.depend.opt
Make*
README
-examples/grundlagen/*.aut
+examples/automath/*.aut
src/*.ml
src/Make*
src/*/*
include Makefile.common
-MATITAC = ../../../claudio/matita/matitac.opt
+MATITAC = ../../../../matita/matita/matitac.opt
-MATITA = ../../../claudio/matita/matita.opt
+MATITA = ../../../../matita/matita/matita.opt
XMLDIR = ../../www/lambdadelta
-INPUT = examples/grundlagen/grundlagen_2.aut
+INPUT = examples/automath/grundlagen_2.aut
-INPUTFAST = examples/grundlagen/grundlagen_1.aut
+INPUTFAST = examples/automath/grundlagen_1.aut
MA = grundlagen_2.ma
matita: $(MA)
@echo " MATITA $<"
- $(H)$(MATITA) $<
+ $(H)cd matita && $(MATITA) $<
matitac: $(MA)
@echo " MATITAC $<"
--- /dev/null
+# Landau's "Grundlagen der Analysis", formal specification in AUTOMATH
+# Copyright (C) 1977, L.S. van Benthem Jutting
+# 1992, revised by F. Wiedijk (http://www.cs.ru.nl/~freek/aut/)
+
++l
+@[a:'prop'][b:'prop']
+imp:=[x:a]b:'prop'
+[a1:a][i:imp(a,b)]
+mp:=<a1>i:b
+a@refimp:=[x:a]x:imp(a,a)
+b@[c:'prop'][i:imp(a,b)][j:imp(b,c)]
+trimp:=[x:a]<<x>i>j:imp(a,c)
+@con:='prim':'prop'
+a@not:=imp(con):'prop'
+wel:=not(not(a)):'prop'
+[a1:a]
+weli:=[x:not(a)]<a1>x:wel(a)
+a@[w:wel(a)]
+et:='prim':a
+a@[c1:con]
+cone:=et([x:not(a)]c1):a
++imp
+b@[i:imp(a,b)][j:imp(not(a),b)]
+th1:=et(b,[x:not(b)]<<trimp(con,i,x)>j>x):b
+b@[n:not(a)]
+th2:=trimp(con,b,n,[x:con]cone(b,x)):imp(a,b)
+b@[n:not(b)][i:imp(a,b)]
+th3:=trimp(con,i,n):not(a)
+b@[a1:a][n:not(b)]
+th4:=[x:imp(a,b)]<a1>th3(n,x):not(imp(a,b))
+b@[n:not(imp(a,b))]
+th5:=et([x:not(a)]<th2(x)>n):a
+th6:=[x:b]<[y:a]x>n:not(b)
+b@[n:not(b)][i:imp(not(a),b)]
+th7:=et(a,th3(not(a),b,n,i)):a
+-imp
+b@[i:imp(not(b),not(a))]
+cp:=[x:a]th7".imp"(b,not(a),weli(x),i):imp(a,b)
+@obvious:=imp(con,con):'prop'
+obviousi:=refimp(con):obvious
+b@ec:=imp(a,not(b)):'prop'
+[n:not(a)]
+eci1:=th2".imp"(not(b),n):ec(a,b)
+b@[n:not(b)]
+eci2:=[x:a]n:ec(a,b)
++ec
+b@[i:imp(a,not(b))]
+th1:=i:ec(a,b)
+b@[i:imp(b,not(a))]
+th2:=[x:a][y:b]<x><y>i:ec(a,b)
+-ec
+b@[e:ec(a,b)]
+comec:=th2".ec"(b,a,e):ec(b,a)
+[a1:a]
+ece1:=<a1>e:not(b)
+e@[b1:b]
+ece2:=th3".imp"(not(b),weli(b,b1),e):not(a)
++*ec
+c@[e:ec(a,b)][i:imp(c,a)]
+th3:=trimp(c,a,not(b),i,e):ec(c,b)
+e@[i:imp(c,b)]
+th4:=comec(c,a,th3(b,a,c,comec(e),i)):ec(a,c)
+-ec
+b@and:=not(ec(a,b)):'prop'
+[a1:a][b1:b]
+andi:=th4".imp"(not(b),a1,weli(b,b1)):and(a,b)
+b@[a1:and(a,b)]
+ande1:=th5".imp"(not(b),a1):a
+ande2:=et(b,th6".imp"(not(b),a1)):b
+comand:=andi(b,a,ande2,ande1):and(b,a)
++and
+b@[n:not(a)]
+th1:=weli(ec,eci1(n)):not(and)
+b@[n:not(b)]
+th2:=weli(ec,eci2(n)):not(and)
+b@[n:not(and)][a1:a]
+th3:=ece1(et(ec,n),a1):not(b)
+n@[b1:b]
+th4:=ece2(et(ec,n),b1):not(a)
+n@th5:=th3"l.imp"(and(b,a),and(a,b),n,[x:and(b,a)]comand(b,a,x)):not(and(b,a))
+c@[a1:and(a,b)][i:imp(a,c)]
+th6:=andi(c,b,<ande1(a1)>i,ande2(a1)):and(c,b)
+a1@[i:imp(b,c)]
+th7:=andi(a,c,ande1(a1),<ande2(a1)>i):and(a,c)
+-and
+b@or:=imp(not(a),b):'prop'
+[a1:a]
+ori1:=th2".imp"(not(a),b,weli(a1)):or(a,b)
+b@[b1:b]
+ori2:=[x:not(a)]b1:or(a,b)
++or
+b@[i:imp(not(a),b)]
+th1:=i:or(a,b)
+b@[i:imp(not(b),a)]
+th2:=[x:not]et(b,th3"l.imp"(not(b),a,x,i)):or(a,b)
+-or
+b@[o:or(a,b)][n:not(a)]
+ore2:=<n>o:b
+o@[n:not(b)]
+ore1:=et(th3".imp"(not(a),b,n,o)):a
+o@comor:=[x:not(b)]ore1(x):or(b,a)
++*or
+b@[n:not(a)][m:not(b)]
+th3:=th4"l.imp"(not(a),b,n,m):not(or(a,b))
+b@[n:not(or(a,b))]
+th4:=th5"l.imp"(not(a),b,n):not(a)
+th5:=th6"l.imp"(not(a),b,n):not(b)
+a@th6:=refimp(not(a)):or(a,not(a))
+-or
+c@[o:or(a,b)][i:imp(a,c)][j:imp(b,c)]
+orapp:=th1".imp"(c,i,trimp(not,b,c,o,j)):c
+c@[d:'prop']
++*or
+o@[i:imp(a,c)]
+th7:=trimp(not(c),not,b,[x:not(c)]th3"l.imp"(a,c,x,i),o):or(c,b)
+o@[i:imp(b,c)]
+th8:=trimp(not(a),b,c,o,i):or(a,c)
+d@[o:or(a,b)][i:imp(a,c)][j:imp(b,d)]
+th9:=th7(a,d,c,th8(a,b,d,o,j),i):or(c,d)
+b@[o:or(a,b)]
+th10:=o:imp(not(a),b)
+th11:=comor(o):imp(not(b),a)
+b@[o:or(not(a),b)]
+th12:=trimp(a,wel(a),b,[x:a]weli(x),o):imp(a,b)
+b@[i:imp(a,b)]
+th13:=trimp(wel(a),a,b,[x:wel(a)]et(x),i):or(not(a),b)
+b@[o:or(not(a),not(b))]
+th14:=weli(ec,th12(not(b),o)):not(and)
+b@[n:not(and)]
+th15:=th13(not(b),et(ec,n)):or(not(a),not(b))
+b@[a1:and(not(a),not(b))]
+th16:=th3(ande1(not(a),not(b),a1),ande2(not(a),not(b),a1)):not(or(a,b))
+b@[n:not(or(a,b))]
+th17:=andi(not(a),not(b),th4(n),th5(n)):and(not(a),not(b))
+-or
+b@orec:=and(or(a,b),ec(a,b)):'prop'
+[o:or(a,b)][e:ec(a,b)]
+oreci:=andi(or(a,b),ec(a,b),o,e):orec(a,b)
++orec
+b@[a1:a][n:not(b)]
+th1:=oreci(ori1(a1),eci2(n)):orec(a,b)
+b@[n:not(a)][b1:b]
+th2:=oreci(ori2(b1),eci1(n)):orec(a,b)
+-orec
+b@[o:orec(a,b)]
+orece1:=ande1(or(a,b),ec,o):or(a,b)
+orece2:=ande2(or(a,b),ec,o):ec(a,b)
+comorec:=oreci(b,a,comor(orece1),comec(orece2)):orec(b,a)
++*orec
+o@[a1:a]
+th3:=ece1(orece2,a1):not(b)
+o@[b1:b]
+th4:=ece2(orece2,b1):not(a)
+o@[n:not(a)]
+th5:=ore2(orece1,n):b
+o@[n:not(b)]
+th6:=ore1(orece1,n):a
+-orec
+b@iff:=and(imp(a,b),imp(b,a)):'prop'
+[i:imp(a,b)][j:imp(b,a)]
+iffi:=andi(imp(a,b),imp(b,a),i,j):iff(a,b)
++iff
+b@[a1:a][b1:b]
+th1:=iffi([x:a]b1,[x:b]a1):iff(a,b)
+b@[n:not(a)][m:not(b)]
+th2:=iffi(th2"l.imp"(n),th2"l.imp"(b,a,m)):iff(a,b)
+-iff
+b@[i:iff(a,b)]
+iffe1:=ande1(imp(a,b),imp(b,a),i):imp(a,b)
+iffe2:=ande2(imp(a,b),imp(b,a),i):imp(b,a)
+comiff:=iffi(b,a,iffe2,iffe1):iff(b,a)
++*iff
+i@[a1:a]
+th3:=<a1>iffe1:b
+i@[b1:b]
+th4:=<b1>iffe2:a
+i@[n:not(a)]
+th5:=th3"l.imp"(b,a,n,iffe2):not(b)
+i@[n:not(b)]
+th6:=th3"l.imp"(n,iffe1):not(a)
+b@[a1:a][n:not(b)]
+th7:=th1"l.and"(imp(a,b),imp(b,a),th4"l.imp"(a1,n)):not(iff(a,b))
+b@[n:not(a)][b1:b]
+th8:=th2"l.and"(imp(a,b),imp(b,a),th4"l.imp"(b,a,b1,n)):not(iff(a,b))
+-iff
+a@refiff:=iffi(a,refimp,refimp):iff(a,a)
+b@[i:iff(a,b)]
+symiff:=comiff(i):iff(b,a)
+c@[i:iff(a,b)][j:iff(b,c)]
+triff:=iffi(a,c,trimp(iffe1(i),iffe1(b,c,j)),trimp(c,b,a,iffe2(b,c,j),iffe2(i))):iff(a,c)
++*iff
+b@[i:iff(a,b)]
+th9:=[x:not(a)]th5(i,x):imp(not(a),not(b))
+th10:=[x:not(b)]th6(i,x):imp(not(b),not(a))
+th11:=iffi(not(a),not(b),th9,th10):iff(not(a),not(b))
+b@[i:imp(not(a),not(b))][j:imp(not(b),not(a))]
+th12:=iffi(cp(j),cp(b,a,i)):iff(a,b)
+b@[o:orec(a,b)]
+th13:=iffi(not(b),orece2(o),comor(orece1(o))):iff(a,not(b))
+th14:=th13(b,a,comorec(o)):iff(b,not(a))
+b@[i:iff(a,not(b))]
+th15:=oreci(comor(b,a,iffe2(not(b),i)),iffe1(not(b),i)):orec(a,b)
+b@[i:iff(b,not(a))]
+th16:=comorec(b,a,th15(b,a,i)):orec(a,b)
+c@[i:iff(a,b)][j:imp(a,c)]
+thimp1:=trimp(b,a,c,iffe2(i),j):imp(b,c)
+i@[j:imp(c,a)]
+thimp2:=trimp(c,a,b,j,iffe1(i)):imp(c,b)
+i@[e:ec(a,c)]
+thec1:=th3"l.ec"(c,b,e,iffe2(i)):ec(b,c)
+i@[e:ec(c,a)]
+thec2:=th4"l.ec"(c,a,b,e,iffe2(i)):ec(c,b)
+i@[a1:and(a,c)]
+thand1:=th6"l.and"(c,b,a1,iffe1(i)):and(b,c)
+i@[a1:and(c,a)]
+thand2:=th7"l.and"(c,a,b,a1,iffe1(i)):and(c,b)
+i@[o:or(a,c)]
+thor1:=th7"l.or"(c,b,o,iffe1(i)):or(b,c)
+i@[o:or(c,a)]
+thor2:=th8"l.or"(c,a,b,o,iffe1(i)):or(c,b)
+i@[o:orec(a,c)]
+thorec1:=oreci(b,c,thor1(orece1(a,c,o)),thec1(orece2(a,c,o))):orec(b,c)
+i@[o:orec(c,a)]
+thorec2:=oreci(c,b,thor2(orece1(c,a,o)),thec2(orece2(c,a,o))):orec(c,b)
+-iff
+@[sigma:'type'][p:[x:sigma]'prop']
+all:=p:'prop'
+[a1:all(sigma,p)][s:sigma]
+alle:=<s>a1:<s>p
++all
+p@[s:sigma][n:not(<s>p)]
+th1:=[x:all(sigma,p)]<<s>x>n:not(all(sigma,p))
+-all
+p@non:=[x:sigma]not(<x>p):[x:sigma]'prop'
+some:=not(non(p)):'prop'
+[s:sigma][sp:<s>p]
+somei:=th1".all"(non(p),s,weli(<s>p,sp)):some(sigma,p)
++some
+p@[n:not(all(sigma,p))][m:non(non(p))][s:sigma]
+t1:=et(<s>p,<s>m):<s>p
+%set etared
+m@t2:=<[x:sigma]t1(x)>n:con
+%reset etared
+n@th1:=[x:non(non(p))]t2(x):some(non(p))
+p@[s:some(non(p))][a1:all(sigma,p)][t:sigma]
+t3:=weli(<t>p,<t>a1):not(not(<t>p))
+a1@t4:=<[x:sigma]t3(x)>s:con
+s@th2:=[x:all(sigma,p)]t4(x):not(all(sigma,p))
+p@[n:not(some(sigma,p))]
+th3:=et(non(p),n):non(p)
+[s:sigma]
+th4:=<s>th3:not(<s>p)
+p@[n:non(p)]
+th5:=weli(non(p),n):not(some(sigma,p))
+-some
+p@[s:some(sigma,p)][x:'prop'][i:[y:sigma]imp(<y>p,x)]
++*some
+i@[n:not(x)][t:sigma]
+t5:=th3"l.imp"(<t>p,x,n,<t>i):not(<t>p)
+n@t6:=mp(some(sigma,p),con,s,th5([y:sigma]t5(y))):con
+-some
+i@someapp:=et(x,[y:not(x)]t6".some"(y)):x
++*some
+p@[q:[x:sigma]'prop'][s:some(sigma,p)][i:[x:sigma]imp(<x>p,<x>q)]
+th6:=someapp(s,some(q),[x:sigma][y:<x>p]somei(q,x,mp(<x>p,<x>q,y,<x>i))):some(q)
+-some
+c@or3:=or(a,or(b,c)):'prop'
+[o:or3(a,b,c)][n:not(a)]
++or3
+th1:=ore2(or(b,c),o,n):or(b,c)
+-or3
+[m:not(b)]
+or3e3:=ore2(b,c,th1".or3",m):c
+o@[n:not(b)]
++*or3
+n@th2:=th2"l.or"(c,a,[x:not(a)]or3e3(x,n)):or(c,a)
+-or3
+n@[m:not(c)]
+or3e1:=ore2(c,a,th2".or3",m):a
+o@[n:not(c)]
++*or3
+n@th3:=th2"l.or"([x:not(b)]or3e1(x,n)):or(a,b)
+-or3
+n@[m:not(a)]
+or3e2:=ore2(th3".or3",m):b
++*or3
+o@th4:=th1"l.or"(b,or(c,a),[x:not(b)]th2(x)):or3(b,c,a)
+th5:=th4(b,c,a,th4):or3(c,a,b)
+-or3
+c@[a1:a]
+or3i1:=ori1(a,or(b,c),a1):or3(a,b,c)
+c@[b1:b]
+or3i2:=ori2(a,or(b,c),ori1(b,c,b1)):or3(a,b,c)
+c@[c1:c]
+or3i3:=ori2(a,or(b,c),ori2(b,c,c1)):or3(a,b,c)
++*or3
+c@[o:or(a,b)]
+th6:=th4"or3"(c,a,b,ori2(c,or(a,b),o)):or3(a,b,c)
+c@[o:or(b,c)]
+th7:=ori2(or(b,c),o):or3(a,b,c)
+c@[o:or(c,a)]
+th8:=th4"or3"(c,a,b,th6(c,a,b,o)):or3(a,b,c)
+-or3
+d@[o:or3(a,b,c)][i:imp(a,d)][j:imp(b,d)][k:imp(c,d)]
+or3app:=orapp(or(b,c),d,o,i,[x:or(b,c)]orapp(b,c,d,x,j,k)):d
+c@and3:=and(a,and(b,c)):'prop'
+[a1:and3(a,b,c)]
+and3e1:=ande1(and(b,c),a1):a
+and3e2:=ande1(b,c,ande2(and(b,c),a1)):b
+and3e3:=ande2(b,c,ande2(and(b,c),a1)):c
+c@[a1:a][b1:b][c1:c]
+and3i:=andi(a,and(b,c),a1,andi(b,c,b1,c1)):and3(a,b,c)
++and3
+c@[a1:and3(a,b,c)]
+th1:=and3i(b,c,a,and3e2(a1),and3e3(a1),and3e1(a1)):and3(b,c,a)
+th2:=th1(b,c,a,th1):and3(c,a,b)
+th3:=andi(and3e1(a1),and3e2(a1)):and(a,b)
+th4:=ande2(and(b,c),a1):and(b,c)
+th5:=th3(c,a,b,th2):and(c,a)
+th6:=and3i(c,b,a,and3e3(a1),and3e2(a1),and3e1(a1)):and3(c,b,a)
+-and3
+c@ec3:=and3(ec,ec(b,c),ec(c,a)):'prop'
+[e:ec3(a,b,c)]
++ec3
+th1:=and3e1(ec,ec(b,c),ec(c,a),e):ec(a,b)
+th2:=and3e2(ec,ec(b,c),ec(c,a),e):ec(b,c)
+th3:=and3e3(ec,ec(b,c),ec(c,a),e):ec(c,a)
+th4:=th1"l.and3"(ec,ec(b,c),ec(c,a),e):ec3(b,c,a)
+th5:=th4(b,c,a,th4):ec3(c,a,b)
+th5a:=and3i(ec(c,b),ec(b,a),ec(a,c),comec(b,c,th2(e)),comec(a,b,th1(e)),comec(c,a,th3(e))):ec3(c,b,a)
+-ec3
+[a1:a]
+ec3e12:=ece1(th1".ec3",a1):not(b)
+ec3e13:=ece2(c,a,th3".ec3",a1):not(c)
+e@[b1:b]
+ec3e23:=ec3e12(b,c,a,th4".ec3",b1):not(c)
+ec3e21:=ec3e13(b,c,a,th4".ec3",b1):not(a)
+e@[c1:c]
+ec3e31:=ec3e12(c,a,b,th5".ec3",c1):not(a)
+ec3e32:=ec3e13(c,a,b,th5".ec3",c1):not(b)
++*ec3
+c@[e:ec(a,b)][f:ec(b,c)][g:ec(c,a)]
+th6:=and3i(ec,ec(b,c),ec(c,a),e,f,g):ec3(a,b,c)
+c@[e:ec3(a,b,c)][o:or(a,b)]
+th7:=orapp(not(c),o,[x:a]ece2(c,a,th3"ec3"(e),x),[x:b]ece1(b,c,th2"ec3"(e),x)):not(c)
+e@[o:or(b,c)]
+th8:=th7(b,c,a,th4"ec3"(e),o):not(a)
+e@[o:or(c,a)]
+th9:=th7(c,a,b,th5"ec3"(e),o):not(b)
+-ec3
+c@[n:not(a)][m:not(b)]
+ec3i1:=th6".ec3"(eci1(n),eci1(b,c,m),eci2(c,a,n)):ec3(a,b,c)
+c@[n:not(b)][m:not(c)]
+ec3i2:=th6".ec3"(eci2(n),eci1(b,c,n),eci1(c,a,m)):ec3(a,b,c)
+c@[n:not(c)][m:not(a)]
+ec3i3:=th6".ec3"(eci1(m),eci2(b,c,n),eci1(c,a,n)):ec3(a,b,c)
++*ec3
+d@[e:'prop'][f:'prop'][o1:or3(a,b,c)][p1:ec3(d,e,f)][i:imp(a,d)][j:imp(b,e)][k:imp(c,f)][d1:d]
+t1:=[x:b]mp(e,con,<x>j,ec3e12(d,e,f,p1,d1)):not(b)
+t2:=[x:c]mp(f,con,<x>k,ec3e13(d,e,f,p1,d1)):not(c)
+th10:=or3e1(o1,t1,t2):a
+k@[e1:e]
+th11:=th10(b,c,a,e,f,d,th4"l.or3"(o1),th4"ec3"(d,e,f,p1),j,k,i,e1):b
+k@[f1:f]
+th12:=th10(c,a,b,f,d,e,th5"l.or3"(o1),th5"ec3"(d,e,f,p1),k,i,j,f1):c
+-ec3
+c@orec3:=and(or3(a,b,c),ec3(a,b,c)):'prop'
+[o:orec3(a,b,c)]
+orec3e1:=ande1(or3(a,b,c),ec3(a,b,c),o):or3(a,b,c)
+orec3e2:=ande2(or3(a,b,c),ec3(a,b,c),o):ec3(a,b,c)
+c@[o:or3(a,b,c)][e:ec3(a,b,c)]
+orec3i:=andi(or3(a,b,c),ec3(a,b,c),o,e):orec3(a,b,c)
++orec3
+c@[o:orec3(a,b,c)]
+th1:=orec3i(b,c,a,th4"l.or3"(orec3e1(o)),th4"l.ec3"(orec3e2(o))):orec3(b,c,a)
+th2:=orec3i(c,a,b,th5"l.or3"(orec3e1(o)),th5"l.ec3"(orec3e2(o))):orec3(c,a,b)
+-orec3
++e
+sigma@[s:sigma][t:sigma]
+is:='prim':'prop'
+s@refis:='prim':is(s,s)
+p@[s:sigma][t:sigma][sp:<s>p][i:is(s,t)]
+isp:='prim':<t>p
+sigma@[s:sigma][t:sigma][i:is(s,t)]
+symis:=isp([x:sigma]is(x,s),s,t,refis(s),i):is(t,s)
+t@[u:sigma][i:is(s,t)][j:is(t,u)]
+tris:=isp([x:sigma]is(x,u),t,s,j,symis(i)):is(s,u)
+u@[i:is(u,s)][j:is(u,t)]
+tris1:=tris(s,u,t,symis(u,s,i),j):is(s,t)
+u@[i:is(s,u)][j:is(t,u)]
+tris2:=tris(s,u,t,i,symis(t,u,j)):is(s,t)
+sp@[i:is(t,s)]
+isp1:=isp(symis(t,s,i)):<t>p
+t@[n:not(is(s,t))]
+symnotis:=th3"l.imp"(is(t,s),is(s,t),n,[x:is(t,s)]symis(t,s,x)):not(is(t,s))
++notis
+u@[n:not(is(s,t))][i:is(s,u)]
+th1:=isp([x:sigma]not(is(x,t)),s,u,n,i):not(is(u,t))
+n@[i:is(u,s)]
+th2:=th1(symis(u,s,i)):not(is(u,t))
+n@[i:is(t,u)]
+th3:=isp([x:sigma]not(is(s,x)),t,u,n,i):not(is(s,u))
+n@[i:is(u,t)]
+th4:=th3(symis(u,t,i)):not(is(s,u))
+u@[v:sigma][n:not(is(s,t))][i:is(s,u)][j:is(t,v)]
+th5:=th3(u,t,v,th1(n,i),j):not(is(u,v))
+-notis
+u@[v:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)]
+tr3is:=tris(s,u,v,tris(i,j),k):is(s,v)
+v@[w:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)][l:is(v,w)]
+tr4is:=tris(s,v,w,tr3is(i,j,k),l):is(s,w)
+p@amone:=[x:sigma][y:sigma][u:<x>p][v:<y>p]is(x,y):'prop'
+[a1:amone(sigma,p)][s:sigma][t:sigma][sp:<s>p][tp:<t>p]
+amonee:=<tp><sp><t><s>a1:is(s,t)
+p@one:=and(amone(sigma,p),some(sigma,p)):'prop'
+[a1:amone(sigma,p)][s:some(sigma,p)]
+onei:=andi(amone(sigma,p),some(sigma,p),a1,s):one(sigma,p)
+p@[o1:one(sigma,p)]
+onee1:=ande1(amone(sigma,p),some(sigma,p),o1):amone(sigma,p)
+onee2:=ande2(amone(sigma,p),some(sigma,p),o1):some(sigma,p)
+ind:='prim':sigma
+oneax:='prim':<ind>p
++one
+[s:sigma][sp:<s>p]
+th1:=amonee(onee1,ind,s,oneax,sp):is(ind,s)
+-one
+sigma@[tau:'type'][f:[x:sigma]tau][s:sigma][t:sigma][i:is(s,t)]
+isf:=isp(sigma,[x:sigma]is(tau,<s>f,<x>f),s,t,refis(tau,<s>f),i):is(tau,<s>f,<t>f)
+f@injective:=all([x:sigma]all([y:sigma]imp(is(tau,<x>f,<y>f),is(x,y)))):'prop'
+[i:injective(f)][s:sigma][t:sigma][j:is(tau,<s>f,<t>f)]
+isfe:=<j><t><s>i:is(s,t)
+f@[t0:tau]
+image:=some([x:sigma]is(tau,t0,<x>f)):'prop'
+f@[s:sigma]
+tofs:=<s>f:tau
+imagei:=somei([x:sigma]is(tau,tofs,<x>f),s,refis(tau,tofs)):image(tofs)
++inj
+i@[ta:tau][tb:tau][j:is(tau,ta,tb)][sa:sigma][sb:sigma][ja:is(tau,ta,tofs(sa))][jb:is(tau,tb,tofs(sb))]
+t1:=tr3is(tau,tofs(sa),ta,tb,tofs(sb),symis(tau,ta,tofs(sa),ja),j,jb):is(tau,tofs(sa),tofs(sb))
+th1:=isfe(sa,sb,t1):is(sa,sb)
+i@[t0:tau]
+th2:=[x:sigma][y:sigma][u:is(tau,t0,<x>f)][v:is(tau,t0,<y>f)]th1(t0,t0,refis(tau,t0),x,y,u,v):amone([x:sigma]is(tau,t0,<x>f))
+[j:image(f,t0)]
+th3:=onei([x:sigma]is(tau,t0,<x>f),th2,j):one([x:sigma]is(tau,t0,<x>f))
+-inj
+i@[t0:tau][j:image(f,t0)]
+soft:=ind([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):sigma
+i@inverse:=[x:tau][u:image(f,x)]soft(x,u):[x:tau][u:image(f,x)]sigma
+j@ists1:=oneax([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):is(tau,t0,tofs(soft(t0,j)))
+ists2:=symis(tau,t0,tofs(soft(t0,j)),ists1):is(tau,tofs(soft(t0,j)),t0)
+i@[ta:tau][ja:image(ta)][tb:tau][jb:image(tb)][j:is(tau,ta,tb)]
+isinv:=th1".inj"(ta,tb,j,soft(ta,ja),soft(tb,jb),ists1(ta,ja),ists1(tb,jb)):is(soft(ta,ja),soft(tb,jb))
+jb@[j:is(soft(ta,ja),soft(tb,jb))]
+isinve:=tr3is(tau,ta,tofs(soft(ta,ja)),tofs(soft(tb,jb)),tb,ists1(ta,ja),isf(soft(ta,ja),soft(tb,jb),j),ists2(tb,jb)):is(tau,ta,tb)
+i@[s:sigma]
+isst1:=isfe(s,soft(tofs(s),imagei(s)),ists1(tofs(s),imagei(s))):is(s,soft(tofs(s),imagei(s)))
+isst2:=symis(s,soft(tofs(s),imagei(s)),isst1):is(soft(tofs(s),imagei(s)),s)
+f@surjective:=all(tau,[x:tau]image(x)):'prop'
+bijective:=and(injective,surjective):'prop'
+[b:bijective(f)]
++*inj
+b@t2:=ande1(injective,surjective,b):injective(f)
+t3:=ande2(injective,surjective,b):surjective(f)
+[t:tau]
+so:=soft(t2,t,<t>t3):sigma
+-inj
+b@invf:=[x:tau]so".inj"(x):[x:tau]sigma
+[s:sigma]
+thinvf1:=tris(s,soft(t2".inj",tofs(s),imagei(s)),<<s>f>invf,isst1(t2".inj",s),isinv(t2".inj",tofs(s),imagei(s),tofs(s),<tofs(s)>t3".inj",refis(tau,tofs(s)))):is(s,<<s>f>invf)
+b@[t:tau]
+thinvf2:=ists1(t2".inj",t,<t>t3".inj"):is(tau,t,<<t>invf>f)
+tau@[upsilon:'type'][f:[x:sigma]tau][g:[x:tau]upsilon]
++*inj
+g@[if:injective(sigma,tau,f)][ig:injective(tau,upsilon,g)]
+h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
+[s:sigma][t:sigma][i:is(upsilon,<s>h,<t>h)]
+t4:=isfe(tau,upsilon,g,ig,<s>f,<t>f,i):is(tau,<s>f,<t>f)
+t5:=isfe(f,if,s,t,t4):is(s,t)
+ig@th4:=[x:sigma][y:sigma][v:is(upsilon,<x>h,<y>h)]t5(x,y,v):injective(sigma,upsilon,[x:sigma]<<x>f>g)
+-inj
++surj
+g@[sf:surjective(sigma,tau,f)][sg:surjective(tau,upsilon,g)]
+h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
+[u:upsilon]
+t1:=<u>sg:image(tau,upsilon,g,u)
+[t:tau][i:is(upsilon,u,<t>g)]
+t2:=<t>sf:image(sigma,tau,f,t)
+[s:sigma][j:is(tau,t,<s>f)]
+t3:=tris(upsilon,u,<t>g,<s>h,i,isf(tau,upsilon,g,t,<s>f,j)):is(upsilon,u,<s>h)
+t4:=somei([x:sigma]is(upsilon,u,<x>h),s,t3):image(sigma,upsilon,h,u)
+i@t5:=someapp([x:sigma]is(tau,t,<x>f),t2,image(sigma,upsilon,h,u),[x:sigma][v:is(tau,t,<x>f)]t4(x,v)):image(sigma,upsilon,h,u)
+u@t6:=someapp(tau,[x:tau]is(upsilon,u,<x>g),t1,image(sigma,upsilon,h,u),[x:tau][v:is(upsilon,u,<x>g)]t5(x,v)):image(sigma,upsilon,h,u)
+sg@th1:=[x:upsilon]t6(x):surjective(sigma,upsilon,[x:sigma]<<x>f>g)
+-surj
++bij
+g@[bf:bijective(sigma,tau,f)][bg:bijective(tau,upsilon,g)]
+h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
+t1:=th4"e.inj"(f,g,ande1(injective(f),surjective(f),bf),ande1(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):injective(sigma,upsilon,h)
+t2:=th1"e.surj"(f,g,ande2(injective(f),surjective(f),bf),ande2(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):surjective(sigma,upsilon,h)
+th1:=andi(injective(sigma,upsilon,h),surjective(sigma,upsilon,h),t1,t2):bijective(sigma,upsilon,[x:sigma]<<x>f>g)
+-bij
+tau@[f:[x:sigma]tau][g:[x:sigma]tau][i:is([x:sigma]tau,f,g)][s:sigma]
+fise:=isp([x:sigma]tau,[y:[x:sigma]tau]is(tau,<s>f,<s>y),f,g,refis(tau,<s>f),i):is(tau,<s>f,<s>g)
+g@[i:[x:sigma]is(tau,<x>f,<x>g)]
+fisi:='prim':is([x:sigma]tau,f,g)
++fis
+g@[i:is([x:sigma]tau,f,g)][s:sigma][t:sigma][j:is(s,t)]
+th1:=tris(tau,<s>f,<t>f,<t>g,isf(f,s,t,j),fise(i,t)):is(tau,<s>f,<t>g)
+-fis
+p@ot:='prim':'type'
+[o1:ot]
+in:='prim':sigma
+inp:='prim':<in>p
+p@otax1:='prim':injective(ot,sigma,[x:ot]in(x))
+[s:sigma][sp:<s>p]
+otax2:='prim':image(ot,sigma,[x:ot]in(x),s)
+o1@[o2:ot][i:is(ot,o1,o2)]
+isini:=isf(ot,sigma,[x:ot]in(x),o1,o2,i):is(in(o1),in(o2))
+o2@[i:is(in(o1),in(o2))]
+isine:=isfe(ot,sigma,[x:ot]in(x),otax1,o1,o2,i):is(ot,o1,o2)
+sp@out:=soft(ot,sigma,[x:ot]in(x),otax1,s,otax2):ot
+[t:sigma][tp:<t>p][i:is(s,t)]
+isouti:=isinv(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(ot,out(s,sp),out(t,tp))
+tp@[i:is(ot,out(s,sp),out(t,tp))]
+isoute:=isinve(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(s,t)
+o1@isoutin:=tris(ot,o1,soft(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1)),out(in(o1),inp(o1)),isst1(ot,sigma,[x:ot]in(x),otax1,o1),isinv(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1),in(o1),otax2(in(o1),inp(o1)),refis(sigma,in(o1)))):is(ot,o1,out(in(o1),inp(o1)))
+sp@isinout:=ists1(ot,sigma,[x:ot]in(x),otax1,s,otax2):is(s,in(out(s,sp)))
+tau@pairtype:='prim':'type'
+[s:sigma][t:tau]
+pair:='prim':pairtype
+tau@[p1:pairtype]
+first:='prim':sigma
+second:='prim':tau
+pairis1:='prim':is(pairtype,pair(first,second),p1)
+pairis2:=symis(pairtype,pair(first,second),p1,pairis1):is(pairtype,p1,pair(first,second))
+t@firstis1:='prim':is(sigma,first(pair),s)
+firstis2:=symis(sigma,first(pair),s,firstis1):is(sigma,s,first(pair))
+secondis1:='prim':is(tau,second(pair),t)
+secondis2:=symis(tau,second(pair),t,secondis1):is(tau,t,second(pair))
+a@[ksi:'type'][x:ksi][y:ksi]
++ite
+[z:ksi]
+prop1:=and(imp(a,is(ksi,z,x)),imp(not(a),is(ksi,z,y))):'prop'
+y@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t1:=ande1(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(a,is(ksi,x1,x))
+t2:=mp(a,is(ksi,x1,x),a1,t1):is(ksi,x1,x)
+t3:=t2(y1,x1,py1,px1):is(ksi,y1,x)
+t4:=tris2(ksi,x1,y1,x,t2,t3):is(ksi,x1,y1)
+a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
+t6:=[x1:a]refis(ksi,x):imp(a,is(ksi,x,x))
+t7:=th2"l.imp"(not(a),is(ksi,x,y),weli(a,a1)):imp(not(a),is(ksi,x,y))
+t8:=andi(imp(a,is(ksi,x,x)),imp(not(a),is(ksi,x,y)),t6,t7):prop1(x)
+t9:=somei(ksi,[t:ksi]prop1(t),x,t8):some(ksi,[t:ksi]prop1(t))
+t10:=onei(ksi,[t:ksi]prop1(t),t5,t9):one(ksi,[t:ksi]prop1(t))
+y@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t11:=ande2(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(not(a),is(ksi,x1,y))
+t12:=mp(not(a),is(ksi,x1,y),n,t11):is(ksi,x1,y)
+t13:=t12(y1,x1,py1,px1):is(ksi,y1,y)
+t14:=tris2(ksi,x1,y1,y,t12,t13):is(ksi,x1,y1)
+n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
+t16:=[x1:not(a)]refis(ksi,y):imp(not(a),is(ksi,y,y))
+t17:=th2"l.imp"(a,is(ksi,y,x),n):imp(a,is(ksi,y,x))
+t18:=andi(imp(a,is(ksi,y,x)),imp(not(a),is(ksi,y,y)),t17,t16):prop1(y)
+t19:=somei(ksi,[t:ksi]prop1(t),y,t18):some(ksi,[t:ksi]prop1(t))
+t20:=onei(ksi,[t:ksi]prop1(t),t15,t19):one(ksi,[t:ksi]prop1(t))
+y@t21:=th1"l.imp"(a,one(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one(ksi,[t:ksi]prop1(t))
+-ite
+ite:=ind(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
++*ite
+y@t22:=oneax(ksi,[t:ksi]prop1(t),t21):prop1(ite)
+t23:=ande1(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(a,is(ksi,ite,x))
+t24:=ande2(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(not(a),is(ksi,ite,y))
+-ite
+y@[a1:a]
+itet:=mp(a,is(ksi,ite,x),a1,t23".ite"):is(ksi,ite,x)
+y@[n:not(a)]
+itef:=mp(not(a),is(ksi,ite,y),n,t24".ite"):is(ksi,ite,y)
+sigma@[s0:sigma][t0:sigma]
++wissel
+[s:sigma]
+wa:=ite(is(s,s0),sigma,t0,s):sigma
+[i:is(s,s0)]
+t1:=itet(is(s,s0),sigma,t0,s,i):is(wa,t0)
+s@[n:not(is(s,s0))]
+t2:=itef(is(s,s0),sigma,t0,s,n):is(wa,s)
+s@wb:=ite(is(s,t0),sigma,s0,wa):sigma
+[i:is(s,t0)]
+t3:=itet(is(s,t0),sigma,s0,wa,i):is(wb,s0)
+s@[n:not(is(s,t0))]
+t4:=itef(is(s,t0),sigma,s0,wa,n):is(wb,wa)
+s@[i:is(s,s0)][j:is(s0,t0)]
+t5:=tris(wb,s0,t0,t3(tris(s,s0,t0,i,j)),j):is(wb,t0)
+i@[n:not(is(s0,t0))]
+t6:=tris(wb,wa,t0,t4(th2"e.notis"(s0,t0,s,n,i)),t1(i)):is(wb,t0)
+i@t7:=th1"l.imp"(is(s0,t0),is(wb,t0),[t:is(s0,t0)]t5(t),[t:not(is(s0,t0))]t6(t)):is(wb,t0)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+t8:=tris(wb,wa,s,t4(o),t2(n)):is(wb,s)
+-wissel
+wissel:=[x:sigma]wb".wissel"(x):[x:sigma]sigma
+[s:sigma][i:is(s,s0)]
+iswissel1:=t7".wissel"(s,i):is(<s>wissel,t0)
+s@[i:is(s,t0)]
+iswissel2:=t3".wissel"(s,i):is(<s>wissel,s0)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+iswissel3:=t8".wissel"(s,n,o):is(<s>wissel,s)
++*wissel
+s@[t:sigma][i:is(wb(s),wb(t))][n:not(is(s,t))][j:is(s,s0)]
+t9:=symnotis(s0,t,th1"e.notis"(s,t,s0,n,j)):not(is(t,s0))
+[k:is(s0,t0)]
+t10:=th3"e.notis"(t,s0,t0,t9,k):not(is(t,t0))
+t11:=tris(wb(s),wb(t),t,i,t8(t,t9,t10)):is(wb(s),t)
+t12:=<tris1(t,t0,wb(s),t11,t7(j))>t10:con
+j@t13:=[v:is(s0,t0)]t12(v):not(is(s0,t0))
+[k:is(t,t0)]
+t14:=tris(wb(s),wb(t),s0,i,t3(t,k)):is(wb(s),s0)
+t15:=t12(tris1(s0,t0,wb(s),t14,t7(j))):con
+j@t16:=[v:is(t,t0)]t15(v):not(is(t,t0))
+t17:=tris(wb(s),wb(t),t,i,t8(t,t9,t16)):is(wb(s),t)
+t18:=t15(tris1(t,t0,wb(s),t17,t7(j))):con
+n@t19:=[v:is(s,s0)]t18(v):not(is(s,s0))
+t20:=t19(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,s0))
+[j:is(s,t0)]
+t21:=symnotis(t0,t,th1"e.notis"(s,t,t0,n,j)):not(is(t,t0))
+t22:=tris(wb(s),wb(t),t,i,t8(t,t20,t21)):is(wb(s),t)
+t23:=<tris1(t,s0,wb(s),t22,t3(j))>t20:con
+n@t24:=[v:is(s,t0)]t23(v):not(is(s,t0))
+t25:=t24(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,t0))
+t26:=tris(wb(s),wb(t),t,i,t8(t,t20,t25)):is(wb(s),t)
+t27:=<tris1(s,t,wb(s),t8(t19,t24),t26)>n:con
+i@t28:=et(is(s,t),[v:not(is(s,t))]t27(v)):is(s,t)
+t0@th1:=[x:sigma][y:sigma][v:is(wb(x),wb(y))]t28(x,y,v):injective(sigma,sigma,wissel)
+s@[i:is(s,s0)]
+t29:=tris2(s,wb(t0),s0,i,t3(t0,refis(t0))):is(s,wb(t0))
+t30:=somei(sigma,[x:sigma]is(s,wb(x)),t0,t29):image(sigma,sigma,wissel,s)
+s@[i:is(s,t0)]
+t31:=tris2(s,wb(s0),t0,i,t7(s0,refis(s0))):is(s,wb(s0))
+t32:=somei(sigma,[x:sigma]is(s,wb(x)),s0,t31):image(sigma,sigma,wissel,s)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+t33:=symis(wb(s),s,t8(n,o)):is(s,wb(s))
+t34:=somei(sigma,[x:sigma]is(s,wb(x)),s,t33):image(sigma,sigma,wissel,s)
+n@t35:=th1"l.imp"(is(s,t0),image(sigma,sigma,wissel,s),[v:is(s,t0)]t32(v),[v:not(is(s,t0))]t34(v)):image(sigma,sigma,wissel,s)
+s@t36:=th1"l.imp"(is(s,s0),image(sigma,sigma,wissel,s),[v:is(s,s0)]t30(v),[v:not(is(s,s0))]t35(v)):image(sigma,sigma,wissel,s)
+t0@th2:=[x:sigma]t36(x):surjective(sigma,sigma,wissel)
+th3:=andi(injective(sigma,sigma,wissel),surjective(sigma,sigma,wissel),th1,th2):bijective(sigma,sigma,wissel)
+-wissel
+tau@[f:[x:sigma]tau][s0:sigma][t0:sigma]
+changef:=[x:sigma]<<x>wissel(s0,t0)>f:[x:sigma]tau
+[s:sigma][i:is(s,s0)]
+changef1:=isf(sigma,tau,f,<s>wissel(s0,t0),t0,iswissel1(s0,t0,s,i)):is(tau,<s>changef,<t0>f)
+s@[i:is(s,t0)]
+changef2:=isf(sigma,tau,f,<s>wissel(s0,t0),s0,iswissel2(s0,t0,s,i)):is(tau,<s>changef,<s0>f)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+changef3:=isf(sigma,tau,f,<s>wissel(s0,t0),s,iswissel3(s0,t0,s,n,o)):is(tau,<s>changef,<s>f)
++*wissel
+t0@[i:injective(f)]
+th4:=th4"e.inj"(sigma,sigma,tau,wissel(s0,t0),f,th1(s0,t0),i):injective(changef)
+t0@[s:surjective(f)]
+th5:=th1"e.surj"(sigma,sigma,tau,wissel(s0,t0),f,th2(s0,t0),s):surjective(changef)
+t0@[b:bijective(f)]
+th6:=th1"e.bij"(sigma,sigma,tau,wissel(s0,t0),f,th3(s0,t0),b):bijective(changef)
+-wissel
+-e
++r
+a@[b:[x:a]'prop']
+imp:=b:'prop'
+[a1:a][i:imp(a,b)]
+mp:=<a1>i:<a1>b
++imp
+b@[n:not(a)]
+%set etared
+th2:=[x:a]cone(<x>b,mp"l"(a,con,x,n)):imp(a,b)
+%reset etared
+-imp
+b@ec:=[x:a]not(<x>b):'prop'
+[n:not(a)]
+eci1:=[x:a]cone(not(<x>b),mp"l"(a,con,x,n)):ec(a,b)
+b@[a1:and(a,b)]
+ande2:=<ande1(a,b,a1)>ande2"l"(a,b,a1):<ande1(a,b,a1)>b
+a@[ksi:'type']
++ite
+[x1:ksi][y1:ksi]
+is:=is"l.e"(ksi,x1,y1):'prop'
+-ite
+[x:[t:a]ksi][y:[t:not(a)]ksi][i:[t:a][u:a]is".ite"(<t>x,<u>x)][j:[t:not(a)][u:not(a)]is".ite"(<t>y,<u>y)]
++*ite
+j@[z:ksi]
+prop1:=and(imp(a,[t:a]is(z,<t>x)),imp(not(a),[t:not(a)]is(z,<t>y))):'prop'
+j@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t1:=ande1"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(a,[t:a]is(x1,<t>x))
+t2:=mp(a,[t:a]is(x1,<t>x),a1,t1):is(x1,<a1>x)
+t3:=t2(y1,x1,py1,px1):is(y1,<a1>x)
+t4:=tris2"l.e"(ksi,x1,y1,<a1>x,t2,t3):is(x1,y1)
+a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
+t6:=<a1>i:imp(a,[t:a]is(<a1>x,<t>x))
+t7:=th2"r.imp"(not(a),[t:not(a)]is(<a1>x,<t>y),weli(a,a1)):imp(not(a),[t:not(a)]is(<a1>x,<t>y))
+t8:=andi(imp(a,[t:a]is(<a1>x,<t>x)),imp(not(a),[t:not(a)]is(<a1>x,<t>y)),t6,t7):prop1(<a1>x)
+t9:=somei(ksi,[t:ksi]prop1(t),<a1>x,t8):some(ksi,[t:ksi]prop1(t))
+t10:=onei"l.e"(ksi,[t:ksi]prop1(t),t5,t9):one"l.e"(ksi,[t:ksi]prop1(t))
+j@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t11:=ande2"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(not(a),[t:not(a)]is(x1,<t>y))
+t12:=mp(not(a),[t:not(a)]is(x1,<t>y),n,t11):is(x1,<n>y)
+t13:=t12(y1,x1,py1,px1):is(y1,<n>y)
+t14:=tris2"l.e"(ksi,x1,y1,<n>y,t12,t13):is(x1,y1)
+n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
+t16:=<n>j:imp(not(a),[t:not(a)]is(<n>y,<t>y))
+t17:=th2"r.imp"(a,[t:a]is(<n>y,<t>x),n):imp(a,[t:a]is(<n>y,<t>x))
+t18:=andi"l"(imp(a,[t:a]is(<n>y,<t>x)),imp(not(a),[t:not(a)]is(<n>y,<t>y)),t17,t16):prop1(<n>y)
+t19:=somei(ksi,[t:ksi]prop1(t),<n>y,t18):some(ksi,[t:ksi]prop1(t))
+t20:=onei"l.e"(ksi,[t:ksi]prop1(t),t15,t19):one"l.e"(ksi,[t:ksi]prop1(t))
+j@t21:=th1"l.imp"(a,one"l.e"(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one"l.e"(ksi,[t:ksi]prop1(t))
+-ite
+j@ite:=ind"l.e"(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
++*ite
+j@t22:=oneax"l.e"(ksi,[t:ksi]prop1(t),t21):prop1(ite)
+t23:=ande1"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(a,[t:a]is(ite,<t>x))
+t24:=ande2"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(not(a),[t:not(a)]is(ite,<t>y))
+-ite
+j@[a1:a]
+itet:=mp(a,[t:a]is".ite"(ite,<t>x),a1,t23".ite"):is".ite"(ksi,ite,<a1>x)
+j@[n:not(a)]
+itef:=mp(not(a),[t:not(a)]is".ite"(ite,<t>y),n,t24".ite"):is".ite"(ksi,ite,<n>y)
+-r
++*e
++st
+sigma@set:='prim':'type'
+[s:sigma][s0:set]
+esti:='prim':'prop'
+p@setof:='prim':set
+[s:sigma][sp:<s>p]
+estii:='prim':esti(s,setof(p))
+s@[e:esti(s,setof(p))]
+estie:='prim':<s>p
+sigma@[s0:set]
+empty:=non([x:sigma]esti(x,s0)):'prop'
+nonempty:=some([x:sigma]esti(x,s0)):'prop'
+[n:[x:sigma]not(esti(x,s0))]
+emptyi:=n:empty(s0)
+s0@[e:empty(s0)][s:sigma]
+emptye:=<s>e:not(esti(s,s0))
+s0@[s:sigma][ses0:esti(s,s0)]
+nonemptyi:=somei([x:sigma]esti(x,s0),s,ses0):nonempty(s0)
+s0@[n:nonempty(s0)][x:'prop'][x1:[y:sigma][z:esti(y,s0)]x]
+nonemptyapp:=someapp([y:sigma]esti(y,s0),n,x,x1):x
+s0@[t0:set]
+incl:=all([x:sigma]imp(esti(x,s0),esti(x,t0))):'prop'
+[e:[x:sigma][y:esti(x,s0)]esti(x,t0)]
+incli:=e:incl(s0,t0)
+t0@[i:incl(s0,t0)][s:sigma][ses0:esti(s,s0)]
+incle:=<ses0><s>i:esti(s,t0)
+s0@refincl:=[x:sigma][y:esti(x,s0)]y:incl(s0,s0)
+t0@disj:=all([x:sigma]ec(esti(x,s0),esti(x,t0))):'prop'
+[n:[x:sigma][y:esti(x,s0)]not(esti(x,t0))]
+disji1:=n:disj(s0,t0)
+t0@[n:[x:sigma][y:esti(x,t0)]not(esti(x,s0))]
+disji2:=[x:sigma]th2"l.ec"(esti(x,s0),esti(x,t0),<x>n):disj(s0,t0)
+t0@[d:disj(s0,t0)][s:sigma][ses0:esti(s,s0)]
+disje1:=ece1(esti(s,s0),esti(s,t0),<s>d,ses0):not(esti(s,t0))
+s@[set0:esti(s,t0)]
+disje2:=ece2(esti(s,s0),esti(s,t0),<s>d,set0):not(esti(s,s0))
+t0@[d:disj(s0,t0)]
+symdisj:=[x:sigma][y:esti(x,t0)]disje2(d,x,y):disj(t0,s0)
++disj
+t0@[s:sigma][ses0:esti(s,s0)][set0:esti(s,t0)]
+th1:=th1"l.all"([x:sigma]ec(esti(x,s0),esti(x,t0)),s,th4"l.imp"(esti(s,s0),not(esti(s,t0)),ses0,weli(esti(s,t0),set0))):not(disj(s0,t0))
+th2:=th1(t0,s0,s,set0,ses0):not(disj(t0,s0))
+-disj
+t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
+issete1:=isp(set,[x:set]esti(s,x),s0,t0,ses0,i):esti(s,t0)
+s@[set0:esti(s,t0)]
+issete2:=isp1(set,[x:set]esti(s,x),t0,s0,set0,i):esti(s,s0)
++isset
+i@th1:=[x:sigma][y:esti(x,s0)]issete1(x,y):incl(s0,t0)
+th2:=[x:sigma][y:esti(x,t0)]issete2(x,y):incl(t0,s0)
+-isset
+t0@[i:incl(s0,t0)][j:incl(t0,s0)]
+isseti:='prim':is(set,s0,t0)
++*isset
+t0@[s:sigma][ses0:esti(s,s0)][n:not(esti(s,t0))]
+th3:=th3"l.imp"(is(set,s0,t0),esti(s,t0),n,[t:is(set,s0,t0)]issete1(t,s,ses0)):not(is(set,s0,t0))
+th4:=symnotis(set,s0,t0,th3):not(is(set,t0,s0))
+s@nissetprop:=and(esti(s,s0),not(esti(s,t0))):'prop'
+[n:not(nissetprop(s0,t0,s))][e:esti(s,s0)]
+t1:=et(esti(s,t0),th3"l.and"(esti(s,s0),not(esti(s,t0)),n,e)):esti(s,t0)
+t0@[n:not(is(set,s0,t0))][m:not(some([x:sigma]nissetprop(s0,t0,x)))][l:non([x:sigma]nissetprop(t0,s0,x))][s:sigma]
+t2:=th4"l.some"([x:sigma]nissetprop(s0,t0,x),m,s):not(nissetprop(s0,t0,s))
+t3:=<s>l:not(nissetprop(t0,s0,s))
+l@t4:=isseti(s0,t0,[x:sigma][y:esti(x,s0)]t1(s0,t0,x,t2(x),y),[x:sigma][y:esti(x,t0)]t1(t0,s0,x,t3(x),y)):is(set,s0,t0)
+m@t5:=th3"l.imp"(non([x:sigma]nissetprop(t0,s0,x)),is(set,s0,t0),n,[y:non([x:sigma]nissetprop(t0,s0,x))]t4(y)):some([x:sigma]nissetprop(t0,s0,x))
+n@th5:=th1"l.or"(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)),[y:not(some([x:sigma]nissetprop(s0,t0,x)))]t5(y)):or(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)))
+-isset
+sigma@[alpha:'type'][sa:[x:alpha]set]
+unmore:=setof([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa))):set
+[s:sigma][a:alpha][seasa:esti(s,<a>sa)]
+eunmore1:=estii([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa)),s,somei(alpha,[y:alpha]esti(s,<y>sa),a,seasa)):esti(s,unmore(sa))
+s@[seun:esti(s,unmore(sa))][x:'prop'][x1:[y:alpha][z:esti(s,<y>sa)]x]
+unmoreapp:=someapp(alpha,[y:alpha]esti(s,<y>sa),estie([z:sigma]some(alpha,[y:alpha]esti(z,<y>sa)),s,seun),x,x1):x
++eq
+sigma@[r:[x:sigma][y:sigma]'prop'][refr1:[x:sigma]<x><x>r][symr1:[x:sigma][y:sigma][t:<y><x>r]<x><y>r][trr1:[x:sigma][y:sigma][z:sigma][t:<y><x>r][u:<z><y>r]<z><x>r][s:sigma]
+refr:=<s>refr1:<s><s>r
+[t:sigma][tsr:<t><s>r]
+symr:=<tsr><t><s>symr1:<s><t>r
+t@[u:sigma][tsr:<t><s>r][utr:<u><t>r]
+trr:=<utr><tsr><u><t><s>trr1:<u><s>r
+u@[sur:<s><u>r][tur:<t><u>r]
+tr1r:=trr(s,u,t,symr(u,s,sur),tur):<t><s>r
+u@[usr:<u><s>r][utr:<u><t>r]
+tr2r:=trr(s,u,t,usr,symr(t,u,utr)):<t><s>r
+s@ecelt:=setof(<s>r):set
++1
+th1:=estii(<s>r,s,refr):esti(s,ecelt(s))
+t@[tsr:<t><s>r]
+th2:=estii(<s>r,t,tsr):esti(t,ecelt(s))
+t@[e:esti(t,ecelt(s))]
+th3:=estie(<s>r,t,e):<t><s>r
+tsr@[u:sigma][e:esti(u,ecelt(s))]
+t1:=th2(t,u,tr1r(t,u,s,tsr,th3(u,e))):esti(u,ecelt(t))
+tsr@th4:=isseti(ecelt(s),ecelt(t),[x:sigma][y:esti(x,ecelt(s))]t1(x,y),[x:sigma][y:esti(x,ecelt(t))]t1(t,s,symr(tsr),x,y)):is(set,ecelt(s),ecelt(t))
+t@[n:not(<t><s>r)][u:sigma][e:esti(u,ecelt(s))]
+t2:=th3"l.imp"(esti(u,ecelt(t)),<t><s>r,n,[x:esti(u,ecelt(t))]tr2r(s,t,u,th3(u,e),th3(t,u,x))):not(esti(u,ecelt(t)))
+n@th5:=[x:sigma][y:esti(x,ecelt(s))]t2(x,y):disj(ecelt(s),ecelt(t))
+s@th6:=nonemptyi(ecelt(s),s,th1):nonempty(ecelt(s))
+-1
+trr1@[s0:set][s:sigma]
+ecp:=is(set,s0,ecelt(s)):'prop'
+s0@anec:=some([x:sigma]ecp(x)):'prop'
++2
+trr1@[s:sigma]
+th1:=somei([x:sigma]ecp(ecelt(s),x),s,refis(set,ecelt(s))):anec(ecelt(s))
+-2
+[ecs0:anec(s0)]
++*2
+ecs0@[s:sigma][ses0:esti(s,s0)][t:sigma][e:ecp(s0,t)]
+t1:=issete1(s0,ecelt(t),e,s,ses0):esti(s,ecelt(t))
+t2:=th4"eq.1"(t,s,th3"eq.1"(t,s,t1)):is(set,ecelt(t),ecelt(s))
+t3:=tris(set,s0,ecelt(t),ecelt(s),e,t2):is(set,s0,ecelt(s))
+ses0@th2:=someapp([x:sigma]ecp(x),ecs0,is(set,s0,ecelt(s)),[x:sigma][y:ecp(x)]t3(x,y)):is(set,s0,ecelt(s))
+[t:sigma][tes0:esti(t,s0)]
+th3:=th3"eq.1"(s,t,issete1(s0,ecelt(s),th2,t,tes0)):<t><s>r
+t@[tsr:<t><s>r]
+th4:=issete2(s0,ecelt(s),th2,t,th2"eq.1"(s,t,tsr)):esti(t,s0)
+ecs0@[s:sigma][e:ecp(s0,s)]
+t4:=isp(set,[x:set]nonempty(x),ecelt(s),s0,th6"eq.1"(s),symis(set,s0,ecelt(s),e)):nonempty(s0)
+ecs0@th5:=someapp([x:sigma]ecp(x),ecs0,nonempty(s0),[x:sigma][y:ecp(x)]t4(x,y)):nonempty(s0)
+-2
++3
+ecs0@[t0:set][ect0:anec(t0)][s:sigma][ses0:esti(s,s0)][t:sigma][tet0:esti(t,t0)][tsr:<t><s>r]
+th1:=tr3is(set,s0,ecelt(s),ecelt(t),t0,th2"eq.2"(s0,ecs0,s,ses0),th4"eq.1"(s,t,tsr),symis(set,t0,ecelt(t),th2"eq.2"(t0,ect0,t,tet0))):is(set,s0,t0)
+tet0@[n:not(<t><s>r)]
+t1:=isp1(set,[x:set]disj(x,ecelt(t)),ecelt(s),s0,th5"eq.1"(s,t,n),th2"eq.2"(s0,ecs0,s,ses0)):disj(s0,ecelt(t))
+th2:=isp1(set,[x:set]disj(s0,x),ecelt(t),t0,t1,th2"eq.2"(t0,ect0,t,tet0)):disj(s0,t0)
+t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
+t2:=issete1(s0,t0,i,s,ses0):esti(s,t0)
+t3:=th1"st.disj"(s0,t0,s,ses0,t2):not(disj(s0,t0))
+i@th3:=nonemptyapp(s0,th5"eq.2"(s0,ecs0),not(disj(s0,t0)),[x:sigma][y:esti(x,s0)]t3(x,y)):not(disj(s0,t0))
+-3
+trr1@ect:=ot(set,[x:set]anec(x)):'type'
+ecs0@ectset:=out(set,[x:set]anec(x),s0,ecs0):ect
+trr1@[s:sigma]
+ectelt:=ectset(ecelt(s),th1".2"(s)):ect
+trr1@[e:ect]
+ecect:=in(set,[x:set]anec(x),e):set
++4
+th1:=inp(set,[x:set]anec(x),e):anec(ecect(e))
+th2:=th5"eq.2"(ecect(e),th1):nonempty(ecect(e))
+[x:'prop'][x1:[y:sigma][z:esti(y,ecect(e))]x]
+th3:=nonemptyapp(ecect(e),th2,x,x1):x
+s@th4:=isinout(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s)):is(set,ecelt(s),ecect(ectelt(s)))
+th5:=issete1(ecelt(s),ecect(ectelt(s)),th4,s,th1"eq.1"(s)):esti(s,ecect(ectelt(s)))
+th6:=eunmore1(ect,[x:ect]ecect(x),s,ectelt(s),th5):esti(s,unmore(ect,[x:ect]ecect(x)))
+e@[s:sigma][see:esti(s,ecect(e))][t:sigma][tee:esti(t,ecect(e))]
+th7:=th3"eq.2"(ecect(e),th1,s,see,t,tee):<t><s>r
+t@[tsr:<t><s>r]
+th8:=th4"eq.2"(ecect(e),th1,s,see,t,tsr):esti(t,ecect(e))
+-4
++5
+[f:ect][i:is(ect,e,f)]
+th1:=isini(set,[x:set]anec(x),e,f,i):is(set,ecect(e),ecect(f))
+f@[i:is(set,ecect(e),ecect(f))]
+th2:=isine(set,[x:set]anec(x),e,f,i):is(ect,e,f)
+f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))][tsr:<t><s>r]
+th3:=th2(th1"eq.3"(ecect(e),th1"eq.4"(e),ecect(f),th1"eq.4"(f),s,see,t,tef,tsr)):is(ect,e,f)
+see@[i:is(ect,e,f)]
+th4:=issete1(ecect(e),ecect(f),th1(i),s,see):esti(s,ecect(f))
+tef@[i:is(ect,e,f)]
+th5:=th3"eq.2"(ecect(f),th1"eq.4"(f),s,th4(i),t,tef):<t><s>r
+trr1@[s:sigma][t:sigma][tsr:<t><s>r]
+th6:=isouti(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s),ecelt(t),th1"eq.2"(t),th4"eq.1"(s,t,tsr)):is(ect,ectelt(s),ectelt(t))
+-5
+trr1@[alpha:'type'][fu:[x:sigma]alpha]
+fixfu:=[x:sigma][y:sigma][z:<y><x>r]is(alpha,<x>fu,<y>fu):'prop'
++10
+[ff:fixfu][e:ect][a1:alpha][s:sigma]
+prop1:=and(esti(s,ecect(e)),is(alpha,<s>fu,a1)):'prop'
+a1@prop2:=some([x:sigma]prop1(x)):'prop'
+e@[s:sigma][see:esti(s,ecect(e))]
+t1:=andi(esti(s,ecect(e)),is(alpha,<s>fu,<s>fu),see,refis(alpha,<s>fu)):prop1(<s>fu,s)
+t2:=somei([x:sigma]prop1(<s>fu,x),s,t1):prop2(<s>fu)
+t3:=somei(alpha,[x:alpha]prop2(x),<s>fu,t2):some(alpha,[x:alpha]prop2(x))
+e@t4:=th3"eq.4"(e,some(alpha,[x:alpha]prop2(x)),[x:sigma][y:esti(x,ecect(e))]t3(x,y)):some(alpha,[x:alpha]prop2(x))
+a1@[b1:alpha][pa1:prop2(a1)][pb1:prop2(b1)][s:sigma][pa1s:prop1(a1,s)][t:sigma][pb1t:prop1(b1,t)]
+t5:=ande1(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):esti(s,ecect(e))
+t6:=ande1(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):esti(t,ecect(e))
+t7:=th7"eq.4"(e,s,t5,t,t6):<t><s>r
+t8:=ande2(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):is(alpha,<s>fu,a1)
+t9:=ande2(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):is(alpha,<t>fu,b1)
+t10:=tr3is(alpha,a1,<s>fu,<t>fu,b1,symis(alpha,<s>fu,a1,t8),<t7><t><s>ff,t9):is(alpha,a1,b1)
+pa1s@t11:=someapp([x:sigma]prop1(b1,x),pb1,is(alpha,a1,b1),[x:sigma][y:prop1(b1,x)]t10(x,y)):is(alpha,a1,b1)
+pb1@t12:=someapp([x:sigma]prop1(a1,x),pa1,is(alpha,a1,b1),[x:sigma][y:prop1(a1,x)]t11(x,y)):is(alpha,a1,b1)
+e@t13:=[x:alpha][y:alpha][u:prop2(x)][v:prop2(y)]t12(x,y,u,v):amone(alpha,[x:alpha]prop2(x))
+t14:=onei(alpha,[x:alpha]prop2(x),t13,t4):one(alpha,[x:alpha]prop2(x))
+-10
+e".10"@indeq:=ind(alpha,[x:alpha]prop2".10"(x),t14".10"):alpha
++*10
+e@th1:=oneax(alpha,[x:alpha]prop2(x),t14):some([x:sigma]and(esti(x,ecect(e)),is(alpha,<x>fu,indeq)))
+[s:sigma][see:esti(s,ecect(e))]
+th2:=t12(<s>fu,indeq,t2(s,see),th1):is(alpha,<s>fu,indeq)
+ff@[s:sigma]
+th3:=th2(ectelt(s),s,th5"eq.4"(s)):is(alpha,<s>fu,indeq(ectelt(s)))
+-10
+alpha@[fu2:[x:sigma][y:sigma]alpha]
+fixfu2:=[x:sigma][y:sigma][z:sigma][u:sigma][v:<y><x>r][w:<u><z>r]is(alpha,<z><x>fu2,<u><y>fu2):'prop'
++11
+[ff2:fixfu2][s:sigma][t:sigma][tsr:<t><s>r][u:sigma]
+t1:=<refr(u)><tsr><u><u><t><s>ff2:is(alpha,<u><s>fu2,<u><t>fu2)
+tsr@t2:=fisi(sigma,alpha,<s>fu2,<t>fu2,[x:sigma]t1(x)):is([x:sigma]alpha,<s>fu2,<t>fu2)
+ff2@[e:ect]
+i:=indeq([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e):[x:sigma]alpha
+[s:sigma][t:sigma][tsr:<t><s>r][u:sigma][uee:esti(u,ecect(e))]
+t3:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,u,uee):is([x:sigma]alpha,<u>fu2,i)
+t4:=fise(alpha,<u>fu2,i,t3,s):is(alpha,<s><u>fu2,<s>i)
+t5:=fise(alpha,<u>fu2,i,t3,t):is(alpha,<t><u>fu2,<t>i)
+t6:=<tsr><refr(u)><t><s><u><u>ff2:is(alpha,<s><u>fu2,<t><u>fu2)
+t7:=tr3is(alpha,<s>i,<s><u>fu2,<t><u>fu2,<t>i,symis(alpha,<s><u>fu2,<s>i,t4),t6,t5):is(alpha,<s>i,<t>i)
+tsr@t8:=th3"eq.4"(e,is(alpha,<s>i,<t>i),[x:sigma][y:esti(x,ecect(e))]t7(x,y)):is(alpha,<s>i,<t>i)
+-11
+e".11"@[f:ect]
+indeq2:=indeq(i".11",[x:sigma][y:sigma][z:<y><x>r]t8".11"(x,y,z),f):alpha
++*11
+f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))]
+t9:=th2"eq.10"(i,[x:sigma][y:sigma][z:<y><x>r]t8(x,y,z),f,t,tef):is(alpha,<t>i,indeq2(e,f))
+t10:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,s,see):is([x:sigma]alpha,<s>fu2,i)
+t11:=fise(alpha,<s>fu2,i,t10,t):is(alpha,<t><s>fu2,<t>i)
+th1:=tris(alpha,<t><s>fu2,<t>i,indeq2,t11,t9):is(alpha,<t><s>fu2,indeq2(e,f))
+ff2@[s:sigma][t:sigma]
+th2:=th1(ectelt(s),ectelt(t),s,th5"eq.4"(s),t,th5"eq.4"(t)):is(alpha,<t><s>fu2,indeq2(ectelt(s),ectelt(t)))
+-11
++landau
++n
+@nat:='prim':'type'
+[x:nat][y:nat]
+is:=is"e"(nat,x,y):'prop'
+nis:=not(is(x,y)):'prop'
+x@[s:set(nat)]
+in:=esti(nat,x,s):'prop'
+@[p:[x:nat]'prop']
+some:=some"l"(nat,p):'prop'
+all:=all"l"(nat,p):'prop'
+one:=one"e"(nat,p):'prop'
+@1:='prim':nat
+suc:='prim':[x:nat]nat
+[x:nat][y:nat][i:is(x,y)]
+ax2:=isf(nat,nat,suc,x,y,i):is(<x>suc,<y>suc)
+@ax3:='prim':[x:nat]nis(<x>suc,1)
+ax4:='prim':[x:nat][y:nat][u:is(<x>suc,<y>suc)]is(x,y)
+[s:set(nat)]
+cond1:=in(1,s):'prop'
+cond2:=all([x:nat]imp(in(x,s),in(<x>suc,s))):'prop'
+@ax5:='prim':[s:set(nat)][u:cond1(s)][v:cond2(s)][x:nat]in(x,s)
+[p:[x:nat]'prop'][1p:<1>p][xsp:[x:nat][y:<x>p]<<x>suc>p][x:nat]
++i1
+s:=setof(nat,p):set(nat)
+t1:=estii(nat,p,1,1p):cond1(s)
+[y:nat][yes:in(y,s)]
+t2:=estie(nat,p,y,yes):<y>p
+t3:=estii(nat,p,<y>suc,<t2><y>xsp):in(<y>suc,s)
+x@t4:=<x><[y:nat][u:in(y,s)]t3(y,u)><t1><s>ax5:in(x,s)
+-i1
+induction:=estie(nat,p,x,t4".i1"):<x>p
+@[x:nat][y:nat][n:nis(x,y)]
++21
+[i:is(<x>suc,<y>suc)]
+t1:=<i><y><x>ax4:is(x,y)
+-21
+satz1:=th3"l.imp"(is(<x>suc,<y>suc),is(x,y),n,[u:is(<x>suc,<y>suc)]t1".21"(u)):nis(<x>suc,<y>suc)
++22
+x@prop1:=nis(<x>suc,x):'prop'
+@t1:=<1>ax3:prop1(1)
+x@[p:prop1(x)]
+t2:=satz1(<x>suc,x,p):prop1(<x>suc)
+-22
+x@satz2:=induction([y:nat]prop1".22"(y),t1".22",[y:nat][u:prop1".22"(y)]t2".22"(y,u),x):nis(<x>suc,x)
++23
+prop1:=or(is(x,1),some([u:nat]is(x,<u>suc))):'prop'
+@t1:=ori1(is(1,1),some([u:nat]is(1,<u>suc)),refis(nat,1)):prop1(1)
+x@t2:=somei(nat,[u:nat]is(<x>suc,<u>suc),x,refis(nat,<x>suc)):some([u:nat]is(<x>suc,<u>suc))
+t3:=ori2(is(<x>suc,1),some([u:nat]is(<x>suc,<u>suc)),t2):prop1(<x>suc)
+t4:=induction([y:nat]prop1(y),t1,[y:nat][u:prop1(y)]t3(y),x):prop1(x)
+-23
+[n:nis(x,1)]
+satz3:=ore2(is(x,1),some([u:nat]is(x,<u>suc)),t4".23",n):some([u:nat]is(x,<u>suc))
+y@[z:nat][i:is(x,<y>suc)][j:is(x,<z>suc)]
++*23
+j@t5:=<tris1(nat,<y>suc,<z>suc,x,i,j)><z><y>ax4:is(y,z)
+x@t6:=[y:nat][z:nat][u:is(x,<y>suc)][v:is(x,<z>suc)]t5(y,z,u,v):amone(nat,[u:nat]is(x,<u>suc))
+-23
+n@satz3a:=onei(nat,[u:nat]is(x,<u>suc),t6".23",satz3):one([u:nat]is(x,<u>suc))
++24
+x@[f:[y:nat]nat]
+prop1:=all([y:nat]is(<<y>suc>f,<<y>f>suc)):'prop'
+prop2:=and(is(<1>f,<x>suc),prop1):'prop'
+x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
+prop3:=is(<y>a,<y>b):'prop'
+pb@t1:=ande1(is(<1>a,<x>suc),prop1(a),pa):is(<1>a,<x>suc)
+t2:=ande1(is(<1>b,<x>suc),prop1(b),pb):is(<1>b,<x>suc)
+t3:=tris2(nat,<1>a,<1>b,<x>suc,t1,t2):prop3(1)
+y@[p:prop3(y)]
+t4:=ax2(<y>a,<y>b,p):is(<<y>a>suc,<<y>b>suc)
+t5:=ande2(is(<1>a,<x>suc),prop1(a),pa):prop1(a)
+t6:=ande2(is(<1>b,<x>suc),prop1(b),pb):prop1(b)
+t7:=<y>t5:is(<<y>suc>a,<<y>a>suc)
+t8:=<y>t6:is(<<y>suc>b,<<y>b>suc)
+t9:=tr3is(nat,<<y>suc>a,<<y>a>suc,<<y>b>suc,<<y>suc>b,t7,t4,symis"e"(nat,<<y>suc>b,<<y>b>suc,t8)):prop3(<y>suc)
+y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
+pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
+x@aa:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
+prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
+@t12:=[x:nat]refis(nat,<<x>suc>suc):prop1(1,suc)
+t13:=andi(is(<1>suc,<1>suc),prop1(1,suc),refis(nat,<1>suc),t12):prop2(1,suc)
+t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),suc,t13):prop4(1)
+x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
+g:=[y:nat]<<y>f>suc:[y:nat]nat
+[y:nat]
+t15:=refis(nat,<y>g):is(<y>g,<<y>f>suc)
+pf@t16:=ande1(is(<1>f,<x>suc),prop1(f),pf):is(<1>f,<x>suc)
+t17:=tris(nat,<1>g,<<1>f>suc,<<x>suc>suc,t15(1),ax2(<1>f,<x>suc,t16)):is(<1>g,<<x>suc>suc)
+y@t18:=ande2(is(<1>f,<x>suc),prop1(f),pf):prop1(f)
+t19:=<y>t18:is(<<y>suc>f,<<y>f>suc)
+t20:=tris2(nat,<<y>suc>f,<y>g,<<y>f>suc,t19,t15):is(<<y>suc>f,<y>g)
+t21:=tris(nat,<<y>suc>g,<<<y>suc>f>suc,<<y>g>suc,t15(<y>suc),ax2(<<y>suc>f,<y>g,t20)):is(<<y>suc>g,<<y>g>suc)
+pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
+t23:=andi(is(<1>g,<<x>suc>suc),prop1(<x>suc,g),t17,t22):prop2(<x>suc,g)
+t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
+p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
+x@bb:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
+-24
+x@satz4:=onei([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),aa".24",bb".24"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,<x>suc),all([y:nat]is(<<y>suc>z,<<y>z>suc))))
+plus:=ind([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),satz4):[y:nat]nat
+y@pl:=<y>plus:nat
++*24
+x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz4):prop2(plus)
+-24
+x@satz4a:=ande1(is(<1>plus,<x>suc),prop1".24"(plus),t26".24"):is(pl(x,1),<x>suc)
++*24
+x@t27:=ande2(is(<1>plus,<x>suc),prop1(plus),t26):prop1(plus)
+-24
+y@satz4b:=<y>t27".24":is(pl(x,<y>suc),<pl(x,y)>suc)
++*24
+@t28:=t11(1,plus(1),suc,t26(1),t13):is"e"([y:nat]nat,plus(1),suc)
+-24
+x@satz4c:=fise(nat,nat,plus(1),suc,t28".24",x):is(pl(1,x),<x>suc)
++*24
+x@t29:=t11(<x>suc,plus(<x>suc),[y:nat]<<y>plus>suc,t26(<x>suc),t23(bb,plus,t26)):is"e"([y:nat]nat,plus(<x>suc),[y:nat]<<y>plus>suc)
+-24
+y@satz4d:=fise(nat,nat,plus(<x>suc),[z:nat]<<z>plus>suc,t29".24",y):is(pl(<x>suc,y),<pl(x,y)>suc)
+x@satz4e:=symis(nat,pl(x,1),<x>suc,satz4a):is(<x>suc,pl(x,1))
+y@satz4f:=symis(nat,pl(x,<y>suc),<pl(x,y)>suc,satz4b):is(<pl(x,y)>suc,pl(x,<y>suc))
+x@satz4g:=symis(nat,pl(1,x),<x>suc,satz4c):is(<x>suc,pl(1,x))
+y@satz4h:=symis(nat,pl(<x>suc,y),<pl(x,y)>suc,satz4d):is(<pl(x,y)>suc,pl(<x>suc,y))
+z@[i:is(x,y)]
+ispl1:=isf(nat,nat,[u:nat]pl(u,z),x,y,i):is(pl(x,z),pl(y,z))
+ispl2:=isf(nat,nat,[u:nat]pl(z,u),x,y,i):is(pl(z,x),pl(z,y))
+z@[u:nat][i:is(x,y)][j:is(z,u)]
+ispl12:=tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
++25
+z@prop1:=is(pl(pl(x,y),z),pl(x,pl(y,z))):'prop'
+y@t1:=tr3is(nat,pl(pl(x,y),1),<pl(x,y)>suc,pl(x,<y>suc),pl(x,pl(y,1)),satz4a(pl(x,y)),satz4f,ispl2(<y>suc,pl(y,1),x,satz4e(y))):prop1(1)
+z@[p:prop1(z)]
+t2:=ax2(pl(pl(x,y),z),pl(x,pl(y,z)),p):is(<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc)
+t3:=tr4is(nat,pl(pl(x,y),<z>suc),<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc,pl(x,<pl(y,z)>suc),pl(x,pl(y,<z>suc)),satz4b(pl(x,y),z),t2,satz4f(x,pl(y,z)),ispl2(<pl(y,z)>suc,pl(y,<z>suc),x,satz4f(y,z))):prop1(<z>suc)
+-25
+z@satz5:=induction([u:nat]prop1".25"(u),t1".25",[u:nat][v:prop1".25"(u)]t3".25"(u,v),z):is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl1:=satz5:is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl2:=symis(nat,pl(pl(x,y),z),pl(x,pl(y,z)),satz5):is(pl(x,pl(y,z)),pl(pl(x,y),z))
++26
+y@prop1:=is(pl(x,y),pl(y,x)):'prop'
+t1:=satz4a(y):is(pl(y,1),<y>suc)
+t2:=satz4c(y):is(pl(1,y),<y>suc)
+t3:=tris2(nat,pl(1,y),pl(y,1),<y>suc,t2,t1):prop1(1,y)
+[p:prop1(x,y)]
+t4:=tris(nat,<pl(x,y)>suc,<pl(y,x)>suc,pl(y,<x>suc),ax2(pl(x,y),pl(y,x),p),satz4f(y,x)):is(<pl(x,y)>suc,pl(y,<x>suc))
+t5:=satz4d:is(pl(<x>suc,y),<pl(x,y)>suc)
+t6:=tris(nat,pl(<x>suc,y),<pl(x,y)>suc,pl(y,<x>suc),t5,t4):prop1(<x>suc,y)
+-26
+y@satz6:=induction([z:nat]prop1".26"(z,y),t3".26",[z:nat][u:prop1".26"(z,y)]t6".26"(z,y,u),x):is(pl(x,y),pl(y,x))
+compl:=satz6:is(pl(x,y),pl(y,x))
++*26
+x@t7:=tris(nat,pl(x,1),<x>suc,pl(1,x),satz4a,satz4g):prop1(1)
+y@[p:prop1(y)]
+t8:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,<pl(y,x)>suc,pl(<y>suc,x),satz4b,ax2(pl(x,y),pl(y,x),p),satz4h(y,x)):prop1(<y>suc)
+y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(pl(x,y),pl(y,x))
+-26
++27
+y@prop1:=nis(y,pl(x,y)):'prop'
+x@t1:=symnotis(nat,<x>suc,1,<x>ax3):nis(1,<x>suc)
+t2:=th4"e.notis"(nat,1,<x>suc,pl(x,1),t1,satz4a):prop1(1)
+y@[p:prop1(y)]
+t3:=satz1(y,pl(x,y),p):nis(<y>suc,<pl(x,y)>suc)
+t4:=th4"e.notis"(nat,<y>suc,<pl(x,y)>suc,pl(x,<y>suc),t3,satz4b):prop1(<y>suc)
+-27
+y@satz7:=induction([z:nat]prop1".27"(z),t2".27",[z:nat][u:prop1".27"(z)]t4".27"(z,u),y):nis(y,pl(x,y))
+z@[n:nis(y,z)]
++28
+prop1:=nis(pl(x,y),pl(x,z)):'prop'
+t1:=satz1(y,z,n):nis(<y>suc,<z>suc)
+t2:=th5"e.notis"(nat,<y>suc,<z>suc,pl(1,y),pl(1,z),t1,satz4g(y),satz4g(z)):prop1(1,y,z,n)
+[p:prop1(x,y,z,n)]
+t3:=satz1(pl(x,y),pl(x,z),p):nis(<pl(x,y)>suc,<pl(x,z)>suc)
+t4:=th5"e.notis"(nat,<pl(x,y)>suc,<pl(x,z)>suc,pl(<x>suc,y),pl(<x>suc,z),t3,satz4h,satz4h(z)):prop1(<x>suc,y,z,n)
+-28
+satz8:=induction([u:nat]prop1".28"(u,y,z,n),t2".28",[u:nat][v:prop1".28"(u,y,z,n)]t4".28"(u,y,z,n,v),x):nis(pl(x,y),pl(x,z))
+z@[i:is(pl(x,y),pl(x,z))]
+satz8a:=th7"l.imp"(is(y,z),nis(pl(x,y),pl(x,z)),weli(is(pl(x,y),pl(x,z)),i),[u:nis(y,z)]satz8(u)):is(y,z)
+z@diffprop:=is(x,pl(y,z)):'prop'
++*28
+y@[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]
+t5:=satz8a(y,u,v,tris1(nat,pl(y,u),pl(y,v),x,du,dv)):is(u,v)
+-28
+y@satz8b:=[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]t5".28"(u,v,du,dv):amone(nat,[z:nat]is(x,pl(y,z)))
++29
+i:=is(x,y):'prop'
+ii:=some([u:nat]diffprop(x,y,u)):'prop'
+iii:=some([v:nat]diffprop(y,x,v)):'prop'
+[one1:i][u:nat]
+t1:=tris(nat,pl(u,x),pl(x,u),pl(y,u),compl(u,x),ispl1(u,one1)):is(pl(u,x),pl(y,u))
+t2:=th3"e.notis"(nat,x,pl(u,x),pl(y,u),satz7(u,x),t1):nis(x,pl(y,u))
+one1@t3:=th5"l.some"(nat,[u:nat]diffprop(u),[u:nat]t2(u)):not(ii)
+y@t4:=th1"l.ec"(i,ii,[z:i]t3(z)):ec(i,ii)
+one1@t5:=t3(y,x,symis(nat,x,y,one1)):not(iii)
+y@t6:=th2"l.ec"(iii,i,[z:i]t5(z)):ec(iii,i)
+[two1:ii][three1:iii][u:nat][du:diffprop(x,y,u)][v:nat][dv:diffprop(y,x,v)]
+t6a:=tr4is(nat,x,pl(y,u),pl(pl(x,v),u),pl(x,pl(v,u)),pl(pl(v,u),x),du,ispl1(y,pl(x,v),u,dv),asspl1(x,v,u),compl(x,pl(v,u))):is(x,pl(pl(v,u),x))
+t7:=mp(is(x,pl(pl(v,u),x)),con,t6a,satz7(pl(v,u),x)):con
+du@t8:=someapp(nat,[v:nat]diffprop(y,x,v),three1,con,[v:nat][dv:diffprop(y,x,v)]t7(v,dv)):con
+three1@t9:=someapp(nat,[u:nat]diffprop(u),two1,con,[u:nat][du:diffprop(u)]t8(u,du)):con
+two1@t10:=[z:iii]t9(z):not(iii)
+y@t11:=th1"l.ec"(ii,iii,[z:ii]t10(z)):ec(ii,iii)
+a:=th6"l.ec3"(i,ii,iii,t4,t11,t6):ec3(i,ii,iii)
+prop1:=or3(i,ii,iii):'prop'
+x@[j:is(x,1)]
+t12:=or3i1(i(1),ii(1),iii(1),j):prop1(1)
+x@[n:nis(x,1)][u:nat][j:is(x,<u>suc)]
+t13:=tris(nat,x,<u>suc,pl(1,u),j,satz4g(u)):is(x,pl(1,u))
+t14:=somei(nat,[z:nat]diffprop(x,1,z),u,t13):ii(1)
+t15:=someapp(nat,[u1:nat]is(x,<u1>suc),satz3(x,n),ii(1),[u1:nat][z:is(x,<u1>suc)]t14(u1,z)):ii(1)
+t16:=or3i2(i(1),ii(1),iii(1),t15):prop1(1)
+n@t16a:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),prop1(1),[u:nat][v:is(x,<u>suc)]t16(u,v)):prop1(1)
+x@t17:=th1"l.imp"(is(x,1),prop1(1),[z:is(x,1)]t12(z),[z:nis(x,1)]t16a(z)):prop1(1)
+y@[p:prop1(y)][one1:i(y)]
+t18:=tris(nat,<y>suc,pl(y,1),pl(x,1),satz4e(y),ispl1(y,x,1,symis(nat,x,y,one1))):is(<y>suc,pl(x,1))
+t19:=somei(nat,[z:nat]diffprop(<y>suc,x,z),1,t18):iii(<y>suc)
+t20:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t19):prop1(<y>suc)
+p@[two1:ii(y)][u:nat][du:diffprop(x,y,u)][j:is(u,1)]
+t21:=tr3is(nat,x,pl(y,u),pl(y,1),<y>suc,du,ispl2(u,1,y,j),satz4a(y)):is(x,<y>suc)
+t22:=or3i1(i(<y>suc),ii(<y>suc),iii(<y>suc),t21):prop1(<y>suc)
+du@[n:nis(u,1)][w:nat][j:is(u,<w>suc)]
+t23:=tris(nat,u,<w>suc,pl(1,w),j,satz4g(w)):is(u,pl(1,w))
+t24:=tr4is(nat,x,pl(y,u),pl(y,pl(1,w)),pl(pl(y,1),w),pl(<y>suc,w),du,ispl2(u,pl(1,w),y,t23),asspl2(y,1,w),ispl1(pl(y,1),<y>suc,w,satz4a(y))):is(x,pl(<y>suc,w))
+t25:=somei(nat,[z:nat]diffprop(x,<y>suc,z),w,t24):ii(<y>suc)
+n@t26:=someapp(nat,[z:nat]is(u,<z>suc),satz3(u,n),ii(<y>suc),[z:nat][v:is(u,<z>suc)]t25(z,v)):ii(<y>suc)
+t27:=or3i2(i(<y>suc),ii(<y>suc),iii(<y>suc),t26):prop1(<y>suc)
+du@t28:=th1"l.imp"(is(u,1),prop1(<y>suc),[z:is(u,1)]t22(z),[z:nis(u,1)]t27(z)):prop1(<y>suc)
+two1@t28a:=someapp(nat,[u:nat]diffprop(u),two1,prop1(<y>suc),[u:nat][du:diffprop(u)]t28(u,du)):prop1(<y>suc)
+p@[three1:iii(y)][v:nat][dv:diffprop(y,x,v)]
+t29:=tris(nat,<y>suc,<pl(x,v)>suc,pl(x,<v>suc),ax2(y,pl(x,v),dv),satz4f(x,v)):is(<y>suc,pl(x,<v>suc))
+t30:=somei(nat,[z:nat]diffprop(<y>suc,x,z),<v>suc,t29):iii(<y>suc)
+three1@t31:=someapp(nat,[v:nat]diffprop(y,x,v),three1,iii(<y>suc),[v:nat][dv:diffprop(y,x,v)]t30(v,dv)):iii(<y>suc)
+t32:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t31):prop1(<y>suc)
+p@t33:=or3app(i(y),ii(y),iii(y),prop1(<y>suc),p,[z:i(y)]t20(z),[z:ii(y)]t28a(z),[z:iii(y)]t32(z)):prop1(<y>suc)
+y@b:=induction([z:nat]prop1(z),t17,[z:nat][u:prop1(z)]t33(z,u),y):or3(i,ii,iii)
+-29
+satz9:=orec3i(i".29",ii".29",iii".29",b".29",a".29"):orec3(is(x,y),some([u:nat]is(x,pl(y,u))),some([v:nat]is(y,pl(x,v))))
+satz9a:=b".29":or3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
+satz9b:=a".29":ec3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
+more:=some([u:nat]diffprop(x,y,u)):'prop'
+less:=some([v:nat]diffprop(y,x,v)):'prop'
+satz10:=satz9:orec3(is(x,y),more(x,y),less(x,y))
+satz10a:=satz9a:or3(is(x,y),more(x,y),less(x,y))
+satz10b:=satz9b:ec3(is(x,y),more(x,y),less(x,y))
+[m:more(x,y)]
+satz11:=m:less(y,x)
+y@[l:less(x,y)]
+satz12:=l:more(y,x)
+y@moreis:=or(more,is(x,y)):'prop'
+lessis:=or(less,is(x,y)):'prop'
+[m:moreis(x,y)]
+satz13:=th9"l.or"(more,is(x,y),less(y,x),is(y,x),m,[z:more]satz11(z),[z:is(x,y)]symis(nat,x,y,z)):lessis(y,x)
+y@[l:lessis(x,y)]
+satz14:=th9"l.or"(less,is(x,y),more(y,x),is(y,x),l,[z:less]satz12(z),[z:is(x,y)]symis(nat,x,y,z)):moreis(y,x)
+z@[i:is(x,y)][m:more(x,z)]
+ismore1:=isp(nat,[u:nat]more(u,z),x,y,m,i):more(y,z)
+i@[m:more(z,x)]
+ismore2:=isp(nat,[u:nat]more(z,u),x,y,m,i):more(z,y)
+i@[l:less(x,z)]
+isless1:=isp(nat,[u:nat]less(u,z),x,y,l,i):less(y,z)
+i@[l:less(z,x)]
+isless2:=isp(nat,[u:nat]less(z,u),x,y,l,i):less(z,y)
+i@[m:moreis(x,z)]
+ismoreis1:=isp(nat,[u:nat]moreis(u,z),x,y,m,i):moreis(y,z)
+i@[m:moreis(z,x)]
+ismoreis2:=isp(nat,[u:nat]moreis(z,u),x,y,m,i):moreis(z,y)
+i@[l:lessis(x,z)]
+islessis1:=isp(nat,[u:nat]lessis(u,z),x,y,l,i):lessis(y,z)
+i@[l:lessis(z,x)]
+islessis2:=isp(nat,[u:nat]lessis(z,u),x,y,l,i):lessis(z,y)
+y@[i:is(x,y)]
+moreisi2:=ori2(more(x,y),is(x,y),i):moreis(x,y)
+lessisi2:=ori2(less(x,y),is(x,y),i):lessis(x,y)
+y@[m:more(x,y)]
+moreisi1:=ori1(more(x,y),is(x,y),m):moreis(x,y)
+y@[l:less(x,y)]
+lessisi1:=ori1(less(x,y),is(x,y),l):lessis(x,y)
+z@[u:nat][i:is(x,y)][j:is(z,u)][m:more(x,z)]
+ismore12:=ismore2(z,u,y,j,ismore1(x,y,z,i,m)):more(y,u)
+j@[l:less(x,z)]
+isless12:=isless2(z,u,y,j,isless1(x,y,z,i,l)):less(y,u)
+j@[m:moreis(x,z)]
+ismoreis12:=ismoreis2(z,u,y,j,ismoreis1(x,y,z,i,m)):moreis(y,u)
+j@[l:lessis(x,z)]
+islessis12:=islessis2(z,u,y,j,islessis1(x,y,z,i,l)):lessis(y,u)
+y@[m:moreis(x,y)]
+satz10c:=th7"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,comor(more(x,y),is(x,y),m)):not(less(x,y))
+y@[l:lessis(x,y)]
+satz10d:=th9"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,l):not(more(x,y))
+y@[n:not(more(x,y))]
+satz10e:=th2"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n):lessis(x,y)
+y@[n:not(less(x,y))]
+satz10f:=comor(is(x,y),more(x,y),th3"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n)):moreis(x,y)
+y@[m:more(x,y)]
+satz10g:=th3"l.or"(less(x,y),is(x,y),ec3e23(is(x,y),more(x,y),less(x,y),satz10b,m),ec3e21(is(x,y),more(x,y),less(x,y),satz10b,m)):not(lessis(x,y))
+y@[l:less(x,y)]
+satz10h:=th3"l.or"(more(x,y),is(x,y),ec3e32(is(x,y),more(x,y),less(x,y),satz10b,l),ec3e31(is(x,y),more(x,y),less(x,y),satz10b,l)):not(moreis(x,y))
+y@[n:not(moreis(x,y))]
+satz10j:=or3e3(is(x,y),more(x,y),less(x,y),satz10a,th5"l.or"(more(x,y),is(x,y),n),th4"l.or"(more(x,y),is(x,y),n)):less(x,y)
+y@[n:not(lessis(x,y))]
+satz10k:=or3e2(is(x,y),more(x,y),less(x,y),satz10a,th4"l.or"(less(x,y),is(x,y),n),th5"l.or"(less(x,y),is(x,y),n)):more(x,y)
+z@[l:less(x,y)][k:less(y,z)]
++315
+[v:nat][dv:diffprop(y,x,v)][w:nat][dw:diffprop(z,y,w)]
+t1:=tr3is(nat,z,pl(y,w),pl(pl(x,v),w),pl(x,pl(v,w)),dw,ispl1(y,pl(x,v),w,dv),asspl1(x,v,w)):is(z,pl(x,pl(v,w)))
+t2:=somei(nat,[u:nat]diffprop(z,x,u),pl(v,w),t1):less(x,z)
+dv@t3:=someapp(nat,[w:nat]diffprop(z,y,w),k,less(x,z),[w:nat][dw:diffprop(z,y,w)]t2(w,dw)):less(x,z)
+-315
+satz15:=someapp(nat,[v:nat]diffprop(y,x,v),l,less(x,z),[v:nat][dv:diffprop(y,x,v)]t3".315"(v,dv)):less(x,z)
+trless:=satz15:less(x,z)
+z@[m:more(x,y)][n:more(y,z)]
+trmore:=satz15(z,y,x,n,m):more(x,z)
++*315
+n@anders:=satz12(z,x,satz15(z,y,x,satz11(y,z,n),satz11(m))):more(x,z)
+-315
+z@[l:lessis(x,y)][k:less(y,z)]
+satz16a:=orapp(less(x,y),is(x,y),less(x,z),l,[u:less(x,y)]trless(u,k),[u:is(x,y)]isless1(y,x,z,symis(nat,x,y,u),k)):less(x,z)
+z@[l:less(x,y)][k:lessis(y,z)]
+satz16b:=orapp(less(y,z),is(y,z),less(x,z),k,[u:less(y,z)]trless(l,u),[u:is(y,z)]isless2(y,z,x,u,l)):less(x,z)
+z@[m:moreis(x,y)][n:more(y,z)]
+satz16c:=satz16b(z,y,x,n,satz13(m)):more(x,z)
+z@[m:more(x,y)][n:moreis(y,z)]
+satz16d:=satz16a(z,y,x,satz13(y,z,n),m):more(x,z)
+z@[l:lessis(x,y)][k:lessis(y,z)]
++317
+[i:is(x,y)][j:is(y,z)]
+t1:=lessisi2(x,z,tris(nat,x,y,z,i,j)):lessis(x,z)
+i@[j:less(y,z)]
+t2:=lessisi1(x,z,satz16a(l,j)):lessis(x,z)
+i@t3:=orapp(less(y,z),is(y,z),lessis(x,z),k,[u:less(y,z)]t2(u),[u:is(y,z)]t1(u)):lessis(x,z)
+k@[j:less(x,y)]
+t4:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
+-317
+satz17:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t4".317"(u),[u:is(x,y)]t3".317"(u)):lessis(x,z)
++*317
+k@[j:less(x,y)]
+t5:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
+k@[i:is(x,y)]
+t6:=islessis1(y,x,z,symis(nat,x,y,i),k):lessis(x,z)
+k@anders:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t5(u),[u:is(x,y)]t6(u)):lessis(x,z)
+-317
+k@trlessis:=satz17:lessis(x,z)
+z@[m:moreis(x,y)][n:moreis(y,z)]
+trmoreis:=satz14(z,x,satz17(z,y,x,satz13(y,z,n),satz13(m))):moreis(x,z)
+y@satz18:=somei(nat,[u:nat]diffprop(pl(x,y),x,u),y,refis(nat,pl(x,y))):more(pl(x,y),x)
+satz18a:=satz18:less(x,pl(x,y))
+x@satz18b:=ismore1(pl(x,1),<x>suc,x,satz4a,satz18(1)):more(<x>suc,x)
+satz18c:=satz18b:less(x,<x>suc)
+z@[m:more(x,y)]
++319
+[u:nat][du:diffprop(u)]
+t1:=tris(nat,x,pl(y,u),pl(u,y),du,compl(y,u)):is(x,pl(u,y))
+t2:=tr3is(nat,pl(x,z),pl(pl(u,y),z),pl(u,pl(y,z)),pl(pl(y,z),u),ispl1(x,pl(u,y),z,t1),asspl1(u,y,z),compl(u,pl(y,z))):is(pl(x,z),pl(pl(y,z),u))
+t3:=somei(nat,[v:nat]diffprop(pl(x,z),pl(y,z),v),u,t2):more(pl(x,z),pl(y,z))
+-319
+satz19a:=someapp(nat,[u:nat]diffprop(u),m,more(pl(x,z),pl(y,z)),[u:nat][v:diffprop(u)]t3".319"(u,v)):more(pl(x,z),pl(y,z))
+z@[i:is(x,y)]
+satz19b:=ispl1(x,y,z,i):is(pl(x,z),pl(y,z))
+z@[l:less(x,y)]
+satz19c:=satz11(pl(y,z),pl(x,z),satz19a(y,x,z,satz12(x,y,l))):less(pl(x,z),pl(y,z))
++*319
+l@anders1:=satz19a(y,x,z,l):less(pl(x,z),pl(y,z))
+-319
+m@satz19d:=ismore12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19a):more(pl(z,x),pl(z,y))
+i@satz19e:=ispl2(x,y,z,i):is(pl(z,x),pl(z,y))
+l@satz19f:=isless12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19c):less(pl(z,x),pl(z,y))
++*319
+l@anders2:=satz19d(y,x,z,l):less(pl(z,x),pl(z,y))
+-319
+z@[u:nat][i:is(x,y)][m:more(z,u)]
+satz19g:=ismore2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19d(z,u,x,m)):more(pl(x,z),pl(y,u))
+satz19h:=ismore12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19g):more(pl(z,x),pl(u,y))
+i@[l:less(z,u)]
+satz19j:=isless2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19f(z,u,x,l)):less(pl(x,z),pl(y,u))
+satz19k:=isless12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19j):less(pl(z,x),pl(u,y))
+z@[m:moreis(x,y)]
++*319
+m@[n:more(x,y)]
+t4:=moreisi1(pl(x,z),pl(y,z),satz19a(n)):moreis(pl(x,z),pl(y,z))
+m@[i:is(x,y)]
+t5:=moreisi2(pl(x,z),pl(y,z),ispl1(x,y,z,i)):moreis(pl(x,z),pl(y,z))
+-319
+m@satz19l:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,z)),m,[u:more(x,y)]t4".319"(u),[u:is(x,y)]t5".319"(u)):moreis(pl(x,z),pl(y,z))
+satz19m:=ismoreis12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19l):moreis(pl(z,x),pl(z,y))
+z@[l:lessis(x,y)]
+satz19n:=satz13(pl(y,z),pl(x,z),satz19l(y,x,z,satz14(l))):lessis(pl(x,z),pl(y,z))
+satz19o:=satz13(pl(z,y),pl(z,x),satz19m(y,x,z,satz14(l))):lessis(pl(z,x),pl(z,y))
++320
+z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
+t2:=satz10b(pl(x,z),pl(y,z)):ec3(is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)))
+-320
+z@[m:more(pl(x,z),pl(y,z))]
+satz20a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),m):more(x,y)
+z@[i:is(pl(x,z),pl(y,z))]
+satz20b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),i):is(x,y)
+z@[l:less(pl(x,z),pl(y,z))]
+satz20c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),l):less(x,y)
++*320
+i@t3:=tr3is(nat,pl(z,x),pl(x,z),pl(y,z),pl(z,y),compl(z,x),i,compl(y,z)):is(pl(z,x),pl(z,y))
+andersb:=satz8a(z,x,y,t3):is(x,y)
+l@andersc:=satz20a(y,x,z,l):less(x,y)
+-320
+z@[m:more(pl(z,x),pl(z,y))]
+satz20d:=satz20a(ismore12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),m)):more(x,y)
+z@[i:is(pl(z,x),pl(z,y))]
+satz20e:=satz20b(tr3is(nat,pl(x,z),pl(z,x),pl(z,y),pl(y,z),compl(x,z),i,compl(z,y))):is(x,y)
+z@[l:less(pl(z,x),pl(z,y))]
+satz20f:=satz20c(isless12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),l)):less(x,y)
+u@[m:more(x,y)][n:more(z,u)]
++321
+t1:=satz19a(x,y,z,m):more(pl(x,z),pl(y,z))
+t2:=ismore12(pl(z,y),pl(y,z),pl(u,y),pl(y,u),compl(z,y),compl(u,y),satz19a(z,u,y,n)):more(pl(y,z),pl(y,u))
+-321
+satz21:=trmore(pl(x,z),pl(y,z),pl(y,u),t1".321",t2".321"):more(pl(x,z),pl(y,u))
++*321
+n@anders:=trmore(pl(x,z),pl(y,z),pl(y,u),satz19a(x,y,z,m),satz19d(z,u,y,n)):more(pl(x,z),pl(y,u))
+-321
+u@[l:less(x,y)][k:less(z,u)]
+satz21a:=satz21(y,x,u,z,l,k):less(pl(x,z),pl(y,u))
++*321
+k@andersa:=satz11(pl(y,u),pl(x,z),satz21(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(pl(x,z),pl(y,u))
+-321
+u@[m:moreis(x,y)][n:more(z,u)]
+satz22a:=orapp(more(x,y),is(x,y),more(pl(x,z),pl(y,u)),m,[v:more(x,y)]satz21(v,n),[v:is(x,y)]satz19g(u,v,n)):more(pl(x,z),pl(y,u))
+u@[m:more(x,y)][n:moreis(z,u)]
+satz22b:=orapp(more(z,u),is(z,u),more(pl(x,z),pl(y,u)),n,[v:more(z,u)]satz21(m,v),[v:is(z,u)]satz19h(z,u,x,y,v,m)):more(pl(x,z),pl(y,u))
+u@[l:lessis(x,y)][k:less(z,u)]
+satz22c:=satz22a(y,x,u,z,satz14(x,y,l),k):less(pl(x,z),pl(y,u))
+u@[l:less(x,y)][k:lessis(z,u)]
+satz22d:=satz22b(y,x,u,z,l,satz14(z,u,k)):less(pl(x,z),pl(y,u))
+u@[m:moreis(x,y)][n:moreis(z,u)]
++323
+[i:is(x,y)][j:is(z,u)]
+t1:=moreisi2(pl(x,z),pl(y,u),tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j))):moreis(pl(x,z),pl(y,u))
+i@[o:more(z,u)]
+t2:=moreisi1(pl(x,z),pl(y,u),satz22a(m,o)):moreis(pl(x,z),pl(y,u))
+i@t3:=orapp(more(z,u),is(z,u),moreis(pl(x,z),pl(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(pl(x,z),pl(y,u))
+n@[o:more(x,y)]
+t4:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
+-323
+satz23:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t4".323"(v),[v:is(x,y)]t3".323"(v)):moreis(pl(x,z),pl(y,u))
++*323
+n@[o:more(x,y)]
+t5:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
+n@[i:is(x,y)]
+t6:=ismoreis2(pl(x,u),pl(y,u),pl(x,z),ispl1(u,i),satz19m(z,u,x,n)):moreis(pl(x,z),pl(y,u))
+n@anders:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(pl(x,z),pl(y,u))
+-323
+u@[l:lessis(x,y)][k:lessis(z,u)]
+satz23a:=satz13(pl(y,u),pl(x,z),satz23(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(pl(x,z),pl(y,u))
++324
+x@[n:nis(x,1)][u:nat][i:is(x,<u>suc)]
+t1:=tris(nat,x,<u>suc,pl(1,u),i,satz4g(u)):is(x,pl(1,u))
+t2:=ismore1(pl(1,u),x,1,symis(nat,x,pl(1,u),t1),satz18(1,u)):more(x,1)
+n@t3:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),more(x,1),[u:nat][v:is(x,<u>suc)]t2(u,v)):more(x,1)
+-324
+x@satz24:=th2"l.or"(more(x,1),is(x,1),[u:nis(x,1)]t3".324"(u)):moreis(x,1)
+satz24a:=satz13(x,1,satz24):lessis(1,x)
+satz24b:=t3".324"(<x>suc,<x>ax3):more(<x>suc,1)
+satz24c:=satz24b:less(1,<x>suc)
+y@[m:more(y,x)]
++325
+[u:nat][du:diffprop(y,x,u)]
+t1:=satz19m(u,1,x,satz24(u)):moreis(pl(x,u),pl(x,1))
+t2:=ismoreis1(pl(x,u),y,pl(x,1),symis(nat,y,pl(x,u),du),t1):moreis(y,pl(x,1))
+-325
+satz25:=someapp(nat,[u:nat]diffprop(y,x,u),m,moreis(y,pl(x,1)),[u:nat][v:diffprop(y,x,u)]t2".325"(u,v)):moreis(y,pl(x,1))
+satz25a:=ismoreis2(pl(x,1),<x>suc,y,satz4a,satz25):moreis(y,<x>suc)
+y@[l:less(y,x)]
+satz25b:=satz13(x,pl(y,1),satz25(y,x,l)):lessis(pl(y,1),x)
+satz25c:=islessis1(pl(y,1),<y>suc,x,satz4a(y),satz25b):lessis(<y>suc,x)
+y@[l:less(y,pl(x,1))]
++326
+[m:more(y,x)]
+t1:=satz25(m):moreis(y,pl(x,1))
+l@t2:=th3"l.imp"(more(y,x),moreis(y,pl(x,1)),satz10h(y,pl(x,1),l),[v:more(y,x)]t1(v)):not(more(y,x))
+-326
+satz26:=satz10e(y,x,t2".326"):lessis(y,x)
+y@[l:less(y,<x>suc)]
+satz26a:=satz26(isless2(<x>suc,pl(x,1),y,satz4e,l)):lessis(y,x)
+y@[m:more(pl(y,1),x)]
+satz26b:=satz14(x,y,satz26(y,x,m)):moreis(y,x)
+y@[m:more(<y>suc,x)]
+satz26c:=satz26b(ismore1(<y>suc,pl(y,1),x,satz4e(y),m)):moreis(y,x)
+@[p:[x:nat]'prop'][n:nat]
++327
+[m:nat]
+lbprop:=imp(<m>p,lessis(n,m)):'prop'
+-327
+lb:=all([x:nat]lbprop".327"(x)):'prop'
+min:=and(lb,<n>p):'prop'
+p@[s:some(p)]
++*327
+s@[n:nat]
+t1:=[x:<n>p]satz24a(n):lbprop(1,n)
+s@t2:=[x:nat]t1(x):lb(1)
+[l:[x:nat]lb(x)][y:nat][yp:<y>p]
+t3:=satz18(y,1):more(pl(y,1),y)
+t4:=satz10g(pl(y,1),y,t3):not(lessis(pl(y,1),y))
+t5:=th4"l.imp"(<y>p,lessis(pl(y,1),y),yp,t4):not(lbprop(pl(y,1),y))
+t6:=th1"l.all"(nat,[x:nat]lbprop(pl(y,1),x),y,t5):not(lb(pl(y,1)))
+t7:=mp(lb(pl(y,1)),con,<pl(y,1)>l,t6):con
+l@t8:=someapp(nat,p,s,con,[x:nat][y:<x>p]t7(x,y)):con
+s@[n:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))][m:nat][l:lb(m)]
+t9:=<m>n:not(and(lb(m),not(lb(pl(m,1)))))
+t10:=et(lb(pl(m,1)),th3"l.and"(lb(m),not(lb(pl(m,1))),t9,l)):lb(pl(m,1))
+t11:=isp(nat,[x:nat]lb(x),pl(m,1),<m>suc,t10,satz4a(m)):lb(<m>suc)
+n@t12:=[x:nat]induction([y:nat]lb(y),t2,[y:nat][z:lb(y)]t11(y,z),x):[x:nat]lb(x)
+s@t13:=[x:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))]t8(t12(x)):some([x:nat]and(lb(x),not(lb(pl(x,1)))))
+[m:nat][a:and(lb(m),not(lb(pl(m,1))))]
+t14:=ande1(lb(m),not(lb(pl(m,1))),a):lb(m)
+t15:=ande2(lb(m),not(lb(pl(m,1))),a):not(lb(pl(m,1)))
+[nmp:not(<m>p)][n:nat][np:<n>p]
+t16:=mp(<n>p,lessis(m,n),np,<n>t14):lessis(m,n)
+t17:=th3"l.imp"(is(m,n),<m>p,nmp,[x:is(m,n)]isp(nat,p,n,m,np,symis(nat,m,n,x))):not(is(m,n))
+t18:=ore1(less(m,n),is(m,n),t16,t17):less(m,n)
+t19:=satz25b(n,m,t18):lessis(pl(m,1),n)
+nmp@t20:=[x:nat][y:<x>p]t19(x,y):lb(pl(m,1))
+t21:=mp(lb(pl(m,1)),con,t20,t15):con
+a@t22:=et(<m>p,[x:not(<m>p)]t21(x)):<m>p
+t23:=andi(lb(m),<m>p,t14,t22):min(m)
+-327
+s@satz27:=th6"l.some"(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))),[x:nat]min(x),t13".327",[x:nat][y:and(lb(x),not(lb(pl(x,1))))]t23".327"(x,y)):some([x:nat]min(p,x))
++*327
+p@[n:non(nat,[x:nat]min(x))][u:nat]
+t24:=[x:<u>p]satz24a(u):lbprop(1,u)
+n@t25:=[x:nat]t24(x):lb(1)
+u@[l:lb(u)]
+t26:=<u>n:not(min(u))
+t27:=th3"l.and"(lb(u),<u>p,t26,l):not(<u>p)
+[v:nat][vp:<v>p]
+t28:=th3"l.imp"(is(u,v),<u>p,t27,[x:is(u,v)]isp1(nat,p,v,u,vp,x)):nis(u,v)
+t29:=mp(<v>p,lessis(u,v),vp,<v>l):lessis(u,v)
+t30:=ore1(less(u,v),is(u,v),t29,t28):less(u,v)
+t31:=satz25c(v,u,t30):lessis(<u>suc,v)
+v@t32:=[x:<v>p]t31(x):lbprop(<u>suc,v)
+l@t33:=[x:nat]t32(x):lb(<u>suc)
+u@t34:=induction([x:nat]lb(x),t25,[x:nat][y:lb(x)]t33(x,y),u):lb(u)
+p@[s:some(p)][u:nat][up:<u>p]
+t35:=satz10g(<u>suc,u,satz18b(u)):not(lessis(<u>suc,u))
+t36:=th4"l.imp"(<u>p,lessis(<u>suc,u),up,t35):not(lbprop(<u>suc,u))
+t37:=th1"l.all"(nat,[x:nat]lbprop(<u>suc,x),u,t36):not(lb(<u>suc))
+t38:=[y:non(nat,[x:nat]min(x))]mp(lb(<u>suc),con,t34(y,<u>suc),t37):some([x:nat]min(x))
+s@anders:=someapp(nat,p,s,some([x:nat]min(x)),[x:nat][y:<x>p]t38(x,y)):some([x:nat]min(x))
+-327
++*327
+p@[n:nat][m:nat][mn:min(p,n)][mm:min(p,m)]
+t39:=ande1(lb(n),<n>p,mn):lb(n)
+t40:=ande1(lb(m),<m>p,mm):lb(m)
+t41:=ande2(lb(n),<n>p,mn):<n>p
+t42:=ande2(lb(m),<m>p,mm):<m>p
+t43:=<m>t39:lbprop(n,m)
+t44:=<n>t40:lbprop(m,n)
+t45:=mp(<m>p,lessis(n,m),t42,t43):lessis(n,m)
+t46:=mp(<n>p,lessis(m,n),t41,t44):lessis(m,n)
+t47:=ore2(more(n,m),is(n,m),satz14(m,n,t46),satz10d(n,m,t45)):is(n,m)
+p@t48:=[x:nat][y:nat][u:min(x)][v:min(y)]t47(x,y,u,v):amone(nat,[x:nat]min(p,x))
+-327
+s@satz27a:=onei(nat,[x:nat]min(p,x),t48".327",satz27):one([x:nat]min(p,x))
++428
+x@[f:[y:nat]nat]
+prop1:=all([y:nat]is(<<y>suc>f,pl(<y>f,x))):'prop'
+prop2:=and(is(<1>f,x),prop1):'prop'
+x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
+prop3:=is(<y>a,<y>b):'prop'
+pb@t1:=ande1(is(<1>a,x),prop1(a),pa):is(<1>a,x)
+t2:=ande1(is(<1>b,x),prop1(b),pb):is(<1>b,x)
+t3:=tris2(nat,<1>a,<1>b,x,t1,t2):prop3(1)
+y@[p:prop3(y)]
+t4:=ispl1(<y>a,<y>b,x,p):is(pl(<y>a,x),pl(<y>b,x))
+t5:=ande2(is(<1>a,x),prop1(a),pa):prop1(a)
+t6:=ande2(is(<1>b,x),prop1(b),pb):prop1(b)
+t7:=<y>t5:is(<<y>suc>a,pl(<y>a,x))
+t8:=<y>t6:is(<<y>suc>b,pl(<y>b,x))
+t9:=tr3is(nat,<<y>suc>a,pl(<y>a,x),pl(<y>b,x),<<y>suc>b,t7,t4,symis(nat,<<y>suc>b,pl(<y>b,x),t8)):prop3(<y>suc)
+y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
+pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
+x@a1:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
+prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
+@id:=[y:nat]y:[y:nat]nat
+t12:=[x:nat]satz4e(x):prop1(1,id)
+t13:=andi(is(<1>id,1),prop1(1,id),refis(nat,1),t12):prop2(1,id)
+t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),id,t13):prop4(1)
+x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
+g:=[y:nat]pl(<y>f,y):[y:nat]nat
+t15:=ande1(is(<1>f,x),prop1(f),pf):is(<1>f,x)
+t16:=tris(nat,<1>g,pl(x,1),<x>suc,ispl1(<1>f,x,1,t15),satz4a(x)):is(<1>g,<x>suc)
+[y:nat]
+t17:=ande2(is(<1>f,x),prop1(f),pf):prop1(f)
+t18:=<y>t17:is(<<y>suc>f,pl(<y>f,x))
+t19:=tris(nat,<<y>suc>g,pl(pl(<y>f,x),<y>suc),pl(<y>f,pl(x,<y>suc)),ispl1(<<y>suc>f,pl(<y>f,x),<y>suc,t18),asspl1(<y>f,x,<y>suc)):is(<<y>suc>g,pl(<y>f,pl(x,<y>suc)))
+t20:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,pl(<x>suc,y),pl(y,<x>suc),satz4b(x,y),satz4h(x,y),compl(<x>suc,y)):is(pl(x,<y>suc),pl(y,<x>suc))
+t21:=tr3is(nat,<<y>suc>g,pl(<y>f,pl(x,<y>suc)),pl(<y>f,pl(y,<x>suc)),pl(<y>g,<x>suc),t19,ispl2(pl(x,<y>suc),pl(y,<x>suc),<y>f,t20),asspl2(<y>f,y,<x>suc)):is(<<y>suc>g,pl(<y>g,<x>suc))
+pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
+t23:=andi(is(<1>g,<x>suc),prop1(<x>suc,g),t16,t22):prop2(<x>suc,g)
+t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
+p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
+x@b1:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
+-428
+x@satz28:=onei([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),a1".428",b1".428"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,x),all([y:nat]is(<<y>suc>z,pl(<y>z,x)))))
+times:=ind([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),satz28):[y:nat]nat
+y@ts:=<y>times:nat
++*428
+x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz28):prop2(times)
+-428
+x@satz28a:=ande1(is(<1>times,x),prop1".428"(times),t26".428"):is(ts(x,1),x)
++*428
+x@t27:=ande2(is(<1>times,x),prop1(times),t26):prop1(times)
+-428
+y@satz28b:=<y>t27".428":is(ts(x,<y>suc),pl(ts(x,y),x))
++*428
+@t28:=t11(1,times(1),id,t26(1),t13):is"e"([y:nat]nat,times(1),id)
+-428
+x@satz28c:=fise(nat,nat,times(1),id".428",t28".428",x):is(ts(1,x),x)
++*428
+x@t29:=t11(<x>suc,times(<x>suc),[y:nat]pl(<y>times,y),t26(<x>suc),t23(b1,times,t26)):is"e"([y:nat]nat,times(<x>suc),[y:nat]pl(<y>times,y))
+-428
+y@satz28d:=fise(nat,nat,times(<x>suc),[z:nat]pl(<z>times,z),t29".428",y):is(ts(<x>suc,y),pl(ts(x,y),y))
+x@satz28e:=symis(nat,ts(x,1),x,satz28a):is(x,ts(x,1))
+y@satz28f:=symis(nat,ts(x,<y>suc),pl(ts(x,y),x),satz28b):is(pl(ts(x,y),x),ts(x,<y>suc))
+x@satz28g:=symis(nat,ts(1,x),x,satz28c):is(x,ts(1,x))
+y@satz28h:=symis(nat,ts(<x>suc,y),pl(ts(x,y),y),satz28d):is(pl(ts(x,y),y),ts(<x>suc,y))
+z@[i:is(x,y)]
+ists1:=isf(nat,nat,[u:nat]ts(u,z),x,y,i):is(ts(x,z),ts(y,z))
+ists2:=isf(nat,nat,[u:nat]ts(z,u),x,y,i):is(ts(z,x),ts(z,y))
+z@[u:nat][i:is(x,y)][j:is(z,u)]
+ists12:=tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
++429
+y@prop1:=is(ts(x,y),ts(y,x)):'prop'
+t1:=satz28a(y):is(ts(y,1),y)
+t2:=satz28c(y):is(ts(1,y),y)
+t3:=tris2(nat,ts(1,y),ts(y,1),y,t2,t1):prop1(1,y)
+[p:prop1(x,y)]
+t4:=tris(nat,pl(ts(x,y),y),pl(ts(y,x),y),ts(y,<x>suc),ispl1(ts(x,y),ts(y,x),y,p),satz28f(y,x)):is(pl(ts(x,y),y),ts(y,<x>suc))
+t5:=satz28d:is(ts(<x>suc,y),pl(ts(x,y),y))
+t6:=tris(nat,ts(<x>suc,y),pl(ts(x,y),y),ts(y,<x>suc),t5,t4):prop1(<x>suc,y)
+-429
+y@satz29:=induction([z:nat]prop1".429"(z,y),t3".429",[z:nat][u:prop1".429"(z,y)]t6".429"(z,y,u),x):is(ts(x,y),ts(y,x))
+comts:=satz29:is(ts(x,y),ts(y,x))
++*429
+x@t7:=tris(nat,ts(x,1),x,ts(1,x),satz28a,satz28g):prop1(1)
+y@[p:prop1(y)]
+t8:=tr3is(nat,ts(x,<y>suc),pl(ts(x,y),x),pl(ts(y,x),x),ts(<y>suc,x),satz28b(x,y),ispl1(ts(x,y),ts(y,x),x,p),satz28h(y,x)):prop1(<y>suc)
+y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(ts(x,y),ts(y,x))
+-429
++430
+z@prop1:=is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z))):'prop'
+y@t1:=tr3is(nat,ts(x,pl(y,1)),ts(x,<y>suc),pl(ts(x,y),x),pl(ts(x,y),ts(x,1)),ists2(pl(y,1),<y>suc,x,satz4a(y)),satz28b,ispl2(x,ts(x,1),ts(x,y),satz28e(x))):prop1(1)
+z@[p:prop1(z)]
+t2:=tr3is(nat,ts(x,pl(y,<z>suc)),ts(x,<pl(y,z)>suc),pl(ts(x,pl(y,z)),x),pl(pl(ts(x,y),ts(x,z)),x),ists2(pl(y,<z>suc),<pl(y,z)>suc,x,satz4b(y,z)),satz28b(x,pl(y,z)),ispl1(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),x,p)):is(ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x))
+t3:=tr3is(nat,ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x),pl(ts(x,y),pl(ts(x,z),x)),pl(ts(x,y),ts(x,<z>suc)),t2,asspl1(ts(x,y),ts(x,z),x),ispl2(pl(ts(x,z),x),ts(x,<z>suc),ts(x,y),satz28f(x,z))):prop1(<z>suc)
+-430
+z@satz30:=induction([u:nat]prop1".430"(u),t1".430",[u:nat][v:prop1".430"(u)]t3".430"(u,v),z):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+disttp1:=tr3is(nat,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz30(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
+disttp2:=satz30:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+distpt1:=symis(nat,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
+distpt2:=symis(nat,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
++431
+prop1:=is(ts(ts(x,y),z),ts(x,ts(y,z))):'prop'
+y@t1:=tris(nat,ts(ts(x,y),1),ts(x,y),ts(x,ts(y,1)),satz28a(ts(x,y)),ists2(y,ts(y,1),x,satz28e(y))):prop1(1)
+z@[p:prop1(z)]
+t2:=tr4is(nat,ts(ts(x,y),<z>suc),pl(ts(ts(x,y),z),ts(x,y)),pl(ts(x,ts(y,z)),ts(x,y)),ts(x,pl(ts(y,z),y)),ts(x,ts(y,<z>suc)),satz28b(ts(x,y),z),ispl1(ts(ts(x,y),z),ts(x,ts(y,z)),ts(x,y),p),distpt2(x,ts(y,z),y),ists2(pl(ts(y,z),y),ts(y,<z>suc),x,satz28f(y,z))):prop1(<z>suc)
+-431
+satz31:=induction([u:nat]prop1".431"(u),t1".431",[u:nat][v:prop1".431"(u)]t2".431"(u,v),z):is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts1:=satz31:is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts2:=symis(nat,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
+[m:more(x,y)]
++432
+[u:nat][du:diffprop(u)]
+t1:=tris(nat,ts(x,z),ts(pl(y,u),z),pl(ts(y,z),ts(u,z)),ists1(x,pl(y,u),z,du),disttp1(y,u,z)):is(ts(x,z),pl(ts(y,z),ts(u,z)))
+t2:=somei(nat,[v:nat]diffprop(ts(x,z),ts(y,z),v),ts(u,z),t1):more(ts(x,z),ts(y,z))
+-432
+satz32a:=someapp(nat,[u:nat]diffprop(u),m,more(ts(x,z),ts(y,z)),[u:nat][v:diffprop(u)]t2".432"(u,v)):more(ts(x,z),ts(y,z))
+z@[i:is(x,y)]
+satz32b:=ists1(x,y,z,i):is(ts(x,z),ts(y,z))
+z@[l:less(x,y)]
+satz32c:=satz11(ts(y,z),ts(x,z),satz32a(y,x,z,satz12(x,y,l))):less(ts(x,z),ts(y,z))
++*432
+l@anders1:=satz32a(y,x,z,l):less(ts(x,z),ts(y,z))
+-432
+m@satz32d:=ismore12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32a):more(ts(z,x),ts(z,y))
+i@satz32e:=ists2(x,y,z,i):is(ts(z,x),ts(z,y))
+l@satz32f:=isless12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32c):less(ts(z,x),ts(z,y))
++*432
+l@anders2:=satz32d(y,x,z,l):less(ts(z,x),ts(z,y))
+-432
+z@[u:nat][i:is(x,y)][m:more(z,u)]
+satz32g:=ismore2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32d(z,u,x,m)):more(ts(x,z),ts(y,u))
+satz32h:=ismore12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32g):more(ts(z,x),ts(u,y))
+i@[l:less(z,u)]
+satz32j:=isless2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32f(z,u,x,l)):less(ts(x,z),ts(y,u))
+satz32k:=isless12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32j):less(ts(z,x),ts(u,y))
+z@[m:moreis(x,y)]
++*432
+m@[n:more(x,y)]
+t3:=moreisi1(ts(x,z),ts(y,z),satz32a(n)):moreis(ts(x,z),ts(y,z))
+m@[i:is(x,y)]
+t4:=moreisi2(ts(x,z),ts(y,z),ists1(x,y,z,i)):moreis(ts(x,z),ts(y,z))
+-432
+m@satz32l:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,z)),m,[u:more(x,y)]t3".432"(u),[u:is(x,y)]t4".432"(u)):moreis(ts(x,z),ts(y,z))
+satz32m:=ismoreis12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32l):moreis(ts(z,x),ts(z,y))
+z@[l:lessis(x,y)]
+satz32n:=satz13(ts(y,z),ts(x,z),satz32l(y,x,z,satz14(l))):lessis(ts(x,z),ts(y,z))
+satz32o:=satz13(ts(z,y),ts(z,x),satz32m(y,x,z,satz14(l))):lessis(ts(z,x),ts(z,y))
++433
+z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
+t2:=satz10b(ts(x,z),ts(y,z)):ec3(is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)))
+-433
+z@[m:more(ts(x,z),ts(y,z))]
+satz33a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),m):more(x,y)
+z@[i:is(ts(x,z),ts(y,z))]
+satz33b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),i):is(x,y)
+z@[l:less(ts(x,z),ts(y,z))]
+satz33c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),l):less(x,y)
++*433
+l@anders:=satz33a(y,x,z,l):less(x,y)
+-433
+u@[m:more(x,y)][n:more(z,u)]
++434
+t1:=satz32a(x,y,z,m):more(ts(x,z),ts(y,z))
+t2:=ismore12(ts(z,y),ts(y,z),ts(u,y),ts(y,u),comts(z,y),comts(u,y),satz32a(z,u,y,n)):more(ts(y,z),ts(y,u))
+-434
+satz34:=trmore(ts(x,z),ts(y,z),ts(y,u),t1".434",t2".434"):more(ts(x,z),ts(y,u))
++*434
+n@anders:=trmore(ts(x,z),ts(y,z),ts(y,u),satz32a(x,y,z,m),satz32d(z,u,y,n)):more(ts(x,z),ts(y,u))
+-434
+u@[l:less(x,y)][k:less(z,u)]
+satz34a:=satz34(y,x,u,z,l,k):less(ts(x,z),ts(y,u))
++*434
+k@andersa:=satz11(ts(y,u),ts(x,z),satz34(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(ts(x,z),ts(y,u))
+-434
+u@[m:moreis(x,y)][n:more(z,u)]
+satz35a:=orapp(more(x,y),is(x,y),more(ts(x,z),ts(y,u)),m,[v:more(x,y)]satz34(v,n),[v:is(x,y)]satz32g(u,v,n)):more(ts(x,z),ts(y,u))
+u@[m:more(x,y)][n:moreis(z,u)]
+satz35b:=orapp(more(z,u),is(z,u),more(ts(x,z),ts(y,u)),n,[v:more(z,u)]satz34(m,v),[v:is(z,u)]satz32h(z,u,x,y,v,m)):more(ts(x,z),ts(y,u))
+u@[l:lessis(x,y)][k:less(z,u)]
+satz35c:=satz35a(y,x,u,z,satz14(x,y,l),k):less(ts(x,z),ts(y,u))
+u@[l:less(x,y)][k:lessis(z,u)]
+satz35d:=satz35b(y,x,u,z,l,satz14(z,u,k)):less(ts(x,z),ts(y,u))
+u@[m:moreis(x,y)][n:moreis(z,u)]
++436
+[i:is(x,y)][j:is(z,u)]
+t1:=moreisi2(ts(x,z),ts(y,u),tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j))):moreis(ts(x,z),ts(y,u))
+i@[o:more(z,u)]
+t2:=moreisi1(ts(x,z),ts(y,u),satz35a(m,o)):moreis(ts(x,z),ts(y,u))
+i@t3:=orapp(more(z,u),is(z,u),moreis(ts(x,z),ts(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(ts(x,z),ts(y,u))
+n@[o:more(x,y)]
+t4:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
+-436
+satz36:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t4".436"(v),[v:is(x,y)]t3".436"(v)):moreis(ts(x,z),ts(y,u))
++*436
+n@[o:more(x,y)]
+t5:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
+n@[i:is(x,y)]
+t6:=ismoreis2(ts(x,u),ts(y,u),ts(x,z),ists1(u,i),satz32m(z,u,x,n)):moreis(ts(x,z),ts(y,u))
+n@anders:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(ts(x,z),ts(y,u))
+-436
+u@[l:lessis(x,y)][k:lessis(z,u)]
+satz36a:=satz13(ts(y,u),ts(x,z),satz36(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(ts(x,z),ts(y,u))
+y@[m:more(x,y)]
++mn
+t1:=onei(nat,[z:nat]diffprop(x,y,z),satz8b(x,y),m):one([z:nat]diffprop(x,y,z))
+-mn
+mn:=ind(nat,[z:nat]diffprop(x,y,z),t1".mn"):nat
++*mn
+m@th1a:=oneax(nat,[z:nat]diffprop(x,y,z),t1):is(x,pl(y,mn(x,y,m)))
+th1b:=symis(nat,x,pl(y,mn(x,y,m)),th1a):is(pl(y,mn(x,y,m)),x)
+th1c:=tris(nat,x,pl(y,mn(x,y,m)),pl(mn(x,y,m),y),th1a,compl(y,mn(x,y,m))):is(x,pl(mn(x,y,m),y))
+th1d:=symis(nat,x,pl(mn(x,y,m),y),th1c):is(pl(mn(x,y,m),y),x)
+y@[z:nat][m:more(x,y)][i:is(pl(y,z),x)]
+th1e:=<th1a(m)><symis(nat,pl(y,z),x,i)><mn(x,y,m)><z>satz8b(x,y):is(z,mn(x,y,m))
+-mn
+z@[u:nat][m:more(x,z)][n:more(y,u)][i:is(x,y)][j:is(z,u)]
++*mn
+j@t2:=tr3is(nat,pl(u,mn(x,z,m)),pl(z,mn(x,z,m)),x,y,ispl1(u,z,mn(x,z,m),symis(nat,z,u,j)),th1b(x,z,m),i):is(pl(u,mn(x,z,m)),y)
+-mn
+j@ismn12:=th1e".mn"(y,u,mn(x,z,m),n,t2".mn"):is(mn(x,z,m),mn(y,u,n))
+@[n:nat]
+1to:=ot(nat,[x:nat]lessis(x,n)):'type'
+[x:nat][l:lessis(x,n)]
+outn:=out(nat,[y:nat]lessis(y,n),x,l):1to(n)
+n@[xn:1to(n)]
+inn:=in"e"(nat,[y:nat]lessis(y,n),xn):nat
+1top:=inp(nat,[y:nat]lessis(y,n),xn):lessis(inn,n)
+l@[y:nat][k:lessis(y,n)][i:is(x,y)]
+isoutni:=isouti(nat,[z:nat]lessis(z,n),x,l,y,k,i):is"e"(1to(n),outn(x,l),outn(y,k))
+k@[i:is"e"(1to(n),outn(x,l),outn(y,k))]
+isoutne:=isoute(nat,[z:nat]lessis(z,n),x,l,y,k,i):is(x,y)
+xn@[yn:1to(n)][i:is"e"(1to(n),xn,yn)]
+isinni:=isini(nat,[z:nat]lessis(z,n),xn,yn,i):is(inn(xn),inn(yn))
+yn@[i:is(inn(xn),inn(yn))]
+isinne:=isine(nat,[z:nat]lessis(z,n),xn,yn,i):is"e"(1to(n),xn,yn)
+xn@isoutinn:=isoutin(nat,[y:nat]lessis(y,n),xn):is"e"(1to(n),xn,outn(inn(xn),1top(xn)))
+l@isinoutn:=isinout(nat,[y:nat]lessis(y,n),x,l):is(x,inn(outn(x,l)))
+@1o:=outn(1,1,lessisi2(1,1,refis(nat,1))):1to(1)
+[u:1to(1)]
++singlet
+u0:=inn(1,u):nat
+t1:=1top(1,u):lessis(u0,1)
+t2:=ore2(more(u0,1),is(u0,1),satz24(u0),satz10d(u0,1,t1)):is(u0,1)
+th1:=tris(1to(1),u,outn(1,u0,t1),1o,isoutinn(1,u),isoutni(1,u0,t1,1,lessisi2(1,1,refis(nat,1)),t2)):is"e"(1to(1),u,1o)
+-singlet
+@2:=pl(1,1):nat
+[x:nat]
++pair
+[l:lessis(x,2)][n:nis(x,2)]
+t1:=satz26(1,x,ore1(less(x,2),is(x,2),l,n)):lessis(x,1)
+t2:=ore2(more(x,1),is(x,1),satz24(x),satz10d(x,1,t1)):is(x,1)
+l@th1:=th2"l.or"(is(x,1),is(x,2),[t:nis(x,2)]t2(t)):or(is(x,1),is(x,2))
+@th2:=th1"e.notis"(nat,<1>suc,1,2,<1>ax3,satz4e(1)):nis(2,1)
+-pair
+@1t:=outn(2,1,satz24a(2)):1to(2)
+2t:=outn(2,2,lessisi2(2,2,refis(nat,2))):1to(2)
++*pair
+@[u:1to(2)]
+u0:=inn(2,u):nat
+t3:=1top(2,u):lessis(u0,2)
+[i:is(u0,1)]
+t4:=isoutni(2,u0,t3,1,satz24a(2),i):is"e"(1to(2),outn(2,u0,t3),1t)
+t5:=tris(1to(2),u,outn(2,u0,t3),1t,isoutinn(2,u),t4):is"e"(1to(2),u,1t)
+u@[i:is(u0,2)]
+t6:=isoutni(2,u0,t3,2,lessisi2(2,2,refis(nat,2)),i):is"e"(1to(2),outn(2,u0,t3),2t)
+t7:=tris(1to(2),u,outn(2,u0,t3),2t,isoutinn(2,u),t6):is"e"(1to(2),u,2t)
+u@th3:=th9"l.or"(is(u0,1),is(u0,2),is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),th1(u0,t3),[t:is(u0,1)]t5(t),[t:is(u0,2)]t7(t)):or(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t))
+@[i:is"e"(1to(2),2t,1t)]
+t9:=isini(nat,[x:nat]lessis(x,2),2t,1t,i):is(u0(2t),u0(1t))
+t10:=tr3is(nat,2,u0(2t),u0(1t),1,isinoutn(2,2,lessisi2(2,2,refis(nat,2))),t9,symis(nat,1,u0(1t),isinoutn(2,1,satz24a(2)))):is(2,1)
+@th4:=th3"l.imp"(is"e"(1to(2),2t,1t),is(2,1),th2,[t:is"e"(1to(2),2t,1t)]t10(t)):not(is"e"(1to(2),2t,1t))
+-pair
+@[alpha:'type']
+pair1type:=[x:1to(2)]alpha:'type'
+[a:alpha][b:alpha]
+pair1:=[x:1to(2)]ite(is"e"(1to(2),x,1t),alpha,a,b):pair1type
+alpha@[p:pair1type]
+first1:=<1t>p:alpha
+second1:=<2t>p:alpha
+b@first1is1:=itet(is"e"(1to(2),1t,1t),alpha,a,b,refis(1to(2),1t)):is"e"(alpha,first1(pair1),a)
+first1is2:=symis(alpha,first1(pair1),a,first1is1):is"e"(alpha,a,first1(pair1))
+second1is1:=itef(is"e"(1to(2),2t,1t),alpha,a,b,th4".pair"):is"e"(alpha,second1(pair1),b)
+second1is2:=symis(alpha,second1(pair1),b,second1is1):is"e"(alpha,b,second1(pair1))
++*pair
+p@[q:pair1type][i:is"e"(alpha,first1(p),first1(q))][j:is"e"(alpha,second1(p),second1(q))][u:1to(2)][u1:is"e"(1to(2),u,1t)]
+t11:=isf(1to(2),alpha,p,u,1t,u1):is"e"(alpha,<u>p,first1(p))
+t12:=symis(alpha,<u>q,first1(q),isf(1to(2),alpha,q,u,1t,u1)):is"e"(alpha,first1(q),<u>q)
+t13:=tr3is(alpha,<u>p,first1(p),first1(q),<u>q,t11,i,t12):is"e"(alpha,<u>p,<u>q)
+u@[u2:is"e"(1to(2),u,2t)]
+t14:=isf(1to(2),alpha,p,u,2t,u2):is"e"(alpha,<u>p,second1(p))
+t15:=symis(alpha,<u>q,second1(q),isf(1to(2),alpha,q,u,2t,u2)):is"e"(alpha,second1(q),<u>q)
+t16:=tr3is(alpha,<u>p,second1(p),second1(q),<u>q,t14,j,t15):is"e"(alpha,<u>p,<u>q)
+u@t17:=orapp(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),is"e"(alpha,<u>p,<u>q),th3(u),[t:is"e"(1to(2),u,1t)]t13(t),[t:is"e"(1to(2),u,2t)]t16(t)):is"e"(alpha,<u>p,<u>q)
+j@th5:=fisi(1to(2),alpha,p,q,[t:1to(2)]t17(t)):is"e"(pair1type,p,q)
+p@q0:=pair1(first1,second1):pair1type
+t18:=first1is1(first1(p),second1):is"e"(alpha,first1(q0),first1(p))
+t19:=second1is1(first1,second1):is"e"(alpha,second1(q0),second1(p))
+-pair
+p@pair1is1:=th5".pair"(q0".pair",p,t18".pair",t19".pair"):is"e"(pair1type,pair1(first1,second1),p)
+pair1is2:=symis(pair1type,pair1(first1,second1),p,pair1is1):is"e"(pair1type,p,pair1(first1,second1))
+@[x:nat]
+lessisi3:=lessisi2(x,x,refis(nat,x)):lessis(x,x)
+1out:=outn(x,1,satz24a(x)):1to(x)
+xout:=outn(x,x,lessisi3(x)):1to(x)
+[y:nat][l:lessis(y,x)][u:1to(y)]
++left
+ui:=inn(y,u):nat
+t1:=1top(y,u):lessis(ui,y)
+t2:=trlessis(ui,y,x,t1,l):lessis(ui,x)
+-left
+left1to:=outn(x,ui".left",t2".left"):1to(x)
+[v:1to(y)][i:is"e"(1to(x),left1to(u),left1to(v))]
++*left
+i@t3:=isoutne(x,ui,t2,ui(v),t2(v),i):is(ui,ui(v))
+-left
+i@thleft1:=isinne(y,u,v,t3".left"):is"e"(1to(y),u,v)
+l@thleft2:=[u:1to(y)][v:1to(y)][t:is"e"(1to(x),left1to(u),left1to(v))]thleft1(u,v,t):injective(1to(y),1to(x),[t:1to(y)]left1to(t))
+y@[u:1to(y)]
++right
+ui:=inn(y,u):nat
+t4:=1top(y,u):lessis(ui,y)
+t5:=satz19o(ui,y,x,t4):lessis(pl(x,ui),pl(x,y))
+-right
+right1to:=outn(pl(x,y),pl(x,ui".right"),t5".right"):1to(pl(x,y))
+[v:1to(y)][i:is"e"(1to(pl(x,y)),right1to(u),right1to(v))]
++*right
+i@t6:=isoutne(pl(x,y),pl(x,ui(u)),t5(u),pl(x,ui(v)),t5(v),i):is(pl(x,ui(u)),pl(x,ui(v)))
+t7:=satz20e(ui(u),ui(v),x,t6):is(ui(u),ui(v))
+-right
+i@thright1:=isinne(y,u,v,t7".right"):is"e"(1to(y),u,v)
+@[alpha:'type'][x:nat][y:nat][l:lessis(y,x)][f:[t:1to(x)]alpha]
+left:=[t:1to(y)]<left1to(x,y,l,t)>f:[t:1to(y)]alpha
+y@[f:[t:1to(pl(x,y))]alpha]
+right:=[t:1to(y)]<right1to(x,y,t)>f:[t:1to(y)]alpha
+y@[i:is(y,x)][f:[t:1to(y)]alpha]
++*left
+f@t4:=lessisi2(y,x,i):lessis(y,x)
+t5:=lessisi2(x,y,symis(nat,y,x,i)):lessis(x,y)
+f1:=left(y,x,t5,f):[t:1to(x)]alpha
+f2:=left(t4,f1):[t:1to(y)]alpha
+[u:1to(y)]
+t6:=isinoutn(x,inn(y,u),trlessis(inn(y,u),y,x,1top(y,u),t4)):is(inn(y,u),inn(x,left1to(x,y,t4,u)))
+t7:=tris(1to(y),u,outn(y,inn(y,u),1top(y,u)),left1to(y,x,t5,left1to(x,y,t4,u)),isoutinn(y,u),isoutni(y,inn(y,u),1top(y,u),inn(x,left1to(x,y,t4,u)),trlessis(inn(x,left1to(x,y,t4,u)),x,y,1top(x,left1to(x,y,t4,u)),t5),t6)):is"e"(1to(y),u,left1to(y,x,t5,left1to(x,y,t4,u)))
+t8:=isf(1to(y),alpha,f,u,left1to(y,x,t5,left1to(x,y,t4,u)),t7):is"e"(alpha,<u>f,<u>f2)
+-left
+f@thleft:=fisi(1to(y),alpha,f,f2".left",[t:1to(y)]t8".left"(t)):is"e"([t:1to(y)]alpha,f,left(x,y,lessisi2(y,x,i),left(y,x,lessisi2(x,y,symis(nat,y,x,i)),f)))
+@frac:=pair1type(nat):'type'
+[x1:nat][x2:nat]
+fr:=pair1(nat,x1,x2):frac
+@[x:frac]
+num:=first1(nat,x):nat
+den:=second1(nat,x):nat
+x2@numis:=first1is1(nat,x1,x2):is(num(fr(x1,x2)),x1)
+isnum:=first1is2(nat,x1,x2):is(x1,num(fr(x1,x2)))
+denis:=second1is1(nat,x1,x2):is(den(fr(x1,x2)),x2)
+isden:=second1is2(nat,x1,x2):is(x2,den(fr(x1,x2)))
+x@1x:=num(x):nat
+2x:=den(x):nat
+fris:=pair1is1(nat,x):is"e"(frac,fr(1x,2x),x)
+isfr:=pair1is2(nat,x):is"e"(frac,x,fr(1x,2x))
+x2@[y1:nat][y2:nat]
+12isnd:=ists12(x1,num(fr(x1,x2)),y2,den(fr(y1,y2)),isnum(x1,x2),isden(y1,y2)):is(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))))
+ndis12:=symis(nat,ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),12isnd):is(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2))
+x@[n1:nat][n2:nat]
+1disnd:=ists1(n1,num(fr(n1,n2)),2x,isnum(n1,n2)):is(ts(n1,2x),ts(num(fr(n1,n2)),2x))
+ndis1d:=symis(nat,ts(n1,2x),ts(num(fr(n1,n2)),2x),1disnd):is(ts(num(fr(n1,n2)),2x),ts(n1,2x))
+n2isnd:=ists2(n2,den(fr(n1,n2)),1x,isden(n1,n2)):is(ts(1x,n2),ts(1x,den(fr(n1,n2))))
+ndisn2:=symis(nat,ts(1x,n2),ts(1x,den(fr(n1,n2))),n2isnd):is(ts(1x,den(fr(n1,n2))),ts(1x,n2))
+x2@[n:nat][i:is(x1,n)]
+isn:=isf(nat,frac,[t:nat]fr(t,x2),x1,n,i):is"e"(frac,fr(x1,x2),fr(n,x2))
+n@[i:is(x2,n)]
+isd:=isf(nat,frac,[t:nat]fr(x1,t),x2,n,i):is"e"(frac,fr(x1,x2),fr(x1,n))
+y2@[i:is(x1,y1)][j:is(x2,y2)]
+isnd:=tris(frac,fr(x1,x2),fr(y1,x2),fr(y1,y2),isn(x1,x2,y1,i),isd(y1,x2,y2,j)):is"e"(frac,fr(x1,x2),fr(y1,y2))
+x@[y:frac]
+1y:=num(y):nat
+2y:=den(y):nat
+eq:=is(ts(1x,2y),ts(1y,2x)):'prop'
+y2@[i:is(ts(x1,y2),ts(y1,x2))]
+eqi12:=tr3is(nat,ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ndis12(x1,x2,y1,y2),i,12isnd(y1,y2,x1,x2)):eq(fr(x1,x2),fr(y1,y2))
+n2@[i:is(ts(1x,n2),ts(n1,2x))]
+eqi1:=isp(frac,[t:frac]eq(t,fr(n1,n2)),fr(1x,2x),x,eqi12(1x,2x,n1,n2,i),fris):eq(x,fr(n1,n2))
+n2@[i:is(ts(n1,2x),ts(1x,n2))]
+eqi2:=isp(frac,[t:frac]eq(fr(n1,n2),t),fr(1x,2x),x,eqi12(n1,n2,1x,2x,i),fris):eq(fr(n1,n2),x)
+x@satz37:=refis(nat,ts(1x,2x)):eq(x,x)
+refeq:=satz37:eq(x,x)
+y@[i:is"e"(frac,x,y)]
+refeq1:=isp(frac,[t:frac]eq(x,t),x,y,refeq,i):eq(x,y)
+refeq2:=isp(frac,[t:frac]eq(t,x),x,y,refeq,i):eq(y,x)
+y2@[i:is(x1,y1)][j:is(x2,y2)]
+eqnd:=refeq1(fr(x1,x2),fr(y1,y2),isnd(i,j)):eq(fr(x1,x2),fr(y1,y2))
+x2@[n:nat][i:is(x1,n)]
+eqn:=refeq1(fr(x1,x2),fr(n,x2),isn(n,i)):eq(fr(x1,x2),fr(n,x2))
+n@[i:is(x2,n)]
+eqd:=refeq1(fr(x1,x2),fr(x1,n),isd(n,i)):eq(fr(x1,x2),fr(x1,n))
+y@[e:eq(x,y)]
+satz38:=symis(nat,ts(1x,2y),ts(1y,2x),e):eq(y,x)
+symeq:=satz38:eq(y,x)
+@[a:nat][b:nat][c:nat][d:nat]
++ii1
+t1:=tris(nat,ts(b,ts(c,d)),ts(ts(b,c),d),ts(d,ts(b,c)),assts2(b,c,d),comts(ts(b,c),d)):is(ts(b,ts(c,d)),ts(d,ts(b,c)))
+-ii1
+stets:=tr4is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(b,c))),ts(ts(a,d),ts(b,c)),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(b,c)),a,t1".ii1"),assts2(a,d,ts(b,c)),ists2(ts(b,c),ts(c,b),ts(a,d),comts(b,c))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
++*ii1
+d@t2:=tr3is(nat,ts(b,ts(c,d)),ts(ts(c,d),b),ts(ts(d,c),b),ts(d,ts(c,b)),comts(b,ts(c,d)),ists1(ts(c,d),ts(d,c),b,comts(c,d)),assts1(d,c,b)):is(ts(b,ts(c,d)),ts(d,ts(c,b)))
+anders:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(c,b))),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(c,b)),a,t2),assts2(a,d,ts(c,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
+-ii1
+y@[z:frac]
+1z:=num(z):nat
+2z:=den(z):nat
+[e:eq(x,y)][f:eq(y,z)]
++139
+t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
+t2:=stets(1x,2y,1y,2z):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)))
+t3:=tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)))
+t4:=tr3is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),symis(nat,ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),t2),t1,t3):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
+-139
+satz39:=satz33b(ts(1x,2z),ts(1z,2x),ts(1y,2y),t4".139"):eq(x,z)
++*139
+f@anders:=tr4is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2z,1y,2y),ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
+-139
+f@treq:=satz39:eq(x,z)
+z@[e:eq(z,x)][f:eq(z,y)]
+treq1:=treq(x,z,y,symeq(z,x,e),f):eq(x,y)
+z@[e:eq(x,z)][f:eq(y,z)]
+treq2:=treq(x,z,y,e,symeq(y,z,f)):eq(x,y)
+z@[u:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)]
+tr3eq:=treq(x,y,u,e,treq(y,z,u,f,g)):eq(x,u)
+u@[v:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)][h:eq(u,v)]
+tr4eq:=tr3eq(x,y,z,v,e,f,treq(z,u,v,g,h)):eq(x,v)
+x@[n:nat]
+satz40:=eqi1(ts(1x,n),ts(2x,n),tris(nat,ts(1x,ts(2x,n)),ts(1x,ts(n,2x)),ts(ts(1x,n),2x),ists2(ts(2x,n),ts(n,2x),1x,comts(2x,n)),assts2(1x,n,2x))):eq(x,fr(ts(1x,n),ts(2x,n)))
+satz40a:=symeq(x,fr(ts(1x,n),ts(2x,n)),satz40):eq(fr(ts(1x,n),ts(2x,n)),x)
+x2@[n:nat]
+satz40b:=eqi12(ts(x1,n),ts(x2,n),tris(nat,ts(x1,ts(x2,n)),ts(x1,ts(n,x2)),ts(ts(x1,n),x2),ists2(ts(x2,n),ts(n,x2),x1,comts(x2,n)),assts2(x1,n,x2))):eq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)))
+satz40c:=symeq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)),satz40b):eq(fr(ts(x1,n),ts(x2,n)),fr(x1,x2))
+y@moref:=more(ts(1x,2y),ts(1y,2x)):'prop'
+lessf:=less(ts(1x,2y),ts(1y,2x)):'prop'
+y2@[m:more(ts(x1,y2),ts(y1,x2))]
+morefi12:=ismore12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),m):moref(fr(x1,x2),fr(y1,y2))
+y2@[l:less(ts(x1,y2),ts(y1,x2))]
+lessfi12:=isless12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),l):lessf(fr(x1,x2),fr(y1,y2))
+n2@[m:more(ts(1x,n2),ts(n1,2x))]
+morefi1:=ismore12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),m):moref(x,fr(n1,n2))
+n2@[m:more(ts(n1,2x),ts(1x,n2))]
+morefi2:=ismore12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),m):moref(fr(n1,n2),x)
+n2@[l:less(ts(1x,n2),ts(n1,2x))]
+lessfi1:=isless12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),l):lessf(x,fr(n1,n2))
+n2@[l:less(ts(n1,2x),ts(1x,n2))]
+lessfi2:=isless12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),l):lessf(fr(n1,n2),x)
+y@satz41:=satz10(ts(1x,2y),ts(1y,2x)):orec3(eq(x,y),moref(x,y),lessf(x,y))
+satz41a:=satz10a(ts(1x,2y),ts(1y,2x)):or3(eq(x,y),moref(x,y),lessf(x,y))
+satz41b:=satz10b(ts(1x,2y),ts(1y,2x)):ec3(eq(x,y),moref(x,y),lessf(x,y))
+[m:moref(x,y)]
+satz42:=satz11(ts(1x,2y),ts(1y,2x),m):lessf(y,x)
+y@[l:lessf(x,y)]
+satz43:=satz12(ts(1x,2y),ts(1y,2x),l):moref(y,x)
+u@1u:=num(u):nat
+2u:=den(u):nat
+[m:moref(x,y)][e:eq(x,z)][f:eq(y,u)]
++244
+t1:=ists12(ts(1y,2u),ts(1u,2y),ts(1z,2x),ts(1x,2z),f,symeq(x,z,e)):is(ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)))
+t2:=tr3is(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)),ts(ts(1u,2z),ts(1x,2y)),stets(1y,2x,1z,2u),t1,stets(1u,2y,1x,2z)):is(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)))
+t3:=ismore1(ts(ts(1u,2z),ts(1x,2y)),ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)),symis(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)),t2),satz32d(ts(1x,2y),ts(1y,2x),ts(1u,2z),m)):more(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)))
+-244
+satz44:=satz33a(ts(1z,2u),ts(1u,2z),ts(1y,2x),ismore1(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1z,2u),ts(1y,2x)),ts(ts(1u,2z),ts(1y,2x)),comts(ts(1y,2x),ts(1z,2u)),t3".244")):moref(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][m:moref(x,z)]
+eqmoref12:=satz44(x,z,y,u,m,e,f):moref(y,u)
+z@[e:eq(x,y)][m:moref(x,z)]
+eqmoref1:=satz44(x,z,y,z,m,e,refeq(z)):moref(y,z)
+e@[m:moref(z,x)]
+eqmoref2:=satz44(z,x,z,y,m,refeq(z),e):moref(z,y)
+u@[l:lessf(x,y)][e:eq(x,z)][f:eq(y,u)]
+satz45:=satz42(u,z,satz44(y,x,u,z,satz43(x,y,l),f,e)):lessf(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][l:lessf(x,z)]
+eqlessf12:=satz45(x,z,y,u,l,e,f):lessf(y,u)
+z@[e:eq(x,y)][l:lessf(x,z)]
+eqlessf1:=satz45(x,z,y,z,l,e,refeq(z)):lessf(y,z)
+e@[l:lessf(z,x)]
+eqlessf2:=satz45(z,x,z,y,l,refeq(z),e):lessf(z,y)
+y@moreq:=or(moref(x,y),eq(x,y)):'prop'
+lesseq:=or(lessf(x,y),eq(x,y)):'prop'
+[e:eq(x,y)]
+moreqi2:=ori2(moref(x,y),eq(x,y),e):moreq(x,y)
+lesseqi2:=ori2(lessf(x,y),eq(x,y),e):lesseq(x,y)
+y@[m:moref(x,y)]
+moreqi1:=ori1(moref(x,y),eq(x,y),m):moreq(x,y)
+y@[l:lessf(x,y)]
+lesseqi1:=ori1(lessf(x,y),eq(x,y),l):lesseq(x,y)
+y@[m:moreq(x,y)]
+satz41c:=th7"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,comor(moref(x,y),eq(x,y),m)):not(lessf(x,y))
+y@[l:lesseq(x,y)]
+satz41d:=th9"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,l):not(moref(x,y))
+y@[n:not(moref(x,y))]
+satz41e:=th2"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n):lesseq(x,y)
+y@[n:not(lessf(x,y))]
+satz41f:=comor(eq(x,y),moref(x,y),th3"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n)):moreq(x,y)
+y@[m:moref(x,y)]
+satz41g:=th3"l.or"(lessf(x,y),eq(x,y),ec3e23(eq(x,y),moref(x,y),lessf(x,y),satz41b,m),ec3e21(eq(x,y),moref(x,y),lessf(x,y),satz41b,m)):not(lesseq(x,y))
+y@[l:lessf(x,y)]
+satz41h:=th3"l.or"(moref(x,y),eq(x,y),ec3e32(eq(x,y),moref(x,y),lessf(x,y),satz41b,l),ec3e31(eq(x,y),moref(x,y),lessf(x,y),satz41b,l)):not(moreq(x,y))
+y@[n:not(moreq(x,y))]
+satz41j:=or3e3(eq(x,y),moref(x,y),lessf(x,y),satz41a,th5"l.or"(moref(x,y),eq(x,y),n),th4"l.or"(moref(x,y),eq(x,y),n)):lessf(x,y)
+y@[n:not(lesseq(x,y))]
+satz41k:=or3e2(eq(x,y),moref(x,y),lessf(x,y),satz41a,th4"l.or"(lessf(x,y),eq(x,y),n),th5"l.or"(lessf(x,y),eq(x,y),n)):moref(x,y)
+u@[m:moreq(x,y)][e:eq(x,z)][f:eq(y,u)]
++246
+[n:moref(x,y)]
+t1:=ori1(moref(z,u),eq(z,u),satz44(n,e,f)):moreq(z,u)
+f@[g:eq(x,y)]
+t2:=ori2(moref(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):moreq(z,u)
+-246
+satz46:=orapp(moref(x,y),eq(x,y),moreq(z,u),m,[t:moref(x,y)]t1".246"(t),[t:eq(x,y)]t2".246"(t)):moreq(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][m:moreq(x,z)]
+eqmoreq12:=satz46(x,z,y,u,m,e,f):moreq(y,u)
+z@[e:eq(x,y)][m:moreq(x,z)]
+eqmoreq1:=satz46(x,z,y,z,m,e,refeq(z)):moreq(y,z)
+e@[m:moreq(z,x)]
+eqmoreq2:=satz46(z,x,z,y,m,refeq(z),e):moreq(z,y)
+u@[l:lesseq(x,y)][e:eq(x,z)][f:eq(y,u)]
++247
+[k:lessf(x,y)]
+t1:=ori1(lessf(z,u),eq(z,u),satz45(k,e,f)):lesseq(z,u)
+f@[g:eq(x,y)]
+t2:=ori2(lessf(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):lesseq(z,u)
+-247
+satz47:=orapp(lessf(x,y),eq(x,y),lesseq(z,u),l,[t:lessf(x,y)]t1".247"(t),[t:eq(x,y)]t2".247"(t)):lesseq(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][l:lesseq(x,z)]
+eqlesseq12:=satz47(x,z,y,u,l,e,f):lesseq(y,u)
+z@[e:eq(x,y)][l:lesseq(x,z)]
+eqlesseq1:=satz47(x,z,y,z,l,e,refeq(z)):lesseq(y,z)
+e@[l:lesseq(z,x)]
+eqlesseq2:=satz47(z,x,z,y,l,refeq(z),e):lesseq(z,y)
+y@[m:moreq(x,y)]
+satz48:=th9"l.or"(moref(x,y),eq(x,y),lessf(y,x),eq(y,x),m,[t:moref(x,y)]satz42(x,y,t),[t:eq(x,y)]satz38(x,y,t)):lesseq(y,x)
+y@[l:lesseq(x,y)]
+satz49:=th9"l.or"(lessf(x,y),eq(x,y),moref(y,x),eq(y,x),l,[t:lessf(x,y)]satz43(x,y,t),[t:eq(x,y)]satz38(x,y,t)):moreq(y,x)
+z@[l:lessf(x,y)][k:lessf(y,z)]
++250
+t1:=satz34a(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),l,k):less(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
+t2:=isless12(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2y,1y,2z),tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))),t1):less(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
+-250
+satz50:=satz33c(ts(1x,2z),ts(1z,2x),ts(1y,2y),t2".250"):lessf(x,z)
+trlessf:=satz50:lessf(x,z)
+z@[m:moref(x,y)][n:moref(y,z)]
+trmoref:=satz43(z,x,satz50(z,y,x,satz42(y,z,n),satz42(x,y,m))):moref(x,z)
+z@[l:lesseq(x,y)][k:lessf(y,z)]
+satz51a:=orapp(lessf(x,y),eq(x,y),lessf(x,z),l,[t:lessf(x,y)]satz50(t,k),[t:eq(x,y)]eqlessf1(y,x,z,symeq(x,y,t),k)):lessf(x,z)
+z@[l:lessf(x,y)][k:lesseq(y,z)]
+satz51b:=orapp(lessf(y,z),eq(y,z),lessf(x,z),k,[t:lessf(y,z)]satz50(l,t),[t:eq(y,z)]eqlessf2(y,z,x,t,l)):lessf(x,z)
+z@[m:moreq(x,y)][n:moref(y,z)]
+satz51c:=satz43(z,x,satz51b(z,y,x,satz42(y,z,n),satz48(x,y,m))):moref(x,z)
+z@[m:moref(x,y)][n:moreq(y,z)]
+satz51d:=satz43(z,x,satz51a(z,y,x,satz48(y,z,n),satz42(x,y,m))):moref(x,z)
+z@[l:lesseq(x,y)][k:lesseq(y,z)]
++252
+[e:eq(x,y)][f:eq(y,z)]
+t1:=ori2(lessf(x,z),eq(x,z),treq(x,y,z,e,f)):lesseq(x,z)
+e@[j:lessf(y,z)]
+t2:=ori1(lessf(x,z),eq(x,z),satz51a(l,j)):lesseq(x,z)
+e@t3:=orapp(lessf(y,z),eq(y,z),lesseq(x,z),k,[t:lessf(y,z)]t2(t),[t:eq(y,z)]t1(t)):lesseq(x,z)
+k@[j:lessf(x,y)]
+t4:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
+-252
+satz52:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t4".252"(t),[t:eq(x,y)]t3".252"(t)):lesseq(x,z)
+trlesseq:=satz52:lesseq(x,z)
++*252
+k@[j:lessf(x,y)]
+t5:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
+k@[e:eq(x,y)]
+t6:=eqlesseq1(y,x,z,symeq(x,y,e),k):lesseq(x,z)
+k@anders:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t5(t),[t:eq(x,y)]t6(t)):lesseq(x,z)
+-252
+z@[m:moreq(x,y)][n:moreq(y,z)]
+trmoreq:=satz49(z,x,satz52(z,y,x,satz48(y,z,n),satz48(x,y,m))):moreq(x,z)
++253
+x@t1:=ismore1(pl(ts(1x,2x),ts(1x,2x)),ts(pl(1x,1x),2x),ts(1x,2x),distpt1(1x,1x,2x),satz18(ts(1x,2x),ts(1x,2x))):more(ts(pl(1x,1x),2x),ts(1x,2x))
+t2:=morefi2(pl(1x,1x),2x,t1):moref(fr(pl(1x,1x),2x),x)
+-253
+x@satz53:=somei(frac,[t:frac]moref(t,x),fr(pl(1x,1x),2x),t2".253"):some"l"(frac,[t:frac]moref(t,x))
++254
+t1:=isless2(pl(ts(1x,2x),ts(1x,2x)),ts(1x,pl(2x,2x)),ts(1x,2x),distpt2(1x,2x,2x),satz18a(ts(1x,2x),ts(1x,2x))):less(ts(1x,2x),ts(1x,pl(2x,2x)))
+t2:=lessfi2(1x,pl(2x,2x),t1):lessf(fr(1x,pl(2x,2x)),x)
+-254
+satz54:=somei(frac,[t:frac]lessf(t,x),fr(1x,pl(2x,2x)),t2".254"):some"l"(frac,[t:frac]lessf(t,x))
+y@[l:lessf(x,y)]
++255
+t1:=satz19f(ts(1x,2y),ts(1y,2x),ts(1x,2x),l):less(pl(ts(1x,2x),ts(1x,2y)),pl(ts(1x,2x),ts(1y,2x)))
+t2:=satz19c(ts(1x,2y),ts(1y,2x),ts(1y,2y),l):less(pl(ts(1x,2y),ts(1y,2y)),pl(ts(1y,2x),ts(1y,2y)))
+t3:=isless12(pl(ts(1x,2x),ts(1x,2y)),ts(1x,pl(2x,2y)),pl(ts(1x,2x),ts(1y,2x)),ts(pl(1x,1y),2x),distpt2(1x,2x,2y),distpt1(1x,1y,2x),t1):less(ts(1x,pl(2x,2y)),ts(pl(1x,1y),2x))
+t4:=lessfi1(pl(1x,1y),pl(2x,2y),t3):lessf(x,fr(pl(1x,1y),pl(2x,2y)))
+t5:=isless12(pl(ts(1x,2y),ts(1y,2y)),ts(pl(1x,1y),2y),pl(ts(1y,2x),ts(1y,2y)),ts(1y,pl(2x,2y)),distpt1(1x,1y,2y),distpt2(1y,2x,2y),t2):less(ts(pl(1x,1y),2y),ts(1y,pl(2x,2y)))
+t6:=lessfi2(y,pl(1x,1y),pl(2x,2y),t5):lessf(fr(pl(1x,1y),pl(2x,2y)),y)
+t7:=andi(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y),t4,t6):and(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y))
+-255
+satz55:=somei(frac,[t:frac]and(lessf(x,t),lessf(t,y)),fr(pl(1x,1y),pl(2x,2y)),t7".255"):some"l"(frac,[t:frac]and(lessf(x,t),lessf(t,y)))
+y@pf:=fr(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)):frac
++ii3
+y2@t1:=ispl12(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ts(y1,x2),ndis12(x1,x2,y1,y2),ndis12(y1,y2,x1,x2)):is(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),pl(ts(x1,y2),ts(y1,x2)))
+t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
+-ii3
+y2@pf12:=isnd(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),ts(den(fr(x1,x2)),den(fr(y1,y2))),pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2),t1".ii3",t2".ii3"):is"e"(frac,pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
++*ii3
+n2@t3:=ispl12(ts(1x,den(fr(n1,n2))),ts(1x,n2),ts(num(fr(n1,n2)),2x),ts(n1,2x),ndisn2(x,n1,n2),ndis1d(x,n1,n2)):is(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),pl(ts(1x,n2),ts(n1,2x)))
+t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
+-ii3
+n2@pf1:=isnd(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),ts(2x,den(fr(n1,n2))),pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2),t3".ii3",t4".ii3"):is"e"(frac,pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
++*ii3
+n2@t5:=ispl12(ts(num(fr(n1,n2)),2x),ts(n1,2x),ts(1x,den(fr(n1,n2))),ts(1x,n2),ndis1d(x,n1,n2),ndisn2(x,n1,n2)):is(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),pl(ts(n1,2x),ts(1x,n2)))
+t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
+-ii3
+n2@pf2:=isnd(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),ts(den(fr(n1,n2)),2x),pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x),t5".ii3",t6".ii3"):is"e"(frac,pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
+y2@pfeq12a:=refeq1(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
+pfeq12b:=refeq2(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf(fr(x1,x2),fr(y1,y2)))
+n2@pfeq1a:=refeq1(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
+pfeq1b:=refeq2(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf(x,fr(n1,n2)))
+pfeq2a:=refeq1(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
+pfeq2b:=refeq2(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf(fr(n1,n2),x))
+u@[e:eq(x,y)][f:eq(z,u)]
++356
+t1:=ists1(ts(1x,2y),ts(1y,2x),ts(2z,2u),e):is(ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)))
+t2:=t1(z,u,x,y,f,e):is(ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)))
+t3:=tr3is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2z),ts(2u,2y)),ts(ts(1x,2y),ts(2u,2z)),ts(ts(1x,2y),ts(2z,2u)),ists2(ts(2y,2u),ts(2u,2y),ts(1x,2z),comts(2y,2u)),stets(1x,2z,2u,2y),ists2(ts(2u,2z),ts(2z,2u),ts(1x,2y),comts(2u,2z))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)))
+t4:=tr4is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)),ts(ts(1y,2u),ts(2z,2x)),ts(ts(1y,2u),ts(2x,2z)),t3,t1,stets(1y,2x,2z,2u),ists2(ts(2z,2x),ts(2x,2z),ts(1y,2u),comts(2z,2x))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)))
+t5:=tr4is(nat,ts(ts(1z,2x),ts(2y,2u)),ts(ts(1z,2u),ts(2y,2x)),ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)),ts(ts(1u,2y),ts(2x,2z)),stets(1z,2x,2y,2u),ists2(ts(2y,2x),ts(2x,2y),ts(1z,2u),comts(2y,2x)),t2,stets(1u,2z,2x,2y)):is(ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)))
+t6:=ispl12(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)),ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)),t4,t5):is(pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))))
+t7:=tr3is(nat,ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)),disttp1(ts(1x,2z),ts(1z,2x),ts(2y,2u)),t6,distpt1(ts(1y,2u),ts(1u,2y),ts(2x,2z))):is(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)))
+-356
+satz56:=eqi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2u),ts(1u,2y)),ts(2y,2u),t7".356"):eq(pf(x,z),pf(y,u))
+eqpf12:=satz56:eq(pf(x,z),pf(y,u))
+z@[e:eq(x,y)]
+eqpf1:=eqpf12(x,y,z,z,e,refeq(z)):eq(pf(x,z),pf(y,z))
+eqpf2:=eqpf12(z,z,x,y,refeq(z),e):eq(pf(z,x),pf(z,y))
+x2@[n:nat]
+satz57:=tr3eq(pf(fr(x1,n),fr(x2,n)),fr(pl(ts(x1,n),ts(x2,n)),ts(n,n)),fr(ts(pl(x1,x2),n),ts(n,n)),fr(pl(x1,x2),n),pfeq12a(x1,n,x2,n),eqn(pl(ts(x1,n),ts(x2,n)),ts(n,n),ts(pl(x1,x2),n),distpt1(x1,x2,n)),satz40c(pl(x1,x2),n,n)):eq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n))
+satz57a:=symeq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n),satz57):eq(fr(pl(x1,x2),n),pf(fr(x1,n),fr(x2,n)))
+y@satz58:=eqnd(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),pl(ts(1y,2x),ts(1x,2y)),ts(2y,2x),compl(ts(1x,2y),ts(1y,2x)),comts(2x,2y)):eq(pf(x,y),pf(y,x))
+compf:=satz58:eq(pf(x,y),pf(y,x))
++359
+z@t1:=tr3is(nat,ts(ts(1y,2x),2z),ts(ts(2x,1y),2z),ts(2x,ts(1y,2z)),ts(ts(1y,2z),2x),ists1(ts(1y,2x),ts(2x,1y),2z,comts(1y,2x)),assts1(2x,1y,2z),comts(2x,ts(1y,2z))):is(ts(ts(1y,2x),2z),ts(ts(1y,2z),2x))
+t2:=ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),t1):is(pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
+t3:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),t2):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
+t4:=tris(nat,ts(1z,ts(2x,2y)),ts(1z,ts(2y,2x)),ts(ts(1z,2y),2x),ists2(ts(2x,2y),ts(2y,2x),1z,comts(2x,2y)),assts2(1z,2y,2x)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
+t5:=ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t3,t4):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)))
+t6:=ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x)):is(pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
+t7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),t5,asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),t6):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
+-359
+z@satz59:=tr3eq(pf(pf(x,y),z),fr(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z)),fr(pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z))),pf(x,pf(y,z)),pfeq2a(z,pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)),eqnd(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z)),t7".359",assts1(2x,2y,2z)),pfeq1b(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z))):eq(pf(pf(x,y),z),pf(x,pf(y,z)))
+asspf1:=satz59:eq(pf(pf(x,y),z),pf(x,pf(y,z)))
+asspf2:=symeq(pf(pf(x,y),z),pf(x,pf(y,z)),asspf1):eq(pf(x,pf(y,z)),pf(pf(x,y),z))
+c@stets1:=tr3is(nat,ts(ts(a,b),c),ts(a,ts(b,c)),ts(a,ts(c,b)),ts(ts(a,c),b),assts1(a,b,c),ists2(ts(b,c),ts(c,b),a,comts(b,c)),assts2(a,c,b)):is(ts(ts(a,b),c),ts(ts(a,c),b))
++*359
+z@t8:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),stets1(1y,2x,2z))):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
+t9:=tris(nat,ts(1z,ts(2x,2y)),ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),assts2(1z,2x,2y),stets1(1z,2x,2y)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
+anderst7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t8,t9),asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x))):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
+-359
++360
+y@t1:=satz18(ts(1x,2y),ts(1y,2x)):more(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y))
+t2:=satz32a(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y),2x,t1):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(ts(1x,2y),2x))
+t3:=tris(nat,ts(ts(1x,2y),2x),ts(1x,ts(2y,2x)),ts(1x,ts(2x,2y)),assts1(1x,2y,2x),ists2(ts(2y,2x),ts(2x,2y),1x,comts(2y,2x))):is(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)))
+t4:=ismore2(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)),ts(pl(ts(1x,2y),ts(1y,2x)),2x),t3,t2):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(1x,ts(2x,2y)))
+-360
+y@satz60:=morefi2(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),t4".360"):moref(pf(x,y),x)
+satz60a:=satz42(pf(x,y),x,satz60):lessf(x,pf(x,y))
+z@[m:moref(x,y)]
++361
+t1:=satz32a(ts(1x,2y),ts(1y,2x),2z,m):more(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z))
+t2:=ismore12(ts(ts(1x,2y),2z),ts(ts(1x,2z),2y),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),stets1(1x,2y,2z),stets1(1y,2x,2z),t1):more(ts(ts(1x,2z),2y),ts(ts(1y,2z),2x))
+t3:=stets1(1z,2x,2y):is(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x))
+t4:=satz19h(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),ts(ts(1x,2z),2y),ts(ts(1y,2z),2x),t3,t2):more(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)))
+t5:=ismore12(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),ts(pl(ts(1x,2z),ts(1z,2x)),2y),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),distpt1(ts(1x,2z),ts(1z,2x),2y),distpt1(ts(1y,2z),ts(1z,2y),2x),t4):more(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x))
+t6:=satz32a(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z,t5):more(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z))
+t7:=ismore12(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)),assts1(pl(ts(1x,2z),ts(1z,2x)),2y,2z),assts1(pl(ts(1y,2z),ts(1z,2y)),2x,2z),t6):more(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)))
+-361
+satz61:=morefi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z),t7".361"):moref(pf(x,z),pf(y,z))
+z@[m:moref(x,y)]
+satz62a:=satz61(m):moref(pf(x,z),pf(y,z))
+z@[e:eq(x,y)]
+satz62b:=eqpf1(x,y,z,e):eq(pf(x,z),pf(y,z))
+z@[l:lessf(x,y)]
+satz62c:=satz42(pf(y,z),pf(x,z),satz61(y,x,z,satz43(l))):lessf(pf(x,z),pf(y,z))
+m@satz62d:=eqmoref12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62a):moref(pf(z,x),pf(z,y))
+e@satz62e:=eqpf2(x,y,z,e):eq(pf(z,x),pf(z,y))
+l@satz62f:=eqlessf12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62c):lessf(pf(z,x),pf(z,y))
+u@[e:eq(x,y)][m:moref(z,u)]
+satz62g:=eqmoref2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62d(z,u,x,m)):moref(pf(x,z),pf(y,u))
+satz62h:=eqmoref12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62g):moref(pf(z,x),pf(u,y))
+e@[l:lessf(z,u)]
+satz62j:=eqlessf2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62f(z,u,x,l)):lessf(pf(x,z),pf(y,u))
+satz62k:=eqlessf12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62j):lessf(pf(z,x),pf(u,y))
++363
+z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
+t2:=satz41b(pf(x,z),pf(y,z)):ec3(eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)))
+-363
+z@[m:moref(pf(x,z),pf(y,z))]
+satz63a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),m):moref(x,y)
+z@[e:eq(pf(x,z),pf(y,z))]
+satz63b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),e):eq(x,y)
+z@[l:lessf(pf(x,z),pf(y,z))]
+satz63c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),l):lessf(x,y)
+z@[m:moref(pf(z,x),pf(z,y))]
+satz63d:=satz63a(eqmoref12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),m)):moref(x,y)
+z@[e:eq(pf(z,x),pf(z,y))]
+satz63e:=satz63b(tr3eq(pf(x,z),pf(z,x),pf(z,y),pf(y,z),compf(x,z),e,compf(z,y))):eq(x,y)
+z@[f:lessf(pf(z,x),pf(z,y))]
+satz63f:=satz63c(eqlessf12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),f)):lessf(x,y)
+u@[m:moref(x,y)][n:moref(z,u)]
++364
+t1:=satz61(x,y,z,m):moref(pf(x,z),pf(y,z))
+t2:=eqmoref12(pf(z,y),pf(y,z),pf(u,y),pf(y,u),compf(z,y),compf(u,y),satz61(z,u,y,n)):moref(pf(y,z),pf(y,u))
+-364
+satz64:=trmoref(pf(x,z),pf(y,z),pf(y,u),t1".364",t2".364"):moref(pf(x,z),pf(y,u))
+u@[l:lessf(x,y)][k:lessf(z,u)]
+satz64a:=satz42(pf(y,u),pf(x,z),satz64(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
+u@[m:moreq(x,y)][n:moref(z,u)]
+satz65a:=orapp(moref(x,y),eq(x,y),moref(pf(x,z),pf(y,u)),m,[v:moref(x,y)]satz64(v,n),[v:eq(x,y)]satz62g(v,n)):moref(pf(x,z),pf(y,u))
+u@[m:moref(x,y)][n:moreq(z,u)]
+satz65b:=orapp(moref(z,u),eq(z,u),moref(pf(x,z),pf(y,u)),n,[v:moref(z,u)]satz64(m,v),[v:eq(z,u)]eqmoref2(pf(y,z),pf(y,u),pf(x,z),eqpf2(z,u,y,v),satz61(x,y,z,m))):moref(pf(x,z),pf(y,u))
+u@[l:lesseq(x,y)][k:lessf(z,u)]
+satz65c:=satz42(pf(y,u),pf(x,z),satz65a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
+u@[l:lessf(x,y)][k:lesseq(z,u)]
+satz65d:=satz42(pf(y,u),pf(x,z),satz65b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(pf(x,z),pf(y,u))
+u@[m:moreq(x,y)][n:moreq(z,u)]
++366
+[e:eq(x,y)][f:eq(z,u)]
+t1:=moreqi2(pf(x,z),pf(y,u),satz56(e,f)):moreq(pf(x,z),pf(y,u))
+e@[o:moref(z,u)]
+t2:=moreqi1(pf(x,z),pf(y,u),satz65a(m,o)):moreq(pf(x,z),pf(y,u))
+e@t3:=orapp(moref(z,u),eq(z,u),moreq(pf(x,z),pf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(pf(x,z),pf(y,u))
+n@[o:moref(x,y)]
+t4:=moreqi1(pf(x,z),pf(y,u),satz65b(o,n)):moreq(pf(x,z),pf(y,u))
+-366
+satz66:=orapp(moref(x,y),eq(x,y),moreq(pf(x,z),pf(y,u)),m,[v:moref(x,y)]t4".366"(v),[v:eq(x,y)]t3".366"(v)):moreq(pf(x,z),pf(y,u))
+u@[l:lesseq(x,y)][k:lesseq(z,u)]
+satz66a:=satz48(pf(y,u),pf(x,z),satz66(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(pf(x,z),pf(y,u))
+y@[l:lesseq(x,y)]
++367
+[v:frac][e:eq(pf(y,v),x)]
+t1:=eqmoref1(pf(y,v),x,y,e,satz60(y,v)):moref(x,y)
+v@t2:=th3"l.imp"(eq(pf(y,v),x),moref(x,y),satz41d(x,y,l),[t:eq(pf(y,v),x)]t1(t)):not(eq(pf(y,v),x))
+-367
+vorbemerkung67:=th5"l.some"(frac,[v:frac]eq(pf(y,v),x),[v:frac]t2".367"(v)):not(some"l"(frac,[t:frac]eq(pf(y,t),x)))
+y@[v:frac][w:frac][e:eq(pf(y,v),x)][f:eq(pf(y,w),x)]
+satz67b:=satz63e(v,w,y,treq2(pf(y,v),pf(y,w),x,e,f)):eq(v,w)
+y@[m:moref(x,y)]
++*367
+m@t3:=onei(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),satz8b(ts(1x,2y),ts(1y,2x)),m):one([t:nat]diffprop(ts(1x,2y),ts(1y,2x),t))
+vo:=ind(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):nat
+t4:=oneax(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):is(ts(1x,2y),pl(ts(1y,2x),vo))
+w:=fr(vo,ts(2x,2y)):frac
+t5:=treq(y,fr(ts(1y,2x),ts(2y,2x)),fr(ts(1y,2x),ts(2x,2y)),satz40(y,2x),eqd(ts(1y,2x),ts(2y,2x),ts(2x,2y),comts(2y,2x))):eq(y,fr(ts(1y,2x),ts(2x,2y)))
+t6:=tr4eq(pf(y,w),pf(fr(ts(1y,2x),ts(2x,2y)),fr(vo,ts(2x,2y))),fr(pl(ts(1y,2x),vo),ts(2x,2y)),fr(ts(1x,2y),ts(2x,2y)),x,eqpf1(y,fr(ts(1y,2x),ts(2x,2y)),w,t5),satz57(ts(1y,2x),vo,ts(2x,2y)),eqn(pl(ts(1y,2x),vo),ts(2x,2y),ts(1x,2y),symis(nat,ts(1x,2y),pl(ts(1y,2x),vo),t4)),satz40a(x,2y)):eq(pf(y,w),x)
+-367
+m@satz67a:=somei(frac,[t:frac]eq(pf(y,t),x),w".367",t6".367"):some"l"(frac,[t:frac]eq(pf(y,t),x))
+mf:=w".367":frac
+satz67c:=t6".367":eq(pf(y,mf(x,y,m)),x)
+satz67d:=symeq(pf(y,mf(x,y,m)),x,satz67c):eq(x,pf(y,mf(x,y,m)))
+y@[v:frac][m:moref(x,y)][e:eq(pf(y,v),x)]
+satz67e:=satz67b(v,mf(x,y,m),e,satz67c(m)):eq(v,mf(x,y,m))
+y@tf:=fr(ts(1x,1y),ts(2x,2y)):frac
++ii4
+y2@t1:=ists12(num(fr(x1,x2)),x1,num(fr(y1,y2)),y1,numis(x1,x2),numis(y1,y2)):is(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(x1,y1))
+t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
+-ii4
+y2@tf12:=isnd(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y1),ts(x2,y2),t1".ii4",t2".ii4"):is"e"(frac,tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
++*ii4
+n2@t3:=ists2(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(1x,num(fr(n1,n2))),ts(1x,n1))
+t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
+-ii4
+n2@tf1:=isnd(ts(1x,num(fr(n1,n2))),ts(2x,den(fr(n1,n2))),ts(1x,n1),ts(2x,n2),t3".ii4",t4".ii4"):is"e"(frac,tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
++*ii4
+n2@t5:=ists1(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(num(fr(n1,n2)),1x),ts(n1,1x))
+t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
+-ii4
+n2@tf2:=isnd(ts(num(fr(n1,n2)),1x),ts(den(fr(n1,n2)),2x),ts(n1,1x),ts(n2,2x),t5".ii4",t6".ii4"):is"e"(frac,tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
+y2@tfeq12a:=refeq1(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
+tfeq12b:=refeq2(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(fr(ts(x1,y1),ts(x2,y2)),tf(fr(x1,x2),fr(y1,y2)))
+n2@tfeq1a:=refeq1(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
+tfeq1b:=refeq2(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(fr(ts(1x,n1),ts(2x,n2)),tf(x,fr(n1,n2)))
+tfeq2a:=refeq1(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
+tfeq2b:=refeq2(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(fr(ts(n1,1x),ts(n2,2x)),tf(fr(n1,n2),x))
+u@[e:eq(x,y)][f:eq(z,u)]
++468
+t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1z,2u),ts(1u,2z),e,f):is(ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)))
+-468
+d@stets2:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(ts(a,b),ts(d,c)),ts(ts(a,c),ts(d,b)),ts(ts(a,c),ts(b,d)),ists2(ts(c,d),ts(d,c),ts(a,b),comts(c,d)),stets(a,b,d,c),ists2(ts(d,b),ts(b,d),ts(a,c),comts(d,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,c),ts(b,d)))
++*468
+f@t2:=tr3is(nat,ts(ts(1x,1z),ts(2y,2u)),ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)),ts(ts(1y,1u),ts(2x,2z)),stets2(1x,1z,2y,2u),t1,stets2(1y,2x,1u,2z)):is(ts(ts(1x,1z),ts(2y,2u)),ts(ts(1y,1u),ts(2x,2z)))
+-468
+f@satz68:=eqi12(ts(1x,1z),ts(2x,2z),ts(1y,1u),ts(2y,2u),t2".468"):eq(tf(x,z),tf(y,u))
+eqtf12:=satz68:eq(tf(x,z),tf(y,u))
+z@[e:eq(x,y)]
+eqtf1:=eqtf12(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
+eqtf2:=eqtf12(z,z,x,y,refeq(z),e):eq(tf(z,x),tf(z,y))
+y@satz69:=eqnd(ts(1x,1y),ts(2x,2y),ts(1y,1x),ts(2y,2x),comts(1x,1y),comts(2x,2y)):eq(tf(x,y),tf(y,x))
+comtf:=satz69:eq(tf(x,y),tf(y,x))
+z@satz70:=tr3eq(tf(tf(x,y),z),fr(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z)),fr(ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z))),tf(x,tf(y,z)),tfeq2a(z,ts(1x,1y),ts(2x,2y)),eqnd(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z),ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z)),assts1(1x,1y,1z),assts1(2x,2y,2z)),tfeq1b(x,ts(1y,1z),ts(2y,2z))):eq(tf(tf(x,y),z),tf(x,tf(y,z)))
+asstf1:=satz70:eq(tf(tf(x,y),z),tf(x,tf(y,z)))
+asstf2:=symeq(tf(tf(x,y),z),tf(x,tf(y,z)),asstf1):eq(tf(x,tf(y,z)),tf(tf(x,y),z))
++471
+t1:=tr3eq(tf(x,pf(y,z)),fr(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z))),fr(pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),ts(2x,ts(2y,2z))),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),tfeq1a(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z)),eqn(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z)),pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),disttp2(1x,ts(1y,2z),ts(1z,2y))),satz57a(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))):eq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))))
+t2:=treq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(ts(1x,1y),2z),ts(ts(2x,2y),2z)),tf(x,y),eqnd(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z)),ts(ts(1x,1y),2z),ts(ts(2x,2y),2z),assts2(1x,1y,2z),assts2(2x,2y,2z)),satz40c(ts(1x,1y),ts(2x,2y),2z)):eq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y))
+t3:=treq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2z,2y))),tf(x,z),eqd(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)),ts(2x,ts(2z,2y)),ists2(ts(2y,2z),ts(2z,2y),2x,comts(2y,2z))),t2(x,z,y)):eq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z))
+-471
+satz71:=treq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),pf(tf(x,y),tf(x,z)),t1".471",eqpf12(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z),t2".471",t3".471")):eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
+disttpf1:=tr3eq(tf(pf(x,y),z),tf(z,pf(x,y)),pf(tf(z,x),tf(z,y)),pf(tf(x,z),tf(y,z)),comtf(pf(x,y),z),satz71(z,x,y),eqpf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y))):eq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)))
+disttpf2:=satz71:eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
+distptf1:=symeq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)),disttpf1):eq(pf(tf(x,z),tf(y,z)),tf(pf(x,y),z))
+distptf2:=symeq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),disttpf2):eq(pf(tf(x,y),tf(x,z)),tf(x,pf(y,z)))
+[m:moref(x,y)]
++472
+t1:=satz32a(ts(1x,2y),ts(1y,2x),ts(1z,2z),m):more(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1y,2x),ts(1z,2z)))
+t2:=ismore12(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,2x),ts(1z,2z)),ts(ts(1y,1z),ts(2x,2z)),stets2(1x,2y,1z,2z),stets2(1y,2x,1z,2z),t1):more(ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,1z),ts(2x,2z)))
+-472
+satz72a:=morefi12(ts(1x,1z),ts(2x,2z),ts(1y,1z),ts(2y,2z),t2".472"):moref(tf(x,z),tf(y,z))
+z@[e:eq(x,y)]
+satz72b:=satz68(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
+z@[l:lessf(x,y)]
+satz72c:=satz42(tf(y,z),tf(x,z),satz72a(y,x,z,satz43(x,y,l))):lessf(tf(x,z),tf(y,z))
+m@satz72d:=eqmoref12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72a):moref(tf(z,x),tf(z,y))
+e@satz72e:=eqtf2(x,y,z,e):eq(tf(z,x),tf(z,y))
+l@satz72f:=eqlessf12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72c):lessf(tf(z,x),tf(z,y))
+u@[e:eq(x,y)][m:moref(z,u)]
+satz72g:=eqmoref2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72d(z,u,x,m)):moref(tf(x,z),tf(y,u))
+satz72h:=eqmoref12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72g):moref(tf(z,x),tf(u,y))
+e@[l:lessf(z,u)]
+satz72j:=eqlessf2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72f(z,u,x,l)):lessf(tf(x,z),tf(y,u))
+satz72k:=eqlessf12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72j):lessf(tf(z,x),tf(u,y))
++473
+z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
+t2:=satz41b(tf(x,z),tf(y,z)):ec3(eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)))
+-473
+z@[m:moref(tf(x,z),tf(y,z))]
+satz73a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),m):moref(x,y)
+z@[e:eq(tf(x,z),tf(y,z))]
+satz73b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),e):eq(x,y)
+z@[l:lessf(tf(x,z),tf(y,z))]
+satz73c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),l):lessf(x,y)
+z@[m:moref(tf(z,x),tf(z,y))]
+satz73d:=satz73a(eqmoref12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),m)):moref(x,y)
+z@[e:eq(tf(z,x),tf(z,y))]
+satz73e:=satz73b(tr3eq(tf(x,z),tf(z,x),tf(z,y),tf(y,z),comtf(x,z),e,comtf(z,y))):eq(x,y)
+z@[l:lessf(tf(z,x),tf(z,y))]
+satz73f:=satz73c(eqlessf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),l)):lessf(x,y)
+u@[m:moref(x,y)][n:moref(z,u)]
++474
+t1:=satz72a(x,y,z,m):moref(tf(x,z),tf(y,z))
+t2:=eqmoref12(tf(z,y),tf(y,z),tf(u,y),tf(y,u),comtf(z,y),comtf(u,y),satz72a(z,u,y,n)):moref(tf(y,z),tf(y,u))
+-474
+satz74:=trmoref(tf(x,z),tf(y,z),tf(y,u),t1".474",t2".474"):moref(tf(x,z),tf(y,u))
+u@[l:lessf(x,y)][k:lessf(z,u)]
+satz74a:=satz42(tf(y,u),tf(x,z),satz74(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
+u@[m:moreq(x,y)][n:moref(z,u)]
+satz75a:=orapp(moref(x,y),eq(x,y),moref(tf(x,z),tf(y,u)),m,[v:moref(x,y)]satz74(v,n),[v:eq(x,y)]satz72g(v,n)):moref(tf(x,z),tf(y,u))
+u@[m:moref(x,y)][n:moreq(z,u)]
+satz75b:=orapp(moref(z,u),eq(z,u),moref(tf(x,z),tf(y,u)),n,[v:moref(z,u)]satz74(m,v),[v:eq(z,u)]eqmoref2(tf(y,z),tf(y,u),tf(x,z),eqtf2(z,u,y,v),satz72a(m))):moref(tf(x,z),tf(y,u))
+u@[l:lesseq(x,y)][k:lessf(z,u)]
+satz75c:=satz42(tf(y,u),tf(x,z),satz75a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
+u@[l:lessf(x,y)][k:lesseq(z,u)]
+satz75d:=satz42(tf(y,u),tf(x,z),satz75b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(tf(x,z),tf(y,u))
+u@[m:moreq(x,y)][n:moreq(z,u)]
++476
+[e:eq(x,y)][f:eq(z,u)]
+t1:=moreqi2(tf(x,z),tf(y,u),satz68(e,f)):moreq(tf(x,z),tf(y,u))
+e@[o:moref(z,u)]
+t2:=moreqi1(tf(x,z),tf(y,u),satz75a(m,o)):moreq(tf(x,z),tf(y,u))
+e@t3:=orapp(moref(z,u),eq(z,u),moreq(tf(x,z),tf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(tf(x,z),tf(y,u))
+n@[o:moref(x,y)]
+t4:=moreqi1(tf(x,z),tf(y,u),satz75b(o,n)):moreq(tf(x,z),tf(y,u))
+-476
+satz76:=orapp(moref(x,y),eq(x,y),moreq(tf(x,z),tf(y,u)),m,[v:moref(x,y)]t4".476"(v),[v:eq(x,y)]t3".476"(v)):moreq(tf(x,z),tf(y,u))
+u@[l:lesseq(x,y)][k:lesseq(z,u)]
+satz76a:=satz48(tf(y,u),tf(x,z),satz76(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(tf(x,z),tf(y,u))
+y@[v:frac][w:frac][e:eq(tf(y,v),x)][f:eq(tf(y,w),x)]
+satz77b:=satz73e(v,w,y,treq2(tf(y,v),tf(y,w),x,e,f)):eq(v,w)
++477
+y@v:=fr(ts(1x,2y),ts(2x,1y)):frac
+t1:=tr4eq(tf(y,v),tf(v,y),fr(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y)),fr(ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y))),x,comtf(y,v),tfeq2a(y,ts(1x,2y),ts(2x,1y)),eqnd(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y),ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y)),tris(nat,ts(ts(1x,2y),1y),ts(1x,ts(2y,1y)),ts(1x,ts(1y,2y)),assts1(1x,2y,1y),ists2(ts(2y,1y),ts(1y,2y),1x,comts(2y,1y))),assts1(2x,1y,2y)),satz40a(x,ts(1y,2y))):eq(tf(y,v),x)
+-477
+y@satz77a:=somei(frac,[t:frac]eq(tf(y,t),x),v".477",t1".477"):some"l"(frac,[t:frac]eq(tf(y,t),x))
++rt
+@eq:=[x:frac][y:frac]eq"n"(x,y):[x:frac][y:frac]'prop'
+refeq:=[x:frac]refeq"n"(x):[x:frac]<x><x>eq
+symeq:=[x:frac][y:frac][t:<y><x>eq]symeq"n"(x,y,t):[x:frac][y:frac][t:<y><x>eq]<x><y>eq
+treq:=[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]treq"n"(x,y,z,t,u):[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]<z><x>eq
+[x:frac][s:set(frac)]
+inf:=esti(frac,x,s):'prop'
+@rat:=ect"eq"(frac,eq,refeq,symeq,treq):'type'
+[x0:rat][y0:rat]
+is:=is"e"(rat,x0,y0):'prop'
+nis:=not(is(x0,y0)):'prop'
+@[p:[x:rat]'prop']
+some:=some"l"(rat,p):'prop'
+all:=all"l"(rat,p):'prop'
+one:=one"e"(rat,p):'prop'
+x0@[s:set(rat)]
+in:=esti(rat,x0,s):'prop'
+x@ratof:=ectelt"eq"(frac,eq,refeq,symeq,treq,x):rat
+x0@class:=ecect"eq"(frac,eq,refeq,symeq,treq,x0):set(frac)
+x@inclass:=th5"eq.4"(frac,eq,refeq,symeq,treq,x):inf(x,class(ratof(x)))
+x0@[x:frac][y:frac][xix0:inf(x,class(x0))][e:eq"n"(x,y)]
+lemmaeq1:=th8"eq.4"(frac,eq,refeq,symeq,treq,x0,x,xix0,y,e):inf(y,class(x0))
+x0@[a:'prop'][a1:[x:frac][xi:inf(x,class(x0))]a]
+ratapp1:=th3"eq.4"(frac,eq,refeq,symeq,treq,x0,a,a1):a
+y0@[a:'prop'][a1:[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]a][x:frac][xix0:inf(x,class(x0))]
++ii5
+t1:=ratapp1(y0,a,[y:frac][yi:inf(y,class(y0))]<yi><xix0><y><x>a1):a
+-ii5
+a1@ratapp2:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t1".ii5"(x,xi)):a
+y0@[z0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]a][x:frac][xix0:inf(x,class(x0))]
++*ii5
+xix0@t2:=ratapp2(y0,z0,a,[y:frac][z:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))]<zi><yi><xix0><z><y><x>a1):a
+-ii5
+a1@ratapp3:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t2".ii5"(x,xi)):a
+z0@[u0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]a][x:frac][xix0:inf(x,class(x0))]
++*ii5
+xix0@t3:=ratapp3(y0,z0,u0,a,[y:frac][z:frac][u:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]<ui><zi><yi><xix0><u><z><y><x>a1):a
+-ii5
+a1@ratapp4:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t3".ii5"(x,xi)):a
+y0@[x1:frac][y1:frac][x1ix0:inf(x1,class(x0))][y1iy0:inf(y1,class(y0))][e:eq"n"(x1,y1)]
+isi:=th3"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,e):is(x0,y0)
+y1iy0@[i:is(x0,y0)]
+ise:=th5"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,i):eq"n"(x1,y1)
+y1iy0@[n:not(eq"n"(x1,y1))]
+nisi:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),n,[t:is(x0,y0)]ise(t)):nis(x0,y0)
+y1iy0@[n:nis(x0,y0)]
+nise:=th3"l.imp"(eq"n"(x1,y1),is(x0,y0),n,[t:eq"n"(x1,y1)]isi(t)):not(eq"n"(x1,y1))
+@[alpha:'type'][f:[x:frac][y:frac]alpha]
+fixf:=fixfu2"eq"(frac,eq,refeq,symeq,treq,alpha,f):'prop'
+y0@[alpha:'type'][f:[x:frac][y:frac]alpha][ff:fixf(alpha,f)]
+indrat:=indeq2"eq"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0):alpha
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+isindrat:=th1"eq.11"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0,x,xix0,y,yiy0):is"e"(alpha,<y><x>f,indrat)
+x0@satz78:=refis(rat,x0):is(x0,x0)
+y0@[i:is(x0,y0)]
+satz79:=symis(rat,x0,y0,i):is(y0,x0)
+z0@[i:is(x0,y0)][j:is(y0,z0)]
+satz80:=tris(rat,x0,y0,z0,i,j):is(x0,z0)
+y0@more:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),moref(x,y)))):'prop'
++*ii5
+y1@propm:=and3(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1)):'prop'
+-ii5
+y0@[m:more(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propm".ii5"(t,u))][u:frac][p:propm".ii5"(t,u)]
++*ii5
+p@t4:=and3e1(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(t,class(x0))
+t5:=and3e2(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(u,class(y0))
+t6:=and3e3(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):moref(t,u)
+t7:=satz44(t,u,x,y,t6,ise(x0,x0,t,x,t4,xix0,refis(rat,x0)),ise(y0,y0,u,y,t5,yiy0,refis(rat,y0))):moref(x,y)
+s@t8:=someapp(frac,[u:frac]propm(t,u),s,moref(x,y),[u:frac][v:propm(t,u)]t7(u,v)):moref(x,y)
+-ii5
+yiy0@also18:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propm".ii5"(t,u)),m,moref(x,y),[t:frac][v:some"l"(frac,[u:frac]propm".ii5"(t,u))]t8".ii5"(t,v)):moref(x,y)
+y1iy0@[m:moref(x1,y1)]
++*ii5
+m@t9:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1),x1ix0,y1iy0,m):propm(x1,y1)
+t10:=somei(frac,[t:frac]propm(x1,t),y1,t9):some"l"(frac,[t:frac]propm(x1,t))
+-ii5
+m@morei:=somei(frac,[u:frac]some"l"(frac,[t:frac]propm".ii5"(u,t)),x1,t10".ii5"):more(x0,y0)
+y1iy0@[m:more(x0,y0)]
+moree:=also18(m,x1,y1,x1ix0,y1iy0):moref(x1,y1)
+z0@[i:is(x0,y0)][m:more(x0,z0)]
+ismore1:=isp(rat,[t:rat]more(t,z0),x0,y0,m,i):more(y0,z0)
+i@[m:more(z0,x0)]
+ismore2:=isp(rat,[t:rat]more(z0,t),x0,y0,m,i):more(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][m:more(x0,z0)]
+ismore12:=ismore2(z0,u0,y0,j,ismore1(x0,y0,z0,i,m)):more(y0,u0)
+y0@less:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),lessf(x,y)))):'prop'
++*ii5
+y1@propl:=and3(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1)):'prop'
+-ii5
+y0@[l:less(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propl".ii5"(t,u))][u:frac][p:propl".ii5"(t,u)]
++*ii5
+p@t11:=and3e1(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(t,class(x0))
+t12:=and3e2(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(u,class(y0))
+t13:=and3e3(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):lessf(t,u)
+t14:=satz45(t,u,x,y,t13,ise(x0,x0,t,x,t11,xix0,refis(rat,x0)),ise(y0,y0,u,y,t12,yiy0,refis(rat,y0))):lessf(x,y)
+s@t15:=someapp(frac,[u:frac]propl(t,u),s,lessf(x,y),[u:frac][v:propl(t,u)]t14(u,v)):lessf(x,y)
+-ii5
+yiy0@also19:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propl".ii5"(t,u)),l,lessf(x,y),[t:frac][v:some"l"(frac,[u:frac]propl".ii5"(t,u))]t15".ii5"(t,v)):lessf(x,y)
+y1iy0@[l:lessf(x1,y1)]
++*ii5
+l@t16:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1),x1ix0,y1iy0,l):propl(x1,y1)
+t17:=somei(frac,[t:frac]propl(x1,t),y1,t16):some"l"(frac,[t:frac]propl(x1,t))
+-ii5
+l@lessi:=somei(frac,[u:frac]some"l"(frac,[t:frac]propl".ii5"(u,t)),x1,t17".ii5"):less(x0,y0)
+y1iy0@[l:less(x0,y0)]
+lesse:=also19(l,x1,y1,x1ix0,y1iy0):lessf(x1,y1)
+z0@[i:is(x0,y0)][l:less(x0,z0)]
+isless1:=isp(rat,[t:rat]less(t,z0),x0,y0,l,i):less(y0,z0)
+i@[l:less(z0,x0)]
+isless2:=isp(rat,[t:rat]less(z0,t),x0,y0,l,i):less(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][l:less(x0,z0)]
+isless12:=isless2(z0,u0,y0,j,isless1(x0,y0,z0,i,l)):less(y0,u0)
++581
+y1iy0@t1:=satz41a(x1,y1):or3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
+[e:eq"n"(x1,y1)]
+t2:=or3i1(is(x0,y0),more(x0,y0),less(x0,y0),isi(e)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+y1iy0@[m:moref(x1,y1)]
+t3:=or3i2(is(x0,y0),more(x0,y0),less(x0,y0),morei(m)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+y1iy0@[l:lessf(x1,y1)]
+t4:=or3i3(is(x0,y0),more(x0,y0),less(x0,y0),lessi(l)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+y1iy0@t5:=or3app(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),or3(is(x0,y0),more(x0,y0),less(x0,y0)),t1,[t:eq"n"(x1,y1)]t2(t),[t:moref(x1,y1)]t3(t),[t:lessf(x1,y1)]t4(t)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+t6:=satz41b(x1,y1):ec3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
+[i:is(x0,y0)]
+t7:=th3"l.imp"(more(x0,y0),moref(x1,y1),ec3e12(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,ise(i)),[t:more(x0,y0)]moree(t)):not(more(x0,y0))
+y1iy0@[m:more(x0,y0)]
+t8:=th3"l.imp"(less(x0,y0),lessf(x1,y1),ec3e23(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,moree(m)),[t:less(x0,y0)]lesse(t)):not(less(x0,y0))
+y1iy0@[l:less(x0,y0)]
+t9:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),ec3e31(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,lesse(l)),[t:is(x0,y0)]ise(t)):nis(x0,y0)
+y1iy0@t10:=th6"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),th1"l.ec"(is(x0,y0),more(x0,y0),[t:is(x0,y0)]t7(t)),th1"l.ec"(more(x0,y0),less(x0,y0),[t:more(x0,y0)]t8(t)),th1"l.ec"(less(x0,y0),is(x0,y0),[t:less(x0,y0)]t9(t))):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
+t11:=orec3i(is(x0,y0),more(x0,y0),less(x0,y0),t5,t10):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
+-581
+y0@satz81:=ratapp2(orec3(is(x0,y0),more(x0,y0),less(x0,y0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t11".581"(x,y,xi,yi)):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
+satz81a:=orec3e1(is(x0,y0),more(x0,y0),less(x0,y0),satz81):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+satz81b:=orec3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
+[m:more(x0,y0)]
++582
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=lessi(y0,x0,y,x,yiy0,xix0,satz42(x,y,moree(x0,y0,x,y,xix0,yiy0,m))):less(y0,x0)
+-582
+satz82:=ratapp2(less(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".582"(x,y,xi,yi)):less(y0,x0)
+y0@[l:less(x0,y0)]
++583
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=morei(y0,x0,y,x,yiy0,xix0,satz43(x,y,lesse(x0,y0,x,y,xix0,yiy0,l))):more(y0,x0)
+-583
+satz83:=ratapp2(more(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".583"(x,y,xi,yi)):more(y0,x0)
+y0@moreis:=or(more(x0,y0),is(x0,y0)):'prop'
+[m:more(x0,y0)]
+moreisi1:=ori1(more,is,m):moreis(x0,y0)
+y0@[i:is(x0,y0)]
+moreisi2:=ori2(more,is,i):moreis(x0,y0)
+y1iy0@[m:moreq(x1,y1)]
+moreisi:=orapp(moref(x1,y1),eq"n"(x1,y1),moreis,m,[t:moref(x1,y1)]moreisi1(morei(t)),[t:eq"n"(x1,y1)]moreisi2(isi(t))):moreis(x0,y0)
+y1iy0@[m:moreis(x0,y0)]
+moreise:=orapp(more,is,moreq(x1,y1),m,[t:more]moreqi1(x1,y1,moree(t)),[t:is]moreqi2(x1,y1,ise(t))):moreq(x1,y1)
+z0@[i:is(x0,y0)][m:moreis(x0,z0)]
+ismoreis1:=isp(rat,[t:rat]moreis(t,z0),x0,y0,m,i):moreis(y0,z0)
+i@[m:moreis(z0,x0)]
+ismoreis2:=isp(rat,[t:rat]moreis(z0,t),x0,y0,m,i):moreis(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][m:moreis(x0,z0)]
+ismoreis12:=ismoreis2(z0,u0,y0,j,ismoreis1(x0,y0,z0,i,m)):moreis(y0,u0)
+y0@lessis:=or(less(x0,y0),is(x0,y0)):'prop'
+[l:less(x0,y0)]
+lessisi1:=ori1(less,is,l):lessis(x0,y0)
+y0@[i:is(x0,y0)]
+lessisi2:=ori2(less,is,i):lessis(x0,y0)
+y1iy0@[l:lesseq(x1,y1)]
+lessisi:=orapp(lessf(x1,y1),eq"n"(x1,y1),lessis,l,[t:lessf(x1,y1)]lessisi1(lessi(t)),[t:eq"n"(x1,y1)]lessisi2(isi(t))):lessis(x0,y0)
+y1iy0@[l:lessis(x0,y0)]
+lessise:=orapp(less,is,lesseq(x1,y1),l,[t:less]lesseqi1(x1,y1,lesse(t)),[t:is]lesseqi2(x1,y1,ise(t))):lesseq(x1,y1)
+z0@[i:is(x0,y0)][l:lessis(x0,z0)]
+islessis1:=isp(rat,[t:rat]lessis(t,z0),x0,y0,l,i):lessis(y0,z0)
+i@[l:lessis(z0,x0)]
+islessis2:=isp(rat,[t:rat]lessis(z0,t),x0,y0,l,i):lessis(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][l:lessis(x0,z0)]
+islessis12:=islessis2(z0,u0,y0,j,islessis1(x0,y0,z0,i,l)):lessis(y0,u0)
+y0@[m:moreis(x0,y0)]
+satz81c:=th7"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,comor(more(x0,y0),is(x0,y0),m)):not(less(x0,y0))
+y0@[l:lessis(x0,y0)]
+satz81d:=th9"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l):not(more(x0,y0))
+y0@[n:not(more(x0,y0))]
+satz81e:=th2"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n):lessis(x0,y0)
+y0@[n:not(less(x0,y0))]
+satz81f:=comor(is(x0,y0),more(x0,y0),th3"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n)):moreis(x0,y0)
+y0@[m:more(x0,y0)]
+satz81g:=th3"l.or"(less(x0,y0),is(x0,y0),ec3e23(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m),ec3e21(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m)):not(lessis(x0,y0))
+y0@[l:less(x0,y0)]
+satz81h:=th3"l.or"(more(x0,y0),is(x0,y0),ec3e32(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l),ec3e31(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l)):not(moreis(x0,y0))
+y0@[n:not(moreis(x0,y0))]
+satz81j:=or3e3(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th5"l.or"(more(x0,y0),is(x0,y0),n),th4"l.or"(more(x0,y0),is(x0,y0),n)):less(x0,y0)
+y0@[n:not(lessis(x0,y0))]
+satz81k:=or3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th4"l.or"(less(x0,y0),is(x0,y0),n),th5"l.or"(less(x0,y0),is(x0,y0),n)):more(x0,y0)
+y0@[m:moreis(x0,y0)]
++584
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=lessisi(y0,x0,y,x,yiy0,xix0,satz48(x,y,moreise(x0,y0,x,y,xix0,yiy0,m))):lessis(y0,x0)
+-584
+satz84:=ratapp2(lessis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".584"(x,y,xi,yi)):lessis(y0,x0)
+y0@[l:lessis(x0,y0)]
++585
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=moreisi(y0,x0,y,x,yiy0,xix0,satz49(x,y,lessise(x0,y0,x,y,xix0,yiy0,l))):moreis(y0,x0)
+-585
+satz85:=ratapp2(moreis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".585"(x,y,xi,yi)):moreis(y0,x0)
+z0@[l:less(x0,y0)][k:less(y0,z0)]
++586
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=lessi(x0,z0,x,z,xix0,ziz0,satz50(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
+-586
+satz86:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".586"(x,y,z,xi,yi,zi)):less(x0,z0)
+trless:=satz86:less(x0,z0)
+z0@[m:more(x0,y0)][n:more(y0,z0)]
+trmore:=satz83(z0,x0,satz86(z0,y0,x0,satz82(y0,z0,n),satz82(m))):more(x0,z0)
+z0@[l:lessis(x0,y0)][k:less(y0,z0)]
++587
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=lessi(x0,z0,x,z,xix0,ziz0,satz51a(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
+-587
+satz87a:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".587"(x,y,z,xi,yi,zi)):less(x0,z0)
+z0@[l:less(x0,y0)][k:lessis(y0,z0)]
++*587
+k@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=lessi(x0,z0,x,z,xix0,ziz0,satz51b(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
+-587
+k@satz87b:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".587"(x,y,z,xi,yi,zi)):less(x0,z0)
+z0@[m:moreis(x0,y0)][n:more(y0,z0)]
+satz87c:=satz83(z0,x0,satz87b(z0,y0,x0,satz82(y0,z0,n),satz84(m))):more(x0,z0)
+z0@[m:more(x0,y0)][n:moreis(y0,z0)]
+satz87d:=satz83(z0,x0,satz87a(z0,y0,x0,satz84(y0,z0,n),satz82(m))):more(x0,z0)
+z0@[l:lessis(x0,y0)][k:lessis(y0,z0)]
++588
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=lessisi(x0,z0,x,z,xix0,ziz0,satz52(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):lessis(x0,z0)
+-588
+satz88:=ratapp3(lessis(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".588"(x,y,z,xi,yi,zi)):lessis(x0,z0)
+trlessis:=satz88:lessis(x0,z0)
+z0@[m:moreis(x0,y0)][n:moreis(y0,z0)]
+trmoreis:=satz85(z0,x0,satz88(z0,y0,x0,satz84(y0,z0,n),satz84(m))):moreis(x0,z0)
++589
+x0@[x:frac][xix0:inf(x,class(x0))][z:frac][m:moref(z,x)]
+t1:=somei(rat,[t:rat]more(t,x0),ratof(z),morei(ratof(z),x0,z,x,inclass(z),xix0,m)):some([t:rat]more(t,x0))
+xix0@t2:=someapp(frac,[t:frac]moref(t,x),satz53(x),some([t:rat]more(t,x0)),[t:frac][u:moref(t,x)]t1(t,u)):some([t:rat]more(t,x0))
+-589
+x0@satz89:=ratapp1(some([t:rat]more(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".589"(x,xi)):some([t:rat]more(t,x0))
++590
+z"rt.589"@[l:lessf(z,x)]
+t1:=somei(rat,[t:rat]less(t,x0),ratof(z),lessi(ratof(z),x0,z,x,inclass(z),xix0,l)):some([t:rat]less(t,x0))
+xix0"rt.589"@t2:=someapp(frac,[t:frac]lessf(t,x),satz54(x),some([t:rat]less(t,x0)),[t:frac][u:lessf(t,x)]t1(t,u)):some([t:rat]less(t,x0))
+-590
+satz90:=ratapp1(some([t:rat]less(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".590"(x,xi)):some([t:rat]less(t,x0))
+y0@[l:less(x0,y0)]
++591
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][z:frac][a:and(lessf(x,z),lessf(z,y))]
+t1:=lessi(x0,ratof(z),x,z,xix0,inclass(z),ande1(lessf(x,z),lessf(z,y),a)):less(x0,ratof(z))
+t2:=lessi(ratof(z),y0,z,y,inclass(z),yiy0,ande2(lessf(x,z),lessf(z,y),a)):less(ratof(z),y0)
+t3:=andi(less(x0,ratof(z)),less(ratof(z),y0),t1,t2):and(less(x0,ratof(z)),less(ratof(z),y0))
+t4:=somei(rat,[t:rat]and(less(x0,t),less(t,y0)),ratof(z),t3):some([t:rat]and(less(x0,t),less(t,y0)))
+yiy0@t5:=someapp(frac,[t:frac]and(lessf(x,t),lessf(t,y)),satz55(x,y,lesse(x,y,xix0,yiy0,l)),some([t:rat]and(less(x0,t),less(t,y0))),[t:frac][u:and(lessf(x,t),lessf(t,y))]t4(t,u)):some([t:rat]and(less(x0,t),less(t,y0)))
+-591
+satz91:=ratapp2(some([t:rat]and(less(x0,t),less(t,y0))),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".591"(x,y,xi,yi)):some([t:rat]and(less(x0,t),less(t,y0)))
+@plusfrt:=[x:frac][y:frac]ratof(pf(x,y)):[x:frac][y:frac]rat
+[x:frac][y:frac][z:frac][u:frac][e:eq"n"(x,y)][f:eq"n"(z,u)]
++*ii5
+f@t18:=isi(ratof(pf(x,z)),ratof(pf(y,u)),pf(x,z),pf(y,u),inclass(pf(x,z)),inclass(pf(y,u)),satz56(x,y,z,u,e,f)):is(<z><x>plusfrt,<u><y>plusfrt)
+-ii5
+@fplusfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t18".ii5"(x,y,z,u,v,w):fixf(rat,plusfrt)
+y0@pl:=indrat(rat,plusfrt,fplusfrt):rat
++*ii5
+y1iy0@t19:=isindrat(rat,plusfrt,fplusfrt,x1,y1,x1ix0,y1iy0):is(ratof(pf(x1,y1)),pl(x0,y0))
+-ii5
+y1iy0@picp:=isp(rat,[t:rat]inf(pf(x1,y1),class(t)),ratof(pf(x1,y1)),pl(x0,y0),inclass(pf(x1,y1)),t19".ii5"):inf(pf(x1,y1),class(pl(x0,y0)))
+z0@[i:is(x0,y0)]
+ispl1:=isf(rat,rat,[t:rat]pl(t,z0),x0,y0,i):is(pl(x0,z0),pl(y0,z0))
+ispl2:=isf(rat,rat,[t:rat]pl(z0,t),x0,y0,i):is(pl(z0,x0),pl(z0,y0))
+u0@[i:is(x0,y0)][j:is(z0,u0)]
+ispl12:=tris(rat,pl(x0,z0),pl(y0,z0),pl(y0,u0),ispl1(i),ispl2(z0,u0,y0,j)):is(pl(x0,z0),pl(y0,u0))
++592
+y1iy0@t1:=isi(pl(x0,y0),pl(y0,x0),pf(x1,y1),pf(y1,x1),picp,picp(y0,x0,y1,x1,y1iy0,x1ix0),satz58(x1,y1)):is(pl(x0,y0),pl(y0,x0))
+-592
+y0@satz92:=ratapp2(is(pl(x0,y0),pl(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".592"(x,y,xi,yi)):is(pl(x0,y0),pl(y0,x0))
+compl:=satz92:is(pl(x0,y0),pl(y0,x0))
++593
+z0@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=picp(pl(x0,y0),z0,pf(x,y),z,picp(x0,y0,x,y,xix0,yiy0),ziz0):inf(pf(pf(x,y),z),class(pl(pl(x0,y0),z0)))
+t2:=picp(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(pf(x,pf(y,z)),class(pl(x0,pl(y0,z0))))
+t3:=isi(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),pf(pf(x,y),z),pf(x,pf(y,z)),t1,t2,satz59(x,y,z)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
+-593
+z0@satz93:=ratapp3(is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".593"(x,y,z,xi,yi,zi)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
+asspl1:=satz93:is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
+asspl2:=symis(rat,pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),satz93):is(pl(x0,pl(y0,z0)),pl(pl(x0,y0),z0))
++594
+y1iy0@t1:=morei(pl(x0,y0),x0,pf(x1,y1),x1,picp,x1ix0,satz60(x1,y1)):more(pl(x0,y0),x0)
+-594
+y0@satz94:=ratapp2(more(pl(x0,y0),x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".594"(x,y,xi,yi)):more(pl(x0,y0),x0)
+satz94a:=satz82(pl(x0,y0),x0,satz94):less(x0,pl(x0,y0))
+z0@[m:more(x0,y0)]
++595
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz61(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
+-595
+satz95:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".595"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
+z0@[m:more(x0,y0)]
++596
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
+-596
+satz96a:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".596"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
+z0@[i:is(x0,y0)]
++*596
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(pl(x0,z0),pl(y0,z0))
+-596
+i@satz96b:=ratapp3(is(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".596"(x,y,z,xi,yi,zi)):is(pl(x0,z0),pl(y0,z0))
+z0@[l:less(x0,y0)]
++*596
+l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t3:=lessi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62c(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l))):less(pl(x0,z0),pl(y0,z0))
+-596
+l@satz96c:=ratapp3(less(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".596"(x,y,z,xi,yi,zi)):less(pl(x0,z0),pl(y0,z0))
++*596
+m@andersa:=satz95(m):more(pl(x0,z0),pl(y0,z0))
+i@andersb:=ispl1(x0,y0,z0,i):is(pl(x0,z0),pl(y0,z0))
+l@andersc:=satz82(pl(y0,z0),pl(x0,z0),satz95(y0,x0,z0,satz83(l))):less(pl(x0,z0),pl(y0,z0))
+-596
+m@satz96d:=ismore12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96a):more(pl(z0,x0),pl(z0,y0))
+i@satz96e:=ispl2(x0,y0,z0,i):is(pl(z0,x0),pl(z0,y0))
+l@satz96f:=isless12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96c):less(pl(z0,x0),pl(z0,y0))
+z0@[m:more(pl(x0,z0),pl(y0,z0))]
++597
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(x0,y0,x,y,xix0,yiy0,satz63a(x,y,z,moree(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
+-597
+satz97a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".597"(x,y,z,xi,yi,zi)):more(x0,y0)
+z0@[i:is(pl(x0,z0),pl(y0,z0))]
++*597
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(x0,y0,x,y,xix0,yiy0,satz63b(x,y,z,ise(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
+-597
+i@satz97b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".597"(x,y,z,xi,yi,zi)):is(x0,y0)
+z0@[l:less(pl(x0,z0),pl(y0,z0))]
++*597
+l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t3:=lessi(x0,y0,x,y,xix0,yiy0,satz63c(x,y,z,lesse(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
+-597
+l@satz97c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".597"(x,y,z,xi,yi,zi)):less(x0,y0)
++*597
+l@anders:=satz82(y0,x0,satz97a(y0,x0,z0,satz83(pl(x0,z0),pl(y0,z0),l))):less(x0,y0)
+-597
+u0@[m:more(x0,y0)][n:more(z0,u0)]
++598
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz64(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
+-598
+satz98:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".598"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
+u0@[l:less(x0,y0)][k:less(z0,u0)]
+satz98a:=satz82(pl(y0,u0),pl(x0,z0),satz98(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
+u0@[m:moreis(x0,y0)][n:more(z0,u0)]
++599
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
+-599
+satz99a:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
+u0@[m:more(x0,y0)][n:moreis(z0,u0)]
++*599
+n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t2:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
+-599
+n@satz99b:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
+u0@[l:lessis(x0,y0)][k:less(z0,u0)]
+satz99c:=satz82(pl(y0,u0),pl(x0,z0),satz99a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
+u0@[l:less(x0,y0)][k:lessis(z0,u0)]
+satz99d:=satz82(pl(y0,u0),pl(x0,z0),satz99b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
+u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
++5100
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=moreisi(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz66(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(pl(x0,z0),pl(y0,u0))
+-5100
+satz100:=ratapp4(moreis(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5100"(x,y,z,u,xi,yi,zi,ui)):moreis(pl(x0,z0),pl(y0,u0))
+u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
+satz100a:=satz84(pl(y0,u0),pl(x0,z0),satz100(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(pl(x0,z0),pl(y0,u0))
+y0@[l:lessis(x0,y0)]
++5101
+[v0:rat][i:is(pl(y0,v0),x0)]
+t1:=ismore1(pl(y0,v0),x0,y0,i,satz94(y0,v0)):more(x0,y0)
+v0@t2:=th3"l.imp"(is(pl(y0,v0),x0),more(x0,y0),satz81d(x0,y0,l),[t:is(pl(y0,v0),x0)]t1(t)):nis(pl(y0,v0),x0)
+-5101
+vorbemerkung101:=th5"l.some"(rat,[v:rat]is(pl(y0,v),x0),[v:rat]t2".5101"(v)):not(some([t:rat]is(pl(y0,t),x0)))
+y0@[m:more(x0,y0)]
++*5101
+m@[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][v:frac][e:eq"n"(pf(y,v),x)]
+t3:=isi(pl(y0,ratof(v)),x0,pf(y,v),x,picp(y0,ratof(v),y,v,yiy0,inclass(v)),xix0,e):is(pl(y0,ratof(v)),x0)
+t4:=somei(rat,[t:rat]is(pl(y0,t),x0),ratof(v),t3):some([t:rat]is(pl(y0,t),x0))
+yiy0@t5:=someapp(frac,[t:frac]eq"n"(pf(y,t),x),satz67a(x,y,moree(x0,y0,x,y,xix0,yiy0,m)),some([t:rat]is(pl(y0,t),x0)),[t:frac][u:eq"n"(pf(y,t),x)]t4(t,u)):some([t:rat]is(pl(y0,t),x0))
+-5101
+m@satz101a:=ratapp2(some([t:rat]is(pl(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".5101"(x,y,xi,yi)):some([t:rat]is(pl(y0,t),x0))
+y0@[v0:rat][w0:rat][i:is(pl(y0,v0),x0)][j:is(pl(y0,w0),x0)]
++*5101
+j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
+t6:=isi(v0,w0,v,w,viv0,wiw0,satz67b(x,y,v,w,ise(pl(y0,v0),x0,pf(y,v),x,picp(y0,v0,y,v,yiy0,viv0),xix0,i),ise(pl(y0,w0),x0,pf(y,w),x,picp(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
+-5101
+j@satz101b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t6".5101"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
++*5101
+y0@t7:=[t:rat][u:rat][v:is(pl(y0,t),x0)][w:is(pl(y0,u),x0)]satz101b(t,u,v,w):amone(rat,[t:rat]is(pl(y0,t),x0))
+-5101
+m@satz101:=onei(rat,[t:rat]is(pl(y0,t),x0),t7".5101",satz101a):one([t:rat]is(pl(y0,t),x0))
+mn:=ind(rat,[t:rat]is(pl(y0,t),x0),satz101):rat
+satz101c:=oneax(rat,[t:rat]is(pl(y0,t),x0),satz101):is(pl(y0,mn(x0,y0,m)),x0)
+satz101d:=symis(rat,pl(y0,mn(x0,y0,m)),x0,satz101c):is(x0,pl(y0,mn(x0,y0,m)))
+satz101e:=tris(rat,pl(mn(x0,y0,m),y0),pl(y0,mn(x0,y0,m)),x0,compl(mn(x0,y0,m),y0),satz101c):is(pl(mn(x0,y0,m),y0),x0)
+satz101f:=symis(rat,pl(mn(x0,y0,m),y0),x0,satz101e):is(x0,pl(mn(x0,y0,m),y0))
+y0@[v0:rat][m:more(x0,y0)][i:is(pl(y0,v0),x0)]
+satz101g:=satz101b(v0,mn(x0,y0,m),i,satz101c(m)):is(v0,mn(x0,y0,m))
+@timesfrt:=[x:frac][y:frac]ratof(tf(x,y)):[x:frac][y:frac]rat
++*ii5
+f@t20:=isi(ratof(tf(x,z)),ratof(tf(y,u)),tf(x,z),tf(y,u),inclass(tf(x,z)),inclass(tf(y,u)),satz68(x,y,z,u,e,f)):is(<z><x>timesfrt,<u><y>timesfrt)
+-ii5
+@ftimesfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t20".ii5"(x,y,z,u,v,w):fixf(rat,timesfrt)
+y0@ts:=indrat(rat,timesfrt,ftimesfrt):rat
++*ii5
+y1iy0@t21:=isindrat(rat,timesfrt,ftimesfrt,x1,y1,x1ix0,y1iy0):is(ratof(tf(x1,y1)),ts(x0,y0))
+-ii5
+y1iy0@tict:=isp(rat,[t:rat]inf(tf(x1,y1),class(t)),ratof(tf(x1,y1)),ts(x0,y0),inclass(tf(x1,y1)),t21".ii5"):inf(tf(x1,y1),class(ts(x0,y0)))
+z0@[i:is(x0,y0)]
+ists1:=isf(rat,rat,[t:rat]ts(t,z0),x0,y0,i):is(ts(x0,z0),ts(y0,z0))
+ists2:=isf(rat,rat,[t:rat]ts(z0,t),x0,y0,i):is(ts(z0,x0),ts(z0,y0))
+u0@[i:is(x0,y0)][j:is(z0,u0)]
+ists12:=tris(rat,ts(x0,z0),ts(y0,z0),ts(y0,u0),ists1(i),ists2(z0,u0,y0,j)):is(ts(x0,z0),ts(y0,u0))
++5102
+y1iy0@t1:=isi(ts(x0,y0),ts(y0,x0),tf(x1,y1),tf(y1,x1),tict,tict(y0,x0,y1,x1,y1iy0,x1ix0),satz69(x1,y1)):is(ts(x0,y0),ts(y0,x0))
+-5102
+y0@satz102:=ratapp2(is(ts(x0,y0),ts(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".5102"(x,y,xi,yi)):is(ts(x0,y0),ts(y0,x0))
+comts:=satz102:is(ts(x0,y0),ts(y0,x0))
++5103
+ziz0"rt.593"@t1:=tict(ts(x0,y0),z0,tf(x,y),z,tict(x0,y0,x,y,xix0,yiy0),ziz0):inf(tf(tf(x,y),z),class(ts(ts(x0,y0),z0)))
+t2:=tict(x0,ts(y0,z0),x,tf(y,z),xix0,tict(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,tf(y,z)),class(ts(x0,ts(y0,z0))))
+t3:=isi(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),tf(tf(x,y),z),tf(x,tf(y,z)),t1,t2,satz70(x,y,z)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
+-5103
+z0@satz103:=ratapp3(is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5103"(x,y,z,xi,yi,zi)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
+assts1:=satz103:is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
+assts2:=symis(rat,ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),satz103):is(ts(x0,ts(y0,z0)),ts(ts(x0,y0),z0))
++5104
+ziz0"rt.593"@t1:=tict(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,pf(y,z)),class(ts(x0,pl(y0,z0))))
+t2:=picp(ts(x0,y0),ts(x0,z0),tf(x,y),tf(x,z),tict(x0,y0,x,y,xix0,yiy0),tict(x0,z0,x,z,xix0,ziz0)):inf(pf(tf(x,y),tf(x,z)),class(pl(ts(x0,y0),ts(x0,z0))))
+t3:=isi(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),t1,t2,satz71(x,y,z)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
+-5104
+satz104:=ratapp3(is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5104"(x,y,z,xi,yi,zi)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
+disttp1:=tr3is(rat,ts(pl(x0,y0),z0),ts(z0,pl(x0,y0)),pl(ts(z0,x0),ts(z0,y0)),pl(ts(x0,z0),ts(y0,z0)),comts(pl(x0,y0),z0),satz104(z0,x0,y0),ispl12(ts(z0,x0),ts(x0,z0),ts(z0,y0),ts(y0,z0),comts(z0,x0),comts(z0,y0))):is(ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)))
+disttp2:=satz104:is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
+distpt1:=symis(rat,ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)),disttp1):is(pl(ts(x0,z0),ts(y0,z0)),ts(pl(x0,y0),z0))
+distpt2:=symis(rat,ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),disttp2):is(pl(ts(x0,y0),ts(x0,z0)),ts(x0,pl(y0,z0)))
+[m:more(x0,y0)]
++5105
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(ts(x0,z0),ts(y0,z0))
+-5105
+satz105a:=ratapp3(more(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5105"(x,y,z,xi,yi,zi)):more(ts(x0,z0),ts(y0,z0))
+z0@[i:is(x0,y0)]
++*5105
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(ts(x0,z0),ts(y0,z0))
+-5105
+i@satz105b:=ratapp3(is(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5105"(x,y,z,xi,yi,zi)):is(ts(x0,z0),ts(y0,z0))
+z0@[l:less(x0,y0)]
++*5105
+l@[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]
+t3:=lessi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xi,zi),tict(y0,z0,y,z,yi,zi),satz72c(x,y,z,lesse(x0,y0,x,y,xi,yi,l))):less(ts(x0,z0),ts(y0,z0))
+-5105
+l@satz105c:=ratapp3(less(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5105"(x,y,z,xi,yi,zi)):less(ts(x0,z0),ts(y0,z0))
++*5105
+i@andersb:=ists1(x0,y0,z0,i):is(ts(x0,z0),ts(y0,z0))
+l@andersc:=satz82(ts(y0,z0),ts(x0,z0),satz105a(y0,x0,z0,satz83(l))):less(ts(x0,z0),ts(y0,z0))
+-5105
+m@satz105d:=ismore12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105a):more(ts(z0,x0),ts(z0,y0))
+i@satz105e:=ists2(x0,y0,z0,i):is(ts(z0,x0),ts(z0,y0))
+l@satz105f:=isless12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105c):less(ts(z0,x0),ts(z0,y0))
+z0@[m:more(ts(x0,z0),ts(y0,z0))]
++5106
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(x0,y0,x,y,xix0,yiy0,satz73a(x,y,z,moree(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
+-5106
+satz106a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5106"(x,y,z,xi,yi,zi)):more(x0,y0)
+z0@[i:is(ts(x0,z0),ts(y0,z0))]
++*5106
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(x0,y0,x,y,xix0,yiy0,satz73b(x,y,z,ise(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
+-5106
+i@satz106b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5106"(x,y,z,xi,yi,zi)):is(x0,y0)
+z0@[l:less(ts(x0,z0),ts(y0,z0))]
++*5106
+l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t3:=lessi(x0,y0,x,y,xix0,yiy0,satz73c(x,y,z,lesse(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
+-5106
+l@satz106c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5106"(x,y,z,xi,yi,zi)):less(x0,y0)
++*5106
+l@anders:=satz82(y0,x0,satz106a(y0,x0,z0,satz83(ts(x0,z0),ts(y0,z0),l))):less(x0,y0)
+-5106
+u0@[m:more(x0,y0)][n:more(z0,u0)]
++5107
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz74(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
+-5107
+satz107:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5107"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
+u0@[l:less(x0,y0)][k:less(z0,u0)]
+satz107a:=satz82(ts(y0,u0),ts(x0,z0),satz107(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
+u0@[m:moreis(x0,y0)][n:more(z0,u0)]
++5108
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
+-5108
+satz108a:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
+u0@[m:more(x0,y0)][n:moreis(z0,u0)]
++*5108
+n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t2:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
+-5108
+n@satz108b:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
+u0@[l:lessis(x0,y0)][k:less(z0,u0)]
+satz108c:=satz82(ts(y0,u0),ts(x0,z0),satz108a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
+u0@[l:less(x0,y0)][k:lessis(z0,u0)]
+satz108d:=satz82(ts(y0,u0),ts(x0,z0),satz108b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
+u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
++5109
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=moreisi(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz76(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(ts(x0,z0),ts(y0,u0))
+-5109
+satz109:=ratapp4(moreis(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5109"(x,y,z,u,xi,yi,zi,ui)):moreis(ts(x0,z0),ts(y0,u0))
+u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
+satz109a:=satz84(ts(y0,u0),ts(x0,z0),satz109(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(ts(x0,z0),ts(y0,u0))
++5110
+y1iy0@[v:frac][e:eq"n"(tf(y1,v),x1)]
+t1:=isi(ts(y0,ratof(v)),x0,tf(y1,v),x1,tict(y0,ratof(v),y1,v,y1iy0,inclass(v)),x1ix0,e):is(ts(y0,ratof(v)),x0)
+t2:=somei(rat,[t:rat]is(ts(y0,t),x0),ratof(v),t1):some([t:rat]is(ts(y0,t),x0))
+y1iy0@t3:=someapp(frac,[t:frac]eq"n"(tf(y1,t),x1),satz77a(x1,y1),some([t:rat]is(ts(y0,t),x0)),[t:frac][u:eq"n"(tf(y1,t),x1)]t2(t,u)):some([t:rat]is(ts(y0,t),x0))
+-5110
+y0@satz110a:=ratapp2(some([t:rat]is(ts(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t3".5110"(x,y,xi,yi)):some([t:rat]is(ts(y0,t),x0))
+[v0:rat][w0:rat][i:is(ts(y0,v0),x0)][j:is(ts(y0,w0),x0)]
++*5110
+j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
+t4:=isi(v0,w0,v,w,viv0,wiw0,satz77b(x,y,v,w,ise(ts(y0,v0),x0,tf(y,v),x,tict(y0,v0,y,v,yiy0,viv0),xix0,i),ise(ts(y0,w0),x0,tf(y,w),x,tict(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
+-5110
+j@satz110b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t4".5110"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
++*5110
+y0@t5:=[t:rat][u:rat][v:is(ts(y0,t),x0)][w:is(ts(y0,u),x0)]satz110b(t,u,v,w):amone(rat,[t:rat]is(ts(y0,t),x0))
+-5110
+y0@satz110:=onei(rat,[t:rat]is(ts(y0,t),x0),t5".5110",satz110a):one([t:rat]is(ts(y0,t),x0))
+-rt
+@[x:nat][y:nat]
++5111
+t1:=tris(nat,ts(num(fr(x,1)),den(fr(y,1))),ts(x,1),x,ndis12(x,1,y,1),satz28a(x)):is(ts(num(fr(x,1)),den(fr(y,1))),x)
+t2:=symis(nat,ts(num(fr(x,1)),den(fr(y,1))),x,t1):is(x,ts(num(fr(x,1)),den(fr(y,1))))
+-5111
+[m:moref(fr(x,1),fr(y,1))]
+satz111a:=ismore12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),m):more(x,y)
+y@[e:eq(fr(x,1),fr(y,1))]
+satz111b:=tr3is(nat,x,ts(num(fr(x,1)),den(fr(y,1))),ts(num(fr(y,1)),den(fr(x,1))),y,t2".5111",e,t1".5111"(y,x)):is(x,y)
+y@[l:lessf(fr(x,1),fr(y,1))]
+satz111c:=isless12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),l):less(x,y)
+y@[m:more(x,y)]
+satz111d:=ismore12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),m):moref(fr(x,1),fr(y,1))
+y@[i:is(x,y)]
+satz111e:=tr3is(nat,ts(num(fr(x,1)),den(fr(y,1))),x,y,ts(num(fr(y,1)),den(fr(x,1))),t1".5111",i,t2".5111"(y,x)):eq(fr(x,1),fr(y,1))
+y@[l:less(x,y)]
+satz111f:=isless12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),l):lessf(fr(x,1),fr(y,1))
++*rt
+@[x0:rat][x:nat]
+natprop:=inf(fr(x,1),class(x0)):'prop'
+x0@natrt:=some"n"([t:nat]natprop(t)):'prop'
++*ii5
+y0@[x:nat][y:nat][npx:natprop(x0,x)][npy:natprop(y0,y)][i:is(x0,y0)]
+t22:=satz111b(x,y,ise(x0,y0,fr(x,1),fr(y,1),npx,npy,i)):is"n"(x,y)
+x0@t23:=[t:nat][u:nat][v:natprop(x0,t)][w:natprop(x0,u)]t22(x0,x0,t,u,v,w,refis(rat,x0)):amone(nat,[t:nat]natprop(x0,t))
+-ii5
+x0@[nx0:natrt(x0)]
+satz111g:=onei(nat,[t:nat]natprop(t),t23".ii5",nx0):one"n"([t:nat]natprop(x0,t))
+nofrt:=ind(nat,[t:nat]natprop(t),satz111g):nat
+inclassn:=oneax(nat,[t:nat]natprop(t),satz111g):inf(fr(nofrt,1),class(x0))
+[y0:rat][ny0:natrt(y0)][i:is(x0,y0)]
+isrten:=t22".ii5"(x0,y0,nofrt(x0,nx0),nofrt(y0,ny0),inclassn(x0,nx0),inclassn(y0,ny0),i):is"n"(nofrt(x0,nx0),nofrt(y0,ny0))
+ny0@[i:is"n"(nofrt(x0,nx0),nofrt(y0,ny0))]
+isrtin:=isi(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),eqn"n"(nofrt(x0,nx0),1,nofrt(y0,ny0),i)):is(x0,y0)
+@[x:nat]
+rtofn:=ratof(fr(x,1)):rat
+natrti:=somei(nat,[t:nat]natprop(rtofn,t),x,inclass(fr(x,1))):natrt(rtofn(x))
+[y:nat][i:is"n"(x,y)]
+isnert:=isf(nat,rat,[t:nat]rtofn(t),x,y,i):is(rtofn(x),rtofn(y))
+y@[i:is(rtofn(x),rtofn(y))]
+isnirt:=t22".ii5"(rtofn(x),rtofn(y),x,y,inclass(fr(x,1)),inclass(fr(y,1)),i):is"n"(x,y)
+nx0@isrtn1:=isi(x0,rtofn(nofrt(x0,nx0)),fr(nofrt(x0,nx0),1),fr(nofrt(x0,nx0),1),inclassn(x0,nx0),inclass(fr(nofrt(x0,nx0),1)),refeq"n"(fr(nofrt(x0,nx0),1))):is(x0,rtofn(nofrt(x0,nx0)))
+x@isnrt1:=t22".ii5"(rtofn(x),rtofn(x),x,nofrt(rtofn(x),natrti(x)),inclass(fr(x,1)),inclassn(rtofn(x),natrti(x)),refis(rat,rtofn(x))):is"n"(x,nofrt(rtofn(x),natrti(x)))
+-rt
+@[x:nat][y:nat]
+satz112a:=satz57(x,y,1):eq(pf(fr(x,1),fr(y,1)),fr(pl(x,y),1))
+satz112b:=treq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),ts(1,1)),fr(ts(x,y),1),tfeq12a(x,1,y,1),eqd(ts(x,y),ts(1,1),1,satz28a(1))):eq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),1))
++*rt
+ny0@satz112c:=lemmaeq1(pl(x0,y0),pf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),picp(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112a(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(pl(x0,y0)))
+satz112d:=somei(nat,[t:nat]natprop(pl(x0,y0),t),pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112c):natrt(pl(x0,y0))
+satz112e:=lemmaeq1(ts(x0,y0),tf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),tict(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112b(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(ts(x0,y0)))
+satz112f:=somei(nat,[t:nat]natprop(ts(x0,y0),t),ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112e):natrt(ts(x0,y0))
+[m:more(x0,y0)]
++5112
+t1:=satz111a(nofrt(x0,nx0),nofrt(y0,ny0),moree(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),m)):more"n"(nofrt(x0,nx0),nofrt(y0,ny0))
+[z:nat][d:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),z)]
+t2:=tris(nat,nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),z),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),d,ispl2"n"(z,nofrt(rtofn(z),natrti(z)),nofrt(y0,ny0),isnrt1(z))):is"n"(nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))))
+t3:=isi(x0,pl(y0,rtofn(z)),fr(nofrt(x0,nx0),1),fr(pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),1),inclassn(x0,nx0),satz112c(y0,ny0,rtofn(z),natrti(z)),eqn(nofrt(x0,nx0),1,pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),t2)):is(x0,pl(y0,rtofn(z)))
+t4:=satz101g(x0,y0,rtofn(z),m,symis(rat,x0,pl(y0,rtofn(z)),t3)):is(rtofn(z),mn(x0,y0,m))
+t5:=isp(rat,[t:rat]natrt(t),rtofn(z),mn(x0,y0,m),natrti(z),t4):natrt(mn(x0,y0,m))
+-5112
+satz112g:=someapp(nat,[t:nat]diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t),t1".5112",natrt(mn(x0,y0,m)),[t:nat][u:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t)]t5".5112"(t,u)):natrt(mn(x0,y0,m))
+@[x:nat][y:nat]
+satz112h:=isi(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),pf(fr(x,1),fr(y,1)),fr(pl"n"(x,y),1),picp(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(pl"n"(x,y),1)),satz112a(x,y)):is(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)))
+satz112j:=isi(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),tf(fr(x,1),fr(y,1)),fr(ts"n"(x,y),1),tict(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(ts"n"(x,y),1)),satz112b(x,y)):is(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)))
++nt
+@natt:=ot(rat,[t:rat]natrt(t)):'type'
+nx0@ntofrt:=out(rat,[t:rat]natrt(t),x0,nx0):natt
+@[xt:natt][yt:natt]
+is:=is"e"(natt,xt,yt):'prop'
+nis:=not(is(xt,yt)):'prop'
+@[p:[x:natt]'prop']
+all:=all"l"(natt,p):'prop'
+some:=some"l"(natt,p):'prop'
+one:=one"e"(natt,p):'prop'
+xt@[st:set(natt)]
+in:=esti(natt,xt,st):'prop'
+xt@rtofnt:=in"e"(rat,[t:rat]natrt(t),xt):rat
+natrti:=inp(rat,[t:rat]natrt(t),xt):natrt(rtofnt(xt))
+ny0@[i:is"rt"(x0,y0)]
+isrtent:=isouti(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is(ntofrt(x0,nx0),ntofrt(y0,ny0))
+ny0@[i:is(ntofrt(x0,nx0),ntofrt(y0,ny0))]
+isrtint:=isoute(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is"rt"(x0,y0)
+yt@[i:is(xt,yt)]
+isntert:=isini(rat,[t:rat]natrt(t),xt,yt,i):is"rt"(rtofnt(xt),rtofnt(yt))
+yt@[i:is"rt"(rtofnt(xt),rtofnt(yt))]
+isntirt:=isine(rat,[t:rat]natrt(t),xt,yt,i):is(xt,yt)
+nx0@isrtnt1:=isinout(rat,[t:rat]natrt(t),x0,nx0):is"rt"(x0,rtofnt(ntofrt(x0,nx0)))
+xt@isntrt1:=isoutin(rat,[t:rat]natrt(t),xt):is(xt,ntofrt(rtofnt(xt),natrti(xt)))
+x@ntofn:=ntofrt(rtofn(x),natrti"rt"(x)):natt
+y@[i:is"n"(x,y)]
+isnent:=isrtent(rtofn(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),isnert(x,y,i)):is(ntofn(x),ntofn(y))
+y@[i:is(ntofn(x),ntofn(y))]
+isnint:=isnirt(x,y,isrtint(rtofn"rt"(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),i)):is"n"(x,y)
+xt@nofnt:=nofrt(rtofnt(xt),natrti(xt)):nat
+yt@[i:is(xt,yt)]
+isnten:=isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),isntert(xt,yt,i)):is"n"(nofnt(xt),nofnt(yt))
+yt@[i:is"n"(nofnt(xt),nofnt(yt))]
+isntin:=isntirt(xt,yt,isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),i)):is(xt,yt)
++ii5
+x@t24:=isrtnt1(rtofn(x),natrti"rt"(x)):is"rt"(rtofn(x),rtofnt(ntofn(x)))
+t25:=isrten(rtofn(x),natrti"rt"(x),rtofnt(ntofn(x)),natrti(ntofn(x)),t24):is"n"(nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)))
+-ii5
+x@isnnt1:=tris(nat,x,nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)),isnrt1(x),t25".ii5"):is"n"(x,nofnt(ntofn(x)))
++*ii5
+xt@t26:=isrtn1(rtofnt(xt),natrti(xt)):is"rt"(rtofnt(xt),rtofn(nofnt(xt)))
+t27:=isrtent(rtofnt(xt),natrti(xt),rtofn(nofnt(xt)),natrti"rt"(nofnt(xt)),t26):is(ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)))
+-ii5
+xt@isntn1:=tris(natt,xt,ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)),isntrt1(xt),t27".ii5"):is(xt,ntofn(nofnt(xt)))
+x@isnnt2:=symis(nat,x,nofnt(ntofn(x)),isnnt1):is"n"(nofnt(ntofn(x)),x)
+xt@isntn2:=symis(natt,xt,ntofn(nofnt(xt)),isntn1):is(ntofn(nofnt(xt)),xt)
+@1t:=ntofn(1):natt
+suct:=[x:natt]ntofn(<nofnt(x)>suc):[x:natt]natt
++5113
+xt@[i:is(<xt>suct,1t)]
+t1:=isnint(<nofnt(xt)>suc,1,i):is"n"(<nofnt(xt)>suc,1)
+-5113
+xt@satz113a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<nofnt(xt)>suc,1),<nofnt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5113"(t)):nis(<xt>suct,1t)
+yt@[i:is(<xt>suct,<yt>suct)]
++*5113
+i"nt"@t2:=isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,i):is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
+-5113
+i@satz113b:=isntin(xt,yt,<t2".5113"><nofnt(yt)><nofnt(xt)>ax4):is(xt,yt)
+@[st:set(natt)]
+cond1:=in(1t,st):'prop'
+cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
+[c1:cond1][c2:cond2]
++*5113
+c2@[x:nat]
+prop1:=in(ntofn(x),st):'prop'
+[p:prop1(x)]
+t3:=<ntofn(x)>c2:imp(in(ntofn(x),st),in(<ntofn(x)>suct,st))
+t4:=mp(in(ntofn(x),st),in(<ntofn(x)>suct,st),p,t3):in(<ntofn(x)>suct,st)
+t5:=isp(nat,[t:nat]in(ntofn(<t>suc),st),nofnt(ntofn(x)),x,t4,isnnt2(x)):prop1(<x>suc)
+-5113
+c2@[xt:natt]
++*5113
+xt@t6:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t5(t,u),nofnt(xt)):in(ntofn(nofnt(xt)),st)
+-5113
+xt@satz113c:=isp(natt,[t:natt]in(t,st),ntofn(nofnt(xt)),xt,t6".5113",isntn2(xt)):in(xt,st)
+@ax3t:=[x:natt]satz113a(x):[x:natt]nis(<x>suct,1t)
+ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz113b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
+ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz113c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
+yt@[n:nis(xt,yt)]
++51
+t1:=th3"l.imp"(is"n"(nofnt(xt),nofnt(yt)),is(xt,yt),n,[t:is"n"(nofnt(xt),nofnt(yt))]isntin(xt,yt,t)):nis"n"(nofnt(xt),nofnt(yt))
+t2:=satz1(nofnt(xt),nofnt(yt),t1):nis"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
+-51
+satz1:=th3"l.imp"(is(<xt>suct,<yt>suct),is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc),t2".51",[t:is(<xt>suct,<yt>suct)]isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,t)):nis(<xt>suct,<yt>suct)
++54
+xt@x:=nofnt(xt):nat
+[ft:[x:natt]natt]
+prop1t:=all([t:natt]is(<<t>suct>ft,<<t>ft>suct)):'prop'
+prop2t:=and(is(<1t>ft,<xt>suct),prop1t):'prop'
+xt@[f:[x:nat]nat]
+prop1:=all"n"([t:nat]is"n"(<<t>suc>f,<<t>f>suc)):'prop'
+prop2:=and(is"n"(<1>f,<x>suc),prop1):'prop'
+ft@g:=[t:nat]nofnt(<ntofn(t)>ft):[x:nat]nat
+[p:prop2t]
+t1:=ande1(is(<1t>ft,<xt>suct),prop1t,p):is(<1t>ft,<xt>suct)
+t2:=tris(nat,<1>g,nofnt(<xt>suct),<x>suc,isnten(<1t>ft,<xt>suct,t1),isnnt2(<x>suc)):is"n"(<1>g,<x>suc)
+t3:=ande2(is(<1t>ft,<xt>suct),prop1t,p):prop1t
+[u:nat]
+ut:=ntofn(u):natt
+t4:=isf(nat,nat,suc,u,nofnt(ut),isnnt1(u)):is"n"(<u>suc,<nofnt(ut)>suc)
+t5:=isf(nat,nat,g,<u>suc,<nofnt(ut)>suc,t4):is"n"(<<u>suc>g,nofnt(<<ut>suct>ft))
+t6:=<ut>t3:is(<<ut>suct>ft,<<ut>ft>suct)
+t7:=isnten(<<ut>suct>ft,<<ut>ft>suct,t6):is"n"(nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct))
+t8:=isnnt2(<<u>g>suc):is"n"(nofnt(<<ut>ft>suct),<<u>g>suc)
+t9:=tr3is(nat,<<u>suc>g,nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct),<<u>g>suc,t5,t7,t8):is"n"(<<u>suc>g,<<u>g>suc)
+p@t10:=[u:nat]t9(u):prop1(g)
+t11:=andi(is"n"(<1>g,<x>suc),prop1(g),t2,t10):prop2(g)
+xt@[a:[t:natt]natt][b:[t:natt]natt][pa:prop2t(a)][pb:prop2t(b)]
+t12:=onee1([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):amone([t:nat]nat,[u:[t:nat]nat]prop2(u))
+t13:=<t11(b,pb)><t11(a,pa)><g(b)><g(a)>t12:is"e"([t:nat]nat,g(a),g(b))
+[yt:natt]
+y:=nofnt(yt):nat
+t14:=fise(nat,nat,g(a),g(b),t13,y):is"n"(nofnt(<ntofn(y)>a),nofnt(<ntofn(y)>b))
+t15:=isntin(<ntofn(y)>a,<ntofn(y)>b,t14):is(<ntofn(y)>a,<ntofn(y)>b)
+t16:=tr3is(natt,<yt>a,<ntofn(y)>a,<ntofn(y)>b,<yt>b,isf(natt,natt,a,yt,ntofn(y),isntn1(yt)),t15,isf(natt,natt,b,ntofn(y),yt,isntn2(yt))):is(<yt>a,<yt>b)
+pb@t17:=fisi(natt,natt,a,b,[t:natt]t16(t)):is"e"([t:natt]natt,a,b)
+xt@t18:=[u:[t:natt]natt][v:[t:natt]natt][w:prop2t(u)][z:prop2t(v)]t17(u,v,w,z):amone([t:natt]natt,[u:[t:natt]natt]prop2t(u))
+t19:=onee2([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):some"l"([t:nat]nat,[u:[t:nat]nat]prop2(u))
+f@gt:=[t:natt]ntofn(<nofnt(t)>f):[x:natt]natt
+[p:prop2]
+t20:=ande1(is"n"(<1>f,<x>suc),prop1,p):is"n"(<1>f,<x>suc)
+t21:=isf(nat,nat,f,nofnt(1t),1,isnnt2(1)):is"n"(<nofnt(1t)>f,<1>f)
+t22:=isnent(<nofnt(1t)>f,<x>suc,tris(nat,<nofnt(1t)>f,<1>f,<x>suc,t21,t20)):is(<1t>gt,<xt>suct)
+t23:=ande2(is"n"(<1>f,<x>suc),prop1,p):prop1
+[zt:natt]
+z:=nofnt(zt):nat
+t24:=isf(nat,nat,f,nofnt(<zt>suct),<z>suc,isnnt2(<z>suc)):is"n"(<nofnt(<zt>suct)>f,<<z>suc>f)
+t25:=<z>t23:is"n"(<<z>suc>f,<<z>f>suc)
+t26:=isf(nat,nat,suc,<z>f,nofnt(<zt>gt),isnnt1(<z>f)):is"n"(<<z>f>suc,<nofnt(<zt>gt)>suc)
+t27:=isnent(<nofnt(<zt>suct)>f,<nofnt(<zt>gt)>suc,tr3is(nat,<nofnt(<zt>suct)>f,<<z>suc>f,<<z>f>suc,<nofnt(<zt>gt)>suc,t24,t25,t26)):is(<<zt>suct>gt,<<zt>gt>suct)
+p@t28:=[u:natt]t27(u):prop1t(gt)
+t29:=andi(is(<1t>gt,<xt>suct),prop1t(gt),t22,t28):prop2t(gt)
+t30:=somei([t:natt]natt,[u:[t:natt]natt]prop2t(u),gt,t29):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
+xt@t31:=someapp([t:nat]nat,[u:[t:nat]nat]prop2(u),t19,some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u)),[u:[t:nat]nat][v:prop2(u)]t30(u,v)):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
+-54
+xt@satz4:=onei([t:natt]natt,[u:[t:natt]natt]prop2t".54"(u),t18".54",t31".54"):one"e"([t:natt]natt,[u:[t:natt]natt]and(is(<1t>u,<xt>suct),all([v:natt]is(<<v>suct>u,<<v>u>suct))))
+yt@pl:=ntofrt(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt))):natt
++*ii5
+yt@t28:=satz112c(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)):inf(fr(pl"n"(nofnt(xt),nofnt(yt)),1),class(pl"rt"(rtofnt(xt),rtofnt(yt))))
+t29:=isi(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),fr(pl"n"(nofnt(xt),nofnt(yt)),1),fr(pl"n"(nofnt(xt),nofnt(yt)),1),t28,inclass(fr(pl"n"(nofnt(xt),nofnt(yt)),1)),refeq"n"(fr(pl"n"(nofnt(xt),nofnt(yt)),1))):is"rt"(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))))
+-ii5
+yt@isplnt:=isrtent(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),natrti"rt"(pl"n"(nofnt(xt),nofnt(yt))),t29".ii5"):is(pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))))
+isntpl:=symis(natt,pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))),isplnt):is(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt))
+ispln:=tris(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(ntofn(pl"n"(nofnt(xt),nofnt(yt)))),nofnt(pl(xt,yt)),isnnt1(pl"n"(nofnt(xt),nofnt(yt))),isnten(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt),isntpl)):is"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)))
+isnpl:=symis(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)),ispln):is"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)))
+[zt:natt]
++55
+t1:=ispl1"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt),isnpl(xt,yt)):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)))
+t2:=ispl2"n"(pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),nofnt(xt),ispln(yt,zt)):is"n"(pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
+t3:=tr3is(nat,pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)),pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t1,satz5(nofnt(xt),nofnt(yt),nofnt(zt)),t2):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
+-55
+satz5:=tr3is(natt,pl(pl(xt,yt),zt),ntofn(pl"n"(nofnt(pl(xt,yt)),nofnt(zt))),ntofn(pl"n"(nofnt(xt),nofnt(pl(yt,zt)))),pl(xt,pl(yt,zt)),isplnt(pl(xt,yt),zt),isnent(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t3".55"),isntpl(xt,pl(yt,zt))):is(pl(pl(xt,yt),zt),pl(xt,pl(yt,zt)))
+diffprop:=is(xt,pl(yt,zt)):'prop'
+[d:diffprop]
+diffprope:=tris(nat,nofnt(xt),nofnt(pl(yt,zt)),pl"n"(nofnt(yt),nofnt(zt)),isnten(xt,pl(yt,zt),d),isnpl(yt,zt)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))
+zt@[d:diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))]
++*ii5
+d@t30:=tris(nat,nofnt(xt),pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),d,ispln(yt,zt)):is"n"(nofnt(xt),nofnt(pl(yt,zt)))
+-ii5
+d@diffpropi:=isntin(xt,pl(yt,zt),t30".ii5"):diffprop
++59
+yt@it:=is(xt,yt):'prop'
+iit:=some([u:natt]diffprop(xt,yt,u)):'prop'
+iiit:=some([u:natt]diffprop(yt,xt,u)):'prop'
+i:=is"n"(nofnt(xt),nofnt(yt)):'prop'
+ii:=some"n"([u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u)):'prop'
+iii:=some"n"([u:nat]diffprop"n"(nofnt(yt),nofnt(xt),u)):'prop'
+[one:i]
+t1:=or3i1(it,iit,iiit,isntin(xt,yt,one)):or3(it,iit,iiit)
+yt@[two:ii][v:nat][d:diffprop"n"(nofnt(xt),nofnt(yt),v)]
+t2:=isp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),v,nofnt(ntofn(v)),d,isnnt1(v)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(ntofn(v)))
+t3:=somei(natt,[u:natt]diffprop(xt,yt,u),ntofn(v),diffpropi(xt,yt,ntofn(v),t2)):iit
+two@t4:=someapp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),two,iit,[u:nat][v:diffprop"n"(nofnt(xt),nofnt(yt),u)]t3(u,v)):iit
+t5:=or3i2(it,iit,iiit,t4):or3(it,iit,iiit)
+yt@[three:iii]
+t6:=or3i3(it,iit,iiit,t4(yt,xt,three)):or3(it,iit,iiit)
+yt@t7:=or3app(i,ii,iii,or3(it,iit,iiit),satz9a(nofnt(xt),nofnt(yt)),[u:i]t1(u),[u:ii]t5(u),[u:iii]t6(u)):or3(it,iit,iiit)
+[onet:it]
+t8:=isnten(xt,yt,onet):i
+yt@[twot:iit][vt:natt][d:diffprop(xt,yt,vt)]
+t9:=somei(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),nofnt(vt),diffprope(xt,yt,vt,d)):ii
+twot@t10:=someapp(natt,[u:natt]diffprop(xt,yt,u),twot,ii,[u:natt][v:diffprop(xt,yt,u)]t9(u,v)):ii
+yt@[threet:iiit]
+t11:=t10(yt,xt,threet):iii
+yt@t12:=satz9b(nofnt(xt),nofnt(yt)):ec3(i,ii,iii)
+onet@t13:=ec3e12(i,ii,iii,t12,t8):not(ii)
+t14:=th3"l.imp"(iit,ii,t13,[x:iit]t10(x)):not(iit)
+yt@t15:=th1"l.ec"(it,iit,[x:it]t14(x)):ec(it,iit)
+twot@t16:=ec3e23(i,ii,iii,t12,t10):not(iii)
+t17:=th3"l.imp"(iiit,iii,t16,[x:iiit]t11(x)):not(iiit)
+yt@t18:=th1"l.ec"(iit,iiit,[x:iit]t17(x)):ec(iit,iiit)
+threet@t19:=ec3e31(i,ii,iii,t12,t11):not(i)
+t20:=th3"l.imp"(it,i,t19,[x:it]t8(x)):not(it)
+yt@t21:=th1"l.ec"(iiit,it,[x:iiit]t20(x)):ec(iiit,it)
+t22:=th6"l.ec3"(it,iit,iiit,t15,t18,t21):ec3(it,iit,iiit)
+-59
+yt@satz9:=orec3i(it".59",iit".59",iiit".59",t7".59",t22".59"):orec3(is(xt,yt),some([u:natt]is(xt,pl(yt,u))),some([u:natt]is(yt,pl(xt,u))))
+more:=more"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[m:more(xt,yt)]
++*ii5
+m@t31:=moree(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+m@moree:=satz111a(nofnt(xt),nofnt(yt),t31".ii5"):more"n"(nofnt(xt),nofnt(yt))
+yt@[m:more"n"(nofnt(xt),nofnt(yt))]
++*ii5
+m@t32:=satz111d(nofnt(xt),nofnt(yt),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+m@morei:=morei"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t32".ii5"):more(xt,yt)
+yt@less:=less"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[l:less(xt,yt)]
++*ii5
+l@t33:=lesse(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+l@lesse:=satz111c(nofnt(xt),nofnt(yt),t33".ii5"):less"n"(nofnt(xt),nofnt(yt))
+yt@[l:less"n"(nofnt(xt),nofnt(yt))]
++*ii5
+l@t34:=satz111f(nofnt(xt),nofnt(yt),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+l@lessi:=lessi"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t34".ii5"):less(xt,yt)
+yt@moreis:=moreis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[m:moreis(xt,yt)]
+moreise:=th9"l.or"(more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),m,[u:more"rt"(rtofnt(xt),rtofnt(yt))]moree(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis"n"(nofnt(xt),nofnt(yt))
+yt@[m:moreis"n"(nofnt(xt),nofnt(yt))]
+moreisi:=th9"l.or"(more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),m,[u:more"n"(nofnt(xt),nofnt(yt))]morei(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis(xt,yt)
+yt@lessis:=lessis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[l:lessis(xt,yt)]
+lessise:=th9"l.or"(less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),l,[u:less"rt"(rtofnt(xt),rtofnt(yt))]lesse(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis"n"(nofnt(xt),nofnt(yt))
+yt@[l:lessis"n"(nofnt(xt),nofnt(yt))]
+lessisi:=th9"l.or"(less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),l,[u:less"n"(nofnt(xt),nofnt(yt))]lessi(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis(xt,yt)
+zt@[l:less(xt,yt)][k:less(yt,zt)]
++515
+t1:=satz15(nofnt(xt),nofnt(yt),nofnt(zt),lesse(xt,yt,l),lesse(yt,zt,k)):less"n"(nofnt(xt),nofnt(zt))
+-515
+satz15:=lessi(xt,zt,t1".515"):less(xt,zt)
+zt@[ut:natt][m:more(xt,yt)][n:more(zt,ut)]
++521
+t1:=satz21(nofnt(xt),nofnt(yt),nofnt(zt),nofnt(ut),moree(xt,yt,m),moree(zt,ut,n)):more"n"(pl"n"(nofnt(xt),nofnt(zt)),pl"n"(nofnt(yt),nofnt(ut)))
+t2:=ismore12"n"(pl"n"(nofnt(xt),nofnt(zt)),nofnt(pl(xt,zt)),pl"n"(nofnt(yt),nofnt(ut)),nofnt(pl(yt,ut)),ispln(xt,zt),ispln(yt,ut),t1):more"n"(nofnt(pl(xt,zt)),nofnt(pl(yt,ut)))
+-521
+satz21:=morei(pl(xt,zt),pl(yt,ut),t2".521"):more(pl(xt,zt),pl(yt,ut))
+@[p:[x:natt]'prop'][n:natt]
+lb:=all([x:natt]imp(<x>p,lessis(n,x))):'prop'
+min:=and(lb,<n>p):'prop'
+p@[s:some(p)]
++527
+q:=[x:nat]<ntofn(x)>p:[x:nat]'prop'
+[n:natt][np:<n>p]
+t1:=isp(natt,p,n,ntofn(nofnt(n)),np,isntn1(n)):<nofnt(n)>q
+t2:=somei(nat,q,nofnt(n),t1):some"n"(q)
+s@t3:=someapp(natt,p,s,some"n"(q),[u:natt][v:<u>p]t2(u,v)):some"n"(q)
+t4:=satz27(q,t3):some"n"([x:nat]min"n"(q,x))
+[m:nat][mqm:min"n"(q,m)]
+t5:=ande1(lb"n"(q,m),<m>q,mqm):lb"n"(q,m)
+[n:nat][nq:<n>q]
+t6:=mp(<n>q,lessis"n"(m,n),nq,<n>t5):lessis"n"(m,n)
+mqm@[n:natt][np:<n>p]
+t7:=t6(nofnt(n),t1(n,np)):lessis"n"(m,nofnt(n))
+t8:=islessis1"n"(m,nofnt(ntofn(m)),nofnt(n),isnnt1(m),t7):lessis"n"(nofnt(ntofn(m)),nofnt(n))
+t9:=lessisi(ntofn(m),n,t8):lessis(ntofn(m),n)
+n@t10:=[u:<n>p]t9(u):imp(<n>p,lessis(ntofn(m),n))
+mqm@t11:=[x:natt]t10(x):lb(ntofn(m))
+t12:=ande2(lb"n"(q,m),<m>q,mqm):<ntofn(m)>p
+t13:=andi(lb(ntofn(m)),<ntofn(m)>p,t11,t12):min(ntofn(m))
+t14:=somei(natt,[x:natt]min(x),ntofn(m),t13):some([x:natt]min(x))
+-527
+satz27:=someapp(nat,[x:nat]min"n"(q".527",x),t4".527",some([x:natt]min(x)),[x:nat][y:min"n"(q".527",x)]t14".527"(x,y)):some([x:natt]min(p,x))
+-nt
+@1rt:=rtofn(1):rat
+x0@[x:frac][xix0:inf(x,class(x0))]
++*ii5
+xix0@t35:=tr3eq(tf(x,fr(1,1)),fr(ts"n"(num(x),1),ts"n"(den(x),1)),fr(num(x),den(x)),x,tfeq1a(x,1,1),eqnd(ts"n"(num(x),1),ts"n"(den(x),1),num(x),den(x),satz28a(num(x)),satz28a(den(x))),refeq1(fr(num(x),den(x)),x,fris(x))):eq"n"(tf(x,fr(1,1)),x)
+t36:=isi(ts(x0,1rt),x0,tf(x,fr(1,1)),x,tict(x0,1rt,x,fr(1,1),xix0,inclass(fr(1,1))),xix0,t35):is(ts(x0,1rt),x0)
+-ii5
+x0@example1a:=ratapp1(x0,is(ts(x0,1rt),x0),[x:frac][xi:inf(x,class(x0))]t36".ii5"(x,xi)):is(ts(x0,1rt),x0)
+example1b:=symis(rat,ts(x0,1rt),x0,example1a):is(x0,ts(x0,1rt))
+example1c:=tris(rat,ts(1rt,x0),ts(x0,1rt),x0,comts(1rt,x0),example1a):is(ts(1rt,x0),x0)
+example1d:=symis(rat,ts(1rt,x0),x0,example1c):is(x0,ts(1rt,x0))
+@[x:frac]
++5114
+t1:=tr3eq(tf(fr(den(x),1),x),fr(ts"n"(den(x),num(x)),ts"n"(1,den(x))),fr(ts"n"(num(x),den(x)),ts"n"(1,den(x))),fr(num(x),1),tfeq2a(x,den(x),1),eqn(ts"n"(den(x),num(x)),ts"n"(1,den(x)),ts"n"(num(x),den(x)),comts"n"(den(x),num(x))),satz40c(num(x),1,den(x))):eq"n"(tf(fr(den(x),1),x),fr(num(x),1))
+-5114
+satz114:=isi(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)),tf(fr(den(x),1),x),fr(num(x),1),tict(rtofn(den(x)),ratof(x),fr(den(x),1),x,inclass(fr(den(x),1)),inclass(x)),inclass(fr(num(x),1)),t1".5114"):is(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)))
+@[x1:nat][x2:nat]
+satz114a:=tr3is(rat,ts(rtofn(x2),ratof(fr(x1,x2))),ts(rtofn(den(fr(x1,x2))),ratof(fr(x1,x2))),rtofn(num(fr(x1,x2))),rtofn(x1),ists1(rtofn(x2),rtofn(den(fr(x1,x2))),ratof(fr(x1,x2)),isnert(x2,den(fr(x1,x2)),isden(x1,x2))),satz114(fr(x1,x2)),isnert(num(fr(x1,x2)),x1,numis(x1,x2))):is(ts(rtofn(x2),ratof(fr(x1,x2))),rtofn(x1))
+x0@[y0:rat]
+ov:=ind(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):rat
+satz110c:=oneax(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):is(ts(y0,ov(x0,y0)),x0)
+satz110d:=symis(rat,ts(y0,ov(x0,y0)),x0,satz110c):is(x0,ts(y0,ov(x0,y0)))
+satz110e:=tris(rat,ts(ov(x0,y0),y0),ts(y0,ov(x0,y0)),x0,comts(ov(x0,y0),y0),satz110c):is(ts(ov(x0,y0),y0),x0)
+satz110f:=symis(rat,ts(ov(x0,y0),y0),x0,satz110e):is(x0,ts(ov(x0,y0),y0))
+[v0:rat][i:is(ts(y0,v0),x0)]
+satz110g:=satz110b(x0,y0,v0,ov(x0,y0),i,satz110c):is(v0,ov(x0,y0))
+x2@satz114b:=satz110b(rtofn(x1),rtofn(x2),ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114a,satz110c(rtofn(x1),rtofn(x2))):is(ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)))
+satz114c:=symis(rat,ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114b):is(ov(rtofn(x1),rtofn(x2)),ratof(fr(x1,x2)))
++5115
+y0@t1:=satz89(ov(y0,x0)):some([t:rat]more(t,ov(y0,x0)))
+[u0:rat][m:more(u0,ov(y0,x0))][u:frac][uiu0:inf(u,class(u0))]
+z:=num(u):nat
+v:=den(u):nat
+t2:=ismore1(u0,ov(rtofn(z),rtofn(v)),ov(y0,x0),tris(rat,u0,ratof(fr(z,v)),ov(rtofn(z),rtofn(v)),isi(u0,ratof(fr(z,v)),u,fr(z,v),uiu0,inclass(fr(z,v)),refeq1(u,fr(z,v),isfr(u))),satz114b(z,v)),m):more(ov(rtofn(z),rtofn(v)),ov(y0,x0))
+t3:=moreisi(rtofn(v),1rt,fr(v,1),fr(1,1),inclass(fr(v,1)),inclass(fr(1,1)),th9"l.or"(more"n"(v,1),is"n"(v,1),moref(fr(v,1),fr(1,1)),eq"n"(fr(v,1),fr(1,1)),satz24(v),[t:more"n"(v,1)]satz111d(v,1,t),[t:is"n"(v,1)]satz111e(v,1,t))):moreis(rtofn(v),1rt)
+t4:=tr3is(rat,ts(rtofn(z),x0),ts(x0,rtofn(z)),ts(x0,ts(ov(rtofn(z),rtofn(v)),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),comts(rtofn(z),x0),ists2(rtofn(z),ts(ov(rtofn(z),rtofn(v)),rtofn(v)),x0,satz110f(rtofn(z),rtofn(v))),assts2(x0,ov(rtofn(z),rtofn(v)),rtofn(v))):is(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)))
+[n:more(rtofn(v),1rt)]
+t5:=ismore1(ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),symis(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),t4),satz105d(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),n)):more(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+t6:=moreisi1(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t5):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+uiu0@[i:is(rtofn(v),1rt)]
+t7:=moreisi2(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),tris(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t4,ists2(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),i))):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+uiu0@t8:=orapp(more(rtofn(v),1rt),is(rtofn(v),1rt),moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt)),t3,[t:more(rtofn(v),1rt)]t6(t),[t:is(rtofn(v),1rt)]t7(t)):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+t9:=ismore12(ts(x0,ov(rtofn(z),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),ts(x0,ov(y0,x0)),y0,example1b(ts(x0,ov(rtofn(z),rtofn(v)))),satz110c(y0,x0),satz105d(ov(rtofn(z),rtofn(v)),ov(y0,x0),x0,t2)):more(ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0)
+t10:=satz87c(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0,t8,t9):more(ts(rtofn(z),x0),y0)
+t11:=somei(nat,[t:nat]more(ts(rtofn(t),x0),y0),z,t10):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
+m@t12:=ratapp1(u0,some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[u:frac][ui:inf(u,class(u0))]t11(u,ui)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
+-5115
+y0@satz115:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[t:rat][u:more(t,ov(y0,x0))]t12".5115"(t,u)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
++*5115
+uiu0@t13:=andi(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0),natrti(z),t10):and(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0))
+t14:=somei(rat,[t:rat]and(natrt(t),more(ts(t,x0),y0)),rtofn(z),t13):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
+m@t15:=ratapp1(u0,some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[u:frac][ui:inf(u,class(u0))]t14(u,ui)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
+-5115
+y0@satz115a:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[t:rat][u:more(t,ov(y0,x0))]t15".5115"(t,u)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
+@[s:set(rat)]
+cutprop1a:=nonempty(rat,s):'prop'
+cutprop1b:=not(all([x:rat]in(x,s))):'prop'
+cutprop1:=and(cutprop1a,cutprop1b):'prop'
+[x0:rat]
+cutprop2a:=all([x:rat]imp(not(in(x,s)),less(x0,x))):'prop'
+s@cutprop2:=all([x:rat]imp(in(x,s),cutprop2a(x))):'prop'
+x0@[y0:rat]
++iii1
+ubprop:=imp(in(y0,s),moreis(x0,y0)):'prop'
+-iii1
+x0@ub:=all([x:rat]ubprop".iii1"(x0,x)):'prop'
+max:=and(ub(x0),in(x0,s)):'prop'
+s@cutprop3:=not(some([x:rat]max(s,x))):'prop'
+cutprop:=and3(cutprop1,cutprop2,cutprop3):'prop'
++*iii1
+y0@lbprop:=imp(in(y0,s),lessis(x0,y0)):'prop'
+-iii1
+x0@lb:=all([x:rat]lbprop".iii1"(x0,x)):'prop'
+min:=and(lb(x0),in(x0,s)):'prop'
+@cut:=ot(set(rat),[x:set(rat)]cutprop(x)):'type'
+[ksi:cut]
+lcl:=in"e"(set(rat),[x:set(rat)]cutprop(x),ksi):set(rat)
+[x0:rat]
+lrt:=in(x0,lcl(ksi)):'prop'
+urt:=not(in(x0,lcl(ksi))):'prop'
+ksi@clcl:=inp(set(rat),[x:set(rat)]cutprop(x),ksi):cutprop(lcl(ksi))
+clcl1:=and3e1(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop1(lcl(ksi))
+clcl2:=and3e2(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop2(lcl(ksi))
+clcl3:=and3e3(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop3(lcl(ksi))
+clcl1a:=ande1(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1a(lcl(ksi))
+clcl1b:=ande2(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1b(lcl(ksi))
+[p:'prop'][p1:[x:rat][t:lrt(ksi,x)]p]
+cutapp1a:=nonemptyapp(rat,lcl,clcl1a,p,p1):p
++*iii1
+ksi@t1:=th1"l.some"(rat,[x:rat]lrt(ksi,x),clcl1b):some([x:rat]urt(ksi,x))
+-iii1
+p@[p1:[x:rat][t:urt(ksi,x)]p]
+cutapp1b:=someapp(rat,[x:rat]urt(ksi,x),t1".iii1",p,p1):p
+ksi@[x0:rat][lx:lrt(ksi,x0)]
++*iii1
+lx@t2:=mp(lrt(ksi,x0),cutprop2a(lcl,x0),lx,<x0>clcl2):cutprop2a(lcl,x0)
+-iii1
+lx@[y0:rat][uy:urt(ksi,y0)]
+cutapp2a:=mp(urt(ksi,y0),less(x0,y0),uy,<y0>t2".iii1"):less(x0,y0)
+cutapp2b:=satz83(x0,y0,cutapp2a):more(y0,x0)
++*iii1
+lx@t3:=th4"l.some"(rat,[x:rat]max(lcl,x),clcl3,x0):not(max(lcl,x0))
+t4:=th4"l.and"(ub(lcl,x0),lrt(ksi,x0),t3,lx):not(ub(lcl,x0))
+t5:=th1"l.some"(rat,[x:rat]ubprop(lcl,x0,x),t4):some([x:rat]not(ubprop(lcl,x0,x)))
+-iii1
+lx@[p:'prop'][p1:[y:rat][t:lrt(ksi,y)][u:less(x0,y)]p][y0:rat][n:not(ubprop".iii1"(lcl,x0,y0))]
++*iii1
+n@t6:=th5"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):lrt(ksi,y0)
+t7:=th6"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):not(moreis(x0,y0))
+t8:=satz81j(x0,y0,t7):less(x0,y0)
+t9:=<t8><t6><y0>p1:p
+-iii1
+p1@cutapp3:=someapp(rat,[y:rat]not(ubprop".iii1"(lcl,x0,y)),t5".iii1",p,[y:rat][t:not(ubprop".iii1"(lcl,x0,y))]t9".iii1"(y,t)):p
+s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))]
++*iii1
+n@t10:=andi(cutprop1a,cutprop1b,nonemptyi(rat,s,x0,i),th1"l.all"(rat,[x:rat]in(x,s),y0,n)):cutprop1
+-iii1
+s@[n:[x:rat]not(max(s,x))]
++*iii1
+n@t11:=th5"l.some"(rat,[x:rat]max(s,x),n):cutprop3
+-iii1
+s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][l:[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]less(x,y)][m:[x:rat]not(max(s,x))]
+cut1:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),l,t11".iii1"(m)):cutprop(s)
++rp
+ksi@[eta:cut]
+is:=is"e"(cut,ksi,eta):'prop'
+nis:=not(is(ksi,eta)):'prop'
+[i:is(ksi,eta)]
+ise:=isini(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is"e"(set(rat),lcl(ksi),lcl(eta))
+[x0:rat][lx:lrt(ksi,x0)]
+ise1:=issete1(rat,lcl(ksi),lcl(eta),ise,x0,lx):lrt(eta,x0)
+eta@[i:is"e"(set(rat),lcl(ksi),lcl(eta))]
+isi:=isine(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is(ksi,eta)
+eta@[l:[x:rat][t:lrt(ksi,x)]lrt(eta,x)][k:[x:rat][t:lrt(eta,x)]lrt(ksi,x)]
+isi1:=isi(isseti(rat,lcl(ksi),lcl(eta),l,k)):is(ksi,eta)
+@[s:set(rat)][cs:cutprop(s)]
+cutof:=out(set(rat),[x:set(rat)]cutprop(x),s,cs):cut
+[x0:rat][i:in(x0,s)]
+ine:=issete1(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,i):lrt(cutof(s,cs),x0)
+x0@[lx:lrt(cutof(s,cs),x0)]
+ini:=issete2(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,lx):in(x0,s)
+s@[t:set(rat)][cs:cutprop(s)][ct:cutprop(t)][i:[x:rat][u:in(x,s)]in(x,t)][j:[x:rat][u:in(x,t)]in(x,s)]
+isi2:=isouti(set(rat),[x:set(rat)]cutprop(x),s,cs,t,ct,isseti(rat,s,t,i,j)):is(cutof(s,cs),cutof(t,ct))
+@[p:[x:cut]'prop']
+all:=all"l"(cut,p):'prop'
+some:=some"l"(cut,p):'prop'
+one:=one"e"(cut,p):'prop'
+ksi@satz116:=refis(cut,ksi):is(ksi,ksi)
+eta@[i:is(ksi,eta)]
+satz117:=symis(cut,ksi,eta,i):is(eta,ksi)
+eta@[zeta:cut][i:is(ksi,eta)][j:is(eta,zeta)]
+satz118:=tris(cut,ksi,eta,zeta,i,j):is(ksi,zeta)
++1119
+@[x0:rat][y0:rat][m:more(x0,y0)]
+t1:=ec3e23(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),m):not(less(x0,y0))
+-1119
+ksi@[x0:rat][ux:urt(ksi,x0)][y0:rat][m:more(y0,x0)]
+satz119:=th3"l.imp"(lrt(ksi,y0),less(y0,x0),t1".1119"(y0,x0,m),[t:lrt(ksi,y0)]cutapp2a(y0,t,x0,ux)):urt(ksi,y0)
+y0@[l:less(x0,y0)]
+satz119a:=satz119(satz83(x0,y0,l)):urt(ksi,y0)
++1120
+@[x0:rat][y0:rat][l:less(x0,y0)]
+t1:=ec3e32(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),l):not(more(x0,y0))
+-1120
+ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][l:less(y0,x0)]
+satz120:=th7"l.imp"(lrt(ksi,y0),more(y0,x0),t1".1120"(y0,x0,l),[t:urt(ksi,y0)]cutapp2b(x0,lx,y0,t)):lrt(ksi,y0)
+y0@[m:more(x0,y0)]
+satz120a:=satz120(satz82(x0,y0,m)):lrt(ksi,y0)
+-rp
+s@[i:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][x0:rat][j:in(x0,s)][y0:rat][n:not(in(y0,s))]
++*iii1
+n@t12:=<y0><j><x0>i:[u:less(y0,x0)]in(y0,s)
+t13:=th3"l.imp"(less(y0,x0),in(y0,s),n,t12):not(less(y0,x0))
+t14:=satz81f(y0,x0,t13):moreis(y0,x0)
+-iii1
+n@[k:is(y0,x0)]
++*iii1
+k@t15:=isp1(rat,[x:rat]in(x,s),x0,y0,j,k):in(y0,s)
+n@t16:=th3"l.imp"(is(y0,x0),in(y0,s),n,[t:is(y0,x0)]t15(t)):nis(y0,x0)
+t17:=ore1(more(y0,x0),is(y0,x0),t14,t16):more(y0,x0)
+t18:=satz82(y0,x0,t17):less(x0,y0)
+i@t19:=[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]t18(x,t,y,u):cutprop2
+-iii1
+s@[s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))][x0:rat][i:in(x0,s)]
++*iii1
+i@t20:=<i><x0>s1:some([y:rat]and(in(y,s),more(y,x0)))
+-iii1
+i@[y0:rat][a:and(in(y0,s),more(y0,x0))]
++*iii1
+a@t21:=ande1(in(y0,s),more(y0,x0),a):in(y0,s)
+t22:=ande2(in(y0,s),more(y0,x0),a):more(y0,x0)
+t23:=satz81g(y0,x0,t22):not(lessis(y0,x0))
+t24:=th3"l.imp"(moreis(x0,y0),lessis(y0,x0),t23,[t:moreis(x0,y0)]satz84(x0,y0,t)):not(moreis(x0,y0))
+t25:=th4"l.imp"(in(y0,s),moreis(x0,y0),t21,t24):not(ubprop(x0,y0))
+t26:=th1"l.all"(rat,[y:rat]ubprop(x0,y),y0,t25):not(ub(s,x0))
+t27:=th1"l.and"(ub(s,x0),in(x0,s),t26):not(max(s,x0))
+i@t28:=someapp(rat,[y:rat]and(in(y,s),more(y,x0)),t20,not(max(s,x0)),[y:rat][t:and(in(y,s),more(y,x0))]t27(y,t)):not(max(s,x0))
+-iii1
+x0@[n:not(in(x0,s))]
++*iii1
+n@t29:=th2"l.and"(ub(x0),in(x0,s),n):not(max(s,x0))
+x0@t30:=th1"l.imp"(in(x0,s),not(max(s,x0)),[u:in(x0,s)]t28(u),[u:not(in(x0,s))]t29(u)):not(max(s,x0))
+s1@t31:=t11([x:rat]t30(x)):cutprop3
+-iii1
+s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][j:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))]
+cut2:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),t19".iii1"(j),t31".iii1"(s1)):cutprop(s)
++*rp
+eta@more:=some"rt"([x:rat]and(lrt(ksi,x),urt(eta,x))):'prop'
+[m:more(ksi,eta)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]p][x0:rat][a:and(lrt(ksi,x0),urt(eta,x0))]
++iii2
+t1:=ande1(lrt(ksi,x0),urt(eta,x0),a):lrt(ksi,x0)
+t2:=ande2(lrt(ksi,x0),urt(eta,x0),a):urt(eta,x0)
+t3:=<t2><t1><x0>p1:p
+-iii2
+p1@moreapp:=someapp(rat,[x:rat]and(lrt(ksi,x),urt(eta,x)),m,p,[x:rat][t:and(lrt(ksi,x),urt(eta,x))]t3".iii2"(x,t)):p
+eta@less:=some"rt"([x:rat]and(urt(ksi,x),lrt(eta,x))):'prop'
+[l:less(ksi,eta)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]p][x0:rat][a:and(urt(ksi,x0),lrt(eta,x0))]
++*iii2
+a@t4:=ande1(urt(ksi,x0),lrt(eta,x0),a):urt(ksi,x0)
+t5:=ande2(urt(ksi,x0),lrt(eta,x0),a):lrt(eta,x0)
+t6:=<t5><t4><x0>p1:p
+-iii2
+p1@lessapp:=someapp(rat,[x:rat]and(urt(ksi,x),lrt(eta,x)),l,p,[x:rat][t:and(urt(ksi,x),lrt(eta,x))]t6".iii2"(x,t)):p
+eta@[m:more(ksi,eta)]
++2121
+[x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
+t1:=andi(urt(eta,x0),lrt(ksi,x0),ux,lx):and(urt(eta,x0),lrt(ksi,x0))
+t2:=somei(rat,[x:rat]and(urt(eta,x),lrt(ksi,x)),x0,t1):less(eta,ksi)
+-2121
+satz121:=moreapp(m,less(eta,ksi),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2".2121"(x,t,u)):less(eta,ksi)
+eta@[l:less(ksi,eta)]
++2122
+[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
+t1:=andi(lrt(eta,x0),urt(ksi,x0),lx,ux):and(lrt(eta,x0),urt(ksi,x0))
+t2:=somei(rat,[x:rat]and(lrt(eta,x),urt(ksi,x)),x0,t1):more(eta,ksi)
+-2122
+satz122:=lessapp(l,more(eta,ksi),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t2".2122"(x,t,u)):more(eta,ksi)
++2123
+eta@[m:more(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
+t1:=th3"st.isset"(rat,lcl(ksi),lcl(eta),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
+t2:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t1,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
+m@t3:=moreapp(ksi,eta,m,not(is(ksi,eta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2(x,t,u)):not(is(ksi,eta))
+eta@t4:=th2"l.ec"(is(ksi,eta),more(ksi,eta),[t:more(ksi,eta)]t3(t)):ec(is(ksi,eta),more(ksi,eta))
+[l:less(ksi,eta)][x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
+t5:=th4"st.isset"(rat,lcl(eta),lcl(ksi),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
+t6:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t5,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
+l@t7:=lessapp(ksi,eta,l,not(is(ksi,eta)),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t6(x,t,u)):not(is(ksi,eta))
+eta@t8:=th1"l.ec"(less(ksi,eta),is(ksi,eta),[t:less(ksi,eta)]t7(t)):ec(less(ksi,eta),is(ksi,eta))
+m@[l:less(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)][y0:rat][uy:urt(ksi,y0)][ly:lrt(eta,y0)]
+t9:=cutapp2a(ksi,x0,lx,y0,uy):less"rt"(x0,y0)
+t10:=cutapp2b(eta,y0,ly,x0,ux):more"rt"(x0,y0)
+t11:=mp(less"rt"(x0,y0),con,t9,ec3e23(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),satz81b(x0,y0),t10)):con
+ux@t12:=lessapp(ksi,eta,l,con,[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t11(x,t,u)):con
+l@t13:=moreapp(ksi,eta,m,con,[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t12(x,t,u)):con
+m@t14:=[t:less(ksi,eta)]t13(t):not(less(ksi,eta))
+eta@t15:=th1"l.ec"(more(ksi,eta),less(ksi,eta),[t:more(ksi,eta)]t14(t)):ec(more(ksi,eta),less(ksi,eta))
+a:=th6"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t4,t15,t8):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+[i:is(ksi,eta)]
+t16:=or3i1(is(ksi,eta),more(ksi,eta),less(ksi,eta),i):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+eta@[n:nis(ksi,eta)]
+t17:=th3"l.imp"(is"e"(set(rat),lcl(ksi),lcl(eta)),is(ksi,eta),n,[t:is"e"(set(rat),lcl(ksi),lcl(eta))]isi(ksi,eta,t)):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
+t18:=th5"st.isset"(rat,lcl(ksi),lcl(eta),t17):or(more(ksi,eta),more(eta,ksi))
+t19:=th8"l.or"(more(ksi,eta),more(eta,ksi),less(ksi,eta),t18,[t:more(eta,ksi)]satz121(eta,ksi,t)):or(more(ksi,eta),less(ksi,eta))
+t20:=th7"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t19):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+eta@b:=th1"l.imp"(is(ksi,eta),or3(is(ksi,eta),more(ksi,eta),less(ksi,eta)),[t:is(ksi,eta)]t16(t),[t:nis(ksi,eta)]t20(t)):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+-2123
+eta@satz123:=orec3i(is(ksi,eta),more(ksi,eta),less(ksi,eta),b".2123",a".2123"):orec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+satz123a:=orec3e1(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+satz123b:=orec3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+moreis:=or(more(ksi,eta),is(ksi,eta)):'prop'
+lessis:=or(less(ksi,eta),is(ksi,eta)):'prop'
+[m:moreis(ksi,eta)]
+satz124:=th9"l.or"(more(ksi,eta),is(ksi,eta),less(eta,ksi),is(eta,ksi),m,[t:more(ksi,eta)]satz121(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):lessis(eta,ksi)
+eta@[l:lessis(ksi,eta)]
+satz125:=th9"l.or"(less(ksi,eta),is(ksi,eta),more(eta,ksi),is(eta,ksi),l,[t:less(ksi,eta)]satz122(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):moreis(eta,ksi)
+zeta@[i:is(ksi,eta)][m:more(ksi,zeta)]
+ismore1:=isp(cut,[u:cut]more(u,zeta),ksi,eta,m,i):more(eta,zeta)
+i@[m:more(zeta,ksi)]
+ismore2:=isp(cut,[u:cut]more(zeta,u),ksi,eta,m,i):more(zeta,eta)
+i@[l:less(ksi,zeta)]
+isless1:=isp(cut,[u:cut]less(u,zeta),ksi,eta,l,i):less(eta,zeta)
+i@[l:less(zeta,ksi)]
+isless2:=isp(cut,[u:cut]less(zeta,u),ksi,eta,l,i):less(zeta,eta)
+i@[m:moreis(ksi,zeta)]
+ismoreis1:=isp(cut,[u:cut]moreis(u,zeta),ksi,eta,m,i):moreis(eta,zeta)
+i@[m:moreis(zeta,ksi)]
+ismoreis2:=isp(cut,[u:cut]moreis(zeta,u),ksi,eta,m,i):moreis(zeta,eta)
+i@[l:lessis(ksi,zeta)]
+islessis1:=isp(cut,[u:cut]lessis(u,zeta),ksi,eta,l,i):lessis(eta,zeta)
+i@[l:lessis(zeta,ksi)]
+islessis2:=isp(cut,[u:cut]lessis(zeta,u),ksi,eta,l,i):lessis(zeta,eta)
+eta@[i:is(ksi,eta)]
+moreisi2:=ori2(more(ksi,eta),is(ksi,eta),i):moreis(ksi,eta)
+lessisi2:=ori2(less(ksi,eta),is(ksi,eta),i):lessis(ksi,eta)
+eta@[m:more(ksi,eta)]
+moreisi1:=ori1(more(ksi,eta),is(ksi,eta),m):moreis(ksi,eta)
+eta@[l:less(ksi,eta)]
+lessisi1:=ori1(less(ksi,eta),is(ksi,eta),l):lessis(ksi,eta)
+zeta@[upsilon:cut][i:is(ksi,eta)][j:is(zeta,upsilon)][m:more(ksi,zeta)]
+ismore12:=ismore2(zeta,upsilon,eta,j,ismore1(ksi,eta,zeta,i,m)):more(eta,upsilon)
+j@[l:less(ksi,zeta)]
+isless12:=isless2(zeta,upsilon,eta,j,isless1(ksi,eta,zeta,i,l)):less(eta,upsilon)
+j@[m:moreis(ksi,zeta)]
+ismoreis12:=ismoreis2(zeta,upsilon,eta,j,ismoreis1(ksi,eta,zeta,i,m)):moreis(eta,upsilon)
+j@[l:lessis(ksi,zeta)]
+islessis12:=islessis2(zeta,upsilon,eta,j,islessis1(ksi,eta,zeta,i,l)):lessis(eta,upsilon)
+eta@[m:moreis(ksi,eta)]
+satz123c:=th7"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,comor(more(ksi,eta),is(ksi,eta),m)):not(less(ksi,eta))
+eta@[l:lessis(ksi,eta)]
+satz123d:=th9"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l):not(more(ksi,eta))
+eta@[n:not(more(ksi,eta))]
+satz123e:=th2"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n):lessis(ksi,eta)
+eta@[n:not(less(ksi,eta))]
+satz123f:=comor(is(ksi,eta),more(ksi,eta),th3"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n)):moreis(ksi,eta)
+eta@[m:more(ksi,eta)]
+satz123g:=th3"l.or"(less(ksi,eta),is(ksi,eta),ec3e23(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m),ec3e21(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m)):not(lessis(ksi,eta))
+eta@[l:less(ksi,eta)]
+satz123h:=th3"l.or"(more(ksi,eta),is(ksi,eta),ec3e32(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l),ec3e31(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l)):not(moreis(ksi,eta))
+eta@[n:not(moreis(ksi,eta))]
+satz123j:=or3e3(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th5"l.or"(more(ksi,eta),is(ksi,eta),n),th4"l.or"(more(ksi,eta),is(ksi,eta),n)):less(ksi,eta)
+eta@[n:not(lessis(ksi,eta))]
+satz123k:=or3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th4"l.or"(less(ksi,eta),is(ksi,eta),n),th5"l.or"(less(ksi,eta),is(ksi,eta),n)):more(ksi,eta)
+zeta@[l:less(ksi,eta)][k:less(eta,zeta)]
++2126
+[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)][y0:rat][uy:urt(eta,y0)][ly:lrt(zeta,y0)]
+t1:=cutapp2a(eta,x0,lx,y0,uy):less"rt"(x0,y0)
+t2:=satz119a(ksi,x0,ux,y0,t1):urt(ksi,y0)
+t3:=andi(urt(ksi,y0),lrt(zeta,y0),t2,ly):and(urt(ksi,y0),lrt(zeta,y0))
+t4:=somei(rat,[x:rat]and(urt(ksi,x),lrt(zeta,x)),y0,t3):less(ksi,zeta)
+lx@t5:=lessapp(eta,zeta,k,less(ksi,zeta),[x:rat][t:urt(eta,x)][u:lrt(zeta,x)]t4(x,t,u)):less(ksi,zeta)
+-2126
+satz126:=lessapp(ksi,eta,l,less(ksi,zeta),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t5".2126"(x,t,u)):less(ksi,zeta)
+trless:=satz126:less(ksi,zeta)
+zeta@[m:more(ksi,eta)][n:more(eta,zeta)]
+trmore:=satz122(zeta,ksi,satz126(zeta,eta,ksi,satz121(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
+zeta@[l:lessis(ksi,eta)][k:less(eta,zeta)]
+satz127a:=orapp(less(ksi,eta),is(ksi,eta),less(ksi,zeta),l,[u:less(ksi,eta)]trless(u,k),[u:is(ksi,eta)]isless1(eta,ksi,zeta,symis(cut,ksi,eta,u),k)):less(ksi,zeta)
+zeta@[l:less(ksi,eta)][k:lessis(eta,zeta)]
+satz127b:=orapp(less(eta,zeta),is(eta,zeta),less(ksi,zeta),k,[u:less(eta,zeta)]trless(l,u),[u:is(eta,zeta)]isless2(eta,zeta,ksi,u,l)):less(ksi,zeta)
+zeta@[m:moreis(ksi,eta)][n:more(eta,zeta)]
+satz127c:=satz122(zeta,ksi,satz127b(zeta,eta,ksi,satz121(eta,zeta,n),satz124(ksi,eta,m))):more(ksi,zeta)
+zeta@[m:more(ksi,eta)][n:moreis(eta,zeta)]
+satz127d:=satz122(zeta,ksi,satz127a(zeta,eta,ksi,satz124(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
+zeta@[l:lessis(ksi,eta)][k:lessis(eta,zeta)]
++2128
+[i:is(ksi,eta)][j:is(eta,zeta)]
+t1:=lessisi2(ksi,zeta,tris(cut,ksi,eta,zeta,i,j)):lessis(ksi,zeta)
+i@[j:less(eta,zeta)]
+t2:=lessisi1(ksi,zeta,satz127a(l,j)):lessis(ksi,zeta)
+i@t3:=orapp(less(eta,zeta),is(eta,zeta),lessis(ksi,zeta),k,[t:less(eta,zeta)]t2(t),[t:is(eta,zeta)]t1(t)):lessis(ksi,zeta)
+k@[j:less(ksi,eta)]
+t4:=lessisi1(ksi,zeta,satz127b(j,k)):lessis(ksi,zeta)
+-2128
+satz128:=orapp(less(ksi,eta),is(ksi,eta),lessis(ksi,zeta),l,[t:less(ksi,eta)]t4".2128"(t),[t:is(ksi,eta)]t3".2128"(t)):lessis(ksi,zeta)
+trlessis:=satz128:lessis(ksi,zeta)
+zeta@[m:moreis(ksi,eta)][n:moreis(eta,zeta)]
+trmoreis:=satz125(zeta,ksi,satz128(zeta,eta,ksi,satz124(eta,zeta,n),satz124(ksi,eta,m))):moreis(ksi,zeta)
+eta@[z0:rat][x0:rat][y0:rat]
+sumprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0))):'prop'
+z0@sumprop:=some"rt"([x:rat]some"rt"([y:rat]sumprop1(z0,x,y))):'prop'
+eta@sum:=setof(rat,[z:rat]sumprop(z)):set(rat)
+x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl(x0,y0))]
++iii3
+t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),lx,ly,i):sumprop1(z0,x0,y0)
+t2:=somei(rat,[y:rat]sumprop1(z0,x0,y),y0,t1):some"rt"([y:rat]sumprop1(z0,x0,y))
+t3:=somei(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),x0,t2):sumprop(z0)
+-iii3
+sum1:=estii(rat,[z:rat]sumprop(z),z0,t3".iii3"):in(z0,sum)
+z0@[i:in(z0,sum)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]p]
++*iii3
+p1@t4:=estie(rat,[z:rat]sumprop(z),z0,i):sumprop(z0)
+-iii3
+p1@[x0:rat][px:some"rt"([y:rat]sumprop1(z0,x0,y))][y0:rat][py:sumprop1(z0,x0,y0)]
++*iii3
+py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(ksi,x0)
+t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(eta,y0)
+t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):is"rt"(z0,pl(x0,y0))
+t8:=<t7><t6><y0><t5><x0>p1:p
+px@t9:=someapp(rat,[y:rat]sumprop1(z0,x0,y),px,p,[y:rat][t:sumprop1(z0,x0,y)]t8(y,t)):p
+-iii3
+p1@sumapp:=someapp(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),t4".iii3",p,[x:rat][t:some"rt"([y:rat]sumprop1(z0,x,y))]t9".iii3"(x,t)):p
+eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
++3129
+[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))]
+t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
+t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
+t3:=isless1"rt"(pl(x0,y0),z0,pl(x1,y1),symis(rat,z0,pl(x0,y0),j),satz98a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,pl(x1,y1))
+t4:=ec3e31(is"rt"(z0,pl(x1,y1)),more"rt"(z0,pl(x1,y1)),less"rt"(z0,pl(x1,y1)),satz81b(z0,pl(x1,y1)),t3):nis"rt"(z0,pl(x1,y1))
+i@t5:=sumapp(ksi,eta,z0,i,nis"rt"(z0,pl(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,pl(x1,y1))
+-3129
+satz129a:=th3"l.imp"(in(pl(x1,y1),sum),nis"rt"(pl(x1,y1),pl(x1,y1)),weli(is"rt"(pl(x1,y1),pl(x1,y1)),refis(rat,pl(x1,y1))),[t:in(pl(x1,y1),sum)]t5".3129"(pl(x1,y1),t)):not(in(pl(x1,y1),sum))
++*3129
+eta@[u0:rat][i:in(u0,sum)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,pl(x0,y0))]
+t6:=isless2"rt"(u0,pl(x0,y0),z0,j,l):less"rt"(z0,pl(x0,y0))
+z1:=ov(z0,pl(x0,y0)):rat
+t7:=isless12"rt"(z0,ts(z1,pl(x0,y0)),pl(x0,y0),ts(1rt,pl(x0,y0)),satz110f(z0,pl(x0,y0)),example1d(pl(x0,y0)),t6):less"rt"(ts(z1,pl(x0,y0)),ts(1rt,pl(x0,y0)))
+t8:=satz106c(z1,1rt,pl(x0,y0),t7):less"rt"(z1,1rt)
+t9:=isless2"rt"(ts(x0,1rt),x0,ts(x0,z1),example1a(x0),satz105f(z1,1rt,x0,t8)):less"rt"(ts(x0,z1),x0)
+t10:=isless2"rt"(ts(y0,1rt),y0,ts(y0,z1),example1a(y0),satz105f(z1,1rt,y0,t8)):less"rt"(ts(y0,z1),y0)
+t11:=satz120(ksi,x0,lx,ts(x0,z1),t9):lrt(ksi,ts(x0,z1))
+t12:=satz120(eta,y0,ly,ts(y0,z1),t10):lrt(eta,ts(y0,z1))
+t13:=tris(rat,pl(ts(x0,z1),ts(y0,z1)),ts(pl(x0,y0),z1),z0,distpt1(x0,y0,z1),satz110c(z0,pl(x0,y0))):is"rt"(pl(ts(x0,z1),ts(y0,z1)),z0)
+t14:=symis(rat,pl(ts(x0,z1),ts(y0,z1)),z0,t13):is"rt"(z0,pl(ts(x0,z1),ts(y0,z1)))
+t15:=sum1(ksi,eta,z0,ts(x0,z1),t11,ts(y0,z1),t12,t14):in(z0,sum)
+l@t16:=sumapp(ksi,eta,u0,i,in(z0,sum),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,pl(x,y))]t15(x,t,y,u,v)):in(z0,sum)
+eta@[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
+t17:=sum1(ksi,eta,pl(x1,y0),x1,lx1,y0,ly,refis(rat,pl(x1,y0))):in(pl(x1,y0),sum)
+t18:=satz96a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(pl(x1,y0),pl(x0,y0))
+t19:=ismore2"rt"(pl(x0,y0),z0,pl(x1,y0),symis(rat,z0,pl(x0,y0),j),t18):more"rt"(pl(x1,y0),z0)
+t20:=andi(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0),t17,t19):and(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0))
+t21:=somei(rat,[y:rat]and(in(y,sum),more"rt"(y,z0)),pl(x1,y0),t20):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
+j@t22:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t21(x,t,u)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
+i@t23:=sumapp(ksi,eta,z0,i,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t22(x,t,y,u,v)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
+eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
+t24:=cut2(sum,pl(x0,y0),sum1(ksi,eta,pl(x0,y0),x0,lx,y0,ly,refis(rat,pl(x0,y0))),pl(x1,y1),satz129a(x1,ux,y1,uy),[x:rat][t:in(x,sum)][y:rat][u:less"rt"(y,x)]t16(x,t,y,u),[x:rat][t:in(x,sum)]t23(x,t)):cutprop(sum)
+ux@t25:=cutapp1b(eta,cutprop(sum),[y:rat][t:urt(eta,y)]t24(y,t)):cutprop(sum)
+ly@t26:=cutapp1b(ksi,cutprop(sum),[x:rat][t:urt(ksi,x)]t25(x,t)):cutprop(sum)
+lx@t27:=cutapp1a(eta,cutprop(sum),[y:rat][t:lrt(eta,y)]t26(y,t)):cutprop(sum)
+-3129
+eta@satz129:=cutapp1a(ksi,cutprop(sum),[x:rat][t:lrt(ksi,x)]t27".3129"(x,t)):cutprop(sum)
+pl:=cutof(sum,satz129):cut
+[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
+lrtpl:=ine(sum,satz129,z0,sum1(z0,x0,lx,y0,ly,i)):lrt(pl(ksi,eta),z0)
+eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
++*iii3
+i@t10:=isp1(rat,[x:rat]not(in(x,sum)),pl"rt"(x0,y0),z0,satz129a(x0,ux,y0,uy),i):not(in(z0,sum))
+-iii3
+i@urtpl:=th3"l.imp"(lrt(pl(ksi,eta),z0),in(z0,sum),t10".iii3",[t:lrt(pl(ksi,eta),z0)]ini(sum,satz129,z0,t)):urt(pl(ksi,eta),z0)
+eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]p]
++*iii3
+p1@t11:=ini(sum,satz129,z0,lz):in(z0,sum)
+-iii3
+p1@plapp:=sumapp(z0,t11".iii3",p,p1):p
+zeta@[i:is(ksi,eta)]
+ispl1:=isf(cut,cut,[u:cut]pl(u,zeta),ksi,eta,i):is(pl(ksi,zeta),pl(eta,zeta))
+ispl2:=isf(cut,cut,[u:cut]pl(zeta,u),ksi,eta,i):is(pl(zeta,ksi),pl(zeta,eta))
+upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
+ispl12:=tris(cut,pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),ispl1(i),ispl2(zeta,upsilon,eta,j)):is(pl(ksi,zeta),pl(eta,upsilon))
++3130
+eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
+t1:=tris(rat,z0,pl"rt"(x0,y0),pl"rt"(y0,x0),i,compl(x0,y0)):is"rt"(z0,pl"rt"(y0,x0))
+t2:=lrtpl(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(pl(eta,ksi),z0)
+lz@t3:=plapp(ksi,eta,z0,lz,lrt(pl(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]t2(x,t,y,u,v)):lrt(pl(eta,ksi),z0)
+-3130
+eta@satz130:=isi1(pl(ksi,eta),pl(eta,ksi),[x:rat][t:lrt(pl(ksi,eta),x)]t3".3130"(x,t),[x:rat][t:lrt(pl(eta,ksi),x)]t3".3130"(eta,ksi,x,t)):is(pl(ksi,eta),pl(eta,ksi))
+compl:=satz130:is(pl(ksi,eta),pl(eta,ksi))
++3131
+zeta@[u0:rat][lu:lrt(pl(pl(ksi,eta),zeta),u0)][v0:rat][lv:lrt(pl(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,pl"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,pl"rt"(x0,y0))]
+t1:=tr3is(rat,u0,pl"rt"(v0,z0),pl"rt"(pl"rt"(x0,y0),z0),pl"rt"(x0,pl"rt"(y0,z0)),i,ispl1"rt"(v0,pl"rt"(x0,y0),z0,j),asspl1(x0,y0,z0)):is"rt"(u0,pl"rt"(x0,pl"rt"(y0,z0)))
+t2:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
+t3:=lrtpl(ksi,pl(eta,zeta),u0,x0,lx,pl"rt"(y0,z0),t2,t1):lrt(pl(ksi,pl(eta,zeta)),u0)
+i@t4:=plapp(ksi,eta,v0,lv,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,pl"rt"(x,y))]t3(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
+lu@t5:=plapp(pl(ksi,eta),zeta,u0,lu,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(pl(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
+u0@[lu:lrt(pl(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,pl"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
+t6:=tr3is(rat,u0,pl"rt"(x0,v0),pl"rt"(x0,pl"rt"(y0,z0)),pl"rt"(pl"rt"(x0,y0),z0),i,ispl2"rt"(v0,pl"rt"(y0,z0),x0,j),asspl2(x0,y0,z0)):is"rt"(u0,pl"rt"(pl"rt"(x0,y0),z0))
+t7:=lrtpl(ksi,eta,pl"rt"(x0,y0),x0,lx,y0,ly,refis(rat,pl"rt"(x0,y0))):lrt(pl(ksi,eta),pl"rt"(x0,y0))
+t8:=lrtpl(pl(ksi,eta),zeta,u0,pl"rt"(x0,y0),t7,z0,lz,t6):lrt(pl(pl(ksi,eta),zeta),u0)
+i@t9:=plapp(eta,zeta,v0,lv,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t8(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
+lu@t10:=plapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t9(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
+-3131
+zeta@satz131:=isi1(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),[x:rat][t:lrt(pl(pl(ksi,eta),zeta),x)]t5".3131"(x,t),[x:rat][t:lrt(pl(ksi,pl(eta,zeta)),x)]t10".3131"(x,t)):is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
+asspl1:=satz131:is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
+asspl2:=symis(cut,pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),satz131):is(pl(ksi,pl(eta,zeta)),pl(pl(ksi,eta),zeta))
+ksi@[a0:rat]
++3132
+[x0:rat][y0:rat]
+prop1:=and(lrt(ksi,x0),urt(ksi,y0)):'prop'
+[p:prop1]
+t1:=cutapp2b(x0,ande1(lrt(ksi,x0),urt(ksi,y0),p),y0,ande2(lrt(ksi,x0),urt(ksi,y0),p)):more"rt"(y0,x0)
+prop2:=is"rt"(mn(y0,x0,t1),a0):'prop'
+y0@prop3:=and(prop1,[t:prop1]prop2(t)):'prop'
+a0@prop4:=some"rt"([x:rat]some"rt"([y:rat]prop3(x,y))):'prop'
+x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
+t2:=cutapp2b(x0,lx,y0,uy):more"rt"(y0,x0)
+[n:nat][m:more"rt"(ts(rtofn(n),a0),mn(y0,x0,t2))]
+t3:=satz96d(ts(rtofn(n),a0),mn(y0,x0,t2),x0,m):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),pl"rt"(x0,mn(y0,x0,t2)))
+t4:=ismore2"rt"(pl"rt"(x0,mn(y0,x0,t2)),y0,pl"rt"(x0,ts(rtofn(n),a0)),satz101c(y0,x0,t2),t3):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),y0)
+t5:=satz119(y0,uy,pl"rt"(x0,ts(rtofn(n),a0)),t4):urt(pl"rt"(x0,ts(rtofn(n),a0)))
+t6:=somei(nat,[x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),n,t5):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
+uy@t7:=someapp(nat,[x:nat]more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2)),satz115(a0,mn(y0,x0,t2)),some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0)))),[x:nat][t:more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2))]t6(x,t)):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
+[u:nat][m:min"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)]
+t8:=ande1(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)
+t9:=ande2(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):urt(pl"rt"(x0,ts(rtofn(u),a0)))
+[i:is"n"(u,1)]
+u0:=pl"rt"(x0,a0):rat
+t10:=tr3is(rat,ts(rtofn(u),a0),ts(1rt,a0),ts(a0,1rt),a0,ists1(rtofn(u),1rt,a0,isnert(u,1,i)),comts(1rt,a0),example1a(a0)):is"rt"(ts(rtofn(u),a0),a0)
+t11:=isp(rat,[x:rat]urt(pl"rt"(x0,x)),ts(rtofn(u),a0),a0,t9,t10):urt(ksi,u0)
+t12:=andi(lrt(ksi,x0),urt(ksi,u0),lx,t11):prop1(x0,u0)
+[p:prop1(x0,u0)]
+t13:=symis(rat,a0,mn(u0,x0,t1(x0,u0,p)),satz101g(u0,x0,a0,t1(x0,u0,p),refis(rat,u0))):prop2(x0,u0,p)
+i@t14:=andi(prop1(x0,u0),[t:prop1(x0,u0)]prop2(x0,u0,t),t12,[t:prop1(x0,u0)]t13(t)):prop3(x0,u0)
+t15:=somei(rat,[y:rat]prop3(x0,y),u0,t14):some"rt"([y:rat]prop3(x0,y))
+t16:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),x0,t15):prop4
+m@[o:more"n"(u,1)]
+t17:=morei(rtofn(u),1rt,fr(u,1),fr(1,1),inclass(fr(u,1)),inclass(fr(1,1)),satz111d(u,1,o)):more"rt"(rtofn(u),1rt)
+um10:=mn(rtofn(u),1rt,t17):rat
+t18:=satz112g(rtofn(u),natrti(u),1rt,natrti(1),t17):natrt(um10)
+um1:=nofrt(um10,t18):nat
+v0:=pl"rt"(x0,ts(um10,a0)):rat
+w0:=pl"rt"(x0,ts(rtofn(u),a0)):rat
+t19:=isless2"rt"(pl"rt"(um10,1rt),rtofn(u),um10,satz101e(rtofn(u),1rt,t17),satz94a(um10,1rt)):less"rt"(um10,rtofn(u))
+t20:=lesse(um10,rtofn(u),fr(um1,1),fr(u,1),inclassn(um10,t18),inclass(fr(u,1)),t19):lessf(fr(um1,1),fr(u,1))
+t21:=satz111c(um1,u,t20):less"n"(um1,u)
+t22:=th3"l.imp"(lessis"n"(u,um1),moreis"n"(um1,u),satz10h(um1,u,t21),[t:lessis"n"(u,um1)]satz14(u,um1,t)):not(lessis"n"(u,um1))
+t23:=et(lrt(pl"rt"(x0,ts(rtofn(um1),a0))),th3"l.imp"(urt(pl"rt"(x0,ts(rtofn(um1),a0))),lessis"n"(u,um1),t22,<um1>t8)):lrt(pl"rt"(x0,ts(rtofn(um1),a0)))
+t24:=isp1(rat,[x:rat]lrt(pl"rt"(x0,ts(x,a0))),rtofn(um1),um10,t23,isrtn1(um10,t18)):lrt(ksi,v0)
+t25:=andi(lrt(ksi,v0),urt(ksi,w0),t24,t9):prop1(v0,w0)
+t26:=tr3is(rat,pl"rt"(ts(um10,a0),a0),pl"rt"(ts(um10,a0),ts(1rt,a0)),ts(pl"rt"(um10,1rt),a0),ts(rtofn(u),a0),ispl2"rt"(a0,ts(1rt,a0),ts(um10,a0),example1d(a0)),distpt1(um10,1rt,a0),ists1(pl"rt"(um10,1rt),rtofn(u),a0,satz101e(rtofn(u),1rt,t17))):is"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0))
+t27:=tris(rat,pl"rt"(v0,a0),pl"rt"(x0,pl"rt"(ts(um10,a0),a0)),w0,asspl1"rt"(x0,ts(um10,a0),a0),ispl2"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0),x0,t26)):is"rt"(pl"rt"(v0,a0),w0)
+[p:prop1(v0,w0)]
+t28:=symis(rat,a0,mn(w0,v0,t1(v0,w0,p)),satz101g(w0,v0,a0,t1(v0,w0,p),t27)):prop2(v0,w0,p)
+o@t29:=andi(prop1(v0,w0),[t:prop1(v0,w0)]prop2(v0,w0,t),t25,[t:prop1(v0,w0)]t28(t)):prop3(v0,w0)
+t30:=somei(rat,[y:rat]prop3(v0,y),w0,t29):some"rt"([y:rat]prop3(v0,y))
+t31:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),v0,t30):prop4
+m@t32:=orapp(more"n"(u,1),is"n"(u,1),prop4,satz24(u),[t:more"n"(u,1)]t31(t),[t:is"n"(u,1)]t16(t)):prop4
+uy@t34:=someapp(nat,[x:nat]min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x),satz27([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),t7),prop4,[x:nat][t:min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x)]t32(x,t)):prop4
+lx@t35:=cutapp1b(prop4,[y:rat][t:urt(ksi,y)]t34(y,t)):prop4
+-3132
+satz132:=cutapp1a(prop4".3132",[x:rat][t:lrt(ksi,x)]t35".3132"(x,t)):some"rt"([x:rat]some"rt"([y:rat]and(and(lrt(ksi,x),urt(ksi,y)),[t:and(lrt(ksi,x),urt(ksi,y))]is"rt"(mn(y,x,cutapp2b(x,ande1(lrt(ksi,x),urt(ksi,y),t),y,ande2(lrt(ksi,x),urt(ksi,y),t))),a0))))
+ksi@[p:'prop'][a0:rat][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),a0)]p]
++*3132
+p1@[x0:rat][s:some"rt"([y:rat]prop3(a0,x0,y))][y0:rat][p3:prop3(a0,x0,y0)]
+t36:=ande1(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop1(a0,x0,y0)
+t37:=ande2"l.r"(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop2(a0,x0,y0,t36)
+t38:=ande1(lrt(ksi,x0),urt(ksi,y0),t36):lrt(ksi,x0)
+t39:=ande2(lrt(ksi,x0),urt(ksi,y0),t36):urt(ksi,y0)
+t40:=satz101g(y0,x0,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),t1(a0,x0,y0,t36),satz101c(y0,x0,cutapp2b(x0,t38,y0,t39))):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)))
+t41:=tris(rat,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)),a0,t40,t37):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),a0)
+t42:=<t41><t39><y0><t38><x0>p1:p
+s@t43:=someapp(rat,[y:rat]prop3(a0,x0,y),s,p,[y:rat][t:prop3(a0,x0,y)]t42(y,t)):p
+-3132
+p1@satz132app:=someapp(rat,[x:rat]some"rt"([y:rat]prop3".3132"(a0,x,y)),satz132(a0),p,[x:rat][t:some"rt"([y:rat]prop3".3132"(a0,x,y))]t43".3132"(x,t)):p
++3133
+eta@[y0:rat][ly:lrt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][uu:urt(ksi,u0)][i:is"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0)]
+t1:=tris(rat,u0,pl"rt"(x0,mn(u0,x0,cutapp2b(x0,lx,u0,uu))),pl"rt"(x0,y0),satz101d(u0,x0,cutapp2b(x0,lx,u0,uu)),ispl2"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0,x0,i)):is"rt"(u0,pl"rt"(x0,y0))
+t2:=lrtpl(ksi,eta,u0,x0,lx,y0,ly,t1):lrt(pl(ksi,eta),u0)
+t3:=andi(lrt(pl(ksi,eta),u0),urt(ksi,u0),t2,uu):and(lrt(pl(ksi,eta),u0),urt(ksi,u0))
+t4:=somei(rat,[x:rat]and(lrt(pl(ksi,eta),x),urt(ksi,x)),u0,t3):more(pl(ksi,eta),ksi)
+ly@t5:=satz132app(ksi,more(pl(ksi,eta),ksi),y0,[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),y0)]t4(x,t,y,u,v)):more(pl(ksi,eta),ksi)
+-3133
+eta@satz133:=cutapp1a(eta,more(pl(ksi,eta),ksi),[x:rat][t:lrt(eta,x)]t5".3133"(x,t)):more(pl(ksi,eta),ksi)
+satz133a:=satz121(pl(ksi,eta),ksi,satz133):less(ksi,pl(ksi,eta))
+zeta@[m:more(ksi,eta)]
++3134
+[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
+t1:=satz119a(eta,y0,uy,x0,l):urt(eta,x0)
+t2:=satz83(y0,x0,l):more"rt"(x0,y0)
+[u0:rat][lu:lrt(zeta,u0)][z0:rat][uz:urt(zeta,z0)][i:is"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2))]
+t3:=tris(rat,z0,pl"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),u0),pl"rt"(mn(x0,y0,t2),u0),satz101f(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),ispl1"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2),u0,i)):is"rt"(z0,pl"rt"(mn(x0,y0,t2),u0))
+t4:=tr3is(rat,pl"rt"(y0,z0),pl"rt"(y0,pl"rt"(mn(x0,y0,t2),u0)),pl"rt"(pl"rt"(y0,mn(x0,y0,t2)),u0),pl"rt"(x0,u0),ispl2"rt"(z0,pl"rt"(mn(x0,y0,t2),u0),y0,t3),asspl2"rt"(y0,mn(x0,y0,t2),u0),ispl1"rt"(pl"rt"(y0,mn(x0,y0,t2)),x0,u0,satz101c(x0,y0,t2))):is"rt"(pl"rt"(y0,z0),pl"rt"(x0,u0))
+t5:=lrtpl(ksi,zeta,pl"rt"(y0,z0),x0,lx,u0,lu,t4):lrt(pl(ksi,zeta),pl"rt"(y0,z0))
+t6:=urtpl(eta,zeta,pl"rt"(y0,z0),y0,uy,z0,uz,refis(rat,pl"rt"(y0,z0))):urt(pl(eta,zeta),pl"rt"(y0,z0))
+t7:=andi(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)),t5,t6):and(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)))
+t8:=somei(rat,[x:rat]and(lrt(pl(ksi,zeta),x),urt(pl(eta,zeta),x)),pl"rt"(y0,z0),t7):more(pl(ksi,zeta),pl(eta,zeta))
+l@t9:=satz132app(zeta,more(pl(ksi,zeta),pl(eta,zeta)),mn(x0,y0,t2),[x:rat][t:lrt(zeta,x)][y:rat][u:urt(zeta,y)][v:is"rt"(mn(y,x,cutapp2b(zeta,x,t,y,u)),mn(x0,y0,t2))]t8(x,t,y,u,v)):more(pl(ksi,zeta),pl(eta,zeta))
+uy@t10:=cutapp3(ksi,y0,ly,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t9(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
+-3134
+satz134:=moreapp(ksi,eta,m,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t10".3134"(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
+zeta@[m:more(ksi,eta)]
+satz135a:=satz134(m):more(pl(ksi,zeta),pl(eta,zeta))
+zeta@[i:is(ksi,eta)]
+satz135b:=ispl1(ksi,eta,zeta,i):is(pl(ksi,zeta),pl(eta,zeta))
+zeta@[l:less(ksi,eta)]
+satz135c:=satz121(pl(eta,zeta),pl(ksi,zeta),satz134(eta,ksi,zeta,satz122(ksi,eta,l))):less(pl(ksi,zeta),pl(eta,zeta))
+m@satz135d:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135a):more(pl(zeta,ksi),pl(zeta,eta))
+i@satz135e:=ispl2(ksi,eta,zeta,i):is(pl(zeta,ksi),pl(zeta,eta))
+l@satz135f:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135c):less(pl(zeta,ksi),pl(zeta,eta))
+upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
+satz135g:=ismore2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135d(zeta,upsilon,ksi,m)):more(pl(ksi,zeta),pl(eta,upsilon))
+satz135h:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135g):more(pl(zeta,ksi),pl(upsilon,eta))
+i@[l:less(zeta,upsilon)]
+satz135j:=isless2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135f(zeta,upsilon,ksi,l)):less(pl(ksi,zeta),pl(eta,upsilon))
+satz135k:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135j):less(pl(zeta,ksi),pl(upsilon,eta))
++3136
+zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+t2:=satz123b(pl(ksi,zeta),pl(eta,zeta)):ec3(is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)))
+-3136
+zeta@[m:more(pl(ksi,zeta),pl(eta,zeta))]
+satz136a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),m):more(ksi,eta)
+zeta@[i:is(pl(ksi,zeta),pl(eta,zeta))]
+satz136b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),i):is(ksi,eta)
+zeta@[l:less(pl(ksi,zeta),pl(eta,zeta))]
+satz136c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),l):less(ksi,eta)
+zeta@[m:more(pl(zeta,ksi),pl(zeta,eta))]
+satz136d:=satz136a(ismore12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),m)):more(ksi,eta)
+zeta@[i:is(pl(zeta,ksi),pl(zeta,eta))]
+satz136e:=satz136b(tr3is(cut,pl(ksi,zeta),pl(zeta,ksi),pl(zeta,eta),pl(eta,zeta),compl(ksi,zeta),i,compl(zeta,eta))):is(ksi,eta)
+zeta@[l:less(pl(zeta,ksi),pl(zeta,eta))]
+satz136f:=satz136c(isless12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),l)):less(ksi,eta)
+upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
++3137
+t1:=satz134(ksi,eta,zeta,m):more(pl(ksi,zeta),pl(eta,zeta))
+t2:=ismore12(pl(zeta,eta),pl(eta,zeta),pl(upsilon,eta),pl(eta,upsilon),compl(zeta,eta),compl(upsilon,eta),satz134(zeta,upsilon,eta,n)):more(pl(eta,zeta),pl(eta,upsilon))
+-3137
+satz137:=trmore(pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),t1".3137",t2".3137"):more(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
+satz137a:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz137(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
+satz138a:=orapp(more(ksi,eta),is(ksi,eta),more(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]satz137(t,n),[t:is(ksi,eta)]satz135g(t,n)):more(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
+satz138b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]satz137(m,t),[t:is(zeta,upsilon)]satz135h(zeta,upsilon,ksi,eta,t,m)):more(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
+satz138c:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
+satz138d:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
++3139
+[i:is(ksi,eta)][j:is(zeta,upsilon)]
+t1:=moreisi2(pl(ksi,zeta),pl(eta,upsilon),ispl12(ksi,eta,zeta,upsilon,i,j)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+i@[o:more(zeta,upsilon)]
+t2:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138a(m,o)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+n@[o:more(ksi,eta)]
+t4:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138b(o,n)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+-3139
+satz139:=orapp(more(ksi,eta),is(ksi,eta),moreis(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]t4".3139"(t),[t:is(ksi,eta)]t3".3139"(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
+satz139a:=satz124(pl(eta,upsilon),pl(ksi,zeta),satz139(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(pl(ksi,zeta),pl(eta,upsilon))
+eta@[l:lessis(ksi,eta)]
++3140
+[phi:cut][i:is(pl(eta,phi),ksi)]
+t1:=ismore1(pl(eta,phi),ksi,eta,i,satz133(eta,phi)):more(ksi,eta)
+phi@t2:=th3"l.imp"(is(pl(eta,phi),ksi),more(ksi,eta),satz123d(ksi,eta,l),[t:is(pl(eta,phi),ksi)]t1(t)):nis(pl(eta,phi),ksi)
+-3140
+vorbemerkung140:=th5"l.some"(cut,[a:cut]is(pl(eta,a),ksi),[a:cut]t2".3140"(a)):not(some([a:cut]is(pl(eta,a),ksi)))
+eta@[phi:cut][psi:cut]
++*3140
+psi@[m:more(phi,psi)]
+t3:=satz135d(phi,psi,eta,m):more(pl(eta,phi),pl(eta,psi))
+t4:=ec3e21(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t3):nis(pl(eta,phi),pl(eta,psi))
+psi@[l:less(phi,psi)]
+t5:=satz135f(phi,psi,eta,l):less(pl(eta,phi),pl(eta,psi))
+t6:=ec3e31(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t5):nis(pl(eta,phi),pl(eta,psi))
+psi@[n:nis(phi,psi)]
+t7:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
+t8:=orapp(more(phi,psi),less(phi,psi),nis(pl(eta,phi),pl(eta,psi)),t7,[t:more(phi,psi)]t4(t),[t:less(phi,psi)]t6(t)):nis(pl(eta,phi),pl(eta,psi))
+-3140
+psi@[i:is(pl(eta,phi),ksi)][j:is(pl(eta,psi),ksi)]
+satz140b:=th7"l.imp"(is(phi,psi),nis(pl(eta,phi),pl(eta,psi)),weli(is(pl(eta,phi),pl(eta,psi)),tris2(cut,pl(eta,phi),pl(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t8".3140"(t)):is(phi,psi)
+eta@[z0:rat][x0:rat][y0:rat]
+diffprop1:=and(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t))):'prop'
+diffprop2:=and3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0)):'prop'
+z0@diffprop:=some"rt"([x:rat]some"rt"([y:rat]diffprop2(z0,x,y))):'prop'
+eta@diff:=setof(rat,[z:rat]diffprop(z)):set(rat)
+x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][m:more"rt"(x0,y0)][i:is"rt"(z0,mn(x0,y0,m))]
++*iii3
+i@[m1:more"rt"(x0,y0)]
+t11a:=tris(rat,z0,mn(x0,y0,m),mn(x0,y0,m1),i,satz101g(x0,y0,mn(x0,y0,m),m1,satz101c(x0,y0,m))):is"rt"(z0,mn(x0,y0,m1))
+i@t12:=andi(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),m,[t:more"rt"(x0,y0)]t11a(t)):diffprop1(z0,x0,y0)
+t13:=and3i(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),lx,uy,t12):diffprop2(z0,x0,y0)
+t14:=somei(rat,[y:rat]diffprop2(z0,x0,y),y0,t13):some"rt"([y:rat]diffprop2(z0,x0,y))
+t15:=somei(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),x0,t14):diffprop(z0)
+-iii3
+i@diff1:=estii(rat,[z:rat]diffprop(z),z0,t15".iii3"):in(z0,diff)
+z0@[i:in(z0,diff)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]p]
++*iii3
+p1@t16:=estie(rat,[z:rat]diffprop(z),z0,i):diffprop(z0)
+-iii3
+p1@[x0:rat][px:some"rt"([y:rat]diffprop2(z0,x0,y))][y0:rat][py:diffprop2(z0,x0,y0)]
++*iii3
+py@t17:=and3e1(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):lrt(ksi,x0)
+t18:=and3e2(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):urt(eta,y0)
+t19:=and3e3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):diffprop1(z0,x0,y0)
+t20:=ande1(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):more"rt"(x0,y0)
+t21:=ande2"l.r"(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):is"rt"(z0,mn(x0,y0,t20))
+t22:=<t21><t20><t18><y0><t17><x0>p1:p
+px@t23:=someapp(rat,[y:rat]diffprop2(z0,x0,y),px,p,[y:rat][t:diffprop2(z0,x0,y)]t22(y,t)):p
+-iii3
+p1@diffapp:=someapp(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),t16".iii3",p,[x:rat][t:some"rt"([y:rat]diffprop2(z0,x,y))]t23".iii3"(x,t)):p
+eta@[m:more(ksi,eta)]
++*3140
+m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
+t9:=t2"rp.3134"(eta,m,y0,ly,uy,x0,lx,l):more"rt"(x0,y0)
+t10:=diff1(mn(x0,y0,t9),x0,lx,y0,uy,t9,refis(rat,mn(x0,y0,t9))):in(mn(x0,y0,t9),diff)
+m"rp"@[x1:rat][ux:urt(ksi,x1)][z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
+t11:=isless12"rt"(mn(x0,y0,n),z0,pl"rt"(mn(x0,y0,n),y0),x0,symis(rat,z0,mn(x0,y0,n),j),satz101e(x0,y0,n),satz94a(mn(x0,y0,n),y0)):less"rt"(z0,x0)
+t12:=trless"rt"(z0,x0,x1,t11,cutapp2a(ksi,x0,lx,x1,ux)):less"rt"(z0,x1)
+t13:=ec3e31(is"rt"(z0,x1),more"rt"(z0,x1),less"rt"(z0,x1),satz81b(z0,x1),t12):nis"rt"(z0,x1)
+i@t14:=diffapp(z0,i,nis"rt"(z0,x1),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t13(x,t,y,u,v,w)):nis"rt"(z0,x1)
+ux@t15:=th3"l.imp"(in(x1,diff),nis"rt"(x1,x1),weli(is"rt"(x1,x1),refis(rat,x1)),[t:in(x1,diff)]t14(x1,t)):not(in(x1,diff))
+m"rp"@[z0:rat][i:in(z0,diff)][u0:rat][l:less"rt"(u0,z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
+t16:=tris(rat,pl"rt"(z0,y0),pl"rt"(mn(x0,y0,n),y0),x0,ispl1"rt"(z0,mn(x0,y0,n),y0,j),satz101e(x0,y0,n)):is"rt"(pl"rt"(z0,y0),x0)
+x2:=pl"rt"(u0,y0):rat
+t17:=isless2"rt"(pl"rt"(z0,y0),x0,x2,t16,satz96c(u0,z0,y0,l)):less"rt"(x2,x0)
+t18:=satz120(ksi,x0,lx,x2,t17):lrt(ksi,x2)
+t19:=ismore1"rt"(pl"rt"(y0,u0),pl"rt"(u0,y0),y0,compl"rt"(y0,u0),satz94(y0,u0)):more"rt"(x2,y0)
+t20:=satz101g(x2,y0,u0,t19,compl"rt"(y0,u0)):is"rt"(u0,mn(x2,y0,t19))
+t21:=diff1(u0,x2,t18,y0,uy,t19,t20):in(u0,diff)
+l@t22:=diffapp(z0,i,in(u0,diff),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t21(x,t,y,u,v,w)):in(u0,diff)
+m"rp"@[z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))][x3:rat][lx3:lrt(ksi,x3)][l:less"rt"(x0,x3)]
+t23:=satz83(x0,x3,l):more"rt"(x3,x0)
+t24:=trmore"rt"(x3,x0,y0,t23,n):more"rt"(x3,y0)
+t25:=ismore12"rt"(x3,pl"rt"(mn(x3,y0,t24),y0),x0,pl"rt"(mn(x0,y0,n),y0),satz101f(x3,y0,t24),satz101f(x0,y0,n),t23):more"rt"(pl"rt"(mn(x3,y0,t24),y0),pl"rt"(mn(x0,y0,n),y0))
+t26:=satz97a(mn(x3,y0,t24),mn(x0,y0,n),y0,t25):more"rt"(mn(x3,y0,t24),mn(x0,y0,n))
+t27:=ismore2"rt"(mn(x0,y0,n),z0,mn(x3,y0,t24),symis(rat,z0,mn(x0,y0,n),j),t26):more"rt"(mn(x3,y0,t24),z0)
+t28:=diff1(mn(x3,y0,t24),x3,lx3,y0,uy,t24,refis(rat,mn(x3,y0,t24))):in(mn(x3,y0,t24),diff)
+t29:=andi(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0),t28,t27):and(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0))
+t30:=somei(rat,[x:rat]and(in(x,diff),more"rt"(x,z0)),mn(x3,y0,t24),t29):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
+j@t31:=cutapp3(ksi,x0,lx,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t30(y,t,u)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
+i@t32:=diffapp(z0,i,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t31(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
+m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)][x1:rat][ux1:urt(ksi,x1)]
+t33:=cut2(diff,mn(x0,y0,t9(y0,ly,uy,x0,lx,l)),t10(y0,ly,uy,x0,lx,l),x1,t15(x1,ux1),[x:rat][t:in(x,diff)][y:rat][u:less"rt"(y,x)]t22(x,t,y,u),[x:rat][t:in(x,diff)]t32(x,t)):cutprop(diff)
+l@t34:=cutapp1b(ksi,cutprop(diff),[x:rat][t:urt(ksi,x)]t33(x,t)):cutprop(diff)
+uy@t35:=cutapp3(ksi,y0,ly,cutprop(diff),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t34(x,t,u)):cutprop(diff)
+-3140
+m@satz140h:=moreapp(ksi,eta,m,cutprop(diff),[x:rat][u:lrt(ksi,x)][v:urt(eta,x)]t35".3140"(x,u,v)):cutprop(diff)
++*3140
+m"rp"@chi:=cutof(diff,satz140h):cut
+[z0:rat][lz:lrt(pl(eta,chi),z0)][y1:rat][ly:lrt(eta,y1)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,pl"rt"(y1,u0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][o:more"rt"(x0,y0)][j:is"rt"(u0,mn(x0,y0,o))]
+t36:=cutapp2b(eta,y1,ly,y0,uy):more"rt"(y0,y1)
+t37:=tr3is(rat,pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),pl"rt"(mn(x0,y0,o),pl"rt"(y1,mn(y0,y1,t36))),pl"rt"(mn(x0,y0,o),y0),x0,asspl1"rt"(mn(x0,y0,o),y1,mn(y0,y1,t36)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t36)),y0,mn(x0,y0,o),satz101c(y0,y1,t36)),satz101e(x0,y0,o)):is"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0)
+t38:=isless2"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0,pl"rt"(mn(x0,y0,o),y1),t37,satz94a(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36))):less"rt"(pl"rt"(mn(x0,y0,o),y1),x0)
+t39:=tr3is(rat,z0,pl"rt"(y1,u0),pl"rt"(u0,y1),pl"rt"(mn(x0,y0,o),y1),i,compl"rt"(y1,u0),ispl1"rt"(u0,mn(x0,y0,o),y1,j)):is"rt"(z0,pl"rt"(mn(x0,y0,o),y1))
+t40:=isless1"rt"(pl"rt"(mn(x0,y0,o),y1),z0,x0,symis(rat,z0,pl"rt"(mn(x0,y0,o),y1),t39),t38):less"rt"(z0,x0)
+t41:=satz120(ksi,x0,lx,z0,t40):lrt(ksi,z0)
+i@t42:=diffapp(u0,ini(diff,satz140h,u0,lu),lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(u0,mn(x,y,v))]t41(x,t,y,u,v,w)):lrt(ksi,z0)
+lz@a:=plapp(eta,chi,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,pl"rt"(x,y))]t42(x,t,y,u,v)):lrt(ksi,z0)
+m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
+t43:=satz83(y0,x0,l):more"rt"(x0,y0)
+[y1:rat][ly1:lrt(eta,y1)][y2:rat][uy2:urt(eta,y2)]
+t44:=cutapp2b(eta,y1,ly1,y2,uy2):more"rt"(y2,y1)
+[i:is"rt"(mn(y2,y1,t44),mn(x0,y0,t43))]
+t45:=cutapp2b(eta,y1,ly1,y0,uy):more"rt"(y0,y1)
+t46:=tris(rat,y2,pl"rt"(mn(y2,y1,t44),y1),pl"rt"(mn(x0,y0,t43),y1),satz101f(y2,y1,t44),ispl1"rt"(mn(y2,y1,t44),mn(x0,y0,t43),y1,i)):is"rt"(y2,pl"rt"(mn(x0,y0,t43),y1))
+t47:=tr4is(rat,pl"rt"(y2,mn(y0,y1,t45)),pl"rt"(pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45)),pl"rt"(mn(x0,y0,t43),pl"rt"(y1,mn(y0,y1,t45))),pl"rt"(mn(x0,y0,t43),y0),x0,ispl1"rt"(y2,pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45),t46),asspl1"rt"(mn(x0,y0,t43),y1,mn(y0,y1,t45)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t45)),y0,mn(x0,y0,t43),satz101c(y0,y1,t45)),satz101e(x0,y0,t43)):is"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0)
+t48:=ismore1"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0,y2,t47,satz94(y2,mn(y0,y1,t45))):more"rt"(x0,y2)
+t49:=satz101g(x0,y2,mn(y0,y1,t45),t48,t47):is"rt"(mn(y0,y1,t45),mn(x0,y2,t48))
+t50:=tris(rat,y0,pl"rt"(mn(y0,y1,t45),y1),pl"rt"(mn(x0,y2,t48),y1),satz101f(y0,y1,t45),ispl1"rt"(mn(y0,y1,t45),mn(x0,y2,t48),y1,t49)):is"rt"(y0,pl"rt"(mn(x0,y2,t48),y1))
+t51:=ine(diff,satz140h,mn(x0,y2,t48),diff1(mn(x0,y2,t48),x0,lx,y2,uy2,t48,refis(rat,mn(x0,y2,t48)))):lrt(chi,mn(x0,y2,t48))
+t52:=lrtpl(eta,chi,y0,y1,ly1,mn(x0,y2,t48),t51,tris(rat,y0,pl"rt"(mn(x0,y2,t48),y1),pl"rt"(y1,mn(x0,y2,t48)),t50,compl"rt"(mn(x0,y2,t48),y1))):lrt(pl(eta,chi),y0)
+l@t53:=satz132app(eta,lrt(pl(eta,chi),y0),mn(x0,y0,t43),[x:rat][t:lrt(eta,x)][y:rat][u:urt(eta,y)][v:is"rt"(mn(y,x,cutapp2b(eta,x,t,y,u)),mn(x0,y0,t43))]t52(x,t,y,u,v)):lrt(pl(eta,chi),y0)
+uy@t54:=cutapp3(ksi,y0,ly,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t53(x,t,u)):lrt(pl(eta,chi),y0)
+ly@[ly0:lrt(eta,y0)][y1:rat][ly1:lrt(ksi,y1)][uy1:urt(eta,y1)]
+t55:=t54(y1,ly1,uy1):lrt(pl(eta,chi),y1)
+t56:=satz120(pl(eta,chi),y1,t55,y0,cutapp2a(eta,y0,ly0,y1,uy1)):lrt(pl(eta,chi),y0)
+ly0@t57:=moreapp(ksi,eta,m,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t56(x,t,u)):lrt(pl(eta,chi),y0)
+ly@b:=th1"l.imp"(lrt(eta,y0),lrt(pl(eta,chi),y0),[t:lrt(eta,y0)]t57(t),[t:urt(eta,y0)]t54(t)):lrt(pl(eta,chi),y0)
+m"rp"@t58:=isi1(pl(eta,chi),ksi,[x:rat][t:lrt(pl(eta,chi),x)]a(x,t),[x:rat][t:lrt(ksi,x)]b(x,t)):is(pl(eta,chi),ksi)
+-3140
+m@satz140a:=somei(cut,[a:cut]is(pl(eta,a),ksi),chi".3140",t58".3140"):some([a:cut]is(pl(eta,a),ksi))
++*3140
+eta@t59:=[c:cut][d:cut][t:is(pl(eta,c),ksi)][u:is(pl(eta,d),ksi)]satz140b(c,d,t,u):amone(cut,[c:cut]is(pl(eta,c),ksi))
+-3140
+m@satz140:=onei(cut,[a:cut]is(pl(eta,a),ksi),t59".3140",satz140a):one([a:cut]is(pl(eta,a),ksi))
+mn:=ind(cut,[a:cut]is(pl(eta,a),ksi),satz140):cut
+satz140c:=oneax(cut,[a:cut]is(pl(eta,a),ksi),satz140):is(pl(eta,mn(ksi,eta,m)),ksi)
+satz140d:=symis(cut,pl(eta,mn(ksi,eta,m)),ksi,satz140c):is(ksi,pl(eta,mn(ksi,eta,m)))
+satz140e:=tris(cut,pl(mn(ksi,eta,m),eta),pl(eta,mn(ksi,eta,m)),ksi,compl(mn(ksi,eta,m),eta),satz140c):is(pl(mn(ksi,eta,m),eta),ksi)
+satz140f:=symis(cut,pl(mn(ksi,eta,m),eta),ksi,satz140e):is(ksi,pl(mn(ksi,eta,m),eta))
+eta@[phi:cut][m:more(ksi,eta)][i:is(pl(eta,phi),ksi)]
+satz140g:=satz140b(phi,mn(ksi,eta,m),i,satz140c(m)):is(phi,mn(ksi,eta,m))
+upsilon@[m:more(ksi,zeta)][n:more(eta,upsilon)][i:is(ksi,eta)][j:is(zeta,upsilon)]
++*3140
+j"rp"@t60:=tr3is(cut,pl(upsilon,mn(ksi,zeta,m)),pl(zeta,mn(ksi,zeta,m)),ksi,eta,ispl1(upsilon,zeta,mn(ksi,zeta,m),symis(cut,zeta,upsilon,j)),satz140c(ksi,zeta,m),i):is(pl(upsilon,mn(ksi,zeta,m)),eta)
+-3140
+j@ismn12:=satz140g(eta,upsilon,mn(ksi,zeta,m),n,t60".3140"):is(mn(ksi,zeta,m),mn(eta,upsilon,n))
+zeta@[m:more(ksi,zeta)][n:more(eta,zeta)][i:is(ksi,eta)]
+ismn1:=ismn12(zeta,m,n,i,refis(cut,zeta)):is(mn(ksi,zeta,m),mn(eta,zeta,n))
+zeta@[m:more(zeta,ksi)][n:more(zeta,eta)][i:is(ksi,eta)]
+ismn2:=ismn12(zeta,zeta,ksi,eta,m,n,refis(cut,zeta),i):is(mn(zeta,ksi,m),mn(zeta,eta,n))
+eta@[z0:rat][x0:rat][y0:rat]
+prodprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0))):'prop'
+z0@prodprop:=some"rt"([x:rat]some"rt"([y:rat]prodprop1(z0,x,y))):'prop'
+eta@prod:=setof(rat,[z:rat]prodprop(z)):set(rat)
+x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts(x0,y0))]
++iii4
+t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),lx,ly,i):prodprop1(z0,x0,y0)
+t2:=somei(rat,[y:rat]prodprop1(z0,x0,y),y0,t1):some"rt"([y:rat]prodprop1(z0,x0,y))
+t3:=somei(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),x0,t2):prodprop(z0)
+-iii4
+prod1:=estii(rat,[z:rat]prodprop(z),z0,t3".iii4"):in(z0,prod)
+z0@[i:in(z0,prod)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]p]
++*iii4
+p1@t4:=estie(rat,[z:rat]prodprop(z),z0,i):prodprop(z0)
+-iii4
+p1@[x0:rat][px:some"rt"([y:rat]prodprop1(z0,x0,y))][y0:rat][py:prodprop1(z0,x0,y0)]
++*iii4
+py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(ksi,x0)
+t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(eta,y0)
+t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):is"rt"(z0,ts(x0,y0))
+t8:=<t7><t6><y0><t5><x0>p1:p
+px@t9:=someapp(rat,[y:rat]prodprop1(z0,x0,y),px,p,[y:rat][t:prodprop1(z0,x0,y)]t8(y,t)):p
+-iii4
+p1@prodapp:=someapp(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),t4".iii4",p,[x:rat][t:some"rt"([y:rat]prodprop1(z0,x,y))]t9".iii4"(x,t)):p
+eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
++4141
+[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))]
+t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
+t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
+t3:=isless1"rt"(ts(x0,y0),z0,ts(x1,y1),symis(rat,z0,ts(x0,y0),j),satz107a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,ts(x1,y1))
+t4:=ec3e31(is"rt"(z0,ts(x1,y1)),more"rt"(z0,ts(x1,y1)),less"rt"(z0,ts(x1,y1)),satz81b(z0,ts(x1,y1)),t3):nis"rt"(z0,ts(x1,y1))
+i@t5:=prodapp(ksi,eta,z0,i,nis"rt"(z0,ts(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,ts(x1,y1))
+-4141
+satz141a:=th3"l.imp"(in(ts(x1,y1),prod),nis"rt"(ts(x1,y1),ts(x1,y1)),weli(is"rt"(ts(x1,y1),ts(x1,y1)),refis(rat,ts(x1,y1))),[t:in(ts(x1,y1),prod)]t5".4141"(ts(x1,y1),t)):not(in(ts(x1,y1),prod))
+-rp
+@[x0:rat][y0:rat]
++4141
+v0:=ts(ov(1rt,y0),x0):rat
+t6:=tr3is(rat,ts(y0,v0),ts(ts(y0,ov(1rt,y0)),x0),ts(1rt,x0),x0,assts2(y0,ov(1rt,y0),x0),ists1(ts(y0,ov(1rt,y0)),1rt,x0,satz110c(1rt,y0)),example1c(x0)):is(ts(y0,v0),x0)
+-4141
+satz141b:=satz110g(x0,y0,v0".4141",t6".4141"):is(ts(ov(1rt,y0),x0),ov(x0,y0))
+satz141c:=symis(rat,ts(ov(1rt,y0),x0),ov(x0,y0),satz141b):is"rt"(ov(x0,y0),ts(ov(1rt,y0),x0))
++*rp
++*4141
+eta@[u0:rat][i:in(u0,prod)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,ts(x0,y0))]
+t7:=isless2"rt"(u0,ts(x0,y0),z0,j,l):less"rt"(z0,ts(x0,y0))
+t8:=tr3is(rat,ts(ov(1rt,x0),ts(x0,y0)),ts(ts(ov(1rt,x0),x0),y0),ts(1rt,y0),y0,assts2(ov(1rt,x0),x0,y0),ists1(ts(ov(1rt,x0),x0),1rt,y0,satz110e(1rt,x0)),example1c(y0)):is"rt"(ts(ov(1rt,x0),ts(x0,y0)),y0)
+t9:=isless12"rt"(ts(ov(1rt,x0),z0),ov(z0,x0),ts(ov(1rt,x0),ts(x0,y0)),y0,satz141b(z0,x0),t8,satz105f(z0,ts(x0,y0),ov(1rt,x0),t7)):less"rt"(ov(z0,x0),y0)
+t10:=satz120(eta,y0,ly,ov(z0,x0),t9):lrt(eta,ov(z0,x0))
+t11:=prod1(z0,x0,lx,ov(z0,x0),t10,satz110d(z0,x0)):in(z0,prod)
+l@t12:=prodapp(u0,i,in(z0,prod),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,ts(x,y))]t11(x,t,y,u,v)):in(z0,prod)
+eta@[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
+t13:=prod1(ts(x1,y0),x1,lx1,y0,ly,refis(rat,ts(x1,y0))):in(ts(x1,y0),prod)
+t14:=satz105a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(ts(x1,y0),ts(x0,y0))
+t15:=ismore2"rt"(ts(x0,y0),z0,ts(x1,y0),symis(rat,z0,ts(x0,y0),j),t14):more"rt"(ts(x1,y0),z0)
+t16:=andi(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0),t13,t15):and(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0))
+t17:=somei(rat,[y:rat]and(in(y,prod),more"rt"(y,z0)),ts(x1,y0),t16):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
+j@t18:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t17(x,t,u)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
+i@t19:=prodapp(z0,i,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t18(x,t,y,u,v)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
+eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
+t20:=cut2(prod,ts(x0,y0),prod1(ts(x0,y0),x0,lx,y0,ly,refis(rat,ts(x0,y0))),ts(x1,y1),satz141a(x1,ux,y1,uy),[x:rat][t:in(x,prod)][y:rat][u:less"rt"(y,x)]t12(x,t,y,u),[x:rat][t:in(x,prod)]t19(x,t)):cutprop(prod)
+ux@t21:=cutapp1b(eta,cutprop(prod),[y:rat][t:urt(eta,y)]t20(y,t)):cutprop(prod)
+ly@t22:=cutapp1b(ksi,cutprop(prod),[x:rat][t:urt(ksi,x)]t21(x,t)):cutprop(prod)
+lx@t23:=cutapp1a(eta,cutprop(prod),[y:rat][t:lrt(eta,y)]t22(y,t)):cutprop(prod)
+-4141
+eta@satz141:=cutapp1a(ksi,cutprop(prod),[x:rat][t:lrt(ksi,x)]t23".4141"(x,t)):cutprop(prod)
+ts:=cutof(prod,satz141):cut
+[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
+lrtts:=ine(prod,satz141,z0,prod1(z0,x0,lx,y0,ly,i)):lrt(ts(ksi,eta),z0)
+eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
++*iii4
+i@t10:=isp1(rat,[x:rat]not(in(x,prod)),ts"rt"(x0,y0),z0,satz141a(x0,ux,y0,uy),i):not(in(z0,prod))
+-iii4
+i@urtts:=th3"l.imp"(lrt(ts(ksi,eta),z0),in(z0,prod),t10".iii4",[t:lrt(ts(ksi,eta),z0)]ini(prod,satz141,z0,t)):urt(ts(ksi,eta),z0)
+eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]p]
++*iii4
+p1@t11:=ini(prod,satz141,z0,lz):in(z0,prod)
+-iii4
+p1@tsapp:=prodapp(z0,t11".iii4",p,p1):p
+zeta@[i:is(ksi,eta)]
+ists1:=isf(cut,cut,[u:cut]ts(u,zeta),ksi,eta,i):is(ts(ksi,zeta),ts(eta,zeta))
+ists2:=isf(cut,cut,[u:cut]ts(zeta,u),ksi,eta,i):is(ts(zeta,ksi),ts(zeta,eta))
+upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
+ists12:=tris(cut,ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),ists1(i),ists2(zeta,upsilon,eta,j)):is(ts(ksi,zeta),ts(eta,upsilon))
++4142
+eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
+t1:=tris(rat,z0,ts"rt"(x0,y0),ts"rt"(y0,x0),i,comts(x0,y0)):is"rt"(z0,ts"rt"(y0,x0))
+t2:=lrtts(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(ts(eta,ksi),z0)
+lz@t3:=tsapp(ksi,eta,z0,lz,lrt(ts(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]t2(x,t,y,u,v)):lrt(ts(eta,ksi),z0)
+-4142
+eta@satz142:=isi1(ts(ksi,eta),ts(eta,ksi),[x:rat][t:lrt(ts(ksi,eta),x)]t3".4142"(x,t),[x:rat][t:lrt(ts(eta,ksi),x)]t3".4142"(eta,ksi,x,t)):is(ts(ksi,eta),ts(eta,ksi))
+comts:=satz142:is(ts(ksi,eta),ts(eta,ksi))
++4143
+zeta@[u0:rat][lu:lrt(ts(ts(ksi,eta),zeta),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,ts"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))]
+t1:=tr3is(rat,u0,ts"rt"(v0,z0),ts"rt"(ts"rt"(x0,y0),z0),ts"rt"(x0,ts"rt"(y0,z0)),i,ists1"rt"(v0,ts"rt"(x0,y0),z0,j),assts1(x0,y0,z0)):is"rt"(u0,ts"rt"(x0,ts"rt"(y0,z0)))
+t2:=lrtts(eta,zeta,ts"rt"(y0,z0),y0,ly,z0,lz,refis(rat,ts"rt"(y0,z0))):lrt(ts(eta,zeta),ts"rt"(y0,z0))
+t3:=lrtts(ksi,ts(eta,zeta),u0,x0,lx,ts"rt"(y0,z0),t2,t1):lrt(ts(ksi,ts(eta,zeta)),u0)
+i@t4:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
+lu@t5:=tsapp(ts(ksi,eta),zeta,u0,lu,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,ts"rt"(x,y))]t4(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
+u0@[lu:lrt(ts(ksi,ts(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(ts(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,ts"rt"(y0,z0))]
+t6:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,ts"rt"(y0,z0)),ts"rt"(ts"rt"(x0,y0),z0),i,ists2"rt"(v0,ts"rt"(y0,z0),x0,j),assts2(x0,y0,z0)):is"rt"(u0,ts"rt"(ts"rt"(x0,y0),z0))
+t7:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
+t8:=lrtts(ts(ksi,eta),zeta,u0,ts"rt"(x0,y0),t7,z0,lz,t6):lrt(ts(ts(ksi,eta),zeta),u0)
+i@t9:=tsapp(eta,zeta,v0,lv,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,ts"rt"(x,y))]t8(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
+lu@t10:=tsapp(ksi,ts(eta,zeta),u0,lu,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(ts(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t9(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
+-4143
+zeta@satz143:=isi1(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),[x:rat][t:lrt(ts(ts(ksi,eta),zeta),x)]t5".4143"(x,t),[x:rat][t:lrt(ts(ksi,ts(eta,zeta)),x)]t10".4143"(x,t)):is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
+assts1:=satz143:is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
+assts2:=symis(cut,ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),satz143):is(ts(ksi,ts(eta,zeta)),ts(ts(ksi,eta),zeta))
++4144
+[u0:rat][lu:lrt(ts(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
+t1:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,pl"rt"(y0,z0)),pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)),i,ists2"rt"(v0,pl"rt"(y0,z0),x0,j),disttp2(x0,y0,z0)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)))
+t2:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
+t3:=lrtts(ksi,zeta,ts"rt"(x0,z0),x0,lx,z0,lz,refis(rat,ts"rt"(x0,z0))):lrt(ts(ksi,zeta),ts"rt"(x0,z0))
+t4:=lrtpl(ts(ksi,eta),ts(ksi,zeta),u0,ts"rt"(x0,y0),t2,ts"rt"(x0,z0),t3,t1):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
+i@t5:=plapp(eta,zeta,v0,lv,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
+lu@t6:=tsapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t5(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
+u0@[lu:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][w0:rat][lw:lrt(ts(ksi,zeta),w0)][i:is"rt"(u0,pl"rt"(v0,w0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][z0:rat][lz:lrt(zeta,z0)][k:is"rt"(w0,ts"rt"(x1,z0))]
+t7:=tris(rat,u0,pl"rt"(v0,w0),pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),i,ispl12"rt"(v0,ts"rt"(x0,y0),w0,ts"rt"(x1,z0),j,k)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)))
+x2:=ite(moreis"rt"(x0,x1),rat,x0,x1):rat
+[m:moreis"rt"(x0,x1)]
+t8:=itet(moreis"rt"(x0,x1),rat,x0,x1,m):is"rt"(x2,x0)
+t9:=isp1(rat,[t:rat]lrt(ksi,t),x0,x2,lx,t8):lrt(ksi,x2)
+t10:=lessisi2"rt"(x0,x2,symis(rat,x2,x0,t8)):lessis"rt"(x0,x2)
+t11:=satz88(x1,x0,x2,satz84(x0,x1,m),t10):lessis"rt"(x1,x2)
+k@[n:not(moreis"rt"(x0,x1))]
+t12:=itef(moreis"rt"(x0,x1),rat,x0,x1,n):is"rt"(x2,x1)
+t13:=isp1(rat,[t:rat]lrt(ksi,t),x1,x2,lx1,t12):lrt(ksi,x2)
+t14:=lessisi2"rt"(x1,x2,symis(rat,x2,x1,t12)):lessis"rt"(x1,x2)
+t15:=lessisi1"rt"(x0,x2,satz87b(x0,x1,x2,satz81j(x0,x1,n),t14)):lessis"rt"(x0,x2)
+k@t16:=th1"l.imp"(moreis"rt"(x0,x1),lrt(ksi,x2),[t:moreis"rt"(x0,x1)]t9(t),[t:not(moreis"rt"(x0,x1))]t13(t)):lrt(ksi,x2)
+t17:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x0,x2),[t:moreis"rt"(x0,x1)]t10(t),[t:not(moreis"rt"(x0,x1))]t15(t)):lessis"rt"(x0,x2)
+t18:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x1,x2),[t:moreis"rt"(x0,x1)]t11(t),[t:not(moreis"rt"(x0,x1))]t14(t)):lessis"rt"(x1,x2)
+t19:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
+t20:=lrtts(ksi,pl(eta,zeta),ts"rt"(x2,pl"rt"(y0,z0)),x2,t16,pl"rt"(y0,z0),t19,refis(rat,ts"rt"(x2,pl"rt"(y0,z0)))):lrt(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)))
+t21:=satz109a(x0,x2,y0,y0,t17,lessisi2"rt"(y0,y0,refis(rat,y0))):lessis"rt"(ts"rt"(x0,y0),ts"rt"(x2,y0))
+t22:=satz109a(x1,x2,z0,z0,t18,lessisi2"rt"(z0,z0,refis(rat,z0))):lessis"rt"(ts"rt"(x1,z0),ts"rt"(x2,z0))
+t23:=islessis12"rt"(pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),u0,pl"rt"(ts"rt"(x2,y0),ts"rt"(x2,z0)),ts"rt"(x2,pl"rt"(y0,z0)),symis(rat,u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),t7),distpt2(x2,y0,z0),satz100a(ts"rt"(x0,y0),ts"rt"(x2,y0),ts"rt"(x1,z0),ts"rt"(x2,z0),t21,t22)):lessis"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))
+t24:=orapp(less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),lrt(ts(ksi,pl(eta,zeta)),u0),t23,[t:less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]satz120(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)),t20,u0,t),[t:is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]isp1(rat,[u:rat]lrt(ts(ksi,pl(eta,zeta)),u),ts"rt"(x2,pl"rt"(y0,z0)),u0,t20,t)):lrt(ts(ksi,pl(eta,zeta)),u0)
+j@t25:=tsapp(ksi,zeta,w0,lw,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(w0,ts"rt"(x,y))]t24(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
+i@t26:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t25(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
+lu@t27:=plapp(ts(ksi,eta),ts(ksi,zeta),u0,lu,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(ts(ksi,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t26(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
+-4144
+satz144:=isi1(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),[x:rat][t:lrt(ts(ksi,pl(eta,zeta)),x)]t6".4144"(x,t),[x:rat][t:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),x)]t27".4144"(x,t)):is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
+disttp1:=tr3is(cut,ts(pl(ksi,eta),zeta),ts(zeta,pl(ksi,eta)),pl(ts(zeta,ksi),ts(zeta,eta)),pl(ts(ksi,zeta),ts(eta,zeta)),comts(pl(ksi,eta),zeta),satz144(zeta,ksi,eta),ispl12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta))):is(ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)))
+disttp2:=satz144:is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
+distpt1:=symis(cut,ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)),disttp1):is(pl(ts(ksi,zeta),ts(eta,zeta)),ts(pl(ksi,eta),zeta))
+distpt2:=symis(cut,ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),disttp2):is(pl(ts(ksi,eta),ts(ksi,zeta)),ts(ksi,pl(eta,zeta)))
+[m:more(ksi,eta)]
++4145
+phi:=mn(ksi,eta,m):cut
+t1:=satz140d(ksi,eta,m):is(ksi,pl(eta,phi))
+t2:=tris(cut,ts(ksi,zeta),ts(pl(eta,phi),zeta),pl(ts(eta,zeta),ts(phi,zeta)),ists1(ksi,pl(eta,phi),zeta,t1),disttp1(eta,phi,zeta)):is(ts(ksi,zeta),pl(ts(eta,zeta),ts(phi,zeta)))
+-4145
+satz145a:=ismore1(pl(ts(eta,zeta),ts(phi".4145",zeta)),ts(ksi,zeta),ts(eta,zeta),symis(cut,ts(ksi,zeta),pl(ts(eta,zeta),ts(phi".4145",zeta)),t2".4145"),satz133(ts(eta,zeta),ts(phi".4145",zeta))):more(ts(ksi,zeta),ts(eta,zeta))
+zeta@[i:is(ksi,eta)]
+satz145b:=ists1(ksi,eta,zeta,i):is(ts(ksi,zeta),ts(eta,zeta))
+zeta@[l:less(ksi,eta)]
+satz145c:=satz121(ts(eta,zeta),ts(ksi,zeta),satz145a(eta,ksi,zeta,satz122(ksi,eta,l))):less(ts(ksi,zeta),ts(eta,zeta))
+m@satz145d:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145a):more(ts(zeta,ksi),ts(zeta,eta))
+i@satz145e:=ists2(ksi,eta,zeta,i):is(ts(zeta,ksi),ts(zeta,eta))
+l@satz145f:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145c):less(ts(zeta,ksi),ts(zeta,eta))
+upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
+satz145g:=ismore2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145d(zeta,upsilon,ksi,m)):more(ts(ksi,zeta),ts(eta,upsilon))
+satz145h:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145g):more(ts(zeta,ksi),ts(upsilon,eta))
+i@[l:less(zeta,upsilon)]
+satz145j:=isless2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145f(zeta,upsilon,ksi,l)):less(ts(ksi,zeta),ts(eta,upsilon))
+satz145k:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145j):less(ts(zeta,ksi),ts(upsilon,eta))
++4146
+zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+t2:=satz123b(ts(ksi,zeta),ts(eta,zeta)):ec3(is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)))
+-4146
+zeta@[m:more(ts(ksi,zeta),ts(eta,zeta))]
+satz146a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),m):more(ksi,eta)
+zeta@[i:is(ts(ksi,zeta),ts(eta,zeta))]
+satz146b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),i):is(ksi,eta)
+zeta@[l:less(ts(ksi,zeta),ts(eta,zeta))]
+satz146c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),l):less(ksi,eta)
+zeta@[m:more(ts(zeta,ksi),ts(zeta,eta))]
+satz146d:=satz146a(ismore12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),m)):more(ksi,eta)
+zeta@[i:is(ts(zeta,ksi),ts(zeta,eta))]
+satz146e:=satz146b(tr3is(cut,ts(ksi,zeta),ts(zeta,ksi),ts(zeta,eta),ts(eta,zeta),comts(ksi,zeta),i,comts(zeta,eta))):is(ksi,eta)
+zeta@[l:less(ts(zeta,ksi),ts(zeta,eta))]
+satz146f:=satz146c(isless12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),l)):less(ksi,eta)
+upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
++4147
+t1:=satz145a(ksi,eta,zeta,m):more(ts(ksi,zeta),ts(eta,zeta))
+t2:=ismore12(ts(zeta,eta),ts(eta,zeta),ts(upsilon,eta),ts(eta,upsilon),comts(zeta,eta),comts(upsilon,eta),satz145a(zeta,upsilon,eta,n)):more(ts(eta,zeta),ts(eta,upsilon))
+-4147
+satz147:=trmore(ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),t1".4147",t2".4147"):more(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
+satz147a:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz147(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
+satz148a:=orapp(more(ksi,eta),is(ksi,eta),more(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]satz147(t,n),[t:is(ksi,eta)]satz145g(t,n)):more(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
+satz148b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]satz147(m,t),[t:is(zeta,upsilon)]satz145h(zeta,upsilon,ksi,eta,t,m)):more(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
+satz148c:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
+satz148d:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
++4149
+[i:is(ksi,eta)][j:is(zeta,upsilon)]
+t1:=moreisi2(ts(ksi,zeta),ts(eta,upsilon),ists12(ksi,eta,zeta,upsilon,i,j)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+i@[o:more(zeta,upsilon)]
+t2:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148a(m,o)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+n@[o:more(ksi,eta)]
+t4:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148b(o,n)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+-4149
+satz149:=orapp(more(ksi,eta),is(ksi,eta),moreis(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]t4".4149"(t),[t:is(ksi,eta)]t3".4149"(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
+satz149a:=satz124(ts(eta,upsilon),ts(ksi,zeta),satz149(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(ts(ksi,zeta),ts(eta,upsilon))
+-rp
+@[r0:rat]
+ratset:=setof(rat,[x:rat]less(x,r0)):set(rat)
++4150
+t1:=satz90(r0):some([x:rat]less(x,r0))
+[x0:rat][l:less(x0,r0)]
+t2:=estii(rat,[x:rat]less(x,r0),x0,l):in(x0,ratset)
+r0@t3:=ec3e13(is(r0,r0),more(r0,r0),less(r0,r0),satz81b(r0,r0),refis(rat,r0)):not(less(r0,r0))
+t4:=th3"l.imp"(in(r0,ratset),less(r0,r0),t3,[t:in(r0,ratset)]estie(rat,[x:rat]less(x,r0),r0,t)):not(in(r0,ratset))
+x0@[i:in(x0,ratset)]
+t5:=estie(rat,[x:rat]less(x,r0),x0,i):less(x0,r0)
+[x1:rat][k:less(x1,x0)]
+t6:=t2(x1,trless(x1,x0,r0,k,t5)):in(x1,ratset)
+i@t7:=satz91(x0,r0,t5):some([x:rat]and(less(x0,x),less(x,r0)))
+[x1:rat][a:and(less(x0,x1),less(x1,r0))]
+t8:=ande1(less(x0,x1),less(x1,r0),a):less(x0,x1)
+t9:=ande2(less(x0,x1),less(x1,r0),a):less(x1,r0)
+t10:=andi(in(x1,ratset),more(x1,x0),t2(x1,t9),satz83(x0,x1,t8)):and(in(x1,ratset),more(x1,x0))
+i@t11:=th6"l.some"(rat,[x:rat]and(less(x0,x),less(x,r0)),[x:rat]and(in(x,ratset),more(x,x0)),t7,[x:rat][t:and(less(x0,x),less(x,r0))]t10(x,t)):some([x:rat]and(in(x,ratset),more(x,x0)))
+l@t12:=cut2(ratset,x0,t2,r0,t4,[x:rat][t:in(x,ratset)][y:rat][u:less(y,x)]t6(x,t,y,u),[x:rat][t:in(x,ratset)]t11(x,t)):cutprop(ratset)
+-4150
+satz150:=someapp(rat,[x:rat]less(x,r0),t1".4150",cutprop(ratset),[x:rat][t:less(x,r0)]t12".4150"(x,t)):cutprop(ratset)
++*rp
+r0@rpofrt:=cutof(ratset,satz150):cut
+[x0:rat][l:less"rt"(x0,r0)]
+lrtrpofrt:=ine(ratset,satz150,x0,t2"rt.4150"(x0,l)):lrt(rpofrt,x0)
+r0@[x0:rat][lx:lrt(rpofrt,x0)]
+lrtrpofrte:=t5"rt.4150"(x0,ini(ratset,satz150,x0,lx)):less"rt"(x0,r0)
+r0@[x0:rat][m:moreis"rt"(x0,r0)]
++*iii4
+m@t12:=satz81c(x0,r0,m):not(less"rt"(x0,r0))
+-iii4
+m@urtrpofrt:=th3"l.imp"(lrt(rpofrt,x0),less"rt"(x0,r0),t12".iii4",[t:lrt(rpofrt,x0)]lrtrpofrte(x0,t)):urt(rpofrt,x0)
+@1rp:=rpofrt(1rt):cut
++4151
+ksi@[z0:rat][lz:lrt(ts(ksi,1rp),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(1rp,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
+t1:=lrtrpofrte(1rt,y0,ly):less"rt"(y0,1rt)
+t2:=isless12"rt"(ts"rt"(x0,y0),z0,ts"rt"(x0,1rt),x0,symis(rat,z0,ts"rt"(x0,y0),i),example1a(x0),satz105f(y0,1rt,x0,t1)):less"rt"(z0,x0)
+t3:=satz120(ksi,x0,lx,z0,t2):lrt(ksi,z0)
+lz@t4:=tsapp(ksi,1rp,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(1rp,y)][v:is"rt"(z0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ksi,z0)
+ksi@[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
+y1:=ts"rt"(ov(1rt,x1),x0):rat
+t5:=isless2"rt"(ts"rt"(ov(1rt,x1),x1),1rt,y1,satz110e(1rt,x1),satz105f(x0,x1,ov(1rt,x1),l)):less"rt"(y1,1rt)
+t6:=lrtrpofrt(1rt,y1,t5):lrt(1rp,y1)
+t7:=tr3is(rat,ts"rt"(x1,y1),ts"rt"(ts"rt"(x1,ov(1rt,x1)),x0),ts"rt"(1rt,x0),x0,assts2"rt"(x1,ov(1rt,x1),x0),ists1"rt"(ts"rt"(x1,ov(1rt,x1)),1rt,x0,satz110c(1rt,x1)),example1c(x0)):is"rt"(ts"rt"(x1,y1),x0)
+t8:=lrtts(ksi,1rp,x0,x1,lx1,y1,t6,symis(rat,ts"rt"(x1,y1),x0,t7)):lrt(ts(ksi,1rp),x0)
+lx@t9:=cutapp3(ksi,x0,lx,lrt(ts(ksi,1rp),x0),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t8(y,t,u)):lrt(ts(ksi,1rp),x0)
+-4151
+ksi@satz151:=isi1(ts(ksi,1rp),ksi,[x:rat][t:lrt(ts(ksi,1rp),x)]t4".4151"(x,t),[x:rat][t:lrt(ksi,x)]t9".4151"(x,t)):is(ts(ksi,1rp),ksi)
+satz151a:=symis(cut,ts(ksi,1rp),ksi,satz151):is(ksi,ts(ksi,1rp))
+satz151b:=tris(cut,ts(1rp,ksi),ts(ksi,1rp),ksi,comts(1rp,ksi),satz151):is(ts(1rp,ksi),ksi)
+satz151c:=symis(cut,ts(1rp,ksi),ksi,satz151b):is(ksi,ts(1rp,ksi))
++4152
+[x0:rat][y0:rat]
+invprop1:=and(urt(ksi,y0),less"rt"(y0,x0)):'prop'
+ksi@[z0:rat][x0:rat]
+invprop2:=and3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0))):'prop'
+z0@invprop:=some"rt"([x:rat]invprop2(z0,x)):'prop'
+ksi@inv:=setof(rat,[z:rat]invprop(z)):set(rat)
+x0@[ux:urt(ksi,x0)][y0:rat][uy:urt(ksi,y0)][l:less"rt"(y0,x0)][i:is"rt"(z0,ov(1rt,x0))]
+t1:=andi(urt(ksi,y0),less"rt"(y0,x0),uy,l):invprop1(x0,y0)
+t2:=somei(rat,[x:rat]invprop1(x0,x),y0,t1):some"rt"([x:rat]invprop1(x0,x))
+t3:=and3i(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),ux,t2,i):invprop2(z0,x0)
+t4:=somei(rat,[x:rat]invprop2(z0,x),x0,t3):invprop(z0)
+inv1:=estii(rat,[z:rat]invprop(z),z0,t4):in(z0,inv)
+z0@[i:in(z0,inv)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]p]
+t5:=estie(rat,[x:rat]invprop(x),z0,i):invprop(z0)
+[x0:rat][px:invprop2(z0,x0)]
+t6:=and3e1(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):urt(ksi,x0)
+t7:=and3e2(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):some"rt"([x:rat]invprop1(x0,x))
+t8:=and3e3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):is"rt"(z0,ov(1rt,x0))
+[y0:rat][py:invprop1(x0,y0)]
+t9:=ande1(urt(ksi,y0),less"rt"(y0,x0),py):urt(ksi,y0)
+t10:=ande2(urt(ksi,y0),less"rt"(y0,x0),py):less"rt"(y0,x0)
+t11:=<t8><t10><t9><y0><t6><x0>p1:p
+px@t12:=someapp(rat,[x:rat]invprop1(x0,x),t7,p,[x:rat][t:invprop1(x0,x)]t11(x,t)):p
+p1@invapp:=someapp(rat,[x:rat]invprop2(z0,x),t5,p,[x:rat][t:invprop2(z0,x)]t12(x,t)):p
+ksi@[x0:rat][ux:urt(ksi,x0)]
+2x0:=pl"rt"(x0,x0):rat
+t13:=satz94a(x0,x0):less"rt"(x0,2x0)
+t14:=satz119a(ksi,x0,ux,2x0,t13):urt(ksi,2x0)
+t15:=inv1(ov(1rt,2x0),2x0,t14,x0,ux,t13,refis(rat,ov(1rt,2x0))):in(ov(1rt,2x0),inv)
+ksi@[x1:rat][lx:lrt(ksi,x1)][x0:rat][ux:urt(ksi,x0)]
+t16:=th3"l.imp"(is"rt"(x0,x1),lrt(ksi,x0),ux,[t:is"rt"(x0,x1)]isp1(rat,[x:rat]lrt(ksi,x),x1,x0,lx,t)):nis"rt"(x0,x1)
+t17:=satz110e(1rt,x0):is"rt"(ts"rt"(ov(1rt,x0),x0),1rt)
+t18:=satz110e(1rt,x1):is"rt"(ts"rt"(ov(1rt,x1),x1),1rt)
+[i:is"rt"(ov(1rt,x0),ov(1rt,x1))]
+t19:=tris(rat,ts"rt"(ov(1rt,x0),x1),ts"rt"(ov(1rt,x1),x1),1rt,ists1"rt"(ov(1rt,x0),ov(1rt,x1),x1,i),t18):is"rt"(ts"rt"(ov(1rt,x0),x1),1rt)
+t20:=satz110b(1rt,ov(1rt,x0),x0,x1,t17,t19):is"rt"(x0,x1)
+ux@t21:=th3"l.imp"(is"rt"(ov(1rt,x0),ov(1rt,x1)),is"rt"(x0,x1),t16,[t:is"rt"(ov(1rt,x0),ov(1rt,x1))]t20(t)):nis"rt"(ov(1rt,x0),ov(1rt,x1))
+lx@[i:in(ov(1rt,x1),inv)]
+t22:=invapp(ov(1rt,x1),i,con,[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(ov(1rt,x1),ov(1rt,x))]<symis(rat,ov(1rt,x1),ov(1rt,x),w)>t21(x,t)):con
+lx@t23:=[t:in(ov(1rt,x1),inv)]t22(t):not(in(ov(1rt,x1),inv))
+ksi@[z0:rat][i:in(z0,inv)][u0:rat][l:less"rt"(u0,z0)][x0:rat][ux:urt(ksi,x0)][j:is"rt"(z0,ov(1rt,x0))]
+t24:=isless2"rt"(z0,ov(1rt,x0),u0,j,l):less"rt"(u0,ov(1rt,x0))
+t25:=tris(rat,ts"rt"(ov(1rt,x0),x0),1rt,ts"rt"(u0,ov(1rt,u0)),satz110e(1rt,x0),satz110d(1rt,u0)):is"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)))
+t26:=isless2"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(u0,x0),t25,satz105c(u0,ov(1rt,x0),x0,t24)):less"rt"(ts"rt"(u0,x0),ts"rt"(u0,ov(1rt,u0)))
+t27:=isless12"rt"(ts"rt"(u0,x0),ts"rt"(x0,u0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(ov(1rt,u0),u0),comts"rt"(u0,x0),comts"rt"(u0,ov(1rt,u0)),t26):less"rt"(ts"rt"(x0,u0),ts"rt"(ov(1rt,u0),u0))
+t28:=satz106c(x0,ov(1rt,u0),u0,t27):less"rt"(x0,ov(1rt,u0))
+t29:=satz119a(x0,ux,ov(1rt,u0),t28):urt(ksi,ov(1rt,u0))
+t30:=satz110e(1rt,u0):is"rt"(ts"rt"(ov(1rt,u0),u0),1rt)
+t31:=satz110g(1rt,ov(1rt,u0),u0,t30):is"rt"(u0,ov(1rt,ov(1rt,u0)))
+t32:=inv1(u0,ov(1rt,u0),t29,x0,ux,t28,t31):in(u0,inv)
+l@t33:=invapp(z0,i,in(u0,inv),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t32(x,t,w)):in(u0,inv)
+i@[x0:rat][ux:urt(ksi,x0)][x1:rat][ux1:urt(ksi,x1)][l:less"rt"(x1,x0)][j:is"rt"(z0,ov(1rt,x0))]
+t34:=satz91(x1,x0,l):some"rt"([x:rat]and(less"rt"(x1,x),less"rt"(x,x0)))
+[x2:rat][a:and(less"rt"(x1,x2),less"rt"(x2,x0))]
+t35:=ande1(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x1,x2)
+t36:=satz119a(ksi,x1,ux1,x2,t35):urt(ksi,x2)
+t37:=inv1(ov(1rt,x2),x2,t36,x1,ux1,t35,refis(rat,ov(1rt,x2))):in(ov(1rt,x2),inv)
+t38:=ande2(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x2,x0)
+t39:=tris(rat,ts"rt"(x0,ov(1rt,x0)),1rt,ts"rt"(x2,ov(1rt,x2)),satz110c(1rt,x0),satz110d(1rt,x2)):is"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
+t40:=isless2"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)),ts"rt"(x2,ov(1rt,x0)),t39,satz105c(x2,x0,ov(1rt,x0),t38)):less"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
+t41:=isless12"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(ov(1rt,x0),x2),ts"rt"(x2,ov(1rt,x2)),ts"rt"(ov(1rt,x2),x2),comts"rt"(x2,ov(1rt,x0)),comts"rt"(x2,ov(1rt,x2)),t40):less"rt"(ts"rt"(ov(1rt,x0),x2),ts"rt"(ov(1rt,x2),x2))
+t42:=satz106c(ov(1rt,x0),ov(1rt,x2),x2,t41):less"rt"(ov(1rt,x0),ov(1rt,x2))
+t43:=ismore2"rt"(ov(1rt,x0),z0,ov(1rt,x2),symis(rat,z0,ov(1rt,x0),j),satz83(ov(1rt,x0),ov(1rt,x2),t42)):more"rt"(ov(1rt,x2),z0)
+t44:=andi(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0),t37,t43):and(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0))
+t45:=somei(rat,[x:rat]and(in(x,inv),more"rt"(x,z0)),ov(1rt,x2),t44):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
+j@t46:=someapp(rat,[x:rat]and(less"rt"(x1,x),less"rt"(x,x0)),t34,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:and(less"rt"(x1,x),less"rt"(x,x0))]t45(x,t)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
+i@t47:=invapp(z0,i,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t46(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
+ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
+t48:=cut2(inv,ov(1rt,pl"rt"(y0,y0)),t15(y0,uy),ov(1rt,x0),t23(x0,lx),[x:rat][t:in(x,inv)][y:rat][u:less"rt"(y,x)]t33(x,t,y,u),[x:rat][t:in(x,inv)]t47(x,t)):cutprop(inv)
+lx@t49:=cutapp1b(ksi,cutprop(inv),[x:rat][t:urt(ksi,x)]t48(x,t)):cutprop(inv)
+ksi@t50:=cutapp1a(ksi,cutprop(inv),[x:rat][t:lrt(ksi,x)]t49(x,t)):cutprop(inv)
+chi:=cutof(inv,t50):cut
+[z0:rat][lz:lrt(ts(ksi,chi),z0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,ts"rt"(x0,u0))][x1:rat][ux:urt(ksi,x1)][j:is"rt"(u0,ov(1rt,x1))]
+t51:=tris(rat,z0,ts"rt"(x0,u0),ts"rt"(x0,ov(1rt,x1)),i,ists2"rt"(u0,ov(1rt,x1),x0,j)):is"rt"(z0,ts"rt"(x0,ov(1rt,x1)))
+t52:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
+t53:=isless12"rt"(ts"rt"(x0,ov(1rt,x1)),z0,ts"rt"(x1,ov(1rt,x1)),1rt,symis(rat,z0,ts"rt"(x0,ov(1rt,x1)),t51),satz110c(1rt,x1),satz105c(x0,x1,ov(1rt,x1),t52)):less"rt"(z0,1rt)
+t54:=lrtrpofrt(1rt,z0,t53):lrt(1rp,z0)
+i@r1:=ini(inv,t50,u0,lu):in(u0,inv)
+r2:=invapp(u0,r1,lrt(1rp,z0),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(u0,ov(1rt,x))]t54(x,t,w)):lrt(1rp,z0)
+lz@r3:=tsapp(ksi,chi,z0,lz,lrt(1rp,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,ts"rt"(x,y))]r2(x,t,y,u,v)):lrt(1rp,z0)
+ksi@[u0:rat][lu:lrt(1rp,u0)]
+t55:=lrtrpofrte(1rt,u0,lu):less"rt"(u0,1rt)
+t56:=satz83(u0,1rt,t55):more"rt"(1rt,u0)
+[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][x2:rat][ux2:urt(ksi,x2)]
+t57:=cutapp2b(x1,lx1,x2,ux2):more"rt"(x2,x1)
+[i:is"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0))]
+t58:=cutapp2a(x0,lx,x2,ux2):less"rt"(x0,x2)
+t59:=satz105f(x0,x2,mn"rt"(1rt,u0,t56),t58):less"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),ts"rt"(mn"rt"(1rt,u0,t56),x2))
+t60:=isless1"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),symis(rat,mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0),i),t59):less"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2))
+t61:=tr4is(rat,pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),ts"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),x2),ts"rt"(1rt,x2),x2,pl"rt"(mn"rt"(x2,x1,t57),x1),distpt1"rt"(mn"rt"(1rt,u0,t56),u0,x2),ists1"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),1rt,x2,satz101e(1rt,u0,t56)),example1c(x2),satz101f(x2,x1,t57)):is"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
+t62:=satz96c(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2),t60):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)))
+t63:=isless2"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),t61,t62):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
+t64:=isless12"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(x1,mn"rt"(x2,x1,t57)),compl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),compl"rt"(mn"rt"(x2,x1,t57),x1),t63):less"rt"(pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(x1,mn"rt"(x2,x1,t57)))
+t65:=satz97c(ts"rt"(u0,x2),x1,mn"rt"(x2,x1,t57),t64):less"rt"(ts"rt"(u0,x2),x1)
+t66:=tr3is(rat,ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),ts"rt"(ts"rt"(ov(1rt,u0),u0),x2),ts"rt"(1rt,x2),x2,assts2"rt"(ov(1rt,u0),u0,x2),ists1"rt"(ts"rt"(ov(1rt,u0),u0),1rt,x2,satz110e(1rt,u0)),example1c(x2)):is"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2)
+t67:=isless12"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2,ts"rt"(ov(1rt,u0),x1),ov(x1,u0),t66,satz141b(x1,u0),satz105f(ts"rt"(u0,x2),x1,ov(1rt,u0),t65)):less"rt"(x2,ov(x1,u0))
+t68:=satz119a(x2,ux2,ov(x1,u0),t67):urt(ksi,ov(x1,u0))
+t69:=satz110e(x1,u0):is"rt"(ts"rt"(ov(x1,u0),u0),x1)
+t70:=tr3is(rat,u0,ov(x1,ov(x1,u0)),ts"rt"(ov(1rt,ov(x1,u0)),x1),ts"rt"(x1,ov(1rt,ov(x1,u0))),satz110g(x1,ov(x1,u0),u0,t69),satz141c(x1,ov(x1,u0)),comts"rt"(ov(1rt,ov(x1,u0)),x1)):is"rt"(u0,ts"rt"(x1,ov(1rt,ov(x1,u0))))
+t71:=inv1(ov(1rt,ov(x1,u0)),ov(x1,u0),t68,x2,ux2,t67,refis(rat,ov(1rt,ov(x1,u0)))):in(ov(1rt,ov(x1,u0)),inv)
+t72:=ine(inv,t50,ov(1rt,ov(x1,u0)),t71):lrt(chi,ov(1rt,ov(x1,u0)))
+t73:=lrtts(ksi,chi,u0,x1,lx1,ov(1rt,ov(x1,u0)),t72,t70):lrt(ts(ksi,chi),u0)
+lx@t74:=satz132app(ksi,lrt(ts(ksi,chi),u0),ts"rt"(mn"rt"(1rt,u0,t56),x0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn"rt"(y,x,cutapp2b(x,t,y,u)),ts"rt"(mn"rt"(1rt,u0,t56),x0))]t73(x,t,y,u,v)):lrt(ts(ksi,chi),u0)
+lu@t75:=cutapp1a(ksi,lrt(ts(ksi,chi),u0),[x:rat][t:lrt(ksi,x)]t74(x,t)):lrt(ts(ksi,chi),u0)
+ksi@t76:=isi1(ts(ksi,chi),1rp,[x:rat][t:lrt(ts(ksi,chi),x)]r3(x,t),[x:rat][t:lrt(1rp,x)]t75(x,t)):is(ts(ksi,chi),1rp)
+-4152
+satz152:=somei(cut,[t:cut]is(ts(ksi,t),1rp),chi".4152",t76".4152"):some([c:cut]is(ts(ksi,c),1rp))
+eta@[phi:cut][psi:cut]
++4153
+[m:more(phi,psi)]
+t1:=satz145d(phi,psi,eta,m):more(ts(eta,phi),ts(eta,psi))
+t2:=ec3e21(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t1):nis(ts(eta,phi),ts(eta,psi))
+psi@[l:less(phi,psi)]
+t3:=satz145f(phi,psi,eta,l):less(ts(eta,phi),ts(eta,psi))
+t4:=ec3e31(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t3):nis(ts(eta,phi),ts(eta,psi))
+psi@[n:nis(phi,psi)]
+t5:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
+t6:=orapp(more(phi,psi),less(phi,psi),nis(ts(eta,phi),ts(eta,psi)),t5,[t:more(phi,psi)]t2(t),[t:less(phi,psi)]t4(t)):nis(ts(eta,phi),ts(eta,psi))
+-4153
+[i:is(ts(eta,phi),ksi)][j:is(ts(eta,psi),ksi)]
+satz153b:=th7"l.imp"(is(phi,psi),nis(ts(eta,phi),ts(eta,psi)),weli(is(ts(eta,phi),ts(eta,psi)),tris2(cut,ts(eta,phi),ts(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t6".4153"(t)):is(phi,psi)
++*4153
+eta@[tau:cut][i:is(ts(eta,tau),1rp)]
+chi:=ts(tau,ksi):cut
+t7:=tr3is(cut,ts(eta,chi),ts(ts(eta,tau),ksi),ts(1rp,ksi),ksi,assts2(eta,tau,ksi),ists1(ts(eta,tau),1rp,ksi,i),satz151b(ksi)):is(ts(eta,chi),ksi)
+t8:=somei(cut,[c:cut]is(ts(eta,c),ksi),chi,t7):some([c:cut]is(ts(eta,c),ksi))
+-4153
+eta@satz153a:=someapp(cut,[c:cut]is(ts(eta,c),1rp),satz152(eta),some([c:cut]is(ts(eta,c),ksi)),[c:cut][t:is(ts(eta,c),1rp)]t8".4153"(c,t)):some([c:cut]is(ts(eta,c),ksi))
++*4153
+eta@t9:=[c:cut][d:cut][t:is(ts(eta,c),ksi)][u:is(ts(eta,d),ksi)]satz153b(c,d,t,u):amone(cut,[c:cut]is(ts(eta,c),ksi))
+-4153
+eta@satz153:=onei(cut,[c:cut]is(ts(eta,c),ksi),t9".4153",satz153a):one([c:cut]is(ts(eta,c),ksi))
+ov:=ind(cut,[a:cut]is(ts(eta,a),ksi),satz153):cut
+satz153c:=oneax(cut,[a:cut]is(ts(eta,a),ksi),satz153):is(ts(eta,ov(ksi,eta)),ksi)
+satz153d:=symis(cut,ts(eta,ov(ksi,eta)),ksi,satz153c):is(ksi,ts(eta,ov(ksi,eta)))
+satz153e:=tris(cut,ts(ov(ksi,eta),eta),ts(eta,ov(ksi,eta)),ksi,comts(ov(ksi,eta),eta),satz153c):is(ts(ov(ksi,eta),eta),ksi)
+satz153f:=symis(cut,ts(ov(ksi,eta),eta),ksi,satz153e):is(ksi,ts(ov(ksi,eta),eta))
+[phi:cut][i:is(ts(eta,phi),ksi)]
+satz153g:=satz153b(phi,ov(ksi,eta),i,satz153c):is(phi,ov(ksi,eta))
+@[ksi:cut]
+ratrp:=image(rat,cut,[x:rat]rpofrt(x),ksi):'prop'
+@[x0:rat]
+ratrpi:=imagei(rat,cut,[x:rat]rpofrt(x),x0):ratrp(rpofrt(x0))
+@[x:nat]
+rpofnt:=rpofrt(rtofn(x)):cut
+ksi@natrp:=image(nat,cut,[x:nat]rpofnt(x),ksi):'prop'
+x@natrpi:=imagei(nat,cut,[y:nat]rpofnt(y),x):natrp(rpofnt(x))
+ksi@[n:natrp(ksi)]
++iii5
+[x:nat][i:is(ksi,rpofnt(x))]
+t1:=somei(rat,[y:rat]is(ksi,rpofrt(y)),rtofn(x),i):ratrp(ksi)
+-iii5
+lemmaiii5:=someapp(nat,[x:nat]is(ksi,rpofnt(x)),n,ratrp(ksi),[x:nat][t:is(ksi,rpofnt(x))]t1".iii5"(x,t)):ratrp(ksi)
+@[x0:rat][y0:rat][m:more"rt"(x0,y0)]
++5154
+t1:=lrtrpofrt(x0,y0,satz82(x0,y0,m)):lrt(rpofrt(x0),y0)
+t2:=urtrpofrt(y0,y0,moreisi2"rt"(y0,y0,refis(rat,y0))):urt(rpofrt(y0),y0)
+t3:=andi(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0),t1,t2):and(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0))
+-5154
+satz154a:=somei(rat,[x:rat]and(lrt(rpofrt(x0),x),urt(rpofrt(y0),x)),y0,t3".5154"):more(rpofrt(x0),rpofrt(y0))
+y0@[i:is"rt"(x0,y0)]
+satz154b:=isf(rat,cut,[x:rat]rpofrt(x),x0,y0,i):is(rpofrt(x0),rpofrt(y0))
+y0@[l:less"rt"(x0,y0)]
+satz154c:=satz121(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,satz83(x0,y0,l))):less(rpofrt(x0),rpofrt(y0))
++*5154
+y0@t4:=satz81a(x0,y0):or3(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0))
+t5:=satz123b(rpofrt(x0),rpofrt(y0)):ec3(is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)))
+-5154
+y0@[m:more(rpofrt(x0),rpofrt(y0))]
+satz154d:=th11"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),m):more"rt"(x0,y0)
+y0@[i:is(rpofrt(x0),rpofrt(y0))]
+satz154e:=th10"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),i):is"rt"(x0,y0)
+y0@[l:less(rpofrt(x0),rpofrt(y0))]
+satz154f:=th12"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),l):less"rt"(x0,y0)
++*iii5
+@t2:=[x:rat][y:rat][t:is(rpofrt(x),rpofrt(y))]satz154e(x,y,t):injective(rat,cut,[x:rat]rpofrt(x))
+-iii5
+y0@[i:is"rt"(x0,y0)]
+isrterp:=satz154b(x0,y0,i):is(rpofrt(x0),rpofrt(y0))
+y0@[i:is(rpofrt(x0),rpofrt(y0))]
+isrtirp:=satz154e(x0,y0,i):is"rt"(x0,y0)
+ksi@[rtksi:ratrp(ksi)]
+rtofrp:=soft(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):rat
+[eta:cut][rteta:ratrp(eta)][i:is(ksi,eta)]
+isrpert:=isinv(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))
+rteta@[i:is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))]
+isrpirt:=isinve(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is(ksi,eta)
+x0@isrtrp1:=isst1(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(x0,rtofrp(rpofrt(x0),ratrpi(x0)))
+isrtrp2:=isst2(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(rtofrp(rpofrt(x0),ratrpi(x0)),x0)
+rtksi@isrprt1:=ists1"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(ksi,rpofrt(rtofrp(ksi,rtksi)))
+isrprt2:=ists2"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(rpofrt(rtofrp(ksi,rtksi)),ksi)
+@[x:nat][y:nat][i:is"n"(x,y)]
+isnterp:=isf(nat,cut,[z:nat]rpofnt(z),x,y,i):is(rpofnt(x),rpofnt(y))
+y@[i:is(rpofnt(x),rpofnt(y))]
+isntirp:=isnirt(x,y,isrtirp(rtofn(x),rtofn(y),i)):is"n"(x,y)
++*iii5
+@t3:=[x:nat][y:nat][t:is(rpofnt(x),rpofnt(y))]isntirp(x,y,t):injective(nat,cut,[x:nat]rpofnt(x))
+-iii5
+ksi@[ntksi:natrp(ksi)]
+ntofrp:=soft(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):nat
+[eta:cut][nteta:natrp(eta)][i:is(ksi,eta)]
+isrpent:=isinv(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))
+nteta@[i:is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))]
+isrpint:=isinve(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is(ksi,eta)
+x@isntrp1:=isst1(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(x,ntofrp(rpofnt(x),natrpi(x)))
+isntrp2:=isst2(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(ntofrp(rpofnt(x),natrpi(x)),x)
+ntksi@isrpnt1:=ists1"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(ksi,rpofnt(ntofrp(ksi,ntksi)))
+isrpnt2:=ists2"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(rpofnt(ntofrp(ksi,ntksi)),ksi)
+@[x0:rat][y0:rat]
++5155
+[z0:rat][lz:lrt(pl(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,pl"rt"(u0,v0))]
+t1:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
+t2:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
+t3:=satz98a(u0,x0,v0,y0,t1,t2):less"rt"(pl"rt"(u0,v0),pl"rt"(x0,y0))
+t4:=isless1"rt"(pl"rt"(u0,v0),z0,pl"rt"(x0,y0),symis(rat,z0,pl"rt"(u0,v0),i),t3):less"rt"(z0,pl"rt"(x0,y0))
+t5:=lrtrpofrt(pl"rt"(x0,y0),z0,t4):lrt(rpofrt(pl"rt"(x0,y0)),z0)
+lz@t6:=plapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(pl"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,pl"rt"(x,y))]t5(x,t,y,u,v)):lrt(rpofrt(pl"rt"(x0,y0)),z0)
+y0@[u0:rat][lu:lrt(rpofrt(pl"rt"(x0,y0)),u0)]
+t7:=lrtrpofrte(pl"rt"(x0,y0),u0,lu):less"rt"(u0,pl"rt"(x0,y0))
+u01:=ov"rt"(u0,pl"rt"(x0,y0)):rat
+t8:=isless12"rt"(u0,ts"rt"(u01,pl"rt"(x0,y0)),pl"rt"(x0,y0),ts"rt"(1rt,pl"rt"(x0,y0)),satz110f(u0,pl"rt"(x0,y0)),example1d(pl"rt"(x0,y0)),t7):less"rt"(ts"rt"(u01,pl"rt"(x0,y0)),ts"rt"(1rt,pl"rt"(x0,y0)))
+t9:=satz106c(u01,1rt,pl"rt"(x0,y0),t8):less"rt"(u01,1rt)
+t10:=tris(rat,u0,ts"rt"(pl"rt"(x0,y0),u01),pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)),satz110d(u0,pl"rt"(x0,y0)),disttp1"rt"(x0,y0,u01)):is"rt"(u0,pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)))
+y0@[l:less"rt"(y0,1rt)]
+t11:=isless12"rt"(ts"rt"(y0,x0),ts"rt"(x0,y0),ts"rt"(1rt,x0),x0,comts"rt"(y0,x0),example1c(x0),satz105c(y0,1rt,x0,l)):less"rt"(ts"rt"(x0,y0),x0)
+t12:=lrtrpofrt(x0,ts"rt"(x0,y0),t11):lrt(rpofrt(x0),ts"rt"(x0,y0))
+lu@t13:=lrtpl(rpofrt(x0),rpofrt(y0),u0,ts"rt"(x0,u01),t12(x0,u01,t9),ts"rt"(y0,u01),t12(y0,u01,t9),t10):lrt(pl(rpofrt(x0),rpofrt(y0)),u0)
+-5155
+satz155a:=isi1(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(pl"rt"(x0,y0)),x)]t13".5155"(x,t),[x:rat][t:lrt(pl(rpofrt(x0),rpofrt(y0)),x)]t6".5155"(x,t)):is(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)))
+[m:more"rt"(x0,y0)]
++*5155
+m@t14:=satz101f(x0,y0,m):is"rt"(x0,pl"rt"(mn"rt"(x0,y0,m),y0))
+t15:=tris(cut,rpofrt(x0),rpofrt(pl"rt"(mn"rt"(x0,y0,m),y0)),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),isrterp(x0,pl"rt"(mn"rt"(x0,y0,m),y0),t14),satz155a(mn"rt"(x0,y0,m),y0)):is(rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)))
+t16:=tris2(cut,pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),compl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),t15):is(pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0))
+-5155
+m@satz155b:=satz140g(rpofrt(x0),rpofrt(y0),rpofrt(mn"rt"(x0,y0,m)),satz154a(x0,y0,m),t16".5155"):is(rpofrt(mn"rt"(x0,y0,m)),mn(rpofrt(x0),rpofrt(y0),satz154a(x0,y0,m)))
++*5155
+y0@[z0:rat][lz:lrt(ts(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,ts"rt"(u0,v0))]
+t17:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
+t18:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
+t19:=satz107a(u0,x0,v0,y0,t17,t18):less"rt"(ts"rt"(u0,v0),ts"rt"(x0,y0))
+t20:=isless1"rt"(ts"rt"(u0,v0),z0,ts"rt"(x0,y0),symis(rat,z0,ts"rt"(u0,v0),i),t19):less"rt"(z0,ts"rt"(x0,y0))
+t21:=lrtrpofrt(ts"rt"(x0,y0),z0,t20):lrt(rpofrt(ts"rt"(x0,y0)),z0)
+lz@t22:=tsapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(ts"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,ts"rt"(x,y))]t21(x,t,y,u,v)):lrt(rpofrt(ts"rt"(x0,y0)),z0)
+y0@[u0:rat][lu:lrt(rpofrt(ts"rt"(x0,y0)),u0)]
+t23:=lrtrpofrte(ts"rt"(x0,y0),u0,lu):less"rt"(u0,ts"rt"(x0,y0))
+[u1:rat][a:and(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)))]
+t24:=ande1(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u0,u1)
+t25:=ande2(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u1,ts"rt"(x0,y0))
+t26:=isless12"rt"(u0,ts"rt"(ov"rt"(u0,u1),u1),u1,ts"rt"(1rt,u1),satz110f(u0,u1),example1d(u1),t24):less"rt"(ts"rt"(ov"rt"(u0,u1),u1),ts"rt"(1rt,u1))
+t27:=satz106c(ov"rt"(u0,u1),1rt,u1,t26):less"rt"(ov"rt"(u0,u1),1rt)
+t28:=isless1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0),satz110f(u1,y0),t25):less"rt"(ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0))
+t29:=satz106c(ov"rt"(u1,y0),x0,y0,t28):less"rt"(ov"rt"(u1,y0),x0)
+t30:=tr3is(rat,u0,ts"rt"(u1,ov"rt"(u0,u1)),ts"rt"(ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1)),ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))),satz110d(u0,u1),ists1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1),satz110f(u1,y0)),assts1"rt"(ov"rt"(u1,y0),y0,ov"rt"(u0,u1))):is"rt"(u0,ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))))
+t31:=lrtts(rpofrt(x0),rpofrt(y0),u0,ov"rt"(u1,y0),lrtrpofrt(x0,ov"rt"(u1,y0),t29),ts"rt"(y0,ov"rt"(u0,u1)),t12(y0,ov"rt"(u0,u1),t27),t30):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
+lu@t32:=someapp(rat,[x:rat]and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0))),satz91(u0,ts"rt"(x0,y0),t23),lrt(ts(rpofrt(x0),rpofrt(y0)),u0),[x:rat][t:and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0)))]t31(x,t)):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
+-5155
+y0@satz155c:=isi1(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(ts"rt"(x0,y0)),x)]t32".5155"(x,t),[x:rat][t:lrt(ts(rpofrt(x0),rpofrt(y0)),x)]t22".5155"(x,t)):is(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)))
++*5155
+y0@t33:=satz110f(x0,y0):is"rt"(x0,ts"rt"(ov"rt"(x0,y0),y0))
+t34:=tris(cut,rpofrt(x0),rpofrt(ts"rt"(ov"rt"(x0,y0),y0)),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),isrterp(x0,ts"rt"(ov"rt"(x0,y0),y0),t33),satz155c(ov"rt"(x0,y0),y0)):is(rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)))
+t35:=tris2(cut,ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),comts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),t34):is(ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0))
+-5155
+y0@satz155d:=satz153g(rpofrt(x0),rpofrt(y0),rpofrt(ov"rt"(x0,y0)),t35".5155"):is(rpofrt(ov"rt"(x0,y0)),ov(rpofrt(x0),rpofrt(y0)))
+@[x:nat][y:nat]
+satz155e:=tris(cut,rpofnt(pl"n"(x,y)),rpofrt(pl"rt"(rtofn(x),rtofn(y))),pl(rpofnt(x),rpofnt(y)),isrterp(rtofn(pl"n"(x,y)),pl"rt"(rtofn(x),rtofn(y)),symis(rat,pl"rt"(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),satz112h(x,y))),satz155a(rtofn(x),rtofn(y))):is(rpofnt(pl"n"(x,y)),pl(rpofnt(x),rpofnt(y)))
+satz155f:=tris(cut,rpofnt(ts"n"(x,y)),rpofrt(ts"rt"(rtofn(x),rtofn(y))),ts(rpofnt(x),rpofnt(y)),isrterp(rtofn(ts"n"(x,y)),ts"rt"(rtofn(x),rtofn(y)),symis(rat,ts"rt"(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),satz112j(x,y))),satz155c(rtofn(x),rtofn(y))):is(rpofnt(ts"n"(x,y)),ts(rpofnt(x),rpofnt(y)))
++nt
+@natt:=ot(cut,[t:cut]natrp(t)):'type'
+[ksi:cut][nksi:natrp(ksi)]
+nttofrp:=out(cut,[t:cut]natrp(t),ksi,nksi):natt
+@[xt:natt][yt:natt]
+is:=is"e"(natt,xt,yt):'prop'
+nis:=not(is(xt,yt)):'prop'
+@[p:[x:natt]'prop']
+all:=all"l"(natt,p):'prop'
+some:=some"l"(natt,p):'prop'
+one:=one"e"(natt,p):'prop'
+xt@[st:set(natt)]
+in:=esti(natt,xt,st):'prop'
+xt@rpofntt:=in"e"(cut,[t:cut]natrp(t),xt):cut
+natrpi:=inp(cut,[t:cut]natrp(t),xt):natrp(rpofntt(xt))
+nksi@[eta:cut][neta:natrp(eta)][i:is"rp"(ksi,eta)]
+isrpentt:=isouti(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is(nttofrp(ksi,nksi),nttofrp(eta,neta))
+neta@[i:is(nttofrp(ksi,nksi),nttofrp(eta,neta))]
+isrpintt:=isoute(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is"rp"(ksi,eta)
+yt@[i:is(xt,yt)]
+isntterp:=isini(cut,[t:cut]natrp(t),xt,yt,i):is"rp"(rpofntt(xt),rpofntt(yt))
+yt@[i:is"rp"(rpofntt(xt),rpofntt(yt))]
+isnttirp:=isine(cut,[t:cut]natrp(t),xt,yt,i):is(xt,yt)
+nksi@isrpntt1:=isinout(cut,[t:cut]natrp(t),ksi,nksi):is"rp"(ksi,rpofntt(nttofrp(ksi,nksi)))
+xt@isnttrp1:=isoutin(cut,[t:cut]natrp(t),xt):is(xt,nttofrp(rpofntt(xt),natrpi(xt)))
+@[x:nat]
+nttofnt:=nttofrp(rpofnt(x),natrpi"rp"(x)):natt
+[y:nat][i:is"n"(x,y)]
+isntentt:=isrpentt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),isnterp(x,y,i)):is(nttofnt(x),nttofnt(y))
+y@[i:is(nttofnt(x),nttofnt(y))]
+isntintt:=isntirp(x,y,isrpintt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),i)):is"n"(x,y)
+xt@ntofntt:=ntofrp(rpofntt(xt),natrpi(xt)):nat
+yt@[i:is(xt,yt)]
+isnttent:=isrpent(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),isntterp(xt,yt,i)):is"n"(ntofntt(xt),ntofntt(yt))
+yt@[i:is"n"(ntofntt(xt),ntofntt(yt))]
+isnttint:=isnttirp(xt,yt,isrpint(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),i)):is(xt,yt)
++iii5
+x@t5:=isrpntt1(rpofnt(x),natrpi"rp"(x)):is"rp"(rpofnt(x),rpofntt(nttofnt(x)))
+t6:=isrpent(rpofnt(x),natrpi"rp"(x),rpofntt(nttofnt(x)),natrpi(nttofnt(x)),t5):is"n"(ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)))
+-iii5
+x@isntntt1:=tris(nat,x,ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)),isntrp1(x),t6".iii5"):is"n"(x,ntofntt(nttofnt(x)))
++*iii5
+xt@t7:=isrpnt1(rpofntt(xt),natrpi(xt)):is"rp"(rpofntt(xt),rpofnt(ntofntt(xt)))
+t8:=isrpentt(rpofntt(xt),natrpi(xt),rpofnt(ntofntt(xt)),natrpi"rp"(ntofntt(xt)),t7):is(nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)))
+-iii5
+xt@isnttnt1:=tris(natt,xt,nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)),isnttrp1(xt),t8".iii5"):is(xt,nttofnt(ntofntt(xt)))
+x@isntntt2:=symis(nat,x,ntofntt(nttofnt(x)),isntntt1):is"n"(ntofntt(nttofnt(x)),x)
+xt@isnttnt2:=symis(natt,xt,nttofnt(ntofntt(xt)),isnttnt1):is(nttofnt(ntofntt(xt)),xt)
+@1t:=nttofnt(1):natt
+suct:=[x:natt]nttofnt(<ntofntt(x)>suc):[x:natt]natt
++5156
+xt@[j:is(<xt>suct,1t)]
+t1:=isntintt(<ntofntt(xt)>suc,1,j):is"n"(<ntofntt(xt)>suc,1)
+-5156
+xt@satz156a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<ntofntt(xt)>suc,1),<ntofntt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5156"(t)):nis(<xt>suct,1t)
+yt@[i:is(<xt>suct,<yt>suct)]
++*5156
+i@t2:=isntintt(<ntofntt(xt)>suc,<ntofntt(yt)>suc,i):is"n"(<ntofntt(xt)>suc,<ntofntt(yt)>suc)
+-5156
+i@satz156b:=isnttint(xt,yt,<t2".5156"><ntofntt(yt)><ntofntt(xt)>ax4):is(xt,yt)
+@[st:set(natt)]
+cond1:=in(1t,st):'prop'
+cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
+[c1:cond1][c2:cond2]
++*5156
+c2@[x:nat]
+prop1:=in(nttofnt(x),st):'prop'
+[p:prop1(x)]
+t3:=<p><nttofnt(x)>c2:in(<nttofnt(x)>suct,st)
+t4:=isp(nat,[t:nat]in(nttofnt(<t>suc),st),ntofntt(nttofnt(x)),x,t3,isntntt2(x)):prop1(<x>suc)
+-5156
+c2@[xt:natt]
++*5156
+xt@t5:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t4(t,u),ntofntt(xt)):in(nttofnt(ntofntt(xt)),st)
+-5156
+xt@satz156c:=isp(natt,[t:natt]in(t,st),nttofnt(ntofntt(xt)),xt,t5".5156",isnttnt2(xt)):in(xt,st)
+@ax3t:=[x:natt]satz156a(x):[x:natt]nis(<x>suct,1t)
+ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz156b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
+ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz156c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
+-nt
++rtt
+@ratt:=ot(cut,[t:cut]ratrp(t)):'type'
+[ksi:cut][rtksi:ratrp(ksi)]
+rttofrp:=out(cut,[t:cut]ratrp(t),ksi,rtksi):ratt
+@[x0t:ratt][y0t:ratt]
+is:=is"e"(ratt,x0t,y0t):'prop'
+nis:=not(is(x0t,y0t)):'prop'
+@[p:[x:ratt]'prop']
+all:=all"l"(ratt,p):'prop'
+some:=some"l"(ratt,p):'prop'
+one:=one"e"(ratt,p):'prop'
+x0t@rpofrtt:=in"e"(cut,[t:cut]ratrp(t),x0t):cut
+ratrpi:=inp(cut,[t:cut]ratrp(t),x0t):ratrp(rpofrtt(x0t))
+rtksi@[eta:cut][rteta:ratrp(eta)][i:is"rp"(ksi,eta)]
+isrpertt:=isouti(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))
+rteta@[i:is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))]
+isrpirtt:=isoute(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is"rp"(ksi,eta)
+y0t@[i:is(x0t,y0t)]
+isrtterp:=isini(cut,[t:cut]ratrp(t),x0t,y0t,i):is"rp"(rpofrtt(x0t),rpofrtt(y0t))
+y0t@[i:is"rp"(rpofrtt(x0t),rpofrtt(y0t))]
+isrttirp:=isine(cut,[t:cut]ratrp(t),x0t,y0t,i):is(x0t,y0t)
+rtksi@isrprtt1:=isinout(cut,[t:cut]ratrp(t),ksi,rtksi):is"rp"(ksi,rpofrtt(rttofrp(ksi,rtksi)))
+x0t@isrttrp1:=isoutin(cut,[t:cut]ratrp(t),x0t):is(x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)))
+@[x0:rat]
+rttofrt:=rttofrp(rpofrt(x0),ratrpi"rp"(x0)):ratt
+[y0:rat][i:is"rt"(x0,y0)]
+isrtertt:=isrpertt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),isrterp(x0,y0,i)):is(rttofrt(x0),rttofrt(y0))
+y0@[i:is(rttofrt(x0),rttofrt(y0))]
+isrtirtt:=isrtirp(x0,y0,isrpirtt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),i)):is"rt"(x0,y0)
+x0t@rtofrtt:=rtofrp(rpofrtt(x0t),ratrpi(x0t)):rat
+y0t@[i:is(x0t,y0t)]
+isrttert:=isrpert(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),isrtterp(x0t,y0t,i)):is"rt"(rtofrtt(x0t),rtofrtt(y0t))
+y0t@[i:is"rt"(rtofrtt(x0t),rtofrtt(y0t))]
+isrttirt:=isrttirp(x0t,y0t,isrpirt(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),i)):is(x0t,y0t)
++iii5
+x0@t9:=isrprtt1(rpofrt(x0),ratrpi"rp"(x0)):is"rp"(rpofrt(x0),rpofrtt(rttofrt(x0)))
+t10:=isrpert(rpofrt(x0),ratrpi"rp"(x0),rpofrtt(rttofrt(x0)),ratrpi(rttofrt(x0)),t9):is"rt"(rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)))
+-iii5
+x0@isrtrtt1:=tris(rat,x0,rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)),isrtrp1(x0),t10".iii5"):is"rt"(x0,rtofrtt(rttofrt(x0)))
++*iii5
+x0t@t11:=isrprt1(rpofrtt(x0t),ratrpi(x0t)):is"rp"(rpofrtt(x0t),rpofrt(rtofrtt(x0t)))
+t12:=isrpertt(rpofrtt(x0t),ratrpi(x0t),rpofrt(rtofrtt(x0t)),ratrpi"rp"(rtofrtt(x0t)),t11):is(rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)))
+-iii5
+x0t@isrttrt1:=tris(ratt,x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)),isrttrp1(x0t),t12".iii5"):is(x0t,rttofrt(rtofrtt(x0t)))
+-rtt
+@[ksi:cut]
+example2:=satz153c(1rp,ksi):is(ts(ksi,ov(1rp,ksi)),1rp)
+[rtksi:ratrp(ksi)]
++5157
+x01:=rtofrp(ksi,rtksi):rat
+ksi@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
+rtksi@[y0:rat][i:in(y0,s1)]
+t1:=estie(rat,[x:rat]urt(ksi,x),y0,i):urt(ksi,y0)
+[m:more"rt"(x01,y0)]
+t2:=lrtrpofrt(x01,y0,satz82(x01,y0,m)):lrt(rpofrt(x01),y0)
+t3:=isp(cut,[x:cut]lrt(x,y0),rpofrt(x01),ksi,t2,isrprt2(ksi,rtksi)):lrt(ksi,y0)
+i@t4:=th3"l.imp"(more"rt"(x01,y0),lrt(ksi,y0),t1,[t:more"rt"(x01,y0)]t3(t)):not(more"rt"(x01,y0))
+t5:=satz81e(x01,y0,t4):lessis"rt"(x01,y0)
+rtksi@t6:=[x:rat][t:in(x,s1)]t5(x,t):lb(s1,x01)
+t7:=urtrpofrt(x01,x01,moreisi2"rt"(x01,x01,refis(rat,x01))):urt(rpofrt(x01),x01)
+t8:=isp(cut,[x:cut]urt(x,x01),rpofrt(x01),ksi,t7,isrprt2(ksi,rtksi)):urt(ksi,x01)
+t9:=estii(rat,[x:rat]urt(ksi,x),x01,t8):in(x01,s1)
+t10:=andi(lb(s1,x01),in(x01,s1),t6,t9):min(s1,x01)
+-5157
+satz157a:=t10".5157":min(setof(rat,[x:rat]urt(ksi,x)),rtofrp(ksi,rtksi))
+satz157b:=somei(rat,[x:rat]min(s1".5157",x),x01".5157",t10".5157"):some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))
+ksi@[x0:rat][m:min(setof(rat,[x:rat]urt(ksi,x)),x0)]
++*5157
+m"rp"@t11:=ande1(lb(s1,x0),in(x0,s1),m):lb(s1,x0)
+t12:=ande2(lb(s1,x0),in(x0,s1),m):in(x0,s1)
+t13:=estie(rat,[x:rat]urt(ksi,x),x0,t12):urt(ksi,x0)
+[y0:rat][ly:lrt(ksi,y0)]
+t14:=cutapp2a(ksi,y0,ly,x0,t13):less"rt"(y0,x0)
+t15:=lrtrpofrt(x0,y0,t14):lrt(rpofrt(x0),y0)
+y0@[uy:urt(ksi,y0)]
+t17:=estii(rat,[x:rat]urt(ksi,x),y0,uy):in(y0,s1)
+t18:=satz85(x0,y0,<t17><y0>t11):moreis"rt"(y0,x0)
+t19:=urtrpofrt(x0,y0,t18):urt(rpofrt(x0),y0)
+y0@t20:=cp(lrt(rpofrt(x0),y0),lrt(ksi,y0),[t:urt(ksi,y0)]t19(t)):imp(lrt(rpofrt(x0),y0),lrt(ksi,y0))
+-5157
+m@satz157c:=isi1(ksi,rpofrt(x0),[x:rat][t:lrt(ksi,x)]t15".5157"(x,t),[x:rat]t20".5157"(x)):is(ksi,rpofrt(x0))
+ksi@[s:some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))]
++*5157
+s@[x0:rat][m:min(s1,x0)]
+t21:=somei(rat,[x:rat]is(ksi,rpofrt(x)),x0,satz157c(x0,m)):ratrp(ksi)
+-5157
+s@satz157d:=someapp(rat,[x:rat]min(s1".5157",x),s,ratrp(ksi),[x:rat][t:min(s1".5157",x)]t21".5157"(x,t)):ratrp(ksi)
+ksi@[x0:rat][lx:lrt(ksi,x0)]
++5158
+x0@xr:=rpofrt(x0):cut
+lx@t1:=urtrpofrt(x0,x0,moreisi2"rt"(x0,x0,refis(rat,x0))):urt(xr,x0)
+t2:=andi(urt(xr,x0),lrt(ksi,x0),t1,lx):and(urt(xr,x0),lrt(ksi,x0))
+-5158
+satz158a:=somei(rat,[x:rat]and(urt(rpofrt(x0),x),lrt(ksi,x)),x0,t2".5158"):less(rpofrt(x0),ksi)
+x0@[ux:urt(ksi,x0)]
++*5158
+ux@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
+[m:min(s1,x0)]
+t3:=symis(cut,ksi,xr,satz157c(ksi,x0,m)):is(xr,ksi)
+t4:=moreisi2(xr,ksi,t3):moreis(xr,ksi)
+ux@[n:not(min(s1,x0))]
+t5:=estii(rat,[x:rat]urt(ksi,x),x0,ux):in(x0,s1)
+t6:=th4"l.and"(lb(s1,x0),in(x0,s1),n,t5):not(lb(s1,x0))
+t7:=th1"l.some"(rat,[x:rat]imp(in(x,s1),lessis"rt"(x0,x)),t6):some"rt"([x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))))
+[y0:rat][o:not(imp(in(y0,s1),lessis"rt"(x0,y0)))]
+t8:=th5"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):in(y0,s1)
+t9:=estie(rat,[x:rat]urt(ksi,x),y0,t8):urt(ksi,y0)
+t10:=th6"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):not(lessis"rt"(x0,y0))
+t11:=satz82(x0,y0,satz81k(x0,y0,t10)):less"rt"(y0,x0)
+t12:=lrtrpofrt(x0,y0,t11):lrt(xr,y0)
+t13:=andi(lrt(xr,y0),urt(ksi,y0),t12,t9):and(lrt(xr,y0),urt(ksi,y0))
+t14:=somei(rat,[x:rat]and(lrt(xr,x),urt(ksi,x)),y0,t13):more(xr,ksi)
+n@t15:=someapp(rat,[x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))),t7,more(xr,ksi),[x:rat][t:not(imp(in(x,s1),lessis"rt"(x0,x)))]t14(x,t)):more(xr,ksi)
+t16:=moreisi1(xr,ksi,t15):moreis(xr,ksi)
+-5158
+ux@satz158b:=th1"l.imp"(min(s1".5158",x0),moreis(rpofrt(x0),ksi),[t:min(s1".5158",x0)]t4".5158"(t),[t:not(min(s1".5158",x0))]t16".5158"(t)):moreis(rpofrt(x0),ksi)
+x0@[l:less(rpofrt(x0),ksi)]
++*5158
+l@t17:=satz123h(xr,ksi,l):not(moreis(xr,ksi))
+t18:=th3"l.imp"(urt(ksi,x0),moreis(xr,ksi),t17,[t:urt(ksi,x0)]satz158b(t)):not(urt(ksi,x0))
+-5158
+l@satz158c:=et(lrt(ksi,x0),t18".5158"):lrt(ksi,x0)
+x0@[m:moreis(rpofrt(x0),ksi)]
++*5158
+m"rp"@t19:=satz123c(xr,ksi,m):not(less(xr,ksi))
+-5158
+m@satz158d:=th3"l.imp"(lrt(ksi,x0),less(rpofrt(x0),ksi),t19".5158",[t:lrt(ksi,x0)]satz158a(t)):urt(ksi,x0)
+ksi@[eta:cut][l:less(ksi,eta)]
++5159
+[x0:rat]
+xr:=rpofrt(x0):cut
+[ux:urt(ksi,x0)][lx:lrt(eta,x0)][z0:rat]
+zr:=rpofrt(z0):cut
+[lz:lrt(eta,z0)][k:less"rt"(x0,z0)]
+t1:=satz127a(ksi,xr,zr,satz124(xr,ksi,satz158b(ksi,x0,ux)),satz154c(x0,z0,k)):less(ksi,zr)
+t2:=andi(less(ksi,zr),less(zr,eta),t1,satz158a(eta,z0,lz)):and(less(ksi,zr),less(zr,eta))
+t3:=somei(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),z0,t2):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
+lx@t4:=cutapp3(eta,x0,lx,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:lrt(eta,x)][u:less"rt"(x0,x)]t3(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
+-5159
+satz159:=lessapp(ksi,eta,l,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t4".5159"(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
++*5159
+x0@[a:and(less(ksi,xr),less(xr,eta))]
+t5:=andi(ratrp(xr),and(less(ksi,xr),less(xr,eta)),ratrpi(x0),a):and3(ratrp(xr),less(ksi,xr),less(xr,eta))
+t6:=somei(cut,[c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)),xr,t5):some([c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)))
+-5159
+l@satz159a:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta))),[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t6".5159"(x,t)):some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta)))
+[p:'prop'][p1:[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),eta)]p]
++*5159
+p1@[y0:rat]
+yr:=rpofrt(y0):cut
+[a:and(less(ksi,yr),less(yr,eta))]
+t7:=ande1(less(ksi,yr),less(yr,eta),a):less(ksi,yr)
+t8:=ande2(less(ksi,yr),less(yr,eta),a):less(yr,eta)
+t9:=<t8><t7><y0>p1:p
+-5159
+p1@satz159app:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,p,[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t9".5159"(x,t)):p
+eta@[z0:rat][m:more(rpofrt(z0),ts(ksi,eta))]
++5160
+zr:=rpofrt(z0):cut
+nm:=mn(zr,ts(ksi,eta),m):cut
+dn:=pl(pl(ksi,eta),1rp):cut
+fr:=ov(nm,dn):cut
+zeta:=ite(less(fr,1rp),cut,fr,1rp):cut
+[l:less(fr,1rp)]
+t1:=itet(less(fr,1rp),cut,fr,1rp,l):is(zeta,fr)
+t2:=lessisi2(zeta,fr,t1):lessis(zeta,fr)
+t3:=lessisi1(zeta,1rp,satz127a(zeta,fr,1rp,t2,l)):lessis(zeta,1rp)
+m@[n:not(less(fr,1rp))]
+t4:=itef(less(fr,1rp),cut,fr,1rp,n):is(zeta,1rp)
+t5:=lessisi2(zeta,1rp,t4):lessis(zeta,1rp)
+t6:=trlessis(zeta,1rp,fr,t5,satz124(fr,1rp,satz123f(fr,1rp,n))):lessis(zeta,fr)
+m@t7:=th1"l.imp"(less(fr,1rp),lessis(zeta,1rp),[t:less(fr,1rp)]t3(t),[t:not(less(fr,1rp))]t5(t)):lessis(zeta,1rp)
+t8:=th1"l.imp"(less(fr,1rp),lessis(zeta,fr),[t:less(fr,1rp)]t2(t),[t:not(less(fr,1rp))]t6(t)):lessis(zeta,fr)
+[z1:rat]
+zr1:=rpofrt(z1):cut
+[l1:less(ksi,zr1)][l2:less(zr1,pl(ksi,zeta))][z2:rat]
+zr2:=rpofrt(z2):cut
+[l3:less(eta,zr2)][l4:less(zr2,pl(eta,zeta))]
+t9:=isless2(ts(pl(ksi,zeta),pl(eta,zeta)),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),ts(zr1,zr2),disttp2(pl(ksi,zeta),eta,zeta),satz147a(zr1,pl(ksi,zeta),zr2,pl(eta,zeta),l2,l4)):less(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)))
+t10:=lessisi2(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),tris(cut,ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(zeta,eta)),pl(ts(ksi,eta),ts(eta,zeta)),disttp1(ksi,zeta,eta),ispl2(ts(zeta,eta),ts(eta,zeta),ts(ksi,eta),comts(zeta,eta)))):lessis(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)))
+t11:=satz149a(pl(ksi,zeta),pl(ksi,1rp),zeta,zeta,satz139a(ksi,ksi,zeta,1rp,lessisi2(ksi,ksi,refis(cut,ksi)),t7),lessisi2(zeta,zeta,refis(cut,zeta))):lessis(ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta))
+t12:=satz139a(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta),t10,t11):lessis(pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
+t13:=satz127b(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),t9,t12):less(ts(zr1,zr2),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
+t14:=tris(cut,pl(eta,pl(ksi,1rp)),pl(pl(eta,ksi),1rp),pl(pl(ksi,eta),1rp),asspl2(eta,ksi,1rp),ispl1(pl(eta,ksi),pl(ksi,eta),1rp,compl(eta,ksi))):is(pl(eta,pl(ksi,1rp)),dn)
+t15:=tris(cut,pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(pl(eta,pl(ksi,1rp)),zeta),ts(dn,zeta),distpt1(eta,pl(ksi,1rp),zeta),ists1(pl(eta,pl(ksi,1rp)),dn,zeta,t14)):is(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta))
+t16:=tris(cut,pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta))),pl(ts(ksi,eta),ts(dn,zeta)),asspl1(ts(ksi,eta),ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ispl2(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta),ts(ksi,eta),t15)):is(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)))
+t17:=isless2(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)),ts(zr1,zr2),t16,t13):less(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)))
+t18:=islessis12(ts(zeta,dn),ts(dn,zeta),ts(fr,dn),nm,comts(zeta,dn),satz153e(nm,dn),satz149a(zeta,fr,dn,dn,t8,lessisi2(dn,dn,refis(cut,dn)))):lessis(ts(dn,zeta),nm)
+t19:=satz139a(ts(ksi,eta),ts(ksi,eta),ts(dn,zeta),nm,lessisi2(ts(ksi,eta),ts(ksi,eta),refis(cut,ts(ksi,eta))),t18):lessis(pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm))
+t20:=satz127b(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm),t17,t19):less(ts(zr1,zr2),pl(ts(ksi,eta),nm))
+t21:=isless2(pl(ts(ksi,eta),nm),zr,ts(zr1,zr2),satz140c(zr,ts(ksi,eta),m),t20):less(ts(zr1,zr2),zr)
+t22:=satz154f(ts"rt"(z1,z2),z0,isless1(ts(zr1,zr2),rpofrt(ts"rt"(z1,z2)),zr,symis(cut,rpofrt(ts"rt"(z1,z2)),ts(zr1,zr2),satz155c(z1,z2)),t21)):less"rt"(ts"rt"(z1,z2),z0)
+x0:=ov"rt"(z0,z2):rat
+xr:=rpofrt(x0):cut
+y0:=z2:rat
+yr:=rpofrt(y0):cut
+t23:=satz110e(z0,z2):is"rt"(ts"rt"(x0,y0),z0)
+t24:=ismore1"rt"(z0,ts"rt"(x0,z2),ts"rt"(z1,z2),symis(rat,ts"rt"(x0,z2),z0,t23),satz83(ts"rt"(z1,z2),z0,t22)):more"rt"(ts"rt"(x0,z2),ts"rt"(z1,z2))
+t25:=satz106a(x0,z1,z2,t24):more"rt"(x0,z1)
+t26:=trmore(xr,zr1,ksi,satz154a(x0,z1,t25),satz122(ksi,zr1,l1)):more(xr,ksi)
+t27:=satz122(eta,yr,l3):more(yr,eta)
+z0@[u0:rat]
+ur:=rpofrt(u0):cut
+[v0:rat]
+vr:=rpofrt(v0):cut
+prop1:=and3(more(ur,ksi),more(vr,eta),is"rt"(ts"rt"(u0,v0),z0)):'prop'
+z0@prop2:=some"rt"([x:rat]some"rt"([y:rat]prop1(x,y))):'prop'
+l4@t28:=and3i(more(xr,ksi),more(yr,eta),is"rt"(ts"rt"(x0,y0),z0),t26,t27,t23):prop1(x0,y0)
+t29:=somei(rat,[y:rat]prop1(x0,y),y0,t28):some"rt"([y:rat]prop1(x0,y))
+t30:=somei(rat,[x:rat]some"rt"([y:rat]prop1(x,y)),x0,t29):prop2
+l2@t31:=satz159app(eta,pl(eta,zeta),satz133a(eta,zeta),prop2,[x:rat][t:less(eta,rpofrt(x))][u:less(rpofrt(x),pl(eta,zeta))]t30(x,t,u)):prop2
+-5160
+satz160:=satz159app(ksi,pl(ksi,zeta".5160"),satz133a(ksi,zeta".5160"),prop2".5160",[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),pl(ksi,zeta".5160"))]t31".5160"(x,t,u)):some"rt"([x:rat]some"rt"([y:rat]and3(more(rpofrt(x),ksi),more(rpofrt(y),eta),is"rt"(ts"rt"(x,y),z0))))
+[p:'prop'][p1:[x:rat][t:more(rpofrt(x),ksi)][y:rat][u:more(rpofrt(y),eta)][v:is"rt"(ts"rt"(x,y),z0)]p]
++*5160
+p1@[x1:rat]
+xr1:=rpofrt(x1):cut
+[px:some"rt"([y:rat]prop1(x1,y))][y1:rat]
+yr1:=rpofrt(y1):cut
+[py:prop1(x1,y1)]
+t32:=and3e1(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(xr1,ksi)
+t33:=and3e2(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(yr1,eta)
+t34:=and3e3(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):is"rt"(ts"rt"(x1,y1),z0)
+t35:=<t34><t33><y1><t32><x1>p1:p
+px@t36:=someapp(rat,[y:rat]prop1(x1,y),px,p,[y:rat][v:prop1(x1,y)]t35(y,v)):p
+-5160
+p1@satz160app:=someapp(rat,[x:rat]some"rt"([y:rat]prop1".5160"(x,y)),satz160,p,[x:rat][t:some"rt"([y:rat]prop1".5160"(x,y))]t36".5160"(x,t)):p
++5161
+@[ksi:cut][eta:cut]
+min:=ite(less(ksi,eta),cut,ksi,eta):cut
+max:=ite(more(ksi,eta),cut,ksi,eta):cut
+[u0:rat]
+ur:=rpofrt(u0):cut
+[lu:lrt(min,u0)]
+t1:=satz158a(min,u0,lu):less(ur,min)
+[l:less(ksi,eta)]
+t2:=isless2(min,ksi,ur,itet(less(ksi,eta),cut,ksi,eta,l),t1):less(ur,ksi)
+t3:=trless(ur,ksi,eta,t2,l):less(ur,eta)
+lu@[n:not(less(ksi,eta))]
+t4:=isless2(min,eta,ur,itef(less(ksi,eta),cut,ksi,eta,n),t1):less(ur,eta)
+t5:=satz127b(ur,eta,ksi,t4,satz124(ksi,eta,satz123f(ksi,eta,n))):less(ur,ksi)
+lu@t6:=th1"l.imp"(less(ksi,eta),less(ur,ksi),[t:less(ksi,eta)]t2(t),[t:not(less(ksi,eta))]t5(t)):less(ur,ksi)
+t7:=th1"l.imp"(less(ksi,eta),less(ur,eta),[t:less(ksi,eta)]t3(t),[t:not(less(ksi,eta))]t4(t)):less(ur,eta)
+u0@[uu:urt(max,u0)]
+t8:=satz158b(max,u0,uu):moreis(ur,max)
+[m:more(ksi,eta)]
+t9:=ismoreis2(max,ksi,ur,itet(more(ksi,eta),cut,ksi,eta,m),t8):moreis(ur,ksi)
+t10:=trmoreis(ur,ksi,eta,t9,moreisi1(ksi,eta,m)):moreis(ur,eta)
+uu@[n:not(more(ksi,eta))]
+t11:=ismoreis2(max,eta,ur,itef(more(ksi,eta),cut,ksi,eta,n),t8):moreis(ur,eta)
+t12:=trmoreis(ur,eta,ksi,t11,satz125(ksi,eta,satz123e(ksi,eta,n))):moreis(ur,ksi)
+uu@t13:=th1"l.imp"(more(ksi,eta),moreis(ur,ksi),[t:more(ksi,eta)]t9(t),[t:not(more(ksi,eta))]t12(t)):moreis(ur,ksi)
+t14:=th1"l.imp"(more(ksi,eta),moreis(ur,eta),[t:more(ksi,eta)]t10(t),[t:not(more(ksi,eta))]t11(t)):moreis(ur,eta)
+-5161
+@[zeta:cut]
++*5161
+zeta@[ksi1:cut][ksi2:cut][m:more(ksi1,ksi2)]
+t15:=satz147(ksi1,ksi2,ksi1,ksi2,m,m):more(ts(ksi1,ksi1),ts(ksi2,ksi2))
+ksi2@sq1:=ts(ksi1,ksi1):cut
+sq2:=ts(ksi2,ksi2):cut
+m@t16:=ec3e21(is(sq1,sq2),more(sq1,sq2),less(sq1,sq2),satz123b(sq1,sq2),t15):nis(sq1,sq2)
+ksi2@[i:is(sq1,zeta)][j:is(sq2,zeta)]
+t17:=tris2(cut,sq1,sq2,zeta,i,j):is(sq1,sq2)
+t18:=[t:more(ksi1,ksi2)]<t17>t16(t):not(more(ksi1,ksi2))
+t19:=[t:less(ksi1,ksi2)]<symis(cut,sq1,sq2,t17)>t16(ksi2,ksi1,satz122(ksi1,ksi2,t)):not(less(ksi1,ksi2))
+t20:=or3e1(is(ksi1,ksi2),more(ksi1,ksi2),less(ksi1,ksi2),satz123a(ksi1,ksi2),t18,t19):is(ksi1,ksi2)
+zeta@t21:=[a:cut][b:cut][t:is(ts(a,a),zeta)][u:is(ts(b,b),zeta)]t20(a,b,t,u):amone(cut,[a:cut]is(ts(a,a),zeta))
+sqrtset:=setof(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta)):set(rat)
+[x0:rat]
+xr:=rpofrt(x0):cut
+[lx:lrt(min(1rp,zeta),x0)]
+t22:=t6(1rp,zeta,x0,lx):less(xr,1rp)
+t23:=t7(1rp,zeta,x0,lx):less(xr,zeta)
+t24:=isless1(xr,ts(xr,1rp),zeta,satz151a(xr),t23):less(ts(xr,1rp),zeta)
+t25:=trless(ts(xr,xr),ts(xr,1rp),zeta,satz148c(xr,xr,xr,1rp,lessisi2(xr,xr,refis(cut,xr)),t22),t24):less(ts(xr,xr),zeta)
+t26:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t25):in(x0,sqrtset)
+x0@[ux:urt(max(1rp,zeta),x0)]
+t27:=t13(1rp,zeta,x0,ux):moreis(xr,1rp)
+t28:=t14(1rp,zeta,x0,ux):moreis(xr,zeta)
+t29:=ismoreis1(xr,ts(xr,1rp),zeta,satz151a(xr),t28):moreis(ts(xr,1rp),zeta)
+t30:=trmoreis(ts(xr,xr),ts(xr,1rp),zeta,satz149(xr,xr,xr,1rp,moreisi2(xr,xr,refis(cut,xr)),t27),t29):moreis(ts(xr,xr),zeta)
+t31:=satz123c(ts(xr,xr),zeta,t30):not(less(ts(xr,xr),zeta))
+t32:=th3"l.imp"(in(x0,sqrtset),less(ts(xr,xr),zeta),t31,[t:in(x0,sqrtset)]estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t)):not(in(x0,sqrtset))
+x0@[i:in(x0,sqrtset)][y0:rat]
+yr:=rpofrt(y0):cut
+[l:less"rt"(y0,x0)]
+i@t33:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,i):less(ts(xr,xr),zeta)
+l@t34:=satz154c(y0,x0,l):less(yr,xr)
+t35:=trless(ts(yr,yr),ts(xr,xr),zeta,satz147a(yr,xr,yr,xr,t34,t34),t33):less(ts(yr,yr),zeta)
+t36:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),y0,t35):in(y0,sqrtset)
+i@t37:=satz122(ts(xr,xr),zeta,t33):more(zeta,ts(xr,xr))
+nm:=mn(zeta,ts(xr,xr),t37):cut
+dn:=pl(xr,pl(xr,1rp)):cut
+fr:=ov(nm,dn):cut
+[z0:rat]
+zr:=rpofrt(z0):cut
+[lz:lrt(min(1rp,fr),z0)]
+t38:=t6(1rp,fr,z0,lz):less(zr,1rp)
+t39:=t7(1rp,fr,z0,lz):less(zr,fr)
+t40:=satz94(x0,z0):more"rt"(pl"rt"(x0,z0),x0)
+t41:=tris(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),ts(pl(xr,zr),pl(xr,zr)),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ists12(rpofrt(pl"rt"(x0,z0)),pl(xr,zr),rpofrt(pl"rt"(x0,z0)),pl(xr,zr),satz155a(x0,z0),satz155a(x0,z0)),disttp2(pl(xr,zr),xr,zr)):is(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)))
+t42:=symis(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),t41):is(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))))
+t43:=lessisi2(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),tris(cut,ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(zr,xr)),pl(ts(xr,xr),ts(xr,zr)),disttp1(xr,zr,xr),ispl2(ts(zr,xr),ts(xr,zr),ts(xr,xr),comts(zr,xr)))):lessis(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)))
+t44:=satz145c(pl(xr,zr),pl(xr,1rp),zr,satz138c(xr,xr,zr,1rp,lessisi2(xr,xr,refis(cut,xr)),t38)):less(ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr))
+t45:=satz138c(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr),t43,t44):less(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)))
+t46:=tris(cut,pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),pl(ts(xr,zr),ts(pl(xr,1rp),zr))),pl(ts(xr,xr),ts(dn,zr)),asspl1(ts(xr,xr),ts(xr,zr),ts(pl(xr,1rp),zr)),ispl2(pl(ts(xr,zr),ts(pl(xr,1rp),zr)),ts(dn,zr),ts(xr,xr),distpt1(xr,pl(xr,1rp),zr))):is(pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)))
+t47:=isless12(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)),t42,t46,t45):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)))
+t48:=isless2(ts(dn,fr),nm,ts(dn,zr),satz153c(nm,dn),satz148c(dn,dn,zr,fr,lessisi2(dn,dn,refis(cut,dn)),t39)):less(ts(dn,zr),nm)
+t49:=satz138c(ts(xr,xr),ts(xr,xr),ts(dn,zr),nm,lessisi2(ts(xr,xr),ts(xr,xr),refis(cut,ts(xr,xr))),t48):less(pl(ts(xr,xr),ts(dn,zr)),pl(ts(xr,xr),nm))
+t50:=isless2(pl(ts(xr,xr),nm),zeta,pl(ts(xr,xr),ts(dn,zr)),satz140c(zeta,ts(xr,xr),t37),t49):less(pl(ts(xr,xr),ts(dn,zr)),zeta)
+t51:=trless(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)),zeta,t47,t50):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),zeta)
+t52:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),pl"rt"(x0,z0),t51):in(pl"rt"(x0,z0),sqrtset)
+t53:=andi(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0),t52,t40):and(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0))
+t54:=somei(rat,[y:rat]and(in(y,sqrtset),more"rt"(y,x0)),pl"rt"(x0,z0),t53):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
+i@t55:=cutapp1a(min(1rp,fr),some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0))),[x:rat][t:lrt(min(1rp,fr),x)]t54(x,t)):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
+x0@[lx:lrt(min(1rp,zeta),x0)][y0:rat][uy:urt(max(1rp,zeta),y0)]
+t56:=cut2(sqrtset,x0,t26(lx),y0,t32(y0,uy),[x:rat][t:in(x,sqrtset)][y:rat][u:less"rt"(y,x)]t36(x,t,y,u),[x:rat][t:in(x,sqrtset)]t55(x,t)):cutprop(sqrtset)
+lx@t57:=cutapp1b(max(1rp,zeta),cutprop(sqrtset),[y:rat][t:urt(max(1rp,zeta),y)]t56(y,t)):cutprop(sqrtset)
+zeta@t58:=cutapp1a(min(1rp,zeta),cutprop(sqrtset),[x:rat][t:lrt(min(1rp,zeta),x)]t57(x,t)):cutprop(sqrtset)
+rtc:=cutof(sqrtset,t58):cut
+@[x0:rat][y0:rat][l:lessis"rt"(x0,y0)]
+t59:=th9"l.or"(less"rt"(x0,y0),is"rt"(x0,y0),less(rpofrt(x0),rpofrt(y0)),is(rpofrt(x0),rpofrt(y0)),l,[t:less"rt"(x0,y0)]satz154c(x0,y0,t),[t:is"rt"(x0,y0)]satz154b(x0,y0,t)):lessis(rpofrt(x0),rpofrt(y0))
+y0@[m:moreis"rt"(x0,y0)]
+t60:=satz125(rpofrt(y0),rpofrt(x0),t59(y0,x0,satz84(x0,y0,m))):moreis(rpofrt(x0),rpofrt(y0))
+zeta@[m:more(ts(rtc,rtc),zeta)]
+t61:=satz121(ts(rtc,rtc),zeta,m):less(zeta,ts(rtc,rtc))
+[z1:rat]
+zr1:=rpofrt(z1):cut
+[l1:less(zeta,zr1)][l2:less(zr1,ts(rtc,rtc))]
+t62:=satz158c(ts(rtc,rtc),z1,l2):lrt(ts(rtc,rtc),z1)
+[x1:rat]
+xr1:=rpofrt(x1):cut
+[lx1:lrt(rtc,x1)][x2:rat]
+xr2:=rpofrt(x2):cut
+[lx2:lrt(rtc,x2)][i:is"rt"(z1,ts"rt"(x1,x2))]
+xm:=ite(more"rt"(x1,x2),rat,x1,x2):rat
+xrm:=rpofrt(xm):cut
+[o:more"rt"(x1,x2)]
+t63:=symis(rat,xm,x1,itet(more"rt"(x1,x2),rat,x1,x2,o)):is"rt"(x1,xm)
+t64:=isp(rat,[x:rat]lrt(rtc,x),x1,xm,lx1,t63):lrt(rtc,xm)
+t65:=lessisi2"rt"(x1,xm,t63):lessis"rt"(x1,xm)
+t66:=lessisi1"rt"(x2,xm,satz87b(x2,x1,xm,satz82(x1,x2,o),t65)):lessis"rt"(x2,xm)
+i@[n:not(more"rt"(x1,x2))]
+t67:=symis(rat,xm,x2,itef(more"rt"(x1,x2),rat,x1,x2,n)):is"rt"(x2,xm)
+t68:=isp(rat,[x:rat]lrt(rtc,x),x2,xm,lx2,t67):lrt(rtc,xm)
+t69:=lessisi2"rt"(x2,xm,t67):lessis"rt"(x2,xm)
+t70:=satz88(x1,x2,xm,satz81e(x1,x2,n),t69):lessis"rt"(x1,xm)
+i@t71:=th1"l.imp"(more"rt"(x1,x2),lrt(rtc,xm),[t:more"rt"(x1,x2)]t64(t),[t:not(more"rt"(x1,x2))]t68(t)):lrt(rtc,xm)
+t72:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x1,xm),[t:more"rt"(x1,x2)]t65(t),[t:not(more"rt"(x1,x2))]t70(t)):lessis"rt"(x1,xm)
+t73:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x2,xm),[t:more"rt"(x1,x2)]t66(t),[t:not(more"rt"(x1,x2))]t69(t)):lessis"rt"(x2,xm)
+t74:=ini(sqrtset,t58,xm,t71):in(xm,sqrtset)
+t75:=t59(x1,xm,t72):lessis(xr1,xrm)
+t76:=t59(x2,xm,t73):lessis(xr2,xrm)
+t77:=tris(cut,zr1,rpofrt(ts"rt"(x1,x2)),ts(xr1,xr2),satz154b(z1,ts"rt"(x1,x2),i),satz155c(x1,x2)):is(zr1,ts(xr1,xr2))
+t78:=islessis1(ts(xr1,xr2),zr1,ts(xrm,xrm),symis(cut,zr1,ts(xr1,xr2),t77),satz149a(xr1,xrm,xr2,xrm,t75,t76)):lessis(zr1,ts(xrm,xrm))
+t79:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),xm,t74):less(ts(xrm,xrm),zeta)
+t80:=satz127a(zr1,ts(xrm,xrm),zeta,t78,t79):less(zr1,zeta)
+t81:=<t80>ec3e23(is(zr1,zeta),more(zr1,zeta),less(zr1,zeta),satz123b(zr1,zeta),satz122(zeta,zr1,l1)):con
+t82:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t81(x,t,y,u,v)):con
+l2@t82a:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t82(x,t,y,u,v)):con
+m@t83:=satz159app(zeta,ts(rtc,rtc),t61,con,[x:rat][t:less(zeta,rpofrt(x))][u:less(rpofrt(x),ts(rtc,rtc))]t82a(x,t,u)):con
+zeta@[l:less(ts(rtc,rtc),zeta)][z2:rat]
+zr2:=rpofrt(z2):cut
+[l3:less(ts(rtc,rtc),zr2)][l4:less(zr2,zeta)]
+t84:=satz122(ts(rtc,rtc),zr2,l3):more(zr2,ts(rtc,rtc))
+[y1:rat]
+yr1:=rpofrt(y1):cut
+[m1:more(yr1,rtc)][y2:rat]
+yr2:=rpofrt(y2):cut
+[m2:more(yr2,rtc)][i:is"rt"(ts"rt"(y1,y2),z2)]
+ym:=ite(less"rt"(y1,y2),rat,y1,y2):rat
+yrm:=rpofrt(ym):cut
+[k:less"rt"(y1,y2)]
+t85:=symis(rat,ym,y1,itet(less"rt"(y1,y2),rat,y1,y2,k)):is"rt"(y1,ym)
+t86:=satz154b(y1,ym,t85):is(yr1,yrm)
+t87:=ismore1(yr1,yrm,rtc,t86,m1):more(yrm,rtc)
+t88:=moreisi2(yr1,yrm,t86):moreis(yr1,yrm)
+t89:=moreisi1(yr2,yrm,satz127d(yr2,yr1,yrm,satz122(yr1,yr2,satz154c(y1,y2,k)),t88)):moreis(yr2,yrm)
+i@[n:not(less"rt"(y1,y2))]
+t90:=symis(rat,ym,y2,itef(less"rt"(y1,y2),rat,y1,y2,n)):is"rt"(y2,ym)
+t91:=satz154b(y2,ym,t90):is(yr2,yrm)
+t92:=ismore1(yr2,yrm,rtc,t91,m2):more(yrm,rtc)
+t93:=moreisi2(yr2,yrm,t91):moreis(yr2,yrm)
+t94:=trmoreis(yr1,yr2,yrm,t60(y1,y2,satz81f(y1,y2,n)),t93):moreis(yr1,yrm)
+i@t95:=th1"l.imp"(less"rt"(y1,y2),more(yrm,rtc),[t:less"rt"(y1,y2)]t87(t),[t:not(less"rt"(y1,y2))]t92(t)):more(yrm,rtc)
+t96:=th1"l.imp"(less"rt"(y1,y2),moreis(yr1,yrm),[t:less"rt"(y1,y2)]t88(t),[t:not(less"rt"(y1,y2))]t94(t)):moreis(yr1,yrm)
+t97:=th1"l.imp"(less"rt"(y1,y2),moreis(yr2,yrm),[t:less"rt"(y1,y2)]t89(t),[t:not(less"rt"(y1,y2))]t93(t)):moreis(yr2,yrm)
+t98:=satz158d(rtc,ym,moreisi1(yrm,rtc,t95)):urt(rtc,ym)
+t99:=th3"l.imp"(in(ym,sqrtset),lrt(rtc,ym),t98,[t:in(ym,sqrtset)]ine(sqrtset,t58,ym,t)):not(in(ym,sqrtset))
+t100:=th3"l.imp"(less(ts(yrm,yrm),zeta),in(ym,sqrtset),t99,[t:less(ts(yrm,yrm),zeta)]estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),ym,t)):not(less(ts(yrm,yrm),zeta))
+t101:=satz123f(ts(yrm,yrm),zeta,t100):moreis(ts(yrm,yrm),zeta)
+t101a:=satz149(yr1,yrm,yr2,yrm,t96,t97):moreis(ts(yr1,yr2),ts(yrm,yrm))
+t102:=ismoreis1(ts(yr1,yr2),zr2,ts(yrm,yrm),tris(cut,ts(yr1,yr2),rpofrt(ts"rt"(y1,y2)),zr2,symis(cut,rpofrt(ts"rt"(y1,y2)),ts(yr1,yr2),satz155c(y1,y2)),satz154b(ts"rt"(y1,y2),z2,i)),t101a):moreis(zr2,ts(yrm,yrm))
+t103:=trmoreis(zr2,ts(yrm,yrm),zeta,t102,t101):moreis(zr2,zeta)
+t104:=<l4>satz123c(zr2,zeta,t103):con
+l4@t105:=satz160app(rtc,rtc,z2,t84,con,[x:rat][t:more(rpofrt(x),rtc)][y:rat][u:more(rpofrt(y),rtc)][v:is"rt"(ts"rt"(x,y),z2)]t104(x,t,y,u,v)):con
+l@t106:=satz159app(ts(rtc,rtc),zeta,l,con,[x:rat][t:less(ts(rtc,rtc),rpofrt(x))][u:less(rpofrt(x),zeta)]t105(x,t,u)):con
+zeta@t107:=or3e1(is(ts(rtc,rtc),zeta),more(ts(rtc,rtc),zeta),less(ts(rtc,rtc),zeta),satz123a(ts(rtc,rtc),zeta),[t:more(ts(rtc,rtc),zeta)]t83(t),[t:less(ts(rtc,rtc),zeta)]t106(t)):is(ts(rtc,rtc),zeta)
+t108:=somei(cut,[a:cut]is(ts(a,a),zeta),rtc,t107):some([a:cut]is(ts(a,a),zeta))
+-5161
+zeta@satz161:=onei(cut,[a:cut]is(ts(a,a),zeta),t21".5161",t108".5161"):one([a:cut]is(ts(a,a),zeta))
+@[ksi:cut]
+irratrp:=not(ratrp(ksi)):'prop'
+-rp
+-rt
++5162
+@[v:nat]
+t1:=tris(nat,pl(v,v),pl(ts(1,v),v),ts(<1>suc,v),ispl1(v,ts(1,v),v,satz28g(v)),satz28h(1,v)):is(pl(v,v),ts(<1>suc,v))
+t2:=isless2(pl(v,v),ts(<1>suc,v),v,t1,satz18a(v,v)):less(v,ts(<1>suc,v))
+[w:nat][l:less(ts(v,v),ts(w,w))]
+t3:=satz10j(v,w,th3"l.imp"(moreis(v,w),moreis(ts(v,v),ts(w,w)),satz10h(ts(v,v),ts(w,w),l),[t:moreis(v,w)]satz36(v,w,v,w,t,t))):less(v,w)
+w@t4:=tris(nat,ts(pl(v,w),v),pl(ts(v,v),ts(w,v)),pl(ts(v,v),ts(v,w)),disttp1(v,w,v),ispl2(ts(w,v),ts(v,w),ts(v,v),comts(w,v))):is(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)))
+t5:=tr3is(nat,ts(pl(v,w),pl(v,w)),pl(ts(pl(v,w),v),ts(pl(v,w),w)),pl(pl(ts(v,v),ts(v,w)),pl(ts(v,w),ts(w,w))),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),disttp2(pl(v,w),v,w),ispl12(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)),ts(pl(v,w),w),pl(ts(v,w),ts(w,w)),t4,disttp1(v,w,w)),asspl2(pl(ts(v,v),ts(v,w)),ts(v,w),ts(w,w))):is(ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)))
+t6:=tris(nat,pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),pl(ts(v,w),ts(v,w))),pl(ts(v,v),ts(<1>suc,ts(v,w))),asspl1(ts(v,v),ts(v,w),ts(v,w)),ispl2(pl(ts(v,w),ts(v,w)),ts(<1>suc,ts(v,w)),ts(v,v),t1(ts(v,w)))):is(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))))
+nun:=tris(nat,ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),t5,ispl1(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w),t6)):is(ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)))
+nun1:=symis(nat,ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),nun):is(pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),ts(pl(v,w),pl(v,w)))
+prop1:=eq(tf(fr(w,v),fr(w,v)),fr(<1>suc,1)):'prop'
+v@prop2:=some([t:nat]prop1(t)):'prop'
+@prop3:=some([u:nat]prop2(u)):'prop'
+[p:prop3]
+y:=ind(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):nat
+t7:=oneax(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):min([u:nat]prop2(u),y)
+t8:=ande1(lb([u:nat]prop2(u),y),prop2(y),t7):lb([u:nat]prop2(u),y)
+t9:=ande2(lb([u:nat]prop2(u),y),prop2(y),t7):prop2(y)
+[x:nat][q:prop1(y,x)]
+t10:=treq1(fr(<1>suc,1),fr(ts(x,x),ts(y,y)),tf(fr(x,y),fr(x,y)),q,tfeq12a(x,y,x,y)):eq(fr(<1>suc,1),fr(ts(x,x),ts(y,y)))
+t11:=tr4is(nat,ts(<1>suc,ts(y,y)),ts(num(fr(<1>suc,1)),den(fr(ts(x,x),ts(y,y)))),ts(num(fr(ts(x,x),ts(y,y))),den(fr(<1>suc,1))),ts(ts(x,x),1),ts(x,x),12isnd(<1>suc,1,ts(x,x),ts(y,y)),t10,ndis12(ts(x,x),ts(y,y),<1>suc,1),satz28a(ts(x,x))):is(ts(<1>suc,ts(y,y)),ts(x,x))
+t12:=isless2(ts(<1>suc,ts(y,y)),ts(x,x),ts(y,y),t11,t2(ts(y,y))):less(ts(y,y),ts(x,x))
+t13:=isless1(ts(ts(<1>suc,y),y),ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)),tris(nat,ts(ts(<1>suc,y),y),ts(<1>suc,ts(y,y)),ts(x,x),assts1(<1>suc,y,y),t11),satz35c(ts(<1>suc,y),ts(<1>suc,y),y,ts(<1>suc,y),lessisi2(ts(<1>suc,y),ts(<1>suc,y),refis(nat,ts(<1>suc,y))),t2(y))):less(ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)))
+t14:=t3(y,x,t12):less(y,x)
+t15:=t3(x,ts(<1>suc,y),t13):less(x,ts(<1>suc,y))
+[u:nat][i:is(x,pl(y,u))]
+t16:=isless12(x,pl(y,u),ts(<1>suc,y),pl(y,y),i,symis(nat,pl(y,y),ts(<1>suc,y),t1(y)),t15):less(pl(y,u),pl(y,y))
+t17:=satz20f(u,y,y,t16):less(u,y)
+[t:nat][j:is(y,pl(u,t))]
+t18:=symis(nat,y,pl(u,t),j):is(pl(u,t),y)
+t19:=tris(nat,ts(x,x),ts(pl(y,u),pl(y,u)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ists12(x,pl(y,u),x,pl(y,u),i,i),nun(y,u)):is(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)))
+t20:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),ispl1(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t),t19),asspl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u),ts(t,t))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))))
+t21:=tr3is(nat,ts(y,u),ts(u,y),ts(u,pl(u,t)),pl(ts(u,u),ts(u,t)),comts(y,u),ists2(y,pl(u,t),u,j),disttp2(u,u,t)):is(ts(y,u),pl(ts(u,u),ts(u,t)))
+t22:=tris(nat,ts(<1>suc,ts(y,u)),ts(<1>suc,pl(ts(u,u),ts(u,t))),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ists2(ts(y,u),pl(ts(u,u),ts(u,t)),<1>suc,t21),disttp2(<1>suc,ts(u,u),ts(u,t))):is(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))))
+t23:=tris(nat,pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(y,y),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),ispl2(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ts(y,y),t22),asspl2(ts(y,y),ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))):is(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))))
+t24:=tr3is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),pl(pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),t20,ispl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t)),t23),asspl1(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))))
+t25:=tr4is(nat,pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),pl(pl(ts(<1>suc,ts(u,t)),ts(u,u)),ts(t,t)),pl(pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t)),ts(pl(u,t),pl(u,t)),ts(y,y),asspl2(ts(<1>suc,ts(u,t)),ts(u,u),ts(t,t)),ispl1(pl(ts(<1>suc,ts(u,t)),ts(u,u)),pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t),compl(ts(<1>suc,ts(u,t)),ts(u,u))),nun1(u,t),ists12(pl(u,t),y,pl(u,t),y,t18,t18)):is(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y))
+t26:=tr4is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),pl(ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u)))),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),t24,ispl2(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u))),t25),compl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),asspl2(ts(y,y),ts(y,y),ts(<1>suc,ts(u,u)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))))
+t27:=tris(nat,pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(y,y)),ts(x,x),t1(ts(y,y)),t11):is(pl(ts(y,y),ts(y,y)),ts(x,x))
+t28:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),pl(ts(x,x),ts(<1>suc,ts(u,u))),t26,ispl1(pl(ts(y,y),ts(y,y)),ts(x,x),ts(<1>suc,ts(u,u)),t27)):is(pl(ts(x,x),ts(t,t)),pl(ts(x,x),ts(<1>suc,ts(u,u))))
+t29:=satz20e(ts(t,t),ts(<1>suc,ts(u,u)),ts(x,x),t28):is(ts(t,t),ts(<1>suc,ts(u,u)))
+t30:=tr4is(nat,ts(num(fr(<1>suc,1)),den(fr(ts(t,t),ts(u,u)))),ts(<1>suc,ts(u,u)),ts(t,t),ts(ts(t,t),1),ts(num(fr(ts(t,t),ts(u,u))),den(fr(<1>suc,1))),ndis12(<1>suc,1,ts(t,t),ts(u,u)),symis(nat,ts(t,t),ts(<1>suc,ts(u,u)),t29),satz28e(ts(t,t)),12isnd(ts(t,t),ts(u,u),<1>suc,1)):eq(fr(<1>suc,1),fr(ts(t,t),ts(u,u)))
+t31:=treq2(tf(fr(t,u),fr(t,u)),fr(<1>suc,1),fr(ts(t,t),ts(u,u)),tfeq12a(t,u,t,u),t30):prop1(u,t)
+t32:=somei(nat,[v:nat]prop1(u,v),t,t31):prop2(u)
+t33:=<t32><u>t8:lessis(y,u)
+t34:=<t33>satz10g(y,u,satz12(u,y,t17)):con
+i@t35:=someapp(nat,[v:nat]diffprop(y,u,v),t17,con,[v:nat][w:diffprop(y,u,v)]t34(v,w)):con
+q@t36:=someapp(nat,[v:nat]diffprop(x,y,v),t14,con,[v:nat][w:diffprop(x,y,v)]t35(v,w)):con
+p@t37:=someapp(nat,[v:nat]prop1(y,v),t9,con,[v:nat][w:prop1(y,v)]t36(v,w)):con
+-5162
++*rt
++5162
+@[x0:rat][i:is(ts(x0,x0),rtofn(<1>suc))][x:frac][xix0:inf(x,class(x0))]
+t38:=ise(ts(x0,x0),rtofn(<1>suc),tf(x,x),fr(<1>suc,1),tict(x0,x0,x,x,xix0,xix0),inclass(fr(<1>suc,1)),i):eq"n"(tf(x,x),fr(<1>suc,1))
+t39:=refeq1(fr(num(x),den(x)),x,fris(x)):eq"n"(fr(num(x),den(x)),x)
+t40:=eqtf12(fr(num(x),den(x)),x,fr(num(x),den(x)),x,t39,t39):eq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x))
+t41:=treq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x),fr(<1>suc,1),t40,t38):prop1"n.5162"(den(x),num(x))
+t42:=somei(nat,[t:nat]prop1"n.5162"(den(x),t),num(x),t41):prop2"n.5162"(den(x))
+t43:=somei(nat,[t:nat]prop2"n.5162"(t),den(x),t42):prop3"n.5162"
+t44:=t37"n.5162"(t43):con
+i@t45:=ratapp1(x0,con,[x:frac][t:inf(x,class(x0))]t44(x,t)):con
+-5162
++*rp
++5162
+@ksi:=ind(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):cut
+t46:=oneax(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):is(ts(ksi,ksi),rpofnt(<1>suc))
+[r:ratrp(ksi)]
+x0:=rtofrp(ksi,r):rat
+t47:=tr3is(cut,rpofrt(ts"rt"(x0,x0)),ts(rpofrt(x0),rpofrt(x0)),ts(ksi,ksi),rpofnt(<1>suc),satz155c(x0,x0),ists12(rpofrt(x0),ksi,rpofrt(x0),ksi,isrprt2(ksi,r),isrprt2(ksi,r)),t46):is(rpofrt(ts"rt"(x0,x0)),rpofnt(<1>suc))
+t48:=isrtirp(ts"rt"(x0,x0),rtofn(<1>suc),t47):is"rt"(ts"rt"(x0,x0),rtofn(<1>suc))
+t49:=t45"rt.5162"(x0,t48):con
+-5162
+@satz162:=somei(cut,[a:cut]irratrp(a),ksi".5162",[t:ratrp(ksi".5162")]t49".5162"(t)):some([a:cut]irratrp(a))
+[zeta:cut]
+sqrt:=ind(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):cut
+thsqrt1:=oneax(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):is(ts(sqrt(zeta),sqrt(zeta)),zeta)
+[ksi:cut][i:is(ts(ksi,ksi),zeta)]
+thsqrt2:=t20".5161"(zeta,ksi,sqrt,i,thsqrt1):is(ksi,sqrt)
+@[ksi:cut][eta:cut][i:is(ksi,eta)]
+issqrt:=isf(cut,cut,[t:cut]sqrt(t),ksi,eta,i):is(sqrt(ksi),sqrt(eta))
+@[ksi:cut][nx:natrp(ksi)][eta:cut][ny:natrp(eta)]
++iiia
+x:=ntofrp(ksi,nx):nat
+y:=ntofrp(eta,ny):nat
+t1:=isrpnt1(ksi,nx):is(ksi,rpofnt(x))
+t2:=isrpnt1(eta,ny):is(eta,rpofnt(y))
+t3:=ispl12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(pl(ksi,eta),pl(rpofnt(x),rpofnt(y)))
+x0:=rtofn(x):rat
+y0:=rtofn(y):rat
+t4:=natrti(x):natrt(x0)
+t5:=natrti(y):natrt(y0)
+t6:=symis(cut,rpofrt(pl"rt"(x0,y0)),pl(rpofnt(x),rpofnt(y)),satz155a(x0,y0)):is(pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)))
+t7:=satz112d(x0,t4,y0,t5):natrt(pl"rt"(x0,y0))
+xpy:=nofrt(pl"rt"(x0,y0),t7):nat
+t8:=isrtn1(pl"rt"(x0,y0),t7):is"rt"(pl"rt"(x0,y0),rtofn(xpy))
+t9:=isrterp(pl"rt"(x0,y0),rtofn(xpy),t8):is(rpofrt(pl"rt"(x0,y0)),rpofnt(xpy))
+t10:=tr3is(cut,pl(ksi,eta),pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)),rpofnt(xpy),t3,t6,t9):is(pl(ksi,eta),rpofnt(xpy))
+-iiia
+natpl:=somei(nat,[t:nat]is(pl(ksi,eta),rpofnt(t)),xpy".iiia",t10".iiia"):natrp(pl(ksi,eta))
++*iiia
+ny@t11:=ists12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(ts(ksi,eta),ts(rpofnt(x),rpofnt(y)))
+t12:=symis(cut,rpofrt(ts"rt"(x0,y0)),ts(rpofnt(x),rpofnt(y)),satz155c(x0,y0)):is(ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)))
+t13:=satz112f(x0,t4,y0,t5):natrt(ts"rt"(x0,y0))
+xty:=nofrt(ts"rt"(x0,y0),t13):nat
+t14:=isrtn1(ts"rt"(x0,y0),t13):is"rt"(ts"rt"(x0,y0),rtofn(xty))
+t15:=isrterp(ts"rt"(x0,y0),rtofn(xty),t14):is(rpofrt(ts"rt"(x0,y0)),rpofnt(xty))
+t16:=tr3is(cut,ts(ksi,eta),ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)),rpofnt(xty),t11,t12,t15):is(ts(ksi,eta),rpofnt(xty))
+-iiia
+ny@natts:=somei(nat,[t:nat]is(ts(ksi,eta),rpofnt(t)),xty".iiia",t16".iiia"):natrp(ts(ksi,eta))
+[m:more(ksi,eta)]
++*iiia
+m@t17:=ismore12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2,m):more(rpofnt(x),rpofnt(y))
+t18:=satz154d(x0,y0,t17):more"rt"(x0,y0)
+t20:=ismn12(ksi,rpofnt(x),eta,rpofnt(y),m,satz154a(x0,y0,t18),t1,t2):is(mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)))
+t21:=symis(cut,rpofrt(mn"rt"(x0,y0,t18)),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),satz155b(x0,y0,t18)):is(mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)))
+t22:=satz112g(x0,t4,y0,t5,t18):natrt(mn"rt"(x0,y0,t18))
+xmy:=nofrt(mn"rt"(x0,y0,t18),t22):nat
+t23:=isrtn1(mn"rt"(x0,y0,t18),t22):is"rt"(mn"rt"(x0,y0,t18),rtofn(xmy))
+t24:=isrterp(mn"rt"(x0,y0,t18),rtofn(xmy),t23):is(rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy))
+t25:=tr3is(cut,mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy),t20,t21,t24):is(mn(ksi,eta,m),rpofnt(xmy))
+-iiia
+m@natmn:=somei(nat,[t:nat]is(mn(ksi,eta,m),rpofnt(t)),xmy".iiia",t25".iiia"):natrp(mn(ksi,eta,m))
+@[p:cut][q:cut][r:cut]
+3pl13:=tr3is(cut,pl(p,pl(q,r)),pl(pl(q,r),p),pl(pl(r,q),p),pl(r,pl(q,p)),compl(p,pl(q,r)),ispl1(pl(q,r),pl(r,q),p,compl(q,r)),asspl1(r,q,p)):is(pl(p,pl(q,r)),pl(r,pl(q,p)))
+[s:cut]
+4pl24:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(s,pl(r,q))),pl(pl(p,s),pl(r,q)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(s,pl(r,q)),p,3pl13(q,r,s)),asspl2(p,s,pl(r,q))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,s),pl(r,q)))
+r@3pl12:=tr3is(cut,pl(p,pl(q,r)),pl(pl(p,q),r),pl(pl(q,p),r),pl(q,pl(p,r)),asspl2(p,q,r),ispl1(pl(p,q),pl(q,p),r,compl(p,q)),asspl1(q,p,r)):is(pl(p,pl(q,r)),pl(q,pl(p,r)))
+s@4pl23:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(r,pl(q,s))),pl(pl(p,r),pl(q,s)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(r,pl(q,s)),p,3pl12(q,r,s)),asspl2(p,r,pl(q,s))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,r),pl(q,s)))
+r@3pl23:=tr3is(cut,pl(pl(p,q),r),pl(p,pl(q,r)),pl(p,pl(r,q)),pl(pl(p,r),q),asspl1(p,q,r),ispl2(pl(q,r),pl(r,q),p,compl(q,r)),asspl2(p,r,q)):is(pl(pl(p,q),r),pl(pl(p,r),q))
+p@a2isapa:=tris(cut,ts(p,pl(1rp,1rp)),pl(ts(p,1rp),ts(p,1rp)),pl(p,p),disttp2(p,1rp,1rp),ispl12(ts(p,1rp),p,ts(p,1rp),p,satz151(p),satz151(p))):is(ts(p,pl(1rp,1rp)),pl(p,p))
+@dif:=pair1type(cut):'type'
+[a1:cut][a2:cut]
+df:=pair1(cut,a1,a2):dif
+@[a:dif]
+stm:=first1(cut,a):cut
+std:=second1(cut,a):cut
+a2@stmis:=first1is1(cut,a1,a2):is(stm(df(a1,a2)),a1)
+isstm:=first1is2(cut,a1,a2):is(a1,stm(df(a1,a2)))
+stdis:=second1is1(cut,a1,a2):is(std(df(a1,a2)),a2)
+isstd:=second1is2(cut,a1,a2):is(a2,std(df(a1,a2)))
+a@1a:=stm(a):cut
+2a:=std(a):cut
+dfis:=pair1is1(cut,a):is"e"(dif,df(1a,2a),a)
+isdf:=pair1is2(cut,a):is"e"(dif,a,df(1a,2a))
+a2@[b1:cut][b2:cut]
+12issmsd:=ispl12(a1,stm(df(a1,a2)),b2,std(df(b1,b2)),isstm(a1,a2),isstd(b1,b2)):is(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))))
+smsdis12:=symis(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),12issmsd):is(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2))
+a@[r1:cut][r2:cut]
+1sdissmsd:=ispl1(r1,stm(df(r1,r2)),2a,isstm(r1,r2)):is(pl(r1,2a),pl(stm(df(r1,r2)),2a))
+smsdis1sd:=symis(cut,pl(r1,2a),pl(stm(df(r1,r2)),2a),1sdissmsd):is(pl(stm(df(r1,r2)),2a),pl(r1,2a))
+sm2issmsd:=ispl2(r2,std(df(r1,r2)),1a,isstd(r1,r2)):is(pl(1a,r2),pl(1a,std(df(r1,r2))))
+smsdissm2:=symis(cut,pl(1a,r2),pl(1a,std(df(r1,r2))),sm2issmsd):is(pl(1a,std(df(r1,r2))),pl(1a,r2))
+a2@[r:cut][i:is(a1,r)]
+issm:=isf(cut,dif,[t:cut]df(t,a2),a1,r,i):is"e"(dif,df(a1,a2),df(r,a2))
+r@[i:is(a2,r)]
+issd:=isf(cut,dif,[t:cut]df(a1,t),a2,r,i):is"e"(dif,df(a1,a2),df(a1,r))
+b2@[i:is(a1,b1)][j:is(a2,b2)]
+issmsd:=tris(dif,df(a1,a2),df(b1,a2),df(b1,b2),issm(a1,a2,b1,i),issd(b1,a2,b2,j)):is"e"(dif,df(a1,a2),df(b1,b2))
+a@[b:dif]
+1b:=stm(b):cut
+2b:=std(b):cut
+eq:=is(pl(1a,2b),pl(1b,2a)):'prop'
+b2@[i:is(pl(a1,b2),pl(b1,a2))]
+eqi12:=tr3is(cut,pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),smsdis12(a1,a2,b1,b2),i,12issmsd(b1,b2,a1,a2)):eq(df(a1,a2),df(b1,b2))
+r2@[i:is(pl(1a,r2),pl(r1,2a))]
+eqi1:=isp(dif,[x:dif]eq(x,df(r1,r2)),df(1a,2a),a,eqi12(1a,2a,r1,r2,i),dfis):eq(a,df(r1,r2))
+r2@[i:is(pl(r1,2a),pl(1a,r2))]
+eqi2:=isp(dif,[x:dif]eq(df(r1,r2),x),df(1a,2a),a,eqi12(r1,r2,1a,2a,i),dfis):eq(df(r1,r2),a)
+b2@[e:eq(df(a1,a2),df(b1,b2))]
+eqe12:=tr3is(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),12issmsd(a1,a2,b1,b2),e,smsdis12(b1,b2,a1,a2)):is(pl(a1,b2),pl(b1,a2))
+a@satzd163:=refis(cut,pl(1a,2a)):eq(a,a)
+refeq:=satzd163:eq(a,a)
+b@[i:is"e"(dif,a,b)]
+refeq1:=isp(dif,[x:dif]eq(a,x),a,b,refeq,i):eq(a,b)
+refeq2:=isp(dif,[x:dif]eq(x,a),a,b,refeq,i):eq(b,a)
+b2@[i:is(a1,b1)][j:is(a2,b2)]
+eqsmsd:=refeq1(df(a1,a2),df(b1,b2),issmsd(i,j)):eq(df(a1,a2),df(b1,b2))
+r@[i:is(a1,r)]
+eqsm:=refeq1(df(a1,a2),df(r,a2),issm(i)):eq(df(a1,a2),df(r,a2))
+r@[i:is(a2,r)]
+eqsd:=refeq1(df(a1,a2),df(a1,r),issd(i)):eq(df(a1,a2),df(a1,r))
+b@[e:eq(a,b)]
+satzd164:=symis(cut,pl(1a,2b),pl(1b,2a),e):eq(b,a)
+symeq:=satzd164:eq(b,a)
+b@[c:dif]
+1c:=stm(c):cut
+2c:=std(c):cut
+[e:eq(a,b)][f:eq(b,c)]
++1d165
+t1:=ispl12(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),e,f):is(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
+t2:=tr4is(cut,pl(pl(1a,2c),pl(1b,2b)),pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2b),pl(1b,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2c,1b,2b),t1,compl(pl(1b,2a),pl(1c,2b)),4pl24(1c,2b,1b,2a)):is(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
+-1d165
+satzd165:=satz136b(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".1d165"):eq(a,c)
+treq:=satzd165:eq(a,c)
+c@[e:eq(c,a)][f:eq(c,b)]
+treq1:=treq(a,c,b,symeq(c,a,e),f):eq(a,b)
+c@[e:eq(a,c)][f:eq(b,c)]
+treq2:=treq(a,c,b,e,symeq(b,c,f)):eq(a,b)
+c@[d:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)]
+tr3eq:=treq(a,b,d,e1,treq(b,c,d,e2,e3)):eq(a,d)
+d@[e:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)][e4:eq(d,e)]
+tr4eq:=tr3eq(a,b,c,e,e1,e2,treq(c,d,e,e3,e4)):eq(a,e)
+a@posd:=more(1a,2a):'prop'
+zero:=is(1a,2a):'prop'
+negd:=less(1a,2a):'prop'
+a2@[m:more(a1,a2)]
+posdi:=ismore12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),m):posd(df(a1,a2))
+a2@[i:is(a1,a2)]
+zeroi:=tr3is(cut,stm(df(a1,a2)),a1,a2,std(df(a1,a2)),stmis(a1,a2),i,isstd(a1,a2)):zero(df(a1,a2))
+a2@[l:less(a1,a2)]
+negdi:=isless12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),l):negd(df(a1,a2))
+a@axrde:=satz123b(1a,2a):ec3(zero(a),posd(a),negd(a))
+axrdo:=satz123a(1a,2a):or3(zero(a),posd(a),negd(a))
+axrd:=orec3i(zero(a),posd(a),negd(a),axrdo,axrde):orec3(zero(a),posd(a),negd(a))
+[p:'prop'][p1:[t:posd(a)]p][p2:[t:zero(a)]p][p3:[t:negd(a)]p]
+rappd:=or3app(zero(a),posd(a),negd(a),p,axrdo,p2,p1,p3):p
+a@[p:posd(a)]
+pnot0d:=ec3e21(zero(a),posd(a),negd(a),axrde,p):not(zero(a))
+pnotnd:=ec3e23(zero(a),posd(a),negd(a),axrde,p):not(negd(a))
+a@[z:zero(a)]
+0notpd:=ec3e12(zero(a),posd(a),negd(a),axrde,z):not(posd(a))
+0notnd:=ec3e13(zero(a),posd(a),negd(a),axrde,z):not(negd(a))
+a@[n:negd(a)]
+nnotpd:=ec3e32(zero(a),posd(a),negd(a),axrde,n):not(posd(a))
+nnot0d:=ec3e31(zero(a),posd(a),negd(a),axrde,n):not(zero(a))
+b@[e:eq(a,b)][p:posd(a)]
++iv1d
+t1:=ismore12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135a(1a,2a,2b,p)):more(pl(1b,2a),pl(2b,2a))
+-iv1d
+eqposd:=satz136a(1b,2b,2a,t1".iv1d"):posd(b)
+e@[z:zero(a)]
++*iv1d
+z@t2:=tr3is(cut,pl(1b,2a),pl(1a,2b),pl(2a,2b),pl(2b,2a),symeq(a,b,e),ispl1(1a,2a,2b,z),compl(2a,2b)):is(pl(1b,2a),pl(2b,2a))
+-iv1d
+z@eqzero:=satz136b(1b,2b,2a,t2".iv1d"):zero(b)
+e@[n:negd(a)]
++*iv1d
+n@t3:=isless12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135c(1a,2a,2b,n)):less(pl(1b,2a),pl(2b,2a))
+-iv1d
+n@eqnegd:=satz136c(1b,2b,2a,t3".iv1d"):negd(b)
+b@[z:zero(a)][y:zero(b)]
+zeroeq:=tris(cut,pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl12(1a,2a,2b,1b,z,symis(cut,1b,2b,y)),compl(2a,1b)):eq(a,b)
+@[r:cut]
+pdofrp:=df(pl(r,1rp),1rp):dif
+ndofrp:=df(1rp,pl(r,1rp)):dif
+[s:cut][i:is(r,s)]
+isrpepd:=refeq1(pdofrp(r),pdofrp(s),isf(cut,dif,[x:cut]pdofrp(x),r,s,i)):eq(pdofrp(r),pdofrp(s))
+isrpend:=refeq1(ndofrp(r),ndofrp(s),isf(cut,dif,[x:cut]ndofrp(x),r,s,i)):eq(ndofrp(r),ndofrp(s))
+s@[e:eq(pdofrp(r),pdofrp(s))]
++*iv1d
+e@t4:=satz136b(pl(r,1rp),pl(s,1rp),1rp,eqe12(pl(r,1rp),1rp,pl(s,1rp),1rp,e)):is(pl(r,1rp),pl(s,1rp))
+-iv1d
+e@isrpipd:=satz136b(r,s,1rp,t4".iv1d"):is(r,s)
+s@[e:eq(ndofrp(r),ndofrp(s))]
++*iv1d
+e@t5:=satz136e(pl(s,1rp),pl(r,1rp),1rp,eqe12(1rp,pl(r,1rp),1rp,pl(s,1rp),e)):is(pl(s,1rp),pl(r,1rp))
+-iv1d
+e@isrpind:=symis(cut,s,r,satz136b(s,r,1rp,t5".iv1d")):is(r,s)
+r@posdirp:=posdi(pl(r,1rp),1rp,ismore1(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133(1rp,r))):posd(pdofrp(r))
+negdirp:=negdi(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):negd(ndofrp(r))
+a@[p:posd(a)]
+rpofpd:=mn(1a,2a,p):cut
++*iv1d
+p@t6:=tr4is(cut,pl(1a,1rp),pl(pl(rpofpd,2a),1rp),pl(rpofpd,pl(2a,1rp)),pl(rpofpd,pl(1rp,2a)),pl(pl(rpofpd,1rp),2a),ispl1(1a,pl(rpofpd,2a),1rp,satz140f(1a,2a,p)),asspl1(rpofpd,2a,1rp),ispl2(pl(2a,1rp),pl(1rp,2a),rpofpd,compl(2a,1rp)),asspl2(rpofpd,1rp,2a)):is(pl(1a,1rp),pl(pl(rpofpd,1rp),2a))
+-iv1d
+p@eqpdrp1:=eqi1(a,pl(rpofpd,1rp),1rp,t6".iv1d"):eq(a,pdofrp(rpofpd(a,p)))
+eqpdrp2:=symeq(a,pdofrp(rpofpd(a,p)),eqpdrp1):eq(pdofrp(rpofpd(a,p)),a)
+a@[n:negd(a)]
+rpofnd:=mn(2a,1a,satz122(1a,2a,n)):cut
++*iv1d
+n@t7:=tr3is(cut,pl(1a,pl(rpofnd,1rp)),pl(pl(1a,rpofnd),1rp),pl(2a,1rp),pl(1rp,2a),asspl2(1a,rpofnd,1rp),ispl1(pl(1a,rpofnd),2a,1rp,satz140c(2a,1a,satz122(1a,2a,n))),compl(2a,1rp)):is(pl(1a,pl(rpofnd,1rp)),pl(1rp,2a))
+-iv1d
+n@eqndrp1:=eqi1(a,1rp,pl(rpofnd,1rp),t7".iv1d"):eq(a,ndofrp(rpofnd(a,n)))
+eqndrp2:=symeq(a,ndofrp(rpofnd(a,n)),eqndrp1):eq(ndofrp(rpofnd(a,n)),a)
+@[h:dif][p:posd(h)][k:dif][q:posd(k)][e:eq(h,k)]
++*iv1d
+e@t8:=tr3eq(pdofrp(rpofpd(h,p)),h,k,pdofrp(rpofpd(k,q)),eqpdrp2(h,p),e,eqpdrp1(k,q)):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
+-iv1d
+e@eqpderp:=isrpipd(rpofpd(h,p),rpofpd(k,q),t8".iv1d"):is(rpofpd(h,p),rpofpd(k,q))
+q@[i:is(rpofpd(h,p),rpofpd(k,q))]
++*iv1d
+i@t9:=isrpepd(rpofpd(h,p),rpofpd(k,q),i):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
+-iv1d
+i@eqpdirp:=tr3eq(h,pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)),k,eqpdrp1(h,p),t9".iv1d",eqpdrp2(k,q)):eq(h,k)
+h@[n:negd(h)][k:dif][o:negd(k)][e:eq(h,k)]
++*iv1d
+e@t10:=tr3eq(ndofrp(rpofnd(h,n)),h,k,ndofrp(rpofnd(k,o)),eqndrp2(h,n),e,eqndrp1(k,o)):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
+-iv1d
+e@eqnderp:=isrpind(rpofnd(h,n),rpofnd(k,o),t10".iv1d"):is(rpofnd(h,n),rpofnd(k,o))
+o@[i:is(rpofnd(h,n),rpofnd(k,o))]
++*iv1d
+i@t11:=isrpend(rpofnd(h,n),rpofnd(k,o),i):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
+-iv1d
+i@eqndirp:=tr3eq(h,ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)),k,eqndrp1(h,n),t11".iv1d",eqndrp2(k,o)):eq(h,k)
+@[r:cut]
++*iv1d
+r@t12:=eqpdrp1(pdofrp(r),posdirp(r)):eq(pdofrp(r),pdofrp(rpofpd(pdofrp(r),posdirp(r))))
+-iv1d
+r@isrppd1:=isrpipd(r,rpofpd(pdofrp(r),posdirp(r)),t12".iv1d"):is(r,rpofpd(pdofrp(r),posdirp(r)))
+isrppd2:=symis(cut,r,rpofpd(pdofrp(r),posdirp(r)),isrppd1):is(rpofpd(pdofrp(r),posdirp(r)),r)
++*iv1d
+r@t13:=eqndrp1(ndofrp(r),negdirp(r)):eq(ndofrp(r),ndofrp(rpofnd(ndofrp(r),negdirp(r))))
+-iv1d
+r@isrpnd1:=isrpind(r,rpofnd(ndofrp(r),negdirp(r)),t13".iv1d"):is(r,rpofnd(ndofrp(r),negdirp(r)))
+isrpnd2:=symis(cut,r,rpofnd(ndofrp(r),negdirp(r)),isrpnd1):is(rpofnd(ndofrp(r),negdirp(r)),r)
+a2@[r:cut]
+lemmad1:=eqi12(a1,a2,pl(a1,r),pl(a2,r),tris(cut,pl(a1,pl(a2,r)),pl(a1,pl(r,a2)),pl(pl(a1,r),a2),ispl2(pl(a2,r),pl(r,a2),a1,compl(a2,r)),asspl2(a1,r,a2))):eq(df(a1,a2),df(pl(a1,r),pl(a2,r)))
+lemmad2:=symeq(df(a1,a2),df(pl(a1,r),pl(a2,r)),lemmad1):eq(df(pl(a1,r),pl(a2,r)),df(a1,a2))
+a@[r:cut]
+lemmad3:=treq(a,df(1a,2a),df(pl(1a,r),pl(2a,r)),refeq1(a,df(1a,2a),isdf),lemmad1(1a,2a,r)):eq(a,df(pl(1a,r),pl(2a,r)))
+lemmad4:=symeq(a,df(pl(1a,r),pl(2a,r)),lemmad3):eq(df(pl(1a,r),pl(2a,r)),a)
+a@absd:=ite(negd(a),dif,df(2a,1a),a):dif
+[n:negd(a)]
+absnd:=refeq1(absd(a),df(2a,1a),itet(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),df(2a,1a))
+a@[n:not(negd(a))]
+absnnd:=refeq1(absd(a),a,itef(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),a)
+a2@[l:less(a1,a2)]
+absdeql:=treq(absd(df(a1,a2)),df(std(df(a1,a2)),stm(df(a1,a2))),df(a2,a1),absnd(df(a1,a2),negdi(a1,a2,l)),eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2))):eq(absd(df(a1,a2)),df(a2,a1))
+a2@[m:moreis(a1,a2)]
+absdeqm:=absnnd(df(a1,a2),th3"l.imp"(negd(df(a1,a2)),less(a1,a2),satz123c(a1,a2,m),[t:negd(df(a1,a2))]isless12(stm(df(a1,a2)),a1,std(df(a1,a2)),a2,stmis(a1,a2),stdis(a1,a2),t))):eq(absd(df(a1,a2)),df(a1,a2))
+b@[e:eq(a,b)]
++iv2d
+[n:negd(a)]
+t1:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
+t2:=tr3eq(absd(a),df(2a,1a),df(2b,1b),absd(b),absnd(a,n),eqi12(2a,1a,2b,1b,t1),symeq(absd(b),df(2b,1b),absnd(b,eqnegd(a,b,e,n)))):eq(absd(a),absd(b))
+e@[n:not(negd(a))]
+t3:=tr3eq(absd(a),a,b,absd(b),absnnd(a,n),e,symeq(absd(b),b,absnnd(b,th3"l.imp"(negd(b),negd(a),n,[t:negd(b)]eqnegd(b,a,symeq(a,b,e),t))))):eq(absd(a),absd(b))
+-iv2d
+eqabsd:=th1"l.imp"(negd(a),eq(absd(a),absd(b)),[t:negd(a)]t2".iv2d"(t),[t:not(negd(a))]t3".iv2d"(t)):eq(absd(a),absd(b))
+a@[p:posd(a)]
+satzd166a:=eqposd(a,absd(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p))),p):posd(absd(a))
+a@[n:negd(a)]
++2d166
+t1:=posdi(2a,1a,satz122(1a,2a,n)):posd(df(2a,1a))
+-2d166
+satzd166b:=eqposd(df(2a,1a),absd(a),symeq(absd(a),df(2a,1a),absnd(a,n)),t1".2d166"):posd(absd(a))
+b@[p:posd(a)][q:posd(b)][e:eq(absd(a),absd(b))]
+satzd166c:=tr3eq(a,absd(a),absd(b),b,symeq(absd(a),a,absnnd(a,pnotnd(a,p))),e,absnnd(b,pnotnd(b,q))):eq(a,b)
+b@[n:negd(a)][o:negd(b)][e:eq(absd(a),absd(b))]
++*2d166
+e@t2:=tr3eq(df(2a,1a),absd(a),absd(b),df(2b,1b),symeq(absd(a),df(2a,1a),absnd(a,n)),e,absnd(b,o)):eq(df(2a,1a),df(2b,1b))
+-2d166
+e@satzd166d:=tr3is(cut,pl(1a,2b),pl(2b,1a),pl(2a,1b),pl(1b,2a),compl(1a,2b),symis(cut,pl(2a,1b),pl(2b,1a),eqe12(2a,1a,2b,1b,t2".2d166")),compl(2a,1b)):eq(a,b)
+a@[n:not(zero(a))]
+satzd166e:=rappd(a,posd(absd(a)),[t:posd(a)]satzd166a(a,t),th2"l.imp"(zero(a),posd(absd(a)),n),[t:negd(a)]satzd166b(a,t)):posd(absd(a))
+a@[z:zero(a)]
+satzd166f:=eqzero(a,absd(a),symeq(absd(a),a,absnnd(a,0notnd(a,z))),z):zero(absd(a))
+b@mored:=more(pl(1a,2b),pl(1b,2a)):'prop'
+b2@[m:more(pl(a1,b2),pl(b1,a2))]
+moredi12:=ismore12(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),12issmsd(a1,a2,b1,b2),12issmsd(b1,b2,a1,a2),m):mored(df(a1,a2),df(b1,b2))
+r2@[m:more(pl(1a,r2),pl(r1,2a))]
+moredi1:=ismore12(pl(1a,r2),pl(1a,std(df(r1,r2))),pl(r1,2a),pl(stm(df(r1,r2)),2a),sm2issmsd(a,r1,r2),1sdissmsd(a,r1,r2),m):mored(a,df(r1,r2))
+r2@[m:more(pl(r1,2a),pl(1a,r2))]
+moredi2:=ismore12(pl(r1,2a),pl(stm(df(r1,r2)),2a),pl(1a,r2),pl(1a,std(df(r1,r2))),1sdissmsd(a,r1,r2),sm2issmsd(a,r1,r2),m):mored(df(r1,r2),a)
+b2@[m:mored(df(a1,a2),df(b1,b2))]
+morede12:=ismore12(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),smsdis12(a1,a2,b1,b2),smsdis12(b1,b2,a1,a2),m):more(pl(a1,b2),pl(b1,a2))
+b@lessd:=less(pl(1a,2b),pl(1b,2a)):'prop'
+[m:mored(a,b)]
+lemmad5:=satz121(pl(1a,2b),pl(1b,2a),m):lessd(b,a)
+b@[l:lessd(a,b)]
+lemmad6:=satz122(pl(1a,2b),pl(1b,2a),l):mored(b,a)
+b2@[l:less(pl(a1,b2),pl(b1,a2))]
+lessdi12:=lemmad5(df(b1,b2),df(a1,a2),moredi12(b1,b2,a1,a2,satz122(pl(a1,b2),pl(b1,a2),l))):lessd(df(a1,a2),df(b1,b2))
+r2@[l:less(pl(1a,r2),pl(r1,2a))]
+lessdi1:=lemmad5(df(r1,r2),a,moredi2(a,r1,r2,satz122(pl(1a,r2),pl(r1,2a),l))):lessd(a,df(r1,r2))
+r2@[l:less(pl(r1,2a),pl(1a,r2))]
+lessdi2:=lemmad5(a,df(r1,r2),moredi1(a,r1,r2,satz122(pl(r1,2a),pl(1a,r2),l))):lessd(df(r1,r2),a)
+b2@[l:lessd(df(a1,a2),df(b1,b2))]
+lessde12:=satz121(pl(b1,a2),pl(a1,b2),morede12(b1,b2,a1,a2,lemmad6(df(a1,a2),df(b1,b2),l))):less(pl(a1,b2),pl(b1,a2))
+b@satzd167:=satz123(pl(1a,2b),pl(1b,2a)):orec3(eq(a,b),mored(a,b),lessd(a,b))
+satzd167a:=satz123a(pl(1a,2b),pl(1b,2a)):or3(eq(a,b),mored(a,b),lessd(a,b))
+satzd167b:=satz123b(pl(1a,2b),pl(1b,2a)):ec3(eq(a,b),mored(a,b),lessd(a,b))
+d@1d:=stm(d):cut
+2d:=std(d):cut
+[e:eq(a,b)][f:eq(c,d)][m:mored(a,c)]
++*iv2d
+m@t4:=tr4is(cut,pl(pl(1b,2d),pl(1c,2a)),pl(pl(1b,2a),pl(1c,2d)),pl(pl(1a,2b),pl(1d,2c)),pl(pl(1a,2c),pl(1d,2b)),pl(pl(1d,2b),pl(1a,2c)),4pl24(1b,2d,1c,2a),ispl12(pl(1b,2a),pl(1a,2b),pl(1c,2d),pl(1d,2c),symeq(a,b,e),f),4pl24(1a,2b,1d,2c),compl(pl(1a,2c),pl(1d,2b))):is(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)))
+t5:=ismore2(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)),pl(pl(1b,2d),pl(1a,2c)),t4,satz135d(pl(1a,2c),pl(1c,2a),pl(1b,2d),m)):more(pl(pl(1b,2d),pl(1a,2c)),pl(pl(1d,2b),pl(1a,2c)))
+-iv2d
+m@eqmored12:=satz136a(pl(1b,2d),pl(1d,2b),pl(1a,2c),t5".iv2d"):mored(b,d)
+f@[l:lessd(a,c)]
+eqlessd12:=lemmad5(d,b,eqmored12(c,d,a,b,f,e,lemmad6(a,c,l))):lessd(b,d)
+c@[e:eq(a,b)][m:mored(a,c)]
+eqmored1:=eqmored12(a,b,c,c,e,refeq(c),m):mored(b,c)
+e@[m:mored(c,a)]
+eqmored2:=eqmored12(c,c,a,b,refeq(c),e,m):mored(c,b)
+e@[l:lessd(a,c)]
+eqlessd1:=eqlessd12(a,b,c,c,e,refeq(c),l):lessd(b,c)
+e@[l:lessd(c,a)]
+eqlessd2:=eqlessd12(c,c,a,b,refeq(c),e,l):lessd(c,b)
+b@moreq:=or(mored(a,b),eq(a,b)):'prop'
+lesseq:=or(lessd(a,b),eq(a,b)):'prop'
+[m:moreq(a,b)]
+satzd168a:=th9"l.or"(mored(a,b),eq(a,b),lessd(b,a),eq(b,a),m,[t:mored(a,b)]lemmad5(a,b,t),[t:eq(a,b)]symeq(a,b,t)):lesseq(b,a)
+b@[l:lesseq(a,b)]
+satzd168b:=th9"l.or"(lessd(a,b),eq(a,b),mored(b,a),eq(b,a),l,[t:lessd(a,b)]lemmad6(a,b,t),[t:eq(a,b)]symeq(a,b,t)):moreq(b,a)
+c@[e:eq(a,b)][m:moreq(a,c)]
+eqmoreq1:=th9"l.or"(mored(a,c),eq(a,c),mored(b,c),eq(b,c),m,[t:mored(a,c)]eqmored1(a,b,c,e,t),[t:eq(a,c)]treq1(b,c,a,e,t)):moreq(b,c)
+e@[m:moreq(c,a)]
+eqmoreq2:=th9"l.or"(mored(c,a),eq(c,a),mored(c,b),eq(c,b),m,[t:mored(c,a)]eqmored2(a,b,c,e,t),[t:eq(c,a)]treq(c,a,b,t,e)):moreq(c,b)
+e@[l:lesseq(a,c)]
+eqlesseq1:=satzd168a(c,b,eqmoreq2(a,b,c,e,satzd168b(a,c,l))):lesseq(b,c)
+e@[l:lesseq(c,a)]
+eqlesseq2:=satzd168a(b,c,eqmoreq1(a,b,c,e,satzd168b(c,a,l))):lesseq(c,b)
+d@[e:eq(a,b)][f:eq(c,d)][m:moreq(a,c)]
+eqmoreq12:=eqmoreq1(a,b,d,e,eqmoreq2(c,d,a,f,m)):moreq(b,d)
+f@[l:lesseq(a,c)]
+eqlesseq12:=eqlesseq1(a,b,d,e,eqlesseq2(c,d,a,f,l)):lesseq(b,d)
+b@[m:mored(a,b)]
+moreqi1:=ori1(mored(a,b),eq(a,b),m):moreq(a,b)
+b@[l:lessd(a,b)]
+lesseqi1:=ori1(lessd(a,b),eq(a,b),l):lesseq(a,b)
+b@[e:eq(a,b)]
+moreqi2:=ori2(mored(a,b),eq(a,b),e):moreq(a,b)
+lesseqi2:=ori2(lessd(a,b),eq(a,b),e):lesseq(a,b)
+b@[m:moreq(a,b)]
+satzd167c:=th7"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,comor(mored(a,b),eq(a,b),m)):not(lessd(a,b))
+b@[l:lesseq(a,b)]
+satzd167d:=th9"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,l):not(mored(a,b))
+b@[n:not(mored(a,b))]
+satzd167e:=th2"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n):lesseq(a,b)
+b@[n:not(lessd(a,b))]
+satzd167f:=comor(eq(a,b),mored(a,b),th3"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n)):moreq(a,b)
+b@[m:mored(a,b)]
+satzd167g:=th3"l.imp"(lesseq(a,b),not(mored(a,b)),weli(mored(a,b),m),[t:lesseq(a,b)]satzd167d(t)):not(lesseq(a,b))
+b@[l:lessd(a,b)]
+satzd167h:=th3"l.imp"(moreq(a,b),not(lessd(a,b)),weli(lessd(a,b),l),[t:moreq(a,b)]satzd167c(t)):not(moreq(a,b))
+b@[n:not(moreq(a,b))]
+satzd167j:=or3e3(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th5"l.or"(mored(a,b),eq(a,b),n),th4"l.or"(mored(a,b),eq(a,b),n)):lessd(a,b)
+b@[n:not(lesseq(a,b))]
+satzd167k:=or3e2(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th4"l.or"(lessd(a,b),eq(a,b),n),th5"l.or"(lessd(a,b),eq(a,b),n)):mored(a,b)
+b@[z:zero(b)][p:posd(a)]
+satzd169a:=ismore12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135a(1a,2a,1b,p)):mored(a,b)
+z@[m:mored(a,b)]
+satzd169b:=satz136d(1a,2a,2b,ismore12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),m)):posd(a)
+z@[n:negd(a)]
+satzd169c:=isless12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135c(1a,2a,1b,n)):lessd(a,b)
+z@[l:lessd(a,b)]
+satzd169d:=satz136f(1a,2a,2b,isless12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),l)):negd(a)
++2d170
+z@[p:posd(a)]
+t1:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166a(a,p))):moreq(absd(a),b)
+z@[y:zero(a)]
+t2:=moreqi2(absd(a),b,treq(absd(a),a,b,absnnd(a,0notnd(a,y)),zeroeq(a,b,y,z))):moreq(absd(a),b)
+z@[n:negd(a)]
+t3:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166b(a,n))):moreq(absd(a),b)
+-2d170
+z@satzd170:=rappd(a,moreq(absd(a),b),[t:posd(a)]t1".2d170"(t),[t:zero(a)]t2".2d170"(t),[t:negd(a)]t3".2d170"(t)):moreq(absd(a),b)
+c@[l:lessd(a,b)][k:lessd(b,c)]
++2d171
+t1:=satz137a(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),l,k):less(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
+t2:=isless12(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1a,2c),pl(1b,2b)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2b,1b,2c),tris(cut,pl(pl(1b,2a),pl(1c,2b)),pl(pl(1b,2b),pl(1c,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1b,2a,1c,2b),compl(pl(1b,2b),pl(1c,2a))),t1):less(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
+-2d171
+satzd171:=satz136c(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".2d171"):lessd(a,c)
+trlessd:=satzd171:lessd(a,c)
+c@[m:mored(a,b)][n:mored(b,c)]
+trmored:=lemmad6(c,a,trlessd(c,b,a,lemmad5(b,c,n),lemmad5(a,b,m))):mored(a,c)
+c@[l:lesseq(a,b)][k:lessd(b,c)]
+satzd172a:=orapp(lessd(a,b),eq(a,b),lessd(a,c),l,[t:lessd(a,b)]trlessd(t,k),[t:eq(a,b)]eqlessd1(b,a,c,symeq(a,b,t),k)):lessd(a,c)
+c@[l:lessd(a,b)][k:lesseq(b,c)]
+satzd172b:=orapp(lessd(b,c),eq(b,c),lessd(a,c),k,[t:lessd(b,c)]trlessd(l,t),[t:eq(b,c)]eqlessd2(b,c,a,t,l)):lessd(a,c)
+c@[m:moreq(a,b)][n:mored(b,c)]
+satzd172c:=lemmad6(c,a,satzd172b(c,b,a,lemmad5(b,c,n),satzd168a(a,b,m))):mored(a,c)
+c@[m:mored(a,b)][n:moreq(b,c)]
+satzd172d:=lemmad6(c,a,satzd172a(c,b,a,satzd168a(b,c,n),lemmad5(a,b,m))):mored(a,c)
+c@[l:lesseq(a,b)][k:lesseq(b,c)]
++2d173
+[j:lessd(a,b)]
+t1:=lesseqi1(a,c,satzd172b(j,k)):lesseq(a,c)
+k@[e:eq(a,b)]
+t2:=eqlesseq1(b,a,c,symeq(a,b,e),k):lesseq(a,c)
+-2d173
+satzd173:=orapp(lessd(a,b),eq(a,b),lesseq(a,c),l,[t:lessd(a,b)]t1".2d173"(t),[t:eq(a,b)]t2".2d173"(t)):lesseq(a,c)
+trlesseq:=satzd173:lesseq(a,c)
+c@[m:moreq(a,b)][n:moreq(b,c)]
+trmoreq:=satzd168b(c,a,trlesseq(c,b,a,satzd168a(b,c,n),satzd168a(a,b,m))):moreq(a,c)
+a@ratd:=[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))):'prop'
+irratd:=not(ratd(a)):'prop'
+b@[e:eq(a,b)][r:ratd(a)]
++*iv2d
+r@[n:not(zero(b))]
+t6:=th3"l.imp"(zero(a),zero(b),n,[t:zero(a)]eqzero(a,b,e,t)):not(zero(a))
+t7:=eqpderp(absd(a),satzd166e(a,t6),absd(b),satzd166e(b,n),eqabsd(a,b,e)):is(rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)))
+t8:=isp(cut,[t:cut]ratrp(t),rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)),<t6>r,t7):ratrp(rpofpd(absd(b),satzd166e(b,n)))
+-iv2d
+r@eqratd:=[t:not(zero(b))]t8".iv2d"(t):ratd(b)
+e@[i:irratd(a)]
+eqirratd:=th3"l.imp"(ratd(b),ratd(a),i,[t:ratd(b)]eqratd(b,a,symeq(a,b,e),t)):irratd(b)
+a@[z:zero(a)]
+ratdi0:=th2"l.r.imp"(not(zero(a)),[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))),weli(zero(a),z)):ratd(a)
+@[r:cut][i:irratrp(r)][x0:rat]
++*iv2d
+x0@[s:ratrp(pl(r,rpofrt(x0)))][y0:rat][j:is(pl(r,rpofrt(x0)),rpofrt(y0))]
+t9:=tris(cut,pl(rpofrt(x0),r),pl(r,rpofrt(x0)),rpofrt(y0),compl(rpofrt(x0),r),j):is(pl(rpofrt(x0),r),rpofrt(y0))
+t10:=ismore1(pl(rpofrt(x0),r),rpofrt(y0),rpofrt(x0),t9,satz133(rpofrt(x0),r)):more(rpofrt(y0),rpofrt(x0))
+t11:=satz154d(y0,x0,t10):more"rt"(y0,x0)
+t12:=satz155b(y0,x0,t11):is(rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
+t13:=satz140g(rpofrt(y0),rpofrt(x0),r,satz154a(y0,x0,t11),t9):is(r,mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
+t14:=tris2(cut,r,rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)),t13,t12):is(r,rpofrt(mn"rt"(y0,x0,t11)))
+t15:=somei(rat,[x:rat]is(r,rpofrt(x)),mn"rt"(y0,x0,t11),t14):ratrp(r)
+s@t16:=someapp(rat,[x:rat]is(pl(r,rpofrt(x0)),rpofrt(x)),s,con,[x:rat][t:is(pl(r,rpofrt(x0)),rpofrt(x))]<t15(x,t)>i):con
+-iv2d
+x0@remark1:=[t:ratrp(pl(r,rpofrt(x0)))]t16".iv2d"(t):irratrp(pl(r,rpofrt(x0)))
++*iv2d
+r@rp:=pdofrp(r):dif
+rn:=ndofrp(r):dif
+t17:=posdirp(r):posd(rp)
+t18:=pnot0d(rp,t17):not(zero(rp))
+t19:=nnot0d(rn,negdirp(r)):not(zero(rn))
+[n:not(zero(rp))]
+t20:=tris2(cut,r,rpofpd(absd(rp),satzd166e(rp,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rp),satzd166e(rp,n),rp,t17,absnnd(rp,pnotnd(rp,t17)))):is(r,rpofpd(absd(rp),satzd166e(rp,n)))
+r@t21:=treq(absd(rn),df(std(rn),stm(rn)),rp,absnd(rn,negdirp(r)),eqsmsd(std(rn),stm(rn),pl(r,1rp),1rp,stdis(1rp,pl(r,1rp)),stmis(1rp,pl(r,1rp)))):eq(absd(rn),rp)
+[n:not(zero(rn))]
+t22:=tris2(cut,r,rpofpd(absd(rn),satzd166e(rn,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rn),satzd166e(rn,n),rp,t17,t21)):is(r,rpofpd(absd(rn),satzd166e(rn,n)))
+r@[s:cut][i:is(r,s)][rr:ratrp(r)]
+t23:=isp(cut,[x:cut]ratrp(x),r,s,rr,i):ratrp(s)
+i@[rs:ratrp(s)]
+t24:=isp1(cut,[x:cut]ratrp(x),s,r,rs,i):ratrp(r)
+-iv2d
+r@[rr:ratrp(r)]
+remark2a:=[t:not(zero(pdofrp(r)))]t23".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t)),t20".iv2d"(t),rr):ratd(pdofrp(r))
+remark2b:=t17".iv2d":posd(pdofrp(r))
+remark3a:=[t:not(zero(ndofrp(r)))]t23".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t)),t22".iv2d"(t),rr):ratd(ndofrp(r))
+remark3b:=negdirp(r):negd(ndofrp(r))
+r@[i:irratrp(r)]
+remark4a:=th3"l.imp"(ratd(pdofrp(r)),ratrp(r),i,[t:ratd(pdofrp(r))]t24".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t18".iv2d")),t20".iv2d"(t18".iv2d"),<t18".iv2d">t)):irratd(pdofrp(r))
+remark4b:=t17".iv2d":posd(pdofrp(r))
+remark5a:=th3"l.imp"(ratd(ndofrp(r)),ratrp(r),i,[t:ratd(ndofrp(r))]t24".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t19".iv2d")),t22".iv2d"(t19".iv2d"),<t19".iv2d">t)):irratd(ndofrp(r))
+remark5b:=negdirp(r):negd(ndofrp(r))
+a@natd:=and(posd(a),[t:posd(a)]natrp(rpofpd(a,t))):'prop'
+[n:natd(a)]
+natposd:=ande1(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):posd(a)
+natderp:=ande2"l.r"(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):natrp(rpofpd(a,natposd(a,n)))
+b@[e:eq(a,b)][n:natd(a)]
++*iv2d
+n"rp"@t25:=eqposd(a,b,e,natposd(a,n)):posd(b)
+[p:posd(b)]
+t26:=eqpderp(a,natposd(a,n),b,p,e):is(rpofpd(a,natposd(a,n)),rpofpd(b,p))
+t27:=isp(cut,[t:cut]natrp(t),rpofpd(a,natposd(a,n)),rpofpd(b,p),natderp(a,n),t26):natrp(rpofpd(b,p))
+-iv2d
+n@eqnatd:=andi(posd(b),[t:posd(b)]natrp(rpofpd(b,t)),t25".iv2d",[t:posd(b)]t27".iv2d"(t)):natd(b)
+@[x:nat]
+pdofnt:=pdofrp(rpofnt(x)):dif
++*iv2d
+x@t28:=posdirp(rpofnt(x)):posd(pdofnt(x))
+[p:posd(pdofnt(x))]
+t29:=isrppd1(rpofnt(x)):is(rpofnt(x),rpofpd(pdofnt(x),t28))
+t30:=eqpderp(pdofnt(x),t28,pdofnt(x),p,refeq(pdofnt(x))):is(rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p))
+t31:=tris(cut,rpofnt(x),rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p),t29,t30):is(rpofnt(x),rpofpd(pdofnt(x),p))
+t32:=isp(cut,[t:cut]natrp(t),rpofnt(x),rpofpd(pdofnt(x),p),natrpi(x),t31):natrp(rpofpd(pdofnt(x),p))
+-iv2d
+x@natdi:=andi(posd(pdofnt(x)),[t:posd(pdofnt(x))]natrp(rpofpd(pdofnt(x),t)),t28".iv2d",[t:posd(pdofnt(x))]t32".iv2d"(t)):natd(pdofnt(x))
+a@intd:=or(zero(a),natd(absd(a))):'prop'
+b@[e:eq(a,b)][i:intd(a)]
++*iv2d
+i"rp"@[z:zero(a)]
+t33:=eqzero(a,b,e,z):zero(b)
+i"rp"@[n:natd(absd(a))]
+t34:=eqnatd(absd(a),absd(b),eqabsd(a,b,e),n):natd(absd(b))
+-iv2d
+i@eqintd:=th9"l.or"(zero(a),natd(absd(a)),zero(b),natd(absd(b)),i,[t:zero(a)]t33".iv2d"(t),[t:natd(absd(a))]t34".iv2d"(t)):intd(b)
+a@[n:natd(a)]
++*iv2d
+n"rp"@t34a:=symeq(absd(a),a,absnnd(a,pnotnd(a,natposd(a,n)))):eq(a,absd(a))
+t35:=eqnatd(a,absd(a),t34a,n):natd(absd(a))
+-iv2d
+n@natintd:=ori2(zero(a),natd(absd(a)),t35".iv2d"):intd(a)
+a@[p:posd(a)][i:intd(a)]
++*iv2d
+i"rp"@t36:=ore2(zero(a),natd(absd(a)),i,pnot0d(a,p)):natd(absd(a))
+-iv2d
+i@posintnatd:=eqnatd(absd(a),a,absnnd(a,pnotnd(a,p)),t36".iv2d"):natd(a)
+a@[z:zero(a)]
+intdi0:=ori1(zero(a),natd(absd(a)),z):intd(a)
+r@[n:natrp(r)]
++*iv2d
+n"rp"@t37:=posdirp(r):posd(pdofrp(r))
+[p:posd(pdofrp(r))]
+t38:=tris(cut,r,rpofpd(pdofrp(r),t37),rpofpd(pdofrp(r),p),isrppd1(r),eqpderp(pdofrp(r),t37,pdofrp(r),p,refeq(pdofrp(r)))):is(r,rpofpd(pdofrp(r),p))
+t39:=isp(cut,[t:cut]natrp(t),r,rpofpd(pdofrp(r),p),n,t38):natrp(rpofpd(pdofrp(r),p))
+-iv2d
+n@remark6a:=andi(posd(pdofrp(r)),[t:posd(pdofrp(r))]natrp(rpofpd(pdofrp(r),t)),t37".iv2d",[t:posd(pdofrp(r))]t39".iv2d"(t)):natd(pdofrp(r))
+remark6:=natintd(pdofrp(r),remark6a):intd(pdofrp(r))
++*iv2d
+n"rp"@t40:=absdeql(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):eq(absd(ndofrp(r)),pdofrp(r))
+t41:=eqnatd(pdofrp(r),absd(ndofrp(r)),symeq(absd(ndofrp(r)),pdofrp(r),t40),remark6a):natd(absd(ndofrp(r)))
+-iv2d
+n@remark7:=ori2(zero(ndofrp(r)),natd(absd(ndofrp(r))),t41".iv2d"):intd(ndofrp(r))
+a@[i:intd(a)]
++2d174
+[n:not(zero(a))]
+t1:=ore2(zero(a),natd(absd(a)),i,n):natd(absd(a))
+t2:=ande2(posd(absd(a)),[t:posd(absd(a))]natrp(rpofpd(absd(a),t)),t1):[t:posd(absd(a))]natrp(rpofpd(absd(a),t))
+t3:=lemmaiii5(rpofpd(absd(a),satzd166e(a,n)),<satzd166e(a,n)>t2):ratrp(rpofpd(absd(a),satzd166e(a,n)))
+-2d174
+satzd174:=[t:not(zero(a))]t3".2d174"(t):ratd(a)
+b@pd:=df(pl(1a,1b),pl(2a,2b)):dif
+b2@pd12:=issmsd(pl(stm(df(a1,a2)),stm(df(b1,b2))),pl(std(df(a1,a2)),std(df(b1,b2))),pl(a1,b1),pl(a2,b2),ispl12(stm(df(a1,a2)),a1,stm(df(b1,b2)),b1,stmis(a1,a2),stmis(b1,b2)),ispl12(std(df(a1,a2)),a2,std(df(b1,b2)),b2,stdis(a1,a2),stdis(b1,b2))):is"e"(dif,pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
+r2@pd1:=issmsd(pl(1a,stm(df(r1,r2))),pl(2a,std(df(r1,r2))),pl(1a,r1),pl(2a,r2),ispl2(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl2(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
+pd2:=issmsd(pl(stm(df(r1,r2)),1a),pl(std(df(r1,r2)),2a),pl(r1,1a),pl(r2,2a),ispl1(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl1(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
+b2@pdeq12a:=refeq1(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
+pdeq12b:=refeq2(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(df(pl(a1,b1),pl(a2,b2)),pd(df(a1,a2),df(b1,b2)))
+r2@pdeq1a:=refeq1(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
+pdeq1b:=refeq2(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(df(pl(1a,r1),pl(2a,r2)),pd(a,df(r1,r2)))
+pdeq2a:=refeq1(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
+pdeq2b:=refeq2(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(df(pl(r1,1a),pl(r2,2a)),pd(df(r1,r2),a))
+b@satzd175:=eqsmsd(pl(1a,1b),pl(2a,2b),pl(1b,1a),pl(2b,2a),compl(1a,1b),compl(2a,2b)):eq(pd(a,b),pd(b,a))
+compd:=satzd175:eq(pd(a,b),pd(b,a))
+c@[e:eq(a,b)]
++iv3d
+t1:=tr3is(cut,pl(pl(1a,1c),pl(2b,2c)),pl(pl(1a,2b),pl(1c,2c)),pl(pl(1b,2a),pl(1c,2c)),pl(pl(1b,1c),pl(2a,2c)),4pl23(1a,1c,2b,2c),ispl1(pl(1a,2b),pl(1b,2a),pl(1c,2c),e),4pl23(1b,2a,1c,2c)):is(pl(pl(1a,1c),pl(2b,2c)),pl(pl(1b,1c),pl(2a,2c)))
+-iv3d
+eqpd1:=eqi12(pl(1a,1c),pl(2a,2c),pl(1b,1c),pl(2b,2c),t1".iv3d"):eq(pd(a,c),pd(b,c))
+eqpd2:=tr3eq(pd(c,a),pd(a,c),pd(b,c),pd(c,b),compd(c,a),eqpd1,compd(b,c)):eq(pd(c,a),pd(c,b))
+d@[e:eq(a,b)][f:eq(c,d)]
+eqpd12:=treq(pd(a,c),pd(b,c),pd(b,d),eqpd1(a,b,c,e),eqpd2(c,d,b,f)):eq(pd(a,c),pd(b,d))
+b@[z:zero(a)]
++*iv3d
+z@t2:=tr4is(cut,pl(pl(1a,1b),2b),pl(1a,pl(1b,2b)),pl(2a,pl(2b,1b)),pl(pl(2a,2b),1b),pl(1b,pl(2a,2b)),asspl1(1a,1b,2b),ispl12(1a,2a,pl(1b,2b),pl(2b,1b),z,compl(1b,2b)),asspl2(2a,2b,1b),compl(pl(2a,2b),1b)):is(pl(pl(1a,1b),2b),pl(1b,pl(2a,2b)))
+-iv3d
+z@pd01:=eqi2(b,pl(1a,1b),pl(2a,2b),t2".iv3d"):eq(pd(a,b),b)
+b@[z:zero(b)]
+pd02:=treq(pd(a,b),pd(b,a),a,compd(a,b),pd01(b,a,z)):eq(pd(a,b),a)
+b@[p:posd(a)][q:posd(b)]
+ppd:=posdi(pl(1a,1b),pl(2a,2b),satz137(1a,2a,1b,2b,p,q)):posd(pd(a,b))
+b@[n:negd(a)][o:negd(b)]
+npd:=negdi(pl(1a,1b),pl(2a,2b),satz137a(1a,2a,1b,2b,n,o)):negd(pd(a,b))
+a@m0d:=df(2a,1a):dif
+a2@m0deqa:=eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2)):eq(m0d(df(a1,a2)),df(a2,a1))
+m0deqb:=symeq(m0d(df(a1,a2)),df(a2,a1),m0deqa):eq(df(a2,a1),m0d(df(a1,a2)))
+b@[e:eq(a,b)]
++*iv3d
+e@t3:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
+-iv3d
+e@eqm0d:=eqi12(2a,1a,2b,1b,t3".iv3d"):eq(m0d(a),m0d(b))
+a@[p:posd(a)]
+satzd176a:=negdi(2a,1a,satz121(1a,2a,p)):negd(m0d(a))
+a@[z:zero(a)]
+satzd176b:=zeroi(2a,1a,symis(cut,1a,2a,z)):zero(m0d(a))
+a@[n:negd(a)]
+satzd176c:=posdi(2a,1a,satz122(1a,2a,n)):posd(m0d(a))
+a@[n:negd(m0d(a))]
+satzd176d:=satz122(2a,1a,isless12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),n)):posd(a)
+a@[z:zero(m0d(a))]
+satzd176e:=symis(cut,2a,1a,tr3is(cut,2a,stm(df(2a,1a)),std(df(2a,1a)),1a,isstm(2a,1a),z,stdis(2a,1a))):zero(a)
+a@[p:posd(m0d(a))]
+satzd176f:=satz121(2a,1a,ismore12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),p)):negd(a)
+a@[z:zero(a)]
+m0d0:=zeroeq(m0d(a),a,satzd176b(a,z),z):eq(m0d(a),a)
++3d177
+a@t1:=tris(dif,m0d(m0d(a)),df(1a,2a),a,issmsd(std(m0d(a)),stm(m0d(a)),1a,2a,stdis(2a,1a),stmis(2a,1a)),dfis(a)):is"e"(dif,m0d(m0d(a)),a)
+-3d177
+a@satzd177:=refeq1(m0d(m0d(a)),a,t1".3d177"):eq(m0d(m0d(a)),a)
+satzd177a:=symeq(m0d(m0d(a)),a,satzd177):eq(a,m0d(m0d(a)))
+b@[e:eq(a,m0d(b))]
+satzd177b:=treq(m0d(a),m0d(m0d(b)),b,eqm0d(a,m0d(b),e),satzd177(b)):eq(m0d(a),b)
+satzd177c:=symeq(m0d(a),b,satzd177b):eq(b,m0d(a))
+b@[e:eq(m0d(a),b)]
+satzd177d:=satzd177c(b,a,symeq(m0d(a),b,e)):eq(a,m0d(b))
+satzd177e:=symeq(a,m0d(b),satzd177d):eq(m0d(b),a)
++3d178
+a@[p:posd(a)]
+t1:=tr3eq(absd(m0d(a)),m0d(m0d(a)),a,absd(a),absnd(m0d(a),satzd176a(a,p)),satzd177(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p)))):eq(absd(m0d(a)),absd(a))
+a@[z:zero(a)]
+t2:=tr3eq(absd(m0d(a)),m0d(a),a,absd(a),absnnd(m0d(a),0notnd(m0d(a),satzd176b(a,z))),m0d0(a,z),symeq(absd(a),a,absnnd(a,0notnd(a,z)))):eq(absd(m0d(a)),absd(a))
+a@[n:negd(a)]
+t3:=treq(absd(m0d(a)),m0d(a),absd(a),absnnd(m0d(a),pnotnd(m0d(a),satzd176c(a,n))),symeq(absd(a),m0d(a),absnd(a,n))):eq(absd(m0d(a)),absd(a))
+-3d178
+a@satzd178:=rappd(a,eq(absd(m0d(a)),absd(a)),[t:posd(a)]t1".3d178"(t),[t:zero(a)]t2".3d178"(t),[t:negd(a)]t3".3d178"(t)):eq(absd(m0d(a)),absd(a))
+satzd178a:=symeq(absd(m0d(a)),absd(a),satzd178):eq(absd(a),absd(m0d(a)))
++3d179
+t1:=pdeq1b(a,2a,1a):eq(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)))
+t2:=zeroi(pl(1a,2a),pl(2a,1a),compl(1a,2a)):zero(df(pl(1a,2a),pl(2a,1a)))
+-3d179
+satzd179:=eqzero(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)),t1".3d179",t2".3d179"):zero(pd(a,m0d(a)))
+satzd179a:=eqzero(pd(a,m0d(a)),pd(m0d(a),a),compd(a,m0d(a)),satzd179):zero(pd(m0d(a),a))
+b@satzd180:=treq(m0d(pd(a,b)),df(pl(2a,2b),pl(1a,1b)),pd(m0d(a),m0d(b)),m0deqa(pl(1a,1b),pl(2a,2b)),pdeq12b(2a,1a,2b,1b)):eq(m0d(pd(a,b)),pd(m0d(a),m0d(b)))
+satzd180a:=symeq(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180):eq(pd(m0d(a),m0d(b)),m0d(pd(a,b)))
+md:=pd(a,m0d(b)):dif
+b2@mdeq12a:=treq(md(df(a1,a2),df(b1,b2)),pd(df(a1,a2),df(b2,b1)),df(pl(a1,b2),pl(a2,b1)),eqpd2(m0d(df(b1,b2)),df(b2,b1),df(a1,a2),m0deqa(b1,b2)),pdeq12a(a1,a2,b2,b1)):eq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)))
+mdeq12b:=symeq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)),mdeq12a):eq(df(pl(a1,b2),pl(a2,b1)),md(df(a1,a2),df(b1,b2)))
+r2@mdeq1a:=treq(md(a,df(r1,r2)),pd(a,df(r2,r1)),df(pl(1a,r2),pl(2a,r1)),eqpd2(m0d(df(r1,r2)),df(r2,r1),a,m0deqa(r1,r2)),pdeq1a(a,r2,r1)):eq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)))
+mdeq1b:=symeq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)),mdeq1a):eq(df(pl(1a,r2),pl(2a,r1)),md(a,df(r1,r2)))
+mdeq2a:=pdeq12a(r1,r2,2a,1a):eq(md(df(r1,r2),a),df(pl(r1,2a),pl(r2,1a)))
+mdeq2b:=pdeq12b(r1,r2,2a,1a):eq(df(pl(r1,2a),pl(r2,1a)),md(df(r1,r2),a))
+c@[e:eq(a,b)]
+eqmd1:=eqpd1(a,b,m0d(c),e):eq(md(a,c),md(b,c))
+eqmd2:=eqpd2(m0d(a),m0d(b),c,eqm0d(a,b,e)):eq(md(c,a),md(c,b))
+d@[e:eq(a,b)][f:eq(c,d)]
+eqmd12:=treq(md(a,c),md(b,c),md(b,d),eqmd1(a,b,c,e),eqmd2(c,d,b,f)):eq(md(a,c),md(b,d))
+b@satzd181:=tr3eq(m0d(md(a,b)),pd(m0d(a),m0d(m0d(b))),pd(m0d(a),b),md(b,a),satzd180(a,m0d(b)),eqpd2(m0d(m0d(b)),b,m0d(a),satzd177(b)),compd(m0d(a),b)):eq(m0d(md(a,b)),md(b,a))
+satzd181a:=symeq(m0d(md(b,a)),md(a,b),satzd181(b,a)):eq(md(a,b),m0d(md(b,a)))
++3d182
+t1:=treq(md(a,b),df(pl(1a,2b),pl(2a,1b)),df(pl(1a,2b),pl(1b,2a)),pdeq1a(a,2b,1b),eqsd(pl(1a,2b),pl(2a,1b),pl(1b,2a),compl(2a,1b))):eq(md(a,b),df(pl(1a,2b),pl(1b,2a)))
+t2:=symeq(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1):eq(df(pl(1a,2b),pl(1b,2a)),md(a,b))
+t3:=stmis(pl(1a,2b),pl(1b,2a)):is(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b))
+t4:=stdis(pl(1a,2b),pl(1b,2a)):is(std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a))
+-3d182
+[p:posd(md(a,b))]
++*3d182
+p@t5:=eqposd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,p):posd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+p@satzd182a:=ismore12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t5".3d182"):mored(a,b)
+b@[z:zero(md(a,b))]
++*3d182
+z@t6:=eqzero(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,z):zero(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+z@satzd182b:=tr3is(cut,pl(1a,2b),stm(df(pl(1a,2b),pl(1b,2a))),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),isstm(pl(1a,2b),pl(1b,2a)),t6".3d182",t4".3d182"):eq(a,b)
+b@[n:negd(md(a,b))]
++*3d182
+n@t7:=eqnegd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,n):negd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+n@satzd182c:=isless12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t7".3d182"):lessd(a,b)
+b@[m:mored(a,b)]
++*3d182
+m@t8:=posdi(pl(1a,2b),pl(1b,2a),m):posd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+m@satzd182d:=eqposd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t8".3d182"):posd(md(a,b))
+b@[e:eq(a,b)]
++*3d182
+e@t9:=zeroi(pl(1a,2b),pl(1b,2a),e):zero(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+e@satzd182e:=eqzero(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t9".3d182"):zero(md(a,b))
+b@[l:lessd(a,b)]
++*3d182
+l@t10:=negdi(pl(1a,2b),pl(1b,2a),l):negd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+l@satzd182f:=eqnegd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t10".3d182"):negd(md(a,b))
++3d183
+b@t1:=tris(cut,pl(1a,2b),pl(2b,1a),pl(stm(m0d(b)),std(m0d(a))),compl(1a,2b),12issmsd(2b,1b,2a,1a)):is(pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))))
+t2:=t1(b,a):is(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))))
+-3d183
+b@[m:mored(a,b)]
+satzd183a:=isless12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad5(a,b,m)):lessd(m0d(a),m0d(b))
+b@[e:eq(a,b)]
+staz183b:=eqm0d(a,b,e):eq(m0d(a),m0d(b))
+b@[l:lessd(a,b)]
+satzd183c:=ismore12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad6(a,b,l)):mored(m0d(a),m0d(b))
+b@[l:lessd(m0d(a),m0d(b))]
+satzd183d:=eqmored12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183c(m0d(a),m0d(b),l)):mored(a,b)
+b@[e:eq(m0d(a),m0d(b))]
+satzd183e:=tr3eq(a,m0d(m0d(a)),m0d(m0d(b)),b,satzd177a(a),eqm0d(m0d(a),m0d(b),e),satzd177(b)):eq(a,b)
+b@[m:mored(m0d(a),m0d(b))]
+satzd183f:=eqlessd12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183a(m0d(a),m0d(b),m)):lessd(a,b)
++3d184
+a@t1:=tr3eq(a,df(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp))),df(pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp))),md(pdofrp(1a),pdofrp(2a)),lemmad3(a,pl(1rp,1rp)),eqsmsd(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp)),pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp)),asspl2(1a,1rp,1rp),3pl12(2a,1rp,1rp)),mdeq12b(pl(1a,1rp),1rp,pl(2a,1rp),1rp)):eq(a,md(pdofrp(1a),pdofrp(2a)))
+t2:=and3i(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))),posdirp(1a),posdirp(2a),t1):and3(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))))
+t3:=somei(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))),pdofrp(2a),t2):some"l"(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))))
+-3d184
+a@satzd184:=somei(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))),pdofrp(1a),t3".3d184"):some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))))
+c@asspd1:=tr3eq(pd(pd(a,b),c),df(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c)),df(pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c))),pd(a,pd(b,c)),pdeq2a(c,pl(1a,1b),pl(2a,2b)),eqsmsd(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c),pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c)),asspl1(1a,1b,1c),asspl1(2a,2b,2c)),pdeq1b(a,pl(1b,1c),pl(2b,2c))):eq(pd(pd(a,b),c),pd(a,pd(b,c)))
+asspd2:=symeq(pd(pd(a,b),c),pd(a,pd(b,c)),asspd1):eq(pd(a,pd(b,c)),pd(pd(a,b),c))
+3pd23:=tr3eq(pd(pd(a,b),c),pd(a,pd(b,c)),pd(a,pd(c,b)),pd(pd(a,c),b),asspd1(a,b,c),eqpd2(pd(b,c),pd(c,b),a,compd(b,c)),asspd2(a,c,b)):eq(pd(pd(a,b),c),pd(pd(a,c),b))
+d@4pd23:=tr3eq(pd(pd(a,b),pd(c,d)),pd(pd(pd(a,b),c),d),pd(pd(pd(a,c),b),d),pd(pd(a,c),pd(b,d)),asspd2(pd(a,b),c,d),eqpd1(pd(pd(a,b),c),pd(pd(a,c),b),d,3pd23),asspd1(pd(a,c),b,d)):eq(pd(pd(a,b),pd(c,d)),pd(pd(a,c),pd(b,d)))
+b@pdmd:=treq(pd(md(a,b),b),pd(a,pd(m0d(b),b)),a,asspd1(a,m0d(b),b),pd02(a,pd(m0d(b),b),satzd179a(b))):eq(pd(md(a,b),b),a)
+mdpd:=treq(md(pd(a,b),b),pd(a,pd(b,m0d(b))),a,asspd1(a,b,m0d(b)),pd02(a,pd(b,m0d(b)),satzd179(b))):eq(md(pd(a,b),b),a)
+d@satzd185:=treq(pd(md(a,b),md(c,d)),pd(pd(a,c),pd(m0d(b),m0d(d))),md(pd(a,c),pd(b,d)),4pd23(a,m0d(b),c,m0d(d)),eqpd2(pd(m0d(b),m0d(d)),m0d(pd(b,d)),pd(a,c),satzd180a(b,d))):eq(pd(md(a,b),md(c,d)),md(pd(a,c),pd(b,d)))
+c@satzd186:=asspd1:eq(pd(pd(a,b),c),pd(a,pd(b,c)))
+b@satzd187a:=treq(pd(b,md(a,b)),pd(md(a,b),b),a,compd(b,md(a,b)),pdmd):eq(pd(b,md(a,b)),a)
+[x:dif][e:eq(pd(b,x),a)]
+satzd187c:=treq(md(a,b),md(pd(x,b),b),x,eqmd1(a,pd(x,b),b,treq1(a,pd(x,b),pd(b,x),e,compd(b,x))),mdpd(x,b)):eq(md(a,b),x)
+satzd187d:=symeq(md(a,b),x,satzd187c):eq(x,md(a,b))
+x@[e:eq(pd(x,b),a)]
+satzd187e:=satzd187c(treq(pd(b,x),pd(x,b),a,compd(b,x),e)):eq(md(a,b),x)
+satzd187f:=symeq(md(a,b),x,satzd187e):eq(x,md(a,b))
++3d188
+c@t1:=tr3eq(md(pd(a,c),pd(b,c)),pd(pd(a,c),pd(m0d(b),m0d(c))),pd(md(a,b),md(c,c)),md(a,b),eqpd2(m0d(pd(b,c)),pd(m0d(b),m0d(c)),pd(a,c),satzd180(b,c)),4pd23(a,c,m0d(b),m0d(c)),pd02(md(a,b),md(c,c),satzd179(c))):eq(md(pd(a,c),pd(b,c)),md(a,b))
+t2:=symeq(md(pd(a,c),pd(b,c)),md(a,b),t1):eq(md(a,b),md(pd(a,c),pd(b,c)))
+-3d188
+c@[m:mored(pd(a,c),pd(b,c))]
++*3d188
+m@t3:=eqposd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182d(pd(a,c),pd(b,c),m)):posd(md(a,b))
+-3d188
+m@satzd188a:=satzd182a(a,b,t3".3d188"):mored(a,b)
+c@[e:eq(pd(a,c),pd(b,c))]
++*3d188
+e@t4:=eqzero(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182e(pd(a,c),pd(b,c),e)):zero(md(a,b))
+-3d188
+e@satzd188b:=satzd182b(a,b,t4".3d188"):eq(a,b)
+c@[l:lessd(pd(a,c),pd(b,c))]
++*3d188
+l@t5:=eqnegd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182f(pd(a,c),pd(b,c),l)):negd(md(a,b))
+-3d188
+l@satzd188c:=satzd182c(a,b,t5".3d188"):lessd(a,b)
+c@[m:mored(a,b)]
++*3d188
+m@t6:=eqposd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182d(a,b,m)):posd(md(pd(a,c),pd(b,c)))
+-3d188
+m@satzd188d:=satzd182a(pd(a,c),pd(b,c),t6".3d188"):mored(pd(a,c),pd(b,c))
+c@[e:eq(a,b)]
+satzd188e:=eqpd1(a,b,c,e):eq(pd(a,c),pd(b,c))
+c@[l:lessd(a,b)]
++*3d188
+l@t7:=eqnegd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182f(a,b,l)):negd(md(pd(a,c),pd(b,c)))
+-3d188
+l@satzd188f:=satzd182c(pd(a,c),pd(b,c),t7".3d188"):lessd(pd(a,c),pd(b,c))
+c@[m:mored(pd(c,a),pd(c,b))]
+satzd188g:=satzd188a(eqmored12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),m)):mored(a,b)
+c@[e:eq(pd(c,a),pd(c,b))]
+satzd188h:=satzd188b(tr3eq(pd(a,c),pd(c,a),pd(c,b),pd(b,c),compd(a,c),e,compd(c,b))):eq(a,b)
+[l:lessd(pd(c,a),pd(c,b))]
+satzd188j:=satzd188c(eqlessd12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),l)):lessd(a,b)
+c@[m:mored(a,b)]
+satzd188k:=eqmored12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188d(m)):mored(pd(c,a),pd(c,b))
+c@[e:eq(a,b)]
+satzd188l:=eqpd2(a,b,c,e):eq(pd(c,a),pd(c,b))
+c@[l:lessd(a,b)]
+satzd188m:=eqlessd12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188f(l)):lessd(pd(c,a),pd(c,b))
+d@[e:eq(a,b)][m:mored(c,d)]
+satzd188n:=eqmored2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188k(c,d,a,m)):mored(pd(a,c),pd(b,d))
+satzd188o:=eqmored12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188n):mored(pd(c,a),pd(d,b))
+e@[l:lessd(c,d)]
+satzd188p:=eqlessd2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188m(c,d,a,l)):lessd(pd(a,c),pd(b,d))
+satzd188q:=eqlessd12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188p):lessd(pd(c,a),pd(d,b))
+d@[m:mored(a,b)][n:mored(c,d)]
+satzd189:=trmored(pd(a,c),pd(b,c),pd(b,d),satzd188d(a,b,c,m),satzd188k(c,d,b,n)):mored(pd(a,c),pd(b,d))
+d@[l:lessd(a,b)][k:lessd(c,d)]
+satzd189a:=lemmad5(pd(b,d),pd(a,c),satzd189(b,a,d,c,lemmad6(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
+d@[m:moreq(a,b)][n:mored(c,d)]
+satzd190a:=orapp(mored(a,b),eq(a,b),mored(pd(a,c),pd(b,d)),m,[t:mored(a,b)]satzd189(t,n),[t:eq(a,b)]satzd188n(t,n)):mored(pd(a,c),pd(b,d))
+d@[m:mored(a,b)][n:moreq(c,d)]
+satzd190b:=eqmored12(pd(c,a),pd(a,c),pd(d,b),pd(b,d),compd(c,a),compd(d,b),satzd190a(c,d,a,b,n,m)):mored(pd(a,c),pd(b,d))
+d@[l:lesseq(a,b)][k:lessd(c,d)]
+satzd190c:=lemmad5(pd(b,d),pd(a,c),satzd190a(b,a,d,c,satzd168b(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
+d@[l:lessd(a,b)][k:lesseq(c,d)]
+satzd190d:=lemmad5(pd(b,d),pd(a,c),satzd190b(b,a,d,c,lemmad6(a,b,l),satzd168b(c,d,k))):lessd(pd(a,c),pd(b,d))
+d@[m:moreq(a,b)][n:moreq(c,d)]
++3d191
+[e:eq(a,b)][f:eq(c,d)]
+t1:=moreqi2(pd(a,c),pd(b,d),eqpd12(a,b,c,d,e,f)):moreq(pd(a,c),pd(b,d))
+e@[o:mored(c,d)]
+t2:=moreqi1(pd(a,c),pd(b,d),satzd190a(m,o)):moreq(pd(a,c),pd(b,d))
+e@t3:=orapp(mored(c,d),eq(c,d),moreq(pd(a,c),pd(b,d)),n,[t:mored(c,d)]t2(t),[t:eq(c,d)]t1(t)):moreq(pd(a,c),pd(b,d))
+n@[o:mored(a,b)]
+t4:=moreqi1(pd(a,c),pd(b,d),satzd190b(o,n)):moreq(pd(a,c),pd(b,d))
+-3d191
+satzd191:=orapp(mored(a,b),eq(a,b),moreq(pd(a,c),pd(b,d)),m,[t:mored(a,b)]t4".3d191"(t),[t:eq(a,b)]t3".3d191"(t)):moreq(pd(a,c),pd(b,d))
+d@[l:lesseq(a,b)][k:lesseq(c,d)]
+satzd191a:=satzd168a(pd(b,d),pd(a,c),satzd191(b,a,d,c,satzd168b(a,b,l),satzd168b(c,d,k))):lesseq(pd(a,c),pd(b,d))
+b@td:=df(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))):dif
++iv4d
+a2@[r:cut]
+t1:=ists1(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(stm(df(a1,a2)),r),ts(a1,r))
+t2:=ists2(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(r,stm(df(a1,a2))),ts(r,a1))
+t3:=ists1(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(std(df(a1,a2)),r),ts(a2,r))
+t4:=ists2(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(r,std(df(a1,a2))),ts(r,a2))
+[s:cut]
+t5:=ispl12(ts(stm(df(a1,a2)),r),ts(a1,r),ts(std(df(a1,a2)),s),ts(a2,s),t1(r),t3(s)):is(pl(ts(stm(df(a1,a2)),r),ts(std(df(a1,a2)),s)),pl(ts(a1,r),ts(a2,s)))
+t6:=ispl12(ts(r,stm(df(a1,a2))),ts(r,a1),ts(s,std(df(a1,a2))),ts(s,a2),t2(r),t4(s)):is(pl(ts(r,stm(df(a1,a2))),ts(s,std(df(a1,a2)))),pl(ts(r,a1),ts(s,a2)))
+t7:=ispl12(ts(std(df(a1,a2)),r),ts(a2,r),ts(stm(df(a1,a2)),s),ts(a1,s),t3(r),t1(s)):is(pl(ts(std(df(a1,a2)),r),ts(stm(df(a1,a2)),s)),pl(ts(a2,r),ts(a1,s)))
+t8:=ispl12(ts(r,std(df(a1,a2))),ts(r,a2),ts(s,stm(df(a1,a2))),ts(s,a1),t4(r),t2(s)):is(pl(ts(r,std(df(a1,a2))),ts(s,stm(df(a1,a2)))),pl(ts(r,a2),ts(s,a1)))
+b2@t9:=tris(cut,pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,stm(df(b1,b2))),ts(a2,std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),t5(a1,a2,stm(df(b1,b2)),std(df(b1,b2))),t6(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)))
+t10:=tris(cut,pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,std(df(b1,b2))),ts(a2,stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)),t5(a1,a2,std(df(b1,b2)),stm(df(b1,b2))),t8(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)))
+-iv4d
+b2@td12:=issmsd(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1)),t9".iv4d",t10".iv4d"):is"e"(dif,td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
+r2@td1:=issmsd(pl(ts(1a,stm(df(r1,r2))),ts(2a,std(df(r1,r2)))),pl(ts(1a,std(df(r1,r2))),ts(2a,stm(df(r1,r2)))),pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1)),t6".iv4d"(r1,r2,1a,2a),t8".iv4d"(r1,r2,1a,2a)):is"e"(dif,td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
+td2:=issmsd(pl(ts(stm(df(r1,r2)),1a),ts(std(df(r1,r2)),2a)),pl(ts(stm(df(r1,r2)),2a),ts(std(df(r1,r2)),1a)),pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a)),t5".iv4d"(r1,r2,1a,2a),t5".iv4d"(r1,r2,2a,1a)):is"e"(dif,td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
+b2@tdeq12a:=refeq1(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
+tdeq12b:=refeq2(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td(df(a1,a2),df(b1,b2)))
+r2@tdeq1a:=refeq1(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
+tdeq1b:=refeq2(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td(a,df(r1,r2)))
+tdeq2a:=refeq1(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
+tdeq2b:=refeq2(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td(df(r1,r2),a))
++4d194
+b@t1:=ispl12(ts(1a,1b),ts(1b,1a),ts(2a,2b),ts(2b,2a),comts(1a,1b),comts(2a,2b)):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1b,1a),ts(2b,2a)))
+t2:=tris(cut,pl(ts(1a,2b),ts(2a,1b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1b,2a),ts(2b,1a)),compl(ts(1a,2b),ts(2a,1b)),ispl12(ts(2a,1b),ts(1b,2a),ts(1a,2b),ts(2b,1a),comts(2a,1b),comts(1a,2b))):is(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,2a),ts(2b,1a)))
+-4d194
+b@satzd194:=eqsmsd(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,1a),ts(2b,2a)),pl(ts(1b,2a),ts(2b,1a)),t1".4d194",t2".4d194"):eq(td(a,b),td(b,a))
+comtd:=satzd194:eq(td(a,b),td(b,a))
+c@[e:eq(a,b)]
++*iv4d
+e@[r:cut]
+t11:=tr3is(cut,pl(ts(1a,r),ts(2b,r)),ts(pl(1a,2b),r),ts(pl(1b,2a),r),pl(ts(1b,r),ts(2a,r)),distpt1(1a,2b,r),ists1(pl(1a,2b),pl(1b,2a),r,e),disttp1(1b,2a,r)):is(pl(ts(1a,r),ts(2b,r)),pl(ts(1b,r),ts(2a,r)))
+e@t12:=tr3is(cut,pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,2c),ts(2a,2c))),pl(pl(ts(1b,1c),ts(2a,1c)),pl(ts(1a,2c),ts(2b,2c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))),4pl24(ts(1a,1c),ts(2a,2c),ts(1b,2c),ts(2b,1c)),ispl12(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,1c),ts(2a,1c)),pl(ts(1b,2c),ts(2a,2c)),pl(ts(1a,2c),ts(2b,2c)),t11(1c),t11(b,a,c,symeq(a,b,e),2c)),4pl24(ts(1b,1c),ts(2a,1c),ts(1a,2c),ts(2b,2c))):is(pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))))
+-iv4d
+e@eqtd1:=eqi12(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)),pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)),t12".iv4d"):eq(td(a,c),td(b,c))
+eqtd2:=tr3eq(td(c,a),td(a,c),td(b,c),td(c,b),comtd(c,a),eqtd1,comtd(b,c)):eq(td(c,a),td(c,b))
+d@[e:eq(a,b)][f:eq(c,d)]
+eqtd12:=treq(td(a,c),td(b,c),td(b,d),eqtd1(a,b,c,e),eqtd2(c,d,b,f)):eq(td(a,c),td(b,d))
+b@[z:zero(a)]
++4d192
+t1:=tris(cut,pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1a,2b),ts(2a,1b)),ispl12(ts(1a,1b),ts(2a,1b),ts(2a,2b),ts(1a,2b),ists1(1a,2a,1b,z),ists1(2a,1a,2b,symis(cut,1a,2a,z))),compl(ts(2a,1b),ts(1a,2b))):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
+-4d192
+satzd192a:=zeroi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t1".4d192"):zero(td(a,b))
+b@[z:zero(b)]
+satzd192b:=eqzero(td(b,a),td(a,b),comtd(b,a),satzd192a(b,a,z)):zero(td(a,b))
+b@[z:zero(a)]
+td01:=satzd192a(z):zero(td(a,b))
+b@[z:zero(b)]
+td02:=satzd192b(z):zero(td(a,b))
+b@satzd197a:=tr3eq(td(m0d(a),b),df(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b))),df(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b))),m0d(td(a,b)),tdeq2a(b,2a,1a),eqsmsd(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b)),compl(ts(2a,1b),ts(1a,2b)),compl(ts(2a,2b),ts(1a,1b))),m0deqb(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))):eq(td(m0d(a),b),m0d(td(a,b)))
+satzd197b:=tr3eq(td(a,m0d(b)),td(m0d(b),a),m0d(td(b,a)),m0d(td(a,b)),comtd(a,m0d(b)),satzd197a(b,a),eqm0d(td(b,a),td(a,b),comtd(b,a))):eq(td(a,m0d(b)),m0d(td(a,b)))
+satzd197c:=treq2(td(m0d(a),b),td(a,m0d(b)),m0d(td(a,b)),satzd197a,satzd197b):eq(td(m0d(a),b),td(a,m0d(b)))
+satzd197d:=symeq(td(m0d(a),b),td(a,m0d(b)),satzd197c):eq(td(a,m0d(b)),td(m0d(a),b))
+satzd197e:=symeq(td(m0d(a),b),m0d(td(a,b)),satzd197a):eq(m0d(td(a,b)),td(m0d(a),b))
+satzd197f:=symeq(td(a,m0d(b)),m0d(td(a,b)),satzd197b):eq(m0d(td(a,b)),td(a,m0d(b)))
+satzd198:=treq(td(m0d(a),m0d(b)),td(a,m0d(m0d(b))),td(a,b),satzd197c(a,m0d(b)),eqtd2(m0d(m0d(b)),b,a,satzd177(b))):eq(td(m0d(a),m0d(b)),td(a,b))
+satzd198a:=symeq(td(m0d(a),m0d(b)),td(a,b),satzd198):eq(td(a,b),td(m0d(a),m0d(b)))
+[p:posd(a)][q:posd(b)]
++*iv4d
+q@[r:cut]
+t13:=tris(cut,pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,pl(mn(1b,2b,q),2b)),ts(r,1b),distpt2(r,mn(1b,2b,q),2b),ists2(pl(mn(1b,2b,q),2b),1b,r,satz140e(1b,2b,q))):is(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b))
+[s:cut]
+t14:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),s),pl(ts(r,1b),s),asspl2(ts(r,mn(1b,2b,q)),ts(r,2b),s),ispl1(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b),s,t13)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s))
+t15:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s),pl(s,ts(r,1b)),t14,compl(ts(r,1b),s)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(s,ts(r,1b)))
+q@t16:=satz135h(pl(ts(1a,2b),ts(2a,2b)),pl(ts(2a,2b),ts(1a,2b)),ts(1a,mn(1b,2b,q)),ts(2a,mn(1b,2b,q)),compl(ts(1a,2b),ts(2a,2b)),satz145a(1a,2a,mn(1b,2b,q),p)):more(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))))
+t17:=ismore12(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))),pl(ts(1a,2b),ts(2a,1b)),t14(1a,ts(2a,2b)),t15(2a,ts(1a,2b)),t16):more(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
+-iv4d
+q@ptdpp:=posdi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t17".iv4d"):posd(td(a,b))
+b@[p:posd(a)][n:negd(b)]
++*iv4d
+n@t18:=eqposd(td(a,m0d(b)),m0d(td(a,b)),satzd197b(a,b),ptdpp(a,m0d(b),p,satzd176c(b,n))):posd(m0d(td(a,b)))
+-iv4d
+n@ntdpn:=satzd176f(td(a,b),t18".iv4d"):negd(td(a,b))
+b@[n:negd(a)][p:posd(b)]
+ntdnp:=eqnegd(td(b,a),td(a,b),comtd(b,a),ntdpn(b,a,p,n)):negd(td(a,b))
+b@[n:negd(a)][o:negd(b)]
+ptdnn:=eqposd(td(m0d(a),m0d(b)),td(a,b),satzd198(a,b),ptdpp(m0d(a),m0d(b),satzd176c(a,n),satzd176c(b,o))):posd(td(a,b))
+b@[n:not(zero(a))][o:not(zero(b))]
++*4d192
+o@[p:posd(a)][q:posd(b)]
+t2:=pnot0d(td(a,b),ptdpp(a,b,p,q)):not(zero(td(a,b)))
+p@[m:negd(b)]
+t3:=nnot0d(td(a,b),ntdpn(a,b,p,m)):not(zero(td(a,b)))
+p@t4:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t2(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t3(t)):not(zero(td(a,b)))
+o@[m:negd(a)][p:posd(b)]
+t5:=nnot0d(td(a,b),ntdnp(a,b,m,p)):not(zero(td(a,b)))
+m@[l:negd(b)]
+t6:=pnot0d(td(a,b),ptdnn(a,b,m,l)):not(zero(td(a,b)))
+m@t7:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t5(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t6(t)):not(zero(td(a,b)))
+-4d192
+o@satzd192d:=rappd(a,not(zero(td(a,b))),[t:posd(a)]t4".4d192"(t),th2"l.imp"(zero(a),not(zero(td(a,b))),n),[t:negd(a)]t7".4d192"(t)):not(zero(td(a,b)))
+b@[z:zero(td(a,b))]
++*4d192
+z@[n:not(zero(a))]
+t8:=et(zero(b),th3"l.imp"(not(zero(b)),not(zero(td(a,b))),weli(zero(td(a,b)),z),[t:not(zero(b))]satzd192d(n,t))):zero(b)
+-4d192
+z@satzd192c:=[t:not(zero(a))]t8".4d192"(t):or(zero(a),zero(b))
++4d193
+b@[p:posd(a)][q:posd(b)]
+t1:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdpp(a,b,p,q))),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+p@[n:negd(b)]
+t2:=treq(absd(td(a,b)),m0d(td(a,b)),td(a,m0d(b)),absnd(td(a,b),ntdpn(a,b,p,n)),satzd197f(a,b)):eq(absd(td(a,b)),td(a,m0d(b)))
+t3:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,m0d(b)),t2,eqtd12(absd(a),a,absd(b),m0d(b),absnnd(a,pnotnd(a,p)),absnd(b,n))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[z:zero(a)]
+t4:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td01(a,b,z)),td01(absd(a),absd(b),satzd166f(a,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[z:zero(b)]
+t5:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td02(a,b,z)),td02(absd(a),absd(b),satzd166f(b,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[n:negd(a)][p:posd(b)]
+t6:=tr3eq(absd(td(a,b)),absd(td(b,a)),td(absd(b),absd(a)),td(absd(a),absd(b)),eqabsd(td(a,b),td(b,a),comtd(a,b)),t3(b,a,p,n),comtd(absd(b),absd(a))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+n@[o:negd(b)]
+t7:=treq(td(absd(a),absd(b)),td(m0d(a),m0d(b)),td(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o)),satzd198(a,b)):eq(td(absd(a),absd(b)),td(a,b))
+t8:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdnn(a,b,n,o))),t7):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[p:posd(a)]
+t9:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t1(p,t),[t:zero(b)]t5(t),[t:negd(b)]t3(p,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[n:negd(a)]
+t10:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t6(n,t),[t:zero(b)]t5(t),[t:negd(b)]t8(n,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
+-4d193
+b@satzd193:=rappd(a,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(a)]t9".4d193"(t),[t:zero(a)]t4".4d193"(t),[t:negd(a)]t10".4d193"(t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
+satzd103a:=symeq(absd(td(a,b)),td(absd(a),absd(b)),satzd193):eq(td(absd(a),absd(b)),absd(td(a,b)))
+@1df:=pdofrp(1rp):dif
++4d195
+a@t1:=tris(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(ts(1a,pl(1rp,1rp)),pl(ts(2a,1rp),2a)),pl(pl(1a,1a),pl(2a,2a)),asspl1(ts(1a,pl(1rp,1rp)),ts(2a,1rp),2a),ispl12(ts(1a,pl(1rp,1rp)),pl(1a,1a),pl(ts(2a,1rp),2a),pl(2a,2a),a2isapa(1a),ispl1(ts(2a,1rp),2a,2a,satz151(2a)))):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(pl(1a,1a),pl(2a,2a)))
+t2:=tris(cut,pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,ts(1a,1rp)),ts(2a,pl(1rp,1rp))),pl(pl(1a,1a),pl(2a,2a)),asspl2(1a,ts(1a,1rp),ts(2a,pl(1rp,1rp))),ispl12(pl(1a,ts(1a,1rp)),pl(1a,1a),ts(2a,pl(1rp,1rp)),pl(2a,2a),ispl2(ts(1a,1rp),1a,1a,satz151(1a)),a2isapa(2a))):is(pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)))
+t3:=tris2(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)),t1,t2):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))))
+-4d195
+a@satzd195:=treq(td(a,1df),df(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),a,tdeq1a(a,pl(1rp,1rp),1rp),eqi2(a,pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp))),t3".4d195")):eq(td(a,1df),a)
+satzd195a:=symeq(td(a,1df),a,satzd195):eq(a,td(a,1df))
+satzd195b:=treq(td(1df,a),td(a,1df),a,comtd(1df,a),satzd195):eq(td(1df,a),a)
+satzd195c:=symeq(td(1df,a),a,satzd195b):eq(a,td(1df,a))
+b@[p:posd(a)][q:posd(b)]
+satzd196a:=symeq(td(absd(a),absd(b)),td(a,b),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(td(a,b),td(absd(a),absd(b)))
+b@[n:negd(a)][o:negd(b)]
+satzd196b:=treq2(td(a,b),td(absd(a),absd(b)),td(m0d(a),m0d(b)),satzd198a(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o))):eq(td(a,b),td(absd(a),absd(b)))
+b@[p:posd(a)][n:negd(b)]
+satzd196c:=treq1(td(a,b),m0d(td(absd(a),absd(b))),td(absd(a),m0d(absd(b))),eqtd12(absd(a),a,m0d(absd(b)),b,absnnd(a,pnotnd(a,p)),satzd177b(absd(b),b,absnd(b,n))),satzd197b(absd(a),absd(b))):eq(td(a,b),m0d(td(absd(a),absd(b))))
+b@[n:negd(a)][p:posd(b)]
+satzd196d:=tr3eq(td(a,b),td(b,a),m0d(td(absd(b),absd(a))),m0d(td(absd(a),absd(b))),comtd(a,b),satzd196c(b,a,p,n),eqm0d(td(absd(b),absd(a)),td(absd(a),absd(b)),comtd(absd(b),absd(a)))):eq(td(a,b),m0d(td(absd(a),absd(b))))
++4d196
+b@p1p2:=and(posd(a),posd(b)):'prop'
+p1n2:=and(posd(a),negd(b)):'prop'
+n1p2:=and(negd(a),posd(b)):'prop'
+n1n2:=and(negd(a),negd(b)):'prop'
+-4d196
+b@[n:not(zero(a))][o:not(zero(b))][e:eq(td(a,b),td(absd(a),absd(b)))]
++*4d196
+o@t1:=ptdpp(absd(a),absd(b),satzd166e(a,n),satzd166e(b,o)):posd(td(absd(a),absd(b)))
+e@t2:=pnotnd(td(a,b),eqposd(td(absd(a),absd(b)),td(a,b),symeq(td(a,b),td(absd(a),absd(b)),e),t1)):not(negd(td(a,b)))
+[p:posd(a)]
+t3:=th3"l.imp"(negd(b),negd(td(a,b)),t2,[t:negd(b)]ntdpn(a,b,p,t)):not(negd(b))
+t4:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t3,o):posd(b)
+t5:=andi(posd(a),posd(b),p,t4):p1p2
+t6:=ori1(p1p2,n1n2,t5):or(p1p2,n1n2)
+e@[m:negd(a)]
+t7:=th3"l.imp"(posd(b),negd(td(a,b)),t2,[t:posd(b)]ntdnp(a,b,m,t)):not(posd(b))
+t8:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t7):negd(b)
+t9:=andi(negd(a),negd(b),m,t8):n1n2
+t10:=ori2(p1p2,n1n2,t9):or(p1p2,n1n2)
+-4d196
+e@satzd196e:=rappd(a,or(p1p2".4d196",n1n2".4d196"),[t:posd(a)]t6".4d196"(t),th2"l.imp"(zero(a),or(p1p2".4d196",n1n2".4d196"),n),[t:negd(a)]t10".4d196"(t)):or(and(posd(a),posd(b)),and(negd(a),negd(b)))
+o@[e:eq(td(a,b),m0d(td(absd(a),absd(b))))]
++*4d196
+o@t11:=satzd176a(td(absd(a),absd(b)),t1):negd(m0d(td(absd(a),absd(b))))
+e@t12:=nnotpd(td(a,b),eqnegd(m0d(td(absd(a),absd(b))),td(a,b),symeq(td(a,b),m0d(td(absd(a),absd(b))),e),t11)):not(posd(td(a,b)))
+[p:posd(a)]
+t13:=th3"l.imp"(posd(b),posd(td(a,b)),t12,[t:posd(b)]ptdpp(a,b,p,t)):not(posd(b))
+t14:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t13):negd(b)
+t15:=andi(posd(a),negd(b),p,t14):p1n2
+t16:=ori1(p1n2,n1p2,t15):or(p1n2,n1p2)
+e@[m:negd(a)]
+t17:=th3"l.imp"(negd(b),posd(td(a,b)),t12,[t:negd(b)]ptdnn(a,b,m,t)):not(negd(b))
+t18:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t17,o):posd(b)
+t19:=andi(negd(a),posd(b),m,t18):n1p2
+t20:=ori2(p1n2,n1p2,t19):or(p1n2,n1p2)
+-4d196
+e@satzd196f:=rappd(a,or(p1n2".4d196",n1p2".4d196"),[t:posd(a)]t16".4d196"(t),th2"l.imp"(zero(a),or(p1n2".4d196",n1p2".4d196"),n),[t:negd(a)]t20".4d196"(t)):or(and(posd(a),negd(b)),and(negd(a),posd(b)))
++4d199
+@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
+t1:=tris(cut,ts(pl(ts(p,r),ts(q,s)),t),pl(ts(ts(p,r),t),ts(ts(q,s),t)),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),disttp1(ts(p,r),ts(q,s),t),ispl12(ts(ts(p,r),t),ts(p,ts(r,t)),ts(ts(q,s),t),ts(q,ts(s,t)),assts1(p,r,t),assts1(q,s,t))):is(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))))
+t2:=tris(cut,pl(ts(q,ts(s,t)),ts(q,ts(r,u))),pl(ts(q,ts(r,u)),ts(q,ts(s,t))),ts(q,pl(ts(r,u),ts(s,t))),compl(ts(q,ts(s,t)),ts(q,ts(r,u))),distpt2(q,ts(r,u),ts(s,t))):is(pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))))
+t3:=tr3is(cut,pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(pl(ts(p,ts(r,t)),ts(q,ts(s,t))),pl(ts(p,ts(s,u)),ts(q,ts(r,u)))),pl(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u)))),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))),ispl12(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),ts(pl(ts(p,s),ts(q,r)),u),pl(ts(p,ts(s,u)),ts(q,ts(r,u))),t1,t1(p,q,s,r,u,t)),4pl23(ts(p,ts(r,t)),ts(q,ts(s,t)),ts(p,ts(s,u)),ts(q,ts(r,u))),ispl12(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),ts(p,pl(ts(r,t),ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))),distpt2(p,ts(r,t),ts(s,u)),t2)):is(pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))))
+-4d199
+c@satzd199:=tr3eq(td(td(a,b),c),df(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c))),df(pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c))))),td(a,td(b,c)),tdeq2a(c,pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))),eqsmsd(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c)),pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c)))),t3".4d199"(1a,2a,1b,2b,1c,2c),t3".4d199"(1a,2a,1b,2b,2c,1c)),tdeq1b(a,pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)))):eq(td(td(a,b),c),td(a,td(b,c)))
+asstd1:=satzd199:eq(td(td(a,b),c),td(a,td(b,c)))
+asstd2:=symeq(td(td(a,b),c),td(a,td(b,c)),satzd199):eq(td(a,td(b,c)),td(td(a,b),c))
++4d201
+@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
+t1:=tris(cut,pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(p,t)),pl(ts(q,s),ts(q,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))),ispl12(ts(p,pl(r,t)),pl(ts(p,r),ts(p,t)),ts(q,pl(s,u)),pl(ts(q,s),ts(q,u)),disttp2(p,r,t),disttp2(q,s,u)),4pl23(ts(p,r),ts(p,t),ts(q,s),ts(q,u))):is(pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))))
+-4d201
+satzd201:=tr3eq(td(a,pd(b,c)),df(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c)))),df(pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c)))),pd(td(a,b),td(a,c)),tdeq1a(a,pl(1b,1c),pl(2b,2c)),eqsmsd(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c))),pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c))),t1".4d201"(1a,2a,1b,2b,1c,2c),t1".4d201"(1a,2a,2b,1b,2c,1c)),pdeq12b(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)))):eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
+disttpd1:=tr3eq(td(pd(a,b),c),td(c,pd(a,b)),pd(td(c,a),td(c,b)),pd(td(a,c),td(b,c)),comtd(pd(a,b),c),satzd201(c,a,b),eqpd12(td(c,a),td(a,c),td(c,b),td(b,c),comtd(c,a),comtd(c,b))):eq(td(pd(a,b),c),pd(td(a,c),td(b,c)))
+disttpd2:=satzd201:eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
+distptd1:=symeq(td(pd(a,b),c),pd(td(a,c),td(b,c)),disttpd1):eq(pd(td(a,c),td(b,c)),td(pd(a,b),c))
+distptd2:=symeq(td(a,pd(b,c)),pd(td(a,b),td(a,c)),disttpd2):eq(pd(td(a,b),td(a,c)),td(a,pd(b,c)))
+satzd202:=treq(td(a,md(b,c)),pd(td(a,b),td(a,m0d(c))),md(td(a,b),td(a,c)),disttpd2(a,b,m0d(c)),eqpd2(td(a,m0d(c)),m0d(td(a,c)),td(a,b),satzd197b(a,c))):eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
+disttmd1:=treq(td(md(a,b),c),pd(td(a,c),td(m0d(b),c)),md(td(a,c),td(b,c)),disttpd1(a,m0d(b),c),eqpd2(td(m0d(b),c),m0d(td(b,c)),td(a,c),satzd197a(b,c))):eq(td(md(a,b),c),md(td(a,c),td(b,c)))
+disttmd2:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
+distmtd1:=symeq(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1):eq(md(td(a,c),td(b,c)),td(md(a,b),c))
+distmtd2:=symeq(td(a,md(b,c)),md(td(a,b),td(a,c)),disttmd2):eq(md(td(a,b),td(a,c)),td(a,md(b,c)))
+satzd200:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
+[m:mored(a,b)]
++4d203
+t1:=satzd182d(a,b,m):posd(md(a,b))
+-4d203
+[p:posd(c)]
++*4d203
+p@t2:=eqposd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ptdpp(md(a,b),c,t1,p)):posd(md(td(a,c),td(b,c)))
+-4d203
+p@satzd203a:=satzd182a(td(a,c),td(b,c),t2".4d203"):mored(td(a,c),td(b,c))
+m@[z:zero(c)]
+satzd203b:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
+m@[n:negd(c)]
++*4d203
+n@t3:=eqnegd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ntdpn(md(a,b),c,t1,n)):negd(md(td(a,c),td(b,c)))
+-4d203
+n@satzd203c:=satzd182c(td(a,c),td(b,c),t3".4d203"):lessd(td(a,c),td(b,c))
+p@satzd203d:=eqmored12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203a):mored(td(c,a),td(c,b))
+z@satzd203e:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
+n@satzd203f:=eqlessd12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203c):lessd(td(c,a),td(c,b))
+c@[l:lessd(a,b)][p:posd(c)]
+satzd203g:=lemmad5(td(b,c),td(a,c),satzd203a(b,a,c,lemmad6(a,b,l),p)):lessd(td(a,c),td(b,c))
+l@[z:zero(c)]
+satzd203h:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
+l@[n:negd(c)]
+satzd203j:=lemmad6(td(b,c),td(a,c),satzd203c(b,a,c,lemmad6(a,b,l),n)):mored(td(a,c),td(b,c))
+p@satzd203k:=lemmad5(td(c,b),td(c,a),satzd203d(b,a,c,lemmad6(a,b,l),p)):lessd(td(c,a),td(c,b))
+z@satzd203l:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
+n@satzd203m:=lemmad6(td(c,b),td(c,a),satzd203f(b,a,c,lemmad6(a,b,l),n)):mored(td(c,a),td(c,b))
++*iv4d
+@[p:cut][q:cut]
+t19:=tris(cut,ts(q,pl(p,1rp)),pl(ts(q,p),ts(q,1rp)),pl(ts(q,p),q),disttp2(q,p,1rp),ispl2(ts(q,1rp),q,ts(q,p),satz151(q))):is(ts(q,pl(p,1rp)),pl(ts(q,p),q))
+[r:cut]
+t20:=tris(cut,pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(pl(ts(q,p),q),r),pl(ts(q,p),pl(q,r)),ispl12(ts(q,pl(p,1rp)),pl(ts(q,p),q),ts(r,1rp),r,t19,satz151(r)),asspl1(ts(q,p),q,r)):is(pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)))
+t21:=tr3is(cut,pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)),pl(ts(q,p),pl(r,q)),compl(ts(r,1rp),ts(q,pl(p,1rp))),t20,ispl2(pl(q,r),pl(r,q),ts(q,p),compl(q,r))):is(pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,p),pl(r,q)))
+a@[p:posd(a)]
+arp:=rpofpd(a,p):cut
+arpi:=ov(1rp,arp):cut
+ai:=pdofrp(arpi):dif
+t22:=tr3eq(td(a,ai),df(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp)))),df(pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a))),df(ts(1a,arpi),ts(2a,arpi)),tdeq1a(a,pl(arpi,1rp),1rp),eqsmsd(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp))),pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a)),t20(arpi,1a,2a),t21(arpi,2a,1a)),lemmad2(ts(1a,arpi),ts(2a,arpi),pl(1a,2a))):eq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)))
+t23:=tr3is(cut,ts(1a,arpi),ts(pl(2a,arp),arpi),pl(ts(2a,arpi),ts(arp,arpi)),pl(ts(2a,arpi),1rp),ists1(1a,pl(2a,arp),arpi,satz140d(1a,2a,p)),disttp1(2a,arp,arpi),ispl2(ts(arp,arpi),1rp,ts(2a,arpi),satz153c(1rp,arp))):is(ts(1a,arpi),pl(ts(2a,arpi),1rp))
+t24:=tr3is(cut,pl(ts(1a,arpi),1rp),pl(pl(ts(2a,arpi),1rp),1rp),pl(ts(2a,arpi),pl(1rp,1rp)),pl(pl(1rp,1rp),ts(2a,arpi)),ispl1(ts(1a,arpi),pl(ts(2a,arpi),1rp),1rp,t23),asspl1(ts(2a,arpi),1rp,1rp),compl(ts(2a,arpi),pl(1rp,1rp))):is(pl(ts(1a,arpi),1rp),pl(pl(1rp,1rp),ts(2a,arpi)))
+t25:=eqi12(ts(1a,arpi),ts(2a,arpi),pl(1rp,1rp),1rp,t24):eq(df(ts(1a,arpi),ts(2a,arpi)),1df)
+t26:=treq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)),1df,t22,t25):eq(td(a,ai),1df)
+t27:=somei(dif,[x:dif]eq(td(a,x),1df),ai,t26):some"l"(dif,[x:dif]eq(td(a,x),1df))
+a@[n:negd(a)]
+t28:=satzd176c(a,n):posd(m0d(a))
+[h:dif][e:eq(td(m0d(a),h),1df)]
+t29:=treq(td(a,m0d(h)),td(m0d(a),h),1df,satzd197d(a,h),e):eq(td(a,m0d(h)),1df)
+t30:=somei(dif,[x:dif]eq(td(a,x),1df),m0d(h),t29):some"l"(dif,[x:dif]eq(td(a,x),1df))
+n@t31:=someapp(dif,[x:dif]eq(td(m0d(a),x),1df),t27(m0d(a),t28),some"l"(dif,[x:dif]eq(td(a,x),1df)),[x:dif][t:eq(td(m0d(a),x),1df)]t30(x,t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
+-iv4d
+a@[n:not(zero(a))]
+lemmad7:=rappd(a,some"l"(dif,[x:dif]eq(td(a,x),1df)),[t:posd(a)]t27".iv4d"(t),th2"l.imp"(zero(a),some"l"(dif,[x:dif]eq(td(a,x),1df)),n),[t:negd(a)]t31".iv4d"(t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
+b@[n:not(zero(b))][h:dif][k:dif][e:eq(td(b,h),a)][f:eq(td(b,k),a)]
++4d204
+t1:=treq2(td(b,h),td(b,k),a,e,f):eq(td(b,h),td(b,k))
+t2:=eqzero(md(td(b,h),td(b,k)),td(b,md(h,k)),distmtd2(b,h,k),satzd182e(td(b,h),td(b,k),t1)):zero(td(b,md(h,k)))
+t3:=ore2(zero(b),zero(md(h,k)),satzd192c(b,md(h,k),t2),n):zero(md(h,k))
+-4d204
+satzd204b:=satzd182b(h,k,t3".4d204"):eq(h,k)
++*4d204
+n@[h:dif][e:eq(td(b,h),1df)]
+t4:=tr3eq(td(b,td(h,a)),td(td(b,h),a),td(1df,a),a,asstd2(b,h,a),eqtd1(td(b,h),1df,a,e),satzd195b(a)):eq(td(b,td(h,a)),a)
+t5:=somei(dif,[x:dif]eq(td(b,x),a),td(h,a),t4):some"l"(dif,[x:dif]eq(td(b,x),a))
+-4d204
+n@satzd204a:=someapp(dif,[x:dif]eq(td(b,x),1df),lemmad7(b,n),some"l"(dif,[x:dif]eq(td(b,x),a)),[x:dif][t:eq(td(b,x),1df)]t5".4d204"(x,t)):some"l"(dif,[x:dif]eq(td(b,x),a))
+@[r:cut][s:cut][m:more(r,s)]
++iv5d
+t1:=ismore12(pl(r,pl(1rp,1rp)),pl(pl(r,1rp),1rp),pl(s,pl(1rp,1rp)),pl(pl(s,1rp),1rp),asspl2(r,1rp,1rp),asspl2(s,1rp,1rp),satz134(r,s,pl(1rp,1rp),m)):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
+-iv5d
+morerpepd:=moredi12(pl(r,1rp),1rp,pl(s,1rp),1rp,t1".iv5d"):mored(pdofrp(r),pdofrp(s))
+s@[m:mored(pdofrp(r),pdofrp(s))]
++*iv5d
+m@t2:=morede12(pl(r,1rp),1rp,pl(s,1rp),1rp,m):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
+-iv5d
+m@morerpipd:=satz136a(r,s,pl(1rp,1rp),ismore12(pl(pl(r,1rp),1rp),pl(r,pl(1rp,1rp)),pl(pl(s,1rp),1rp),pl(s,pl(1rp,1rp)),asspl1(r,1rp,1rp),asspl1(s,1rp,1rp),t2".iv5d")):more(r,s)
+s@[l:less(r,s)]
+lessrpepd:=lemmad5(pdofrp(s),pdofrp(r),morerpepd(s,r,satz122(r,s,l))):lessd(pdofrp(r),pdofrp(s))
+s@[l:lessd(pdofrp(r),pdofrp(s))]
+lessrpipd:=satz121(s,r,morerpipd(s,r,lemmad6(pdofrp(r),pdofrp(s),l))):less(r,s)
++*iv5d
+@i:=1rp:cut
+2:=pl(i,i):cut
+r@rp1:=pl(r,i):cut
+s@sp1:=pl(s,i):cut
+rps:=pl(r,s):cut
+rs:=ts(r,s):cut
+t3:=tris(cut,pl(pl(rp1,sp1),i),pl(pl(rps,2),i),pl(pl(rps,i),2),ispl1(pl(rp1,sp1),pl(rps,2),i,4pl23(r,i,s,i)),3pl23(rps,2,i)):is(pl(pl(rp1,sp1),i),pl(pl(rps,i),2))
+t4:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(rp1,sp1),2),pdofrp(rps),pdeq12a(rp1,i,sp1,i),eqi12(pl(rp1,sp1),2,pl(rps,i),i,t3)):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(rps))
+-iv5d
+s@lemmad8:=t4".iv5d":eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
++*iv5d
+s@t5:=tris(cut,ts(r,sp1),pl(rs,ts(r,i)),pl(rs,r),disttp2(r,s,i),ispl2(ts(r,i),r,rs,satz151(r))):is(ts(r,sp1),pl(rs,r))
+t6:=tr4is(cut,ts(rp1,sp1),pl(ts(r,sp1),ts(i,sp1)),pl(pl(rs,r),sp1),pl(pl(pl(rs,r),s),i),pl(pl(rs,rps),i),disttp1(r,i,sp1),ispl12(ts(r,sp1),pl(rs,r),ts(i,sp1),sp1,t5,satz151b(sp1)),asspl2(pl(rs,r),s,i),ispl1(pl(pl(rs,r),s),pl(rs,rps),i,asspl1(rs,r,s))):is(ts(rp1,sp1),pl(pl(rs,rps),i))
+t7:=tr3is(cut,pl(ts(rp1,sp1),ts(i,i)),pl(pl(pl(rs,rps),i),i),pl(pl(rs,rps),2),pl(rs,pl(rps,2)),ispl12(ts(rp1,sp1),pl(pl(rs,rps),i),ts(i,i),i,t6,satz151(i)),asspl1(pl(rs,rps),i,i),asspl1(rs,rps,2)):is(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)))
+t8:=tris(cut,pl(ts(rp1,i),ts(i,sp1)),pl(rp1,sp1),pl(rps,2),ispl12(ts(rp1,i),rp1,ts(i,sp1),sp1,satz151(rp1),satz151b(sp1)),4pl23(r,i,s,i)):is(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2))
+t9:=tris(cut,pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,i),pl(rps,2)),pl(pl(rs,pl(rps,2)),i),ispl2(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2),pl(rs,i),t8),3pl23(rs,i,pl(rps,2))):is(pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i))
+t10:=tris2(cut,pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i),ispl1(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)),i,t7),t9):is(pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))))
+t11:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1))),pdofrp(rs),tdeq12a(rp1,i,sp1,i),eqi12(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1)),pl(rs,i),i,t10)):eq(td(pdofrp(r),pdofrp(s)),pdofrp(rs))
+-iv5d
+s@lemmad9:=t11".iv5d":eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
+@[r:cut][s0:set(cut)]
+in:=esti(cut,r,s0):'prop'
+@[s0:set(cut)][t0:set(cut)][p0:all([x:cut]or(in(x,s0),in(x,t0)))][p1a:nonempty(cut,s0)][p1b:nonempty(cut,t0)][p2:all([x:cut][t:in(x,s0)]all([y:cut][u:in(y,t0)]less(x,y)))]
++5p205
+t0@[r:cut]
+prop1:=all([x:cut][t:less(x,r)]in(x,s0)):'prop'
+prop2:=all([x:cut][t:more(x,r)]in(x,t0)):'prop'
+prop3:=and(prop1,prop2):'prop'
+p2@[r1:cut][r2:cut][pr1:prop3(r1)][pr2:prop3(r2)]
+t1:=ande2(prop1(r1),prop2(r1),pr1):prop2(r1)
+t2:=ande1(prop1(r2),prop2(r2),pr2):prop1(r2)
+[l:less(r1,r2)][x0:rat]
+rx:=rpofrt(x0):cut
+[l1:less(r1,rx)][l2:less(rx,r2)]
+t3:=<l2><rx>t2:in(rx,s0)
+t4:=<satz122(r1,rx,l1)><rx>t1:in(rx,t0)
+t5:=<refis(cut,rx)>ec3e31(is(rx,rx),more(rx,rx),less(rx,rx),satz123b(rx,rx),<t4><rx><t3><rx>p2):con
+l@t6:=satz159app(r1,r2,l,con,[x:rat][t:less(r1,rpofrt(x))][u:less(rpofrt(x),r2)]t5(x,t,u)):con
+pr2@t7:=[t:less(r1,r2)]t6(t):not(less(r1,r2))
+t8:=[t:more(r1,r2)]t6(r2,r1,pr2,pr1,satz121(r1,r2,t)):not(more(r1,r2))
+t9:=or3e1(is(r1,r2),more(r1,r2),less(r1,r2),satz123a(r1,r2),t8,t7):is(r1,r2)
+p2@t10:=[x:cut][y:cut][t:prop3(x)][u:prop3(y)]t9(x,y,t,u):amone(cut,[x:cut]prop3(x))
+[x0:rat]
+schnittprop:=some([y:cut]and(in(y,s0),lrt(y,x0))):'prop'
+p2@schnittset:=setof(rat,[x:rat]schnittprop(x)):set(rat)
+[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)]
+t11:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
+t12:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t11):schnittprop(x0)
+t13:=estii(rat,[x:rat]schnittprop(x),x0,t12):in"rt"(x0,schnittset)
+r@[i:in(r,t0)][x0:rat][ux:urt(r,x0)][s:cut][j:in(s,s0)]
+t14:=satz122(s,r,<i><r><j><s>p2):more(r,s)
+t15:=satz158b(r,x0,ux):moreis(rpofrt(x0),r)
+t16:=moreisi1(rpofrt(x0),s,satz127c(rpofrt(x0),r,s,t15,t14)):moreis(rpofrt(x0),s)
+t17:=satz158d(s,x0,t16):urt(s,x0)
+s@t18:=weli(ec(in(s,s0),lrt(s,x0)),[t:in(s,s0)]t17(t)):not(and(in(s,s0),lrt(s,x0)))
+ux@t19:=th5"l.some"(cut,[y:cut]and(in(y,s0),lrt(y,x0)),[y:cut]t18(y)):not(schnittprop(x0))
+t20:=th3"l.imp"(in"rt"(x0,schnittset),schnittprop(x0),t19,[t:in"rt"(x0,schnittset)]estie(rat,[x:rat]schnittprop(x),x0,t)):not(in"rt"(x0,schnittset))
+p2@[x0:rat][i:in"rt"(x0,schnittset)][y0:rat][l:less"rt"(y0,x0)]
+i@t21:=estie(rat,[x:rat]schnittprop(x),x0,i):schnittprop(x0)
+l@[r:cut][a:and(in(r,s0),lrt(r,x0))]
+t22:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
+t23:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
+t24:=satz120(r,x0,t23,y0,l):lrt(r,y0)
+t25:=andi(in(r,s0),lrt(r,y0),t22,t24):and(in(r,s0),lrt(r,y0))
+t26:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t25):schnittprop(y0)
+l@t27:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,schnittprop(y0),[y:cut][r:and(in(y,s0),lrt(y,x0))]t26(y,r)):schnittprop(y0)
+t28:=estii(rat,[x:rat]schnittprop(x),y0,t27):in"rt"(y0,schnittset)
+i@[r:cut][a:and(in(r,s0),lrt(r,x0))]
+t29:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
+t30:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
+[y0:rat][ly:lrt(r,y0)][l:less"rt"(x0,y0)]
+t31:=andi(in(r,s0),lrt(r,y0),t29,ly):and(in(r,s0),lrt(r,y0))
+t32:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t31):schnittprop(y0)
+t33:=estii(rat,[x:rat]schnittprop(x),y0,t32):in"rt"(y0,schnittset)
+t34:=satz83(x0,y0,l):more"rt"(y0,x0)
+t35:=andi(in"rt"(y0,schnittset),more"rt"(y0,x0),t33,t34):and(in"rt"(y0,schnittset),more"rt"(y0,x0))
+t36:=somei(rat,[y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)),y0,t35):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
+a@t37:=cutapp3(r,x0,t30,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:rat][t:lrt(r,y)][u:less"rt"(x0,y)]t36(y,t,u)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
+i@t38:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:cut][t:and(in(y,s0),lrt(y,x0))]t37(y,t)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
+p2@[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)][s:cut][j:in(s,t0)][y0:rat][uy:urt(s,y0)]
+t39:=cut2(schnittset,x0,t13(r,i,x0,lx),y0,t20(s,j,y0,uy),[x:rat][t:in"rt"(x,schnittset)][y:rat][u:less"rt"(y,x)]t28(x,t,y,u),[x:rat][t:in"rt"(x,schnittset)]t38(x,t)):cutprop(schnittset)
+j@t40:=cutapp1b(s,cutprop(schnittset),[x:rat][t:urt(s,x)]t39(x,t)):cutprop(schnittset)
+lx@t41:=nonemptyapp(cut,t0,p1b,cutprop(schnittset),[y:cut][t:in(y,t0)]t40(y,t)):cutprop(schnittset)
+i@t42:=cutapp1a(r,cutprop(schnittset),[x:rat][t:lrt(r,x)]t41(x,t)):cutprop(schnittset)
+p2@t43:=nonemptyapp(cut,s0,p1a,cutprop(schnittset),[y:cut][t:in(y,s0)]t42(y,t)):cutprop(schnittset)
+snt:=cutof(schnittset,t43):cut
+[r:cut][l:less(r,snt)][x0:rat][ux:urt(r,x0)][lx:lrt(snt,x0)]
+t44:=ini(schnittset,t43,x0,lx):in"rt"(x0,schnittset)
+t45:=estie(rat,[x:rat]schnittprop(x),x0,t44):schnittprop(x0)
+[s:cut][a:and(in(s,s0),lrt(s,x0))]
+t46:=ande1(in(s,s0),lrt(s,x0),a):in(s,s0)
+t47:=ande2(in(s,s0),lrt(s,x0),a):lrt(s,x0)
+t48:=andi(urt(r,x0),lrt(s,x0),ux,t47):and(urt(r,x0),lrt(s,x0))
+t49:=somei(rat,[x:rat]and(urt(r,x),lrt(s,x)),x0,t48):less(r,s)
+t50:=ec3e23(is(s,r),more(s,r),less(s,r),satz123b(s,r),satz122(r,s,t49)):not(less(s,r))
+t51:=th3"l.imp"(in(r,t0),less(s,r),t50,<r><t46><s>p2):not(in(r,t0))
+t52:=ore1(in(r,s0),in(r,t0),<r>p0,t51):in(r,s0)
+lx@t53:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t45,in(r,s0),[y:cut][t:and(in(y,s0),lrt(y,x0))]t52(y,t)):in(r,s0)
+l@t54:=lessapp(r,snt,l,in(r,s0),[x:rat][t:urt(r,x)][u:lrt(snt,x)]t53(x,t,u)):in(r,s0)
+r@[m:more(r,snt)][x0:rat][lx:lrt(r,x0)][ux:urt(snt,x0)][i:in(r,s0)]
+t55:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
+t56:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t55):schnittprop(x0)
+t57:=estii(rat,[x:rat]schnittprop(x),x0,t56):in"rt"(x0,schnittset)
+t58:=ine(schnittset,t43,x0,t57):lrt(snt,x0)
+ux@t59:=th3"l.imp"(in(r,s0),lrt(snt,x0),ux,[t:in(r,s0)]t58(t)):not(in(r,s0))
+t60:=ore2(in(r,s0),in(r,t0),<r>p0,t59):in(r,t0)
+m@t61:=moreapp(r,snt,m,in(r,t0),[x:rat][t:lrt(r,x)][u:urt(snt,x)]t60(x,t,u)):in(r,t0)
+p2@t62:=andi(prop1(snt),prop2(snt),[x:cut][t:less(x,snt)]t54(x,t),[x:cut][t:more(x,snt)]t61(x,t)):prop3(snt)
+t63:=somei(cut,[x:cut]prop3(x),snt,t62):some([x:cut]prop3(x))
+-5p205
+satzp205:=onei(cut,[x:cut]prop3".5p205"(x),t10".5p205",t63".5p205"):one([x:cut]and(all([y:cut][t:less(y,x)]in(y,s0)),all([y:cut][t:more(y,x)]in(y,t0))))
+schnitt:=ind(cut,[x:cut]prop3".5p205"(x),satzp205):cut
+satzp205a:=ande1(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:less(x,schnitt)]in(x,s0))
+satzp205b:=ande2(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:more(x,schnitt)]in(x,t0))
+@[r:cut][s:cut]
++ivad
+@i:=1rp:cut
+r@r1:=pl(r,i):cut
+s@s1:=pl(s,i):cut
+rps:=pl(r,s):cut
+@2:=pl(i,i):cut
+s@t1:=pdeq12a(r1,i,s1,i):eq(pd(pdofrp(r),pdofrp(s)),df(pl(r1,s1),2))
+t2:=tris(cut,pl(r1,s1),pl(rps,2),pl(pl(rps,i),i),4pl23(r,i,s,i),asspl2(rps,i,i)):is(pl(r1,s1),pl(pl(rps,i),i))
+t3:=ispl1(pl(r1,s1),pl(pl(rps,i),i),i,t2):is(pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i))
+t4:=tris(cut,pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i),pl(pl(rps,i),2),t3,asspl1(pl(rps,i),i,i)):is(pl(pl(r1,s1),i),pl(pl(rps,i),2))
+t5:=eqi12(pl(r1,s1),2,pl(rps,i),i,t4):eq(df(pl(r1,s1),2),pdofrp(rps))
+-ivad
+lemmaivad1:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(pl(r,1rp),pl(s,1rp)),pl(1rp,1rp)),pdofrp(pl(r,s)),t1".ivad",t5".ivad"):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
++*ivad
+s@rs:=ts(r,s):cut
+t6:=tdeq12a(r1,i,s1,i):eq(td(pdofrp(r),pdofrp(s)),df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))))
+t7:=tris(cut,ts(r1,s),pl(rs,ts(i,s)),pl(rs,s),disttp1(r,i,s),ispl2(ts(i,s),s,rs,satz151b(s))):is(ts(r1,s),pl(rs,s))
+t8:=tr3is(cut,ts(r1,s1),pl(ts(r1,s),ts(r1,i)),pl(pl(rs,s),r1),pl(pl(rs,i),rps),disttp2(r1,s,i),ispl12(ts(r1,s),pl(rs,s),ts(r1,i),r1,t7,satz151(r1)),4pl24(rs,s,r,i)):is(ts(r1,s1),pl(pl(rs,i),rps))
+t9:=tris(cut,pl(ts(r1,s1),ts(i,i)),pl(pl(pl(rs,i),rps),i),pl(pl(rs,i),pl(rps,i)),ispl12(ts(r1,s1),pl(pl(rs,i),rps),ts(i,i),i,t8,satz151(i)),asspl1(pl(rs,i),rps,i)):is(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)))
+t10:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(pl(rs,i),pl(rps,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),ispl1(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)),i,t9),asspl1(pl(rs,i),pl(rps,i),i)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)))
+t11:=tr3is(cut,pl(pl(rps,i),i),pl(rps,2),pl(r1,s1),pl(ts(r1,i),ts(i,s1)),asspl1(rps,i,i),4pl23(r,s,i,i),ispl12(r1,ts(r1,i),s1,ts(i,s1),satz151a(r1),satz151c(s1))):is(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)))
+t12:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))),t10,ispl2(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)),pl(rs,i),t11)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))))
+t13:=eqi12(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1)),pl(rs,i),i,t12):eq(df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))),pdofrp(rs))
+-ivad
+s@lemmaivad2:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(pl(r,1rp),pl(s,1rp)),ts(1rp,1rp)),pl(ts(pl(r,1rp),1rp),ts(1rp,pl(s,1rp)))),pdofrp(ts(r,s)),t6".ivad",t13".ivad"):eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
+[m:mored(pdofrp(r),pdofrp(s))]
++*ivad
+m@t14:=morede12(r1,i,s1,i,m):more(pl(r1,i),pl(s1,i))
+t15:=satz136a(r1,s1,i,t14):more(r1,s1)
+-ivad
+m@lemmaivad3:=satz136a(r,s,1rp,t15".ivad"):more(r,s)
+@[c:dif][a:dif][b:dif][n:not(negd(a))][o:not(negd(b))][e:eq(td(a,a),c)][f:eq(td(b,b),c)]
++d161
+t1:=treq2(td(a,a),td(b,b),c,e,f):eq(td(a,a),td(b,b))
+t2:=treq(pd(md(td(a,a),td(a,b)),td(b,a)),pd(md(td(a,a),td(a,b)),td(a,b)),td(a,a),eqpd2(td(b,a),td(a,b),md(td(a,a),td(a,b)),comtd(b,a)),pdmd(td(a,a),td(a,b))):eq(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a))
+t3:=tr4eq(td(pd(a,b),md(a,b)),pd(td(a,md(a,b)),td(b,md(a,b))),pd(md(td(a,a),td(a,b)),md(td(b,a),td(b,b))),md(pd(md(td(a,a),td(a,b)),td(b,a)),td(b,b)),md(td(a,a),td(b,b)),disttpd1(a,b,md(a,b)),eqpd12(td(a,md(a,b)),md(td(a,a),td(a,b)),td(b,md(a,b)),md(td(b,a),td(b,b)),disttmd2(a,a,b),disttmd2(b,a,b)),asspd2(md(td(a,a),td(a,b)),td(b,a),m0d(td(b,b))),eqmd1(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a),td(b,b),t2)):eq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)))
+t4:=eqzero(md(td(a,a),td(b,b)),td(pd(a,b),md(a,b)),symeq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)),t3),satzd182e(td(a,a),td(b,b),t1)):zero(td(pd(a,b),md(a,b)))
+t5:=satzd192c(pd(a,b),md(a,b),t4):or(zero(pd(a,b)),zero(md(a,b)))
+[z:zero(a)]
+t6:=eqzero(td(a,a),td(b,b),t1,td01(a,a,z)):zero(td(b,b))
+t7:=th1"l.imp"(zero(b),zero(b),refimp(zero(b)),satzd192c(b,b,t6)):zero(b)
+t8:=zeroeq(a,b,z,t7):eq(a,b)
+f@[p:not(zero(a))]
+t9:=or3e2(zero(a),posd(a),negd(a),axrdo(a),n,p):posd(a)
+t10:=th3"l.imp"(zero(b),zero(a),p,[t:zero(b)]t7(b,a,o,n,f,e,t)):not(zero(b))
+t11:=t9(b,a,o,n,f,e,t10):posd(b)
+t12:=pnot0d(pd(a,b),ppd(a,b,t9,t11)):not(zero(pd(a,b)))
+t13:=ore2(zero(pd(a,b)),zero(md(a,b)),t5,t12):zero(md(a,b))
+t14:=satzd182b(a,b,t13):eq(a,b)
+-d161
+satzd161b:=th1"l.imp"(zero(a),eq(a,b),[t:zero(a)]t8".d161"(t),[t:not(zero(a))]t14".d161"(t)):eq(a,b)
+c@[n:not(negd(c))]
++*d161
+n@[z:zero(c)]
+t15:=zeroeq(td(c,c),c,td01(c,c,z),z):eq(td(c,c),c)
+t16:=andi(not(negd(c)),eq(td(c,c),c),n,t15):and(not(negd(c)),eq(td(c,c),c))
+t17:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),c,t16):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
+n@[o:not(zero(c))]
+t18:=or3e2(zero(c),posd(c),negd(c),axrdo(c),n,o):posd(c)
+crp:=rpofpd(c,t18):cut
+srp:=sqrt(crp):cut
+s:=pdofrp(srp):dif
+t19:=tr3eq(td(s,s),pdofrp(ts(srp,srp)),pdofrp(crp),c,lemmaivad2(srp,srp),isrpepd(ts(srp,srp),crp,thsqrt1(crp)),eqpdrp2(c,t18)):eq(td(s,s),c)
+t20:=andi(not(negd(s)),eq(td(s,s),c),pnotnd(s,posdirp(srp)),t19):and(not(negd(s)),eq(td(s,s),c))
+t21:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),s,t20):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
+-d161
+n@satzd161a:=th1"l.imp"(zero(c),some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c))),[t:zero(c)]t17".d161"(t),[t:not(zero(c))]t21".d161"(t)):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
+@[a:dif][i:intd(a)]
++intd
+[z:zero(a)]
+t1:=ori1(zero(absd(a)),natd(absd(absd(a))),satzd166f(a,z)):intd(absd(a))
+i@[n:natd(absd(a))]
+t2:=natintd(absd(a),n):intd(absd(a))
+-intd
+intabsd:=orapp(zero(a),natd(absd(a)),intd(absd(a)),i,[t:zero(a)]t1".intd"(t),[t:natd(absd(a))]t2".intd"(t)):intd(absd(a))
++*intd
+n@t4:=eqnatd(absd(a),absd(m0d(a)),satzd178a(a),n):natd(absd(m0d(a)))
+-intd
+i@intm0d:=th9"l.or"(zero(a),natd(absd(a)),zero(m0d(a)),natd(absd(m0d(a))),i,[t:zero(a)]satzd176b(a,t),[t:natd(absd(a))]t4".intd"(t)):intd(m0d(a))
+a@[b:dif][i:intd(a)][j:intd(b)]
++*intd
+j@[z:zero(a)]
+t5:=symeq(pd(a,b),b,pd01(a,b,z)):eq(b,pd(a,b))
+t6:=eqintd(b,pd(a,b),t5,j):intd(pd(a,b))
+j@[z:zero(b)]
+t7:=symeq(pd(a,b),a,pd02(a,b,z)):eq(a,pd(a,b))
+t8:=eqintd(a,pd(a,b),t7,i):intd(pd(a,b))
+a@[i:intd(a)][p:posd(a)]
+t9:=<p>ande2(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),posintnatd(a,p,i)):natrp(rpofpd(a,p))
+j@[pp:posd(pd(a,b))]
+apb1:=rpofpd(pd(a,b),pp):cut
+[p:posd(a)]
+a1:=rpofpd(a,p):cut
+[q:posd(b)]
+b1:=rpofpd(b,q):cut
+t10:=natpl(a1,t9(a,i,p),b1,t9(b,j,q)):natrp(pl(a1,b1))
+t11:=eqpd12(a,pdofrp(a1),b,pdofrp(b1),eqpdrp1(a,p),eqpdrp1(b,q)):eq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)))
+t12:=treq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)),pdofrp(pl(a1,b1)),t11,lemmaivad1(a1,b1)):eq(pd(a,b),pdofrp(pl(a1,b1)))
+t13:=tris(cut,apb1,rpofpd(pdofrp(pl(a1,b1)),posdirp(pl(a1,b1))),pl(a1,b1),eqpderp(pd(a,b),pp,pdofrp(pl(a1,b1)),posdirp(pl(a1,b1)),t12),isrppd2(pl(a1,b1))):is(apb1,pl(a1,b1))
+t14:=isp1(cut,[t:cut]natrp(t),pl(a1,b1),apb1,t10,t13):natrp(apb1)
+t15:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t14(t,p,q)):natd(pd(a,b))
+t16:=natintd(pd(a,b),t15):intd(pd(a,b))
+p@[n:negd(b)]
+t17:=satzd176c(b,n):posd(m0d(b))
+b2:=rpofpd(m0d(b),t17):cut
+t18:=eqpd2(b,m0d(m0d(b)),a,satzd177a(b)):eq(pd(a,b),md(a,m0d(b)))
+t19:=eqposd(pd(a,b),md(a,m0d(b)),t18,pp):posd(md(a,m0d(b)))
+t20:=satzd182a(a,m0d(b),t19):mored(a,m0d(b))
+t21:=eqmored12(a,pdofrp(a1),m0d(b),pdofrp(b2),eqpdrp1(a,p),eqpdrp1(m0d(b),t17),t20):mored(pdofrp(a1),pdofrp(b2))
+t22:=lemmaivad3(a1,b2,t21):more(a1,b2)
+t23:=natmn(a1,t9(a,i,p),b2,t9(m0d(b),intm0d(b,j),t17),t22):natrp(mn(a1,b2,t22))
+t24:=eqpd12(m0d(b),pdofrp(b2),pd(a,b),pdofrp(apb1),eqpdrp1(m0d(b),t17),eqpdrp1(pd(a,b),pp)):eq(pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)))
+t25:=tr4eq(a,md(pd(a,b),b),pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)),pdofrp(pl(b2,apb1)),symeq(md(pd(a,b),b),a,mdpd(a,b)),compd(pd(a,b),m0d(b)),t24,lemmaivad1(b2,apb1)):eq(a,pdofrp(pl(b2,apb1)))
+t26:=tris2(cut,pl(b2,apb1),a1,rpofpd(pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1))),isrppd1(pl(b2,apb1)),eqpderp(a,p,pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1)),t25)):is(pl(b2,apb1),a1)
+t27:=satz140g(a1,b2,apb1,t22,t26):is(apb1,mn(a1,b2,t22))
+t28:=isp1(cut,[t:cut]natrp(t),mn(a1,b2,t22),apb1,t23,t27):natrp(apb1)
+t29:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t28(t,p,n)):natd(pd(a,b))
+t30:=natintd(pd(a,b),t29):intd(pd(a,b))
+p@t31:=rappd(b,intd(pd(a,b)),[t:posd(b)]t16(t),[t:zero(b)]t8(t),[t:negd(b)]t30(t)):intd(pd(a,b))
+pp@[n:negd(a)]
+t31a:=th3"l.imp"(negd(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:negd(b)]npd(a,b,n,t)):not(negd(b))
+t32:=th3"l.imp"(zero(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:zero(b)]eqnegd(a,pd(a,b),symeq(pd(a,b),a,pd02(a,b,t)),n)):not(zero(b))
+t33:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t31a,t32):posd(b)
+t34:=eqposd(pd(a,b),pd(b,a),compd(a,b),pp):posd(pd(b,a))
+t35:=t30(b,a,j,i,t34,t33,n):intd(pd(b,a))
+t36:=eqintd(pd(b,a),pd(a,b),compd(b,a),t35):intd(pd(a,b))
+pp@t37:=rappd(a,intd(pd(a,b)),[t:posd(a)]t31(t),[t:zero(a)]t6(t),[t:negd(a)]t36(t)):intd(pd(a,b))
+j@[0p:zero(pd(a,b))]
+t38:=intdi0(pd(a,b),0p):intd(pd(a,b))
+j@[np:negd(pd(a,b))]
+t39:=satzd176c(pd(a,b),np):posd(m0d(pd(a,b)))
+t40:=eqposd(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180(a,b),t39):posd(pd(m0d(a),m0d(b)))
+t41:=t37(m0d(a),m0d(b),intm0d(a,i),intm0d(b,j),t40):intd(pd(m0d(a),m0d(b)))
+t42:=eqintd(pd(m0d(a),m0d(b)),m0d(pd(a,b)),satzd180a(a,b),t41):intd(m0d(pd(a,b)))
+t43:=intm0d(m0d(pd(a,b)),t42):intd(m0d(m0d(pd(a,b))))
+t44:=eqintd(m0d(m0d(pd(a,b))),pd(a,b),satzd177(pd(a,b)),t43):intd(pd(a,b))
+-intd
+j@intpd:=rappd(pd(a,b),intd(pd(a,b)),[t:posd(pd(a,b))]t37".intd"(t),[t:zero(pd(a,b))]t38".intd"(t),[t:negd(pd(a,b))]t44".intd"(t)):intd(pd(a,b))
+intmd:=intpd(a,m0d(b),i,intm0d(b,j)):intd(md(a,b))
++*intd
+j@[n:not(zero(td(a,b)))]
+t45:=th3"l.imp"(zero(a),zero(td(a,b)),n,[t:zero(a)]td01(a,b,t)):not(zero(a))
+t46:=th3"l.imp"(zero(b),zero(td(a,b)),n,[t:zero(b)]td02(a,b,t)):not(zero(b))
+t47:=satzd166e(a,t45):posd(absd(a))
+a3:=rpofpd(absd(a),t47):cut
+t48:=satzd166e(b,t46):posd(absd(b))
+b3:=rpofpd(absd(b),t48):cut
+t49:=natts(a3,t9(absd(a),intabsd(a,i),t47),b3,t9(absd(b),intabsd(b,j),t48)):natrp(ts(a3,b3))
+t50:=satzd166e(td(a,b),n):posd(absd(td(a,b)))
+[p:posd(absd(td(a,b)))]
+atb3:=rpofpd(absd(td(a,b)),p):cut
+t51:=eqtd12(absd(a),pdofrp(a3),absd(b),pdofrp(b3),eqpdrp1(absd(a),t47),eqpdrp1(absd(b),t48)):eq(td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)))
+t52:=tr3eq(absd(td(a,b)),td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)),pdofrp(ts(a3,b3)),satzd193(a,b),t51,lemmaivad2(a3,b3)):eq(absd(td(a,b)),pdofrp(ts(a3,b3)))
+t53:=tris2(cut,atb3,ts(a3,b3),rpofpd(pdofrp(ts(a3,b3)),posdirp(ts(a3,b3))),eqpderp(absd(td(a,b)),p,pdofrp(ts(a3,b3)),posdirp(ts(a3,b3)),t52),isrppd1(ts(a3,b3))):is(atb3,ts(a3,b3))
+t54:=isp1(cut,[t:cut]natrp(t),ts(a3,b3),atb3,t49,t53):natrp(atb3)
+n@t55:=andi(posd(absd(td(a,b))),[t:posd(absd(td(a,b)))]natrp(atb3(t)),t50,[t:posd(absd(td(a,b)))]t54(t)):natd(absd(td(a,b)))
+-intd
+j@inttd:=[t:not(zero(td(a,b)))]t55".intd"(t):intd(td(a,b))
++r
+@eq:=[x:dif][y:dif]eq"rp"(x,y):[x:dif][y:dif]'prop'
+refeq:=[x:dif]refeq"rp"(x):[x:dif]<x><x>eq
+symeq:=[x:dif][y:dif][t:<y><x>eq]symeq"rp"(x,y,t):[x:dif][y:dif][t:<y><x>eq]<x><y>eq
+treq:=[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]treq"rp"(x,y,z,t,u):[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]<z><x>eq
+[a:dif][s:set(dif)]
+inn:=esti(dif,a,s):'prop'
+@real:=ect"eq"(dif,eq,refeq,symeq,treq):'type'
+[r:real][s:real]
+is:=is"e"(real,r,s):'prop'
+nis:=not(is(r,s)):'prop'
+@[p:[x:real]'prop']
+some:=some"l"(real,p):'prop'
+all:=all"l"(real,p):'prop'
+one:=one"e"(real,p):'prop'
+r@[s0:set(real)]
+in:=esti(real,r,s0):'prop'
+a@realof:=ectelt"eq"(dif,eq,refeq,symeq,treq,a):real
+r@class:=ecect"eq"(dif,eq,refeq,symeq,treq,r):set(dif)
+a@innclass:=th5"eq.4"(dif,eq,refeq,symeq,treq,a):inn(a,class(realof(a)))
+r@[a:dif][b:dif][e:eq"rp"(a,b)][air:inn(a,class(r))]
+eqinn:=th8"eq.4"(dif,eq,refeq,symeq,treq,r,a,air,b,e):inn(b,class(r))
+r@[p:'prop'][p1:[x:dif][xi:inn(x,class(r))]p]
+realapp1:=th3"eq.4"(dif,eq,refeq,symeq,treq,r,p,p1):p
+r@[s:real][p:'prop'][p1:[x:dif][y:dif][xi:inn(x,class(r))][yi:inn(y,class(s))]p]
++ivr1
+[a:dif][air:inn(a,class(r))]
+t1:=realapp1(s,p,[y:dif]<air><y><a>p1):p
+-ivr1
+realapp2:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t1".ivr1"(x,xi)):p
+s@[t:real][p:'prop'][p1:[x:dif][y:dif][z:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))]p]
++*ivr1
+p1@[a:dif][air:inn(a,class(r))]
+t2:=realapp2(s,t,p,[y:dif][z:dif]<air><z><y><a>p1):p
+-ivr1
+p1@realapp3:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t2".ivr1"(x,xi)):p
+t@[u:real][p:'prop'][p1:[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]p]
++*ivr1
+p1@[a:dif][air:inn(a,class(r))]
+t3:=realapp3(s,t,u,p,[y:dif][z:dif][v:dif]<air><v><z><y><a>p1):p
+-ivr1
+p1@realapp4:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t3".ivr1"(x,xi)):p
+s@[a1:dif][b1:dif][a1ir:inn(a1,class(r))][b1is:inn(b1,class(s))][e:eq"rp"(a1,b1)]
+isin:=th3"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,e):is(r,s)
+b1is@[i:is(r,s)]
+isex:=th5"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,i):eq"rp"(a1,b1)
+b1is@[n:not(eq"rp"(a1,b1))]
+nisin:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),n,[t:is(r,s)]isex(t)):nis(r,s)
+b1is@[n:nis(r,s)]
+nisex:=th3"l.imp"(eq"rp"(a1,b1),is(r,s),n,[t:eq"rp"(a1,b1)]isin(t)):not(eq"rp"(a1,b1))
+@[alpha:'type'][f:[x:dif]alpha]
+fixf:=fixfu"eq"(dif,eq,refeq,symeq,treq,alpha,f):'prop'
+[ff:fixf(alpha,f)][r0:real]
+indreal:=indeq"eq"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0):alpha
+[a:dif][air:inn(a,class(r0))]
+isindreal:=th2"eq.10"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0,a,air):is"e"(alpha,<a>f,indreal)
+alpha@[g:[x:dif][y:dif]alpha]
+fixf2:=fixfu2"eq"(dif,eq,refeq,symeq,treq,alpha,g):'prop'
+[ff2:fixf2(alpha,g)][r0:real][s0:real]
+indreal2:=indeq2"eq"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0):alpha
+[a:dif][b:dif][air:inn(a,class(r0))][bis:inn(b,class(s0))]
+isindreal2:=th1"eq.11"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0,a,air,b,bis):is"e"(alpha,<b><a>g,indreal2)
+@0:=realof(df(1rp,1rp)):real
+r@[a0:dif][a0ir:inn(a0,class(r))][z:zero(a0)]
+0in:=isin(r,0,a0,df(1rp,1rp),a0ir,innclass(df(1rp,1rp)),zeroeq(a0,df(1rp,1rp),z,zeroi(1rp,1rp,refis(cut,1rp)))):is(r,0)
+a0ir@[i:is(r,0)]
+0ex:=eqzero(df(1rp,1rp),a0,isex(0,r,df(1rp,1rp),a0,innclass(df(1rp,1rp)),a0ir,symis(real,r,0,i)),tris(cut,stm(df(1rp,1rp)),1rp,std(df(1rp,1rp)),stmis(1rp,1rp),isstd(1rp,1rp))):zero(a0)
++*ivr1
+a0@propp:=and(inn(a0,class(r)),posd(a0)):'prop'
+-ivr1
+r@pos:=some"l"(dif,[x:dif]propp".ivr1"(x)):'prop'
+a0ir@[p:posd(a0)]
++*ivr1
+p@t4:=andi(inn(a0,class(r)),posd(a0),a0ir,p):propp(a0)
+-ivr1
+p@posin:=somei(dif,[x:dif]propp".ivr1"(x),a0,t4".ivr1"):pos(r)
+a0ir@[p:pos(r)]
++*ivr1
+p@[a:dif][q1:propp(a)]
+t5:=ande1(inn(a,class(r)),posd(a),q1):inn(a,class(r))
+t6:=ande2(inn(a,class(r)),posd(a),q1):posd(a)
+t7:=eqposd(a,a0,isex(r,r,a,a0,t5,a0ir,refis(real,r)),t6):posd(a0)
+-ivr1
+p@posex:=someapp(dif,[x:dif]propp".ivr1"(x),p,posd(a0),[x:dif][t:propp".ivr1"(x)]t7".ivr1"(x,t)):posd(a0)
++*ivr1
+a0@propn:=and(inn(a0,class(r)),negd(a0)):'prop'
+-ivr1
+r@neg:=some"l"(dif,[x:dif]propn".ivr1"(x)):'prop'
+a0ir@[n:negd(a0)]
++*ivr1
+n@t8:=andi(inn(a0,class(r)),negd(a0),a0ir,n):propn(a0)
+-ivr1
+n@negin:=somei(dif,[x:dif]propn".ivr1"(x),a0,t8".ivr1"):neg(r)
+a0ir@[n:neg(r)]
++*ivr1
+n@[a:dif][pl:propn(a)]
+t9:=ande1(inn(a,class(r)),negd(a),pl):inn(a,class(r))
+t10:=ande2(inn(a,class(r)),negd(a),pl):negd(a)
+t11:=eqnegd(a,a0,isex(r,r,a,a0,t9,a0ir,refis(real,r)),t10):negd(a0)
+-ivr1
+n@negex:=someapp(dif,[x:dif]propn".ivr1"(x),n,negd(a0),[x:dif][t:propn".ivr1"(x)]t11".ivr1"(x,t)):negd(a0)
++*ivr1
+a0ir@[p:posd(a0)]
+t12:=or3i2(is(r,0),pos(r),neg(r),posin(p)):or3(is(r,0),pos(r),neg(r))
+a0ir@[z:zero(a0)]
+t13:=or3i1(is(r,0),pos(r),neg(r),0in(z)):or3(is(r,0),pos(r),neg(r))
+a0ir@[n:negd(a0)]
+t14:=or3i3(is(r,0),pos(r),neg(r),negin(n)):or3(is(r,0),pos(r),neg(r))
+a0ir@t15:=rappd(a0,or3(is(r,0),pos(r),neg(r)),[t:posd(a0)]t12(t),[t:zero(a0)]t13(t),[t:negd(a0)]t14(t)):or3(is(r,0),pos(r),neg(r))
+-ivr1
+r@axrlo:=realapp1(r,or3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t15".ivr1"(x,xi)):or3(is(r,0),pos(r),neg(r))
++*ivr1
+a0ir@[i:is(r,0)]
+t16:=th3"l.imp"(pos(r),posd(a0),0notpd(a0,0ex(i)),[t:pos(r)]posex(t)):not(pos(r))
+a0ir@[p:pos(r)]
+t17:=th3"l.imp"(neg(r),negd(a0),pnotnd(a0,posex(p)),[t:neg(r)]negex(t)):not(neg(r))
+a0ir@[n:neg(r)]
+t18:=th3"l.imp"(is(r,0),zero(a0),nnot0d(a0,negex(n)),[t:is(r,0)]0ex(t)):not(is(r,0))
+a0ir@t19:=th6"l.ec3"(is(r,0),pos(r),neg(r),[t:is(r,0)]t16(t),[t:pos(r)]t17(t),[t:neg(r)]t18(t)):ec3(is(r,0),pos(r),neg(r))
+-ivr1
+r@axrle:=realapp1(r,ec3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t19".ivr1"(x,xi)):ec3(is(r,0),pos(r),neg(r))
+axrl:=orec3i(is(r,0),pos(r),neg(r),axrlo,axrle):orec3(is(r,0),pos(r),neg(r))
+[p:'prop'][p1:[t:pos(r)]p][p2:[t:is(r,0)]p][p3:[t:neg(r)]p]
+rapp:=or3app(is(r,0),pos(r),neg(r),p,axrlo,p2,p1,p3):p
+r@[p:pos(r)]
+pnotn:=ec3e23(is(r,0),pos(r),neg(r),axrle,p):not(neg(r))
+pnot0:=ec3e21(is(r,0),pos(r),neg(r),axrle,p):nis(r,0)
+r@[i:is(r,0)]
+0notp:=ec3e12(is(r,0),pos(r),neg(r),axrle,i):not(pos(r))
+0notn:=ec3e13(is(r,0),pos(r),neg(r),axrle,i):not(neg(r))
+r@[n:neg(r)]
+nnotp:=ec3e32(is(r,0),pos(r),neg(r),axrle,n):not(pos(r))
+nnot0:=ec3e31(is(r,0),pos(r),neg(r),axrle,n):nis(r,0)
+s@[i:is(r,s)][p:pos(r)]
+ispos:=isp(real,[x:real]pos(x),r,s,p,i):pos(s)
+i@[n:neg(r)]
+isneg:=isp(real,[x:real]neg(x),r,s,n,i):neg(s)
+@[r0:cut]
+pofrp:=realof(pdofrp(r0)):real
+nofrp:=realof(ndofrp(r0)):real
+[s0:cut][i:is"rp"(r0,s0)]
+isrpep:=isf(cut,real,[x:cut]pofrp(x),r0,s0,i):is(pofrp(r0),pofrp(s0))
+isrpen:=isf(cut,real,[x:cut]nofrp(x),r0,s0,i):is(nofrp(r0),nofrp(s0))
+s0@[i:is(pofrp(r0),pofrp(s0))]
++*ivr1
+i"r"@t20:=isex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),i):eq"rp"(pdofrp(r0),pdofrp(s0))
+-ivr1
+i@isrpip:=isrpipd(r0,s0,t20".ivr1"):is"rp"(r0,s0)
+s0@[i:is(nofrp(r0),nofrp(s0))]
++*ivr1
+i"r"@t21:=isex(nofrp(r0),nofrp(s0),ndofrp(r0),ndofrp(s0),innclass(ndofrp(r0)),innclass(ndofrp(s0)),i):eq"rp"(ndofrp(r0),ndofrp(s0))
+-ivr1
+i@isrpin:=isrpind(r0,s0,t21".ivr1"):is"rp"(r0,s0)
+r0@posi:=posin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),posdirp(r0)):pos(pofrp(r0))
+negi:=negin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),negdirp(r0)):neg(nofrp(r0))
+s@[r0:cut][s0:cut][i:is(r,pofrp(r0))][j:is(s,pofrp(s0))][k:is(r,s)]
++*ivr1
+k@t22:=isrpip(r0,s0,tr3is(real,pofrp(r0),r,s,pofrp(s0),symis(real,r,pofrp(r0),i),k,j)):is"rp"(r0,s0)
+r@t23:=[x:cut][y:cut][t:is(r,pofrp(x))][u:is(r,pofrp(y))]t22(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,pofrp(x)))
+a0ir@[p1:pos(r)]
+t24:=posex(p1):posd(a0)
+pr:=rpofpd(a0,t24):cut
+t25:=isin(r,pofrp(pr),a0,pdofrp(pr),a0ir,innclass(pdofrp(pr)),eqpdrp1(a0,t24)):is(r,pofrp(pr))
+t26:=somei(cut,[x:cut]is(r,pofrp(x)),pr,t25):some"rp"([x:cut]is(r,pofrp(x)))
+-ivr1
+r@[p:pos(r)]
++*ivr1
+p"r"@t27:=realapp1(some"rp"([x:cut]is(r,pofrp(x))),[x:dif][t:inn(x,class(r))]t26(x,t,p)):some"rp"([x:cut]is(r,pofrp(x)))
+t28:=onei(cut,[x:cut]is(r,pofrp(x)),t23,t27):one"rp"([x:cut]is(r,pofrp(x)))
+-ivr1
+p@rpofp:=ind(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):cut
+isprp1:=oneax(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):is(r,pofrp(rpofp(r,p)))
+isprp2:=symis(real,r,pofrp(rpofp(r,p)),isprp1):is(pofrp(rpofp(r,p)),r)
+@[r1:real][p:pos(r1)][s1:real][q:pos(s1)][i:is(r1,s1)]
+isperp:=t22".ivr1"(r1,s1,rpofp(r1,p),rpofp(s1,q),isprp1(r1,p),isprp1(s1,q),i):is"rp"(rpofp(r1,p),rpofp(s1,q))
+q@[i:is"rp"(rpofp(r1,p),rpofp(s1,q))]
+ispirp:=tr3is(real,r1,pofrp(rpofp(r1,p)),pofrp(rpofp(s1,q)),s1,isprp1(r1,p),isrpep(rpofp(r1,p),rpofp(s1,q),i),isprp2(s1,q)):is(r1,s1)
+@[r0:cut]
+isrpp1:=t22".ivr1"(pofrp(r0),pofrp(r0),r0,rpofp(pofrp(r0),posi(r0)),refis(real,pofrp(r0)),isprp1(pofrp(r0),posi(r0)),refis(real,pofrp(r0))):is"rp"(r0,rpofp(pofrp(r0),posi(r0)))
+isrpp2:=symis(cut,r0,rpofp(pofrp(r0),posi(r0)),isrpp1):is"rp"(rpofp(pofrp(r0),posi(r0)),r0)
+s@[r0:cut][s0:cut][i:is(r,nofrp(r0))][j:is(s,nofrp(s0))][k:is(r,s)]
++*ivr1
+k@t29:=isrpin(r0,s0,tr3is(real,nofrp(r0),r,s,nofrp(s0),symis(real,r,nofrp(r0),i),k,j)):is"rp"(r0,s0)
+r@t30:=[x:cut][y:cut][t:is(r,nofrp(x))][u:is(r,nofrp(y))]t29(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,nofrp(x)))
+a0ir@[n1:neg(r)]
+t31:=negex(n1):negd(a0)
+nr:=rpofnd(a0,t31):cut
+t32:=isin(r,nofrp(nr),a0,ndofrp(nr),a0ir,innclass(ndofrp(nr)),eqndrp1(a0,t31)):is(r,nofrp(nr))
+t33:=somei(cut,[x:cut]is(r,nofrp(x)),nr,t32):some"rp"([x:cut]is(r,nofrp(x)))
+-ivr1
+r@[n:neg(r)]
++*ivr1
+n"r"@t34:=realapp1(some"rp"([x:cut]is(r,nofrp(x))),[x:dif][t:inn(x,class(r))]t33(x,t,n)):some"rp"([x:cut]is(r,nofrp(x)))
+t35:=onei(cut,[x:cut]is(r,nofrp(x)),t30,t34):one"rp"([x:cut]is(r,nofrp(x)))
+-ivr1
+n@rpofn:=ind(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):cut
+isnrp1:=oneax(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):is(r,nofrp(rpofn(r,n)))
+isnrp2:=symis(real,r,nofrp(rpofn(r,n)),isnrp1):is(nofrp(rpofn(r,n)),r)
+@[r1:real][n:neg(r1)][s1:real][m:neg(s1)][i:is(r1,s1)]
+isnerp:=t29".ivr1"(r1,s1,rpofn(r1,n),rpofn(s1,m),isnrp1(r1,n),isnrp1(s1,m),i):is"rp"(rpofn(r1,n),rpofn(s1,m))
+m@[i:is"rp"(rpofn(r1,n),rpofn(s1,m))]
+isnirp:=tr3is(real,r1,nofrp(rpofn(r1,n)),nofrp(rpofn(s1,m)),s1,isnrp1(r1,n),isrpen(rpofn(r1,n),rpofn(s1,m),i),isnrp2(s1,m)):is(r1,s1)
+@[r0:cut]
+isrpn1:=t29".ivr1"(nofrp(r0),nofrp(r0),r0,rpofn(nofrp(r0),negi(r0)),refis(real,nofrp(r0)),isnrp1(nofrp(r0),negi(r0)),refis(real,nofrp(r0))):is"rp"(r0,rpofn(nofrp(r0),negi(r0)))
+isrpn2:=symis(cut,r0,rpofn(nofrp(r0),negi(r0)),isrpn1):is"rp"(rpofn(nofrp(r0),negi(r0)),r0)
+r@satz163:=refis(real,r):is(r,r)
+s@[i:is(r,s)]
+satz164:=symis(real,r,s,i):is(s,r)
+t@[i:is(r,s)][j:is(s,t)]
+satz165:=tris(real,r,s,t,i,j):is(r,t)
+@absdr:=[x:dif]realof(absd(x)):[x:dif]real
++ivr2
+[a:dif][b:dif][e:eq"rp"(a,b)]
+t1:=isin(realof(absd(a)),realof(absd(b)),absd(a),absd(b),innclass(absd(a)),innclass(absd(b)),eqabsd(a,b,e)):is(<a>absdr,<b>absdr)
+-ivr2
+fabsdr:=[x:dif][y:dif][t:<y><x>eq]t1".ivr2"(x,y,t):fixf(real,absdr)
+r@abs:=indreal(real,absdr,fabsdr,r):real
++*ivr2
+a0ir@t2:=isindreal(real,absdr,fabsdr,r,a0,a0ir):is(realof(absd(a0)),abs(r))
+-ivr2
+a0ir@aica:=isp(real,[x:real]inn(absd(a0),class(x)),realof(absd(a0)),abs(r),innclass(absd(a0)),t2".ivr2"):inn(absd(a0),class(abs(r)))
+s@[i:is(r,s)]
+isabs:=isf(real,real,[x:real]abs(x),r,s,i):is(abs(r),abs(s))
++2r166
+a0ir@[p:pos(r)]
+t1:=satzd166a(a0,posex(p)):posd(absd(a0))
+t2:=posin(abs(r),absd(a0),aica,t1):pos(abs(r))
+-2r166
+r@[p:pos(r)]
+satz166a:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t2".2r166"(x,t,p)):pos(abs(r))
++*2r166
+a0ir@[n:neg(r)]
+t3:=satzd166b(a0,negex(n)):posd(absd(a0))
+t4:=posin(abs(r),absd(a0),aica,t3):pos(abs(r))
+-2r166
+r@[n:neg(r)]
+satz166b:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t4".2r166"(x,t,n)):pos(abs(r))
++*2r166
+b1is@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
+t5:=satzd166c(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
+t6:=isin(t5):is(r,s)
+-2r166
+s@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
+satz166c:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".2r166"(x,y,t,u,p,q,i)):is(r,s)
++*2r166
+b1is@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
+t7:=satzd166d(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
+t8:=isin(t7):is(r,s)
+-2r166
+s@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
+satz166d:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".2r166"(x,y,t,u,n,o,i)):is(r,s)
+r@[n:nis(r,0)]
+satz166e:=rapp(r,pos(abs(r)),[t:pos(r)]satz166a(t),th2"l.imp"(is(r,0),pos(abs(r)),n),[t:neg(r)]satz166b(t)):pos(abs(r))
++*2r166
+a0ir@[i:is(r,0)]
+t9:=satzd166f(a0,0ex(i)):zero(absd(a0))
+t10:=0in(abs(r),absd(a0),aica,t9):is(abs(r),0)
+-2r166
+r@[i:is(r,0)]
+satz166f:=realapp1(is(abs(r),0),[x:dif][t:inn(x,class(r))]t10".2r166"(x,t,i)):is(abs(r),0)
+s@more:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),mored(x,y)))):'prop'
++*ivr2
+b1@propm:=and3(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1)):'prop'
+-ivr2
+b1is@[m:mored(a1,b1)]
++*ivr2
+m@t3:=and3i(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1),a1ir,b1is,m):propm(a1,b1)
+t4:=somei(dif,[x:dif]propm(a1,x),b1,t3):some"l"(dif,[x:dif]propm(a1,x))
+-ivr2
+m@morein:=somei(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),a1,t4".ivr2"):more(r,s)
+b1is@[m:more(r,s)]
++*ivr2
+m@[a:dif][sa:some"l"(dif,[x:dif]propm(a,x))][b:dif][p2:propm(a,b)]
+t5:=and3e1(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(a,class(r))
+t6:=and3e2(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(b,class(s))
+t7:=and3e3(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):mored(a,b)
+t8:=eqmored12(a,a1,b,b1,isex(r,r,a,a1,t5,a1ir,refis(real,r)),isex(s,s,b,b1,t6,b1is,refis(real,s)),t7):mored(a1,b1)
+sa@t9:=someapp(dif,[x:dif]propm(a,x),sa,mored(a1,b1),[x:dif][t:propm(a,x)]t8(x,t)):mored(a1,b1)
+-ivr2
+m@moreex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),m,mored(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propm".ivr2"(x,y))]t9".ivr2"(x,t)):mored(a1,b1)
+s@less:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),lessd(x,y)))):'prop'
++*ivr2
+b1@propl:=and3(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1)):'prop'
+-ivr2
+b1is@[l:lessd(a1,b1)]
++*ivr2
+l@t10:=and3i(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1),a1ir,b1is,l):propl(a1,b1)
+t11:=somei(dif,[x:dif]propl(a1,x),b1,t10):some"l"(dif,[x:dif]propl(a1,x))
+-ivr2
+l@lessin:=somei(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),a1,t11".ivr2"):less(r,s)
+b1is@[l:less(r,s)]
++*ivr2
+l@[a:dif][sa:some"l"(dif,[x:dif]propl(a,x))][b:dif][p2:propl(a,b)]
+t12:=and3e1(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(a,class(r))
+t13:=and3e2(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(b,class(s))
+t14:=and3e3(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):lessd(a,b)
+t15:=eqlessd12(a,a1,b,b1,isex(r,r,a,a1,t12,a1ir,refis(real,r)),isex(s,s,b,b1,t13,b1is,refis(real,s)),t14):lessd(a1,b1)
+sa@t16:=someapp(dif,[x:dif]propl(a,x),sa,lessd(a1,b1),[x:dif][t:propl(a,x)]t15(x,t)):lessd(a1,b1)
+-ivr2
+l@lessex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),l,lessd(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propl".ivr2"(x,y))]t16".ivr2"(x,t)):lessd(a1,b1)
+t@[i:is(r,s)][m:more(r,t)]
+ismore1:=isp(real,[x:real]more(x,t),r,s,m,i):more(s,t)
+i@[m:more(t,r)]
+ismore2:=isp(real,[x:real]more(t,x),r,s,m,i):more(t,s)
+i@[l:less(r,t)]
+isless1:=isp(real,[x:real]less(x,t),r,s,l,i):less(s,t)
+i@[l:less(t,r)]
+isless2:=isp(real,[x:real]less(t,x),r,s,l,i):less(t,s)
+u@[i:is(r,s)][j:is(t,u)][m:more(r,t)]
+ismore12:=ismore2(t,u,s,j,ismore1(r,s,t,i,m)):more(s,u)
+j@[l:less(r,t)]
+isless12:=isless2(t,u,s,j,isless1(r,s,t,i,l)):less(s,u)
++*ivr2
+b1is@[m:more(r,s)]
+t17:=lemmad5(a1,b1,moreex(m)):lessd(b1,a1)
+t18:=lessin(s,r,b1,a1,b1is,a1ir,t17):less(s,r)
+-ivr2
+s@[m:more(r,s)]
+lemma1:=realapp2(less(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t18".ivr2"(x,y,t,u,m)):less(s,r)
++*ivr2
+b1is@[l:less(r,s)]
+t19:=lemmad6(a1,b1,lessex(l)):mored(b1,a1)
+t20:=morein(s,r,b1,a1,b1is,a1ir,t19):more(s,r)
+-ivr2
+s@[l:less(r,s)]
+lemma2:=realapp2(more(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t20".ivr2"(x,y,t,u,l)):more(s,r)
++2r167
+b1is@t1:=satzd167a(a1,b1):or3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
+[e:eq"rp"(a1,b1)]
+t2:=or3i1(is(r,s),more(r,s),less(r,s),isin(e)):or3(is(r,s),more(r,s),less(r,s))
+b1is@[m:mored(a1,b1)]
+t3:=or3i2(is(r,s),more(r,s),less(r,s),morein(m)):or3(is(r,s),more(r,s),less(r,s))
+b1is@[l:lessd(a1,b1)]
+t4:=or3i3(is(r,s),more(r,s),less(r,s),lessin(l)):or3(is(r,s),more(r,s),less(r,s))
+b1is@t5:=or3app(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),or3(is(r,s),more(r,s),less(r,s)),t1,[t:eq"rp"(a1,b1)]t2(t),[t:mored(a1,b1)]t3(t),[t:lessd(a1,b1)]t4(t)):or3(is(r,s),more(r,s),less(r,s))
+t6:=satzd167b(a1,b1):ec3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
+[i:is(r,s)]
+t7:=th3"l.imp"(more(r,s),mored(a1,b1),ec3e12(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,isex(i)),[t:more(r,s)]moreex(t)):not(more(r,s))
+b1is@[m:more(r,s)]
+t8:=th3"l.imp"(less(r,s),lessd(a1,b1),ec3e23(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,moreex(m)),[t:less(r,s)]lessex(t)):not(less(r,s))
+b1is@[l:less(r,s)]
+t9:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),ec3e31(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,lessex(l)),[t:is(r,s)]isex(t)):not(is(r,s))
+b1is@t10:=th6"l.ec3"(is(r,s),more(r,s),less(r,s),th1"l.ec"(is(r,s),more(r,s),[t:is(r,s)]t7(t)),th1"l.ec"(more(r,s),less(r,s),[t:more(r,s)]t8(t)),th1"l.ec"(less(r,s),is(r,s),[t:less(r,s)]t9(t))):ec3(is(r,s),more(r,s),less(r,s))
+t11:=orec3i(is(r,s),more(r,s),less(r,s),t5,t10):orec3(is(r,s),more(r,s),less(r,s))
+-2r167
+s@satz167:=realapp2(orec3(is(r,s),more(r,s),less(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".2r167"(x,y,t,u)):orec3(is(r,s),more(r,s),less(r,s))
+satz167a:=orec3e1(is(r,s),more(r,s),less(r,s),satz167):or3(is(r,s),more(r,s),less(r,s))
+satz167b:=orec3e2(is(r,s),more(r,s),less(r,s),satz167):ec3(is(r,s),more(r,s),less(r,s))
+moreis:=or(more(r,s),is(r,s)):'prop'
+lessis:=or(less(r,s),is(r,s)):'prop'
+[m:moreis(r,s)]
+satz168a:=th9"l.or"(more(r,s),is(r,s),less(s,r),is(s,r),m,[t:more(r,s)]lemma1(t),[t:is(r,s)]symis(real,r,s,t)):lessis(s,r)
+s@[l:lessis(r,s)]
+satz168b:=th9"l.or"(less(r,s),is(r,s),more(s,r),is(s,r),l,[t:less(r,s)]lemma2(t),[t:is(r,s)]symis(real,r,s,t)):moreis(s,r)
+t@[i:is(r,s)][m:moreis(r,t)]
+ismoreis1:=isp(real,[x:real]moreis(x,t),r,s,m,i):moreis(s,t)
+i@[m:moreis(t,r)]
+ismoreis2:=isp(real,[x:real]moreis(t,x),r,s,m,i):moreis(t,s)
+i@[l:lessis(r,t)]
+islessis1:=isp(real,[x:real]lessis(x,t),r,s,l,i):lessis(s,t)
+i@[l:lessis(t,r)]
+islessis2:=isp(real,[x:real]lessis(t,x),r,s,l,i):lessis(t,s)
+u@[i:is(r,s)][j:is(t,u)][m:moreis(r,t)]
+ismoreis12:=ismoreis2(t,u,s,j,ismoreis1(r,s,t,i,m)):moreis(s,u)
+j@[l:lessis(r,t)]
+islessis12:=islessis2(t,u,s,j,islessis1(r,s,t,i,l)):lessis(s,u)
+s@[m:more(r,s)]
+moreisi1:=ori1(more(r,s),is(r,s),m):moreis(r,s)
+s@[l:less(r,s)]
+lessisi1:=ori1(less(r,s),is(r,s),l):lessis(r,s)
+s@[i:is(r,s)]
+moreisi2:=ori2(more(r,s),is(r,s),i):moreis(r,s)
+lessisi2:=ori2(less(r,s),is(r,s),i):lessis(r,s)
+b1is@[m:moreq(a1,b1)]
+moreisin:=orapp(mored(a1,b1),eq"rp"(a1,b1),moreis(r,s),m,[t:mored(a1,b1)]moreisi1(morein(t)),[t:eq"rp"(a1,b1)]moreisi2(isin(t))):moreis(r,s)
+b1is@[m:moreis(r,s)]
+moreisex:=orapp(more(r,s),is(r,s),moreq(a1,b1),m,[t:more(r,s)]moreqi1(a1,b1,moreex(t)),[t:is(r,s)]moreqi2(a1,b1,isex(t))):moreq(a1,b1)
+b1is@[l:lesseq(a1,b1)]
+lessisin:=orapp(lessd(a1,b1),eq"rp"(a1,b1),lessis(r,s),l,[t:lessd(a1,b1)]lessisi1(lessin(t)),[t:eq"rp"(a1,b1)]lessisi2(isin(t))):lessis(r,s)
+b1is@[l:lessis(r,s)]
+lessisex:=orapp(less(r,s),is(r,s),lesseq(a1,b1),l,[t:less(r,s)]lesseqi1(a1,b1,lessex(t)),[t:is(r,s)]lesseqi2(a1,b1,isex(t))):lesseq(a1,b1)
+s@[m:moreis(r,s)]
+satz167c:=th7"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,comor(more(r,s),is(r,s),m)):not(less(r,s))
+s@[l:lessis(r,s)]
+satz167d:=th9"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,l):not(more(r,s))
+s@[n:not(more(r,s))]
+satz167e:=th2"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n):lessis(r,s)
+s@[n:not(less(r,s))]
+s@[n:not(less(r,s))]
+satz167f:=comor(is(r,s),more(r,s),th3"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n)):moreis(r,s)
+s@[m:more(r,s)]
+satz167g:=th3"l.imp"(lessis(r,s),not(more(r,s)),weli(more(r,s),m),[t:lessis(r,s)]satz167d(t)):not(lessis(r,s))
+s@[l:less(r,s)]
+satz167h:=th3"l.imp"(moreis(r,s),not(less(r,s)),weli(less(r,s),l),[t:moreis(r,s)]satz167c(t)):not(moreis(r,s))
+s@[n:not(moreis(r,s))]
+satz167j:=or3e3(is(r,s),more(r,s),less(r,s),satz167a,th5"l.or"(more(r,s),is(r,s),n),th4"l.or"(more(r,s),is(r,s),n)):less(r,s)
+s@[n:not(lessis(r,s))]
+satz167k:=or3e2(is(r,s),more(r,s),less(r,s),satz167a,th4"l.or"(less(r,s),is(r,s),n),th5"l.or"(less(r,s),is(r,s),n)):more(r,s)
+r@[p:pos(r)]
++2r169
+[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t1:=satzd169a(a,b,0ex(0,b,bi0,refis(real,0)),posex(a,air,p)):mored(a,b)
+t2:=morein(r,0,a,b,air,bi0,t1):more(r,0)
+-2r169
+satz169a:=realapp2(r,0,more(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r169"(x,y,t,u)):more(r,0)
+r@[m:more(r,0)]
++*2r169
+m@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t3:=satzd169b(a,b,0ex(0,b,bi0,refis(real,0)),moreex(r,0,a,b,air,bi0,m)):posd(a)
+t4:=posin(r,a,air,t3):pos(r)
+-2r169
+m@satz169b:=realapp2(r,0,pos(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t4".2r169"(x,y,t,u)):pos(r)
+r@[n:neg(r)]
++*2r169
+n@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t5:=satzd169c(a,b,0ex(0,b,bi0,refis(real,0)),negex(a,air,n)):lessd(a,b)
+t6:=lessin(r,0,a,b,air,bi0,t5):less(r,0)
+-2r169
+n@satz169c:=realapp2(r,0,less(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t6".2r169"(x,y,t,u)):less(r,0)
+r@[l:less(r,0)]
++*2r169
+l@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t7:=satzd169d(a,b,0ex(0,b,bi0,refis(real,0)),lessex(r,0,a,b,air,bi0,l)):negd(a)
+t8:=negin(r,a,air,t7):neg(r)
+-2r169
+l@satz169d:=realapp2(r,0,neg(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t8".2r169"(x,y,t,u)):neg(r)
++2r170
+r@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t1:=satzd170(a,b,0ex(0,b,bi0,refis(real,0))):moreq(absd(a),b)
+t2:=moreisin(abs(r),0,absd(a),b,aica(r,a,air),bi0,t1):moreis(abs(r),0)
+-2r170
+r@satz170:=realapp2(r,0,moreis(abs(r),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r170"(x,y,t,u)):moreis(abs(r),0)
+satz170a:=th3"l.imp"(neg(abs(r)),less(abs(r),0),satz167c(abs(r),0,satz170),[t:neg(abs(r))]satz169c(abs(r),t)):not(neg(abs(r)))
+t@[l:less(r,s)][k:less(s,t)]
++2r171
+[a:dif][b:dif][c:dif][air:inn(a,class(r))][bis:inn(b,class(s))][cit:inn(c,class(t))]
+t1:=satzd171(a,b,c,lessex(r,s,a,b,air,bis,l),lessex(s,t,b,c,bis,cit,k)):lessd(a,c)
+t2:=lessin(r,t,a,c,air,cit,t1):less(r,t)
+-2r171
+satz171:=realapp3(r,s,t,less(r,t),[x:dif][y:dif][z:dif][w:inn(x,class(r))][u:inn(y,class(s))][v:inn(z,class(t))]t2".2r171"(x,y,z,w,u,v)):less(r,t)
+trless:=satz171:less(r,t)
+t@[m:more(r,s)][n:more(s,t)]
+trmore:=lemma2(t,r,trless(t,s,r,lemma1(s,t,n),lemma1(r,s,m))):more(r,t)
+t@[a2:dif][b2:dif][c2:dif][a2ir:inn(a2,class(r))][b2is:inn(b2,class(s))][c2it:inn(c2,class(t))]
++2r172
+[l:lessis(r,s)][k:less(s,t)]
+t1:=satzd172a(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
+t2:=lessin(r,t,a2,c2,a2ir,c2it,t1):less(r,t)
+-2r172
+t@[l:lessis(r,s)][k:less(s,t)]
+satz172a:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
++*2r172
+c2it@[l:less(r,s)][k:lessis(s,t)]
+t3:=satzd172b(a2,b2,c2,lessex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
+t4:=lessin(r,t,a2,c2,a2ir,c2it,t3):less(r,t)
+-2r172
+t@[l:less(r,s)][k:lessis(s,t)]
+satz172b:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
+t@[m:moreis(r,s)][n:more(s,t)]
+satz172c:=lemma2(t,r,satz172b(t,s,r,lemma1(s,t,n),satz168a(m))):more(r,t)
+t@[m:more(r,s)][n:moreis(s,t)]
+satz172d:=lemma2(t,r,satz172a(t,s,r,satz168a(s,t,n),lemma1(m))):more(r,t)
++2r173
+c2it@[l:lessis(r,s)][k:lessis(s,t)]
+t1:=satzd173(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lesseq(a2,c2)
+t2:=lessisin(r,t,a2,c2,a2ir,c2it,t1):lessis(r,t)
+-2r173
+t@[l:lessis(r,s)][k:lessis(s,t)]
+satz173:=realapp3(lessis(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r173"(x,y,z,u,v,w,l,k)):lessis(r,t)
+trlessis:=satz173:lessis(r,t)
+t@[m:moreis(r,s)][n:moreis(s,t)]
+trmoreis:=satz168b(t,r,trlessis(t,s,r,satz168a(s,t,n),satz168a(m))):moreis(r,t)
+r@ratrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),ratd(x))):'prop'
+a0ir@[r1:ratd(a0)]
++*ivr2
+r1@t21:=andi(inn(a0,class(r)),ratd(a0),a0ir,r1):and(inn(a0,class(r)),ratd(a0))
+-ivr2
+r1@ratrlin:=somei(dif,[x:dif]and(inn(x,class(r)),ratd(x)),a0,t21".ivr2"):ratrl(r)
+a0ir@[rr:ratrl(r)]
++*ivr2
+rr@[a:dif][b:and(inn(a,class(r)),ratd(a))]
+t22:=ande1(inn(a,class(r)),ratd(a),b):inn(a,class(r))
+t23:=ande2(inn(a,class(r)),ratd(a),b):ratd(a)
+t24:=eqratd(a,a0,isex(r,r,a,a0,t22,a0ir,refis(real,r)),t23):ratd(a0)
+-ivr2
+rr@ratrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),ratd(x)),rr,ratd(a0),[x:dif][t:and(inn(x,class(r)),ratd(x))]t24".ivr2"(x,t)):ratd(a0)
+r@irratrl:=not(ratrl(r)):'prop'
+@[r0:cut][rr:ratrp(r0)]
+remark2:=ratrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark2a(r0,rr)):ratrl(pofrp(r0))
+remark3:=ratrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark3a(r0,rr)):ratrl(nofrp(r0))
+r0@[ir:irratrp(r0)]
+remark4:=th3"l.imp"(ratrl(pofrp(r0)),ratd(pdofrp(r0)),remark4a(r0,ir),[t:ratrl(pofrp(r0))]ratrlex(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),t)):irratrl(pofrp(r0))
+remark5:=th3"l.imp"(ratrl(nofrp(r0)),ratd(ndofrp(r0)),remark5a(r0,ir),[t:ratrl(nofrp(r0))]ratrlex(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),t)):irratrl(nofrp(r0))
+r@natrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),natd(x))):'prop'
+a0ir@[n:natd(a0)]
++*ivr2
+n@t25:=andi(inn(a0,class(r)),natd(a0),a0ir,n):and(inn(a0,class(r)),natd(a0))
+-ivr2
+n@natrlin:=somei(dif,[x:dif]and(inn(x,class(r)),natd(x)),a0,t25".ivr2"):natrl(r)
+a0ir@[n:natrl(r)]
++*ivr2
+n@[a:dif][b:and(inn(a,class(r)),natd(a))]
+t26:=ande1(inn(a,class(r)),natd(a),b):inn(a,class(r))
+t27:=ande2(inn(a,class(r)),natd(a),b):natd(a)
+t28:=eqnatd(a,a0,isex(r,r,a,a0,t26,a0ir,refis(real,r)),t27):natd(a0)
+-ivr2
+n@natrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),natd(x)),n,natd(a0),[x:dif][t:and(inn(x,class(r)),natd(x))]t28".ivr2"(x,t)):natd(a0)
++*ivr2
+a0ir@[n:natrl(r)]
+t29:=natposd(a0,natrlex(n)):posd(a0)
+t30:=posin(t29):pos(r)
+-ivr2
+r@[n:natrl(r)]
+natpos:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t30".ivr2"(x,t,n)):pos(r)
+@[x:nat]
+rlofnt:=realof(pdofnt(x)):real
+natrli:=natrlin(rlofnt(x),pdofnt(x),innclass(pdofnt(x)),natdi(x)):natrl(rlofnt(x))
+[y:nat][i:is"n"(x,y)]
+isnterl:=isf(nat,real,[u:nat]rlofnt(u),x,y,i):is(rlofnt(x),rlofnt(y))
+y@[i:is(rlofnt(x),rlofnt(y))]
+isntirl:=isntirp(x,y,isrpip(rpofnt(x),rpofnt(y),i)):is"n"(x,y)
++*ivr2
+@t31:=[x:nat][y:nat][t:is(rlofnt(x),rlofnt(y))]isntirl(x,y,t):injective(nat,real,[x:nat]rlofnt(x))
+a0ir@[n:natrl(r)]
+t32:=natposd(a0,natrlex(n)):posd(a0)
+ap:=rpofpd(a0,t32):cut
+t33:=natderp(a0,natrlex(n)):natrp(ap)
+x0:=ntofrp(ap,t33):nat
+t34:=isrpepd(ap,rpofnt(x0),isrpnt1(ap,t33)):eq"rp"(pdofrp(ap),pdofnt(x0))
+t35:=treq"rp"(a0,pdofrp(ap),pdofnt(x0),eqpdrp1(a0,t32),t34):eq"rp"(a0,pdofnt(x0))
+t36:=isin(r,rlofnt(x0),a0,pdofnt(x0),a0ir,innclass(pdofnt(x0)),t35):is(r,rlofnt(x0))
+t37:=somei(nat,[x:nat]is(r,rlofnt(x)),x0,t36):image(nat,real,[x:nat]rlofnt(x),r)
+-ivr2
+r@[n:natrl(r)]
+natimage:=realapp1(image(nat,real,[x:nat]rlofnt(x),r),[x:dif][t:inn(x,class(r))]t37".ivr2"(x,t,n)):image(nat,real,[x:nat]rlofnt(x),r)
+r@[i:image(nat,real,[x:nat]rlofnt(x),r)]
++*ivr2
+i"r"@[x:nat][j:is(r,rlofnt(x))]
+t38:=isp1(real,[u:real]natrl(u),rlofnt(x),r,natrli(x),j):natrl(r)
+-ivr2
+i@imagenat:=someapp(nat,[u:nat]is(r,rlofnt(u)),i,natrl(r),[u:nat][v:is(r,rlofnt(u))]t38".ivr2"(u,v)):natrl(r)
+r@[n:natrl(r)]
+ntofrl:=soft(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):nat
+@[r1:real][n:natrl(r1)][s1:real][m:natrl(s1)][i:is(r1,s1)]
+isrlent:=isinv(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is"n"(ntofrl(r1,n),ntofrl(s1,m))
+m@[i:is"n"(ntofrl(r1,n),ntofrl(s1,m))]
+isrlint:=isinve(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is(r1,s1)
+r@[n:natrl(r)]
+isrlnt1:=ists1"e"(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):is(r,rlofnt(ntofrl(r,n)))
+isrlnt2:=symis(real,r,rlofnt(ntofrl(r,n)),isrlnt1):is(rlofnt(ntofrl(r,n)),r)
+@[x:nat]
++*ivr2
+x"r"@xn:=soft(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x)):nat
+t39:=isinv(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x),rlofnt(x),natimage(rlofnt(x),natrli(x)),refis(real,rlofnt(x))):is"n"(xn,ntofrl(rlofnt(x),natrli(x)))
+-ivr2
+x@isntrl1:=tris(nat,x,xn".ivr2",ntofrl(rlofnt(x),natrli(x)),isst1(nat,real,[u:nat]rlofnt(u),t31".ivr2",x),t39".ivr2"):is"n"(x,ntofrl(rlofnt(x),natrli(x)))
+isntrl2:=symis(nat,x,ntofrl(rlofnt(x),natrli(x)),isntrl1):is"n"(ntofrl(rlofnt(x),natrli(x)),x)
+r@intrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),intd(x))):'prop'
+a0ir@[i:intd(a0)]
++*ivr2
+i@t40:=andi(inn(a0,class(r)),intd(a0),a0ir,i):and(inn(a0,class(r)),intd(a0))
+-ivr2
+i@intrlin:=somei(dif,[x:dif]and(inn(x,class(r)),intd(x)),a0,t40".ivr2"):intrl(r)
+a0ir@[i:intrl(r)]
++*ivr2
+i@[a:dif][b:and(inn(a,class(r)),intd(a))]
+t41:=ande1(inn(a,class(r)),intd(a),b):inn(a,class(r))
+t42:=ande2(inn(a,class(r)),intd(a),b):intd(a)
+t43:=eqintd(a,a0,isex(r,r,a,a0,t41,a0ir,refis(real,r)),t42):intd(a0)
+-ivr2
+i@intrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),intd(x)),i,intd(a0),[x:dif][t:and(inn(x,class(r)),intd(x))]t43".ivr2"(x,t)):intd(a0)
++*ivr2
+a0ir@[n:natrl(r)]
+t44:=natintd(a0,natrlex(n)):intd(a0)
+t45:=intrlin(t44):intrl(r)
+-ivr2
+r@[n:natrl(r)]
+natintrl:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t45".ivr2"(x,t,n)):intrl(r)
++*ivr2
+a0ir@[p:pos(r)][i:intrl(r)]
+t46:=posintnatd(a0,posex(p),intrlex(i)):natd(a0)
+t47:=natrlin(t46):natrl(r)
+-ivr2
+r@[p:pos(r)][i:intrl(r)]
+posintnatrl:=realapp1(natrl(r),[x:dif][t:inn(x,class(r))]t47".ivr2"(x,t,p,i)):natrl(r)
++*ivr2
+a0ir@[i2:is(r,0)]
+t48:=intdi0(a0,0ex(i2)):intd(a0)
+t49:=intrlin(t48):intrl(r)
+-ivr2
+r@[i:is(r,0)]
+intrli0:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t49".ivr2"(x,t,i)):intrl(r)
+r0@[n:natrp(r0)]
+remark6:=intrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark6"rp"(r0,n)):intrl(pofrp(r0))
+remark7:=intrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark7"rp"(r0,n)):intrl(nofrp(r0))
++2r174
+a0ir@[i:intrl(r)]
+t1:=satzd174(a0,intrlex(i)):ratd(a0)
+t2:=ratrlin(t1):ratrl(r)
+-2r174
+r@[i:intrl(r)]
+satz174:=realapp1(ratrl(r),[x:dif][t:inn(x,class(r))]t2".2r174"(x,t,i)):ratrl(r)
+@plusdr:=[x:dif][y:dif]realof(pd(x,y)):[x:dif][y:dif]real
++ivr3
+[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
+t1:=isin(realof(pd(a,c)),realof(pd(b,d)),pd(a,c),pd(b,d),innclass(pd(a,c)),innclass(pd(b,d)),eqpd12(a,b,c,d,e,f)):is(<c><a>plusdr,<d><b>plusdr)
+-ivr3
+fplusdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr3"(x,y,z,v,t,u):fixf2(real,plusdr)
+s@pl:=indreal2(real,plusdr,fplusdr,r,s):real
++*ivr3
+b1is@t2:=isindreal2(real,plusdr,fplusdr,r,s,a1,b1,a1ir,b1is):is(realof(pd(a1,b1)),pl(r,s))
+-ivr3
+b1is@picp:=isp(real,[x:real]inn(pd(a1,b1),class(x)),realof(pd(a1,b1)),pl(r,s),innclass(pd(a1,b1)),t2".ivr3"):inn(pd(a1,b1),class(pl(r,s)))
+t@[i:is(r,s)]
+ispl1:=isf(real,real,[x:real]pl(x,t),r,s,i):is(pl(r,t),pl(s,t))
+ispl2:=isf(real,real,[x:real]pl(t,x),r,s,i):is(pl(t,r),pl(t,s))
+u@[i:is(r,s)][j:is(t,u)]
+ispl12:=tris(real,pl(r,t),pl(s,t),pl(s,u),ispl1(i),ispl2(t,u,s,j)):is(pl(r,t),pl(s,u))
++3r175
+b1is@t1:=satzd175(a1,b1):eq"rp"(pd(a1,b1),pd(b1,a1))
+t2:=isin(pl(r,s),pl(s,r),pd(a1,b1),pd(b1,a1),picp,picp(s,r,b1,a1,b1is,a1ir),t1):is(pl(r,s),pl(s,r))
+-3r175
+s@satz175:=realapp2(is(pl(r,s),pl(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r175"(x,y,t,u)):is(pl(r,s),pl(s,r))
+compl:=satz175:is(pl(r,s),pl(s,r))
++*ivr3
+b1is@[i:is(r,0)]
+t3:=pd01(a1,b1,0ex(r,a1,a1ir,i)):eq"rp"(pd(a1,b1),b1)
+t4:=isin(pl(r,s),s,pd(a1,b1),b1,picp,b1is,t3):is(pl(r,s),s)
+-ivr3
+s@[i:is(r,0)]
+pl01:=realapp2(is(pl(r,s),s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr3"(x,y,t,u,i)):is(pl(r,s),s)
+s@[i:is(s,0)]
+pl02:=tris(real,pl(r,s),pl(s,r),r,compl,pl01(s,r,i)):is(pl(r,s),r)
++*ivr3
+b1is@[p:pos(r)][q:pos(s)]
+t5:=ppd(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(pd(a1,b1))
+t6:=posin(pl(r,s),pd(a1,b1),picp,t5):pos(pl(r,s))
+-ivr3
+s@[p:pos(r)][q:pos(s)]
+pospl:=realapp2(pos(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr3"(x,y,t,u,p,q)):pos(pl(r,s))
++*ivr3
+b1is@[n:neg(r)][o:neg(s)]
+t7:=npd(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):negd(pd(a1,b1))
+t8:=negin(pl(r,s),pd(a1,b1),picp,t7):neg(pl(r,s))
+-ivr3
+s@[n:neg(r)][o:neg(s)]
+negpl:=realapp2(neg(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".ivr3"(x,y,t,u,n,o)):neg(pl(r,s))
+@m0dr:=[x:dif]realof(m0d(x)):[x:dif]real
++*ivr3
+@[a:dif][b:dif][e:eq"rp"(a,b)]
+t5a:=isin(realof(m0d(a)),realof(m0d(b)),m0d(a),m0d(b),innclass(m0d(a)),innclass(m0d(b)),eqm0d(a,b,e)):is(<a>m0dr,<b>m0dr)
+-ivr3
+@fm0dr:=[x:dif][y:dif][t:<y><x>eq]t5a".ivr3"(x,y,t):fixf(real,m0dr)
+r@m0:=indreal(real,m0dr,fm0dr,r):real
++*ivr3
+a0ir@t6a:=isindreal(real,m0dr,fm0dr,r,a0,a0ir):is(realof(m0d(a0)),m0(r))
+-ivr3
+a0ir@micm0:=isp(real,[x:real]inn(m0d(a0),class(x)),realof(m0d(a0)),m0(r),innclass(m0d(a0)),t6a".ivr3"):inn(m0d(a0),class(m0(r)))
+s@[i:is(r,s)]
+ism0:=isf(real,real,[x:real]m0(x),r,s,i):is(m0(r),m0(s))
++*ivr3
+a0ir@[n:neg(r)]
+t7a:=absnd(a0,negex(n)):eq"rp"(absd(a0),m0d(a0))
+t8a:=isin(abs(r),m0(r),absd(a0),m0d(a0),aica,micm0,t7a):is(abs(r),m0(r))
+-ivr3
+r@[n:neg(r)]
+absn:=realapp1(is(abs(r),m0(r)),[x:dif][t:inn(x,class(r))]t8a".ivr3"(x,t,n)):is(abs(r),m0(r))
++*ivr3
+a0ir@[nn:not(neg(r))]
+t9:=absnnd(a0,th3"l.imp"(negd(a0),neg(r),nn,[t:negd(a0)]negin(t))):eq"rp"(absd(a0),a0)
+t10:=isin(abs(r),r,absd(a0),a0,aica,a0ir,t9):is(abs(r),r)
+-ivr3
+r@[nn:not(neg(r))]
+absnn:=realapp1(is(abs(r),r),[x:dif][t:inn(x,class(r))]t10".ivr3"(x,t,nn)):is(abs(r),r)
+r@[p:pos(r)]
+absp:=absnn(r,pnotn(r,p)):is(abs(r),r)
+r@[i:is(r,0)]
+abs0:=tris(real,abs(r),r,0,absnn(r,0notn(r,i)),i):is(abs(r),0)
++3r176
+a0ir@[p:pos(r)]
+t1:=satzd176a(a0,posex(p)):negd(m0d(a0))
+t2:=negin(m0(r),m0d(a0),micm0,t1):neg(m0(r))
+-3r176
+r@[p:pos(r)]
+satz176a:=realapp1(neg(m0(r)),[x:dif][t:inn(x,class(r))]t2".3r176"(x,t,p)):neg(m0(r))
++*3r176
+a0ir@[i:is(r,0)]
+t3:=satzd176b(a0,0ex(i)):zero(m0d(a0))
+t4:=0in(m0(r),m0d(a0),micm0,t3):is(m0(r),0)
+-3r176
+r@[i:is(r,0)]
+satz176b:=realapp1(is(m0(r),0),[x:dif][t:inn(x,class(r))]t4".3r176"(x,t,i)):is(m0(r),0)
++*3r176
+a0ir@[n:neg(r)]
+t5:=satzd176c(a0,negex(n)):posd(m0d(a0))
+t6:=posin(m0(r),m0d(a0),micm0,t5):pos(m0(r))
+-3r176
+r@[n:neg(r)]
+satz176c:=realapp1(pos(m0(r)),[x:dif][t:inn(x,class(r))]t6".3r176"(x,t,n)):pos(m0(r))
++*3r176
+a0ir@[n:neg(m0(r))]
+t7:=satzd176d(a0,negex(m0(r),m0d(a0),micm0,n)):posd(a0)
+t8:=posin(t7):pos(r)
+-3r176
+r@[n:neg(m0(r))]
+satz176d:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t8".3r176"(x,t,n)):pos(r)
++*3r176
+a0ir@[i:is(m0(r),0)]
+t9:=satzd176e(a0,0ex(m0(r),m0d(a0),micm0,i)):zero(a0)
+t10:=0in(t9):is(r,0)
+-3r176
+r@[i:is(m0(r),0)]
+satz176e:=realapp1(is(r,0),[x:dif][t:inn(x,class(r))]t10".3r176"(x,t,i)):is(r,0)
++*3r176
+a0ir@[p:pos(m0(r))]
+t11:=satzd176f(a0,posex(m0(r),m0d(a0),micm0,p)):negd(a0)
+t12:=negin(t11):neg(r)
+-3r176
+r@[p:pos(m0(r))]
+satz176f:=realapp1(neg(r),[x:dif][t:inn(x,class(r))]t12".3r176"(x,t,p)):neg(r)
++3r177
+a0ir@t1:=isin(m0(m0(r)),r,m0d(m0d(a0)),a0,micm0(m0(r),m0d(a0),micm0),a0ir,satzd177(a0)):is(m0(m0(r)),r)
+-3r177
+r@satz177:=realapp1(is(m0(m0(r)),r),[x:dif][t:inn(x,class(r))]t1".3r177"(x,t)):is(m0(m0(r)),r)
+satz177a:=symis(real,m0(m0(r)),r,satz177):is(r,m0(m0(r)))
+s@[i:is(r,m0(s))]
+satz177b:=tris(real,m0(r),m0(m0(s)),s,ism0(r,m0(s),i),satz177(s)):is(m0(r),s)
+satz177c:=symis(real,m0(r),s,satz177b):is(s,m0(r))
+s@[i:is(m0(r),s)]
+satz177d:=satz177c(s,r,symis(real,m0(r),s,i)):is(r,m0(s))
+satz177e:=symis(real,r,m0(s),satz177d):is(m0(s),r)
++3r178
+a0ir@t1:=isin(abs(m0(r)),abs(r),absd(m0d(a0)),absd(a0),aica(m0(r),m0d(a0),micm0),aica,satzd178(a0)):is(abs(m0(r)),abs(r))
+-3r178
+r@satz178:=realapp1(is(abs(m0(r)),abs(r)),[x:dif][t:inn(x,class(r))]t1".3r178"(x,t)):is(abs(m0(r)),abs(r))
+satz178a:=symis(real,abs(m0(r)),abs(r),satz178):is(abs(r),abs(m0(r)))
++3r179
+a0ir@t1:=0in(pl(r,m0(r)),pd(a0,m0d(a0)),picp(r,m0(r),a0,m0d(a0),a0ir,micm0),satzd179(a0)):is(pl(r,m0(r)),0)
+-3r179
+satz179:=realapp1(is(pl(r,m0(r)),0),[x:dif][t:inn(x,class(r))]t1".3r179"(x,t)):is(pl(r,m0(r)),0)
+satz179a:=tris(real,pl(m0(r),r),pl(r,m0(r)),0,compl(m0(r),r),satz179):is(pl(m0(r),r),0)
++3r180
+b1is@t1:=isin(m0(pl(r,s)),pl(m0(r),m0(s)),m0d(pd(a1,b1)),pd(m0d(a1),m0d(b1)),micm0(pl(r,s),pd(a1,b1),picp),picp(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is)),satzd180(a1,b1)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
+-3r180
+s@satz180:=realapp2(is(m0(pl(r,s)),pl(m0(r),m0(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t1".3r180"(x,y,t,u)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
+satz180a:=symis(real,m0(pl(r,s)),pl(m0(r),m0(s)),satz180):is(pl(m0(r),m0(s)),m0(pl(r,s)))
+mn:=pl(r,m0(s)):real
+b1is@micmn:=picp(r,m0(s),a1,m0d(b1),a1ir,micm0(s,b1,b1is)):inn(md(a1,b1),class(mn(r,s)))
+t@[i:is(r,s)]
+ismn1:=ispl1(r,s,m0(t),i):is(mn(r,t),mn(s,t))
+ismn2:=ispl2(m0(r),m0(s),t,ism0(r,s,i)):is(mn(t,r),mn(t,s))
+u@[i:is(r,s)][j:is(t,u)]
+ismn12:=ispl12(r,s,m0(t),m0(u),i,ism0(t,u,j)):is(mn(r,t),mn(s,u))
+s@satz181:=tr3is(real,m0(mn(r,s)),pl(m0(r),m0(m0(s))),pl(m0(r),s),mn(s,r),satz180(r,m0(s)),ispl2(m0(m0(s)),s,m0(r),satz177(s)),compl(m0(r),s)):is(m0(mn(r,s)),mn(s,r))
+satz181a:=symis(real,m0(mn(s,r)),mn(r,s),satz181(s,r)):is(mn(r,s),m0(mn(s,r)))
++3r182
+b1is@[p:pos(mn(r,s))]
+t1:=satzd182a(a1,b1,posex(mn(r,s),md(a1,b1),micmn,p)):mored(a1,b1)
+t2:=morein(t1):more(r,s)
+-3r182
+[p:pos(mn(r,s))]
+satz182a:=realapp2(more(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r182"(x,y,t,u,p)):more(r,s)
++*3r182
+b1is@[i:is(mn(r,s),0)]
+t3:=satzd182b(a1,b1,0ex(mn(r,s),md(a1,b1),micmn,i)):eq"rp"(a1,b1)
+t4:=isin(t3):is(r,s)
+-3r182
+s@[i:is(mn(r,s),0)]
+satz182b:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r182"(x,y,t,u,i)):is(r,s)
++*3r182
+b1is@[n:neg(mn(r,s))]
+t5:=satzd182c(a1,b1,negex(mn(r,s),md(a1,b1),micmn,n)):lessd(a1,b1)
+t6:=lessin(t5):less(r,s)
+-3r182
+s@[n:neg(mn(r,s))]
+satz182c:=realapp2(less(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".3r182"(x,y,t,u,n)):less(r,s)
++*3r182
+b1is@[m:more(r,s)]
+t7:=satzd182d(a1,b1,moreex(m)):posd(md(a1,b1))
+t8:=posin(mn(r,s),md(a1,b1),micmn,t7):pos(mn(r,s))
+-3r182
+s@[m:more(r,s)]
+satz182d:=realapp2(pos(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".3r182"(x,y,t,u,m)):pos(mn(r,s))
++*3r182
+b1is@[i:is(r,s)]
+t9:=satzd182e(a1,b1,isex(i)):zero(md(a1,b1))
+t10:=0in(mn(r,s),md(a1,b1),micmn,t9):is(mn(r,s),0)
+-3r182
+s@[i:is(r,s)]
+satz182e:=realapp2(is(mn(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t10".3r182"(x,y,t,u,i)):is(mn(r,s),0)
++*3r182
+b1is@[l:less(r,s)]
+t11:=satzd182f(a1,b1,lessex(l)):negd(md(a1,b1))
+t12:=negin(mn(r,s),md(a1,b1),micmn,t11):neg(mn(r,s))
+-3r182
+s@[l:less(r,s)]
+satz182f:=realapp2(neg(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t12".3r182"(x,y,t,u,l)):neg(mn(r,s))
++3r183
+b1is@[m:more(r,s)]
+t1:=satzd183a(a1,b1,moreex(m)):lessd(m0d(a1),m0d(b1))
+t2:=lessin(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t1):less(m0(r),m0(s))
+-3r183
+s@[m:more(r,s)]
+satz183a:=realapp2(less(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r183"(x,y,t,u,m)):less(m0(r),m0(s))
+s@[i:is(r,s)]
+satz183b:=ism0(r,s,i):is(m0(r),m0(s))
++*3r183
+b1is@[l:less(r,s)]
+t3:=satzd183c(a1,b1,lessex(l)):mored(m0d(a1),m0d(b1))
+t4:=morein(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t3):more(m0(r),m0(s))
+-3r183
+s@[l:less(r,s)]
+satz183c:=realapp2(more(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r183"(x,y,t,u,l)):more(m0(r),m0(s))
+s@[l:less(m0(r),m0(s))]
+satz183d:=ismore12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183c(m0(r),m0(s),l)):more(r,s)
+s@[i:is(m0(r),m0(s))]
+satz183e:=tr3is(real,r,m0(m0(r)),m0(m0(s)),s,satz177a(r),ism0(m0(r),m0(s),i),satz177(s)):is(r,s)
+s@[m:more(m0(r),m0(s))]
+satz183f:=isless12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183a(m0(r),m0(s),m)):less(r,s)
++3r184
+t@prop1:=and3(pos(s),pos(t),is(r,mn(s,t))):'prop'
+s@prop2:=some([x:real]prop1(x)):'prop'
+r@prop3:=some([x:real]prop2(x)):'prop'
+a0ir@[a:dif][b:dif]
+prop1d:=and3(posd(a),posd(b),eq"rp"(a0,md(a,b))):'prop'
+a@prop2d:=some"l"(dif,[x:dif]prop1d(x)):'prop'
+[p2:prop2d(a)][b:dif][p1:prop1d(a,b)]
+t1:=and3e1(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(a)
+t2:=and3e2(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(b)
+t3:=and3e3(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):eq"rp"(a0,md(a,b))
+p2@ra:=realof(a):real
+p1@rb:=realof(b):real
+t4:=innclass(a):inn(a,class(ra))
+t5:=innclass(b):inn(b,class(rb))
+t6:=isin(r,mn(ra,rb),a0,md(a,b),a0ir,micmn(ra,rb,a,b,t4,t5),t3):is(r,mn(ra,rb))
+t7:=and3i(pos(ra),pos(rb),is(r,mn(ra,rb)),posin(ra,a,t4,t1),posin(rb,b,t5,t2),t6):prop1(ra,rb)
+t8:=somei(real,[x:real]prop1(ra,x),rb,t7):prop2(ra)
+p2@t9:=someapp(dif,[x:dif]prop1d(a,x),p2,prop2(ra),[x:dif][t:prop1d(a,x)]t8(x,t)):prop2(ra)
+t10:=somei(real,[x:real]prop2(x),ra,t9):prop3
+a0ir@t11:=someapp(dif,[x:dif]prop2d(x),satzd184(a0),prop3,[x:dif][t:prop2d(x)]t10(x,t)):prop3
+-3r184
+r@satz184:=realapp1(prop3".3r184",[x:dif][t:inn(x,class(r))]t11".3r184"(x,t)):some([x:real]some([y:real]and3(pos(x),pos(y),is(r,mn(x,y)))))
+u@[a3:dif][b3:dif][c3:dif][d3:dif][a3ir:inn(a3,class(r))][b3is:inn(b3,class(s))][c3it:inn(c3,class(t))][d3iu:inn(d3,class(u))]
++3r185
+t1:=satzd185(a3,b3,c3,d3):eq"rp"(pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)))
+t2:=isin(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)),pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)),picp(mn(r,s),mn(t,u),md(a3,b3),md(c3,d3),micmn(r,s,a3,b3,a3ir,b3is),micmn(t,u,c3,d3,c3it,d3iu)),micmn(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu)),t1):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
+-3r185
+u@satz185:=realapp4(is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u))),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r185"(x,y,z,v,xi,yi,zi,vi)):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
++3r186
+c2it@t1:=satzd186(a2,b2,c2):eq"rp"(pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)))
+t2:=isin(pl(pl(r,s),t),pl(r,pl(s,t)),pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)),picp(pl(r,s),t,pd(a2,b2),c2,picp(r,s,a2,b2,a2ir,b2is),c2it),picp(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),t1):is(pl(pl(r,s),t),pl(r,pl(s,t)))
+-3r186
+t@satz186:=realapp3(is(pl(pl(r,s),t),pl(r,pl(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r186"(x,y,z,u,v,w)):is(pl(pl(r,s),t),pl(r,pl(s,t)))
+asspl1:=satz186:is(pl(pl(r,s),t),pl(r,pl(s,t)))
+asspl2:=symis(real,pl(pl(r,s),t),pl(r,pl(s,t)),satz186):is(pl(r,pl(s,t)),pl(pl(r,s),t))
+s@plmn:=tris(real,pl(mn(r,s),s),pl(r,pl(m0(s),s)),r,asspl1(r,m0(s),s),pl02(r,pl(m0(s),s),satz179a(s))):is(pl(mn(r,s),s),r)
+mnpl:=tris(real,mn(pl(r,s),s),pl(r,pl(s,m0(s))),r,asspl1(r,s,m0(s)),pl02(r,pl(s,m0(s)),satz179(s))):is(mn(pl(r,s),s),r)
+satz187a:=tris(real,pl(s,mn(r,s)),pl(mn(r,s),s),r,compl(s,mn(r,s)),plmn):is(pl(s,mn(r,s)),r)
+satz187b:=somei(real,[x:real]is(pl(s,x),r),mn(r,s),satz187a):some([x:real]is(pl(s,x),r))
+[x:real][i:is(pl(s,x),r)]
+satz187c:=tris(real,mn(r,s),mn(pl(x,s),s),x,ismn1(r,pl(x,s),s,tris1(real,r,pl(x,s),pl(s,x),i,compl(s,x))),mnpl(x,s)):is(mn(r,s),x)
+satz187d:=symis(real,mn(r,s),x,satz187c):is(x,mn(r,s))
+x@[i:is(pl(x,s),r)]
+satz187e:=satz187c(tris(real,pl(s,x),pl(x,s),r,compl(s,x),i)):is(mn(r,s),x)
+satz187f:=symis(real,mn(r,s),x,satz187e):is(x,mn(r,s))
++3r187
+s@[x:real][y:real][i:is(pl(s,x),r)][j:is(pl(s,y),r)]
+t1:=tris1(real,x,y,mn(r,s),satz187c(x,i),satz187c(y,j)):is(x,y)
+s@t2:=[x:real][y:real][t:is(pl(s,x),r)][u:is(pl(s,y),r)]t1(x,y,t,u):amone(real,[x:real]is(pl(s,x),r))
+-3r187
+s@satz187:=onei(real,[x:real]is(pl(s,x),r),t2".3r187",satz187b):one([x:real]is(pl(s,x),r))
++3r188
+c2it@[m:more(pl(r,t),pl(s,t))]
+t1:=satzd188a(a2,b2,c2,moreex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),m)):mored(a2,b2)
+t2:=morein(r,s,a2,b2,a2ir,b2is,t1):more(r,s)
+-3r188
+t@[m:more(pl(r,t),pl(s,t))]
+satz188a:=realapp3(more(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r188"(x,y,z,u,v,w,m)):more(r,s)
++*3r188
+c2it@[i:is(pl(r,t),pl(s,t))]
+t3:=satzd188b(a2,b2,c2,isex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),i)):eq"rp"(a2,b2)
+t4:=isin(r,s,a2,b2,a2ir,b2is,t3):is(r,s)
+-3r188
+t@[i:is(pl(r,t),pl(s,t))]
+satz188b:=realapp3(is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".3r188"(x,y,z,u,v,w,i)):is(r,s)
++*3r188
+c2it@[l:less(pl(r,t),pl(s,t))]
+t5:=satzd188c(a2,b2,c2,lessex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),l)):lessd(a2,b2)
+t6:=lessin(r,s,a2,b2,a2ir,b2is,t5):less(r,s)
+-3r188
+t@[l:less(pl(r,t),pl(s,t))]
+satz188c:=realapp3(less(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t6".3r188"(x,y,z,u,v,w,l)):less(r,s)
++*3r188
+c2it@[m:more(r,s)]
+t7:=satzd188d(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m)):mored(pd(a2,c2),pd(b2,c2))
+t8:=morein(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t7):more(pl(r,t),pl(s,t))
+-3r188
+t@[m:more(r,s)]
+satz188d:=realapp3(more(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t8".3r188"(x,y,z,u,v,w,m)):more(pl(r,t),pl(s,t))
+t@[i:is(r,s)]
+satz188e:=ispl1(r,s,t,i):is(pl(r,t),pl(s,t))
++*3r188
+c2it@[l:less(r,s)]
+t9:=satzd188f(a2,b2,c2,lessex(r,s,a2,b2,a2ir,b2is,l)):lessd(pd(a2,c2),pd(b2,c2))
+t10:=lessin(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t9):less(pl(r,t),pl(s,t))
+-3r188
+t@[l:less(r,s)]
+satz188f:=realapp3(less(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t10".3r188"(x,y,z,u,v,w,l)):less(pl(r,t),pl(s,t))
+t@[m:more(pl(t,r),pl(t,s))]
+satz188g:=satz188a(ismore12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),m)):more(r,s)
+t@[i:is(pl(t,r),pl(t,s))]
+satz188h:=satz188b(tr3is(real,pl(r,t),pl(t,r),pl(t,s),pl(s,t),compl(r,t),i,compl(t,s))):is(r,s)
+t@[l:less(pl(t,r),pl(t,s))]
+satz188j:=satz188c(isless12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),l)):less(r,s)
+t@[m:more(r,s)]
+satz188k:=ismore12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188d(m)):more(pl(t,r),pl(t,s))
+t@[i:is(r,s)]
+satz188l:=ispl2(r,s,t,i):is(pl(t,r),pl(t,s))
+t@[l:less(r,s)]
+satz188m:=isless12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188f(l)):less(pl(t,r),pl(t,s))
+u@[i:is(r,s)][m:more(t,u)]
+satz188n:=ismore2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188k(t,u,r,m)):more(pl(r,t),pl(s,u))
+satz188o:=ismore12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188n):more(pl(t,r),pl(u,s))
+i@[l:less(t,u)]
+satz188p:=isless2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188m(t,u,r,l)):less(pl(r,t),pl(s,u))
+satz188q:=isless12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188p):less(pl(t,r),pl(u,s))
+u@[m:more(r,s)][n:more(t,u)]
+satz189:=trmore(pl(r,t),pl(s,t),pl(s,u),satz188d(m),satz188k(t,u,s,n)):more(pl(r,t),pl(s,u))
+u@[l:less(r,s)][k:less(t,u)]
+satz189a:=lemma1(pl(s,u),pl(r,t),satz189(s,r,u,t,lemma2(r,s,l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
+u@[m:moreis(r,s)][n:more(t,u)]
+satz190a:=orapp(more(r,s),is(r,s),more(pl(r,t),pl(s,u)),m,[v:more(r,s)]satz189(v,n),[v:is(r,s)]satz188n(v,n)):more(pl(r,t),pl(s,u))
+u@[m:more(r,s)][n:moreis(t,u)]
+satz190b:=ismore12(pl(t,r),pl(r,t),pl(u,s),pl(s,u),compl(t,r),compl(u,s),satz190a(t,u,r,s,n,m)):more(pl(r,t),pl(s,u))
+u@[l:lessis(r,s)][k:less(t,u)]
+satz190c:=lemma1(pl(s,u),pl(r,t),satz190a(s,r,u,t,satz168b(l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
+u@[l:less(r,s)][k:lessis(t,u)]
+satz190d:=lemma1(pl(s,u),pl(r,t),satz190b(s,r,u,t,lemma2(l),satz168b(t,u,k))):less(pl(r,t),pl(s,u))
++3r191
+d3iu@[m:moreis(r,s)][n:moreis(t,u)]
+t1:=satzd191(a3,b3,c3,d3,moreisex(r,s,a3,b3,a3ir,b3is,m),moreisex(t,u,c3,d3,c3it,d3iu,n)):moreq(pd(a3,c3),pd(b3,d3))
+t2:=moreisin(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu),t1):moreis(pl(r,t),pl(s,u))
+-3r191
+u@[m:moreis(r,s)][n:moreis(t,u)]
+satz191:=realapp4(moreis(pl(r,t),pl(s,u)),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r191"(x,y,z,v,xi,yi,zi,vi,m,n)):moreis(pl(r,t),pl(s,u))
+u@[l:lessis(r,s)][k:lessis(t,u)]
+satz191a:=satz168a(pl(s,u),pl(r,t),satz191(s,r,u,t,satz168b(l),satz168b(t,u,k))):lessis(pl(r,t),pl(s,u))
+@timesdr:=[x:dif][y:dif]realof(td(x,y)):[x:dif][y:dif]real
++ivr4
+[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
+t1:=isin(realof(td(a,c)),realof(td(b,d)),td(a,c),td(b,d),innclass(td(a,c)),innclass(td(b,d)),eqtd12(a,b,c,d,e,f)):is(<c><a>timesdr,<d><b>timesdr)
+-ivr4
+ftimesdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr4"(x,y,z,v,t,u):fixf2(real,timesdr)
+s@ts:=indreal2(real,timesdr,ftimesdr,r,s):real
++*ivr4
+b1is@t2:=isindreal2(real,timesdr,ftimesdr,r,s,a1,b1,a1ir,b1is):is(realof(td(a1,b1)),ts(r,s))
+-ivr4
+b1is@tict:=isp(real,[x:real]inn(td(a1,b1),class(x)),realof(td(a1,b1)),ts(r,s),innclass(td(a1,b1)),t2".ivr4"):inn(td(a1,b1),class(ts(r,s)))
+t@[i:is(r,s)]
+ists1:=isf(real,real,[x:real]ts(x,t),r,s,i):is(ts(r,t),ts(s,t))
+ists2:=isf(real,real,[x:real]ts(t,x),r,s,i):is(ts(t,r),ts(t,s))
+u@[i:is(r,s)][j:is(t,u)]
+ists12:=tris(real,ts(r,t),ts(s,t),ts(s,u),ists1(i),ists2(t,u,s,j)):is(ts(r,t),ts(s,u))
++4r192
+b1is@[i:is(r,0)]
+t1:=satzd192a(a1,b1,0ex(r,a1,a1ir,i)):zero(td(a1,b1))
+t2:=0in(ts(r,s),td(a1,b1),tict,t1):is(ts(r,s),0)
+-4r192
+s@[i:is(r,0)]
+satz192a:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r192"(x,y,t,u,i)):is(ts(r,s),0)
++*4r192
+b1is@[i:is(s,0)]
+t3:=satzd192b(a1,b1,0ex(s,b1,b1is,i)):zero(td(a1,b1))
+t4:=0in(ts(r,s),td(a1,b1),tict,t3):is(ts(r,s),0)
+-4r192
+s@[i:is(s,0)]
+satz192b:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".4r192"(x,y,t,u,i)):is(ts(r,s),0)
++*4r192
+b1is@[i:is(ts(r,s),0)]
+t5:=satzd192c(a1,b1,0ex(ts(r,s),td(a1,b1),tict,i)):or(zero(a1),zero(b1))
+t6:=th9"l.or"(zero(a1),zero(b1),is(r,0),is(s,0),t5,[t:zero(a1)]0in(r,a1,a1ir,t),[t:zero(b1)]0in(s,b1,b1is,t)):or(is(r,0),is(s,0))
+-4r192
+s@[i:is(ts(r,s),0)]
+satz192c:=realapp2(or(is(r,0),is(s,0)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".4r192"(x,y,t,u,i)):or(is(r,0),is(s,0))
+s@[n:nis(r,0)][o:nis(s,0)]
+satz192d:=th3"l.imp"(is(ts(r,s),0),or(is(r,0),is(s,0)),th3"l.or"(is(r,0),is(s,0),n,o),[t:is(ts(r,s),0)]satz192c(t)):nis(ts(r,s),0)
+s@[i:is(r,0)]
+ts01:=satz192a(i):is(ts(r,s),0)
+s@[i:is(s,0)]
+ts02:=satz192b(i):is(ts(r,s),0)
++4r193
+b1is@t1:=satzd193(a1,b1):eq"rp"(absd(td(a1,b1)),td(absd(a1),absd(b1)))
+t2:=isin(abs(ts(r,s)),ts(abs(r),abs(s)),absd(td(a1,b1)),td(absd(a1),absd(b1)),aica(ts(r,s),td(a1,b1),tict),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(abs(ts(r,s)),ts(abs(r),abs(s)))
+-4r193
+s@satz193:=realapp2(is(abs(ts(r,s)),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r193"(x,y,t,u)):is(abs(ts(r,s)),ts(abs(r),abs(s)))
+satz193a:=symis(real,abs(ts(r,s)),ts(abs(r),abs(s)),satz193):is(ts(abs(r),abs(s)),abs(ts(r,s)))
++4r194
+b1is@t1:=satzd194(a1,b1):eq"rp"(td(a1,b1),td(b1,a1))
+t2:=isin(ts(r,s),ts(s,r),td(a1,b1),td(b1,a1),tict,tict(s,r,b1,a1,b1is,a1ir),t1):is(ts(r,s),ts(s,r))
+-4r194
+satz194:=realapp2(is(ts(r,s),ts(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r194"(x,y,t,u)):is(ts(r,s),ts(s,r))
+comts:=satz194:is(ts(r,s),ts(s,r))
+@1rl:=realof(1df):real
+pos1:=posin(1rl,1df,innclass(1df),posdirp(1rp)):pos(1rl)
+natrl1:=natrli(1):natrl(1rl)
+intrl1:=natintrl(1rl,natrl1):intrl(1rl)
++4r195
+a0ir@t1:=satzd195(a0):eq"rp"(td(a0,1df),a0)
+t2:=isin(ts(r,1rl),r,td(a0,1df),a0,tict(r,1rl,a0,1df,a0ir,innclass(1df)),a0ir,t1):is(ts(r,1rl),r)
+-4r195
+r@satz195:=realapp1(is(ts(r,1rl),r),[x:dif][t:inn(x,class(r))]t2".4r195"(x,t)):is(ts(r,1rl),r)
+satz195a:=symis(real,ts(r,1rl),r,satz195):is(r,ts(r,1rl))
+satz195b:=tris(real,ts(1rl,r),ts(r,1rl),r,comts(1rl,r),satz195):is(ts(1rl,r),r)
+satz195c:=symis(real,ts(1rl,r),r,satz195b):is(r,ts(1rl,r))
+s@[p:pos(r)][q:pos(s)]
+satz196a:=symis(real,ts(abs(r),abs(s)),ts(r,s),ists12(abs(r),r,abs(s),s,absp(r,p),absp(s,q))):is(ts(r,s),ts(abs(r),abs(s)))
++4r196
+b1is@[n:neg(r)][o:neg(s)]
+t1:=satzd196b(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):eq"rp"(td(a1,b1),td(absd(a1),absd(b1)))
+t2:=isin(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(ts(r,s),ts(abs(r),abs(s)))
+-4r196
+s@[n:neg(r)][o:neg(s)]
+satz196b:=realapp2(is(ts(r,s),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r196"(x,y,t,u,n,o)):is(ts(r,s),ts(abs(r),abs(s)))
++*4r196
+b1is@[p:pos(r)][n:neg(s)]
+t1a:=satzd196c(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):eq"rp"(td(a1,b1),m0d(td(absd(a1),absd(b1))))
+t2a:=isin(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),t1a):is(ts(r,s),m0(ts(abs(r),abs(s))))
+-4r196
+s@[p:pos(r)][n:neg(s)]
+satz196c:=realapp2(is(ts(r,s),m0(ts(abs(r),abs(s)))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2a".4r196"(x,y,t,u,p,n)):is(ts(r,s),m0(ts(abs(r),abs(s))))
+s@[n:neg(r)][p:pos(s)]
+satz196d:=tr3is(real,ts(r,s),ts(s,r),m0(ts(abs(s),abs(r))),m0(ts(abs(r),abs(s))),comts(r,s),satz196c(s,r,p,n),ism0(ts(abs(s),abs(r)),ts(abs(r),abs(s)),comts(abs(s),abs(r)))):is(ts(r,s),m0(ts(abs(r),abs(s))))
++*4r196
+a0ir@[n:not(is(r,0))]
+t3:=th3"l.imp"(zero(a0),is(r,0),n,[t:zero(a0)]0in(t)):not(zero(a0))
+b1is@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
+t4:=satzd196e(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),i)):or(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)))
+[a:and(posd(a1),posd(b1))]
+t5:=andi(pos(r),pos(s),posin(r,a1,a1ir,ande1(posd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(posd(a1),posd(b1),a))):and(pos(r),pos(s))
+i@[a:and(negd(a1),negd(b1))]
+t6:=andi(neg(r),neg(s),negin(r,a1,a1ir,ande1(negd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(negd(a1),negd(b1),a))):and(neg(r),neg(s))
+i@t7:=th9"l.or"(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)),and(pos(r),pos(s)),and(neg(r),neg(s)),t4,[t:and(posd(a1),posd(b1))]t5(t),[t:and(negd(a1),negd(b1))]t6(t)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
+-4r196
+s@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
+satz196e:=realapp2(or(and(pos(r),pos(s)),and(neg(r),neg(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
++*4r196
+o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
+t8:=satzd196f(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),i)):or(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)))
+[a:and(posd(a1),negd(b1))]
+t9:=andi(pos(r),neg(s),posin(r,a1,a1ir,ande1(posd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(posd(a1),negd(b1),a))):and(pos(r),neg(s))
+i@[a:and(negd(a1),posd(b1))]
+t10:=andi(neg(r),pos(s),negin(r,a1,a1ir,ande1(negd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(negd(a1),posd(b1),a))):and(neg(r),pos(s))
+i@t11:=th9"l.or"(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)),and(pos(r),neg(s)),and(neg(r),pos(s)),t8,[t:and(posd(a1),negd(b1))]t9(t),[t:and(negd(a1),posd(b1))]t10(t)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
+-4r196
+o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
+satz196f:=realapp2(or(and(pos(r),neg(s)),and(neg(r),pos(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
+s@[p:pos(ts(r,s))]
++*4r196
+p"r"@t12:=th3"l.imp"(is(r,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
+t13:=th3"l.imp"(is(s,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
+t14:=tris1(real,ts(r,s),ts(abs(r),abs(s)),abs(ts(r,s)),absp(ts(r,s),p),satz193(r,s)):is(ts(r,s),ts(abs(r),abs(s)))
+-4r196
+p@satz196g:=satz196e(t12".4r196",t13".4r196",t14".4r196"):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
+s@[n:neg(ts(r,s))]
++*4r196
+n"r"@t15:=th3"l.imp"(is(r,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
+t16:=th3"l.imp"(is(s,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
+t17:=satz177c(ts(abs(r),abs(s)),ts(r,s),tris(real,ts(abs(r),abs(s)),abs(ts(r,s)),m0(ts(r,s)),satz193a(r,s),absn(ts(r,s),n))):is(ts(r,s),m0(ts(abs(r),abs(s))))
+-4r196
+n@satz196h:=satz196f(t15".4r196",t16".4r196",t17".4r196"):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
++4r197
+b1is@t1:=satzd197a(a1,b1):eq"rp"(td(m0d(a1),b1),m0d(td(a1,b1)))
+t2:=isin(ts(m0(r),s),m0(ts(r,s)),td(m0d(a1),b1),m0d(td(a1,b1)),tict(m0(r),s,m0d(a1),b1,micm0(r,a1,a1ir),b1is),micm0(ts(r,s),td(a1,b1),tict),t1):is(ts(m0(r),s),m0(ts(r,s)))
+-4r197
+s@satz197a:=realapp2(is(ts(m0(r),s),m0(ts(r,s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r197"(x,y,t,u)):is(ts(m0(r),s),m0(ts(r,s)))
+satz197b:=tr3is(real,ts(r,m0(s)),ts(m0(s),r),m0(ts(s,r)),m0(ts(r,s)),comts(r,m0(s)),satz197a(s,r),ism0(ts(s,r),ts(r,s),comts(s,r))):is(ts(r,m0(s)),m0(ts(r,s)))
+satz197c:=tris2(real,ts(m0(r),s),ts(r,m0(s)),m0(ts(r,s)),satz197a,satz197b):is(ts(m0(r),s),ts(r,m0(s)))
+satz197d:=symis(real,ts(m0(r),s),ts(r,m0(s)),satz197c):is(ts(r,m0(s)),ts(m0(r),s))
+satz197e:=symis(real,ts(m0(r),s),m0(ts(r,s)),satz197a):is(m0(ts(r,s)),ts(m0(r),s))
+satz197f:=symis(real,ts(r,m0(s)),m0(ts(r,s)),satz197b):is(m0(ts(r,s)),ts(r,m0(s)))
+satz198:=tris(real,ts(m0(r),m0(s)),ts(r,m0(m0(s))),ts(r,s),satz197c(r,m0(s)),ists2(m0(m0(s)),s,r,satz177(s))):is(ts(m0(r),m0(s)),ts(r,s))
+satz198a:=symis(real,ts(m0(r),m0(s)),ts(r,s),satz198):is(ts(r,s),ts(m0(r),m0(s)))
++*ivr4
+b1is@[p:pos(r)][q:pos(s)]
+t3:=ptdpp(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(td(a1,b1))
+t4:=posin(ts(r,s),td(a1,b1),tict,t3):pos(ts(r,s))
+-ivr4
+s@[p:pos(r)][q:pos(s)]
+postspp:=realapp2(pos(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr4"(x,y,t,u,p,q)):pos(ts(r,s))
++*ivr4
+p@[n:neg(s)]
+t5:=ntdpn(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):negd(td(a1,b1))
+t6:=negin(ts(r,s),td(a1,b1),tict,t5):neg(ts(r,s))
+-ivr4
+s@[p:pos(r)][n:neg(s)]
+negtspn:=realapp2(neg(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr4"(x,y,t,u,p,n)):neg(ts(r,s))
+s@[n:neg(r)][p:pos(s)]
+negtsnp:=isneg(ts(s,r),ts(r,s),comts(s,r),negtspn(s,r,p,n)):neg(ts(r,s))
+s@[n:neg(r)][o:neg(s)]
+postsnn:=ispos(ts(m0(r),m0(s)),ts(r,s),satz198,postspp(m0(r),m0(s),satz176c(r,n),satz176c(s,o))):pos(ts(r,s))
+r@[n:nis(r,0)]
+possq:=rapp(r,pos(ts(r,r)),[t:pos(r)]postspp(r,r,t,t),th2"l.imp"(is(r,0),pos(ts(r,r)),n),[t:neg(r)]postsnn(r,r,t,t)):pos(ts(r,r))
+r@nnegsq:=th1"l.imp"(is(r,0),not(neg(ts(r,r))),[t:is(r,0)]0notn(ts(r,r),satz192a(r,r,t)),[t:nis(r,0)]pnotn(ts(r,r),possq(r,t))):not(neg(ts(r,r)))
++4r199
+c2it@t1:=satzd199(a2,b2,c2):eq"rp"(td(td(a2,b2),c2),td(a2,td(b2,c2)))
+t2:=isin(ts(ts(r,s),t),ts(r,ts(s,t)),td(td(a2,b2),c2),td(a2,td(b2,c2)),tict(ts(r,s),t,td(a2,b2),c2,tict(r,s,a2,b2,a2ir,b2is),c2it),tict(r,ts(s,t),a2,td(b2,c2),a2ir,tict(s,t,b2,c2,b2is,c2it)),t1):is(ts(ts(r,s),t),ts(r,ts(s,t)))
+-4r199
+t@satz199:=realapp3(is(ts(ts(r,s),t),ts(r,ts(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r199"(x,y,z,u,v,w)):is(ts(ts(r,s),t),ts(r,ts(s,t)))
+assts1:=satz199:is(ts(ts(r,s),t),ts(r,ts(s,t)))
+assts2:=symis(real,ts(ts(r,s),t),ts(r,ts(s,t)),satz199):is(ts(r,ts(s,t)),ts(ts(r,s),t))
++4r201
+c2it@t1:=satzd201(a2,b2,c2):eq"rp"(td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)))
+t2:=isin(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)),tict(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),picp(ts(r,s),ts(r,t),td(a2,b2),td(a2,c2),tict(r,s,a2,b2,a2ir,b2is),tict(r,t,a2,c2,a2ir,c2it)),t1):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
+-4r201
+satz201:=realapp3(is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r201"(x,y,z,u,v,w)):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
+disttp1:=tr3is(real,ts(pl(r,s),t),ts(t,pl(r,s)),pl(ts(t,r),ts(t,s)),pl(ts(r,t),ts(s,t)),comts(pl(r,s),t),satz201(t,r,s),ispl12(ts(t,r),ts(r,t),ts(t,s),ts(s,t),comts(t,r),comts(t,s))):is(ts(pl(r,s),t),pl(ts(r,t),ts(s,t)))
+disttp2:=satz201:is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
+distpt1:=symis(real,ts(pl(r,s),t),pl(ts(r,t),ts(s,t)),disttp1):is(pl(ts(r,t),ts(s,t)),ts(pl(r,s),t))
+distpt2:=symis(real,ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),disttp2):is(pl(ts(r,s),ts(r,t)),ts(r,pl(s,t)))
+satz202:=tris(real,ts(r,mn(s,t)),pl(ts(r,s),ts(r,m0(t))),mn(ts(r,s),ts(r,t)),disttp2(r,s,m0(t)),ispl2(ts(r,m0(t)),m0(ts(r,t)),ts(r,s),satz197b(r,t))):is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
+disttm1:=tris(real,ts(mn(r,s),t),pl(ts(r,t),ts(m0(s),t)),mn(ts(r,t),ts(s,t)),disttp1(r,m0(s),t),ispl2(ts(m0(s),t),m0(ts(s,t)),ts(r,t),satz197a(s,t))):is(ts(mn(r,s),t),mn(ts(r,t),ts(s,t)))
+disttm2:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
+distmt1:=symis(real,ts(mn(r,s),t),mn(ts(r,t),ts(s,t)),disttm1):is(mn(ts(r,t),ts(s,t)),ts(mn(r,s),t))
+distmt2:=symis(real,ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)),disttm2):is(mn(ts(r,s),ts(r,t)),ts(r,mn(s,t)))
+satz200:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
++4r203
+c2it@[m:more(r,s)][p:pos(t)]
+t1:=satzd203a(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),posex(t,c2,c2it,p)):mored(td(a2,c2),td(b2,c2))
+t2:=morein(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t1):more(ts(r,t),ts(s,t))
+-4r203
+[m:more(r,s)][p:pos(t)]
+satz203a:=realapp3(more(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r203"(x,y,z,u,v,w,m,p)):more(ts(r,t),ts(s,t))
+m@[i:is(t,0)]
+satz203b:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
++*4r203
+m@[n:neg(t)]
+t3:=satzd203c(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),negex(t,c2,c2it,n)):lessd(td(a2,c2),td(b2,c2))
+t4:=lessin(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t3):less(ts(r,t),ts(s,t))
+-4r203
+m@[n:neg(t)]
+satz203c:=realapp3(less(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".4r203"(x,y,z,u,v,w,m,n)):less(ts(r,t),ts(s,t))
+p@satz203d:=ismore12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203a):more(ts(t,r),ts(t,s))
+i@satz203e:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
+n@satz203f:=isless12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203c):less(ts(t,r),ts(t,s))
+t@[l:less(r,s)][p:pos(t)]
+satz203g:=lemma1(ts(s,t),ts(r,t),satz203a(s,r,t,lemma2(r,s,l),p)):less(ts(r,t),ts(s,t))
+l@[i:is(t,0)]
+satz203h:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
+l@[n:neg(t)]
+satz203j:=lemma2(ts(s,t),ts(r,t),satz203c(s,r,t,lemma2(r,s,l),n)):more(ts(r,t),ts(s,t))
+p@satz203k:=lemma1(ts(t,s),ts(t,r),satz203d(s,r,t,lemma2(r,s,l),p)):less(ts(t,r),ts(t,s))
+i@satz203l:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
+n@satz203m:=lemma2(ts(t,s),ts(t,r),satz203f(s,r,t,lemma2(r,s,l),n)):more(ts(t,r),ts(t,s))
++4r204
+a0ir@[n1:nis(r,0)]
+t1:=th3"l.imp"(zero(a0),is(r,0),n1,[t:zero(a0)]0in(t)):not(zero(a0))
+d3iu@[n1:nis(s,0)][i:is(ts(s,t),r)][j:is(ts(s,u),r)]
+t2:=satzd204b(a3,b3,t1(s,b3,b3is,n1),c3,d3,isex(ts(s,t),r,td(b3,c3),a3,tict(s,t,b3,c3,b3is,c3it),a3ir,i),isex(ts(s,u),r,td(b3,d3),a3,tict(s,u,b3,d3,b3is,d3iu),a3ir,j)):eq"rp"(c3,d3)
+t3:=isin(t,u,c3,d3,c3it,d3iu,t2):is(t,u)
+-4r204
+s@[n:nis(s,0)][x:real][y:real][i:is(ts(s,x),r)][j:is(ts(s,y),r)]
+satz204b:=realapp4(x,y,is(x,y),[z:dif][u:dif][v:dif][w:dif][zi:inn(z,class(r))][ui:inn(u,class(s))][vi:inn(v,class(x))][wi:inn(w,class(y))]t3".4r204"(x,y,z,u,v,w,zi,ui,vi,wi,n,i,j)):is(x,y)
++*4r204
+b1is@[n1:nis(s,0)]
+t4:=satzd204a(a1,b1,t1(s,b1,b1is,n1)):some"l"(dif,[x:dif]eq"rp"(td(b1,x),a1))
+[a:dif][e:eq"rp"(td(b1,a),a1)]
+ar:=realof(a):real
+t5:=isin(ts(s,ar),r,td(b1,a),a1,tict(s,ar,b1,a,b1is,innclass(a)),a1ir,e):is(ts(s,ar),r)
+t6:=somei(real,[x:real]is(ts(s,x),r),ar,t5):some([x:real]is(ts(s,x),r))
+n1@t7:=someapp(dif,[x:dif]eq"rp"(td(b1,x),a1),t4,some([x:real]is(ts(s,x),r)),[x:dif][t:eq"rp"(td(b1,x),a1)]t6(x,t)):some([x:real]is(ts(s,x),r))
+-4r204
+n@satz204a:=realapp2(some([x:real]is(ts(s,x),r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r204"(x,y,t,u,n)):some([x:real]is(ts(s,x),r))
+satz204:=onei(real,[x:real]is(ts(s,x),r),[x:real][y:real][t:is(ts(s,x),r)][u:is(ts(s,y),r)]satz204b(x,y,t,u),satz204a):one([x:real]is(ts(s,x),r))
+ov:=ind(real,[x:real]is(ts(s,x),r),satz204):real
+satz204c:=oneax(real,[x:real]is(ts(s,x),r),satz204):is(ts(s,ov(r,s,n)),r)
+satz204d:=symis(real,ts(s,ov(r,s,n)),r,satz204c):is(r,ts(s,ov(r,s,n)))
+satz204e:=tris(real,ts(ov(r,s,n),s),ts(s,ov(r,s,n)),r,comts(ov(r,s,n),s),satz204c):is(ts(ov(r,s,n),s),r)
+satz204f:=symis(real,ts(ov(r,s,n),s),r,satz204e):is(r,ts(ov(r,s,n),s))
+s@[x:real][n:nis(s,0)][i:is(ts(s,x),r)]
+satz204g:=satz204b(n,x,ov(r,s,n),i,satz204c(n)):is(x,ov(r,s,n))
+s@[n:nis(s,0)][p:pos(r)][q:pos(s)]
++*4r204
+n@ros:=ov(r,s,n):real
+p@t8:=ispos(r,ts(s,ros),satz204d(n),p):pos(ts(s,ros))
+q@t9:=th1"l.and"(neg(s),neg(ros),pnotn(s,q)):not(and(neg(s),neg(ros)))
+t10:=ore1(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t9):and(pos(s),pos(ros))
+-4r204
+q@posovpp:=ande2(pos(s),pos(ov(r,s,n)),t10".4r204"):pos(ov(r,s,n))
+p@[m:neg(s)]
++*4r204
+m@t11:=th1"l.and"(pos(s),pos(ros),nnotp(s,m)):not(and(pos(s),pos(ros)))
+t12:=ore2(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t11):and(neg(s),neg(ros))
+-4r204
+m@negovpn:=ande2(neg(s),neg(ov(r,s,n)),t12".4r204"):neg(ov(r,s,n))
+n@[m:neg(r)][p:pos(s)]
++*4r204
+m@t13:=isneg(r,ts(s,ros),satz204d(n),m):neg(ts(s,ros))
+p@t14:=th1"l.and"(neg(s),pos(ros),pnotn(s,p)):not(and(neg(s),pos(ros)))
+t15:=ore1(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t14):and(pos(s),neg(ros))
+-4r204
+p@negovnp:=ande2(pos(s),neg(ov(r,s,n)),t15".4r204"):neg(ov(r,s,n))
+m@[l:neg(s)]
++*4r204
+l@t16:=th1"l.and"(pos(s),neg(ros),nnotp(s,l)):not(and(pos(s),neg(ros)))
+t17:=ore2(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t16):and(neg(s),pos(ros))
+-4r204
+l@posovnn:=ande2(neg(s),pos(ov(r,s,n)),t17".4r204"):pos(ov(r,s,n))
+@[r0:cut][s0:cut][m:more"rp"(r0,s0)]
+morerpep:=morein(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),morerpepd(r0,s0,m)):more(pofrp(r0),pofrp(s0))
+s0@[m:more(pofrp(r0),pofrp(s0))]
+morerpip:=morerpipd(r0,s0,moreex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),m)):more"rp"(r0,s0)
+s0@[l:less"rp"(r0,s0)]
+lessrpep:=lemma1(pofrp(s0),pofrp(r0),morerpep(s0,r0,satz122(r0,s0,l))):less(pofrp(r0),pofrp(s0))
+s0@[l:less(pofrp(r0),pofrp(s0))]
+lessrpip:=satz121(s0,r0,morerpip(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
+s@[p:pos(r)][q:pos(s)][m:more(r,s)]
+q@[m:more(r,s)]
++ivr5
+t1:=ismore12(r,pofrp(rpofp(r,p)),s,pofrp(rpofp(s,q)),isprp1(r,p),isprp1(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
+-ivr5
+moreperp:=morerpip(rpofp(r,p),rpofp(s,q),t1".ivr5"):more"rp"(rpofp(r,p),rpofp(s,q))
+q@[m:more"rp"(rpofp(r,p),rpofp(s,q))]
++*ivr5
+m@t2:=morerpep(rpofp(r,p),rpofp(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
+-ivr5
+m@morepirp:=ismore12(pofrp(rpofp(r,p)),r,pofrp(rpofp(s,q)),s,isprp2(r,p),isprp2(s,q),t2".ivr5"):more(r,s)
+q@[l:less(r,s)]
+lessperp:=satz121(rpofp(s,q),rpofp(r,p),moreperp(s,r,q,p,lemma2(r,s,l))):less"rp"(rpofp(r,p),rpofp(s,q))
+q@[l:less"rp"(rpofp(r,p),rpofp(s,q))]
+lesspirp:=lemma1(s,r,morepirp(s,r,q,p,satz122(rpofp(r,p),rpofp(s,q),l))):less(r,s)
+r@s01:=setof(real,[x:real]lessis(x,r)):set(real)
+s02:=setof(real,[x:real]more(x,r)):set(real)
++5r205
+s@[n:not(in(s,s01))]
+t1:=th3"l.imp"(lessis(s,r),in(s,s01),n,[t:lessis(s,r)]estii(real,[x:real]lessis(x,r),s,t)):not(lessis(s,r))
+t2:=estii(real,[x:real]more(x,r),s,satz167k(s,r,t1)):in(s,s02)
+-5r205
+vb00:=[x:real][t:not(in(x,s01))]t2".5r205"(x,t):all([x:real]or(in(x,s01),in(x,s02)))
++*5r205
+r@t3:=estii(real,[x:real]lessis(x,r),r,lessisi2(r,r,refis(real,r))):in(r,s01)
+-5r205
+r@vb01a:=nonemptyi(real,s01,r,t3".5r205"):nonempty(real,s01)
++*5r205
+r@t4:=ismore2(pl(r,0),r,pl(r,1rl),pl02(r,0,refis(real,0)),satz188k(1rl,0,r,satz169a(1rl,pos1))):more(pl(r,1rl),r)
+t5:=estii(real,[x:real]more(x,r),pl(r,1rl),t4):in(pl(r,1rl),s02)
+-5r205
+r@vb01b:=nonemptyi(real,s02,pl(r,1rl),t5".5r205"):nonempty(real,s02)
++*5r205
+s@[i:in(s,s01)][t:real][j:in(t,s02)]
+t6:=satz172a(s,r,t,estie(real,[x:real]lessis(x,r),s,i),lemma1(t,r,estie(real,[x:real]more(x,r),t,j))):less(s,t)
+-5r205
+r@vb02:=[x:real][t:in(x,s01)][y:real][u:in(y,s02)]t6".5r205"(x,t,y,u):all([x:real][t:in(x,s01)]all([y:real][u:in(y,s02)]less(x,y)))
+s@[l:less(s,r)]
+vb03a:=estii(real,[x:real]lessis(x,r),s,lessisi1(s,r,l)):in(s,s01)
+s@[m:more(s,r)]
+vb03b:=estii(real,[x:real]more(x,r),s,m):in(s,s02)
+r@s11:=setof(real,[x:real]less(x,r)):set(real)
+s12:=setof(real,[x:real]moreis(x,r)):set(real)
++*5r205
+s@[n:not(in(s,s11))]
+t7:=th3"l.imp"(less(s,r),in(s,s11),n,[t:less(s,r)]estii(real,[x:real]less(x,r),s,t)):not(less(s,r))
+t8:=estii(real,[x:real]moreis(x,r),s,satz167f(s,r,t7)):in(s,s12)
+-5r205
+r@vb10:=[x:real][t:not(in(x,s11))]t8".5r205"(x,t):all([x:real]or(in(x,s11),in(x,s12)))
++*5r205
+r@t9:=isless2(pl(r,0),r,mn(r,1rl),pl02(r,0,refis(real,0)),satz188m(m0(1rl),0,r,satz169c(m0(1rl),satz176a(1rl,pos1)))):less(mn(r,1rl),r)
+t10:=estii(real,[x:real]less(x,r),mn(r,1rl),t9):in(mn(r,1rl),s11)
+-5r205
+r@vb11a:=nonemptyi(real,s11,mn(r,1rl),t10".5r205"):nonempty(real,s11)
++*5r205
+r@t11:=estii(real,[x:real]moreis(x,r),r,moreisi2(r,r,refis(real,r))):in(r,s12)
+-5r205
+r@vb11b:=nonemptyi(real,s12,r,t11".5r205"):nonempty(real,s12)
++*5r205
+s@[i:in(s,s11)][t:real][j:in(t,s12)]
+t12:=satz172b(s,r,t,estie(real,[x:real]less(x,r),s,i),satz168a(t,r,estie(real,[x:real]moreis(x,r),t,j))):less(s,t)
+-5r205
+r@vb12:=[x:real][t:in(x,s11)][y:real][u:in(y,s12)]t12".5r205"(x,t,y,u):all([x:real][t:in(x,s11)]all([y:real][u:in(y,s12)]less(x,y)))
+s@[l:less(s,r)]
+vb13a:=estii(real,[x:real]less(x,r),s,l):in(s,s11)
+s@[m:more(s,r)]
+vb13b:=estii(real,[x:real]moreis(x,r),s,moreisi1(s,r,m)):in(s,s12)
+@2rl:=pl(1rl,1rl):real
+pos2:=pospl(1rl,1rl,pos1,pos1):pos(2rl)
+half:=ov(1rl,2rl,pnot0(2rl,pos2)):real
+poshalf:=posovpp(1rl,2rl,pnot0(2rl,pos2),pos1,pos2):pos(half)
++*ivr5
+r@t3:=tris(real,pl(r,r),pl(ts(1rl,r),ts(1rl,r)),ts(2rl,r),ispl12(r,ts(1rl,r),r,ts(1rl,r),satz195c(r),satz195c(r)),distpt1(1rl,1rl,r)):is(pl(r,r),ts(2rl,r))
+t4:=tr4is(real,ts(half,pl(r,r)),ts(half,ts(2rl,r)),ts(ts(half,2rl),r),ts(1rl,r),r,ists2(pl(r,r),ts(2rl,r),half,t3),assts2(half,2rl,r),ists1(ts(half,2rl),1rl,r,satz204e(1rl,2rl,pnot0(2rl,pos2))),satz195b(r)):is(ts(half,pl(r,r)),r)
+-ivr5
+s@[l:less(r,s)]
++*ivr5
+l@t5:=satz203k(pl(r,r),pl(r,s),half,satz188m(r,s,r,l),poshalf):less(ts(half,pl(r,r)),ts(half,pl(r,s)))
+-ivr5
+l@lemma3:=isless1(ts(half,pl(r,r)),r,ts(half,pl(r,s)),t4".ivr5",t5".ivr5"):less(r,ts(half,pl(r,s)))
++*ivr5
+l@t6:=satz203k(pl(r,s),pl(s,s),half,satz188f(r,s,s,l),poshalf):less(ts(half,pl(r,s)),ts(half,pl(s,s)))
+-ivr5
+l@lemma4:=isless2(ts(half,pl(s,s)),s,ts(half,pl(r,s)),t4".ivr5"(s),t6".ivr5"):less(ts(half,pl(r,s)),s)
+[p:pos(r)]
+lemma5:=satz169b(s,trmore(s,r,0,lemma2(r,s,l),satz169a(r,p))):pos(s)
+@[s1:set(real)][s2:set(real)][p0:all([x:real]or(in(x,s1),in(x,s2)))][p1a:nonempty(real,s1)][p1b:nonempty(real,s2)][p2:all([x:real][t:in(x,s1)]all([y:real][u:in(y,s2)]less(x,y)))]
++*5r205
+s2@[r:real]
+prop1:=all([x:real][t:less(x,r)]in(x,s1)):'prop'
+prop2:=all([x:real][t:more(x,r)]in(x,s2)):'prop'
+prop3:=and(prop1,prop2):'prop'
+p2@[x:real][y:real][px:prop3(x)][py:prop3(y)][l:less(x,y)]
+mxy:=ts(half,pl(x,y)):real
+t13:=lemma2(x,mxy,lemma3(x,y,l)):more(mxy,x)
+t14:=lemma4(x,y,l):less(mxy,y)
+t15:=<t14><mxy>ande1(prop1(y),prop2(y),py):in(mxy,s1)
+t16:=<t13><mxy>ande2(prop1(x),prop2(x),px):in(mxy,s2)
+t17:=<t16><mxy><t15><mxy>p2:less(mxy,mxy)
+t18:=<refis(real,mxy)>ec3e31(is(mxy,mxy),more(mxy,mxy),less(mxy,mxy),satz167b(mxy,mxy),t17):con
+py@t19:=[t:less(x,y)]t18(t):not(less(x,y))
+t20:=[t:more(x,y)]t18(y,x,py,px,lemma1(x,y,t)):not(more(x,y))
+t21:=or3e1(is(x,y),more(x,y),less(x,y),satz167a(x,y),t20,t19):is(x,y)
+p2@t22:=[x:real][y:real][t:prop3(x)][u:prop3(y)]t21(x,y,t,u):amone(real,[x:real]prop3(x))
+[case1:some([x:real]and(pos(x),in(x,s1)))][r:real][a:and(pos(r),in(r,s1))]
+t23:=ande1(pos(r),in(r,s1),a):pos(r)
+t24:=ande2(pos(r),in(r,s1),a):in(r,s1)
+sc1:=setof(cut,[x:cut]in(pofrp(x),s1)):set(cut)
+sc2:=setof(cut,[x:cut]in(pofrp(x),s2)):set(cut)
+[r0:cut][i:in(pofrp(r0),s1)]
+t25:=estii(cut,[x:cut]in(pofrp(x),s1),r0,i):in"rp"(r0,sc1)
+r0@[i:in"rp"(r0,sc1)]
+t26:=estie(cut,[x:cut]in(pofrp(x),s1),r0,i):in(pofrp(r0),s1)
+r0@[i:in(pofrp(r0),s2)]
+t27:=estii(cut,[x:cut]in(pofrp(x),s2),r0,i):in"rp"(r0,sc2)
+r0@[i:in"rp"(r0,sc2)]
+t28:=estie(cut,[x:cut]in(pofrp(x),s2),r0,i):in(pofrp(r0),s2)
+r0@t29:=th9"l.or"(in(pofrp(r0),s1),in(pofrp(r0),s2),in"rp"(r0,sc1),in"rp"(r0,sc2),<pofrp(r0)>p0,[t:in(pofrp(r0),s1)]t25(t),[t:in(pofrp(r0),s2)]t27(t)):or(in"rp"(r0,sc1),in"rp"(r0,sc2))
+a@pr1:=rpofp(r,t23):cut
+t30:=isp(real,[x:real]in(x,s1),r,pofrp(pr1),t24,isprp1(r,t23)):in(pofrp(pr1),s1)
+t31:=nonemptyi(cut,sc1,pr1,t25(pr1,t30)):nonempty(cut,sc1)
+[s:real][i:in(s,s2)]
+t32:=<i><s><t24><r>p2:less(r,s)
+t33:=lemma5(r,s,t32,t23):pos(s)
+ps1:=rpofp(s,t33):cut
+t34:=isp(real,[x:real]in(x,s2),s,pofrp(ps1),i,isprp1(s,t33)):in(pofrp(ps1),s2)
+t35:=nonemptyi(cut,sc2,ps1,t27(ps1,t34)):nonempty(cut,sc2)
+a@t36:=nonemptyapp(real,s2,p1b,nonempty(cut,sc2),[x:real][t:in(x,s2)]t35(x,t)):nonempty(cut,sc2)
+r0@[i:in"rp"(r0,sc1)][s0:cut][j:in"rp"(s0,sc2)]
+t37:=<t28(s0,j)><pofrp(s0)><t26(r0,i)><pofrp(r0)>p2:less(pofrp(r0),pofrp(s0))
+t38:=lessrpip(r0,s0,t37):less"rp"(r0,s0)
+a@stc:=schnitt(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):cut
+t39:=satzp205a(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:less"rp"(x,stc)]in"rp"(x,sc1))
+t40:=satzp205b(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:more"rp"(x,stc)]in"rp"(x,sc2))
+stp:=pofrp(stc):real
+t41:=posi(stc):pos(stp)
+[s:real][l:less(s,stp)][p:pos(s)]
+ps2:=rpofp(s,p):cut
+t42:=lessrpip(ps2,stc,isless1(s,pofrp(ps2),stp,isprp1(s,p),l)):less"rp"(ps2,stc)
+t43:=<t42><ps2>t39:in"rp"(ps2,sc1)
+t44:=isp(real,[x:real]in(x,s1),pofrp(ps2),s,t26(ps2,t43),isprp2(s,p)):in(s,s1)
+l@[n:not(pos(s))][i:in(s,s2)]
+t45:=<i><s><t24><r>p2:less(r,s)
+t46:=<lemma5(r,s,t45,t23)>n:con
+n@t47:=ore1(in(s,s1),in(s,s2),<s>p0,[t:in(s,s2)]t46(t)):in(s,s1)
+l@t48:=th1"l.imp"(pos(s),in(s,s1),[t:pos(s)]t44(t),[t:not(pos(s))]t47(t)):in(s,s1)
+s@[m:more(s,stp)]
+t49:=lemma5(stp,s,lemma1(s,stp,m),t41):pos(s)
+ps3:=rpofp(s,t49):cut
+t50:=morerpip(ps3,stc,ismore1(s,pofrp(ps3),stp,isprp1(s,t49),m)):more"rp"(ps3,stc)
+t51:=<t50><ps3>t40:in"rp"(ps3,sc2)
+t52:=isp(real,[x:real]in(x,s2),pofrp(ps3),s,t28(ps3,t51),isprp2(s,t49)):in(s,s2)
+a@t53:=andi(prop1(stp),prop2(stp),[x:real][t:less(x,stp)]t48(x,t),[x:real][t:more(x,stp)]t52(x,t)):prop3(stp)
+t54:=somei(real,[x:real]prop3(x),stp,t53):some([x:real]prop3(x))
+case1@t55:=someapp(real,[x:real]and(pos(x),in(x,s1)),case1,some([x:real]prop3(x)),[x:real][t:and(pos(x),in(x,s1))]t54(x,t)):some([x:real]prop3(x))
+p2@[case2:some([x:real]and(neg(x),in(x,s2)))]
+sp1:=setof(real,[x:real]in(m0(x),s1)):set(real)
+sp2:=setof(real,[x:real]in(m0(x),s2)):set(real)
+[r:real][i:in(m0(r),s1)]
+t56:=estii(real,[x:real]in(m0(x),s1),r,i):in(r,sp1)
+r@[i:in(r,sp1)]
+t57:=estie(real,[x:real]in(m0(x),s1),r,i):in(m0(r),s1)
+r@[i:in(m0(r),s2)]
+t58:=estii(real,[x:real]in(m0(x),s2),r,i):in(r,sp2)
+r@[i:in(r,sp2)]
+t59:=estie(real,[x:real]in(m0(x),s2),r,i):in(m0(r),s2)
+r@t60:=comor(in(r,sp1),in(r,sp2),th9"l.or"(in(m0(r),s1),in(m0(r),s2),in(r,sp1),in(r,sp2),<m0(r)>p0,[t:in(m0(r),s1)]t56(t),[t:in(m0(r),s2)]t58(t))):or(in(r,sp2),in(r,sp1))
+[i:in(r,s2)]
+t61:=t58(m0(r),isp(real,[x:real]in(x,s2),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp2)
+t62:=nonemptyi(real,sp2,m0(r),t61):nonempty(real,sp2)
+case2@t63:=nonemptyapp(real,s2,p1b,nonempty(real,sp2),[x:real][t:in(x,s2)]t62(x,t)):nonempty(real,sp2)
+r@[i:in(r,s1)]
+t64:=t56(m0(r),isp(real,[x:real]in(x,s1),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp1)
+t65:=nonemptyi(real,sp1,m0(r),t64):nonempty(real,sp1)
+case2@t66:=nonemptyapp(real,s1,p1a,nonempty(real,sp1),[x:real][t:in(x,s1)]t65(x,t)):nonempty(real,sp1)
+r@[i:in(r,sp2)][s:real][j:in(s,sp1)]
+t67:=<t59(r,i)><m0(r)><t57(s,j)><m0(s)>p2:less(m0(s),m0(r))
+t68:=lemma1(s,r,satz183d(s,r,t67)):less(r,s)
+r@[a:and(neg(r),in(r,s2))]
+t69:=satz176c(r,ande1(neg(r),in(r,s2),a)):pos(m0(r))
+t70:=isp(real,[x:real]in(x,s2),r,m0(m0(r)),ande2(neg(r),in(r,s2),a),satz177a(r)):in(m0(m0(r)),s2)
+t71:=andi(pos(m0(r)),in(m0(r),sp2),t69,t58(m0(r),t70)):and(pos(m0(r)),in(m0(r),sp2))
+t72:=somei(real,[x:real]and(pos(x),in(x,sp2)),m0(r),t71):some([x:real]and(pos(x),in(x,sp2)))
+case2@t73:=someapp(real,[x:real]and(neg(x),in(x,s2)),case2,some([x:real]and(pos(x),in(x,sp2))),[x:real][t:and(neg(x),in(x,s2))]t72(x,t)):some([x:real]and(pos(x),in(x,sp2)))
+t74:=t55(sp2,sp1,[x:real]t60(x),t63,t66,[x:real][t:in(x,sp2)][y:real][u:in(y,sp1)]t68(x,t,y,u),t73):some([x:real]prop3(sp2,sp1,x))
+[r:real][p:prop3(sp2,sp1,r)][s:real][l:less(s,m0(r))]
+t75:=ismore2(m0(m0(r)),r,m0(s),satz177(r),satz183c(s,m0(r),l)):more(m0(s),r)
+t76:=<t75><m0(s)>ande2(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp1)
+t77:=isp(real,[x:real]in(x,s1),m0(m0(s)),s,t57(m0(s),t76),satz177(s)):in(s,s1)
+s@[m:more(s,m0(r))]
+t78:=isless2(m0(m0(r)),r,m0(s),satz177(r),satz183a(s,m0(r),m)):less(m0(s),r)
+t79:=<t78><m0(s)>ande1(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp2)
+t80:=isp(real,[x:real]in(x,s2),m0(m0(s)),s,t59(m0(s),t79),satz177(s)):in(s,s2)
+p@t81:=andi(prop1(m0(r)),prop2(m0(r)),[x:real][t:less(x,m0(r))]t77(x,t),[x:real][t:more(x,m0(r))]t80(x,t)):prop3(m0(r))
+t82:=somei(real,[x:real]prop3(x),m0(r),t81):some([x:real]prop3(x))
+case2@t83:=someapp(real,[x:real]prop3(sp2,sp1,x),t74,some([x:real]prop3(x)),[x:real][t:prop3(sp2,sp1,x)]t82(x,t)):some([x:real]prop3(x))
+p2@[notcase1:not(some([x:real]and(pos(x),in(x,s1))))][notcase2:not(some([x:real]and(neg(x),in(x,s2))))][r:real][l:less(r,0)]
+t84:=th4"l.some"(real,[x:real]and(neg(x),in(x,s2)),notcase2,r):not(and(neg(r),in(r,s2)))
+t85:=th3"l.and"(neg(r),in(r,s2),t84,satz169d(r,l)):not(in(r,s2))
+t86:=ore1(in(r,s1),in(r,s2),<r>p0,t85):in(r,s1)
+r@[m:more(r,0)]
+t87:=th4"l.some"(real,[x:real]and(pos(x),in(x,s1)),notcase1,r):not(and(pos(r),in(r,s1)))
+t88:=th3"l.and"(pos(r),in(r,s1),t87,satz169b(r,m)):not(in(r,s1))
+t89:=ore2(in(r,s1),in(r,s2),<r>p0,t88):in(r,s2)
+notcase2@t90:=andi(prop1(0),prop2(0),[x:real][t:less(x,0)]t86(x,t),[x:real][t:more(x,0)]t89(x,t)):prop3(0)
+t91:=somei(real,[x:real]prop3(x),0,t90):some([x:real]prop3(x))
+notcase1@t92:=th1"l.imp"(some([x:real]and(neg(x),in(x,s2))),some([x:real]prop3(x)),[t:some([x:real]and(neg(x),in(x,s2)))]t83(t),[t:not(some([x:real]and(neg(x),in(x,s2))))]t91(t)):some([x:real]prop3(x))
+p2@t93:=th1"l.imp"(some([x:real]and(pos(x),in(x,s1))),some([x:real]prop3(x)),[t:some([x:real]and(pos(x),in(x,s1)))]t55(t),[t:not(some([x:real]and(pos(x),in(x,s1))))]t92(t)):some([x:real]prop3(x))
+t94:=onei(real,[x:real]prop3(x),t22,t93):one([x:real]prop3(x))
+-5r205
+p2@satz205:=t94".5r205":one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
+dedekind:=satz205:one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
+schnitt:=ind(real,[x:real]prop3".5r205"(x),satz205):real
+[r:real][l:less(r,schnitt)]
+satz205a:=<l><r>ande1(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s1)
+r@[m:more(r,schnitt)]
+satz205b:=<m><r>ande2(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s2)
+@[r0:cut][s0:cut]
++iva
+dr:=pdofrp(r0):dif
+ds:=pdofrp(s0):dif
+t1:=lemmaivad1(r0,s0):eq"rp"(pd(dr,ds),pdofrp(pl"rp"(r0,s0)))
+-iva
+lemmaiva1:=isin(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)),pd(pdofrp(r0),pdofrp(s0)),pdofrp(pl"rp"(r0,s0)),picp(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(pl"rp"(r0,s0))),t1".iva"):is(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)))
++*iva
+s0@t2:=lemmaivad2(r0,s0):eq"rp"(td(dr,ds),pdofrp(ts"rp"(r0,s0)))
+-iva
+s0@lemmaiva2:=isin(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)),td(pdofrp(r0),pdofrp(s0)),pdofrp(ts"rp"(r0,s0)),tict(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(ts"rp"(r0,s0))),t2".iva"):is(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)))
+[m:more(pofrp(r0),pofrp(s0))]
++*iva
+m@t3:=moreex(pofrp(r0),pofrp(s0),dr,ds,innclass(dr),innclass(ds),m):mored(dr,ds)
+-iva
+m@lemmaiva3:=lemmaivad3(r0,s0,t3".iva"):more"rp"(r0,s0)
+s0@[m:more"rp"(r0,s0)]
++*iva
+m@[l:less(pofrp(r0),pofrp(s0))]
+t4:=satz121(s0,r0,lemmaiva3(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
+m@t5:=ec3e23(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):not(less"rp"(r0,s0))
+t6:=th3"l.imp"(less(pofrp(r0),pofrp(s0)),less"rp"(r0,s0),t5,[t:less(pofrp(r0),pofrp(s0))]t4(t)):not(less(pofrp(r0),pofrp(s0)))
+t7:=ec3e21(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):nis"rp"(r0,s0)
+t8:=th3"l.imp"(is(pofrp(r0),pofrp(s0)),is"rp"(r0,s0),t7,[t:is(pofrp(r0),pofrp(s0))]isrpip(r0,s0,t)):nis(pofrp(r0),pofrp(s0))
+-iva
+m@lemmaiva4:=or3e2(is(pofrp(r0),pofrp(s0)),more(pofrp(r0),pofrp(s0)),less(pofrp(r0),pofrp(s0)),satz167a(pofrp(r0),pofrp(s0)),t6".iva",t8".iva"):more(pofrp(r0),pofrp(s0))
+@[x:nat][y:nat][m:more(rlofnt(x),rlofnt(y))]
++*iva
+m@t9:=lemmaiva3(rpofnt(x),rpofnt(y),m):more"rp"(rpofnt(x),rpofnt(y))
+t10:=satz154d(rtofn(x),rtofn(y),t9):more"rt"(rtofn(x),rtofn(y))
+t11:=moree"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t10):moref(fr(x,1),fr(y,1))
+-iva
+m@lemmaiva5:=satz111a(x,y,t11".iva"):more"n"(x,y)
+y@[m:more"n"(x,y)]
++*iva
+m@t12:=satz111d(x,y,m):moref(fr(x,1),fr(y,1))
+t13:=morei"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t12):more"rt"(rtofn(x),rtofn(y))
+t14:=satz154a(rtofn(x),rtofn(y),t13):more"rp"(rpofnt(x),rpofnt(y))
+-iva
+m@lemmaiva6:=lemmaiva4(rpofnt(x),rpofnt(y),t14".iva"):more(rlofnt(x),rlofnt(y))
+@[r:real]
++int
+a0ir@[i:intrl(r)]
+t1:=intabsd(a0,intrlex(r,a0,a0ir,i)):intd(absd(a0))
+t2:=intrlin(abs(r),absd(a0),aica,t1):intrl(abs(r))
+-int
+[i:intrl(r)]
+intabs:=realapp1(r,intrl(abs(r)),[x:dif][t:inn(x,class(r))]t2".int"(r,x,t,i)):intrl(abs(r))
++*int
+i@t3:=intm0d(a0,intrlex(r,a0,a0ir,i)):intd(m0d(a0))
+t4:=intrlin(m0(r),m0d(a0),micm0,t3):intrl(m0(r))
+-int
+i@intm0:=realapp1(r,intrl(m0(r)),[x:dif][t:inn(x,class(r))]t4".int"(r,x,t,i)):intrl(m0(r))
++*int
+b1is@[i:intrl(r)][j:intrl(s)]
+t5:=intpd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(pd(a1,b1))
+t6:=intrlin(pl(r,s),pd(a1,b1),picp,t5):intrl(pl(r,s))
+-int
+i@[s:real][j:intrl(s)]
+intpl:=realapp2(r,s,intrl(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".int"(r,s,x,y,t,u,i,j)):intrl(pl(r,s))
+intmn:=intpl(r,i,m0(s),intm0(s,j)):intrl(mn(r,s))
++*int
+j@t7:=inttd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(td(a1,b1))
+t8:=intrlin(ts(r,s),td(a1,b1),tict,t7):intrl(ts(r,s))
+-int
+j@intts:=realapp2(r,s,intrl(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".int"(r,s,x,y,t,u,i,j)):intrl(ts(r,s))
+r@[n:natrl(r)]
++ivr24
+t1:=satz24a(ntofrl(r,n)):lessis"n"(1,ntofrl(r,n))
+t2:=th3"l.imp"(more(1rl,r),more"n"(1,ntofrl(r,n)),satz10d(1,ntofrl(r,n),t1),[t:more(1rl,r)]lemmaiva5(1,ntofrl(r,n),ismore2(r,rlofnt(ntofrl(r,n)),1rl,isrlnt1(r,n),t))):not(more(1rl,r))
+-ivr24
+satzr24:=satz167e(1rl,r,t2".ivr24"):lessis(1rl,r)
+r@[i:intrl(r)][s:real][j:intrl(s)][l:less(r,s)]
++ivr25
+t1:=satz182d(s,r,lemma2(r,s,l)):pos(mn(s,r))
+t2:=intmn(s,j,r,i):intrl(mn(s,r))
+t3:=posintnatrl(mn(s,r),t1,t2):natrl(mn(s,r))
+t4:=satzr24(mn(s,r),t3):lessis(1rl,mn(s,r))
+t5:=th9"l.or"(less(1rl,mn(s,r)),is(1rl,mn(s,r)),less(pl(1rl,r),pl(mn(s,r),r)),is(pl(1rl,r),pl(mn(s,r),r)),t4,[t:less(1rl,mn(s,r))]satz188f(1rl,mn(s,r),r,t),[t:is(1rl,mn(s,r))]ispl1(1rl,mn(s,r),r,t)):lessis(pl(1rl,r),pl(mn(s,r),r))
+-ivr25
+satzr25:=islessis12(pl(1rl,r),pl(r,1rl),pl(mn(s,r),r),s,compl(1rl,r),plmn(s,r),t5".ivr25"):lessis(pl(r,1rl),s)
+@[x:nat][y:nat]
++ivr155
+t1:=lemmaiva1(rpofnt(x),rpofnt(y)):is(pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
+t2:=isrpep(rpofnt(pl"n"(x,y)),pl"rp"(rpofnt(x),rpofnt(y)),satz155e(x,y)):is(rlofnt(pl"n"(x,y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
+-ivr155
+satzr155a:=tris2(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))),t2".ivr155",t1".ivr155"):is(rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)))
+satzr155b:=symis(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),satzr155a):is(pl(rlofnt(x),rlofnt(y)),rlofnt(pl"n"(x,y)))
++*ivr155
+y@t3:=lemmaiva2(rpofnt(x),rpofnt(y)):is(ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
+t4:=isrpep(rpofnt(ts"n"(x,y)),ts"rp"(rpofnt(x),rpofnt(y)),satz155f(x,y)):is(rlofnt(ts"n"(x,y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
+-ivr155
+y@satzr155c:=tris2(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))),t4".ivr155",t3".ivr155"):is(rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)))
+satzr155d:=symis(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),satzr155c):is(ts(rlofnt(x),rlofnt(y)),rlofnt(ts"n"(x,y)))
+@[t:real][r:real][s:real][a:and(not(neg(r)),is(ts(r,r),t))][b:and(not(neg(s)),is(ts(s,s),t))]
++7r161
+[c0:dif][cit:inn(c0,class(t))][a0:dif][air:inn(a0,class(r))][b0:dif][bis:inn(b0,class(s))]
+t1:=th3"l.imp"(negd(a0),neg(r),ande1(not(neg(r)),is(ts(r,r),t),a),[u:negd(a0)]negin(r,a0,air,u)):not(negd(a0))
+t2:=th3"l.imp"(negd(b0),neg(s),ande1(not(neg(s)),is(ts(s,s),t),b),[u:negd(b0)]negin(s,b0,bis,u)):not(negd(b0))
+t3:=isex(ts(r,r),t,td(a0,a0),c0,tict(r,r,a0,a0,air,air),cit,ande2(not(neg(r)),is(ts(r,r),t),a)):eq"rp"(td(a0,a0),c0)
+t4:=isex(ts(s,s),t,td(b0,b0),c0,tict(s,s,b0,b0,bis,bis),cit,ande2(not(neg(s)),is(ts(s,s),t),b)):eq"rp"(td(b0,b0),c0)
+t5:=isin(r,s,a0,b0,air,bis,satzd161b(c0,a0,b0,t1,t2,t3,t4)):is(r,s)
+-7r161
+satzr161b:=realapp3(t,r,s,is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(t))][v:inn(y,class(r))][w:inn(z,class(s))]t5".7r161"(x,u,y,v,z,w)):is(r,s)
+t@[n:not(neg(t))]
++*7r161
+n@[c0:dif][cit:inn(c0,class(t))]
+t6:=th3"l.imp"(negd(c0),neg(t),n,[u:negd(c0)]negin(t,c0,cit,u)):not(negd(c0))
+[a0:dif][a:and(not(negd(a0)),eq"rp"(td(a0,a0),c0))]
+ar:=realof(a0):real
+t7:=th3"l.imp"(neg(ar),negd(a0),ande1(not(negd(a0)),eq"rp"(td(a0,a0),c0),a),[u:neg(ar)]negex(ar,a0,innclass(a0),u)):not(neg(ar))
+t8:=isin(ts(ar,ar),t,td(a0,a0),c0,tict(ar,ar,a0,a0,innclass(a0),innclass(a0)),cit,ande2(not(negd(a0)),eq"rp"(td(a0,a0),c0),a)):is(ts(ar,ar),t)
+t9:=andi(not(neg(ar)),is(ts(ar,ar),t),t7,t8):and(not(neg(ar)),is(ts(ar,ar),t))
+t10:=somei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),ar,t9):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
+cit@t11:=someapp(dif,[x:dif]and(not(negd(x)),eq"rp"(td(x,x),c0)),satzd161a(c0,t6),some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:and(not(negd(x)),eq"rp"(td(x,x),c0))]t10(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
+-7r161
+n@satzr161a:=realapp1(t,some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:inn(x,class(t))]t11".7r161"(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
+satzr161:=onei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),[u:real][v:real][a:and(not(neg(u)),is(ts(u,u),t))][b:and(not(neg(v)),is(ts(v,v),t))]satzr161b(u,v,a,b),satzr161a):one([u:real]and(not(neg(u)),is(ts(u,u),t)))
+sqrt:=ind(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):real
++*7r161
+n@t12:=oneax(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):and(not(neg(sqrt)),is(ts(sqrt,sqrt),t))
+-7r161
+n@thsqrt1a:=ande1(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):not(neg(sqrt))
+thsqrt1b:=ande2(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):is(ts(sqrt,sqrt),t)
+[x:real][o:not(neg(x))][i:is(ts(x,x),t)]
+thsqrt2:=satzr161b(x,sqrt,andi(not(neg(x)),is(ts(x,x),t),o,i),t12".7r161"):is(x,sqrt(t,n))
+o@[i:is(t,ts(x,x))]
+thsqrt3:=symis(real,x,sqrt(t,n),thsqrt2(symis(real,t,ts(x,x),i))):is(sqrt(t,n),x)
+@[r:real][s:real][n:not(neg(r))][o:not(neg(s))][i:is(r,s)]
+issqrt:=thsqrt2(s,o,sqrt(r,n),thsqrt1a(r,n),tris(real,ts(sqrt(r,n),sqrt(r,n)),r,s,thsqrt1b(r,n),i)):is(sqrt(r,n),sqrt(s,o))
+r@[n:not(neg(r))][i:is(r,0)]
+sqrt0:=thsqrt3(r,n,0,0notn(0,refis(real,0)),tris2(real,r,ts(0,0),0,i,ts01(0,0,refis(real,0)))):is(sqrt(r,n),0)
+n@[o:nis(r,0)]
++sqrt
+t1:=th3"l.imp"(is(sqrt(r,n),0),is(r,0),o,[t:is(sqrt(r,n),0)]tris1(real,r,0,ts(sqrt(r,n),sqrt(r,n)),thsqrt1b(r,n),ts01(sqrt(r,n),sqrt(r,n),t))):nis(sqrt(r,n),0)
+-sqrt
+sqrtnot0:=or3e2(is(sqrt(r,n),0),pos(sqrt(r,n)),neg(sqrt(r,n)),axrlo(sqrt(r,n)),thsqrt1a(r,n),t1".sqrt"):pos(sqrt(r,n))
+@[r:real][s:real][t:real][n:nis(t,0)]
++v0
+t1:=tr3is(real,ts(t,ts(r,ov(s,t,n))),ts(ts(r,ov(s,t,n)),t),ts(r,ts(ov(s,t,n),t)),ts(r,s),comts(t,ts(r,ov(s,t,n))),assts1(r,ov(s,t,n),t),ists2(ts(ov(s,t,n),t),s,r,satz204e(s,t,n))):is(ts(t,ts(r,ov(s,t,n))),ts(r,s))
+-v0
+lemma6:=satz204g(ts(r,s),t,ts(r,ov(s,t,n)),n,t1".v0"):is(ts(r,ov(s,t,n)),ov(ts(r,s),t,n))
++*v0
+n@t2:=tris(real,ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(ts(t,ov(r,t,n)),ts(t,ov(s,t,n))),pl(r,s),disttp2(t,ov(r,t,n),ov(s,t,n)),ispl12(ts(t,ov(r,t,n)),r,ts(t,ov(s,t,n)),s,satz204c(r,t,n),satz204c(s,t,n))):is(ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(r,s))
+-v0
+n@lemma7:=satz204g(pl(r,s),t,pl(ov(r,t,n),ov(s,t,n)),n,t2".v0"):is(pl(ov(r,t,n),ov(s,t,n)),ov(pl(r,s),t,n))
+r@[n:nis(r,0)]
+lemma8:=satz204b(r,r,n,ov(r,r,n),1rl,satz204c(r,r,n),satz195(r)):is(ov(r,r,n),1rl)
+lemma9:=ore2(is(r,0),is(ov(0,r,n),0),satz192c(r,ov(0,r,n),satz204c(0,r,n)),n):is(ov(0,r,n),0)
+r@[i:is(r,m0(r))]
++*v0
+i@[p:pos(m0(r))]
+t3:=<isneg(r,m0(r),i,satz176f(r,p))>pnotn(m0(r),p):con
+i@[n:neg(m0(r))]
+t4:=<ispos(r,m0(r),i,satz176d(r,n))>nnotp(m0(r),n):con
+-v0
+i@lemma10:=satz176e(r,or3e1(is(m0(r),0),pos(m0(r)),neg(m0(r)),axrlo(m0(r)),[t:pos(m0(r))]t3".v0"(t),[t:neg(m0(r))]t4".v0"(t))):is(r,0)
+r@lemma11:=satz167f(ts(r,r),0,th3"l.imp"(less(ts(r,r),0),neg(ts(r,r)),nnegsq(r),[t:less(ts(r,r),0)]satz169d(ts(r,r),t))):moreis(ts(r,r),0)
+lemma12:=rapp(r,is(ts(r,r),ts(abs(r),abs(r))),[t:pos(r)]satz196a(r,r,t,t),[t:is(r,0)]tris2(real,ts(r,r),ts(abs(r),abs(r)),0,ts01(r,r,t),ts01(abs(r),abs(r),abs0(r,t))),[t:neg(r)]satz196b(r,r,t,t)):is(ts(r,r),ts(abs(r),abs(r)))
+@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
++shift
+t1:=satz190a(x,x,1rl,0,moreisi2(x,x,refis(real,x)),satz169a(1rl,natpos(1rl,natrl1))):more(pl(x,1rl),pl(x,0))
+t2:=ismore2(pl(x,0),x,pl(x,1rl),pl02(x,0,refis(real,0)),t1):more(pl(x,1rl),x)
+t3:=satz172d(pl(x,1rl),x,y,t2,satz168b(y,x,ly)):more(pl(x,1rl),y)
+t4:=satz182d(pl(x,1rl),y,t3):pos(mn(pl(x,1rl),y))
+t5:=intmn(pl(x,1rl),intpl(x,ix,1rl,intrl1),y,iy):intrl(mn(pl(x,1rl),y))
+t6:=posintnatrl(mn(pl(x,1rl),y),t4,t5):natrl(mn(pl(x,1rl),y))
+-shift
+shiftl:=ntofrl(mn(pl(x,1rl),y),t6".shift"):nat
+[n:1to(shiftl)]
++*shift
+n@n1:=inn"n"(shiftl,n):nat
+t7:=1top(shiftl,n):lessis"n"(n1,shiftl)
+n2:=rlofnt(n1):real
+t8:=natintrl(n2,natrli(n1)):intrl(n2)
+-shift
+n@shiftr:=mn(pl(n2".shift",y),1rl):real
+intshiftr:=intmn(pl(n2".shift",y),intpl(n2".shift",t8".shift",y,iy),1rl,intrl1):intrl(shiftr)
+[m:1to(shiftl)][i:is(shiftr(n),shiftr(m))]
++*shift
+n@t8a:=tris(real,mn(pl(shiftr(n),1rl),y),mn(pl(n2,y),y),n2,ismn1(pl(mn(pl(n2,y),1rl),1rl),pl(n2,y),y,plmn(pl(n2,y),1rl)),mnpl(n2,y)):is(mn(pl(shiftr(n),1rl),y),n2)
+i@t9a:=ismn1(pl(shiftr(n),1rl),pl(shiftr(m),1rl),y,ispl1(shiftr(n),shiftr(m),1rl,i)):is(mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y))
+t10a:=tr3is(real,n2(n),mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y),n2(m),symis(real,mn(pl(shiftr(n),1rl),y),n2,t8a),t9a,t8a(m)):is(n2(n),n2(m))
+t11a:=isntirl(n1(n),n1(m),t10a):is"n"(n1(n),n1(m))
+-shift
+i@iseshiftr:=isinne(shiftl,n,m,t11a".shift"):is"e"(1to(shiftl),n,m)
++*shift
+n@[m:more(shiftr,x)]
+t9:=satz188d(shiftr,x,1rl,m):more(pl(shiftr,1rl),pl(x,1rl))
+t10:=ismore1(pl(shiftr,1rl),pl(n2,y),pl(x,1rl),plmn(pl(n2,y),1rl),t9):more(pl(n2,y),pl(x,1rl))
+t11:=satz188d(pl(n2,y),pl(x,1rl),m0(y),t10):more(mn(pl(n2,y),y),mn(pl(x,1rl),y))
+t12:=ismore1(mn(pl(n2,y),y),n2,mn(pl(x,1rl),y),mnpl(n2,y),t11):more(n2,mn(pl(x,1rl),y))
+t13:=ismore12(n2,rlofnt(ntofrl(n2,natrli(n1))),mn(pl(x,1rl),y),rlofnt(ntofrl(mn(pl(x,1rl),y),t6)),isrlnt1(n2,natrli(n1)),isrlnt1(mn(pl(x,1rl),y),t6),t12):more(rlofnt(ntofrl(n2,natrli(n1))),rlofnt(shiftl))
+t14:=lemmaiva5(ntofrl(n2,natrli(n1)),shiftl,t13):more"n"(ntofrl(n2,natrli(n1)),shiftl)
+t15:=ismore1"n"(ntofrl(n2,natrli(n1)),n1,shiftl,isntrl2(n1),t14):more"n"(n1,shiftl)
+n@t16:=th3"l.imp"(more(shiftr,x),more"n"(n1,shiftl),satz10d(n1,shiftl,t7),[t:more(shiftr,x)]t15(t)):not(more(shiftr,x))
+-shift
+n@shiftrls:=satz167e(shiftr,x,t16".shift"):lessis(shiftr,x)
++*shift
+n@[m:more(y,shiftr)]
+t17:=satz188d(y,shiftr,1rl,m):more(pl(y,1rl),pl(shiftr,1rl))
+t18:=ismore12(pl(y,1rl),pl(1rl,y),pl(shiftr,1rl),pl(n2,y),compl(y,1rl),plmn(pl(n2,y),1rl),t17):more(pl(1rl,y),pl(n2,y))
+t19:=satz188a(1rl,n2,y,t18):more(1rl,n2)
+t20:=lemmaiva5(1,n1,t19):more"n"(1,n1)
+n@t21:=th3"l.imp"(more(y,shiftr),more"n"(1,n1),satz10d(1,n1,satz24a(n1)),[t:more(y,shiftr)]t20(t)):not(more(y,shiftr))
+-shift
+n@lsshiftr:=satz167e(y,shiftr,t21".shift"):lessis(y,shiftr)
+ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
++*shift
+a@t22:=and3e1(intrl(u),lessis(y,u),lessis(u,x),a):intrl(u)
+t23:=and3e2(intrl(u),lessis(y,u),lessis(u,x),a):lessis(y,u)
+t24:=and3e3(intrl(u),lessis(y,u),lessis(u,x),a):lessis(u,x)
+[l:less(u,x)]
+t25:=satz188f(pl(u,1rl),pl(x,1rl),m0"r"(y),satz188f(u,x,1rl,l)):less(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
+a@[i:is(u,x)]
+t26:=ismn1(pl(u,1rl),pl(x,1rl),y,ispl1(u,x,1rl,i)):is(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
+a@t27:=th9"l.or"(less(u,x),is(u,x),less(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),is(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),t24,[t:less(u,x)]t25(t),[t:is(u,x)]t26(t)):lessis(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
+ul:=shiftl(u,t22,y,iy,t23):nat
+t28:=islessis12(mn(pl(u,1rl),y),rlofnt(ul),mn(pl(x,1rl),y),rlofnt(shiftl),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isrlnt1(mn(pl(x,1rl),y),t6),t27):lessis(rlofnt(ul),rlofnt(shiftl))
+t29:=th3"l.imp"(more"n"(ul,shiftl),more(rlofnt(ul),rlofnt(shiftl)),satz167d(rlofnt(ul),rlofnt(shiftl),t28),[t:more"n"(ul,shiftl)]lemmaiva6(ul,shiftl,t)):not(more"n"(ul,shiftl))
+t30:=satz10e(ul,shiftl,t29):lessis"n"(ul,shiftl)
+-shift
+a@shiftl1:=outn(shiftl,ul".shift",t30".shift"):1to(shiftl)
++*shift
+a@t31:=isinoutn(shiftl,ul,t30):is"n"(ul,n1(shiftl1))
+t32:=tris(real,mn(pl(u,1rl),y),rlofnt(ul),n2(shiftl1),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isnterl(ul,n1(shiftl1),t31)):is(mn(pl(u,1rl),y),n2(shiftl1))
+t33:=tris(real,mn(pl(mn(pl(u,1rl),y),y),1rl),mn(pl(u,1rl),1rl),u,ismn1(pl(mn(pl(u,1rl),y),y),pl(u,1rl),1rl,plmn(pl(u,1rl),y)),mnpl(u,1rl)):is(mn(pl(mn(pl(u,1rl),y),y),1rl),u)
+-shift
+a@shiftinv1:=tris1(real,u,shiftr(shiftl1),mn(pl(mn(pl(u,1rl),y),y),1rl),t33".shift",ismn1(pl(mn(pl(u,1rl),y),y),pl(n2".shift"(shiftl1),y),1rl,ispl1(mn(pl(u,1rl),y),n2".shift"(shiftl1),y,t32".shift"))):is(u,shiftr(shiftl1))
+shiftinv2:=symis(real,u,shiftr(shiftl1),shiftinv1):is(shiftr(shiftl1),u)
+ly@[alpha:'type']
+seq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]alpha:'type'
+[s:seq]
+proofsirrelevant:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is(t,u)]is"e"(alpha,<tl><lt><it><t>s,<ul><lu><iu><u>s):'prop'
+alpha@[f:seq]
+shiftf:=[t:1to(shiftl)]<shiftrls(t)><lsshiftr(t)><intshiftr(t)><shiftr(t)>f:[t:1to(shiftl)]alpha
+ly@[s:seq(real)]
+inseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]and3(intrl(<w><v><u><t>s),lessis(y,<w><v><u><t>s),lessis(<w><v><u><t>s,x)):'prop'
+injseq:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is"r"(<tl><lt><it><t>s,<ul><lu><iu><u>s)]is"r"(t,u):'prop'
+[u:real][v:real][a:and3(intrl(v),lessis(y,v),lessis(v,x))]
++*shift
+a@prop1:=is(u,<t24(v,a)><t23(v,a)><t22(v,a)><v>s):'prop'
+-shift
+v@improp:=and(and3(intrl(v),lessis(y,v),lessis(v,x)),[t:and3(intrl(v),lessis(y,v),lessis(v,x))]prop1".shift"(t)):'prop'
+u@imseq:=some([t:real]improp(u,t)):'prop'
+s@surjseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]imseq(t):'prop'
+perm:=and(injseq,surjseq):'prop'
+[ins:inseq(s)]
++*shift
+ins@[n:1to(shiftl)]
+ns:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>s:real
+t34:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ins:and3(intrl(ns),lessis(y,ns),lessis(ns,x))
+-shift
+ins@shiftseq:=[t:1to(shiftl)]shiftl1(ns".shift"(t),t34".shift"(t)):[t:1to(shiftl)]1to(shiftl)
+[js:injseq(s)]
++*shift
+js@[n:1to(shiftl)][m:1to(shiftl)][i:is"e"(1to(shiftl),<n>shiftseq,<m>shiftseq)]
+t35:=isoutne(shiftl,ul(ns(n),t34(n)),t30(ns(n),t34(n)),ul(ns(m),t34(m)),t30(ns(m),t34(m)),i):is"n"(ul(ns(n),t34(n)),ul(ns(m),t34(m)))
+t36:=isrlint(mn(pl(ns(n),1rl),y),t6(ns(n),t22(ns(n),t34(n)),y,iy,t23(ns(n),t34(n))),mn(pl(ns(m),1rl),y),t6(ns(m),t22(ns(m),t34(m)),y,iy,t23(ns(m),t34(m))),t35):is(mn(pl(ns(n),1rl),y),mn(pl(ns(m),1rl),y))
+t37:=satz188b(ns(n),ns(m),1rl,satz188b(pl(ns(n),1rl),pl(ns(m),1rl),m0"r"(y),t36)):is(ns(n),ns(m))
+t38:=<t37><shiftrls(m)><lsshiftr(m)><intshiftr(m)><shiftr(m)><shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>js:is(shiftr(n),shiftr(m))
+t39:=satz188b(n2(n),n2(m),y,satz188b(pl(n2(n),y),pl(n2(m),y),m0(1rl),t38)):is(n2(n),n2(m))
+t40:=isntirl(n1(n),n1(m),t39):is"n"(n1(n),n1(m))
+t41:=isinne(shiftl,n,m,t40):is"e"(1to(shiftl),n,m)
+-shift
+js@injshiftseq:=[t:1to(shiftl)][u:1to(shiftl)][v:is"e"(1to(shiftl),<t>shiftseq,<u>shiftseq)]t41".shift"(t,u,v):injective(1to(shiftl),1to(shiftl),shiftseq)
+ins@[pri:proofsirrelevant(real,s)][ss:surjseq(s)]
++*shift
+ss@[n:1to(shiftl)]
+t42:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ss:imseq(shiftr(n))
+[u:real][p:improp(shiftr(n),u)]
+t43:=ande1(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):and3(intrl(u),lessis(y,u),lessis(u,x))
+t44:=ande2"l.r"(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):is(shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s)
+ul1:=shiftl1(u,t43):1to(shiftl)
+t45:=<shiftinv1(u,t43)><shiftrls(ul1)><lsshiftr(ul1)><intshiftr(ul1)><shiftr(ul1)><t24(u,t43)><t23(u,t43)><t22(u,t43)><u>pri:is(<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1))
+t46:=shiftinv1(ns(ul1),t34(ul1)):is(ns(ul1),shiftr(<ul1>shiftseq))
+t47:=tr3is(real,shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1),shiftr(<ul1>shiftseq),t44,t45,t46):is(shiftr(n),shiftr(<ul1>shiftseq))
+t48:=iseshiftr(n,<ul1>shiftseq,t47):is"e"(1to(shiftl),n,<ul1>shiftseq)
+t49:=somei(1to(shiftl),[t:1to(shiftl)]is"e"(1to(shiftl),n,<t>shiftseq),ul1,t48):image(1to(shiftl),1to(shiftl),shiftseq,n)
+n@t50:=someapp(real,[t:real]improp(shiftr(n),t),t42,image(1to(shiftl),1to(shiftl),shiftseq,n),[t:real][u:improp(shiftr(n),t)]t49(t,u)):image(1to(shiftl),1to(shiftl),shiftseq,n)
+-shift
+ss@surjshiftseq:=[t:1to(shiftl)]t50".shift"(t):surjective(1to(shiftl),1to(shiftl),shiftseq)
+pri@[ps:perm(s)]
+bijshiftseq:=andi(injective(1to(shiftl),1to(shiftl),shiftseq),surjective(1to(shiftl),1to(shiftl),shiftseq),injshiftseq(ande1(injseq(s),surjseq(s),ps)),surjshiftseq(ande2(injseq(s),surjseq(s),ps))):bijective(1to(shiftl),1to(shiftl),shiftseq)
++c
+@complex:=pair1type(real):'type'
+cx:=complex:'type'
+[x:complex][y:complex]
+is:=is"e"(cx,x,y):'prop'
+nis:=not(is(x,y)):'prop'
+@[p:[t:complex]'prop']
+some:=some"l"(cx,p):'prop'
+all:=all"l"(cx,p):'prop'
+one:=one"e"(cx,p):'prop'
+@[a:real][b:real]
+pli:=pair1(real,a,b):complex
+x@re:=first1(real,x):real
+im:=second1(real,x):real
+b@reis:=first1is1(real,a,b):is"r"(re(pli(a,b)),a)
+isre:=first1is2(real,a,b):is"r"(a,re(pli(a,b)))
+imis:=second1is1(real,a,b):is"r"(im(pli(a,b)),b)
+isim:=second1is2(real,a,b):is"r"(b,im(pli(a,b)))
+x@pliis:=pair1is1(real,x):is(pli(re(x),im(x)),x)
+ispli:=pair1is2(real,x):is(x,pli(re(x),im(x)))
+y@[i:is(x,y)]
+iscere:=isf(cx,real,[t:cx]re(t),x,y,i):is"r"(re(x),re(y))
+isceim:=isf(cx,real,[t:cx]im(t),x,y,i):is"r"(im(x),im(y))
+b@[c:real][i:is"r"(a,b)]
+isrecx1:=isf(real,cx,[t:real]pli(t,c),a,b,i):is(pli(a,c),pli(b,c))
+isrecx2:=isf(real,cx,[t:real]pli(c,t),a,b,i):is(pli(c,a),pli(c,b))
+c@[d:real][i:is"r"(a,b)][j:is"r"(c,d)]
+isrecx12:=tris(cx,pli(a,c),pli(b,c),pli(b,d),isrecx1(a,b,c,i),isrecx2(c,d,b,j)):is(pli(a,c),pli(b,d))
+x@satz206:=refis(cx,x):is(x,x)
+y@[i:is(x,y)]
+satz207:=symis(cx,x,y,i):is(y,x)
+y@[z:complex][i:is(x,y)][j:is(y,z)]
+satz208:=tris(cx,x,y,z,i,j):is(x,z)
+@0c:=pli(0,0):complex
+1c:=pli(1rl,0):complex
+y@pl:=pli(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))):complex
+d@plis12a:=isrecx12(pl"r"(re(pli(a,b)),re(pli(c,d))),pl"r"(a,c),pl"r"(im(pli(a,b)),im(pli(c,d))),pl"r"(b,d),ispl12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ispl12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)))
+plis12b:=symis(cx,pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)),plis12a):is(pli(pl"r"(a,c),pl"r"(b,d)),pl(pli(a,b),pli(c,d)))
+x@[r:real][s:real]
+plis1a:=isrecx12(pl"r"(re(pli(r,s)),re(x)),pl"r"(r,re(x)),pl"r"(im(pli(r,s)),im(x)),pl"r"(s,im(x)),ispl1(re(pli(r,s)),r,re(x),reis(r,s)),ispl1(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))))
+plis1b:=symis(cx,pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))),plis1a):is(pli(pl"r"(r,re(x)),pl"r"(s,im(x))),pl(pli(r,s),x))
+plis2a:=isrecx12(pl"r"(re(x),re(pli(r,s))),pl"r"(re(x),r),pl"r"(im(x),im(pli(r,s))),pl"r"(im(x),s),ispl2(re(pli(r,s)),r,re(x),reis(r,s)),ispl2(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)))
+plis2b:=symis(cx,pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)),plis2a):is(pli(pl"r"(re(x),r),pl"r"(im(x),s)),pl(x,pli(r,s)))
+z@[i:is(x,y)]
+ispl1:=isf(cx,cx,[t:cx]pl(t,z),x,y,i):is(pl(x,z),pl(y,z))
+ispl2:=isf(cx,cx,[t:cx]pl(z,t),x,y,i):is(pl(z,x),pl(z,y))
+z@[u:complex][i:is(x,y)][j:is(z,u)]
+ispl12:=tris(cx,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
+y@satz209:=isrecx12(pl"r"(re(x),re(y)),pl"r"(re(y),re(x)),pl"r"(im(x),im(y)),pl"r"(im(y),im(x)),compl(re(x),re(y)),compl(im(x),im(y))):is(pl(x,y),pl(y,x))
+compl:=satz209:is(pl(x,y),pl(y,x))
+x@satz210:=tr3is(cx,pl(x,0c),pli(pl"r"(re(x),0),pl"r"(im(x),0)),pli(re(x),im(x)),x,plis2a(x,0,0),isrecx12(pl"r"(re(x),0),re(x),pl"r"(im(x),0),im(x),pl02(re(x),0,refis(real,0)),pl02(im(x),0,refis(real,0))),pliis(x)):is(pl(x,0c),x)
+satz210a:=symis(cx,pl(x,0c),x,satz210):is(x,pl(x,0c))
+satz210b:=tris(cx,pl(0c,x),pl(x,0c),x,compl(0c,x),satz210):is(pl(0c,x),x)
+satz210c:=symis(cx,pl(0c,x),x,satz210b):is(x,pl(0c,x))
+z@satz211:=tr3is(cx,pl(pl(x,y),z),pli(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(pl"r"(im(x),im(y)),im(z))),pli(pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(im(x),pl"r"(im(y),im(z)))),pl(x,pl(y,z)),plis1a(z,pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(pl"r"(im(x),im(y)),im(z)),pl"r"(im(x),pl"r"(im(y),im(z))),asspl1(re(x),re(y),re(z)),asspl1(im(x),im(y),im(z))),plis2b(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z)))):is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl1:=satz211:is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl2:=symis(cx,pl(pl(x,y),z),pl(x,pl(y,z)),asspl1):is(pl(x,pl(y,z)),pl(pl(x,y),z))
+y@[u:complex][i:is(pl(y,u),x)]
++2212
+t1:=tris(real,pl"r"(re(y),re(u)),re(pl(y,u)),re(x),isre(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),iscere(pl(y,u),x,i)):is"r"(pl"r"(re(y),re(u)),re(x))
+t2:=tris(real,pl"r"(im(y),im(u)),im(pl(y,u)),im(x),isim(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),isceim(pl(y,u),x,i)):is"r"(pl"r"(im(y),im(u)),im(x))
+t3:=satz187d(re(x),re(y),re(u),t1):is"r"(re(u),mn(re(x),re(y)))
+t4:=satz187d(im(x),im(y),im(u),t2):is"r"(im(u),mn(im(x),im(y)))
+-2212
+satz212a:=tris(cx,u,pli(re(u),im(u)),pli(mn(re(x),re(y)),mn(im(x),im(y))),ispli(u),isrecx12(re(u),mn(re(x),re(y)),im(u),mn(im(x),im(y)),t3".2212",t4".2212")):is(u,pli(mn(re(x),re(y)),mn(im(x),im(y))))
+y@satz212b:=tr3is(cx,pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),pli(pl"r"(re(y),mn(re(x),re(y))),pl"r"(im(y),mn(im(x),im(y)))),pli(re(x),im(x)),x,plis2a(y,mn(re(x),re(y)),mn(im(x),im(y))),isrecx12(pl"r"(re(y),mn(re(x),re(y))),re(x),pl"r"(im(y),mn(im(x),im(y))),im(x),satz187a(re(x),re(y)),satz187a(im(x),im(y))),pliis(x)):is(pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),x)
+satz212c:=somei(cx,[t:cx]is(pl(y,t),x),pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212b):some([t:complex]is(pl(y,t),x))
+satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212a(t,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
+%satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
+mn:=pli(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))):complex
+d@mnis12a:=isrecx12(mn"r"(re(pli(a,b)),re(pli(c,d))),mn"r"(a,c),mn"r"(im(pli(a,b)),im(pli(c,d))),mn"r"(b,d),ismn12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ismn12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)))
+mnis12b:=symis(cx,mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)),mnis12a):is(pli(mn"r"(a,c),mn"r"(b,d)),mn(pli(a,b),pli(c,d)))
+x@[r:real][s:real]
+mnis1a:=isrecx12(mn"r"(re(pli(r,s)),re(x)),mn"r"(r,re(x)),mn"r"(im(pli(r,s)),im(x)),mn"r"(s,im(x)),ismn1(re(pli(r,s)),r,re(x),reis(r,s)),ismn1(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))))
+mnis1b:=symis(cx,mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mnis1a):is(pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mn(pli(r,s),x))
+mnis2a:=isrecx12(mn"r"(re(x),re(pli(r,s))),mn"r"(re(x),r),mn"r"(im(x),im(pli(r,s))),mn"r"(im(x),s),ismn2(re(pli(r,s)),r,re(x),reis(r,s)),ismn2(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)))
+mnis2b:=symis(cx,mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)),mnis2a):is(pli(mn"r"(re(x),r),mn"r"(im(x),s)),mn(x,pli(r,s)))
+z@[i:is(x,y)]
+ismn1:=isf(cx,cx,[t:cx]mn(t,z),x,y,i):is(mn(x,z),mn(y,z))
+ismn2:=isf(cx,cx,[t:cx]mn(z,t),x,y,i):is(mn(z,x),mn(z,y))
+z@[u:complex][i:is(x,y)][j:is(z,u)]
+ismn12:=tris(cx,mn(x,z),mn(y,z),mn(y,u),ismn1(x,y,z,i),ismn2(z,u,y,j)):is(mn(x,z),mn(y,u))
+y@[u:complex][i:is(pl(y,u),x)]
+satz212d:=satz212a(u,i):is(u,mn(x,y))
+satz212e:=symis(cx,u,mn(x,y),satz212d):is(mn(x,y),u)
+u@[i:is(pl(u,y),x)]
+satz212f:=satz212d(tris(cx,pl(y,u),pl(u,y),x,compl(y,u),i)):is(u,mn(x,y))
+satz212g:=symis(cx,u,mn(x,y),satz212f):is(mn(x,y),u)
+y@satz212h:=satz212b:is(pl(y,mn(x,y)),x)
+[i:is(mn(x,y),0c)]
++2213
+t1:=tr3is(real,mn"r"(re(x),re(y)),re(mn(x,y)),re(0c),0,isre(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),iscere(mn(x,y),0c,i),reis(0,0)):is"r"(mn"r"(re(x),re(y)),0)
+t2:=tr3is(real,mn"r"(im(x),im(y)),im(mn(x,y)),im(0c),0,isim(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),isceim(mn(x,y),0c,i),imis(0,0)):is"r"(mn"r"(im(x),im(y)),0)
+t3:=satz182b(re(x),re(y),t1):is"r"(re(x),re(y))
+t4:=satz182b(im(x),im(y),t2):is"r"(im(x),im(y))
+-2213
+satz213a:=tr3is(cx,x,pli(re(x),im(x)),pli(re(y),im(y)),y,ispli(x),isrecx12(re(x),re(y),im(x),im(y),t3".2213",t4".2213"),pliis(y)):is(x,y)
+y@[i:is(x,y)]
++*2213
+i@t5:=satz182e(re(x),re(y),iscere(x,y,i)):is"r"(mn"r"(re(x),re(y)),0)
+t6:=satz182e(im(x),im(y),isceim(x,y,i)):is"r"(mn"r"(im(x),im(y)),0)
+-2213
+i@satz213b:=isrecx12(mn"r"(re(x),re(y)),0,mn"r"(im(x),im(y)),0,t5".2213",t6".2213"):is(mn(x,y),0c)
+x@m0:=mn(0c,x):complex
+satz214:=isrecx12(mn"r"(re(0c),re(x)),m0"r"(re(x)),mn"r"(im(0c),im(x)),m0"r"(im(x)),pl01(re(0c),m0"r"(re(x)),reis(0,0)),pl01(im(0c),m0"r"(im(x)),imis(0,0))):is(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))))
+satz214a:=symis(cx,m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214):is(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x))
+b@m0isa:=tris(cx,m0(pli(a,b)),pli(m0"r"(re(pli(a,b))),m0"r"(im(pli(a,b)))),pli(m0"r"(a),m0"r"(b)),satz214(pli(a,b)),isrecx12(m0"r"(re(pli(a,b))),m0"r"(a),m0"r"(im(pli(a,b))),m0"r"(b),ism0(re(pli(a,b)),a,reis(a,b)),ism0(im(pli(a,b)),b,imis(a,b)))):is(m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)))
+m0isb:=symis(cx,m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)),m0isa):is(pli(m0"r"(a),m0"r"(b)),m0(pli(a,b)))
+y@[i:is(x,y)]
+ism0:=isf(cx,cx,[t:cx]m0(t),x,y,i):is(m0(x),m0(y))
+x@satz215:=tr4is(cx,m0(m0(x)),m0(pli(m0"r"(re(x)),m0"r"(im(x)))),pli(m0"r"(m0"r"(re(x))),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,ism0(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214),m0isa(m0"r"(re(x)),m0"r"(im(x))),isrecx12(m0"r"(m0"r"(re(x))),re(x),m0"r"(m0"r"(im(x))),im(x),satz177(re(x)),satz177(im(x))),pliis(x)):is(m0(m0(x)),x)
+satz215a:=symis(cx,m0(m0(x)),x,satz215):is(x,m0(m0(x)))
+y@[i:is(x,m0(y))]
+satz215b:=tris(cx,m0(x),m0(m0(y)),y,ism0(x,m0(y),i),satz215(y)):is(m0(x),y)
+satz215c:=symis(cx,m0(x),y,satz215b):is(y,m0(x))
+y@[i:is(m0(x),y)]
+satz215d:=satz215c(y,x,symis(cx,m0(x),y,i)):is(x,m0(y))
+satz215e:=symis(cx,x,m0(y),satz215d):is(m0(y),x)
+x@satz216:=tr3is(cx,pl(x,m0(x)),pl(x,pli(m0"r"(re(x)),m0"r"(im(x)))),pli(pl"r"(re(x),m0"r"(re(x))),pl"r"(im(x),m0"r"(im(x)))),0c,ispl2(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),x,satz214(x)),plis2a(x,m0"r"(re(x)),m0"r"(im(x))),isrecx12(pl"r"(re(x),m0"r"(re(x))),0,pl"r"(im(x),m0"r"(im(x))),0,satz179(re(x)),satz179(im(x)))):is(pl(x,m0(x)),0c)
++2216
+anders:=satz212h(0c,x):is(pl(x,m0(x)),0c)
+-2216
+satz216a:=tris(cx,pl(m0(x),x),pl(x,m0(x)),0c,compl(m0(x),x),satz216):is(pl(m0(x),x),0c)
+y@satz217:=tr4is(cx,m0(pl(x,y)),pli(m0"r"(pl"r"(re(x),re(y))),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(m0"r"(re(x)),m0"r"(re(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(pli(m0"r"(re(x)),m0"r"(im(x))),pli(m0"r"(re(y)),m0"r"(im(y)))),pl(m0(x),m0(y)),m0isa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(m0"r"(pl"r"(re(x),re(y))),pl"r"(m0"r"(re(x)),m0"r"(re(y))),m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),satz180(re(x),re(y)),satz180(im(x),im(y))),plis12b(m0"r"(re(x)),m0"r"(im(x)),m0"r"(re(y)),m0"r"(im(y))),ispl12(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),satz214a(x),satz214a(y))):is(m0(pl(x,y)),pl(m0(x),m0(y)))
+satz217a:=symis(cx,m0(pl(x,y)),pl(m0(x),m0(y)),satz217):is(pl(m0(x),m0(y)),m0(pl(x,y)))
+satz218:=tris(cx,mn(x,y),pl(x,pli(m0"r"(re(y)),m0"r"(im(y)))),pl(x,m0(y)),plis2b(x,m0"r"(re(y)),m0"r"(im(y))),ispl2(pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),x,satz214a(y))):is(mn(x,y),pl(x,m0(y)))
+satz218a:=symis(cx,mn(x,y),pl(x,m0(y)),satz218):is(pl(x,m0(y)),mn(x,y))
++2219
+t1:=tr3is(cx,m0(mn(x,y)),m0(pl(x,m0(y))),pl(m0(x),m0(m0(y))),pl(m0(x),y),ism0(mn(x,y),pl(x,m0(y)),satz218),satz217(x,m0(y)),ispl2(m0(m0(y)),y,m0(x),satz215(y))):is(m0(mn(x,y)),pl(m0(x),y))
+-2219
+satz219:=tr3is(cx,m0(mn(x,y)),pl(m0(x),y),pl(y,m0(x)),mn(y,x),t1".2219",compl(m0(x),y),satz218a(y,x)):is(m0(mn(x,y)),mn(y,x))
+satz219a:=symis(cx,m0(mn(y,x)),mn(x,y),satz219(y,x)):is(mn(x,y),m0(mn(y,x)))
+ts:=pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))):complex
+rets:=mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))):real
+imts:=pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))):real
++v3
+d@t1:=ismn12"r"(ts"r"(re(pli(a,b)),re(pli(c,d))),ts"r"(a,c),ts"r"(im(pli(a,b)),im(pli(c,d))),ts"r"(b,d),ists12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ists12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is"r"(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)))
+t2:=ispl12"r"(ts"r"(re(pli(a,b)),im(pli(c,d))),ts"r"(a,d),ts"r"(im(pli(a,b)),re(pli(c,d))),ts"r"(b,c),ists12(re(pli(a,b)),a,im(pli(c,d)),d,reis(a,b),imis(c,d)),ists12(im(pli(a,b)),b,re(pli(c,d)),c,imis(a,b),reis(c,d))):is"r"(imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)))
+-v3
+d@tsis12a:=isrecx12(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)),imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)),t1".v3",t2".v3"):is(ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))))
+tsis12b:=symis(cx,ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),tsis12a):is(pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),ts(pli(a,b),pli(c,d)))
+x@[r:real][s:real]
++*v3
+s@t3:=ismn12"r"(ts"r"(re(pli(r,s)),re(x)),ts"r"(r,re(x)),ts"r"(im(pli(r,s)),im(x)),ts"r"(s,im(x)),ists1(re(pli(r,s)),r,re(x),reis(r,s)),ists1(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))))
+t4:=ispl12"r"(ts"r"(re(pli(r,s)),im(x)),ts"r"(r,im(x)),ts"r"(im(pli(r,s)),re(x)),ts"r"(s,re(x)),ists1(re(pli(r,s)),r,im(x),reis(r,s)),ists1(im(pli(r,s)),s,re(x),imis(r,s))):is"r"(imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))))
+-v3
+s@tsis1a:=isrecx12(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))),t3".v3",t4".v3"):is(ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))))
+tsis1b:=symis(cx,ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),tsis1a):is(pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),ts(pli(r,s),x))
++*v3
+s@t5:=ismn12"r"(ts"r"(re(x),re(pli(r,s))),ts"r"(re(x),r),ts"r"(im(x),im(pli(r,s))),ts"r"(im(x),s),ists2(re(pli(r,s)),r,re(x),reis(r,s)),ists2(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)))
+t6:=ispl12"r"(ts"r"(re(x),im(pli(r,s))),ts"r"(re(x),s),ts"r"(im(x),re(pli(r,s))),ts"r"(im(x),r),ists2(im(pli(r,s)),s,re(x),imis(r,s)),ists2(re(pli(r,s)),r,im(x),reis(r,s))):is"r"(imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)))
+-v3
+s@tsis2a:=isrecx12(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)),t5".v3",t6".v3"):is(ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))))
+tsis2b:=symis(cx,ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),tsis2a):is(pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),ts(x,pli(r,s)))
+z@[i:is(x,y)]
+ists1:=isf(cx,cx,[t:cx]ts(t,z),x,y,i):is(ts(x,z),ts(y,z))
+ists2:=isf(cx,cx,[t:cx]ts(z,t),x,y,i):is(ts(z,x),ts(z,y))
+z@[u:complex][i:is(x,y)][j:is(z,u)]
+ists12:=tris(cx,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
++3220
+y@t1:=ismn12"r"(ts"r"(re(x),re(y)),ts"r"(re(y),re(x)),ts"r"(im(x),im(y)),ts"r"(im(y),im(x)),comts(re(x),re(y)),comts(im(x),im(y))):is"r"(rets(x,y),rets(y,x))
+t2:=tris(real,imts(x,y),pl"r"(ts"r"(im(x),re(y)),ts"r"(re(x),im(y))),imts(y,x),compl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(ts"r"(im(x),re(y)),ts"r"(re(y),im(x)),ts"r"(re(x),im(y)),ts"r"(im(y),re(x)),comts(im(x),re(y)),comts(re(x),im(y)))):is"r"(imts(x,y),imts(y,x))
+-3220
+y@satz220:=isrecx12(rets(x,y),rets(y,x),imts(x,y),imts(y,x),t1".3220",t2".3220"):is(ts(x,y),ts(y,x))
+comts:=satz220:is(ts(x,y),ts(y,x))
+x@[i:is(x,0c)]
+lemma1:=tris(real,re(x),re(0c),0,iscere(x,0c,i),reis(0,0)):is"r"(re(x),0)
+lemma2:=tris(real,im(x),im(0c),0,isceim(x,0c,i),imis(0,0)):is"r"(im(x),0)
+x@mod2:=pl"r"(ts"r"(re(x),re(x)),ts"r"(im(x),im(x))):real
+i@lemma3:=tris(real,mod2,pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),0,ts01(re(x),re(x),lemma1),ts01(im(x),im(x),lemma2)),pl01(0,0,refis(real,0))):is"r"(mod2(x),0)
+x@[n:nis(x,0c)]
++*v3
+x@re2:=ts"r"(re(x),re(x)):real
+im2:=ts"r"(im(x),im(x)):real
+n@[i:is"r"(re(x),0)]
+t7:=th3"l.imp"(is"r"(im(x),0),is(x,0c),n,[t:is"r"(im(x),0)]tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,i,t))):nis"r"(im(x),0)
+t8:=ispos(im2,mod2,symis(real,mod2,im2,pl01(re2,im2,ts01(re(x),re(x),i))),possq(im(x),t7)):pos(mod2)
+n@[o:nis"r"(re(x),0)][i:is"r"(im(x),0)]
+t9:=ispos(re2,mod2,symis(real,mod2,re2,pl02(re2,im2,ts01(im(x),im(x),i))),possq(re(x),o)):pos(mod2)
+o@[p:nis"r"(im(x),0)]
+t10:=pospl(re2,im2,possq(re(x),o),possq(im(x),p)):pos(mod2)
+o@t11:=th1"l.imp"(is"r"(im(x),0),pos(mod2),[t:is"r"(im(x),0)]t9(t),[t:nis"r"(im(x),0)]t10(t)):pos(mod2)
+-v3
+n@lemma4:=th1"l.imp"(is"r"(re(x),0),pos(mod2),[t:is"r"(re(x),0)]t8".v3"(t),[t:nis"r"(re(x),0)]t11".v3"(t)):pos(mod2(x))
+x@lemma5:=th1"l.imp"(is(x,0c),not(neg(mod2)),[t:is(x,0c)]0notn(mod2,lemma3(t)),[t:nis(x,0c)]pnotn(mod2,lemma4(t))):not(neg(mod2(x)))
+y@[i:is(x,0c)]
++3221
+t1:=lemma1(x,i):is"r"(re(x),0)
+t2:=lemma2(x,i):is"r"(im(x),0)
+t3:=tris(real,rets(x,y),mn"r"(0,0),0,ismn12"r"(ts"r"(re(x),re(y)),0,ts"r"(im(x),im(y)),0,ts01(re(x),re(y),t1),ts01(im(x),im(y),t2)),satz187c(0,0,0,pl02(0,0,refis(real,0)))):is"r"(rets(x,y),0)
+t4:=tris(real,imts(x,y),pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),im(y)),0,ts"r"(im(x),re(y)),0,ts01(re(x),im(y),t1),ts01(im(x),re(y),t2)),pl02(0,0,refis(real,0))):is"r"(imts(x,y),0)
+-3221
+satz221a:=isrecx12(rets(x,y),0,imts(x,y),0,t3".3221",t4".3221"):is(ts(x,y),0c)
+y@[i:is(y,0c)]
+satz221b:=tris(cx,ts(x,y),ts(y,x),0c,comts(x,y),satz221a(y,x,i)):is(ts(x,y),0c)
+y@[i:is(ts(x,y),0c)]
++*3221
+i@[n:nis(y,0c)]
+t5:=lemma4(y,n):pos(mod2(y))
+t6:=tris1(real,rets(x,y),0,re(ts(x,y)),reis(rets(x,y),imts(x,y)),lemma1(ts(x,y),i)):is"r"(rets(x,y),0)
+t7:=tris1(real,imts(x,y),0,im(ts(x,y)),imis(rets(x,y),imts(x,y)),lemma2(ts(x,y),i)):is"r"(imts(x,y),0)
+t8:=tris(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(0,0),0,ispl12"r"(ts"r"(rets(x,y),re(y)),0,ts"r"(imts(x,y),im(y)),0,ts01(rets(x,y),re(y),t6),ts01(imts(x,y),im(y),t7)),pl02(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),0)
+y@ii1r:=ts"r"(ts"r"(im(x),im(y)),re(y)):real
+i1ir:=ts"r"(im(x),ts"r"(im(y),re(y))):real
+ir1i:=ts"r"(ts"r"(im(x),re(y)),im(y)):real
+i1ri:=ts"r"(im(x),ts"r"(re(y),im(y))):real
+rr1r:=ts"r"(ts"r"(re(x),re(y)),re(y)):real
+r1rr:=ts"r"(re(x),ts"r"(re(y),re(y))):real
+ri1r:=ts"r"(ts"r"(re(x),im(y)),re(y)):real
+r1ir:=ts"r"(re(x),ts"r"(im(y),re(y))):real
+ri1i:=ts"r"(ts"r"(re(x),im(y)),im(y)):real
+r1ii:=ts"r"(re(x),ts"r"(im(y),im(y))):real
+n@t9:=tris(real,ii1r,i1ir,i1ri,assts1(im(x),im(y),re(y)),ists2"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),im(x),comts"r"(im(y),re(y)))):is"r"(ii1r,i1ri)
+t10:=tris(real,ts"r"(rets(x,y),re(y)),mn"r"(rr1r,ii1r),mn"r"(r1rr,i1ri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(y)),ismn12"r"(rr1r,r1rr,ii1r,i1ri,assts1(re(x),re(y),re(y)),t9)):is"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri))
+t11:=tr3is(real,ts"r"(imts(x,y),im(y)),pl"r"(ri1i,ir1i),pl"r"(r1ii,i1ri),pl"r"(i1ri,r1ii),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(y)),ispl12"r"(ri1i,r1ii,ir1i,i1ri,assts1(re(x),im(y),im(y)),assts1(im(x),re(y),im(y))),compl"r"(r1ii,i1ri)):is"r"(ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii))
+t12:=tr4is(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(mn"r"(r1rr,i1ri),pl"r"(i1ri,r1ii)),pl"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1ii),pl"r"(r1rr,r1ii),ts"r"(re(x),mod2(y)),ispl12"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri),ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii),t10,t11),asspl2"r"(mn"r"(r1rr,i1ri),i1ri,r1ii),ispl1"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1rr,r1ii,plmn(r1rr,i1ri)),distpt2(re(x),ts"r"(re(y),re(y)),ts"r"(im(y),im(y)))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),ts"r"(re(x),mod2(y)))
+t13:=tris1(real,ts"r"(re(x),mod2(y)),0,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),t12,t8):is"r"(ts"r"(re(x),mod2(y)),0)
+t14:=ore1(is"r"(re(x),0),is"r"(mod2(y),0),satz192c(re(x),mod2(y),t13),pnot0(mod2(y),t5)):is"r"(re(x),0)
+t15:=tris1(real,ts"r"(im(x),im(y)),0,ts"r"(re(x),re(y)),satz182b(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),t6),ts01(re(x),re(y),t14)):is"r"(ts"r"(im(x),im(y)),0)
+t16:=tris1(real,ts"r"(im(x),re(y)),0,imts(x,y),pl01(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),ts01(re(x),im(y),t14)),t7):is"r"(ts"r"(im(x),re(y)),0)
+[j:is"r"(re(y),0)]
+t17:=t7"c.v3"(y,n,j):nis"r"(im(y),0)
+t18:=ore1(is"r"(im(x),0),is"r"(im(y),0),satz192c(im(x),im(y),t15),t17):is"r"(im(x),0)
+n@[o:nis"r"(re(y),0)]
+t19:=ore1(is"r"(im(x),0),is"r"(re(y),0),satz192c(im(x),re(y),t16),o):is"r"(im(x),0)
+n@t20:=th1"l.imp"(is"r"(re(y),0),is"r"(im(x),0),[t:is"r"(re(y),0)]t18(t),[t:nis"r"(re(y),0)]t19(t)):is"r"(im(x),0)
+t21:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t14,t20)):is(x,0c)
+-3221
+i@satz221c:=th2"l.or"(is(x,0c),is(y,0c),[t:nis(y,0c)]t21".3221"(t)):or(is(x,0c),is(y,0c))
+y@[n:nis(x,0c)][o:nis(y,0c)]
+satz221d:=th3"l.imp"(is(ts(x,y),0c),or(is(x,0c),is(y,0c)),th3"l.or"(is(x,0c),is(y,0c),n,o),[t:is(ts(x,y),0c)]satz221c(t)):nis(ts(x,y),0c)
++3222
+x@t1:=tris(real,mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),mn"r"(re(x),0),re(x),ismn12"r"(ts"r"(re(x),1rl),re(x),ts"r"(im(x),0),0,satz195(re(x)),ts02(im(x),0,refis(real,0))),pl02(re(x),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x))
+t2:=tris(real,pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),pl"r"(0,im(x)),im(x),ispl12"r"(ts"r"(re(x),0),0,ts"r"(im(x),1rl),im(x),ts02(re(x),0,refis(real,0)),satz195(im(x))),pl01(0,im(x),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x))
+-3222
+x@satz222:=tr3is(cx,ts(x,1c),pli(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl))),pli(re(x),im(x)),x,tsis2a(x,1rl,0),isrecx12(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x),t1".3222",t2".3222"),pliis(x)):is(ts(x,1c),x)
+satz222a:=symis(cx,ts(x,1c),x,satz222):is(x,ts(x,1c))
+satz222b:=tris(cx,ts(1c,x),ts(x,1c),x,comts(1c,x),satz222):is(ts(1c,x),x)
+satz222c:=symis(cx,ts(1c,x),x,satz222b):is(x,ts(1c,x))
++3223
+t1:=tris(real,mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),mn"r"(m0"r"(re(x)),0),m0"r"(re(x)),ismn12"r"(ts"r"(re(x),m0"r"(1rl)),m0"r"(re(x)),ts"r"(im(x),m0"r"(0)),0,tris(real,ts"r"(re(x),m0"r"(1rl)),m0"r"(ts"r"(re(x),1rl)),m0"r"(re(x)),satz197b(re(x),1rl),ism0"r"(ts"r"(re(x),1rl),re(x),satz195(re(x)))),ts02(im(x),m0"r"(0),satz176b(0,refis(real,0)))),pl02(m0"r"(re(x)),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)))
+t2:=tris(real,pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),pl"r"(0,m0"r"(im(x))),m0"r"(im(x)),ispl12"r"(ts"r"(re(x),m0"r"(0)),0,ts"r"(im(x),m0"r"(1rl)),m0"r"(im(x)),ts02(re(x),m0"r"(0),satz176b(0,refis(real,0))),tris(real,ts"r"(im(x),m0"r"(1rl)),m0"r"(ts"r"(im(x),1rl)),m0"r"(im(x)),satz197b(im(x),1rl),ism0"r"(ts"r"(im(x),1rl),im(x),satz195(im(x))))),pl01(0,m0"r"(im(x)),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)))
+-3223
+satz223:=tr4is(cx,ts(x,m0(1c)),ts(x,pli(m0"r"(1rl),m0"r"(0))),pli(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl)))),pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),ists2(m0(1c),pli(m0"r"(1rl),m0"r"(0)),x,m0isa(1rl,0)),tsis2a(x,m0"r"(1rl),m0"r"(0)),isrecx12(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)),t1".3223",t2".3223"),satz214a(x)):is(ts(x,m0(1c)),m0(x))
+satz223a:=symis(cx,ts(x,m0(1c)),m0(x),satz223):is(m0(x),ts(x,m0(1c)))
+satz223b:=tris(cx,ts(m0(1c),x),ts(x,m0(1c)),m0(x),comts(m0(1c),x),satz223):is(ts(m0(1c),x),m0(x))
+satz223c:=symis(cx,ts(m0(1c),x),m0(x),satz223b):is(m0(x),ts(m0(1c),x))
++3224
+y@rxry:=ts"r"(re(x),re(y)):real
+ixiy:=ts"r"(im(x),im(y)):real
+rxiy:=ts"r"(re(x),im(y)):real
+ixry:=ts"r"(im(x),re(y)):real
+t1:=tr4is(real,mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),mn"r"(m0"r"(rxry),m0"r"(ixiy)),pl"r"(m0"r"(rxry),ixiy),mn"r"(ixiy,rxry),m0"r"(mn"r"(rxry,ixiy)),ismn12"r"(ts"r"(m0"r"(re(x)),re(y)),m0"r"(rxry),ts"r"(m0"r"(im(x)),im(y)),m0"r"(ixiy),satz197a(re(x),re(y)),satz197a(im(x),im(y))),ispl2"r"(m0"r"(m0"r"(ixiy)),ixiy,m0"r"(rxry),satz177(ixiy)),compl"r"(m0"r"(rxry),ixiy),satz181a(ixiy,rxry)):is"r"(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(rxry,ixiy)))
+t2:=tris(real,pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),mn"r"(m0"r"(rxiy),ixry),m0"r"(pl"r"(rxiy,ixry)),ispl12"r"(ts"r"(m0"r"(re(x)),im(y)),m0"r"(rxiy),ts"r"(m0"r"(im(x)),re(y)),m0"r"(ixry),satz197a(re(x),im(y)),satz197a(im(x),re(y))),satz180a(rxiy,ixry)):is"r"(pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(rxiy,ixry)))
+-3224
+y@satz224a:=tr4is(cx,ts(m0(x),y),ts(pli(m0"r"(re(x)),m0"r"(im(x))),y),pli(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y)))),pli(m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))),m0(ts(x,y)),ists1(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),y,satz214(x)),tsis1a(y,m0"r"(re(x)),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))),t1".3224",t2".3224"),m0isb(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))):is(ts(m0(x),y),m0(ts(x,y)))
+satz224b:=tr3is(cx,ts(x,m0(y)),ts(m0(y),x),m0(ts(y,x)),m0(ts(x,y)),comts(x,m0(y)),satz224a(y,x),ism0(ts(y,x),ts(x,y),comts(y,x))):is(ts(x,m0(y)),m0(ts(x,y)))
+satz224c:=tris2(cx,ts(m0(x),y),ts(x,m0(y)),m0(ts(x,y)),satz224a,satz224b):is(ts(m0(x),y),ts(x,m0(y)))
+satz224d:=symis(cx,ts(m0(x),y),ts(x,m0(y)),satz224c):is(ts(x,m0(y)),ts(m0(x),y))
+satz224e:=symis(cx,ts(m0(x),y),m0(ts(x,y)),satz224a):is(m0(ts(x,y)),ts(m0(x),y))
+satz224f:=symis(cx,ts(x,m0(y)),m0(ts(x,y)),satz224b):is(m0(ts(x,y)),ts(x,m0(y)))
+satz225:=tris(cx,ts(m0(x),m0(y)),ts(x,m0(m0(y))),ts(x,y),satz224c(x,m0(y)),ists2(m0(m0(y)),y,x,satz215(y))):is(ts(m0(x),m0(y)),ts(x,y))
+satz225a:=symis(cx,ts(m0(x),m0(y)),ts(x,y),satz225):is(ts(x,y),ts(m0(x),m0(y)))
++3226
+z@rrr:=ts"r"(ts"r"(re(x),re(y)),re(z)):real
+iir:=ts"r"(ts"r"(im(x),im(y)),re(z)):real
+rii:=ts"r"(ts"r"(re(x),im(y)),im(z)):real
+iri:=ts"r"(ts"r"(im(x),re(y)),im(z)):real
+rri:=ts"r"(ts"r"(re(x),re(y)),im(z)):real
+iii:=ts"r"(ts"r"(im(x),im(y)),im(z)):real
+rir:=ts"r"(ts"r"(re(x),im(y)),re(z)):real
+irr:=ts"r"(ts"r"(im(x),re(y)),re(z)):real
+t1:=tr3is(real,mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(mn"r"(rrr,iir),pl"r"(rii,iri)),pl"r"(rrr,pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri)))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),ismn12"r"(ts"r"(rets(x,y),re(z)),mn"r"(rrr,iir),ts"r"(imts(x,y),im(z)),pl"r"(rii,iri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(z))),asspl1"r"(rrr,m0"r"(iir),m0"r"(pl"r"(rii,iri))),ispl2"r"(pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri))),m0"r"(pl"r"(iir,pl"r"(rii,iri))),rrr,satz180a(iir,pl"r"(rii,iri)))):is"r"(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))))
+t2:=tr3is(real,pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),pl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),pl"r"(pl"r"(rir,irr),mn"r"(rri,iii)),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),ispl12"r"(ts"r"(rets(x,y),im(z)),mn"r"(rri,iii),ts"r"(imts(x,y),re(z)),pl"r"(rir,irr),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),im(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),re(z))),compl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),asspl2"r"(pl"r"(rir,irr),rri,m0"r"(iii))):is"r"(pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii))
+t3:=tris(cx,ts(ts(x,y),z),pli(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z)))),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),tsis1a(z,rets(x,y),imts(x,y)),isrecx12(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),t1,t2)):is(ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)))
+c@t4:=tris(real,ts"r"(ts"r"(a,b),c),ts"r"(a,ts"r"(b,c)),ts"r"(ts"r"(b,c),a),assts1(a,b,c),comts"r"(a,ts"r"(b,c))):is"r"(ts"r"(ts"r"(a,b),c),ts"r"(ts"r"(b,c),a))
+t5:=tris(real,pl"r"(pl"r"(a,b),c),pl"r"(c,pl"r"(a,b)),pl"r"(pl"r"(c,a),b),compl"r"(pl"r"(a,b),c),asspl2"r"(c,a,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(c,a),b))
+t6:=tris(real,pl"r"(a,pl"r"(b,c)),pl"r"(pl"r"(b,c),a),pl"r"(b,pl"r"(c,a)),compl"r"(a,pl"r"(b,c)),asspl1"r"(b,c,a)):is"r"(pl"r"(a,pl"r"(b,c)),pl"r"(b,pl"r"(c,a)))
+z@rrr1:=rrr(y,z,x):real
+iir1:=iir(y,z,x):real
+rii1:=rii(y,z,x):real
+iri1:=iri(y,z,x):real
+rri1:=rri(y,z,x):real
+iii1:=iii(y,z,x):real
+rir1:=rir(y,z,x):real
+irr1:=irr(y,z,x):real
+t7:=tris(real,pl"r"(iir,pl"r"(rii,iri)),pl"r"(rii,pl"r"(iri,iir)),pl"r"(iir1,pl"r"(rii1,iri1)),t6(iir,rii,iri),ispl12"r"(rii,iir1,pl"r"(iri,iir),pl"r"(rii1,iri1),t4(re(x),im(y),im(z)),ispl12"r"(iri,rii1,iir,iri1,t4(im(x),re(y),im(z)),t4(im(x),im(y),re(z))))):is"r"(pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)))
+t8:=tris(real,pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rri,rir),irr),pl"r"(pl"r"(rir1,irr1),rri1),t5(rir,irr,rri),ispl12"r"(pl"r"(rri,rir),pl"r"(rir1,irr1),irr,rri1,ispl12"r"(rri,rir1,rir,irr1,t4(re(x),re(y),im(z)),t4(re(x),im(y),re(z))),t4(im(x),re(y),re(z)))):is"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1))
+t9:=ismn12"r"(rrr,rrr1,pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)),t4(re(x),re(y),re(z)),t7):is"r"(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))))
+t10:=ismn12"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1),iii,iii1,t8,t4(im(x),im(y),im(z))):is"r"(mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1))
+t11:=tris(cx,ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t3,isrecx12(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1),t9,t10)):is(ts(ts(x,y),z),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
+t12:=tris(cx,ts(x,ts(y,z)),ts(ts(y,z),x),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),comts(x,ts(y,z)),t3(y,z,x)):is(ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
+t13:=tris2(cx,ts(ts(x,y),z),ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t11,t12):is(ts(ts(x,y),z),ts(x,ts(y,z)))
+-3226
+z@satz226:=t13".3226":is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts1:=satz226:is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts2:=symis(cx,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
++3227
+c@t1:=tr3is(real,pl"r"(pl"r"(a,b),c),pl"r"(a,pl"r"(b,c)),pl"r"(a,pl"r"(c,b)),pl"r"(pl"r"(a,c),b),asspl1"r"(a,b,c),ispl2"r"(pl"r"(b,c),pl"r"(c,b),a,compl"r"(b,c)),asspl2"r"(a,c,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b))
+d@t2:=tr3is(real,pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(pl"r"(a,b),c),d),pl"r"(pl"r"(pl"r"(a,c),b),d),pl"r"(pl"r"(a,c),pl"r"(b,d)),asspl2"r"(pl"r"(a,b),c,d),ispl1"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b),d,t1),asspl1"r"(pl"r"(a,c),b,d)):is"r"(pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,c),pl"r"(b,d)))
+t3:=tris(real,mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,b),pl"r"(m0"r"(c),m0"r"(d))),pl"r"(mn"r"(a,c),mn"r"(b,d)),ispl2"r"(m0"r"(pl"r"(c,d)),pl"r"(m0"r"(c),m0"r"(d)),pl"r"(a,b),satz180(c,d)),t2(a,b,m0"r"(c),m0"r"(d))):is"r"(mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(mn"r"(a,c),mn"r"(b,d)))
+z@t4:=tris(real,mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),mn"r"(pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))),pl"r"(rets(x,y),rets(x,z)),ismn12"r"(ts"r"(re(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),ts"r"(im(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z))),disttp2(re(x),re(y),re(z)),disttp2(im(x),im(y),im(z))),t3(ts"r"(re(x),re(y)),ts"r"(re(x),re(z)),ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))):is"r"(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)))
+t5:=tris(real,pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))),pl"r"(imts(x,y),imts(x,z)),ispl12"r"(ts"r"(re(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z))),disttp2(re(x),im(y),im(z)),disttp2(im(x),re(y),re(z))),t2(ts"r"(re(x),im(y)),ts"r"(re(x),im(z)),ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))):is"r"(pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)))
+t6:=tr3is(cx,ts(x,pl(y,z)),pli(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))))),pli(pl"r"(rets(x,y),rets(x,z)),pl"r"(imts(x,y),imts(x,z))),pl(ts(x,y),ts(x,z)),tsis2a(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z))),isrecx12(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)),t4,t5),plis12b(rets(x,y),imts(x,y),rets(x,z),imts(x,z))):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+-3227
+satz227:=t6".3227":is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+disttp1:=tr3is(cx,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz227(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
+disttp2:=satz227:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+distpt1:=symis(cx,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
+distpt2:=symis(cx,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
+satz228:=tr4is(cx,ts(x,mn(y,z)),ts(x,pl(y,m0(z))),pl(ts(x,y),ts(x,m0(z))),pl(ts(x,y),m0(ts(x,z))),mn(ts(x,y),ts(x,z)),ists2(mn(y,z),pl(y,m0(z)),x,satz218(y,z)),disttp2(x,y,m0(z)),ispl2(ts(x,m0(z)),m0(ts(x,z)),ts(x,y),satz224b(x,z)),satz218a(ts(x,y),ts(x,z))):is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
+disttm1:=tr3is(cx,ts(mn(x,y),z),ts(z,mn(x,y)),mn(ts(z,x),ts(z,y)),mn(ts(x,z),ts(y,z)),comts(mn(x,y),z),satz228(z,x,y),ismn12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(mn(x,y),z),mn(ts(x,z),ts(y,z)))
+disttm2:=satz228:is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
+distmt1:=symis(cx,ts(mn(x,y),z),mn(ts(x,z),ts(y,z)),disttm1):is(mn(ts(x,z),ts(y,z)),ts(mn(x,y),z))
+distmt2:=symis(cx,ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)),disttm2):is(mn(ts(x,y),ts(x,z)),ts(x,mn(y,z)))
+y@[n:nis(y,0c)][u1:complex][u2:complex][i:is(ts(y,u1),x)][j:is(ts(y,u2),x)]
++3229
+t1:=tris2(cx,ts(y,u1),ts(y,u2),x,i,j):is(ts(y,u1),ts(y,u2))
+t2:=tris(cx,ts(y,mn(u1,u2)),mn(ts(y,u1),ts(y,u2)),0c,disttm2(y,u1,u2),satz213b(ts(y,u1),ts(y,u2),t1)):is(ts(y,mn(u1,u2)),0c)
+t3:=ore2(is(y,0c),is(mn(u1,u2),0c),satz221c(y,mn(u1,u2),t2),n):is(mn(u1,u2),0c)
+-3229
+satz229b:=satz213a(u1,u2,t3".3229"):is(u1,u2)
++*3229
+n@t4:=pnot0(mod2(y),lemma4(y,n)):nis"r"(mod2(y),0)
+u:=ts(pli(ov(re(y),mod2(y),t4),m0"r"(ov(im(y),mod2(y),t4))),x):complex
+[v:real]
+dd:=ov(v,mod2(y),t4):real
+n@t5:=tr3is(real,m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),m0"r"(m0"r"(ts"r"(im(y),dd(im(y))))),ts"r"(im(y),dd(im(y))),dd(ts"r"(im(y),im(y))),ism0"r"(ts"r"(im(y),m0"r"(dd(im(y)))),m0"r"(ts"r"(im(y),dd(im(y)))),satz197b(im(y),dd(im(y)))),satz177(ts"r"(im(y),dd(im(y)))),lemma6(im(y),im(y),mod2(y),t4)):is"r"(m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))))
+t6:=tr3is(real,mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(dd(ts"r"(re(y),re(y))),dd(ts"r"(im(y),im(y)))),dd(mod2(y)),1rl,ispl12"r"(ts"r"(re(y),dd(re(y))),dd(ts"r"(re(y),re(y))),m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))),lemma6(re(y),re(y),mod2(y),t4),t5),lemma7(ts"r"(re(y),re(y)),ts"r"(im(y),im(y)),mod2(y),t4),lemma8(mod2(y),t4)):is"r"(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl)
+t7:=tris(real,ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(m0"r"(re(y)),dd(im(y))),dd(ts"r"(m0"r"(re(y)),im(y))),satz197d(re(y),dd(im(y))),lemma6(m0"r"(re(y)),im(y),mod2(y),t4)):is"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))))
+t8:=tris(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),pl"r"(dd(ts"r"(m0"r"(re(y)),im(y))),dd(ts"r"(im(y),re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),ispl12"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))),ts"r"(im(y),dd(re(y))),dd(ts"r"(im(y),re(y))),t7,lemma6(im(y),re(y),mod2(y),t4)),lemma7(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)),mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))))
+t9:=tr3is(real,pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),pl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),mn"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y))),0,ispl1"r"(ts"r"(m0"r"(re(y)),im(y)),m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y)),satz197a(re(y),im(y))),compl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),satz182e(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),comts"r"(im(y),re(y)))):is"r"(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0)
+t10:=tr3is(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),dd(0),0,t8,isf(real,real,[t:real]dd(t),pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0,t9),lemma9(mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0)
+t11:=tris(cx,ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),pli(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y))))),1c,tsis2a(y,dd(re(y)),m0"r"(dd(im(y)))),isrecx12(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0,t6,t10)):is(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c)
+t12:=tr3is(cx,ts(y,u),ts(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),x),ts(1c,x),x,assts2(y,pli(dd(re(y)),m0"r"(dd(im(y)))),x),ists1(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c,x,t11),satz222b(x)):is(ts(y,u),x)
+-3229
+n@satz229a:=somei(cx,[t:cx]is(ts(y,t),x),u".3229",t12".3229"):some([t:cx]is(ts(y,t),x))
+satz229:=onei(cx,[t:cx]is(ts(y,t),x),[t:cx][u:cx][v:is(ts(y,t),x)][w:is(ts(y,u),x)]satz229b(t,u,v,w),satz229a):one([t:cx]is(ts(y,t),x))
+ov:=ind(cx,[t:cx]is(ts(y,t),x),satz229):complex
+satz229c:=oneax(cx,[t:cx]is(ts(y,t),x),satz229):is(ts(y,ov(x,y,n)),x)
+satz229d:=symis(cx,ts(y,ov(x,y,n)),x,satz229c):is(x,ts(y,ov(x,y,n)))
+satz229e:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c):is(ts(ov(x,y,n),y),x)
+satz229f:=symis(cx,ts(ov(x,y,n),y),x,satz229e):is(x,ts(ov(x,y,n),y))
+y@[u:complex][n:nis(y,0c)][i:is(ts(y,u),x)]
+satz229g:=satz229b(n,u,ov(x,y,n),i,satz229c(n)):is(u,ov(x,y,n))
+satz229h:=symis(cx,u,ov(x,y,n),satz229g):is(ov(x,y,n),u)
+n@[i:is(ts(u,y),x)]
+satz229j:=satz229g(tris(cx,ts(y,u),ts(u,y),x,comts(y,u),i)):is(u,ov(x,y,n))
+satz229k:=symis(cx,u,ov(x,y,n),satz229j):is(ov(x,y,n),u)
+z@[i:is(x,y)][n:nis(z,0c)]
+isov1:=isf(cx,cx,[t:cx]ov(t,z,n),x,y,i):is(ov(x,z,n),ov(y,z,n))
+i@[n:nis(x,0c)][o:nis(y,0c)]
+isov2:=satz229h(z,x,ov(z,y,o),n,tris(cx,ts(x,ov(z,y,o)),ts(y,ov(z,y,o)),z,ists1(x,y,ov(z,y,o),i),satz229c(z,y,o))):is(ov(z,x,n),ov(z,y,o))
+z@[u:complex][i:is(x,y)][j:is(z,u)][n:nis(z,0c)][o:nis(u,0c)]
+isov12:=tris(cx,ov(x,z,n),ov(y,z,n),ov(y,u,o),isov1(x,y,z,i,n),isov2(z,u,y,j,n,o)):is(ov(x,z,n),ov(y,u,o))
+y@satz230:=tris(cx,pl(mn(x,y),y),pl(y,mn(x,y)),x,compl(mn(x,y),y),satz212h(x,y)):is(pl(mn(x,y),y),x)
+satz231:=satz212e(pl(x,y),y,x,compl(y,x)):is(mn(pl(x,y),y),x)
+satz232:=satz212e(x,mn(x,y),y,satz230):is(mn(x,mn(x,y)),y)
++4233
+z@t1:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(mn(mn(x,y),z),pl(y,z)),pl(mn(mn(x,y),z),pl(z,y)),pl(pl(mn(mn(x,y),z),z),y),compl(pl(y,z),mn(mn(x,y),z)),ispl2(pl(y,z),pl(z,y),mn(mn(x,y),z),compl(y,z)),asspl2(mn(mn(x,y),z),z,y)):is(pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y))
+t2:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y),pl(mn(x,y),y),x,t1,ispl1(pl(mn(mn(x,y),z),z),mn(x,y),y,satz230(mn(x,y),z)),satz230(x,y)):is(pl(pl(y,z),mn(mn(x,y),z)),x)
+-4233
+z@satz233:=satz212d(x,pl(y,z),mn(mn(x,y),z),t2".4233"):is(mn(mn(x,y),z),mn(x,pl(y,z)))
+satz234:=satz212g(pl(x,y),z,pl(x,mn(y,z)),tris(cx,pl(pl(x,mn(y,z)),z),pl(x,pl(mn(y,z),z)),pl(x,y),asspl1(x,mn(y,z),z),ispl2(pl(mn(y,z),z),y,x,satz230(y,z)))):is(mn(pl(x,y),z),pl(x,mn(y,z)))
+satz234a:=symis(cx,mn(pl(x,y),z),pl(x,mn(y,z)),satz234):is(pl(x,mn(y,z)),mn(pl(x,y),z))
+satz234b:=tr3is(cx,mn(pl(x,y),z),mn(pl(y,x),z),pl(y,mn(x,z)),pl(mn(x,z),y),ismn1(pl(x,y),pl(y,x),z,compl(x,y)),satz234(y,x,z),compl(y,mn(x,z))):is(mn(pl(x,y),z),pl(mn(x,z),y))
+satz234c:=symis(cx,mn(pl(x,y),z),pl(mn(x,z),y),satz234b):is(pl(mn(x,z),y),mn(pl(x,y),z))
+satz235:=satz212f(x,mn(y,z),pl(mn(x,y),z),tr3is(cx,pl(pl(mn(x,y),z),mn(y,z)),pl(mn(x,y),pl(z,mn(y,z))),pl(mn(x,y),y),x,asspl1(mn(x,y),z,mn(y,z)),ispl2(pl(z,mn(y,z)),y,mn(x,y),satz212h(y,z)),satz230(x,y))):is(pl(mn(x,y),z),mn(x,mn(y,z)))
+satz235a:=symis(cx,pl(mn(x,y),z),mn(x,mn(y,z)),satz235):is(mn(x,mn(y,z)),pl(mn(x,y),z))
+satz235b:=tris(cx,mn(x,mn(y,z)),pl(mn(x,y),z),mn(pl(x,z),y),satz235a,satz234c(x,z,y)):is(mn(x,mn(y,z)),mn(pl(x,z),y))
+satz235c:=tris(cx,mn(x,mn(y,z)),mn(pl(x,z),y),mn(pl(z,x),y),satz235b,ismn1(pl(x,z),pl(z,x),y,compl(x,z))):is(mn(x,mn(y,z)),mn(pl(z,x),y))
+satz236:=satz212g(pl(x,z),pl(y,z),mn(x,y),tris(cx,pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y)))):is(mn(pl(x,z),pl(y,z)),mn(x,y))
+satz236a:=tris(cx,mn(pl(z,x),pl(z,y)),mn(pl(x,z),pl(y,z)),mn(x,y),ismn12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y)),satz236):is(mn(pl(z,x),pl(z,y)),mn(x,y))
+[u:complex]
++4237
+t1:=tr3is(cx,pl(mn(z,u),pl(u,y)),pl(pl(mn(z,u),u),y),pl(z,y),pl(y,z),asspl2(mn(z,u),u,y),ispl1(pl(mn(z,u),u),z,y,satz230(z,u)),compl(z,y)):is(pl(mn(z,u),pl(u,y)),pl(y,z))
+t2:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(pl(mn(x,y),mn(z,u)),pl(u,y)),pl(mn(x,y),pl(mn(z,u),pl(u,y))),pl(mn(x,y),pl(y,z)),ispl2(pl(y,u),pl(u,y),pl(mn(x,y),mn(z,u)),compl(y,u)),asspl1(mn(x,y),mn(z,u),pl(u,y)),ispl2(pl(mn(z,u),pl(u,y)),pl(y,z),mn(x,y),t1)):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)))
+t3:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),t2,asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y))):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(x,z))
+-4237
+satz237:=satz212f(pl(x,z),pl(y,u),pl(mn(x,y),mn(z,u)),t3".4237"):is(pl(mn(x,y),mn(z,u)),mn(pl(x,z),pl(y,u)))
++4238
+t1:=tris(cx,pl(pl(x,u),z),pl(x,pl(u,z)),pl(x,pl(z,u)),asspl1(x,u,z),ispl2(pl(u,z),pl(z,u),x,compl(u,z))):is(pl(pl(x,u),z),pl(x,pl(z,u)))
+t2:=tr3is(cx,pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(pl(pl(x,u),z),pl(pl(y,z),u)),mn(pl(x,pl(z,u)),pl(y,pl(z,u))),mn(x,y),satz237(pl(x,u),pl(y,z),z,u),ismn12(pl(pl(x,u),z),pl(x,pl(z,u)),pl(pl(y,z),u),pl(y,pl(z,u)),t1,asspl1(y,z,u)),satz236(x,y,pl(z,u))):is(pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(x,y))
+-4238
+satz238:=satz212g(mn(x,y),mn(z,u),mn(pl(x,u),pl(y,z)),t2".4238"):is(mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)))
+[i:is(mn(x,y),mn(z,u))]
++4239
+t1:=tris1(cx,mn(pl(x,u),pl(y,z)),0c,mn(mn(x,y),mn(z,u)),satz238,satz213b(mn(x,y),mn(z,u),i)):is(mn(pl(x,u),pl(y,z)),0c)
+-4239
+satz239a:=satz213a(pl(x,u),pl(y,z),t1".4239"):is(pl(x,u),pl(y,z))
+u@[i:is(pl(x,u),pl(y,z))]
++*4239
+i@t2:=tris(cx,mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)),0c,satz238,satz213b(pl(x,u),pl(y,z),i)):is(mn(mn(x,y),mn(z,u)),0c)
+-4239
+i@satz239b:=satz213a(mn(x,y),mn(z,u),t2".4239"):is(mn(x,y),mn(z,u))
+y@[n:nis(y,0c)]
+satz240:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c(x,y,n)):is(ts(ov(x,y,n),y),x)
+satz241:=satz229h(ts(x,y),y,x,n,comts(y,x)):is(ov(ts(x,y),y,n),x)
+y@[n:nis(x,0c)][o:nis(y,0c)]
+lemma6:=th3"l.imp"(is(ov(x,y,o),0c),is(x,0c),n,[t:is(ov(x,y,o),0c)]tris1(cx,x,0c,ts(y,ov(x,y,o)),satz229c(x,y,o),satz221b(y,ov(x,y,o),t))):nis(ov(x,y,o),0c)
+satz242:=satz229h(x,ov(x,y,o),y,lemma6,satz240(o)):is(ov(x,ov(x,y,o),lemma6),y)
+z@[n:nis(y,0c)][o:nis(z,0c)]
++5243
+t1:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ov(ov(x,y,n),z,o),ts(y,z)),ts(ov(ov(x,y,n),z,o),ts(z,y)),ts(ts(ov(ov(x,y,n),z,o),z),y),comts(ts(y,z),ov(ov(x,y,n),z,o)),ists2(ts(y,z),ts(z,y),ov(ov(x,y,n),z,o),comts(y,z)),assts2(ov(ov(x,y,n),z,o),z,y)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y))
+t2:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y),ts(ov(x,y,n),y),x,t1,ists1(ts(ov(ov(x,y,n),z,o),z),ov(x,y,n),y,satz240(ov(x,y,n),z,o)),satz240(x,y,n)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),x)
+-5243
+satz243:=satz229g(x,ts(y,z),ov(ov(x,y,n),z,o),satz221d(y,z,n,o),t2".5243"):is(ov(ov(x,y,n),z,o),ov(x,ts(y,z),satz221d(y,z,n,o)))
+z@[n:nis(z,0c)]
+satz244:=satz229k(ts(x,y),z,ts(x,ov(y,z,n)),n,tris(cx,ts(ts(x,ov(y,z,n)),z),ts(x,ts(ov(y,z,n),z)),ts(x,y),assts1(x,ov(y,z,n),z),ists2(ts(ov(y,z,n),z),y,x,satz240(y,z,n)))):is(ov(ts(x,y),z,n),ts(x,ov(y,z,n)))
+satz244a:=symis(cx,ov(ts(x,y),z,n),ts(x,ov(y,z,n)),satz244):is(ts(x,ov(y,z,n)),ov(ts(x,y),z,n))
+satz244b:=tr3is(cx,ov(ts(x,y),z,n),ov(ts(y,x),z,n),ts(y,ov(x,z,n)),ts(ov(x,z,n),y),isov1(ts(x,y),ts(y,x),z,comts(x,y),n),satz244(y,x,z,n),comts(y,ov(x,z,n))):is(ov(ts(x,y),z,n),ts(ov(x,z,n),y))
+satz244c:=symis(cx,ov(ts(x,y),z,n),ts(ov(x,z,n),y),satz244b):is(ts(ov(x,z,n),y),ov(ts(x,y),z,n))
+z@[n:nis(y,0c)][o:nis(z,0c)]
+satz245:=satz229j(x,ov(y,z,o),ts(ov(x,y,n),z),lemma6(y,z,n,o),tr3is(cx,ts(ts(ov(x,y,n),z),ov(y,z,o)),ts(ov(x,y,n),ts(z,ov(y,z,o))),ts(ov(x,y,n),y),x,assts1(ov(x,y,n),z,ov(y,z,o)),ists2(ts(z,ov(y,z,o)),y,ov(x,y,n),satz229c(y,z,o)),satz240(x,y,n))):is(ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)))
+satz245a:=symis(cx,ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)),satz245):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z))
+satz245b:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z),ov(ts(x,z),y,n),satz245a,satz244c(x,z,y,n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n))
+satz245c:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n),ov(ts(z,x),y,n),satz245b,isov1(ts(x,z),ts(z,x),y,comts(x,z),n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(z,x),y,n))
+satz246:=satz229k(ts(x,z),ts(y,z),ov(x,y,n),satz221d(y,z,n,o),tris(cx,ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n)))):is(ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n))
+satz246a:=tris(cx,ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n),isov12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y),satz221d(z,y,o,n),satz221d(y,z,n,o)),satz246):is(ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(x,y,n))
+z@[u:complex][n:nis(y,0c)][o:nis(u,0c)]
++5247
+t1:=tr3is(cx,ts(ov(z,u,o),ts(u,y)),ts(ts(ov(z,u,o),u),y),ts(z,y),ts(y,z),assts2(ov(z,u,o),u,y),ists1(ts(ov(z,u,o),u),z,y,satz240(z,u,o)),comts(z,y)):is(ts(ov(z,u,o),ts(u,y)),ts(y,z))
+t2:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ts(ov(x,y,n),ov(z,u,o)),ts(u,y)),ts(ov(x,y,n),ts(ov(z,u,o),ts(u,y))),ts(ov(x,y,n),ts(y,z)),ists2(ts(y,u),ts(u,y),ts(ov(x,y,n),ov(z,u,o)),comts(y,u)),assts1(ov(x,y,n),ov(z,u,o),ts(u,y)),ists2(ts(ov(z,u,o),ts(u,y)),ts(y,z),ov(x,y,n),t1)):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)))
+t3:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),t2,assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n))):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(x,z))
+-5247
+satz247:=satz229j(ts(x,z),ts(y,u),ts(ov(x,y,n),ov(z,u,o)),satz221d(y,u,n,o),t3".5247"):is(ts(ov(x,y,n),ov(z,u,o)),ov(ts(x,z),ts(y,u),satz221d(y,u,n,o)))
+u@[n:nis(y,0c)][o:nis(z,0c)][p:nis(u,0c)]
++5248
+t1:=tris(cx,ts(ts(x,u),z),ts(x,ts(u,z)),ts(x,ts(z,u)),assts1(x,u,z),ists2(ts(u,z),ts(z,u),x,comts(u,z))):is(ts(ts(x,u),z),ts(x,ts(z,u)))
+t2:=tr3is(cx,ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(ts(ts(x,u),z),ts(ts(y,z),u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p)),ov(ts(x,ts(z,u)),ts(y,ts(z,u)),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),ov(x,y,n),satz247(ts(x,u),ts(y,z),z,u,satz221d(y,z,n,o),p),isov12(ts(ts(x,u),z),ts(x,ts(z,u)),ts(ts(y,z),u),ts(y,ts(z,u)),t1,assts1(y,z,u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),satz246(x,y,ts(z,u),n,satz221d(z,u,o,p))):is(ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(x,y,n))
+-5248
+satz248:=satz229k(ov(x,y,n),ov(z,u,p),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),lemma6(z,u,o,p),t2".5248"):is(ov(ov(x,y,n),ov(z,u,p),lemma6(z,u,o,p)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)))
+x@[n:nis(x,0c)]
+satz249:=satz229h(0c,x,0c,n,satz221b(x,0c,refis(cx,0c))):is(ov(0c,x,n),0c)
+satz250:=satz229h(x,x,1c,n,satz222(x)):is(ov(x,x,n),1c)
+y@[n:nis(y,0c)][i:is(x,y)]
+satz251a:=tris(cx,ov(x,y,n),ov(x,x,th2"e.notis"(cx,y,0c,x,n,i)),1c,isov2(y,x,x,symis(cx,x,y,i),n,th2"e.notis"(cx,y,0c,x,n,i)),satz250(x,th2"e.notis"(cx,y,0c,x,n,i))):is(ov(x,y,n),1c)
+n@[i:is(ov(x,y,n),1c)]
+satz251b:=tr3is(cx,x,ts(y,ov(x,y,n)),ts(y,1c),y,satz229d(x,y,n),ists2(ov(x,y,n),1c,y,i),satz222(y)):is(x,y)
+u@[n:nis(y,0c)][o:nis(u,0c)][i:is(ov(x,y,n),ov(z,u,o))]
++5252
+[j:is(z,0c)]
+t1:=tr3is(cx,ov(x,y,n),ov(z,u,o),ov(0c,u,o),0c,i,isov1(z,0c,u,j,o),satz249(u,o)):is(ov(x,y,n),0c)
+t2:=tris(cx,x,ts(y,ov(x,y,n)),0c,satz229d(x,y,n),satz221b(y,ov(x,y,n),t1)):is(x,0c)
+t3:=tris2(cx,ts(x,u),ts(y,z),0c,satz221a(x,u,t2),satz221b(y,z,j)):is(ts(x,u),ts(y,z))
+i@[p:nis(z,0c)]
+t4:=tris1(cx,ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),satz248(x,y,z,u,n,p,o),satz251a(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),i)):is(ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c)
+t5:=satz251b(ts(x,u),ts(y,z),satz221d(y,z,n,p),t4):is(ts(x,u),ts(y,z))
+-5252
+satz252a:=th1"l.imp"(is(z,0c),is(ts(x,u),ts(y,z)),[t:is(z,0c)]t3".5252"(t),[t:nis(z,0c)]t5".5252"(t)):is(ts(x,u),ts(y,z))
+o@[i:is(ts(x,u),ts(y,z))]
++*5252
+i@[j:is(z,0c)]
+t6:=tris(cx,ts(x,u),ts(y,z),0c,i,satz221b(y,z,j)):is(ts(x,u),0c)
+t7:=ore1(is(x,0c),is(u,0c),satz221c(x,u,t6),o):is(x,0c)
+t8:=tris2(cx,ov(x,y,n),ov(z,u,o),0c,tris(cx,ov(x,y,n),ov(0c,y,n),0c,isov1(x,0c,y,t7,n),satz249(y,n)),tris(cx,ov(z,u,o),ov(0c,u,o),0c,isov1(z,0c,u,j,o),satz249(u,o))):is(ov(x,y,n),ov(z,u,o))
+i@[p:nis(z,0c)]
+t9:=tris(cx,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,satz248(x,y,z,u,n,p,o),satz251a(ts(x,u),ts(y,z),satz221d(y,z,n,p),i)):is(ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),1c)
+t10:=satz251b(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),t9):is(ov(x,y,n),ov(z,u,o))
+-5252
+i@satz252b:=th1"l.imp"(is(z,0c),is(ov(x,y,n),ov(z,u,o)),[t:is(z,0c)]t8".5252"(t),[t:nis(z,0c)]t10".5252"(t)):is(ov(x,y,n),ov(z,u,o))
+z@[n:nis(y,0c)]
+satz253:=satz229g(pl(x,z),y,pl(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,pl(ov(x,y,n),ov(z,y,n))),pl(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),pl(x,z),disttp2(y,ov(x,y,n),ov(z,y,n)),ispl12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(pl(ov(x,y,n),ov(z,y,n)),ov(pl(x,z),y,n))
+z@[n:nis(z,0c)]
+distop:=symis(cx,pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n),satz253(x,z,y,n)):is(ov(pl(x,y),z,n),pl(ov(x,z,n),ov(y,z,n)))
+distpo:=satz253(x,z,y,n):is(pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n))
+u@[n:nis(y,0c)][o:nis(u,0c)]
+satz254:=tris1(cx,pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),pl(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ispl12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz253(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
+z@[n:nis(y,0c)]
+satz255:=satz229g(mn(x,z),y,mn(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,mn(ov(x,y,n),ov(z,y,n))),mn(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),mn(x,z),disttm2(y,ov(x,y,n),ov(z,y,n)),ismn12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(mn(ov(x,y,n),ov(z,y,n)),ov(mn(x,z),y,n))
+z@[n:nis(z,0c)]
+distom:=symis(cx,mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n),satz255(x,z,y,n)):is(ov(mn(x,y),z,n),mn(ov(x,z,n),ov(y,z,n)))
+distmo:=satz255(x,z,y,n):is(mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n))
+u@[n:nis(y,0c)][o:nis(u,0c)]
+satz256:=tris1(cx,mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),mn(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ismn12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz255(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
+x@conj:=pli(re(x),m0"r"(im(x))):complex
+b@conjisa:=isrecx12(re(pli(a,b)),a,m0"r"(im(pli(a,b))),m0"r"(b),reis(a,b),ism0"r"(im(pli(a,b)),b,imis(a,b))):is(conj(pli(a,b)),pli(a,m0"r"(b)))
+conjisb:=symis(cx,conj(pli(a,b)),pli(a,m0"r"(b)),conjisa):is(pli(a,m0"r"(b)),conj(pli(a,b)))
+y@[i:is(x,y)]
+isconj:=isf(cx,cx,[t:cx]conj(t),x,y,i):is(conj(x),conj(y))
+x@satz257:=tr3is(cx,conj(conj(x)),pli(re(x),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,conjisa(re(x),m0"r"(im(x))),isrecx2(m0"r"(m0"r"(im(x))),im(x),re(x),satz177(im(x))),pliis(x)):is(conj(conj(x)),x)
+[i:is(x,0c)]
+satz258a:=tr3is(cx,conj(x),conj(0c),pli(0,m0"r"(0)),0c,isconj(x,0c,i),conjisa(0,0),isrecx2(m0"r"(0),0,0,satz176b(0,refis(real,0)))):is(conj(x),0c)
+x@[i:is(conj(x),0c)]
++6258
+t1:=tris(real,re(x),re(conj(x)),0,isre(re(x),m0"r"(im(x))),lemma1(conj(x),i)):is"r"(re(x),0)
+t2:=satz176e(im(x),tris(real,m0"r"(im(x)),im(conj(x)),0,isim(re(x),m0"r"(im(x))),lemma2(conj(x),i))):is"r"(im(x),0)
+-6258
+satz258b:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t1".6258",t2".6258")):is(x,0c)
++*6258
+i@anders:=tris1(cx,x,0c,conj(conj(x)),satz257,satz258a(conj(x),i)):is(x,0c)
+-6258
+x@[n:nis(x,0c)]
+satz258c:=th3"l.imp"(is(conj(x),0c),is(x,0c),n,[t:is(conj(x),0c)]satz258b(t)):nis(conj(x),0c)
+x@[i:is(conj(x),x)]
++6259
+t1:=tris(real,m0"r"(im(x)),im(conj(x)),im(x),isim(re(x),m0"r"(im(x))),isceim(conj(x),x,i)):is"r"(m0"r"(im(x)),im(x))
+-6259
+satz259a:=lemma10(im(x),symis(real,m0"r"(im(x)),im(x),t1".6259")):is"r"(im(x),0)
+x@[i:is"r"(im(x),0)]
+satz259b:=tris(cx,conj(x),pli(re(x),im(x)),x,isrecx2(m0"r"(im(x)),im(x),re(x),tris2(real,m0"r"(im(x)),im(x),0,satz176b(im(x),i),i)),pliis(x)):is(conj(x),x)
+x@[i:is(x,conj(x))]
+satz269c:=satz259a(x,symis(cx,x,conj(x),i)):is"r"(im(x),0)
+x@[i:is"r"(im(x),0)]
+satz269d:=symis(cx,conj(x),x,satz259b(i)):is(x,conj(x))
+y@satz260:=tr3is(cx,conj(pl(x,y)),pli(pl"r"(re(x),re(y)),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(re(x),re(y)),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(conj(x),conj(y)),conjisa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx2(m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),pl"r"(re(x),re(y)),satz180(im(x),im(y))),plis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(pl(x,y)),pl(conj(x),conj(y)))
+satz260a:=symis(cx,conj(pl(x,y)),pl(conj(x),conj(y)),satz260):is(pl(conj(x),conj(y)),conj(pl(x,y)))
++6261
+t1:=tris(real,m0"r"(imts(x,y)),pl"r"(m0"r"(ts"r"(re(x),im(y))),m0"r"(ts"r"(im(x),re(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),satz180(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(m0"r"(ts"r"(re(x),im(y))),ts"r"(re(x),m0"r"(im(y))),m0"r"(ts"r"(im(x),re(y))),ts"r"(m0"r"(im(x)),re(y)),satz197f(re(x),im(y)),satz197e(im(x),re(y)))):is"r"(m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))))
+-6261
+satz261:=tr3is(cx,conj(ts(x,y)),pli(rets(x,y),m0"r"(imts(x,y))),pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y)))),ts(conj(x),conj(y)),conjisa(rets(x,y),imts(x,y)),isrecx12(rets(x,y),mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),ismn2"r"(ts"r"(im(x),im(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y))),ts"r"(re(x),re(y)),satz198a(im(x),im(y))),t1".6261"),tsis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(ts(x,y)),ts(conj(x),conj(y)))
+satz261a:=symis(cx,conj(ts(x,y)),ts(conj(x),conj(y)),satz261):is(ts(conj(x),conj(y)),conj(ts(x,y)))
++6262
+t1:=symis(cx,pl(mn(x,y),y),x,satz230(x,y)):is(x,pl(mn(x,y),y))
+t2:=tris(cx,conj(x),conj(pl(mn(x,y),y)),pl(conj(mn(x,y)),conj(y)),isconj(x,pl(mn(x,y),y),t1),satz260(mn(x,y),y)):is(conj(x),pl(conj(mn(x,y)),conj(y)))
+-6262
+satz262:=satz212f(conj(x),conj(y),conj(mn(x,y)),symis(cx,conj(x),pl(conj(mn(x,y)),conj(y)),t2".6262")):is(conj(mn(x,y)),mn(conj(x),conj(y)))
+satz262a:=symis(cx,conj(mn(x,y)),mn(conj(x),conj(y)),satz262):is(mn(conj(x),conj(y)),conj(mn(x,y)))
+[n:nis(y,0c)]
++6263
+t1:=satz229f(x,y,n):is(x,ts(ov(x,y,n),y))
+t2:=isconj(x,ts(ov(x,y,n),y),t1):is(conj(x),conj(ts(ov(x,y,n),y)))
+t3:=satz261(ov(x,y,n),y):is(conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)))
+t4:=tris(cx,conj(x),conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)),t2,t3):is(conj(x),ts(conj(ov(x,y,n)),conj(y)))
+t5:=satz258c(y,n):nis(conj(y),0c)
+-6263
+satz263:=satz229j(conj(x),conj(y),conj(ov(x,y,n)),t5".6263",symis(cx,conj(x),ts(conj(ov(x,y,n)),conj(y)),t4".6263")):is(conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)))
+satz263a:=symis(cx,conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)),satz263):is(ov(conj(x),conj(y),satz258c(y,n)),conj(ov(x,y,n)))
+x@mod:=sqrt(mod2(x),lemma5(x)):real
+y@[i:is(x,y)]
+ismod:=isf(cx,real,[t:cx]mod(t),x,y,i):is"r"(mod(x),mod(y))
+x@[n:nis(x,0c)]
+satz264a:=sqrtnot0(mod2(x),lemma5(x),pnot0(mod2(x),lemma4(x,n))):pos(mod(x))
+x@[i:is(x,0c)]
+satz264b:=sqrt0(mod2(x),lemma5(x),lemma3(x,i)):is"r"(mod(x),0)
+x@satz264c:=thsqrt1a(mod2(x),lemma5(x)):not(neg(mod(x)))
+satz264d:=satz167f(mod(x),0,th3"l.imp"(less(mod(x),0),neg(mod(x)),satz264c,[t:less(mod(x),0)]satz169d(mod(x),t))):moreis(mod(x),0)
++7265
+t1:=symis(real,ts"r"(mod(x),mod(x)),mod2(x),thsqrt1b(mod2(x),lemma5(x))):is"r"(mod2(x),ts"r"(mod(x),mod(x)))
+t2:=tris(real,pl"r"(ts"r"(re(x),re(x)),0),ts"r"(re(x),re(x)),ts"r"(abs(re(x)),abs(re(x))),pl02(ts"r"(re(x),re(x)),0,refis(real,0)),lemma12"r"(re(x))):is"r"(pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))))
+t3:=satz191(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),ts"r"(im(x),im(x)),0,moreisi2(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),refis(real,ts"r"(re(x),re(x)))),lemma11"r"(im(x))):moreis(mod2(x),pl"r"(ts"r"(re(x),re(x)),0))
+t4:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))),t1,t2,t3):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(re(x)),abs(re(x))))
+t5:=tris(real,pl"r"(0,ts"r"(im(x),im(x))),ts"r"(im(x),im(x)),ts"r"(abs(im(x)),abs(im(x))),pl01(0,ts"r"(im(x),im(x)),refis(real,0)),lemma12"r"(im(x))):is"r"(pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))))
+t6:=satz191(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),lemma11"r"(re(x)),moreisi2(ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),refis(real,ts"r"(im(x),im(x))))):moreis(mod2(x),pl"r"(0,ts"r"(im(x),im(x))))
+t7:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))),t1,t5,t6):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(im(x)),abs(im(x))))
+@[r:real][s:real][m:moreis(ts"r"(r,r),ts"r"(s,s))][n:moreis(r,0)][l:less(r,s)]
+t8:=lemma2"r"(r,s,l):more(s,r)
+t9:=satz169b(s,satz172d(s,r,0,t8,n)):pos(s)
+[o:more(r,0)]
+t10:=trmore(ts"r"(s,s),ts"r"(r,s),ts"r"(r,r),satz203a(s,r,s,t8,t9),satz203d(s,r,r,t8,satz169b(r,o))):more(ts"r"(s,s),ts"r"(r,r))
+l@[i:is"r"(r,0)]
+t11:=ismore2(0,ts"r"(r,r),ts"r"(s,s),symis(real,ts"r"(r,r),0,ts01(r,r,i)),satz169a(ts"r"(s,s),possq(s,pnot0(s,t9)))):more(ts"r"(s,s),ts"r"(r,r))
+l@t12:=lemma1"r"(ts"r"(s,s),ts"r"(r,r),orapp(more(r,0),is"r"(r,0),more(ts"r"(s,s),ts"r"(r,r)),n,[t:more(r,0)]t10(t),[t:is"r"(r,0)]t11(t))):less(ts"r"(r,r),ts"r"(s,s))
+n@t13:=satz167f(r,s,[t:less(r,s)]<t12(t)>satz167c(ts"r"(r,r),ts"r"(s,s),m)):moreis(r,s)
+-7265
+satz265a:=t13".7265"(mod(x),abs(re(x)),t4".7265",satz264d(x)):moreis(mod(x),abs(re(x)))
+satz265b:=t13".7265"(mod(x),abs(im(x)),t7".7265",satz264d(x)):moreis(mod(x),abs(im(x)))
+@[r:real][s:real][i:is(ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)))][n:not(neg(r))][o:not(neg(s))]
++7266
+@[t:real]
+t1:=pl02(ts"r"(t,t),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t))
+t2:=tris(real,pl"r"(ts"r"(t,0),ts"r"(0,t)),ts"r"(t,0),0,pl02(ts"r"(t,0),ts"r"(0,t),ts01(0,t,refis(real,0))),ts02(t,0,refis(real,0))):is"r"(pl"r"(ts"r"(t,0),ts"r"(0,t)),0)
+t3:=tris(cx,ts(pli(t,0),pli(t,0)),pli(mn"r"(ts"r"(t,t),ts"r"(0,0)),pl"r"(ts"r"(t,0),ts"r"(0,t))),pli(ts"r"(t,t),0),tsis12a(t,0,t,0),isrecx12(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t),pl"r"(ts"r"(t,0),ts"r"(0,t)),0,t1,t2)):is(ts(pli(t,0),pli(t,0)),pli(ts"r"(t,t),0))
+o@t4:=tr3is(cx,pli(ts"r"(r,r),0),ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)),pli(ts"r"(s,s),0),symis(cx,ts(pli(r,0),pli(r,0)),pli(ts"r"(r,r),0),t3(r)),i,t3(s)):is(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0))
+t5:=tr3is(real,ts"r"(r,r),re(pli(ts"r"(r,r),0)),re(pli(ts"r"(s,s),0)),ts"r"(s,s),isre(ts"r"(r,r),0),iscere(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0),t4),reis(ts"r"(s,s),0)):is"r"(ts"r"(r,r),ts"r"(s,s))
+t6:=andi(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)),n,t5):and(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)))
+t7:=andi(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)),o,refis(real,ts"r"(s,s))):and(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)))
+-7266
+satz266:=satzr161b(ts"r"(s,s),r,s,t6".7266",t7".7266"):is"r"(r,s)
++7267
+x@t1:=tris(cx,ts(pli(mod(x),0),pli(mod(x),0)),pli(ts"r"(mod(x),mod(x)),0),pli(mod2(x),0),t3"c.7266"(mod(x)),isrecx1(ts"r"(mod(x),mod(x)),mod2(x),0,thsqrt1b(mod2(x),lemma5(x)))):is(ts(pli(mod(x),0),pli(mod(x),0)),pli(mod2(x),0))
+t2:=ispl2"r"(m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(im(x),im(x)),ts"r"(re(x),re(x)),tris(real,m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),satz197e(im(x),m0"r"(im(x))),satz198(im(x),im(x)))):is"r"(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x))
+t3:=tris(real,pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),pl"r"(m0"r"(ts"r"(re(x),im(x))),ts"r"(re(x),im(x))),0,ispl12"r"(ts"r"(re(x),m0"r"(im(x))),m0"r"(ts"r"(re(x),im(x))),ts"r"(im(x),re(x)),ts"r"(re(x),im(x)),satz197b(re(x),im(x)),comts"r"(im(x),re(x))),satz179a(ts"r"(re(x),im(x)))):is"r"(pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0)
+t4:=tris(cx,ts(x,conj(x)),pli(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x)))),pli(mod2(x),0),tsis2a(x,re(x),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0,t2,t3)):is(ts(x,conj(x)),pli(mod2(x),0))
+-7267
+x@satz267:=tris2(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),pli(mod2(x),0),t1".7267",t4".7267"):is(ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)))
+satz267a:=symis(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),satz267):is(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)))
++7268
+z@t1:=tr3is(cx,ts(x,ts(y,z)),ts(ts(x,y),z),ts(ts(y,x),z),ts(y,ts(x,z)),assts2(x,y,z),ists1(ts(x,y),ts(y,x),z,comts(x,y)),assts1(y,x,z)):is(ts(x,ts(y,z)),ts(y,ts(x,z)))
+[u:complex]
+t2:=tr3is(cx,ts(ts(x,y),ts(z,u)),ts(x,ts(y,ts(z,u))),ts(x,ts(z,ts(y,u))),ts(ts(x,z),ts(y,u)),assts1(x,y,ts(z,u)),ists2(ts(y,ts(z,u)),ts(z,ts(y,u)),x,t1(y,z,u)),assts2(x,z,ts(y,u))):is(ts(ts(x,y),ts(z,u)),ts(ts(x,z),ts(y,u)))
+y@t3:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,y),conj(ts(x,y))),ts(ts(x,y),ts(conj(x),conj(y))),ts(ts(x,conj(x)),ts(y,conj(y))),satz267(ts(x,y)),ists2(conj(ts(x,y)),ts(conj(x),conj(y)),ts(x,y),satz261(x,y)),t2(x,y,conj(x),conj(y))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))))
+t4:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))),ts(ts(pli(mod(x),0),pli(mod(x),0)),ts(pli(mod(y),0),pli(mod(y),0))),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),t3,ists12(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)),ts(y,conj(y)),ts(pli(mod(y),0),pli(mod(y),0)),satz267a(x),satz267a(y)),t2(pli(mod(x),0),pli(mod(x),0),pli(mod(y),0),pli(mod(y),0))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))))
+@[r:real][s:real]
+t5:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
+t6:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
+t7:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t5,t6)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
+y@t8:=tris(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)),t4,ists12(ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),t7(mod(x),mod(y)),t7(mod(x),mod(y)))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)))
+[n:neg(ts"r"(mod(x),mod(y)))]
+t9:=orapp(and(pos(mod(x)),neg(mod(y))),and(neg(mod(x)),pos(mod(y))),con,satz196h(mod(x),mod(y),n),[t:and(pos(mod(x)),neg(mod(y)))]<ande2(pos(mod(x)),neg(mod(y)),t)>satz264c(y),[t:and(neg(mod(x)),pos(mod(y)))]<ande1(neg(mod(x)),pos(mod(y)),t)>satz264c(x)):con
+-7268
+y@satz268:=satz266(mod(ts(x,y)),ts"r"(mod(x),mod(y)),t8".7268",satz264c(ts(x,y)),[t:neg(ts"r"(mod(x),mod(y)))]t9".7268"(t)):is"r"(mod(ts(x,y)),ts"r"(mod(x),mod(y)))
+satz268a:=symis(real,mod(ts(x,y)),ts"r"(mod(x),mod(y)),satz268):is"r"(ts"r"(mod(x),mod(y)),mod(ts(x,y)))
+[n:nis(y,0c)]
++7269
+t1:=pnot0(mod(y),satz264a(y,n)):nis"r"(mod(y),0)
+t2:=tris1(real,ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),mod(ts(ov(x,y,n),y)),satz268(ov(x,y,n),y),ismod(ts(ov(x,y,n),y),x,satz240(x,y,n))):is"r"(ts"r"(mod(ov(x,y,n)),mod(y)),mod(x))
+t3:=satz204g(mod(x),mod(y),mod(ov(x,y,n)),t1,tris(real,ts"r"(mod(y),mod(ov(x,y,n))),ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),comts"r"(mod(y),mod(ov(x,y,n))),t2)):is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),t1))
+-7269
+satz269:=t3".7269":is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),pnot0(mod(y),satz264a(y,n))))
+y@[i:is(pl(x,y),1c)]
++7270
+@[r:real]
+t1:=th1"l.imp"(neg(r),moreis(abs(r),r),[t:neg(r)]moreisi1(abs(r),r,trmore(abs(r),0,r,satz169a(abs(r),satz166b(r,t)),lemma2"r"(r,0,satz169c(r,t)))),[t:not(neg(r))]moreisi2(abs(r),r,absnn(r,t))):moreis(abs(r),r)
+x@t2:=trmoreis(mod(x),abs(re(x)),re(x),satz265a(x),t1(re(x))):moreis(mod(x),re(x))
+i@t3:=tr3is(real,pl"r"(re(x),re(y)),re(pl(x,y)),re(1c),1rl,isre(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),iscere(pl(x,y),1c,i),reis(1rl,0)):is"r"(pl"r"(re(x),re(y)),1rl)
+-7270
+satz270:=ismoreis2(pl"r"(re(x),re(y)),1rl,pl"r"(mod(x),mod(y)),t3".7270",satz191(mod(x),re(x),mod(y),re(y),t2".7270",t2".7270"(y))):moreis(pl"r"(mod(x),mod(y)),1rl)
++7271
+y@[i:is(pl(x,y),0c)]
+t1:=satz264b(pl(x,y),i):is"r"(mod(pl(x,y)),0)
+t2:=ismoreis2(pl"r"(0,0),mod(pl(x,y)),pl"r"(mod(x),mod(y)),tris2(real,pl"r"(0,0),mod(pl(x,y)),0,pl01(0,0,refis(real,0)),t1),satz191(mod(x),0,mod(y),0,satz264d(x),satz264d(y))):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
+y@[n:nis(pl(x,y),0c)]
+t3:=pnot0(mod(pl(x,y)),satz264a(pl(x,y),n)):nis"r"(mod(pl(x,y)),0)
+t4:=tris(cx,pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),ov(pl(x,y),pl(x,y),n),1c,satz253(x,pl(x,y),y,n),satz250(pl(x,y),n)):is(pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),1c)
+t5:=satz270(ov(x,pl(x,y),n),ov(y,pl(x,y),n),t4):moreis(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),1rl)
+fx:=ov"r"(mod(x),mod(pl(x,y)),t3):real
+fy:=ov"r"(mod(y),mod(pl(x,y)),t3):real
+t6:=ismoreis1(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),pl"r"(fx,fy),1rl,ispl12"r"(mod(ov(x,pl(x,y),n)),fx,mod(ov(y,pl(x,y),n)),fy,satz269(x,pl(x,y),n),satz269(y,pl(x,y),n)),t5):moreis(pl"r"(fx,fy),1rl)
+prl:=ts"r"(pl"r"(fx,fy),mod(pl(x,y))):real
+prr:=ts"r"(1rl,mod(pl(x,y))):real
+t7:=orapp(more(pl"r"(fx,fy),1rl),is"r"(pl"r"(fx,fy),1rl),moreis(prl,prr),t6,[t:more(pl"r"(fx,fy),1rl)]moreisi1(prl,prr,satz203a(pl"r"(fx,fy),1rl,mod(pl(x,y)),t,satz264a(pl(x,y),n))),[t:is"r"(pl"r"(fx,fy),1rl)]moreisi2(prl,prr,ists1"r"(pl"r"(fx,fy),1rl,mod(pl(x,y)),t))):moreis(prl,prr)
+t8:=tris(real,prl,pl"r"(ts"r"(fx,mod(pl(x,y))),ts"r"(fy,mod(pl(x,y)))),pl"r"(mod(x),mod(y)),disttp1"r"(fx,fy,mod(pl(x,y))),ispl12"r"(ts"r"(fx,mod(pl(x,y))),mod(x),ts"r"(fy,mod(pl(x,y))),mod(y),satz204e(mod(x),mod(pl(x,y)),t3),satz204e(mod(y),mod(pl(x,y)),t3))):is"r"(prl,pl"r"(mod(x),mod(y)))
+t9:=satz195b(mod(pl(x,y))):is"r"(prr,mod(pl(x,y)))
+t10:=ismoreis12(prl,pl"r"(mod(x),mod(y)),prr,mod(pl(x,y)),t8,t9,t7):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
+y@t11:=th1"l.imp"(is(pl(x,y),0c),moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y))),[t:is(pl(x,y),0c)]t2(t),[t:nis(pl(x,y),0c)]t10(t)):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
+-7271
+y@satz271:=satz168a(pl"r"(mod(x),mod(y)),mod(pl(x,y)),t11".7271"):lessis(mod(pl(x,y)),pl"r"(mod(x),mod(y)))
+satz271a:=t11".7271":moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
++7272
+x@t1:=tris(real,re(m0(x)),re(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(re(x)),iscere(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),reis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(re(m0(x)),m0"r"(re(x)))
+t2:=tris(real,ts"r"(re(m0(x)),re(m0(x))),ts"r"(m0"r"(re(x)),m0"r"(re(x))),ts"r"(re(x),re(x)),ists12"r"(re(m0(x)),m0"r"(re(x)),re(m0(x)),m0"r"(re(x)),t1,t1),satz198(re(x),re(x))):is"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)))
+t3:=tris(real,im(m0(x)),im(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(im(x)),isceim(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),imis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(im(m0(x)),m0"r"(im(x)))
+t4:=tris(real,ts"r"(im(m0(x)),im(m0(x))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),ists12"r"(im(m0(x)),m0"r"(im(x)),im(m0(x)),m0"r"(im(x)),t3,t3),satz198(im(x),im(x))):is"r"(ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)))
+t5:=ispl12"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)),ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)),t2,t4):is"r"(mod2(m0(x)),mod2(x))
+-7272
+x@satz272:=issqrt(mod2(m0(x)),mod2(x),lemma5(m0(x)),lemma5(x),t5".7272"):is"r"(mod(m0(x)),mod(x))
+satz272a:=symis(real,mod(m0(x)),mod(x),satz272):is"r"(mod(x),mod(m0(x)))
++7273
+y@sum:=pl"r"(mod(y),mod(mn(x,y))):real
+t1:=islessis1(mod(pl(y,mn(x,y))),mod(x),sum,ismod(pl(y,mn(x,y)),x,satz212h(x,y)),satz271(y,mn(x,y))):lessis(mod(x),sum)
+t2:=th9"l.or"(less(mod(x),sum),is"r"(mod(x),sum),less(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),is"r"(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),t1,[t:less(mod(x),sum)]satz188f(mod(x),sum,m0"r"(mod(y)),t),[t:is"r"(mod(x),sum)]ismn1"r"(mod(x),sum,mod(y),t)):lessis(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y)))
+t3:=tris(real,mn"r"(sum,mod(y)),mn"r"(pl"r"(mod(mn(x,y)),mod(y)),mod(y)),mod(mn(x,y)),ismn1"r"(sum,pl"r"(mod(mn(x,y)),mod(y)),mod(y),compl"r"(mod(y),mod(mn(x,y)))),mnpl(mod(mn(x,y)),mod(y))):is"r"(mn"r"(sum,mod(y)),mod(mn(x,y)))
+t4:=satz168b(mn"r"(mod(x),mod(y)),mod(mn(x,y)),islessis2(mn"r"(sum,mod(y)),mod(mn(x,y)),mn"r"(mod(x),mod(y)),t3,t2)):moreis(mod(mn(x,y)),mn"r"(mod(x),mod(y)))
+t5:=ismoreis12(mod(mn(y,x)),mod(mn(x,y)),mn"r"(mod(y),mod(x)),m0"r"(mn"r"(mod(x),mod(y))),tris1(real,mod(mn(y,x)),mod(mn(x,y)),mod(m0(mn(x,y))),ismod(m0(mn(x,y)),mn(y,x),satz219(x,y)),satz272(mn(x,y))),satz181a(mod(y),mod(x)),t4(y,x)):moreis(mod(mn(x,y)),m0"r"(mn"r"(mod(x),mod(y))))
+@[r:real][s:real][m:moreis(r,s)][n:moreis(r,m0"r"(s))]
+r@t6:=th9"l.or"(neg(r),not(neg(r)),is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r),th6"l.or"(neg(r)),[t:neg(r)]absn(r,t),[t:not(neg(r))]absnn(r,t)):or(is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r))
+n@t7:=orapp(is"r"(abs(s),m0"r"(s)),is"r"(abs(s),s),moreis(r,abs(s)),t6(s),[t:is"r"(abs(s),m0"r"(s))]ismoreis2(m0"r"(s),abs(s),r,symis(real,abs(s),m0"r"(s),t),n),[t:is"r"(abs(s),s)]ismoreis2(s,abs(s),r,symis(real,abs(s),s,t),m)):moreis(r,abs(s))
+-7273
+y@satz273:=t7".7273"(mod(mn(x,y)),mn"r"(mod(x),mod(y)),t4".7273",t5".7273"):moreis(mod(mn(x,y)),abs(mn"r"(mod(x),mod(y))))
+-c
+-r
+-rp
+-rt
+@[x:nat][y:nat]
++8274
+prop1:=some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)):'prop'
+x@prop2:=all([y:nat]imp(less(x,y),not(prop1(y)))):'prop'
+@[y:nat][l:less(1,y)][f:[t:1to(1)]1to(y)]
+1y:=1out(y):1to(y)
+yy:=xout(y):1to(y)
+[i:is"e"(1to(y),1y,yy)]
+t1:=isoutne(y,1,satz24a(y),y,lessisi3(y),i):is(1,y)
+f@t2:=ec3e31(is(1,y),more(1,y),less(1,y),satz10b(1,y),l):nis(1,y)
+t3:=th3"l.imp"(is"e"(1to(y),1y,yy),is(1,y),t2,[t:is"e"(1to(y),1y,yy)]t1(t)):not(is"e"(1to(y),1y,yy))
+[u:1to(1)]
+t4:=isf(1to(1),1to(y),f,u,1o,th1"n.singlet"(u)):is"e"(1to(y),<u>f,<1o>f)
+f@[i:is"e"(1to(y),<1o>f,1y)][u:1to(1)]
+t5:=th2"e.notis"(1to(y),1y,yy,<u>f,t3,tris(1to(y),<u>f,<1o>f,1y,t4(u),i)):not(is"e"(1to(y),<u>f,yy))
+i@t6:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),yy,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,yy,t5(u))):not(image(1to(1),1to(y),f,yy))
+t7:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),yy,t6):not(surjective(1to(1),1to(y),f))
+f@[n:not(is"e"(1to(y),<1o>f,1y))][u:1to(1)]
+t8:=th2"e.notis"(1to(y),<1o>f,1y,<u>f,n,t4(u)):not(is"e"(1to(y),<u>f,1y))
+n@t9:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),1y,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,1y,t8(u))):not(image(1to(1),1to(y),f,1y))
+t10:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),1y,t9):not(surjective(1to(1),1to(y),f))
+f@t11:=th1"l.imp"(is"e"(1to(y),<1o>f,1y),not(surjective(1to(1),1to(y),f)),[t:is"e"(1to(y),<1o>f,1y)]t7(t),[t:not(is"e"(1to(y),<1o>f,1y))]t10(t)):not(surjective(1to(1),1to(y),f))
+t12:=th2"l.and"(injective(1to(1),1to(y),f),surjective(1to(1),1to(y),f),t11):not(bijective(1to(1),1to(y),f))
+l@t13:=th5"l.some"([t:1to(1)]1to(y),[f:[t:1to(1)]1to(y)]bijective(1to(1),1to(y),f),[f:[t:1to(1)]1to(y)]t12(f)):not(prop1(1,y))
+@t14:=[y:nat][t:less(1,y)]t13(y,t):prop2(1)
+x@[p:prop2(x)][y:nat][l:less(<x>suc,y)]
+x@xs:=<x>suc:nat
+l@xxs:=xout(xs):1to(<x>suc)
+yy1:=xout(y):1to(y)
+t15:=trless(1,<x>suc,y,satz24c(x),l):less(1,y)
+ym1:=mn(y,1,t15):nat
+t16:=isless12(<x>suc,pl(x,1),y,pl(ym1,1),satz4e(x),th1c"n.mn"(y,1,t15),l):less(pl(x,1),pl(ym1,1))
+t17:=satz20c(x,ym1,1,t16):less(x,ym1)
+t18:=isless2(pl(ym1,1),y,ym1,th1d"n.mn"(y,1,t15),satz18a(ym1,1)):less(ym1,y)
+[f:[t:1to(xs)]1to(y)][b:bijective(1to(xs),1to(y),f)]
+t19:=ande1(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):injective(1to(xs),1to(y),f)
+t20:=ande2(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):surjective(1to(xs),1to(y),f)
+[i:is"e"(1to(y),<xxs>f,yy1)][u:1to(x)]
+u1:=inn(x,u):nat
+t21:=satz16a(u1,x,xs,1top(x,u),satz18c(x)):less(u1,xs)
+t22:=ec3e31(is(u1,xs),more(u1,xs),less(u1,xs),satz10b(u1,xs),t21):nis(u1,xs)
+t23:=lessisi1(u1,xs,t21):lessis(u1,xs)
+u2:=outn(xs,u1,t23):1to(xs)
+t24:=th3"l.imp"(is"e"(1to(xs),u2,xxs),is(u1,xs),t22,[t:is"e"(1to(xs),u2,xxs)]isoutne(xs,u1,t23,xs,lessisi3(xs),t)):not(is"e"(1to(xs),u2,xxs))
+[j:is"e"(1to(y),<u2>f,yy1)]
+t25:=tris2(1to(y),<u2>f,<xxs>f,yy1,j,i):is"e"(1to(y),<u2>f,<xxs>f)
+t26:=isfe(1to(xs),1to(y),f,t19,u2,xxs,t25):is"e"(1to(xs),u2,xxs)
+u@t27:=th3"l.imp"(is"e"(1to(y),<u2>f,yy1),is"e"(1to(xs),u2,xxs),t24,[t:is"e"(1to(y),<u2>f,yy1)]t26(t)):not(is"e"(1to(y),<u2>f,yy1))
+w1:=inn(y,<u2>f):nat
+[j:is(w1,y)]
+t28:=tris(1to(y),<u2>f,outn(y,w1,1top(y,<u2>f)),yy1,isoutinn(y,<u2>f),isoutni(y,w1,1top(y,<u2>f),y,lessisi3(y),j)):is"e"(1to(y),<u2>f,yy1)
+u@t29:=th3"l.imp"(is(w1,y),is"e"(1to(y),<u2>f,yy1),t27,[t:is(w1,y)]t28(t)):nis(w1,y)
+t30:=ore1(less(w1,y),is(w1,y),1top(y,<u2>f),t29):less(w1,y)
+t31:=islessis2(y,pl(ym1,1),pl(w1,1),th1c"n.mn"(y,1,t15),satz25b(y,w1,t30)):lessis(pl(w1,1),pl(ym1,1))
+t32:=th9"l.or"(less(pl(w1,1),pl(ym1,1)),is(pl(w1,1),pl(ym1,1)),less(w1,ym1),is(w1,ym1),t31,[t:less(pl(w1,1),pl(ym1,1))]satz20c(w1,ym1,1,t),[t:is(pl(w1,1),pl(ym1,1))]satz20b(w1,ym1,1,t)):lessis(w1,ym1)
+w2:=outn(ym1,w1,t32):1to(ym1)
+i@f1:=[t:1to(x)]w2(t):[t:1to(x)]1to(ym1)
+u@[v:1to(x)][j:is"e"(1to(ym1),<u>f1,<v>f1)]
+t33:=isoutne(ym1,w1(u),t32(u),w1(v),t32(v),j):is(w1(u),w1(v))
+t34:=isinne(y,<u2(u)>f,<u2(v)>f,t33):is"e"(1to(y),<u2(u)>f,<u2(v)>f)
+t35:=<t34><u2(v)><u2(u)>t19:is"e"(1to(xs),u2(u),u2(v))
+t36:=isoutne(xs,u1(u),t23(u),u1(v),t23(v),t35):is(u1(u),u1(v))
+t37:=isinne(x,u,v,t36):is"e"(1to(x),u,v)
+i@[v:1to(ym1)]
+v1:=inn(ym1,v):nat
+t38:=satz16a(v1,ym1,y,1top(ym1,v),t18):less(v1,y)
+t39:=ec3e31(is(v1,y),more(v1,y),less(v1,y),satz10b(v1,y),t38):nis(v1,y)
+t40:=lessisi1(v1,y,t38):lessis(v1,y)
+v2:=outn(y,v1,t40):1to(y)
+w3:=<v2>invf(1to(xs),1to(y),f,b):1to(xs)
+t41:=thinvf2(1to(xs),1to(y),f,b,v2):is"e"(1to(y),v2,<w3>f)
+[j:is"e"(1to(xs),w3,xxs)]
+t42:=isf(1to(xs),1to(y),f,w3,xxs,j):is"e"(1to(y),<w3>f,<xxs>f)
+t43:=tr3is(1to(y),v2,<w3>f,<xxs>f,yy1,t41,t42,i):is"e"(1to(y),v2,yy1)
+t44:=isoutne(y,v1,t40,y,lessisi3(y),t43):is(v1,y)
+v@t45:=th3"l.imp"(is"e"(1to(xs),w3,xxs),is(v1,y),t39,[t:is"e"(1to(xs),w3,xxs)]t44(t)):not(is"e"(1to(xs),w3,xxs))
+w4:=inn(xs,w3):nat
+[j:is(w4,xs)]
+t46:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),xxs,isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),xs,lessisi3(xs),j)):is"e"(1to(xs),w3,xxs)
+v@t47:=th3"l.imp"(is(w4,xs),is"e"(1to(xs),w3,xxs),t45,[t:is(w4,xs)]t46(t)):nis(w4,xs)
+t48:=ore1(less(w4,xs),is(w4,xs),1top(xs,w3),t47):less(w4,xs)
+t49:=satz26a(x,w4,t48):lessis(w4,x)
+w5:=outn(x,w4,t49):1to(x)
+t50:=isinoutn(x,w4,t49):is(w4,u1(w5))
+t51:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),u2(w5),isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),u1(w5),t23(w5),t50)):is"e"(1to(xs),w3,u2(w5))
+t52:=isf(1to(xs),1to(y),f,w3,u2(w5),t51):is"e"(1to(y),<w3>f,<u2(w5)>f)
+t53:=tris(1to(y),v2,<w3>f,<u2(w5)>f,t41,t52):is"e"(1to(y),v2,<u2(w5)>f)
+t54:=tris(nat,v1,inn(y,v2),w1(w5),isinoutn(y,v1,t40),isinni(y,v2,<u2(w5)>f,t53)):is(v1,w1(w5))
+t55:=tris(1to(ym1),v,outn(ym1,v1,1top(ym1,v)),w2(w5),isoutinn(ym1,v),isoutni(ym1,v1,1top(ym1,v),w1(w5),t32(w5),t54)):is"e"(1to(ym1),v,<w5>f1)
+t56:=somei(1to(x),[t:1to(x)]is"e"(1to(ym1),v,<t>f1),w5,t55):image(1to(x),1to(ym1),f1,v)
+i@t57:=andi(injective(1to(x),1to(ym1),f1),surjective(1to(x),1to(ym1),f1),[u:1to(x)][v:1to(x)][t:is"e"(1to(ym1),<u>f1,<v>f1)]t37(u,v,t),[u:1to(ym1)]t56(u)):bijective(1to(x),1to(ym1),f1)
+t58:=somei([t:1to(x)]1to(ym1),[g:[t:1to(x)]1to(ym1)]bijective(1to(x),1to(ym1),g),f1,t57):prop1(ym1)
+t59:=<t58><t17><ym1>p:con
+b@[n:not(is"e"(1to(y),<xxs>f,yy1))]
+m0:=<yy1>invf(1to(xs),1to(y),f,b):1to(xs)
+t60:=thinvf2(1to(xs),1to(y),f,b,yy1):is"e"(1to(y),yy1,<m0>f)
+f2:=changef(1to(xs),1to(y),f,m0,xxs):[t:1to(xs)]1to(y)
+t61:=changef2(1to(xs),1to(y),f,m0,xxs,xxs,refis(1to(xs),xxs)):is"e"(1to(y),<xxs>f2,<m0>f)
+t62:=tris2(1to(y),<xxs>f2,yy1,<m0>f,t61,t60):is"e"(1to(y),<xxs>f2,yy1)
+t63:=th6"e.wissel"(1to(xs),1to(y),f,m0,xxs,b):bijective(1to(xs),1to(y),f2)
+t64:=t59(f2,t63,t62):con
+b@t65:=th1"l.imp"(is"e"(1to(y),<xxs>f,yy1),con,[t:is"e"(1to(y),<xxs>f,yy1)]t59(t),[t:not(is"e"(1to(y),<xxs>f,yy1))]t64(t)):con
+l@t65a:=th5"l.some"([t:1to(xs)]1to(y),[f:[t:1to(xs)]1to(y)]bijective(1to(xs),1to(y),f),[f:[t:1to(xs)]1to(y)][t:bijective(1to(xs),1to(y),f)]t65(f,t)):not(prop1(xs,y))
+p@t66:=[y:nat][t:less(xs,y)]t65a(y,t):prop2(xs)
+x@t67:=induction([t:nat]prop2(t),t14,[t:nat][u:prop2(t)]t66(t,u),x):prop2(x)
+-8274
+[l:less(x,y)]
+satz274:=<l><y>t67".8274":not(some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)))
+[f:[t:1to(x)]1to(y)]
+satz274a:=th4"l.some"([t:1to(x)]1to(y),[g:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),g),satz274,f):not(bijective(1to(x),1to(y),f))
++*rt
++*rp
++*r
++*c
+@[x:nat][u:1to(x)]
+inn:=inn"n"(x,u):nat
+@[q:[t:cx][u:cx]cx][x:nat][f:[t:1to(x)]cx]
+x@[n:1to(x)][o:not(is"e"(1to(x),n,xout(x)))]
++8275
+t1:=th3"l.imp"(is"n"(inn(x,n),x),is"e"(1to(x),n,xout(x)),o,[t:is"n"(inn(x,n),x)]tris(1to(x),n,outn(x,inn(x,n),1top(x,n)),xout(x),isoutinn(x,n),isoutni(x,inn(x,n),1top(x,n),x,lessisi3(x),t))):not(is"n"(inn(x,n),x))
+t2:=ore1(less"n"(inn(x,n),x),is"n"(inn(x,n),x),1top(x,n),t1):less"n"(inn(x,n),x)
+-8275
+lemma275:=satz25c(x,inn(x,n),t2".8275"):lessis"n"(<inn(x,n)>suc,x)
+f@[g:[t:1to(x)]cx]
+recprop:=and(is(<1out(x)>g,<1out(x)>f),[t:1to(x)][u:not(is"e"(1to(x),t,xout(x)))]is(<outn(x,<inn(x,t)>suc,lemma275(t,u))>g,<<outn(x,<inn(x,t)>suc,lemma275(t,u))>f><<t>g>q)):'prop'
++*8275
+x@1o:=1out(x):1to(x)
+xo:=xout(x):1to(x)
+[u:nat][l:lessis"n"(<u>suc,x)]
+t11:=satz16b(u,<u>suc,x,satz18c(u),l):less"n"(u,x)
+t12:=lessisi1"n"(u,x,t11):lessis"n"(u,x)
+ux:=outn(x,u,t12):1to(x)
+t13:=ec3e31(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11):nis"n"(u,x)
+t14:=th3"l.imp"(is"e"(1to(x),ux,xo),is"n"(u,x),t13,[t:is"e"(1to(x),ux,xo)]isoutne(x,u,t12,x,lessisi3(x),t)):not(is"e"(1to(x),ux,xo))
+t15:=isf(nat,nat,suc,u,inn(x,ux),isinoutn(x,u,t12)):is"n"(<u>suc,<inn(x,ux)>suc)
+t16:=isoutni(x,<u>suc,l,<inn(x,ux)>suc,lemma275(ux,t14),t15):is"e"(1to(x),outn(x,<u>suc,l),outn(x,<inn(x,ux)>suc,lemma275(ux,t14)))
+x@[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
+ns:=outn(x,<inn(x,n)>suc,lemma275(n,o)):1to(x)
+f@[g:[t:1to(x)]cx]
+prop1:=is(<1o>g,<1o>f):'prop'
+prop2:=[t:1to(x)][u:not(is"e"(1to(x),t,xo))]is(<ns(t,u)>g,<<ns(t,u)>f><<t>g>q):'prop'
+[pg:recprop(g)]
+t3:=ande1(prop1,prop2,pg):prop1
+[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
+t4:=<o><n>ande2(prop1,prop2,pg):is(<ns(n,o)>g,<<ns(n,o)>f><<n>g>q)
+pg@[u:nat][l:lessis"n"(<u>suc,x)]
+t17:=isf(1to(x),cx,g,outn(x,<u>suc,l),ns(ux(u,l),t14(u,l)),t16(u,l)):is(<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g)
+t18:=tris(cx,<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,t17,t4(pg,ux(u,l),t14(u,l))):is(<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q)
+g@[h:[t:1to(x)]cx][u:nat][l:lessis"n"(u,x)]
+prop3:=is(<outn(x,u,l)>g,<outn(x,u,l)>h):'prop'
+u@prop4:=and(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(t)):'prop'
+prop5:=or(prop4,more"n"(u,x)):'prop'
+h@[pg:recprop(g)][ph:recprop(h)][l:lessis"n"(1,x)]
+t5:=isoutni(x,1,l,1,satz24a(x),refis(nat,1)):is"e"(1to(x),outn(x,1,l),1o)
+t6:=isf(1to(x),cx,g,outn(x,1,l),1o,t5):is(<outn(x,1,l)>g,<1o>g)
+t7:=tris(cx,<outn(x,1,l)>g,<1o>g,<1o>f,t6,t3(pg)):is(<outn(x,1,l)>g,<1o>f)
+t8:=tris2(cx,<outn(x,1,l)>g,<outn(x,1,l)>h,<1o>f,t7,t7(h,g,ph,pg,l)):prop3(1,l)
+ph@t9:=andi(lessis"n"(1,x),[t:lessis"n"(1,x)]prop3(1,t),satz24a(x),[t:lessis"n"(1,x)]t8(t)):prop4(1)
+t10:=ori1(prop4(1),more"n"(1,x),t9):prop5(1)
+[u:nat][p:prop5(u)][l:lessis"n"(<u>suc,x)]
+t19:=ec3e32(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11(u,l)):not(more"n"(u,x))
+t20:=ore1(prop4(u),more"n"(u,x),p,t19):prop4(u)
+t21:=<t12(u,l)>ande2(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(u,t),t20):prop3(u,t12(u,l))
+t22:=isf(cx,cx,[t:cx]<<ns(ux(u,l),t14(u,l))>f><t>q,<ux(u,l)>g,<ux(u,l)>h,t21):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q)
+t23:=symis(cx,<outn(x,<u>suc,l)>h,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,t18(h,ph,u,l)):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h)
+t24:=tr3is(cx,<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h,t18(g,pg,u,l),t22,t23):prop3(<u>suc,l)
+t25:=andi(lessis"n"(<u>suc,x),[t:lessis"n"(<u>suc,x)]prop3(<u>suc,t),l,[t:lessis"n"(<u>suc,x)]t24(t)):prop4(<u>suc)
+t26:=ori1(prop4(<u>suc),more"n"(<u>suc,x),t25):prop5(<u>suc)
+p@[n:not(lessis"n"(<u>suc,x))]
+t27:=satz10k(<u>suc,x,n):more"n"(<u>suc,x)
+t28:=ori2(prop4(<u>suc),more"n"(<u>suc,x),t27):prop5(<u>suc)
+p@t29:=th1"l.imp"(lessis"n"(<u>suc,x),prop5(<u>suc),[t:lessis"n"(<u>suc,x)]t26(t),[t:not(lessis"n"(<u>suc,x))]t28(t)):prop5(<u>suc)
+u@t30:=induction([v:nat]prop5(v),t10,[v:nat][t:prop5(v)]t29(v,t),u):prop5(u)
+ph@[n:1to(x)]
+t31:=isf(1to(x),cx,g,n,outn(x,inn(x,n),1top(x,n)),isoutinn(x,n)):is(<n>g,<outn(x,inn(x,n),1top(x,n))>g)
+t32:=satz10d(inn(x,n),x,1top(x,n)):not(more"n"(inn(x,n),x))
+t33:=ore1(prop4(inn(x,n)),more"n"(inn(x,n),x),t30(inn(x,n)),t32):prop4(inn(x,n))
+t34:=<1top(x,n)>ande2(lessis"n"(inn(x,n),x),[t:lessis"n"(inn(x,n),x)]prop3(inn(x,n),t),t33):prop3(inn(x,n),1top(x,n))
+t35:=symis(cx,<n>h,<outn(x,inn(x,n),1top(x,n))>h,t31(h,g,ph,pg,n)):is(<outn(x,inn(x,n),1top(x,n))>h,<n>h)
+t36:=tr3is(cx,<n>g,<outn(x,inn(x,n),1top(x,n))>g,<outn(x,inn(x,n),1top(x,n))>h,<n>h,t31,t34,t35):is(<n>g,<n>h)
+ph@t37:=fisi(1to(x),cx,g,h,[t:1to(x)]t36(t)):is"e"([t:1to(x)]cx,g,h)
+f@prop6:=some"l"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(g)):'prop'
+x@prop7:=all"l"([t:1to(x)]cx,[f:[t:1to(x)]cx]prop6(f)):'prop'
+q@[f:[t:1to(1)]cx]
+t38:=refis(cx,<1o(1)>f):prop1(1,f,f)
+[n:1to(1)][o:not(is"e"(1to(1),n,xo(1)))]
+t39:=<th1"n.singlet"(n)>o:con
+t40:=cone(is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q),t39):is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q)
+f@t41:=andi(prop1(1,f,f),prop2(1,f,f),t38,[t:1to(1)][u:not(is"e"(1to(1),t,xo(1)))]t40(t,u)):recprop(1,f,f)
+t42:=somei([t:1to(1)]cx,[g:[t:1to(1)]cx]recprop(1,f,g),f,t41):prop6(1,f)
+q@t43:=[f:[t:1to(1)]cx]t42(f):prop7(1)
+x@[p:prop7(x)]
+xs:=<x>suc:nat
+[f:[t:1to(xs)]cx]
+f1:=left(cx,xs,x,lessisi1"n"(x,xs,satz18c(x)),f):[t:1to(x)]cx
+t44:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f1,g)][v:recprop(x,f1,h)]t37(f1,g,h,u,v),<f1>p):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g))
+g1:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):[t:1to(x)]cx
+t45:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):recprop(x,f1,g1)
+[n:1to(xs)]
+nxs:=is"e"(1to(xs),n,xo(xs)):'prop'
+[o:not(nxs)]
+t46:=satz26a(x,inn(xs,n),t2(xs,n,o)):lessis"n"(inn(xs,n),x)
+n1:=outn(x,inn(xs,n),t46):1to(x)
+b:=<n1>g1:cx
+[o1:not(nxs)]
+t47:=isoutni(x,inn(xs,n),t46(o),inn(xs,n),t46(o1),refis(nat,inn(xs,n))):is"e"(1to(x),n1(o),n1(o1))
+t48:=isf(1to(x),cx,g1,n1(o),n1(o1),t47):is(b(o),b(o1))
+f@a:=<<xo(xs)>f><<xo(x)>g1>q:cx
+n@c:=ite"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u)):cx
+[i:nxs]
+t49:=itet"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),i):is(c,a)
+o@t50:=itef"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),o):is(c,b)
+f@g2:=[t:1to(xs)]c(t):[t:1to(xs)]cx
+t51:=th3"l.imp"(is"e"(1to(xs),1o(xs),xo(xs)),is"n"(1,xs),symnotis(nat,xs,1,<x>ax3),[t:is"e"(1to(xs),1o(xs),xo(xs))]isoutne(xs,1,satz24a(xs),xs,lessisi3(xs),t)):not(is"e"(1to(xs),1o(xs),xo(xs)))
+t52:=t50(1o(xs),t51):is(c(1o(xs)),b(1o(xs),t51))
+t53:=isinoutn(xs,1,satz24a(xs)):is"n"(1,inn(xs,1o(xs)))
+t54:=isoutni(x,1,satz24a(x),inn(xs,1o(xs)),t46(1o(xs),t51),t53):is"e"(1to(x),1o(x),n1(1o(xs),t51))
+t55:=isf(1to(x),cx,g1,1o(x),n1(1o(xs),t51),t54):is(<1o(x)>g1,b(1o(xs),t51))
+t56:=tris2(cx,c(1o(xs)),<1o(x)>g1,b(1o(xs),t51),t52,t55):is(c(1o(xs)),<1o(x)>g1)
+t57:=tris(cx,c(1o(xs)),<1o(x)>g1,<1o(x)>f1,t56,t3(x,f1,g1,t45)):is(c(1o(xs)),<1o(x)>f1)
+t58:=isinoutn(x,1,satz24a(x)):is"n"(1,inn(x,1o(x)))
+t59:=isoutni(xs,1,satz24a(xs),inn(x,1o(x)),trlessis"n"(inn(x,1o(x)),x,xs,1top(x,1o(x)),lessisi1"n"(x,xs,satz18c(x))),t58):is"e"(1to(xs),1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)))
+t60:=isf(1to(xs),cx,f,1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)),t59):is(<1o(xs)>f,<1o(x)>f1)
+t61:=tris2(cx,c(1o(xs)),<1o(xs)>f,<1o(x)>f1,t57,t60):prop1(xs,f,g2)
+o@[i:is"e"(1to(xs),ns(xs,n,o),xo(xs))]
+t62:=isoutne(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),i):is"n"(<inn(xs,n)>suc,xs)
+t63:=<t62><x><inn(xs,n)>ax4:is"n"(inn(xs,n),x)
+t64:=isoutni(x,inn(xs,n),t46,x,lessisi3(x),t63):is"e"(1to(x),n1,xo(x))
+t65:=isf(1to(x),cx,g1,xo(x),n1,symis(1to(x),n1,xo(x),t64)):is(<xo(x)>g1,b)
+t66:=tris2(cx,<xo(x)>g1,c,b,t65,t50):is(<xo(x)>g1,c)
+t67:=isf(cx,cx,[t:cx]<<xo(xs)>f><t>q,<xo(x)>g1,c,t66):is(a,<<xo(xs)>f><c>q)
+t68:=isf(1to(xs),cx,f,xo(xs),ns(xs,n,o),symis(1to(xs),ns(xs,n,o),xo(xs),i)):is(<xo(xs)>f,<ns(xs,n,o)>f)
+t69:=isf(cx,cx,<c>q,<xo(xs)>f,<ns(xs,n,o)>f,t68):is(<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q)
+t70:=tr3is(cx,c(ns(xs,n,o)),a,<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q,t49(ns(xs,n,o),i),t67,t69):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
+o@[o1:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))][i:is"e"(1to(x),n1,xo(x))]
+t71:=isoutne(x,inn(xs,n),t46,x,lessisi3(x),i):is"n"(inn(xs,n),x)
+t72:=ax2(inn(xs,n),x,t71):is"n"(<inn(xs,n)>suc,xs)
+t73:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),t72):is"e"(1to(xs),ns(xs,n,o),xo(xs))
+o1@t74:=th3"l.imp"(is"e"(1to(x),n1,xo(x)),is"e"(1to(xs),ns(xs,n,o),xo(xs)),o1,[t:is"e"(1to(x),n1,xo(x))]t73(t)):not(is"e"(1to(x),n1,xo(x)))
+t75:=isinoutn(x,inn(xs,n),t46):is"n"(inn(xs,n),inn(x,n1))
+t76:=ax2(inn(xs,n),inn(x,n1),t75):is"n"(<inn(xs,n)>suc,<inn(x,n1)>suc)
+t77:=isinoutn(xs,<inn(xs,n)>suc,lemma275(xs,n,o)):is"n"(<inn(xs,n)>suc,inn(xs,ns(xs,n,o)))
+t78:=tris1(nat,inn(xs,ns(xs,n,o)),<inn(x,n1)>suc,<inn(xs,n)>suc,t77,t76):is"n"(inn(xs,ns(xs,n,o)),<inn(x,n1)>suc)
+t79:=isoutni(x,inn(xs,ns(xs,n,o)),t46(ns(xs,n,o),o1),<inn(x,n1)>suc,lemma275(x,n1,t74),t78):is"e"(1to(x),n1(ns(xs,n,o),o1),ns(n1,t74))
+t80:=isf(1to(x),cx,g1,n1(ns(xs,n,o),o1),ns(n1,t74),t79):is(b(ns(xs,n,o),o1),<ns(n1,t74)>g1)
+t81:=isinoutn(x,<inn(x,n1)>suc,lemma275(x,n1,t74)):is"n"(<inn(x,n1)>suc,inn(x,ns(n1,t74)))
+t82:=tris(nat,<inn(xs,n)>suc,<inn(x,n1)>suc,inn(x,ns(n1,t74)),t76,t81):is"n"(<inn(xs,n)>suc,inn(x,ns(n1,t74)))
+t83:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),inn(x,ns(n1,t74)),trlessis"n"(inn(x,ns(n1,t74)),x,xs,1top(x,ns(n1,t74)),lessisi1"n"(x,xs,satz18c(x))),t82):is"e"(1to(xs),ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)))
+t84:=isf(1to(xs),cx,f,ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)),t83):is(<ns(xs,n,o)>f,<ns(n1,t74)>f1)
+t85:=isf(cx,cx,<b>q,<ns(xs,n,o)>f,<ns(n1,t74)>f1,t84):is(<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q)
+t86:=isf(cx,cx,[t:cx]<<ns(xs,n,o)>f><t>q,c,b,t50):is(<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q)
+t87:=tr3is(cx,c(ns(xs,n,o)),b(ns(xs,n,o),o1),<ns(n1,t74)>g1,<<ns(n1,t74)>f1><b>q,t50(ns(xs,n,o),o1),t80,t4(f1,g1,t45,n1,t74)):is(c(ns(xs,n,o)),<<ns(n1,t74)>f1><b>q)
+t88:=tris(cx,<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q,t86,t85):is(<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q)
+t89:=tris2(cx,c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q,t87,t88):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
+o@t90:=th1"l.imp"(is"e"(1to(xs),ns(xs,n,o),xo(xs)),is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q),[t:is"e"(1to(xs),ns(xs,n,o),xo(xs))]t70(t),[t:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))]t89(t)):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
+f@t91:=[t:1to(xs)][u:not(nxs(t))]t90(t,u):prop2(xs,f,g2)
+t92:=andi(prop1(xs,f,g2),prop2(xs,f,g2),t61,t91):recprop(xs,f,g2)
+t93:=somei([t:1to(xs)]cx,[g:[t:1to(xs)]cx]recprop(xs,f,g),g2,t92):prop6(xs,f)
+p@t94:=[f:[t:1to(xs)]cx]t93(f):prop7(xs)
+x@t95:=induction([y:nat]prop7(y),t43,[y:nat][t:prop7(y)]t94(y,t),x):prop7(x)
+[f:[t:1to(x)]cx]
+t96:=<f>t95:prop6(x,f)
+t97:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f,g)][v:recprop(x,f,h)]t37(f,g,h,u,v),t96):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
+-8275
+f@satz275:=t97".8275"(f):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
+recf:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):[t:1to(x)]cx
+satz275a:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):recprop(x,f,recf)
+[n:1to(x)]
+rec:=<n>recf:cx
+f@satz275b:=t3".8275"(x,f,recf,satz275a):is(rec(1out(x)),<1out(x)>f)
+n@[o:not(is"e"(1to(x),n,xout(x)))]
+sucx:=ns".8275"(n,o):1to(x)
+satz275c:=t4".8275"(x,f,recf,satz275a,n,o):is(rec(sucx(n,o)),<<sucx(n,o)>f><rec(n)>q)
+f@[g:[t:1to(x)]cx][r:recprop(x,f,g)]
+satz275d:=t37".8275"(x,f,g,recf,r,satz275a):is"e"([t:1to(x)]cx,g,recf)
+[n:1to(x)]
+satz275e:=fise(1to(x),cx,g,recf,satz275d,n):is(<n>g,rec(n))
+x@[y:nat]
++*8275
+y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
+fl:=left(cx,x,y,l,f):[t:1to(y)]cx
+rf:=recf(x,f):[t:1to(x)]cx
+rfl:=left(cx,x,y,l,rf):[t:1to(y)]cx
+t98:=isinoutn(y,1,satz24a(y)):is"n"(1,inn(y,1out(y)))
+t99:=isoutni(x,1,satz24a(x),inn(y,1out(y)),trlessis"n"(inn(y,1out(y)),y,x,1top(y,1out(y)),l),t98):is"e"(1to(x),1out(x),left1to(x,y,l,1out(y)))
+t100:=isp(1to(x),[t:1to(x)]is(<t>rf,<t>f),1out(x),left1to(x,y,l,1out(y)),t3(x,f,rf,satz275a(x,f)),t99):prop1(y,fl,rfl)
+[n:1to(y)][o:not(is"e"(1to(y),n,xout(y)))]
+t100a:=th3"l.imp"(is"n"(inn(y,n),y),is"e"(1to(y),n,xout(y)),o,[t:is"n"(inn(y,n),y)]tris(1to(y),n,outn(y,inn(y,n),1top(y,n)),xout(y),isoutinn(y,n),isoutni(y,inn(y,n),1top(y,n),y,lessisi3(y),t))):not(is"n"(inn(y,n),y))
+t100b:=ore1(less"n"(inn(y,n),y),is"n"(inn(y,n),y),1top(y,n),t100a):less"n"(inn(y,n),y)
+t101:=satz16b(inn(y,n),y,x,t100b,l):less"n"(inn(y,n),x)
+t102:=ec3e31(is"n"(inn(y,n),x),more"n"(inn(y,n),x),less"n"(inn(y,n),x),satz10b(inn(y,n),x),t101):nis"n"(inn(y,n),x)
+t103:=th3"l.imp"(is"e"(1to(x),left1to(x,y,l,n),xout(x)),is"n"(inn(y,n),x),t102,[t:is"e"(1to(x),left1to(x,y,l,n),xout(x))]isoutne(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l),x,lessisi3(x),t)):not(is"e"(1to(x),left1to(x,y,l,n),xout(x)))
+t104:=t4(x,f,rf,satz275a(x,f),left1to(x,y,l,n),t103):is(<ns(x,left1to(x,y,l,n),t103)>rf,<<ns(x,left1to(x,y,l,n),t103)>f><<n>rfl>q)
+t105:=isinoutn(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l)):is"n"(inn(y,n),inn(x,left1to(x,y,l,n)))
+t106:=ax2(inn(y,n),inn(x,left1to(x,y,l,n)),t105):is"n"(<inn(y,n)>suc,<inn(x,left1to(x,y,l,n))>suc)
+t107:=isinoutn(y,<inn(y,n)>suc,lemma275(y,n,o)):is"n"(<inn(y,n)>suc,inn(y,ns(y,n,o)))
+t108:=tris1(nat,<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)),<inn(y,n)>suc,t106,t107):is"n"(<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)))
+t109:=isoutni(x,<inn(x,left1to(x,y,l,n))>suc,lemma275(x,left1to(x,y,l,n),t103),inn(y,ns(y,n,o)),trlessis"n"(inn(y,ns(y,n,o)),y,x,1top(y,ns(y,n,o)),l),t108):is"e"(1to(x),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)))
+t110:=isp(1to(x),[t:1to(x)]is(<t>rf,<<t>f><<n>rfl>q),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)),t104,t109):is(<ns(y,n,o)>rfl,<<ns(y,n,o)>fl><<n>rfl>q)
+f@t111:=[t:1to(y)][u:not(is"e"(1to(y),t,xout(y)))]t110(t,u):prop2(y,fl,rfl)
+t112:=andi(prop1(y,fl,rfl),prop2(y,fl,rfl),t100,t111):recprop(y,fl,rfl)
+-8275
+y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
+satz275f:=satz275d(y,fl".8275"(l,f),rfl".8275"(l,f),t112".8275"(l,f)):is"e"([t:1to(y)]cx,left(cx,x,y,l,recf(x,f)),recf(y,left(cx,x,y,l,f)))
+x@[f:[t:1to(pl"n"(x,1))]cx]
++8276
+xs:=<x>suc:nat
+x1:=pl"n"(x,1):nat
+t1:=lessisi1"n"(x,x1,satz18a(x,1)):lessis"n"(x,x1)
+t2:=lessisi1"n"(x,xs,satz18c(x)):lessis"n"(x,xs)
+t3:=lessisi2"n"(xs,x1,satz4e(x)):lessis"n"(xs,x1)
+fx:=left(cx,x1,x,t1,f):[t:1to(x)]cx
+f1:=left(cx,x1,xs,t3,f):[t:1to(xs)]cx
+f1x:=f1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
+g1:=g2"c.8275"(x,t95"c.8275"(x),f1):[t:1to(xs)]cx
+g1x:=g1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
+g:=left(cx,x1,xs,t3,recf(x1,f)):[t:1to(xs)]cx
+t4:=t49"c.8275"(x,t95"c.8275"(x),f1,xout(xs),refis(1to(xs),xout(xs))):is(<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q)
+t5:=satz275d(xs,f1,g1,t92"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(xs)]cx,g1,recf(xs,f1))
+t6:=satz275f(x1,xs,t3,f):is"e"([t:1to(xs)]cx,g,recf(xs,f1))
+t7:=tris2([t:1to(xs)]cx,g,g1,recf(xs,f1),t6,t5):is"e"([t:1to(xs)]cx,g,g1)
+t8:=fise(1to(xs),cx,g,g1,t7,xout(xs)):is(<xout(xs)>g,<xout(xs)>g1)
+t9:=tris(cx,<xout(xs)>g,<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q,t8,t4):is(<xout(xs)>g,<<xout(xs)>f1><<xout(x)>g1x>q)
+[n:1to(x)]
+t10:=isinoutn(xs,inn(x,n),trlessis"n"(inn(x,n),x,xs,1top(x,n),t2)):is"n"(inn(x,n),inn(xs,left1to(xs,x,t2,n)))
+t11:=isoutni(x1,inn(x,n),trlessis"n"(inn(x,n),x,x1,1top(x,n),t1),inn(xs,left1to(xs,x,t2,n)),trlessis"n"(inn(xs,left1to(xs,x,t2,n)),xs,x1,1top(xs,left1to(xs,x,t2,n)),t3),t10):is"e"(1to(x1),left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)))
+t12:=isf(1to(x1),cx,f,left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)),t11):is(<n>fx,<n>f1x)
+f@t13:=fisi(1to(x),cx,fx,f1x,[t:1to(x)]t12(t)):is"e"([t:1to(x)]cx,fx,f1x)
+t14:=isf([t:1to(x)]cx,[t:1to(x)]cx,[u:[t:1to(x)]cx]recf(x,u),fx,f1x,t13):is"e"([t:1to(x)]cx,recf(x,fx),recf(x,f1x))
+t15:=satz275d(x,f1x,g1x,t45"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(x)]cx,g1x,recf(x,f1x))
+t16:=tris2([t:1to(x)]cx,g1x,recf(x,fx),recf(x,f1x),t15,t14):is"e"([t:1to(x)]cx,g1x,recf(x,fx))
+t17:=fise(1to(x),cx,g1x,recf(x,fx),t16,xout(x)):is(<xout(x)>g1x,<xout(x)>recf(x,fx))
+t18:=isinoutn(xs,xs,lessisi3(xs)):is"n"(xs,inn(xs,xout(xs)))
+t19:=tris(nat,x1,xs,inn(xs,xout(xs)),satz4a(x),t18):is"n"(x1,inn(xs,xout(xs)))
+t20:=isoutni(x1,x1,lessisi3(x1),inn(xs,xout(xs)),trlessis"n"(inn(xs,xout(xs)),xs,x1,1top(xs,xout(xs)),t3),t19):is"e"(1to(x1),xout(x1),left1to(x1,xs,t3,xout(xs)))
+t21:=isp1(1to(x1),[t:1to(x1)]is(<t>recf(x1,f),<<t>f><<xout(x)>g1x>q),left1to(x1,xs,t3,xout(xs)),xout(x1),t9,t20):is(<xout(x1)>recf(x1,f),<<xout(x1)>f><<xout(x)>g1x>q)
+t22:=isf(cx,cx,[t:cx]<<xout(x1)>f><t>q,<xout(x)>g1x,<xout(x)>recf(x,fx),t17):is(<<xout(x1)>f><<xout(x)>g1x>q,<<xout(x1)>f><<xout(x)>recf(x,fx)>q)
+-8276
+satz276:=tris(cx,<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>g1x".8276">q,<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,fx".8276")>q,t21".8276",t22".8276"):is(<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
+x@[f:[u:1to(x)]cx]
+smpr:=rec(x,f,xout(x)):cx
+@[x:nat][f:[u:1to(x)]cx]
+sum:=smpr([t:cx][u:cx]pl(t,u),x,f):cx
+prod:=smpr([t:cx][u:cx]ts(t,u),x,f):cx
+q@[f:[u:1to(1)]cx]
++8277
+t1:=isoutni(1,1,satz24a(1),1,lessisi3(1),refis(nat,1)):is"e"(1to(1),1out(1),xout(1))
+-8277
+satz277:=isp(1to(1),[t:1to(1)]is(rec(1,f,t),<t>f),1out(1),xout(1),satz275b(1,f),t1".8277"):is(smpr(1,f),<xout(1)>f)
+q@[x:nat][f:[u:1to(pl"n"(x,1))]cx]
+satz278:=satz276(x,f):is(smpr(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><smpr(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
+x@[f:[u:1to(x)]cx][y:nat][i:is"n"(y,x)]
++v8
+t1:=lessisi2"n"(y,x,i):lessis"n"(y,x)
+f0:=left(cx,x,y,t1,f):[t:1to(y)]cx
+t2:=fise(1to(y),cx,left(cx,x,y,t1,recf(x,f)),recf(y,f0),satz275f(x,y,t1,f),xout(y)):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(y,f0))
+t3:=tris1(nat,inn(y,xout(y)),x,y,isinoutn(y,y,lessisi3(y)),i):is"n"(inn(y,xout(y)),x)
+t4:=isoutni(x,inn(y,xout(y)),trlessis"n"(inn(y,xout(y)),y,x,1top(y,xout(y)),t1),x,lessisi3(x),t3):is"e"(1to(x),left1to(x,y,t1,xout(y)),xout(x))
+t5:=isf(1to(x),cx,recf(x,f),left1to(x,y,t1,xout(y)),xout(x),t4):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(x,f))
+-v8
+issmpr:=tris1(cx,smpr(y,f0".v8"),smpr(x,f),<left1to(x,y,t1".v8",xout(y))>recf(x,f),t2".v8",t5".v8"):is(smpr(y,left(cx,x,y,lessisi2"n"(y,x,i),f)),smpr(x,f))
+@[z:complex][x:nat]
++8279
+xr:=rlofnt(x):real
+prop1:=is(sum(x,[t:1to(x)]z),ts(z,pli(xr,0))):'prop'
+z@t1:=satz277([t:cx][u:cx]pl(t,u),[t:1to(1)]z):is(sum(1,[t:1to(1)]z),z)
+t2:=tris(cx,sum(1,[t:1to(1)]z),z,ts(z,1c),t1,satz222a(z)):prop1(1)
+x@[p:prop1(x)]
+t3:=satz278([t:cx][u:cx]pl(t,u),x,[t:1to(pl"n"(x,1))]z):is(sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z))
+t4:=ispl12(sum(x,[t:1to(x)]z),ts(z,pli(xr,0)),z,ts(z,1c),p,satz222a(z)):is(pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)))
+t5:=distpt2(z,pli(xr,0),1c):is(pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)))
+t6:=plis12a(xr,0,1rl,0):is(pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)))
+t7:=isrecx12(pl"r"(xr,1rl),rlofnt(pl"n"(x,1)),pl"r"(0,0),0,satzr155b(x,1),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0))
+t8:=tris(cx,pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0),t6,t7):is(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0))
+t9:=ists2(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0),z,t8):is(ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)))
+t10:=tr4is(cx,sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)),t3,t4,t5,t9):prop1(pl"n"(x,1))
+t11:=isp(nat,[t:nat]prop1(t),pl"n"(x,1),<x>suc,t10,satz4a(x)):prop1(<x>suc)
+-8279
+satz279:=induction([t:nat]prop1".8279"(t),t2".8279",[u:nat][t:prop1".8279"(u)]t11".8279"(u,t),x):is(sum(x,[t:1to(x)]z),ts(z,pli(rlofnt(x),0)))
+q@[f:[t:1to(2)]cx]
++8280
+t1:=lessisi1"n"(1,2,satz18a(1,1)):lessis"n"(1,2)
+f1:=left(cx,2,1,t1,f):[t:1to(1)]cx
+t2:=satz278(q,1,f):is(smpr(2,f),<<xout(2)>f><smpr(1,f1)>q)
+t3:=satz277(q,f1):is(smpr(1,f1),<xout(1)>f1)
+t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+t5:=isoutni(2,1,satz24a(2),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,2,1top(1,xout(1)),t1),t4):is"e"(1to(2),1out(2),left1to(2,1,t1,xout(1)))
+t6:=isf(1to(2),cx,f,1out(2),left1to(2,1,t1,xout(1)),t5):is(<1out(2)>f,<xout(1)>f1)
+t7:=tris2(cx,smpr(1,f1),<1out(2)>f,<xout(1)>f1,t3,t6):is(smpr(1,f1),<1out(2)>f)
+t8:=isf(cx,cx,[t:cx]<<xout(2)>f><t>q,smpr(1,f1),<1out(2)>f,t7):is(<<xout(2)>f><smpr(1,f1)>q,<<xout(2)>f><<1out(2)>f>q)
+-8280
+satz280:=tris(cx,smpr(2,f),<<xout(2)>f><smpr(1,f1".8280")>q,<<xout(2)>f><<1out(2)>f>q,t2".8280",t8".8280"):is(smpr(2,f),<<xout(2)>f><<1out(2)>f>q)
+q@assoc:=[x:cx][y:cx][z:cx]is(<z><<y><x>q>q,<<z><y>q><x>q):'prop'
+@assocp1:=[x:cx][y:cx][z:cx]asspl1(x,y,z):assoc([x:cx][y:cx]pl(x,y))
+assocts:=[x:cx][y:cx][z:cx]assts1(x,y,z):assoc([x:cx][y:cx]ts(x,y))
+q@[a:assoc][z:cx][u:cx][v:cx]
+assq1:=<v><u><z>a:is(<v><<u><z>q>q,<<v><u>q><z>q)
+assq2:=symis(cx,<v><<u><z>q>q,<<v><u>q><z>q,assq1):is(<<v><u>q><z>q,<v><<u><z>q>q)
+q@[a:assoc(q)][x:nat][y:nat][f:[t:1to(pl"n"(x,y))]cx]
++8281
+y@t1:=lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)):lessis"n"(x,pl"n"(x,y))
+f@f1:=left(cx,pl"n"(x,y),x,t1,f):[t:1to(x)]cx
+f2:=right(cx,x,y,f):[t:1to(y)]cx
+prop1:=is(smpr(pl"n"(x,y),f),<smpr(y,f2)><smpr(x,f1)>q):'prop'
+y@prop2:=all"l"([t:1to(pl"n"(x,y))]cx,[u:[t:1to(pl"n"(x,y))]cx]prop1(u)):'prop'
+x@[f0:[t:1to(pl"n"(x,1))]cx]
+t2:=satz278(q,x,f0):is(smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q)
+t3:=satz277(q,f2(1,f0)):is(smpr(1,f2(1,f0)),<xout(1)>f2(1,f0))
+t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+t5:=ispl2"n"(1,inn(1,xout(1)),x,t4):is"n"(pl"n"(x,1),pl"n"(x,inn(1,xout(1))))
+t6:=isoutni(pl"n"(x,1),pl"n"(x,1),lessisi3(pl"n"(x,1)),pl"n"(x,inn(1,xout(1))),satz19o(inn(1,xout(1)),1,x,1top(1,xout(1))),t5):is"e"(1to(pl"n"(x,1)),xout(pl"n"(x,1)),right1to(x,1,xout(1)))
+t7:=isf(1to(pl"n"(x,1)),cx,f0,xout(pl"n"(x,1)),right1to(x,1,xout(1)),t6):is(<xout(pl"n"(x,1))>f0,<xout(1)>f2(1,f0))
+t8:=tris2(cx,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),<xout(1)>f2(1,f0),t7,t3):is(<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)))
+t9:=isf(cx,cx,<smpr(x,f1(1,f0))>q,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),t8):is(<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q)
+t10:=tris(cx,smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q,t2,t9):prop1(1,f0)
+x@t11:=[u:[t:1to(pl"n"(x,1))]cx]t10(u):prop2(1)
+y@yp1:=pl"n"(y,1):nat
+xpy:=pl"n"(x,y):nat
+xpy1:=pl"n"(x,yp1):nat
+xyp1:=pl"n"(xpy,1):nat
+t12:=lessisi2"n"(xyp1,xpy1,asspl1"n"(x,y,1)):lessis"n"(xyp1,xpy1)
+[p:prop2(y)][f:[t:1to(xpy1)]cx]
+t13:=isinoutn(xyp1,xyp1,lessisi3(xyp1)):is"n"(xyp1,inn(xyp1,xout(xyp1)))
+t14:=tris(nat,xpy1,xyp1,inn(xyp1,xout(xyp1)),asspl2"n"(x,y,1),t13):is"n"(xpy1,inn(xyp1,xout(xyp1)))
+t15:=isoutni(xpy1,xpy1,lessisi3(xpy1),inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),t14):is"e"(1to(xpy1),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)))
+t16:=isf(1to(xpy1),cx,recf(xpy1,f),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),t15):is(smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)))
+fr:=left(cx,xpy1,xyp1,t12,f):[t:1to(xyp1)]cx
+t17:=satz275f(xpy1,xyp1,t12,f):is"e"([t:1to(xyp1)]cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr))
+t18:=fise(1to(xyp1),cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr),t17,xout(xyp1)):is(<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr))
+t19:=lessisi1"n"(xpy,xyp1,satz18a(xpy,1)):lessis"n"(xpy,xyp1)
+frr:=left(cx,xyp1,xpy,t19,fr):[t:1to(xpy)]cx
+t20:=satz278(xpy,fr):is(smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q)
+t21:=isf(cx,cx,[u:cx]<<xout(xyp1)>fr><u>q,smpr(xpy,frr),<smpr(y,f2(frr))><smpr(x,f1(frr))>q,<frr>p):is(<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
+t22:=assq1(a,smpr(x,f1(frr)),smpr(y,f2(frr)),<xout(xyp1)>fr):is(<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q)
+t23:=lessisi1"n"(y,yp1,satz18a(y,1)):lessis"n"(y,yp1)
+fy:=left(cx,yp1,y,t23,f2(yp1,f)):[t:1to(y)]cx
+t24:=satz278(y,f2(yp1,f)):is(smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
+t25:=isinoutn(yp1,yp1,lessisi3(yp1)):is"n"(yp1,inn(yp1,xout(yp1)))
+t26:=ispl2"n"(yp1,inn(yp1,xout(yp1)),x,t25):is"n"(xpy1,pl"n"(x,inn(yp1,xout(yp1))))
+t27:=tris1(nat,inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))),xpy1,t14,t26):is"n"(inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))))
+t28:=isoutni(xpy1,inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),pl"n"(x,inn(yp1,xout(yp1))),satz19o(inn(yp1,xout(yp1)),yp1,x,1top(yp1,xout(yp1))),t27):is"e"(1to(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)))
+t29:=isf(1to(xpy1),cx,f,left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)),t28):is(<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f))
+t30:=isf(cx,cx,<smpr(y,f2(frr))>q,<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f),t29):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q)
+[n:1to(y)]
+n0:=inn(y,n):nat
+nyp1:=left1to(yp1,y,t23,n):1to(yp1)
+t31:=isinoutn(yp1,n0,trlessis"n"(n0,y,yp1,1top(y,n),t23)):is"n"(n0,inn(yp1,nyp1))
+t32:=ispl2"n"(n0,inn(yp1,nyp1),x,t31):is"n"(pl"n"(x,n0),pl"n"(x,inn(yp1,nyp1)))
+nxpy:=right1to(x,y,n):1to(xpy)
+nxyp1:=left1to(xyp1,xpy,t19,nxpy):1to(xyp1)
+t33:=isinoutn(xyp1,inn(xpy,nxpy),trlessis"n"(inn(xpy,nxpy),xpy,xyp1,1top(xpy,nxpy),t19)):is"n"(inn(xpy,nxpy),inn(xyp1,nxyp1))
+t34:=isinoutn(xpy,pl"n"(x,n0),satz19o(n0,y,x,1top(y,n))):is"n"(pl"n"(x,n0),inn(xpy,nxpy))
+t35:=tris(nat,pl"n"(x,n0),inn(xpy,nxpy),inn(xyp1,nxyp1),t34,t33):is"n"(pl"n"(x,n0),inn(xyp1,nxyp1))
+t36:=tris1(nat,pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1),pl"n"(x,n0),t32,t35):is"n"(pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1))
+t37:=isoutni(xpy1,pl"n"(x,inn(yp1,nyp1)),satz19o(inn(yp1,nyp1),yp1,x,1top(yp1,nyp1)),inn(xyp1,nxyp1),trlessis"n"(inn(xyp1,nxyp1),xyp1,xpy1,1top(xyp1,nxyp1),t12),t36):is"e"(1to(xpy1),right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1))
+t38:=isf(1to(xpy1),cx,f,right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1),t37):is(<n>fy,<n>f2(frr))
+f@t39:=fisi(1to(y),cx,fy,f2(frr),[u:1to(y)]t38(u)):is"e"([u:1to(y)]cx,fy,f2(frr))
+t40:=isf([u:1to(y)]cx,cx,[t:[u:1to(y)]cx]smpr(y,t),fy,f2(frr),t39):is(smpr(y,fy),smpr(y,f2(frr)))
+t41:=isf(cx,cx,[t:cx]<<xout(yp1)>f2(yp1,f)><t>q,smpr(y,f2(frr)),smpr(y,fy),symis(cx,smpr(y,fy),smpr(y,f2(frr)),t40)):is(<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
+t41a:=tris(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t30,t41):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
+t42:=tris2(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t41a,t24):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)))
+t43:=isf(cx,cx,<smpr(x,f1(frr))>q,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),t42):is(<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q)
+[m:1to(x)]
+m0:=inn(x,m):nat
+mxpy:=left1to(xpy,x,t1,m):1to(xpy)
+mxyp1:=left1to(xyp1,xpy,t19,mxpy):1to(xyp1)
+t44:=isinoutn(xyp1,inn(xpy,mxpy),trlessis"n"(inn(xpy,mxpy),xpy,xyp1,1top(xpy,mxpy),t19)):is"n"(inn(xpy,mxpy),inn(xyp1,mxyp1))
+t45:=isinoutn(xpy,m0,trlessis"n"(m0,x,xpy,1top(x,m),t1)):is"n"(m0,inn(xpy,mxpy))
+t46:=tris(nat,m0,inn(xpy,mxpy),inn(xyp1,mxyp1),t45,t44):is"n"(m0,inn(xyp1,mxyp1))
+t47:=isoutni(xpy1,m0,trlessis"n"(m0,x,xpy1,1top(x,m),t1(yp1)),inn(xyp1,mxyp1),trlessis"n"(inn(xyp1,mxyp1),xyp1,xpy1,1top(xyp1,mxyp1),t12),t46):is"e"(1to(xpy1),left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1))
+t48:=isf(1to(xpy1),cx,f,left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1),t47):is(<m>f1(x,yp1,f),<m>f1(x,y,frr))
+f@t49:=fisi(1to(x),cx,f1(x,yp1,f),f1(x,y,frr),[u:1to(x)]t48(u)):is"e"([u:1to(x)]cx,f1(x,yp1,f),f1(x,y,frr))
+t50:=isf([u:1to(x)]cx,cx,[t:[u:1to(x)]cx]smpr(x,t),f1(yp1,f),f1(frr),t49):is(smpr(x,f1(yp1,f)),smpr(x,f1(frr)))
+t51:=isf(cx,cx,[t:cx]<smpr(yp1,f2(yp1,f))><t>q,smpr(x,f1(frr)),smpr(x,f1(yp1,f)),symis(cx,smpr(x,f1(yp1,f)),smpr(x,f1(frr)),t50)):is(<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q)
+t52:=tr4is(cx,smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,t16,t18,t20,t21):is(smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
+t53:=tr4is(cx,smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q,t52,t22,t43,t51):prop1(yp1,f)
+p@t54:=[u:[t:1to(xpy1)]cx]t53(u):prop2(yp1)
+t55:=isp(nat,[t:nat]prop2(t),yp1,<y>suc,t54,satz4a(y)):prop2(<y>suc)
+y@t56:=induction([t:nat]prop2(t),t11,[z:nat][t:prop2(z)]t55(z,t),y):prop2(y)
+-8281
+satz281:=<f>t56".8281":is(smpr(pl"n"(x,y),f),<smpr(y,right(cx,x,y,f))><smpr(x,left(cx,pl"n"(x,y),x,lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)),f))>q)
+q@commut:=[x:cx][y:cx]is(<y><x>q,<x><y>q):'prop'
+@commutpl:=[x:cx][y:cx]compl(x,y):commut([x:cx][y:cx]pl(x,y))
+commutts:=[x:cx][y:cx]comts(x,y):commut([x:cx][y:cx]ts(x,y))
+q@[c:commut][z:cx][u:cx]
+comq:=<u><z>c:is(<u><z>q,<z><u>q)
+a@[c:commut(q)][x:nat][f:[t:1to(x)]cx][g:[t:1to(x)]cx]
++8282
+prop1:=is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q):'prop'
+x@prop2:=all"l"([t:1to(x)]cx,[u:[t:1to(x)]cx]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]prop1(u,v))):'prop'
+c@[f0:[t:1to(1)]cx][g0:[t:1to(1)]cx]
+t1:=satz277([t:1to(1)]<<t>g0><<t>f0>q):is(smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<<xout(1)>g0><<xout(1)>f0>q)
+t2:=isf(cx,cx,<smpr(1,f0)>q,smpr(1,g0),<xout(1)>g0,satz277(g0)):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q)
+t3:=isf(cx,cx,[t:cx]<<xout(1)>g0><t>q,smpr(1,f0),<xout(1)>f0,satz277(f0)):is(<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
+t4:=tris(cx,<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t2,t3):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
+t5:=tris2(cx,smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t1,t4):prop1(1,f0,g0)
+c@t6:=[u:[t:1to(1)]cx][v:[t:1to(1)]cx]t5(u,v):prop2(1)
+x@xp1:=pl"n"(x,1):nat
+[p:prop2(x)][f:[t:1to(xp1)]cx][g:[t:1to(xp1)]cx]
+c@[u:cx][v:cx][w:cx][z:cx]
+t7:=assq2(a,<v><u>q,w,z):is(<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q)
+t8:=comq(c,<v><u>q,w):is(<w><<v><u>q>q,<<v><u>q><w>q)
+t9:=assq2(a,w,u,v):is(<<v><u>q><w>q,<v><<u><w>q>q)
+t10:=tris(cx,<w><<v><u>q>q,<<v><u>q><w>q,<v><<u><w>q>q,t8,t9):is(<w><<v><u>q>q,<v><<u><w>q>q)
+t11:=isf(cx,cx,[t:cx]<z><t>q,<w><<v><u>q>q,<v><<u><w>q>q,t10):is(<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q)
+t12:=assq1(a,<u><w>q,v,z):is(<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q)
+t13:=comq(c,w,u):is(<u><w>q,<w><u>q)
+t14:=isf(cx,cx,[t:cx]<<z><v>q><t>q,<u><w>q,<w><u>q,t13):is(<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q)
+t15:=tr4is(cx,<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q,t7,t11,t12,t14):is(<<z><w>q><<v><u>q>q,<<z><v>q><<w><u>q>q)
+g@t16:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
+sfx:=smpr(x,left(cx,xp1,x,t16,f)):cx
+sgx:=smpr(x,left(cx,xp1,x,t16,g)):cx
+h:=[t:1to(xp1)]<<t>g><<t>f>q:[t:1to(xp1)]cx
+shx:=smpr(x,left(cx,xp1,x,t16,h)):cx
+t17:=satz278(x,h):is(smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q)
+t18:=<left(cx,xp1,x,t16,g)><left(cx,xp1,x,t16,f)>p:is(shx,<sgx><sfx>q)
+t19:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><<xout(xp1)>f>q><t>q,shx,<sgx><sfx>q,t18):is(<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q)
+t20:=t15(sfx,sgx,<xout(xp1)>f,<xout(xp1)>g):is(<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
+t21:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><sfx>q,satz278(x,f)):is(<<xout(xp1)>f><sfx>q,smpr(xp1,f))
+t22:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><sgx>q><t>q,<<xout(xp1)>f><sfx>q,smpr(xp1,f),t21):is(<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q)
+t23:=symis(cx,smpr(xp1,g),<<xout(xp1)>g><sgx>q,satz278(x,g)):is(<<xout(xp1)>g><sgx>q,smpr(xp1,g))
+t24:=isf(cx,cx,<smpr(xp1,f)>q,<<xout(xp1)>g><sgx>q,smpr(xp1,g),t23):is(<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q)
+t25:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,t17,t19,t20):is(smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
+t26:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q,t25,t22,t24):prop1(xp1,f,g)
+p@t27:=[u:[t:1to(xp1)]cx][v:[t:1to(xp1)]cx]t26(u,v):prop2(xp1)
+t28:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t27,satz4a(x)):prop2(<x>suc)
+x@t29:=induction([t:nat]prop2(t),t6,[y:nat][t:prop2(y)]t28(y,t),x):prop2(x)
+-8282
+satz282:=<g><f>t29".8282":is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q)
+x@[s:[t:1to(x)]1to(x)][b:bijective(1to(x),1to(x),s)][f:[t:1to(x)]cx]
++8283
+s@[f:[t:1to(x)]cx]
+g:=[t:1to(x)]<<t>s>f:[t:1to(x)]cx
+prop1:=is(smpr(x,g),smpr(x,f)):'prop'
+x@prop2:=all"l"([t:1to(x)]1to(x),[u:[t:1to(x)]1to(x)]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]imp(bijective(1to(x),1to(x),u),prop1(u,v)))):'prop'
+c@[s:[t:1to(1)]1to(1)][f:[t:1to(1)]cx]
+t1:=tris2(1to(1),<xout(1)>s,xout(1),1o"n",th1"n.singlet"(<xout(1)>s),th1"n.singlet"(xout(1))):is"e"(1to(1),<xout(1)>s,xout(1))
+t2:=satz277(g(1,s,f)):is(smpr(1,g(1,s,f)),<xout(1)>g(1,s,f))
+t3:=isf(1to(1),cx,f,<xout(1)>s,xout(1),t1):is(<xout(1)>g(1,s,f),<xout(1)>f)
+t4:=symis(cx,smpr(1,f),<xout(1)>f,satz277(f)):is(<xout(1)>f,smpr(1,f))
+t5:=tr3is(cx,smpr(1,g(1,s,f)),<xout(1)>g(1,s,f),<xout(1)>f,smpr(1,f),t2,t3,t4):prop1(1,s,f)
+c@t6:=[u:[t:1to(1)]1to(1)][v:[t:1to(1)]cx][w:bijective(1to(1),1to(1),u)]t5(u,v):prop2(1)
+x@xp1:=pl"n"(x,1):nat
+t7:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
+[p:prop2(x)][s:[t:1to(xp1)]1to(xp1)][f:[t:1to(xp1)]cx][b:bijective(1to(xp1),1to(xp1),s)]
+t8:=ande1(injective(1to(xp1),1to(xp1),s),surjective(1to(xp1),1to(xp1),s),b):injective(1to(xp1),1to(xp1),s)
+[case1:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))][u:1to(x)]
+u1:=left1to(xp1,x,t7,u):1to(xp1)
+n1:=inn(xp1,<u1>s):nat
+[i:is"n"(n1,xp1)]
+t9:=tr3is(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),xout(xp1),<xout(xp1)>s,isoutinn(xp1,<u1>s),isoutni(xp1,n1,1top(xp1,<u1>s),xp1,lessisi3(xp1),i),symis(1to(xp1),<xout(xp1)>s,xout(xp1),case1)):is"e"(1to(xp1),<u1>s,<xout(xp1)>s)
+t10:=isfe(1to(xp1),1to(xp1),s,t8,u1,xout(xp1),t9):is"e"(1to(xp1),u1,xout(xp1))
+t11:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t10):is"n"(inn(x,u),xp1)
+t12:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
+t13:=<t11>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t12):con
+u@t14:=ore1(less"n"(n1,xp1),is"n"(n1,xp1),1top(xp1,<u1>s),[t:is"n"(n1,xp1)]t13(t)):less"n"(n1,xp1)
+t15:=satz26(x,n1,t14):lessis"n"(n1,x)
+w1:=outn(x,n1,t15):1to(x)
+case1@s01:=[t:1to(x)]w1(t):[t:1to(x)]1to(x)
+u@[v:1to(x)][i:is"e"(1to(x),w1(u),w1(v))]
+t16:=isoutne(x,n1(u),t15(u),n1(v),t15(v),i):is"n"(n1(u),n1(v))
+t17:=<isinne(xp1,<u1(u)>s,<u1(v)>s,t16)><u1(v)><u1(u)>t8:is"e"(1to(xp1),u1(u),u1(v))
+t18:=thleft1(xp1,x,t7,u,v,t17):is"e"(1to(x),u,v)
+u@u2:=<u1>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
+n2:=inn(xp1,u2):nat
+[i:is"n"(n2,xp1)]
+t19:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),xout(xp1),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),xp1,lessisi3(xp1),i)):is"e"(1to(xp1),u2,xout(xp1))
+t20:=tr3is(1to(xp1),u1,<u2>s,<xout(xp1)>s,xout(xp1),thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,xout(xp1),t19),case1):is"e"(1to(xp1),u1,xout(xp1))
+t21:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t20):is"n"(inn(x,u),xp1)
+t22:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
+t23:=<t21>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t22):con
+u@t24:=ore1(less"n"(n2,xp1),is"n"(n2,xp1),1top(xp1,u2),[t:is"n"(n2,xp1)]t23(t)):less"n"(n2,xp1)
+t25:=satz26(x,n2,t24):lessis"n"(n2,x)
+w2:=outn(x,n2,t25):1to(x)
+t26:=isinoutn(x,n2,t25):is"n"(n2,inn(x,w2))
+t27:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),u1(w2),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),inn(x,w2),trlessis"n"(inn(x,w2),x,xp1,1top(x,w2),t7),t26)):is"e"(1to(xp1),u2,u1(w2))
+t28:=tris(1to(xp1),u1,<u2>s,<u1(w2)>s,thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,u1(w2),t27)):is"e"(1to(xp1),u1,<u1(w2)>s)
+t29:=tris(nat,inn(x,u),inn(xp1,u1),n1(w2),isinoutn(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7)),isinni(xp1,u1,<u1(w2)>s,t28)):is"n"(inn(x,u),n1(w2))
+t30:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w1(w2),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),n1(w2),t15(w2),t29)):is"e"(1to(x),u,w1(w2))
+t31:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w1(t)),w2,t30):image(1to(x),1to(x),s01,u)
+case1@t32:=andi(injective(1to(x),1to(x),s01),surjective(1to(x),1to(x),s01),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s01,<u>s01)]t18(t,u,v),[t:1to(x)]t31(t)):bijective(1to(x),1to(x),s01)
+f01:=left(cx,xp1,x,t7,f):[t:1to(x)]cx
+t33:=<t32><f01><s01>p:prop1(s01,f01)
+g1:=left(cx,xp1,x,t7,g(xp1,s,f)):[t:1to(x)]cx
+g2:=g(x,s01,f01):[t:1to(x)]cx
+u@t33a:=isoutinn(xp1,<u1>s):is"e"(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)))
+t34:=isinoutn(x,n1,t15):is"n"(n1,inn(x,w1))
+t35:=isoutni(xp1,n1,1top(xp1,<u1>s),inn(x,w1),trlessis"n"(inn(x,w1),x,xp1,1top(x,w1),t7),t34):is"e"(1to(xp1),outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1))
+t36:=tris(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1),t33a,t35):is"e"(1to(xp1),<u1>s,left1to(xp1,x,t7,w1))
+t37:=isf(1to(xp1),cx,f,<u1>s,left1to(xp1,x,t7,w1),t36):is(<u>g1,<u>g2)
+case1@t38:=fisi(1to(x),cx,g1,g2,[t:1to(x)]t37(t)):is"e"([t:1to(x)]cx,g1,g2)
+t39:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g1,g2,t38):is(smpr(x,g1),smpr(x,g2))
+t40:=tris(cx,smpr(x,g1),smpr(x,g2),smpr(x,f01),t39,t33):is(smpr(x,g1),smpr(x,f01))
+t41:=isf(1to(xp1),cx,f,<xout(xp1)>s,xout(xp1),case1):is(<xout(xp1)>g(xp1,s,f),<xout(xp1)>f)
+t42:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q)
+t43:=isf(cx,cx,<smpr(x,g1)>q,<xout(xp1)>g(xp1,s,f),<xout(xp1)>f,t41):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q)
+t44:=isf(cx,cx,[t:cx]<<xout(xp1)>f><t>q,smpr(x,g1),smpr(x,f01),t40):is(<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q)
+t45:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><smpr(x,f01)>q,satz278(x,f)):is(<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f))
+t46:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f),t42,t43,t44,t45):prop1(xp1,s,f)
+b@1px:=pl"n"(1,x):nat
+[case2:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))][u:1to(x)]
+u3:=right1to(1,x,u):1to(1px)
+case2@t47:=lessisi2"n"(1px,xp1,compl"n"(1,x)):lessis"n"(1px,xp1)
+s02:=left(1to(xp1),xp1,1px,t47,s):[t:1to(1px)]1to(xp1)
+u@n3:=inn(xp1,<u3>s02):nat
+[i:is"n"(n3,1)]
+t48:=tr3is(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),1out(xp1),<1out(xp1)>s,isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),1,satz24a(xp1),i),symis(1to(xp1),<1out(xp1)>s,1out(xp1),case2)):is"e"(1to(xp1),<u3>s02,<1out(xp1)>s)
+t49:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3),1out(xp1),t48):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
+t50:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t49):is"n"(inn(1px,u3),1)
+t51:=isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))):is"n"(pl"n"(1,inn(x,u)),inn(1px,u3))
+t52:=ismore1"n"(pl"n"(1,inn(x,u)),inn(1px,u3),1,t51,satz18(1,inn(x,u))):more"n"(inn(1px,u3),1)
+t53:=<t50>ec3e21(is"n"(inn(1px,u3),1),more"n"(inn(1px,u3),1),less"n"(inn(1px,u3),1),satz10b(inn(1px,u3),1),t52):con
+u@t54:=ore1(more"n"(n3,1),is"n"(n3,1),satz24(n3),[t:is"n"(n3,1)]t53(t)):more"n"(n3,1)
+nm1:=mn"n"(n3,1,t54):nat
+t54a:=islessis1"n"(n3,pl"n"(nm1,1),xp1,th1c"n.mn"(n3,1,t54),1top(xp1,<u3>s02)):lessis"n"(pl"n"(nm1,1),xp1)
+t55:=th9"l.or"(less"n"(pl"n"(nm1,1),xp1),is"n"(pl"n"(nm1,1),xp1),less"n"(nm1,x),is"n"(nm1,x),t54a,[t:less"n"(pl"n"(nm1,1),xp1)]satz20c(nm1,x,1,t),[t:is"n"(pl"n"(nm1,1),xp1)]satz20b(nm1,x,1,t)):lessis"n"(nm1,x)
+w3:=outn(x,nm1,t55):1to(x)
+case2@s03:=[t:1to(x)]w3(t):[t:1to(x)]1to(x)
+u@[v:1to(x)][i:is"e"(1to(x),w3(u),w3(v))]
+t56:=isoutne(x,nm1(u),t55(u),nm1(v),t55(v),i):is"n"(nm1(u),nm1(v))
+t57:=tr3is(nat,n3(u),pl"n"(nm1(u),1),pl"n"(nm1(v),1),n3(v),th1c"n.mn"(n3(u),1,t54(u)),ispl1"n"(nm1(u),nm1(v),1,t56),th1d"n.mn"(n3(v),1,t54(v))):is"n"(n3(u),n3(v))
+t58:=isinne(xp1,<u3(u)>s02,<u3(v)>s02,t57):is"e"(1to(xp1),<u3(u)>s02,<u3(v)>s02)
+t59:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)),t58):is"e"(1to(xp1),left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)))
+t60:=thleft1(xp1,1px,t47,u3(u),u3(v),t59):is"e"(1to(1px),u3(u),u3(v))
+t61:=thright1(1,x,u,v,t60):is"e"(1to(x),u,v)
+case2@s04:=left(1to(xp1),xp1,1px,t47,invf(1to(xp1),1to(xp1),s,b)):[t:1to(1px)]1to(xp1)
+u@u4:=<u3>s04:1to(xp1)
+n4:=inn(xp1,u4):nat
+[i:is"n"(n4,1)]
+t62:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),1out(xp1),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),1,satz24a(xp1),i)):is"e"(1to(xp1),u4,1out(xp1))
+t63:=tr3is(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<1out(xp1)>s,1out(xp1),thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,1out(xp1),t62),case2):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
+t64:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t63):is"n"(inn(1px,u3),1)
+t65:=tris(nat,pl"n"(1,inn(x,u)),inn(1px,u3),1,isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),t64):is"n"(pl"n"(1,inn(x,u)),1)
+t66:=<t65>ec3e21(is"n"(pl"n"(1,inn(x,u)),1),more"n"(pl"n"(1,inn(x,u)),1),less"n"(pl"n"(1,inn(x,u)),1),satz10b(pl"n"(1,inn(x,u)),1),satz18(1,inn(x,u))):con
+u@t67:=ore1(more"n"(n4,1),is"n"(n4,1),satz24(n4),[t:is"n"(n4,1)]t66(t)):more"n"(n4,1)
+nm2:=mn"n"(n4,1,t67):nat
+t68:=islessis1"n"(n4,pl"n"(nm2,1),xp1,th1c"n.mn"(n4,1,t67),1top(xp1,u4)):lessis"n"(pl"n"(nm2,1),xp1)
+t69:=th9"l.or"(less"n"(pl"n"(nm2,1),xp1),is"n"(pl"n"(nm2,1),xp1),less"n"(nm2,x),is"n"(nm2,x),t68,[t:less"n"(pl"n"(nm2,1),xp1)]satz20c(nm2,x,1,t),[t:is"n"(pl"n"(nm2,1),xp1)]satz20b(nm2,x,1,t)):lessis"n"(nm2,x)
+w4:=outn(x,nm2,t69):1to(x)
+t70:=isinoutn(x,nm2,t69):is"n"(nm2,inn(x,w4))
+t71:=tr3is(nat,n4,pl"n"(1,nm2),pl"n"(1,inn(x,w4)),inn(1px,u3(w4)),th1a"n.mn"(n4,1,t67),ispl2"n"(nm2,inn(x,w4),1,t70),isinoutn(1px,pl"n"(1,inn(x,w4)),satz19o(inn(x,w4),x,1,1top(x,w4)))):is"n"(n4,inn(1px,u3(w4)))
+t72:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),left1to(xp1,1px,t47,u3(w4)),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),inn(1px,u3(w4)),trlessis"n"(inn(1px,u3(w4)),1px,xp1,1top(1px,u3(w4)),t47),t71)):is"e"(1to(xp1),u4,left1to(xp1,1px,t47,u3(w4)))
+t73:=tris(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<u3(w4)>s02,thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,left1to(xp1,1px,t47,u3(w4)),t72)):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),<u3(w4)>s02)
+t74:=tr3is(nat,pl"n"(1,inn(x,u)),inn(1px,u3),inn(xp1,left1to(xp1,1px,t47,u3)),n3(w4),isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),isinoutn(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47)),isinni(xp1,left1to(xp1,1px,t47,u3),<u3(w4)>s02,t73)):is"n"(pl"n"(1,inn(x,u)),n3(w4))
+t75:=th1e"n.mn"(n3(w4),1,inn(x,u),t54(w4),t74):is"n"(inn(x,u),nm1(w4))
+t76:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w3(w4),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),nm1(w4),t55(w4),t75)):is"e"(1to(x),u,w3(w4))
+t77:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w3(t)),w4,t76):image(1to(x),1to(x),s03,u)
+case2@t78:=andi(injective(1to(x),1to(x),s03),surjective(1to(x),1to(x),s03),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s03,<u>s03)]t61(t,u,v),[t:1to(x)]t77(t)):bijective(1to(x),1to(x),s03)
+f02:=left(cx,xp1,1px,t47,f):[t:1to(1px)]cx
+f03:=right(cx,1,x,f02):[t:1to(x)]cx
+t79:=<t78><f03><s03>p:prop1(s03,f03)
+g3:=left(cx,xp1,1px,t47,g(xp1,s,f)):[t:1to(1px)]cx
+g4:=right(cx,1,x,g3):[t:1to(x)]cx
+g5:=g(x,s03,f03):[t:1to(x)]cx
+u@t80:=tr3is(nat,n3,pl"n"(1,nm1),pl"n"(1,inn(x,w3)),inn(1px,right1to(1,x,w3)),th1a"n.mn"(n3,1,t54),ispl2"n"(nm1,inn(x,w3),1,isinoutn(x,nm1,t55)),isinoutn(1px,pl"n"(1,inn(x,w3)),satz19o(inn(x,w3),x,1,1top(x,w3)))):is"n"(n3,inn(1px,right1to(1,x,w3)))
+t81:=tris(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),left1to(xp1,1px,t47,right1to(1,x,w3)),isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),inn(1px,right1to(1,x,w3)),trlessis"n"(inn(1px,right1to(1,x,w3)),1px,xp1,1top(1px,right1to(1,x,w3)),t47),t80)):is"e"(1to(xp1),<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)))
+t82:=isf(1to(xp1),cx,f,<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)),t81):is(<u>g4,<u>g5)
+case2@t83:=fisi(1to(x),cx,g4,g5,[t:1to(x)]t82(t)):is"e"([t:1to(x)]cx,g4,g5)
+t85:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g4,g5,t83):is(smpr(x,g4),smpr(x,g5))
+t86:=tris(cx,smpr(x,g4),smpr(x,g5),smpr(x,f03),t85,t79):is(smpr(x,g4),smpr(x,f03))
+t87:=lessisi1"n"(1,1px,satz18a(1,x)):lessis"n"(1,1px)
+g6:=left(cx,1px,1,t87,g3):[t:1to(1)]cx
+f04:=left(cx,1px,1,t87,f02):[t:1to(1)]cx
+t87a:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+1d:=left1to(1px,1,t87,xout(1)):1to(1px)
+t87b:=isinoutn(1px,inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,1px,1top(1,xout(1)),t87)):is"n"(inn(1,xout(1)),inn(1px,1d))
+t88:=tris(nat,1,inn(1,xout(1)),inn(1px,1d),t87a,t87b):is"n"(1,inn(1px,1d))
+1e:=left1to(xp1,1px,t47,1d):1to(xp1)
+t88a:=isoutni(xp1,1,satz24a(xp1),inn(1px,1d),trlessis"n"(inn(1px,1d),1px,xp1,1top(1px,1d),t47),t88):is"e"(1to(xp1),1out(xp1),1e)
+t88b:=isf(1to(xp1),1to(xp1),s,1e,1out(xp1),symis(1to(xp1),1out(xp1),1e,t88a)):is"e"(1to(xp1),<1e>s,<1out(xp1)>s)
+t89:=tr3is(1to(xp1),<1e>s,<1out(xp1)>s,1out(xp1),1e,t88b,case2,t88a):is"e"(1to(xp1),<1e>s,1e)
+t89a:=tr3is(cx,smpr(1,g6),<xout(1)>g6,<xout(1)>f04,smpr(1,f04),satz277(g6),isf(1to(xp1),cx,f,<1e>s,1e,t89),symis(cx,smpr(1,f04),<xout(1)>f04,satz277(f04))):is(smpr(1,g6),smpr(1,f04))
+t90:=satz281(1,x,g3):is(smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q)
+t91:=isf(cx,cx,<smpr(1,g6)>q,smpr(x,g4),smpr(x,f03),t86):is(<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q)
+t92:=isf(cx,cx,[t:cx]<smpr(x,f03)><t>q,smpr(1,g6),smpr(1,f04),t89a):is(<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q)
+t93:=symis(cx,smpr(1px,f02),<smpr(x,f03)><smpr(1,f04)>q,satz281(1,x,f02)):is(<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02))
+t94:=tr4is(cx,smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02),t90,t91,t92,t93):is(smpr(1px,g3),smpr(1px,f02))
+t95:=issmpr(xp1,f,1px,compl"n"(1,x)):is(smpr(1px,f02),smpr(xp1,f))
+t96:=symis(cx,smpr(1px,g3),smpr(xp1,g(xp1,s,f)),issmpr(xp1,g(xp1,s,f),1px,compl"n"(1,x))):is(smpr(xp1,g(xp1,s,f)),smpr(1px,g3))
+t97:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(1px,g3),smpr(1px,f02),smpr(xp1,f),t96,t94,t95):prop1(xp1,s,f)
+b@[not1:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))][not2:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]
+a0:=<1out(xp1)>s:1to(xp1)
+b0:=<1out(xp1)>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
+t98:=thinvf2(1to(xp1),1to(xp1),s,b,1out(xp1)):is"e"(1to(xp1),1out(xp1),<b0>s)
+t99:=not2:not(is"e"(1to(xp1),a0,1out(xp1)))
+t100:=symnotis(1to(xp1),<1out(xp1)>s,<b0>s,th3"e.notis"(1to(xp1),<1out(xp1)>s,1out(xp1),<b0>s,not2,t98)):not(is"e"(1to(xp1),<b0>s,<1out(xp1)>s))
+t101:=th3"l.imp"(is"e"(1to(xp1),b0,1out(xp1)),is"e"(1to(xp1),<b0>s,<1out(xp1)>s),t100,[t:is"e"(1to(xp1),b0,1out(xp1))]isf(1to(xp1),1to(xp1),s,b0,1out(xp1),t)):not(is"e"(1to(xp1),b0,1out(xp1)))
+s1:=changef(1to(xp1),1to(xp1),s,1out(xp1),b0):[t:1to(xp1)]1to(xp1)
+[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
+t102:=changef1(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,<b0>s)
+t103:=tris2(1to(xp1),<u>s1,1out(xp1),<b0>s,t102,t98):is"e"(1to(xp1),<u>s1,1out(xp1))
+u@[i:is"e"(1to(xp1),u,b0)]
+t104:=changef2(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,a0)
+u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
+t105:=changef3(1to(xp1),1to(xp1),s,1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
+not2@t106:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),b0,b):bijective(1to(xp1),1to(xp1),s1)
+[alpha:not(is"e"(1to(xp1),a0,xout(xp1)))]
+s2:=wissel(1to(xp1),1out(xp1),a0):[t:1to(xp1)]1to(xp1)
+t107:=th3"e.wissel"(1to(xp1),1out(xp1),a0):bijective(1to(xp1),1to(xp1),s2)
+[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
+t108:=iswissel1(1to(xp1),1out(xp1),a0,<u>s1,t103(u,i)):is"e"(1to(xp1),<<u>s1>s2,a0)
+t109:=tris2(1to(xp1),<u>s,<<u>s1>s2,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t108):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+u@[i:is"e"(1to(xp1),u,b0)]
+t110:=iswissel2(1to(xp1),1out(xp1),a0,<u>s1,t104(u,i)):is"e"(1to(xp1),<<u>s1>s2,1out(xp1))
+t111:=tris2(1to(xp1),<u>s,<<u>s1>s2,1out(xp1),tris2(1to(xp1),<u>s,1out(xp1),<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),t98),t110):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))][i:is"e"(1to(xp1),<u>s1,1out(xp1))]
+t112:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,1out(xp1),tris2(1to(xp1),<u>s1,<1out(xp1)>s1,1out(xp1),i,t103(1out(xp1),refis(1to(xp1),1out(xp1))))):is"e"(1to(xp1),u,1out(xp1))
+o@t113:=th3"l.imp"(is"e"(1to(xp1),<u>s1,1out(xp1)),is"e"(1to(xp1),u,1out(xp1)),n,[t:is"e"(1to(xp1),<u>s1,1out(xp1))]t112(t)):not(is"e"(1to(xp1),<u>s1,1out(xp1)))
+[i:is"e"(1to(xp1),<u>s1,a0)]
+t114:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,b0,tris2(1to(xp1),<u>s1,<b0>s1,a0,i,t104(b0,refis(1to(xp1),b0)))):is"e"(1to(xp1),u,b0)
+o@t115:=th3"l.imp"(is"e"(1to(xp1),<u>s1,a0),is"e"(1to(xp1),u,b0),o,[t:is"e"(1to(xp1),<u>s1,a0)]t114(t)):not(is"e"(1to(xp1),<u>s1,a0))
+t116:=iswissel3(1to(xp1),1out(xp1),a0,<u>s1,t113,t115):is"e"(1to(xp1),<<u>s1>s2,<u>s1)
+t117:=symis(1to(xp1),<<u>s1>s2,<u>s,tris(1to(xp1),<<u>s1>s2,<u>s1,<u>s,t116,t105(u,n,o))):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+n@t118:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,b0)]t111(t),[t:not(is"e"(1to(xp1),u,b0))]t117(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+u@t119:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,1out(xp1))]t109(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t118(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+alpha@t120:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s1>s2,[t:1to(xp1)]t119(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s1>s2)
+not2@t121:=t103(1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s1,1out(xp1))
+t121a:=ec3e21(is"n"(xp1,1),more"n"(xp1,1),less"n"(xp1,1),satz10b(xp1,1),ismore1"n"(1px,xp1,1,compl"n"(1,x),satz18(1,x))):nis"n"(xp1,1)
+t122:=th3"l.imp"(is"e"(1to(xp1),xout(xp1),1out(xp1)),is"n"(xp1,1),t121a,[t:is"e"(1to(xp1),xout(xp1),1out(xp1))]isoutne(xp1,xp1,lessisi3(xp1),1,satz24a(xp1),t)):not(is"e"(1to(xp1),xout(xp1),1out(xp1)))
+alpha@t123:=symnotis(1to(xp1),a0,xout(xp1),alpha):not(is"e"(1to(xp1),xout(xp1),a0))
+t124:=iswissel3(1to(xp1),1out(xp1),a0,xout(xp1),t122,t123):is"e"(1to(xp1),<xout(xp1)>s2,xout(xp1))
+t125:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s1>s2,t120):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))))
+t126:=t97(s1,g(xp1,s2,f),t106,t121):is(smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)))
+t127:=t46(s2,f,t107,t124):is(smpr(xp1,g(xp1,s2,f)),smpr(xp1,f))
+t128:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)),smpr(xp1,f),t125,t126,t127):prop1(xp1,s,f)
+not2@[i3:is"e"(1to(xp1),a0,xout(xp1))][beta:not(is"e"(1to(xp1),b0,xout(xp1)))]
+s3:=wissel(1to(xp1),1out(xp1),b0):[t:1to(xp1)]1to(xp1)
+t129:=th3"e.wissel"(1to(xp1),1out(xp1),b0):bijective(1to(xp1),1to(xp1),s3)
+[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
+t130:=t104(<u>s3,iswissel1(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,a0)
+t131:=tris2(1to(xp1),<u>s,<<u>s3>s1,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t130):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+u@[i:is"e"(1to(xp1),u,b0)]
+t132:=t103(<u>s3,iswissel2(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,1out(xp1))
+t133:=tris2(1to(xp1),<u>s,<<u>s3>s1,<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),tris(1to(xp1),<<u>s3>s1,1out(xp1),<b0>s,t132,t98)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
+t134:=iswissel3(1to(xp1),1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s3,u)
+t135:=isf(1to(xp1),1to(xp1),s1,<u>s3,u,t134):is"e"(1to(xp1),<<u>s3>s1,<u>s1)
+t136:=t105(u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
+t139:=symis(1to(xp1),<<u>s3>s1,<u>s,tris(1to(xp1),<<u>s3>s1,<u>s1,<u>s,t135,t136)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+n@t140:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,b0)]t133(t),[t:not(is"e"(1to(xp1),u,b0))]t139(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+u@t141:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,1out(xp1))]t131(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t140(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+beta@t142:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s3>s1,[t:1to(xp1)]t141(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s3>s1)
+t143:=symnotis(1to(xp1),b0,xout(xp1),beta):not(is"e"(1to(xp1),xout(xp1),b0))
+t144:=iswissel3(1to(xp1),1out(xp1),b0,xout(xp1),t122,t143):is"e"(1to(xp1),<xout(xp1)>s3,xout(xp1))
+t145:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s3>s1,t142):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))))
+t146:=t46(s3,g(xp1,s1,f),t129,t144):is(smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)))
+t147:=t97(s1,f,t106,t121):is(smpr(xp1,g(xp1,s1,f)),smpr(xp1,f))
+t148:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)),smpr(xp1,f),t145,t146,t147):prop1(xp1,s,f)
+i3@[gamma:is"e"(1to(xp1),b0,xout(xp1))][i:is"n"(x,1)]
+t149:=ispl1"n"(1,x,1,symis(nat,x,1,i)):is"n"(2,xp1)
+t150:=lessisi2"n"(2,xp1,t149):lessis"n"(2,xp1)
+f05:=left(cx,xp1,2,t150,f):[t:1to(2)]cx
+s05:=left(1to(xp1),xp1,2,t150,s):[t:1to(2)]1to(xp1)
+g7:=left(cx,xp1,2,t150,g(xp1,s,f)):[t:1to(2)]cx
+t151:=issmpr(xp1,f,2,t149):is(smpr(2,f05),smpr(xp1,f))
+t152:=issmpr(xp1,g(xp1,s,f),2,t149):is(smpr(2,g7),smpr(xp1,g(xp1,s,f)))
+t153:=satz280(f05):is(smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q)
+t154:=satz280(g7):is(smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q)
+t155:=tris1(nat,inn(2,xout(2)),xp1,2,isinoutn(2,2,lessisi3(2)),t149):is"n"(inn(2,xout(2)),xp1)
+t156:=isoutni(xp1,inn(2,xout(2)),trlessis"n"(inn(2,xout(2)),2,xp1,1top(2,xout(2)),t150),xp1,lessisi3(xp1),t155):is"e"(1to(xp1),left1to(xp1,2,t150,xout(2)),xout(xp1))
+t157:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,xout(2)),xout(xp1),t156):is"e"(1to(xp1),<xout(2)>s05,<xout(xp1)>s)
+t158:=symis(nat,1,inn(2,1out(2)),isinoutn(2,1,satz24a(2))):is"n"(inn(2,1out(2)),1)
+t159:=isoutni(xp1,inn(2,1out(2)),trlessis"n"(inn(2,1out(2)),2,xp1,1top(2,1out(2)),t150),1,satz24a(xp1),t158):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1))
+t160:=tr3is(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1),<b0>s,<xout(xp1)>s,t159,t98,isf(1to(xp1),1to(xp1),s,b0,xout(xp1),gamma)):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),<xout(xp1)>s)
+t161:=tris2(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)),<xout(xp1)>s,t157,t160):is"e"(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)))
+t163:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,1out(2)),1out(xp1),t159):is"e"(1to(xp1),<1out(2)>s05,<1out(xp1)>s)
+t164:=tris(1to(xp1),<1out(2)>s05,<1out(xp1)>s,xout(xp1),t163,i3):is"e"(1to(xp1),<1out(2)>s05,xout(xp1))
+t165:=tris2(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)),xout(xp1),t164,t156):is"e"(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)))
+t166:=isf(1to(xp1),cx,f,<xout(2)>s05,left1to(xp1,2,t150,1out(2)),t161):is(<xout(2)>g7,<1out(2)>f05)
+t167:=isf(1to(xp1),cx,f,<1out(2)>s05,left1to(xp1,2,t150,xout(2)),t165):is(<1out(2)>g7,<xout(2)>f05)
+t168:=isf(cx,cx,<<1out(2)>g7>q,<xout(2)>g7,<1out(2)>f05,t166):is(<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q)
+t169:=comq(c,<1out(2)>g7,<1out(2)>f05):is(<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q)
+t170:=isf(cx,cx,<<1out(2)>f05>q,<1out(2)>g7,<xout(2)>f05,t167):is(<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q)
+t171:=tr4is(cx,smpr(xp1,g(xp1,s,f)),smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q,symis(cx,smpr(2,g7),smpr(xp1,g(xp1,s,f)),t152),t154,t168,t169):is(smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q)
+t172:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q,smpr(2,f05),smpr(xp1,f),t171,t170,symis(cx,smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q,t153),t151):prop1(xp1,s,f)
+trivial:=t172:prop1(xp1,s,f)
+gamma@[n:nis"n"(x,1)]
+t173:=ore1(more"n"(x,1),is"n"(x,1),satz24(x),n):more"n"(x,1)
+xm1:=mn"n"(x,1,t173):nat
+s4:=changef(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1)):[t:1to(xp1)]1to(xp1)
+t174:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),b):bijective(1to(xp1),1to(xp1),s4)
+t175:=changef2(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),xout(xp1),refis(1to(xp1),xout(xp1))):is"e"(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s)
+t176:=symis(1to(xp1),a0,xout(xp1),i3):is"e"(1to(xp1),xout(xp1),<1out(xp1)>s)
+t177:=tris2(1to(xp1),<xout(xp1)>s4,xout(xp1),<1out(xp1)>s,t175,t176):is"e"(1to(xp1),<xout(xp1)>s4,xout(xp1))
+t178:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
+g8:=left(cx,xp1,x,t178,g(xp1,s,f)):[t:1to(x)]cx
+t179:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q)
+t180:=th1b"n.mn"(x,1,t173):is"n"(pl"n"(1,xm1),x)
+t181:=lessisi2"n"(pl"n"(1,xm1),x,t180):lessis"n"(pl"n"(1,xm1),x)
+g9:=left(cx,x,pl"n"(1,xm1),t181,g8):[t:1to(pl"n"(1,xm1))]cx
+t182:=symis(cx,smpr(pl"n"(1,xm1),g9),smpr(x,g8),issmpr(x,g8,pl"n"(1,xm1),t180)):is(smpr(x,g8),smpr(pl"n"(1,xm1),g9))
+g10:=right(cx,1,xm1,g9):[t:1to(xm1)]cx
+t183:=lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)):lessis"n"(1,pl"n"(1,xm1))
+g11:=left(cx,pl"n"(1,xm1),1,t183,g9):[t:1to(1)]cx
+t184:=satz281(a,1,xm1,g9):is(smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q)
+t185:=satz277(g11):is(smpr(1,g11),<xout(1)>g11)
+t186:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+1a:=left1to(pl"n"(1,xm1),1,t183,xout(1)):1to(pl"n"(1,xm1))
+t187:=isinoutn(pl"n"(1,xm1),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,pl"n"(1,xm1),1top(1,xout(1)),t183)):is"n"(inn(1,xout(1)),inn(pl"n"(1,xm1),1a))
+1b:=left1to(x,pl"n"(1,xm1),t181,1a):1to(x)
+t188:=isinoutn(x,inn(pl"n"(1,xm1),1a),trlessis"n"(inn(pl"n"(1,xm1),1a),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),1a),t181)):is"n"(inn(pl"n"(1,xm1),1a),inn(x,1b))
+t189:=tr3is(nat,1,inn(1,xout(1)),inn(pl"n"(1,xm1),1a),inn(x,1b),t186,t187,t188):is"n"(1,inn(x,1b))
+1c:=left1to(xp1,x,t178,1b):1to(xp1)
+t190:=isoutni(xp1,1,satz24a(xp1),inn(x,1b),trlessis"n"(inn(x,1b),x,xp1,1top(x,1b),t178),t189):is"e"(1to(xp1),1out(xp1),1c)
+t191:=isf(1to(xp1),cx,g(xp1,s,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s,f),<xout(1)>g11)
+t192:=tris2(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(1)>g11,t185,t191):is(smpr(1,g11),<1out(xp1)>g(xp1,s,f))
+t193:=symis(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s,t175):is"e"(1to(xp1),<1out(xp1)>s,<xout(xp1)>s4)
+t194:=isf(1to(xp1),cx,f,<1out(xp1)>s,<xout(xp1)>s4,t193):is(<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f))
+t195:=tris(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f),t192,t194):is(smpr(1,g11),<xout(xp1)>g(xp1,s4,f))
+t196:=isf(cx,cx,[t:cx]<smpr(xm1,g10)><t>q,smpr(1,g11),<xout(xp1)>g(xp1,s4,f),t195):is(<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
+t197:=tr3is(cx,smpr(x,g8),smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t182,t184,t196):is(smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
+t198:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s,f)><t>q,smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t197):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q)
+t199:=assq1(a,<xout(xp1)>g(xp1,s4,f),smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q)
+t200:=comq(c,<xout(xp1)>g(xp1,s4,f),<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q):is(<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
+g12:=left(cx,xp1,x,t178,g(xp1,s4,f)):[t:1to(x)]cx
+g13:=left(cx,x,pl"n"(1,xm1),t181,g12):[t:1to(pl"n"(1,xm1))]cx
+g14:=right(cx,1,xm1,g13):[t:1to(xm1)]cx
+g15:=left(cx,pl"n"(1,xm1),1,lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)),g13):[t:1to(1)]cx
+t201:=satz278(x,g(xp1,s4,f)):is(smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
+t202:=symis(cx,smpr(pl"n"(1,xm1),g13),smpr(x,g12),issmpr(x,g12,pl"n"(1,xm1),t180)):is(smpr(x,g12),smpr(pl"n"(1,xm1),g13))
+t203:=satz281(a,1,xm1,g13):is(smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q)
+t204:=satz277(g15):is(smpr(1,g15),<xout(1)>g15)
+t205:=isf(1to(xp1),cx,g(xp1,s4,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s4,f),<xout(1)>g15)
+t206:=tris2(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(1)>g15,t204,t205):is(smpr(1,g15),<1out(xp1)>g(xp1,s4,f))
+t207:=changef1(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s4,<xout(xp1)>s)
+t208:=isf(1to(xp1),cx,f,<1out(xp1)>s4,<xout(xp1)>s,t207):is(<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f))
+t209:=tris(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f),t206,t208):is(smpr(1,g15),<xout(xp1)>g(xp1,s,f))
+t210:=isf(cx,cx,[t:cx]<smpr(xm1,g14)><t>q,smpr(1,g15),<xout(xp1)>g(xp1,s,f),t209):is(<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+t211:=tr3is(cx,smpr(x,g12),smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t202,t203,t210):is(smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+[u:1to(xm1)]
+ua:=right1to(1,xm1,u):1to(pl"n"(1,xm1))
+ub:=left1to(x,pl"n"(1,xm1),t181,ua):1to(x)
+uc:=left1to(xp1,x,t178,ub):1to(xp1)
+[i:is"e"(1to(xp1),uc,xout(xp1))]
+t212:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),xp1,lessisi3(xp1),i):is"n"(inn(x,ub),xp1)
+t213:=satz16a(inn(x,ub),x,xp1,1top(x,ub),satz18a(x,1)):less"n"(inn(x,ub),xp1)
+t214:=<t212>ec3e31(is"n"(inn(x,ub),xp1),more"n"(inn(x,ub),xp1),less"n"(inn(x,ub),xp1),satz10b(inn(x,ub),xp1),t213):con
+u@t215:=[t:is"e"(1to(xp1),uc,xout(xp1))]t214(t):not(is"e"(1to(xp1),uc,xout(xp1)))
+[i:is"e"(1to(xp1),uc,1out(xp1))]
+t216:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),1,satz24a(xp1),i):is"n"(inn(x,ub),1)
+t217:=isinoutn(x,inn(pl"n"(1,xm1),ua),trlessis"n"(inn(pl"n"(1,xm1),ua),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),ua),t181)):is"n"(inn(pl"n"(1,xm1),ua),inn(x,ub))
+t218:=isinoutn(pl"n"(1,xm1),pl"n"(1,inn(xm1,u)),satz19o(inn(xm1,u),xm1,1,1top(xm1,u))):is"n"(pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua))
+t219:=tr3is(nat,pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua),inn(x,ub),1,t218,t217,t216):is"n"(pl"n"(1,inn(xm1,u)),1)
+t220:=satz18(1,inn(xm1,u)):more"n"(pl"n"(1,inn(xm1,u)),1)
+t221:=<t219>ec3e21(is"n"(pl"n"(1,inn(xm1,u)),1),more"n"(pl"n"(1,inn(xm1,u)),1),less"n"(pl"n"(1,inn(xm1,u)),1),satz10b(pl"n"(1,inn(xm1,u)),1),t220):con
+u@t222:=[t:is"e"(1to(xp1),uc,1out(xp1))]t221(t):not(is"e"(1to(xp1),uc,1out(xp1)))
+t223:=changef3(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),uc,t222,t215):is"e"(1to(xp1),<uc>s4,<uc>s)
+t224:=isf(1to(xp1),cx,f,<uc>s4,<uc>s,t223):is(<u>g14,<u>g10)
+n@t225:=fisi(1to(xm1),cx,g10,g14,[t:1to(xm1)]symis(cx,<t>g14,<t>g10,t224(t))):is"e"([t:1to(xm1)]cx,g10,g14)
+t226:=isf([t:1to(xm1)]cx,cx,[u:[t:1to(xm1)]cx]smpr(xm1,u),g10,g14,t225):is(smpr(xm1,g10),smpr(xm1,g14))
+t227:=comq(c,smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q)
+t228:=isf(cx,cx,<<xout(xp1)>g(xp1,s,f)>q,smpr(xm1,g10),smpr(xm1,g14),t226):is(<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+t229:=tris(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t227,t228):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+t230:=tris2(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t229,t211):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12))
+t231:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s4,f)><t>q,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),t230):is(<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
+t232:=symis(cx,smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,t201):is(<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)))
+t233:=t46(s4,f,t174,t177):is(smpr(xp1,g(xp1,s4,f)),smpr(xp1,f))
+t234:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,t179,t198,t199,t200):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
+t235:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)),smpr(xp1,f),t234,t231,t232,t233):prop1(xp1,s,f)
+gamma@t236:=th1"l.imp"(is"n"(x,1),prop1(xp1,s,f),[t:is"n"(x,1)]t172(t),[t:not(is"n"(x,1))]t235(t)):prop1(xp1,s,f)
+i3@t237:=th1"l.imp"(is"e"(1to(xp1),b0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),b0,xout(xp1))]t236(t),[t:not(is"e"(1to(xp1),b0,xout(xp1)))]t148(t)):prop1(xp1,s,f)
+not2@t238:=th1"l.imp"(is"e"(1to(xp1),a0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),a0,xout(xp1))]t237(t),[t:not(is"e"(1to(xp1),a0,xout(xp1)))]t128(t)):prop1(xp1,s,f)
+not1@t239:=th1"l.imp"(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))]t97(t),[t:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]t238(t)):prop1(xp1,s,f)
+b@t240:=th1"l.imp"(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))]t46(t),[t:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))]t239(t)):prop1(xp1,s,f)
+p@t241:=[u:[t:1to(xp1)]1to(xp1)][v:[t:1to(xp1)]cx][w:bijective(1to(xp1),1to(xp1),u)]t240(u,v,w):prop2(xp1)
+t242:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t241,satz4a(x)):prop2(<x>suc)
+x@t243:=induction([t:nat]prop2(t),t6,[t:nat][u:prop2(t)]t242(t,u),x):prop2(x)
+-8283
+satz283:=<b><f><s>t243".8283":is(smpr(x,[t:1to(x)]<<t>s>f),smpr(x,f))
+@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
+shiftl:=shiftl"r"(x,ix,y,iy,ly):nat
+[n:1to(shiftl)]
+shiftr:=shiftr"r"(x,ix,y,iy,ly,n):real
+intshiftr:=intshiftr"r"(x,ix,y,iy,ly,n):intrl(shiftr)
+shiftrls:=shiftrls"r"(x,ix,y,iy,ly,n):lessis(shiftr,x)
+lsshiftr:=lsshiftr"r"(x,ix,y,iy,ly,n):lessis(y,shiftr)
+[m:1to(shiftl)][i:is"r"(shiftr(n),shiftr(m))]
+iseshiftr:=iseshiftr"r"(x,ix,y,iy,ly,n,m,i):is"e"(1to(shiftl),n,m)
+ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
+shiftl1:=shiftl1"r"(x,ix,y,iy,ly,u,a):1to(shiftl)
+shiftinv1:=shiftinv1"r"(x,ix,y,iy,ly,u,a):is"r"(u,shiftr(shiftl1))
+shiftinv2:=shiftinv2"r"(x,ix,y,iy,ly,u,a):is"r"(shiftr(shiftl1),u)
+ly@[f:seq(x,ix,y,iy,ly,cx)]
+shiftf:=shiftf(x,ix,y,iy,ly,cx,f):[t:1to(shiftl)]cx
+[q:[t:cx][u:cx]cx]
+smpri:=smpr(q,shiftl,shiftf):cx
+f@[pi:proofsirrelevant(x,ix,y,iy,ly,cx,f)][q:[t:cx][u:cx]cx][a:assoc(q)][u:real][iu:intrl(u)][l:lessis(y,u)][k:less(u,x)][v:real][iv:intrl(v)][lv:lessis(y,v)][kv:lessis(v,u)]
++8284
+t1:=lessisi1(v,x,satz172a(v,u,x,kv,k)):lessis(v,x)
+-8284
+k@lft:=[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]<t1".8284"(t,v,lt,kt)><lt><v><t>f:[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]cx
+iv@[lv:lessis(pl"r"(u,1rl),v)][kv:lessis(v,x)]
++*8284
+x@[y:real]
+pl:=pl"r"(x,y):real
+mn:=mn"r"(x,y):real
+x@p1:=pl"r"(x,1rl):real
+kv@t2:=satz190c(u,u,0,1rl,lessisi2(u,u,refis(real,u)),lemma1"r"(1rl,0,satz169a(1rl,natpos(1rl,natrl1)))):less(pl(u,0),p1(u))
+t3:=isless1(pl(u,0),u,p1(u),pl02"r"(u,0,refis(real,0)),t2):less(u,p1(u))
+t4:=lessisi1(y,v,satz172b(y,p1(u),v,satz172a(y,u,p1(u),l,t3),lv)):lessis(y,v)
+-8284
+k@rgt:=[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]<kt><t4".8284"(t,v,lt,kt)><v><t>f:[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]cx
++*8284
+k@t5:=intpl(u,iu,1rl,intrl1):intrl(p1(u))
+t6:=satzr25(u,iu,x,ix,k):lessis(p1(u),x)
+t7:=tr3is(real,pl(mn(p1(u),y),mn(p1(x),p1(u))),pl(mn(p1(x),p1(u)),mn(p1(u),y)),mn(pl(mn(p1(x),p1(u)),p1(u)),y),mn(p1(x),y),compl"r"(mn(p1(u),y),mn(p1(x),p1(u))),asspl2"r"(mn(p1(x),p1(u)),p1(u),m0"r"(y)),ismn1"r"(pl(mn(p1(x),p1(u)),p1(u)),p1(x),y,plmn(p1(x),p1(u)))):is"r"(pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y))
+sxy:=shiftl(x,ix,y,iy,ly):nat
+suy:=shiftl(u,iu,y,iy,l):nat
+sxu:=shiftl(x,ix,p1(u),t5,t6):nat
+t8:=tr4is(real,rlofnt(pl"n"(suy,sxu)),pl(rlofnt(suy),rlofnt(sxu)),pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y),rlofnt(sxy),satzr155a(suy,sxu),ispl12"r"(rlofnt(suy),mn(p1(u),y),rlofnt(sxu),mn(p1(x),p1(u)),isrlnt2(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l)),isrlnt2(mn(p1(x),p1(u)),t6"r.shift"(x,ix,p1(u),t5,t6))),t7,isrlnt1(mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly))):is"r"(rlofnt(pl"n"(suy,sxu)),rlofnt(sxy))
+t9:=isntirl(pl"n"(suy,sxu),sxy,t8):is"n"(pl"n"(suy,sxu),sxy)
+t10:=lessisi2"n"(pl"n"(suy,sxu),sxy,t9):lessis"n"(pl"n"(suy,sxu),sxy)
+f1:=left(cx,sxy,pl"n"(suy,sxu),t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(pl"n"(suy,sxu))]cx
+t11:=issmpr(q,sxy,shiftf(x,ix,y,iy,ly,f),pl"n"(suy,sxu),t9):is(smpr(q,pl"n"(suy,sxu),f1),smpri(x,ix,y,iy,ly,f,q))
+fr:=right(cx,suy,sxu,f1):[t:1to(sxu)]cx
+t12:=lessisi1"n"(suy,pl"n"(suy,sxu),satz18a(suy,sxu)):lessis"n"(suy,pl"n"(suy,sxu))
+fl:=left(cx,pl"n"(suy,sxu),suy,t12,f1):[t:1to(suy)]cx
+t12a:=satz281(q,a,suy,sxu,f1):is(smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q)
+[n:1to(sxu)]
+t13:=isinoutn(pl"n"(suy,sxu),pl"n"(suy,inn(sxu,n)),satz19o(inn(sxu,n),sxu,suy,1top(sxu,n))):is"n"(pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)))
+t14:=isinoutn(sxy,inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),trlessis"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),right1to(suy,sxu,n)),t10)):is"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n))))
+n1:=left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n)):1to(sxy)
+t15:=tris(nat,pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,n1),t13,t14):is"n"(pl"n"(suy,inn(sxu,n)),inn(sxy,n1))
+t16:=isnterl(pl"n"(suy,inn(sxu,n)),inn(sxy,n1),t15):is"r"(rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)))
+t17:=satzr155b(suy,inn(sxu,n)):is"r"(pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))))
+t18:=ispl1"r"(mn(p1(u),y),rlofnt(suy),rlofnt(inn(sxu,n)),isrlnt1(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l))):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))))
+t19:=tr3is(real,pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)),t18,t17,t16):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)))
+t20:=ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)),y,t19):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxy,n1)),y))
+t21:=tr3is(real,pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y),pl(rlofnt(inn(sxu,n)),pl(mn(p1(u),y),y)),pl(rlofnt(inn(sxu,n)),p1(u)),ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y,compl"r"(mn(p1(u),y),rlofnt(inn(sxu,n)))),asspl1"r"(rlofnt(inn(sxu,n)),mn(p1(u),y),y),ispl2"r"(pl(mn(p1(u),y),y),p1(u),rlofnt(inn(sxu,n)),plmn(p1(u),y))):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxu,n)),p1(u)))
+t22:=tris1(real,pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),t20,t21):is"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)))
+t23:=ismn1"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),1rl,t22):is"r"(shiftr(x,ix,y,iy,ly,n1),shiftr(x,ix,p1(u),t5,t6,n))
+t24:=intshiftr(x,ix,y,iy,ly,n1):intrl(shiftr(x,ix,y,iy,ly,n1))
+t25:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,shiftr(x,ix,y,iy,ly,n1))
+t26:=shiftrls(x,ix,y,iy,ly,n1):lessis(shiftr(x,ix,y,iy,ly,n1),x)
+t27:=intshiftr(x,ix,p1(u),t5,t6,n):intrl(shiftr(x,ix,p1(u),t5,t6,n))
+t28:=lsshiftr(x,ix,p1(u),t5,t6,n):lessis(p1(u),shiftr(x,ix,p1(u),t5,t6,n))
+t29:=shiftrls(x,ix,p1(u),t5,t6,n):lessis(shiftr(x,ix,p1(u),t5,t6,n),x)
+t30:=t4(shiftr(x,ix,p1(u),t5,t6,n),t27,t28,t29):lessis(y,shiftr(x,ix,p1(u),t5,t6,n))
+t31:=<t23><t29><t30><t27><shiftr(x,ix,p1(u),t5,t6,n)><t26><t25><t24><shiftr(x,ix,y,iy,ly,n1)>pi:is(<n>fr,<n>shiftf(x,ix,p1(u),t5,t6,rgt))
+k@t32:=fisi(1to(sxu),cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt),[t:1to(sxu)]t31(t)):is"e"([t:1to(sxu)]cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt))
+t33:=isf([t:1to(sxu)]cx,cx,[v:[t:1to(sxu)]cx]smpr(q,sxu,v),fr,shiftf(x,ix,p1(u),t5,t6,rgt),t32):is(smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q))
+t34:=isf(cx,cx,<smpr(q,suy,fl)>q,smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q),t33):is(<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q)
+[n:1to(suy)]
+t35:=isinoutn(pl"n"(suy,sxu),inn(suy,n),trlessis"n"(inn(suy,n),suy,pl"n"(suy,sxu),1top(suy,n),t12)):is"n"(inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)))
+t36:=isinoutn(sxy,inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),trlessis"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),t10)):is"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n))))
+n2:=left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n)):1to(sxy)
+t37:=tris(nat,inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,n2),t35,t36):is"n"(inn(suy,n),inn(sxy,n2))
+t38:=isnterl(inn(suy,n),inn(sxy,n2),t37):is"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)))
+t39:=ispl1"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)),y,t38):is"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y))
+t40:=ismn1"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y),1rl,t39):is"r"(shiftr(u,iu,y,iy,l,n),shiftr(x,ix,y,iy,ly,n2))
+t41:=intshiftr(u,iu,y,iy,l,n):intrl(shiftr(u,iu,y,iy,l,n))
+t42:=lsshiftr(u,iu,y,iy,l,n):lessis(y,shiftr(u,iu,y,iy,l,n))
+t43:=shiftrls(u,iu,y,iy,l,n):lessis(shiftr(u,iu,y,iy,l,n),u)
+t44:=t1(shiftr(u,iu,y,iy,l,n),t41,t42,t43):lessis(shiftr(u,iu,y,iy,l,n),x)
+t45:=intshiftr(x,ix,y,iy,ly,n2):intrl(shiftr(x,ix,y,iy,ly,n2))
+t46:=lsshiftr(x,ix,y,iy,ly,n2):lessis(y,shiftr(x,ix,y,iy,ly,n2))
+t47:=shiftrls(x,ix,y,iy,ly,n2):lessis(shiftr(x,ix,y,iy,ly,n2),x)
+t48:=<t40><t47><t46><t45><shiftr(x,ix,y,iy,ly,n2)><t44><t42><t41><shiftr(u,iu,y,iy,l,n)>pi:is(<n>shiftf(u,iu,y,iy,l,lft),<n>fl)
+t49:=symis(cx,<n>shiftf(u,iu,y,iy,l,lft),<n>fl,t48):is(<n>fl,<n>shiftf(u,iu,y,iy,l,lft))
+k@t50:=fisi(1to(suy),cx,fl,shiftf(u,iu,y,iy,l,lft),[t:1to(suy)]t49(t)):is"e"([t:1to(suy)]cx,fl,shiftf(u,iu,y,iy,l,lft))
+t51:=isf([t:1to(suy)]cx,cx,[v:[t:1to(suy)]cx]smpr(q,suy,v),fl,shiftf(u,iu,y,iy,l,lft),t50):is(smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q))
+t52:=isf(cx,cx,[t:cx]<smpri(x,ix,p1(u),t5,t6,rgt,q)><t>q,smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q),t51):is(<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
+t53:=tr3is(cx,smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,t12a,t34,t52):is(smpr(q,pl"n"(suy,sxu),f1),<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
+-8284
+k@satz284:=tris1(cx,smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,smpr(q,pl"n"(suy".8284",sxu".8284"),f1".8284"),t11".8284",t53".8284"):is(smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
+q@[v:real][iv:intrl(v)][w:real][iw:intrl(w)][lw:lessis(pl"r"(y,v),w)][kw:lessis(w,pl"r"(x,v))]
++8285
+x@[y:real]
+pl:=pl"r"(x,y):real
+mn:=mn"r"(x,y):real
+x@p1:=pl"r"(x,1rl):real
+kw@t1:=th9"l.or"(less(pl(y,v),w),is"r"(pl(y,v),w),less(mn(pl(y,v),v),mn(w,v)),is"r"(mn(pl(y,v),v),mn(w,v)),lw,[t:less(pl(y,v),w)]satz188f(pl(y,v),w,m0"r"(v),t),[t:is"r"(pl(y,v),w)]ismn1"r"(pl(y,v),w,v,t)):lessis(mn(pl(y,v),v),mn(w,v))
+t2:=islessis1(mn(pl(y,v),v),y,mn(w,v),mnpl(y,v),t1):lessis(y,mn(w,v))
+t3:=th9"l.or"(less(w,pl(x,v)),is"r"(w,pl(x,v)),less(mn(w,v),mn(pl(x,v),v)),is"r"(mn(w,v),mn(pl(x,v),v)),kw,[t:less(w,pl(x,v))]satz188f(w,pl(x,v),m0"r"(v),t),[t:is"r"(w,pl(x,v))]ismn1"r"(w,pl(x,v),v,t)):lessis(mn(w,v),mn(pl(x,v),v))
+t4:=islessis2(mn(pl(x,v),v),x,mn(w,v),mnpl(x,v),t3):lessis(mn(w,v),x)
+-8285
+iv@sft:=[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]<t4".8285"(t,w,lt,kt)><t2".8285"(t,w,lt,kt)><intmn(t,w,v,iv)><mn"r"(t,v)>f:[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]cx
++*8285
+iv@t5:=tris(real,m0"r"(pl(y,v)),m0"r"(pl(v,y)),pl(m0"r"(v),m0"r"(y)),ism0"r"(pl(y,v),pl(v,y),compl"r"(y,v)),satz180(v,y)):is"r"(m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)))
+t6:=tr3is(real,mn(pl(1rl,pl(x,v)),v),pl(1rl,mn(pl(x,v),v)),pl(1rl,x),p1(x),asspl1"r"(1rl,pl(x,v),m0"r"(v)),ispl2"r"(mn(pl(x,v),v),x,1rl,mnpl(x,v)),compl"r"(1rl,x)):is"r"(mn(pl(1rl,pl(x,v)),v),p1(x))
+t7:=tr3is(real,mn(p1(pl(x,v)),pl(y,v)),pl(pl(1rl,pl(x,v)),pl(m0"r"(v),m0"r"(y))),mn(mn(pl(1rl,pl(x,v)),v),y),mn(p1(x),y),ispl12"r"(p1(pl(x,v)),pl(1rl,pl(x,v)),m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)),compl"r"(pl(x,v),1rl),t5),asspl2"r"(pl(1rl,pl(x,v)),m0"r"(v),m0"r"(y)),ismn1"r"(mn(pl(1rl,pl(x,v)),v),p1(x),y,t6)):is"r"(mn(p1(pl(x,v)),pl(y,v)),mn(p1(x),y))
+t8:=th9"l.or"(less(y,x),is"r"(y,x),less(pl(y,v),pl(x,v)),is"r"(pl(y,v),pl(x,v)),ly,[t:less(y,x)]satz188f(y,x,v,t),[t:is"r"(y,x)]ispl1"r"(y,x,v,t)):lessis(pl(y,v),pl(x,v))
+s0:=shiftl(x,ix,y,iy,ly):nat
+sv:=shiftl(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8):nat
+t9:=isrlent(mn(p1(pl(x,v)),pl(y,v)),t6"r.shift"(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8),mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly),t7):is"n"(sv,s0)
+t10:=lessisi2"n"(sv,s0,t9):lessis"n"(sv,s0)
+f1:=left(cx,s0,sv,t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(sv)]cx
+t11:=issmpr(q,s0,shiftf(x,ix,y,iy,ly,f),sv,t9):is(smpr(q,sv,f1),smpri(x,ix,y,iy,ly,f,q))
+[n:1to(sv)]
+t12:=isinoutn(s0,inn(sv,n),trlessis"n"(inn(sv,n),sv,s0,1top(sv,n),t10)):is"n"(inn(sv,n),inn(s0,left1to(s0,sv,t10,n)))
+n1:=left1to(s0,sv,t10,n):1to(s0)
+t13:=isnterl(inn(sv,n),inn(s0,n1),t12):is"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)))
+t14:=tris(real,mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(sv,n)),mn(pl(y,v),v)),pl(rlofnt(inn(s0,n1)),y),asspl1"r"(rlofnt(inn(sv,n)),pl(y,v),m0"r"(v)),ispl12"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)),mn(pl(y,v),v),y,t13,mnpl(y,v))):is"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y))
+st0:=shiftr(x,ix,y,iy,ly,n1):real
+stv:=shiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):real
+t15:=tr4is(real,mn(stv,v),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(1rl),m0"r"(v))),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(v),m0"r"(1rl))),mn(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),1rl),st0,asspl1"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(1rl),m0"r"(v)),ispl2"r"(pl(m0"r"(1rl),m0"r"(v)),pl(m0"r"(v),m0"r"(1rl)),pl(rlofnt(inn(sv,n)),pl(y,v)),compl"r"(m0"r"(1rl),m0"r"(v))),asspl2"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(v),m0"r"(1rl)),ismn1"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y),1rl,t14)):is"r"(mn(stv,v),st0)
+t16:=intshiftr(x,ix,y,iy,ly,n1):intrl(st0)
+t17:=shiftrls(x,ix,y,iy,ly,n1):lessis(st0,x)
+t18:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,st0)
+t19:=intshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):intrl(stv)
+t20:=shiftrls(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(stv,pl(x,v))
+t21:=lsshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(pl(y,v),stv)
+t22:=intmn(stv,t19,v,iv):intrl(mn(stv,v))
+t23:=t2(stv,t19,t21,t20):lessis(y,mn(stv,v))
+t24:=t4(stv,t19,t21,t20):lessis(mn(stv,v),x)
+t25:=<t15><t17><t18><t16><st0><t24><t23><t22><mn(stv,v)>pi:is(<n>shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),<n>f1)
+iv@t26:=fisi(1to(sv),cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,[t:1to(sv)]t25(t)):is"e"([t:1to(sv)]cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1)
+t27:=isf([t:1to(sv)]cx,cx,[w:[t:1to(sv)]cx]smpr(q,sv,w),shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,t26):is(smpri(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft,q),smpr(q,sv,f1))
+-8285
+iv@lemma285:=t8".8285":lessis(pl"r"(y,v),pl"r"(x,v))
+satz285:=tris(cx,smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpr(q,sv".8285",f1".8285"),smpri(x,ix,y,iy,ly,f,q),t27".8285",t11".8285"):is(smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpri(x,ix,y,iy,ly,f,q))
+ly@[s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][f:seq(x,ix,y,iy,ly,cx)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)]
+us:=<ul><lu><iu><u>s:real
++8286
+t1:=<ul><lu><iu><u>ins:and3(intrl(us),lessis(y,us),lessis(us,x))
+-8286
+inseqe1:=t22"r.shift"(x,ix,y,iy,ly,us,t1".8286"):intrl(us)
+inseqe2:=t23"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(y,us)
+inseqe3:=t24"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(us,x)
+usf:=<inseqe3><inseqe2><inseqe1><us>f:cx
+f@permseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]usf(t,u,v,w):[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]cx
+q@[a:assoc(q)][c:commut(q)][s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][pri:proofsirrelevant(x,ix,y,iy,ly,real,s)][ps:perm(x,ix,y,iy,ly,s)]
++*8286
+ps@ss:=shiftseq(x,ix,y,iy,ly,s,ins):[t:1to(shiftl)]1to(shiftl)
+t2:=satz283(q,a,c,shiftl,ss,bijshiftseq(x,ix,y,iy,ly,s,ins,pri,ps),shiftf(f)):is(smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)),smpri(f,q))
+[n:1to(shiftl)]
+ns:=us(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):real
+t3:=shiftinv1(ns,t34"r.shift"(x,ix,y,iy,ly,s,ins,n)):is"r"(ns,shiftr(<n>ss))
+t4:=inseqe1(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):intrl(ns)
+t5:=inseqe2(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(y,ns)
+t6:=inseqe3(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(ns,x)
+t7:=intshiftr(<n>ss):intrl(shiftr(<n>ss))
+t8:=lsshiftr(<n>ss):lessis(y,shiftr(<n>ss))
+t9:=shiftrls(<n>ss):lessis(shiftr(<n>ss),x)
+t10:=<t3><t9><t8><t7><shiftr(<n>ss)><t6><t5><t4><ns>pi:is(<n>shiftf(permseq(s,ins,f)),<<n>ss>shiftf(f))
+ps@t11:=fisi(1to(shiftl),cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),[t:1to(shiftl)]t10(t)):is"e"([t:1to(shiftl)]cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f))
+t12:=isf([t:1to(shiftl)]cx,cx,[u:[t:1to(shiftl)]cx]smpr(q,shiftl,u),shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),t11):is(smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)))
+-8286
+ps@satz286:=tris(cx,smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss".8286">shiftf(f)),smpri(f,q),t12".8286",t2".8286"):is(smpri(permseq(s,ins,f),q),smpri(f,q))
+@[x:nat][f:[t:1to(x)]cx]
+modf:=[t:1to(x)]pli(mod(<t>f),0):[t:1to(x)]cx
++8287
+[r:real]
+prop1:=lessis(mod(sum(x,f)),r):'prop'
+prop2:=is(sum(x,modf(f)),pli(r,0)):'prop'
+prop3:=and(prop1,prop2):'prop'
+f@prop4:=some"r"([t:real]prop3(t)):'prop'
+x@prop5:=[u:[t:1to(x)]cx]prop4(u):'prop'
+@[f:[t:1to(1)]cx]
+t1:=satz277([t:cx][u:cx]pl(t,u),f):is(sum(1,f),<xout(1)>f)
+t2:=ismod(sum(1,f),<xout(1)>f,t1):is"r"(mod(sum(1,f)),mod(<xout(1)>f))
+t3:=lessisi2(mod(sum(1,f)),mod(<xout(1)>f),t2):prop1(1,f,mod(<xout(1)>f))
+t4:=satz277([t:cx][u:cx]pl(t,u),modf(1,f)):prop2(1,f,mod(<xout(1)>f))
+t5:=andi(prop1(1,f,mod(<xout(1)>f)),prop2(1,f,mod(<xout(1)>f)),t3,t4):prop3(1,f,mod(<xout(1)>f))
+t6:=somei(real,[t:real]prop3(1,f,t),mod(<xout(1)>f),t5):prop4(1,f)
+@t7:=[u:[t:1to(1)]cx]t6(u):prop5(1)
+x@[p:prop5(x)][f:[t:1to(pl"n"(x,1))]cx]
+t8:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
+lf:=left(cx,pl"n"(x,1),x,t8,f):[t:1to(x)]cx
+[r:real][pr:prop3(lf,r)]
+t9:=ande1(prop1(lf,r),prop2(lf,r),pr):prop1(lf,r)
+t10:=ande2(prop1(lf,r),prop2(lf,r),pr):prop2(lf,r)
+t11:=satz278([t:cx][u:cx]pl(t,u),x,f):is(sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f))
+t12:=ismod(pl(sum(x,lf),<xout(pl"n"(x,1))>f),sum(pl"n"(x,1),f),symis(cx,sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f),t11)):is"r"(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)))
+m:=mod(<xout(pl"n"(x,1))>f):real
+t13:=islessis1(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),t12,satz271(sum(x,lf),<xout(pl"n"(x,1))>f)):lessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m))
+t14:=th9"l.or"(less(mod(sum(x,lf)),r),is"r"(mod(sum(x,lf)),r),less(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),is"r"(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),t9,[t:less(mod(sum(x,lf)),r)]satz188f(mod(sum(x,lf)),r,m,t),[t:is"r"(mod(sum(x,lf)),r)]ispl1"r"(mod(sum(x,lf)),r,m,t)):lessis(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m))
+t15:=trlessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),pl"r"(r,m),t13,t14):prop1(pl"n"(x,1),f,pl"r"(r,m))
+lmf:=left(cx,pl"n"(x,1),x,t8,modf(pl"n"(x,1),f)):[t:1to(x)]cx
+t16:=satz278([t:cx][u:cx]pl(t,u),x,modf(pl"n"(x,1),f)):is(sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)))
+t17:=ispl1(sum(x,lmf),pli(r,0),pli(m,0),t10):is(pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)))
+t18:=plis12a(r,0,m,0):is(pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)))
+t19:=isrecx2(pl"r"(0,0),0,pl"r"(r,m),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0))
+t20:=tr4is(cx,sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0),t16,t17,t18,t19):prop2(pl"n"(x,1),f,pl"r"(r,m))
+t21:=andi(prop1(pl"n"(x,1),f,pl"r"(r,m)),prop2(pl"n"(x,1),f,pl"r"(r,m)),t15,t20):prop3(pl"n"(x,1),f,pl"r"(r,m))
+t22:=somei(real,[t:real]prop3(pl"n"(x,1),f,t),pl"r"(r,m),t21):prop4(pl"n"(x,1),f)
+f@t23:=someapp(real,[t:real]prop3(lf,t),<lf>p,prop4(pl"n"(x,1),f),[t:real][u:prop3(lf,t)]t22(t,u)):prop4(pl"n"(x,1),f)
+p@t25:=[u:[t:1to(pl"n"(x,1))]cx]t23(u):prop5(pl"n"(x,1))
+t26:=isp(nat,[t:nat]prop5(t),pl"n"(x,1),<x>suc,t25,satz4a(x)):prop5(<x>suc)
+-8287
+satz287:=<f>induction([t:nat]prop5".8287"(t),t7".8287",[t:nat][u:prop5".8287"(t)]t26".8287"(t,u),x):some"r"([t:real]and(lessis(mod(sum(x,f)),t),is(sum(x,modf(f)),pli(t,0))))
++8288
+prop1:=is(pli(mod(prod(x,f)),0),prod(x,modf(f))):'prop'
+x@prop2:=[u:[t:1to(x)]cx]prop1(u):'prop'
+@[f:[t:1to(1)]cx]
+t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
+t2:=ismod(prod(1,f),<xout(1)>f,t1):is"r"(mod(prod(1,f)),mod(<xout(1)>f))
+t3:=isrecx1(mod(prod(1,f)),mod(<xout(1)>f),0,t2):is(pli(mod(prod(1,f)),0),pli(mod(<xout(1)>f),0))
+t4:=satz277([t:cx][u:cx]ts(t,u),modf(1,f)):is(prod(1,modf(1,f)),pli(mod(<xout(1)>f),0))
+t5:=tris2(cx,pli(mod(prod(1,f)),0),prod(1,modf(1,f)),pli(mod(<xout(1)>f),0),t3,t4):prop1(1,f)
+@t6:=[u:[t:1to(1)]cx]t5(u):prop2(1)
+x@[p:prop2(x)][f:[t:1to(pl"n"(x,1))]cx]
+t7:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
+lf:=left(cx,pl"n"(x,1),x,t7,f):[t:1to(x)]cx
+t8:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
+m:=mod(<xout(pl"n"(x,1))>f):real
+t9:=ismod(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),t8):is"r"(mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)))
+t10:=satz268(prod(x,lf),<xout(pl"n"(x,1))>f):is"r"(mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m))
+t11:=tris(real,mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m),t9,t10):is"r"(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m))
+t12:=isrecx1(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m),0,t11):is(pli(mod(prod(pl"n"(x,1),f)),0),pli(ts"r"(mod(prod(x,lf)),m),0))
+lmf:=left(cx,pl"n"(x,1),x,t7,modf(pl"n"(x,1),f)):[t:1to(x)]cx
+t13:=satz278([t:cx][u:cx]ts(t,u),x,modf(pl"n"(x,1),f)):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)))
+t14:=symis(cx,pli(mod(prod(x,lf)),0),prod(x,lmf),<lf>p):is(prod(x,lmf),pli(mod(prod(x,lf)),0))
+t15:=ists1(prod(x,lmf),pli(mod(prod(x,lf)),0),pli(m,0),t14):is(ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)))
+t16:=tsis12a(mod(prod(x,lf)),0,m,0):is(ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))))
+t17:=tris(real,mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),mn"r"(ts"r"(mod(prod(x,lf)),m),0),ts"r"(mod(prod(x,lf)),m),ismn2"r"(ts"r"(0,0),0,ts"r"(mod(prod(x,lf)),m),ts01"r"(0,0,refis(real,0))),pl02"r"(ts"r"(mod(prod(x,lf)),m),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m))
+t18:=tris(real,pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),pl"r"(0,0),0,ispl12"r"(ts"r"(mod(prod(x,lf)),0),0,ts"r"(0,m),0,ts02"r"(mod(prod(x,lf)),0,refis(real,0)),ts01"r"(0,m,refis(real,0))),pl01"r"(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0)
+t19:=isrecx12(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0,t17,t18):is(pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0))
+t20:=tr4is(cx,prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0),t13,t15,t16,t19):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0))
+t21:=tris2(cx,pli(mod(prod(pl"n"(x,1),f)),0),prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0),t12,t20):prop1(pl"n"(x,1),f)
+p@t21a:=[u:[t:1to(pl"n"(x,1))]cx]t21(u):prop2(pl"n"(x,1))
+t22:=isp(nat,[t:nat]prop2(t),pl"n"(x,1),<x>suc,t21a,satz4a(x)):prop2(<x>suc)
+-8288
+satz288:=<f>induction([t:nat]prop2".8288"(t),t6".8288",[t:nat][u:prop2".8288"(t)]t22".8288"(t,u),x):is(pli(mod(prod(x,f)),0),prod(x,modf(f)))
++8289
+prop1:=is(prod(x,f),0c):'prop'
+prop2:=some"l"(1to(x),[t:1to(x)]is(<t>f,0c)):'prop'
+prop3:=iff(prop1,prop2):'prop'
+x@prop4:=[u:[t:1to(x)]cx]prop3(u):'prop'
+@[f:[t:1to(1)]cx]
+t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
+[p:prop1(1,f)]
+t2:=tris1(cx,<xout(1)>f,0c,prod(1,f),t1,p):is(<xout(1)>f,0c)
+t3:=somei(1to(1),[t:1to(1)]is(<t>f,0c),xout(1),t2):prop2(1,f)
+f@[p:prop2(1,f)][u:1to(1)][i:is(<u>f,0c)]
+t4:=th1"n.singlet"(u):is"e"(1to(1),u,xout(1))
+t5:=tr3is(cx,prod(1,f),<xout(1)>f,<u>f,0c,t1,isf(1to(1),cx,f,xout(1),u,symis(1to(1),u,xout(1),t4)),i):prop1(1,f)
+p@t6:=someapp(1to(1),[t:1to(1)]is(<t>f,0c),p,prop1(1,f),[t:1to(1)][u:is(<t>f,0c)]t5(t,u)):prop1(1,f)
+f@t7:=iffi(prop1(1,f),prop2(1,f),[t:prop1(1,f)]t3(t),[t:prop2(1,f)]t6(t)):prop3(1,f)
+@t8:=[u:[t:1to(1)]cx]t7(u):prop4(1)
+x@[p:prop4(x)][f:[t:1to(pl"n"(x,1))]cx]
+t9:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
+lf:=left(cx,pl"n"(x,1),x,t9,f):[t:1to(x)]cx
+t10:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
+[q:prop1(pl"n"(x,1),f)]
+t11:=tris1(cx,ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,prod(pl"n"(x,1),f),t10,q):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+t12:=satz221c(prod(x,lf),<xout(pl"n"(x,1))>f,t11):or(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c))
+[i:is(prod(x,lf),0c)]
+t13:=th3"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,i):prop2(x,lf)
+[n:1to(x)][j:is(<n>lf,0c)]
+t14:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),left1to(pl"n"(x,1),x,t9,n),j):prop2(pl"n"(x,1),f)
+i@t15:=someapp(1to(x),[t:1to(x)]is(<t>lf,0c),t13,prop2(pl"n"(x,1),f),[t:1to(x)][u:is(<t>lf,0c)]t14(t,u)):prop2(pl"n"(x,1),f)
+q@[i:is(<xout(pl"n"(x,1))>f,0c)]
+t16:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),xout(pl"n"(x,1)),i):prop2(pl"n"(x,1),f)
+q@t17:=orapp(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c),prop2(pl"n"(x,1),f),t12,[t:is(prod(x,lf),0c)]t15(t),[t:is(<xout(pl"n"(x,1))>f,0c)]t16(t)):prop2(pl"n"(x,1),f)
+f@[q:prop2(pl"n"(x,1),f)][n:1to(pl"n"(x,1))][i:is(<n>f,0c)][j:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]
+t18:=tris1(cx,<xout(pl"n"(x,1))>f,0c,<n>f,isf(1to(pl"n"(x,1)),cx,f,n,xout(pl"n"(x,1)),j),i):is(<xout(pl"n"(x,1))>f,0c)
+t20:=satz221b(prod(x,lf),<xout(pl"n"(x,1))>f,t18):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+i@[m:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]
+n1:=inn(pl"n"(x,1),n):nat
+[j:is"n"(n1,pl"n"(x,1))]
+t21:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),pl"n"(x,1),lessisi3(pl"n"(x,1)),j):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)))
+t22:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)),isoutinn(pl"n"(x,1),n),t21):is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))
+m@t23:=th3"l.imp"(is"n"(n1,pl"n"(x,1)),is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),m,[t:is"n"(n1,pl"n"(x,1))]t22(t)):nis"n"(n1,pl"n"(x,1))
+t24:=ore1(less"n"(n1,pl"n"(x,1)),is"n"(n1,pl"n"(x,1)),1top(pl"n"(x,1),n),t23):less"n"(n1,pl"n"(x,1))
+t25:=satz26(x,n1,t24):lessis"n"(n1,x)
+n2:=outn(x,n1,t25):1to(x)
+t26:=isinoutn(x,n1,t25):is"n"(n1,inn(x,n2))
+t27:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),inn(x,n2),trlessis"n"(inn(x,n2),x,pl"n"(x,1),1top(x,n2),t9),t26):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2))
+t28:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2),isoutinn(pl"n"(x,1),n),t27):is"e"(1to(pl"n"(x,1)),n,left1to(pl"n"(x,1),x,t9,n2))
+t29:=isf(1to(pl"n"(x,1)),cx,f,n,left1to(pl"n"(x,1),x,t9,n2),t28):is(<n>f,<n2>lf)
+t30:=tris1(cx,<n2>lf,0c,<n>f,t29,i):is(<n2>lf,0c)
+t31:=somei(1to(x),[t:1to(x)]is(<t>lf,0c),n2,t30):prop2(x,lf)
+t32:=th4"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,t31):prop1(x,lf)
+t34:=satz221a(prod(x,lf),<xout(pl"n"(x,1))>f,t32):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+i@t35:=th1"l.imp"(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c),[t:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]t20(t),[t:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]t34(t)):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+t36:=tris(cx,prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,t10,t35):prop1(pl"n"(x,1),f)
+q@t37:=someapp(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),q,prop1(pl"n"(x,1),f),[t:1to(pl"n"(x,1))][u:is(<t>f,0c)]t36(t,u)):prop1(pl"n"(x,1),f)
+f@t38:=iffi(prop1(pl"n"(x,1),f),prop2(pl"n"(x,1),f),[t:prop1(pl"n"(x,1),f)]t17(t),[t:prop2(pl"n"(x,1),f)]t37(t)):prop3(pl"n"(x,1),f)
+p@t39:=[u:[t:1to(pl"n"(x,1))]cx]t38(u):prop4(pl"n"(x,1))
+t40:=isp(nat,[t:nat]prop4(t),pl"n"(x,1),<x>suc,t39,satz4a(x)):prop4(<x>suc)
+-8289
+satz289:=<f>induction([t:nat]prop4".8289"(t),t8".8289",[t:nat][u:prop4".8289"(t)]t40".8289"(t,u),x):iff(is(prod(x,f),0c),some"l"(1to(x),[t:1to(x)]is(<t>f,0c)))
+[i:is(prod(x,f),0c)]
+satz289a:=th3"l.iff"(prop1".8289",prop2".8289",satz289,i):some"l"(1to(x),[t:1to(x)]is(<t>f,0c))
+f@[n:1to(x)][i:is(<n>f,0c)]
++*8289
+i"c"@t41:=somei(1to(x),[t:1to(x)]is(<t>f,0c),n,i):prop2
+-8289
+i@satz289b:=th4"l.iff"(prop1".8289",prop2".8289",satz289,t41".8289"):is(prod(x,f),0c)
+@[x:complex][m:real][mi:intrl(m)][o:or(nis(x,0c),pos(m))]
++v9
+[p:pos(m)]
+t1:=posintnatrl(m,p,mi):natrl(m)
+m1:=ntofrl(m,t1):nat
+pw1:=prod(m1,[t:1to(m1)]x):cx
+-v9
+x@[y:complex][m:real][n:real][i:is(x,y)][j:is"r"(m,n)][mi1:intrl(m)][ni1:intrl(n)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(n))]
++*v9
+oy@[mp:pos(m)][np:pos(n)]
+m0:=m1(x,m,mi1,ox,mp):nat
+n0:=m1(y,n,ni1,oy,np):nat
+t2:=isrlent(m,t1(x,m,mi1,ox,mp),n,t1(y,n,ni1,oy,np),j):is"n"(m0,n0)
+t3:=lessisi2"n"(m0,n0,t2):lessis"n"(m0,n0)
+t4:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]y,m0,t2):is(prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np))
+t5:=fisi(1to(m0),cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),[t:1to(m0)]i):is"e"([t:1to(m0)]cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y))
+t6:=isf([t:1to(m0)]cx,cx,[u:[t:1to(m0)]cx]prod(m0,u),[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),t5):is(pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)))
+t7:=tris(cx,pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np),t6,t4):is(pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,np))
+p@[p1:pos(m)]
+t8:=t7(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,p,p1):is(pw1(p),pw1(p1))
+p@[n:nis(x,0c)]
+t9:=th5"l.some"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c),[t:1to(m1)]n):not(some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)))
+t10:=th3"l.imp"(is(pw1,0c),some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)),t9,[t:is(pw1,0c)]satz289a(m1,[u:1to(m1)]x,t)):nis(pw1,0c)
+o@[n:neg(m)]
+mi@t11:=intabs(m,mi):intrl(abs(m))
+n@t12:=satz166b(m,n):pos(abs(m))
+t13:=ori2(nis(x,0c),pos(abs(m)),t12):or(nis(x,0c),pos(abs(m)))
+t14:=ore1(nis(x,0c),pos(m),o,nnotp(m,n)):nis(x,0c)
+t15:=t10(abs(m),t11,t13,t12,t14):nis(pw1(abs(m),t11,t13,t12),0c)
+pw2:=ov(1c,pw1(abs(m),t11,t13,t12),t15):cx
+oy@[nm:neg(m)][nn:neg(n)]
+pwm:=pw1(x,abs(m),t11(x,m,mi1),t13(x,m,mi1,ox,nm),t12(x,m,mi1,ox,nm)):cx
+pwn:=pw1(y,abs(n),t11(y,n,ni1),t13(y,n,ni1,oy,nn),t12(y,n,ni1,oy,nn)):cx
+t16:=t7(abs(m),abs(n),i,isabs(m,n,j),t11(x,m,mi1),t11(y,n,ni1),t13(x,m,mi1,ox,nm),t13(y,n,ni1,oy,nn),t12(x,m,mi1,ox,nm),t12(y,n,ni1,oy,nn)):is(pwm,pwn)
+t17:=isov2(pwm,pwn,1c,t16,t15(x,m,mi1,ox,nm),t15(y,n,ni1,oy,nn)):is(pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,nn))
+n@[n1:neg(m)]
+t18:=t17(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,n,n1):is(pw2(n),pw2(n1))
+o@pw3:=ite"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c)):cx
+n@t19:=itet"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),n):is(pw3,pw2(n))
+o@[nn:not(neg(m))]
+t20:=itef"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),nn):is(pw3,1c)
+nm@t21:=isp(real,[t:real]neg(t),m,n,nm,j):neg(n)
+t22:=t19(x,m,mi1,ox,nm):is(pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm))
+t23:=symis(cx,pw3(y,n,ni1,oy),pw2(y,n,ni1,oy,t21),t19(y,n,ni1,oy,t21)):is(pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy))
+t24:=tr3is(cx,pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy),t22,t17(t21),t23):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
+oy@[nn:not(neg(m))]
+t25:=isp(real,[t:real]not(neg(t)),m,n,nn,j):not(neg(n))
+t26:=t20(x,m,mi1,ox,nn):is(pw3(x,m,mi1,ox),1c)
+t27:=t20(y,n,ni1,oy,t25):is(pw3(y,n,ni1,oy),1c)
+t28:=tris2(cx,pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),1c,t26,t27):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
+oy@t29:=th1"l.imp"(neg(m),is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy)),[t:neg(m)]t24(t),[t:not(neg(m))]t28(t)):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
+-v9
+o@pw:=ite"l.r"(pos(m),cx,[t:pos(m)]pw1".v9"(t),[t:not(pos(m))]pw3".v9",[t:pos(m)][u:pos(m)]t8".v9"(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3".v9")):cx
++*v9
+p@t30:=itet"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),p):is(pw,pw1(p))
+o@[n:not(pos(m))]
+t31:=itef"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),n):is(pw,pw3)
+o@[i:is"r"(m,0)]
+t32:=tris(cx,pw,pw3,1c,t31(0notp(m,i)),t20(0notn(m,i))):is(pw,1c)
+o@[n:neg(m)]
+t33:=tris(cx,pw,pw3,pw2(n),t31(nnotp(m,n)),t19(n)):is(pw,pw2(n))
+-v9
+o@[p:pos(m)]
+posexp:=t30".v9"(p):is(pw(x,m,mi,o),prod(ntofrl(m,posintnatrl(m,p,mi)),[t:1to(ntofrl(m,posintnatrl(m,p,mi)))]x))
+[n:nis(x,0c)]
+lemmapw1:=th2"e.notis"(cx,pw1".v9"(p),0c,pw,t10".v9"(p,n),posexp):nis(pw(x,m,mi,o),0c)
+o@[i:is"r"(m,0)]
+0exp:=t32".v9"(i):is(pw(x,m,mi,o),1c)
+o@[n:neg(m)]
+lemmapw2:=t14".v9"(n):nis(x,0c)
+lemmapw3:=t13".v9"(n):or(nis(x,0c),pos(abs(m)))
++*v9
+n@t34:=t30(abs(m),t11,t13(n),t12(n)):is(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)))
+t35:=isov2(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)),1c,t34,lemmapw1(abs(m),t11,t13(n),t12(n),t14(n)),t15(n)):is(ov(1c,pw(x,abs(m),t11,t13(n)),lemmapw1(abs(m),t11,t13(n),t12(n),t14(n))),pw2(n))
+-v9
+n@negexp:=tris2(cx,pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)),pw2".v9"(n),t33".v9"(n),t35".v9"(n)):is(pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)))
++*v9
+mp@t36:=isp(real,[t:real]pos(t),m,n,mp,j):pos(n)
+t37:=t30(x,m,mi1,ox,mp):is(pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp))
+t38:=symis(cx,pw(y,n,ni1,oy),pw1(y,n,ni1,oy,t36),t30(y,n,ni1,oy,t36)):is(pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy))
+t39:=tr3is(cx,pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy),t37,t7(t36),t38):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
+oy@[np:not(pos(m))]
+t40:=isp(real,[t:real]not(pos(t)),m,n,np,j):not(pos(n))
+t41:=t31(x,m,mi1,ox,np):is(pw(x,m,mi1,ox),pw3(x,m,mi1,ox))
+t42:=symis(cx,pw(y,n,ni1,oy),pw3(y,n,ni1,oy),t31(y,n,ni1,oy,t40)):is(pw3(y,n,ni1,oy),pw(y,n,ni1,oy))
+t43:=tr3is(cx,pw(x,m,mi1,ox),pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),pw(y,n,ni1,oy),t41,t29,t42):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
+-v9
+oy@ispw12:=th1"l.imp"(pos(m),is(pw(x,m,mi1,ox),pw(y,n,ni1,oy)),[t:pos(m)]t39".v9"(t),[t:not(pos(m))]t43".v9"(t)):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
+m@[i:is(x,y)][mi:intrl(m)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(m))]
+ispw1:=ispw12(x,y,m,m,i,refis(real,m),mi,mi,ox,oy):is(pw(x,m,mi,ox),pw(y,m,mi,oy))
+x@[m:real][n:real][i:is"r"(m,n)][mi:intrl(m)][ni:intrl(n)][om:or(nis(x,0c),pos(m))][on:or(nis(x,0c),pos(n))]
+ispw2:=ispw12(x,x,m,n,refis(cx,x),i,mi,ni,om,on):is(pw(x,m,mi,om),pw(x,n,ni,on))
+o@[n:nis(x,0c)]
++9290
+[p:pos(m)]
+t1:=lemmapw1(p,n):nis(pw(x,m,mi,o),0c)
+@[i:is(1c,0c)]
+t2:=tr3is(real,1rl,re(1c),re(0c),0,isre(1rl,0),iscere(1c,0c,i),reis(0,0)):is"r"(1rl,0)
+-9290
+@1not0:=th3"l.imp"(is(1c,0c),is"r"(1rl,0),pnot0(1rl,pos1),[t:is(1c,0c)]t2".9290"(t)):nis(1c,0c)
++*9290
+n@[i:is"r"(m,0)]
+t4:=th2"e.notis"(cx,1c,0c,pw(x,m,mi,o),1not0,0exp(i)):nis(pw(x,m,mi,o),0c)
+n@[nm:neg(m)]
+p0:=pw(x,abs(m),intabs(m,mi),lemmapw3(nm)):cx
+t5:=lemmapw1(x,abs(m),intabs(m,mi),lemmapw3(nm),satz166b(m,nm),lemmapw2(nm)):nis(p0,0c)
+t6:=tris(cx,ts(pw(x,m,mi,o),p0),ts(ov(1c,p0,t5),p0),1c,ists1(pw(x,m,mi,o),ov(1c,p0,t5),p0,negexp(nm)),satz229e(1c,p0,t5)):is(ts(pw(x,m,mi,o),p0),1c)
+t7:=th2"e.notis"(cx,1c,0c,ts(pw(x,m,mi,o),p0),1not0,t6):nis(ts(pw(x,m,mi,o),p0),0c)
+t8:=th3"l.imp"(is(pw(x,m,mi,o),0c),is(ts(pw(x,m,mi,o),p0),0c),t7,[t:is(pw(x,m,mi,o),0c)]satz221a(pw(x,m,mi,o),p0,t)):nis(pw(x,m,mi,o),0c)
+-9290
+n@satz290:=rapp(m,nis(pw(x,m,mi,o),0c),[t:pos(m)]t1".9290"(t),[t:is"r"(m,0)]t4".9290"(t),[t:neg(m)]t8".9290"(t)):nis(pw(x,m,mi,o),0c)
+x@lemma291:=ori2(nis(x,0c),pos(1rl),pos1):or(nis(x,0c),pos(1rl))
++9291
+1a:=ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)):nat
+t1:=posexp(x,1rl,intrl1,lemma291,pos1):is(pw(x,1rl,intrl1,lemma291),prod(1a,[t:1to(1a)]x))
+t2:=tris(nat,1,ntofrl(1rl,natrl1),ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)),isntrl1(1),isrlent(1rl,natrl1,1rl,posintnatrl(1rl,pos1,intrl1),refis(real,1rl))):is"n"(1,1a)
+t3:=lessisi2"n"(1,1a,t2):lessis"n"(1,1a)
+t4:=issmpr([t:cx][u:cx]ts(t,u),1a,[t:1to(1a)]x,1,t2):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),prod(1a,[t:1to(1a)]x))
+t5:=satz277([t:cx][u:cx]ts(t,u),left(cx,1a,1,t3,[t:1to(1a)]x)):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),x)
+t6:=tris1(cx,prod(1a,[t:1to(1a)]x),x,prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),t4,t5):is(prod(1a,[t:1to(1a)]x),x)
+-9291
+satz291:=tris(cx,pw(x,1rl,intrl1,lemma291),prod(1a".9291",[t:1to(1a".9291")]x),x,t1".9291",t6".9291"):is(pw(x,1rl,intrl1,lemma291),x)
+[y:cx][m:real][mi:intrl(m)][o:or(and(nis(x,0c),nis(y,0c)),pos(m))]
++9292
+[a:and(nis(x,0c),nis(y,0c))]
+t1:=ande1(nis(x,0c),nis(y,0c),a):nis(x,0c)
+t2:=ande2(nis(x,0c),nis(y,0c),a):nis(y,0c)
+t3:=satz221d(x,y,t1,t2):nis(ts(x,y),0c)
+-9292
+lemma292a:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(x,0c),o,[t:and(nis(x,0c),nis(y,0c))]t1".9292"(t)):or(nis(x,0c),pos(m))
+lemma292b:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(y,0c),o,[t:and(nis(x,0c),nis(y,0c))]t2".9292"(t)):or(nis(y,0c),pos(m))
+lemma292c:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(ts(x,y),0c),o,[t:and(nis(x,0c),nis(y,0c))]t3".9292"(t)):or(nis(ts(x,y),0c),pos(m))
++*9292
+x@[n:nat]
+nr:=rlofnt(n):real
+t4:=natintrl(nr,natrli(n)):intrl(nr)
+t5:=ori2(nis(x,0c),pos(nr),natpos(nr,natrli(n))):or(nis(x,0c),pos(nr))
+p0:=pw(x,nr,t4,t5):cx
+x@t6:=tris(cx,p0(1),pw(x,1rl,intrl1,lemma291(x)),x,ispw1(x,x,1rl,refis(cx,x),intrl1,t5(1),lemma291(x)),satz291(x)):is(p0(1),x)
+n@n0:=ntofrl(nr,posintnatrl(nr,natpos(nr,natrli(n)),t4)):nat
+t7:=tris(nat,n,ntofrl(nr,natrli(n)),n0,isntrl1(n),isrlent(nr,natrli(n),nr,posintnatrl(nr,natpos(nr,natrli(n)),t4),refis(real,nr))):is"n"(n,n0)
+t8:=lessisi2"n"(n,n0,t7):lessis"n"(n,n0)
+t9:=posexp(x,nr,t4,t5,natpos(nr,natrli(n))):is(p0,prod(n0,[t:1to(n0)]x))
+t10:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]x,n,t7):is(prod(n,left(cx,n0,n,t8,[t:1to(n0)]x)),prod(n0,[t:1to(n0)]x))
+t11:=tris2(cx,p0,prod(n,[t:1to(n)]x),prod(n0,[t:1to(n0)]x),t9,t10):is(p0,prod(n,[t:1to(n)]x))
+n1:=pl"n"(n,1):nat
+t12:=lessisi1"n"(n,n1,satz18a(n,1)):lessis"n"(n,n1)
+t13:=satz278([t:cx][u:cx]ts(t,u),n,[t:1to(n1)]x):is(prod(n1,[t:1to(n1)]x),ts(prod(n,left(cx,n1,n,t12,[t:1to(n1)]x)),x))
+t14:=ists1(p0,prod(n,[t:1to(n)]x),x,t11):is(ts(p0,x),ts(prod(n,[t:1to(n)]x),x))
+t15:=tris2(cx,prod(n1,[t:1to(n1)]x),ts(p0,x),ts(prod(n,[t:1to(n)]x),x),t13,t14):is(prod(n1,[t:1to(n1)]x),ts(p0,x))
+t16:=tris(cx,p0(n1),prod(n1,[t:1to(n1)]x),ts(p0,x),t11(n1),t15):is(p0(n1),ts(p0(n),x))
+y@[n:nat]
+prop1:=is(p0(ts(x,y),n),ts(p0(x,n),p0(y,n))):'prop'
+y@t17:=ists12(p0(x,1),x,p0(y,1),y,t6(x),t6(y)):is(ts(p0(x,1),p0(y,1)),ts(x,y))
+t18:=tris2(cx,p0(ts(x,y),1),ts(p0(x,1),p0(y,1)),ts(x,y),t6(ts(x,y)),t17):prop1(1)
+n@[p:prop1(n)]
+t19:=ists1(p0(ts(x,y),n),ts(p0(x,n),p0(y,n)),ts(x,y),p):is(ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)))
+t20:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),x),ts(p0(x,n),ts(p0(y,n),x)),ts(p0(x,n),ts(x,p0(y,n))),ts(ts(p0(x,n),x),p0(y,n)),assts1(p0(x,n),p0(y,n),x),ists2(ts(p0(y,n),x),ts(x,p0(y,n)),p0(x,n),comts(p0(y,n),x)),assts2(p0(x,n),x,p0(y,n))):is(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)))
+t21:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(ts(p0(x,n),p0(y,n)),x),y),ts(ts(ts(p0(x,n),x),p0(y,n)),y),ts(ts(p0(x,n),x),ts(p0(y,n),y)),assts2(ts(p0(x,n),p0(y,n)),x,y),ists1(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)),y,t20),assts1(ts(p0(x,n),x),p0(y,n),y)):is(ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
+t22:=tr3is(cx,p0(ts(x,y),n1(n)),ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t16(ts(x,y),n),t19,t21):is(p0(ts(x,y),n1(n)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
+t23:=ists12(p0(x,n1(n)),ts(p0(x,n),x),p0(y,n1(n)),ts(p0(y,n),y),t16(x,n),t16(y,n)):is(ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
+t24:=tris2(cx,p0(ts(x,y),n1(n)),ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t22,t23):prop1(n1(n))
+t25:=isp(nat,[t:nat]prop1(t),n1(n),<n>suc,t24,satz4a(n)):prop1(<n>suc)
+n@t26:=induction([t:nat]prop1(t),t18,[t:nat][u:prop1(t)]t25(t,u),n):prop1
+o@prop2:=is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b))):'prop'
+[p:pos(m)]
+t28:=posintnatrl(m,p,mi):natrl(m)
+m0:=ntofrl(m,t28):nat
+t29:=isrlnt1(m,t28):is"r"(m,nr(m0))
+t30:=isrlnt2(m,t28):is"r"(nr(m0),m)
+t31:=ispw2(ts(x,y),m,nr(m0),t29,mi,t4(ts(x,y),m0),lemma292c,t5(ts(x,y),m0)):is(pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0))
+t32:=ists12(p0(x,m0),pw(x,m,mi,lemma292a),p0(y,m0),pw(y,m,mi,lemma292b),ispw2(x,nr(m0),m,t30,t4(x,m0),mi,t5(x,m0),lemma292a),ispw2(y,nr(m0),m,t30,t4(y,m0),mi,t5(y,m0),lemma292b)):is(ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
+t33:=tr3is(cx,pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0),ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),t31,t26(m0),t32):prop2
+o@[i:is"r"(m,0)]
+t34:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(1c,1c),1c,ists12(pw(x,m,mi,lemma292a),1c,pw(y,m,mi,lemma292b),1c,0exp(x,m,mi,lemma292a,i),0exp(y,m,mi,lemma292b,i)),satz222(1c)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c)
+t35:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c,0exp(ts(x,y),m,mi,lemma292c,i),t34):prop2
+o@[n:neg(m)]
+t36:=intabs(m,mi):intrl(abs(m))
+t37:=ori2(and(nis(x,0c),nis(y,0c)),pos(abs(m)),satz166b(m,n)):or(and(nis(x,0c),nis(y,0c)),pos(abs(m)))
+t38:=lemma292a(abs(m),t36,t37):or(nis(x,0c),pos(abs(m)))
+t39:=lemma292b(abs(m),t36,t37):or(nis(y,0c),pos(abs(m)))
+t40:=lemma292c(abs(m),t36,t37):or(nis(ts(x,y),0c),pos(abs(m)))
+t41:=lemmapw3(x,m,mi,lemma292a,n):or(nis(x,0c),pos(abs(m)))
+t42:=lemmapw3(y,m,mi,lemma292b,n):or(nis(y,0c),pos(abs(m)))
+t43:=lemmapw3(ts(x,y),m,mi,lemma292c,n):or(nis(ts(x,y),0c),pos(abs(m)))
+t44:=ispw2(ts(x,y),abs(m),abs(m),refis(real,abs(m)),t36,t36,t43,t40):is(pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40))
+t45:=t33(abs(m),t36,t37,satz166b(m,n)):is(pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)))
+t46:=ists12(pw(x,abs(m),t36,t38),pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t39),pw(y,abs(m),t36,t42),ispw2(x,abs(m),abs(m),refis(real,abs(m)),t36,t36,t38,t41),ispw2(y,abs(m),abs(m),refis(real,abs(m)),t36,t36,t39,t42)):is(ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
+t47:=tr3is(cx,pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t44,t45,t46):is(pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
+t48:=lemmapw1(x,abs(m),t36,t41,satz166b(m,n),lemmapw2(x,m,mi,lemma292a,n)):nis(pw(x,abs(m),t36,t41),0c)
+t49:=lemmapw1(y,abs(m),t36,t42,satz166b(m,n),lemmapw2(y,m,mi,lemma292b,n)):nis(pw(y,abs(m),t36,t42),0c)
+t50:=lemmapw1(ts(x,y),abs(m),t36,t43,satz166b(m,n),lemmapw2(ts(x,y),m,mi,lemma292c,n)):nis(pw(ts(x,y),abs(m),t36,t43),0c)
+t51:=satz221d(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42),t48,t49):nis(ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),0c)
+t52:=negexp(ts(x,y),m,mi,lemma292c,n):is(pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50))
+t53:=isov12(1c,ts(1c,1c),pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),satz222a(1c),t47,t50,t51):is(ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t54:=tris(cx,pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t52,t53):is(pw(ts(x,y),m,mi,lemma292c),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t55:=ists12(pw(x,m,mi,lemma292a),ov(1c,pw(x,abs(m),t36,t41),t48),pw(y,m,mi,lemma292b),ov(1c,pw(y,abs(m),t36,t42),t49),negexp(x,m,mi,lemma292a,n),negexp(y,m,mi,lemma292b,n)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)))
+t56:=satz247(1c,pw(x,abs(m),t36,t41),1c,pw(y,abs(m),t36,t42),t48,t49):is(ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t57:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t55,t56):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t58:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t54,t57):prop2
+-9292
+o@satz292:=rapp(m,prop2".9292",[t:pos(m)]t33".9292"(t),[t:is"r"(m,0)]t35".9292"(t),[t:neg(m)]t58".9292"(t)):is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
+@[m:real]
+lemma293:=ori1(nis(1c,0c),pos(m),1not0):or(nis(1c,0c),pos(m))
+[mi:intrl(m)]
++9293
+t1:=ori1(and(nis(1c,0c),nis(1c,0c)),pos(m),andi(nis(1c,0c),nis(1c,0c),1not0,1not0)):or(and(nis(1c,0c),nis(1c,0c)),pos(m))
+1m:=pw(1c,m,mi,lemma293):cx
+t2:=satz222(1m):is(ts(1m,1c),1m)
+t3:=ispw1(1c,ts(1c,1c),m,satz222a(1c),mi,lemma293,lemma292c(1c,1c,m,mi,t1)):is(1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)))
+t4:=satz292(1c,1c,m,mi,t1):is(pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))))
+t5:=ists12(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),1m,pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1)),1m,ispw1(1c,1c,m,refis(cx,1c),mi,lemma292a(1c,1c,m,mi,t1),lemma293),ispw1(1c,1c,m,refis(cx,1c),mi,lemma292b(1c,1c,m,mi,t1),lemma293)):is(ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m))
+t6:=tr4is(cx,ts(1m,1c),1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m),t2,t3,t4,t5):is(ts(1m,1c),ts(1m,1m))
+t7:=tris(cx,ts(1m,mn(1m,1c)),mn(ts(1m,1m),ts(1m,1c)),0c,disttm2(1m,1m,1c),satz213b(ts(1m,1m),ts(1m,1c),symis(cx,ts(1m,1c),ts(1m,1m),t6))):is(ts(1m,mn(1m,1c)),0c)
+t8:=ore2(is(1m,0c),is(mn(1m,1c),0c),satz221c(1m,mn(1m,1c),t7),satz290(1c,m,mi,lemma293,1not0)):is(mn(1m,1c),0c)
+-9293
+satz293:=satz213a(1m".9293",1c,t8".9293"):is(pw(1c,m,mi,lemma293),1c)
+x@[m:real][n:real][mi:intrl(m)][ni:intrl(n)][o:or(nis(x,0c),and(pos(m),pos(n)))]
++9294
+[a:and(pos(m),pos(n))]
+t1:=ande1(pos(m),pos(n),a):pos(m)
+t2:=ande2(pos(m),pos(n),a):pos(n)
+t3:=pospl(m,n,t1,t2):pos(pl"r"(m,n))
+-9294
+lemma294a:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(m),o,[t:and(pos(m),pos(n))]t1".9294"(t)):or(nis(x,0c),pos(m))
+lemma294b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(n),o,[t:and(pos(m),pos(n))]t2".9294"(t)):or(nis(x,0c),pos(n))
+lemma294c:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(pl"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9294"(t)):or(nis(x,0c),pos(pl"r"(m,n)))
++*9294
+o@prop1:=is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c)):'prop'
+a@m1:=ntofrl(m,posintnatrl(m,t1,mi)):nat
+n1:=ntofrl(n,posintnatrl(n,t2,ni)):nat
+t4:=ists12(pw(x,m,mi,lemma294a),prod(m1,[t:1to(m1)]x),pw(x,n,ni,lemma294b),prod(n1,[t:1to(n1)]x),posexp(x,m,mi,lemma294a,t1),posexp(x,n,ni,lemma294b,t2)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
+p1:=ntofrl(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni))):nat
+t5:=posexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t3):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(p1,[t:1to(p1)]x))
+t6:=tris(real,pl"r"(m,n),pl"r"(rlofnt(m1),rlofnt(n1)),rlofnt(pl"n"(m1,n1)),ispl12"r"(m,rlofnt(m1),n,rlofnt(n1),isrlnt1(m,posintnatrl(m,t1,mi)),isrlnt1(n,posintnatrl(n,t2,ni))),satzr155b(m1,n1)):is"r"(pl"r"(m,n),rlofnt(pl"n"(m1,n1)))
+t7:=tris2(nat,pl"n"(m1,n1),p1,ntofrl(rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1))),isntrl1(pl"n"(m1,n1)),isrlent(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni)),rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1)),t6)):is"n"(pl"n"(m1,n1),p1)
+t8:=lessisi2"n"(pl"n"(m1,n1),p1,t7):lessis"n"(pl"n"(m1,n1),p1)
+t9:=issmpr([t:cx][u:cx]ts(t,u),p1,[t:1to(p1)]x,pl"n"(m1,n1),t7):is(prod(pl"n"(m1,n1),left(cx,p1,pl"n"(m1,n1),t8,[t:1to(p1)]x)),prod(p1,[t:1to(p1)]x))
+t10:=tris2(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),prod(p1,[t:1to(p1)]x),t5,t9):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x))
+t11:=lessisi1"n"(m1,pl"n"(m1,n1),satz18a(m1,n1)):lessis"n"(m1,pl"n"(m1,n1))
+t12:=satz281([t:cx][u:cx]ts(t,u),assocts,m1,n1,[t:1to(pl"n"(m1,n1))]x):is(prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,left(cx,pl"n"(m1,n1),m1,t11,[t:1to(pl"n"(m1,n1))]x)),prod(n1,right(cx,m1,n1,[t:1to(pl"n"(m1,n1))]x))))
+t13:=tris(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t10,t12):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
+t14:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t4,t13):prop1
+o@[na:not(and(pos(m),pos(n)))]
+t15:=ore1(nis(x,0c),and(pos(m),pos(n)),o,na):nis(x,0c)
+t16:=th15"l.or"(pos(m),pos(n),na):or(not(pos(m)),not(pos(n)))
+o@am:=abs(m):real
+an:=abs(n):real
+ap:=abs(pl"r"(m,n)):real
+t17:=intabs(m,mi):intrl(am)
+t18:=intabs(n,ni):intrl(an)
+t19:=intabs(pl"r"(m,n),intpl(m,mi,n,ni)):intrl(ap)
+na@[nm:neg(m)][nn:neg(n)]
+t20:=andi(pos(am),pos(an),satz166e(m,nnot0(m,nm)),satz166e(n,nnot0(n,nn))):and(pos(am),pos(an))
+t21:=ori2(nis(x,0c),and(pos(am),pos(an)),t20):or(nis(x,0c),and(pos(am),pos(an)))
+t22:=lemmapw3(x,m,mi,lemma294a,nm):or(nis(x,0c),pos(am))
+t23:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
+t24:=lemma294a(x,am,an,t17,t18,t21):or(nis(x,0c),pos(am))
+t25:=lemma294b(x,am,an,t17,t18,t21):or(nis(x,0c),pos(an))
+t26:=ists12(pw(x,am,t17,t22),pw(x,am,t17,t24),pw(x,an,t18,t23),pw(x,an,t18,t25),ispw1(x,x,am,refis(cx,x),t17,t22,t24),ispw1(x,x,an,refis(cx,x),t18,t23,t25)):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)))
+t27:=lemma294c(x,am,an,t17,t18,t21):or(nis(x,0c),pos(pl"r"(am,an)))
+t28:=t14(x,am,an,t17,t18,t21,t20):is(ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27))
+t29:=tr3is(real,pl"r"(am,an),pl"r"(m0"r"(m),m0"r"(n)),m0"r"(pl"r"(m,n)),ap,ispl12"r"(am,m0"r"(m),an,m0"r"(n),absn(m,nm),absn(n,nn)),satz180a(m,n),symis(real,ap,m0"r"(pl"r"(m,n)),absn(pl"r"(m,n),negpl(m,n,nm,nn)))):is"r"(pl"r"(am,an),ap)
+t30:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn)):or(nis(x,0c),pos(ap))
+t31:=ispw2(x,pl"r"(am,an),ap,t29,intpl(am,t17,an,t18),t19,t27,t30):is(pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30))
+t32:=tr3is(cx,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30),t26,t28,t31):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30))
+t33:=lemmapw1(x,am,t17,t22,satz166b(m,nm),lemmapw2(x,m,mi,lemma294a,nm)):nis(pw(x,am,t17,t22),0c)
+t34:=lemmapw1(x,an,t18,t23,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t23),0c)
+t35:=lemmapw1(x,ap,t19,t30,satz166b(pl"r"(m,n),negpl(m,n,nm,nn)),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):nis(pw(x,ap,t19,t30),0c)
+t36:=ists12(pw(x,m,mi,lemma294a),ov(1c,pw(x,am,t17,t22),t33),pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t23),t34),negexp(x,m,mi,lemma294a,nm),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)))
+t37:=satz221d(pw(x,am,t17,t22),pw(x,an,t18,t23),t33,t34):nis(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),0c)
+t38:=satz247(1c,pw(x,am,t17,t22),1c,pw(x,an,t18,t23),t33,t34):is(ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37))
+t39:=isov12(ts(1c,1c),1c,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30),satz222(1c),t32,t37,t35):is(ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35))
+t40:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t30),t35),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):is(ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t41:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t36,t38,t39,t40):prop1
+na@[pm:pos(m)][nn:neg(n)]
+t42:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
+t43:=lemmapw1(x,an,t18,t42,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t42),0c)
+t44:=ists2(pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t42),t43),pw(x,m,mi,lemma294a),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)))
+t45:=satz244a(pw(x,m,mi,lemma294a),1c,pw(x,an,t18,t42),t43):is(ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43))
+t46:=isov1(ts(pw(x,m,mi,lemma294a),1c),pw(x,m,mi,lemma294a),pw(x,an,t18,t42),satz222(pw(x,m,mi,lemma294a)),t43):is(ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+t47:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t44,t45,t46):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+[casea:more(m,an)]
+t48:=satz182d(m,an,casea):pos(mn"r"(m,an))
+t49:=satz166e(n,nnot0(n,nn)):pos(an)
+t50:=andi(pos(an),pos(mn"r"(m,an)),t49,t48):and(pos(an),pos(mn"r"(m,an)))
+t51:=ori2(nis(x,0c),and(pos(an),pos(mn"r"(m,an))),t50):or(nis(x,0c),and(pos(an),pos(mn"r"(m,an))))
+t52:=intmn(m,mi,an,t18):intrl(mn"r"(m,an))
+t53:=lemma294a(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(an))
+t54:=lemma294b(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(mn"r"(m,an)))
+t55:=lemma294c(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(pl"r"(an,mn"r"(m,an))))
+t56:=intpl(an,t18,mn"r"(m,an),t52):intrl(pl"r"(an,mn"r"(m,an)))
+t57:=t14(x,an,mn"r"(m,an),t18,t52,t51,t50):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55))
+t58:=satz187a(m,an):is"r"(pl"r"(an,mn"r"(m,an)),m)
+t59:=ispw2(x,pl"r"(an,mn"r"(m,an)),m,t58,t56,mi,t55,lemma294a):is(pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a))
+t60:=tris(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a),t57,t59):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a))
+t61:=ispw1(x,x,an,refis(cx,x),t18,t53,t42):is(pw(x,an,t18,t53),pw(x,an,t18,t42))
+t62:=isp1(cx,[t:cx]nis(t,0c),pw(x,an,t18,t42),pw(x,an,t18,t53),t43,t61):nis(pw(x,an,t18,t53),0c)
+t63:=isov12(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a),pw(x,an,t18,t53),pw(x,an,t18,t42),t60,t61,t62,t43):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+t64:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t63):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62))
+t65:=satz229h(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54),t62,refis(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)))):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54))
+t66:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
+t67:=ispw2(x,mn"r"(m,an),pl"r"(m,n),t66,t52,intpl(m,mi,n,ni),t54,lemma294c):is(pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t68:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t64,t65,t67):prop1
+nn@[caseb:is"r"(m,an)]
+t69:=ispw2(x,m,an,caseb,mi,t18,lemma294a,t42):is(pw(x,m,mi,lemma294a),pw(x,an,t18,t42))
+t70:=satz251a(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43,t69):is(ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c)
+t71:=tr3is(real,pl"r"(m,n),mn"r"(m,m0"r"(n)),mn"r"(m,an),0,ispl2"r"(n,m0"r"(m0"r"(n)),m,satz177a(n)),ismn2"r"(m0"r"(n),an,m,symis(real,an,m0"r"(n),absn(n,nn))),satz182e(m,an,caseb)):is"r"(pl"r"(m,n),0)
+t72:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),1c,0exp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t71)):is(1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t73:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t47,t70,t72):prop1
+nn@[casec:less(m,an)]
+t74:=satz182d(an,m,lemma2"r"(m,an,casec)):pos(mn"r"(an,m))
+t75:=andi(pos(m),pos(mn"r"(an,m)),pm,t74):and(pos(m),pos(mn"r"(an,m)))
+t76:=ori2(nis(x,0c),and(pos(m),pos(mn"r"(an,m))),t75):or(nis(x,0c),and(pos(m),pos(mn"r"(an,m))))
+t77:=intmn(an,t18,m,mi):intrl(mn"r"(an,m))
+t78:=lemma294a(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(m))
+t79:=lemma294b(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(mn"r"(an,m)))
+t80:=lemma294c(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(pl"r"(m,mn"r"(an,m))))
+t81:=intpl(m,mi,mn"r"(an,m),t77):intrl(pl"r"(m,mn"r"(an,m)))
+t81a:=t14(x,m,mn"r"(an,m),mi,t77,t76,t75):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80))
+t82:=satz187a(an,m):is"r"(pl"r"(m,mn"r"(an,m)),an)
+t83:=ispw2(x,pl"r"(m,mn"r"(an,m)),an,t82,t81,t18,t80,t42):is(pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42))
+t84:=tris(cx,ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42),t81a,t83):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42))
+t85:=satz290(x,m,mi,t78,t15):nis(pw(x,m,mi,t78),0c)
+t86:=satz290(x,mn"r"(an,m),t77,t79,t15):nis(pw(x,mn"r"(an,m),t77,t79),0c)
+t87:=satz221d(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79),t85,t86):nis(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),0c)
+t88:=satz222(pw(x,m,mi,t78)):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78))
+t89:=ispw1(x,x,m,refis(cx,x),mi,t78,lemma294a):is(pw(x,m,mi,t78),pw(x,m,mi,lemma294a))
+t90:=tris(cx,ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78),pw(x,m,mi,lemma294a),t88,t89):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a))
+t91:=isov12(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42),t90,t84,t87,t43):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+t92:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t91):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87))
+t93:=satz246a(1c,pw(x,mn"r"(an,m),t77,t79),pw(x,m,mi,t78),t86,t85):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86))
+t94:=satz182f(m,an,casec):neg(mn"r"(m,an))
+t94a:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
+t95:=tr3is(real,mn"r"(an,m),m0"r"(mn"r"(m,an)),abs(mn"r"(m,an)),ap,satz181a(an,m),symis(real,abs(mn"r"(m,an)),m0"r"(mn"r"(m,an)),absn(mn"r"(m,an),t94)),isabs(mn"r"(m,an),pl"r"(m,n),t94a)):is"r"(mn"r"(an,m),ap)
+t96:=isp(real,[t:real]neg(t),mn"r"(m,an),pl"r"(m,n),t94,t94a):neg(pl"r"(m,n))
+t97:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96):or(nis(x,0c),pos(ap))
+t98:=lemmapw1(x,ap,t19,t97,satz166b(pl"r"(m,n),t96),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):nis(pw(x,ap,t19,t97),0c)
+t99:=ispw2(x,mn"r"(an,m),ap,t95,t77,t19,t79,t97):is(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97))
+t100:=isov2(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97),1c,t99,t86,t98):is(ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98))
+t101:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t97),t98),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):is(ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t102:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t92,t93,t100,t101):prop1
+nn@t103:=or3app(is"r"(m,an),more(m,an),less(m,an),prop1,satz167a(m,an),[t:is"r"(m,an)]t73(t),[t:more(m,an)]t68(t),[t:less(m,an)]t102(t)):prop1
+na@[nm:neg(m)][qn:pos(n)]
+na@t104:=ori1(nis(x,0c),and(pos(n),pos(m)),t15):or(nis(x,0c),and(pos(n),pos(m)))
+t104a:=th5"l.and"(pos(m),pos(n),na):not(and(pos(n),pos(m)))
+t105:=lemma294a(x,n,m,ni,mi,t104):or(nis(x,0c),pos(n))
+t106:=lemma294b(x,n,m,ni,mi,t104):or(nis(x,0c),pos(m))
+t107:=lemma294c(x,n,m,ni,mi,t104):or(nis(x,0c),pos(pl"r"(n,m)))
+t108:=ists12(pw(x,m,mi,lemma294a),pw(x,m,mi,t106),pw(x,n,ni,lemma294b),pw(x,n,ni,t105),ispw1(x,x,m,refis(cx,x),mi,lemma294a,t106),ispw1(x,x,n,refis(cx,x),ni,lemma294b,t105)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)))
+t109:=comts(pw(x,m,mi,t106),pw(x,n,ni,t105)):is(ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)))
+qn@t110:=t103(x,n,m,ni,mi,t104,t104a,qn,nm):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
+na@t111:=ispw2(x,pl"r"(n,m),pl"r"(m,n),compl"r"(n,m),intpl(n,ni,m,mi),intpl(m,mi,n,ni),t107,lemma294c):is(pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+qn@t112:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t110,t111):prop1
+na@[i:is"r"(m,0)]
+t113:=ists1(pw(x,m,mi,lemma294a),1c,pw(x,n,ni,lemma294b),0exp(x,m,mi,lemma294a,i)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)))
+t114:=satz222b(pw(x,n,ni,lemma294b)):is(ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b))
+t115:=symis(real,pl"r"(m,n),n,pl01"r"(m,n,i)):is"r"(n,pl"r"(m,n))
+t116:=ispw2(x,n,pl"r"(m,n),t115,ni,intpl(m,mi,n,ni),lemma294b,lemma294c):is(pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t117:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t113,t114,t116):prop1
+na@[i:is"r"(n,0)]
+t118:=t117(x,n,m,ni,mi,t104,t104a,i):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
+t119:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t118,t111):prop1
+na@[pm:pos(m)]
+t120:=ore2(not(pos(m)),not(pos(n)),t16,weli(pos(m),pm)):not(pos(n))
+t121:=rapp(n,prop1,th2"l.imp"(pos(n),prop1,t120),[t:is"r"(n,0)]t119(t),[t:neg(n)]t103(pm,t)):prop1
+na@[nm:neg(m)]
+t122:=rapp(n,prop1,[t:pos(n)]t112(nm,t),[t:is"r"(n,0)]t119(t),[t:neg(n)]t41(nm,t)):prop1
+na@t123:=rapp(m,prop1,[t:pos(m)]t121(t),[t:is"r"(m,0)]t117(t),[t:neg(m)]t122(t)):prop1
+-9294
+o@satz294:=th1"l.imp"(and(pos(m),pos(n)),prop1".9294",[t:and(pos(m),pos(n))]t14".9294"(t),[t:not(and(pos(m),pos(n)))]t123".9294"(t)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+ni@[o:nis(x,0c)]
+lemma295a:=ori1(nis(x,0c),pos(m),o):or(nis(x,0c),pos(m))
+lemma295b:=ori1(nis(x,0c),pos(n),o):or(nis(x,0c),pos(n))
+lemma295c:=ori1(nis(x,0c),pos(mn"r"(m,n)),o):or(nis(x,0c),pos(mn"r"(m,n)))
++9295
+t1:=ori1(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)),o):or(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)))
+t2:=intmn(m,mi,n,ni):intrl(mn"r"(m,n))
+t3:=lemma294a(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(mn"r"(m,n)))
+t4:=lemma294b(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(n))
+t5:=lemma294c(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(pl"r"(mn"r"(m,n),n)))
+t6:=ists12(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,lemma295b),pw(x,n,ni,t4),ispw1(x,x,mn"r"(m,n),refis(cx,x),t2,lemma295c,t3),ispw1(x,x,n,refis(cx,x),ni,lemma295b,t4)):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)))
+t7:=satz294(x,mn"r"(m,n),n,t2,ni,t1):is(ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5))
+t8:=plmn(m,n):is"r"(pl"r"(mn"r"(m,n),n),m)
+t9:=ispw2(x,pl"r"(mn"r"(m,n),n),m,t8,intpl(mn"r"(m,n),t2,n,ni),mi,t5,lemma295a):is(pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a))
+t10:=tr3is(cx,ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a),t6,t7,t9):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),pw(x,m,mi,lemma295a))
+t11:=satz290(x,n,ni,lemma295b,o):nis(pw(x,n,ni,lemma295b),0c)
+-9295
+satz295:=satz229k(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),pw(x,mn"r"(m,n),t2".9295",lemma295c),t11".9295",t10".9295"):is(ov(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),satz290(x,n,ni,lemma295b,o)),pw(x,mn"r"(m,n),intmn(m,mi,n,ni),lemma295c))
+m@[mi:intrl(m)][n:nis(x,0c)]
+lemma296:=ori1(nis(x,0c),pos(m),n):or(nis(x,0c),pos(m))
++9296
+t1:=intrli0(0,refis(real,0)):intrl(0)
+t2:=lemma295a(x,0,m,t1,mi,n):or(nis(x,0c),pos(0))
+t3:=lemma295b(x,0,m,t1,mi,n):or(nis(x,0c),pos(m))
+t4:=lemma295c(x,0,m,t1,mi,n):or(nis(x,0c),pos(mn"r"(0,m)))
+t5:=satz290(x,m,mi,lemma296,n):nis(pw(x,m,mi,lemma296),0c)
+t6:=satz290(x,m,mi,t3,n):nis(pw(x,m,mi,t3),0c)
+t7:=symis(cx,pw(x,0,t1,t2),1c,0exp(x,0,t1,t2,refis(real,0))):is(1c,pw(x,0,t1,t2))
+t8:=ispw1(x,x,m,refis(cx,x),mi,lemma296,t3):is(pw(x,m,mi,lemma296),pw(x,m,mi,t3))
+t9:=isov12(1c,pw(x,0,t1,t2),pw(x,m,mi,lemma296),pw(x,m,mi,t3),t7,t8,t5,t6):is(ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6))
+t10:=satz295(x,0,m,t1,mi,n):is(ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4))
+t11:=pl01(0,m0"r"(m),refis(real,0)):is"r"(mn"r"(0,m),m0"r"(m))
+t12:=lemma296(x,m0"r"(m),intm0(m,mi),n):or(nis(x,0c),pos(m0"r"(m)))
+t13:=ispw2(x,mn"r"(0,m),m0"r"(m),t11,intmn(0,t1,m,mi),intm0(m,mi),t4,t12):is(pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12))
+t14:=tr3is(cx,ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12),t9,t10,t13):is(ov(1c,pw(x,m,mi,lemma296),t5),pw(x,m0"r"(m),intm0(m,mi),t12))
+-9296
+satz296:=t14".9296":is(ov(1c,pw(x,m,mi,lemma296),satz290(x,m,mi,lemma296,n)),pw(x,m0"r"(m),intm0(m,mi),lemma296(m0"r"(m),intm0(m,mi),n)))
+ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
++9297
+[p:nis(x,0c)]
+t1:=satz290(x,m,mi,lemma294a(o),p):nis(pw(x,m,mi,lemma294a(o)),0c)
+o@[a:and(pos(m),pos(n))]
+t2:=ande2(pos(m),pos(n),a):pos(n)
+t3:=postspp(m,n,ande1(pos(m),pos(n),a),t2):pos(ts"r"(m,n))
+-9297
+lemma297a:=th9"l.or"(nis(x,0c),and(pos(m),pos(n)),nis(pw(x,m,mi,lemma294a(o)),0c),pos(n),o,[t:nis(x,0c)]t1".9297"(t),[t:and(pos(m),pos(n))]t2".9297"(t)):or(nis(pw(x,m,mi,lemma294a(o)),0c),pos(n))
+lemma297b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(ts"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9297"(t)):or(nis(x,0c),pos(ts"r"(m,n)))
+mi@[o:or(nis(x,0c),pos(m))][i:is(x,0c)]
++*9297
+i@t4:=ore2(nis(x,0c),pos(m),o,weli(is(x,0c),i)):pos(m)
+m1:=ntofrl(m,posintnatrl(m,t4,mi)):nat
+t5:=posexp(x,m,mi,o,t4):is(pw(x,m,mi,o),prod(m1,[t:1to(m1)]x))
+t6:=satz289b(m1,[t:1to(m1)]x,xout(m1),i):is(prod(m1,[t:1to(m1)]x),0c)
+t7:=tris(cx,pw(x,m,mi,o),prod(m1,[t:1to(m1)]x),0c,t5,t6):is(pw(x,m,mi,o),0c)
+-9297
+i@pw0:=t7".9297":is(pw(x,m,mi,o),0c)
+ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
++*9297
+ni@t8:=intts(m,mi,n,ni):intrl(ts"r"(m,n))
+o@prop1:=is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o))):'prop'
+[i:is(x,0c)]
+t9:=pw0(x,m,mi,lemma294a(o),i):is(pw(x,m,mi,lemma294a(o)),0c)
+t10:=pw0(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o),t9):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),0c)
+t11:=pw0(x,ts"r"(m,n),t8,lemma297b(o),i):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),0c)
+t12:=tris2(cx,pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),0c,t10,t11):prop1
+m@[mi:intrl(m)][p:nis(x,0c)]
+t13:=ori1(nis(x,0c),pos(m),p):or(nis(x,0c),pos(m))
+p0:=pw(x,m,mi,t13):cx
+[n:nat]
+nr:=rlofnt(n):real
+t14:=natintrl(nr,natrli(n)):intrl(nr)
+t15:=ori2(nis(p0,0c),pos(nr),natpos(nr,natrli(n))):or(nis(p0,0c),pos(nr))
+t16:=ori1(nis(x,0c),pos(ts"r"(m,nr)),p):or(nis(x,0c),pos(ts"r"(m,nr)))
+t17:=intts(m,mi,nr,t14):intrl(ts"r"(m,nr))
+prop2:=is(pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16)):'prop'
+p@t18:=ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t15(1),lemma291(p0)):is(pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)))
+t19:=satz291(p0):is(pw(p0,1rl,intrl1,lemma291(p0)),p0)
+t20:=ispw2(x,m,ts"r"(m,1rl),satz195a(m),mi,t17(1),t13,t16(1)):is(p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)))
+t21:=tr3is(cx,pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)),t18,t19,t20):prop2(1)
+n@[p2:prop2(n)]
+n1:=pl"n"(n,1):nat
+t22:=satz290(x,m,mi,t13,p):nis(p0,0c)
+t23:=ori1(nis(p0,0c),and(pos(nr),pos(1rl)),t22):or(nis(p0,0c),and(pos(nr),pos(1rl)))
+t24:=lemma294a(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(nr))
+t25:=lemma294b(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(1rl))
+t26:=lemma294c(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(pl"r"(nr,1rl)))
+t27:=ispw2(p0,nr(n1),pl"r"(nr,1rl),satzr155a(n,1),t14(n1),intpl(nr,t14,1rl,intrl1),t15(n1),t26):is(pw(p0,nr(n1),t14(n1),t15(n1)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
+t27a:=satz294(p0,nr,1rl,t14,intrl1,t23):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
+t28:=tris2(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26),t27,t27a):is(pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)))
+t29:=ori1(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)),p):or(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)))
+t30:=lemma294a(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(ts"r"(m,nr)))
+t31:=lemma294b(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(m))
+t32:=lemma294c(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(pl"r"(ts"r"(m,nr),m)))
+t33:=tr3is(cx,pw(p0,nr,t14,t24),pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16),pw(x,ts"r"(m,nr),t17,t30),ispw1(p0,p0,nr,refis(cx,p0),t14,t24,t15),p2,ispw1(x,x,ts"r"(m,nr),refis(cx,x),t17,t16,t30)):is(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30))
+t34:=tr3is(cx,pw(p0,1rl,intrl1,t25),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,m,mi,t31),ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t25,lemma291(p0)),t19,ispw1(x,x,m,refis(cx,x),mi,t13,t31)):is(pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31))
+t35:=ists12(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30),pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31),t33,t34):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)))
+t36:=satz294(x,ts"r"(m,nr),m,t17,mi,t29):is(ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32))
+t37:=tr3is(real,pl"r"(ts"r"(m,nr),m),pl"r"(ts"r"(m,nr),ts"r"(m,1rl)),ts"r"(m,pl"r"(nr,1rl)),ts"r"(m,nr(n1)),ispl2"r"(m,ts"r"(m,1rl),ts"r"(m,nr),satz195a(m)),distpt2"r"(m,nr,1rl),ists2"r"(pl"r"(nr,1rl),nr(n1),m,satzr155b(n,1))):is"r"(pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)))
+t38:=ispw2(x,pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)),t37,intpl(ts"r"(m,nr),t17,m,mi),t17(n1),t32,t16(n1)):is(pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)))
+t39:=tr4is(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)),t28,t35,t36,t38):prop2(n1)
+t40:=isp(nat,[t:nat]prop2(t),n1,<n>suc,t39,satz4a(n)):prop2(<n>suc)
+n@t41:=induction([t:nat]prop2(t),t21,[t:nat][u:prop2(t)]t40(t,u),n):prop2(n)
+o@[p:nis(x,0c)][q:pos(n)]
+t42:=posintnatrl(n,q,ni):natrl(n)
+n0:=ntofrl(n,t42):nat
+t43:=isrlnt1(n,t42):is"r"(n,rlofnt(n0))
+t44:=isrlnt2(n,t42):is"r"(rlofnt(n0),n)
+o@p1:=pw(x,m,mi,lemma294a(o)):cx
+q@t44a:=ispw2(x,m,m,refis(real,m),mi,mi,lemma294a(o),t13(mi,p)):is(p1,p0(mi,p))
+t45:=ispw12(p1,p0(mi,p),n,rlofnt(n0),t44a,t43,ni,t14(mi,p,n0),lemma297a(o),t15(mi,p,n0)):is(pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)))
+t46:=t41(mi,p,n0):is(pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)))
+t47:=ists2"r"(rlofnt(n0),n,m,t44):is"r"(ts"r"(m,rlofnt(n0)),ts"r"(m,n))
+t48:=ispw2(x,ts"r"(m,rlofnt(n0)),ts"r"(m,n),t47,t17(mi,p,n0),t8,t16(mi,p,n0),lemma297b(o)):is(pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)))
+t49:=tr3is(cx,pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)),t45,t46,t48):prop1
+p@[i:is"r"(n,0)]
+t50:=0exp(p1,n,ni,lemma297a(o),i):is(pw(p1,n,ni,lemma297a(o)),1c)
+t51:=ts02"r"(m,n,i):is"r"(ts"r"(m,n),0)
+t52:=0exp(x,ts"r"(m,n),t8,lemma297b(o),t51):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),1c)
+t53:=tris2(cx,pw(p1,n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),1c,t50,t52):prop1
+p@[q:neg(n)]
+an:=abs(n):real
+t54:=intabs(n,ni):intrl(an)
+t55:=ori1(nis(x,0c),and(pos(m),pos(an)),p):or(nis(x,0c),and(pos(m),pos(an)))
+p1t55:=p1(an,mi,t54,t55):cx
+t56:=satz166e(n,nnot0(n,q)):pos(an)
+t56a:=lemma294a(an,mi,t54,t55):or(nis(x,0c),pos(m))
+t57:=lemma297a(an,mi,t54,t55):or(nis(p1t55,0c),pos(an))
+t58:=lemma297b(an,mi,t54,t55):or(nis(x,0c),pos(ts"r"(m,an)))
+t59:=t49(an,mi,t54,t55,p,t56):is(pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58))
+t60:=satz177c(an,n,absn(n,q)):is"r"(n,m0"r"(an))
+t61:=intm0(an,t54):intrl(m0"r"(an))
+t62:=satz290(x,m,mi,t56a,p):nis(p1t55,0c)
+t63:=lemma296(p1t55,an,t54,t62):or(nis(p1t55,0c),pos(an))
+t64:=satz290(p1t55,an,t54,t63,t62):nis(pw(p1t55,an,t54,t63),0c)
+t65:=lemma296(p1t55,m0"r"(an),t61,t62):or(nis(p1t55,0c),pos(m0"r"(an)))
+t66:=satz296(p1t55,an,t54,t62):is(ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65))
+t67:=ispw1(x,x,m,refis(cx,x),mi,lemma294a(o),t56a):is(p1,p1t55)
+t68:=ispw12(p1,p1t55,n,m0"r"(an),t67,t60,ni,t61,lemma297a(o),t65):is(pw(p1,n,ni,lemma297a(o)),pw(p1t55,m0"r"(an),t61,t65))
+t69:=tris2(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65),t68,t66):is(pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64))
+t70:=tris(real,m0"r"(ts"r"(m,an)),ts"r"(m,m0"r"(an)),ts"r"(m,n),satz197f(m,an),ists2"r"(m0"r"(an),n,m,symis(real,n,m0"r"(an),t60))):is"r"(m0"r"(ts"r"(m,an)),ts"r"(m,n))
+t71:=intm0(ts"r"(m,an),t8(an,mi,t54)):intrl(m0"r"(ts"r"(m,an)))
+t72:=lemma296(x,ts"r"(m,an),t8(an,mi,t54),p):or(nis(x,0c),pos(ts"r"(m,an)))
+t73:=satz290(x,ts"r"(m,an),t8(an,mi,t54),t72,p):nis(pw(x,ts"r"(m,an),t8(an,mi,t54),t72),0c)
+t74:=lemma296(x,m0"r"(ts"r"(m,an)),t71,p):or(nis(x,0c),pos(m0"r"(ts"r"(m,an))))
+t75:=satz296(x,ts"r"(m,an),t8(an,mi,t54),p):is(ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74))
+t76:=ispw2(x,m0"r"(ts"r"(m,an)),ts"r"(m,n),t70,t71,t8,t74,lemma297b(o)):is(pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)))
+t77:=ispw1(p1t55,p1t55,an,refis(cx,p1t55),t54,t63,t57):is(pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57))
+t78:=ispw1(x,x,ts"r"(m,an),refis(cx,x),t8(an,mi,t54),t58,t72):is(pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
+t79:=tr3is(cx,pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t77,t59,t78):is(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
+t80:=isov2(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),1c,t79,t64,t73):is(ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73))
+t81:=tr4is(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)),t69,t80,t75,t76):prop1
+p@t82:=rapp(n,prop1,[t:pos(n)]t49(t),[t:is"r"(n,0)]t53(t),[t:neg(n)]t81(t)):prop1
+-9297
+o@satz297:=th1"l.imp"(is(x,0c),prop1".9297",[t:is(x,0c)]t12".9297"(t),[t:nis(x,0c)]t82".9297"(t)):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),intts(m,mi,n,ni),lemma297b(o)))
+@[r:real][s:real]
++10298
+t1:=tris(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),pl"r"(0,0)),pli(pl"r"(r,s),0),plis12a(r,0,s,0),isrecx2(pl"r"(0,0),0,pl"r"(r,s),pl01(0,0,refis(real,0)))):is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
+-10298
+satz298a:=symis(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0),t1".10298"):is(pli(pl"r"(r,s),0),pl(pli(r,0),pli(s,0)))
+satz298b:=t1".10298":is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
++*10298
+s@t2:=tris(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),mn"r"(0,0)),pli(mn"r"(r,s),0),mnis12a(r,0,s,0),isrecx2(mn"r"(0,0),0,mn"r"(r,s),pl02(0,m0"r"(0),satz176b(0,refis(real,0))))):is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
+-10298
+s@satz298c:=symis(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0),t2".10298"):is(pli(mn"r"(r,s),0),mn(pli(r,0),pli(s,0)))
+satz298d:=t2".10298":is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
++*10298
+s@t3:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
+t4:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
+t5:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t3,t4)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
+-10298
+s@satz298e:=symis(cx,ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0),t5".10298"):is(pli(ts"r"(r,s),0),ts(pli(r,0),pli(s,0)))
+satz298f:=t5".10298":is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
+[n:nis"r"(s,0)]
++*10298
+n@[i:is(pli(s,0),0c)]
+t6:=tr3is(real,s,re(pli(s,0)),re(0c),0,isre(s,0),iscere(pli(s,0),0c,i),reis(0,0)):is"r"(s,0)
+-10298
+n@lemma298:=th3"l.imp"(is(pli(s,0),0c),is"r"(s,0),n,[t:is(pli(s,0),0c)]t6".10298"(t)):nis(pli(s,0),0c)
++*10298
+n@t7:=tris(cx,ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(ts"r"(s,ov"r"(r,s,n)),0),pli(r,0),t5(s,ov"r"(r,s,n)),isrecx1(ts"r"(s,ov"r"(r,s,n)),r,0,satz204c(r,s,n))):is(ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(r,0))
+-10298
+n@satz298g:=satz229g(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(pli(ov"r"(r,s,n),0),ov(pli(r,0),pli(s,0),lemma298))
+satz298h:=satz229h(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(ov(pli(r,0),pli(s,0),lemma298),pli(ov"r"(r,s,n),0))
++*10298
+r@t8:=tris(cx,m0(pli(r,0)),pli(m0"r"(r),m0"r"(0)),pli(m0"r"(r),0),m0isa(r,0),isrecx2(m0"r"(0),0,m0"r"(r),satz176b(0,refis(real,0)))):is(m0(pli(r,0)),pli(m0"r"(r),0))
+-10298
+r@satz298j:=symis(cx,m0(pli(r,0)),pli(m0"r"(r),0),t8".10298"):is(pli(m0"r"(r),0),m0(pli(r,0)))
+satz298k:=t8".10298":is(m0(pli(r,0)),pli(m0"r"(r),0))
++*10298
+r@t9:=tris(real,mod2(pli(r,0)),ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(r,r),pl02(ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(im(pli(r,0)),im(pli(r,0))),ts01(im(pli(r,0)),im(pli(r,0)),imis(r,0))),ists12"r"(re(pli(r,0)),r,re(pli(r,0)),r,reis(r,0),reis(r,0))):is"r"(mod2(pli(r,0)),ts"r"(r,r))
+ar:=abs(r):real
+[p:pos(r)]
+t10:=satz196a(r,r,p,p):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+r@[i:is"r"(r,0)]
+t11:=tris2(real,ts"r"(r,r),ts"r"(ar,ar),0,ts01(r,r,i),ts01(ar,ar,abs0(r,i))):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+r@[n:neg(r)]
+t12:=satz196b(r,r,n,n):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+r@t13:=rapp(r,is"r"(ts"r"(r,r),ts"r"(ar,ar)),[t:pos(r)]t10(t),[t:is"r"(r,0)]t11(t),[t:neg(r)]t12(t)):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+t14:=tris(real,mod2(pli(r,0)),ts"r"(r,r),ts"r"(ar,ar),t9,t13):is"r"(mod2(pli(r,0)),ts"r"(ar,ar))
+t15:=th1"l.imp"(is"r"(r,0),not(neg(ar)),[t:is"r"(r,0)]0notn(ar,abs0(r,t)),[t:nis"r"(r,0)]pnotn(ar,satz166e(r,t))):not(neg(ar))
+-10298
+r@satz298l:=thsqrt3(mod2(pli(r,0)),lemma5(pli(r,0)),abs(r),t15".10298",t14".10298"):is"r"(mod(pli(r,0)),abs(r))
+satz298m:=symis(real,mod(pli(r,0)),abs(r),satz298l):is"r"(abs(r),mod(pli(r,0)))
+cofrl:=pli(r,0):complex
+s@[i:is(cofrl(r),cofrl(s))]
+isrlic:=tr3is(real,r,re(cofrl(r)),re(cofrl(s)),s,isre(r,0),iscere(cofrl(r),cofrl(s),i),reis(s,0)):is"r"(r,s)
+s@[i:is"r"(r,s)]
+isrlec:=isrecx1(r,s,0,i):is(cofrl(r),cofrl(s))
++v10
+@t1:=[t:real][u:real][v:is(cofrl(t),cofrl(u))]isrlic(t,u,v):injective(real,cx,[t:real]cofrl(t))
+-v10
+@[x:cx]
+realc:=image(real,cx,[t:real]cofrl(t),x):'prop'
+r@reali:=imagei(real,cx,[t:real]cofrl(t),r):realc(cofrl(r))
+x@[rx:realc(x)]
+rlofc:=soft(real,cx,[t:real]cofrl(t),t1".v10",x,rx):real
+[y:cx][ry:realc(y)][i:is"r"(rlofc(x,rx),rlofc(y,ry))]
+iscirl:=isinve(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is(x,y)
+ry@[i:is(x,y)]
+iscerl:=isinv(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is"r"(rlofc(x,rx),rlofc(y,ry))
+r@isrlc1:=isst1(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(r,rlofc(cofrl(r),reali(r)))
+isrlc2:=isst2(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(rlofc(cofrl(r),reali(r)),r)
+rx@iscrl1:=ists1"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(x,cofrl(rlofc(x,rx)))
+iscrl2:=ists2"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(cofrl(rlofc(x,rx)),x)
+@[n:nat]
+cofn:=cofrl(rlofnt(n)):complex
+[m:nat][i:is"n"(n,m)]
+isnec:=isrlec(rlofnt(n),rlofnt(m),isnterl(n,m,i)):is(cofn(n),cofn(m))
+m@[i:is(cofn(n),cofn(m))]
+isnic:=isntirl(n,m,isrlic(rlofnt(n),rlofnt(m),i)):is"n"(n,m)
++*v10
+@t2:=[t:nat][u:nat][v:is(cofn(t),cofn(u))]isnic(t,u,v):injective(nat,cx,[t:nat]cofn(t))
+-v10
+x@natc:=image(nat,cx,[t:nat]cofn(t),x):'prop'
+n@nati:=imagei(nat,cx,[t:nat]cofn(t),n):natc(cofn(n))
+x@[nx:natc(x)]
+nofc:=soft(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):nat
+[y:cx][ny:natc(y)][i:is(x,y)]
+iscen:=isinv(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is"n"(nofc(x,nx),nofc(y,ny))
+ny@[i:is"n"(nofc(x,nx),nofc(y,ny))]
+iscin:=isinve(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is(x,y)
+n@isnc1:=isst1(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(n,nofc(cofn(n),nati(n)))
+isnc2:=isst2(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(nofc(cofn(n),nati(n)),n)
+nx@iscn1:=ists1"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(x,cofn(nofc(x,nx)))
+iscn2:=ists2"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(cofn(nofc(x,nx)),x)
+@natt:=ot(cx,[t:cx]natc(t)):'type'
+[nt:natt]
+cofnt:=in"e"(cx,[t:cx]natc(t),nt):cx
+natti:=inp(cx,[t:cx]natc(t),nt):natc(cofnt(nt))
+[mt:natt][i:is"e"(natt,nt,mt)]
+isntec:=isini(cx,[t:cx]natc(t),nt,mt,i):is(cofnt(nt),cofnt(mt))
+mt@[i:is(cofnt(nt),cofnt(mt))]
+isntic:=isine(cx,[t:cx]natc(t),nt,mt,i):is"e"(natt,nt,mt)
+nx@ntofc:=out(cx,[t:cx]natc(t),x,nx):natt
+ny@[i:is(x,y)]
+iscent:=isouti(cx,[t:cx]natc(t),x,nx,y,ny,i):is"e"(natt,ntofc(x,nx),ntofc(y,ny))
+ny@[i:is"e"(natt,ntofc(x,nx),ntofc(y,ny))]
+iscint:=isoute(cx,[t:cx]natc(t),x,nx,y,ny,i):is(x,y)
+nt@isntc1:=isoutin(cx,[t:cx]natc(t),nt):is"e"(natt,nt,ntofc(cofnt(nt),natti(nt)))
+isntc2:=symis(natt,nt,ntofc(cofnt(nt),natti(nt)),isntc1):is"e"(natt,ntofc(cofnt(nt),natti(nt)),nt)
+nx@iscnt1:=isinout(cx,[t:cx]natc(t),x,nx):is(x,cofnt(ntofc(x,nx)))
+iscnt2:=symis(cx,x,cofnt(ntofc(x,nx)),iscnt1):is(cofnt(ntofc(x,nx)),x)
+n@ntofn:=ntofc(cofn(n),nati(n)):natt
+m@[i:is"n"(n,m)]
+isnent:=iscent(cofn(n),nati(n),cofn(m),nati(m),isnec(n,m,i)):is"e"(natt,ntofn(n),ntofn(m))
+m@[i:is"e"(natt,ntofn(n),ntofn(m))]
+isnint:=isnic(n,m,iscint(cofn(n),nati(n),cofn(m),nati(m),i)):is"n"(n,m)
+nt@nofnt:=nofc(cofnt(nt),natti(nt)):nat
+mt@[i:is"e"(natt,nt,mt)]
+isnter:=iscen(cofnt(nt),natti(nt),cofnt(mt),natti(mt),isntec(nt,mt,i)):is"n"(nofnt(nt),nofnt(mt))
+mt@[i:is"n"(nofnt(nt),nofnt(mt))]
+isntin:=isntic(nt,mt,iscin(cofnt(nt),natti(nt),cofnt(mt),natti(mt),i)):is"e"(natt,nt,mt)
++*v10
+n@t3:=iscnt1(cofn(n),nati(n)):is(cofn(n),cofnt(ntofn(n)))
+-v10
+n@isnnt1:=tris(nat,n,nofc(cofn(n),nati(n)),nofnt(ntofn(n)),isnc1(n),iscen(cofn(n),nati(n),cofnt(ntofn(n)),natti(ntofn(n)),t3".v10")):is"n"(n,nofnt(ntofn(n)))
+isnnt2:=symis(nat,n,nofnt(ntofn(n)),isnnt1):is"n"(nofnt(ntofn(n)),n)
++*v10
+nt@t4:=iscn1(cofnt(nt),natti(nt)):is(cofnt(nt),cofn(nofnt(nt)))
+-v10
+nt@isntn1:=tris(natt,nt,ntofc(cofnt(nt),natti(nt)),ntofn(nofnt(nt)),isntc1(nt),iscent(cofnt(nt),natti(nt),cofn(nofnt(nt)),nati(nofnt(nt)),t4".v10")):is"e"(natt,nt,ntofn(nofnt(nt)))
+isntn2:=symis(natt,nt,ntofn(nofnt(nt)),isntn1):is"e"(natt,ntofn(nofnt(nt)),nt)
+@1t:=ntofn(1):natt
+suct:=[t:natt]ntofn(<nofnt(t)>suc):[t:natt]natt
++10299
+nt@[i:is"e"(natt,<nt>suct,1t)]
+t1:=isnint(<nofnt(nt)>suc,1,i):is"n"(<nofnt(nt)>suc,1)
+-10299
+nt@satz299a:=th3"l.imp"(is"e"(natt,<nt>suct,1t),is"n"(<nofnt(nt)>suc,1),<nofnt(nt)>ax3,[t:is"e"(natt,<nt>suct,1t)]t1".10299"(t)):not(is"e"(natt,<nt>suct,1t))
+@ax3t:=[t:natt]satz299a(t):[t:natt]not(is"e"(natt,<t>suct,1t))
+mt@[i:is"e"(natt,<nt>suct,<mt>suct)]
++*10299
+i"c"@t2:=isnint(<nofnt(nt)>suc,<nofnt(mt)>suc,i):is"n"(<nofnt(nt)>suc,<nofnt(mt)>suc)
+t3:=<t2><nofnt(mt)><nofnt(nt)>ax4:is"n"(nofnt(nt),nofnt(mt))
+-10299
+i@satz299b:=isntin(nt,mt,t3".10299"):is"e"(natt,nt,mt)
+@ax4t:=[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]satz299b(t,u,v):[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]is"e"(natt,t,u)
+[s:set(natt)]
+cond1t:=esti(natt,1t,s):'prop'
+cond2t:=all"l"(natt,[t:natt]imp(esti(natt,t,s),esti(natt,<t>suct,s))):'prop'
+[c1:cond1t][c2:cond2t]
++*10299
+c2@[n:nat]
+prop1:=esti(natt,ntofn(n),s):'prop'
+c2@t4:=c1:prop1(1)
+n@[p:prop1(n)]
+t5:=<p><ntofn(n)>c2:esti(natt,ntofn(<nofnt(ntofn(n))>suc),s)
+t6:=isp(nat,[t:nat]esti(natt,ntofn(<t>suc),s),nofnt(ntofn(n)),n,t5,isnnt2(n)):prop1(<n>suc)
+c2@[nt:natt]
+t7:=induction([t:nat]prop1(t),t4,[t:nat][u:prop1(t)]t6(t,u),nofnt(nt)):prop1(nofnt(nt))
+-10299
+c2@satz299c:=[t:natt]isp(natt,[u:natt]esti(natt,u,s),ntofn(nofnt(t)),t,t7".10299"(t),isntn2(t)):[t:natt]esti(natt,t,s)
+@ax5t:=[t:set(natt)][u:cond1t(t)][v:cond2t(t)]satz299c(t,u,v):[t:set(natt)][u:cond1t(t)][v:cond2t(t)][w:natt]esti(natt,w,t)
+ic:=pli(0,1rl):complex
++10300
+t1:=tsis12a(0,1rl,0,1rl):is(ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))))
+t2:=tris(real,mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(ts"r"(1rl,1rl)),m0"r"(1rl),pl01(ts"r"(0,0),m0"r"(ts"r"(1rl,1rl)),ts01(0,0,refis(real,0))),ism0"r"(ts"r"(1rl,1rl),1rl,satz195(1rl))):is"r"(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl))
+t3:=tris(real,pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),ts"r"(1rl,0),0,pl01(ts"r"(0,1rl),ts"r"(1rl,0),ts01(0,1rl,refis(real,0))),ts02(1rl,0,refis(real,0))):is"r"(pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0)
+t4:=isrecx12(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0,t2,t3):is(pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)))
+t5:=satz298j(1rl):is(cofrl(m0"r"(1rl)),m0(1c))
+-10300
+satz2300:=tr3is(cx,ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)),m0(1c),t1".10300",t4".10300",t5".10300"):is(ts(ic,ic),m0(1c))
+[r:real][s:real]
++10301
+t1:=tsis12a(s,0,0,1rl):is(ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))))
+t2:=tris(real,mn"r"(ts"r"(s,0),ts"r"(0,1rl)),m0"r"(ts"r"(0,1rl)),0,pl01(ts"r"(s,0),m0"r"(ts"r"(0,1rl)),ts02(s,0,refis(real,0))),satz176b(ts"r"(0,1rl),ts01(0,1rl,refis(real,0)))):is"r"(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0)
+t3:=tris(real,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),ts"r"(s,1rl),s,pl02(ts"r"(s,1rl),ts"r"(0,0),ts01(0,0,refis(real,0))),satz195(s)):is"r"(pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s)
+t4:=isrecx12(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s,t2,t3):is(pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s))
+t5:=tris(cx,ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s),t1,t4):is(ts(cofrl(s),ic),pli(0,s))
+t6:=ispl2(ts(cofrl(s),ic),pli(0,s),cofrl(r),t5):is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)))
+t7:=plis12a(r,0,0,s):is(pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)))
+t8:=isrecx12(pl"r"(r,0),r,pl"r"(0,s),s,pl02(r,0,refis(real,0)),pl01(0,s,refis(real,0))):is(pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s))
+-10301
+satz301a:=tr3is(cx,pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s),t6".10301",t7".10301",t8".10301"):is"e"(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s))
+satz301b:=symis(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s),satz301a):is(pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)))
+@[x:complex]
+satz301c:=tris(cx,x,pli(re(x),im(x)),pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),ispli(x),satz301b(re(x),im(x))):is(x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)))
+satz301d:=symis(cx,x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),satz301c):is(pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),x)
+s@[t:real][u:real][i:is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)))]
++*10301
+i@t9:=tr3is(cx,pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)),pli(t,u),satz301b(r,s),i,satz301a(t,u)):is(pli(r,s),pli(t,u))
+-10301
+i@satz301e:=tr3is(real,r,re(pli(r,s)),re(pli(t,u)),t,isre(r,s),iscere(pli(r,s),pli(t,u),t9".10301"),reis(t,u)):is"r"(r,t)
+satz301f:=tr3is(real,s,im(pli(r,s)),im(pli(t,u)),u,isim(r,s),isceim(pli(r,s),pli(t,u),t9".10301"),imis(t,u)):is"r"(s,u)
+-c
+-r
+-rp
+-rt
+-n
+-landau
+-eq
+-st
+-e
+-l
--- /dev/null
+# Landau's "Grundlagen der Analysis", formal specification in AUTOMATH
+# Copyright (C) 1977, L.S. van Benthem Jutting
+# 1992, revised by F. Wiedijk (http://www.cs.ru.nl/~freek/aut/)
+# 2008, revised by F. Guidi to remove the eta-reductions
+
++l
+@[a:'prop'][b:'prop']
+imp:=[x:a]b:'prop'
+[a1:a][i:imp(a,b)]
+mp:=<a1>i:b
+a@refimp:=[x:a]x:imp(a,a)
+b@[c:'prop'][i:imp(a,b)][j:imp(b,c)]
+trimp:=[x:a]<<x>i>j:imp(a,c)
+@con:='prim':'prop'
+a@not:=imp(con):'prop'
+wel:=not(not(a)):'prop'
+[a1:a]
+weli:=[x:not(a)]<a1>x:wel(a)
+a@[w:wel(a)]
+et:='prim':a
+a@[c1:con]
+cone:=et([x:not(a)]c1):a
++imp
+b@[i:imp(a,b)][j:imp(not(a),b)]
+th1:=et(b,[x:not(b)]<<trimp(con,i,x)>j>x):b
+b@[n:not(a)]
+th2:=trimp(con,b,n,[x:con]cone(b,x)):imp(a,b)
+b@[n:not(b)][i:imp(a,b)]
+th3:=trimp(con,i,n):not(a)
+b@[a1:a][n:not(b)]
+th4:=[x:imp(a,b)]<a1>th3(n,x):not(imp(a,b))
+b@[n:not(imp(a,b))]
+th5:=et([x:not(a)]<th2(x)>n):a
+th6:=[x:b]<[y:a]x>n:not(b)
+b@[n:not(b)][i:imp(not(a),b)]
+th7:=et(a,th3(not(a),b,n,i)):a
+-imp
+b@[i:imp(not(b),not(a))]
+cp:=[x:a]th7".imp"(b,not(a),weli(x),i):imp(a,b)
+@obvious:=imp(con,con):'prop'
+obviousi:=refimp(con):obvious
+b@ec:=imp(a,not(b)):'prop'
+[n:not(a)]
+eci1:=th2".imp"(not(b),n):ec(a,b)
+b@[n:not(b)]
+eci2:=[x:a]n:ec(a,b)
++ec
+b@[i:imp(a,not(b))]
+th1:=i:ec(a,b)
+b@[i:imp(b,not(a))]
+th2:=[x:a][y:b]<x><y>i:ec(a,b)
+-ec
+b@[e:ec(a,b)]
+comec:=th2".ec"(b,a,e):ec(b,a)
+[a1:a]
+ece1:=<a1>e:not(b)
+e@[b1:b]
+ece2:=th3".imp"(not(b),weli(b,b1),e):not(a)
++*ec
+c@[e:ec(a,b)][i:imp(c,a)]
+th3:=trimp(c,a,not(b),i,e):ec(c,b)
+e@[i:imp(c,b)]
+th4:=comec(c,a,th3(b,a,c,comec(e),i)):ec(a,c)
+-ec
+b@and:=not(ec(a,b)):'prop'
+[a1:a][b1:b]
+andi:=th4".imp"(not(b),a1,weli(b,b1)):and(a,b)
+b@[a1:and(a,b)]
+ande1:=th5".imp"(not(b),a1):a
+ande2:=et(b,th6".imp"(not(b),a1)):b
+comand:=andi(b,a,ande2,ande1):and(b,a)
++and
+b@[n:not(a)]
+th1:=weli(ec,eci1(n)):not(and)
+b@[n:not(b)]
+th2:=weli(ec,eci2(n)):not(and)
+b@[n:not(and)][a1:a]
+th3:=ece1(et(ec,n),a1):not(b)
+n@[b1:b]
+th4:=ece2(et(ec,n),b1):not(a)
+n@th5:=th3"l.imp"(and(b,a),and(a,b),n,[x:and(b,a)]comand(b,a,x)):not(and(b,a))
+c@[a1:and(a,b)][i:imp(a,c)]
+th6:=andi(c,b,<ande1(a1)>i,ande2(a1)):and(c,b)
+a1@[i:imp(b,c)]
+th7:=andi(a,c,ande1(a1),<ande2(a1)>i):and(a,c)
+-and
+b@or:=imp(not(a),b):'prop'
+[a1:a]
+ori1:=th2".imp"(not(a),b,weli(a1)):or(a,b)
+b@[b1:b]
+ori2:=[x:not(a)]b1:or(a,b)
++or
+b@[i:imp(not(a),b)]
+th1:=i:or(a,b)
+b@[i:imp(not(b),a)]
+th2:=[x:not]et(b,th3"l.imp"(not(b),a,x,i)):or(a,b)
+-or
+b@[o:or(a,b)][n:not(a)]
+ore2:=<n>o:b
+o@[n:not(b)]
+ore1:=et(th3".imp"(not(a),b,n,o)):a
+o@comor:=[x:not(b)]ore1(x):or(b,a)
++*or
+b@[n:not(a)][m:not(b)]
+th3:=th4"l.imp"(not(a),b,n,m):not(or(a,b))
+b@[n:not(or(a,b))]
+th4:=th5"l.imp"(not(a),b,n):not(a)
+th5:=th6"l.imp"(not(a),b,n):not(b)
+a@th6:=refimp(not(a)):or(a,not(a))
+-or
+c@[o:or(a,b)][i:imp(a,c)][j:imp(b,c)]
+orapp:=th1".imp"(c,i,trimp(not,b,c,o,j)):c
+c@[d:'prop']
++*or
+o@[i:imp(a,c)]
+th7:=trimp(not(c),not,b,[x:not(c)]th3"l.imp"(a,c,x,i),o):or(c,b)
+o@[i:imp(b,c)]
+th8:=trimp(not(a),b,c,o,i):or(a,c)
+d@[o:or(a,b)][i:imp(a,c)][j:imp(b,d)]
+th9:=th7(a,d,c,th8(a,b,d,o,j),i):or(c,d)
+b@[o:or(a,b)]
+th10:=o:imp(not(a),b)
+th11:=comor(o):imp(not(b),a)
+b@[o:or(not(a),b)]
+th12:=trimp(a,wel(a),b,[x:a]weli(x),o):imp(a,b)
+b@[i:imp(a,b)]
+th13:=trimp(wel(a),a,b,[x:wel(a)]et(x),i):or(not(a),b)
+b@[o:or(not(a),not(b))]
+th14:=weli(ec,th12(not(b),o)):not(and)
+b@[n:not(and)]
+th15:=th13(not(b),et(ec,n)):or(not(a),not(b))
+b@[a1:and(not(a),not(b))]
+th16:=th3(ande1(not(a),not(b),a1),ande2(not(a),not(b),a1)):not(or(a,b))
+b@[n:not(or(a,b))]
+th17:=andi(not(a),not(b),th4(n),th5(n)):and(not(a),not(b))
+-or
+b@orec:=and(or(a,b),ec(a,b)):'prop'
+[o:or(a,b)][e:ec(a,b)]
+oreci:=andi(or(a,b),ec(a,b),o,e):orec(a,b)
++orec
+b@[a1:a][n:not(b)]
+th1:=oreci(ori1(a1),eci2(n)):orec(a,b)
+b@[n:not(a)][b1:b]
+th2:=oreci(ori2(b1),eci1(n)):orec(a,b)
+-orec
+b@[o:orec(a,b)]
+orece1:=ande1(or(a,b),ec,o):or(a,b)
+orece2:=ande2(or(a,b),ec,o):ec(a,b)
+comorec:=oreci(b,a,comor(orece1),comec(orece2)):orec(b,a)
++*orec
+o@[a1:a]
+th3:=ece1(orece2,a1):not(b)
+o@[b1:b]
+th4:=ece2(orece2,b1):not(a)
+o@[n:not(a)]
+th5:=ore2(orece1,n):b
+o@[n:not(b)]
+th6:=ore1(orece1,n):a
+-orec
+b@iff:=and(imp(a,b),imp(b,a)):'prop'
+[i:imp(a,b)][j:imp(b,a)]
+iffi:=andi(imp(a,b),imp(b,a),i,j):iff(a,b)
++iff
+b@[a1:a][b1:b]
+th1:=iffi([x:a]b1,[x:b]a1):iff(a,b)
+b@[n:not(a)][m:not(b)]
+th2:=iffi(th2"l.imp"(n),th2"l.imp"(b,a,m)):iff(a,b)
+-iff
+b@[i:iff(a,b)]
+iffe1:=ande1(imp(a,b),imp(b,a),i):imp(a,b)
+iffe2:=ande2(imp(a,b),imp(b,a),i):imp(b,a)
+comiff:=iffi(b,a,iffe2,iffe1):iff(b,a)
++*iff
+i@[a1:a]
+th3:=<a1>iffe1:b
+i@[b1:b]
+th4:=<b1>iffe2:a
+i@[n:not(a)]
+th5:=th3"l.imp"(b,a,n,iffe2):not(b)
+i@[n:not(b)]
+th6:=th3"l.imp"(n,iffe1):not(a)
+b@[a1:a][n:not(b)]
+th7:=th1"l.and"(imp(a,b),imp(b,a),th4"l.imp"(a1,n)):not(iff(a,b))
+b@[n:not(a)][b1:b]
+th8:=th2"l.and"(imp(a,b),imp(b,a),th4"l.imp"(b,a,b1,n)):not(iff(a,b))
+-iff
+a@refiff:=iffi(a,refimp,refimp):iff(a,a)
+b@[i:iff(a,b)]
+symiff:=comiff(i):iff(b,a)
+c@[i:iff(a,b)][j:iff(b,c)]
+triff:=iffi(a,c,trimp(iffe1(i),iffe1(b,c,j)),trimp(c,b,a,iffe2(b,c,j),iffe2(i))):iff(a,c)
++*iff
+b@[i:iff(a,b)]
+th9:=[x:not(a)]th5(i,x):imp(not(a),not(b))
+th10:=[x:not(b)]th6(i,x):imp(not(b),not(a))
+th11:=iffi(not(a),not(b),th9,th10):iff(not(a),not(b))
+b@[i:imp(not(a),not(b))][j:imp(not(b),not(a))]
+th12:=iffi(cp(j),cp(b,a,i)):iff(a,b)
+b@[o:orec(a,b)]
+th13:=iffi(not(b),orece2(o),comor(orece1(o))):iff(a,not(b))
+th14:=th13(b,a,comorec(o)):iff(b,not(a))
+b@[i:iff(a,not(b))]
+th15:=oreci(comor(b,a,iffe2(not(b),i)),iffe1(not(b),i)):orec(a,b)
+b@[i:iff(b,not(a))]
+th16:=comorec(b,a,th15(b,a,i)):orec(a,b)
+c@[i:iff(a,b)][j:imp(a,c)]
+thimp1:=trimp(b,a,c,iffe2(i),j):imp(b,c)
+i@[j:imp(c,a)]
+thimp2:=trimp(c,a,b,j,iffe1(i)):imp(c,b)
+i@[e:ec(a,c)]
+thec1:=th3"l.ec"(c,b,e,iffe2(i)):ec(b,c)
+i@[e:ec(c,a)]
+thec2:=th4"l.ec"(c,a,b,e,iffe2(i)):ec(c,b)
+i@[a1:and(a,c)]
+thand1:=th6"l.and"(c,b,a1,iffe1(i)):and(b,c)
+i@[a1:and(c,a)]
+thand2:=th7"l.and"(c,a,b,a1,iffe1(i)):and(c,b)
+i@[o:or(a,c)]
+thor1:=th7"l.or"(c,b,o,iffe1(i)):or(b,c)
+i@[o:or(c,a)]
+thor2:=th8"l.or"(c,a,b,o,iffe1(i)):or(c,b)
+i@[o:orec(a,c)]
+thorec1:=oreci(b,c,thor1(orece1(a,c,o)),thec1(orece2(a,c,o))):orec(b,c)
+i@[o:orec(c,a)]
+thorec2:=oreci(c,b,thor2(orece1(c,a,o)),thec2(orece2(c,a,o))):orec(c,b)
+-iff
+@[sigma:'type'][p:[x:sigma]'prop']
+%suggestion by van Daalen to remove the first eta-reduction
+%all:=p:'prop' %original line
+all:=[x:sigma]<x>p:'prop'
+%end of suggestion
+[a1:all(sigma,p)][s:sigma]
+alle:=<s>a1:<s>p
++all
+p@[s:sigma][n:not(<s>p)]
+th1:=[x:all(sigma,p)]<<s>x>n:not(all(sigma,p))
+-all
+p@non:=[x:sigma]not(<x>p):[x:sigma]'prop'
+some:=not(non(p)):'prop'
+[s:sigma][sp:<s>p]
+somei:=th1".all"(non(p),s,weli(<s>p,sp)):some(sigma,p)
++some
+p@[n:not(all(sigma,p))][m:non(non(p))][s:sigma]
+t1:=et(<s>p,<s>m):<s>p
+%set etared
+m@t2:=<[x:sigma]t1(x)>n:con
+%reset etared
+n@th1:=[x:non(non(p))]t2(x):some(non(p))
+p@[s:some(non(p))][a1:all(sigma,p)][t:sigma]
+t3:=weli(<t>p,<t>a1):not(not(<t>p))
+a1@t4:=<[x:sigma]t3(x)>s:con
+s@th2:=[x:all(sigma,p)]t4(x):not(all(sigma,p))
+p@[n:not(some(sigma,p))]
+th3:=et(non(p),n):non(p)
+[s:sigma]
+th4:=<s>th3:not(<s>p)
+p@[n:non(p)]
+th5:=weli(non(p),n):not(some(sigma,p))
+-some
+p@[s:some(sigma,p)][x:'prop'][i:[y:sigma]imp(<y>p,x)]
++*some
+i@[n:not(x)][t:sigma]
+t5:=th3"l.imp"(<t>p,x,n,<t>i):not(<t>p)
+n@t6:=mp(some(sigma,p),con,s,th5([y:sigma]t5(y))):con
+-some
+i@someapp:=et(x,[y:not(x)]t6".some"(y)):x
++*some
+p@[q:[x:sigma]'prop'][s:some(sigma,p)][i:[x:sigma]imp(<x>p,<x>q)]
+th6:=someapp(s,some(q),[x:sigma][y:<x>p]somei(q,x,mp(<x>p,<x>q,y,<x>i))):some(q)
+-some
+c@or3:=or(a,or(b,c)):'prop'
+[o:or3(a,b,c)][n:not(a)]
++or3
+th1:=ore2(or(b,c),o,n):or(b,c)
+-or3
+[m:not(b)]
+or3e3:=ore2(b,c,th1".or3",m):c
+o@[n:not(b)]
++*or3
+n@th2:=th2"l.or"(c,a,[x:not(a)]or3e3(x,n)):or(c,a)
+-or3
+n@[m:not(c)]
+or3e1:=ore2(c,a,th2".or3",m):a
+o@[n:not(c)]
++*or3
+n@th3:=th2"l.or"([x:not(b)]or3e1(x,n)):or(a,b)
+-or3
+n@[m:not(a)]
+or3e2:=ore2(th3".or3",m):b
++*or3
+o@th4:=th1"l.or"(b,or(c,a),[x:not(b)]th2(x)):or3(b,c,a)
+th5:=th4(b,c,a,th4):or3(c,a,b)
+-or3
+c@[a1:a]
+or3i1:=ori1(a,or(b,c),a1):or3(a,b,c)
+c@[b1:b]
+or3i2:=ori2(a,or(b,c),ori1(b,c,b1)):or3(a,b,c)
+c@[c1:c]
+or3i3:=ori2(a,or(b,c),ori2(b,c,c1)):or3(a,b,c)
++*or3
+c@[o:or(a,b)]
+th6:=th4"or3"(c,a,b,ori2(c,or(a,b),o)):or3(a,b,c)
+c@[o:or(b,c)]
+th7:=ori2(or(b,c),o):or3(a,b,c)
+c@[o:or(c,a)]
+th8:=th4"or3"(c,a,b,th6(c,a,b,o)):or3(a,b,c)
+-or3
+d@[o:or3(a,b,c)][i:imp(a,d)][j:imp(b,d)][k:imp(c,d)]
+or3app:=orapp(or(b,c),d,o,i,[x:or(b,c)]orapp(b,c,d,x,j,k)):d
+c@and3:=and(a,and(b,c)):'prop'
+[a1:and3(a,b,c)]
+and3e1:=ande1(and(b,c),a1):a
+and3e2:=ande1(b,c,ande2(and(b,c),a1)):b
+and3e3:=ande2(b,c,ande2(and(b,c),a1)):c
+c@[a1:a][b1:b][c1:c]
+and3i:=andi(a,and(b,c),a1,andi(b,c,b1,c1)):and3(a,b,c)
++and3
+c@[a1:and3(a,b,c)]
+th1:=and3i(b,c,a,and3e2(a1),and3e3(a1),and3e1(a1)):and3(b,c,a)
+th2:=th1(b,c,a,th1):and3(c,a,b)
+th3:=andi(and3e1(a1),and3e2(a1)):and(a,b)
+th4:=ande2(and(b,c),a1):and(b,c)
+th5:=th3(c,a,b,th2):and(c,a)
+th6:=and3i(c,b,a,and3e3(a1),and3e2(a1),and3e1(a1)):and3(c,b,a)
+-and3
+c@ec3:=and3(ec,ec(b,c),ec(c,a)):'prop'
+[e:ec3(a,b,c)]
++ec3
+th1:=and3e1(ec,ec(b,c),ec(c,a),e):ec(a,b)
+th2:=and3e2(ec,ec(b,c),ec(c,a),e):ec(b,c)
+th3:=and3e3(ec,ec(b,c),ec(c,a),e):ec(c,a)
+th4:=th1"l.and3"(ec,ec(b,c),ec(c,a),e):ec3(b,c,a)
+th5:=th4(b,c,a,th4):ec3(c,a,b)
+th5a:=and3i(ec(c,b),ec(b,a),ec(a,c),comec(b,c,th2(e)),comec(a,b,th1(e)),comec(c,a,th3(e))):ec3(c,b,a)
+-ec3
+[a1:a]
+ec3e12:=ece1(th1".ec3",a1):not(b)
+ec3e13:=ece2(c,a,th3".ec3",a1):not(c)
+e@[b1:b]
+ec3e23:=ec3e12(b,c,a,th4".ec3",b1):not(c)
+ec3e21:=ec3e13(b,c,a,th4".ec3",b1):not(a)
+e@[c1:c]
+ec3e31:=ec3e12(c,a,b,th5".ec3",c1):not(a)
+ec3e32:=ec3e13(c,a,b,th5".ec3",c1):not(b)
++*ec3
+c@[e:ec(a,b)][f:ec(b,c)][g:ec(c,a)]
+th6:=and3i(ec,ec(b,c),ec(c,a),e,f,g):ec3(a,b,c)
+c@[e:ec3(a,b,c)][o:or(a,b)]
+th7:=orapp(not(c),o,[x:a]ece2(c,a,th3"ec3"(e),x),[x:b]ece1(b,c,th2"ec3"(e),x)):not(c)
+e@[o:or(b,c)]
+th8:=th7(b,c,a,th4"ec3"(e),o):not(a)
+e@[o:or(c,a)]
+th9:=th7(c,a,b,th5"ec3"(e),o):not(b)
+-ec3
+c@[n:not(a)][m:not(b)]
+ec3i1:=th6".ec3"(eci1(n),eci1(b,c,m),eci2(c,a,n)):ec3(a,b,c)
+c@[n:not(b)][m:not(c)]
+ec3i2:=th6".ec3"(eci2(n),eci1(b,c,n),eci1(c,a,m)):ec3(a,b,c)
+c@[n:not(c)][m:not(a)]
+ec3i3:=th6".ec3"(eci1(m),eci2(b,c,n),eci1(c,a,n)):ec3(a,b,c)
++*ec3
+d@[e:'prop'][f:'prop'][o1:or3(a,b,c)][p1:ec3(d,e,f)][i:imp(a,d)][j:imp(b,e)][k:imp(c,f)][d1:d]
+t1:=[x:b]mp(e,con,<x>j,ec3e12(d,e,f,p1,d1)):not(b)
+t2:=[x:c]mp(f,con,<x>k,ec3e13(d,e,f,p1,d1)):not(c)
+th10:=or3e1(o1,t1,t2):a
+k@[e1:e]
+th11:=th10(b,c,a,e,f,d,th4"l.or3"(o1),th4"ec3"(d,e,f,p1),j,k,i,e1):b
+k@[f1:f]
+th12:=th10(c,a,b,f,d,e,th5"l.or3"(o1),th5"ec3"(d,e,f,p1),k,i,j,f1):c
+-ec3
+c@orec3:=and(or3(a,b,c),ec3(a,b,c)):'prop'
+[o:orec3(a,b,c)]
+orec3e1:=ande1(or3(a,b,c),ec3(a,b,c),o):or3(a,b,c)
+orec3e2:=ande2(or3(a,b,c),ec3(a,b,c),o):ec3(a,b,c)
+c@[o:or3(a,b,c)][e:ec3(a,b,c)]
+orec3i:=andi(or3(a,b,c),ec3(a,b,c),o,e):orec3(a,b,c)
++orec3
+c@[o:orec3(a,b,c)]
+th1:=orec3i(b,c,a,th4"l.or3"(orec3e1(o)),th4"l.ec3"(orec3e2(o))):orec3(b,c,a)
+th2:=orec3i(c,a,b,th5"l.or3"(orec3e1(o)),th5"l.ec3"(orec3e2(o))):orec3(c,a,b)
+-orec3
++e
+sigma@[s:sigma][t:sigma]
+is:='prim':'prop'
+s@refis:='prim':is(s,s)
+p@[s:sigma][t:sigma][sp:<s>p][i:is(s,t)]
+isp:='prim':<t>p
+sigma@[s:sigma][t:sigma][i:is(s,t)]
+symis:=isp([x:sigma]is(x,s),s,t,refis(s),i):is(t,s)
+t@[u:sigma][i:is(s,t)][j:is(t,u)]
+tris:=isp([x:sigma]is(x,u),t,s,j,symis(i)):is(s,u)
+u@[i:is(u,s)][j:is(u,t)]
+tris1:=tris(s,u,t,symis(u,s,i),j):is(s,t)
+u@[i:is(s,u)][j:is(t,u)]
+tris2:=tris(s,u,t,i,symis(t,u,j)):is(s,t)
+sp@[i:is(t,s)]
+isp1:=isp(symis(t,s,i)):<t>p
+t@[n:not(is(s,t))]
+symnotis:=th3"l.imp"(is(t,s),is(s,t),n,[x:is(t,s)]symis(t,s,x)):not(is(t,s))
++notis
+u@[n:not(is(s,t))][i:is(s,u)]
+th1:=isp([x:sigma]not(is(x,t)),s,u,n,i):not(is(u,t))
+n@[i:is(u,s)]
+th2:=th1(symis(u,s,i)):not(is(u,t))
+n@[i:is(t,u)]
+th3:=isp([x:sigma]not(is(s,x)),t,u,n,i):not(is(s,u))
+n@[i:is(u,t)]
+th4:=th3(symis(u,t,i)):not(is(s,u))
+u@[v:sigma][n:not(is(s,t))][i:is(s,u)][j:is(t,v)]
+th5:=th3(u,t,v,th1(n,i),j):not(is(u,v))
+-notis
+u@[v:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)]
+tr3is:=tris(s,u,v,tris(i,j),k):is(s,v)
+v@[w:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)][l:is(v,w)]
+tr4is:=tris(s,v,w,tr3is(i,j,k),l):is(s,w)
+p@amone:=[x:sigma][y:sigma][u:<x>p][v:<y>p]is(x,y):'prop'
+[a1:amone(sigma,p)][s:sigma][t:sigma][sp:<s>p][tp:<t>p]
+amonee:=<tp><sp><t><s>a1:is(s,t)
+p@one:=and(amone(sigma,p),some(sigma,p)):'prop'
+[a1:amone(sigma,p)][s:some(sigma,p)]
+onei:=andi(amone(sigma,p),some(sigma,p),a1,s):one(sigma,p)
+p@[o1:one(sigma,p)]
+onee1:=ande1(amone(sigma,p),some(sigma,p),o1):amone(sigma,p)
+onee2:=ande2(amone(sigma,p),some(sigma,p),o1):some(sigma,p)
+ind:='prim':sigma
+oneax:='prim':<ind>p
++one
+[s:sigma][sp:<s>p]
+th1:=amonee(onee1,ind,s,oneax,sp):is(ind,s)
+-one
+sigma@[tau:'type'][f:[x:sigma]tau][s:sigma][t:sigma][i:is(s,t)]
+isf:=isp(sigma,[x:sigma]is(tau,<s>f,<x>f),s,t,refis(tau,<s>f),i):is(tau,<s>f,<t>f)
+f@injective:=all([x:sigma]all([y:sigma]imp(is(tau,<x>f,<y>f),is(x,y)))):'prop'
+[i:injective(f)][s:sigma][t:sigma][j:is(tau,<s>f,<t>f)]
+isfe:=<j><t><s>i:is(s,t)
+f@[t0:tau]
+image:=some([x:sigma]is(tau,t0,<x>f)):'prop'
+f@[s:sigma]
+tofs:=<s>f:tau
+imagei:=somei([x:sigma]is(tau,tofs,<x>f),s,refis(tau,tofs)):image(tofs)
++inj
+i@[ta:tau][tb:tau][j:is(tau,ta,tb)][sa:sigma][sb:sigma][ja:is(tau,ta,tofs(sa))][jb:is(tau,tb,tofs(sb))]
+t1:=tr3is(tau,tofs(sa),ta,tb,tofs(sb),symis(tau,ta,tofs(sa),ja),j,jb):is(tau,tofs(sa),tofs(sb))
+th1:=isfe(sa,sb,t1):is(sa,sb)
+i@[t0:tau]
+th2:=[x:sigma][y:sigma][u:is(tau,t0,<x>f)][v:is(tau,t0,<y>f)]th1(t0,t0,refis(tau,t0),x,y,u,v):amone([x:sigma]is(tau,t0,<x>f))
+[j:image(f,t0)]
+th3:=onei([x:sigma]is(tau,t0,<x>f),th2,j):one([x:sigma]is(tau,t0,<x>f))
+-inj
+i@[t0:tau][j:image(f,t0)]
+soft:=ind([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):sigma
+i@inverse:=[x:tau][u:image(f,x)]soft(x,u):[x:tau][u:image(f,x)]sigma
+j@ists1:=oneax([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):is(tau,t0,tofs(soft(t0,j)))
+ists2:=symis(tau,t0,tofs(soft(t0,j)),ists1):is(tau,tofs(soft(t0,j)),t0)
+i@[ta:tau][ja:image(ta)][tb:tau][jb:image(tb)][j:is(tau,ta,tb)]
+isinv:=th1".inj"(ta,tb,j,soft(ta,ja),soft(tb,jb),ists1(ta,ja),ists1(tb,jb)):is(soft(ta,ja),soft(tb,jb))
+jb@[j:is(soft(ta,ja),soft(tb,jb))]
+isinve:=tr3is(tau,ta,tofs(soft(ta,ja)),tofs(soft(tb,jb)),tb,ists1(ta,ja),isf(soft(ta,ja),soft(tb,jb),j),ists2(tb,jb)):is(tau,ta,tb)
+i@[s:sigma]
+isst1:=isfe(s,soft(tofs(s),imagei(s)),ists1(tofs(s),imagei(s))):is(s,soft(tofs(s),imagei(s)))
+isst2:=symis(s,soft(tofs(s),imagei(s)),isst1):is(soft(tofs(s),imagei(s)),s)
+f@surjective:=all(tau,[x:tau]image(x)):'prop'
+bijective:=and(injective,surjective):'prop'
+[b:bijective(f)]
++*inj
+b@t2:=ande1(injective,surjective,b):injective(f)
+t3:=ande2(injective,surjective,b):surjective(f)
+[t:tau]
+so:=soft(t2,t,<t>t3):sigma
+-inj
+b@invf:=[x:tau]so".inj"(x):[x:tau]sigma
+[s:sigma]
+thinvf1:=tris(s,soft(t2".inj",tofs(s),imagei(s)),<<s>f>invf,isst1(t2".inj",s),isinv(t2".inj",tofs(s),imagei(s),tofs(s),<tofs(s)>t3".inj",refis(tau,tofs(s)))):is(s,<<s>f>invf)
+b@[t:tau]
+thinvf2:=ists1(t2".inj",t,<t>t3".inj"):is(tau,t,<<t>invf>f)
+tau@[upsilon:'type'][f:[x:sigma]tau][g:[x:tau]upsilon]
++*inj
+g@[if:injective(sigma,tau,f)][ig:injective(tau,upsilon,g)]
+h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
+[s:sigma][t:sigma][i:is(upsilon,<s>h,<t>h)]
+t4:=isfe(tau,upsilon,g,ig,<s>f,<t>f,i):is(tau,<s>f,<t>f)
+t5:=isfe(f,if,s,t,t4):is(s,t)
+ig@th4:=[x:sigma][y:sigma][v:is(upsilon,<x>h,<y>h)]t5(x,y,v):injective(sigma,upsilon,[x:sigma]<<x>f>g)
+-inj
++surj
+g@[sf:surjective(sigma,tau,f)][sg:surjective(tau,upsilon,g)]
+h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
+[u:upsilon]
+t1:=<u>sg:image(tau,upsilon,g,u)
+[t:tau][i:is(upsilon,u,<t>g)]
+t2:=<t>sf:image(sigma,tau,f,t)
+[s:sigma][j:is(tau,t,<s>f)]
+t3:=tris(upsilon,u,<t>g,<s>h,i,isf(tau,upsilon,g,t,<s>f,j)):is(upsilon,u,<s>h)
+t4:=somei([x:sigma]is(upsilon,u,<x>h),s,t3):image(sigma,upsilon,h,u)
+i@t5:=someapp([x:sigma]is(tau,t,<x>f),t2,image(sigma,upsilon,h,u),[x:sigma][v:is(tau,t,<x>f)]t4(x,v)):image(sigma,upsilon,h,u)
+u@t6:=someapp(tau,[x:tau]is(upsilon,u,<x>g),t1,image(sigma,upsilon,h,u),[x:tau][v:is(upsilon,u,<x>g)]t5(x,v)):image(sigma,upsilon,h,u)
+sg@th1:=[x:upsilon]t6(x):surjective(sigma,upsilon,[x:sigma]<<x>f>g)
+-surj
++bij
+g@[bf:bijective(sigma,tau,f)][bg:bijective(tau,upsilon,g)]
+h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
+t1:=th4"e.inj"(f,g,ande1(injective(f),surjective(f),bf),ande1(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):injective(sigma,upsilon,h)
+t2:=th1"e.surj"(f,g,ande2(injective(f),surjective(f),bf),ande2(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):surjective(sigma,upsilon,h)
+th1:=andi(injective(sigma,upsilon,h),surjective(sigma,upsilon,h),t1,t2):bijective(sigma,upsilon,[x:sigma]<<x>f>g)
+-bij
+tau@[f:[x:sigma]tau][g:[x:sigma]tau][i:is([x:sigma]tau,f,g)][s:sigma]
+fise:=isp([x:sigma]tau,[y:[x:sigma]tau]is(tau,<s>f,<s>y),f,g,refis(tau,<s>f),i):is(tau,<s>f,<s>g)
+g@[i:[x:sigma]is(tau,<x>f,<x>g)]
+fisi:='prim':is([x:sigma]tau,f,g)
++fis
+g@[i:is([x:sigma]tau,f,g)][s:sigma][t:sigma][j:is(s,t)]
+th1:=tris(tau,<s>f,<t>f,<t>g,isf(f,s,t,j),fise(i,t)):is(tau,<s>f,<t>g)
+-fis
+p@ot:='prim':'type'
+[o1:ot]
+in:='prim':sigma
+inp:='prim':<in>p
+p@otax1:='prim':injective(ot,sigma,[x:ot]in(x))
+[s:sigma][sp:<s>p]
+otax2:='prim':image(ot,sigma,[x:ot]in(x),s)
+o1@[o2:ot][i:is(ot,o1,o2)]
+isini:=isf(ot,sigma,[x:ot]in(x),o1,o2,i):is(in(o1),in(o2))
+o2@[i:is(in(o1),in(o2))]
+isine:=isfe(ot,sigma,[x:ot]in(x),otax1,o1,o2,i):is(ot,o1,o2)
+sp@out:=soft(ot,sigma,[x:ot]in(x),otax1,s,otax2):ot
+[t:sigma][tp:<t>p][i:is(s,t)]
+isouti:=isinv(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(ot,out(s,sp),out(t,tp))
+tp@[i:is(ot,out(s,sp),out(t,tp))]
+isoute:=isinve(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(s,t)
+o1@isoutin:=tris(ot,o1,soft(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1)),out(in(o1),inp(o1)),isst1(ot,sigma,[x:ot]in(x),otax1,o1),isinv(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1),in(o1),otax2(in(o1),inp(o1)),refis(sigma,in(o1)))):is(ot,o1,out(in(o1),inp(o1)))
+sp@isinout:=ists1(ot,sigma,[x:ot]in(x),otax1,s,otax2):is(s,in(out(s,sp)))
+tau@pairtype:='prim':'type'
+[s:sigma][t:tau]
+pair:='prim':pairtype
+tau@[p1:pairtype]
+first:='prim':sigma
+second:='prim':tau
+pairis1:='prim':is(pairtype,pair(first,second),p1)
+pairis2:=symis(pairtype,pair(first,second),p1,pairis1):is(pairtype,p1,pair(first,second))
+t@firstis1:='prim':is(sigma,first(pair),s)
+firstis2:=symis(sigma,first(pair),s,firstis1):is(sigma,s,first(pair))
+secondis1:='prim':is(tau,second(pair),t)
+secondis2:=symis(tau,second(pair),t,secondis1):is(tau,t,second(pair))
+a@[ksi:'type'][x:ksi][y:ksi]
++ite
+[z:ksi]
+prop1:=and(imp(a,is(ksi,z,x)),imp(not(a),is(ksi,z,y))):'prop'
+y@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t1:=ande1(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(a,is(ksi,x1,x))
+t2:=mp(a,is(ksi,x1,x),a1,t1):is(ksi,x1,x)
+t3:=t2(y1,x1,py1,px1):is(ksi,y1,x)
+t4:=tris2(ksi,x1,y1,x,t2,t3):is(ksi,x1,y1)
+a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
+t6:=[x1:a]refis(ksi,x):imp(a,is(ksi,x,x))
+t7:=th2"l.imp"(not(a),is(ksi,x,y),weli(a,a1)):imp(not(a),is(ksi,x,y))
+t8:=andi(imp(a,is(ksi,x,x)),imp(not(a),is(ksi,x,y)),t6,t7):prop1(x)
+t9:=somei(ksi,[t:ksi]prop1(t),x,t8):some(ksi,[t:ksi]prop1(t))
+t10:=onei(ksi,[t:ksi]prop1(t),t5,t9):one(ksi,[t:ksi]prop1(t))
+y@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t11:=ande2(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(not(a),is(ksi,x1,y))
+t12:=mp(not(a),is(ksi,x1,y),n,t11):is(ksi,x1,y)
+t13:=t12(y1,x1,py1,px1):is(ksi,y1,y)
+t14:=tris2(ksi,x1,y1,y,t12,t13):is(ksi,x1,y1)
+n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
+t16:=[x1:not(a)]refis(ksi,y):imp(not(a),is(ksi,y,y))
+t17:=th2"l.imp"(a,is(ksi,y,x),n):imp(a,is(ksi,y,x))
+t18:=andi(imp(a,is(ksi,y,x)),imp(not(a),is(ksi,y,y)),t17,t16):prop1(y)
+t19:=somei(ksi,[t:ksi]prop1(t),y,t18):some(ksi,[t:ksi]prop1(t))
+t20:=onei(ksi,[t:ksi]prop1(t),t15,t19):one(ksi,[t:ksi]prop1(t))
+y@t21:=th1"l.imp"(a,one(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one(ksi,[t:ksi]prop1(t))
+-ite
+ite:=ind(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
++*ite
+y@t22:=oneax(ksi,[t:ksi]prop1(t),t21):prop1(ite)
+t23:=ande1(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(a,is(ksi,ite,x))
+t24:=ande2(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(not(a),is(ksi,ite,y))
+-ite
+y@[a1:a]
+itet:=mp(a,is(ksi,ite,x),a1,t23".ite"):is(ksi,ite,x)
+y@[n:not(a)]
+itef:=mp(not(a),is(ksi,ite,y),n,t24".ite"):is(ksi,ite,y)
+sigma@[s0:sigma][t0:sigma]
++wissel
+[s:sigma]
+wa:=ite(is(s,s0),sigma,t0,s):sigma
+[i:is(s,s0)]
+t1:=itet(is(s,s0),sigma,t0,s,i):is(wa,t0)
+s@[n:not(is(s,s0))]
+t2:=itef(is(s,s0),sigma,t0,s,n):is(wa,s)
+s@wb:=ite(is(s,t0),sigma,s0,wa):sigma
+[i:is(s,t0)]
+t3:=itet(is(s,t0),sigma,s0,wa,i):is(wb,s0)
+s@[n:not(is(s,t0))]
+t4:=itef(is(s,t0),sigma,s0,wa,n):is(wb,wa)
+s@[i:is(s,s0)][j:is(s0,t0)]
+t5:=tris(wb,s0,t0,t3(tris(s,s0,t0,i,j)),j):is(wb,t0)
+i@[n:not(is(s0,t0))]
+t6:=tris(wb,wa,t0,t4(th2"e.notis"(s0,t0,s,n,i)),t1(i)):is(wb,t0)
+i@t7:=th1"l.imp"(is(s0,t0),is(wb,t0),[t:is(s0,t0)]t5(t),[t:not(is(s0,t0))]t6(t)):is(wb,t0)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+t8:=tris(wb,wa,s,t4(o),t2(n)):is(wb,s)
+-wissel
+wissel:=[x:sigma]wb".wissel"(x):[x:sigma]sigma
+[s:sigma][i:is(s,s0)]
+iswissel1:=t7".wissel"(s,i):is(<s>wissel,t0)
+s@[i:is(s,t0)]
+iswissel2:=t3".wissel"(s,i):is(<s>wissel,s0)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+iswissel3:=t8".wissel"(s,n,o):is(<s>wissel,s)
++*wissel
+s@[t:sigma][i:is(wb(s),wb(t))][n:not(is(s,t))][j:is(s,s0)]
+t9:=symnotis(s0,t,th1"e.notis"(s,t,s0,n,j)):not(is(t,s0))
+[k:is(s0,t0)]
+t10:=th3"e.notis"(t,s0,t0,t9,k):not(is(t,t0))
+t11:=tris(wb(s),wb(t),t,i,t8(t,t9,t10)):is(wb(s),t)
+t12:=<tris1(t,t0,wb(s),t11,t7(j))>t10:con
+j@t13:=[v:is(s0,t0)]t12(v):not(is(s0,t0))
+[k:is(t,t0)]
+t14:=tris(wb(s),wb(t),s0,i,t3(t,k)):is(wb(s),s0)
+t15:=t12(tris1(s0,t0,wb(s),t14,t7(j))):con
+j@t16:=[v:is(t,t0)]t15(v):not(is(t,t0))
+t17:=tris(wb(s),wb(t),t,i,t8(t,t9,t16)):is(wb(s),t)
+t18:=t15(tris1(t,t0,wb(s),t17,t7(j))):con
+n@t19:=[v:is(s,s0)]t18(v):not(is(s,s0))
+t20:=t19(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,s0))
+[j:is(s,t0)]
+t21:=symnotis(t0,t,th1"e.notis"(s,t,t0,n,j)):not(is(t,t0))
+t22:=tris(wb(s),wb(t),t,i,t8(t,t20,t21)):is(wb(s),t)
+t23:=<tris1(t,s0,wb(s),t22,t3(j))>t20:con
+n@t24:=[v:is(s,t0)]t23(v):not(is(s,t0))
+t25:=t24(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,t0))
+t26:=tris(wb(s),wb(t),t,i,t8(t,t20,t25)):is(wb(s),t)
+t27:=<tris1(s,t,wb(s),t8(t19,t24),t26)>n:con
+i@t28:=et(is(s,t),[v:not(is(s,t))]t27(v)):is(s,t)
+t0@th1:=[x:sigma][y:sigma][v:is(wb(x),wb(y))]t28(x,y,v):injective(sigma,sigma,wissel)
+s@[i:is(s,s0)]
+t29:=tris2(s,wb(t0),s0,i,t3(t0,refis(t0))):is(s,wb(t0))
+t30:=somei(sigma,[x:sigma]is(s,wb(x)),t0,t29):image(sigma,sigma,wissel,s)
+s@[i:is(s,t0)]
+t31:=tris2(s,wb(s0),t0,i,t7(s0,refis(s0))):is(s,wb(s0))
+t32:=somei(sigma,[x:sigma]is(s,wb(x)),s0,t31):image(sigma,sigma,wissel,s)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+t33:=symis(wb(s),s,t8(n,o)):is(s,wb(s))
+t34:=somei(sigma,[x:sigma]is(s,wb(x)),s,t33):image(sigma,sigma,wissel,s)
+n@t35:=th1"l.imp"(is(s,t0),image(sigma,sigma,wissel,s),[v:is(s,t0)]t32(v),[v:not(is(s,t0))]t34(v)):image(sigma,sigma,wissel,s)
+s@t36:=th1"l.imp"(is(s,s0),image(sigma,sigma,wissel,s),[v:is(s,s0)]t30(v),[v:not(is(s,s0))]t35(v)):image(sigma,sigma,wissel,s)
+t0@th2:=[x:sigma]t36(x):surjective(sigma,sigma,wissel)
+th3:=andi(injective(sigma,sigma,wissel),surjective(sigma,sigma,wissel),th1,th2):bijective(sigma,sigma,wissel)
+-wissel
+tau@[f:[x:sigma]tau][s0:sigma][t0:sigma]
+changef:=[x:sigma]<<x>wissel(s0,t0)>f:[x:sigma]tau
+[s:sigma][i:is(s,s0)]
+changef1:=isf(sigma,tau,f,<s>wissel(s0,t0),t0,iswissel1(s0,t0,s,i)):is(tau,<s>changef,<t0>f)
+s@[i:is(s,t0)]
+changef2:=isf(sigma,tau,f,<s>wissel(s0,t0),s0,iswissel2(s0,t0,s,i)):is(tau,<s>changef,<s0>f)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+changef3:=isf(sigma,tau,f,<s>wissel(s0,t0),s,iswissel3(s0,t0,s,n,o)):is(tau,<s>changef,<s>f)
++*wissel
+t0@[i:injective(f)]
+th4:=th4"e.inj"(sigma,sigma,tau,wissel(s0,t0),f,th1(s0,t0),i):injective(changef)
+t0@[s:surjective(f)]
+th5:=th1"e.surj"(sigma,sigma,tau,wissel(s0,t0),f,th2(s0,t0),s):surjective(changef)
+t0@[b:bijective(f)]
+th6:=th1"e.bij"(sigma,sigma,tau,wissel(s0,t0),f,th3(s0,t0),b):bijective(changef)
+-wissel
+-e
++r
+a@[b:[x:a]'prop']
+%suggestion by van Daalen to remove the second eta-reduction
+%imp:=b:'prop' %original line
+imp:=[x:a]<x>b:'prop'
+%end of suggestion
+[a1:a][i:imp(a,b)]
+mp:=<a1>i:<a1>b
++imp
+b@[n:not(a)]
+%set etared
+th2:=[x:a]cone(<x>b,mp"l"(a,con,x,n)):imp(a,b)
+%reset etared
+-imp
+b@ec:=[x:a]not(<x>b):'prop'
+[n:not(a)]
+eci1:=[x:a]cone(not(<x>b),mp"l"(a,con,x,n)):ec(a,b)
+b@[a1:and(a,b)]
+ande2:=<ande1(a,b,a1)>ande2"l"(a,b,a1):<ande1(a,b,a1)>b
+a@[ksi:'type']
++ite
+[x1:ksi][y1:ksi]
+is:=is"l.e"(ksi,x1,y1):'prop'
+-ite
+[x:[t:a]ksi][y:[t:not(a)]ksi][i:[t:a][u:a]is".ite"(<t>x,<u>x)][j:[t:not(a)][u:not(a)]is".ite"(<t>y,<u>y)]
++*ite
+j@[z:ksi]
+prop1:=and(imp(a,[t:a]is(z,<t>x)),imp(not(a),[t:not(a)]is(z,<t>y))):'prop'
+j@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t1:=ande1"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(a,[t:a]is(x1,<t>x))
+t2:=mp(a,[t:a]is(x1,<t>x),a1,t1):is(x1,<a1>x)
+t3:=t2(y1,x1,py1,px1):is(y1,<a1>x)
+t4:=tris2"l.e"(ksi,x1,y1,<a1>x,t2,t3):is(x1,y1)
+a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
+t6:=<a1>i:imp(a,[t:a]is(<a1>x,<t>x))
+t7:=th2"r.imp"(not(a),[t:not(a)]is(<a1>x,<t>y),weli(a,a1)):imp(not(a),[t:not(a)]is(<a1>x,<t>y))
+t8:=andi(imp(a,[t:a]is(<a1>x,<t>x)),imp(not(a),[t:not(a)]is(<a1>x,<t>y)),t6,t7):prop1(<a1>x)
+t9:=somei(ksi,[t:ksi]prop1(t),<a1>x,t8):some(ksi,[t:ksi]prop1(t))
+t10:=onei"l.e"(ksi,[t:ksi]prop1(t),t5,t9):one"l.e"(ksi,[t:ksi]prop1(t))
+j@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t11:=ande2"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(not(a),[t:not(a)]is(x1,<t>y))
+t12:=mp(not(a),[t:not(a)]is(x1,<t>y),n,t11):is(x1,<n>y)
+t13:=t12(y1,x1,py1,px1):is(y1,<n>y)
+t14:=tris2"l.e"(ksi,x1,y1,<n>y,t12,t13):is(x1,y1)
+n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
+t16:=<n>j:imp(not(a),[t:not(a)]is(<n>y,<t>y))
+t17:=th2"r.imp"(a,[t:a]is(<n>y,<t>x),n):imp(a,[t:a]is(<n>y,<t>x))
+t18:=andi"l"(imp(a,[t:a]is(<n>y,<t>x)),imp(not(a),[t:not(a)]is(<n>y,<t>y)),t17,t16):prop1(<n>y)
+t19:=somei(ksi,[t:ksi]prop1(t),<n>y,t18):some(ksi,[t:ksi]prop1(t))
+t20:=onei"l.e"(ksi,[t:ksi]prop1(t),t15,t19):one"l.e"(ksi,[t:ksi]prop1(t))
+j@t21:=th1"l.imp"(a,one"l.e"(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one"l.e"(ksi,[t:ksi]prop1(t))
+-ite
+j@ite:=ind"l.e"(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
++*ite
+j@t22:=oneax"l.e"(ksi,[t:ksi]prop1(t),t21):prop1(ite)
+t23:=ande1"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(a,[t:a]is(ite,<t>x))
+t24:=ande2"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(not(a),[t:not(a)]is(ite,<t>y))
+-ite
+j@[a1:a]
+itet:=mp(a,[t:a]is".ite"(ite,<t>x),a1,t23".ite"):is".ite"(ksi,ite,<a1>x)
+j@[n:not(a)]
+itef:=mp(not(a),[t:not(a)]is".ite"(ite,<t>y),n,t24".ite"):is".ite"(ksi,ite,<n>y)
+-r
++*e
++st
+sigma@set:='prim':'type'
+[s:sigma][s0:set]
+esti:='prim':'prop'
+p@setof:='prim':set
+[s:sigma][sp:<s>p]
+estii:='prim':esti(s,setof(p))
+s@[e:esti(s,setof(p))]
+estie:='prim':<s>p
+sigma@[s0:set]
+empty:=non([x:sigma]esti(x,s0)):'prop'
+nonempty:=some([x:sigma]esti(x,s0)):'prop'
+[n:[x:sigma]not(esti(x,s0))]
+emptyi:=n:empty(s0)
+s0@[e:empty(s0)][s:sigma]
+emptye:=<s>e:not(esti(s,s0))
+s0@[s:sigma][ses0:esti(s,s0)]
+nonemptyi:=somei([x:sigma]esti(x,s0),s,ses0):nonempty(s0)
+s0@[n:nonempty(s0)][x:'prop'][x1:[y:sigma][z:esti(y,s0)]x]
+nonemptyapp:=someapp([y:sigma]esti(y,s0),n,x,x1):x
+s0@[t0:set]
+incl:=all([x:sigma]imp(esti(x,s0),esti(x,t0))):'prop'
+[e:[x:sigma][y:esti(x,s0)]esti(x,t0)]
+incli:=e:incl(s0,t0)
+t0@[i:incl(s0,t0)][s:sigma][ses0:esti(s,s0)]
+incle:=<ses0><s>i:esti(s,t0)
+s0@refincl:=[x:sigma][y:esti(x,s0)]y:incl(s0,s0)
+t0@disj:=all([x:sigma]ec(esti(x,s0),esti(x,t0))):'prop'
+[n:[x:sigma][y:esti(x,s0)]not(esti(x,t0))]
+disji1:=n:disj(s0,t0)
+t0@[n:[x:sigma][y:esti(x,t0)]not(esti(x,s0))]
+disji2:=[x:sigma]th2"l.ec"(esti(x,s0),esti(x,t0),<x>n):disj(s0,t0)
+t0@[d:disj(s0,t0)][s:sigma][ses0:esti(s,s0)]
+disje1:=ece1(esti(s,s0),esti(s,t0),<s>d,ses0):not(esti(s,t0))
+s@[set0:esti(s,t0)]
+disje2:=ece2(esti(s,s0),esti(s,t0),<s>d,set0):not(esti(s,s0))
+t0@[d:disj(s0,t0)]
+symdisj:=[x:sigma][y:esti(x,t0)]disje2(d,x,y):disj(t0,s0)
++disj
+t0@[s:sigma][ses0:esti(s,s0)][set0:esti(s,t0)]
+th1:=th1"l.all"([x:sigma]ec(esti(x,s0),esti(x,t0)),s,th4"l.imp"(esti(s,s0),not(esti(s,t0)),ses0,weli(esti(s,t0),set0))):not(disj(s0,t0))
+th2:=th1(t0,s0,s,set0,ses0):not(disj(t0,s0))
+-disj
+t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
+issete1:=isp(set,[x:set]esti(s,x),s0,t0,ses0,i):esti(s,t0)
+s@[set0:esti(s,t0)]
+issete2:=isp1(set,[x:set]esti(s,x),t0,s0,set0,i):esti(s,s0)
++isset
+i@th1:=[x:sigma][y:esti(x,s0)]issete1(x,y):incl(s0,t0)
+th2:=[x:sigma][y:esti(x,t0)]issete2(x,y):incl(t0,s0)
+-isset
+t0@[i:incl(s0,t0)][j:incl(t0,s0)]
+isseti:='prim':is(set,s0,t0)
++*isset
+t0@[s:sigma][ses0:esti(s,s0)][n:not(esti(s,t0))]
+th3:=th3"l.imp"(is(set,s0,t0),esti(s,t0),n,[t:is(set,s0,t0)]issete1(t,s,ses0)):not(is(set,s0,t0))
+th4:=symnotis(set,s0,t0,th3):not(is(set,t0,s0))
+s@nissetprop:=and(esti(s,s0),not(esti(s,t0))):'prop'
+[n:not(nissetprop(s0,t0,s))][e:esti(s,s0)]
+t1:=et(esti(s,t0),th3"l.and"(esti(s,s0),not(esti(s,t0)),n,e)):esti(s,t0)
+t0@[n:not(is(set,s0,t0))][m:not(some([x:sigma]nissetprop(s0,t0,x)))][l:non([x:sigma]nissetprop(t0,s0,x))][s:sigma]
+t2:=th4"l.some"([x:sigma]nissetprop(s0,t0,x),m,s):not(nissetprop(s0,t0,s))
+t3:=<s>l:not(nissetprop(t0,s0,s))
+l@t4:=isseti(s0,t0,[x:sigma][y:esti(x,s0)]t1(s0,t0,x,t2(x),y),[x:sigma][y:esti(x,t0)]t1(t0,s0,x,t3(x),y)):is(set,s0,t0)
+m@t5:=th3"l.imp"(non([x:sigma]nissetprop(t0,s0,x)),is(set,s0,t0),n,[y:non([x:sigma]nissetprop(t0,s0,x))]t4(y)):some([x:sigma]nissetprop(t0,s0,x))
+n@th5:=th1"l.or"(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)),[y:not(some([x:sigma]nissetprop(s0,t0,x)))]t5(y)):or(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)))
+-isset
+sigma@[alpha:'type'][sa:[x:alpha]set]
+unmore:=setof([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa))):set
+[s:sigma][a:alpha][seasa:esti(s,<a>sa)]
+eunmore1:=estii([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa)),s,somei(alpha,[y:alpha]esti(s,<y>sa),a,seasa)):esti(s,unmore(sa))
+s@[seun:esti(s,unmore(sa))][x:'prop'][x1:[y:alpha][z:esti(s,<y>sa)]x]
+unmoreapp:=someapp(alpha,[y:alpha]esti(s,<y>sa),estie([z:sigma]some(alpha,[y:alpha]esti(z,<y>sa)),s,seun),x,x1):x
++eq
+sigma@[r:[x:sigma][y:sigma]'prop'][refr1:[x:sigma]<x><x>r][symr1:[x:sigma][y:sigma][t:<y><x>r]<x><y>r][trr1:[x:sigma][y:sigma][z:sigma][t:<y><x>r][u:<z><y>r]<z><x>r][s:sigma]
+refr:=<s>refr1:<s><s>r
+[t:sigma][tsr:<t><s>r]
+symr:=<tsr><t><s>symr1:<s><t>r
+t@[u:sigma][tsr:<t><s>r][utr:<u><t>r]
+trr:=<utr><tsr><u><t><s>trr1:<u><s>r
+u@[sur:<s><u>r][tur:<t><u>r]
+tr1r:=trr(s,u,t,symr(u,s,sur),tur):<t><s>r
+u@[usr:<u><s>r][utr:<u><t>r]
+tr2r:=trr(s,u,t,usr,symr(t,u,utr)):<t><s>r
+s@ecelt:=setof(<s>r):set
++1
+th1:=estii(<s>r,s,refr):esti(s,ecelt(s))
+t@[tsr:<t><s>r]
+th2:=estii(<s>r,t,tsr):esti(t,ecelt(s))
+t@[e:esti(t,ecelt(s))]
+th3:=estie(<s>r,t,e):<t><s>r
+tsr@[u:sigma][e:esti(u,ecelt(s))]
+t1:=th2(t,u,tr1r(t,u,s,tsr,th3(u,e))):esti(u,ecelt(t))
+tsr@th4:=isseti(ecelt(s),ecelt(t),[x:sigma][y:esti(x,ecelt(s))]t1(x,y),[x:sigma][y:esti(x,ecelt(t))]t1(t,s,symr(tsr),x,y)):is(set,ecelt(s),ecelt(t))
+t@[n:not(<t><s>r)][u:sigma][e:esti(u,ecelt(s))]
+t2:=th3"l.imp"(esti(u,ecelt(t)),<t><s>r,n,[x:esti(u,ecelt(t))]tr2r(s,t,u,th3(u,e),th3(t,u,x))):not(esti(u,ecelt(t)))
+n@th5:=[x:sigma][y:esti(x,ecelt(s))]t2(x,y):disj(ecelt(s),ecelt(t))
+s@th6:=nonemptyi(ecelt(s),s,th1):nonempty(ecelt(s))
+-1
+trr1@[s0:set][s:sigma]
+ecp:=is(set,s0,ecelt(s)):'prop'
+s0@anec:=some([x:sigma]ecp(x)):'prop'
++2
+trr1@[s:sigma]
+th1:=somei([x:sigma]ecp(ecelt(s),x),s,refis(set,ecelt(s))):anec(ecelt(s))
+-2
+[ecs0:anec(s0)]
++*2
+ecs0@[s:sigma][ses0:esti(s,s0)][t:sigma][e:ecp(s0,t)]
+t1:=issete1(s0,ecelt(t),e,s,ses0):esti(s,ecelt(t))
+t2:=th4"eq.1"(t,s,th3"eq.1"(t,s,t1)):is(set,ecelt(t),ecelt(s))
+t3:=tris(set,s0,ecelt(t),ecelt(s),e,t2):is(set,s0,ecelt(s))
+ses0@th2:=someapp([x:sigma]ecp(x),ecs0,is(set,s0,ecelt(s)),[x:sigma][y:ecp(x)]t3(x,y)):is(set,s0,ecelt(s))
+[t:sigma][tes0:esti(t,s0)]
+th3:=th3"eq.1"(s,t,issete1(s0,ecelt(s),th2,t,tes0)):<t><s>r
+t@[tsr:<t><s>r]
+th4:=issete2(s0,ecelt(s),th2,t,th2"eq.1"(s,t,tsr)):esti(t,s0)
+ecs0@[s:sigma][e:ecp(s0,s)]
+t4:=isp(set,[x:set]nonempty(x),ecelt(s),s0,th6"eq.1"(s),symis(set,s0,ecelt(s),e)):nonempty(s0)
+ecs0@th5:=someapp([x:sigma]ecp(x),ecs0,nonempty(s0),[x:sigma][y:ecp(x)]t4(x,y)):nonempty(s0)
+-2
++3
+ecs0@[t0:set][ect0:anec(t0)][s:sigma][ses0:esti(s,s0)][t:sigma][tet0:esti(t,t0)][tsr:<t><s>r]
+th1:=tr3is(set,s0,ecelt(s),ecelt(t),t0,th2"eq.2"(s0,ecs0,s,ses0),th4"eq.1"(s,t,tsr),symis(set,t0,ecelt(t),th2"eq.2"(t0,ect0,t,tet0))):is(set,s0,t0)
+tet0@[n:not(<t><s>r)]
+t1:=isp1(set,[x:set]disj(x,ecelt(t)),ecelt(s),s0,th5"eq.1"(s,t,n),th2"eq.2"(s0,ecs0,s,ses0)):disj(s0,ecelt(t))
+th2:=isp1(set,[x:set]disj(s0,x),ecelt(t),t0,t1,th2"eq.2"(t0,ect0,t,tet0)):disj(s0,t0)
+t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
+t2:=issete1(s0,t0,i,s,ses0):esti(s,t0)
+t3:=th1"st.disj"(s0,t0,s,ses0,t2):not(disj(s0,t0))
+i@th3:=nonemptyapp(s0,th5"eq.2"(s0,ecs0),not(disj(s0,t0)),[x:sigma][y:esti(x,s0)]t3(x,y)):not(disj(s0,t0))
+-3
+trr1@ect:=ot(set,[x:set]anec(x)):'type'
+ecs0@ectset:=out(set,[x:set]anec(x),s0,ecs0):ect
+trr1@[s:sigma]
+ectelt:=ectset(ecelt(s),th1".2"(s)):ect
+trr1@[e:ect]
+ecect:=in(set,[x:set]anec(x),e):set
++4
+th1:=inp(set,[x:set]anec(x),e):anec(ecect(e))
+th2:=th5"eq.2"(ecect(e),th1):nonempty(ecect(e))
+[x:'prop'][x1:[y:sigma][z:esti(y,ecect(e))]x]
+th3:=nonemptyapp(ecect(e),th2,x,x1):x
+s@th4:=isinout(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s)):is(set,ecelt(s),ecect(ectelt(s)))
+th5:=issete1(ecelt(s),ecect(ectelt(s)),th4,s,th1"eq.1"(s)):esti(s,ecect(ectelt(s)))
+th6:=eunmore1(ect,[x:ect]ecect(x),s,ectelt(s),th5):esti(s,unmore(ect,[x:ect]ecect(x)))
+e@[s:sigma][see:esti(s,ecect(e))][t:sigma][tee:esti(t,ecect(e))]
+th7:=th3"eq.2"(ecect(e),th1,s,see,t,tee):<t><s>r
+t@[tsr:<t><s>r]
+th8:=th4"eq.2"(ecect(e),th1,s,see,t,tsr):esti(t,ecect(e))
+-4
++5
+[f:ect][i:is(ect,e,f)]
+th1:=isini(set,[x:set]anec(x),e,f,i):is(set,ecect(e),ecect(f))
+f@[i:is(set,ecect(e),ecect(f))]
+th2:=isine(set,[x:set]anec(x),e,f,i):is(ect,e,f)
+f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))][tsr:<t><s>r]
+th3:=th2(th1"eq.3"(ecect(e),th1"eq.4"(e),ecect(f),th1"eq.4"(f),s,see,t,tef,tsr)):is(ect,e,f)
+see@[i:is(ect,e,f)]
+th4:=issete1(ecect(e),ecect(f),th1(i),s,see):esti(s,ecect(f))
+tef@[i:is(ect,e,f)]
+th5:=th3"eq.2"(ecect(f),th1"eq.4"(f),s,th4(i),t,tef):<t><s>r
+trr1@[s:sigma][t:sigma][tsr:<t><s>r]
+th6:=isouti(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s),ecelt(t),th1"eq.2"(t),th4"eq.1"(s,t,tsr)):is(ect,ectelt(s),ectelt(t))
+-5
+trr1@[alpha:'type'][fu:[x:sigma]alpha]
+fixfu:=[x:sigma][y:sigma][z:<y><x>r]is(alpha,<x>fu,<y>fu):'prop'
++10
+[ff:fixfu][e:ect][a1:alpha][s:sigma]
+prop1:=and(esti(s,ecect(e)),is(alpha,<s>fu,a1)):'prop'
+a1@prop2:=some([x:sigma]prop1(x)):'prop'
+e@[s:sigma][see:esti(s,ecect(e))]
+t1:=andi(esti(s,ecect(e)),is(alpha,<s>fu,<s>fu),see,refis(alpha,<s>fu)):prop1(<s>fu,s)
+t2:=somei([x:sigma]prop1(<s>fu,x),s,t1):prop2(<s>fu)
+t3:=somei(alpha,[x:alpha]prop2(x),<s>fu,t2):some(alpha,[x:alpha]prop2(x))
+e@t4:=th3"eq.4"(e,some(alpha,[x:alpha]prop2(x)),[x:sigma][y:esti(x,ecect(e))]t3(x,y)):some(alpha,[x:alpha]prop2(x))
+a1@[b1:alpha][pa1:prop2(a1)][pb1:prop2(b1)][s:sigma][pa1s:prop1(a1,s)][t:sigma][pb1t:prop1(b1,t)]
+t5:=ande1(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):esti(s,ecect(e))
+t6:=ande1(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):esti(t,ecect(e))
+t7:=th7"eq.4"(e,s,t5,t,t6):<t><s>r
+t8:=ande2(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):is(alpha,<s>fu,a1)
+t9:=ande2(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):is(alpha,<t>fu,b1)
+t10:=tr3is(alpha,a1,<s>fu,<t>fu,b1,symis(alpha,<s>fu,a1,t8),<t7><t><s>ff,t9):is(alpha,a1,b1)
+pa1s@t11:=someapp([x:sigma]prop1(b1,x),pb1,is(alpha,a1,b1),[x:sigma][y:prop1(b1,x)]t10(x,y)):is(alpha,a1,b1)
+pb1@t12:=someapp([x:sigma]prop1(a1,x),pa1,is(alpha,a1,b1),[x:sigma][y:prop1(a1,x)]t11(x,y)):is(alpha,a1,b1)
+e@t13:=[x:alpha][y:alpha][u:prop2(x)][v:prop2(y)]t12(x,y,u,v):amone(alpha,[x:alpha]prop2(x))
+t14:=onei(alpha,[x:alpha]prop2(x),t13,t4):one(alpha,[x:alpha]prop2(x))
+-10
+e".10"@indeq:=ind(alpha,[x:alpha]prop2".10"(x),t14".10"):alpha
++*10
+e@th1:=oneax(alpha,[x:alpha]prop2(x),t14):some([x:sigma]and(esti(x,ecect(e)),is(alpha,<x>fu,indeq)))
+[s:sigma][see:esti(s,ecect(e))]
+th2:=t12(<s>fu,indeq,t2(s,see),th1):is(alpha,<s>fu,indeq)
+ff@[s:sigma]
+th3:=th2(ectelt(s),s,th5"eq.4"(s)):is(alpha,<s>fu,indeq(ectelt(s)))
+-10
+alpha@[fu2:[x:sigma][y:sigma]alpha]
+fixfu2:=[x:sigma][y:sigma][z:sigma][u:sigma][v:<y><x>r][w:<u><z>r]is(alpha,<z><x>fu2,<u><y>fu2):'prop'
++11
+[ff2:fixfu2][s:sigma][t:sigma][tsr:<t><s>r][u:sigma]
+t1:=<refr(u)><tsr><u><u><t><s>ff2:is(alpha,<u><s>fu2,<u><t>fu2)
+tsr@t2:=fisi(sigma,alpha,<s>fu2,<t>fu2,[x:sigma]t1(x)):is([x:sigma]alpha,<s>fu2,<t>fu2)
+ff2@[e:ect]
+i:=indeq([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e):[x:sigma]alpha
+[s:sigma][t:sigma][tsr:<t><s>r][u:sigma][uee:esti(u,ecect(e))]
+t3:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,u,uee):is([x:sigma]alpha,<u>fu2,i)
+t4:=fise(alpha,<u>fu2,i,t3,s):is(alpha,<s><u>fu2,<s>i)
+t5:=fise(alpha,<u>fu2,i,t3,t):is(alpha,<t><u>fu2,<t>i)
+t6:=<tsr><refr(u)><t><s><u><u>ff2:is(alpha,<s><u>fu2,<t><u>fu2)
+t7:=tr3is(alpha,<s>i,<s><u>fu2,<t><u>fu2,<t>i,symis(alpha,<s><u>fu2,<s>i,t4),t6,t5):is(alpha,<s>i,<t>i)
+tsr@t8:=th3"eq.4"(e,is(alpha,<s>i,<t>i),[x:sigma][y:esti(x,ecect(e))]t7(x,y)):is(alpha,<s>i,<t>i)
+-11
+e".11"@[f:ect]
+indeq2:=indeq(i".11",[x:sigma][y:sigma][z:<y><x>r]t8".11"(x,y,z),f):alpha
++*11
+f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))]
+t9:=th2"eq.10"(i,[x:sigma][y:sigma][z:<y><x>r]t8(x,y,z),f,t,tef):is(alpha,<t>i,indeq2(e,f))
+t10:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,s,see):is([x:sigma]alpha,<s>fu2,i)
+t11:=fise(alpha,<s>fu2,i,t10,t):is(alpha,<t><s>fu2,<t>i)
+th1:=tris(alpha,<t><s>fu2,<t>i,indeq2,t11,t9):is(alpha,<t><s>fu2,indeq2(e,f))
+ff2@[s:sigma][t:sigma]
+th2:=th1(ectelt(s),ectelt(t),s,th5"eq.4"(s),t,th5"eq.4"(t)):is(alpha,<t><s>fu2,indeq2(ectelt(s),ectelt(t)))
+-11
++landau
++n
+@nat:='prim':'type'
+[x:nat][y:nat]
+is:=is"e"(nat,x,y):'prop'
+nis:=not(is(x,y)):'prop'
+x@[s:set(nat)]
+in:=esti(nat,x,s):'prop'
+@[p:[x:nat]'prop']
+some:=some"l"(nat,p):'prop'
+all:=all"l"(nat,p):'prop'
+one:=one"e"(nat,p):'prop'
+@1:='prim':nat
+suc:='prim':[x:nat]nat
+[x:nat][y:nat][i:is(x,y)]
+ax2:=isf(nat,nat,suc,x,y,i):is(<x>suc,<y>suc)
+@ax3:='prim':[x:nat]nis(<x>suc,1)
+ax4:='prim':[x:nat][y:nat][u:is(<x>suc,<y>suc)]is(x,y)
+[s:set(nat)]
+cond1:=in(1,s):'prop'
+cond2:=all([x:nat]imp(in(x,s),in(<x>suc,s))):'prop'
+@ax5:='prim':[s:set(nat)][u:cond1(s)][v:cond2(s)][x:nat]in(x,s)
+[p:[x:nat]'prop'][1p:<1>p][xsp:[x:nat][y:<x>p]<<x>suc>p][x:nat]
++i1
+s:=setof(nat,p):set(nat)
+t1:=estii(nat,p,1,1p):cond1(s)
+[y:nat][yes:in(y,s)]
+t2:=estie(nat,p,y,yes):<y>p
+t3:=estii(nat,p,<y>suc,<t2><y>xsp):in(<y>suc,s)
+x@t4:=<x><[y:nat][u:in(y,s)]t3(y,u)><t1><s>ax5:in(x,s)
+-i1
+induction:=estie(nat,p,x,t4".i1"):<x>p
+@[x:nat][y:nat][n:nis(x,y)]
++21
+[i:is(<x>suc,<y>suc)]
+t1:=<i><y><x>ax4:is(x,y)
+-21
+satz1:=th3"l.imp"(is(<x>suc,<y>suc),is(x,y),n,[u:is(<x>suc,<y>suc)]t1".21"(u)):nis(<x>suc,<y>suc)
++22
+x@prop1:=nis(<x>suc,x):'prop'
+@t1:=<1>ax3:prop1(1)
+x@[p:prop1(x)]
+t2:=satz1(<x>suc,x,p):prop1(<x>suc)
+-22
+x@satz2:=induction([y:nat]prop1".22"(y),t1".22",[y:nat][u:prop1".22"(y)]t2".22"(y,u),x):nis(<x>suc,x)
++23
+prop1:=or(is(x,1),some([u:nat]is(x,<u>suc))):'prop'
+@t1:=ori1(is(1,1),some([u:nat]is(1,<u>suc)),refis(nat,1)):prop1(1)
+x@t2:=somei(nat,[u:nat]is(<x>suc,<u>suc),x,refis(nat,<x>suc)):some([u:nat]is(<x>suc,<u>suc))
+t3:=ori2(is(<x>suc,1),some([u:nat]is(<x>suc,<u>suc)),t2):prop1(<x>suc)
+t4:=induction([y:nat]prop1(y),t1,[y:nat][u:prop1(y)]t3(y),x):prop1(x)
+-23
+[n:nis(x,1)]
+satz3:=ore2(is(x,1),some([u:nat]is(x,<u>suc)),t4".23",n):some([u:nat]is(x,<u>suc))
+y@[z:nat][i:is(x,<y>suc)][j:is(x,<z>suc)]
++*23
+j@t5:=<tris1(nat,<y>suc,<z>suc,x,i,j)><z><y>ax4:is(y,z)
+x@t6:=[y:nat][z:nat][u:is(x,<y>suc)][v:is(x,<z>suc)]t5(y,z,u,v):amone(nat,[u:nat]is(x,<u>suc))
+-23
+n@satz3a:=onei(nat,[u:nat]is(x,<u>suc),t6".23",satz3):one([u:nat]is(x,<u>suc))
++24
+x@[f:[y:nat]nat]
+prop1:=all([y:nat]is(<<y>suc>f,<<y>f>suc)):'prop'
+prop2:=and(is(<1>f,<x>suc),prop1):'prop'
+x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
+prop3:=is(<y>a,<y>b):'prop'
+pb@t1:=ande1(is(<1>a,<x>suc),prop1(a),pa):is(<1>a,<x>suc)
+t2:=ande1(is(<1>b,<x>suc),prop1(b),pb):is(<1>b,<x>suc)
+t3:=tris2(nat,<1>a,<1>b,<x>suc,t1,t2):prop3(1)
+y@[p:prop3(y)]
+t4:=ax2(<y>a,<y>b,p):is(<<y>a>suc,<<y>b>suc)
+t5:=ande2(is(<1>a,<x>suc),prop1(a),pa):prop1(a)
+t6:=ande2(is(<1>b,<x>suc),prop1(b),pb):prop1(b)
+t7:=<y>t5:is(<<y>suc>a,<<y>a>suc)
+t8:=<y>t6:is(<<y>suc>b,<<y>b>suc)
+t9:=tr3is(nat,<<y>suc>a,<<y>a>suc,<<y>b>suc,<<y>suc>b,t7,t4,symis"e"(nat,<<y>suc>b,<<y>b>suc,t8)):prop3(<y>suc)
+y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
+pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
+x@aa:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
+prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
+@t12:=[x:nat]refis(nat,<<x>suc>suc):prop1(1,suc)
+t13:=andi(is(<1>suc,<1>suc),prop1(1,suc),refis(nat,<1>suc),t12):prop2(1,suc)
+t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),suc,t13):prop4(1)
+x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
+g:=[y:nat]<<y>f>suc:[y:nat]nat
+[y:nat]
+t15:=refis(nat,<y>g):is(<y>g,<<y>f>suc)
+pf@t16:=ande1(is(<1>f,<x>suc),prop1(f),pf):is(<1>f,<x>suc)
+t17:=tris(nat,<1>g,<<1>f>suc,<<x>suc>suc,t15(1),ax2(<1>f,<x>suc,t16)):is(<1>g,<<x>suc>suc)
+y@t18:=ande2(is(<1>f,<x>suc),prop1(f),pf):prop1(f)
+t19:=<y>t18:is(<<y>suc>f,<<y>f>suc)
+t20:=tris2(nat,<<y>suc>f,<y>g,<<y>f>suc,t19,t15):is(<<y>suc>f,<y>g)
+t21:=tris(nat,<<y>suc>g,<<<y>suc>f>suc,<<y>g>suc,t15(<y>suc),ax2(<<y>suc>f,<y>g,t20)):is(<<y>suc>g,<<y>g>suc)
+pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
+t23:=andi(is(<1>g,<<x>suc>suc),prop1(<x>suc,g),t17,t22):prop2(<x>suc,g)
+t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
+p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
+x@bb:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
+-24
+x@satz4:=onei([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),aa".24",bb".24"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,<x>suc),all([y:nat]is(<<y>suc>z,<<y>z>suc))))
+plus:=ind([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),satz4):[y:nat]nat
+y@pl:=<y>plus:nat
++*24
+x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz4):prop2(plus)
+-24
+x@satz4a:=ande1(is(<1>plus,<x>suc),prop1".24"(plus),t26".24"):is(pl(x,1),<x>suc)
++*24
+x@t27:=ande2(is(<1>plus,<x>suc),prop1(plus),t26):prop1(plus)
+-24
+y@satz4b:=<y>t27".24":is(pl(x,<y>suc),<pl(x,y)>suc)
++*24
+@t28:=t11(1,plus(1),suc,t26(1),t13):is"e"([y:nat]nat,plus(1),suc)
+-24
+x@satz4c:=fise(nat,nat,plus(1),suc,t28".24",x):is(pl(1,x),<x>suc)
++*24
+x@t29:=t11(<x>suc,plus(<x>suc),[y:nat]<<y>plus>suc,t26(<x>suc),t23(bb,plus,t26)):is"e"([y:nat]nat,plus(<x>suc),[y:nat]<<y>plus>suc)
+-24
+y@satz4d:=fise(nat,nat,plus(<x>suc),[z:nat]<<z>plus>suc,t29".24",y):is(pl(<x>suc,y),<pl(x,y)>suc)
+x@satz4e:=symis(nat,pl(x,1),<x>suc,satz4a):is(<x>suc,pl(x,1))
+y@satz4f:=symis(nat,pl(x,<y>suc),<pl(x,y)>suc,satz4b):is(<pl(x,y)>suc,pl(x,<y>suc))
+x@satz4g:=symis(nat,pl(1,x),<x>suc,satz4c):is(<x>suc,pl(1,x))
+y@satz4h:=symis(nat,pl(<x>suc,y),<pl(x,y)>suc,satz4d):is(<pl(x,y)>suc,pl(<x>suc,y))
+z@[i:is(x,y)]
+ispl1:=isf(nat,nat,[u:nat]pl(u,z),x,y,i):is(pl(x,z),pl(y,z))
+ispl2:=isf(nat,nat,[u:nat]pl(z,u),x,y,i):is(pl(z,x),pl(z,y))
+z@[u:nat][i:is(x,y)][j:is(z,u)]
+ispl12:=tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
++25
+z@prop1:=is(pl(pl(x,y),z),pl(x,pl(y,z))):'prop'
+y@t1:=tr3is(nat,pl(pl(x,y),1),<pl(x,y)>suc,pl(x,<y>suc),pl(x,pl(y,1)),satz4a(pl(x,y)),satz4f,ispl2(<y>suc,pl(y,1),x,satz4e(y))):prop1(1)
+z@[p:prop1(z)]
+t2:=ax2(pl(pl(x,y),z),pl(x,pl(y,z)),p):is(<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc)
+t3:=tr4is(nat,pl(pl(x,y),<z>suc),<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc,pl(x,<pl(y,z)>suc),pl(x,pl(y,<z>suc)),satz4b(pl(x,y),z),t2,satz4f(x,pl(y,z)),ispl2(<pl(y,z)>suc,pl(y,<z>suc),x,satz4f(y,z))):prop1(<z>suc)
+-25
+z@satz5:=induction([u:nat]prop1".25"(u),t1".25",[u:nat][v:prop1".25"(u)]t3".25"(u,v),z):is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl1:=satz5:is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl2:=symis(nat,pl(pl(x,y),z),pl(x,pl(y,z)),satz5):is(pl(x,pl(y,z)),pl(pl(x,y),z))
++26
+y@prop1:=is(pl(x,y),pl(y,x)):'prop'
+t1:=satz4a(y):is(pl(y,1),<y>suc)
+t2:=satz4c(y):is(pl(1,y),<y>suc)
+t3:=tris2(nat,pl(1,y),pl(y,1),<y>suc,t2,t1):prop1(1,y)
+[p:prop1(x,y)]
+t4:=tris(nat,<pl(x,y)>suc,<pl(y,x)>suc,pl(y,<x>suc),ax2(pl(x,y),pl(y,x),p),satz4f(y,x)):is(<pl(x,y)>suc,pl(y,<x>suc))
+t5:=satz4d:is(pl(<x>suc,y),<pl(x,y)>suc)
+t6:=tris(nat,pl(<x>suc,y),<pl(x,y)>suc,pl(y,<x>suc),t5,t4):prop1(<x>suc,y)
+-26
+y@satz6:=induction([z:nat]prop1".26"(z,y),t3".26",[z:nat][u:prop1".26"(z,y)]t6".26"(z,y,u),x):is(pl(x,y),pl(y,x))
+compl:=satz6:is(pl(x,y),pl(y,x))
++*26
+x@t7:=tris(nat,pl(x,1),<x>suc,pl(1,x),satz4a,satz4g):prop1(1)
+y@[p:prop1(y)]
+t8:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,<pl(y,x)>suc,pl(<y>suc,x),satz4b,ax2(pl(x,y),pl(y,x),p),satz4h(y,x)):prop1(<y>suc)
+y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(pl(x,y),pl(y,x))
+-26
++27
+y@prop1:=nis(y,pl(x,y)):'prop'
+x@t1:=symnotis(nat,<x>suc,1,<x>ax3):nis(1,<x>suc)
+t2:=th4"e.notis"(nat,1,<x>suc,pl(x,1),t1,satz4a):prop1(1)
+y@[p:prop1(y)]
+t3:=satz1(y,pl(x,y),p):nis(<y>suc,<pl(x,y)>suc)
+t4:=th4"e.notis"(nat,<y>suc,<pl(x,y)>suc,pl(x,<y>suc),t3,satz4b):prop1(<y>suc)
+-27
+y@satz7:=induction([z:nat]prop1".27"(z),t2".27",[z:nat][u:prop1".27"(z)]t4".27"(z,u),y):nis(y,pl(x,y))
+z@[n:nis(y,z)]
++28
+prop1:=nis(pl(x,y),pl(x,z)):'prop'
+t1:=satz1(y,z,n):nis(<y>suc,<z>suc)
+t2:=th5"e.notis"(nat,<y>suc,<z>suc,pl(1,y),pl(1,z),t1,satz4g(y),satz4g(z)):prop1(1,y,z,n)
+[p:prop1(x,y,z,n)]
+t3:=satz1(pl(x,y),pl(x,z),p):nis(<pl(x,y)>suc,<pl(x,z)>suc)
+t4:=th5"e.notis"(nat,<pl(x,y)>suc,<pl(x,z)>suc,pl(<x>suc,y),pl(<x>suc,z),t3,satz4h,satz4h(z)):prop1(<x>suc,y,z,n)
+-28
+satz8:=induction([u:nat]prop1".28"(u,y,z,n),t2".28",[u:nat][v:prop1".28"(u,y,z,n)]t4".28"(u,y,z,n,v),x):nis(pl(x,y),pl(x,z))
+z@[i:is(pl(x,y),pl(x,z))]
+satz8a:=th7"l.imp"(is(y,z),nis(pl(x,y),pl(x,z)),weli(is(pl(x,y),pl(x,z)),i),[u:nis(y,z)]satz8(u)):is(y,z)
+z@diffprop:=is(x,pl(y,z)):'prop'
++*28
+y@[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]
+t5:=satz8a(y,u,v,tris1(nat,pl(y,u),pl(y,v),x,du,dv)):is(u,v)
+-28
+y@satz8b:=[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]t5".28"(u,v,du,dv):amone(nat,[z:nat]is(x,pl(y,z)))
++29
+i:=is(x,y):'prop'
+ii:=some([u:nat]diffprop(x,y,u)):'prop'
+iii:=some([v:nat]diffprop(y,x,v)):'prop'
+[one1:i][u:nat]
+t1:=tris(nat,pl(u,x),pl(x,u),pl(y,u),compl(u,x),ispl1(u,one1)):is(pl(u,x),pl(y,u))
+t2:=th3"e.notis"(nat,x,pl(u,x),pl(y,u),satz7(u,x),t1):nis(x,pl(y,u))
+one1@t3:=th5"l.some"(nat,[u:nat]diffprop(u),[u:nat]t2(u)):not(ii)
+y@t4:=th1"l.ec"(i,ii,[z:i]t3(z)):ec(i,ii)
+one1@t5:=t3(y,x,symis(nat,x,y,one1)):not(iii)
+y@t6:=th2"l.ec"(iii,i,[z:i]t5(z)):ec(iii,i)
+[two1:ii][three1:iii][u:nat][du:diffprop(x,y,u)][v:nat][dv:diffprop(y,x,v)]
+t6a:=tr4is(nat,x,pl(y,u),pl(pl(x,v),u),pl(x,pl(v,u)),pl(pl(v,u),x),du,ispl1(y,pl(x,v),u,dv),asspl1(x,v,u),compl(x,pl(v,u))):is(x,pl(pl(v,u),x))
+t7:=mp(is(x,pl(pl(v,u),x)),con,t6a,satz7(pl(v,u),x)):con
+du@t8:=someapp(nat,[v:nat]diffprop(y,x,v),three1,con,[v:nat][dv:diffprop(y,x,v)]t7(v,dv)):con
+three1@t9:=someapp(nat,[u:nat]diffprop(u),two1,con,[u:nat][du:diffprop(u)]t8(u,du)):con
+two1@t10:=[z:iii]t9(z):not(iii)
+y@t11:=th1"l.ec"(ii,iii,[z:ii]t10(z)):ec(ii,iii)
+a:=th6"l.ec3"(i,ii,iii,t4,t11,t6):ec3(i,ii,iii)
+prop1:=or3(i,ii,iii):'prop'
+x@[j:is(x,1)]
+t12:=or3i1(i(1),ii(1),iii(1),j):prop1(1)
+x@[n:nis(x,1)][u:nat][j:is(x,<u>suc)]
+t13:=tris(nat,x,<u>suc,pl(1,u),j,satz4g(u)):is(x,pl(1,u))
+t14:=somei(nat,[z:nat]diffprop(x,1,z),u,t13):ii(1)
+t15:=someapp(nat,[u1:nat]is(x,<u1>suc),satz3(x,n),ii(1),[u1:nat][z:is(x,<u1>suc)]t14(u1,z)):ii(1)
+t16:=or3i2(i(1),ii(1),iii(1),t15):prop1(1)
+n@t16a:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),prop1(1),[u:nat][v:is(x,<u>suc)]t16(u,v)):prop1(1)
+x@t17:=th1"l.imp"(is(x,1),prop1(1),[z:is(x,1)]t12(z),[z:nis(x,1)]t16a(z)):prop1(1)
+y@[p:prop1(y)][one1:i(y)]
+t18:=tris(nat,<y>suc,pl(y,1),pl(x,1),satz4e(y),ispl1(y,x,1,symis(nat,x,y,one1))):is(<y>suc,pl(x,1))
+t19:=somei(nat,[z:nat]diffprop(<y>suc,x,z),1,t18):iii(<y>suc)
+t20:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t19):prop1(<y>suc)
+p@[two1:ii(y)][u:nat][du:diffprop(x,y,u)][j:is(u,1)]
+t21:=tr3is(nat,x,pl(y,u),pl(y,1),<y>suc,du,ispl2(u,1,y,j),satz4a(y)):is(x,<y>suc)
+t22:=or3i1(i(<y>suc),ii(<y>suc),iii(<y>suc),t21):prop1(<y>suc)
+du@[n:nis(u,1)][w:nat][j:is(u,<w>suc)]
+t23:=tris(nat,u,<w>suc,pl(1,w),j,satz4g(w)):is(u,pl(1,w))
+t24:=tr4is(nat,x,pl(y,u),pl(y,pl(1,w)),pl(pl(y,1),w),pl(<y>suc,w),du,ispl2(u,pl(1,w),y,t23),asspl2(y,1,w),ispl1(pl(y,1),<y>suc,w,satz4a(y))):is(x,pl(<y>suc,w))
+t25:=somei(nat,[z:nat]diffprop(x,<y>suc,z),w,t24):ii(<y>suc)
+n@t26:=someapp(nat,[z:nat]is(u,<z>suc),satz3(u,n),ii(<y>suc),[z:nat][v:is(u,<z>suc)]t25(z,v)):ii(<y>suc)
+t27:=or3i2(i(<y>suc),ii(<y>suc),iii(<y>suc),t26):prop1(<y>suc)
+du@t28:=th1"l.imp"(is(u,1),prop1(<y>suc),[z:is(u,1)]t22(z),[z:nis(u,1)]t27(z)):prop1(<y>suc)
+two1@t28a:=someapp(nat,[u:nat]diffprop(u),two1,prop1(<y>suc),[u:nat][du:diffprop(u)]t28(u,du)):prop1(<y>suc)
+p@[three1:iii(y)][v:nat][dv:diffprop(y,x,v)]
+t29:=tris(nat,<y>suc,<pl(x,v)>suc,pl(x,<v>suc),ax2(y,pl(x,v),dv),satz4f(x,v)):is(<y>suc,pl(x,<v>suc))
+t30:=somei(nat,[z:nat]diffprop(<y>suc,x,z),<v>suc,t29):iii(<y>suc)
+three1@t31:=someapp(nat,[v:nat]diffprop(y,x,v),three1,iii(<y>suc),[v:nat][dv:diffprop(y,x,v)]t30(v,dv)):iii(<y>suc)
+t32:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t31):prop1(<y>suc)
+p@t33:=or3app(i(y),ii(y),iii(y),prop1(<y>suc),p,[z:i(y)]t20(z),[z:ii(y)]t28a(z),[z:iii(y)]t32(z)):prop1(<y>suc)
+y@b:=induction([z:nat]prop1(z),t17,[z:nat][u:prop1(z)]t33(z,u),y):or3(i,ii,iii)
+-29
+satz9:=orec3i(i".29",ii".29",iii".29",b".29",a".29"):orec3(is(x,y),some([u:nat]is(x,pl(y,u))),some([v:nat]is(y,pl(x,v))))
+satz9a:=b".29":or3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
+satz9b:=a".29":ec3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
+more:=some([u:nat]diffprop(x,y,u)):'prop'
+less:=some([v:nat]diffprop(y,x,v)):'prop'
+satz10:=satz9:orec3(is(x,y),more(x,y),less(x,y))
+satz10a:=satz9a:or3(is(x,y),more(x,y),less(x,y))
+satz10b:=satz9b:ec3(is(x,y),more(x,y),less(x,y))
+[m:more(x,y)]
+satz11:=m:less(y,x)
+y@[l:less(x,y)]
+satz12:=l:more(y,x)
+y@moreis:=or(more,is(x,y)):'prop'
+lessis:=or(less,is(x,y)):'prop'
+[m:moreis(x,y)]
+satz13:=th9"l.or"(more,is(x,y),less(y,x),is(y,x),m,[z:more]satz11(z),[z:is(x,y)]symis(nat,x,y,z)):lessis(y,x)
+y@[l:lessis(x,y)]
+satz14:=th9"l.or"(less,is(x,y),more(y,x),is(y,x),l,[z:less]satz12(z),[z:is(x,y)]symis(nat,x,y,z)):moreis(y,x)
+z@[i:is(x,y)][m:more(x,z)]
+ismore1:=isp(nat,[u:nat]more(u,z),x,y,m,i):more(y,z)
+i@[m:more(z,x)]
+ismore2:=isp(nat,[u:nat]more(z,u),x,y,m,i):more(z,y)
+i@[l:less(x,z)]
+isless1:=isp(nat,[u:nat]less(u,z),x,y,l,i):less(y,z)
+i@[l:less(z,x)]
+isless2:=isp(nat,[u:nat]less(z,u),x,y,l,i):less(z,y)
+i@[m:moreis(x,z)]
+ismoreis1:=isp(nat,[u:nat]moreis(u,z),x,y,m,i):moreis(y,z)
+i@[m:moreis(z,x)]
+ismoreis2:=isp(nat,[u:nat]moreis(z,u),x,y,m,i):moreis(z,y)
+i@[l:lessis(x,z)]
+islessis1:=isp(nat,[u:nat]lessis(u,z),x,y,l,i):lessis(y,z)
+i@[l:lessis(z,x)]
+islessis2:=isp(nat,[u:nat]lessis(z,u),x,y,l,i):lessis(z,y)
+y@[i:is(x,y)]
+moreisi2:=ori2(more(x,y),is(x,y),i):moreis(x,y)
+lessisi2:=ori2(less(x,y),is(x,y),i):lessis(x,y)
+y@[m:more(x,y)]
+moreisi1:=ori1(more(x,y),is(x,y),m):moreis(x,y)
+y@[l:less(x,y)]
+lessisi1:=ori1(less(x,y),is(x,y),l):lessis(x,y)
+z@[u:nat][i:is(x,y)][j:is(z,u)][m:more(x,z)]
+ismore12:=ismore2(z,u,y,j,ismore1(x,y,z,i,m)):more(y,u)
+j@[l:less(x,z)]
+isless12:=isless2(z,u,y,j,isless1(x,y,z,i,l)):less(y,u)
+j@[m:moreis(x,z)]
+ismoreis12:=ismoreis2(z,u,y,j,ismoreis1(x,y,z,i,m)):moreis(y,u)
+j@[l:lessis(x,z)]
+islessis12:=islessis2(z,u,y,j,islessis1(x,y,z,i,l)):lessis(y,u)
+y@[m:moreis(x,y)]
+satz10c:=th7"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,comor(more(x,y),is(x,y),m)):not(less(x,y))
+y@[l:lessis(x,y)]
+satz10d:=th9"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,l):not(more(x,y))
+y@[n:not(more(x,y))]
+satz10e:=th2"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n):lessis(x,y)
+y@[n:not(less(x,y))]
+satz10f:=comor(is(x,y),more(x,y),th3"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n)):moreis(x,y)
+y@[m:more(x,y)]
+satz10g:=th3"l.or"(less(x,y),is(x,y),ec3e23(is(x,y),more(x,y),less(x,y),satz10b,m),ec3e21(is(x,y),more(x,y),less(x,y),satz10b,m)):not(lessis(x,y))
+y@[l:less(x,y)]
+satz10h:=th3"l.or"(more(x,y),is(x,y),ec3e32(is(x,y),more(x,y),less(x,y),satz10b,l),ec3e31(is(x,y),more(x,y),less(x,y),satz10b,l)):not(moreis(x,y))
+y@[n:not(moreis(x,y))]
+satz10j:=or3e3(is(x,y),more(x,y),less(x,y),satz10a,th5"l.or"(more(x,y),is(x,y),n),th4"l.or"(more(x,y),is(x,y),n)):less(x,y)
+y@[n:not(lessis(x,y))]
+satz10k:=or3e2(is(x,y),more(x,y),less(x,y),satz10a,th4"l.or"(less(x,y),is(x,y),n),th5"l.or"(less(x,y),is(x,y),n)):more(x,y)
+z@[l:less(x,y)][k:less(y,z)]
++315
+[v:nat][dv:diffprop(y,x,v)][w:nat][dw:diffprop(z,y,w)]
+t1:=tr3is(nat,z,pl(y,w),pl(pl(x,v),w),pl(x,pl(v,w)),dw,ispl1(y,pl(x,v),w,dv),asspl1(x,v,w)):is(z,pl(x,pl(v,w)))
+t2:=somei(nat,[u:nat]diffprop(z,x,u),pl(v,w),t1):less(x,z)
+dv@t3:=someapp(nat,[w:nat]diffprop(z,y,w),k,less(x,z),[w:nat][dw:diffprop(z,y,w)]t2(w,dw)):less(x,z)
+-315
+satz15:=someapp(nat,[v:nat]diffprop(y,x,v),l,less(x,z),[v:nat][dv:diffprop(y,x,v)]t3".315"(v,dv)):less(x,z)
+trless:=satz15:less(x,z)
+z@[m:more(x,y)][n:more(y,z)]
+trmore:=satz15(z,y,x,n,m):more(x,z)
++*315
+n@anders:=satz12(z,x,satz15(z,y,x,satz11(y,z,n),satz11(m))):more(x,z)
+-315
+z@[l:lessis(x,y)][k:less(y,z)]
+satz16a:=orapp(less(x,y),is(x,y),less(x,z),l,[u:less(x,y)]trless(u,k),[u:is(x,y)]isless1(y,x,z,symis(nat,x,y,u),k)):less(x,z)
+z@[l:less(x,y)][k:lessis(y,z)]
+satz16b:=orapp(less(y,z),is(y,z),less(x,z),k,[u:less(y,z)]trless(l,u),[u:is(y,z)]isless2(y,z,x,u,l)):less(x,z)
+z@[m:moreis(x,y)][n:more(y,z)]
+satz16c:=satz16b(z,y,x,n,satz13(m)):more(x,z)
+z@[m:more(x,y)][n:moreis(y,z)]
+satz16d:=satz16a(z,y,x,satz13(y,z,n),m):more(x,z)
+z@[l:lessis(x,y)][k:lessis(y,z)]
++317
+[i:is(x,y)][j:is(y,z)]
+t1:=lessisi2(x,z,tris(nat,x,y,z,i,j)):lessis(x,z)
+i@[j:less(y,z)]
+t2:=lessisi1(x,z,satz16a(l,j)):lessis(x,z)
+i@t3:=orapp(less(y,z),is(y,z),lessis(x,z),k,[u:less(y,z)]t2(u),[u:is(y,z)]t1(u)):lessis(x,z)
+k@[j:less(x,y)]
+t4:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
+-317
+satz17:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t4".317"(u),[u:is(x,y)]t3".317"(u)):lessis(x,z)
++*317
+k@[j:less(x,y)]
+t5:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
+k@[i:is(x,y)]
+t6:=islessis1(y,x,z,symis(nat,x,y,i),k):lessis(x,z)
+k@anders:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t5(u),[u:is(x,y)]t6(u)):lessis(x,z)
+-317
+k@trlessis:=satz17:lessis(x,z)
+z@[m:moreis(x,y)][n:moreis(y,z)]
+trmoreis:=satz14(z,x,satz17(z,y,x,satz13(y,z,n),satz13(m))):moreis(x,z)
+y@satz18:=somei(nat,[u:nat]diffprop(pl(x,y),x,u),y,refis(nat,pl(x,y))):more(pl(x,y),x)
+satz18a:=satz18:less(x,pl(x,y))
+x@satz18b:=ismore1(pl(x,1),<x>suc,x,satz4a,satz18(1)):more(<x>suc,x)
+satz18c:=satz18b:less(x,<x>suc)
+z@[m:more(x,y)]
++319
+[u:nat][du:diffprop(u)]
+t1:=tris(nat,x,pl(y,u),pl(u,y),du,compl(y,u)):is(x,pl(u,y))
+t2:=tr3is(nat,pl(x,z),pl(pl(u,y),z),pl(u,pl(y,z)),pl(pl(y,z),u),ispl1(x,pl(u,y),z,t1),asspl1(u,y,z),compl(u,pl(y,z))):is(pl(x,z),pl(pl(y,z),u))
+t3:=somei(nat,[v:nat]diffprop(pl(x,z),pl(y,z),v),u,t2):more(pl(x,z),pl(y,z))
+-319
+satz19a:=someapp(nat,[u:nat]diffprop(u),m,more(pl(x,z),pl(y,z)),[u:nat][v:diffprop(u)]t3".319"(u,v)):more(pl(x,z),pl(y,z))
+z@[i:is(x,y)]
+satz19b:=ispl1(x,y,z,i):is(pl(x,z),pl(y,z))
+z@[l:less(x,y)]
+satz19c:=satz11(pl(y,z),pl(x,z),satz19a(y,x,z,satz12(x,y,l))):less(pl(x,z),pl(y,z))
++*319
+l@anders1:=satz19a(y,x,z,l):less(pl(x,z),pl(y,z))
+-319
+m@satz19d:=ismore12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19a):more(pl(z,x),pl(z,y))
+i@satz19e:=ispl2(x,y,z,i):is(pl(z,x),pl(z,y))
+l@satz19f:=isless12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19c):less(pl(z,x),pl(z,y))
++*319
+l@anders2:=satz19d(y,x,z,l):less(pl(z,x),pl(z,y))
+-319
+z@[u:nat][i:is(x,y)][m:more(z,u)]
+satz19g:=ismore2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19d(z,u,x,m)):more(pl(x,z),pl(y,u))
+satz19h:=ismore12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19g):more(pl(z,x),pl(u,y))
+i@[l:less(z,u)]
+satz19j:=isless2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19f(z,u,x,l)):less(pl(x,z),pl(y,u))
+satz19k:=isless12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19j):less(pl(z,x),pl(u,y))
+z@[m:moreis(x,y)]
++*319
+m@[n:more(x,y)]
+t4:=moreisi1(pl(x,z),pl(y,z),satz19a(n)):moreis(pl(x,z),pl(y,z))
+m@[i:is(x,y)]
+t5:=moreisi2(pl(x,z),pl(y,z),ispl1(x,y,z,i)):moreis(pl(x,z),pl(y,z))
+-319
+m@satz19l:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,z)),m,[u:more(x,y)]t4".319"(u),[u:is(x,y)]t5".319"(u)):moreis(pl(x,z),pl(y,z))
+satz19m:=ismoreis12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19l):moreis(pl(z,x),pl(z,y))
+z@[l:lessis(x,y)]
+satz19n:=satz13(pl(y,z),pl(x,z),satz19l(y,x,z,satz14(l))):lessis(pl(x,z),pl(y,z))
+satz19o:=satz13(pl(z,y),pl(z,x),satz19m(y,x,z,satz14(l))):lessis(pl(z,x),pl(z,y))
++320
+z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
+t2:=satz10b(pl(x,z),pl(y,z)):ec3(is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)))
+-320
+z@[m:more(pl(x,z),pl(y,z))]
+satz20a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),m):more(x,y)
+z@[i:is(pl(x,z),pl(y,z))]
+satz20b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),i):is(x,y)
+z@[l:less(pl(x,z),pl(y,z))]
+satz20c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),l):less(x,y)
++*320
+i@t3:=tr3is(nat,pl(z,x),pl(x,z),pl(y,z),pl(z,y),compl(z,x),i,compl(y,z)):is(pl(z,x),pl(z,y))
+andersb:=satz8a(z,x,y,t3):is(x,y)
+l@andersc:=satz20a(y,x,z,l):less(x,y)
+-320
+z@[m:more(pl(z,x),pl(z,y))]
+satz20d:=satz20a(ismore12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),m)):more(x,y)
+z@[i:is(pl(z,x),pl(z,y))]
+satz20e:=satz20b(tr3is(nat,pl(x,z),pl(z,x),pl(z,y),pl(y,z),compl(x,z),i,compl(z,y))):is(x,y)
+z@[l:less(pl(z,x),pl(z,y))]
+satz20f:=satz20c(isless12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),l)):less(x,y)
+u@[m:more(x,y)][n:more(z,u)]
++321
+t1:=satz19a(x,y,z,m):more(pl(x,z),pl(y,z))
+t2:=ismore12(pl(z,y),pl(y,z),pl(u,y),pl(y,u),compl(z,y),compl(u,y),satz19a(z,u,y,n)):more(pl(y,z),pl(y,u))
+-321
+satz21:=trmore(pl(x,z),pl(y,z),pl(y,u),t1".321",t2".321"):more(pl(x,z),pl(y,u))
++*321
+n@anders:=trmore(pl(x,z),pl(y,z),pl(y,u),satz19a(x,y,z,m),satz19d(z,u,y,n)):more(pl(x,z),pl(y,u))
+-321
+u@[l:less(x,y)][k:less(z,u)]
+satz21a:=satz21(y,x,u,z,l,k):less(pl(x,z),pl(y,u))
++*321
+k@andersa:=satz11(pl(y,u),pl(x,z),satz21(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(pl(x,z),pl(y,u))
+-321
+u@[m:moreis(x,y)][n:more(z,u)]
+satz22a:=orapp(more(x,y),is(x,y),more(pl(x,z),pl(y,u)),m,[v:more(x,y)]satz21(v,n),[v:is(x,y)]satz19g(u,v,n)):more(pl(x,z),pl(y,u))
+u@[m:more(x,y)][n:moreis(z,u)]
+satz22b:=orapp(more(z,u),is(z,u),more(pl(x,z),pl(y,u)),n,[v:more(z,u)]satz21(m,v),[v:is(z,u)]satz19h(z,u,x,y,v,m)):more(pl(x,z),pl(y,u))
+u@[l:lessis(x,y)][k:less(z,u)]
+satz22c:=satz22a(y,x,u,z,satz14(x,y,l),k):less(pl(x,z),pl(y,u))
+u@[l:less(x,y)][k:lessis(z,u)]
+satz22d:=satz22b(y,x,u,z,l,satz14(z,u,k)):less(pl(x,z),pl(y,u))
+u@[m:moreis(x,y)][n:moreis(z,u)]
++323
+[i:is(x,y)][j:is(z,u)]
+t1:=moreisi2(pl(x,z),pl(y,u),tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j))):moreis(pl(x,z),pl(y,u))
+i@[o:more(z,u)]
+t2:=moreisi1(pl(x,z),pl(y,u),satz22a(m,o)):moreis(pl(x,z),pl(y,u))
+i@t3:=orapp(more(z,u),is(z,u),moreis(pl(x,z),pl(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(pl(x,z),pl(y,u))
+n@[o:more(x,y)]
+t4:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
+-323
+satz23:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t4".323"(v),[v:is(x,y)]t3".323"(v)):moreis(pl(x,z),pl(y,u))
++*323
+n@[o:more(x,y)]
+t5:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
+n@[i:is(x,y)]
+t6:=ismoreis2(pl(x,u),pl(y,u),pl(x,z),ispl1(u,i),satz19m(z,u,x,n)):moreis(pl(x,z),pl(y,u))
+n@anders:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(pl(x,z),pl(y,u))
+-323
+u@[l:lessis(x,y)][k:lessis(z,u)]
+satz23a:=satz13(pl(y,u),pl(x,z),satz23(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(pl(x,z),pl(y,u))
++324
+x@[n:nis(x,1)][u:nat][i:is(x,<u>suc)]
+t1:=tris(nat,x,<u>suc,pl(1,u),i,satz4g(u)):is(x,pl(1,u))
+t2:=ismore1(pl(1,u),x,1,symis(nat,x,pl(1,u),t1),satz18(1,u)):more(x,1)
+n@t3:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),more(x,1),[u:nat][v:is(x,<u>suc)]t2(u,v)):more(x,1)
+-324
+x@satz24:=th2"l.or"(more(x,1),is(x,1),[u:nis(x,1)]t3".324"(u)):moreis(x,1)
+satz24a:=satz13(x,1,satz24):lessis(1,x)
+satz24b:=t3".324"(<x>suc,<x>ax3):more(<x>suc,1)
+satz24c:=satz24b:less(1,<x>suc)
+y@[m:more(y,x)]
++325
+[u:nat][du:diffprop(y,x,u)]
+t1:=satz19m(u,1,x,satz24(u)):moreis(pl(x,u),pl(x,1))
+t2:=ismoreis1(pl(x,u),y,pl(x,1),symis(nat,y,pl(x,u),du),t1):moreis(y,pl(x,1))
+-325
+satz25:=someapp(nat,[u:nat]diffprop(y,x,u),m,moreis(y,pl(x,1)),[u:nat][v:diffprop(y,x,u)]t2".325"(u,v)):moreis(y,pl(x,1))
+satz25a:=ismoreis2(pl(x,1),<x>suc,y,satz4a,satz25):moreis(y,<x>suc)
+y@[l:less(y,x)]
+satz25b:=satz13(x,pl(y,1),satz25(y,x,l)):lessis(pl(y,1),x)
+satz25c:=islessis1(pl(y,1),<y>suc,x,satz4a(y),satz25b):lessis(<y>suc,x)
+y@[l:less(y,pl(x,1))]
++326
+[m:more(y,x)]
+t1:=satz25(m):moreis(y,pl(x,1))
+l@t2:=th3"l.imp"(more(y,x),moreis(y,pl(x,1)),satz10h(y,pl(x,1),l),[v:more(y,x)]t1(v)):not(more(y,x))
+-326
+satz26:=satz10e(y,x,t2".326"):lessis(y,x)
+y@[l:less(y,<x>suc)]
+satz26a:=satz26(isless2(<x>suc,pl(x,1),y,satz4e,l)):lessis(y,x)
+y@[m:more(pl(y,1),x)]
+satz26b:=satz14(x,y,satz26(y,x,m)):moreis(y,x)
+y@[m:more(<y>suc,x)]
+satz26c:=satz26b(ismore1(<y>suc,pl(y,1),x,satz4e(y),m)):moreis(y,x)
+@[p:[x:nat]'prop'][n:nat]
++327
+[m:nat]
+lbprop:=imp(<m>p,lessis(n,m)):'prop'
+-327
+lb:=all([x:nat]lbprop".327"(x)):'prop'
+min:=and(lb,<n>p):'prop'
+p@[s:some(p)]
++*327
+s@[n:nat]
+t1:=[x:<n>p]satz24a(n):lbprop(1,n)
+s@t2:=[x:nat]t1(x):lb(1)
+[l:[x:nat]lb(x)][y:nat][yp:<y>p]
+t3:=satz18(y,1):more(pl(y,1),y)
+t4:=satz10g(pl(y,1),y,t3):not(lessis(pl(y,1),y))
+t5:=th4"l.imp"(<y>p,lessis(pl(y,1),y),yp,t4):not(lbprop(pl(y,1),y))
+t6:=th1"l.all"(nat,[x:nat]lbprop(pl(y,1),x),y,t5):not(lb(pl(y,1)))
+t7:=mp(lb(pl(y,1)),con,<pl(y,1)>l,t6):con
+l@t8:=someapp(nat,p,s,con,[x:nat][y:<x>p]t7(x,y)):con
+s@[n:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))][m:nat][l:lb(m)]
+t9:=<m>n:not(and(lb(m),not(lb(pl(m,1)))))
+t10:=et(lb(pl(m,1)),th3"l.and"(lb(m),not(lb(pl(m,1))),t9,l)):lb(pl(m,1))
+t11:=isp(nat,[x:nat]lb(x),pl(m,1),<m>suc,t10,satz4a(m)):lb(<m>suc)
+n@t12:=[x:nat]induction([y:nat]lb(y),t2,[y:nat][z:lb(y)]t11(y,z),x):[x:nat]lb(x)
+s@t13:=[x:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))]t8(t12(x)):some([x:nat]and(lb(x),not(lb(pl(x,1)))))
+[m:nat][a:and(lb(m),not(lb(pl(m,1))))]
+t14:=ande1(lb(m),not(lb(pl(m,1))),a):lb(m)
+t15:=ande2(lb(m),not(lb(pl(m,1))),a):not(lb(pl(m,1)))
+[nmp:not(<m>p)][n:nat][np:<n>p]
+t16:=mp(<n>p,lessis(m,n),np,<n>t14):lessis(m,n)
+t17:=th3"l.imp"(is(m,n),<m>p,nmp,[x:is(m,n)]isp(nat,p,n,m,np,symis(nat,m,n,x))):not(is(m,n))
+t18:=ore1(less(m,n),is(m,n),t16,t17):less(m,n)
+t19:=satz25b(n,m,t18):lessis(pl(m,1),n)
+nmp@t20:=[x:nat][y:<x>p]t19(x,y):lb(pl(m,1))
+t21:=mp(lb(pl(m,1)),con,t20,t15):con
+a@t22:=et(<m>p,[x:not(<m>p)]t21(x)):<m>p
+t23:=andi(lb(m),<m>p,t14,t22):min(m)
+-327
+s@satz27:=th6"l.some"(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))),[x:nat]min(x),t13".327",[x:nat][y:and(lb(x),not(lb(pl(x,1))))]t23".327"(x,y)):some([x:nat]min(p,x))
++*327
+p@[n:non(nat,[x:nat]min(x))][u:nat]
+t24:=[x:<u>p]satz24a(u):lbprop(1,u)
+n@t25:=[x:nat]t24(x):lb(1)
+u@[l:lb(u)]
+t26:=<u>n:not(min(u))
+t27:=th3"l.and"(lb(u),<u>p,t26,l):not(<u>p)
+[v:nat][vp:<v>p]
+t28:=th3"l.imp"(is(u,v),<u>p,t27,[x:is(u,v)]isp1(nat,p,v,u,vp,x)):nis(u,v)
+t29:=mp(<v>p,lessis(u,v),vp,<v>l):lessis(u,v)
+t30:=ore1(less(u,v),is(u,v),t29,t28):less(u,v)
+t31:=satz25c(v,u,t30):lessis(<u>suc,v)
+v@t32:=[x:<v>p]t31(x):lbprop(<u>suc,v)
+l@t33:=[x:nat]t32(x):lb(<u>suc)
+u@t34:=induction([x:nat]lb(x),t25,[x:nat][y:lb(x)]t33(x,y),u):lb(u)
+p@[s:some(p)][u:nat][up:<u>p]
+t35:=satz10g(<u>suc,u,satz18b(u)):not(lessis(<u>suc,u))
+t36:=th4"l.imp"(<u>p,lessis(<u>suc,u),up,t35):not(lbprop(<u>suc,u))
+t37:=th1"l.all"(nat,[x:nat]lbprop(<u>suc,x),u,t36):not(lb(<u>suc))
+t38:=[y:non(nat,[x:nat]min(x))]mp(lb(<u>suc),con,t34(y,<u>suc),t37):some([x:nat]min(x))
+s@anders:=someapp(nat,p,s,some([x:nat]min(x)),[x:nat][y:<x>p]t38(x,y)):some([x:nat]min(x))
+-327
++*327
+p@[n:nat][m:nat][mn:min(p,n)][mm:min(p,m)]
+t39:=ande1(lb(n),<n>p,mn):lb(n)
+t40:=ande1(lb(m),<m>p,mm):lb(m)
+t41:=ande2(lb(n),<n>p,mn):<n>p
+t42:=ande2(lb(m),<m>p,mm):<m>p
+t43:=<m>t39:lbprop(n,m)
+t44:=<n>t40:lbprop(m,n)
+t45:=mp(<m>p,lessis(n,m),t42,t43):lessis(n,m)
+t46:=mp(<n>p,lessis(m,n),t41,t44):lessis(m,n)
+t47:=ore2(more(n,m),is(n,m),satz14(m,n,t46),satz10d(n,m,t45)):is(n,m)
+p@t48:=[x:nat][y:nat][u:min(x)][v:min(y)]t47(x,y,u,v):amone(nat,[x:nat]min(p,x))
+-327
+s@satz27a:=onei(nat,[x:nat]min(p,x),t48".327",satz27):one([x:nat]min(p,x))
++428
+x@[f:[y:nat]nat]
+prop1:=all([y:nat]is(<<y>suc>f,pl(<y>f,x))):'prop'
+prop2:=and(is(<1>f,x),prop1):'prop'
+x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
+prop3:=is(<y>a,<y>b):'prop'
+pb@t1:=ande1(is(<1>a,x),prop1(a),pa):is(<1>a,x)
+t2:=ande1(is(<1>b,x),prop1(b),pb):is(<1>b,x)
+t3:=tris2(nat,<1>a,<1>b,x,t1,t2):prop3(1)
+y@[p:prop3(y)]
+t4:=ispl1(<y>a,<y>b,x,p):is(pl(<y>a,x),pl(<y>b,x))
+t5:=ande2(is(<1>a,x),prop1(a),pa):prop1(a)
+t6:=ande2(is(<1>b,x),prop1(b),pb):prop1(b)
+t7:=<y>t5:is(<<y>suc>a,pl(<y>a,x))
+t8:=<y>t6:is(<<y>suc>b,pl(<y>b,x))
+t9:=tr3is(nat,<<y>suc>a,pl(<y>a,x),pl(<y>b,x),<<y>suc>b,t7,t4,symis(nat,<<y>suc>b,pl(<y>b,x),t8)):prop3(<y>suc)
+y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
+pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
+x@a1:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
+prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
+@id:=[y:nat]y:[y:nat]nat
+t12:=[x:nat]satz4e(x):prop1(1,id)
+t13:=andi(is(<1>id,1),prop1(1,id),refis(nat,1),t12):prop2(1,id)
+t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),id,t13):prop4(1)
+x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
+g:=[y:nat]pl(<y>f,y):[y:nat]nat
+t15:=ande1(is(<1>f,x),prop1(f),pf):is(<1>f,x)
+t16:=tris(nat,<1>g,pl(x,1),<x>suc,ispl1(<1>f,x,1,t15),satz4a(x)):is(<1>g,<x>suc)
+[y:nat]
+t17:=ande2(is(<1>f,x),prop1(f),pf):prop1(f)
+t18:=<y>t17:is(<<y>suc>f,pl(<y>f,x))
+t19:=tris(nat,<<y>suc>g,pl(pl(<y>f,x),<y>suc),pl(<y>f,pl(x,<y>suc)),ispl1(<<y>suc>f,pl(<y>f,x),<y>suc,t18),asspl1(<y>f,x,<y>suc)):is(<<y>suc>g,pl(<y>f,pl(x,<y>suc)))
+t20:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,pl(<x>suc,y),pl(y,<x>suc),satz4b(x,y),satz4h(x,y),compl(<x>suc,y)):is(pl(x,<y>suc),pl(y,<x>suc))
+t21:=tr3is(nat,<<y>suc>g,pl(<y>f,pl(x,<y>suc)),pl(<y>f,pl(y,<x>suc)),pl(<y>g,<x>suc),t19,ispl2(pl(x,<y>suc),pl(y,<x>suc),<y>f,t20),asspl2(<y>f,y,<x>suc)):is(<<y>suc>g,pl(<y>g,<x>suc))
+pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
+t23:=andi(is(<1>g,<x>suc),prop1(<x>suc,g),t16,t22):prop2(<x>suc,g)
+t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
+p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
+x@b1:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
+-428
+x@satz28:=onei([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),a1".428",b1".428"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,x),all([y:nat]is(<<y>suc>z,pl(<y>z,x)))))
+times:=ind([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),satz28):[y:nat]nat
+y@ts:=<y>times:nat
++*428
+x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz28):prop2(times)
+-428
+x@satz28a:=ande1(is(<1>times,x),prop1".428"(times),t26".428"):is(ts(x,1),x)
++*428
+x@t27:=ande2(is(<1>times,x),prop1(times),t26):prop1(times)
+-428
+y@satz28b:=<y>t27".428":is(ts(x,<y>suc),pl(ts(x,y),x))
++*428
+@t28:=t11(1,times(1),id,t26(1),t13):is"e"([y:nat]nat,times(1),id)
+-428
+x@satz28c:=fise(nat,nat,times(1),id".428",t28".428",x):is(ts(1,x),x)
++*428
+x@t29:=t11(<x>suc,times(<x>suc),[y:nat]pl(<y>times,y),t26(<x>suc),t23(b1,times,t26)):is"e"([y:nat]nat,times(<x>suc),[y:nat]pl(<y>times,y))
+-428
+y@satz28d:=fise(nat,nat,times(<x>suc),[z:nat]pl(<z>times,z),t29".428",y):is(ts(<x>suc,y),pl(ts(x,y),y))
+x@satz28e:=symis(nat,ts(x,1),x,satz28a):is(x,ts(x,1))
+y@satz28f:=symis(nat,ts(x,<y>suc),pl(ts(x,y),x),satz28b):is(pl(ts(x,y),x),ts(x,<y>suc))
+x@satz28g:=symis(nat,ts(1,x),x,satz28c):is(x,ts(1,x))
+y@satz28h:=symis(nat,ts(<x>suc,y),pl(ts(x,y),y),satz28d):is(pl(ts(x,y),y),ts(<x>suc,y))
+z@[i:is(x,y)]
+ists1:=isf(nat,nat,[u:nat]ts(u,z),x,y,i):is(ts(x,z),ts(y,z))
+ists2:=isf(nat,nat,[u:nat]ts(z,u),x,y,i):is(ts(z,x),ts(z,y))
+z@[u:nat][i:is(x,y)][j:is(z,u)]
+ists12:=tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
++429
+y@prop1:=is(ts(x,y),ts(y,x)):'prop'
+t1:=satz28a(y):is(ts(y,1),y)
+t2:=satz28c(y):is(ts(1,y),y)
+t3:=tris2(nat,ts(1,y),ts(y,1),y,t2,t1):prop1(1,y)
+[p:prop1(x,y)]
+t4:=tris(nat,pl(ts(x,y),y),pl(ts(y,x),y),ts(y,<x>suc),ispl1(ts(x,y),ts(y,x),y,p),satz28f(y,x)):is(pl(ts(x,y),y),ts(y,<x>suc))
+t5:=satz28d:is(ts(<x>suc,y),pl(ts(x,y),y))
+t6:=tris(nat,ts(<x>suc,y),pl(ts(x,y),y),ts(y,<x>suc),t5,t4):prop1(<x>suc,y)
+-429
+y@satz29:=induction([z:nat]prop1".429"(z,y),t3".429",[z:nat][u:prop1".429"(z,y)]t6".429"(z,y,u),x):is(ts(x,y),ts(y,x))
+comts:=satz29:is(ts(x,y),ts(y,x))
++*429
+x@t7:=tris(nat,ts(x,1),x,ts(1,x),satz28a,satz28g):prop1(1)
+y@[p:prop1(y)]
+t8:=tr3is(nat,ts(x,<y>suc),pl(ts(x,y),x),pl(ts(y,x),x),ts(<y>suc,x),satz28b(x,y),ispl1(ts(x,y),ts(y,x),x,p),satz28h(y,x)):prop1(<y>suc)
+y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(ts(x,y),ts(y,x))
+-429
++430
+z@prop1:=is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z))):'prop'
+y@t1:=tr3is(nat,ts(x,pl(y,1)),ts(x,<y>suc),pl(ts(x,y),x),pl(ts(x,y),ts(x,1)),ists2(pl(y,1),<y>suc,x,satz4a(y)),satz28b,ispl2(x,ts(x,1),ts(x,y),satz28e(x))):prop1(1)
+z@[p:prop1(z)]
+t2:=tr3is(nat,ts(x,pl(y,<z>suc)),ts(x,<pl(y,z)>suc),pl(ts(x,pl(y,z)),x),pl(pl(ts(x,y),ts(x,z)),x),ists2(pl(y,<z>suc),<pl(y,z)>suc,x,satz4b(y,z)),satz28b(x,pl(y,z)),ispl1(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),x,p)):is(ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x))
+t3:=tr3is(nat,ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x),pl(ts(x,y),pl(ts(x,z),x)),pl(ts(x,y),ts(x,<z>suc)),t2,asspl1(ts(x,y),ts(x,z),x),ispl2(pl(ts(x,z),x),ts(x,<z>suc),ts(x,y),satz28f(x,z))):prop1(<z>suc)
+-430
+z@satz30:=induction([u:nat]prop1".430"(u),t1".430",[u:nat][v:prop1".430"(u)]t3".430"(u,v),z):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+disttp1:=tr3is(nat,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz30(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
+disttp2:=satz30:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+distpt1:=symis(nat,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
+distpt2:=symis(nat,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
++431
+prop1:=is(ts(ts(x,y),z),ts(x,ts(y,z))):'prop'
+y@t1:=tris(nat,ts(ts(x,y),1),ts(x,y),ts(x,ts(y,1)),satz28a(ts(x,y)),ists2(y,ts(y,1),x,satz28e(y))):prop1(1)
+z@[p:prop1(z)]
+t2:=tr4is(nat,ts(ts(x,y),<z>suc),pl(ts(ts(x,y),z),ts(x,y)),pl(ts(x,ts(y,z)),ts(x,y)),ts(x,pl(ts(y,z),y)),ts(x,ts(y,<z>suc)),satz28b(ts(x,y),z),ispl1(ts(ts(x,y),z),ts(x,ts(y,z)),ts(x,y),p),distpt2(x,ts(y,z),y),ists2(pl(ts(y,z),y),ts(y,<z>suc),x,satz28f(y,z))):prop1(<z>suc)
+-431
+satz31:=induction([u:nat]prop1".431"(u),t1".431",[u:nat][v:prop1".431"(u)]t2".431"(u,v),z):is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts1:=satz31:is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts2:=symis(nat,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
+[m:more(x,y)]
++432
+[u:nat][du:diffprop(u)]
+t1:=tris(nat,ts(x,z),ts(pl(y,u),z),pl(ts(y,z),ts(u,z)),ists1(x,pl(y,u),z,du),disttp1(y,u,z)):is(ts(x,z),pl(ts(y,z),ts(u,z)))
+t2:=somei(nat,[v:nat]diffprop(ts(x,z),ts(y,z),v),ts(u,z),t1):more(ts(x,z),ts(y,z))
+-432
+satz32a:=someapp(nat,[u:nat]diffprop(u),m,more(ts(x,z),ts(y,z)),[u:nat][v:diffprop(u)]t2".432"(u,v)):more(ts(x,z),ts(y,z))
+z@[i:is(x,y)]
+satz32b:=ists1(x,y,z,i):is(ts(x,z),ts(y,z))
+z@[l:less(x,y)]
+satz32c:=satz11(ts(y,z),ts(x,z),satz32a(y,x,z,satz12(x,y,l))):less(ts(x,z),ts(y,z))
++*432
+l@anders1:=satz32a(y,x,z,l):less(ts(x,z),ts(y,z))
+-432
+m@satz32d:=ismore12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32a):more(ts(z,x),ts(z,y))
+i@satz32e:=ists2(x,y,z,i):is(ts(z,x),ts(z,y))
+l@satz32f:=isless12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32c):less(ts(z,x),ts(z,y))
++*432
+l@anders2:=satz32d(y,x,z,l):less(ts(z,x),ts(z,y))
+-432
+z@[u:nat][i:is(x,y)][m:more(z,u)]
+satz32g:=ismore2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32d(z,u,x,m)):more(ts(x,z),ts(y,u))
+satz32h:=ismore12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32g):more(ts(z,x),ts(u,y))
+i@[l:less(z,u)]
+satz32j:=isless2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32f(z,u,x,l)):less(ts(x,z),ts(y,u))
+satz32k:=isless12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32j):less(ts(z,x),ts(u,y))
+z@[m:moreis(x,y)]
++*432
+m@[n:more(x,y)]
+t3:=moreisi1(ts(x,z),ts(y,z),satz32a(n)):moreis(ts(x,z),ts(y,z))
+m@[i:is(x,y)]
+t4:=moreisi2(ts(x,z),ts(y,z),ists1(x,y,z,i)):moreis(ts(x,z),ts(y,z))
+-432
+m@satz32l:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,z)),m,[u:more(x,y)]t3".432"(u),[u:is(x,y)]t4".432"(u)):moreis(ts(x,z),ts(y,z))
+satz32m:=ismoreis12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32l):moreis(ts(z,x),ts(z,y))
+z@[l:lessis(x,y)]
+satz32n:=satz13(ts(y,z),ts(x,z),satz32l(y,x,z,satz14(l))):lessis(ts(x,z),ts(y,z))
+satz32o:=satz13(ts(z,y),ts(z,x),satz32m(y,x,z,satz14(l))):lessis(ts(z,x),ts(z,y))
++433
+z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
+t2:=satz10b(ts(x,z),ts(y,z)):ec3(is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)))
+-433
+z@[m:more(ts(x,z),ts(y,z))]
+satz33a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),m):more(x,y)
+z@[i:is(ts(x,z),ts(y,z))]
+satz33b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),i):is(x,y)
+z@[l:less(ts(x,z),ts(y,z))]
+satz33c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),l):less(x,y)
++*433
+l@anders:=satz33a(y,x,z,l):less(x,y)
+-433
+u@[m:more(x,y)][n:more(z,u)]
++434
+t1:=satz32a(x,y,z,m):more(ts(x,z),ts(y,z))
+t2:=ismore12(ts(z,y),ts(y,z),ts(u,y),ts(y,u),comts(z,y),comts(u,y),satz32a(z,u,y,n)):more(ts(y,z),ts(y,u))
+-434
+satz34:=trmore(ts(x,z),ts(y,z),ts(y,u),t1".434",t2".434"):more(ts(x,z),ts(y,u))
++*434
+n@anders:=trmore(ts(x,z),ts(y,z),ts(y,u),satz32a(x,y,z,m),satz32d(z,u,y,n)):more(ts(x,z),ts(y,u))
+-434
+u@[l:less(x,y)][k:less(z,u)]
+satz34a:=satz34(y,x,u,z,l,k):less(ts(x,z),ts(y,u))
++*434
+k@andersa:=satz11(ts(y,u),ts(x,z),satz34(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(ts(x,z),ts(y,u))
+-434
+u@[m:moreis(x,y)][n:more(z,u)]
+satz35a:=orapp(more(x,y),is(x,y),more(ts(x,z),ts(y,u)),m,[v:more(x,y)]satz34(v,n),[v:is(x,y)]satz32g(u,v,n)):more(ts(x,z),ts(y,u))
+u@[m:more(x,y)][n:moreis(z,u)]
+satz35b:=orapp(more(z,u),is(z,u),more(ts(x,z),ts(y,u)),n,[v:more(z,u)]satz34(m,v),[v:is(z,u)]satz32h(z,u,x,y,v,m)):more(ts(x,z),ts(y,u))
+u@[l:lessis(x,y)][k:less(z,u)]
+satz35c:=satz35a(y,x,u,z,satz14(x,y,l),k):less(ts(x,z),ts(y,u))
+u@[l:less(x,y)][k:lessis(z,u)]
+satz35d:=satz35b(y,x,u,z,l,satz14(z,u,k)):less(ts(x,z),ts(y,u))
+u@[m:moreis(x,y)][n:moreis(z,u)]
++436
+[i:is(x,y)][j:is(z,u)]
+t1:=moreisi2(ts(x,z),ts(y,u),tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j))):moreis(ts(x,z),ts(y,u))
+i@[o:more(z,u)]
+t2:=moreisi1(ts(x,z),ts(y,u),satz35a(m,o)):moreis(ts(x,z),ts(y,u))
+i@t3:=orapp(more(z,u),is(z,u),moreis(ts(x,z),ts(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(ts(x,z),ts(y,u))
+n@[o:more(x,y)]
+t4:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
+-436
+satz36:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t4".436"(v),[v:is(x,y)]t3".436"(v)):moreis(ts(x,z),ts(y,u))
++*436
+n@[o:more(x,y)]
+t5:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
+n@[i:is(x,y)]
+t6:=ismoreis2(ts(x,u),ts(y,u),ts(x,z),ists1(u,i),satz32m(z,u,x,n)):moreis(ts(x,z),ts(y,u))
+n@anders:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(ts(x,z),ts(y,u))
+-436
+u@[l:lessis(x,y)][k:lessis(z,u)]
+satz36a:=satz13(ts(y,u),ts(x,z),satz36(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(ts(x,z),ts(y,u))
+y@[m:more(x,y)]
++mn
+t1:=onei(nat,[z:nat]diffprop(x,y,z),satz8b(x,y),m):one([z:nat]diffprop(x,y,z))
+-mn
+mn:=ind(nat,[z:nat]diffprop(x,y,z),t1".mn"):nat
++*mn
+m@th1a:=oneax(nat,[z:nat]diffprop(x,y,z),t1):is(x,pl(y,mn(x,y,m)))
+th1b:=symis(nat,x,pl(y,mn(x,y,m)),th1a):is(pl(y,mn(x,y,m)),x)
+th1c:=tris(nat,x,pl(y,mn(x,y,m)),pl(mn(x,y,m),y),th1a,compl(y,mn(x,y,m))):is(x,pl(mn(x,y,m),y))
+th1d:=symis(nat,x,pl(mn(x,y,m),y),th1c):is(pl(mn(x,y,m),y),x)
+y@[z:nat][m:more(x,y)][i:is(pl(y,z),x)]
+th1e:=<th1a(m)><symis(nat,pl(y,z),x,i)><mn(x,y,m)><z>satz8b(x,y):is(z,mn(x,y,m))
+-mn
+z@[u:nat][m:more(x,z)][n:more(y,u)][i:is(x,y)][j:is(z,u)]
++*mn
+j@t2:=tr3is(nat,pl(u,mn(x,z,m)),pl(z,mn(x,z,m)),x,y,ispl1(u,z,mn(x,z,m),symis(nat,z,u,j)),th1b(x,z,m),i):is(pl(u,mn(x,z,m)),y)
+-mn
+j@ismn12:=th1e".mn"(y,u,mn(x,z,m),n,t2".mn"):is(mn(x,z,m),mn(y,u,n))
+@[n:nat]
+1to:=ot(nat,[x:nat]lessis(x,n)):'type'
+[x:nat][l:lessis(x,n)]
+outn:=out(nat,[y:nat]lessis(y,n),x,l):1to(n)
+n@[xn:1to(n)]
+inn:=in"e"(nat,[y:nat]lessis(y,n),xn):nat
+1top:=inp(nat,[y:nat]lessis(y,n),xn):lessis(inn,n)
+l@[y:nat][k:lessis(y,n)][i:is(x,y)]
+isoutni:=isouti(nat,[z:nat]lessis(z,n),x,l,y,k,i):is"e"(1to(n),outn(x,l),outn(y,k))
+k@[i:is"e"(1to(n),outn(x,l),outn(y,k))]
+isoutne:=isoute(nat,[z:nat]lessis(z,n),x,l,y,k,i):is(x,y)
+xn@[yn:1to(n)][i:is"e"(1to(n),xn,yn)]
+isinni:=isini(nat,[z:nat]lessis(z,n),xn,yn,i):is(inn(xn),inn(yn))
+yn@[i:is(inn(xn),inn(yn))]
+isinne:=isine(nat,[z:nat]lessis(z,n),xn,yn,i):is"e"(1to(n),xn,yn)
+xn@isoutinn:=isoutin(nat,[y:nat]lessis(y,n),xn):is"e"(1to(n),xn,outn(inn(xn),1top(xn)))
+l@isinoutn:=isinout(nat,[y:nat]lessis(y,n),x,l):is(x,inn(outn(x,l)))
+@1o:=outn(1,1,lessisi2(1,1,refis(nat,1))):1to(1)
+[u:1to(1)]
++singlet
+u0:=inn(1,u):nat
+t1:=1top(1,u):lessis(u0,1)
+t2:=ore2(more(u0,1),is(u0,1),satz24(u0),satz10d(u0,1,t1)):is(u0,1)
+th1:=tris(1to(1),u,outn(1,u0,t1),1o,isoutinn(1,u),isoutni(1,u0,t1,1,lessisi2(1,1,refis(nat,1)),t2)):is"e"(1to(1),u,1o)
+-singlet
+@2:=pl(1,1):nat
+[x:nat]
++pair
+[l:lessis(x,2)][n:nis(x,2)]
+t1:=satz26(1,x,ore1(less(x,2),is(x,2),l,n)):lessis(x,1)
+t2:=ore2(more(x,1),is(x,1),satz24(x),satz10d(x,1,t1)):is(x,1)
+l@th1:=th2"l.or"(is(x,1),is(x,2),[t:nis(x,2)]t2(t)):or(is(x,1),is(x,2))
+@th2:=th1"e.notis"(nat,<1>suc,1,2,<1>ax3,satz4e(1)):nis(2,1)
+-pair
+@1t:=outn(2,1,satz24a(2)):1to(2)
+2t:=outn(2,2,lessisi2(2,2,refis(nat,2))):1to(2)
++*pair
+@[u:1to(2)]
+u0:=inn(2,u):nat
+t3:=1top(2,u):lessis(u0,2)
+[i:is(u0,1)]
+t4:=isoutni(2,u0,t3,1,satz24a(2),i):is"e"(1to(2),outn(2,u0,t3),1t)
+t5:=tris(1to(2),u,outn(2,u0,t3),1t,isoutinn(2,u),t4):is"e"(1to(2),u,1t)
+u@[i:is(u0,2)]
+t6:=isoutni(2,u0,t3,2,lessisi2(2,2,refis(nat,2)),i):is"e"(1to(2),outn(2,u0,t3),2t)
+t7:=tris(1to(2),u,outn(2,u0,t3),2t,isoutinn(2,u),t6):is"e"(1to(2),u,2t)
+u@th3:=th9"l.or"(is(u0,1),is(u0,2),is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),th1(u0,t3),[t:is(u0,1)]t5(t),[t:is(u0,2)]t7(t)):or(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t))
+@[i:is"e"(1to(2),2t,1t)]
+t9:=isini(nat,[x:nat]lessis(x,2),2t,1t,i):is(u0(2t),u0(1t))
+t10:=tr3is(nat,2,u0(2t),u0(1t),1,isinoutn(2,2,lessisi2(2,2,refis(nat,2))),t9,symis(nat,1,u0(1t),isinoutn(2,1,satz24a(2)))):is(2,1)
+@th4:=th3"l.imp"(is"e"(1to(2),2t,1t),is(2,1),th2,[t:is"e"(1to(2),2t,1t)]t10(t)):not(is"e"(1to(2),2t,1t))
+-pair
+@[alpha:'type']
+pair1type:=[x:1to(2)]alpha:'type'
+[a:alpha][b:alpha]
+pair1:=[x:1to(2)]ite(is"e"(1to(2),x,1t),alpha,a,b):pair1type
+alpha@[p:pair1type]
+first1:=<1t>p:alpha
+second1:=<2t>p:alpha
+b@first1is1:=itet(is"e"(1to(2),1t,1t),alpha,a,b,refis(1to(2),1t)):is"e"(alpha,first1(pair1),a)
+first1is2:=symis(alpha,first1(pair1),a,first1is1):is"e"(alpha,a,first1(pair1))
+second1is1:=itef(is"e"(1to(2),2t,1t),alpha,a,b,th4".pair"):is"e"(alpha,second1(pair1),b)
+second1is2:=symis(alpha,second1(pair1),b,second1is1):is"e"(alpha,b,second1(pair1))
++*pair
+p@[q:pair1type][i:is"e"(alpha,first1(p),first1(q))][j:is"e"(alpha,second1(p),second1(q))][u:1to(2)][u1:is"e"(1to(2),u,1t)]
+t11:=isf(1to(2),alpha,p,u,1t,u1):is"e"(alpha,<u>p,first1(p))
+t12:=symis(alpha,<u>q,first1(q),isf(1to(2),alpha,q,u,1t,u1)):is"e"(alpha,first1(q),<u>q)
+t13:=tr3is(alpha,<u>p,first1(p),first1(q),<u>q,t11,i,t12):is"e"(alpha,<u>p,<u>q)
+u@[u2:is"e"(1to(2),u,2t)]
+t14:=isf(1to(2),alpha,p,u,2t,u2):is"e"(alpha,<u>p,second1(p))
+t15:=symis(alpha,<u>q,second1(q),isf(1to(2),alpha,q,u,2t,u2)):is"e"(alpha,second1(q),<u>q)
+t16:=tr3is(alpha,<u>p,second1(p),second1(q),<u>q,t14,j,t15):is"e"(alpha,<u>p,<u>q)
+u@t17:=orapp(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),is"e"(alpha,<u>p,<u>q),th3(u),[t:is"e"(1to(2),u,1t)]t13(t),[t:is"e"(1to(2),u,2t)]t16(t)):is"e"(alpha,<u>p,<u>q)
+j@th5:=fisi(1to(2),alpha,p,q,[t:1to(2)]t17(t)):is"e"(pair1type,p,q)
+p@q0:=pair1(first1,second1):pair1type
+t18:=first1is1(first1(p),second1):is"e"(alpha,first1(q0),first1(p))
+t19:=second1is1(first1,second1):is"e"(alpha,second1(q0),second1(p))
+-pair
+p@pair1is1:=th5".pair"(q0".pair",p,t18".pair",t19".pair"):is"e"(pair1type,pair1(first1,second1),p)
+pair1is2:=symis(pair1type,pair1(first1,second1),p,pair1is1):is"e"(pair1type,p,pair1(first1,second1))
+@[x:nat]
+lessisi3:=lessisi2(x,x,refis(nat,x)):lessis(x,x)
+1out:=outn(x,1,satz24a(x)):1to(x)
+xout:=outn(x,x,lessisi3(x)):1to(x)
+[y:nat][l:lessis(y,x)][u:1to(y)]
++left
+ui:=inn(y,u):nat
+t1:=1top(y,u):lessis(ui,y)
+t2:=trlessis(ui,y,x,t1,l):lessis(ui,x)
+-left
+left1to:=outn(x,ui".left",t2".left"):1to(x)
+[v:1to(y)][i:is"e"(1to(x),left1to(u),left1to(v))]
++*left
+i@t3:=isoutne(x,ui,t2,ui(v),t2(v),i):is(ui,ui(v))
+-left
+i@thleft1:=isinne(y,u,v,t3".left"):is"e"(1to(y),u,v)
+l@thleft2:=[u:1to(y)][v:1to(y)][t:is"e"(1to(x),left1to(u),left1to(v))]thleft1(u,v,t):injective(1to(y),1to(x),[t:1to(y)]left1to(t))
+y@[u:1to(y)]
++right
+ui:=inn(y,u):nat
+t4:=1top(y,u):lessis(ui,y)
+t5:=satz19o(ui,y,x,t4):lessis(pl(x,ui),pl(x,y))
+-right
+right1to:=outn(pl(x,y),pl(x,ui".right"),t5".right"):1to(pl(x,y))
+[v:1to(y)][i:is"e"(1to(pl(x,y)),right1to(u),right1to(v))]
++*right
+i@t6:=isoutne(pl(x,y),pl(x,ui(u)),t5(u),pl(x,ui(v)),t5(v),i):is(pl(x,ui(u)),pl(x,ui(v)))
+t7:=satz20e(ui(u),ui(v),x,t6):is(ui(u),ui(v))
+-right
+i@thright1:=isinne(y,u,v,t7".right"):is"e"(1to(y),u,v)
+@[alpha:'type'][x:nat][y:nat][l:lessis(y,x)][f:[t:1to(x)]alpha]
+left:=[t:1to(y)]<left1to(x,y,l,t)>f:[t:1to(y)]alpha
+y@[f:[t:1to(pl(x,y))]alpha]
+right:=[t:1to(y)]<right1to(x,y,t)>f:[t:1to(y)]alpha
+y@[i:is(y,x)][f:[t:1to(y)]alpha]
++*left
+f@t4:=lessisi2(y,x,i):lessis(y,x)
+t5:=lessisi2(x,y,symis(nat,y,x,i)):lessis(x,y)
+f1:=left(y,x,t5,f):[t:1to(x)]alpha
+f2:=left(t4,f1):[t:1to(y)]alpha
+[u:1to(y)]
+t6:=isinoutn(x,inn(y,u),trlessis(inn(y,u),y,x,1top(y,u),t4)):is(inn(y,u),inn(x,left1to(x,y,t4,u)))
+t7:=tris(1to(y),u,outn(y,inn(y,u),1top(y,u)),left1to(y,x,t5,left1to(x,y,t4,u)),isoutinn(y,u),isoutni(y,inn(y,u),1top(y,u),inn(x,left1to(x,y,t4,u)),trlessis(inn(x,left1to(x,y,t4,u)),x,y,1top(x,left1to(x,y,t4,u)),t5),t6)):is"e"(1to(y),u,left1to(y,x,t5,left1to(x,y,t4,u)))
+t8:=isf(1to(y),alpha,f,u,left1to(y,x,t5,left1to(x,y,t4,u)),t7):is"e"(alpha,<u>f,<u>f2)
+-left
+f@thleft:=fisi(1to(y),alpha,f,f2".left",[t:1to(y)]t8".left"(t)):is"e"([t:1to(y)]alpha,f,left(x,y,lessisi2(y,x,i),left(y,x,lessisi2(x,y,symis(nat,y,x,i)),f)))
+@frac:=pair1type(nat):'type'
+[x1:nat][x2:nat]
+fr:=pair1(nat,x1,x2):frac
+@[x:frac]
+num:=first1(nat,x):nat
+den:=second1(nat,x):nat
+x2@numis:=first1is1(nat,x1,x2):is(num(fr(x1,x2)),x1)
+isnum:=first1is2(nat,x1,x2):is(x1,num(fr(x1,x2)))
+denis:=second1is1(nat,x1,x2):is(den(fr(x1,x2)),x2)
+isden:=second1is2(nat,x1,x2):is(x2,den(fr(x1,x2)))
+x@1x:=num(x):nat
+2x:=den(x):nat
+fris:=pair1is1(nat,x):is"e"(frac,fr(1x,2x),x)
+isfr:=pair1is2(nat,x):is"e"(frac,x,fr(1x,2x))
+x2@[y1:nat][y2:nat]
+12isnd:=ists12(x1,num(fr(x1,x2)),y2,den(fr(y1,y2)),isnum(x1,x2),isden(y1,y2)):is(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))))
+ndis12:=symis(nat,ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),12isnd):is(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2))
+x@[n1:nat][n2:nat]
+1disnd:=ists1(n1,num(fr(n1,n2)),2x,isnum(n1,n2)):is(ts(n1,2x),ts(num(fr(n1,n2)),2x))
+ndis1d:=symis(nat,ts(n1,2x),ts(num(fr(n1,n2)),2x),1disnd):is(ts(num(fr(n1,n2)),2x),ts(n1,2x))
+n2isnd:=ists2(n2,den(fr(n1,n2)),1x,isden(n1,n2)):is(ts(1x,n2),ts(1x,den(fr(n1,n2))))
+ndisn2:=symis(nat,ts(1x,n2),ts(1x,den(fr(n1,n2))),n2isnd):is(ts(1x,den(fr(n1,n2))),ts(1x,n2))
+x2@[n:nat][i:is(x1,n)]
+isn:=isf(nat,frac,[t:nat]fr(t,x2),x1,n,i):is"e"(frac,fr(x1,x2),fr(n,x2))
+n@[i:is(x2,n)]
+isd:=isf(nat,frac,[t:nat]fr(x1,t),x2,n,i):is"e"(frac,fr(x1,x2),fr(x1,n))
+y2@[i:is(x1,y1)][j:is(x2,y2)]
+isnd:=tris(frac,fr(x1,x2),fr(y1,x2),fr(y1,y2),isn(x1,x2,y1,i),isd(y1,x2,y2,j)):is"e"(frac,fr(x1,x2),fr(y1,y2))
+x@[y:frac]
+1y:=num(y):nat
+2y:=den(y):nat
+eq:=is(ts(1x,2y),ts(1y,2x)):'prop'
+y2@[i:is(ts(x1,y2),ts(y1,x2))]
+eqi12:=tr3is(nat,ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ndis12(x1,x2,y1,y2),i,12isnd(y1,y2,x1,x2)):eq(fr(x1,x2),fr(y1,y2))
+n2@[i:is(ts(1x,n2),ts(n1,2x))]
+eqi1:=isp(frac,[t:frac]eq(t,fr(n1,n2)),fr(1x,2x),x,eqi12(1x,2x,n1,n2,i),fris):eq(x,fr(n1,n2))
+n2@[i:is(ts(n1,2x),ts(1x,n2))]
+eqi2:=isp(frac,[t:frac]eq(fr(n1,n2),t),fr(1x,2x),x,eqi12(n1,n2,1x,2x,i),fris):eq(fr(n1,n2),x)
+x@satz37:=refis(nat,ts(1x,2x)):eq(x,x)
+refeq:=satz37:eq(x,x)
+y@[i:is"e"(frac,x,y)]
+refeq1:=isp(frac,[t:frac]eq(x,t),x,y,refeq,i):eq(x,y)
+refeq2:=isp(frac,[t:frac]eq(t,x),x,y,refeq,i):eq(y,x)
+y2@[i:is(x1,y1)][j:is(x2,y2)]
+eqnd:=refeq1(fr(x1,x2),fr(y1,y2),isnd(i,j)):eq(fr(x1,x2),fr(y1,y2))
+x2@[n:nat][i:is(x1,n)]
+eqn:=refeq1(fr(x1,x2),fr(n,x2),isn(n,i)):eq(fr(x1,x2),fr(n,x2))
+n@[i:is(x2,n)]
+eqd:=refeq1(fr(x1,x2),fr(x1,n),isd(n,i)):eq(fr(x1,x2),fr(x1,n))
+y@[e:eq(x,y)]
+satz38:=symis(nat,ts(1x,2y),ts(1y,2x),e):eq(y,x)
+symeq:=satz38:eq(y,x)
+@[a:nat][b:nat][c:nat][d:nat]
++ii1
+t1:=tris(nat,ts(b,ts(c,d)),ts(ts(b,c),d),ts(d,ts(b,c)),assts2(b,c,d),comts(ts(b,c),d)):is(ts(b,ts(c,d)),ts(d,ts(b,c)))
+-ii1
+stets:=tr4is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(b,c))),ts(ts(a,d),ts(b,c)),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(b,c)),a,t1".ii1"),assts2(a,d,ts(b,c)),ists2(ts(b,c),ts(c,b),ts(a,d),comts(b,c))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
++*ii1
+d@t2:=tr3is(nat,ts(b,ts(c,d)),ts(ts(c,d),b),ts(ts(d,c),b),ts(d,ts(c,b)),comts(b,ts(c,d)),ists1(ts(c,d),ts(d,c),b,comts(c,d)),assts1(d,c,b)):is(ts(b,ts(c,d)),ts(d,ts(c,b)))
+anders:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(c,b))),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(c,b)),a,t2),assts2(a,d,ts(c,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
+-ii1
+y@[z:frac]
+1z:=num(z):nat
+2z:=den(z):nat
+[e:eq(x,y)][f:eq(y,z)]
++139
+t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
+t2:=stets(1x,2y,1y,2z):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)))
+t3:=tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)))
+t4:=tr3is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),symis(nat,ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),t2),t1,t3):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
+-139
+satz39:=satz33b(ts(1x,2z),ts(1z,2x),ts(1y,2y),t4".139"):eq(x,z)
++*139
+f@anders:=tr4is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2z,1y,2y),ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
+-139
+f@treq:=satz39:eq(x,z)
+z@[e:eq(z,x)][f:eq(z,y)]
+treq1:=treq(x,z,y,symeq(z,x,e),f):eq(x,y)
+z@[e:eq(x,z)][f:eq(y,z)]
+treq2:=treq(x,z,y,e,symeq(y,z,f)):eq(x,y)
+z@[u:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)]
+tr3eq:=treq(x,y,u,e,treq(y,z,u,f,g)):eq(x,u)
+u@[v:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)][h:eq(u,v)]
+tr4eq:=tr3eq(x,y,z,v,e,f,treq(z,u,v,g,h)):eq(x,v)
+x@[n:nat]
+satz40:=eqi1(ts(1x,n),ts(2x,n),tris(nat,ts(1x,ts(2x,n)),ts(1x,ts(n,2x)),ts(ts(1x,n),2x),ists2(ts(2x,n),ts(n,2x),1x,comts(2x,n)),assts2(1x,n,2x))):eq(x,fr(ts(1x,n),ts(2x,n)))
+satz40a:=symeq(x,fr(ts(1x,n),ts(2x,n)),satz40):eq(fr(ts(1x,n),ts(2x,n)),x)
+x2@[n:nat]
+satz40b:=eqi12(ts(x1,n),ts(x2,n),tris(nat,ts(x1,ts(x2,n)),ts(x1,ts(n,x2)),ts(ts(x1,n),x2),ists2(ts(x2,n),ts(n,x2),x1,comts(x2,n)),assts2(x1,n,x2))):eq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)))
+satz40c:=symeq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)),satz40b):eq(fr(ts(x1,n),ts(x2,n)),fr(x1,x2))
+y@moref:=more(ts(1x,2y),ts(1y,2x)):'prop'
+lessf:=less(ts(1x,2y),ts(1y,2x)):'prop'
+y2@[m:more(ts(x1,y2),ts(y1,x2))]
+morefi12:=ismore12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),m):moref(fr(x1,x2),fr(y1,y2))
+y2@[l:less(ts(x1,y2),ts(y1,x2))]
+lessfi12:=isless12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),l):lessf(fr(x1,x2),fr(y1,y2))
+n2@[m:more(ts(1x,n2),ts(n1,2x))]
+morefi1:=ismore12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),m):moref(x,fr(n1,n2))
+n2@[m:more(ts(n1,2x),ts(1x,n2))]
+morefi2:=ismore12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),m):moref(fr(n1,n2),x)
+n2@[l:less(ts(1x,n2),ts(n1,2x))]
+lessfi1:=isless12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),l):lessf(x,fr(n1,n2))
+n2@[l:less(ts(n1,2x),ts(1x,n2))]
+lessfi2:=isless12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),l):lessf(fr(n1,n2),x)
+y@satz41:=satz10(ts(1x,2y),ts(1y,2x)):orec3(eq(x,y),moref(x,y),lessf(x,y))
+satz41a:=satz10a(ts(1x,2y),ts(1y,2x)):or3(eq(x,y),moref(x,y),lessf(x,y))
+satz41b:=satz10b(ts(1x,2y),ts(1y,2x)):ec3(eq(x,y),moref(x,y),lessf(x,y))
+[m:moref(x,y)]
+satz42:=satz11(ts(1x,2y),ts(1y,2x),m):lessf(y,x)
+y@[l:lessf(x,y)]
+satz43:=satz12(ts(1x,2y),ts(1y,2x),l):moref(y,x)
+u@1u:=num(u):nat
+2u:=den(u):nat
+[m:moref(x,y)][e:eq(x,z)][f:eq(y,u)]
++244
+t1:=ists12(ts(1y,2u),ts(1u,2y),ts(1z,2x),ts(1x,2z),f,symeq(x,z,e)):is(ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)))
+t2:=tr3is(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)),ts(ts(1u,2z),ts(1x,2y)),stets(1y,2x,1z,2u),t1,stets(1u,2y,1x,2z)):is(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)))
+t3:=ismore1(ts(ts(1u,2z),ts(1x,2y)),ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)),symis(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)),t2),satz32d(ts(1x,2y),ts(1y,2x),ts(1u,2z),m)):more(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)))
+-244
+satz44:=satz33a(ts(1z,2u),ts(1u,2z),ts(1y,2x),ismore1(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1z,2u),ts(1y,2x)),ts(ts(1u,2z),ts(1y,2x)),comts(ts(1y,2x),ts(1z,2u)),t3".244")):moref(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][m:moref(x,z)]
+eqmoref12:=satz44(x,z,y,u,m,e,f):moref(y,u)
+z@[e:eq(x,y)][m:moref(x,z)]
+eqmoref1:=satz44(x,z,y,z,m,e,refeq(z)):moref(y,z)
+e@[m:moref(z,x)]
+eqmoref2:=satz44(z,x,z,y,m,refeq(z),e):moref(z,y)
+u@[l:lessf(x,y)][e:eq(x,z)][f:eq(y,u)]
+satz45:=satz42(u,z,satz44(y,x,u,z,satz43(x,y,l),f,e)):lessf(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][l:lessf(x,z)]
+eqlessf12:=satz45(x,z,y,u,l,e,f):lessf(y,u)
+z@[e:eq(x,y)][l:lessf(x,z)]
+eqlessf1:=satz45(x,z,y,z,l,e,refeq(z)):lessf(y,z)
+e@[l:lessf(z,x)]
+eqlessf2:=satz45(z,x,z,y,l,refeq(z),e):lessf(z,y)
+y@moreq:=or(moref(x,y),eq(x,y)):'prop'
+lesseq:=or(lessf(x,y),eq(x,y)):'prop'
+[e:eq(x,y)]
+moreqi2:=ori2(moref(x,y),eq(x,y),e):moreq(x,y)
+lesseqi2:=ori2(lessf(x,y),eq(x,y),e):lesseq(x,y)
+y@[m:moref(x,y)]
+moreqi1:=ori1(moref(x,y),eq(x,y),m):moreq(x,y)
+y@[l:lessf(x,y)]
+lesseqi1:=ori1(lessf(x,y),eq(x,y),l):lesseq(x,y)
+y@[m:moreq(x,y)]
+satz41c:=th7"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,comor(moref(x,y),eq(x,y),m)):not(lessf(x,y))
+y@[l:lesseq(x,y)]
+satz41d:=th9"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,l):not(moref(x,y))
+y@[n:not(moref(x,y))]
+satz41e:=th2"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n):lesseq(x,y)
+y@[n:not(lessf(x,y))]
+satz41f:=comor(eq(x,y),moref(x,y),th3"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n)):moreq(x,y)
+y@[m:moref(x,y)]
+satz41g:=th3"l.or"(lessf(x,y),eq(x,y),ec3e23(eq(x,y),moref(x,y),lessf(x,y),satz41b,m),ec3e21(eq(x,y),moref(x,y),lessf(x,y),satz41b,m)):not(lesseq(x,y))
+y@[l:lessf(x,y)]
+satz41h:=th3"l.or"(moref(x,y),eq(x,y),ec3e32(eq(x,y),moref(x,y),lessf(x,y),satz41b,l),ec3e31(eq(x,y),moref(x,y),lessf(x,y),satz41b,l)):not(moreq(x,y))
+y@[n:not(moreq(x,y))]
+satz41j:=or3e3(eq(x,y),moref(x,y),lessf(x,y),satz41a,th5"l.or"(moref(x,y),eq(x,y),n),th4"l.or"(moref(x,y),eq(x,y),n)):lessf(x,y)
+y@[n:not(lesseq(x,y))]
+satz41k:=or3e2(eq(x,y),moref(x,y),lessf(x,y),satz41a,th4"l.or"(lessf(x,y),eq(x,y),n),th5"l.or"(lessf(x,y),eq(x,y),n)):moref(x,y)
+u@[m:moreq(x,y)][e:eq(x,z)][f:eq(y,u)]
++246
+[n:moref(x,y)]
+t1:=ori1(moref(z,u),eq(z,u),satz44(n,e,f)):moreq(z,u)
+f@[g:eq(x,y)]
+t2:=ori2(moref(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):moreq(z,u)
+-246
+satz46:=orapp(moref(x,y),eq(x,y),moreq(z,u),m,[t:moref(x,y)]t1".246"(t),[t:eq(x,y)]t2".246"(t)):moreq(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][m:moreq(x,z)]
+eqmoreq12:=satz46(x,z,y,u,m,e,f):moreq(y,u)
+z@[e:eq(x,y)][m:moreq(x,z)]
+eqmoreq1:=satz46(x,z,y,z,m,e,refeq(z)):moreq(y,z)
+e@[m:moreq(z,x)]
+eqmoreq2:=satz46(z,x,z,y,m,refeq(z),e):moreq(z,y)
+u@[l:lesseq(x,y)][e:eq(x,z)][f:eq(y,u)]
++247
+[k:lessf(x,y)]
+t1:=ori1(lessf(z,u),eq(z,u),satz45(k,e,f)):lesseq(z,u)
+f@[g:eq(x,y)]
+t2:=ori2(lessf(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):lesseq(z,u)
+-247
+satz47:=orapp(lessf(x,y),eq(x,y),lesseq(z,u),l,[t:lessf(x,y)]t1".247"(t),[t:eq(x,y)]t2".247"(t)):lesseq(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][l:lesseq(x,z)]
+eqlesseq12:=satz47(x,z,y,u,l,e,f):lesseq(y,u)
+z@[e:eq(x,y)][l:lesseq(x,z)]
+eqlesseq1:=satz47(x,z,y,z,l,e,refeq(z)):lesseq(y,z)
+e@[l:lesseq(z,x)]
+eqlesseq2:=satz47(z,x,z,y,l,refeq(z),e):lesseq(z,y)
+y@[m:moreq(x,y)]
+satz48:=th9"l.or"(moref(x,y),eq(x,y),lessf(y,x),eq(y,x),m,[t:moref(x,y)]satz42(x,y,t),[t:eq(x,y)]satz38(x,y,t)):lesseq(y,x)
+y@[l:lesseq(x,y)]
+satz49:=th9"l.or"(lessf(x,y),eq(x,y),moref(y,x),eq(y,x),l,[t:lessf(x,y)]satz43(x,y,t),[t:eq(x,y)]satz38(x,y,t)):moreq(y,x)
+z@[l:lessf(x,y)][k:lessf(y,z)]
++250
+t1:=satz34a(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),l,k):less(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
+t2:=isless12(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2y,1y,2z),tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))),t1):less(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
+-250
+satz50:=satz33c(ts(1x,2z),ts(1z,2x),ts(1y,2y),t2".250"):lessf(x,z)
+trlessf:=satz50:lessf(x,z)
+z@[m:moref(x,y)][n:moref(y,z)]
+trmoref:=satz43(z,x,satz50(z,y,x,satz42(y,z,n),satz42(x,y,m))):moref(x,z)
+z@[l:lesseq(x,y)][k:lessf(y,z)]
+satz51a:=orapp(lessf(x,y),eq(x,y),lessf(x,z),l,[t:lessf(x,y)]satz50(t,k),[t:eq(x,y)]eqlessf1(y,x,z,symeq(x,y,t),k)):lessf(x,z)
+z@[l:lessf(x,y)][k:lesseq(y,z)]
+satz51b:=orapp(lessf(y,z),eq(y,z),lessf(x,z),k,[t:lessf(y,z)]satz50(l,t),[t:eq(y,z)]eqlessf2(y,z,x,t,l)):lessf(x,z)
+z@[m:moreq(x,y)][n:moref(y,z)]
+satz51c:=satz43(z,x,satz51b(z,y,x,satz42(y,z,n),satz48(x,y,m))):moref(x,z)
+z@[m:moref(x,y)][n:moreq(y,z)]
+satz51d:=satz43(z,x,satz51a(z,y,x,satz48(y,z,n),satz42(x,y,m))):moref(x,z)
+z@[l:lesseq(x,y)][k:lesseq(y,z)]
++252
+[e:eq(x,y)][f:eq(y,z)]
+t1:=ori2(lessf(x,z),eq(x,z),treq(x,y,z,e,f)):lesseq(x,z)
+e@[j:lessf(y,z)]
+t2:=ori1(lessf(x,z),eq(x,z),satz51a(l,j)):lesseq(x,z)
+e@t3:=orapp(lessf(y,z),eq(y,z),lesseq(x,z),k,[t:lessf(y,z)]t2(t),[t:eq(y,z)]t1(t)):lesseq(x,z)
+k@[j:lessf(x,y)]
+t4:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
+-252
+satz52:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t4".252"(t),[t:eq(x,y)]t3".252"(t)):lesseq(x,z)
+trlesseq:=satz52:lesseq(x,z)
++*252
+k@[j:lessf(x,y)]
+t5:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
+k@[e:eq(x,y)]
+t6:=eqlesseq1(y,x,z,symeq(x,y,e),k):lesseq(x,z)
+k@anders:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t5(t),[t:eq(x,y)]t6(t)):lesseq(x,z)
+-252
+z@[m:moreq(x,y)][n:moreq(y,z)]
+trmoreq:=satz49(z,x,satz52(z,y,x,satz48(y,z,n),satz48(x,y,m))):moreq(x,z)
++253
+x@t1:=ismore1(pl(ts(1x,2x),ts(1x,2x)),ts(pl(1x,1x),2x),ts(1x,2x),distpt1(1x,1x,2x),satz18(ts(1x,2x),ts(1x,2x))):more(ts(pl(1x,1x),2x),ts(1x,2x))
+t2:=morefi2(pl(1x,1x),2x,t1):moref(fr(pl(1x,1x),2x),x)
+-253
+x@satz53:=somei(frac,[t:frac]moref(t,x),fr(pl(1x,1x),2x),t2".253"):some"l"(frac,[t:frac]moref(t,x))
++254
+t1:=isless2(pl(ts(1x,2x),ts(1x,2x)),ts(1x,pl(2x,2x)),ts(1x,2x),distpt2(1x,2x,2x),satz18a(ts(1x,2x),ts(1x,2x))):less(ts(1x,2x),ts(1x,pl(2x,2x)))
+t2:=lessfi2(1x,pl(2x,2x),t1):lessf(fr(1x,pl(2x,2x)),x)
+-254
+satz54:=somei(frac,[t:frac]lessf(t,x),fr(1x,pl(2x,2x)),t2".254"):some"l"(frac,[t:frac]lessf(t,x))
+y@[l:lessf(x,y)]
++255
+t1:=satz19f(ts(1x,2y),ts(1y,2x),ts(1x,2x),l):less(pl(ts(1x,2x),ts(1x,2y)),pl(ts(1x,2x),ts(1y,2x)))
+t2:=satz19c(ts(1x,2y),ts(1y,2x),ts(1y,2y),l):less(pl(ts(1x,2y),ts(1y,2y)),pl(ts(1y,2x),ts(1y,2y)))
+t3:=isless12(pl(ts(1x,2x),ts(1x,2y)),ts(1x,pl(2x,2y)),pl(ts(1x,2x),ts(1y,2x)),ts(pl(1x,1y),2x),distpt2(1x,2x,2y),distpt1(1x,1y,2x),t1):less(ts(1x,pl(2x,2y)),ts(pl(1x,1y),2x))
+t4:=lessfi1(pl(1x,1y),pl(2x,2y),t3):lessf(x,fr(pl(1x,1y),pl(2x,2y)))
+t5:=isless12(pl(ts(1x,2y),ts(1y,2y)),ts(pl(1x,1y),2y),pl(ts(1y,2x),ts(1y,2y)),ts(1y,pl(2x,2y)),distpt1(1x,1y,2y),distpt2(1y,2x,2y),t2):less(ts(pl(1x,1y),2y),ts(1y,pl(2x,2y)))
+t6:=lessfi2(y,pl(1x,1y),pl(2x,2y),t5):lessf(fr(pl(1x,1y),pl(2x,2y)),y)
+t7:=andi(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y),t4,t6):and(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y))
+-255
+satz55:=somei(frac,[t:frac]and(lessf(x,t),lessf(t,y)),fr(pl(1x,1y),pl(2x,2y)),t7".255"):some"l"(frac,[t:frac]and(lessf(x,t),lessf(t,y)))
+y@pf:=fr(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)):frac
++ii3
+y2@t1:=ispl12(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ts(y1,x2),ndis12(x1,x2,y1,y2),ndis12(y1,y2,x1,x2)):is(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),pl(ts(x1,y2),ts(y1,x2)))
+t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
+-ii3
+y2@pf12:=isnd(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),ts(den(fr(x1,x2)),den(fr(y1,y2))),pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2),t1".ii3",t2".ii3"):is"e"(frac,pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
++*ii3
+n2@t3:=ispl12(ts(1x,den(fr(n1,n2))),ts(1x,n2),ts(num(fr(n1,n2)),2x),ts(n1,2x),ndisn2(x,n1,n2),ndis1d(x,n1,n2)):is(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),pl(ts(1x,n2),ts(n1,2x)))
+t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
+-ii3
+n2@pf1:=isnd(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),ts(2x,den(fr(n1,n2))),pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2),t3".ii3",t4".ii3"):is"e"(frac,pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
++*ii3
+n2@t5:=ispl12(ts(num(fr(n1,n2)),2x),ts(n1,2x),ts(1x,den(fr(n1,n2))),ts(1x,n2),ndis1d(x,n1,n2),ndisn2(x,n1,n2)):is(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),pl(ts(n1,2x),ts(1x,n2)))
+t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
+-ii3
+n2@pf2:=isnd(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),ts(den(fr(n1,n2)),2x),pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x),t5".ii3",t6".ii3"):is"e"(frac,pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
+y2@pfeq12a:=refeq1(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
+pfeq12b:=refeq2(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf(fr(x1,x2),fr(y1,y2)))
+n2@pfeq1a:=refeq1(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
+pfeq1b:=refeq2(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf(x,fr(n1,n2)))
+pfeq2a:=refeq1(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
+pfeq2b:=refeq2(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf(fr(n1,n2),x))
+u@[e:eq(x,y)][f:eq(z,u)]
++356
+t1:=ists1(ts(1x,2y),ts(1y,2x),ts(2z,2u),e):is(ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)))
+t2:=t1(z,u,x,y,f,e):is(ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)))
+t3:=tr3is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2z),ts(2u,2y)),ts(ts(1x,2y),ts(2u,2z)),ts(ts(1x,2y),ts(2z,2u)),ists2(ts(2y,2u),ts(2u,2y),ts(1x,2z),comts(2y,2u)),stets(1x,2z,2u,2y),ists2(ts(2u,2z),ts(2z,2u),ts(1x,2y),comts(2u,2z))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)))
+t4:=tr4is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)),ts(ts(1y,2u),ts(2z,2x)),ts(ts(1y,2u),ts(2x,2z)),t3,t1,stets(1y,2x,2z,2u),ists2(ts(2z,2x),ts(2x,2z),ts(1y,2u),comts(2z,2x))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)))
+t5:=tr4is(nat,ts(ts(1z,2x),ts(2y,2u)),ts(ts(1z,2u),ts(2y,2x)),ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)),ts(ts(1u,2y),ts(2x,2z)),stets(1z,2x,2y,2u),ists2(ts(2y,2x),ts(2x,2y),ts(1z,2u),comts(2y,2x)),t2,stets(1u,2z,2x,2y)):is(ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)))
+t6:=ispl12(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)),ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)),t4,t5):is(pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))))
+t7:=tr3is(nat,ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)),disttp1(ts(1x,2z),ts(1z,2x),ts(2y,2u)),t6,distpt1(ts(1y,2u),ts(1u,2y),ts(2x,2z))):is(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)))
+-356
+satz56:=eqi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2u),ts(1u,2y)),ts(2y,2u),t7".356"):eq(pf(x,z),pf(y,u))
+eqpf12:=satz56:eq(pf(x,z),pf(y,u))
+z@[e:eq(x,y)]
+eqpf1:=eqpf12(x,y,z,z,e,refeq(z)):eq(pf(x,z),pf(y,z))
+eqpf2:=eqpf12(z,z,x,y,refeq(z),e):eq(pf(z,x),pf(z,y))
+x2@[n:nat]
+satz57:=tr3eq(pf(fr(x1,n),fr(x2,n)),fr(pl(ts(x1,n),ts(x2,n)),ts(n,n)),fr(ts(pl(x1,x2),n),ts(n,n)),fr(pl(x1,x2),n),pfeq12a(x1,n,x2,n),eqn(pl(ts(x1,n),ts(x2,n)),ts(n,n),ts(pl(x1,x2),n),distpt1(x1,x2,n)),satz40c(pl(x1,x2),n,n)):eq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n))
+satz57a:=symeq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n),satz57):eq(fr(pl(x1,x2),n),pf(fr(x1,n),fr(x2,n)))
+y@satz58:=eqnd(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),pl(ts(1y,2x),ts(1x,2y)),ts(2y,2x),compl(ts(1x,2y),ts(1y,2x)),comts(2x,2y)):eq(pf(x,y),pf(y,x))
+compf:=satz58:eq(pf(x,y),pf(y,x))
++359
+z@t1:=tr3is(nat,ts(ts(1y,2x),2z),ts(ts(2x,1y),2z),ts(2x,ts(1y,2z)),ts(ts(1y,2z),2x),ists1(ts(1y,2x),ts(2x,1y),2z,comts(1y,2x)),assts1(2x,1y,2z),comts(2x,ts(1y,2z))):is(ts(ts(1y,2x),2z),ts(ts(1y,2z),2x))
+t2:=ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),t1):is(pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
+t3:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),t2):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
+t4:=tris(nat,ts(1z,ts(2x,2y)),ts(1z,ts(2y,2x)),ts(ts(1z,2y),2x),ists2(ts(2x,2y),ts(2y,2x),1z,comts(2x,2y)),assts2(1z,2y,2x)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
+t5:=ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t3,t4):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)))
+t6:=ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x)):is(pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
+t7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),t5,asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),t6):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
+-359
+z@satz59:=tr3eq(pf(pf(x,y),z),fr(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z)),fr(pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z))),pf(x,pf(y,z)),pfeq2a(z,pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)),eqnd(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z)),t7".359",assts1(2x,2y,2z)),pfeq1b(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z))):eq(pf(pf(x,y),z),pf(x,pf(y,z)))
+asspf1:=satz59:eq(pf(pf(x,y),z),pf(x,pf(y,z)))
+asspf2:=symeq(pf(pf(x,y),z),pf(x,pf(y,z)),asspf1):eq(pf(x,pf(y,z)),pf(pf(x,y),z))
+c@stets1:=tr3is(nat,ts(ts(a,b),c),ts(a,ts(b,c)),ts(a,ts(c,b)),ts(ts(a,c),b),assts1(a,b,c),ists2(ts(b,c),ts(c,b),a,comts(b,c)),assts2(a,c,b)):is(ts(ts(a,b),c),ts(ts(a,c),b))
++*359
+z@t8:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),stets1(1y,2x,2z))):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
+t9:=tris(nat,ts(1z,ts(2x,2y)),ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),assts2(1z,2x,2y),stets1(1z,2x,2y)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
+anderst7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t8,t9),asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x))):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
+-359
++360
+y@t1:=satz18(ts(1x,2y),ts(1y,2x)):more(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y))
+t2:=satz32a(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y),2x,t1):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(ts(1x,2y),2x))
+t3:=tris(nat,ts(ts(1x,2y),2x),ts(1x,ts(2y,2x)),ts(1x,ts(2x,2y)),assts1(1x,2y,2x),ists2(ts(2y,2x),ts(2x,2y),1x,comts(2y,2x))):is(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)))
+t4:=ismore2(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)),ts(pl(ts(1x,2y),ts(1y,2x)),2x),t3,t2):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(1x,ts(2x,2y)))
+-360
+y@satz60:=morefi2(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),t4".360"):moref(pf(x,y),x)
+satz60a:=satz42(pf(x,y),x,satz60):lessf(x,pf(x,y))
+z@[m:moref(x,y)]
++361
+t1:=satz32a(ts(1x,2y),ts(1y,2x),2z,m):more(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z))
+t2:=ismore12(ts(ts(1x,2y),2z),ts(ts(1x,2z),2y),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),stets1(1x,2y,2z),stets1(1y,2x,2z),t1):more(ts(ts(1x,2z),2y),ts(ts(1y,2z),2x))
+t3:=stets1(1z,2x,2y):is(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x))
+t4:=satz19h(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),ts(ts(1x,2z),2y),ts(ts(1y,2z),2x),t3,t2):more(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)))
+t5:=ismore12(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),ts(pl(ts(1x,2z),ts(1z,2x)),2y),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),distpt1(ts(1x,2z),ts(1z,2x),2y),distpt1(ts(1y,2z),ts(1z,2y),2x),t4):more(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x))
+t6:=satz32a(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z,t5):more(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z))
+t7:=ismore12(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)),assts1(pl(ts(1x,2z),ts(1z,2x)),2y,2z),assts1(pl(ts(1y,2z),ts(1z,2y)),2x,2z),t6):more(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)))
+-361
+satz61:=morefi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z),t7".361"):moref(pf(x,z),pf(y,z))
+z@[m:moref(x,y)]
+satz62a:=satz61(m):moref(pf(x,z),pf(y,z))
+z@[e:eq(x,y)]
+satz62b:=eqpf1(x,y,z,e):eq(pf(x,z),pf(y,z))
+z@[l:lessf(x,y)]
+satz62c:=satz42(pf(y,z),pf(x,z),satz61(y,x,z,satz43(l))):lessf(pf(x,z),pf(y,z))
+m@satz62d:=eqmoref12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62a):moref(pf(z,x),pf(z,y))
+e@satz62e:=eqpf2(x,y,z,e):eq(pf(z,x),pf(z,y))
+l@satz62f:=eqlessf12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62c):lessf(pf(z,x),pf(z,y))
+u@[e:eq(x,y)][m:moref(z,u)]
+satz62g:=eqmoref2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62d(z,u,x,m)):moref(pf(x,z),pf(y,u))
+satz62h:=eqmoref12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62g):moref(pf(z,x),pf(u,y))
+e@[l:lessf(z,u)]
+satz62j:=eqlessf2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62f(z,u,x,l)):lessf(pf(x,z),pf(y,u))
+satz62k:=eqlessf12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62j):lessf(pf(z,x),pf(u,y))
++363
+z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
+t2:=satz41b(pf(x,z),pf(y,z)):ec3(eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)))
+-363
+z@[m:moref(pf(x,z),pf(y,z))]
+satz63a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),m):moref(x,y)
+z@[e:eq(pf(x,z),pf(y,z))]
+satz63b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),e):eq(x,y)
+z@[l:lessf(pf(x,z),pf(y,z))]
+satz63c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),l):lessf(x,y)
+z@[m:moref(pf(z,x),pf(z,y))]
+satz63d:=satz63a(eqmoref12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),m)):moref(x,y)
+z@[e:eq(pf(z,x),pf(z,y))]
+satz63e:=satz63b(tr3eq(pf(x,z),pf(z,x),pf(z,y),pf(y,z),compf(x,z),e,compf(z,y))):eq(x,y)
+z@[f:lessf(pf(z,x),pf(z,y))]
+satz63f:=satz63c(eqlessf12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),f)):lessf(x,y)
+u@[m:moref(x,y)][n:moref(z,u)]
++364
+t1:=satz61(x,y,z,m):moref(pf(x,z),pf(y,z))
+t2:=eqmoref12(pf(z,y),pf(y,z),pf(u,y),pf(y,u),compf(z,y),compf(u,y),satz61(z,u,y,n)):moref(pf(y,z),pf(y,u))
+-364
+satz64:=trmoref(pf(x,z),pf(y,z),pf(y,u),t1".364",t2".364"):moref(pf(x,z),pf(y,u))
+u@[l:lessf(x,y)][k:lessf(z,u)]
+satz64a:=satz42(pf(y,u),pf(x,z),satz64(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
+u@[m:moreq(x,y)][n:moref(z,u)]
+satz65a:=orapp(moref(x,y),eq(x,y),moref(pf(x,z),pf(y,u)),m,[v:moref(x,y)]satz64(v,n),[v:eq(x,y)]satz62g(v,n)):moref(pf(x,z),pf(y,u))
+u@[m:moref(x,y)][n:moreq(z,u)]
+satz65b:=orapp(moref(z,u),eq(z,u),moref(pf(x,z),pf(y,u)),n,[v:moref(z,u)]satz64(m,v),[v:eq(z,u)]eqmoref2(pf(y,z),pf(y,u),pf(x,z),eqpf2(z,u,y,v),satz61(x,y,z,m))):moref(pf(x,z),pf(y,u))
+u@[l:lesseq(x,y)][k:lessf(z,u)]
+satz65c:=satz42(pf(y,u),pf(x,z),satz65a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
+u@[l:lessf(x,y)][k:lesseq(z,u)]
+satz65d:=satz42(pf(y,u),pf(x,z),satz65b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(pf(x,z),pf(y,u))
+u@[m:moreq(x,y)][n:moreq(z,u)]
++366
+[e:eq(x,y)][f:eq(z,u)]
+t1:=moreqi2(pf(x,z),pf(y,u),satz56(e,f)):moreq(pf(x,z),pf(y,u))
+e@[o:moref(z,u)]
+t2:=moreqi1(pf(x,z),pf(y,u),satz65a(m,o)):moreq(pf(x,z),pf(y,u))
+e@t3:=orapp(moref(z,u),eq(z,u),moreq(pf(x,z),pf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(pf(x,z),pf(y,u))
+n@[o:moref(x,y)]
+t4:=moreqi1(pf(x,z),pf(y,u),satz65b(o,n)):moreq(pf(x,z),pf(y,u))
+-366
+satz66:=orapp(moref(x,y),eq(x,y),moreq(pf(x,z),pf(y,u)),m,[v:moref(x,y)]t4".366"(v),[v:eq(x,y)]t3".366"(v)):moreq(pf(x,z),pf(y,u))
+u@[l:lesseq(x,y)][k:lesseq(z,u)]
+satz66a:=satz48(pf(y,u),pf(x,z),satz66(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(pf(x,z),pf(y,u))
+y@[l:lesseq(x,y)]
++367
+[v:frac][e:eq(pf(y,v),x)]
+t1:=eqmoref1(pf(y,v),x,y,e,satz60(y,v)):moref(x,y)
+v@t2:=th3"l.imp"(eq(pf(y,v),x),moref(x,y),satz41d(x,y,l),[t:eq(pf(y,v),x)]t1(t)):not(eq(pf(y,v),x))
+-367
+vorbemerkung67:=th5"l.some"(frac,[v:frac]eq(pf(y,v),x),[v:frac]t2".367"(v)):not(some"l"(frac,[t:frac]eq(pf(y,t),x)))
+y@[v:frac][w:frac][e:eq(pf(y,v),x)][f:eq(pf(y,w),x)]
+satz67b:=satz63e(v,w,y,treq2(pf(y,v),pf(y,w),x,e,f)):eq(v,w)
+y@[m:moref(x,y)]
++*367
+m@t3:=onei(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),satz8b(ts(1x,2y),ts(1y,2x)),m):one([t:nat]diffprop(ts(1x,2y),ts(1y,2x),t))
+vo:=ind(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):nat
+t4:=oneax(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):is(ts(1x,2y),pl(ts(1y,2x),vo))
+w:=fr(vo,ts(2x,2y)):frac
+t5:=treq(y,fr(ts(1y,2x),ts(2y,2x)),fr(ts(1y,2x),ts(2x,2y)),satz40(y,2x),eqd(ts(1y,2x),ts(2y,2x),ts(2x,2y),comts(2y,2x))):eq(y,fr(ts(1y,2x),ts(2x,2y)))
+t6:=tr4eq(pf(y,w),pf(fr(ts(1y,2x),ts(2x,2y)),fr(vo,ts(2x,2y))),fr(pl(ts(1y,2x),vo),ts(2x,2y)),fr(ts(1x,2y),ts(2x,2y)),x,eqpf1(y,fr(ts(1y,2x),ts(2x,2y)),w,t5),satz57(ts(1y,2x),vo,ts(2x,2y)),eqn(pl(ts(1y,2x),vo),ts(2x,2y),ts(1x,2y),symis(nat,ts(1x,2y),pl(ts(1y,2x),vo),t4)),satz40a(x,2y)):eq(pf(y,w),x)
+-367
+m@satz67a:=somei(frac,[t:frac]eq(pf(y,t),x),w".367",t6".367"):some"l"(frac,[t:frac]eq(pf(y,t),x))
+mf:=w".367":frac
+satz67c:=t6".367":eq(pf(y,mf(x,y,m)),x)
+satz67d:=symeq(pf(y,mf(x,y,m)),x,satz67c):eq(x,pf(y,mf(x,y,m)))
+y@[v:frac][m:moref(x,y)][e:eq(pf(y,v),x)]
+satz67e:=satz67b(v,mf(x,y,m),e,satz67c(m)):eq(v,mf(x,y,m))
+y@tf:=fr(ts(1x,1y),ts(2x,2y)):frac
++ii4
+y2@t1:=ists12(num(fr(x1,x2)),x1,num(fr(y1,y2)),y1,numis(x1,x2),numis(y1,y2)):is(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(x1,y1))
+t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
+-ii4
+y2@tf12:=isnd(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y1),ts(x2,y2),t1".ii4",t2".ii4"):is"e"(frac,tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
++*ii4
+n2@t3:=ists2(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(1x,num(fr(n1,n2))),ts(1x,n1))
+t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
+-ii4
+n2@tf1:=isnd(ts(1x,num(fr(n1,n2))),ts(2x,den(fr(n1,n2))),ts(1x,n1),ts(2x,n2),t3".ii4",t4".ii4"):is"e"(frac,tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
++*ii4
+n2@t5:=ists1(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(num(fr(n1,n2)),1x),ts(n1,1x))
+t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
+-ii4
+n2@tf2:=isnd(ts(num(fr(n1,n2)),1x),ts(den(fr(n1,n2)),2x),ts(n1,1x),ts(n2,2x),t5".ii4",t6".ii4"):is"e"(frac,tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
+y2@tfeq12a:=refeq1(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
+tfeq12b:=refeq2(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(fr(ts(x1,y1),ts(x2,y2)),tf(fr(x1,x2),fr(y1,y2)))
+n2@tfeq1a:=refeq1(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
+tfeq1b:=refeq2(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(fr(ts(1x,n1),ts(2x,n2)),tf(x,fr(n1,n2)))
+tfeq2a:=refeq1(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
+tfeq2b:=refeq2(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(fr(ts(n1,1x),ts(n2,2x)),tf(fr(n1,n2),x))
+u@[e:eq(x,y)][f:eq(z,u)]
++468
+t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1z,2u),ts(1u,2z),e,f):is(ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)))
+-468
+d@stets2:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(ts(a,b),ts(d,c)),ts(ts(a,c),ts(d,b)),ts(ts(a,c),ts(b,d)),ists2(ts(c,d),ts(d,c),ts(a,b),comts(c,d)),stets(a,b,d,c),ists2(ts(d,b),ts(b,d),ts(a,c),comts(d,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,c),ts(b,d)))
++*468
+f@t2:=tr3is(nat,ts(ts(1x,1z),ts(2y,2u)),ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)),ts(ts(1y,1u),ts(2x,2z)),stets2(1x,1z,2y,2u),t1,stets2(1y,2x,1u,2z)):is(ts(ts(1x,1z),ts(2y,2u)),ts(ts(1y,1u),ts(2x,2z)))
+-468
+f@satz68:=eqi12(ts(1x,1z),ts(2x,2z),ts(1y,1u),ts(2y,2u),t2".468"):eq(tf(x,z),tf(y,u))
+eqtf12:=satz68:eq(tf(x,z),tf(y,u))
+z@[e:eq(x,y)]
+eqtf1:=eqtf12(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
+eqtf2:=eqtf12(z,z,x,y,refeq(z),e):eq(tf(z,x),tf(z,y))
+y@satz69:=eqnd(ts(1x,1y),ts(2x,2y),ts(1y,1x),ts(2y,2x),comts(1x,1y),comts(2x,2y)):eq(tf(x,y),tf(y,x))
+comtf:=satz69:eq(tf(x,y),tf(y,x))
+z@satz70:=tr3eq(tf(tf(x,y),z),fr(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z)),fr(ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z))),tf(x,tf(y,z)),tfeq2a(z,ts(1x,1y),ts(2x,2y)),eqnd(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z),ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z)),assts1(1x,1y,1z),assts1(2x,2y,2z)),tfeq1b(x,ts(1y,1z),ts(2y,2z))):eq(tf(tf(x,y),z),tf(x,tf(y,z)))
+asstf1:=satz70:eq(tf(tf(x,y),z),tf(x,tf(y,z)))
+asstf2:=symeq(tf(tf(x,y),z),tf(x,tf(y,z)),asstf1):eq(tf(x,tf(y,z)),tf(tf(x,y),z))
++471
+t1:=tr3eq(tf(x,pf(y,z)),fr(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z))),fr(pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),ts(2x,ts(2y,2z))),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),tfeq1a(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z)),eqn(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z)),pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),disttp2(1x,ts(1y,2z),ts(1z,2y))),satz57a(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))):eq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))))
+t2:=treq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(ts(1x,1y),2z),ts(ts(2x,2y),2z)),tf(x,y),eqnd(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z)),ts(ts(1x,1y),2z),ts(ts(2x,2y),2z),assts2(1x,1y,2z),assts2(2x,2y,2z)),satz40c(ts(1x,1y),ts(2x,2y),2z)):eq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y))
+t3:=treq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2z,2y))),tf(x,z),eqd(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)),ts(2x,ts(2z,2y)),ists2(ts(2y,2z),ts(2z,2y),2x,comts(2y,2z))),t2(x,z,y)):eq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z))
+-471
+satz71:=treq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),pf(tf(x,y),tf(x,z)),t1".471",eqpf12(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z),t2".471",t3".471")):eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
+disttpf1:=tr3eq(tf(pf(x,y),z),tf(z,pf(x,y)),pf(tf(z,x),tf(z,y)),pf(tf(x,z),tf(y,z)),comtf(pf(x,y),z),satz71(z,x,y),eqpf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y))):eq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)))
+disttpf2:=satz71:eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
+distptf1:=symeq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)),disttpf1):eq(pf(tf(x,z),tf(y,z)),tf(pf(x,y),z))
+distptf2:=symeq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),disttpf2):eq(pf(tf(x,y),tf(x,z)),tf(x,pf(y,z)))
+[m:moref(x,y)]
++472
+t1:=satz32a(ts(1x,2y),ts(1y,2x),ts(1z,2z),m):more(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1y,2x),ts(1z,2z)))
+t2:=ismore12(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,2x),ts(1z,2z)),ts(ts(1y,1z),ts(2x,2z)),stets2(1x,2y,1z,2z),stets2(1y,2x,1z,2z),t1):more(ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,1z),ts(2x,2z)))
+-472
+satz72a:=morefi12(ts(1x,1z),ts(2x,2z),ts(1y,1z),ts(2y,2z),t2".472"):moref(tf(x,z),tf(y,z))
+z@[e:eq(x,y)]
+satz72b:=satz68(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
+z@[l:lessf(x,y)]
+satz72c:=satz42(tf(y,z),tf(x,z),satz72a(y,x,z,satz43(x,y,l))):lessf(tf(x,z),tf(y,z))
+m@satz72d:=eqmoref12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72a):moref(tf(z,x),tf(z,y))
+e@satz72e:=eqtf2(x,y,z,e):eq(tf(z,x),tf(z,y))
+l@satz72f:=eqlessf12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72c):lessf(tf(z,x),tf(z,y))
+u@[e:eq(x,y)][m:moref(z,u)]
+satz72g:=eqmoref2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72d(z,u,x,m)):moref(tf(x,z),tf(y,u))
+satz72h:=eqmoref12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72g):moref(tf(z,x),tf(u,y))
+e@[l:lessf(z,u)]
+satz72j:=eqlessf2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72f(z,u,x,l)):lessf(tf(x,z),tf(y,u))
+satz72k:=eqlessf12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72j):lessf(tf(z,x),tf(u,y))
++473
+z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
+t2:=satz41b(tf(x,z),tf(y,z)):ec3(eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)))
+-473
+z@[m:moref(tf(x,z),tf(y,z))]
+satz73a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),m):moref(x,y)
+z@[e:eq(tf(x,z),tf(y,z))]
+satz73b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),e):eq(x,y)
+z@[l:lessf(tf(x,z),tf(y,z))]
+satz73c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),l):lessf(x,y)
+z@[m:moref(tf(z,x),tf(z,y))]
+satz73d:=satz73a(eqmoref12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),m)):moref(x,y)
+z@[e:eq(tf(z,x),tf(z,y))]
+satz73e:=satz73b(tr3eq(tf(x,z),tf(z,x),tf(z,y),tf(y,z),comtf(x,z),e,comtf(z,y))):eq(x,y)
+z@[l:lessf(tf(z,x),tf(z,y))]
+satz73f:=satz73c(eqlessf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),l)):lessf(x,y)
+u@[m:moref(x,y)][n:moref(z,u)]
++474
+t1:=satz72a(x,y,z,m):moref(tf(x,z),tf(y,z))
+t2:=eqmoref12(tf(z,y),tf(y,z),tf(u,y),tf(y,u),comtf(z,y),comtf(u,y),satz72a(z,u,y,n)):moref(tf(y,z),tf(y,u))
+-474
+satz74:=trmoref(tf(x,z),tf(y,z),tf(y,u),t1".474",t2".474"):moref(tf(x,z),tf(y,u))
+u@[l:lessf(x,y)][k:lessf(z,u)]
+satz74a:=satz42(tf(y,u),tf(x,z),satz74(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
+u@[m:moreq(x,y)][n:moref(z,u)]
+satz75a:=orapp(moref(x,y),eq(x,y),moref(tf(x,z),tf(y,u)),m,[v:moref(x,y)]satz74(v,n),[v:eq(x,y)]satz72g(v,n)):moref(tf(x,z),tf(y,u))
+u@[m:moref(x,y)][n:moreq(z,u)]
+satz75b:=orapp(moref(z,u),eq(z,u),moref(tf(x,z),tf(y,u)),n,[v:moref(z,u)]satz74(m,v),[v:eq(z,u)]eqmoref2(tf(y,z),tf(y,u),tf(x,z),eqtf2(z,u,y,v),satz72a(m))):moref(tf(x,z),tf(y,u))
+u@[l:lesseq(x,y)][k:lessf(z,u)]
+satz75c:=satz42(tf(y,u),tf(x,z),satz75a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
+u@[l:lessf(x,y)][k:lesseq(z,u)]
+satz75d:=satz42(tf(y,u),tf(x,z),satz75b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(tf(x,z),tf(y,u))
+u@[m:moreq(x,y)][n:moreq(z,u)]
++476
+[e:eq(x,y)][f:eq(z,u)]
+t1:=moreqi2(tf(x,z),tf(y,u),satz68(e,f)):moreq(tf(x,z),tf(y,u))
+e@[o:moref(z,u)]
+t2:=moreqi1(tf(x,z),tf(y,u),satz75a(m,o)):moreq(tf(x,z),tf(y,u))
+e@t3:=orapp(moref(z,u),eq(z,u),moreq(tf(x,z),tf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(tf(x,z),tf(y,u))
+n@[o:moref(x,y)]
+t4:=moreqi1(tf(x,z),tf(y,u),satz75b(o,n)):moreq(tf(x,z),tf(y,u))
+-476
+satz76:=orapp(moref(x,y),eq(x,y),moreq(tf(x,z),tf(y,u)),m,[v:moref(x,y)]t4".476"(v),[v:eq(x,y)]t3".476"(v)):moreq(tf(x,z),tf(y,u))
+u@[l:lesseq(x,y)][k:lesseq(z,u)]
+satz76a:=satz48(tf(y,u),tf(x,z),satz76(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(tf(x,z),tf(y,u))
+y@[v:frac][w:frac][e:eq(tf(y,v),x)][f:eq(tf(y,w),x)]
+satz77b:=satz73e(v,w,y,treq2(tf(y,v),tf(y,w),x,e,f)):eq(v,w)
++477
+y@v:=fr(ts(1x,2y),ts(2x,1y)):frac
+t1:=tr4eq(tf(y,v),tf(v,y),fr(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y)),fr(ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y))),x,comtf(y,v),tfeq2a(y,ts(1x,2y),ts(2x,1y)),eqnd(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y),ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y)),tris(nat,ts(ts(1x,2y),1y),ts(1x,ts(2y,1y)),ts(1x,ts(1y,2y)),assts1(1x,2y,1y),ists2(ts(2y,1y),ts(1y,2y),1x,comts(2y,1y))),assts1(2x,1y,2y)),satz40a(x,ts(1y,2y))):eq(tf(y,v),x)
+-477
+y@satz77a:=somei(frac,[t:frac]eq(tf(y,t),x),v".477",t1".477"):some"l"(frac,[t:frac]eq(tf(y,t),x))
++rt
+@eq:=[x:frac][y:frac]eq"n"(x,y):[x:frac][y:frac]'prop'
+refeq:=[x:frac]refeq"n"(x):[x:frac]<x><x>eq
+symeq:=[x:frac][y:frac][t:<y><x>eq]symeq"n"(x,y,t):[x:frac][y:frac][t:<y><x>eq]<x><y>eq
+treq:=[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]treq"n"(x,y,z,t,u):[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]<z><x>eq
+[x:frac][s:set(frac)]
+inf:=esti(frac,x,s):'prop'
+@rat:=ect"eq"(frac,eq,refeq,symeq,treq):'type'
+[x0:rat][y0:rat]
+is:=is"e"(rat,x0,y0):'prop'
+nis:=not(is(x0,y0)):'prop'
+@[p:[x:rat]'prop']
+some:=some"l"(rat,p):'prop'
+all:=all"l"(rat,p):'prop'
+one:=one"e"(rat,p):'prop'
+x0@[s:set(rat)]
+in:=esti(rat,x0,s):'prop'
+x@ratof:=ectelt"eq"(frac,eq,refeq,symeq,treq,x):rat
+x0@class:=ecect"eq"(frac,eq,refeq,symeq,treq,x0):set(frac)
+x@inclass:=th5"eq.4"(frac,eq,refeq,symeq,treq,x):inf(x,class(ratof(x)))
+x0@[x:frac][y:frac][xix0:inf(x,class(x0))][e:eq"n"(x,y)]
+lemmaeq1:=th8"eq.4"(frac,eq,refeq,symeq,treq,x0,x,xix0,y,e):inf(y,class(x0))
+x0@[a:'prop'][a1:[x:frac][xi:inf(x,class(x0))]a]
+ratapp1:=th3"eq.4"(frac,eq,refeq,symeq,treq,x0,a,a1):a
+y0@[a:'prop'][a1:[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]a][x:frac][xix0:inf(x,class(x0))]
++ii5
+t1:=ratapp1(y0,a,[y:frac][yi:inf(y,class(y0))]<yi><xix0><y><x>a1):a
+-ii5
+a1@ratapp2:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t1".ii5"(x,xi)):a
+y0@[z0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]a][x:frac][xix0:inf(x,class(x0))]
++*ii5
+xix0@t2:=ratapp2(y0,z0,a,[y:frac][z:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))]<zi><yi><xix0><z><y><x>a1):a
+-ii5
+a1@ratapp3:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t2".ii5"(x,xi)):a
+z0@[u0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]a][x:frac][xix0:inf(x,class(x0))]
++*ii5
+xix0@t3:=ratapp3(y0,z0,u0,a,[y:frac][z:frac][u:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]<ui><zi><yi><xix0><u><z><y><x>a1):a
+-ii5
+a1@ratapp4:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t3".ii5"(x,xi)):a
+y0@[x1:frac][y1:frac][x1ix0:inf(x1,class(x0))][y1iy0:inf(y1,class(y0))][e:eq"n"(x1,y1)]
+isi:=th3"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,e):is(x0,y0)
+y1iy0@[i:is(x0,y0)]
+ise:=th5"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,i):eq"n"(x1,y1)
+y1iy0@[n:not(eq"n"(x1,y1))]
+nisi:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),n,[t:is(x0,y0)]ise(t)):nis(x0,y0)
+y1iy0@[n:nis(x0,y0)]
+nise:=th3"l.imp"(eq"n"(x1,y1),is(x0,y0),n,[t:eq"n"(x1,y1)]isi(t)):not(eq"n"(x1,y1))
+@[alpha:'type'][f:[x:frac][y:frac]alpha]
+fixf:=fixfu2"eq"(frac,eq,refeq,symeq,treq,alpha,f):'prop'
+y0@[alpha:'type'][f:[x:frac][y:frac]alpha][ff:fixf(alpha,f)]
+indrat:=indeq2"eq"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0):alpha
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+isindrat:=th1"eq.11"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0,x,xix0,y,yiy0):is"e"(alpha,<y><x>f,indrat)
+x0@satz78:=refis(rat,x0):is(x0,x0)
+y0@[i:is(x0,y0)]
+satz79:=symis(rat,x0,y0,i):is(y0,x0)
+z0@[i:is(x0,y0)][j:is(y0,z0)]
+satz80:=tris(rat,x0,y0,z0,i,j):is(x0,z0)
+y0@more:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),moref(x,y)))):'prop'
++*ii5
+y1@propm:=and3(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1)):'prop'
+-ii5
+y0@[m:more(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propm".ii5"(t,u))][u:frac][p:propm".ii5"(t,u)]
++*ii5
+p@t4:=and3e1(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(t,class(x0))
+t5:=and3e2(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(u,class(y0))
+t6:=and3e3(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):moref(t,u)
+t7:=satz44(t,u,x,y,t6,ise(x0,x0,t,x,t4,xix0,refis(rat,x0)),ise(y0,y0,u,y,t5,yiy0,refis(rat,y0))):moref(x,y)
+s@t8:=someapp(frac,[u:frac]propm(t,u),s,moref(x,y),[u:frac][v:propm(t,u)]t7(u,v)):moref(x,y)
+-ii5
+yiy0@also18:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propm".ii5"(t,u)),m,moref(x,y),[t:frac][v:some"l"(frac,[u:frac]propm".ii5"(t,u))]t8".ii5"(t,v)):moref(x,y)
+y1iy0@[m:moref(x1,y1)]
++*ii5
+m@t9:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1),x1ix0,y1iy0,m):propm(x1,y1)
+t10:=somei(frac,[t:frac]propm(x1,t),y1,t9):some"l"(frac,[t:frac]propm(x1,t))
+-ii5
+m@morei:=somei(frac,[u:frac]some"l"(frac,[t:frac]propm".ii5"(u,t)),x1,t10".ii5"):more(x0,y0)
+y1iy0@[m:more(x0,y0)]
+moree:=also18(m,x1,y1,x1ix0,y1iy0):moref(x1,y1)
+z0@[i:is(x0,y0)][m:more(x0,z0)]
+ismore1:=isp(rat,[t:rat]more(t,z0),x0,y0,m,i):more(y0,z0)
+i@[m:more(z0,x0)]
+ismore2:=isp(rat,[t:rat]more(z0,t),x0,y0,m,i):more(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][m:more(x0,z0)]
+ismore12:=ismore2(z0,u0,y0,j,ismore1(x0,y0,z0,i,m)):more(y0,u0)
+y0@less:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),lessf(x,y)))):'prop'
++*ii5
+y1@propl:=and3(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1)):'prop'
+-ii5
+y0@[l:less(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propl".ii5"(t,u))][u:frac][p:propl".ii5"(t,u)]
++*ii5
+p@t11:=and3e1(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(t,class(x0))
+t12:=and3e2(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(u,class(y0))
+t13:=and3e3(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):lessf(t,u)
+t14:=satz45(t,u,x,y,t13,ise(x0,x0,t,x,t11,xix0,refis(rat,x0)),ise(y0,y0,u,y,t12,yiy0,refis(rat,y0))):lessf(x,y)
+s@t15:=someapp(frac,[u:frac]propl(t,u),s,lessf(x,y),[u:frac][v:propl(t,u)]t14(u,v)):lessf(x,y)
+-ii5
+yiy0@also19:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propl".ii5"(t,u)),l,lessf(x,y),[t:frac][v:some"l"(frac,[u:frac]propl".ii5"(t,u))]t15".ii5"(t,v)):lessf(x,y)
+y1iy0@[l:lessf(x1,y1)]
++*ii5
+l@t16:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1),x1ix0,y1iy0,l):propl(x1,y1)
+t17:=somei(frac,[t:frac]propl(x1,t),y1,t16):some"l"(frac,[t:frac]propl(x1,t))
+-ii5
+l@lessi:=somei(frac,[u:frac]some"l"(frac,[t:frac]propl".ii5"(u,t)),x1,t17".ii5"):less(x0,y0)
+y1iy0@[l:less(x0,y0)]
+lesse:=also19(l,x1,y1,x1ix0,y1iy0):lessf(x1,y1)
+z0@[i:is(x0,y0)][l:less(x0,z0)]
+isless1:=isp(rat,[t:rat]less(t,z0),x0,y0,l,i):less(y0,z0)
+i@[l:less(z0,x0)]
+isless2:=isp(rat,[t:rat]less(z0,t),x0,y0,l,i):less(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][l:less(x0,z0)]
+isless12:=isless2(z0,u0,y0,j,isless1(x0,y0,z0,i,l)):less(y0,u0)
++581
+y1iy0@t1:=satz41a(x1,y1):or3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
+[e:eq"n"(x1,y1)]
+t2:=or3i1(is(x0,y0),more(x0,y0),less(x0,y0),isi(e)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+y1iy0@[m:moref(x1,y1)]
+t3:=or3i2(is(x0,y0),more(x0,y0),less(x0,y0),morei(m)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+y1iy0@[l:lessf(x1,y1)]
+t4:=or3i3(is(x0,y0),more(x0,y0),less(x0,y0),lessi(l)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+y1iy0@t5:=or3app(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),or3(is(x0,y0),more(x0,y0),less(x0,y0)),t1,[t:eq"n"(x1,y1)]t2(t),[t:moref(x1,y1)]t3(t),[t:lessf(x1,y1)]t4(t)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+t6:=satz41b(x1,y1):ec3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
+[i:is(x0,y0)]
+t7:=th3"l.imp"(more(x0,y0),moref(x1,y1),ec3e12(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,ise(i)),[t:more(x0,y0)]moree(t)):not(more(x0,y0))
+y1iy0@[m:more(x0,y0)]
+t8:=th3"l.imp"(less(x0,y0),lessf(x1,y1),ec3e23(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,moree(m)),[t:less(x0,y0)]lesse(t)):not(less(x0,y0))
+y1iy0@[l:less(x0,y0)]
+t9:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),ec3e31(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,lesse(l)),[t:is(x0,y0)]ise(t)):nis(x0,y0)
+y1iy0@t10:=th6"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),th1"l.ec"(is(x0,y0),more(x0,y0),[t:is(x0,y0)]t7(t)),th1"l.ec"(more(x0,y0),less(x0,y0),[t:more(x0,y0)]t8(t)),th1"l.ec"(less(x0,y0),is(x0,y0),[t:less(x0,y0)]t9(t))):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
+t11:=orec3i(is(x0,y0),more(x0,y0),less(x0,y0),t5,t10):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
+-581
+y0@satz81:=ratapp2(orec3(is(x0,y0),more(x0,y0),less(x0,y0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t11".581"(x,y,xi,yi)):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
+satz81a:=orec3e1(is(x0,y0),more(x0,y0),less(x0,y0),satz81):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+satz81b:=orec3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
+[m:more(x0,y0)]
++582
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=lessi(y0,x0,y,x,yiy0,xix0,satz42(x,y,moree(x0,y0,x,y,xix0,yiy0,m))):less(y0,x0)
+-582
+satz82:=ratapp2(less(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".582"(x,y,xi,yi)):less(y0,x0)
+y0@[l:less(x0,y0)]
++583
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=morei(y0,x0,y,x,yiy0,xix0,satz43(x,y,lesse(x0,y0,x,y,xix0,yiy0,l))):more(y0,x0)
+-583
+satz83:=ratapp2(more(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".583"(x,y,xi,yi)):more(y0,x0)
+y0@moreis:=or(more(x0,y0),is(x0,y0)):'prop'
+[m:more(x0,y0)]
+moreisi1:=ori1(more,is,m):moreis(x0,y0)
+y0@[i:is(x0,y0)]
+moreisi2:=ori2(more,is,i):moreis(x0,y0)
+y1iy0@[m:moreq(x1,y1)]
+moreisi:=orapp(moref(x1,y1),eq"n"(x1,y1),moreis,m,[t:moref(x1,y1)]moreisi1(morei(t)),[t:eq"n"(x1,y1)]moreisi2(isi(t))):moreis(x0,y0)
+y1iy0@[m:moreis(x0,y0)]
+moreise:=orapp(more,is,moreq(x1,y1),m,[t:more]moreqi1(x1,y1,moree(t)),[t:is]moreqi2(x1,y1,ise(t))):moreq(x1,y1)
+z0@[i:is(x0,y0)][m:moreis(x0,z0)]
+ismoreis1:=isp(rat,[t:rat]moreis(t,z0),x0,y0,m,i):moreis(y0,z0)
+i@[m:moreis(z0,x0)]
+ismoreis2:=isp(rat,[t:rat]moreis(z0,t),x0,y0,m,i):moreis(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][m:moreis(x0,z0)]
+ismoreis12:=ismoreis2(z0,u0,y0,j,ismoreis1(x0,y0,z0,i,m)):moreis(y0,u0)
+y0@lessis:=or(less(x0,y0),is(x0,y0)):'prop'
+[l:less(x0,y0)]
+lessisi1:=ori1(less,is,l):lessis(x0,y0)
+y0@[i:is(x0,y0)]
+lessisi2:=ori2(less,is,i):lessis(x0,y0)
+y1iy0@[l:lesseq(x1,y1)]
+lessisi:=orapp(lessf(x1,y1),eq"n"(x1,y1),lessis,l,[t:lessf(x1,y1)]lessisi1(lessi(t)),[t:eq"n"(x1,y1)]lessisi2(isi(t))):lessis(x0,y0)
+y1iy0@[l:lessis(x0,y0)]
+lessise:=orapp(less,is,lesseq(x1,y1),l,[t:less]lesseqi1(x1,y1,lesse(t)),[t:is]lesseqi2(x1,y1,ise(t))):lesseq(x1,y1)
+z0@[i:is(x0,y0)][l:lessis(x0,z0)]
+islessis1:=isp(rat,[t:rat]lessis(t,z0),x0,y0,l,i):lessis(y0,z0)
+i@[l:lessis(z0,x0)]
+islessis2:=isp(rat,[t:rat]lessis(z0,t),x0,y0,l,i):lessis(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][l:lessis(x0,z0)]
+islessis12:=islessis2(z0,u0,y0,j,islessis1(x0,y0,z0,i,l)):lessis(y0,u0)
+y0@[m:moreis(x0,y0)]
+satz81c:=th7"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,comor(more(x0,y0),is(x0,y0),m)):not(less(x0,y0))
+y0@[l:lessis(x0,y0)]
+satz81d:=th9"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l):not(more(x0,y0))
+y0@[n:not(more(x0,y0))]
+satz81e:=th2"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n):lessis(x0,y0)
+y0@[n:not(less(x0,y0))]
+satz81f:=comor(is(x0,y0),more(x0,y0),th3"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n)):moreis(x0,y0)
+y0@[m:more(x0,y0)]
+satz81g:=th3"l.or"(less(x0,y0),is(x0,y0),ec3e23(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m),ec3e21(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m)):not(lessis(x0,y0))
+y0@[l:less(x0,y0)]
+satz81h:=th3"l.or"(more(x0,y0),is(x0,y0),ec3e32(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l),ec3e31(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l)):not(moreis(x0,y0))
+y0@[n:not(moreis(x0,y0))]
+satz81j:=or3e3(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th5"l.or"(more(x0,y0),is(x0,y0),n),th4"l.or"(more(x0,y0),is(x0,y0),n)):less(x0,y0)
+y0@[n:not(lessis(x0,y0))]
+satz81k:=or3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th4"l.or"(less(x0,y0),is(x0,y0),n),th5"l.or"(less(x0,y0),is(x0,y0),n)):more(x0,y0)
+y0@[m:moreis(x0,y0)]
++584
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=lessisi(y0,x0,y,x,yiy0,xix0,satz48(x,y,moreise(x0,y0,x,y,xix0,yiy0,m))):lessis(y0,x0)
+-584
+satz84:=ratapp2(lessis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".584"(x,y,xi,yi)):lessis(y0,x0)
+y0@[l:lessis(x0,y0)]
++585
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=moreisi(y0,x0,y,x,yiy0,xix0,satz49(x,y,lessise(x0,y0,x,y,xix0,yiy0,l))):moreis(y0,x0)
+-585
+satz85:=ratapp2(moreis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".585"(x,y,xi,yi)):moreis(y0,x0)
+z0@[l:less(x0,y0)][k:less(y0,z0)]
++586
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=lessi(x0,z0,x,z,xix0,ziz0,satz50(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
+-586
+satz86:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".586"(x,y,z,xi,yi,zi)):less(x0,z0)
+trless:=satz86:less(x0,z0)
+z0@[m:more(x0,y0)][n:more(y0,z0)]
+trmore:=satz83(z0,x0,satz86(z0,y0,x0,satz82(y0,z0,n),satz82(m))):more(x0,z0)
+z0@[l:lessis(x0,y0)][k:less(y0,z0)]
++587
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=lessi(x0,z0,x,z,xix0,ziz0,satz51a(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
+-587
+satz87a:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".587"(x,y,z,xi,yi,zi)):less(x0,z0)
+z0@[l:less(x0,y0)][k:lessis(y0,z0)]
++*587
+k@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=lessi(x0,z0,x,z,xix0,ziz0,satz51b(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
+-587
+k@satz87b:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".587"(x,y,z,xi,yi,zi)):less(x0,z0)
+z0@[m:moreis(x0,y0)][n:more(y0,z0)]
+satz87c:=satz83(z0,x0,satz87b(z0,y0,x0,satz82(y0,z0,n),satz84(m))):more(x0,z0)
+z0@[m:more(x0,y0)][n:moreis(y0,z0)]
+satz87d:=satz83(z0,x0,satz87a(z0,y0,x0,satz84(y0,z0,n),satz82(m))):more(x0,z0)
+z0@[l:lessis(x0,y0)][k:lessis(y0,z0)]
++588
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=lessisi(x0,z0,x,z,xix0,ziz0,satz52(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):lessis(x0,z0)
+-588
+satz88:=ratapp3(lessis(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".588"(x,y,z,xi,yi,zi)):lessis(x0,z0)
+trlessis:=satz88:lessis(x0,z0)
+z0@[m:moreis(x0,y0)][n:moreis(y0,z0)]
+trmoreis:=satz85(z0,x0,satz88(z0,y0,x0,satz84(y0,z0,n),satz84(m))):moreis(x0,z0)
++589
+x0@[x:frac][xix0:inf(x,class(x0))][z:frac][m:moref(z,x)]
+t1:=somei(rat,[t:rat]more(t,x0),ratof(z),morei(ratof(z),x0,z,x,inclass(z),xix0,m)):some([t:rat]more(t,x0))
+xix0@t2:=someapp(frac,[t:frac]moref(t,x),satz53(x),some([t:rat]more(t,x0)),[t:frac][u:moref(t,x)]t1(t,u)):some([t:rat]more(t,x0))
+-589
+x0@satz89:=ratapp1(some([t:rat]more(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".589"(x,xi)):some([t:rat]more(t,x0))
++590
+z"rt.589"@[l:lessf(z,x)]
+t1:=somei(rat,[t:rat]less(t,x0),ratof(z),lessi(ratof(z),x0,z,x,inclass(z),xix0,l)):some([t:rat]less(t,x0))
+xix0"rt.589"@t2:=someapp(frac,[t:frac]lessf(t,x),satz54(x),some([t:rat]less(t,x0)),[t:frac][u:lessf(t,x)]t1(t,u)):some([t:rat]less(t,x0))
+-590
+satz90:=ratapp1(some([t:rat]less(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".590"(x,xi)):some([t:rat]less(t,x0))
+y0@[l:less(x0,y0)]
++591
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][z:frac][a:and(lessf(x,z),lessf(z,y))]
+t1:=lessi(x0,ratof(z),x,z,xix0,inclass(z),ande1(lessf(x,z),lessf(z,y),a)):less(x0,ratof(z))
+t2:=lessi(ratof(z),y0,z,y,inclass(z),yiy0,ande2(lessf(x,z),lessf(z,y),a)):less(ratof(z),y0)
+t3:=andi(less(x0,ratof(z)),less(ratof(z),y0),t1,t2):and(less(x0,ratof(z)),less(ratof(z),y0))
+t4:=somei(rat,[t:rat]and(less(x0,t),less(t,y0)),ratof(z),t3):some([t:rat]and(less(x0,t),less(t,y0)))
+yiy0@t5:=someapp(frac,[t:frac]and(lessf(x,t),lessf(t,y)),satz55(x,y,lesse(x,y,xix0,yiy0,l)),some([t:rat]and(less(x0,t),less(t,y0))),[t:frac][u:and(lessf(x,t),lessf(t,y))]t4(t,u)):some([t:rat]and(less(x0,t),less(t,y0)))
+-591
+satz91:=ratapp2(some([t:rat]and(less(x0,t),less(t,y0))),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".591"(x,y,xi,yi)):some([t:rat]and(less(x0,t),less(t,y0)))
+@plusfrt:=[x:frac][y:frac]ratof(pf(x,y)):[x:frac][y:frac]rat
+[x:frac][y:frac][z:frac][u:frac][e:eq"n"(x,y)][f:eq"n"(z,u)]
++*ii5
+f@t18:=isi(ratof(pf(x,z)),ratof(pf(y,u)),pf(x,z),pf(y,u),inclass(pf(x,z)),inclass(pf(y,u)),satz56(x,y,z,u,e,f)):is(<z><x>plusfrt,<u><y>plusfrt)
+-ii5
+@fplusfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t18".ii5"(x,y,z,u,v,w):fixf(rat,plusfrt)
+y0@pl:=indrat(rat,plusfrt,fplusfrt):rat
++*ii5
+y1iy0@t19:=isindrat(rat,plusfrt,fplusfrt,x1,y1,x1ix0,y1iy0):is(ratof(pf(x1,y1)),pl(x0,y0))
+-ii5
+y1iy0@picp:=isp(rat,[t:rat]inf(pf(x1,y1),class(t)),ratof(pf(x1,y1)),pl(x0,y0),inclass(pf(x1,y1)),t19".ii5"):inf(pf(x1,y1),class(pl(x0,y0)))
+z0@[i:is(x0,y0)]
+ispl1:=isf(rat,rat,[t:rat]pl(t,z0),x0,y0,i):is(pl(x0,z0),pl(y0,z0))
+ispl2:=isf(rat,rat,[t:rat]pl(z0,t),x0,y0,i):is(pl(z0,x0),pl(z0,y0))
+u0@[i:is(x0,y0)][j:is(z0,u0)]
+ispl12:=tris(rat,pl(x0,z0),pl(y0,z0),pl(y0,u0),ispl1(i),ispl2(z0,u0,y0,j)):is(pl(x0,z0),pl(y0,u0))
++592
+y1iy0@t1:=isi(pl(x0,y0),pl(y0,x0),pf(x1,y1),pf(y1,x1),picp,picp(y0,x0,y1,x1,y1iy0,x1ix0),satz58(x1,y1)):is(pl(x0,y0),pl(y0,x0))
+-592
+y0@satz92:=ratapp2(is(pl(x0,y0),pl(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".592"(x,y,xi,yi)):is(pl(x0,y0),pl(y0,x0))
+compl:=satz92:is(pl(x0,y0),pl(y0,x0))
++593
+z0@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=picp(pl(x0,y0),z0,pf(x,y),z,picp(x0,y0,x,y,xix0,yiy0),ziz0):inf(pf(pf(x,y),z),class(pl(pl(x0,y0),z0)))
+t2:=picp(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(pf(x,pf(y,z)),class(pl(x0,pl(y0,z0))))
+t3:=isi(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),pf(pf(x,y),z),pf(x,pf(y,z)),t1,t2,satz59(x,y,z)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
+-593
+z0@satz93:=ratapp3(is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".593"(x,y,z,xi,yi,zi)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
+asspl1:=satz93:is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
+asspl2:=symis(rat,pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),satz93):is(pl(x0,pl(y0,z0)),pl(pl(x0,y0),z0))
++594
+y1iy0@t1:=morei(pl(x0,y0),x0,pf(x1,y1),x1,picp,x1ix0,satz60(x1,y1)):more(pl(x0,y0),x0)
+-594
+y0@satz94:=ratapp2(more(pl(x0,y0),x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".594"(x,y,xi,yi)):more(pl(x0,y0),x0)
+satz94a:=satz82(pl(x0,y0),x0,satz94):less(x0,pl(x0,y0))
+z0@[m:more(x0,y0)]
++595
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz61(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
+-595
+satz95:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".595"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
+z0@[m:more(x0,y0)]
++596
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
+-596
+satz96a:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".596"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
+z0@[i:is(x0,y0)]
++*596
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(pl(x0,z0),pl(y0,z0))
+-596
+i@satz96b:=ratapp3(is(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".596"(x,y,z,xi,yi,zi)):is(pl(x0,z0),pl(y0,z0))
+z0@[l:less(x0,y0)]
++*596
+l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t3:=lessi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62c(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l))):less(pl(x0,z0),pl(y0,z0))
+-596
+l@satz96c:=ratapp3(less(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".596"(x,y,z,xi,yi,zi)):less(pl(x0,z0),pl(y0,z0))
++*596
+m@andersa:=satz95(m):more(pl(x0,z0),pl(y0,z0))
+i@andersb:=ispl1(x0,y0,z0,i):is(pl(x0,z0),pl(y0,z0))
+l@andersc:=satz82(pl(y0,z0),pl(x0,z0),satz95(y0,x0,z0,satz83(l))):less(pl(x0,z0),pl(y0,z0))
+-596
+m@satz96d:=ismore12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96a):more(pl(z0,x0),pl(z0,y0))
+i@satz96e:=ispl2(x0,y0,z0,i):is(pl(z0,x0),pl(z0,y0))
+l@satz96f:=isless12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96c):less(pl(z0,x0),pl(z0,y0))
+z0@[m:more(pl(x0,z0),pl(y0,z0))]
++597
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(x0,y0,x,y,xix0,yiy0,satz63a(x,y,z,moree(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
+-597
+satz97a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".597"(x,y,z,xi,yi,zi)):more(x0,y0)
+z0@[i:is(pl(x0,z0),pl(y0,z0))]
++*597
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(x0,y0,x,y,xix0,yiy0,satz63b(x,y,z,ise(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
+-597
+i@satz97b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".597"(x,y,z,xi,yi,zi)):is(x0,y0)
+z0@[l:less(pl(x0,z0),pl(y0,z0))]
++*597
+l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t3:=lessi(x0,y0,x,y,xix0,yiy0,satz63c(x,y,z,lesse(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
+-597
+l@satz97c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".597"(x,y,z,xi,yi,zi)):less(x0,y0)
++*597
+l@anders:=satz82(y0,x0,satz97a(y0,x0,z0,satz83(pl(x0,z0),pl(y0,z0),l))):less(x0,y0)
+-597
+u0@[m:more(x0,y0)][n:more(z0,u0)]
++598
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz64(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
+-598
+satz98:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".598"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
+u0@[l:less(x0,y0)][k:less(z0,u0)]
+satz98a:=satz82(pl(y0,u0),pl(x0,z0),satz98(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
+u0@[m:moreis(x0,y0)][n:more(z0,u0)]
++599
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
+-599
+satz99a:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
+u0@[m:more(x0,y0)][n:moreis(z0,u0)]
++*599
+n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t2:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
+-599
+n@satz99b:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
+u0@[l:lessis(x0,y0)][k:less(z0,u0)]
+satz99c:=satz82(pl(y0,u0),pl(x0,z0),satz99a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
+u0@[l:less(x0,y0)][k:lessis(z0,u0)]
+satz99d:=satz82(pl(y0,u0),pl(x0,z0),satz99b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
+u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
++5100
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=moreisi(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz66(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(pl(x0,z0),pl(y0,u0))
+-5100
+satz100:=ratapp4(moreis(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5100"(x,y,z,u,xi,yi,zi,ui)):moreis(pl(x0,z0),pl(y0,u0))
+u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
+satz100a:=satz84(pl(y0,u0),pl(x0,z0),satz100(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(pl(x0,z0),pl(y0,u0))
+y0@[l:lessis(x0,y0)]
++5101
+[v0:rat][i:is(pl(y0,v0),x0)]
+t1:=ismore1(pl(y0,v0),x0,y0,i,satz94(y0,v0)):more(x0,y0)
+v0@t2:=th3"l.imp"(is(pl(y0,v0),x0),more(x0,y0),satz81d(x0,y0,l),[t:is(pl(y0,v0),x0)]t1(t)):nis(pl(y0,v0),x0)
+-5101
+vorbemerkung101:=th5"l.some"(rat,[v:rat]is(pl(y0,v),x0),[v:rat]t2".5101"(v)):not(some([t:rat]is(pl(y0,t),x0)))
+y0@[m:more(x0,y0)]
++*5101
+m@[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][v:frac][e:eq"n"(pf(y,v),x)]
+t3:=isi(pl(y0,ratof(v)),x0,pf(y,v),x,picp(y0,ratof(v),y,v,yiy0,inclass(v)),xix0,e):is(pl(y0,ratof(v)),x0)
+t4:=somei(rat,[t:rat]is(pl(y0,t),x0),ratof(v),t3):some([t:rat]is(pl(y0,t),x0))
+yiy0@t5:=someapp(frac,[t:frac]eq"n"(pf(y,t),x),satz67a(x,y,moree(x0,y0,x,y,xix0,yiy0,m)),some([t:rat]is(pl(y0,t),x0)),[t:frac][u:eq"n"(pf(y,t),x)]t4(t,u)):some([t:rat]is(pl(y0,t),x0))
+-5101
+m@satz101a:=ratapp2(some([t:rat]is(pl(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".5101"(x,y,xi,yi)):some([t:rat]is(pl(y0,t),x0))
+y0@[v0:rat][w0:rat][i:is(pl(y0,v0),x0)][j:is(pl(y0,w0),x0)]
++*5101
+j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
+t6:=isi(v0,w0,v,w,viv0,wiw0,satz67b(x,y,v,w,ise(pl(y0,v0),x0,pf(y,v),x,picp(y0,v0,y,v,yiy0,viv0),xix0,i),ise(pl(y0,w0),x0,pf(y,w),x,picp(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
+-5101
+j@satz101b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t6".5101"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
++*5101
+y0@t7:=[t:rat][u:rat][v:is(pl(y0,t),x0)][w:is(pl(y0,u),x0)]satz101b(t,u,v,w):amone(rat,[t:rat]is(pl(y0,t),x0))
+-5101
+m@satz101:=onei(rat,[t:rat]is(pl(y0,t),x0),t7".5101",satz101a):one([t:rat]is(pl(y0,t),x0))
+mn:=ind(rat,[t:rat]is(pl(y0,t),x0),satz101):rat
+satz101c:=oneax(rat,[t:rat]is(pl(y0,t),x0),satz101):is(pl(y0,mn(x0,y0,m)),x0)
+satz101d:=symis(rat,pl(y0,mn(x0,y0,m)),x0,satz101c):is(x0,pl(y0,mn(x0,y0,m)))
+satz101e:=tris(rat,pl(mn(x0,y0,m),y0),pl(y0,mn(x0,y0,m)),x0,compl(mn(x0,y0,m),y0),satz101c):is(pl(mn(x0,y0,m),y0),x0)
+satz101f:=symis(rat,pl(mn(x0,y0,m),y0),x0,satz101e):is(x0,pl(mn(x0,y0,m),y0))
+y0@[v0:rat][m:more(x0,y0)][i:is(pl(y0,v0),x0)]
+satz101g:=satz101b(v0,mn(x0,y0,m),i,satz101c(m)):is(v0,mn(x0,y0,m))
+@timesfrt:=[x:frac][y:frac]ratof(tf(x,y)):[x:frac][y:frac]rat
++*ii5
+f@t20:=isi(ratof(tf(x,z)),ratof(tf(y,u)),tf(x,z),tf(y,u),inclass(tf(x,z)),inclass(tf(y,u)),satz68(x,y,z,u,e,f)):is(<z><x>timesfrt,<u><y>timesfrt)
+-ii5
+@ftimesfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t20".ii5"(x,y,z,u,v,w):fixf(rat,timesfrt)
+y0@ts:=indrat(rat,timesfrt,ftimesfrt):rat
++*ii5
+y1iy0@t21:=isindrat(rat,timesfrt,ftimesfrt,x1,y1,x1ix0,y1iy0):is(ratof(tf(x1,y1)),ts(x0,y0))
+-ii5
+y1iy0@tict:=isp(rat,[t:rat]inf(tf(x1,y1),class(t)),ratof(tf(x1,y1)),ts(x0,y0),inclass(tf(x1,y1)),t21".ii5"):inf(tf(x1,y1),class(ts(x0,y0)))
+z0@[i:is(x0,y0)]
+ists1:=isf(rat,rat,[t:rat]ts(t,z0),x0,y0,i):is(ts(x0,z0),ts(y0,z0))
+ists2:=isf(rat,rat,[t:rat]ts(z0,t),x0,y0,i):is(ts(z0,x0),ts(z0,y0))
+u0@[i:is(x0,y0)][j:is(z0,u0)]
+ists12:=tris(rat,ts(x0,z0),ts(y0,z0),ts(y0,u0),ists1(i),ists2(z0,u0,y0,j)):is(ts(x0,z0),ts(y0,u0))
++5102
+y1iy0@t1:=isi(ts(x0,y0),ts(y0,x0),tf(x1,y1),tf(y1,x1),tict,tict(y0,x0,y1,x1,y1iy0,x1ix0),satz69(x1,y1)):is(ts(x0,y0),ts(y0,x0))
+-5102
+y0@satz102:=ratapp2(is(ts(x0,y0),ts(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".5102"(x,y,xi,yi)):is(ts(x0,y0),ts(y0,x0))
+comts:=satz102:is(ts(x0,y0),ts(y0,x0))
++5103
+ziz0"rt.593"@t1:=tict(ts(x0,y0),z0,tf(x,y),z,tict(x0,y0,x,y,xix0,yiy0),ziz0):inf(tf(tf(x,y),z),class(ts(ts(x0,y0),z0)))
+t2:=tict(x0,ts(y0,z0),x,tf(y,z),xix0,tict(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,tf(y,z)),class(ts(x0,ts(y0,z0))))
+t3:=isi(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),tf(tf(x,y),z),tf(x,tf(y,z)),t1,t2,satz70(x,y,z)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
+-5103
+z0@satz103:=ratapp3(is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5103"(x,y,z,xi,yi,zi)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
+assts1:=satz103:is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
+assts2:=symis(rat,ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),satz103):is(ts(x0,ts(y0,z0)),ts(ts(x0,y0),z0))
++5104
+ziz0"rt.593"@t1:=tict(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,pf(y,z)),class(ts(x0,pl(y0,z0))))
+t2:=picp(ts(x0,y0),ts(x0,z0),tf(x,y),tf(x,z),tict(x0,y0,x,y,xix0,yiy0),tict(x0,z0,x,z,xix0,ziz0)):inf(pf(tf(x,y),tf(x,z)),class(pl(ts(x0,y0),ts(x0,z0))))
+t3:=isi(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),t1,t2,satz71(x,y,z)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
+-5104
+satz104:=ratapp3(is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5104"(x,y,z,xi,yi,zi)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
+disttp1:=tr3is(rat,ts(pl(x0,y0),z0),ts(z0,pl(x0,y0)),pl(ts(z0,x0),ts(z0,y0)),pl(ts(x0,z0),ts(y0,z0)),comts(pl(x0,y0),z0),satz104(z0,x0,y0),ispl12(ts(z0,x0),ts(x0,z0),ts(z0,y0),ts(y0,z0),comts(z0,x0),comts(z0,y0))):is(ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)))
+disttp2:=satz104:is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
+distpt1:=symis(rat,ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)),disttp1):is(pl(ts(x0,z0),ts(y0,z0)),ts(pl(x0,y0),z0))
+distpt2:=symis(rat,ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),disttp2):is(pl(ts(x0,y0),ts(x0,z0)),ts(x0,pl(y0,z0)))
+[m:more(x0,y0)]
++5105
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(ts(x0,z0),ts(y0,z0))
+-5105
+satz105a:=ratapp3(more(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5105"(x,y,z,xi,yi,zi)):more(ts(x0,z0),ts(y0,z0))
+z0@[i:is(x0,y0)]
++*5105
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(ts(x0,z0),ts(y0,z0))
+-5105
+i@satz105b:=ratapp3(is(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5105"(x,y,z,xi,yi,zi)):is(ts(x0,z0),ts(y0,z0))
+z0@[l:less(x0,y0)]
++*5105
+l@[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]
+t3:=lessi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xi,zi),tict(y0,z0,y,z,yi,zi),satz72c(x,y,z,lesse(x0,y0,x,y,xi,yi,l))):less(ts(x0,z0),ts(y0,z0))
+-5105
+l@satz105c:=ratapp3(less(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5105"(x,y,z,xi,yi,zi)):less(ts(x0,z0),ts(y0,z0))
++*5105
+i@andersb:=ists1(x0,y0,z0,i):is(ts(x0,z0),ts(y0,z0))
+l@andersc:=satz82(ts(y0,z0),ts(x0,z0),satz105a(y0,x0,z0,satz83(l))):less(ts(x0,z0),ts(y0,z0))
+-5105
+m@satz105d:=ismore12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105a):more(ts(z0,x0),ts(z0,y0))
+i@satz105e:=ists2(x0,y0,z0,i):is(ts(z0,x0),ts(z0,y0))
+l@satz105f:=isless12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105c):less(ts(z0,x0),ts(z0,y0))
+z0@[m:more(ts(x0,z0),ts(y0,z0))]
++5106
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(x0,y0,x,y,xix0,yiy0,satz73a(x,y,z,moree(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
+-5106
+satz106a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5106"(x,y,z,xi,yi,zi)):more(x0,y0)
+z0@[i:is(ts(x0,z0),ts(y0,z0))]
++*5106
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(x0,y0,x,y,xix0,yiy0,satz73b(x,y,z,ise(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
+-5106
+i@satz106b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5106"(x,y,z,xi,yi,zi)):is(x0,y0)
+z0@[l:less(ts(x0,z0),ts(y0,z0))]
++*5106
+l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t3:=lessi(x0,y0,x,y,xix0,yiy0,satz73c(x,y,z,lesse(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
+-5106
+l@satz106c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5106"(x,y,z,xi,yi,zi)):less(x0,y0)
++*5106
+l@anders:=satz82(y0,x0,satz106a(y0,x0,z0,satz83(ts(x0,z0),ts(y0,z0),l))):less(x0,y0)
+-5106
+u0@[m:more(x0,y0)][n:more(z0,u0)]
++5107
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz74(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
+-5107
+satz107:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5107"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
+u0@[l:less(x0,y0)][k:less(z0,u0)]
+satz107a:=satz82(ts(y0,u0),ts(x0,z0),satz107(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
+u0@[m:moreis(x0,y0)][n:more(z0,u0)]
++5108
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
+-5108
+satz108a:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
+u0@[m:more(x0,y0)][n:moreis(z0,u0)]
++*5108
+n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t2:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
+-5108
+n@satz108b:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
+u0@[l:lessis(x0,y0)][k:less(z0,u0)]
+satz108c:=satz82(ts(y0,u0),ts(x0,z0),satz108a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
+u0@[l:less(x0,y0)][k:lessis(z0,u0)]
+satz108d:=satz82(ts(y0,u0),ts(x0,z0),satz108b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
+u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
++5109
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=moreisi(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz76(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(ts(x0,z0),ts(y0,u0))
+-5109
+satz109:=ratapp4(moreis(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5109"(x,y,z,u,xi,yi,zi,ui)):moreis(ts(x0,z0),ts(y0,u0))
+u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
+satz109a:=satz84(ts(y0,u0),ts(x0,z0),satz109(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(ts(x0,z0),ts(y0,u0))
++5110
+y1iy0@[v:frac][e:eq"n"(tf(y1,v),x1)]
+t1:=isi(ts(y0,ratof(v)),x0,tf(y1,v),x1,tict(y0,ratof(v),y1,v,y1iy0,inclass(v)),x1ix0,e):is(ts(y0,ratof(v)),x0)
+t2:=somei(rat,[t:rat]is(ts(y0,t),x0),ratof(v),t1):some([t:rat]is(ts(y0,t),x0))
+y1iy0@t3:=someapp(frac,[t:frac]eq"n"(tf(y1,t),x1),satz77a(x1,y1),some([t:rat]is(ts(y0,t),x0)),[t:frac][u:eq"n"(tf(y1,t),x1)]t2(t,u)):some([t:rat]is(ts(y0,t),x0))
+-5110
+y0@satz110a:=ratapp2(some([t:rat]is(ts(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t3".5110"(x,y,xi,yi)):some([t:rat]is(ts(y0,t),x0))
+[v0:rat][w0:rat][i:is(ts(y0,v0),x0)][j:is(ts(y0,w0),x0)]
++*5110
+j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
+t4:=isi(v0,w0,v,w,viv0,wiw0,satz77b(x,y,v,w,ise(ts(y0,v0),x0,tf(y,v),x,tict(y0,v0,y,v,yiy0,viv0),xix0,i),ise(ts(y0,w0),x0,tf(y,w),x,tict(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
+-5110
+j@satz110b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t4".5110"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
++*5110
+y0@t5:=[t:rat][u:rat][v:is(ts(y0,t),x0)][w:is(ts(y0,u),x0)]satz110b(t,u,v,w):amone(rat,[t:rat]is(ts(y0,t),x0))
+-5110
+y0@satz110:=onei(rat,[t:rat]is(ts(y0,t),x0),t5".5110",satz110a):one([t:rat]is(ts(y0,t),x0))
+-rt
+@[x:nat][y:nat]
++5111
+t1:=tris(nat,ts(num(fr(x,1)),den(fr(y,1))),ts(x,1),x,ndis12(x,1,y,1),satz28a(x)):is(ts(num(fr(x,1)),den(fr(y,1))),x)
+t2:=symis(nat,ts(num(fr(x,1)),den(fr(y,1))),x,t1):is(x,ts(num(fr(x,1)),den(fr(y,1))))
+-5111
+[m:moref(fr(x,1),fr(y,1))]
+satz111a:=ismore12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),m):more(x,y)
+y@[e:eq(fr(x,1),fr(y,1))]
+satz111b:=tr3is(nat,x,ts(num(fr(x,1)),den(fr(y,1))),ts(num(fr(y,1)),den(fr(x,1))),y,t2".5111",e,t1".5111"(y,x)):is(x,y)
+y@[l:lessf(fr(x,1),fr(y,1))]
+satz111c:=isless12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),l):less(x,y)
+y@[m:more(x,y)]
+satz111d:=ismore12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),m):moref(fr(x,1),fr(y,1))
+y@[i:is(x,y)]
+satz111e:=tr3is(nat,ts(num(fr(x,1)),den(fr(y,1))),x,y,ts(num(fr(y,1)),den(fr(x,1))),t1".5111",i,t2".5111"(y,x)):eq(fr(x,1),fr(y,1))
+y@[l:less(x,y)]
+satz111f:=isless12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),l):lessf(fr(x,1),fr(y,1))
++*rt
+@[x0:rat][x:nat]
+natprop:=inf(fr(x,1),class(x0)):'prop'
+x0@natrt:=some"n"([t:nat]natprop(t)):'prop'
++*ii5
+y0@[x:nat][y:nat][npx:natprop(x0,x)][npy:natprop(y0,y)][i:is(x0,y0)]
+t22:=satz111b(x,y,ise(x0,y0,fr(x,1),fr(y,1),npx,npy,i)):is"n"(x,y)
+x0@t23:=[t:nat][u:nat][v:natprop(x0,t)][w:natprop(x0,u)]t22(x0,x0,t,u,v,w,refis(rat,x0)):amone(nat,[t:nat]natprop(x0,t))
+-ii5
+x0@[nx0:natrt(x0)]
+satz111g:=onei(nat,[t:nat]natprop(t),t23".ii5",nx0):one"n"([t:nat]natprop(x0,t))
+nofrt:=ind(nat,[t:nat]natprop(t),satz111g):nat
+inclassn:=oneax(nat,[t:nat]natprop(t),satz111g):inf(fr(nofrt,1),class(x0))
+[y0:rat][ny0:natrt(y0)][i:is(x0,y0)]
+isrten:=t22".ii5"(x0,y0,nofrt(x0,nx0),nofrt(y0,ny0),inclassn(x0,nx0),inclassn(y0,ny0),i):is"n"(nofrt(x0,nx0),nofrt(y0,ny0))
+ny0@[i:is"n"(nofrt(x0,nx0),nofrt(y0,ny0))]
+isrtin:=isi(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),eqn"n"(nofrt(x0,nx0),1,nofrt(y0,ny0),i)):is(x0,y0)
+@[x:nat]
+rtofn:=ratof(fr(x,1)):rat
+natrti:=somei(nat,[t:nat]natprop(rtofn,t),x,inclass(fr(x,1))):natrt(rtofn(x))
+[y:nat][i:is"n"(x,y)]
+isnert:=isf(nat,rat,[t:nat]rtofn(t),x,y,i):is(rtofn(x),rtofn(y))
+y@[i:is(rtofn(x),rtofn(y))]
+isnirt:=t22".ii5"(rtofn(x),rtofn(y),x,y,inclass(fr(x,1)),inclass(fr(y,1)),i):is"n"(x,y)
+nx0@isrtn1:=isi(x0,rtofn(nofrt(x0,nx0)),fr(nofrt(x0,nx0),1),fr(nofrt(x0,nx0),1),inclassn(x0,nx0),inclass(fr(nofrt(x0,nx0),1)),refeq"n"(fr(nofrt(x0,nx0),1))):is(x0,rtofn(nofrt(x0,nx0)))
+x@isnrt1:=t22".ii5"(rtofn(x),rtofn(x),x,nofrt(rtofn(x),natrti(x)),inclass(fr(x,1)),inclassn(rtofn(x),natrti(x)),refis(rat,rtofn(x))):is"n"(x,nofrt(rtofn(x),natrti(x)))
+-rt
+@[x:nat][y:nat]
+satz112a:=satz57(x,y,1):eq(pf(fr(x,1),fr(y,1)),fr(pl(x,y),1))
+satz112b:=treq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),ts(1,1)),fr(ts(x,y),1),tfeq12a(x,1,y,1),eqd(ts(x,y),ts(1,1),1,satz28a(1))):eq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),1))
++*rt
+ny0@satz112c:=lemmaeq1(pl(x0,y0),pf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),picp(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112a(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(pl(x0,y0)))
+satz112d:=somei(nat,[t:nat]natprop(pl(x0,y0),t),pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112c):natrt(pl(x0,y0))
+satz112e:=lemmaeq1(ts(x0,y0),tf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),tict(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112b(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(ts(x0,y0)))
+satz112f:=somei(nat,[t:nat]natprop(ts(x0,y0),t),ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112e):natrt(ts(x0,y0))
+[m:more(x0,y0)]
++5112
+t1:=satz111a(nofrt(x0,nx0),nofrt(y0,ny0),moree(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),m)):more"n"(nofrt(x0,nx0),nofrt(y0,ny0))
+[z:nat][d:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),z)]
+t2:=tris(nat,nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),z),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),d,ispl2"n"(z,nofrt(rtofn(z),natrti(z)),nofrt(y0,ny0),isnrt1(z))):is"n"(nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))))
+t3:=isi(x0,pl(y0,rtofn(z)),fr(nofrt(x0,nx0),1),fr(pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),1),inclassn(x0,nx0),satz112c(y0,ny0,rtofn(z),natrti(z)),eqn(nofrt(x0,nx0),1,pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),t2)):is(x0,pl(y0,rtofn(z)))
+t4:=satz101g(x0,y0,rtofn(z),m,symis(rat,x0,pl(y0,rtofn(z)),t3)):is(rtofn(z),mn(x0,y0,m))
+t5:=isp(rat,[t:rat]natrt(t),rtofn(z),mn(x0,y0,m),natrti(z),t4):natrt(mn(x0,y0,m))
+-5112
+satz112g:=someapp(nat,[t:nat]diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t),t1".5112",natrt(mn(x0,y0,m)),[t:nat][u:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t)]t5".5112"(t,u)):natrt(mn(x0,y0,m))
+@[x:nat][y:nat]
+satz112h:=isi(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),pf(fr(x,1),fr(y,1)),fr(pl"n"(x,y),1),picp(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(pl"n"(x,y),1)),satz112a(x,y)):is(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)))
+satz112j:=isi(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),tf(fr(x,1),fr(y,1)),fr(ts"n"(x,y),1),tict(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(ts"n"(x,y),1)),satz112b(x,y)):is(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)))
++nt
+@natt:=ot(rat,[t:rat]natrt(t)):'type'
+nx0@ntofrt:=out(rat,[t:rat]natrt(t),x0,nx0):natt
+@[xt:natt][yt:natt]
+is:=is"e"(natt,xt,yt):'prop'
+nis:=not(is(xt,yt)):'prop'
+@[p:[x:natt]'prop']
+all:=all"l"(natt,p):'prop'
+some:=some"l"(natt,p):'prop'
+one:=one"e"(natt,p):'prop'
+xt@[st:set(natt)]
+in:=esti(natt,xt,st):'prop'
+xt@rtofnt:=in"e"(rat,[t:rat]natrt(t),xt):rat
+natrti:=inp(rat,[t:rat]natrt(t),xt):natrt(rtofnt(xt))
+ny0@[i:is"rt"(x0,y0)]
+isrtent:=isouti(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is(ntofrt(x0,nx0),ntofrt(y0,ny0))
+ny0@[i:is(ntofrt(x0,nx0),ntofrt(y0,ny0))]
+isrtint:=isoute(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is"rt"(x0,y0)
+yt@[i:is(xt,yt)]
+isntert:=isini(rat,[t:rat]natrt(t),xt,yt,i):is"rt"(rtofnt(xt),rtofnt(yt))
+yt@[i:is"rt"(rtofnt(xt),rtofnt(yt))]
+isntirt:=isine(rat,[t:rat]natrt(t),xt,yt,i):is(xt,yt)
+nx0@isrtnt1:=isinout(rat,[t:rat]natrt(t),x0,nx0):is"rt"(x0,rtofnt(ntofrt(x0,nx0)))
+xt@isntrt1:=isoutin(rat,[t:rat]natrt(t),xt):is(xt,ntofrt(rtofnt(xt),natrti(xt)))
+x@ntofn:=ntofrt(rtofn(x),natrti"rt"(x)):natt
+y@[i:is"n"(x,y)]
+isnent:=isrtent(rtofn(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),isnert(x,y,i)):is(ntofn(x),ntofn(y))
+y@[i:is(ntofn(x),ntofn(y))]
+isnint:=isnirt(x,y,isrtint(rtofn"rt"(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),i)):is"n"(x,y)
+xt@nofnt:=nofrt(rtofnt(xt),natrti(xt)):nat
+yt@[i:is(xt,yt)]
+isnten:=isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),isntert(xt,yt,i)):is"n"(nofnt(xt),nofnt(yt))
+yt@[i:is"n"(nofnt(xt),nofnt(yt))]
+isntin:=isntirt(xt,yt,isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),i)):is(xt,yt)
++ii5
+x@t24:=isrtnt1(rtofn(x),natrti"rt"(x)):is"rt"(rtofn(x),rtofnt(ntofn(x)))
+t25:=isrten(rtofn(x),natrti"rt"(x),rtofnt(ntofn(x)),natrti(ntofn(x)),t24):is"n"(nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)))
+-ii5
+x@isnnt1:=tris(nat,x,nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)),isnrt1(x),t25".ii5"):is"n"(x,nofnt(ntofn(x)))
++*ii5
+xt@t26:=isrtn1(rtofnt(xt),natrti(xt)):is"rt"(rtofnt(xt),rtofn(nofnt(xt)))
+t27:=isrtent(rtofnt(xt),natrti(xt),rtofn(nofnt(xt)),natrti"rt"(nofnt(xt)),t26):is(ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)))
+-ii5
+xt@isntn1:=tris(natt,xt,ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)),isntrt1(xt),t27".ii5"):is(xt,ntofn(nofnt(xt)))
+x@isnnt2:=symis(nat,x,nofnt(ntofn(x)),isnnt1):is"n"(nofnt(ntofn(x)),x)
+xt@isntn2:=symis(natt,xt,ntofn(nofnt(xt)),isntn1):is(ntofn(nofnt(xt)),xt)
+@1t:=ntofn(1):natt
+suct:=[x:natt]ntofn(<nofnt(x)>suc):[x:natt]natt
++5113
+xt@[i:is(<xt>suct,1t)]
+t1:=isnint(<nofnt(xt)>suc,1,i):is"n"(<nofnt(xt)>suc,1)
+-5113
+xt@satz113a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<nofnt(xt)>suc,1),<nofnt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5113"(t)):nis(<xt>suct,1t)
+yt@[i:is(<xt>suct,<yt>suct)]
++*5113
+i"nt"@t2:=isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,i):is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
+-5113
+i@satz113b:=isntin(xt,yt,<t2".5113"><nofnt(yt)><nofnt(xt)>ax4):is(xt,yt)
+@[st:set(natt)]
+cond1:=in(1t,st):'prop'
+cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
+[c1:cond1][c2:cond2]
++*5113
+c2@[x:nat]
+prop1:=in(ntofn(x),st):'prop'
+[p:prop1(x)]
+t3:=<ntofn(x)>c2:imp(in(ntofn(x),st),in(<ntofn(x)>suct,st))
+t4:=mp(in(ntofn(x),st),in(<ntofn(x)>suct,st),p,t3):in(<ntofn(x)>suct,st)
+t5:=isp(nat,[t:nat]in(ntofn(<t>suc),st),nofnt(ntofn(x)),x,t4,isnnt2(x)):prop1(<x>suc)
+-5113
+c2@[xt:natt]
++*5113
+xt@t6:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t5(t,u),nofnt(xt)):in(ntofn(nofnt(xt)),st)
+-5113
+xt@satz113c:=isp(natt,[t:natt]in(t,st),ntofn(nofnt(xt)),xt,t6".5113",isntn2(xt)):in(xt,st)
+@ax3t:=[x:natt]satz113a(x):[x:natt]nis(<x>suct,1t)
+ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz113b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
+ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz113c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
+yt@[n:nis(xt,yt)]
++51
+t1:=th3"l.imp"(is"n"(nofnt(xt),nofnt(yt)),is(xt,yt),n,[t:is"n"(nofnt(xt),nofnt(yt))]isntin(xt,yt,t)):nis"n"(nofnt(xt),nofnt(yt))
+t2:=satz1(nofnt(xt),nofnt(yt),t1):nis"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
+-51
+satz1:=th3"l.imp"(is(<xt>suct,<yt>suct),is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc),t2".51",[t:is(<xt>suct,<yt>suct)]isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,t)):nis(<xt>suct,<yt>suct)
++54
+xt@x:=nofnt(xt):nat
+[ft:[x:natt]natt]
+prop1t:=all([t:natt]is(<<t>suct>ft,<<t>ft>suct)):'prop'
+prop2t:=and(is(<1t>ft,<xt>suct),prop1t):'prop'
+xt@[f:[x:nat]nat]
+prop1:=all"n"([t:nat]is"n"(<<t>suc>f,<<t>f>suc)):'prop'
+prop2:=and(is"n"(<1>f,<x>suc),prop1):'prop'
+ft@g:=[t:nat]nofnt(<ntofn(t)>ft):[x:nat]nat
+[p:prop2t]
+t1:=ande1(is(<1t>ft,<xt>suct),prop1t,p):is(<1t>ft,<xt>suct)
+t2:=tris(nat,<1>g,nofnt(<xt>suct),<x>suc,isnten(<1t>ft,<xt>suct,t1),isnnt2(<x>suc)):is"n"(<1>g,<x>suc)
+t3:=ande2(is(<1t>ft,<xt>suct),prop1t,p):prop1t
+[u:nat]
+ut:=ntofn(u):natt
+t4:=isf(nat,nat,suc,u,nofnt(ut),isnnt1(u)):is"n"(<u>suc,<nofnt(ut)>suc)
+t5:=isf(nat,nat,g,<u>suc,<nofnt(ut)>suc,t4):is"n"(<<u>suc>g,nofnt(<<ut>suct>ft))
+t6:=<ut>t3:is(<<ut>suct>ft,<<ut>ft>suct)
+t7:=isnten(<<ut>suct>ft,<<ut>ft>suct,t6):is"n"(nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct))
+t8:=isnnt2(<<u>g>suc):is"n"(nofnt(<<ut>ft>suct),<<u>g>suc)
+t9:=tr3is(nat,<<u>suc>g,nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct),<<u>g>suc,t5,t7,t8):is"n"(<<u>suc>g,<<u>g>suc)
+p@t10:=[u:nat]t9(u):prop1(g)
+t11:=andi(is"n"(<1>g,<x>suc),prop1(g),t2,t10):prop2(g)
+xt@[a:[t:natt]natt][b:[t:natt]natt][pa:prop2t(a)][pb:prop2t(b)]
+t12:=onee1([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):amone([t:nat]nat,[u:[t:nat]nat]prop2(u))
+t13:=<t11(b,pb)><t11(a,pa)><g(b)><g(a)>t12:is"e"([t:nat]nat,g(a),g(b))
+[yt:natt]
+y:=nofnt(yt):nat
+t14:=fise(nat,nat,g(a),g(b),t13,y):is"n"(nofnt(<ntofn(y)>a),nofnt(<ntofn(y)>b))
+t15:=isntin(<ntofn(y)>a,<ntofn(y)>b,t14):is(<ntofn(y)>a,<ntofn(y)>b)
+t16:=tr3is(natt,<yt>a,<ntofn(y)>a,<ntofn(y)>b,<yt>b,isf(natt,natt,a,yt,ntofn(y),isntn1(yt)),t15,isf(natt,natt,b,ntofn(y),yt,isntn2(yt))):is(<yt>a,<yt>b)
+pb@t17:=fisi(natt,natt,a,b,[t:natt]t16(t)):is"e"([t:natt]natt,a,b)
+xt@t18:=[u:[t:natt]natt][v:[t:natt]natt][w:prop2t(u)][z:prop2t(v)]t17(u,v,w,z):amone([t:natt]natt,[u:[t:natt]natt]prop2t(u))
+t19:=onee2([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):some"l"([t:nat]nat,[u:[t:nat]nat]prop2(u))
+f@gt:=[t:natt]ntofn(<nofnt(t)>f):[x:natt]natt
+[p:prop2]
+t20:=ande1(is"n"(<1>f,<x>suc),prop1,p):is"n"(<1>f,<x>suc)
+t21:=isf(nat,nat,f,nofnt(1t),1,isnnt2(1)):is"n"(<nofnt(1t)>f,<1>f)
+t22:=isnent(<nofnt(1t)>f,<x>suc,tris(nat,<nofnt(1t)>f,<1>f,<x>suc,t21,t20)):is(<1t>gt,<xt>suct)
+t23:=ande2(is"n"(<1>f,<x>suc),prop1,p):prop1
+[zt:natt]
+z:=nofnt(zt):nat
+t24:=isf(nat,nat,f,nofnt(<zt>suct),<z>suc,isnnt2(<z>suc)):is"n"(<nofnt(<zt>suct)>f,<<z>suc>f)
+t25:=<z>t23:is"n"(<<z>suc>f,<<z>f>suc)
+t26:=isf(nat,nat,suc,<z>f,nofnt(<zt>gt),isnnt1(<z>f)):is"n"(<<z>f>suc,<nofnt(<zt>gt)>suc)
+t27:=isnent(<nofnt(<zt>suct)>f,<nofnt(<zt>gt)>suc,tr3is(nat,<nofnt(<zt>suct)>f,<<z>suc>f,<<z>f>suc,<nofnt(<zt>gt)>suc,t24,t25,t26)):is(<<zt>suct>gt,<<zt>gt>suct)
+p@t28:=[u:natt]t27(u):prop1t(gt)
+t29:=andi(is(<1t>gt,<xt>suct),prop1t(gt),t22,t28):prop2t(gt)
+t30:=somei([t:natt]natt,[u:[t:natt]natt]prop2t(u),gt,t29):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
+xt@t31:=someapp([t:nat]nat,[u:[t:nat]nat]prop2(u),t19,some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u)),[u:[t:nat]nat][v:prop2(u)]t30(u,v)):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
+-54
+xt@satz4:=onei([t:natt]natt,[u:[t:natt]natt]prop2t".54"(u),t18".54",t31".54"):one"e"([t:natt]natt,[u:[t:natt]natt]and(is(<1t>u,<xt>suct),all([v:natt]is(<<v>suct>u,<<v>u>suct))))
+yt@pl:=ntofrt(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt))):natt
++*ii5
+yt@t28:=satz112c(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)):inf(fr(pl"n"(nofnt(xt),nofnt(yt)),1),class(pl"rt"(rtofnt(xt),rtofnt(yt))))
+t29:=isi(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),fr(pl"n"(nofnt(xt),nofnt(yt)),1),fr(pl"n"(nofnt(xt),nofnt(yt)),1),t28,inclass(fr(pl"n"(nofnt(xt),nofnt(yt)),1)),refeq"n"(fr(pl"n"(nofnt(xt),nofnt(yt)),1))):is"rt"(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))))
+-ii5
+yt@isplnt:=isrtent(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),natrti"rt"(pl"n"(nofnt(xt),nofnt(yt))),t29".ii5"):is(pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))))
+isntpl:=symis(natt,pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))),isplnt):is(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt))
+ispln:=tris(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(ntofn(pl"n"(nofnt(xt),nofnt(yt)))),nofnt(pl(xt,yt)),isnnt1(pl"n"(nofnt(xt),nofnt(yt))),isnten(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt),isntpl)):is"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)))
+isnpl:=symis(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)),ispln):is"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)))
+[zt:natt]
++55
+t1:=ispl1"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt),isnpl(xt,yt)):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)))
+t2:=ispl2"n"(pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),nofnt(xt),ispln(yt,zt)):is"n"(pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
+t3:=tr3is(nat,pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)),pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t1,satz5(nofnt(xt),nofnt(yt),nofnt(zt)),t2):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
+-55
+satz5:=tr3is(natt,pl(pl(xt,yt),zt),ntofn(pl"n"(nofnt(pl(xt,yt)),nofnt(zt))),ntofn(pl"n"(nofnt(xt),nofnt(pl(yt,zt)))),pl(xt,pl(yt,zt)),isplnt(pl(xt,yt),zt),isnent(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t3".55"),isntpl(xt,pl(yt,zt))):is(pl(pl(xt,yt),zt),pl(xt,pl(yt,zt)))
+diffprop:=is(xt,pl(yt,zt)):'prop'
+[d:diffprop]
+diffprope:=tris(nat,nofnt(xt),nofnt(pl(yt,zt)),pl"n"(nofnt(yt),nofnt(zt)),isnten(xt,pl(yt,zt),d),isnpl(yt,zt)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))
+zt@[d:diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))]
++*ii5
+d@t30:=tris(nat,nofnt(xt),pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),d,ispln(yt,zt)):is"n"(nofnt(xt),nofnt(pl(yt,zt)))
+-ii5
+d@diffpropi:=isntin(xt,pl(yt,zt),t30".ii5"):diffprop
++59
+yt@it:=is(xt,yt):'prop'
+iit:=some([u:natt]diffprop(xt,yt,u)):'prop'
+iiit:=some([u:natt]diffprop(yt,xt,u)):'prop'
+i:=is"n"(nofnt(xt),nofnt(yt)):'prop'
+ii:=some"n"([u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u)):'prop'
+iii:=some"n"([u:nat]diffprop"n"(nofnt(yt),nofnt(xt),u)):'prop'
+[one:i]
+t1:=or3i1(it,iit,iiit,isntin(xt,yt,one)):or3(it,iit,iiit)
+yt@[two:ii][v:nat][d:diffprop"n"(nofnt(xt),nofnt(yt),v)]
+t2:=isp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),v,nofnt(ntofn(v)),d,isnnt1(v)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(ntofn(v)))
+t3:=somei(natt,[u:natt]diffprop(xt,yt,u),ntofn(v),diffpropi(xt,yt,ntofn(v),t2)):iit
+two@t4:=someapp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),two,iit,[u:nat][v:diffprop"n"(nofnt(xt),nofnt(yt),u)]t3(u,v)):iit
+t5:=or3i2(it,iit,iiit,t4):or3(it,iit,iiit)
+yt@[three:iii]
+t6:=or3i3(it,iit,iiit,t4(yt,xt,three)):or3(it,iit,iiit)
+yt@t7:=or3app(i,ii,iii,or3(it,iit,iiit),satz9a(nofnt(xt),nofnt(yt)),[u:i]t1(u),[u:ii]t5(u),[u:iii]t6(u)):or3(it,iit,iiit)
+[onet:it]
+t8:=isnten(xt,yt,onet):i
+yt@[twot:iit][vt:natt][d:diffprop(xt,yt,vt)]
+t9:=somei(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),nofnt(vt),diffprope(xt,yt,vt,d)):ii
+twot@t10:=someapp(natt,[u:natt]diffprop(xt,yt,u),twot,ii,[u:natt][v:diffprop(xt,yt,u)]t9(u,v)):ii
+yt@[threet:iiit]
+t11:=t10(yt,xt,threet):iii
+yt@t12:=satz9b(nofnt(xt),nofnt(yt)):ec3(i,ii,iii)
+onet@t13:=ec3e12(i,ii,iii,t12,t8):not(ii)
+t14:=th3"l.imp"(iit,ii,t13,[x:iit]t10(x)):not(iit)
+yt@t15:=th1"l.ec"(it,iit,[x:it]t14(x)):ec(it,iit)
+twot@t16:=ec3e23(i,ii,iii,t12,t10):not(iii)
+t17:=th3"l.imp"(iiit,iii,t16,[x:iiit]t11(x)):not(iiit)
+yt@t18:=th1"l.ec"(iit,iiit,[x:iit]t17(x)):ec(iit,iiit)
+threet@t19:=ec3e31(i,ii,iii,t12,t11):not(i)
+t20:=th3"l.imp"(it,i,t19,[x:it]t8(x)):not(it)
+yt@t21:=th1"l.ec"(iiit,it,[x:iiit]t20(x)):ec(iiit,it)
+t22:=th6"l.ec3"(it,iit,iiit,t15,t18,t21):ec3(it,iit,iiit)
+-59
+yt@satz9:=orec3i(it".59",iit".59",iiit".59",t7".59",t22".59"):orec3(is(xt,yt),some([u:natt]is(xt,pl(yt,u))),some([u:natt]is(yt,pl(xt,u))))
+more:=more"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[m:more(xt,yt)]
++*ii5
+m@t31:=moree(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+m@moree:=satz111a(nofnt(xt),nofnt(yt),t31".ii5"):more"n"(nofnt(xt),nofnt(yt))
+yt@[m:more"n"(nofnt(xt),nofnt(yt))]
++*ii5
+m@t32:=satz111d(nofnt(xt),nofnt(yt),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+m@morei:=morei"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t32".ii5"):more(xt,yt)
+yt@less:=less"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[l:less(xt,yt)]
++*ii5
+l@t33:=lesse(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+l@lesse:=satz111c(nofnt(xt),nofnt(yt),t33".ii5"):less"n"(nofnt(xt),nofnt(yt))
+yt@[l:less"n"(nofnt(xt),nofnt(yt))]
++*ii5
+l@t34:=satz111f(nofnt(xt),nofnt(yt),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+l@lessi:=lessi"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t34".ii5"):less(xt,yt)
+yt@moreis:=moreis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[m:moreis(xt,yt)]
+moreise:=th9"l.or"(more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),m,[u:more"rt"(rtofnt(xt),rtofnt(yt))]moree(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis"n"(nofnt(xt),nofnt(yt))
+yt@[m:moreis"n"(nofnt(xt),nofnt(yt))]
+moreisi:=th9"l.or"(more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),m,[u:more"n"(nofnt(xt),nofnt(yt))]morei(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis(xt,yt)
+yt@lessis:=lessis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[l:lessis(xt,yt)]
+lessise:=th9"l.or"(less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),l,[u:less"rt"(rtofnt(xt),rtofnt(yt))]lesse(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis"n"(nofnt(xt),nofnt(yt))
+yt@[l:lessis"n"(nofnt(xt),nofnt(yt))]
+lessisi:=th9"l.or"(less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),l,[u:less"n"(nofnt(xt),nofnt(yt))]lessi(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis(xt,yt)
+zt@[l:less(xt,yt)][k:less(yt,zt)]
++515
+t1:=satz15(nofnt(xt),nofnt(yt),nofnt(zt),lesse(xt,yt,l),lesse(yt,zt,k)):less"n"(nofnt(xt),nofnt(zt))
+-515
+satz15:=lessi(xt,zt,t1".515"):less(xt,zt)
+zt@[ut:natt][m:more(xt,yt)][n:more(zt,ut)]
++521
+t1:=satz21(nofnt(xt),nofnt(yt),nofnt(zt),nofnt(ut),moree(xt,yt,m),moree(zt,ut,n)):more"n"(pl"n"(nofnt(xt),nofnt(zt)),pl"n"(nofnt(yt),nofnt(ut)))
+t2:=ismore12"n"(pl"n"(nofnt(xt),nofnt(zt)),nofnt(pl(xt,zt)),pl"n"(nofnt(yt),nofnt(ut)),nofnt(pl(yt,ut)),ispln(xt,zt),ispln(yt,ut),t1):more"n"(nofnt(pl(xt,zt)),nofnt(pl(yt,ut)))
+-521
+satz21:=morei(pl(xt,zt),pl(yt,ut),t2".521"):more(pl(xt,zt),pl(yt,ut))
+@[p:[x:natt]'prop'][n:natt]
+lb:=all([x:natt]imp(<x>p,lessis(n,x))):'prop'
+min:=and(lb,<n>p):'prop'
+p@[s:some(p)]
++527
+q:=[x:nat]<ntofn(x)>p:[x:nat]'prop'
+[n:natt][np:<n>p]
+t1:=isp(natt,p,n,ntofn(nofnt(n)),np,isntn1(n)):<nofnt(n)>q
+t2:=somei(nat,q,nofnt(n),t1):some"n"(q)
+s@t3:=someapp(natt,p,s,some"n"(q),[u:natt][v:<u>p]t2(u,v)):some"n"(q)
+t4:=satz27(q,t3):some"n"([x:nat]min"n"(q,x))
+[m:nat][mqm:min"n"(q,m)]
+t5:=ande1(lb"n"(q,m),<m>q,mqm):lb"n"(q,m)
+[n:nat][nq:<n>q]
+t6:=mp(<n>q,lessis"n"(m,n),nq,<n>t5):lessis"n"(m,n)
+mqm@[n:natt][np:<n>p]
+t7:=t6(nofnt(n),t1(n,np)):lessis"n"(m,nofnt(n))
+t8:=islessis1"n"(m,nofnt(ntofn(m)),nofnt(n),isnnt1(m),t7):lessis"n"(nofnt(ntofn(m)),nofnt(n))
+t9:=lessisi(ntofn(m),n,t8):lessis(ntofn(m),n)
+n@t10:=[u:<n>p]t9(u):imp(<n>p,lessis(ntofn(m),n))
+mqm@t11:=[x:natt]t10(x):lb(ntofn(m))
+t12:=ande2(lb"n"(q,m),<m>q,mqm):<ntofn(m)>p
+t13:=andi(lb(ntofn(m)),<ntofn(m)>p,t11,t12):min(ntofn(m))
+t14:=somei(natt,[x:natt]min(x),ntofn(m),t13):some([x:natt]min(x))
+-527
+satz27:=someapp(nat,[x:nat]min"n"(q".527",x),t4".527",some([x:natt]min(x)),[x:nat][y:min"n"(q".527",x)]t14".527"(x,y)):some([x:natt]min(p,x))
+-nt
+@1rt:=rtofn(1):rat
+x0@[x:frac][xix0:inf(x,class(x0))]
++*ii5
+xix0@t35:=tr3eq(tf(x,fr(1,1)),fr(ts"n"(num(x),1),ts"n"(den(x),1)),fr(num(x),den(x)),x,tfeq1a(x,1,1),eqnd(ts"n"(num(x),1),ts"n"(den(x),1),num(x),den(x),satz28a(num(x)),satz28a(den(x))),refeq1(fr(num(x),den(x)),x,fris(x))):eq"n"(tf(x,fr(1,1)),x)
+t36:=isi(ts(x0,1rt),x0,tf(x,fr(1,1)),x,tict(x0,1rt,x,fr(1,1),xix0,inclass(fr(1,1))),xix0,t35):is(ts(x0,1rt),x0)
+-ii5
+x0@example1a:=ratapp1(x0,is(ts(x0,1rt),x0),[x:frac][xi:inf(x,class(x0))]t36".ii5"(x,xi)):is(ts(x0,1rt),x0)
+example1b:=symis(rat,ts(x0,1rt),x0,example1a):is(x0,ts(x0,1rt))
+example1c:=tris(rat,ts(1rt,x0),ts(x0,1rt),x0,comts(1rt,x0),example1a):is(ts(1rt,x0),x0)
+example1d:=symis(rat,ts(1rt,x0),x0,example1c):is(x0,ts(1rt,x0))
+@[x:frac]
++5114
+t1:=tr3eq(tf(fr(den(x),1),x),fr(ts"n"(den(x),num(x)),ts"n"(1,den(x))),fr(ts"n"(num(x),den(x)),ts"n"(1,den(x))),fr(num(x),1),tfeq2a(x,den(x),1),eqn(ts"n"(den(x),num(x)),ts"n"(1,den(x)),ts"n"(num(x),den(x)),comts"n"(den(x),num(x))),satz40c(num(x),1,den(x))):eq"n"(tf(fr(den(x),1),x),fr(num(x),1))
+-5114
+satz114:=isi(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)),tf(fr(den(x),1),x),fr(num(x),1),tict(rtofn(den(x)),ratof(x),fr(den(x),1),x,inclass(fr(den(x),1)),inclass(x)),inclass(fr(num(x),1)),t1".5114"):is(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)))
+@[x1:nat][x2:nat]
+satz114a:=tr3is(rat,ts(rtofn(x2),ratof(fr(x1,x2))),ts(rtofn(den(fr(x1,x2))),ratof(fr(x1,x2))),rtofn(num(fr(x1,x2))),rtofn(x1),ists1(rtofn(x2),rtofn(den(fr(x1,x2))),ratof(fr(x1,x2)),isnert(x2,den(fr(x1,x2)),isden(x1,x2))),satz114(fr(x1,x2)),isnert(num(fr(x1,x2)),x1,numis(x1,x2))):is(ts(rtofn(x2),ratof(fr(x1,x2))),rtofn(x1))
+x0@[y0:rat]
+ov:=ind(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):rat
+satz110c:=oneax(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):is(ts(y0,ov(x0,y0)),x0)
+satz110d:=symis(rat,ts(y0,ov(x0,y0)),x0,satz110c):is(x0,ts(y0,ov(x0,y0)))
+satz110e:=tris(rat,ts(ov(x0,y0),y0),ts(y0,ov(x0,y0)),x0,comts(ov(x0,y0),y0),satz110c):is(ts(ov(x0,y0),y0),x0)
+satz110f:=symis(rat,ts(ov(x0,y0),y0),x0,satz110e):is(x0,ts(ov(x0,y0),y0))
+[v0:rat][i:is(ts(y0,v0),x0)]
+satz110g:=satz110b(x0,y0,v0,ov(x0,y0),i,satz110c):is(v0,ov(x0,y0))
+x2@satz114b:=satz110b(rtofn(x1),rtofn(x2),ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114a,satz110c(rtofn(x1),rtofn(x2))):is(ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)))
+satz114c:=symis(rat,ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114b):is(ov(rtofn(x1),rtofn(x2)),ratof(fr(x1,x2)))
++5115
+y0@t1:=satz89(ov(y0,x0)):some([t:rat]more(t,ov(y0,x0)))
+[u0:rat][m:more(u0,ov(y0,x0))][u:frac][uiu0:inf(u,class(u0))]
+z:=num(u):nat
+v:=den(u):nat
+t2:=ismore1(u0,ov(rtofn(z),rtofn(v)),ov(y0,x0),tris(rat,u0,ratof(fr(z,v)),ov(rtofn(z),rtofn(v)),isi(u0,ratof(fr(z,v)),u,fr(z,v),uiu0,inclass(fr(z,v)),refeq1(u,fr(z,v),isfr(u))),satz114b(z,v)),m):more(ov(rtofn(z),rtofn(v)),ov(y0,x0))
+t3:=moreisi(rtofn(v),1rt,fr(v,1),fr(1,1),inclass(fr(v,1)),inclass(fr(1,1)),th9"l.or"(more"n"(v,1),is"n"(v,1),moref(fr(v,1),fr(1,1)),eq"n"(fr(v,1),fr(1,1)),satz24(v),[t:more"n"(v,1)]satz111d(v,1,t),[t:is"n"(v,1)]satz111e(v,1,t))):moreis(rtofn(v),1rt)
+t4:=tr3is(rat,ts(rtofn(z),x0),ts(x0,rtofn(z)),ts(x0,ts(ov(rtofn(z),rtofn(v)),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),comts(rtofn(z),x0),ists2(rtofn(z),ts(ov(rtofn(z),rtofn(v)),rtofn(v)),x0,satz110f(rtofn(z),rtofn(v))),assts2(x0,ov(rtofn(z),rtofn(v)),rtofn(v))):is(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)))
+[n:more(rtofn(v),1rt)]
+t5:=ismore1(ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),symis(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),t4),satz105d(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),n)):more(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+t6:=moreisi1(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t5):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+uiu0@[i:is(rtofn(v),1rt)]
+t7:=moreisi2(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),tris(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t4,ists2(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),i))):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+uiu0@t8:=orapp(more(rtofn(v),1rt),is(rtofn(v),1rt),moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt)),t3,[t:more(rtofn(v),1rt)]t6(t),[t:is(rtofn(v),1rt)]t7(t)):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+t9:=ismore12(ts(x0,ov(rtofn(z),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),ts(x0,ov(y0,x0)),y0,example1b(ts(x0,ov(rtofn(z),rtofn(v)))),satz110c(y0,x0),satz105d(ov(rtofn(z),rtofn(v)),ov(y0,x0),x0,t2)):more(ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0)
+t10:=satz87c(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0,t8,t9):more(ts(rtofn(z),x0),y0)
+t11:=somei(nat,[t:nat]more(ts(rtofn(t),x0),y0),z,t10):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
+m@t12:=ratapp1(u0,some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[u:frac][ui:inf(u,class(u0))]t11(u,ui)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
+-5115
+y0@satz115:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[t:rat][u:more(t,ov(y0,x0))]t12".5115"(t,u)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
++*5115
+uiu0@t13:=andi(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0),natrti(z),t10):and(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0))
+t14:=somei(rat,[t:rat]and(natrt(t),more(ts(t,x0),y0)),rtofn(z),t13):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
+m@t15:=ratapp1(u0,some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[u:frac][ui:inf(u,class(u0))]t14(u,ui)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
+-5115
+y0@satz115a:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[t:rat][u:more(t,ov(y0,x0))]t15".5115"(t,u)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
+@[s:set(rat)]
+cutprop1a:=nonempty(rat,s):'prop'
+cutprop1b:=not(all([x:rat]in(x,s))):'prop'
+cutprop1:=and(cutprop1a,cutprop1b):'prop'
+[x0:rat]
+cutprop2a:=all([x:rat]imp(not(in(x,s)),less(x0,x))):'prop'
+s@cutprop2:=all([x:rat]imp(in(x,s),cutprop2a(x))):'prop'
+x0@[y0:rat]
++iii1
+ubprop:=imp(in(y0,s),moreis(x0,y0)):'prop'
+-iii1
+x0@ub:=all([x:rat]ubprop".iii1"(x0,x)):'prop'
+max:=and(ub(x0),in(x0,s)):'prop'
+s@cutprop3:=not(some([x:rat]max(s,x))):'prop'
+cutprop:=and3(cutprop1,cutprop2,cutprop3):'prop'
++*iii1
+y0@lbprop:=imp(in(y0,s),lessis(x0,y0)):'prop'
+-iii1
+x0@lb:=all([x:rat]lbprop".iii1"(x0,x)):'prop'
+min:=and(lb(x0),in(x0,s)):'prop'
+@cut:=ot(set(rat),[x:set(rat)]cutprop(x)):'type'
+[ksi:cut]
+lcl:=in"e"(set(rat),[x:set(rat)]cutprop(x),ksi):set(rat)
+[x0:rat]
+lrt:=in(x0,lcl(ksi)):'prop'
+urt:=not(in(x0,lcl(ksi))):'prop'
+ksi@clcl:=inp(set(rat),[x:set(rat)]cutprop(x),ksi):cutprop(lcl(ksi))
+clcl1:=and3e1(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop1(lcl(ksi))
+clcl2:=and3e2(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop2(lcl(ksi))
+clcl3:=and3e3(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop3(lcl(ksi))
+clcl1a:=ande1(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1a(lcl(ksi))
+clcl1b:=ande2(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1b(lcl(ksi))
+[p:'prop'][p1:[x:rat][t:lrt(ksi,x)]p]
+cutapp1a:=nonemptyapp(rat,lcl,clcl1a,p,p1):p
++*iii1
+ksi@t1:=th1"l.some"(rat,[x:rat]lrt(ksi,x),clcl1b):some([x:rat]urt(ksi,x))
+-iii1
+p@[p1:[x:rat][t:urt(ksi,x)]p]
+cutapp1b:=someapp(rat,[x:rat]urt(ksi,x),t1".iii1",p,p1):p
+ksi@[x0:rat][lx:lrt(ksi,x0)]
++*iii1
+lx@t2:=mp(lrt(ksi,x0),cutprop2a(lcl,x0),lx,<x0>clcl2):cutprop2a(lcl,x0)
+-iii1
+lx@[y0:rat][uy:urt(ksi,y0)]
+cutapp2a:=mp(urt(ksi,y0),less(x0,y0),uy,<y0>t2".iii1"):less(x0,y0)
+cutapp2b:=satz83(x0,y0,cutapp2a):more(y0,x0)
++*iii1
+lx@t3:=th4"l.some"(rat,[x:rat]max(lcl,x),clcl3,x0):not(max(lcl,x0))
+t4:=th4"l.and"(ub(lcl,x0),lrt(ksi,x0),t3,lx):not(ub(lcl,x0))
+t5:=th1"l.some"(rat,[x:rat]ubprop(lcl,x0,x),t4):some([x:rat]not(ubprop(lcl,x0,x)))
+-iii1
+lx@[p:'prop'][p1:[y:rat][t:lrt(ksi,y)][u:less(x0,y)]p][y0:rat][n:not(ubprop".iii1"(lcl,x0,y0))]
++*iii1
+n@t6:=th5"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):lrt(ksi,y0)
+t7:=th6"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):not(moreis(x0,y0))
+t8:=satz81j(x0,y0,t7):less(x0,y0)
+t9:=<t8><t6><y0>p1:p
+-iii1
+p1@cutapp3:=someapp(rat,[y:rat]not(ubprop".iii1"(lcl,x0,y)),t5".iii1",p,[y:rat][t:not(ubprop".iii1"(lcl,x0,y))]t9".iii1"(y,t)):p
+s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))]
++*iii1
+n@t10:=andi(cutprop1a,cutprop1b,nonemptyi(rat,s,x0,i),th1"l.all"(rat,[x:rat]in(x,s),y0,n)):cutprop1
+-iii1
+s@[n:[x:rat]not(max(s,x))]
++*iii1
+n@t11:=th5"l.some"(rat,[x:rat]max(s,x),n):cutprop3
+-iii1
+s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][l:[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]less(x,y)][m:[x:rat]not(max(s,x))]
+cut1:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),l,t11".iii1"(m)):cutprop(s)
++rp
+ksi@[eta:cut]
+is:=is"e"(cut,ksi,eta):'prop'
+nis:=not(is(ksi,eta)):'prop'
+[i:is(ksi,eta)]
+ise:=isini(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is"e"(set(rat),lcl(ksi),lcl(eta))
+[x0:rat][lx:lrt(ksi,x0)]
+ise1:=issete1(rat,lcl(ksi),lcl(eta),ise,x0,lx):lrt(eta,x0)
+eta@[i:is"e"(set(rat),lcl(ksi),lcl(eta))]
+isi:=isine(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is(ksi,eta)
+eta@[l:[x:rat][t:lrt(ksi,x)]lrt(eta,x)][k:[x:rat][t:lrt(eta,x)]lrt(ksi,x)]
+isi1:=isi(isseti(rat,lcl(ksi),lcl(eta),l,k)):is(ksi,eta)
+@[s:set(rat)][cs:cutprop(s)]
+cutof:=out(set(rat),[x:set(rat)]cutprop(x),s,cs):cut
+[x0:rat][i:in(x0,s)]
+ine:=issete1(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,i):lrt(cutof(s,cs),x0)
+x0@[lx:lrt(cutof(s,cs),x0)]
+ini:=issete2(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,lx):in(x0,s)
+s@[t:set(rat)][cs:cutprop(s)][ct:cutprop(t)][i:[x:rat][u:in(x,s)]in(x,t)][j:[x:rat][u:in(x,t)]in(x,s)]
+isi2:=isouti(set(rat),[x:set(rat)]cutprop(x),s,cs,t,ct,isseti(rat,s,t,i,j)):is(cutof(s,cs),cutof(t,ct))
+@[p:[x:cut]'prop']
+all:=all"l"(cut,p):'prop'
+some:=some"l"(cut,p):'prop'
+one:=one"e"(cut,p):'prop'
+ksi@satz116:=refis(cut,ksi):is(ksi,ksi)
+eta@[i:is(ksi,eta)]
+satz117:=symis(cut,ksi,eta,i):is(eta,ksi)
+eta@[zeta:cut][i:is(ksi,eta)][j:is(eta,zeta)]
+satz118:=tris(cut,ksi,eta,zeta,i,j):is(ksi,zeta)
++1119
+@[x0:rat][y0:rat][m:more(x0,y0)]
+t1:=ec3e23(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),m):not(less(x0,y0))
+-1119
+ksi@[x0:rat][ux:urt(ksi,x0)][y0:rat][m:more(y0,x0)]
+satz119:=th3"l.imp"(lrt(ksi,y0),less(y0,x0),t1".1119"(y0,x0,m),[t:lrt(ksi,y0)]cutapp2a(y0,t,x0,ux)):urt(ksi,y0)
+y0@[l:less(x0,y0)]
+satz119a:=satz119(satz83(x0,y0,l)):urt(ksi,y0)
++1120
+@[x0:rat][y0:rat][l:less(x0,y0)]
+t1:=ec3e32(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),l):not(more(x0,y0))
+-1120
+ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][l:less(y0,x0)]
+satz120:=th7"l.imp"(lrt(ksi,y0),more(y0,x0),t1".1120"(y0,x0,l),[t:urt(ksi,y0)]cutapp2b(x0,lx,y0,t)):lrt(ksi,y0)
+y0@[m:more(x0,y0)]
+satz120a:=satz120(satz82(x0,y0,m)):lrt(ksi,y0)
+-rp
+s@[i:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][x0:rat][j:in(x0,s)][y0:rat][n:not(in(y0,s))]
++*iii1
+n@t12:=<y0><j><x0>i:[u:less(y0,x0)]in(y0,s)
+t13:=th3"l.imp"(less(y0,x0),in(y0,s),n,t12):not(less(y0,x0))
+t14:=satz81f(y0,x0,t13):moreis(y0,x0)
+-iii1
+n@[k:is(y0,x0)]
++*iii1
+k@t15:=isp1(rat,[x:rat]in(x,s),x0,y0,j,k):in(y0,s)
+n@t16:=th3"l.imp"(is(y0,x0),in(y0,s),n,[t:is(y0,x0)]t15(t)):nis(y0,x0)
+t17:=ore1(more(y0,x0),is(y0,x0),t14,t16):more(y0,x0)
+t18:=satz82(y0,x0,t17):less(x0,y0)
+i@t19:=[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]t18(x,t,y,u):cutprop2
+-iii1
+s@[s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))][x0:rat][i:in(x0,s)]
++*iii1
+i@t20:=<i><x0>s1:some([y:rat]and(in(y,s),more(y,x0)))
+-iii1
+i@[y0:rat][a:and(in(y0,s),more(y0,x0))]
++*iii1
+a@t21:=ande1(in(y0,s),more(y0,x0),a):in(y0,s)
+t22:=ande2(in(y0,s),more(y0,x0),a):more(y0,x0)
+t23:=satz81g(y0,x0,t22):not(lessis(y0,x0))
+t24:=th3"l.imp"(moreis(x0,y0),lessis(y0,x0),t23,[t:moreis(x0,y0)]satz84(x0,y0,t)):not(moreis(x0,y0))
+t25:=th4"l.imp"(in(y0,s),moreis(x0,y0),t21,t24):not(ubprop(x0,y0))
+t26:=th1"l.all"(rat,[y:rat]ubprop(x0,y),y0,t25):not(ub(s,x0))
+t27:=th1"l.and"(ub(s,x0),in(x0,s),t26):not(max(s,x0))
+i@t28:=someapp(rat,[y:rat]and(in(y,s),more(y,x0)),t20,not(max(s,x0)),[y:rat][t:and(in(y,s),more(y,x0))]t27(y,t)):not(max(s,x0))
+-iii1
+x0@[n:not(in(x0,s))]
++*iii1
+n@t29:=th2"l.and"(ub(x0),in(x0,s),n):not(max(s,x0))
+x0@t30:=th1"l.imp"(in(x0,s),not(max(s,x0)),[u:in(x0,s)]t28(u),[u:not(in(x0,s))]t29(u)):not(max(s,x0))
+s1@t31:=t11([x:rat]t30(x)):cutprop3
+-iii1
+s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][j:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))]
+cut2:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),t19".iii1"(j),t31".iii1"(s1)):cutprop(s)
++*rp
+eta@more:=some"rt"([x:rat]and(lrt(ksi,x),urt(eta,x))):'prop'
+[m:more(ksi,eta)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]p][x0:rat][a:and(lrt(ksi,x0),urt(eta,x0))]
++iii2
+t1:=ande1(lrt(ksi,x0),urt(eta,x0),a):lrt(ksi,x0)
+t2:=ande2(lrt(ksi,x0),urt(eta,x0),a):urt(eta,x0)
+t3:=<t2><t1><x0>p1:p
+-iii2
+p1@moreapp:=someapp(rat,[x:rat]and(lrt(ksi,x),urt(eta,x)),m,p,[x:rat][t:and(lrt(ksi,x),urt(eta,x))]t3".iii2"(x,t)):p
+eta@less:=some"rt"([x:rat]and(urt(ksi,x),lrt(eta,x))):'prop'
+[l:less(ksi,eta)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]p][x0:rat][a:and(urt(ksi,x0),lrt(eta,x0))]
++*iii2
+a@t4:=ande1(urt(ksi,x0),lrt(eta,x0),a):urt(ksi,x0)
+t5:=ande2(urt(ksi,x0),lrt(eta,x0),a):lrt(eta,x0)
+t6:=<t5><t4><x0>p1:p
+-iii2
+p1@lessapp:=someapp(rat,[x:rat]and(urt(ksi,x),lrt(eta,x)),l,p,[x:rat][t:and(urt(ksi,x),lrt(eta,x))]t6".iii2"(x,t)):p
+eta@[m:more(ksi,eta)]
++2121
+[x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
+t1:=andi(urt(eta,x0),lrt(ksi,x0),ux,lx):and(urt(eta,x0),lrt(ksi,x0))
+t2:=somei(rat,[x:rat]and(urt(eta,x),lrt(ksi,x)),x0,t1):less(eta,ksi)
+-2121
+satz121:=moreapp(m,less(eta,ksi),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2".2121"(x,t,u)):less(eta,ksi)
+eta@[l:less(ksi,eta)]
++2122
+[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
+t1:=andi(lrt(eta,x0),urt(ksi,x0),lx,ux):and(lrt(eta,x0),urt(ksi,x0))
+t2:=somei(rat,[x:rat]and(lrt(eta,x),urt(ksi,x)),x0,t1):more(eta,ksi)
+-2122
+satz122:=lessapp(l,more(eta,ksi),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t2".2122"(x,t,u)):more(eta,ksi)
++2123
+eta@[m:more(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
+t1:=th3"st.isset"(rat,lcl(ksi),lcl(eta),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
+t2:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t1,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
+m@t3:=moreapp(ksi,eta,m,not(is(ksi,eta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2(x,t,u)):not(is(ksi,eta))
+eta@t4:=th2"l.ec"(is(ksi,eta),more(ksi,eta),[t:more(ksi,eta)]t3(t)):ec(is(ksi,eta),more(ksi,eta))
+[l:less(ksi,eta)][x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
+t5:=th4"st.isset"(rat,lcl(eta),lcl(ksi),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
+t6:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t5,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
+l@t7:=lessapp(ksi,eta,l,not(is(ksi,eta)),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t6(x,t,u)):not(is(ksi,eta))
+eta@t8:=th1"l.ec"(less(ksi,eta),is(ksi,eta),[t:less(ksi,eta)]t7(t)):ec(less(ksi,eta),is(ksi,eta))
+m@[l:less(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)][y0:rat][uy:urt(ksi,y0)][ly:lrt(eta,y0)]
+t9:=cutapp2a(ksi,x0,lx,y0,uy):less"rt"(x0,y0)
+t10:=cutapp2b(eta,y0,ly,x0,ux):more"rt"(x0,y0)
+t11:=mp(less"rt"(x0,y0),con,t9,ec3e23(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),satz81b(x0,y0),t10)):con
+ux@t12:=lessapp(ksi,eta,l,con,[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t11(x,t,u)):con
+l@t13:=moreapp(ksi,eta,m,con,[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t12(x,t,u)):con
+m@t14:=[t:less(ksi,eta)]t13(t):not(less(ksi,eta))
+eta@t15:=th1"l.ec"(more(ksi,eta),less(ksi,eta),[t:more(ksi,eta)]t14(t)):ec(more(ksi,eta),less(ksi,eta))
+a:=th6"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t4,t15,t8):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+[i:is(ksi,eta)]
+t16:=or3i1(is(ksi,eta),more(ksi,eta),less(ksi,eta),i):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+eta@[n:nis(ksi,eta)]
+t17:=th3"l.imp"(is"e"(set(rat),lcl(ksi),lcl(eta)),is(ksi,eta),n,[t:is"e"(set(rat),lcl(ksi),lcl(eta))]isi(ksi,eta,t)):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
+t18:=th5"st.isset"(rat,lcl(ksi),lcl(eta),t17):or(more(ksi,eta),more(eta,ksi))
+t19:=th8"l.or"(more(ksi,eta),more(eta,ksi),less(ksi,eta),t18,[t:more(eta,ksi)]satz121(eta,ksi,t)):or(more(ksi,eta),less(ksi,eta))
+t20:=th7"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t19):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+eta@b:=th1"l.imp"(is(ksi,eta),or3(is(ksi,eta),more(ksi,eta),less(ksi,eta)),[t:is(ksi,eta)]t16(t),[t:nis(ksi,eta)]t20(t)):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+-2123
+eta@satz123:=orec3i(is(ksi,eta),more(ksi,eta),less(ksi,eta),b".2123",a".2123"):orec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+satz123a:=orec3e1(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+satz123b:=orec3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+moreis:=or(more(ksi,eta),is(ksi,eta)):'prop'
+lessis:=or(less(ksi,eta),is(ksi,eta)):'prop'
+[m:moreis(ksi,eta)]
+satz124:=th9"l.or"(more(ksi,eta),is(ksi,eta),less(eta,ksi),is(eta,ksi),m,[t:more(ksi,eta)]satz121(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):lessis(eta,ksi)
+eta@[l:lessis(ksi,eta)]
+satz125:=th9"l.or"(less(ksi,eta),is(ksi,eta),more(eta,ksi),is(eta,ksi),l,[t:less(ksi,eta)]satz122(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):moreis(eta,ksi)
+zeta@[i:is(ksi,eta)][m:more(ksi,zeta)]
+ismore1:=isp(cut,[u:cut]more(u,zeta),ksi,eta,m,i):more(eta,zeta)
+i@[m:more(zeta,ksi)]
+ismore2:=isp(cut,[u:cut]more(zeta,u),ksi,eta,m,i):more(zeta,eta)
+i@[l:less(ksi,zeta)]
+isless1:=isp(cut,[u:cut]less(u,zeta),ksi,eta,l,i):less(eta,zeta)
+i@[l:less(zeta,ksi)]
+isless2:=isp(cut,[u:cut]less(zeta,u),ksi,eta,l,i):less(zeta,eta)
+i@[m:moreis(ksi,zeta)]
+ismoreis1:=isp(cut,[u:cut]moreis(u,zeta),ksi,eta,m,i):moreis(eta,zeta)
+i@[m:moreis(zeta,ksi)]
+ismoreis2:=isp(cut,[u:cut]moreis(zeta,u),ksi,eta,m,i):moreis(zeta,eta)
+i@[l:lessis(ksi,zeta)]
+islessis1:=isp(cut,[u:cut]lessis(u,zeta),ksi,eta,l,i):lessis(eta,zeta)
+i@[l:lessis(zeta,ksi)]
+islessis2:=isp(cut,[u:cut]lessis(zeta,u),ksi,eta,l,i):lessis(zeta,eta)
+eta@[i:is(ksi,eta)]
+moreisi2:=ori2(more(ksi,eta),is(ksi,eta),i):moreis(ksi,eta)
+lessisi2:=ori2(less(ksi,eta),is(ksi,eta),i):lessis(ksi,eta)
+eta@[m:more(ksi,eta)]
+moreisi1:=ori1(more(ksi,eta),is(ksi,eta),m):moreis(ksi,eta)
+eta@[l:less(ksi,eta)]
+lessisi1:=ori1(less(ksi,eta),is(ksi,eta),l):lessis(ksi,eta)
+zeta@[upsilon:cut][i:is(ksi,eta)][j:is(zeta,upsilon)][m:more(ksi,zeta)]
+ismore12:=ismore2(zeta,upsilon,eta,j,ismore1(ksi,eta,zeta,i,m)):more(eta,upsilon)
+j@[l:less(ksi,zeta)]
+isless12:=isless2(zeta,upsilon,eta,j,isless1(ksi,eta,zeta,i,l)):less(eta,upsilon)
+j@[m:moreis(ksi,zeta)]
+ismoreis12:=ismoreis2(zeta,upsilon,eta,j,ismoreis1(ksi,eta,zeta,i,m)):moreis(eta,upsilon)
+j@[l:lessis(ksi,zeta)]
+islessis12:=islessis2(zeta,upsilon,eta,j,islessis1(ksi,eta,zeta,i,l)):lessis(eta,upsilon)
+eta@[m:moreis(ksi,eta)]
+satz123c:=th7"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,comor(more(ksi,eta),is(ksi,eta),m)):not(less(ksi,eta))
+eta@[l:lessis(ksi,eta)]
+satz123d:=th9"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l):not(more(ksi,eta))
+eta@[n:not(more(ksi,eta))]
+satz123e:=th2"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n):lessis(ksi,eta)
+eta@[n:not(less(ksi,eta))]
+satz123f:=comor(is(ksi,eta),more(ksi,eta),th3"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n)):moreis(ksi,eta)
+eta@[m:more(ksi,eta)]
+satz123g:=th3"l.or"(less(ksi,eta),is(ksi,eta),ec3e23(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m),ec3e21(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m)):not(lessis(ksi,eta))
+eta@[l:less(ksi,eta)]
+satz123h:=th3"l.or"(more(ksi,eta),is(ksi,eta),ec3e32(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l),ec3e31(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l)):not(moreis(ksi,eta))
+eta@[n:not(moreis(ksi,eta))]
+satz123j:=or3e3(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th5"l.or"(more(ksi,eta),is(ksi,eta),n),th4"l.or"(more(ksi,eta),is(ksi,eta),n)):less(ksi,eta)
+eta@[n:not(lessis(ksi,eta))]
+satz123k:=or3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th4"l.or"(less(ksi,eta),is(ksi,eta),n),th5"l.or"(less(ksi,eta),is(ksi,eta),n)):more(ksi,eta)
+zeta@[l:less(ksi,eta)][k:less(eta,zeta)]
++2126
+[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)][y0:rat][uy:urt(eta,y0)][ly:lrt(zeta,y0)]
+t1:=cutapp2a(eta,x0,lx,y0,uy):less"rt"(x0,y0)
+t2:=satz119a(ksi,x0,ux,y0,t1):urt(ksi,y0)
+t3:=andi(urt(ksi,y0),lrt(zeta,y0),t2,ly):and(urt(ksi,y0),lrt(zeta,y0))
+t4:=somei(rat,[x:rat]and(urt(ksi,x),lrt(zeta,x)),y0,t3):less(ksi,zeta)
+lx@t5:=lessapp(eta,zeta,k,less(ksi,zeta),[x:rat][t:urt(eta,x)][u:lrt(zeta,x)]t4(x,t,u)):less(ksi,zeta)
+-2126
+satz126:=lessapp(ksi,eta,l,less(ksi,zeta),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t5".2126"(x,t,u)):less(ksi,zeta)
+trless:=satz126:less(ksi,zeta)
+zeta@[m:more(ksi,eta)][n:more(eta,zeta)]
+trmore:=satz122(zeta,ksi,satz126(zeta,eta,ksi,satz121(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
+zeta@[l:lessis(ksi,eta)][k:less(eta,zeta)]
+satz127a:=orapp(less(ksi,eta),is(ksi,eta),less(ksi,zeta),l,[u:less(ksi,eta)]trless(u,k),[u:is(ksi,eta)]isless1(eta,ksi,zeta,symis(cut,ksi,eta,u),k)):less(ksi,zeta)
+zeta@[l:less(ksi,eta)][k:lessis(eta,zeta)]
+satz127b:=orapp(less(eta,zeta),is(eta,zeta),less(ksi,zeta),k,[u:less(eta,zeta)]trless(l,u),[u:is(eta,zeta)]isless2(eta,zeta,ksi,u,l)):less(ksi,zeta)
+zeta@[m:moreis(ksi,eta)][n:more(eta,zeta)]
+satz127c:=satz122(zeta,ksi,satz127b(zeta,eta,ksi,satz121(eta,zeta,n),satz124(ksi,eta,m))):more(ksi,zeta)
+zeta@[m:more(ksi,eta)][n:moreis(eta,zeta)]
+satz127d:=satz122(zeta,ksi,satz127a(zeta,eta,ksi,satz124(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
+zeta@[l:lessis(ksi,eta)][k:lessis(eta,zeta)]
++2128
+[i:is(ksi,eta)][j:is(eta,zeta)]
+t1:=lessisi2(ksi,zeta,tris(cut,ksi,eta,zeta,i,j)):lessis(ksi,zeta)
+i@[j:less(eta,zeta)]
+t2:=lessisi1(ksi,zeta,satz127a(l,j)):lessis(ksi,zeta)
+i@t3:=orapp(less(eta,zeta),is(eta,zeta),lessis(ksi,zeta),k,[t:less(eta,zeta)]t2(t),[t:is(eta,zeta)]t1(t)):lessis(ksi,zeta)
+k@[j:less(ksi,eta)]
+t4:=lessisi1(ksi,zeta,satz127b(j,k)):lessis(ksi,zeta)
+-2128
+satz128:=orapp(less(ksi,eta),is(ksi,eta),lessis(ksi,zeta),l,[t:less(ksi,eta)]t4".2128"(t),[t:is(ksi,eta)]t3".2128"(t)):lessis(ksi,zeta)
+trlessis:=satz128:lessis(ksi,zeta)
+zeta@[m:moreis(ksi,eta)][n:moreis(eta,zeta)]
+trmoreis:=satz125(zeta,ksi,satz128(zeta,eta,ksi,satz124(eta,zeta,n),satz124(ksi,eta,m))):moreis(ksi,zeta)
+eta@[z0:rat][x0:rat][y0:rat]
+sumprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0))):'prop'
+z0@sumprop:=some"rt"([x:rat]some"rt"([y:rat]sumprop1(z0,x,y))):'prop'
+eta@sum:=setof(rat,[z:rat]sumprop(z)):set(rat)
+x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl(x0,y0))]
++iii3
+t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),lx,ly,i):sumprop1(z0,x0,y0)
+t2:=somei(rat,[y:rat]sumprop1(z0,x0,y),y0,t1):some"rt"([y:rat]sumprop1(z0,x0,y))
+t3:=somei(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),x0,t2):sumprop(z0)
+-iii3
+sum1:=estii(rat,[z:rat]sumprop(z),z0,t3".iii3"):in(z0,sum)
+z0@[i:in(z0,sum)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]p]
++*iii3
+p1@t4:=estie(rat,[z:rat]sumprop(z),z0,i):sumprop(z0)
+-iii3
+p1@[x0:rat][px:some"rt"([y:rat]sumprop1(z0,x0,y))][y0:rat][py:sumprop1(z0,x0,y0)]
++*iii3
+py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(ksi,x0)
+t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(eta,y0)
+t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):is"rt"(z0,pl(x0,y0))
+t8:=<t7><t6><y0><t5><x0>p1:p
+px@t9:=someapp(rat,[y:rat]sumprop1(z0,x0,y),px,p,[y:rat][t:sumprop1(z0,x0,y)]t8(y,t)):p
+-iii3
+p1@sumapp:=someapp(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),t4".iii3",p,[x:rat][t:some"rt"([y:rat]sumprop1(z0,x,y))]t9".iii3"(x,t)):p
+eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
++3129
+[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))]
+t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
+t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
+t3:=isless1"rt"(pl(x0,y0),z0,pl(x1,y1),symis(rat,z0,pl(x0,y0),j),satz98a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,pl(x1,y1))
+t4:=ec3e31(is"rt"(z0,pl(x1,y1)),more"rt"(z0,pl(x1,y1)),less"rt"(z0,pl(x1,y1)),satz81b(z0,pl(x1,y1)),t3):nis"rt"(z0,pl(x1,y1))
+i@t5:=sumapp(ksi,eta,z0,i,nis"rt"(z0,pl(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,pl(x1,y1))
+-3129
+satz129a:=th3"l.imp"(in(pl(x1,y1),sum),nis"rt"(pl(x1,y1),pl(x1,y1)),weli(is"rt"(pl(x1,y1),pl(x1,y1)),refis(rat,pl(x1,y1))),[t:in(pl(x1,y1),sum)]t5".3129"(pl(x1,y1),t)):not(in(pl(x1,y1),sum))
++*3129
+eta@[u0:rat][i:in(u0,sum)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,pl(x0,y0))]
+t6:=isless2"rt"(u0,pl(x0,y0),z0,j,l):less"rt"(z0,pl(x0,y0))
+z1:=ov(z0,pl(x0,y0)):rat
+t7:=isless12"rt"(z0,ts(z1,pl(x0,y0)),pl(x0,y0),ts(1rt,pl(x0,y0)),satz110f(z0,pl(x0,y0)),example1d(pl(x0,y0)),t6):less"rt"(ts(z1,pl(x0,y0)),ts(1rt,pl(x0,y0)))
+t8:=satz106c(z1,1rt,pl(x0,y0),t7):less"rt"(z1,1rt)
+t9:=isless2"rt"(ts(x0,1rt),x0,ts(x0,z1),example1a(x0),satz105f(z1,1rt,x0,t8)):less"rt"(ts(x0,z1),x0)
+t10:=isless2"rt"(ts(y0,1rt),y0,ts(y0,z1),example1a(y0),satz105f(z1,1rt,y0,t8)):less"rt"(ts(y0,z1),y0)
+t11:=satz120(ksi,x0,lx,ts(x0,z1),t9):lrt(ksi,ts(x0,z1))
+t12:=satz120(eta,y0,ly,ts(y0,z1),t10):lrt(eta,ts(y0,z1))
+t13:=tris(rat,pl(ts(x0,z1),ts(y0,z1)),ts(pl(x0,y0),z1),z0,distpt1(x0,y0,z1),satz110c(z0,pl(x0,y0))):is"rt"(pl(ts(x0,z1),ts(y0,z1)),z0)
+t14:=symis(rat,pl(ts(x0,z1),ts(y0,z1)),z0,t13):is"rt"(z0,pl(ts(x0,z1),ts(y0,z1)))
+t15:=sum1(ksi,eta,z0,ts(x0,z1),t11,ts(y0,z1),t12,t14):in(z0,sum)
+l@t16:=sumapp(ksi,eta,u0,i,in(z0,sum),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,pl(x,y))]t15(x,t,y,u,v)):in(z0,sum)
+eta@[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
+t17:=sum1(ksi,eta,pl(x1,y0),x1,lx1,y0,ly,refis(rat,pl(x1,y0))):in(pl(x1,y0),sum)
+t18:=satz96a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(pl(x1,y0),pl(x0,y0))
+t19:=ismore2"rt"(pl(x0,y0),z0,pl(x1,y0),symis(rat,z0,pl(x0,y0),j),t18):more"rt"(pl(x1,y0),z0)
+t20:=andi(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0),t17,t19):and(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0))
+t21:=somei(rat,[y:rat]and(in(y,sum),more"rt"(y,z0)),pl(x1,y0),t20):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
+j@t22:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t21(x,t,u)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
+i@t23:=sumapp(ksi,eta,z0,i,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t22(x,t,y,u,v)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
+eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
+t24:=cut2(sum,pl(x0,y0),sum1(ksi,eta,pl(x0,y0),x0,lx,y0,ly,refis(rat,pl(x0,y0))),pl(x1,y1),satz129a(x1,ux,y1,uy),[x:rat][t:in(x,sum)][y:rat][u:less"rt"(y,x)]t16(x,t,y,u),[x:rat][t:in(x,sum)]t23(x,t)):cutprop(sum)
+ux@t25:=cutapp1b(eta,cutprop(sum),[y:rat][t:urt(eta,y)]t24(y,t)):cutprop(sum)
+ly@t26:=cutapp1b(ksi,cutprop(sum),[x:rat][t:urt(ksi,x)]t25(x,t)):cutprop(sum)
+lx@t27:=cutapp1a(eta,cutprop(sum),[y:rat][t:lrt(eta,y)]t26(y,t)):cutprop(sum)
+-3129
+eta@satz129:=cutapp1a(ksi,cutprop(sum),[x:rat][t:lrt(ksi,x)]t27".3129"(x,t)):cutprop(sum)
+pl:=cutof(sum,satz129):cut
+[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
+lrtpl:=ine(sum,satz129,z0,sum1(z0,x0,lx,y0,ly,i)):lrt(pl(ksi,eta),z0)
+eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
++*iii3
+i@t10:=isp1(rat,[x:rat]not(in(x,sum)),pl"rt"(x0,y0),z0,satz129a(x0,ux,y0,uy),i):not(in(z0,sum))
+-iii3
+i@urtpl:=th3"l.imp"(lrt(pl(ksi,eta),z0),in(z0,sum),t10".iii3",[t:lrt(pl(ksi,eta),z0)]ini(sum,satz129,z0,t)):urt(pl(ksi,eta),z0)
+eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]p]
++*iii3
+p1@t11:=ini(sum,satz129,z0,lz):in(z0,sum)
+-iii3
+p1@plapp:=sumapp(z0,t11".iii3",p,p1):p
+zeta@[i:is(ksi,eta)]
+ispl1:=isf(cut,cut,[u:cut]pl(u,zeta),ksi,eta,i):is(pl(ksi,zeta),pl(eta,zeta))
+ispl2:=isf(cut,cut,[u:cut]pl(zeta,u),ksi,eta,i):is(pl(zeta,ksi),pl(zeta,eta))
+upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
+ispl12:=tris(cut,pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),ispl1(i),ispl2(zeta,upsilon,eta,j)):is(pl(ksi,zeta),pl(eta,upsilon))
++3130
+eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
+t1:=tris(rat,z0,pl"rt"(x0,y0),pl"rt"(y0,x0),i,compl(x0,y0)):is"rt"(z0,pl"rt"(y0,x0))
+t2:=lrtpl(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(pl(eta,ksi),z0)
+lz@t3:=plapp(ksi,eta,z0,lz,lrt(pl(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]t2(x,t,y,u,v)):lrt(pl(eta,ksi),z0)
+-3130
+eta@satz130:=isi1(pl(ksi,eta),pl(eta,ksi),[x:rat][t:lrt(pl(ksi,eta),x)]t3".3130"(x,t),[x:rat][t:lrt(pl(eta,ksi),x)]t3".3130"(eta,ksi,x,t)):is(pl(ksi,eta),pl(eta,ksi))
+compl:=satz130:is(pl(ksi,eta),pl(eta,ksi))
++3131
+zeta@[u0:rat][lu:lrt(pl(pl(ksi,eta),zeta),u0)][v0:rat][lv:lrt(pl(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,pl"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,pl"rt"(x0,y0))]
+t1:=tr3is(rat,u0,pl"rt"(v0,z0),pl"rt"(pl"rt"(x0,y0),z0),pl"rt"(x0,pl"rt"(y0,z0)),i,ispl1"rt"(v0,pl"rt"(x0,y0),z0,j),asspl1(x0,y0,z0)):is"rt"(u0,pl"rt"(x0,pl"rt"(y0,z0)))
+t2:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
+t3:=lrtpl(ksi,pl(eta,zeta),u0,x0,lx,pl"rt"(y0,z0),t2,t1):lrt(pl(ksi,pl(eta,zeta)),u0)
+i@t4:=plapp(ksi,eta,v0,lv,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,pl"rt"(x,y))]t3(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
+lu@t5:=plapp(pl(ksi,eta),zeta,u0,lu,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(pl(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
+u0@[lu:lrt(pl(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,pl"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
+t6:=tr3is(rat,u0,pl"rt"(x0,v0),pl"rt"(x0,pl"rt"(y0,z0)),pl"rt"(pl"rt"(x0,y0),z0),i,ispl2"rt"(v0,pl"rt"(y0,z0),x0,j),asspl2(x0,y0,z0)):is"rt"(u0,pl"rt"(pl"rt"(x0,y0),z0))
+t7:=lrtpl(ksi,eta,pl"rt"(x0,y0),x0,lx,y0,ly,refis(rat,pl"rt"(x0,y0))):lrt(pl(ksi,eta),pl"rt"(x0,y0))
+t8:=lrtpl(pl(ksi,eta),zeta,u0,pl"rt"(x0,y0),t7,z0,lz,t6):lrt(pl(pl(ksi,eta),zeta),u0)
+i@t9:=plapp(eta,zeta,v0,lv,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t8(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
+lu@t10:=plapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t9(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
+-3131
+zeta@satz131:=isi1(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),[x:rat][t:lrt(pl(pl(ksi,eta),zeta),x)]t5".3131"(x,t),[x:rat][t:lrt(pl(ksi,pl(eta,zeta)),x)]t10".3131"(x,t)):is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
+asspl1:=satz131:is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
+asspl2:=symis(cut,pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),satz131):is(pl(ksi,pl(eta,zeta)),pl(pl(ksi,eta),zeta))
+ksi@[a0:rat]
++3132
+[x0:rat][y0:rat]
+prop1:=and(lrt(ksi,x0),urt(ksi,y0)):'prop'
+[p:prop1]
+t1:=cutapp2b(x0,ande1(lrt(ksi,x0),urt(ksi,y0),p),y0,ande2(lrt(ksi,x0),urt(ksi,y0),p)):more"rt"(y0,x0)
+prop2:=is"rt"(mn(y0,x0,t1),a0):'prop'
+y0@prop3:=and(prop1,[t:prop1]prop2(t)):'prop'
+a0@prop4:=some"rt"([x:rat]some"rt"([y:rat]prop3(x,y))):'prop'
+x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
+t2:=cutapp2b(x0,lx,y0,uy):more"rt"(y0,x0)
+[n:nat][m:more"rt"(ts(rtofn(n),a0),mn(y0,x0,t2))]
+t3:=satz96d(ts(rtofn(n),a0),mn(y0,x0,t2),x0,m):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),pl"rt"(x0,mn(y0,x0,t2)))
+t4:=ismore2"rt"(pl"rt"(x0,mn(y0,x0,t2)),y0,pl"rt"(x0,ts(rtofn(n),a0)),satz101c(y0,x0,t2),t3):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),y0)
+t5:=satz119(y0,uy,pl"rt"(x0,ts(rtofn(n),a0)),t4):urt(pl"rt"(x0,ts(rtofn(n),a0)))
+t6:=somei(nat,[x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),n,t5):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
+uy@t7:=someapp(nat,[x:nat]more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2)),satz115(a0,mn(y0,x0,t2)),some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0)))),[x:nat][t:more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2))]t6(x,t)):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
+[u:nat][m:min"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)]
+t8:=ande1(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)
+t9:=ande2(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):urt(pl"rt"(x0,ts(rtofn(u),a0)))
+[i:is"n"(u,1)]
+u0:=pl"rt"(x0,a0):rat
+t10:=tr3is(rat,ts(rtofn(u),a0),ts(1rt,a0),ts(a0,1rt),a0,ists1(rtofn(u),1rt,a0,isnert(u,1,i)),comts(1rt,a0),example1a(a0)):is"rt"(ts(rtofn(u),a0),a0)
+t11:=isp(rat,[x:rat]urt(pl"rt"(x0,x)),ts(rtofn(u),a0),a0,t9,t10):urt(ksi,u0)
+t12:=andi(lrt(ksi,x0),urt(ksi,u0),lx,t11):prop1(x0,u0)
+[p:prop1(x0,u0)]
+t13:=symis(rat,a0,mn(u0,x0,t1(x0,u0,p)),satz101g(u0,x0,a0,t1(x0,u0,p),refis(rat,u0))):prop2(x0,u0,p)
+i@t14:=andi(prop1(x0,u0),[t:prop1(x0,u0)]prop2(x0,u0,t),t12,[t:prop1(x0,u0)]t13(t)):prop3(x0,u0)
+t15:=somei(rat,[y:rat]prop3(x0,y),u0,t14):some"rt"([y:rat]prop3(x0,y))
+t16:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),x0,t15):prop4
+m@[o:more"n"(u,1)]
+t17:=morei(rtofn(u),1rt,fr(u,1),fr(1,1),inclass(fr(u,1)),inclass(fr(1,1)),satz111d(u,1,o)):more"rt"(rtofn(u),1rt)
+um10:=mn(rtofn(u),1rt,t17):rat
+t18:=satz112g(rtofn(u),natrti(u),1rt,natrti(1),t17):natrt(um10)
+um1:=nofrt(um10,t18):nat
+v0:=pl"rt"(x0,ts(um10,a0)):rat
+w0:=pl"rt"(x0,ts(rtofn(u),a0)):rat
+t19:=isless2"rt"(pl"rt"(um10,1rt),rtofn(u),um10,satz101e(rtofn(u),1rt,t17),satz94a(um10,1rt)):less"rt"(um10,rtofn(u))
+t20:=lesse(um10,rtofn(u),fr(um1,1),fr(u,1),inclassn(um10,t18),inclass(fr(u,1)),t19):lessf(fr(um1,1),fr(u,1))
+t21:=satz111c(um1,u,t20):less"n"(um1,u)
+t22:=th3"l.imp"(lessis"n"(u,um1),moreis"n"(um1,u),satz10h(um1,u,t21),[t:lessis"n"(u,um1)]satz14(u,um1,t)):not(lessis"n"(u,um1))
+t23:=et(lrt(pl"rt"(x0,ts(rtofn(um1),a0))),th3"l.imp"(urt(pl"rt"(x0,ts(rtofn(um1),a0))),lessis"n"(u,um1),t22,<um1>t8)):lrt(pl"rt"(x0,ts(rtofn(um1),a0)))
+t24:=isp1(rat,[x:rat]lrt(pl"rt"(x0,ts(x,a0))),rtofn(um1),um10,t23,isrtn1(um10,t18)):lrt(ksi,v0)
+t25:=andi(lrt(ksi,v0),urt(ksi,w0),t24,t9):prop1(v0,w0)
+t26:=tr3is(rat,pl"rt"(ts(um10,a0),a0),pl"rt"(ts(um10,a0),ts(1rt,a0)),ts(pl"rt"(um10,1rt),a0),ts(rtofn(u),a0),ispl2"rt"(a0,ts(1rt,a0),ts(um10,a0),example1d(a0)),distpt1(um10,1rt,a0),ists1(pl"rt"(um10,1rt),rtofn(u),a0,satz101e(rtofn(u),1rt,t17))):is"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0))
+t27:=tris(rat,pl"rt"(v0,a0),pl"rt"(x0,pl"rt"(ts(um10,a0),a0)),w0,asspl1"rt"(x0,ts(um10,a0),a0),ispl2"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0),x0,t26)):is"rt"(pl"rt"(v0,a0),w0)
+[p:prop1(v0,w0)]
+t28:=symis(rat,a0,mn(w0,v0,t1(v0,w0,p)),satz101g(w0,v0,a0,t1(v0,w0,p),t27)):prop2(v0,w0,p)
+o@t29:=andi(prop1(v0,w0),[t:prop1(v0,w0)]prop2(v0,w0,t),t25,[t:prop1(v0,w0)]t28(t)):prop3(v0,w0)
+t30:=somei(rat,[y:rat]prop3(v0,y),w0,t29):some"rt"([y:rat]prop3(v0,y))
+t31:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),v0,t30):prop4
+m@t32:=orapp(more"n"(u,1),is"n"(u,1),prop4,satz24(u),[t:more"n"(u,1)]t31(t),[t:is"n"(u,1)]t16(t)):prop4
+uy@t34:=someapp(nat,[x:nat]min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x),satz27([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),t7),prop4,[x:nat][t:min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x)]t32(x,t)):prop4
+lx@t35:=cutapp1b(prop4,[y:rat][t:urt(ksi,y)]t34(y,t)):prop4
+-3132
+satz132:=cutapp1a(prop4".3132",[x:rat][t:lrt(ksi,x)]t35".3132"(x,t)):some"rt"([x:rat]some"rt"([y:rat]and(and(lrt(ksi,x),urt(ksi,y)),[t:and(lrt(ksi,x),urt(ksi,y))]is"rt"(mn(y,x,cutapp2b(x,ande1(lrt(ksi,x),urt(ksi,y),t),y,ande2(lrt(ksi,x),urt(ksi,y),t))),a0))))
+ksi@[p:'prop'][a0:rat][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),a0)]p]
++*3132
+p1@[x0:rat][s:some"rt"([y:rat]prop3(a0,x0,y))][y0:rat][p3:prop3(a0,x0,y0)]
+t36:=ande1(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop1(a0,x0,y0)
+t37:=ande2"l.r"(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop2(a0,x0,y0,t36)
+t38:=ande1(lrt(ksi,x0),urt(ksi,y0),t36):lrt(ksi,x0)
+t39:=ande2(lrt(ksi,x0),urt(ksi,y0),t36):urt(ksi,y0)
+t40:=satz101g(y0,x0,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),t1(a0,x0,y0,t36),satz101c(y0,x0,cutapp2b(x0,t38,y0,t39))):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)))
+t41:=tris(rat,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)),a0,t40,t37):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),a0)
+t42:=<t41><t39><y0><t38><x0>p1:p
+s@t43:=someapp(rat,[y:rat]prop3(a0,x0,y),s,p,[y:rat][t:prop3(a0,x0,y)]t42(y,t)):p
+-3132
+p1@satz132app:=someapp(rat,[x:rat]some"rt"([y:rat]prop3".3132"(a0,x,y)),satz132(a0),p,[x:rat][t:some"rt"([y:rat]prop3".3132"(a0,x,y))]t43".3132"(x,t)):p
++3133
+eta@[y0:rat][ly:lrt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][uu:urt(ksi,u0)][i:is"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0)]
+t1:=tris(rat,u0,pl"rt"(x0,mn(u0,x0,cutapp2b(x0,lx,u0,uu))),pl"rt"(x0,y0),satz101d(u0,x0,cutapp2b(x0,lx,u0,uu)),ispl2"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0,x0,i)):is"rt"(u0,pl"rt"(x0,y0))
+t2:=lrtpl(ksi,eta,u0,x0,lx,y0,ly,t1):lrt(pl(ksi,eta),u0)
+t3:=andi(lrt(pl(ksi,eta),u0),urt(ksi,u0),t2,uu):and(lrt(pl(ksi,eta),u0),urt(ksi,u0))
+t4:=somei(rat,[x:rat]and(lrt(pl(ksi,eta),x),urt(ksi,x)),u0,t3):more(pl(ksi,eta),ksi)
+ly@t5:=satz132app(ksi,more(pl(ksi,eta),ksi),y0,[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),y0)]t4(x,t,y,u,v)):more(pl(ksi,eta),ksi)
+-3133
+eta@satz133:=cutapp1a(eta,more(pl(ksi,eta),ksi),[x:rat][t:lrt(eta,x)]t5".3133"(x,t)):more(pl(ksi,eta),ksi)
+satz133a:=satz121(pl(ksi,eta),ksi,satz133):less(ksi,pl(ksi,eta))
+zeta@[m:more(ksi,eta)]
++3134
+[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
+t1:=satz119a(eta,y0,uy,x0,l):urt(eta,x0)
+t2:=satz83(y0,x0,l):more"rt"(x0,y0)
+[u0:rat][lu:lrt(zeta,u0)][z0:rat][uz:urt(zeta,z0)][i:is"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2))]
+t3:=tris(rat,z0,pl"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),u0),pl"rt"(mn(x0,y0,t2),u0),satz101f(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),ispl1"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2),u0,i)):is"rt"(z0,pl"rt"(mn(x0,y0,t2),u0))
+t4:=tr3is(rat,pl"rt"(y0,z0),pl"rt"(y0,pl"rt"(mn(x0,y0,t2),u0)),pl"rt"(pl"rt"(y0,mn(x0,y0,t2)),u0),pl"rt"(x0,u0),ispl2"rt"(z0,pl"rt"(mn(x0,y0,t2),u0),y0,t3),asspl2"rt"(y0,mn(x0,y0,t2),u0),ispl1"rt"(pl"rt"(y0,mn(x0,y0,t2)),x0,u0,satz101c(x0,y0,t2))):is"rt"(pl"rt"(y0,z0),pl"rt"(x0,u0))
+t5:=lrtpl(ksi,zeta,pl"rt"(y0,z0),x0,lx,u0,lu,t4):lrt(pl(ksi,zeta),pl"rt"(y0,z0))
+t6:=urtpl(eta,zeta,pl"rt"(y0,z0),y0,uy,z0,uz,refis(rat,pl"rt"(y0,z0))):urt(pl(eta,zeta),pl"rt"(y0,z0))
+t7:=andi(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)),t5,t6):and(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)))
+t8:=somei(rat,[x:rat]and(lrt(pl(ksi,zeta),x),urt(pl(eta,zeta),x)),pl"rt"(y0,z0),t7):more(pl(ksi,zeta),pl(eta,zeta))
+l@t9:=satz132app(zeta,more(pl(ksi,zeta),pl(eta,zeta)),mn(x0,y0,t2),[x:rat][t:lrt(zeta,x)][y:rat][u:urt(zeta,y)][v:is"rt"(mn(y,x,cutapp2b(zeta,x,t,y,u)),mn(x0,y0,t2))]t8(x,t,y,u,v)):more(pl(ksi,zeta),pl(eta,zeta))
+uy@t10:=cutapp3(ksi,y0,ly,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t9(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
+-3134
+satz134:=moreapp(ksi,eta,m,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t10".3134"(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
+zeta@[m:more(ksi,eta)]
+satz135a:=satz134(m):more(pl(ksi,zeta),pl(eta,zeta))
+zeta@[i:is(ksi,eta)]
+satz135b:=ispl1(ksi,eta,zeta,i):is(pl(ksi,zeta),pl(eta,zeta))
+zeta@[l:less(ksi,eta)]
+satz135c:=satz121(pl(eta,zeta),pl(ksi,zeta),satz134(eta,ksi,zeta,satz122(ksi,eta,l))):less(pl(ksi,zeta),pl(eta,zeta))
+m@satz135d:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135a):more(pl(zeta,ksi),pl(zeta,eta))
+i@satz135e:=ispl2(ksi,eta,zeta,i):is(pl(zeta,ksi),pl(zeta,eta))
+l@satz135f:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135c):less(pl(zeta,ksi),pl(zeta,eta))
+upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
+satz135g:=ismore2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135d(zeta,upsilon,ksi,m)):more(pl(ksi,zeta),pl(eta,upsilon))
+satz135h:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135g):more(pl(zeta,ksi),pl(upsilon,eta))
+i@[l:less(zeta,upsilon)]
+satz135j:=isless2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135f(zeta,upsilon,ksi,l)):less(pl(ksi,zeta),pl(eta,upsilon))
+satz135k:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135j):less(pl(zeta,ksi),pl(upsilon,eta))
++3136
+zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+t2:=satz123b(pl(ksi,zeta),pl(eta,zeta)):ec3(is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)))
+-3136
+zeta@[m:more(pl(ksi,zeta),pl(eta,zeta))]
+satz136a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),m):more(ksi,eta)
+zeta@[i:is(pl(ksi,zeta),pl(eta,zeta))]
+satz136b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),i):is(ksi,eta)
+zeta@[l:less(pl(ksi,zeta),pl(eta,zeta))]
+satz136c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),l):less(ksi,eta)
+zeta@[m:more(pl(zeta,ksi),pl(zeta,eta))]
+satz136d:=satz136a(ismore12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),m)):more(ksi,eta)
+zeta@[i:is(pl(zeta,ksi),pl(zeta,eta))]
+satz136e:=satz136b(tr3is(cut,pl(ksi,zeta),pl(zeta,ksi),pl(zeta,eta),pl(eta,zeta),compl(ksi,zeta),i,compl(zeta,eta))):is(ksi,eta)
+zeta@[l:less(pl(zeta,ksi),pl(zeta,eta))]
+satz136f:=satz136c(isless12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),l)):less(ksi,eta)
+upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
++3137
+t1:=satz134(ksi,eta,zeta,m):more(pl(ksi,zeta),pl(eta,zeta))
+t2:=ismore12(pl(zeta,eta),pl(eta,zeta),pl(upsilon,eta),pl(eta,upsilon),compl(zeta,eta),compl(upsilon,eta),satz134(zeta,upsilon,eta,n)):more(pl(eta,zeta),pl(eta,upsilon))
+-3137
+satz137:=trmore(pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),t1".3137",t2".3137"):more(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
+satz137a:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz137(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
+satz138a:=orapp(more(ksi,eta),is(ksi,eta),more(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]satz137(t,n),[t:is(ksi,eta)]satz135g(t,n)):more(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
+satz138b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]satz137(m,t),[t:is(zeta,upsilon)]satz135h(zeta,upsilon,ksi,eta,t,m)):more(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
+satz138c:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
+satz138d:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
++3139
+[i:is(ksi,eta)][j:is(zeta,upsilon)]
+t1:=moreisi2(pl(ksi,zeta),pl(eta,upsilon),ispl12(ksi,eta,zeta,upsilon,i,j)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+i@[o:more(zeta,upsilon)]
+t2:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138a(m,o)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+n@[o:more(ksi,eta)]
+t4:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138b(o,n)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+-3139
+satz139:=orapp(more(ksi,eta),is(ksi,eta),moreis(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]t4".3139"(t),[t:is(ksi,eta)]t3".3139"(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
+satz139a:=satz124(pl(eta,upsilon),pl(ksi,zeta),satz139(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(pl(ksi,zeta),pl(eta,upsilon))
+eta@[l:lessis(ksi,eta)]
++3140
+[phi:cut][i:is(pl(eta,phi),ksi)]
+t1:=ismore1(pl(eta,phi),ksi,eta,i,satz133(eta,phi)):more(ksi,eta)
+phi@t2:=th3"l.imp"(is(pl(eta,phi),ksi),more(ksi,eta),satz123d(ksi,eta,l),[t:is(pl(eta,phi),ksi)]t1(t)):nis(pl(eta,phi),ksi)
+-3140
+vorbemerkung140:=th5"l.some"(cut,[a:cut]is(pl(eta,a),ksi),[a:cut]t2".3140"(a)):not(some([a:cut]is(pl(eta,a),ksi)))
+eta@[phi:cut][psi:cut]
++*3140
+psi@[m:more(phi,psi)]
+t3:=satz135d(phi,psi,eta,m):more(pl(eta,phi),pl(eta,psi))
+t4:=ec3e21(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t3):nis(pl(eta,phi),pl(eta,psi))
+psi@[l:less(phi,psi)]
+t5:=satz135f(phi,psi,eta,l):less(pl(eta,phi),pl(eta,psi))
+t6:=ec3e31(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t5):nis(pl(eta,phi),pl(eta,psi))
+psi@[n:nis(phi,psi)]
+t7:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
+t8:=orapp(more(phi,psi),less(phi,psi),nis(pl(eta,phi),pl(eta,psi)),t7,[t:more(phi,psi)]t4(t),[t:less(phi,psi)]t6(t)):nis(pl(eta,phi),pl(eta,psi))
+-3140
+psi@[i:is(pl(eta,phi),ksi)][j:is(pl(eta,psi),ksi)]
+satz140b:=th7"l.imp"(is(phi,psi),nis(pl(eta,phi),pl(eta,psi)),weli(is(pl(eta,phi),pl(eta,psi)),tris2(cut,pl(eta,phi),pl(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t8".3140"(t)):is(phi,psi)
+eta@[z0:rat][x0:rat][y0:rat]
+diffprop1:=and(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t))):'prop'
+diffprop2:=and3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0)):'prop'
+z0@diffprop:=some"rt"([x:rat]some"rt"([y:rat]diffprop2(z0,x,y))):'prop'
+eta@diff:=setof(rat,[z:rat]diffprop(z)):set(rat)
+x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][m:more"rt"(x0,y0)][i:is"rt"(z0,mn(x0,y0,m))]
++*iii3
+i@[m1:more"rt"(x0,y0)]
+t11a:=tris(rat,z0,mn(x0,y0,m),mn(x0,y0,m1),i,satz101g(x0,y0,mn(x0,y0,m),m1,satz101c(x0,y0,m))):is"rt"(z0,mn(x0,y0,m1))
+i@t12:=andi(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),m,[t:more"rt"(x0,y0)]t11a(t)):diffprop1(z0,x0,y0)
+t13:=and3i(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),lx,uy,t12):diffprop2(z0,x0,y0)
+t14:=somei(rat,[y:rat]diffprop2(z0,x0,y),y0,t13):some"rt"([y:rat]diffprop2(z0,x0,y))
+t15:=somei(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),x0,t14):diffprop(z0)
+-iii3
+i@diff1:=estii(rat,[z:rat]diffprop(z),z0,t15".iii3"):in(z0,diff)
+z0@[i:in(z0,diff)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]p]
++*iii3
+p1@t16:=estie(rat,[z:rat]diffprop(z),z0,i):diffprop(z0)
+-iii3
+p1@[x0:rat][px:some"rt"([y:rat]diffprop2(z0,x0,y))][y0:rat][py:diffprop2(z0,x0,y0)]
++*iii3
+py@t17:=and3e1(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):lrt(ksi,x0)
+t18:=and3e2(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):urt(eta,y0)
+t19:=and3e3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):diffprop1(z0,x0,y0)
+t20:=ande1(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):more"rt"(x0,y0)
+t21:=ande2"l.r"(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):is"rt"(z0,mn(x0,y0,t20))
+t22:=<t21><t20><t18><y0><t17><x0>p1:p
+px@t23:=someapp(rat,[y:rat]diffprop2(z0,x0,y),px,p,[y:rat][t:diffprop2(z0,x0,y)]t22(y,t)):p
+-iii3
+p1@diffapp:=someapp(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),t16".iii3",p,[x:rat][t:some"rt"([y:rat]diffprop2(z0,x,y))]t23".iii3"(x,t)):p
+eta@[m:more(ksi,eta)]
++*3140
+m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
+t9:=t2"rp.3134"(eta,m,y0,ly,uy,x0,lx,l):more"rt"(x0,y0)
+t10:=diff1(mn(x0,y0,t9),x0,lx,y0,uy,t9,refis(rat,mn(x0,y0,t9))):in(mn(x0,y0,t9),diff)
+m"rp"@[x1:rat][ux:urt(ksi,x1)][z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
+t11:=isless12"rt"(mn(x0,y0,n),z0,pl"rt"(mn(x0,y0,n),y0),x0,symis(rat,z0,mn(x0,y0,n),j),satz101e(x0,y0,n),satz94a(mn(x0,y0,n),y0)):less"rt"(z0,x0)
+t12:=trless"rt"(z0,x0,x1,t11,cutapp2a(ksi,x0,lx,x1,ux)):less"rt"(z0,x1)
+t13:=ec3e31(is"rt"(z0,x1),more"rt"(z0,x1),less"rt"(z0,x1),satz81b(z0,x1),t12):nis"rt"(z0,x1)
+i@t14:=diffapp(z0,i,nis"rt"(z0,x1),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t13(x,t,y,u,v,w)):nis"rt"(z0,x1)
+ux@t15:=th3"l.imp"(in(x1,diff),nis"rt"(x1,x1),weli(is"rt"(x1,x1),refis(rat,x1)),[t:in(x1,diff)]t14(x1,t)):not(in(x1,diff))
+m"rp"@[z0:rat][i:in(z0,diff)][u0:rat][l:less"rt"(u0,z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
+t16:=tris(rat,pl"rt"(z0,y0),pl"rt"(mn(x0,y0,n),y0),x0,ispl1"rt"(z0,mn(x0,y0,n),y0,j),satz101e(x0,y0,n)):is"rt"(pl"rt"(z0,y0),x0)
+x2:=pl"rt"(u0,y0):rat
+t17:=isless2"rt"(pl"rt"(z0,y0),x0,x2,t16,satz96c(u0,z0,y0,l)):less"rt"(x2,x0)
+t18:=satz120(ksi,x0,lx,x2,t17):lrt(ksi,x2)
+t19:=ismore1"rt"(pl"rt"(y0,u0),pl"rt"(u0,y0),y0,compl"rt"(y0,u0),satz94(y0,u0)):more"rt"(x2,y0)
+t20:=satz101g(x2,y0,u0,t19,compl"rt"(y0,u0)):is"rt"(u0,mn(x2,y0,t19))
+t21:=diff1(u0,x2,t18,y0,uy,t19,t20):in(u0,diff)
+l@t22:=diffapp(z0,i,in(u0,diff),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t21(x,t,y,u,v,w)):in(u0,diff)
+m"rp"@[z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))][x3:rat][lx3:lrt(ksi,x3)][l:less"rt"(x0,x3)]
+t23:=satz83(x0,x3,l):more"rt"(x3,x0)
+t24:=trmore"rt"(x3,x0,y0,t23,n):more"rt"(x3,y0)
+t25:=ismore12"rt"(x3,pl"rt"(mn(x3,y0,t24),y0),x0,pl"rt"(mn(x0,y0,n),y0),satz101f(x3,y0,t24),satz101f(x0,y0,n),t23):more"rt"(pl"rt"(mn(x3,y0,t24),y0),pl"rt"(mn(x0,y0,n),y0))
+t26:=satz97a(mn(x3,y0,t24),mn(x0,y0,n),y0,t25):more"rt"(mn(x3,y0,t24),mn(x0,y0,n))
+t27:=ismore2"rt"(mn(x0,y0,n),z0,mn(x3,y0,t24),symis(rat,z0,mn(x0,y0,n),j),t26):more"rt"(mn(x3,y0,t24),z0)
+t28:=diff1(mn(x3,y0,t24),x3,lx3,y0,uy,t24,refis(rat,mn(x3,y0,t24))):in(mn(x3,y0,t24),diff)
+t29:=andi(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0),t28,t27):and(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0))
+t30:=somei(rat,[x:rat]and(in(x,diff),more"rt"(x,z0)),mn(x3,y0,t24),t29):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
+j@t31:=cutapp3(ksi,x0,lx,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t30(y,t,u)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
+i@t32:=diffapp(z0,i,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t31(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
+m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)][x1:rat][ux1:urt(ksi,x1)]
+t33:=cut2(diff,mn(x0,y0,t9(y0,ly,uy,x0,lx,l)),t10(y0,ly,uy,x0,lx,l),x1,t15(x1,ux1),[x:rat][t:in(x,diff)][y:rat][u:less"rt"(y,x)]t22(x,t,y,u),[x:rat][t:in(x,diff)]t32(x,t)):cutprop(diff)
+l@t34:=cutapp1b(ksi,cutprop(diff),[x:rat][t:urt(ksi,x)]t33(x,t)):cutprop(diff)
+uy@t35:=cutapp3(ksi,y0,ly,cutprop(diff),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t34(x,t,u)):cutprop(diff)
+-3140
+m@satz140h:=moreapp(ksi,eta,m,cutprop(diff),[x:rat][u:lrt(ksi,x)][v:urt(eta,x)]t35".3140"(x,u,v)):cutprop(diff)
++*3140
+m"rp"@chi:=cutof(diff,satz140h):cut
+[z0:rat][lz:lrt(pl(eta,chi),z0)][y1:rat][ly:lrt(eta,y1)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,pl"rt"(y1,u0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][o:more"rt"(x0,y0)][j:is"rt"(u0,mn(x0,y0,o))]
+t36:=cutapp2b(eta,y1,ly,y0,uy):more"rt"(y0,y1)
+t37:=tr3is(rat,pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),pl"rt"(mn(x0,y0,o),pl"rt"(y1,mn(y0,y1,t36))),pl"rt"(mn(x0,y0,o),y0),x0,asspl1"rt"(mn(x0,y0,o),y1,mn(y0,y1,t36)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t36)),y0,mn(x0,y0,o),satz101c(y0,y1,t36)),satz101e(x0,y0,o)):is"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0)
+t38:=isless2"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0,pl"rt"(mn(x0,y0,o),y1),t37,satz94a(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36))):less"rt"(pl"rt"(mn(x0,y0,o),y1),x0)
+t39:=tr3is(rat,z0,pl"rt"(y1,u0),pl"rt"(u0,y1),pl"rt"(mn(x0,y0,o),y1),i,compl"rt"(y1,u0),ispl1"rt"(u0,mn(x0,y0,o),y1,j)):is"rt"(z0,pl"rt"(mn(x0,y0,o),y1))
+t40:=isless1"rt"(pl"rt"(mn(x0,y0,o),y1),z0,x0,symis(rat,z0,pl"rt"(mn(x0,y0,o),y1),t39),t38):less"rt"(z0,x0)
+t41:=satz120(ksi,x0,lx,z0,t40):lrt(ksi,z0)
+i@t42:=diffapp(u0,ini(diff,satz140h,u0,lu),lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(u0,mn(x,y,v))]t41(x,t,y,u,v,w)):lrt(ksi,z0)
+lz@a:=plapp(eta,chi,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,pl"rt"(x,y))]t42(x,t,y,u,v)):lrt(ksi,z0)
+m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
+t43:=satz83(y0,x0,l):more"rt"(x0,y0)
+[y1:rat][ly1:lrt(eta,y1)][y2:rat][uy2:urt(eta,y2)]
+t44:=cutapp2b(eta,y1,ly1,y2,uy2):more"rt"(y2,y1)
+[i:is"rt"(mn(y2,y1,t44),mn(x0,y0,t43))]
+t45:=cutapp2b(eta,y1,ly1,y0,uy):more"rt"(y0,y1)
+t46:=tris(rat,y2,pl"rt"(mn(y2,y1,t44),y1),pl"rt"(mn(x0,y0,t43),y1),satz101f(y2,y1,t44),ispl1"rt"(mn(y2,y1,t44),mn(x0,y0,t43),y1,i)):is"rt"(y2,pl"rt"(mn(x0,y0,t43),y1))
+t47:=tr4is(rat,pl"rt"(y2,mn(y0,y1,t45)),pl"rt"(pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45)),pl"rt"(mn(x0,y0,t43),pl"rt"(y1,mn(y0,y1,t45))),pl"rt"(mn(x0,y0,t43),y0),x0,ispl1"rt"(y2,pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45),t46),asspl1"rt"(mn(x0,y0,t43),y1,mn(y0,y1,t45)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t45)),y0,mn(x0,y0,t43),satz101c(y0,y1,t45)),satz101e(x0,y0,t43)):is"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0)
+t48:=ismore1"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0,y2,t47,satz94(y2,mn(y0,y1,t45))):more"rt"(x0,y2)
+t49:=satz101g(x0,y2,mn(y0,y1,t45),t48,t47):is"rt"(mn(y0,y1,t45),mn(x0,y2,t48))
+t50:=tris(rat,y0,pl"rt"(mn(y0,y1,t45),y1),pl"rt"(mn(x0,y2,t48),y1),satz101f(y0,y1,t45),ispl1"rt"(mn(y0,y1,t45),mn(x0,y2,t48),y1,t49)):is"rt"(y0,pl"rt"(mn(x0,y2,t48),y1))
+t51:=ine(diff,satz140h,mn(x0,y2,t48),diff1(mn(x0,y2,t48),x0,lx,y2,uy2,t48,refis(rat,mn(x0,y2,t48)))):lrt(chi,mn(x0,y2,t48))
+t52:=lrtpl(eta,chi,y0,y1,ly1,mn(x0,y2,t48),t51,tris(rat,y0,pl"rt"(mn(x0,y2,t48),y1),pl"rt"(y1,mn(x0,y2,t48)),t50,compl"rt"(mn(x0,y2,t48),y1))):lrt(pl(eta,chi),y0)
+l@t53:=satz132app(eta,lrt(pl(eta,chi),y0),mn(x0,y0,t43),[x:rat][t:lrt(eta,x)][y:rat][u:urt(eta,y)][v:is"rt"(mn(y,x,cutapp2b(eta,x,t,y,u)),mn(x0,y0,t43))]t52(x,t,y,u,v)):lrt(pl(eta,chi),y0)
+uy@t54:=cutapp3(ksi,y0,ly,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t53(x,t,u)):lrt(pl(eta,chi),y0)
+ly@[ly0:lrt(eta,y0)][y1:rat][ly1:lrt(ksi,y1)][uy1:urt(eta,y1)]
+t55:=t54(y1,ly1,uy1):lrt(pl(eta,chi),y1)
+t56:=satz120(pl(eta,chi),y1,t55,y0,cutapp2a(eta,y0,ly0,y1,uy1)):lrt(pl(eta,chi),y0)
+ly0@t57:=moreapp(ksi,eta,m,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t56(x,t,u)):lrt(pl(eta,chi),y0)
+ly@b:=th1"l.imp"(lrt(eta,y0),lrt(pl(eta,chi),y0),[t:lrt(eta,y0)]t57(t),[t:urt(eta,y0)]t54(t)):lrt(pl(eta,chi),y0)
+m"rp"@t58:=isi1(pl(eta,chi),ksi,[x:rat][t:lrt(pl(eta,chi),x)]a(x,t),[x:rat][t:lrt(ksi,x)]b(x,t)):is(pl(eta,chi),ksi)
+-3140
+m@satz140a:=somei(cut,[a:cut]is(pl(eta,a),ksi),chi".3140",t58".3140"):some([a:cut]is(pl(eta,a),ksi))
++*3140
+eta@t59:=[c:cut][d:cut][t:is(pl(eta,c),ksi)][u:is(pl(eta,d),ksi)]satz140b(c,d,t,u):amone(cut,[c:cut]is(pl(eta,c),ksi))
+-3140
+m@satz140:=onei(cut,[a:cut]is(pl(eta,a),ksi),t59".3140",satz140a):one([a:cut]is(pl(eta,a),ksi))
+mn:=ind(cut,[a:cut]is(pl(eta,a),ksi),satz140):cut
+satz140c:=oneax(cut,[a:cut]is(pl(eta,a),ksi),satz140):is(pl(eta,mn(ksi,eta,m)),ksi)
+satz140d:=symis(cut,pl(eta,mn(ksi,eta,m)),ksi,satz140c):is(ksi,pl(eta,mn(ksi,eta,m)))
+satz140e:=tris(cut,pl(mn(ksi,eta,m),eta),pl(eta,mn(ksi,eta,m)),ksi,compl(mn(ksi,eta,m),eta),satz140c):is(pl(mn(ksi,eta,m),eta),ksi)
+satz140f:=symis(cut,pl(mn(ksi,eta,m),eta),ksi,satz140e):is(ksi,pl(mn(ksi,eta,m),eta))
+eta@[phi:cut][m:more(ksi,eta)][i:is(pl(eta,phi),ksi)]
+satz140g:=satz140b(phi,mn(ksi,eta,m),i,satz140c(m)):is(phi,mn(ksi,eta,m))
+upsilon@[m:more(ksi,zeta)][n:more(eta,upsilon)][i:is(ksi,eta)][j:is(zeta,upsilon)]
++*3140
+j"rp"@t60:=tr3is(cut,pl(upsilon,mn(ksi,zeta,m)),pl(zeta,mn(ksi,zeta,m)),ksi,eta,ispl1(upsilon,zeta,mn(ksi,zeta,m),symis(cut,zeta,upsilon,j)),satz140c(ksi,zeta,m),i):is(pl(upsilon,mn(ksi,zeta,m)),eta)
+-3140
+j@ismn12:=satz140g(eta,upsilon,mn(ksi,zeta,m),n,t60".3140"):is(mn(ksi,zeta,m),mn(eta,upsilon,n))
+zeta@[m:more(ksi,zeta)][n:more(eta,zeta)][i:is(ksi,eta)]
+ismn1:=ismn12(zeta,m,n,i,refis(cut,zeta)):is(mn(ksi,zeta,m),mn(eta,zeta,n))
+zeta@[m:more(zeta,ksi)][n:more(zeta,eta)][i:is(ksi,eta)]
+ismn2:=ismn12(zeta,zeta,ksi,eta,m,n,refis(cut,zeta),i):is(mn(zeta,ksi,m),mn(zeta,eta,n))
+eta@[z0:rat][x0:rat][y0:rat]
+prodprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0))):'prop'
+z0@prodprop:=some"rt"([x:rat]some"rt"([y:rat]prodprop1(z0,x,y))):'prop'
+eta@prod:=setof(rat,[z:rat]prodprop(z)):set(rat)
+x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts(x0,y0))]
++iii4
+t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),lx,ly,i):prodprop1(z0,x0,y0)
+t2:=somei(rat,[y:rat]prodprop1(z0,x0,y),y0,t1):some"rt"([y:rat]prodprop1(z0,x0,y))
+t3:=somei(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),x0,t2):prodprop(z0)
+-iii4
+prod1:=estii(rat,[z:rat]prodprop(z),z0,t3".iii4"):in(z0,prod)
+z0@[i:in(z0,prod)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]p]
++*iii4
+p1@t4:=estie(rat,[z:rat]prodprop(z),z0,i):prodprop(z0)
+-iii4
+p1@[x0:rat][px:some"rt"([y:rat]prodprop1(z0,x0,y))][y0:rat][py:prodprop1(z0,x0,y0)]
++*iii4
+py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(ksi,x0)
+t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(eta,y0)
+t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):is"rt"(z0,ts(x0,y0))
+t8:=<t7><t6><y0><t5><x0>p1:p
+px@t9:=someapp(rat,[y:rat]prodprop1(z0,x0,y),px,p,[y:rat][t:prodprop1(z0,x0,y)]t8(y,t)):p
+-iii4
+p1@prodapp:=someapp(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),t4".iii4",p,[x:rat][t:some"rt"([y:rat]prodprop1(z0,x,y))]t9".iii4"(x,t)):p
+eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
++4141
+[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))]
+t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
+t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
+t3:=isless1"rt"(ts(x0,y0),z0,ts(x1,y1),symis(rat,z0,ts(x0,y0),j),satz107a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,ts(x1,y1))
+t4:=ec3e31(is"rt"(z0,ts(x1,y1)),more"rt"(z0,ts(x1,y1)),less"rt"(z0,ts(x1,y1)),satz81b(z0,ts(x1,y1)),t3):nis"rt"(z0,ts(x1,y1))
+i@t5:=prodapp(ksi,eta,z0,i,nis"rt"(z0,ts(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,ts(x1,y1))
+-4141
+satz141a:=th3"l.imp"(in(ts(x1,y1),prod),nis"rt"(ts(x1,y1),ts(x1,y1)),weli(is"rt"(ts(x1,y1),ts(x1,y1)),refis(rat,ts(x1,y1))),[t:in(ts(x1,y1),prod)]t5".4141"(ts(x1,y1),t)):not(in(ts(x1,y1),prod))
+-rp
+@[x0:rat][y0:rat]
++4141
+v0:=ts(ov(1rt,y0),x0):rat
+t6:=tr3is(rat,ts(y0,v0),ts(ts(y0,ov(1rt,y0)),x0),ts(1rt,x0),x0,assts2(y0,ov(1rt,y0),x0),ists1(ts(y0,ov(1rt,y0)),1rt,x0,satz110c(1rt,y0)),example1c(x0)):is(ts(y0,v0),x0)
+-4141
+satz141b:=satz110g(x0,y0,v0".4141",t6".4141"):is(ts(ov(1rt,y0),x0),ov(x0,y0))
+satz141c:=symis(rat,ts(ov(1rt,y0),x0),ov(x0,y0),satz141b):is"rt"(ov(x0,y0),ts(ov(1rt,y0),x0))
++*rp
++*4141
+eta@[u0:rat][i:in(u0,prod)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,ts(x0,y0))]
+t7:=isless2"rt"(u0,ts(x0,y0),z0,j,l):less"rt"(z0,ts(x0,y0))
+t8:=tr3is(rat,ts(ov(1rt,x0),ts(x0,y0)),ts(ts(ov(1rt,x0),x0),y0),ts(1rt,y0),y0,assts2(ov(1rt,x0),x0,y0),ists1(ts(ov(1rt,x0),x0),1rt,y0,satz110e(1rt,x0)),example1c(y0)):is"rt"(ts(ov(1rt,x0),ts(x0,y0)),y0)
+t9:=isless12"rt"(ts(ov(1rt,x0),z0),ov(z0,x0),ts(ov(1rt,x0),ts(x0,y0)),y0,satz141b(z0,x0),t8,satz105f(z0,ts(x0,y0),ov(1rt,x0),t7)):less"rt"(ov(z0,x0),y0)
+t10:=satz120(eta,y0,ly,ov(z0,x0),t9):lrt(eta,ov(z0,x0))
+t11:=prod1(z0,x0,lx,ov(z0,x0),t10,satz110d(z0,x0)):in(z0,prod)
+l@t12:=prodapp(u0,i,in(z0,prod),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,ts(x,y))]t11(x,t,y,u,v)):in(z0,prod)
+eta@[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
+t13:=prod1(ts(x1,y0),x1,lx1,y0,ly,refis(rat,ts(x1,y0))):in(ts(x1,y0),prod)
+t14:=satz105a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(ts(x1,y0),ts(x0,y0))
+t15:=ismore2"rt"(ts(x0,y0),z0,ts(x1,y0),symis(rat,z0,ts(x0,y0),j),t14):more"rt"(ts(x1,y0),z0)
+t16:=andi(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0),t13,t15):and(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0))
+t17:=somei(rat,[y:rat]and(in(y,prod),more"rt"(y,z0)),ts(x1,y0),t16):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
+j@t18:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t17(x,t,u)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
+i@t19:=prodapp(z0,i,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t18(x,t,y,u,v)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
+eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
+t20:=cut2(prod,ts(x0,y0),prod1(ts(x0,y0),x0,lx,y0,ly,refis(rat,ts(x0,y0))),ts(x1,y1),satz141a(x1,ux,y1,uy),[x:rat][t:in(x,prod)][y:rat][u:less"rt"(y,x)]t12(x,t,y,u),[x:rat][t:in(x,prod)]t19(x,t)):cutprop(prod)
+ux@t21:=cutapp1b(eta,cutprop(prod),[y:rat][t:urt(eta,y)]t20(y,t)):cutprop(prod)
+ly@t22:=cutapp1b(ksi,cutprop(prod),[x:rat][t:urt(ksi,x)]t21(x,t)):cutprop(prod)
+lx@t23:=cutapp1a(eta,cutprop(prod),[y:rat][t:lrt(eta,y)]t22(y,t)):cutprop(prod)
+-4141
+eta@satz141:=cutapp1a(ksi,cutprop(prod),[x:rat][t:lrt(ksi,x)]t23".4141"(x,t)):cutprop(prod)
+ts:=cutof(prod,satz141):cut
+[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
+lrtts:=ine(prod,satz141,z0,prod1(z0,x0,lx,y0,ly,i)):lrt(ts(ksi,eta),z0)
+eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
++*iii4
+i@t10:=isp1(rat,[x:rat]not(in(x,prod)),ts"rt"(x0,y0),z0,satz141a(x0,ux,y0,uy),i):not(in(z0,prod))
+-iii4
+i@urtts:=th3"l.imp"(lrt(ts(ksi,eta),z0),in(z0,prod),t10".iii4",[t:lrt(ts(ksi,eta),z0)]ini(prod,satz141,z0,t)):urt(ts(ksi,eta),z0)
+eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]p]
++*iii4
+p1@t11:=ini(prod,satz141,z0,lz):in(z0,prod)
+-iii4
+p1@tsapp:=prodapp(z0,t11".iii4",p,p1):p
+zeta@[i:is(ksi,eta)]
+ists1:=isf(cut,cut,[u:cut]ts(u,zeta),ksi,eta,i):is(ts(ksi,zeta),ts(eta,zeta))
+ists2:=isf(cut,cut,[u:cut]ts(zeta,u),ksi,eta,i):is(ts(zeta,ksi),ts(zeta,eta))
+upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
+ists12:=tris(cut,ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),ists1(i),ists2(zeta,upsilon,eta,j)):is(ts(ksi,zeta),ts(eta,upsilon))
++4142
+eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
+t1:=tris(rat,z0,ts"rt"(x0,y0),ts"rt"(y0,x0),i,comts(x0,y0)):is"rt"(z0,ts"rt"(y0,x0))
+t2:=lrtts(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(ts(eta,ksi),z0)
+lz@t3:=tsapp(ksi,eta,z0,lz,lrt(ts(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]t2(x,t,y,u,v)):lrt(ts(eta,ksi),z0)
+-4142
+eta@satz142:=isi1(ts(ksi,eta),ts(eta,ksi),[x:rat][t:lrt(ts(ksi,eta),x)]t3".4142"(x,t),[x:rat][t:lrt(ts(eta,ksi),x)]t3".4142"(eta,ksi,x,t)):is(ts(ksi,eta),ts(eta,ksi))
+comts:=satz142:is(ts(ksi,eta),ts(eta,ksi))
++4143
+zeta@[u0:rat][lu:lrt(ts(ts(ksi,eta),zeta),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,ts"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))]
+t1:=tr3is(rat,u0,ts"rt"(v0,z0),ts"rt"(ts"rt"(x0,y0),z0),ts"rt"(x0,ts"rt"(y0,z0)),i,ists1"rt"(v0,ts"rt"(x0,y0),z0,j),assts1(x0,y0,z0)):is"rt"(u0,ts"rt"(x0,ts"rt"(y0,z0)))
+t2:=lrtts(eta,zeta,ts"rt"(y0,z0),y0,ly,z0,lz,refis(rat,ts"rt"(y0,z0))):lrt(ts(eta,zeta),ts"rt"(y0,z0))
+t3:=lrtts(ksi,ts(eta,zeta),u0,x0,lx,ts"rt"(y0,z0),t2,t1):lrt(ts(ksi,ts(eta,zeta)),u0)
+i@t4:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
+lu@t5:=tsapp(ts(ksi,eta),zeta,u0,lu,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,ts"rt"(x,y))]t4(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
+u0@[lu:lrt(ts(ksi,ts(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(ts(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,ts"rt"(y0,z0))]
+t6:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,ts"rt"(y0,z0)),ts"rt"(ts"rt"(x0,y0),z0),i,ists2"rt"(v0,ts"rt"(y0,z0),x0,j),assts2(x0,y0,z0)):is"rt"(u0,ts"rt"(ts"rt"(x0,y0),z0))
+t7:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
+t8:=lrtts(ts(ksi,eta),zeta,u0,ts"rt"(x0,y0),t7,z0,lz,t6):lrt(ts(ts(ksi,eta),zeta),u0)
+i@t9:=tsapp(eta,zeta,v0,lv,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,ts"rt"(x,y))]t8(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
+lu@t10:=tsapp(ksi,ts(eta,zeta),u0,lu,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(ts(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t9(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
+-4143
+zeta@satz143:=isi1(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),[x:rat][t:lrt(ts(ts(ksi,eta),zeta),x)]t5".4143"(x,t),[x:rat][t:lrt(ts(ksi,ts(eta,zeta)),x)]t10".4143"(x,t)):is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
+assts1:=satz143:is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
+assts2:=symis(cut,ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),satz143):is(ts(ksi,ts(eta,zeta)),ts(ts(ksi,eta),zeta))
++4144
+[u0:rat][lu:lrt(ts(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
+t1:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,pl"rt"(y0,z0)),pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)),i,ists2"rt"(v0,pl"rt"(y0,z0),x0,j),disttp2(x0,y0,z0)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)))
+t2:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
+t3:=lrtts(ksi,zeta,ts"rt"(x0,z0),x0,lx,z0,lz,refis(rat,ts"rt"(x0,z0))):lrt(ts(ksi,zeta),ts"rt"(x0,z0))
+t4:=lrtpl(ts(ksi,eta),ts(ksi,zeta),u0,ts"rt"(x0,y0),t2,ts"rt"(x0,z0),t3,t1):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
+i@t5:=plapp(eta,zeta,v0,lv,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
+lu@t6:=tsapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t5(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
+u0@[lu:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][w0:rat][lw:lrt(ts(ksi,zeta),w0)][i:is"rt"(u0,pl"rt"(v0,w0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][z0:rat][lz:lrt(zeta,z0)][k:is"rt"(w0,ts"rt"(x1,z0))]
+t7:=tris(rat,u0,pl"rt"(v0,w0),pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),i,ispl12"rt"(v0,ts"rt"(x0,y0),w0,ts"rt"(x1,z0),j,k)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)))
+x2:=ite(moreis"rt"(x0,x1),rat,x0,x1):rat
+[m:moreis"rt"(x0,x1)]
+t8:=itet(moreis"rt"(x0,x1),rat,x0,x1,m):is"rt"(x2,x0)
+t9:=isp1(rat,[t:rat]lrt(ksi,t),x0,x2,lx,t8):lrt(ksi,x2)
+t10:=lessisi2"rt"(x0,x2,symis(rat,x2,x0,t8)):lessis"rt"(x0,x2)
+t11:=satz88(x1,x0,x2,satz84(x0,x1,m),t10):lessis"rt"(x1,x2)
+k@[n:not(moreis"rt"(x0,x1))]
+t12:=itef(moreis"rt"(x0,x1),rat,x0,x1,n):is"rt"(x2,x1)
+t13:=isp1(rat,[t:rat]lrt(ksi,t),x1,x2,lx1,t12):lrt(ksi,x2)
+t14:=lessisi2"rt"(x1,x2,symis(rat,x2,x1,t12)):lessis"rt"(x1,x2)
+t15:=lessisi1"rt"(x0,x2,satz87b(x0,x1,x2,satz81j(x0,x1,n),t14)):lessis"rt"(x0,x2)
+k@t16:=th1"l.imp"(moreis"rt"(x0,x1),lrt(ksi,x2),[t:moreis"rt"(x0,x1)]t9(t),[t:not(moreis"rt"(x0,x1))]t13(t)):lrt(ksi,x2)
+t17:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x0,x2),[t:moreis"rt"(x0,x1)]t10(t),[t:not(moreis"rt"(x0,x1))]t15(t)):lessis"rt"(x0,x2)
+t18:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x1,x2),[t:moreis"rt"(x0,x1)]t11(t),[t:not(moreis"rt"(x0,x1))]t14(t)):lessis"rt"(x1,x2)
+t19:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
+t20:=lrtts(ksi,pl(eta,zeta),ts"rt"(x2,pl"rt"(y0,z0)),x2,t16,pl"rt"(y0,z0),t19,refis(rat,ts"rt"(x2,pl"rt"(y0,z0)))):lrt(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)))
+t21:=satz109a(x0,x2,y0,y0,t17,lessisi2"rt"(y0,y0,refis(rat,y0))):lessis"rt"(ts"rt"(x0,y0),ts"rt"(x2,y0))
+t22:=satz109a(x1,x2,z0,z0,t18,lessisi2"rt"(z0,z0,refis(rat,z0))):lessis"rt"(ts"rt"(x1,z0),ts"rt"(x2,z0))
+t23:=islessis12"rt"(pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),u0,pl"rt"(ts"rt"(x2,y0),ts"rt"(x2,z0)),ts"rt"(x2,pl"rt"(y0,z0)),symis(rat,u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),t7),distpt2(x2,y0,z0),satz100a(ts"rt"(x0,y0),ts"rt"(x2,y0),ts"rt"(x1,z0),ts"rt"(x2,z0),t21,t22)):lessis"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))
+t24:=orapp(less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),lrt(ts(ksi,pl(eta,zeta)),u0),t23,[t:less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]satz120(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)),t20,u0,t),[t:is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]isp1(rat,[u:rat]lrt(ts(ksi,pl(eta,zeta)),u),ts"rt"(x2,pl"rt"(y0,z0)),u0,t20,t)):lrt(ts(ksi,pl(eta,zeta)),u0)
+j@t25:=tsapp(ksi,zeta,w0,lw,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(w0,ts"rt"(x,y))]t24(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
+i@t26:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t25(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
+lu@t27:=plapp(ts(ksi,eta),ts(ksi,zeta),u0,lu,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(ts(ksi,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t26(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
+-4144
+satz144:=isi1(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),[x:rat][t:lrt(ts(ksi,pl(eta,zeta)),x)]t6".4144"(x,t),[x:rat][t:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),x)]t27".4144"(x,t)):is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
+disttp1:=tr3is(cut,ts(pl(ksi,eta),zeta),ts(zeta,pl(ksi,eta)),pl(ts(zeta,ksi),ts(zeta,eta)),pl(ts(ksi,zeta),ts(eta,zeta)),comts(pl(ksi,eta),zeta),satz144(zeta,ksi,eta),ispl12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta))):is(ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)))
+disttp2:=satz144:is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
+distpt1:=symis(cut,ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)),disttp1):is(pl(ts(ksi,zeta),ts(eta,zeta)),ts(pl(ksi,eta),zeta))
+distpt2:=symis(cut,ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),disttp2):is(pl(ts(ksi,eta),ts(ksi,zeta)),ts(ksi,pl(eta,zeta)))
+[m:more(ksi,eta)]
++4145
+phi:=mn(ksi,eta,m):cut
+t1:=satz140d(ksi,eta,m):is(ksi,pl(eta,phi))
+t2:=tris(cut,ts(ksi,zeta),ts(pl(eta,phi),zeta),pl(ts(eta,zeta),ts(phi,zeta)),ists1(ksi,pl(eta,phi),zeta,t1),disttp1(eta,phi,zeta)):is(ts(ksi,zeta),pl(ts(eta,zeta),ts(phi,zeta)))
+-4145
+satz145a:=ismore1(pl(ts(eta,zeta),ts(phi".4145",zeta)),ts(ksi,zeta),ts(eta,zeta),symis(cut,ts(ksi,zeta),pl(ts(eta,zeta),ts(phi".4145",zeta)),t2".4145"),satz133(ts(eta,zeta),ts(phi".4145",zeta))):more(ts(ksi,zeta),ts(eta,zeta))
+zeta@[i:is(ksi,eta)]
+satz145b:=ists1(ksi,eta,zeta,i):is(ts(ksi,zeta),ts(eta,zeta))
+zeta@[l:less(ksi,eta)]
+satz145c:=satz121(ts(eta,zeta),ts(ksi,zeta),satz145a(eta,ksi,zeta,satz122(ksi,eta,l))):less(ts(ksi,zeta),ts(eta,zeta))
+m@satz145d:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145a):more(ts(zeta,ksi),ts(zeta,eta))
+i@satz145e:=ists2(ksi,eta,zeta,i):is(ts(zeta,ksi),ts(zeta,eta))
+l@satz145f:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145c):less(ts(zeta,ksi),ts(zeta,eta))
+upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
+satz145g:=ismore2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145d(zeta,upsilon,ksi,m)):more(ts(ksi,zeta),ts(eta,upsilon))
+satz145h:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145g):more(ts(zeta,ksi),ts(upsilon,eta))
+i@[l:less(zeta,upsilon)]
+satz145j:=isless2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145f(zeta,upsilon,ksi,l)):less(ts(ksi,zeta),ts(eta,upsilon))
+satz145k:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145j):less(ts(zeta,ksi),ts(upsilon,eta))
++4146
+zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+t2:=satz123b(ts(ksi,zeta),ts(eta,zeta)):ec3(is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)))
+-4146
+zeta@[m:more(ts(ksi,zeta),ts(eta,zeta))]
+satz146a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),m):more(ksi,eta)
+zeta@[i:is(ts(ksi,zeta),ts(eta,zeta))]
+satz146b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),i):is(ksi,eta)
+zeta@[l:less(ts(ksi,zeta),ts(eta,zeta))]
+satz146c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),l):less(ksi,eta)
+zeta@[m:more(ts(zeta,ksi),ts(zeta,eta))]
+satz146d:=satz146a(ismore12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),m)):more(ksi,eta)
+zeta@[i:is(ts(zeta,ksi),ts(zeta,eta))]
+satz146e:=satz146b(tr3is(cut,ts(ksi,zeta),ts(zeta,ksi),ts(zeta,eta),ts(eta,zeta),comts(ksi,zeta),i,comts(zeta,eta))):is(ksi,eta)
+zeta@[l:less(ts(zeta,ksi),ts(zeta,eta))]
+satz146f:=satz146c(isless12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),l)):less(ksi,eta)
+upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
++4147
+t1:=satz145a(ksi,eta,zeta,m):more(ts(ksi,zeta),ts(eta,zeta))
+t2:=ismore12(ts(zeta,eta),ts(eta,zeta),ts(upsilon,eta),ts(eta,upsilon),comts(zeta,eta),comts(upsilon,eta),satz145a(zeta,upsilon,eta,n)):more(ts(eta,zeta),ts(eta,upsilon))
+-4147
+satz147:=trmore(ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),t1".4147",t2".4147"):more(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
+satz147a:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz147(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
+satz148a:=orapp(more(ksi,eta),is(ksi,eta),more(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]satz147(t,n),[t:is(ksi,eta)]satz145g(t,n)):more(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
+satz148b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]satz147(m,t),[t:is(zeta,upsilon)]satz145h(zeta,upsilon,ksi,eta,t,m)):more(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
+satz148c:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
+satz148d:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
++4149
+[i:is(ksi,eta)][j:is(zeta,upsilon)]
+t1:=moreisi2(ts(ksi,zeta),ts(eta,upsilon),ists12(ksi,eta,zeta,upsilon,i,j)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+i@[o:more(zeta,upsilon)]
+t2:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148a(m,o)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+n@[o:more(ksi,eta)]
+t4:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148b(o,n)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+-4149
+satz149:=orapp(more(ksi,eta),is(ksi,eta),moreis(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]t4".4149"(t),[t:is(ksi,eta)]t3".4149"(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
+satz149a:=satz124(ts(eta,upsilon),ts(ksi,zeta),satz149(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(ts(ksi,zeta),ts(eta,upsilon))
+-rp
+@[r0:rat]
+ratset:=setof(rat,[x:rat]less(x,r0)):set(rat)
++4150
+t1:=satz90(r0):some([x:rat]less(x,r0))
+[x0:rat][l:less(x0,r0)]
+t2:=estii(rat,[x:rat]less(x,r0),x0,l):in(x0,ratset)
+r0@t3:=ec3e13(is(r0,r0),more(r0,r0),less(r0,r0),satz81b(r0,r0),refis(rat,r0)):not(less(r0,r0))
+t4:=th3"l.imp"(in(r0,ratset),less(r0,r0),t3,[t:in(r0,ratset)]estie(rat,[x:rat]less(x,r0),r0,t)):not(in(r0,ratset))
+x0@[i:in(x0,ratset)]
+t5:=estie(rat,[x:rat]less(x,r0),x0,i):less(x0,r0)
+[x1:rat][k:less(x1,x0)]
+t6:=t2(x1,trless(x1,x0,r0,k,t5)):in(x1,ratset)
+i@t7:=satz91(x0,r0,t5):some([x:rat]and(less(x0,x),less(x,r0)))
+[x1:rat][a:and(less(x0,x1),less(x1,r0))]
+t8:=ande1(less(x0,x1),less(x1,r0),a):less(x0,x1)
+t9:=ande2(less(x0,x1),less(x1,r0),a):less(x1,r0)
+t10:=andi(in(x1,ratset),more(x1,x0),t2(x1,t9),satz83(x0,x1,t8)):and(in(x1,ratset),more(x1,x0))
+i@t11:=th6"l.some"(rat,[x:rat]and(less(x0,x),less(x,r0)),[x:rat]and(in(x,ratset),more(x,x0)),t7,[x:rat][t:and(less(x0,x),less(x,r0))]t10(x,t)):some([x:rat]and(in(x,ratset),more(x,x0)))
+l@t12:=cut2(ratset,x0,t2,r0,t4,[x:rat][t:in(x,ratset)][y:rat][u:less(y,x)]t6(x,t,y,u),[x:rat][t:in(x,ratset)]t11(x,t)):cutprop(ratset)
+-4150
+satz150:=someapp(rat,[x:rat]less(x,r0),t1".4150",cutprop(ratset),[x:rat][t:less(x,r0)]t12".4150"(x,t)):cutprop(ratset)
++*rp
+r0@rpofrt:=cutof(ratset,satz150):cut
+[x0:rat][l:less"rt"(x0,r0)]
+lrtrpofrt:=ine(ratset,satz150,x0,t2"rt.4150"(x0,l)):lrt(rpofrt,x0)
+r0@[x0:rat][lx:lrt(rpofrt,x0)]
+lrtrpofrte:=t5"rt.4150"(x0,ini(ratset,satz150,x0,lx)):less"rt"(x0,r0)
+r0@[x0:rat][m:moreis"rt"(x0,r0)]
++*iii4
+m@t12:=satz81c(x0,r0,m):not(less"rt"(x0,r0))
+-iii4
+m@urtrpofrt:=th3"l.imp"(lrt(rpofrt,x0),less"rt"(x0,r0),t12".iii4",[t:lrt(rpofrt,x0)]lrtrpofrte(x0,t)):urt(rpofrt,x0)
+@1rp:=rpofrt(1rt):cut
++4151
+ksi@[z0:rat][lz:lrt(ts(ksi,1rp),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(1rp,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
+t1:=lrtrpofrte(1rt,y0,ly):less"rt"(y0,1rt)
+t2:=isless12"rt"(ts"rt"(x0,y0),z0,ts"rt"(x0,1rt),x0,symis(rat,z0,ts"rt"(x0,y0),i),example1a(x0),satz105f(y0,1rt,x0,t1)):less"rt"(z0,x0)
+t3:=satz120(ksi,x0,lx,z0,t2):lrt(ksi,z0)
+lz@t4:=tsapp(ksi,1rp,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(1rp,y)][v:is"rt"(z0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ksi,z0)
+ksi@[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
+y1:=ts"rt"(ov(1rt,x1),x0):rat
+t5:=isless2"rt"(ts"rt"(ov(1rt,x1),x1),1rt,y1,satz110e(1rt,x1),satz105f(x0,x1,ov(1rt,x1),l)):less"rt"(y1,1rt)
+t6:=lrtrpofrt(1rt,y1,t5):lrt(1rp,y1)
+t7:=tr3is(rat,ts"rt"(x1,y1),ts"rt"(ts"rt"(x1,ov(1rt,x1)),x0),ts"rt"(1rt,x0),x0,assts2"rt"(x1,ov(1rt,x1),x0),ists1"rt"(ts"rt"(x1,ov(1rt,x1)),1rt,x0,satz110c(1rt,x1)),example1c(x0)):is"rt"(ts"rt"(x1,y1),x0)
+t8:=lrtts(ksi,1rp,x0,x1,lx1,y1,t6,symis(rat,ts"rt"(x1,y1),x0,t7)):lrt(ts(ksi,1rp),x0)
+lx@t9:=cutapp3(ksi,x0,lx,lrt(ts(ksi,1rp),x0),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t8(y,t,u)):lrt(ts(ksi,1rp),x0)
+-4151
+ksi@satz151:=isi1(ts(ksi,1rp),ksi,[x:rat][t:lrt(ts(ksi,1rp),x)]t4".4151"(x,t),[x:rat][t:lrt(ksi,x)]t9".4151"(x,t)):is(ts(ksi,1rp),ksi)
+satz151a:=symis(cut,ts(ksi,1rp),ksi,satz151):is(ksi,ts(ksi,1rp))
+satz151b:=tris(cut,ts(1rp,ksi),ts(ksi,1rp),ksi,comts(1rp,ksi),satz151):is(ts(1rp,ksi),ksi)
+satz151c:=symis(cut,ts(1rp,ksi),ksi,satz151b):is(ksi,ts(1rp,ksi))
++4152
+[x0:rat][y0:rat]
+invprop1:=and(urt(ksi,y0),less"rt"(y0,x0)):'prop'
+ksi@[z0:rat][x0:rat]
+invprop2:=and3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0))):'prop'
+z0@invprop:=some"rt"([x:rat]invprop2(z0,x)):'prop'
+ksi@inv:=setof(rat,[z:rat]invprop(z)):set(rat)
+x0@[ux:urt(ksi,x0)][y0:rat][uy:urt(ksi,y0)][l:less"rt"(y0,x0)][i:is"rt"(z0,ov(1rt,x0))]
+t1:=andi(urt(ksi,y0),less"rt"(y0,x0),uy,l):invprop1(x0,y0)
+t2:=somei(rat,[x:rat]invprop1(x0,x),y0,t1):some"rt"([x:rat]invprop1(x0,x))
+t3:=and3i(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),ux,t2,i):invprop2(z0,x0)
+t4:=somei(rat,[x:rat]invprop2(z0,x),x0,t3):invprop(z0)
+inv1:=estii(rat,[z:rat]invprop(z),z0,t4):in(z0,inv)
+z0@[i:in(z0,inv)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]p]
+t5:=estie(rat,[x:rat]invprop(x),z0,i):invprop(z0)
+[x0:rat][px:invprop2(z0,x0)]
+t6:=and3e1(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):urt(ksi,x0)
+t7:=and3e2(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):some"rt"([x:rat]invprop1(x0,x))
+t8:=and3e3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):is"rt"(z0,ov(1rt,x0))
+[y0:rat][py:invprop1(x0,y0)]
+t9:=ande1(urt(ksi,y0),less"rt"(y0,x0),py):urt(ksi,y0)
+t10:=ande2(urt(ksi,y0),less"rt"(y0,x0),py):less"rt"(y0,x0)
+t11:=<t8><t10><t9><y0><t6><x0>p1:p
+px@t12:=someapp(rat,[x:rat]invprop1(x0,x),t7,p,[x:rat][t:invprop1(x0,x)]t11(x,t)):p
+p1@invapp:=someapp(rat,[x:rat]invprop2(z0,x),t5,p,[x:rat][t:invprop2(z0,x)]t12(x,t)):p
+ksi@[x0:rat][ux:urt(ksi,x0)]
+2x0:=pl"rt"(x0,x0):rat
+t13:=satz94a(x0,x0):less"rt"(x0,2x0)
+t14:=satz119a(ksi,x0,ux,2x0,t13):urt(ksi,2x0)
+t15:=inv1(ov(1rt,2x0),2x0,t14,x0,ux,t13,refis(rat,ov(1rt,2x0))):in(ov(1rt,2x0),inv)
+ksi@[x1:rat][lx:lrt(ksi,x1)][x0:rat][ux:urt(ksi,x0)]
+t16:=th3"l.imp"(is"rt"(x0,x1),lrt(ksi,x0),ux,[t:is"rt"(x0,x1)]isp1(rat,[x:rat]lrt(ksi,x),x1,x0,lx,t)):nis"rt"(x0,x1)
+t17:=satz110e(1rt,x0):is"rt"(ts"rt"(ov(1rt,x0),x0),1rt)
+t18:=satz110e(1rt,x1):is"rt"(ts"rt"(ov(1rt,x1),x1),1rt)
+[i:is"rt"(ov(1rt,x0),ov(1rt,x1))]
+t19:=tris(rat,ts"rt"(ov(1rt,x0),x1),ts"rt"(ov(1rt,x1),x1),1rt,ists1"rt"(ov(1rt,x0),ov(1rt,x1),x1,i),t18):is"rt"(ts"rt"(ov(1rt,x0),x1),1rt)
+t20:=satz110b(1rt,ov(1rt,x0),x0,x1,t17,t19):is"rt"(x0,x1)
+ux@t21:=th3"l.imp"(is"rt"(ov(1rt,x0),ov(1rt,x1)),is"rt"(x0,x1),t16,[t:is"rt"(ov(1rt,x0),ov(1rt,x1))]t20(t)):nis"rt"(ov(1rt,x0),ov(1rt,x1))
+lx@[i:in(ov(1rt,x1),inv)]
+t22:=invapp(ov(1rt,x1),i,con,[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(ov(1rt,x1),ov(1rt,x))]<symis(rat,ov(1rt,x1),ov(1rt,x),w)>t21(x,t)):con
+lx@t23:=[t:in(ov(1rt,x1),inv)]t22(t):not(in(ov(1rt,x1),inv))
+ksi@[z0:rat][i:in(z0,inv)][u0:rat][l:less"rt"(u0,z0)][x0:rat][ux:urt(ksi,x0)][j:is"rt"(z0,ov(1rt,x0))]
+t24:=isless2"rt"(z0,ov(1rt,x0),u0,j,l):less"rt"(u0,ov(1rt,x0))
+t25:=tris(rat,ts"rt"(ov(1rt,x0),x0),1rt,ts"rt"(u0,ov(1rt,u0)),satz110e(1rt,x0),satz110d(1rt,u0)):is"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)))
+t26:=isless2"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(u0,x0),t25,satz105c(u0,ov(1rt,x0),x0,t24)):less"rt"(ts"rt"(u0,x0),ts"rt"(u0,ov(1rt,u0)))
+t27:=isless12"rt"(ts"rt"(u0,x0),ts"rt"(x0,u0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(ov(1rt,u0),u0),comts"rt"(u0,x0),comts"rt"(u0,ov(1rt,u0)),t26):less"rt"(ts"rt"(x0,u0),ts"rt"(ov(1rt,u0),u0))
+t28:=satz106c(x0,ov(1rt,u0),u0,t27):less"rt"(x0,ov(1rt,u0))
+t29:=satz119a(x0,ux,ov(1rt,u0),t28):urt(ksi,ov(1rt,u0))
+t30:=satz110e(1rt,u0):is"rt"(ts"rt"(ov(1rt,u0),u0),1rt)
+t31:=satz110g(1rt,ov(1rt,u0),u0,t30):is"rt"(u0,ov(1rt,ov(1rt,u0)))
+t32:=inv1(u0,ov(1rt,u0),t29,x0,ux,t28,t31):in(u0,inv)
+l@t33:=invapp(z0,i,in(u0,inv),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t32(x,t,w)):in(u0,inv)
+i@[x0:rat][ux:urt(ksi,x0)][x1:rat][ux1:urt(ksi,x1)][l:less"rt"(x1,x0)][j:is"rt"(z0,ov(1rt,x0))]
+t34:=satz91(x1,x0,l):some"rt"([x:rat]and(less"rt"(x1,x),less"rt"(x,x0)))
+[x2:rat][a:and(less"rt"(x1,x2),less"rt"(x2,x0))]
+t35:=ande1(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x1,x2)
+t36:=satz119a(ksi,x1,ux1,x2,t35):urt(ksi,x2)
+t37:=inv1(ov(1rt,x2),x2,t36,x1,ux1,t35,refis(rat,ov(1rt,x2))):in(ov(1rt,x2),inv)
+t38:=ande2(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x2,x0)
+t39:=tris(rat,ts"rt"(x0,ov(1rt,x0)),1rt,ts"rt"(x2,ov(1rt,x2)),satz110c(1rt,x0),satz110d(1rt,x2)):is"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
+t40:=isless2"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)),ts"rt"(x2,ov(1rt,x0)),t39,satz105c(x2,x0,ov(1rt,x0),t38)):less"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
+t41:=isless12"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(ov(1rt,x0),x2),ts"rt"(x2,ov(1rt,x2)),ts"rt"(ov(1rt,x2),x2),comts"rt"(x2,ov(1rt,x0)),comts"rt"(x2,ov(1rt,x2)),t40):less"rt"(ts"rt"(ov(1rt,x0),x2),ts"rt"(ov(1rt,x2),x2))
+t42:=satz106c(ov(1rt,x0),ov(1rt,x2),x2,t41):less"rt"(ov(1rt,x0),ov(1rt,x2))
+t43:=ismore2"rt"(ov(1rt,x0),z0,ov(1rt,x2),symis(rat,z0,ov(1rt,x0),j),satz83(ov(1rt,x0),ov(1rt,x2),t42)):more"rt"(ov(1rt,x2),z0)
+t44:=andi(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0),t37,t43):and(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0))
+t45:=somei(rat,[x:rat]and(in(x,inv),more"rt"(x,z0)),ov(1rt,x2),t44):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
+j@t46:=someapp(rat,[x:rat]and(less"rt"(x1,x),less"rt"(x,x0)),t34,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:and(less"rt"(x1,x),less"rt"(x,x0))]t45(x,t)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
+i@t47:=invapp(z0,i,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t46(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
+ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
+t48:=cut2(inv,ov(1rt,pl"rt"(y0,y0)),t15(y0,uy),ov(1rt,x0),t23(x0,lx),[x:rat][t:in(x,inv)][y:rat][u:less"rt"(y,x)]t33(x,t,y,u),[x:rat][t:in(x,inv)]t47(x,t)):cutprop(inv)
+lx@t49:=cutapp1b(ksi,cutprop(inv),[x:rat][t:urt(ksi,x)]t48(x,t)):cutprop(inv)
+ksi@t50:=cutapp1a(ksi,cutprop(inv),[x:rat][t:lrt(ksi,x)]t49(x,t)):cutprop(inv)
+chi:=cutof(inv,t50):cut
+[z0:rat][lz:lrt(ts(ksi,chi),z0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,ts"rt"(x0,u0))][x1:rat][ux:urt(ksi,x1)][j:is"rt"(u0,ov(1rt,x1))]
+t51:=tris(rat,z0,ts"rt"(x0,u0),ts"rt"(x0,ov(1rt,x1)),i,ists2"rt"(u0,ov(1rt,x1),x0,j)):is"rt"(z0,ts"rt"(x0,ov(1rt,x1)))
+t52:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
+t53:=isless12"rt"(ts"rt"(x0,ov(1rt,x1)),z0,ts"rt"(x1,ov(1rt,x1)),1rt,symis(rat,z0,ts"rt"(x0,ov(1rt,x1)),t51),satz110c(1rt,x1),satz105c(x0,x1,ov(1rt,x1),t52)):less"rt"(z0,1rt)
+t54:=lrtrpofrt(1rt,z0,t53):lrt(1rp,z0)
+i@r1:=ini(inv,t50,u0,lu):in(u0,inv)
+r2:=invapp(u0,r1,lrt(1rp,z0),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(u0,ov(1rt,x))]t54(x,t,w)):lrt(1rp,z0)
+lz@r3:=tsapp(ksi,chi,z0,lz,lrt(1rp,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,ts"rt"(x,y))]r2(x,t,y,u,v)):lrt(1rp,z0)
+ksi@[u0:rat][lu:lrt(1rp,u0)]
+t55:=lrtrpofrte(1rt,u0,lu):less"rt"(u0,1rt)
+t56:=satz83(u0,1rt,t55):more"rt"(1rt,u0)
+[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][x2:rat][ux2:urt(ksi,x2)]
+t57:=cutapp2b(x1,lx1,x2,ux2):more"rt"(x2,x1)
+[i:is"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0))]
+t58:=cutapp2a(x0,lx,x2,ux2):less"rt"(x0,x2)
+t59:=satz105f(x0,x2,mn"rt"(1rt,u0,t56),t58):less"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),ts"rt"(mn"rt"(1rt,u0,t56),x2))
+t60:=isless1"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),symis(rat,mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0),i),t59):less"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2))
+t61:=tr4is(rat,pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),ts"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),x2),ts"rt"(1rt,x2),x2,pl"rt"(mn"rt"(x2,x1,t57),x1),distpt1"rt"(mn"rt"(1rt,u0,t56),u0,x2),ists1"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),1rt,x2,satz101e(1rt,u0,t56)),example1c(x2),satz101f(x2,x1,t57)):is"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
+t62:=satz96c(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2),t60):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)))
+t63:=isless2"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),t61,t62):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
+t64:=isless12"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(x1,mn"rt"(x2,x1,t57)),compl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),compl"rt"(mn"rt"(x2,x1,t57),x1),t63):less"rt"(pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(x1,mn"rt"(x2,x1,t57)))
+t65:=satz97c(ts"rt"(u0,x2),x1,mn"rt"(x2,x1,t57),t64):less"rt"(ts"rt"(u0,x2),x1)
+t66:=tr3is(rat,ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),ts"rt"(ts"rt"(ov(1rt,u0),u0),x2),ts"rt"(1rt,x2),x2,assts2"rt"(ov(1rt,u0),u0,x2),ists1"rt"(ts"rt"(ov(1rt,u0),u0),1rt,x2,satz110e(1rt,u0)),example1c(x2)):is"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2)
+t67:=isless12"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2,ts"rt"(ov(1rt,u0),x1),ov(x1,u0),t66,satz141b(x1,u0),satz105f(ts"rt"(u0,x2),x1,ov(1rt,u0),t65)):less"rt"(x2,ov(x1,u0))
+t68:=satz119a(x2,ux2,ov(x1,u0),t67):urt(ksi,ov(x1,u0))
+t69:=satz110e(x1,u0):is"rt"(ts"rt"(ov(x1,u0),u0),x1)
+t70:=tr3is(rat,u0,ov(x1,ov(x1,u0)),ts"rt"(ov(1rt,ov(x1,u0)),x1),ts"rt"(x1,ov(1rt,ov(x1,u0))),satz110g(x1,ov(x1,u0),u0,t69),satz141c(x1,ov(x1,u0)),comts"rt"(ov(1rt,ov(x1,u0)),x1)):is"rt"(u0,ts"rt"(x1,ov(1rt,ov(x1,u0))))
+t71:=inv1(ov(1rt,ov(x1,u0)),ov(x1,u0),t68,x2,ux2,t67,refis(rat,ov(1rt,ov(x1,u0)))):in(ov(1rt,ov(x1,u0)),inv)
+t72:=ine(inv,t50,ov(1rt,ov(x1,u0)),t71):lrt(chi,ov(1rt,ov(x1,u0)))
+t73:=lrtts(ksi,chi,u0,x1,lx1,ov(1rt,ov(x1,u0)),t72,t70):lrt(ts(ksi,chi),u0)
+lx@t74:=satz132app(ksi,lrt(ts(ksi,chi),u0),ts"rt"(mn"rt"(1rt,u0,t56),x0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn"rt"(y,x,cutapp2b(x,t,y,u)),ts"rt"(mn"rt"(1rt,u0,t56),x0))]t73(x,t,y,u,v)):lrt(ts(ksi,chi),u0)
+lu@t75:=cutapp1a(ksi,lrt(ts(ksi,chi),u0),[x:rat][t:lrt(ksi,x)]t74(x,t)):lrt(ts(ksi,chi),u0)
+ksi@t76:=isi1(ts(ksi,chi),1rp,[x:rat][t:lrt(ts(ksi,chi),x)]r3(x,t),[x:rat][t:lrt(1rp,x)]t75(x,t)):is(ts(ksi,chi),1rp)
+-4152
+satz152:=somei(cut,[t:cut]is(ts(ksi,t),1rp),chi".4152",t76".4152"):some([c:cut]is(ts(ksi,c),1rp))
+eta@[phi:cut][psi:cut]
++4153
+[m:more(phi,psi)]
+t1:=satz145d(phi,psi,eta,m):more(ts(eta,phi),ts(eta,psi))
+t2:=ec3e21(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t1):nis(ts(eta,phi),ts(eta,psi))
+psi@[l:less(phi,psi)]
+t3:=satz145f(phi,psi,eta,l):less(ts(eta,phi),ts(eta,psi))
+t4:=ec3e31(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t3):nis(ts(eta,phi),ts(eta,psi))
+psi@[n:nis(phi,psi)]
+t5:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
+t6:=orapp(more(phi,psi),less(phi,psi),nis(ts(eta,phi),ts(eta,psi)),t5,[t:more(phi,psi)]t2(t),[t:less(phi,psi)]t4(t)):nis(ts(eta,phi),ts(eta,psi))
+-4153
+[i:is(ts(eta,phi),ksi)][j:is(ts(eta,psi),ksi)]
+satz153b:=th7"l.imp"(is(phi,psi),nis(ts(eta,phi),ts(eta,psi)),weli(is(ts(eta,phi),ts(eta,psi)),tris2(cut,ts(eta,phi),ts(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t6".4153"(t)):is(phi,psi)
++*4153
+eta@[tau:cut][i:is(ts(eta,tau),1rp)]
+chi:=ts(tau,ksi):cut
+t7:=tr3is(cut,ts(eta,chi),ts(ts(eta,tau),ksi),ts(1rp,ksi),ksi,assts2(eta,tau,ksi),ists1(ts(eta,tau),1rp,ksi,i),satz151b(ksi)):is(ts(eta,chi),ksi)
+t8:=somei(cut,[c:cut]is(ts(eta,c),ksi),chi,t7):some([c:cut]is(ts(eta,c),ksi))
+-4153
+eta@satz153a:=someapp(cut,[c:cut]is(ts(eta,c),1rp),satz152(eta),some([c:cut]is(ts(eta,c),ksi)),[c:cut][t:is(ts(eta,c),1rp)]t8".4153"(c,t)):some([c:cut]is(ts(eta,c),ksi))
++*4153
+eta@t9:=[c:cut][d:cut][t:is(ts(eta,c),ksi)][u:is(ts(eta,d),ksi)]satz153b(c,d,t,u):amone(cut,[c:cut]is(ts(eta,c),ksi))
+-4153
+eta@satz153:=onei(cut,[c:cut]is(ts(eta,c),ksi),t9".4153",satz153a):one([c:cut]is(ts(eta,c),ksi))
+ov:=ind(cut,[a:cut]is(ts(eta,a),ksi),satz153):cut
+satz153c:=oneax(cut,[a:cut]is(ts(eta,a),ksi),satz153):is(ts(eta,ov(ksi,eta)),ksi)
+satz153d:=symis(cut,ts(eta,ov(ksi,eta)),ksi,satz153c):is(ksi,ts(eta,ov(ksi,eta)))
+satz153e:=tris(cut,ts(ov(ksi,eta),eta),ts(eta,ov(ksi,eta)),ksi,comts(ov(ksi,eta),eta),satz153c):is(ts(ov(ksi,eta),eta),ksi)
+satz153f:=symis(cut,ts(ov(ksi,eta),eta),ksi,satz153e):is(ksi,ts(ov(ksi,eta),eta))
+[phi:cut][i:is(ts(eta,phi),ksi)]
+satz153g:=satz153b(phi,ov(ksi,eta),i,satz153c):is(phi,ov(ksi,eta))
+@[ksi:cut]
+ratrp:=image(rat,cut,[x:rat]rpofrt(x),ksi):'prop'
+@[x0:rat]
+ratrpi:=imagei(rat,cut,[x:rat]rpofrt(x),x0):ratrp(rpofrt(x0))
+@[x:nat]
+rpofnt:=rpofrt(rtofn(x)):cut
+ksi@natrp:=image(nat,cut,[x:nat]rpofnt(x),ksi):'prop'
+x@natrpi:=imagei(nat,cut,[y:nat]rpofnt(y),x):natrp(rpofnt(x))
+ksi@[n:natrp(ksi)]
++iii5
+[x:nat][i:is(ksi,rpofnt(x))]
+t1:=somei(rat,[y:rat]is(ksi,rpofrt(y)),rtofn(x),i):ratrp(ksi)
+-iii5
+lemmaiii5:=someapp(nat,[x:nat]is(ksi,rpofnt(x)),n,ratrp(ksi),[x:nat][t:is(ksi,rpofnt(x))]t1".iii5"(x,t)):ratrp(ksi)
+@[x0:rat][y0:rat][m:more"rt"(x0,y0)]
++5154
+t1:=lrtrpofrt(x0,y0,satz82(x0,y0,m)):lrt(rpofrt(x0),y0)
+t2:=urtrpofrt(y0,y0,moreisi2"rt"(y0,y0,refis(rat,y0))):urt(rpofrt(y0),y0)
+t3:=andi(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0),t1,t2):and(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0))
+-5154
+satz154a:=somei(rat,[x:rat]and(lrt(rpofrt(x0),x),urt(rpofrt(y0),x)),y0,t3".5154"):more(rpofrt(x0),rpofrt(y0))
+y0@[i:is"rt"(x0,y0)]
+satz154b:=isf(rat,cut,[x:rat]rpofrt(x),x0,y0,i):is(rpofrt(x0),rpofrt(y0))
+y0@[l:less"rt"(x0,y0)]
+satz154c:=satz121(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,satz83(x0,y0,l))):less(rpofrt(x0),rpofrt(y0))
++*5154
+y0@t4:=satz81a(x0,y0):or3(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0))
+t5:=satz123b(rpofrt(x0),rpofrt(y0)):ec3(is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)))
+-5154
+y0@[m:more(rpofrt(x0),rpofrt(y0))]
+satz154d:=th11"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),m):more"rt"(x0,y0)
+y0@[i:is(rpofrt(x0),rpofrt(y0))]
+satz154e:=th10"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),i):is"rt"(x0,y0)
+y0@[l:less(rpofrt(x0),rpofrt(y0))]
+satz154f:=th12"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),l):less"rt"(x0,y0)
++*iii5
+@t2:=[x:rat][y:rat][t:is(rpofrt(x),rpofrt(y))]satz154e(x,y,t):injective(rat,cut,[x:rat]rpofrt(x))
+-iii5
+y0@[i:is"rt"(x0,y0)]
+isrterp:=satz154b(x0,y0,i):is(rpofrt(x0),rpofrt(y0))
+y0@[i:is(rpofrt(x0),rpofrt(y0))]
+isrtirp:=satz154e(x0,y0,i):is"rt"(x0,y0)
+ksi@[rtksi:ratrp(ksi)]
+rtofrp:=soft(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):rat
+[eta:cut][rteta:ratrp(eta)][i:is(ksi,eta)]
+isrpert:=isinv(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))
+rteta@[i:is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))]
+isrpirt:=isinve(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is(ksi,eta)
+x0@isrtrp1:=isst1(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(x0,rtofrp(rpofrt(x0),ratrpi(x0)))
+isrtrp2:=isst2(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(rtofrp(rpofrt(x0),ratrpi(x0)),x0)
+rtksi@isrprt1:=ists1"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(ksi,rpofrt(rtofrp(ksi,rtksi)))
+isrprt2:=ists2"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(rpofrt(rtofrp(ksi,rtksi)),ksi)
+@[x:nat][y:nat][i:is"n"(x,y)]
+isnterp:=isf(nat,cut,[z:nat]rpofnt(z),x,y,i):is(rpofnt(x),rpofnt(y))
+y@[i:is(rpofnt(x),rpofnt(y))]
+isntirp:=isnirt(x,y,isrtirp(rtofn(x),rtofn(y),i)):is"n"(x,y)
++*iii5
+@t3:=[x:nat][y:nat][t:is(rpofnt(x),rpofnt(y))]isntirp(x,y,t):injective(nat,cut,[x:nat]rpofnt(x))
+-iii5
+ksi@[ntksi:natrp(ksi)]
+ntofrp:=soft(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):nat
+[eta:cut][nteta:natrp(eta)][i:is(ksi,eta)]
+isrpent:=isinv(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))
+nteta@[i:is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))]
+isrpint:=isinve(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is(ksi,eta)
+x@isntrp1:=isst1(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(x,ntofrp(rpofnt(x),natrpi(x)))
+isntrp2:=isst2(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(ntofrp(rpofnt(x),natrpi(x)),x)
+ntksi@isrpnt1:=ists1"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(ksi,rpofnt(ntofrp(ksi,ntksi)))
+isrpnt2:=ists2"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(rpofnt(ntofrp(ksi,ntksi)),ksi)
+@[x0:rat][y0:rat]
++5155
+[z0:rat][lz:lrt(pl(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,pl"rt"(u0,v0))]
+t1:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
+t2:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
+t3:=satz98a(u0,x0,v0,y0,t1,t2):less"rt"(pl"rt"(u0,v0),pl"rt"(x0,y0))
+t4:=isless1"rt"(pl"rt"(u0,v0),z0,pl"rt"(x0,y0),symis(rat,z0,pl"rt"(u0,v0),i),t3):less"rt"(z0,pl"rt"(x0,y0))
+t5:=lrtrpofrt(pl"rt"(x0,y0),z0,t4):lrt(rpofrt(pl"rt"(x0,y0)),z0)
+lz@t6:=plapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(pl"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,pl"rt"(x,y))]t5(x,t,y,u,v)):lrt(rpofrt(pl"rt"(x0,y0)),z0)
+y0@[u0:rat][lu:lrt(rpofrt(pl"rt"(x0,y0)),u0)]
+t7:=lrtrpofrte(pl"rt"(x0,y0),u0,lu):less"rt"(u0,pl"rt"(x0,y0))
+u01:=ov"rt"(u0,pl"rt"(x0,y0)):rat
+t8:=isless12"rt"(u0,ts"rt"(u01,pl"rt"(x0,y0)),pl"rt"(x0,y0),ts"rt"(1rt,pl"rt"(x0,y0)),satz110f(u0,pl"rt"(x0,y0)),example1d(pl"rt"(x0,y0)),t7):less"rt"(ts"rt"(u01,pl"rt"(x0,y0)),ts"rt"(1rt,pl"rt"(x0,y0)))
+t9:=satz106c(u01,1rt,pl"rt"(x0,y0),t8):less"rt"(u01,1rt)
+t10:=tris(rat,u0,ts"rt"(pl"rt"(x0,y0),u01),pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)),satz110d(u0,pl"rt"(x0,y0)),disttp1"rt"(x0,y0,u01)):is"rt"(u0,pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)))
+y0@[l:less"rt"(y0,1rt)]
+t11:=isless12"rt"(ts"rt"(y0,x0),ts"rt"(x0,y0),ts"rt"(1rt,x0),x0,comts"rt"(y0,x0),example1c(x0),satz105c(y0,1rt,x0,l)):less"rt"(ts"rt"(x0,y0),x0)
+t12:=lrtrpofrt(x0,ts"rt"(x0,y0),t11):lrt(rpofrt(x0),ts"rt"(x0,y0))
+lu@t13:=lrtpl(rpofrt(x0),rpofrt(y0),u0,ts"rt"(x0,u01),t12(x0,u01,t9),ts"rt"(y0,u01),t12(y0,u01,t9),t10):lrt(pl(rpofrt(x0),rpofrt(y0)),u0)
+-5155
+satz155a:=isi1(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(pl"rt"(x0,y0)),x)]t13".5155"(x,t),[x:rat][t:lrt(pl(rpofrt(x0),rpofrt(y0)),x)]t6".5155"(x,t)):is(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)))
+[m:more"rt"(x0,y0)]
++*5155
+m@t14:=satz101f(x0,y0,m):is"rt"(x0,pl"rt"(mn"rt"(x0,y0,m),y0))
+t15:=tris(cut,rpofrt(x0),rpofrt(pl"rt"(mn"rt"(x0,y0,m),y0)),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),isrterp(x0,pl"rt"(mn"rt"(x0,y0,m),y0),t14),satz155a(mn"rt"(x0,y0,m),y0)):is(rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)))
+t16:=tris2(cut,pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),compl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),t15):is(pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0))
+-5155
+m@satz155b:=satz140g(rpofrt(x0),rpofrt(y0),rpofrt(mn"rt"(x0,y0,m)),satz154a(x0,y0,m),t16".5155"):is(rpofrt(mn"rt"(x0,y0,m)),mn(rpofrt(x0),rpofrt(y0),satz154a(x0,y0,m)))
++*5155
+y0@[z0:rat][lz:lrt(ts(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,ts"rt"(u0,v0))]
+t17:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
+t18:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
+t19:=satz107a(u0,x0,v0,y0,t17,t18):less"rt"(ts"rt"(u0,v0),ts"rt"(x0,y0))
+t20:=isless1"rt"(ts"rt"(u0,v0),z0,ts"rt"(x0,y0),symis(rat,z0,ts"rt"(u0,v0),i),t19):less"rt"(z0,ts"rt"(x0,y0))
+t21:=lrtrpofrt(ts"rt"(x0,y0),z0,t20):lrt(rpofrt(ts"rt"(x0,y0)),z0)
+lz@t22:=tsapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(ts"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,ts"rt"(x,y))]t21(x,t,y,u,v)):lrt(rpofrt(ts"rt"(x0,y0)),z0)
+y0@[u0:rat][lu:lrt(rpofrt(ts"rt"(x0,y0)),u0)]
+t23:=lrtrpofrte(ts"rt"(x0,y0),u0,lu):less"rt"(u0,ts"rt"(x0,y0))
+[u1:rat][a:and(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)))]
+t24:=ande1(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u0,u1)
+t25:=ande2(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u1,ts"rt"(x0,y0))
+t26:=isless12"rt"(u0,ts"rt"(ov"rt"(u0,u1),u1),u1,ts"rt"(1rt,u1),satz110f(u0,u1),example1d(u1),t24):less"rt"(ts"rt"(ov"rt"(u0,u1),u1),ts"rt"(1rt,u1))
+t27:=satz106c(ov"rt"(u0,u1),1rt,u1,t26):less"rt"(ov"rt"(u0,u1),1rt)
+t28:=isless1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0),satz110f(u1,y0),t25):less"rt"(ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0))
+t29:=satz106c(ov"rt"(u1,y0),x0,y0,t28):less"rt"(ov"rt"(u1,y0),x0)
+t30:=tr3is(rat,u0,ts"rt"(u1,ov"rt"(u0,u1)),ts"rt"(ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1)),ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))),satz110d(u0,u1),ists1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1),satz110f(u1,y0)),assts1"rt"(ov"rt"(u1,y0),y0,ov"rt"(u0,u1))):is"rt"(u0,ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))))
+t31:=lrtts(rpofrt(x0),rpofrt(y0),u0,ov"rt"(u1,y0),lrtrpofrt(x0,ov"rt"(u1,y0),t29),ts"rt"(y0,ov"rt"(u0,u1)),t12(y0,ov"rt"(u0,u1),t27),t30):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
+lu@t32:=someapp(rat,[x:rat]and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0))),satz91(u0,ts"rt"(x0,y0),t23),lrt(ts(rpofrt(x0),rpofrt(y0)),u0),[x:rat][t:and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0)))]t31(x,t)):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
+-5155
+y0@satz155c:=isi1(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(ts"rt"(x0,y0)),x)]t32".5155"(x,t),[x:rat][t:lrt(ts(rpofrt(x0),rpofrt(y0)),x)]t22".5155"(x,t)):is(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)))
++*5155
+y0@t33:=satz110f(x0,y0):is"rt"(x0,ts"rt"(ov"rt"(x0,y0),y0))
+t34:=tris(cut,rpofrt(x0),rpofrt(ts"rt"(ov"rt"(x0,y0),y0)),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),isrterp(x0,ts"rt"(ov"rt"(x0,y0),y0),t33),satz155c(ov"rt"(x0,y0),y0)):is(rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)))
+t35:=tris2(cut,ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),comts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),t34):is(ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0))
+-5155
+y0@satz155d:=satz153g(rpofrt(x0),rpofrt(y0),rpofrt(ov"rt"(x0,y0)),t35".5155"):is(rpofrt(ov"rt"(x0,y0)),ov(rpofrt(x0),rpofrt(y0)))
+@[x:nat][y:nat]
+satz155e:=tris(cut,rpofnt(pl"n"(x,y)),rpofrt(pl"rt"(rtofn(x),rtofn(y))),pl(rpofnt(x),rpofnt(y)),isrterp(rtofn(pl"n"(x,y)),pl"rt"(rtofn(x),rtofn(y)),symis(rat,pl"rt"(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),satz112h(x,y))),satz155a(rtofn(x),rtofn(y))):is(rpofnt(pl"n"(x,y)),pl(rpofnt(x),rpofnt(y)))
+satz155f:=tris(cut,rpofnt(ts"n"(x,y)),rpofrt(ts"rt"(rtofn(x),rtofn(y))),ts(rpofnt(x),rpofnt(y)),isrterp(rtofn(ts"n"(x,y)),ts"rt"(rtofn(x),rtofn(y)),symis(rat,ts"rt"(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),satz112j(x,y))),satz155c(rtofn(x),rtofn(y))):is(rpofnt(ts"n"(x,y)),ts(rpofnt(x),rpofnt(y)))
++nt
+@natt:=ot(cut,[t:cut]natrp(t)):'type'
+[ksi:cut][nksi:natrp(ksi)]
+nttofrp:=out(cut,[t:cut]natrp(t),ksi,nksi):natt
+@[xt:natt][yt:natt]
+is:=is"e"(natt,xt,yt):'prop'
+nis:=not(is(xt,yt)):'prop'
+@[p:[x:natt]'prop']
+all:=all"l"(natt,p):'prop'
+some:=some"l"(natt,p):'prop'
+one:=one"e"(natt,p):'prop'
+xt@[st:set(natt)]
+in:=esti(natt,xt,st):'prop'
+xt@rpofntt:=in"e"(cut,[t:cut]natrp(t),xt):cut
+natrpi:=inp(cut,[t:cut]natrp(t),xt):natrp(rpofntt(xt))
+nksi@[eta:cut][neta:natrp(eta)][i:is"rp"(ksi,eta)]
+isrpentt:=isouti(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is(nttofrp(ksi,nksi),nttofrp(eta,neta))
+neta@[i:is(nttofrp(ksi,nksi),nttofrp(eta,neta))]
+isrpintt:=isoute(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is"rp"(ksi,eta)
+yt@[i:is(xt,yt)]
+isntterp:=isini(cut,[t:cut]natrp(t),xt,yt,i):is"rp"(rpofntt(xt),rpofntt(yt))
+yt@[i:is"rp"(rpofntt(xt),rpofntt(yt))]
+isnttirp:=isine(cut,[t:cut]natrp(t),xt,yt,i):is(xt,yt)
+nksi@isrpntt1:=isinout(cut,[t:cut]natrp(t),ksi,nksi):is"rp"(ksi,rpofntt(nttofrp(ksi,nksi)))
+xt@isnttrp1:=isoutin(cut,[t:cut]natrp(t),xt):is(xt,nttofrp(rpofntt(xt),natrpi(xt)))
+@[x:nat]
+nttofnt:=nttofrp(rpofnt(x),natrpi"rp"(x)):natt
+[y:nat][i:is"n"(x,y)]
+isntentt:=isrpentt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),isnterp(x,y,i)):is(nttofnt(x),nttofnt(y))
+y@[i:is(nttofnt(x),nttofnt(y))]
+isntintt:=isntirp(x,y,isrpintt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),i)):is"n"(x,y)
+xt@ntofntt:=ntofrp(rpofntt(xt),natrpi(xt)):nat
+yt@[i:is(xt,yt)]
+isnttent:=isrpent(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),isntterp(xt,yt,i)):is"n"(ntofntt(xt),ntofntt(yt))
+yt@[i:is"n"(ntofntt(xt),ntofntt(yt))]
+isnttint:=isnttirp(xt,yt,isrpint(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),i)):is(xt,yt)
++iii5
+x@t5:=isrpntt1(rpofnt(x),natrpi"rp"(x)):is"rp"(rpofnt(x),rpofntt(nttofnt(x)))
+t6:=isrpent(rpofnt(x),natrpi"rp"(x),rpofntt(nttofnt(x)),natrpi(nttofnt(x)),t5):is"n"(ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)))
+-iii5
+x@isntntt1:=tris(nat,x,ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)),isntrp1(x),t6".iii5"):is"n"(x,ntofntt(nttofnt(x)))
++*iii5
+xt@t7:=isrpnt1(rpofntt(xt),natrpi(xt)):is"rp"(rpofntt(xt),rpofnt(ntofntt(xt)))
+t8:=isrpentt(rpofntt(xt),natrpi(xt),rpofnt(ntofntt(xt)),natrpi"rp"(ntofntt(xt)),t7):is(nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)))
+-iii5
+xt@isnttnt1:=tris(natt,xt,nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)),isnttrp1(xt),t8".iii5"):is(xt,nttofnt(ntofntt(xt)))
+x@isntntt2:=symis(nat,x,ntofntt(nttofnt(x)),isntntt1):is"n"(ntofntt(nttofnt(x)),x)
+xt@isnttnt2:=symis(natt,xt,nttofnt(ntofntt(xt)),isnttnt1):is(nttofnt(ntofntt(xt)),xt)
+@1t:=nttofnt(1):natt
+suct:=[x:natt]nttofnt(<ntofntt(x)>suc):[x:natt]natt
++5156
+xt@[j:is(<xt>suct,1t)]
+t1:=isntintt(<ntofntt(xt)>suc,1,j):is"n"(<ntofntt(xt)>suc,1)
+-5156
+xt@satz156a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<ntofntt(xt)>suc,1),<ntofntt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5156"(t)):nis(<xt>suct,1t)
+yt@[i:is(<xt>suct,<yt>suct)]
++*5156
+i@t2:=isntintt(<ntofntt(xt)>suc,<ntofntt(yt)>suc,i):is"n"(<ntofntt(xt)>suc,<ntofntt(yt)>suc)
+-5156
+i@satz156b:=isnttint(xt,yt,<t2".5156"><ntofntt(yt)><ntofntt(xt)>ax4):is(xt,yt)
+@[st:set(natt)]
+cond1:=in(1t,st):'prop'
+cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
+[c1:cond1][c2:cond2]
++*5156
+c2@[x:nat]
+prop1:=in(nttofnt(x),st):'prop'
+[p:prop1(x)]
+t3:=<p><nttofnt(x)>c2:in(<nttofnt(x)>suct,st)
+t4:=isp(nat,[t:nat]in(nttofnt(<t>suc),st),ntofntt(nttofnt(x)),x,t3,isntntt2(x)):prop1(<x>suc)
+-5156
+c2@[xt:natt]
++*5156
+xt@t5:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t4(t,u),ntofntt(xt)):in(nttofnt(ntofntt(xt)),st)
+-5156
+xt@satz156c:=isp(natt,[t:natt]in(t,st),nttofnt(ntofntt(xt)),xt,t5".5156",isnttnt2(xt)):in(xt,st)
+@ax3t:=[x:natt]satz156a(x):[x:natt]nis(<x>suct,1t)
+ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz156b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
+ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz156c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
+-nt
++rtt
+@ratt:=ot(cut,[t:cut]ratrp(t)):'type'
+[ksi:cut][rtksi:ratrp(ksi)]
+rttofrp:=out(cut,[t:cut]ratrp(t),ksi,rtksi):ratt
+@[x0t:ratt][y0t:ratt]
+is:=is"e"(ratt,x0t,y0t):'prop'
+nis:=not(is(x0t,y0t)):'prop'
+@[p:[x:ratt]'prop']
+all:=all"l"(ratt,p):'prop'
+some:=some"l"(ratt,p):'prop'
+one:=one"e"(ratt,p):'prop'
+x0t@rpofrtt:=in"e"(cut,[t:cut]ratrp(t),x0t):cut
+ratrpi:=inp(cut,[t:cut]ratrp(t),x0t):ratrp(rpofrtt(x0t))
+rtksi@[eta:cut][rteta:ratrp(eta)][i:is"rp"(ksi,eta)]
+isrpertt:=isouti(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))
+rteta@[i:is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))]
+isrpirtt:=isoute(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is"rp"(ksi,eta)
+y0t@[i:is(x0t,y0t)]
+isrtterp:=isini(cut,[t:cut]ratrp(t),x0t,y0t,i):is"rp"(rpofrtt(x0t),rpofrtt(y0t))
+y0t@[i:is"rp"(rpofrtt(x0t),rpofrtt(y0t))]
+isrttirp:=isine(cut,[t:cut]ratrp(t),x0t,y0t,i):is(x0t,y0t)
+rtksi@isrprtt1:=isinout(cut,[t:cut]ratrp(t),ksi,rtksi):is"rp"(ksi,rpofrtt(rttofrp(ksi,rtksi)))
+x0t@isrttrp1:=isoutin(cut,[t:cut]ratrp(t),x0t):is(x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)))
+@[x0:rat]
+rttofrt:=rttofrp(rpofrt(x0),ratrpi"rp"(x0)):ratt
+[y0:rat][i:is"rt"(x0,y0)]
+isrtertt:=isrpertt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),isrterp(x0,y0,i)):is(rttofrt(x0),rttofrt(y0))
+y0@[i:is(rttofrt(x0),rttofrt(y0))]
+isrtirtt:=isrtirp(x0,y0,isrpirtt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),i)):is"rt"(x0,y0)
+x0t@rtofrtt:=rtofrp(rpofrtt(x0t),ratrpi(x0t)):rat
+y0t@[i:is(x0t,y0t)]
+isrttert:=isrpert(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),isrtterp(x0t,y0t,i)):is"rt"(rtofrtt(x0t),rtofrtt(y0t))
+y0t@[i:is"rt"(rtofrtt(x0t),rtofrtt(y0t))]
+isrttirt:=isrttirp(x0t,y0t,isrpirt(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),i)):is(x0t,y0t)
++iii5
+x0@t9:=isrprtt1(rpofrt(x0),ratrpi"rp"(x0)):is"rp"(rpofrt(x0),rpofrtt(rttofrt(x0)))
+t10:=isrpert(rpofrt(x0),ratrpi"rp"(x0),rpofrtt(rttofrt(x0)),ratrpi(rttofrt(x0)),t9):is"rt"(rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)))
+-iii5
+x0@isrtrtt1:=tris(rat,x0,rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)),isrtrp1(x0),t10".iii5"):is"rt"(x0,rtofrtt(rttofrt(x0)))
++*iii5
+x0t@t11:=isrprt1(rpofrtt(x0t),ratrpi(x0t)):is"rp"(rpofrtt(x0t),rpofrt(rtofrtt(x0t)))
+t12:=isrpertt(rpofrtt(x0t),ratrpi(x0t),rpofrt(rtofrtt(x0t)),ratrpi"rp"(rtofrtt(x0t)),t11):is(rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)))
+-iii5
+x0t@isrttrt1:=tris(ratt,x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)),isrttrp1(x0t),t12".iii5"):is(x0t,rttofrt(rtofrtt(x0t)))
+-rtt
+@[ksi:cut]
+example2:=satz153c(1rp,ksi):is(ts(ksi,ov(1rp,ksi)),1rp)
+[rtksi:ratrp(ksi)]
++5157
+x01:=rtofrp(ksi,rtksi):rat
+ksi@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
+rtksi@[y0:rat][i:in(y0,s1)]
+t1:=estie(rat,[x:rat]urt(ksi,x),y0,i):urt(ksi,y0)
+[m:more"rt"(x01,y0)]
+t2:=lrtrpofrt(x01,y0,satz82(x01,y0,m)):lrt(rpofrt(x01),y0)
+t3:=isp(cut,[x:cut]lrt(x,y0),rpofrt(x01),ksi,t2,isrprt2(ksi,rtksi)):lrt(ksi,y0)
+i@t4:=th3"l.imp"(more"rt"(x01,y0),lrt(ksi,y0),t1,[t:more"rt"(x01,y0)]t3(t)):not(more"rt"(x01,y0))
+t5:=satz81e(x01,y0,t4):lessis"rt"(x01,y0)
+rtksi@t6:=[x:rat][t:in(x,s1)]t5(x,t):lb(s1,x01)
+t7:=urtrpofrt(x01,x01,moreisi2"rt"(x01,x01,refis(rat,x01))):urt(rpofrt(x01),x01)
+t8:=isp(cut,[x:cut]urt(x,x01),rpofrt(x01),ksi,t7,isrprt2(ksi,rtksi)):urt(ksi,x01)
+t9:=estii(rat,[x:rat]urt(ksi,x),x01,t8):in(x01,s1)
+t10:=andi(lb(s1,x01),in(x01,s1),t6,t9):min(s1,x01)
+-5157
+satz157a:=t10".5157":min(setof(rat,[x:rat]urt(ksi,x)),rtofrp(ksi,rtksi))
+satz157b:=somei(rat,[x:rat]min(s1".5157",x),x01".5157",t10".5157"):some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))
+ksi@[x0:rat][m:min(setof(rat,[x:rat]urt(ksi,x)),x0)]
++*5157
+m"rp"@t11:=ande1(lb(s1,x0),in(x0,s1),m):lb(s1,x0)
+t12:=ande2(lb(s1,x0),in(x0,s1),m):in(x0,s1)
+t13:=estie(rat,[x:rat]urt(ksi,x),x0,t12):urt(ksi,x0)
+[y0:rat][ly:lrt(ksi,y0)]
+t14:=cutapp2a(ksi,y0,ly,x0,t13):less"rt"(y0,x0)
+t15:=lrtrpofrt(x0,y0,t14):lrt(rpofrt(x0),y0)
+y0@[uy:urt(ksi,y0)]
+t17:=estii(rat,[x:rat]urt(ksi,x),y0,uy):in(y0,s1)
+t18:=satz85(x0,y0,<t17><y0>t11):moreis"rt"(y0,x0)
+t19:=urtrpofrt(x0,y0,t18):urt(rpofrt(x0),y0)
+y0@t20:=cp(lrt(rpofrt(x0),y0),lrt(ksi,y0),[t:urt(ksi,y0)]t19(t)):imp(lrt(rpofrt(x0),y0),lrt(ksi,y0))
+-5157
+m@satz157c:=isi1(ksi,rpofrt(x0),[x:rat][t:lrt(ksi,x)]t15".5157"(x,t),[x:rat]t20".5157"(x)):is(ksi,rpofrt(x0))
+ksi@[s:some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))]
++*5157
+s@[x0:rat][m:min(s1,x0)]
+t21:=somei(rat,[x:rat]is(ksi,rpofrt(x)),x0,satz157c(x0,m)):ratrp(ksi)
+-5157
+s@satz157d:=someapp(rat,[x:rat]min(s1".5157",x),s,ratrp(ksi),[x:rat][t:min(s1".5157",x)]t21".5157"(x,t)):ratrp(ksi)
+ksi@[x0:rat][lx:lrt(ksi,x0)]
++5158
+x0@xr:=rpofrt(x0):cut
+lx@t1:=urtrpofrt(x0,x0,moreisi2"rt"(x0,x0,refis(rat,x0))):urt(xr,x0)
+t2:=andi(urt(xr,x0),lrt(ksi,x0),t1,lx):and(urt(xr,x0),lrt(ksi,x0))
+-5158
+satz158a:=somei(rat,[x:rat]and(urt(rpofrt(x0),x),lrt(ksi,x)),x0,t2".5158"):less(rpofrt(x0),ksi)
+x0@[ux:urt(ksi,x0)]
++*5158
+ux@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
+[m:min(s1,x0)]
+t3:=symis(cut,ksi,xr,satz157c(ksi,x0,m)):is(xr,ksi)
+t4:=moreisi2(xr,ksi,t3):moreis(xr,ksi)
+ux@[n:not(min(s1,x0))]
+t5:=estii(rat,[x:rat]urt(ksi,x),x0,ux):in(x0,s1)
+t6:=th4"l.and"(lb(s1,x0),in(x0,s1),n,t5):not(lb(s1,x0))
+t7:=th1"l.some"(rat,[x:rat]imp(in(x,s1),lessis"rt"(x0,x)),t6):some"rt"([x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))))
+[y0:rat][o:not(imp(in(y0,s1),lessis"rt"(x0,y0)))]
+t8:=th5"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):in(y0,s1)
+t9:=estie(rat,[x:rat]urt(ksi,x),y0,t8):urt(ksi,y0)
+t10:=th6"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):not(lessis"rt"(x0,y0))
+t11:=satz82(x0,y0,satz81k(x0,y0,t10)):less"rt"(y0,x0)
+t12:=lrtrpofrt(x0,y0,t11):lrt(xr,y0)
+t13:=andi(lrt(xr,y0),urt(ksi,y0),t12,t9):and(lrt(xr,y0),urt(ksi,y0))
+t14:=somei(rat,[x:rat]and(lrt(xr,x),urt(ksi,x)),y0,t13):more(xr,ksi)
+n@t15:=someapp(rat,[x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))),t7,more(xr,ksi),[x:rat][t:not(imp(in(x,s1),lessis"rt"(x0,x)))]t14(x,t)):more(xr,ksi)
+t16:=moreisi1(xr,ksi,t15):moreis(xr,ksi)
+-5158
+ux@satz158b:=th1"l.imp"(min(s1".5158",x0),moreis(rpofrt(x0),ksi),[t:min(s1".5158",x0)]t4".5158"(t),[t:not(min(s1".5158",x0))]t16".5158"(t)):moreis(rpofrt(x0),ksi)
+x0@[l:less(rpofrt(x0),ksi)]
++*5158
+l@t17:=satz123h(xr,ksi,l):not(moreis(xr,ksi))
+t18:=th3"l.imp"(urt(ksi,x0),moreis(xr,ksi),t17,[t:urt(ksi,x0)]satz158b(t)):not(urt(ksi,x0))
+-5158
+l@satz158c:=et(lrt(ksi,x0),t18".5158"):lrt(ksi,x0)
+x0@[m:moreis(rpofrt(x0),ksi)]
++*5158
+m"rp"@t19:=satz123c(xr,ksi,m):not(less(xr,ksi))
+-5158
+m@satz158d:=th3"l.imp"(lrt(ksi,x0),less(rpofrt(x0),ksi),t19".5158",[t:lrt(ksi,x0)]satz158a(t)):urt(ksi,x0)
+ksi@[eta:cut][l:less(ksi,eta)]
++5159
+[x0:rat]
+xr:=rpofrt(x0):cut
+[ux:urt(ksi,x0)][lx:lrt(eta,x0)][z0:rat]
+zr:=rpofrt(z0):cut
+[lz:lrt(eta,z0)][k:less"rt"(x0,z0)]
+t1:=satz127a(ksi,xr,zr,satz124(xr,ksi,satz158b(ksi,x0,ux)),satz154c(x0,z0,k)):less(ksi,zr)
+t2:=andi(less(ksi,zr),less(zr,eta),t1,satz158a(eta,z0,lz)):and(less(ksi,zr),less(zr,eta))
+t3:=somei(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),z0,t2):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
+lx@t4:=cutapp3(eta,x0,lx,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:lrt(eta,x)][u:less"rt"(x0,x)]t3(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
+-5159
+satz159:=lessapp(ksi,eta,l,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t4".5159"(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
++*5159
+x0@[a:and(less(ksi,xr),less(xr,eta))]
+t5:=andi(ratrp(xr),and(less(ksi,xr),less(xr,eta)),ratrpi(x0),a):and3(ratrp(xr),less(ksi,xr),less(xr,eta))
+t6:=somei(cut,[c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)),xr,t5):some([c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)))
+-5159
+l@satz159a:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta))),[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t6".5159"(x,t)):some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta)))
+[p:'prop'][p1:[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),eta)]p]
++*5159
+p1@[y0:rat]
+yr:=rpofrt(y0):cut
+[a:and(less(ksi,yr),less(yr,eta))]
+t7:=ande1(less(ksi,yr),less(yr,eta),a):less(ksi,yr)
+t8:=ande2(less(ksi,yr),less(yr,eta),a):less(yr,eta)
+t9:=<t8><t7><y0>p1:p
+-5159
+p1@satz159app:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,p,[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t9".5159"(x,t)):p
+eta@[z0:rat][m:more(rpofrt(z0),ts(ksi,eta))]
++5160
+zr:=rpofrt(z0):cut
+nm:=mn(zr,ts(ksi,eta),m):cut
+dn:=pl(pl(ksi,eta),1rp):cut
+fr:=ov(nm,dn):cut
+zeta:=ite(less(fr,1rp),cut,fr,1rp):cut
+[l:less(fr,1rp)]
+t1:=itet(less(fr,1rp),cut,fr,1rp,l):is(zeta,fr)
+t2:=lessisi2(zeta,fr,t1):lessis(zeta,fr)
+t3:=lessisi1(zeta,1rp,satz127a(zeta,fr,1rp,t2,l)):lessis(zeta,1rp)
+m@[n:not(less(fr,1rp))]
+t4:=itef(less(fr,1rp),cut,fr,1rp,n):is(zeta,1rp)
+t5:=lessisi2(zeta,1rp,t4):lessis(zeta,1rp)
+t6:=trlessis(zeta,1rp,fr,t5,satz124(fr,1rp,satz123f(fr,1rp,n))):lessis(zeta,fr)
+m@t7:=th1"l.imp"(less(fr,1rp),lessis(zeta,1rp),[t:less(fr,1rp)]t3(t),[t:not(less(fr,1rp))]t5(t)):lessis(zeta,1rp)
+t8:=th1"l.imp"(less(fr,1rp),lessis(zeta,fr),[t:less(fr,1rp)]t2(t),[t:not(less(fr,1rp))]t6(t)):lessis(zeta,fr)
+[z1:rat]
+zr1:=rpofrt(z1):cut
+[l1:less(ksi,zr1)][l2:less(zr1,pl(ksi,zeta))][z2:rat]
+zr2:=rpofrt(z2):cut
+[l3:less(eta,zr2)][l4:less(zr2,pl(eta,zeta))]
+t9:=isless2(ts(pl(ksi,zeta),pl(eta,zeta)),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),ts(zr1,zr2),disttp2(pl(ksi,zeta),eta,zeta),satz147a(zr1,pl(ksi,zeta),zr2,pl(eta,zeta),l2,l4)):less(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)))
+t10:=lessisi2(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),tris(cut,ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(zeta,eta)),pl(ts(ksi,eta),ts(eta,zeta)),disttp1(ksi,zeta,eta),ispl2(ts(zeta,eta),ts(eta,zeta),ts(ksi,eta),comts(zeta,eta)))):lessis(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)))
+t11:=satz149a(pl(ksi,zeta),pl(ksi,1rp),zeta,zeta,satz139a(ksi,ksi,zeta,1rp,lessisi2(ksi,ksi,refis(cut,ksi)),t7),lessisi2(zeta,zeta,refis(cut,zeta))):lessis(ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta))
+t12:=satz139a(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta),t10,t11):lessis(pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
+t13:=satz127b(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),t9,t12):less(ts(zr1,zr2),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
+t14:=tris(cut,pl(eta,pl(ksi,1rp)),pl(pl(eta,ksi),1rp),pl(pl(ksi,eta),1rp),asspl2(eta,ksi,1rp),ispl1(pl(eta,ksi),pl(ksi,eta),1rp,compl(eta,ksi))):is(pl(eta,pl(ksi,1rp)),dn)
+t15:=tris(cut,pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(pl(eta,pl(ksi,1rp)),zeta),ts(dn,zeta),distpt1(eta,pl(ksi,1rp),zeta),ists1(pl(eta,pl(ksi,1rp)),dn,zeta,t14)):is(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta))
+t16:=tris(cut,pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta))),pl(ts(ksi,eta),ts(dn,zeta)),asspl1(ts(ksi,eta),ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ispl2(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta),ts(ksi,eta),t15)):is(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)))
+t17:=isless2(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)),ts(zr1,zr2),t16,t13):less(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)))
+t18:=islessis12(ts(zeta,dn),ts(dn,zeta),ts(fr,dn),nm,comts(zeta,dn),satz153e(nm,dn),satz149a(zeta,fr,dn,dn,t8,lessisi2(dn,dn,refis(cut,dn)))):lessis(ts(dn,zeta),nm)
+t19:=satz139a(ts(ksi,eta),ts(ksi,eta),ts(dn,zeta),nm,lessisi2(ts(ksi,eta),ts(ksi,eta),refis(cut,ts(ksi,eta))),t18):lessis(pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm))
+t20:=satz127b(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm),t17,t19):less(ts(zr1,zr2),pl(ts(ksi,eta),nm))
+t21:=isless2(pl(ts(ksi,eta),nm),zr,ts(zr1,zr2),satz140c(zr,ts(ksi,eta),m),t20):less(ts(zr1,zr2),zr)
+t22:=satz154f(ts"rt"(z1,z2),z0,isless1(ts(zr1,zr2),rpofrt(ts"rt"(z1,z2)),zr,symis(cut,rpofrt(ts"rt"(z1,z2)),ts(zr1,zr2),satz155c(z1,z2)),t21)):less"rt"(ts"rt"(z1,z2),z0)
+x0:=ov"rt"(z0,z2):rat
+xr:=rpofrt(x0):cut
+y0:=z2:rat
+yr:=rpofrt(y0):cut
+t23:=satz110e(z0,z2):is"rt"(ts"rt"(x0,y0),z0)
+t24:=ismore1"rt"(z0,ts"rt"(x0,z2),ts"rt"(z1,z2),symis(rat,ts"rt"(x0,z2),z0,t23),satz83(ts"rt"(z1,z2),z0,t22)):more"rt"(ts"rt"(x0,z2),ts"rt"(z1,z2))
+t25:=satz106a(x0,z1,z2,t24):more"rt"(x0,z1)
+t26:=trmore(xr,zr1,ksi,satz154a(x0,z1,t25),satz122(ksi,zr1,l1)):more(xr,ksi)
+t27:=satz122(eta,yr,l3):more(yr,eta)
+z0@[u0:rat]
+ur:=rpofrt(u0):cut
+[v0:rat]
+vr:=rpofrt(v0):cut
+prop1:=and3(more(ur,ksi),more(vr,eta),is"rt"(ts"rt"(u0,v0),z0)):'prop'
+z0@prop2:=some"rt"([x:rat]some"rt"([y:rat]prop1(x,y))):'prop'
+l4@t28:=and3i(more(xr,ksi),more(yr,eta),is"rt"(ts"rt"(x0,y0),z0),t26,t27,t23):prop1(x0,y0)
+t29:=somei(rat,[y:rat]prop1(x0,y),y0,t28):some"rt"([y:rat]prop1(x0,y))
+t30:=somei(rat,[x:rat]some"rt"([y:rat]prop1(x,y)),x0,t29):prop2
+l2@t31:=satz159app(eta,pl(eta,zeta),satz133a(eta,zeta),prop2,[x:rat][t:less(eta,rpofrt(x))][u:less(rpofrt(x),pl(eta,zeta))]t30(x,t,u)):prop2
+-5160
+satz160:=satz159app(ksi,pl(ksi,zeta".5160"),satz133a(ksi,zeta".5160"),prop2".5160",[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),pl(ksi,zeta".5160"))]t31".5160"(x,t,u)):some"rt"([x:rat]some"rt"([y:rat]and3(more(rpofrt(x),ksi),more(rpofrt(y),eta),is"rt"(ts"rt"(x,y),z0))))
+[p:'prop'][p1:[x:rat][t:more(rpofrt(x),ksi)][y:rat][u:more(rpofrt(y),eta)][v:is"rt"(ts"rt"(x,y),z0)]p]
++*5160
+p1@[x1:rat]
+xr1:=rpofrt(x1):cut
+[px:some"rt"([y:rat]prop1(x1,y))][y1:rat]
+yr1:=rpofrt(y1):cut
+[py:prop1(x1,y1)]
+t32:=and3e1(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(xr1,ksi)
+t33:=and3e2(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(yr1,eta)
+t34:=and3e3(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):is"rt"(ts"rt"(x1,y1),z0)
+t35:=<t34><t33><y1><t32><x1>p1:p
+px@t36:=someapp(rat,[y:rat]prop1(x1,y),px,p,[y:rat][v:prop1(x1,y)]t35(y,v)):p
+-5160
+p1@satz160app:=someapp(rat,[x:rat]some"rt"([y:rat]prop1".5160"(x,y)),satz160,p,[x:rat][t:some"rt"([y:rat]prop1".5160"(x,y))]t36".5160"(x,t)):p
++5161
+@[ksi:cut][eta:cut]
+min:=ite(less(ksi,eta),cut,ksi,eta):cut
+max:=ite(more(ksi,eta),cut,ksi,eta):cut
+[u0:rat]
+ur:=rpofrt(u0):cut
+[lu:lrt(min,u0)]
+t1:=satz158a(min,u0,lu):less(ur,min)
+[l:less(ksi,eta)]
+t2:=isless2(min,ksi,ur,itet(less(ksi,eta),cut,ksi,eta,l),t1):less(ur,ksi)
+t3:=trless(ur,ksi,eta,t2,l):less(ur,eta)
+lu@[n:not(less(ksi,eta))]
+t4:=isless2(min,eta,ur,itef(less(ksi,eta),cut,ksi,eta,n),t1):less(ur,eta)
+t5:=satz127b(ur,eta,ksi,t4,satz124(ksi,eta,satz123f(ksi,eta,n))):less(ur,ksi)
+lu@t6:=th1"l.imp"(less(ksi,eta),less(ur,ksi),[t:less(ksi,eta)]t2(t),[t:not(less(ksi,eta))]t5(t)):less(ur,ksi)
+t7:=th1"l.imp"(less(ksi,eta),less(ur,eta),[t:less(ksi,eta)]t3(t),[t:not(less(ksi,eta))]t4(t)):less(ur,eta)
+u0@[uu:urt(max,u0)]
+t8:=satz158b(max,u0,uu):moreis(ur,max)
+[m:more(ksi,eta)]
+t9:=ismoreis2(max,ksi,ur,itet(more(ksi,eta),cut,ksi,eta,m),t8):moreis(ur,ksi)
+t10:=trmoreis(ur,ksi,eta,t9,moreisi1(ksi,eta,m)):moreis(ur,eta)
+uu@[n:not(more(ksi,eta))]
+t11:=ismoreis2(max,eta,ur,itef(more(ksi,eta),cut,ksi,eta,n),t8):moreis(ur,eta)
+t12:=trmoreis(ur,eta,ksi,t11,satz125(ksi,eta,satz123e(ksi,eta,n))):moreis(ur,ksi)
+uu@t13:=th1"l.imp"(more(ksi,eta),moreis(ur,ksi),[t:more(ksi,eta)]t9(t),[t:not(more(ksi,eta))]t12(t)):moreis(ur,ksi)
+t14:=th1"l.imp"(more(ksi,eta),moreis(ur,eta),[t:more(ksi,eta)]t10(t),[t:not(more(ksi,eta))]t11(t)):moreis(ur,eta)
+-5161
+@[zeta:cut]
++*5161
+zeta@[ksi1:cut][ksi2:cut][m:more(ksi1,ksi2)]
+t15:=satz147(ksi1,ksi2,ksi1,ksi2,m,m):more(ts(ksi1,ksi1),ts(ksi2,ksi2))
+ksi2@sq1:=ts(ksi1,ksi1):cut
+sq2:=ts(ksi2,ksi2):cut
+m@t16:=ec3e21(is(sq1,sq2),more(sq1,sq2),less(sq1,sq2),satz123b(sq1,sq2),t15):nis(sq1,sq2)
+ksi2@[i:is(sq1,zeta)][j:is(sq2,zeta)]
+t17:=tris2(cut,sq1,sq2,zeta,i,j):is(sq1,sq2)
+t18:=[t:more(ksi1,ksi2)]<t17>t16(t):not(more(ksi1,ksi2))
+t19:=[t:less(ksi1,ksi2)]<symis(cut,sq1,sq2,t17)>t16(ksi2,ksi1,satz122(ksi1,ksi2,t)):not(less(ksi1,ksi2))
+t20:=or3e1(is(ksi1,ksi2),more(ksi1,ksi2),less(ksi1,ksi2),satz123a(ksi1,ksi2),t18,t19):is(ksi1,ksi2)
+zeta@t21:=[a:cut][b:cut][t:is(ts(a,a),zeta)][u:is(ts(b,b),zeta)]t20(a,b,t,u):amone(cut,[a:cut]is(ts(a,a),zeta))
+sqrtset:=setof(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta)):set(rat)
+[x0:rat]
+xr:=rpofrt(x0):cut
+[lx:lrt(min(1rp,zeta),x0)]
+t22:=t6(1rp,zeta,x0,lx):less(xr,1rp)
+t23:=t7(1rp,zeta,x0,lx):less(xr,zeta)
+t24:=isless1(xr,ts(xr,1rp),zeta,satz151a(xr),t23):less(ts(xr,1rp),zeta)
+t25:=trless(ts(xr,xr),ts(xr,1rp),zeta,satz148c(xr,xr,xr,1rp,lessisi2(xr,xr,refis(cut,xr)),t22),t24):less(ts(xr,xr),zeta)
+t26:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t25):in(x0,sqrtset)
+x0@[ux:urt(max(1rp,zeta),x0)]
+t27:=t13(1rp,zeta,x0,ux):moreis(xr,1rp)
+t28:=t14(1rp,zeta,x0,ux):moreis(xr,zeta)
+t29:=ismoreis1(xr,ts(xr,1rp),zeta,satz151a(xr),t28):moreis(ts(xr,1rp),zeta)
+t30:=trmoreis(ts(xr,xr),ts(xr,1rp),zeta,satz149(xr,xr,xr,1rp,moreisi2(xr,xr,refis(cut,xr)),t27),t29):moreis(ts(xr,xr),zeta)
+t31:=satz123c(ts(xr,xr),zeta,t30):not(less(ts(xr,xr),zeta))
+t32:=th3"l.imp"(in(x0,sqrtset),less(ts(xr,xr),zeta),t31,[t:in(x0,sqrtset)]estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t)):not(in(x0,sqrtset))
+x0@[i:in(x0,sqrtset)][y0:rat]
+yr:=rpofrt(y0):cut
+[l:less"rt"(y0,x0)]
+i@t33:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,i):less(ts(xr,xr),zeta)
+l@t34:=satz154c(y0,x0,l):less(yr,xr)
+t35:=trless(ts(yr,yr),ts(xr,xr),zeta,satz147a(yr,xr,yr,xr,t34,t34),t33):less(ts(yr,yr),zeta)
+t36:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),y0,t35):in(y0,sqrtset)
+i@t37:=satz122(ts(xr,xr),zeta,t33):more(zeta,ts(xr,xr))
+nm:=mn(zeta,ts(xr,xr),t37):cut
+dn:=pl(xr,pl(xr,1rp)):cut
+fr:=ov(nm,dn):cut
+[z0:rat]
+zr:=rpofrt(z0):cut
+[lz:lrt(min(1rp,fr),z0)]
+t38:=t6(1rp,fr,z0,lz):less(zr,1rp)
+t39:=t7(1rp,fr,z0,lz):less(zr,fr)
+t40:=satz94(x0,z0):more"rt"(pl"rt"(x0,z0),x0)
+t41:=tris(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),ts(pl(xr,zr),pl(xr,zr)),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ists12(rpofrt(pl"rt"(x0,z0)),pl(xr,zr),rpofrt(pl"rt"(x0,z0)),pl(xr,zr),satz155a(x0,z0),satz155a(x0,z0)),disttp2(pl(xr,zr),xr,zr)):is(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)))
+t42:=symis(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),t41):is(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))))
+t43:=lessisi2(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),tris(cut,ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(zr,xr)),pl(ts(xr,xr),ts(xr,zr)),disttp1(xr,zr,xr),ispl2(ts(zr,xr),ts(xr,zr),ts(xr,xr),comts(zr,xr)))):lessis(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)))
+t44:=satz145c(pl(xr,zr),pl(xr,1rp),zr,satz138c(xr,xr,zr,1rp,lessisi2(xr,xr,refis(cut,xr)),t38)):less(ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr))
+t45:=satz138c(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr),t43,t44):less(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)))
+t46:=tris(cut,pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),pl(ts(xr,zr),ts(pl(xr,1rp),zr))),pl(ts(xr,xr),ts(dn,zr)),asspl1(ts(xr,xr),ts(xr,zr),ts(pl(xr,1rp),zr)),ispl2(pl(ts(xr,zr),ts(pl(xr,1rp),zr)),ts(dn,zr),ts(xr,xr),distpt1(xr,pl(xr,1rp),zr))):is(pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)))
+t47:=isless12(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)),t42,t46,t45):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)))
+t48:=isless2(ts(dn,fr),nm,ts(dn,zr),satz153c(nm,dn),satz148c(dn,dn,zr,fr,lessisi2(dn,dn,refis(cut,dn)),t39)):less(ts(dn,zr),nm)
+t49:=satz138c(ts(xr,xr),ts(xr,xr),ts(dn,zr),nm,lessisi2(ts(xr,xr),ts(xr,xr),refis(cut,ts(xr,xr))),t48):less(pl(ts(xr,xr),ts(dn,zr)),pl(ts(xr,xr),nm))
+t50:=isless2(pl(ts(xr,xr),nm),zeta,pl(ts(xr,xr),ts(dn,zr)),satz140c(zeta,ts(xr,xr),t37),t49):less(pl(ts(xr,xr),ts(dn,zr)),zeta)
+t51:=trless(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)),zeta,t47,t50):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),zeta)
+t52:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),pl"rt"(x0,z0),t51):in(pl"rt"(x0,z0),sqrtset)
+t53:=andi(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0),t52,t40):and(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0))
+t54:=somei(rat,[y:rat]and(in(y,sqrtset),more"rt"(y,x0)),pl"rt"(x0,z0),t53):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
+i@t55:=cutapp1a(min(1rp,fr),some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0))),[x:rat][t:lrt(min(1rp,fr),x)]t54(x,t)):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
+x0@[lx:lrt(min(1rp,zeta),x0)][y0:rat][uy:urt(max(1rp,zeta),y0)]
+t56:=cut2(sqrtset,x0,t26(lx),y0,t32(y0,uy),[x:rat][t:in(x,sqrtset)][y:rat][u:less"rt"(y,x)]t36(x,t,y,u),[x:rat][t:in(x,sqrtset)]t55(x,t)):cutprop(sqrtset)
+lx@t57:=cutapp1b(max(1rp,zeta),cutprop(sqrtset),[y:rat][t:urt(max(1rp,zeta),y)]t56(y,t)):cutprop(sqrtset)
+zeta@t58:=cutapp1a(min(1rp,zeta),cutprop(sqrtset),[x:rat][t:lrt(min(1rp,zeta),x)]t57(x,t)):cutprop(sqrtset)
+rtc:=cutof(sqrtset,t58):cut
+@[x0:rat][y0:rat][l:lessis"rt"(x0,y0)]
+t59:=th9"l.or"(less"rt"(x0,y0),is"rt"(x0,y0),less(rpofrt(x0),rpofrt(y0)),is(rpofrt(x0),rpofrt(y0)),l,[t:less"rt"(x0,y0)]satz154c(x0,y0,t),[t:is"rt"(x0,y0)]satz154b(x0,y0,t)):lessis(rpofrt(x0),rpofrt(y0))
+y0@[m:moreis"rt"(x0,y0)]
+t60:=satz125(rpofrt(y0),rpofrt(x0),t59(y0,x0,satz84(x0,y0,m))):moreis(rpofrt(x0),rpofrt(y0))
+zeta@[m:more(ts(rtc,rtc),zeta)]
+t61:=satz121(ts(rtc,rtc),zeta,m):less(zeta,ts(rtc,rtc))
+[z1:rat]
+zr1:=rpofrt(z1):cut
+[l1:less(zeta,zr1)][l2:less(zr1,ts(rtc,rtc))]
+t62:=satz158c(ts(rtc,rtc),z1,l2):lrt(ts(rtc,rtc),z1)
+[x1:rat]
+xr1:=rpofrt(x1):cut
+[lx1:lrt(rtc,x1)][x2:rat]
+xr2:=rpofrt(x2):cut
+[lx2:lrt(rtc,x2)][i:is"rt"(z1,ts"rt"(x1,x2))]
+xm:=ite(more"rt"(x1,x2),rat,x1,x2):rat
+xrm:=rpofrt(xm):cut
+[o:more"rt"(x1,x2)]
+t63:=symis(rat,xm,x1,itet(more"rt"(x1,x2),rat,x1,x2,o)):is"rt"(x1,xm)
+t64:=isp(rat,[x:rat]lrt(rtc,x),x1,xm,lx1,t63):lrt(rtc,xm)
+t65:=lessisi2"rt"(x1,xm,t63):lessis"rt"(x1,xm)
+t66:=lessisi1"rt"(x2,xm,satz87b(x2,x1,xm,satz82(x1,x2,o),t65)):lessis"rt"(x2,xm)
+i@[n:not(more"rt"(x1,x2))]
+t67:=symis(rat,xm,x2,itef(more"rt"(x1,x2),rat,x1,x2,n)):is"rt"(x2,xm)
+t68:=isp(rat,[x:rat]lrt(rtc,x),x2,xm,lx2,t67):lrt(rtc,xm)
+t69:=lessisi2"rt"(x2,xm,t67):lessis"rt"(x2,xm)
+t70:=satz88(x1,x2,xm,satz81e(x1,x2,n),t69):lessis"rt"(x1,xm)
+i@t71:=th1"l.imp"(more"rt"(x1,x2),lrt(rtc,xm),[t:more"rt"(x1,x2)]t64(t),[t:not(more"rt"(x1,x2))]t68(t)):lrt(rtc,xm)
+t72:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x1,xm),[t:more"rt"(x1,x2)]t65(t),[t:not(more"rt"(x1,x2))]t70(t)):lessis"rt"(x1,xm)
+t73:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x2,xm),[t:more"rt"(x1,x2)]t66(t),[t:not(more"rt"(x1,x2))]t69(t)):lessis"rt"(x2,xm)
+t74:=ini(sqrtset,t58,xm,t71):in(xm,sqrtset)
+t75:=t59(x1,xm,t72):lessis(xr1,xrm)
+t76:=t59(x2,xm,t73):lessis(xr2,xrm)
+t77:=tris(cut,zr1,rpofrt(ts"rt"(x1,x2)),ts(xr1,xr2),satz154b(z1,ts"rt"(x1,x2),i),satz155c(x1,x2)):is(zr1,ts(xr1,xr2))
+t78:=islessis1(ts(xr1,xr2),zr1,ts(xrm,xrm),symis(cut,zr1,ts(xr1,xr2),t77),satz149a(xr1,xrm,xr2,xrm,t75,t76)):lessis(zr1,ts(xrm,xrm))
+t79:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),xm,t74):less(ts(xrm,xrm),zeta)
+t80:=satz127a(zr1,ts(xrm,xrm),zeta,t78,t79):less(zr1,zeta)
+t81:=<t80>ec3e23(is(zr1,zeta),more(zr1,zeta),less(zr1,zeta),satz123b(zr1,zeta),satz122(zeta,zr1,l1)):con
+t82:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t81(x,t,y,u,v)):con
+l2@t82a:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t82(x,t,y,u,v)):con
+m@t83:=satz159app(zeta,ts(rtc,rtc),t61,con,[x:rat][t:less(zeta,rpofrt(x))][u:less(rpofrt(x),ts(rtc,rtc))]t82a(x,t,u)):con
+zeta@[l:less(ts(rtc,rtc),zeta)][z2:rat]
+zr2:=rpofrt(z2):cut
+[l3:less(ts(rtc,rtc),zr2)][l4:less(zr2,zeta)]
+t84:=satz122(ts(rtc,rtc),zr2,l3):more(zr2,ts(rtc,rtc))
+[y1:rat]
+yr1:=rpofrt(y1):cut
+[m1:more(yr1,rtc)][y2:rat]
+yr2:=rpofrt(y2):cut
+[m2:more(yr2,rtc)][i:is"rt"(ts"rt"(y1,y2),z2)]
+ym:=ite(less"rt"(y1,y2),rat,y1,y2):rat
+yrm:=rpofrt(ym):cut
+[k:less"rt"(y1,y2)]
+t85:=symis(rat,ym,y1,itet(less"rt"(y1,y2),rat,y1,y2,k)):is"rt"(y1,ym)
+t86:=satz154b(y1,ym,t85):is(yr1,yrm)
+t87:=ismore1(yr1,yrm,rtc,t86,m1):more(yrm,rtc)
+t88:=moreisi2(yr1,yrm,t86):moreis(yr1,yrm)
+t89:=moreisi1(yr2,yrm,satz127d(yr2,yr1,yrm,satz122(yr1,yr2,satz154c(y1,y2,k)),t88)):moreis(yr2,yrm)
+i@[n:not(less"rt"(y1,y2))]
+t90:=symis(rat,ym,y2,itef(less"rt"(y1,y2),rat,y1,y2,n)):is"rt"(y2,ym)
+t91:=satz154b(y2,ym,t90):is(yr2,yrm)
+t92:=ismore1(yr2,yrm,rtc,t91,m2):more(yrm,rtc)
+t93:=moreisi2(yr2,yrm,t91):moreis(yr2,yrm)
+t94:=trmoreis(yr1,yr2,yrm,t60(y1,y2,satz81f(y1,y2,n)),t93):moreis(yr1,yrm)
+i@t95:=th1"l.imp"(less"rt"(y1,y2),more(yrm,rtc),[t:less"rt"(y1,y2)]t87(t),[t:not(less"rt"(y1,y2))]t92(t)):more(yrm,rtc)
+t96:=th1"l.imp"(less"rt"(y1,y2),moreis(yr1,yrm),[t:less"rt"(y1,y2)]t88(t),[t:not(less"rt"(y1,y2))]t94(t)):moreis(yr1,yrm)
+t97:=th1"l.imp"(less"rt"(y1,y2),moreis(yr2,yrm),[t:less"rt"(y1,y2)]t89(t),[t:not(less"rt"(y1,y2))]t93(t)):moreis(yr2,yrm)
+t98:=satz158d(rtc,ym,moreisi1(yrm,rtc,t95)):urt(rtc,ym)
+t99:=th3"l.imp"(in(ym,sqrtset),lrt(rtc,ym),t98,[t:in(ym,sqrtset)]ine(sqrtset,t58,ym,t)):not(in(ym,sqrtset))
+t100:=th3"l.imp"(less(ts(yrm,yrm),zeta),in(ym,sqrtset),t99,[t:less(ts(yrm,yrm),zeta)]estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),ym,t)):not(less(ts(yrm,yrm),zeta))
+t101:=satz123f(ts(yrm,yrm),zeta,t100):moreis(ts(yrm,yrm),zeta)
+t101a:=satz149(yr1,yrm,yr2,yrm,t96,t97):moreis(ts(yr1,yr2),ts(yrm,yrm))
+t102:=ismoreis1(ts(yr1,yr2),zr2,ts(yrm,yrm),tris(cut,ts(yr1,yr2),rpofrt(ts"rt"(y1,y2)),zr2,symis(cut,rpofrt(ts"rt"(y1,y2)),ts(yr1,yr2),satz155c(y1,y2)),satz154b(ts"rt"(y1,y2),z2,i)),t101a):moreis(zr2,ts(yrm,yrm))
+t103:=trmoreis(zr2,ts(yrm,yrm),zeta,t102,t101):moreis(zr2,zeta)
+t104:=<l4>satz123c(zr2,zeta,t103):con
+l4@t105:=satz160app(rtc,rtc,z2,t84,con,[x:rat][t:more(rpofrt(x),rtc)][y:rat][u:more(rpofrt(y),rtc)][v:is"rt"(ts"rt"(x,y),z2)]t104(x,t,y,u,v)):con
+l@t106:=satz159app(ts(rtc,rtc),zeta,l,con,[x:rat][t:less(ts(rtc,rtc),rpofrt(x))][u:less(rpofrt(x),zeta)]t105(x,t,u)):con
+zeta@t107:=or3e1(is(ts(rtc,rtc),zeta),more(ts(rtc,rtc),zeta),less(ts(rtc,rtc),zeta),satz123a(ts(rtc,rtc),zeta),[t:more(ts(rtc,rtc),zeta)]t83(t),[t:less(ts(rtc,rtc),zeta)]t106(t)):is(ts(rtc,rtc),zeta)
+t108:=somei(cut,[a:cut]is(ts(a,a),zeta),rtc,t107):some([a:cut]is(ts(a,a),zeta))
+-5161
+zeta@satz161:=onei(cut,[a:cut]is(ts(a,a),zeta),t21".5161",t108".5161"):one([a:cut]is(ts(a,a),zeta))
+@[ksi:cut]
+irratrp:=not(ratrp(ksi)):'prop'
+-rp
+-rt
++5162
+@[v:nat]
+t1:=tris(nat,pl(v,v),pl(ts(1,v),v),ts(<1>suc,v),ispl1(v,ts(1,v),v,satz28g(v)),satz28h(1,v)):is(pl(v,v),ts(<1>suc,v))
+t2:=isless2(pl(v,v),ts(<1>suc,v),v,t1,satz18a(v,v)):less(v,ts(<1>suc,v))
+[w:nat][l:less(ts(v,v),ts(w,w))]
+t3:=satz10j(v,w,th3"l.imp"(moreis(v,w),moreis(ts(v,v),ts(w,w)),satz10h(ts(v,v),ts(w,w),l),[t:moreis(v,w)]satz36(v,w,v,w,t,t))):less(v,w)
+w@t4:=tris(nat,ts(pl(v,w),v),pl(ts(v,v),ts(w,v)),pl(ts(v,v),ts(v,w)),disttp1(v,w,v),ispl2(ts(w,v),ts(v,w),ts(v,v),comts(w,v))):is(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)))
+t5:=tr3is(nat,ts(pl(v,w),pl(v,w)),pl(ts(pl(v,w),v),ts(pl(v,w),w)),pl(pl(ts(v,v),ts(v,w)),pl(ts(v,w),ts(w,w))),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),disttp2(pl(v,w),v,w),ispl12(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)),ts(pl(v,w),w),pl(ts(v,w),ts(w,w)),t4,disttp1(v,w,w)),asspl2(pl(ts(v,v),ts(v,w)),ts(v,w),ts(w,w))):is(ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)))
+t6:=tris(nat,pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),pl(ts(v,w),ts(v,w))),pl(ts(v,v),ts(<1>suc,ts(v,w))),asspl1(ts(v,v),ts(v,w),ts(v,w)),ispl2(pl(ts(v,w),ts(v,w)),ts(<1>suc,ts(v,w)),ts(v,v),t1(ts(v,w)))):is(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))))
+nun:=tris(nat,ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),t5,ispl1(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w),t6)):is(ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)))
+nun1:=symis(nat,ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),nun):is(pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),ts(pl(v,w),pl(v,w)))
+prop1:=eq(tf(fr(w,v),fr(w,v)),fr(<1>suc,1)):'prop'
+v@prop2:=some([t:nat]prop1(t)):'prop'
+@prop3:=some([u:nat]prop2(u)):'prop'
+[p:prop3]
+y:=ind(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):nat
+t7:=oneax(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):min([u:nat]prop2(u),y)
+t8:=ande1(lb([u:nat]prop2(u),y),prop2(y),t7):lb([u:nat]prop2(u),y)
+t9:=ande2(lb([u:nat]prop2(u),y),prop2(y),t7):prop2(y)
+[x:nat][q:prop1(y,x)]
+t10:=treq1(fr(<1>suc,1),fr(ts(x,x),ts(y,y)),tf(fr(x,y),fr(x,y)),q,tfeq12a(x,y,x,y)):eq(fr(<1>suc,1),fr(ts(x,x),ts(y,y)))
+t11:=tr4is(nat,ts(<1>suc,ts(y,y)),ts(num(fr(<1>suc,1)),den(fr(ts(x,x),ts(y,y)))),ts(num(fr(ts(x,x),ts(y,y))),den(fr(<1>suc,1))),ts(ts(x,x),1),ts(x,x),12isnd(<1>suc,1,ts(x,x),ts(y,y)),t10,ndis12(ts(x,x),ts(y,y),<1>suc,1),satz28a(ts(x,x))):is(ts(<1>suc,ts(y,y)),ts(x,x))
+t12:=isless2(ts(<1>suc,ts(y,y)),ts(x,x),ts(y,y),t11,t2(ts(y,y))):less(ts(y,y),ts(x,x))
+t13:=isless1(ts(ts(<1>suc,y),y),ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)),tris(nat,ts(ts(<1>suc,y),y),ts(<1>suc,ts(y,y)),ts(x,x),assts1(<1>suc,y,y),t11),satz35c(ts(<1>suc,y),ts(<1>suc,y),y,ts(<1>suc,y),lessisi2(ts(<1>suc,y),ts(<1>suc,y),refis(nat,ts(<1>suc,y))),t2(y))):less(ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)))
+t14:=t3(y,x,t12):less(y,x)
+t15:=t3(x,ts(<1>suc,y),t13):less(x,ts(<1>suc,y))
+[u:nat][i:is(x,pl(y,u))]
+t16:=isless12(x,pl(y,u),ts(<1>suc,y),pl(y,y),i,symis(nat,pl(y,y),ts(<1>suc,y),t1(y)),t15):less(pl(y,u),pl(y,y))
+t17:=satz20f(u,y,y,t16):less(u,y)
+[t:nat][j:is(y,pl(u,t))]
+t18:=symis(nat,y,pl(u,t),j):is(pl(u,t),y)
+t19:=tris(nat,ts(x,x),ts(pl(y,u),pl(y,u)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ists12(x,pl(y,u),x,pl(y,u),i,i),nun(y,u)):is(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)))
+t20:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),ispl1(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t),t19),asspl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u),ts(t,t))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))))
+t21:=tr3is(nat,ts(y,u),ts(u,y),ts(u,pl(u,t)),pl(ts(u,u),ts(u,t)),comts(y,u),ists2(y,pl(u,t),u,j),disttp2(u,u,t)):is(ts(y,u),pl(ts(u,u),ts(u,t)))
+t22:=tris(nat,ts(<1>suc,ts(y,u)),ts(<1>suc,pl(ts(u,u),ts(u,t))),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ists2(ts(y,u),pl(ts(u,u),ts(u,t)),<1>suc,t21),disttp2(<1>suc,ts(u,u),ts(u,t))):is(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))))
+t23:=tris(nat,pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(y,y),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),ispl2(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ts(y,y),t22),asspl2(ts(y,y),ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))):is(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))))
+t24:=tr3is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),pl(pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),t20,ispl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t)),t23),asspl1(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))))
+t25:=tr4is(nat,pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),pl(pl(ts(<1>suc,ts(u,t)),ts(u,u)),ts(t,t)),pl(pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t)),ts(pl(u,t),pl(u,t)),ts(y,y),asspl2(ts(<1>suc,ts(u,t)),ts(u,u),ts(t,t)),ispl1(pl(ts(<1>suc,ts(u,t)),ts(u,u)),pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t),compl(ts(<1>suc,ts(u,t)),ts(u,u))),nun1(u,t),ists12(pl(u,t),y,pl(u,t),y,t18,t18)):is(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y))
+t26:=tr4is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),pl(ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u)))),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),t24,ispl2(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u))),t25),compl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),asspl2(ts(y,y),ts(y,y),ts(<1>suc,ts(u,u)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))))
+t27:=tris(nat,pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(y,y)),ts(x,x),t1(ts(y,y)),t11):is(pl(ts(y,y),ts(y,y)),ts(x,x))
+t28:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),pl(ts(x,x),ts(<1>suc,ts(u,u))),t26,ispl1(pl(ts(y,y),ts(y,y)),ts(x,x),ts(<1>suc,ts(u,u)),t27)):is(pl(ts(x,x),ts(t,t)),pl(ts(x,x),ts(<1>suc,ts(u,u))))
+t29:=satz20e(ts(t,t),ts(<1>suc,ts(u,u)),ts(x,x),t28):is(ts(t,t),ts(<1>suc,ts(u,u)))
+t30:=tr4is(nat,ts(num(fr(<1>suc,1)),den(fr(ts(t,t),ts(u,u)))),ts(<1>suc,ts(u,u)),ts(t,t),ts(ts(t,t),1),ts(num(fr(ts(t,t),ts(u,u))),den(fr(<1>suc,1))),ndis12(<1>suc,1,ts(t,t),ts(u,u)),symis(nat,ts(t,t),ts(<1>suc,ts(u,u)),t29),satz28e(ts(t,t)),12isnd(ts(t,t),ts(u,u),<1>suc,1)):eq(fr(<1>suc,1),fr(ts(t,t),ts(u,u)))
+t31:=treq2(tf(fr(t,u),fr(t,u)),fr(<1>suc,1),fr(ts(t,t),ts(u,u)),tfeq12a(t,u,t,u),t30):prop1(u,t)
+t32:=somei(nat,[v:nat]prop1(u,v),t,t31):prop2(u)
+t33:=<t32><u>t8:lessis(y,u)
+t34:=<t33>satz10g(y,u,satz12(u,y,t17)):con
+i@t35:=someapp(nat,[v:nat]diffprop(y,u,v),t17,con,[v:nat][w:diffprop(y,u,v)]t34(v,w)):con
+q@t36:=someapp(nat,[v:nat]diffprop(x,y,v),t14,con,[v:nat][w:diffprop(x,y,v)]t35(v,w)):con
+p@t37:=someapp(nat,[v:nat]prop1(y,v),t9,con,[v:nat][w:prop1(y,v)]t36(v,w)):con
+-5162
++*rt
++5162
+@[x0:rat][i:is(ts(x0,x0),rtofn(<1>suc))][x:frac][xix0:inf(x,class(x0))]
+t38:=ise(ts(x0,x0),rtofn(<1>suc),tf(x,x),fr(<1>suc,1),tict(x0,x0,x,x,xix0,xix0),inclass(fr(<1>suc,1)),i):eq"n"(tf(x,x),fr(<1>suc,1))
+t39:=refeq1(fr(num(x),den(x)),x,fris(x)):eq"n"(fr(num(x),den(x)),x)
+t40:=eqtf12(fr(num(x),den(x)),x,fr(num(x),den(x)),x,t39,t39):eq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x))
+t41:=treq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x),fr(<1>suc,1),t40,t38):prop1"n.5162"(den(x),num(x))
+t42:=somei(nat,[t:nat]prop1"n.5162"(den(x),t),num(x),t41):prop2"n.5162"(den(x))
+t43:=somei(nat,[t:nat]prop2"n.5162"(t),den(x),t42):prop3"n.5162"
+t44:=t37"n.5162"(t43):con
+i@t45:=ratapp1(x0,con,[x:frac][t:inf(x,class(x0))]t44(x,t)):con
+-5162
++*rp
++5162
+@ksi:=ind(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):cut
+t46:=oneax(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):is(ts(ksi,ksi),rpofnt(<1>suc))
+[r:ratrp(ksi)]
+x0:=rtofrp(ksi,r):rat
+t47:=tr3is(cut,rpofrt(ts"rt"(x0,x0)),ts(rpofrt(x0),rpofrt(x0)),ts(ksi,ksi),rpofnt(<1>suc),satz155c(x0,x0),ists12(rpofrt(x0),ksi,rpofrt(x0),ksi,isrprt2(ksi,r),isrprt2(ksi,r)),t46):is(rpofrt(ts"rt"(x0,x0)),rpofnt(<1>suc))
+t48:=isrtirp(ts"rt"(x0,x0),rtofn(<1>suc),t47):is"rt"(ts"rt"(x0,x0),rtofn(<1>suc))
+t49:=t45"rt.5162"(x0,t48):con
+-5162
+@satz162:=somei(cut,[a:cut]irratrp(a),ksi".5162",[t:ratrp(ksi".5162")]t49".5162"(t)):some([a:cut]irratrp(a))
+[zeta:cut]
+sqrt:=ind(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):cut
+thsqrt1:=oneax(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):is(ts(sqrt(zeta),sqrt(zeta)),zeta)
+[ksi:cut][i:is(ts(ksi,ksi),zeta)]
+thsqrt2:=t20".5161"(zeta,ksi,sqrt,i,thsqrt1):is(ksi,sqrt)
+@[ksi:cut][eta:cut][i:is(ksi,eta)]
+issqrt:=isf(cut,cut,[t:cut]sqrt(t),ksi,eta,i):is(sqrt(ksi),sqrt(eta))
+@[ksi:cut][nx:natrp(ksi)][eta:cut][ny:natrp(eta)]
++iiia
+x:=ntofrp(ksi,nx):nat
+y:=ntofrp(eta,ny):nat
+t1:=isrpnt1(ksi,nx):is(ksi,rpofnt(x))
+t2:=isrpnt1(eta,ny):is(eta,rpofnt(y))
+t3:=ispl12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(pl(ksi,eta),pl(rpofnt(x),rpofnt(y)))
+x0:=rtofn(x):rat
+y0:=rtofn(y):rat
+t4:=natrti(x):natrt(x0)
+t5:=natrti(y):natrt(y0)
+t6:=symis(cut,rpofrt(pl"rt"(x0,y0)),pl(rpofnt(x),rpofnt(y)),satz155a(x0,y0)):is(pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)))
+t7:=satz112d(x0,t4,y0,t5):natrt(pl"rt"(x0,y0))
+xpy:=nofrt(pl"rt"(x0,y0),t7):nat
+t8:=isrtn1(pl"rt"(x0,y0),t7):is"rt"(pl"rt"(x0,y0),rtofn(xpy))
+t9:=isrterp(pl"rt"(x0,y0),rtofn(xpy),t8):is(rpofrt(pl"rt"(x0,y0)),rpofnt(xpy))
+t10:=tr3is(cut,pl(ksi,eta),pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)),rpofnt(xpy),t3,t6,t9):is(pl(ksi,eta),rpofnt(xpy))
+-iiia
+natpl:=somei(nat,[t:nat]is(pl(ksi,eta),rpofnt(t)),xpy".iiia",t10".iiia"):natrp(pl(ksi,eta))
++*iiia
+ny@t11:=ists12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(ts(ksi,eta),ts(rpofnt(x),rpofnt(y)))
+t12:=symis(cut,rpofrt(ts"rt"(x0,y0)),ts(rpofnt(x),rpofnt(y)),satz155c(x0,y0)):is(ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)))
+t13:=satz112f(x0,t4,y0,t5):natrt(ts"rt"(x0,y0))
+xty:=nofrt(ts"rt"(x0,y0),t13):nat
+t14:=isrtn1(ts"rt"(x0,y0),t13):is"rt"(ts"rt"(x0,y0),rtofn(xty))
+t15:=isrterp(ts"rt"(x0,y0),rtofn(xty),t14):is(rpofrt(ts"rt"(x0,y0)),rpofnt(xty))
+t16:=tr3is(cut,ts(ksi,eta),ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)),rpofnt(xty),t11,t12,t15):is(ts(ksi,eta),rpofnt(xty))
+-iiia
+ny@natts:=somei(nat,[t:nat]is(ts(ksi,eta),rpofnt(t)),xty".iiia",t16".iiia"):natrp(ts(ksi,eta))
+[m:more(ksi,eta)]
++*iiia
+m@t17:=ismore12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2,m):more(rpofnt(x),rpofnt(y))
+t18:=satz154d(x0,y0,t17):more"rt"(x0,y0)
+t20:=ismn12(ksi,rpofnt(x),eta,rpofnt(y),m,satz154a(x0,y0,t18),t1,t2):is(mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)))
+t21:=symis(cut,rpofrt(mn"rt"(x0,y0,t18)),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),satz155b(x0,y0,t18)):is(mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)))
+t22:=satz112g(x0,t4,y0,t5,t18):natrt(mn"rt"(x0,y0,t18))
+xmy:=nofrt(mn"rt"(x0,y0,t18),t22):nat
+t23:=isrtn1(mn"rt"(x0,y0,t18),t22):is"rt"(mn"rt"(x0,y0,t18),rtofn(xmy))
+t24:=isrterp(mn"rt"(x0,y0,t18),rtofn(xmy),t23):is(rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy))
+t25:=tr3is(cut,mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy),t20,t21,t24):is(mn(ksi,eta,m),rpofnt(xmy))
+-iiia
+m@natmn:=somei(nat,[t:nat]is(mn(ksi,eta,m),rpofnt(t)),xmy".iiia",t25".iiia"):natrp(mn(ksi,eta,m))
+@[p:cut][q:cut][r:cut]
+3pl13:=tr3is(cut,pl(p,pl(q,r)),pl(pl(q,r),p),pl(pl(r,q),p),pl(r,pl(q,p)),compl(p,pl(q,r)),ispl1(pl(q,r),pl(r,q),p,compl(q,r)),asspl1(r,q,p)):is(pl(p,pl(q,r)),pl(r,pl(q,p)))
+[s:cut]
+4pl24:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(s,pl(r,q))),pl(pl(p,s),pl(r,q)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(s,pl(r,q)),p,3pl13(q,r,s)),asspl2(p,s,pl(r,q))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,s),pl(r,q)))
+r@3pl12:=tr3is(cut,pl(p,pl(q,r)),pl(pl(p,q),r),pl(pl(q,p),r),pl(q,pl(p,r)),asspl2(p,q,r),ispl1(pl(p,q),pl(q,p),r,compl(p,q)),asspl1(q,p,r)):is(pl(p,pl(q,r)),pl(q,pl(p,r)))
+s@4pl23:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(r,pl(q,s))),pl(pl(p,r),pl(q,s)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(r,pl(q,s)),p,3pl12(q,r,s)),asspl2(p,r,pl(q,s))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,r),pl(q,s)))
+r@3pl23:=tr3is(cut,pl(pl(p,q),r),pl(p,pl(q,r)),pl(p,pl(r,q)),pl(pl(p,r),q),asspl1(p,q,r),ispl2(pl(q,r),pl(r,q),p,compl(q,r)),asspl2(p,r,q)):is(pl(pl(p,q),r),pl(pl(p,r),q))
+p@a2isapa:=tris(cut,ts(p,pl(1rp,1rp)),pl(ts(p,1rp),ts(p,1rp)),pl(p,p),disttp2(p,1rp,1rp),ispl12(ts(p,1rp),p,ts(p,1rp),p,satz151(p),satz151(p))):is(ts(p,pl(1rp,1rp)),pl(p,p))
+@dif:=pair1type(cut):'type'
+[a1:cut][a2:cut]
+df:=pair1(cut,a1,a2):dif
+@[a:dif]
+stm:=first1(cut,a):cut
+std:=second1(cut,a):cut
+a2@stmis:=first1is1(cut,a1,a2):is(stm(df(a1,a2)),a1)
+isstm:=first1is2(cut,a1,a2):is(a1,stm(df(a1,a2)))
+stdis:=second1is1(cut,a1,a2):is(std(df(a1,a2)),a2)
+isstd:=second1is2(cut,a1,a2):is(a2,std(df(a1,a2)))
+a@1a:=stm(a):cut
+2a:=std(a):cut
+dfis:=pair1is1(cut,a):is"e"(dif,df(1a,2a),a)
+isdf:=pair1is2(cut,a):is"e"(dif,a,df(1a,2a))
+a2@[b1:cut][b2:cut]
+12issmsd:=ispl12(a1,stm(df(a1,a2)),b2,std(df(b1,b2)),isstm(a1,a2),isstd(b1,b2)):is(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))))
+smsdis12:=symis(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),12issmsd):is(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2))
+a@[r1:cut][r2:cut]
+1sdissmsd:=ispl1(r1,stm(df(r1,r2)),2a,isstm(r1,r2)):is(pl(r1,2a),pl(stm(df(r1,r2)),2a))
+smsdis1sd:=symis(cut,pl(r1,2a),pl(stm(df(r1,r2)),2a),1sdissmsd):is(pl(stm(df(r1,r2)),2a),pl(r1,2a))
+sm2issmsd:=ispl2(r2,std(df(r1,r2)),1a,isstd(r1,r2)):is(pl(1a,r2),pl(1a,std(df(r1,r2))))
+smsdissm2:=symis(cut,pl(1a,r2),pl(1a,std(df(r1,r2))),sm2issmsd):is(pl(1a,std(df(r1,r2))),pl(1a,r2))
+a2@[r:cut][i:is(a1,r)]
+issm:=isf(cut,dif,[t:cut]df(t,a2),a1,r,i):is"e"(dif,df(a1,a2),df(r,a2))
+r@[i:is(a2,r)]
+issd:=isf(cut,dif,[t:cut]df(a1,t),a2,r,i):is"e"(dif,df(a1,a2),df(a1,r))
+b2@[i:is(a1,b1)][j:is(a2,b2)]
+issmsd:=tris(dif,df(a1,a2),df(b1,a2),df(b1,b2),issm(a1,a2,b1,i),issd(b1,a2,b2,j)):is"e"(dif,df(a1,a2),df(b1,b2))
+a@[b:dif]
+1b:=stm(b):cut
+2b:=std(b):cut
+eq:=is(pl(1a,2b),pl(1b,2a)):'prop'
+b2@[i:is(pl(a1,b2),pl(b1,a2))]
+eqi12:=tr3is(cut,pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),smsdis12(a1,a2,b1,b2),i,12issmsd(b1,b2,a1,a2)):eq(df(a1,a2),df(b1,b2))
+r2@[i:is(pl(1a,r2),pl(r1,2a))]
+eqi1:=isp(dif,[x:dif]eq(x,df(r1,r2)),df(1a,2a),a,eqi12(1a,2a,r1,r2,i),dfis):eq(a,df(r1,r2))
+r2@[i:is(pl(r1,2a),pl(1a,r2))]
+eqi2:=isp(dif,[x:dif]eq(df(r1,r2),x),df(1a,2a),a,eqi12(r1,r2,1a,2a,i),dfis):eq(df(r1,r2),a)
+b2@[e:eq(df(a1,a2),df(b1,b2))]
+eqe12:=tr3is(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),12issmsd(a1,a2,b1,b2),e,smsdis12(b1,b2,a1,a2)):is(pl(a1,b2),pl(b1,a2))
+a@satzd163:=refis(cut,pl(1a,2a)):eq(a,a)
+refeq:=satzd163:eq(a,a)
+b@[i:is"e"(dif,a,b)]
+refeq1:=isp(dif,[x:dif]eq(a,x),a,b,refeq,i):eq(a,b)
+refeq2:=isp(dif,[x:dif]eq(x,a),a,b,refeq,i):eq(b,a)
+b2@[i:is(a1,b1)][j:is(a2,b2)]
+eqsmsd:=refeq1(df(a1,a2),df(b1,b2),issmsd(i,j)):eq(df(a1,a2),df(b1,b2))
+r@[i:is(a1,r)]
+eqsm:=refeq1(df(a1,a2),df(r,a2),issm(i)):eq(df(a1,a2),df(r,a2))
+r@[i:is(a2,r)]
+eqsd:=refeq1(df(a1,a2),df(a1,r),issd(i)):eq(df(a1,a2),df(a1,r))
+b@[e:eq(a,b)]
+satzd164:=symis(cut,pl(1a,2b),pl(1b,2a),e):eq(b,a)
+symeq:=satzd164:eq(b,a)
+b@[c:dif]
+1c:=stm(c):cut
+2c:=std(c):cut
+[e:eq(a,b)][f:eq(b,c)]
++1d165
+t1:=ispl12(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),e,f):is(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
+t2:=tr4is(cut,pl(pl(1a,2c),pl(1b,2b)),pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2b),pl(1b,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2c,1b,2b),t1,compl(pl(1b,2a),pl(1c,2b)),4pl24(1c,2b,1b,2a)):is(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
+-1d165
+satzd165:=satz136b(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".1d165"):eq(a,c)
+treq:=satzd165:eq(a,c)
+c@[e:eq(c,a)][f:eq(c,b)]
+treq1:=treq(a,c,b,symeq(c,a,e),f):eq(a,b)
+c@[e:eq(a,c)][f:eq(b,c)]
+treq2:=treq(a,c,b,e,symeq(b,c,f)):eq(a,b)
+c@[d:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)]
+tr3eq:=treq(a,b,d,e1,treq(b,c,d,e2,e3)):eq(a,d)
+d@[e:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)][e4:eq(d,e)]
+tr4eq:=tr3eq(a,b,c,e,e1,e2,treq(c,d,e,e3,e4)):eq(a,e)
+a@posd:=more(1a,2a):'prop'
+zero:=is(1a,2a):'prop'
+negd:=less(1a,2a):'prop'
+a2@[m:more(a1,a2)]
+posdi:=ismore12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),m):posd(df(a1,a2))
+a2@[i:is(a1,a2)]
+zeroi:=tr3is(cut,stm(df(a1,a2)),a1,a2,std(df(a1,a2)),stmis(a1,a2),i,isstd(a1,a2)):zero(df(a1,a2))
+a2@[l:less(a1,a2)]
+negdi:=isless12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),l):negd(df(a1,a2))
+a@axrde:=satz123b(1a,2a):ec3(zero(a),posd(a),negd(a))
+axrdo:=satz123a(1a,2a):or3(zero(a),posd(a),negd(a))
+axrd:=orec3i(zero(a),posd(a),negd(a),axrdo,axrde):orec3(zero(a),posd(a),negd(a))
+[p:'prop'][p1:[t:posd(a)]p][p2:[t:zero(a)]p][p3:[t:negd(a)]p]
+rappd:=or3app(zero(a),posd(a),negd(a),p,axrdo,p2,p1,p3):p
+a@[p:posd(a)]
+pnot0d:=ec3e21(zero(a),posd(a),negd(a),axrde,p):not(zero(a))
+pnotnd:=ec3e23(zero(a),posd(a),negd(a),axrde,p):not(negd(a))
+a@[z:zero(a)]
+0notpd:=ec3e12(zero(a),posd(a),negd(a),axrde,z):not(posd(a))
+0notnd:=ec3e13(zero(a),posd(a),negd(a),axrde,z):not(negd(a))
+a@[n:negd(a)]
+nnotpd:=ec3e32(zero(a),posd(a),negd(a),axrde,n):not(posd(a))
+nnot0d:=ec3e31(zero(a),posd(a),negd(a),axrde,n):not(zero(a))
+b@[e:eq(a,b)][p:posd(a)]
++iv1d
+t1:=ismore12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135a(1a,2a,2b,p)):more(pl(1b,2a),pl(2b,2a))
+-iv1d
+eqposd:=satz136a(1b,2b,2a,t1".iv1d"):posd(b)
+e@[z:zero(a)]
++*iv1d
+z@t2:=tr3is(cut,pl(1b,2a),pl(1a,2b),pl(2a,2b),pl(2b,2a),symeq(a,b,e),ispl1(1a,2a,2b,z),compl(2a,2b)):is(pl(1b,2a),pl(2b,2a))
+-iv1d
+z@eqzero:=satz136b(1b,2b,2a,t2".iv1d"):zero(b)
+e@[n:negd(a)]
++*iv1d
+n@t3:=isless12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135c(1a,2a,2b,n)):less(pl(1b,2a),pl(2b,2a))
+-iv1d
+n@eqnegd:=satz136c(1b,2b,2a,t3".iv1d"):negd(b)
+b@[z:zero(a)][y:zero(b)]
+zeroeq:=tris(cut,pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl12(1a,2a,2b,1b,z,symis(cut,1b,2b,y)),compl(2a,1b)):eq(a,b)
+@[r:cut]
+pdofrp:=df(pl(r,1rp),1rp):dif
+ndofrp:=df(1rp,pl(r,1rp)):dif
+[s:cut][i:is(r,s)]
+isrpepd:=refeq1(pdofrp(r),pdofrp(s),isf(cut,dif,[x:cut]pdofrp(x),r,s,i)):eq(pdofrp(r),pdofrp(s))
+isrpend:=refeq1(ndofrp(r),ndofrp(s),isf(cut,dif,[x:cut]ndofrp(x),r,s,i)):eq(ndofrp(r),ndofrp(s))
+s@[e:eq(pdofrp(r),pdofrp(s))]
++*iv1d
+e@t4:=satz136b(pl(r,1rp),pl(s,1rp),1rp,eqe12(pl(r,1rp),1rp,pl(s,1rp),1rp,e)):is(pl(r,1rp),pl(s,1rp))
+-iv1d
+e@isrpipd:=satz136b(r,s,1rp,t4".iv1d"):is(r,s)
+s@[e:eq(ndofrp(r),ndofrp(s))]
++*iv1d
+e@t5:=satz136e(pl(s,1rp),pl(r,1rp),1rp,eqe12(1rp,pl(r,1rp),1rp,pl(s,1rp),e)):is(pl(s,1rp),pl(r,1rp))
+-iv1d
+e@isrpind:=symis(cut,s,r,satz136b(s,r,1rp,t5".iv1d")):is(r,s)
+r@posdirp:=posdi(pl(r,1rp),1rp,ismore1(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133(1rp,r))):posd(pdofrp(r))
+negdirp:=negdi(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):negd(ndofrp(r))
+a@[p:posd(a)]
+rpofpd:=mn(1a,2a,p):cut
++*iv1d
+p@t6:=tr4is(cut,pl(1a,1rp),pl(pl(rpofpd,2a),1rp),pl(rpofpd,pl(2a,1rp)),pl(rpofpd,pl(1rp,2a)),pl(pl(rpofpd,1rp),2a),ispl1(1a,pl(rpofpd,2a),1rp,satz140f(1a,2a,p)),asspl1(rpofpd,2a,1rp),ispl2(pl(2a,1rp),pl(1rp,2a),rpofpd,compl(2a,1rp)),asspl2(rpofpd,1rp,2a)):is(pl(1a,1rp),pl(pl(rpofpd,1rp),2a))
+-iv1d
+p@eqpdrp1:=eqi1(a,pl(rpofpd,1rp),1rp,t6".iv1d"):eq(a,pdofrp(rpofpd(a,p)))
+eqpdrp2:=symeq(a,pdofrp(rpofpd(a,p)),eqpdrp1):eq(pdofrp(rpofpd(a,p)),a)
+a@[n:negd(a)]
+rpofnd:=mn(2a,1a,satz122(1a,2a,n)):cut
++*iv1d
+n@t7:=tr3is(cut,pl(1a,pl(rpofnd,1rp)),pl(pl(1a,rpofnd),1rp),pl(2a,1rp),pl(1rp,2a),asspl2(1a,rpofnd,1rp),ispl1(pl(1a,rpofnd),2a,1rp,satz140c(2a,1a,satz122(1a,2a,n))),compl(2a,1rp)):is(pl(1a,pl(rpofnd,1rp)),pl(1rp,2a))
+-iv1d
+n@eqndrp1:=eqi1(a,1rp,pl(rpofnd,1rp),t7".iv1d"):eq(a,ndofrp(rpofnd(a,n)))
+eqndrp2:=symeq(a,ndofrp(rpofnd(a,n)),eqndrp1):eq(ndofrp(rpofnd(a,n)),a)
+@[h:dif][p:posd(h)][k:dif][q:posd(k)][e:eq(h,k)]
++*iv1d
+e@t8:=tr3eq(pdofrp(rpofpd(h,p)),h,k,pdofrp(rpofpd(k,q)),eqpdrp2(h,p),e,eqpdrp1(k,q)):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
+-iv1d
+e@eqpderp:=isrpipd(rpofpd(h,p),rpofpd(k,q),t8".iv1d"):is(rpofpd(h,p),rpofpd(k,q))
+q@[i:is(rpofpd(h,p),rpofpd(k,q))]
++*iv1d
+i@t9:=isrpepd(rpofpd(h,p),rpofpd(k,q),i):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
+-iv1d
+i@eqpdirp:=tr3eq(h,pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)),k,eqpdrp1(h,p),t9".iv1d",eqpdrp2(k,q)):eq(h,k)
+h@[n:negd(h)][k:dif][o:negd(k)][e:eq(h,k)]
++*iv1d
+e@t10:=tr3eq(ndofrp(rpofnd(h,n)),h,k,ndofrp(rpofnd(k,o)),eqndrp2(h,n),e,eqndrp1(k,o)):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
+-iv1d
+e@eqnderp:=isrpind(rpofnd(h,n),rpofnd(k,o),t10".iv1d"):is(rpofnd(h,n),rpofnd(k,o))
+o@[i:is(rpofnd(h,n),rpofnd(k,o))]
++*iv1d
+i@t11:=isrpend(rpofnd(h,n),rpofnd(k,o),i):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
+-iv1d
+i@eqndirp:=tr3eq(h,ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)),k,eqndrp1(h,n),t11".iv1d",eqndrp2(k,o)):eq(h,k)
+@[r:cut]
++*iv1d
+r@t12:=eqpdrp1(pdofrp(r),posdirp(r)):eq(pdofrp(r),pdofrp(rpofpd(pdofrp(r),posdirp(r))))
+-iv1d
+r@isrppd1:=isrpipd(r,rpofpd(pdofrp(r),posdirp(r)),t12".iv1d"):is(r,rpofpd(pdofrp(r),posdirp(r)))
+isrppd2:=symis(cut,r,rpofpd(pdofrp(r),posdirp(r)),isrppd1):is(rpofpd(pdofrp(r),posdirp(r)),r)
++*iv1d
+r@t13:=eqndrp1(ndofrp(r),negdirp(r)):eq(ndofrp(r),ndofrp(rpofnd(ndofrp(r),negdirp(r))))
+-iv1d
+r@isrpnd1:=isrpind(r,rpofnd(ndofrp(r),negdirp(r)),t13".iv1d"):is(r,rpofnd(ndofrp(r),negdirp(r)))
+isrpnd2:=symis(cut,r,rpofnd(ndofrp(r),negdirp(r)),isrpnd1):is(rpofnd(ndofrp(r),negdirp(r)),r)
+a2@[r:cut]
+lemmad1:=eqi12(a1,a2,pl(a1,r),pl(a2,r),tris(cut,pl(a1,pl(a2,r)),pl(a1,pl(r,a2)),pl(pl(a1,r),a2),ispl2(pl(a2,r),pl(r,a2),a1,compl(a2,r)),asspl2(a1,r,a2))):eq(df(a1,a2),df(pl(a1,r),pl(a2,r)))
+lemmad2:=symeq(df(a1,a2),df(pl(a1,r),pl(a2,r)),lemmad1):eq(df(pl(a1,r),pl(a2,r)),df(a1,a2))
+a@[r:cut]
+lemmad3:=treq(a,df(1a,2a),df(pl(1a,r),pl(2a,r)),refeq1(a,df(1a,2a),isdf),lemmad1(1a,2a,r)):eq(a,df(pl(1a,r),pl(2a,r)))
+lemmad4:=symeq(a,df(pl(1a,r),pl(2a,r)),lemmad3):eq(df(pl(1a,r),pl(2a,r)),a)
+a@absd:=ite(negd(a),dif,df(2a,1a),a):dif
+[n:negd(a)]
+absnd:=refeq1(absd(a),df(2a,1a),itet(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),df(2a,1a))
+a@[n:not(negd(a))]
+absnnd:=refeq1(absd(a),a,itef(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),a)
+a2@[l:less(a1,a2)]
+absdeql:=treq(absd(df(a1,a2)),df(std(df(a1,a2)),stm(df(a1,a2))),df(a2,a1),absnd(df(a1,a2),negdi(a1,a2,l)),eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2))):eq(absd(df(a1,a2)),df(a2,a1))
+a2@[m:moreis(a1,a2)]
+absdeqm:=absnnd(df(a1,a2),th3"l.imp"(negd(df(a1,a2)),less(a1,a2),satz123c(a1,a2,m),[t:negd(df(a1,a2))]isless12(stm(df(a1,a2)),a1,std(df(a1,a2)),a2,stmis(a1,a2),stdis(a1,a2),t))):eq(absd(df(a1,a2)),df(a1,a2))
+b@[e:eq(a,b)]
++iv2d
+[n:negd(a)]
+t1:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
+t2:=tr3eq(absd(a),df(2a,1a),df(2b,1b),absd(b),absnd(a,n),eqi12(2a,1a,2b,1b,t1),symeq(absd(b),df(2b,1b),absnd(b,eqnegd(a,b,e,n)))):eq(absd(a),absd(b))
+e@[n:not(negd(a))]
+t3:=tr3eq(absd(a),a,b,absd(b),absnnd(a,n),e,symeq(absd(b),b,absnnd(b,th3"l.imp"(negd(b),negd(a),n,[t:negd(b)]eqnegd(b,a,symeq(a,b,e),t))))):eq(absd(a),absd(b))
+-iv2d
+eqabsd:=th1"l.imp"(negd(a),eq(absd(a),absd(b)),[t:negd(a)]t2".iv2d"(t),[t:not(negd(a))]t3".iv2d"(t)):eq(absd(a),absd(b))
+a@[p:posd(a)]
+satzd166a:=eqposd(a,absd(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p))),p):posd(absd(a))
+a@[n:negd(a)]
++2d166
+t1:=posdi(2a,1a,satz122(1a,2a,n)):posd(df(2a,1a))
+-2d166
+satzd166b:=eqposd(df(2a,1a),absd(a),symeq(absd(a),df(2a,1a),absnd(a,n)),t1".2d166"):posd(absd(a))
+b@[p:posd(a)][q:posd(b)][e:eq(absd(a),absd(b))]
+satzd166c:=tr3eq(a,absd(a),absd(b),b,symeq(absd(a),a,absnnd(a,pnotnd(a,p))),e,absnnd(b,pnotnd(b,q))):eq(a,b)
+b@[n:negd(a)][o:negd(b)][e:eq(absd(a),absd(b))]
++*2d166
+e@t2:=tr3eq(df(2a,1a),absd(a),absd(b),df(2b,1b),symeq(absd(a),df(2a,1a),absnd(a,n)),e,absnd(b,o)):eq(df(2a,1a),df(2b,1b))
+-2d166
+e@satzd166d:=tr3is(cut,pl(1a,2b),pl(2b,1a),pl(2a,1b),pl(1b,2a),compl(1a,2b),symis(cut,pl(2a,1b),pl(2b,1a),eqe12(2a,1a,2b,1b,t2".2d166")),compl(2a,1b)):eq(a,b)
+a@[n:not(zero(a))]
+satzd166e:=rappd(a,posd(absd(a)),[t:posd(a)]satzd166a(a,t),th2"l.imp"(zero(a),posd(absd(a)),n),[t:negd(a)]satzd166b(a,t)):posd(absd(a))
+a@[z:zero(a)]
+satzd166f:=eqzero(a,absd(a),symeq(absd(a),a,absnnd(a,0notnd(a,z))),z):zero(absd(a))
+b@mored:=more(pl(1a,2b),pl(1b,2a)):'prop'
+b2@[m:more(pl(a1,b2),pl(b1,a2))]
+moredi12:=ismore12(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),12issmsd(a1,a2,b1,b2),12issmsd(b1,b2,a1,a2),m):mored(df(a1,a2),df(b1,b2))
+r2@[m:more(pl(1a,r2),pl(r1,2a))]
+moredi1:=ismore12(pl(1a,r2),pl(1a,std(df(r1,r2))),pl(r1,2a),pl(stm(df(r1,r2)),2a),sm2issmsd(a,r1,r2),1sdissmsd(a,r1,r2),m):mored(a,df(r1,r2))
+r2@[m:more(pl(r1,2a),pl(1a,r2))]
+moredi2:=ismore12(pl(r1,2a),pl(stm(df(r1,r2)),2a),pl(1a,r2),pl(1a,std(df(r1,r2))),1sdissmsd(a,r1,r2),sm2issmsd(a,r1,r2),m):mored(df(r1,r2),a)
+b2@[m:mored(df(a1,a2),df(b1,b2))]
+morede12:=ismore12(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),smsdis12(a1,a2,b1,b2),smsdis12(b1,b2,a1,a2),m):more(pl(a1,b2),pl(b1,a2))
+b@lessd:=less(pl(1a,2b),pl(1b,2a)):'prop'
+[m:mored(a,b)]
+lemmad5:=satz121(pl(1a,2b),pl(1b,2a),m):lessd(b,a)
+b@[l:lessd(a,b)]
+lemmad6:=satz122(pl(1a,2b),pl(1b,2a),l):mored(b,a)
+b2@[l:less(pl(a1,b2),pl(b1,a2))]
+lessdi12:=lemmad5(df(b1,b2),df(a1,a2),moredi12(b1,b2,a1,a2,satz122(pl(a1,b2),pl(b1,a2),l))):lessd(df(a1,a2),df(b1,b2))
+r2@[l:less(pl(1a,r2),pl(r1,2a))]
+lessdi1:=lemmad5(df(r1,r2),a,moredi2(a,r1,r2,satz122(pl(1a,r2),pl(r1,2a),l))):lessd(a,df(r1,r2))
+r2@[l:less(pl(r1,2a),pl(1a,r2))]
+lessdi2:=lemmad5(a,df(r1,r2),moredi1(a,r1,r2,satz122(pl(r1,2a),pl(1a,r2),l))):lessd(df(r1,r2),a)
+b2@[l:lessd(df(a1,a2),df(b1,b2))]
+lessde12:=satz121(pl(b1,a2),pl(a1,b2),morede12(b1,b2,a1,a2,lemmad6(df(a1,a2),df(b1,b2),l))):less(pl(a1,b2),pl(b1,a2))
+b@satzd167:=satz123(pl(1a,2b),pl(1b,2a)):orec3(eq(a,b),mored(a,b),lessd(a,b))
+satzd167a:=satz123a(pl(1a,2b),pl(1b,2a)):or3(eq(a,b),mored(a,b),lessd(a,b))
+satzd167b:=satz123b(pl(1a,2b),pl(1b,2a)):ec3(eq(a,b),mored(a,b),lessd(a,b))
+d@1d:=stm(d):cut
+2d:=std(d):cut
+[e:eq(a,b)][f:eq(c,d)][m:mored(a,c)]
++*iv2d
+m@t4:=tr4is(cut,pl(pl(1b,2d),pl(1c,2a)),pl(pl(1b,2a),pl(1c,2d)),pl(pl(1a,2b),pl(1d,2c)),pl(pl(1a,2c),pl(1d,2b)),pl(pl(1d,2b),pl(1a,2c)),4pl24(1b,2d,1c,2a),ispl12(pl(1b,2a),pl(1a,2b),pl(1c,2d),pl(1d,2c),symeq(a,b,e),f),4pl24(1a,2b,1d,2c),compl(pl(1a,2c),pl(1d,2b))):is(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)))
+t5:=ismore2(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)),pl(pl(1b,2d),pl(1a,2c)),t4,satz135d(pl(1a,2c),pl(1c,2a),pl(1b,2d),m)):more(pl(pl(1b,2d),pl(1a,2c)),pl(pl(1d,2b),pl(1a,2c)))
+-iv2d
+m@eqmored12:=satz136a(pl(1b,2d),pl(1d,2b),pl(1a,2c),t5".iv2d"):mored(b,d)
+f@[l:lessd(a,c)]
+eqlessd12:=lemmad5(d,b,eqmored12(c,d,a,b,f,e,lemmad6(a,c,l))):lessd(b,d)
+c@[e:eq(a,b)][m:mored(a,c)]
+eqmored1:=eqmored12(a,b,c,c,e,refeq(c),m):mored(b,c)
+e@[m:mored(c,a)]
+eqmored2:=eqmored12(c,c,a,b,refeq(c),e,m):mored(c,b)
+e@[l:lessd(a,c)]
+eqlessd1:=eqlessd12(a,b,c,c,e,refeq(c),l):lessd(b,c)
+e@[l:lessd(c,a)]
+eqlessd2:=eqlessd12(c,c,a,b,refeq(c),e,l):lessd(c,b)
+b@moreq:=or(mored(a,b),eq(a,b)):'prop'
+lesseq:=or(lessd(a,b),eq(a,b)):'prop'
+[m:moreq(a,b)]
+satzd168a:=th9"l.or"(mored(a,b),eq(a,b),lessd(b,a),eq(b,a),m,[t:mored(a,b)]lemmad5(a,b,t),[t:eq(a,b)]symeq(a,b,t)):lesseq(b,a)
+b@[l:lesseq(a,b)]
+satzd168b:=th9"l.or"(lessd(a,b),eq(a,b),mored(b,a),eq(b,a),l,[t:lessd(a,b)]lemmad6(a,b,t),[t:eq(a,b)]symeq(a,b,t)):moreq(b,a)
+c@[e:eq(a,b)][m:moreq(a,c)]
+eqmoreq1:=th9"l.or"(mored(a,c),eq(a,c),mored(b,c),eq(b,c),m,[t:mored(a,c)]eqmored1(a,b,c,e,t),[t:eq(a,c)]treq1(b,c,a,e,t)):moreq(b,c)
+e@[m:moreq(c,a)]
+eqmoreq2:=th9"l.or"(mored(c,a),eq(c,a),mored(c,b),eq(c,b),m,[t:mored(c,a)]eqmored2(a,b,c,e,t),[t:eq(c,a)]treq(c,a,b,t,e)):moreq(c,b)
+e@[l:lesseq(a,c)]
+eqlesseq1:=satzd168a(c,b,eqmoreq2(a,b,c,e,satzd168b(a,c,l))):lesseq(b,c)
+e@[l:lesseq(c,a)]
+eqlesseq2:=satzd168a(b,c,eqmoreq1(a,b,c,e,satzd168b(c,a,l))):lesseq(c,b)
+d@[e:eq(a,b)][f:eq(c,d)][m:moreq(a,c)]
+eqmoreq12:=eqmoreq1(a,b,d,e,eqmoreq2(c,d,a,f,m)):moreq(b,d)
+f@[l:lesseq(a,c)]
+eqlesseq12:=eqlesseq1(a,b,d,e,eqlesseq2(c,d,a,f,l)):lesseq(b,d)
+b@[m:mored(a,b)]
+moreqi1:=ori1(mored(a,b),eq(a,b),m):moreq(a,b)
+b@[l:lessd(a,b)]
+lesseqi1:=ori1(lessd(a,b),eq(a,b),l):lesseq(a,b)
+b@[e:eq(a,b)]
+moreqi2:=ori2(mored(a,b),eq(a,b),e):moreq(a,b)
+lesseqi2:=ori2(lessd(a,b),eq(a,b),e):lesseq(a,b)
+b@[m:moreq(a,b)]
+satzd167c:=th7"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,comor(mored(a,b),eq(a,b),m)):not(lessd(a,b))
+b@[l:lesseq(a,b)]
+satzd167d:=th9"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,l):not(mored(a,b))
+b@[n:not(mored(a,b))]
+satzd167e:=th2"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n):lesseq(a,b)
+b@[n:not(lessd(a,b))]
+satzd167f:=comor(eq(a,b),mored(a,b),th3"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n)):moreq(a,b)
+b@[m:mored(a,b)]
+satzd167g:=th3"l.imp"(lesseq(a,b),not(mored(a,b)),weli(mored(a,b),m),[t:lesseq(a,b)]satzd167d(t)):not(lesseq(a,b))
+b@[l:lessd(a,b)]
+satzd167h:=th3"l.imp"(moreq(a,b),not(lessd(a,b)),weli(lessd(a,b),l),[t:moreq(a,b)]satzd167c(t)):not(moreq(a,b))
+b@[n:not(moreq(a,b))]
+satzd167j:=or3e3(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th5"l.or"(mored(a,b),eq(a,b),n),th4"l.or"(mored(a,b),eq(a,b),n)):lessd(a,b)
+b@[n:not(lesseq(a,b))]
+satzd167k:=or3e2(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th4"l.or"(lessd(a,b),eq(a,b),n),th5"l.or"(lessd(a,b),eq(a,b),n)):mored(a,b)
+b@[z:zero(b)][p:posd(a)]
+satzd169a:=ismore12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135a(1a,2a,1b,p)):mored(a,b)
+z@[m:mored(a,b)]
+satzd169b:=satz136d(1a,2a,2b,ismore12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),m)):posd(a)
+z@[n:negd(a)]
+satzd169c:=isless12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135c(1a,2a,1b,n)):lessd(a,b)
+z@[l:lessd(a,b)]
+satzd169d:=satz136f(1a,2a,2b,isless12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),l)):negd(a)
++2d170
+z@[p:posd(a)]
+t1:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166a(a,p))):moreq(absd(a),b)
+z@[y:zero(a)]
+t2:=moreqi2(absd(a),b,treq(absd(a),a,b,absnnd(a,0notnd(a,y)),zeroeq(a,b,y,z))):moreq(absd(a),b)
+z@[n:negd(a)]
+t3:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166b(a,n))):moreq(absd(a),b)
+-2d170
+z@satzd170:=rappd(a,moreq(absd(a),b),[t:posd(a)]t1".2d170"(t),[t:zero(a)]t2".2d170"(t),[t:negd(a)]t3".2d170"(t)):moreq(absd(a),b)
+c@[l:lessd(a,b)][k:lessd(b,c)]
++2d171
+t1:=satz137a(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),l,k):less(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
+t2:=isless12(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1a,2c),pl(1b,2b)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2b,1b,2c),tris(cut,pl(pl(1b,2a),pl(1c,2b)),pl(pl(1b,2b),pl(1c,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1b,2a,1c,2b),compl(pl(1b,2b),pl(1c,2a))),t1):less(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
+-2d171
+satzd171:=satz136c(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".2d171"):lessd(a,c)
+trlessd:=satzd171:lessd(a,c)
+c@[m:mored(a,b)][n:mored(b,c)]
+trmored:=lemmad6(c,a,trlessd(c,b,a,lemmad5(b,c,n),lemmad5(a,b,m))):mored(a,c)
+c@[l:lesseq(a,b)][k:lessd(b,c)]
+satzd172a:=orapp(lessd(a,b),eq(a,b),lessd(a,c),l,[t:lessd(a,b)]trlessd(t,k),[t:eq(a,b)]eqlessd1(b,a,c,symeq(a,b,t),k)):lessd(a,c)
+c@[l:lessd(a,b)][k:lesseq(b,c)]
+satzd172b:=orapp(lessd(b,c),eq(b,c),lessd(a,c),k,[t:lessd(b,c)]trlessd(l,t),[t:eq(b,c)]eqlessd2(b,c,a,t,l)):lessd(a,c)
+c@[m:moreq(a,b)][n:mored(b,c)]
+satzd172c:=lemmad6(c,a,satzd172b(c,b,a,lemmad5(b,c,n),satzd168a(a,b,m))):mored(a,c)
+c@[m:mored(a,b)][n:moreq(b,c)]
+satzd172d:=lemmad6(c,a,satzd172a(c,b,a,satzd168a(b,c,n),lemmad5(a,b,m))):mored(a,c)
+c@[l:lesseq(a,b)][k:lesseq(b,c)]
++2d173
+[j:lessd(a,b)]
+t1:=lesseqi1(a,c,satzd172b(j,k)):lesseq(a,c)
+k@[e:eq(a,b)]
+t2:=eqlesseq1(b,a,c,symeq(a,b,e),k):lesseq(a,c)
+-2d173
+satzd173:=orapp(lessd(a,b),eq(a,b),lesseq(a,c),l,[t:lessd(a,b)]t1".2d173"(t),[t:eq(a,b)]t2".2d173"(t)):lesseq(a,c)
+trlesseq:=satzd173:lesseq(a,c)
+c@[m:moreq(a,b)][n:moreq(b,c)]
+trmoreq:=satzd168b(c,a,trlesseq(c,b,a,satzd168a(b,c,n),satzd168a(a,b,m))):moreq(a,c)
+a@ratd:=[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))):'prop'
+irratd:=not(ratd(a)):'prop'
+b@[e:eq(a,b)][r:ratd(a)]
++*iv2d
+r@[n:not(zero(b))]
+t6:=th3"l.imp"(zero(a),zero(b),n,[t:zero(a)]eqzero(a,b,e,t)):not(zero(a))
+t7:=eqpderp(absd(a),satzd166e(a,t6),absd(b),satzd166e(b,n),eqabsd(a,b,e)):is(rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)))
+t8:=isp(cut,[t:cut]ratrp(t),rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)),<t6>r,t7):ratrp(rpofpd(absd(b),satzd166e(b,n)))
+-iv2d
+r@eqratd:=[t:not(zero(b))]t8".iv2d"(t):ratd(b)
+e@[i:irratd(a)]
+eqirratd:=th3"l.imp"(ratd(b),ratd(a),i,[t:ratd(b)]eqratd(b,a,symeq(a,b,e),t)):irratd(b)
+a@[z:zero(a)]
+ratdi0:=th2"l.r.imp"(not(zero(a)),[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))),weli(zero(a),z)):ratd(a)
+@[r:cut][i:irratrp(r)][x0:rat]
++*iv2d
+x0@[s:ratrp(pl(r,rpofrt(x0)))][y0:rat][j:is(pl(r,rpofrt(x0)),rpofrt(y0))]
+t9:=tris(cut,pl(rpofrt(x0),r),pl(r,rpofrt(x0)),rpofrt(y0),compl(rpofrt(x0),r),j):is(pl(rpofrt(x0),r),rpofrt(y0))
+t10:=ismore1(pl(rpofrt(x0),r),rpofrt(y0),rpofrt(x0),t9,satz133(rpofrt(x0),r)):more(rpofrt(y0),rpofrt(x0))
+t11:=satz154d(y0,x0,t10):more"rt"(y0,x0)
+t12:=satz155b(y0,x0,t11):is(rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
+t13:=satz140g(rpofrt(y0),rpofrt(x0),r,satz154a(y0,x0,t11),t9):is(r,mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
+t14:=tris2(cut,r,rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)),t13,t12):is(r,rpofrt(mn"rt"(y0,x0,t11)))
+t15:=somei(rat,[x:rat]is(r,rpofrt(x)),mn"rt"(y0,x0,t11),t14):ratrp(r)
+s@t16:=someapp(rat,[x:rat]is(pl(r,rpofrt(x0)),rpofrt(x)),s,con,[x:rat][t:is(pl(r,rpofrt(x0)),rpofrt(x))]<t15(x,t)>i):con
+-iv2d
+x0@remark1:=[t:ratrp(pl(r,rpofrt(x0)))]t16".iv2d"(t):irratrp(pl(r,rpofrt(x0)))
++*iv2d
+r@rp:=pdofrp(r):dif
+rn:=ndofrp(r):dif
+t17:=posdirp(r):posd(rp)
+t18:=pnot0d(rp,t17):not(zero(rp))
+t19:=nnot0d(rn,negdirp(r)):not(zero(rn))
+[n:not(zero(rp))]
+t20:=tris2(cut,r,rpofpd(absd(rp),satzd166e(rp,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rp),satzd166e(rp,n),rp,t17,absnnd(rp,pnotnd(rp,t17)))):is(r,rpofpd(absd(rp),satzd166e(rp,n)))
+r@t21:=treq(absd(rn),df(std(rn),stm(rn)),rp,absnd(rn,negdirp(r)),eqsmsd(std(rn),stm(rn),pl(r,1rp),1rp,stdis(1rp,pl(r,1rp)),stmis(1rp,pl(r,1rp)))):eq(absd(rn),rp)
+[n:not(zero(rn))]
+t22:=tris2(cut,r,rpofpd(absd(rn),satzd166e(rn,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rn),satzd166e(rn,n),rp,t17,t21)):is(r,rpofpd(absd(rn),satzd166e(rn,n)))
+r@[s:cut][i:is(r,s)][rr:ratrp(r)]
+t23:=isp(cut,[x:cut]ratrp(x),r,s,rr,i):ratrp(s)
+i@[rs:ratrp(s)]
+t24:=isp1(cut,[x:cut]ratrp(x),s,r,rs,i):ratrp(r)
+-iv2d
+r@[rr:ratrp(r)]
+remark2a:=[t:not(zero(pdofrp(r)))]t23".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t)),t20".iv2d"(t),rr):ratd(pdofrp(r))
+remark2b:=t17".iv2d":posd(pdofrp(r))
+remark3a:=[t:not(zero(ndofrp(r)))]t23".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t)),t22".iv2d"(t),rr):ratd(ndofrp(r))
+remark3b:=negdirp(r):negd(ndofrp(r))
+r@[i:irratrp(r)]
+remark4a:=th3"l.imp"(ratd(pdofrp(r)),ratrp(r),i,[t:ratd(pdofrp(r))]t24".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t18".iv2d")),t20".iv2d"(t18".iv2d"),<t18".iv2d">t)):irratd(pdofrp(r))
+remark4b:=t17".iv2d":posd(pdofrp(r))
+remark5a:=th3"l.imp"(ratd(ndofrp(r)),ratrp(r),i,[t:ratd(ndofrp(r))]t24".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t19".iv2d")),t22".iv2d"(t19".iv2d"),<t19".iv2d">t)):irratd(ndofrp(r))
+remark5b:=negdirp(r):negd(ndofrp(r))
+a@natd:=and(posd(a),[t:posd(a)]natrp(rpofpd(a,t))):'prop'
+[n:natd(a)]
+natposd:=ande1(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):posd(a)
+natderp:=ande2"l.r"(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):natrp(rpofpd(a,natposd(a,n)))
+b@[e:eq(a,b)][n:natd(a)]
++*iv2d
+n"rp"@t25:=eqposd(a,b,e,natposd(a,n)):posd(b)
+[p:posd(b)]
+t26:=eqpderp(a,natposd(a,n),b,p,e):is(rpofpd(a,natposd(a,n)),rpofpd(b,p))
+t27:=isp(cut,[t:cut]natrp(t),rpofpd(a,natposd(a,n)),rpofpd(b,p),natderp(a,n),t26):natrp(rpofpd(b,p))
+-iv2d
+n@eqnatd:=andi(posd(b),[t:posd(b)]natrp(rpofpd(b,t)),t25".iv2d",[t:posd(b)]t27".iv2d"(t)):natd(b)
+@[x:nat]
+pdofnt:=pdofrp(rpofnt(x)):dif
++*iv2d
+x@t28:=posdirp(rpofnt(x)):posd(pdofnt(x))
+[p:posd(pdofnt(x))]
+t29:=isrppd1(rpofnt(x)):is(rpofnt(x),rpofpd(pdofnt(x),t28))
+t30:=eqpderp(pdofnt(x),t28,pdofnt(x),p,refeq(pdofnt(x))):is(rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p))
+t31:=tris(cut,rpofnt(x),rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p),t29,t30):is(rpofnt(x),rpofpd(pdofnt(x),p))
+t32:=isp(cut,[t:cut]natrp(t),rpofnt(x),rpofpd(pdofnt(x),p),natrpi(x),t31):natrp(rpofpd(pdofnt(x),p))
+-iv2d
+x@natdi:=andi(posd(pdofnt(x)),[t:posd(pdofnt(x))]natrp(rpofpd(pdofnt(x),t)),t28".iv2d",[t:posd(pdofnt(x))]t32".iv2d"(t)):natd(pdofnt(x))
+a@intd:=or(zero(a),natd(absd(a))):'prop'
+b@[e:eq(a,b)][i:intd(a)]
++*iv2d
+i"rp"@[z:zero(a)]
+t33:=eqzero(a,b,e,z):zero(b)
+i"rp"@[n:natd(absd(a))]
+t34:=eqnatd(absd(a),absd(b),eqabsd(a,b,e),n):natd(absd(b))
+-iv2d
+i@eqintd:=th9"l.or"(zero(a),natd(absd(a)),zero(b),natd(absd(b)),i,[t:zero(a)]t33".iv2d"(t),[t:natd(absd(a))]t34".iv2d"(t)):intd(b)
+a@[n:natd(a)]
++*iv2d
+n"rp"@t34a:=symeq(absd(a),a,absnnd(a,pnotnd(a,natposd(a,n)))):eq(a,absd(a))
+t35:=eqnatd(a,absd(a),t34a,n):natd(absd(a))
+-iv2d
+n@natintd:=ori2(zero(a),natd(absd(a)),t35".iv2d"):intd(a)
+a@[p:posd(a)][i:intd(a)]
++*iv2d
+i"rp"@t36:=ore2(zero(a),natd(absd(a)),i,pnot0d(a,p)):natd(absd(a))
+-iv2d
+i@posintnatd:=eqnatd(absd(a),a,absnnd(a,pnotnd(a,p)),t36".iv2d"):natd(a)
+a@[z:zero(a)]
+intdi0:=ori1(zero(a),natd(absd(a)),z):intd(a)
+r@[n:natrp(r)]
++*iv2d
+n"rp"@t37:=posdirp(r):posd(pdofrp(r))
+[p:posd(pdofrp(r))]
+t38:=tris(cut,r,rpofpd(pdofrp(r),t37),rpofpd(pdofrp(r),p),isrppd1(r),eqpderp(pdofrp(r),t37,pdofrp(r),p,refeq(pdofrp(r)))):is(r,rpofpd(pdofrp(r),p))
+t39:=isp(cut,[t:cut]natrp(t),r,rpofpd(pdofrp(r),p),n,t38):natrp(rpofpd(pdofrp(r),p))
+-iv2d
+n@remark6a:=andi(posd(pdofrp(r)),[t:posd(pdofrp(r))]natrp(rpofpd(pdofrp(r),t)),t37".iv2d",[t:posd(pdofrp(r))]t39".iv2d"(t)):natd(pdofrp(r))
+remark6:=natintd(pdofrp(r),remark6a):intd(pdofrp(r))
++*iv2d
+n"rp"@t40:=absdeql(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):eq(absd(ndofrp(r)),pdofrp(r))
+t41:=eqnatd(pdofrp(r),absd(ndofrp(r)),symeq(absd(ndofrp(r)),pdofrp(r),t40),remark6a):natd(absd(ndofrp(r)))
+-iv2d
+n@remark7:=ori2(zero(ndofrp(r)),natd(absd(ndofrp(r))),t41".iv2d"):intd(ndofrp(r))
+a@[i:intd(a)]
++2d174
+[n:not(zero(a))]
+t1:=ore2(zero(a),natd(absd(a)),i,n):natd(absd(a))
+t2:=ande2(posd(absd(a)),[t:posd(absd(a))]natrp(rpofpd(absd(a),t)),t1):[t:posd(absd(a))]natrp(rpofpd(absd(a),t))
+t3:=lemmaiii5(rpofpd(absd(a),satzd166e(a,n)),<satzd166e(a,n)>t2):ratrp(rpofpd(absd(a),satzd166e(a,n)))
+-2d174
+satzd174:=[t:not(zero(a))]t3".2d174"(t):ratd(a)
+b@pd:=df(pl(1a,1b),pl(2a,2b)):dif
+b2@pd12:=issmsd(pl(stm(df(a1,a2)),stm(df(b1,b2))),pl(std(df(a1,a2)),std(df(b1,b2))),pl(a1,b1),pl(a2,b2),ispl12(stm(df(a1,a2)),a1,stm(df(b1,b2)),b1,stmis(a1,a2),stmis(b1,b2)),ispl12(std(df(a1,a2)),a2,std(df(b1,b2)),b2,stdis(a1,a2),stdis(b1,b2))):is"e"(dif,pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
+r2@pd1:=issmsd(pl(1a,stm(df(r1,r2))),pl(2a,std(df(r1,r2))),pl(1a,r1),pl(2a,r2),ispl2(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl2(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
+pd2:=issmsd(pl(stm(df(r1,r2)),1a),pl(std(df(r1,r2)),2a),pl(r1,1a),pl(r2,2a),ispl1(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl1(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
+b2@pdeq12a:=refeq1(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
+pdeq12b:=refeq2(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(df(pl(a1,b1),pl(a2,b2)),pd(df(a1,a2),df(b1,b2)))
+r2@pdeq1a:=refeq1(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
+pdeq1b:=refeq2(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(df(pl(1a,r1),pl(2a,r2)),pd(a,df(r1,r2)))
+pdeq2a:=refeq1(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
+pdeq2b:=refeq2(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(df(pl(r1,1a),pl(r2,2a)),pd(df(r1,r2),a))
+b@satzd175:=eqsmsd(pl(1a,1b),pl(2a,2b),pl(1b,1a),pl(2b,2a),compl(1a,1b),compl(2a,2b)):eq(pd(a,b),pd(b,a))
+compd:=satzd175:eq(pd(a,b),pd(b,a))
+c@[e:eq(a,b)]
++iv3d
+t1:=tr3is(cut,pl(pl(1a,1c),pl(2b,2c)),pl(pl(1a,2b),pl(1c,2c)),pl(pl(1b,2a),pl(1c,2c)),pl(pl(1b,1c),pl(2a,2c)),4pl23(1a,1c,2b,2c),ispl1(pl(1a,2b),pl(1b,2a),pl(1c,2c),e),4pl23(1b,2a,1c,2c)):is(pl(pl(1a,1c),pl(2b,2c)),pl(pl(1b,1c),pl(2a,2c)))
+-iv3d
+eqpd1:=eqi12(pl(1a,1c),pl(2a,2c),pl(1b,1c),pl(2b,2c),t1".iv3d"):eq(pd(a,c),pd(b,c))
+eqpd2:=tr3eq(pd(c,a),pd(a,c),pd(b,c),pd(c,b),compd(c,a),eqpd1,compd(b,c)):eq(pd(c,a),pd(c,b))
+d@[e:eq(a,b)][f:eq(c,d)]
+eqpd12:=treq(pd(a,c),pd(b,c),pd(b,d),eqpd1(a,b,c,e),eqpd2(c,d,b,f)):eq(pd(a,c),pd(b,d))
+b@[z:zero(a)]
++*iv3d
+z@t2:=tr4is(cut,pl(pl(1a,1b),2b),pl(1a,pl(1b,2b)),pl(2a,pl(2b,1b)),pl(pl(2a,2b),1b),pl(1b,pl(2a,2b)),asspl1(1a,1b,2b),ispl12(1a,2a,pl(1b,2b),pl(2b,1b),z,compl(1b,2b)),asspl2(2a,2b,1b),compl(pl(2a,2b),1b)):is(pl(pl(1a,1b),2b),pl(1b,pl(2a,2b)))
+-iv3d
+z@pd01:=eqi2(b,pl(1a,1b),pl(2a,2b),t2".iv3d"):eq(pd(a,b),b)
+b@[z:zero(b)]
+pd02:=treq(pd(a,b),pd(b,a),a,compd(a,b),pd01(b,a,z)):eq(pd(a,b),a)
+b@[p:posd(a)][q:posd(b)]
+ppd:=posdi(pl(1a,1b),pl(2a,2b),satz137(1a,2a,1b,2b,p,q)):posd(pd(a,b))
+b@[n:negd(a)][o:negd(b)]
+npd:=negdi(pl(1a,1b),pl(2a,2b),satz137a(1a,2a,1b,2b,n,o)):negd(pd(a,b))
+a@m0d:=df(2a,1a):dif
+a2@m0deqa:=eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2)):eq(m0d(df(a1,a2)),df(a2,a1))
+m0deqb:=symeq(m0d(df(a1,a2)),df(a2,a1),m0deqa):eq(df(a2,a1),m0d(df(a1,a2)))
+b@[e:eq(a,b)]
++*iv3d
+e@t3:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
+-iv3d
+e@eqm0d:=eqi12(2a,1a,2b,1b,t3".iv3d"):eq(m0d(a),m0d(b))
+a@[p:posd(a)]
+satzd176a:=negdi(2a,1a,satz121(1a,2a,p)):negd(m0d(a))
+a@[z:zero(a)]
+satzd176b:=zeroi(2a,1a,symis(cut,1a,2a,z)):zero(m0d(a))
+a@[n:negd(a)]
+satzd176c:=posdi(2a,1a,satz122(1a,2a,n)):posd(m0d(a))
+a@[n:negd(m0d(a))]
+satzd176d:=satz122(2a,1a,isless12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),n)):posd(a)
+a@[z:zero(m0d(a))]
+satzd176e:=symis(cut,2a,1a,tr3is(cut,2a,stm(df(2a,1a)),std(df(2a,1a)),1a,isstm(2a,1a),z,stdis(2a,1a))):zero(a)
+a@[p:posd(m0d(a))]
+satzd176f:=satz121(2a,1a,ismore12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),p)):negd(a)
+a@[z:zero(a)]
+m0d0:=zeroeq(m0d(a),a,satzd176b(a,z),z):eq(m0d(a),a)
++3d177
+a@t1:=tris(dif,m0d(m0d(a)),df(1a,2a),a,issmsd(std(m0d(a)),stm(m0d(a)),1a,2a,stdis(2a,1a),stmis(2a,1a)),dfis(a)):is"e"(dif,m0d(m0d(a)),a)
+-3d177
+a@satzd177:=refeq1(m0d(m0d(a)),a,t1".3d177"):eq(m0d(m0d(a)),a)
+satzd177a:=symeq(m0d(m0d(a)),a,satzd177):eq(a,m0d(m0d(a)))
+b@[e:eq(a,m0d(b))]
+satzd177b:=treq(m0d(a),m0d(m0d(b)),b,eqm0d(a,m0d(b),e),satzd177(b)):eq(m0d(a),b)
+satzd177c:=symeq(m0d(a),b,satzd177b):eq(b,m0d(a))
+b@[e:eq(m0d(a),b)]
+satzd177d:=satzd177c(b,a,symeq(m0d(a),b,e)):eq(a,m0d(b))
+satzd177e:=symeq(a,m0d(b),satzd177d):eq(m0d(b),a)
++3d178
+a@[p:posd(a)]
+t1:=tr3eq(absd(m0d(a)),m0d(m0d(a)),a,absd(a),absnd(m0d(a),satzd176a(a,p)),satzd177(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p)))):eq(absd(m0d(a)),absd(a))
+a@[z:zero(a)]
+t2:=tr3eq(absd(m0d(a)),m0d(a),a,absd(a),absnnd(m0d(a),0notnd(m0d(a),satzd176b(a,z))),m0d0(a,z),symeq(absd(a),a,absnnd(a,0notnd(a,z)))):eq(absd(m0d(a)),absd(a))
+a@[n:negd(a)]
+t3:=treq(absd(m0d(a)),m0d(a),absd(a),absnnd(m0d(a),pnotnd(m0d(a),satzd176c(a,n))),symeq(absd(a),m0d(a),absnd(a,n))):eq(absd(m0d(a)),absd(a))
+-3d178
+a@satzd178:=rappd(a,eq(absd(m0d(a)),absd(a)),[t:posd(a)]t1".3d178"(t),[t:zero(a)]t2".3d178"(t),[t:negd(a)]t3".3d178"(t)):eq(absd(m0d(a)),absd(a))
+satzd178a:=symeq(absd(m0d(a)),absd(a),satzd178):eq(absd(a),absd(m0d(a)))
++3d179
+t1:=pdeq1b(a,2a,1a):eq(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)))
+t2:=zeroi(pl(1a,2a),pl(2a,1a),compl(1a,2a)):zero(df(pl(1a,2a),pl(2a,1a)))
+-3d179
+satzd179:=eqzero(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)),t1".3d179",t2".3d179"):zero(pd(a,m0d(a)))
+satzd179a:=eqzero(pd(a,m0d(a)),pd(m0d(a),a),compd(a,m0d(a)),satzd179):zero(pd(m0d(a),a))
+b@satzd180:=treq(m0d(pd(a,b)),df(pl(2a,2b),pl(1a,1b)),pd(m0d(a),m0d(b)),m0deqa(pl(1a,1b),pl(2a,2b)),pdeq12b(2a,1a,2b,1b)):eq(m0d(pd(a,b)),pd(m0d(a),m0d(b)))
+satzd180a:=symeq(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180):eq(pd(m0d(a),m0d(b)),m0d(pd(a,b)))
+md:=pd(a,m0d(b)):dif
+b2@mdeq12a:=treq(md(df(a1,a2),df(b1,b2)),pd(df(a1,a2),df(b2,b1)),df(pl(a1,b2),pl(a2,b1)),eqpd2(m0d(df(b1,b2)),df(b2,b1),df(a1,a2),m0deqa(b1,b2)),pdeq12a(a1,a2,b2,b1)):eq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)))
+mdeq12b:=symeq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)),mdeq12a):eq(df(pl(a1,b2),pl(a2,b1)),md(df(a1,a2),df(b1,b2)))
+r2@mdeq1a:=treq(md(a,df(r1,r2)),pd(a,df(r2,r1)),df(pl(1a,r2),pl(2a,r1)),eqpd2(m0d(df(r1,r2)),df(r2,r1),a,m0deqa(r1,r2)),pdeq1a(a,r2,r1)):eq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)))
+mdeq1b:=symeq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)),mdeq1a):eq(df(pl(1a,r2),pl(2a,r1)),md(a,df(r1,r2)))
+mdeq2a:=pdeq12a(r1,r2,2a,1a):eq(md(df(r1,r2),a),df(pl(r1,2a),pl(r2,1a)))
+mdeq2b:=pdeq12b(r1,r2,2a,1a):eq(df(pl(r1,2a),pl(r2,1a)),md(df(r1,r2),a))
+c@[e:eq(a,b)]
+eqmd1:=eqpd1(a,b,m0d(c),e):eq(md(a,c),md(b,c))
+eqmd2:=eqpd2(m0d(a),m0d(b),c,eqm0d(a,b,e)):eq(md(c,a),md(c,b))
+d@[e:eq(a,b)][f:eq(c,d)]
+eqmd12:=treq(md(a,c),md(b,c),md(b,d),eqmd1(a,b,c,e),eqmd2(c,d,b,f)):eq(md(a,c),md(b,d))
+b@satzd181:=tr3eq(m0d(md(a,b)),pd(m0d(a),m0d(m0d(b))),pd(m0d(a),b),md(b,a),satzd180(a,m0d(b)),eqpd2(m0d(m0d(b)),b,m0d(a),satzd177(b)),compd(m0d(a),b)):eq(m0d(md(a,b)),md(b,a))
+satzd181a:=symeq(m0d(md(b,a)),md(a,b),satzd181(b,a)):eq(md(a,b),m0d(md(b,a)))
++3d182
+t1:=treq(md(a,b),df(pl(1a,2b),pl(2a,1b)),df(pl(1a,2b),pl(1b,2a)),pdeq1a(a,2b,1b),eqsd(pl(1a,2b),pl(2a,1b),pl(1b,2a),compl(2a,1b))):eq(md(a,b),df(pl(1a,2b),pl(1b,2a)))
+t2:=symeq(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1):eq(df(pl(1a,2b),pl(1b,2a)),md(a,b))
+t3:=stmis(pl(1a,2b),pl(1b,2a)):is(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b))
+t4:=stdis(pl(1a,2b),pl(1b,2a)):is(std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a))
+-3d182
+[p:posd(md(a,b))]
++*3d182
+p@t5:=eqposd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,p):posd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+p@satzd182a:=ismore12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t5".3d182"):mored(a,b)
+b@[z:zero(md(a,b))]
++*3d182
+z@t6:=eqzero(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,z):zero(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+z@satzd182b:=tr3is(cut,pl(1a,2b),stm(df(pl(1a,2b),pl(1b,2a))),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),isstm(pl(1a,2b),pl(1b,2a)),t6".3d182",t4".3d182"):eq(a,b)
+b@[n:negd(md(a,b))]
++*3d182
+n@t7:=eqnegd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,n):negd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+n@satzd182c:=isless12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t7".3d182"):lessd(a,b)
+b@[m:mored(a,b)]
++*3d182
+m@t8:=posdi(pl(1a,2b),pl(1b,2a),m):posd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+m@satzd182d:=eqposd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t8".3d182"):posd(md(a,b))
+b@[e:eq(a,b)]
++*3d182
+e@t9:=zeroi(pl(1a,2b),pl(1b,2a),e):zero(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+e@satzd182e:=eqzero(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t9".3d182"):zero(md(a,b))
+b@[l:lessd(a,b)]
++*3d182
+l@t10:=negdi(pl(1a,2b),pl(1b,2a),l):negd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+l@satzd182f:=eqnegd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t10".3d182"):negd(md(a,b))
++3d183
+b@t1:=tris(cut,pl(1a,2b),pl(2b,1a),pl(stm(m0d(b)),std(m0d(a))),compl(1a,2b),12issmsd(2b,1b,2a,1a)):is(pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))))
+t2:=t1(b,a):is(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))))
+-3d183
+b@[m:mored(a,b)]
+satzd183a:=isless12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad5(a,b,m)):lessd(m0d(a),m0d(b))
+b@[e:eq(a,b)]
+staz183b:=eqm0d(a,b,e):eq(m0d(a),m0d(b))
+b@[l:lessd(a,b)]
+satzd183c:=ismore12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad6(a,b,l)):mored(m0d(a),m0d(b))
+b@[l:lessd(m0d(a),m0d(b))]
+satzd183d:=eqmored12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183c(m0d(a),m0d(b),l)):mored(a,b)
+b@[e:eq(m0d(a),m0d(b))]
+satzd183e:=tr3eq(a,m0d(m0d(a)),m0d(m0d(b)),b,satzd177a(a),eqm0d(m0d(a),m0d(b),e),satzd177(b)):eq(a,b)
+b@[m:mored(m0d(a),m0d(b))]
+satzd183f:=eqlessd12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183a(m0d(a),m0d(b),m)):lessd(a,b)
++3d184
+a@t1:=tr3eq(a,df(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp))),df(pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp))),md(pdofrp(1a),pdofrp(2a)),lemmad3(a,pl(1rp,1rp)),eqsmsd(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp)),pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp)),asspl2(1a,1rp,1rp),3pl12(2a,1rp,1rp)),mdeq12b(pl(1a,1rp),1rp,pl(2a,1rp),1rp)):eq(a,md(pdofrp(1a),pdofrp(2a)))
+t2:=and3i(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))),posdirp(1a),posdirp(2a),t1):and3(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))))
+t3:=somei(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))),pdofrp(2a),t2):some"l"(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))))
+-3d184
+a@satzd184:=somei(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))),pdofrp(1a),t3".3d184"):some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))))
+c@asspd1:=tr3eq(pd(pd(a,b),c),df(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c)),df(pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c))),pd(a,pd(b,c)),pdeq2a(c,pl(1a,1b),pl(2a,2b)),eqsmsd(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c),pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c)),asspl1(1a,1b,1c),asspl1(2a,2b,2c)),pdeq1b(a,pl(1b,1c),pl(2b,2c))):eq(pd(pd(a,b),c),pd(a,pd(b,c)))
+asspd2:=symeq(pd(pd(a,b),c),pd(a,pd(b,c)),asspd1):eq(pd(a,pd(b,c)),pd(pd(a,b),c))
+3pd23:=tr3eq(pd(pd(a,b),c),pd(a,pd(b,c)),pd(a,pd(c,b)),pd(pd(a,c),b),asspd1(a,b,c),eqpd2(pd(b,c),pd(c,b),a,compd(b,c)),asspd2(a,c,b)):eq(pd(pd(a,b),c),pd(pd(a,c),b))
+d@4pd23:=tr3eq(pd(pd(a,b),pd(c,d)),pd(pd(pd(a,b),c),d),pd(pd(pd(a,c),b),d),pd(pd(a,c),pd(b,d)),asspd2(pd(a,b),c,d),eqpd1(pd(pd(a,b),c),pd(pd(a,c),b),d,3pd23),asspd1(pd(a,c),b,d)):eq(pd(pd(a,b),pd(c,d)),pd(pd(a,c),pd(b,d)))
+b@pdmd:=treq(pd(md(a,b),b),pd(a,pd(m0d(b),b)),a,asspd1(a,m0d(b),b),pd02(a,pd(m0d(b),b),satzd179a(b))):eq(pd(md(a,b),b),a)
+mdpd:=treq(md(pd(a,b),b),pd(a,pd(b,m0d(b))),a,asspd1(a,b,m0d(b)),pd02(a,pd(b,m0d(b)),satzd179(b))):eq(md(pd(a,b),b),a)
+d@satzd185:=treq(pd(md(a,b),md(c,d)),pd(pd(a,c),pd(m0d(b),m0d(d))),md(pd(a,c),pd(b,d)),4pd23(a,m0d(b),c,m0d(d)),eqpd2(pd(m0d(b),m0d(d)),m0d(pd(b,d)),pd(a,c),satzd180a(b,d))):eq(pd(md(a,b),md(c,d)),md(pd(a,c),pd(b,d)))
+c@satzd186:=asspd1:eq(pd(pd(a,b),c),pd(a,pd(b,c)))
+b@satzd187a:=treq(pd(b,md(a,b)),pd(md(a,b),b),a,compd(b,md(a,b)),pdmd):eq(pd(b,md(a,b)),a)
+[x:dif][e:eq(pd(b,x),a)]
+satzd187c:=treq(md(a,b),md(pd(x,b),b),x,eqmd1(a,pd(x,b),b,treq1(a,pd(x,b),pd(b,x),e,compd(b,x))),mdpd(x,b)):eq(md(a,b),x)
+satzd187d:=symeq(md(a,b),x,satzd187c):eq(x,md(a,b))
+x@[e:eq(pd(x,b),a)]
+satzd187e:=satzd187c(treq(pd(b,x),pd(x,b),a,compd(b,x),e)):eq(md(a,b),x)
+satzd187f:=symeq(md(a,b),x,satzd187e):eq(x,md(a,b))
++3d188
+c@t1:=tr3eq(md(pd(a,c),pd(b,c)),pd(pd(a,c),pd(m0d(b),m0d(c))),pd(md(a,b),md(c,c)),md(a,b),eqpd2(m0d(pd(b,c)),pd(m0d(b),m0d(c)),pd(a,c),satzd180(b,c)),4pd23(a,c,m0d(b),m0d(c)),pd02(md(a,b),md(c,c),satzd179(c))):eq(md(pd(a,c),pd(b,c)),md(a,b))
+t2:=symeq(md(pd(a,c),pd(b,c)),md(a,b),t1):eq(md(a,b),md(pd(a,c),pd(b,c)))
+-3d188
+c@[m:mored(pd(a,c),pd(b,c))]
++*3d188
+m@t3:=eqposd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182d(pd(a,c),pd(b,c),m)):posd(md(a,b))
+-3d188
+m@satzd188a:=satzd182a(a,b,t3".3d188"):mored(a,b)
+c@[e:eq(pd(a,c),pd(b,c))]
++*3d188
+e@t4:=eqzero(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182e(pd(a,c),pd(b,c),e)):zero(md(a,b))
+-3d188
+e@satzd188b:=satzd182b(a,b,t4".3d188"):eq(a,b)
+c@[l:lessd(pd(a,c),pd(b,c))]
++*3d188
+l@t5:=eqnegd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182f(pd(a,c),pd(b,c),l)):negd(md(a,b))
+-3d188
+l@satzd188c:=satzd182c(a,b,t5".3d188"):lessd(a,b)
+c@[m:mored(a,b)]
++*3d188
+m@t6:=eqposd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182d(a,b,m)):posd(md(pd(a,c),pd(b,c)))
+-3d188
+m@satzd188d:=satzd182a(pd(a,c),pd(b,c),t6".3d188"):mored(pd(a,c),pd(b,c))
+c@[e:eq(a,b)]
+satzd188e:=eqpd1(a,b,c,e):eq(pd(a,c),pd(b,c))
+c@[l:lessd(a,b)]
++*3d188
+l@t7:=eqnegd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182f(a,b,l)):negd(md(pd(a,c),pd(b,c)))
+-3d188
+l@satzd188f:=satzd182c(pd(a,c),pd(b,c),t7".3d188"):lessd(pd(a,c),pd(b,c))
+c@[m:mored(pd(c,a),pd(c,b))]
+satzd188g:=satzd188a(eqmored12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),m)):mored(a,b)
+c@[e:eq(pd(c,a),pd(c,b))]
+satzd188h:=satzd188b(tr3eq(pd(a,c),pd(c,a),pd(c,b),pd(b,c),compd(a,c),e,compd(c,b))):eq(a,b)
+[l:lessd(pd(c,a),pd(c,b))]
+satzd188j:=satzd188c(eqlessd12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),l)):lessd(a,b)
+c@[m:mored(a,b)]
+satzd188k:=eqmored12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188d(m)):mored(pd(c,a),pd(c,b))
+c@[e:eq(a,b)]
+satzd188l:=eqpd2(a,b,c,e):eq(pd(c,a),pd(c,b))
+c@[l:lessd(a,b)]
+satzd188m:=eqlessd12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188f(l)):lessd(pd(c,a),pd(c,b))
+d@[e:eq(a,b)][m:mored(c,d)]
+satzd188n:=eqmored2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188k(c,d,a,m)):mored(pd(a,c),pd(b,d))
+satzd188o:=eqmored12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188n):mored(pd(c,a),pd(d,b))
+e@[l:lessd(c,d)]
+satzd188p:=eqlessd2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188m(c,d,a,l)):lessd(pd(a,c),pd(b,d))
+satzd188q:=eqlessd12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188p):lessd(pd(c,a),pd(d,b))
+d@[m:mored(a,b)][n:mored(c,d)]
+satzd189:=trmored(pd(a,c),pd(b,c),pd(b,d),satzd188d(a,b,c,m),satzd188k(c,d,b,n)):mored(pd(a,c),pd(b,d))
+d@[l:lessd(a,b)][k:lessd(c,d)]
+satzd189a:=lemmad5(pd(b,d),pd(a,c),satzd189(b,a,d,c,lemmad6(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
+d@[m:moreq(a,b)][n:mored(c,d)]
+satzd190a:=orapp(mored(a,b),eq(a,b),mored(pd(a,c),pd(b,d)),m,[t:mored(a,b)]satzd189(t,n),[t:eq(a,b)]satzd188n(t,n)):mored(pd(a,c),pd(b,d))
+d@[m:mored(a,b)][n:moreq(c,d)]
+satzd190b:=eqmored12(pd(c,a),pd(a,c),pd(d,b),pd(b,d),compd(c,a),compd(d,b),satzd190a(c,d,a,b,n,m)):mored(pd(a,c),pd(b,d))
+d@[l:lesseq(a,b)][k:lessd(c,d)]
+satzd190c:=lemmad5(pd(b,d),pd(a,c),satzd190a(b,a,d,c,satzd168b(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
+d@[l:lessd(a,b)][k:lesseq(c,d)]
+satzd190d:=lemmad5(pd(b,d),pd(a,c),satzd190b(b,a,d,c,lemmad6(a,b,l),satzd168b(c,d,k))):lessd(pd(a,c),pd(b,d))
+d@[m:moreq(a,b)][n:moreq(c,d)]
++3d191
+[e:eq(a,b)][f:eq(c,d)]
+t1:=moreqi2(pd(a,c),pd(b,d),eqpd12(a,b,c,d,e,f)):moreq(pd(a,c),pd(b,d))
+e@[o:mored(c,d)]
+t2:=moreqi1(pd(a,c),pd(b,d),satzd190a(m,o)):moreq(pd(a,c),pd(b,d))
+e@t3:=orapp(mored(c,d),eq(c,d),moreq(pd(a,c),pd(b,d)),n,[t:mored(c,d)]t2(t),[t:eq(c,d)]t1(t)):moreq(pd(a,c),pd(b,d))
+n@[o:mored(a,b)]
+t4:=moreqi1(pd(a,c),pd(b,d),satzd190b(o,n)):moreq(pd(a,c),pd(b,d))
+-3d191
+satzd191:=orapp(mored(a,b),eq(a,b),moreq(pd(a,c),pd(b,d)),m,[t:mored(a,b)]t4".3d191"(t),[t:eq(a,b)]t3".3d191"(t)):moreq(pd(a,c),pd(b,d))
+d@[l:lesseq(a,b)][k:lesseq(c,d)]
+satzd191a:=satzd168a(pd(b,d),pd(a,c),satzd191(b,a,d,c,satzd168b(a,b,l),satzd168b(c,d,k))):lesseq(pd(a,c),pd(b,d))
+b@td:=df(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))):dif
++iv4d
+a2@[r:cut]
+t1:=ists1(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(stm(df(a1,a2)),r),ts(a1,r))
+t2:=ists2(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(r,stm(df(a1,a2))),ts(r,a1))
+t3:=ists1(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(std(df(a1,a2)),r),ts(a2,r))
+t4:=ists2(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(r,std(df(a1,a2))),ts(r,a2))
+[s:cut]
+t5:=ispl12(ts(stm(df(a1,a2)),r),ts(a1,r),ts(std(df(a1,a2)),s),ts(a2,s),t1(r),t3(s)):is(pl(ts(stm(df(a1,a2)),r),ts(std(df(a1,a2)),s)),pl(ts(a1,r),ts(a2,s)))
+t6:=ispl12(ts(r,stm(df(a1,a2))),ts(r,a1),ts(s,std(df(a1,a2))),ts(s,a2),t2(r),t4(s)):is(pl(ts(r,stm(df(a1,a2))),ts(s,std(df(a1,a2)))),pl(ts(r,a1),ts(s,a2)))
+t7:=ispl12(ts(std(df(a1,a2)),r),ts(a2,r),ts(stm(df(a1,a2)),s),ts(a1,s),t3(r),t1(s)):is(pl(ts(std(df(a1,a2)),r),ts(stm(df(a1,a2)),s)),pl(ts(a2,r),ts(a1,s)))
+t8:=ispl12(ts(r,std(df(a1,a2))),ts(r,a2),ts(s,stm(df(a1,a2))),ts(s,a1),t4(r),t2(s)):is(pl(ts(r,std(df(a1,a2))),ts(s,stm(df(a1,a2)))),pl(ts(r,a2),ts(s,a1)))
+b2@t9:=tris(cut,pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,stm(df(b1,b2))),ts(a2,std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),t5(a1,a2,stm(df(b1,b2)),std(df(b1,b2))),t6(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)))
+t10:=tris(cut,pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,std(df(b1,b2))),ts(a2,stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)),t5(a1,a2,std(df(b1,b2)),stm(df(b1,b2))),t8(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)))
+-iv4d
+b2@td12:=issmsd(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1)),t9".iv4d",t10".iv4d"):is"e"(dif,td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
+r2@td1:=issmsd(pl(ts(1a,stm(df(r1,r2))),ts(2a,std(df(r1,r2)))),pl(ts(1a,std(df(r1,r2))),ts(2a,stm(df(r1,r2)))),pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1)),t6".iv4d"(r1,r2,1a,2a),t8".iv4d"(r1,r2,1a,2a)):is"e"(dif,td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
+td2:=issmsd(pl(ts(stm(df(r1,r2)),1a),ts(std(df(r1,r2)),2a)),pl(ts(stm(df(r1,r2)),2a),ts(std(df(r1,r2)),1a)),pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a)),t5".iv4d"(r1,r2,1a,2a),t5".iv4d"(r1,r2,2a,1a)):is"e"(dif,td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
+b2@tdeq12a:=refeq1(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
+tdeq12b:=refeq2(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td(df(a1,a2),df(b1,b2)))
+r2@tdeq1a:=refeq1(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
+tdeq1b:=refeq2(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td(a,df(r1,r2)))
+tdeq2a:=refeq1(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
+tdeq2b:=refeq2(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td(df(r1,r2),a))
++4d194
+b@t1:=ispl12(ts(1a,1b),ts(1b,1a),ts(2a,2b),ts(2b,2a),comts(1a,1b),comts(2a,2b)):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1b,1a),ts(2b,2a)))
+t2:=tris(cut,pl(ts(1a,2b),ts(2a,1b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1b,2a),ts(2b,1a)),compl(ts(1a,2b),ts(2a,1b)),ispl12(ts(2a,1b),ts(1b,2a),ts(1a,2b),ts(2b,1a),comts(2a,1b),comts(1a,2b))):is(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,2a),ts(2b,1a)))
+-4d194
+b@satzd194:=eqsmsd(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,1a),ts(2b,2a)),pl(ts(1b,2a),ts(2b,1a)),t1".4d194",t2".4d194"):eq(td(a,b),td(b,a))
+comtd:=satzd194:eq(td(a,b),td(b,a))
+c@[e:eq(a,b)]
++*iv4d
+e@[r:cut]
+t11:=tr3is(cut,pl(ts(1a,r),ts(2b,r)),ts(pl(1a,2b),r),ts(pl(1b,2a),r),pl(ts(1b,r),ts(2a,r)),distpt1(1a,2b,r),ists1(pl(1a,2b),pl(1b,2a),r,e),disttp1(1b,2a,r)):is(pl(ts(1a,r),ts(2b,r)),pl(ts(1b,r),ts(2a,r)))
+e@t12:=tr3is(cut,pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,2c),ts(2a,2c))),pl(pl(ts(1b,1c),ts(2a,1c)),pl(ts(1a,2c),ts(2b,2c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))),4pl24(ts(1a,1c),ts(2a,2c),ts(1b,2c),ts(2b,1c)),ispl12(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,1c),ts(2a,1c)),pl(ts(1b,2c),ts(2a,2c)),pl(ts(1a,2c),ts(2b,2c)),t11(1c),t11(b,a,c,symeq(a,b,e),2c)),4pl24(ts(1b,1c),ts(2a,1c),ts(1a,2c),ts(2b,2c))):is(pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))))
+-iv4d
+e@eqtd1:=eqi12(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)),pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)),t12".iv4d"):eq(td(a,c),td(b,c))
+eqtd2:=tr3eq(td(c,a),td(a,c),td(b,c),td(c,b),comtd(c,a),eqtd1,comtd(b,c)):eq(td(c,a),td(c,b))
+d@[e:eq(a,b)][f:eq(c,d)]
+eqtd12:=treq(td(a,c),td(b,c),td(b,d),eqtd1(a,b,c,e),eqtd2(c,d,b,f)):eq(td(a,c),td(b,d))
+b@[z:zero(a)]
++4d192
+t1:=tris(cut,pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1a,2b),ts(2a,1b)),ispl12(ts(1a,1b),ts(2a,1b),ts(2a,2b),ts(1a,2b),ists1(1a,2a,1b,z),ists1(2a,1a,2b,symis(cut,1a,2a,z))),compl(ts(2a,1b),ts(1a,2b))):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
+-4d192
+satzd192a:=zeroi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t1".4d192"):zero(td(a,b))
+b@[z:zero(b)]
+satzd192b:=eqzero(td(b,a),td(a,b),comtd(b,a),satzd192a(b,a,z)):zero(td(a,b))
+b@[z:zero(a)]
+td01:=satzd192a(z):zero(td(a,b))
+b@[z:zero(b)]
+td02:=satzd192b(z):zero(td(a,b))
+b@satzd197a:=tr3eq(td(m0d(a),b),df(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b))),df(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b))),m0d(td(a,b)),tdeq2a(b,2a,1a),eqsmsd(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b)),compl(ts(2a,1b),ts(1a,2b)),compl(ts(2a,2b),ts(1a,1b))),m0deqb(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))):eq(td(m0d(a),b),m0d(td(a,b)))
+satzd197b:=tr3eq(td(a,m0d(b)),td(m0d(b),a),m0d(td(b,a)),m0d(td(a,b)),comtd(a,m0d(b)),satzd197a(b,a),eqm0d(td(b,a),td(a,b),comtd(b,a))):eq(td(a,m0d(b)),m0d(td(a,b)))
+satzd197c:=treq2(td(m0d(a),b),td(a,m0d(b)),m0d(td(a,b)),satzd197a,satzd197b):eq(td(m0d(a),b),td(a,m0d(b)))
+satzd197d:=symeq(td(m0d(a),b),td(a,m0d(b)),satzd197c):eq(td(a,m0d(b)),td(m0d(a),b))
+satzd197e:=symeq(td(m0d(a),b),m0d(td(a,b)),satzd197a):eq(m0d(td(a,b)),td(m0d(a),b))
+satzd197f:=symeq(td(a,m0d(b)),m0d(td(a,b)),satzd197b):eq(m0d(td(a,b)),td(a,m0d(b)))
+satzd198:=treq(td(m0d(a),m0d(b)),td(a,m0d(m0d(b))),td(a,b),satzd197c(a,m0d(b)),eqtd2(m0d(m0d(b)),b,a,satzd177(b))):eq(td(m0d(a),m0d(b)),td(a,b))
+satzd198a:=symeq(td(m0d(a),m0d(b)),td(a,b),satzd198):eq(td(a,b),td(m0d(a),m0d(b)))
+[p:posd(a)][q:posd(b)]
++*iv4d
+q@[r:cut]
+t13:=tris(cut,pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,pl(mn(1b,2b,q),2b)),ts(r,1b),distpt2(r,mn(1b,2b,q),2b),ists2(pl(mn(1b,2b,q),2b),1b,r,satz140e(1b,2b,q))):is(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b))
+[s:cut]
+t14:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),s),pl(ts(r,1b),s),asspl2(ts(r,mn(1b,2b,q)),ts(r,2b),s),ispl1(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b),s,t13)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s))
+t15:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s),pl(s,ts(r,1b)),t14,compl(ts(r,1b),s)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(s,ts(r,1b)))
+q@t16:=satz135h(pl(ts(1a,2b),ts(2a,2b)),pl(ts(2a,2b),ts(1a,2b)),ts(1a,mn(1b,2b,q)),ts(2a,mn(1b,2b,q)),compl(ts(1a,2b),ts(2a,2b)),satz145a(1a,2a,mn(1b,2b,q),p)):more(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))))
+t17:=ismore12(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))),pl(ts(1a,2b),ts(2a,1b)),t14(1a,ts(2a,2b)),t15(2a,ts(1a,2b)),t16):more(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
+-iv4d
+q@ptdpp:=posdi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t17".iv4d"):posd(td(a,b))
+b@[p:posd(a)][n:negd(b)]
++*iv4d
+n@t18:=eqposd(td(a,m0d(b)),m0d(td(a,b)),satzd197b(a,b),ptdpp(a,m0d(b),p,satzd176c(b,n))):posd(m0d(td(a,b)))
+-iv4d
+n@ntdpn:=satzd176f(td(a,b),t18".iv4d"):negd(td(a,b))
+b@[n:negd(a)][p:posd(b)]
+ntdnp:=eqnegd(td(b,a),td(a,b),comtd(b,a),ntdpn(b,a,p,n)):negd(td(a,b))
+b@[n:negd(a)][o:negd(b)]
+ptdnn:=eqposd(td(m0d(a),m0d(b)),td(a,b),satzd198(a,b),ptdpp(m0d(a),m0d(b),satzd176c(a,n),satzd176c(b,o))):posd(td(a,b))
+b@[n:not(zero(a))][o:not(zero(b))]
++*4d192
+o@[p:posd(a)][q:posd(b)]
+t2:=pnot0d(td(a,b),ptdpp(a,b,p,q)):not(zero(td(a,b)))
+p@[m:negd(b)]
+t3:=nnot0d(td(a,b),ntdpn(a,b,p,m)):not(zero(td(a,b)))
+p@t4:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t2(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t3(t)):not(zero(td(a,b)))
+o@[m:negd(a)][p:posd(b)]
+t5:=nnot0d(td(a,b),ntdnp(a,b,m,p)):not(zero(td(a,b)))
+m@[l:negd(b)]
+t6:=pnot0d(td(a,b),ptdnn(a,b,m,l)):not(zero(td(a,b)))
+m@t7:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t5(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t6(t)):not(zero(td(a,b)))
+-4d192
+o@satzd192d:=rappd(a,not(zero(td(a,b))),[t:posd(a)]t4".4d192"(t),th2"l.imp"(zero(a),not(zero(td(a,b))),n),[t:negd(a)]t7".4d192"(t)):not(zero(td(a,b)))
+b@[z:zero(td(a,b))]
++*4d192
+z@[n:not(zero(a))]
+t8:=et(zero(b),th3"l.imp"(not(zero(b)),not(zero(td(a,b))),weli(zero(td(a,b)),z),[t:not(zero(b))]satzd192d(n,t))):zero(b)
+-4d192
+z@satzd192c:=[t:not(zero(a))]t8".4d192"(t):or(zero(a),zero(b))
++4d193
+b@[p:posd(a)][q:posd(b)]
+t1:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdpp(a,b,p,q))),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+p@[n:negd(b)]
+t2:=treq(absd(td(a,b)),m0d(td(a,b)),td(a,m0d(b)),absnd(td(a,b),ntdpn(a,b,p,n)),satzd197f(a,b)):eq(absd(td(a,b)),td(a,m0d(b)))
+t3:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,m0d(b)),t2,eqtd12(absd(a),a,absd(b),m0d(b),absnnd(a,pnotnd(a,p)),absnd(b,n))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[z:zero(a)]
+t4:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td01(a,b,z)),td01(absd(a),absd(b),satzd166f(a,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[z:zero(b)]
+t5:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td02(a,b,z)),td02(absd(a),absd(b),satzd166f(b,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[n:negd(a)][p:posd(b)]
+t6:=tr3eq(absd(td(a,b)),absd(td(b,a)),td(absd(b),absd(a)),td(absd(a),absd(b)),eqabsd(td(a,b),td(b,a),comtd(a,b)),t3(b,a,p,n),comtd(absd(b),absd(a))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+n@[o:negd(b)]
+t7:=treq(td(absd(a),absd(b)),td(m0d(a),m0d(b)),td(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o)),satzd198(a,b)):eq(td(absd(a),absd(b)),td(a,b))
+t8:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdnn(a,b,n,o))),t7):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[p:posd(a)]
+t9:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t1(p,t),[t:zero(b)]t5(t),[t:negd(b)]t3(p,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[n:negd(a)]
+t10:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t6(n,t),[t:zero(b)]t5(t),[t:negd(b)]t8(n,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
+-4d193
+b@satzd193:=rappd(a,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(a)]t9".4d193"(t),[t:zero(a)]t4".4d193"(t),[t:negd(a)]t10".4d193"(t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
+satzd103a:=symeq(absd(td(a,b)),td(absd(a),absd(b)),satzd193):eq(td(absd(a),absd(b)),absd(td(a,b)))
+@1df:=pdofrp(1rp):dif
++4d195
+a@t1:=tris(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(ts(1a,pl(1rp,1rp)),pl(ts(2a,1rp),2a)),pl(pl(1a,1a),pl(2a,2a)),asspl1(ts(1a,pl(1rp,1rp)),ts(2a,1rp),2a),ispl12(ts(1a,pl(1rp,1rp)),pl(1a,1a),pl(ts(2a,1rp),2a),pl(2a,2a),a2isapa(1a),ispl1(ts(2a,1rp),2a,2a,satz151(2a)))):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(pl(1a,1a),pl(2a,2a)))
+t2:=tris(cut,pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,ts(1a,1rp)),ts(2a,pl(1rp,1rp))),pl(pl(1a,1a),pl(2a,2a)),asspl2(1a,ts(1a,1rp),ts(2a,pl(1rp,1rp))),ispl12(pl(1a,ts(1a,1rp)),pl(1a,1a),ts(2a,pl(1rp,1rp)),pl(2a,2a),ispl2(ts(1a,1rp),1a,1a,satz151(1a)),a2isapa(2a))):is(pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)))
+t3:=tris2(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)),t1,t2):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))))
+-4d195
+a@satzd195:=treq(td(a,1df),df(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),a,tdeq1a(a,pl(1rp,1rp),1rp),eqi2(a,pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp))),t3".4d195")):eq(td(a,1df),a)
+satzd195a:=symeq(td(a,1df),a,satzd195):eq(a,td(a,1df))
+satzd195b:=treq(td(1df,a),td(a,1df),a,comtd(1df,a),satzd195):eq(td(1df,a),a)
+satzd195c:=symeq(td(1df,a),a,satzd195b):eq(a,td(1df,a))
+b@[p:posd(a)][q:posd(b)]
+satzd196a:=symeq(td(absd(a),absd(b)),td(a,b),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(td(a,b),td(absd(a),absd(b)))
+b@[n:negd(a)][o:negd(b)]
+satzd196b:=treq2(td(a,b),td(absd(a),absd(b)),td(m0d(a),m0d(b)),satzd198a(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o))):eq(td(a,b),td(absd(a),absd(b)))
+b@[p:posd(a)][n:negd(b)]
+satzd196c:=treq1(td(a,b),m0d(td(absd(a),absd(b))),td(absd(a),m0d(absd(b))),eqtd12(absd(a),a,m0d(absd(b)),b,absnnd(a,pnotnd(a,p)),satzd177b(absd(b),b,absnd(b,n))),satzd197b(absd(a),absd(b))):eq(td(a,b),m0d(td(absd(a),absd(b))))
+b@[n:negd(a)][p:posd(b)]
+satzd196d:=tr3eq(td(a,b),td(b,a),m0d(td(absd(b),absd(a))),m0d(td(absd(a),absd(b))),comtd(a,b),satzd196c(b,a,p,n),eqm0d(td(absd(b),absd(a)),td(absd(a),absd(b)),comtd(absd(b),absd(a)))):eq(td(a,b),m0d(td(absd(a),absd(b))))
++4d196
+b@p1p2:=and(posd(a),posd(b)):'prop'
+p1n2:=and(posd(a),negd(b)):'prop'
+n1p2:=and(negd(a),posd(b)):'prop'
+n1n2:=and(negd(a),negd(b)):'prop'
+-4d196
+b@[n:not(zero(a))][o:not(zero(b))][e:eq(td(a,b),td(absd(a),absd(b)))]
++*4d196
+o@t1:=ptdpp(absd(a),absd(b),satzd166e(a,n),satzd166e(b,o)):posd(td(absd(a),absd(b)))
+e@t2:=pnotnd(td(a,b),eqposd(td(absd(a),absd(b)),td(a,b),symeq(td(a,b),td(absd(a),absd(b)),e),t1)):not(negd(td(a,b)))
+[p:posd(a)]
+t3:=th3"l.imp"(negd(b),negd(td(a,b)),t2,[t:negd(b)]ntdpn(a,b,p,t)):not(negd(b))
+t4:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t3,o):posd(b)
+t5:=andi(posd(a),posd(b),p,t4):p1p2
+t6:=ori1(p1p2,n1n2,t5):or(p1p2,n1n2)
+e@[m:negd(a)]
+t7:=th3"l.imp"(posd(b),negd(td(a,b)),t2,[t:posd(b)]ntdnp(a,b,m,t)):not(posd(b))
+t8:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t7):negd(b)
+t9:=andi(negd(a),negd(b),m,t8):n1n2
+t10:=ori2(p1p2,n1n2,t9):or(p1p2,n1n2)
+-4d196
+e@satzd196e:=rappd(a,or(p1p2".4d196",n1n2".4d196"),[t:posd(a)]t6".4d196"(t),th2"l.imp"(zero(a),or(p1p2".4d196",n1n2".4d196"),n),[t:negd(a)]t10".4d196"(t)):or(and(posd(a),posd(b)),and(negd(a),negd(b)))
+o@[e:eq(td(a,b),m0d(td(absd(a),absd(b))))]
++*4d196
+o@t11:=satzd176a(td(absd(a),absd(b)),t1):negd(m0d(td(absd(a),absd(b))))
+e@t12:=nnotpd(td(a,b),eqnegd(m0d(td(absd(a),absd(b))),td(a,b),symeq(td(a,b),m0d(td(absd(a),absd(b))),e),t11)):not(posd(td(a,b)))
+[p:posd(a)]
+t13:=th3"l.imp"(posd(b),posd(td(a,b)),t12,[t:posd(b)]ptdpp(a,b,p,t)):not(posd(b))
+t14:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t13):negd(b)
+t15:=andi(posd(a),negd(b),p,t14):p1n2
+t16:=ori1(p1n2,n1p2,t15):or(p1n2,n1p2)
+e@[m:negd(a)]
+t17:=th3"l.imp"(negd(b),posd(td(a,b)),t12,[t:negd(b)]ptdnn(a,b,m,t)):not(negd(b))
+t18:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t17,o):posd(b)
+t19:=andi(negd(a),posd(b),m,t18):n1p2
+t20:=ori2(p1n2,n1p2,t19):or(p1n2,n1p2)
+-4d196
+e@satzd196f:=rappd(a,or(p1n2".4d196",n1p2".4d196"),[t:posd(a)]t16".4d196"(t),th2"l.imp"(zero(a),or(p1n2".4d196",n1p2".4d196"),n),[t:negd(a)]t20".4d196"(t)):or(and(posd(a),negd(b)),and(negd(a),posd(b)))
++4d199
+@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
+t1:=tris(cut,ts(pl(ts(p,r),ts(q,s)),t),pl(ts(ts(p,r),t),ts(ts(q,s),t)),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),disttp1(ts(p,r),ts(q,s),t),ispl12(ts(ts(p,r),t),ts(p,ts(r,t)),ts(ts(q,s),t),ts(q,ts(s,t)),assts1(p,r,t),assts1(q,s,t))):is(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))))
+t2:=tris(cut,pl(ts(q,ts(s,t)),ts(q,ts(r,u))),pl(ts(q,ts(r,u)),ts(q,ts(s,t))),ts(q,pl(ts(r,u),ts(s,t))),compl(ts(q,ts(s,t)),ts(q,ts(r,u))),distpt2(q,ts(r,u),ts(s,t))):is(pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))))
+t3:=tr3is(cut,pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(pl(ts(p,ts(r,t)),ts(q,ts(s,t))),pl(ts(p,ts(s,u)),ts(q,ts(r,u)))),pl(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u)))),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))),ispl12(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),ts(pl(ts(p,s),ts(q,r)),u),pl(ts(p,ts(s,u)),ts(q,ts(r,u))),t1,t1(p,q,s,r,u,t)),4pl23(ts(p,ts(r,t)),ts(q,ts(s,t)),ts(p,ts(s,u)),ts(q,ts(r,u))),ispl12(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),ts(p,pl(ts(r,t),ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))),distpt2(p,ts(r,t),ts(s,u)),t2)):is(pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))))
+-4d199
+c@satzd199:=tr3eq(td(td(a,b),c),df(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c))),df(pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c))))),td(a,td(b,c)),tdeq2a(c,pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))),eqsmsd(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c)),pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c)))),t3".4d199"(1a,2a,1b,2b,1c,2c),t3".4d199"(1a,2a,1b,2b,2c,1c)),tdeq1b(a,pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)))):eq(td(td(a,b),c),td(a,td(b,c)))
+asstd1:=satzd199:eq(td(td(a,b),c),td(a,td(b,c)))
+asstd2:=symeq(td(td(a,b),c),td(a,td(b,c)),satzd199):eq(td(a,td(b,c)),td(td(a,b),c))
++4d201
+@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
+t1:=tris(cut,pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(p,t)),pl(ts(q,s),ts(q,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))),ispl12(ts(p,pl(r,t)),pl(ts(p,r),ts(p,t)),ts(q,pl(s,u)),pl(ts(q,s),ts(q,u)),disttp2(p,r,t),disttp2(q,s,u)),4pl23(ts(p,r),ts(p,t),ts(q,s),ts(q,u))):is(pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))))
+-4d201
+satzd201:=tr3eq(td(a,pd(b,c)),df(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c)))),df(pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c)))),pd(td(a,b),td(a,c)),tdeq1a(a,pl(1b,1c),pl(2b,2c)),eqsmsd(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c))),pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c))),t1".4d201"(1a,2a,1b,2b,1c,2c),t1".4d201"(1a,2a,2b,1b,2c,1c)),pdeq12b(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)))):eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
+disttpd1:=tr3eq(td(pd(a,b),c),td(c,pd(a,b)),pd(td(c,a),td(c,b)),pd(td(a,c),td(b,c)),comtd(pd(a,b),c),satzd201(c,a,b),eqpd12(td(c,a),td(a,c),td(c,b),td(b,c),comtd(c,a),comtd(c,b))):eq(td(pd(a,b),c),pd(td(a,c),td(b,c)))
+disttpd2:=satzd201:eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
+distptd1:=symeq(td(pd(a,b),c),pd(td(a,c),td(b,c)),disttpd1):eq(pd(td(a,c),td(b,c)),td(pd(a,b),c))
+distptd2:=symeq(td(a,pd(b,c)),pd(td(a,b),td(a,c)),disttpd2):eq(pd(td(a,b),td(a,c)),td(a,pd(b,c)))
+satzd202:=treq(td(a,md(b,c)),pd(td(a,b),td(a,m0d(c))),md(td(a,b),td(a,c)),disttpd2(a,b,m0d(c)),eqpd2(td(a,m0d(c)),m0d(td(a,c)),td(a,b),satzd197b(a,c))):eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
+disttmd1:=treq(td(md(a,b),c),pd(td(a,c),td(m0d(b),c)),md(td(a,c),td(b,c)),disttpd1(a,m0d(b),c),eqpd2(td(m0d(b),c),m0d(td(b,c)),td(a,c),satzd197a(b,c))):eq(td(md(a,b),c),md(td(a,c),td(b,c)))
+disttmd2:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
+distmtd1:=symeq(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1):eq(md(td(a,c),td(b,c)),td(md(a,b),c))
+distmtd2:=symeq(td(a,md(b,c)),md(td(a,b),td(a,c)),disttmd2):eq(md(td(a,b),td(a,c)),td(a,md(b,c)))
+satzd200:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
+[m:mored(a,b)]
++4d203
+t1:=satzd182d(a,b,m):posd(md(a,b))
+-4d203
+[p:posd(c)]
++*4d203
+p@t2:=eqposd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ptdpp(md(a,b),c,t1,p)):posd(md(td(a,c),td(b,c)))
+-4d203
+p@satzd203a:=satzd182a(td(a,c),td(b,c),t2".4d203"):mored(td(a,c),td(b,c))
+m@[z:zero(c)]
+satzd203b:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
+m@[n:negd(c)]
++*4d203
+n@t3:=eqnegd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ntdpn(md(a,b),c,t1,n)):negd(md(td(a,c),td(b,c)))
+-4d203
+n@satzd203c:=satzd182c(td(a,c),td(b,c),t3".4d203"):lessd(td(a,c),td(b,c))
+p@satzd203d:=eqmored12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203a):mored(td(c,a),td(c,b))
+z@satzd203e:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
+n@satzd203f:=eqlessd12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203c):lessd(td(c,a),td(c,b))
+c@[l:lessd(a,b)][p:posd(c)]
+satzd203g:=lemmad5(td(b,c),td(a,c),satzd203a(b,a,c,lemmad6(a,b,l),p)):lessd(td(a,c),td(b,c))
+l@[z:zero(c)]
+satzd203h:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
+l@[n:negd(c)]
+satzd203j:=lemmad6(td(b,c),td(a,c),satzd203c(b,a,c,lemmad6(a,b,l),n)):mored(td(a,c),td(b,c))
+p@satzd203k:=lemmad5(td(c,b),td(c,a),satzd203d(b,a,c,lemmad6(a,b,l),p)):lessd(td(c,a),td(c,b))
+z@satzd203l:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
+n@satzd203m:=lemmad6(td(c,b),td(c,a),satzd203f(b,a,c,lemmad6(a,b,l),n)):mored(td(c,a),td(c,b))
++*iv4d
+@[p:cut][q:cut]
+t19:=tris(cut,ts(q,pl(p,1rp)),pl(ts(q,p),ts(q,1rp)),pl(ts(q,p),q),disttp2(q,p,1rp),ispl2(ts(q,1rp),q,ts(q,p),satz151(q))):is(ts(q,pl(p,1rp)),pl(ts(q,p),q))
+[r:cut]
+t20:=tris(cut,pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(pl(ts(q,p),q),r),pl(ts(q,p),pl(q,r)),ispl12(ts(q,pl(p,1rp)),pl(ts(q,p),q),ts(r,1rp),r,t19,satz151(r)),asspl1(ts(q,p),q,r)):is(pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)))
+t21:=tr3is(cut,pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)),pl(ts(q,p),pl(r,q)),compl(ts(r,1rp),ts(q,pl(p,1rp))),t20,ispl2(pl(q,r),pl(r,q),ts(q,p),compl(q,r))):is(pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,p),pl(r,q)))
+a@[p:posd(a)]
+arp:=rpofpd(a,p):cut
+arpi:=ov(1rp,arp):cut
+ai:=pdofrp(arpi):dif
+t22:=tr3eq(td(a,ai),df(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp)))),df(pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a))),df(ts(1a,arpi),ts(2a,arpi)),tdeq1a(a,pl(arpi,1rp),1rp),eqsmsd(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp))),pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a)),t20(arpi,1a,2a),t21(arpi,2a,1a)),lemmad2(ts(1a,arpi),ts(2a,arpi),pl(1a,2a))):eq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)))
+t23:=tr3is(cut,ts(1a,arpi),ts(pl(2a,arp),arpi),pl(ts(2a,arpi),ts(arp,arpi)),pl(ts(2a,arpi),1rp),ists1(1a,pl(2a,arp),arpi,satz140d(1a,2a,p)),disttp1(2a,arp,arpi),ispl2(ts(arp,arpi),1rp,ts(2a,arpi),satz153c(1rp,arp))):is(ts(1a,arpi),pl(ts(2a,arpi),1rp))
+t24:=tr3is(cut,pl(ts(1a,arpi),1rp),pl(pl(ts(2a,arpi),1rp),1rp),pl(ts(2a,arpi),pl(1rp,1rp)),pl(pl(1rp,1rp),ts(2a,arpi)),ispl1(ts(1a,arpi),pl(ts(2a,arpi),1rp),1rp,t23),asspl1(ts(2a,arpi),1rp,1rp),compl(ts(2a,arpi),pl(1rp,1rp))):is(pl(ts(1a,arpi),1rp),pl(pl(1rp,1rp),ts(2a,arpi)))
+t25:=eqi12(ts(1a,arpi),ts(2a,arpi),pl(1rp,1rp),1rp,t24):eq(df(ts(1a,arpi),ts(2a,arpi)),1df)
+t26:=treq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)),1df,t22,t25):eq(td(a,ai),1df)
+t27:=somei(dif,[x:dif]eq(td(a,x),1df),ai,t26):some"l"(dif,[x:dif]eq(td(a,x),1df))
+a@[n:negd(a)]
+t28:=satzd176c(a,n):posd(m0d(a))
+[h:dif][e:eq(td(m0d(a),h),1df)]
+t29:=treq(td(a,m0d(h)),td(m0d(a),h),1df,satzd197d(a,h),e):eq(td(a,m0d(h)),1df)
+t30:=somei(dif,[x:dif]eq(td(a,x),1df),m0d(h),t29):some"l"(dif,[x:dif]eq(td(a,x),1df))
+n@t31:=someapp(dif,[x:dif]eq(td(m0d(a),x),1df),t27(m0d(a),t28),some"l"(dif,[x:dif]eq(td(a,x),1df)),[x:dif][t:eq(td(m0d(a),x),1df)]t30(x,t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
+-iv4d
+a@[n:not(zero(a))]
+lemmad7:=rappd(a,some"l"(dif,[x:dif]eq(td(a,x),1df)),[t:posd(a)]t27".iv4d"(t),th2"l.imp"(zero(a),some"l"(dif,[x:dif]eq(td(a,x),1df)),n),[t:negd(a)]t31".iv4d"(t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
+b@[n:not(zero(b))][h:dif][k:dif][e:eq(td(b,h),a)][f:eq(td(b,k),a)]
++4d204
+t1:=treq2(td(b,h),td(b,k),a,e,f):eq(td(b,h),td(b,k))
+t2:=eqzero(md(td(b,h),td(b,k)),td(b,md(h,k)),distmtd2(b,h,k),satzd182e(td(b,h),td(b,k),t1)):zero(td(b,md(h,k)))
+t3:=ore2(zero(b),zero(md(h,k)),satzd192c(b,md(h,k),t2),n):zero(md(h,k))
+-4d204
+satzd204b:=satzd182b(h,k,t3".4d204"):eq(h,k)
++*4d204
+n@[h:dif][e:eq(td(b,h),1df)]
+t4:=tr3eq(td(b,td(h,a)),td(td(b,h),a),td(1df,a),a,asstd2(b,h,a),eqtd1(td(b,h),1df,a,e),satzd195b(a)):eq(td(b,td(h,a)),a)
+t5:=somei(dif,[x:dif]eq(td(b,x),a),td(h,a),t4):some"l"(dif,[x:dif]eq(td(b,x),a))
+-4d204
+n@satzd204a:=someapp(dif,[x:dif]eq(td(b,x),1df),lemmad7(b,n),some"l"(dif,[x:dif]eq(td(b,x),a)),[x:dif][t:eq(td(b,x),1df)]t5".4d204"(x,t)):some"l"(dif,[x:dif]eq(td(b,x),a))
+@[r:cut][s:cut][m:more(r,s)]
++iv5d
+t1:=ismore12(pl(r,pl(1rp,1rp)),pl(pl(r,1rp),1rp),pl(s,pl(1rp,1rp)),pl(pl(s,1rp),1rp),asspl2(r,1rp,1rp),asspl2(s,1rp,1rp),satz134(r,s,pl(1rp,1rp),m)):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
+-iv5d
+morerpepd:=moredi12(pl(r,1rp),1rp,pl(s,1rp),1rp,t1".iv5d"):mored(pdofrp(r),pdofrp(s))
+s@[m:mored(pdofrp(r),pdofrp(s))]
++*iv5d
+m@t2:=morede12(pl(r,1rp),1rp,pl(s,1rp),1rp,m):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
+-iv5d
+m@morerpipd:=satz136a(r,s,pl(1rp,1rp),ismore12(pl(pl(r,1rp),1rp),pl(r,pl(1rp,1rp)),pl(pl(s,1rp),1rp),pl(s,pl(1rp,1rp)),asspl1(r,1rp,1rp),asspl1(s,1rp,1rp),t2".iv5d")):more(r,s)
+s@[l:less(r,s)]
+lessrpepd:=lemmad5(pdofrp(s),pdofrp(r),morerpepd(s,r,satz122(r,s,l))):lessd(pdofrp(r),pdofrp(s))
+s@[l:lessd(pdofrp(r),pdofrp(s))]
+lessrpipd:=satz121(s,r,morerpipd(s,r,lemmad6(pdofrp(r),pdofrp(s),l))):less(r,s)
++*iv5d
+@i:=1rp:cut
+2:=pl(i,i):cut
+r@rp1:=pl(r,i):cut
+s@sp1:=pl(s,i):cut
+rps:=pl(r,s):cut
+rs:=ts(r,s):cut
+t3:=tris(cut,pl(pl(rp1,sp1),i),pl(pl(rps,2),i),pl(pl(rps,i),2),ispl1(pl(rp1,sp1),pl(rps,2),i,4pl23(r,i,s,i)),3pl23(rps,2,i)):is(pl(pl(rp1,sp1),i),pl(pl(rps,i),2))
+t4:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(rp1,sp1),2),pdofrp(rps),pdeq12a(rp1,i,sp1,i),eqi12(pl(rp1,sp1),2,pl(rps,i),i,t3)):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(rps))
+-iv5d
+s@lemmad8:=t4".iv5d":eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
++*iv5d
+s@t5:=tris(cut,ts(r,sp1),pl(rs,ts(r,i)),pl(rs,r),disttp2(r,s,i),ispl2(ts(r,i),r,rs,satz151(r))):is(ts(r,sp1),pl(rs,r))
+t6:=tr4is(cut,ts(rp1,sp1),pl(ts(r,sp1),ts(i,sp1)),pl(pl(rs,r),sp1),pl(pl(pl(rs,r),s),i),pl(pl(rs,rps),i),disttp1(r,i,sp1),ispl12(ts(r,sp1),pl(rs,r),ts(i,sp1),sp1,t5,satz151b(sp1)),asspl2(pl(rs,r),s,i),ispl1(pl(pl(rs,r),s),pl(rs,rps),i,asspl1(rs,r,s))):is(ts(rp1,sp1),pl(pl(rs,rps),i))
+t7:=tr3is(cut,pl(ts(rp1,sp1),ts(i,i)),pl(pl(pl(rs,rps),i),i),pl(pl(rs,rps),2),pl(rs,pl(rps,2)),ispl12(ts(rp1,sp1),pl(pl(rs,rps),i),ts(i,i),i,t6,satz151(i)),asspl1(pl(rs,rps),i,i),asspl1(rs,rps,2)):is(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)))
+t8:=tris(cut,pl(ts(rp1,i),ts(i,sp1)),pl(rp1,sp1),pl(rps,2),ispl12(ts(rp1,i),rp1,ts(i,sp1),sp1,satz151(rp1),satz151b(sp1)),4pl23(r,i,s,i)):is(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2))
+t9:=tris(cut,pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,i),pl(rps,2)),pl(pl(rs,pl(rps,2)),i),ispl2(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2),pl(rs,i),t8),3pl23(rs,i,pl(rps,2))):is(pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i))
+t10:=tris2(cut,pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i),ispl1(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)),i,t7),t9):is(pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))))
+t11:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1))),pdofrp(rs),tdeq12a(rp1,i,sp1,i),eqi12(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1)),pl(rs,i),i,t10)):eq(td(pdofrp(r),pdofrp(s)),pdofrp(rs))
+-iv5d
+s@lemmad9:=t11".iv5d":eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
+@[r:cut][s0:set(cut)]
+in:=esti(cut,r,s0):'prop'
+@[s0:set(cut)][t0:set(cut)][p0:all([x:cut]or(in(x,s0),in(x,t0)))][p1a:nonempty(cut,s0)][p1b:nonempty(cut,t0)][p2:all([x:cut][t:in(x,s0)]all([y:cut][u:in(y,t0)]less(x,y)))]
++5p205
+t0@[r:cut]
+prop1:=all([x:cut][t:less(x,r)]in(x,s0)):'prop'
+prop2:=all([x:cut][t:more(x,r)]in(x,t0)):'prop'
+prop3:=and(prop1,prop2):'prop'
+p2@[r1:cut][r2:cut][pr1:prop3(r1)][pr2:prop3(r2)]
+t1:=ande2(prop1(r1),prop2(r1),pr1):prop2(r1)
+t2:=ande1(prop1(r2),prop2(r2),pr2):prop1(r2)
+[l:less(r1,r2)][x0:rat]
+rx:=rpofrt(x0):cut
+[l1:less(r1,rx)][l2:less(rx,r2)]
+t3:=<l2><rx>t2:in(rx,s0)
+t4:=<satz122(r1,rx,l1)><rx>t1:in(rx,t0)
+t5:=<refis(cut,rx)>ec3e31(is(rx,rx),more(rx,rx),less(rx,rx),satz123b(rx,rx),<t4><rx><t3><rx>p2):con
+l@t6:=satz159app(r1,r2,l,con,[x:rat][t:less(r1,rpofrt(x))][u:less(rpofrt(x),r2)]t5(x,t,u)):con
+pr2@t7:=[t:less(r1,r2)]t6(t):not(less(r1,r2))
+t8:=[t:more(r1,r2)]t6(r2,r1,pr2,pr1,satz121(r1,r2,t)):not(more(r1,r2))
+t9:=or3e1(is(r1,r2),more(r1,r2),less(r1,r2),satz123a(r1,r2),t8,t7):is(r1,r2)
+p2@t10:=[x:cut][y:cut][t:prop3(x)][u:prop3(y)]t9(x,y,t,u):amone(cut,[x:cut]prop3(x))
+[x0:rat]
+schnittprop:=some([y:cut]and(in(y,s0),lrt(y,x0))):'prop'
+p2@schnittset:=setof(rat,[x:rat]schnittprop(x)):set(rat)
+[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)]
+t11:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
+t12:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t11):schnittprop(x0)
+t13:=estii(rat,[x:rat]schnittprop(x),x0,t12):in"rt"(x0,schnittset)
+r@[i:in(r,t0)][x0:rat][ux:urt(r,x0)][s:cut][j:in(s,s0)]
+t14:=satz122(s,r,<i><r><j><s>p2):more(r,s)
+t15:=satz158b(r,x0,ux):moreis(rpofrt(x0),r)
+t16:=moreisi1(rpofrt(x0),s,satz127c(rpofrt(x0),r,s,t15,t14)):moreis(rpofrt(x0),s)
+t17:=satz158d(s,x0,t16):urt(s,x0)
+s@t18:=weli(ec(in(s,s0),lrt(s,x0)),[t:in(s,s0)]t17(t)):not(and(in(s,s0),lrt(s,x0)))
+ux@t19:=th5"l.some"(cut,[y:cut]and(in(y,s0),lrt(y,x0)),[y:cut]t18(y)):not(schnittprop(x0))
+t20:=th3"l.imp"(in"rt"(x0,schnittset),schnittprop(x0),t19,[t:in"rt"(x0,schnittset)]estie(rat,[x:rat]schnittprop(x),x0,t)):not(in"rt"(x0,schnittset))
+p2@[x0:rat][i:in"rt"(x0,schnittset)][y0:rat][l:less"rt"(y0,x0)]
+i@t21:=estie(rat,[x:rat]schnittprop(x),x0,i):schnittprop(x0)
+l@[r:cut][a:and(in(r,s0),lrt(r,x0))]
+t22:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
+t23:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
+t24:=satz120(r,x0,t23,y0,l):lrt(r,y0)
+t25:=andi(in(r,s0),lrt(r,y0),t22,t24):and(in(r,s0),lrt(r,y0))
+t26:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t25):schnittprop(y0)
+l@t27:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,schnittprop(y0),[y:cut][r:and(in(y,s0),lrt(y,x0))]t26(y,r)):schnittprop(y0)
+t28:=estii(rat,[x:rat]schnittprop(x),y0,t27):in"rt"(y0,schnittset)
+i@[r:cut][a:and(in(r,s0),lrt(r,x0))]
+t29:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
+t30:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
+[y0:rat][ly:lrt(r,y0)][l:less"rt"(x0,y0)]
+t31:=andi(in(r,s0),lrt(r,y0),t29,ly):and(in(r,s0),lrt(r,y0))
+t32:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t31):schnittprop(y0)
+t33:=estii(rat,[x:rat]schnittprop(x),y0,t32):in"rt"(y0,schnittset)
+t34:=satz83(x0,y0,l):more"rt"(y0,x0)
+t35:=andi(in"rt"(y0,schnittset),more"rt"(y0,x0),t33,t34):and(in"rt"(y0,schnittset),more"rt"(y0,x0))
+t36:=somei(rat,[y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)),y0,t35):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
+a@t37:=cutapp3(r,x0,t30,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:rat][t:lrt(r,y)][u:less"rt"(x0,y)]t36(y,t,u)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
+i@t38:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:cut][t:and(in(y,s0),lrt(y,x0))]t37(y,t)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
+p2@[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)][s:cut][j:in(s,t0)][y0:rat][uy:urt(s,y0)]
+t39:=cut2(schnittset,x0,t13(r,i,x0,lx),y0,t20(s,j,y0,uy),[x:rat][t:in"rt"(x,schnittset)][y:rat][u:less"rt"(y,x)]t28(x,t,y,u),[x:rat][t:in"rt"(x,schnittset)]t38(x,t)):cutprop(schnittset)
+j@t40:=cutapp1b(s,cutprop(schnittset),[x:rat][t:urt(s,x)]t39(x,t)):cutprop(schnittset)
+lx@t41:=nonemptyapp(cut,t0,p1b,cutprop(schnittset),[y:cut][t:in(y,t0)]t40(y,t)):cutprop(schnittset)
+i@t42:=cutapp1a(r,cutprop(schnittset),[x:rat][t:lrt(r,x)]t41(x,t)):cutprop(schnittset)
+p2@t43:=nonemptyapp(cut,s0,p1a,cutprop(schnittset),[y:cut][t:in(y,s0)]t42(y,t)):cutprop(schnittset)
+snt:=cutof(schnittset,t43):cut
+[r:cut][l:less(r,snt)][x0:rat][ux:urt(r,x0)][lx:lrt(snt,x0)]
+t44:=ini(schnittset,t43,x0,lx):in"rt"(x0,schnittset)
+t45:=estie(rat,[x:rat]schnittprop(x),x0,t44):schnittprop(x0)
+[s:cut][a:and(in(s,s0),lrt(s,x0))]
+t46:=ande1(in(s,s0),lrt(s,x0),a):in(s,s0)
+t47:=ande2(in(s,s0),lrt(s,x0),a):lrt(s,x0)
+t48:=andi(urt(r,x0),lrt(s,x0),ux,t47):and(urt(r,x0),lrt(s,x0))
+t49:=somei(rat,[x:rat]and(urt(r,x),lrt(s,x)),x0,t48):less(r,s)
+t50:=ec3e23(is(s,r),more(s,r),less(s,r),satz123b(s,r),satz122(r,s,t49)):not(less(s,r))
+t51:=th3"l.imp"(in(r,t0),less(s,r),t50,<r><t46><s>p2):not(in(r,t0))
+t52:=ore1(in(r,s0),in(r,t0),<r>p0,t51):in(r,s0)
+lx@t53:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t45,in(r,s0),[y:cut][t:and(in(y,s0),lrt(y,x0))]t52(y,t)):in(r,s0)
+l@t54:=lessapp(r,snt,l,in(r,s0),[x:rat][t:urt(r,x)][u:lrt(snt,x)]t53(x,t,u)):in(r,s0)
+r@[m:more(r,snt)][x0:rat][lx:lrt(r,x0)][ux:urt(snt,x0)][i:in(r,s0)]
+t55:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
+t56:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t55):schnittprop(x0)
+t57:=estii(rat,[x:rat]schnittprop(x),x0,t56):in"rt"(x0,schnittset)
+t58:=ine(schnittset,t43,x0,t57):lrt(snt,x0)
+ux@t59:=th3"l.imp"(in(r,s0),lrt(snt,x0),ux,[t:in(r,s0)]t58(t)):not(in(r,s0))
+t60:=ore2(in(r,s0),in(r,t0),<r>p0,t59):in(r,t0)
+m@t61:=moreapp(r,snt,m,in(r,t0),[x:rat][t:lrt(r,x)][u:urt(snt,x)]t60(x,t,u)):in(r,t0)
+p2@t62:=andi(prop1(snt),prop2(snt),[x:cut][t:less(x,snt)]t54(x,t),[x:cut][t:more(x,snt)]t61(x,t)):prop3(snt)
+t63:=somei(cut,[x:cut]prop3(x),snt,t62):some([x:cut]prop3(x))
+-5p205
+satzp205:=onei(cut,[x:cut]prop3".5p205"(x),t10".5p205",t63".5p205"):one([x:cut]and(all([y:cut][t:less(y,x)]in(y,s0)),all([y:cut][t:more(y,x)]in(y,t0))))
+schnitt:=ind(cut,[x:cut]prop3".5p205"(x),satzp205):cut
+satzp205a:=ande1(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:less(x,schnitt)]in(x,s0))
+satzp205b:=ande2(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:more(x,schnitt)]in(x,t0))
+@[r:cut][s:cut]
++ivad
+@i:=1rp:cut
+r@r1:=pl(r,i):cut
+s@s1:=pl(s,i):cut
+rps:=pl(r,s):cut
+@2:=pl(i,i):cut
+s@t1:=pdeq12a(r1,i,s1,i):eq(pd(pdofrp(r),pdofrp(s)),df(pl(r1,s1),2))
+t2:=tris(cut,pl(r1,s1),pl(rps,2),pl(pl(rps,i),i),4pl23(r,i,s,i),asspl2(rps,i,i)):is(pl(r1,s1),pl(pl(rps,i),i))
+t3:=ispl1(pl(r1,s1),pl(pl(rps,i),i),i,t2):is(pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i))
+t4:=tris(cut,pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i),pl(pl(rps,i),2),t3,asspl1(pl(rps,i),i,i)):is(pl(pl(r1,s1),i),pl(pl(rps,i),2))
+t5:=eqi12(pl(r1,s1),2,pl(rps,i),i,t4):eq(df(pl(r1,s1),2),pdofrp(rps))
+-ivad
+lemmaivad1:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(pl(r,1rp),pl(s,1rp)),pl(1rp,1rp)),pdofrp(pl(r,s)),t1".ivad",t5".ivad"):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
++*ivad
+s@rs:=ts(r,s):cut
+t6:=tdeq12a(r1,i,s1,i):eq(td(pdofrp(r),pdofrp(s)),df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))))
+t7:=tris(cut,ts(r1,s),pl(rs,ts(i,s)),pl(rs,s),disttp1(r,i,s),ispl2(ts(i,s),s,rs,satz151b(s))):is(ts(r1,s),pl(rs,s))
+t8:=tr3is(cut,ts(r1,s1),pl(ts(r1,s),ts(r1,i)),pl(pl(rs,s),r1),pl(pl(rs,i),rps),disttp2(r1,s,i),ispl12(ts(r1,s),pl(rs,s),ts(r1,i),r1,t7,satz151(r1)),4pl24(rs,s,r,i)):is(ts(r1,s1),pl(pl(rs,i),rps))
+t9:=tris(cut,pl(ts(r1,s1),ts(i,i)),pl(pl(pl(rs,i),rps),i),pl(pl(rs,i),pl(rps,i)),ispl12(ts(r1,s1),pl(pl(rs,i),rps),ts(i,i),i,t8,satz151(i)),asspl1(pl(rs,i),rps,i)):is(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)))
+t10:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(pl(rs,i),pl(rps,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),ispl1(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)),i,t9),asspl1(pl(rs,i),pl(rps,i),i)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)))
+t11:=tr3is(cut,pl(pl(rps,i),i),pl(rps,2),pl(r1,s1),pl(ts(r1,i),ts(i,s1)),asspl1(rps,i,i),4pl23(r,s,i,i),ispl12(r1,ts(r1,i),s1,ts(i,s1),satz151a(r1),satz151c(s1))):is(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)))
+t12:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))),t10,ispl2(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)),pl(rs,i),t11)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))))
+t13:=eqi12(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1)),pl(rs,i),i,t12):eq(df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))),pdofrp(rs))
+-ivad
+s@lemmaivad2:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(pl(r,1rp),pl(s,1rp)),ts(1rp,1rp)),pl(ts(pl(r,1rp),1rp),ts(1rp,pl(s,1rp)))),pdofrp(ts(r,s)),t6".ivad",t13".ivad"):eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
+[m:mored(pdofrp(r),pdofrp(s))]
++*ivad
+m@t14:=morede12(r1,i,s1,i,m):more(pl(r1,i),pl(s1,i))
+t15:=satz136a(r1,s1,i,t14):more(r1,s1)
+-ivad
+m@lemmaivad3:=satz136a(r,s,1rp,t15".ivad"):more(r,s)
+@[c:dif][a:dif][b:dif][n:not(negd(a))][o:not(negd(b))][e:eq(td(a,a),c)][f:eq(td(b,b),c)]
++d161
+t1:=treq2(td(a,a),td(b,b),c,e,f):eq(td(a,a),td(b,b))
+t2:=treq(pd(md(td(a,a),td(a,b)),td(b,a)),pd(md(td(a,a),td(a,b)),td(a,b)),td(a,a),eqpd2(td(b,a),td(a,b),md(td(a,a),td(a,b)),comtd(b,a)),pdmd(td(a,a),td(a,b))):eq(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a))
+t3:=tr4eq(td(pd(a,b),md(a,b)),pd(td(a,md(a,b)),td(b,md(a,b))),pd(md(td(a,a),td(a,b)),md(td(b,a),td(b,b))),md(pd(md(td(a,a),td(a,b)),td(b,a)),td(b,b)),md(td(a,a),td(b,b)),disttpd1(a,b,md(a,b)),eqpd12(td(a,md(a,b)),md(td(a,a),td(a,b)),td(b,md(a,b)),md(td(b,a),td(b,b)),disttmd2(a,a,b),disttmd2(b,a,b)),asspd2(md(td(a,a),td(a,b)),td(b,a),m0d(td(b,b))),eqmd1(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a),td(b,b),t2)):eq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)))
+t4:=eqzero(md(td(a,a),td(b,b)),td(pd(a,b),md(a,b)),symeq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)),t3),satzd182e(td(a,a),td(b,b),t1)):zero(td(pd(a,b),md(a,b)))
+t5:=satzd192c(pd(a,b),md(a,b),t4):or(zero(pd(a,b)),zero(md(a,b)))
+[z:zero(a)]
+t6:=eqzero(td(a,a),td(b,b),t1,td01(a,a,z)):zero(td(b,b))
+t7:=th1"l.imp"(zero(b),zero(b),refimp(zero(b)),satzd192c(b,b,t6)):zero(b)
+t8:=zeroeq(a,b,z,t7):eq(a,b)
+f@[p:not(zero(a))]
+t9:=or3e2(zero(a),posd(a),negd(a),axrdo(a),n,p):posd(a)
+t10:=th3"l.imp"(zero(b),zero(a),p,[t:zero(b)]t7(b,a,o,n,f,e,t)):not(zero(b))
+t11:=t9(b,a,o,n,f,e,t10):posd(b)
+t12:=pnot0d(pd(a,b),ppd(a,b,t9,t11)):not(zero(pd(a,b)))
+t13:=ore2(zero(pd(a,b)),zero(md(a,b)),t5,t12):zero(md(a,b))
+t14:=satzd182b(a,b,t13):eq(a,b)
+-d161
+satzd161b:=th1"l.imp"(zero(a),eq(a,b),[t:zero(a)]t8".d161"(t),[t:not(zero(a))]t14".d161"(t)):eq(a,b)
+c@[n:not(negd(c))]
++*d161
+n@[z:zero(c)]
+t15:=zeroeq(td(c,c),c,td01(c,c,z),z):eq(td(c,c),c)
+t16:=andi(not(negd(c)),eq(td(c,c),c),n,t15):and(not(negd(c)),eq(td(c,c),c))
+t17:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),c,t16):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
+n@[o:not(zero(c))]
+t18:=or3e2(zero(c),posd(c),negd(c),axrdo(c),n,o):posd(c)
+crp:=rpofpd(c,t18):cut
+srp:=sqrt(crp):cut
+s:=pdofrp(srp):dif
+t19:=tr3eq(td(s,s),pdofrp(ts(srp,srp)),pdofrp(crp),c,lemmaivad2(srp,srp),isrpepd(ts(srp,srp),crp,thsqrt1(crp)),eqpdrp2(c,t18)):eq(td(s,s),c)
+t20:=andi(not(negd(s)),eq(td(s,s),c),pnotnd(s,posdirp(srp)),t19):and(not(negd(s)),eq(td(s,s),c))
+t21:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),s,t20):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
+-d161
+n@satzd161a:=th1"l.imp"(zero(c),some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c))),[t:zero(c)]t17".d161"(t),[t:not(zero(c))]t21".d161"(t)):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
+@[a:dif][i:intd(a)]
++intd
+[z:zero(a)]
+t1:=ori1(zero(absd(a)),natd(absd(absd(a))),satzd166f(a,z)):intd(absd(a))
+i@[n:natd(absd(a))]
+t2:=natintd(absd(a),n):intd(absd(a))
+-intd
+intabsd:=orapp(zero(a),natd(absd(a)),intd(absd(a)),i,[t:zero(a)]t1".intd"(t),[t:natd(absd(a))]t2".intd"(t)):intd(absd(a))
++*intd
+n@t4:=eqnatd(absd(a),absd(m0d(a)),satzd178a(a),n):natd(absd(m0d(a)))
+-intd
+i@intm0d:=th9"l.or"(zero(a),natd(absd(a)),zero(m0d(a)),natd(absd(m0d(a))),i,[t:zero(a)]satzd176b(a,t),[t:natd(absd(a))]t4".intd"(t)):intd(m0d(a))
+a@[b:dif][i:intd(a)][j:intd(b)]
++*intd
+j@[z:zero(a)]
+t5:=symeq(pd(a,b),b,pd01(a,b,z)):eq(b,pd(a,b))
+t6:=eqintd(b,pd(a,b),t5,j):intd(pd(a,b))
+j@[z:zero(b)]
+t7:=symeq(pd(a,b),a,pd02(a,b,z)):eq(a,pd(a,b))
+t8:=eqintd(a,pd(a,b),t7,i):intd(pd(a,b))
+a@[i:intd(a)][p:posd(a)]
+t9:=<p>ande2(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),posintnatd(a,p,i)):natrp(rpofpd(a,p))
+j@[pp:posd(pd(a,b))]
+apb1:=rpofpd(pd(a,b),pp):cut
+[p:posd(a)]
+a1:=rpofpd(a,p):cut
+[q:posd(b)]
+b1:=rpofpd(b,q):cut
+t10:=natpl(a1,t9(a,i,p),b1,t9(b,j,q)):natrp(pl(a1,b1))
+t11:=eqpd12(a,pdofrp(a1),b,pdofrp(b1),eqpdrp1(a,p),eqpdrp1(b,q)):eq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)))
+t12:=treq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)),pdofrp(pl(a1,b1)),t11,lemmaivad1(a1,b1)):eq(pd(a,b),pdofrp(pl(a1,b1)))
+t13:=tris(cut,apb1,rpofpd(pdofrp(pl(a1,b1)),posdirp(pl(a1,b1))),pl(a1,b1),eqpderp(pd(a,b),pp,pdofrp(pl(a1,b1)),posdirp(pl(a1,b1)),t12),isrppd2(pl(a1,b1))):is(apb1,pl(a1,b1))
+t14:=isp1(cut,[t:cut]natrp(t),pl(a1,b1),apb1,t10,t13):natrp(apb1)
+t15:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t14(t,p,q)):natd(pd(a,b))
+t16:=natintd(pd(a,b),t15):intd(pd(a,b))
+p@[n:negd(b)]
+t17:=satzd176c(b,n):posd(m0d(b))
+b2:=rpofpd(m0d(b),t17):cut
+t18:=eqpd2(b,m0d(m0d(b)),a,satzd177a(b)):eq(pd(a,b),md(a,m0d(b)))
+t19:=eqposd(pd(a,b),md(a,m0d(b)),t18,pp):posd(md(a,m0d(b)))
+t20:=satzd182a(a,m0d(b),t19):mored(a,m0d(b))
+t21:=eqmored12(a,pdofrp(a1),m0d(b),pdofrp(b2),eqpdrp1(a,p),eqpdrp1(m0d(b),t17),t20):mored(pdofrp(a1),pdofrp(b2))
+t22:=lemmaivad3(a1,b2,t21):more(a1,b2)
+t23:=natmn(a1,t9(a,i,p),b2,t9(m0d(b),intm0d(b,j),t17),t22):natrp(mn(a1,b2,t22))
+t24:=eqpd12(m0d(b),pdofrp(b2),pd(a,b),pdofrp(apb1),eqpdrp1(m0d(b),t17),eqpdrp1(pd(a,b),pp)):eq(pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)))
+t25:=tr4eq(a,md(pd(a,b),b),pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)),pdofrp(pl(b2,apb1)),symeq(md(pd(a,b),b),a,mdpd(a,b)),compd(pd(a,b),m0d(b)),t24,lemmaivad1(b2,apb1)):eq(a,pdofrp(pl(b2,apb1)))
+t26:=tris2(cut,pl(b2,apb1),a1,rpofpd(pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1))),isrppd1(pl(b2,apb1)),eqpderp(a,p,pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1)),t25)):is(pl(b2,apb1),a1)
+t27:=satz140g(a1,b2,apb1,t22,t26):is(apb1,mn(a1,b2,t22))
+t28:=isp1(cut,[t:cut]natrp(t),mn(a1,b2,t22),apb1,t23,t27):natrp(apb1)
+t29:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t28(t,p,n)):natd(pd(a,b))
+t30:=natintd(pd(a,b),t29):intd(pd(a,b))
+p@t31:=rappd(b,intd(pd(a,b)),[t:posd(b)]t16(t),[t:zero(b)]t8(t),[t:negd(b)]t30(t)):intd(pd(a,b))
+pp@[n:negd(a)]
+t31a:=th3"l.imp"(negd(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:negd(b)]npd(a,b,n,t)):not(negd(b))
+t32:=th3"l.imp"(zero(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:zero(b)]eqnegd(a,pd(a,b),symeq(pd(a,b),a,pd02(a,b,t)),n)):not(zero(b))
+t33:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t31a,t32):posd(b)
+t34:=eqposd(pd(a,b),pd(b,a),compd(a,b),pp):posd(pd(b,a))
+t35:=t30(b,a,j,i,t34,t33,n):intd(pd(b,a))
+t36:=eqintd(pd(b,a),pd(a,b),compd(b,a),t35):intd(pd(a,b))
+pp@t37:=rappd(a,intd(pd(a,b)),[t:posd(a)]t31(t),[t:zero(a)]t6(t),[t:negd(a)]t36(t)):intd(pd(a,b))
+j@[0p:zero(pd(a,b))]
+t38:=intdi0(pd(a,b),0p):intd(pd(a,b))
+j@[np:negd(pd(a,b))]
+t39:=satzd176c(pd(a,b),np):posd(m0d(pd(a,b)))
+t40:=eqposd(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180(a,b),t39):posd(pd(m0d(a),m0d(b)))
+t41:=t37(m0d(a),m0d(b),intm0d(a,i),intm0d(b,j),t40):intd(pd(m0d(a),m0d(b)))
+t42:=eqintd(pd(m0d(a),m0d(b)),m0d(pd(a,b)),satzd180a(a,b),t41):intd(m0d(pd(a,b)))
+t43:=intm0d(m0d(pd(a,b)),t42):intd(m0d(m0d(pd(a,b))))
+t44:=eqintd(m0d(m0d(pd(a,b))),pd(a,b),satzd177(pd(a,b)),t43):intd(pd(a,b))
+-intd
+j@intpd:=rappd(pd(a,b),intd(pd(a,b)),[t:posd(pd(a,b))]t37".intd"(t),[t:zero(pd(a,b))]t38".intd"(t),[t:negd(pd(a,b))]t44".intd"(t)):intd(pd(a,b))
+intmd:=intpd(a,m0d(b),i,intm0d(b,j)):intd(md(a,b))
++*intd
+j@[n:not(zero(td(a,b)))]
+t45:=th3"l.imp"(zero(a),zero(td(a,b)),n,[t:zero(a)]td01(a,b,t)):not(zero(a))
+t46:=th3"l.imp"(zero(b),zero(td(a,b)),n,[t:zero(b)]td02(a,b,t)):not(zero(b))
+t47:=satzd166e(a,t45):posd(absd(a))
+a3:=rpofpd(absd(a),t47):cut
+t48:=satzd166e(b,t46):posd(absd(b))
+b3:=rpofpd(absd(b),t48):cut
+t49:=natts(a3,t9(absd(a),intabsd(a,i),t47),b3,t9(absd(b),intabsd(b,j),t48)):natrp(ts(a3,b3))
+t50:=satzd166e(td(a,b),n):posd(absd(td(a,b)))
+[p:posd(absd(td(a,b)))]
+atb3:=rpofpd(absd(td(a,b)),p):cut
+t51:=eqtd12(absd(a),pdofrp(a3),absd(b),pdofrp(b3),eqpdrp1(absd(a),t47),eqpdrp1(absd(b),t48)):eq(td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)))
+t52:=tr3eq(absd(td(a,b)),td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)),pdofrp(ts(a3,b3)),satzd193(a,b),t51,lemmaivad2(a3,b3)):eq(absd(td(a,b)),pdofrp(ts(a3,b3)))
+t53:=tris2(cut,atb3,ts(a3,b3),rpofpd(pdofrp(ts(a3,b3)),posdirp(ts(a3,b3))),eqpderp(absd(td(a,b)),p,pdofrp(ts(a3,b3)),posdirp(ts(a3,b3)),t52),isrppd1(ts(a3,b3))):is(atb3,ts(a3,b3))
+t54:=isp1(cut,[t:cut]natrp(t),ts(a3,b3),atb3,t49,t53):natrp(atb3)
+n@t55:=andi(posd(absd(td(a,b))),[t:posd(absd(td(a,b)))]natrp(atb3(t)),t50,[t:posd(absd(td(a,b)))]t54(t)):natd(absd(td(a,b)))
+-intd
+j@inttd:=[t:not(zero(td(a,b)))]t55".intd"(t):intd(td(a,b))
++r
+@eq:=[x:dif][y:dif]eq"rp"(x,y):[x:dif][y:dif]'prop'
+refeq:=[x:dif]refeq"rp"(x):[x:dif]<x><x>eq
+symeq:=[x:dif][y:dif][t:<y><x>eq]symeq"rp"(x,y,t):[x:dif][y:dif][t:<y><x>eq]<x><y>eq
+treq:=[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]treq"rp"(x,y,z,t,u):[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]<z><x>eq
+[a:dif][s:set(dif)]
+inn:=esti(dif,a,s):'prop'
+@real:=ect"eq"(dif,eq,refeq,symeq,treq):'type'
+[r:real][s:real]
+is:=is"e"(real,r,s):'prop'
+nis:=not(is(r,s)):'prop'
+@[p:[x:real]'prop']
+some:=some"l"(real,p):'prop'
+all:=all"l"(real,p):'prop'
+one:=one"e"(real,p):'prop'
+r@[s0:set(real)]
+in:=esti(real,r,s0):'prop'
+a@realof:=ectelt"eq"(dif,eq,refeq,symeq,treq,a):real
+r@class:=ecect"eq"(dif,eq,refeq,symeq,treq,r):set(dif)
+a@innclass:=th5"eq.4"(dif,eq,refeq,symeq,treq,a):inn(a,class(realof(a)))
+r@[a:dif][b:dif][e:eq"rp"(a,b)][air:inn(a,class(r))]
+eqinn:=th8"eq.4"(dif,eq,refeq,symeq,treq,r,a,air,b,e):inn(b,class(r))
+r@[p:'prop'][p1:[x:dif][xi:inn(x,class(r))]p]
+realapp1:=th3"eq.4"(dif,eq,refeq,symeq,treq,r,p,p1):p
+r@[s:real][p:'prop'][p1:[x:dif][y:dif][xi:inn(x,class(r))][yi:inn(y,class(s))]p]
++ivr1
+[a:dif][air:inn(a,class(r))]
+t1:=realapp1(s,p,[y:dif]<air><y><a>p1):p
+-ivr1
+realapp2:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t1".ivr1"(x,xi)):p
+s@[t:real][p:'prop'][p1:[x:dif][y:dif][z:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))]p]
++*ivr1
+p1@[a:dif][air:inn(a,class(r))]
+t2:=realapp2(s,t,p,[y:dif][z:dif]<air><z><y><a>p1):p
+-ivr1
+p1@realapp3:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t2".ivr1"(x,xi)):p
+t@[u:real][p:'prop'][p1:[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]p]
++*ivr1
+p1@[a:dif][air:inn(a,class(r))]
+t3:=realapp3(s,t,u,p,[y:dif][z:dif][v:dif]<air><v><z><y><a>p1):p
+-ivr1
+p1@realapp4:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t3".ivr1"(x,xi)):p
+s@[a1:dif][b1:dif][a1ir:inn(a1,class(r))][b1is:inn(b1,class(s))][e:eq"rp"(a1,b1)]
+isin:=th3"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,e):is(r,s)
+b1is@[i:is(r,s)]
+isex:=th5"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,i):eq"rp"(a1,b1)
+b1is@[n:not(eq"rp"(a1,b1))]
+nisin:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),n,[t:is(r,s)]isex(t)):nis(r,s)
+b1is@[n:nis(r,s)]
+nisex:=th3"l.imp"(eq"rp"(a1,b1),is(r,s),n,[t:eq"rp"(a1,b1)]isin(t)):not(eq"rp"(a1,b1))
+@[alpha:'type'][f:[x:dif]alpha]
+fixf:=fixfu"eq"(dif,eq,refeq,symeq,treq,alpha,f):'prop'
+[ff:fixf(alpha,f)][r0:real]
+indreal:=indeq"eq"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0):alpha
+[a:dif][air:inn(a,class(r0))]
+isindreal:=th2"eq.10"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0,a,air):is"e"(alpha,<a>f,indreal)
+alpha@[g:[x:dif][y:dif]alpha]
+fixf2:=fixfu2"eq"(dif,eq,refeq,symeq,treq,alpha,g):'prop'
+[ff2:fixf2(alpha,g)][r0:real][s0:real]
+indreal2:=indeq2"eq"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0):alpha
+[a:dif][b:dif][air:inn(a,class(r0))][bis:inn(b,class(s0))]
+isindreal2:=th1"eq.11"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0,a,air,b,bis):is"e"(alpha,<b><a>g,indreal2)
+@0:=realof(df(1rp,1rp)):real
+r@[a0:dif][a0ir:inn(a0,class(r))][z:zero(a0)]
+0in:=isin(r,0,a0,df(1rp,1rp),a0ir,innclass(df(1rp,1rp)),zeroeq(a0,df(1rp,1rp),z,zeroi(1rp,1rp,refis(cut,1rp)))):is(r,0)
+a0ir@[i:is(r,0)]
+0ex:=eqzero(df(1rp,1rp),a0,isex(0,r,df(1rp,1rp),a0,innclass(df(1rp,1rp)),a0ir,symis(real,r,0,i)),tris(cut,stm(df(1rp,1rp)),1rp,std(df(1rp,1rp)),stmis(1rp,1rp),isstd(1rp,1rp))):zero(a0)
++*ivr1
+a0@propp:=and(inn(a0,class(r)),posd(a0)):'prop'
+-ivr1
+r@pos:=some"l"(dif,[x:dif]propp".ivr1"(x)):'prop'
+a0ir@[p:posd(a0)]
++*ivr1
+p@t4:=andi(inn(a0,class(r)),posd(a0),a0ir,p):propp(a0)
+-ivr1
+p@posin:=somei(dif,[x:dif]propp".ivr1"(x),a0,t4".ivr1"):pos(r)
+a0ir@[p:pos(r)]
++*ivr1
+p@[a:dif][q1:propp(a)]
+t5:=ande1(inn(a,class(r)),posd(a),q1):inn(a,class(r))
+t6:=ande2(inn(a,class(r)),posd(a),q1):posd(a)
+t7:=eqposd(a,a0,isex(r,r,a,a0,t5,a0ir,refis(real,r)),t6):posd(a0)
+-ivr1
+p@posex:=someapp(dif,[x:dif]propp".ivr1"(x),p,posd(a0),[x:dif][t:propp".ivr1"(x)]t7".ivr1"(x,t)):posd(a0)
++*ivr1
+a0@propn:=and(inn(a0,class(r)),negd(a0)):'prop'
+-ivr1
+r@neg:=some"l"(dif,[x:dif]propn".ivr1"(x)):'prop'
+a0ir@[n:negd(a0)]
++*ivr1
+n@t8:=andi(inn(a0,class(r)),negd(a0),a0ir,n):propn(a0)
+-ivr1
+n@negin:=somei(dif,[x:dif]propn".ivr1"(x),a0,t8".ivr1"):neg(r)
+a0ir@[n:neg(r)]
++*ivr1
+n@[a:dif][pl:propn(a)]
+t9:=ande1(inn(a,class(r)),negd(a),pl):inn(a,class(r))
+t10:=ande2(inn(a,class(r)),negd(a),pl):negd(a)
+t11:=eqnegd(a,a0,isex(r,r,a,a0,t9,a0ir,refis(real,r)),t10):negd(a0)
+-ivr1
+n@negex:=someapp(dif,[x:dif]propn".ivr1"(x),n,negd(a0),[x:dif][t:propn".ivr1"(x)]t11".ivr1"(x,t)):negd(a0)
++*ivr1
+a0ir@[p:posd(a0)]
+t12:=or3i2(is(r,0),pos(r),neg(r),posin(p)):or3(is(r,0),pos(r),neg(r))
+a0ir@[z:zero(a0)]
+t13:=or3i1(is(r,0),pos(r),neg(r),0in(z)):or3(is(r,0),pos(r),neg(r))
+a0ir@[n:negd(a0)]
+t14:=or3i3(is(r,0),pos(r),neg(r),negin(n)):or3(is(r,0),pos(r),neg(r))
+a0ir@t15:=rappd(a0,or3(is(r,0),pos(r),neg(r)),[t:posd(a0)]t12(t),[t:zero(a0)]t13(t),[t:negd(a0)]t14(t)):or3(is(r,0),pos(r),neg(r))
+-ivr1
+r@axrlo:=realapp1(r,or3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t15".ivr1"(x,xi)):or3(is(r,0),pos(r),neg(r))
++*ivr1
+a0ir@[i:is(r,0)]
+t16:=th3"l.imp"(pos(r),posd(a0),0notpd(a0,0ex(i)),[t:pos(r)]posex(t)):not(pos(r))
+a0ir@[p:pos(r)]
+t17:=th3"l.imp"(neg(r),negd(a0),pnotnd(a0,posex(p)),[t:neg(r)]negex(t)):not(neg(r))
+a0ir@[n:neg(r)]
+t18:=th3"l.imp"(is(r,0),zero(a0),nnot0d(a0,negex(n)),[t:is(r,0)]0ex(t)):not(is(r,0))
+a0ir@t19:=th6"l.ec3"(is(r,0),pos(r),neg(r),[t:is(r,0)]t16(t),[t:pos(r)]t17(t),[t:neg(r)]t18(t)):ec3(is(r,0),pos(r),neg(r))
+-ivr1
+r@axrle:=realapp1(r,ec3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t19".ivr1"(x,xi)):ec3(is(r,0),pos(r),neg(r))
+axrl:=orec3i(is(r,0),pos(r),neg(r),axrlo,axrle):orec3(is(r,0),pos(r),neg(r))
+[p:'prop'][p1:[t:pos(r)]p][p2:[t:is(r,0)]p][p3:[t:neg(r)]p]
+rapp:=or3app(is(r,0),pos(r),neg(r),p,axrlo,p2,p1,p3):p
+r@[p:pos(r)]
+pnotn:=ec3e23(is(r,0),pos(r),neg(r),axrle,p):not(neg(r))
+pnot0:=ec3e21(is(r,0),pos(r),neg(r),axrle,p):nis(r,0)
+r@[i:is(r,0)]
+0notp:=ec3e12(is(r,0),pos(r),neg(r),axrle,i):not(pos(r))
+0notn:=ec3e13(is(r,0),pos(r),neg(r),axrle,i):not(neg(r))
+r@[n:neg(r)]
+nnotp:=ec3e32(is(r,0),pos(r),neg(r),axrle,n):not(pos(r))
+nnot0:=ec3e31(is(r,0),pos(r),neg(r),axrle,n):nis(r,0)
+s@[i:is(r,s)][p:pos(r)]
+ispos:=isp(real,[x:real]pos(x),r,s,p,i):pos(s)
+i@[n:neg(r)]
+isneg:=isp(real,[x:real]neg(x),r,s,n,i):neg(s)
+@[r0:cut]
+pofrp:=realof(pdofrp(r0)):real
+nofrp:=realof(ndofrp(r0)):real
+[s0:cut][i:is"rp"(r0,s0)]
+isrpep:=isf(cut,real,[x:cut]pofrp(x),r0,s0,i):is(pofrp(r0),pofrp(s0))
+isrpen:=isf(cut,real,[x:cut]nofrp(x),r0,s0,i):is(nofrp(r0),nofrp(s0))
+s0@[i:is(pofrp(r0),pofrp(s0))]
++*ivr1
+i"r"@t20:=isex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),i):eq"rp"(pdofrp(r0),pdofrp(s0))
+-ivr1
+i@isrpip:=isrpipd(r0,s0,t20".ivr1"):is"rp"(r0,s0)
+s0@[i:is(nofrp(r0),nofrp(s0))]
++*ivr1
+i"r"@t21:=isex(nofrp(r0),nofrp(s0),ndofrp(r0),ndofrp(s0),innclass(ndofrp(r0)),innclass(ndofrp(s0)),i):eq"rp"(ndofrp(r0),ndofrp(s0))
+-ivr1
+i@isrpin:=isrpind(r0,s0,t21".ivr1"):is"rp"(r0,s0)
+r0@posi:=posin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),posdirp(r0)):pos(pofrp(r0))
+negi:=negin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),negdirp(r0)):neg(nofrp(r0))
+s@[r0:cut][s0:cut][i:is(r,pofrp(r0))][j:is(s,pofrp(s0))][k:is(r,s)]
++*ivr1
+k@t22:=isrpip(r0,s0,tr3is(real,pofrp(r0),r,s,pofrp(s0),symis(real,r,pofrp(r0),i),k,j)):is"rp"(r0,s0)
+r@t23:=[x:cut][y:cut][t:is(r,pofrp(x))][u:is(r,pofrp(y))]t22(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,pofrp(x)))
+a0ir@[p1:pos(r)]
+t24:=posex(p1):posd(a0)
+pr:=rpofpd(a0,t24):cut
+t25:=isin(r,pofrp(pr),a0,pdofrp(pr),a0ir,innclass(pdofrp(pr)),eqpdrp1(a0,t24)):is(r,pofrp(pr))
+t26:=somei(cut,[x:cut]is(r,pofrp(x)),pr,t25):some"rp"([x:cut]is(r,pofrp(x)))
+-ivr1
+r@[p:pos(r)]
++*ivr1
+p"r"@t27:=realapp1(some"rp"([x:cut]is(r,pofrp(x))),[x:dif][t:inn(x,class(r))]t26(x,t,p)):some"rp"([x:cut]is(r,pofrp(x)))
+t28:=onei(cut,[x:cut]is(r,pofrp(x)),t23,t27):one"rp"([x:cut]is(r,pofrp(x)))
+-ivr1
+p@rpofp:=ind(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):cut
+isprp1:=oneax(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):is(r,pofrp(rpofp(r,p)))
+isprp2:=symis(real,r,pofrp(rpofp(r,p)),isprp1):is(pofrp(rpofp(r,p)),r)
+@[r1:real][p:pos(r1)][s1:real][q:pos(s1)][i:is(r1,s1)]
+isperp:=t22".ivr1"(r1,s1,rpofp(r1,p),rpofp(s1,q),isprp1(r1,p),isprp1(s1,q),i):is"rp"(rpofp(r1,p),rpofp(s1,q))
+q@[i:is"rp"(rpofp(r1,p),rpofp(s1,q))]
+ispirp:=tr3is(real,r1,pofrp(rpofp(r1,p)),pofrp(rpofp(s1,q)),s1,isprp1(r1,p),isrpep(rpofp(r1,p),rpofp(s1,q),i),isprp2(s1,q)):is(r1,s1)
+@[r0:cut]
+isrpp1:=t22".ivr1"(pofrp(r0),pofrp(r0),r0,rpofp(pofrp(r0),posi(r0)),refis(real,pofrp(r0)),isprp1(pofrp(r0),posi(r0)),refis(real,pofrp(r0))):is"rp"(r0,rpofp(pofrp(r0),posi(r0)))
+isrpp2:=symis(cut,r0,rpofp(pofrp(r0),posi(r0)),isrpp1):is"rp"(rpofp(pofrp(r0),posi(r0)),r0)
+s@[r0:cut][s0:cut][i:is(r,nofrp(r0))][j:is(s,nofrp(s0))][k:is(r,s)]
++*ivr1
+k@t29:=isrpin(r0,s0,tr3is(real,nofrp(r0),r,s,nofrp(s0),symis(real,r,nofrp(r0),i),k,j)):is"rp"(r0,s0)
+r@t30:=[x:cut][y:cut][t:is(r,nofrp(x))][u:is(r,nofrp(y))]t29(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,nofrp(x)))
+a0ir@[n1:neg(r)]
+t31:=negex(n1):negd(a0)
+nr:=rpofnd(a0,t31):cut
+t32:=isin(r,nofrp(nr),a0,ndofrp(nr),a0ir,innclass(ndofrp(nr)),eqndrp1(a0,t31)):is(r,nofrp(nr))
+t33:=somei(cut,[x:cut]is(r,nofrp(x)),nr,t32):some"rp"([x:cut]is(r,nofrp(x)))
+-ivr1
+r@[n:neg(r)]
++*ivr1
+n"r"@t34:=realapp1(some"rp"([x:cut]is(r,nofrp(x))),[x:dif][t:inn(x,class(r))]t33(x,t,n)):some"rp"([x:cut]is(r,nofrp(x)))
+t35:=onei(cut,[x:cut]is(r,nofrp(x)),t30,t34):one"rp"([x:cut]is(r,nofrp(x)))
+-ivr1
+n@rpofn:=ind(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):cut
+isnrp1:=oneax(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):is(r,nofrp(rpofn(r,n)))
+isnrp2:=symis(real,r,nofrp(rpofn(r,n)),isnrp1):is(nofrp(rpofn(r,n)),r)
+@[r1:real][n:neg(r1)][s1:real][m:neg(s1)][i:is(r1,s1)]
+isnerp:=t29".ivr1"(r1,s1,rpofn(r1,n),rpofn(s1,m),isnrp1(r1,n),isnrp1(s1,m),i):is"rp"(rpofn(r1,n),rpofn(s1,m))
+m@[i:is"rp"(rpofn(r1,n),rpofn(s1,m))]
+isnirp:=tr3is(real,r1,nofrp(rpofn(r1,n)),nofrp(rpofn(s1,m)),s1,isnrp1(r1,n),isrpen(rpofn(r1,n),rpofn(s1,m),i),isnrp2(s1,m)):is(r1,s1)
+@[r0:cut]
+isrpn1:=t29".ivr1"(nofrp(r0),nofrp(r0),r0,rpofn(nofrp(r0),negi(r0)),refis(real,nofrp(r0)),isnrp1(nofrp(r0),negi(r0)),refis(real,nofrp(r0))):is"rp"(r0,rpofn(nofrp(r0),negi(r0)))
+isrpn2:=symis(cut,r0,rpofn(nofrp(r0),negi(r0)),isrpn1):is"rp"(rpofn(nofrp(r0),negi(r0)),r0)
+r@satz163:=refis(real,r):is(r,r)
+s@[i:is(r,s)]
+satz164:=symis(real,r,s,i):is(s,r)
+t@[i:is(r,s)][j:is(s,t)]
+satz165:=tris(real,r,s,t,i,j):is(r,t)
+@absdr:=[x:dif]realof(absd(x)):[x:dif]real
++ivr2
+[a:dif][b:dif][e:eq"rp"(a,b)]
+t1:=isin(realof(absd(a)),realof(absd(b)),absd(a),absd(b),innclass(absd(a)),innclass(absd(b)),eqabsd(a,b,e)):is(<a>absdr,<b>absdr)
+-ivr2
+fabsdr:=[x:dif][y:dif][t:<y><x>eq]t1".ivr2"(x,y,t):fixf(real,absdr)
+r@abs:=indreal(real,absdr,fabsdr,r):real
++*ivr2
+a0ir@t2:=isindreal(real,absdr,fabsdr,r,a0,a0ir):is(realof(absd(a0)),abs(r))
+-ivr2
+a0ir@aica:=isp(real,[x:real]inn(absd(a0),class(x)),realof(absd(a0)),abs(r),innclass(absd(a0)),t2".ivr2"):inn(absd(a0),class(abs(r)))
+s@[i:is(r,s)]
+isabs:=isf(real,real,[x:real]abs(x),r,s,i):is(abs(r),abs(s))
++2r166
+a0ir@[p:pos(r)]
+t1:=satzd166a(a0,posex(p)):posd(absd(a0))
+t2:=posin(abs(r),absd(a0),aica,t1):pos(abs(r))
+-2r166
+r@[p:pos(r)]
+satz166a:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t2".2r166"(x,t,p)):pos(abs(r))
++*2r166
+a0ir@[n:neg(r)]
+t3:=satzd166b(a0,negex(n)):posd(absd(a0))
+t4:=posin(abs(r),absd(a0),aica,t3):pos(abs(r))
+-2r166
+r@[n:neg(r)]
+satz166b:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t4".2r166"(x,t,n)):pos(abs(r))
++*2r166
+b1is@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
+t5:=satzd166c(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
+t6:=isin(t5):is(r,s)
+-2r166
+s@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
+satz166c:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".2r166"(x,y,t,u,p,q,i)):is(r,s)
++*2r166
+b1is@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
+t7:=satzd166d(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
+t8:=isin(t7):is(r,s)
+-2r166
+s@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
+satz166d:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".2r166"(x,y,t,u,n,o,i)):is(r,s)
+r@[n:nis(r,0)]
+satz166e:=rapp(r,pos(abs(r)),[t:pos(r)]satz166a(t),th2"l.imp"(is(r,0),pos(abs(r)),n),[t:neg(r)]satz166b(t)):pos(abs(r))
++*2r166
+a0ir@[i:is(r,0)]
+t9:=satzd166f(a0,0ex(i)):zero(absd(a0))
+t10:=0in(abs(r),absd(a0),aica,t9):is(abs(r),0)
+-2r166
+r@[i:is(r,0)]
+satz166f:=realapp1(is(abs(r),0),[x:dif][t:inn(x,class(r))]t10".2r166"(x,t,i)):is(abs(r),0)
+s@more:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),mored(x,y)))):'prop'
++*ivr2
+b1@propm:=and3(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1)):'prop'
+-ivr2
+b1is@[m:mored(a1,b1)]
++*ivr2
+m@t3:=and3i(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1),a1ir,b1is,m):propm(a1,b1)
+t4:=somei(dif,[x:dif]propm(a1,x),b1,t3):some"l"(dif,[x:dif]propm(a1,x))
+-ivr2
+m@morein:=somei(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),a1,t4".ivr2"):more(r,s)
+b1is@[m:more(r,s)]
++*ivr2
+m@[a:dif][sa:some"l"(dif,[x:dif]propm(a,x))][b:dif][p2:propm(a,b)]
+t5:=and3e1(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(a,class(r))
+t6:=and3e2(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(b,class(s))
+t7:=and3e3(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):mored(a,b)
+t8:=eqmored12(a,a1,b,b1,isex(r,r,a,a1,t5,a1ir,refis(real,r)),isex(s,s,b,b1,t6,b1is,refis(real,s)),t7):mored(a1,b1)
+sa@t9:=someapp(dif,[x:dif]propm(a,x),sa,mored(a1,b1),[x:dif][t:propm(a,x)]t8(x,t)):mored(a1,b1)
+-ivr2
+m@moreex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),m,mored(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propm".ivr2"(x,y))]t9".ivr2"(x,t)):mored(a1,b1)
+s@less:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),lessd(x,y)))):'prop'
++*ivr2
+b1@propl:=and3(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1)):'prop'
+-ivr2
+b1is@[l:lessd(a1,b1)]
++*ivr2
+l@t10:=and3i(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1),a1ir,b1is,l):propl(a1,b1)
+t11:=somei(dif,[x:dif]propl(a1,x),b1,t10):some"l"(dif,[x:dif]propl(a1,x))
+-ivr2
+l@lessin:=somei(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),a1,t11".ivr2"):less(r,s)
+b1is@[l:less(r,s)]
++*ivr2
+l@[a:dif][sa:some"l"(dif,[x:dif]propl(a,x))][b:dif][p2:propl(a,b)]
+t12:=and3e1(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(a,class(r))
+t13:=and3e2(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(b,class(s))
+t14:=and3e3(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):lessd(a,b)
+t15:=eqlessd12(a,a1,b,b1,isex(r,r,a,a1,t12,a1ir,refis(real,r)),isex(s,s,b,b1,t13,b1is,refis(real,s)),t14):lessd(a1,b1)
+sa@t16:=someapp(dif,[x:dif]propl(a,x),sa,lessd(a1,b1),[x:dif][t:propl(a,x)]t15(x,t)):lessd(a1,b1)
+-ivr2
+l@lessex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),l,lessd(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propl".ivr2"(x,y))]t16".ivr2"(x,t)):lessd(a1,b1)
+t@[i:is(r,s)][m:more(r,t)]
+ismore1:=isp(real,[x:real]more(x,t),r,s,m,i):more(s,t)
+i@[m:more(t,r)]
+ismore2:=isp(real,[x:real]more(t,x),r,s,m,i):more(t,s)
+i@[l:less(r,t)]
+isless1:=isp(real,[x:real]less(x,t),r,s,l,i):less(s,t)
+i@[l:less(t,r)]
+isless2:=isp(real,[x:real]less(t,x),r,s,l,i):less(t,s)
+u@[i:is(r,s)][j:is(t,u)][m:more(r,t)]
+ismore12:=ismore2(t,u,s,j,ismore1(r,s,t,i,m)):more(s,u)
+j@[l:less(r,t)]
+isless12:=isless2(t,u,s,j,isless1(r,s,t,i,l)):less(s,u)
++*ivr2
+b1is@[m:more(r,s)]
+t17:=lemmad5(a1,b1,moreex(m)):lessd(b1,a1)
+t18:=lessin(s,r,b1,a1,b1is,a1ir,t17):less(s,r)
+-ivr2
+s@[m:more(r,s)]
+lemma1:=realapp2(less(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t18".ivr2"(x,y,t,u,m)):less(s,r)
++*ivr2
+b1is@[l:less(r,s)]
+t19:=lemmad6(a1,b1,lessex(l)):mored(b1,a1)
+t20:=morein(s,r,b1,a1,b1is,a1ir,t19):more(s,r)
+-ivr2
+s@[l:less(r,s)]
+lemma2:=realapp2(more(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t20".ivr2"(x,y,t,u,l)):more(s,r)
++2r167
+b1is@t1:=satzd167a(a1,b1):or3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
+[e:eq"rp"(a1,b1)]
+t2:=or3i1(is(r,s),more(r,s),less(r,s),isin(e)):or3(is(r,s),more(r,s),less(r,s))
+b1is@[m:mored(a1,b1)]
+t3:=or3i2(is(r,s),more(r,s),less(r,s),morein(m)):or3(is(r,s),more(r,s),less(r,s))
+b1is@[l:lessd(a1,b1)]
+t4:=or3i3(is(r,s),more(r,s),less(r,s),lessin(l)):or3(is(r,s),more(r,s),less(r,s))
+b1is@t5:=or3app(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),or3(is(r,s),more(r,s),less(r,s)),t1,[t:eq"rp"(a1,b1)]t2(t),[t:mored(a1,b1)]t3(t),[t:lessd(a1,b1)]t4(t)):or3(is(r,s),more(r,s),less(r,s))
+t6:=satzd167b(a1,b1):ec3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
+[i:is(r,s)]
+t7:=th3"l.imp"(more(r,s),mored(a1,b1),ec3e12(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,isex(i)),[t:more(r,s)]moreex(t)):not(more(r,s))
+b1is@[m:more(r,s)]
+t8:=th3"l.imp"(less(r,s),lessd(a1,b1),ec3e23(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,moreex(m)),[t:less(r,s)]lessex(t)):not(less(r,s))
+b1is@[l:less(r,s)]
+t9:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),ec3e31(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,lessex(l)),[t:is(r,s)]isex(t)):not(is(r,s))
+b1is@t10:=th6"l.ec3"(is(r,s),more(r,s),less(r,s),th1"l.ec"(is(r,s),more(r,s),[t:is(r,s)]t7(t)),th1"l.ec"(more(r,s),less(r,s),[t:more(r,s)]t8(t)),th1"l.ec"(less(r,s),is(r,s),[t:less(r,s)]t9(t))):ec3(is(r,s),more(r,s),less(r,s))
+t11:=orec3i(is(r,s),more(r,s),less(r,s),t5,t10):orec3(is(r,s),more(r,s),less(r,s))
+-2r167
+s@satz167:=realapp2(orec3(is(r,s),more(r,s),less(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".2r167"(x,y,t,u)):orec3(is(r,s),more(r,s),less(r,s))
+satz167a:=orec3e1(is(r,s),more(r,s),less(r,s),satz167):or3(is(r,s),more(r,s),less(r,s))
+satz167b:=orec3e2(is(r,s),more(r,s),less(r,s),satz167):ec3(is(r,s),more(r,s),less(r,s))
+moreis:=or(more(r,s),is(r,s)):'prop'
+lessis:=or(less(r,s),is(r,s)):'prop'
+[m:moreis(r,s)]
+satz168a:=th9"l.or"(more(r,s),is(r,s),less(s,r),is(s,r),m,[t:more(r,s)]lemma1(t),[t:is(r,s)]symis(real,r,s,t)):lessis(s,r)
+s@[l:lessis(r,s)]
+satz168b:=th9"l.or"(less(r,s),is(r,s),more(s,r),is(s,r),l,[t:less(r,s)]lemma2(t),[t:is(r,s)]symis(real,r,s,t)):moreis(s,r)
+t@[i:is(r,s)][m:moreis(r,t)]
+ismoreis1:=isp(real,[x:real]moreis(x,t),r,s,m,i):moreis(s,t)
+i@[m:moreis(t,r)]
+ismoreis2:=isp(real,[x:real]moreis(t,x),r,s,m,i):moreis(t,s)
+i@[l:lessis(r,t)]
+islessis1:=isp(real,[x:real]lessis(x,t),r,s,l,i):lessis(s,t)
+i@[l:lessis(t,r)]
+islessis2:=isp(real,[x:real]lessis(t,x),r,s,l,i):lessis(t,s)
+u@[i:is(r,s)][j:is(t,u)][m:moreis(r,t)]
+ismoreis12:=ismoreis2(t,u,s,j,ismoreis1(r,s,t,i,m)):moreis(s,u)
+j@[l:lessis(r,t)]
+islessis12:=islessis2(t,u,s,j,islessis1(r,s,t,i,l)):lessis(s,u)
+s@[m:more(r,s)]
+moreisi1:=ori1(more(r,s),is(r,s),m):moreis(r,s)
+s@[l:less(r,s)]
+lessisi1:=ori1(less(r,s),is(r,s),l):lessis(r,s)
+s@[i:is(r,s)]
+moreisi2:=ori2(more(r,s),is(r,s),i):moreis(r,s)
+lessisi2:=ori2(less(r,s),is(r,s),i):lessis(r,s)
+b1is@[m:moreq(a1,b1)]
+moreisin:=orapp(mored(a1,b1),eq"rp"(a1,b1),moreis(r,s),m,[t:mored(a1,b1)]moreisi1(morein(t)),[t:eq"rp"(a1,b1)]moreisi2(isin(t))):moreis(r,s)
+b1is@[m:moreis(r,s)]
+moreisex:=orapp(more(r,s),is(r,s),moreq(a1,b1),m,[t:more(r,s)]moreqi1(a1,b1,moreex(t)),[t:is(r,s)]moreqi2(a1,b1,isex(t))):moreq(a1,b1)
+b1is@[l:lesseq(a1,b1)]
+lessisin:=orapp(lessd(a1,b1),eq"rp"(a1,b1),lessis(r,s),l,[t:lessd(a1,b1)]lessisi1(lessin(t)),[t:eq"rp"(a1,b1)]lessisi2(isin(t))):lessis(r,s)
+b1is@[l:lessis(r,s)]
+lessisex:=orapp(less(r,s),is(r,s),lesseq(a1,b1),l,[t:less(r,s)]lesseqi1(a1,b1,lessex(t)),[t:is(r,s)]lesseqi2(a1,b1,isex(t))):lesseq(a1,b1)
+s@[m:moreis(r,s)]
+satz167c:=th7"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,comor(more(r,s),is(r,s),m)):not(less(r,s))
+s@[l:lessis(r,s)]
+satz167d:=th9"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,l):not(more(r,s))
+s@[n:not(more(r,s))]
+satz167e:=th2"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n):lessis(r,s)
+s@[n:not(less(r,s))]
+s@[n:not(less(r,s))]
+satz167f:=comor(is(r,s),more(r,s),th3"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n)):moreis(r,s)
+s@[m:more(r,s)]
+satz167g:=th3"l.imp"(lessis(r,s),not(more(r,s)),weli(more(r,s),m),[t:lessis(r,s)]satz167d(t)):not(lessis(r,s))
+s@[l:less(r,s)]
+satz167h:=th3"l.imp"(moreis(r,s),not(less(r,s)),weli(less(r,s),l),[t:moreis(r,s)]satz167c(t)):not(moreis(r,s))
+s@[n:not(moreis(r,s))]
+satz167j:=or3e3(is(r,s),more(r,s),less(r,s),satz167a,th5"l.or"(more(r,s),is(r,s),n),th4"l.or"(more(r,s),is(r,s),n)):less(r,s)
+s@[n:not(lessis(r,s))]
+satz167k:=or3e2(is(r,s),more(r,s),less(r,s),satz167a,th4"l.or"(less(r,s),is(r,s),n),th5"l.or"(less(r,s),is(r,s),n)):more(r,s)
+r@[p:pos(r)]
++2r169
+[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t1:=satzd169a(a,b,0ex(0,b,bi0,refis(real,0)),posex(a,air,p)):mored(a,b)
+t2:=morein(r,0,a,b,air,bi0,t1):more(r,0)
+-2r169
+satz169a:=realapp2(r,0,more(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r169"(x,y,t,u)):more(r,0)
+r@[m:more(r,0)]
++*2r169
+m@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t3:=satzd169b(a,b,0ex(0,b,bi0,refis(real,0)),moreex(r,0,a,b,air,bi0,m)):posd(a)
+t4:=posin(r,a,air,t3):pos(r)
+-2r169
+m@satz169b:=realapp2(r,0,pos(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t4".2r169"(x,y,t,u)):pos(r)
+r@[n:neg(r)]
++*2r169
+n@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t5:=satzd169c(a,b,0ex(0,b,bi0,refis(real,0)),negex(a,air,n)):lessd(a,b)
+t6:=lessin(r,0,a,b,air,bi0,t5):less(r,0)
+-2r169
+n@satz169c:=realapp2(r,0,less(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t6".2r169"(x,y,t,u)):less(r,0)
+r@[l:less(r,0)]
++*2r169
+l@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t7:=satzd169d(a,b,0ex(0,b,bi0,refis(real,0)),lessex(r,0,a,b,air,bi0,l)):negd(a)
+t8:=negin(r,a,air,t7):neg(r)
+-2r169
+l@satz169d:=realapp2(r,0,neg(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t8".2r169"(x,y,t,u)):neg(r)
++2r170
+r@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t1:=satzd170(a,b,0ex(0,b,bi0,refis(real,0))):moreq(absd(a),b)
+t2:=moreisin(abs(r),0,absd(a),b,aica(r,a,air),bi0,t1):moreis(abs(r),0)
+-2r170
+r@satz170:=realapp2(r,0,moreis(abs(r),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r170"(x,y,t,u)):moreis(abs(r),0)
+satz170a:=th3"l.imp"(neg(abs(r)),less(abs(r),0),satz167c(abs(r),0,satz170),[t:neg(abs(r))]satz169c(abs(r),t)):not(neg(abs(r)))
+t@[l:less(r,s)][k:less(s,t)]
++2r171
+[a:dif][b:dif][c:dif][air:inn(a,class(r))][bis:inn(b,class(s))][cit:inn(c,class(t))]
+t1:=satzd171(a,b,c,lessex(r,s,a,b,air,bis,l),lessex(s,t,b,c,bis,cit,k)):lessd(a,c)
+t2:=lessin(r,t,a,c,air,cit,t1):less(r,t)
+-2r171
+satz171:=realapp3(r,s,t,less(r,t),[x:dif][y:dif][z:dif][w:inn(x,class(r))][u:inn(y,class(s))][v:inn(z,class(t))]t2".2r171"(x,y,z,w,u,v)):less(r,t)
+trless:=satz171:less(r,t)
+t@[m:more(r,s)][n:more(s,t)]
+trmore:=lemma2(t,r,trless(t,s,r,lemma1(s,t,n),lemma1(r,s,m))):more(r,t)
+t@[a2:dif][b2:dif][c2:dif][a2ir:inn(a2,class(r))][b2is:inn(b2,class(s))][c2it:inn(c2,class(t))]
++2r172
+[l:lessis(r,s)][k:less(s,t)]
+t1:=satzd172a(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
+t2:=lessin(r,t,a2,c2,a2ir,c2it,t1):less(r,t)
+-2r172
+t@[l:lessis(r,s)][k:less(s,t)]
+satz172a:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
++*2r172
+c2it@[l:less(r,s)][k:lessis(s,t)]
+t3:=satzd172b(a2,b2,c2,lessex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
+t4:=lessin(r,t,a2,c2,a2ir,c2it,t3):less(r,t)
+-2r172
+t@[l:less(r,s)][k:lessis(s,t)]
+satz172b:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
+t@[m:moreis(r,s)][n:more(s,t)]
+satz172c:=lemma2(t,r,satz172b(t,s,r,lemma1(s,t,n),satz168a(m))):more(r,t)
+t@[m:more(r,s)][n:moreis(s,t)]
+satz172d:=lemma2(t,r,satz172a(t,s,r,satz168a(s,t,n),lemma1(m))):more(r,t)
++2r173
+c2it@[l:lessis(r,s)][k:lessis(s,t)]
+t1:=satzd173(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lesseq(a2,c2)
+t2:=lessisin(r,t,a2,c2,a2ir,c2it,t1):lessis(r,t)
+-2r173
+t@[l:lessis(r,s)][k:lessis(s,t)]
+satz173:=realapp3(lessis(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r173"(x,y,z,u,v,w,l,k)):lessis(r,t)
+trlessis:=satz173:lessis(r,t)
+t@[m:moreis(r,s)][n:moreis(s,t)]
+trmoreis:=satz168b(t,r,trlessis(t,s,r,satz168a(s,t,n),satz168a(m))):moreis(r,t)
+r@ratrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),ratd(x))):'prop'
+a0ir@[r1:ratd(a0)]
++*ivr2
+r1@t21:=andi(inn(a0,class(r)),ratd(a0),a0ir,r1):and(inn(a0,class(r)),ratd(a0))
+-ivr2
+r1@ratrlin:=somei(dif,[x:dif]and(inn(x,class(r)),ratd(x)),a0,t21".ivr2"):ratrl(r)
+a0ir@[rr:ratrl(r)]
++*ivr2
+rr@[a:dif][b:and(inn(a,class(r)),ratd(a))]
+t22:=ande1(inn(a,class(r)),ratd(a),b):inn(a,class(r))
+t23:=ande2(inn(a,class(r)),ratd(a),b):ratd(a)
+t24:=eqratd(a,a0,isex(r,r,a,a0,t22,a0ir,refis(real,r)),t23):ratd(a0)
+-ivr2
+rr@ratrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),ratd(x)),rr,ratd(a0),[x:dif][t:and(inn(x,class(r)),ratd(x))]t24".ivr2"(x,t)):ratd(a0)
+r@irratrl:=not(ratrl(r)):'prop'
+@[r0:cut][rr:ratrp(r0)]
+remark2:=ratrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark2a(r0,rr)):ratrl(pofrp(r0))
+remark3:=ratrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark3a(r0,rr)):ratrl(nofrp(r0))
+r0@[ir:irratrp(r0)]
+remark4:=th3"l.imp"(ratrl(pofrp(r0)),ratd(pdofrp(r0)),remark4a(r0,ir),[t:ratrl(pofrp(r0))]ratrlex(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),t)):irratrl(pofrp(r0))
+remark5:=th3"l.imp"(ratrl(nofrp(r0)),ratd(ndofrp(r0)),remark5a(r0,ir),[t:ratrl(nofrp(r0))]ratrlex(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),t)):irratrl(nofrp(r0))
+r@natrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),natd(x))):'prop'
+a0ir@[n:natd(a0)]
++*ivr2
+n@t25:=andi(inn(a0,class(r)),natd(a0),a0ir,n):and(inn(a0,class(r)),natd(a0))
+-ivr2
+n@natrlin:=somei(dif,[x:dif]and(inn(x,class(r)),natd(x)),a0,t25".ivr2"):natrl(r)
+a0ir@[n:natrl(r)]
++*ivr2
+n@[a:dif][b:and(inn(a,class(r)),natd(a))]
+t26:=ande1(inn(a,class(r)),natd(a),b):inn(a,class(r))
+t27:=ande2(inn(a,class(r)),natd(a),b):natd(a)
+t28:=eqnatd(a,a0,isex(r,r,a,a0,t26,a0ir,refis(real,r)),t27):natd(a0)
+-ivr2
+n@natrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),natd(x)),n,natd(a0),[x:dif][t:and(inn(x,class(r)),natd(x))]t28".ivr2"(x,t)):natd(a0)
++*ivr2
+a0ir@[n:natrl(r)]
+t29:=natposd(a0,natrlex(n)):posd(a0)
+t30:=posin(t29):pos(r)
+-ivr2
+r@[n:natrl(r)]
+natpos:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t30".ivr2"(x,t,n)):pos(r)
+@[x:nat]
+rlofnt:=realof(pdofnt(x)):real
+natrli:=natrlin(rlofnt(x),pdofnt(x),innclass(pdofnt(x)),natdi(x)):natrl(rlofnt(x))
+[y:nat][i:is"n"(x,y)]
+isnterl:=isf(nat,real,[u:nat]rlofnt(u),x,y,i):is(rlofnt(x),rlofnt(y))
+y@[i:is(rlofnt(x),rlofnt(y))]
+isntirl:=isntirp(x,y,isrpip(rpofnt(x),rpofnt(y),i)):is"n"(x,y)
++*ivr2
+@t31:=[x:nat][y:nat][t:is(rlofnt(x),rlofnt(y))]isntirl(x,y,t):injective(nat,real,[x:nat]rlofnt(x))
+a0ir@[n:natrl(r)]
+t32:=natposd(a0,natrlex(n)):posd(a0)
+ap:=rpofpd(a0,t32):cut
+t33:=natderp(a0,natrlex(n)):natrp(ap)
+x0:=ntofrp(ap,t33):nat
+t34:=isrpepd(ap,rpofnt(x0),isrpnt1(ap,t33)):eq"rp"(pdofrp(ap),pdofnt(x0))
+t35:=treq"rp"(a0,pdofrp(ap),pdofnt(x0),eqpdrp1(a0,t32),t34):eq"rp"(a0,pdofnt(x0))
+t36:=isin(r,rlofnt(x0),a0,pdofnt(x0),a0ir,innclass(pdofnt(x0)),t35):is(r,rlofnt(x0))
+t37:=somei(nat,[x:nat]is(r,rlofnt(x)),x0,t36):image(nat,real,[x:nat]rlofnt(x),r)
+-ivr2
+r@[n:natrl(r)]
+natimage:=realapp1(image(nat,real,[x:nat]rlofnt(x),r),[x:dif][t:inn(x,class(r))]t37".ivr2"(x,t,n)):image(nat,real,[x:nat]rlofnt(x),r)
+r@[i:image(nat,real,[x:nat]rlofnt(x),r)]
++*ivr2
+i"r"@[x:nat][j:is(r,rlofnt(x))]
+t38:=isp1(real,[u:real]natrl(u),rlofnt(x),r,natrli(x),j):natrl(r)
+-ivr2
+i@imagenat:=someapp(nat,[u:nat]is(r,rlofnt(u)),i,natrl(r),[u:nat][v:is(r,rlofnt(u))]t38".ivr2"(u,v)):natrl(r)
+r@[n:natrl(r)]
+ntofrl:=soft(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):nat
+@[r1:real][n:natrl(r1)][s1:real][m:natrl(s1)][i:is(r1,s1)]
+isrlent:=isinv(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is"n"(ntofrl(r1,n),ntofrl(s1,m))
+m@[i:is"n"(ntofrl(r1,n),ntofrl(s1,m))]
+isrlint:=isinve(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is(r1,s1)
+r@[n:natrl(r)]
+isrlnt1:=ists1"e"(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):is(r,rlofnt(ntofrl(r,n)))
+isrlnt2:=symis(real,r,rlofnt(ntofrl(r,n)),isrlnt1):is(rlofnt(ntofrl(r,n)),r)
+@[x:nat]
++*ivr2
+x"r"@xn:=soft(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x)):nat
+t39:=isinv(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x),rlofnt(x),natimage(rlofnt(x),natrli(x)),refis(real,rlofnt(x))):is"n"(xn,ntofrl(rlofnt(x),natrli(x)))
+-ivr2
+x@isntrl1:=tris(nat,x,xn".ivr2",ntofrl(rlofnt(x),natrli(x)),isst1(nat,real,[u:nat]rlofnt(u),t31".ivr2",x),t39".ivr2"):is"n"(x,ntofrl(rlofnt(x),natrli(x)))
+isntrl2:=symis(nat,x,ntofrl(rlofnt(x),natrli(x)),isntrl1):is"n"(ntofrl(rlofnt(x),natrli(x)),x)
+r@intrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),intd(x))):'prop'
+a0ir@[i:intd(a0)]
++*ivr2
+i@t40:=andi(inn(a0,class(r)),intd(a0),a0ir,i):and(inn(a0,class(r)),intd(a0))
+-ivr2
+i@intrlin:=somei(dif,[x:dif]and(inn(x,class(r)),intd(x)),a0,t40".ivr2"):intrl(r)
+a0ir@[i:intrl(r)]
++*ivr2
+i@[a:dif][b:and(inn(a,class(r)),intd(a))]
+t41:=ande1(inn(a,class(r)),intd(a),b):inn(a,class(r))
+t42:=ande2(inn(a,class(r)),intd(a),b):intd(a)
+t43:=eqintd(a,a0,isex(r,r,a,a0,t41,a0ir,refis(real,r)),t42):intd(a0)
+-ivr2
+i@intrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),intd(x)),i,intd(a0),[x:dif][t:and(inn(x,class(r)),intd(x))]t43".ivr2"(x,t)):intd(a0)
++*ivr2
+a0ir@[n:natrl(r)]
+t44:=natintd(a0,natrlex(n)):intd(a0)
+t45:=intrlin(t44):intrl(r)
+-ivr2
+r@[n:natrl(r)]
+natintrl:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t45".ivr2"(x,t,n)):intrl(r)
++*ivr2
+a0ir@[p:pos(r)][i:intrl(r)]
+t46:=posintnatd(a0,posex(p),intrlex(i)):natd(a0)
+t47:=natrlin(t46):natrl(r)
+-ivr2
+r@[p:pos(r)][i:intrl(r)]
+posintnatrl:=realapp1(natrl(r),[x:dif][t:inn(x,class(r))]t47".ivr2"(x,t,p,i)):natrl(r)
++*ivr2
+a0ir@[i2:is(r,0)]
+t48:=intdi0(a0,0ex(i2)):intd(a0)
+t49:=intrlin(t48):intrl(r)
+-ivr2
+r@[i:is(r,0)]
+intrli0:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t49".ivr2"(x,t,i)):intrl(r)
+r0@[n:natrp(r0)]
+remark6:=intrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark6"rp"(r0,n)):intrl(pofrp(r0))
+remark7:=intrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark7"rp"(r0,n)):intrl(nofrp(r0))
++2r174
+a0ir@[i:intrl(r)]
+t1:=satzd174(a0,intrlex(i)):ratd(a0)
+t2:=ratrlin(t1):ratrl(r)
+-2r174
+r@[i:intrl(r)]
+satz174:=realapp1(ratrl(r),[x:dif][t:inn(x,class(r))]t2".2r174"(x,t,i)):ratrl(r)
+@plusdr:=[x:dif][y:dif]realof(pd(x,y)):[x:dif][y:dif]real
++ivr3
+[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
+t1:=isin(realof(pd(a,c)),realof(pd(b,d)),pd(a,c),pd(b,d),innclass(pd(a,c)),innclass(pd(b,d)),eqpd12(a,b,c,d,e,f)):is(<c><a>plusdr,<d><b>plusdr)
+-ivr3
+fplusdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr3"(x,y,z,v,t,u):fixf2(real,plusdr)
+s@pl:=indreal2(real,plusdr,fplusdr,r,s):real
++*ivr3
+b1is@t2:=isindreal2(real,plusdr,fplusdr,r,s,a1,b1,a1ir,b1is):is(realof(pd(a1,b1)),pl(r,s))
+-ivr3
+b1is@picp:=isp(real,[x:real]inn(pd(a1,b1),class(x)),realof(pd(a1,b1)),pl(r,s),innclass(pd(a1,b1)),t2".ivr3"):inn(pd(a1,b1),class(pl(r,s)))
+t@[i:is(r,s)]
+ispl1:=isf(real,real,[x:real]pl(x,t),r,s,i):is(pl(r,t),pl(s,t))
+ispl2:=isf(real,real,[x:real]pl(t,x),r,s,i):is(pl(t,r),pl(t,s))
+u@[i:is(r,s)][j:is(t,u)]
+ispl12:=tris(real,pl(r,t),pl(s,t),pl(s,u),ispl1(i),ispl2(t,u,s,j)):is(pl(r,t),pl(s,u))
++3r175
+b1is@t1:=satzd175(a1,b1):eq"rp"(pd(a1,b1),pd(b1,a1))
+t2:=isin(pl(r,s),pl(s,r),pd(a1,b1),pd(b1,a1),picp,picp(s,r,b1,a1,b1is,a1ir),t1):is(pl(r,s),pl(s,r))
+-3r175
+s@satz175:=realapp2(is(pl(r,s),pl(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r175"(x,y,t,u)):is(pl(r,s),pl(s,r))
+compl:=satz175:is(pl(r,s),pl(s,r))
++*ivr3
+b1is@[i:is(r,0)]
+t3:=pd01(a1,b1,0ex(r,a1,a1ir,i)):eq"rp"(pd(a1,b1),b1)
+t4:=isin(pl(r,s),s,pd(a1,b1),b1,picp,b1is,t3):is(pl(r,s),s)
+-ivr3
+s@[i:is(r,0)]
+pl01:=realapp2(is(pl(r,s),s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr3"(x,y,t,u,i)):is(pl(r,s),s)
+s@[i:is(s,0)]
+pl02:=tris(real,pl(r,s),pl(s,r),r,compl,pl01(s,r,i)):is(pl(r,s),r)
++*ivr3
+b1is@[p:pos(r)][q:pos(s)]
+t5:=ppd(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(pd(a1,b1))
+t6:=posin(pl(r,s),pd(a1,b1),picp,t5):pos(pl(r,s))
+-ivr3
+s@[p:pos(r)][q:pos(s)]
+pospl:=realapp2(pos(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr3"(x,y,t,u,p,q)):pos(pl(r,s))
++*ivr3
+b1is@[n:neg(r)][o:neg(s)]
+t7:=npd(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):negd(pd(a1,b1))
+t8:=negin(pl(r,s),pd(a1,b1),picp,t7):neg(pl(r,s))
+-ivr3
+s@[n:neg(r)][o:neg(s)]
+negpl:=realapp2(neg(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".ivr3"(x,y,t,u,n,o)):neg(pl(r,s))
+@m0dr:=[x:dif]realof(m0d(x)):[x:dif]real
++*ivr3
+@[a:dif][b:dif][e:eq"rp"(a,b)]
+t5a:=isin(realof(m0d(a)),realof(m0d(b)),m0d(a),m0d(b),innclass(m0d(a)),innclass(m0d(b)),eqm0d(a,b,e)):is(<a>m0dr,<b>m0dr)
+-ivr3
+@fm0dr:=[x:dif][y:dif][t:<y><x>eq]t5a".ivr3"(x,y,t):fixf(real,m0dr)
+r@m0:=indreal(real,m0dr,fm0dr,r):real
++*ivr3
+a0ir@t6a:=isindreal(real,m0dr,fm0dr,r,a0,a0ir):is(realof(m0d(a0)),m0(r))
+-ivr3
+a0ir@micm0:=isp(real,[x:real]inn(m0d(a0),class(x)),realof(m0d(a0)),m0(r),innclass(m0d(a0)),t6a".ivr3"):inn(m0d(a0),class(m0(r)))
+s@[i:is(r,s)]
+ism0:=isf(real,real,[x:real]m0(x),r,s,i):is(m0(r),m0(s))
++*ivr3
+a0ir@[n:neg(r)]
+t7a:=absnd(a0,negex(n)):eq"rp"(absd(a0),m0d(a0))
+t8a:=isin(abs(r),m0(r),absd(a0),m0d(a0),aica,micm0,t7a):is(abs(r),m0(r))
+-ivr3
+r@[n:neg(r)]
+absn:=realapp1(is(abs(r),m0(r)),[x:dif][t:inn(x,class(r))]t8a".ivr3"(x,t,n)):is(abs(r),m0(r))
++*ivr3
+a0ir@[nn:not(neg(r))]
+t9:=absnnd(a0,th3"l.imp"(negd(a0),neg(r),nn,[t:negd(a0)]negin(t))):eq"rp"(absd(a0),a0)
+t10:=isin(abs(r),r,absd(a0),a0,aica,a0ir,t9):is(abs(r),r)
+-ivr3
+r@[nn:not(neg(r))]
+absnn:=realapp1(is(abs(r),r),[x:dif][t:inn(x,class(r))]t10".ivr3"(x,t,nn)):is(abs(r),r)
+r@[p:pos(r)]
+absp:=absnn(r,pnotn(r,p)):is(abs(r),r)
+r@[i:is(r,0)]
+abs0:=tris(real,abs(r),r,0,absnn(r,0notn(r,i)),i):is(abs(r),0)
++3r176
+a0ir@[p:pos(r)]
+t1:=satzd176a(a0,posex(p)):negd(m0d(a0))
+t2:=negin(m0(r),m0d(a0),micm0,t1):neg(m0(r))
+-3r176
+r@[p:pos(r)]
+satz176a:=realapp1(neg(m0(r)),[x:dif][t:inn(x,class(r))]t2".3r176"(x,t,p)):neg(m0(r))
++*3r176
+a0ir@[i:is(r,0)]
+t3:=satzd176b(a0,0ex(i)):zero(m0d(a0))
+t4:=0in(m0(r),m0d(a0),micm0,t3):is(m0(r),0)
+-3r176
+r@[i:is(r,0)]
+satz176b:=realapp1(is(m0(r),0),[x:dif][t:inn(x,class(r))]t4".3r176"(x,t,i)):is(m0(r),0)
++*3r176
+a0ir@[n:neg(r)]
+t5:=satzd176c(a0,negex(n)):posd(m0d(a0))
+t6:=posin(m0(r),m0d(a0),micm0,t5):pos(m0(r))
+-3r176
+r@[n:neg(r)]
+satz176c:=realapp1(pos(m0(r)),[x:dif][t:inn(x,class(r))]t6".3r176"(x,t,n)):pos(m0(r))
++*3r176
+a0ir@[n:neg(m0(r))]
+t7:=satzd176d(a0,negex(m0(r),m0d(a0),micm0,n)):posd(a0)
+t8:=posin(t7):pos(r)
+-3r176
+r@[n:neg(m0(r))]
+satz176d:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t8".3r176"(x,t,n)):pos(r)
++*3r176
+a0ir@[i:is(m0(r),0)]
+t9:=satzd176e(a0,0ex(m0(r),m0d(a0),micm0,i)):zero(a0)
+t10:=0in(t9):is(r,0)
+-3r176
+r@[i:is(m0(r),0)]
+satz176e:=realapp1(is(r,0),[x:dif][t:inn(x,class(r))]t10".3r176"(x,t,i)):is(r,0)
++*3r176
+a0ir@[p:pos(m0(r))]
+t11:=satzd176f(a0,posex(m0(r),m0d(a0),micm0,p)):negd(a0)
+t12:=negin(t11):neg(r)
+-3r176
+r@[p:pos(m0(r))]
+satz176f:=realapp1(neg(r),[x:dif][t:inn(x,class(r))]t12".3r176"(x,t,p)):neg(r)
++3r177
+a0ir@t1:=isin(m0(m0(r)),r,m0d(m0d(a0)),a0,micm0(m0(r),m0d(a0),micm0),a0ir,satzd177(a0)):is(m0(m0(r)),r)
+-3r177
+r@satz177:=realapp1(is(m0(m0(r)),r),[x:dif][t:inn(x,class(r))]t1".3r177"(x,t)):is(m0(m0(r)),r)
+satz177a:=symis(real,m0(m0(r)),r,satz177):is(r,m0(m0(r)))
+s@[i:is(r,m0(s))]
+satz177b:=tris(real,m0(r),m0(m0(s)),s,ism0(r,m0(s),i),satz177(s)):is(m0(r),s)
+satz177c:=symis(real,m0(r),s,satz177b):is(s,m0(r))
+s@[i:is(m0(r),s)]
+satz177d:=satz177c(s,r,symis(real,m0(r),s,i)):is(r,m0(s))
+satz177e:=symis(real,r,m0(s),satz177d):is(m0(s),r)
++3r178
+a0ir@t1:=isin(abs(m0(r)),abs(r),absd(m0d(a0)),absd(a0),aica(m0(r),m0d(a0),micm0),aica,satzd178(a0)):is(abs(m0(r)),abs(r))
+-3r178
+r@satz178:=realapp1(is(abs(m0(r)),abs(r)),[x:dif][t:inn(x,class(r))]t1".3r178"(x,t)):is(abs(m0(r)),abs(r))
+satz178a:=symis(real,abs(m0(r)),abs(r),satz178):is(abs(r),abs(m0(r)))
++3r179
+a0ir@t1:=0in(pl(r,m0(r)),pd(a0,m0d(a0)),picp(r,m0(r),a0,m0d(a0),a0ir,micm0),satzd179(a0)):is(pl(r,m0(r)),0)
+-3r179
+satz179:=realapp1(is(pl(r,m0(r)),0),[x:dif][t:inn(x,class(r))]t1".3r179"(x,t)):is(pl(r,m0(r)),0)
+satz179a:=tris(real,pl(m0(r),r),pl(r,m0(r)),0,compl(m0(r),r),satz179):is(pl(m0(r),r),0)
++3r180
+b1is@t1:=isin(m0(pl(r,s)),pl(m0(r),m0(s)),m0d(pd(a1,b1)),pd(m0d(a1),m0d(b1)),micm0(pl(r,s),pd(a1,b1),picp),picp(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is)),satzd180(a1,b1)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
+-3r180
+s@satz180:=realapp2(is(m0(pl(r,s)),pl(m0(r),m0(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t1".3r180"(x,y,t,u)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
+satz180a:=symis(real,m0(pl(r,s)),pl(m0(r),m0(s)),satz180):is(pl(m0(r),m0(s)),m0(pl(r,s)))
+mn:=pl(r,m0(s)):real
+b1is@micmn:=picp(r,m0(s),a1,m0d(b1),a1ir,micm0(s,b1,b1is)):inn(md(a1,b1),class(mn(r,s)))
+t@[i:is(r,s)]
+ismn1:=ispl1(r,s,m0(t),i):is(mn(r,t),mn(s,t))
+ismn2:=ispl2(m0(r),m0(s),t,ism0(r,s,i)):is(mn(t,r),mn(t,s))
+u@[i:is(r,s)][j:is(t,u)]
+ismn12:=ispl12(r,s,m0(t),m0(u),i,ism0(t,u,j)):is(mn(r,t),mn(s,u))
+s@satz181:=tr3is(real,m0(mn(r,s)),pl(m0(r),m0(m0(s))),pl(m0(r),s),mn(s,r),satz180(r,m0(s)),ispl2(m0(m0(s)),s,m0(r),satz177(s)),compl(m0(r),s)):is(m0(mn(r,s)),mn(s,r))
+satz181a:=symis(real,m0(mn(s,r)),mn(r,s),satz181(s,r)):is(mn(r,s),m0(mn(s,r)))
++3r182
+b1is@[p:pos(mn(r,s))]
+t1:=satzd182a(a1,b1,posex(mn(r,s),md(a1,b1),micmn,p)):mored(a1,b1)
+t2:=morein(t1):more(r,s)
+-3r182
+[p:pos(mn(r,s))]
+satz182a:=realapp2(more(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r182"(x,y,t,u,p)):more(r,s)
++*3r182
+b1is@[i:is(mn(r,s),0)]
+t3:=satzd182b(a1,b1,0ex(mn(r,s),md(a1,b1),micmn,i)):eq"rp"(a1,b1)
+t4:=isin(t3):is(r,s)
+-3r182
+s@[i:is(mn(r,s),0)]
+satz182b:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r182"(x,y,t,u,i)):is(r,s)
++*3r182
+b1is@[n:neg(mn(r,s))]
+t5:=satzd182c(a1,b1,negex(mn(r,s),md(a1,b1),micmn,n)):lessd(a1,b1)
+t6:=lessin(t5):less(r,s)
+-3r182
+s@[n:neg(mn(r,s))]
+satz182c:=realapp2(less(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".3r182"(x,y,t,u,n)):less(r,s)
++*3r182
+b1is@[m:more(r,s)]
+t7:=satzd182d(a1,b1,moreex(m)):posd(md(a1,b1))
+t8:=posin(mn(r,s),md(a1,b1),micmn,t7):pos(mn(r,s))
+-3r182
+s@[m:more(r,s)]
+satz182d:=realapp2(pos(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".3r182"(x,y,t,u,m)):pos(mn(r,s))
++*3r182
+b1is@[i:is(r,s)]
+t9:=satzd182e(a1,b1,isex(i)):zero(md(a1,b1))
+t10:=0in(mn(r,s),md(a1,b1),micmn,t9):is(mn(r,s),0)
+-3r182
+s@[i:is(r,s)]
+satz182e:=realapp2(is(mn(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t10".3r182"(x,y,t,u,i)):is(mn(r,s),0)
++*3r182
+b1is@[l:less(r,s)]
+t11:=satzd182f(a1,b1,lessex(l)):negd(md(a1,b1))
+t12:=negin(mn(r,s),md(a1,b1),micmn,t11):neg(mn(r,s))
+-3r182
+s@[l:less(r,s)]
+satz182f:=realapp2(neg(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t12".3r182"(x,y,t,u,l)):neg(mn(r,s))
++3r183
+b1is@[m:more(r,s)]
+t1:=satzd183a(a1,b1,moreex(m)):lessd(m0d(a1),m0d(b1))
+t2:=lessin(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t1):less(m0(r),m0(s))
+-3r183
+s@[m:more(r,s)]
+satz183a:=realapp2(less(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r183"(x,y,t,u,m)):less(m0(r),m0(s))
+s@[i:is(r,s)]
+satz183b:=ism0(r,s,i):is(m0(r),m0(s))
++*3r183
+b1is@[l:less(r,s)]
+t3:=satzd183c(a1,b1,lessex(l)):mored(m0d(a1),m0d(b1))
+t4:=morein(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t3):more(m0(r),m0(s))
+-3r183
+s@[l:less(r,s)]
+satz183c:=realapp2(more(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r183"(x,y,t,u,l)):more(m0(r),m0(s))
+s@[l:less(m0(r),m0(s))]
+satz183d:=ismore12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183c(m0(r),m0(s),l)):more(r,s)
+s@[i:is(m0(r),m0(s))]
+satz183e:=tr3is(real,r,m0(m0(r)),m0(m0(s)),s,satz177a(r),ism0(m0(r),m0(s),i),satz177(s)):is(r,s)
+s@[m:more(m0(r),m0(s))]
+satz183f:=isless12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183a(m0(r),m0(s),m)):less(r,s)
++3r184
+t@prop1:=and3(pos(s),pos(t),is(r,mn(s,t))):'prop'
+s@prop2:=some([x:real]prop1(x)):'prop'
+r@prop3:=some([x:real]prop2(x)):'prop'
+a0ir@[a:dif][b:dif]
+prop1d:=and3(posd(a),posd(b),eq"rp"(a0,md(a,b))):'prop'
+a@prop2d:=some"l"(dif,[x:dif]prop1d(x)):'prop'
+[p2:prop2d(a)][b:dif][p1:prop1d(a,b)]
+t1:=and3e1(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(a)
+t2:=and3e2(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(b)
+t3:=and3e3(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):eq"rp"(a0,md(a,b))
+p2@ra:=realof(a):real
+p1@rb:=realof(b):real
+t4:=innclass(a):inn(a,class(ra))
+t5:=innclass(b):inn(b,class(rb))
+t6:=isin(r,mn(ra,rb),a0,md(a,b),a0ir,micmn(ra,rb,a,b,t4,t5),t3):is(r,mn(ra,rb))
+t7:=and3i(pos(ra),pos(rb),is(r,mn(ra,rb)),posin(ra,a,t4,t1),posin(rb,b,t5,t2),t6):prop1(ra,rb)
+t8:=somei(real,[x:real]prop1(ra,x),rb,t7):prop2(ra)
+p2@t9:=someapp(dif,[x:dif]prop1d(a,x),p2,prop2(ra),[x:dif][t:prop1d(a,x)]t8(x,t)):prop2(ra)
+t10:=somei(real,[x:real]prop2(x),ra,t9):prop3
+a0ir@t11:=someapp(dif,[x:dif]prop2d(x),satzd184(a0),prop3,[x:dif][t:prop2d(x)]t10(x,t)):prop3
+-3r184
+r@satz184:=realapp1(prop3".3r184",[x:dif][t:inn(x,class(r))]t11".3r184"(x,t)):some([x:real]some([y:real]and3(pos(x),pos(y),is(r,mn(x,y)))))
+u@[a3:dif][b3:dif][c3:dif][d3:dif][a3ir:inn(a3,class(r))][b3is:inn(b3,class(s))][c3it:inn(c3,class(t))][d3iu:inn(d3,class(u))]
++3r185
+t1:=satzd185(a3,b3,c3,d3):eq"rp"(pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)))
+t2:=isin(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)),pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)),picp(mn(r,s),mn(t,u),md(a3,b3),md(c3,d3),micmn(r,s,a3,b3,a3ir,b3is),micmn(t,u,c3,d3,c3it,d3iu)),micmn(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu)),t1):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
+-3r185
+u@satz185:=realapp4(is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u))),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r185"(x,y,z,v,xi,yi,zi,vi)):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
++3r186
+c2it@t1:=satzd186(a2,b2,c2):eq"rp"(pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)))
+t2:=isin(pl(pl(r,s),t),pl(r,pl(s,t)),pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)),picp(pl(r,s),t,pd(a2,b2),c2,picp(r,s,a2,b2,a2ir,b2is),c2it),picp(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),t1):is(pl(pl(r,s),t),pl(r,pl(s,t)))
+-3r186
+t@satz186:=realapp3(is(pl(pl(r,s),t),pl(r,pl(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r186"(x,y,z,u,v,w)):is(pl(pl(r,s),t),pl(r,pl(s,t)))
+asspl1:=satz186:is(pl(pl(r,s),t),pl(r,pl(s,t)))
+asspl2:=symis(real,pl(pl(r,s),t),pl(r,pl(s,t)),satz186):is(pl(r,pl(s,t)),pl(pl(r,s),t))
+s@plmn:=tris(real,pl(mn(r,s),s),pl(r,pl(m0(s),s)),r,asspl1(r,m0(s),s),pl02(r,pl(m0(s),s),satz179a(s))):is(pl(mn(r,s),s),r)
+mnpl:=tris(real,mn(pl(r,s),s),pl(r,pl(s,m0(s))),r,asspl1(r,s,m0(s)),pl02(r,pl(s,m0(s)),satz179(s))):is(mn(pl(r,s),s),r)
+satz187a:=tris(real,pl(s,mn(r,s)),pl(mn(r,s),s),r,compl(s,mn(r,s)),plmn):is(pl(s,mn(r,s)),r)
+satz187b:=somei(real,[x:real]is(pl(s,x),r),mn(r,s),satz187a):some([x:real]is(pl(s,x),r))
+[x:real][i:is(pl(s,x),r)]
+satz187c:=tris(real,mn(r,s),mn(pl(x,s),s),x,ismn1(r,pl(x,s),s,tris1(real,r,pl(x,s),pl(s,x),i,compl(s,x))),mnpl(x,s)):is(mn(r,s),x)
+satz187d:=symis(real,mn(r,s),x,satz187c):is(x,mn(r,s))
+x@[i:is(pl(x,s),r)]
+satz187e:=satz187c(tris(real,pl(s,x),pl(x,s),r,compl(s,x),i)):is(mn(r,s),x)
+satz187f:=symis(real,mn(r,s),x,satz187e):is(x,mn(r,s))
++3r187
+s@[x:real][y:real][i:is(pl(s,x),r)][j:is(pl(s,y),r)]
+t1:=tris1(real,x,y,mn(r,s),satz187c(x,i),satz187c(y,j)):is(x,y)
+s@t2:=[x:real][y:real][t:is(pl(s,x),r)][u:is(pl(s,y),r)]t1(x,y,t,u):amone(real,[x:real]is(pl(s,x),r))
+-3r187
+s@satz187:=onei(real,[x:real]is(pl(s,x),r),t2".3r187",satz187b):one([x:real]is(pl(s,x),r))
++3r188
+c2it@[m:more(pl(r,t),pl(s,t))]
+t1:=satzd188a(a2,b2,c2,moreex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),m)):mored(a2,b2)
+t2:=morein(r,s,a2,b2,a2ir,b2is,t1):more(r,s)
+-3r188
+t@[m:more(pl(r,t),pl(s,t))]
+satz188a:=realapp3(more(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r188"(x,y,z,u,v,w,m)):more(r,s)
++*3r188
+c2it@[i:is(pl(r,t),pl(s,t))]
+t3:=satzd188b(a2,b2,c2,isex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),i)):eq"rp"(a2,b2)
+t4:=isin(r,s,a2,b2,a2ir,b2is,t3):is(r,s)
+-3r188
+t@[i:is(pl(r,t),pl(s,t))]
+satz188b:=realapp3(is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".3r188"(x,y,z,u,v,w,i)):is(r,s)
++*3r188
+c2it@[l:less(pl(r,t),pl(s,t))]
+t5:=satzd188c(a2,b2,c2,lessex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),l)):lessd(a2,b2)
+t6:=lessin(r,s,a2,b2,a2ir,b2is,t5):less(r,s)
+-3r188
+t@[l:less(pl(r,t),pl(s,t))]
+satz188c:=realapp3(less(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t6".3r188"(x,y,z,u,v,w,l)):less(r,s)
++*3r188
+c2it@[m:more(r,s)]
+t7:=satzd188d(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m)):mored(pd(a2,c2),pd(b2,c2))
+t8:=morein(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t7):more(pl(r,t),pl(s,t))
+-3r188
+t@[m:more(r,s)]
+satz188d:=realapp3(more(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t8".3r188"(x,y,z,u,v,w,m)):more(pl(r,t),pl(s,t))
+t@[i:is(r,s)]
+satz188e:=ispl1(r,s,t,i):is(pl(r,t),pl(s,t))
++*3r188
+c2it@[l:less(r,s)]
+t9:=satzd188f(a2,b2,c2,lessex(r,s,a2,b2,a2ir,b2is,l)):lessd(pd(a2,c2),pd(b2,c2))
+t10:=lessin(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t9):less(pl(r,t),pl(s,t))
+-3r188
+t@[l:less(r,s)]
+satz188f:=realapp3(less(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t10".3r188"(x,y,z,u,v,w,l)):less(pl(r,t),pl(s,t))
+t@[m:more(pl(t,r),pl(t,s))]
+satz188g:=satz188a(ismore12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),m)):more(r,s)
+t@[i:is(pl(t,r),pl(t,s))]
+satz188h:=satz188b(tr3is(real,pl(r,t),pl(t,r),pl(t,s),pl(s,t),compl(r,t),i,compl(t,s))):is(r,s)
+t@[l:less(pl(t,r),pl(t,s))]
+satz188j:=satz188c(isless12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),l)):less(r,s)
+t@[m:more(r,s)]
+satz188k:=ismore12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188d(m)):more(pl(t,r),pl(t,s))
+t@[i:is(r,s)]
+satz188l:=ispl2(r,s,t,i):is(pl(t,r),pl(t,s))
+t@[l:less(r,s)]
+satz188m:=isless12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188f(l)):less(pl(t,r),pl(t,s))
+u@[i:is(r,s)][m:more(t,u)]
+satz188n:=ismore2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188k(t,u,r,m)):more(pl(r,t),pl(s,u))
+satz188o:=ismore12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188n):more(pl(t,r),pl(u,s))
+i@[l:less(t,u)]
+satz188p:=isless2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188m(t,u,r,l)):less(pl(r,t),pl(s,u))
+satz188q:=isless12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188p):less(pl(t,r),pl(u,s))
+u@[m:more(r,s)][n:more(t,u)]
+satz189:=trmore(pl(r,t),pl(s,t),pl(s,u),satz188d(m),satz188k(t,u,s,n)):more(pl(r,t),pl(s,u))
+u@[l:less(r,s)][k:less(t,u)]
+satz189a:=lemma1(pl(s,u),pl(r,t),satz189(s,r,u,t,lemma2(r,s,l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
+u@[m:moreis(r,s)][n:more(t,u)]
+satz190a:=orapp(more(r,s),is(r,s),more(pl(r,t),pl(s,u)),m,[v:more(r,s)]satz189(v,n),[v:is(r,s)]satz188n(v,n)):more(pl(r,t),pl(s,u))
+u@[m:more(r,s)][n:moreis(t,u)]
+satz190b:=ismore12(pl(t,r),pl(r,t),pl(u,s),pl(s,u),compl(t,r),compl(u,s),satz190a(t,u,r,s,n,m)):more(pl(r,t),pl(s,u))
+u@[l:lessis(r,s)][k:less(t,u)]
+satz190c:=lemma1(pl(s,u),pl(r,t),satz190a(s,r,u,t,satz168b(l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
+u@[l:less(r,s)][k:lessis(t,u)]
+satz190d:=lemma1(pl(s,u),pl(r,t),satz190b(s,r,u,t,lemma2(l),satz168b(t,u,k))):less(pl(r,t),pl(s,u))
++3r191
+d3iu@[m:moreis(r,s)][n:moreis(t,u)]
+t1:=satzd191(a3,b3,c3,d3,moreisex(r,s,a3,b3,a3ir,b3is,m),moreisex(t,u,c3,d3,c3it,d3iu,n)):moreq(pd(a3,c3),pd(b3,d3))
+t2:=moreisin(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu),t1):moreis(pl(r,t),pl(s,u))
+-3r191
+u@[m:moreis(r,s)][n:moreis(t,u)]
+satz191:=realapp4(moreis(pl(r,t),pl(s,u)),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r191"(x,y,z,v,xi,yi,zi,vi,m,n)):moreis(pl(r,t),pl(s,u))
+u@[l:lessis(r,s)][k:lessis(t,u)]
+satz191a:=satz168a(pl(s,u),pl(r,t),satz191(s,r,u,t,satz168b(l),satz168b(t,u,k))):lessis(pl(r,t),pl(s,u))
+@timesdr:=[x:dif][y:dif]realof(td(x,y)):[x:dif][y:dif]real
++ivr4
+[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
+t1:=isin(realof(td(a,c)),realof(td(b,d)),td(a,c),td(b,d),innclass(td(a,c)),innclass(td(b,d)),eqtd12(a,b,c,d,e,f)):is(<c><a>timesdr,<d><b>timesdr)
+-ivr4
+ftimesdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr4"(x,y,z,v,t,u):fixf2(real,timesdr)
+s@ts:=indreal2(real,timesdr,ftimesdr,r,s):real
++*ivr4
+b1is@t2:=isindreal2(real,timesdr,ftimesdr,r,s,a1,b1,a1ir,b1is):is(realof(td(a1,b1)),ts(r,s))
+-ivr4
+b1is@tict:=isp(real,[x:real]inn(td(a1,b1),class(x)),realof(td(a1,b1)),ts(r,s),innclass(td(a1,b1)),t2".ivr4"):inn(td(a1,b1),class(ts(r,s)))
+t@[i:is(r,s)]
+ists1:=isf(real,real,[x:real]ts(x,t),r,s,i):is(ts(r,t),ts(s,t))
+ists2:=isf(real,real,[x:real]ts(t,x),r,s,i):is(ts(t,r),ts(t,s))
+u@[i:is(r,s)][j:is(t,u)]
+ists12:=tris(real,ts(r,t),ts(s,t),ts(s,u),ists1(i),ists2(t,u,s,j)):is(ts(r,t),ts(s,u))
++4r192
+b1is@[i:is(r,0)]
+t1:=satzd192a(a1,b1,0ex(r,a1,a1ir,i)):zero(td(a1,b1))
+t2:=0in(ts(r,s),td(a1,b1),tict,t1):is(ts(r,s),0)
+-4r192
+s@[i:is(r,0)]
+satz192a:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r192"(x,y,t,u,i)):is(ts(r,s),0)
++*4r192
+b1is@[i:is(s,0)]
+t3:=satzd192b(a1,b1,0ex(s,b1,b1is,i)):zero(td(a1,b1))
+t4:=0in(ts(r,s),td(a1,b1),tict,t3):is(ts(r,s),0)
+-4r192
+s@[i:is(s,0)]
+satz192b:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".4r192"(x,y,t,u,i)):is(ts(r,s),0)
++*4r192
+b1is@[i:is(ts(r,s),0)]
+t5:=satzd192c(a1,b1,0ex(ts(r,s),td(a1,b1),tict,i)):or(zero(a1),zero(b1))
+t6:=th9"l.or"(zero(a1),zero(b1),is(r,0),is(s,0),t5,[t:zero(a1)]0in(r,a1,a1ir,t),[t:zero(b1)]0in(s,b1,b1is,t)):or(is(r,0),is(s,0))
+-4r192
+s@[i:is(ts(r,s),0)]
+satz192c:=realapp2(or(is(r,0),is(s,0)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".4r192"(x,y,t,u,i)):or(is(r,0),is(s,0))
+s@[n:nis(r,0)][o:nis(s,0)]
+satz192d:=th3"l.imp"(is(ts(r,s),0),or(is(r,0),is(s,0)),th3"l.or"(is(r,0),is(s,0),n,o),[t:is(ts(r,s),0)]satz192c(t)):nis(ts(r,s),0)
+s@[i:is(r,0)]
+ts01:=satz192a(i):is(ts(r,s),0)
+s@[i:is(s,0)]
+ts02:=satz192b(i):is(ts(r,s),0)
++4r193
+b1is@t1:=satzd193(a1,b1):eq"rp"(absd(td(a1,b1)),td(absd(a1),absd(b1)))
+t2:=isin(abs(ts(r,s)),ts(abs(r),abs(s)),absd(td(a1,b1)),td(absd(a1),absd(b1)),aica(ts(r,s),td(a1,b1),tict),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(abs(ts(r,s)),ts(abs(r),abs(s)))
+-4r193
+s@satz193:=realapp2(is(abs(ts(r,s)),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r193"(x,y,t,u)):is(abs(ts(r,s)),ts(abs(r),abs(s)))
+satz193a:=symis(real,abs(ts(r,s)),ts(abs(r),abs(s)),satz193):is(ts(abs(r),abs(s)),abs(ts(r,s)))
++4r194
+b1is@t1:=satzd194(a1,b1):eq"rp"(td(a1,b1),td(b1,a1))
+t2:=isin(ts(r,s),ts(s,r),td(a1,b1),td(b1,a1),tict,tict(s,r,b1,a1,b1is,a1ir),t1):is(ts(r,s),ts(s,r))
+-4r194
+satz194:=realapp2(is(ts(r,s),ts(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r194"(x,y,t,u)):is(ts(r,s),ts(s,r))
+comts:=satz194:is(ts(r,s),ts(s,r))
+@1rl:=realof(1df):real
+pos1:=posin(1rl,1df,innclass(1df),posdirp(1rp)):pos(1rl)
+natrl1:=natrli(1):natrl(1rl)
+intrl1:=natintrl(1rl,natrl1):intrl(1rl)
++4r195
+a0ir@t1:=satzd195(a0):eq"rp"(td(a0,1df),a0)
+t2:=isin(ts(r,1rl),r,td(a0,1df),a0,tict(r,1rl,a0,1df,a0ir,innclass(1df)),a0ir,t1):is(ts(r,1rl),r)
+-4r195
+r@satz195:=realapp1(is(ts(r,1rl),r),[x:dif][t:inn(x,class(r))]t2".4r195"(x,t)):is(ts(r,1rl),r)
+satz195a:=symis(real,ts(r,1rl),r,satz195):is(r,ts(r,1rl))
+satz195b:=tris(real,ts(1rl,r),ts(r,1rl),r,comts(1rl,r),satz195):is(ts(1rl,r),r)
+satz195c:=symis(real,ts(1rl,r),r,satz195b):is(r,ts(1rl,r))
+s@[p:pos(r)][q:pos(s)]
+satz196a:=symis(real,ts(abs(r),abs(s)),ts(r,s),ists12(abs(r),r,abs(s),s,absp(r,p),absp(s,q))):is(ts(r,s),ts(abs(r),abs(s)))
++4r196
+b1is@[n:neg(r)][o:neg(s)]
+t1:=satzd196b(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):eq"rp"(td(a1,b1),td(absd(a1),absd(b1)))
+t2:=isin(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(ts(r,s),ts(abs(r),abs(s)))
+-4r196
+s@[n:neg(r)][o:neg(s)]
+satz196b:=realapp2(is(ts(r,s),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r196"(x,y,t,u,n,o)):is(ts(r,s),ts(abs(r),abs(s)))
++*4r196
+b1is@[p:pos(r)][n:neg(s)]
+t1a:=satzd196c(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):eq"rp"(td(a1,b1),m0d(td(absd(a1),absd(b1))))
+t2a:=isin(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),t1a):is(ts(r,s),m0(ts(abs(r),abs(s))))
+-4r196
+s@[p:pos(r)][n:neg(s)]
+satz196c:=realapp2(is(ts(r,s),m0(ts(abs(r),abs(s)))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2a".4r196"(x,y,t,u,p,n)):is(ts(r,s),m0(ts(abs(r),abs(s))))
+s@[n:neg(r)][p:pos(s)]
+satz196d:=tr3is(real,ts(r,s),ts(s,r),m0(ts(abs(s),abs(r))),m0(ts(abs(r),abs(s))),comts(r,s),satz196c(s,r,p,n),ism0(ts(abs(s),abs(r)),ts(abs(r),abs(s)),comts(abs(s),abs(r)))):is(ts(r,s),m0(ts(abs(r),abs(s))))
++*4r196
+a0ir@[n:not(is(r,0))]
+t3:=th3"l.imp"(zero(a0),is(r,0),n,[t:zero(a0)]0in(t)):not(zero(a0))
+b1is@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
+t4:=satzd196e(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),i)):or(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)))
+[a:and(posd(a1),posd(b1))]
+t5:=andi(pos(r),pos(s),posin(r,a1,a1ir,ande1(posd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(posd(a1),posd(b1),a))):and(pos(r),pos(s))
+i@[a:and(negd(a1),negd(b1))]
+t6:=andi(neg(r),neg(s),negin(r,a1,a1ir,ande1(negd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(negd(a1),negd(b1),a))):and(neg(r),neg(s))
+i@t7:=th9"l.or"(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)),and(pos(r),pos(s)),and(neg(r),neg(s)),t4,[t:and(posd(a1),posd(b1))]t5(t),[t:and(negd(a1),negd(b1))]t6(t)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
+-4r196
+s@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
+satz196e:=realapp2(or(and(pos(r),pos(s)),and(neg(r),neg(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
++*4r196
+o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
+t8:=satzd196f(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),i)):or(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)))
+[a:and(posd(a1),negd(b1))]
+t9:=andi(pos(r),neg(s),posin(r,a1,a1ir,ande1(posd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(posd(a1),negd(b1),a))):and(pos(r),neg(s))
+i@[a:and(negd(a1),posd(b1))]
+t10:=andi(neg(r),pos(s),negin(r,a1,a1ir,ande1(negd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(negd(a1),posd(b1),a))):and(neg(r),pos(s))
+i@t11:=th9"l.or"(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)),and(pos(r),neg(s)),and(neg(r),pos(s)),t8,[t:and(posd(a1),negd(b1))]t9(t),[t:and(negd(a1),posd(b1))]t10(t)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
+-4r196
+o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
+satz196f:=realapp2(or(and(pos(r),neg(s)),and(neg(r),pos(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
+s@[p:pos(ts(r,s))]
++*4r196
+p"r"@t12:=th3"l.imp"(is(r,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
+t13:=th3"l.imp"(is(s,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
+t14:=tris1(real,ts(r,s),ts(abs(r),abs(s)),abs(ts(r,s)),absp(ts(r,s),p),satz193(r,s)):is(ts(r,s),ts(abs(r),abs(s)))
+-4r196
+p@satz196g:=satz196e(t12".4r196",t13".4r196",t14".4r196"):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
+s@[n:neg(ts(r,s))]
++*4r196
+n"r"@t15:=th3"l.imp"(is(r,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
+t16:=th3"l.imp"(is(s,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
+t17:=satz177c(ts(abs(r),abs(s)),ts(r,s),tris(real,ts(abs(r),abs(s)),abs(ts(r,s)),m0(ts(r,s)),satz193a(r,s),absn(ts(r,s),n))):is(ts(r,s),m0(ts(abs(r),abs(s))))
+-4r196
+n@satz196h:=satz196f(t15".4r196",t16".4r196",t17".4r196"):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
++4r197
+b1is@t1:=satzd197a(a1,b1):eq"rp"(td(m0d(a1),b1),m0d(td(a1,b1)))
+t2:=isin(ts(m0(r),s),m0(ts(r,s)),td(m0d(a1),b1),m0d(td(a1,b1)),tict(m0(r),s,m0d(a1),b1,micm0(r,a1,a1ir),b1is),micm0(ts(r,s),td(a1,b1),tict),t1):is(ts(m0(r),s),m0(ts(r,s)))
+-4r197
+s@satz197a:=realapp2(is(ts(m0(r),s),m0(ts(r,s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r197"(x,y,t,u)):is(ts(m0(r),s),m0(ts(r,s)))
+satz197b:=tr3is(real,ts(r,m0(s)),ts(m0(s),r),m0(ts(s,r)),m0(ts(r,s)),comts(r,m0(s)),satz197a(s,r),ism0(ts(s,r),ts(r,s),comts(s,r))):is(ts(r,m0(s)),m0(ts(r,s)))
+satz197c:=tris2(real,ts(m0(r),s),ts(r,m0(s)),m0(ts(r,s)),satz197a,satz197b):is(ts(m0(r),s),ts(r,m0(s)))
+satz197d:=symis(real,ts(m0(r),s),ts(r,m0(s)),satz197c):is(ts(r,m0(s)),ts(m0(r),s))
+satz197e:=symis(real,ts(m0(r),s),m0(ts(r,s)),satz197a):is(m0(ts(r,s)),ts(m0(r),s))
+satz197f:=symis(real,ts(r,m0(s)),m0(ts(r,s)),satz197b):is(m0(ts(r,s)),ts(r,m0(s)))
+satz198:=tris(real,ts(m0(r),m0(s)),ts(r,m0(m0(s))),ts(r,s),satz197c(r,m0(s)),ists2(m0(m0(s)),s,r,satz177(s))):is(ts(m0(r),m0(s)),ts(r,s))
+satz198a:=symis(real,ts(m0(r),m0(s)),ts(r,s),satz198):is(ts(r,s),ts(m0(r),m0(s)))
++*ivr4
+b1is@[p:pos(r)][q:pos(s)]
+t3:=ptdpp(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(td(a1,b1))
+t4:=posin(ts(r,s),td(a1,b1),tict,t3):pos(ts(r,s))
+-ivr4
+s@[p:pos(r)][q:pos(s)]
+postspp:=realapp2(pos(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr4"(x,y,t,u,p,q)):pos(ts(r,s))
++*ivr4
+p@[n:neg(s)]
+t5:=ntdpn(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):negd(td(a1,b1))
+t6:=negin(ts(r,s),td(a1,b1),tict,t5):neg(ts(r,s))
+-ivr4
+s@[p:pos(r)][n:neg(s)]
+negtspn:=realapp2(neg(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr4"(x,y,t,u,p,n)):neg(ts(r,s))
+s@[n:neg(r)][p:pos(s)]
+negtsnp:=isneg(ts(s,r),ts(r,s),comts(s,r),negtspn(s,r,p,n)):neg(ts(r,s))
+s@[n:neg(r)][o:neg(s)]
+postsnn:=ispos(ts(m0(r),m0(s)),ts(r,s),satz198,postspp(m0(r),m0(s),satz176c(r,n),satz176c(s,o))):pos(ts(r,s))
+r@[n:nis(r,0)]
+possq:=rapp(r,pos(ts(r,r)),[t:pos(r)]postspp(r,r,t,t),th2"l.imp"(is(r,0),pos(ts(r,r)),n),[t:neg(r)]postsnn(r,r,t,t)):pos(ts(r,r))
+r@nnegsq:=th1"l.imp"(is(r,0),not(neg(ts(r,r))),[t:is(r,0)]0notn(ts(r,r),satz192a(r,r,t)),[t:nis(r,0)]pnotn(ts(r,r),possq(r,t))):not(neg(ts(r,r)))
++4r199
+c2it@t1:=satzd199(a2,b2,c2):eq"rp"(td(td(a2,b2),c2),td(a2,td(b2,c2)))
+t2:=isin(ts(ts(r,s),t),ts(r,ts(s,t)),td(td(a2,b2),c2),td(a2,td(b2,c2)),tict(ts(r,s),t,td(a2,b2),c2,tict(r,s,a2,b2,a2ir,b2is),c2it),tict(r,ts(s,t),a2,td(b2,c2),a2ir,tict(s,t,b2,c2,b2is,c2it)),t1):is(ts(ts(r,s),t),ts(r,ts(s,t)))
+-4r199
+t@satz199:=realapp3(is(ts(ts(r,s),t),ts(r,ts(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r199"(x,y,z,u,v,w)):is(ts(ts(r,s),t),ts(r,ts(s,t)))
+assts1:=satz199:is(ts(ts(r,s),t),ts(r,ts(s,t)))
+assts2:=symis(real,ts(ts(r,s),t),ts(r,ts(s,t)),satz199):is(ts(r,ts(s,t)),ts(ts(r,s),t))
++4r201
+c2it@t1:=satzd201(a2,b2,c2):eq"rp"(td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)))
+t2:=isin(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)),tict(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),picp(ts(r,s),ts(r,t),td(a2,b2),td(a2,c2),tict(r,s,a2,b2,a2ir,b2is),tict(r,t,a2,c2,a2ir,c2it)),t1):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
+-4r201
+satz201:=realapp3(is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r201"(x,y,z,u,v,w)):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
+disttp1:=tr3is(real,ts(pl(r,s),t),ts(t,pl(r,s)),pl(ts(t,r),ts(t,s)),pl(ts(r,t),ts(s,t)),comts(pl(r,s),t),satz201(t,r,s),ispl12(ts(t,r),ts(r,t),ts(t,s),ts(s,t),comts(t,r),comts(t,s))):is(ts(pl(r,s),t),pl(ts(r,t),ts(s,t)))
+disttp2:=satz201:is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
+distpt1:=symis(real,ts(pl(r,s),t),pl(ts(r,t),ts(s,t)),disttp1):is(pl(ts(r,t),ts(s,t)),ts(pl(r,s),t))
+distpt2:=symis(real,ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),disttp2):is(pl(ts(r,s),ts(r,t)),ts(r,pl(s,t)))
+satz202:=tris(real,ts(r,mn(s,t)),pl(ts(r,s),ts(r,m0(t))),mn(ts(r,s),ts(r,t)),disttp2(r,s,m0(t)),ispl2(ts(r,m0(t)),m0(ts(r,t)),ts(r,s),satz197b(r,t))):is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
+disttm1:=tris(real,ts(mn(r,s),t),pl(ts(r,t),ts(m0(s),t)),mn(ts(r,t),ts(s,t)),disttp1(r,m0(s),t),ispl2(ts(m0(s),t),m0(ts(s,t)),ts(r,t),satz197a(s,t))):is(ts(mn(r,s),t),mn(ts(r,t),ts(s,t)))
+disttm2:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
+distmt1:=symis(real,ts(mn(r,s),t),mn(ts(r,t),ts(s,t)),disttm1):is(mn(ts(r,t),ts(s,t)),ts(mn(r,s),t))
+distmt2:=symis(real,ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)),disttm2):is(mn(ts(r,s),ts(r,t)),ts(r,mn(s,t)))
+satz200:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
++4r203
+c2it@[m:more(r,s)][p:pos(t)]
+t1:=satzd203a(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),posex(t,c2,c2it,p)):mored(td(a2,c2),td(b2,c2))
+t2:=morein(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t1):more(ts(r,t),ts(s,t))
+-4r203
+[m:more(r,s)][p:pos(t)]
+satz203a:=realapp3(more(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r203"(x,y,z,u,v,w,m,p)):more(ts(r,t),ts(s,t))
+m@[i:is(t,0)]
+satz203b:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
++*4r203
+m@[n:neg(t)]
+t3:=satzd203c(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),negex(t,c2,c2it,n)):lessd(td(a2,c2),td(b2,c2))
+t4:=lessin(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t3):less(ts(r,t),ts(s,t))
+-4r203
+m@[n:neg(t)]
+satz203c:=realapp3(less(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".4r203"(x,y,z,u,v,w,m,n)):less(ts(r,t),ts(s,t))
+p@satz203d:=ismore12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203a):more(ts(t,r),ts(t,s))
+i@satz203e:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
+n@satz203f:=isless12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203c):less(ts(t,r),ts(t,s))
+t@[l:less(r,s)][p:pos(t)]
+satz203g:=lemma1(ts(s,t),ts(r,t),satz203a(s,r,t,lemma2(r,s,l),p)):less(ts(r,t),ts(s,t))
+l@[i:is(t,0)]
+satz203h:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
+l@[n:neg(t)]
+satz203j:=lemma2(ts(s,t),ts(r,t),satz203c(s,r,t,lemma2(r,s,l),n)):more(ts(r,t),ts(s,t))
+p@satz203k:=lemma1(ts(t,s),ts(t,r),satz203d(s,r,t,lemma2(r,s,l),p)):less(ts(t,r),ts(t,s))
+i@satz203l:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
+n@satz203m:=lemma2(ts(t,s),ts(t,r),satz203f(s,r,t,lemma2(r,s,l),n)):more(ts(t,r),ts(t,s))
++4r204
+a0ir@[n1:nis(r,0)]
+t1:=th3"l.imp"(zero(a0),is(r,0),n1,[t:zero(a0)]0in(t)):not(zero(a0))
+d3iu@[n1:nis(s,0)][i:is(ts(s,t),r)][j:is(ts(s,u),r)]
+t2:=satzd204b(a3,b3,t1(s,b3,b3is,n1),c3,d3,isex(ts(s,t),r,td(b3,c3),a3,tict(s,t,b3,c3,b3is,c3it),a3ir,i),isex(ts(s,u),r,td(b3,d3),a3,tict(s,u,b3,d3,b3is,d3iu),a3ir,j)):eq"rp"(c3,d3)
+t3:=isin(t,u,c3,d3,c3it,d3iu,t2):is(t,u)
+-4r204
+s@[n:nis(s,0)][x:real][y:real][i:is(ts(s,x),r)][j:is(ts(s,y),r)]
+satz204b:=realapp4(x,y,is(x,y),[z:dif][u:dif][v:dif][w:dif][zi:inn(z,class(r))][ui:inn(u,class(s))][vi:inn(v,class(x))][wi:inn(w,class(y))]t3".4r204"(x,y,z,u,v,w,zi,ui,vi,wi,n,i,j)):is(x,y)
++*4r204
+b1is@[n1:nis(s,0)]
+t4:=satzd204a(a1,b1,t1(s,b1,b1is,n1)):some"l"(dif,[x:dif]eq"rp"(td(b1,x),a1))
+[a:dif][e:eq"rp"(td(b1,a),a1)]
+ar:=realof(a):real
+t5:=isin(ts(s,ar),r,td(b1,a),a1,tict(s,ar,b1,a,b1is,innclass(a)),a1ir,e):is(ts(s,ar),r)
+t6:=somei(real,[x:real]is(ts(s,x),r),ar,t5):some([x:real]is(ts(s,x),r))
+n1@t7:=someapp(dif,[x:dif]eq"rp"(td(b1,x),a1),t4,some([x:real]is(ts(s,x),r)),[x:dif][t:eq"rp"(td(b1,x),a1)]t6(x,t)):some([x:real]is(ts(s,x),r))
+-4r204
+n@satz204a:=realapp2(some([x:real]is(ts(s,x),r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r204"(x,y,t,u,n)):some([x:real]is(ts(s,x),r))
+satz204:=onei(real,[x:real]is(ts(s,x),r),[x:real][y:real][t:is(ts(s,x),r)][u:is(ts(s,y),r)]satz204b(x,y,t,u),satz204a):one([x:real]is(ts(s,x),r))
+ov:=ind(real,[x:real]is(ts(s,x),r),satz204):real
+satz204c:=oneax(real,[x:real]is(ts(s,x),r),satz204):is(ts(s,ov(r,s,n)),r)
+satz204d:=symis(real,ts(s,ov(r,s,n)),r,satz204c):is(r,ts(s,ov(r,s,n)))
+satz204e:=tris(real,ts(ov(r,s,n),s),ts(s,ov(r,s,n)),r,comts(ov(r,s,n),s),satz204c):is(ts(ov(r,s,n),s),r)
+satz204f:=symis(real,ts(ov(r,s,n),s),r,satz204e):is(r,ts(ov(r,s,n),s))
+s@[x:real][n:nis(s,0)][i:is(ts(s,x),r)]
+satz204g:=satz204b(n,x,ov(r,s,n),i,satz204c(n)):is(x,ov(r,s,n))
+s@[n:nis(s,0)][p:pos(r)][q:pos(s)]
++*4r204
+n@ros:=ov(r,s,n):real
+p@t8:=ispos(r,ts(s,ros),satz204d(n),p):pos(ts(s,ros))
+q@t9:=th1"l.and"(neg(s),neg(ros),pnotn(s,q)):not(and(neg(s),neg(ros)))
+t10:=ore1(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t9):and(pos(s),pos(ros))
+-4r204
+q@posovpp:=ande2(pos(s),pos(ov(r,s,n)),t10".4r204"):pos(ov(r,s,n))
+p@[m:neg(s)]
++*4r204
+m@t11:=th1"l.and"(pos(s),pos(ros),nnotp(s,m)):not(and(pos(s),pos(ros)))
+t12:=ore2(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t11):and(neg(s),neg(ros))
+-4r204
+m@negovpn:=ande2(neg(s),neg(ov(r,s,n)),t12".4r204"):neg(ov(r,s,n))
+n@[m:neg(r)][p:pos(s)]
++*4r204
+m@t13:=isneg(r,ts(s,ros),satz204d(n),m):neg(ts(s,ros))
+p@t14:=th1"l.and"(neg(s),pos(ros),pnotn(s,p)):not(and(neg(s),pos(ros)))
+t15:=ore1(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t14):and(pos(s),neg(ros))
+-4r204
+p@negovnp:=ande2(pos(s),neg(ov(r,s,n)),t15".4r204"):neg(ov(r,s,n))
+m@[l:neg(s)]
++*4r204
+l@t16:=th1"l.and"(pos(s),neg(ros),nnotp(s,l)):not(and(pos(s),neg(ros)))
+t17:=ore2(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t16):and(neg(s),pos(ros))
+-4r204
+l@posovnn:=ande2(neg(s),pos(ov(r,s,n)),t17".4r204"):pos(ov(r,s,n))
+@[r0:cut][s0:cut][m:more"rp"(r0,s0)]
+morerpep:=morein(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),morerpepd(r0,s0,m)):more(pofrp(r0),pofrp(s0))
+s0@[m:more(pofrp(r0),pofrp(s0))]
+morerpip:=morerpipd(r0,s0,moreex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),m)):more"rp"(r0,s0)
+s0@[l:less"rp"(r0,s0)]
+lessrpep:=lemma1(pofrp(s0),pofrp(r0),morerpep(s0,r0,satz122(r0,s0,l))):less(pofrp(r0),pofrp(s0))
+s0@[l:less(pofrp(r0),pofrp(s0))]
+lessrpip:=satz121(s0,r0,morerpip(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
+s@[p:pos(r)][q:pos(s)][m:more(r,s)]
+q@[m:more(r,s)]
++ivr5
+t1:=ismore12(r,pofrp(rpofp(r,p)),s,pofrp(rpofp(s,q)),isprp1(r,p),isprp1(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
+-ivr5
+moreperp:=morerpip(rpofp(r,p),rpofp(s,q),t1".ivr5"):more"rp"(rpofp(r,p),rpofp(s,q))
+q@[m:more"rp"(rpofp(r,p),rpofp(s,q))]
++*ivr5
+m@t2:=morerpep(rpofp(r,p),rpofp(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
+-ivr5
+m@morepirp:=ismore12(pofrp(rpofp(r,p)),r,pofrp(rpofp(s,q)),s,isprp2(r,p),isprp2(s,q),t2".ivr5"):more(r,s)
+q@[l:less(r,s)]
+lessperp:=satz121(rpofp(s,q),rpofp(r,p),moreperp(s,r,q,p,lemma2(r,s,l))):less"rp"(rpofp(r,p),rpofp(s,q))
+q@[l:less"rp"(rpofp(r,p),rpofp(s,q))]
+lesspirp:=lemma1(s,r,morepirp(s,r,q,p,satz122(rpofp(r,p),rpofp(s,q),l))):less(r,s)
+r@s01:=setof(real,[x:real]lessis(x,r)):set(real)
+s02:=setof(real,[x:real]more(x,r)):set(real)
++5r205
+s@[n:not(in(s,s01))]
+t1:=th3"l.imp"(lessis(s,r),in(s,s01),n,[t:lessis(s,r)]estii(real,[x:real]lessis(x,r),s,t)):not(lessis(s,r))
+t2:=estii(real,[x:real]more(x,r),s,satz167k(s,r,t1)):in(s,s02)
+-5r205
+vb00:=[x:real][t:not(in(x,s01))]t2".5r205"(x,t):all([x:real]or(in(x,s01),in(x,s02)))
++*5r205
+r@t3:=estii(real,[x:real]lessis(x,r),r,lessisi2(r,r,refis(real,r))):in(r,s01)
+-5r205
+r@vb01a:=nonemptyi(real,s01,r,t3".5r205"):nonempty(real,s01)
++*5r205
+r@t4:=ismore2(pl(r,0),r,pl(r,1rl),pl02(r,0,refis(real,0)),satz188k(1rl,0,r,satz169a(1rl,pos1))):more(pl(r,1rl),r)
+t5:=estii(real,[x:real]more(x,r),pl(r,1rl),t4):in(pl(r,1rl),s02)
+-5r205
+r@vb01b:=nonemptyi(real,s02,pl(r,1rl),t5".5r205"):nonempty(real,s02)
++*5r205
+s@[i:in(s,s01)][t:real][j:in(t,s02)]
+t6:=satz172a(s,r,t,estie(real,[x:real]lessis(x,r),s,i),lemma1(t,r,estie(real,[x:real]more(x,r),t,j))):less(s,t)
+-5r205
+r@vb02:=[x:real][t:in(x,s01)][y:real][u:in(y,s02)]t6".5r205"(x,t,y,u):all([x:real][t:in(x,s01)]all([y:real][u:in(y,s02)]less(x,y)))
+s@[l:less(s,r)]
+vb03a:=estii(real,[x:real]lessis(x,r),s,lessisi1(s,r,l)):in(s,s01)
+s@[m:more(s,r)]
+vb03b:=estii(real,[x:real]more(x,r),s,m):in(s,s02)
+r@s11:=setof(real,[x:real]less(x,r)):set(real)
+s12:=setof(real,[x:real]moreis(x,r)):set(real)
++*5r205
+s@[n:not(in(s,s11))]
+t7:=th3"l.imp"(less(s,r),in(s,s11),n,[t:less(s,r)]estii(real,[x:real]less(x,r),s,t)):not(less(s,r))
+t8:=estii(real,[x:real]moreis(x,r),s,satz167f(s,r,t7)):in(s,s12)
+-5r205
+r@vb10:=[x:real][t:not(in(x,s11))]t8".5r205"(x,t):all([x:real]or(in(x,s11),in(x,s12)))
++*5r205
+r@t9:=isless2(pl(r,0),r,mn(r,1rl),pl02(r,0,refis(real,0)),satz188m(m0(1rl),0,r,satz169c(m0(1rl),satz176a(1rl,pos1)))):less(mn(r,1rl),r)
+t10:=estii(real,[x:real]less(x,r),mn(r,1rl),t9):in(mn(r,1rl),s11)
+-5r205
+r@vb11a:=nonemptyi(real,s11,mn(r,1rl),t10".5r205"):nonempty(real,s11)
++*5r205
+r@t11:=estii(real,[x:real]moreis(x,r),r,moreisi2(r,r,refis(real,r))):in(r,s12)
+-5r205
+r@vb11b:=nonemptyi(real,s12,r,t11".5r205"):nonempty(real,s12)
++*5r205
+s@[i:in(s,s11)][t:real][j:in(t,s12)]
+t12:=satz172b(s,r,t,estie(real,[x:real]less(x,r),s,i),satz168a(t,r,estie(real,[x:real]moreis(x,r),t,j))):less(s,t)
+-5r205
+r@vb12:=[x:real][t:in(x,s11)][y:real][u:in(y,s12)]t12".5r205"(x,t,y,u):all([x:real][t:in(x,s11)]all([y:real][u:in(y,s12)]less(x,y)))
+s@[l:less(s,r)]
+vb13a:=estii(real,[x:real]less(x,r),s,l):in(s,s11)
+s@[m:more(s,r)]
+vb13b:=estii(real,[x:real]moreis(x,r),s,moreisi1(s,r,m)):in(s,s12)
+@2rl:=pl(1rl,1rl):real
+pos2:=pospl(1rl,1rl,pos1,pos1):pos(2rl)
+half:=ov(1rl,2rl,pnot0(2rl,pos2)):real
+poshalf:=posovpp(1rl,2rl,pnot0(2rl,pos2),pos1,pos2):pos(half)
++*ivr5
+r@t3:=tris(real,pl(r,r),pl(ts(1rl,r),ts(1rl,r)),ts(2rl,r),ispl12(r,ts(1rl,r),r,ts(1rl,r),satz195c(r),satz195c(r)),distpt1(1rl,1rl,r)):is(pl(r,r),ts(2rl,r))
+t4:=tr4is(real,ts(half,pl(r,r)),ts(half,ts(2rl,r)),ts(ts(half,2rl),r),ts(1rl,r),r,ists2(pl(r,r),ts(2rl,r),half,t3),assts2(half,2rl,r),ists1(ts(half,2rl),1rl,r,satz204e(1rl,2rl,pnot0(2rl,pos2))),satz195b(r)):is(ts(half,pl(r,r)),r)
+-ivr5
+s@[l:less(r,s)]
++*ivr5
+l@t5:=satz203k(pl(r,r),pl(r,s),half,satz188m(r,s,r,l),poshalf):less(ts(half,pl(r,r)),ts(half,pl(r,s)))
+-ivr5
+l@lemma3:=isless1(ts(half,pl(r,r)),r,ts(half,pl(r,s)),t4".ivr5",t5".ivr5"):less(r,ts(half,pl(r,s)))
++*ivr5
+l@t6:=satz203k(pl(r,s),pl(s,s),half,satz188f(r,s,s,l),poshalf):less(ts(half,pl(r,s)),ts(half,pl(s,s)))
+-ivr5
+l@lemma4:=isless2(ts(half,pl(s,s)),s,ts(half,pl(r,s)),t4".ivr5"(s),t6".ivr5"):less(ts(half,pl(r,s)),s)
+[p:pos(r)]
+lemma5:=satz169b(s,trmore(s,r,0,lemma2(r,s,l),satz169a(r,p))):pos(s)
+@[s1:set(real)][s2:set(real)][p0:all([x:real]or(in(x,s1),in(x,s2)))][p1a:nonempty(real,s1)][p1b:nonempty(real,s2)][p2:all([x:real][t:in(x,s1)]all([y:real][u:in(y,s2)]less(x,y)))]
++*5r205
+s2@[r:real]
+prop1:=all([x:real][t:less(x,r)]in(x,s1)):'prop'
+prop2:=all([x:real][t:more(x,r)]in(x,s2)):'prop'
+prop3:=and(prop1,prop2):'prop'
+p2@[x:real][y:real][px:prop3(x)][py:prop3(y)][l:less(x,y)]
+mxy:=ts(half,pl(x,y)):real
+t13:=lemma2(x,mxy,lemma3(x,y,l)):more(mxy,x)
+t14:=lemma4(x,y,l):less(mxy,y)
+t15:=<t14><mxy>ande1(prop1(y),prop2(y),py):in(mxy,s1)
+t16:=<t13><mxy>ande2(prop1(x),prop2(x),px):in(mxy,s2)
+t17:=<t16><mxy><t15><mxy>p2:less(mxy,mxy)
+t18:=<refis(real,mxy)>ec3e31(is(mxy,mxy),more(mxy,mxy),less(mxy,mxy),satz167b(mxy,mxy),t17):con
+py@t19:=[t:less(x,y)]t18(t):not(less(x,y))
+t20:=[t:more(x,y)]t18(y,x,py,px,lemma1(x,y,t)):not(more(x,y))
+t21:=or3e1(is(x,y),more(x,y),less(x,y),satz167a(x,y),t20,t19):is(x,y)
+p2@t22:=[x:real][y:real][t:prop3(x)][u:prop3(y)]t21(x,y,t,u):amone(real,[x:real]prop3(x))
+[case1:some([x:real]and(pos(x),in(x,s1)))][r:real][a:and(pos(r),in(r,s1))]
+t23:=ande1(pos(r),in(r,s1),a):pos(r)
+t24:=ande2(pos(r),in(r,s1),a):in(r,s1)
+sc1:=setof(cut,[x:cut]in(pofrp(x),s1)):set(cut)
+sc2:=setof(cut,[x:cut]in(pofrp(x),s2)):set(cut)
+[r0:cut][i:in(pofrp(r0),s1)]
+t25:=estii(cut,[x:cut]in(pofrp(x),s1),r0,i):in"rp"(r0,sc1)
+r0@[i:in"rp"(r0,sc1)]
+t26:=estie(cut,[x:cut]in(pofrp(x),s1),r0,i):in(pofrp(r0),s1)
+r0@[i:in(pofrp(r0),s2)]
+t27:=estii(cut,[x:cut]in(pofrp(x),s2),r0,i):in"rp"(r0,sc2)
+r0@[i:in"rp"(r0,sc2)]
+t28:=estie(cut,[x:cut]in(pofrp(x),s2),r0,i):in(pofrp(r0),s2)
+r0@t29:=th9"l.or"(in(pofrp(r0),s1),in(pofrp(r0),s2),in"rp"(r0,sc1),in"rp"(r0,sc2),<pofrp(r0)>p0,[t:in(pofrp(r0),s1)]t25(t),[t:in(pofrp(r0),s2)]t27(t)):or(in"rp"(r0,sc1),in"rp"(r0,sc2))
+a@pr1:=rpofp(r,t23):cut
+t30:=isp(real,[x:real]in(x,s1),r,pofrp(pr1),t24,isprp1(r,t23)):in(pofrp(pr1),s1)
+t31:=nonemptyi(cut,sc1,pr1,t25(pr1,t30)):nonempty(cut,sc1)
+[s:real][i:in(s,s2)]
+t32:=<i><s><t24><r>p2:less(r,s)
+t33:=lemma5(r,s,t32,t23):pos(s)
+ps1:=rpofp(s,t33):cut
+t34:=isp(real,[x:real]in(x,s2),s,pofrp(ps1),i,isprp1(s,t33)):in(pofrp(ps1),s2)
+t35:=nonemptyi(cut,sc2,ps1,t27(ps1,t34)):nonempty(cut,sc2)
+a@t36:=nonemptyapp(real,s2,p1b,nonempty(cut,sc2),[x:real][t:in(x,s2)]t35(x,t)):nonempty(cut,sc2)
+r0@[i:in"rp"(r0,sc1)][s0:cut][j:in"rp"(s0,sc2)]
+t37:=<t28(s0,j)><pofrp(s0)><t26(r0,i)><pofrp(r0)>p2:less(pofrp(r0),pofrp(s0))
+t38:=lessrpip(r0,s0,t37):less"rp"(r0,s0)
+a@stc:=schnitt(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):cut
+t39:=satzp205a(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:less"rp"(x,stc)]in"rp"(x,sc1))
+t40:=satzp205b(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:more"rp"(x,stc)]in"rp"(x,sc2))
+stp:=pofrp(stc):real
+t41:=posi(stc):pos(stp)
+[s:real][l:less(s,stp)][p:pos(s)]
+ps2:=rpofp(s,p):cut
+t42:=lessrpip(ps2,stc,isless1(s,pofrp(ps2),stp,isprp1(s,p),l)):less"rp"(ps2,stc)
+t43:=<t42><ps2>t39:in"rp"(ps2,sc1)
+t44:=isp(real,[x:real]in(x,s1),pofrp(ps2),s,t26(ps2,t43),isprp2(s,p)):in(s,s1)
+l@[n:not(pos(s))][i:in(s,s2)]
+t45:=<i><s><t24><r>p2:less(r,s)
+t46:=<lemma5(r,s,t45,t23)>n:con
+n@t47:=ore1(in(s,s1),in(s,s2),<s>p0,[t:in(s,s2)]t46(t)):in(s,s1)
+l@t48:=th1"l.imp"(pos(s),in(s,s1),[t:pos(s)]t44(t),[t:not(pos(s))]t47(t)):in(s,s1)
+s@[m:more(s,stp)]
+t49:=lemma5(stp,s,lemma1(s,stp,m),t41):pos(s)
+ps3:=rpofp(s,t49):cut
+t50:=morerpip(ps3,stc,ismore1(s,pofrp(ps3),stp,isprp1(s,t49),m)):more"rp"(ps3,stc)
+t51:=<t50><ps3>t40:in"rp"(ps3,sc2)
+t52:=isp(real,[x:real]in(x,s2),pofrp(ps3),s,t28(ps3,t51),isprp2(s,t49)):in(s,s2)
+a@t53:=andi(prop1(stp),prop2(stp),[x:real][t:less(x,stp)]t48(x,t),[x:real][t:more(x,stp)]t52(x,t)):prop3(stp)
+t54:=somei(real,[x:real]prop3(x),stp,t53):some([x:real]prop3(x))
+case1@t55:=someapp(real,[x:real]and(pos(x),in(x,s1)),case1,some([x:real]prop3(x)),[x:real][t:and(pos(x),in(x,s1))]t54(x,t)):some([x:real]prop3(x))
+p2@[case2:some([x:real]and(neg(x),in(x,s2)))]
+sp1:=setof(real,[x:real]in(m0(x),s1)):set(real)
+sp2:=setof(real,[x:real]in(m0(x),s2)):set(real)
+[r:real][i:in(m0(r),s1)]
+t56:=estii(real,[x:real]in(m0(x),s1),r,i):in(r,sp1)
+r@[i:in(r,sp1)]
+t57:=estie(real,[x:real]in(m0(x),s1),r,i):in(m0(r),s1)
+r@[i:in(m0(r),s2)]
+t58:=estii(real,[x:real]in(m0(x),s2),r,i):in(r,sp2)
+r@[i:in(r,sp2)]
+t59:=estie(real,[x:real]in(m0(x),s2),r,i):in(m0(r),s2)
+r@t60:=comor(in(r,sp1),in(r,sp2),th9"l.or"(in(m0(r),s1),in(m0(r),s2),in(r,sp1),in(r,sp2),<m0(r)>p0,[t:in(m0(r),s1)]t56(t),[t:in(m0(r),s2)]t58(t))):or(in(r,sp2),in(r,sp1))
+[i:in(r,s2)]
+t61:=t58(m0(r),isp(real,[x:real]in(x,s2),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp2)
+t62:=nonemptyi(real,sp2,m0(r),t61):nonempty(real,sp2)
+case2@t63:=nonemptyapp(real,s2,p1b,nonempty(real,sp2),[x:real][t:in(x,s2)]t62(x,t)):nonempty(real,sp2)
+r@[i:in(r,s1)]
+t64:=t56(m0(r),isp(real,[x:real]in(x,s1),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp1)
+t65:=nonemptyi(real,sp1,m0(r),t64):nonempty(real,sp1)
+case2@t66:=nonemptyapp(real,s1,p1a,nonempty(real,sp1),[x:real][t:in(x,s1)]t65(x,t)):nonempty(real,sp1)
+r@[i:in(r,sp2)][s:real][j:in(s,sp1)]
+t67:=<t59(r,i)><m0(r)><t57(s,j)><m0(s)>p2:less(m0(s),m0(r))
+t68:=lemma1(s,r,satz183d(s,r,t67)):less(r,s)
+r@[a:and(neg(r),in(r,s2))]
+t69:=satz176c(r,ande1(neg(r),in(r,s2),a)):pos(m0(r))
+t70:=isp(real,[x:real]in(x,s2),r,m0(m0(r)),ande2(neg(r),in(r,s2),a),satz177a(r)):in(m0(m0(r)),s2)
+t71:=andi(pos(m0(r)),in(m0(r),sp2),t69,t58(m0(r),t70)):and(pos(m0(r)),in(m0(r),sp2))
+t72:=somei(real,[x:real]and(pos(x),in(x,sp2)),m0(r),t71):some([x:real]and(pos(x),in(x,sp2)))
+case2@t73:=someapp(real,[x:real]and(neg(x),in(x,s2)),case2,some([x:real]and(pos(x),in(x,sp2))),[x:real][t:and(neg(x),in(x,s2))]t72(x,t)):some([x:real]and(pos(x),in(x,sp2)))
+t74:=t55(sp2,sp1,[x:real]t60(x),t63,t66,[x:real][t:in(x,sp2)][y:real][u:in(y,sp1)]t68(x,t,y,u),t73):some([x:real]prop3(sp2,sp1,x))
+[r:real][p:prop3(sp2,sp1,r)][s:real][l:less(s,m0(r))]
+t75:=ismore2(m0(m0(r)),r,m0(s),satz177(r),satz183c(s,m0(r),l)):more(m0(s),r)
+t76:=<t75><m0(s)>ande2(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp1)
+t77:=isp(real,[x:real]in(x,s1),m0(m0(s)),s,t57(m0(s),t76),satz177(s)):in(s,s1)
+s@[m:more(s,m0(r))]
+t78:=isless2(m0(m0(r)),r,m0(s),satz177(r),satz183a(s,m0(r),m)):less(m0(s),r)
+t79:=<t78><m0(s)>ande1(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp2)
+t80:=isp(real,[x:real]in(x,s2),m0(m0(s)),s,t59(m0(s),t79),satz177(s)):in(s,s2)
+p@t81:=andi(prop1(m0(r)),prop2(m0(r)),[x:real][t:less(x,m0(r))]t77(x,t),[x:real][t:more(x,m0(r))]t80(x,t)):prop3(m0(r))
+t82:=somei(real,[x:real]prop3(x),m0(r),t81):some([x:real]prop3(x))
+case2@t83:=someapp(real,[x:real]prop3(sp2,sp1,x),t74,some([x:real]prop3(x)),[x:real][t:prop3(sp2,sp1,x)]t82(x,t)):some([x:real]prop3(x))
+p2@[notcase1:not(some([x:real]and(pos(x),in(x,s1))))][notcase2:not(some([x:real]and(neg(x),in(x,s2))))][r:real][l:less(r,0)]
+t84:=th4"l.some"(real,[x:real]and(neg(x),in(x,s2)),notcase2,r):not(and(neg(r),in(r,s2)))
+t85:=th3"l.and"(neg(r),in(r,s2),t84,satz169d(r,l)):not(in(r,s2))
+t86:=ore1(in(r,s1),in(r,s2),<r>p0,t85):in(r,s1)
+r@[m:more(r,0)]
+t87:=th4"l.some"(real,[x:real]and(pos(x),in(x,s1)),notcase1,r):not(and(pos(r),in(r,s1)))
+t88:=th3"l.and"(pos(r),in(r,s1),t87,satz169b(r,m)):not(in(r,s1))
+t89:=ore2(in(r,s1),in(r,s2),<r>p0,t88):in(r,s2)
+notcase2@t90:=andi(prop1(0),prop2(0),[x:real][t:less(x,0)]t86(x,t),[x:real][t:more(x,0)]t89(x,t)):prop3(0)
+t91:=somei(real,[x:real]prop3(x),0,t90):some([x:real]prop3(x))
+notcase1@t92:=th1"l.imp"(some([x:real]and(neg(x),in(x,s2))),some([x:real]prop3(x)),[t:some([x:real]and(neg(x),in(x,s2)))]t83(t),[t:not(some([x:real]and(neg(x),in(x,s2))))]t91(t)):some([x:real]prop3(x))
+p2@t93:=th1"l.imp"(some([x:real]and(pos(x),in(x,s1))),some([x:real]prop3(x)),[t:some([x:real]and(pos(x),in(x,s1)))]t55(t),[t:not(some([x:real]and(pos(x),in(x,s1))))]t92(t)):some([x:real]prop3(x))
+t94:=onei(real,[x:real]prop3(x),t22,t93):one([x:real]prop3(x))
+-5r205
+p2@satz205:=t94".5r205":one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
+dedekind:=satz205:one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
+schnitt:=ind(real,[x:real]prop3".5r205"(x),satz205):real
+[r:real][l:less(r,schnitt)]
+satz205a:=<l><r>ande1(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s1)
+r@[m:more(r,schnitt)]
+satz205b:=<m><r>ande2(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s2)
+@[r0:cut][s0:cut]
++iva
+dr:=pdofrp(r0):dif
+ds:=pdofrp(s0):dif
+t1:=lemmaivad1(r0,s0):eq"rp"(pd(dr,ds),pdofrp(pl"rp"(r0,s0)))
+-iva
+lemmaiva1:=isin(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)),pd(pdofrp(r0),pdofrp(s0)),pdofrp(pl"rp"(r0,s0)),picp(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(pl"rp"(r0,s0))),t1".iva"):is(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)))
++*iva
+s0@t2:=lemmaivad2(r0,s0):eq"rp"(td(dr,ds),pdofrp(ts"rp"(r0,s0)))
+-iva
+s0@lemmaiva2:=isin(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)),td(pdofrp(r0),pdofrp(s0)),pdofrp(ts"rp"(r0,s0)),tict(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(ts"rp"(r0,s0))),t2".iva"):is(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)))
+[m:more(pofrp(r0),pofrp(s0))]
++*iva
+m@t3:=moreex(pofrp(r0),pofrp(s0),dr,ds,innclass(dr),innclass(ds),m):mored(dr,ds)
+-iva
+m@lemmaiva3:=lemmaivad3(r0,s0,t3".iva"):more"rp"(r0,s0)
+s0@[m:more"rp"(r0,s0)]
++*iva
+m@[l:less(pofrp(r0),pofrp(s0))]
+t4:=satz121(s0,r0,lemmaiva3(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
+m@t5:=ec3e23(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):not(less"rp"(r0,s0))
+t6:=th3"l.imp"(less(pofrp(r0),pofrp(s0)),less"rp"(r0,s0),t5,[t:less(pofrp(r0),pofrp(s0))]t4(t)):not(less(pofrp(r0),pofrp(s0)))
+t7:=ec3e21(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):nis"rp"(r0,s0)
+t8:=th3"l.imp"(is(pofrp(r0),pofrp(s0)),is"rp"(r0,s0),t7,[t:is(pofrp(r0),pofrp(s0))]isrpip(r0,s0,t)):nis(pofrp(r0),pofrp(s0))
+-iva
+m@lemmaiva4:=or3e2(is(pofrp(r0),pofrp(s0)),more(pofrp(r0),pofrp(s0)),less(pofrp(r0),pofrp(s0)),satz167a(pofrp(r0),pofrp(s0)),t6".iva",t8".iva"):more(pofrp(r0),pofrp(s0))
+@[x:nat][y:nat][m:more(rlofnt(x),rlofnt(y))]
++*iva
+m@t9:=lemmaiva3(rpofnt(x),rpofnt(y),m):more"rp"(rpofnt(x),rpofnt(y))
+t10:=satz154d(rtofn(x),rtofn(y),t9):more"rt"(rtofn(x),rtofn(y))
+t11:=moree"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t10):moref(fr(x,1),fr(y,1))
+-iva
+m@lemmaiva5:=satz111a(x,y,t11".iva"):more"n"(x,y)
+y@[m:more"n"(x,y)]
++*iva
+m@t12:=satz111d(x,y,m):moref(fr(x,1),fr(y,1))
+t13:=morei"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t12):more"rt"(rtofn(x),rtofn(y))
+t14:=satz154a(rtofn(x),rtofn(y),t13):more"rp"(rpofnt(x),rpofnt(y))
+-iva
+m@lemmaiva6:=lemmaiva4(rpofnt(x),rpofnt(y),t14".iva"):more(rlofnt(x),rlofnt(y))
+@[r:real]
++int
+a0ir@[i:intrl(r)]
+t1:=intabsd(a0,intrlex(r,a0,a0ir,i)):intd(absd(a0))
+t2:=intrlin(abs(r),absd(a0),aica,t1):intrl(abs(r))
+-int
+[i:intrl(r)]
+intabs:=realapp1(r,intrl(abs(r)),[x:dif][t:inn(x,class(r))]t2".int"(r,x,t,i)):intrl(abs(r))
++*int
+i@t3:=intm0d(a0,intrlex(r,a0,a0ir,i)):intd(m0d(a0))
+t4:=intrlin(m0(r),m0d(a0),micm0,t3):intrl(m0(r))
+-int
+i@intm0:=realapp1(r,intrl(m0(r)),[x:dif][t:inn(x,class(r))]t4".int"(r,x,t,i)):intrl(m0(r))
++*int
+b1is@[i:intrl(r)][j:intrl(s)]
+t5:=intpd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(pd(a1,b1))
+t6:=intrlin(pl(r,s),pd(a1,b1),picp,t5):intrl(pl(r,s))
+-int
+i@[s:real][j:intrl(s)]
+intpl:=realapp2(r,s,intrl(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".int"(r,s,x,y,t,u,i,j)):intrl(pl(r,s))
+intmn:=intpl(r,i,m0(s),intm0(s,j)):intrl(mn(r,s))
++*int
+j@t7:=inttd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(td(a1,b1))
+t8:=intrlin(ts(r,s),td(a1,b1),tict,t7):intrl(ts(r,s))
+-int
+j@intts:=realapp2(r,s,intrl(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".int"(r,s,x,y,t,u,i,j)):intrl(ts(r,s))
+r@[n:natrl(r)]
++ivr24
+t1:=satz24a(ntofrl(r,n)):lessis"n"(1,ntofrl(r,n))
+t2:=th3"l.imp"(more(1rl,r),more"n"(1,ntofrl(r,n)),satz10d(1,ntofrl(r,n),t1),[t:more(1rl,r)]lemmaiva5(1,ntofrl(r,n),ismore2(r,rlofnt(ntofrl(r,n)),1rl,isrlnt1(r,n),t))):not(more(1rl,r))
+-ivr24
+satzr24:=satz167e(1rl,r,t2".ivr24"):lessis(1rl,r)
+r@[i:intrl(r)][s:real][j:intrl(s)][l:less(r,s)]
++ivr25
+t1:=satz182d(s,r,lemma2(r,s,l)):pos(mn(s,r))
+t2:=intmn(s,j,r,i):intrl(mn(s,r))
+t3:=posintnatrl(mn(s,r),t1,t2):natrl(mn(s,r))
+t4:=satzr24(mn(s,r),t3):lessis(1rl,mn(s,r))
+t5:=th9"l.or"(less(1rl,mn(s,r)),is(1rl,mn(s,r)),less(pl(1rl,r),pl(mn(s,r),r)),is(pl(1rl,r),pl(mn(s,r),r)),t4,[t:less(1rl,mn(s,r))]satz188f(1rl,mn(s,r),r,t),[t:is(1rl,mn(s,r))]ispl1(1rl,mn(s,r),r,t)):lessis(pl(1rl,r),pl(mn(s,r),r))
+-ivr25
+satzr25:=islessis12(pl(1rl,r),pl(r,1rl),pl(mn(s,r),r),s,compl(1rl,r),plmn(s,r),t5".ivr25"):lessis(pl(r,1rl),s)
+@[x:nat][y:nat]
++ivr155
+t1:=lemmaiva1(rpofnt(x),rpofnt(y)):is(pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
+t2:=isrpep(rpofnt(pl"n"(x,y)),pl"rp"(rpofnt(x),rpofnt(y)),satz155e(x,y)):is(rlofnt(pl"n"(x,y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
+-ivr155
+satzr155a:=tris2(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))),t2".ivr155",t1".ivr155"):is(rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)))
+satzr155b:=symis(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),satzr155a):is(pl(rlofnt(x),rlofnt(y)),rlofnt(pl"n"(x,y)))
++*ivr155
+y@t3:=lemmaiva2(rpofnt(x),rpofnt(y)):is(ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
+t4:=isrpep(rpofnt(ts"n"(x,y)),ts"rp"(rpofnt(x),rpofnt(y)),satz155f(x,y)):is(rlofnt(ts"n"(x,y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
+-ivr155
+y@satzr155c:=tris2(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))),t4".ivr155",t3".ivr155"):is(rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)))
+satzr155d:=symis(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),satzr155c):is(ts(rlofnt(x),rlofnt(y)),rlofnt(ts"n"(x,y)))
+@[t:real][r:real][s:real][a:and(not(neg(r)),is(ts(r,r),t))][b:and(not(neg(s)),is(ts(s,s),t))]
++7r161
+[c0:dif][cit:inn(c0,class(t))][a0:dif][air:inn(a0,class(r))][b0:dif][bis:inn(b0,class(s))]
+t1:=th3"l.imp"(negd(a0),neg(r),ande1(not(neg(r)),is(ts(r,r),t),a),[u:negd(a0)]negin(r,a0,air,u)):not(negd(a0))
+t2:=th3"l.imp"(negd(b0),neg(s),ande1(not(neg(s)),is(ts(s,s),t),b),[u:negd(b0)]negin(s,b0,bis,u)):not(negd(b0))
+t3:=isex(ts(r,r),t,td(a0,a0),c0,tict(r,r,a0,a0,air,air),cit,ande2(not(neg(r)),is(ts(r,r),t),a)):eq"rp"(td(a0,a0),c0)
+t4:=isex(ts(s,s),t,td(b0,b0),c0,tict(s,s,b0,b0,bis,bis),cit,ande2(not(neg(s)),is(ts(s,s),t),b)):eq"rp"(td(b0,b0),c0)
+t5:=isin(r,s,a0,b0,air,bis,satzd161b(c0,a0,b0,t1,t2,t3,t4)):is(r,s)
+-7r161
+satzr161b:=realapp3(t,r,s,is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(t))][v:inn(y,class(r))][w:inn(z,class(s))]t5".7r161"(x,u,y,v,z,w)):is(r,s)
+t@[n:not(neg(t))]
++*7r161
+n@[c0:dif][cit:inn(c0,class(t))]
+t6:=th3"l.imp"(negd(c0),neg(t),n,[u:negd(c0)]negin(t,c0,cit,u)):not(negd(c0))
+[a0:dif][a:and(not(negd(a0)),eq"rp"(td(a0,a0),c0))]
+ar:=realof(a0):real
+t7:=th3"l.imp"(neg(ar),negd(a0),ande1(not(negd(a0)),eq"rp"(td(a0,a0),c0),a),[u:neg(ar)]negex(ar,a0,innclass(a0),u)):not(neg(ar))
+t8:=isin(ts(ar,ar),t,td(a0,a0),c0,tict(ar,ar,a0,a0,innclass(a0),innclass(a0)),cit,ande2(not(negd(a0)),eq"rp"(td(a0,a0),c0),a)):is(ts(ar,ar),t)
+t9:=andi(not(neg(ar)),is(ts(ar,ar),t),t7,t8):and(not(neg(ar)),is(ts(ar,ar),t))
+t10:=somei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),ar,t9):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
+cit@t11:=someapp(dif,[x:dif]and(not(negd(x)),eq"rp"(td(x,x),c0)),satzd161a(c0,t6),some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:and(not(negd(x)),eq"rp"(td(x,x),c0))]t10(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
+-7r161
+n@satzr161a:=realapp1(t,some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:inn(x,class(t))]t11".7r161"(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
+satzr161:=onei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),[u:real][v:real][a:and(not(neg(u)),is(ts(u,u),t))][b:and(not(neg(v)),is(ts(v,v),t))]satzr161b(u,v,a,b),satzr161a):one([u:real]and(not(neg(u)),is(ts(u,u),t)))
+sqrt:=ind(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):real
++*7r161
+n@t12:=oneax(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):and(not(neg(sqrt)),is(ts(sqrt,sqrt),t))
+-7r161
+n@thsqrt1a:=ande1(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):not(neg(sqrt))
+thsqrt1b:=ande2(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):is(ts(sqrt,sqrt),t)
+[x:real][o:not(neg(x))][i:is(ts(x,x),t)]
+thsqrt2:=satzr161b(x,sqrt,andi(not(neg(x)),is(ts(x,x),t),o,i),t12".7r161"):is(x,sqrt(t,n))
+o@[i:is(t,ts(x,x))]
+thsqrt3:=symis(real,x,sqrt(t,n),thsqrt2(symis(real,t,ts(x,x),i))):is(sqrt(t,n),x)
+@[r:real][s:real][n:not(neg(r))][o:not(neg(s))][i:is(r,s)]
+issqrt:=thsqrt2(s,o,sqrt(r,n),thsqrt1a(r,n),tris(real,ts(sqrt(r,n),sqrt(r,n)),r,s,thsqrt1b(r,n),i)):is(sqrt(r,n),sqrt(s,o))
+r@[n:not(neg(r))][i:is(r,0)]
+sqrt0:=thsqrt3(r,n,0,0notn(0,refis(real,0)),tris2(real,r,ts(0,0),0,i,ts01(0,0,refis(real,0)))):is(sqrt(r,n),0)
+n@[o:nis(r,0)]
++sqrt
+t1:=th3"l.imp"(is(sqrt(r,n),0),is(r,0),o,[t:is(sqrt(r,n),0)]tris1(real,r,0,ts(sqrt(r,n),sqrt(r,n)),thsqrt1b(r,n),ts01(sqrt(r,n),sqrt(r,n),t))):nis(sqrt(r,n),0)
+-sqrt
+sqrtnot0:=or3e2(is(sqrt(r,n),0),pos(sqrt(r,n)),neg(sqrt(r,n)),axrlo(sqrt(r,n)),thsqrt1a(r,n),t1".sqrt"):pos(sqrt(r,n))
+@[r:real][s:real][t:real][n:nis(t,0)]
++v0
+t1:=tr3is(real,ts(t,ts(r,ov(s,t,n))),ts(ts(r,ov(s,t,n)),t),ts(r,ts(ov(s,t,n),t)),ts(r,s),comts(t,ts(r,ov(s,t,n))),assts1(r,ov(s,t,n),t),ists2(ts(ov(s,t,n),t),s,r,satz204e(s,t,n))):is(ts(t,ts(r,ov(s,t,n))),ts(r,s))
+-v0
+lemma6:=satz204g(ts(r,s),t,ts(r,ov(s,t,n)),n,t1".v0"):is(ts(r,ov(s,t,n)),ov(ts(r,s),t,n))
++*v0
+n@t2:=tris(real,ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(ts(t,ov(r,t,n)),ts(t,ov(s,t,n))),pl(r,s),disttp2(t,ov(r,t,n),ov(s,t,n)),ispl12(ts(t,ov(r,t,n)),r,ts(t,ov(s,t,n)),s,satz204c(r,t,n),satz204c(s,t,n))):is(ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(r,s))
+-v0
+n@lemma7:=satz204g(pl(r,s),t,pl(ov(r,t,n),ov(s,t,n)),n,t2".v0"):is(pl(ov(r,t,n),ov(s,t,n)),ov(pl(r,s),t,n))
+r@[n:nis(r,0)]
+lemma8:=satz204b(r,r,n,ov(r,r,n),1rl,satz204c(r,r,n),satz195(r)):is(ov(r,r,n),1rl)
+lemma9:=ore2(is(r,0),is(ov(0,r,n),0),satz192c(r,ov(0,r,n),satz204c(0,r,n)),n):is(ov(0,r,n),0)
+r@[i:is(r,m0(r))]
++*v0
+i@[p:pos(m0(r))]
+t3:=<isneg(r,m0(r),i,satz176f(r,p))>pnotn(m0(r),p):con
+i@[n:neg(m0(r))]
+t4:=<ispos(r,m0(r),i,satz176d(r,n))>nnotp(m0(r),n):con
+-v0
+i@lemma10:=satz176e(r,or3e1(is(m0(r),0),pos(m0(r)),neg(m0(r)),axrlo(m0(r)),[t:pos(m0(r))]t3".v0"(t),[t:neg(m0(r))]t4".v0"(t))):is(r,0)
+r@lemma11:=satz167f(ts(r,r),0,th3"l.imp"(less(ts(r,r),0),neg(ts(r,r)),nnegsq(r),[t:less(ts(r,r),0)]satz169d(ts(r,r),t))):moreis(ts(r,r),0)
+lemma12:=rapp(r,is(ts(r,r),ts(abs(r),abs(r))),[t:pos(r)]satz196a(r,r,t,t),[t:is(r,0)]tris2(real,ts(r,r),ts(abs(r),abs(r)),0,ts01(r,r,t),ts01(abs(r),abs(r),abs0(r,t))),[t:neg(r)]satz196b(r,r,t,t)):is(ts(r,r),ts(abs(r),abs(r)))
+@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
++shift
+t1:=satz190a(x,x,1rl,0,moreisi2(x,x,refis(real,x)),satz169a(1rl,natpos(1rl,natrl1))):more(pl(x,1rl),pl(x,0))
+t2:=ismore2(pl(x,0),x,pl(x,1rl),pl02(x,0,refis(real,0)),t1):more(pl(x,1rl),x)
+t3:=satz172d(pl(x,1rl),x,y,t2,satz168b(y,x,ly)):more(pl(x,1rl),y)
+t4:=satz182d(pl(x,1rl),y,t3):pos(mn(pl(x,1rl),y))
+t5:=intmn(pl(x,1rl),intpl(x,ix,1rl,intrl1),y,iy):intrl(mn(pl(x,1rl),y))
+t6:=posintnatrl(mn(pl(x,1rl),y),t4,t5):natrl(mn(pl(x,1rl),y))
+-shift
+shiftl:=ntofrl(mn(pl(x,1rl),y),t6".shift"):nat
+[n:1to(shiftl)]
++*shift
+n@n1:=inn"n"(shiftl,n):nat
+t7:=1top(shiftl,n):lessis"n"(n1,shiftl)
+n2:=rlofnt(n1):real
+t8:=natintrl(n2,natrli(n1)):intrl(n2)
+-shift
+n@shiftr:=mn(pl(n2".shift",y),1rl):real
+intshiftr:=intmn(pl(n2".shift",y),intpl(n2".shift",t8".shift",y,iy),1rl,intrl1):intrl(shiftr)
+[m:1to(shiftl)][i:is(shiftr(n),shiftr(m))]
++*shift
+n@t8a:=tris(real,mn(pl(shiftr(n),1rl),y),mn(pl(n2,y),y),n2,ismn1(pl(mn(pl(n2,y),1rl),1rl),pl(n2,y),y,plmn(pl(n2,y),1rl)),mnpl(n2,y)):is(mn(pl(shiftr(n),1rl),y),n2)
+i@t9a:=ismn1(pl(shiftr(n),1rl),pl(shiftr(m),1rl),y,ispl1(shiftr(n),shiftr(m),1rl,i)):is(mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y))
+t10a:=tr3is(real,n2(n),mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y),n2(m),symis(real,mn(pl(shiftr(n),1rl),y),n2,t8a),t9a,t8a(m)):is(n2(n),n2(m))
+t11a:=isntirl(n1(n),n1(m),t10a):is"n"(n1(n),n1(m))
+-shift
+i@iseshiftr:=isinne(shiftl,n,m,t11a".shift"):is"e"(1to(shiftl),n,m)
++*shift
+n@[m:more(shiftr,x)]
+t9:=satz188d(shiftr,x,1rl,m):more(pl(shiftr,1rl),pl(x,1rl))
+t10:=ismore1(pl(shiftr,1rl),pl(n2,y),pl(x,1rl),plmn(pl(n2,y),1rl),t9):more(pl(n2,y),pl(x,1rl))
+t11:=satz188d(pl(n2,y),pl(x,1rl),m0(y),t10):more(mn(pl(n2,y),y),mn(pl(x,1rl),y))
+t12:=ismore1(mn(pl(n2,y),y),n2,mn(pl(x,1rl),y),mnpl(n2,y),t11):more(n2,mn(pl(x,1rl),y))
+t13:=ismore12(n2,rlofnt(ntofrl(n2,natrli(n1))),mn(pl(x,1rl),y),rlofnt(ntofrl(mn(pl(x,1rl),y),t6)),isrlnt1(n2,natrli(n1)),isrlnt1(mn(pl(x,1rl),y),t6),t12):more(rlofnt(ntofrl(n2,natrli(n1))),rlofnt(shiftl))
+t14:=lemmaiva5(ntofrl(n2,natrli(n1)),shiftl,t13):more"n"(ntofrl(n2,natrli(n1)),shiftl)
+t15:=ismore1"n"(ntofrl(n2,natrli(n1)),n1,shiftl,isntrl2(n1),t14):more"n"(n1,shiftl)
+n@t16:=th3"l.imp"(more(shiftr,x),more"n"(n1,shiftl),satz10d(n1,shiftl,t7),[t:more(shiftr,x)]t15(t)):not(more(shiftr,x))
+-shift
+n@shiftrls:=satz167e(shiftr,x,t16".shift"):lessis(shiftr,x)
++*shift
+n@[m:more(y,shiftr)]
+t17:=satz188d(y,shiftr,1rl,m):more(pl(y,1rl),pl(shiftr,1rl))
+t18:=ismore12(pl(y,1rl),pl(1rl,y),pl(shiftr,1rl),pl(n2,y),compl(y,1rl),plmn(pl(n2,y),1rl),t17):more(pl(1rl,y),pl(n2,y))
+t19:=satz188a(1rl,n2,y,t18):more(1rl,n2)
+t20:=lemmaiva5(1,n1,t19):more"n"(1,n1)
+n@t21:=th3"l.imp"(more(y,shiftr),more"n"(1,n1),satz10d(1,n1,satz24a(n1)),[t:more(y,shiftr)]t20(t)):not(more(y,shiftr))
+-shift
+n@lsshiftr:=satz167e(y,shiftr,t21".shift"):lessis(y,shiftr)
+ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
++*shift
+a@t22:=and3e1(intrl(u),lessis(y,u),lessis(u,x),a):intrl(u)
+t23:=and3e2(intrl(u),lessis(y,u),lessis(u,x),a):lessis(y,u)
+t24:=and3e3(intrl(u),lessis(y,u),lessis(u,x),a):lessis(u,x)
+[l:less(u,x)]
+t25:=satz188f(pl(u,1rl),pl(x,1rl),m0"r"(y),satz188f(u,x,1rl,l)):less(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
+a@[i:is(u,x)]
+t26:=ismn1(pl(u,1rl),pl(x,1rl),y,ispl1(u,x,1rl,i)):is(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
+a@t27:=th9"l.or"(less(u,x),is(u,x),less(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),is(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),t24,[t:less(u,x)]t25(t),[t:is(u,x)]t26(t)):lessis(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
+ul:=shiftl(u,t22,y,iy,t23):nat
+t28:=islessis12(mn(pl(u,1rl),y),rlofnt(ul),mn(pl(x,1rl),y),rlofnt(shiftl),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isrlnt1(mn(pl(x,1rl),y),t6),t27):lessis(rlofnt(ul),rlofnt(shiftl))
+t29:=th3"l.imp"(more"n"(ul,shiftl),more(rlofnt(ul),rlofnt(shiftl)),satz167d(rlofnt(ul),rlofnt(shiftl),t28),[t:more"n"(ul,shiftl)]lemmaiva6(ul,shiftl,t)):not(more"n"(ul,shiftl))
+t30:=satz10e(ul,shiftl,t29):lessis"n"(ul,shiftl)
+-shift
+a@shiftl1:=outn(shiftl,ul".shift",t30".shift"):1to(shiftl)
++*shift
+a@t31:=isinoutn(shiftl,ul,t30):is"n"(ul,n1(shiftl1))
+t32:=tris(real,mn(pl(u,1rl),y),rlofnt(ul),n2(shiftl1),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isnterl(ul,n1(shiftl1),t31)):is(mn(pl(u,1rl),y),n2(shiftl1))
+t33:=tris(real,mn(pl(mn(pl(u,1rl),y),y),1rl),mn(pl(u,1rl),1rl),u,ismn1(pl(mn(pl(u,1rl),y),y),pl(u,1rl),1rl,plmn(pl(u,1rl),y)),mnpl(u,1rl)):is(mn(pl(mn(pl(u,1rl),y),y),1rl),u)
+-shift
+a@shiftinv1:=tris1(real,u,shiftr(shiftl1),mn(pl(mn(pl(u,1rl),y),y),1rl),t33".shift",ismn1(pl(mn(pl(u,1rl),y),y),pl(n2".shift"(shiftl1),y),1rl,ispl1(mn(pl(u,1rl),y),n2".shift"(shiftl1),y,t32".shift"))):is(u,shiftr(shiftl1))
+shiftinv2:=symis(real,u,shiftr(shiftl1),shiftinv1):is(shiftr(shiftl1),u)
+ly@[alpha:'type']
+seq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]alpha:'type'
+[s:seq]
+proofsirrelevant:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is(t,u)]is"e"(alpha,<tl><lt><it><t>s,<ul><lu><iu><u>s):'prop'
+alpha@[f:seq]
+shiftf:=[t:1to(shiftl)]<shiftrls(t)><lsshiftr(t)><intshiftr(t)><shiftr(t)>f:[t:1to(shiftl)]alpha
+ly@[s:seq(real)]
+inseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]and3(intrl(<w><v><u><t>s),lessis(y,<w><v><u><t>s),lessis(<w><v><u><t>s,x)):'prop'
+injseq:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is"r"(<tl><lt><it><t>s,<ul><lu><iu><u>s)]is"r"(t,u):'prop'
+[u:real][v:real][a:and3(intrl(v),lessis(y,v),lessis(v,x))]
++*shift
+a@prop1:=is(u,<t24(v,a)><t23(v,a)><t22(v,a)><v>s):'prop'
+-shift
+v@improp:=and(and3(intrl(v),lessis(y,v),lessis(v,x)),[t:and3(intrl(v),lessis(y,v),lessis(v,x))]prop1".shift"(t)):'prop'
+u@imseq:=some([t:real]improp(u,t)):'prop'
+s@surjseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]imseq(t):'prop'
+perm:=and(injseq,surjseq):'prop'
+[ins:inseq(s)]
++*shift
+ins@[n:1to(shiftl)]
+ns:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>s:real
+t34:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ins:and3(intrl(ns),lessis(y,ns),lessis(ns,x))
+-shift
+ins@shiftseq:=[t:1to(shiftl)]shiftl1(ns".shift"(t),t34".shift"(t)):[t:1to(shiftl)]1to(shiftl)
+[js:injseq(s)]
++*shift
+js@[n:1to(shiftl)][m:1to(shiftl)][i:is"e"(1to(shiftl),<n>shiftseq,<m>shiftseq)]
+t35:=isoutne(shiftl,ul(ns(n),t34(n)),t30(ns(n),t34(n)),ul(ns(m),t34(m)),t30(ns(m),t34(m)),i):is"n"(ul(ns(n),t34(n)),ul(ns(m),t34(m)))
+t36:=isrlint(mn(pl(ns(n),1rl),y),t6(ns(n),t22(ns(n),t34(n)),y,iy,t23(ns(n),t34(n))),mn(pl(ns(m),1rl),y),t6(ns(m),t22(ns(m),t34(m)),y,iy,t23(ns(m),t34(m))),t35):is(mn(pl(ns(n),1rl),y),mn(pl(ns(m),1rl),y))
+t37:=satz188b(ns(n),ns(m),1rl,satz188b(pl(ns(n),1rl),pl(ns(m),1rl),m0"r"(y),t36)):is(ns(n),ns(m))
+t38:=<t37><shiftrls(m)><lsshiftr(m)><intshiftr(m)><shiftr(m)><shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>js:is(shiftr(n),shiftr(m))
+t39:=satz188b(n2(n),n2(m),y,satz188b(pl(n2(n),y),pl(n2(m),y),m0(1rl),t38)):is(n2(n),n2(m))
+t40:=isntirl(n1(n),n1(m),t39):is"n"(n1(n),n1(m))
+t41:=isinne(shiftl,n,m,t40):is"e"(1to(shiftl),n,m)
+-shift
+js@injshiftseq:=[t:1to(shiftl)][u:1to(shiftl)][v:is"e"(1to(shiftl),<t>shiftseq,<u>shiftseq)]t41".shift"(t,u,v):injective(1to(shiftl),1to(shiftl),shiftseq)
+ins@[pri:proofsirrelevant(real,s)][ss:surjseq(s)]
++*shift
+ss@[n:1to(shiftl)]
+t42:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ss:imseq(shiftr(n))
+[u:real][p:improp(shiftr(n),u)]
+t43:=ande1(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):and3(intrl(u),lessis(y,u),lessis(u,x))
+t44:=ande2"l.r"(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):is(shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s)
+ul1:=shiftl1(u,t43):1to(shiftl)
+t45:=<shiftinv1(u,t43)><shiftrls(ul1)><lsshiftr(ul1)><intshiftr(ul1)><shiftr(ul1)><t24(u,t43)><t23(u,t43)><t22(u,t43)><u>pri:is(<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1))
+t46:=shiftinv1(ns(ul1),t34(ul1)):is(ns(ul1),shiftr(<ul1>shiftseq))
+t47:=tr3is(real,shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1),shiftr(<ul1>shiftseq),t44,t45,t46):is(shiftr(n),shiftr(<ul1>shiftseq))
+t48:=iseshiftr(n,<ul1>shiftseq,t47):is"e"(1to(shiftl),n,<ul1>shiftseq)
+t49:=somei(1to(shiftl),[t:1to(shiftl)]is"e"(1to(shiftl),n,<t>shiftseq),ul1,t48):image(1to(shiftl),1to(shiftl),shiftseq,n)
+n@t50:=someapp(real,[t:real]improp(shiftr(n),t),t42,image(1to(shiftl),1to(shiftl),shiftseq,n),[t:real][u:improp(shiftr(n),t)]t49(t,u)):image(1to(shiftl),1to(shiftl),shiftseq,n)
+-shift
+ss@surjshiftseq:=[t:1to(shiftl)]t50".shift"(t):surjective(1to(shiftl),1to(shiftl),shiftseq)
+pri@[ps:perm(s)]
+bijshiftseq:=andi(injective(1to(shiftl),1to(shiftl),shiftseq),surjective(1to(shiftl),1to(shiftl),shiftseq),injshiftseq(ande1(injseq(s),surjseq(s),ps)),surjshiftseq(ande2(injseq(s),surjseq(s),ps))):bijective(1to(shiftl),1to(shiftl),shiftseq)
++c
+@complex:=pair1type(real):'type'
+cx:=complex:'type'
+[x:complex][y:complex]
+is:=is"e"(cx,x,y):'prop'
+nis:=not(is(x,y)):'prop'
+@[p:[t:complex]'prop']
+some:=some"l"(cx,p):'prop'
+all:=all"l"(cx,p):'prop'
+one:=one"e"(cx,p):'prop'
+@[a:real][b:real]
+pli:=pair1(real,a,b):complex
+x@re:=first1(real,x):real
+im:=second1(real,x):real
+b@reis:=first1is1(real,a,b):is"r"(re(pli(a,b)),a)
+isre:=first1is2(real,a,b):is"r"(a,re(pli(a,b)))
+imis:=second1is1(real,a,b):is"r"(im(pli(a,b)),b)
+isim:=second1is2(real,a,b):is"r"(b,im(pli(a,b)))
+x@pliis:=pair1is1(real,x):is(pli(re(x),im(x)),x)
+ispli:=pair1is2(real,x):is(x,pli(re(x),im(x)))
+y@[i:is(x,y)]
+iscere:=isf(cx,real,[t:cx]re(t),x,y,i):is"r"(re(x),re(y))
+isceim:=isf(cx,real,[t:cx]im(t),x,y,i):is"r"(im(x),im(y))
+b@[c:real][i:is"r"(a,b)]
+isrecx1:=isf(real,cx,[t:real]pli(t,c),a,b,i):is(pli(a,c),pli(b,c))
+isrecx2:=isf(real,cx,[t:real]pli(c,t),a,b,i):is(pli(c,a),pli(c,b))
+c@[d:real][i:is"r"(a,b)][j:is"r"(c,d)]
+isrecx12:=tris(cx,pli(a,c),pli(b,c),pli(b,d),isrecx1(a,b,c,i),isrecx2(c,d,b,j)):is(pli(a,c),pli(b,d))
+x@satz206:=refis(cx,x):is(x,x)
+y@[i:is(x,y)]
+satz207:=symis(cx,x,y,i):is(y,x)
+y@[z:complex][i:is(x,y)][j:is(y,z)]
+satz208:=tris(cx,x,y,z,i,j):is(x,z)
+@0c:=pli(0,0):complex
+1c:=pli(1rl,0):complex
+y@pl:=pli(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))):complex
+d@plis12a:=isrecx12(pl"r"(re(pli(a,b)),re(pli(c,d))),pl"r"(a,c),pl"r"(im(pli(a,b)),im(pli(c,d))),pl"r"(b,d),ispl12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ispl12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)))
+plis12b:=symis(cx,pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)),plis12a):is(pli(pl"r"(a,c),pl"r"(b,d)),pl(pli(a,b),pli(c,d)))
+x@[r:real][s:real]
+plis1a:=isrecx12(pl"r"(re(pli(r,s)),re(x)),pl"r"(r,re(x)),pl"r"(im(pli(r,s)),im(x)),pl"r"(s,im(x)),ispl1(re(pli(r,s)),r,re(x),reis(r,s)),ispl1(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))))
+plis1b:=symis(cx,pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))),plis1a):is(pli(pl"r"(r,re(x)),pl"r"(s,im(x))),pl(pli(r,s),x))
+plis2a:=isrecx12(pl"r"(re(x),re(pli(r,s))),pl"r"(re(x),r),pl"r"(im(x),im(pli(r,s))),pl"r"(im(x),s),ispl2(re(pli(r,s)),r,re(x),reis(r,s)),ispl2(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)))
+plis2b:=symis(cx,pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)),plis2a):is(pli(pl"r"(re(x),r),pl"r"(im(x),s)),pl(x,pli(r,s)))
+z@[i:is(x,y)]
+ispl1:=isf(cx,cx,[t:cx]pl(t,z),x,y,i):is(pl(x,z),pl(y,z))
+ispl2:=isf(cx,cx,[t:cx]pl(z,t),x,y,i):is(pl(z,x),pl(z,y))
+z@[u:complex][i:is(x,y)][j:is(z,u)]
+ispl12:=tris(cx,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
+y@satz209:=isrecx12(pl"r"(re(x),re(y)),pl"r"(re(y),re(x)),pl"r"(im(x),im(y)),pl"r"(im(y),im(x)),compl(re(x),re(y)),compl(im(x),im(y))):is(pl(x,y),pl(y,x))
+compl:=satz209:is(pl(x,y),pl(y,x))
+x@satz210:=tr3is(cx,pl(x,0c),pli(pl"r"(re(x),0),pl"r"(im(x),0)),pli(re(x),im(x)),x,plis2a(x,0,0),isrecx12(pl"r"(re(x),0),re(x),pl"r"(im(x),0),im(x),pl02(re(x),0,refis(real,0)),pl02(im(x),0,refis(real,0))),pliis(x)):is(pl(x,0c),x)
+satz210a:=symis(cx,pl(x,0c),x,satz210):is(x,pl(x,0c))
+satz210b:=tris(cx,pl(0c,x),pl(x,0c),x,compl(0c,x),satz210):is(pl(0c,x),x)
+satz210c:=symis(cx,pl(0c,x),x,satz210b):is(x,pl(0c,x))
+z@satz211:=tr3is(cx,pl(pl(x,y),z),pli(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(pl"r"(im(x),im(y)),im(z))),pli(pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(im(x),pl"r"(im(y),im(z)))),pl(x,pl(y,z)),plis1a(z,pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(pl"r"(im(x),im(y)),im(z)),pl"r"(im(x),pl"r"(im(y),im(z))),asspl1(re(x),re(y),re(z)),asspl1(im(x),im(y),im(z))),plis2b(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z)))):is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl1:=satz211:is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl2:=symis(cx,pl(pl(x,y),z),pl(x,pl(y,z)),asspl1):is(pl(x,pl(y,z)),pl(pl(x,y),z))
+y@[u:complex][i:is(pl(y,u),x)]
++2212
+t1:=tris(real,pl"r"(re(y),re(u)),re(pl(y,u)),re(x),isre(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),iscere(pl(y,u),x,i)):is"r"(pl"r"(re(y),re(u)),re(x))
+t2:=tris(real,pl"r"(im(y),im(u)),im(pl(y,u)),im(x),isim(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),isceim(pl(y,u),x,i)):is"r"(pl"r"(im(y),im(u)),im(x))
+t3:=satz187d(re(x),re(y),re(u),t1):is"r"(re(u),mn(re(x),re(y)))
+t4:=satz187d(im(x),im(y),im(u),t2):is"r"(im(u),mn(im(x),im(y)))
+-2212
+satz212a:=tris(cx,u,pli(re(u),im(u)),pli(mn(re(x),re(y)),mn(im(x),im(y))),ispli(u),isrecx12(re(u),mn(re(x),re(y)),im(u),mn(im(x),im(y)),t3".2212",t4".2212")):is(u,pli(mn(re(x),re(y)),mn(im(x),im(y))))
+y@satz212b:=tr3is(cx,pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),pli(pl"r"(re(y),mn(re(x),re(y))),pl"r"(im(y),mn(im(x),im(y)))),pli(re(x),im(x)),x,plis2a(y,mn(re(x),re(y)),mn(im(x),im(y))),isrecx12(pl"r"(re(y),mn(re(x),re(y))),re(x),pl"r"(im(y),mn(im(x),im(y))),im(x),satz187a(re(x),re(y)),satz187a(im(x),im(y))),pliis(x)):is(pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),x)
+satz212c:=somei(cx,[t:cx]is(pl(y,t),x),pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212b):some([t:complex]is(pl(y,t),x))
+satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212a(t,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
+%satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
+mn:=pli(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))):complex
+d@mnis12a:=isrecx12(mn"r"(re(pli(a,b)),re(pli(c,d))),mn"r"(a,c),mn"r"(im(pli(a,b)),im(pli(c,d))),mn"r"(b,d),ismn12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ismn12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)))
+mnis12b:=symis(cx,mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)),mnis12a):is(pli(mn"r"(a,c),mn"r"(b,d)),mn(pli(a,b),pli(c,d)))
+x@[r:real][s:real]
+mnis1a:=isrecx12(mn"r"(re(pli(r,s)),re(x)),mn"r"(r,re(x)),mn"r"(im(pli(r,s)),im(x)),mn"r"(s,im(x)),ismn1(re(pli(r,s)),r,re(x),reis(r,s)),ismn1(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))))
+mnis1b:=symis(cx,mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mnis1a):is(pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mn(pli(r,s),x))
+mnis2a:=isrecx12(mn"r"(re(x),re(pli(r,s))),mn"r"(re(x),r),mn"r"(im(x),im(pli(r,s))),mn"r"(im(x),s),ismn2(re(pli(r,s)),r,re(x),reis(r,s)),ismn2(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)))
+mnis2b:=symis(cx,mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)),mnis2a):is(pli(mn"r"(re(x),r),mn"r"(im(x),s)),mn(x,pli(r,s)))
+z@[i:is(x,y)]
+ismn1:=isf(cx,cx,[t:cx]mn(t,z),x,y,i):is(mn(x,z),mn(y,z))
+ismn2:=isf(cx,cx,[t:cx]mn(z,t),x,y,i):is(mn(z,x),mn(z,y))
+z@[u:complex][i:is(x,y)][j:is(z,u)]
+ismn12:=tris(cx,mn(x,z),mn(y,z),mn(y,u),ismn1(x,y,z,i),ismn2(z,u,y,j)):is(mn(x,z),mn(y,u))
+y@[u:complex][i:is(pl(y,u),x)]
+satz212d:=satz212a(u,i):is(u,mn(x,y))
+satz212e:=symis(cx,u,mn(x,y),satz212d):is(mn(x,y),u)
+u@[i:is(pl(u,y),x)]
+satz212f:=satz212d(tris(cx,pl(y,u),pl(u,y),x,compl(y,u),i)):is(u,mn(x,y))
+satz212g:=symis(cx,u,mn(x,y),satz212f):is(mn(x,y),u)
+y@satz212h:=satz212b:is(pl(y,mn(x,y)),x)
+[i:is(mn(x,y),0c)]
++2213
+t1:=tr3is(real,mn"r"(re(x),re(y)),re(mn(x,y)),re(0c),0,isre(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),iscere(mn(x,y),0c,i),reis(0,0)):is"r"(mn"r"(re(x),re(y)),0)
+t2:=tr3is(real,mn"r"(im(x),im(y)),im(mn(x,y)),im(0c),0,isim(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),isceim(mn(x,y),0c,i),imis(0,0)):is"r"(mn"r"(im(x),im(y)),0)
+t3:=satz182b(re(x),re(y),t1):is"r"(re(x),re(y))
+t4:=satz182b(im(x),im(y),t2):is"r"(im(x),im(y))
+-2213
+satz213a:=tr3is(cx,x,pli(re(x),im(x)),pli(re(y),im(y)),y,ispli(x),isrecx12(re(x),re(y),im(x),im(y),t3".2213",t4".2213"),pliis(y)):is(x,y)
+y@[i:is(x,y)]
++*2213
+i@t5:=satz182e(re(x),re(y),iscere(x,y,i)):is"r"(mn"r"(re(x),re(y)),0)
+t6:=satz182e(im(x),im(y),isceim(x,y,i)):is"r"(mn"r"(im(x),im(y)),0)
+-2213
+i@satz213b:=isrecx12(mn"r"(re(x),re(y)),0,mn"r"(im(x),im(y)),0,t5".2213",t6".2213"):is(mn(x,y),0c)
+x@m0:=mn(0c,x):complex
+satz214:=isrecx12(mn"r"(re(0c),re(x)),m0"r"(re(x)),mn"r"(im(0c),im(x)),m0"r"(im(x)),pl01(re(0c),m0"r"(re(x)),reis(0,0)),pl01(im(0c),m0"r"(im(x)),imis(0,0))):is(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))))
+satz214a:=symis(cx,m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214):is(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x))
+b@m0isa:=tris(cx,m0(pli(a,b)),pli(m0"r"(re(pli(a,b))),m0"r"(im(pli(a,b)))),pli(m0"r"(a),m0"r"(b)),satz214(pli(a,b)),isrecx12(m0"r"(re(pli(a,b))),m0"r"(a),m0"r"(im(pli(a,b))),m0"r"(b),ism0(re(pli(a,b)),a,reis(a,b)),ism0(im(pli(a,b)),b,imis(a,b)))):is(m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)))
+m0isb:=symis(cx,m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)),m0isa):is(pli(m0"r"(a),m0"r"(b)),m0(pli(a,b)))
+y@[i:is(x,y)]
+ism0:=isf(cx,cx,[t:cx]m0(t),x,y,i):is(m0(x),m0(y))
+x@satz215:=tr4is(cx,m0(m0(x)),m0(pli(m0"r"(re(x)),m0"r"(im(x)))),pli(m0"r"(m0"r"(re(x))),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,ism0(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214),m0isa(m0"r"(re(x)),m0"r"(im(x))),isrecx12(m0"r"(m0"r"(re(x))),re(x),m0"r"(m0"r"(im(x))),im(x),satz177(re(x)),satz177(im(x))),pliis(x)):is(m0(m0(x)),x)
+satz215a:=symis(cx,m0(m0(x)),x,satz215):is(x,m0(m0(x)))
+y@[i:is(x,m0(y))]
+satz215b:=tris(cx,m0(x),m0(m0(y)),y,ism0(x,m0(y),i),satz215(y)):is(m0(x),y)
+satz215c:=symis(cx,m0(x),y,satz215b):is(y,m0(x))
+y@[i:is(m0(x),y)]
+satz215d:=satz215c(y,x,symis(cx,m0(x),y,i)):is(x,m0(y))
+satz215e:=symis(cx,x,m0(y),satz215d):is(m0(y),x)
+x@satz216:=tr3is(cx,pl(x,m0(x)),pl(x,pli(m0"r"(re(x)),m0"r"(im(x)))),pli(pl"r"(re(x),m0"r"(re(x))),pl"r"(im(x),m0"r"(im(x)))),0c,ispl2(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),x,satz214(x)),plis2a(x,m0"r"(re(x)),m0"r"(im(x))),isrecx12(pl"r"(re(x),m0"r"(re(x))),0,pl"r"(im(x),m0"r"(im(x))),0,satz179(re(x)),satz179(im(x)))):is(pl(x,m0(x)),0c)
++2216
+anders:=satz212h(0c,x):is(pl(x,m0(x)),0c)
+-2216
+satz216a:=tris(cx,pl(m0(x),x),pl(x,m0(x)),0c,compl(m0(x),x),satz216):is(pl(m0(x),x),0c)
+y@satz217:=tr4is(cx,m0(pl(x,y)),pli(m0"r"(pl"r"(re(x),re(y))),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(m0"r"(re(x)),m0"r"(re(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(pli(m0"r"(re(x)),m0"r"(im(x))),pli(m0"r"(re(y)),m0"r"(im(y)))),pl(m0(x),m0(y)),m0isa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(m0"r"(pl"r"(re(x),re(y))),pl"r"(m0"r"(re(x)),m0"r"(re(y))),m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),satz180(re(x),re(y)),satz180(im(x),im(y))),plis12b(m0"r"(re(x)),m0"r"(im(x)),m0"r"(re(y)),m0"r"(im(y))),ispl12(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),satz214a(x),satz214a(y))):is(m0(pl(x,y)),pl(m0(x),m0(y)))
+satz217a:=symis(cx,m0(pl(x,y)),pl(m0(x),m0(y)),satz217):is(pl(m0(x),m0(y)),m0(pl(x,y)))
+satz218:=tris(cx,mn(x,y),pl(x,pli(m0"r"(re(y)),m0"r"(im(y)))),pl(x,m0(y)),plis2b(x,m0"r"(re(y)),m0"r"(im(y))),ispl2(pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),x,satz214a(y))):is(mn(x,y),pl(x,m0(y)))
+satz218a:=symis(cx,mn(x,y),pl(x,m0(y)),satz218):is(pl(x,m0(y)),mn(x,y))
++2219
+t1:=tr3is(cx,m0(mn(x,y)),m0(pl(x,m0(y))),pl(m0(x),m0(m0(y))),pl(m0(x),y),ism0(mn(x,y),pl(x,m0(y)),satz218),satz217(x,m0(y)),ispl2(m0(m0(y)),y,m0(x),satz215(y))):is(m0(mn(x,y)),pl(m0(x),y))
+-2219
+satz219:=tr3is(cx,m0(mn(x,y)),pl(m0(x),y),pl(y,m0(x)),mn(y,x),t1".2219",compl(m0(x),y),satz218a(y,x)):is(m0(mn(x,y)),mn(y,x))
+satz219a:=symis(cx,m0(mn(y,x)),mn(x,y),satz219(y,x)):is(mn(x,y),m0(mn(y,x)))
+ts:=pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))):complex
+rets:=mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))):real
+imts:=pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))):real
++v3
+d@t1:=ismn12"r"(ts"r"(re(pli(a,b)),re(pli(c,d))),ts"r"(a,c),ts"r"(im(pli(a,b)),im(pli(c,d))),ts"r"(b,d),ists12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ists12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is"r"(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)))
+t2:=ispl12"r"(ts"r"(re(pli(a,b)),im(pli(c,d))),ts"r"(a,d),ts"r"(im(pli(a,b)),re(pli(c,d))),ts"r"(b,c),ists12(re(pli(a,b)),a,im(pli(c,d)),d,reis(a,b),imis(c,d)),ists12(im(pli(a,b)),b,re(pli(c,d)),c,imis(a,b),reis(c,d))):is"r"(imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)))
+-v3
+d@tsis12a:=isrecx12(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)),imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)),t1".v3",t2".v3"):is(ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))))
+tsis12b:=symis(cx,ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),tsis12a):is(pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),ts(pli(a,b),pli(c,d)))
+x@[r:real][s:real]
++*v3
+s@t3:=ismn12"r"(ts"r"(re(pli(r,s)),re(x)),ts"r"(r,re(x)),ts"r"(im(pli(r,s)),im(x)),ts"r"(s,im(x)),ists1(re(pli(r,s)),r,re(x),reis(r,s)),ists1(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))))
+t4:=ispl12"r"(ts"r"(re(pli(r,s)),im(x)),ts"r"(r,im(x)),ts"r"(im(pli(r,s)),re(x)),ts"r"(s,re(x)),ists1(re(pli(r,s)),r,im(x),reis(r,s)),ists1(im(pli(r,s)),s,re(x),imis(r,s))):is"r"(imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))))
+-v3
+s@tsis1a:=isrecx12(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))),t3".v3",t4".v3"):is(ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))))
+tsis1b:=symis(cx,ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),tsis1a):is(pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),ts(pli(r,s),x))
++*v3
+s@t5:=ismn12"r"(ts"r"(re(x),re(pli(r,s))),ts"r"(re(x),r),ts"r"(im(x),im(pli(r,s))),ts"r"(im(x),s),ists2(re(pli(r,s)),r,re(x),reis(r,s)),ists2(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)))
+t6:=ispl12"r"(ts"r"(re(x),im(pli(r,s))),ts"r"(re(x),s),ts"r"(im(x),re(pli(r,s))),ts"r"(im(x),r),ists2(im(pli(r,s)),s,re(x),imis(r,s)),ists2(re(pli(r,s)),r,im(x),reis(r,s))):is"r"(imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)))
+-v3
+s@tsis2a:=isrecx12(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)),t5".v3",t6".v3"):is(ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))))
+tsis2b:=symis(cx,ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),tsis2a):is(pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),ts(x,pli(r,s)))
+z@[i:is(x,y)]
+ists1:=isf(cx,cx,[t:cx]ts(t,z),x,y,i):is(ts(x,z),ts(y,z))
+ists2:=isf(cx,cx,[t:cx]ts(z,t),x,y,i):is(ts(z,x),ts(z,y))
+z@[u:complex][i:is(x,y)][j:is(z,u)]
+ists12:=tris(cx,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
++3220
+y@t1:=ismn12"r"(ts"r"(re(x),re(y)),ts"r"(re(y),re(x)),ts"r"(im(x),im(y)),ts"r"(im(y),im(x)),comts(re(x),re(y)),comts(im(x),im(y))):is"r"(rets(x,y),rets(y,x))
+t2:=tris(real,imts(x,y),pl"r"(ts"r"(im(x),re(y)),ts"r"(re(x),im(y))),imts(y,x),compl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(ts"r"(im(x),re(y)),ts"r"(re(y),im(x)),ts"r"(re(x),im(y)),ts"r"(im(y),re(x)),comts(im(x),re(y)),comts(re(x),im(y)))):is"r"(imts(x,y),imts(y,x))
+-3220
+y@satz220:=isrecx12(rets(x,y),rets(y,x),imts(x,y),imts(y,x),t1".3220",t2".3220"):is(ts(x,y),ts(y,x))
+comts:=satz220:is(ts(x,y),ts(y,x))
+x@[i:is(x,0c)]
+lemma1:=tris(real,re(x),re(0c),0,iscere(x,0c,i),reis(0,0)):is"r"(re(x),0)
+lemma2:=tris(real,im(x),im(0c),0,isceim(x,0c,i),imis(0,0)):is"r"(im(x),0)
+x@mod2:=pl"r"(ts"r"(re(x),re(x)),ts"r"(im(x),im(x))):real
+i@lemma3:=tris(real,mod2,pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),0,ts01(re(x),re(x),lemma1),ts01(im(x),im(x),lemma2)),pl01(0,0,refis(real,0))):is"r"(mod2(x),0)
+x@[n:nis(x,0c)]
++*v3
+x@re2:=ts"r"(re(x),re(x)):real
+im2:=ts"r"(im(x),im(x)):real
+n@[i:is"r"(re(x),0)]
+t7:=th3"l.imp"(is"r"(im(x),0),is(x,0c),n,[t:is"r"(im(x),0)]tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,i,t))):nis"r"(im(x),0)
+t8:=ispos(im2,mod2,symis(real,mod2,im2,pl01(re2,im2,ts01(re(x),re(x),i))),possq(im(x),t7)):pos(mod2)
+n@[o:nis"r"(re(x),0)][i:is"r"(im(x),0)]
+t9:=ispos(re2,mod2,symis(real,mod2,re2,pl02(re2,im2,ts01(im(x),im(x),i))),possq(re(x),o)):pos(mod2)
+o@[p:nis"r"(im(x),0)]
+t10:=pospl(re2,im2,possq(re(x),o),possq(im(x),p)):pos(mod2)
+o@t11:=th1"l.imp"(is"r"(im(x),0),pos(mod2),[t:is"r"(im(x),0)]t9(t),[t:nis"r"(im(x),0)]t10(t)):pos(mod2)
+-v3
+n@lemma4:=th1"l.imp"(is"r"(re(x),0),pos(mod2),[t:is"r"(re(x),0)]t8".v3"(t),[t:nis"r"(re(x),0)]t11".v3"(t)):pos(mod2(x))
+x@lemma5:=th1"l.imp"(is(x,0c),not(neg(mod2)),[t:is(x,0c)]0notn(mod2,lemma3(t)),[t:nis(x,0c)]pnotn(mod2,lemma4(t))):not(neg(mod2(x)))
+y@[i:is(x,0c)]
++3221
+t1:=lemma1(x,i):is"r"(re(x),0)
+t2:=lemma2(x,i):is"r"(im(x),0)
+t3:=tris(real,rets(x,y),mn"r"(0,0),0,ismn12"r"(ts"r"(re(x),re(y)),0,ts"r"(im(x),im(y)),0,ts01(re(x),re(y),t1),ts01(im(x),im(y),t2)),satz187c(0,0,0,pl02(0,0,refis(real,0)))):is"r"(rets(x,y),0)
+t4:=tris(real,imts(x,y),pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),im(y)),0,ts"r"(im(x),re(y)),0,ts01(re(x),im(y),t1),ts01(im(x),re(y),t2)),pl02(0,0,refis(real,0))):is"r"(imts(x,y),0)
+-3221
+satz221a:=isrecx12(rets(x,y),0,imts(x,y),0,t3".3221",t4".3221"):is(ts(x,y),0c)
+y@[i:is(y,0c)]
+satz221b:=tris(cx,ts(x,y),ts(y,x),0c,comts(x,y),satz221a(y,x,i)):is(ts(x,y),0c)
+y@[i:is(ts(x,y),0c)]
++*3221
+i@[n:nis(y,0c)]
+t5:=lemma4(y,n):pos(mod2(y))
+t6:=tris1(real,rets(x,y),0,re(ts(x,y)),reis(rets(x,y),imts(x,y)),lemma1(ts(x,y),i)):is"r"(rets(x,y),0)
+t7:=tris1(real,imts(x,y),0,im(ts(x,y)),imis(rets(x,y),imts(x,y)),lemma2(ts(x,y),i)):is"r"(imts(x,y),0)
+t8:=tris(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(0,0),0,ispl12"r"(ts"r"(rets(x,y),re(y)),0,ts"r"(imts(x,y),im(y)),0,ts01(rets(x,y),re(y),t6),ts01(imts(x,y),im(y),t7)),pl02(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),0)
+y@ii1r:=ts"r"(ts"r"(im(x),im(y)),re(y)):real
+i1ir:=ts"r"(im(x),ts"r"(im(y),re(y))):real
+ir1i:=ts"r"(ts"r"(im(x),re(y)),im(y)):real
+i1ri:=ts"r"(im(x),ts"r"(re(y),im(y))):real
+rr1r:=ts"r"(ts"r"(re(x),re(y)),re(y)):real
+r1rr:=ts"r"(re(x),ts"r"(re(y),re(y))):real
+ri1r:=ts"r"(ts"r"(re(x),im(y)),re(y)):real
+r1ir:=ts"r"(re(x),ts"r"(im(y),re(y))):real
+ri1i:=ts"r"(ts"r"(re(x),im(y)),im(y)):real
+r1ii:=ts"r"(re(x),ts"r"(im(y),im(y))):real
+n@t9:=tris(real,ii1r,i1ir,i1ri,assts1(im(x),im(y),re(y)),ists2"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),im(x),comts"r"(im(y),re(y)))):is"r"(ii1r,i1ri)
+t10:=tris(real,ts"r"(rets(x,y),re(y)),mn"r"(rr1r,ii1r),mn"r"(r1rr,i1ri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(y)),ismn12"r"(rr1r,r1rr,ii1r,i1ri,assts1(re(x),re(y),re(y)),t9)):is"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri))
+t11:=tr3is(real,ts"r"(imts(x,y),im(y)),pl"r"(ri1i,ir1i),pl"r"(r1ii,i1ri),pl"r"(i1ri,r1ii),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(y)),ispl12"r"(ri1i,r1ii,ir1i,i1ri,assts1(re(x),im(y),im(y)),assts1(im(x),re(y),im(y))),compl"r"(r1ii,i1ri)):is"r"(ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii))
+t12:=tr4is(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(mn"r"(r1rr,i1ri),pl"r"(i1ri,r1ii)),pl"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1ii),pl"r"(r1rr,r1ii),ts"r"(re(x),mod2(y)),ispl12"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri),ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii),t10,t11),asspl2"r"(mn"r"(r1rr,i1ri),i1ri,r1ii),ispl1"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1rr,r1ii,plmn(r1rr,i1ri)),distpt2(re(x),ts"r"(re(y),re(y)),ts"r"(im(y),im(y)))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),ts"r"(re(x),mod2(y)))
+t13:=tris1(real,ts"r"(re(x),mod2(y)),0,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),t12,t8):is"r"(ts"r"(re(x),mod2(y)),0)
+t14:=ore1(is"r"(re(x),0),is"r"(mod2(y),0),satz192c(re(x),mod2(y),t13),pnot0(mod2(y),t5)):is"r"(re(x),0)
+t15:=tris1(real,ts"r"(im(x),im(y)),0,ts"r"(re(x),re(y)),satz182b(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),t6),ts01(re(x),re(y),t14)):is"r"(ts"r"(im(x),im(y)),0)
+t16:=tris1(real,ts"r"(im(x),re(y)),0,imts(x,y),pl01(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),ts01(re(x),im(y),t14)),t7):is"r"(ts"r"(im(x),re(y)),0)
+[j:is"r"(re(y),0)]
+t17:=t7"c.v3"(y,n,j):nis"r"(im(y),0)
+t18:=ore1(is"r"(im(x),0),is"r"(im(y),0),satz192c(im(x),im(y),t15),t17):is"r"(im(x),0)
+n@[o:nis"r"(re(y),0)]
+t19:=ore1(is"r"(im(x),0),is"r"(re(y),0),satz192c(im(x),re(y),t16),o):is"r"(im(x),0)
+n@t20:=th1"l.imp"(is"r"(re(y),0),is"r"(im(x),0),[t:is"r"(re(y),0)]t18(t),[t:nis"r"(re(y),0)]t19(t)):is"r"(im(x),0)
+t21:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t14,t20)):is(x,0c)
+-3221
+i@satz221c:=th2"l.or"(is(x,0c),is(y,0c),[t:nis(y,0c)]t21".3221"(t)):or(is(x,0c),is(y,0c))
+y@[n:nis(x,0c)][o:nis(y,0c)]
+satz221d:=th3"l.imp"(is(ts(x,y),0c),or(is(x,0c),is(y,0c)),th3"l.or"(is(x,0c),is(y,0c),n,o),[t:is(ts(x,y),0c)]satz221c(t)):nis(ts(x,y),0c)
++3222
+x@t1:=tris(real,mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),mn"r"(re(x),0),re(x),ismn12"r"(ts"r"(re(x),1rl),re(x),ts"r"(im(x),0),0,satz195(re(x)),ts02(im(x),0,refis(real,0))),pl02(re(x),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x))
+t2:=tris(real,pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),pl"r"(0,im(x)),im(x),ispl12"r"(ts"r"(re(x),0),0,ts"r"(im(x),1rl),im(x),ts02(re(x),0,refis(real,0)),satz195(im(x))),pl01(0,im(x),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x))
+-3222
+x@satz222:=tr3is(cx,ts(x,1c),pli(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl))),pli(re(x),im(x)),x,tsis2a(x,1rl,0),isrecx12(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x),t1".3222",t2".3222"),pliis(x)):is(ts(x,1c),x)
+satz222a:=symis(cx,ts(x,1c),x,satz222):is(x,ts(x,1c))
+satz222b:=tris(cx,ts(1c,x),ts(x,1c),x,comts(1c,x),satz222):is(ts(1c,x),x)
+satz222c:=symis(cx,ts(1c,x),x,satz222b):is(x,ts(1c,x))
++3223
+t1:=tris(real,mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),mn"r"(m0"r"(re(x)),0),m0"r"(re(x)),ismn12"r"(ts"r"(re(x),m0"r"(1rl)),m0"r"(re(x)),ts"r"(im(x),m0"r"(0)),0,tris(real,ts"r"(re(x),m0"r"(1rl)),m0"r"(ts"r"(re(x),1rl)),m0"r"(re(x)),satz197b(re(x),1rl),ism0"r"(ts"r"(re(x),1rl),re(x),satz195(re(x)))),ts02(im(x),m0"r"(0),satz176b(0,refis(real,0)))),pl02(m0"r"(re(x)),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)))
+t2:=tris(real,pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),pl"r"(0,m0"r"(im(x))),m0"r"(im(x)),ispl12"r"(ts"r"(re(x),m0"r"(0)),0,ts"r"(im(x),m0"r"(1rl)),m0"r"(im(x)),ts02(re(x),m0"r"(0),satz176b(0,refis(real,0))),tris(real,ts"r"(im(x),m0"r"(1rl)),m0"r"(ts"r"(im(x),1rl)),m0"r"(im(x)),satz197b(im(x),1rl),ism0"r"(ts"r"(im(x),1rl),im(x),satz195(im(x))))),pl01(0,m0"r"(im(x)),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)))
+-3223
+satz223:=tr4is(cx,ts(x,m0(1c)),ts(x,pli(m0"r"(1rl),m0"r"(0))),pli(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl)))),pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),ists2(m0(1c),pli(m0"r"(1rl),m0"r"(0)),x,m0isa(1rl,0)),tsis2a(x,m0"r"(1rl),m0"r"(0)),isrecx12(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)),t1".3223",t2".3223"),satz214a(x)):is(ts(x,m0(1c)),m0(x))
+satz223a:=symis(cx,ts(x,m0(1c)),m0(x),satz223):is(m0(x),ts(x,m0(1c)))
+satz223b:=tris(cx,ts(m0(1c),x),ts(x,m0(1c)),m0(x),comts(m0(1c),x),satz223):is(ts(m0(1c),x),m0(x))
+satz223c:=symis(cx,ts(m0(1c),x),m0(x),satz223b):is(m0(x),ts(m0(1c),x))
++3224
+y@rxry:=ts"r"(re(x),re(y)):real
+ixiy:=ts"r"(im(x),im(y)):real
+rxiy:=ts"r"(re(x),im(y)):real
+ixry:=ts"r"(im(x),re(y)):real
+t1:=tr4is(real,mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),mn"r"(m0"r"(rxry),m0"r"(ixiy)),pl"r"(m0"r"(rxry),ixiy),mn"r"(ixiy,rxry),m0"r"(mn"r"(rxry,ixiy)),ismn12"r"(ts"r"(m0"r"(re(x)),re(y)),m0"r"(rxry),ts"r"(m0"r"(im(x)),im(y)),m0"r"(ixiy),satz197a(re(x),re(y)),satz197a(im(x),im(y))),ispl2"r"(m0"r"(m0"r"(ixiy)),ixiy,m0"r"(rxry),satz177(ixiy)),compl"r"(m0"r"(rxry),ixiy),satz181a(ixiy,rxry)):is"r"(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(rxry,ixiy)))
+t2:=tris(real,pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),mn"r"(m0"r"(rxiy),ixry),m0"r"(pl"r"(rxiy,ixry)),ispl12"r"(ts"r"(m0"r"(re(x)),im(y)),m0"r"(rxiy),ts"r"(m0"r"(im(x)),re(y)),m0"r"(ixry),satz197a(re(x),im(y)),satz197a(im(x),re(y))),satz180a(rxiy,ixry)):is"r"(pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(rxiy,ixry)))
+-3224
+y@satz224a:=tr4is(cx,ts(m0(x),y),ts(pli(m0"r"(re(x)),m0"r"(im(x))),y),pli(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y)))),pli(m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))),m0(ts(x,y)),ists1(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),y,satz214(x)),tsis1a(y,m0"r"(re(x)),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))),t1".3224",t2".3224"),m0isb(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))):is(ts(m0(x),y),m0(ts(x,y)))
+satz224b:=tr3is(cx,ts(x,m0(y)),ts(m0(y),x),m0(ts(y,x)),m0(ts(x,y)),comts(x,m0(y)),satz224a(y,x),ism0(ts(y,x),ts(x,y),comts(y,x))):is(ts(x,m0(y)),m0(ts(x,y)))
+satz224c:=tris2(cx,ts(m0(x),y),ts(x,m0(y)),m0(ts(x,y)),satz224a,satz224b):is(ts(m0(x),y),ts(x,m0(y)))
+satz224d:=symis(cx,ts(m0(x),y),ts(x,m0(y)),satz224c):is(ts(x,m0(y)),ts(m0(x),y))
+satz224e:=symis(cx,ts(m0(x),y),m0(ts(x,y)),satz224a):is(m0(ts(x,y)),ts(m0(x),y))
+satz224f:=symis(cx,ts(x,m0(y)),m0(ts(x,y)),satz224b):is(m0(ts(x,y)),ts(x,m0(y)))
+satz225:=tris(cx,ts(m0(x),m0(y)),ts(x,m0(m0(y))),ts(x,y),satz224c(x,m0(y)),ists2(m0(m0(y)),y,x,satz215(y))):is(ts(m0(x),m0(y)),ts(x,y))
+satz225a:=symis(cx,ts(m0(x),m0(y)),ts(x,y),satz225):is(ts(x,y),ts(m0(x),m0(y)))
++3226
+z@rrr:=ts"r"(ts"r"(re(x),re(y)),re(z)):real
+iir:=ts"r"(ts"r"(im(x),im(y)),re(z)):real
+rii:=ts"r"(ts"r"(re(x),im(y)),im(z)):real
+iri:=ts"r"(ts"r"(im(x),re(y)),im(z)):real
+rri:=ts"r"(ts"r"(re(x),re(y)),im(z)):real
+iii:=ts"r"(ts"r"(im(x),im(y)),im(z)):real
+rir:=ts"r"(ts"r"(re(x),im(y)),re(z)):real
+irr:=ts"r"(ts"r"(im(x),re(y)),re(z)):real
+t1:=tr3is(real,mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(mn"r"(rrr,iir),pl"r"(rii,iri)),pl"r"(rrr,pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri)))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),ismn12"r"(ts"r"(rets(x,y),re(z)),mn"r"(rrr,iir),ts"r"(imts(x,y),im(z)),pl"r"(rii,iri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(z))),asspl1"r"(rrr,m0"r"(iir),m0"r"(pl"r"(rii,iri))),ispl2"r"(pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri))),m0"r"(pl"r"(iir,pl"r"(rii,iri))),rrr,satz180a(iir,pl"r"(rii,iri)))):is"r"(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))))
+t2:=tr3is(real,pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),pl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),pl"r"(pl"r"(rir,irr),mn"r"(rri,iii)),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),ispl12"r"(ts"r"(rets(x,y),im(z)),mn"r"(rri,iii),ts"r"(imts(x,y),re(z)),pl"r"(rir,irr),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),im(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),re(z))),compl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),asspl2"r"(pl"r"(rir,irr),rri,m0"r"(iii))):is"r"(pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii))
+t3:=tris(cx,ts(ts(x,y),z),pli(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z)))),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),tsis1a(z,rets(x,y),imts(x,y)),isrecx12(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),t1,t2)):is(ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)))
+c@t4:=tris(real,ts"r"(ts"r"(a,b),c),ts"r"(a,ts"r"(b,c)),ts"r"(ts"r"(b,c),a),assts1(a,b,c),comts"r"(a,ts"r"(b,c))):is"r"(ts"r"(ts"r"(a,b),c),ts"r"(ts"r"(b,c),a))
+t5:=tris(real,pl"r"(pl"r"(a,b),c),pl"r"(c,pl"r"(a,b)),pl"r"(pl"r"(c,a),b),compl"r"(pl"r"(a,b),c),asspl2"r"(c,a,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(c,a),b))
+t6:=tris(real,pl"r"(a,pl"r"(b,c)),pl"r"(pl"r"(b,c),a),pl"r"(b,pl"r"(c,a)),compl"r"(a,pl"r"(b,c)),asspl1"r"(b,c,a)):is"r"(pl"r"(a,pl"r"(b,c)),pl"r"(b,pl"r"(c,a)))
+z@rrr1:=rrr(y,z,x):real
+iir1:=iir(y,z,x):real
+rii1:=rii(y,z,x):real
+iri1:=iri(y,z,x):real
+rri1:=rri(y,z,x):real
+iii1:=iii(y,z,x):real
+rir1:=rir(y,z,x):real
+irr1:=irr(y,z,x):real
+t7:=tris(real,pl"r"(iir,pl"r"(rii,iri)),pl"r"(rii,pl"r"(iri,iir)),pl"r"(iir1,pl"r"(rii1,iri1)),t6(iir,rii,iri),ispl12"r"(rii,iir1,pl"r"(iri,iir),pl"r"(rii1,iri1),t4(re(x),im(y),im(z)),ispl12"r"(iri,rii1,iir,iri1,t4(im(x),re(y),im(z)),t4(im(x),im(y),re(z))))):is"r"(pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)))
+t8:=tris(real,pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rri,rir),irr),pl"r"(pl"r"(rir1,irr1),rri1),t5(rir,irr,rri),ispl12"r"(pl"r"(rri,rir),pl"r"(rir1,irr1),irr,rri1,ispl12"r"(rri,rir1,rir,irr1,t4(re(x),re(y),im(z)),t4(re(x),im(y),re(z))),t4(im(x),re(y),re(z)))):is"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1))
+t9:=ismn12"r"(rrr,rrr1,pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)),t4(re(x),re(y),re(z)),t7):is"r"(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))))
+t10:=ismn12"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1),iii,iii1,t8,t4(im(x),im(y),im(z))):is"r"(mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1))
+t11:=tris(cx,ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t3,isrecx12(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1),t9,t10)):is(ts(ts(x,y),z),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
+t12:=tris(cx,ts(x,ts(y,z)),ts(ts(y,z),x),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),comts(x,ts(y,z)),t3(y,z,x)):is(ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
+t13:=tris2(cx,ts(ts(x,y),z),ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t11,t12):is(ts(ts(x,y),z),ts(x,ts(y,z)))
+-3226
+z@satz226:=t13".3226":is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts1:=satz226:is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts2:=symis(cx,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
++3227
+c@t1:=tr3is(real,pl"r"(pl"r"(a,b),c),pl"r"(a,pl"r"(b,c)),pl"r"(a,pl"r"(c,b)),pl"r"(pl"r"(a,c),b),asspl1"r"(a,b,c),ispl2"r"(pl"r"(b,c),pl"r"(c,b),a,compl"r"(b,c)),asspl2"r"(a,c,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b))
+d@t2:=tr3is(real,pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(pl"r"(a,b),c),d),pl"r"(pl"r"(pl"r"(a,c),b),d),pl"r"(pl"r"(a,c),pl"r"(b,d)),asspl2"r"(pl"r"(a,b),c,d),ispl1"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b),d,t1),asspl1"r"(pl"r"(a,c),b,d)):is"r"(pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,c),pl"r"(b,d)))
+t3:=tris(real,mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,b),pl"r"(m0"r"(c),m0"r"(d))),pl"r"(mn"r"(a,c),mn"r"(b,d)),ispl2"r"(m0"r"(pl"r"(c,d)),pl"r"(m0"r"(c),m0"r"(d)),pl"r"(a,b),satz180(c,d)),t2(a,b,m0"r"(c),m0"r"(d))):is"r"(mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(mn"r"(a,c),mn"r"(b,d)))
+z@t4:=tris(real,mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),mn"r"(pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))),pl"r"(rets(x,y),rets(x,z)),ismn12"r"(ts"r"(re(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),ts"r"(im(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z))),disttp2(re(x),re(y),re(z)),disttp2(im(x),im(y),im(z))),t3(ts"r"(re(x),re(y)),ts"r"(re(x),re(z)),ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))):is"r"(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)))
+t5:=tris(real,pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))),pl"r"(imts(x,y),imts(x,z)),ispl12"r"(ts"r"(re(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z))),disttp2(re(x),im(y),im(z)),disttp2(im(x),re(y),re(z))),t2(ts"r"(re(x),im(y)),ts"r"(re(x),im(z)),ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))):is"r"(pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)))
+t6:=tr3is(cx,ts(x,pl(y,z)),pli(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))))),pli(pl"r"(rets(x,y),rets(x,z)),pl"r"(imts(x,y),imts(x,z))),pl(ts(x,y),ts(x,z)),tsis2a(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z))),isrecx12(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)),t4,t5),plis12b(rets(x,y),imts(x,y),rets(x,z),imts(x,z))):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+-3227
+satz227:=t6".3227":is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+disttp1:=tr3is(cx,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz227(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
+disttp2:=satz227:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+distpt1:=symis(cx,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
+distpt2:=symis(cx,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
+satz228:=tr4is(cx,ts(x,mn(y,z)),ts(x,pl(y,m0(z))),pl(ts(x,y),ts(x,m0(z))),pl(ts(x,y),m0(ts(x,z))),mn(ts(x,y),ts(x,z)),ists2(mn(y,z),pl(y,m0(z)),x,satz218(y,z)),disttp2(x,y,m0(z)),ispl2(ts(x,m0(z)),m0(ts(x,z)),ts(x,y),satz224b(x,z)),satz218a(ts(x,y),ts(x,z))):is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
+disttm1:=tr3is(cx,ts(mn(x,y),z),ts(z,mn(x,y)),mn(ts(z,x),ts(z,y)),mn(ts(x,z),ts(y,z)),comts(mn(x,y),z),satz228(z,x,y),ismn12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(mn(x,y),z),mn(ts(x,z),ts(y,z)))
+disttm2:=satz228:is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
+distmt1:=symis(cx,ts(mn(x,y),z),mn(ts(x,z),ts(y,z)),disttm1):is(mn(ts(x,z),ts(y,z)),ts(mn(x,y),z))
+distmt2:=symis(cx,ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)),disttm2):is(mn(ts(x,y),ts(x,z)),ts(x,mn(y,z)))
+y@[n:nis(y,0c)][u1:complex][u2:complex][i:is(ts(y,u1),x)][j:is(ts(y,u2),x)]
++3229
+t1:=tris2(cx,ts(y,u1),ts(y,u2),x,i,j):is(ts(y,u1),ts(y,u2))
+t2:=tris(cx,ts(y,mn(u1,u2)),mn(ts(y,u1),ts(y,u2)),0c,disttm2(y,u1,u2),satz213b(ts(y,u1),ts(y,u2),t1)):is(ts(y,mn(u1,u2)),0c)
+t3:=ore2(is(y,0c),is(mn(u1,u2),0c),satz221c(y,mn(u1,u2),t2),n):is(mn(u1,u2),0c)
+-3229
+satz229b:=satz213a(u1,u2,t3".3229"):is(u1,u2)
++*3229
+n@t4:=pnot0(mod2(y),lemma4(y,n)):nis"r"(mod2(y),0)
+u:=ts(pli(ov(re(y),mod2(y),t4),m0"r"(ov(im(y),mod2(y),t4))),x):complex
+[v:real]
+dd:=ov(v,mod2(y),t4):real
+n@t5:=tr3is(real,m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),m0"r"(m0"r"(ts"r"(im(y),dd(im(y))))),ts"r"(im(y),dd(im(y))),dd(ts"r"(im(y),im(y))),ism0"r"(ts"r"(im(y),m0"r"(dd(im(y)))),m0"r"(ts"r"(im(y),dd(im(y)))),satz197b(im(y),dd(im(y)))),satz177(ts"r"(im(y),dd(im(y)))),lemma6(im(y),im(y),mod2(y),t4)):is"r"(m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))))
+t6:=tr3is(real,mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(dd(ts"r"(re(y),re(y))),dd(ts"r"(im(y),im(y)))),dd(mod2(y)),1rl,ispl12"r"(ts"r"(re(y),dd(re(y))),dd(ts"r"(re(y),re(y))),m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))),lemma6(re(y),re(y),mod2(y),t4),t5),lemma7(ts"r"(re(y),re(y)),ts"r"(im(y),im(y)),mod2(y),t4),lemma8(mod2(y),t4)):is"r"(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl)
+t7:=tris(real,ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(m0"r"(re(y)),dd(im(y))),dd(ts"r"(m0"r"(re(y)),im(y))),satz197d(re(y),dd(im(y))),lemma6(m0"r"(re(y)),im(y),mod2(y),t4)):is"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))))
+t8:=tris(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),pl"r"(dd(ts"r"(m0"r"(re(y)),im(y))),dd(ts"r"(im(y),re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),ispl12"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))),ts"r"(im(y),dd(re(y))),dd(ts"r"(im(y),re(y))),t7,lemma6(im(y),re(y),mod2(y),t4)),lemma7(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)),mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))))
+t9:=tr3is(real,pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),pl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),mn"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y))),0,ispl1"r"(ts"r"(m0"r"(re(y)),im(y)),m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y)),satz197a(re(y),im(y))),compl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),satz182e(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),comts"r"(im(y),re(y)))):is"r"(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0)
+t10:=tr3is(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),dd(0),0,t8,isf(real,real,[t:real]dd(t),pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0,t9),lemma9(mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0)
+t11:=tris(cx,ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),pli(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y))))),1c,tsis2a(y,dd(re(y)),m0"r"(dd(im(y)))),isrecx12(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0,t6,t10)):is(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c)
+t12:=tr3is(cx,ts(y,u),ts(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),x),ts(1c,x),x,assts2(y,pli(dd(re(y)),m0"r"(dd(im(y)))),x),ists1(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c,x,t11),satz222b(x)):is(ts(y,u),x)
+-3229
+n@satz229a:=somei(cx,[t:cx]is(ts(y,t),x),u".3229",t12".3229"):some([t:cx]is(ts(y,t),x))
+satz229:=onei(cx,[t:cx]is(ts(y,t),x),[t:cx][u:cx][v:is(ts(y,t),x)][w:is(ts(y,u),x)]satz229b(t,u,v,w),satz229a):one([t:cx]is(ts(y,t),x))
+ov:=ind(cx,[t:cx]is(ts(y,t),x),satz229):complex
+satz229c:=oneax(cx,[t:cx]is(ts(y,t),x),satz229):is(ts(y,ov(x,y,n)),x)
+satz229d:=symis(cx,ts(y,ov(x,y,n)),x,satz229c):is(x,ts(y,ov(x,y,n)))
+satz229e:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c):is(ts(ov(x,y,n),y),x)
+satz229f:=symis(cx,ts(ov(x,y,n),y),x,satz229e):is(x,ts(ov(x,y,n),y))
+y@[u:complex][n:nis(y,0c)][i:is(ts(y,u),x)]
+satz229g:=satz229b(n,u,ov(x,y,n),i,satz229c(n)):is(u,ov(x,y,n))
+satz229h:=symis(cx,u,ov(x,y,n),satz229g):is(ov(x,y,n),u)
+n@[i:is(ts(u,y),x)]
+satz229j:=satz229g(tris(cx,ts(y,u),ts(u,y),x,comts(y,u),i)):is(u,ov(x,y,n))
+satz229k:=symis(cx,u,ov(x,y,n),satz229j):is(ov(x,y,n),u)
+z@[i:is(x,y)][n:nis(z,0c)]
+isov1:=isf(cx,cx,[t:cx]ov(t,z,n),x,y,i):is(ov(x,z,n),ov(y,z,n))
+i@[n:nis(x,0c)][o:nis(y,0c)]
+isov2:=satz229h(z,x,ov(z,y,o),n,tris(cx,ts(x,ov(z,y,o)),ts(y,ov(z,y,o)),z,ists1(x,y,ov(z,y,o),i),satz229c(z,y,o))):is(ov(z,x,n),ov(z,y,o))
+z@[u:complex][i:is(x,y)][j:is(z,u)][n:nis(z,0c)][o:nis(u,0c)]
+isov12:=tris(cx,ov(x,z,n),ov(y,z,n),ov(y,u,o),isov1(x,y,z,i,n),isov2(z,u,y,j,n,o)):is(ov(x,z,n),ov(y,u,o))
+y@satz230:=tris(cx,pl(mn(x,y),y),pl(y,mn(x,y)),x,compl(mn(x,y),y),satz212h(x,y)):is(pl(mn(x,y),y),x)
+satz231:=satz212e(pl(x,y),y,x,compl(y,x)):is(mn(pl(x,y),y),x)
+satz232:=satz212e(x,mn(x,y),y,satz230):is(mn(x,mn(x,y)),y)
++4233
+z@t1:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(mn(mn(x,y),z),pl(y,z)),pl(mn(mn(x,y),z),pl(z,y)),pl(pl(mn(mn(x,y),z),z),y),compl(pl(y,z),mn(mn(x,y),z)),ispl2(pl(y,z),pl(z,y),mn(mn(x,y),z),compl(y,z)),asspl2(mn(mn(x,y),z),z,y)):is(pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y))
+t2:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y),pl(mn(x,y),y),x,t1,ispl1(pl(mn(mn(x,y),z),z),mn(x,y),y,satz230(mn(x,y),z)),satz230(x,y)):is(pl(pl(y,z),mn(mn(x,y),z)),x)
+-4233
+z@satz233:=satz212d(x,pl(y,z),mn(mn(x,y),z),t2".4233"):is(mn(mn(x,y),z),mn(x,pl(y,z)))
+satz234:=satz212g(pl(x,y),z,pl(x,mn(y,z)),tris(cx,pl(pl(x,mn(y,z)),z),pl(x,pl(mn(y,z),z)),pl(x,y),asspl1(x,mn(y,z),z),ispl2(pl(mn(y,z),z),y,x,satz230(y,z)))):is(mn(pl(x,y),z),pl(x,mn(y,z)))
+satz234a:=symis(cx,mn(pl(x,y),z),pl(x,mn(y,z)),satz234):is(pl(x,mn(y,z)),mn(pl(x,y),z))
+satz234b:=tr3is(cx,mn(pl(x,y),z),mn(pl(y,x),z),pl(y,mn(x,z)),pl(mn(x,z),y),ismn1(pl(x,y),pl(y,x),z,compl(x,y)),satz234(y,x,z),compl(y,mn(x,z))):is(mn(pl(x,y),z),pl(mn(x,z),y))
+satz234c:=symis(cx,mn(pl(x,y),z),pl(mn(x,z),y),satz234b):is(pl(mn(x,z),y),mn(pl(x,y),z))
+satz235:=satz212f(x,mn(y,z),pl(mn(x,y),z),tr3is(cx,pl(pl(mn(x,y),z),mn(y,z)),pl(mn(x,y),pl(z,mn(y,z))),pl(mn(x,y),y),x,asspl1(mn(x,y),z,mn(y,z)),ispl2(pl(z,mn(y,z)),y,mn(x,y),satz212h(y,z)),satz230(x,y))):is(pl(mn(x,y),z),mn(x,mn(y,z)))
+satz235a:=symis(cx,pl(mn(x,y),z),mn(x,mn(y,z)),satz235):is(mn(x,mn(y,z)),pl(mn(x,y),z))
+satz235b:=tris(cx,mn(x,mn(y,z)),pl(mn(x,y),z),mn(pl(x,z),y),satz235a,satz234c(x,z,y)):is(mn(x,mn(y,z)),mn(pl(x,z),y))
+satz235c:=tris(cx,mn(x,mn(y,z)),mn(pl(x,z),y),mn(pl(z,x),y),satz235b,ismn1(pl(x,z),pl(z,x),y,compl(x,z))):is(mn(x,mn(y,z)),mn(pl(z,x),y))
+satz236:=satz212g(pl(x,z),pl(y,z),mn(x,y),tris(cx,pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y)))):is(mn(pl(x,z),pl(y,z)),mn(x,y))
+satz236a:=tris(cx,mn(pl(z,x),pl(z,y)),mn(pl(x,z),pl(y,z)),mn(x,y),ismn12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y)),satz236):is(mn(pl(z,x),pl(z,y)),mn(x,y))
+[u:complex]
++4237
+t1:=tr3is(cx,pl(mn(z,u),pl(u,y)),pl(pl(mn(z,u),u),y),pl(z,y),pl(y,z),asspl2(mn(z,u),u,y),ispl1(pl(mn(z,u),u),z,y,satz230(z,u)),compl(z,y)):is(pl(mn(z,u),pl(u,y)),pl(y,z))
+t2:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(pl(mn(x,y),mn(z,u)),pl(u,y)),pl(mn(x,y),pl(mn(z,u),pl(u,y))),pl(mn(x,y),pl(y,z)),ispl2(pl(y,u),pl(u,y),pl(mn(x,y),mn(z,u)),compl(y,u)),asspl1(mn(x,y),mn(z,u),pl(u,y)),ispl2(pl(mn(z,u),pl(u,y)),pl(y,z),mn(x,y),t1)):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)))
+t3:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),t2,asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y))):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(x,z))
+-4237
+satz237:=satz212f(pl(x,z),pl(y,u),pl(mn(x,y),mn(z,u)),t3".4237"):is(pl(mn(x,y),mn(z,u)),mn(pl(x,z),pl(y,u)))
++4238
+t1:=tris(cx,pl(pl(x,u),z),pl(x,pl(u,z)),pl(x,pl(z,u)),asspl1(x,u,z),ispl2(pl(u,z),pl(z,u),x,compl(u,z))):is(pl(pl(x,u),z),pl(x,pl(z,u)))
+t2:=tr3is(cx,pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(pl(pl(x,u),z),pl(pl(y,z),u)),mn(pl(x,pl(z,u)),pl(y,pl(z,u))),mn(x,y),satz237(pl(x,u),pl(y,z),z,u),ismn12(pl(pl(x,u),z),pl(x,pl(z,u)),pl(pl(y,z),u),pl(y,pl(z,u)),t1,asspl1(y,z,u)),satz236(x,y,pl(z,u))):is(pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(x,y))
+-4238
+satz238:=satz212g(mn(x,y),mn(z,u),mn(pl(x,u),pl(y,z)),t2".4238"):is(mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)))
+[i:is(mn(x,y),mn(z,u))]
++4239
+t1:=tris1(cx,mn(pl(x,u),pl(y,z)),0c,mn(mn(x,y),mn(z,u)),satz238,satz213b(mn(x,y),mn(z,u),i)):is(mn(pl(x,u),pl(y,z)),0c)
+-4239
+satz239a:=satz213a(pl(x,u),pl(y,z),t1".4239"):is(pl(x,u),pl(y,z))
+u@[i:is(pl(x,u),pl(y,z))]
++*4239
+i@t2:=tris(cx,mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)),0c,satz238,satz213b(pl(x,u),pl(y,z),i)):is(mn(mn(x,y),mn(z,u)),0c)
+-4239
+i@satz239b:=satz213a(mn(x,y),mn(z,u),t2".4239"):is(mn(x,y),mn(z,u))
+y@[n:nis(y,0c)]
+satz240:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c(x,y,n)):is(ts(ov(x,y,n),y),x)
+satz241:=satz229h(ts(x,y),y,x,n,comts(y,x)):is(ov(ts(x,y),y,n),x)
+y@[n:nis(x,0c)][o:nis(y,0c)]
+lemma6:=th3"l.imp"(is(ov(x,y,o),0c),is(x,0c),n,[t:is(ov(x,y,o),0c)]tris1(cx,x,0c,ts(y,ov(x,y,o)),satz229c(x,y,o),satz221b(y,ov(x,y,o),t))):nis(ov(x,y,o),0c)
+satz242:=satz229h(x,ov(x,y,o),y,lemma6,satz240(o)):is(ov(x,ov(x,y,o),lemma6),y)
+z@[n:nis(y,0c)][o:nis(z,0c)]
++5243
+t1:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ov(ov(x,y,n),z,o),ts(y,z)),ts(ov(ov(x,y,n),z,o),ts(z,y)),ts(ts(ov(ov(x,y,n),z,o),z),y),comts(ts(y,z),ov(ov(x,y,n),z,o)),ists2(ts(y,z),ts(z,y),ov(ov(x,y,n),z,o),comts(y,z)),assts2(ov(ov(x,y,n),z,o),z,y)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y))
+t2:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y),ts(ov(x,y,n),y),x,t1,ists1(ts(ov(ov(x,y,n),z,o),z),ov(x,y,n),y,satz240(ov(x,y,n),z,o)),satz240(x,y,n)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),x)
+-5243
+satz243:=satz229g(x,ts(y,z),ov(ov(x,y,n),z,o),satz221d(y,z,n,o),t2".5243"):is(ov(ov(x,y,n),z,o),ov(x,ts(y,z),satz221d(y,z,n,o)))
+z@[n:nis(z,0c)]
+satz244:=satz229k(ts(x,y),z,ts(x,ov(y,z,n)),n,tris(cx,ts(ts(x,ov(y,z,n)),z),ts(x,ts(ov(y,z,n),z)),ts(x,y),assts1(x,ov(y,z,n),z),ists2(ts(ov(y,z,n),z),y,x,satz240(y,z,n)))):is(ov(ts(x,y),z,n),ts(x,ov(y,z,n)))
+satz244a:=symis(cx,ov(ts(x,y),z,n),ts(x,ov(y,z,n)),satz244):is(ts(x,ov(y,z,n)),ov(ts(x,y),z,n))
+satz244b:=tr3is(cx,ov(ts(x,y),z,n),ov(ts(y,x),z,n),ts(y,ov(x,z,n)),ts(ov(x,z,n),y),isov1(ts(x,y),ts(y,x),z,comts(x,y),n),satz244(y,x,z,n),comts(y,ov(x,z,n))):is(ov(ts(x,y),z,n),ts(ov(x,z,n),y))
+satz244c:=symis(cx,ov(ts(x,y),z,n),ts(ov(x,z,n),y),satz244b):is(ts(ov(x,z,n),y),ov(ts(x,y),z,n))
+z@[n:nis(y,0c)][o:nis(z,0c)]
+satz245:=satz229j(x,ov(y,z,o),ts(ov(x,y,n),z),lemma6(y,z,n,o),tr3is(cx,ts(ts(ov(x,y,n),z),ov(y,z,o)),ts(ov(x,y,n),ts(z,ov(y,z,o))),ts(ov(x,y,n),y),x,assts1(ov(x,y,n),z,ov(y,z,o)),ists2(ts(z,ov(y,z,o)),y,ov(x,y,n),satz229c(y,z,o)),satz240(x,y,n))):is(ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)))
+satz245a:=symis(cx,ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)),satz245):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z))
+satz245b:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z),ov(ts(x,z),y,n),satz245a,satz244c(x,z,y,n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n))
+satz245c:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n),ov(ts(z,x),y,n),satz245b,isov1(ts(x,z),ts(z,x),y,comts(x,z),n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(z,x),y,n))
+satz246:=satz229k(ts(x,z),ts(y,z),ov(x,y,n),satz221d(y,z,n,o),tris(cx,ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n)))):is(ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n))
+satz246a:=tris(cx,ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n),isov12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y),satz221d(z,y,o,n),satz221d(y,z,n,o)),satz246):is(ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(x,y,n))
+z@[u:complex][n:nis(y,0c)][o:nis(u,0c)]
++5247
+t1:=tr3is(cx,ts(ov(z,u,o),ts(u,y)),ts(ts(ov(z,u,o),u),y),ts(z,y),ts(y,z),assts2(ov(z,u,o),u,y),ists1(ts(ov(z,u,o),u),z,y,satz240(z,u,o)),comts(z,y)):is(ts(ov(z,u,o),ts(u,y)),ts(y,z))
+t2:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ts(ov(x,y,n),ov(z,u,o)),ts(u,y)),ts(ov(x,y,n),ts(ov(z,u,o),ts(u,y))),ts(ov(x,y,n),ts(y,z)),ists2(ts(y,u),ts(u,y),ts(ov(x,y,n),ov(z,u,o)),comts(y,u)),assts1(ov(x,y,n),ov(z,u,o),ts(u,y)),ists2(ts(ov(z,u,o),ts(u,y)),ts(y,z),ov(x,y,n),t1)):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)))
+t3:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),t2,assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n))):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(x,z))
+-5247
+satz247:=satz229j(ts(x,z),ts(y,u),ts(ov(x,y,n),ov(z,u,o)),satz221d(y,u,n,o),t3".5247"):is(ts(ov(x,y,n),ov(z,u,o)),ov(ts(x,z),ts(y,u),satz221d(y,u,n,o)))
+u@[n:nis(y,0c)][o:nis(z,0c)][p:nis(u,0c)]
++5248
+t1:=tris(cx,ts(ts(x,u),z),ts(x,ts(u,z)),ts(x,ts(z,u)),assts1(x,u,z),ists2(ts(u,z),ts(z,u),x,comts(u,z))):is(ts(ts(x,u),z),ts(x,ts(z,u)))
+t2:=tr3is(cx,ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(ts(ts(x,u),z),ts(ts(y,z),u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p)),ov(ts(x,ts(z,u)),ts(y,ts(z,u)),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),ov(x,y,n),satz247(ts(x,u),ts(y,z),z,u,satz221d(y,z,n,o),p),isov12(ts(ts(x,u),z),ts(x,ts(z,u)),ts(ts(y,z),u),ts(y,ts(z,u)),t1,assts1(y,z,u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),satz246(x,y,ts(z,u),n,satz221d(z,u,o,p))):is(ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(x,y,n))
+-5248
+satz248:=satz229k(ov(x,y,n),ov(z,u,p),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),lemma6(z,u,o,p),t2".5248"):is(ov(ov(x,y,n),ov(z,u,p),lemma6(z,u,o,p)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)))
+x@[n:nis(x,0c)]
+satz249:=satz229h(0c,x,0c,n,satz221b(x,0c,refis(cx,0c))):is(ov(0c,x,n),0c)
+satz250:=satz229h(x,x,1c,n,satz222(x)):is(ov(x,x,n),1c)
+y@[n:nis(y,0c)][i:is(x,y)]
+satz251a:=tris(cx,ov(x,y,n),ov(x,x,th2"e.notis"(cx,y,0c,x,n,i)),1c,isov2(y,x,x,symis(cx,x,y,i),n,th2"e.notis"(cx,y,0c,x,n,i)),satz250(x,th2"e.notis"(cx,y,0c,x,n,i))):is(ov(x,y,n),1c)
+n@[i:is(ov(x,y,n),1c)]
+satz251b:=tr3is(cx,x,ts(y,ov(x,y,n)),ts(y,1c),y,satz229d(x,y,n),ists2(ov(x,y,n),1c,y,i),satz222(y)):is(x,y)
+u@[n:nis(y,0c)][o:nis(u,0c)][i:is(ov(x,y,n),ov(z,u,o))]
++5252
+[j:is(z,0c)]
+t1:=tr3is(cx,ov(x,y,n),ov(z,u,o),ov(0c,u,o),0c,i,isov1(z,0c,u,j,o),satz249(u,o)):is(ov(x,y,n),0c)
+t2:=tris(cx,x,ts(y,ov(x,y,n)),0c,satz229d(x,y,n),satz221b(y,ov(x,y,n),t1)):is(x,0c)
+t3:=tris2(cx,ts(x,u),ts(y,z),0c,satz221a(x,u,t2),satz221b(y,z,j)):is(ts(x,u),ts(y,z))
+i@[p:nis(z,0c)]
+t4:=tris1(cx,ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),satz248(x,y,z,u,n,p,o),satz251a(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),i)):is(ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c)
+t5:=satz251b(ts(x,u),ts(y,z),satz221d(y,z,n,p),t4):is(ts(x,u),ts(y,z))
+-5252
+satz252a:=th1"l.imp"(is(z,0c),is(ts(x,u),ts(y,z)),[t:is(z,0c)]t3".5252"(t),[t:nis(z,0c)]t5".5252"(t)):is(ts(x,u),ts(y,z))
+o@[i:is(ts(x,u),ts(y,z))]
++*5252
+i@[j:is(z,0c)]
+t6:=tris(cx,ts(x,u),ts(y,z),0c,i,satz221b(y,z,j)):is(ts(x,u),0c)
+t7:=ore1(is(x,0c),is(u,0c),satz221c(x,u,t6),o):is(x,0c)
+t8:=tris2(cx,ov(x,y,n),ov(z,u,o),0c,tris(cx,ov(x,y,n),ov(0c,y,n),0c,isov1(x,0c,y,t7,n),satz249(y,n)),tris(cx,ov(z,u,o),ov(0c,u,o),0c,isov1(z,0c,u,j,o),satz249(u,o))):is(ov(x,y,n),ov(z,u,o))
+i@[p:nis(z,0c)]
+t9:=tris(cx,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,satz248(x,y,z,u,n,p,o),satz251a(ts(x,u),ts(y,z),satz221d(y,z,n,p),i)):is(ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),1c)
+t10:=satz251b(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),t9):is(ov(x,y,n),ov(z,u,o))
+-5252
+i@satz252b:=th1"l.imp"(is(z,0c),is(ov(x,y,n),ov(z,u,o)),[t:is(z,0c)]t8".5252"(t),[t:nis(z,0c)]t10".5252"(t)):is(ov(x,y,n),ov(z,u,o))
+z@[n:nis(y,0c)]
+satz253:=satz229g(pl(x,z),y,pl(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,pl(ov(x,y,n),ov(z,y,n))),pl(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),pl(x,z),disttp2(y,ov(x,y,n),ov(z,y,n)),ispl12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(pl(ov(x,y,n),ov(z,y,n)),ov(pl(x,z),y,n))
+z@[n:nis(z,0c)]
+distop:=symis(cx,pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n),satz253(x,z,y,n)):is(ov(pl(x,y),z,n),pl(ov(x,z,n),ov(y,z,n)))
+distpo:=satz253(x,z,y,n):is(pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n))
+u@[n:nis(y,0c)][o:nis(u,0c)]
+satz254:=tris1(cx,pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),pl(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ispl12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz253(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
+z@[n:nis(y,0c)]
+satz255:=satz229g(mn(x,z),y,mn(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,mn(ov(x,y,n),ov(z,y,n))),mn(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),mn(x,z),disttm2(y,ov(x,y,n),ov(z,y,n)),ismn12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(mn(ov(x,y,n),ov(z,y,n)),ov(mn(x,z),y,n))
+z@[n:nis(z,0c)]
+distom:=symis(cx,mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n),satz255(x,z,y,n)):is(ov(mn(x,y),z,n),mn(ov(x,z,n),ov(y,z,n)))
+distmo:=satz255(x,z,y,n):is(mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n))
+u@[n:nis(y,0c)][o:nis(u,0c)]
+satz256:=tris1(cx,mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),mn(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ismn12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz255(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
+x@conj:=pli(re(x),m0"r"(im(x))):complex
+b@conjisa:=isrecx12(re(pli(a,b)),a,m0"r"(im(pli(a,b))),m0"r"(b),reis(a,b),ism0"r"(im(pli(a,b)),b,imis(a,b))):is(conj(pli(a,b)),pli(a,m0"r"(b)))
+conjisb:=symis(cx,conj(pli(a,b)),pli(a,m0"r"(b)),conjisa):is(pli(a,m0"r"(b)),conj(pli(a,b)))
+y@[i:is(x,y)]
+isconj:=isf(cx,cx,[t:cx]conj(t),x,y,i):is(conj(x),conj(y))
+x@satz257:=tr3is(cx,conj(conj(x)),pli(re(x),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,conjisa(re(x),m0"r"(im(x))),isrecx2(m0"r"(m0"r"(im(x))),im(x),re(x),satz177(im(x))),pliis(x)):is(conj(conj(x)),x)
+[i:is(x,0c)]
+satz258a:=tr3is(cx,conj(x),conj(0c),pli(0,m0"r"(0)),0c,isconj(x,0c,i),conjisa(0,0),isrecx2(m0"r"(0),0,0,satz176b(0,refis(real,0)))):is(conj(x),0c)
+x@[i:is(conj(x),0c)]
++6258
+t1:=tris(real,re(x),re(conj(x)),0,isre(re(x),m0"r"(im(x))),lemma1(conj(x),i)):is"r"(re(x),0)
+t2:=satz176e(im(x),tris(real,m0"r"(im(x)),im(conj(x)),0,isim(re(x),m0"r"(im(x))),lemma2(conj(x),i))):is"r"(im(x),0)
+-6258
+satz258b:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t1".6258",t2".6258")):is(x,0c)
++*6258
+i@anders:=tris1(cx,x,0c,conj(conj(x)),satz257,satz258a(conj(x),i)):is(x,0c)
+-6258
+x@[n:nis(x,0c)]
+satz258c:=th3"l.imp"(is(conj(x),0c),is(x,0c),n,[t:is(conj(x),0c)]satz258b(t)):nis(conj(x),0c)
+x@[i:is(conj(x),x)]
++6259
+t1:=tris(real,m0"r"(im(x)),im(conj(x)),im(x),isim(re(x),m0"r"(im(x))),isceim(conj(x),x,i)):is"r"(m0"r"(im(x)),im(x))
+-6259
+satz259a:=lemma10(im(x),symis(real,m0"r"(im(x)),im(x),t1".6259")):is"r"(im(x),0)
+x@[i:is"r"(im(x),0)]
+satz259b:=tris(cx,conj(x),pli(re(x),im(x)),x,isrecx2(m0"r"(im(x)),im(x),re(x),tris2(real,m0"r"(im(x)),im(x),0,satz176b(im(x),i),i)),pliis(x)):is(conj(x),x)
+x@[i:is(x,conj(x))]
+satz269c:=satz259a(x,symis(cx,x,conj(x),i)):is"r"(im(x),0)
+x@[i:is"r"(im(x),0)]
+satz269d:=symis(cx,conj(x),x,satz259b(i)):is(x,conj(x))
+y@satz260:=tr3is(cx,conj(pl(x,y)),pli(pl"r"(re(x),re(y)),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(re(x),re(y)),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(conj(x),conj(y)),conjisa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx2(m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),pl"r"(re(x),re(y)),satz180(im(x),im(y))),plis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(pl(x,y)),pl(conj(x),conj(y)))
+satz260a:=symis(cx,conj(pl(x,y)),pl(conj(x),conj(y)),satz260):is(pl(conj(x),conj(y)),conj(pl(x,y)))
++6261
+t1:=tris(real,m0"r"(imts(x,y)),pl"r"(m0"r"(ts"r"(re(x),im(y))),m0"r"(ts"r"(im(x),re(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),satz180(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(m0"r"(ts"r"(re(x),im(y))),ts"r"(re(x),m0"r"(im(y))),m0"r"(ts"r"(im(x),re(y))),ts"r"(m0"r"(im(x)),re(y)),satz197f(re(x),im(y)),satz197e(im(x),re(y)))):is"r"(m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))))
+-6261
+satz261:=tr3is(cx,conj(ts(x,y)),pli(rets(x,y),m0"r"(imts(x,y))),pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y)))),ts(conj(x),conj(y)),conjisa(rets(x,y),imts(x,y)),isrecx12(rets(x,y),mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),ismn2"r"(ts"r"(im(x),im(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y))),ts"r"(re(x),re(y)),satz198a(im(x),im(y))),t1".6261"),tsis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(ts(x,y)),ts(conj(x),conj(y)))
+satz261a:=symis(cx,conj(ts(x,y)),ts(conj(x),conj(y)),satz261):is(ts(conj(x),conj(y)),conj(ts(x,y)))
++6262
+t1:=symis(cx,pl(mn(x,y),y),x,satz230(x,y)):is(x,pl(mn(x,y),y))
+t2:=tris(cx,conj(x),conj(pl(mn(x,y),y)),pl(conj(mn(x,y)),conj(y)),isconj(x,pl(mn(x,y),y),t1),satz260(mn(x,y),y)):is(conj(x),pl(conj(mn(x,y)),conj(y)))
+-6262
+satz262:=satz212f(conj(x),conj(y),conj(mn(x,y)),symis(cx,conj(x),pl(conj(mn(x,y)),conj(y)),t2".6262")):is(conj(mn(x,y)),mn(conj(x),conj(y)))
+satz262a:=symis(cx,conj(mn(x,y)),mn(conj(x),conj(y)),satz262):is(mn(conj(x),conj(y)),conj(mn(x,y)))
+[n:nis(y,0c)]
++6263
+t1:=satz229f(x,y,n):is(x,ts(ov(x,y,n),y))
+t2:=isconj(x,ts(ov(x,y,n),y),t1):is(conj(x),conj(ts(ov(x,y,n),y)))
+t3:=satz261(ov(x,y,n),y):is(conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)))
+t4:=tris(cx,conj(x),conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)),t2,t3):is(conj(x),ts(conj(ov(x,y,n)),conj(y)))
+t5:=satz258c(y,n):nis(conj(y),0c)
+-6263
+satz263:=satz229j(conj(x),conj(y),conj(ov(x,y,n)),t5".6263",symis(cx,conj(x),ts(conj(ov(x,y,n)),conj(y)),t4".6263")):is(conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)))
+satz263a:=symis(cx,conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)),satz263):is(ov(conj(x),conj(y),satz258c(y,n)),conj(ov(x,y,n)))
+x@mod:=sqrt(mod2(x),lemma5(x)):real
+y@[i:is(x,y)]
+ismod:=isf(cx,real,[t:cx]mod(t),x,y,i):is"r"(mod(x),mod(y))
+x@[n:nis(x,0c)]
+satz264a:=sqrtnot0(mod2(x),lemma5(x),pnot0(mod2(x),lemma4(x,n))):pos(mod(x))
+x@[i:is(x,0c)]
+satz264b:=sqrt0(mod2(x),lemma5(x),lemma3(x,i)):is"r"(mod(x),0)
+x@satz264c:=thsqrt1a(mod2(x),lemma5(x)):not(neg(mod(x)))
+satz264d:=satz167f(mod(x),0,th3"l.imp"(less(mod(x),0),neg(mod(x)),satz264c,[t:less(mod(x),0)]satz169d(mod(x),t))):moreis(mod(x),0)
++7265
+t1:=symis(real,ts"r"(mod(x),mod(x)),mod2(x),thsqrt1b(mod2(x),lemma5(x))):is"r"(mod2(x),ts"r"(mod(x),mod(x)))
+t2:=tris(real,pl"r"(ts"r"(re(x),re(x)),0),ts"r"(re(x),re(x)),ts"r"(abs(re(x)),abs(re(x))),pl02(ts"r"(re(x),re(x)),0,refis(real,0)),lemma12"r"(re(x))):is"r"(pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))))
+t3:=satz191(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),ts"r"(im(x),im(x)),0,moreisi2(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),refis(real,ts"r"(re(x),re(x)))),lemma11"r"(im(x))):moreis(mod2(x),pl"r"(ts"r"(re(x),re(x)),0))
+t4:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))),t1,t2,t3):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(re(x)),abs(re(x))))
+t5:=tris(real,pl"r"(0,ts"r"(im(x),im(x))),ts"r"(im(x),im(x)),ts"r"(abs(im(x)),abs(im(x))),pl01(0,ts"r"(im(x),im(x)),refis(real,0)),lemma12"r"(im(x))):is"r"(pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))))
+t6:=satz191(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),lemma11"r"(re(x)),moreisi2(ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),refis(real,ts"r"(im(x),im(x))))):moreis(mod2(x),pl"r"(0,ts"r"(im(x),im(x))))
+t7:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))),t1,t5,t6):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(im(x)),abs(im(x))))
+@[r:real][s:real][m:moreis(ts"r"(r,r),ts"r"(s,s))][n:moreis(r,0)][l:less(r,s)]
+t8:=lemma2"r"(r,s,l):more(s,r)
+t9:=satz169b(s,satz172d(s,r,0,t8,n)):pos(s)
+[o:more(r,0)]
+t10:=trmore(ts"r"(s,s),ts"r"(r,s),ts"r"(r,r),satz203a(s,r,s,t8,t9),satz203d(s,r,r,t8,satz169b(r,o))):more(ts"r"(s,s),ts"r"(r,r))
+l@[i:is"r"(r,0)]
+t11:=ismore2(0,ts"r"(r,r),ts"r"(s,s),symis(real,ts"r"(r,r),0,ts01(r,r,i)),satz169a(ts"r"(s,s),possq(s,pnot0(s,t9)))):more(ts"r"(s,s),ts"r"(r,r))
+l@t12:=lemma1"r"(ts"r"(s,s),ts"r"(r,r),orapp(more(r,0),is"r"(r,0),more(ts"r"(s,s),ts"r"(r,r)),n,[t:more(r,0)]t10(t),[t:is"r"(r,0)]t11(t))):less(ts"r"(r,r),ts"r"(s,s))
+n@t13:=satz167f(r,s,[t:less(r,s)]<t12(t)>satz167c(ts"r"(r,r),ts"r"(s,s),m)):moreis(r,s)
+-7265
+satz265a:=t13".7265"(mod(x),abs(re(x)),t4".7265",satz264d(x)):moreis(mod(x),abs(re(x)))
+satz265b:=t13".7265"(mod(x),abs(im(x)),t7".7265",satz264d(x)):moreis(mod(x),abs(im(x)))
+@[r:real][s:real][i:is(ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)))][n:not(neg(r))][o:not(neg(s))]
++7266
+@[t:real]
+t1:=pl02(ts"r"(t,t),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t))
+t2:=tris(real,pl"r"(ts"r"(t,0),ts"r"(0,t)),ts"r"(t,0),0,pl02(ts"r"(t,0),ts"r"(0,t),ts01(0,t,refis(real,0))),ts02(t,0,refis(real,0))):is"r"(pl"r"(ts"r"(t,0),ts"r"(0,t)),0)
+t3:=tris(cx,ts(pli(t,0),pli(t,0)),pli(mn"r"(ts"r"(t,t),ts"r"(0,0)),pl"r"(ts"r"(t,0),ts"r"(0,t))),pli(ts"r"(t,t),0),tsis12a(t,0,t,0),isrecx12(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t),pl"r"(ts"r"(t,0),ts"r"(0,t)),0,t1,t2)):is(ts(pli(t,0),pli(t,0)),pli(ts"r"(t,t),0))
+o@t4:=tr3is(cx,pli(ts"r"(r,r),0),ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)),pli(ts"r"(s,s),0),symis(cx,ts(pli(r,0),pli(r,0)),pli(ts"r"(r,r),0),t3(r)),i,t3(s)):is(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0))
+t5:=tr3is(real,ts"r"(r,r),re(pli(ts"r"(r,r),0)),re(pli(ts"r"(s,s),0)),ts"r"(s,s),isre(ts"r"(r,r),0),iscere(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0),t4),reis(ts"r"(s,s),0)):is"r"(ts"r"(r,r),ts"r"(s,s))
+t6:=andi(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)),n,t5):and(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)))
+t7:=andi(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)),o,refis(real,ts"r"(s,s))):and(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)))
+-7266
+satz266:=satzr161b(ts"r"(s,s),r,s,t6".7266",t7".7266"):is"r"(r,s)
++7267
+x@t1:=tris(cx,ts(pli(mod(x),0),pli(mod(x),0)),pli(ts"r"(mod(x),mod(x)),0),pli(mod2(x),0),t3"c.7266"(mod(x)),isrecx1(ts"r"(mod(x),mod(x)),mod2(x),0,thsqrt1b(mod2(x),lemma5(x)))):is(ts(pli(mod(x),0),pli(mod(x),0)),pli(mod2(x),0))
+t2:=ispl2"r"(m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(im(x),im(x)),ts"r"(re(x),re(x)),tris(real,m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),satz197e(im(x),m0"r"(im(x))),satz198(im(x),im(x)))):is"r"(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x))
+t3:=tris(real,pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),pl"r"(m0"r"(ts"r"(re(x),im(x))),ts"r"(re(x),im(x))),0,ispl12"r"(ts"r"(re(x),m0"r"(im(x))),m0"r"(ts"r"(re(x),im(x))),ts"r"(im(x),re(x)),ts"r"(re(x),im(x)),satz197b(re(x),im(x)),comts"r"(im(x),re(x))),satz179a(ts"r"(re(x),im(x)))):is"r"(pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0)
+t4:=tris(cx,ts(x,conj(x)),pli(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x)))),pli(mod2(x),0),tsis2a(x,re(x),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0,t2,t3)):is(ts(x,conj(x)),pli(mod2(x),0))
+-7267
+x@satz267:=tris2(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),pli(mod2(x),0),t1".7267",t4".7267"):is(ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)))
+satz267a:=symis(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),satz267):is(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)))
++7268
+z@t1:=tr3is(cx,ts(x,ts(y,z)),ts(ts(x,y),z),ts(ts(y,x),z),ts(y,ts(x,z)),assts2(x,y,z),ists1(ts(x,y),ts(y,x),z,comts(x,y)),assts1(y,x,z)):is(ts(x,ts(y,z)),ts(y,ts(x,z)))
+[u:complex]
+t2:=tr3is(cx,ts(ts(x,y),ts(z,u)),ts(x,ts(y,ts(z,u))),ts(x,ts(z,ts(y,u))),ts(ts(x,z),ts(y,u)),assts1(x,y,ts(z,u)),ists2(ts(y,ts(z,u)),ts(z,ts(y,u)),x,t1(y,z,u)),assts2(x,z,ts(y,u))):is(ts(ts(x,y),ts(z,u)),ts(ts(x,z),ts(y,u)))
+y@t3:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,y),conj(ts(x,y))),ts(ts(x,y),ts(conj(x),conj(y))),ts(ts(x,conj(x)),ts(y,conj(y))),satz267(ts(x,y)),ists2(conj(ts(x,y)),ts(conj(x),conj(y)),ts(x,y),satz261(x,y)),t2(x,y,conj(x),conj(y))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))))
+t4:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))),ts(ts(pli(mod(x),0),pli(mod(x),0)),ts(pli(mod(y),0),pli(mod(y),0))),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),t3,ists12(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)),ts(y,conj(y)),ts(pli(mod(y),0),pli(mod(y),0)),satz267a(x),satz267a(y)),t2(pli(mod(x),0),pli(mod(x),0),pli(mod(y),0),pli(mod(y),0))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))))
+@[r:real][s:real]
+t5:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
+t6:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
+t7:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t5,t6)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
+y@t8:=tris(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)),t4,ists12(ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),t7(mod(x),mod(y)),t7(mod(x),mod(y)))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)))
+[n:neg(ts"r"(mod(x),mod(y)))]
+t9:=orapp(and(pos(mod(x)),neg(mod(y))),and(neg(mod(x)),pos(mod(y))),con,satz196h(mod(x),mod(y),n),[t:and(pos(mod(x)),neg(mod(y)))]<ande2(pos(mod(x)),neg(mod(y)),t)>satz264c(y),[t:and(neg(mod(x)),pos(mod(y)))]<ande1(neg(mod(x)),pos(mod(y)),t)>satz264c(x)):con
+-7268
+y@satz268:=satz266(mod(ts(x,y)),ts"r"(mod(x),mod(y)),t8".7268",satz264c(ts(x,y)),[t:neg(ts"r"(mod(x),mod(y)))]t9".7268"(t)):is"r"(mod(ts(x,y)),ts"r"(mod(x),mod(y)))
+satz268a:=symis(real,mod(ts(x,y)),ts"r"(mod(x),mod(y)),satz268):is"r"(ts"r"(mod(x),mod(y)),mod(ts(x,y)))
+[n:nis(y,0c)]
++7269
+t1:=pnot0(mod(y),satz264a(y,n)):nis"r"(mod(y),0)
+t2:=tris1(real,ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),mod(ts(ov(x,y,n),y)),satz268(ov(x,y,n),y),ismod(ts(ov(x,y,n),y),x,satz240(x,y,n))):is"r"(ts"r"(mod(ov(x,y,n)),mod(y)),mod(x))
+t3:=satz204g(mod(x),mod(y),mod(ov(x,y,n)),t1,tris(real,ts"r"(mod(y),mod(ov(x,y,n))),ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),comts"r"(mod(y),mod(ov(x,y,n))),t2)):is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),t1))
+-7269
+satz269:=t3".7269":is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),pnot0(mod(y),satz264a(y,n))))
+y@[i:is(pl(x,y),1c)]
++7270
+@[r:real]
+t1:=th1"l.imp"(neg(r),moreis(abs(r),r),[t:neg(r)]moreisi1(abs(r),r,trmore(abs(r),0,r,satz169a(abs(r),satz166b(r,t)),lemma2"r"(r,0,satz169c(r,t)))),[t:not(neg(r))]moreisi2(abs(r),r,absnn(r,t))):moreis(abs(r),r)
+x@t2:=trmoreis(mod(x),abs(re(x)),re(x),satz265a(x),t1(re(x))):moreis(mod(x),re(x))
+i@t3:=tr3is(real,pl"r"(re(x),re(y)),re(pl(x,y)),re(1c),1rl,isre(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),iscere(pl(x,y),1c,i),reis(1rl,0)):is"r"(pl"r"(re(x),re(y)),1rl)
+-7270
+satz270:=ismoreis2(pl"r"(re(x),re(y)),1rl,pl"r"(mod(x),mod(y)),t3".7270",satz191(mod(x),re(x),mod(y),re(y),t2".7270",t2".7270"(y))):moreis(pl"r"(mod(x),mod(y)),1rl)
++7271
+y@[i:is(pl(x,y),0c)]
+t1:=satz264b(pl(x,y),i):is"r"(mod(pl(x,y)),0)
+t2:=ismoreis2(pl"r"(0,0),mod(pl(x,y)),pl"r"(mod(x),mod(y)),tris2(real,pl"r"(0,0),mod(pl(x,y)),0,pl01(0,0,refis(real,0)),t1),satz191(mod(x),0,mod(y),0,satz264d(x),satz264d(y))):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
+y@[n:nis(pl(x,y),0c)]
+t3:=pnot0(mod(pl(x,y)),satz264a(pl(x,y),n)):nis"r"(mod(pl(x,y)),0)
+t4:=tris(cx,pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),ov(pl(x,y),pl(x,y),n),1c,satz253(x,pl(x,y),y,n),satz250(pl(x,y),n)):is(pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),1c)
+t5:=satz270(ov(x,pl(x,y),n),ov(y,pl(x,y),n),t4):moreis(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),1rl)
+fx:=ov"r"(mod(x),mod(pl(x,y)),t3):real
+fy:=ov"r"(mod(y),mod(pl(x,y)),t3):real
+t6:=ismoreis1(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),pl"r"(fx,fy),1rl,ispl12"r"(mod(ov(x,pl(x,y),n)),fx,mod(ov(y,pl(x,y),n)),fy,satz269(x,pl(x,y),n),satz269(y,pl(x,y),n)),t5):moreis(pl"r"(fx,fy),1rl)
+prl:=ts"r"(pl"r"(fx,fy),mod(pl(x,y))):real
+prr:=ts"r"(1rl,mod(pl(x,y))):real
+t7:=orapp(more(pl"r"(fx,fy),1rl),is"r"(pl"r"(fx,fy),1rl),moreis(prl,prr),t6,[t:more(pl"r"(fx,fy),1rl)]moreisi1(prl,prr,satz203a(pl"r"(fx,fy),1rl,mod(pl(x,y)),t,satz264a(pl(x,y),n))),[t:is"r"(pl"r"(fx,fy),1rl)]moreisi2(prl,prr,ists1"r"(pl"r"(fx,fy),1rl,mod(pl(x,y)),t))):moreis(prl,prr)
+t8:=tris(real,prl,pl"r"(ts"r"(fx,mod(pl(x,y))),ts"r"(fy,mod(pl(x,y)))),pl"r"(mod(x),mod(y)),disttp1"r"(fx,fy,mod(pl(x,y))),ispl12"r"(ts"r"(fx,mod(pl(x,y))),mod(x),ts"r"(fy,mod(pl(x,y))),mod(y),satz204e(mod(x),mod(pl(x,y)),t3),satz204e(mod(y),mod(pl(x,y)),t3))):is"r"(prl,pl"r"(mod(x),mod(y)))
+t9:=satz195b(mod(pl(x,y))):is"r"(prr,mod(pl(x,y)))
+t10:=ismoreis12(prl,pl"r"(mod(x),mod(y)),prr,mod(pl(x,y)),t8,t9,t7):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
+y@t11:=th1"l.imp"(is(pl(x,y),0c),moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y))),[t:is(pl(x,y),0c)]t2(t),[t:nis(pl(x,y),0c)]t10(t)):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
+-7271
+y@satz271:=satz168a(pl"r"(mod(x),mod(y)),mod(pl(x,y)),t11".7271"):lessis(mod(pl(x,y)),pl"r"(mod(x),mod(y)))
+satz271a:=t11".7271":moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
++7272
+x@t1:=tris(real,re(m0(x)),re(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(re(x)),iscere(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),reis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(re(m0(x)),m0"r"(re(x)))
+t2:=tris(real,ts"r"(re(m0(x)),re(m0(x))),ts"r"(m0"r"(re(x)),m0"r"(re(x))),ts"r"(re(x),re(x)),ists12"r"(re(m0(x)),m0"r"(re(x)),re(m0(x)),m0"r"(re(x)),t1,t1),satz198(re(x),re(x))):is"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)))
+t3:=tris(real,im(m0(x)),im(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(im(x)),isceim(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),imis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(im(m0(x)),m0"r"(im(x)))
+t4:=tris(real,ts"r"(im(m0(x)),im(m0(x))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),ists12"r"(im(m0(x)),m0"r"(im(x)),im(m0(x)),m0"r"(im(x)),t3,t3),satz198(im(x),im(x))):is"r"(ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)))
+t5:=ispl12"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)),ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)),t2,t4):is"r"(mod2(m0(x)),mod2(x))
+-7272
+x@satz272:=issqrt(mod2(m0(x)),mod2(x),lemma5(m0(x)),lemma5(x),t5".7272"):is"r"(mod(m0(x)),mod(x))
+satz272a:=symis(real,mod(m0(x)),mod(x),satz272):is"r"(mod(x),mod(m0(x)))
++7273
+y@sum:=pl"r"(mod(y),mod(mn(x,y))):real
+t1:=islessis1(mod(pl(y,mn(x,y))),mod(x),sum,ismod(pl(y,mn(x,y)),x,satz212h(x,y)),satz271(y,mn(x,y))):lessis(mod(x),sum)
+t2:=th9"l.or"(less(mod(x),sum),is"r"(mod(x),sum),less(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),is"r"(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),t1,[t:less(mod(x),sum)]satz188f(mod(x),sum,m0"r"(mod(y)),t),[t:is"r"(mod(x),sum)]ismn1"r"(mod(x),sum,mod(y),t)):lessis(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y)))
+t3:=tris(real,mn"r"(sum,mod(y)),mn"r"(pl"r"(mod(mn(x,y)),mod(y)),mod(y)),mod(mn(x,y)),ismn1"r"(sum,pl"r"(mod(mn(x,y)),mod(y)),mod(y),compl"r"(mod(y),mod(mn(x,y)))),mnpl(mod(mn(x,y)),mod(y))):is"r"(mn"r"(sum,mod(y)),mod(mn(x,y)))
+t4:=satz168b(mn"r"(mod(x),mod(y)),mod(mn(x,y)),islessis2(mn"r"(sum,mod(y)),mod(mn(x,y)),mn"r"(mod(x),mod(y)),t3,t2)):moreis(mod(mn(x,y)),mn"r"(mod(x),mod(y)))
+t5:=ismoreis12(mod(mn(y,x)),mod(mn(x,y)),mn"r"(mod(y),mod(x)),m0"r"(mn"r"(mod(x),mod(y))),tris1(real,mod(mn(y,x)),mod(mn(x,y)),mod(m0(mn(x,y))),ismod(m0(mn(x,y)),mn(y,x),satz219(x,y)),satz272(mn(x,y))),satz181a(mod(y),mod(x)),t4(y,x)):moreis(mod(mn(x,y)),m0"r"(mn"r"(mod(x),mod(y))))
+@[r:real][s:real][m:moreis(r,s)][n:moreis(r,m0"r"(s))]
+r@t6:=th9"l.or"(neg(r),not(neg(r)),is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r),th6"l.or"(neg(r)),[t:neg(r)]absn(r,t),[t:not(neg(r))]absnn(r,t)):or(is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r))
+n@t7:=orapp(is"r"(abs(s),m0"r"(s)),is"r"(abs(s),s),moreis(r,abs(s)),t6(s),[t:is"r"(abs(s),m0"r"(s))]ismoreis2(m0"r"(s),abs(s),r,symis(real,abs(s),m0"r"(s),t),n),[t:is"r"(abs(s),s)]ismoreis2(s,abs(s),r,symis(real,abs(s),s,t),m)):moreis(r,abs(s))
+-7273
+y@satz273:=t7".7273"(mod(mn(x,y)),mn"r"(mod(x),mod(y)),t4".7273",t5".7273"):moreis(mod(mn(x,y)),abs(mn"r"(mod(x),mod(y))))
+-c
+-r
+-rp
+-rt
+@[x:nat][y:nat]
++8274
+prop1:=some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)):'prop'
+x@prop2:=all([y:nat]imp(less(x,y),not(prop1(y)))):'prop'
+@[y:nat][l:less(1,y)][f:[t:1to(1)]1to(y)]
+1y:=1out(y):1to(y)
+yy:=xout(y):1to(y)
+[i:is"e"(1to(y),1y,yy)]
+t1:=isoutne(y,1,satz24a(y),y,lessisi3(y),i):is(1,y)
+f@t2:=ec3e31(is(1,y),more(1,y),less(1,y),satz10b(1,y),l):nis(1,y)
+t3:=th3"l.imp"(is"e"(1to(y),1y,yy),is(1,y),t2,[t:is"e"(1to(y),1y,yy)]t1(t)):not(is"e"(1to(y),1y,yy))
+[u:1to(1)]
+t4:=isf(1to(1),1to(y),f,u,1o,th1"n.singlet"(u)):is"e"(1to(y),<u>f,<1o>f)
+f@[i:is"e"(1to(y),<1o>f,1y)][u:1to(1)]
+t5:=th2"e.notis"(1to(y),1y,yy,<u>f,t3,tris(1to(y),<u>f,<1o>f,1y,t4(u),i)):not(is"e"(1to(y),<u>f,yy))
+i@t6:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),yy,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,yy,t5(u))):not(image(1to(1),1to(y),f,yy))
+t7:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),yy,t6):not(surjective(1to(1),1to(y),f))
+f@[n:not(is"e"(1to(y),<1o>f,1y))][u:1to(1)]
+t8:=th2"e.notis"(1to(y),<1o>f,1y,<u>f,n,t4(u)):not(is"e"(1to(y),<u>f,1y))
+n@t9:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),1y,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,1y,t8(u))):not(image(1to(1),1to(y),f,1y))
+t10:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),1y,t9):not(surjective(1to(1),1to(y),f))
+f@t11:=th1"l.imp"(is"e"(1to(y),<1o>f,1y),not(surjective(1to(1),1to(y),f)),[t:is"e"(1to(y),<1o>f,1y)]t7(t),[t:not(is"e"(1to(y),<1o>f,1y))]t10(t)):not(surjective(1to(1),1to(y),f))
+t12:=th2"l.and"(injective(1to(1),1to(y),f),surjective(1to(1),1to(y),f),t11):not(bijective(1to(1),1to(y),f))
+l@t13:=th5"l.some"([t:1to(1)]1to(y),[f:[t:1to(1)]1to(y)]bijective(1to(1),1to(y),f),[f:[t:1to(1)]1to(y)]t12(f)):not(prop1(1,y))
+@t14:=[y:nat][t:less(1,y)]t13(y,t):prop2(1)
+x@[p:prop2(x)][y:nat][l:less(<x>suc,y)]
+x@xs:=<x>suc:nat
+l@xxs:=xout(xs):1to(<x>suc)
+yy1:=xout(y):1to(y)
+t15:=trless(1,<x>suc,y,satz24c(x),l):less(1,y)
+ym1:=mn(y,1,t15):nat
+t16:=isless12(<x>suc,pl(x,1),y,pl(ym1,1),satz4e(x),th1c"n.mn"(y,1,t15),l):less(pl(x,1),pl(ym1,1))
+t17:=satz20c(x,ym1,1,t16):less(x,ym1)
+t18:=isless2(pl(ym1,1),y,ym1,th1d"n.mn"(y,1,t15),satz18a(ym1,1)):less(ym1,y)
+[f:[t:1to(xs)]1to(y)][b:bijective(1to(xs),1to(y),f)]
+t19:=ande1(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):injective(1to(xs),1to(y),f)
+t20:=ande2(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):surjective(1to(xs),1to(y),f)
+[i:is"e"(1to(y),<xxs>f,yy1)][u:1to(x)]
+u1:=inn(x,u):nat
+t21:=satz16a(u1,x,xs,1top(x,u),satz18c(x)):less(u1,xs)
+t22:=ec3e31(is(u1,xs),more(u1,xs),less(u1,xs),satz10b(u1,xs),t21):nis(u1,xs)
+t23:=lessisi1(u1,xs,t21):lessis(u1,xs)
+u2:=outn(xs,u1,t23):1to(xs)
+t24:=th3"l.imp"(is"e"(1to(xs),u2,xxs),is(u1,xs),t22,[t:is"e"(1to(xs),u2,xxs)]isoutne(xs,u1,t23,xs,lessisi3(xs),t)):not(is"e"(1to(xs),u2,xxs))
+[j:is"e"(1to(y),<u2>f,yy1)]
+t25:=tris2(1to(y),<u2>f,<xxs>f,yy1,j,i):is"e"(1to(y),<u2>f,<xxs>f)
+t26:=isfe(1to(xs),1to(y),f,t19,u2,xxs,t25):is"e"(1to(xs),u2,xxs)
+u@t27:=th3"l.imp"(is"e"(1to(y),<u2>f,yy1),is"e"(1to(xs),u2,xxs),t24,[t:is"e"(1to(y),<u2>f,yy1)]t26(t)):not(is"e"(1to(y),<u2>f,yy1))
+w1:=inn(y,<u2>f):nat
+[j:is(w1,y)]
+t28:=tris(1to(y),<u2>f,outn(y,w1,1top(y,<u2>f)),yy1,isoutinn(y,<u2>f),isoutni(y,w1,1top(y,<u2>f),y,lessisi3(y),j)):is"e"(1to(y),<u2>f,yy1)
+u@t29:=th3"l.imp"(is(w1,y),is"e"(1to(y),<u2>f,yy1),t27,[t:is(w1,y)]t28(t)):nis(w1,y)
+t30:=ore1(less(w1,y),is(w1,y),1top(y,<u2>f),t29):less(w1,y)
+t31:=islessis2(y,pl(ym1,1),pl(w1,1),th1c"n.mn"(y,1,t15),satz25b(y,w1,t30)):lessis(pl(w1,1),pl(ym1,1))
+t32:=th9"l.or"(less(pl(w1,1),pl(ym1,1)),is(pl(w1,1),pl(ym1,1)),less(w1,ym1),is(w1,ym1),t31,[t:less(pl(w1,1),pl(ym1,1))]satz20c(w1,ym1,1,t),[t:is(pl(w1,1),pl(ym1,1))]satz20b(w1,ym1,1,t)):lessis(w1,ym1)
+w2:=outn(ym1,w1,t32):1to(ym1)
+i@f1:=[t:1to(x)]w2(t):[t:1to(x)]1to(ym1)
+u@[v:1to(x)][j:is"e"(1to(ym1),<u>f1,<v>f1)]
+t33:=isoutne(ym1,w1(u),t32(u),w1(v),t32(v),j):is(w1(u),w1(v))
+t34:=isinne(y,<u2(u)>f,<u2(v)>f,t33):is"e"(1to(y),<u2(u)>f,<u2(v)>f)
+t35:=<t34><u2(v)><u2(u)>t19:is"e"(1to(xs),u2(u),u2(v))
+t36:=isoutne(xs,u1(u),t23(u),u1(v),t23(v),t35):is(u1(u),u1(v))
+t37:=isinne(x,u,v,t36):is"e"(1to(x),u,v)
+i@[v:1to(ym1)]
+v1:=inn(ym1,v):nat
+t38:=satz16a(v1,ym1,y,1top(ym1,v),t18):less(v1,y)
+t39:=ec3e31(is(v1,y),more(v1,y),less(v1,y),satz10b(v1,y),t38):nis(v1,y)
+t40:=lessisi1(v1,y,t38):lessis(v1,y)
+v2:=outn(y,v1,t40):1to(y)
+w3:=<v2>invf(1to(xs),1to(y),f,b):1to(xs)
+t41:=thinvf2(1to(xs),1to(y),f,b,v2):is"e"(1to(y),v2,<w3>f)
+[j:is"e"(1to(xs),w3,xxs)]
+t42:=isf(1to(xs),1to(y),f,w3,xxs,j):is"e"(1to(y),<w3>f,<xxs>f)
+t43:=tr3is(1to(y),v2,<w3>f,<xxs>f,yy1,t41,t42,i):is"e"(1to(y),v2,yy1)
+t44:=isoutne(y,v1,t40,y,lessisi3(y),t43):is(v1,y)
+v@t45:=th3"l.imp"(is"e"(1to(xs),w3,xxs),is(v1,y),t39,[t:is"e"(1to(xs),w3,xxs)]t44(t)):not(is"e"(1to(xs),w3,xxs))
+w4:=inn(xs,w3):nat
+[j:is(w4,xs)]
+t46:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),xxs,isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),xs,lessisi3(xs),j)):is"e"(1to(xs),w3,xxs)
+v@t47:=th3"l.imp"(is(w4,xs),is"e"(1to(xs),w3,xxs),t45,[t:is(w4,xs)]t46(t)):nis(w4,xs)
+t48:=ore1(less(w4,xs),is(w4,xs),1top(xs,w3),t47):less(w4,xs)
+t49:=satz26a(x,w4,t48):lessis(w4,x)
+w5:=outn(x,w4,t49):1to(x)
+t50:=isinoutn(x,w4,t49):is(w4,u1(w5))
+t51:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),u2(w5),isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),u1(w5),t23(w5),t50)):is"e"(1to(xs),w3,u2(w5))
+t52:=isf(1to(xs),1to(y),f,w3,u2(w5),t51):is"e"(1to(y),<w3>f,<u2(w5)>f)
+t53:=tris(1to(y),v2,<w3>f,<u2(w5)>f,t41,t52):is"e"(1to(y),v2,<u2(w5)>f)
+t54:=tris(nat,v1,inn(y,v2),w1(w5),isinoutn(y,v1,t40),isinni(y,v2,<u2(w5)>f,t53)):is(v1,w1(w5))
+t55:=tris(1to(ym1),v,outn(ym1,v1,1top(ym1,v)),w2(w5),isoutinn(ym1,v),isoutni(ym1,v1,1top(ym1,v),w1(w5),t32(w5),t54)):is"e"(1to(ym1),v,<w5>f1)
+t56:=somei(1to(x),[t:1to(x)]is"e"(1to(ym1),v,<t>f1),w5,t55):image(1to(x),1to(ym1),f1,v)
+i@t57:=andi(injective(1to(x),1to(ym1),f1),surjective(1to(x),1to(ym1),f1),[u:1to(x)][v:1to(x)][t:is"e"(1to(ym1),<u>f1,<v>f1)]t37(u,v,t),[u:1to(ym1)]t56(u)):bijective(1to(x),1to(ym1),f1)
+t58:=somei([t:1to(x)]1to(ym1),[g:[t:1to(x)]1to(ym1)]bijective(1to(x),1to(ym1),g),f1,t57):prop1(ym1)
+t59:=<t58><t17><ym1>p:con
+b@[n:not(is"e"(1to(y),<xxs>f,yy1))]
+m0:=<yy1>invf(1to(xs),1to(y),f,b):1to(xs)
+t60:=thinvf2(1to(xs),1to(y),f,b,yy1):is"e"(1to(y),yy1,<m0>f)
+f2:=changef(1to(xs),1to(y),f,m0,xxs):[t:1to(xs)]1to(y)
+t61:=changef2(1to(xs),1to(y),f,m0,xxs,xxs,refis(1to(xs),xxs)):is"e"(1to(y),<xxs>f2,<m0>f)
+t62:=tris2(1to(y),<xxs>f2,yy1,<m0>f,t61,t60):is"e"(1to(y),<xxs>f2,yy1)
+t63:=th6"e.wissel"(1to(xs),1to(y),f,m0,xxs,b):bijective(1to(xs),1to(y),f2)
+t64:=t59(f2,t63,t62):con
+b@t65:=th1"l.imp"(is"e"(1to(y),<xxs>f,yy1),con,[t:is"e"(1to(y),<xxs>f,yy1)]t59(t),[t:not(is"e"(1to(y),<xxs>f,yy1))]t64(t)):con
+l@t65a:=th5"l.some"([t:1to(xs)]1to(y),[f:[t:1to(xs)]1to(y)]bijective(1to(xs),1to(y),f),[f:[t:1to(xs)]1to(y)][t:bijective(1to(xs),1to(y),f)]t65(f,t)):not(prop1(xs,y))
+p@t66:=[y:nat][t:less(xs,y)]t65a(y,t):prop2(xs)
+x@t67:=induction([t:nat]prop2(t),t14,[t:nat][u:prop2(t)]t66(t,u),x):prop2(x)
+-8274
+[l:less(x,y)]
+satz274:=<l><y>t67".8274":not(some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)))
+[f:[t:1to(x)]1to(y)]
+satz274a:=th4"l.some"([t:1to(x)]1to(y),[g:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),g),satz274,f):not(bijective(1to(x),1to(y),f))
++*rt
++*rp
++*r
++*c
+@[x:nat][u:1to(x)]
+inn:=inn"n"(x,u):nat
+@[q:[t:cx][u:cx]cx][x:nat][f:[t:1to(x)]cx]
+x@[n:1to(x)][o:not(is"e"(1to(x),n,xout(x)))]
++8275
+t1:=th3"l.imp"(is"n"(inn(x,n),x),is"e"(1to(x),n,xout(x)),o,[t:is"n"(inn(x,n),x)]tris(1to(x),n,outn(x,inn(x,n),1top(x,n)),xout(x),isoutinn(x,n),isoutni(x,inn(x,n),1top(x,n),x,lessisi3(x),t))):not(is"n"(inn(x,n),x))
+t2:=ore1(less"n"(inn(x,n),x),is"n"(inn(x,n),x),1top(x,n),t1):less"n"(inn(x,n),x)
+-8275
+lemma275:=satz25c(x,inn(x,n),t2".8275"):lessis"n"(<inn(x,n)>suc,x)
+f@[g:[t:1to(x)]cx]
+recprop:=and(is(<1out(x)>g,<1out(x)>f),[t:1to(x)][u:not(is"e"(1to(x),t,xout(x)))]is(<outn(x,<inn(x,t)>suc,lemma275(t,u))>g,<<outn(x,<inn(x,t)>suc,lemma275(t,u))>f><<t>g>q)):'prop'
++*8275
+x@1o:=1out(x):1to(x)
+xo:=xout(x):1to(x)
+[u:nat][l:lessis"n"(<u>suc,x)]
+t11:=satz16b(u,<u>suc,x,satz18c(u),l):less"n"(u,x)
+t12:=lessisi1"n"(u,x,t11):lessis"n"(u,x)
+ux:=outn(x,u,t12):1to(x)
+t13:=ec3e31(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11):nis"n"(u,x)
+t14:=th3"l.imp"(is"e"(1to(x),ux,xo),is"n"(u,x),t13,[t:is"e"(1to(x),ux,xo)]isoutne(x,u,t12,x,lessisi3(x),t)):not(is"e"(1to(x),ux,xo))
+t15:=isf(nat,nat,suc,u,inn(x,ux),isinoutn(x,u,t12)):is"n"(<u>suc,<inn(x,ux)>suc)
+t16:=isoutni(x,<u>suc,l,<inn(x,ux)>suc,lemma275(ux,t14),t15):is"e"(1to(x),outn(x,<u>suc,l),outn(x,<inn(x,ux)>suc,lemma275(ux,t14)))
+x@[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
+ns:=outn(x,<inn(x,n)>suc,lemma275(n,o)):1to(x)
+f@[g:[t:1to(x)]cx]
+prop1:=is(<1o>g,<1o>f):'prop'
+prop2:=[t:1to(x)][u:not(is"e"(1to(x),t,xo))]is(<ns(t,u)>g,<<ns(t,u)>f><<t>g>q):'prop'
+[pg:recprop(g)]
+t3:=ande1(prop1,prop2,pg):prop1
+[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
+t4:=<o><n>ande2(prop1,prop2,pg):is(<ns(n,o)>g,<<ns(n,o)>f><<n>g>q)
+pg@[u:nat][l:lessis"n"(<u>suc,x)]
+t17:=isf(1to(x),cx,g,outn(x,<u>suc,l),ns(ux(u,l),t14(u,l)),t16(u,l)):is(<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g)
+t18:=tris(cx,<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,t17,t4(pg,ux(u,l),t14(u,l))):is(<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q)
+g@[h:[t:1to(x)]cx][u:nat][l:lessis"n"(u,x)]
+prop3:=is(<outn(x,u,l)>g,<outn(x,u,l)>h):'prop'
+u@prop4:=and(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(t)):'prop'
+prop5:=or(prop4,more"n"(u,x)):'prop'
+h@[pg:recprop(g)][ph:recprop(h)][l:lessis"n"(1,x)]
+t5:=isoutni(x,1,l,1,satz24a(x),refis(nat,1)):is"e"(1to(x),outn(x,1,l),1o)
+t6:=isf(1to(x),cx,g,outn(x,1,l),1o,t5):is(<outn(x,1,l)>g,<1o>g)
+t7:=tris(cx,<outn(x,1,l)>g,<1o>g,<1o>f,t6,t3(pg)):is(<outn(x,1,l)>g,<1o>f)
+t8:=tris2(cx,<outn(x,1,l)>g,<outn(x,1,l)>h,<1o>f,t7,t7(h,g,ph,pg,l)):prop3(1,l)
+ph@t9:=andi(lessis"n"(1,x),[t:lessis"n"(1,x)]prop3(1,t),satz24a(x),[t:lessis"n"(1,x)]t8(t)):prop4(1)
+t10:=ori1(prop4(1),more"n"(1,x),t9):prop5(1)
+[u:nat][p:prop5(u)][l:lessis"n"(<u>suc,x)]
+t19:=ec3e32(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11(u,l)):not(more"n"(u,x))
+t20:=ore1(prop4(u),more"n"(u,x),p,t19):prop4(u)
+t21:=<t12(u,l)>ande2(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(u,t),t20):prop3(u,t12(u,l))
+t22:=isf(cx,cx,[t:cx]<<ns(ux(u,l),t14(u,l))>f><t>q,<ux(u,l)>g,<ux(u,l)>h,t21):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q)
+t23:=symis(cx,<outn(x,<u>suc,l)>h,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,t18(h,ph,u,l)):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h)
+t24:=tr3is(cx,<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h,t18(g,pg,u,l),t22,t23):prop3(<u>suc,l)
+t25:=andi(lessis"n"(<u>suc,x),[t:lessis"n"(<u>suc,x)]prop3(<u>suc,t),l,[t:lessis"n"(<u>suc,x)]t24(t)):prop4(<u>suc)
+t26:=ori1(prop4(<u>suc),more"n"(<u>suc,x),t25):prop5(<u>suc)
+p@[n:not(lessis"n"(<u>suc,x))]
+t27:=satz10k(<u>suc,x,n):more"n"(<u>suc,x)
+t28:=ori2(prop4(<u>suc),more"n"(<u>suc,x),t27):prop5(<u>suc)
+p@t29:=th1"l.imp"(lessis"n"(<u>suc,x),prop5(<u>suc),[t:lessis"n"(<u>suc,x)]t26(t),[t:not(lessis"n"(<u>suc,x))]t28(t)):prop5(<u>suc)
+u@t30:=induction([v:nat]prop5(v),t10,[v:nat][t:prop5(v)]t29(v,t),u):prop5(u)
+ph@[n:1to(x)]
+t31:=isf(1to(x),cx,g,n,outn(x,inn(x,n),1top(x,n)),isoutinn(x,n)):is(<n>g,<outn(x,inn(x,n),1top(x,n))>g)
+t32:=satz10d(inn(x,n),x,1top(x,n)):not(more"n"(inn(x,n),x))
+t33:=ore1(prop4(inn(x,n)),more"n"(inn(x,n),x),t30(inn(x,n)),t32):prop4(inn(x,n))
+t34:=<1top(x,n)>ande2(lessis"n"(inn(x,n),x),[t:lessis"n"(inn(x,n),x)]prop3(inn(x,n),t),t33):prop3(inn(x,n),1top(x,n))
+t35:=symis(cx,<n>h,<outn(x,inn(x,n),1top(x,n))>h,t31(h,g,ph,pg,n)):is(<outn(x,inn(x,n),1top(x,n))>h,<n>h)
+t36:=tr3is(cx,<n>g,<outn(x,inn(x,n),1top(x,n))>g,<outn(x,inn(x,n),1top(x,n))>h,<n>h,t31,t34,t35):is(<n>g,<n>h)
+ph@t37:=fisi(1to(x),cx,g,h,[t:1to(x)]t36(t)):is"e"([t:1to(x)]cx,g,h)
+f@prop6:=some"l"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(g)):'prop'
+x@prop7:=all"l"([t:1to(x)]cx,[f:[t:1to(x)]cx]prop6(f)):'prop'
+q@[f:[t:1to(1)]cx]
+t38:=refis(cx,<1o(1)>f):prop1(1,f,f)
+[n:1to(1)][o:not(is"e"(1to(1),n,xo(1)))]
+t39:=<th1"n.singlet"(n)>o:con
+t40:=cone(is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q),t39):is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q)
+f@t41:=andi(prop1(1,f,f),prop2(1,f,f),t38,[t:1to(1)][u:not(is"e"(1to(1),t,xo(1)))]t40(t,u)):recprop(1,f,f)
+t42:=somei([t:1to(1)]cx,[g:[t:1to(1)]cx]recprop(1,f,g),f,t41):prop6(1,f)
+q@t43:=[f:[t:1to(1)]cx]t42(f):prop7(1)
+x@[p:prop7(x)]
+xs:=<x>suc:nat
+[f:[t:1to(xs)]cx]
+f1:=left(cx,xs,x,lessisi1"n"(x,xs,satz18c(x)),f):[t:1to(x)]cx
+t44:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f1,g)][v:recprop(x,f1,h)]t37(f1,g,h,u,v),<f1>p):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g))
+g1:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):[t:1to(x)]cx
+t45:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):recprop(x,f1,g1)
+[n:1to(xs)]
+nxs:=is"e"(1to(xs),n,xo(xs)):'prop'
+[o:not(nxs)]
+t46:=satz26a(x,inn(xs,n),t2(xs,n,o)):lessis"n"(inn(xs,n),x)
+n1:=outn(x,inn(xs,n),t46):1to(x)
+b:=<n1>g1:cx
+[o1:not(nxs)]
+t47:=isoutni(x,inn(xs,n),t46(o),inn(xs,n),t46(o1),refis(nat,inn(xs,n))):is"e"(1to(x),n1(o),n1(o1))
+t48:=isf(1to(x),cx,g1,n1(o),n1(o1),t47):is(b(o),b(o1))
+f@a:=<<xo(xs)>f><<xo(x)>g1>q:cx
+n@c:=ite"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u)):cx
+[i:nxs]
+t49:=itet"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),i):is(c,a)
+o@t50:=itef"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),o):is(c,b)
+f@g2:=[t:1to(xs)]c(t):[t:1to(xs)]cx
+t51:=th3"l.imp"(is"e"(1to(xs),1o(xs),xo(xs)),is"n"(1,xs),symnotis(nat,xs,1,<x>ax3),[t:is"e"(1to(xs),1o(xs),xo(xs))]isoutne(xs,1,satz24a(xs),xs,lessisi3(xs),t)):not(is"e"(1to(xs),1o(xs),xo(xs)))
+t52:=t50(1o(xs),t51):is(c(1o(xs)),b(1o(xs),t51))
+t53:=isinoutn(xs,1,satz24a(xs)):is"n"(1,inn(xs,1o(xs)))
+t54:=isoutni(x,1,satz24a(x),inn(xs,1o(xs)),t46(1o(xs),t51),t53):is"e"(1to(x),1o(x),n1(1o(xs),t51))
+t55:=isf(1to(x),cx,g1,1o(x),n1(1o(xs),t51),t54):is(<1o(x)>g1,b(1o(xs),t51))
+t56:=tris2(cx,c(1o(xs)),<1o(x)>g1,b(1o(xs),t51),t52,t55):is(c(1o(xs)),<1o(x)>g1)
+t57:=tris(cx,c(1o(xs)),<1o(x)>g1,<1o(x)>f1,t56,t3(x,f1,g1,t45)):is(c(1o(xs)),<1o(x)>f1)
+t58:=isinoutn(x,1,satz24a(x)):is"n"(1,inn(x,1o(x)))
+t59:=isoutni(xs,1,satz24a(xs),inn(x,1o(x)),trlessis"n"(inn(x,1o(x)),x,xs,1top(x,1o(x)),lessisi1"n"(x,xs,satz18c(x))),t58):is"e"(1to(xs),1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)))
+t60:=isf(1to(xs),cx,f,1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)),t59):is(<1o(xs)>f,<1o(x)>f1)
+t61:=tris2(cx,c(1o(xs)),<1o(xs)>f,<1o(x)>f1,t57,t60):prop1(xs,f,g2)
+o@[i:is"e"(1to(xs),ns(xs,n,o),xo(xs))]
+t62:=isoutne(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),i):is"n"(<inn(xs,n)>suc,xs)
+t63:=<t62><x><inn(xs,n)>ax4:is"n"(inn(xs,n),x)
+t64:=isoutni(x,inn(xs,n),t46,x,lessisi3(x),t63):is"e"(1to(x),n1,xo(x))
+t65:=isf(1to(x),cx,g1,xo(x),n1,symis(1to(x),n1,xo(x),t64)):is(<xo(x)>g1,b)
+t66:=tris2(cx,<xo(x)>g1,c,b,t65,t50):is(<xo(x)>g1,c)
+t67:=isf(cx,cx,[t:cx]<<xo(xs)>f><t>q,<xo(x)>g1,c,t66):is(a,<<xo(xs)>f><c>q)
+t68:=isf(1to(xs),cx,f,xo(xs),ns(xs,n,o),symis(1to(xs),ns(xs,n,o),xo(xs),i)):is(<xo(xs)>f,<ns(xs,n,o)>f)
+t69:=isf(cx,cx,<c>q,<xo(xs)>f,<ns(xs,n,o)>f,t68):is(<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q)
+t70:=tr3is(cx,c(ns(xs,n,o)),a,<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q,t49(ns(xs,n,o),i),t67,t69):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
+o@[o1:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))][i:is"e"(1to(x),n1,xo(x))]
+t71:=isoutne(x,inn(xs,n),t46,x,lessisi3(x),i):is"n"(inn(xs,n),x)
+t72:=ax2(inn(xs,n),x,t71):is"n"(<inn(xs,n)>suc,xs)
+t73:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),t72):is"e"(1to(xs),ns(xs,n,o),xo(xs))
+o1@t74:=th3"l.imp"(is"e"(1to(x),n1,xo(x)),is"e"(1to(xs),ns(xs,n,o),xo(xs)),o1,[t:is"e"(1to(x),n1,xo(x))]t73(t)):not(is"e"(1to(x),n1,xo(x)))
+t75:=isinoutn(x,inn(xs,n),t46):is"n"(inn(xs,n),inn(x,n1))
+t76:=ax2(inn(xs,n),inn(x,n1),t75):is"n"(<inn(xs,n)>suc,<inn(x,n1)>suc)
+t77:=isinoutn(xs,<inn(xs,n)>suc,lemma275(xs,n,o)):is"n"(<inn(xs,n)>suc,inn(xs,ns(xs,n,o)))
+t78:=tris1(nat,inn(xs,ns(xs,n,o)),<inn(x,n1)>suc,<inn(xs,n)>suc,t77,t76):is"n"(inn(xs,ns(xs,n,o)),<inn(x,n1)>suc)
+t79:=isoutni(x,inn(xs,ns(xs,n,o)),t46(ns(xs,n,o),o1),<inn(x,n1)>suc,lemma275(x,n1,t74),t78):is"e"(1to(x),n1(ns(xs,n,o),o1),ns(n1,t74))
+t80:=isf(1to(x),cx,g1,n1(ns(xs,n,o),o1),ns(n1,t74),t79):is(b(ns(xs,n,o),o1),<ns(n1,t74)>g1)
+t81:=isinoutn(x,<inn(x,n1)>suc,lemma275(x,n1,t74)):is"n"(<inn(x,n1)>suc,inn(x,ns(n1,t74)))
+t82:=tris(nat,<inn(xs,n)>suc,<inn(x,n1)>suc,inn(x,ns(n1,t74)),t76,t81):is"n"(<inn(xs,n)>suc,inn(x,ns(n1,t74)))
+t83:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),inn(x,ns(n1,t74)),trlessis"n"(inn(x,ns(n1,t74)),x,xs,1top(x,ns(n1,t74)),lessisi1"n"(x,xs,satz18c(x))),t82):is"e"(1to(xs),ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)))
+t84:=isf(1to(xs),cx,f,ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)),t83):is(<ns(xs,n,o)>f,<ns(n1,t74)>f1)
+t85:=isf(cx,cx,<b>q,<ns(xs,n,o)>f,<ns(n1,t74)>f1,t84):is(<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q)
+t86:=isf(cx,cx,[t:cx]<<ns(xs,n,o)>f><t>q,c,b,t50):is(<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q)
+t87:=tr3is(cx,c(ns(xs,n,o)),b(ns(xs,n,o),o1),<ns(n1,t74)>g1,<<ns(n1,t74)>f1><b>q,t50(ns(xs,n,o),o1),t80,t4(f1,g1,t45,n1,t74)):is(c(ns(xs,n,o)),<<ns(n1,t74)>f1><b>q)
+t88:=tris(cx,<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q,t86,t85):is(<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q)
+t89:=tris2(cx,c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q,t87,t88):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
+o@t90:=th1"l.imp"(is"e"(1to(xs),ns(xs,n,o),xo(xs)),is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q),[t:is"e"(1to(xs),ns(xs,n,o),xo(xs))]t70(t),[t:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))]t89(t)):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
+f@t91:=[t:1to(xs)][u:not(nxs(t))]t90(t,u):prop2(xs,f,g2)
+t92:=andi(prop1(xs,f,g2),prop2(xs,f,g2),t61,t91):recprop(xs,f,g2)
+t93:=somei([t:1to(xs)]cx,[g:[t:1to(xs)]cx]recprop(xs,f,g),g2,t92):prop6(xs,f)
+p@t94:=[f:[t:1to(xs)]cx]t93(f):prop7(xs)
+x@t95:=induction([y:nat]prop7(y),t43,[y:nat][t:prop7(y)]t94(y,t),x):prop7(x)
+[f:[t:1to(x)]cx]
+t96:=<f>t95:prop6(x,f)
+t97:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f,g)][v:recprop(x,f,h)]t37(f,g,h,u,v),t96):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
+-8275
+f@satz275:=t97".8275"(f):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
+recf:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):[t:1to(x)]cx
+satz275a:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):recprop(x,f,recf)
+[n:1to(x)]
+rec:=<n>recf:cx
+f@satz275b:=t3".8275"(x,f,recf,satz275a):is(rec(1out(x)),<1out(x)>f)
+n@[o:not(is"e"(1to(x),n,xout(x)))]
+sucx:=ns".8275"(n,o):1to(x)
+satz275c:=t4".8275"(x,f,recf,satz275a,n,o):is(rec(sucx(n,o)),<<sucx(n,o)>f><rec(n)>q)
+f@[g:[t:1to(x)]cx][r:recprop(x,f,g)]
+satz275d:=t37".8275"(x,f,g,recf,r,satz275a):is"e"([t:1to(x)]cx,g,recf)
+[n:1to(x)]
+satz275e:=fise(1to(x),cx,g,recf,satz275d,n):is(<n>g,rec(n))
+x@[y:nat]
++*8275
+y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
+fl:=left(cx,x,y,l,f):[t:1to(y)]cx
+rf:=recf(x,f):[t:1to(x)]cx
+rfl:=left(cx,x,y,l,rf):[t:1to(y)]cx
+t98:=isinoutn(y,1,satz24a(y)):is"n"(1,inn(y,1out(y)))
+t99:=isoutni(x,1,satz24a(x),inn(y,1out(y)),trlessis"n"(inn(y,1out(y)),y,x,1top(y,1out(y)),l),t98):is"e"(1to(x),1out(x),left1to(x,y,l,1out(y)))
+t100:=isp(1to(x),[t:1to(x)]is(<t>rf,<t>f),1out(x),left1to(x,y,l,1out(y)),t3(x,f,rf,satz275a(x,f)),t99):prop1(y,fl,rfl)
+[n:1to(y)][o:not(is"e"(1to(y),n,xout(y)))]
+t100a:=th3"l.imp"(is"n"(inn(y,n),y),is"e"(1to(y),n,xout(y)),o,[t:is"n"(inn(y,n),y)]tris(1to(y),n,outn(y,inn(y,n),1top(y,n)),xout(y),isoutinn(y,n),isoutni(y,inn(y,n),1top(y,n),y,lessisi3(y),t))):not(is"n"(inn(y,n),y))
+t100b:=ore1(less"n"(inn(y,n),y),is"n"(inn(y,n),y),1top(y,n),t100a):less"n"(inn(y,n),y)
+t101:=satz16b(inn(y,n),y,x,t100b,l):less"n"(inn(y,n),x)
+t102:=ec3e31(is"n"(inn(y,n),x),more"n"(inn(y,n),x),less"n"(inn(y,n),x),satz10b(inn(y,n),x),t101):nis"n"(inn(y,n),x)
+t103:=th3"l.imp"(is"e"(1to(x),left1to(x,y,l,n),xout(x)),is"n"(inn(y,n),x),t102,[t:is"e"(1to(x),left1to(x,y,l,n),xout(x))]isoutne(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l),x,lessisi3(x),t)):not(is"e"(1to(x),left1to(x,y,l,n),xout(x)))
+t104:=t4(x,f,rf,satz275a(x,f),left1to(x,y,l,n),t103):is(<ns(x,left1to(x,y,l,n),t103)>rf,<<ns(x,left1to(x,y,l,n),t103)>f><<n>rfl>q)
+t105:=isinoutn(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l)):is"n"(inn(y,n),inn(x,left1to(x,y,l,n)))
+t106:=ax2(inn(y,n),inn(x,left1to(x,y,l,n)),t105):is"n"(<inn(y,n)>suc,<inn(x,left1to(x,y,l,n))>suc)
+t107:=isinoutn(y,<inn(y,n)>suc,lemma275(y,n,o)):is"n"(<inn(y,n)>suc,inn(y,ns(y,n,o)))
+t108:=tris1(nat,<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)),<inn(y,n)>suc,t106,t107):is"n"(<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)))
+t109:=isoutni(x,<inn(x,left1to(x,y,l,n))>suc,lemma275(x,left1to(x,y,l,n),t103),inn(y,ns(y,n,o)),trlessis"n"(inn(y,ns(y,n,o)),y,x,1top(y,ns(y,n,o)),l),t108):is"e"(1to(x),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)))
+t110:=isp(1to(x),[t:1to(x)]is(<t>rf,<<t>f><<n>rfl>q),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)),t104,t109):is(<ns(y,n,o)>rfl,<<ns(y,n,o)>fl><<n>rfl>q)
+f@t111:=[t:1to(y)][u:not(is"e"(1to(y),t,xout(y)))]t110(t,u):prop2(y,fl,rfl)
+t112:=andi(prop1(y,fl,rfl),prop2(y,fl,rfl),t100,t111):recprop(y,fl,rfl)
+-8275
+y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
+satz275f:=satz275d(y,fl".8275"(l,f),rfl".8275"(l,f),t112".8275"(l,f)):is"e"([t:1to(y)]cx,left(cx,x,y,l,recf(x,f)),recf(y,left(cx,x,y,l,f)))
+x@[f:[t:1to(pl"n"(x,1))]cx]
++8276
+xs:=<x>suc:nat
+x1:=pl"n"(x,1):nat
+t1:=lessisi1"n"(x,x1,satz18a(x,1)):lessis"n"(x,x1)
+t2:=lessisi1"n"(x,xs,satz18c(x)):lessis"n"(x,xs)
+t3:=lessisi2"n"(xs,x1,satz4e(x)):lessis"n"(xs,x1)
+fx:=left(cx,x1,x,t1,f):[t:1to(x)]cx
+f1:=left(cx,x1,xs,t3,f):[t:1to(xs)]cx
+f1x:=f1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
+g1:=g2"c.8275"(x,t95"c.8275"(x),f1):[t:1to(xs)]cx
+g1x:=g1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
+g:=left(cx,x1,xs,t3,recf(x1,f)):[t:1to(xs)]cx
+t4:=t49"c.8275"(x,t95"c.8275"(x),f1,xout(xs),refis(1to(xs),xout(xs))):is(<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q)
+t5:=satz275d(xs,f1,g1,t92"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(xs)]cx,g1,recf(xs,f1))
+t6:=satz275f(x1,xs,t3,f):is"e"([t:1to(xs)]cx,g,recf(xs,f1))
+t7:=tris2([t:1to(xs)]cx,g,g1,recf(xs,f1),t6,t5):is"e"([t:1to(xs)]cx,g,g1)
+t8:=fise(1to(xs),cx,g,g1,t7,xout(xs)):is(<xout(xs)>g,<xout(xs)>g1)
+t9:=tris(cx,<xout(xs)>g,<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q,t8,t4):is(<xout(xs)>g,<<xout(xs)>f1><<xout(x)>g1x>q)
+[n:1to(x)]
+t10:=isinoutn(xs,inn(x,n),trlessis"n"(inn(x,n),x,xs,1top(x,n),t2)):is"n"(inn(x,n),inn(xs,left1to(xs,x,t2,n)))
+t11:=isoutni(x1,inn(x,n),trlessis"n"(inn(x,n),x,x1,1top(x,n),t1),inn(xs,left1to(xs,x,t2,n)),trlessis"n"(inn(xs,left1to(xs,x,t2,n)),xs,x1,1top(xs,left1to(xs,x,t2,n)),t3),t10):is"e"(1to(x1),left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)))
+t12:=isf(1to(x1),cx,f,left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)),t11):is(<n>fx,<n>f1x)
+f@t13:=fisi(1to(x),cx,fx,f1x,[t:1to(x)]t12(t)):is"e"([t:1to(x)]cx,fx,f1x)
+t14:=isf([t:1to(x)]cx,[t:1to(x)]cx,[u:[t:1to(x)]cx]recf(x,u),fx,f1x,t13):is"e"([t:1to(x)]cx,recf(x,fx),recf(x,f1x))
+t15:=satz275d(x,f1x,g1x,t45"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(x)]cx,g1x,recf(x,f1x))
+t16:=tris2([t:1to(x)]cx,g1x,recf(x,fx),recf(x,f1x),t15,t14):is"e"([t:1to(x)]cx,g1x,recf(x,fx))
+t17:=fise(1to(x),cx,g1x,recf(x,fx),t16,xout(x)):is(<xout(x)>g1x,<xout(x)>recf(x,fx))
+t18:=isinoutn(xs,xs,lessisi3(xs)):is"n"(xs,inn(xs,xout(xs)))
+t19:=tris(nat,x1,xs,inn(xs,xout(xs)),satz4a(x),t18):is"n"(x1,inn(xs,xout(xs)))
+t20:=isoutni(x1,x1,lessisi3(x1),inn(xs,xout(xs)),trlessis"n"(inn(xs,xout(xs)),xs,x1,1top(xs,xout(xs)),t3),t19):is"e"(1to(x1),xout(x1),left1to(x1,xs,t3,xout(xs)))
+t21:=isp1(1to(x1),[t:1to(x1)]is(<t>recf(x1,f),<<t>f><<xout(x)>g1x>q),left1to(x1,xs,t3,xout(xs)),xout(x1),t9,t20):is(<xout(x1)>recf(x1,f),<<xout(x1)>f><<xout(x)>g1x>q)
+t22:=isf(cx,cx,[t:cx]<<xout(x1)>f><t>q,<xout(x)>g1x,<xout(x)>recf(x,fx),t17):is(<<xout(x1)>f><<xout(x)>g1x>q,<<xout(x1)>f><<xout(x)>recf(x,fx)>q)
+-8276
+satz276:=tris(cx,<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>g1x".8276">q,<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,fx".8276")>q,t21".8276",t22".8276"):is(<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
+x@[f:[u:1to(x)]cx]
+smpr:=rec(x,f,xout(x)):cx
+@[x:nat][f:[u:1to(x)]cx]
+sum:=smpr([t:cx][u:cx]pl(t,u),x,f):cx
+prod:=smpr([t:cx][u:cx]ts(t,u),x,f):cx
+q@[f:[u:1to(1)]cx]
++8277
+t1:=isoutni(1,1,satz24a(1),1,lessisi3(1),refis(nat,1)):is"e"(1to(1),1out(1),xout(1))
+-8277
+satz277:=isp(1to(1),[t:1to(1)]is(rec(1,f,t),<t>f),1out(1),xout(1),satz275b(1,f),t1".8277"):is(smpr(1,f),<xout(1)>f)
+q@[x:nat][f:[u:1to(pl"n"(x,1))]cx]
+satz278:=satz276(x,f):is(smpr(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><smpr(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
+x@[f:[u:1to(x)]cx][y:nat][i:is"n"(y,x)]
++v8
+t1:=lessisi2"n"(y,x,i):lessis"n"(y,x)
+f0:=left(cx,x,y,t1,f):[t:1to(y)]cx
+t2:=fise(1to(y),cx,left(cx,x,y,t1,recf(x,f)),recf(y,f0),satz275f(x,y,t1,f),xout(y)):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(y,f0))
+t3:=tris1(nat,inn(y,xout(y)),x,y,isinoutn(y,y,lessisi3(y)),i):is"n"(inn(y,xout(y)),x)
+t4:=isoutni(x,inn(y,xout(y)),trlessis"n"(inn(y,xout(y)),y,x,1top(y,xout(y)),t1),x,lessisi3(x),t3):is"e"(1to(x),left1to(x,y,t1,xout(y)),xout(x))
+t5:=isf(1to(x),cx,recf(x,f),left1to(x,y,t1,xout(y)),xout(x),t4):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(x,f))
+-v8
+issmpr:=tris1(cx,smpr(y,f0".v8"),smpr(x,f),<left1to(x,y,t1".v8",xout(y))>recf(x,f),t2".v8",t5".v8"):is(smpr(y,left(cx,x,y,lessisi2"n"(y,x,i),f)),smpr(x,f))
+@[z:complex][x:nat]
++8279
+xr:=rlofnt(x):real
+prop1:=is(sum(x,[t:1to(x)]z),ts(z,pli(xr,0))):'prop'
+z@t1:=satz277([t:cx][u:cx]pl(t,u),[t:1to(1)]z):is(sum(1,[t:1to(1)]z),z)
+t2:=tris(cx,sum(1,[t:1to(1)]z),z,ts(z,1c),t1,satz222a(z)):prop1(1)
+x@[p:prop1(x)]
+t3:=satz278([t:cx][u:cx]pl(t,u),x,[t:1to(pl"n"(x,1))]z):is(sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z))
+t4:=ispl12(sum(x,[t:1to(x)]z),ts(z,pli(xr,0)),z,ts(z,1c),p,satz222a(z)):is(pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)))
+t5:=distpt2(z,pli(xr,0),1c):is(pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)))
+t6:=plis12a(xr,0,1rl,0):is(pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)))
+t7:=isrecx12(pl"r"(xr,1rl),rlofnt(pl"n"(x,1)),pl"r"(0,0),0,satzr155b(x,1),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0))
+t8:=tris(cx,pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0),t6,t7):is(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0))
+t9:=ists2(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0),z,t8):is(ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)))
+t10:=tr4is(cx,sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)),t3,t4,t5,t9):prop1(pl"n"(x,1))
+t11:=isp(nat,[t:nat]prop1(t),pl"n"(x,1),<x>suc,t10,satz4a(x)):prop1(<x>suc)
+-8279
+satz279:=induction([t:nat]prop1".8279"(t),t2".8279",[u:nat][t:prop1".8279"(u)]t11".8279"(u,t),x):is(sum(x,[t:1to(x)]z),ts(z,pli(rlofnt(x),0)))
+q@[f:[t:1to(2)]cx]
++8280
+t1:=lessisi1"n"(1,2,satz18a(1,1)):lessis"n"(1,2)
+f1:=left(cx,2,1,t1,f):[t:1to(1)]cx
+t2:=satz278(q,1,f):is(smpr(2,f),<<xout(2)>f><smpr(1,f1)>q)
+t3:=satz277(q,f1):is(smpr(1,f1),<xout(1)>f1)
+t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+t5:=isoutni(2,1,satz24a(2),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,2,1top(1,xout(1)),t1),t4):is"e"(1to(2),1out(2),left1to(2,1,t1,xout(1)))
+t6:=isf(1to(2),cx,f,1out(2),left1to(2,1,t1,xout(1)),t5):is(<1out(2)>f,<xout(1)>f1)
+t7:=tris2(cx,smpr(1,f1),<1out(2)>f,<xout(1)>f1,t3,t6):is(smpr(1,f1),<1out(2)>f)
+t8:=isf(cx,cx,[t:cx]<<xout(2)>f><t>q,smpr(1,f1),<1out(2)>f,t7):is(<<xout(2)>f><smpr(1,f1)>q,<<xout(2)>f><<1out(2)>f>q)
+-8280
+satz280:=tris(cx,smpr(2,f),<<xout(2)>f><smpr(1,f1".8280")>q,<<xout(2)>f><<1out(2)>f>q,t2".8280",t8".8280"):is(smpr(2,f),<<xout(2)>f><<1out(2)>f>q)
+q@assoc:=[x:cx][y:cx][z:cx]is(<z><<y><x>q>q,<<z><y>q><x>q):'prop'
+@assocp1:=[x:cx][y:cx][z:cx]asspl1(x,y,z):assoc([x:cx][y:cx]pl(x,y))
+assocts:=[x:cx][y:cx][z:cx]assts1(x,y,z):assoc([x:cx][y:cx]ts(x,y))
+q@[a:assoc][z:cx][u:cx][v:cx]
+assq1:=<v><u><z>a:is(<v><<u><z>q>q,<<v><u>q><z>q)
+assq2:=symis(cx,<v><<u><z>q>q,<<v><u>q><z>q,assq1):is(<<v><u>q><z>q,<v><<u><z>q>q)
+q@[a:assoc(q)][x:nat][y:nat][f:[t:1to(pl"n"(x,y))]cx]
++8281
+y@t1:=lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)):lessis"n"(x,pl"n"(x,y))
+f@f1:=left(cx,pl"n"(x,y),x,t1,f):[t:1to(x)]cx
+f2:=right(cx,x,y,f):[t:1to(y)]cx
+prop1:=is(smpr(pl"n"(x,y),f),<smpr(y,f2)><smpr(x,f1)>q):'prop'
+y@prop2:=all"l"([t:1to(pl"n"(x,y))]cx,[u:[t:1to(pl"n"(x,y))]cx]prop1(u)):'prop'
+x@[f0:[t:1to(pl"n"(x,1))]cx]
+t2:=satz278(q,x,f0):is(smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q)
+t3:=satz277(q,f2(1,f0)):is(smpr(1,f2(1,f0)),<xout(1)>f2(1,f0))
+t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+t5:=ispl2"n"(1,inn(1,xout(1)),x,t4):is"n"(pl"n"(x,1),pl"n"(x,inn(1,xout(1))))
+t6:=isoutni(pl"n"(x,1),pl"n"(x,1),lessisi3(pl"n"(x,1)),pl"n"(x,inn(1,xout(1))),satz19o(inn(1,xout(1)),1,x,1top(1,xout(1))),t5):is"e"(1to(pl"n"(x,1)),xout(pl"n"(x,1)),right1to(x,1,xout(1)))
+t7:=isf(1to(pl"n"(x,1)),cx,f0,xout(pl"n"(x,1)),right1to(x,1,xout(1)),t6):is(<xout(pl"n"(x,1))>f0,<xout(1)>f2(1,f0))
+t8:=tris2(cx,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),<xout(1)>f2(1,f0),t7,t3):is(<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)))
+t9:=isf(cx,cx,<smpr(x,f1(1,f0))>q,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),t8):is(<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q)
+t10:=tris(cx,smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q,t2,t9):prop1(1,f0)
+x@t11:=[u:[t:1to(pl"n"(x,1))]cx]t10(u):prop2(1)
+y@yp1:=pl"n"(y,1):nat
+xpy:=pl"n"(x,y):nat
+xpy1:=pl"n"(x,yp1):nat
+xyp1:=pl"n"(xpy,1):nat
+t12:=lessisi2"n"(xyp1,xpy1,asspl1"n"(x,y,1)):lessis"n"(xyp1,xpy1)
+[p:prop2(y)][f:[t:1to(xpy1)]cx]
+t13:=isinoutn(xyp1,xyp1,lessisi3(xyp1)):is"n"(xyp1,inn(xyp1,xout(xyp1)))
+t14:=tris(nat,xpy1,xyp1,inn(xyp1,xout(xyp1)),asspl2"n"(x,y,1),t13):is"n"(xpy1,inn(xyp1,xout(xyp1)))
+t15:=isoutni(xpy1,xpy1,lessisi3(xpy1),inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),t14):is"e"(1to(xpy1),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)))
+t16:=isf(1to(xpy1),cx,recf(xpy1,f),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),t15):is(smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)))
+fr:=left(cx,xpy1,xyp1,t12,f):[t:1to(xyp1)]cx
+t17:=satz275f(xpy1,xyp1,t12,f):is"e"([t:1to(xyp1)]cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr))
+t18:=fise(1to(xyp1),cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr),t17,xout(xyp1)):is(<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr))
+t19:=lessisi1"n"(xpy,xyp1,satz18a(xpy,1)):lessis"n"(xpy,xyp1)
+frr:=left(cx,xyp1,xpy,t19,fr):[t:1to(xpy)]cx
+t20:=satz278(xpy,fr):is(smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q)
+t21:=isf(cx,cx,[u:cx]<<xout(xyp1)>fr><u>q,smpr(xpy,frr),<smpr(y,f2(frr))><smpr(x,f1(frr))>q,<frr>p):is(<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
+t22:=assq1(a,smpr(x,f1(frr)),smpr(y,f2(frr)),<xout(xyp1)>fr):is(<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q)
+t23:=lessisi1"n"(y,yp1,satz18a(y,1)):lessis"n"(y,yp1)
+fy:=left(cx,yp1,y,t23,f2(yp1,f)):[t:1to(y)]cx
+t24:=satz278(y,f2(yp1,f)):is(smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
+t25:=isinoutn(yp1,yp1,lessisi3(yp1)):is"n"(yp1,inn(yp1,xout(yp1)))
+t26:=ispl2"n"(yp1,inn(yp1,xout(yp1)),x,t25):is"n"(xpy1,pl"n"(x,inn(yp1,xout(yp1))))
+t27:=tris1(nat,inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))),xpy1,t14,t26):is"n"(inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))))
+t28:=isoutni(xpy1,inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),pl"n"(x,inn(yp1,xout(yp1))),satz19o(inn(yp1,xout(yp1)),yp1,x,1top(yp1,xout(yp1))),t27):is"e"(1to(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)))
+t29:=isf(1to(xpy1),cx,f,left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)),t28):is(<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f))
+t30:=isf(cx,cx,<smpr(y,f2(frr))>q,<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f),t29):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q)
+[n:1to(y)]
+n0:=inn(y,n):nat
+nyp1:=left1to(yp1,y,t23,n):1to(yp1)
+t31:=isinoutn(yp1,n0,trlessis"n"(n0,y,yp1,1top(y,n),t23)):is"n"(n0,inn(yp1,nyp1))
+t32:=ispl2"n"(n0,inn(yp1,nyp1),x,t31):is"n"(pl"n"(x,n0),pl"n"(x,inn(yp1,nyp1)))
+nxpy:=right1to(x,y,n):1to(xpy)
+nxyp1:=left1to(xyp1,xpy,t19,nxpy):1to(xyp1)
+t33:=isinoutn(xyp1,inn(xpy,nxpy),trlessis"n"(inn(xpy,nxpy),xpy,xyp1,1top(xpy,nxpy),t19)):is"n"(inn(xpy,nxpy),inn(xyp1,nxyp1))
+t34:=isinoutn(xpy,pl"n"(x,n0),satz19o(n0,y,x,1top(y,n))):is"n"(pl"n"(x,n0),inn(xpy,nxpy))
+t35:=tris(nat,pl"n"(x,n0),inn(xpy,nxpy),inn(xyp1,nxyp1),t34,t33):is"n"(pl"n"(x,n0),inn(xyp1,nxyp1))
+t36:=tris1(nat,pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1),pl"n"(x,n0),t32,t35):is"n"(pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1))
+t37:=isoutni(xpy1,pl"n"(x,inn(yp1,nyp1)),satz19o(inn(yp1,nyp1),yp1,x,1top(yp1,nyp1)),inn(xyp1,nxyp1),trlessis"n"(inn(xyp1,nxyp1),xyp1,xpy1,1top(xyp1,nxyp1),t12),t36):is"e"(1to(xpy1),right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1))
+t38:=isf(1to(xpy1),cx,f,right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1),t37):is(<n>fy,<n>f2(frr))
+f@t39:=fisi(1to(y),cx,fy,f2(frr),[u:1to(y)]t38(u)):is"e"([u:1to(y)]cx,fy,f2(frr))
+t40:=isf([u:1to(y)]cx,cx,[t:[u:1to(y)]cx]smpr(y,t),fy,f2(frr),t39):is(smpr(y,fy),smpr(y,f2(frr)))
+t41:=isf(cx,cx,[t:cx]<<xout(yp1)>f2(yp1,f)><t>q,smpr(y,f2(frr)),smpr(y,fy),symis(cx,smpr(y,fy),smpr(y,f2(frr)),t40)):is(<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
+t41a:=tris(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t30,t41):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
+t42:=tris2(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t41a,t24):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)))
+t43:=isf(cx,cx,<smpr(x,f1(frr))>q,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),t42):is(<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q)
+[m:1to(x)]
+m0:=inn(x,m):nat
+mxpy:=left1to(xpy,x,t1,m):1to(xpy)
+mxyp1:=left1to(xyp1,xpy,t19,mxpy):1to(xyp1)
+t44:=isinoutn(xyp1,inn(xpy,mxpy),trlessis"n"(inn(xpy,mxpy),xpy,xyp1,1top(xpy,mxpy),t19)):is"n"(inn(xpy,mxpy),inn(xyp1,mxyp1))
+t45:=isinoutn(xpy,m0,trlessis"n"(m0,x,xpy,1top(x,m),t1)):is"n"(m0,inn(xpy,mxpy))
+t46:=tris(nat,m0,inn(xpy,mxpy),inn(xyp1,mxyp1),t45,t44):is"n"(m0,inn(xyp1,mxyp1))
+t47:=isoutni(xpy1,m0,trlessis"n"(m0,x,xpy1,1top(x,m),t1(yp1)),inn(xyp1,mxyp1),trlessis"n"(inn(xyp1,mxyp1),xyp1,xpy1,1top(xyp1,mxyp1),t12),t46):is"e"(1to(xpy1),left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1))
+t48:=isf(1to(xpy1),cx,f,left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1),t47):is(<m>f1(x,yp1,f),<m>f1(x,y,frr))
+f@t49:=fisi(1to(x),cx,f1(x,yp1,f),f1(x,y,frr),[u:1to(x)]t48(u)):is"e"([u:1to(x)]cx,f1(x,yp1,f),f1(x,y,frr))
+t50:=isf([u:1to(x)]cx,cx,[t:[u:1to(x)]cx]smpr(x,t),f1(yp1,f),f1(frr),t49):is(smpr(x,f1(yp1,f)),smpr(x,f1(frr)))
+t51:=isf(cx,cx,[t:cx]<smpr(yp1,f2(yp1,f))><t>q,smpr(x,f1(frr)),smpr(x,f1(yp1,f)),symis(cx,smpr(x,f1(yp1,f)),smpr(x,f1(frr)),t50)):is(<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q)
+t52:=tr4is(cx,smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,t16,t18,t20,t21):is(smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
+t53:=tr4is(cx,smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q,t52,t22,t43,t51):prop1(yp1,f)
+p@t54:=[u:[t:1to(xpy1)]cx]t53(u):prop2(yp1)
+t55:=isp(nat,[t:nat]prop2(t),yp1,<y>suc,t54,satz4a(y)):prop2(<y>suc)
+y@t56:=induction([t:nat]prop2(t),t11,[z:nat][t:prop2(z)]t55(z,t),y):prop2(y)
+-8281
+satz281:=<f>t56".8281":is(smpr(pl"n"(x,y),f),<smpr(y,right(cx,x,y,f))><smpr(x,left(cx,pl"n"(x,y),x,lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)),f))>q)
+q@commut:=[x:cx][y:cx]is(<y><x>q,<x><y>q):'prop'
+@commutpl:=[x:cx][y:cx]compl(x,y):commut([x:cx][y:cx]pl(x,y))
+commutts:=[x:cx][y:cx]comts(x,y):commut([x:cx][y:cx]ts(x,y))
+q@[c:commut][z:cx][u:cx]
+comq:=<u><z>c:is(<u><z>q,<z><u>q)
+a@[c:commut(q)][x:nat][f:[t:1to(x)]cx][g:[t:1to(x)]cx]
++8282
+prop1:=is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q):'prop'
+x@prop2:=all"l"([t:1to(x)]cx,[u:[t:1to(x)]cx]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]prop1(u,v))):'prop'
+c@[f0:[t:1to(1)]cx][g0:[t:1to(1)]cx]
+t1:=satz277([t:1to(1)]<<t>g0><<t>f0>q):is(smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<<xout(1)>g0><<xout(1)>f0>q)
+t2:=isf(cx,cx,<smpr(1,f0)>q,smpr(1,g0),<xout(1)>g0,satz277(g0)):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q)
+t3:=isf(cx,cx,[t:cx]<<xout(1)>g0><t>q,smpr(1,f0),<xout(1)>f0,satz277(f0)):is(<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
+t4:=tris(cx,<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t2,t3):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
+t5:=tris2(cx,smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t1,t4):prop1(1,f0,g0)
+c@t6:=[u:[t:1to(1)]cx][v:[t:1to(1)]cx]t5(u,v):prop2(1)
+x@xp1:=pl"n"(x,1):nat
+[p:prop2(x)][f:[t:1to(xp1)]cx][g:[t:1to(xp1)]cx]
+c@[u:cx][v:cx][w:cx][z:cx]
+t7:=assq2(a,<v><u>q,w,z):is(<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q)
+t8:=comq(c,<v><u>q,w):is(<w><<v><u>q>q,<<v><u>q><w>q)
+t9:=assq2(a,w,u,v):is(<<v><u>q><w>q,<v><<u><w>q>q)
+t10:=tris(cx,<w><<v><u>q>q,<<v><u>q><w>q,<v><<u><w>q>q,t8,t9):is(<w><<v><u>q>q,<v><<u><w>q>q)
+t11:=isf(cx,cx,[t:cx]<z><t>q,<w><<v><u>q>q,<v><<u><w>q>q,t10):is(<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q)
+t12:=assq1(a,<u><w>q,v,z):is(<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q)
+t13:=comq(c,w,u):is(<u><w>q,<w><u>q)
+t14:=isf(cx,cx,[t:cx]<<z><v>q><t>q,<u><w>q,<w><u>q,t13):is(<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q)
+t15:=tr4is(cx,<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q,t7,t11,t12,t14):is(<<z><w>q><<v><u>q>q,<<z><v>q><<w><u>q>q)
+g@t16:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
+sfx:=smpr(x,left(cx,xp1,x,t16,f)):cx
+sgx:=smpr(x,left(cx,xp1,x,t16,g)):cx
+h:=[t:1to(xp1)]<<t>g><<t>f>q:[t:1to(xp1)]cx
+shx:=smpr(x,left(cx,xp1,x,t16,h)):cx
+t17:=satz278(x,h):is(smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q)
+t18:=<left(cx,xp1,x,t16,g)><left(cx,xp1,x,t16,f)>p:is(shx,<sgx><sfx>q)
+t19:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><<xout(xp1)>f>q><t>q,shx,<sgx><sfx>q,t18):is(<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q)
+t20:=t15(sfx,sgx,<xout(xp1)>f,<xout(xp1)>g):is(<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
+t21:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><sfx>q,satz278(x,f)):is(<<xout(xp1)>f><sfx>q,smpr(xp1,f))
+t22:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><sgx>q><t>q,<<xout(xp1)>f><sfx>q,smpr(xp1,f),t21):is(<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q)
+t23:=symis(cx,smpr(xp1,g),<<xout(xp1)>g><sgx>q,satz278(x,g)):is(<<xout(xp1)>g><sgx>q,smpr(xp1,g))
+t24:=isf(cx,cx,<smpr(xp1,f)>q,<<xout(xp1)>g><sgx>q,smpr(xp1,g),t23):is(<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q)
+t25:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,t17,t19,t20):is(smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
+t26:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q,t25,t22,t24):prop1(xp1,f,g)
+p@t27:=[u:[t:1to(xp1)]cx][v:[t:1to(xp1)]cx]t26(u,v):prop2(xp1)
+t28:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t27,satz4a(x)):prop2(<x>suc)
+x@t29:=induction([t:nat]prop2(t),t6,[y:nat][t:prop2(y)]t28(y,t),x):prop2(x)
+-8282
+satz282:=<g><f>t29".8282":is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q)
+x@[s:[t:1to(x)]1to(x)][b:bijective(1to(x),1to(x),s)][f:[t:1to(x)]cx]
++8283
+s@[f:[t:1to(x)]cx]
+g:=[t:1to(x)]<<t>s>f:[t:1to(x)]cx
+prop1:=is(smpr(x,g),smpr(x,f)):'prop'
+x@prop2:=all"l"([t:1to(x)]1to(x),[u:[t:1to(x)]1to(x)]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]imp(bijective(1to(x),1to(x),u),prop1(u,v)))):'prop'
+c@[s:[t:1to(1)]1to(1)][f:[t:1to(1)]cx]
+t1:=tris2(1to(1),<xout(1)>s,xout(1),1o"n",th1"n.singlet"(<xout(1)>s),th1"n.singlet"(xout(1))):is"e"(1to(1),<xout(1)>s,xout(1))
+t2:=satz277(g(1,s,f)):is(smpr(1,g(1,s,f)),<xout(1)>g(1,s,f))
+t3:=isf(1to(1),cx,f,<xout(1)>s,xout(1),t1):is(<xout(1)>g(1,s,f),<xout(1)>f)
+t4:=symis(cx,smpr(1,f),<xout(1)>f,satz277(f)):is(<xout(1)>f,smpr(1,f))
+t5:=tr3is(cx,smpr(1,g(1,s,f)),<xout(1)>g(1,s,f),<xout(1)>f,smpr(1,f),t2,t3,t4):prop1(1,s,f)
+c@t6:=[u:[t:1to(1)]1to(1)][v:[t:1to(1)]cx][w:bijective(1to(1),1to(1),u)]t5(u,v):prop2(1)
+x@xp1:=pl"n"(x,1):nat
+t7:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
+[p:prop2(x)][s:[t:1to(xp1)]1to(xp1)][f:[t:1to(xp1)]cx][b:bijective(1to(xp1),1to(xp1),s)]
+t8:=ande1(injective(1to(xp1),1to(xp1),s),surjective(1to(xp1),1to(xp1),s),b):injective(1to(xp1),1to(xp1),s)
+[case1:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))][u:1to(x)]
+u1:=left1to(xp1,x,t7,u):1to(xp1)
+n1:=inn(xp1,<u1>s):nat
+[i:is"n"(n1,xp1)]
+t9:=tr3is(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),xout(xp1),<xout(xp1)>s,isoutinn(xp1,<u1>s),isoutni(xp1,n1,1top(xp1,<u1>s),xp1,lessisi3(xp1),i),symis(1to(xp1),<xout(xp1)>s,xout(xp1),case1)):is"e"(1to(xp1),<u1>s,<xout(xp1)>s)
+t10:=isfe(1to(xp1),1to(xp1),s,t8,u1,xout(xp1),t9):is"e"(1to(xp1),u1,xout(xp1))
+t11:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t10):is"n"(inn(x,u),xp1)
+t12:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
+t13:=<t11>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t12):con
+u@t14:=ore1(less"n"(n1,xp1),is"n"(n1,xp1),1top(xp1,<u1>s),[t:is"n"(n1,xp1)]t13(t)):less"n"(n1,xp1)
+t15:=satz26(x,n1,t14):lessis"n"(n1,x)
+w1:=outn(x,n1,t15):1to(x)
+case1@s01:=[t:1to(x)]w1(t):[t:1to(x)]1to(x)
+u@[v:1to(x)][i:is"e"(1to(x),w1(u),w1(v))]
+t16:=isoutne(x,n1(u),t15(u),n1(v),t15(v),i):is"n"(n1(u),n1(v))
+t17:=<isinne(xp1,<u1(u)>s,<u1(v)>s,t16)><u1(v)><u1(u)>t8:is"e"(1to(xp1),u1(u),u1(v))
+t18:=thleft1(xp1,x,t7,u,v,t17):is"e"(1to(x),u,v)
+u@u2:=<u1>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
+n2:=inn(xp1,u2):nat
+[i:is"n"(n2,xp1)]
+t19:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),xout(xp1),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),xp1,lessisi3(xp1),i)):is"e"(1to(xp1),u2,xout(xp1))
+t20:=tr3is(1to(xp1),u1,<u2>s,<xout(xp1)>s,xout(xp1),thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,xout(xp1),t19),case1):is"e"(1to(xp1),u1,xout(xp1))
+t21:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t20):is"n"(inn(x,u),xp1)
+t22:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
+t23:=<t21>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t22):con
+u@t24:=ore1(less"n"(n2,xp1),is"n"(n2,xp1),1top(xp1,u2),[t:is"n"(n2,xp1)]t23(t)):less"n"(n2,xp1)
+t25:=satz26(x,n2,t24):lessis"n"(n2,x)
+w2:=outn(x,n2,t25):1to(x)
+t26:=isinoutn(x,n2,t25):is"n"(n2,inn(x,w2))
+t27:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),u1(w2),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),inn(x,w2),trlessis"n"(inn(x,w2),x,xp1,1top(x,w2),t7),t26)):is"e"(1to(xp1),u2,u1(w2))
+t28:=tris(1to(xp1),u1,<u2>s,<u1(w2)>s,thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,u1(w2),t27)):is"e"(1to(xp1),u1,<u1(w2)>s)
+t29:=tris(nat,inn(x,u),inn(xp1,u1),n1(w2),isinoutn(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7)),isinni(xp1,u1,<u1(w2)>s,t28)):is"n"(inn(x,u),n1(w2))
+t30:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w1(w2),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),n1(w2),t15(w2),t29)):is"e"(1to(x),u,w1(w2))
+t31:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w1(t)),w2,t30):image(1to(x),1to(x),s01,u)
+case1@t32:=andi(injective(1to(x),1to(x),s01),surjective(1to(x),1to(x),s01),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s01,<u>s01)]t18(t,u,v),[t:1to(x)]t31(t)):bijective(1to(x),1to(x),s01)
+f01:=left(cx,xp1,x,t7,f):[t:1to(x)]cx
+t33:=<t32><f01><s01>p:prop1(s01,f01)
+g1:=left(cx,xp1,x,t7,g(xp1,s,f)):[t:1to(x)]cx
+g2:=g(x,s01,f01):[t:1to(x)]cx
+u@t33a:=isoutinn(xp1,<u1>s):is"e"(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)))
+t34:=isinoutn(x,n1,t15):is"n"(n1,inn(x,w1))
+t35:=isoutni(xp1,n1,1top(xp1,<u1>s),inn(x,w1),trlessis"n"(inn(x,w1),x,xp1,1top(x,w1),t7),t34):is"e"(1to(xp1),outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1))
+t36:=tris(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1),t33a,t35):is"e"(1to(xp1),<u1>s,left1to(xp1,x,t7,w1))
+t37:=isf(1to(xp1),cx,f,<u1>s,left1to(xp1,x,t7,w1),t36):is(<u>g1,<u>g2)
+case1@t38:=fisi(1to(x),cx,g1,g2,[t:1to(x)]t37(t)):is"e"([t:1to(x)]cx,g1,g2)
+t39:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g1,g2,t38):is(smpr(x,g1),smpr(x,g2))
+t40:=tris(cx,smpr(x,g1),smpr(x,g2),smpr(x,f01),t39,t33):is(smpr(x,g1),smpr(x,f01))
+t41:=isf(1to(xp1),cx,f,<xout(xp1)>s,xout(xp1),case1):is(<xout(xp1)>g(xp1,s,f),<xout(xp1)>f)
+t42:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q)
+t43:=isf(cx,cx,<smpr(x,g1)>q,<xout(xp1)>g(xp1,s,f),<xout(xp1)>f,t41):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q)
+t44:=isf(cx,cx,[t:cx]<<xout(xp1)>f><t>q,smpr(x,g1),smpr(x,f01),t40):is(<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q)
+t45:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><smpr(x,f01)>q,satz278(x,f)):is(<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f))
+t46:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f),t42,t43,t44,t45):prop1(xp1,s,f)
+b@1px:=pl"n"(1,x):nat
+[case2:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))][u:1to(x)]
+u3:=right1to(1,x,u):1to(1px)
+case2@t47:=lessisi2"n"(1px,xp1,compl"n"(1,x)):lessis"n"(1px,xp1)
+s02:=left(1to(xp1),xp1,1px,t47,s):[t:1to(1px)]1to(xp1)
+u@n3:=inn(xp1,<u3>s02):nat
+[i:is"n"(n3,1)]
+t48:=tr3is(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),1out(xp1),<1out(xp1)>s,isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),1,satz24a(xp1),i),symis(1to(xp1),<1out(xp1)>s,1out(xp1),case2)):is"e"(1to(xp1),<u3>s02,<1out(xp1)>s)
+t49:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3),1out(xp1),t48):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
+t50:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t49):is"n"(inn(1px,u3),1)
+t51:=isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))):is"n"(pl"n"(1,inn(x,u)),inn(1px,u3))
+t52:=ismore1"n"(pl"n"(1,inn(x,u)),inn(1px,u3),1,t51,satz18(1,inn(x,u))):more"n"(inn(1px,u3),1)
+t53:=<t50>ec3e21(is"n"(inn(1px,u3),1),more"n"(inn(1px,u3),1),less"n"(inn(1px,u3),1),satz10b(inn(1px,u3),1),t52):con
+u@t54:=ore1(more"n"(n3,1),is"n"(n3,1),satz24(n3),[t:is"n"(n3,1)]t53(t)):more"n"(n3,1)
+nm1:=mn"n"(n3,1,t54):nat
+t54a:=islessis1"n"(n3,pl"n"(nm1,1),xp1,th1c"n.mn"(n3,1,t54),1top(xp1,<u3>s02)):lessis"n"(pl"n"(nm1,1),xp1)
+t55:=th9"l.or"(less"n"(pl"n"(nm1,1),xp1),is"n"(pl"n"(nm1,1),xp1),less"n"(nm1,x),is"n"(nm1,x),t54a,[t:less"n"(pl"n"(nm1,1),xp1)]satz20c(nm1,x,1,t),[t:is"n"(pl"n"(nm1,1),xp1)]satz20b(nm1,x,1,t)):lessis"n"(nm1,x)
+w3:=outn(x,nm1,t55):1to(x)
+case2@s03:=[t:1to(x)]w3(t):[t:1to(x)]1to(x)
+u@[v:1to(x)][i:is"e"(1to(x),w3(u),w3(v))]
+t56:=isoutne(x,nm1(u),t55(u),nm1(v),t55(v),i):is"n"(nm1(u),nm1(v))
+t57:=tr3is(nat,n3(u),pl"n"(nm1(u),1),pl"n"(nm1(v),1),n3(v),th1c"n.mn"(n3(u),1,t54(u)),ispl1"n"(nm1(u),nm1(v),1,t56),th1d"n.mn"(n3(v),1,t54(v))):is"n"(n3(u),n3(v))
+t58:=isinne(xp1,<u3(u)>s02,<u3(v)>s02,t57):is"e"(1to(xp1),<u3(u)>s02,<u3(v)>s02)
+t59:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)),t58):is"e"(1to(xp1),left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)))
+t60:=thleft1(xp1,1px,t47,u3(u),u3(v),t59):is"e"(1to(1px),u3(u),u3(v))
+t61:=thright1(1,x,u,v,t60):is"e"(1to(x),u,v)
+case2@s04:=left(1to(xp1),xp1,1px,t47,invf(1to(xp1),1to(xp1),s,b)):[t:1to(1px)]1to(xp1)
+u@u4:=<u3>s04:1to(xp1)
+n4:=inn(xp1,u4):nat
+[i:is"n"(n4,1)]
+t62:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),1out(xp1),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),1,satz24a(xp1),i)):is"e"(1to(xp1),u4,1out(xp1))
+t63:=tr3is(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<1out(xp1)>s,1out(xp1),thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,1out(xp1),t62),case2):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
+t64:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t63):is"n"(inn(1px,u3),1)
+t65:=tris(nat,pl"n"(1,inn(x,u)),inn(1px,u3),1,isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),t64):is"n"(pl"n"(1,inn(x,u)),1)
+t66:=<t65>ec3e21(is"n"(pl"n"(1,inn(x,u)),1),more"n"(pl"n"(1,inn(x,u)),1),less"n"(pl"n"(1,inn(x,u)),1),satz10b(pl"n"(1,inn(x,u)),1),satz18(1,inn(x,u))):con
+u@t67:=ore1(more"n"(n4,1),is"n"(n4,1),satz24(n4),[t:is"n"(n4,1)]t66(t)):more"n"(n4,1)
+nm2:=mn"n"(n4,1,t67):nat
+t68:=islessis1"n"(n4,pl"n"(nm2,1),xp1,th1c"n.mn"(n4,1,t67),1top(xp1,u4)):lessis"n"(pl"n"(nm2,1),xp1)
+t69:=th9"l.or"(less"n"(pl"n"(nm2,1),xp1),is"n"(pl"n"(nm2,1),xp1),less"n"(nm2,x),is"n"(nm2,x),t68,[t:less"n"(pl"n"(nm2,1),xp1)]satz20c(nm2,x,1,t),[t:is"n"(pl"n"(nm2,1),xp1)]satz20b(nm2,x,1,t)):lessis"n"(nm2,x)
+w4:=outn(x,nm2,t69):1to(x)
+t70:=isinoutn(x,nm2,t69):is"n"(nm2,inn(x,w4))
+t71:=tr3is(nat,n4,pl"n"(1,nm2),pl"n"(1,inn(x,w4)),inn(1px,u3(w4)),th1a"n.mn"(n4,1,t67),ispl2"n"(nm2,inn(x,w4),1,t70),isinoutn(1px,pl"n"(1,inn(x,w4)),satz19o(inn(x,w4),x,1,1top(x,w4)))):is"n"(n4,inn(1px,u3(w4)))
+t72:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),left1to(xp1,1px,t47,u3(w4)),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),inn(1px,u3(w4)),trlessis"n"(inn(1px,u3(w4)),1px,xp1,1top(1px,u3(w4)),t47),t71)):is"e"(1to(xp1),u4,left1to(xp1,1px,t47,u3(w4)))
+t73:=tris(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<u3(w4)>s02,thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,left1to(xp1,1px,t47,u3(w4)),t72)):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),<u3(w4)>s02)
+t74:=tr3is(nat,pl"n"(1,inn(x,u)),inn(1px,u3),inn(xp1,left1to(xp1,1px,t47,u3)),n3(w4),isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),isinoutn(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47)),isinni(xp1,left1to(xp1,1px,t47,u3),<u3(w4)>s02,t73)):is"n"(pl"n"(1,inn(x,u)),n3(w4))
+t75:=th1e"n.mn"(n3(w4),1,inn(x,u),t54(w4),t74):is"n"(inn(x,u),nm1(w4))
+t76:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w3(w4),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),nm1(w4),t55(w4),t75)):is"e"(1to(x),u,w3(w4))
+t77:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w3(t)),w4,t76):image(1to(x),1to(x),s03,u)
+case2@t78:=andi(injective(1to(x),1to(x),s03),surjective(1to(x),1to(x),s03),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s03,<u>s03)]t61(t,u,v),[t:1to(x)]t77(t)):bijective(1to(x),1to(x),s03)
+f02:=left(cx,xp1,1px,t47,f):[t:1to(1px)]cx
+f03:=right(cx,1,x,f02):[t:1to(x)]cx
+t79:=<t78><f03><s03>p:prop1(s03,f03)
+g3:=left(cx,xp1,1px,t47,g(xp1,s,f)):[t:1to(1px)]cx
+g4:=right(cx,1,x,g3):[t:1to(x)]cx
+g5:=g(x,s03,f03):[t:1to(x)]cx
+u@t80:=tr3is(nat,n3,pl"n"(1,nm1),pl"n"(1,inn(x,w3)),inn(1px,right1to(1,x,w3)),th1a"n.mn"(n3,1,t54),ispl2"n"(nm1,inn(x,w3),1,isinoutn(x,nm1,t55)),isinoutn(1px,pl"n"(1,inn(x,w3)),satz19o(inn(x,w3),x,1,1top(x,w3)))):is"n"(n3,inn(1px,right1to(1,x,w3)))
+t81:=tris(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),left1to(xp1,1px,t47,right1to(1,x,w3)),isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),inn(1px,right1to(1,x,w3)),trlessis"n"(inn(1px,right1to(1,x,w3)),1px,xp1,1top(1px,right1to(1,x,w3)),t47),t80)):is"e"(1to(xp1),<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)))
+t82:=isf(1to(xp1),cx,f,<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)),t81):is(<u>g4,<u>g5)
+case2@t83:=fisi(1to(x),cx,g4,g5,[t:1to(x)]t82(t)):is"e"([t:1to(x)]cx,g4,g5)
+t85:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g4,g5,t83):is(smpr(x,g4),smpr(x,g5))
+t86:=tris(cx,smpr(x,g4),smpr(x,g5),smpr(x,f03),t85,t79):is(smpr(x,g4),smpr(x,f03))
+t87:=lessisi1"n"(1,1px,satz18a(1,x)):lessis"n"(1,1px)
+g6:=left(cx,1px,1,t87,g3):[t:1to(1)]cx
+f04:=left(cx,1px,1,t87,f02):[t:1to(1)]cx
+t87a:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+1d:=left1to(1px,1,t87,xout(1)):1to(1px)
+t87b:=isinoutn(1px,inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,1px,1top(1,xout(1)),t87)):is"n"(inn(1,xout(1)),inn(1px,1d))
+t88:=tris(nat,1,inn(1,xout(1)),inn(1px,1d),t87a,t87b):is"n"(1,inn(1px,1d))
+1e:=left1to(xp1,1px,t47,1d):1to(xp1)
+t88a:=isoutni(xp1,1,satz24a(xp1),inn(1px,1d),trlessis"n"(inn(1px,1d),1px,xp1,1top(1px,1d),t47),t88):is"e"(1to(xp1),1out(xp1),1e)
+t88b:=isf(1to(xp1),1to(xp1),s,1e,1out(xp1),symis(1to(xp1),1out(xp1),1e,t88a)):is"e"(1to(xp1),<1e>s,<1out(xp1)>s)
+t89:=tr3is(1to(xp1),<1e>s,<1out(xp1)>s,1out(xp1),1e,t88b,case2,t88a):is"e"(1to(xp1),<1e>s,1e)
+t89a:=tr3is(cx,smpr(1,g6),<xout(1)>g6,<xout(1)>f04,smpr(1,f04),satz277(g6),isf(1to(xp1),cx,f,<1e>s,1e,t89),symis(cx,smpr(1,f04),<xout(1)>f04,satz277(f04))):is(smpr(1,g6),smpr(1,f04))
+t90:=satz281(1,x,g3):is(smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q)
+t91:=isf(cx,cx,<smpr(1,g6)>q,smpr(x,g4),smpr(x,f03),t86):is(<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q)
+t92:=isf(cx,cx,[t:cx]<smpr(x,f03)><t>q,smpr(1,g6),smpr(1,f04),t89a):is(<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q)
+t93:=symis(cx,smpr(1px,f02),<smpr(x,f03)><smpr(1,f04)>q,satz281(1,x,f02)):is(<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02))
+t94:=tr4is(cx,smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02),t90,t91,t92,t93):is(smpr(1px,g3),smpr(1px,f02))
+t95:=issmpr(xp1,f,1px,compl"n"(1,x)):is(smpr(1px,f02),smpr(xp1,f))
+t96:=symis(cx,smpr(1px,g3),smpr(xp1,g(xp1,s,f)),issmpr(xp1,g(xp1,s,f),1px,compl"n"(1,x))):is(smpr(xp1,g(xp1,s,f)),smpr(1px,g3))
+t97:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(1px,g3),smpr(1px,f02),smpr(xp1,f),t96,t94,t95):prop1(xp1,s,f)
+b@[not1:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))][not2:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]
+a0:=<1out(xp1)>s:1to(xp1)
+b0:=<1out(xp1)>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
+t98:=thinvf2(1to(xp1),1to(xp1),s,b,1out(xp1)):is"e"(1to(xp1),1out(xp1),<b0>s)
+t99:=not2:not(is"e"(1to(xp1),a0,1out(xp1)))
+t100:=symnotis(1to(xp1),<1out(xp1)>s,<b0>s,th3"e.notis"(1to(xp1),<1out(xp1)>s,1out(xp1),<b0>s,not2,t98)):not(is"e"(1to(xp1),<b0>s,<1out(xp1)>s))
+t101:=th3"l.imp"(is"e"(1to(xp1),b0,1out(xp1)),is"e"(1to(xp1),<b0>s,<1out(xp1)>s),t100,[t:is"e"(1to(xp1),b0,1out(xp1))]isf(1to(xp1),1to(xp1),s,b0,1out(xp1),t)):not(is"e"(1to(xp1),b0,1out(xp1)))
+s1:=changef(1to(xp1),1to(xp1),s,1out(xp1),b0):[t:1to(xp1)]1to(xp1)
+[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
+t102:=changef1(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,<b0>s)
+t103:=tris2(1to(xp1),<u>s1,1out(xp1),<b0>s,t102,t98):is"e"(1to(xp1),<u>s1,1out(xp1))
+u@[i:is"e"(1to(xp1),u,b0)]
+t104:=changef2(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,a0)
+u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
+t105:=changef3(1to(xp1),1to(xp1),s,1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
+not2@t106:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),b0,b):bijective(1to(xp1),1to(xp1),s1)
+[alpha:not(is"e"(1to(xp1),a0,xout(xp1)))]
+s2:=wissel(1to(xp1),1out(xp1),a0):[t:1to(xp1)]1to(xp1)
+t107:=th3"e.wissel"(1to(xp1),1out(xp1),a0):bijective(1to(xp1),1to(xp1),s2)
+[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
+t108:=iswissel1(1to(xp1),1out(xp1),a0,<u>s1,t103(u,i)):is"e"(1to(xp1),<<u>s1>s2,a0)
+t109:=tris2(1to(xp1),<u>s,<<u>s1>s2,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t108):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+u@[i:is"e"(1to(xp1),u,b0)]
+t110:=iswissel2(1to(xp1),1out(xp1),a0,<u>s1,t104(u,i)):is"e"(1to(xp1),<<u>s1>s2,1out(xp1))
+t111:=tris2(1to(xp1),<u>s,<<u>s1>s2,1out(xp1),tris2(1to(xp1),<u>s,1out(xp1),<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),t98),t110):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))][i:is"e"(1to(xp1),<u>s1,1out(xp1))]
+t112:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,1out(xp1),tris2(1to(xp1),<u>s1,<1out(xp1)>s1,1out(xp1),i,t103(1out(xp1),refis(1to(xp1),1out(xp1))))):is"e"(1to(xp1),u,1out(xp1))
+o@t113:=th3"l.imp"(is"e"(1to(xp1),<u>s1,1out(xp1)),is"e"(1to(xp1),u,1out(xp1)),n,[t:is"e"(1to(xp1),<u>s1,1out(xp1))]t112(t)):not(is"e"(1to(xp1),<u>s1,1out(xp1)))
+[i:is"e"(1to(xp1),<u>s1,a0)]
+t114:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,b0,tris2(1to(xp1),<u>s1,<b0>s1,a0,i,t104(b0,refis(1to(xp1),b0)))):is"e"(1to(xp1),u,b0)
+o@t115:=th3"l.imp"(is"e"(1to(xp1),<u>s1,a0),is"e"(1to(xp1),u,b0),o,[t:is"e"(1to(xp1),<u>s1,a0)]t114(t)):not(is"e"(1to(xp1),<u>s1,a0))
+t116:=iswissel3(1to(xp1),1out(xp1),a0,<u>s1,t113,t115):is"e"(1to(xp1),<<u>s1>s2,<u>s1)
+t117:=symis(1to(xp1),<<u>s1>s2,<u>s,tris(1to(xp1),<<u>s1>s2,<u>s1,<u>s,t116,t105(u,n,o))):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+n@t118:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,b0)]t111(t),[t:not(is"e"(1to(xp1),u,b0))]t117(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+u@t119:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,1out(xp1))]t109(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t118(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+alpha@t120:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s1>s2,[t:1to(xp1)]t119(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s1>s2)
+not2@t121:=t103(1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s1,1out(xp1))
+t121a:=ec3e21(is"n"(xp1,1),more"n"(xp1,1),less"n"(xp1,1),satz10b(xp1,1),ismore1"n"(1px,xp1,1,compl"n"(1,x),satz18(1,x))):nis"n"(xp1,1)
+t122:=th3"l.imp"(is"e"(1to(xp1),xout(xp1),1out(xp1)),is"n"(xp1,1),t121a,[t:is"e"(1to(xp1),xout(xp1),1out(xp1))]isoutne(xp1,xp1,lessisi3(xp1),1,satz24a(xp1),t)):not(is"e"(1to(xp1),xout(xp1),1out(xp1)))
+alpha@t123:=symnotis(1to(xp1),a0,xout(xp1),alpha):not(is"e"(1to(xp1),xout(xp1),a0))
+t124:=iswissel3(1to(xp1),1out(xp1),a0,xout(xp1),t122,t123):is"e"(1to(xp1),<xout(xp1)>s2,xout(xp1))
+t125:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s1>s2,t120):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))))
+t126:=t97(s1,g(xp1,s2,f),t106,t121):is(smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)))
+t127:=t46(s2,f,t107,t124):is(smpr(xp1,g(xp1,s2,f)),smpr(xp1,f))
+t128:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)),smpr(xp1,f),t125,t126,t127):prop1(xp1,s,f)
+not2@[i3:is"e"(1to(xp1),a0,xout(xp1))][beta:not(is"e"(1to(xp1),b0,xout(xp1)))]
+s3:=wissel(1to(xp1),1out(xp1),b0):[t:1to(xp1)]1to(xp1)
+t129:=th3"e.wissel"(1to(xp1),1out(xp1),b0):bijective(1to(xp1),1to(xp1),s3)
+[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
+t130:=t104(<u>s3,iswissel1(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,a0)
+t131:=tris2(1to(xp1),<u>s,<<u>s3>s1,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t130):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+u@[i:is"e"(1to(xp1),u,b0)]
+t132:=t103(<u>s3,iswissel2(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,1out(xp1))
+t133:=tris2(1to(xp1),<u>s,<<u>s3>s1,<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),tris(1to(xp1),<<u>s3>s1,1out(xp1),<b0>s,t132,t98)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
+t134:=iswissel3(1to(xp1),1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s3,u)
+t135:=isf(1to(xp1),1to(xp1),s1,<u>s3,u,t134):is"e"(1to(xp1),<<u>s3>s1,<u>s1)
+t136:=t105(u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
+t139:=symis(1to(xp1),<<u>s3>s1,<u>s,tris(1to(xp1),<<u>s3>s1,<u>s1,<u>s,t135,t136)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+n@t140:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,b0)]t133(t),[t:not(is"e"(1to(xp1),u,b0))]t139(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+u@t141:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,1out(xp1))]t131(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t140(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+beta@t142:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s3>s1,[t:1to(xp1)]t141(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s3>s1)
+t143:=symnotis(1to(xp1),b0,xout(xp1),beta):not(is"e"(1to(xp1),xout(xp1),b0))
+t144:=iswissel3(1to(xp1),1out(xp1),b0,xout(xp1),t122,t143):is"e"(1to(xp1),<xout(xp1)>s3,xout(xp1))
+t145:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s3>s1,t142):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))))
+t146:=t46(s3,g(xp1,s1,f),t129,t144):is(smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)))
+t147:=t97(s1,f,t106,t121):is(smpr(xp1,g(xp1,s1,f)),smpr(xp1,f))
+t148:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)),smpr(xp1,f),t145,t146,t147):prop1(xp1,s,f)
+i3@[gamma:is"e"(1to(xp1),b0,xout(xp1))][i:is"n"(x,1)]
+t149:=ispl1"n"(1,x,1,symis(nat,x,1,i)):is"n"(2,xp1)
+t150:=lessisi2"n"(2,xp1,t149):lessis"n"(2,xp1)
+f05:=left(cx,xp1,2,t150,f):[t:1to(2)]cx
+s05:=left(1to(xp1),xp1,2,t150,s):[t:1to(2)]1to(xp1)
+g7:=left(cx,xp1,2,t150,g(xp1,s,f)):[t:1to(2)]cx
+t151:=issmpr(xp1,f,2,t149):is(smpr(2,f05),smpr(xp1,f))
+t152:=issmpr(xp1,g(xp1,s,f),2,t149):is(smpr(2,g7),smpr(xp1,g(xp1,s,f)))
+t153:=satz280(f05):is(smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q)
+t154:=satz280(g7):is(smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q)
+t155:=tris1(nat,inn(2,xout(2)),xp1,2,isinoutn(2,2,lessisi3(2)),t149):is"n"(inn(2,xout(2)),xp1)
+t156:=isoutni(xp1,inn(2,xout(2)),trlessis"n"(inn(2,xout(2)),2,xp1,1top(2,xout(2)),t150),xp1,lessisi3(xp1),t155):is"e"(1to(xp1),left1to(xp1,2,t150,xout(2)),xout(xp1))
+t157:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,xout(2)),xout(xp1),t156):is"e"(1to(xp1),<xout(2)>s05,<xout(xp1)>s)
+t158:=symis(nat,1,inn(2,1out(2)),isinoutn(2,1,satz24a(2))):is"n"(inn(2,1out(2)),1)
+t159:=isoutni(xp1,inn(2,1out(2)),trlessis"n"(inn(2,1out(2)),2,xp1,1top(2,1out(2)),t150),1,satz24a(xp1),t158):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1))
+t160:=tr3is(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1),<b0>s,<xout(xp1)>s,t159,t98,isf(1to(xp1),1to(xp1),s,b0,xout(xp1),gamma)):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),<xout(xp1)>s)
+t161:=tris2(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)),<xout(xp1)>s,t157,t160):is"e"(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)))
+t163:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,1out(2)),1out(xp1),t159):is"e"(1to(xp1),<1out(2)>s05,<1out(xp1)>s)
+t164:=tris(1to(xp1),<1out(2)>s05,<1out(xp1)>s,xout(xp1),t163,i3):is"e"(1to(xp1),<1out(2)>s05,xout(xp1))
+t165:=tris2(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)),xout(xp1),t164,t156):is"e"(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)))
+t166:=isf(1to(xp1),cx,f,<xout(2)>s05,left1to(xp1,2,t150,1out(2)),t161):is(<xout(2)>g7,<1out(2)>f05)
+t167:=isf(1to(xp1),cx,f,<1out(2)>s05,left1to(xp1,2,t150,xout(2)),t165):is(<1out(2)>g7,<xout(2)>f05)
+t168:=isf(cx,cx,<<1out(2)>g7>q,<xout(2)>g7,<1out(2)>f05,t166):is(<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q)
+t169:=comq(c,<1out(2)>g7,<1out(2)>f05):is(<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q)
+t170:=isf(cx,cx,<<1out(2)>f05>q,<1out(2)>g7,<xout(2)>f05,t167):is(<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q)
+t171:=tr4is(cx,smpr(xp1,g(xp1,s,f)),smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q,symis(cx,smpr(2,g7),smpr(xp1,g(xp1,s,f)),t152),t154,t168,t169):is(smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q)
+t172:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q,smpr(2,f05),smpr(xp1,f),t171,t170,symis(cx,smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q,t153),t151):prop1(xp1,s,f)
+trivial:=t172:prop1(xp1,s,f)
+gamma@[n:nis"n"(x,1)]
+t173:=ore1(more"n"(x,1),is"n"(x,1),satz24(x),n):more"n"(x,1)
+xm1:=mn"n"(x,1,t173):nat
+s4:=changef(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1)):[t:1to(xp1)]1to(xp1)
+t174:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),b):bijective(1to(xp1),1to(xp1),s4)
+t175:=changef2(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),xout(xp1),refis(1to(xp1),xout(xp1))):is"e"(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s)
+t176:=symis(1to(xp1),a0,xout(xp1),i3):is"e"(1to(xp1),xout(xp1),<1out(xp1)>s)
+t177:=tris2(1to(xp1),<xout(xp1)>s4,xout(xp1),<1out(xp1)>s,t175,t176):is"e"(1to(xp1),<xout(xp1)>s4,xout(xp1))
+t178:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
+g8:=left(cx,xp1,x,t178,g(xp1,s,f)):[t:1to(x)]cx
+t179:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q)
+t180:=th1b"n.mn"(x,1,t173):is"n"(pl"n"(1,xm1),x)
+t181:=lessisi2"n"(pl"n"(1,xm1),x,t180):lessis"n"(pl"n"(1,xm1),x)
+g9:=left(cx,x,pl"n"(1,xm1),t181,g8):[t:1to(pl"n"(1,xm1))]cx
+t182:=symis(cx,smpr(pl"n"(1,xm1),g9),smpr(x,g8),issmpr(x,g8,pl"n"(1,xm1),t180)):is(smpr(x,g8),smpr(pl"n"(1,xm1),g9))
+g10:=right(cx,1,xm1,g9):[t:1to(xm1)]cx
+t183:=lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)):lessis"n"(1,pl"n"(1,xm1))
+g11:=left(cx,pl"n"(1,xm1),1,t183,g9):[t:1to(1)]cx
+t184:=satz281(a,1,xm1,g9):is(smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q)
+t185:=satz277(g11):is(smpr(1,g11),<xout(1)>g11)
+t186:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+1a:=left1to(pl"n"(1,xm1),1,t183,xout(1)):1to(pl"n"(1,xm1))
+t187:=isinoutn(pl"n"(1,xm1),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,pl"n"(1,xm1),1top(1,xout(1)),t183)):is"n"(inn(1,xout(1)),inn(pl"n"(1,xm1),1a))
+1b:=left1to(x,pl"n"(1,xm1),t181,1a):1to(x)
+t188:=isinoutn(x,inn(pl"n"(1,xm1),1a),trlessis"n"(inn(pl"n"(1,xm1),1a),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),1a),t181)):is"n"(inn(pl"n"(1,xm1),1a),inn(x,1b))
+t189:=tr3is(nat,1,inn(1,xout(1)),inn(pl"n"(1,xm1),1a),inn(x,1b),t186,t187,t188):is"n"(1,inn(x,1b))
+1c:=left1to(xp1,x,t178,1b):1to(xp1)
+t190:=isoutni(xp1,1,satz24a(xp1),inn(x,1b),trlessis"n"(inn(x,1b),x,xp1,1top(x,1b),t178),t189):is"e"(1to(xp1),1out(xp1),1c)
+t191:=isf(1to(xp1),cx,g(xp1,s,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s,f),<xout(1)>g11)
+t192:=tris2(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(1)>g11,t185,t191):is(smpr(1,g11),<1out(xp1)>g(xp1,s,f))
+t193:=symis(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s,t175):is"e"(1to(xp1),<1out(xp1)>s,<xout(xp1)>s4)
+t194:=isf(1to(xp1),cx,f,<1out(xp1)>s,<xout(xp1)>s4,t193):is(<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f))
+t195:=tris(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f),t192,t194):is(smpr(1,g11),<xout(xp1)>g(xp1,s4,f))
+t196:=isf(cx,cx,[t:cx]<smpr(xm1,g10)><t>q,smpr(1,g11),<xout(xp1)>g(xp1,s4,f),t195):is(<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
+t197:=tr3is(cx,smpr(x,g8),smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t182,t184,t196):is(smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
+t198:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s,f)><t>q,smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t197):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q)
+t199:=assq1(a,<xout(xp1)>g(xp1,s4,f),smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q)
+t200:=comq(c,<xout(xp1)>g(xp1,s4,f),<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q):is(<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
+g12:=left(cx,xp1,x,t178,g(xp1,s4,f)):[t:1to(x)]cx
+g13:=left(cx,x,pl"n"(1,xm1),t181,g12):[t:1to(pl"n"(1,xm1))]cx
+g14:=right(cx,1,xm1,g13):[t:1to(xm1)]cx
+g15:=left(cx,pl"n"(1,xm1),1,lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)),g13):[t:1to(1)]cx
+t201:=satz278(x,g(xp1,s4,f)):is(smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
+t202:=symis(cx,smpr(pl"n"(1,xm1),g13),smpr(x,g12),issmpr(x,g12,pl"n"(1,xm1),t180)):is(smpr(x,g12),smpr(pl"n"(1,xm1),g13))
+t203:=satz281(a,1,xm1,g13):is(smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q)
+t204:=satz277(g15):is(smpr(1,g15),<xout(1)>g15)
+t205:=isf(1to(xp1),cx,g(xp1,s4,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s4,f),<xout(1)>g15)
+t206:=tris2(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(1)>g15,t204,t205):is(smpr(1,g15),<1out(xp1)>g(xp1,s4,f))
+t207:=changef1(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s4,<xout(xp1)>s)
+t208:=isf(1to(xp1),cx,f,<1out(xp1)>s4,<xout(xp1)>s,t207):is(<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f))
+t209:=tris(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f),t206,t208):is(smpr(1,g15),<xout(xp1)>g(xp1,s,f))
+t210:=isf(cx,cx,[t:cx]<smpr(xm1,g14)><t>q,smpr(1,g15),<xout(xp1)>g(xp1,s,f),t209):is(<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+t211:=tr3is(cx,smpr(x,g12),smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t202,t203,t210):is(smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+[u:1to(xm1)]
+ua:=right1to(1,xm1,u):1to(pl"n"(1,xm1))
+ub:=left1to(x,pl"n"(1,xm1),t181,ua):1to(x)
+uc:=left1to(xp1,x,t178,ub):1to(xp1)
+[i:is"e"(1to(xp1),uc,xout(xp1))]
+t212:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),xp1,lessisi3(xp1),i):is"n"(inn(x,ub),xp1)
+t213:=satz16a(inn(x,ub),x,xp1,1top(x,ub),satz18a(x,1)):less"n"(inn(x,ub),xp1)
+t214:=<t212>ec3e31(is"n"(inn(x,ub),xp1),more"n"(inn(x,ub),xp1),less"n"(inn(x,ub),xp1),satz10b(inn(x,ub),xp1),t213):con
+u@t215:=[t:is"e"(1to(xp1),uc,xout(xp1))]t214(t):not(is"e"(1to(xp1),uc,xout(xp1)))
+[i:is"e"(1to(xp1),uc,1out(xp1))]
+t216:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),1,satz24a(xp1),i):is"n"(inn(x,ub),1)
+t217:=isinoutn(x,inn(pl"n"(1,xm1),ua),trlessis"n"(inn(pl"n"(1,xm1),ua),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),ua),t181)):is"n"(inn(pl"n"(1,xm1),ua),inn(x,ub))
+t218:=isinoutn(pl"n"(1,xm1),pl"n"(1,inn(xm1,u)),satz19o(inn(xm1,u),xm1,1,1top(xm1,u))):is"n"(pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua))
+t219:=tr3is(nat,pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua),inn(x,ub),1,t218,t217,t216):is"n"(pl"n"(1,inn(xm1,u)),1)
+t220:=satz18(1,inn(xm1,u)):more"n"(pl"n"(1,inn(xm1,u)),1)
+t221:=<t219>ec3e21(is"n"(pl"n"(1,inn(xm1,u)),1),more"n"(pl"n"(1,inn(xm1,u)),1),less"n"(pl"n"(1,inn(xm1,u)),1),satz10b(pl"n"(1,inn(xm1,u)),1),t220):con
+u@t222:=[t:is"e"(1to(xp1),uc,1out(xp1))]t221(t):not(is"e"(1to(xp1),uc,1out(xp1)))
+t223:=changef3(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),uc,t222,t215):is"e"(1to(xp1),<uc>s4,<uc>s)
+t224:=isf(1to(xp1),cx,f,<uc>s4,<uc>s,t223):is(<u>g14,<u>g10)
+n@t225:=fisi(1to(xm1),cx,g10,g14,[t:1to(xm1)]symis(cx,<t>g14,<t>g10,t224(t))):is"e"([t:1to(xm1)]cx,g10,g14)
+t226:=isf([t:1to(xm1)]cx,cx,[u:[t:1to(xm1)]cx]smpr(xm1,u),g10,g14,t225):is(smpr(xm1,g10),smpr(xm1,g14))
+t227:=comq(c,smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q)
+t228:=isf(cx,cx,<<xout(xp1)>g(xp1,s,f)>q,smpr(xm1,g10),smpr(xm1,g14),t226):is(<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+t229:=tris(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t227,t228):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+t230:=tris2(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t229,t211):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12))
+t231:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s4,f)><t>q,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),t230):is(<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
+t232:=symis(cx,smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,t201):is(<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)))
+t233:=t46(s4,f,t174,t177):is(smpr(xp1,g(xp1,s4,f)),smpr(xp1,f))
+t234:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,t179,t198,t199,t200):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
+t235:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)),smpr(xp1,f),t234,t231,t232,t233):prop1(xp1,s,f)
+gamma@t236:=th1"l.imp"(is"n"(x,1),prop1(xp1,s,f),[t:is"n"(x,1)]t172(t),[t:not(is"n"(x,1))]t235(t)):prop1(xp1,s,f)
+i3@t237:=th1"l.imp"(is"e"(1to(xp1),b0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),b0,xout(xp1))]t236(t),[t:not(is"e"(1to(xp1),b0,xout(xp1)))]t148(t)):prop1(xp1,s,f)
+not2@t238:=th1"l.imp"(is"e"(1to(xp1),a0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),a0,xout(xp1))]t237(t),[t:not(is"e"(1to(xp1),a0,xout(xp1)))]t128(t)):prop1(xp1,s,f)
+not1@t239:=th1"l.imp"(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))]t97(t),[t:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]t238(t)):prop1(xp1,s,f)
+b@t240:=th1"l.imp"(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))]t46(t),[t:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))]t239(t)):prop1(xp1,s,f)
+p@t241:=[u:[t:1to(xp1)]1to(xp1)][v:[t:1to(xp1)]cx][w:bijective(1to(xp1),1to(xp1),u)]t240(u,v,w):prop2(xp1)
+t242:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t241,satz4a(x)):prop2(<x>suc)
+x@t243:=induction([t:nat]prop2(t),t6,[t:nat][u:prop2(t)]t242(t,u),x):prop2(x)
+-8283
+satz283:=<b><f><s>t243".8283":is(smpr(x,[t:1to(x)]<<t>s>f),smpr(x,f))
+@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
+shiftl:=shiftl"r"(x,ix,y,iy,ly):nat
+[n:1to(shiftl)]
+shiftr:=shiftr"r"(x,ix,y,iy,ly,n):real
+intshiftr:=intshiftr"r"(x,ix,y,iy,ly,n):intrl(shiftr)
+shiftrls:=shiftrls"r"(x,ix,y,iy,ly,n):lessis(shiftr,x)
+lsshiftr:=lsshiftr"r"(x,ix,y,iy,ly,n):lessis(y,shiftr)
+[m:1to(shiftl)][i:is"r"(shiftr(n),shiftr(m))]
+iseshiftr:=iseshiftr"r"(x,ix,y,iy,ly,n,m,i):is"e"(1to(shiftl),n,m)
+ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
+shiftl1:=shiftl1"r"(x,ix,y,iy,ly,u,a):1to(shiftl)
+shiftinv1:=shiftinv1"r"(x,ix,y,iy,ly,u,a):is"r"(u,shiftr(shiftl1))
+shiftinv2:=shiftinv2"r"(x,ix,y,iy,ly,u,a):is"r"(shiftr(shiftl1),u)
+ly@[f:seq(x,ix,y,iy,ly,cx)]
+shiftf:=shiftf(x,ix,y,iy,ly,cx,f):[t:1to(shiftl)]cx
+[q:[t:cx][u:cx]cx]
+smpri:=smpr(q,shiftl,shiftf):cx
+f@[pi:proofsirrelevant(x,ix,y,iy,ly,cx,f)][q:[t:cx][u:cx]cx][a:assoc(q)][u:real][iu:intrl(u)][l:lessis(y,u)][k:less(u,x)][v:real][iv:intrl(v)][lv:lessis(y,v)][kv:lessis(v,u)]
++8284
+t1:=lessisi1(v,x,satz172a(v,u,x,kv,k)):lessis(v,x)
+-8284
+k@lft:=[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]<t1".8284"(t,v,lt,kt)><lt><v><t>f:[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]cx
+iv@[lv:lessis(pl"r"(u,1rl),v)][kv:lessis(v,x)]
++*8284
+x@[y:real]
+pl:=pl"r"(x,y):real
+mn:=mn"r"(x,y):real
+x@p1:=pl"r"(x,1rl):real
+kv@t2:=satz190c(u,u,0,1rl,lessisi2(u,u,refis(real,u)),lemma1"r"(1rl,0,satz169a(1rl,natpos(1rl,natrl1)))):less(pl(u,0),p1(u))
+t3:=isless1(pl(u,0),u,p1(u),pl02"r"(u,0,refis(real,0)),t2):less(u,p1(u))
+t4:=lessisi1(y,v,satz172b(y,p1(u),v,satz172a(y,u,p1(u),l,t3),lv)):lessis(y,v)
+-8284
+k@rgt:=[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]<kt><t4".8284"(t,v,lt,kt)><v><t>f:[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]cx
++*8284
+k@t5:=intpl(u,iu,1rl,intrl1):intrl(p1(u))
+t6:=satzr25(u,iu,x,ix,k):lessis(p1(u),x)
+t7:=tr3is(real,pl(mn(p1(u),y),mn(p1(x),p1(u))),pl(mn(p1(x),p1(u)),mn(p1(u),y)),mn(pl(mn(p1(x),p1(u)),p1(u)),y),mn(p1(x),y),compl"r"(mn(p1(u),y),mn(p1(x),p1(u))),asspl2"r"(mn(p1(x),p1(u)),p1(u),m0"r"(y)),ismn1"r"(pl(mn(p1(x),p1(u)),p1(u)),p1(x),y,plmn(p1(x),p1(u)))):is"r"(pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y))
+sxy:=shiftl(x,ix,y,iy,ly):nat
+suy:=shiftl(u,iu,y,iy,l):nat
+sxu:=shiftl(x,ix,p1(u),t5,t6):nat
+t8:=tr4is(real,rlofnt(pl"n"(suy,sxu)),pl(rlofnt(suy),rlofnt(sxu)),pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y),rlofnt(sxy),satzr155a(suy,sxu),ispl12"r"(rlofnt(suy),mn(p1(u),y),rlofnt(sxu),mn(p1(x),p1(u)),isrlnt2(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l)),isrlnt2(mn(p1(x),p1(u)),t6"r.shift"(x,ix,p1(u),t5,t6))),t7,isrlnt1(mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly))):is"r"(rlofnt(pl"n"(suy,sxu)),rlofnt(sxy))
+t9:=isntirl(pl"n"(suy,sxu),sxy,t8):is"n"(pl"n"(suy,sxu),sxy)
+t10:=lessisi2"n"(pl"n"(suy,sxu),sxy,t9):lessis"n"(pl"n"(suy,sxu),sxy)
+f1:=left(cx,sxy,pl"n"(suy,sxu),t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(pl"n"(suy,sxu))]cx
+t11:=issmpr(q,sxy,shiftf(x,ix,y,iy,ly,f),pl"n"(suy,sxu),t9):is(smpr(q,pl"n"(suy,sxu),f1),smpri(x,ix,y,iy,ly,f,q))
+fr:=right(cx,suy,sxu,f1):[t:1to(sxu)]cx
+t12:=lessisi1"n"(suy,pl"n"(suy,sxu),satz18a(suy,sxu)):lessis"n"(suy,pl"n"(suy,sxu))
+fl:=left(cx,pl"n"(suy,sxu),suy,t12,f1):[t:1to(suy)]cx
+t12a:=satz281(q,a,suy,sxu,f1):is(smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q)
+[n:1to(sxu)]
+t13:=isinoutn(pl"n"(suy,sxu),pl"n"(suy,inn(sxu,n)),satz19o(inn(sxu,n),sxu,suy,1top(sxu,n))):is"n"(pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)))
+t14:=isinoutn(sxy,inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),trlessis"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),right1to(suy,sxu,n)),t10)):is"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n))))
+n1:=left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n)):1to(sxy)
+t15:=tris(nat,pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,n1),t13,t14):is"n"(pl"n"(suy,inn(sxu,n)),inn(sxy,n1))
+t16:=isnterl(pl"n"(suy,inn(sxu,n)),inn(sxy,n1),t15):is"r"(rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)))
+t17:=satzr155b(suy,inn(sxu,n)):is"r"(pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))))
+t18:=ispl1"r"(mn(p1(u),y),rlofnt(suy),rlofnt(inn(sxu,n)),isrlnt1(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l))):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))))
+t19:=tr3is(real,pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)),t18,t17,t16):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)))
+t20:=ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)),y,t19):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxy,n1)),y))
+t21:=tr3is(real,pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y),pl(rlofnt(inn(sxu,n)),pl(mn(p1(u),y),y)),pl(rlofnt(inn(sxu,n)),p1(u)),ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y,compl"r"(mn(p1(u),y),rlofnt(inn(sxu,n)))),asspl1"r"(rlofnt(inn(sxu,n)),mn(p1(u),y),y),ispl2"r"(pl(mn(p1(u),y),y),p1(u),rlofnt(inn(sxu,n)),plmn(p1(u),y))):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxu,n)),p1(u)))
+t22:=tris1(real,pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),t20,t21):is"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)))
+t23:=ismn1"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),1rl,t22):is"r"(shiftr(x,ix,y,iy,ly,n1),shiftr(x,ix,p1(u),t5,t6,n))
+t24:=intshiftr(x,ix,y,iy,ly,n1):intrl(shiftr(x,ix,y,iy,ly,n1))
+t25:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,shiftr(x,ix,y,iy,ly,n1))
+t26:=shiftrls(x,ix,y,iy,ly,n1):lessis(shiftr(x,ix,y,iy,ly,n1),x)
+t27:=intshiftr(x,ix,p1(u),t5,t6,n):intrl(shiftr(x,ix,p1(u),t5,t6,n))
+t28:=lsshiftr(x,ix,p1(u),t5,t6,n):lessis(p1(u),shiftr(x,ix,p1(u),t5,t6,n))
+t29:=shiftrls(x,ix,p1(u),t5,t6,n):lessis(shiftr(x,ix,p1(u),t5,t6,n),x)
+t30:=t4(shiftr(x,ix,p1(u),t5,t6,n),t27,t28,t29):lessis(y,shiftr(x,ix,p1(u),t5,t6,n))
+t31:=<t23><t29><t30><t27><shiftr(x,ix,p1(u),t5,t6,n)><t26><t25><t24><shiftr(x,ix,y,iy,ly,n1)>pi:is(<n>fr,<n>shiftf(x,ix,p1(u),t5,t6,rgt))
+k@t32:=fisi(1to(sxu),cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt),[t:1to(sxu)]t31(t)):is"e"([t:1to(sxu)]cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt))
+t33:=isf([t:1to(sxu)]cx,cx,[v:[t:1to(sxu)]cx]smpr(q,sxu,v),fr,shiftf(x,ix,p1(u),t5,t6,rgt),t32):is(smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q))
+t34:=isf(cx,cx,<smpr(q,suy,fl)>q,smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q),t33):is(<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q)
+[n:1to(suy)]
+t35:=isinoutn(pl"n"(suy,sxu),inn(suy,n),trlessis"n"(inn(suy,n),suy,pl"n"(suy,sxu),1top(suy,n),t12)):is"n"(inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)))
+t36:=isinoutn(sxy,inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),trlessis"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),t10)):is"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n))))
+n2:=left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n)):1to(sxy)
+t37:=tris(nat,inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,n2),t35,t36):is"n"(inn(suy,n),inn(sxy,n2))
+t38:=isnterl(inn(suy,n),inn(sxy,n2),t37):is"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)))
+t39:=ispl1"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)),y,t38):is"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y))
+t40:=ismn1"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y),1rl,t39):is"r"(shiftr(u,iu,y,iy,l,n),shiftr(x,ix,y,iy,ly,n2))
+t41:=intshiftr(u,iu,y,iy,l,n):intrl(shiftr(u,iu,y,iy,l,n))
+t42:=lsshiftr(u,iu,y,iy,l,n):lessis(y,shiftr(u,iu,y,iy,l,n))
+t43:=shiftrls(u,iu,y,iy,l,n):lessis(shiftr(u,iu,y,iy,l,n),u)
+t44:=t1(shiftr(u,iu,y,iy,l,n),t41,t42,t43):lessis(shiftr(u,iu,y,iy,l,n),x)
+t45:=intshiftr(x,ix,y,iy,ly,n2):intrl(shiftr(x,ix,y,iy,ly,n2))
+t46:=lsshiftr(x,ix,y,iy,ly,n2):lessis(y,shiftr(x,ix,y,iy,ly,n2))
+t47:=shiftrls(x,ix,y,iy,ly,n2):lessis(shiftr(x,ix,y,iy,ly,n2),x)
+t48:=<t40><t47><t46><t45><shiftr(x,ix,y,iy,ly,n2)><t44><t42><t41><shiftr(u,iu,y,iy,l,n)>pi:is(<n>shiftf(u,iu,y,iy,l,lft),<n>fl)
+t49:=symis(cx,<n>shiftf(u,iu,y,iy,l,lft),<n>fl,t48):is(<n>fl,<n>shiftf(u,iu,y,iy,l,lft))
+k@t50:=fisi(1to(suy),cx,fl,shiftf(u,iu,y,iy,l,lft),[t:1to(suy)]t49(t)):is"e"([t:1to(suy)]cx,fl,shiftf(u,iu,y,iy,l,lft))
+t51:=isf([t:1to(suy)]cx,cx,[v:[t:1to(suy)]cx]smpr(q,suy,v),fl,shiftf(u,iu,y,iy,l,lft),t50):is(smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q))
+t52:=isf(cx,cx,[t:cx]<smpri(x,ix,p1(u),t5,t6,rgt,q)><t>q,smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q),t51):is(<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
+t53:=tr3is(cx,smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,t12a,t34,t52):is(smpr(q,pl"n"(suy,sxu),f1),<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
+-8284
+k@satz284:=tris1(cx,smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,smpr(q,pl"n"(suy".8284",sxu".8284"),f1".8284"),t11".8284",t53".8284"):is(smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
+q@[v:real][iv:intrl(v)][w:real][iw:intrl(w)][lw:lessis(pl"r"(y,v),w)][kw:lessis(w,pl"r"(x,v))]
++8285
+x@[y:real]
+pl:=pl"r"(x,y):real
+mn:=mn"r"(x,y):real
+x@p1:=pl"r"(x,1rl):real
+kw@t1:=th9"l.or"(less(pl(y,v),w),is"r"(pl(y,v),w),less(mn(pl(y,v),v),mn(w,v)),is"r"(mn(pl(y,v),v),mn(w,v)),lw,[t:less(pl(y,v),w)]satz188f(pl(y,v),w,m0"r"(v),t),[t:is"r"(pl(y,v),w)]ismn1"r"(pl(y,v),w,v,t)):lessis(mn(pl(y,v),v),mn(w,v))
+t2:=islessis1(mn(pl(y,v),v),y,mn(w,v),mnpl(y,v),t1):lessis(y,mn(w,v))
+t3:=th9"l.or"(less(w,pl(x,v)),is"r"(w,pl(x,v)),less(mn(w,v),mn(pl(x,v),v)),is"r"(mn(w,v),mn(pl(x,v),v)),kw,[t:less(w,pl(x,v))]satz188f(w,pl(x,v),m0"r"(v),t),[t:is"r"(w,pl(x,v))]ismn1"r"(w,pl(x,v),v,t)):lessis(mn(w,v),mn(pl(x,v),v))
+t4:=islessis2(mn(pl(x,v),v),x,mn(w,v),mnpl(x,v),t3):lessis(mn(w,v),x)
+-8285
+iv@sft:=[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]<t4".8285"(t,w,lt,kt)><t2".8285"(t,w,lt,kt)><intmn(t,w,v,iv)><mn"r"(t,v)>f:[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]cx
++*8285
+iv@t5:=tris(real,m0"r"(pl(y,v)),m0"r"(pl(v,y)),pl(m0"r"(v),m0"r"(y)),ism0"r"(pl(y,v),pl(v,y),compl"r"(y,v)),satz180(v,y)):is"r"(m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)))
+t6:=tr3is(real,mn(pl(1rl,pl(x,v)),v),pl(1rl,mn(pl(x,v),v)),pl(1rl,x),p1(x),asspl1"r"(1rl,pl(x,v),m0"r"(v)),ispl2"r"(mn(pl(x,v),v),x,1rl,mnpl(x,v)),compl"r"(1rl,x)):is"r"(mn(pl(1rl,pl(x,v)),v),p1(x))
+t7:=tr3is(real,mn(p1(pl(x,v)),pl(y,v)),pl(pl(1rl,pl(x,v)),pl(m0"r"(v),m0"r"(y))),mn(mn(pl(1rl,pl(x,v)),v),y),mn(p1(x),y),ispl12"r"(p1(pl(x,v)),pl(1rl,pl(x,v)),m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)),compl"r"(pl(x,v),1rl),t5),asspl2"r"(pl(1rl,pl(x,v)),m0"r"(v),m0"r"(y)),ismn1"r"(mn(pl(1rl,pl(x,v)),v),p1(x),y,t6)):is"r"(mn(p1(pl(x,v)),pl(y,v)),mn(p1(x),y))
+t8:=th9"l.or"(less(y,x),is"r"(y,x),less(pl(y,v),pl(x,v)),is"r"(pl(y,v),pl(x,v)),ly,[t:less(y,x)]satz188f(y,x,v,t),[t:is"r"(y,x)]ispl1"r"(y,x,v,t)):lessis(pl(y,v),pl(x,v))
+s0:=shiftl(x,ix,y,iy,ly):nat
+sv:=shiftl(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8):nat
+t9:=isrlent(mn(p1(pl(x,v)),pl(y,v)),t6"r.shift"(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8),mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly),t7):is"n"(sv,s0)
+t10:=lessisi2"n"(sv,s0,t9):lessis"n"(sv,s0)
+f1:=left(cx,s0,sv,t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(sv)]cx
+t11:=issmpr(q,s0,shiftf(x,ix,y,iy,ly,f),sv,t9):is(smpr(q,sv,f1),smpri(x,ix,y,iy,ly,f,q))
+[n:1to(sv)]
+t12:=isinoutn(s0,inn(sv,n),trlessis"n"(inn(sv,n),sv,s0,1top(sv,n),t10)):is"n"(inn(sv,n),inn(s0,left1to(s0,sv,t10,n)))
+n1:=left1to(s0,sv,t10,n):1to(s0)
+t13:=isnterl(inn(sv,n),inn(s0,n1),t12):is"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)))
+t14:=tris(real,mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(sv,n)),mn(pl(y,v),v)),pl(rlofnt(inn(s0,n1)),y),asspl1"r"(rlofnt(inn(sv,n)),pl(y,v),m0"r"(v)),ispl12"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)),mn(pl(y,v),v),y,t13,mnpl(y,v))):is"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y))
+st0:=shiftr(x,ix,y,iy,ly,n1):real
+stv:=shiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):real
+t15:=tr4is(real,mn(stv,v),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(1rl),m0"r"(v))),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(v),m0"r"(1rl))),mn(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),1rl),st0,asspl1"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(1rl),m0"r"(v)),ispl2"r"(pl(m0"r"(1rl),m0"r"(v)),pl(m0"r"(v),m0"r"(1rl)),pl(rlofnt(inn(sv,n)),pl(y,v)),compl"r"(m0"r"(1rl),m0"r"(v))),asspl2"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(v),m0"r"(1rl)),ismn1"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y),1rl,t14)):is"r"(mn(stv,v),st0)
+t16:=intshiftr(x,ix,y,iy,ly,n1):intrl(st0)
+t17:=shiftrls(x,ix,y,iy,ly,n1):lessis(st0,x)
+t18:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,st0)
+t19:=intshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):intrl(stv)
+t20:=shiftrls(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(stv,pl(x,v))
+t21:=lsshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(pl(y,v),stv)
+t22:=intmn(stv,t19,v,iv):intrl(mn(stv,v))
+t23:=t2(stv,t19,t21,t20):lessis(y,mn(stv,v))
+t24:=t4(stv,t19,t21,t20):lessis(mn(stv,v),x)
+t25:=<t15><t17><t18><t16><st0><t24><t23><t22><mn(stv,v)>pi:is(<n>shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),<n>f1)
+iv@t26:=fisi(1to(sv),cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,[t:1to(sv)]t25(t)):is"e"([t:1to(sv)]cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1)
+t27:=isf([t:1to(sv)]cx,cx,[w:[t:1to(sv)]cx]smpr(q,sv,w),shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,t26):is(smpri(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft,q),smpr(q,sv,f1))
+-8285
+iv@lemma285:=t8".8285":lessis(pl"r"(y,v),pl"r"(x,v))
+satz285:=tris(cx,smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpr(q,sv".8285",f1".8285"),smpri(x,ix,y,iy,ly,f,q),t27".8285",t11".8285"):is(smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpri(x,ix,y,iy,ly,f,q))
+ly@[s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][f:seq(x,ix,y,iy,ly,cx)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)]
+us:=<ul><lu><iu><u>s:real
++8286
+t1:=<ul><lu><iu><u>ins:and3(intrl(us),lessis(y,us),lessis(us,x))
+-8286
+inseqe1:=t22"r.shift"(x,ix,y,iy,ly,us,t1".8286"):intrl(us)
+inseqe2:=t23"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(y,us)
+inseqe3:=t24"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(us,x)
+usf:=<inseqe3><inseqe2><inseqe1><us>f:cx
+f@permseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]usf(t,u,v,w):[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]cx
+q@[a:assoc(q)][c:commut(q)][s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][pri:proofsirrelevant(x,ix,y,iy,ly,real,s)][ps:perm(x,ix,y,iy,ly,s)]
++*8286
+ps@ss:=shiftseq(x,ix,y,iy,ly,s,ins):[t:1to(shiftl)]1to(shiftl)
+t2:=satz283(q,a,c,shiftl,ss,bijshiftseq(x,ix,y,iy,ly,s,ins,pri,ps),shiftf(f)):is(smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)),smpri(f,q))
+[n:1to(shiftl)]
+ns:=us(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):real
+t3:=shiftinv1(ns,t34"r.shift"(x,ix,y,iy,ly,s,ins,n)):is"r"(ns,shiftr(<n>ss))
+t4:=inseqe1(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):intrl(ns)
+t5:=inseqe2(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(y,ns)
+t6:=inseqe3(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(ns,x)
+t7:=intshiftr(<n>ss):intrl(shiftr(<n>ss))
+t8:=lsshiftr(<n>ss):lessis(y,shiftr(<n>ss))
+t9:=shiftrls(<n>ss):lessis(shiftr(<n>ss),x)
+t10:=<t3><t9><t8><t7><shiftr(<n>ss)><t6><t5><t4><ns>pi:is(<n>shiftf(permseq(s,ins,f)),<<n>ss>shiftf(f))
+ps@t11:=fisi(1to(shiftl),cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),[t:1to(shiftl)]t10(t)):is"e"([t:1to(shiftl)]cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f))
+t12:=isf([t:1to(shiftl)]cx,cx,[u:[t:1to(shiftl)]cx]smpr(q,shiftl,u),shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),t11):is(smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)))
+-8286
+ps@satz286:=tris(cx,smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss".8286">shiftf(f)),smpri(f,q),t12".8286",t2".8286"):is(smpri(permseq(s,ins,f),q),smpri(f,q))
+@[x:nat][f:[t:1to(x)]cx]
+modf:=[t:1to(x)]pli(mod(<t>f),0):[t:1to(x)]cx
++8287
+[r:real]
+prop1:=lessis(mod(sum(x,f)),r):'prop'
+prop2:=is(sum(x,modf(f)),pli(r,0)):'prop'
+prop3:=and(prop1,prop2):'prop'
+f@prop4:=some"r"([t:real]prop3(t)):'prop'
+x@prop5:=[u:[t:1to(x)]cx]prop4(u):'prop'
+@[f:[t:1to(1)]cx]
+t1:=satz277([t:cx][u:cx]pl(t,u),f):is(sum(1,f),<xout(1)>f)
+t2:=ismod(sum(1,f),<xout(1)>f,t1):is"r"(mod(sum(1,f)),mod(<xout(1)>f))
+t3:=lessisi2(mod(sum(1,f)),mod(<xout(1)>f),t2):prop1(1,f,mod(<xout(1)>f))
+t4:=satz277([t:cx][u:cx]pl(t,u),modf(1,f)):prop2(1,f,mod(<xout(1)>f))
+t5:=andi(prop1(1,f,mod(<xout(1)>f)),prop2(1,f,mod(<xout(1)>f)),t3,t4):prop3(1,f,mod(<xout(1)>f))
+t6:=somei(real,[t:real]prop3(1,f,t),mod(<xout(1)>f),t5):prop4(1,f)
+@t7:=[u:[t:1to(1)]cx]t6(u):prop5(1)
+x@[p:prop5(x)][f:[t:1to(pl"n"(x,1))]cx]
+t8:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
+lf:=left(cx,pl"n"(x,1),x,t8,f):[t:1to(x)]cx
+[r:real][pr:prop3(lf,r)]
+t9:=ande1(prop1(lf,r),prop2(lf,r),pr):prop1(lf,r)
+t10:=ande2(prop1(lf,r),prop2(lf,r),pr):prop2(lf,r)
+t11:=satz278([t:cx][u:cx]pl(t,u),x,f):is(sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f))
+t12:=ismod(pl(sum(x,lf),<xout(pl"n"(x,1))>f),sum(pl"n"(x,1),f),symis(cx,sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f),t11)):is"r"(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)))
+m:=mod(<xout(pl"n"(x,1))>f):real
+t13:=islessis1(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),t12,satz271(sum(x,lf),<xout(pl"n"(x,1))>f)):lessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m))
+t14:=th9"l.or"(less(mod(sum(x,lf)),r),is"r"(mod(sum(x,lf)),r),less(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),is"r"(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),t9,[t:less(mod(sum(x,lf)),r)]satz188f(mod(sum(x,lf)),r,m,t),[t:is"r"(mod(sum(x,lf)),r)]ispl1"r"(mod(sum(x,lf)),r,m,t)):lessis(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m))
+t15:=trlessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),pl"r"(r,m),t13,t14):prop1(pl"n"(x,1),f,pl"r"(r,m))
+lmf:=left(cx,pl"n"(x,1),x,t8,modf(pl"n"(x,1),f)):[t:1to(x)]cx
+t16:=satz278([t:cx][u:cx]pl(t,u),x,modf(pl"n"(x,1),f)):is(sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)))
+t17:=ispl1(sum(x,lmf),pli(r,0),pli(m,0),t10):is(pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)))
+t18:=plis12a(r,0,m,0):is(pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)))
+t19:=isrecx2(pl"r"(0,0),0,pl"r"(r,m),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0))
+t20:=tr4is(cx,sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0),t16,t17,t18,t19):prop2(pl"n"(x,1),f,pl"r"(r,m))
+t21:=andi(prop1(pl"n"(x,1),f,pl"r"(r,m)),prop2(pl"n"(x,1),f,pl"r"(r,m)),t15,t20):prop3(pl"n"(x,1),f,pl"r"(r,m))
+t22:=somei(real,[t:real]prop3(pl"n"(x,1),f,t),pl"r"(r,m),t21):prop4(pl"n"(x,1),f)
+f@t23:=someapp(real,[t:real]prop3(lf,t),<lf>p,prop4(pl"n"(x,1),f),[t:real][u:prop3(lf,t)]t22(t,u)):prop4(pl"n"(x,1),f)
+p@t25:=[u:[t:1to(pl"n"(x,1))]cx]t23(u):prop5(pl"n"(x,1))
+t26:=isp(nat,[t:nat]prop5(t),pl"n"(x,1),<x>suc,t25,satz4a(x)):prop5(<x>suc)
+-8287
+satz287:=<f>induction([t:nat]prop5".8287"(t),t7".8287",[t:nat][u:prop5".8287"(t)]t26".8287"(t,u),x):some"r"([t:real]and(lessis(mod(sum(x,f)),t),is(sum(x,modf(f)),pli(t,0))))
++8288
+prop1:=is(pli(mod(prod(x,f)),0),prod(x,modf(f))):'prop'
+x@prop2:=[u:[t:1to(x)]cx]prop1(u):'prop'
+@[f:[t:1to(1)]cx]
+t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
+t2:=ismod(prod(1,f),<xout(1)>f,t1):is"r"(mod(prod(1,f)),mod(<xout(1)>f))
+t3:=isrecx1(mod(prod(1,f)),mod(<xout(1)>f),0,t2):is(pli(mod(prod(1,f)),0),pli(mod(<xout(1)>f),0))
+t4:=satz277([t:cx][u:cx]ts(t,u),modf(1,f)):is(prod(1,modf(1,f)),pli(mod(<xout(1)>f),0))
+t5:=tris2(cx,pli(mod(prod(1,f)),0),prod(1,modf(1,f)),pli(mod(<xout(1)>f),0),t3,t4):prop1(1,f)
+@t6:=[u:[t:1to(1)]cx]t5(u):prop2(1)
+x@[p:prop2(x)][f:[t:1to(pl"n"(x,1))]cx]
+t7:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
+lf:=left(cx,pl"n"(x,1),x,t7,f):[t:1to(x)]cx
+t8:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
+m:=mod(<xout(pl"n"(x,1))>f):real
+t9:=ismod(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),t8):is"r"(mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)))
+t10:=satz268(prod(x,lf),<xout(pl"n"(x,1))>f):is"r"(mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m))
+t11:=tris(real,mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m),t9,t10):is"r"(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m))
+t12:=isrecx1(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m),0,t11):is(pli(mod(prod(pl"n"(x,1),f)),0),pli(ts"r"(mod(prod(x,lf)),m),0))
+lmf:=left(cx,pl"n"(x,1),x,t7,modf(pl"n"(x,1),f)):[t:1to(x)]cx
+t13:=satz278([t:cx][u:cx]ts(t,u),x,modf(pl"n"(x,1),f)):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)))
+t14:=symis(cx,pli(mod(prod(x,lf)),0),prod(x,lmf),<lf>p):is(prod(x,lmf),pli(mod(prod(x,lf)),0))
+t15:=ists1(prod(x,lmf),pli(mod(prod(x,lf)),0),pli(m,0),t14):is(ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)))
+t16:=tsis12a(mod(prod(x,lf)),0,m,0):is(ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))))
+t17:=tris(real,mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),mn"r"(ts"r"(mod(prod(x,lf)),m),0),ts"r"(mod(prod(x,lf)),m),ismn2"r"(ts"r"(0,0),0,ts"r"(mod(prod(x,lf)),m),ts01"r"(0,0,refis(real,0))),pl02"r"(ts"r"(mod(prod(x,lf)),m),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m))
+t18:=tris(real,pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),pl"r"(0,0),0,ispl12"r"(ts"r"(mod(prod(x,lf)),0),0,ts"r"(0,m),0,ts02"r"(mod(prod(x,lf)),0,refis(real,0)),ts01"r"(0,m,refis(real,0))),pl01"r"(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0)
+t19:=isrecx12(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0,t17,t18):is(pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0))
+t20:=tr4is(cx,prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0),t13,t15,t16,t19):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0))
+t21:=tris2(cx,pli(mod(prod(pl"n"(x,1),f)),0),prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0),t12,t20):prop1(pl"n"(x,1),f)
+p@t21a:=[u:[t:1to(pl"n"(x,1))]cx]t21(u):prop2(pl"n"(x,1))
+t22:=isp(nat,[t:nat]prop2(t),pl"n"(x,1),<x>suc,t21a,satz4a(x)):prop2(<x>suc)
+-8288
+satz288:=<f>induction([t:nat]prop2".8288"(t),t6".8288",[t:nat][u:prop2".8288"(t)]t22".8288"(t,u),x):is(pli(mod(prod(x,f)),0),prod(x,modf(f)))
++8289
+prop1:=is(prod(x,f),0c):'prop'
+prop2:=some"l"(1to(x),[t:1to(x)]is(<t>f,0c)):'prop'
+prop3:=iff(prop1,prop2):'prop'
+x@prop4:=[u:[t:1to(x)]cx]prop3(u):'prop'
+@[f:[t:1to(1)]cx]
+t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
+[p:prop1(1,f)]
+t2:=tris1(cx,<xout(1)>f,0c,prod(1,f),t1,p):is(<xout(1)>f,0c)
+t3:=somei(1to(1),[t:1to(1)]is(<t>f,0c),xout(1),t2):prop2(1,f)
+f@[p:prop2(1,f)][u:1to(1)][i:is(<u>f,0c)]
+t4:=th1"n.singlet"(u):is"e"(1to(1),u,xout(1))
+t5:=tr3is(cx,prod(1,f),<xout(1)>f,<u>f,0c,t1,isf(1to(1),cx,f,xout(1),u,symis(1to(1),u,xout(1),t4)),i):prop1(1,f)
+p@t6:=someapp(1to(1),[t:1to(1)]is(<t>f,0c),p,prop1(1,f),[t:1to(1)][u:is(<t>f,0c)]t5(t,u)):prop1(1,f)
+f@t7:=iffi(prop1(1,f),prop2(1,f),[t:prop1(1,f)]t3(t),[t:prop2(1,f)]t6(t)):prop3(1,f)
+@t8:=[u:[t:1to(1)]cx]t7(u):prop4(1)
+x@[p:prop4(x)][f:[t:1to(pl"n"(x,1))]cx]
+t9:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
+lf:=left(cx,pl"n"(x,1),x,t9,f):[t:1to(x)]cx
+t10:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
+[q:prop1(pl"n"(x,1),f)]
+t11:=tris1(cx,ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,prod(pl"n"(x,1),f),t10,q):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+t12:=satz221c(prod(x,lf),<xout(pl"n"(x,1))>f,t11):or(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c))
+[i:is(prod(x,lf),0c)]
+t13:=th3"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,i):prop2(x,lf)
+[n:1to(x)][j:is(<n>lf,0c)]
+t14:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),left1to(pl"n"(x,1),x,t9,n),j):prop2(pl"n"(x,1),f)
+i@t15:=someapp(1to(x),[t:1to(x)]is(<t>lf,0c),t13,prop2(pl"n"(x,1),f),[t:1to(x)][u:is(<t>lf,0c)]t14(t,u)):prop2(pl"n"(x,1),f)
+q@[i:is(<xout(pl"n"(x,1))>f,0c)]
+t16:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),xout(pl"n"(x,1)),i):prop2(pl"n"(x,1),f)
+q@t17:=orapp(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c),prop2(pl"n"(x,1),f),t12,[t:is(prod(x,lf),0c)]t15(t),[t:is(<xout(pl"n"(x,1))>f,0c)]t16(t)):prop2(pl"n"(x,1),f)
+f@[q:prop2(pl"n"(x,1),f)][n:1to(pl"n"(x,1))][i:is(<n>f,0c)][j:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]
+t18:=tris1(cx,<xout(pl"n"(x,1))>f,0c,<n>f,isf(1to(pl"n"(x,1)),cx,f,n,xout(pl"n"(x,1)),j),i):is(<xout(pl"n"(x,1))>f,0c)
+t20:=satz221b(prod(x,lf),<xout(pl"n"(x,1))>f,t18):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+i@[m:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]
+n1:=inn(pl"n"(x,1),n):nat
+[j:is"n"(n1,pl"n"(x,1))]
+t21:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),pl"n"(x,1),lessisi3(pl"n"(x,1)),j):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)))
+t22:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)),isoutinn(pl"n"(x,1),n),t21):is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))
+m@t23:=th3"l.imp"(is"n"(n1,pl"n"(x,1)),is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),m,[t:is"n"(n1,pl"n"(x,1))]t22(t)):nis"n"(n1,pl"n"(x,1))
+t24:=ore1(less"n"(n1,pl"n"(x,1)),is"n"(n1,pl"n"(x,1)),1top(pl"n"(x,1),n),t23):less"n"(n1,pl"n"(x,1))
+t25:=satz26(x,n1,t24):lessis"n"(n1,x)
+n2:=outn(x,n1,t25):1to(x)
+t26:=isinoutn(x,n1,t25):is"n"(n1,inn(x,n2))
+t27:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),inn(x,n2),trlessis"n"(inn(x,n2),x,pl"n"(x,1),1top(x,n2),t9),t26):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2))
+t28:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2),isoutinn(pl"n"(x,1),n),t27):is"e"(1to(pl"n"(x,1)),n,left1to(pl"n"(x,1),x,t9,n2))
+t29:=isf(1to(pl"n"(x,1)),cx,f,n,left1to(pl"n"(x,1),x,t9,n2),t28):is(<n>f,<n2>lf)
+t30:=tris1(cx,<n2>lf,0c,<n>f,t29,i):is(<n2>lf,0c)
+t31:=somei(1to(x),[t:1to(x)]is(<t>lf,0c),n2,t30):prop2(x,lf)
+t32:=th4"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,t31):prop1(x,lf)
+t34:=satz221a(prod(x,lf),<xout(pl"n"(x,1))>f,t32):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+i@t35:=th1"l.imp"(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c),[t:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]t20(t),[t:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]t34(t)):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+t36:=tris(cx,prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,t10,t35):prop1(pl"n"(x,1),f)
+q@t37:=someapp(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),q,prop1(pl"n"(x,1),f),[t:1to(pl"n"(x,1))][u:is(<t>f,0c)]t36(t,u)):prop1(pl"n"(x,1),f)
+f@t38:=iffi(prop1(pl"n"(x,1),f),prop2(pl"n"(x,1),f),[t:prop1(pl"n"(x,1),f)]t17(t),[t:prop2(pl"n"(x,1),f)]t37(t)):prop3(pl"n"(x,1),f)
+p@t39:=[u:[t:1to(pl"n"(x,1))]cx]t38(u):prop4(pl"n"(x,1))
+t40:=isp(nat,[t:nat]prop4(t),pl"n"(x,1),<x>suc,t39,satz4a(x)):prop4(<x>suc)
+-8289
+satz289:=<f>induction([t:nat]prop4".8289"(t),t8".8289",[t:nat][u:prop4".8289"(t)]t40".8289"(t,u),x):iff(is(prod(x,f),0c),some"l"(1to(x),[t:1to(x)]is(<t>f,0c)))
+[i:is(prod(x,f),0c)]
+satz289a:=th3"l.iff"(prop1".8289",prop2".8289",satz289,i):some"l"(1to(x),[t:1to(x)]is(<t>f,0c))
+f@[n:1to(x)][i:is(<n>f,0c)]
++*8289
+i"c"@t41:=somei(1to(x),[t:1to(x)]is(<t>f,0c),n,i):prop2
+-8289
+i@satz289b:=th4"l.iff"(prop1".8289",prop2".8289",satz289,t41".8289"):is(prod(x,f),0c)
+@[x:complex][m:real][mi:intrl(m)][o:or(nis(x,0c),pos(m))]
++v9
+[p:pos(m)]
+t1:=posintnatrl(m,p,mi):natrl(m)
+m1:=ntofrl(m,t1):nat
+pw1:=prod(m1,[t:1to(m1)]x):cx
+-v9
+x@[y:complex][m:real][n:real][i:is(x,y)][j:is"r"(m,n)][mi1:intrl(m)][ni1:intrl(n)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(n))]
++*v9
+oy@[mp:pos(m)][np:pos(n)]
+m0:=m1(x,m,mi1,ox,mp):nat
+n0:=m1(y,n,ni1,oy,np):nat
+t2:=isrlent(m,t1(x,m,mi1,ox,mp),n,t1(y,n,ni1,oy,np),j):is"n"(m0,n0)
+t3:=lessisi2"n"(m0,n0,t2):lessis"n"(m0,n0)
+t4:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]y,m0,t2):is(prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np))
+t5:=fisi(1to(m0),cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),[t:1to(m0)]i):is"e"([t:1to(m0)]cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y))
+t6:=isf([t:1to(m0)]cx,cx,[u:[t:1to(m0)]cx]prod(m0,u),[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),t5):is(pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)))
+t7:=tris(cx,pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np),t6,t4):is(pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,np))
+p@[p1:pos(m)]
+t8:=t7(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,p,p1):is(pw1(p),pw1(p1))
+p@[n:nis(x,0c)]
+t9:=th5"l.some"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c),[t:1to(m1)]n):not(some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)))
+t10:=th3"l.imp"(is(pw1,0c),some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)),t9,[t:is(pw1,0c)]satz289a(m1,[u:1to(m1)]x,t)):nis(pw1,0c)
+o@[n:neg(m)]
+mi@t11:=intabs(m,mi):intrl(abs(m))
+n@t12:=satz166b(m,n):pos(abs(m))
+t13:=ori2(nis(x,0c),pos(abs(m)),t12):or(nis(x,0c),pos(abs(m)))
+t14:=ore1(nis(x,0c),pos(m),o,nnotp(m,n)):nis(x,0c)
+t15:=t10(abs(m),t11,t13,t12,t14):nis(pw1(abs(m),t11,t13,t12),0c)
+pw2:=ov(1c,pw1(abs(m),t11,t13,t12),t15):cx
+oy@[nm:neg(m)][nn:neg(n)]
+pwm:=pw1(x,abs(m),t11(x,m,mi1),t13(x,m,mi1,ox,nm),t12(x,m,mi1,ox,nm)):cx
+pwn:=pw1(y,abs(n),t11(y,n,ni1),t13(y,n,ni1,oy,nn),t12(y,n,ni1,oy,nn)):cx
+t16:=t7(abs(m),abs(n),i,isabs(m,n,j),t11(x,m,mi1),t11(y,n,ni1),t13(x,m,mi1,ox,nm),t13(y,n,ni1,oy,nn),t12(x,m,mi1,ox,nm),t12(y,n,ni1,oy,nn)):is(pwm,pwn)
+t17:=isov2(pwm,pwn,1c,t16,t15(x,m,mi1,ox,nm),t15(y,n,ni1,oy,nn)):is(pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,nn))
+n@[n1:neg(m)]
+t18:=t17(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,n,n1):is(pw2(n),pw2(n1))
+o@pw3:=ite"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c)):cx
+n@t19:=itet"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),n):is(pw3,pw2(n))
+o@[nn:not(neg(m))]
+t20:=itef"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),nn):is(pw3,1c)
+nm@t21:=isp(real,[t:real]neg(t),m,n,nm,j):neg(n)
+t22:=t19(x,m,mi1,ox,nm):is(pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm))
+t23:=symis(cx,pw3(y,n,ni1,oy),pw2(y,n,ni1,oy,t21),t19(y,n,ni1,oy,t21)):is(pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy))
+t24:=tr3is(cx,pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy),t22,t17(t21),t23):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
+oy@[nn:not(neg(m))]
+t25:=isp(real,[t:real]not(neg(t)),m,n,nn,j):not(neg(n))
+t26:=t20(x,m,mi1,ox,nn):is(pw3(x,m,mi1,ox),1c)
+t27:=t20(y,n,ni1,oy,t25):is(pw3(y,n,ni1,oy),1c)
+t28:=tris2(cx,pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),1c,t26,t27):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
+oy@t29:=th1"l.imp"(neg(m),is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy)),[t:neg(m)]t24(t),[t:not(neg(m))]t28(t)):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
+-v9
+o@pw:=ite"l.r"(pos(m),cx,[t:pos(m)]pw1".v9"(t),[t:not(pos(m))]pw3".v9",[t:pos(m)][u:pos(m)]t8".v9"(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3".v9")):cx
++*v9
+p@t30:=itet"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),p):is(pw,pw1(p))
+o@[n:not(pos(m))]
+t31:=itef"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),n):is(pw,pw3)
+o@[i:is"r"(m,0)]
+t32:=tris(cx,pw,pw3,1c,t31(0notp(m,i)),t20(0notn(m,i))):is(pw,1c)
+o@[n:neg(m)]
+t33:=tris(cx,pw,pw3,pw2(n),t31(nnotp(m,n)),t19(n)):is(pw,pw2(n))
+-v9
+o@[p:pos(m)]
+posexp:=t30".v9"(p):is(pw(x,m,mi,o),prod(ntofrl(m,posintnatrl(m,p,mi)),[t:1to(ntofrl(m,posintnatrl(m,p,mi)))]x))
+[n:nis(x,0c)]
+lemmapw1:=th2"e.notis"(cx,pw1".v9"(p),0c,pw,t10".v9"(p,n),posexp):nis(pw(x,m,mi,o),0c)
+o@[i:is"r"(m,0)]
+0exp:=t32".v9"(i):is(pw(x,m,mi,o),1c)
+o@[n:neg(m)]
+lemmapw2:=t14".v9"(n):nis(x,0c)
+lemmapw3:=t13".v9"(n):or(nis(x,0c),pos(abs(m)))
++*v9
+n@t34:=t30(abs(m),t11,t13(n),t12(n)):is(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)))
+t35:=isov2(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)),1c,t34,lemmapw1(abs(m),t11,t13(n),t12(n),t14(n)),t15(n)):is(ov(1c,pw(x,abs(m),t11,t13(n)),lemmapw1(abs(m),t11,t13(n),t12(n),t14(n))),pw2(n))
+-v9
+n@negexp:=tris2(cx,pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)),pw2".v9"(n),t33".v9"(n),t35".v9"(n)):is(pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)))
++*v9
+mp@t36:=isp(real,[t:real]pos(t),m,n,mp,j):pos(n)
+t37:=t30(x,m,mi1,ox,mp):is(pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp))
+t38:=symis(cx,pw(y,n,ni1,oy),pw1(y,n,ni1,oy,t36),t30(y,n,ni1,oy,t36)):is(pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy))
+t39:=tr3is(cx,pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy),t37,t7(t36),t38):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
+oy@[np:not(pos(m))]
+t40:=isp(real,[t:real]not(pos(t)),m,n,np,j):not(pos(n))
+t41:=t31(x,m,mi1,ox,np):is(pw(x,m,mi1,ox),pw3(x,m,mi1,ox))
+t42:=symis(cx,pw(y,n,ni1,oy),pw3(y,n,ni1,oy),t31(y,n,ni1,oy,t40)):is(pw3(y,n,ni1,oy),pw(y,n,ni1,oy))
+t43:=tr3is(cx,pw(x,m,mi1,ox),pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),pw(y,n,ni1,oy),t41,t29,t42):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
+-v9
+oy@ispw12:=th1"l.imp"(pos(m),is(pw(x,m,mi1,ox),pw(y,n,ni1,oy)),[t:pos(m)]t39".v9"(t),[t:not(pos(m))]t43".v9"(t)):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
+m@[i:is(x,y)][mi:intrl(m)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(m))]
+ispw1:=ispw12(x,y,m,m,i,refis(real,m),mi,mi,ox,oy):is(pw(x,m,mi,ox),pw(y,m,mi,oy))
+x@[m:real][n:real][i:is"r"(m,n)][mi:intrl(m)][ni:intrl(n)][om:or(nis(x,0c),pos(m))][on:or(nis(x,0c),pos(n))]
+ispw2:=ispw12(x,x,m,n,refis(cx,x),i,mi,ni,om,on):is(pw(x,m,mi,om),pw(x,n,ni,on))
+o@[n:nis(x,0c)]
++9290
+[p:pos(m)]
+t1:=lemmapw1(p,n):nis(pw(x,m,mi,o),0c)
+@[i:is(1c,0c)]
+t2:=tr3is(real,1rl,re(1c),re(0c),0,isre(1rl,0),iscere(1c,0c,i),reis(0,0)):is"r"(1rl,0)
+-9290
+@1not0:=th3"l.imp"(is(1c,0c),is"r"(1rl,0),pnot0(1rl,pos1),[t:is(1c,0c)]t2".9290"(t)):nis(1c,0c)
++*9290
+n@[i:is"r"(m,0)]
+t4:=th2"e.notis"(cx,1c,0c,pw(x,m,mi,o),1not0,0exp(i)):nis(pw(x,m,mi,o),0c)
+n@[nm:neg(m)]
+p0:=pw(x,abs(m),intabs(m,mi),lemmapw3(nm)):cx
+t5:=lemmapw1(x,abs(m),intabs(m,mi),lemmapw3(nm),satz166b(m,nm),lemmapw2(nm)):nis(p0,0c)
+t6:=tris(cx,ts(pw(x,m,mi,o),p0),ts(ov(1c,p0,t5),p0),1c,ists1(pw(x,m,mi,o),ov(1c,p0,t5),p0,negexp(nm)),satz229e(1c,p0,t5)):is(ts(pw(x,m,mi,o),p0),1c)
+t7:=th2"e.notis"(cx,1c,0c,ts(pw(x,m,mi,o),p0),1not0,t6):nis(ts(pw(x,m,mi,o),p0),0c)
+t8:=th3"l.imp"(is(pw(x,m,mi,o),0c),is(ts(pw(x,m,mi,o),p0),0c),t7,[t:is(pw(x,m,mi,o),0c)]satz221a(pw(x,m,mi,o),p0,t)):nis(pw(x,m,mi,o),0c)
+-9290
+n@satz290:=rapp(m,nis(pw(x,m,mi,o),0c),[t:pos(m)]t1".9290"(t),[t:is"r"(m,0)]t4".9290"(t),[t:neg(m)]t8".9290"(t)):nis(pw(x,m,mi,o),0c)
+x@lemma291:=ori2(nis(x,0c),pos(1rl),pos1):or(nis(x,0c),pos(1rl))
++9291
+1a:=ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)):nat
+t1:=posexp(x,1rl,intrl1,lemma291,pos1):is(pw(x,1rl,intrl1,lemma291),prod(1a,[t:1to(1a)]x))
+t2:=tris(nat,1,ntofrl(1rl,natrl1),ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)),isntrl1(1),isrlent(1rl,natrl1,1rl,posintnatrl(1rl,pos1,intrl1),refis(real,1rl))):is"n"(1,1a)
+t3:=lessisi2"n"(1,1a,t2):lessis"n"(1,1a)
+t4:=issmpr([t:cx][u:cx]ts(t,u),1a,[t:1to(1a)]x,1,t2):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),prod(1a,[t:1to(1a)]x))
+t5:=satz277([t:cx][u:cx]ts(t,u),left(cx,1a,1,t3,[t:1to(1a)]x)):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),x)
+t6:=tris1(cx,prod(1a,[t:1to(1a)]x),x,prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),t4,t5):is(prod(1a,[t:1to(1a)]x),x)
+-9291
+satz291:=tris(cx,pw(x,1rl,intrl1,lemma291),prod(1a".9291",[t:1to(1a".9291")]x),x,t1".9291",t6".9291"):is(pw(x,1rl,intrl1,lemma291),x)
+[y:cx][m:real][mi:intrl(m)][o:or(and(nis(x,0c),nis(y,0c)),pos(m))]
++9292
+[a:and(nis(x,0c),nis(y,0c))]
+t1:=ande1(nis(x,0c),nis(y,0c),a):nis(x,0c)
+t2:=ande2(nis(x,0c),nis(y,0c),a):nis(y,0c)
+t3:=satz221d(x,y,t1,t2):nis(ts(x,y),0c)
+-9292
+lemma292a:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(x,0c),o,[t:and(nis(x,0c),nis(y,0c))]t1".9292"(t)):or(nis(x,0c),pos(m))
+lemma292b:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(y,0c),o,[t:and(nis(x,0c),nis(y,0c))]t2".9292"(t)):or(nis(y,0c),pos(m))
+lemma292c:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(ts(x,y),0c),o,[t:and(nis(x,0c),nis(y,0c))]t3".9292"(t)):or(nis(ts(x,y),0c),pos(m))
++*9292
+x@[n:nat]
+nr:=rlofnt(n):real
+t4:=natintrl(nr,natrli(n)):intrl(nr)
+t5:=ori2(nis(x,0c),pos(nr),natpos(nr,natrli(n))):or(nis(x,0c),pos(nr))
+p0:=pw(x,nr,t4,t5):cx
+x@t6:=tris(cx,p0(1),pw(x,1rl,intrl1,lemma291(x)),x,ispw1(x,x,1rl,refis(cx,x),intrl1,t5(1),lemma291(x)),satz291(x)):is(p0(1),x)
+n@n0:=ntofrl(nr,posintnatrl(nr,natpos(nr,natrli(n)),t4)):nat
+t7:=tris(nat,n,ntofrl(nr,natrli(n)),n0,isntrl1(n),isrlent(nr,natrli(n),nr,posintnatrl(nr,natpos(nr,natrli(n)),t4),refis(real,nr))):is"n"(n,n0)
+t8:=lessisi2"n"(n,n0,t7):lessis"n"(n,n0)
+t9:=posexp(x,nr,t4,t5,natpos(nr,natrli(n))):is(p0,prod(n0,[t:1to(n0)]x))
+t10:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]x,n,t7):is(prod(n,left(cx,n0,n,t8,[t:1to(n0)]x)),prod(n0,[t:1to(n0)]x))
+t11:=tris2(cx,p0,prod(n,[t:1to(n)]x),prod(n0,[t:1to(n0)]x),t9,t10):is(p0,prod(n,[t:1to(n)]x))
+n1:=pl"n"(n,1):nat
+t12:=lessisi1"n"(n,n1,satz18a(n,1)):lessis"n"(n,n1)
+t13:=satz278([t:cx][u:cx]ts(t,u),n,[t:1to(n1)]x):is(prod(n1,[t:1to(n1)]x),ts(prod(n,left(cx,n1,n,t12,[t:1to(n1)]x)),x))
+t14:=ists1(p0,prod(n,[t:1to(n)]x),x,t11):is(ts(p0,x),ts(prod(n,[t:1to(n)]x),x))
+t15:=tris2(cx,prod(n1,[t:1to(n1)]x),ts(p0,x),ts(prod(n,[t:1to(n)]x),x),t13,t14):is(prod(n1,[t:1to(n1)]x),ts(p0,x))
+t16:=tris(cx,p0(n1),prod(n1,[t:1to(n1)]x),ts(p0,x),t11(n1),t15):is(p0(n1),ts(p0(n),x))
+y@[n:nat]
+prop1:=is(p0(ts(x,y),n),ts(p0(x,n),p0(y,n))):'prop'
+y@t17:=ists12(p0(x,1),x,p0(y,1),y,t6(x),t6(y)):is(ts(p0(x,1),p0(y,1)),ts(x,y))
+t18:=tris2(cx,p0(ts(x,y),1),ts(p0(x,1),p0(y,1)),ts(x,y),t6(ts(x,y)),t17):prop1(1)
+n@[p:prop1(n)]
+t19:=ists1(p0(ts(x,y),n),ts(p0(x,n),p0(y,n)),ts(x,y),p):is(ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)))
+t20:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),x),ts(p0(x,n),ts(p0(y,n),x)),ts(p0(x,n),ts(x,p0(y,n))),ts(ts(p0(x,n),x),p0(y,n)),assts1(p0(x,n),p0(y,n),x),ists2(ts(p0(y,n),x),ts(x,p0(y,n)),p0(x,n),comts(p0(y,n),x)),assts2(p0(x,n),x,p0(y,n))):is(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)))
+t21:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(ts(p0(x,n),p0(y,n)),x),y),ts(ts(ts(p0(x,n),x),p0(y,n)),y),ts(ts(p0(x,n),x),ts(p0(y,n),y)),assts2(ts(p0(x,n),p0(y,n)),x,y),ists1(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)),y,t20),assts1(ts(p0(x,n),x),p0(y,n),y)):is(ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
+t22:=tr3is(cx,p0(ts(x,y),n1(n)),ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t16(ts(x,y),n),t19,t21):is(p0(ts(x,y),n1(n)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
+t23:=ists12(p0(x,n1(n)),ts(p0(x,n),x),p0(y,n1(n)),ts(p0(y,n),y),t16(x,n),t16(y,n)):is(ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
+t24:=tris2(cx,p0(ts(x,y),n1(n)),ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t22,t23):prop1(n1(n))
+t25:=isp(nat,[t:nat]prop1(t),n1(n),<n>suc,t24,satz4a(n)):prop1(<n>suc)
+n@t26:=induction([t:nat]prop1(t),t18,[t:nat][u:prop1(t)]t25(t,u),n):prop1
+o@prop2:=is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b))):'prop'
+[p:pos(m)]
+t28:=posintnatrl(m,p,mi):natrl(m)
+m0:=ntofrl(m,t28):nat
+t29:=isrlnt1(m,t28):is"r"(m,nr(m0))
+t30:=isrlnt2(m,t28):is"r"(nr(m0),m)
+t31:=ispw2(ts(x,y),m,nr(m0),t29,mi,t4(ts(x,y),m0),lemma292c,t5(ts(x,y),m0)):is(pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0))
+t32:=ists12(p0(x,m0),pw(x,m,mi,lemma292a),p0(y,m0),pw(y,m,mi,lemma292b),ispw2(x,nr(m0),m,t30,t4(x,m0),mi,t5(x,m0),lemma292a),ispw2(y,nr(m0),m,t30,t4(y,m0),mi,t5(y,m0),lemma292b)):is(ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
+t33:=tr3is(cx,pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0),ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),t31,t26(m0),t32):prop2
+o@[i:is"r"(m,0)]
+t34:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(1c,1c),1c,ists12(pw(x,m,mi,lemma292a),1c,pw(y,m,mi,lemma292b),1c,0exp(x,m,mi,lemma292a,i),0exp(y,m,mi,lemma292b,i)),satz222(1c)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c)
+t35:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c,0exp(ts(x,y),m,mi,lemma292c,i),t34):prop2
+o@[n:neg(m)]
+t36:=intabs(m,mi):intrl(abs(m))
+t37:=ori2(and(nis(x,0c),nis(y,0c)),pos(abs(m)),satz166b(m,n)):or(and(nis(x,0c),nis(y,0c)),pos(abs(m)))
+t38:=lemma292a(abs(m),t36,t37):or(nis(x,0c),pos(abs(m)))
+t39:=lemma292b(abs(m),t36,t37):or(nis(y,0c),pos(abs(m)))
+t40:=lemma292c(abs(m),t36,t37):or(nis(ts(x,y),0c),pos(abs(m)))
+t41:=lemmapw3(x,m,mi,lemma292a,n):or(nis(x,0c),pos(abs(m)))
+t42:=lemmapw3(y,m,mi,lemma292b,n):or(nis(y,0c),pos(abs(m)))
+t43:=lemmapw3(ts(x,y),m,mi,lemma292c,n):or(nis(ts(x,y),0c),pos(abs(m)))
+t44:=ispw2(ts(x,y),abs(m),abs(m),refis(real,abs(m)),t36,t36,t43,t40):is(pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40))
+t45:=t33(abs(m),t36,t37,satz166b(m,n)):is(pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)))
+t46:=ists12(pw(x,abs(m),t36,t38),pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t39),pw(y,abs(m),t36,t42),ispw2(x,abs(m),abs(m),refis(real,abs(m)),t36,t36,t38,t41),ispw2(y,abs(m),abs(m),refis(real,abs(m)),t36,t36,t39,t42)):is(ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
+t47:=tr3is(cx,pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t44,t45,t46):is(pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
+t48:=lemmapw1(x,abs(m),t36,t41,satz166b(m,n),lemmapw2(x,m,mi,lemma292a,n)):nis(pw(x,abs(m),t36,t41),0c)
+t49:=lemmapw1(y,abs(m),t36,t42,satz166b(m,n),lemmapw2(y,m,mi,lemma292b,n)):nis(pw(y,abs(m),t36,t42),0c)
+t50:=lemmapw1(ts(x,y),abs(m),t36,t43,satz166b(m,n),lemmapw2(ts(x,y),m,mi,lemma292c,n)):nis(pw(ts(x,y),abs(m),t36,t43),0c)
+t51:=satz221d(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42),t48,t49):nis(ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),0c)
+t52:=negexp(ts(x,y),m,mi,lemma292c,n):is(pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50))
+t53:=isov12(1c,ts(1c,1c),pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),satz222a(1c),t47,t50,t51):is(ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t54:=tris(cx,pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t52,t53):is(pw(ts(x,y),m,mi,lemma292c),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t55:=ists12(pw(x,m,mi,lemma292a),ov(1c,pw(x,abs(m),t36,t41),t48),pw(y,m,mi,lemma292b),ov(1c,pw(y,abs(m),t36,t42),t49),negexp(x,m,mi,lemma292a,n),negexp(y,m,mi,lemma292b,n)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)))
+t56:=satz247(1c,pw(x,abs(m),t36,t41),1c,pw(y,abs(m),t36,t42),t48,t49):is(ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t57:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t55,t56):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t58:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t54,t57):prop2
+-9292
+o@satz292:=rapp(m,prop2".9292",[t:pos(m)]t33".9292"(t),[t:is"r"(m,0)]t35".9292"(t),[t:neg(m)]t58".9292"(t)):is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
+@[m:real]
+lemma293:=ori1(nis(1c,0c),pos(m),1not0):or(nis(1c,0c),pos(m))
+[mi:intrl(m)]
++9293
+t1:=ori1(and(nis(1c,0c),nis(1c,0c)),pos(m),andi(nis(1c,0c),nis(1c,0c),1not0,1not0)):or(and(nis(1c,0c),nis(1c,0c)),pos(m))
+1m:=pw(1c,m,mi,lemma293):cx
+t2:=satz222(1m):is(ts(1m,1c),1m)
+t3:=ispw1(1c,ts(1c,1c),m,satz222a(1c),mi,lemma293,lemma292c(1c,1c,m,mi,t1)):is(1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)))
+t4:=satz292(1c,1c,m,mi,t1):is(pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))))
+t5:=ists12(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),1m,pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1)),1m,ispw1(1c,1c,m,refis(cx,1c),mi,lemma292a(1c,1c,m,mi,t1),lemma293),ispw1(1c,1c,m,refis(cx,1c),mi,lemma292b(1c,1c,m,mi,t1),lemma293)):is(ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m))
+t6:=tr4is(cx,ts(1m,1c),1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m),t2,t3,t4,t5):is(ts(1m,1c),ts(1m,1m))
+t7:=tris(cx,ts(1m,mn(1m,1c)),mn(ts(1m,1m),ts(1m,1c)),0c,disttm2(1m,1m,1c),satz213b(ts(1m,1m),ts(1m,1c),symis(cx,ts(1m,1c),ts(1m,1m),t6))):is(ts(1m,mn(1m,1c)),0c)
+t8:=ore2(is(1m,0c),is(mn(1m,1c),0c),satz221c(1m,mn(1m,1c),t7),satz290(1c,m,mi,lemma293,1not0)):is(mn(1m,1c),0c)
+-9293
+satz293:=satz213a(1m".9293",1c,t8".9293"):is(pw(1c,m,mi,lemma293),1c)
+x@[m:real][n:real][mi:intrl(m)][ni:intrl(n)][o:or(nis(x,0c),and(pos(m),pos(n)))]
++9294
+[a:and(pos(m),pos(n))]
+t1:=ande1(pos(m),pos(n),a):pos(m)
+t2:=ande2(pos(m),pos(n),a):pos(n)
+t3:=pospl(m,n,t1,t2):pos(pl"r"(m,n))
+-9294
+lemma294a:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(m),o,[t:and(pos(m),pos(n))]t1".9294"(t)):or(nis(x,0c),pos(m))
+lemma294b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(n),o,[t:and(pos(m),pos(n))]t2".9294"(t)):or(nis(x,0c),pos(n))
+lemma294c:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(pl"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9294"(t)):or(nis(x,0c),pos(pl"r"(m,n)))
++*9294
+o@prop1:=is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c)):'prop'
+a@m1:=ntofrl(m,posintnatrl(m,t1,mi)):nat
+n1:=ntofrl(n,posintnatrl(n,t2,ni)):nat
+t4:=ists12(pw(x,m,mi,lemma294a),prod(m1,[t:1to(m1)]x),pw(x,n,ni,lemma294b),prod(n1,[t:1to(n1)]x),posexp(x,m,mi,lemma294a,t1),posexp(x,n,ni,lemma294b,t2)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
+p1:=ntofrl(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni))):nat
+t5:=posexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t3):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(p1,[t:1to(p1)]x))
+t6:=tris(real,pl"r"(m,n),pl"r"(rlofnt(m1),rlofnt(n1)),rlofnt(pl"n"(m1,n1)),ispl12"r"(m,rlofnt(m1),n,rlofnt(n1),isrlnt1(m,posintnatrl(m,t1,mi)),isrlnt1(n,posintnatrl(n,t2,ni))),satzr155b(m1,n1)):is"r"(pl"r"(m,n),rlofnt(pl"n"(m1,n1)))
+t7:=tris2(nat,pl"n"(m1,n1),p1,ntofrl(rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1))),isntrl1(pl"n"(m1,n1)),isrlent(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni)),rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1)),t6)):is"n"(pl"n"(m1,n1),p1)
+t8:=lessisi2"n"(pl"n"(m1,n1),p1,t7):lessis"n"(pl"n"(m1,n1),p1)
+t9:=issmpr([t:cx][u:cx]ts(t,u),p1,[t:1to(p1)]x,pl"n"(m1,n1),t7):is(prod(pl"n"(m1,n1),left(cx,p1,pl"n"(m1,n1),t8,[t:1to(p1)]x)),prod(p1,[t:1to(p1)]x))
+t10:=tris2(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),prod(p1,[t:1to(p1)]x),t5,t9):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x))
+t11:=lessisi1"n"(m1,pl"n"(m1,n1),satz18a(m1,n1)):lessis"n"(m1,pl"n"(m1,n1))
+t12:=satz281([t:cx][u:cx]ts(t,u),assocts,m1,n1,[t:1to(pl"n"(m1,n1))]x):is(prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,left(cx,pl"n"(m1,n1),m1,t11,[t:1to(pl"n"(m1,n1))]x)),prod(n1,right(cx,m1,n1,[t:1to(pl"n"(m1,n1))]x))))
+t13:=tris(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t10,t12):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
+t14:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t4,t13):prop1
+o@[na:not(and(pos(m),pos(n)))]
+t15:=ore1(nis(x,0c),and(pos(m),pos(n)),o,na):nis(x,0c)
+t16:=th15"l.or"(pos(m),pos(n),na):or(not(pos(m)),not(pos(n)))
+o@am:=abs(m):real
+an:=abs(n):real
+ap:=abs(pl"r"(m,n)):real
+t17:=intabs(m,mi):intrl(am)
+t18:=intabs(n,ni):intrl(an)
+t19:=intabs(pl"r"(m,n),intpl(m,mi,n,ni)):intrl(ap)
+na@[nm:neg(m)][nn:neg(n)]
+t20:=andi(pos(am),pos(an),satz166e(m,nnot0(m,nm)),satz166e(n,nnot0(n,nn))):and(pos(am),pos(an))
+t21:=ori2(nis(x,0c),and(pos(am),pos(an)),t20):or(nis(x,0c),and(pos(am),pos(an)))
+t22:=lemmapw3(x,m,mi,lemma294a,nm):or(nis(x,0c),pos(am))
+t23:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
+t24:=lemma294a(x,am,an,t17,t18,t21):or(nis(x,0c),pos(am))
+t25:=lemma294b(x,am,an,t17,t18,t21):or(nis(x,0c),pos(an))
+t26:=ists12(pw(x,am,t17,t22),pw(x,am,t17,t24),pw(x,an,t18,t23),pw(x,an,t18,t25),ispw1(x,x,am,refis(cx,x),t17,t22,t24),ispw1(x,x,an,refis(cx,x),t18,t23,t25)):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)))
+t27:=lemma294c(x,am,an,t17,t18,t21):or(nis(x,0c),pos(pl"r"(am,an)))
+t28:=t14(x,am,an,t17,t18,t21,t20):is(ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27))
+t29:=tr3is(real,pl"r"(am,an),pl"r"(m0"r"(m),m0"r"(n)),m0"r"(pl"r"(m,n)),ap,ispl12"r"(am,m0"r"(m),an,m0"r"(n),absn(m,nm),absn(n,nn)),satz180a(m,n),symis(real,ap,m0"r"(pl"r"(m,n)),absn(pl"r"(m,n),negpl(m,n,nm,nn)))):is"r"(pl"r"(am,an),ap)
+t30:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn)):or(nis(x,0c),pos(ap))
+t31:=ispw2(x,pl"r"(am,an),ap,t29,intpl(am,t17,an,t18),t19,t27,t30):is(pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30))
+t32:=tr3is(cx,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30),t26,t28,t31):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30))
+t33:=lemmapw1(x,am,t17,t22,satz166b(m,nm),lemmapw2(x,m,mi,lemma294a,nm)):nis(pw(x,am,t17,t22),0c)
+t34:=lemmapw1(x,an,t18,t23,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t23),0c)
+t35:=lemmapw1(x,ap,t19,t30,satz166b(pl"r"(m,n),negpl(m,n,nm,nn)),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):nis(pw(x,ap,t19,t30),0c)
+t36:=ists12(pw(x,m,mi,lemma294a),ov(1c,pw(x,am,t17,t22),t33),pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t23),t34),negexp(x,m,mi,lemma294a,nm),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)))
+t37:=satz221d(pw(x,am,t17,t22),pw(x,an,t18,t23),t33,t34):nis(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),0c)
+t38:=satz247(1c,pw(x,am,t17,t22),1c,pw(x,an,t18,t23),t33,t34):is(ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37))
+t39:=isov12(ts(1c,1c),1c,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30),satz222(1c),t32,t37,t35):is(ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35))
+t40:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t30),t35),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):is(ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t41:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t36,t38,t39,t40):prop1
+na@[pm:pos(m)][nn:neg(n)]
+t42:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
+t43:=lemmapw1(x,an,t18,t42,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t42),0c)
+t44:=ists2(pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t42),t43),pw(x,m,mi,lemma294a),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)))
+t45:=satz244a(pw(x,m,mi,lemma294a),1c,pw(x,an,t18,t42),t43):is(ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43))
+t46:=isov1(ts(pw(x,m,mi,lemma294a),1c),pw(x,m,mi,lemma294a),pw(x,an,t18,t42),satz222(pw(x,m,mi,lemma294a)),t43):is(ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+t47:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t44,t45,t46):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+[casea:more(m,an)]
+t48:=satz182d(m,an,casea):pos(mn"r"(m,an))
+t49:=satz166e(n,nnot0(n,nn)):pos(an)
+t50:=andi(pos(an),pos(mn"r"(m,an)),t49,t48):and(pos(an),pos(mn"r"(m,an)))
+t51:=ori2(nis(x,0c),and(pos(an),pos(mn"r"(m,an))),t50):or(nis(x,0c),and(pos(an),pos(mn"r"(m,an))))
+t52:=intmn(m,mi,an,t18):intrl(mn"r"(m,an))
+t53:=lemma294a(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(an))
+t54:=lemma294b(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(mn"r"(m,an)))
+t55:=lemma294c(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(pl"r"(an,mn"r"(m,an))))
+t56:=intpl(an,t18,mn"r"(m,an),t52):intrl(pl"r"(an,mn"r"(m,an)))
+t57:=t14(x,an,mn"r"(m,an),t18,t52,t51,t50):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55))
+t58:=satz187a(m,an):is"r"(pl"r"(an,mn"r"(m,an)),m)
+t59:=ispw2(x,pl"r"(an,mn"r"(m,an)),m,t58,t56,mi,t55,lemma294a):is(pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a))
+t60:=tris(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a),t57,t59):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a))
+t61:=ispw1(x,x,an,refis(cx,x),t18,t53,t42):is(pw(x,an,t18,t53),pw(x,an,t18,t42))
+t62:=isp1(cx,[t:cx]nis(t,0c),pw(x,an,t18,t42),pw(x,an,t18,t53),t43,t61):nis(pw(x,an,t18,t53),0c)
+t63:=isov12(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a),pw(x,an,t18,t53),pw(x,an,t18,t42),t60,t61,t62,t43):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+t64:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t63):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62))
+t65:=satz229h(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54),t62,refis(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)))):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54))
+t66:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
+t67:=ispw2(x,mn"r"(m,an),pl"r"(m,n),t66,t52,intpl(m,mi,n,ni),t54,lemma294c):is(pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t68:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t64,t65,t67):prop1
+nn@[caseb:is"r"(m,an)]
+t69:=ispw2(x,m,an,caseb,mi,t18,lemma294a,t42):is(pw(x,m,mi,lemma294a),pw(x,an,t18,t42))
+t70:=satz251a(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43,t69):is(ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c)
+t71:=tr3is(real,pl"r"(m,n),mn"r"(m,m0"r"(n)),mn"r"(m,an),0,ispl2"r"(n,m0"r"(m0"r"(n)),m,satz177a(n)),ismn2"r"(m0"r"(n),an,m,symis(real,an,m0"r"(n),absn(n,nn))),satz182e(m,an,caseb)):is"r"(pl"r"(m,n),0)
+t72:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),1c,0exp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t71)):is(1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t73:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t47,t70,t72):prop1
+nn@[casec:less(m,an)]
+t74:=satz182d(an,m,lemma2"r"(m,an,casec)):pos(mn"r"(an,m))
+t75:=andi(pos(m),pos(mn"r"(an,m)),pm,t74):and(pos(m),pos(mn"r"(an,m)))
+t76:=ori2(nis(x,0c),and(pos(m),pos(mn"r"(an,m))),t75):or(nis(x,0c),and(pos(m),pos(mn"r"(an,m))))
+t77:=intmn(an,t18,m,mi):intrl(mn"r"(an,m))
+t78:=lemma294a(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(m))
+t79:=lemma294b(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(mn"r"(an,m)))
+t80:=lemma294c(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(pl"r"(m,mn"r"(an,m))))
+t81:=intpl(m,mi,mn"r"(an,m),t77):intrl(pl"r"(m,mn"r"(an,m)))
+t81a:=t14(x,m,mn"r"(an,m),mi,t77,t76,t75):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80))
+t82:=satz187a(an,m):is"r"(pl"r"(m,mn"r"(an,m)),an)
+t83:=ispw2(x,pl"r"(m,mn"r"(an,m)),an,t82,t81,t18,t80,t42):is(pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42))
+t84:=tris(cx,ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42),t81a,t83):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42))
+t85:=satz290(x,m,mi,t78,t15):nis(pw(x,m,mi,t78),0c)
+t86:=satz290(x,mn"r"(an,m),t77,t79,t15):nis(pw(x,mn"r"(an,m),t77,t79),0c)
+t87:=satz221d(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79),t85,t86):nis(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),0c)
+t88:=satz222(pw(x,m,mi,t78)):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78))
+t89:=ispw1(x,x,m,refis(cx,x),mi,t78,lemma294a):is(pw(x,m,mi,t78),pw(x,m,mi,lemma294a))
+t90:=tris(cx,ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78),pw(x,m,mi,lemma294a),t88,t89):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a))
+t91:=isov12(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42),t90,t84,t87,t43):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+t92:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t91):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87))
+t93:=satz246a(1c,pw(x,mn"r"(an,m),t77,t79),pw(x,m,mi,t78),t86,t85):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86))
+t94:=satz182f(m,an,casec):neg(mn"r"(m,an))
+t94a:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
+t95:=tr3is(real,mn"r"(an,m),m0"r"(mn"r"(m,an)),abs(mn"r"(m,an)),ap,satz181a(an,m),symis(real,abs(mn"r"(m,an)),m0"r"(mn"r"(m,an)),absn(mn"r"(m,an),t94)),isabs(mn"r"(m,an),pl"r"(m,n),t94a)):is"r"(mn"r"(an,m),ap)
+t96:=isp(real,[t:real]neg(t),mn"r"(m,an),pl"r"(m,n),t94,t94a):neg(pl"r"(m,n))
+t97:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96):or(nis(x,0c),pos(ap))
+t98:=lemmapw1(x,ap,t19,t97,satz166b(pl"r"(m,n),t96),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):nis(pw(x,ap,t19,t97),0c)
+t99:=ispw2(x,mn"r"(an,m),ap,t95,t77,t19,t79,t97):is(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97))
+t100:=isov2(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97),1c,t99,t86,t98):is(ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98))
+t101:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t97),t98),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):is(ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t102:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t92,t93,t100,t101):prop1
+nn@t103:=or3app(is"r"(m,an),more(m,an),less(m,an),prop1,satz167a(m,an),[t:is"r"(m,an)]t73(t),[t:more(m,an)]t68(t),[t:less(m,an)]t102(t)):prop1
+na@[nm:neg(m)][qn:pos(n)]
+na@t104:=ori1(nis(x,0c),and(pos(n),pos(m)),t15):or(nis(x,0c),and(pos(n),pos(m)))
+t104a:=th5"l.and"(pos(m),pos(n),na):not(and(pos(n),pos(m)))
+t105:=lemma294a(x,n,m,ni,mi,t104):or(nis(x,0c),pos(n))
+t106:=lemma294b(x,n,m,ni,mi,t104):or(nis(x,0c),pos(m))
+t107:=lemma294c(x,n,m,ni,mi,t104):or(nis(x,0c),pos(pl"r"(n,m)))
+t108:=ists12(pw(x,m,mi,lemma294a),pw(x,m,mi,t106),pw(x,n,ni,lemma294b),pw(x,n,ni,t105),ispw1(x,x,m,refis(cx,x),mi,lemma294a,t106),ispw1(x,x,n,refis(cx,x),ni,lemma294b,t105)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)))
+t109:=comts(pw(x,m,mi,t106),pw(x,n,ni,t105)):is(ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)))
+qn@t110:=t103(x,n,m,ni,mi,t104,t104a,qn,nm):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
+na@t111:=ispw2(x,pl"r"(n,m),pl"r"(m,n),compl"r"(n,m),intpl(n,ni,m,mi),intpl(m,mi,n,ni),t107,lemma294c):is(pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+qn@t112:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t110,t111):prop1
+na@[i:is"r"(m,0)]
+t113:=ists1(pw(x,m,mi,lemma294a),1c,pw(x,n,ni,lemma294b),0exp(x,m,mi,lemma294a,i)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)))
+t114:=satz222b(pw(x,n,ni,lemma294b)):is(ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b))
+t115:=symis(real,pl"r"(m,n),n,pl01"r"(m,n,i)):is"r"(n,pl"r"(m,n))
+t116:=ispw2(x,n,pl"r"(m,n),t115,ni,intpl(m,mi,n,ni),lemma294b,lemma294c):is(pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t117:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t113,t114,t116):prop1
+na@[i:is"r"(n,0)]
+t118:=t117(x,n,m,ni,mi,t104,t104a,i):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
+t119:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t118,t111):prop1
+na@[pm:pos(m)]
+t120:=ore2(not(pos(m)),not(pos(n)),t16,weli(pos(m),pm)):not(pos(n))
+t121:=rapp(n,prop1,th2"l.imp"(pos(n),prop1,t120),[t:is"r"(n,0)]t119(t),[t:neg(n)]t103(pm,t)):prop1
+na@[nm:neg(m)]
+t122:=rapp(n,prop1,[t:pos(n)]t112(nm,t),[t:is"r"(n,0)]t119(t),[t:neg(n)]t41(nm,t)):prop1
+na@t123:=rapp(m,prop1,[t:pos(m)]t121(t),[t:is"r"(m,0)]t117(t),[t:neg(m)]t122(t)):prop1
+-9294
+o@satz294:=th1"l.imp"(and(pos(m),pos(n)),prop1".9294",[t:and(pos(m),pos(n))]t14".9294"(t),[t:not(and(pos(m),pos(n)))]t123".9294"(t)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+ni@[o:nis(x,0c)]
+lemma295a:=ori1(nis(x,0c),pos(m),o):or(nis(x,0c),pos(m))
+lemma295b:=ori1(nis(x,0c),pos(n),o):or(nis(x,0c),pos(n))
+lemma295c:=ori1(nis(x,0c),pos(mn"r"(m,n)),o):or(nis(x,0c),pos(mn"r"(m,n)))
++9295
+t1:=ori1(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)),o):or(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)))
+t2:=intmn(m,mi,n,ni):intrl(mn"r"(m,n))
+t3:=lemma294a(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(mn"r"(m,n)))
+t4:=lemma294b(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(n))
+t5:=lemma294c(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(pl"r"(mn"r"(m,n),n)))
+t6:=ists12(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,lemma295b),pw(x,n,ni,t4),ispw1(x,x,mn"r"(m,n),refis(cx,x),t2,lemma295c,t3),ispw1(x,x,n,refis(cx,x),ni,lemma295b,t4)):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)))
+t7:=satz294(x,mn"r"(m,n),n,t2,ni,t1):is(ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5))
+t8:=plmn(m,n):is"r"(pl"r"(mn"r"(m,n),n),m)
+t9:=ispw2(x,pl"r"(mn"r"(m,n),n),m,t8,intpl(mn"r"(m,n),t2,n,ni),mi,t5,lemma295a):is(pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a))
+t10:=tr3is(cx,ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a),t6,t7,t9):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),pw(x,m,mi,lemma295a))
+t11:=satz290(x,n,ni,lemma295b,o):nis(pw(x,n,ni,lemma295b),0c)
+-9295
+satz295:=satz229k(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),pw(x,mn"r"(m,n),t2".9295",lemma295c),t11".9295",t10".9295"):is(ov(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),satz290(x,n,ni,lemma295b,o)),pw(x,mn"r"(m,n),intmn(m,mi,n,ni),lemma295c))
+m@[mi:intrl(m)][n:nis(x,0c)]
+lemma296:=ori1(nis(x,0c),pos(m),n):or(nis(x,0c),pos(m))
++9296
+t1:=intrli0(0,refis(real,0)):intrl(0)
+t2:=lemma295a(x,0,m,t1,mi,n):or(nis(x,0c),pos(0))
+t3:=lemma295b(x,0,m,t1,mi,n):or(nis(x,0c),pos(m))
+t4:=lemma295c(x,0,m,t1,mi,n):or(nis(x,0c),pos(mn"r"(0,m)))
+t5:=satz290(x,m,mi,lemma296,n):nis(pw(x,m,mi,lemma296),0c)
+t6:=satz290(x,m,mi,t3,n):nis(pw(x,m,mi,t3),0c)
+t7:=symis(cx,pw(x,0,t1,t2),1c,0exp(x,0,t1,t2,refis(real,0))):is(1c,pw(x,0,t1,t2))
+t8:=ispw1(x,x,m,refis(cx,x),mi,lemma296,t3):is(pw(x,m,mi,lemma296),pw(x,m,mi,t3))
+t9:=isov12(1c,pw(x,0,t1,t2),pw(x,m,mi,lemma296),pw(x,m,mi,t3),t7,t8,t5,t6):is(ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6))
+t10:=satz295(x,0,m,t1,mi,n):is(ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4))
+t11:=pl01(0,m0"r"(m),refis(real,0)):is"r"(mn"r"(0,m),m0"r"(m))
+t12:=lemma296(x,m0"r"(m),intm0(m,mi),n):or(nis(x,0c),pos(m0"r"(m)))
+t13:=ispw2(x,mn"r"(0,m),m0"r"(m),t11,intmn(0,t1,m,mi),intm0(m,mi),t4,t12):is(pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12))
+t14:=tr3is(cx,ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12),t9,t10,t13):is(ov(1c,pw(x,m,mi,lemma296),t5),pw(x,m0"r"(m),intm0(m,mi),t12))
+-9296
+satz296:=t14".9296":is(ov(1c,pw(x,m,mi,lemma296),satz290(x,m,mi,lemma296,n)),pw(x,m0"r"(m),intm0(m,mi),lemma296(m0"r"(m),intm0(m,mi),n)))
+ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
++9297
+[p:nis(x,0c)]
+t1:=satz290(x,m,mi,lemma294a(o),p):nis(pw(x,m,mi,lemma294a(o)),0c)
+o@[a:and(pos(m),pos(n))]
+t2:=ande2(pos(m),pos(n),a):pos(n)
+t3:=postspp(m,n,ande1(pos(m),pos(n),a),t2):pos(ts"r"(m,n))
+-9297
+lemma297a:=th9"l.or"(nis(x,0c),and(pos(m),pos(n)),nis(pw(x,m,mi,lemma294a(o)),0c),pos(n),o,[t:nis(x,0c)]t1".9297"(t),[t:and(pos(m),pos(n))]t2".9297"(t)):or(nis(pw(x,m,mi,lemma294a(o)),0c),pos(n))
+lemma297b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(ts"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9297"(t)):or(nis(x,0c),pos(ts"r"(m,n)))
+mi@[o:or(nis(x,0c),pos(m))][i:is(x,0c)]
++*9297
+i@t4:=ore2(nis(x,0c),pos(m),o,weli(is(x,0c),i)):pos(m)
+m1:=ntofrl(m,posintnatrl(m,t4,mi)):nat
+t5:=posexp(x,m,mi,o,t4):is(pw(x,m,mi,o),prod(m1,[t:1to(m1)]x))
+t6:=satz289b(m1,[t:1to(m1)]x,xout(m1),i):is(prod(m1,[t:1to(m1)]x),0c)
+t7:=tris(cx,pw(x,m,mi,o),prod(m1,[t:1to(m1)]x),0c,t5,t6):is(pw(x,m,mi,o),0c)
+-9297
+i@pw0:=t7".9297":is(pw(x,m,mi,o),0c)
+ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
++*9297
+ni@t8:=intts(m,mi,n,ni):intrl(ts"r"(m,n))
+o@prop1:=is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o))):'prop'
+[i:is(x,0c)]
+t9:=pw0(x,m,mi,lemma294a(o),i):is(pw(x,m,mi,lemma294a(o)),0c)
+t10:=pw0(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o),t9):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),0c)
+t11:=pw0(x,ts"r"(m,n),t8,lemma297b(o),i):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),0c)
+t12:=tris2(cx,pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),0c,t10,t11):prop1
+m@[mi:intrl(m)][p:nis(x,0c)]
+t13:=ori1(nis(x,0c),pos(m),p):or(nis(x,0c),pos(m))
+p0:=pw(x,m,mi,t13):cx
+[n:nat]
+nr:=rlofnt(n):real
+t14:=natintrl(nr,natrli(n)):intrl(nr)
+t15:=ori2(nis(p0,0c),pos(nr),natpos(nr,natrli(n))):or(nis(p0,0c),pos(nr))
+t16:=ori1(nis(x,0c),pos(ts"r"(m,nr)),p):or(nis(x,0c),pos(ts"r"(m,nr)))
+t17:=intts(m,mi,nr,t14):intrl(ts"r"(m,nr))
+prop2:=is(pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16)):'prop'
+p@t18:=ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t15(1),lemma291(p0)):is(pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)))
+t19:=satz291(p0):is(pw(p0,1rl,intrl1,lemma291(p0)),p0)
+t20:=ispw2(x,m,ts"r"(m,1rl),satz195a(m),mi,t17(1),t13,t16(1)):is(p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)))
+t21:=tr3is(cx,pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)),t18,t19,t20):prop2(1)
+n@[p2:prop2(n)]
+n1:=pl"n"(n,1):nat
+t22:=satz290(x,m,mi,t13,p):nis(p0,0c)
+t23:=ori1(nis(p0,0c),and(pos(nr),pos(1rl)),t22):or(nis(p0,0c),and(pos(nr),pos(1rl)))
+t24:=lemma294a(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(nr))
+t25:=lemma294b(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(1rl))
+t26:=lemma294c(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(pl"r"(nr,1rl)))
+t27:=ispw2(p0,nr(n1),pl"r"(nr,1rl),satzr155a(n,1),t14(n1),intpl(nr,t14,1rl,intrl1),t15(n1),t26):is(pw(p0,nr(n1),t14(n1),t15(n1)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
+t27a:=satz294(p0,nr,1rl,t14,intrl1,t23):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
+t28:=tris2(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26),t27,t27a):is(pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)))
+t29:=ori1(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)),p):or(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)))
+t30:=lemma294a(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(ts"r"(m,nr)))
+t31:=lemma294b(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(m))
+t32:=lemma294c(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(pl"r"(ts"r"(m,nr),m)))
+t33:=tr3is(cx,pw(p0,nr,t14,t24),pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16),pw(x,ts"r"(m,nr),t17,t30),ispw1(p0,p0,nr,refis(cx,p0),t14,t24,t15),p2,ispw1(x,x,ts"r"(m,nr),refis(cx,x),t17,t16,t30)):is(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30))
+t34:=tr3is(cx,pw(p0,1rl,intrl1,t25),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,m,mi,t31),ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t25,lemma291(p0)),t19,ispw1(x,x,m,refis(cx,x),mi,t13,t31)):is(pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31))
+t35:=ists12(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30),pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31),t33,t34):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)))
+t36:=satz294(x,ts"r"(m,nr),m,t17,mi,t29):is(ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32))
+t37:=tr3is(real,pl"r"(ts"r"(m,nr),m),pl"r"(ts"r"(m,nr),ts"r"(m,1rl)),ts"r"(m,pl"r"(nr,1rl)),ts"r"(m,nr(n1)),ispl2"r"(m,ts"r"(m,1rl),ts"r"(m,nr),satz195a(m)),distpt2"r"(m,nr,1rl),ists2"r"(pl"r"(nr,1rl),nr(n1),m,satzr155b(n,1))):is"r"(pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)))
+t38:=ispw2(x,pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)),t37,intpl(ts"r"(m,nr),t17,m,mi),t17(n1),t32,t16(n1)):is(pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)))
+t39:=tr4is(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)),t28,t35,t36,t38):prop2(n1)
+t40:=isp(nat,[t:nat]prop2(t),n1,<n>suc,t39,satz4a(n)):prop2(<n>suc)
+n@t41:=induction([t:nat]prop2(t),t21,[t:nat][u:prop2(t)]t40(t,u),n):prop2(n)
+o@[p:nis(x,0c)][q:pos(n)]
+t42:=posintnatrl(n,q,ni):natrl(n)
+n0:=ntofrl(n,t42):nat
+t43:=isrlnt1(n,t42):is"r"(n,rlofnt(n0))
+t44:=isrlnt2(n,t42):is"r"(rlofnt(n0),n)
+o@p1:=pw(x,m,mi,lemma294a(o)):cx
+q@t44a:=ispw2(x,m,m,refis(real,m),mi,mi,lemma294a(o),t13(mi,p)):is(p1,p0(mi,p))
+t45:=ispw12(p1,p0(mi,p),n,rlofnt(n0),t44a,t43,ni,t14(mi,p,n0),lemma297a(o),t15(mi,p,n0)):is(pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)))
+t46:=t41(mi,p,n0):is(pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)))
+t47:=ists2"r"(rlofnt(n0),n,m,t44):is"r"(ts"r"(m,rlofnt(n0)),ts"r"(m,n))
+t48:=ispw2(x,ts"r"(m,rlofnt(n0)),ts"r"(m,n),t47,t17(mi,p,n0),t8,t16(mi,p,n0),lemma297b(o)):is(pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)))
+t49:=tr3is(cx,pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)),t45,t46,t48):prop1
+p@[i:is"r"(n,0)]
+t50:=0exp(p1,n,ni,lemma297a(o),i):is(pw(p1,n,ni,lemma297a(o)),1c)
+t51:=ts02"r"(m,n,i):is"r"(ts"r"(m,n),0)
+t52:=0exp(x,ts"r"(m,n),t8,lemma297b(o),t51):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),1c)
+t53:=tris2(cx,pw(p1,n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),1c,t50,t52):prop1
+p@[q:neg(n)]
+an:=abs(n):real
+t54:=intabs(n,ni):intrl(an)
+t55:=ori1(nis(x,0c),and(pos(m),pos(an)),p):or(nis(x,0c),and(pos(m),pos(an)))
+p1t55:=p1(an,mi,t54,t55):cx
+t56:=satz166e(n,nnot0(n,q)):pos(an)
+t56a:=lemma294a(an,mi,t54,t55):or(nis(x,0c),pos(m))
+t57:=lemma297a(an,mi,t54,t55):or(nis(p1t55,0c),pos(an))
+t58:=lemma297b(an,mi,t54,t55):or(nis(x,0c),pos(ts"r"(m,an)))
+t59:=t49(an,mi,t54,t55,p,t56):is(pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58))
+t60:=satz177c(an,n,absn(n,q)):is"r"(n,m0"r"(an))
+t61:=intm0(an,t54):intrl(m0"r"(an))
+t62:=satz290(x,m,mi,t56a,p):nis(p1t55,0c)
+t63:=lemma296(p1t55,an,t54,t62):or(nis(p1t55,0c),pos(an))
+t64:=satz290(p1t55,an,t54,t63,t62):nis(pw(p1t55,an,t54,t63),0c)
+t65:=lemma296(p1t55,m0"r"(an),t61,t62):or(nis(p1t55,0c),pos(m0"r"(an)))
+t66:=satz296(p1t55,an,t54,t62):is(ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65))
+t67:=ispw1(x,x,m,refis(cx,x),mi,lemma294a(o),t56a):is(p1,p1t55)
+t68:=ispw12(p1,p1t55,n,m0"r"(an),t67,t60,ni,t61,lemma297a(o),t65):is(pw(p1,n,ni,lemma297a(o)),pw(p1t55,m0"r"(an),t61,t65))
+t69:=tris2(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65),t68,t66):is(pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64))
+t70:=tris(real,m0"r"(ts"r"(m,an)),ts"r"(m,m0"r"(an)),ts"r"(m,n),satz197f(m,an),ists2"r"(m0"r"(an),n,m,symis(real,n,m0"r"(an),t60))):is"r"(m0"r"(ts"r"(m,an)),ts"r"(m,n))
+t71:=intm0(ts"r"(m,an),t8(an,mi,t54)):intrl(m0"r"(ts"r"(m,an)))
+t72:=lemma296(x,ts"r"(m,an),t8(an,mi,t54),p):or(nis(x,0c),pos(ts"r"(m,an)))
+t73:=satz290(x,ts"r"(m,an),t8(an,mi,t54),t72,p):nis(pw(x,ts"r"(m,an),t8(an,mi,t54),t72),0c)
+t74:=lemma296(x,m0"r"(ts"r"(m,an)),t71,p):or(nis(x,0c),pos(m0"r"(ts"r"(m,an))))
+t75:=satz296(x,ts"r"(m,an),t8(an,mi,t54),p):is(ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74))
+t76:=ispw2(x,m0"r"(ts"r"(m,an)),ts"r"(m,n),t70,t71,t8,t74,lemma297b(o)):is(pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)))
+t77:=ispw1(p1t55,p1t55,an,refis(cx,p1t55),t54,t63,t57):is(pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57))
+t78:=ispw1(x,x,ts"r"(m,an),refis(cx,x),t8(an,mi,t54),t58,t72):is(pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
+t79:=tr3is(cx,pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t77,t59,t78):is(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
+t80:=isov2(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),1c,t79,t64,t73):is(ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73))
+t81:=tr4is(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)),t69,t80,t75,t76):prop1
+p@t82:=rapp(n,prop1,[t:pos(n)]t49(t),[t:is"r"(n,0)]t53(t),[t:neg(n)]t81(t)):prop1
+-9297
+o@satz297:=th1"l.imp"(is(x,0c),prop1".9297",[t:is(x,0c)]t12".9297"(t),[t:nis(x,0c)]t82".9297"(t)):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),intts(m,mi,n,ni),lemma297b(o)))
+@[r:real][s:real]
++10298
+t1:=tris(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),pl"r"(0,0)),pli(pl"r"(r,s),0),plis12a(r,0,s,0),isrecx2(pl"r"(0,0),0,pl"r"(r,s),pl01(0,0,refis(real,0)))):is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
+-10298
+satz298a:=symis(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0),t1".10298"):is(pli(pl"r"(r,s),0),pl(pli(r,0),pli(s,0)))
+satz298b:=t1".10298":is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
++*10298
+s@t2:=tris(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),mn"r"(0,0)),pli(mn"r"(r,s),0),mnis12a(r,0,s,0),isrecx2(mn"r"(0,0),0,mn"r"(r,s),pl02(0,m0"r"(0),satz176b(0,refis(real,0))))):is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
+-10298
+s@satz298c:=symis(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0),t2".10298"):is(pli(mn"r"(r,s),0),mn(pli(r,0),pli(s,0)))
+satz298d:=t2".10298":is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
++*10298
+s@t3:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
+t4:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
+t5:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t3,t4)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
+-10298
+s@satz298e:=symis(cx,ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0),t5".10298"):is(pli(ts"r"(r,s),0),ts(pli(r,0),pli(s,0)))
+satz298f:=t5".10298":is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
+[n:nis"r"(s,0)]
++*10298
+n@[i:is(pli(s,0),0c)]
+t6:=tr3is(real,s,re(pli(s,0)),re(0c),0,isre(s,0),iscere(pli(s,0),0c,i),reis(0,0)):is"r"(s,0)
+-10298
+n@lemma298:=th3"l.imp"(is(pli(s,0),0c),is"r"(s,0),n,[t:is(pli(s,0),0c)]t6".10298"(t)):nis(pli(s,0),0c)
++*10298
+n@t7:=tris(cx,ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(ts"r"(s,ov"r"(r,s,n)),0),pli(r,0),t5(s,ov"r"(r,s,n)),isrecx1(ts"r"(s,ov"r"(r,s,n)),r,0,satz204c(r,s,n))):is(ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(r,0))
+-10298
+n@satz298g:=satz229g(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(pli(ov"r"(r,s,n),0),ov(pli(r,0),pli(s,0),lemma298))
+satz298h:=satz229h(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(ov(pli(r,0),pli(s,0),lemma298),pli(ov"r"(r,s,n),0))
++*10298
+r@t8:=tris(cx,m0(pli(r,0)),pli(m0"r"(r),m0"r"(0)),pli(m0"r"(r),0),m0isa(r,0),isrecx2(m0"r"(0),0,m0"r"(r),satz176b(0,refis(real,0)))):is(m0(pli(r,0)),pli(m0"r"(r),0))
+-10298
+r@satz298j:=symis(cx,m0(pli(r,0)),pli(m0"r"(r),0),t8".10298"):is(pli(m0"r"(r),0),m0(pli(r,0)))
+satz298k:=t8".10298":is(m0(pli(r,0)),pli(m0"r"(r),0))
++*10298
+r@t9:=tris(real,mod2(pli(r,0)),ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(r,r),pl02(ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(im(pli(r,0)),im(pli(r,0))),ts01(im(pli(r,0)),im(pli(r,0)),imis(r,0))),ists12"r"(re(pli(r,0)),r,re(pli(r,0)),r,reis(r,0),reis(r,0))):is"r"(mod2(pli(r,0)),ts"r"(r,r))
+ar:=abs(r):real
+[p:pos(r)]
+t10:=satz196a(r,r,p,p):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+r@[i:is"r"(r,0)]
+t11:=tris2(real,ts"r"(r,r),ts"r"(ar,ar),0,ts01(r,r,i),ts01(ar,ar,abs0(r,i))):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+r@[n:neg(r)]
+t12:=satz196b(r,r,n,n):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+r@t13:=rapp(r,is"r"(ts"r"(r,r),ts"r"(ar,ar)),[t:pos(r)]t10(t),[t:is"r"(r,0)]t11(t),[t:neg(r)]t12(t)):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+t14:=tris(real,mod2(pli(r,0)),ts"r"(r,r),ts"r"(ar,ar),t9,t13):is"r"(mod2(pli(r,0)),ts"r"(ar,ar))
+t15:=th1"l.imp"(is"r"(r,0),not(neg(ar)),[t:is"r"(r,0)]0notn(ar,abs0(r,t)),[t:nis"r"(r,0)]pnotn(ar,satz166e(r,t))):not(neg(ar))
+-10298
+r@satz298l:=thsqrt3(mod2(pli(r,0)),lemma5(pli(r,0)),abs(r),t15".10298",t14".10298"):is"r"(mod(pli(r,0)),abs(r))
+satz298m:=symis(real,mod(pli(r,0)),abs(r),satz298l):is"r"(abs(r),mod(pli(r,0)))
+cofrl:=pli(r,0):complex
+s@[i:is(cofrl(r),cofrl(s))]
+isrlic:=tr3is(real,r,re(cofrl(r)),re(cofrl(s)),s,isre(r,0),iscere(cofrl(r),cofrl(s),i),reis(s,0)):is"r"(r,s)
+s@[i:is"r"(r,s)]
+isrlec:=isrecx1(r,s,0,i):is(cofrl(r),cofrl(s))
++v10
+@t1:=[t:real][u:real][v:is(cofrl(t),cofrl(u))]isrlic(t,u,v):injective(real,cx,[t:real]cofrl(t))
+-v10
+@[x:cx]
+realc:=image(real,cx,[t:real]cofrl(t),x):'prop'
+r@reali:=imagei(real,cx,[t:real]cofrl(t),r):realc(cofrl(r))
+x@[rx:realc(x)]
+rlofc:=soft(real,cx,[t:real]cofrl(t),t1".v10",x,rx):real
+[y:cx][ry:realc(y)][i:is"r"(rlofc(x,rx),rlofc(y,ry))]
+iscirl:=isinve(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is(x,y)
+ry@[i:is(x,y)]
+iscerl:=isinv(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is"r"(rlofc(x,rx),rlofc(y,ry))
+r@isrlc1:=isst1(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(r,rlofc(cofrl(r),reali(r)))
+isrlc2:=isst2(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(rlofc(cofrl(r),reali(r)),r)
+rx@iscrl1:=ists1"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(x,cofrl(rlofc(x,rx)))
+iscrl2:=ists2"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(cofrl(rlofc(x,rx)),x)
+@[n:nat]
+cofn:=cofrl(rlofnt(n)):complex
+[m:nat][i:is"n"(n,m)]
+isnec:=isrlec(rlofnt(n),rlofnt(m),isnterl(n,m,i)):is(cofn(n),cofn(m))
+m@[i:is(cofn(n),cofn(m))]
+isnic:=isntirl(n,m,isrlic(rlofnt(n),rlofnt(m),i)):is"n"(n,m)
++*v10
+@t2:=[t:nat][u:nat][v:is(cofn(t),cofn(u))]isnic(t,u,v):injective(nat,cx,[t:nat]cofn(t))
+-v10
+x@natc:=image(nat,cx,[t:nat]cofn(t),x):'prop'
+n@nati:=imagei(nat,cx,[t:nat]cofn(t),n):natc(cofn(n))
+x@[nx:natc(x)]
+nofc:=soft(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):nat
+[y:cx][ny:natc(y)][i:is(x,y)]
+iscen:=isinv(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is"n"(nofc(x,nx),nofc(y,ny))
+ny@[i:is"n"(nofc(x,nx),nofc(y,ny))]
+iscin:=isinve(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is(x,y)
+n@isnc1:=isst1(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(n,nofc(cofn(n),nati(n)))
+isnc2:=isst2(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(nofc(cofn(n),nati(n)),n)
+nx@iscn1:=ists1"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(x,cofn(nofc(x,nx)))
+iscn2:=ists2"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(cofn(nofc(x,nx)),x)
+@natt:=ot(cx,[t:cx]natc(t)):'type'
+[nt:natt]
+cofnt:=in"e"(cx,[t:cx]natc(t),nt):cx
+natti:=inp(cx,[t:cx]natc(t),nt):natc(cofnt(nt))
+[mt:natt][i:is"e"(natt,nt,mt)]
+isntec:=isini(cx,[t:cx]natc(t),nt,mt,i):is(cofnt(nt),cofnt(mt))
+mt@[i:is(cofnt(nt),cofnt(mt))]
+isntic:=isine(cx,[t:cx]natc(t),nt,mt,i):is"e"(natt,nt,mt)
+nx@ntofc:=out(cx,[t:cx]natc(t),x,nx):natt
+ny@[i:is(x,y)]
+iscent:=isouti(cx,[t:cx]natc(t),x,nx,y,ny,i):is"e"(natt,ntofc(x,nx),ntofc(y,ny))
+ny@[i:is"e"(natt,ntofc(x,nx),ntofc(y,ny))]
+iscint:=isoute(cx,[t:cx]natc(t),x,nx,y,ny,i):is(x,y)
+nt@isntc1:=isoutin(cx,[t:cx]natc(t),nt):is"e"(natt,nt,ntofc(cofnt(nt),natti(nt)))
+isntc2:=symis(natt,nt,ntofc(cofnt(nt),natti(nt)),isntc1):is"e"(natt,ntofc(cofnt(nt),natti(nt)),nt)
+nx@iscnt1:=isinout(cx,[t:cx]natc(t),x,nx):is(x,cofnt(ntofc(x,nx)))
+iscnt2:=symis(cx,x,cofnt(ntofc(x,nx)),iscnt1):is(cofnt(ntofc(x,nx)),x)
+n@ntofn:=ntofc(cofn(n),nati(n)):natt
+m@[i:is"n"(n,m)]
+isnent:=iscent(cofn(n),nati(n),cofn(m),nati(m),isnec(n,m,i)):is"e"(natt,ntofn(n),ntofn(m))
+m@[i:is"e"(natt,ntofn(n),ntofn(m))]
+isnint:=isnic(n,m,iscint(cofn(n),nati(n),cofn(m),nati(m),i)):is"n"(n,m)
+nt@nofnt:=nofc(cofnt(nt),natti(nt)):nat
+mt@[i:is"e"(natt,nt,mt)]
+isnter:=iscen(cofnt(nt),natti(nt),cofnt(mt),natti(mt),isntec(nt,mt,i)):is"n"(nofnt(nt),nofnt(mt))
+mt@[i:is"n"(nofnt(nt),nofnt(mt))]
+isntin:=isntic(nt,mt,iscin(cofnt(nt),natti(nt),cofnt(mt),natti(mt),i)):is"e"(natt,nt,mt)
++*v10
+n@t3:=iscnt1(cofn(n),nati(n)):is(cofn(n),cofnt(ntofn(n)))
+-v10
+n@isnnt1:=tris(nat,n,nofc(cofn(n),nati(n)),nofnt(ntofn(n)),isnc1(n),iscen(cofn(n),nati(n),cofnt(ntofn(n)),natti(ntofn(n)),t3".v10")):is"n"(n,nofnt(ntofn(n)))
+isnnt2:=symis(nat,n,nofnt(ntofn(n)),isnnt1):is"n"(nofnt(ntofn(n)),n)
++*v10
+nt@t4:=iscn1(cofnt(nt),natti(nt)):is(cofnt(nt),cofn(nofnt(nt)))
+-v10
+nt@isntn1:=tris(natt,nt,ntofc(cofnt(nt),natti(nt)),ntofn(nofnt(nt)),isntc1(nt),iscent(cofnt(nt),natti(nt),cofn(nofnt(nt)),nati(nofnt(nt)),t4".v10")):is"e"(natt,nt,ntofn(nofnt(nt)))
+isntn2:=symis(natt,nt,ntofn(nofnt(nt)),isntn1):is"e"(natt,ntofn(nofnt(nt)),nt)
+@1t:=ntofn(1):natt
+suct:=[t:natt]ntofn(<nofnt(t)>suc):[t:natt]natt
++10299
+nt@[i:is"e"(natt,<nt>suct,1t)]
+t1:=isnint(<nofnt(nt)>suc,1,i):is"n"(<nofnt(nt)>suc,1)
+-10299
+nt@satz299a:=th3"l.imp"(is"e"(natt,<nt>suct,1t),is"n"(<nofnt(nt)>suc,1),<nofnt(nt)>ax3,[t:is"e"(natt,<nt>suct,1t)]t1".10299"(t)):not(is"e"(natt,<nt>suct,1t))
+@ax3t:=[t:natt]satz299a(t):[t:natt]not(is"e"(natt,<t>suct,1t))
+mt@[i:is"e"(natt,<nt>suct,<mt>suct)]
++*10299
+i"c"@t2:=isnint(<nofnt(nt)>suc,<nofnt(mt)>suc,i):is"n"(<nofnt(nt)>suc,<nofnt(mt)>suc)
+t3:=<t2><nofnt(mt)><nofnt(nt)>ax4:is"n"(nofnt(nt),nofnt(mt))
+-10299
+i@satz299b:=isntin(nt,mt,t3".10299"):is"e"(natt,nt,mt)
+@ax4t:=[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]satz299b(t,u,v):[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]is"e"(natt,t,u)
+[s:set(natt)]
+cond1t:=esti(natt,1t,s):'prop'
+cond2t:=all"l"(natt,[t:natt]imp(esti(natt,t,s),esti(natt,<t>suct,s))):'prop'
+[c1:cond1t][c2:cond2t]
++*10299
+c2@[n:nat]
+prop1:=esti(natt,ntofn(n),s):'prop'
+c2@t4:=c1:prop1(1)
+n@[p:prop1(n)]
+t5:=<p><ntofn(n)>c2:esti(natt,ntofn(<nofnt(ntofn(n))>suc),s)
+t6:=isp(nat,[t:nat]esti(natt,ntofn(<t>suc),s),nofnt(ntofn(n)),n,t5,isnnt2(n)):prop1(<n>suc)
+c2@[nt:natt]
+t7:=induction([t:nat]prop1(t),t4,[t:nat][u:prop1(t)]t6(t,u),nofnt(nt)):prop1(nofnt(nt))
+-10299
+c2@satz299c:=[t:natt]isp(natt,[u:natt]esti(natt,u,s),ntofn(nofnt(t)),t,t7".10299"(t),isntn2(t)):[t:natt]esti(natt,t,s)
+@ax5t:=[t:set(natt)][u:cond1t(t)][v:cond2t(t)]satz299c(t,u,v):[t:set(natt)][u:cond1t(t)][v:cond2t(t)][w:natt]esti(natt,w,t)
+ic:=pli(0,1rl):complex
++10300
+t1:=tsis12a(0,1rl,0,1rl):is(ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))))
+t2:=tris(real,mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(ts"r"(1rl,1rl)),m0"r"(1rl),pl01(ts"r"(0,0),m0"r"(ts"r"(1rl,1rl)),ts01(0,0,refis(real,0))),ism0"r"(ts"r"(1rl,1rl),1rl,satz195(1rl))):is"r"(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl))
+t3:=tris(real,pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),ts"r"(1rl,0),0,pl01(ts"r"(0,1rl),ts"r"(1rl,0),ts01(0,1rl,refis(real,0))),ts02(1rl,0,refis(real,0))):is"r"(pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0)
+t4:=isrecx12(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0,t2,t3):is(pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)))
+t5:=satz298j(1rl):is(cofrl(m0"r"(1rl)),m0(1c))
+-10300
+satz2300:=tr3is(cx,ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)),m0(1c),t1".10300",t4".10300",t5".10300"):is(ts(ic,ic),m0(1c))
+[r:real][s:real]
++10301
+t1:=tsis12a(s,0,0,1rl):is(ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))))
+t2:=tris(real,mn"r"(ts"r"(s,0),ts"r"(0,1rl)),m0"r"(ts"r"(0,1rl)),0,pl01(ts"r"(s,0),m0"r"(ts"r"(0,1rl)),ts02(s,0,refis(real,0))),satz176b(ts"r"(0,1rl),ts01(0,1rl,refis(real,0)))):is"r"(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0)
+t3:=tris(real,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),ts"r"(s,1rl),s,pl02(ts"r"(s,1rl),ts"r"(0,0),ts01(0,0,refis(real,0))),satz195(s)):is"r"(pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s)
+t4:=isrecx12(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s,t2,t3):is(pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s))
+t5:=tris(cx,ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s),t1,t4):is(ts(cofrl(s),ic),pli(0,s))
+t6:=ispl2(ts(cofrl(s),ic),pli(0,s),cofrl(r),t5):is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)))
+t7:=plis12a(r,0,0,s):is(pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)))
+t8:=isrecx12(pl"r"(r,0),r,pl"r"(0,s),s,pl02(r,0,refis(real,0)),pl01(0,s,refis(real,0))):is(pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s))
+-10301
+satz301a:=tr3is(cx,pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s),t6".10301",t7".10301",t8".10301"):is"e"(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s))
+satz301b:=symis(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s),satz301a):is(pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)))
+@[x:complex]
+satz301c:=tris(cx,x,pli(re(x),im(x)),pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),ispli(x),satz301b(re(x),im(x))):is(x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)))
+satz301d:=symis(cx,x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),satz301c):is(pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),x)
+s@[t:real][u:real][i:is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)))]
++*10301
+i@t9:=tr3is(cx,pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)),pli(t,u),satz301b(r,s),i,satz301a(t,u)):is(pli(r,s),pli(t,u))
+-10301
+i@satz301e:=tr3is(real,r,re(pli(r,s)),re(pli(t,u)),t,isre(r,s),iscere(pli(r,s),pli(t,u),t9".10301"),reis(t,u)):is"r"(r,t)
+satz301f:=tr3is(real,s,im(pli(r,s)),im(pli(t,u)),u,isim(r,s),isceim(pli(r,s),pli(t,u),t9".10301"),imis(t,u)):is"r"(s,u)
+-c
+-r
+-rp
+-rt
+-n
+-landau
+-eq
+-st
+-e
+-l
--- /dev/null
+# Landau's "Grundlagen der Analysis", formal specification in AUTOMATH
+# Copyright (C) 1977, L.S. van Benthem Jutting
+# 1992, revised by F. Wiedijk (http://www.cs.ru.nl/~freek/aut/)
+# 2008, revised by F. Guidi to remove the eta-reductions
+# 2014, revised by F. Guidi to suggest @-typing removal
+
++l
+@[a:'prop'][b:'prop']
+imp:=[x:a]b:'prop'
+[a1:a][i:imp(a,b)]
+mp:=<a1>i:b
+a@refimp:=[x:a]x:imp(a,a)
+b@[c:'prop'][i:imp(a,b)][j:imp(b,c)]
+trimp:=[x:a]<<x>i>j:imp(a,c)
+@con:='prim':'prop'
+a@not:=imp(con):'prop'
+wel:=not(not(a)):'prop'
+[a1:a]
+weli:=[x:not(a)]<a1>x:wel(a)
+a@[w:wel(a)]
+et:='prim':a
+a@[c1:con]
+cone:=et([x:not(a)]c1):a
++imp
+b@[i:imp(a,b)][j:imp(not(a),b)]
+th1:=et(b,[x:not(b)]<<trimp(con,i,x)>j>x):b
+b@[n:not(a)]
+th2:=trimp(con,b,n,[x:con]cone(b,x)):imp(a,b)
+b@[n:not(b)][i:imp(a,b)]
+th3:=trimp(con,i,n):not(a)
+b@[a1:a][n:not(b)]
+th4:=[x:imp(a,b)]<a1>th3(n,x):not(imp(a,b))
+b@[n:not(imp(a,b))]
+th5:=et([x:not(a)]<th2(x)>n):a
+th6:=[x:b]<[y:a]x>n:not(b)
+b@[n:not(b)][i:imp(not(a),b)]
+th7:=et(a,th3(not(a),b,n,i)):a
+-imp
+b@[i:imp(not(b),not(a))]
+cp:=[x:a]th7".imp"(b,not(a),weli(x),i):imp(a,b)
+@obvious:=imp(con,con):'prop'
+obviousi:=refimp(con):obvious
+b@ec:=imp(a,not(b)):'prop'
+[n:not(a)]
+eci1:=th2".imp"(not(b),n):ec(a,b)
+b@[n:not(b)]
+eci2:=[x:a]n:ec(a,b)
++ec
+b@[i:imp(a,not(b))]
+th1:=i:ec(a,b)
+b@[i:imp(b,not(a))]
+th2:=[x:a][y:b]<x><y>i:ec(a,b)
+-ec
+b@[e:ec(a,b)]
+comec:=th2".ec"(b,a,e):ec(b,a)
+[a1:a]
+ece1:=<a1>e:not(b)
+e@[b1:b]
+ece2:=th3".imp"(not(b),weli(b,b1),e):not(a)
++*ec
+c@[e:ec(a,b)][i:imp(c,a)]
+th3:=trimp(c,a,not(b),i,e):ec(c,b)
+e@[i:imp(c,b)]
+th4:=comec(c,a,th3(b,a,c,comec(e),i)):ec(a,c)
+-ec
+b@and:=not(ec(a,b)):'prop'
+[a1:a][b1:b]
+andi:=th4".imp"(not(b),a1,weli(b,b1)):and(a,b)
+b@[a1:and(a,b)]
+ande1:=th5".imp"(not(b),a1):a
+ande2:=et(b,th6".imp"(not(b),a1)):b
+comand:=andi(b,a,ande2,ande1):and(b,a)
++and
+b@[n:not(a)]
+th1:=weli(ec,eci1(n)):not(and)
+b@[n:not(b)]
+th2:=weli(ec,eci2(n)):not(and)
+b@[n:not(and)][a1:a]
+th3:=ece1(et(ec,n),a1):not(b)
+n@[b1:b]
+th4:=ece2(et(ec,n),b1):not(a)
+n@th5:=th3"l.imp"(and(b,a),and(a,b),n,[x:and(b,a)]comand(b,a,x)):not(and(b,a))
+c@[a1:and(a,b)][i:imp(a,c)]
+th6:=andi(c,b,<ande1(a1)>i,ande2(a1)):and(c,b)
+a1@[i:imp(b,c)]
+th7:=andi(a,c,ande1(a1),<ande2(a1)>i):and(a,c)
+-and
+b@or:=imp(not(a),b):'prop'
+[a1:a]
+ori1:=th2".imp"(not(a),b,weli(a1)):or(a,b)
+b@[b1:b]
+ori2:=[x:not(a)]b1:or(a,b)
++or
+b@[i:imp(not(a),b)]
+th1:=i:or(a,b)
+b@[i:imp(not(b),a)]
+th2:=[x:not]et(b,th3"l.imp"(not(b),a,x,i)):or(a,b)
+-or
+b@[o:or(a,b)][n:not(a)]
+ore2:=<n>o:b
+o@[n:not(b)]
+ore1:=et(th3".imp"(not(a),b,n,o)):a
+o@comor:=[x:not(b)]ore1(x):or(b,a)
++*or
+b@[n:not(a)][m:not(b)]
+th3:=th4"l.imp"(not(a),b,n,m):not(or(a,b))
+b@[n:not(or(a,b))]
+th4:=th5"l.imp"(not(a),b,n):not(a)
+th5:=th6"l.imp"(not(a),b,n):not(b)
+a@th6:=refimp(not(a)):or(a,not(a))
+-or
+c@[o:or(a,b)][i:imp(a,c)][j:imp(b,c)]
+orapp:=th1".imp"(c,i,trimp(not,b,c,o,j)):c
+c@[d:'prop']
++*or
+o@[i:imp(a,c)]
+th7:=trimp(not(c),not,b,[x:not(c)]th3"l.imp"(a,c,x,i),o):or(c,b)
+o@[i:imp(b,c)]
+th8:=trimp(not(a),b,c,o,i):or(a,c)
+d@[o:or(a,b)][i:imp(a,c)][j:imp(b,d)]
+th9:=th7(a,d,c,th8(a,b,d,o,j),i):or(c,d)
+b@[o:or(a,b)]
+th10:=o:imp(not(a),b)
+th11:=comor(o):imp(not(b),a)
+b@[o:or(not(a),b)]
+th12:=trimp(a,wel(a),b,[x:a]weli(x),o):imp(a,b)
+b@[i:imp(a,b)]
+th13:=trimp(wel(a),a,b,[x:wel(a)]et(x),i):or(not(a),b)
+b@[o:or(not(a),not(b))]
+th14:=weli(ec,th12(not(b),o)):not(and)
+b@[n:not(and)]
+th15:=th13(not(b),et(ec,n)):or(not(a),not(b))
+b@[a1:and(not(a),not(b))]
+th16:=th3(ande1(not(a),not(b),a1),ande2(not(a),not(b),a1)):not(or(a,b))
+b@[n:not(or(a,b))]
+th17:=andi(not(a),not(b),th4(n),th5(n)):and(not(a),not(b))
+-or
+b@orec:=and(or(a,b),ec(a,b)):'prop'
+[o:or(a,b)][e:ec(a,b)]
+oreci:=andi(or(a,b),ec(a,b),o,e):orec(a,b)
++orec
+b@[a1:a][n:not(b)]
+th1:=oreci(ori1(a1),eci2(n)):orec(a,b)
+b@[n:not(a)][b1:b]
+th2:=oreci(ori2(b1),eci1(n)):orec(a,b)
+-orec
+b@[o:orec(a,b)]
+orece1:=ande1(or(a,b),ec,o):or(a,b)
+orece2:=ande2(or(a,b),ec,o):ec(a,b)
+comorec:=oreci(b,a,comor(orece1),comec(orece2)):orec(b,a)
++*orec
+o@[a1:a]
+th3:=ece1(orece2,a1):not(b)
+o@[b1:b]
+th4:=ece2(orece2,b1):not(a)
+o@[n:not(a)]
+th5:=ore2(orece1,n):b
+o@[n:not(b)]
+th6:=ore1(orece1,n):a
+-orec
+b@iff:=and(imp(a,b),imp(b,a)):'prop'
+[i:imp(a,b)][j:imp(b,a)]
+iffi:=andi(imp(a,b),imp(b,a),i,j):iff(a,b)
++iff
+b@[a1:a][b1:b]
+th1:=iffi([x:a]b1,[x:b]a1):iff(a,b)
+b@[n:not(a)][m:not(b)]
+th2:=iffi(th2"l.imp"(n),th2"l.imp"(b,a,m)):iff(a,b)
+-iff
+b@[i:iff(a,b)]
+iffe1:=ande1(imp(a,b),imp(b,a),i):imp(a,b)
+iffe2:=ande2(imp(a,b),imp(b,a),i):imp(b,a)
+comiff:=iffi(b,a,iffe2,iffe1):iff(b,a)
++*iff
+i@[a1:a]
+th3:=<a1>iffe1:b
+i@[b1:b]
+th4:=<b1>iffe2:a
+i@[n:not(a)]
+th5:=th3"l.imp"(b,a,n,iffe2):not(b)
+i@[n:not(b)]
+th6:=th3"l.imp"(n,iffe1):not(a)
+b@[a1:a][n:not(b)]
+th7:=th1"l.and"(imp(a,b),imp(b,a),th4"l.imp"(a1,n)):not(iff(a,b))
+b@[n:not(a)][b1:b]
+th8:=th2"l.and"(imp(a,b),imp(b,a),th4"l.imp"(b,a,b1,n)):not(iff(a,b))
+-iff
+a@refiff:=iffi(a,refimp,refimp):iff(a,a)
+b@[i:iff(a,b)]
+symiff:=comiff(i):iff(b,a)
+c@[i:iff(a,b)][j:iff(b,c)]
+triff:=iffi(a,c,trimp(iffe1(i),iffe1(b,c,j)),trimp(c,b,a,iffe2(b,c,j),iffe2(i))):iff(a,c)
++*iff
+b@[i:iff(a,b)]
+th9:=[x:not(a)]th5(i,x):imp(not(a),not(b))
+th10:=[x:not(b)]th6(i,x):imp(not(b),not(a))
+th11:=iffi(not(a),not(b),th9,th10):iff(not(a),not(b))
+b@[i:imp(not(a),not(b))][j:imp(not(b),not(a))]
+th12:=iffi(cp(j),cp(b,a,i)):iff(a,b)
+b@[o:orec(a,b)]
+th13:=iffi(not(b),orece2(o),comor(orece1(o))):iff(a,not(b))
+th14:=th13(b,a,comorec(o)):iff(b,not(a))
+b@[i:iff(a,not(b))]
+th15:=oreci(comor(b,a,iffe2(not(b),i)),iffe1(not(b),i)):orec(a,b)
+b@[i:iff(b,not(a))]
+th16:=comorec(b,a,th15(b,a,i)):orec(a,b)
+c@[i:iff(a,b)][j:imp(a,c)]
+thimp1:=trimp(b,a,c,iffe2(i),j):imp(b,c)
+i@[j:imp(c,a)]
+thimp2:=trimp(c,a,b,j,iffe1(i)):imp(c,b)
+i@[e:ec(a,c)]
+thec1:=th3"l.ec"(c,b,e,iffe2(i)):ec(b,c)
+i@[e:ec(c,a)]
+thec2:=th4"l.ec"(c,a,b,e,iffe2(i)):ec(c,b)
+i@[a1:and(a,c)]
+thand1:=th6"l.and"(c,b,a1,iffe1(i)):and(b,c)
+i@[a1:and(c,a)]
+thand2:=th7"l.and"(c,a,b,a1,iffe1(i)):and(c,b)
+i@[o:or(a,c)]
+thor1:=th7"l.or"(c,b,o,iffe1(i)):or(b,c)
+i@[o:or(c,a)]
+thor2:=th8"l.or"(c,a,b,o,iffe1(i)):or(c,b)
+i@[o:orec(a,c)]
+thorec1:=oreci(b,c,thor1(orece1(a,c,o)),thec1(orece2(a,c,o))):orec(b,c)
+i@[o:orec(c,a)]
+thorec2:=oreci(c,b,thor2(orece1(c,a,o)),thec2(orece2(c,a,o))):orec(c,b)
+-iff
+@[sigma:'type'][p:[x:sigma]'prop']
+%suggestion by van Daalen to remove the first eta-reduction
+%all:=p:'prop' %original line
+all:=[x:sigma]<x>p:'prop'
+%end of suggestion
+[a1:all(sigma,p)][s:sigma]
+alle:=<s>a1:<s>p
++all
+p@[s:sigma][n:not(<s>p)]
+th1:=[x:all(sigma,p)]<<s>x>n:not(all(sigma,p))
+-all
+p@non:=[x:sigma]not(<x>p):[x:sigma]'prop'
+some:=not(non(p)):'prop'
+{ to validate }
+[s:sigma][sp:<s>p]
+somei:=th1".all"(non(p),s,weli(<s>p,sp)):some(sigma,p)
++some
+p@[n:not(all(sigma,p))][m:non(non(p))][s:sigma]
+t1:=et(<s>p,<s>m):<s>p
+%set etared
+m@t2:=<[x:sigma]t1(x)>n:con
+%reset etared
+n@th1:=[x:non(non(p))]t2(x):some(non(p))
+p@[s:some(non(p))][a1:all(sigma,p)][t:sigma]
+t3:=weli(<t>p,<t>a1):not(not(<t>p))
+a1@t4:=<[x:sigma]t3(x)>s:con
+s@th2:=[x:all(sigma,p)]t4(x):not(all(sigma,p))
+p@[n:not(some(sigma,p))]
+th3:=et(non(p),n):non(p)
+[s:sigma]
+th4:=<s>th3:not(<s>p)
+p@[n:non(p)]
+th5:=weli(non(p),n):not(some(sigma,p))
+-some
+p@[s:some(sigma,p)][x:'prop'][i:[y:sigma]imp(<y>p,x)]
++*some
+i@[n:not(x)][t:sigma]
+t5:=th3"l.imp"(<t>p,x,n,<t>i):not(<t>p)
+n@t6:=mp(some(sigma,p),con,s,th5([y:sigma]t5(y))):con
+-some
+i@someapp:=et(x,[y:not(x)]t6".some"(y)):x
++*some
+p@[q:[x:sigma]'prop'][s:some(sigma,p)][i:[x:sigma]imp(<x>p,<x>q)]
+th6:=someapp(s,some(q),[x:sigma][y:<x>p]somei(q,x,mp(<x>p,<x>q,y,<x>i))):some(q)
+-some
+c@or3:=or(a,or(b,c)):'prop'
+[o:or3(a,b,c)][n:not(a)]
++or3
+th1:=ore2(or(b,c),o,n):or(b,c)
+-or3
+[m:not(b)]
+or3e3:=ore2(b,c,th1".or3",m):c
+o@[n:not(b)]
++*or3
+n@th2:=th2"l.or"(c,a,[x:not(a)]or3e3(x,n)):or(c,a)
+-or3
+n@[m:not(c)]
+or3e1:=ore2(c,a,th2".or3",m):a
+o@[n:not(c)]
++*or3
+n@th3:=th2"l.or"([x:not(b)]or3e1(x,n)):or(a,b)
+-or3
+n@[m:not(a)]
+or3e2:=ore2(th3".or3",m):b
++*or3
+o@th4:=th1"l.or"(b,or(c,a),[x:not(b)]th2(x)):or3(b,c,a)
+th5:=th4(b,c,a,th4):or3(c,a,b)
+-or3
+c@[a1:a]
+or3i1:=ori1(a,or(b,c),a1):or3(a,b,c)
+c@[b1:b]
+or3i2:=ori2(a,or(b,c),ori1(b,c,b1)):or3(a,b,c)
+c@[c1:c]
+or3i3:=ori2(a,or(b,c),ori2(b,c,c1)):or3(a,b,c)
++*or3
+c@[o:or(a,b)]
+th6:=th4"or3"(c,a,b,ori2(c,or(a,b),o)):or3(a,b,c)
+c@[o:or(b,c)]
+th7:=ori2(or(b,c),o):or3(a,b,c)
+c@[o:or(c,a)]
+th8:=th4"or3"(c,a,b,th6(c,a,b,o)):or3(a,b,c)
+-or3
+d@[o:or3(a,b,c)][i:imp(a,d)][j:imp(b,d)][k:imp(c,d)]
+or3app:=orapp(or(b,c),d,o,i,[x:or(b,c)]orapp(b,c,d,x,j,k)):d
+c@and3:=and(a,and(b,c)):'prop'
+[a1:and3(a,b,c)]
+and3e1:=ande1(and(b,c),a1):a
+and3e2:=ande1(b,c,ande2(and(b,c),a1)):b
+and3e3:=ande2(b,c,ande2(and(b,c),a1)):c
+c@[a1:a][b1:b][c1:c]
+and3i:=andi(a,and(b,c),a1,andi(b,c,b1,c1)):and3(a,b,c)
++and3
+c@[a1:and3(a,b,c)]
+th1:=and3i(b,c,a,and3e2(a1),and3e3(a1),and3e1(a1)):and3(b,c,a)
+th2:=th1(b,c,a,th1):and3(c,a,b)
+th3:=andi(and3e1(a1),and3e2(a1)):and(a,b)
+th4:=ande2(and(b,c),a1):and(b,c)
+th5:=th3(c,a,b,th2):and(c,a)
+th6:=and3i(c,b,a,and3e3(a1),and3e2(a1),and3e1(a1)):and3(c,b,a)
+-and3
+c@ec3:=and3(ec,ec(b,c),ec(c,a)):'prop'
+[e:ec3(a,b,c)]
++ec3
+th1:=and3e1(ec,ec(b,c),ec(c,a),e):ec(a,b)
+th2:=and3e2(ec,ec(b,c),ec(c,a),e):ec(b,c)
+th3:=and3e3(ec,ec(b,c),ec(c,a),e):ec(c,a)
+th4:=th1"l.and3"(ec,ec(b,c),ec(c,a),e):ec3(b,c,a)
+th5:=th4(b,c,a,th4):ec3(c,a,b)
+th5a:=and3i(ec(c,b),ec(b,a),ec(a,c),comec(b,c,th2(e)),comec(a,b,th1(e)),comec(c,a,th3(e))):ec3(c,b,a)
+-ec3
+[a1:a]
+ec3e12:=ece1(th1".ec3",a1):not(b)
+ec3e13:=ece2(c,a,th3".ec3",a1):not(c)
+e@[b1:b]
+ec3e23:=ec3e12(b,c,a,th4".ec3",b1):not(c)
+ec3e21:=ec3e13(b,c,a,th4".ec3",b1):not(a)
+e@[c1:c]
+ec3e31:=ec3e12(c,a,b,th5".ec3",c1):not(a)
+ec3e32:=ec3e13(c,a,b,th5".ec3",c1):not(b)
++*ec3
+c@[e:ec(a,b)][f:ec(b,c)][g:ec(c,a)]
+th6:=and3i(ec,ec(b,c),ec(c,a),e,f,g):ec3(a,b,c)
+c@[e:ec3(a,b,c)][o:or(a,b)]
+th7:=orapp(not(c),o,[x:a]ece2(c,a,th3"ec3"(e),x),[x:b]ece1(b,c,th2"ec3"(e),x)):not(c)
+e@[o:or(b,c)]
+th8:=th7(b,c,a,th4"ec3"(e),o):not(a)
+e@[o:or(c,a)]
+th9:=th7(c,a,b,th5"ec3"(e),o):not(b)
+-ec3
+c@[n:not(a)][m:not(b)]
+ec3i1:=th6".ec3"(eci1(n),eci1(b,c,m),eci2(c,a,n)):ec3(a,b,c)
+c@[n:not(b)][m:not(c)]
+ec3i2:=th6".ec3"(eci2(n),eci1(b,c,n),eci1(c,a,m)):ec3(a,b,c)
+c@[n:not(c)][m:not(a)]
+ec3i3:=th6".ec3"(eci1(m),eci2(b,c,n),eci1(c,a,n)):ec3(a,b,c)
++*ec3
+d@[e:'prop'][f:'prop'][o1:or3(a,b,c)][p1:ec3(d,e,f)][i:imp(a,d)][j:imp(b,e)][k:imp(c,f)][d1:d]
+t1:=[x:b]mp(e,con,<x>j,ec3e12(d,e,f,p1,d1)):not(b)
+t2:=[x:c]mp(f,con,<x>k,ec3e13(d,e,f,p1,d1)):not(c)
+th10:=or3e1(o1,t1,t2):a
+k@[e1:e]
+th11:=th10(b,c,a,e,f,d,th4"l.or3"(o1),th4"ec3"(d,e,f,p1),j,k,i,e1):b
+k@[f1:f]
+th12:=th10(c,a,b,f,d,e,th5"l.or3"(o1),th5"ec3"(d,e,f,p1),k,i,j,f1):c
+-ec3
+c@orec3:=and(or3(a,b,c),ec3(a,b,c)):'prop'
+[o:orec3(a,b,c)]
+orec3e1:=ande1(or3(a,b,c),ec3(a,b,c),o):or3(a,b,c)
+orec3e2:=ande2(or3(a,b,c),ec3(a,b,c),o):ec3(a,b,c)
+c@[o:or3(a,b,c)][e:ec3(a,b,c)]
+orec3i:=andi(or3(a,b,c),ec3(a,b,c),o,e):orec3(a,b,c)
++orec3
+c@[o:orec3(a,b,c)]
+th1:=orec3i(b,c,a,th4"l.or3"(orec3e1(o)),th4"l.ec3"(orec3e2(o))):orec3(b,c,a)
+th2:=orec3i(c,a,b,th5"l.or3"(orec3e1(o)),th5"l.ec3"(orec3e2(o))):orec3(c,a,b)
+-orec3
++e
+sigma@[s:sigma][t:sigma]
+is:='prim':'prop'
+s@refis:='prim':is(s,s)
+p@[s:sigma][t:sigma][sp:<s>p][i:is(s,t)]
+isp:='prim':<t>p
+sigma@[s:sigma][t:sigma][i:is(s,t)]
+symis:=isp([x:sigma]is(x,s),s,t,refis(s),i):is(t,s)
+t@[u:sigma][i:is(s,t)][j:is(t,u)]
+tris:=isp([x:sigma]is(x,u),t,s,j,symis(i)):is(s,u)
+u@[i:is(u,s)][j:is(u,t)]
+tris1:=tris(s,u,t,symis(u,s,i),j):is(s,t)
+u@[i:is(s,u)][j:is(t,u)]
+tris2:=tris(s,u,t,i,symis(t,u,j)):is(s,t)
+sp@[i:is(t,s)]
+isp1:=isp(symis(t,s,i)):<t>p
+t@[n:not(is(s,t))]
+symnotis:=th3"l.imp"(is(t,s),is(s,t),n,[x:is(t,s)]symis(t,s,x)):not(is(t,s))
++notis
+u@[n:not(is(s,t))][i:is(s,u)]
+th1:=isp([x:sigma]not(is(x,t)),s,u,n,i):not(is(u,t))
+n@[i:is(u,s)]
+th2:=th1(symis(u,s,i)):not(is(u,t))
+n@[i:is(t,u)]
+th3:=isp([x:sigma]not(is(s,x)),t,u,n,i):not(is(s,u))
+n@[i:is(u,t)]
+th4:=th3(symis(u,t,i)):not(is(s,u))
+u@[v:sigma][n:not(is(s,t))][i:is(s,u)][j:is(t,v)]
+th5:=th3(u,t,v,th1(n,i),j):not(is(u,v))
+-notis
+u@[v:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)]
+tr3is:=tris(s,u,v,tris(i,j),k):is(s,v)
+v@[w:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)][l:is(v,w)]
+tr4is:=tris(s,v,w,tr3is(i,j,k),l):is(s,w)
+p@amone:=[x:sigma][y:sigma][u:<x>p][v:<y>p]is(x,y):'prop'
+[a1:amone(sigma,p)][s:sigma][t:sigma][sp:<s>p][tp:<t>p]
+amonee:=<tp><sp><t><s>a1:is(s,t)
+p@one:=and(amone(sigma,p),some(sigma,p)):'prop'
+[a1:amone(sigma,p)][s:some(sigma,p)]
+onei:=andi(amone(sigma,p),some(sigma,p),a1,s):one(sigma,p)
+p@[o1:one(sigma,p)]
+onee1:=ande1(amone(sigma,p),some(sigma,p),o1):amone(sigma,p)
+onee2:=ande2(amone(sigma,p),some(sigma,p),o1):some(sigma,p)
+ind:='prim':sigma
+oneax:='prim':<ind>p
++one
+[s:sigma][sp:<s>p]
+th1:=amonee(onee1,ind,s,oneax,sp):is(ind,s)
+-one
+sigma@[tau:'type'][f:[x:sigma]tau][s:sigma][t:sigma][i:is(s,t)]
+isf:=isp(sigma,[x:sigma]is(tau,<s>f,<x>f),s,t,refis(tau,<s>f),i):is(tau,<s>f,<t>f)
+f@injective:=all([x:sigma]all([y:sigma]imp(is(tau,<x>f,<y>f),is(x,y)))):'prop'
+[i:injective(f)][s:sigma][t:sigma][j:is(tau,<s>f,<t>f)]
+isfe:=<j><t><s>i:is(s,t)
+f@[t0:tau]
+image:=some([x:sigma]is(tau,t0,<x>f)):'prop'
+f@[s:sigma]
+tofs:=<s>f:tau
+imagei:=somei([x:sigma]is(tau,tofs,<x>f),s,refis(tau,tofs)):image(tofs)
++inj
+i@[ta:tau][tb:tau][j:is(tau,ta,tb)][sa:sigma][sb:sigma][ja:is(tau,ta,tofs(sa))][jb:is(tau,tb,tofs(sb))]
+t1:=tr3is(tau,tofs(sa),ta,tb,tofs(sb),symis(tau,ta,tofs(sa),ja),j,jb):is(tau,tofs(sa),tofs(sb))
+th1:=isfe(sa,sb,t1):is(sa,sb)
+i@[t0:tau]
+th2:=[x:sigma][y:sigma][u:is(tau,t0,<x>f)][v:is(tau,t0,<y>f)]th1(t0,t0,refis(tau,t0),x,y,u,v):amone([x:sigma]is(tau,t0,<x>f))
+[j:image(f,t0)]
+th3:=onei([x:sigma]is(tau,t0,<x>f),th2,j):one([x:sigma]is(tau,t0,<x>f))
+-inj
+i@[t0:tau][j:image(f,t0)]
+soft:=ind([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):sigma
+i@inverse:=[x:tau][u:image(f,x)]soft(x,u):[x:tau][u:image(f,x)]sigma
+j@ists1:=oneax([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):is(tau,t0,tofs(soft(t0,j)))
+ists2:=symis(tau,t0,tofs(soft(t0,j)),ists1):is(tau,tofs(soft(t0,j)),t0)
+i@[ta:tau][ja:image(ta)][tb:tau][jb:image(tb)][j:is(tau,ta,tb)]
+isinv:=th1".inj"(ta,tb,j,soft(ta,ja),soft(tb,jb),ists1(ta,ja),ists1(tb,jb)):is(soft(ta,ja),soft(tb,jb))
+jb@[j:is(soft(ta,ja),soft(tb,jb))]
+isinve:=tr3is(tau,ta,tofs(soft(ta,ja)),tofs(soft(tb,jb)),tb,ists1(ta,ja),isf(soft(ta,ja),soft(tb,jb),j),ists2(tb,jb)):is(tau,ta,tb)
+i@[s:sigma]
+isst1:=isfe(s,soft(tofs(s),imagei(s)),ists1(tofs(s),imagei(s))):is(s,soft(tofs(s),imagei(s)))
+isst2:=symis(s,soft(tofs(s),imagei(s)),isst1):is(soft(tofs(s),imagei(s)),s)
+f@surjective:=all(tau,[x:tau]image(x)):'prop'
+bijective:=and(injective,surjective):'prop'
+[b:bijective(f)]
++*inj
+b@t2:=ande1(injective,surjective,b):injective(f)
+t3:=ande2(injective,surjective,b):surjective(f)
+[t:tau]
+so:=soft(t2,t,<t>t3):sigma
+-inj
+b@invf:=[x:tau]so".inj"(x):[x:tau]sigma
+[s:sigma]
+thinvf1:=tris(s,soft(t2".inj",tofs(s),imagei(s)),<<s>f>invf,isst1(t2".inj",s),isinv(t2".inj",tofs(s),imagei(s),tofs(s),<tofs(s)>t3".inj",refis(tau,tofs(s)))):is(s,<<s>f>invf)
+b@[t:tau]
+thinvf2:=ists1(t2".inj",t,<t>t3".inj"):is(tau,t,<<t>invf>f)
+tau@[upsilon:'type'][f:[x:sigma]tau][g:[x:tau]upsilon]
++*inj
+g@[if:injective(sigma,tau,f)][ig:injective(tau,upsilon,g)]
+h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
+[s:sigma][t:sigma][i:is(upsilon,<s>h,<t>h)]
+t4:=isfe(tau,upsilon,g,ig,<s>f,<t>f,i):is(tau,<s>f,<t>f)
+t5:=isfe(f,if,s,t,t4):is(s,t)
+ig@th4:=[x:sigma][y:sigma][v:is(upsilon,<x>h,<y>h)]t5(x,y,v):injective(sigma,upsilon,[x:sigma]<<x>f>g)
+-inj
++surj
+g@[sf:surjective(sigma,tau,f)][sg:surjective(tau,upsilon,g)]
+h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
+[u:upsilon]
+t1:=<u>sg:image(tau,upsilon,g,u)
+[t:tau][i:is(upsilon,u,<t>g)]
+t2:=<t>sf:image(sigma,tau,f,t)
+[s:sigma][j:is(tau,t,<s>f)]
+t3:=tris(upsilon,u,<t>g,<s>h,i,isf(tau,upsilon,g,t,<s>f,j)):is(upsilon,u,<s>h)
+t4:=somei([x:sigma]is(upsilon,u,<x>h),s,t3):image(sigma,upsilon,h,u)
+i@t5:=someapp([x:sigma]is(tau,t,<x>f),t2,image(sigma,upsilon,h,u),[x:sigma][v:is(tau,t,<x>f)]t4(x,v)):image(sigma,upsilon,h,u)
+u@t6:=someapp(tau,[x:tau]is(upsilon,u,<x>g),t1,image(sigma,upsilon,h,u),[x:tau][v:is(upsilon,u,<x>g)]t5(x,v)):image(sigma,upsilon,h,u)
+sg@th1:=[x:upsilon]t6(x):surjective(sigma,upsilon,[x:sigma]<<x>f>g)
+-surj
++bij
+g@[bf:bijective(sigma,tau,f)][bg:bijective(tau,upsilon,g)]
+h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
+t1:=th4"e.inj"(f,g,ande1(injective(f),surjective(f),bf),ande1(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):injective(sigma,upsilon,h)
+t2:=th1"e.surj"(f,g,ande2(injective(f),surjective(f),bf),ande2(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):surjective(sigma,upsilon,h)
+th1:=andi(injective(sigma,upsilon,h),surjective(sigma,upsilon,h),t1,t2):bijective(sigma,upsilon,[x:sigma]<<x>f>g)
+-bij
+tau@[f:[x:sigma]tau][g:[x:sigma]tau][i:is([x:sigma]tau,f,g)][s:sigma]
+fise:=isp([x:sigma]tau,[y:[x:sigma]tau]is(tau,<s>f,<s>y),f,g,refis(tau,<s>f),i):is(tau,<s>f,<s>g)
+g@[i:[x:sigma]is(tau,<x>f,<x>g)]
+fisi:='prim':is([x:sigma]tau,f,g)
++fis
+g@[i:is([x:sigma]tau,f,g)][s:sigma][t:sigma][j:is(s,t)]
+th1:=tris(tau,<s>f,<t>f,<t>g,isf(f,s,t,j),fise(i,t)):is(tau,<s>f,<t>g)
+-fis
+p@ot:='prim':'type'
+[o1:ot]
+in:='prim':sigma
+inp:='prim':<in>p
+p@otax1:='prim':injective(ot,sigma,[x:ot]in(x))
+[s:sigma][sp:<s>p]
+otax2:='prim':image(ot,sigma,[x:ot]in(x),s)
+o1@[o2:ot][i:is(ot,o1,o2)]
+isini:=isf(ot,sigma,[x:ot]in(x),o1,o2,i):is(in(o1),in(o2))
+o2@[i:is(in(o1),in(o2))]
+isine:=isfe(ot,sigma,[x:ot]in(x),otax1,o1,o2,i):is(ot,o1,o2)
+sp@out:=soft(ot,sigma,[x:ot]in(x),otax1,s,otax2):ot
+[t:sigma][tp:<t>p][i:is(s,t)]
+isouti:=isinv(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(ot,out(s,sp),out(t,tp))
+tp@[i:is(ot,out(s,sp),out(t,tp))]
+isoute:=isinve(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(s,t)
+o1@isoutin:=tris(ot,o1,soft(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1)),out(in(o1),inp(o1)),isst1(ot,sigma,[x:ot]in(x),otax1,o1),isinv(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1),in(o1),otax2(in(o1),inp(o1)),refis(sigma,in(o1)))):is(ot,o1,out(in(o1),inp(o1)))
+sp@isinout:=ists1(ot,sigma,[x:ot]in(x),otax1,s,otax2):is(s,in(out(s,sp)))
+tau@pairtype:='prim':'type'
+[s:sigma][t:tau]
+pair:='prim':pairtype
+tau@[p1:pairtype]
+first:='prim':sigma
+second:='prim':tau
+pairis1:='prim':is(pairtype,pair(first,second),p1)
+pairis2:=symis(pairtype,pair(first,second),p1,pairis1):is(pairtype,p1,pair(first,second))
+t@firstis1:='prim':is(sigma,first(pair),s)
+firstis2:=symis(sigma,first(pair),s,firstis1):is(sigma,s,first(pair))
+secondis1:='prim':is(tau,second(pair),t)
+secondis2:=symis(tau,second(pair),t,secondis1):is(tau,t,second(pair))
+a@[ksi:'type'][x:ksi][y:ksi]
++ite
+[z:ksi]
+prop1:=and(imp(a,is(ksi,z,x)),imp(not(a),is(ksi,z,y))):'prop'
+y@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t1:=ande1(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(a,is(ksi,x1,x))
+t2:=mp(a,is(ksi,x1,x),a1,t1):is(ksi,x1,x)
+t3:=t2(y1,x1,py1,px1):is(ksi,y1,x)
+t4:=tris2(ksi,x1,y1,x,t2,t3):is(ksi,x1,y1)
+a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
+t6:=[x1:a]refis(ksi,x):imp(a,is(ksi,x,x))
+t7:=th2"l.imp"(not(a),is(ksi,x,y),weli(a,a1)):imp(not(a),is(ksi,x,y))
+t8:=andi(imp(a,is(ksi,x,x)),imp(not(a),is(ksi,x,y)),t6,t7):prop1(x)
+t9:=somei(ksi,[t:ksi]prop1(t),x,t8):some(ksi,[t:ksi]prop1(t))
+t10:=onei(ksi,[t:ksi]prop1(t),t5,t9):one(ksi,[t:ksi]prop1(t))
+y@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t11:=ande2(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(not(a),is(ksi,x1,y))
+t12:=mp(not(a),is(ksi,x1,y),n,t11):is(ksi,x1,y)
+t13:=t12(y1,x1,py1,px1):is(ksi,y1,y)
+t14:=tris2(ksi,x1,y1,y,t12,t13):is(ksi,x1,y1)
+n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
+t16:=[x1:not(a)]refis(ksi,y):imp(not(a),is(ksi,y,y))
+t17:=th2"l.imp"(a,is(ksi,y,x),n):imp(a,is(ksi,y,x))
+t18:=andi(imp(a,is(ksi,y,x)),imp(not(a),is(ksi,y,y)),t17,t16):prop1(y)
+t19:=somei(ksi,[t:ksi]prop1(t),y,t18):some(ksi,[t:ksi]prop1(t))
+t20:=onei(ksi,[t:ksi]prop1(t),t15,t19):one(ksi,[t:ksi]prop1(t))
+y@t21:=th1"l.imp"(a,one(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one(ksi,[t:ksi]prop1(t))
+-ite
+ite:=ind(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
++*ite
+y@t22:=oneax(ksi,[t:ksi]prop1(t),t21):prop1(ite)
+t23:=ande1(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(a,is(ksi,ite,x))
+t24:=ande2(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(not(a),is(ksi,ite,y))
+-ite
+y@[a1:a]
+itet:=mp(a,is(ksi,ite,x),a1,t23".ite"):is(ksi,ite,x)
+y@[n:not(a)]
+itef:=mp(not(a),is(ksi,ite,y),n,t24".ite"):is(ksi,ite,y)
+sigma@[s0:sigma][t0:sigma]
++wissel
+[s:sigma]
+wa:=ite(is(s,s0),sigma,t0,s):sigma
+[i:is(s,s0)]
+t1:=itet(is(s,s0),sigma,t0,s,i):is(wa,t0)
+s@[n:not(is(s,s0))]
+t2:=itef(is(s,s0),sigma,t0,s,n):is(wa,s)
+s@wb:=ite(is(s,t0),sigma,s0,wa):sigma
+[i:is(s,t0)]
+t3:=itet(is(s,t0),sigma,s0,wa,i):is(wb,s0)
+s@[n:not(is(s,t0))]
+t4:=itef(is(s,t0),sigma,s0,wa,n):is(wb,wa)
+s@[i:is(s,s0)][j:is(s0,t0)]
+t5:=tris(wb,s0,t0,t3(tris(s,s0,t0,i,j)),j):is(wb,t0)
+i@[n:not(is(s0,t0))]
+t6:=tris(wb,wa,t0,t4(th2"e.notis"(s0,t0,s,n,i)),t1(i)):is(wb,t0)
+i@t7:=th1"l.imp"(is(s0,t0),is(wb,t0),[t:is(s0,t0)]t5(t),[t:not(is(s0,t0))]t6(t)):is(wb,t0)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+t8:=tris(wb,wa,s,t4(o),t2(n)):is(wb,s)
+-wissel
+wissel:=[x:sigma]wb".wissel"(x):[x:sigma]sigma
+[s:sigma][i:is(s,s0)]
+iswissel1:=t7".wissel"(s,i):is(<s>wissel,t0)
+s@[i:is(s,t0)]
+iswissel2:=t3".wissel"(s,i):is(<s>wissel,s0)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+iswissel3:=t8".wissel"(s,n,o):is(<s>wissel,s)
++*wissel
+s@[t:sigma][i:is(wb(s),wb(t))][n:not(is(s,t))][j:is(s,s0)]
+t9:=symnotis(s0,t,th1"e.notis"(s,t,s0,n,j)):not(is(t,s0))
+[k:is(s0,t0)]
+t10:=th3"e.notis"(t,s0,t0,t9,k):not(is(t,t0))
+t11:=tris(wb(s),wb(t),t,i,t8(t,t9,t10)):is(wb(s),t)
+t12:=<tris1(t,t0,wb(s),t11,t7(j))>t10:con
+j@t13:=[v:is(s0,t0)]t12(v):not(is(s0,t0))
+[k:is(t,t0)]
+t14:=tris(wb(s),wb(t),s0,i,t3(t,k)):is(wb(s),s0)
+t15:=t12(tris1(s0,t0,wb(s),t14,t7(j))):con
+j@t16:=[v:is(t,t0)]t15(v):not(is(t,t0))
+t17:=tris(wb(s),wb(t),t,i,t8(t,t9,t16)):is(wb(s),t)
+t18:=t15(tris1(t,t0,wb(s),t17,t7(j))):con
+n@t19:=[v:is(s,s0)]t18(v):not(is(s,s0))
+t20:=t19(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,s0))
+[j:is(s,t0)]
+t21:=symnotis(t0,t,th1"e.notis"(s,t,t0,n,j)):not(is(t,t0))
+t22:=tris(wb(s),wb(t),t,i,t8(t,t20,t21)):is(wb(s),t)
+t23:=<tris1(t,s0,wb(s),t22,t3(j))>t20:con
+n@t24:=[v:is(s,t0)]t23(v):not(is(s,t0))
+t25:=t24(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,t0))
+t26:=tris(wb(s),wb(t),t,i,t8(t,t20,t25)):is(wb(s),t)
+t27:=<tris1(s,t,wb(s),t8(t19,t24),t26)>n:con
+i@t28:=et(is(s,t),[v:not(is(s,t))]t27(v)):is(s,t)
+t0@th1:=[x:sigma][y:sigma][v:is(wb(x),wb(y))]t28(x,y,v):injective(sigma,sigma,wissel)
+s@[i:is(s,s0)]
+t29:=tris2(s,wb(t0),s0,i,t3(t0,refis(t0))):is(s,wb(t0))
+t30:=somei(sigma,[x:sigma]is(s,wb(x)),t0,t29):image(sigma,sigma,wissel,s)
+s@[i:is(s,t0)]
+t31:=tris2(s,wb(s0),t0,i,t7(s0,refis(s0))):is(s,wb(s0))
+t32:=somei(sigma,[x:sigma]is(s,wb(x)),s0,t31):image(sigma,sigma,wissel,s)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+t33:=symis(wb(s),s,t8(n,o)):is(s,wb(s))
+t34:=somei(sigma,[x:sigma]is(s,wb(x)),s,t33):image(sigma,sigma,wissel,s)
+n@t35:=th1"l.imp"(is(s,t0),image(sigma,sigma,wissel,s),[v:is(s,t0)]t32(v),[v:not(is(s,t0))]t34(v)):image(sigma,sigma,wissel,s)
+s@t36:=th1"l.imp"(is(s,s0),image(sigma,sigma,wissel,s),[v:is(s,s0)]t30(v),[v:not(is(s,s0))]t35(v)):image(sigma,sigma,wissel,s)
+t0@th2:=[x:sigma]t36(x):surjective(sigma,sigma,wissel)
+th3:=andi(injective(sigma,sigma,wissel),surjective(sigma,sigma,wissel),th1,th2):bijective(sigma,sigma,wissel)
+-wissel
+tau@[f:[x:sigma]tau][s0:sigma][t0:sigma]
+changef:=[x:sigma]<<x>wissel(s0,t0)>f:[x:sigma]tau
+[s:sigma][i:is(s,s0)]
+changef1:=isf(sigma,tau,f,<s>wissel(s0,t0),t0,iswissel1(s0,t0,s,i)):is(tau,<s>changef,<t0>f)
+s@[i:is(s,t0)]
+changef2:=isf(sigma,tau,f,<s>wissel(s0,t0),s0,iswissel2(s0,t0,s,i)):is(tau,<s>changef,<s0>f)
+s@[n:not(is(s,s0))][o:not(is(s,t0))]
+changef3:=isf(sigma,tau,f,<s>wissel(s0,t0),s,iswissel3(s0,t0,s,n,o)):is(tau,<s>changef,<s>f)
++*wissel
+t0@[i:injective(f)]
+th4:=th4"e.inj"(sigma,sigma,tau,wissel(s0,t0),f,th1(s0,t0),i):injective(changef)
+t0@[s:surjective(f)]
+th5:=th1"e.surj"(sigma,sigma,tau,wissel(s0,t0),f,th2(s0,t0),s):surjective(changef)
+t0@[b:bijective(f)]
+th6:=th1"e.bij"(sigma,sigma,tau,wissel(s0,t0),f,th3(s0,t0),b):bijective(changef)
+-wissel
+-e
++r
+a@[b:[x:a]'prop']
+%suggestion by van Daalen to remove the second eta-reduction
+%imp:=b:'prop' %original line
+imp:=[x:a]<x>b:'prop'
+%end of suggestion
+[a1:a][i:imp(a,b)]
+mp:=<a1>i:<a1>b
++imp
+b@[n:not(a)]
+%set etared
+th2:=[x:a]cone(<x>b,mp"l"(a,con,x,n)):imp(a,b)
+%reset etared
+-imp
+b@ec:=[x:a]not(<x>b):'prop'
+[n:not(a)]
+eci1:=[x:a]cone(not(<x>b),mp"l"(a,con,x,n)):ec(a,b)
+%suggestion by Guidi to remove @-typing by adding imp-introduction
+b@[a1:and(a,b)] %original line
+ande2:=<ande1(a,b,a1)>ande2"l"(a,b,a1):<ande1(a,b,a1)>b %original line
+%b@[a1:and(a,imp(a,b))]
+%ande2:=<ande1(a,imp(a,b),a1)>ande2"l"(a,imp(a,b),a1):<ande1(a,imp(a,b),a1)>b
+%end of suggestion
+a@[ksi:'type']
++ite
+[x1:ksi][y1:ksi]
+is:=is"l.e"(ksi,x1,y1):'prop'
+-ite
+[x:[t:a]ksi][y:[t:not(a)]ksi][i:[t:a][u:a]is".ite"(<t>x,<u>x)][j:[t:not(a)][u:not(a)]is".ite"(<t>y,<u>y)]
++*ite
+j@[z:ksi]
+prop1:=and(imp(a,[t:a]is(z,<t>x)),imp(not(a),[t:not(a)]is(z,<t>y))):'prop'
+j@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t1:=ande1"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(a,[t:a]is(x1,<t>x))
+t2:=mp(a,[t:a]is(x1,<t>x),a1,t1):is(x1,<a1>x)
+t3:=t2(y1,x1,py1,px1):is(y1,<a1>x)
+t4:=tris2"l.e"(ksi,x1,y1,<a1>x,t2,t3):is(x1,y1)
+a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
+t6:=<a1>i:imp(a,[t:a]is(<a1>x,<t>x))
+t7:=th2"r.imp"(not(a),[t:not(a)]is(<a1>x,<t>y),weli(a,a1)):imp(not(a),[t:not(a)]is(<a1>x,<t>y))
+t8:=andi(imp(a,[t:a]is(<a1>x,<t>x)),imp(not(a),[t:not(a)]is(<a1>x,<t>y)),t6,t7):prop1(<a1>x)
+t9:=somei(ksi,[t:ksi]prop1(t),<a1>x,t8):some(ksi,[t:ksi]prop1(t))
+t10:=onei"l.e"(ksi,[t:ksi]prop1(t),t5,t9):one"l.e"(ksi,[t:ksi]prop1(t))
+j@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
+t11:=ande2"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(not(a),[t:not(a)]is(x1,<t>y))
+t12:=mp(not(a),[t:not(a)]is(x1,<t>y),n,t11):is(x1,<n>y)
+t13:=t12(y1,x1,py1,px1):is(y1,<n>y)
+t14:=tris2"l.e"(ksi,x1,y1,<n>y,t12,t13):is(x1,y1)
+n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
+t16:=<n>j:imp(not(a),[t:not(a)]is(<n>y,<t>y))
+t17:=th2"r.imp"(a,[t:a]is(<n>y,<t>x),n):imp(a,[t:a]is(<n>y,<t>x))
+t18:=andi"l"(imp(a,[t:a]is(<n>y,<t>x)),imp(not(a),[t:not(a)]is(<n>y,<t>y)),t17,t16):prop1(<n>y)
+t19:=somei(ksi,[t:ksi]prop1(t),<n>y,t18):some(ksi,[t:ksi]prop1(t))
+t20:=onei"l.e"(ksi,[t:ksi]prop1(t),t15,t19):one"l.e"(ksi,[t:ksi]prop1(t))
+j@t21:=th1"l.imp"(a,one"l.e"(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one"l.e"(ksi,[t:ksi]prop1(t))
+-ite
+j@ite:=ind"l.e"(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
++*ite
+j@t22:=oneax"l.e"(ksi,[t:ksi]prop1(t),t21):prop1(ite)
+t23:=ande1"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(a,[t:a]is(ite,<t>x))
+t24:=ande2"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(not(a),[t:not(a)]is(ite,<t>y))
+-ite
+j@[a1:a]
+itet:=mp(a,[t:a]is".ite"(ite,<t>x),a1,t23".ite"):is".ite"(ksi,ite,<a1>x)
+j@[n:not(a)]
+itef:=mp(not(a),[t:not(a)]is".ite"(ite,<t>y),n,t24".ite"):is".ite"(ksi,ite,<n>y)
+-r
++*e
++st
+sigma@set:='prim':'type'
+[s:sigma][s0:set]
+esti:='prim':'prop'
+p@setof:='prim':set
+[s:sigma][sp:<s>p]
+estii:='prim':esti(s,setof(p))
+s@[e:esti(s,setof(p))]
+estie:='prim':<s>p
+sigma@[s0:set]
+empty:=non([x:sigma]esti(x,s0)):'prop'
+nonempty:=some([x:sigma]esti(x,s0)):'prop'
+[n:[x:sigma]not(esti(x,s0))]
+emptyi:=n:empty(s0)
+s0@[e:empty(s0)][s:sigma]
+emptye:=<s>e:not(esti(s,s0))
+s0@[s:sigma][ses0:esti(s,s0)]
+nonemptyi:=somei([x:sigma]esti(x,s0),s,ses0):nonempty(s0)
+s0@[n:nonempty(s0)][x:'prop'][x1:[y:sigma][z:esti(y,s0)]x]
+nonemptyapp:=someapp([y:sigma]esti(y,s0),n,x,x1):x
+s0@[t0:set]
+incl:=all([x:sigma]imp(esti(x,s0),esti(x,t0))):'prop'
+[e:[x:sigma][y:esti(x,s0)]esti(x,t0)]
+incli:=e:incl(s0,t0)
+t0@[i:incl(s0,t0)][s:sigma][ses0:esti(s,s0)]
+incle:=<ses0><s>i:esti(s,t0)
+s0@refincl:=[x:sigma][y:esti(x,s0)]y:incl(s0,s0)
+t0@disj:=all([x:sigma]ec(esti(x,s0),esti(x,t0))):'prop'
+[n:[x:sigma][y:esti(x,s0)]not(esti(x,t0))]
+disji1:=n:disj(s0,t0)
+t0@[n:[x:sigma][y:esti(x,t0)]not(esti(x,s0))]
+disji2:=[x:sigma]th2"l.ec"(esti(x,s0),esti(x,t0),<x>n):disj(s0,t0)
+t0@[d:disj(s0,t0)][s:sigma][ses0:esti(s,s0)]
+disje1:=ece1(esti(s,s0),esti(s,t0),<s>d,ses0):not(esti(s,t0))
+s@[set0:esti(s,t0)]
+disje2:=ece2(esti(s,s0),esti(s,t0),<s>d,set0):not(esti(s,s0))
+t0@[d:disj(s0,t0)]
+symdisj:=[x:sigma][y:esti(x,t0)]disje2(d,x,y):disj(t0,s0)
++disj
+t0@[s:sigma][ses0:esti(s,s0)][set0:esti(s,t0)]
+th1:=th1"l.all"([x:sigma]ec(esti(x,s0),esti(x,t0)),s,th4"l.imp"(esti(s,s0),not(esti(s,t0)),ses0,weli(esti(s,t0),set0))):not(disj(s0,t0))
+th2:=th1(t0,s0,s,set0,ses0):not(disj(t0,s0))
+-disj
+t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
+issete1:=isp(set,[x:set]esti(s,x),s0,t0,ses0,i):esti(s,t0)
+s@[set0:esti(s,t0)]
+issete2:=isp1(set,[x:set]esti(s,x),t0,s0,set0,i):esti(s,s0)
++isset
+i@th1:=[x:sigma][y:esti(x,s0)]issete1(x,y):incl(s0,t0)
+th2:=[x:sigma][y:esti(x,t0)]issete2(x,y):incl(t0,s0)
+-isset
+t0@[i:incl(s0,t0)][j:incl(t0,s0)]
+isseti:='prim':is(set,s0,t0)
++*isset
+t0@[s:sigma][ses0:esti(s,s0)][n:not(esti(s,t0))]
+th3:=th3"l.imp"(is(set,s0,t0),esti(s,t0),n,[t:is(set,s0,t0)]issete1(t,s,ses0)):not(is(set,s0,t0))
+th4:=symnotis(set,s0,t0,th3):not(is(set,t0,s0))
+s@nissetprop:=and(esti(s,s0),not(esti(s,t0))):'prop'
+[n:not(nissetprop(s0,t0,s))][e:esti(s,s0)]
+t1:=et(esti(s,t0),th3"l.and"(esti(s,s0),not(esti(s,t0)),n,e)):esti(s,t0)
+t0@[n:not(is(set,s0,t0))][m:not(some([x:sigma]nissetprop(s0,t0,x)))][l:non([x:sigma]nissetprop(t0,s0,x))][s:sigma]
+t2:=th4"l.some"([x:sigma]nissetprop(s0,t0,x),m,s):not(nissetprop(s0,t0,s))
+t3:=<s>l:not(nissetprop(t0,s0,s))
+l@t4:=isseti(s0,t0,[x:sigma][y:esti(x,s0)]t1(s0,t0,x,t2(x),y),[x:sigma][y:esti(x,t0)]t1(t0,s0,x,t3(x),y)):is(set,s0,t0)
+m@t5:=th3"l.imp"(non([x:sigma]nissetprop(t0,s0,x)),is(set,s0,t0),n,[y:non([x:sigma]nissetprop(t0,s0,x))]t4(y)):some([x:sigma]nissetprop(t0,s0,x))
+n@th5:=th1"l.or"(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)),[y:not(some([x:sigma]nissetprop(s0,t0,x)))]t5(y)):or(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)))
+-isset
+sigma@[alpha:'type'][sa:[x:alpha]set]
+unmore:=setof([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa))):set
+[s:sigma][a:alpha][seasa:esti(s,<a>sa)]
+eunmore1:=estii([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa)),s,somei(alpha,[y:alpha]esti(s,<y>sa),a,seasa)):esti(s,unmore(sa))
+s@[seun:esti(s,unmore(sa))][x:'prop'][x1:[y:alpha][z:esti(s,<y>sa)]x]
+unmoreapp:=someapp(alpha,[y:alpha]esti(s,<y>sa),estie([z:sigma]some(alpha,[y:alpha]esti(z,<y>sa)),s,seun),x,x1):x
++eq
+sigma@[r:[x:sigma][y:sigma]'prop'][refr1:[x:sigma]<x><x>r][symr1:[x:sigma][y:sigma][t:<y><x>r]<x><y>r][trr1:[x:sigma][y:sigma][z:sigma][t:<y><x>r][u:<z><y>r]<z><x>r][s:sigma]
+refr:=<s>refr1:<s><s>r
+[t:sigma][tsr:<t><s>r]
+symr:=<tsr><t><s>symr1:<s><t>r
+t@[u:sigma][tsr:<t><s>r][utr:<u><t>r]
+trr:=<utr><tsr><u><t><s>trr1:<u><s>r
+u@[sur:<s><u>r][tur:<t><u>r]
+tr1r:=trr(s,u,t,symr(u,s,sur),tur):<t><s>r
+u@[usr:<u><s>r][utr:<u><t>r]
+tr2r:=trr(s,u,t,usr,symr(t,u,utr)):<t><s>r
+s@ecelt:=setof(<s>r):set
++1
+th1:=estii(<s>r,s,refr):esti(s,ecelt(s))
+t@[tsr:<t><s>r]
+th2:=estii(<s>r,t,tsr):esti(t,ecelt(s))
+t@[e:esti(t,ecelt(s))]
+th3:=estie(<s>r,t,e):<t><s>r
+tsr@[u:sigma][e:esti(u,ecelt(s))]
+t1:=th2(t,u,tr1r(t,u,s,tsr,th3(u,e))):esti(u,ecelt(t))
+tsr@th4:=isseti(ecelt(s),ecelt(t),[x:sigma][y:esti(x,ecelt(s))]t1(x,y),[x:sigma][y:esti(x,ecelt(t))]t1(t,s,symr(tsr),x,y)):is(set,ecelt(s),ecelt(t))
+t@[n:not(<t><s>r)][u:sigma][e:esti(u,ecelt(s))]
+t2:=th3"l.imp"(esti(u,ecelt(t)),<t><s>r,n,[x:esti(u,ecelt(t))]tr2r(s,t,u,th3(u,e),th3(t,u,x))):not(esti(u,ecelt(t)))
+n@th5:=[x:sigma][y:esti(x,ecelt(s))]t2(x,y):disj(ecelt(s),ecelt(t))
+s@th6:=nonemptyi(ecelt(s),s,th1):nonempty(ecelt(s))
+-1
+trr1@[s0:set][s:sigma]
+ecp:=is(set,s0,ecelt(s)):'prop'
+s0@anec:=some([x:sigma]ecp(x)):'prop'
++2
+trr1@[s:sigma]
+th1:=somei([x:sigma]ecp(ecelt(s),x),s,refis(set,ecelt(s))):anec(ecelt(s))
+-2
+[ecs0:anec(s0)]
++*2
+ecs0@[s:sigma][ses0:esti(s,s0)][t:sigma][e:ecp(s0,t)]
+t1:=issete1(s0,ecelt(t),e,s,ses0):esti(s,ecelt(t))
+t2:=th4"eq.1"(t,s,th3"eq.1"(t,s,t1)):is(set,ecelt(t),ecelt(s))
+t3:=tris(set,s0,ecelt(t),ecelt(s),e,t2):is(set,s0,ecelt(s))
+ses0@th2:=someapp([x:sigma]ecp(x),ecs0,is(set,s0,ecelt(s)),[x:sigma][y:ecp(x)]t3(x,y)):is(set,s0,ecelt(s))
+[t:sigma][tes0:esti(t,s0)]
+th3:=th3"eq.1"(s,t,issete1(s0,ecelt(s),th2,t,tes0)):<t><s>r
+t@[tsr:<t><s>r]
+th4:=issete2(s0,ecelt(s),th2,t,th2"eq.1"(s,t,tsr)):esti(t,s0)
+ecs0@[s:sigma][e:ecp(s0,s)]
+t4:=isp(set,[x:set]nonempty(x),ecelt(s),s0,th6"eq.1"(s),symis(set,s0,ecelt(s),e)):nonempty(s0)
+ecs0@th5:=someapp([x:sigma]ecp(x),ecs0,nonempty(s0),[x:sigma][y:ecp(x)]t4(x,y)):nonempty(s0)
+-2
++3
+ecs0@[t0:set][ect0:anec(t0)][s:sigma][ses0:esti(s,s0)][t:sigma][tet0:esti(t,t0)][tsr:<t><s>r]
+th1:=tr3is(set,s0,ecelt(s),ecelt(t),t0,th2"eq.2"(s0,ecs0,s,ses0),th4"eq.1"(s,t,tsr),symis(set,t0,ecelt(t),th2"eq.2"(t0,ect0,t,tet0))):is(set,s0,t0)
+tet0@[n:not(<t><s>r)]
+t1:=isp1(set,[x:set]disj(x,ecelt(t)),ecelt(s),s0,th5"eq.1"(s,t,n),th2"eq.2"(s0,ecs0,s,ses0)):disj(s0,ecelt(t))
+th2:=isp1(set,[x:set]disj(s0,x),ecelt(t),t0,t1,th2"eq.2"(t0,ect0,t,tet0)):disj(s0,t0)
+t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
+t2:=issete1(s0,t0,i,s,ses0):esti(s,t0)
+t3:=th1"st.disj"(s0,t0,s,ses0,t2):not(disj(s0,t0))
+i@th3:=nonemptyapp(s0,th5"eq.2"(s0,ecs0),not(disj(s0,t0)),[x:sigma][y:esti(x,s0)]t3(x,y)):not(disj(s0,t0))
+-3
+trr1@ect:=ot(set,[x:set]anec(x)):'type'
+ecs0@ectset:=out(set,[x:set]anec(x),s0,ecs0):ect
+trr1@[s:sigma]
+ectelt:=ectset(ecelt(s),th1".2"(s)):ect
+trr1@[e:ect]
+ecect:=in(set,[x:set]anec(x),e):set
++4
+th1:=inp(set,[x:set]anec(x),e):anec(ecect(e))
+th2:=th5"eq.2"(ecect(e),th1):nonempty(ecect(e))
+[x:'prop'][x1:[y:sigma][z:esti(y,ecect(e))]x]
+th3:=nonemptyapp(ecect(e),th2,x,x1):x
+s@th4:=isinout(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s)):is(set,ecelt(s),ecect(ectelt(s)))
+th5:=issete1(ecelt(s),ecect(ectelt(s)),th4,s,th1"eq.1"(s)):esti(s,ecect(ectelt(s)))
+th6:=eunmore1(ect,[x:ect]ecect(x),s,ectelt(s),th5):esti(s,unmore(ect,[x:ect]ecect(x)))
+e@[s:sigma][see:esti(s,ecect(e))][t:sigma][tee:esti(t,ecect(e))]
+th7:=th3"eq.2"(ecect(e),th1,s,see,t,tee):<t><s>r
+t@[tsr:<t><s>r]
+th8:=th4"eq.2"(ecect(e),th1,s,see,t,tsr):esti(t,ecect(e))
+-4
++5
+[f:ect][i:is(ect,e,f)]
+th1:=isini(set,[x:set]anec(x),e,f,i):is(set,ecect(e),ecect(f))
+f@[i:is(set,ecect(e),ecect(f))]
+th2:=isine(set,[x:set]anec(x),e,f,i):is(ect,e,f)
+f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))][tsr:<t><s>r]
+th3:=th2(th1"eq.3"(ecect(e),th1"eq.4"(e),ecect(f),th1"eq.4"(f),s,see,t,tef,tsr)):is(ect,e,f)
+see@[i:is(ect,e,f)]
+th4:=issete1(ecect(e),ecect(f),th1(i),s,see):esti(s,ecect(f))
+tef@[i:is(ect,e,f)]
+th5:=th3"eq.2"(ecect(f),th1"eq.4"(f),s,th4(i),t,tef):<t><s>r
+trr1@[s:sigma][t:sigma][tsr:<t><s>r]
+th6:=isouti(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s),ecelt(t),th1"eq.2"(t),th4"eq.1"(s,t,tsr)):is(ect,ectelt(s),ectelt(t))
+-5
+trr1@[alpha:'type'][fu:[x:sigma]alpha]
+fixfu:=[x:sigma][y:sigma][z:<y><x>r]is(alpha,<x>fu,<y>fu):'prop'
++10
+[ff:fixfu][e:ect][a1:alpha][s:sigma]
+prop1:=and(esti(s,ecect(e)),is(alpha,<s>fu,a1)):'prop'
+a1@prop2:=some([x:sigma]prop1(x)):'prop'
+e@[s:sigma][see:esti(s,ecect(e))]
+t1:=andi(esti(s,ecect(e)),is(alpha,<s>fu,<s>fu),see,refis(alpha,<s>fu)):prop1(<s>fu,s)
+t2:=somei([x:sigma]prop1(<s>fu,x),s,t1):prop2(<s>fu)
+t3:=somei(alpha,[x:alpha]prop2(x),<s>fu,t2):some(alpha,[x:alpha]prop2(x))
+e@t4:=th3"eq.4"(e,some(alpha,[x:alpha]prop2(x)),[x:sigma][y:esti(x,ecect(e))]t3(x,y)):some(alpha,[x:alpha]prop2(x))
+a1@[b1:alpha][pa1:prop2(a1)][pb1:prop2(b1)][s:sigma][pa1s:prop1(a1,s)][t:sigma][pb1t:prop1(b1,t)]
+t5:=ande1(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):esti(s,ecect(e))
+t6:=ande1(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):esti(t,ecect(e))
+t7:=th7"eq.4"(e,s,t5,t,t6):<t><s>r
+t8:=ande2(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):is(alpha,<s>fu,a1)
+t9:=ande2(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):is(alpha,<t>fu,b1)
+t10:=tr3is(alpha,a1,<s>fu,<t>fu,b1,symis(alpha,<s>fu,a1,t8),<t7><t><s>ff,t9):is(alpha,a1,b1)
+pa1s@t11:=someapp([x:sigma]prop1(b1,x),pb1,is(alpha,a1,b1),[x:sigma][y:prop1(b1,x)]t10(x,y)):is(alpha,a1,b1)
+pb1@t12:=someapp([x:sigma]prop1(a1,x),pa1,is(alpha,a1,b1),[x:sigma][y:prop1(a1,x)]t11(x,y)):is(alpha,a1,b1)
+e@t13:=[x:alpha][y:alpha][u:prop2(x)][v:prop2(y)]t12(x,y,u,v):amone(alpha,[x:alpha]prop2(x))
+t14:=onei(alpha,[x:alpha]prop2(x),t13,t4):one(alpha,[x:alpha]prop2(x))
+-10
+e".10"@indeq:=ind(alpha,[x:alpha]prop2".10"(x),t14".10"):alpha
++*10
+e@th1:=oneax(alpha,[x:alpha]prop2(x),t14):some([x:sigma]and(esti(x,ecect(e)),is(alpha,<x>fu,indeq)))
+[s:sigma][see:esti(s,ecect(e))]
+th2:=t12(<s>fu,indeq,t2(s,see),th1):is(alpha,<s>fu,indeq)
+ff@[s:sigma]
+th3:=th2(ectelt(s),s,th5"eq.4"(s)):is(alpha,<s>fu,indeq(ectelt(s)))
+-10
+alpha@[fu2:[x:sigma][y:sigma]alpha]
+fixfu2:=[x:sigma][y:sigma][z:sigma][u:sigma][v:<y><x>r][w:<u><z>r]is(alpha,<z><x>fu2,<u><y>fu2):'prop'
++11
+[ff2:fixfu2][s:sigma][t:sigma][tsr:<t><s>r][u:sigma]
+t1:=<refr(u)><tsr><u><u><t><s>ff2:is(alpha,<u><s>fu2,<u><t>fu2)
+tsr@t2:=fisi(sigma,alpha,<s>fu2,<t>fu2,[x:sigma]t1(x)):is([x:sigma]alpha,<s>fu2,<t>fu2)
+ff2@[e:ect]
+i:=indeq([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e):[x:sigma]alpha
+[s:sigma][t:sigma][tsr:<t><s>r][u:sigma][uee:esti(u,ecect(e))]
+t3:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,u,uee):is([x:sigma]alpha,<u>fu2,i)
+t4:=fise(alpha,<u>fu2,i,t3,s):is(alpha,<s><u>fu2,<s>i)
+t5:=fise(alpha,<u>fu2,i,t3,t):is(alpha,<t><u>fu2,<t>i)
+t6:=<tsr><refr(u)><t><s><u><u>ff2:is(alpha,<s><u>fu2,<t><u>fu2)
+t7:=tr3is(alpha,<s>i,<s><u>fu2,<t><u>fu2,<t>i,symis(alpha,<s><u>fu2,<s>i,t4),t6,t5):is(alpha,<s>i,<t>i)
+tsr@t8:=th3"eq.4"(e,is(alpha,<s>i,<t>i),[x:sigma][y:esti(x,ecect(e))]t7(x,y)):is(alpha,<s>i,<t>i)
+-11
+e".11"@[f:ect]
+indeq2:=indeq(i".11",[x:sigma][y:sigma][z:<y><x>r]t8".11"(x,y,z),f):alpha
++*11
+f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))]
+t9:=th2"eq.10"(i,[x:sigma][y:sigma][z:<y><x>r]t8(x,y,z),f,t,tef):is(alpha,<t>i,indeq2(e,f))
+t10:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,s,see):is([x:sigma]alpha,<s>fu2,i)
+t11:=fise(alpha,<s>fu2,i,t10,t):is(alpha,<t><s>fu2,<t>i)
+th1:=tris(alpha,<t><s>fu2,<t>i,indeq2,t11,t9):is(alpha,<t><s>fu2,indeq2(e,f))
+ff2@[s:sigma][t:sigma]
+th2:=th1(ectelt(s),ectelt(t),s,th5"eq.4"(s),t,th5"eq.4"(t)):is(alpha,<t><s>fu2,indeq2(ectelt(s),ectelt(t)))
+-11
++landau
++n
+@nat:='prim':'type'
+[x:nat][y:nat]
+is:=is"e"(nat,x,y):'prop'
+nis:=not(is(x,y)):'prop'
+x@[s:set(nat)]
+in:=esti(nat,x,s):'prop'
+@[p:[x:nat]'prop']
+some:=some"l"(nat,p):'prop'
+all:=all"l"(nat,p):'prop'
+one:=one"e"(nat,p):'prop'
+@1:='prim':nat
+suc:='prim':[x:nat]nat
+[x:nat][y:nat][i:is(x,y)]
+ax2:=isf(nat,nat,suc,x,y,i):is(<x>suc,<y>suc)
+@ax3:='prim':[x:nat]nis(<x>suc,1)
+ax4:='prim':[x:nat][y:nat][u:is(<x>suc,<y>suc)]is(x,y)
+[s:set(nat)]
+cond1:=in(1,s):'prop'
+cond2:=all([x:nat]imp(in(x,s),in(<x>suc,s))):'prop'
+@ax5:='prim':[s:set(nat)][u:cond1(s)][v:cond2(s)][x:nat]in(x,s)
+[p:[x:nat]'prop'][1p:<1>p][xsp:[x:nat][y:<x>p]<<x>suc>p][x:nat]
++i1
+s:=setof(nat,p):set(nat)
+t1:=estii(nat,p,1,1p):cond1(s)
+[y:nat][yes:in(y,s)]
+t2:=estie(nat,p,y,yes):<y>p
+t3:=estii(nat,p,<y>suc,<t2><y>xsp):in(<y>suc,s)
+x@t4:=<x><[y:nat][u:in(y,s)]t3(y,u)><t1><s>ax5:in(x,s)
+-i1
+induction:=estie(nat,p,x,t4".i1"):<x>p
+@[x:nat][y:nat][n:nis(x,y)]
++21
+[i:is(<x>suc,<y>suc)]
+t1:=<i><y><x>ax4:is(x,y)
+-21
+satz1:=th3"l.imp"(is(<x>suc,<y>suc),is(x,y),n,[u:is(<x>suc,<y>suc)]t1".21"(u)):nis(<x>suc,<y>suc)
++22
+x@prop1:=nis(<x>suc,x):'prop'
+@t1:=<1>ax3:prop1(1)
+x@[p:prop1(x)]
+t2:=satz1(<x>suc,x,p):prop1(<x>suc)
+-22
+x@satz2:=induction([y:nat]prop1".22"(y),t1".22",[y:nat][u:prop1".22"(y)]t2".22"(y,u),x):nis(<x>suc,x)
++23
+prop1:=or(is(x,1),some([u:nat]is(x,<u>suc))):'prop'
+@t1:=ori1(is(1,1),some([u:nat]is(1,<u>suc)),refis(nat,1)):prop1(1)
+x@t2:=somei(nat,[u:nat]is(<x>suc,<u>suc),x,refis(nat,<x>suc)):some([u:nat]is(<x>suc,<u>suc))
+t3:=ori2(is(<x>suc,1),some([u:nat]is(<x>suc,<u>suc)),t2):prop1(<x>suc)
+t4:=induction([y:nat]prop1(y),t1,[y:nat][u:prop1(y)]t3(y),x):prop1(x)
+-23
+[n:nis(x,1)]
+satz3:=ore2(is(x,1),some([u:nat]is(x,<u>suc)),t4".23",n):some([u:nat]is(x,<u>suc))
+y@[z:nat][i:is(x,<y>suc)][j:is(x,<z>suc)]
++*23
+j@t5:=<tris1(nat,<y>suc,<z>suc,x,i,j)><z><y>ax4:is(y,z)
+x@t6:=[y:nat][z:nat][u:is(x,<y>suc)][v:is(x,<z>suc)]t5(y,z,u,v):amone(nat,[u:nat]is(x,<u>suc))
+-23
+n@satz3a:=onei(nat,[u:nat]is(x,<u>suc),t6".23",satz3):one([u:nat]is(x,<u>suc))
++24
+x@[f:[y:nat]nat]
+prop1:=all([y:nat]is(<<y>suc>f,<<y>f>suc)):'prop'
+prop2:=and(is(<1>f,<x>suc),prop1):'prop'
+x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
+prop3:=is(<y>a,<y>b):'prop'
+pb@t1:=ande1(is(<1>a,<x>suc),prop1(a),pa):is(<1>a,<x>suc)
+t2:=ande1(is(<1>b,<x>suc),prop1(b),pb):is(<1>b,<x>suc)
+t3:=tris2(nat,<1>a,<1>b,<x>suc,t1,t2):prop3(1)
+y@[p:prop3(y)]
+t4:=ax2(<y>a,<y>b,p):is(<<y>a>suc,<<y>b>suc)
+t5:=ande2(is(<1>a,<x>suc),prop1(a),pa):prop1(a)
+t6:=ande2(is(<1>b,<x>suc),prop1(b),pb):prop1(b)
+t7:=<y>t5:is(<<y>suc>a,<<y>a>suc)
+t8:=<y>t6:is(<<y>suc>b,<<y>b>suc)
+t9:=tr3is(nat,<<y>suc>a,<<y>a>suc,<<y>b>suc,<<y>suc>b,t7,t4,symis"e"(nat,<<y>suc>b,<<y>b>suc,t8)):prop3(<y>suc)
+y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
+pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
+x@aa:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
+prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
+@t12:=[x:nat]refis(nat,<<x>suc>suc):prop1(1,suc)
+t13:=andi(is(<1>suc,<1>suc),prop1(1,suc),refis(nat,<1>suc),t12):prop2(1,suc)
+t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),suc,t13):prop4(1)
+x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
+g:=[y:nat]<<y>f>suc:[y:nat]nat
+[y:nat]
+t15:=refis(nat,<y>g):is(<y>g,<<y>f>suc)
+pf@t16:=ande1(is(<1>f,<x>suc),prop1(f),pf):is(<1>f,<x>suc)
+t17:=tris(nat,<1>g,<<1>f>suc,<<x>suc>suc,t15(1),ax2(<1>f,<x>suc,t16)):is(<1>g,<<x>suc>suc)
+y@t18:=ande2(is(<1>f,<x>suc),prop1(f),pf):prop1(f)
+t19:=<y>t18:is(<<y>suc>f,<<y>f>suc)
+t20:=tris2(nat,<<y>suc>f,<y>g,<<y>f>suc,t19,t15):is(<<y>suc>f,<y>g)
+t21:=tris(nat,<<y>suc>g,<<<y>suc>f>suc,<<y>g>suc,t15(<y>suc),ax2(<<y>suc>f,<y>g,t20)):is(<<y>suc>g,<<y>g>suc)
+pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
+t23:=andi(is(<1>g,<<x>suc>suc),prop1(<x>suc,g),t17,t22):prop2(<x>suc,g)
+t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
+p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
+x@bb:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
+-24
+x@satz4:=onei([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),aa".24",bb".24"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,<x>suc),all([y:nat]is(<<y>suc>z,<<y>z>suc))))
+plus:=ind([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),satz4):[y:nat]nat
+y@pl:=<y>plus:nat
++*24
+x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz4):prop2(plus)
+-24
+x@satz4a:=ande1(is(<1>plus,<x>suc),prop1".24"(plus),t26".24"):is(pl(x,1),<x>suc)
++*24
+x@t27:=ande2(is(<1>plus,<x>suc),prop1(plus),t26):prop1(plus)
+-24
+y@satz4b:=<y>t27".24":is(pl(x,<y>suc),<pl(x,y)>suc)
++*24
+@t28:=t11(1,plus(1),suc,t26(1),t13):is"e"([y:nat]nat,plus(1),suc)
+-24
+x@satz4c:=fise(nat,nat,plus(1),suc,t28".24",x):is(pl(1,x),<x>suc)
++*24
+x@t29:=t11(<x>suc,plus(<x>suc),[y:nat]<<y>plus>suc,t26(<x>suc),t23(bb,plus,t26)):is"e"([y:nat]nat,plus(<x>suc),[y:nat]<<y>plus>suc)
+-24
+y@satz4d:=fise(nat,nat,plus(<x>suc),[z:nat]<<z>plus>suc,t29".24",y):is(pl(<x>suc,y),<pl(x,y)>suc)
+x@satz4e:=symis(nat,pl(x,1),<x>suc,satz4a):is(<x>suc,pl(x,1))
+y@satz4f:=symis(nat,pl(x,<y>suc),<pl(x,y)>suc,satz4b):is(<pl(x,y)>suc,pl(x,<y>suc))
+x@satz4g:=symis(nat,pl(1,x),<x>suc,satz4c):is(<x>suc,pl(1,x))
+y@satz4h:=symis(nat,pl(<x>suc,y),<pl(x,y)>suc,satz4d):is(<pl(x,y)>suc,pl(<x>suc,y))
+z@[i:is(x,y)]
+ispl1:=isf(nat,nat,[u:nat]pl(u,z),x,y,i):is(pl(x,z),pl(y,z))
+ispl2:=isf(nat,nat,[u:nat]pl(z,u),x,y,i):is(pl(z,x),pl(z,y))
+z@[u:nat][i:is(x,y)][j:is(z,u)]
+ispl12:=tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
++25
+z@prop1:=is(pl(pl(x,y),z),pl(x,pl(y,z))):'prop'
+y@t1:=tr3is(nat,pl(pl(x,y),1),<pl(x,y)>suc,pl(x,<y>suc),pl(x,pl(y,1)),satz4a(pl(x,y)),satz4f,ispl2(<y>suc,pl(y,1),x,satz4e(y))):prop1(1)
+z@[p:prop1(z)]
+t2:=ax2(pl(pl(x,y),z),pl(x,pl(y,z)),p):is(<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc)
+t3:=tr4is(nat,pl(pl(x,y),<z>suc),<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc,pl(x,<pl(y,z)>suc),pl(x,pl(y,<z>suc)),satz4b(pl(x,y),z),t2,satz4f(x,pl(y,z)),ispl2(<pl(y,z)>suc,pl(y,<z>suc),x,satz4f(y,z))):prop1(<z>suc)
+-25
+z@satz5:=induction([u:nat]prop1".25"(u),t1".25",[u:nat][v:prop1".25"(u)]t3".25"(u,v),z):is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl1:=satz5:is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl2:=symis(nat,pl(pl(x,y),z),pl(x,pl(y,z)),satz5):is(pl(x,pl(y,z)),pl(pl(x,y),z))
++26
+y@prop1:=is(pl(x,y),pl(y,x)):'prop'
+t1:=satz4a(y):is(pl(y,1),<y>suc)
+t2:=satz4c(y):is(pl(1,y),<y>suc)
+t3:=tris2(nat,pl(1,y),pl(y,1),<y>suc,t2,t1):prop1(1,y)
+[p:prop1(x,y)]
+t4:=tris(nat,<pl(x,y)>suc,<pl(y,x)>suc,pl(y,<x>suc),ax2(pl(x,y),pl(y,x),p),satz4f(y,x)):is(<pl(x,y)>suc,pl(y,<x>suc))
+t5:=satz4d:is(pl(<x>suc,y),<pl(x,y)>suc)
+t6:=tris(nat,pl(<x>suc,y),<pl(x,y)>suc,pl(y,<x>suc),t5,t4):prop1(<x>suc,y)
+-26
+y@satz6:=induction([z:nat]prop1".26"(z,y),t3".26",[z:nat][u:prop1".26"(z,y)]t6".26"(z,y,u),x):is(pl(x,y),pl(y,x))
+compl:=satz6:is(pl(x,y),pl(y,x))
++*26
+x@t7:=tris(nat,pl(x,1),<x>suc,pl(1,x),satz4a,satz4g):prop1(1)
+y@[p:prop1(y)]
+t8:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,<pl(y,x)>suc,pl(<y>suc,x),satz4b,ax2(pl(x,y),pl(y,x),p),satz4h(y,x)):prop1(<y>suc)
+y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(pl(x,y),pl(y,x))
+-26
++27
+y@prop1:=nis(y,pl(x,y)):'prop'
+x@t1:=symnotis(nat,<x>suc,1,<x>ax3):nis(1,<x>suc)
+t2:=th4"e.notis"(nat,1,<x>suc,pl(x,1),t1,satz4a):prop1(1)
+y@[p:prop1(y)]
+t3:=satz1(y,pl(x,y),p):nis(<y>suc,<pl(x,y)>suc)
+t4:=th4"e.notis"(nat,<y>suc,<pl(x,y)>suc,pl(x,<y>suc),t3,satz4b):prop1(<y>suc)
+-27
+y@satz7:=induction([z:nat]prop1".27"(z),t2".27",[z:nat][u:prop1".27"(z)]t4".27"(z,u),y):nis(y,pl(x,y))
+z@[n:nis(y,z)]
++28
+prop1:=nis(pl(x,y),pl(x,z)):'prop'
+t1:=satz1(y,z,n):nis(<y>suc,<z>suc)
+t2:=th5"e.notis"(nat,<y>suc,<z>suc,pl(1,y),pl(1,z),t1,satz4g(y),satz4g(z)):prop1(1,y,z,n)
+[p:prop1(x,y,z,n)]
+t3:=satz1(pl(x,y),pl(x,z),p):nis(<pl(x,y)>suc,<pl(x,z)>suc)
+t4:=th5"e.notis"(nat,<pl(x,y)>suc,<pl(x,z)>suc,pl(<x>suc,y),pl(<x>suc,z),t3,satz4h,satz4h(z)):prop1(<x>suc,y,z,n)
+-28
+satz8:=induction([u:nat]prop1".28"(u,y,z,n),t2".28",[u:nat][v:prop1".28"(u,y,z,n)]t4".28"(u,y,z,n,v),x):nis(pl(x,y),pl(x,z))
+z@[i:is(pl(x,y),pl(x,z))]
+satz8a:=th7"l.imp"(is(y,z),nis(pl(x,y),pl(x,z)),weli(is(pl(x,y),pl(x,z)),i),[u:nis(y,z)]satz8(u)):is(y,z)
+z@diffprop:=is(x,pl(y,z)):'prop'
++*28
+y@[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]
+t5:=satz8a(y,u,v,tris1(nat,pl(y,u),pl(y,v),x,du,dv)):is(u,v)
+-28
+y@satz8b:=[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]t5".28"(u,v,du,dv):amone(nat,[z:nat]is(x,pl(y,z)))
++29
+i:=is(x,y):'prop'
+ii:=some([u:nat]diffprop(x,y,u)):'prop'
+iii:=some([v:nat]diffprop(y,x,v)):'prop'
+[one1:i][u:nat]
+t1:=tris(nat,pl(u,x),pl(x,u),pl(y,u),compl(u,x),ispl1(u,one1)):is(pl(u,x),pl(y,u))
+t2:=th3"e.notis"(nat,x,pl(u,x),pl(y,u),satz7(u,x),t1):nis(x,pl(y,u))
+one1@t3:=th5"l.some"(nat,[u:nat]diffprop(u),[u:nat]t2(u)):not(ii)
+y@t4:=th1"l.ec"(i,ii,[z:i]t3(z)):ec(i,ii)
+one1@t5:=t3(y,x,symis(nat,x,y,one1)):not(iii)
+y@t6:=th2"l.ec"(iii,i,[z:i]t5(z)):ec(iii,i)
+[two1:ii][three1:iii][u:nat][du:diffprop(x,y,u)][v:nat][dv:diffprop(y,x,v)]
+t6a:=tr4is(nat,x,pl(y,u),pl(pl(x,v),u),pl(x,pl(v,u)),pl(pl(v,u),x),du,ispl1(y,pl(x,v),u,dv),asspl1(x,v,u),compl(x,pl(v,u))):is(x,pl(pl(v,u),x))
+t7:=mp(is(x,pl(pl(v,u),x)),con,t6a,satz7(pl(v,u),x)):con
+du@t8:=someapp(nat,[v:nat]diffprop(y,x,v),three1,con,[v:nat][dv:diffprop(y,x,v)]t7(v,dv)):con
+three1@t9:=someapp(nat,[u:nat]diffprop(u),two1,con,[u:nat][du:diffprop(u)]t8(u,du)):con
+two1@t10:=[z:iii]t9(z):not(iii)
+y@t11:=th1"l.ec"(ii,iii,[z:ii]t10(z)):ec(ii,iii)
+a:=th6"l.ec3"(i,ii,iii,t4,t11,t6):ec3(i,ii,iii)
+prop1:=or3(i,ii,iii):'prop'
+x@[j:is(x,1)]
+t12:=or3i1(i(1),ii(1),iii(1),j):prop1(1)
+x@[n:nis(x,1)][u:nat][j:is(x,<u>suc)]
+t13:=tris(nat,x,<u>suc,pl(1,u),j,satz4g(u)):is(x,pl(1,u))
+t14:=somei(nat,[z:nat]diffprop(x,1,z),u,t13):ii(1)
+t15:=someapp(nat,[u1:nat]is(x,<u1>suc),satz3(x,n),ii(1),[u1:nat][z:is(x,<u1>suc)]t14(u1,z)):ii(1)
+t16:=or3i2(i(1),ii(1),iii(1),t15):prop1(1)
+n@t16a:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),prop1(1),[u:nat][v:is(x,<u>suc)]t16(u,v)):prop1(1)
+x@t17:=th1"l.imp"(is(x,1),prop1(1),[z:is(x,1)]t12(z),[z:nis(x,1)]t16a(z)):prop1(1)
+y@[p:prop1(y)][one1:i(y)]
+t18:=tris(nat,<y>suc,pl(y,1),pl(x,1),satz4e(y),ispl1(y,x,1,symis(nat,x,y,one1))):is(<y>suc,pl(x,1))
+t19:=somei(nat,[z:nat]diffprop(<y>suc,x,z),1,t18):iii(<y>suc)
+t20:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t19):prop1(<y>suc)
+p@[two1:ii(y)][u:nat][du:diffprop(x,y,u)][j:is(u,1)]
+t21:=tr3is(nat,x,pl(y,u),pl(y,1),<y>suc,du,ispl2(u,1,y,j),satz4a(y)):is(x,<y>suc)
+t22:=or3i1(i(<y>suc),ii(<y>suc),iii(<y>suc),t21):prop1(<y>suc)
+du@[n:nis(u,1)][w:nat][j:is(u,<w>suc)]
+t23:=tris(nat,u,<w>suc,pl(1,w),j,satz4g(w)):is(u,pl(1,w))
+t24:=tr4is(nat,x,pl(y,u),pl(y,pl(1,w)),pl(pl(y,1),w),pl(<y>suc,w),du,ispl2(u,pl(1,w),y,t23),asspl2(y,1,w),ispl1(pl(y,1),<y>suc,w,satz4a(y))):is(x,pl(<y>suc,w))
+t25:=somei(nat,[z:nat]diffprop(x,<y>suc,z),w,t24):ii(<y>suc)
+n@t26:=someapp(nat,[z:nat]is(u,<z>suc),satz3(u,n),ii(<y>suc),[z:nat][v:is(u,<z>suc)]t25(z,v)):ii(<y>suc)
+t27:=or3i2(i(<y>suc),ii(<y>suc),iii(<y>suc),t26):prop1(<y>suc)
+du@t28:=th1"l.imp"(is(u,1),prop1(<y>suc),[z:is(u,1)]t22(z),[z:nis(u,1)]t27(z)):prop1(<y>suc)
+two1@t28a:=someapp(nat,[u:nat]diffprop(u),two1,prop1(<y>suc),[u:nat][du:diffprop(u)]t28(u,du)):prop1(<y>suc)
+p@[three1:iii(y)][v:nat][dv:diffprop(y,x,v)]
+t29:=tris(nat,<y>suc,<pl(x,v)>suc,pl(x,<v>suc),ax2(y,pl(x,v),dv),satz4f(x,v)):is(<y>suc,pl(x,<v>suc))
+t30:=somei(nat,[z:nat]diffprop(<y>suc,x,z),<v>suc,t29):iii(<y>suc)
+three1@t31:=someapp(nat,[v:nat]diffprop(y,x,v),three1,iii(<y>suc),[v:nat][dv:diffprop(y,x,v)]t30(v,dv)):iii(<y>suc)
+t32:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t31):prop1(<y>suc)
+p@t33:=or3app(i(y),ii(y),iii(y),prop1(<y>suc),p,[z:i(y)]t20(z),[z:ii(y)]t28a(z),[z:iii(y)]t32(z)):prop1(<y>suc)
+y@b:=induction([z:nat]prop1(z),t17,[z:nat][u:prop1(z)]t33(z,u),y):or3(i,ii,iii)
+-29
+satz9:=orec3i(i".29",ii".29",iii".29",b".29",a".29"):orec3(is(x,y),some([u:nat]is(x,pl(y,u))),some([v:nat]is(y,pl(x,v))))
+satz9a:=b".29":or3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
+satz9b:=a".29":ec3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
+more:=some([u:nat]diffprop(x,y,u)):'prop'
+less:=some([v:nat]diffprop(y,x,v)):'prop'
+satz10:=satz9:orec3(is(x,y),more(x,y),less(x,y))
+satz10a:=satz9a:or3(is(x,y),more(x,y),less(x,y))
+satz10b:=satz9b:ec3(is(x,y),more(x,y),less(x,y))
+[m:more(x,y)]
+satz11:=m:less(y,x)
+y@[l:less(x,y)]
+satz12:=l:more(y,x)
+y@moreis:=or(more,is(x,y)):'prop'
+lessis:=or(less,is(x,y)):'prop'
+[m:moreis(x,y)]
+satz13:=th9"l.or"(more,is(x,y),less(y,x),is(y,x),m,[z:more]satz11(z),[z:is(x,y)]symis(nat,x,y,z)):lessis(y,x)
+y@[l:lessis(x,y)]
+satz14:=th9"l.or"(less,is(x,y),more(y,x),is(y,x),l,[z:less]satz12(z),[z:is(x,y)]symis(nat,x,y,z)):moreis(y,x)
+z@[i:is(x,y)][m:more(x,z)]
+ismore1:=isp(nat,[u:nat]more(u,z),x,y,m,i):more(y,z)
+i@[m:more(z,x)]
+ismore2:=isp(nat,[u:nat]more(z,u),x,y,m,i):more(z,y)
+i@[l:less(x,z)]
+isless1:=isp(nat,[u:nat]less(u,z),x,y,l,i):less(y,z)
+i@[l:less(z,x)]
+isless2:=isp(nat,[u:nat]less(z,u),x,y,l,i):less(z,y)
+i@[m:moreis(x,z)]
+ismoreis1:=isp(nat,[u:nat]moreis(u,z),x,y,m,i):moreis(y,z)
+i@[m:moreis(z,x)]
+ismoreis2:=isp(nat,[u:nat]moreis(z,u),x,y,m,i):moreis(z,y)
+i@[l:lessis(x,z)]
+islessis1:=isp(nat,[u:nat]lessis(u,z),x,y,l,i):lessis(y,z)
+i@[l:lessis(z,x)]
+islessis2:=isp(nat,[u:nat]lessis(z,u),x,y,l,i):lessis(z,y)
+y@[i:is(x,y)]
+moreisi2:=ori2(more(x,y),is(x,y),i):moreis(x,y)
+lessisi2:=ori2(less(x,y),is(x,y),i):lessis(x,y)
+y@[m:more(x,y)]
+moreisi1:=ori1(more(x,y),is(x,y),m):moreis(x,y)
+y@[l:less(x,y)]
+lessisi1:=ori1(less(x,y),is(x,y),l):lessis(x,y)
+z@[u:nat][i:is(x,y)][j:is(z,u)][m:more(x,z)]
+ismore12:=ismore2(z,u,y,j,ismore1(x,y,z,i,m)):more(y,u)
+j@[l:less(x,z)]
+isless12:=isless2(z,u,y,j,isless1(x,y,z,i,l)):less(y,u)
+j@[m:moreis(x,z)]
+ismoreis12:=ismoreis2(z,u,y,j,ismoreis1(x,y,z,i,m)):moreis(y,u)
+j@[l:lessis(x,z)]
+islessis12:=islessis2(z,u,y,j,islessis1(x,y,z,i,l)):lessis(y,u)
+y@[m:moreis(x,y)]
+satz10c:=th7"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,comor(more(x,y),is(x,y),m)):not(less(x,y))
+y@[l:lessis(x,y)]
+satz10d:=th9"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,l):not(more(x,y))
+y@[n:not(more(x,y))]
+satz10e:=th2"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n):lessis(x,y)
+y@[n:not(less(x,y))]
+satz10f:=comor(is(x,y),more(x,y),th3"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n)):moreis(x,y)
+y@[m:more(x,y)]
+satz10g:=th3"l.or"(less(x,y),is(x,y),ec3e23(is(x,y),more(x,y),less(x,y),satz10b,m),ec3e21(is(x,y),more(x,y),less(x,y),satz10b,m)):not(lessis(x,y))
+y@[l:less(x,y)]
+satz10h:=th3"l.or"(more(x,y),is(x,y),ec3e32(is(x,y),more(x,y),less(x,y),satz10b,l),ec3e31(is(x,y),more(x,y),less(x,y),satz10b,l)):not(moreis(x,y))
+y@[n:not(moreis(x,y))]
+satz10j:=or3e3(is(x,y),more(x,y),less(x,y),satz10a,th5"l.or"(more(x,y),is(x,y),n),th4"l.or"(more(x,y),is(x,y),n)):less(x,y)
+y@[n:not(lessis(x,y))]
+satz10k:=or3e2(is(x,y),more(x,y),less(x,y),satz10a,th4"l.or"(less(x,y),is(x,y),n),th5"l.or"(less(x,y),is(x,y),n)):more(x,y)
+z@[l:less(x,y)][k:less(y,z)]
++315
+[v:nat][dv:diffprop(y,x,v)][w:nat][dw:diffprop(z,y,w)]
+t1:=tr3is(nat,z,pl(y,w),pl(pl(x,v),w),pl(x,pl(v,w)),dw,ispl1(y,pl(x,v),w,dv),asspl1(x,v,w)):is(z,pl(x,pl(v,w)))
+t2:=somei(nat,[u:nat]diffprop(z,x,u),pl(v,w),t1):less(x,z)
+dv@t3:=someapp(nat,[w:nat]diffprop(z,y,w),k,less(x,z),[w:nat][dw:diffprop(z,y,w)]t2(w,dw)):less(x,z)
+-315
+satz15:=someapp(nat,[v:nat]diffprop(y,x,v),l,less(x,z),[v:nat][dv:diffprop(y,x,v)]t3".315"(v,dv)):less(x,z)
+trless:=satz15:less(x,z)
+z@[m:more(x,y)][n:more(y,z)]
+trmore:=satz15(z,y,x,n,m):more(x,z)
++*315
+n@anders:=satz12(z,x,satz15(z,y,x,satz11(y,z,n),satz11(m))):more(x,z)
+-315
+z@[l:lessis(x,y)][k:less(y,z)]
+satz16a:=orapp(less(x,y),is(x,y),less(x,z),l,[u:less(x,y)]trless(u,k),[u:is(x,y)]isless1(y,x,z,symis(nat,x,y,u),k)):less(x,z)
+z@[l:less(x,y)][k:lessis(y,z)]
+satz16b:=orapp(less(y,z),is(y,z),less(x,z),k,[u:less(y,z)]trless(l,u),[u:is(y,z)]isless2(y,z,x,u,l)):less(x,z)
+z@[m:moreis(x,y)][n:more(y,z)]
+satz16c:=satz16b(z,y,x,n,satz13(m)):more(x,z)
+z@[m:more(x,y)][n:moreis(y,z)]
+satz16d:=satz16a(z,y,x,satz13(y,z,n),m):more(x,z)
+z@[l:lessis(x,y)][k:lessis(y,z)]
++317
+[i:is(x,y)][j:is(y,z)]
+t1:=lessisi2(x,z,tris(nat,x,y,z,i,j)):lessis(x,z)
+i@[j:less(y,z)]
+t2:=lessisi1(x,z,satz16a(l,j)):lessis(x,z)
+i@t3:=orapp(less(y,z),is(y,z),lessis(x,z),k,[u:less(y,z)]t2(u),[u:is(y,z)]t1(u)):lessis(x,z)
+k@[j:less(x,y)]
+t4:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
+-317
+satz17:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t4".317"(u),[u:is(x,y)]t3".317"(u)):lessis(x,z)
++*317
+k@[j:less(x,y)]
+t5:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
+k@[i:is(x,y)]
+t6:=islessis1(y,x,z,symis(nat,x,y,i),k):lessis(x,z)
+k@anders:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t5(u),[u:is(x,y)]t6(u)):lessis(x,z)
+-317
+k@trlessis:=satz17:lessis(x,z)
+z@[m:moreis(x,y)][n:moreis(y,z)]
+trmoreis:=satz14(z,x,satz17(z,y,x,satz13(y,z,n),satz13(m))):moreis(x,z)
+y@satz18:=somei(nat,[u:nat]diffprop(pl(x,y),x,u),y,refis(nat,pl(x,y))):more(pl(x,y),x)
+satz18a:=satz18:less(x,pl(x,y))
+x@satz18b:=ismore1(pl(x,1),<x>suc,x,satz4a,satz18(1)):more(<x>suc,x)
+satz18c:=satz18b:less(x,<x>suc)
+z@[m:more(x,y)]
++319
+[u:nat][du:diffprop(u)]
+t1:=tris(nat,x,pl(y,u),pl(u,y),du,compl(y,u)):is(x,pl(u,y))
+t2:=tr3is(nat,pl(x,z),pl(pl(u,y),z),pl(u,pl(y,z)),pl(pl(y,z),u),ispl1(x,pl(u,y),z,t1),asspl1(u,y,z),compl(u,pl(y,z))):is(pl(x,z),pl(pl(y,z),u))
+t3:=somei(nat,[v:nat]diffprop(pl(x,z),pl(y,z),v),u,t2):more(pl(x,z),pl(y,z))
+-319
+satz19a:=someapp(nat,[u:nat]diffprop(u),m,more(pl(x,z),pl(y,z)),[u:nat][v:diffprop(u)]t3".319"(u,v)):more(pl(x,z),pl(y,z))
+z@[i:is(x,y)]
+satz19b:=ispl1(x,y,z,i):is(pl(x,z),pl(y,z))
+z@[l:less(x,y)]
+satz19c:=satz11(pl(y,z),pl(x,z),satz19a(y,x,z,satz12(x,y,l))):less(pl(x,z),pl(y,z))
++*319
+l@anders1:=satz19a(y,x,z,l):less(pl(x,z),pl(y,z))
+-319
+m@satz19d:=ismore12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19a):more(pl(z,x),pl(z,y))
+i@satz19e:=ispl2(x,y,z,i):is(pl(z,x),pl(z,y))
+l@satz19f:=isless12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19c):less(pl(z,x),pl(z,y))
++*319
+l@anders2:=satz19d(y,x,z,l):less(pl(z,x),pl(z,y))
+-319
+z@[u:nat][i:is(x,y)][m:more(z,u)]
+satz19g:=ismore2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19d(z,u,x,m)):more(pl(x,z),pl(y,u))
+satz19h:=ismore12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19g):more(pl(z,x),pl(u,y))
+i@[l:less(z,u)]
+satz19j:=isless2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19f(z,u,x,l)):less(pl(x,z),pl(y,u))
+satz19k:=isless12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19j):less(pl(z,x),pl(u,y))
+z@[m:moreis(x,y)]
++*319
+m@[n:more(x,y)]
+t4:=moreisi1(pl(x,z),pl(y,z),satz19a(n)):moreis(pl(x,z),pl(y,z))
+m@[i:is(x,y)]
+t5:=moreisi2(pl(x,z),pl(y,z),ispl1(x,y,z,i)):moreis(pl(x,z),pl(y,z))
+-319
+m@satz19l:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,z)),m,[u:more(x,y)]t4".319"(u),[u:is(x,y)]t5".319"(u)):moreis(pl(x,z),pl(y,z))
+satz19m:=ismoreis12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19l):moreis(pl(z,x),pl(z,y))
+z@[l:lessis(x,y)]
+satz19n:=satz13(pl(y,z),pl(x,z),satz19l(y,x,z,satz14(l))):lessis(pl(x,z),pl(y,z))
+satz19o:=satz13(pl(z,y),pl(z,x),satz19m(y,x,z,satz14(l))):lessis(pl(z,x),pl(z,y))
++320
+z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
+t2:=satz10b(pl(x,z),pl(y,z)):ec3(is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)))
+-320
+z@[m:more(pl(x,z),pl(y,z))]
+satz20a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),m):more(x,y)
+z@[i:is(pl(x,z),pl(y,z))]
+satz20b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),i):is(x,y)
+z@[l:less(pl(x,z),pl(y,z))]
+satz20c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),l):less(x,y)
++*320
+i@t3:=tr3is(nat,pl(z,x),pl(x,z),pl(y,z),pl(z,y),compl(z,x),i,compl(y,z)):is(pl(z,x),pl(z,y))
+andersb:=satz8a(z,x,y,t3):is(x,y)
+l@andersc:=satz20a(y,x,z,l):less(x,y)
+-320
+z@[m:more(pl(z,x),pl(z,y))]
+satz20d:=satz20a(ismore12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),m)):more(x,y)
+z@[i:is(pl(z,x),pl(z,y))]
+satz20e:=satz20b(tr3is(nat,pl(x,z),pl(z,x),pl(z,y),pl(y,z),compl(x,z),i,compl(z,y))):is(x,y)
+z@[l:less(pl(z,x),pl(z,y))]
+satz20f:=satz20c(isless12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),l)):less(x,y)
+u@[m:more(x,y)][n:more(z,u)]
++321
+t1:=satz19a(x,y,z,m):more(pl(x,z),pl(y,z))
+t2:=ismore12(pl(z,y),pl(y,z),pl(u,y),pl(y,u),compl(z,y),compl(u,y),satz19a(z,u,y,n)):more(pl(y,z),pl(y,u))
+-321
+satz21:=trmore(pl(x,z),pl(y,z),pl(y,u),t1".321",t2".321"):more(pl(x,z),pl(y,u))
++*321
+n@anders:=trmore(pl(x,z),pl(y,z),pl(y,u),satz19a(x,y,z,m),satz19d(z,u,y,n)):more(pl(x,z),pl(y,u))
+-321
+u@[l:less(x,y)][k:less(z,u)]
+satz21a:=satz21(y,x,u,z,l,k):less(pl(x,z),pl(y,u))
++*321
+k@andersa:=satz11(pl(y,u),pl(x,z),satz21(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(pl(x,z),pl(y,u))
+-321
+u@[m:moreis(x,y)][n:more(z,u)]
+satz22a:=orapp(more(x,y),is(x,y),more(pl(x,z),pl(y,u)),m,[v:more(x,y)]satz21(v,n),[v:is(x,y)]satz19g(u,v,n)):more(pl(x,z),pl(y,u))
+u@[m:more(x,y)][n:moreis(z,u)]
+satz22b:=orapp(more(z,u),is(z,u),more(pl(x,z),pl(y,u)),n,[v:more(z,u)]satz21(m,v),[v:is(z,u)]satz19h(z,u,x,y,v,m)):more(pl(x,z),pl(y,u))
+u@[l:lessis(x,y)][k:less(z,u)]
+satz22c:=satz22a(y,x,u,z,satz14(x,y,l),k):less(pl(x,z),pl(y,u))
+u@[l:less(x,y)][k:lessis(z,u)]
+satz22d:=satz22b(y,x,u,z,l,satz14(z,u,k)):less(pl(x,z),pl(y,u))
+u@[m:moreis(x,y)][n:moreis(z,u)]
++323
+[i:is(x,y)][j:is(z,u)]
+t1:=moreisi2(pl(x,z),pl(y,u),tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j))):moreis(pl(x,z),pl(y,u))
+i@[o:more(z,u)]
+t2:=moreisi1(pl(x,z),pl(y,u),satz22a(m,o)):moreis(pl(x,z),pl(y,u))
+i@t3:=orapp(more(z,u),is(z,u),moreis(pl(x,z),pl(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(pl(x,z),pl(y,u))
+n@[o:more(x,y)]
+t4:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
+-323
+satz23:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t4".323"(v),[v:is(x,y)]t3".323"(v)):moreis(pl(x,z),pl(y,u))
++*323
+n@[o:more(x,y)]
+t5:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
+n@[i:is(x,y)]
+t6:=ismoreis2(pl(x,u),pl(y,u),pl(x,z),ispl1(u,i),satz19m(z,u,x,n)):moreis(pl(x,z),pl(y,u))
+n@anders:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(pl(x,z),pl(y,u))
+-323
+u@[l:lessis(x,y)][k:lessis(z,u)]
+satz23a:=satz13(pl(y,u),pl(x,z),satz23(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(pl(x,z),pl(y,u))
++324
+x@[n:nis(x,1)][u:nat][i:is(x,<u>suc)]
+t1:=tris(nat,x,<u>suc,pl(1,u),i,satz4g(u)):is(x,pl(1,u))
+t2:=ismore1(pl(1,u),x,1,symis(nat,x,pl(1,u),t1),satz18(1,u)):more(x,1)
+n@t3:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),more(x,1),[u:nat][v:is(x,<u>suc)]t2(u,v)):more(x,1)
+-324
+x@satz24:=th2"l.or"(more(x,1),is(x,1),[u:nis(x,1)]t3".324"(u)):moreis(x,1)
+satz24a:=satz13(x,1,satz24):lessis(1,x)
+satz24b:=t3".324"(<x>suc,<x>ax3):more(<x>suc,1)
+satz24c:=satz24b:less(1,<x>suc)
+y@[m:more(y,x)]
++325
+[u:nat][du:diffprop(y,x,u)]
+t1:=satz19m(u,1,x,satz24(u)):moreis(pl(x,u),pl(x,1))
+t2:=ismoreis1(pl(x,u),y,pl(x,1),symis(nat,y,pl(x,u),du),t1):moreis(y,pl(x,1))
+-325
+satz25:=someapp(nat,[u:nat]diffprop(y,x,u),m,moreis(y,pl(x,1)),[u:nat][v:diffprop(y,x,u)]t2".325"(u,v)):moreis(y,pl(x,1))
+satz25a:=ismoreis2(pl(x,1),<x>suc,y,satz4a,satz25):moreis(y,<x>suc)
+y@[l:less(y,x)]
+satz25b:=satz13(x,pl(y,1),satz25(y,x,l)):lessis(pl(y,1),x)
+satz25c:=islessis1(pl(y,1),<y>suc,x,satz4a(y),satz25b):lessis(<y>suc,x)
+y@[l:less(y,pl(x,1))]
++326
+[m:more(y,x)]
+t1:=satz25(m):moreis(y,pl(x,1))
+l@t2:=th3"l.imp"(more(y,x),moreis(y,pl(x,1)),satz10h(y,pl(x,1),l),[v:more(y,x)]t1(v)):not(more(y,x))
+-326
+satz26:=satz10e(y,x,t2".326"):lessis(y,x)
+y@[l:less(y,<x>suc)]
+satz26a:=satz26(isless2(<x>suc,pl(x,1),y,satz4e,l)):lessis(y,x)
+y@[m:more(pl(y,1),x)]
+satz26b:=satz14(x,y,satz26(y,x,m)):moreis(y,x)
+y@[m:more(<y>suc,x)]
+satz26c:=satz26b(ismore1(<y>suc,pl(y,1),x,satz4e(y),m)):moreis(y,x)
+@[p:[x:nat]'prop'][n:nat]
++327
+[m:nat]
+lbprop:=imp(<m>p,lessis(n,m)):'prop'
+-327
+lb:=all([x:nat]lbprop".327"(x)):'prop'
+min:=and(lb,<n>p):'prop'
+p@[s:some(p)]
++*327
+s@[n:nat]
+t1:=[x:<n>p]satz24a(n):lbprop(1,n)
+s@t2:=[x:nat]t1(x):lb(1)
+[l:[x:nat]lb(x)][y:nat][yp:<y>p]
+t3:=satz18(y,1):more(pl(y,1),y)
+t4:=satz10g(pl(y,1),y,t3):not(lessis(pl(y,1),y))
+t5:=th4"l.imp"(<y>p,lessis(pl(y,1),y),yp,t4):not(lbprop(pl(y,1),y))
+t6:=th1"l.all"(nat,[x:nat]lbprop(pl(y,1),x),y,t5):not(lb(pl(y,1)))
+t7:=mp(lb(pl(y,1)),con,<pl(y,1)>l,t6):con
+l@t8:=someapp(nat,p,s,con,[x:nat][y:<x>p]t7(x,y)):con
+s@[n:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))][m:nat][l:lb(m)]
+t9:=<m>n:not(and(lb(m),not(lb(pl(m,1)))))
+t10:=et(lb(pl(m,1)),th3"l.and"(lb(m),not(lb(pl(m,1))),t9,l)):lb(pl(m,1))
+t11:=isp(nat,[x:nat]lb(x),pl(m,1),<m>suc,t10,satz4a(m)):lb(<m>suc)
+n@t12:=[x:nat]induction([y:nat]lb(y),t2,[y:nat][z:lb(y)]t11(y,z),x):[x:nat]lb(x)
+s@t13:=[x:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))]t8(t12(x)):some([x:nat]and(lb(x),not(lb(pl(x,1)))))
+[m:nat][a:and(lb(m),not(lb(pl(m,1))))]
+t14:=ande1(lb(m),not(lb(pl(m,1))),a):lb(m)
+t15:=ande2(lb(m),not(lb(pl(m,1))),a):not(lb(pl(m,1)))
+[nmp:not(<m>p)][n:nat][np:<n>p]
+t16:=mp(<n>p,lessis(m,n),np,<n>t14):lessis(m,n)
+t17:=th3"l.imp"(is(m,n),<m>p,nmp,[x:is(m,n)]isp(nat,p,n,m,np,symis(nat,m,n,x))):not(is(m,n))
+t18:=ore1(less(m,n),is(m,n),t16,t17):less(m,n)
+t19:=satz25b(n,m,t18):lessis(pl(m,1),n)
+nmp@t20:=[x:nat][y:<x>p]t19(x,y):lb(pl(m,1))
+t21:=mp(lb(pl(m,1)),con,t20,t15):con
+a@t22:=et(<m>p,[x:not(<m>p)]t21(x)):<m>p
+t23:=andi(lb(m),<m>p,t14,t22):min(m)
+-327
+s@satz27:=th6"l.some"(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))),[x:nat]min(x),t13".327",[x:nat][y:and(lb(x),not(lb(pl(x,1))))]t23".327"(x,y)):some([x:nat]min(p,x))
++*327
+p@[n:non(nat,[x:nat]min(x))][u:nat]
+t24:=[x:<u>p]satz24a(u):lbprop(1,u)
+n@t25:=[x:nat]t24(x):lb(1)
+u@[l:lb(u)]
+t26:=<u>n:not(min(u))
+t27:=th3"l.and"(lb(u),<u>p,t26,l):not(<u>p)
+[v:nat][vp:<v>p]
+t28:=th3"l.imp"(is(u,v),<u>p,t27,[x:is(u,v)]isp1(nat,p,v,u,vp,x)):nis(u,v)
+t29:=mp(<v>p,lessis(u,v),vp,<v>l):lessis(u,v)
+t30:=ore1(less(u,v),is(u,v),t29,t28):less(u,v)
+t31:=satz25c(v,u,t30):lessis(<u>suc,v)
+v@t32:=[x:<v>p]t31(x):lbprop(<u>suc,v)
+l@t33:=[x:nat]t32(x):lb(<u>suc)
+u@t34:=induction([x:nat]lb(x),t25,[x:nat][y:lb(x)]t33(x,y),u):lb(u)
+p@[s:some(p)][u:nat][up:<u>p]
+t35:=satz10g(<u>suc,u,satz18b(u)):not(lessis(<u>suc,u))
+t36:=th4"l.imp"(<u>p,lessis(<u>suc,u),up,t35):not(lbprop(<u>suc,u))
+t37:=th1"l.all"(nat,[x:nat]lbprop(<u>suc,x),u,t36):not(lb(<u>suc))
+t38:=[y:non(nat,[x:nat]min(x))]mp(lb(<u>suc),con,t34(y,<u>suc),t37):some([x:nat]min(x))
+s@anders:=someapp(nat,p,s,some([x:nat]min(x)),[x:nat][y:<x>p]t38(x,y)):some([x:nat]min(x))
+-327
++*327
+p@[n:nat][m:nat][mn:min(p,n)][mm:min(p,m)]
+t39:=ande1(lb(n),<n>p,mn):lb(n)
+t40:=ande1(lb(m),<m>p,mm):lb(m)
+t41:=ande2(lb(n),<n>p,mn):<n>p
+t42:=ande2(lb(m),<m>p,mm):<m>p
+t43:=<m>t39:lbprop(n,m)
+t44:=<n>t40:lbprop(m,n)
+t45:=mp(<m>p,lessis(n,m),t42,t43):lessis(n,m)
+t46:=mp(<n>p,lessis(m,n),t41,t44):lessis(m,n)
+t47:=ore2(more(n,m),is(n,m),satz14(m,n,t46),satz10d(n,m,t45)):is(n,m)
+p@t48:=[x:nat][y:nat][u:min(x)][v:min(y)]t47(x,y,u,v):amone(nat,[x:nat]min(p,x))
+-327
+s@satz27a:=onei(nat,[x:nat]min(p,x),t48".327",satz27):one([x:nat]min(p,x))
++428
+x@[f:[y:nat]nat]
+prop1:=all([y:nat]is(<<y>suc>f,pl(<y>f,x))):'prop'
+prop2:=and(is(<1>f,x),prop1):'prop'
+x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
+prop3:=is(<y>a,<y>b):'prop'
+pb@t1:=ande1(is(<1>a,x),prop1(a),pa):is(<1>a,x)
+t2:=ande1(is(<1>b,x),prop1(b),pb):is(<1>b,x)
+t3:=tris2(nat,<1>a,<1>b,x,t1,t2):prop3(1)
+y@[p:prop3(y)]
+t4:=ispl1(<y>a,<y>b,x,p):is(pl(<y>a,x),pl(<y>b,x))
+t5:=ande2(is(<1>a,x),prop1(a),pa):prop1(a)
+t6:=ande2(is(<1>b,x),prop1(b),pb):prop1(b)
+t7:=<y>t5:is(<<y>suc>a,pl(<y>a,x))
+t8:=<y>t6:is(<<y>suc>b,pl(<y>b,x))
+t9:=tr3is(nat,<<y>suc>a,pl(<y>a,x),pl(<y>b,x),<<y>suc>b,t7,t4,symis(nat,<<y>suc>b,pl(<y>b,x),t8)):prop3(<y>suc)
+y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
+pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
+x@a1:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
+prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
+@id:=[y:nat]y:[y:nat]nat
+t12:=[x:nat]satz4e(x):prop1(1,id)
+t13:=andi(is(<1>id,1),prop1(1,id),refis(nat,1),t12):prop2(1,id)
+t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),id,t13):prop4(1)
+x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
+g:=[y:nat]pl(<y>f,y):[y:nat]nat
+t15:=ande1(is(<1>f,x),prop1(f),pf):is(<1>f,x)
+t16:=tris(nat,<1>g,pl(x,1),<x>suc,ispl1(<1>f,x,1,t15),satz4a(x)):is(<1>g,<x>suc)
+[y:nat]
+t17:=ande2(is(<1>f,x),prop1(f),pf):prop1(f)
+t18:=<y>t17:is(<<y>suc>f,pl(<y>f,x))
+t19:=tris(nat,<<y>suc>g,pl(pl(<y>f,x),<y>suc),pl(<y>f,pl(x,<y>suc)),ispl1(<<y>suc>f,pl(<y>f,x),<y>suc,t18),asspl1(<y>f,x,<y>suc)):is(<<y>suc>g,pl(<y>f,pl(x,<y>suc)))
+t20:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,pl(<x>suc,y),pl(y,<x>suc),satz4b(x,y),satz4h(x,y),compl(<x>suc,y)):is(pl(x,<y>suc),pl(y,<x>suc))
+t21:=tr3is(nat,<<y>suc>g,pl(<y>f,pl(x,<y>suc)),pl(<y>f,pl(y,<x>suc)),pl(<y>g,<x>suc),t19,ispl2(pl(x,<y>suc),pl(y,<x>suc),<y>f,t20),asspl2(<y>f,y,<x>suc)):is(<<y>suc>g,pl(<y>g,<x>suc))
+pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
+t23:=andi(is(<1>g,<x>suc),prop1(<x>suc,g),t16,t22):prop2(<x>suc,g)
+t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
+p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
+x@b1:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
+-428
+x@satz28:=onei([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),a1".428",b1".428"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,x),all([y:nat]is(<<y>suc>z,pl(<y>z,x)))))
+times:=ind([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),satz28):[y:nat]nat
+y@ts:=<y>times:nat
++*428
+x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz28):prop2(times)
+-428
+x@satz28a:=ande1(is(<1>times,x),prop1".428"(times),t26".428"):is(ts(x,1),x)
++*428
+x@t27:=ande2(is(<1>times,x),prop1(times),t26):prop1(times)
+-428
+y@satz28b:=<y>t27".428":is(ts(x,<y>suc),pl(ts(x,y),x))
++*428
+@t28:=t11(1,times(1),id,t26(1),t13):is"e"([y:nat]nat,times(1),id)
+-428
+x@satz28c:=fise(nat,nat,times(1),id".428",t28".428",x):is(ts(1,x),x)
++*428
+x@t29:=t11(<x>suc,times(<x>suc),[y:nat]pl(<y>times,y),t26(<x>suc),t23(b1,times,t26)):is"e"([y:nat]nat,times(<x>suc),[y:nat]pl(<y>times,y))
+-428
+y@satz28d:=fise(nat,nat,times(<x>suc),[z:nat]pl(<z>times,z),t29".428",y):is(ts(<x>suc,y),pl(ts(x,y),y))
+x@satz28e:=symis(nat,ts(x,1),x,satz28a):is(x,ts(x,1))
+y@satz28f:=symis(nat,ts(x,<y>suc),pl(ts(x,y),x),satz28b):is(pl(ts(x,y),x),ts(x,<y>suc))
+x@satz28g:=symis(nat,ts(1,x),x,satz28c):is(x,ts(1,x))
+y@satz28h:=symis(nat,ts(<x>suc,y),pl(ts(x,y),y),satz28d):is(pl(ts(x,y),y),ts(<x>suc,y))
+z@[i:is(x,y)]
+ists1:=isf(nat,nat,[u:nat]ts(u,z),x,y,i):is(ts(x,z),ts(y,z))
+ists2:=isf(nat,nat,[u:nat]ts(z,u),x,y,i):is(ts(z,x),ts(z,y))
+z@[u:nat][i:is(x,y)][j:is(z,u)]
+ists12:=tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
++429
+y@prop1:=is(ts(x,y),ts(y,x)):'prop'
+t1:=satz28a(y):is(ts(y,1),y)
+t2:=satz28c(y):is(ts(1,y),y)
+t3:=tris2(nat,ts(1,y),ts(y,1),y,t2,t1):prop1(1,y)
+[p:prop1(x,y)]
+t4:=tris(nat,pl(ts(x,y),y),pl(ts(y,x),y),ts(y,<x>suc),ispl1(ts(x,y),ts(y,x),y,p),satz28f(y,x)):is(pl(ts(x,y),y),ts(y,<x>suc))
+t5:=satz28d:is(ts(<x>suc,y),pl(ts(x,y),y))
+t6:=tris(nat,ts(<x>suc,y),pl(ts(x,y),y),ts(y,<x>suc),t5,t4):prop1(<x>suc,y)
+-429
+y@satz29:=induction([z:nat]prop1".429"(z,y),t3".429",[z:nat][u:prop1".429"(z,y)]t6".429"(z,y,u),x):is(ts(x,y),ts(y,x))
+comts:=satz29:is(ts(x,y),ts(y,x))
++*429
+x@t7:=tris(nat,ts(x,1),x,ts(1,x),satz28a,satz28g):prop1(1)
+y@[p:prop1(y)]
+t8:=tr3is(nat,ts(x,<y>suc),pl(ts(x,y),x),pl(ts(y,x),x),ts(<y>suc,x),satz28b(x,y),ispl1(ts(x,y),ts(y,x),x,p),satz28h(y,x)):prop1(<y>suc)
+y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(ts(x,y),ts(y,x))
+-429
++430
+z@prop1:=is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z))):'prop'
+y@t1:=tr3is(nat,ts(x,pl(y,1)),ts(x,<y>suc),pl(ts(x,y),x),pl(ts(x,y),ts(x,1)),ists2(pl(y,1),<y>suc,x,satz4a(y)),satz28b,ispl2(x,ts(x,1),ts(x,y),satz28e(x))):prop1(1)
+z@[p:prop1(z)]
+t2:=tr3is(nat,ts(x,pl(y,<z>suc)),ts(x,<pl(y,z)>suc),pl(ts(x,pl(y,z)),x),pl(pl(ts(x,y),ts(x,z)),x),ists2(pl(y,<z>suc),<pl(y,z)>suc,x,satz4b(y,z)),satz28b(x,pl(y,z)),ispl1(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),x,p)):is(ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x))
+t3:=tr3is(nat,ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x),pl(ts(x,y),pl(ts(x,z),x)),pl(ts(x,y),ts(x,<z>suc)),t2,asspl1(ts(x,y),ts(x,z),x),ispl2(pl(ts(x,z),x),ts(x,<z>suc),ts(x,y),satz28f(x,z))):prop1(<z>suc)
+-430
+z@satz30:=induction([u:nat]prop1".430"(u),t1".430",[u:nat][v:prop1".430"(u)]t3".430"(u,v),z):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+disttp1:=tr3is(nat,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz30(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
+disttp2:=satz30:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+distpt1:=symis(nat,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
+distpt2:=symis(nat,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
++431
+prop1:=is(ts(ts(x,y),z),ts(x,ts(y,z))):'prop'
+y@t1:=tris(nat,ts(ts(x,y),1),ts(x,y),ts(x,ts(y,1)),satz28a(ts(x,y)),ists2(y,ts(y,1),x,satz28e(y))):prop1(1)
+z@[p:prop1(z)]
+t2:=tr4is(nat,ts(ts(x,y),<z>suc),pl(ts(ts(x,y),z),ts(x,y)),pl(ts(x,ts(y,z)),ts(x,y)),ts(x,pl(ts(y,z),y)),ts(x,ts(y,<z>suc)),satz28b(ts(x,y),z),ispl1(ts(ts(x,y),z),ts(x,ts(y,z)),ts(x,y),p),distpt2(x,ts(y,z),y),ists2(pl(ts(y,z),y),ts(y,<z>suc),x,satz28f(y,z))):prop1(<z>suc)
+-431
+satz31:=induction([u:nat]prop1".431"(u),t1".431",[u:nat][v:prop1".431"(u)]t2".431"(u,v),z):is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts1:=satz31:is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts2:=symis(nat,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
+[m:more(x,y)]
++432
+[u:nat][du:diffprop(u)]
+t1:=tris(nat,ts(x,z),ts(pl(y,u),z),pl(ts(y,z),ts(u,z)),ists1(x,pl(y,u),z,du),disttp1(y,u,z)):is(ts(x,z),pl(ts(y,z),ts(u,z)))
+t2:=somei(nat,[v:nat]diffprop(ts(x,z),ts(y,z),v),ts(u,z),t1):more(ts(x,z),ts(y,z))
+-432
+satz32a:=someapp(nat,[u:nat]diffprop(u),m,more(ts(x,z),ts(y,z)),[u:nat][v:diffprop(u)]t2".432"(u,v)):more(ts(x,z),ts(y,z))
+z@[i:is(x,y)]
+satz32b:=ists1(x,y,z,i):is(ts(x,z),ts(y,z))
+z@[l:less(x,y)]
+satz32c:=satz11(ts(y,z),ts(x,z),satz32a(y,x,z,satz12(x,y,l))):less(ts(x,z),ts(y,z))
++*432
+l@anders1:=satz32a(y,x,z,l):less(ts(x,z),ts(y,z))
+-432
+m@satz32d:=ismore12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32a):more(ts(z,x),ts(z,y))
+i@satz32e:=ists2(x,y,z,i):is(ts(z,x),ts(z,y))
+l@satz32f:=isless12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32c):less(ts(z,x),ts(z,y))
++*432
+l@anders2:=satz32d(y,x,z,l):less(ts(z,x),ts(z,y))
+-432
+z@[u:nat][i:is(x,y)][m:more(z,u)]
+satz32g:=ismore2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32d(z,u,x,m)):more(ts(x,z),ts(y,u))
+satz32h:=ismore12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32g):more(ts(z,x),ts(u,y))
+i@[l:less(z,u)]
+satz32j:=isless2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32f(z,u,x,l)):less(ts(x,z),ts(y,u))
+satz32k:=isless12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32j):less(ts(z,x),ts(u,y))
+z@[m:moreis(x,y)]
++*432
+m@[n:more(x,y)]
+t3:=moreisi1(ts(x,z),ts(y,z),satz32a(n)):moreis(ts(x,z),ts(y,z))
+m@[i:is(x,y)]
+t4:=moreisi2(ts(x,z),ts(y,z),ists1(x,y,z,i)):moreis(ts(x,z),ts(y,z))
+-432
+m@satz32l:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,z)),m,[u:more(x,y)]t3".432"(u),[u:is(x,y)]t4".432"(u)):moreis(ts(x,z),ts(y,z))
+satz32m:=ismoreis12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32l):moreis(ts(z,x),ts(z,y))
+z@[l:lessis(x,y)]
+satz32n:=satz13(ts(y,z),ts(x,z),satz32l(y,x,z,satz14(l))):lessis(ts(x,z),ts(y,z))
+satz32o:=satz13(ts(z,y),ts(z,x),satz32m(y,x,z,satz14(l))):lessis(ts(z,x),ts(z,y))
++433
+z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
+t2:=satz10b(ts(x,z),ts(y,z)):ec3(is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)))
+-433
+z@[m:more(ts(x,z),ts(y,z))]
+satz33a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),m):more(x,y)
+z@[i:is(ts(x,z),ts(y,z))]
+satz33b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),i):is(x,y)
+z@[l:less(ts(x,z),ts(y,z))]
+satz33c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),l):less(x,y)
++*433
+l@anders:=satz33a(y,x,z,l):less(x,y)
+-433
+u@[m:more(x,y)][n:more(z,u)]
++434
+t1:=satz32a(x,y,z,m):more(ts(x,z),ts(y,z))
+t2:=ismore12(ts(z,y),ts(y,z),ts(u,y),ts(y,u),comts(z,y),comts(u,y),satz32a(z,u,y,n)):more(ts(y,z),ts(y,u))
+-434
+satz34:=trmore(ts(x,z),ts(y,z),ts(y,u),t1".434",t2".434"):more(ts(x,z),ts(y,u))
++*434
+n@anders:=trmore(ts(x,z),ts(y,z),ts(y,u),satz32a(x,y,z,m),satz32d(z,u,y,n)):more(ts(x,z),ts(y,u))
+-434
+u@[l:less(x,y)][k:less(z,u)]
+satz34a:=satz34(y,x,u,z,l,k):less(ts(x,z),ts(y,u))
++*434
+k@andersa:=satz11(ts(y,u),ts(x,z),satz34(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(ts(x,z),ts(y,u))
+-434
+u@[m:moreis(x,y)][n:more(z,u)]
+satz35a:=orapp(more(x,y),is(x,y),more(ts(x,z),ts(y,u)),m,[v:more(x,y)]satz34(v,n),[v:is(x,y)]satz32g(u,v,n)):more(ts(x,z),ts(y,u))
+u@[m:more(x,y)][n:moreis(z,u)]
+satz35b:=orapp(more(z,u),is(z,u),more(ts(x,z),ts(y,u)),n,[v:more(z,u)]satz34(m,v),[v:is(z,u)]satz32h(z,u,x,y,v,m)):more(ts(x,z),ts(y,u))
+u@[l:lessis(x,y)][k:less(z,u)]
+satz35c:=satz35a(y,x,u,z,satz14(x,y,l),k):less(ts(x,z),ts(y,u))
+u@[l:less(x,y)][k:lessis(z,u)]
+satz35d:=satz35b(y,x,u,z,l,satz14(z,u,k)):less(ts(x,z),ts(y,u))
+u@[m:moreis(x,y)][n:moreis(z,u)]
++436
+[i:is(x,y)][j:is(z,u)]
+t1:=moreisi2(ts(x,z),ts(y,u),tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j))):moreis(ts(x,z),ts(y,u))
+i@[o:more(z,u)]
+t2:=moreisi1(ts(x,z),ts(y,u),satz35a(m,o)):moreis(ts(x,z),ts(y,u))
+i@t3:=orapp(more(z,u),is(z,u),moreis(ts(x,z),ts(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(ts(x,z),ts(y,u))
+n@[o:more(x,y)]
+t4:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
+-436
+satz36:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t4".436"(v),[v:is(x,y)]t3".436"(v)):moreis(ts(x,z),ts(y,u))
++*436
+n@[o:more(x,y)]
+t5:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
+n@[i:is(x,y)]
+t6:=ismoreis2(ts(x,u),ts(y,u),ts(x,z),ists1(u,i),satz32m(z,u,x,n)):moreis(ts(x,z),ts(y,u))
+n@anders:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(ts(x,z),ts(y,u))
+-436
+u@[l:lessis(x,y)][k:lessis(z,u)]
+satz36a:=satz13(ts(y,u),ts(x,z),satz36(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(ts(x,z),ts(y,u))
+y@[m:more(x,y)]
++mn
+t1:=onei(nat,[z:nat]diffprop(x,y,z),satz8b(x,y),m):one([z:nat]diffprop(x,y,z))
+-mn
+mn:=ind(nat,[z:nat]diffprop(x,y,z),t1".mn"):nat
++*mn
+m@th1a:=oneax(nat,[z:nat]diffprop(x,y,z),t1):is(x,pl(y,mn(x,y,m)))
+th1b:=symis(nat,x,pl(y,mn(x,y,m)),th1a):is(pl(y,mn(x,y,m)),x)
+th1c:=tris(nat,x,pl(y,mn(x,y,m)),pl(mn(x,y,m),y),th1a,compl(y,mn(x,y,m))):is(x,pl(mn(x,y,m),y))
+th1d:=symis(nat,x,pl(mn(x,y,m),y),th1c):is(pl(mn(x,y,m),y),x)
+y@[z:nat][m:more(x,y)][i:is(pl(y,z),x)]
+th1e:=<th1a(m)><symis(nat,pl(y,z),x,i)><mn(x,y,m)><z>satz8b(x,y):is(z,mn(x,y,m))
+-mn
+z@[u:nat][m:more(x,z)][n:more(y,u)][i:is(x,y)][j:is(z,u)]
++*mn
+j@t2:=tr3is(nat,pl(u,mn(x,z,m)),pl(z,mn(x,z,m)),x,y,ispl1(u,z,mn(x,z,m),symis(nat,z,u,j)),th1b(x,z,m),i):is(pl(u,mn(x,z,m)),y)
+-mn
+j@ismn12:=th1e".mn"(y,u,mn(x,z,m),n,t2".mn"):is(mn(x,z,m),mn(y,u,n))
+@[n:nat]
+1to:=ot(nat,[x:nat]lessis(x,n)):'type'
+[x:nat][l:lessis(x,n)]
+outn:=out(nat,[y:nat]lessis(y,n),x,l):1to(n)
+n@[xn:1to(n)]
+inn:=in"e"(nat,[y:nat]lessis(y,n),xn):nat
+1top:=inp(nat,[y:nat]lessis(y,n),xn):lessis(inn,n)
+l@[y:nat][k:lessis(y,n)][i:is(x,y)]
+isoutni:=isouti(nat,[z:nat]lessis(z,n),x,l,y,k,i):is"e"(1to(n),outn(x,l),outn(y,k))
+k@[i:is"e"(1to(n),outn(x,l),outn(y,k))]
+isoutne:=isoute(nat,[z:nat]lessis(z,n),x,l,y,k,i):is(x,y)
+xn@[yn:1to(n)][i:is"e"(1to(n),xn,yn)]
+isinni:=isini(nat,[z:nat]lessis(z,n),xn,yn,i):is(inn(xn),inn(yn))
+yn@[i:is(inn(xn),inn(yn))]
+isinne:=isine(nat,[z:nat]lessis(z,n),xn,yn,i):is"e"(1to(n),xn,yn)
+xn@isoutinn:=isoutin(nat,[y:nat]lessis(y,n),xn):is"e"(1to(n),xn,outn(inn(xn),1top(xn)))
+l@isinoutn:=isinout(nat,[y:nat]lessis(y,n),x,l):is(x,inn(outn(x,l)))
+@1o:=outn(1,1,lessisi2(1,1,refis(nat,1))):1to(1)
+[u:1to(1)]
++singlet
+u0:=inn(1,u):nat
+t1:=1top(1,u):lessis(u0,1)
+t2:=ore2(more(u0,1),is(u0,1),satz24(u0),satz10d(u0,1,t1)):is(u0,1)
+th1:=tris(1to(1),u,outn(1,u0,t1),1o,isoutinn(1,u),isoutni(1,u0,t1,1,lessisi2(1,1,refis(nat,1)),t2)):is"e"(1to(1),u,1o)
+-singlet
+@2:=pl(1,1):nat
+[x:nat]
++pair
+[l:lessis(x,2)][n:nis(x,2)]
+t1:=satz26(1,x,ore1(less(x,2),is(x,2),l,n)):lessis(x,1)
+t2:=ore2(more(x,1),is(x,1),satz24(x),satz10d(x,1,t1)):is(x,1)
+l@th1:=th2"l.or"(is(x,1),is(x,2),[t:nis(x,2)]t2(t)):or(is(x,1),is(x,2))
+@th2:=th1"e.notis"(nat,<1>suc,1,2,<1>ax3,satz4e(1)):nis(2,1)
+-pair
+@1t:=outn(2,1,satz24a(2)):1to(2)
+2t:=outn(2,2,lessisi2(2,2,refis(nat,2))):1to(2)
++*pair
+@[u:1to(2)]
+u0:=inn(2,u):nat
+t3:=1top(2,u):lessis(u0,2)
+[i:is(u0,1)]
+t4:=isoutni(2,u0,t3,1,satz24a(2),i):is"e"(1to(2),outn(2,u0,t3),1t)
+t5:=tris(1to(2),u,outn(2,u0,t3),1t,isoutinn(2,u),t4):is"e"(1to(2),u,1t)
+u@[i:is(u0,2)]
+t6:=isoutni(2,u0,t3,2,lessisi2(2,2,refis(nat,2)),i):is"e"(1to(2),outn(2,u0,t3),2t)
+t7:=tris(1to(2),u,outn(2,u0,t3),2t,isoutinn(2,u),t6):is"e"(1to(2),u,2t)
+u@th3:=th9"l.or"(is(u0,1),is(u0,2),is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),th1(u0,t3),[t:is(u0,1)]t5(t),[t:is(u0,2)]t7(t)):or(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t))
+@[i:is"e"(1to(2),2t,1t)]
+t9:=isini(nat,[x:nat]lessis(x,2),2t,1t,i):is(u0(2t),u0(1t))
+t10:=tr3is(nat,2,u0(2t),u0(1t),1,isinoutn(2,2,lessisi2(2,2,refis(nat,2))),t9,symis(nat,1,u0(1t),isinoutn(2,1,satz24a(2)))):is(2,1)
+@th4:=th3"l.imp"(is"e"(1to(2),2t,1t),is(2,1),th2,[t:is"e"(1to(2),2t,1t)]t10(t)):not(is"e"(1to(2),2t,1t))
+-pair
+@[alpha:'type']
+pair1type:=[x:1to(2)]alpha:'type'
+[a:alpha][b:alpha]
+pair1:=[x:1to(2)]ite(is"e"(1to(2),x,1t),alpha,a,b):pair1type
+alpha@[p:pair1type]
+first1:=<1t>p:alpha
+second1:=<2t>p:alpha
+b@first1is1:=itet(is"e"(1to(2),1t,1t),alpha,a,b,refis(1to(2),1t)):is"e"(alpha,first1(pair1),a)
+first1is2:=symis(alpha,first1(pair1),a,first1is1):is"e"(alpha,a,first1(pair1))
+second1is1:=itef(is"e"(1to(2),2t,1t),alpha,a,b,th4".pair"):is"e"(alpha,second1(pair1),b)
+second1is2:=symis(alpha,second1(pair1),b,second1is1):is"e"(alpha,b,second1(pair1))
++*pair
+p@[q:pair1type][i:is"e"(alpha,first1(p),first1(q))][j:is"e"(alpha,second1(p),second1(q))][u:1to(2)][u1:is"e"(1to(2),u,1t)]
+t11:=isf(1to(2),alpha,p,u,1t,u1):is"e"(alpha,<u>p,first1(p))
+t12:=symis(alpha,<u>q,first1(q),isf(1to(2),alpha,q,u,1t,u1)):is"e"(alpha,first1(q),<u>q)
+t13:=tr3is(alpha,<u>p,first1(p),first1(q),<u>q,t11,i,t12):is"e"(alpha,<u>p,<u>q)
+u@[u2:is"e"(1to(2),u,2t)]
+t14:=isf(1to(2),alpha,p,u,2t,u2):is"e"(alpha,<u>p,second1(p))
+t15:=symis(alpha,<u>q,second1(q),isf(1to(2),alpha,q,u,2t,u2)):is"e"(alpha,second1(q),<u>q)
+t16:=tr3is(alpha,<u>p,second1(p),second1(q),<u>q,t14,j,t15):is"e"(alpha,<u>p,<u>q)
+u@t17:=orapp(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),is"e"(alpha,<u>p,<u>q),th3(u),[t:is"e"(1to(2),u,1t)]t13(t),[t:is"e"(1to(2),u,2t)]t16(t)):is"e"(alpha,<u>p,<u>q)
+j@th5:=fisi(1to(2),alpha,p,q,[t:1to(2)]t17(t)):is"e"(pair1type,p,q)
+p@q0:=pair1(first1,second1):pair1type
+t18:=first1is1(first1(p),second1):is"e"(alpha,first1(q0),first1(p))
+t19:=second1is1(first1,second1):is"e"(alpha,second1(q0),second1(p))
+-pair
+p@pair1is1:=th5".pair"(q0".pair",p,t18".pair",t19".pair"):is"e"(pair1type,pair1(first1,second1),p)
+pair1is2:=symis(pair1type,pair1(first1,second1),p,pair1is1):is"e"(pair1type,p,pair1(first1,second1))
+@[x:nat]
+lessisi3:=lessisi2(x,x,refis(nat,x)):lessis(x,x)
+1out:=outn(x,1,satz24a(x)):1to(x)
+xout:=outn(x,x,lessisi3(x)):1to(x)
+[y:nat][l:lessis(y,x)][u:1to(y)]
++left
+ui:=inn(y,u):nat
+t1:=1top(y,u):lessis(ui,y)
+t2:=trlessis(ui,y,x,t1,l):lessis(ui,x)
+-left
+left1to:=outn(x,ui".left",t2".left"):1to(x)
+[v:1to(y)][i:is"e"(1to(x),left1to(u),left1to(v))]
++*left
+i@t3:=isoutne(x,ui,t2,ui(v),t2(v),i):is(ui,ui(v))
+-left
+i@thleft1:=isinne(y,u,v,t3".left"):is"e"(1to(y),u,v)
+l@thleft2:=[u:1to(y)][v:1to(y)][t:is"e"(1to(x),left1to(u),left1to(v))]thleft1(u,v,t):injective(1to(y),1to(x),[t:1to(y)]left1to(t))
+y@[u:1to(y)]
++right
+ui:=inn(y,u):nat
+t4:=1top(y,u):lessis(ui,y)
+t5:=satz19o(ui,y,x,t4):lessis(pl(x,ui),pl(x,y))
+-right
+right1to:=outn(pl(x,y),pl(x,ui".right"),t5".right"):1to(pl(x,y))
+[v:1to(y)][i:is"e"(1to(pl(x,y)),right1to(u),right1to(v))]
++*right
+i@t6:=isoutne(pl(x,y),pl(x,ui(u)),t5(u),pl(x,ui(v)),t5(v),i):is(pl(x,ui(u)),pl(x,ui(v)))
+t7:=satz20e(ui(u),ui(v),x,t6):is(ui(u),ui(v))
+-right
+i@thright1:=isinne(y,u,v,t7".right"):is"e"(1to(y),u,v)
+@[alpha:'type'][x:nat][y:nat][l:lessis(y,x)][f:[t:1to(x)]alpha]
+left:=[t:1to(y)]<left1to(x,y,l,t)>f:[t:1to(y)]alpha
+y@[f:[t:1to(pl(x,y))]alpha]
+right:=[t:1to(y)]<right1to(x,y,t)>f:[t:1to(y)]alpha
+y@[i:is(y,x)][f:[t:1to(y)]alpha]
++*left
+f@t4:=lessisi2(y,x,i):lessis(y,x)
+t5:=lessisi2(x,y,symis(nat,y,x,i)):lessis(x,y)
+f1:=left(y,x,t5,f):[t:1to(x)]alpha
+f2:=left(t4,f1):[t:1to(y)]alpha
+[u:1to(y)]
+t6:=isinoutn(x,inn(y,u),trlessis(inn(y,u),y,x,1top(y,u),t4)):is(inn(y,u),inn(x,left1to(x,y,t4,u)))
+t7:=tris(1to(y),u,outn(y,inn(y,u),1top(y,u)),left1to(y,x,t5,left1to(x,y,t4,u)),isoutinn(y,u),isoutni(y,inn(y,u),1top(y,u),inn(x,left1to(x,y,t4,u)),trlessis(inn(x,left1to(x,y,t4,u)),x,y,1top(x,left1to(x,y,t4,u)),t5),t6)):is"e"(1to(y),u,left1to(y,x,t5,left1to(x,y,t4,u)))
+t8:=isf(1to(y),alpha,f,u,left1to(y,x,t5,left1to(x,y,t4,u)),t7):is"e"(alpha,<u>f,<u>f2)
+-left
+f@thleft:=fisi(1to(y),alpha,f,f2".left",[t:1to(y)]t8".left"(t)):is"e"([t:1to(y)]alpha,f,left(x,y,lessisi2(y,x,i),left(y,x,lessisi2(x,y,symis(nat,y,x,i)),f)))
+@frac:=pair1type(nat):'type'
+[x1:nat][x2:nat]
+fr:=pair1(nat,x1,x2):frac
+@[x:frac]
+num:=first1(nat,x):nat
+den:=second1(nat,x):nat
+x2@numis:=first1is1(nat,x1,x2):is(num(fr(x1,x2)),x1)
+isnum:=first1is2(nat,x1,x2):is(x1,num(fr(x1,x2)))
+denis:=second1is1(nat,x1,x2):is(den(fr(x1,x2)),x2)
+isden:=second1is2(nat,x1,x2):is(x2,den(fr(x1,x2)))
+x@1x:=num(x):nat
+2x:=den(x):nat
+fris:=pair1is1(nat,x):is"e"(frac,fr(1x,2x),x)
+isfr:=pair1is2(nat,x):is"e"(frac,x,fr(1x,2x))
+x2@[y1:nat][y2:nat]
+12isnd:=ists12(x1,num(fr(x1,x2)),y2,den(fr(y1,y2)),isnum(x1,x2),isden(y1,y2)):is(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))))
+ndis12:=symis(nat,ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),12isnd):is(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2))
+x@[n1:nat][n2:nat]
+1disnd:=ists1(n1,num(fr(n1,n2)),2x,isnum(n1,n2)):is(ts(n1,2x),ts(num(fr(n1,n2)),2x))
+ndis1d:=symis(nat,ts(n1,2x),ts(num(fr(n1,n2)),2x),1disnd):is(ts(num(fr(n1,n2)),2x),ts(n1,2x))
+n2isnd:=ists2(n2,den(fr(n1,n2)),1x,isden(n1,n2)):is(ts(1x,n2),ts(1x,den(fr(n1,n2))))
+ndisn2:=symis(nat,ts(1x,n2),ts(1x,den(fr(n1,n2))),n2isnd):is(ts(1x,den(fr(n1,n2))),ts(1x,n2))
+x2@[n:nat][i:is(x1,n)]
+isn:=isf(nat,frac,[t:nat]fr(t,x2),x1,n,i):is"e"(frac,fr(x1,x2),fr(n,x2))
+n@[i:is(x2,n)]
+isd:=isf(nat,frac,[t:nat]fr(x1,t),x2,n,i):is"e"(frac,fr(x1,x2),fr(x1,n))
+y2@[i:is(x1,y1)][j:is(x2,y2)]
+isnd:=tris(frac,fr(x1,x2),fr(y1,x2),fr(y1,y2),isn(x1,x2,y1,i),isd(y1,x2,y2,j)):is"e"(frac,fr(x1,x2),fr(y1,y2))
+x@[y:frac]
+1y:=num(y):nat
+2y:=den(y):nat
+eq:=is(ts(1x,2y),ts(1y,2x)):'prop'
+y2@[i:is(ts(x1,y2),ts(y1,x2))]
+eqi12:=tr3is(nat,ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ndis12(x1,x2,y1,y2),i,12isnd(y1,y2,x1,x2)):eq(fr(x1,x2),fr(y1,y2))
+n2@[i:is(ts(1x,n2),ts(n1,2x))]
+eqi1:=isp(frac,[t:frac]eq(t,fr(n1,n2)),fr(1x,2x),x,eqi12(1x,2x,n1,n2,i),fris):eq(x,fr(n1,n2))
+n2@[i:is(ts(n1,2x),ts(1x,n2))]
+eqi2:=isp(frac,[t:frac]eq(fr(n1,n2),t),fr(1x,2x),x,eqi12(n1,n2,1x,2x,i),fris):eq(fr(n1,n2),x)
+x@satz37:=refis(nat,ts(1x,2x)):eq(x,x)
+refeq:=satz37:eq(x,x)
+y@[i:is"e"(frac,x,y)]
+refeq1:=isp(frac,[t:frac]eq(x,t),x,y,refeq,i):eq(x,y)
+refeq2:=isp(frac,[t:frac]eq(t,x),x,y,refeq,i):eq(y,x)
+y2@[i:is(x1,y1)][j:is(x2,y2)]
+eqnd:=refeq1(fr(x1,x2),fr(y1,y2),isnd(i,j)):eq(fr(x1,x2),fr(y1,y2))
+x2@[n:nat][i:is(x1,n)]
+eqn:=refeq1(fr(x1,x2),fr(n,x2),isn(n,i)):eq(fr(x1,x2),fr(n,x2))
+n@[i:is(x2,n)]
+eqd:=refeq1(fr(x1,x2),fr(x1,n),isd(n,i)):eq(fr(x1,x2),fr(x1,n))
+y@[e:eq(x,y)]
+satz38:=symis(nat,ts(1x,2y),ts(1y,2x),e):eq(y,x)
+symeq:=satz38:eq(y,x)
+@[a:nat][b:nat][c:nat][d:nat]
++ii1
+t1:=tris(nat,ts(b,ts(c,d)),ts(ts(b,c),d),ts(d,ts(b,c)),assts2(b,c,d),comts(ts(b,c),d)):is(ts(b,ts(c,d)),ts(d,ts(b,c)))
+-ii1
+stets:=tr4is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(b,c))),ts(ts(a,d),ts(b,c)),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(b,c)),a,t1".ii1"),assts2(a,d,ts(b,c)),ists2(ts(b,c),ts(c,b),ts(a,d),comts(b,c))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
++*ii1
+d@t2:=tr3is(nat,ts(b,ts(c,d)),ts(ts(c,d),b),ts(ts(d,c),b),ts(d,ts(c,b)),comts(b,ts(c,d)),ists1(ts(c,d),ts(d,c),b,comts(c,d)),assts1(d,c,b)):is(ts(b,ts(c,d)),ts(d,ts(c,b)))
+anders:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(c,b))),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(c,b)),a,t2),assts2(a,d,ts(c,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
+-ii1
+y@[z:frac]
+1z:=num(z):nat
+2z:=den(z):nat
+[e:eq(x,y)][f:eq(y,z)]
++139
+t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
+t2:=stets(1x,2y,1y,2z):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)))
+t3:=tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)))
+t4:=tr3is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),symis(nat,ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),t2),t1,t3):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
+-139
+satz39:=satz33b(ts(1x,2z),ts(1z,2x),ts(1y,2y),t4".139"):eq(x,z)
++*139
+f@anders:=tr4is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2z,1y,2y),ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
+-139
+f@treq:=satz39:eq(x,z)
+z@[e:eq(z,x)][f:eq(z,y)]
+treq1:=treq(x,z,y,symeq(z,x,e),f):eq(x,y)
+z@[e:eq(x,z)][f:eq(y,z)]
+treq2:=treq(x,z,y,e,symeq(y,z,f)):eq(x,y)
+z@[u:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)]
+tr3eq:=treq(x,y,u,e,treq(y,z,u,f,g)):eq(x,u)
+u@[v:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)][h:eq(u,v)]
+tr4eq:=tr3eq(x,y,z,v,e,f,treq(z,u,v,g,h)):eq(x,v)
+x@[n:nat]
+satz40:=eqi1(ts(1x,n),ts(2x,n),tris(nat,ts(1x,ts(2x,n)),ts(1x,ts(n,2x)),ts(ts(1x,n),2x),ists2(ts(2x,n),ts(n,2x),1x,comts(2x,n)),assts2(1x,n,2x))):eq(x,fr(ts(1x,n),ts(2x,n)))
+satz40a:=symeq(x,fr(ts(1x,n),ts(2x,n)),satz40):eq(fr(ts(1x,n),ts(2x,n)),x)
+x2@[n:nat]
+satz40b:=eqi12(ts(x1,n),ts(x2,n),tris(nat,ts(x1,ts(x2,n)),ts(x1,ts(n,x2)),ts(ts(x1,n),x2),ists2(ts(x2,n),ts(n,x2),x1,comts(x2,n)),assts2(x1,n,x2))):eq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)))
+satz40c:=symeq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)),satz40b):eq(fr(ts(x1,n),ts(x2,n)),fr(x1,x2))
+y@moref:=more(ts(1x,2y),ts(1y,2x)):'prop'
+lessf:=less(ts(1x,2y),ts(1y,2x)):'prop'
+y2@[m:more(ts(x1,y2),ts(y1,x2))]
+morefi12:=ismore12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),m):moref(fr(x1,x2),fr(y1,y2))
+y2@[l:less(ts(x1,y2),ts(y1,x2))]
+lessfi12:=isless12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),l):lessf(fr(x1,x2),fr(y1,y2))
+n2@[m:more(ts(1x,n2),ts(n1,2x))]
+morefi1:=ismore12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),m):moref(x,fr(n1,n2))
+n2@[m:more(ts(n1,2x),ts(1x,n2))]
+morefi2:=ismore12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),m):moref(fr(n1,n2),x)
+n2@[l:less(ts(1x,n2),ts(n1,2x))]
+lessfi1:=isless12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),l):lessf(x,fr(n1,n2))
+n2@[l:less(ts(n1,2x),ts(1x,n2))]
+lessfi2:=isless12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),l):lessf(fr(n1,n2),x)
+y@satz41:=satz10(ts(1x,2y),ts(1y,2x)):orec3(eq(x,y),moref(x,y),lessf(x,y))
+satz41a:=satz10a(ts(1x,2y),ts(1y,2x)):or3(eq(x,y),moref(x,y),lessf(x,y))
+satz41b:=satz10b(ts(1x,2y),ts(1y,2x)):ec3(eq(x,y),moref(x,y),lessf(x,y))
+[m:moref(x,y)]
+satz42:=satz11(ts(1x,2y),ts(1y,2x),m):lessf(y,x)
+y@[l:lessf(x,y)]
+satz43:=satz12(ts(1x,2y),ts(1y,2x),l):moref(y,x)
+u@1u:=num(u):nat
+2u:=den(u):nat
+[m:moref(x,y)][e:eq(x,z)][f:eq(y,u)]
++244
+t1:=ists12(ts(1y,2u),ts(1u,2y),ts(1z,2x),ts(1x,2z),f,symeq(x,z,e)):is(ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)))
+t2:=tr3is(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)),ts(ts(1u,2z),ts(1x,2y)),stets(1y,2x,1z,2u),t1,stets(1u,2y,1x,2z)):is(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)))
+t3:=ismore1(ts(ts(1u,2z),ts(1x,2y)),ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)),symis(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)),t2),satz32d(ts(1x,2y),ts(1y,2x),ts(1u,2z),m)):more(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)))
+-244
+satz44:=satz33a(ts(1z,2u),ts(1u,2z),ts(1y,2x),ismore1(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1z,2u),ts(1y,2x)),ts(ts(1u,2z),ts(1y,2x)),comts(ts(1y,2x),ts(1z,2u)),t3".244")):moref(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][m:moref(x,z)]
+eqmoref12:=satz44(x,z,y,u,m,e,f):moref(y,u)
+z@[e:eq(x,y)][m:moref(x,z)]
+eqmoref1:=satz44(x,z,y,z,m,e,refeq(z)):moref(y,z)
+e@[m:moref(z,x)]
+eqmoref2:=satz44(z,x,z,y,m,refeq(z),e):moref(z,y)
+u@[l:lessf(x,y)][e:eq(x,z)][f:eq(y,u)]
+satz45:=satz42(u,z,satz44(y,x,u,z,satz43(x,y,l),f,e)):lessf(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][l:lessf(x,z)]
+eqlessf12:=satz45(x,z,y,u,l,e,f):lessf(y,u)
+z@[e:eq(x,y)][l:lessf(x,z)]
+eqlessf1:=satz45(x,z,y,z,l,e,refeq(z)):lessf(y,z)
+e@[l:lessf(z,x)]
+eqlessf2:=satz45(z,x,z,y,l,refeq(z),e):lessf(z,y)
+y@moreq:=or(moref(x,y),eq(x,y)):'prop'
+lesseq:=or(lessf(x,y),eq(x,y)):'prop'
+[e:eq(x,y)]
+moreqi2:=ori2(moref(x,y),eq(x,y),e):moreq(x,y)
+lesseqi2:=ori2(lessf(x,y),eq(x,y),e):lesseq(x,y)
+y@[m:moref(x,y)]
+moreqi1:=ori1(moref(x,y),eq(x,y),m):moreq(x,y)
+y@[l:lessf(x,y)]
+lesseqi1:=ori1(lessf(x,y),eq(x,y),l):lesseq(x,y)
+y@[m:moreq(x,y)]
+satz41c:=th7"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,comor(moref(x,y),eq(x,y),m)):not(lessf(x,y))
+y@[l:lesseq(x,y)]
+satz41d:=th9"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,l):not(moref(x,y))
+y@[n:not(moref(x,y))]
+satz41e:=th2"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n):lesseq(x,y)
+y@[n:not(lessf(x,y))]
+satz41f:=comor(eq(x,y),moref(x,y),th3"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n)):moreq(x,y)
+y@[m:moref(x,y)]
+satz41g:=th3"l.or"(lessf(x,y),eq(x,y),ec3e23(eq(x,y),moref(x,y),lessf(x,y),satz41b,m),ec3e21(eq(x,y),moref(x,y),lessf(x,y),satz41b,m)):not(lesseq(x,y))
+y@[l:lessf(x,y)]
+satz41h:=th3"l.or"(moref(x,y),eq(x,y),ec3e32(eq(x,y),moref(x,y),lessf(x,y),satz41b,l),ec3e31(eq(x,y),moref(x,y),lessf(x,y),satz41b,l)):not(moreq(x,y))
+y@[n:not(moreq(x,y))]
+satz41j:=or3e3(eq(x,y),moref(x,y),lessf(x,y),satz41a,th5"l.or"(moref(x,y),eq(x,y),n),th4"l.or"(moref(x,y),eq(x,y),n)):lessf(x,y)
+y@[n:not(lesseq(x,y))]
+satz41k:=or3e2(eq(x,y),moref(x,y),lessf(x,y),satz41a,th4"l.or"(lessf(x,y),eq(x,y),n),th5"l.or"(lessf(x,y),eq(x,y),n)):moref(x,y)
+u@[m:moreq(x,y)][e:eq(x,z)][f:eq(y,u)]
++246
+[n:moref(x,y)]
+t1:=ori1(moref(z,u),eq(z,u),satz44(n,e,f)):moreq(z,u)
+f@[g:eq(x,y)]
+t2:=ori2(moref(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):moreq(z,u)
+-246
+satz46:=orapp(moref(x,y),eq(x,y),moreq(z,u),m,[t:moref(x,y)]t1".246"(t),[t:eq(x,y)]t2".246"(t)):moreq(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][m:moreq(x,z)]
+eqmoreq12:=satz46(x,z,y,u,m,e,f):moreq(y,u)
+z@[e:eq(x,y)][m:moreq(x,z)]
+eqmoreq1:=satz46(x,z,y,z,m,e,refeq(z)):moreq(y,z)
+e@[m:moreq(z,x)]
+eqmoreq2:=satz46(z,x,z,y,m,refeq(z),e):moreq(z,y)
+u@[l:lesseq(x,y)][e:eq(x,z)][f:eq(y,u)]
++247
+[k:lessf(x,y)]
+t1:=ori1(lessf(z,u),eq(z,u),satz45(k,e,f)):lesseq(z,u)
+f@[g:eq(x,y)]
+t2:=ori2(lessf(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):lesseq(z,u)
+-247
+satz47:=orapp(lessf(x,y),eq(x,y),lesseq(z,u),l,[t:lessf(x,y)]t1".247"(t),[t:eq(x,y)]t2".247"(t)):lesseq(z,u)
+u@[e:eq(x,y)][f:eq(z,u)][l:lesseq(x,z)]
+eqlesseq12:=satz47(x,z,y,u,l,e,f):lesseq(y,u)
+z@[e:eq(x,y)][l:lesseq(x,z)]
+eqlesseq1:=satz47(x,z,y,z,l,e,refeq(z)):lesseq(y,z)
+e@[l:lesseq(z,x)]
+eqlesseq2:=satz47(z,x,z,y,l,refeq(z),e):lesseq(z,y)
+y@[m:moreq(x,y)]
+satz48:=th9"l.or"(moref(x,y),eq(x,y),lessf(y,x),eq(y,x),m,[t:moref(x,y)]satz42(x,y,t),[t:eq(x,y)]satz38(x,y,t)):lesseq(y,x)
+y@[l:lesseq(x,y)]
+satz49:=th9"l.or"(lessf(x,y),eq(x,y),moref(y,x),eq(y,x),l,[t:lessf(x,y)]satz43(x,y,t),[t:eq(x,y)]satz38(x,y,t)):moreq(y,x)
+z@[l:lessf(x,y)][k:lessf(y,z)]
++250
+t1:=satz34a(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),l,k):less(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
+t2:=isless12(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2y,1y,2z),tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))),t1):less(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
+-250
+satz50:=satz33c(ts(1x,2z),ts(1z,2x),ts(1y,2y),t2".250"):lessf(x,z)
+trlessf:=satz50:lessf(x,z)
+z@[m:moref(x,y)][n:moref(y,z)]
+trmoref:=satz43(z,x,satz50(z,y,x,satz42(y,z,n),satz42(x,y,m))):moref(x,z)
+z@[l:lesseq(x,y)][k:lessf(y,z)]
+satz51a:=orapp(lessf(x,y),eq(x,y),lessf(x,z),l,[t:lessf(x,y)]satz50(t,k),[t:eq(x,y)]eqlessf1(y,x,z,symeq(x,y,t),k)):lessf(x,z)
+z@[l:lessf(x,y)][k:lesseq(y,z)]
+satz51b:=orapp(lessf(y,z),eq(y,z),lessf(x,z),k,[t:lessf(y,z)]satz50(l,t),[t:eq(y,z)]eqlessf2(y,z,x,t,l)):lessf(x,z)
+z@[m:moreq(x,y)][n:moref(y,z)]
+satz51c:=satz43(z,x,satz51b(z,y,x,satz42(y,z,n),satz48(x,y,m))):moref(x,z)
+z@[m:moref(x,y)][n:moreq(y,z)]
+satz51d:=satz43(z,x,satz51a(z,y,x,satz48(y,z,n),satz42(x,y,m))):moref(x,z)
+z@[l:lesseq(x,y)][k:lesseq(y,z)]
++252
+[e:eq(x,y)][f:eq(y,z)]
+t1:=ori2(lessf(x,z),eq(x,z),treq(x,y,z,e,f)):lesseq(x,z)
+e@[j:lessf(y,z)]
+t2:=ori1(lessf(x,z),eq(x,z),satz51a(l,j)):lesseq(x,z)
+e@t3:=orapp(lessf(y,z),eq(y,z),lesseq(x,z),k,[t:lessf(y,z)]t2(t),[t:eq(y,z)]t1(t)):lesseq(x,z)
+k@[j:lessf(x,y)]
+t4:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
+-252
+satz52:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t4".252"(t),[t:eq(x,y)]t3".252"(t)):lesseq(x,z)
+trlesseq:=satz52:lesseq(x,z)
++*252
+k@[j:lessf(x,y)]
+t5:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
+k@[e:eq(x,y)]
+t6:=eqlesseq1(y,x,z,symeq(x,y,e),k):lesseq(x,z)
+k@anders:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t5(t),[t:eq(x,y)]t6(t)):lesseq(x,z)
+-252
+z@[m:moreq(x,y)][n:moreq(y,z)]
+trmoreq:=satz49(z,x,satz52(z,y,x,satz48(y,z,n),satz48(x,y,m))):moreq(x,z)
++253
+x@t1:=ismore1(pl(ts(1x,2x),ts(1x,2x)),ts(pl(1x,1x),2x),ts(1x,2x),distpt1(1x,1x,2x),satz18(ts(1x,2x),ts(1x,2x))):more(ts(pl(1x,1x),2x),ts(1x,2x))
+t2:=morefi2(pl(1x,1x),2x,t1):moref(fr(pl(1x,1x),2x),x)
+-253
+x@satz53:=somei(frac,[t:frac]moref(t,x),fr(pl(1x,1x),2x),t2".253"):some"l"(frac,[t:frac]moref(t,x))
++254
+t1:=isless2(pl(ts(1x,2x),ts(1x,2x)),ts(1x,pl(2x,2x)),ts(1x,2x),distpt2(1x,2x,2x),satz18a(ts(1x,2x),ts(1x,2x))):less(ts(1x,2x),ts(1x,pl(2x,2x)))
+t2:=lessfi2(1x,pl(2x,2x),t1):lessf(fr(1x,pl(2x,2x)),x)
+-254
+satz54:=somei(frac,[t:frac]lessf(t,x),fr(1x,pl(2x,2x)),t2".254"):some"l"(frac,[t:frac]lessf(t,x))
+y@[l:lessf(x,y)]
++255
+t1:=satz19f(ts(1x,2y),ts(1y,2x),ts(1x,2x),l):less(pl(ts(1x,2x),ts(1x,2y)),pl(ts(1x,2x),ts(1y,2x)))
+t2:=satz19c(ts(1x,2y),ts(1y,2x),ts(1y,2y),l):less(pl(ts(1x,2y),ts(1y,2y)),pl(ts(1y,2x),ts(1y,2y)))
+t3:=isless12(pl(ts(1x,2x),ts(1x,2y)),ts(1x,pl(2x,2y)),pl(ts(1x,2x),ts(1y,2x)),ts(pl(1x,1y),2x),distpt2(1x,2x,2y),distpt1(1x,1y,2x),t1):less(ts(1x,pl(2x,2y)),ts(pl(1x,1y),2x))
+t4:=lessfi1(pl(1x,1y),pl(2x,2y),t3):lessf(x,fr(pl(1x,1y),pl(2x,2y)))
+t5:=isless12(pl(ts(1x,2y),ts(1y,2y)),ts(pl(1x,1y),2y),pl(ts(1y,2x),ts(1y,2y)),ts(1y,pl(2x,2y)),distpt1(1x,1y,2y),distpt2(1y,2x,2y),t2):less(ts(pl(1x,1y),2y),ts(1y,pl(2x,2y)))
+t6:=lessfi2(y,pl(1x,1y),pl(2x,2y),t5):lessf(fr(pl(1x,1y),pl(2x,2y)),y)
+t7:=andi(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y),t4,t6):and(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y))
+-255
+satz55:=somei(frac,[t:frac]and(lessf(x,t),lessf(t,y)),fr(pl(1x,1y),pl(2x,2y)),t7".255"):some"l"(frac,[t:frac]and(lessf(x,t),lessf(t,y)))
+y@pf:=fr(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)):frac
++ii3
+y2@t1:=ispl12(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ts(y1,x2),ndis12(x1,x2,y1,y2),ndis12(y1,y2,x1,x2)):is(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),pl(ts(x1,y2),ts(y1,x2)))
+t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
+-ii3
+y2@pf12:=isnd(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),ts(den(fr(x1,x2)),den(fr(y1,y2))),pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2),t1".ii3",t2".ii3"):is"e"(frac,pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
++*ii3
+n2@t3:=ispl12(ts(1x,den(fr(n1,n2))),ts(1x,n2),ts(num(fr(n1,n2)),2x),ts(n1,2x),ndisn2(x,n1,n2),ndis1d(x,n1,n2)):is(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),pl(ts(1x,n2),ts(n1,2x)))
+t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
+-ii3
+n2@pf1:=isnd(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),ts(2x,den(fr(n1,n2))),pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2),t3".ii3",t4".ii3"):is"e"(frac,pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
++*ii3
+n2@t5:=ispl12(ts(num(fr(n1,n2)),2x),ts(n1,2x),ts(1x,den(fr(n1,n2))),ts(1x,n2),ndis1d(x,n1,n2),ndisn2(x,n1,n2)):is(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),pl(ts(n1,2x),ts(1x,n2)))
+t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
+-ii3
+n2@pf2:=isnd(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),ts(den(fr(n1,n2)),2x),pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x),t5".ii3",t6".ii3"):is"e"(frac,pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
+y2@pfeq12a:=refeq1(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
+pfeq12b:=refeq2(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf(fr(x1,x2),fr(y1,y2)))
+n2@pfeq1a:=refeq1(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
+pfeq1b:=refeq2(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf(x,fr(n1,n2)))
+pfeq2a:=refeq1(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
+pfeq2b:=refeq2(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf(fr(n1,n2),x))
+u@[e:eq(x,y)][f:eq(z,u)]
++356
+t1:=ists1(ts(1x,2y),ts(1y,2x),ts(2z,2u),e):is(ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)))
+t2:=t1(z,u,x,y,f,e):is(ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)))
+t3:=tr3is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2z),ts(2u,2y)),ts(ts(1x,2y),ts(2u,2z)),ts(ts(1x,2y),ts(2z,2u)),ists2(ts(2y,2u),ts(2u,2y),ts(1x,2z),comts(2y,2u)),stets(1x,2z,2u,2y),ists2(ts(2u,2z),ts(2z,2u),ts(1x,2y),comts(2u,2z))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)))
+t4:=tr4is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)),ts(ts(1y,2u),ts(2z,2x)),ts(ts(1y,2u),ts(2x,2z)),t3,t1,stets(1y,2x,2z,2u),ists2(ts(2z,2x),ts(2x,2z),ts(1y,2u),comts(2z,2x))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)))
+t5:=tr4is(nat,ts(ts(1z,2x),ts(2y,2u)),ts(ts(1z,2u),ts(2y,2x)),ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)),ts(ts(1u,2y),ts(2x,2z)),stets(1z,2x,2y,2u),ists2(ts(2y,2x),ts(2x,2y),ts(1z,2u),comts(2y,2x)),t2,stets(1u,2z,2x,2y)):is(ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)))
+t6:=ispl12(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)),ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)),t4,t5):is(pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))))
+t7:=tr3is(nat,ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)),disttp1(ts(1x,2z),ts(1z,2x),ts(2y,2u)),t6,distpt1(ts(1y,2u),ts(1u,2y),ts(2x,2z))):is(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)))
+-356
+satz56:=eqi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2u),ts(1u,2y)),ts(2y,2u),t7".356"):eq(pf(x,z),pf(y,u))
+eqpf12:=satz56:eq(pf(x,z),pf(y,u))
+z@[e:eq(x,y)]
+eqpf1:=eqpf12(x,y,z,z,e,refeq(z)):eq(pf(x,z),pf(y,z))
+eqpf2:=eqpf12(z,z,x,y,refeq(z),e):eq(pf(z,x),pf(z,y))
+x2@[n:nat]
+satz57:=tr3eq(pf(fr(x1,n),fr(x2,n)),fr(pl(ts(x1,n),ts(x2,n)),ts(n,n)),fr(ts(pl(x1,x2),n),ts(n,n)),fr(pl(x1,x2),n),pfeq12a(x1,n,x2,n),eqn(pl(ts(x1,n),ts(x2,n)),ts(n,n),ts(pl(x1,x2),n),distpt1(x1,x2,n)),satz40c(pl(x1,x2),n,n)):eq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n))
+satz57a:=symeq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n),satz57):eq(fr(pl(x1,x2),n),pf(fr(x1,n),fr(x2,n)))
+y@satz58:=eqnd(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),pl(ts(1y,2x),ts(1x,2y)),ts(2y,2x),compl(ts(1x,2y),ts(1y,2x)),comts(2x,2y)):eq(pf(x,y),pf(y,x))
+compf:=satz58:eq(pf(x,y),pf(y,x))
++359
+z@t1:=tr3is(nat,ts(ts(1y,2x),2z),ts(ts(2x,1y),2z),ts(2x,ts(1y,2z)),ts(ts(1y,2z),2x),ists1(ts(1y,2x),ts(2x,1y),2z,comts(1y,2x)),assts1(2x,1y,2z),comts(2x,ts(1y,2z))):is(ts(ts(1y,2x),2z),ts(ts(1y,2z),2x))
+t2:=ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),t1):is(pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
+t3:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),t2):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
+t4:=tris(nat,ts(1z,ts(2x,2y)),ts(1z,ts(2y,2x)),ts(ts(1z,2y),2x),ists2(ts(2x,2y),ts(2y,2x),1z,comts(2x,2y)),assts2(1z,2y,2x)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
+t5:=ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t3,t4):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)))
+t6:=ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x)):is(pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
+t7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),t5,asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),t6):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
+-359
+z@satz59:=tr3eq(pf(pf(x,y),z),fr(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z)),fr(pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z))),pf(x,pf(y,z)),pfeq2a(z,pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)),eqnd(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z)),t7".359",assts1(2x,2y,2z)),pfeq1b(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z))):eq(pf(pf(x,y),z),pf(x,pf(y,z)))
+asspf1:=satz59:eq(pf(pf(x,y),z),pf(x,pf(y,z)))
+asspf2:=symeq(pf(pf(x,y),z),pf(x,pf(y,z)),asspf1):eq(pf(x,pf(y,z)),pf(pf(x,y),z))
+c@stets1:=tr3is(nat,ts(ts(a,b),c),ts(a,ts(b,c)),ts(a,ts(c,b)),ts(ts(a,c),b),assts1(a,b,c),ists2(ts(b,c),ts(c,b),a,comts(b,c)),assts2(a,c,b)):is(ts(ts(a,b),c),ts(ts(a,c),b))
++*359
+z@t8:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),stets1(1y,2x,2z))):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
+t9:=tris(nat,ts(1z,ts(2x,2y)),ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),assts2(1z,2x,2y),stets1(1z,2x,2y)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
+anderst7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t8,t9),asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x))):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
+-359
++360
+y@t1:=satz18(ts(1x,2y),ts(1y,2x)):more(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y))
+t2:=satz32a(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y),2x,t1):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(ts(1x,2y),2x))
+t3:=tris(nat,ts(ts(1x,2y),2x),ts(1x,ts(2y,2x)),ts(1x,ts(2x,2y)),assts1(1x,2y,2x),ists2(ts(2y,2x),ts(2x,2y),1x,comts(2y,2x))):is(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)))
+t4:=ismore2(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)),ts(pl(ts(1x,2y),ts(1y,2x)),2x),t3,t2):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(1x,ts(2x,2y)))
+-360
+y@satz60:=morefi2(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),t4".360"):moref(pf(x,y),x)
+satz60a:=satz42(pf(x,y),x,satz60):lessf(x,pf(x,y))
+z@[m:moref(x,y)]
++361
+t1:=satz32a(ts(1x,2y),ts(1y,2x),2z,m):more(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z))
+t2:=ismore12(ts(ts(1x,2y),2z),ts(ts(1x,2z),2y),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),stets1(1x,2y,2z),stets1(1y,2x,2z),t1):more(ts(ts(1x,2z),2y),ts(ts(1y,2z),2x))
+t3:=stets1(1z,2x,2y):is(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x))
+t4:=satz19h(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),ts(ts(1x,2z),2y),ts(ts(1y,2z),2x),t3,t2):more(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)))
+t5:=ismore12(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),ts(pl(ts(1x,2z),ts(1z,2x)),2y),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),distpt1(ts(1x,2z),ts(1z,2x),2y),distpt1(ts(1y,2z),ts(1z,2y),2x),t4):more(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x))
+t6:=satz32a(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z,t5):more(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z))
+t7:=ismore12(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)),assts1(pl(ts(1x,2z),ts(1z,2x)),2y,2z),assts1(pl(ts(1y,2z),ts(1z,2y)),2x,2z),t6):more(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)))
+-361
+satz61:=morefi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z),t7".361"):moref(pf(x,z),pf(y,z))
+z@[m:moref(x,y)]
+satz62a:=satz61(m):moref(pf(x,z),pf(y,z))
+z@[e:eq(x,y)]
+satz62b:=eqpf1(x,y,z,e):eq(pf(x,z),pf(y,z))
+z@[l:lessf(x,y)]
+satz62c:=satz42(pf(y,z),pf(x,z),satz61(y,x,z,satz43(l))):lessf(pf(x,z),pf(y,z))
+m@satz62d:=eqmoref12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62a):moref(pf(z,x),pf(z,y))
+e@satz62e:=eqpf2(x,y,z,e):eq(pf(z,x),pf(z,y))
+l@satz62f:=eqlessf12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62c):lessf(pf(z,x),pf(z,y))
+u@[e:eq(x,y)][m:moref(z,u)]
+satz62g:=eqmoref2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62d(z,u,x,m)):moref(pf(x,z),pf(y,u))
+satz62h:=eqmoref12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62g):moref(pf(z,x),pf(u,y))
+e@[l:lessf(z,u)]
+satz62j:=eqlessf2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62f(z,u,x,l)):lessf(pf(x,z),pf(y,u))
+satz62k:=eqlessf12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62j):lessf(pf(z,x),pf(u,y))
++363
+z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
+t2:=satz41b(pf(x,z),pf(y,z)):ec3(eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)))
+-363
+z@[m:moref(pf(x,z),pf(y,z))]
+satz63a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),m):moref(x,y)
+z@[e:eq(pf(x,z),pf(y,z))]
+satz63b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),e):eq(x,y)
+z@[l:lessf(pf(x,z),pf(y,z))]
+satz63c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),l):lessf(x,y)
+z@[m:moref(pf(z,x),pf(z,y))]
+satz63d:=satz63a(eqmoref12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),m)):moref(x,y)
+z@[e:eq(pf(z,x),pf(z,y))]
+satz63e:=satz63b(tr3eq(pf(x,z),pf(z,x),pf(z,y),pf(y,z),compf(x,z),e,compf(z,y))):eq(x,y)
+z@[f:lessf(pf(z,x),pf(z,y))]
+satz63f:=satz63c(eqlessf12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),f)):lessf(x,y)
+u@[m:moref(x,y)][n:moref(z,u)]
++364
+t1:=satz61(x,y,z,m):moref(pf(x,z),pf(y,z))
+t2:=eqmoref12(pf(z,y),pf(y,z),pf(u,y),pf(y,u),compf(z,y),compf(u,y),satz61(z,u,y,n)):moref(pf(y,z),pf(y,u))
+-364
+satz64:=trmoref(pf(x,z),pf(y,z),pf(y,u),t1".364",t2".364"):moref(pf(x,z),pf(y,u))
+u@[l:lessf(x,y)][k:lessf(z,u)]
+satz64a:=satz42(pf(y,u),pf(x,z),satz64(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
+u@[m:moreq(x,y)][n:moref(z,u)]
+satz65a:=orapp(moref(x,y),eq(x,y),moref(pf(x,z),pf(y,u)),m,[v:moref(x,y)]satz64(v,n),[v:eq(x,y)]satz62g(v,n)):moref(pf(x,z),pf(y,u))
+u@[m:moref(x,y)][n:moreq(z,u)]
+satz65b:=orapp(moref(z,u),eq(z,u),moref(pf(x,z),pf(y,u)),n,[v:moref(z,u)]satz64(m,v),[v:eq(z,u)]eqmoref2(pf(y,z),pf(y,u),pf(x,z),eqpf2(z,u,y,v),satz61(x,y,z,m))):moref(pf(x,z),pf(y,u))
+u@[l:lesseq(x,y)][k:lessf(z,u)]
+satz65c:=satz42(pf(y,u),pf(x,z),satz65a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
+u@[l:lessf(x,y)][k:lesseq(z,u)]
+satz65d:=satz42(pf(y,u),pf(x,z),satz65b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(pf(x,z),pf(y,u))
+u@[m:moreq(x,y)][n:moreq(z,u)]
++366
+[e:eq(x,y)][f:eq(z,u)]
+t1:=moreqi2(pf(x,z),pf(y,u),satz56(e,f)):moreq(pf(x,z),pf(y,u))
+e@[o:moref(z,u)]
+t2:=moreqi1(pf(x,z),pf(y,u),satz65a(m,o)):moreq(pf(x,z),pf(y,u))
+e@t3:=orapp(moref(z,u),eq(z,u),moreq(pf(x,z),pf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(pf(x,z),pf(y,u))
+n@[o:moref(x,y)]
+t4:=moreqi1(pf(x,z),pf(y,u),satz65b(o,n)):moreq(pf(x,z),pf(y,u))
+-366
+satz66:=orapp(moref(x,y),eq(x,y),moreq(pf(x,z),pf(y,u)),m,[v:moref(x,y)]t4".366"(v),[v:eq(x,y)]t3".366"(v)):moreq(pf(x,z),pf(y,u))
+u@[l:lesseq(x,y)][k:lesseq(z,u)]
+satz66a:=satz48(pf(y,u),pf(x,z),satz66(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(pf(x,z),pf(y,u))
+y@[l:lesseq(x,y)]
++367
+[v:frac][e:eq(pf(y,v),x)]
+t1:=eqmoref1(pf(y,v),x,y,e,satz60(y,v)):moref(x,y)
+v@t2:=th3"l.imp"(eq(pf(y,v),x),moref(x,y),satz41d(x,y,l),[t:eq(pf(y,v),x)]t1(t)):not(eq(pf(y,v),x))
+-367
+vorbemerkung67:=th5"l.some"(frac,[v:frac]eq(pf(y,v),x),[v:frac]t2".367"(v)):not(some"l"(frac,[t:frac]eq(pf(y,t),x)))
+y@[v:frac][w:frac][e:eq(pf(y,v),x)][f:eq(pf(y,w),x)]
+satz67b:=satz63e(v,w,y,treq2(pf(y,v),pf(y,w),x,e,f)):eq(v,w)
+y@[m:moref(x,y)]
++*367
+m@t3:=onei(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),satz8b(ts(1x,2y),ts(1y,2x)),m):one([t:nat]diffprop(ts(1x,2y),ts(1y,2x),t))
+vo:=ind(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):nat
+t4:=oneax(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):is(ts(1x,2y),pl(ts(1y,2x),vo))
+w:=fr(vo,ts(2x,2y)):frac
+t5:=treq(y,fr(ts(1y,2x),ts(2y,2x)),fr(ts(1y,2x),ts(2x,2y)),satz40(y,2x),eqd(ts(1y,2x),ts(2y,2x),ts(2x,2y),comts(2y,2x))):eq(y,fr(ts(1y,2x),ts(2x,2y)))
+t6:=tr4eq(pf(y,w),pf(fr(ts(1y,2x),ts(2x,2y)),fr(vo,ts(2x,2y))),fr(pl(ts(1y,2x),vo),ts(2x,2y)),fr(ts(1x,2y),ts(2x,2y)),x,eqpf1(y,fr(ts(1y,2x),ts(2x,2y)),w,t5),satz57(ts(1y,2x),vo,ts(2x,2y)),eqn(pl(ts(1y,2x),vo),ts(2x,2y),ts(1x,2y),symis(nat,ts(1x,2y),pl(ts(1y,2x),vo),t4)),satz40a(x,2y)):eq(pf(y,w),x)
+-367
+m@satz67a:=somei(frac,[t:frac]eq(pf(y,t),x),w".367",t6".367"):some"l"(frac,[t:frac]eq(pf(y,t),x))
+mf:=w".367":frac
+satz67c:=t6".367":eq(pf(y,mf(x,y,m)),x)
+satz67d:=symeq(pf(y,mf(x,y,m)),x,satz67c):eq(x,pf(y,mf(x,y,m)))
+y@[v:frac][m:moref(x,y)][e:eq(pf(y,v),x)]
+satz67e:=satz67b(v,mf(x,y,m),e,satz67c(m)):eq(v,mf(x,y,m))
+y@tf:=fr(ts(1x,1y),ts(2x,2y)):frac
++ii4
+y2@t1:=ists12(num(fr(x1,x2)),x1,num(fr(y1,y2)),y1,numis(x1,x2),numis(y1,y2)):is(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(x1,y1))
+t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
+-ii4
+y2@tf12:=isnd(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y1),ts(x2,y2),t1".ii4",t2".ii4"):is"e"(frac,tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
++*ii4
+n2@t3:=ists2(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(1x,num(fr(n1,n2))),ts(1x,n1))
+t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
+-ii4
+n2@tf1:=isnd(ts(1x,num(fr(n1,n2))),ts(2x,den(fr(n1,n2))),ts(1x,n1),ts(2x,n2),t3".ii4",t4".ii4"):is"e"(frac,tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
++*ii4
+n2@t5:=ists1(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(num(fr(n1,n2)),1x),ts(n1,1x))
+t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
+-ii4
+n2@tf2:=isnd(ts(num(fr(n1,n2)),1x),ts(den(fr(n1,n2)),2x),ts(n1,1x),ts(n2,2x),t5".ii4",t6".ii4"):is"e"(frac,tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
+y2@tfeq12a:=refeq1(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
+tfeq12b:=refeq2(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(fr(ts(x1,y1),ts(x2,y2)),tf(fr(x1,x2),fr(y1,y2)))
+n2@tfeq1a:=refeq1(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
+tfeq1b:=refeq2(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(fr(ts(1x,n1),ts(2x,n2)),tf(x,fr(n1,n2)))
+tfeq2a:=refeq1(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
+tfeq2b:=refeq2(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(fr(ts(n1,1x),ts(n2,2x)),tf(fr(n1,n2),x))
+u@[e:eq(x,y)][f:eq(z,u)]
++468
+t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1z,2u),ts(1u,2z),e,f):is(ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)))
+-468
+d@stets2:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(ts(a,b),ts(d,c)),ts(ts(a,c),ts(d,b)),ts(ts(a,c),ts(b,d)),ists2(ts(c,d),ts(d,c),ts(a,b),comts(c,d)),stets(a,b,d,c),ists2(ts(d,b),ts(b,d),ts(a,c),comts(d,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,c),ts(b,d)))
++*468
+f@t2:=tr3is(nat,ts(ts(1x,1z),ts(2y,2u)),ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)),ts(ts(1y,1u),ts(2x,2z)),stets2(1x,1z,2y,2u),t1,stets2(1y,2x,1u,2z)):is(ts(ts(1x,1z),ts(2y,2u)),ts(ts(1y,1u),ts(2x,2z)))
+-468
+f@satz68:=eqi12(ts(1x,1z),ts(2x,2z),ts(1y,1u),ts(2y,2u),t2".468"):eq(tf(x,z),tf(y,u))
+eqtf12:=satz68:eq(tf(x,z),tf(y,u))
+z@[e:eq(x,y)]
+eqtf1:=eqtf12(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
+eqtf2:=eqtf12(z,z,x,y,refeq(z),e):eq(tf(z,x),tf(z,y))
+y@satz69:=eqnd(ts(1x,1y),ts(2x,2y),ts(1y,1x),ts(2y,2x),comts(1x,1y),comts(2x,2y)):eq(tf(x,y),tf(y,x))
+comtf:=satz69:eq(tf(x,y),tf(y,x))
+z@satz70:=tr3eq(tf(tf(x,y),z),fr(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z)),fr(ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z))),tf(x,tf(y,z)),tfeq2a(z,ts(1x,1y),ts(2x,2y)),eqnd(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z),ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z)),assts1(1x,1y,1z),assts1(2x,2y,2z)),tfeq1b(x,ts(1y,1z),ts(2y,2z))):eq(tf(tf(x,y),z),tf(x,tf(y,z)))
+asstf1:=satz70:eq(tf(tf(x,y),z),tf(x,tf(y,z)))
+asstf2:=symeq(tf(tf(x,y),z),tf(x,tf(y,z)),asstf1):eq(tf(x,tf(y,z)),tf(tf(x,y),z))
++471
+t1:=tr3eq(tf(x,pf(y,z)),fr(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z))),fr(pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),ts(2x,ts(2y,2z))),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),tfeq1a(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z)),eqn(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z)),pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),disttp2(1x,ts(1y,2z),ts(1z,2y))),satz57a(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))):eq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))))
+t2:=treq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(ts(1x,1y),2z),ts(ts(2x,2y),2z)),tf(x,y),eqnd(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z)),ts(ts(1x,1y),2z),ts(ts(2x,2y),2z),assts2(1x,1y,2z),assts2(2x,2y,2z)),satz40c(ts(1x,1y),ts(2x,2y),2z)):eq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y))
+t3:=treq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2z,2y))),tf(x,z),eqd(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)),ts(2x,ts(2z,2y)),ists2(ts(2y,2z),ts(2z,2y),2x,comts(2y,2z))),t2(x,z,y)):eq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z))
+-471
+satz71:=treq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),pf(tf(x,y),tf(x,z)),t1".471",eqpf12(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z),t2".471",t3".471")):eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
+disttpf1:=tr3eq(tf(pf(x,y),z),tf(z,pf(x,y)),pf(tf(z,x),tf(z,y)),pf(tf(x,z),tf(y,z)),comtf(pf(x,y),z),satz71(z,x,y),eqpf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y))):eq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)))
+disttpf2:=satz71:eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
+distptf1:=symeq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)),disttpf1):eq(pf(tf(x,z),tf(y,z)),tf(pf(x,y),z))
+distptf2:=symeq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),disttpf2):eq(pf(tf(x,y),tf(x,z)),tf(x,pf(y,z)))
+[m:moref(x,y)]
++472
+t1:=satz32a(ts(1x,2y),ts(1y,2x),ts(1z,2z),m):more(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1y,2x),ts(1z,2z)))
+t2:=ismore12(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,2x),ts(1z,2z)),ts(ts(1y,1z),ts(2x,2z)),stets2(1x,2y,1z,2z),stets2(1y,2x,1z,2z),t1):more(ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,1z),ts(2x,2z)))
+-472
+satz72a:=morefi12(ts(1x,1z),ts(2x,2z),ts(1y,1z),ts(2y,2z),t2".472"):moref(tf(x,z),tf(y,z))
+z@[e:eq(x,y)]
+satz72b:=satz68(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
+z@[l:lessf(x,y)]
+satz72c:=satz42(tf(y,z),tf(x,z),satz72a(y,x,z,satz43(x,y,l))):lessf(tf(x,z),tf(y,z))
+m@satz72d:=eqmoref12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72a):moref(tf(z,x),tf(z,y))
+e@satz72e:=eqtf2(x,y,z,e):eq(tf(z,x),tf(z,y))
+l@satz72f:=eqlessf12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72c):lessf(tf(z,x),tf(z,y))
+u@[e:eq(x,y)][m:moref(z,u)]
+satz72g:=eqmoref2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72d(z,u,x,m)):moref(tf(x,z),tf(y,u))
+satz72h:=eqmoref12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72g):moref(tf(z,x),tf(u,y))
+e@[l:lessf(z,u)]
+satz72j:=eqlessf2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72f(z,u,x,l)):lessf(tf(x,z),tf(y,u))
+satz72k:=eqlessf12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72j):lessf(tf(z,x),tf(u,y))
++473
+z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
+t2:=satz41b(tf(x,z),tf(y,z)):ec3(eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)))
+-473
+z@[m:moref(tf(x,z),tf(y,z))]
+satz73a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),m):moref(x,y)
+z@[e:eq(tf(x,z),tf(y,z))]
+satz73b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),e):eq(x,y)
+z@[l:lessf(tf(x,z),tf(y,z))]
+satz73c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),l):lessf(x,y)
+z@[m:moref(tf(z,x),tf(z,y))]
+satz73d:=satz73a(eqmoref12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),m)):moref(x,y)
+z@[e:eq(tf(z,x),tf(z,y))]
+satz73e:=satz73b(tr3eq(tf(x,z),tf(z,x),tf(z,y),tf(y,z),comtf(x,z),e,comtf(z,y))):eq(x,y)
+z@[l:lessf(tf(z,x),tf(z,y))]
+satz73f:=satz73c(eqlessf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),l)):lessf(x,y)
+u@[m:moref(x,y)][n:moref(z,u)]
++474
+t1:=satz72a(x,y,z,m):moref(tf(x,z),tf(y,z))
+t2:=eqmoref12(tf(z,y),tf(y,z),tf(u,y),tf(y,u),comtf(z,y),comtf(u,y),satz72a(z,u,y,n)):moref(tf(y,z),tf(y,u))
+-474
+satz74:=trmoref(tf(x,z),tf(y,z),tf(y,u),t1".474",t2".474"):moref(tf(x,z),tf(y,u))
+u@[l:lessf(x,y)][k:lessf(z,u)]
+satz74a:=satz42(tf(y,u),tf(x,z),satz74(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
+u@[m:moreq(x,y)][n:moref(z,u)]
+satz75a:=orapp(moref(x,y),eq(x,y),moref(tf(x,z),tf(y,u)),m,[v:moref(x,y)]satz74(v,n),[v:eq(x,y)]satz72g(v,n)):moref(tf(x,z),tf(y,u))
+u@[m:moref(x,y)][n:moreq(z,u)]
+satz75b:=orapp(moref(z,u),eq(z,u),moref(tf(x,z),tf(y,u)),n,[v:moref(z,u)]satz74(m,v),[v:eq(z,u)]eqmoref2(tf(y,z),tf(y,u),tf(x,z),eqtf2(z,u,y,v),satz72a(m))):moref(tf(x,z),tf(y,u))
+u@[l:lesseq(x,y)][k:lessf(z,u)]
+satz75c:=satz42(tf(y,u),tf(x,z),satz75a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
+u@[l:lessf(x,y)][k:lesseq(z,u)]
+satz75d:=satz42(tf(y,u),tf(x,z),satz75b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(tf(x,z),tf(y,u))
+u@[m:moreq(x,y)][n:moreq(z,u)]
++476
+[e:eq(x,y)][f:eq(z,u)]
+t1:=moreqi2(tf(x,z),tf(y,u),satz68(e,f)):moreq(tf(x,z),tf(y,u))
+e@[o:moref(z,u)]
+t2:=moreqi1(tf(x,z),tf(y,u),satz75a(m,o)):moreq(tf(x,z),tf(y,u))
+e@t3:=orapp(moref(z,u),eq(z,u),moreq(tf(x,z),tf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(tf(x,z),tf(y,u))
+n@[o:moref(x,y)]
+t4:=moreqi1(tf(x,z),tf(y,u),satz75b(o,n)):moreq(tf(x,z),tf(y,u))
+-476
+satz76:=orapp(moref(x,y),eq(x,y),moreq(tf(x,z),tf(y,u)),m,[v:moref(x,y)]t4".476"(v),[v:eq(x,y)]t3".476"(v)):moreq(tf(x,z),tf(y,u))
+u@[l:lesseq(x,y)][k:lesseq(z,u)]
+satz76a:=satz48(tf(y,u),tf(x,z),satz76(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(tf(x,z),tf(y,u))
+y@[v:frac][w:frac][e:eq(tf(y,v),x)][f:eq(tf(y,w),x)]
+satz77b:=satz73e(v,w,y,treq2(tf(y,v),tf(y,w),x,e,f)):eq(v,w)
++477
+y@v:=fr(ts(1x,2y),ts(2x,1y)):frac
+t1:=tr4eq(tf(y,v),tf(v,y),fr(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y)),fr(ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y))),x,comtf(y,v),tfeq2a(y,ts(1x,2y),ts(2x,1y)),eqnd(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y),ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y)),tris(nat,ts(ts(1x,2y),1y),ts(1x,ts(2y,1y)),ts(1x,ts(1y,2y)),assts1(1x,2y,1y),ists2(ts(2y,1y),ts(1y,2y),1x,comts(2y,1y))),assts1(2x,1y,2y)),satz40a(x,ts(1y,2y))):eq(tf(y,v),x)
+-477
+y@satz77a:=somei(frac,[t:frac]eq(tf(y,t),x),v".477",t1".477"):some"l"(frac,[t:frac]eq(tf(y,t),x))
++rt
+@eq:=[x:frac][y:frac]eq"n"(x,y):[x:frac][y:frac]'prop'
+refeq:=[x:frac]refeq"n"(x):[x:frac]<x><x>eq
+symeq:=[x:frac][y:frac][t:<y><x>eq]symeq"n"(x,y,t):[x:frac][y:frac][t:<y><x>eq]<x><y>eq
+treq:=[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]treq"n"(x,y,z,t,u):[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]<z><x>eq
+[x:frac][s:set(frac)]
+inf:=esti(frac,x,s):'prop'
+@rat:=ect"eq"(frac,eq,refeq,symeq,treq):'type'
+[x0:rat][y0:rat]
+is:=is"e"(rat,x0,y0):'prop'
+nis:=not(is(x0,y0)):'prop'
+@[p:[x:rat]'prop']
+some:=some"l"(rat,p):'prop'
+all:=all"l"(rat,p):'prop'
+one:=one"e"(rat,p):'prop'
+x0@[s:set(rat)]
+in:=esti(rat,x0,s):'prop'
+x@ratof:=ectelt"eq"(frac,eq,refeq,symeq,treq,x):rat
+x0@class:=ecect"eq"(frac,eq,refeq,symeq,treq,x0):set(frac)
+x@inclass:=th5"eq.4"(frac,eq,refeq,symeq,treq,x):inf(x,class(ratof(x)))
+x0@[x:frac][y:frac][xix0:inf(x,class(x0))][e:eq"n"(x,y)]
+lemmaeq1:=th8"eq.4"(frac,eq,refeq,symeq,treq,x0,x,xix0,y,e):inf(y,class(x0))
+x0@[a:'prop'][a1:[x:frac][xi:inf(x,class(x0))]a]
+ratapp1:=th3"eq.4"(frac,eq,refeq,symeq,treq,x0,a,a1):a
+y0@[a:'prop'][a1:[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]a][x:frac][xix0:inf(x,class(x0))]
++ii5
+t1:=ratapp1(y0,a,[y:frac][yi:inf(y,class(y0))]<yi><xix0><y><x>a1):a
+-ii5
+a1@ratapp2:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t1".ii5"(x,xi)):a
+y0@[z0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]a][x:frac][xix0:inf(x,class(x0))]
++*ii5
+xix0@t2:=ratapp2(y0,z0,a,[y:frac][z:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))]<zi><yi><xix0><z><y><x>a1):a
+-ii5
+a1@ratapp3:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t2".ii5"(x,xi)):a
+z0@[u0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]a][x:frac][xix0:inf(x,class(x0))]
++*ii5
+xix0@t3:=ratapp3(y0,z0,u0,a,[y:frac][z:frac][u:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]<ui><zi><yi><xix0><u><z><y><x>a1):a
+-ii5
+a1@ratapp4:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t3".ii5"(x,xi)):a
+y0@[x1:frac][y1:frac][x1ix0:inf(x1,class(x0))][y1iy0:inf(y1,class(y0))][e:eq"n"(x1,y1)]
+isi:=th3"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,e):is(x0,y0)
+y1iy0@[i:is(x0,y0)]
+ise:=th5"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,i):eq"n"(x1,y1)
+y1iy0@[n:not(eq"n"(x1,y1))]
+nisi:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),n,[t:is(x0,y0)]ise(t)):nis(x0,y0)
+y1iy0@[n:nis(x0,y0)]
+nise:=th3"l.imp"(eq"n"(x1,y1),is(x0,y0),n,[t:eq"n"(x1,y1)]isi(t)):not(eq"n"(x1,y1))
+@[alpha:'type'][f:[x:frac][y:frac]alpha]
+fixf:=fixfu2"eq"(frac,eq,refeq,symeq,treq,alpha,f):'prop'
+y0@[alpha:'type'][f:[x:frac][y:frac]alpha][ff:fixf(alpha,f)]
+indrat:=indeq2"eq"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0):alpha
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+isindrat:=th1"eq.11"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0,x,xix0,y,yiy0):is"e"(alpha,<y><x>f,indrat)
+x0@satz78:=refis(rat,x0):is(x0,x0)
+y0@[i:is(x0,y0)]
+satz79:=symis(rat,x0,y0,i):is(y0,x0)
+z0@[i:is(x0,y0)][j:is(y0,z0)]
+satz80:=tris(rat,x0,y0,z0,i,j):is(x0,z0)
+y0@more:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),moref(x,y)))):'prop'
++*ii5
+y1@propm:=and3(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1)):'prop'
+-ii5
+y0@[m:more(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propm".ii5"(t,u))][u:frac][p:propm".ii5"(t,u)]
++*ii5
+p@t4:=and3e1(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(t,class(x0))
+t5:=and3e2(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(u,class(y0))
+t6:=and3e3(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):moref(t,u)
+t7:=satz44(t,u,x,y,t6,ise(x0,x0,t,x,t4,xix0,refis(rat,x0)),ise(y0,y0,u,y,t5,yiy0,refis(rat,y0))):moref(x,y)
+s@t8:=someapp(frac,[u:frac]propm(t,u),s,moref(x,y),[u:frac][v:propm(t,u)]t7(u,v)):moref(x,y)
+-ii5
+yiy0@also18:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propm".ii5"(t,u)),m,moref(x,y),[t:frac][v:some"l"(frac,[u:frac]propm".ii5"(t,u))]t8".ii5"(t,v)):moref(x,y)
+y1iy0@[m:moref(x1,y1)]
++*ii5
+m@t9:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1),x1ix0,y1iy0,m):propm(x1,y1)
+t10:=somei(frac,[t:frac]propm(x1,t),y1,t9):some"l"(frac,[t:frac]propm(x1,t))
+-ii5
+m@morei:=somei(frac,[u:frac]some"l"(frac,[t:frac]propm".ii5"(u,t)),x1,t10".ii5"):more(x0,y0)
+y1iy0@[m:more(x0,y0)]
+moree:=also18(m,x1,y1,x1ix0,y1iy0):moref(x1,y1)
+z0@[i:is(x0,y0)][m:more(x0,z0)]
+ismore1:=isp(rat,[t:rat]more(t,z0),x0,y0,m,i):more(y0,z0)
+i@[m:more(z0,x0)]
+ismore2:=isp(rat,[t:rat]more(z0,t),x0,y0,m,i):more(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][m:more(x0,z0)]
+ismore12:=ismore2(z0,u0,y0,j,ismore1(x0,y0,z0,i,m)):more(y0,u0)
+y0@less:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),lessf(x,y)))):'prop'
++*ii5
+y1@propl:=and3(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1)):'prop'
+-ii5
+y0@[l:less(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propl".ii5"(t,u))][u:frac][p:propl".ii5"(t,u)]
++*ii5
+p@t11:=and3e1(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(t,class(x0))
+t12:=and3e2(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(u,class(y0))
+t13:=and3e3(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):lessf(t,u)
+t14:=satz45(t,u,x,y,t13,ise(x0,x0,t,x,t11,xix0,refis(rat,x0)),ise(y0,y0,u,y,t12,yiy0,refis(rat,y0))):lessf(x,y)
+s@t15:=someapp(frac,[u:frac]propl(t,u),s,lessf(x,y),[u:frac][v:propl(t,u)]t14(u,v)):lessf(x,y)
+-ii5
+yiy0@also19:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propl".ii5"(t,u)),l,lessf(x,y),[t:frac][v:some"l"(frac,[u:frac]propl".ii5"(t,u))]t15".ii5"(t,v)):lessf(x,y)
+y1iy0@[l:lessf(x1,y1)]
++*ii5
+l@t16:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1),x1ix0,y1iy0,l):propl(x1,y1)
+t17:=somei(frac,[t:frac]propl(x1,t),y1,t16):some"l"(frac,[t:frac]propl(x1,t))
+-ii5
+l@lessi:=somei(frac,[u:frac]some"l"(frac,[t:frac]propl".ii5"(u,t)),x1,t17".ii5"):less(x0,y0)
+y1iy0@[l:less(x0,y0)]
+lesse:=also19(l,x1,y1,x1ix0,y1iy0):lessf(x1,y1)
+z0@[i:is(x0,y0)][l:less(x0,z0)]
+isless1:=isp(rat,[t:rat]less(t,z0),x0,y0,l,i):less(y0,z0)
+i@[l:less(z0,x0)]
+isless2:=isp(rat,[t:rat]less(z0,t),x0,y0,l,i):less(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][l:less(x0,z0)]
+isless12:=isless2(z0,u0,y0,j,isless1(x0,y0,z0,i,l)):less(y0,u0)
++581
+y1iy0@t1:=satz41a(x1,y1):or3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
+[e:eq"n"(x1,y1)]
+t2:=or3i1(is(x0,y0),more(x0,y0),less(x0,y0),isi(e)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+y1iy0@[m:moref(x1,y1)]
+t3:=or3i2(is(x0,y0),more(x0,y0),less(x0,y0),morei(m)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+y1iy0@[l:lessf(x1,y1)]
+t4:=or3i3(is(x0,y0),more(x0,y0),less(x0,y0),lessi(l)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+y1iy0@t5:=or3app(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),or3(is(x0,y0),more(x0,y0),less(x0,y0)),t1,[t:eq"n"(x1,y1)]t2(t),[t:moref(x1,y1)]t3(t),[t:lessf(x1,y1)]t4(t)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+t6:=satz41b(x1,y1):ec3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
+[i:is(x0,y0)]
+t7:=th3"l.imp"(more(x0,y0),moref(x1,y1),ec3e12(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,ise(i)),[t:more(x0,y0)]moree(t)):not(more(x0,y0))
+y1iy0@[m:more(x0,y0)]
+t8:=th3"l.imp"(less(x0,y0),lessf(x1,y1),ec3e23(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,moree(m)),[t:less(x0,y0)]lesse(t)):not(less(x0,y0))
+y1iy0@[l:less(x0,y0)]
+t9:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),ec3e31(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,lesse(l)),[t:is(x0,y0)]ise(t)):nis(x0,y0)
+y1iy0@t10:=th6"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),th1"l.ec"(is(x0,y0),more(x0,y0),[t:is(x0,y0)]t7(t)),th1"l.ec"(more(x0,y0),less(x0,y0),[t:more(x0,y0)]t8(t)),th1"l.ec"(less(x0,y0),is(x0,y0),[t:less(x0,y0)]t9(t))):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
+t11:=orec3i(is(x0,y0),more(x0,y0),less(x0,y0),t5,t10):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
+-581
+y0@satz81:=ratapp2(orec3(is(x0,y0),more(x0,y0),less(x0,y0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t11".581"(x,y,xi,yi)):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
+satz81a:=orec3e1(is(x0,y0),more(x0,y0),less(x0,y0),satz81):or3(is(x0,y0),more(x0,y0),less(x0,y0))
+satz81b:=orec3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
+[m:more(x0,y0)]
++582
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=lessi(y0,x0,y,x,yiy0,xix0,satz42(x,y,moree(x0,y0,x,y,xix0,yiy0,m))):less(y0,x0)
+-582
+satz82:=ratapp2(less(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".582"(x,y,xi,yi)):less(y0,x0)
+y0@[l:less(x0,y0)]
++583
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=morei(y0,x0,y,x,yiy0,xix0,satz43(x,y,lesse(x0,y0,x,y,xix0,yiy0,l))):more(y0,x0)
+-583
+satz83:=ratapp2(more(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".583"(x,y,xi,yi)):more(y0,x0)
+y0@moreis:=or(more(x0,y0),is(x0,y0)):'prop'
+[m:more(x0,y0)]
+moreisi1:=ori1(more,is,m):moreis(x0,y0)
+y0@[i:is(x0,y0)]
+moreisi2:=ori2(more,is,i):moreis(x0,y0)
+y1iy0@[m:moreq(x1,y1)]
+moreisi:=orapp(moref(x1,y1),eq"n"(x1,y1),moreis,m,[t:moref(x1,y1)]moreisi1(morei(t)),[t:eq"n"(x1,y1)]moreisi2(isi(t))):moreis(x0,y0)
+y1iy0@[m:moreis(x0,y0)]
+moreise:=orapp(more,is,moreq(x1,y1),m,[t:more]moreqi1(x1,y1,moree(t)),[t:is]moreqi2(x1,y1,ise(t))):moreq(x1,y1)
+z0@[i:is(x0,y0)][m:moreis(x0,z0)]
+ismoreis1:=isp(rat,[t:rat]moreis(t,z0),x0,y0,m,i):moreis(y0,z0)
+i@[m:moreis(z0,x0)]
+ismoreis2:=isp(rat,[t:rat]moreis(z0,t),x0,y0,m,i):moreis(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][m:moreis(x0,z0)]
+ismoreis12:=ismoreis2(z0,u0,y0,j,ismoreis1(x0,y0,z0,i,m)):moreis(y0,u0)
+y0@lessis:=or(less(x0,y0),is(x0,y0)):'prop'
+[l:less(x0,y0)]
+lessisi1:=ori1(less,is,l):lessis(x0,y0)
+y0@[i:is(x0,y0)]
+lessisi2:=ori2(less,is,i):lessis(x0,y0)
+y1iy0@[l:lesseq(x1,y1)]
+lessisi:=orapp(lessf(x1,y1),eq"n"(x1,y1),lessis,l,[t:lessf(x1,y1)]lessisi1(lessi(t)),[t:eq"n"(x1,y1)]lessisi2(isi(t))):lessis(x0,y0)
+y1iy0@[l:lessis(x0,y0)]
+lessise:=orapp(less,is,lesseq(x1,y1),l,[t:less]lesseqi1(x1,y1,lesse(t)),[t:is]lesseqi2(x1,y1,ise(t))):lesseq(x1,y1)
+z0@[i:is(x0,y0)][l:lessis(x0,z0)]
+islessis1:=isp(rat,[t:rat]lessis(t,z0),x0,y0,l,i):lessis(y0,z0)
+i@[l:lessis(z0,x0)]
+islessis2:=isp(rat,[t:rat]lessis(z0,t),x0,y0,l,i):lessis(z0,y0)
+u0@[i:is(x0,y0)][j:is(z0,u0)][l:lessis(x0,z0)]
+islessis12:=islessis2(z0,u0,y0,j,islessis1(x0,y0,z0,i,l)):lessis(y0,u0)
+y0@[m:moreis(x0,y0)]
+satz81c:=th7"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,comor(more(x0,y0),is(x0,y0),m)):not(less(x0,y0))
+y0@[l:lessis(x0,y0)]
+satz81d:=th9"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l):not(more(x0,y0))
+y0@[n:not(more(x0,y0))]
+satz81e:=th2"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n):lessis(x0,y0)
+y0@[n:not(less(x0,y0))]
+satz81f:=comor(is(x0,y0),more(x0,y0),th3"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n)):moreis(x0,y0)
+y0@[m:more(x0,y0)]
+satz81g:=th3"l.or"(less(x0,y0),is(x0,y0),ec3e23(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m),ec3e21(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m)):not(lessis(x0,y0))
+y0@[l:less(x0,y0)]
+satz81h:=th3"l.or"(more(x0,y0),is(x0,y0),ec3e32(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l),ec3e31(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l)):not(moreis(x0,y0))
+y0@[n:not(moreis(x0,y0))]
+satz81j:=or3e3(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th5"l.or"(more(x0,y0),is(x0,y0),n),th4"l.or"(more(x0,y0),is(x0,y0),n)):less(x0,y0)
+y0@[n:not(lessis(x0,y0))]
+satz81k:=or3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th4"l.or"(less(x0,y0),is(x0,y0),n),th5"l.or"(less(x0,y0),is(x0,y0),n)):more(x0,y0)
+y0@[m:moreis(x0,y0)]
++584
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=lessisi(y0,x0,y,x,yiy0,xix0,satz48(x,y,moreise(x0,y0,x,y,xix0,yiy0,m))):lessis(y0,x0)
+-584
+satz84:=ratapp2(lessis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".584"(x,y,xi,yi)):lessis(y0,x0)
+y0@[l:lessis(x0,y0)]
++585
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
+t1:=moreisi(y0,x0,y,x,yiy0,xix0,satz49(x,y,lessise(x0,y0,x,y,xix0,yiy0,l))):moreis(y0,x0)
+-585
+satz85:=ratapp2(moreis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".585"(x,y,xi,yi)):moreis(y0,x0)
+z0@[l:less(x0,y0)][k:less(y0,z0)]
++586
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=lessi(x0,z0,x,z,xix0,ziz0,satz50(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
+-586
+satz86:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".586"(x,y,z,xi,yi,zi)):less(x0,z0)
+trless:=satz86:less(x0,z0)
+z0@[m:more(x0,y0)][n:more(y0,z0)]
+trmore:=satz83(z0,x0,satz86(z0,y0,x0,satz82(y0,z0,n),satz82(m))):more(x0,z0)
+z0@[l:lessis(x0,y0)][k:less(y0,z0)]
++587
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=lessi(x0,z0,x,z,xix0,ziz0,satz51a(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
+-587
+satz87a:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".587"(x,y,z,xi,yi,zi)):less(x0,z0)
+z0@[l:less(x0,y0)][k:lessis(y0,z0)]
++*587
+k@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=lessi(x0,z0,x,z,xix0,ziz0,satz51b(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
+-587
+k@satz87b:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".587"(x,y,z,xi,yi,zi)):less(x0,z0)
+z0@[m:moreis(x0,y0)][n:more(y0,z0)]
+satz87c:=satz83(z0,x0,satz87b(z0,y0,x0,satz82(y0,z0,n),satz84(m))):more(x0,z0)
+z0@[m:more(x0,y0)][n:moreis(y0,z0)]
+satz87d:=satz83(z0,x0,satz87a(z0,y0,x0,satz84(y0,z0,n),satz82(m))):more(x0,z0)
+z0@[l:lessis(x0,y0)][k:lessis(y0,z0)]
++588
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=lessisi(x0,z0,x,z,xix0,ziz0,satz52(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):lessis(x0,z0)
+-588
+satz88:=ratapp3(lessis(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".588"(x,y,z,xi,yi,zi)):lessis(x0,z0)
+trlessis:=satz88:lessis(x0,z0)
+z0@[m:moreis(x0,y0)][n:moreis(y0,z0)]
+trmoreis:=satz85(z0,x0,satz88(z0,y0,x0,satz84(y0,z0,n),satz84(m))):moreis(x0,z0)
++589
+x0@[x:frac][xix0:inf(x,class(x0))][z:frac][m:moref(z,x)]
+t1:=somei(rat,[t:rat]more(t,x0),ratof(z),morei(ratof(z),x0,z,x,inclass(z),xix0,m)):some([t:rat]more(t,x0))
+xix0@t2:=someapp(frac,[t:frac]moref(t,x),satz53(x),some([t:rat]more(t,x0)),[t:frac][u:moref(t,x)]t1(t,u)):some([t:rat]more(t,x0))
+-589
+x0@satz89:=ratapp1(some([t:rat]more(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".589"(x,xi)):some([t:rat]more(t,x0))
++590
+z"rt.589"@[l:lessf(z,x)]
+t1:=somei(rat,[t:rat]less(t,x0),ratof(z),lessi(ratof(z),x0,z,x,inclass(z),xix0,l)):some([t:rat]less(t,x0))
+xix0"rt.589"@t2:=someapp(frac,[t:frac]lessf(t,x),satz54(x),some([t:rat]less(t,x0)),[t:frac][u:lessf(t,x)]t1(t,u)):some([t:rat]less(t,x0))
+-590
+satz90:=ratapp1(some([t:rat]less(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".590"(x,xi)):some([t:rat]less(t,x0))
+y0@[l:less(x0,y0)]
++591
+[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][z:frac][a:and(lessf(x,z),lessf(z,y))]
+t1:=lessi(x0,ratof(z),x,z,xix0,inclass(z),ande1(lessf(x,z),lessf(z,y),a)):less(x0,ratof(z))
+t2:=lessi(ratof(z),y0,z,y,inclass(z),yiy0,ande2(lessf(x,z),lessf(z,y),a)):less(ratof(z),y0)
+t3:=andi(less(x0,ratof(z)),less(ratof(z),y0),t1,t2):and(less(x0,ratof(z)),less(ratof(z),y0))
+t4:=somei(rat,[t:rat]and(less(x0,t),less(t,y0)),ratof(z),t3):some([t:rat]and(less(x0,t),less(t,y0)))
+yiy0@t5:=someapp(frac,[t:frac]and(lessf(x,t),lessf(t,y)),satz55(x,y,lesse(x,y,xix0,yiy0,l)),some([t:rat]and(less(x0,t),less(t,y0))),[t:frac][u:and(lessf(x,t),lessf(t,y))]t4(t,u)):some([t:rat]and(less(x0,t),less(t,y0)))
+-591
+satz91:=ratapp2(some([t:rat]and(less(x0,t),less(t,y0))),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".591"(x,y,xi,yi)):some([t:rat]and(less(x0,t),less(t,y0)))
+@plusfrt:=[x:frac][y:frac]ratof(pf(x,y)):[x:frac][y:frac]rat
+[x:frac][y:frac][z:frac][u:frac][e:eq"n"(x,y)][f:eq"n"(z,u)]
++*ii5
+f@t18:=isi(ratof(pf(x,z)),ratof(pf(y,u)),pf(x,z),pf(y,u),inclass(pf(x,z)),inclass(pf(y,u)),satz56(x,y,z,u,e,f)):is(<z><x>plusfrt,<u><y>plusfrt)
+-ii5
+@fplusfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t18".ii5"(x,y,z,u,v,w):fixf(rat,plusfrt)
+y0@pl:=indrat(rat,plusfrt,fplusfrt):rat
++*ii5
+y1iy0@t19:=isindrat(rat,plusfrt,fplusfrt,x1,y1,x1ix0,y1iy0):is(ratof(pf(x1,y1)),pl(x0,y0))
+-ii5
+y1iy0@picp:=isp(rat,[t:rat]inf(pf(x1,y1),class(t)),ratof(pf(x1,y1)),pl(x0,y0),inclass(pf(x1,y1)),t19".ii5"):inf(pf(x1,y1),class(pl(x0,y0)))
+z0@[i:is(x0,y0)]
+ispl1:=isf(rat,rat,[t:rat]pl(t,z0),x0,y0,i):is(pl(x0,z0),pl(y0,z0))
+ispl2:=isf(rat,rat,[t:rat]pl(z0,t),x0,y0,i):is(pl(z0,x0),pl(z0,y0))
+u0@[i:is(x0,y0)][j:is(z0,u0)]
+ispl12:=tris(rat,pl(x0,z0),pl(y0,z0),pl(y0,u0),ispl1(i),ispl2(z0,u0,y0,j)):is(pl(x0,z0),pl(y0,u0))
++592
+y1iy0@t1:=isi(pl(x0,y0),pl(y0,x0),pf(x1,y1),pf(y1,x1),picp,picp(y0,x0,y1,x1,y1iy0,x1ix0),satz58(x1,y1)):is(pl(x0,y0),pl(y0,x0))
+-592
+y0@satz92:=ratapp2(is(pl(x0,y0),pl(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".592"(x,y,xi,yi)):is(pl(x0,y0),pl(y0,x0))
+compl:=satz92:is(pl(x0,y0),pl(y0,x0))
++593
+z0@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=picp(pl(x0,y0),z0,pf(x,y),z,picp(x0,y0,x,y,xix0,yiy0),ziz0):inf(pf(pf(x,y),z),class(pl(pl(x0,y0),z0)))
+t2:=picp(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(pf(x,pf(y,z)),class(pl(x0,pl(y0,z0))))
+t3:=isi(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),pf(pf(x,y),z),pf(x,pf(y,z)),t1,t2,satz59(x,y,z)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
+-593
+z0@satz93:=ratapp3(is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".593"(x,y,z,xi,yi,zi)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
+asspl1:=satz93:is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
+asspl2:=symis(rat,pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),satz93):is(pl(x0,pl(y0,z0)),pl(pl(x0,y0),z0))
++594
+y1iy0@t1:=morei(pl(x0,y0),x0,pf(x1,y1),x1,picp,x1ix0,satz60(x1,y1)):more(pl(x0,y0),x0)
+-594
+y0@satz94:=ratapp2(more(pl(x0,y0),x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".594"(x,y,xi,yi)):more(pl(x0,y0),x0)
+satz94a:=satz82(pl(x0,y0),x0,satz94):less(x0,pl(x0,y0))
+z0@[m:more(x0,y0)]
++595
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz61(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
+-595
+satz95:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".595"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
+z0@[m:more(x0,y0)]
++596
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
+-596
+satz96a:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".596"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
+z0@[i:is(x0,y0)]
++*596
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(pl(x0,z0),pl(y0,z0))
+-596
+i@satz96b:=ratapp3(is(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".596"(x,y,z,xi,yi,zi)):is(pl(x0,z0),pl(y0,z0))
+z0@[l:less(x0,y0)]
++*596
+l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t3:=lessi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62c(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l))):less(pl(x0,z0),pl(y0,z0))
+-596
+l@satz96c:=ratapp3(less(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".596"(x,y,z,xi,yi,zi)):less(pl(x0,z0),pl(y0,z0))
++*596
+m@andersa:=satz95(m):more(pl(x0,z0),pl(y0,z0))
+i@andersb:=ispl1(x0,y0,z0,i):is(pl(x0,z0),pl(y0,z0))
+l@andersc:=satz82(pl(y0,z0),pl(x0,z0),satz95(y0,x0,z0,satz83(l))):less(pl(x0,z0),pl(y0,z0))
+-596
+m@satz96d:=ismore12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96a):more(pl(z0,x0),pl(z0,y0))
+i@satz96e:=ispl2(x0,y0,z0,i):is(pl(z0,x0),pl(z0,y0))
+l@satz96f:=isless12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96c):less(pl(z0,x0),pl(z0,y0))
+z0@[m:more(pl(x0,z0),pl(y0,z0))]
++597
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(x0,y0,x,y,xix0,yiy0,satz63a(x,y,z,moree(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
+-597
+satz97a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".597"(x,y,z,xi,yi,zi)):more(x0,y0)
+z0@[i:is(pl(x0,z0),pl(y0,z0))]
++*597
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(x0,y0,x,y,xix0,yiy0,satz63b(x,y,z,ise(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
+-597
+i@satz97b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".597"(x,y,z,xi,yi,zi)):is(x0,y0)
+z0@[l:less(pl(x0,z0),pl(y0,z0))]
++*597
+l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t3:=lessi(x0,y0,x,y,xix0,yiy0,satz63c(x,y,z,lesse(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
+-597
+l@satz97c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".597"(x,y,z,xi,yi,zi)):less(x0,y0)
++*597
+l@anders:=satz82(y0,x0,satz97a(y0,x0,z0,satz83(pl(x0,z0),pl(y0,z0),l))):less(x0,y0)
+-597
+u0@[m:more(x0,y0)][n:more(z0,u0)]
++598
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz64(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
+-598
+satz98:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".598"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
+u0@[l:less(x0,y0)][k:less(z0,u0)]
+satz98a:=satz82(pl(y0,u0),pl(x0,z0),satz98(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
+u0@[m:moreis(x0,y0)][n:more(z0,u0)]
++599
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
+-599
+satz99a:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
+u0@[m:more(x0,y0)][n:moreis(z0,u0)]
++*599
+n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t2:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
+-599
+n@satz99b:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
+u0@[l:lessis(x0,y0)][k:less(z0,u0)]
+satz99c:=satz82(pl(y0,u0),pl(x0,z0),satz99a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
+u0@[l:less(x0,y0)][k:lessis(z0,u0)]
+satz99d:=satz82(pl(y0,u0),pl(x0,z0),satz99b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
+u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
++5100
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=moreisi(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz66(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(pl(x0,z0),pl(y0,u0))
+-5100
+satz100:=ratapp4(moreis(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5100"(x,y,z,u,xi,yi,zi,ui)):moreis(pl(x0,z0),pl(y0,u0))
+u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
+satz100a:=satz84(pl(y0,u0),pl(x0,z0),satz100(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(pl(x0,z0),pl(y0,u0))
+y0@[l:lessis(x0,y0)]
++5101
+[v0:rat][i:is(pl(y0,v0),x0)]
+t1:=ismore1(pl(y0,v0),x0,y0,i,satz94(y0,v0)):more(x0,y0)
+v0@t2:=th3"l.imp"(is(pl(y0,v0),x0),more(x0,y0),satz81d(x0,y0,l),[t:is(pl(y0,v0),x0)]t1(t)):nis(pl(y0,v0),x0)
+-5101
+vorbemerkung101:=th5"l.some"(rat,[v:rat]is(pl(y0,v),x0),[v:rat]t2".5101"(v)):not(some([t:rat]is(pl(y0,t),x0)))
+y0@[m:more(x0,y0)]
++*5101
+m@[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][v:frac][e:eq"n"(pf(y,v),x)]
+t3:=isi(pl(y0,ratof(v)),x0,pf(y,v),x,picp(y0,ratof(v),y,v,yiy0,inclass(v)),xix0,e):is(pl(y0,ratof(v)),x0)
+t4:=somei(rat,[t:rat]is(pl(y0,t),x0),ratof(v),t3):some([t:rat]is(pl(y0,t),x0))
+yiy0@t5:=someapp(frac,[t:frac]eq"n"(pf(y,t),x),satz67a(x,y,moree(x0,y0,x,y,xix0,yiy0,m)),some([t:rat]is(pl(y0,t),x0)),[t:frac][u:eq"n"(pf(y,t),x)]t4(t,u)):some([t:rat]is(pl(y0,t),x0))
+-5101
+m@satz101a:=ratapp2(some([t:rat]is(pl(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".5101"(x,y,xi,yi)):some([t:rat]is(pl(y0,t),x0))
+y0@[v0:rat][w0:rat][i:is(pl(y0,v0),x0)][j:is(pl(y0,w0),x0)]
++*5101
+j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
+t6:=isi(v0,w0,v,w,viv0,wiw0,satz67b(x,y,v,w,ise(pl(y0,v0),x0,pf(y,v),x,picp(y0,v0,y,v,yiy0,viv0),xix0,i),ise(pl(y0,w0),x0,pf(y,w),x,picp(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
+-5101
+j@satz101b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t6".5101"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
++*5101
+y0@t7:=[t:rat][u:rat][v:is(pl(y0,t),x0)][w:is(pl(y0,u),x0)]satz101b(t,u,v,w):amone(rat,[t:rat]is(pl(y0,t),x0))
+-5101
+m@satz101:=onei(rat,[t:rat]is(pl(y0,t),x0),t7".5101",satz101a):one([t:rat]is(pl(y0,t),x0))
+mn:=ind(rat,[t:rat]is(pl(y0,t),x0),satz101):rat
+satz101c:=oneax(rat,[t:rat]is(pl(y0,t),x0),satz101):is(pl(y0,mn(x0,y0,m)),x0)
+satz101d:=symis(rat,pl(y0,mn(x0,y0,m)),x0,satz101c):is(x0,pl(y0,mn(x0,y0,m)))
+satz101e:=tris(rat,pl(mn(x0,y0,m),y0),pl(y0,mn(x0,y0,m)),x0,compl(mn(x0,y0,m),y0),satz101c):is(pl(mn(x0,y0,m),y0),x0)
+satz101f:=symis(rat,pl(mn(x0,y0,m),y0),x0,satz101e):is(x0,pl(mn(x0,y0,m),y0))
+y0@[v0:rat][m:more(x0,y0)][i:is(pl(y0,v0),x0)]
+satz101g:=satz101b(v0,mn(x0,y0,m),i,satz101c(m)):is(v0,mn(x0,y0,m))
+@timesfrt:=[x:frac][y:frac]ratof(tf(x,y)):[x:frac][y:frac]rat
++*ii5
+f@t20:=isi(ratof(tf(x,z)),ratof(tf(y,u)),tf(x,z),tf(y,u),inclass(tf(x,z)),inclass(tf(y,u)),satz68(x,y,z,u,e,f)):is(<z><x>timesfrt,<u><y>timesfrt)
+-ii5
+@ftimesfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t20".ii5"(x,y,z,u,v,w):fixf(rat,timesfrt)
+y0@ts:=indrat(rat,timesfrt,ftimesfrt):rat
++*ii5
+y1iy0@t21:=isindrat(rat,timesfrt,ftimesfrt,x1,y1,x1ix0,y1iy0):is(ratof(tf(x1,y1)),ts(x0,y0))
+-ii5
+y1iy0@tict:=isp(rat,[t:rat]inf(tf(x1,y1),class(t)),ratof(tf(x1,y1)),ts(x0,y0),inclass(tf(x1,y1)),t21".ii5"):inf(tf(x1,y1),class(ts(x0,y0)))
+z0@[i:is(x0,y0)]
+ists1:=isf(rat,rat,[t:rat]ts(t,z0),x0,y0,i):is(ts(x0,z0),ts(y0,z0))
+ists2:=isf(rat,rat,[t:rat]ts(z0,t),x0,y0,i):is(ts(z0,x0),ts(z0,y0))
+u0@[i:is(x0,y0)][j:is(z0,u0)]
+ists12:=tris(rat,ts(x0,z0),ts(y0,z0),ts(y0,u0),ists1(i),ists2(z0,u0,y0,j)):is(ts(x0,z0),ts(y0,u0))
++5102
+y1iy0@t1:=isi(ts(x0,y0),ts(y0,x0),tf(x1,y1),tf(y1,x1),tict,tict(y0,x0,y1,x1,y1iy0,x1ix0),satz69(x1,y1)):is(ts(x0,y0),ts(y0,x0))
+-5102
+y0@satz102:=ratapp2(is(ts(x0,y0),ts(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".5102"(x,y,xi,yi)):is(ts(x0,y0),ts(y0,x0))
+comts:=satz102:is(ts(x0,y0),ts(y0,x0))
++5103
+ziz0"rt.593"@t1:=tict(ts(x0,y0),z0,tf(x,y),z,tict(x0,y0,x,y,xix0,yiy0),ziz0):inf(tf(tf(x,y),z),class(ts(ts(x0,y0),z0)))
+t2:=tict(x0,ts(y0,z0),x,tf(y,z),xix0,tict(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,tf(y,z)),class(ts(x0,ts(y0,z0))))
+t3:=isi(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),tf(tf(x,y),z),tf(x,tf(y,z)),t1,t2,satz70(x,y,z)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
+-5103
+z0@satz103:=ratapp3(is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5103"(x,y,z,xi,yi,zi)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
+assts1:=satz103:is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
+assts2:=symis(rat,ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),satz103):is(ts(x0,ts(y0,z0)),ts(ts(x0,y0),z0))
++5104
+ziz0"rt.593"@t1:=tict(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,pf(y,z)),class(ts(x0,pl(y0,z0))))
+t2:=picp(ts(x0,y0),ts(x0,z0),tf(x,y),tf(x,z),tict(x0,y0,x,y,xix0,yiy0),tict(x0,z0,x,z,xix0,ziz0)):inf(pf(tf(x,y),tf(x,z)),class(pl(ts(x0,y0),ts(x0,z0))))
+t3:=isi(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),t1,t2,satz71(x,y,z)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
+-5104
+satz104:=ratapp3(is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5104"(x,y,z,xi,yi,zi)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
+disttp1:=tr3is(rat,ts(pl(x0,y0),z0),ts(z0,pl(x0,y0)),pl(ts(z0,x0),ts(z0,y0)),pl(ts(x0,z0),ts(y0,z0)),comts(pl(x0,y0),z0),satz104(z0,x0,y0),ispl12(ts(z0,x0),ts(x0,z0),ts(z0,y0),ts(y0,z0),comts(z0,x0),comts(z0,y0))):is(ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)))
+disttp2:=satz104:is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
+distpt1:=symis(rat,ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)),disttp1):is(pl(ts(x0,z0),ts(y0,z0)),ts(pl(x0,y0),z0))
+distpt2:=symis(rat,ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),disttp2):is(pl(ts(x0,y0),ts(x0,z0)),ts(x0,pl(y0,z0)))
+[m:more(x0,y0)]
++5105
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(ts(x0,z0),ts(y0,z0))
+-5105
+satz105a:=ratapp3(more(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5105"(x,y,z,xi,yi,zi)):more(ts(x0,z0),ts(y0,z0))
+z0@[i:is(x0,y0)]
++*5105
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(ts(x0,z0),ts(y0,z0))
+-5105
+i@satz105b:=ratapp3(is(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5105"(x,y,z,xi,yi,zi)):is(ts(x0,z0),ts(y0,z0))
+z0@[l:less(x0,y0)]
++*5105
+l@[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]
+t3:=lessi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xi,zi),tict(y0,z0,y,z,yi,zi),satz72c(x,y,z,lesse(x0,y0,x,y,xi,yi,l))):less(ts(x0,z0),ts(y0,z0))
+-5105
+l@satz105c:=ratapp3(less(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5105"(x,y,z,xi,yi,zi)):less(ts(x0,z0),ts(y0,z0))
++*5105
+i@andersb:=ists1(x0,y0,z0,i):is(ts(x0,z0),ts(y0,z0))
+l@andersc:=satz82(ts(y0,z0),ts(x0,z0),satz105a(y0,x0,z0,satz83(l))):less(ts(x0,z0),ts(y0,z0))
+-5105
+m@satz105d:=ismore12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105a):more(ts(z0,x0),ts(z0,y0))
+i@satz105e:=ists2(x0,y0,z0,i):is(ts(z0,x0),ts(z0,y0))
+l@satz105f:=isless12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105c):less(ts(z0,x0),ts(z0,y0))
+z0@[m:more(ts(x0,z0),ts(y0,z0))]
++5106
+[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t1:=morei(x0,y0,x,y,xix0,yiy0,satz73a(x,y,z,moree(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
+-5106
+satz106a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5106"(x,y,z,xi,yi,zi)):more(x0,y0)
+z0@[i:is(ts(x0,z0),ts(y0,z0))]
++*5106
+i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t2:=isi(x0,y0,x,y,xix0,yiy0,satz73b(x,y,z,ise(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
+-5106
+i@satz106b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5106"(x,y,z,xi,yi,zi)):is(x0,y0)
+z0@[l:less(ts(x0,z0),ts(y0,z0))]
++*5106
+l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
+t3:=lessi(x0,y0,x,y,xix0,yiy0,satz73c(x,y,z,lesse(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
+-5106
+l@satz106c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5106"(x,y,z,xi,yi,zi)):less(x0,y0)
++*5106
+l@anders:=satz82(y0,x0,satz106a(y0,x0,z0,satz83(ts(x0,z0),ts(y0,z0),l))):less(x0,y0)
+-5106
+u0@[m:more(x0,y0)][n:more(z0,u0)]
++5107
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz74(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
+-5107
+satz107:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5107"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
+u0@[l:less(x0,y0)][k:less(z0,u0)]
+satz107a:=satz82(ts(y0,u0),ts(x0,z0),satz107(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
+u0@[m:moreis(x0,y0)][n:more(z0,u0)]
++5108
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
+-5108
+satz108a:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
+u0@[m:more(x0,y0)][n:moreis(z0,u0)]
++*5108
+n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t2:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
+-5108
+n@satz108b:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
+u0@[l:lessis(x0,y0)][k:less(z0,u0)]
+satz108c:=satz82(ts(y0,u0),ts(x0,z0),satz108a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
+u0@[l:less(x0,y0)][k:lessis(z0,u0)]
+satz108d:=satz82(ts(y0,u0),ts(x0,z0),satz108b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
+u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
++5109
+[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
+t1:=moreisi(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz76(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(ts(x0,z0),ts(y0,u0))
+-5109
+satz109:=ratapp4(moreis(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5109"(x,y,z,u,xi,yi,zi,ui)):moreis(ts(x0,z0),ts(y0,u0))
+u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
+satz109a:=satz84(ts(y0,u0),ts(x0,z0),satz109(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(ts(x0,z0),ts(y0,u0))
++5110
+y1iy0@[v:frac][e:eq"n"(tf(y1,v),x1)]
+t1:=isi(ts(y0,ratof(v)),x0,tf(y1,v),x1,tict(y0,ratof(v),y1,v,y1iy0,inclass(v)),x1ix0,e):is(ts(y0,ratof(v)),x0)
+t2:=somei(rat,[t:rat]is(ts(y0,t),x0),ratof(v),t1):some([t:rat]is(ts(y0,t),x0))
+y1iy0@t3:=someapp(frac,[t:frac]eq"n"(tf(y1,t),x1),satz77a(x1,y1),some([t:rat]is(ts(y0,t),x0)),[t:frac][u:eq"n"(tf(y1,t),x1)]t2(t,u)):some([t:rat]is(ts(y0,t),x0))
+-5110
+y0@satz110a:=ratapp2(some([t:rat]is(ts(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t3".5110"(x,y,xi,yi)):some([t:rat]is(ts(y0,t),x0))
+[v0:rat][w0:rat][i:is(ts(y0,v0),x0)][j:is(ts(y0,w0),x0)]
++*5110
+j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
+t4:=isi(v0,w0,v,w,viv0,wiw0,satz77b(x,y,v,w,ise(ts(y0,v0),x0,tf(y,v),x,tict(y0,v0,y,v,yiy0,viv0),xix0,i),ise(ts(y0,w0),x0,tf(y,w),x,tict(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
+-5110
+j@satz110b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t4".5110"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
++*5110
+y0@t5:=[t:rat][u:rat][v:is(ts(y0,t),x0)][w:is(ts(y0,u),x0)]satz110b(t,u,v,w):amone(rat,[t:rat]is(ts(y0,t),x0))
+-5110
+y0@satz110:=onei(rat,[t:rat]is(ts(y0,t),x0),t5".5110",satz110a):one([t:rat]is(ts(y0,t),x0))
+-rt
+@[x:nat][y:nat]
++5111
+t1:=tris(nat,ts(num(fr(x,1)),den(fr(y,1))),ts(x,1),x,ndis12(x,1,y,1),satz28a(x)):is(ts(num(fr(x,1)),den(fr(y,1))),x)
+t2:=symis(nat,ts(num(fr(x,1)),den(fr(y,1))),x,t1):is(x,ts(num(fr(x,1)),den(fr(y,1))))
+-5111
+[m:moref(fr(x,1),fr(y,1))]
+satz111a:=ismore12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),m):more(x,y)
+y@[e:eq(fr(x,1),fr(y,1))]
+satz111b:=tr3is(nat,x,ts(num(fr(x,1)),den(fr(y,1))),ts(num(fr(y,1)),den(fr(x,1))),y,t2".5111",e,t1".5111"(y,x)):is(x,y)
+y@[l:lessf(fr(x,1),fr(y,1))]
+satz111c:=isless12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),l):less(x,y)
+y@[m:more(x,y)]
+satz111d:=ismore12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),m):moref(fr(x,1),fr(y,1))
+y@[i:is(x,y)]
+satz111e:=tr3is(nat,ts(num(fr(x,1)),den(fr(y,1))),x,y,ts(num(fr(y,1)),den(fr(x,1))),t1".5111",i,t2".5111"(y,x)):eq(fr(x,1),fr(y,1))
+y@[l:less(x,y)]
+satz111f:=isless12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),l):lessf(fr(x,1),fr(y,1))
++*rt
+@[x0:rat][x:nat]
+natprop:=inf(fr(x,1),class(x0)):'prop'
+x0@natrt:=some"n"([t:nat]natprop(t)):'prop'
++*ii5
+y0@[x:nat][y:nat][npx:natprop(x0,x)][npy:natprop(y0,y)][i:is(x0,y0)]
+t22:=satz111b(x,y,ise(x0,y0,fr(x,1),fr(y,1),npx,npy,i)):is"n"(x,y)
+x0@t23:=[t:nat][u:nat][v:natprop(x0,t)][w:natprop(x0,u)]t22(x0,x0,t,u,v,w,refis(rat,x0)):amone(nat,[t:nat]natprop(x0,t))
+-ii5
+x0@[nx0:natrt(x0)]
+satz111g:=onei(nat,[t:nat]natprop(t),t23".ii5",nx0):one"n"([t:nat]natprop(x0,t))
+nofrt:=ind(nat,[t:nat]natprop(t),satz111g):nat
+inclassn:=oneax(nat,[t:nat]natprop(t),satz111g):inf(fr(nofrt,1),class(x0))
+[y0:rat][ny0:natrt(y0)][i:is(x0,y0)]
+isrten:=t22".ii5"(x0,y0,nofrt(x0,nx0),nofrt(y0,ny0),inclassn(x0,nx0),inclassn(y0,ny0),i):is"n"(nofrt(x0,nx0),nofrt(y0,ny0))
+ny0@[i:is"n"(nofrt(x0,nx0),nofrt(y0,ny0))]
+isrtin:=isi(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),eqn"n"(nofrt(x0,nx0),1,nofrt(y0,ny0),i)):is(x0,y0)
+@[x:nat]
+rtofn:=ratof(fr(x,1)):rat
+natrti:=somei(nat,[t:nat]natprop(rtofn,t),x,inclass(fr(x,1))):natrt(rtofn(x))
+[y:nat][i:is"n"(x,y)]
+isnert:=isf(nat,rat,[t:nat]rtofn(t),x,y,i):is(rtofn(x),rtofn(y))
+y@[i:is(rtofn(x),rtofn(y))]
+isnirt:=t22".ii5"(rtofn(x),rtofn(y),x,y,inclass(fr(x,1)),inclass(fr(y,1)),i):is"n"(x,y)
+nx0@isrtn1:=isi(x0,rtofn(nofrt(x0,nx0)),fr(nofrt(x0,nx0),1),fr(nofrt(x0,nx0),1),inclassn(x0,nx0),inclass(fr(nofrt(x0,nx0),1)),refeq"n"(fr(nofrt(x0,nx0),1))):is(x0,rtofn(nofrt(x0,nx0)))
+x@isnrt1:=t22".ii5"(rtofn(x),rtofn(x),x,nofrt(rtofn(x),natrti(x)),inclass(fr(x,1)),inclassn(rtofn(x),natrti(x)),refis(rat,rtofn(x))):is"n"(x,nofrt(rtofn(x),natrti(x)))
+-rt
+@[x:nat][y:nat]
+satz112a:=satz57(x,y,1):eq(pf(fr(x,1),fr(y,1)),fr(pl(x,y),1))
+satz112b:=treq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),ts(1,1)),fr(ts(x,y),1),tfeq12a(x,1,y,1),eqd(ts(x,y),ts(1,1),1,satz28a(1))):eq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),1))
++*rt
+ny0@satz112c:=lemmaeq1(pl(x0,y0),pf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),picp(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112a(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(pl(x0,y0)))
+satz112d:=somei(nat,[t:nat]natprop(pl(x0,y0),t),pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112c):natrt(pl(x0,y0))
+satz112e:=lemmaeq1(ts(x0,y0),tf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),tict(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112b(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(ts(x0,y0)))
+satz112f:=somei(nat,[t:nat]natprop(ts(x0,y0),t),ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112e):natrt(ts(x0,y0))
+[m:more(x0,y0)]
++5112
+t1:=satz111a(nofrt(x0,nx0),nofrt(y0,ny0),moree(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),m)):more"n"(nofrt(x0,nx0),nofrt(y0,ny0))
+[z:nat][d:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),z)]
+t2:=tris(nat,nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),z),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),d,ispl2"n"(z,nofrt(rtofn(z),natrti(z)),nofrt(y0,ny0),isnrt1(z))):is"n"(nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))))
+t3:=isi(x0,pl(y0,rtofn(z)),fr(nofrt(x0,nx0),1),fr(pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),1),inclassn(x0,nx0),satz112c(y0,ny0,rtofn(z),natrti(z)),eqn(nofrt(x0,nx0),1,pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),t2)):is(x0,pl(y0,rtofn(z)))
+t4:=satz101g(x0,y0,rtofn(z),m,symis(rat,x0,pl(y0,rtofn(z)),t3)):is(rtofn(z),mn(x0,y0,m))
+t5:=isp(rat,[t:rat]natrt(t),rtofn(z),mn(x0,y0,m),natrti(z),t4):natrt(mn(x0,y0,m))
+-5112
+satz112g:=someapp(nat,[t:nat]diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t),t1".5112",natrt(mn(x0,y0,m)),[t:nat][u:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t)]t5".5112"(t,u)):natrt(mn(x0,y0,m))
+@[x:nat][y:nat]
+satz112h:=isi(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),pf(fr(x,1),fr(y,1)),fr(pl"n"(x,y),1),picp(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(pl"n"(x,y),1)),satz112a(x,y)):is(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)))
+satz112j:=isi(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),tf(fr(x,1),fr(y,1)),fr(ts"n"(x,y),1),tict(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(ts"n"(x,y),1)),satz112b(x,y)):is(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)))
++nt
+@natt:=ot(rat,[t:rat]natrt(t)):'type'
+nx0@ntofrt:=out(rat,[t:rat]natrt(t),x0,nx0):natt
+@[xt:natt][yt:natt]
+is:=is"e"(natt,xt,yt):'prop'
+nis:=not(is(xt,yt)):'prop'
+@[p:[x:natt]'prop']
+all:=all"l"(natt,p):'prop'
+some:=some"l"(natt,p):'prop'
+one:=one"e"(natt,p):'prop'
+xt@[st:set(natt)]
+in:=esti(natt,xt,st):'prop'
+xt@rtofnt:=in"e"(rat,[t:rat]natrt(t),xt):rat
+natrti:=inp(rat,[t:rat]natrt(t),xt):natrt(rtofnt(xt))
+ny0@[i:is"rt"(x0,y0)]
+isrtent:=isouti(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is(ntofrt(x0,nx0),ntofrt(y0,ny0))
+ny0@[i:is(ntofrt(x0,nx0),ntofrt(y0,ny0))]
+isrtint:=isoute(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is"rt"(x0,y0)
+yt@[i:is(xt,yt)]
+isntert:=isini(rat,[t:rat]natrt(t),xt,yt,i):is"rt"(rtofnt(xt),rtofnt(yt))
+yt@[i:is"rt"(rtofnt(xt),rtofnt(yt))]
+isntirt:=isine(rat,[t:rat]natrt(t),xt,yt,i):is(xt,yt)
+nx0@isrtnt1:=isinout(rat,[t:rat]natrt(t),x0,nx0):is"rt"(x0,rtofnt(ntofrt(x0,nx0)))
+xt@isntrt1:=isoutin(rat,[t:rat]natrt(t),xt):is(xt,ntofrt(rtofnt(xt),natrti(xt)))
+x@ntofn:=ntofrt(rtofn(x),natrti"rt"(x)):natt
+y@[i:is"n"(x,y)]
+isnent:=isrtent(rtofn(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),isnert(x,y,i)):is(ntofn(x),ntofn(y))
+y@[i:is(ntofn(x),ntofn(y))]
+isnint:=isnirt(x,y,isrtint(rtofn"rt"(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),i)):is"n"(x,y)
+xt@nofnt:=nofrt(rtofnt(xt),natrti(xt)):nat
+yt@[i:is(xt,yt)]
+isnten:=isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),isntert(xt,yt,i)):is"n"(nofnt(xt),nofnt(yt))
+yt@[i:is"n"(nofnt(xt),nofnt(yt))]
+isntin:=isntirt(xt,yt,isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),i)):is(xt,yt)
++ii5
+x@t24:=isrtnt1(rtofn(x),natrti"rt"(x)):is"rt"(rtofn(x),rtofnt(ntofn(x)))
+t25:=isrten(rtofn(x),natrti"rt"(x),rtofnt(ntofn(x)),natrti(ntofn(x)),t24):is"n"(nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)))
+-ii5
+x@isnnt1:=tris(nat,x,nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)),isnrt1(x),t25".ii5"):is"n"(x,nofnt(ntofn(x)))
++*ii5
+xt@t26:=isrtn1(rtofnt(xt),natrti(xt)):is"rt"(rtofnt(xt),rtofn(nofnt(xt)))
+t27:=isrtent(rtofnt(xt),natrti(xt),rtofn(nofnt(xt)),natrti"rt"(nofnt(xt)),t26):is(ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)))
+-ii5
+xt@isntn1:=tris(natt,xt,ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)),isntrt1(xt),t27".ii5"):is(xt,ntofn(nofnt(xt)))
+x@isnnt2:=symis(nat,x,nofnt(ntofn(x)),isnnt1):is"n"(nofnt(ntofn(x)),x)
+xt@isntn2:=symis(natt,xt,ntofn(nofnt(xt)),isntn1):is(ntofn(nofnt(xt)),xt)
+@1t:=ntofn(1):natt
+suct:=[x:natt]ntofn(<nofnt(x)>suc):[x:natt]natt
++5113
+xt@[i:is(<xt>suct,1t)]
+t1:=isnint(<nofnt(xt)>suc,1,i):is"n"(<nofnt(xt)>suc,1)
+-5113
+xt@satz113a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<nofnt(xt)>suc,1),<nofnt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5113"(t)):nis(<xt>suct,1t)
+yt@[i:is(<xt>suct,<yt>suct)]
++*5113
+i"nt"@t2:=isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,i):is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
+-5113
+i@satz113b:=isntin(xt,yt,<t2".5113"><nofnt(yt)><nofnt(xt)>ax4):is(xt,yt)
+@[st:set(natt)]
+cond1:=in(1t,st):'prop'
+cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
+[c1:cond1][c2:cond2]
++*5113
+c2@[x:nat]
+prop1:=in(ntofn(x),st):'prop'
+[p:prop1(x)]
+t3:=<ntofn(x)>c2:imp(in(ntofn(x),st),in(<ntofn(x)>suct,st))
+t4:=mp(in(ntofn(x),st),in(<ntofn(x)>suct,st),p,t3):in(<ntofn(x)>suct,st)
+t5:=isp(nat,[t:nat]in(ntofn(<t>suc),st),nofnt(ntofn(x)),x,t4,isnnt2(x)):prop1(<x>suc)
+-5113
+c2@[xt:natt]
++*5113
+xt@t6:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t5(t,u),nofnt(xt)):in(ntofn(nofnt(xt)),st)
+-5113
+xt@satz113c:=isp(natt,[t:natt]in(t,st),ntofn(nofnt(xt)),xt,t6".5113",isntn2(xt)):in(xt,st)
+@ax3t:=[x:natt]satz113a(x):[x:natt]nis(<x>suct,1t)
+ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz113b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
+ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz113c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
+yt@[n:nis(xt,yt)]
++51
+t1:=th3"l.imp"(is"n"(nofnt(xt),nofnt(yt)),is(xt,yt),n,[t:is"n"(nofnt(xt),nofnt(yt))]isntin(xt,yt,t)):nis"n"(nofnt(xt),nofnt(yt))
+t2:=satz1(nofnt(xt),nofnt(yt),t1):nis"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
+-51
+satz1:=th3"l.imp"(is(<xt>suct,<yt>suct),is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc),t2".51",[t:is(<xt>suct,<yt>suct)]isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,t)):nis(<xt>suct,<yt>suct)
++54
+xt@x:=nofnt(xt):nat
+[ft:[x:natt]natt]
+prop1t:=all([t:natt]is(<<t>suct>ft,<<t>ft>suct)):'prop'
+prop2t:=and(is(<1t>ft,<xt>suct),prop1t):'prop'
+xt@[f:[x:nat]nat]
+prop1:=all"n"([t:nat]is"n"(<<t>suc>f,<<t>f>suc)):'prop'
+prop2:=and(is"n"(<1>f,<x>suc),prop1):'prop'
+ft@g:=[t:nat]nofnt(<ntofn(t)>ft):[x:nat]nat
+[p:prop2t]
+t1:=ande1(is(<1t>ft,<xt>suct),prop1t,p):is(<1t>ft,<xt>suct)
+t2:=tris(nat,<1>g,nofnt(<xt>suct),<x>suc,isnten(<1t>ft,<xt>suct,t1),isnnt2(<x>suc)):is"n"(<1>g,<x>suc)
+t3:=ande2(is(<1t>ft,<xt>suct),prop1t,p):prop1t
+[u:nat]
+ut:=ntofn(u):natt
+t4:=isf(nat,nat,suc,u,nofnt(ut),isnnt1(u)):is"n"(<u>suc,<nofnt(ut)>suc)
+t5:=isf(nat,nat,g,<u>suc,<nofnt(ut)>suc,t4):is"n"(<<u>suc>g,nofnt(<<ut>suct>ft))
+t6:=<ut>t3:is(<<ut>suct>ft,<<ut>ft>suct)
+t7:=isnten(<<ut>suct>ft,<<ut>ft>suct,t6):is"n"(nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct))
+t8:=isnnt2(<<u>g>suc):is"n"(nofnt(<<ut>ft>suct),<<u>g>suc)
+t9:=tr3is(nat,<<u>suc>g,nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct),<<u>g>suc,t5,t7,t8):is"n"(<<u>suc>g,<<u>g>suc)
+p@t10:=[u:nat]t9(u):prop1(g)
+t11:=andi(is"n"(<1>g,<x>suc),prop1(g),t2,t10):prop2(g)
+xt@[a:[t:natt]natt][b:[t:natt]natt][pa:prop2t(a)][pb:prop2t(b)]
+t12:=onee1([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):amone([t:nat]nat,[u:[t:nat]nat]prop2(u))
+t13:=<t11(b,pb)><t11(a,pa)><g(b)><g(a)>t12:is"e"([t:nat]nat,g(a),g(b))
+[yt:natt]
+y:=nofnt(yt):nat
+t14:=fise(nat,nat,g(a),g(b),t13,y):is"n"(nofnt(<ntofn(y)>a),nofnt(<ntofn(y)>b))
+t15:=isntin(<ntofn(y)>a,<ntofn(y)>b,t14):is(<ntofn(y)>a,<ntofn(y)>b)
+t16:=tr3is(natt,<yt>a,<ntofn(y)>a,<ntofn(y)>b,<yt>b,isf(natt,natt,a,yt,ntofn(y),isntn1(yt)),t15,isf(natt,natt,b,ntofn(y),yt,isntn2(yt))):is(<yt>a,<yt>b)
+pb@t17:=fisi(natt,natt,a,b,[t:natt]t16(t)):is"e"([t:natt]natt,a,b)
+xt@t18:=[u:[t:natt]natt][v:[t:natt]natt][w:prop2t(u)][z:prop2t(v)]t17(u,v,w,z):amone([t:natt]natt,[u:[t:natt]natt]prop2t(u))
+t19:=onee2([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):some"l"([t:nat]nat,[u:[t:nat]nat]prop2(u))
+f@gt:=[t:natt]ntofn(<nofnt(t)>f):[x:natt]natt
+[p:prop2]
+t20:=ande1(is"n"(<1>f,<x>suc),prop1,p):is"n"(<1>f,<x>suc)
+t21:=isf(nat,nat,f,nofnt(1t),1,isnnt2(1)):is"n"(<nofnt(1t)>f,<1>f)
+t22:=isnent(<nofnt(1t)>f,<x>suc,tris(nat,<nofnt(1t)>f,<1>f,<x>suc,t21,t20)):is(<1t>gt,<xt>suct)
+t23:=ande2(is"n"(<1>f,<x>suc),prop1,p):prop1
+[zt:natt]
+z:=nofnt(zt):nat
+t24:=isf(nat,nat,f,nofnt(<zt>suct),<z>suc,isnnt2(<z>suc)):is"n"(<nofnt(<zt>suct)>f,<<z>suc>f)
+t25:=<z>t23:is"n"(<<z>suc>f,<<z>f>suc)
+t26:=isf(nat,nat,suc,<z>f,nofnt(<zt>gt),isnnt1(<z>f)):is"n"(<<z>f>suc,<nofnt(<zt>gt)>suc)
+t27:=isnent(<nofnt(<zt>suct)>f,<nofnt(<zt>gt)>suc,tr3is(nat,<nofnt(<zt>suct)>f,<<z>suc>f,<<z>f>suc,<nofnt(<zt>gt)>suc,t24,t25,t26)):is(<<zt>suct>gt,<<zt>gt>suct)
+p@t28:=[u:natt]t27(u):prop1t(gt)
+t29:=andi(is(<1t>gt,<xt>suct),prop1t(gt),t22,t28):prop2t(gt)
+t30:=somei([t:natt]natt,[u:[t:natt]natt]prop2t(u),gt,t29):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
+xt@t31:=someapp([t:nat]nat,[u:[t:nat]nat]prop2(u),t19,some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u)),[u:[t:nat]nat][v:prop2(u)]t30(u,v)):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
+-54
+xt@satz4:=onei([t:natt]natt,[u:[t:natt]natt]prop2t".54"(u),t18".54",t31".54"):one"e"([t:natt]natt,[u:[t:natt]natt]and(is(<1t>u,<xt>suct),all([v:natt]is(<<v>suct>u,<<v>u>suct))))
+yt@pl:=ntofrt(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt))):natt
++*ii5
+yt@t28:=satz112c(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)):inf(fr(pl"n"(nofnt(xt),nofnt(yt)),1),class(pl"rt"(rtofnt(xt),rtofnt(yt))))
+t29:=isi(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),fr(pl"n"(nofnt(xt),nofnt(yt)),1),fr(pl"n"(nofnt(xt),nofnt(yt)),1),t28,inclass(fr(pl"n"(nofnt(xt),nofnt(yt)),1)),refeq"n"(fr(pl"n"(nofnt(xt),nofnt(yt)),1))):is"rt"(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))))
+-ii5
+yt@isplnt:=isrtent(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),natrti"rt"(pl"n"(nofnt(xt),nofnt(yt))),t29".ii5"):is(pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))))
+isntpl:=symis(natt,pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))),isplnt):is(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt))
+ispln:=tris(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(ntofn(pl"n"(nofnt(xt),nofnt(yt)))),nofnt(pl(xt,yt)),isnnt1(pl"n"(nofnt(xt),nofnt(yt))),isnten(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt),isntpl)):is"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)))
+isnpl:=symis(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)),ispln):is"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)))
+[zt:natt]
++55
+t1:=ispl1"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt),isnpl(xt,yt)):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)))
+t2:=ispl2"n"(pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),nofnt(xt),ispln(yt,zt)):is"n"(pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
+t3:=tr3is(nat,pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)),pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t1,satz5(nofnt(xt),nofnt(yt),nofnt(zt)),t2):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
+-55
+satz5:=tr3is(natt,pl(pl(xt,yt),zt),ntofn(pl"n"(nofnt(pl(xt,yt)),nofnt(zt))),ntofn(pl"n"(nofnt(xt),nofnt(pl(yt,zt)))),pl(xt,pl(yt,zt)),isplnt(pl(xt,yt),zt),isnent(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t3".55"),isntpl(xt,pl(yt,zt))):is(pl(pl(xt,yt),zt),pl(xt,pl(yt,zt)))
+diffprop:=is(xt,pl(yt,zt)):'prop'
+[d:diffprop]
+diffprope:=tris(nat,nofnt(xt),nofnt(pl(yt,zt)),pl"n"(nofnt(yt),nofnt(zt)),isnten(xt,pl(yt,zt),d),isnpl(yt,zt)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))
+zt@[d:diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))]
++*ii5
+d@t30:=tris(nat,nofnt(xt),pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),d,ispln(yt,zt)):is"n"(nofnt(xt),nofnt(pl(yt,zt)))
+-ii5
+d@diffpropi:=isntin(xt,pl(yt,zt),t30".ii5"):diffprop
++59
+yt@it:=is(xt,yt):'prop'
+iit:=some([u:natt]diffprop(xt,yt,u)):'prop'
+iiit:=some([u:natt]diffprop(yt,xt,u)):'prop'
+i:=is"n"(nofnt(xt),nofnt(yt)):'prop'
+ii:=some"n"([u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u)):'prop'
+iii:=some"n"([u:nat]diffprop"n"(nofnt(yt),nofnt(xt),u)):'prop'
+[one:i]
+t1:=or3i1(it,iit,iiit,isntin(xt,yt,one)):or3(it,iit,iiit)
+yt@[two:ii][v:nat][d:diffprop"n"(nofnt(xt),nofnt(yt),v)]
+t2:=isp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),v,nofnt(ntofn(v)),d,isnnt1(v)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(ntofn(v)))
+t3:=somei(natt,[u:natt]diffprop(xt,yt,u),ntofn(v),diffpropi(xt,yt,ntofn(v),t2)):iit
+two@t4:=someapp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),two,iit,[u:nat][v:diffprop"n"(nofnt(xt),nofnt(yt),u)]t3(u,v)):iit
+t5:=or3i2(it,iit,iiit,t4):or3(it,iit,iiit)
+yt@[three:iii]
+t6:=or3i3(it,iit,iiit,t4(yt,xt,three)):or3(it,iit,iiit)
+yt@t7:=or3app(i,ii,iii,or3(it,iit,iiit),satz9a(nofnt(xt),nofnt(yt)),[u:i]t1(u),[u:ii]t5(u),[u:iii]t6(u)):or3(it,iit,iiit)
+[onet:it]
+t8:=isnten(xt,yt,onet):i
+yt@[twot:iit][vt:natt][d:diffprop(xt,yt,vt)]
+t9:=somei(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),nofnt(vt),diffprope(xt,yt,vt,d)):ii
+twot@t10:=someapp(natt,[u:natt]diffprop(xt,yt,u),twot,ii,[u:natt][v:diffprop(xt,yt,u)]t9(u,v)):ii
+yt@[threet:iiit]
+t11:=t10(yt,xt,threet):iii
+yt@t12:=satz9b(nofnt(xt),nofnt(yt)):ec3(i,ii,iii)
+onet@t13:=ec3e12(i,ii,iii,t12,t8):not(ii)
+t14:=th3"l.imp"(iit,ii,t13,[x:iit]t10(x)):not(iit)
+yt@t15:=th1"l.ec"(it,iit,[x:it]t14(x)):ec(it,iit)
+twot@t16:=ec3e23(i,ii,iii,t12,t10):not(iii)
+t17:=th3"l.imp"(iiit,iii,t16,[x:iiit]t11(x)):not(iiit)
+yt@t18:=th1"l.ec"(iit,iiit,[x:iit]t17(x)):ec(iit,iiit)
+threet@t19:=ec3e31(i,ii,iii,t12,t11):not(i)
+t20:=th3"l.imp"(it,i,t19,[x:it]t8(x)):not(it)
+yt@t21:=th1"l.ec"(iiit,it,[x:iiit]t20(x)):ec(iiit,it)
+t22:=th6"l.ec3"(it,iit,iiit,t15,t18,t21):ec3(it,iit,iiit)
+-59
+yt@satz9:=orec3i(it".59",iit".59",iiit".59",t7".59",t22".59"):orec3(is(xt,yt),some([u:natt]is(xt,pl(yt,u))),some([u:natt]is(yt,pl(xt,u))))
+more:=more"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[m:more(xt,yt)]
++*ii5
+m@t31:=moree(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+m@moree:=satz111a(nofnt(xt),nofnt(yt),t31".ii5"):more"n"(nofnt(xt),nofnt(yt))
+yt@[m:more"n"(nofnt(xt),nofnt(yt))]
++*ii5
+m@t32:=satz111d(nofnt(xt),nofnt(yt),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+m@morei:=morei"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t32".ii5"):more(xt,yt)
+yt@less:=less"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[l:less(xt,yt)]
++*ii5
+l@t33:=lesse(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+l@lesse:=satz111c(nofnt(xt),nofnt(yt),t33".ii5"):less"n"(nofnt(xt),nofnt(yt))
+yt@[l:less"n"(nofnt(xt),nofnt(yt))]
++*ii5
+l@t34:=satz111f(nofnt(xt),nofnt(yt),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
+-ii5
+l@lessi:=lessi"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t34".ii5"):less(xt,yt)
+yt@moreis:=moreis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[m:moreis(xt,yt)]
+moreise:=th9"l.or"(more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),m,[u:more"rt"(rtofnt(xt),rtofnt(yt))]moree(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis"n"(nofnt(xt),nofnt(yt))
+yt@[m:moreis"n"(nofnt(xt),nofnt(yt))]
+moreisi:=th9"l.or"(more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),m,[u:more"n"(nofnt(xt),nofnt(yt))]morei(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis(xt,yt)
+yt@lessis:=lessis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
+[l:lessis(xt,yt)]
+lessise:=th9"l.or"(less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),l,[u:less"rt"(rtofnt(xt),rtofnt(yt))]lesse(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis"n"(nofnt(xt),nofnt(yt))
+yt@[l:lessis"n"(nofnt(xt),nofnt(yt))]
+lessisi:=th9"l.or"(less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),l,[u:less"n"(nofnt(xt),nofnt(yt))]lessi(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis(xt,yt)
+zt@[l:less(xt,yt)][k:less(yt,zt)]
++515
+t1:=satz15(nofnt(xt),nofnt(yt),nofnt(zt),lesse(xt,yt,l),lesse(yt,zt,k)):less"n"(nofnt(xt),nofnt(zt))
+-515
+satz15:=lessi(xt,zt,t1".515"):less(xt,zt)
+zt@[ut:natt][m:more(xt,yt)][n:more(zt,ut)]
++521
+t1:=satz21(nofnt(xt),nofnt(yt),nofnt(zt),nofnt(ut),moree(xt,yt,m),moree(zt,ut,n)):more"n"(pl"n"(nofnt(xt),nofnt(zt)),pl"n"(nofnt(yt),nofnt(ut)))
+t2:=ismore12"n"(pl"n"(nofnt(xt),nofnt(zt)),nofnt(pl(xt,zt)),pl"n"(nofnt(yt),nofnt(ut)),nofnt(pl(yt,ut)),ispln(xt,zt),ispln(yt,ut),t1):more"n"(nofnt(pl(xt,zt)),nofnt(pl(yt,ut)))
+-521
+satz21:=morei(pl(xt,zt),pl(yt,ut),t2".521"):more(pl(xt,zt),pl(yt,ut))
+@[p:[x:natt]'prop'][n:natt]
+lb:=all([x:natt]imp(<x>p,lessis(n,x))):'prop'
+min:=and(lb,<n>p):'prop'
+p@[s:some(p)]
++527
+q:=[x:nat]<ntofn(x)>p:[x:nat]'prop'
+[n:natt][np:<n>p]
+t1:=isp(natt,p,n,ntofn(nofnt(n)),np,isntn1(n)):<nofnt(n)>q
+t2:=somei(nat,q,nofnt(n),t1):some"n"(q)
+s@t3:=someapp(natt,p,s,some"n"(q),[u:natt][v:<u>p]t2(u,v)):some"n"(q)
+t4:=satz27(q,t3):some"n"([x:nat]min"n"(q,x))
+[m:nat][mqm:min"n"(q,m)]
+t5:=ande1(lb"n"(q,m),<m>q,mqm):lb"n"(q,m)
+[n:nat][nq:<n>q]
+t6:=mp(<n>q,lessis"n"(m,n),nq,<n>t5):lessis"n"(m,n)
+mqm@[n:natt][np:<n>p]
+t7:=t6(nofnt(n),t1(n,np)):lessis"n"(m,nofnt(n))
+t8:=islessis1"n"(m,nofnt(ntofn(m)),nofnt(n),isnnt1(m),t7):lessis"n"(nofnt(ntofn(m)),nofnt(n))
+t9:=lessisi(ntofn(m),n,t8):lessis(ntofn(m),n)
+n@t10:=[u:<n>p]t9(u):imp(<n>p,lessis(ntofn(m),n))
+mqm@t11:=[x:natt]t10(x):lb(ntofn(m))
+t12:=ande2(lb"n"(q,m),<m>q,mqm):<ntofn(m)>p
+t13:=andi(lb(ntofn(m)),<ntofn(m)>p,t11,t12):min(ntofn(m))
+t14:=somei(natt,[x:natt]min(x),ntofn(m),t13):some([x:natt]min(x))
+-527
+satz27:=someapp(nat,[x:nat]min"n"(q".527",x),t4".527",some([x:natt]min(x)),[x:nat][y:min"n"(q".527",x)]t14".527"(x,y)):some([x:natt]min(p,x))
+-nt
+@1rt:=rtofn(1):rat
+x0@[x:frac][xix0:inf(x,class(x0))]
++*ii5
+xix0@t35:=tr3eq(tf(x,fr(1,1)),fr(ts"n"(num(x),1),ts"n"(den(x),1)),fr(num(x),den(x)),x,tfeq1a(x,1,1),eqnd(ts"n"(num(x),1),ts"n"(den(x),1),num(x),den(x),satz28a(num(x)),satz28a(den(x))),refeq1(fr(num(x),den(x)),x,fris(x))):eq"n"(tf(x,fr(1,1)),x)
+t36:=isi(ts(x0,1rt),x0,tf(x,fr(1,1)),x,tict(x0,1rt,x,fr(1,1),xix0,inclass(fr(1,1))),xix0,t35):is(ts(x0,1rt),x0)
+-ii5
+x0@example1a:=ratapp1(x0,is(ts(x0,1rt),x0),[x:frac][xi:inf(x,class(x0))]t36".ii5"(x,xi)):is(ts(x0,1rt),x0)
+example1b:=symis(rat,ts(x0,1rt),x0,example1a):is(x0,ts(x0,1rt))
+example1c:=tris(rat,ts(1rt,x0),ts(x0,1rt),x0,comts(1rt,x0),example1a):is(ts(1rt,x0),x0)
+example1d:=symis(rat,ts(1rt,x0),x0,example1c):is(x0,ts(1rt,x0))
+@[x:frac]
++5114
+t1:=tr3eq(tf(fr(den(x),1),x),fr(ts"n"(den(x),num(x)),ts"n"(1,den(x))),fr(ts"n"(num(x),den(x)),ts"n"(1,den(x))),fr(num(x),1),tfeq2a(x,den(x),1),eqn(ts"n"(den(x),num(x)),ts"n"(1,den(x)),ts"n"(num(x),den(x)),comts"n"(den(x),num(x))),satz40c(num(x),1,den(x))):eq"n"(tf(fr(den(x),1),x),fr(num(x),1))
+-5114
+satz114:=isi(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)),tf(fr(den(x),1),x),fr(num(x),1),tict(rtofn(den(x)),ratof(x),fr(den(x),1),x,inclass(fr(den(x),1)),inclass(x)),inclass(fr(num(x),1)),t1".5114"):is(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)))
+@[x1:nat][x2:nat]
+satz114a:=tr3is(rat,ts(rtofn(x2),ratof(fr(x1,x2))),ts(rtofn(den(fr(x1,x2))),ratof(fr(x1,x2))),rtofn(num(fr(x1,x2))),rtofn(x1),ists1(rtofn(x2),rtofn(den(fr(x1,x2))),ratof(fr(x1,x2)),isnert(x2,den(fr(x1,x2)),isden(x1,x2))),satz114(fr(x1,x2)),isnert(num(fr(x1,x2)),x1,numis(x1,x2))):is(ts(rtofn(x2),ratof(fr(x1,x2))),rtofn(x1))
+x0@[y0:rat]
+ov:=ind(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):rat
+satz110c:=oneax(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):is(ts(y0,ov(x0,y0)),x0)
+satz110d:=symis(rat,ts(y0,ov(x0,y0)),x0,satz110c):is(x0,ts(y0,ov(x0,y0)))
+satz110e:=tris(rat,ts(ov(x0,y0),y0),ts(y0,ov(x0,y0)),x0,comts(ov(x0,y0),y0),satz110c):is(ts(ov(x0,y0),y0),x0)
+satz110f:=symis(rat,ts(ov(x0,y0),y0),x0,satz110e):is(x0,ts(ov(x0,y0),y0))
+[v0:rat][i:is(ts(y0,v0),x0)]
+satz110g:=satz110b(x0,y0,v0,ov(x0,y0),i,satz110c):is(v0,ov(x0,y0))
+x2@satz114b:=satz110b(rtofn(x1),rtofn(x2),ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114a,satz110c(rtofn(x1),rtofn(x2))):is(ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)))
+satz114c:=symis(rat,ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114b):is(ov(rtofn(x1),rtofn(x2)),ratof(fr(x1,x2)))
++5115
+y0@t1:=satz89(ov(y0,x0)):some([t:rat]more(t,ov(y0,x0)))
+[u0:rat][m:more(u0,ov(y0,x0))][u:frac][uiu0:inf(u,class(u0))]
+z:=num(u):nat
+v:=den(u):nat
+t2:=ismore1(u0,ov(rtofn(z),rtofn(v)),ov(y0,x0),tris(rat,u0,ratof(fr(z,v)),ov(rtofn(z),rtofn(v)),isi(u0,ratof(fr(z,v)),u,fr(z,v),uiu0,inclass(fr(z,v)),refeq1(u,fr(z,v),isfr(u))),satz114b(z,v)),m):more(ov(rtofn(z),rtofn(v)),ov(y0,x0))
+t3:=moreisi(rtofn(v),1rt,fr(v,1),fr(1,1),inclass(fr(v,1)),inclass(fr(1,1)),th9"l.or"(more"n"(v,1),is"n"(v,1),moref(fr(v,1),fr(1,1)),eq"n"(fr(v,1),fr(1,1)),satz24(v),[t:more"n"(v,1)]satz111d(v,1,t),[t:is"n"(v,1)]satz111e(v,1,t))):moreis(rtofn(v),1rt)
+t4:=tr3is(rat,ts(rtofn(z),x0),ts(x0,rtofn(z)),ts(x0,ts(ov(rtofn(z),rtofn(v)),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),comts(rtofn(z),x0),ists2(rtofn(z),ts(ov(rtofn(z),rtofn(v)),rtofn(v)),x0,satz110f(rtofn(z),rtofn(v))),assts2(x0,ov(rtofn(z),rtofn(v)),rtofn(v))):is(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)))
+[n:more(rtofn(v),1rt)]
+t5:=ismore1(ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),symis(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),t4),satz105d(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),n)):more(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+t6:=moreisi1(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t5):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+uiu0@[i:is(rtofn(v),1rt)]
+t7:=moreisi2(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),tris(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t4,ists2(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),i))):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+uiu0@t8:=orapp(more(rtofn(v),1rt),is(rtofn(v),1rt),moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt)),t3,[t:more(rtofn(v),1rt)]t6(t),[t:is(rtofn(v),1rt)]t7(t)):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
+t9:=ismore12(ts(x0,ov(rtofn(z),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),ts(x0,ov(y0,x0)),y0,example1b(ts(x0,ov(rtofn(z),rtofn(v)))),satz110c(y0,x0),satz105d(ov(rtofn(z),rtofn(v)),ov(y0,x0),x0,t2)):more(ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0)
+t10:=satz87c(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0,t8,t9):more(ts(rtofn(z),x0),y0)
+t11:=somei(nat,[t:nat]more(ts(rtofn(t),x0),y0),z,t10):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
+m@t12:=ratapp1(u0,some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[u:frac][ui:inf(u,class(u0))]t11(u,ui)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
+-5115
+y0@satz115:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[t:rat][u:more(t,ov(y0,x0))]t12".5115"(t,u)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
++*5115
+uiu0@t13:=andi(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0),natrti(z),t10):and(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0))
+t14:=somei(rat,[t:rat]and(natrt(t),more(ts(t,x0),y0)),rtofn(z),t13):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
+m@t15:=ratapp1(u0,some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[u:frac][ui:inf(u,class(u0))]t14(u,ui)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
+-5115
+y0@satz115a:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[t:rat][u:more(t,ov(y0,x0))]t15".5115"(t,u)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
+@[s:set(rat)]
+cutprop1a:=nonempty(rat,s):'prop'
+cutprop1b:=not(all([x:rat]in(x,s))):'prop'
+cutprop1:=and(cutprop1a,cutprop1b):'prop'
+[x0:rat]
+cutprop2a:=all([x:rat]imp(not(in(x,s)),less(x0,x))):'prop'
+s@cutprop2:=all([x:rat]imp(in(x,s),cutprop2a(x))):'prop'
+x0@[y0:rat]
++iii1
+ubprop:=imp(in(y0,s),moreis(x0,y0)):'prop'
+-iii1
+x0@ub:=all([x:rat]ubprop".iii1"(x0,x)):'prop'
+max:=and(ub(x0),in(x0,s)):'prop'
+s@cutprop3:=not(some([x:rat]max(s,x))):'prop'
+cutprop:=and3(cutprop1,cutprop2,cutprop3):'prop'
++*iii1
+y0@lbprop:=imp(in(y0,s),lessis(x0,y0)):'prop'
+-iii1
+x0@lb:=all([x:rat]lbprop".iii1"(x0,x)):'prop'
+min:=and(lb(x0),in(x0,s)):'prop'
+@cut:=ot(set(rat),[x:set(rat)]cutprop(x)):'type'
+[ksi:cut]
+lcl:=in"e"(set(rat),[x:set(rat)]cutprop(x),ksi):set(rat)
+[x0:rat]
+lrt:=in(x0,lcl(ksi)):'prop'
+urt:=not(in(x0,lcl(ksi))):'prop'
+ksi@clcl:=inp(set(rat),[x:set(rat)]cutprop(x),ksi):cutprop(lcl(ksi))
+clcl1:=and3e1(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop1(lcl(ksi))
+clcl2:=and3e2(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop2(lcl(ksi))
+clcl3:=and3e3(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop3(lcl(ksi))
+clcl1a:=ande1(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1a(lcl(ksi))
+clcl1b:=ande2(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1b(lcl(ksi))
+[p:'prop'][p1:[x:rat][t:lrt(ksi,x)]p]
+cutapp1a:=nonemptyapp(rat,lcl,clcl1a,p,p1):p
++*iii1
+ksi@t1:=th1"l.some"(rat,[x:rat]lrt(ksi,x),clcl1b):some([x:rat]urt(ksi,x))
+-iii1
+p@[p1:[x:rat][t:urt(ksi,x)]p]
+cutapp1b:=someapp(rat,[x:rat]urt(ksi,x),t1".iii1",p,p1):p
+ksi@[x0:rat][lx:lrt(ksi,x0)]
++*iii1
+lx@t2:=mp(lrt(ksi,x0),cutprop2a(lcl,x0),lx,<x0>clcl2):cutprop2a(lcl,x0)
+-iii1
+lx@[y0:rat][uy:urt(ksi,y0)]
+cutapp2a:=mp(urt(ksi,y0),less(x0,y0),uy,<y0>t2".iii1"):less(x0,y0)
+cutapp2b:=satz83(x0,y0,cutapp2a):more(y0,x0)
++*iii1
+lx@t3:=th4"l.some"(rat,[x:rat]max(lcl,x),clcl3,x0):not(max(lcl,x0))
+t4:=th4"l.and"(ub(lcl,x0),lrt(ksi,x0),t3,lx):not(ub(lcl,x0))
+t5:=th1"l.some"(rat,[x:rat]ubprop(lcl,x0,x),t4):some([x:rat]not(ubprop(lcl,x0,x)))
+-iii1
+lx@[p:'prop'][p1:[y:rat][t:lrt(ksi,y)][u:less(x0,y)]p][y0:rat][n:not(ubprop".iii1"(lcl,x0,y0))]
++*iii1
+n@t6:=th5"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):lrt(ksi,y0)
+t7:=th6"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):not(moreis(x0,y0))
+t8:=satz81j(x0,y0,t7):less(x0,y0)
+t9:=<t8><t6><y0>p1:p
+-iii1
+p1@cutapp3:=someapp(rat,[y:rat]not(ubprop".iii1"(lcl,x0,y)),t5".iii1",p,[y:rat][t:not(ubprop".iii1"(lcl,x0,y))]t9".iii1"(y,t)):p
+s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))]
++*iii1
+n@t10:=andi(cutprop1a,cutprop1b,nonemptyi(rat,s,x0,i),th1"l.all"(rat,[x:rat]in(x,s),y0,n)):cutprop1
+-iii1
+s@[n:[x:rat]not(max(s,x))]
++*iii1
+n@t11:=th5"l.some"(rat,[x:rat]max(s,x),n):cutprop3
+-iii1
+s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][l:[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]less(x,y)][m:[x:rat]not(max(s,x))]
+cut1:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),l,t11".iii1"(m)):cutprop(s)
++rp
+ksi@[eta:cut]
+is:=is"e"(cut,ksi,eta):'prop'
+nis:=not(is(ksi,eta)):'prop'
+[i:is(ksi,eta)]
+ise:=isini(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is"e"(set(rat),lcl(ksi),lcl(eta))
+[x0:rat][lx:lrt(ksi,x0)]
+ise1:=issete1(rat,lcl(ksi),lcl(eta),ise,x0,lx):lrt(eta,x0)
+eta@[i:is"e"(set(rat),lcl(ksi),lcl(eta))]
+isi:=isine(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is(ksi,eta)
+eta@[l:[x:rat][t:lrt(ksi,x)]lrt(eta,x)][k:[x:rat][t:lrt(eta,x)]lrt(ksi,x)]
+isi1:=isi(isseti(rat,lcl(ksi),lcl(eta),l,k)):is(ksi,eta)
+@[s:set(rat)][cs:cutprop(s)]
+cutof:=out(set(rat),[x:set(rat)]cutprop(x),s,cs):cut
+[x0:rat][i:in(x0,s)]
+ine:=issete1(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,i):lrt(cutof(s,cs),x0)
+x0@[lx:lrt(cutof(s,cs),x0)]
+ini:=issete2(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,lx):in(x0,s)
+s@[t:set(rat)][cs:cutprop(s)][ct:cutprop(t)][i:[x:rat][u:in(x,s)]in(x,t)][j:[x:rat][u:in(x,t)]in(x,s)]
+isi2:=isouti(set(rat),[x:set(rat)]cutprop(x),s,cs,t,ct,isseti(rat,s,t,i,j)):is(cutof(s,cs),cutof(t,ct))
+@[p:[x:cut]'prop']
+all:=all"l"(cut,p):'prop'
+some:=some"l"(cut,p):'prop'
+one:=one"e"(cut,p):'prop'
+ksi@satz116:=refis(cut,ksi):is(ksi,ksi)
+eta@[i:is(ksi,eta)]
+satz117:=symis(cut,ksi,eta,i):is(eta,ksi)
+eta@[zeta:cut][i:is(ksi,eta)][j:is(eta,zeta)]
+satz118:=tris(cut,ksi,eta,zeta,i,j):is(ksi,zeta)
++1119
+@[x0:rat][y0:rat][m:more(x0,y0)]
+t1:=ec3e23(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),m):not(less(x0,y0))
+-1119
+ksi@[x0:rat][ux:urt(ksi,x0)][y0:rat][m:more(y0,x0)]
+satz119:=th3"l.imp"(lrt(ksi,y0),less(y0,x0),t1".1119"(y0,x0,m),[t:lrt(ksi,y0)]cutapp2a(y0,t,x0,ux)):urt(ksi,y0)
+y0@[l:less(x0,y0)]
+satz119a:=satz119(satz83(x0,y0,l)):urt(ksi,y0)
++1120
+@[x0:rat][y0:rat][l:less(x0,y0)]
+t1:=ec3e32(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),l):not(more(x0,y0))
+-1120
+ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][l:less(y0,x0)]
+satz120:=th7"l.imp"(lrt(ksi,y0),more(y0,x0),t1".1120"(y0,x0,l),[t:urt(ksi,y0)]cutapp2b(x0,lx,y0,t)):lrt(ksi,y0)
+y0@[m:more(x0,y0)]
+satz120a:=satz120(satz82(x0,y0,m)):lrt(ksi,y0)
+-rp
+s@[i:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][x0:rat][j:in(x0,s)][y0:rat][n:not(in(y0,s))]
++*iii1
+n@t12:=<y0><j><x0>i:[u:less(y0,x0)]in(y0,s)
+t13:=th3"l.imp"(less(y0,x0),in(y0,s),n,t12):not(less(y0,x0))
+t14:=satz81f(y0,x0,t13):moreis(y0,x0)
+-iii1
+n@[k:is(y0,x0)]
++*iii1
+k@t15:=isp1(rat,[x:rat]in(x,s),x0,y0,j,k):in(y0,s)
+n@t16:=th3"l.imp"(is(y0,x0),in(y0,s),n,[t:is(y0,x0)]t15(t)):nis(y0,x0)
+t17:=ore1(more(y0,x0),is(y0,x0),t14,t16):more(y0,x0)
+t18:=satz82(y0,x0,t17):less(x0,y0)
+i@t19:=[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]t18(x,t,y,u):cutprop2
+-iii1
+s@[s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))][x0:rat][i:in(x0,s)]
++*iii1
+i@t20:=<i><x0>s1:some([y:rat]and(in(y,s),more(y,x0)))
+-iii1
+i@[y0:rat][a:and(in(y0,s),more(y0,x0))]
++*iii1
+a@t21:=ande1(in(y0,s),more(y0,x0),a):in(y0,s)
+t22:=ande2(in(y0,s),more(y0,x0),a):more(y0,x0)
+t23:=satz81g(y0,x0,t22):not(lessis(y0,x0))
+t24:=th3"l.imp"(moreis(x0,y0),lessis(y0,x0),t23,[t:moreis(x0,y0)]satz84(x0,y0,t)):not(moreis(x0,y0))
+t25:=th4"l.imp"(in(y0,s),moreis(x0,y0),t21,t24):not(ubprop(x0,y0))
+t26:=th1"l.all"(rat,[y:rat]ubprop(x0,y),y0,t25):not(ub(s,x0))
+t27:=th1"l.and"(ub(s,x0),in(x0,s),t26):not(max(s,x0))
+i@t28:=someapp(rat,[y:rat]and(in(y,s),more(y,x0)),t20,not(max(s,x0)),[y:rat][t:and(in(y,s),more(y,x0))]t27(y,t)):not(max(s,x0))
+-iii1
+x0@[n:not(in(x0,s))]
++*iii1
+n@t29:=th2"l.and"(ub(x0),in(x0,s),n):not(max(s,x0))
+x0@t30:=th1"l.imp"(in(x0,s),not(max(s,x0)),[u:in(x0,s)]t28(u),[u:not(in(x0,s))]t29(u)):not(max(s,x0))
+s1@t31:=t11([x:rat]t30(x)):cutprop3
+-iii1
+s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][j:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))]
+cut2:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),t19".iii1"(j),t31".iii1"(s1)):cutprop(s)
++*rp
+eta@more:=some"rt"([x:rat]and(lrt(ksi,x),urt(eta,x))):'prop'
+[m:more(ksi,eta)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]p][x0:rat][a:and(lrt(ksi,x0),urt(eta,x0))]
++iii2
+t1:=ande1(lrt(ksi,x0),urt(eta,x0),a):lrt(ksi,x0)
+t2:=ande2(lrt(ksi,x0),urt(eta,x0),a):urt(eta,x0)
+t3:=<t2><t1><x0>p1:p
+-iii2
+p1@moreapp:=someapp(rat,[x:rat]and(lrt(ksi,x),urt(eta,x)),m,p,[x:rat][t:and(lrt(ksi,x),urt(eta,x))]t3".iii2"(x,t)):p
+eta@less:=some"rt"([x:rat]and(urt(ksi,x),lrt(eta,x))):'prop'
+[l:less(ksi,eta)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]p][x0:rat][a:and(urt(ksi,x0),lrt(eta,x0))]
++*iii2
+a@t4:=ande1(urt(ksi,x0),lrt(eta,x0),a):urt(ksi,x0)
+t5:=ande2(urt(ksi,x0),lrt(eta,x0),a):lrt(eta,x0)
+t6:=<t5><t4><x0>p1:p
+-iii2
+p1@lessapp:=someapp(rat,[x:rat]and(urt(ksi,x),lrt(eta,x)),l,p,[x:rat][t:and(urt(ksi,x),lrt(eta,x))]t6".iii2"(x,t)):p
+eta@[m:more(ksi,eta)]
++2121
+[x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
+t1:=andi(urt(eta,x0),lrt(ksi,x0),ux,lx):and(urt(eta,x0),lrt(ksi,x0))
+t2:=somei(rat,[x:rat]and(urt(eta,x),lrt(ksi,x)),x0,t1):less(eta,ksi)
+-2121
+satz121:=moreapp(m,less(eta,ksi),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2".2121"(x,t,u)):less(eta,ksi)
+eta@[l:less(ksi,eta)]
++2122
+[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
+t1:=andi(lrt(eta,x0),urt(ksi,x0),lx,ux):and(lrt(eta,x0),urt(ksi,x0))
+t2:=somei(rat,[x:rat]and(lrt(eta,x),urt(ksi,x)),x0,t1):more(eta,ksi)
+-2122
+satz122:=lessapp(l,more(eta,ksi),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t2".2122"(x,t,u)):more(eta,ksi)
++2123
+eta@[m:more(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
+t1:=th3"st.isset"(rat,lcl(ksi),lcl(eta),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
+t2:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t1,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
+m@t3:=moreapp(ksi,eta,m,not(is(ksi,eta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2(x,t,u)):not(is(ksi,eta))
+eta@t4:=th2"l.ec"(is(ksi,eta),more(ksi,eta),[t:more(ksi,eta)]t3(t)):ec(is(ksi,eta),more(ksi,eta))
+[l:less(ksi,eta)][x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
+t5:=th4"st.isset"(rat,lcl(eta),lcl(ksi),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
+t6:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t5,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
+l@t7:=lessapp(ksi,eta,l,not(is(ksi,eta)),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t6(x,t,u)):not(is(ksi,eta))
+eta@t8:=th1"l.ec"(less(ksi,eta),is(ksi,eta),[t:less(ksi,eta)]t7(t)):ec(less(ksi,eta),is(ksi,eta))
+m@[l:less(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)][y0:rat][uy:urt(ksi,y0)][ly:lrt(eta,y0)]
+t9:=cutapp2a(ksi,x0,lx,y0,uy):less"rt"(x0,y0)
+t10:=cutapp2b(eta,y0,ly,x0,ux):more"rt"(x0,y0)
+t11:=mp(less"rt"(x0,y0),con,t9,ec3e23(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),satz81b(x0,y0),t10)):con
+ux@t12:=lessapp(ksi,eta,l,con,[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t11(x,t,u)):con
+l@t13:=moreapp(ksi,eta,m,con,[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t12(x,t,u)):con
+m@t14:=[t:less(ksi,eta)]t13(t):not(less(ksi,eta))
+eta@t15:=th1"l.ec"(more(ksi,eta),less(ksi,eta),[t:more(ksi,eta)]t14(t)):ec(more(ksi,eta),less(ksi,eta))
+a:=th6"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t4,t15,t8):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+[i:is(ksi,eta)]
+t16:=or3i1(is(ksi,eta),more(ksi,eta),less(ksi,eta),i):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+eta@[n:nis(ksi,eta)]
+t17:=th3"l.imp"(is"e"(set(rat),lcl(ksi),lcl(eta)),is(ksi,eta),n,[t:is"e"(set(rat),lcl(ksi),lcl(eta))]isi(ksi,eta,t)):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
+t18:=th5"st.isset"(rat,lcl(ksi),lcl(eta),t17):or(more(ksi,eta),more(eta,ksi))
+t19:=th8"l.or"(more(ksi,eta),more(eta,ksi),less(ksi,eta),t18,[t:more(eta,ksi)]satz121(eta,ksi,t)):or(more(ksi,eta),less(ksi,eta))
+t20:=th7"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t19):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+eta@b:=th1"l.imp"(is(ksi,eta),or3(is(ksi,eta),more(ksi,eta),less(ksi,eta)),[t:is(ksi,eta)]t16(t),[t:nis(ksi,eta)]t20(t)):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+-2123
+eta@satz123:=orec3i(is(ksi,eta),more(ksi,eta),less(ksi,eta),b".2123",a".2123"):orec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+satz123a:=orec3e1(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+satz123b:=orec3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+moreis:=or(more(ksi,eta),is(ksi,eta)):'prop'
+lessis:=or(less(ksi,eta),is(ksi,eta)):'prop'
+[m:moreis(ksi,eta)]
+satz124:=th9"l.or"(more(ksi,eta),is(ksi,eta),less(eta,ksi),is(eta,ksi),m,[t:more(ksi,eta)]satz121(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):lessis(eta,ksi)
+eta@[l:lessis(ksi,eta)]
+satz125:=th9"l.or"(less(ksi,eta),is(ksi,eta),more(eta,ksi),is(eta,ksi),l,[t:less(ksi,eta)]satz122(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):moreis(eta,ksi)
+zeta@[i:is(ksi,eta)][m:more(ksi,zeta)]
+ismore1:=isp(cut,[u:cut]more(u,zeta),ksi,eta,m,i):more(eta,zeta)
+i@[m:more(zeta,ksi)]
+ismore2:=isp(cut,[u:cut]more(zeta,u),ksi,eta,m,i):more(zeta,eta)
+i@[l:less(ksi,zeta)]
+isless1:=isp(cut,[u:cut]less(u,zeta),ksi,eta,l,i):less(eta,zeta)
+i@[l:less(zeta,ksi)]
+isless2:=isp(cut,[u:cut]less(zeta,u),ksi,eta,l,i):less(zeta,eta)
+i@[m:moreis(ksi,zeta)]
+ismoreis1:=isp(cut,[u:cut]moreis(u,zeta),ksi,eta,m,i):moreis(eta,zeta)
+i@[m:moreis(zeta,ksi)]
+ismoreis2:=isp(cut,[u:cut]moreis(zeta,u),ksi,eta,m,i):moreis(zeta,eta)
+i@[l:lessis(ksi,zeta)]
+islessis1:=isp(cut,[u:cut]lessis(u,zeta),ksi,eta,l,i):lessis(eta,zeta)
+i@[l:lessis(zeta,ksi)]
+islessis2:=isp(cut,[u:cut]lessis(zeta,u),ksi,eta,l,i):lessis(zeta,eta)
+eta@[i:is(ksi,eta)]
+moreisi2:=ori2(more(ksi,eta),is(ksi,eta),i):moreis(ksi,eta)
+lessisi2:=ori2(less(ksi,eta),is(ksi,eta),i):lessis(ksi,eta)
+eta@[m:more(ksi,eta)]
+moreisi1:=ori1(more(ksi,eta),is(ksi,eta),m):moreis(ksi,eta)
+eta@[l:less(ksi,eta)]
+lessisi1:=ori1(less(ksi,eta),is(ksi,eta),l):lessis(ksi,eta)
+zeta@[upsilon:cut][i:is(ksi,eta)][j:is(zeta,upsilon)][m:more(ksi,zeta)]
+ismore12:=ismore2(zeta,upsilon,eta,j,ismore1(ksi,eta,zeta,i,m)):more(eta,upsilon)
+j@[l:less(ksi,zeta)]
+isless12:=isless2(zeta,upsilon,eta,j,isless1(ksi,eta,zeta,i,l)):less(eta,upsilon)
+j@[m:moreis(ksi,zeta)]
+ismoreis12:=ismoreis2(zeta,upsilon,eta,j,ismoreis1(ksi,eta,zeta,i,m)):moreis(eta,upsilon)
+j@[l:lessis(ksi,zeta)]
+islessis12:=islessis2(zeta,upsilon,eta,j,islessis1(ksi,eta,zeta,i,l)):lessis(eta,upsilon)
+eta@[m:moreis(ksi,eta)]
+satz123c:=th7"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,comor(more(ksi,eta),is(ksi,eta),m)):not(less(ksi,eta))
+eta@[l:lessis(ksi,eta)]
+satz123d:=th9"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l):not(more(ksi,eta))
+eta@[n:not(more(ksi,eta))]
+satz123e:=th2"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n):lessis(ksi,eta)
+eta@[n:not(less(ksi,eta))]
+satz123f:=comor(is(ksi,eta),more(ksi,eta),th3"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n)):moreis(ksi,eta)
+eta@[m:more(ksi,eta)]
+satz123g:=th3"l.or"(less(ksi,eta),is(ksi,eta),ec3e23(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m),ec3e21(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m)):not(lessis(ksi,eta))
+eta@[l:less(ksi,eta)]
+satz123h:=th3"l.or"(more(ksi,eta),is(ksi,eta),ec3e32(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l),ec3e31(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l)):not(moreis(ksi,eta))
+eta@[n:not(moreis(ksi,eta))]
+satz123j:=or3e3(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th5"l.or"(more(ksi,eta),is(ksi,eta),n),th4"l.or"(more(ksi,eta),is(ksi,eta),n)):less(ksi,eta)
+eta@[n:not(lessis(ksi,eta))]
+satz123k:=or3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th4"l.or"(less(ksi,eta),is(ksi,eta),n),th5"l.or"(less(ksi,eta),is(ksi,eta),n)):more(ksi,eta)
+zeta@[l:less(ksi,eta)][k:less(eta,zeta)]
++2126
+[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)][y0:rat][uy:urt(eta,y0)][ly:lrt(zeta,y0)]
+t1:=cutapp2a(eta,x0,lx,y0,uy):less"rt"(x0,y0)
+t2:=satz119a(ksi,x0,ux,y0,t1):urt(ksi,y0)
+t3:=andi(urt(ksi,y0),lrt(zeta,y0),t2,ly):and(urt(ksi,y0),lrt(zeta,y0))
+t4:=somei(rat,[x:rat]and(urt(ksi,x),lrt(zeta,x)),y0,t3):less(ksi,zeta)
+lx@t5:=lessapp(eta,zeta,k,less(ksi,zeta),[x:rat][t:urt(eta,x)][u:lrt(zeta,x)]t4(x,t,u)):less(ksi,zeta)
+-2126
+satz126:=lessapp(ksi,eta,l,less(ksi,zeta),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t5".2126"(x,t,u)):less(ksi,zeta)
+trless:=satz126:less(ksi,zeta)
+zeta@[m:more(ksi,eta)][n:more(eta,zeta)]
+trmore:=satz122(zeta,ksi,satz126(zeta,eta,ksi,satz121(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
+zeta@[l:lessis(ksi,eta)][k:less(eta,zeta)]
+satz127a:=orapp(less(ksi,eta),is(ksi,eta),less(ksi,zeta),l,[u:less(ksi,eta)]trless(u,k),[u:is(ksi,eta)]isless1(eta,ksi,zeta,symis(cut,ksi,eta,u),k)):less(ksi,zeta)
+zeta@[l:less(ksi,eta)][k:lessis(eta,zeta)]
+satz127b:=orapp(less(eta,zeta),is(eta,zeta),less(ksi,zeta),k,[u:less(eta,zeta)]trless(l,u),[u:is(eta,zeta)]isless2(eta,zeta,ksi,u,l)):less(ksi,zeta)
+zeta@[m:moreis(ksi,eta)][n:more(eta,zeta)]
+satz127c:=satz122(zeta,ksi,satz127b(zeta,eta,ksi,satz121(eta,zeta,n),satz124(ksi,eta,m))):more(ksi,zeta)
+zeta@[m:more(ksi,eta)][n:moreis(eta,zeta)]
+satz127d:=satz122(zeta,ksi,satz127a(zeta,eta,ksi,satz124(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
+zeta@[l:lessis(ksi,eta)][k:lessis(eta,zeta)]
++2128
+[i:is(ksi,eta)][j:is(eta,zeta)]
+t1:=lessisi2(ksi,zeta,tris(cut,ksi,eta,zeta,i,j)):lessis(ksi,zeta)
+i@[j:less(eta,zeta)]
+t2:=lessisi1(ksi,zeta,satz127a(l,j)):lessis(ksi,zeta)
+i@t3:=orapp(less(eta,zeta),is(eta,zeta),lessis(ksi,zeta),k,[t:less(eta,zeta)]t2(t),[t:is(eta,zeta)]t1(t)):lessis(ksi,zeta)
+k@[j:less(ksi,eta)]
+t4:=lessisi1(ksi,zeta,satz127b(j,k)):lessis(ksi,zeta)
+-2128
+satz128:=orapp(less(ksi,eta),is(ksi,eta),lessis(ksi,zeta),l,[t:less(ksi,eta)]t4".2128"(t),[t:is(ksi,eta)]t3".2128"(t)):lessis(ksi,zeta)
+trlessis:=satz128:lessis(ksi,zeta)
+zeta@[m:moreis(ksi,eta)][n:moreis(eta,zeta)]
+trmoreis:=satz125(zeta,ksi,satz128(zeta,eta,ksi,satz124(eta,zeta,n),satz124(ksi,eta,m))):moreis(ksi,zeta)
+eta@[z0:rat][x0:rat][y0:rat]
+sumprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0))):'prop'
+z0@sumprop:=some"rt"([x:rat]some"rt"([y:rat]sumprop1(z0,x,y))):'prop'
+eta@sum:=setof(rat,[z:rat]sumprop(z)):set(rat)
+x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl(x0,y0))]
++iii3
+t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),lx,ly,i):sumprop1(z0,x0,y0)
+t2:=somei(rat,[y:rat]sumprop1(z0,x0,y),y0,t1):some"rt"([y:rat]sumprop1(z0,x0,y))
+t3:=somei(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),x0,t2):sumprop(z0)
+-iii3
+sum1:=estii(rat,[z:rat]sumprop(z),z0,t3".iii3"):in(z0,sum)
+z0@[i:in(z0,sum)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]p]
++*iii3
+p1@t4:=estie(rat,[z:rat]sumprop(z),z0,i):sumprop(z0)
+-iii3
+p1@[x0:rat][px:some"rt"([y:rat]sumprop1(z0,x0,y))][y0:rat][py:sumprop1(z0,x0,y0)]
++*iii3
+py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(ksi,x0)
+t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(eta,y0)
+t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):is"rt"(z0,pl(x0,y0))
+t8:=<t7><t6><y0><t5><x0>p1:p
+px@t9:=someapp(rat,[y:rat]sumprop1(z0,x0,y),px,p,[y:rat][t:sumprop1(z0,x0,y)]t8(y,t)):p
+-iii3
+p1@sumapp:=someapp(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),t4".iii3",p,[x:rat][t:some"rt"([y:rat]sumprop1(z0,x,y))]t9".iii3"(x,t)):p
+eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
++3129
+[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))]
+t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
+t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
+t3:=isless1"rt"(pl(x0,y0),z0,pl(x1,y1),symis(rat,z0,pl(x0,y0),j),satz98a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,pl(x1,y1))
+t4:=ec3e31(is"rt"(z0,pl(x1,y1)),more"rt"(z0,pl(x1,y1)),less"rt"(z0,pl(x1,y1)),satz81b(z0,pl(x1,y1)),t3):nis"rt"(z0,pl(x1,y1))
+i@t5:=sumapp(ksi,eta,z0,i,nis"rt"(z0,pl(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,pl(x1,y1))
+-3129
+satz129a:=th3"l.imp"(in(pl(x1,y1),sum),nis"rt"(pl(x1,y1),pl(x1,y1)),weli(is"rt"(pl(x1,y1),pl(x1,y1)),refis(rat,pl(x1,y1))),[t:in(pl(x1,y1),sum)]t5".3129"(pl(x1,y1),t)):not(in(pl(x1,y1),sum))
++*3129
+eta@[u0:rat][i:in(u0,sum)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,pl(x0,y0))]
+t6:=isless2"rt"(u0,pl(x0,y0),z0,j,l):less"rt"(z0,pl(x0,y0))
+z1:=ov(z0,pl(x0,y0)):rat
+t7:=isless12"rt"(z0,ts(z1,pl(x0,y0)),pl(x0,y0),ts(1rt,pl(x0,y0)),satz110f(z0,pl(x0,y0)),example1d(pl(x0,y0)),t6):less"rt"(ts(z1,pl(x0,y0)),ts(1rt,pl(x0,y0)))
+t8:=satz106c(z1,1rt,pl(x0,y0),t7):less"rt"(z1,1rt)
+t9:=isless2"rt"(ts(x0,1rt),x0,ts(x0,z1),example1a(x0),satz105f(z1,1rt,x0,t8)):less"rt"(ts(x0,z1),x0)
+t10:=isless2"rt"(ts(y0,1rt),y0,ts(y0,z1),example1a(y0),satz105f(z1,1rt,y0,t8)):less"rt"(ts(y0,z1),y0)
+t11:=satz120(ksi,x0,lx,ts(x0,z1),t9):lrt(ksi,ts(x0,z1))
+t12:=satz120(eta,y0,ly,ts(y0,z1),t10):lrt(eta,ts(y0,z1))
+t13:=tris(rat,pl(ts(x0,z1),ts(y0,z1)),ts(pl(x0,y0),z1),z0,distpt1(x0,y0,z1),satz110c(z0,pl(x0,y0))):is"rt"(pl(ts(x0,z1),ts(y0,z1)),z0)
+t14:=symis(rat,pl(ts(x0,z1),ts(y0,z1)),z0,t13):is"rt"(z0,pl(ts(x0,z1),ts(y0,z1)))
+t15:=sum1(ksi,eta,z0,ts(x0,z1),t11,ts(y0,z1),t12,t14):in(z0,sum)
+l@t16:=sumapp(ksi,eta,u0,i,in(z0,sum),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,pl(x,y))]t15(x,t,y,u,v)):in(z0,sum)
+eta@[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
+t17:=sum1(ksi,eta,pl(x1,y0),x1,lx1,y0,ly,refis(rat,pl(x1,y0))):in(pl(x1,y0),sum)
+t18:=satz96a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(pl(x1,y0),pl(x0,y0))
+t19:=ismore2"rt"(pl(x0,y0),z0,pl(x1,y0),symis(rat,z0,pl(x0,y0),j),t18):more"rt"(pl(x1,y0),z0)
+t20:=andi(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0),t17,t19):and(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0))
+t21:=somei(rat,[y:rat]and(in(y,sum),more"rt"(y,z0)),pl(x1,y0),t20):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
+j@t22:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t21(x,t,u)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
+i@t23:=sumapp(ksi,eta,z0,i,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t22(x,t,y,u,v)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
+eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
+t24:=cut2(sum,pl(x0,y0),sum1(ksi,eta,pl(x0,y0),x0,lx,y0,ly,refis(rat,pl(x0,y0))),pl(x1,y1),satz129a(x1,ux,y1,uy),[x:rat][t:in(x,sum)][y:rat][u:less"rt"(y,x)]t16(x,t,y,u),[x:rat][t:in(x,sum)]t23(x,t)):cutprop(sum)
+ux@t25:=cutapp1b(eta,cutprop(sum),[y:rat][t:urt(eta,y)]t24(y,t)):cutprop(sum)
+ly@t26:=cutapp1b(ksi,cutprop(sum),[x:rat][t:urt(ksi,x)]t25(x,t)):cutprop(sum)
+lx@t27:=cutapp1a(eta,cutprop(sum),[y:rat][t:lrt(eta,y)]t26(y,t)):cutprop(sum)
+-3129
+eta@satz129:=cutapp1a(ksi,cutprop(sum),[x:rat][t:lrt(ksi,x)]t27".3129"(x,t)):cutprop(sum)
+pl:=cutof(sum,satz129):cut
+[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
+lrtpl:=ine(sum,satz129,z0,sum1(z0,x0,lx,y0,ly,i)):lrt(pl(ksi,eta),z0)
+eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
++*iii3
+i@t10:=isp1(rat,[x:rat]not(in(x,sum)),pl"rt"(x0,y0),z0,satz129a(x0,ux,y0,uy),i):not(in(z0,sum))
+-iii3
+i@urtpl:=th3"l.imp"(lrt(pl(ksi,eta),z0),in(z0,sum),t10".iii3",[t:lrt(pl(ksi,eta),z0)]ini(sum,satz129,z0,t)):urt(pl(ksi,eta),z0)
+eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]p]
++*iii3
+p1@t11:=ini(sum,satz129,z0,lz):in(z0,sum)
+-iii3
+p1@plapp:=sumapp(z0,t11".iii3",p,p1):p
+zeta@[i:is(ksi,eta)]
+ispl1:=isf(cut,cut,[u:cut]pl(u,zeta),ksi,eta,i):is(pl(ksi,zeta),pl(eta,zeta))
+ispl2:=isf(cut,cut,[u:cut]pl(zeta,u),ksi,eta,i):is(pl(zeta,ksi),pl(zeta,eta))
+upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
+ispl12:=tris(cut,pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),ispl1(i),ispl2(zeta,upsilon,eta,j)):is(pl(ksi,zeta),pl(eta,upsilon))
++3130
+eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
+t1:=tris(rat,z0,pl"rt"(x0,y0),pl"rt"(y0,x0),i,compl(x0,y0)):is"rt"(z0,pl"rt"(y0,x0))
+t2:=lrtpl(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(pl(eta,ksi),z0)
+lz@t3:=plapp(ksi,eta,z0,lz,lrt(pl(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]t2(x,t,y,u,v)):lrt(pl(eta,ksi),z0)
+-3130
+eta@satz130:=isi1(pl(ksi,eta),pl(eta,ksi),[x:rat][t:lrt(pl(ksi,eta),x)]t3".3130"(x,t),[x:rat][t:lrt(pl(eta,ksi),x)]t3".3130"(eta,ksi,x,t)):is(pl(ksi,eta),pl(eta,ksi))
+compl:=satz130:is(pl(ksi,eta),pl(eta,ksi))
++3131
+zeta@[u0:rat][lu:lrt(pl(pl(ksi,eta),zeta),u0)][v0:rat][lv:lrt(pl(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,pl"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,pl"rt"(x0,y0))]
+t1:=tr3is(rat,u0,pl"rt"(v0,z0),pl"rt"(pl"rt"(x0,y0),z0),pl"rt"(x0,pl"rt"(y0,z0)),i,ispl1"rt"(v0,pl"rt"(x0,y0),z0,j),asspl1(x0,y0,z0)):is"rt"(u0,pl"rt"(x0,pl"rt"(y0,z0)))
+t2:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
+t3:=lrtpl(ksi,pl(eta,zeta),u0,x0,lx,pl"rt"(y0,z0),t2,t1):lrt(pl(ksi,pl(eta,zeta)),u0)
+i@t4:=plapp(ksi,eta,v0,lv,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,pl"rt"(x,y))]t3(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
+lu@t5:=plapp(pl(ksi,eta),zeta,u0,lu,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(pl(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
+u0@[lu:lrt(pl(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,pl"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
+t6:=tr3is(rat,u0,pl"rt"(x0,v0),pl"rt"(x0,pl"rt"(y0,z0)),pl"rt"(pl"rt"(x0,y0),z0),i,ispl2"rt"(v0,pl"rt"(y0,z0),x0,j),asspl2(x0,y0,z0)):is"rt"(u0,pl"rt"(pl"rt"(x0,y0),z0))
+t7:=lrtpl(ksi,eta,pl"rt"(x0,y0),x0,lx,y0,ly,refis(rat,pl"rt"(x0,y0))):lrt(pl(ksi,eta),pl"rt"(x0,y0))
+t8:=lrtpl(pl(ksi,eta),zeta,u0,pl"rt"(x0,y0),t7,z0,lz,t6):lrt(pl(pl(ksi,eta),zeta),u0)
+i@t9:=plapp(eta,zeta,v0,lv,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t8(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
+lu@t10:=plapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t9(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
+-3131
+zeta@satz131:=isi1(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),[x:rat][t:lrt(pl(pl(ksi,eta),zeta),x)]t5".3131"(x,t),[x:rat][t:lrt(pl(ksi,pl(eta,zeta)),x)]t10".3131"(x,t)):is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
+asspl1:=satz131:is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
+asspl2:=symis(cut,pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),satz131):is(pl(ksi,pl(eta,zeta)),pl(pl(ksi,eta),zeta))
+ksi@[a0:rat]
++3132
+[x0:rat][y0:rat]
+prop1:=and(lrt(ksi,x0),urt(ksi,y0)):'prop'
+[p:prop1]
+t1:=cutapp2b(x0,ande1(lrt(ksi,x0),urt(ksi,y0),p),y0,ande2(lrt(ksi,x0),urt(ksi,y0),p)):more"rt"(y0,x0)
+prop2:=is"rt"(mn(y0,x0,t1),a0):'prop'
+y0@prop3:=and(prop1,[t:prop1]prop2(t)):'prop'
+a0@prop4:=some"rt"([x:rat]some"rt"([y:rat]prop3(x,y))):'prop'
+x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
+t2:=cutapp2b(x0,lx,y0,uy):more"rt"(y0,x0)
+[n:nat][m:more"rt"(ts(rtofn(n),a0),mn(y0,x0,t2))]
+t3:=satz96d(ts(rtofn(n),a0),mn(y0,x0,t2),x0,m):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),pl"rt"(x0,mn(y0,x0,t2)))
+t4:=ismore2"rt"(pl"rt"(x0,mn(y0,x0,t2)),y0,pl"rt"(x0,ts(rtofn(n),a0)),satz101c(y0,x0,t2),t3):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),y0)
+t5:=satz119(y0,uy,pl"rt"(x0,ts(rtofn(n),a0)),t4):urt(pl"rt"(x0,ts(rtofn(n),a0)))
+t6:=somei(nat,[x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),n,t5):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
+uy@t7:=someapp(nat,[x:nat]more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2)),satz115(a0,mn(y0,x0,t2)),some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0)))),[x:nat][t:more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2))]t6(x,t)):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
+[u:nat][m:min"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)]
+t8:=ande1(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)
+t9:=ande2(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):urt(pl"rt"(x0,ts(rtofn(u),a0)))
+[i:is"n"(u,1)]
+u0:=pl"rt"(x0,a0):rat
+t10:=tr3is(rat,ts(rtofn(u),a0),ts(1rt,a0),ts(a0,1rt),a0,ists1(rtofn(u),1rt,a0,isnert(u,1,i)),comts(1rt,a0),example1a(a0)):is"rt"(ts(rtofn(u),a0),a0)
+t11:=isp(rat,[x:rat]urt(pl"rt"(x0,x)),ts(rtofn(u),a0),a0,t9,t10):urt(ksi,u0)
+t12:=andi(lrt(ksi,x0),urt(ksi,u0),lx,t11):prop1(x0,u0)
+[p:prop1(x0,u0)]
+t13:=symis(rat,a0,mn(u0,x0,t1(x0,u0,p)),satz101g(u0,x0,a0,t1(x0,u0,p),refis(rat,u0))):prop2(x0,u0,p)
+i@t14:=andi(prop1(x0,u0),[t:prop1(x0,u0)]prop2(x0,u0,t),t12,[t:prop1(x0,u0)]t13(t)):prop3(x0,u0)
+t15:=somei(rat,[y:rat]prop3(x0,y),u0,t14):some"rt"([y:rat]prop3(x0,y))
+t16:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),x0,t15):prop4
+m@[o:more"n"(u,1)]
+t17:=morei(rtofn(u),1rt,fr(u,1),fr(1,1),inclass(fr(u,1)),inclass(fr(1,1)),satz111d(u,1,o)):more"rt"(rtofn(u),1rt)
+um10:=mn(rtofn(u),1rt,t17):rat
+t18:=satz112g(rtofn(u),natrti(u),1rt,natrti(1),t17):natrt(um10)
+um1:=nofrt(um10,t18):nat
+v0:=pl"rt"(x0,ts(um10,a0)):rat
+w0:=pl"rt"(x0,ts(rtofn(u),a0)):rat
+t19:=isless2"rt"(pl"rt"(um10,1rt),rtofn(u),um10,satz101e(rtofn(u),1rt,t17),satz94a(um10,1rt)):less"rt"(um10,rtofn(u))
+t20:=lesse(um10,rtofn(u),fr(um1,1),fr(u,1),inclassn(um10,t18),inclass(fr(u,1)),t19):lessf(fr(um1,1),fr(u,1))
+t21:=satz111c(um1,u,t20):less"n"(um1,u)
+t22:=th3"l.imp"(lessis"n"(u,um1),moreis"n"(um1,u),satz10h(um1,u,t21),[t:lessis"n"(u,um1)]satz14(u,um1,t)):not(lessis"n"(u,um1))
+t23:=et(lrt(pl"rt"(x0,ts(rtofn(um1),a0))),th3"l.imp"(urt(pl"rt"(x0,ts(rtofn(um1),a0))),lessis"n"(u,um1),t22,<um1>t8)):lrt(pl"rt"(x0,ts(rtofn(um1),a0)))
+t24:=isp1(rat,[x:rat]lrt(pl"rt"(x0,ts(x,a0))),rtofn(um1),um10,t23,isrtn1(um10,t18)):lrt(ksi,v0)
+t25:=andi(lrt(ksi,v0),urt(ksi,w0),t24,t9):prop1(v0,w0)
+t26:=tr3is(rat,pl"rt"(ts(um10,a0),a0),pl"rt"(ts(um10,a0),ts(1rt,a0)),ts(pl"rt"(um10,1rt),a0),ts(rtofn(u),a0),ispl2"rt"(a0,ts(1rt,a0),ts(um10,a0),example1d(a0)),distpt1(um10,1rt,a0),ists1(pl"rt"(um10,1rt),rtofn(u),a0,satz101e(rtofn(u),1rt,t17))):is"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0))
+t27:=tris(rat,pl"rt"(v0,a0),pl"rt"(x0,pl"rt"(ts(um10,a0),a0)),w0,asspl1"rt"(x0,ts(um10,a0),a0),ispl2"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0),x0,t26)):is"rt"(pl"rt"(v0,a0),w0)
+[p:prop1(v0,w0)]
+t28:=symis(rat,a0,mn(w0,v0,t1(v0,w0,p)),satz101g(w0,v0,a0,t1(v0,w0,p),t27)):prop2(v0,w0,p)
+o@t29:=andi(prop1(v0,w0),[t:prop1(v0,w0)]prop2(v0,w0,t),t25,[t:prop1(v0,w0)]t28(t)):prop3(v0,w0)
+t30:=somei(rat,[y:rat]prop3(v0,y),w0,t29):some"rt"([y:rat]prop3(v0,y))
+t31:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),v0,t30):prop4
+m@t32:=orapp(more"n"(u,1),is"n"(u,1),prop4,satz24(u),[t:more"n"(u,1)]t31(t),[t:is"n"(u,1)]t16(t)):prop4
+uy@t34:=someapp(nat,[x:nat]min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x),satz27([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),t7),prop4,[x:nat][t:min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x)]t32(x,t)):prop4
+lx@t35:=cutapp1b(prop4,[y:rat][t:urt(ksi,y)]t34(y,t)):prop4
+-3132
+satz132:=cutapp1a(prop4".3132",[x:rat][t:lrt(ksi,x)]t35".3132"(x,t)):some"rt"([x:rat]some"rt"([y:rat]and(and(lrt(ksi,x),urt(ksi,y)),[t:and(lrt(ksi,x),urt(ksi,y))]is"rt"(mn(y,x,cutapp2b(x,ande1(lrt(ksi,x),urt(ksi,y),t),y,ande2(lrt(ksi,x),urt(ksi,y),t))),a0))))
+ksi@[p:'prop'][a0:rat][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),a0)]p]
++*3132
+p1@[x0:rat][s:some"rt"([y:rat]prop3(a0,x0,y))][y0:rat][p3:prop3(a0,x0,y0)]
+t36:=ande1(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop1(a0,x0,y0)
+t37:=ande2"l.r"(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop2(a0,x0,y0,t36)
+t38:=ande1(lrt(ksi,x0),urt(ksi,y0),t36):lrt(ksi,x0)
+t39:=ande2(lrt(ksi,x0),urt(ksi,y0),t36):urt(ksi,y0)
+t40:=satz101g(y0,x0,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),t1(a0,x0,y0,t36),satz101c(y0,x0,cutapp2b(x0,t38,y0,t39))):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)))
+t41:=tris(rat,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)),a0,t40,t37):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),a0)
+t42:=<t41><t39><y0><t38><x0>p1:p
+s@t43:=someapp(rat,[y:rat]prop3(a0,x0,y),s,p,[y:rat][t:prop3(a0,x0,y)]t42(y,t)):p
+-3132
+p1@satz132app:=someapp(rat,[x:rat]some"rt"([y:rat]prop3".3132"(a0,x,y)),satz132(a0),p,[x:rat][t:some"rt"([y:rat]prop3".3132"(a0,x,y))]t43".3132"(x,t)):p
++3133
+eta@[y0:rat][ly:lrt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][uu:urt(ksi,u0)][i:is"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0)]
+t1:=tris(rat,u0,pl"rt"(x0,mn(u0,x0,cutapp2b(x0,lx,u0,uu))),pl"rt"(x0,y0),satz101d(u0,x0,cutapp2b(x0,lx,u0,uu)),ispl2"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0,x0,i)):is"rt"(u0,pl"rt"(x0,y0))
+t2:=lrtpl(ksi,eta,u0,x0,lx,y0,ly,t1):lrt(pl(ksi,eta),u0)
+t3:=andi(lrt(pl(ksi,eta),u0),urt(ksi,u0),t2,uu):and(lrt(pl(ksi,eta),u0),urt(ksi,u0))
+t4:=somei(rat,[x:rat]and(lrt(pl(ksi,eta),x),urt(ksi,x)),u0,t3):more(pl(ksi,eta),ksi)
+ly@t5:=satz132app(ksi,more(pl(ksi,eta),ksi),y0,[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),y0)]t4(x,t,y,u,v)):more(pl(ksi,eta),ksi)
+-3133
+eta@satz133:=cutapp1a(eta,more(pl(ksi,eta),ksi),[x:rat][t:lrt(eta,x)]t5".3133"(x,t)):more(pl(ksi,eta),ksi)
+satz133a:=satz121(pl(ksi,eta),ksi,satz133):less(ksi,pl(ksi,eta))
+zeta@[m:more(ksi,eta)]
++3134
+[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
+t1:=satz119a(eta,y0,uy,x0,l):urt(eta,x0)
+t2:=satz83(y0,x0,l):more"rt"(x0,y0)
+[u0:rat][lu:lrt(zeta,u0)][z0:rat][uz:urt(zeta,z0)][i:is"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2))]
+t3:=tris(rat,z0,pl"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),u0),pl"rt"(mn(x0,y0,t2),u0),satz101f(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),ispl1"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2),u0,i)):is"rt"(z0,pl"rt"(mn(x0,y0,t2),u0))
+t4:=tr3is(rat,pl"rt"(y0,z0),pl"rt"(y0,pl"rt"(mn(x0,y0,t2),u0)),pl"rt"(pl"rt"(y0,mn(x0,y0,t2)),u0),pl"rt"(x0,u0),ispl2"rt"(z0,pl"rt"(mn(x0,y0,t2),u0),y0,t3),asspl2"rt"(y0,mn(x0,y0,t2),u0),ispl1"rt"(pl"rt"(y0,mn(x0,y0,t2)),x0,u0,satz101c(x0,y0,t2))):is"rt"(pl"rt"(y0,z0),pl"rt"(x0,u0))
+t5:=lrtpl(ksi,zeta,pl"rt"(y0,z0),x0,lx,u0,lu,t4):lrt(pl(ksi,zeta),pl"rt"(y0,z0))
+t6:=urtpl(eta,zeta,pl"rt"(y0,z0),y0,uy,z0,uz,refis(rat,pl"rt"(y0,z0))):urt(pl(eta,zeta),pl"rt"(y0,z0))
+t7:=andi(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)),t5,t6):and(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)))
+t8:=somei(rat,[x:rat]and(lrt(pl(ksi,zeta),x),urt(pl(eta,zeta),x)),pl"rt"(y0,z0),t7):more(pl(ksi,zeta),pl(eta,zeta))
+l@t9:=satz132app(zeta,more(pl(ksi,zeta),pl(eta,zeta)),mn(x0,y0,t2),[x:rat][t:lrt(zeta,x)][y:rat][u:urt(zeta,y)][v:is"rt"(mn(y,x,cutapp2b(zeta,x,t,y,u)),mn(x0,y0,t2))]t8(x,t,y,u,v)):more(pl(ksi,zeta),pl(eta,zeta))
+uy@t10:=cutapp3(ksi,y0,ly,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t9(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
+-3134
+satz134:=moreapp(ksi,eta,m,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t10".3134"(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
+zeta@[m:more(ksi,eta)]
+satz135a:=satz134(m):more(pl(ksi,zeta),pl(eta,zeta))
+zeta@[i:is(ksi,eta)]
+satz135b:=ispl1(ksi,eta,zeta,i):is(pl(ksi,zeta),pl(eta,zeta))
+zeta@[l:less(ksi,eta)]
+satz135c:=satz121(pl(eta,zeta),pl(ksi,zeta),satz134(eta,ksi,zeta,satz122(ksi,eta,l))):less(pl(ksi,zeta),pl(eta,zeta))
+m@satz135d:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135a):more(pl(zeta,ksi),pl(zeta,eta))
+i@satz135e:=ispl2(ksi,eta,zeta,i):is(pl(zeta,ksi),pl(zeta,eta))
+l@satz135f:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135c):less(pl(zeta,ksi),pl(zeta,eta))
+upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
+satz135g:=ismore2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135d(zeta,upsilon,ksi,m)):more(pl(ksi,zeta),pl(eta,upsilon))
+satz135h:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135g):more(pl(zeta,ksi),pl(upsilon,eta))
+i@[l:less(zeta,upsilon)]
+satz135j:=isless2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135f(zeta,upsilon,ksi,l)):less(pl(ksi,zeta),pl(eta,upsilon))
+satz135k:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135j):less(pl(zeta,ksi),pl(upsilon,eta))
++3136
+zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+t2:=satz123b(pl(ksi,zeta),pl(eta,zeta)):ec3(is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)))
+-3136
+zeta@[m:more(pl(ksi,zeta),pl(eta,zeta))]
+satz136a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),m):more(ksi,eta)
+zeta@[i:is(pl(ksi,zeta),pl(eta,zeta))]
+satz136b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),i):is(ksi,eta)
+zeta@[l:less(pl(ksi,zeta),pl(eta,zeta))]
+satz136c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),l):less(ksi,eta)
+zeta@[m:more(pl(zeta,ksi),pl(zeta,eta))]
+satz136d:=satz136a(ismore12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),m)):more(ksi,eta)
+zeta@[i:is(pl(zeta,ksi),pl(zeta,eta))]
+satz136e:=satz136b(tr3is(cut,pl(ksi,zeta),pl(zeta,ksi),pl(zeta,eta),pl(eta,zeta),compl(ksi,zeta),i,compl(zeta,eta))):is(ksi,eta)
+zeta@[l:less(pl(zeta,ksi),pl(zeta,eta))]
+satz136f:=satz136c(isless12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),l)):less(ksi,eta)
+upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
++3137
+t1:=satz134(ksi,eta,zeta,m):more(pl(ksi,zeta),pl(eta,zeta))
+t2:=ismore12(pl(zeta,eta),pl(eta,zeta),pl(upsilon,eta),pl(eta,upsilon),compl(zeta,eta),compl(upsilon,eta),satz134(zeta,upsilon,eta,n)):more(pl(eta,zeta),pl(eta,upsilon))
+-3137
+satz137:=trmore(pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),t1".3137",t2".3137"):more(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
+satz137a:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz137(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
+satz138a:=orapp(more(ksi,eta),is(ksi,eta),more(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]satz137(t,n),[t:is(ksi,eta)]satz135g(t,n)):more(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
+satz138b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]satz137(m,t),[t:is(zeta,upsilon)]satz135h(zeta,upsilon,ksi,eta,t,m)):more(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
+satz138c:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
+satz138d:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
++3139
+[i:is(ksi,eta)][j:is(zeta,upsilon)]
+t1:=moreisi2(pl(ksi,zeta),pl(eta,upsilon),ispl12(ksi,eta,zeta,upsilon,i,j)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+i@[o:more(zeta,upsilon)]
+t2:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138a(m,o)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+n@[o:more(ksi,eta)]
+t4:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138b(o,n)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+-3139
+satz139:=orapp(more(ksi,eta),is(ksi,eta),moreis(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]t4".3139"(t),[t:is(ksi,eta)]t3".3139"(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
+satz139a:=satz124(pl(eta,upsilon),pl(ksi,zeta),satz139(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(pl(ksi,zeta),pl(eta,upsilon))
+eta@[l:lessis(ksi,eta)]
++3140
+[phi:cut][i:is(pl(eta,phi),ksi)]
+t1:=ismore1(pl(eta,phi),ksi,eta,i,satz133(eta,phi)):more(ksi,eta)
+phi@t2:=th3"l.imp"(is(pl(eta,phi),ksi),more(ksi,eta),satz123d(ksi,eta,l),[t:is(pl(eta,phi),ksi)]t1(t)):nis(pl(eta,phi),ksi)
+-3140
+vorbemerkung140:=th5"l.some"(cut,[a:cut]is(pl(eta,a),ksi),[a:cut]t2".3140"(a)):not(some([a:cut]is(pl(eta,a),ksi)))
+eta@[phi:cut][psi:cut]
++*3140
+psi@[m:more(phi,psi)]
+t3:=satz135d(phi,psi,eta,m):more(pl(eta,phi),pl(eta,psi))
+t4:=ec3e21(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t3):nis(pl(eta,phi),pl(eta,psi))
+psi@[l:less(phi,psi)]
+t5:=satz135f(phi,psi,eta,l):less(pl(eta,phi),pl(eta,psi))
+t6:=ec3e31(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t5):nis(pl(eta,phi),pl(eta,psi))
+psi@[n:nis(phi,psi)]
+t7:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
+t8:=orapp(more(phi,psi),less(phi,psi),nis(pl(eta,phi),pl(eta,psi)),t7,[t:more(phi,psi)]t4(t),[t:less(phi,psi)]t6(t)):nis(pl(eta,phi),pl(eta,psi))
+-3140
+psi@[i:is(pl(eta,phi),ksi)][j:is(pl(eta,psi),ksi)]
+satz140b:=th7"l.imp"(is(phi,psi),nis(pl(eta,phi),pl(eta,psi)),weli(is(pl(eta,phi),pl(eta,psi)),tris2(cut,pl(eta,phi),pl(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t8".3140"(t)):is(phi,psi)
+eta@[z0:rat][x0:rat][y0:rat]
+diffprop1:=and(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t))):'prop'
+diffprop2:=and3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0)):'prop'
+z0@diffprop:=some"rt"([x:rat]some"rt"([y:rat]diffprop2(z0,x,y))):'prop'
+eta@diff:=setof(rat,[z:rat]diffprop(z)):set(rat)
+x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][m:more"rt"(x0,y0)][i:is"rt"(z0,mn(x0,y0,m))]
++*iii3
+i@[m1:more"rt"(x0,y0)]
+t11a:=tris(rat,z0,mn(x0,y0,m),mn(x0,y0,m1),i,satz101g(x0,y0,mn(x0,y0,m),m1,satz101c(x0,y0,m))):is"rt"(z0,mn(x0,y0,m1))
+i@t12:=andi(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),m,[t:more"rt"(x0,y0)]t11a(t)):diffprop1(z0,x0,y0)
+t13:=and3i(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),lx,uy,t12):diffprop2(z0,x0,y0)
+t14:=somei(rat,[y:rat]diffprop2(z0,x0,y),y0,t13):some"rt"([y:rat]diffprop2(z0,x0,y))
+t15:=somei(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),x0,t14):diffprop(z0)
+-iii3
+i@diff1:=estii(rat,[z:rat]diffprop(z),z0,t15".iii3"):in(z0,diff)
+z0@[i:in(z0,diff)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]p]
++*iii3
+p1@t16:=estie(rat,[z:rat]diffprop(z),z0,i):diffprop(z0)
+-iii3
+p1@[x0:rat][px:some"rt"([y:rat]diffprop2(z0,x0,y))][y0:rat][py:diffprop2(z0,x0,y0)]
++*iii3
+py@t17:=and3e1(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):lrt(ksi,x0)
+t18:=and3e2(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):urt(eta,y0)
+t19:=and3e3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):diffprop1(z0,x0,y0)
+t20:=ande1(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):more"rt"(x0,y0)
+t21:=ande2"l.r"(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):is"rt"(z0,mn(x0,y0,t20))
+t22:=<t21><t20><t18><y0><t17><x0>p1:p
+px@t23:=someapp(rat,[y:rat]diffprop2(z0,x0,y),px,p,[y:rat][t:diffprop2(z0,x0,y)]t22(y,t)):p
+-iii3
+p1@diffapp:=someapp(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),t16".iii3",p,[x:rat][t:some"rt"([y:rat]diffprop2(z0,x,y))]t23".iii3"(x,t)):p
+eta@[m:more(ksi,eta)]
++*3140
+m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
+t9:=t2"rp.3134"(eta,m,y0,ly,uy,x0,lx,l):more"rt"(x0,y0)
+t10:=diff1(mn(x0,y0,t9),x0,lx,y0,uy,t9,refis(rat,mn(x0,y0,t9))):in(mn(x0,y0,t9),diff)
+m"rp"@[x1:rat][ux:urt(ksi,x1)][z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
+t11:=isless12"rt"(mn(x0,y0,n),z0,pl"rt"(mn(x0,y0,n),y0),x0,symis(rat,z0,mn(x0,y0,n),j),satz101e(x0,y0,n),satz94a(mn(x0,y0,n),y0)):less"rt"(z0,x0)
+t12:=trless"rt"(z0,x0,x1,t11,cutapp2a(ksi,x0,lx,x1,ux)):less"rt"(z0,x1)
+t13:=ec3e31(is"rt"(z0,x1),more"rt"(z0,x1),less"rt"(z0,x1),satz81b(z0,x1),t12):nis"rt"(z0,x1)
+i@t14:=diffapp(z0,i,nis"rt"(z0,x1),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t13(x,t,y,u,v,w)):nis"rt"(z0,x1)
+ux@t15:=th3"l.imp"(in(x1,diff),nis"rt"(x1,x1),weli(is"rt"(x1,x1),refis(rat,x1)),[t:in(x1,diff)]t14(x1,t)):not(in(x1,diff))
+m"rp"@[z0:rat][i:in(z0,diff)][u0:rat][l:less"rt"(u0,z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
+t16:=tris(rat,pl"rt"(z0,y0),pl"rt"(mn(x0,y0,n),y0),x0,ispl1"rt"(z0,mn(x0,y0,n),y0,j),satz101e(x0,y0,n)):is"rt"(pl"rt"(z0,y0),x0)
+x2:=pl"rt"(u0,y0):rat
+t17:=isless2"rt"(pl"rt"(z0,y0),x0,x2,t16,satz96c(u0,z0,y0,l)):less"rt"(x2,x0)
+t18:=satz120(ksi,x0,lx,x2,t17):lrt(ksi,x2)
+t19:=ismore1"rt"(pl"rt"(y0,u0),pl"rt"(u0,y0),y0,compl"rt"(y0,u0),satz94(y0,u0)):more"rt"(x2,y0)
+t20:=satz101g(x2,y0,u0,t19,compl"rt"(y0,u0)):is"rt"(u0,mn(x2,y0,t19))
+t21:=diff1(u0,x2,t18,y0,uy,t19,t20):in(u0,diff)
+l@t22:=diffapp(z0,i,in(u0,diff),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t21(x,t,y,u,v,w)):in(u0,diff)
+m"rp"@[z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))][x3:rat][lx3:lrt(ksi,x3)][l:less"rt"(x0,x3)]
+t23:=satz83(x0,x3,l):more"rt"(x3,x0)
+t24:=trmore"rt"(x3,x0,y0,t23,n):more"rt"(x3,y0)
+t25:=ismore12"rt"(x3,pl"rt"(mn(x3,y0,t24),y0),x0,pl"rt"(mn(x0,y0,n),y0),satz101f(x3,y0,t24),satz101f(x0,y0,n),t23):more"rt"(pl"rt"(mn(x3,y0,t24),y0),pl"rt"(mn(x0,y0,n),y0))
+t26:=satz97a(mn(x3,y0,t24),mn(x0,y0,n),y0,t25):more"rt"(mn(x3,y0,t24),mn(x0,y0,n))
+t27:=ismore2"rt"(mn(x0,y0,n),z0,mn(x3,y0,t24),symis(rat,z0,mn(x0,y0,n),j),t26):more"rt"(mn(x3,y0,t24),z0)
+t28:=diff1(mn(x3,y0,t24),x3,lx3,y0,uy,t24,refis(rat,mn(x3,y0,t24))):in(mn(x3,y0,t24),diff)
+t29:=andi(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0),t28,t27):and(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0))
+t30:=somei(rat,[x:rat]and(in(x,diff),more"rt"(x,z0)),mn(x3,y0,t24),t29):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
+j@t31:=cutapp3(ksi,x0,lx,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t30(y,t,u)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
+i@t32:=diffapp(z0,i,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t31(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
+m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)][x1:rat][ux1:urt(ksi,x1)]
+t33:=cut2(diff,mn(x0,y0,t9(y0,ly,uy,x0,lx,l)),t10(y0,ly,uy,x0,lx,l),x1,t15(x1,ux1),[x:rat][t:in(x,diff)][y:rat][u:less"rt"(y,x)]t22(x,t,y,u),[x:rat][t:in(x,diff)]t32(x,t)):cutprop(diff)
+l@t34:=cutapp1b(ksi,cutprop(diff),[x:rat][t:urt(ksi,x)]t33(x,t)):cutprop(diff)
+uy@t35:=cutapp3(ksi,y0,ly,cutprop(diff),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t34(x,t,u)):cutprop(diff)
+-3140
+m@satz140h:=moreapp(ksi,eta,m,cutprop(diff),[x:rat][u:lrt(ksi,x)][v:urt(eta,x)]t35".3140"(x,u,v)):cutprop(diff)
++*3140
+m"rp"@chi:=cutof(diff,satz140h):cut
+[z0:rat][lz:lrt(pl(eta,chi),z0)][y1:rat][ly:lrt(eta,y1)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,pl"rt"(y1,u0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][o:more"rt"(x0,y0)][j:is"rt"(u0,mn(x0,y0,o))]
+t36:=cutapp2b(eta,y1,ly,y0,uy):more"rt"(y0,y1)
+t37:=tr3is(rat,pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),pl"rt"(mn(x0,y0,o),pl"rt"(y1,mn(y0,y1,t36))),pl"rt"(mn(x0,y0,o),y0),x0,asspl1"rt"(mn(x0,y0,o),y1,mn(y0,y1,t36)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t36)),y0,mn(x0,y0,o),satz101c(y0,y1,t36)),satz101e(x0,y0,o)):is"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0)
+t38:=isless2"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0,pl"rt"(mn(x0,y0,o),y1),t37,satz94a(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36))):less"rt"(pl"rt"(mn(x0,y0,o),y1),x0)
+t39:=tr3is(rat,z0,pl"rt"(y1,u0),pl"rt"(u0,y1),pl"rt"(mn(x0,y0,o),y1),i,compl"rt"(y1,u0),ispl1"rt"(u0,mn(x0,y0,o),y1,j)):is"rt"(z0,pl"rt"(mn(x0,y0,o),y1))
+t40:=isless1"rt"(pl"rt"(mn(x0,y0,o),y1),z0,x0,symis(rat,z0,pl"rt"(mn(x0,y0,o),y1),t39),t38):less"rt"(z0,x0)
+t41:=satz120(ksi,x0,lx,z0,t40):lrt(ksi,z0)
+i@t42:=diffapp(u0,ini(diff,satz140h,u0,lu),lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(u0,mn(x,y,v))]t41(x,t,y,u,v,w)):lrt(ksi,z0)
+lz@a:=plapp(eta,chi,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,pl"rt"(x,y))]t42(x,t,y,u,v)):lrt(ksi,z0)
+m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
+t43:=satz83(y0,x0,l):more"rt"(x0,y0)
+[y1:rat][ly1:lrt(eta,y1)][y2:rat][uy2:urt(eta,y2)]
+t44:=cutapp2b(eta,y1,ly1,y2,uy2):more"rt"(y2,y1)
+[i:is"rt"(mn(y2,y1,t44),mn(x0,y0,t43))]
+t45:=cutapp2b(eta,y1,ly1,y0,uy):more"rt"(y0,y1)
+t46:=tris(rat,y2,pl"rt"(mn(y2,y1,t44),y1),pl"rt"(mn(x0,y0,t43),y1),satz101f(y2,y1,t44),ispl1"rt"(mn(y2,y1,t44),mn(x0,y0,t43),y1,i)):is"rt"(y2,pl"rt"(mn(x0,y0,t43),y1))
+t47:=tr4is(rat,pl"rt"(y2,mn(y0,y1,t45)),pl"rt"(pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45)),pl"rt"(mn(x0,y0,t43),pl"rt"(y1,mn(y0,y1,t45))),pl"rt"(mn(x0,y0,t43),y0),x0,ispl1"rt"(y2,pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45),t46),asspl1"rt"(mn(x0,y0,t43),y1,mn(y0,y1,t45)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t45)),y0,mn(x0,y0,t43),satz101c(y0,y1,t45)),satz101e(x0,y0,t43)):is"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0)
+t48:=ismore1"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0,y2,t47,satz94(y2,mn(y0,y1,t45))):more"rt"(x0,y2)
+t49:=satz101g(x0,y2,mn(y0,y1,t45),t48,t47):is"rt"(mn(y0,y1,t45),mn(x0,y2,t48))
+t50:=tris(rat,y0,pl"rt"(mn(y0,y1,t45),y1),pl"rt"(mn(x0,y2,t48),y1),satz101f(y0,y1,t45),ispl1"rt"(mn(y0,y1,t45),mn(x0,y2,t48),y1,t49)):is"rt"(y0,pl"rt"(mn(x0,y2,t48),y1))
+t51:=ine(diff,satz140h,mn(x0,y2,t48),diff1(mn(x0,y2,t48),x0,lx,y2,uy2,t48,refis(rat,mn(x0,y2,t48)))):lrt(chi,mn(x0,y2,t48))
+t52:=lrtpl(eta,chi,y0,y1,ly1,mn(x0,y2,t48),t51,tris(rat,y0,pl"rt"(mn(x0,y2,t48),y1),pl"rt"(y1,mn(x0,y2,t48)),t50,compl"rt"(mn(x0,y2,t48),y1))):lrt(pl(eta,chi),y0)
+l@t53:=satz132app(eta,lrt(pl(eta,chi),y0),mn(x0,y0,t43),[x:rat][t:lrt(eta,x)][y:rat][u:urt(eta,y)][v:is"rt"(mn(y,x,cutapp2b(eta,x,t,y,u)),mn(x0,y0,t43))]t52(x,t,y,u,v)):lrt(pl(eta,chi),y0)
+uy@t54:=cutapp3(ksi,y0,ly,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t53(x,t,u)):lrt(pl(eta,chi),y0)
+ly@[ly0:lrt(eta,y0)][y1:rat][ly1:lrt(ksi,y1)][uy1:urt(eta,y1)]
+t55:=t54(y1,ly1,uy1):lrt(pl(eta,chi),y1)
+t56:=satz120(pl(eta,chi),y1,t55,y0,cutapp2a(eta,y0,ly0,y1,uy1)):lrt(pl(eta,chi),y0)
+ly0@t57:=moreapp(ksi,eta,m,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t56(x,t,u)):lrt(pl(eta,chi),y0)
+ly@b:=th1"l.imp"(lrt(eta,y0),lrt(pl(eta,chi),y0),[t:lrt(eta,y0)]t57(t),[t:urt(eta,y0)]t54(t)):lrt(pl(eta,chi),y0)
+m"rp"@t58:=isi1(pl(eta,chi),ksi,[x:rat][t:lrt(pl(eta,chi),x)]a(x,t),[x:rat][t:lrt(ksi,x)]b(x,t)):is(pl(eta,chi),ksi)
+-3140
+m@satz140a:=somei(cut,[a:cut]is(pl(eta,a),ksi),chi".3140",t58".3140"):some([a:cut]is(pl(eta,a),ksi))
++*3140
+eta@t59:=[c:cut][d:cut][t:is(pl(eta,c),ksi)][u:is(pl(eta,d),ksi)]satz140b(c,d,t,u):amone(cut,[c:cut]is(pl(eta,c),ksi))
+-3140
+m@satz140:=onei(cut,[a:cut]is(pl(eta,a),ksi),t59".3140",satz140a):one([a:cut]is(pl(eta,a),ksi))
+mn:=ind(cut,[a:cut]is(pl(eta,a),ksi),satz140):cut
+satz140c:=oneax(cut,[a:cut]is(pl(eta,a),ksi),satz140):is(pl(eta,mn(ksi,eta,m)),ksi)
+satz140d:=symis(cut,pl(eta,mn(ksi,eta,m)),ksi,satz140c):is(ksi,pl(eta,mn(ksi,eta,m)))
+satz140e:=tris(cut,pl(mn(ksi,eta,m),eta),pl(eta,mn(ksi,eta,m)),ksi,compl(mn(ksi,eta,m),eta),satz140c):is(pl(mn(ksi,eta,m),eta),ksi)
+satz140f:=symis(cut,pl(mn(ksi,eta,m),eta),ksi,satz140e):is(ksi,pl(mn(ksi,eta,m),eta))
+eta@[phi:cut][m:more(ksi,eta)][i:is(pl(eta,phi),ksi)]
+satz140g:=satz140b(phi,mn(ksi,eta,m),i,satz140c(m)):is(phi,mn(ksi,eta,m))
+upsilon@[m:more(ksi,zeta)][n:more(eta,upsilon)][i:is(ksi,eta)][j:is(zeta,upsilon)]
++*3140
+j"rp"@t60:=tr3is(cut,pl(upsilon,mn(ksi,zeta,m)),pl(zeta,mn(ksi,zeta,m)),ksi,eta,ispl1(upsilon,zeta,mn(ksi,zeta,m),symis(cut,zeta,upsilon,j)),satz140c(ksi,zeta,m),i):is(pl(upsilon,mn(ksi,zeta,m)),eta)
+-3140
+j@ismn12:=satz140g(eta,upsilon,mn(ksi,zeta,m),n,t60".3140"):is(mn(ksi,zeta,m),mn(eta,upsilon,n))
+zeta@[m:more(ksi,zeta)][n:more(eta,zeta)][i:is(ksi,eta)]
+ismn1:=ismn12(zeta,m,n,i,refis(cut,zeta)):is(mn(ksi,zeta,m),mn(eta,zeta,n))
+zeta@[m:more(zeta,ksi)][n:more(zeta,eta)][i:is(ksi,eta)]
+ismn2:=ismn12(zeta,zeta,ksi,eta,m,n,refis(cut,zeta),i):is(mn(zeta,ksi,m),mn(zeta,eta,n))
+eta@[z0:rat][x0:rat][y0:rat]
+prodprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0))):'prop'
+z0@prodprop:=some"rt"([x:rat]some"rt"([y:rat]prodprop1(z0,x,y))):'prop'
+eta@prod:=setof(rat,[z:rat]prodprop(z)):set(rat)
+x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts(x0,y0))]
++iii4
+t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),lx,ly,i):prodprop1(z0,x0,y0)
+t2:=somei(rat,[y:rat]prodprop1(z0,x0,y),y0,t1):some"rt"([y:rat]prodprop1(z0,x0,y))
+t3:=somei(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),x0,t2):prodprop(z0)
+-iii4
+prod1:=estii(rat,[z:rat]prodprop(z),z0,t3".iii4"):in(z0,prod)
+z0@[i:in(z0,prod)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]p]
++*iii4
+p1@t4:=estie(rat,[z:rat]prodprop(z),z0,i):prodprop(z0)
+-iii4
+p1@[x0:rat][px:some"rt"([y:rat]prodprop1(z0,x0,y))][y0:rat][py:prodprop1(z0,x0,y0)]
++*iii4
+py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(ksi,x0)
+t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(eta,y0)
+t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):is"rt"(z0,ts(x0,y0))
+t8:=<t7><t6><y0><t5><x0>p1:p
+px@t9:=someapp(rat,[y:rat]prodprop1(z0,x0,y),px,p,[y:rat][t:prodprop1(z0,x0,y)]t8(y,t)):p
+-iii4
+p1@prodapp:=someapp(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),t4".iii4",p,[x:rat][t:some"rt"([y:rat]prodprop1(z0,x,y))]t9".iii4"(x,t)):p
+eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
++4141
+[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))]
+t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
+t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
+t3:=isless1"rt"(ts(x0,y0),z0,ts(x1,y1),symis(rat,z0,ts(x0,y0),j),satz107a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,ts(x1,y1))
+t4:=ec3e31(is"rt"(z0,ts(x1,y1)),more"rt"(z0,ts(x1,y1)),less"rt"(z0,ts(x1,y1)),satz81b(z0,ts(x1,y1)),t3):nis"rt"(z0,ts(x1,y1))
+i@t5:=prodapp(ksi,eta,z0,i,nis"rt"(z0,ts(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,ts(x1,y1))
+-4141
+satz141a:=th3"l.imp"(in(ts(x1,y1),prod),nis"rt"(ts(x1,y1),ts(x1,y1)),weli(is"rt"(ts(x1,y1),ts(x1,y1)),refis(rat,ts(x1,y1))),[t:in(ts(x1,y1),prod)]t5".4141"(ts(x1,y1),t)):not(in(ts(x1,y1),prod))
+-rp
+@[x0:rat][y0:rat]
++4141
+v0:=ts(ov(1rt,y0),x0):rat
+t6:=tr3is(rat,ts(y0,v0),ts(ts(y0,ov(1rt,y0)),x0),ts(1rt,x0),x0,assts2(y0,ov(1rt,y0),x0),ists1(ts(y0,ov(1rt,y0)),1rt,x0,satz110c(1rt,y0)),example1c(x0)):is(ts(y0,v0),x0)
+-4141
+satz141b:=satz110g(x0,y0,v0".4141",t6".4141"):is(ts(ov(1rt,y0),x0),ov(x0,y0))
+satz141c:=symis(rat,ts(ov(1rt,y0),x0),ov(x0,y0),satz141b):is"rt"(ov(x0,y0),ts(ov(1rt,y0),x0))
++*rp
++*4141
+eta@[u0:rat][i:in(u0,prod)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,ts(x0,y0))]
+t7:=isless2"rt"(u0,ts(x0,y0),z0,j,l):less"rt"(z0,ts(x0,y0))
+t8:=tr3is(rat,ts(ov(1rt,x0),ts(x0,y0)),ts(ts(ov(1rt,x0),x0),y0),ts(1rt,y0),y0,assts2(ov(1rt,x0),x0,y0),ists1(ts(ov(1rt,x0),x0),1rt,y0,satz110e(1rt,x0)),example1c(y0)):is"rt"(ts(ov(1rt,x0),ts(x0,y0)),y0)
+t9:=isless12"rt"(ts(ov(1rt,x0),z0),ov(z0,x0),ts(ov(1rt,x0),ts(x0,y0)),y0,satz141b(z0,x0),t8,satz105f(z0,ts(x0,y0),ov(1rt,x0),t7)):less"rt"(ov(z0,x0),y0)
+t10:=satz120(eta,y0,ly,ov(z0,x0),t9):lrt(eta,ov(z0,x0))
+t11:=prod1(z0,x0,lx,ov(z0,x0),t10,satz110d(z0,x0)):in(z0,prod)
+l@t12:=prodapp(u0,i,in(z0,prod),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,ts(x,y))]t11(x,t,y,u,v)):in(z0,prod)
+eta@[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
+t13:=prod1(ts(x1,y0),x1,lx1,y0,ly,refis(rat,ts(x1,y0))):in(ts(x1,y0),prod)
+t14:=satz105a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(ts(x1,y0),ts(x0,y0))
+t15:=ismore2"rt"(ts(x0,y0),z0,ts(x1,y0),symis(rat,z0,ts(x0,y0),j),t14):more"rt"(ts(x1,y0),z0)
+t16:=andi(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0),t13,t15):and(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0))
+t17:=somei(rat,[y:rat]and(in(y,prod),more"rt"(y,z0)),ts(x1,y0),t16):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
+j@t18:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t17(x,t,u)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
+i@t19:=prodapp(z0,i,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t18(x,t,y,u,v)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
+eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
+t20:=cut2(prod,ts(x0,y0),prod1(ts(x0,y0),x0,lx,y0,ly,refis(rat,ts(x0,y0))),ts(x1,y1),satz141a(x1,ux,y1,uy),[x:rat][t:in(x,prod)][y:rat][u:less"rt"(y,x)]t12(x,t,y,u),[x:rat][t:in(x,prod)]t19(x,t)):cutprop(prod)
+ux@t21:=cutapp1b(eta,cutprop(prod),[y:rat][t:urt(eta,y)]t20(y,t)):cutprop(prod)
+ly@t22:=cutapp1b(ksi,cutprop(prod),[x:rat][t:urt(ksi,x)]t21(x,t)):cutprop(prod)
+lx@t23:=cutapp1a(eta,cutprop(prod),[y:rat][t:lrt(eta,y)]t22(y,t)):cutprop(prod)
+-4141
+eta@satz141:=cutapp1a(ksi,cutprop(prod),[x:rat][t:lrt(ksi,x)]t23".4141"(x,t)):cutprop(prod)
+ts:=cutof(prod,satz141):cut
+[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
+lrtts:=ine(prod,satz141,z0,prod1(z0,x0,lx,y0,ly,i)):lrt(ts(ksi,eta),z0)
+eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
++*iii4
+i@t10:=isp1(rat,[x:rat]not(in(x,prod)),ts"rt"(x0,y0),z0,satz141a(x0,ux,y0,uy),i):not(in(z0,prod))
+-iii4
+i@urtts:=th3"l.imp"(lrt(ts(ksi,eta),z0),in(z0,prod),t10".iii4",[t:lrt(ts(ksi,eta),z0)]ini(prod,satz141,z0,t)):urt(ts(ksi,eta),z0)
+eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]p]
++*iii4
+p1@t11:=ini(prod,satz141,z0,lz):in(z0,prod)
+-iii4
+p1@tsapp:=prodapp(z0,t11".iii4",p,p1):p
+zeta@[i:is(ksi,eta)]
+ists1:=isf(cut,cut,[u:cut]ts(u,zeta),ksi,eta,i):is(ts(ksi,zeta),ts(eta,zeta))
+ists2:=isf(cut,cut,[u:cut]ts(zeta,u),ksi,eta,i):is(ts(zeta,ksi),ts(zeta,eta))
+upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
+ists12:=tris(cut,ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),ists1(i),ists2(zeta,upsilon,eta,j)):is(ts(ksi,zeta),ts(eta,upsilon))
++4142
+eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
+t1:=tris(rat,z0,ts"rt"(x0,y0),ts"rt"(y0,x0),i,comts(x0,y0)):is"rt"(z0,ts"rt"(y0,x0))
+t2:=lrtts(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(ts(eta,ksi),z0)
+lz@t3:=tsapp(ksi,eta,z0,lz,lrt(ts(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]t2(x,t,y,u,v)):lrt(ts(eta,ksi),z0)
+-4142
+eta@satz142:=isi1(ts(ksi,eta),ts(eta,ksi),[x:rat][t:lrt(ts(ksi,eta),x)]t3".4142"(x,t),[x:rat][t:lrt(ts(eta,ksi),x)]t3".4142"(eta,ksi,x,t)):is(ts(ksi,eta),ts(eta,ksi))
+comts:=satz142:is(ts(ksi,eta),ts(eta,ksi))
++4143
+zeta@[u0:rat][lu:lrt(ts(ts(ksi,eta),zeta),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,ts"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))]
+t1:=tr3is(rat,u0,ts"rt"(v0,z0),ts"rt"(ts"rt"(x0,y0),z0),ts"rt"(x0,ts"rt"(y0,z0)),i,ists1"rt"(v0,ts"rt"(x0,y0),z0,j),assts1(x0,y0,z0)):is"rt"(u0,ts"rt"(x0,ts"rt"(y0,z0)))
+t2:=lrtts(eta,zeta,ts"rt"(y0,z0),y0,ly,z0,lz,refis(rat,ts"rt"(y0,z0))):lrt(ts(eta,zeta),ts"rt"(y0,z0))
+t3:=lrtts(ksi,ts(eta,zeta),u0,x0,lx,ts"rt"(y0,z0),t2,t1):lrt(ts(ksi,ts(eta,zeta)),u0)
+i@t4:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
+lu@t5:=tsapp(ts(ksi,eta),zeta,u0,lu,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,ts"rt"(x,y))]t4(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
+u0@[lu:lrt(ts(ksi,ts(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(ts(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,ts"rt"(y0,z0))]
+t6:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,ts"rt"(y0,z0)),ts"rt"(ts"rt"(x0,y0),z0),i,ists2"rt"(v0,ts"rt"(y0,z0),x0,j),assts2(x0,y0,z0)):is"rt"(u0,ts"rt"(ts"rt"(x0,y0),z0))
+t7:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
+t8:=lrtts(ts(ksi,eta),zeta,u0,ts"rt"(x0,y0),t7,z0,lz,t6):lrt(ts(ts(ksi,eta),zeta),u0)
+i@t9:=tsapp(eta,zeta,v0,lv,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,ts"rt"(x,y))]t8(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
+lu@t10:=tsapp(ksi,ts(eta,zeta),u0,lu,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(ts(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t9(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
+-4143
+zeta@satz143:=isi1(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),[x:rat][t:lrt(ts(ts(ksi,eta),zeta),x)]t5".4143"(x,t),[x:rat][t:lrt(ts(ksi,ts(eta,zeta)),x)]t10".4143"(x,t)):is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
+assts1:=satz143:is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
+assts2:=symis(cut,ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),satz143):is(ts(ksi,ts(eta,zeta)),ts(ts(ksi,eta),zeta))
++4144
+[u0:rat][lu:lrt(ts(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
+t1:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,pl"rt"(y0,z0)),pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)),i,ists2"rt"(v0,pl"rt"(y0,z0),x0,j),disttp2(x0,y0,z0)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)))
+t2:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
+t3:=lrtts(ksi,zeta,ts"rt"(x0,z0),x0,lx,z0,lz,refis(rat,ts"rt"(x0,z0))):lrt(ts(ksi,zeta),ts"rt"(x0,z0))
+t4:=lrtpl(ts(ksi,eta),ts(ksi,zeta),u0,ts"rt"(x0,y0),t2,ts"rt"(x0,z0),t3,t1):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
+i@t5:=plapp(eta,zeta,v0,lv,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
+lu@t6:=tsapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t5(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
+u0@[lu:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][w0:rat][lw:lrt(ts(ksi,zeta),w0)][i:is"rt"(u0,pl"rt"(v0,w0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][z0:rat][lz:lrt(zeta,z0)][k:is"rt"(w0,ts"rt"(x1,z0))]
+t7:=tris(rat,u0,pl"rt"(v0,w0),pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),i,ispl12"rt"(v0,ts"rt"(x0,y0),w0,ts"rt"(x1,z0),j,k)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)))
+x2:=ite(moreis"rt"(x0,x1),rat,x0,x1):rat
+[m:moreis"rt"(x0,x1)]
+t8:=itet(moreis"rt"(x0,x1),rat,x0,x1,m):is"rt"(x2,x0)
+t9:=isp1(rat,[t:rat]lrt(ksi,t),x0,x2,lx,t8):lrt(ksi,x2)
+t10:=lessisi2"rt"(x0,x2,symis(rat,x2,x0,t8)):lessis"rt"(x0,x2)
+t11:=satz88(x1,x0,x2,satz84(x0,x1,m),t10):lessis"rt"(x1,x2)
+k@[n:not(moreis"rt"(x0,x1))]
+t12:=itef(moreis"rt"(x0,x1),rat,x0,x1,n):is"rt"(x2,x1)
+t13:=isp1(rat,[t:rat]lrt(ksi,t),x1,x2,lx1,t12):lrt(ksi,x2)
+t14:=lessisi2"rt"(x1,x2,symis(rat,x2,x1,t12)):lessis"rt"(x1,x2)
+t15:=lessisi1"rt"(x0,x2,satz87b(x0,x1,x2,satz81j(x0,x1,n),t14)):lessis"rt"(x0,x2)
+k@t16:=th1"l.imp"(moreis"rt"(x0,x1),lrt(ksi,x2),[t:moreis"rt"(x0,x1)]t9(t),[t:not(moreis"rt"(x0,x1))]t13(t)):lrt(ksi,x2)
+t17:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x0,x2),[t:moreis"rt"(x0,x1)]t10(t),[t:not(moreis"rt"(x0,x1))]t15(t)):lessis"rt"(x0,x2)
+t18:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x1,x2),[t:moreis"rt"(x0,x1)]t11(t),[t:not(moreis"rt"(x0,x1))]t14(t)):lessis"rt"(x1,x2)
+t19:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
+t20:=lrtts(ksi,pl(eta,zeta),ts"rt"(x2,pl"rt"(y0,z0)),x2,t16,pl"rt"(y0,z0),t19,refis(rat,ts"rt"(x2,pl"rt"(y0,z0)))):lrt(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)))
+t21:=satz109a(x0,x2,y0,y0,t17,lessisi2"rt"(y0,y0,refis(rat,y0))):lessis"rt"(ts"rt"(x0,y0),ts"rt"(x2,y0))
+t22:=satz109a(x1,x2,z0,z0,t18,lessisi2"rt"(z0,z0,refis(rat,z0))):lessis"rt"(ts"rt"(x1,z0),ts"rt"(x2,z0))
+t23:=islessis12"rt"(pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),u0,pl"rt"(ts"rt"(x2,y0),ts"rt"(x2,z0)),ts"rt"(x2,pl"rt"(y0,z0)),symis(rat,u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),t7),distpt2(x2,y0,z0),satz100a(ts"rt"(x0,y0),ts"rt"(x2,y0),ts"rt"(x1,z0),ts"rt"(x2,z0),t21,t22)):lessis"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))
+t24:=orapp(less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),lrt(ts(ksi,pl(eta,zeta)),u0),t23,[t:less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]satz120(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)),t20,u0,t),[t:is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]isp1(rat,[u:rat]lrt(ts(ksi,pl(eta,zeta)),u),ts"rt"(x2,pl"rt"(y0,z0)),u0,t20,t)):lrt(ts(ksi,pl(eta,zeta)),u0)
+j@t25:=tsapp(ksi,zeta,w0,lw,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(w0,ts"rt"(x,y))]t24(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
+i@t26:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t25(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
+lu@t27:=plapp(ts(ksi,eta),ts(ksi,zeta),u0,lu,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(ts(ksi,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t26(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
+-4144
+satz144:=isi1(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),[x:rat][t:lrt(ts(ksi,pl(eta,zeta)),x)]t6".4144"(x,t),[x:rat][t:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),x)]t27".4144"(x,t)):is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
+disttp1:=tr3is(cut,ts(pl(ksi,eta),zeta),ts(zeta,pl(ksi,eta)),pl(ts(zeta,ksi),ts(zeta,eta)),pl(ts(ksi,zeta),ts(eta,zeta)),comts(pl(ksi,eta),zeta),satz144(zeta,ksi,eta),ispl12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta))):is(ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)))
+disttp2:=satz144:is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
+distpt1:=symis(cut,ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)),disttp1):is(pl(ts(ksi,zeta),ts(eta,zeta)),ts(pl(ksi,eta),zeta))
+distpt2:=symis(cut,ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),disttp2):is(pl(ts(ksi,eta),ts(ksi,zeta)),ts(ksi,pl(eta,zeta)))
+[m:more(ksi,eta)]
++4145
+phi:=mn(ksi,eta,m):cut
+t1:=satz140d(ksi,eta,m):is(ksi,pl(eta,phi))
+t2:=tris(cut,ts(ksi,zeta),ts(pl(eta,phi),zeta),pl(ts(eta,zeta),ts(phi,zeta)),ists1(ksi,pl(eta,phi),zeta,t1),disttp1(eta,phi,zeta)):is(ts(ksi,zeta),pl(ts(eta,zeta),ts(phi,zeta)))
+-4145
+satz145a:=ismore1(pl(ts(eta,zeta),ts(phi".4145",zeta)),ts(ksi,zeta),ts(eta,zeta),symis(cut,ts(ksi,zeta),pl(ts(eta,zeta),ts(phi".4145",zeta)),t2".4145"),satz133(ts(eta,zeta),ts(phi".4145",zeta))):more(ts(ksi,zeta),ts(eta,zeta))
+zeta@[i:is(ksi,eta)]
+satz145b:=ists1(ksi,eta,zeta,i):is(ts(ksi,zeta),ts(eta,zeta))
+zeta@[l:less(ksi,eta)]
+satz145c:=satz121(ts(eta,zeta),ts(ksi,zeta),satz145a(eta,ksi,zeta,satz122(ksi,eta,l))):less(ts(ksi,zeta),ts(eta,zeta))
+m@satz145d:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145a):more(ts(zeta,ksi),ts(zeta,eta))
+i@satz145e:=ists2(ksi,eta,zeta,i):is(ts(zeta,ksi),ts(zeta,eta))
+l@satz145f:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145c):less(ts(zeta,ksi),ts(zeta,eta))
+upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
+satz145g:=ismore2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145d(zeta,upsilon,ksi,m)):more(ts(ksi,zeta),ts(eta,upsilon))
+satz145h:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145g):more(ts(zeta,ksi),ts(upsilon,eta))
+i@[l:less(zeta,upsilon)]
+satz145j:=isless2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145f(zeta,upsilon,ksi,l)):less(ts(ksi,zeta),ts(eta,upsilon))
+satz145k:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145j):less(ts(zeta,ksi),ts(upsilon,eta))
++4146
+zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
+t2:=satz123b(ts(ksi,zeta),ts(eta,zeta)):ec3(is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)))
+-4146
+zeta@[m:more(ts(ksi,zeta),ts(eta,zeta))]
+satz146a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),m):more(ksi,eta)
+zeta@[i:is(ts(ksi,zeta),ts(eta,zeta))]
+satz146b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),i):is(ksi,eta)
+zeta@[l:less(ts(ksi,zeta),ts(eta,zeta))]
+satz146c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),l):less(ksi,eta)
+zeta@[m:more(ts(zeta,ksi),ts(zeta,eta))]
+satz146d:=satz146a(ismore12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),m)):more(ksi,eta)
+zeta@[i:is(ts(zeta,ksi),ts(zeta,eta))]
+satz146e:=satz146b(tr3is(cut,ts(ksi,zeta),ts(zeta,ksi),ts(zeta,eta),ts(eta,zeta),comts(ksi,zeta),i,comts(zeta,eta))):is(ksi,eta)
+zeta@[l:less(ts(zeta,ksi),ts(zeta,eta))]
+satz146f:=satz146c(isless12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),l)):less(ksi,eta)
+upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
++4147
+t1:=satz145a(ksi,eta,zeta,m):more(ts(ksi,zeta),ts(eta,zeta))
+t2:=ismore12(ts(zeta,eta),ts(eta,zeta),ts(upsilon,eta),ts(eta,upsilon),comts(zeta,eta),comts(upsilon,eta),satz145a(zeta,upsilon,eta,n)):more(ts(eta,zeta),ts(eta,upsilon))
+-4147
+satz147:=trmore(ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),t1".4147",t2".4147"):more(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
+satz147a:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz147(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
+satz148a:=orapp(more(ksi,eta),is(ksi,eta),more(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]satz147(t,n),[t:is(ksi,eta)]satz145g(t,n)):more(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
+satz148b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]satz147(m,t),[t:is(zeta,upsilon)]satz145h(zeta,upsilon,ksi,eta,t,m)):more(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
+satz148c:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
+satz148d:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
++4149
+[i:is(ksi,eta)][j:is(zeta,upsilon)]
+t1:=moreisi2(ts(ksi,zeta),ts(eta,upsilon),ists12(ksi,eta,zeta,upsilon,i,j)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+i@[o:more(zeta,upsilon)]
+t2:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148a(m,o)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+n@[o:more(ksi,eta)]
+t4:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148b(o,n)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+-4149
+satz149:=orapp(more(ksi,eta),is(ksi,eta),moreis(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]t4".4149"(t),[t:is(ksi,eta)]t3".4149"(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
+upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
+satz149a:=satz124(ts(eta,upsilon),ts(ksi,zeta),satz149(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(ts(ksi,zeta),ts(eta,upsilon))
+-rp
+@[r0:rat]
+ratset:=setof(rat,[x:rat]less(x,r0)):set(rat)
++4150
+t1:=satz90(r0):some([x:rat]less(x,r0))
+[x0:rat][l:less(x0,r0)]
+t2:=estii(rat,[x:rat]less(x,r0),x0,l):in(x0,ratset)
+r0@t3:=ec3e13(is(r0,r0),more(r0,r0),less(r0,r0),satz81b(r0,r0),refis(rat,r0)):not(less(r0,r0))
+t4:=th3"l.imp"(in(r0,ratset),less(r0,r0),t3,[t:in(r0,ratset)]estie(rat,[x:rat]less(x,r0),r0,t)):not(in(r0,ratset))
+x0@[i:in(x0,ratset)]
+t5:=estie(rat,[x:rat]less(x,r0),x0,i):less(x0,r0)
+[x1:rat][k:less(x1,x0)]
+t6:=t2(x1,trless(x1,x0,r0,k,t5)):in(x1,ratset)
+i@t7:=satz91(x0,r0,t5):some([x:rat]and(less(x0,x),less(x,r0)))
+[x1:rat][a:and(less(x0,x1),less(x1,r0))]
+t8:=ande1(less(x0,x1),less(x1,r0),a):less(x0,x1)
+t9:=ande2(less(x0,x1),less(x1,r0),a):less(x1,r0)
+t10:=andi(in(x1,ratset),more(x1,x0),t2(x1,t9),satz83(x0,x1,t8)):and(in(x1,ratset),more(x1,x0))
+i@t11:=th6"l.some"(rat,[x:rat]and(less(x0,x),less(x,r0)),[x:rat]and(in(x,ratset),more(x,x0)),t7,[x:rat][t:and(less(x0,x),less(x,r0))]t10(x,t)):some([x:rat]and(in(x,ratset),more(x,x0)))
+l@t12:=cut2(ratset,x0,t2,r0,t4,[x:rat][t:in(x,ratset)][y:rat][u:less(y,x)]t6(x,t,y,u),[x:rat][t:in(x,ratset)]t11(x,t)):cutprop(ratset)
+-4150
+satz150:=someapp(rat,[x:rat]less(x,r0),t1".4150",cutprop(ratset),[x:rat][t:less(x,r0)]t12".4150"(x,t)):cutprop(ratset)
++*rp
+r0@rpofrt:=cutof(ratset,satz150):cut
+[x0:rat][l:less"rt"(x0,r0)]
+lrtrpofrt:=ine(ratset,satz150,x0,t2"rt.4150"(x0,l)):lrt(rpofrt,x0)
+r0@[x0:rat][lx:lrt(rpofrt,x0)]
+lrtrpofrte:=t5"rt.4150"(x0,ini(ratset,satz150,x0,lx)):less"rt"(x0,r0)
+r0@[x0:rat][m:moreis"rt"(x0,r0)]
++*iii4
+m@t12:=satz81c(x0,r0,m):not(less"rt"(x0,r0))
+-iii4
+m@urtrpofrt:=th3"l.imp"(lrt(rpofrt,x0),less"rt"(x0,r0),t12".iii4",[t:lrt(rpofrt,x0)]lrtrpofrte(x0,t)):urt(rpofrt,x0)
+@1rp:=rpofrt(1rt):cut
++4151
+ksi@[z0:rat][lz:lrt(ts(ksi,1rp),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(1rp,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
+t1:=lrtrpofrte(1rt,y0,ly):less"rt"(y0,1rt)
+t2:=isless12"rt"(ts"rt"(x0,y0),z0,ts"rt"(x0,1rt),x0,symis(rat,z0,ts"rt"(x0,y0),i),example1a(x0),satz105f(y0,1rt,x0,t1)):less"rt"(z0,x0)
+t3:=satz120(ksi,x0,lx,z0,t2):lrt(ksi,z0)
+lz@t4:=tsapp(ksi,1rp,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(1rp,y)][v:is"rt"(z0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ksi,z0)
+ksi@[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
+y1:=ts"rt"(ov(1rt,x1),x0):rat
+t5:=isless2"rt"(ts"rt"(ov(1rt,x1),x1),1rt,y1,satz110e(1rt,x1),satz105f(x0,x1,ov(1rt,x1),l)):less"rt"(y1,1rt)
+t6:=lrtrpofrt(1rt,y1,t5):lrt(1rp,y1)
+t7:=tr3is(rat,ts"rt"(x1,y1),ts"rt"(ts"rt"(x1,ov(1rt,x1)),x0),ts"rt"(1rt,x0),x0,assts2"rt"(x1,ov(1rt,x1),x0),ists1"rt"(ts"rt"(x1,ov(1rt,x1)),1rt,x0,satz110c(1rt,x1)),example1c(x0)):is"rt"(ts"rt"(x1,y1),x0)
+t8:=lrtts(ksi,1rp,x0,x1,lx1,y1,t6,symis(rat,ts"rt"(x1,y1),x0,t7)):lrt(ts(ksi,1rp),x0)
+lx@t9:=cutapp3(ksi,x0,lx,lrt(ts(ksi,1rp),x0),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t8(y,t,u)):lrt(ts(ksi,1rp),x0)
+-4151
+ksi@satz151:=isi1(ts(ksi,1rp),ksi,[x:rat][t:lrt(ts(ksi,1rp),x)]t4".4151"(x,t),[x:rat][t:lrt(ksi,x)]t9".4151"(x,t)):is(ts(ksi,1rp),ksi)
+satz151a:=symis(cut,ts(ksi,1rp),ksi,satz151):is(ksi,ts(ksi,1rp))
+satz151b:=tris(cut,ts(1rp,ksi),ts(ksi,1rp),ksi,comts(1rp,ksi),satz151):is(ts(1rp,ksi),ksi)
+satz151c:=symis(cut,ts(1rp,ksi),ksi,satz151b):is(ksi,ts(1rp,ksi))
++4152
+[x0:rat][y0:rat]
+invprop1:=and(urt(ksi,y0),less"rt"(y0,x0)):'prop'
+ksi@[z0:rat][x0:rat]
+invprop2:=and3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0))):'prop'
+z0@invprop:=some"rt"([x:rat]invprop2(z0,x)):'prop'
+ksi@inv:=setof(rat,[z:rat]invprop(z)):set(rat)
+x0@[ux:urt(ksi,x0)][y0:rat][uy:urt(ksi,y0)][l:less"rt"(y0,x0)][i:is"rt"(z0,ov(1rt,x0))]
+t1:=andi(urt(ksi,y0),less"rt"(y0,x0),uy,l):invprop1(x0,y0)
+t2:=somei(rat,[x:rat]invprop1(x0,x),y0,t1):some"rt"([x:rat]invprop1(x0,x))
+t3:=and3i(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),ux,t2,i):invprop2(z0,x0)
+t4:=somei(rat,[x:rat]invprop2(z0,x),x0,t3):invprop(z0)
+inv1:=estii(rat,[z:rat]invprop(z),z0,t4):in(z0,inv)
+z0@[i:in(z0,inv)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]p]
+t5:=estie(rat,[x:rat]invprop(x),z0,i):invprop(z0)
+[x0:rat][px:invprop2(z0,x0)]
+t6:=and3e1(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):urt(ksi,x0)
+t7:=and3e2(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):some"rt"([x:rat]invprop1(x0,x))
+t8:=and3e3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):is"rt"(z0,ov(1rt,x0))
+[y0:rat][py:invprop1(x0,y0)]
+t9:=ande1(urt(ksi,y0),less"rt"(y0,x0),py):urt(ksi,y0)
+t10:=ande2(urt(ksi,y0),less"rt"(y0,x0),py):less"rt"(y0,x0)
+t11:=<t8><t10><t9><y0><t6><x0>p1:p
+px@t12:=someapp(rat,[x:rat]invprop1(x0,x),t7,p,[x:rat][t:invprop1(x0,x)]t11(x,t)):p
+p1@invapp:=someapp(rat,[x:rat]invprop2(z0,x),t5,p,[x:rat][t:invprop2(z0,x)]t12(x,t)):p
+ksi@[x0:rat][ux:urt(ksi,x0)]
+2x0:=pl"rt"(x0,x0):rat
+t13:=satz94a(x0,x0):less"rt"(x0,2x0)
+t14:=satz119a(ksi,x0,ux,2x0,t13):urt(ksi,2x0)
+t15:=inv1(ov(1rt,2x0),2x0,t14,x0,ux,t13,refis(rat,ov(1rt,2x0))):in(ov(1rt,2x0),inv)
+ksi@[x1:rat][lx:lrt(ksi,x1)][x0:rat][ux:urt(ksi,x0)]
+t16:=th3"l.imp"(is"rt"(x0,x1),lrt(ksi,x0),ux,[t:is"rt"(x0,x1)]isp1(rat,[x:rat]lrt(ksi,x),x1,x0,lx,t)):nis"rt"(x0,x1)
+t17:=satz110e(1rt,x0):is"rt"(ts"rt"(ov(1rt,x0),x0),1rt)
+t18:=satz110e(1rt,x1):is"rt"(ts"rt"(ov(1rt,x1),x1),1rt)
+[i:is"rt"(ov(1rt,x0),ov(1rt,x1))]
+t19:=tris(rat,ts"rt"(ov(1rt,x0),x1),ts"rt"(ov(1rt,x1),x1),1rt,ists1"rt"(ov(1rt,x0),ov(1rt,x1),x1,i),t18):is"rt"(ts"rt"(ov(1rt,x0),x1),1rt)
+t20:=satz110b(1rt,ov(1rt,x0),x0,x1,t17,t19):is"rt"(x0,x1)
+ux@t21:=th3"l.imp"(is"rt"(ov(1rt,x0),ov(1rt,x1)),is"rt"(x0,x1),t16,[t:is"rt"(ov(1rt,x0),ov(1rt,x1))]t20(t)):nis"rt"(ov(1rt,x0),ov(1rt,x1))
+lx@[i:in(ov(1rt,x1),inv)]
+t22:=invapp(ov(1rt,x1),i,con,[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(ov(1rt,x1),ov(1rt,x))]<symis(rat,ov(1rt,x1),ov(1rt,x),w)>t21(x,t)):con
+lx@t23:=[t:in(ov(1rt,x1),inv)]t22(t):not(in(ov(1rt,x1),inv))
+ksi@[z0:rat][i:in(z0,inv)][u0:rat][l:less"rt"(u0,z0)][x0:rat][ux:urt(ksi,x0)][j:is"rt"(z0,ov(1rt,x0))]
+t24:=isless2"rt"(z0,ov(1rt,x0),u0,j,l):less"rt"(u0,ov(1rt,x0))
+t25:=tris(rat,ts"rt"(ov(1rt,x0),x0),1rt,ts"rt"(u0,ov(1rt,u0)),satz110e(1rt,x0),satz110d(1rt,u0)):is"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)))
+t26:=isless2"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(u0,x0),t25,satz105c(u0,ov(1rt,x0),x0,t24)):less"rt"(ts"rt"(u0,x0),ts"rt"(u0,ov(1rt,u0)))
+t27:=isless12"rt"(ts"rt"(u0,x0),ts"rt"(x0,u0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(ov(1rt,u0),u0),comts"rt"(u0,x0),comts"rt"(u0,ov(1rt,u0)),t26):less"rt"(ts"rt"(x0,u0),ts"rt"(ov(1rt,u0),u0))
+t28:=satz106c(x0,ov(1rt,u0),u0,t27):less"rt"(x0,ov(1rt,u0))
+t29:=satz119a(x0,ux,ov(1rt,u0),t28):urt(ksi,ov(1rt,u0))
+t30:=satz110e(1rt,u0):is"rt"(ts"rt"(ov(1rt,u0),u0),1rt)
+t31:=satz110g(1rt,ov(1rt,u0),u0,t30):is"rt"(u0,ov(1rt,ov(1rt,u0)))
+t32:=inv1(u0,ov(1rt,u0),t29,x0,ux,t28,t31):in(u0,inv)
+l@t33:=invapp(z0,i,in(u0,inv),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t32(x,t,w)):in(u0,inv)
+i@[x0:rat][ux:urt(ksi,x0)][x1:rat][ux1:urt(ksi,x1)][l:less"rt"(x1,x0)][j:is"rt"(z0,ov(1rt,x0))]
+t34:=satz91(x1,x0,l):some"rt"([x:rat]and(less"rt"(x1,x),less"rt"(x,x0)))
+[x2:rat][a:and(less"rt"(x1,x2),less"rt"(x2,x0))]
+t35:=ande1(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x1,x2)
+t36:=satz119a(ksi,x1,ux1,x2,t35):urt(ksi,x2)
+t37:=inv1(ov(1rt,x2),x2,t36,x1,ux1,t35,refis(rat,ov(1rt,x2))):in(ov(1rt,x2),inv)
+t38:=ande2(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x2,x0)
+t39:=tris(rat,ts"rt"(x0,ov(1rt,x0)),1rt,ts"rt"(x2,ov(1rt,x2)),satz110c(1rt,x0),satz110d(1rt,x2)):is"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
+t40:=isless2"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)),ts"rt"(x2,ov(1rt,x0)),t39,satz105c(x2,x0,ov(1rt,x0),t38)):less"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
+t41:=isless12"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(ov(1rt,x0),x2),ts"rt"(x2,ov(1rt,x2)),ts"rt"(ov(1rt,x2),x2),comts"rt"(x2,ov(1rt,x0)),comts"rt"(x2,ov(1rt,x2)),t40):less"rt"(ts"rt"(ov(1rt,x0),x2),ts"rt"(ov(1rt,x2),x2))
+t42:=satz106c(ov(1rt,x0),ov(1rt,x2),x2,t41):less"rt"(ov(1rt,x0),ov(1rt,x2))
+t43:=ismore2"rt"(ov(1rt,x0),z0,ov(1rt,x2),symis(rat,z0,ov(1rt,x0),j),satz83(ov(1rt,x0),ov(1rt,x2),t42)):more"rt"(ov(1rt,x2),z0)
+t44:=andi(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0),t37,t43):and(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0))
+t45:=somei(rat,[x:rat]and(in(x,inv),more"rt"(x,z0)),ov(1rt,x2),t44):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
+j@t46:=someapp(rat,[x:rat]and(less"rt"(x1,x),less"rt"(x,x0)),t34,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:and(less"rt"(x1,x),less"rt"(x,x0))]t45(x,t)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
+i@t47:=invapp(z0,i,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t46(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
+ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
+t48:=cut2(inv,ov(1rt,pl"rt"(y0,y0)),t15(y0,uy),ov(1rt,x0),t23(x0,lx),[x:rat][t:in(x,inv)][y:rat][u:less"rt"(y,x)]t33(x,t,y,u),[x:rat][t:in(x,inv)]t47(x,t)):cutprop(inv)
+lx@t49:=cutapp1b(ksi,cutprop(inv),[x:rat][t:urt(ksi,x)]t48(x,t)):cutprop(inv)
+ksi@t50:=cutapp1a(ksi,cutprop(inv),[x:rat][t:lrt(ksi,x)]t49(x,t)):cutprop(inv)
+chi:=cutof(inv,t50):cut
+[z0:rat][lz:lrt(ts(ksi,chi),z0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,ts"rt"(x0,u0))][x1:rat][ux:urt(ksi,x1)][j:is"rt"(u0,ov(1rt,x1))]
+t51:=tris(rat,z0,ts"rt"(x0,u0),ts"rt"(x0,ov(1rt,x1)),i,ists2"rt"(u0,ov(1rt,x1),x0,j)):is"rt"(z0,ts"rt"(x0,ov(1rt,x1)))
+t52:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
+t53:=isless12"rt"(ts"rt"(x0,ov(1rt,x1)),z0,ts"rt"(x1,ov(1rt,x1)),1rt,symis(rat,z0,ts"rt"(x0,ov(1rt,x1)),t51),satz110c(1rt,x1),satz105c(x0,x1,ov(1rt,x1),t52)):less"rt"(z0,1rt)
+t54:=lrtrpofrt(1rt,z0,t53):lrt(1rp,z0)
+i@r1:=ini(inv,t50,u0,lu):in(u0,inv)
+r2:=invapp(u0,r1,lrt(1rp,z0),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(u0,ov(1rt,x))]t54(x,t,w)):lrt(1rp,z0)
+lz@r3:=tsapp(ksi,chi,z0,lz,lrt(1rp,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,ts"rt"(x,y))]r2(x,t,y,u,v)):lrt(1rp,z0)
+ksi@[u0:rat][lu:lrt(1rp,u0)]
+t55:=lrtrpofrte(1rt,u0,lu):less"rt"(u0,1rt)
+t56:=satz83(u0,1rt,t55):more"rt"(1rt,u0)
+[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][x2:rat][ux2:urt(ksi,x2)]
+t57:=cutapp2b(x1,lx1,x2,ux2):more"rt"(x2,x1)
+[i:is"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0))]
+t58:=cutapp2a(x0,lx,x2,ux2):less"rt"(x0,x2)
+t59:=satz105f(x0,x2,mn"rt"(1rt,u0,t56),t58):less"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),ts"rt"(mn"rt"(1rt,u0,t56),x2))
+t60:=isless1"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),symis(rat,mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0),i),t59):less"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2))
+t61:=tr4is(rat,pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),ts"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),x2),ts"rt"(1rt,x2),x2,pl"rt"(mn"rt"(x2,x1,t57),x1),distpt1"rt"(mn"rt"(1rt,u0,t56),u0,x2),ists1"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),1rt,x2,satz101e(1rt,u0,t56)),example1c(x2),satz101f(x2,x1,t57)):is"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
+t62:=satz96c(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2),t60):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)))
+t63:=isless2"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),t61,t62):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
+t64:=isless12"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(x1,mn"rt"(x2,x1,t57)),compl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),compl"rt"(mn"rt"(x2,x1,t57),x1),t63):less"rt"(pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(x1,mn"rt"(x2,x1,t57)))
+t65:=satz97c(ts"rt"(u0,x2),x1,mn"rt"(x2,x1,t57),t64):less"rt"(ts"rt"(u0,x2),x1)
+t66:=tr3is(rat,ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),ts"rt"(ts"rt"(ov(1rt,u0),u0),x2),ts"rt"(1rt,x2),x2,assts2"rt"(ov(1rt,u0),u0,x2),ists1"rt"(ts"rt"(ov(1rt,u0),u0),1rt,x2,satz110e(1rt,u0)),example1c(x2)):is"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2)
+t67:=isless12"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2,ts"rt"(ov(1rt,u0),x1),ov(x1,u0),t66,satz141b(x1,u0),satz105f(ts"rt"(u0,x2),x1,ov(1rt,u0),t65)):less"rt"(x2,ov(x1,u0))
+t68:=satz119a(x2,ux2,ov(x1,u0),t67):urt(ksi,ov(x1,u0))
+t69:=satz110e(x1,u0):is"rt"(ts"rt"(ov(x1,u0),u0),x1)
+t70:=tr3is(rat,u0,ov(x1,ov(x1,u0)),ts"rt"(ov(1rt,ov(x1,u0)),x1),ts"rt"(x1,ov(1rt,ov(x1,u0))),satz110g(x1,ov(x1,u0),u0,t69),satz141c(x1,ov(x1,u0)),comts"rt"(ov(1rt,ov(x1,u0)),x1)):is"rt"(u0,ts"rt"(x1,ov(1rt,ov(x1,u0))))
+t71:=inv1(ov(1rt,ov(x1,u0)),ov(x1,u0),t68,x2,ux2,t67,refis(rat,ov(1rt,ov(x1,u0)))):in(ov(1rt,ov(x1,u0)),inv)
+t72:=ine(inv,t50,ov(1rt,ov(x1,u0)),t71):lrt(chi,ov(1rt,ov(x1,u0)))
+t73:=lrtts(ksi,chi,u0,x1,lx1,ov(1rt,ov(x1,u0)),t72,t70):lrt(ts(ksi,chi),u0)
+lx@t74:=satz132app(ksi,lrt(ts(ksi,chi),u0),ts"rt"(mn"rt"(1rt,u0,t56),x0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn"rt"(y,x,cutapp2b(x,t,y,u)),ts"rt"(mn"rt"(1rt,u0,t56),x0))]t73(x,t,y,u,v)):lrt(ts(ksi,chi),u0)
+lu@t75:=cutapp1a(ksi,lrt(ts(ksi,chi),u0),[x:rat][t:lrt(ksi,x)]t74(x,t)):lrt(ts(ksi,chi),u0)
+ksi@t76:=isi1(ts(ksi,chi),1rp,[x:rat][t:lrt(ts(ksi,chi),x)]r3(x,t),[x:rat][t:lrt(1rp,x)]t75(x,t)):is(ts(ksi,chi),1rp)
+-4152
+satz152:=somei(cut,[t:cut]is(ts(ksi,t),1rp),chi".4152",t76".4152"):some([c:cut]is(ts(ksi,c),1rp))
+eta@[phi:cut][psi:cut]
++4153
+[m:more(phi,psi)]
+t1:=satz145d(phi,psi,eta,m):more(ts(eta,phi),ts(eta,psi))
+t2:=ec3e21(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t1):nis(ts(eta,phi),ts(eta,psi))
+psi@[l:less(phi,psi)]
+t3:=satz145f(phi,psi,eta,l):less(ts(eta,phi),ts(eta,psi))
+t4:=ec3e31(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t3):nis(ts(eta,phi),ts(eta,psi))
+psi@[n:nis(phi,psi)]
+t5:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
+t6:=orapp(more(phi,psi),less(phi,psi),nis(ts(eta,phi),ts(eta,psi)),t5,[t:more(phi,psi)]t2(t),[t:less(phi,psi)]t4(t)):nis(ts(eta,phi),ts(eta,psi))
+-4153
+[i:is(ts(eta,phi),ksi)][j:is(ts(eta,psi),ksi)]
+satz153b:=th7"l.imp"(is(phi,psi),nis(ts(eta,phi),ts(eta,psi)),weli(is(ts(eta,phi),ts(eta,psi)),tris2(cut,ts(eta,phi),ts(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t6".4153"(t)):is(phi,psi)
++*4153
+eta@[tau:cut][i:is(ts(eta,tau),1rp)]
+chi:=ts(tau,ksi):cut
+t7:=tr3is(cut,ts(eta,chi),ts(ts(eta,tau),ksi),ts(1rp,ksi),ksi,assts2(eta,tau,ksi),ists1(ts(eta,tau),1rp,ksi,i),satz151b(ksi)):is(ts(eta,chi),ksi)
+t8:=somei(cut,[c:cut]is(ts(eta,c),ksi),chi,t7):some([c:cut]is(ts(eta,c),ksi))
+-4153
+eta@satz153a:=someapp(cut,[c:cut]is(ts(eta,c),1rp),satz152(eta),some([c:cut]is(ts(eta,c),ksi)),[c:cut][t:is(ts(eta,c),1rp)]t8".4153"(c,t)):some([c:cut]is(ts(eta,c),ksi))
++*4153
+eta@t9:=[c:cut][d:cut][t:is(ts(eta,c),ksi)][u:is(ts(eta,d),ksi)]satz153b(c,d,t,u):amone(cut,[c:cut]is(ts(eta,c),ksi))
+-4153
+eta@satz153:=onei(cut,[c:cut]is(ts(eta,c),ksi),t9".4153",satz153a):one([c:cut]is(ts(eta,c),ksi))
+ov:=ind(cut,[a:cut]is(ts(eta,a),ksi),satz153):cut
+satz153c:=oneax(cut,[a:cut]is(ts(eta,a),ksi),satz153):is(ts(eta,ov(ksi,eta)),ksi)
+satz153d:=symis(cut,ts(eta,ov(ksi,eta)),ksi,satz153c):is(ksi,ts(eta,ov(ksi,eta)))
+satz153e:=tris(cut,ts(ov(ksi,eta),eta),ts(eta,ov(ksi,eta)),ksi,comts(ov(ksi,eta),eta),satz153c):is(ts(ov(ksi,eta),eta),ksi)
+satz153f:=symis(cut,ts(ov(ksi,eta),eta),ksi,satz153e):is(ksi,ts(ov(ksi,eta),eta))
+[phi:cut][i:is(ts(eta,phi),ksi)]
+satz153g:=satz153b(phi,ov(ksi,eta),i,satz153c):is(phi,ov(ksi,eta))
+@[ksi:cut]
+ratrp:=image(rat,cut,[x:rat]rpofrt(x),ksi):'prop'
+@[x0:rat]
+ratrpi:=imagei(rat,cut,[x:rat]rpofrt(x),x0):ratrp(rpofrt(x0))
+@[x:nat]
+rpofnt:=rpofrt(rtofn(x)):cut
+ksi@natrp:=image(nat,cut,[x:nat]rpofnt(x),ksi):'prop'
+x@natrpi:=imagei(nat,cut,[y:nat]rpofnt(y),x):natrp(rpofnt(x))
+ksi@[n:natrp(ksi)]
++iii5
+[x:nat][i:is(ksi,rpofnt(x))]
+t1:=somei(rat,[y:rat]is(ksi,rpofrt(y)),rtofn(x),i):ratrp(ksi)
+-iii5
+lemmaiii5:=someapp(nat,[x:nat]is(ksi,rpofnt(x)),n,ratrp(ksi),[x:nat][t:is(ksi,rpofnt(x))]t1".iii5"(x,t)):ratrp(ksi)
+@[x0:rat][y0:rat][m:more"rt"(x0,y0)]
++5154
+t1:=lrtrpofrt(x0,y0,satz82(x0,y0,m)):lrt(rpofrt(x0),y0)
+t2:=urtrpofrt(y0,y0,moreisi2"rt"(y0,y0,refis(rat,y0))):urt(rpofrt(y0),y0)
+t3:=andi(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0),t1,t2):and(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0))
+-5154
+satz154a:=somei(rat,[x:rat]and(lrt(rpofrt(x0),x),urt(rpofrt(y0),x)),y0,t3".5154"):more(rpofrt(x0),rpofrt(y0))
+y0@[i:is"rt"(x0,y0)]
+satz154b:=isf(rat,cut,[x:rat]rpofrt(x),x0,y0,i):is(rpofrt(x0),rpofrt(y0))
+y0@[l:less"rt"(x0,y0)]
+satz154c:=satz121(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,satz83(x0,y0,l))):less(rpofrt(x0),rpofrt(y0))
++*5154
+y0@t4:=satz81a(x0,y0):or3(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0))
+t5:=satz123b(rpofrt(x0),rpofrt(y0)):ec3(is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)))
+-5154
+y0@[m:more(rpofrt(x0),rpofrt(y0))]
+satz154d:=th11"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),m):more"rt"(x0,y0)
+y0@[i:is(rpofrt(x0),rpofrt(y0))]
+satz154e:=th10"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),i):is"rt"(x0,y0)
+y0@[l:less(rpofrt(x0),rpofrt(y0))]
+satz154f:=th12"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),l):less"rt"(x0,y0)
++*iii5
+@t2:=[x:rat][y:rat][t:is(rpofrt(x),rpofrt(y))]satz154e(x,y,t):injective(rat,cut,[x:rat]rpofrt(x))
+-iii5
+y0@[i:is"rt"(x0,y0)]
+isrterp:=satz154b(x0,y0,i):is(rpofrt(x0),rpofrt(y0))
+y0@[i:is(rpofrt(x0),rpofrt(y0))]
+isrtirp:=satz154e(x0,y0,i):is"rt"(x0,y0)
+ksi@[rtksi:ratrp(ksi)]
+rtofrp:=soft(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):rat
+[eta:cut][rteta:ratrp(eta)][i:is(ksi,eta)]
+isrpert:=isinv(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))
+rteta@[i:is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))]
+isrpirt:=isinve(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is(ksi,eta)
+x0@isrtrp1:=isst1(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(x0,rtofrp(rpofrt(x0),ratrpi(x0)))
+isrtrp2:=isst2(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(rtofrp(rpofrt(x0),ratrpi(x0)),x0)
+rtksi@isrprt1:=ists1"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(ksi,rpofrt(rtofrp(ksi,rtksi)))
+isrprt2:=ists2"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(rpofrt(rtofrp(ksi,rtksi)),ksi)
+@[x:nat][y:nat][i:is"n"(x,y)]
+isnterp:=isf(nat,cut,[z:nat]rpofnt(z),x,y,i):is(rpofnt(x),rpofnt(y))
+y@[i:is(rpofnt(x),rpofnt(y))]
+isntirp:=isnirt(x,y,isrtirp(rtofn(x),rtofn(y),i)):is"n"(x,y)
++*iii5
+@t3:=[x:nat][y:nat][t:is(rpofnt(x),rpofnt(y))]isntirp(x,y,t):injective(nat,cut,[x:nat]rpofnt(x))
+-iii5
+ksi@[ntksi:natrp(ksi)]
+ntofrp:=soft(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):nat
+[eta:cut][nteta:natrp(eta)][i:is(ksi,eta)]
+isrpent:=isinv(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))
+nteta@[i:is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))]
+isrpint:=isinve(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is(ksi,eta)
+x@isntrp1:=isst1(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(x,ntofrp(rpofnt(x),natrpi(x)))
+isntrp2:=isst2(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(ntofrp(rpofnt(x),natrpi(x)),x)
+ntksi@isrpnt1:=ists1"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(ksi,rpofnt(ntofrp(ksi,ntksi)))
+isrpnt2:=ists2"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(rpofnt(ntofrp(ksi,ntksi)),ksi)
+@[x0:rat][y0:rat]
++5155
+[z0:rat][lz:lrt(pl(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,pl"rt"(u0,v0))]
+t1:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
+t2:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
+t3:=satz98a(u0,x0,v0,y0,t1,t2):less"rt"(pl"rt"(u0,v0),pl"rt"(x0,y0))
+t4:=isless1"rt"(pl"rt"(u0,v0),z0,pl"rt"(x0,y0),symis(rat,z0,pl"rt"(u0,v0),i),t3):less"rt"(z0,pl"rt"(x0,y0))
+t5:=lrtrpofrt(pl"rt"(x0,y0),z0,t4):lrt(rpofrt(pl"rt"(x0,y0)),z0)
+lz@t6:=plapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(pl"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,pl"rt"(x,y))]t5(x,t,y,u,v)):lrt(rpofrt(pl"rt"(x0,y0)),z0)
+y0@[u0:rat][lu:lrt(rpofrt(pl"rt"(x0,y0)),u0)]
+t7:=lrtrpofrte(pl"rt"(x0,y0),u0,lu):less"rt"(u0,pl"rt"(x0,y0))
+u01:=ov"rt"(u0,pl"rt"(x0,y0)):rat
+t8:=isless12"rt"(u0,ts"rt"(u01,pl"rt"(x0,y0)),pl"rt"(x0,y0),ts"rt"(1rt,pl"rt"(x0,y0)),satz110f(u0,pl"rt"(x0,y0)),example1d(pl"rt"(x0,y0)),t7):less"rt"(ts"rt"(u01,pl"rt"(x0,y0)),ts"rt"(1rt,pl"rt"(x0,y0)))
+t9:=satz106c(u01,1rt,pl"rt"(x0,y0),t8):less"rt"(u01,1rt)
+t10:=tris(rat,u0,ts"rt"(pl"rt"(x0,y0),u01),pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)),satz110d(u0,pl"rt"(x0,y0)),disttp1"rt"(x0,y0,u01)):is"rt"(u0,pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)))
+y0@[l:less"rt"(y0,1rt)]
+t11:=isless12"rt"(ts"rt"(y0,x0),ts"rt"(x0,y0),ts"rt"(1rt,x0),x0,comts"rt"(y0,x0),example1c(x0),satz105c(y0,1rt,x0,l)):less"rt"(ts"rt"(x0,y0),x0)
+t12:=lrtrpofrt(x0,ts"rt"(x0,y0),t11):lrt(rpofrt(x0),ts"rt"(x0,y0))
+lu@t13:=lrtpl(rpofrt(x0),rpofrt(y0),u0,ts"rt"(x0,u01),t12(x0,u01,t9),ts"rt"(y0,u01),t12(y0,u01,t9),t10):lrt(pl(rpofrt(x0),rpofrt(y0)),u0)
+-5155
+satz155a:=isi1(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(pl"rt"(x0,y0)),x)]t13".5155"(x,t),[x:rat][t:lrt(pl(rpofrt(x0),rpofrt(y0)),x)]t6".5155"(x,t)):is(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)))
+[m:more"rt"(x0,y0)]
++*5155
+m@t14:=satz101f(x0,y0,m):is"rt"(x0,pl"rt"(mn"rt"(x0,y0,m),y0))
+t15:=tris(cut,rpofrt(x0),rpofrt(pl"rt"(mn"rt"(x0,y0,m),y0)),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),isrterp(x0,pl"rt"(mn"rt"(x0,y0,m),y0),t14),satz155a(mn"rt"(x0,y0,m),y0)):is(rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)))
+t16:=tris2(cut,pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),compl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),t15):is(pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0))
+-5155
+m@satz155b:=satz140g(rpofrt(x0),rpofrt(y0),rpofrt(mn"rt"(x0,y0,m)),satz154a(x0,y0,m),t16".5155"):is(rpofrt(mn"rt"(x0,y0,m)),mn(rpofrt(x0),rpofrt(y0),satz154a(x0,y0,m)))
++*5155
+y0@[z0:rat][lz:lrt(ts(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,ts"rt"(u0,v0))]
+t17:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
+t18:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
+t19:=satz107a(u0,x0,v0,y0,t17,t18):less"rt"(ts"rt"(u0,v0),ts"rt"(x0,y0))
+t20:=isless1"rt"(ts"rt"(u0,v0),z0,ts"rt"(x0,y0),symis(rat,z0,ts"rt"(u0,v0),i),t19):less"rt"(z0,ts"rt"(x0,y0))
+t21:=lrtrpofrt(ts"rt"(x0,y0),z0,t20):lrt(rpofrt(ts"rt"(x0,y0)),z0)
+lz@t22:=tsapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(ts"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,ts"rt"(x,y))]t21(x,t,y,u,v)):lrt(rpofrt(ts"rt"(x0,y0)),z0)
+y0@[u0:rat][lu:lrt(rpofrt(ts"rt"(x0,y0)),u0)]
+t23:=lrtrpofrte(ts"rt"(x0,y0),u0,lu):less"rt"(u0,ts"rt"(x0,y0))
+[u1:rat][a:and(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)))]
+t24:=ande1(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u0,u1)
+t25:=ande2(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u1,ts"rt"(x0,y0))
+t26:=isless12"rt"(u0,ts"rt"(ov"rt"(u0,u1),u1),u1,ts"rt"(1rt,u1),satz110f(u0,u1),example1d(u1),t24):less"rt"(ts"rt"(ov"rt"(u0,u1),u1),ts"rt"(1rt,u1))
+t27:=satz106c(ov"rt"(u0,u1),1rt,u1,t26):less"rt"(ov"rt"(u0,u1),1rt)
+t28:=isless1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0),satz110f(u1,y0),t25):less"rt"(ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0))
+t29:=satz106c(ov"rt"(u1,y0),x0,y0,t28):less"rt"(ov"rt"(u1,y0),x0)
+t30:=tr3is(rat,u0,ts"rt"(u1,ov"rt"(u0,u1)),ts"rt"(ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1)),ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))),satz110d(u0,u1),ists1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1),satz110f(u1,y0)),assts1"rt"(ov"rt"(u1,y0),y0,ov"rt"(u0,u1))):is"rt"(u0,ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))))
+t31:=lrtts(rpofrt(x0),rpofrt(y0),u0,ov"rt"(u1,y0),lrtrpofrt(x0,ov"rt"(u1,y0),t29),ts"rt"(y0,ov"rt"(u0,u1)),t12(y0,ov"rt"(u0,u1),t27),t30):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
+lu@t32:=someapp(rat,[x:rat]and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0))),satz91(u0,ts"rt"(x0,y0),t23),lrt(ts(rpofrt(x0),rpofrt(y0)),u0),[x:rat][t:and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0)))]t31(x,t)):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
+-5155
+y0@satz155c:=isi1(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(ts"rt"(x0,y0)),x)]t32".5155"(x,t),[x:rat][t:lrt(ts(rpofrt(x0),rpofrt(y0)),x)]t22".5155"(x,t)):is(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)))
++*5155
+y0@t33:=satz110f(x0,y0):is"rt"(x0,ts"rt"(ov"rt"(x0,y0),y0))
+t34:=tris(cut,rpofrt(x0),rpofrt(ts"rt"(ov"rt"(x0,y0),y0)),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),isrterp(x0,ts"rt"(ov"rt"(x0,y0),y0),t33),satz155c(ov"rt"(x0,y0),y0)):is(rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)))
+t35:=tris2(cut,ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),comts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),t34):is(ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0))
+-5155
+y0@satz155d:=satz153g(rpofrt(x0),rpofrt(y0),rpofrt(ov"rt"(x0,y0)),t35".5155"):is(rpofrt(ov"rt"(x0,y0)),ov(rpofrt(x0),rpofrt(y0)))
+@[x:nat][y:nat]
+satz155e:=tris(cut,rpofnt(pl"n"(x,y)),rpofrt(pl"rt"(rtofn(x),rtofn(y))),pl(rpofnt(x),rpofnt(y)),isrterp(rtofn(pl"n"(x,y)),pl"rt"(rtofn(x),rtofn(y)),symis(rat,pl"rt"(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),satz112h(x,y))),satz155a(rtofn(x),rtofn(y))):is(rpofnt(pl"n"(x,y)),pl(rpofnt(x),rpofnt(y)))
+satz155f:=tris(cut,rpofnt(ts"n"(x,y)),rpofrt(ts"rt"(rtofn(x),rtofn(y))),ts(rpofnt(x),rpofnt(y)),isrterp(rtofn(ts"n"(x,y)),ts"rt"(rtofn(x),rtofn(y)),symis(rat,ts"rt"(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),satz112j(x,y))),satz155c(rtofn(x),rtofn(y))):is(rpofnt(ts"n"(x,y)),ts(rpofnt(x),rpofnt(y)))
++nt
+@natt:=ot(cut,[t:cut]natrp(t)):'type'
+[ksi:cut][nksi:natrp(ksi)]
+nttofrp:=out(cut,[t:cut]natrp(t),ksi,nksi):natt
+@[xt:natt][yt:natt]
+is:=is"e"(natt,xt,yt):'prop'
+nis:=not(is(xt,yt)):'prop'
+@[p:[x:natt]'prop']
+all:=all"l"(natt,p):'prop'
+some:=some"l"(natt,p):'prop'
+one:=one"e"(natt,p):'prop'
+xt@[st:set(natt)]
+in:=esti(natt,xt,st):'prop'
+xt@rpofntt:=in"e"(cut,[t:cut]natrp(t),xt):cut
+natrpi:=inp(cut,[t:cut]natrp(t),xt):natrp(rpofntt(xt))
+nksi@[eta:cut][neta:natrp(eta)][i:is"rp"(ksi,eta)]
+isrpentt:=isouti(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is(nttofrp(ksi,nksi),nttofrp(eta,neta))
+neta@[i:is(nttofrp(ksi,nksi),nttofrp(eta,neta))]
+isrpintt:=isoute(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is"rp"(ksi,eta)
+yt@[i:is(xt,yt)]
+isntterp:=isini(cut,[t:cut]natrp(t),xt,yt,i):is"rp"(rpofntt(xt),rpofntt(yt))
+yt@[i:is"rp"(rpofntt(xt),rpofntt(yt))]
+isnttirp:=isine(cut,[t:cut]natrp(t),xt,yt,i):is(xt,yt)
+nksi@isrpntt1:=isinout(cut,[t:cut]natrp(t),ksi,nksi):is"rp"(ksi,rpofntt(nttofrp(ksi,nksi)))
+xt@isnttrp1:=isoutin(cut,[t:cut]natrp(t),xt):is(xt,nttofrp(rpofntt(xt),natrpi(xt)))
+@[x:nat]
+nttofnt:=nttofrp(rpofnt(x),natrpi"rp"(x)):natt
+[y:nat][i:is"n"(x,y)]
+isntentt:=isrpentt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),isnterp(x,y,i)):is(nttofnt(x),nttofnt(y))
+y@[i:is(nttofnt(x),nttofnt(y))]
+isntintt:=isntirp(x,y,isrpintt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),i)):is"n"(x,y)
+xt@ntofntt:=ntofrp(rpofntt(xt),natrpi(xt)):nat
+yt@[i:is(xt,yt)]
+isnttent:=isrpent(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),isntterp(xt,yt,i)):is"n"(ntofntt(xt),ntofntt(yt))
+yt@[i:is"n"(ntofntt(xt),ntofntt(yt))]
+isnttint:=isnttirp(xt,yt,isrpint(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),i)):is(xt,yt)
++iii5
+x@t5:=isrpntt1(rpofnt(x),natrpi"rp"(x)):is"rp"(rpofnt(x),rpofntt(nttofnt(x)))
+t6:=isrpent(rpofnt(x),natrpi"rp"(x),rpofntt(nttofnt(x)),natrpi(nttofnt(x)),t5):is"n"(ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)))
+-iii5
+x@isntntt1:=tris(nat,x,ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)),isntrp1(x),t6".iii5"):is"n"(x,ntofntt(nttofnt(x)))
++*iii5
+xt@t7:=isrpnt1(rpofntt(xt),natrpi(xt)):is"rp"(rpofntt(xt),rpofnt(ntofntt(xt)))
+t8:=isrpentt(rpofntt(xt),natrpi(xt),rpofnt(ntofntt(xt)),natrpi"rp"(ntofntt(xt)),t7):is(nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)))
+-iii5
+xt@isnttnt1:=tris(natt,xt,nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)),isnttrp1(xt),t8".iii5"):is(xt,nttofnt(ntofntt(xt)))
+x@isntntt2:=symis(nat,x,ntofntt(nttofnt(x)),isntntt1):is"n"(ntofntt(nttofnt(x)),x)
+xt@isnttnt2:=symis(natt,xt,nttofnt(ntofntt(xt)),isnttnt1):is(nttofnt(ntofntt(xt)),xt)
+@1t:=nttofnt(1):natt
+suct:=[x:natt]nttofnt(<ntofntt(x)>suc):[x:natt]natt
++5156
+xt@[j:is(<xt>suct,1t)]
+t1:=isntintt(<ntofntt(xt)>suc,1,j):is"n"(<ntofntt(xt)>suc,1)
+-5156
+xt@satz156a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<ntofntt(xt)>suc,1),<ntofntt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5156"(t)):nis(<xt>suct,1t)
+yt@[i:is(<xt>suct,<yt>suct)]
++*5156
+i@t2:=isntintt(<ntofntt(xt)>suc,<ntofntt(yt)>suc,i):is"n"(<ntofntt(xt)>suc,<ntofntt(yt)>suc)
+-5156
+i@satz156b:=isnttint(xt,yt,<t2".5156"><ntofntt(yt)><ntofntt(xt)>ax4):is(xt,yt)
+@[st:set(natt)]
+cond1:=in(1t,st):'prop'
+cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
+[c1:cond1][c2:cond2]
++*5156
+c2@[x:nat]
+prop1:=in(nttofnt(x),st):'prop'
+[p:prop1(x)]
+t3:=<p><nttofnt(x)>c2:in(<nttofnt(x)>suct,st)
+t4:=isp(nat,[t:nat]in(nttofnt(<t>suc),st),ntofntt(nttofnt(x)),x,t3,isntntt2(x)):prop1(<x>suc)
+-5156
+c2@[xt:natt]
++*5156
+xt@t5:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t4(t,u),ntofntt(xt)):in(nttofnt(ntofntt(xt)),st)
+-5156
+xt@satz156c:=isp(natt,[t:natt]in(t,st),nttofnt(ntofntt(xt)),xt,t5".5156",isnttnt2(xt)):in(xt,st)
+@ax3t:=[x:natt]satz156a(x):[x:natt]nis(<x>suct,1t)
+ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz156b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
+ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz156c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
+-nt
++rtt
+@ratt:=ot(cut,[t:cut]ratrp(t)):'type'
+[ksi:cut][rtksi:ratrp(ksi)]
+rttofrp:=out(cut,[t:cut]ratrp(t),ksi,rtksi):ratt
+@[x0t:ratt][y0t:ratt]
+is:=is"e"(ratt,x0t,y0t):'prop'
+nis:=not(is(x0t,y0t)):'prop'
+@[p:[x:ratt]'prop']
+all:=all"l"(ratt,p):'prop'
+some:=some"l"(ratt,p):'prop'
+one:=one"e"(ratt,p):'prop'
+x0t@rpofrtt:=in"e"(cut,[t:cut]ratrp(t),x0t):cut
+ratrpi:=inp(cut,[t:cut]ratrp(t),x0t):ratrp(rpofrtt(x0t))
+rtksi@[eta:cut][rteta:ratrp(eta)][i:is"rp"(ksi,eta)]
+isrpertt:=isouti(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))
+rteta@[i:is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))]
+isrpirtt:=isoute(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is"rp"(ksi,eta)
+y0t@[i:is(x0t,y0t)]
+isrtterp:=isini(cut,[t:cut]ratrp(t),x0t,y0t,i):is"rp"(rpofrtt(x0t),rpofrtt(y0t))
+y0t@[i:is"rp"(rpofrtt(x0t),rpofrtt(y0t))]
+isrttirp:=isine(cut,[t:cut]ratrp(t),x0t,y0t,i):is(x0t,y0t)
+rtksi@isrprtt1:=isinout(cut,[t:cut]ratrp(t),ksi,rtksi):is"rp"(ksi,rpofrtt(rttofrp(ksi,rtksi)))
+x0t@isrttrp1:=isoutin(cut,[t:cut]ratrp(t),x0t):is(x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)))
+@[x0:rat]
+rttofrt:=rttofrp(rpofrt(x0),ratrpi"rp"(x0)):ratt
+[y0:rat][i:is"rt"(x0,y0)]
+isrtertt:=isrpertt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),isrterp(x0,y0,i)):is(rttofrt(x0),rttofrt(y0))
+y0@[i:is(rttofrt(x0),rttofrt(y0))]
+isrtirtt:=isrtirp(x0,y0,isrpirtt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),i)):is"rt"(x0,y0)
+x0t@rtofrtt:=rtofrp(rpofrtt(x0t),ratrpi(x0t)):rat
+y0t@[i:is(x0t,y0t)]
+isrttert:=isrpert(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),isrtterp(x0t,y0t,i)):is"rt"(rtofrtt(x0t),rtofrtt(y0t))
+y0t@[i:is"rt"(rtofrtt(x0t),rtofrtt(y0t))]
+isrttirt:=isrttirp(x0t,y0t,isrpirt(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),i)):is(x0t,y0t)
++iii5
+x0@t9:=isrprtt1(rpofrt(x0),ratrpi"rp"(x0)):is"rp"(rpofrt(x0),rpofrtt(rttofrt(x0)))
+t10:=isrpert(rpofrt(x0),ratrpi"rp"(x0),rpofrtt(rttofrt(x0)),ratrpi(rttofrt(x0)),t9):is"rt"(rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)))
+-iii5
+x0@isrtrtt1:=tris(rat,x0,rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)),isrtrp1(x0),t10".iii5"):is"rt"(x0,rtofrtt(rttofrt(x0)))
++*iii5
+x0t@t11:=isrprt1(rpofrtt(x0t),ratrpi(x0t)):is"rp"(rpofrtt(x0t),rpofrt(rtofrtt(x0t)))
+t12:=isrpertt(rpofrtt(x0t),ratrpi(x0t),rpofrt(rtofrtt(x0t)),ratrpi"rp"(rtofrtt(x0t)),t11):is(rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)))
+-iii5
+x0t@isrttrt1:=tris(ratt,x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)),isrttrp1(x0t),t12".iii5"):is(x0t,rttofrt(rtofrtt(x0t)))
+-rtt
+@[ksi:cut]
+example2:=satz153c(1rp,ksi):is(ts(ksi,ov(1rp,ksi)),1rp)
+[rtksi:ratrp(ksi)]
++5157
+x01:=rtofrp(ksi,rtksi):rat
+ksi@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
+rtksi@[y0:rat][i:in(y0,s1)]
+t1:=estie(rat,[x:rat]urt(ksi,x),y0,i):urt(ksi,y0)
+[m:more"rt"(x01,y0)]
+t2:=lrtrpofrt(x01,y0,satz82(x01,y0,m)):lrt(rpofrt(x01),y0)
+t3:=isp(cut,[x:cut]lrt(x,y0),rpofrt(x01),ksi,t2,isrprt2(ksi,rtksi)):lrt(ksi,y0)
+i@t4:=th3"l.imp"(more"rt"(x01,y0),lrt(ksi,y0),t1,[t:more"rt"(x01,y0)]t3(t)):not(more"rt"(x01,y0))
+t5:=satz81e(x01,y0,t4):lessis"rt"(x01,y0)
+rtksi@t6:=[x:rat][t:in(x,s1)]t5(x,t):lb(s1,x01)
+t7:=urtrpofrt(x01,x01,moreisi2"rt"(x01,x01,refis(rat,x01))):urt(rpofrt(x01),x01)
+t8:=isp(cut,[x:cut]urt(x,x01),rpofrt(x01),ksi,t7,isrprt2(ksi,rtksi)):urt(ksi,x01)
+t9:=estii(rat,[x:rat]urt(ksi,x),x01,t8):in(x01,s1)
+t10:=andi(lb(s1,x01),in(x01,s1),t6,t9):min(s1,x01)
+-5157
+satz157a:=t10".5157":min(setof(rat,[x:rat]urt(ksi,x)),rtofrp(ksi,rtksi))
+satz157b:=somei(rat,[x:rat]min(s1".5157",x),x01".5157",t10".5157"):some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))
+ksi@[x0:rat][m:min(setof(rat,[x:rat]urt(ksi,x)),x0)]
++*5157
+m"rp"@t11:=ande1(lb(s1,x0),in(x0,s1),m):lb(s1,x0)
+t12:=ande2(lb(s1,x0),in(x0,s1),m):in(x0,s1)
+t13:=estie(rat,[x:rat]urt(ksi,x),x0,t12):urt(ksi,x0)
+[y0:rat][ly:lrt(ksi,y0)]
+t14:=cutapp2a(ksi,y0,ly,x0,t13):less"rt"(y0,x0)
+t15:=lrtrpofrt(x0,y0,t14):lrt(rpofrt(x0),y0)
+y0@[uy:urt(ksi,y0)]
+t17:=estii(rat,[x:rat]urt(ksi,x),y0,uy):in(y0,s1)
+t18:=satz85(x0,y0,<t17><y0>t11):moreis"rt"(y0,x0)
+t19:=urtrpofrt(x0,y0,t18):urt(rpofrt(x0),y0)
+y0@t20:=cp(lrt(rpofrt(x0),y0),lrt(ksi,y0),[t:urt(ksi,y0)]t19(t)):imp(lrt(rpofrt(x0),y0),lrt(ksi,y0))
+-5157
+m@satz157c:=isi1(ksi,rpofrt(x0),[x:rat][t:lrt(ksi,x)]t15".5157"(x,t),[x:rat]t20".5157"(x)):is(ksi,rpofrt(x0))
+ksi@[s:some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))]
++*5157
+s@[x0:rat][m:min(s1,x0)]
+t21:=somei(rat,[x:rat]is(ksi,rpofrt(x)),x0,satz157c(x0,m)):ratrp(ksi)
+-5157
+s@satz157d:=someapp(rat,[x:rat]min(s1".5157",x),s,ratrp(ksi),[x:rat][t:min(s1".5157",x)]t21".5157"(x,t)):ratrp(ksi)
+ksi@[x0:rat][lx:lrt(ksi,x0)]
++5158
+x0@xr:=rpofrt(x0):cut
+lx@t1:=urtrpofrt(x0,x0,moreisi2"rt"(x0,x0,refis(rat,x0))):urt(xr,x0)
+t2:=andi(urt(xr,x0),lrt(ksi,x0),t1,lx):and(urt(xr,x0),lrt(ksi,x0))
+-5158
+satz158a:=somei(rat,[x:rat]and(urt(rpofrt(x0),x),lrt(ksi,x)),x0,t2".5158"):less(rpofrt(x0),ksi)
+x0@[ux:urt(ksi,x0)]
++*5158
+ux@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
+[m:min(s1,x0)]
+t3:=symis(cut,ksi,xr,satz157c(ksi,x0,m)):is(xr,ksi)
+t4:=moreisi2(xr,ksi,t3):moreis(xr,ksi)
+ux@[n:not(min(s1,x0))]
+t5:=estii(rat,[x:rat]urt(ksi,x),x0,ux):in(x0,s1)
+t6:=th4"l.and"(lb(s1,x0),in(x0,s1),n,t5):not(lb(s1,x0))
+t7:=th1"l.some"(rat,[x:rat]imp(in(x,s1),lessis"rt"(x0,x)),t6):some"rt"([x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))))
+[y0:rat][o:not(imp(in(y0,s1),lessis"rt"(x0,y0)))]
+t8:=th5"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):in(y0,s1)
+t9:=estie(rat,[x:rat]urt(ksi,x),y0,t8):urt(ksi,y0)
+t10:=th6"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):not(lessis"rt"(x0,y0))
+t11:=satz82(x0,y0,satz81k(x0,y0,t10)):less"rt"(y0,x0)
+t12:=lrtrpofrt(x0,y0,t11):lrt(xr,y0)
+t13:=andi(lrt(xr,y0),urt(ksi,y0),t12,t9):and(lrt(xr,y0),urt(ksi,y0))
+t14:=somei(rat,[x:rat]and(lrt(xr,x),urt(ksi,x)),y0,t13):more(xr,ksi)
+n@t15:=someapp(rat,[x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))),t7,more(xr,ksi),[x:rat][t:not(imp(in(x,s1),lessis"rt"(x0,x)))]t14(x,t)):more(xr,ksi)
+t16:=moreisi1(xr,ksi,t15):moreis(xr,ksi)
+-5158
+ux@satz158b:=th1"l.imp"(min(s1".5158",x0),moreis(rpofrt(x0),ksi),[t:min(s1".5158",x0)]t4".5158"(t),[t:not(min(s1".5158",x0))]t16".5158"(t)):moreis(rpofrt(x0),ksi)
+x0@[l:less(rpofrt(x0),ksi)]
++*5158
+l@t17:=satz123h(xr,ksi,l):not(moreis(xr,ksi))
+t18:=th3"l.imp"(urt(ksi,x0),moreis(xr,ksi),t17,[t:urt(ksi,x0)]satz158b(t)):not(urt(ksi,x0))
+-5158
+l@satz158c:=et(lrt(ksi,x0),t18".5158"):lrt(ksi,x0)
+x0@[m:moreis(rpofrt(x0),ksi)]
++*5158
+m"rp"@t19:=satz123c(xr,ksi,m):not(less(xr,ksi))
+-5158
+m@satz158d:=th3"l.imp"(lrt(ksi,x0),less(rpofrt(x0),ksi),t19".5158",[t:lrt(ksi,x0)]satz158a(t)):urt(ksi,x0)
+ksi@[eta:cut][l:less(ksi,eta)]
++5159
+[x0:rat]
+xr:=rpofrt(x0):cut
+[ux:urt(ksi,x0)][lx:lrt(eta,x0)][z0:rat]
+zr:=rpofrt(z0):cut
+[lz:lrt(eta,z0)][k:less"rt"(x0,z0)]
+t1:=satz127a(ksi,xr,zr,satz124(xr,ksi,satz158b(ksi,x0,ux)),satz154c(x0,z0,k)):less(ksi,zr)
+t2:=andi(less(ksi,zr),less(zr,eta),t1,satz158a(eta,z0,lz)):and(less(ksi,zr),less(zr,eta))
+t3:=somei(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),z0,t2):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
+lx@t4:=cutapp3(eta,x0,lx,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:lrt(eta,x)][u:less"rt"(x0,x)]t3(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
+-5159
+satz159:=lessapp(ksi,eta,l,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t4".5159"(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
++*5159
+x0@[a:and(less(ksi,xr),less(xr,eta))]
+t5:=andi(ratrp(xr),and(less(ksi,xr),less(xr,eta)),ratrpi(x0),a):and3(ratrp(xr),less(ksi,xr),less(xr,eta))
+t6:=somei(cut,[c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)),xr,t5):some([c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)))
+-5159
+l@satz159a:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta))),[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t6".5159"(x,t)):some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta)))
+[p:'prop'][p1:[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),eta)]p]
++*5159
+p1@[y0:rat]
+yr:=rpofrt(y0):cut
+[a:and(less(ksi,yr),less(yr,eta))]
+t7:=ande1(less(ksi,yr),less(yr,eta),a):less(ksi,yr)
+t8:=ande2(less(ksi,yr),less(yr,eta),a):less(yr,eta)
+t9:=<t8><t7><y0>p1:p
+-5159
+p1@satz159app:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,p,[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t9".5159"(x,t)):p
+eta@[z0:rat][m:more(rpofrt(z0),ts(ksi,eta))]
++5160
+zr:=rpofrt(z0):cut
+nm:=mn(zr,ts(ksi,eta),m):cut
+dn:=pl(pl(ksi,eta),1rp):cut
+fr:=ov(nm,dn):cut
+zeta:=ite(less(fr,1rp),cut,fr,1rp):cut
+[l:less(fr,1rp)]
+t1:=itet(less(fr,1rp),cut,fr,1rp,l):is(zeta,fr)
+t2:=lessisi2(zeta,fr,t1):lessis(zeta,fr)
+t3:=lessisi1(zeta,1rp,satz127a(zeta,fr,1rp,t2,l)):lessis(zeta,1rp)
+m@[n:not(less(fr,1rp))]
+t4:=itef(less(fr,1rp),cut,fr,1rp,n):is(zeta,1rp)
+t5:=lessisi2(zeta,1rp,t4):lessis(zeta,1rp)
+t6:=trlessis(zeta,1rp,fr,t5,satz124(fr,1rp,satz123f(fr,1rp,n))):lessis(zeta,fr)
+m@t7:=th1"l.imp"(less(fr,1rp),lessis(zeta,1rp),[t:less(fr,1rp)]t3(t),[t:not(less(fr,1rp))]t5(t)):lessis(zeta,1rp)
+t8:=th1"l.imp"(less(fr,1rp),lessis(zeta,fr),[t:less(fr,1rp)]t2(t),[t:not(less(fr,1rp))]t6(t)):lessis(zeta,fr)
+[z1:rat]
+zr1:=rpofrt(z1):cut
+[l1:less(ksi,zr1)][l2:less(zr1,pl(ksi,zeta))][z2:rat]
+zr2:=rpofrt(z2):cut
+[l3:less(eta,zr2)][l4:less(zr2,pl(eta,zeta))]
+t9:=isless2(ts(pl(ksi,zeta),pl(eta,zeta)),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),ts(zr1,zr2),disttp2(pl(ksi,zeta),eta,zeta),satz147a(zr1,pl(ksi,zeta),zr2,pl(eta,zeta),l2,l4)):less(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)))
+t10:=lessisi2(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),tris(cut,ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(zeta,eta)),pl(ts(ksi,eta),ts(eta,zeta)),disttp1(ksi,zeta,eta),ispl2(ts(zeta,eta),ts(eta,zeta),ts(ksi,eta),comts(zeta,eta)))):lessis(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)))
+t11:=satz149a(pl(ksi,zeta),pl(ksi,1rp),zeta,zeta,satz139a(ksi,ksi,zeta,1rp,lessisi2(ksi,ksi,refis(cut,ksi)),t7),lessisi2(zeta,zeta,refis(cut,zeta))):lessis(ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta))
+t12:=satz139a(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta),t10,t11):lessis(pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
+t13:=satz127b(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),t9,t12):less(ts(zr1,zr2),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
+t14:=tris(cut,pl(eta,pl(ksi,1rp)),pl(pl(eta,ksi),1rp),pl(pl(ksi,eta),1rp),asspl2(eta,ksi,1rp),ispl1(pl(eta,ksi),pl(ksi,eta),1rp,compl(eta,ksi))):is(pl(eta,pl(ksi,1rp)),dn)
+t15:=tris(cut,pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(pl(eta,pl(ksi,1rp)),zeta),ts(dn,zeta),distpt1(eta,pl(ksi,1rp),zeta),ists1(pl(eta,pl(ksi,1rp)),dn,zeta,t14)):is(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta))
+t16:=tris(cut,pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta))),pl(ts(ksi,eta),ts(dn,zeta)),asspl1(ts(ksi,eta),ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ispl2(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta),ts(ksi,eta),t15)):is(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)))
+t17:=isless2(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)),ts(zr1,zr2),t16,t13):less(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)))
+t18:=islessis12(ts(zeta,dn),ts(dn,zeta),ts(fr,dn),nm,comts(zeta,dn),satz153e(nm,dn),satz149a(zeta,fr,dn,dn,t8,lessisi2(dn,dn,refis(cut,dn)))):lessis(ts(dn,zeta),nm)
+t19:=satz139a(ts(ksi,eta),ts(ksi,eta),ts(dn,zeta),nm,lessisi2(ts(ksi,eta),ts(ksi,eta),refis(cut,ts(ksi,eta))),t18):lessis(pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm))
+t20:=satz127b(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm),t17,t19):less(ts(zr1,zr2),pl(ts(ksi,eta),nm))
+t21:=isless2(pl(ts(ksi,eta),nm),zr,ts(zr1,zr2),satz140c(zr,ts(ksi,eta),m),t20):less(ts(zr1,zr2),zr)
+t22:=satz154f(ts"rt"(z1,z2),z0,isless1(ts(zr1,zr2),rpofrt(ts"rt"(z1,z2)),zr,symis(cut,rpofrt(ts"rt"(z1,z2)),ts(zr1,zr2),satz155c(z1,z2)),t21)):less"rt"(ts"rt"(z1,z2),z0)
+x0:=ov"rt"(z0,z2):rat
+xr:=rpofrt(x0):cut
+y0:=z2:rat
+yr:=rpofrt(y0):cut
+t23:=satz110e(z0,z2):is"rt"(ts"rt"(x0,y0),z0)
+t24:=ismore1"rt"(z0,ts"rt"(x0,z2),ts"rt"(z1,z2),symis(rat,ts"rt"(x0,z2),z0,t23),satz83(ts"rt"(z1,z2),z0,t22)):more"rt"(ts"rt"(x0,z2),ts"rt"(z1,z2))
+t25:=satz106a(x0,z1,z2,t24):more"rt"(x0,z1)
+t26:=trmore(xr,zr1,ksi,satz154a(x0,z1,t25),satz122(ksi,zr1,l1)):more(xr,ksi)
+t27:=satz122(eta,yr,l3):more(yr,eta)
+z0@[u0:rat]
+ur:=rpofrt(u0):cut
+[v0:rat]
+vr:=rpofrt(v0):cut
+prop1:=and3(more(ur,ksi),more(vr,eta),is"rt"(ts"rt"(u0,v0),z0)):'prop'
+z0@prop2:=some"rt"([x:rat]some"rt"([y:rat]prop1(x,y))):'prop'
+l4@t28:=and3i(more(xr,ksi),more(yr,eta),is"rt"(ts"rt"(x0,y0),z0),t26,t27,t23):prop1(x0,y0)
+t29:=somei(rat,[y:rat]prop1(x0,y),y0,t28):some"rt"([y:rat]prop1(x0,y))
+t30:=somei(rat,[x:rat]some"rt"([y:rat]prop1(x,y)),x0,t29):prop2
+l2@t31:=satz159app(eta,pl(eta,zeta),satz133a(eta,zeta),prop2,[x:rat][t:less(eta,rpofrt(x))][u:less(rpofrt(x),pl(eta,zeta))]t30(x,t,u)):prop2
+-5160
+satz160:=satz159app(ksi,pl(ksi,zeta".5160"),satz133a(ksi,zeta".5160"),prop2".5160",[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),pl(ksi,zeta".5160"))]t31".5160"(x,t,u)):some"rt"([x:rat]some"rt"([y:rat]and3(more(rpofrt(x),ksi),more(rpofrt(y),eta),is"rt"(ts"rt"(x,y),z0))))
+[p:'prop'][p1:[x:rat][t:more(rpofrt(x),ksi)][y:rat][u:more(rpofrt(y),eta)][v:is"rt"(ts"rt"(x,y),z0)]p]
++*5160
+p1@[x1:rat]
+xr1:=rpofrt(x1):cut
+[px:some"rt"([y:rat]prop1(x1,y))][y1:rat]
+yr1:=rpofrt(y1):cut
+[py:prop1(x1,y1)]
+t32:=and3e1(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(xr1,ksi)
+t33:=and3e2(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(yr1,eta)
+t34:=and3e3(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):is"rt"(ts"rt"(x1,y1),z0)
+t35:=<t34><t33><y1><t32><x1>p1:p
+px@t36:=someapp(rat,[y:rat]prop1(x1,y),px,p,[y:rat][v:prop1(x1,y)]t35(y,v)):p
+-5160
+p1@satz160app:=someapp(rat,[x:rat]some"rt"([y:rat]prop1".5160"(x,y)),satz160,p,[x:rat][t:some"rt"([y:rat]prop1".5160"(x,y))]t36".5160"(x,t)):p
++5161
+@[ksi:cut][eta:cut]
+min:=ite(less(ksi,eta),cut,ksi,eta):cut
+max:=ite(more(ksi,eta),cut,ksi,eta):cut
+[u0:rat]
+ur:=rpofrt(u0):cut
+[lu:lrt(min,u0)]
+t1:=satz158a(min,u0,lu):less(ur,min)
+[l:less(ksi,eta)]
+t2:=isless2(min,ksi,ur,itet(less(ksi,eta),cut,ksi,eta,l),t1):less(ur,ksi)
+t3:=trless(ur,ksi,eta,t2,l):less(ur,eta)
+lu@[n:not(less(ksi,eta))]
+t4:=isless2(min,eta,ur,itef(less(ksi,eta),cut,ksi,eta,n),t1):less(ur,eta)
+t5:=satz127b(ur,eta,ksi,t4,satz124(ksi,eta,satz123f(ksi,eta,n))):less(ur,ksi)
+lu@t6:=th1"l.imp"(less(ksi,eta),less(ur,ksi),[t:less(ksi,eta)]t2(t),[t:not(less(ksi,eta))]t5(t)):less(ur,ksi)
+t7:=th1"l.imp"(less(ksi,eta),less(ur,eta),[t:less(ksi,eta)]t3(t),[t:not(less(ksi,eta))]t4(t)):less(ur,eta)
+u0@[uu:urt(max,u0)]
+t8:=satz158b(max,u0,uu):moreis(ur,max)
+[m:more(ksi,eta)]
+t9:=ismoreis2(max,ksi,ur,itet(more(ksi,eta),cut,ksi,eta,m),t8):moreis(ur,ksi)
+t10:=trmoreis(ur,ksi,eta,t9,moreisi1(ksi,eta,m)):moreis(ur,eta)
+uu@[n:not(more(ksi,eta))]
+t11:=ismoreis2(max,eta,ur,itef(more(ksi,eta),cut,ksi,eta,n),t8):moreis(ur,eta)
+t12:=trmoreis(ur,eta,ksi,t11,satz125(ksi,eta,satz123e(ksi,eta,n))):moreis(ur,ksi)
+uu@t13:=th1"l.imp"(more(ksi,eta),moreis(ur,ksi),[t:more(ksi,eta)]t9(t),[t:not(more(ksi,eta))]t12(t)):moreis(ur,ksi)
+t14:=th1"l.imp"(more(ksi,eta),moreis(ur,eta),[t:more(ksi,eta)]t10(t),[t:not(more(ksi,eta))]t11(t)):moreis(ur,eta)
+-5161
+@[zeta:cut]
++*5161
+zeta@[ksi1:cut][ksi2:cut][m:more(ksi1,ksi2)]
+t15:=satz147(ksi1,ksi2,ksi1,ksi2,m,m):more(ts(ksi1,ksi1),ts(ksi2,ksi2))
+ksi2@sq1:=ts(ksi1,ksi1):cut
+sq2:=ts(ksi2,ksi2):cut
+m@t16:=ec3e21(is(sq1,sq2),more(sq1,sq2),less(sq1,sq2),satz123b(sq1,sq2),t15):nis(sq1,sq2)
+ksi2@[i:is(sq1,zeta)][j:is(sq2,zeta)]
+t17:=tris2(cut,sq1,sq2,zeta,i,j):is(sq1,sq2)
+t18:=[t:more(ksi1,ksi2)]<t17>t16(t):not(more(ksi1,ksi2))
+t19:=[t:less(ksi1,ksi2)]<symis(cut,sq1,sq2,t17)>t16(ksi2,ksi1,satz122(ksi1,ksi2,t)):not(less(ksi1,ksi2))
+t20:=or3e1(is(ksi1,ksi2),more(ksi1,ksi2),less(ksi1,ksi2),satz123a(ksi1,ksi2),t18,t19):is(ksi1,ksi2)
+zeta@t21:=[a:cut][b:cut][t:is(ts(a,a),zeta)][u:is(ts(b,b),zeta)]t20(a,b,t,u):amone(cut,[a:cut]is(ts(a,a),zeta))
+sqrtset:=setof(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta)):set(rat)
+[x0:rat]
+xr:=rpofrt(x0):cut
+[lx:lrt(min(1rp,zeta),x0)]
+t22:=t6(1rp,zeta,x0,lx):less(xr,1rp)
+t23:=t7(1rp,zeta,x0,lx):less(xr,zeta)
+t24:=isless1(xr,ts(xr,1rp),zeta,satz151a(xr),t23):less(ts(xr,1rp),zeta)
+t25:=trless(ts(xr,xr),ts(xr,1rp),zeta,satz148c(xr,xr,xr,1rp,lessisi2(xr,xr,refis(cut,xr)),t22),t24):less(ts(xr,xr),zeta)
+t26:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t25):in(x0,sqrtset)
+x0@[ux:urt(max(1rp,zeta),x0)]
+t27:=t13(1rp,zeta,x0,ux):moreis(xr,1rp)
+t28:=t14(1rp,zeta,x0,ux):moreis(xr,zeta)
+t29:=ismoreis1(xr,ts(xr,1rp),zeta,satz151a(xr),t28):moreis(ts(xr,1rp),zeta)
+t30:=trmoreis(ts(xr,xr),ts(xr,1rp),zeta,satz149(xr,xr,xr,1rp,moreisi2(xr,xr,refis(cut,xr)),t27),t29):moreis(ts(xr,xr),zeta)
+t31:=satz123c(ts(xr,xr),zeta,t30):not(less(ts(xr,xr),zeta))
+t32:=th3"l.imp"(in(x0,sqrtset),less(ts(xr,xr),zeta),t31,[t:in(x0,sqrtset)]estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t)):not(in(x0,sqrtset))
+x0@[i:in(x0,sqrtset)][y0:rat]
+yr:=rpofrt(y0):cut
+[l:less"rt"(y0,x0)]
+i@t33:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,i):less(ts(xr,xr),zeta)
+l@t34:=satz154c(y0,x0,l):less(yr,xr)
+t35:=trless(ts(yr,yr),ts(xr,xr),zeta,satz147a(yr,xr,yr,xr,t34,t34),t33):less(ts(yr,yr),zeta)
+t36:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),y0,t35):in(y0,sqrtset)
+i@t37:=satz122(ts(xr,xr),zeta,t33):more(zeta,ts(xr,xr))
+nm:=mn(zeta,ts(xr,xr),t37):cut
+dn:=pl(xr,pl(xr,1rp)):cut
+fr:=ov(nm,dn):cut
+[z0:rat]
+zr:=rpofrt(z0):cut
+[lz:lrt(min(1rp,fr),z0)]
+t38:=t6(1rp,fr,z0,lz):less(zr,1rp)
+t39:=t7(1rp,fr,z0,lz):less(zr,fr)
+t40:=satz94(x0,z0):more"rt"(pl"rt"(x0,z0),x0)
+t41:=tris(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),ts(pl(xr,zr),pl(xr,zr)),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ists12(rpofrt(pl"rt"(x0,z0)),pl(xr,zr),rpofrt(pl"rt"(x0,z0)),pl(xr,zr),satz155a(x0,z0),satz155a(x0,z0)),disttp2(pl(xr,zr),xr,zr)):is(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)))
+t42:=symis(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),t41):is(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))))
+t43:=lessisi2(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),tris(cut,ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(zr,xr)),pl(ts(xr,xr),ts(xr,zr)),disttp1(xr,zr,xr),ispl2(ts(zr,xr),ts(xr,zr),ts(xr,xr),comts(zr,xr)))):lessis(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)))
+t44:=satz145c(pl(xr,zr),pl(xr,1rp),zr,satz138c(xr,xr,zr,1rp,lessisi2(xr,xr,refis(cut,xr)),t38)):less(ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr))
+t45:=satz138c(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr),t43,t44):less(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)))
+t46:=tris(cut,pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),pl(ts(xr,zr),ts(pl(xr,1rp),zr))),pl(ts(xr,xr),ts(dn,zr)),asspl1(ts(xr,xr),ts(xr,zr),ts(pl(xr,1rp),zr)),ispl2(pl(ts(xr,zr),ts(pl(xr,1rp),zr)),ts(dn,zr),ts(xr,xr),distpt1(xr,pl(xr,1rp),zr))):is(pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)))
+t47:=isless12(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)),t42,t46,t45):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)))
+t48:=isless2(ts(dn,fr),nm,ts(dn,zr),satz153c(nm,dn),satz148c(dn,dn,zr,fr,lessisi2(dn,dn,refis(cut,dn)),t39)):less(ts(dn,zr),nm)
+t49:=satz138c(ts(xr,xr),ts(xr,xr),ts(dn,zr),nm,lessisi2(ts(xr,xr),ts(xr,xr),refis(cut,ts(xr,xr))),t48):less(pl(ts(xr,xr),ts(dn,zr)),pl(ts(xr,xr),nm))
+t50:=isless2(pl(ts(xr,xr),nm),zeta,pl(ts(xr,xr),ts(dn,zr)),satz140c(zeta,ts(xr,xr),t37),t49):less(pl(ts(xr,xr),ts(dn,zr)),zeta)
+t51:=trless(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)),zeta,t47,t50):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),zeta)
+t52:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),pl"rt"(x0,z0),t51):in(pl"rt"(x0,z0),sqrtset)
+t53:=andi(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0),t52,t40):and(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0))
+t54:=somei(rat,[y:rat]and(in(y,sqrtset),more"rt"(y,x0)),pl"rt"(x0,z0),t53):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
+i@t55:=cutapp1a(min(1rp,fr),some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0))),[x:rat][t:lrt(min(1rp,fr),x)]t54(x,t)):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
+x0@[lx:lrt(min(1rp,zeta),x0)][y0:rat][uy:urt(max(1rp,zeta),y0)]
+t56:=cut2(sqrtset,x0,t26(lx),y0,t32(y0,uy),[x:rat][t:in(x,sqrtset)][y:rat][u:less"rt"(y,x)]t36(x,t,y,u),[x:rat][t:in(x,sqrtset)]t55(x,t)):cutprop(sqrtset)
+lx@t57:=cutapp1b(max(1rp,zeta),cutprop(sqrtset),[y:rat][t:urt(max(1rp,zeta),y)]t56(y,t)):cutprop(sqrtset)
+zeta@t58:=cutapp1a(min(1rp,zeta),cutprop(sqrtset),[x:rat][t:lrt(min(1rp,zeta),x)]t57(x,t)):cutprop(sqrtset)
+rtc:=cutof(sqrtset,t58):cut
+@[x0:rat][y0:rat][l:lessis"rt"(x0,y0)]
+t59:=th9"l.or"(less"rt"(x0,y0),is"rt"(x0,y0),less(rpofrt(x0),rpofrt(y0)),is(rpofrt(x0),rpofrt(y0)),l,[t:less"rt"(x0,y0)]satz154c(x0,y0,t),[t:is"rt"(x0,y0)]satz154b(x0,y0,t)):lessis(rpofrt(x0),rpofrt(y0))
+y0@[m:moreis"rt"(x0,y0)]
+t60:=satz125(rpofrt(y0),rpofrt(x0),t59(y0,x0,satz84(x0,y0,m))):moreis(rpofrt(x0),rpofrt(y0))
+zeta@[m:more(ts(rtc,rtc),zeta)]
+t61:=satz121(ts(rtc,rtc),zeta,m):less(zeta,ts(rtc,rtc))
+[z1:rat]
+zr1:=rpofrt(z1):cut
+[l1:less(zeta,zr1)][l2:less(zr1,ts(rtc,rtc))]
+t62:=satz158c(ts(rtc,rtc),z1,l2):lrt(ts(rtc,rtc),z1)
+[x1:rat]
+xr1:=rpofrt(x1):cut
+[lx1:lrt(rtc,x1)][x2:rat]
+xr2:=rpofrt(x2):cut
+[lx2:lrt(rtc,x2)][i:is"rt"(z1,ts"rt"(x1,x2))]
+xm:=ite(more"rt"(x1,x2),rat,x1,x2):rat
+xrm:=rpofrt(xm):cut
+[o:more"rt"(x1,x2)]
+t63:=symis(rat,xm,x1,itet(more"rt"(x1,x2),rat,x1,x2,o)):is"rt"(x1,xm)
+t64:=isp(rat,[x:rat]lrt(rtc,x),x1,xm,lx1,t63):lrt(rtc,xm)
+t65:=lessisi2"rt"(x1,xm,t63):lessis"rt"(x1,xm)
+t66:=lessisi1"rt"(x2,xm,satz87b(x2,x1,xm,satz82(x1,x2,o),t65)):lessis"rt"(x2,xm)
+i@[n:not(more"rt"(x1,x2))]
+t67:=symis(rat,xm,x2,itef(more"rt"(x1,x2),rat,x1,x2,n)):is"rt"(x2,xm)
+t68:=isp(rat,[x:rat]lrt(rtc,x),x2,xm,lx2,t67):lrt(rtc,xm)
+t69:=lessisi2"rt"(x2,xm,t67):lessis"rt"(x2,xm)
+t70:=satz88(x1,x2,xm,satz81e(x1,x2,n),t69):lessis"rt"(x1,xm)
+i@t71:=th1"l.imp"(more"rt"(x1,x2),lrt(rtc,xm),[t:more"rt"(x1,x2)]t64(t),[t:not(more"rt"(x1,x2))]t68(t)):lrt(rtc,xm)
+t72:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x1,xm),[t:more"rt"(x1,x2)]t65(t),[t:not(more"rt"(x1,x2))]t70(t)):lessis"rt"(x1,xm)
+t73:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x2,xm),[t:more"rt"(x1,x2)]t66(t),[t:not(more"rt"(x1,x2))]t69(t)):lessis"rt"(x2,xm)
+t74:=ini(sqrtset,t58,xm,t71):in(xm,sqrtset)
+t75:=t59(x1,xm,t72):lessis(xr1,xrm)
+t76:=t59(x2,xm,t73):lessis(xr2,xrm)
+t77:=tris(cut,zr1,rpofrt(ts"rt"(x1,x2)),ts(xr1,xr2),satz154b(z1,ts"rt"(x1,x2),i),satz155c(x1,x2)):is(zr1,ts(xr1,xr2))
+t78:=islessis1(ts(xr1,xr2),zr1,ts(xrm,xrm),symis(cut,zr1,ts(xr1,xr2),t77),satz149a(xr1,xrm,xr2,xrm,t75,t76)):lessis(zr1,ts(xrm,xrm))
+t79:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),xm,t74):less(ts(xrm,xrm),zeta)
+t80:=satz127a(zr1,ts(xrm,xrm),zeta,t78,t79):less(zr1,zeta)
+t81:=<t80>ec3e23(is(zr1,zeta),more(zr1,zeta),less(zr1,zeta),satz123b(zr1,zeta),satz122(zeta,zr1,l1)):con
+t82:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t81(x,t,y,u,v)):con
+l2@t82a:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t82(x,t,y,u,v)):con
+m@t83:=satz159app(zeta,ts(rtc,rtc),t61,con,[x:rat][t:less(zeta,rpofrt(x))][u:less(rpofrt(x),ts(rtc,rtc))]t82a(x,t,u)):con
+zeta@[l:less(ts(rtc,rtc),zeta)][z2:rat]
+zr2:=rpofrt(z2):cut
+[l3:less(ts(rtc,rtc),zr2)][l4:less(zr2,zeta)]
+t84:=satz122(ts(rtc,rtc),zr2,l3):more(zr2,ts(rtc,rtc))
+[y1:rat]
+yr1:=rpofrt(y1):cut
+[m1:more(yr1,rtc)][y2:rat]
+yr2:=rpofrt(y2):cut
+[m2:more(yr2,rtc)][i:is"rt"(ts"rt"(y1,y2),z2)]
+ym:=ite(less"rt"(y1,y2),rat,y1,y2):rat
+yrm:=rpofrt(ym):cut
+[k:less"rt"(y1,y2)]
+t85:=symis(rat,ym,y1,itet(less"rt"(y1,y2),rat,y1,y2,k)):is"rt"(y1,ym)
+t86:=satz154b(y1,ym,t85):is(yr1,yrm)
+t87:=ismore1(yr1,yrm,rtc,t86,m1):more(yrm,rtc)
+t88:=moreisi2(yr1,yrm,t86):moreis(yr1,yrm)
+t89:=moreisi1(yr2,yrm,satz127d(yr2,yr1,yrm,satz122(yr1,yr2,satz154c(y1,y2,k)),t88)):moreis(yr2,yrm)
+i@[n:not(less"rt"(y1,y2))]
+t90:=symis(rat,ym,y2,itef(less"rt"(y1,y2),rat,y1,y2,n)):is"rt"(y2,ym)
+t91:=satz154b(y2,ym,t90):is(yr2,yrm)
+t92:=ismore1(yr2,yrm,rtc,t91,m2):more(yrm,rtc)
+t93:=moreisi2(yr2,yrm,t91):moreis(yr2,yrm)
+t94:=trmoreis(yr1,yr2,yrm,t60(y1,y2,satz81f(y1,y2,n)),t93):moreis(yr1,yrm)
+i@t95:=th1"l.imp"(less"rt"(y1,y2),more(yrm,rtc),[t:less"rt"(y1,y2)]t87(t),[t:not(less"rt"(y1,y2))]t92(t)):more(yrm,rtc)
+t96:=th1"l.imp"(less"rt"(y1,y2),moreis(yr1,yrm),[t:less"rt"(y1,y2)]t88(t),[t:not(less"rt"(y1,y2))]t94(t)):moreis(yr1,yrm)
+t97:=th1"l.imp"(less"rt"(y1,y2),moreis(yr2,yrm),[t:less"rt"(y1,y2)]t89(t),[t:not(less"rt"(y1,y2))]t93(t)):moreis(yr2,yrm)
+t98:=satz158d(rtc,ym,moreisi1(yrm,rtc,t95)):urt(rtc,ym)
+t99:=th3"l.imp"(in(ym,sqrtset),lrt(rtc,ym),t98,[t:in(ym,sqrtset)]ine(sqrtset,t58,ym,t)):not(in(ym,sqrtset))
+t100:=th3"l.imp"(less(ts(yrm,yrm),zeta),in(ym,sqrtset),t99,[t:less(ts(yrm,yrm),zeta)]estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),ym,t)):not(less(ts(yrm,yrm),zeta))
+t101:=satz123f(ts(yrm,yrm),zeta,t100):moreis(ts(yrm,yrm),zeta)
+t101a:=satz149(yr1,yrm,yr2,yrm,t96,t97):moreis(ts(yr1,yr2),ts(yrm,yrm))
+t102:=ismoreis1(ts(yr1,yr2),zr2,ts(yrm,yrm),tris(cut,ts(yr1,yr2),rpofrt(ts"rt"(y1,y2)),zr2,symis(cut,rpofrt(ts"rt"(y1,y2)),ts(yr1,yr2),satz155c(y1,y2)),satz154b(ts"rt"(y1,y2),z2,i)),t101a):moreis(zr2,ts(yrm,yrm))
+t103:=trmoreis(zr2,ts(yrm,yrm),zeta,t102,t101):moreis(zr2,zeta)
+t104:=<l4>satz123c(zr2,zeta,t103):con
+l4@t105:=satz160app(rtc,rtc,z2,t84,con,[x:rat][t:more(rpofrt(x),rtc)][y:rat][u:more(rpofrt(y),rtc)][v:is"rt"(ts"rt"(x,y),z2)]t104(x,t,y,u,v)):con
+l@t106:=satz159app(ts(rtc,rtc),zeta,l,con,[x:rat][t:less(ts(rtc,rtc),rpofrt(x))][u:less(rpofrt(x),zeta)]t105(x,t,u)):con
+zeta@t107:=or3e1(is(ts(rtc,rtc),zeta),more(ts(rtc,rtc),zeta),less(ts(rtc,rtc),zeta),satz123a(ts(rtc,rtc),zeta),[t:more(ts(rtc,rtc),zeta)]t83(t),[t:less(ts(rtc,rtc),zeta)]t106(t)):is(ts(rtc,rtc),zeta)
+t108:=somei(cut,[a:cut]is(ts(a,a),zeta),rtc,t107):some([a:cut]is(ts(a,a),zeta))
+-5161
+zeta@satz161:=onei(cut,[a:cut]is(ts(a,a),zeta),t21".5161",t108".5161"):one([a:cut]is(ts(a,a),zeta))
+@[ksi:cut]
+irratrp:=not(ratrp(ksi)):'prop'
+-rp
+-rt
++5162
+@[v:nat]
+t1:=tris(nat,pl(v,v),pl(ts(1,v),v),ts(<1>suc,v),ispl1(v,ts(1,v),v,satz28g(v)),satz28h(1,v)):is(pl(v,v),ts(<1>suc,v))
+t2:=isless2(pl(v,v),ts(<1>suc,v),v,t1,satz18a(v,v)):less(v,ts(<1>suc,v))
+[w:nat][l:less(ts(v,v),ts(w,w))]
+t3:=satz10j(v,w,th3"l.imp"(moreis(v,w),moreis(ts(v,v),ts(w,w)),satz10h(ts(v,v),ts(w,w),l),[t:moreis(v,w)]satz36(v,w,v,w,t,t))):less(v,w)
+w@t4:=tris(nat,ts(pl(v,w),v),pl(ts(v,v),ts(w,v)),pl(ts(v,v),ts(v,w)),disttp1(v,w,v),ispl2(ts(w,v),ts(v,w),ts(v,v),comts(w,v))):is(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)))
+t5:=tr3is(nat,ts(pl(v,w),pl(v,w)),pl(ts(pl(v,w),v),ts(pl(v,w),w)),pl(pl(ts(v,v),ts(v,w)),pl(ts(v,w),ts(w,w))),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),disttp2(pl(v,w),v,w),ispl12(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)),ts(pl(v,w),w),pl(ts(v,w),ts(w,w)),t4,disttp1(v,w,w)),asspl2(pl(ts(v,v),ts(v,w)),ts(v,w),ts(w,w))):is(ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)))
+t6:=tris(nat,pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),pl(ts(v,w),ts(v,w))),pl(ts(v,v),ts(<1>suc,ts(v,w))),asspl1(ts(v,v),ts(v,w),ts(v,w)),ispl2(pl(ts(v,w),ts(v,w)),ts(<1>suc,ts(v,w)),ts(v,v),t1(ts(v,w)))):is(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))))
+nun:=tris(nat,ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),t5,ispl1(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w),t6)):is(ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)))
+nun1:=symis(nat,ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),nun):is(pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),ts(pl(v,w),pl(v,w)))
+prop1:=eq(tf(fr(w,v),fr(w,v)),fr(<1>suc,1)):'prop'
+v@prop2:=some([t:nat]prop1(t)):'prop'
+@prop3:=some([u:nat]prop2(u)):'prop'
+[p:prop3]
+y:=ind(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):nat
+t7:=oneax(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):min([u:nat]prop2(u),y)
+t8:=ande1(lb([u:nat]prop2(u),y),prop2(y),t7):lb([u:nat]prop2(u),y)
+t9:=ande2(lb([u:nat]prop2(u),y),prop2(y),t7):prop2(y)
+[x:nat][q:prop1(y,x)]
+t10:=treq1(fr(<1>suc,1),fr(ts(x,x),ts(y,y)),tf(fr(x,y),fr(x,y)),q,tfeq12a(x,y,x,y)):eq(fr(<1>suc,1),fr(ts(x,x),ts(y,y)))
+t11:=tr4is(nat,ts(<1>suc,ts(y,y)),ts(num(fr(<1>suc,1)),den(fr(ts(x,x),ts(y,y)))),ts(num(fr(ts(x,x),ts(y,y))),den(fr(<1>suc,1))),ts(ts(x,x),1),ts(x,x),12isnd(<1>suc,1,ts(x,x),ts(y,y)),t10,ndis12(ts(x,x),ts(y,y),<1>suc,1),satz28a(ts(x,x))):is(ts(<1>suc,ts(y,y)),ts(x,x))
+t12:=isless2(ts(<1>suc,ts(y,y)),ts(x,x),ts(y,y),t11,t2(ts(y,y))):less(ts(y,y),ts(x,x))
+t13:=isless1(ts(ts(<1>suc,y),y),ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)),tris(nat,ts(ts(<1>suc,y),y),ts(<1>suc,ts(y,y)),ts(x,x),assts1(<1>suc,y,y),t11),satz35c(ts(<1>suc,y),ts(<1>suc,y),y,ts(<1>suc,y),lessisi2(ts(<1>suc,y),ts(<1>suc,y),refis(nat,ts(<1>suc,y))),t2(y))):less(ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)))
+t14:=t3(y,x,t12):less(y,x)
+t15:=t3(x,ts(<1>suc,y),t13):less(x,ts(<1>suc,y))
+[u:nat][i:is(x,pl(y,u))]
+t16:=isless12(x,pl(y,u),ts(<1>suc,y),pl(y,y),i,symis(nat,pl(y,y),ts(<1>suc,y),t1(y)),t15):less(pl(y,u),pl(y,y))
+t17:=satz20f(u,y,y,t16):less(u,y)
+[t:nat][j:is(y,pl(u,t))]
+t18:=symis(nat,y,pl(u,t),j):is(pl(u,t),y)
+t19:=tris(nat,ts(x,x),ts(pl(y,u),pl(y,u)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ists12(x,pl(y,u),x,pl(y,u),i,i),nun(y,u)):is(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)))
+t20:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),ispl1(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t),t19),asspl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u),ts(t,t))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))))
+t21:=tr3is(nat,ts(y,u),ts(u,y),ts(u,pl(u,t)),pl(ts(u,u),ts(u,t)),comts(y,u),ists2(y,pl(u,t),u,j),disttp2(u,u,t)):is(ts(y,u),pl(ts(u,u),ts(u,t)))
+t22:=tris(nat,ts(<1>suc,ts(y,u)),ts(<1>suc,pl(ts(u,u),ts(u,t))),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ists2(ts(y,u),pl(ts(u,u),ts(u,t)),<1>suc,t21),disttp2(<1>suc,ts(u,u),ts(u,t))):is(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))))
+t23:=tris(nat,pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(y,y),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),ispl2(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ts(y,y),t22),asspl2(ts(y,y),ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))):is(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))))
+t24:=tr3is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),pl(pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),t20,ispl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t)),t23),asspl1(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))))
+t25:=tr4is(nat,pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),pl(pl(ts(<1>suc,ts(u,t)),ts(u,u)),ts(t,t)),pl(pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t)),ts(pl(u,t),pl(u,t)),ts(y,y),asspl2(ts(<1>suc,ts(u,t)),ts(u,u),ts(t,t)),ispl1(pl(ts(<1>suc,ts(u,t)),ts(u,u)),pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t),compl(ts(<1>suc,ts(u,t)),ts(u,u))),nun1(u,t),ists12(pl(u,t),y,pl(u,t),y,t18,t18)):is(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y))
+t26:=tr4is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),pl(ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u)))),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),t24,ispl2(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u))),t25),compl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),asspl2(ts(y,y),ts(y,y),ts(<1>suc,ts(u,u)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))))
+t27:=tris(nat,pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(y,y)),ts(x,x),t1(ts(y,y)),t11):is(pl(ts(y,y),ts(y,y)),ts(x,x))
+t28:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),pl(ts(x,x),ts(<1>suc,ts(u,u))),t26,ispl1(pl(ts(y,y),ts(y,y)),ts(x,x),ts(<1>suc,ts(u,u)),t27)):is(pl(ts(x,x),ts(t,t)),pl(ts(x,x),ts(<1>suc,ts(u,u))))
+t29:=satz20e(ts(t,t),ts(<1>suc,ts(u,u)),ts(x,x),t28):is(ts(t,t),ts(<1>suc,ts(u,u)))
+t30:=tr4is(nat,ts(num(fr(<1>suc,1)),den(fr(ts(t,t),ts(u,u)))),ts(<1>suc,ts(u,u)),ts(t,t),ts(ts(t,t),1),ts(num(fr(ts(t,t),ts(u,u))),den(fr(<1>suc,1))),ndis12(<1>suc,1,ts(t,t),ts(u,u)),symis(nat,ts(t,t),ts(<1>suc,ts(u,u)),t29),satz28e(ts(t,t)),12isnd(ts(t,t),ts(u,u),<1>suc,1)):eq(fr(<1>suc,1),fr(ts(t,t),ts(u,u)))
+t31:=treq2(tf(fr(t,u),fr(t,u)),fr(<1>suc,1),fr(ts(t,t),ts(u,u)),tfeq12a(t,u,t,u),t30):prop1(u,t)
+t32:=somei(nat,[v:nat]prop1(u,v),t,t31):prop2(u)
+t33:=<t32><u>t8:lessis(y,u)
+t34:=<t33>satz10g(y,u,satz12(u,y,t17)):con
+i@t35:=someapp(nat,[v:nat]diffprop(y,u,v),t17,con,[v:nat][w:diffprop(y,u,v)]t34(v,w)):con
+q@t36:=someapp(nat,[v:nat]diffprop(x,y,v),t14,con,[v:nat][w:diffprop(x,y,v)]t35(v,w)):con
+p@t37:=someapp(nat,[v:nat]prop1(y,v),t9,con,[v:nat][w:prop1(y,v)]t36(v,w)):con
+-5162
++*rt
++5162
+@[x0:rat][i:is(ts(x0,x0),rtofn(<1>suc))][x:frac][xix0:inf(x,class(x0))]
+t38:=ise(ts(x0,x0),rtofn(<1>suc),tf(x,x),fr(<1>suc,1),tict(x0,x0,x,x,xix0,xix0),inclass(fr(<1>suc,1)),i):eq"n"(tf(x,x),fr(<1>suc,1))
+t39:=refeq1(fr(num(x),den(x)),x,fris(x)):eq"n"(fr(num(x),den(x)),x)
+t40:=eqtf12(fr(num(x),den(x)),x,fr(num(x),den(x)),x,t39,t39):eq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x))
+t41:=treq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x),fr(<1>suc,1),t40,t38):prop1"n.5162"(den(x),num(x))
+t42:=somei(nat,[t:nat]prop1"n.5162"(den(x),t),num(x),t41):prop2"n.5162"(den(x))
+t43:=somei(nat,[t:nat]prop2"n.5162"(t),den(x),t42):prop3"n.5162"
+t44:=t37"n.5162"(t43):con
+i@t45:=ratapp1(x0,con,[x:frac][t:inf(x,class(x0))]t44(x,t)):con
+-5162
++*rp
++5162
+@ksi:=ind(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):cut
+t46:=oneax(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):is(ts(ksi,ksi),rpofnt(<1>suc))
+[r:ratrp(ksi)]
+x0:=rtofrp(ksi,r):rat
+t47:=tr3is(cut,rpofrt(ts"rt"(x0,x0)),ts(rpofrt(x0),rpofrt(x0)),ts(ksi,ksi),rpofnt(<1>suc),satz155c(x0,x0),ists12(rpofrt(x0),ksi,rpofrt(x0),ksi,isrprt2(ksi,r),isrprt2(ksi,r)),t46):is(rpofrt(ts"rt"(x0,x0)),rpofnt(<1>suc))
+t48:=isrtirp(ts"rt"(x0,x0),rtofn(<1>suc),t47):is"rt"(ts"rt"(x0,x0),rtofn(<1>suc))
+t49:=t45"rt.5162"(x0,t48):con
+-5162
+@satz162:=somei(cut,[a:cut]irratrp(a),ksi".5162",[t:ratrp(ksi".5162")]t49".5162"(t)):some([a:cut]irratrp(a))
+[zeta:cut]
+sqrt:=ind(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):cut
+thsqrt1:=oneax(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):is(ts(sqrt(zeta),sqrt(zeta)),zeta)
+[ksi:cut][i:is(ts(ksi,ksi),zeta)]
+thsqrt2:=t20".5161"(zeta,ksi,sqrt,i,thsqrt1):is(ksi,sqrt)
+@[ksi:cut][eta:cut][i:is(ksi,eta)]
+issqrt:=isf(cut,cut,[t:cut]sqrt(t),ksi,eta,i):is(sqrt(ksi),sqrt(eta))
+@[ksi:cut][nx:natrp(ksi)][eta:cut][ny:natrp(eta)]
++iiia
+x:=ntofrp(ksi,nx):nat
+y:=ntofrp(eta,ny):nat
+t1:=isrpnt1(ksi,nx):is(ksi,rpofnt(x))
+t2:=isrpnt1(eta,ny):is(eta,rpofnt(y))
+t3:=ispl12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(pl(ksi,eta),pl(rpofnt(x),rpofnt(y)))
+x0:=rtofn(x):rat
+y0:=rtofn(y):rat
+t4:=natrti(x):natrt(x0)
+t5:=natrti(y):natrt(y0)
+t6:=symis(cut,rpofrt(pl"rt"(x0,y0)),pl(rpofnt(x),rpofnt(y)),satz155a(x0,y0)):is(pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)))
+t7:=satz112d(x0,t4,y0,t5):natrt(pl"rt"(x0,y0))
+xpy:=nofrt(pl"rt"(x0,y0),t7):nat
+t8:=isrtn1(pl"rt"(x0,y0),t7):is"rt"(pl"rt"(x0,y0),rtofn(xpy))
+t9:=isrterp(pl"rt"(x0,y0),rtofn(xpy),t8):is(rpofrt(pl"rt"(x0,y0)),rpofnt(xpy))
+t10:=tr3is(cut,pl(ksi,eta),pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)),rpofnt(xpy),t3,t6,t9):is(pl(ksi,eta),rpofnt(xpy))
+-iiia
+natpl:=somei(nat,[t:nat]is(pl(ksi,eta),rpofnt(t)),xpy".iiia",t10".iiia"):natrp(pl(ksi,eta))
++*iiia
+ny@t11:=ists12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(ts(ksi,eta),ts(rpofnt(x),rpofnt(y)))
+t12:=symis(cut,rpofrt(ts"rt"(x0,y0)),ts(rpofnt(x),rpofnt(y)),satz155c(x0,y0)):is(ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)))
+t13:=satz112f(x0,t4,y0,t5):natrt(ts"rt"(x0,y0))
+xty:=nofrt(ts"rt"(x0,y0),t13):nat
+t14:=isrtn1(ts"rt"(x0,y0),t13):is"rt"(ts"rt"(x0,y0),rtofn(xty))
+t15:=isrterp(ts"rt"(x0,y0),rtofn(xty),t14):is(rpofrt(ts"rt"(x0,y0)),rpofnt(xty))
+t16:=tr3is(cut,ts(ksi,eta),ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)),rpofnt(xty),t11,t12,t15):is(ts(ksi,eta),rpofnt(xty))
+-iiia
+ny@natts:=somei(nat,[t:nat]is(ts(ksi,eta),rpofnt(t)),xty".iiia",t16".iiia"):natrp(ts(ksi,eta))
+[m:more(ksi,eta)]
++*iiia
+m@t17:=ismore12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2,m):more(rpofnt(x),rpofnt(y))
+t18:=satz154d(x0,y0,t17):more"rt"(x0,y0)
+t20:=ismn12(ksi,rpofnt(x),eta,rpofnt(y),m,satz154a(x0,y0,t18),t1,t2):is(mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)))
+t21:=symis(cut,rpofrt(mn"rt"(x0,y0,t18)),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),satz155b(x0,y0,t18)):is(mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)))
+t22:=satz112g(x0,t4,y0,t5,t18):natrt(mn"rt"(x0,y0,t18))
+xmy:=nofrt(mn"rt"(x0,y0,t18),t22):nat
+t23:=isrtn1(mn"rt"(x0,y0,t18),t22):is"rt"(mn"rt"(x0,y0,t18),rtofn(xmy))
+t24:=isrterp(mn"rt"(x0,y0,t18),rtofn(xmy),t23):is(rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy))
+t25:=tr3is(cut,mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy),t20,t21,t24):is(mn(ksi,eta,m),rpofnt(xmy))
+-iiia
+m@natmn:=somei(nat,[t:nat]is(mn(ksi,eta,m),rpofnt(t)),xmy".iiia",t25".iiia"):natrp(mn(ksi,eta,m))
+@[p:cut][q:cut][r:cut]
+3pl13:=tr3is(cut,pl(p,pl(q,r)),pl(pl(q,r),p),pl(pl(r,q),p),pl(r,pl(q,p)),compl(p,pl(q,r)),ispl1(pl(q,r),pl(r,q),p,compl(q,r)),asspl1(r,q,p)):is(pl(p,pl(q,r)),pl(r,pl(q,p)))
+[s:cut]
+4pl24:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(s,pl(r,q))),pl(pl(p,s),pl(r,q)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(s,pl(r,q)),p,3pl13(q,r,s)),asspl2(p,s,pl(r,q))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,s),pl(r,q)))
+r@3pl12:=tr3is(cut,pl(p,pl(q,r)),pl(pl(p,q),r),pl(pl(q,p),r),pl(q,pl(p,r)),asspl2(p,q,r),ispl1(pl(p,q),pl(q,p),r,compl(p,q)),asspl1(q,p,r)):is(pl(p,pl(q,r)),pl(q,pl(p,r)))
+s@4pl23:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(r,pl(q,s))),pl(pl(p,r),pl(q,s)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(r,pl(q,s)),p,3pl12(q,r,s)),asspl2(p,r,pl(q,s))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,r),pl(q,s)))
+r@3pl23:=tr3is(cut,pl(pl(p,q),r),pl(p,pl(q,r)),pl(p,pl(r,q)),pl(pl(p,r),q),asspl1(p,q,r),ispl2(pl(q,r),pl(r,q),p,compl(q,r)),asspl2(p,r,q)):is(pl(pl(p,q),r),pl(pl(p,r),q))
+p@a2isapa:=tris(cut,ts(p,pl(1rp,1rp)),pl(ts(p,1rp),ts(p,1rp)),pl(p,p),disttp2(p,1rp,1rp),ispl12(ts(p,1rp),p,ts(p,1rp),p,satz151(p),satz151(p))):is(ts(p,pl(1rp,1rp)),pl(p,p))
+@dif:=pair1type(cut):'type'
+[a1:cut][a2:cut]
+df:=pair1(cut,a1,a2):dif
+@[a:dif]
+stm:=first1(cut,a):cut
+std:=second1(cut,a):cut
+a2@stmis:=first1is1(cut,a1,a2):is(stm(df(a1,a2)),a1)
+isstm:=first1is2(cut,a1,a2):is(a1,stm(df(a1,a2)))
+stdis:=second1is1(cut,a1,a2):is(std(df(a1,a2)),a2)
+isstd:=second1is2(cut,a1,a2):is(a2,std(df(a1,a2)))
+a@1a:=stm(a):cut
+2a:=std(a):cut
+dfis:=pair1is1(cut,a):is"e"(dif,df(1a,2a),a)
+isdf:=pair1is2(cut,a):is"e"(dif,a,df(1a,2a))
+a2@[b1:cut][b2:cut]
+12issmsd:=ispl12(a1,stm(df(a1,a2)),b2,std(df(b1,b2)),isstm(a1,a2),isstd(b1,b2)):is(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))))
+smsdis12:=symis(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),12issmsd):is(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2))
+a@[r1:cut][r2:cut]
+1sdissmsd:=ispl1(r1,stm(df(r1,r2)),2a,isstm(r1,r2)):is(pl(r1,2a),pl(stm(df(r1,r2)),2a))
+smsdis1sd:=symis(cut,pl(r1,2a),pl(stm(df(r1,r2)),2a),1sdissmsd):is(pl(stm(df(r1,r2)),2a),pl(r1,2a))
+sm2issmsd:=ispl2(r2,std(df(r1,r2)),1a,isstd(r1,r2)):is(pl(1a,r2),pl(1a,std(df(r1,r2))))
+smsdissm2:=symis(cut,pl(1a,r2),pl(1a,std(df(r1,r2))),sm2issmsd):is(pl(1a,std(df(r1,r2))),pl(1a,r2))
+a2@[r:cut][i:is(a1,r)]
+issm:=isf(cut,dif,[t:cut]df(t,a2),a1,r,i):is"e"(dif,df(a1,a2),df(r,a2))
+r@[i:is(a2,r)]
+issd:=isf(cut,dif,[t:cut]df(a1,t),a2,r,i):is"e"(dif,df(a1,a2),df(a1,r))
+b2@[i:is(a1,b1)][j:is(a2,b2)]
+issmsd:=tris(dif,df(a1,a2),df(b1,a2),df(b1,b2),issm(a1,a2,b1,i),issd(b1,a2,b2,j)):is"e"(dif,df(a1,a2),df(b1,b2))
+a@[b:dif]
+1b:=stm(b):cut
+2b:=std(b):cut
+eq:=is(pl(1a,2b),pl(1b,2a)):'prop'
+b2@[i:is(pl(a1,b2),pl(b1,a2))]
+eqi12:=tr3is(cut,pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),smsdis12(a1,a2,b1,b2),i,12issmsd(b1,b2,a1,a2)):eq(df(a1,a2),df(b1,b2))
+r2@[i:is(pl(1a,r2),pl(r1,2a))]
+eqi1:=isp(dif,[x:dif]eq(x,df(r1,r2)),df(1a,2a),a,eqi12(1a,2a,r1,r2,i),dfis):eq(a,df(r1,r2))
+r2@[i:is(pl(r1,2a),pl(1a,r2))]
+eqi2:=isp(dif,[x:dif]eq(df(r1,r2),x),df(1a,2a),a,eqi12(r1,r2,1a,2a,i),dfis):eq(df(r1,r2),a)
+b2@[e:eq(df(a1,a2),df(b1,b2))]
+eqe12:=tr3is(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),12issmsd(a1,a2,b1,b2),e,smsdis12(b1,b2,a1,a2)):is(pl(a1,b2),pl(b1,a2))
+a@satzd163:=refis(cut,pl(1a,2a)):eq(a,a)
+refeq:=satzd163:eq(a,a)
+b@[i:is"e"(dif,a,b)]
+refeq1:=isp(dif,[x:dif]eq(a,x),a,b,refeq,i):eq(a,b)
+refeq2:=isp(dif,[x:dif]eq(x,a),a,b,refeq,i):eq(b,a)
+b2@[i:is(a1,b1)][j:is(a2,b2)]
+eqsmsd:=refeq1(df(a1,a2),df(b1,b2),issmsd(i,j)):eq(df(a1,a2),df(b1,b2))
+r@[i:is(a1,r)]
+eqsm:=refeq1(df(a1,a2),df(r,a2),issm(i)):eq(df(a1,a2),df(r,a2))
+r@[i:is(a2,r)]
+eqsd:=refeq1(df(a1,a2),df(a1,r),issd(i)):eq(df(a1,a2),df(a1,r))
+b@[e:eq(a,b)]
+satzd164:=symis(cut,pl(1a,2b),pl(1b,2a),e):eq(b,a)
+symeq:=satzd164:eq(b,a)
+b@[c:dif]
+1c:=stm(c):cut
+2c:=std(c):cut
+[e:eq(a,b)][f:eq(b,c)]
++1d165
+t1:=ispl12(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),e,f):is(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
+t2:=tr4is(cut,pl(pl(1a,2c),pl(1b,2b)),pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2b),pl(1b,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2c,1b,2b),t1,compl(pl(1b,2a),pl(1c,2b)),4pl24(1c,2b,1b,2a)):is(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
+-1d165
+satzd165:=satz136b(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".1d165"):eq(a,c)
+treq:=satzd165:eq(a,c)
+c@[e:eq(c,a)][f:eq(c,b)]
+treq1:=treq(a,c,b,symeq(c,a,e),f):eq(a,b)
+c@[e:eq(a,c)][f:eq(b,c)]
+treq2:=treq(a,c,b,e,symeq(b,c,f)):eq(a,b)
+c@[d:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)]
+tr3eq:=treq(a,b,d,e1,treq(b,c,d,e2,e3)):eq(a,d)
+d@[e:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)][e4:eq(d,e)]
+tr4eq:=tr3eq(a,b,c,e,e1,e2,treq(c,d,e,e3,e4)):eq(a,e)
+a@posd:=more(1a,2a):'prop'
+zero:=is(1a,2a):'prop'
+negd:=less(1a,2a):'prop'
+a2@[m:more(a1,a2)]
+posdi:=ismore12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),m):posd(df(a1,a2))
+a2@[i:is(a1,a2)]
+zeroi:=tr3is(cut,stm(df(a1,a2)),a1,a2,std(df(a1,a2)),stmis(a1,a2),i,isstd(a1,a2)):zero(df(a1,a2))
+a2@[l:less(a1,a2)]
+negdi:=isless12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),l):negd(df(a1,a2))
+a@axrde:=satz123b(1a,2a):ec3(zero(a),posd(a),negd(a))
+axrdo:=satz123a(1a,2a):or3(zero(a),posd(a),negd(a))
+axrd:=orec3i(zero(a),posd(a),negd(a),axrdo,axrde):orec3(zero(a),posd(a),negd(a))
+[p:'prop'][p1:[t:posd(a)]p][p2:[t:zero(a)]p][p3:[t:negd(a)]p]
+rappd:=or3app(zero(a),posd(a),negd(a),p,axrdo,p2,p1,p3):p
+a@[p:posd(a)]
+pnot0d:=ec3e21(zero(a),posd(a),negd(a),axrde,p):not(zero(a))
+pnotnd:=ec3e23(zero(a),posd(a),negd(a),axrde,p):not(negd(a))
+a@[z:zero(a)]
+0notpd:=ec3e12(zero(a),posd(a),negd(a),axrde,z):not(posd(a))
+0notnd:=ec3e13(zero(a),posd(a),negd(a),axrde,z):not(negd(a))
+a@[n:negd(a)]
+nnotpd:=ec3e32(zero(a),posd(a),negd(a),axrde,n):not(posd(a))
+nnot0d:=ec3e31(zero(a),posd(a),negd(a),axrde,n):not(zero(a))
+b@[e:eq(a,b)][p:posd(a)]
++iv1d
+t1:=ismore12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135a(1a,2a,2b,p)):more(pl(1b,2a),pl(2b,2a))
+-iv1d
+eqposd:=satz136a(1b,2b,2a,t1".iv1d"):posd(b)
+e@[z:zero(a)]
++*iv1d
+z@t2:=tr3is(cut,pl(1b,2a),pl(1a,2b),pl(2a,2b),pl(2b,2a),symeq(a,b,e),ispl1(1a,2a,2b,z),compl(2a,2b)):is(pl(1b,2a),pl(2b,2a))
+-iv1d
+z@eqzero:=satz136b(1b,2b,2a,t2".iv1d"):zero(b)
+e@[n:negd(a)]
++*iv1d
+n@t3:=isless12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135c(1a,2a,2b,n)):less(pl(1b,2a),pl(2b,2a))
+-iv1d
+n@eqnegd:=satz136c(1b,2b,2a,t3".iv1d"):negd(b)
+b@[z:zero(a)][y:zero(b)]
+zeroeq:=tris(cut,pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl12(1a,2a,2b,1b,z,symis(cut,1b,2b,y)),compl(2a,1b)):eq(a,b)
+@[r:cut]
+pdofrp:=df(pl(r,1rp),1rp):dif
+ndofrp:=df(1rp,pl(r,1rp)):dif
+[s:cut][i:is(r,s)]
+isrpepd:=refeq1(pdofrp(r),pdofrp(s),isf(cut,dif,[x:cut]pdofrp(x),r,s,i)):eq(pdofrp(r),pdofrp(s))
+isrpend:=refeq1(ndofrp(r),ndofrp(s),isf(cut,dif,[x:cut]ndofrp(x),r,s,i)):eq(ndofrp(r),ndofrp(s))
+s@[e:eq(pdofrp(r),pdofrp(s))]
++*iv1d
+e@t4:=satz136b(pl(r,1rp),pl(s,1rp),1rp,eqe12(pl(r,1rp),1rp,pl(s,1rp),1rp,e)):is(pl(r,1rp),pl(s,1rp))
+-iv1d
+e@isrpipd:=satz136b(r,s,1rp,t4".iv1d"):is(r,s)
+s@[e:eq(ndofrp(r),ndofrp(s))]
++*iv1d
+e@t5:=satz136e(pl(s,1rp),pl(r,1rp),1rp,eqe12(1rp,pl(r,1rp),1rp,pl(s,1rp),e)):is(pl(s,1rp),pl(r,1rp))
+-iv1d
+e@isrpind:=symis(cut,s,r,satz136b(s,r,1rp,t5".iv1d")):is(r,s)
+r@posdirp:=posdi(pl(r,1rp),1rp,ismore1(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133(1rp,r))):posd(pdofrp(r))
+negdirp:=negdi(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):negd(ndofrp(r))
+a@[p:posd(a)]
+rpofpd:=mn(1a,2a,p):cut
++*iv1d
+p@t6:=tr4is(cut,pl(1a,1rp),pl(pl(rpofpd,2a),1rp),pl(rpofpd,pl(2a,1rp)),pl(rpofpd,pl(1rp,2a)),pl(pl(rpofpd,1rp),2a),ispl1(1a,pl(rpofpd,2a),1rp,satz140f(1a,2a,p)),asspl1(rpofpd,2a,1rp),ispl2(pl(2a,1rp),pl(1rp,2a),rpofpd,compl(2a,1rp)),asspl2(rpofpd,1rp,2a)):is(pl(1a,1rp),pl(pl(rpofpd,1rp),2a))
+-iv1d
+p@eqpdrp1:=eqi1(a,pl(rpofpd,1rp),1rp,t6".iv1d"):eq(a,pdofrp(rpofpd(a,p)))
+eqpdrp2:=symeq(a,pdofrp(rpofpd(a,p)),eqpdrp1):eq(pdofrp(rpofpd(a,p)),a)
+a@[n:negd(a)]
+rpofnd:=mn(2a,1a,satz122(1a,2a,n)):cut
++*iv1d
+n@t7:=tr3is(cut,pl(1a,pl(rpofnd,1rp)),pl(pl(1a,rpofnd),1rp),pl(2a,1rp),pl(1rp,2a),asspl2(1a,rpofnd,1rp),ispl1(pl(1a,rpofnd),2a,1rp,satz140c(2a,1a,satz122(1a,2a,n))),compl(2a,1rp)):is(pl(1a,pl(rpofnd,1rp)),pl(1rp,2a))
+-iv1d
+n@eqndrp1:=eqi1(a,1rp,pl(rpofnd,1rp),t7".iv1d"):eq(a,ndofrp(rpofnd(a,n)))
+eqndrp2:=symeq(a,ndofrp(rpofnd(a,n)),eqndrp1):eq(ndofrp(rpofnd(a,n)),a)
+@[h:dif][p:posd(h)][k:dif][q:posd(k)][e:eq(h,k)]
++*iv1d
+e@t8:=tr3eq(pdofrp(rpofpd(h,p)),h,k,pdofrp(rpofpd(k,q)),eqpdrp2(h,p),e,eqpdrp1(k,q)):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
+-iv1d
+e@eqpderp:=isrpipd(rpofpd(h,p),rpofpd(k,q),t8".iv1d"):is(rpofpd(h,p),rpofpd(k,q))
+q@[i:is(rpofpd(h,p),rpofpd(k,q))]
++*iv1d
+i@t9:=isrpepd(rpofpd(h,p),rpofpd(k,q),i):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
+-iv1d
+i@eqpdirp:=tr3eq(h,pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)),k,eqpdrp1(h,p),t9".iv1d",eqpdrp2(k,q)):eq(h,k)
+h@[n:negd(h)][k:dif][o:negd(k)][e:eq(h,k)]
++*iv1d
+e@t10:=tr3eq(ndofrp(rpofnd(h,n)),h,k,ndofrp(rpofnd(k,o)),eqndrp2(h,n),e,eqndrp1(k,o)):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
+-iv1d
+e@eqnderp:=isrpind(rpofnd(h,n),rpofnd(k,o),t10".iv1d"):is(rpofnd(h,n),rpofnd(k,o))
+o@[i:is(rpofnd(h,n),rpofnd(k,o))]
++*iv1d
+i@t11:=isrpend(rpofnd(h,n),rpofnd(k,o),i):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
+-iv1d
+i@eqndirp:=tr3eq(h,ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)),k,eqndrp1(h,n),t11".iv1d",eqndrp2(k,o)):eq(h,k)
+@[r:cut]
++*iv1d
+r@t12:=eqpdrp1(pdofrp(r),posdirp(r)):eq(pdofrp(r),pdofrp(rpofpd(pdofrp(r),posdirp(r))))
+-iv1d
+r@isrppd1:=isrpipd(r,rpofpd(pdofrp(r),posdirp(r)),t12".iv1d"):is(r,rpofpd(pdofrp(r),posdirp(r)))
+isrppd2:=symis(cut,r,rpofpd(pdofrp(r),posdirp(r)),isrppd1):is(rpofpd(pdofrp(r),posdirp(r)),r)
++*iv1d
+r@t13:=eqndrp1(ndofrp(r),negdirp(r)):eq(ndofrp(r),ndofrp(rpofnd(ndofrp(r),negdirp(r))))
+-iv1d
+r@isrpnd1:=isrpind(r,rpofnd(ndofrp(r),negdirp(r)),t13".iv1d"):is(r,rpofnd(ndofrp(r),negdirp(r)))
+isrpnd2:=symis(cut,r,rpofnd(ndofrp(r),negdirp(r)),isrpnd1):is(rpofnd(ndofrp(r),negdirp(r)),r)
+a2@[r:cut]
+lemmad1:=eqi12(a1,a2,pl(a1,r),pl(a2,r),tris(cut,pl(a1,pl(a2,r)),pl(a1,pl(r,a2)),pl(pl(a1,r),a2),ispl2(pl(a2,r),pl(r,a2),a1,compl(a2,r)),asspl2(a1,r,a2))):eq(df(a1,a2),df(pl(a1,r),pl(a2,r)))
+lemmad2:=symeq(df(a1,a2),df(pl(a1,r),pl(a2,r)),lemmad1):eq(df(pl(a1,r),pl(a2,r)),df(a1,a2))
+a@[r:cut]
+lemmad3:=treq(a,df(1a,2a),df(pl(1a,r),pl(2a,r)),refeq1(a,df(1a,2a),isdf),lemmad1(1a,2a,r)):eq(a,df(pl(1a,r),pl(2a,r)))
+lemmad4:=symeq(a,df(pl(1a,r),pl(2a,r)),lemmad3):eq(df(pl(1a,r),pl(2a,r)),a)
+a@absd:=ite(negd(a),dif,df(2a,1a),a):dif
+[n:negd(a)]
+absnd:=refeq1(absd(a),df(2a,1a),itet(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),df(2a,1a))
+a@[n:not(negd(a))]
+absnnd:=refeq1(absd(a),a,itef(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),a)
+a2@[l:less(a1,a2)]
+absdeql:=treq(absd(df(a1,a2)),df(std(df(a1,a2)),stm(df(a1,a2))),df(a2,a1),absnd(df(a1,a2),negdi(a1,a2,l)),eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2))):eq(absd(df(a1,a2)),df(a2,a1))
+a2@[m:moreis(a1,a2)]
+absdeqm:=absnnd(df(a1,a2),th3"l.imp"(negd(df(a1,a2)),less(a1,a2),satz123c(a1,a2,m),[t:negd(df(a1,a2))]isless12(stm(df(a1,a2)),a1,std(df(a1,a2)),a2,stmis(a1,a2),stdis(a1,a2),t))):eq(absd(df(a1,a2)),df(a1,a2))
+b@[e:eq(a,b)]
++iv2d
+[n:negd(a)]
+t1:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
+t2:=tr3eq(absd(a),df(2a,1a),df(2b,1b),absd(b),absnd(a,n),eqi12(2a,1a,2b,1b,t1),symeq(absd(b),df(2b,1b),absnd(b,eqnegd(a,b,e,n)))):eq(absd(a),absd(b))
+e@[n:not(negd(a))]
+t3:=tr3eq(absd(a),a,b,absd(b),absnnd(a,n),e,symeq(absd(b),b,absnnd(b,th3"l.imp"(negd(b),negd(a),n,[t:negd(b)]eqnegd(b,a,symeq(a,b,e),t))))):eq(absd(a),absd(b))
+-iv2d
+eqabsd:=th1"l.imp"(negd(a),eq(absd(a),absd(b)),[t:negd(a)]t2".iv2d"(t),[t:not(negd(a))]t3".iv2d"(t)):eq(absd(a),absd(b))
+a@[p:posd(a)]
+satzd166a:=eqposd(a,absd(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p))),p):posd(absd(a))
+a@[n:negd(a)]
++2d166
+t1:=posdi(2a,1a,satz122(1a,2a,n)):posd(df(2a,1a))
+-2d166
+satzd166b:=eqposd(df(2a,1a),absd(a),symeq(absd(a),df(2a,1a),absnd(a,n)),t1".2d166"):posd(absd(a))
+b@[p:posd(a)][q:posd(b)][e:eq(absd(a),absd(b))]
+satzd166c:=tr3eq(a,absd(a),absd(b),b,symeq(absd(a),a,absnnd(a,pnotnd(a,p))),e,absnnd(b,pnotnd(b,q))):eq(a,b)
+b@[n:negd(a)][o:negd(b)][e:eq(absd(a),absd(b))]
++*2d166
+e@t2:=tr3eq(df(2a,1a),absd(a),absd(b),df(2b,1b),symeq(absd(a),df(2a,1a),absnd(a,n)),e,absnd(b,o)):eq(df(2a,1a),df(2b,1b))
+-2d166
+e@satzd166d:=tr3is(cut,pl(1a,2b),pl(2b,1a),pl(2a,1b),pl(1b,2a),compl(1a,2b),symis(cut,pl(2a,1b),pl(2b,1a),eqe12(2a,1a,2b,1b,t2".2d166")),compl(2a,1b)):eq(a,b)
+a@[n:not(zero(a))]
+satzd166e:=rappd(a,posd(absd(a)),[t:posd(a)]satzd166a(a,t),th2"l.imp"(zero(a),posd(absd(a)),n),[t:negd(a)]satzd166b(a,t)):posd(absd(a))
+a@[z:zero(a)]
+satzd166f:=eqzero(a,absd(a),symeq(absd(a),a,absnnd(a,0notnd(a,z))),z):zero(absd(a))
+b@mored:=more(pl(1a,2b),pl(1b,2a)):'prop'
+b2@[m:more(pl(a1,b2),pl(b1,a2))]
+moredi12:=ismore12(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),12issmsd(a1,a2,b1,b2),12issmsd(b1,b2,a1,a2),m):mored(df(a1,a2),df(b1,b2))
+r2@[m:more(pl(1a,r2),pl(r1,2a))]
+moredi1:=ismore12(pl(1a,r2),pl(1a,std(df(r1,r2))),pl(r1,2a),pl(stm(df(r1,r2)),2a),sm2issmsd(a,r1,r2),1sdissmsd(a,r1,r2),m):mored(a,df(r1,r2))
+r2@[m:more(pl(r1,2a),pl(1a,r2))]
+moredi2:=ismore12(pl(r1,2a),pl(stm(df(r1,r2)),2a),pl(1a,r2),pl(1a,std(df(r1,r2))),1sdissmsd(a,r1,r2),sm2issmsd(a,r1,r2),m):mored(df(r1,r2),a)
+b2@[m:mored(df(a1,a2),df(b1,b2))]
+morede12:=ismore12(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),smsdis12(a1,a2,b1,b2),smsdis12(b1,b2,a1,a2),m):more(pl(a1,b2),pl(b1,a2))
+b@lessd:=less(pl(1a,2b),pl(1b,2a)):'prop'
+[m:mored(a,b)]
+lemmad5:=satz121(pl(1a,2b),pl(1b,2a),m):lessd(b,a)
+b@[l:lessd(a,b)]
+lemmad6:=satz122(pl(1a,2b),pl(1b,2a),l):mored(b,a)
+b2@[l:less(pl(a1,b2),pl(b1,a2))]
+lessdi12:=lemmad5(df(b1,b2),df(a1,a2),moredi12(b1,b2,a1,a2,satz122(pl(a1,b2),pl(b1,a2),l))):lessd(df(a1,a2),df(b1,b2))
+r2@[l:less(pl(1a,r2),pl(r1,2a))]
+lessdi1:=lemmad5(df(r1,r2),a,moredi2(a,r1,r2,satz122(pl(1a,r2),pl(r1,2a),l))):lessd(a,df(r1,r2))
+r2@[l:less(pl(r1,2a),pl(1a,r2))]
+lessdi2:=lemmad5(a,df(r1,r2),moredi1(a,r1,r2,satz122(pl(r1,2a),pl(1a,r2),l))):lessd(df(r1,r2),a)
+b2@[l:lessd(df(a1,a2),df(b1,b2))]
+lessde12:=satz121(pl(b1,a2),pl(a1,b2),morede12(b1,b2,a1,a2,lemmad6(df(a1,a2),df(b1,b2),l))):less(pl(a1,b2),pl(b1,a2))
+b@satzd167:=satz123(pl(1a,2b),pl(1b,2a)):orec3(eq(a,b),mored(a,b),lessd(a,b))
+satzd167a:=satz123a(pl(1a,2b),pl(1b,2a)):or3(eq(a,b),mored(a,b),lessd(a,b))
+satzd167b:=satz123b(pl(1a,2b),pl(1b,2a)):ec3(eq(a,b),mored(a,b),lessd(a,b))
+d@1d:=stm(d):cut
+2d:=std(d):cut
+[e:eq(a,b)][f:eq(c,d)][m:mored(a,c)]
++*iv2d
+m@t4:=tr4is(cut,pl(pl(1b,2d),pl(1c,2a)),pl(pl(1b,2a),pl(1c,2d)),pl(pl(1a,2b),pl(1d,2c)),pl(pl(1a,2c),pl(1d,2b)),pl(pl(1d,2b),pl(1a,2c)),4pl24(1b,2d,1c,2a),ispl12(pl(1b,2a),pl(1a,2b),pl(1c,2d),pl(1d,2c),symeq(a,b,e),f),4pl24(1a,2b,1d,2c),compl(pl(1a,2c),pl(1d,2b))):is(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)))
+t5:=ismore2(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)),pl(pl(1b,2d),pl(1a,2c)),t4,satz135d(pl(1a,2c),pl(1c,2a),pl(1b,2d),m)):more(pl(pl(1b,2d),pl(1a,2c)),pl(pl(1d,2b),pl(1a,2c)))
+-iv2d
+m@eqmored12:=satz136a(pl(1b,2d),pl(1d,2b),pl(1a,2c),t5".iv2d"):mored(b,d)
+f@[l:lessd(a,c)]
+eqlessd12:=lemmad5(d,b,eqmored12(c,d,a,b,f,e,lemmad6(a,c,l))):lessd(b,d)
+c@[e:eq(a,b)][m:mored(a,c)]
+eqmored1:=eqmored12(a,b,c,c,e,refeq(c),m):mored(b,c)
+e@[m:mored(c,a)]
+eqmored2:=eqmored12(c,c,a,b,refeq(c),e,m):mored(c,b)
+e@[l:lessd(a,c)]
+eqlessd1:=eqlessd12(a,b,c,c,e,refeq(c),l):lessd(b,c)
+e@[l:lessd(c,a)]
+eqlessd2:=eqlessd12(c,c,a,b,refeq(c),e,l):lessd(c,b)
+b@moreq:=or(mored(a,b),eq(a,b)):'prop'
+lesseq:=or(lessd(a,b),eq(a,b)):'prop'
+[m:moreq(a,b)]
+satzd168a:=th9"l.or"(mored(a,b),eq(a,b),lessd(b,a),eq(b,a),m,[t:mored(a,b)]lemmad5(a,b,t),[t:eq(a,b)]symeq(a,b,t)):lesseq(b,a)
+b@[l:lesseq(a,b)]
+satzd168b:=th9"l.or"(lessd(a,b),eq(a,b),mored(b,a),eq(b,a),l,[t:lessd(a,b)]lemmad6(a,b,t),[t:eq(a,b)]symeq(a,b,t)):moreq(b,a)
+c@[e:eq(a,b)][m:moreq(a,c)]
+eqmoreq1:=th9"l.or"(mored(a,c),eq(a,c),mored(b,c),eq(b,c),m,[t:mored(a,c)]eqmored1(a,b,c,e,t),[t:eq(a,c)]treq1(b,c,a,e,t)):moreq(b,c)
+e@[m:moreq(c,a)]
+eqmoreq2:=th9"l.or"(mored(c,a),eq(c,a),mored(c,b),eq(c,b),m,[t:mored(c,a)]eqmored2(a,b,c,e,t),[t:eq(c,a)]treq(c,a,b,t,e)):moreq(c,b)
+e@[l:lesseq(a,c)]
+eqlesseq1:=satzd168a(c,b,eqmoreq2(a,b,c,e,satzd168b(a,c,l))):lesseq(b,c)
+e@[l:lesseq(c,a)]
+eqlesseq2:=satzd168a(b,c,eqmoreq1(a,b,c,e,satzd168b(c,a,l))):lesseq(c,b)
+d@[e:eq(a,b)][f:eq(c,d)][m:moreq(a,c)]
+eqmoreq12:=eqmoreq1(a,b,d,e,eqmoreq2(c,d,a,f,m)):moreq(b,d)
+f@[l:lesseq(a,c)]
+eqlesseq12:=eqlesseq1(a,b,d,e,eqlesseq2(c,d,a,f,l)):lesseq(b,d)
+b@[m:mored(a,b)]
+moreqi1:=ori1(mored(a,b),eq(a,b),m):moreq(a,b)
+b@[l:lessd(a,b)]
+lesseqi1:=ori1(lessd(a,b),eq(a,b),l):lesseq(a,b)
+b@[e:eq(a,b)]
+moreqi2:=ori2(mored(a,b),eq(a,b),e):moreq(a,b)
+lesseqi2:=ori2(lessd(a,b),eq(a,b),e):lesseq(a,b)
+b@[m:moreq(a,b)]
+satzd167c:=th7"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,comor(mored(a,b),eq(a,b),m)):not(lessd(a,b))
+b@[l:lesseq(a,b)]
+satzd167d:=th9"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,l):not(mored(a,b))
+b@[n:not(mored(a,b))]
+satzd167e:=th2"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n):lesseq(a,b)
+b@[n:not(lessd(a,b))]
+satzd167f:=comor(eq(a,b),mored(a,b),th3"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n)):moreq(a,b)
+b@[m:mored(a,b)]
+satzd167g:=th3"l.imp"(lesseq(a,b),not(mored(a,b)),weli(mored(a,b),m),[t:lesseq(a,b)]satzd167d(t)):not(lesseq(a,b))
+b@[l:lessd(a,b)]
+satzd167h:=th3"l.imp"(moreq(a,b),not(lessd(a,b)),weli(lessd(a,b),l),[t:moreq(a,b)]satzd167c(t)):not(moreq(a,b))
+b@[n:not(moreq(a,b))]
+satzd167j:=or3e3(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th5"l.or"(mored(a,b),eq(a,b),n),th4"l.or"(mored(a,b),eq(a,b),n)):lessd(a,b)
+b@[n:not(lesseq(a,b))]
+satzd167k:=or3e2(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th4"l.or"(lessd(a,b),eq(a,b),n),th5"l.or"(lessd(a,b),eq(a,b),n)):mored(a,b)
+b@[z:zero(b)][p:posd(a)]
+satzd169a:=ismore12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135a(1a,2a,1b,p)):mored(a,b)
+z@[m:mored(a,b)]
+satzd169b:=satz136d(1a,2a,2b,ismore12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),m)):posd(a)
+z@[n:negd(a)]
+satzd169c:=isless12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135c(1a,2a,1b,n)):lessd(a,b)
+z@[l:lessd(a,b)]
+satzd169d:=satz136f(1a,2a,2b,isless12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),l)):negd(a)
++2d170
+z@[p:posd(a)]
+t1:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166a(a,p))):moreq(absd(a),b)
+z@[y:zero(a)]
+t2:=moreqi2(absd(a),b,treq(absd(a),a,b,absnnd(a,0notnd(a,y)),zeroeq(a,b,y,z))):moreq(absd(a),b)
+z@[n:negd(a)]
+t3:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166b(a,n))):moreq(absd(a),b)
+-2d170
+z@satzd170:=rappd(a,moreq(absd(a),b),[t:posd(a)]t1".2d170"(t),[t:zero(a)]t2".2d170"(t),[t:negd(a)]t3".2d170"(t)):moreq(absd(a),b)
+c@[l:lessd(a,b)][k:lessd(b,c)]
++2d171
+t1:=satz137a(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),l,k):less(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
+t2:=isless12(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1a,2c),pl(1b,2b)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2b,1b,2c),tris(cut,pl(pl(1b,2a),pl(1c,2b)),pl(pl(1b,2b),pl(1c,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1b,2a,1c,2b),compl(pl(1b,2b),pl(1c,2a))),t1):less(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
+-2d171
+satzd171:=satz136c(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".2d171"):lessd(a,c)
+trlessd:=satzd171:lessd(a,c)
+c@[m:mored(a,b)][n:mored(b,c)]
+trmored:=lemmad6(c,a,trlessd(c,b,a,lemmad5(b,c,n),lemmad5(a,b,m))):mored(a,c)
+c@[l:lesseq(a,b)][k:lessd(b,c)]
+satzd172a:=orapp(lessd(a,b),eq(a,b),lessd(a,c),l,[t:lessd(a,b)]trlessd(t,k),[t:eq(a,b)]eqlessd1(b,a,c,symeq(a,b,t),k)):lessd(a,c)
+c@[l:lessd(a,b)][k:lesseq(b,c)]
+satzd172b:=orapp(lessd(b,c),eq(b,c),lessd(a,c),k,[t:lessd(b,c)]trlessd(l,t),[t:eq(b,c)]eqlessd2(b,c,a,t,l)):lessd(a,c)
+c@[m:moreq(a,b)][n:mored(b,c)]
+satzd172c:=lemmad6(c,a,satzd172b(c,b,a,lemmad5(b,c,n),satzd168a(a,b,m))):mored(a,c)
+c@[m:mored(a,b)][n:moreq(b,c)]
+satzd172d:=lemmad6(c,a,satzd172a(c,b,a,satzd168a(b,c,n),lemmad5(a,b,m))):mored(a,c)
+c@[l:lesseq(a,b)][k:lesseq(b,c)]
++2d173
+[j:lessd(a,b)]
+t1:=lesseqi1(a,c,satzd172b(j,k)):lesseq(a,c)
+k@[e:eq(a,b)]
+t2:=eqlesseq1(b,a,c,symeq(a,b,e),k):lesseq(a,c)
+-2d173
+satzd173:=orapp(lessd(a,b),eq(a,b),lesseq(a,c),l,[t:lessd(a,b)]t1".2d173"(t),[t:eq(a,b)]t2".2d173"(t)):lesseq(a,c)
+trlesseq:=satzd173:lesseq(a,c)
+c@[m:moreq(a,b)][n:moreq(b,c)]
+trmoreq:=satzd168b(c,a,trlesseq(c,b,a,satzd168a(b,c,n),satzd168a(a,b,m))):moreq(a,c)
+a@ratd:=[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))):'prop'
+irratd:=not(ratd(a)):'prop'
+b@[e:eq(a,b)][r:ratd(a)]
++*iv2d
+r@[n:not(zero(b))]
+t6:=th3"l.imp"(zero(a),zero(b),n,[t:zero(a)]eqzero(a,b,e,t)):not(zero(a))
+t7:=eqpderp(absd(a),satzd166e(a,t6),absd(b),satzd166e(b,n),eqabsd(a,b,e)):is(rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)))
+t8:=isp(cut,[t:cut]ratrp(t),rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)),<t6>r,t7):ratrp(rpofpd(absd(b),satzd166e(b,n)))
+-iv2d
+r@eqratd:=[t:not(zero(b))]t8".iv2d"(t):ratd(b)
+e@[i:irratd(a)]
+eqirratd:=th3"l.imp"(ratd(b),ratd(a),i,[t:ratd(b)]eqratd(b,a,symeq(a,b,e),t)):irratd(b)
+a@[z:zero(a)]
+ratdi0:=th2"l.r.imp"(not(zero(a)),[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))),weli(zero(a),z)):ratd(a)
+@[r:cut][i:irratrp(r)][x0:rat]
++*iv2d
+x0@[s:ratrp(pl(r,rpofrt(x0)))][y0:rat][j:is(pl(r,rpofrt(x0)),rpofrt(y0))]
+t9:=tris(cut,pl(rpofrt(x0),r),pl(r,rpofrt(x0)),rpofrt(y0),compl(rpofrt(x0),r),j):is(pl(rpofrt(x0),r),rpofrt(y0))
+t10:=ismore1(pl(rpofrt(x0),r),rpofrt(y0),rpofrt(x0),t9,satz133(rpofrt(x0),r)):more(rpofrt(y0),rpofrt(x0))
+t11:=satz154d(y0,x0,t10):more"rt"(y0,x0)
+t12:=satz155b(y0,x0,t11):is(rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
+t13:=satz140g(rpofrt(y0),rpofrt(x0),r,satz154a(y0,x0,t11),t9):is(r,mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
+t14:=tris2(cut,r,rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)),t13,t12):is(r,rpofrt(mn"rt"(y0,x0,t11)))
+t15:=somei(rat,[x:rat]is(r,rpofrt(x)),mn"rt"(y0,x0,t11),t14):ratrp(r)
+s@t16:=someapp(rat,[x:rat]is(pl(r,rpofrt(x0)),rpofrt(x)),s,con,[x:rat][t:is(pl(r,rpofrt(x0)),rpofrt(x))]<t15(x,t)>i):con
+-iv2d
+x0@remark1:=[t:ratrp(pl(r,rpofrt(x0)))]t16".iv2d"(t):irratrp(pl(r,rpofrt(x0)))
++*iv2d
+r@rp:=pdofrp(r):dif
+rn:=ndofrp(r):dif
+t17:=posdirp(r):posd(rp)
+t18:=pnot0d(rp,t17):not(zero(rp))
+t19:=nnot0d(rn,negdirp(r)):not(zero(rn))
+[n:not(zero(rp))]
+t20:=tris2(cut,r,rpofpd(absd(rp),satzd166e(rp,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rp),satzd166e(rp,n),rp,t17,absnnd(rp,pnotnd(rp,t17)))):is(r,rpofpd(absd(rp),satzd166e(rp,n)))
+r@t21:=treq(absd(rn),df(std(rn),stm(rn)),rp,absnd(rn,negdirp(r)),eqsmsd(std(rn),stm(rn),pl(r,1rp),1rp,stdis(1rp,pl(r,1rp)),stmis(1rp,pl(r,1rp)))):eq(absd(rn),rp)
+[n:not(zero(rn))]
+t22:=tris2(cut,r,rpofpd(absd(rn),satzd166e(rn,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rn),satzd166e(rn,n),rp,t17,t21)):is(r,rpofpd(absd(rn),satzd166e(rn,n)))
+r@[s:cut][i:is(r,s)][rr:ratrp(r)]
+t23:=isp(cut,[x:cut]ratrp(x),r,s,rr,i):ratrp(s)
+i@[rs:ratrp(s)]
+t24:=isp1(cut,[x:cut]ratrp(x),s,r,rs,i):ratrp(r)
+-iv2d
+r@[rr:ratrp(r)]
+remark2a:=[t:not(zero(pdofrp(r)))]t23".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t)),t20".iv2d"(t),rr):ratd(pdofrp(r))
+remark2b:=t17".iv2d":posd(pdofrp(r))
+remark3a:=[t:not(zero(ndofrp(r)))]t23".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t)),t22".iv2d"(t),rr):ratd(ndofrp(r))
+remark3b:=negdirp(r):negd(ndofrp(r))
+r@[i:irratrp(r)]
+remark4a:=th3"l.imp"(ratd(pdofrp(r)),ratrp(r),i,[t:ratd(pdofrp(r))]t24".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t18".iv2d")),t20".iv2d"(t18".iv2d"),<t18".iv2d">t)):irratd(pdofrp(r))
+remark4b:=t17".iv2d":posd(pdofrp(r))
+remark5a:=th3"l.imp"(ratd(ndofrp(r)),ratrp(r),i,[t:ratd(ndofrp(r))]t24".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t19".iv2d")),t22".iv2d"(t19".iv2d"),<t19".iv2d">t)):irratd(ndofrp(r))
+remark5b:=negdirp(r):negd(ndofrp(r))
+a@natd:=and(posd(a),[t:posd(a)]natrp(rpofpd(a,t))):'prop'
+[n:natd(a)]
+natposd:=ande1(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):posd(a)
+natderp:=ande2"l.r"(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):natrp(rpofpd(a,natposd(a,n)))
+b@[e:eq(a,b)][n:natd(a)]
++*iv2d
+n"rp"@t25:=eqposd(a,b,e,natposd(a,n)):posd(b)
+[p:posd(b)]
+t26:=eqpderp(a,natposd(a,n),b,p,e):is(rpofpd(a,natposd(a,n)),rpofpd(b,p))
+t27:=isp(cut,[t:cut]natrp(t),rpofpd(a,natposd(a,n)),rpofpd(b,p),natderp(a,n),t26):natrp(rpofpd(b,p))
+-iv2d
+n@eqnatd:=andi(posd(b),[t:posd(b)]natrp(rpofpd(b,t)),t25".iv2d",[t:posd(b)]t27".iv2d"(t)):natd(b)
+@[x:nat]
+pdofnt:=pdofrp(rpofnt(x)):dif
++*iv2d
+x@t28:=posdirp(rpofnt(x)):posd(pdofnt(x))
+[p:posd(pdofnt(x))]
+t29:=isrppd1(rpofnt(x)):is(rpofnt(x),rpofpd(pdofnt(x),t28))
+t30:=eqpderp(pdofnt(x),t28,pdofnt(x),p,refeq(pdofnt(x))):is(rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p))
+t31:=tris(cut,rpofnt(x),rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p),t29,t30):is(rpofnt(x),rpofpd(pdofnt(x),p))
+t32:=isp(cut,[t:cut]natrp(t),rpofnt(x),rpofpd(pdofnt(x),p),natrpi(x),t31):natrp(rpofpd(pdofnt(x),p))
+-iv2d
+x@natdi:=andi(posd(pdofnt(x)),[t:posd(pdofnt(x))]natrp(rpofpd(pdofnt(x),t)),t28".iv2d",[t:posd(pdofnt(x))]t32".iv2d"(t)):natd(pdofnt(x))
+a@intd:=or(zero(a),natd(absd(a))):'prop'
+b@[e:eq(a,b)][i:intd(a)]
++*iv2d
+i"rp"@[z:zero(a)]
+t33:=eqzero(a,b,e,z):zero(b)
+i"rp"@[n:natd(absd(a))]
+t34:=eqnatd(absd(a),absd(b),eqabsd(a,b,e),n):natd(absd(b))
+-iv2d
+i@eqintd:=th9"l.or"(zero(a),natd(absd(a)),zero(b),natd(absd(b)),i,[t:zero(a)]t33".iv2d"(t),[t:natd(absd(a))]t34".iv2d"(t)):intd(b)
+a@[n:natd(a)]
++*iv2d
+n"rp"@t34a:=symeq(absd(a),a,absnnd(a,pnotnd(a,natposd(a,n)))):eq(a,absd(a))
+t35:=eqnatd(a,absd(a),t34a,n):natd(absd(a))
+-iv2d
+n@natintd:=ori2(zero(a),natd(absd(a)),t35".iv2d"):intd(a)
+a@[p:posd(a)][i:intd(a)]
++*iv2d
+i"rp"@t36:=ore2(zero(a),natd(absd(a)),i,pnot0d(a,p)):natd(absd(a))
+-iv2d
+i@posintnatd:=eqnatd(absd(a),a,absnnd(a,pnotnd(a,p)),t36".iv2d"):natd(a)
+a@[z:zero(a)]
+intdi0:=ori1(zero(a),natd(absd(a)),z):intd(a)
+r@[n:natrp(r)]
++*iv2d
+n"rp"@t37:=posdirp(r):posd(pdofrp(r))
+[p:posd(pdofrp(r))]
+t38:=tris(cut,r,rpofpd(pdofrp(r),t37),rpofpd(pdofrp(r),p),isrppd1(r),eqpderp(pdofrp(r),t37,pdofrp(r),p,refeq(pdofrp(r)))):is(r,rpofpd(pdofrp(r),p))
+t39:=isp(cut,[t:cut]natrp(t),r,rpofpd(pdofrp(r),p),n,t38):natrp(rpofpd(pdofrp(r),p))
+-iv2d
+n@remark6a:=andi(posd(pdofrp(r)),[t:posd(pdofrp(r))]natrp(rpofpd(pdofrp(r),t)),t37".iv2d",[t:posd(pdofrp(r))]t39".iv2d"(t)):natd(pdofrp(r))
+remark6:=natintd(pdofrp(r),remark6a):intd(pdofrp(r))
++*iv2d
+n"rp"@t40:=absdeql(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):eq(absd(ndofrp(r)),pdofrp(r))
+t41:=eqnatd(pdofrp(r),absd(ndofrp(r)),symeq(absd(ndofrp(r)),pdofrp(r),t40),remark6a):natd(absd(ndofrp(r)))
+-iv2d
+n@remark7:=ori2(zero(ndofrp(r)),natd(absd(ndofrp(r))),t41".iv2d"):intd(ndofrp(r))
+a@[i:intd(a)]
++2d174
+[n:not(zero(a))]
+t1:=ore2(zero(a),natd(absd(a)),i,n):natd(absd(a))
+t2:=ande2(posd(absd(a)),[t:posd(absd(a))]natrp(rpofpd(absd(a),t)),t1):[t:posd(absd(a))]natrp(rpofpd(absd(a),t))
+t3:=lemmaiii5(rpofpd(absd(a),satzd166e(a,n)),<satzd166e(a,n)>t2):ratrp(rpofpd(absd(a),satzd166e(a,n)))
+-2d174
+satzd174:=[t:not(zero(a))]t3".2d174"(t):ratd(a)
+b@pd:=df(pl(1a,1b),pl(2a,2b)):dif
+b2@pd12:=issmsd(pl(stm(df(a1,a2)),stm(df(b1,b2))),pl(std(df(a1,a2)),std(df(b1,b2))),pl(a1,b1),pl(a2,b2),ispl12(stm(df(a1,a2)),a1,stm(df(b1,b2)),b1,stmis(a1,a2),stmis(b1,b2)),ispl12(std(df(a1,a2)),a2,std(df(b1,b2)),b2,stdis(a1,a2),stdis(b1,b2))):is"e"(dif,pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
+r2@pd1:=issmsd(pl(1a,stm(df(r1,r2))),pl(2a,std(df(r1,r2))),pl(1a,r1),pl(2a,r2),ispl2(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl2(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
+pd2:=issmsd(pl(stm(df(r1,r2)),1a),pl(std(df(r1,r2)),2a),pl(r1,1a),pl(r2,2a),ispl1(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl1(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
+b2@pdeq12a:=refeq1(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
+pdeq12b:=refeq2(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(df(pl(a1,b1),pl(a2,b2)),pd(df(a1,a2),df(b1,b2)))
+r2@pdeq1a:=refeq1(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
+pdeq1b:=refeq2(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(df(pl(1a,r1),pl(2a,r2)),pd(a,df(r1,r2)))
+pdeq2a:=refeq1(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
+pdeq2b:=refeq2(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(df(pl(r1,1a),pl(r2,2a)),pd(df(r1,r2),a))
+b@satzd175:=eqsmsd(pl(1a,1b),pl(2a,2b),pl(1b,1a),pl(2b,2a),compl(1a,1b),compl(2a,2b)):eq(pd(a,b),pd(b,a))
+compd:=satzd175:eq(pd(a,b),pd(b,a))
+c@[e:eq(a,b)]
++iv3d
+t1:=tr3is(cut,pl(pl(1a,1c),pl(2b,2c)),pl(pl(1a,2b),pl(1c,2c)),pl(pl(1b,2a),pl(1c,2c)),pl(pl(1b,1c),pl(2a,2c)),4pl23(1a,1c,2b,2c),ispl1(pl(1a,2b),pl(1b,2a),pl(1c,2c),e),4pl23(1b,2a,1c,2c)):is(pl(pl(1a,1c),pl(2b,2c)),pl(pl(1b,1c),pl(2a,2c)))
+-iv3d
+eqpd1:=eqi12(pl(1a,1c),pl(2a,2c),pl(1b,1c),pl(2b,2c),t1".iv3d"):eq(pd(a,c),pd(b,c))
+eqpd2:=tr3eq(pd(c,a),pd(a,c),pd(b,c),pd(c,b),compd(c,a),eqpd1,compd(b,c)):eq(pd(c,a),pd(c,b))
+d@[e:eq(a,b)][f:eq(c,d)]
+eqpd12:=treq(pd(a,c),pd(b,c),pd(b,d),eqpd1(a,b,c,e),eqpd2(c,d,b,f)):eq(pd(a,c),pd(b,d))
+b@[z:zero(a)]
++*iv3d
+z@t2:=tr4is(cut,pl(pl(1a,1b),2b),pl(1a,pl(1b,2b)),pl(2a,pl(2b,1b)),pl(pl(2a,2b),1b),pl(1b,pl(2a,2b)),asspl1(1a,1b,2b),ispl12(1a,2a,pl(1b,2b),pl(2b,1b),z,compl(1b,2b)),asspl2(2a,2b,1b),compl(pl(2a,2b),1b)):is(pl(pl(1a,1b),2b),pl(1b,pl(2a,2b)))
+-iv3d
+z@pd01:=eqi2(b,pl(1a,1b),pl(2a,2b),t2".iv3d"):eq(pd(a,b),b)
+b@[z:zero(b)]
+pd02:=treq(pd(a,b),pd(b,a),a,compd(a,b),pd01(b,a,z)):eq(pd(a,b),a)
+b@[p:posd(a)][q:posd(b)]
+ppd:=posdi(pl(1a,1b),pl(2a,2b),satz137(1a,2a,1b,2b,p,q)):posd(pd(a,b))
+b@[n:negd(a)][o:negd(b)]
+npd:=negdi(pl(1a,1b),pl(2a,2b),satz137a(1a,2a,1b,2b,n,o)):negd(pd(a,b))
+a@m0d:=df(2a,1a):dif
+a2@m0deqa:=eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2)):eq(m0d(df(a1,a2)),df(a2,a1))
+m0deqb:=symeq(m0d(df(a1,a2)),df(a2,a1),m0deqa):eq(df(a2,a1),m0d(df(a1,a2)))
+b@[e:eq(a,b)]
++*iv3d
+e@t3:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
+-iv3d
+e@eqm0d:=eqi12(2a,1a,2b,1b,t3".iv3d"):eq(m0d(a),m0d(b))
+a@[p:posd(a)]
+satzd176a:=negdi(2a,1a,satz121(1a,2a,p)):negd(m0d(a))
+a@[z:zero(a)]
+satzd176b:=zeroi(2a,1a,symis(cut,1a,2a,z)):zero(m0d(a))
+a@[n:negd(a)]
+satzd176c:=posdi(2a,1a,satz122(1a,2a,n)):posd(m0d(a))
+a@[n:negd(m0d(a))]
+satzd176d:=satz122(2a,1a,isless12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),n)):posd(a)
+a@[z:zero(m0d(a))]
+satzd176e:=symis(cut,2a,1a,tr3is(cut,2a,stm(df(2a,1a)),std(df(2a,1a)),1a,isstm(2a,1a),z,stdis(2a,1a))):zero(a)
+a@[p:posd(m0d(a))]
+satzd176f:=satz121(2a,1a,ismore12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),p)):negd(a)
+a@[z:zero(a)]
+m0d0:=zeroeq(m0d(a),a,satzd176b(a,z),z):eq(m0d(a),a)
++3d177
+a@t1:=tris(dif,m0d(m0d(a)),df(1a,2a),a,issmsd(std(m0d(a)),stm(m0d(a)),1a,2a,stdis(2a,1a),stmis(2a,1a)),dfis(a)):is"e"(dif,m0d(m0d(a)),a)
+-3d177
+a@satzd177:=refeq1(m0d(m0d(a)),a,t1".3d177"):eq(m0d(m0d(a)),a)
+satzd177a:=symeq(m0d(m0d(a)),a,satzd177):eq(a,m0d(m0d(a)))
+b@[e:eq(a,m0d(b))]
+satzd177b:=treq(m0d(a),m0d(m0d(b)),b,eqm0d(a,m0d(b),e),satzd177(b)):eq(m0d(a),b)
+satzd177c:=symeq(m0d(a),b,satzd177b):eq(b,m0d(a))
+b@[e:eq(m0d(a),b)]
+satzd177d:=satzd177c(b,a,symeq(m0d(a),b,e)):eq(a,m0d(b))
+satzd177e:=symeq(a,m0d(b),satzd177d):eq(m0d(b),a)
++3d178
+a@[p:posd(a)]
+t1:=tr3eq(absd(m0d(a)),m0d(m0d(a)),a,absd(a),absnd(m0d(a),satzd176a(a,p)),satzd177(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p)))):eq(absd(m0d(a)),absd(a))
+a@[z:zero(a)]
+t2:=tr3eq(absd(m0d(a)),m0d(a),a,absd(a),absnnd(m0d(a),0notnd(m0d(a),satzd176b(a,z))),m0d0(a,z),symeq(absd(a),a,absnnd(a,0notnd(a,z)))):eq(absd(m0d(a)),absd(a))
+a@[n:negd(a)]
+t3:=treq(absd(m0d(a)),m0d(a),absd(a),absnnd(m0d(a),pnotnd(m0d(a),satzd176c(a,n))),symeq(absd(a),m0d(a),absnd(a,n))):eq(absd(m0d(a)),absd(a))
+-3d178
+a@satzd178:=rappd(a,eq(absd(m0d(a)),absd(a)),[t:posd(a)]t1".3d178"(t),[t:zero(a)]t2".3d178"(t),[t:negd(a)]t3".3d178"(t)):eq(absd(m0d(a)),absd(a))
+satzd178a:=symeq(absd(m0d(a)),absd(a),satzd178):eq(absd(a),absd(m0d(a)))
++3d179
+t1:=pdeq1b(a,2a,1a):eq(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)))
+t2:=zeroi(pl(1a,2a),pl(2a,1a),compl(1a,2a)):zero(df(pl(1a,2a),pl(2a,1a)))
+-3d179
+satzd179:=eqzero(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)),t1".3d179",t2".3d179"):zero(pd(a,m0d(a)))
+satzd179a:=eqzero(pd(a,m0d(a)),pd(m0d(a),a),compd(a,m0d(a)),satzd179):zero(pd(m0d(a),a))
+b@satzd180:=treq(m0d(pd(a,b)),df(pl(2a,2b),pl(1a,1b)),pd(m0d(a),m0d(b)),m0deqa(pl(1a,1b),pl(2a,2b)),pdeq12b(2a,1a,2b,1b)):eq(m0d(pd(a,b)),pd(m0d(a),m0d(b)))
+satzd180a:=symeq(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180):eq(pd(m0d(a),m0d(b)),m0d(pd(a,b)))
+md:=pd(a,m0d(b)):dif
+b2@mdeq12a:=treq(md(df(a1,a2),df(b1,b2)),pd(df(a1,a2),df(b2,b1)),df(pl(a1,b2),pl(a2,b1)),eqpd2(m0d(df(b1,b2)),df(b2,b1),df(a1,a2),m0deqa(b1,b2)),pdeq12a(a1,a2,b2,b1)):eq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)))
+mdeq12b:=symeq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)),mdeq12a):eq(df(pl(a1,b2),pl(a2,b1)),md(df(a1,a2),df(b1,b2)))
+r2@mdeq1a:=treq(md(a,df(r1,r2)),pd(a,df(r2,r1)),df(pl(1a,r2),pl(2a,r1)),eqpd2(m0d(df(r1,r2)),df(r2,r1),a,m0deqa(r1,r2)),pdeq1a(a,r2,r1)):eq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)))
+mdeq1b:=symeq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)),mdeq1a):eq(df(pl(1a,r2),pl(2a,r1)),md(a,df(r1,r2)))
+mdeq2a:=pdeq12a(r1,r2,2a,1a):eq(md(df(r1,r2),a),df(pl(r1,2a),pl(r2,1a)))
+mdeq2b:=pdeq12b(r1,r2,2a,1a):eq(df(pl(r1,2a),pl(r2,1a)),md(df(r1,r2),a))
+c@[e:eq(a,b)]
+eqmd1:=eqpd1(a,b,m0d(c),e):eq(md(a,c),md(b,c))
+eqmd2:=eqpd2(m0d(a),m0d(b),c,eqm0d(a,b,e)):eq(md(c,a),md(c,b))
+d@[e:eq(a,b)][f:eq(c,d)]
+eqmd12:=treq(md(a,c),md(b,c),md(b,d),eqmd1(a,b,c,e),eqmd2(c,d,b,f)):eq(md(a,c),md(b,d))
+b@satzd181:=tr3eq(m0d(md(a,b)),pd(m0d(a),m0d(m0d(b))),pd(m0d(a),b),md(b,a),satzd180(a,m0d(b)),eqpd2(m0d(m0d(b)),b,m0d(a),satzd177(b)),compd(m0d(a),b)):eq(m0d(md(a,b)),md(b,a))
+satzd181a:=symeq(m0d(md(b,a)),md(a,b),satzd181(b,a)):eq(md(a,b),m0d(md(b,a)))
++3d182
+t1:=treq(md(a,b),df(pl(1a,2b),pl(2a,1b)),df(pl(1a,2b),pl(1b,2a)),pdeq1a(a,2b,1b),eqsd(pl(1a,2b),pl(2a,1b),pl(1b,2a),compl(2a,1b))):eq(md(a,b),df(pl(1a,2b),pl(1b,2a)))
+t2:=symeq(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1):eq(df(pl(1a,2b),pl(1b,2a)),md(a,b))
+t3:=stmis(pl(1a,2b),pl(1b,2a)):is(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b))
+t4:=stdis(pl(1a,2b),pl(1b,2a)):is(std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a))
+-3d182
+[p:posd(md(a,b))]
++*3d182
+p@t5:=eqposd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,p):posd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+p@satzd182a:=ismore12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t5".3d182"):mored(a,b)
+b@[z:zero(md(a,b))]
++*3d182
+z@t6:=eqzero(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,z):zero(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+z@satzd182b:=tr3is(cut,pl(1a,2b),stm(df(pl(1a,2b),pl(1b,2a))),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),isstm(pl(1a,2b),pl(1b,2a)),t6".3d182",t4".3d182"):eq(a,b)
+b@[n:negd(md(a,b))]
++*3d182
+n@t7:=eqnegd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,n):negd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+n@satzd182c:=isless12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t7".3d182"):lessd(a,b)
+b@[m:mored(a,b)]
++*3d182
+m@t8:=posdi(pl(1a,2b),pl(1b,2a),m):posd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+m@satzd182d:=eqposd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t8".3d182"):posd(md(a,b))
+b@[e:eq(a,b)]
++*3d182
+e@t9:=zeroi(pl(1a,2b),pl(1b,2a),e):zero(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+e@satzd182e:=eqzero(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t9".3d182"):zero(md(a,b))
+b@[l:lessd(a,b)]
++*3d182
+l@t10:=negdi(pl(1a,2b),pl(1b,2a),l):negd(df(pl(1a,2b),pl(1b,2a)))
+-3d182
+l@satzd182f:=eqnegd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t10".3d182"):negd(md(a,b))
++3d183
+b@t1:=tris(cut,pl(1a,2b),pl(2b,1a),pl(stm(m0d(b)),std(m0d(a))),compl(1a,2b),12issmsd(2b,1b,2a,1a)):is(pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))))
+t2:=t1(b,a):is(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))))
+-3d183
+b@[m:mored(a,b)]
+satzd183a:=isless12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad5(a,b,m)):lessd(m0d(a),m0d(b))
+b@[e:eq(a,b)]
+staz183b:=eqm0d(a,b,e):eq(m0d(a),m0d(b))
+b@[l:lessd(a,b)]
+satzd183c:=ismore12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad6(a,b,l)):mored(m0d(a),m0d(b))
+b@[l:lessd(m0d(a),m0d(b))]
+satzd183d:=eqmored12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183c(m0d(a),m0d(b),l)):mored(a,b)
+b@[e:eq(m0d(a),m0d(b))]
+satzd183e:=tr3eq(a,m0d(m0d(a)),m0d(m0d(b)),b,satzd177a(a),eqm0d(m0d(a),m0d(b),e),satzd177(b)):eq(a,b)
+b@[m:mored(m0d(a),m0d(b))]
+satzd183f:=eqlessd12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183a(m0d(a),m0d(b),m)):lessd(a,b)
++3d184
+a@t1:=tr3eq(a,df(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp))),df(pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp))),md(pdofrp(1a),pdofrp(2a)),lemmad3(a,pl(1rp,1rp)),eqsmsd(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp)),pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp)),asspl2(1a,1rp,1rp),3pl12(2a,1rp,1rp)),mdeq12b(pl(1a,1rp),1rp,pl(2a,1rp),1rp)):eq(a,md(pdofrp(1a),pdofrp(2a)))
+t2:=and3i(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))),posdirp(1a),posdirp(2a),t1):and3(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))))
+t3:=somei(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))),pdofrp(2a),t2):some"l"(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))))
+-3d184
+a@satzd184:=somei(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))),pdofrp(1a),t3".3d184"):some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))))
+c@asspd1:=tr3eq(pd(pd(a,b),c),df(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c)),df(pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c))),pd(a,pd(b,c)),pdeq2a(c,pl(1a,1b),pl(2a,2b)),eqsmsd(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c),pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c)),asspl1(1a,1b,1c),asspl1(2a,2b,2c)),pdeq1b(a,pl(1b,1c),pl(2b,2c))):eq(pd(pd(a,b),c),pd(a,pd(b,c)))
+asspd2:=symeq(pd(pd(a,b),c),pd(a,pd(b,c)),asspd1):eq(pd(a,pd(b,c)),pd(pd(a,b),c))
+3pd23:=tr3eq(pd(pd(a,b),c),pd(a,pd(b,c)),pd(a,pd(c,b)),pd(pd(a,c),b),asspd1(a,b,c),eqpd2(pd(b,c),pd(c,b),a,compd(b,c)),asspd2(a,c,b)):eq(pd(pd(a,b),c),pd(pd(a,c),b))
+d@4pd23:=tr3eq(pd(pd(a,b),pd(c,d)),pd(pd(pd(a,b),c),d),pd(pd(pd(a,c),b),d),pd(pd(a,c),pd(b,d)),asspd2(pd(a,b),c,d),eqpd1(pd(pd(a,b),c),pd(pd(a,c),b),d,3pd23),asspd1(pd(a,c),b,d)):eq(pd(pd(a,b),pd(c,d)),pd(pd(a,c),pd(b,d)))
+b@pdmd:=treq(pd(md(a,b),b),pd(a,pd(m0d(b),b)),a,asspd1(a,m0d(b),b),pd02(a,pd(m0d(b),b),satzd179a(b))):eq(pd(md(a,b),b),a)
+mdpd:=treq(md(pd(a,b),b),pd(a,pd(b,m0d(b))),a,asspd1(a,b,m0d(b)),pd02(a,pd(b,m0d(b)),satzd179(b))):eq(md(pd(a,b),b),a)
+d@satzd185:=treq(pd(md(a,b),md(c,d)),pd(pd(a,c),pd(m0d(b),m0d(d))),md(pd(a,c),pd(b,d)),4pd23(a,m0d(b),c,m0d(d)),eqpd2(pd(m0d(b),m0d(d)),m0d(pd(b,d)),pd(a,c),satzd180a(b,d))):eq(pd(md(a,b),md(c,d)),md(pd(a,c),pd(b,d)))
+c@satzd186:=asspd1:eq(pd(pd(a,b),c),pd(a,pd(b,c)))
+b@satzd187a:=treq(pd(b,md(a,b)),pd(md(a,b),b),a,compd(b,md(a,b)),pdmd):eq(pd(b,md(a,b)),a)
+[x:dif][e:eq(pd(b,x),a)]
+satzd187c:=treq(md(a,b),md(pd(x,b),b),x,eqmd1(a,pd(x,b),b,treq1(a,pd(x,b),pd(b,x),e,compd(b,x))),mdpd(x,b)):eq(md(a,b),x)
+satzd187d:=symeq(md(a,b),x,satzd187c):eq(x,md(a,b))
+x@[e:eq(pd(x,b),a)]
+satzd187e:=satzd187c(treq(pd(b,x),pd(x,b),a,compd(b,x),e)):eq(md(a,b),x)
+satzd187f:=symeq(md(a,b),x,satzd187e):eq(x,md(a,b))
++3d188
+c@t1:=tr3eq(md(pd(a,c),pd(b,c)),pd(pd(a,c),pd(m0d(b),m0d(c))),pd(md(a,b),md(c,c)),md(a,b),eqpd2(m0d(pd(b,c)),pd(m0d(b),m0d(c)),pd(a,c),satzd180(b,c)),4pd23(a,c,m0d(b),m0d(c)),pd02(md(a,b),md(c,c),satzd179(c))):eq(md(pd(a,c),pd(b,c)),md(a,b))
+t2:=symeq(md(pd(a,c),pd(b,c)),md(a,b),t1):eq(md(a,b),md(pd(a,c),pd(b,c)))
+-3d188
+c@[m:mored(pd(a,c),pd(b,c))]
++*3d188
+m@t3:=eqposd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182d(pd(a,c),pd(b,c),m)):posd(md(a,b))
+-3d188
+m@satzd188a:=satzd182a(a,b,t3".3d188"):mored(a,b)
+c@[e:eq(pd(a,c),pd(b,c))]
++*3d188
+e@t4:=eqzero(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182e(pd(a,c),pd(b,c),e)):zero(md(a,b))
+-3d188
+e@satzd188b:=satzd182b(a,b,t4".3d188"):eq(a,b)
+c@[l:lessd(pd(a,c),pd(b,c))]
++*3d188
+l@t5:=eqnegd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182f(pd(a,c),pd(b,c),l)):negd(md(a,b))
+-3d188
+l@satzd188c:=satzd182c(a,b,t5".3d188"):lessd(a,b)
+c@[m:mored(a,b)]
++*3d188
+m@t6:=eqposd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182d(a,b,m)):posd(md(pd(a,c),pd(b,c)))
+-3d188
+m@satzd188d:=satzd182a(pd(a,c),pd(b,c),t6".3d188"):mored(pd(a,c),pd(b,c))
+c@[e:eq(a,b)]
+satzd188e:=eqpd1(a,b,c,e):eq(pd(a,c),pd(b,c))
+c@[l:lessd(a,b)]
++*3d188
+l@t7:=eqnegd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182f(a,b,l)):negd(md(pd(a,c),pd(b,c)))
+-3d188
+l@satzd188f:=satzd182c(pd(a,c),pd(b,c),t7".3d188"):lessd(pd(a,c),pd(b,c))
+c@[m:mored(pd(c,a),pd(c,b))]
+satzd188g:=satzd188a(eqmored12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),m)):mored(a,b)
+c@[e:eq(pd(c,a),pd(c,b))]
+satzd188h:=satzd188b(tr3eq(pd(a,c),pd(c,a),pd(c,b),pd(b,c),compd(a,c),e,compd(c,b))):eq(a,b)
+[l:lessd(pd(c,a),pd(c,b))]
+satzd188j:=satzd188c(eqlessd12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),l)):lessd(a,b)
+c@[m:mored(a,b)]
+satzd188k:=eqmored12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188d(m)):mored(pd(c,a),pd(c,b))
+c@[e:eq(a,b)]
+satzd188l:=eqpd2(a,b,c,e):eq(pd(c,a),pd(c,b))
+c@[l:lessd(a,b)]
+satzd188m:=eqlessd12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188f(l)):lessd(pd(c,a),pd(c,b))
+d@[e:eq(a,b)][m:mored(c,d)]
+satzd188n:=eqmored2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188k(c,d,a,m)):mored(pd(a,c),pd(b,d))
+satzd188o:=eqmored12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188n):mored(pd(c,a),pd(d,b))
+e@[l:lessd(c,d)]
+satzd188p:=eqlessd2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188m(c,d,a,l)):lessd(pd(a,c),pd(b,d))
+satzd188q:=eqlessd12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188p):lessd(pd(c,a),pd(d,b))
+d@[m:mored(a,b)][n:mored(c,d)]
+satzd189:=trmored(pd(a,c),pd(b,c),pd(b,d),satzd188d(a,b,c,m),satzd188k(c,d,b,n)):mored(pd(a,c),pd(b,d))
+d@[l:lessd(a,b)][k:lessd(c,d)]
+satzd189a:=lemmad5(pd(b,d),pd(a,c),satzd189(b,a,d,c,lemmad6(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
+d@[m:moreq(a,b)][n:mored(c,d)]
+satzd190a:=orapp(mored(a,b),eq(a,b),mored(pd(a,c),pd(b,d)),m,[t:mored(a,b)]satzd189(t,n),[t:eq(a,b)]satzd188n(t,n)):mored(pd(a,c),pd(b,d))
+d@[m:mored(a,b)][n:moreq(c,d)]
+satzd190b:=eqmored12(pd(c,a),pd(a,c),pd(d,b),pd(b,d),compd(c,a),compd(d,b),satzd190a(c,d,a,b,n,m)):mored(pd(a,c),pd(b,d))
+d@[l:lesseq(a,b)][k:lessd(c,d)]
+satzd190c:=lemmad5(pd(b,d),pd(a,c),satzd190a(b,a,d,c,satzd168b(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
+d@[l:lessd(a,b)][k:lesseq(c,d)]
+satzd190d:=lemmad5(pd(b,d),pd(a,c),satzd190b(b,a,d,c,lemmad6(a,b,l),satzd168b(c,d,k))):lessd(pd(a,c),pd(b,d))
+d@[m:moreq(a,b)][n:moreq(c,d)]
++3d191
+[e:eq(a,b)][f:eq(c,d)]
+t1:=moreqi2(pd(a,c),pd(b,d),eqpd12(a,b,c,d,e,f)):moreq(pd(a,c),pd(b,d))
+e@[o:mored(c,d)]
+t2:=moreqi1(pd(a,c),pd(b,d),satzd190a(m,o)):moreq(pd(a,c),pd(b,d))
+e@t3:=orapp(mored(c,d),eq(c,d),moreq(pd(a,c),pd(b,d)),n,[t:mored(c,d)]t2(t),[t:eq(c,d)]t1(t)):moreq(pd(a,c),pd(b,d))
+n@[o:mored(a,b)]
+t4:=moreqi1(pd(a,c),pd(b,d),satzd190b(o,n)):moreq(pd(a,c),pd(b,d))
+-3d191
+satzd191:=orapp(mored(a,b),eq(a,b),moreq(pd(a,c),pd(b,d)),m,[t:mored(a,b)]t4".3d191"(t),[t:eq(a,b)]t3".3d191"(t)):moreq(pd(a,c),pd(b,d))
+d@[l:lesseq(a,b)][k:lesseq(c,d)]
+satzd191a:=satzd168a(pd(b,d),pd(a,c),satzd191(b,a,d,c,satzd168b(a,b,l),satzd168b(c,d,k))):lesseq(pd(a,c),pd(b,d))
+b@td:=df(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))):dif
++iv4d
+a2@[r:cut]
+t1:=ists1(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(stm(df(a1,a2)),r),ts(a1,r))
+t2:=ists2(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(r,stm(df(a1,a2))),ts(r,a1))
+t3:=ists1(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(std(df(a1,a2)),r),ts(a2,r))
+t4:=ists2(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(r,std(df(a1,a2))),ts(r,a2))
+[s:cut]
+t5:=ispl12(ts(stm(df(a1,a2)),r),ts(a1,r),ts(std(df(a1,a2)),s),ts(a2,s),t1(r),t3(s)):is(pl(ts(stm(df(a1,a2)),r),ts(std(df(a1,a2)),s)),pl(ts(a1,r),ts(a2,s)))
+t6:=ispl12(ts(r,stm(df(a1,a2))),ts(r,a1),ts(s,std(df(a1,a2))),ts(s,a2),t2(r),t4(s)):is(pl(ts(r,stm(df(a1,a2))),ts(s,std(df(a1,a2)))),pl(ts(r,a1),ts(s,a2)))
+t7:=ispl12(ts(std(df(a1,a2)),r),ts(a2,r),ts(stm(df(a1,a2)),s),ts(a1,s),t3(r),t1(s)):is(pl(ts(std(df(a1,a2)),r),ts(stm(df(a1,a2)),s)),pl(ts(a2,r),ts(a1,s)))
+t8:=ispl12(ts(r,std(df(a1,a2))),ts(r,a2),ts(s,stm(df(a1,a2))),ts(s,a1),t4(r),t2(s)):is(pl(ts(r,std(df(a1,a2))),ts(s,stm(df(a1,a2)))),pl(ts(r,a2),ts(s,a1)))
+b2@t9:=tris(cut,pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,stm(df(b1,b2))),ts(a2,std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),t5(a1,a2,stm(df(b1,b2)),std(df(b1,b2))),t6(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)))
+t10:=tris(cut,pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,std(df(b1,b2))),ts(a2,stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)),t5(a1,a2,std(df(b1,b2)),stm(df(b1,b2))),t8(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)))
+-iv4d
+b2@td12:=issmsd(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1)),t9".iv4d",t10".iv4d"):is"e"(dif,td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
+r2@td1:=issmsd(pl(ts(1a,stm(df(r1,r2))),ts(2a,std(df(r1,r2)))),pl(ts(1a,std(df(r1,r2))),ts(2a,stm(df(r1,r2)))),pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1)),t6".iv4d"(r1,r2,1a,2a),t8".iv4d"(r1,r2,1a,2a)):is"e"(dif,td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
+td2:=issmsd(pl(ts(stm(df(r1,r2)),1a),ts(std(df(r1,r2)),2a)),pl(ts(stm(df(r1,r2)),2a),ts(std(df(r1,r2)),1a)),pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a)),t5".iv4d"(r1,r2,1a,2a),t5".iv4d"(r1,r2,2a,1a)):is"e"(dif,td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
+b2@tdeq12a:=refeq1(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
+tdeq12b:=refeq2(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td(df(a1,a2),df(b1,b2)))
+r2@tdeq1a:=refeq1(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
+tdeq1b:=refeq2(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td(a,df(r1,r2)))
+tdeq2a:=refeq1(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
+tdeq2b:=refeq2(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td(df(r1,r2),a))
++4d194
+b@t1:=ispl12(ts(1a,1b),ts(1b,1a),ts(2a,2b),ts(2b,2a),comts(1a,1b),comts(2a,2b)):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1b,1a),ts(2b,2a)))
+t2:=tris(cut,pl(ts(1a,2b),ts(2a,1b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1b,2a),ts(2b,1a)),compl(ts(1a,2b),ts(2a,1b)),ispl12(ts(2a,1b),ts(1b,2a),ts(1a,2b),ts(2b,1a),comts(2a,1b),comts(1a,2b))):is(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,2a),ts(2b,1a)))
+-4d194
+b@satzd194:=eqsmsd(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,1a),ts(2b,2a)),pl(ts(1b,2a),ts(2b,1a)),t1".4d194",t2".4d194"):eq(td(a,b),td(b,a))
+comtd:=satzd194:eq(td(a,b),td(b,a))
+c@[e:eq(a,b)]
++*iv4d
+e@[r:cut]
+t11:=tr3is(cut,pl(ts(1a,r),ts(2b,r)),ts(pl(1a,2b),r),ts(pl(1b,2a),r),pl(ts(1b,r),ts(2a,r)),distpt1(1a,2b,r),ists1(pl(1a,2b),pl(1b,2a),r,e),disttp1(1b,2a,r)):is(pl(ts(1a,r),ts(2b,r)),pl(ts(1b,r),ts(2a,r)))
+e@t12:=tr3is(cut,pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,2c),ts(2a,2c))),pl(pl(ts(1b,1c),ts(2a,1c)),pl(ts(1a,2c),ts(2b,2c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))),4pl24(ts(1a,1c),ts(2a,2c),ts(1b,2c),ts(2b,1c)),ispl12(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,1c),ts(2a,1c)),pl(ts(1b,2c),ts(2a,2c)),pl(ts(1a,2c),ts(2b,2c)),t11(1c),t11(b,a,c,symeq(a,b,e),2c)),4pl24(ts(1b,1c),ts(2a,1c),ts(1a,2c),ts(2b,2c))):is(pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))))
+-iv4d
+e@eqtd1:=eqi12(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)),pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)),t12".iv4d"):eq(td(a,c),td(b,c))
+eqtd2:=tr3eq(td(c,a),td(a,c),td(b,c),td(c,b),comtd(c,a),eqtd1,comtd(b,c)):eq(td(c,a),td(c,b))
+d@[e:eq(a,b)][f:eq(c,d)]
+eqtd12:=treq(td(a,c),td(b,c),td(b,d),eqtd1(a,b,c,e),eqtd2(c,d,b,f)):eq(td(a,c),td(b,d))
+b@[z:zero(a)]
++4d192
+t1:=tris(cut,pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1a,2b),ts(2a,1b)),ispl12(ts(1a,1b),ts(2a,1b),ts(2a,2b),ts(1a,2b),ists1(1a,2a,1b,z),ists1(2a,1a,2b,symis(cut,1a,2a,z))),compl(ts(2a,1b),ts(1a,2b))):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
+-4d192
+satzd192a:=zeroi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t1".4d192"):zero(td(a,b))
+b@[z:zero(b)]
+satzd192b:=eqzero(td(b,a),td(a,b),comtd(b,a),satzd192a(b,a,z)):zero(td(a,b))
+b@[z:zero(a)]
+td01:=satzd192a(z):zero(td(a,b))
+b@[z:zero(b)]
+td02:=satzd192b(z):zero(td(a,b))
+b@satzd197a:=tr3eq(td(m0d(a),b),df(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b))),df(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b))),m0d(td(a,b)),tdeq2a(b,2a,1a),eqsmsd(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b)),compl(ts(2a,1b),ts(1a,2b)),compl(ts(2a,2b),ts(1a,1b))),m0deqb(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))):eq(td(m0d(a),b),m0d(td(a,b)))
+satzd197b:=tr3eq(td(a,m0d(b)),td(m0d(b),a),m0d(td(b,a)),m0d(td(a,b)),comtd(a,m0d(b)),satzd197a(b,a),eqm0d(td(b,a),td(a,b),comtd(b,a))):eq(td(a,m0d(b)),m0d(td(a,b)))
+satzd197c:=treq2(td(m0d(a),b),td(a,m0d(b)),m0d(td(a,b)),satzd197a,satzd197b):eq(td(m0d(a),b),td(a,m0d(b)))
+satzd197d:=symeq(td(m0d(a),b),td(a,m0d(b)),satzd197c):eq(td(a,m0d(b)),td(m0d(a),b))
+satzd197e:=symeq(td(m0d(a),b),m0d(td(a,b)),satzd197a):eq(m0d(td(a,b)),td(m0d(a),b))
+satzd197f:=symeq(td(a,m0d(b)),m0d(td(a,b)),satzd197b):eq(m0d(td(a,b)),td(a,m0d(b)))
+satzd198:=treq(td(m0d(a),m0d(b)),td(a,m0d(m0d(b))),td(a,b),satzd197c(a,m0d(b)),eqtd2(m0d(m0d(b)),b,a,satzd177(b))):eq(td(m0d(a),m0d(b)),td(a,b))
+satzd198a:=symeq(td(m0d(a),m0d(b)),td(a,b),satzd198):eq(td(a,b),td(m0d(a),m0d(b)))
+[p:posd(a)][q:posd(b)]
++*iv4d
+q@[r:cut]
+t13:=tris(cut,pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,pl(mn(1b,2b,q),2b)),ts(r,1b),distpt2(r,mn(1b,2b,q),2b),ists2(pl(mn(1b,2b,q),2b),1b,r,satz140e(1b,2b,q))):is(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b))
+[s:cut]
+t14:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),s),pl(ts(r,1b),s),asspl2(ts(r,mn(1b,2b,q)),ts(r,2b),s),ispl1(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b),s,t13)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s))
+t15:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s),pl(s,ts(r,1b)),t14,compl(ts(r,1b),s)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(s,ts(r,1b)))
+q@t16:=satz135h(pl(ts(1a,2b),ts(2a,2b)),pl(ts(2a,2b),ts(1a,2b)),ts(1a,mn(1b,2b,q)),ts(2a,mn(1b,2b,q)),compl(ts(1a,2b),ts(2a,2b)),satz145a(1a,2a,mn(1b,2b,q),p)):more(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))))
+t17:=ismore12(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))),pl(ts(1a,2b),ts(2a,1b)),t14(1a,ts(2a,2b)),t15(2a,ts(1a,2b)),t16):more(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
+-iv4d
+q@ptdpp:=posdi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t17".iv4d"):posd(td(a,b))
+b@[p:posd(a)][n:negd(b)]
++*iv4d
+n@t18:=eqposd(td(a,m0d(b)),m0d(td(a,b)),satzd197b(a,b),ptdpp(a,m0d(b),p,satzd176c(b,n))):posd(m0d(td(a,b)))
+-iv4d
+n@ntdpn:=satzd176f(td(a,b),t18".iv4d"):negd(td(a,b))
+b@[n:negd(a)][p:posd(b)]
+ntdnp:=eqnegd(td(b,a),td(a,b),comtd(b,a),ntdpn(b,a,p,n)):negd(td(a,b))
+b@[n:negd(a)][o:negd(b)]
+ptdnn:=eqposd(td(m0d(a),m0d(b)),td(a,b),satzd198(a,b),ptdpp(m0d(a),m0d(b),satzd176c(a,n),satzd176c(b,o))):posd(td(a,b))
+b@[n:not(zero(a))][o:not(zero(b))]
++*4d192
+o@[p:posd(a)][q:posd(b)]
+t2:=pnot0d(td(a,b),ptdpp(a,b,p,q)):not(zero(td(a,b)))
+p@[m:negd(b)]
+t3:=nnot0d(td(a,b),ntdpn(a,b,p,m)):not(zero(td(a,b)))
+p@t4:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t2(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t3(t)):not(zero(td(a,b)))
+o@[m:negd(a)][p:posd(b)]
+t5:=nnot0d(td(a,b),ntdnp(a,b,m,p)):not(zero(td(a,b)))
+m@[l:negd(b)]
+t6:=pnot0d(td(a,b),ptdnn(a,b,m,l)):not(zero(td(a,b)))
+m@t7:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t5(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t6(t)):not(zero(td(a,b)))
+-4d192
+o@satzd192d:=rappd(a,not(zero(td(a,b))),[t:posd(a)]t4".4d192"(t),th2"l.imp"(zero(a),not(zero(td(a,b))),n),[t:negd(a)]t7".4d192"(t)):not(zero(td(a,b)))
+b@[z:zero(td(a,b))]
++*4d192
+z@[n:not(zero(a))]
+t8:=et(zero(b),th3"l.imp"(not(zero(b)),not(zero(td(a,b))),weli(zero(td(a,b)),z),[t:not(zero(b))]satzd192d(n,t))):zero(b)
+-4d192
+z@satzd192c:=[t:not(zero(a))]t8".4d192"(t):or(zero(a),zero(b))
++4d193
+b@[p:posd(a)][q:posd(b)]
+t1:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdpp(a,b,p,q))),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+p@[n:negd(b)]
+t2:=treq(absd(td(a,b)),m0d(td(a,b)),td(a,m0d(b)),absnd(td(a,b),ntdpn(a,b,p,n)),satzd197f(a,b)):eq(absd(td(a,b)),td(a,m0d(b)))
+t3:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,m0d(b)),t2,eqtd12(absd(a),a,absd(b),m0d(b),absnnd(a,pnotnd(a,p)),absnd(b,n))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[z:zero(a)]
+t4:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td01(a,b,z)),td01(absd(a),absd(b),satzd166f(a,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[z:zero(b)]
+t5:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td02(a,b,z)),td02(absd(a),absd(b),satzd166f(b,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[n:negd(a)][p:posd(b)]
+t6:=tr3eq(absd(td(a,b)),absd(td(b,a)),td(absd(b),absd(a)),td(absd(a),absd(b)),eqabsd(td(a,b),td(b,a),comtd(a,b)),t3(b,a,p,n),comtd(absd(b),absd(a))):eq(absd(td(a,b)),td(absd(a),absd(b)))
+n@[o:negd(b)]
+t7:=treq(td(absd(a),absd(b)),td(m0d(a),m0d(b)),td(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o)),satzd198(a,b)):eq(td(absd(a),absd(b)),td(a,b))
+t8:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdnn(a,b,n,o))),t7):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[p:posd(a)]
+t9:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t1(p,t),[t:zero(b)]t5(t),[t:negd(b)]t3(p,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
+b@[n:negd(a)]
+t10:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t6(n,t),[t:zero(b)]t5(t),[t:negd(b)]t8(n,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
+-4d193
+b@satzd193:=rappd(a,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(a)]t9".4d193"(t),[t:zero(a)]t4".4d193"(t),[t:negd(a)]t10".4d193"(t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
+satzd103a:=symeq(absd(td(a,b)),td(absd(a),absd(b)),satzd193):eq(td(absd(a),absd(b)),absd(td(a,b)))
+@1df:=pdofrp(1rp):dif
++4d195
+a@t1:=tris(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(ts(1a,pl(1rp,1rp)),pl(ts(2a,1rp),2a)),pl(pl(1a,1a),pl(2a,2a)),asspl1(ts(1a,pl(1rp,1rp)),ts(2a,1rp),2a),ispl12(ts(1a,pl(1rp,1rp)),pl(1a,1a),pl(ts(2a,1rp),2a),pl(2a,2a),a2isapa(1a),ispl1(ts(2a,1rp),2a,2a,satz151(2a)))):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(pl(1a,1a),pl(2a,2a)))
+t2:=tris(cut,pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,ts(1a,1rp)),ts(2a,pl(1rp,1rp))),pl(pl(1a,1a),pl(2a,2a)),asspl2(1a,ts(1a,1rp),ts(2a,pl(1rp,1rp))),ispl12(pl(1a,ts(1a,1rp)),pl(1a,1a),ts(2a,pl(1rp,1rp)),pl(2a,2a),ispl2(ts(1a,1rp),1a,1a,satz151(1a)),a2isapa(2a))):is(pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)))
+t3:=tris2(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)),t1,t2):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))))
+-4d195
+a@satzd195:=treq(td(a,1df),df(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),a,tdeq1a(a,pl(1rp,1rp),1rp),eqi2(a,pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp))),t3".4d195")):eq(td(a,1df),a)
+satzd195a:=symeq(td(a,1df),a,satzd195):eq(a,td(a,1df))
+satzd195b:=treq(td(1df,a),td(a,1df),a,comtd(1df,a),satzd195):eq(td(1df,a),a)
+satzd195c:=symeq(td(1df,a),a,satzd195b):eq(a,td(1df,a))
+b@[p:posd(a)][q:posd(b)]
+satzd196a:=symeq(td(absd(a),absd(b)),td(a,b),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(td(a,b),td(absd(a),absd(b)))
+b@[n:negd(a)][o:negd(b)]
+satzd196b:=treq2(td(a,b),td(absd(a),absd(b)),td(m0d(a),m0d(b)),satzd198a(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o))):eq(td(a,b),td(absd(a),absd(b)))
+b@[p:posd(a)][n:negd(b)]
+satzd196c:=treq1(td(a,b),m0d(td(absd(a),absd(b))),td(absd(a),m0d(absd(b))),eqtd12(absd(a),a,m0d(absd(b)),b,absnnd(a,pnotnd(a,p)),satzd177b(absd(b),b,absnd(b,n))),satzd197b(absd(a),absd(b))):eq(td(a,b),m0d(td(absd(a),absd(b))))
+b@[n:negd(a)][p:posd(b)]
+satzd196d:=tr3eq(td(a,b),td(b,a),m0d(td(absd(b),absd(a))),m0d(td(absd(a),absd(b))),comtd(a,b),satzd196c(b,a,p,n),eqm0d(td(absd(b),absd(a)),td(absd(a),absd(b)),comtd(absd(b),absd(a)))):eq(td(a,b),m0d(td(absd(a),absd(b))))
++4d196
+b@p1p2:=and(posd(a),posd(b)):'prop'
+p1n2:=and(posd(a),negd(b)):'prop'
+n1p2:=and(negd(a),posd(b)):'prop'
+n1n2:=and(negd(a),negd(b)):'prop'
+-4d196
+b@[n:not(zero(a))][o:not(zero(b))][e:eq(td(a,b),td(absd(a),absd(b)))]
++*4d196
+o@t1:=ptdpp(absd(a),absd(b),satzd166e(a,n),satzd166e(b,o)):posd(td(absd(a),absd(b)))
+e@t2:=pnotnd(td(a,b),eqposd(td(absd(a),absd(b)),td(a,b),symeq(td(a,b),td(absd(a),absd(b)),e),t1)):not(negd(td(a,b)))
+[p:posd(a)]
+t3:=th3"l.imp"(negd(b),negd(td(a,b)),t2,[t:negd(b)]ntdpn(a,b,p,t)):not(negd(b))
+t4:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t3,o):posd(b)
+t5:=andi(posd(a),posd(b),p,t4):p1p2
+t6:=ori1(p1p2,n1n2,t5):or(p1p2,n1n2)
+e@[m:negd(a)]
+t7:=th3"l.imp"(posd(b),negd(td(a,b)),t2,[t:posd(b)]ntdnp(a,b,m,t)):not(posd(b))
+t8:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t7):negd(b)
+t9:=andi(negd(a),negd(b),m,t8):n1n2
+t10:=ori2(p1p2,n1n2,t9):or(p1p2,n1n2)
+-4d196
+e@satzd196e:=rappd(a,or(p1p2".4d196",n1n2".4d196"),[t:posd(a)]t6".4d196"(t),th2"l.imp"(zero(a),or(p1p2".4d196",n1n2".4d196"),n),[t:negd(a)]t10".4d196"(t)):or(and(posd(a),posd(b)),and(negd(a),negd(b)))
+o@[e:eq(td(a,b),m0d(td(absd(a),absd(b))))]
++*4d196
+o@t11:=satzd176a(td(absd(a),absd(b)),t1):negd(m0d(td(absd(a),absd(b))))
+e@t12:=nnotpd(td(a,b),eqnegd(m0d(td(absd(a),absd(b))),td(a,b),symeq(td(a,b),m0d(td(absd(a),absd(b))),e),t11)):not(posd(td(a,b)))
+[p:posd(a)]
+t13:=th3"l.imp"(posd(b),posd(td(a,b)),t12,[t:posd(b)]ptdpp(a,b,p,t)):not(posd(b))
+t14:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t13):negd(b)
+t15:=andi(posd(a),negd(b),p,t14):p1n2
+t16:=ori1(p1n2,n1p2,t15):or(p1n2,n1p2)
+e@[m:negd(a)]
+t17:=th3"l.imp"(negd(b),posd(td(a,b)),t12,[t:negd(b)]ptdnn(a,b,m,t)):not(negd(b))
+t18:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t17,o):posd(b)
+t19:=andi(negd(a),posd(b),m,t18):n1p2
+t20:=ori2(p1n2,n1p2,t19):or(p1n2,n1p2)
+-4d196
+e@satzd196f:=rappd(a,or(p1n2".4d196",n1p2".4d196"),[t:posd(a)]t16".4d196"(t),th2"l.imp"(zero(a),or(p1n2".4d196",n1p2".4d196"),n),[t:negd(a)]t20".4d196"(t)):or(and(posd(a),negd(b)),and(negd(a),posd(b)))
++4d199
+@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
+t1:=tris(cut,ts(pl(ts(p,r),ts(q,s)),t),pl(ts(ts(p,r),t),ts(ts(q,s),t)),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),disttp1(ts(p,r),ts(q,s),t),ispl12(ts(ts(p,r),t),ts(p,ts(r,t)),ts(ts(q,s),t),ts(q,ts(s,t)),assts1(p,r,t),assts1(q,s,t))):is(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))))
+t2:=tris(cut,pl(ts(q,ts(s,t)),ts(q,ts(r,u))),pl(ts(q,ts(r,u)),ts(q,ts(s,t))),ts(q,pl(ts(r,u),ts(s,t))),compl(ts(q,ts(s,t)),ts(q,ts(r,u))),distpt2(q,ts(r,u),ts(s,t))):is(pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))))
+t3:=tr3is(cut,pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(pl(ts(p,ts(r,t)),ts(q,ts(s,t))),pl(ts(p,ts(s,u)),ts(q,ts(r,u)))),pl(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u)))),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))),ispl12(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),ts(pl(ts(p,s),ts(q,r)),u),pl(ts(p,ts(s,u)),ts(q,ts(r,u))),t1,t1(p,q,s,r,u,t)),4pl23(ts(p,ts(r,t)),ts(q,ts(s,t)),ts(p,ts(s,u)),ts(q,ts(r,u))),ispl12(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),ts(p,pl(ts(r,t),ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))),distpt2(p,ts(r,t),ts(s,u)),t2)):is(pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))))
+-4d199
+c@satzd199:=tr3eq(td(td(a,b),c),df(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c))),df(pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c))))),td(a,td(b,c)),tdeq2a(c,pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))),eqsmsd(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c)),pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c)))),t3".4d199"(1a,2a,1b,2b,1c,2c),t3".4d199"(1a,2a,1b,2b,2c,1c)),tdeq1b(a,pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)))):eq(td(td(a,b),c),td(a,td(b,c)))
+asstd1:=satzd199:eq(td(td(a,b),c),td(a,td(b,c)))
+asstd2:=symeq(td(td(a,b),c),td(a,td(b,c)),satzd199):eq(td(a,td(b,c)),td(td(a,b),c))
++4d201
+@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
+t1:=tris(cut,pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(p,t)),pl(ts(q,s),ts(q,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))),ispl12(ts(p,pl(r,t)),pl(ts(p,r),ts(p,t)),ts(q,pl(s,u)),pl(ts(q,s),ts(q,u)),disttp2(p,r,t),disttp2(q,s,u)),4pl23(ts(p,r),ts(p,t),ts(q,s),ts(q,u))):is(pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))))
+-4d201
+satzd201:=tr3eq(td(a,pd(b,c)),df(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c)))),df(pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c)))),pd(td(a,b),td(a,c)),tdeq1a(a,pl(1b,1c),pl(2b,2c)),eqsmsd(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c))),pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c))),t1".4d201"(1a,2a,1b,2b,1c,2c),t1".4d201"(1a,2a,2b,1b,2c,1c)),pdeq12b(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)))):eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
+disttpd1:=tr3eq(td(pd(a,b),c),td(c,pd(a,b)),pd(td(c,a),td(c,b)),pd(td(a,c),td(b,c)),comtd(pd(a,b),c),satzd201(c,a,b),eqpd12(td(c,a),td(a,c),td(c,b),td(b,c),comtd(c,a),comtd(c,b))):eq(td(pd(a,b),c),pd(td(a,c),td(b,c)))
+disttpd2:=satzd201:eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
+distptd1:=symeq(td(pd(a,b),c),pd(td(a,c),td(b,c)),disttpd1):eq(pd(td(a,c),td(b,c)),td(pd(a,b),c))
+distptd2:=symeq(td(a,pd(b,c)),pd(td(a,b),td(a,c)),disttpd2):eq(pd(td(a,b),td(a,c)),td(a,pd(b,c)))
+satzd202:=treq(td(a,md(b,c)),pd(td(a,b),td(a,m0d(c))),md(td(a,b),td(a,c)),disttpd2(a,b,m0d(c)),eqpd2(td(a,m0d(c)),m0d(td(a,c)),td(a,b),satzd197b(a,c))):eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
+disttmd1:=treq(td(md(a,b),c),pd(td(a,c),td(m0d(b),c)),md(td(a,c),td(b,c)),disttpd1(a,m0d(b),c),eqpd2(td(m0d(b),c),m0d(td(b,c)),td(a,c),satzd197a(b,c))):eq(td(md(a,b),c),md(td(a,c),td(b,c)))
+disttmd2:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
+distmtd1:=symeq(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1):eq(md(td(a,c),td(b,c)),td(md(a,b),c))
+distmtd2:=symeq(td(a,md(b,c)),md(td(a,b),td(a,c)),disttmd2):eq(md(td(a,b),td(a,c)),td(a,md(b,c)))
+satzd200:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
+[m:mored(a,b)]
++4d203
+t1:=satzd182d(a,b,m):posd(md(a,b))
+-4d203
+[p:posd(c)]
++*4d203
+p@t2:=eqposd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ptdpp(md(a,b),c,t1,p)):posd(md(td(a,c),td(b,c)))
+-4d203
+p@satzd203a:=satzd182a(td(a,c),td(b,c),t2".4d203"):mored(td(a,c),td(b,c))
+m@[z:zero(c)]
+satzd203b:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
+m@[n:negd(c)]
++*4d203
+n@t3:=eqnegd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ntdpn(md(a,b),c,t1,n)):negd(md(td(a,c),td(b,c)))
+-4d203
+n@satzd203c:=satzd182c(td(a,c),td(b,c),t3".4d203"):lessd(td(a,c),td(b,c))
+p@satzd203d:=eqmored12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203a):mored(td(c,a),td(c,b))
+z@satzd203e:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
+n@satzd203f:=eqlessd12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203c):lessd(td(c,a),td(c,b))
+c@[l:lessd(a,b)][p:posd(c)]
+satzd203g:=lemmad5(td(b,c),td(a,c),satzd203a(b,a,c,lemmad6(a,b,l),p)):lessd(td(a,c),td(b,c))
+l@[z:zero(c)]
+satzd203h:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
+l@[n:negd(c)]
+satzd203j:=lemmad6(td(b,c),td(a,c),satzd203c(b,a,c,lemmad6(a,b,l),n)):mored(td(a,c),td(b,c))
+p@satzd203k:=lemmad5(td(c,b),td(c,a),satzd203d(b,a,c,lemmad6(a,b,l),p)):lessd(td(c,a),td(c,b))
+z@satzd203l:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
+n@satzd203m:=lemmad6(td(c,b),td(c,a),satzd203f(b,a,c,lemmad6(a,b,l),n)):mored(td(c,a),td(c,b))
++*iv4d
+@[p:cut][q:cut]
+t19:=tris(cut,ts(q,pl(p,1rp)),pl(ts(q,p),ts(q,1rp)),pl(ts(q,p),q),disttp2(q,p,1rp),ispl2(ts(q,1rp),q,ts(q,p),satz151(q))):is(ts(q,pl(p,1rp)),pl(ts(q,p),q))
+[r:cut]
+t20:=tris(cut,pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(pl(ts(q,p),q),r),pl(ts(q,p),pl(q,r)),ispl12(ts(q,pl(p,1rp)),pl(ts(q,p),q),ts(r,1rp),r,t19,satz151(r)),asspl1(ts(q,p),q,r)):is(pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)))
+t21:=tr3is(cut,pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)),pl(ts(q,p),pl(r,q)),compl(ts(r,1rp),ts(q,pl(p,1rp))),t20,ispl2(pl(q,r),pl(r,q),ts(q,p),compl(q,r))):is(pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,p),pl(r,q)))
+a@[p:posd(a)]
+arp:=rpofpd(a,p):cut
+arpi:=ov(1rp,arp):cut
+ai:=pdofrp(arpi):dif
+t22:=tr3eq(td(a,ai),df(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp)))),df(pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a))),df(ts(1a,arpi),ts(2a,arpi)),tdeq1a(a,pl(arpi,1rp),1rp),eqsmsd(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp))),pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a)),t20(arpi,1a,2a),t21(arpi,2a,1a)),lemmad2(ts(1a,arpi),ts(2a,arpi),pl(1a,2a))):eq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)))
+t23:=tr3is(cut,ts(1a,arpi),ts(pl(2a,arp),arpi),pl(ts(2a,arpi),ts(arp,arpi)),pl(ts(2a,arpi),1rp),ists1(1a,pl(2a,arp),arpi,satz140d(1a,2a,p)),disttp1(2a,arp,arpi),ispl2(ts(arp,arpi),1rp,ts(2a,arpi),satz153c(1rp,arp))):is(ts(1a,arpi),pl(ts(2a,arpi),1rp))
+t24:=tr3is(cut,pl(ts(1a,arpi),1rp),pl(pl(ts(2a,arpi),1rp),1rp),pl(ts(2a,arpi),pl(1rp,1rp)),pl(pl(1rp,1rp),ts(2a,arpi)),ispl1(ts(1a,arpi),pl(ts(2a,arpi),1rp),1rp,t23),asspl1(ts(2a,arpi),1rp,1rp),compl(ts(2a,arpi),pl(1rp,1rp))):is(pl(ts(1a,arpi),1rp),pl(pl(1rp,1rp),ts(2a,arpi)))
+t25:=eqi12(ts(1a,arpi),ts(2a,arpi),pl(1rp,1rp),1rp,t24):eq(df(ts(1a,arpi),ts(2a,arpi)),1df)
+t26:=treq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)),1df,t22,t25):eq(td(a,ai),1df)
+t27:=somei(dif,[x:dif]eq(td(a,x),1df),ai,t26):some"l"(dif,[x:dif]eq(td(a,x),1df))
+a@[n:negd(a)]
+t28:=satzd176c(a,n):posd(m0d(a))
+[h:dif][e:eq(td(m0d(a),h),1df)]
+t29:=treq(td(a,m0d(h)),td(m0d(a),h),1df,satzd197d(a,h),e):eq(td(a,m0d(h)),1df)
+t30:=somei(dif,[x:dif]eq(td(a,x),1df),m0d(h),t29):some"l"(dif,[x:dif]eq(td(a,x),1df))
+n@t31:=someapp(dif,[x:dif]eq(td(m0d(a),x),1df),t27(m0d(a),t28),some"l"(dif,[x:dif]eq(td(a,x),1df)),[x:dif][t:eq(td(m0d(a),x),1df)]t30(x,t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
+-iv4d
+a@[n:not(zero(a))]
+lemmad7:=rappd(a,some"l"(dif,[x:dif]eq(td(a,x),1df)),[t:posd(a)]t27".iv4d"(t),th2"l.imp"(zero(a),some"l"(dif,[x:dif]eq(td(a,x),1df)),n),[t:negd(a)]t31".iv4d"(t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
+b@[n:not(zero(b))][h:dif][k:dif][e:eq(td(b,h),a)][f:eq(td(b,k),a)]
++4d204
+t1:=treq2(td(b,h),td(b,k),a,e,f):eq(td(b,h),td(b,k))
+t2:=eqzero(md(td(b,h),td(b,k)),td(b,md(h,k)),distmtd2(b,h,k),satzd182e(td(b,h),td(b,k),t1)):zero(td(b,md(h,k)))
+t3:=ore2(zero(b),zero(md(h,k)),satzd192c(b,md(h,k),t2),n):zero(md(h,k))
+-4d204
+satzd204b:=satzd182b(h,k,t3".4d204"):eq(h,k)
++*4d204
+n@[h:dif][e:eq(td(b,h),1df)]
+t4:=tr3eq(td(b,td(h,a)),td(td(b,h),a),td(1df,a),a,asstd2(b,h,a),eqtd1(td(b,h),1df,a,e),satzd195b(a)):eq(td(b,td(h,a)),a)
+t5:=somei(dif,[x:dif]eq(td(b,x),a),td(h,a),t4):some"l"(dif,[x:dif]eq(td(b,x),a))
+-4d204
+n@satzd204a:=someapp(dif,[x:dif]eq(td(b,x),1df),lemmad7(b,n),some"l"(dif,[x:dif]eq(td(b,x),a)),[x:dif][t:eq(td(b,x),1df)]t5".4d204"(x,t)):some"l"(dif,[x:dif]eq(td(b,x),a))
+@[r:cut][s:cut][m:more(r,s)]
++iv5d
+t1:=ismore12(pl(r,pl(1rp,1rp)),pl(pl(r,1rp),1rp),pl(s,pl(1rp,1rp)),pl(pl(s,1rp),1rp),asspl2(r,1rp,1rp),asspl2(s,1rp,1rp),satz134(r,s,pl(1rp,1rp),m)):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
+-iv5d
+morerpepd:=moredi12(pl(r,1rp),1rp,pl(s,1rp),1rp,t1".iv5d"):mored(pdofrp(r),pdofrp(s))
+s@[m:mored(pdofrp(r),pdofrp(s))]
++*iv5d
+m@t2:=morede12(pl(r,1rp),1rp,pl(s,1rp),1rp,m):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
+-iv5d
+m@morerpipd:=satz136a(r,s,pl(1rp,1rp),ismore12(pl(pl(r,1rp),1rp),pl(r,pl(1rp,1rp)),pl(pl(s,1rp),1rp),pl(s,pl(1rp,1rp)),asspl1(r,1rp,1rp),asspl1(s,1rp,1rp),t2".iv5d")):more(r,s)
+s@[l:less(r,s)]
+lessrpepd:=lemmad5(pdofrp(s),pdofrp(r),morerpepd(s,r,satz122(r,s,l))):lessd(pdofrp(r),pdofrp(s))
+s@[l:lessd(pdofrp(r),pdofrp(s))]
+lessrpipd:=satz121(s,r,morerpipd(s,r,lemmad6(pdofrp(r),pdofrp(s),l))):less(r,s)
++*iv5d
+@i:=1rp:cut
+2:=pl(i,i):cut
+r@rp1:=pl(r,i):cut
+s@sp1:=pl(s,i):cut
+rps:=pl(r,s):cut
+rs:=ts(r,s):cut
+t3:=tris(cut,pl(pl(rp1,sp1),i),pl(pl(rps,2),i),pl(pl(rps,i),2),ispl1(pl(rp1,sp1),pl(rps,2),i,4pl23(r,i,s,i)),3pl23(rps,2,i)):is(pl(pl(rp1,sp1),i),pl(pl(rps,i),2))
+t4:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(rp1,sp1),2),pdofrp(rps),pdeq12a(rp1,i,sp1,i),eqi12(pl(rp1,sp1),2,pl(rps,i),i,t3)):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(rps))
+-iv5d
+s@lemmad8:=t4".iv5d":eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
++*iv5d
+s@t5:=tris(cut,ts(r,sp1),pl(rs,ts(r,i)),pl(rs,r),disttp2(r,s,i),ispl2(ts(r,i),r,rs,satz151(r))):is(ts(r,sp1),pl(rs,r))
+t6:=tr4is(cut,ts(rp1,sp1),pl(ts(r,sp1),ts(i,sp1)),pl(pl(rs,r),sp1),pl(pl(pl(rs,r),s),i),pl(pl(rs,rps),i),disttp1(r,i,sp1),ispl12(ts(r,sp1),pl(rs,r),ts(i,sp1),sp1,t5,satz151b(sp1)),asspl2(pl(rs,r),s,i),ispl1(pl(pl(rs,r),s),pl(rs,rps),i,asspl1(rs,r,s))):is(ts(rp1,sp1),pl(pl(rs,rps),i))
+t7:=tr3is(cut,pl(ts(rp1,sp1),ts(i,i)),pl(pl(pl(rs,rps),i),i),pl(pl(rs,rps),2),pl(rs,pl(rps,2)),ispl12(ts(rp1,sp1),pl(pl(rs,rps),i),ts(i,i),i,t6,satz151(i)),asspl1(pl(rs,rps),i,i),asspl1(rs,rps,2)):is(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)))
+t8:=tris(cut,pl(ts(rp1,i),ts(i,sp1)),pl(rp1,sp1),pl(rps,2),ispl12(ts(rp1,i),rp1,ts(i,sp1),sp1,satz151(rp1),satz151b(sp1)),4pl23(r,i,s,i)):is(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2))
+t9:=tris(cut,pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,i),pl(rps,2)),pl(pl(rs,pl(rps,2)),i),ispl2(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2),pl(rs,i),t8),3pl23(rs,i,pl(rps,2))):is(pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i))
+t10:=tris2(cut,pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i),ispl1(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)),i,t7),t9):is(pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))))
+t11:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1))),pdofrp(rs),tdeq12a(rp1,i,sp1,i),eqi12(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1)),pl(rs,i),i,t10)):eq(td(pdofrp(r),pdofrp(s)),pdofrp(rs))
+-iv5d
+s@lemmad9:=t11".iv5d":eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
+@[r:cut][s0:set(cut)]
+in:=esti(cut,r,s0):'prop'
+@[s0:set(cut)][t0:set(cut)][p0:all([x:cut]or(in(x,s0),in(x,t0)))][p1a:nonempty(cut,s0)][p1b:nonempty(cut,t0)][p2:all([x:cut][t:in(x,s0)]all([y:cut][u:in(y,t0)]less(x,y)))]
++5p205
+t0@[r:cut]
+prop1:=all([x:cut][t:less(x,r)]in(x,s0)):'prop'
+prop2:=all([x:cut][t:more(x,r)]in(x,t0)):'prop'
+prop3:=and(prop1,prop2):'prop'
+p2@[r1:cut][r2:cut][pr1:prop3(r1)][pr2:prop3(r2)]
+t1:=ande2(prop1(r1),prop2(r1),pr1):prop2(r1)
+t2:=ande1(prop1(r2),prop2(r2),pr2):prop1(r2)
+[l:less(r1,r2)][x0:rat]
+rx:=rpofrt(x0):cut
+[l1:less(r1,rx)][l2:less(rx,r2)]
+t3:=<l2><rx>t2:in(rx,s0)
+t4:=<satz122(r1,rx,l1)><rx>t1:in(rx,t0)
+t5:=<refis(cut,rx)>ec3e31(is(rx,rx),more(rx,rx),less(rx,rx),satz123b(rx,rx),<t4><rx><t3><rx>p2):con
+l@t6:=satz159app(r1,r2,l,con,[x:rat][t:less(r1,rpofrt(x))][u:less(rpofrt(x),r2)]t5(x,t,u)):con
+pr2@t7:=[t:less(r1,r2)]t6(t):not(less(r1,r2))
+t8:=[t:more(r1,r2)]t6(r2,r1,pr2,pr1,satz121(r1,r2,t)):not(more(r1,r2))
+t9:=or3e1(is(r1,r2),more(r1,r2),less(r1,r2),satz123a(r1,r2),t8,t7):is(r1,r2)
+p2@t10:=[x:cut][y:cut][t:prop3(x)][u:prop3(y)]t9(x,y,t,u):amone(cut,[x:cut]prop3(x))
+[x0:rat]
+schnittprop:=some([y:cut]and(in(y,s0),lrt(y,x0))):'prop'
+p2@schnittset:=setof(rat,[x:rat]schnittprop(x)):set(rat)
+[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)]
+t11:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
+t12:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t11):schnittprop(x0)
+t13:=estii(rat,[x:rat]schnittprop(x),x0,t12):in"rt"(x0,schnittset)
+r@[i:in(r,t0)][x0:rat][ux:urt(r,x0)][s:cut][j:in(s,s0)]
+t14:=satz122(s,r,<i><r><j><s>p2):more(r,s)
+t15:=satz158b(r,x0,ux):moreis(rpofrt(x0),r)
+t16:=moreisi1(rpofrt(x0),s,satz127c(rpofrt(x0),r,s,t15,t14)):moreis(rpofrt(x0),s)
+t17:=satz158d(s,x0,t16):urt(s,x0)
+s@t18:=weli(ec(in(s,s0),lrt(s,x0)),[t:in(s,s0)]t17(t)):not(and(in(s,s0),lrt(s,x0)))
+ux@t19:=th5"l.some"(cut,[y:cut]and(in(y,s0),lrt(y,x0)),[y:cut]t18(y)):not(schnittprop(x0))
+t20:=th3"l.imp"(in"rt"(x0,schnittset),schnittprop(x0),t19,[t:in"rt"(x0,schnittset)]estie(rat,[x:rat]schnittprop(x),x0,t)):not(in"rt"(x0,schnittset))
+p2@[x0:rat][i:in"rt"(x0,schnittset)][y0:rat][l:less"rt"(y0,x0)]
+i@t21:=estie(rat,[x:rat]schnittprop(x),x0,i):schnittprop(x0)
+l@[r:cut][a:and(in(r,s0),lrt(r,x0))]
+t22:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
+t23:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
+t24:=satz120(r,x0,t23,y0,l):lrt(r,y0)
+t25:=andi(in(r,s0),lrt(r,y0),t22,t24):and(in(r,s0),lrt(r,y0))
+t26:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t25):schnittprop(y0)
+l@t27:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,schnittprop(y0),[y:cut][r:and(in(y,s0),lrt(y,x0))]t26(y,r)):schnittprop(y0)
+t28:=estii(rat,[x:rat]schnittprop(x),y0,t27):in"rt"(y0,schnittset)
+i@[r:cut][a:and(in(r,s0),lrt(r,x0))]
+t29:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
+t30:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
+[y0:rat][ly:lrt(r,y0)][l:less"rt"(x0,y0)]
+t31:=andi(in(r,s0),lrt(r,y0),t29,ly):and(in(r,s0),lrt(r,y0))
+t32:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t31):schnittprop(y0)
+t33:=estii(rat,[x:rat]schnittprop(x),y0,t32):in"rt"(y0,schnittset)
+t34:=satz83(x0,y0,l):more"rt"(y0,x0)
+t35:=andi(in"rt"(y0,schnittset),more"rt"(y0,x0),t33,t34):and(in"rt"(y0,schnittset),more"rt"(y0,x0))
+t36:=somei(rat,[y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)),y0,t35):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
+a@t37:=cutapp3(r,x0,t30,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:rat][t:lrt(r,y)][u:less"rt"(x0,y)]t36(y,t,u)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
+i@t38:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:cut][t:and(in(y,s0),lrt(y,x0))]t37(y,t)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
+p2@[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)][s:cut][j:in(s,t0)][y0:rat][uy:urt(s,y0)]
+t39:=cut2(schnittset,x0,t13(r,i,x0,lx),y0,t20(s,j,y0,uy),[x:rat][t:in"rt"(x,schnittset)][y:rat][u:less"rt"(y,x)]t28(x,t,y,u),[x:rat][t:in"rt"(x,schnittset)]t38(x,t)):cutprop(schnittset)
+j@t40:=cutapp1b(s,cutprop(schnittset),[x:rat][t:urt(s,x)]t39(x,t)):cutprop(schnittset)
+lx@t41:=nonemptyapp(cut,t0,p1b,cutprop(schnittset),[y:cut][t:in(y,t0)]t40(y,t)):cutprop(schnittset)
+i@t42:=cutapp1a(r,cutprop(schnittset),[x:rat][t:lrt(r,x)]t41(x,t)):cutprop(schnittset)
+p2@t43:=nonemptyapp(cut,s0,p1a,cutprop(schnittset),[y:cut][t:in(y,s0)]t42(y,t)):cutprop(schnittset)
+snt:=cutof(schnittset,t43):cut
+[r:cut][l:less(r,snt)][x0:rat][ux:urt(r,x0)][lx:lrt(snt,x0)]
+t44:=ini(schnittset,t43,x0,lx):in"rt"(x0,schnittset)
+t45:=estie(rat,[x:rat]schnittprop(x),x0,t44):schnittprop(x0)
+[s:cut][a:and(in(s,s0),lrt(s,x0))]
+t46:=ande1(in(s,s0),lrt(s,x0),a):in(s,s0)
+t47:=ande2(in(s,s0),lrt(s,x0),a):lrt(s,x0)
+t48:=andi(urt(r,x0),lrt(s,x0),ux,t47):and(urt(r,x0),lrt(s,x0))
+t49:=somei(rat,[x:rat]and(urt(r,x),lrt(s,x)),x0,t48):less(r,s)
+t50:=ec3e23(is(s,r),more(s,r),less(s,r),satz123b(s,r),satz122(r,s,t49)):not(less(s,r))
+t51:=th3"l.imp"(in(r,t0),less(s,r),t50,<r><t46><s>p2):not(in(r,t0))
+t52:=ore1(in(r,s0),in(r,t0),<r>p0,t51):in(r,s0)
+lx@t53:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t45,in(r,s0),[y:cut][t:and(in(y,s0),lrt(y,x0))]t52(y,t)):in(r,s0)
+l@t54:=lessapp(r,snt,l,in(r,s0),[x:rat][t:urt(r,x)][u:lrt(snt,x)]t53(x,t,u)):in(r,s0)
+r@[m:more(r,snt)][x0:rat][lx:lrt(r,x0)][ux:urt(snt,x0)][i:in(r,s0)]
+t55:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
+t56:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t55):schnittprop(x0)
+t57:=estii(rat,[x:rat]schnittprop(x),x0,t56):in"rt"(x0,schnittset)
+t58:=ine(schnittset,t43,x0,t57):lrt(snt,x0)
+ux@t59:=th3"l.imp"(in(r,s0),lrt(snt,x0),ux,[t:in(r,s0)]t58(t)):not(in(r,s0))
+t60:=ore2(in(r,s0),in(r,t0),<r>p0,t59):in(r,t0)
+m@t61:=moreapp(r,snt,m,in(r,t0),[x:rat][t:lrt(r,x)][u:urt(snt,x)]t60(x,t,u)):in(r,t0)
+p2@t62:=andi(prop1(snt),prop2(snt),[x:cut][t:less(x,snt)]t54(x,t),[x:cut][t:more(x,snt)]t61(x,t)):prop3(snt)
+t63:=somei(cut,[x:cut]prop3(x),snt,t62):some([x:cut]prop3(x))
+-5p205
+satzp205:=onei(cut,[x:cut]prop3".5p205"(x),t10".5p205",t63".5p205"):one([x:cut]and(all([y:cut][t:less(y,x)]in(y,s0)),all([y:cut][t:more(y,x)]in(y,t0))))
+schnitt:=ind(cut,[x:cut]prop3".5p205"(x),satzp205):cut
+satzp205a:=ande1(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:less(x,schnitt)]in(x,s0))
+satzp205b:=ande2(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:more(x,schnitt)]in(x,t0))
+@[r:cut][s:cut]
++ivad
+@i:=1rp:cut
+r@r1:=pl(r,i):cut
+s@s1:=pl(s,i):cut
+rps:=pl(r,s):cut
+@2:=pl(i,i):cut
+s@t1:=pdeq12a(r1,i,s1,i):eq(pd(pdofrp(r),pdofrp(s)),df(pl(r1,s1),2))
+t2:=tris(cut,pl(r1,s1),pl(rps,2),pl(pl(rps,i),i),4pl23(r,i,s,i),asspl2(rps,i,i)):is(pl(r1,s1),pl(pl(rps,i),i))
+t3:=ispl1(pl(r1,s1),pl(pl(rps,i),i),i,t2):is(pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i))
+t4:=tris(cut,pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i),pl(pl(rps,i),2),t3,asspl1(pl(rps,i),i,i)):is(pl(pl(r1,s1),i),pl(pl(rps,i),2))
+t5:=eqi12(pl(r1,s1),2,pl(rps,i),i,t4):eq(df(pl(r1,s1),2),pdofrp(rps))
+-ivad
+lemmaivad1:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(pl(r,1rp),pl(s,1rp)),pl(1rp,1rp)),pdofrp(pl(r,s)),t1".ivad",t5".ivad"):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
++*ivad
+s@rs:=ts(r,s):cut
+t6:=tdeq12a(r1,i,s1,i):eq(td(pdofrp(r),pdofrp(s)),df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))))
+t7:=tris(cut,ts(r1,s),pl(rs,ts(i,s)),pl(rs,s),disttp1(r,i,s),ispl2(ts(i,s),s,rs,satz151b(s))):is(ts(r1,s),pl(rs,s))
+t8:=tr3is(cut,ts(r1,s1),pl(ts(r1,s),ts(r1,i)),pl(pl(rs,s),r1),pl(pl(rs,i),rps),disttp2(r1,s,i),ispl12(ts(r1,s),pl(rs,s),ts(r1,i),r1,t7,satz151(r1)),4pl24(rs,s,r,i)):is(ts(r1,s1),pl(pl(rs,i),rps))
+t9:=tris(cut,pl(ts(r1,s1),ts(i,i)),pl(pl(pl(rs,i),rps),i),pl(pl(rs,i),pl(rps,i)),ispl12(ts(r1,s1),pl(pl(rs,i),rps),ts(i,i),i,t8,satz151(i)),asspl1(pl(rs,i),rps,i)):is(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)))
+t10:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(pl(rs,i),pl(rps,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),ispl1(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)),i,t9),asspl1(pl(rs,i),pl(rps,i),i)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)))
+t11:=tr3is(cut,pl(pl(rps,i),i),pl(rps,2),pl(r1,s1),pl(ts(r1,i),ts(i,s1)),asspl1(rps,i,i),4pl23(r,s,i,i),ispl12(r1,ts(r1,i),s1,ts(i,s1),satz151a(r1),satz151c(s1))):is(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)))
+t12:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))),t10,ispl2(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)),pl(rs,i),t11)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))))
+t13:=eqi12(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1)),pl(rs,i),i,t12):eq(df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))),pdofrp(rs))
+-ivad
+s@lemmaivad2:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(pl(r,1rp),pl(s,1rp)),ts(1rp,1rp)),pl(ts(pl(r,1rp),1rp),ts(1rp,pl(s,1rp)))),pdofrp(ts(r,s)),t6".ivad",t13".ivad"):eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
+[m:mored(pdofrp(r),pdofrp(s))]
++*ivad
+m@t14:=morede12(r1,i,s1,i,m):more(pl(r1,i),pl(s1,i))
+t15:=satz136a(r1,s1,i,t14):more(r1,s1)
+-ivad
+m@lemmaivad3:=satz136a(r,s,1rp,t15".ivad"):more(r,s)
+@[c:dif][a:dif][b:dif][n:not(negd(a))][o:not(negd(b))][e:eq(td(a,a),c)][f:eq(td(b,b),c)]
++d161
+t1:=treq2(td(a,a),td(b,b),c,e,f):eq(td(a,a),td(b,b))
+t2:=treq(pd(md(td(a,a),td(a,b)),td(b,a)),pd(md(td(a,a),td(a,b)),td(a,b)),td(a,a),eqpd2(td(b,a),td(a,b),md(td(a,a),td(a,b)),comtd(b,a)),pdmd(td(a,a),td(a,b))):eq(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a))
+t3:=tr4eq(td(pd(a,b),md(a,b)),pd(td(a,md(a,b)),td(b,md(a,b))),pd(md(td(a,a),td(a,b)),md(td(b,a),td(b,b))),md(pd(md(td(a,a),td(a,b)),td(b,a)),td(b,b)),md(td(a,a),td(b,b)),disttpd1(a,b,md(a,b)),eqpd12(td(a,md(a,b)),md(td(a,a),td(a,b)),td(b,md(a,b)),md(td(b,a),td(b,b)),disttmd2(a,a,b),disttmd2(b,a,b)),asspd2(md(td(a,a),td(a,b)),td(b,a),m0d(td(b,b))),eqmd1(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a),td(b,b),t2)):eq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)))
+t4:=eqzero(md(td(a,a),td(b,b)),td(pd(a,b),md(a,b)),symeq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)),t3),satzd182e(td(a,a),td(b,b),t1)):zero(td(pd(a,b),md(a,b)))
+t5:=satzd192c(pd(a,b),md(a,b),t4):or(zero(pd(a,b)),zero(md(a,b)))
+[z:zero(a)]
+t6:=eqzero(td(a,a),td(b,b),t1,td01(a,a,z)):zero(td(b,b))
+t7:=th1"l.imp"(zero(b),zero(b),refimp(zero(b)),satzd192c(b,b,t6)):zero(b)
+t8:=zeroeq(a,b,z,t7):eq(a,b)
+f@[p:not(zero(a))]
+t9:=or3e2(zero(a),posd(a),negd(a),axrdo(a),n,p):posd(a)
+t10:=th3"l.imp"(zero(b),zero(a),p,[t:zero(b)]t7(b,a,o,n,f,e,t)):not(zero(b))
+t11:=t9(b,a,o,n,f,e,t10):posd(b)
+t12:=pnot0d(pd(a,b),ppd(a,b,t9,t11)):not(zero(pd(a,b)))
+t13:=ore2(zero(pd(a,b)),zero(md(a,b)),t5,t12):zero(md(a,b))
+t14:=satzd182b(a,b,t13):eq(a,b)
+-d161
+satzd161b:=th1"l.imp"(zero(a),eq(a,b),[t:zero(a)]t8".d161"(t),[t:not(zero(a))]t14".d161"(t)):eq(a,b)
+c@[n:not(negd(c))]
++*d161
+n@[z:zero(c)]
+t15:=zeroeq(td(c,c),c,td01(c,c,z),z):eq(td(c,c),c)
+t16:=andi(not(negd(c)),eq(td(c,c),c),n,t15):and(not(negd(c)),eq(td(c,c),c))
+t17:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),c,t16):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
+n@[o:not(zero(c))]
+t18:=or3e2(zero(c),posd(c),negd(c),axrdo(c),n,o):posd(c)
+crp:=rpofpd(c,t18):cut
+srp:=sqrt(crp):cut
+s:=pdofrp(srp):dif
+t19:=tr3eq(td(s,s),pdofrp(ts(srp,srp)),pdofrp(crp),c,lemmaivad2(srp,srp),isrpepd(ts(srp,srp),crp,thsqrt1(crp)),eqpdrp2(c,t18)):eq(td(s,s),c)
+t20:=andi(not(negd(s)),eq(td(s,s),c),pnotnd(s,posdirp(srp)),t19):and(not(negd(s)),eq(td(s,s),c))
+t21:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),s,t20):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
+-d161
+n@satzd161a:=th1"l.imp"(zero(c),some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c))),[t:zero(c)]t17".d161"(t),[t:not(zero(c))]t21".d161"(t)):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
+@[a:dif][i:intd(a)]
++intd
+[z:zero(a)]
+t1:=ori1(zero(absd(a)),natd(absd(absd(a))),satzd166f(a,z)):intd(absd(a))
+i@[n:natd(absd(a))]
+t2:=natintd(absd(a),n):intd(absd(a))
+-intd
+intabsd:=orapp(zero(a),natd(absd(a)),intd(absd(a)),i,[t:zero(a)]t1".intd"(t),[t:natd(absd(a))]t2".intd"(t)):intd(absd(a))
++*intd
+n@t4:=eqnatd(absd(a),absd(m0d(a)),satzd178a(a),n):natd(absd(m0d(a)))
+-intd
+i@intm0d:=th9"l.or"(zero(a),natd(absd(a)),zero(m0d(a)),natd(absd(m0d(a))),i,[t:zero(a)]satzd176b(a,t),[t:natd(absd(a))]t4".intd"(t)):intd(m0d(a))
+a@[b:dif][i:intd(a)][j:intd(b)]
++*intd
+j@[z:zero(a)]
+t5:=symeq(pd(a,b),b,pd01(a,b,z)):eq(b,pd(a,b))
+t6:=eqintd(b,pd(a,b),t5,j):intd(pd(a,b))
+j@[z:zero(b)]
+t7:=symeq(pd(a,b),a,pd02(a,b,z)):eq(a,pd(a,b))
+t8:=eqintd(a,pd(a,b),t7,i):intd(pd(a,b))
+a@[i:intd(a)][p:posd(a)]
+t9:=<p>ande2(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),posintnatd(a,p,i)):natrp(rpofpd(a,p))
+j@[pp:posd(pd(a,b))]
+apb1:=rpofpd(pd(a,b),pp):cut
+[p:posd(a)]
+a1:=rpofpd(a,p):cut
+[q:posd(b)]
+b1:=rpofpd(b,q):cut
+t10:=natpl(a1,t9(a,i,p),b1,t9(b,j,q)):natrp(pl(a1,b1))
+t11:=eqpd12(a,pdofrp(a1),b,pdofrp(b1),eqpdrp1(a,p),eqpdrp1(b,q)):eq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)))
+t12:=treq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)),pdofrp(pl(a1,b1)),t11,lemmaivad1(a1,b1)):eq(pd(a,b),pdofrp(pl(a1,b1)))
+t13:=tris(cut,apb1,rpofpd(pdofrp(pl(a1,b1)),posdirp(pl(a1,b1))),pl(a1,b1),eqpderp(pd(a,b),pp,pdofrp(pl(a1,b1)),posdirp(pl(a1,b1)),t12),isrppd2(pl(a1,b1))):is(apb1,pl(a1,b1))
+t14:=isp1(cut,[t:cut]natrp(t),pl(a1,b1),apb1,t10,t13):natrp(apb1)
+t15:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t14(t,p,q)):natd(pd(a,b))
+t16:=natintd(pd(a,b),t15):intd(pd(a,b))
+p@[n:negd(b)]
+t17:=satzd176c(b,n):posd(m0d(b))
+b2:=rpofpd(m0d(b),t17):cut
+t18:=eqpd2(b,m0d(m0d(b)),a,satzd177a(b)):eq(pd(a,b),md(a,m0d(b)))
+t19:=eqposd(pd(a,b),md(a,m0d(b)),t18,pp):posd(md(a,m0d(b)))
+t20:=satzd182a(a,m0d(b),t19):mored(a,m0d(b))
+t21:=eqmored12(a,pdofrp(a1),m0d(b),pdofrp(b2),eqpdrp1(a,p),eqpdrp1(m0d(b),t17),t20):mored(pdofrp(a1),pdofrp(b2))
+t22:=lemmaivad3(a1,b2,t21):more(a1,b2)
+t23:=natmn(a1,t9(a,i,p),b2,t9(m0d(b),intm0d(b,j),t17),t22):natrp(mn(a1,b2,t22))
+t24:=eqpd12(m0d(b),pdofrp(b2),pd(a,b),pdofrp(apb1),eqpdrp1(m0d(b),t17),eqpdrp1(pd(a,b),pp)):eq(pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)))
+t25:=tr4eq(a,md(pd(a,b),b),pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)),pdofrp(pl(b2,apb1)),symeq(md(pd(a,b),b),a,mdpd(a,b)),compd(pd(a,b),m0d(b)),t24,lemmaivad1(b2,apb1)):eq(a,pdofrp(pl(b2,apb1)))
+t26:=tris2(cut,pl(b2,apb1),a1,rpofpd(pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1))),isrppd1(pl(b2,apb1)),eqpderp(a,p,pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1)),t25)):is(pl(b2,apb1),a1)
+t27:=satz140g(a1,b2,apb1,t22,t26):is(apb1,mn(a1,b2,t22))
+t28:=isp1(cut,[t:cut]natrp(t),mn(a1,b2,t22),apb1,t23,t27):natrp(apb1)
+t29:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t28(t,p,n)):natd(pd(a,b))
+t30:=natintd(pd(a,b),t29):intd(pd(a,b))
+p@t31:=rappd(b,intd(pd(a,b)),[t:posd(b)]t16(t),[t:zero(b)]t8(t),[t:negd(b)]t30(t)):intd(pd(a,b))
+pp@[n:negd(a)]
+t31a:=th3"l.imp"(negd(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:negd(b)]npd(a,b,n,t)):not(negd(b))
+t32:=th3"l.imp"(zero(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:zero(b)]eqnegd(a,pd(a,b),symeq(pd(a,b),a,pd02(a,b,t)),n)):not(zero(b))
+t33:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t31a,t32):posd(b)
+t34:=eqposd(pd(a,b),pd(b,a),compd(a,b),pp):posd(pd(b,a))
+t35:=t30(b,a,j,i,t34,t33,n):intd(pd(b,a))
+t36:=eqintd(pd(b,a),pd(a,b),compd(b,a),t35):intd(pd(a,b))
+pp@t37:=rappd(a,intd(pd(a,b)),[t:posd(a)]t31(t),[t:zero(a)]t6(t),[t:negd(a)]t36(t)):intd(pd(a,b))
+j@[0p:zero(pd(a,b))]
+t38:=intdi0(pd(a,b),0p):intd(pd(a,b))
+j@[np:negd(pd(a,b))]
+t39:=satzd176c(pd(a,b),np):posd(m0d(pd(a,b)))
+t40:=eqposd(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180(a,b),t39):posd(pd(m0d(a),m0d(b)))
+t41:=t37(m0d(a),m0d(b),intm0d(a,i),intm0d(b,j),t40):intd(pd(m0d(a),m0d(b)))
+t42:=eqintd(pd(m0d(a),m0d(b)),m0d(pd(a,b)),satzd180a(a,b),t41):intd(m0d(pd(a,b)))
+t43:=intm0d(m0d(pd(a,b)),t42):intd(m0d(m0d(pd(a,b))))
+t44:=eqintd(m0d(m0d(pd(a,b))),pd(a,b),satzd177(pd(a,b)),t43):intd(pd(a,b))
+-intd
+j@intpd:=rappd(pd(a,b),intd(pd(a,b)),[t:posd(pd(a,b))]t37".intd"(t),[t:zero(pd(a,b))]t38".intd"(t),[t:negd(pd(a,b))]t44".intd"(t)):intd(pd(a,b))
+intmd:=intpd(a,m0d(b),i,intm0d(b,j)):intd(md(a,b))
++*intd
+j@[n:not(zero(td(a,b)))]
+t45:=th3"l.imp"(zero(a),zero(td(a,b)),n,[t:zero(a)]td01(a,b,t)):not(zero(a))
+t46:=th3"l.imp"(zero(b),zero(td(a,b)),n,[t:zero(b)]td02(a,b,t)):not(zero(b))
+t47:=satzd166e(a,t45):posd(absd(a))
+a3:=rpofpd(absd(a),t47):cut
+t48:=satzd166e(b,t46):posd(absd(b))
+b3:=rpofpd(absd(b),t48):cut
+t49:=natts(a3,t9(absd(a),intabsd(a,i),t47),b3,t9(absd(b),intabsd(b,j),t48)):natrp(ts(a3,b3))
+t50:=satzd166e(td(a,b),n):posd(absd(td(a,b)))
+[p:posd(absd(td(a,b)))]
+atb3:=rpofpd(absd(td(a,b)),p):cut
+t51:=eqtd12(absd(a),pdofrp(a3),absd(b),pdofrp(b3),eqpdrp1(absd(a),t47),eqpdrp1(absd(b),t48)):eq(td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)))
+t52:=tr3eq(absd(td(a,b)),td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)),pdofrp(ts(a3,b3)),satzd193(a,b),t51,lemmaivad2(a3,b3)):eq(absd(td(a,b)),pdofrp(ts(a3,b3)))
+t53:=tris2(cut,atb3,ts(a3,b3),rpofpd(pdofrp(ts(a3,b3)),posdirp(ts(a3,b3))),eqpderp(absd(td(a,b)),p,pdofrp(ts(a3,b3)),posdirp(ts(a3,b3)),t52),isrppd1(ts(a3,b3))):is(atb3,ts(a3,b3))
+t54:=isp1(cut,[t:cut]natrp(t),ts(a3,b3),atb3,t49,t53):natrp(atb3)
+n@t55:=andi(posd(absd(td(a,b))),[t:posd(absd(td(a,b)))]natrp(atb3(t)),t50,[t:posd(absd(td(a,b)))]t54(t)):natd(absd(td(a,b)))
+-intd
+j@inttd:=[t:not(zero(td(a,b)))]t55".intd"(t):intd(td(a,b))
++r
+@eq:=[x:dif][y:dif]eq"rp"(x,y):[x:dif][y:dif]'prop'
+refeq:=[x:dif]refeq"rp"(x):[x:dif]<x><x>eq
+symeq:=[x:dif][y:dif][t:<y><x>eq]symeq"rp"(x,y,t):[x:dif][y:dif][t:<y><x>eq]<x><y>eq
+treq:=[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]treq"rp"(x,y,z,t,u):[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]<z><x>eq
+[a:dif][s:set(dif)]
+inn:=esti(dif,a,s):'prop'
+@real:=ect"eq"(dif,eq,refeq,symeq,treq):'type'
+[r:real][s:real]
+is:=is"e"(real,r,s):'prop'
+nis:=not(is(r,s)):'prop'
+@[p:[x:real]'prop']
+some:=some"l"(real,p):'prop'
+all:=all"l"(real,p):'prop'
+one:=one"e"(real,p):'prop'
+r@[s0:set(real)]
+in:=esti(real,r,s0):'prop'
+a@realof:=ectelt"eq"(dif,eq,refeq,symeq,treq,a):real
+r@class:=ecect"eq"(dif,eq,refeq,symeq,treq,r):set(dif)
+a@innclass:=th5"eq.4"(dif,eq,refeq,symeq,treq,a):inn(a,class(realof(a)))
+r@[a:dif][b:dif][e:eq"rp"(a,b)][air:inn(a,class(r))]
+eqinn:=th8"eq.4"(dif,eq,refeq,symeq,treq,r,a,air,b,e):inn(b,class(r))
+r@[p:'prop'][p1:[x:dif][xi:inn(x,class(r))]p]
+realapp1:=th3"eq.4"(dif,eq,refeq,symeq,treq,r,p,p1):p
+r@[s:real][p:'prop'][p1:[x:dif][y:dif][xi:inn(x,class(r))][yi:inn(y,class(s))]p]
++ivr1
+[a:dif][air:inn(a,class(r))]
+t1:=realapp1(s,p,[y:dif]<air><y><a>p1):p
+-ivr1
+realapp2:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t1".ivr1"(x,xi)):p
+s@[t:real][p:'prop'][p1:[x:dif][y:dif][z:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))]p]
++*ivr1
+p1@[a:dif][air:inn(a,class(r))]
+t2:=realapp2(s,t,p,[y:dif][z:dif]<air><z><y><a>p1):p
+-ivr1
+p1@realapp3:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t2".ivr1"(x,xi)):p
+t@[u:real][p:'prop'][p1:[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]p]
++*ivr1
+p1@[a:dif][air:inn(a,class(r))]
+t3:=realapp3(s,t,u,p,[y:dif][z:dif][v:dif]<air><v><z><y><a>p1):p
+-ivr1
+p1@realapp4:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t3".ivr1"(x,xi)):p
+s@[a1:dif][b1:dif][a1ir:inn(a1,class(r))][b1is:inn(b1,class(s))][e:eq"rp"(a1,b1)]
+isin:=th3"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,e):is(r,s)
+b1is@[i:is(r,s)]
+isex:=th5"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,i):eq"rp"(a1,b1)
+b1is@[n:not(eq"rp"(a1,b1))]
+nisin:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),n,[t:is(r,s)]isex(t)):nis(r,s)
+b1is@[n:nis(r,s)]
+nisex:=th3"l.imp"(eq"rp"(a1,b1),is(r,s),n,[t:eq"rp"(a1,b1)]isin(t)):not(eq"rp"(a1,b1))
+@[alpha:'type'][f:[x:dif]alpha]
+fixf:=fixfu"eq"(dif,eq,refeq,symeq,treq,alpha,f):'prop'
+[ff:fixf(alpha,f)][r0:real]
+indreal:=indeq"eq"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0):alpha
+[a:dif][air:inn(a,class(r0))]
+isindreal:=th2"eq.10"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0,a,air):is"e"(alpha,<a>f,indreal)
+alpha@[g:[x:dif][y:dif]alpha]
+fixf2:=fixfu2"eq"(dif,eq,refeq,symeq,treq,alpha,g):'prop'
+[ff2:fixf2(alpha,g)][r0:real][s0:real]
+indreal2:=indeq2"eq"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0):alpha
+[a:dif][b:dif][air:inn(a,class(r0))][bis:inn(b,class(s0))]
+isindreal2:=th1"eq.11"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0,a,air,b,bis):is"e"(alpha,<b><a>g,indreal2)
+@0:=realof(df(1rp,1rp)):real
+r@[a0:dif][a0ir:inn(a0,class(r))][z:zero(a0)]
+0in:=isin(r,0,a0,df(1rp,1rp),a0ir,innclass(df(1rp,1rp)),zeroeq(a0,df(1rp,1rp),z,zeroi(1rp,1rp,refis(cut,1rp)))):is(r,0)
+a0ir@[i:is(r,0)]
+0ex:=eqzero(df(1rp,1rp),a0,isex(0,r,df(1rp,1rp),a0,innclass(df(1rp,1rp)),a0ir,symis(real,r,0,i)),tris(cut,stm(df(1rp,1rp)),1rp,std(df(1rp,1rp)),stmis(1rp,1rp),isstd(1rp,1rp))):zero(a0)
++*ivr1
+a0@propp:=and(inn(a0,class(r)),posd(a0)):'prop'
+-ivr1
+r@pos:=some"l"(dif,[x:dif]propp".ivr1"(x)):'prop'
+a0ir@[p:posd(a0)]
++*ivr1
+p@t4:=andi(inn(a0,class(r)),posd(a0),a0ir,p):propp(a0)
+-ivr1
+p@posin:=somei(dif,[x:dif]propp".ivr1"(x),a0,t4".ivr1"):pos(r)
+a0ir@[p:pos(r)]
++*ivr1
+p@[a:dif][q1:propp(a)]
+t5:=ande1(inn(a,class(r)),posd(a),q1):inn(a,class(r))
+t6:=ande2(inn(a,class(r)),posd(a),q1):posd(a)
+t7:=eqposd(a,a0,isex(r,r,a,a0,t5,a0ir,refis(real,r)),t6):posd(a0)
+-ivr1
+p@posex:=someapp(dif,[x:dif]propp".ivr1"(x),p,posd(a0),[x:dif][t:propp".ivr1"(x)]t7".ivr1"(x,t)):posd(a0)
++*ivr1
+a0@propn:=and(inn(a0,class(r)),negd(a0)):'prop'
+-ivr1
+r@neg:=some"l"(dif,[x:dif]propn".ivr1"(x)):'prop'
+a0ir@[n:negd(a0)]
++*ivr1
+n@t8:=andi(inn(a0,class(r)),negd(a0),a0ir,n):propn(a0)
+-ivr1
+n@negin:=somei(dif,[x:dif]propn".ivr1"(x),a0,t8".ivr1"):neg(r)
+a0ir@[n:neg(r)]
++*ivr1
+n@[a:dif][pl:propn(a)]
+t9:=ande1(inn(a,class(r)),negd(a),pl):inn(a,class(r))
+t10:=ande2(inn(a,class(r)),negd(a),pl):negd(a)
+t11:=eqnegd(a,a0,isex(r,r,a,a0,t9,a0ir,refis(real,r)),t10):negd(a0)
+-ivr1
+n@negex:=someapp(dif,[x:dif]propn".ivr1"(x),n,negd(a0),[x:dif][t:propn".ivr1"(x)]t11".ivr1"(x,t)):negd(a0)
++*ivr1
+a0ir@[p:posd(a0)]
+t12:=or3i2(is(r,0),pos(r),neg(r),posin(p)):or3(is(r,0),pos(r),neg(r))
+a0ir@[z:zero(a0)]
+t13:=or3i1(is(r,0),pos(r),neg(r),0in(z)):or3(is(r,0),pos(r),neg(r))
+a0ir@[n:negd(a0)]
+t14:=or3i3(is(r,0),pos(r),neg(r),negin(n)):or3(is(r,0),pos(r),neg(r))
+a0ir@t15:=rappd(a0,or3(is(r,0),pos(r),neg(r)),[t:posd(a0)]t12(t),[t:zero(a0)]t13(t),[t:negd(a0)]t14(t)):or3(is(r,0),pos(r),neg(r))
+-ivr1
+r@axrlo:=realapp1(r,or3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t15".ivr1"(x,xi)):or3(is(r,0),pos(r),neg(r))
++*ivr1
+a0ir@[i:is(r,0)]
+t16:=th3"l.imp"(pos(r),posd(a0),0notpd(a0,0ex(i)),[t:pos(r)]posex(t)):not(pos(r))
+a0ir@[p:pos(r)]
+t17:=th3"l.imp"(neg(r),negd(a0),pnotnd(a0,posex(p)),[t:neg(r)]negex(t)):not(neg(r))
+a0ir@[n:neg(r)]
+t18:=th3"l.imp"(is(r,0),zero(a0),nnot0d(a0,negex(n)),[t:is(r,0)]0ex(t)):not(is(r,0))
+a0ir@t19:=th6"l.ec3"(is(r,0),pos(r),neg(r),[t:is(r,0)]t16(t),[t:pos(r)]t17(t),[t:neg(r)]t18(t)):ec3(is(r,0),pos(r),neg(r))
+-ivr1
+r@axrle:=realapp1(r,ec3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t19".ivr1"(x,xi)):ec3(is(r,0),pos(r),neg(r))
+axrl:=orec3i(is(r,0),pos(r),neg(r),axrlo,axrle):orec3(is(r,0),pos(r),neg(r))
+[p:'prop'][p1:[t:pos(r)]p][p2:[t:is(r,0)]p][p3:[t:neg(r)]p]
+rapp:=or3app(is(r,0),pos(r),neg(r),p,axrlo,p2,p1,p3):p
+r@[p:pos(r)]
+pnotn:=ec3e23(is(r,0),pos(r),neg(r),axrle,p):not(neg(r))
+pnot0:=ec3e21(is(r,0),pos(r),neg(r),axrle,p):nis(r,0)
+r@[i:is(r,0)]
+0notp:=ec3e12(is(r,0),pos(r),neg(r),axrle,i):not(pos(r))
+0notn:=ec3e13(is(r,0),pos(r),neg(r),axrle,i):not(neg(r))
+r@[n:neg(r)]
+nnotp:=ec3e32(is(r,0),pos(r),neg(r),axrle,n):not(pos(r))
+nnot0:=ec3e31(is(r,0),pos(r),neg(r),axrle,n):nis(r,0)
+s@[i:is(r,s)][p:pos(r)]
+ispos:=isp(real,[x:real]pos(x),r,s,p,i):pos(s)
+i@[n:neg(r)]
+isneg:=isp(real,[x:real]neg(x),r,s,n,i):neg(s)
+@[r0:cut]
+pofrp:=realof(pdofrp(r0)):real
+nofrp:=realof(ndofrp(r0)):real
+[s0:cut][i:is"rp"(r0,s0)]
+isrpep:=isf(cut,real,[x:cut]pofrp(x),r0,s0,i):is(pofrp(r0),pofrp(s0))
+isrpen:=isf(cut,real,[x:cut]nofrp(x),r0,s0,i):is(nofrp(r0),nofrp(s0))
+s0@[i:is(pofrp(r0),pofrp(s0))]
++*ivr1
+i"r"@t20:=isex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),i):eq"rp"(pdofrp(r0),pdofrp(s0))
+-ivr1
+i@isrpip:=isrpipd(r0,s0,t20".ivr1"):is"rp"(r0,s0)
+s0@[i:is(nofrp(r0),nofrp(s0))]
++*ivr1
+i"r"@t21:=isex(nofrp(r0),nofrp(s0),ndofrp(r0),ndofrp(s0),innclass(ndofrp(r0)),innclass(ndofrp(s0)),i):eq"rp"(ndofrp(r0),ndofrp(s0))
+-ivr1
+i@isrpin:=isrpind(r0,s0,t21".ivr1"):is"rp"(r0,s0)
+r0@posi:=posin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),posdirp(r0)):pos(pofrp(r0))
+negi:=negin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),negdirp(r0)):neg(nofrp(r0))
+s@[r0:cut][s0:cut][i:is(r,pofrp(r0))][j:is(s,pofrp(s0))][k:is(r,s)]
++*ivr1
+k@t22:=isrpip(r0,s0,tr3is(real,pofrp(r0),r,s,pofrp(s0),symis(real,r,pofrp(r0),i),k,j)):is"rp"(r0,s0)
+r@t23:=[x:cut][y:cut][t:is(r,pofrp(x))][u:is(r,pofrp(y))]t22(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,pofrp(x)))
+a0ir@[p1:pos(r)]
+t24:=posex(p1):posd(a0)
+pr:=rpofpd(a0,t24):cut
+t25:=isin(r,pofrp(pr),a0,pdofrp(pr),a0ir,innclass(pdofrp(pr)),eqpdrp1(a0,t24)):is(r,pofrp(pr))
+t26:=somei(cut,[x:cut]is(r,pofrp(x)),pr,t25):some"rp"([x:cut]is(r,pofrp(x)))
+-ivr1
+r@[p:pos(r)]
++*ivr1
+p"r"@t27:=realapp1(some"rp"([x:cut]is(r,pofrp(x))),[x:dif][t:inn(x,class(r))]t26(x,t,p)):some"rp"([x:cut]is(r,pofrp(x)))
+t28:=onei(cut,[x:cut]is(r,pofrp(x)),t23,t27):one"rp"([x:cut]is(r,pofrp(x)))
+-ivr1
+p@rpofp:=ind(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):cut
+isprp1:=oneax(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):is(r,pofrp(rpofp(r,p)))
+isprp2:=symis(real,r,pofrp(rpofp(r,p)),isprp1):is(pofrp(rpofp(r,p)),r)
+@[r1:real][p:pos(r1)][s1:real][q:pos(s1)][i:is(r1,s1)]
+isperp:=t22".ivr1"(r1,s1,rpofp(r1,p),rpofp(s1,q),isprp1(r1,p),isprp1(s1,q),i):is"rp"(rpofp(r1,p),rpofp(s1,q))
+q@[i:is"rp"(rpofp(r1,p),rpofp(s1,q))]
+ispirp:=tr3is(real,r1,pofrp(rpofp(r1,p)),pofrp(rpofp(s1,q)),s1,isprp1(r1,p),isrpep(rpofp(r1,p),rpofp(s1,q),i),isprp2(s1,q)):is(r1,s1)
+@[r0:cut]
+isrpp1:=t22".ivr1"(pofrp(r0),pofrp(r0),r0,rpofp(pofrp(r0),posi(r0)),refis(real,pofrp(r0)),isprp1(pofrp(r0),posi(r0)),refis(real,pofrp(r0))):is"rp"(r0,rpofp(pofrp(r0),posi(r0)))
+isrpp2:=symis(cut,r0,rpofp(pofrp(r0),posi(r0)),isrpp1):is"rp"(rpofp(pofrp(r0),posi(r0)),r0)
+s@[r0:cut][s0:cut][i:is(r,nofrp(r0))][j:is(s,nofrp(s0))][k:is(r,s)]
++*ivr1
+k@t29:=isrpin(r0,s0,tr3is(real,nofrp(r0),r,s,nofrp(s0),symis(real,r,nofrp(r0),i),k,j)):is"rp"(r0,s0)
+r@t30:=[x:cut][y:cut][t:is(r,nofrp(x))][u:is(r,nofrp(y))]t29(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,nofrp(x)))
+a0ir@[n1:neg(r)]
+t31:=negex(n1):negd(a0)
+nr:=rpofnd(a0,t31):cut
+t32:=isin(r,nofrp(nr),a0,ndofrp(nr),a0ir,innclass(ndofrp(nr)),eqndrp1(a0,t31)):is(r,nofrp(nr))
+t33:=somei(cut,[x:cut]is(r,nofrp(x)),nr,t32):some"rp"([x:cut]is(r,nofrp(x)))
+-ivr1
+r@[n:neg(r)]
++*ivr1
+n"r"@t34:=realapp1(some"rp"([x:cut]is(r,nofrp(x))),[x:dif][t:inn(x,class(r))]t33(x,t,n)):some"rp"([x:cut]is(r,nofrp(x)))
+t35:=onei(cut,[x:cut]is(r,nofrp(x)),t30,t34):one"rp"([x:cut]is(r,nofrp(x)))
+-ivr1
+n@rpofn:=ind(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):cut
+isnrp1:=oneax(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):is(r,nofrp(rpofn(r,n)))
+isnrp2:=symis(real,r,nofrp(rpofn(r,n)),isnrp1):is(nofrp(rpofn(r,n)),r)
+@[r1:real][n:neg(r1)][s1:real][m:neg(s1)][i:is(r1,s1)]
+isnerp:=t29".ivr1"(r1,s1,rpofn(r1,n),rpofn(s1,m),isnrp1(r1,n),isnrp1(s1,m),i):is"rp"(rpofn(r1,n),rpofn(s1,m))
+m@[i:is"rp"(rpofn(r1,n),rpofn(s1,m))]
+isnirp:=tr3is(real,r1,nofrp(rpofn(r1,n)),nofrp(rpofn(s1,m)),s1,isnrp1(r1,n),isrpen(rpofn(r1,n),rpofn(s1,m),i),isnrp2(s1,m)):is(r1,s1)
+@[r0:cut]
+isrpn1:=t29".ivr1"(nofrp(r0),nofrp(r0),r0,rpofn(nofrp(r0),negi(r0)),refis(real,nofrp(r0)),isnrp1(nofrp(r0),negi(r0)),refis(real,nofrp(r0))):is"rp"(r0,rpofn(nofrp(r0),negi(r0)))
+isrpn2:=symis(cut,r0,rpofn(nofrp(r0),negi(r0)),isrpn1):is"rp"(rpofn(nofrp(r0),negi(r0)),r0)
+r@satz163:=refis(real,r):is(r,r)
+s@[i:is(r,s)]
+satz164:=symis(real,r,s,i):is(s,r)
+t@[i:is(r,s)][j:is(s,t)]
+satz165:=tris(real,r,s,t,i,j):is(r,t)
+@absdr:=[x:dif]realof(absd(x)):[x:dif]real
++ivr2
+[a:dif][b:dif][e:eq"rp"(a,b)]
+t1:=isin(realof(absd(a)),realof(absd(b)),absd(a),absd(b),innclass(absd(a)),innclass(absd(b)),eqabsd(a,b,e)):is(<a>absdr,<b>absdr)
+-ivr2
+fabsdr:=[x:dif][y:dif][t:<y><x>eq]t1".ivr2"(x,y,t):fixf(real,absdr)
+r@abs:=indreal(real,absdr,fabsdr,r):real
++*ivr2
+a0ir@t2:=isindreal(real,absdr,fabsdr,r,a0,a0ir):is(realof(absd(a0)),abs(r))
+-ivr2
+a0ir@aica:=isp(real,[x:real]inn(absd(a0),class(x)),realof(absd(a0)),abs(r),innclass(absd(a0)),t2".ivr2"):inn(absd(a0),class(abs(r)))
+s@[i:is(r,s)]
+isabs:=isf(real,real,[x:real]abs(x),r,s,i):is(abs(r),abs(s))
++2r166
+a0ir@[p:pos(r)]
+t1:=satzd166a(a0,posex(p)):posd(absd(a0))
+t2:=posin(abs(r),absd(a0),aica,t1):pos(abs(r))
+-2r166
+r@[p:pos(r)]
+satz166a:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t2".2r166"(x,t,p)):pos(abs(r))
++*2r166
+a0ir@[n:neg(r)]
+t3:=satzd166b(a0,negex(n)):posd(absd(a0))
+t4:=posin(abs(r),absd(a0),aica,t3):pos(abs(r))
+-2r166
+r@[n:neg(r)]
+satz166b:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t4".2r166"(x,t,n)):pos(abs(r))
++*2r166
+b1is@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
+t5:=satzd166c(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
+t6:=isin(t5):is(r,s)
+-2r166
+s@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
+satz166c:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".2r166"(x,y,t,u,p,q,i)):is(r,s)
++*2r166
+b1is@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
+t7:=satzd166d(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
+t8:=isin(t7):is(r,s)
+-2r166
+s@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
+satz166d:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".2r166"(x,y,t,u,n,o,i)):is(r,s)
+r@[n:nis(r,0)]
+satz166e:=rapp(r,pos(abs(r)),[t:pos(r)]satz166a(t),th2"l.imp"(is(r,0),pos(abs(r)),n),[t:neg(r)]satz166b(t)):pos(abs(r))
++*2r166
+a0ir@[i:is(r,0)]
+t9:=satzd166f(a0,0ex(i)):zero(absd(a0))
+t10:=0in(abs(r),absd(a0),aica,t9):is(abs(r),0)
+-2r166
+r@[i:is(r,0)]
+satz166f:=realapp1(is(abs(r),0),[x:dif][t:inn(x,class(r))]t10".2r166"(x,t,i)):is(abs(r),0)
+s@more:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),mored(x,y)))):'prop'
++*ivr2
+b1@propm:=and3(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1)):'prop'
+-ivr2
+b1is@[m:mored(a1,b1)]
++*ivr2
+m@t3:=and3i(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1),a1ir,b1is,m):propm(a1,b1)
+t4:=somei(dif,[x:dif]propm(a1,x),b1,t3):some"l"(dif,[x:dif]propm(a1,x))
+-ivr2
+m@morein:=somei(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),a1,t4".ivr2"):more(r,s)
+b1is@[m:more(r,s)]
++*ivr2
+m@[a:dif][sa:some"l"(dif,[x:dif]propm(a,x))][b:dif][p2:propm(a,b)]
+t5:=and3e1(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(a,class(r))
+t6:=and3e2(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(b,class(s))
+t7:=and3e3(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):mored(a,b)
+t8:=eqmored12(a,a1,b,b1,isex(r,r,a,a1,t5,a1ir,refis(real,r)),isex(s,s,b,b1,t6,b1is,refis(real,s)),t7):mored(a1,b1)
+sa@t9:=someapp(dif,[x:dif]propm(a,x),sa,mored(a1,b1),[x:dif][t:propm(a,x)]t8(x,t)):mored(a1,b1)
+-ivr2
+m@moreex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),m,mored(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propm".ivr2"(x,y))]t9".ivr2"(x,t)):mored(a1,b1)
+s@less:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),lessd(x,y)))):'prop'
++*ivr2
+b1@propl:=and3(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1)):'prop'
+-ivr2
+b1is@[l:lessd(a1,b1)]
++*ivr2
+l@t10:=and3i(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1),a1ir,b1is,l):propl(a1,b1)
+t11:=somei(dif,[x:dif]propl(a1,x),b1,t10):some"l"(dif,[x:dif]propl(a1,x))
+-ivr2
+l@lessin:=somei(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),a1,t11".ivr2"):less(r,s)
+b1is@[l:less(r,s)]
++*ivr2
+l@[a:dif][sa:some"l"(dif,[x:dif]propl(a,x))][b:dif][p2:propl(a,b)]
+t12:=and3e1(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(a,class(r))
+t13:=and3e2(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(b,class(s))
+t14:=and3e3(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):lessd(a,b)
+t15:=eqlessd12(a,a1,b,b1,isex(r,r,a,a1,t12,a1ir,refis(real,r)),isex(s,s,b,b1,t13,b1is,refis(real,s)),t14):lessd(a1,b1)
+sa@t16:=someapp(dif,[x:dif]propl(a,x),sa,lessd(a1,b1),[x:dif][t:propl(a,x)]t15(x,t)):lessd(a1,b1)
+-ivr2
+l@lessex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),l,lessd(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propl".ivr2"(x,y))]t16".ivr2"(x,t)):lessd(a1,b1)
+t@[i:is(r,s)][m:more(r,t)]
+ismore1:=isp(real,[x:real]more(x,t),r,s,m,i):more(s,t)
+i@[m:more(t,r)]
+ismore2:=isp(real,[x:real]more(t,x),r,s,m,i):more(t,s)
+i@[l:less(r,t)]
+isless1:=isp(real,[x:real]less(x,t),r,s,l,i):less(s,t)
+i@[l:less(t,r)]
+isless2:=isp(real,[x:real]less(t,x),r,s,l,i):less(t,s)
+u@[i:is(r,s)][j:is(t,u)][m:more(r,t)]
+ismore12:=ismore2(t,u,s,j,ismore1(r,s,t,i,m)):more(s,u)
+j@[l:less(r,t)]
+isless12:=isless2(t,u,s,j,isless1(r,s,t,i,l)):less(s,u)
++*ivr2
+b1is@[m:more(r,s)]
+t17:=lemmad5(a1,b1,moreex(m)):lessd(b1,a1)
+t18:=lessin(s,r,b1,a1,b1is,a1ir,t17):less(s,r)
+-ivr2
+s@[m:more(r,s)]
+lemma1:=realapp2(less(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t18".ivr2"(x,y,t,u,m)):less(s,r)
++*ivr2
+b1is@[l:less(r,s)]
+t19:=lemmad6(a1,b1,lessex(l)):mored(b1,a1)
+t20:=morein(s,r,b1,a1,b1is,a1ir,t19):more(s,r)
+-ivr2
+s@[l:less(r,s)]
+lemma2:=realapp2(more(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t20".ivr2"(x,y,t,u,l)):more(s,r)
++2r167
+b1is@t1:=satzd167a(a1,b1):or3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
+[e:eq"rp"(a1,b1)]
+t2:=or3i1(is(r,s),more(r,s),less(r,s),isin(e)):or3(is(r,s),more(r,s),less(r,s))
+b1is@[m:mored(a1,b1)]
+t3:=or3i2(is(r,s),more(r,s),less(r,s),morein(m)):or3(is(r,s),more(r,s),less(r,s))
+b1is@[l:lessd(a1,b1)]
+t4:=or3i3(is(r,s),more(r,s),less(r,s),lessin(l)):or3(is(r,s),more(r,s),less(r,s))
+b1is@t5:=or3app(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),or3(is(r,s),more(r,s),less(r,s)),t1,[t:eq"rp"(a1,b1)]t2(t),[t:mored(a1,b1)]t3(t),[t:lessd(a1,b1)]t4(t)):or3(is(r,s),more(r,s),less(r,s))
+t6:=satzd167b(a1,b1):ec3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
+[i:is(r,s)]
+t7:=th3"l.imp"(more(r,s),mored(a1,b1),ec3e12(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,isex(i)),[t:more(r,s)]moreex(t)):not(more(r,s))
+b1is@[m:more(r,s)]
+t8:=th3"l.imp"(less(r,s),lessd(a1,b1),ec3e23(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,moreex(m)),[t:less(r,s)]lessex(t)):not(less(r,s))
+b1is@[l:less(r,s)]
+t9:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),ec3e31(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,lessex(l)),[t:is(r,s)]isex(t)):not(is(r,s))
+b1is@t10:=th6"l.ec3"(is(r,s),more(r,s),less(r,s),th1"l.ec"(is(r,s),more(r,s),[t:is(r,s)]t7(t)),th1"l.ec"(more(r,s),less(r,s),[t:more(r,s)]t8(t)),th1"l.ec"(less(r,s),is(r,s),[t:less(r,s)]t9(t))):ec3(is(r,s),more(r,s),less(r,s))
+t11:=orec3i(is(r,s),more(r,s),less(r,s),t5,t10):orec3(is(r,s),more(r,s),less(r,s))
+-2r167
+s@satz167:=realapp2(orec3(is(r,s),more(r,s),less(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".2r167"(x,y,t,u)):orec3(is(r,s),more(r,s),less(r,s))
+satz167a:=orec3e1(is(r,s),more(r,s),less(r,s),satz167):or3(is(r,s),more(r,s),less(r,s))
+satz167b:=orec3e2(is(r,s),more(r,s),less(r,s),satz167):ec3(is(r,s),more(r,s),less(r,s))
+moreis:=or(more(r,s),is(r,s)):'prop'
+lessis:=or(less(r,s),is(r,s)):'prop'
+[m:moreis(r,s)]
+satz168a:=th9"l.or"(more(r,s),is(r,s),less(s,r),is(s,r),m,[t:more(r,s)]lemma1(t),[t:is(r,s)]symis(real,r,s,t)):lessis(s,r)
+s@[l:lessis(r,s)]
+satz168b:=th9"l.or"(less(r,s),is(r,s),more(s,r),is(s,r),l,[t:less(r,s)]lemma2(t),[t:is(r,s)]symis(real,r,s,t)):moreis(s,r)
+t@[i:is(r,s)][m:moreis(r,t)]
+ismoreis1:=isp(real,[x:real]moreis(x,t),r,s,m,i):moreis(s,t)
+i@[m:moreis(t,r)]
+ismoreis2:=isp(real,[x:real]moreis(t,x),r,s,m,i):moreis(t,s)
+i@[l:lessis(r,t)]
+islessis1:=isp(real,[x:real]lessis(x,t),r,s,l,i):lessis(s,t)
+i@[l:lessis(t,r)]
+islessis2:=isp(real,[x:real]lessis(t,x),r,s,l,i):lessis(t,s)
+u@[i:is(r,s)][j:is(t,u)][m:moreis(r,t)]
+ismoreis12:=ismoreis2(t,u,s,j,ismoreis1(r,s,t,i,m)):moreis(s,u)
+j@[l:lessis(r,t)]
+islessis12:=islessis2(t,u,s,j,islessis1(r,s,t,i,l)):lessis(s,u)
+s@[m:more(r,s)]
+moreisi1:=ori1(more(r,s),is(r,s),m):moreis(r,s)
+s@[l:less(r,s)]
+lessisi1:=ori1(less(r,s),is(r,s),l):lessis(r,s)
+s@[i:is(r,s)]
+moreisi2:=ori2(more(r,s),is(r,s),i):moreis(r,s)
+lessisi2:=ori2(less(r,s),is(r,s),i):lessis(r,s)
+b1is@[m:moreq(a1,b1)]
+moreisin:=orapp(mored(a1,b1),eq"rp"(a1,b1),moreis(r,s),m,[t:mored(a1,b1)]moreisi1(morein(t)),[t:eq"rp"(a1,b1)]moreisi2(isin(t))):moreis(r,s)
+b1is@[m:moreis(r,s)]
+moreisex:=orapp(more(r,s),is(r,s),moreq(a1,b1),m,[t:more(r,s)]moreqi1(a1,b1,moreex(t)),[t:is(r,s)]moreqi2(a1,b1,isex(t))):moreq(a1,b1)
+b1is@[l:lesseq(a1,b1)]
+lessisin:=orapp(lessd(a1,b1),eq"rp"(a1,b1),lessis(r,s),l,[t:lessd(a1,b1)]lessisi1(lessin(t)),[t:eq"rp"(a1,b1)]lessisi2(isin(t))):lessis(r,s)
+b1is@[l:lessis(r,s)]
+lessisex:=orapp(less(r,s),is(r,s),lesseq(a1,b1),l,[t:less(r,s)]lesseqi1(a1,b1,lessex(t)),[t:is(r,s)]lesseqi2(a1,b1,isex(t))):lesseq(a1,b1)
+s@[m:moreis(r,s)]
+satz167c:=th7"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,comor(more(r,s),is(r,s),m)):not(less(r,s))
+s@[l:lessis(r,s)]
+satz167d:=th9"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,l):not(more(r,s))
+s@[n:not(more(r,s))]
+satz167e:=th2"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n):lessis(r,s)
+s@[n:not(less(r,s))]
+s@[n:not(less(r,s))]
+satz167f:=comor(is(r,s),more(r,s),th3"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n)):moreis(r,s)
+s@[m:more(r,s)]
+satz167g:=th3"l.imp"(lessis(r,s),not(more(r,s)),weli(more(r,s),m),[t:lessis(r,s)]satz167d(t)):not(lessis(r,s))
+s@[l:less(r,s)]
+satz167h:=th3"l.imp"(moreis(r,s),not(less(r,s)),weli(less(r,s),l),[t:moreis(r,s)]satz167c(t)):not(moreis(r,s))
+s@[n:not(moreis(r,s))]
+satz167j:=or3e3(is(r,s),more(r,s),less(r,s),satz167a,th5"l.or"(more(r,s),is(r,s),n),th4"l.or"(more(r,s),is(r,s),n)):less(r,s)
+s@[n:not(lessis(r,s))]
+satz167k:=or3e2(is(r,s),more(r,s),less(r,s),satz167a,th4"l.or"(less(r,s),is(r,s),n),th5"l.or"(less(r,s),is(r,s),n)):more(r,s)
+r@[p:pos(r)]
++2r169
+[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t1:=satzd169a(a,b,0ex(0,b,bi0,refis(real,0)),posex(a,air,p)):mored(a,b)
+t2:=morein(r,0,a,b,air,bi0,t1):more(r,0)
+-2r169
+satz169a:=realapp2(r,0,more(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r169"(x,y,t,u)):more(r,0)
+r@[m:more(r,0)]
++*2r169
+m@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t3:=satzd169b(a,b,0ex(0,b,bi0,refis(real,0)),moreex(r,0,a,b,air,bi0,m)):posd(a)
+t4:=posin(r,a,air,t3):pos(r)
+-2r169
+m@satz169b:=realapp2(r,0,pos(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t4".2r169"(x,y,t,u)):pos(r)
+r@[n:neg(r)]
++*2r169
+n@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t5:=satzd169c(a,b,0ex(0,b,bi0,refis(real,0)),negex(a,air,n)):lessd(a,b)
+t6:=lessin(r,0,a,b,air,bi0,t5):less(r,0)
+-2r169
+n@satz169c:=realapp2(r,0,less(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t6".2r169"(x,y,t,u)):less(r,0)
+r@[l:less(r,0)]
++*2r169
+l@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t7:=satzd169d(a,b,0ex(0,b,bi0,refis(real,0)),lessex(r,0,a,b,air,bi0,l)):negd(a)
+t8:=negin(r,a,air,t7):neg(r)
+-2r169
+l@satz169d:=realapp2(r,0,neg(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t8".2r169"(x,y,t,u)):neg(r)
++2r170
+r@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
+t1:=satzd170(a,b,0ex(0,b,bi0,refis(real,0))):moreq(absd(a),b)
+t2:=moreisin(abs(r),0,absd(a),b,aica(r,a,air),bi0,t1):moreis(abs(r),0)
+-2r170
+r@satz170:=realapp2(r,0,moreis(abs(r),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r170"(x,y,t,u)):moreis(abs(r),0)
+satz170a:=th3"l.imp"(neg(abs(r)),less(abs(r),0),satz167c(abs(r),0,satz170),[t:neg(abs(r))]satz169c(abs(r),t)):not(neg(abs(r)))
+t@[l:less(r,s)][k:less(s,t)]
++2r171
+[a:dif][b:dif][c:dif][air:inn(a,class(r))][bis:inn(b,class(s))][cit:inn(c,class(t))]
+t1:=satzd171(a,b,c,lessex(r,s,a,b,air,bis,l),lessex(s,t,b,c,bis,cit,k)):lessd(a,c)
+t2:=lessin(r,t,a,c,air,cit,t1):less(r,t)
+-2r171
+satz171:=realapp3(r,s,t,less(r,t),[x:dif][y:dif][z:dif][w:inn(x,class(r))][u:inn(y,class(s))][v:inn(z,class(t))]t2".2r171"(x,y,z,w,u,v)):less(r,t)
+trless:=satz171:less(r,t)
+t@[m:more(r,s)][n:more(s,t)]
+trmore:=lemma2(t,r,trless(t,s,r,lemma1(s,t,n),lemma1(r,s,m))):more(r,t)
+t@[a2:dif][b2:dif][c2:dif][a2ir:inn(a2,class(r))][b2is:inn(b2,class(s))][c2it:inn(c2,class(t))]
++2r172
+[l:lessis(r,s)][k:less(s,t)]
+t1:=satzd172a(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
+t2:=lessin(r,t,a2,c2,a2ir,c2it,t1):less(r,t)
+-2r172
+t@[l:lessis(r,s)][k:less(s,t)]
+satz172a:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
++*2r172
+c2it@[l:less(r,s)][k:lessis(s,t)]
+t3:=satzd172b(a2,b2,c2,lessex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
+t4:=lessin(r,t,a2,c2,a2ir,c2it,t3):less(r,t)
+-2r172
+t@[l:less(r,s)][k:lessis(s,t)]
+satz172b:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
+t@[m:moreis(r,s)][n:more(s,t)]
+satz172c:=lemma2(t,r,satz172b(t,s,r,lemma1(s,t,n),satz168a(m))):more(r,t)
+t@[m:more(r,s)][n:moreis(s,t)]
+satz172d:=lemma2(t,r,satz172a(t,s,r,satz168a(s,t,n),lemma1(m))):more(r,t)
++2r173
+c2it@[l:lessis(r,s)][k:lessis(s,t)]
+t1:=satzd173(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lesseq(a2,c2)
+t2:=lessisin(r,t,a2,c2,a2ir,c2it,t1):lessis(r,t)
+-2r173
+t@[l:lessis(r,s)][k:lessis(s,t)]
+satz173:=realapp3(lessis(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r173"(x,y,z,u,v,w,l,k)):lessis(r,t)
+trlessis:=satz173:lessis(r,t)
+t@[m:moreis(r,s)][n:moreis(s,t)]
+trmoreis:=satz168b(t,r,trlessis(t,s,r,satz168a(s,t,n),satz168a(m))):moreis(r,t)
+r@ratrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),ratd(x))):'prop'
+a0ir@[r1:ratd(a0)]
++*ivr2
+r1@t21:=andi(inn(a0,class(r)),ratd(a0),a0ir,r1):and(inn(a0,class(r)),ratd(a0))
+-ivr2
+r1@ratrlin:=somei(dif,[x:dif]and(inn(x,class(r)),ratd(x)),a0,t21".ivr2"):ratrl(r)
+a0ir@[rr:ratrl(r)]
++*ivr2
+rr@[a:dif][b:and(inn(a,class(r)),ratd(a))]
+t22:=ande1(inn(a,class(r)),ratd(a),b):inn(a,class(r))
+t23:=ande2(inn(a,class(r)),ratd(a),b):ratd(a)
+t24:=eqratd(a,a0,isex(r,r,a,a0,t22,a0ir,refis(real,r)),t23):ratd(a0)
+-ivr2
+rr@ratrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),ratd(x)),rr,ratd(a0),[x:dif][t:and(inn(x,class(r)),ratd(x))]t24".ivr2"(x,t)):ratd(a0)
+r@irratrl:=not(ratrl(r)):'prop'
+@[r0:cut][rr:ratrp(r0)]
+remark2:=ratrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark2a(r0,rr)):ratrl(pofrp(r0))
+remark3:=ratrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark3a(r0,rr)):ratrl(nofrp(r0))
+r0@[ir:irratrp(r0)]
+remark4:=th3"l.imp"(ratrl(pofrp(r0)),ratd(pdofrp(r0)),remark4a(r0,ir),[t:ratrl(pofrp(r0))]ratrlex(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),t)):irratrl(pofrp(r0))
+remark5:=th3"l.imp"(ratrl(nofrp(r0)),ratd(ndofrp(r0)),remark5a(r0,ir),[t:ratrl(nofrp(r0))]ratrlex(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),t)):irratrl(nofrp(r0))
+r@natrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),natd(x))):'prop'
+a0ir@[n:natd(a0)]
++*ivr2
+n@t25:=andi(inn(a0,class(r)),natd(a0),a0ir,n):and(inn(a0,class(r)),natd(a0))
+-ivr2
+n@natrlin:=somei(dif,[x:dif]and(inn(x,class(r)),natd(x)),a0,t25".ivr2"):natrl(r)
+a0ir@[n:natrl(r)]
++*ivr2
+n@[a:dif][b:and(inn(a,class(r)),natd(a))]
+t26:=ande1(inn(a,class(r)),natd(a),b):inn(a,class(r))
+t27:=ande2(inn(a,class(r)),natd(a),b):natd(a)
+t28:=eqnatd(a,a0,isex(r,r,a,a0,t26,a0ir,refis(real,r)),t27):natd(a0)
+-ivr2
+n@natrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),natd(x)),n,natd(a0),[x:dif][t:and(inn(x,class(r)),natd(x))]t28".ivr2"(x,t)):natd(a0)
++*ivr2
+a0ir@[n:natrl(r)]
+t29:=natposd(a0,natrlex(n)):posd(a0)
+t30:=posin(t29):pos(r)
+-ivr2
+r@[n:natrl(r)]
+natpos:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t30".ivr2"(x,t,n)):pos(r)
+@[x:nat]
+rlofnt:=realof(pdofnt(x)):real
+natrli:=natrlin(rlofnt(x),pdofnt(x),innclass(pdofnt(x)),natdi(x)):natrl(rlofnt(x))
+[y:nat][i:is"n"(x,y)]
+isnterl:=isf(nat,real,[u:nat]rlofnt(u),x,y,i):is(rlofnt(x),rlofnt(y))
+y@[i:is(rlofnt(x),rlofnt(y))]
+isntirl:=isntirp(x,y,isrpip(rpofnt(x),rpofnt(y),i)):is"n"(x,y)
++*ivr2
+@t31:=[x:nat][y:nat][t:is(rlofnt(x),rlofnt(y))]isntirl(x,y,t):injective(nat,real,[x:nat]rlofnt(x))
+a0ir@[n:natrl(r)]
+t32:=natposd(a0,natrlex(n)):posd(a0)
+ap:=rpofpd(a0,t32):cut
+t33:=natderp(a0,natrlex(n)):natrp(ap)
+x0:=ntofrp(ap,t33):nat
+t34:=isrpepd(ap,rpofnt(x0),isrpnt1(ap,t33)):eq"rp"(pdofrp(ap),pdofnt(x0))
+t35:=treq"rp"(a0,pdofrp(ap),pdofnt(x0),eqpdrp1(a0,t32),t34):eq"rp"(a0,pdofnt(x0))
+t36:=isin(r,rlofnt(x0),a0,pdofnt(x0),a0ir,innclass(pdofnt(x0)),t35):is(r,rlofnt(x0))
+t37:=somei(nat,[x:nat]is(r,rlofnt(x)),x0,t36):image(nat,real,[x:nat]rlofnt(x),r)
+-ivr2
+r@[n:natrl(r)]
+natimage:=realapp1(image(nat,real,[x:nat]rlofnt(x),r),[x:dif][t:inn(x,class(r))]t37".ivr2"(x,t,n)):image(nat,real,[x:nat]rlofnt(x),r)
+r@[i:image(nat,real,[x:nat]rlofnt(x),r)]
++*ivr2
+i"r"@[x:nat][j:is(r,rlofnt(x))]
+t38:=isp1(real,[u:real]natrl(u),rlofnt(x),r,natrli(x),j):natrl(r)
+-ivr2
+i@imagenat:=someapp(nat,[u:nat]is(r,rlofnt(u)),i,natrl(r),[u:nat][v:is(r,rlofnt(u))]t38".ivr2"(u,v)):natrl(r)
+r@[n:natrl(r)]
+ntofrl:=soft(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):nat
+@[r1:real][n:natrl(r1)][s1:real][m:natrl(s1)][i:is(r1,s1)]
+isrlent:=isinv(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is"n"(ntofrl(r1,n),ntofrl(s1,m))
+m@[i:is"n"(ntofrl(r1,n),ntofrl(s1,m))]
+isrlint:=isinve(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is(r1,s1)
+r@[n:natrl(r)]
+isrlnt1:=ists1"e"(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):is(r,rlofnt(ntofrl(r,n)))
+isrlnt2:=symis(real,r,rlofnt(ntofrl(r,n)),isrlnt1):is(rlofnt(ntofrl(r,n)),r)
+@[x:nat]
++*ivr2
+x"r"@xn:=soft(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x)):nat
+t39:=isinv(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x),rlofnt(x),natimage(rlofnt(x),natrli(x)),refis(real,rlofnt(x))):is"n"(xn,ntofrl(rlofnt(x),natrli(x)))
+-ivr2
+x@isntrl1:=tris(nat,x,xn".ivr2",ntofrl(rlofnt(x),natrli(x)),isst1(nat,real,[u:nat]rlofnt(u),t31".ivr2",x),t39".ivr2"):is"n"(x,ntofrl(rlofnt(x),natrli(x)))
+isntrl2:=symis(nat,x,ntofrl(rlofnt(x),natrli(x)),isntrl1):is"n"(ntofrl(rlofnt(x),natrli(x)),x)
+r@intrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),intd(x))):'prop'
+a0ir@[i:intd(a0)]
++*ivr2
+i@t40:=andi(inn(a0,class(r)),intd(a0),a0ir,i):and(inn(a0,class(r)),intd(a0))
+-ivr2
+i@intrlin:=somei(dif,[x:dif]and(inn(x,class(r)),intd(x)),a0,t40".ivr2"):intrl(r)
+a0ir@[i:intrl(r)]
++*ivr2
+i@[a:dif][b:and(inn(a,class(r)),intd(a))]
+t41:=ande1(inn(a,class(r)),intd(a),b):inn(a,class(r))
+t42:=ande2(inn(a,class(r)),intd(a),b):intd(a)
+t43:=eqintd(a,a0,isex(r,r,a,a0,t41,a0ir,refis(real,r)),t42):intd(a0)
+-ivr2
+i@intrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),intd(x)),i,intd(a0),[x:dif][t:and(inn(x,class(r)),intd(x))]t43".ivr2"(x,t)):intd(a0)
++*ivr2
+a0ir@[n:natrl(r)]
+t44:=natintd(a0,natrlex(n)):intd(a0)
+t45:=intrlin(t44):intrl(r)
+-ivr2
+r@[n:natrl(r)]
+natintrl:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t45".ivr2"(x,t,n)):intrl(r)
++*ivr2
+a0ir@[p:pos(r)][i:intrl(r)]
+t46:=posintnatd(a0,posex(p),intrlex(i)):natd(a0)
+t47:=natrlin(t46):natrl(r)
+-ivr2
+r@[p:pos(r)][i:intrl(r)]
+posintnatrl:=realapp1(natrl(r),[x:dif][t:inn(x,class(r))]t47".ivr2"(x,t,p,i)):natrl(r)
++*ivr2
+a0ir@[i2:is(r,0)]
+t48:=intdi0(a0,0ex(i2)):intd(a0)
+t49:=intrlin(t48):intrl(r)
+-ivr2
+r@[i:is(r,0)]
+intrli0:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t49".ivr2"(x,t,i)):intrl(r)
+r0@[n:natrp(r0)]
+remark6:=intrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark6"rp"(r0,n)):intrl(pofrp(r0))
+remark7:=intrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark7"rp"(r0,n)):intrl(nofrp(r0))
++2r174
+a0ir@[i:intrl(r)]
+t1:=satzd174(a0,intrlex(i)):ratd(a0)
+t2:=ratrlin(t1):ratrl(r)
+-2r174
+r@[i:intrl(r)]
+satz174:=realapp1(ratrl(r),[x:dif][t:inn(x,class(r))]t2".2r174"(x,t,i)):ratrl(r)
+@plusdr:=[x:dif][y:dif]realof(pd(x,y)):[x:dif][y:dif]real
++ivr3
+[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
+t1:=isin(realof(pd(a,c)),realof(pd(b,d)),pd(a,c),pd(b,d),innclass(pd(a,c)),innclass(pd(b,d)),eqpd12(a,b,c,d,e,f)):is(<c><a>plusdr,<d><b>plusdr)
+-ivr3
+fplusdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr3"(x,y,z,v,t,u):fixf2(real,plusdr)
+s@pl:=indreal2(real,plusdr,fplusdr,r,s):real
++*ivr3
+b1is@t2:=isindreal2(real,plusdr,fplusdr,r,s,a1,b1,a1ir,b1is):is(realof(pd(a1,b1)),pl(r,s))
+-ivr3
+b1is@picp:=isp(real,[x:real]inn(pd(a1,b1),class(x)),realof(pd(a1,b1)),pl(r,s),innclass(pd(a1,b1)),t2".ivr3"):inn(pd(a1,b1),class(pl(r,s)))
+t@[i:is(r,s)]
+ispl1:=isf(real,real,[x:real]pl(x,t),r,s,i):is(pl(r,t),pl(s,t))
+ispl2:=isf(real,real,[x:real]pl(t,x),r,s,i):is(pl(t,r),pl(t,s))
+u@[i:is(r,s)][j:is(t,u)]
+ispl12:=tris(real,pl(r,t),pl(s,t),pl(s,u),ispl1(i),ispl2(t,u,s,j)):is(pl(r,t),pl(s,u))
++3r175
+b1is@t1:=satzd175(a1,b1):eq"rp"(pd(a1,b1),pd(b1,a1))
+t2:=isin(pl(r,s),pl(s,r),pd(a1,b1),pd(b1,a1),picp,picp(s,r,b1,a1,b1is,a1ir),t1):is(pl(r,s),pl(s,r))
+-3r175
+s@satz175:=realapp2(is(pl(r,s),pl(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r175"(x,y,t,u)):is(pl(r,s),pl(s,r))
+compl:=satz175:is(pl(r,s),pl(s,r))
++*ivr3
+b1is@[i:is(r,0)]
+t3:=pd01(a1,b1,0ex(r,a1,a1ir,i)):eq"rp"(pd(a1,b1),b1)
+t4:=isin(pl(r,s),s,pd(a1,b1),b1,picp,b1is,t3):is(pl(r,s),s)
+-ivr3
+s@[i:is(r,0)]
+pl01:=realapp2(is(pl(r,s),s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr3"(x,y,t,u,i)):is(pl(r,s),s)
+s@[i:is(s,0)]
+pl02:=tris(real,pl(r,s),pl(s,r),r,compl,pl01(s,r,i)):is(pl(r,s),r)
++*ivr3
+b1is@[p:pos(r)][q:pos(s)]
+t5:=ppd(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(pd(a1,b1))
+t6:=posin(pl(r,s),pd(a1,b1),picp,t5):pos(pl(r,s))
+-ivr3
+s@[p:pos(r)][q:pos(s)]
+pospl:=realapp2(pos(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr3"(x,y,t,u,p,q)):pos(pl(r,s))
++*ivr3
+b1is@[n:neg(r)][o:neg(s)]
+t7:=npd(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):negd(pd(a1,b1))
+t8:=negin(pl(r,s),pd(a1,b1),picp,t7):neg(pl(r,s))
+-ivr3
+s@[n:neg(r)][o:neg(s)]
+negpl:=realapp2(neg(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".ivr3"(x,y,t,u,n,o)):neg(pl(r,s))
+@m0dr:=[x:dif]realof(m0d(x)):[x:dif]real
++*ivr3
+@[a:dif][b:dif][e:eq"rp"(a,b)]
+t5a:=isin(realof(m0d(a)),realof(m0d(b)),m0d(a),m0d(b),innclass(m0d(a)),innclass(m0d(b)),eqm0d(a,b,e)):is(<a>m0dr,<b>m0dr)
+-ivr3
+@fm0dr:=[x:dif][y:dif][t:<y><x>eq]t5a".ivr3"(x,y,t):fixf(real,m0dr)
+r@m0:=indreal(real,m0dr,fm0dr,r):real
++*ivr3
+a0ir@t6a:=isindreal(real,m0dr,fm0dr,r,a0,a0ir):is(realof(m0d(a0)),m0(r))
+-ivr3
+a0ir@micm0:=isp(real,[x:real]inn(m0d(a0),class(x)),realof(m0d(a0)),m0(r),innclass(m0d(a0)),t6a".ivr3"):inn(m0d(a0),class(m0(r)))
+s@[i:is(r,s)]
+ism0:=isf(real,real,[x:real]m0(x),r,s,i):is(m0(r),m0(s))
++*ivr3
+a0ir@[n:neg(r)]
+t7a:=absnd(a0,negex(n)):eq"rp"(absd(a0),m0d(a0))
+t8a:=isin(abs(r),m0(r),absd(a0),m0d(a0),aica,micm0,t7a):is(abs(r),m0(r))
+-ivr3
+r@[n:neg(r)]
+absn:=realapp1(is(abs(r),m0(r)),[x:dif][t:inn(x,class(r))]t8a".ivr3"(x,t,n)):is(abs(r),m0(r))
++*ivr3
+a0ir@[nn:not(neg(r))]
+t9:=absnnd(a0,th3"l.imp"(negd(a0),neg(r),nn,[t:negd(a0)]negin(t))):eq"rp"(absd(a0),a0)
+t10:=isin(abs(r),r,absd(a0),a0,aica,a0ir,t9):is(abs(r),r)
+-ivr3
+r@[nn:not(neg(r))]
+absnn:=realapp1(is(abs(r),r),[x:dif][t:inn(x,class(r))]t10".ivr3"(x,t,nn)):is(abs(r),r)
+r@[p:pos(r)]
+absp:=absnn(r,pnotn(r,p)):is(abs(r),r)
+r@[i:is(r,0)]
+abs0:=tris(real,abs(r),r,0,absnn(r,0notn(r,i)),i):is(abs(r),0)
++3r176
+a0ir@[p:pos(r)]
+t1:=satzd176a(a0,posex(p)):negd(m0d(a0))
+t2:=negin(m0(r),m0d(a0),micm0,t1):neg(m0(r))
+-3r176
+r@[p:pos(r)]
+satz176a:=realapp1(neg(m0(r)),[x:dif][t:inn(x,class(r))]t2".3r176"(x,t,p)):neg(m0(r))
++*3r176
+a0ir@[i:is(r,0)]
+t3:=satzd176b(a0,0ex(i)):zero(m0d(a0))
+t4:=0in(m0(r),m0d(a0),micm0,t3):is(m0(r),0)
+-3r176
+r@[i:is(r,0)]
+satz176b:=realapp1(is(m0(r),0),[x:dif][t:inn(x,class(r))]t4".3r176"(x,t,i)):is(m0(r),0)
++*3r176
+a0ir@[n:neg(r)]
+t5:=satzd176c(a0,negex(n)):posd(m0d(a0))
+t6:=posin(m0(r),m0d(a0),micm0,t5):pos(m0(r))
+-3r176
+r@[n:neg(r)]
+satz176c:=realapp1(pos(m0(r)),[x:dif][t:inn(x,class(r))]t6".3r176"(x,t,n)):pos(m0(r))
++*3r176
+a0ir@[n:neg(m0(r))]
+t7:=satzd176d(a0,negex(m0(r),m0d(a0),micm0,n)):posd(a0)
+t8:=posin(t7):pos(r)
+-3r176
+r@[n:neg(m0(r))]
+satz176d:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t8".3r176"(x,t,n)):pos(r)
++*3r176
+a0ir@[i:is(m0(r),0)]
+t9:=satzd176e(a0,0ex(m0(r),m0d(a0),micm0,i)):zero(a0)
+t10:=0in(t9):is(r,0)
+-3r176
+r@[i:is(m0(r),0)]
+satz176e:=realapp1(is(r,0),[x:dif][t:inn(x,class(r))]t10".3r176"(x,t,i)):is(r,0)
++*3r176
+a0ir@[p:pos(m0(r))]
+t11:=satzd176f(a0,posex(m0(r),m0d(a0),micm0,p)):negd(a0)
+t12:=negin(t11):neg(r)
+-3r176
+r@[p:pos(m0(r))]
+satz176f:=realapp1(neg(r),[x:dif][t:inn(x,class(r))]t12".3r176"(x,t,p)):neg(r)
++3r177
+a0ir@t1:=isin(m0(m0(r)),r,m0d(m0d(a0)),a0,micm0(m0(r),m0d(a0),micm0),a0ir,satzd177(a0)):is(m0(m0(r)),r)
+-3r177
+r@satz177:=realapp1(is(m0(m0(r)),r),[x:dif][t:inn(x,class(r))]t1".3r177"(x,t)):is(m0(m0(r)),r)
+satz177a:=symis(real,m0(m0(r)),r,satz177):is(r,m0(m0(r)))
+s@[i:is(r,m0(s))]
+satz177b:=tris(real,m0(r),m0(m0(s)),s,ism0(r,m0(s),i),satz177(s)):is(m0(r),s)
+satz177c:=symis(real,m0(r),s,satz177b):is(s,m0(r))
+s@[i:is(m0(r),s)]
+satz177d:=satz177c(s,r,symis(real,m0(r),s,i)):is(r,m0(s))
+satz177e:=symis(real,r,m0(s),satz177d):is(m0(s),r)
++3r178
+a0ir@t1:=isin(abs(m0(r)),abs(r),absd(m0d(a0)),absd(a0),aica(m0(r),m0d(a0),micm0),aica,satzd178(a0)):is(abs(m0(r)),abs(r))
+-3r178
+r@satz178:=realapp1(is(abs(m0(r)),abs(r)),[x:dif][t:inn(x,class(r))]t1".3r178"(x,t)):is(abs(m0(r)),abs(r))
+satz178a:=symis(real,abs(m0(r)),abs(r),satz178):is(abs(r),abs(m0(r)))
++3r179
+a0ir@t1:=0in(pl(r,m0(r)),pd(a0,m0d(a0)),picp(r,m0(r),a0,m0d(a0),a0ir,micm0),satzd179(a0)):is(pl(r,m0(r)),0)
+-3r179
+satz179:=realapp1(is(pl(r,m0(r)),0),[x:dif][t:inn(x,class(r))]t1".3r179"(x,t)):is(pl(r,m0(r)),0)
+satz179a:=tris(real,pl(m0(r),r),pl(r,m0(r)),0,compl(m0(r),r),satz179):is(pl(m0(r),r),0)
++3r180
+b1is@t1:=isin(m0(pl(r,s)),pl(m0(r),m0(s)),m0d(pd(a1,b1)),pd(m0d(a1),m0d(b1)),micm0(pl(r,s),pd(a1,b1),picp),picp(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is)),satzd180(a1,b1)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
+-3r180
+s@satz180:=realapp2(is(m0(pl(r,s)),pl(m0(r),m0(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t1".3r180"(x,y,t,u)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
+satz180a:=symis(real,m0(pl(r,s)),pl(m0(r),m0(s)),satz180):is(pl(m0(r),m0(s)),m0(pl(r,s)))
+mn:=pl(r,m0(s)):real
+b1is@micmn:=picp(r,m0(s),a1,m0d(b1),a1ir,micm0(s,b1,b1is)):inn(md(a1,b1),class(mn(r,s)))
+t@[i:is(r,s)]
+ismn1:=ispl1(r,s,m0(t),i):is(mn(r,t),mn(s,t))
+ismn2:=ispl2(m0(r),m0(s),t,ism0(r,s,i)):is(mn(t,r),mn(t,s))
+u@[i:is(r,s)][j:is(t,u)]
+ismn12:=ispl12(r,s,m0(t),m0(u),i,ism0(t,u,j)):is(mn(r,t),mn(s,u))
+s@satz181:=tr3is(real,m0(mn(r,s)),pl(m0(r),m0(m0(s))),pl(m0(r),s),mn(s,r),satz180(r,m0(s)),ispl2(m0(m0(s)),s,m0(r),satz177(s)),compl(m0(r),s)):is(m0(mn(r,s)),mn(s,r))
+satz181a:=symis(real,m0(mn(s,r)),mn(r,s),satz181(s,r)):is(mn(r,s),m0(mn(s,r)))
++3r182
+b1is@[p:pos(mn(r,s))]
+t1:=satzd182a(a1,b1,posex(mn(r,s),md(a1,b1),micmn,p)):mored(a1,b1)
+t2:=morein(t1):more(r,s)
+-3r182
+[p:pos(mn(r,s))]
+satz182a:=realapp2(more(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r182"(x,y,t,u,p)):more(r,s)
++*3r182
+b1is@[i:is(mn(r,s),0)]
+t3:=satzd182b(a1,b1,0ex(mn(r,s),md(a1,b1),micmn,i)):eq"rp"(a1,b1)
+t4:=isin(t3):is(r,s)
+-3r182
+s@[i:is(mn(r,s),0)]
+satz182b:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r182"(x,y,t,u,i)):is(r,s)
++*3r182
+b1is@[n:neg(mn(r,s))]
+t5:=satzd182c(a1,b1,negex(mn(r,s),md(a1,b1),micmn,n)):lessd(a1,b1)
+t6:=lessin(t5):less(r,s)
+-3r182
+s@[n:neg(mn(r,s))]
+satz182c:=realapp2(less(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".3r182"(x,y,t,u,n)):less(r,s)
++*3r182
+b1is@[m:more(r,s)]
+t7:=satzd182d(a1,b1,moreex(m)):posd(md(a1,b1))
+t8:=posin(mn(r,s),md(a1,b1),micmn,t7):pos(mn(r,s))
+-3r182
+s@[m:more(r,s)]
+satz182d:=realapp2(pos(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".3r182"(x,y,t,u,m)):pos(mn(r,s))
++*3r182
+b1is@[i:is(r,s)]
+t9:=satzd182e(a1,b1,isex(i)):zero(md(a1,b1))
+t10:=0in(mn(r,s),md(a1,b1),micmn,t9):is(mn(r,s),0)
+-3r182
+s@[i:is(r,s)]
+satz182e:=realapp2(is(mn(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t10".3r182"(x,y,t,u,i)):is(mn(r,s),0)
++*3r182
+b1is@[l:less(r,s)]
+t11:=satzd182f(a1,b1,lessex(l)):negd(md(a1,b1))
+t12:=negin(mn(r,s),md(a1,b1),micmn,t11):neg(mn(r,s))
+-3r182
+s@[l:less(r,s)]
+satz182f:=realapp2(neg(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t12".3r182"(x,y,t,u,l)):neg(mn(r,s))
++3r183
+b1is@[m:more(r,s)]
+t1:=satzd183a(a1,b1,moreex(m)):lessd(m0d(a1),m0d(b1))
+t2:=lessin(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t1):less(m0(r),m0(s))
+-3r183
+s@[m:more(r,s)]
+satz183a:=realapp2(less(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r183"(x,y,t,u,m)):less(m0(r),m0(s))
+s@[i:is(r,s)]
+satz183b:=ism0(r,s,i):is(m0(r),m0(s))
++*3r183
+b1is@[l:less(r,s)]
+t3:=satzd183c(a1,b1,lessex(l)):mored(m0d(a1),m0d(b1))
+t4:=morein(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t3):more(m0(r),m0(s))
+-3r183
+s@[l:less(r,s)]
+satz183c:=realapp2(more(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r183"(x,y,t,u,l)):more(m0(r),m0(s))
+s@[l:less(m0(r),m0(s))]
+satz183d:=ismore12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183c(m0(r),m0(s),l)):more(r,s)
+s@[i:is(m0(r),m0(s))]
+satz183e:=tr3is(real,r,m0(m0(r)),m0(m0(s)),s,satz177a(r),ism0(m0(r),m0(s),i),satz177(s)):is(r,s)
+s@[m:more(m0(r),m0(s))]
+satz183f:=isless12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183a(m0(r),m0(s),m)):less(r,s)
++3r184
+t@prop1:=and3(pos(s),pos(t),is(r,mn(s,t))):'prop'
+s@prop2:=some([x:real]prop1(x)):'prop'
+r@prop3:=some([x:real]prop2(x)):'prop'
+a0ir@[a:dif][b:dif]
+prop1d:=and3(posd(a),posd(b),eq"rp"(a0,md(a,b))):'prop'
+a@prop2d:=some"l"(dif,[x:dif]prop1d(x)):'prop'
+[p2:prop2d(a)][b:dif][p1:prop1d(a,b)]
+t1:=and3e1(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(a)
+t2:=and3e2(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(b)
+t3:=and3e3(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):eq"rp"(a0,md(a,b))
+p2@ra:=realof(a):real
+p1@rb:=realof(b):real
+t4:=innclass(a):inn(a,class(ra))
+t5:=innclass(b):inn(b,class(rb))
+t6:=isin(r,mn(ra,rb),a0,md(a,b),a0ir,micmn(ra,rb,a,b,t4,t5),t3):is(r,mn(ra,rb))
+t7:=and3i(pos(ra),pos(rb),is(r,mn(ra,rb)),posin(ra,a,t4,t1),posin(rb,b,t5,t2),t6):prop1(ra,rb)
+t8:=somei(real,[x:real]prop1(ra,x),rb,t7):prop2(ra)
+p2@t9:=someapp(dif,[x:dif]prop1d(a,x),p2,prop2(ra),[x:dif][t:prop1d(a,x)]t8(x,t)):prop2(ra)
+t10:=somei(real,[x:real]prop2(x),ra,t9):prop3
+a0ir@t11:=someapp(dif,[x:dif]prop2d(x),satzd184(a0),prop3,[x:dif][t:prop2d(x)]t10(x,t)):prop3
+-3r184
+r@satz184:=realapp1(prop3".3r184",[x:dif][t:inn(x,class(r))]t11".3r184"(x,t)):some([x:real]some([y:real]and3(pos(x),pos(y),is(r,mn(x,y)))))
+u@[a3:dif][b3:dif][c3:dif][d3:dif][a3ir:inn(a3,class(r))][b3is:inn(b3,class(s))][c3it:inn(c3,class(t))][d3iu:inn(d3,class(u))]
++3r185
+t1:=satzd185(a3,b3,c3,d3):eq"rp"(pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)))
+t2:=isin(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)),pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)),picp(mn(r,s),mn(t,u),md(a3,b3),md(c3,d3),micmn(r,s,a3,b3,a3ir,b3is),micmn(t,u,c3,d3,c3it,d3iu)),micmn(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu)),t1):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
+-3r185
+u@satz185:=realapp4(is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u))),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r185"(x,y,z,v,xi,yi,zi,vi)):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
++3r186
+c2it@t1:=satzd186(a2,b2,c2):eq"rp"(pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)))
+t2:=isin(pl(pl(r,s),t),pl(r,pl(s,t)),pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)),picp(pl(r,s),t,pd(a2,b2),c2,picp(r,s,a2,b2,a2ir,b2is),c2it),picp(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),t1):is(pl(pl(r,s),t),pl(r,pl(s,t)))
+-3r186
+t@satz186:=realapp3(is(pl(pl(r,s),t),pl(r,pl(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r186"(x,y,z,u,v,w)):is(pl(pl(r,s),t),pl(r,pl(s,t)))
+asspl1:=satz186:is(pl(pl(r,s),t),pl(r,pl(s,t)))
+asspl2:=symis(real,pl(pl(r,s),t),pl(r,pl(s,t)),satz186):is(pl(r,pl(s,t)),pl(pl(r,s),t))
+s@plmn:=tris(real,pl(mn(r,s),s),pl(r,pl(m0(s),s)),r,asspl1(r,m0(s),s),pl02(r,pl(m0(s),s),satz179a(s))):is(pl(mn(r,s),s),r)
+mnpl:=tris(real,mn(pl(r,s),s),pl(r,pl(s,m0(s))),r,asspl1(r,s,m0(s)),pl02(r,pl(s,m0(s)),satz179(s))):is(mn(pl(r,s),s),r)
+satz187a:=tris(real,pl(s,mn(r,s)),pl(mn(r,s),s),r,compl(s,mn(r,s)),plmn):is(pl(s,mn(r,s)),r)
+satz187b:=somei(real,[x:real]is(pl(s,x),r),mn(r,s),satz187a):some([x:real]is(pl(s,x),r))
+[x:real][i:is(pl(s,x),r)]
+satz187c:=tris(real,mn(r,s),mn(pl(x,s),s),x,ismn1(r,pl(x,s),s,tris1(real,r,pl(x,s),pl(s,x),i,compl(s,x))),mnpl(x,s)):is(mn(r,s),x)
+satz187d:=symis(real,mn(r,s),x,satz187c):is(x,mn(r,s))
+x@[i:is(pl(x,s),r)]
+satz187e:=satz187c(tris(real,pl(s,x),pl(x,s),r,compl(s,x),i)):is(mn(r,s),x)
+satz187f:=symis(real,mn(r,s),x,satz187e):is(x,mn(r,s))
++3r187
+s@[x:real][y:real][i:is(pl(s,x),r)][j:is(pl(s,y),r)]
+t1:=tris1(real,x,y,mn(r,s),satz187c(x,i),satz187c(y,j)):is(x,y)
+s@t2:=[x:real][y:real][t:is(pl(s,x),r)][u:is(pl(s,y),r)]t1(x,y,t,u):amone(real,[x:real]is(pl(s,x),r))
+-3r187
+s@satz187:=onei(real,[x:real]is(pl(s,x),r),t2".3r187",satz187b):one([x:real]is(pl(s,x),r))
++3r188
+c2it@[m:more(pl(r,t),pl(s,t))]
+t1:=satzd188a(a2,b2,c2,moreex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),m)):mored(a2,b2)
+t2:=morein(r,s,a2,b2,a2ir,b2is,t1):more(r,s)
+-3r188
+t@[m:more(pl(r,t),pl(s,t))]
+satz188a:=realapp3(more(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r188"(x,y,z,u,v,w,m)):more(r,s)
++*3r188
+c2it@[i:is(pl(r,t),pl(s,t))]
+t3:=satzd188b(a2,b2,c2,isex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),i)):eq"rp"(a2,b2)
+t4:=isin(r,s,a2,b2,a2ir,b2is,t3):is(r,s)
+-3r188
+t@[i:is(pl(r,t),pl(s,t))]
+satz188b:=realapp3(is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".3r188"(x,y,z,u,v,w,i)):is(r,s)
++*3r188
+c2it@[l:less(pl(r,t),pl(s,t))]
+t5:=satzd188c(a2,b2,c2,lessex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),l)):lessd(a2,b2)
+t6:=lessin(r,s,a2,b2,a2ir,b2is,t5):less(r,s)
+-3r188
+t@[l:less(pl(r,t),pl(s,t))]
+satz188c:=realapp3(less(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t6".3r188"(x,y,z,u,v,w,l)):less(r,s)
++*3r188
+c2it@[m:more(r,s)]
+t7:=satzd188d(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m)):mored(pd(a2,c2),pd(b2,c2))
+t8:=morein(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t7):more(pl(r,t),pl(s,t))
+-3r188
+t@[m:more(r,s)]
+satz188d:=realapp3(more(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t8".3r188"(x,y,z,u,v,w,m)):more(pl(r,t),pl(s,t))
+t@[i:is(r,s)]
+satz188e:=ispl1(r,s,t,i):is(pl(r,t),pl(s,t))
++*3r188
+c2it@[l:less(r,s)]
+t9:=satzd188f(a2,b2,c2,lessex(r,s,a2,b2,a2ir,b2is,l)):lessd(pd(a2,c2),pd(b2,c2))
+t10:=lessin(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t9):less(pl(r,t),pl(s,t))
+-3r188
+t@[l:less(r,s)]
+satz188f:=realapp3(less(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t10".3r188"(x,y,z,u,v,w,l)):less(pl(r,t),pl(s,t))
+t@[m:more(pl(t,r),pl(t,s))]
+satz188g:=satz188a(ismore12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),m)):more(r,s)
+t@[i:is(pl(t,r),pl(t,s))]
+satz188h:=satz188b(tr3is(real,pl(r,t),pl(t,r),pl(t,s),pl(s,t),compl(r,t),i,compl(t,s))):is(r,s)
+t@[l:less(pl(t,r),pl(t,s))]
+satz188j:=satz188c(isless12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),l)):less(r,s)
+t@[m:more(r,s)]
+satz188k:=ismore12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188d(m)):more(pl(t,r),pl(t,s))
+t@[i:is(r,s)]
+satz188l:=ispl2(r,s,t,i):is(pl(t,r),pl(t,s))
+t@[l:less(r,s)]
+satz188m:=isless12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188f(l)):less(pl(t,r),pl(t,s))
+u@[i:is(r,s)][m:more(t,u)]
+satz188n:=ismore2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188k(t,u,r,m)):more(pl(r,t),pl(s,u))
+satz188o:=ismore12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188n):more(pl(t,r),pl(u,s))
+i@[l:less(t,u)]
+satz188p:=isless2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188m(t,u,r,l)):less(pl(r,t),pl(s,u))
+satz188q:=isless12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188p):less(pl(t,r),pl(u,s))
+u@[m:more(r,s)][n:more(t,u)]
+satz189:=trmore(pl(r,t),pl(s,t),pl(s,u),satz188d(m),satz188k(t,u,s,n)):more(pl(r,t),pl(s,u))
+u@[l:less(r,s)][k:less(t,u)]
+satz189a:=lemma1(pl(s,u),pl(r,t),satz189(s,r,u,t,lemma2(r,s,l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
+u@[m:moreis(r,s)][n:more(t,u)]
+satz190a:=orapp(more(r,s),is(r,s),more(pl(r,t),pl(s,u)),m,[v:more(r,s)]satz189(v,n),[v:is(r,s)]satz188n(v,n)):more(pl(r,t),pl(s,u))
+u@[m:more(r,s)][n:moreis(t,u)]
+satz190b:=ismore12(pl(t,r),pl(r,t),pl(u,s),pl(s,u),compl(t,r),compl(u,s),satz190a(t,u,r,s,n,m)):more(pl(r,t),pl(s,u))
+u@[l:lessis(r,s)][k:less(t,u)]
+satz190c:=lemma1(pl(s,u),pl(r,t),satz190a(s,r,u,t,satz168b(l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
+u@[l:less(r,s)][k:lessis(t,u)]
+satz190d:=lemma1(pl(s,u),pl(r,t),satz190b(s,r,u,t,lemma2(l),satz168b(t,u,k))):less(pl(r,t),pl(s,u))
++3r191
+d3iu@[m:moreis(r,s)][n:moreis(t,u)]
+t1:=satzd191(a3,b3,c3,d3,moreisex(r,s,a3,b3,a3ir,b3is,m),moreisex(t,u,c3,d3,c3it,d3iu,n)):moreq(pd(a3,c3),pd(b3,d3))
+t2:=moreisin(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu),t1):moreis(pl(r,t),pl(s,u))
+-3r191
+u@[m:moreis(r,s)][n:moreis(t,u)]
+satz191:=realapp4(moreis(pl(r,t),pl(s,u)),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r191"(x,y,z,v,xi,yi,zi,vi,m,n)):moreis(pl(r,t),pl(s,u))
+u@[l:lessis(r,s)][k:lessis(t,u)]
+satz191a:=satz168a(pl(s,u),pl(r,t),satz191(s,r,u,t,satz168b(l),satz168b(t,u,k))):lessis(pl(r,t),pl(s,u))
+@timesdr:=[x:dif][y:dif]realof(td(x,y)):[x:dif][y:dif]real
++ivr4
+[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
+t1:=isin(realof(td(a,c)),realof(td(b,d)),td(a,c),td(b,d),innclass(td(a,c)),innclass(td(b,d)),eqtd12(a,b,c,d,e,f)):is(<c><a>timesdr,<d><b>timesdr)
+-ivr4
+ftimesdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr4"(x,y,z,v,t,u):fixf2(real,timesdr)
+s@ts:=indreal2(real,timesdr,ftimesdr,r,s):real
++*ivr4
+b1is@t2:=isindreal2(real,timesdr,ftimesdr,r,s,a1,b1,a1ir,b1is):is(realof(td(a1,b1)),ts(r,s))
+-ivr4
+b1is@tict:=isp(real,[x:real]inn(td(a1,b1),class(x)),realof(td(a1,b1)),ts(r,s),innclass(td(a1,b1)),t2".ivr4"):inn(td(a1,b1),class(ts(r,s)))
+t@[i:is(r,s)]
+ists1:=isf(real,real,[x:real]ts(x,t),r,s,i):is(ts(r,t),ts(s,t))
+ists2:=isf(real,real,[x:real]ts(t,x),r,s,i):is(ts(t,r),ts(t,s))
+u@[i:is(r,s)][j:is(t,u)]
+ists12:=tris(real,ts(r,t),ts(s,t),ts(s,u),ists1(i),ists2(t,u,s,j)):is(ts(r,t),ts(s,u))
++4r192
+b1is@[i:is(r,0)]
+t1:=satzd192a(a1,b1,0ex(r,a1,a1ir,i)):zero(td(a1,b1))
+t2:=0in(ts(r,s),td(a1,b1),tict,t1):is(ts(r,s),0)
+-4r192
+s@[i:is(r,0)]
+satz192a:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r192"(x,y,t,u,i)):is(ts(r,s),0)
++*4r192
+b1is@[i:is(s,0)]
+t3:=satzd192b(a1,b1,0ex(s,b1,b1is,i)):zero(td(a1,b1))
+t4:=0in(ts(r,s),td(a1,b1),tict,t3):is(ts(r,s),0)
+-4r192
+s@[i:is(s,0)]
+satz192b:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".4r192"(x,y,t,u,i)):is(ts(r,s),0)
++*4r192
+b1is@[i:is(ts(r,s),0)]
+t5:=satzd192c(a1,b1,0ex(ts(r,s),td(a1,b1),tict,i)):or(zero(a1),zero(b1))
+t6:=th9"l.or"(zero(a1),zero(b1),is(r,0),is(s,0),t5,[t:zero(a1)]0in(r,a1,a1ir,t),[t:zero(b1)]0in(s,b1,b1is,t)):or(is(r,0),is(s,0))
+-4r192
+s@[i:is(ts(r,s),0)]
+satz192c:=realapp2(or(is(r,0),is(s,0)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".4r192"(x,y,t,u,i)):or(is(r,0),is(s,0))
+s@[n:nis(r,0)][o:nis(s,0)]
+satz192d:=th3"l.imp"(is(ts(r,s),0),or(is(r,0),is(s,0)),th3"l.or"(is(r,0),is(s,0),n,o),[t:is(ts(r,s),0)]satz192c(t)):nis(ts(r,s),0)
+s@[i:is(r,0)]
+ts01:=satz192a(i):is(ts(r,s),0)
+s@[i:is(s,0)]
+ts02:=satz192b(i):is(ts(r,s),0)
++4r193
+b1is@t1:=satzd193(a1,b1):eq"rp"(absd(td(a1,b1)),td(absd(a1),absd(b1)))
+t2:=isin(abs(ts(r,s)),ts(abs(r),abs(s)),absd(td(a1,b1)),td(absd(a1),absd(b1)),aica(ts(r,s),td(a1,b1),tict),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(abs(ts(r,s)),ts(abs(r),abs(s)))
+-4r193
+s@satz193:=realapp2(is(abs(ts(r,s)),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r193"(x,y,t,u)):is(abs(ts(r,s)),ts(abs(r),abs(s)))
+satz193a:=symis(real,abs(ts(r,s)),ts(abs(r),abs(s)),satz193):is(ts(abs(r),abs(s)),abs(ts(r,s)))
++4r194
+b1is@t1:=satzd194(a1,b1):eq"rp"(td(a1,b1),td(b1,a1))
+t2:=isin(ts(r,s),ts(s,r),td(a1,b1),td(b1,a1),tict,tict(s,r,b1,a1,b1is,a1ir),t1):is(ts(r,s),ts(s,r))
+-4r194
+satz194:=realapp2(is(ts(r,s),ts(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r194"(x,y,t,u)):is(ts(r,s),ts(s,r))
+comts:=satz194:is(ts(r,s),ts(s,r))
+@1rl:=realof(1df):real
+pos1:=posin(1rl,1df,innclass(1df),posdirp(1rp)):pos(1rl)
+natrl1:=natrli(1):natrl(1rl)
+intrl1:=natintrl(1rl,natrl1):intrl(1rl)
++4r195
+a0ir@t1:=satzd195(a0):eq"rp"(td(a0,1df),a0)
+t2:=isin(ts(r,1rl),r,td(a0,1df),a0,tict(r,1rl,a0,1df,a0ir,innclass(1df)),a0ir,t1):is(ts(r,1rl),r)
+-4r195
+r@satz195:=realapp1(is(ts(r,1rl),r),[x:dif][t:inn(x,class(r))]t2".4r195"(x,t)):is(ts(r,1rl),r)
+satz195a:=symis(real,ts(r,1rl),r,satz195):is(r,ts(r,1rl))
+satz195b:=tris(real,ts(1rl,r),ts(r,1rl),r,comts(1rl,r),satz195):is(ts(1rl,r),r)
+satz195c:=symis(real,ts(1rl,r),r,satz195b):is(r,ts(1rl,r))
+s@[p:pos(r)][q:pos(s)]
+satz196a:=symis(real,ts(abs(r),abs(s)),ts(r,s),ists12(abs(r),r,abs(s),s,absp(r,p),absp(s,q))):is(ts(r,s),ts(abs(r),abs(s)))
++4r196
+b1is@[n:neg(r)][o:neg(s)]
+t1:=satzd196b(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):eq"rp"(td(a1,b1),td(absd(a1),absd(b1)))
+t2:=isin(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(ts(r,s),ts(abs(r),abs(s)))
+-4r196
+s@[n:neg(r)][o:neg(s)]
+satz196b:=realapp2(is(ts(r,s),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r196"(x,y,t,u,n,o)):is(ts(r,s),ts(abs(r),abs(s)))
++*4r196
+b1is@[p:pos(r)][n:neg(s)]
+t1a:=satzd196c(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):eq"rp"(td(a1,b1),m0d(td(absd(a1),absd(b1))))
+t2a:=isin(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),t1a):is(ts(r,s),m0(ts(abs(r),abs(s))))
+-4r196
+s@[p:pos(r)][n:neg(s)]
+satz196c:=realapp2(is(ts(r,s),m0(ts(abs(r),abs(s)))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2a".4r196"(x,y,t,u,p,n)):is(ts(r,s),m0(ts(abs(r),abs(s))))
+s@[n:neg(r)][p:pos(s)]
+satz196d:=tr3is(real,ts(r,s),ts(s,r),m0(ts(abs(s),abs(r))),m0(ts(abs(r),abs(s))),comts(r,s),satz196c(s,r,p,n),ism0(ts(abs(s),abs(r)),ts(abs(r),abs(s)),comts(abs(s),abs(r)))):is(ts(r,s),m0(ts(abs(r),abs(s))))
++*4r196
+a0ir@[n:not(is(r,0))]
+t3:=th3"l.imp"(zero(a0),is(r,0),n,[t:zero(a0)]0in(t)):not(zero(a0))
+b1is@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
+t4:=satzd196e(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),i)):or(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)))
+[a:and(posd(a1),posd(b1))]
+t5:=andi(pos(r),pos(s),posin(r,a1,a1ir,ande1(posd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(posd(a1),posd(b1),a))):and(pos(r),pos(s))
+i@[a:and(negd(a1),negd(b1))]
+t6:=andi(neg(r),neg(s),negin(r,a1,a1ir,ande1(negd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(negd(a1),negd(b1),a))):and(neg(r),neg(s))
+i@t7:=th9"l.or"(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)),and(pos(r),pos(s)),and(neg(r),neg(s)),t4,[t:and(posd(a1),posd(b1))]t5(t),[t:and(negd(a1),negd(b1))]t6(t)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
+-4r196
+s@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
+satz196e:=realapp2(or(and(pos(r),pos(s)),and(neg(r),neg(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
++*4r196
+o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
+t8:=satzd196f(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),i)):or(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)))
+[a:and(posd(a1),negd(b1))]
+t9:=andi(pos(r),neg(s),posin(r,a1,a1ir,ande1(posd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(posd(a1),negd(b1),a))):and(pos(r),neg(s))
+i@[a:and(negd(a1),posd(b1))]
+t10:=andi(neg(r),pos(s),negin(r,a1,a1ir,ande1(negd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(negd(a1),posd(b1),a))):and(neg(r),pos(s))
+i@t11:=th9"l.or"(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)),and(pos(r),neg(s)),and(neg(r),pos(s)),t8,[t:and(posd(a1),negd(b1))]t9(t),[t:and(negd(a1),posd(b1))]t10(t)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
+-4r196
+o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
+satz196f:=realapp2(or(and(pos(r),neg(s)),and(neg(r),pos(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
+s@[p:pos(ts(r,s))]
++*4r196
+p"r"@t12:=th3"l.imp"(is(r,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
+t13:=th3"l.imp"(is(s,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
+t14:=tris1(real,ts(r,s),ts(abs(r),abs(s)),abs(ts(r,s)),absp(ts(r,s),p),satz193(r,s)):is(ts(r,s),ts(abs(r),abs(s)))
+-4r196
+p@satz196g:=satz196e(t12".4r196",t13".4r196",t14".4r196"):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
+s@[n:neg(ts(r,s))]
++*4r196
+n"r"@t15:=th3"l.imp"(is(r,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
+t16:=th3"l.imp"(is(s,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
+t17:=satz177c(ts(abs(r),abs(s)),ts(r,s),tris(real,ts(abs(r),abs(s)),abs(ts(r,s)),m0(ts(r,s)),satz193a(r,s),absn(ts(r,s),n))):is(ts(r,s),m0(ts(abs(r),abs(s))))
+-4r196
+n@satz196h:=satz196f(t15".4r196",t16".4r196",t17".4r196"):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
++4r197
+b1is@t1:=satzd197a(a1,b1):eq"rp"(td(m0d(a1),b1),m0d(td(a1,b1)))
+t2:=isin(ts(m0(r),s),m0(ts(r,s)),td(m0d(a1),b1),m0d(td(a1,b1)),tict(m0(r),s,m0d(a1),b1,micm0(r,a1,a1ir),b1is),micm0(ts(r,s),td(a1,b1),tict),t1):is(ts(m0(r),s),m0(ts(r,s)))
+-4r197
+s@satz197a:=realapp2(is(ts(m0(r),s),m0(ts(r,s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r197"(x,y,t,u)):is(ts(m0(r),s),m0(ts(r,s)))
+satz197b:=tr3is(real,ts(r,m0(s)),ts(m0(s),r),m0(ts(s,r)),m0(ts(r,s)),comts(r,m0(s)),satz197a(s,r),ism0(ts(s,r),ts(r,s),comts(s,r))):is(ts(r,m0(s)),m0(ts(r,s)))
+satz197c:=tris2(real,ts(m0(r),s),ts(r,m0(s)),m0(ts(r,s)),satz197a,satz197b):is(ts(m0(r),s),ts(r,m0(s)))
+satz197d:=symis(real,ts(m0(r),s),ts(r,m0(s)),satz197c):is(ts(r,m0(s)),ts(m0(r),s))
+satz197e:=symis(real,ts(m0(r),s),m0(ts(r,s)),satz197a):is(m0(ts(r,s)),ts(m0(r),s))
+satz197f:=symis(real,ts(r,m0(s)),m0(ts(r,s)),satz197b):is(m0(ts(r,s)),ts(r,m0(s)))
+satz198:=tris(real,ts(m0(r),m0(s)),ts(r,m0(m0(s))),ts(r,s),satz197c(r,m0(s)),ists2(m0(m0(s)),s,r,satz177(s))):is(ts(m0(r),m0(s)),ts(r,s))
+satz198a:=symis(real,ts(m0(r),m0(s)),ts(r,s),satz198):is(ts(r,s),ts(m0(r),m0(s)))
++*ivr4
+b1is@[p:pos(r)][q:pos(s)]
+t3:=ptdpp(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(td(a1,b1))
+t4:=posin(ts(r,s),td(a1,b1),tict,t3):pos(ts(r,s))
+-ivr4
+s@[p:pos(r)][q:pos(s)]
+postspp:=realapp2(pos(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr4"(x,y,t,u,p,q)):pos(ts(r,s))
++*ivr4
+p@[n:neg(s)]
+t5:=ntdpn(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):negd(td(a1,b1))
+t6:=negin(ts(r,s),td(a1,b1),tict,t5):neg(ts(r,s))
+-ivr4
+s@[p:pos(r)][n:neg(s)]
+negtspn:=realapp2(neg(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr4"(x,y,t,u,p,n)):neg(ts(r,s))
+s@[n:neg(r)][p:pos(s)]
+negtsnp:=isneg(ts(s,r),ts(r,s),comts(s,r),negtspn(s,r,p,n)):neg(ts(r,s))
+s@[n:neg(r)][o:neg(s)]
+postsnn:=ispos(ts(m0(r),m0(s)),ts(r,s),satz198,postspp(m0(r),m0(s),satz176c(r,n),satz176c(s,o))):pos(ts(r,s))
+r@[n:nis(r,0)]
+possq:=rapp(r,pos(ts(r,r)),[t:pos(r)]postspp(r,r,t,t),th2"l.imp"(is(r,0),pos(ts(r,r)),n),[t:neg(r)]postsnn(r,r,t,t)):pos(ts(r,r))
+r@nnegsq:=th1"l.imp"(is(r,0),not(neg(ts(r,r))),[t:is(r,0)]0notn(ts(r,r),satz192a(r,r,t)),[t:nis(r,0)]pnotn(ts(r,r),possq(r,t))):not(neg(ts(r,r)))
++4r199
+c2it@t1:=satzd199(a2,b2,c2):eq"rp"(td(td(a2,b2),c2),td(a2,td(b2,c2)))
+t2:=isin(ts(ts(r,s),t),ts(r,ts(s,t)),td(td(a2,b2),c2),td(a2,td(b2,c2)),tict(ts(r,s),t,td(a2,b2),c2,tict(r,s,a2,b2,a2ir,b2is),c2it),tict(r,ts(s,t),a2,td(b2,c2),a2ir,tict(s,t,b2,c2,b2is,c2it)),t1):is(ts(ts(r,s),t),ts(r,ts(s,t)))
+-4r199
+t@satz199:=realapp3(is(ts(ts(r,s),t),ts(r,ts(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r199"(x,y,z,u,v,w)):is(ts(ts(r,s),t),ts(r,ts(s,t)))
+assts1:=satz199:is(ts(ts(r,s),t),ts(r,ts(s,t)))
+assts2:=symis(real,ts(ts(r,s),t),ts(r,ts(s,t)),satz199):is(ts(r,ts(s,t)),ts(ts(r,s),t))
++4r201
+c2it@t1:=satzd201(a2,b2,c2):eq"rp"(td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)))
+t2:=isin(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)),tict(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),picp(ts(r,s),ts(r,t),td(a2,b2),td(a2,c2),tict(r,s,a2,b2,a2ir,b2is),tict(r,t,a2,c2,a2ir,c2it)),t1):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
+-4r201
+satz201:=realapp3(is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r201"(x,y,z,u,v,w)):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
+disttp1:=tr3is(real,ts(pl(r,s),t),ts(t,pl(r,s)),pl(ts(t,r),ts(t,s)),pl(ts(r,t),ts(s,t)),comts(pl(r,s),t),satz201(t,r,s),ispl12(ts(t,r),ts(r,t),ts(t,s),ts(s,t),comts(t,r),comts(t,s))):is(ts(pl(r,s),t),pl(ts(r,t),ts(s,t)))
+disttp2:=satz201:is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
+distpt1:=symis(real,ts(pl(r,s),t),pl(ts(r,t),ts(s,t)),disttp1):is(pl(ts(r,t),ts(s,t)),ts(pl(r,s),t))
+distpt2:=symis(real,ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),disttp2):is(pl(ts(r,s),ts(r,t)),ts(r,pl(s,t)))
+satz202:=tris(real,ts(r,mn(s,t)),pl(ts(r,s),ts(r,m0(t))),mn(ts(r,s),ts(r,t)),disttp2(r,s,m0(t)),ispl2(ts(r,m0(t)),m0(ts(r,t)),ts(r,s),satz197b(r,t))):is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
+disttm1:=tris(real,ts(mn(r,s),t),pl(ts(r,t),ts(m0(s),t)),mn(ts(r,t),ts(s,t)),disttp1(r,m0(s),t),ispl2(ts(m0(s),t),m0(ts(s,t)),ts(r,t),satz197a(s,t))):is(ts(mn(r,s),t),mn(ts(r,t),ts(s,t)))
+disttm2:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
+distmt1:=symis(real,ts(mn(r,s),t),mn(ts(r,t),ts(s,t)),disttm1):is(mn(ts(r,t),ts(s,t)),ts(mn(r,s),t))
+distmt2:=symis(real,ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)),disttm2):is(mn(ts(r,s),ts(r,t)),ts(r,mn(s,t)))
+satz200:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
++4r203
+c2it@[m:more(r,s)][p:pos(t)]
+t1:=satzd203a(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),posex(t,c2,c2it,p)):mored(td(a2,c2),td(b2,c2))
+t2:=morein(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t1):more(ts(r,t),ts(s,t))
+-4r203
+[m:more(r,s)][p:pos(t)]
+satz203a:=realapp3(more(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r203"(x,y,z,u,v,w,m,p)):more(ts(r,t),ts(s,t))
+m@[i:is(t,0)]
+satz203b:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
++*4r203
+m@[n:neg(t)]
+t3:=satzd203c(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),negex(t,c2,c2it,n)):lessd(td(a2,c2),td(b2,c2))
+t4:=lessin(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t3):less(ts(r,t),ts(s,t))
+-4r203
+m@[n:neg(t)]
+satz203c:=realapp3(less(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".4r203"(x,y,z,u,v,w,m,n)):less(ts(r,t),ts(s,t))
+p@satz203d:=ismore12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203a):more(ts(t,r),ts(t,s))
+i@satz203e:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
+n@satz203f:=isless12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203c):less(ts(t,r),ts(t,s))
+t@[l:less(r,s)][p:pos(t)]
+satz203g:=lemma1(ts(s,t),ts(r,t),satz203a(s,r,t,lemma2(r,s,l),p)):less(ts(r,t),ts(s,t))
+l@[i:is(t,0)]
+satz203h:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
+l@[n:neg(t)]
+satz203j:=lemma2(ts(s,t),ts(r,t),satz203c(s,r,t,lemma2(r,s,l),n)):more(ts(r,t),ts(s,t))
+p@satz203k:=lemma1(ts(t,s),ts(t,r),satz203d(s,r,t,lemma2(r,s,l),p)):less(ts(t,r),ts(t,s))
+i@satz203l:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
+n@satz203m:=lemma2(ts(t,s),ts(t,r),satz203f(s,r,t,lemma2(r,s,l),n)):more(ts(t,r),ts(t,s))
++4r204
+a0ir@[n1:nis(r,0)]
+t1:=th3"l.imp"(zero(a0),is(r,0),n1,[t:zero(a0)]0in(t)):not(zero(a0))
+d3iu@[n1:nis(s,0)][i:is(ts(s,t),r)][j:is(ts(s,u),r)]
+t2:=satzd204b(a3,b3,t1(s,b3,b3is,n1),c3,d3,isex(ts(s,t),r,td(b3,c3),a3,tict(s,t,b3,c3,b3is,c3it),a3ir,i),isex(ts(s,u),r,td(b3,d3),a3,tict(s,u,b3,d3,b3is,d3iu),a3ir,j)):eq"rp"(c3,d3)
+t3:=isin(t,u,c3,d3,c3it,d3iu,t2):is(t,u)
+-4r204
+s@[n:nis(s,0)][x:real][y:real][i:is(ts(s,x),r)][j:is(ts(s,y),r)]
+satz204b:=realapp4(x,y,is(x,y),[z:dif][u:dif][v:dif][w:dif][zi:inn(z,class(r))][ui:inn(u,class(s))][vi:inn(v,class(x))][wi:inn(w,class(y))]t3".4r204"(x,y,z,u,v,w,zi,ui,vi,wi,n,i,j)):is(x,y)
++*4r204
+b1is@[n1:nis(s,0)]
+t4:=satzd204a(a1,b1,t1(s,b1,b1is,n1)):some"l"(dif,[x:dif]eq"rp"(td(b1,x),a1))
+[a:dif][e:eq"rp"(td(b1,a),a1)]
+ar:=realof(a):real
+t5:=isin(ts(s,ar),r,td(b1,a),a1,tict(s,ar,b1,a,b1is,innclass(a)),a1ir,e):is(ts(s,ar),r)
+t6:=somei(real,[x:real]is(ts(s,x),r),ar,t5):some([x:real]is(ts(s,x),r))
+n1@t7:=someapp(dif,[x:dif]eq"rp"(td(b1,x),a1),t4,some([x:real]is(ts(s,x),r)),[x:dif][t:eq"rp"(td(b1,x),a1)]t6(x,t)):some([x:real]is(ts(s,x),r))
+-4r204
+n@satz204a:=realapp2(some([x:real]is(ts(s,x),r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r204"(x,y,t,u,n)):some([x:real]is(ts(s,x),r))
+satz204:=onei(real,[x:real]is(ts(s,x),r),[x:real][y:real][t:is(ts(s,x),r)][u:is(ts(s,y),r)]satz204b(x,y,t,u),satz204a):one([x:real]is(ts(s,x),r))
+ov:=ind(real,[x:real]is(ts(s,x),r),satz204):real
+satz204c:=oneax(real,[x:real]is(ts(s,x),r),satz204):is(ts(s,ov(r,s,n)),r)
+satz204d:=symis(real,ts(s,ov(r,s,n)),r,satz204c):is(r,ts(s,ov(r,s,n)))
+satz204e:=tris(real,ts(ov(r,s,n),s),ts(s,ov(r,s,n)),r,comts(ov(r,s,n),s),satz204c):is(ts(ov(r,s,n),s),r)
+satz204f:=symis(real,ts(ov(r,s,n),s),r,satz204e):is(r,ts(ov(r,s,n),s))
+s@[x:real][n:nis(s,0)][i:is(ts(s,x),r)]
+satz204g:=satz204b(n,x,ov(r,s,n),i,satz204c(n)):is(x,ov(r,s,n))
+s@[n:nis(s,0)][p:pos(r)][q:pos(s)]
++*4r204
+n@ros:=ov(r,s,n):real
+p@t8:=ispos(r,ts(s,ros),satz204d(n),p):pos(ts(s,ros))
+q@t9:=th1"l.and"(neg(s),neg(ros),pnotn(s,q)):not(and(neg(s),neg(ros)))
+t10:=ore1(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t9):and(pos(s),pos(ros))
+-4r204
+q@posovpp:=ande2(pos(s),pos(ov(r,s,n)),t10".4r204"):pos(ov(r,s,n))
+p@[m:neg(s)]
++*4r204
+m@t11:=th1"l.and"(pos(s),pos(ros),nnotp(s,m)):not(and(pos(s),pos(ros)))
+t12:=ore2(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t11):and(neg(s),neg(ros))
+-4r204
+m@negovpn:=ande2(neg(s),neg(ov(r,s,n)),t12".4r204"):neg(ov(r,s,n))
+n@[m:neg(r)][p:pos(s)]
++*4r204
+m@t13:=isneg(r,ts(s,ros),satz204d(n),m):neg(ts(s,ros))
+p@t14:=th1"l.and"(neg(s),pos(ros),pnotn(s,p)):not(and(neg(s),pos(ros)))
+t15:=ore1(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t14):and(pos(s),neg(ros))
+-4r204
+p@negovnp:=ande2(pos(s),neg(ov(r,s,n)),t15".4r204"):neg(ov(r,s,n))
+m@[l:neg(s)]
++*4r204
+l@t16:=th1"l.and"(pos(s),neg(ros),nnotp(s,l)):not(and(pos(s),neg(ros)))
+t17:=ore2(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t16):and(neg(s),pos(ros))
+-4r204
+l@posovnn:=ande2(neg(s),pos(ov(r,s,n)),t17".4r204"):pos(ov(r,s,n))
+@[r0:cut][s0:cut][m:more"rp"(r0,s0)]
+morerpep:=morein(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),morerpepd(r0,s0,m)):more(pofrp(r0),pofrp(s0))
+s0@[m:more(pofrp(r0),pofrp(s0))]
+morerpip:=morerpipd(r0,s0,moreex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),m)):more"rp"(r0,s0)
+s0@[l:less"rp"(r0,s0)]
+lessrpep:=lemma1(pofrp(s0),pofrp(r0),morerpep(s0,r0,satz122(r0,s0,l))):less(pofrp(r0),pofrp(s0))
+s0@[l:less(pofrp(r0),pofrp(s0))]
+lessrpip:=satz121(s0,r0,morerpip(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
+s@[p:pos(r)][q:pos(s)][m:more(r,s)]
+q@[m:more(r,s)]
++ivr5
+t1:=ismore12(r,pofrp(rpofp(r,p)),s,pofrp(rpofp(s,q)),isprp1(r,p),isprp1(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
+-ivr5
+moreperp:=morerpip(rpofp(r,p),rpofp(s,q),t1".ivr5"):more"rp"(rpofp(r,p),rpofp(s,q))
+q@[m:more"rp"(rpofp(r,p),rpofp(s,q))]
++*ivr5
+m@t2:=morerpep(rpofp(r,p),rpofp(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
+-ivr5
+m@morepirp:=ismore12(pofrp(rpofp(r,p)),r,pofrp(rpofp(s,q)),s,isprp2(r,p),isprp2(s,q),t2".ivr5"):more(r,s)
+q@[l:less(r,s)]
+lessperp:=satz121(rpofp(s,q),rpofp(r,p),moreperp(s,r,q,p,lemma2(r,s,l))):less"rp"(rpofp(r,p),rpofp(s,q))
+q@[l:less"rp"(rpofp(r,p),rpofp(s,q))]
+lesspirp:=lemma1(s,r,morepirp(s,r,q,p,satz122(rpofp(r,p),rpofp(s,q),l))):less(r,s)
+r@s01:=setof(real,[x:real]lessis(x,r)):set(real)
+s02:=setof(real,[x:real]more(x,r)):set(real)
++5r205
+s@[n:not(in(s,s01))]
+t1:=th3"l.imp"(lessis(s,r),in(s,s01),n,[t:lessis(s,r)]estii(real,[x:real]lessis(x,r),s,t)):not(lessis(s,r))
+t2:=estii(real,[x:real]more(x,r),s,satz167k(s,r,t1)):in(s,s02)
+-5r205
+vb00:=[x:real][t:not(in(x,s01))]t2".5r205"(x,t):all([x:real]or(in(x,s01),in(x,s02)))
++*5r205
+r@t3:=estii(real,[x:real]lessis(x,r),r,lessisi2(r,r,refis(real,r))):in(r,s01)
+-5r205
+r@vb01a:=nonemptyi(real,s01,r,t3".5r205"):nonempty(real,s01)
++*5r205
+r@t4:=ismore2(pl(r,0),r,pl(r,1rl),pl02(r,0,refis(real,0)),satz188k(1rl,0,r,satz169a(1rl,pos1))):more(pl(r,1rl),r)
+t5:=estii(real,[x:real]more(x,r),pl(r,1rl),t4):in(pl(r,1rl),s02)
+-5r205
+r@vb01b:=nonemptyi(real,s02,pl(r,1rl),t5".5r205"):nonempty(real,s02)
++*5r205
+s@[i:in(s,s01)][t:real][j:in(t,s02)]
+t6:=satz172a(s,r,t,estie(real,[x:real]lessis(x,r),s,i),lemma1(t,r,estie(real,[x:real]more(x,r),t,j))):less(s,t)
+-5r205
+r@vb02:=[x:real][t:in(x,s01)][y:real][u:in(y,s02)]t6".5r205"(x,t,y,u):all([x:real][t:in(x,s01)]all([y:real][u:in(y,s02)]less(x,y)))
+s@[l:less(s,r)]
+vb03a:=estii(real,[x:real]lessis(x,r),s,lessisi1(s,r,l)):in(s,s01)
+s@[m:more(s,r)]
+vb03b:=estii(real,[x:real]more(x,r),s,m):in(s,s02)
+r@s11:=setof(real,[x:real]less(x,r)):set(real)
+s12:=setof(real,[x:real]moreis(x,r)):set(real)
++*5r205
+s@[n:not(in(s,s11))]
+t7:=th3"l.imp"(less(s,r),in(s,s11),n,[t:less(s,r)]estii(real,[x:real]less(x,r),s,t)):not(less(s,r))
+t8:=estii(real,[x:real]moreis(x,r),s,satz167f(s,r,t7)):in(s,s12)
+-5r205
+r@vb10:=[x:real][t:not(in(x,s11))]t8".5r205"(x,t):all([x:real]or(in(x,s11),in(x,s12)))
++*5r205
+r@t9:=isless2(pl(r,0),r,mn(r,1rl),pl02(r,0,refis(real,0)),satz188m(m0(1rl),0,r,satz169c(m0(1rl),satz176a(1rl,pos1)))):less(mn(r,1rl),r)
+t10:=estii(real,[x:real]less(x,r),mn(r,1rl),t9):in(mn(r,1rl),s11)
+-5r205
+r@vb11a:=nonemptyi(real,s11,mn(r,1rl),t10".5r205"):nonempty(real,s11)
++*5r205
+r@t11:=estii(real,[x:real]moreis(x,r),r,moreisi2(r,r,refis(real,r))):in(r,s12)
+-5r205
+r@vb11b:=nonemptyi(real,s12,r,t11".5r205"):nonempty(real,s12)
++*5r205
+s@[i:in(s,s11)][t:real][j:in(t,s12)]
+t12:=satz172b(s,r,t,estie(real,[x:real]less(x,r),s,i),satz168a(t,r,estie(real,[x:real]moreis(x,r),t,j))):less(s,t)
+-5r205
+r@vb12:=[x:real][t:in(x,s11)][y:real][u:in(y,s12)]t12".5r205"(x,t,y,u):all([x:real][t:in(x,s11)]all([y:real][u:in(y,s12)]less(x,y)))
+s@[l:less(s,r)]
+vb13a:=estii(real,[x:real]less(x,r),s,l):in(s,s11)
+s@[m:more(s,r)]
+vb13b:=estii(real,[x:real]moreis(x,r),s,moreisi1(s,r,m)):in(s,s12)
+@2rl:=pl(1rl,1rl):real
+pos2:=pospl(1rl,1rl,pos1,pos1):pos(2rl)
+half:=ov(1rl,2rl,pnot0(2rl,pos2)):real
+poshalf:=posovpp(1rl,2rl,pnot0(2rl,pos2),pos1,pos2):pos(half)
++*ivr5
+r@t3:=tris(real,pl(r,r),pl(ts(1rl,r),ts(1rl,r)),ts(2rl,r),ispl12(r,ts(1rl,r),r,ts(1rl,r),satz195c(r),satz195c(r)),distpt1(1rl,1rl,r)):is(pl(r,r),ts(2rl,r))
+t4:=tr4is(real,ts(half,pl(r,r)),ts(half,ts(2rl,r)),ts(ts(half,2rl),r),ts(1rl,r),r,ists2(pl(r,r),ts(2rl,r),half,t3),assts2(half,2rl,r),ists1(ts(half,2rl),1rl,r,satz204e(1rl,2rl,pnot0(2rl,pos2))),satz195b(r)):is(ts(half,pl(r,r)),r)
+-ivr5
+s@[l:less(r,s)]
++*ivr5
+l@t5:=satz203k(pl(r,r),pl(r,s),half,satz188m(r,s,r,l),poshalf):less(ts(half,pl(r,r)),ts(half,pl(r,s)))
+-ivr5
+l@lemma3:=isless1(ts(half,pl(r,r)),r,ts(half,pl(r,s)),t4".ivr5",t5".ivr5"):less(r,ts(half,pl(r,s)))
++*ivr5
+l@t6:=satz203k(pl(r,s),pl(s,s),half,satz188f(r,s,s,l),poshalf):less(ts(half,pl(r,s)),ts(half,pl(s,s)))
+-ivr5
+l@lemma4:=isless2(ts(half,pl(s,s)),s,ts(half,pl(r,s)),t4".ivr5"(s),t6".ivr5"):less(ts(half,pl(r,s)),s)
+[p:pos(r)]
+lemma5:=satz169b(s,trmore(s,r,0,lemma2(r,s,l),satz169a(r,p))):pos(s)
+@[s1:set(real)][s2:set(real)][p0:all([x:real]or(in(x,s1),in(x,s2)))][p1a:nonempty(real,s1)][p1b:nonempty(real,s2)][p2:all([x:real][t:in(x,s1)]all([y:real][u:in(y,s2)]less(x,y)))]
++*5r205
+s2@[r:real]
+prop1:=all([x:real][t:less(x,r)]in(x,s1)):'prop'
+prop2:=all([x:real][t:more(x,r)]in(x,s2)):'prop'
+prop3:=and(prop1,prop2):'prop'
+p2@[x:real][y:real][px:prop3(x)][py:prop3(y)][l:less(x,y)]
+mxy:=ts(half,pl(x,y)):real
+t13:=lemma2(x,mxy,lemma3(x,y,l)):more(mxy,x)
+t14:=lemma4(x,y,l):less(mxy,y)
+t15:=<t14><mxy>ande1(prop1(y),prop2(y),py):in(mxy,s1)
+t16:=<t13><mxy>ande2(prop1(x),prop2(x),px):in(mxy,s2)
+t17:=<t16><mxy><t15><mxy>p2:less(mxy,mxy)
+t18:=<refis(real,mxy)>ec3e31(is(mxy,mxy),more(mxy,mxy),less(mxy,mxy),satz167b(mxy,mxy),t17):con
+py@t19:=[t:less(x,y)]t18(t):not(less(x,y))
+t20:=[t:more(x,y)]t18(y,x,py,px,lemma1(x,y,t)):not(more(x,y))
+t21:=or3e1(is(x,y),more(x,y),less(x,y),satz167a(x,y),t20,t19):is(x,y)
+p2@t22:=[x:real][y:real][t:prop3(x)][u:prop3(y)]t21(x,y,t,u):amone(real,[x:real]prop3(x))
+[case1:some([x:real]and(pos(x),in(x,s1)))][r:real][a:and(pos(r),in(r,s1))]
+t23:=ande1(pos(r),in(r,s1),a):pos(r)
+t24:=ande2(pos(r),in(r,s1),a):in(r,s1)
+sc1:=setof(cut,[x:cut]in(pofrp(x),s1)):set(cut)
+sc2:=setof(cut,[x:cut]in(pofrp(x),s2)):set(cut)
+[r0:cut][i:in(pofrp(r0),s1)]
+t25:=estii(cut,[x:cut]in(pofrp(x),s1),r0,i):in"rp"(r0,sc1)
+r0@[i:in"rp"(r0,sc1)]
+t26:=estie(cut,[x:cut]in(pofrp(x),s1),r0,i):in(pofrp(r0),s1)
+r0@[i:in(pofrp(r0),s2)]
+t27:=estii(cut,[x:cut]in(pofrp(x),s2),r0,i):in"rp"(r0,sc2)
+r0@[i:in"rp"(r0,sc2)]
+t28:=estie(cut,[x:cut]in(pofrp(x),s2),r0,i):in(pofrp(r0),s2)
+r0@t29:=th9"l.or"(in(pofrp(r0),s1),in(pofrp(r0),s2),in"rp"(r0,sc1),in"rp"(r0,sc2),<pofrp(r0)>p0,[t:in(pofrp(r0),s1)]t25(t),[t:in(pofrp(r0),s2)]t27(t)):or(in"rp"(r0,sc1),in"rp"(r0,sc2))
+a@pr1:=rpofp(r,t23):cut
+t30:=isp(real,[x:real]in(x,s1),r,pofrp(pr1),t24,isprp1(r,t23)):in(pofrp(pr1),s1)
+t31:=nonemptyi(cut,sc1,pr1,t25(pr1,t30)):nonempty(cut,sc1)
+[s:real][i:in(s,s2)]
+t32:=<i><s><t24><r>p2:less(r,s)
+t33:=lemma5(r,s,t32,t23):pos(s)
+ps1:=rpofp(s,t33):cut
+t34:=isp(real,[x:real]in(x,s2),s,pofrp(ps1),i,isprp1(s,t33)):in(pofrp(ps1),s2)
+t35:=nonemptyi(cut,sc2,ps1,t27(ps1,t34)):nonempty(cut,sc2)
+a@t36:=nonemptyapp(real,s2,p1b,nonempty(cut,sc2),[x:real][t:in(x,s2)]t35(x,t)):nonempty(cut,sc2)
+r0@[i:in"rp"(r0,sc1)][s0:cut][j:in"rp"(s0,sc2)]
+t37:=<t28(s0,j)><pofrp(s0)><t26(r0,i)><pofrp(r0)>p2:less(pofrp(r0),pofrp(s0))
+t38:=lessrpip(r0,s0,t37):less"rp"(r0,s0)
+a@stc:=schnitt(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):cut
+t39:=satzp205a(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:less"rp"(x,stc)]in"rp"(x,sc1))
+t40:=satzp205b(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:more"rp"(x,stc)]in"rp"(x,sc2))
+stp:=pofrp(stc):real
+t41:=posi(stc):pos(stp)
+[s:real][l:less(s,stp)][p:pos(s)]
+ps2:=rpofp(s,p):cut
+t42:=lessrpip(ps2,stc,isless1(s,pofrp(ps2),stp,isprp1(s,p),l)):less"rp"(ps2,stc)
+t43:=<t42><ps2>t39:in"rp"(ps2,sc1)
+t44:=isp(real,[x:real]in(x,s1),pofrp(ps2),s,t26(ps2,t43),isprp2(s,p)):in(s,s1)
+l@[n:not(pos(s))][i:in(s,s2)]
+t45:=<i><s><t24><r>p2:less(r,s)
+t46:=<lemma5(r,s,t45,t23)>n:con
+n@t47:=ore1(in(s,s1),in(s,s2),<s>p0,[t:in(s,s2)]t46(t)):in(s,s1)
+l@t48:=th1"l.imp"(pos(s),in(s,s1),[t:pos(s)]t44(t),[t:not(pos(s))]t47(t)):in(s,s1)
+s@[m:more(s,stp)]
+t49:=lemma5(stp,s,lemma1(s,stp,m),t41):pos(s)
+ps3:=rpofp(s,t49):cut
+t50:=morerpip(ps3,stc,ismore1(s,pofrp(ps3),stp,isprp1(s,t49),m)):more"rp"(ps3,stc)
+t51:=<t50><ps3>t40:in"rp"(ps3,sc2)
+t52:=isp(real,[x:real]in(x,s2),pofrp(ps3),s,t28(ps3,t51),isprp2(s,t49)):in(s,s2)
+a@t53:=andi(prop1(stp),prop2(stp),[x:real][t:less(x,stp)]t48(x,t),[x:real][t:more(x,stp)]t52(x,t)):prop3(stp)
+t54:=somei(real,[x:real]prop3(x),stp,t53):some([x:real]prop3(x))
+case1@t55:=someapp(real,[x:real]and(pos(x),in(x,s1)),case1,some([x:real]prop3(x)),[x:real][t:and(pos(x),in(x,s1))]t54(x,t)):some([x:real]prop3(x))
+p2@[case2:some([x:real]and(neg(x),in(x,s2)))]
+sp1:=setof(real,[x:real]in(m0(x),s1)):set(real)
+sp2:=setof(real,[x:real]in(m0(x),s2)):set(real)
+[r:real][i:in(m0(r),s1)]
+t56:=estii(real,[x:real]in(m0(x),s1),r,i):in(r,sp1)
+r@[i:in(r,sp1)]
+t57:=estie(real,[x:real]in(m0(x),s1),r,i):in(m0(r),s1)
+r@[i:in(m0(r),s2)]
+t58:=estii(real,[x:real]in(m0(x),s2),r,i):in(r,sp2)
+r@[i:in(r,sp2)]
+t59:=estie(real,[x:real]in(m0(x),s2),r,i):in(m0(r),s2)
+r@t60:=comor(in(r,sp1),in(r,sp2),th9"l.or"(in(m0(r),s1),in(m0(r),s2),in(r,sp1),in(r,sp2),<m0(r)>p0,[t:in(m0(r),s1)]t56(t),[t:in(m0(r),s2)]t58(t))):or(in(r,sp2),in(r,sp1))
+[i:in(r,s2)]
+t61:=t58(m0(r),isp(real,[x:real]in(x,s2),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp2)
+t62:=nonemptyi(real,sp2,m0(r),t61):nonempty(real,sp2)
+case2@t63:=nonemptyapp(real,s2,p1b,nonempty(real,sp2),[x:real][t:in(x,s2)]t62(x,t)):nonempty(real,sp2)
+r@[i:in(r,s1)]
+t64:=t56(m0(r),isp(real,[x:real]in(x,s1),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp1)
+t65:=nonemptyi(real,sp1,m0(r),t64):nonempty(real,sp1)
+case2@t66:=nonemptyapp(real,s1,p1a,nonempty(real,sp1),[x:real][t:in(x,s1)]t65(x,t)):nonempty(real,sp1)
+r@[i:in(r,sp2)][s:real][j:in(s,sp1)]
+t67:=<t59(r,i)><m0(r)><t57(s,j)><m0(s)>p2:less(m0(s),m0(r))
+t68:=lemma1(s,r,satz183d(s,r,t67)):less(r,s)
+r@[a:and(neg(r),in(r,s2))]
+t69:=satz176c(r,ande1(neg(r),in(r,s2),a)):pos(m0(r))
+t70:=isp(real,[x:real]in(x,s2),r,m0(m0(r)),ande2(neg(r),in(r,s2),a),satz177a(r)):in(m0(m0(r)),s2)
+t71:=andi(pos(m0(r)),in(m0(r),sp2),t69,t58(m0(r),t70)):and(pos(m0(r)),in(m0(r),sp2))
+t72:=somei(real,[x:real]and(pos(x),in(x,sp2)),m0(r),t71):some([x:real]and(pos(x),in(x,sp2)))
+case2@t73:=someapp(real,[x:real]and(neg(x),in(x,s2)),case2,some([x:real]and(pos(x),in(x,sp2))),[x:real][t:and(neg(x),in(x,s2))]t72(x,t)):some([x:real]and(pos(x),in(x,sp2)))
+t74:=t55(sp2,sp1,[x:real]t60(x),t63,t66,[x:real][t:in(x,sp2)][y:real][u:in(y,sp1)]t68(x,t,y,u),t73):some([x:real]prop3(sp2,sp1,x))
+[r:real][p:prop3(sp2,sp1,r)][s:real][l:less(s,m0(r))]
+t75:=ismore2(m0(m0(r)),r,m0(s),satz177(r),satz183c(s,m0(r),l)):more(m0(s),r)
+t76:=<t75><m0(s)>ande2(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp1)
+t77:=isp(real,[x:real]in(x,s1),m0(m0(s)),s,t57(m0(s),t76),satz177(s)):in(s,s1)
+s@[m:more(s,m0(r))]
+t78:=isless2(m0(m0(r)),r,m0(s),satz177(r),satz183a(s,m0(r),m)):less(m0(s),r)
+t79:=<t78><m0(s)>ande1(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp2)
+t80:=isp(real,[x:real]in(x,s2),m0(m0(s)),s,t59(m0(s),t79),satz177(s)):in(s,s2)
+p@t81:=andi(prop1(m0(r)),prop2(m0(r)),[x:real][t:less(x,m0(r))]t77(x,t),[x:real][t:more(x,m0(r))]t80(x,t)):prop3(m0(r))
+t82:=somei(real,[x:real]prop3(x),m0(r),t81):some([x:real]prop3(x))
+case2@t83:=someapp(real,[x:real]prop3(sp2,sp1,x),t74,some([x:real]prop3(x)),[x:real][t:prop3(sp2,sp1,x)]t82(x,t)):some([x:real]prop3(x))
+p2@[notcase1:not(some([x:real]and(pos(x),in(x,s1))))][notcase2:not(some([x:real]and(neg(x),in(x,s2))))][r:real][l:less(r,0)]
+t84:=th4"l.some"(real,[x:real]and(neg(x),in(x,s2)),notcase2,r):not(and(neg(r),in(r,s2)))
+t85:=th3"l.and"(neg(r),in(r,s2),t84,satz169d(r,l)):not(in(r,s2))
+t86:=ore1(in(r,s1),in(r,s2),<r>p0,t85):in(r,s1)
+r@[m:more(r,0)]
+t87:=th4"l.some"(real,[x:real]and(pos(x),in(x,s1)),notcase1,r):not(and(pos(r),in(r,s1)))
+t88:=th3"l.and"(pos(r),in(r,s1),t87,satz169b(r,m)):not(in(r,s1))
+t89:=ore2(in(r,s1),in(r,s2),<r>p0,t88):in(r,s2)
+notcase2@t90:=andi(prop1(0),prop2(0),[x:real][t:less(x,0)]t86(x,t),[x:real][t:more(x,0)]t89(x,t)):prop3(0)
+t91:=somei(real,[x:real]prop3(x),0,t90):some([x:real]prop3(x))
+notcase1@t92:=th1"l.imp"(some([x:real]and(neg(x),in(x,s2))),some([x:real]prop3(x)),[t:some([x:real]and(neg(x),in(x,s2)))]t83(t),[t:not(some([x:real]and(neg(x),in(x,s2))))]t91(t)):some([x:real]prop3(x))
+p2@t93:=th1"l.imp"(some([x:real]and(pos(x),in(x,s1))),some([x:real]prop3(x)),[t:some([x:real]and(pos(x),in(x,s1)))]t55(t),[t:not(some([x:real]and(pos(x),in(x,s1))))]t92(t)):some([x:real]prop3(x))
+t94:=onei(real,[x:real]prop3(x),t22,t93):one([x:real]prop3(x))
+-5r205
+p2@satz205:=t94".5r205":one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
+dedekind:=satz205:one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
+schnitt:=ind(real,[x:real]prop3".5r205"(x),satz205):real
+[r:real][l:less(r,schnitt)]
+satz205a:=<l><r>ande1(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s1)
+r@[m:more(r,schnitt)]
+satz205b:=<m><r>ande2(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s2)
+@[r0:cut][s0:cut]
++iva
+dr:=pdofrp(r0):dif
+ds:=pdofrp(s0):dif
+t1:=lemmaivad1(r0,s0):eq"rp"(pd(dr,ds),pdofrp(pl"rp"(r0,s0)))
+-iva
+lemmaiva1:=isin(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)),pd(pdofrp(r0),pdofrp(s0)),pdofrp(pl"rp"(r0,s0)),picp(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(pl"rp"(r0,s0))),t1".iva"):is(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)))
++*iva
+s0@t2:=lemmaivad2(r0,s0):eq"rp"(td(dr,ds),pdofrp(ts"rp"(r0,s0)))
+-iva
+s0@lemmaiva2:=isin(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)),td(pdofrp(r0),pdofrp(s0)),pdofrp(ts"rp"(r0,s0)),tict(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(ts"rp"(r0,s0))),t2".iva"):is(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)))
+[m:more(pofrp(r0),pofrp(s0))]
++*iva
+m@t3:=moreex(pofrp(r0),pofrp(s0),dr,ds,innclass(dr),innclass(ds),m):mored(dr,ds)
+-iva
+m@lemmaiva3:=lemmaivad3(r0,s0,t3".iva"):more"rp"(r0,s0)
+s0@[m:more"rp"(r0,s0)]
++*iva
+m@[l:less(pofrp(r0),pofrp(s0))]
+t4:=satz121(s0,r0,lemmaiva3(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
+m@t5:=ec3e23(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):not(less"rp"(r0,s0))
+t6:=th3"l.imp"(less(pofrp(r0),pofrp(s0)),less"rp"(r0,s0),t5,[t:less(pofrp(r0),pofrp(s0))]t4(t)):not(less(pofrp(r0),pofrp(s0)))
+t7:=ec3e21(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):nis"rp"(r0,s0)
+t8:=th3"l.imp"(is(pofrp(r0),pofrp(s0)),is"rp"(r0,s0),t7,[t:is(pofrp(r0),pofrp(s0))]isrpip(r0,s0,t)):nis(pofrp(r0),pofrp(s0))
+-iva
+m@lemmaiva4:=or3e2(is(pofrp(r0),pofrp(s0)),more(pofrp(r0),pofrp(s0)),less(pofrp(r0),pofrp(s0)),satz167a(pofrp(r0),pofrp(s0)),t6".iva",t8".iva"):more(pofrp(r0),pofrp(s0))
+@[x:nat][y:nat][m:more(rlofnt(x),rlofnt(y))]
++*iva
+m@t9:=lemmaiva3(rpofnt(x),rpofnt(y),m):more"rp"(rpofnt(x),rpofnt(y))
+t10:=satz154d(rtofn(x),rtofn(y),t9):more"rt"(rtofn(x),rtofn(y))
+t11:=moree"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t10):moref(fr(x,1),fr(y,1))
+-iva
+m@lemmaiva5:=satz111a(x,y,t11".iva"):more"n"(x,y)
+y@[m:more"n"(x,y)]
++*iva
+m@t12:=satz111d(x,y,m):moref(fr(x,1),fr(y,1))
+t13:=morei"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t12):more"rt"(rtofn(x),rtofn(y))
+t14:=satz154a(rtofn(x),rtofn(y),t13):more"rp"(rpofnt(x),rpofnt(y))
+-iva
+m@lemmaiva6:=lemmaiva4(rpofnt(x),rpofnt(y),t14".iva"):more(rlofnt(x),rlofnt(y))
+@[r:real]
++int
+a0ir@[i:intrl(r)]
+t1:=intabsd(a0,intrlex(r,a0,a0ir,i)):intd(absd(a0))
+t2:=intrlin(abs(r),absd(a0),aica,t1):intrl(abs(r))
+-int
+[i:intrl(r)]
+intabs:=realapp1(r,intrl(abs(r)),[x:dif][t:inn(x,class(r))]t2".int"(r,x,t,i)):intrl(abs(r))
++*int
+i@t3:=intm0d(a0,intrlex(r,a0,a0ir,i)):intd(m0d(a0))
+t4:=intrlin(m0(r),m0d(a0),micm0,t3):intrl(m0(r))
+-int
+i@intm0:=realapp1(r,intrl(m0(r)),[x:dif][t:inn(x,class(r))]t4".int"(r,x,t,i)):intrl(m0(r))
++*int
+b1is@[i:intrl(r)][j:intrl(s)]
+t5:=intpd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(pd(a1,b1))
+t6:=intrlin(pl(r,s),pd(a1,b1),picp,t5):intrl(pl(r,s))
+-int
+i@[s:real][j:intrl(s)]
+intpl:=realapp2(r,s,intrl(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".int"(r,s,x,y,t,u,i,j)):intrl(pl(r,s))
+intmn:=intpl(r,i,m0(s),intm0(s,j)):intrl(mn(r,s))
++*int
+j@t7:=inttd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(td(a1,b1))
+t8:=intrlin(ts(r,s),td(a1,b1),tict,t7):intrl(ts(r,s))
+-int
+j@intts:=realapp2(r,s,intrl(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".int"(r,s,x,y,t,u,i,j)):intrl(ts(r,s))
+r@[n:natrl(r)]
++ivr24
+t1:=satz24a(ntofrl(r,n)):lessis"n"(1,ntofrl(r,n))
+t2:=th3"l.imp"(more(1rl,r),more"n"(1,ntofrl(r,n)),satz10d(1,ntofrl(r,n),t1),[t:more(1rl,r)]lemmaiva5(1,ntofrl(r,n),ismore2(r,rlofnt(ntofrl(r,n)),1rl,isrlnt1(r,n),t))):not(more(1rl,r))
+-ivr24
+satzr24:=satz167e(1rl,r,t2".ivr24"):lessis(1rl,r)
+r@[i:intrl(r)][s:real][j:intrl(s)][l:less(r,s)]
++ivr25
+t1:=satz182d(s,r,lemma2(r,s,l)):pos(mn(s,r))
+t2:=intmn(s,j,r,i):intrl(mn(s,r))
+t3:=posintnatrl(mn(s,r),t1,t2):natrl(mn(s,r))
+t4:=satzr24(mn(s,r),t3):lessis(1rl,mn(s,r))
+t5:=th9"l.or"(less(1rl,mn(s,r)),is(1rl,mn(s,r)),less(pl(1rl,r),pl(mn(s,r),r)),is(pl(1rl,r),pl(mn(s,r),r)),t4,[t:less(1rl,mn(s,r))]satz188f(1rl,mn(s,r),r,t),[t:is(1rl,mn(s,r))]ispl1(1rl,mn(s,r),r,t)):lessis(pl(1rl,r),pl(mn(s,r),r))
+-ivr25
+satzr25:=islessis12(pl(1rl,r),pl(r,1rl),pl(mn(s,r),r),s,compl(1rl,r),plmn(s,r),t5".ivr25"):lessis(pl(r,1rl),s)
+@[x:nat][y:nat]
++ivr155
+t1:=lemmaiva1(rpofnt(x),rpofnt(y)):is(pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
+t2:=isrpep(rpofnt(pl"n"(x,y)),pl"rp"(rpofnt(x),rpofnt(y)),satz155e(x,y)):is(rlofnt(pl"n"(x,y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
+-ivr155
+satzr155a:=tris2(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))),t2".ivr155",t1".ivr155"):is(rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)))
+satzr155b:=symis(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),satzr155a):is(pl(rlofnt(x),rlofnt(y)),rlofnt(pl"n"(x,y)))
++*ivr155
+y@t3:=lemmaiva2(rpofnt(x),rpofnt(y)):is(ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
+t4:=isrpep(rpofnt(ts"n"(x,y)),ts"rp"(rpofnt(x),rpofnt(y)),satz155f(x,y)):is(rlofnt(ts"n"(x,y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
+-ivr155
+y@satzr155c:=tris2(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))),t4".ivr155",t3".ivr155"):is(rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)))
+satzr155d:=symis(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),satzr155c):is(ts(rlofnt(x),rlofnt(y)),rlofnt(ts"n"(x,y)))
+@[t:real][r:real][s:real][a:and(not(neg(r)),is(ts(r,r),t))][b:and(not(neg(s)),is(ts(s,s),t))]
++7r161
+[c0:dif][cit:inn(c0,class(t))][a0:dif][air:inn(a0,class(r))][b0:dif][bis:inn(b0,class(s))]
+t1:=th3"l.imp"(negd(a0),neg(r),ande1(not(neg(r)),is(ts(r,r),t),a),[u:negd(a0)]negin(r,a0,air,u)):not(negd(a0))
+t2:=th3"l.imp"(negd(b0),neg(s),ande1(not(neg(s)),is(ts(s,s),t),b),[u:negd(b0)]negin(s,b0,bis,u)):not(negd(b0))
+t3:=isex(ts(r,r),t,td(a0,a0),c0,tict(r,r,a0,a0,air,air),cit,ande2(not(neg(r)),is(ts(r,r),t),a)):eq"rp"(td(a0,a0),c0)
+t4:=isex(ts(s,s),t,td(b0,b0),c0,tict(s,s,b0,b0,bis,bis),cit,ande2(not(neg(s)),is(ts(s,s),t),b)):eq"rp"(td(b0,b0),c0)
+t5:=isin(r,s,a0,b0,air,bis,satzd161b(c0,a0,b0,t1,t2,t3,t4)):is(r,s)
+-7r161
+satzr161b:=realapp3(t,r,s,is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(t))][v:inn(y,class(r))][w:inn(z,class(s))]t5".7r161"(x,u,y,v,z,w)):is(r,s)
+t@[n:not(neg(t))]
++*7r161
+n@[c0:dif][cit:inn(c0,class(t))]
+t6:=th3"l.imp"(negd(c0),neg(t),n,[u:negd(c0)]negin(t,c0,cit,u)):not(negd(c0))
+[a0:dif][a:and(not(negd(a0)),eq"rp"(td(a0,a0),c0))]
+ar:=realof(a0):real
+t7:=th3"l.imp"(neg(ar),negd(a0),ande1(not(negd(a0)),eq"rp"(td(a0,a0),c0),a),[u:neg(ar)]negex(ar,a0,innclass(a0),u)):not(neg(ar))
+t8:=isin(ts(ar,ar),t,td(a0,a0),c0,tict(ar,ar,a0,a0,innclass(a0),innclass(a0)),cit,ande2(not(negd(a0)),eq"rp"(td(a0,a0),c0),a)):is(ts(ar,ar),t)
+t9:=andi(not(neg(ar)),is(ts(ar,ar),t),t7,t8):and(not(neg(ar)),is(ts(ar,ar),t))
+t10:=somei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),ar,t9):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
+cit@t11:=someapp(dif,[x:dif]and(not(negd(x)),eq"rp"(td(x,x),c0)),satzd161a(c0,t6),some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:and(not(negd(x)),eq"rp"(td(x,x),c0))]t10(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
+-7r161
+n@satzr161a:=realapp1(t,some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:inn(x,class(t))]t11".7r161"(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
+satzr161:=onei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),[u:real][v:real][a:and(not(neg(u)),is(ts(u,u),t))][b:and(not(neg(v)),is(ts(v,v),t))]satzr161b(u,v,a,b),satzr161a):one([u:real]and(not(neg(u)),is(ts(u,u),t)))
+sqrt:=ind(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):real
++*7r161
+n@t12:=oneax(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):and(not(neg(sqrt)),is(ts(sqrt,sqrt),t))
+-7r161
+n@thsqrt1a:=ande1(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):not(neg(sqrt))
+thsqrt1b:=ande2(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):is(ts(sqrt,sqrt),t)
+[x:real][o:not(neg(x))][i:is(ts(x,x),t)]
+thsqrt2:=satzr161b(x,sqrt,andi(not(neg(x)),is(ts(x,x),t),o,i),t12".7r161"):is(x,sqrt(t,n))
+o@[i:is(t,ts(x,x))]
+thsqrt3:=symis(real,x,sqrt(t,n),thsqrt2(symis(real,t,ts(x,x),i))):is(sqrt(t,n),x)
+@[r:real][s:real][n:not(neg(r))][o:not(neg(s))][i:is(r,s)]
+issqrt:=thsqrt2(s,o,sqrt(r,n),thsqrt1a(r,n),tris(real,ts(sqrt(r,n),sqrt(r,n)),r,s,thsqrt1b(r,n),i)):is(sqrt(r,n),sqrt(s,o))
+r@[n:not(neg(r))][i:is(r,0)]
+sqrt0:=thsqrt3(r,n,0,0notn(0,refis(real,0)),tris2(real,r,ts(0,0),0,i,ts01(0,0,refis(real,0)))):is(sqrt(r,n),0)
+n@[o:nis(r,0)]
++sqrt
+t1:=th3"l.imp"(is(sqrt(r,n),0),is(r,0),o,[t:is(sqrt(r,n),0)]tris1(real,r,0,ts(sqrt(r,n),sqrt(r,n)),thsqrt1b(r,n),ts01(sqrt(r,n),sqrt(r,n),t))):nis(sqrt(r,n),0)
+-sqrt
+sqrtnot0:=or3e2(is(sqrt(r,n),0),pos(sqrt(r,n)),neg(sqrt(r,n)),axrlo(sqrt(r,n)),thsqrt1a(r,n),t1".sqrt"):pos(sqrt(r,n))
+@[r:real][s:real][t:real][n:nis(t,0)]
++v0
+t1:=tr3is(real,ts(t,ts(r,ov(s,t,n))),ts(ts(r,ov(s,t,n)),t),ts(r,ts(ov(s,t,n),t)),ts(r,s),comts(t,ts(r,ov(s,t,n))),assts1(r,ov(s,t,n),t),ists2(ts(ov(s,t,n),t),s,r,satz204e(s,t,n))):is(ts(t,ts(r,ov(s,t,n))),ts(r,s))
+-v0
+lemma6:=satz204g(ts(r,s),t,ts(r,ov(s,t,n)),n,t1".v0"):is(ts(r,ov(s,t,n)),ov(ts(r,s),t,n))
++*v0
+n@t2:=tris(real,ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(ts(t,ov(r,t,n)),ts(t,ov(s,t,n))),pl(r,s),disttp2(t,ov(r,t,n),ov(s,t,n)),ispl12(ts(t,ov(r,t,n)),r,ts(t,ov(s,t,n)),s,satz204c(r,t,n),satz204c(s,t,n))):is(ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(r,s))
+-v0
+n@lemma7:=satz204g(pl(r,s),t,pl(ov(r,t,n),ov(s,t,n)),n,t2".v0"):is(pl(ov(r,t,n),ov(s,t,n)),ov(pl(r,s),t,n))
+r@[n:nis(r,0)]
+lemma8:=satz204b(r,r,n,ov(r,r,n),1rl,satz204c(r,r,n),satz195(r)):is(ov(r,r,n),1rl)
+lemma9:=ore2(is(r,0),is(ov(0,r,n),0),satz192c(r,ov(0,r,n),satz204c(0,r,n)),n):is(ov(0,r,n),0)
+r@[i:is(r,m0(r))]
++*v0
+i@[p:pos(m0(r))]
+t3:=<isneg(r,m0(r),i,satz176f(r,p))>pnotn(m0(r),p):con
+i@[n:neg(m0(r))]
+t4:=<ispos(r,m0(r),i,satz176d(r,n))>nnotp(m0(r),n):con
+-v0
+i@lemma10:=satz176e(r,or3e1(is(m0(r),0),pos(m0(r)),neg(m0(r)),axrlo(m0(r)),[t:pos(m0(r))]t3".v0"(t),[t:neg(m0(r))]t4".v0"(t))):is(r,0)
+r@lemma11:=satz167f(ts(r,r),0,th3"l.imp"(less(ts(r,r),0),neg(ts(r,r)),nnegsq(r),[t:less(ts(r,r),0)]satz169d(ts(r,r),t))):moreis(ts(r,r),0)
+lemma12:=rapp(r,is(ts(r,r),ts(abs(r),abs(r))),[t:pos(r)]satz196a(r,r,t,t),[t:is(r,0)]tris2(real,ts(r,r),ts(abs(r),abs(r)),0,ts01(r,r,t),ts01(abs(r),abs(r),abs0(r,t))),[t:neg(r)]satz196b(r,r,t,t)):is(ts(r,r),ts(abs(r),abs(r)))
+@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
++shift
+t1:=satz190a(x,x,1rl,0,moreisi2(x,x,refis(real,x)),satz169a(1rl,natpos(1rl,natrl1))):more(pl(x,1rl),pl(x,0))
+t2:=ismore2(pl(x,0),x,pl(x,1rl),pl02(x,0,refis(real,0)),t1):more(pl(x,1rl),x)
+t3:=satz172d(pl(x,1rl),x,y,t2,satz168b(y,x,ly)):more(pl(x,1rl),y)
+t4:=satz182d(pl(x,1rl),y,t3):pos(mn(pl(x,1rl),y))
+t5:=intmn(pl(x,1rl),intpl(x,ix,1rl,intrl1),y,iy):intrl(mn(pl(x,1rl),y))
+t6:=posintnatrl(mn(pl(x,1rl),y),t4,t5):natrl(mn(pl(x,1rl),y))
+-shift
+shiftl:=ntofrl(mn(pl(x,1rl),y),t6".shift"):nat
+[n:1to(shiftl)]
++*shift
+n@n1:=inn"n"(shiftl,n):nat
+t7:=1top(shiftl,n):lessis"n"(n1,shiftl)
+n2:=rlofnt(n1):real
+t8:=natintrl(n2,natrli(n1)):intrl(n2)
+-shift
+n@shiftr:=mn(pl(n2".shift",y),1rl):real
+intshiftr:=intmn(pl(n2".shift",y),intpl(n2".shift",t8".shift",y,iy),1rl,intrl1):intrl(shiftr)
+[m:1to(shiftl)][i:is(shiftr(n),shiftr(m))]
++*shift
+n@t8a:=tris(real,mn(pl(shiftr(n),1rl),y),mn(pl(n2,y),y),n2,ismn1(pl(mn(pl(n2,y),1rl),1rl),pl(n2,y),y,plmn(pl(n2,y),1rl)),mnpl(n2,y)):is(mn(pl(shiftr(n),1rl),y),n2)
+i@t9a:=ismn1(pl(shiftr(n),1rl),pl(shiftr(m),1rl),y,ispl1(shiftr(n),shiftr(m),1rl,i)):is(mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y))
+t10a:=tr3is(real,n2(n),mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y),n2(m),symis(real,mn(pl(shiftr(n),1rl),y),n2,t8a),t9a,t8a(m)):is(n2(n),n2(m))
+t11a:=isntirl(n1(n),n1(m),t10a):is"n"(n1(n),n1(m))
+-shift
+i@iseshiftr:=isinne(shiftl,n,m,t11a".shift"):is"e"(1to(shiftl),n,m)
++*shift
+n@[m:more(shiftr,x)]
+t9:=satz188d(shiftr,x,1rl,m):more(pl(shiftr,1rl),pl(x,1rl))
+t10:=ismore1(pl(shiftr,1rl),pl(n2,y),pl(x,1rl),plmn(pl(n2,y),1rl),t9):more(pl(n2,y),pl(x,1rl))
+t11:=satz188d(pl(n2,y),pl(x,1rl),m0(y),t10):more(mn(pl(n2,y),y),mn(pl(x,1rl),y))
+t12:=ismore1(mn(pl(n2,y),y),n2,mn(pl(x,1rl),y),mnpl(n2,y),t11):more(n2,mn(pl(x,1rl),y))
+t13:=ismore12(n2,rlofnt(ntofrl(n2,natrli(n1))),mn(pl(x,1rl),y),rlofnt(ntofrl(mn(pl(x,1rl),y),t6)),isrlnt1(n2,natrli(n1)),isrlnt1(mn(pl(x,1rl),y),t6),t12):more(rlofnt(ntofrl(n2,natrli(n1))),rlofnt(shiftl))
+t14:=lemmaiva5(ntofrl(n2,natrli(n1)),shiftl,t13):more"n"(ntofrl(n2,natrli(n1)),shiftl)
+t15:=ismore1"n"(ntofrl(n2,natrli(n1)),n1,shiftl,isntrl2(n1),t14):more"n"(n1,shiftl)
+n@t16:=th3"l.imp"(more(shiftr,x),more"n"(n1,shiftl),satz10d(n1,shiftl,t7),[t:more(shiftr,x)]t15(t)):not(more(shiftr,x))
+-shift
+n@shiftrls:=satz167e(shiftr,x,t16".shift"):lessis(shiftr,x)
++*shift
+n@[m:more(y,shiftr)]
+t17:=satz188d(y,shiftr,1rl,m):more(pl(y,1rl),pl(shiftr,1rl))
+t18:=ismore12(pl(y,1rl),pl(1rl,y),pl(shiftr,1rl),pl(n2,y),compl(y,1rl),plmn(pl(n2,y),1rl),t17):more(pl(1rl,y),pl(n2,y))
+t19:=satz188a(1rl,n2,y,t18):more(1rl,n2)
+t20:=lemmaiva5(1,n1,t19):more"n"(1,n1)
+n@t21:=th3"l.imp"(more(y,shiftr),more"n"(1,n1),satz10d(1,n1,satz24a(n1)),[t:more(y,shiftr)]t20(t)):not(more(y,shiftr))
+-shift
+n@lsshiftr:=satz167e(y,shiftr,t21".shift"):lessis(y,shiftr)
+ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
++*shift
+a@t22:=and3e1(intrl(u),lessis(y,u),lessis(u,x),a):intrl(u)
+t23:=and3e2(intrl(u),lessis(y,u),lessis(u,x),a):lessis(y,u)
+t24:=and3e3(intrl(u),lessis(y,u),lessis(u,x),a):lessis(u,x)
+[l:less(u,x)]
+t25:=satz188f(pl(u,1rl),pl(x,1rl),m0"r"(y),satz188f(u,x,1rl,l)):less(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
+a@[i:is(u,x)]
+t26:=ismn1(pl(u,1rl),pl(x,1rl),y,ispl1(u,x,1rl,i)):is(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
+a@t27:=th9"l.or"(less(u,x),is(u,x),less(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),is(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),t24,[t:less(u,x)]t25(t),[t:is(u,x)]t26(t)):lessis(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
+ul:=shiftl(u,t22,y,iy,t23):nat
+t28:=islessis12(mn(pl(u,1rl),y),rlofnt(ul),mn(pl(x,1rl),y),rlofnt(shiftl),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isrlnt1(mn(pl(x,1rl),y),t6),t27):lessis(rlofnt(ul),rlofnt(shiftl))
+t29:=th3"l.imp"(more"n"(ul,shiftl),more(rlofnt(ul),rlofnt(shiftl)),satz167d(rlofnt(ul),rlofnt(shiftl),t28),[t:more"n"(ul,shiftl)]lemmaiva6(ul,shiftl,t)):not(more"n"(ul,shiftl))
+t30:=satz10e(ul,shiftl,t29):lessis"n"(ul,shiftl)
+-shift
+a@shiftl1:=outn(shiftl,ul".shift",t30".shift"):1to(shiftl)
++*shift
+a@t31:=isinoutn(shiftl,ul,t30):is"n"(ul,n1(shiftl1))
+t32:=tris(real,mn(pl(u,1rl),y),rlofnt(ul),n2(shiftl1),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isnterl(ul,n1(shiftl1),t31)):is(mn(pl(u,1rl),y),n2(shiftl1))
+t33:=tris(real,mn(pl(mn(pl(u,1rl),y),y),1rl),mn(pl(u,1rl),1rl),u,ismn1(pl(mn(pl(u,1rl),y),y),pl(u,1rl),1rl,plmn(pl(u,1rl),y)),mnpl(u,1rl)):is(mn(pl(mn(pl(u,1rl),y),y),1rl),u)
+-shift
+a@shiftinv1:=tris1(real,u,shiftr(shiftl1),mn(pl(mn(pl(u,1rl),y),y),1rl),t33".shift",ismn1(pl(mn(pl(u,1rl),y),y),pl(n2".shift"(shiftl1),y),1rl,ispl1(mn(pl(u,1rl),y),n2".shift"(shiftl1),y,t32".shift"))):is(u,shiftr(shiftl1))
+shiftinv2:=symis(real,u,shiftr(shiftl1),shiftinv1):is(shiftr(shiftl1),u)
+ly@[alpha:'type']
+seq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]alpha:'type'
+[s:seq]
+proofsirrelevant:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is(t,u)]is"e"(alpha,<tl><lt><it><t>s,<ul><lu><iu><u>s):'prop'
+alpha@[f:seq]
+shiftf:=[t:1to(shiftl)]<shiftrls(t)><lsshiftr(t)><intshiftr(t)><shiftr(t)>f:[t:1to(shiftl)]alpha
+ly@[s:seq(real)]
+inseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]and3(intrl(<w><v><u><t>s),lessis(y,<w><v><u><t>s),lessis(<w><v><u><t>s,x)):'prop'
+injseq:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is"r"(<tl><lt><it><t>s,<ul><lu><iu><u>s)]is"r"(t,u):'prop'
+[u:real][v:real][a:and3(intrl(v),lessis(y,v),lessis(v,x))]
++*shift
+a@prop1:=is(u,<t24(v,a)><t23(v,a)><t22(v,a)><v>s):'prop'
+-shift
+v@improp:=and(and3(intrl(v),lessis(y,v),lessis(v,x)),[t:and3(intrl(v),lessis(y,v),lessis(v,x))]prop1".shift"(t)):'prop'
+u@imseq:=some([t:real]improp(u,t)):'prop'
+s@surjseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]imseq(t):'prop'
+perm:=and(injseq,surjseq):'prop'
+[ins:inseq(s)]
++*shift
+ins@[n:1to(shiftl)]
+ns:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>s:real
+t34:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ins:and3(intrl(ns),lessis(y,ns),lessis(ns,x))
+-shift
+ins@shiftseq:=[t:1to(shiftl)]shiftl1(ns".shift"(t),t34".shift"(t)):[t:1to(shiftl)]1to(shiftl)
+[js:injseq(s)]
++*shift
+js@[n:1to(shiftl)][m:1to(shiftl)][i:is"e"(1to(shiftl),<n>shiftseq,<m>shiftseq)]
+t35:=isoutne(shiftl,ul(ns(n),t34(n)),t30(ns(n),t34(n)),ul(ns(m),t34(m)),t30(ns(m),t34(m)),i):is"n"(ul(ns(n),t34(n)),ul(ns(m),t34(m)))
+t36:=isrlint(mn(pl(ns(n),1rl),y),t6(ns(n),t22(ns(n),t34(n)),y,iy,t23(ns(n),t34(n))),mn(pl(ns(m),1rl),y),t6(ns(m),t22(ns(m),t34(m)),y,iy,t23(ns(m),t34(m))),t35):is(mn(pl(ns(n),1rl),y),mn(pl(ns(m),1rl),y))
+t37:=satz188b(ns(n),ns(m),1rl,satz188b(pl(ns(n),1rl),pl(ns(m),1rl),m0"r"(y),t36)):is(ns(n),ns(m))
+t38:=<t37><shiftrls(m)><lsshiftr(m)><intshiftr(m)><shiftr(m)><shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>js:is(shiftr(n),shiftr(m))
+t39:=satz188b(n2(n),n2(m),y,satz188b(pl(n2(n),y),pl(n2(m),y),m0(1rl),t38)):is(n2(n),n2(m))
+t40:=isntirl(n1(n),n1(m),t39):is"n"(n1(n),n1(m))
+t41:=isinne(shiftl,n,m,t40):is"e"(1to(shiftl),n,m)
+-shift
+js@injshiftseq:=[t:1to(shiftl)][u:1to(shiftl)][v:is"e"(1to(shiftl),<t>shiftseq,<u>shiftseq)]t41".shift"(t,u,v):injective(1to(shiftl),1to(shiftl),shiftseq)
+ins@[pri:proofsirrelevant(real,s)][ss:surjseq(s)]
++*shift
+ss@[n:1to(shiftl)]
+t42:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ss:imseq(shiftr(n))
+[u:real][p:improp(shiftr(n),u)]
+t43:=ande1(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):and3(intrl(u),lessis(y,u),lessis(u,x))
+t44:=ande2"l.r"(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):is(shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s)
+ul1:=shiftl1(u,t43):1to(shiftl)
+t45:=<shiftinv1(u,t43)><shiftrls(ul1)><lsshiftr(ul1)><intshiftr(ul1)><shiftr(ul1)><t24(u,t43)><t23(u,t43)><t22(u,t43)><u>pri:is(<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1))
+t46:=shiftinv1(ns(ul1),t34(ul1)):is(ns(ul1),shiftr(<ul1>shiftseq))
+t47:=tr3is(real,shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1),shiftr(<ul1>shiftseq),t44,t45,t46):is(shiftr(n),shiftr(<ul1>shiftseq))
+t48:=iseshiftr(n,<ul1>shiftseq,t47):is"e"(1to(shiftl),n,<ul1>shiftseq)
+t49:=somei(1to(shiftl),[t:1to(shiftl)]is"e"(1to(shiftl),n,<t>shiftseq),ul1,t48):image(1to(shiftl),1to(shiftl),shiftseq,n)
+n@t50:=someapp(real,[t:real]improp(shiftr(n),t),t42,image(1to(shiftl),1to(shiftl),shiftseq,n),[t:real][u:improp(shiftr(n),t)]t49(t,u)):image(1to(shiftl),1to(shiftl),shiftseq,n)
+-shift
+ss@surjshiftseq:=[t:1to(shiftl)]t50".shift"(t):surjective(1to(shiftl),1to(shiftl),shiftseq)
+pri@[ps:perm(s)]
+bijshiftseq:=andi(injective(1to(shiftl),1to(shiftl),shiftseq),surjective(1to(shiftl),1to(shiftl),shiftseq),injshiftseq(ande1(injseq(s),surjseq(s),ps)),surjshiftseq(ande2(injseq(s),surjseq(s),ps))):bijective(1to(shiftl),1to(shiftl),shiftseq)
++c
+@complex:=pair1type(real):'type'
+cx:=complex:'type'
+[x:complex][y:complex]
+is:=is"e"(cx,x,y):'prop'
+nis:=not(is(x,y)):'prop'
+@[p:[t:complex]'prop']
+some:=some"l"(cx,p):'prop'
+all:=all"l"(cx,p):'prop'
+one:=one"e"(cx,p):'prop'
+@[a:real][b:real]
+pli:=pair1(real,a,b):complex
+x@re:=first1(real,x):real
+im:=second1(real,x):real
+b@reis:=first1is1(real,a,b):is"r"(re(pli(a,b)),a)
+isre:=first1is2(real,a,b):is"r"(a,re(pli(a,b)))
+imis:=second1is1(real,a,b):is"r"(im(pli(a,b)),b)
+isim:=second1is2(real,a,b):is"r"(b,im(pli(a,b)))
+x@pliis:=pair1is1(real,x):is(pli(re(x),im(x)),x)
+ispli:=pair1is2(real,x):is(x,pli(re(x),im(x)))
+y@[i:is(x,y)]
+iscere:=isf(cx,real,[t:cx]re(t),x,y,i):is"r"(re(x),re(y))
+isceim:=isf(cx,real,[t:cx]im(t),x,y,i):is"r"(im(x),im(y))
+b@[c:real][i:is"r"(a,b)]
+isrecx1:=isf(real,cx,[t:real]pli(t,c),a,b,i):is(pli(a,c),pli(b,c))
+isrecx2:=isf(real,cx,[t:real]pli(c,t),a,b,i):is(pli(c,a),pli(c,b))
+c@[d:real][i:is"r"(a,b)][j:is"r"(c,d)]
+isrecx12:=tris(cx,pli(a,c),pli(b,c),pli(b,d),isrecx1(a,b,c,i),isrecx2(c,d,b,j)):is(pli(a,c),pli(b,d))
+x@satz206:=refis(cx,x):is(x,x)
+y@[i:is(x,y)]
+satz207:=symis(cx,x,y,i):is(y,x)
+y@[z:complex][i:is(x,y)][j:is(y,z)]
+satz208:=tris(cx,x,y,z,i,j):is(x,z)
+@0c:=pli(0,0):complex
+1c:=pli(1rl,0):complex
+y@pl:=pli(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))):complex
+d@plis12a:=isrecx12(pl"r"(re(pli(a,b)),re(pli(c,d))),pl"r"(a,c),pl"r"(im(pli(a,b)),im(pli(c,d))),pl"r"(b,d),ispl12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ispl12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)))
+plis12b:=symis(cx,pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)),plis12a):is(pli(pl"r"(a,c),pl"r"(b,d)),pl(pli(a,b),pli(c,d)))
+x@[r:real][s:real]
+plis1a:=isrecx12(pl"r"(re(pli(r,s)),re(x)),pl"r"(r,re(x)),pl"r"(im(pli(r,s)),im(x)),pl"r"(s,im(x)),ispl1(re(pli(r,s)),r,re(x),reis(r,s)),ispl1(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))))
+plis1b:=symis(cx,pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))),plis1a):is(pli(pl"r"(r,re(x)),pl"r"(s,im(x))),pl(pli(r,s),x))
+plis2a:=isrecx12(pl"r"(re(x),re(pli(r,s))),pl"r"(re(x),r),pl"r"(im(x),im(pli(r,s))),pl"r"(im(x),s),ispl2(re(pli(r,s)),r,re(x),reis(r,s)),ispl2(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)))
+plis2b:=symis(cx,pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)),plis2a):is(pli(pl"r"(re(x),r),pl"r"(im(x),s)),pl(x,pli(r,s)))
+z@[i:is(x,y)]
+ispl1:=isf(cx,cx,[t:cx]pl(t,z),x,y,i):is(pl(x,z),pl(y,z))
+ispl2:=isf(cx,cx,[t:cx]pl(z,t),x,y,i):is(pl(z,x),pl(z,y))
+z@[u:complex][i:is(x,y)][j:is(z,u)]
+ispl12:=tris(cx,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
+y@satz209:=isrecx12(pl"r"(re(x),re(y)),pl"r"(re(y),re(x)),pl"r"(im(x),im(y)),pl"r"(im(y),im(x)),compl(re(x),re(y)),compl(im(x),im(y))):is(pl(x,y),pl(y,x))
+compl:=satz209:is(pl(x,y),pl(y,x))
+x@satz210:=tr3is(cx,pl(x,0c),pli(pl"r"(re(x),0),pl"r"(im(x),0)),pli(re(x),im(x)),x,plis2a(x,0,0),isrecx12(pl"r"(re(x),0),re(x),pl"r"(im(x),0),im(x),pl02(re(x),0,refis(real,0)),pl02(im(x),0,refis(real,0))),pliis(x)):is(pl(x,0c),x)
+satz210a:=symis(cx,pl(x,0c),x,satz210):is(x,pl(x,0c))
+satz210b:=tris(cx,pl(0c,x),pl(x,0c),x,compl(0c,x),satz210):is(pl(0c,x),x)
+satz210c:=symis(cx,pl(0c,x),x,satz210b):is(x,pl(0c,x))
+z@satz211:=tr3is(cx,pl(pl(x,y),z),pli(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(pl"r"(im(x),im(y)),im(z))),pli(pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(im(x),pl"r"(im(y),im(z)))),pl(x,pl(y,z)),plis1a(z,pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(pl"r"(im(x),im(y)),im(z)),pl"r"(im(x),pl"r"(im(y),im(z))),asspl1(re(x),re(y),re(z)),asspl1(im(x),im(y),im(z))),plis2b(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z)))):is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl1:=satz211:is(pl(pl(x,y),z),pl(x,pl(y,z)))
+asspl2:=symis(cx,pl(pl(x,y),z),pl(x,pl(y,z)),asspl1):is(pl(x,pl(y,z)),pl(pl(x,y),z))
+y@[u:complex][i:is(pl(y,u),x)]
++2212
+t1:=tris(real,pl"r"(re(y),re(u)),re(pl(y,u)),re(x),isre(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),iscere(pl(y,u),x,i)):is"r"(pl"r"(re(y),re(u)),re(x))
+t2:=tris(real,pl"r"(im(y),im(u)),im(pl(y,u)),im(x),isim(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),isceim(pl(y,u),x,i)):is"r"(pl"r"(im(y),im(u)),im(x))
+t3:=satz187d(re(x),re(y),re(u),t1):is"r"(re(u),mn(re(x),re(y)))
+t4:=satz187d(im(x),im(y),im(u),t2):is"r"(im(u),mn(im(x),im(y)))
+-2212
+satz212a:=tris(cx,u,pli(re(u),im(u)),pli(mn(re(x),re(y)),mn(im(x),im(y))),ispli(u),isrecx12(re(u),mn(re(x),re(y)),im(u),mn(im(x),im(y)),t3".2212",t4".2212")):is(u,pli(mn(re(x),re(y)),mn(im(x),im(y))))
+y@satz212b:=tr3is(cx,pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),pli(pl"r"(re(y),mn(re(x),re(y))),pl"r"(im(y),mn(im(x),im(y)))),pli(re(x),im(x)),x,plis2a(y,mn(re(x),re(y)),mn(im(x),im(y))),isrecx12(pl"r"(re(y),mn(re(x),re(y))),re(x),pl"r"(im(y),mn(im(x),im(y))),im(x),satz187a(re(x),re(y)),satz187a(im(x),im(y))),pliis(x)):is(pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),x)
+satz212c:=somei(cx,[t:cx]is(pl(y,t),x),pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212b):some([t:complex]is(pl(y,t),x))
+satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212a(t,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
+%satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
+mn:=pli(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))):complex
+d@mnis12a:=isrecx12(mn"r"(re(pli(a,b)),re(pli(c,d))),mn"r"(a,c),mn"r"(im(pli(a,b)),im(pli(c,d))),mn"r"(b,d),ismn12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ismn12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)))
+mnis12b:=symis(cx,mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)),mnis12a):is(pli(mn"r"(a,c),mn"r"(b,d)),mn(pli(a,b),pli(c,d)))
+x@[r:real][s:real]
+mnis1a:=isrecx12(mn"r"(re(pli(r,s)),re(x)),mn"r"(r,re(x)),mn"r"(im(pli(r,s)),im(x)),mn"r"(s,im(x)),ismn1(re(pli(r,s)),r,re(x),reis(r,s)),ismn1(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))))
+mnis1b:=symis(cx,mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mnis1a):is(pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mn(pli(r,s),x))
+mnis2a:=isrecx12(mn"r"(re(x),re(pli(r,s))),mn"r"(re(x),r),mn"r"(im(x),im(pli(r,s))),mn"r"(im(x),s),ismn2(re(pli(r,s)),r,re(x),reis(r,s)),ismn2(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)))
+mnis2b:=symis(cx,mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)),mnis2a):is(pli(mn"r"(re(x),r),mn"r"(im(x),s)),mn(x,pli(r,s)))
+z@[i:is(x,y)]
+ismn1:=isf(cx,cx,[t:cx]mn(t,z),x,y,i):is(mn(x,z),mn(y,z))
+ismn2:=isf(cx,cx,[t:cx]mn(z,t),x,y,i):is(mn(z,x),mn(z,y))
+z@[u:complex][i:is(x,y)][j:is(z,u)]
+ismn12:=tris(cx,mn(x,z),mn(y,z),mn(y,u),ismn1(x,y,z,i),ismn2(z,u,y,j)):is(mn(x,z),mn(y,u))
+y@[u:complex][i:is(pl(y,u),x)]
+satz212d:=satz212a(u,i):is(u,mn(x,y))
+satz212e:=symis(cx,u,mn(x,y),satz212d):is(mn(x,y),u)
+u@[i:is(pl(u,y),x)]
+satz212f:=satz212d(tris(cx,pl(y,u),pl(u,y),x,compl(y,u),i)):is(u,mn(x,y))
+satz212g:=symis(cx,u,mn(x,y),satz212f):is(mn(x,y),u)
+y@satz212h:=satz212b:is(pl(y,mn(x,y)),x)
+[i:is(mn(x,y),0c)]
++2213
+t1:=tr3is(real,mn"r"(re(x),re(y)),re(mn(x,y)),re(0c),0,isre(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),iscere(mn(x,y),0c,i),reis(0,0)):is"r"(mn"r"(re(x),re(y)),0)
+t2:=tr3is(real,mn"r"(im(x),im(y)),im(mn(x,y)),im(0c),0,isim(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),isceim(mn(x,y),0c,i),imis(0,0)):is"r"(mn"r"(im(x),im(y)),0)
+t3:=satz182b(re(x),re(y),t1):is"r"(re(x),re(y))
+t4:=satz182b(im(x),im(y),t2):is"r"(im(x),im(y))
+-2213
+satz213a:=tr3is(cx,x,pli(re(x),im(x)),pli(re(y),im(y)),y,ispli(x),isrecx12(re(x),re(y),im(x),im(y),t3".2213",t4".2213"),pliis(y)):is(x,y)
+y@[i:is(x,y)]
++*2213
+i@t5:=satz182e(re(x),re(y),iscere(x,y,i)):is"r"(mn"r"(re(x),re(y)),0)
+t6:=satz182e(im(x),im(y),isceim(x,y,i)):is"r"(mn"r"(im(x),im(y)),0)
+-2213
+i@satz213b:=isrecx12(mn"r"(re(x),re(y)),0,mn"r"(im(x),im(y)),0,t5".2213",t6".2213"):is(mn(x,y),0c)
+x@m0:=mn(0c,x):complex
+satz214:=isrecx12(mn"r"(re(0c),re(x)),m0"r"(re(x)),mn"r"(im(0c),im(x)),m0"r"(im(x)),pl01(re(0c),m0"r"(re(x)),reis(0,0)),pl01(im(0c),m0"r"(im(x)),imis(0,0))):is(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))))
+satz214a:=symis(cx,m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214):is(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x))
+b@m0isa:=tris(cx,m0(pli(a,b)),pli(m0"r"(re(pli(a,b))),m0"r"(im(pli(a,b)))),pli(m0"r"(a),m0"r"(b)),satz214(pli(a,b)),isrecx12(m0"r"(re(pli(a,b))),m0"r"(a),m0"r"(im(pli(a,b))),m0"r"(b),ism0(re(pli(a,b)),a,reis(a,b)),ism0(im(pli(a,b)),b,imis(a,b)))):is(m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)))
+m0isb:=symis(cx,m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)),m0isa):is(pli(m0"r"(a),m0"r"(b)),m0(pli(a,b)))
+y@[i:is(x,y)]
+ism0:=isf(cx,cx,[t:cx]m0(t),x,y,i):is(m0(x),m0(y))
+x@satz215:=tr4is(cx,m0(m0(x)),m0(pli(m0"r"(re(x)),m0"r"(im(x)))),pli(m0"r"(m0"r"(re(x))),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,ism0(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214),m0isa(m0"r"(re(x)),m0"r"(im(x))),isrecx12(m0"r"(m0"r"(re(x))),re(x),m0"r"(m0"r"(im(x))),im(x),satz177(re(x)),satz177(im(x))),pliis(x)):is(m0(m0(x)),x)
+satz215a:=symis(cx,m0(m0(x)),x,satz215):is(x,m0(m0(x)))
+y@[i:is(x,m0(y))]
+satz215b:=tris(cx,m0(x),m0(m0(y)),y,ism0(x,m0(y),i),satz215(y)):is(m0(x),y)
+satz215c:=symis(cx,m0(x),y,satz215b):is(y,m0(x))
+y@[i:is(m0(x),y)]
+satz215d:=satz215c(y,x,symis(cx,m0(x),y,i)):is(x,m0(y))
+satz215e:=symis(cx,x,m0(y),satz215d):is(m0(y),x)
+x@satz216:=tr3is(cx,pl(x,m0(x)),pl(x,pli(m0"r"(re(x)),m0"r"(im(x)))),pli(pl"r"(re(x),m0"r"(re(x))),pl"r"(im(x),m0"r"(im(x)))),0c,ispl2(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),x,satz214(x)),plis2a(x,m0"r"(re(x)),m0"r"(im(x))),isrecx12(pl"r"(re(x),m0"r"(re(x))),0,pl"r"(im(x),m0"r"(im(x))),0,satz179(re(x)),satz179(im(x)))):is(pl(x,m0(x)),0c)
++2216
+anders:=satz212h(0c,x):is(pl(x,m0(x)),0c)
+-2216
+satz216a:=tris(cx,pl(m0(x),x),pl(x,m0(x)),0c,compl(m0(x),x),satz216):is(pl(m0(x),x),0c)
+y@satz217:=tr4is(cx,m0(pl(x,y)),pli(m0"r"(pl"r"(re(x),re(y))),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(m0"r"(re(x)),m0"r"(re(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(pli(m0"r"(re(x)),m0"r"(im(x))),pli(m0"r"(re(y)),m0"r"(im(y)))),pl(m0(x),m0(y)),m0isa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(m0"r"(pl"r"(re(x),re(y))),pl"r"(m0"r"(re(x)),m0"r"(re(y))),m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),satz180(re(x),re(y)),satz180(im(x),im(y))),plis12b(m0"r"(re(x)),m0"r"(im(x)),m0"r"(re(y)),m0"r"(im(y))),ispl12(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),satz214a(x),satz214a(y))):is(m0(pl(x,y)),pl(m0(x),m0(y)))
+satz217a:=symis(cx,m0(pl(x,y)),pl(m0(x),m0(y)),satz217):is(pl(m0(x),m0(y)),m0(pl(x,y)))
+satz218:=tris(cx,mn(x,y),pl(x,pli(m0"r"(re(y)),m0"r"(im(y)))),pl(x,m0(y)),plis2b(x,m0"r"(re(y)),m0"r"(im(y))),ispl2(pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),x,satz214a(y))):is(mn(x,y),pl(x,m0(y)))
+satz218a:=symis(cx,mn(x,y),pl(x,m0(y)),satz218):is(pl(x,m0(y)),mn(x,y))
++2219
+t1:=tr3is(cx,m0(mn(x,y)),m0(pl(x,m0(y))),pl(m0(x),m0(m0(y))),pl(m0(x),y),ism0(mn(x,y),pl(x,m0(y)),satz218),satz217(x,m0(y)),ispl2(m0(m0(y)),y,m0(x),satz215(y))):is(m0(mn(x,y)),pl(m0(x),y))
+-2219
+satz219:=tr3is(cx,m0(mn(x,y)),pl(m0(x),y),pl(y,m0(x)),mn(y,x),t1".2219",compl(m0(x),y),satz218a(y,x)):is(m0(mn(x,y)),mn(y,x))
+satz219a:=symis(cx,m0(mn(y,x)),mn(x,y),satz219(y,x)):is(mn(x,y),m0(mn(y,x)))
+ts:=pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))):complex
+rets:=mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))):real
+imts:=pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))):real
++v3
+d@t1:=ismn12"r"(ts"r"(re(pli(a,b)),re(pli(c,d))),ts"r"(a,c),ts"r"(im(pli(a,b)),im(pli(c,d))),ts"r"(b,d),ists12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ists12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is"r"(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)))
+t2:=ispl12"r"(ts"r"(re(pli(a,b)),im(pli(c,d))),ts"r"(a,d),ts"r"(im(pli(a,b)),re(pli(c,d))),ts"r"(b,c),ists12(re(pli(a,b)),a,im(pli(c,d)),d,reis(a,b),imis(c,d)),ists12(im(pli(a,b)),b,re(pli(c,d)),c,imis(a,b),reis(c,d))):is"r"(imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)))
+-v3
+d@tsis12a:=isrecx12(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)),imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)),t1".v3",t2".v3"):is(ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))))
+tsis12b:=symis(cx,ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),tsis12a):is(pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),ts(pli(a,b),pli(c,d)))
+x@[r:real][s:real]
++*v3
+s@t3:=ismn12"r"(ts"r"(re(pli(r,s)),re(x)),ts"r"(r,re(x)),ts"r"(im(pli(r,s)),im(x)),ts"r"(s,im(x)),ists1(re(pli(r,s)),r,re(x),reis(r,s)),ists1(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))))
+t4:=ispl12"r"(ts"r"(re(pli(r,s)),im(x)),ts"r"(r,im(x)),ts"r"(im(pli(r,s)),re(x)),ts"r"(s,re(x)),ists1(re(pli(r,s)),r,im(x),reis(r,s)),ists1(im(pli(r,s)),s,re(x),imis(r,s))):is"r"(imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))))
+-v3
+s@tsis1a:=isrecx12(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))),t3".v3",t4".v3"):is(ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))))
+tsis1b:=symis(cx,ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),tsis1a):is(pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),ts(pli(r,s),x))
++*v3
+s@t5:=ismn12"r"(ts"r"(re(x),re(pli(r,s))),ts"r"(re(x),r),ts"r"(im(x),im(pli(r,s))),ts"r"(im(x),s),ists2(re(pli(r,s)),r,re(x),reis(r,s)),ists2(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)))
+t6:=ispl12"r"(ts"r"(re(x),im(pli(r,s))),ts"r"(re(x),s),ts"r"(im(x),re(pli(r,s))),ts"r"(im(x),r),ists2(im(pli(r,s)),s,re(x),imis(r,s)),ists2(re(pli(r,s)),r,im(x),reis(r,s))):is"r"(imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)))
+-v3
+s@tsis2a:=isrecx12(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)),t5".v3",t6".v3"):is(ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))))
+tsis2b:=symis(cx,ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),tsis2a):is(pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),ts(x,pli(r,s)))
+z@[i:is(x,y)]
+ists1:=isf(cx,cx,[t:cx]ts(t,z),x,y,i):is(ts(x,z),ts(y,z))
+ists2:=isf(cx,cx,[t:cx]ts(z,t),x,y,i):is(ts(z,x),ts(z,y))
+z@[u:complex][i:is(x,y)][j:is(z,u)]
+ists12:=tris(cx,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
++3220
+y@t1:=ismn12"r"(ts"r"(re(x),re(y)),ts"r"(re(y),re(x)),ts"r"(im(x),im(y)),ts"r"(im(y),im(x)),comts(re(x),re(y)),comts(im(x),im(y))):is"r"(rets(x,y),rets(y,x))
+t2:=tris(real,imts(x,y),pl"r"(ts"r"(im(x),re(y)),ts"r"(re(x),im(y))),imts(y,x),compl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(ts"r"(im(x),re(y)),ts"r"(re(y),im(x)),ts"r"(re(x),im(y)),ts"r"(im(y),re(x)),comts(im(x),re(y)),comts(re(x),im(y)))):is"r"(imts(x,y),imts(y,x))
+-3220
+y@satz220:=isrecx12(rets(x,y),rets(y,x),imts(x,y),imts(y,x),t1".3220",t2".3220"):is(ts(x,y),ts(y,x))
+comts:=satz220:is(ts(x,y),ts(y,x))
+x@[i:is(x,0c)]
+lemma1:=tris(real,re(x),re(0c),0,iscere(x,0c,i),reis(0,0)):is"r"(re(x),0)
+lemma2:=tris(real,im(x),im(0c),0,isceim(x,0c,i),imis(0,0)):is"r"(im(x),0)
+x@mod2:=pl"r"(ts"r"(re(x),re(x)),ts"r"(im(x),im(x))):real
+i@lemma3:=tris(real,mod2,pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),0,ts01(re(x),re(x),lemma1),ts01(im(x),im(x),lemma2)),pl01(0,0,refis(real,0))):is"r"(mod2(x),0)
+x@[n:nis(x,0c)]
++*v3
+x@re2:=ts"r"(re(x),re(x)):real
+im2:=ts"r"(im(x),im(x)):real
+n@[i:is"r"(re(x),0)]
+t7:=th3"l.imp"(is"r"(im(x),0),is(x,0c),n,[t:is"r"(im(x),0)]tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,i,t))):nis"r"(im(x),0)
+t8:=ispos(im2,mod2,symis(real,mod2,im2,pl01(re2,im2,ts01(re(x),re(x),i))),possq(im(x),t7)):pos(mod2)
+n@[o:nis"r"(re(x),0)][i:is"r"(im(x),0)]
+t9:=ispos(re2,mod2,symis(real,mod2,re2,pl02(re2,im2,ts01(im(x),im(x),i))),possq(re(x),o)):pos(mod2)
+o@[p:nis"r"(im(x),0)]
+t10:=pospl(re2,im2,possq(re(x),o),possq(im(x),p)):pos(mod2)
+o@t11:=th1"l.imp"(is"r"(im(x),0),pos(mod2),[t:is"r"(im(x),0)]t9(t),[t:nis"r"(im(x),0)]t10(t)):pos(mod2)
+-v3
+n@lemma4:=th1"l.imp"(is"r"(re(x),0),pos(mod2),[t:is"r"(re(x),0)]t8".v3"(t),[t:nis"r"(re(x),0)]t11".v3"(t)):pos(mod2(x))
+x@lemma5:=th1"l.imp"(is(x,0c),not(neg(mod2)),[t:is(x,0c)]0notn(mod2,lemma3(t)),[t:nis(x,0c)]pnotn(mod2,lemma4(t))):not(neg(mod2(x)))
+y@[i:is(x,0c)]
++3221
+t1:=lemma1(x,i):is"r"(re(x),0)
+t2:=lemma2(x,i):is"r"(im(x),0)
+t3:=tris(real,rets(x,y),mn"r"(0,0),0,ismn12"r"(ts"r"(re(x),re(y)),0,ts"r"(im(x),im(y)),0,ts01(re(x),re(y),t1),ts01(im(x),im(y),t2)),satz187c(0,0,0,pl02(0,0,refis(real,0)))):is"r"(rets(x,y),0)
+t4:=tris(real,imts(x,y),pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),im(y)),0,ts"r"(im(x),re(y)),0,ts01(re(x),im(y),t1),ts01(im(x),re(y),t2)),pl02(0,0,refis(real,0))):is"r"(imts(x,y),0)
+-3221
+satz221a:=isrecx12(rets(x,y),0,imts(x,y),0,t3".3221",t4".3221"):is(ts(x,y),0c)
+y@[i:is(y,0c)]
+satz221b:=tris(cx,ts(x,y),ts(y,x),0c,comts(x,y),satz221a(y,x,i)):is(ts(x,y),0c)
+y@[i:is(ts(x,y),0c)]
++*3221
+i@[n:nis(y,0c)]
+t5:=lemma4(y,n):pos(mod2(y))
+t6:=tris1(real,rets(x,y),0,re(ts(x,y)),reis(rets(x,y),imts(x,y)),lemma1(ts(x,y),i)):is"r"(rets(x,y),0)
+t7:=tris1(real,imts(x,y),0,im(ts(x,y)),imis(rets(x,y),imts(x,y)),lemma2(ts(x,y),i)):is"r"(imts(x,y),0)
+t8:=tris(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(0,0),0,ispl12"r"(ts"r"(rets(x,y),re(y)),0,ts"r"(imts(x,y),im(y)),0,ts01(rets(x,y),re(y),t6),ts01(imts(x,y),im(y),t7)),pl02(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),0)
+y@ii1r:=ts"r"(ts"r"(im(x),im(y)),re(y)):real
+i1ir:=ts"r"(im(x),ts"r"(im(y),re(y))):real
+ir1i:=ts"r"(ts"r"(im(x),re(y)),im(y)):real
+i1ri:=ts"r"(im(x),ts"r"(re(y),im(y))):real
+rr1r:=ts"r"(ts"r"(re(x),re(y)),re(y)):real
+r1rr:=ts"r"(re(x),ts"r"(re(y),re(y))):real
+ri1r:=ts"r"(ts"r"(re(x),im(y)),re(y)):real
+r1ir:=ts"r"(re(x),ts"r"(im(y),re(y))):real
+ri1i:=ts"r"(ts"r"(re(x),im(y)),im(y)):real
+r1ii:=ts"r"(re(x),ts"r"(im(y),im(y))):real
+n@t9:=tris(real,ii1r,i1ir,i1ri,assts1(im(x),im(y),re(y)),ists2"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),im(x),comts"r"(im(y),re(y)))):is"r"(ii1r,i1ri)
+t10:=tris(real,ts"r"(rets(x,y),re(y)),mn"r"(rr1r,ii1r),mn"r"(r1rr,i1ri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(y)),ismn12"r"(rr1r,r1rr,ii1r,i1ri,assts1(re(x),re(y),re(y)),t9)):is"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri))
+t11:=tr3is(real,ts"r"(imts(x,y),im(y)),pl"r"(ri1i,ir1i),pl"r"(r1ii,i1ri),pl"r"(i1ri,r1ii),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(y)),ispl12"r"(ri1i,r1ii,ir1i,i1ri,assts1(re(x),im(y),im(y)),assts1(im(x),re(y),im(y))),compl"r"(r1ii,i1ri)):is"r"(ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii))
+t12:=tr4is(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(mn"r"(r1rr,i1ri),pl"r"(i1ri,r1ii)),pl"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1ii),pl"r"(r1rr,r1ii),ts"r"(re(x),mod2(y)),ispl12"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri),ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii),t10,t11),asspl2"r"(mn"r"(r1rr,i1ri),i1ri,r1ii),ispl1"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1rr,r1ii,plmn(r1rr,i1ri)),distpt2(re(x),ts"r"(re(y),re(y)),ts"r"(im(y),im(y)))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),ts"r"(re(x),mod2(y)))
+t13:=tris1(real,ts"r"(re(x),mod2(y)),0,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),t12,t8):is"r"(ts"r"(re(x),mod2(y)),0)
+t14:=ore1(is"r"(re(x),0),is"r"(mod2(y),0),satz192c(re(x),mod2(y),t13),pnot0(mod2(y),t5)):is"r"(re(x),0)
+t15:=tris1(real,ts"r"(im(x),im(y)),0,ts"r"(re(x),re(y)),satz182b(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),t6),ts01(re(x),re(y),t14)):is"r"(ts"r"(im(x),im(y)),0)
+t16:=tris1(real,ts"r"(im(x),re(y)),0,imts(x,y),pl01(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),ts01(re(x),im(y),t14)),t7):is"r"(ts"r"(im(x),re(y)),0)
+[j:is"r"(re(y),0)]
+t17:=t7"c.v3"(y,n,j):nis"r"(im(y),0)
+t18:=ore1(is"r"(im(x),0),is"r"(im(y),0),satz192c(im(x),im(y),t15),t17):is"r"(im(x),0)
+n@[o:nis"r"(re(y),0)]
+t19:=ore1(is"r"(im(x),0),is"r"(re(y),0),satz192c(im(x),re(y),t16),o):is"r"(im(x),0)
+n@t20:=th1"l.imp"(is"r"(re(y),0),is"r"(im(x),0),[t:is"r"(re(y),0)]t18(t),[t:nis"r"(re(y),0)]t19(t)):is"r"(im(x),0)
+t21:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t14,t20)):is(x,0c)
+-3221
+i@satz221c:=th2"l.or"(is(x,0c),is(y,0c),[t:nis(y,0c)]t21".3221"(t)):or(is(x,0c),is(y,0c))
+y@[n:nis(x,0c)][o:nis(y,0c)]
+satz221d:=th3"l.imp"(is(ts(x,y),0c),or(is(x,0c),is(y,0c)),th3"l.or"(is(x,0c),is(y,0c),n,o),[t:is(ts(x,y),0c)]satz221c(t)):nis(ts(x,y),0c)
++3222
+x@t1:=tris(real,mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),mn"r"(re(x),0),re(x),ismn12"r"(ts"r"(re(x),1rl),re(x),ts"r"(im(x),0),0,satz195(re(x)),ts02(im(x),0,refis(real,0))),pl02(re(x),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x))
+t2:=tris(real,pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),pl"r"(0,im(x)),im(x),ispl12"r"(ts"r"(re(x),0),0,ts"r"(im(x),1rl),im(x),ts02(re(x),0,refis(real,0)),satz195(im(x))),pl01(0,im(x),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x))
+-3222
+x@satz222:=tr3is(cx,ts(x,1c),pli(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl))),pli(re(x),im(x)),x,tsis2a(x,1rl,0),isrecx12(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x),t1".3222",t2".3222"),pliis(x)):is(ts(x,1c),x)
+satz222a:=symis(cx,ts(x,1c),x,satz222):is(x,ts(x,1c))
+satz222b:=tris(cx,ts(1c,x),ts(x,1c),x,comts(1c,x),satz222):is(ts(1c,x),x)
+satz222c:=symis(cx,ts(1c,x),x,satz222b):is(x,ts(1c,x))
++3223
+t1:=tris(real,mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),mn"r"(m0"r"(re(x)),0),m0"r"(re(x)),ismn12"r"(ts"r"(re(x),m0"r"(1rl)),m0"r"(re(x)),ts"r"(im(x),m0"r"(0)),0,tris(real,ts"r"(re(x),m0"r"(1rl)),m0"r"(ts"r"(re(x),1rl)),m0"r"(re(x)),satz197b(re(x),1rl),ism0"r"(ts"r"(re(x),1rl),re(x),satz195(re(x)))),ts02(im(x),m0"r"(0),satz176b(0,refis(real,0)))),pl02(m0"r"(re(x)),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)))
+t2:=tris(real,pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),pl"r"(0,m0"r"(im(x))),m0"r"(im(x)),ispl12"r"(ts"r"(re(x),m0"r"(0)),0,ts"r"(im(x),m0"r"(1rl)),m0"r"(im(x)),ts02(re(x),m0"r"(0),satz176b(0,refis(real,0))),tris(real,ts"r"(im(x),m0"r"(1rl)),m0"r"(ts"r"(im(x),1rl)),m0"r"(im(x)),satz197b(im(x),1rl),ism0"r"(ts"r"(im(x),1rl),im(x),satz195(im(x))))),pl01(0,m0"r"(im(x)),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)))
+-3223
+satz223:=tr4is(cx,ts(x,m0(1c)),ts(x,pli(m0"r"(1rl),m0"r"(0))),pli(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl)))),pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),ists2(m0(1c),pli(m0"r"(1rl),m0"r"(0)),x,m0isa(1rl,0)),tsis2a(x,m0"r"(1rl),m0"r"(0)),isrecx12(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)),t1".3223",t2".3223"),satz214a(x)):is(ts(x,m0(1c)),m0(x))
+satz223a:=symis(cx,ts(x,m0(1c)),m0(x),satz223):is(m0(x),ts(x,m0(1c)))
+satz223b:=tris(cx,ts(m0(1c),x),ts(x,m0(1c)),m0(x),comts(m0(1c),x),satz223):is(ts(m0(1c),x),m0(x))
+satz223c:=symis(cx,ts(m0(1c),x),m0(x),satz223b):is(m0(x),ts(m0(1c),x))
++3224
+y@rxry:=ts"r"(re(x),re(y)):real
+ixiy:=ts"r"(im(x),im(y)):real
+rxiy:=ts"r"(re(x),im(y)):real
+ixry:=ts"r"(im(x),re(y)):real
+t1:=tr4is(real,mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),mn"r"(m0"r"(rxry),m0"r"(ixiy)),pl"r"(m0"r"(rxry),ixiy),mn"r"(ixiy,rxry),m0"r"(mn"r"(rxry,ixiy)),ismn12"r"(ts"r"(m0"r"(re(x)),re(y)),m0"r"(rxry),ts"r"(m0"r"(im(x)),im(y)),m0"r"(ixiy),satz197a(re(x),re(y)),satz197a(im(x),im(y))),ispl2"r"(m0"r"(m0"r"(ixiy)),ixiy,m0"r"(rxry),satz177(ixiy)),compl"r"(m0"r"(rxry),ixiy),satz181a(ixiy,rxry)):is"r"(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(rxry,ixiy)))
+t2:=tris(real,pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),mn"r"(m0"r"(rxiy),ixry),m0"r"(pl"r"(rxiy,ixry)),ispl12"r"(ts"r"(m0"r"(re(x)),im(y)),m0"r"(rxiy),ts"r"(m0"r"(im(x)),re(y)),m0"r"(ixry),satz197a(re(x),im(y)),satz197a(im(x),re(y))),satz180a(rxiy,ixry)):is"r"(pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(rxiy,ixry)))
+-3224
+y@satz224a:=tr4is(cx,ts(m0(x),y),ts(pli(m0"r"(re(x)),m0"r"(im(x))),y),pli(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y)))),pli(m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))),m0(ts(x,y)),ists1(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),y,satz214(x)),tsis1a(y,m0"r"(re(x)),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))),t1".3224",t2".3224"),m0isb(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))):is(ts(m0(x),y),m0(ts(x,y)))
+satz224b:=tr3is(cx,ts(x,m0(y)),ts(m0(y),x),m0(ts(y,x)),m0(ts(x,y)),comts(x,m0(y)),satz224a(y,x),ism0(ts(y,x),ts(x,y),comts(y,x))):is(ts(x,m0(y)),m0(ts(x,y)))
+satz224c:=tris2(cx,ts(m0(x),y),ts(x,m0(y)),m0(ts(x,y)),satz224a,satz224b):is(ts(m0(x),y),ts(x,m0(y)))
+satz224d:=symis(cx,ts(m0(x),y),ts(x,m0(y)),satz224c):is(ts(x,m0(y)),ts(m0(x),y))
+satz224e:=symis(cx,ts(m0(x),y),m0(ts(x,y)),satz224a):is(m0(ts(x,y)),ts(m0(x),y))
+satz224f:=symis(cx,ts(x,m0(y)),m0(ts(x,y)),satz224b):is(m0(ts(x,y)),ts(x,m0(y)))
+satz225:=tris(cx,ts(m0(x),m0(y)),ts(x,m0(m0(y))),ts(x,y),satz224c(x,m0(y)),ists2(m0(m0(y)),y,x,satz215(y))):is(ts(m0(x),m0(y)),ts(x,y))
+satz225a:=symis(cx,ts(m0(x),m0(y)),ts(x,y),satz225):is(ts(x,y),ts(m0(x),m0(y)))
++3226
+z@rrr:=ts"r"(ts"r"(re(x),re(y)),re(z)):real
+iir:=ts"r"(ts"r"(im(x),im(y)),re(z)):real
+rii:=ts"r"(ts"r"(re(x),im(y)),im(z)):real
+iri:=ts"r"(ts"r"(im(x),re(y)),im(z)):real
+rri:=ts"r"(ts"r"(re(x),re(y)),im(z)):real
+iii:=ts"r"(ts"r"(im(x),im(y)),im(z)):real
+rir:=ts"r"(ts"r"(re(x),im(y)),re(z)):real
+irr:=ts"r"(ts"r"(im(x),re(y)),re(z)):real
+t1:=tr3is(real,mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(mn"r"(rrr,iir),pl"r"(rii,iri)),pl"r"(rrr,pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri)))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),ismn12"r"(ts"r"(rets(x,y),re(z)),mn"r"(rrr,iir),ts"r"(imts(x,y),im(z)),pl"r"(rii,iri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(z))),asspl1"r"(rrr,m0"r"(iir),m0"r"(pl"r"(rii,iri))),ispl2"r"(pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri))),m0"r"(pl"r"(iir,pl"r"(rii,iri))),rrr,satz180a(iir,pl"r"(rii,iri)))):is"r"(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))))
+t2:=tr3is(real,pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),pl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),pl"r"(pl"r"(rir,irr),mn"r"(rri,iii)),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),ispl12"r"(ts"r"(rets(x,y),im(z)),mn"r"(rri,iii),ts"r"(imts(x,y),re(z)),pl"r"(rir,irr),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),im(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),re(z))),compl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),asspl2"r"(pl"r"(rir,irr),rri,m0"r"(iii))):is"r"(pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii))
+t3:=tris(cx,ts(ts(x,y),z),pli(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z)))),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),tsis1a(z,rets(x,y),imts(x,y)),isrecx12(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),t1,t2)):is(ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)))
+c@t4:=tris(real,ts"r"(ts"r"(a,b),c),ts"r"(a,ts"r"(b,c)),ts"r"(ts"r"(b,c),a),assts1(a,b,c),comts"r"(a,ts"r"(b,c))):is"r"(ts"r"(ts"r"(a,b),c),ts"r"(ts"r"(b,c),a))
+t5:=tris(real,pl"r"(pl"r"(a,b),c),pl"r"(c,pl"r"(a,b)),pl"r"(pl"r"(c,a),b),compl"r"(pl"r"(a,b),c),asspl2"r"(c,a,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(c,a),b))
+t6:=tris(real,pl"r"(a,pl"r"(b,c)),pl"r"(pl"r"(b,c),a),pl"r"(b,pl"r"(c,a)),compl"r"(a,pl"r"(b,c)),asspl1"r"(b,c,a)):is"r"(pl"r"(a,pl"r"(b,c)),pl"r"(b,pl"r"(c,a)))
+z@rrr1:=rrr(y,z,x):real
+iir1:=iir(y,z,x):real
+rii1:=rii(y,z,x):real
+iri1:=iri(y,z,x):real
+rri1:=rri(y,z,x):real
+iii1:=iii(y,z,x):real
+rir1:=rir(y,z,x):real
+irr1:=irr(y,z,x):real
+t7:=tris(real,pl"r"(iir,pl"r"(rii,iri)),pl"r"(rii,pl"r"(iri,iir)),pl"r"(iir1,pl"r"(rii1,iri1)),t6(iir,rii,iri),ispl12"r"(rii,iir1,pl"r"(iri,iir),pl"r"(rii1,iri1),t4(re(x),im(y),im(z)),ispl12"r"(iri,rii1,iir,iri1,t4(im(x),re(y),im(z)),t4(im(x),im(y),re(z))))):is"r"(pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)))
+t8:=tris(real,pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rri,rir),irr),pl"r"(pl"r"(rir1,irr1),rri1),t5(rir,irr,rri),ispl12"r"(pl"r"(rri,rir),pl"r"(rir1,irr1),irr,rri1,ispl12"r"(rri,rir1,rir,irr1,t4(re(x),re(y),im(z)),t4(re(x),im(y),re(z))),t4(im(x),re(y),re(z)))):is"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1))
+t9:=ismn12"r"(rrr,rrr1,pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)),t4(re(x),re(y),re(z)),t7):is"r"(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))))
+t10:=ismn12"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1),iii,iii1,t8,t4(im(x),im(y),im(z))):is"r"(mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1))
+t11:=tris(cx,ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t3,isrecx12(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1),t9,t10)):is(ts(ts(x,y),z),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
+t12:=tris(cx,ts(x,ts(y,z)),ts(ts(y,z),x),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),comts(x,ts(y,z)),t3(y,z,x)):is(ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
+t13:=tris2(cx,ts(ts(x,y),z),ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t11,t12):is(ts(ts(x,y),z),ts(x,ts(y,z)))
+-3226
+z@satz226:=t13".3226":is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts1:=satz226:is(ts(ts(x,y),z),ts(x,ts(y,z)))
+assts2:=symis(cx,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
++3227
+c@t1:=tr3is(real,pl"r"(pl"r"(a,b),c),pl"r"(a,pl"r"(b,c)),pl"r"(a,pl"r"(c,b)),pl"r"(pl"r"(a,c),b),asspl1"r"(a,b,c),ispl2"r"(pl"r"(b,c),pl"r"(c,b),a,compl"r"(b,c)),asspl2"r"(a,c,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b))
+d@t2:=tr3is(real,pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(pl"r"(a,b),c),d),pl"r"(pl"r"(pl"r"(a,c),b),d),pl"r"(pl"r"(a,c),pl"r"(b,d)),asspl2"r"(pl"r"(a,b),c,d),ispl1"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b),d,t1),asspl1"r"(pl"r"(a,c),b,d)):is"r"(pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,c),pl"r"(b,d)))
+t3:=tris(real,mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,b),pl"r"(m0"r"(c),m0"r"(d))),pl"r"(mn"r"(a,c),mn"r"(b,d)),ispl2"r"(m0"r"(pl"r"(c,d)),pl"r"(m0"r"(c),m0"r"(d)),pl"r"(a,b),satz180(c,d)),t2(a,b,m0"r"(c),m0"r"(d))):is"r"(mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(mn"r"(a,c),mn"r"(b,d)))
+z@t4:=tris(real,mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),mn"r"(pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))),pl"r"(rets(x,y),rets(x,z)),ismn12"r"(ts"r"(re(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),ts"r"(im(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z))),disttp2(re(x),re(y),re(z)),disttp2(im(x),im(y),im(z))),t3(ts"r"(re(x),re(y)),ts"r"(re(x),re(z)),ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))):is"r"(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)))
+t5:=tris(real,pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))),pl"r"(imts(x,y),imts(x,z)),ispl12"r"(ts"r"(re(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z))),disttp2(re(x),im(y),im(z)),disttp2(im(x),re(y),re(z))),t2(ts"r"(re(x),im(y)),ts"r"(re(x),im(z)),ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))):is"r"(pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)))
+t6:=tr3is(cx,ts(x,pl(y,z)),pli(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))))),pli(pl"r"(rets(x,y),rets(x,z)),pl"r"(imts(x,y),imts(x,z))),pl(ts(x,y),ts(x,z)),tsis2a(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z))),isrecx12(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)),t4,t5),plis12b(rets(x,y),imts(x,y),rets(x,z),imts(x,z))):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+-3227
+satz227:=t6".3227":is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+disttp1:=tr3is(cx,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz227(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
+disttp2:=satz227:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
+distpt1:=symis(cx,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
+distpt2:=symis(cx,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
+satz228:=tr4is(cx,ts(x,mn(y,z)),ts(x,pl(y,m0(z))),pl(ts(x,y),ts(x,m0(z))),pl(ts(x,y),m0(ts(x,z))),mn(ts(x,y),ts(x,z)),ists2(mn(y,z),pl(y,m0(z)),x,satz218(y,z)),disttp2(x,y,m0(z)),ispl2(ts(x,m0(z)),m0(ts(x,z)),ts(x,y),satz224b(x,z)),satz218a(ts(x,y),ts(x,z))):is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
+disttm1:=tr3is(cx,ts(mn(x,y),z),ts(z,mn(x,y)),mn(ts(z,x),ts(z,y)),mn(ts(x,z),ts(y,z)),comts(mn(x,y),z),satz228(z,x,y),ismn12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(mn(x,y),z),mn(ts(x,z),ts(y,z)))
+disttm2:=satz228:is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
+distmt1:=symis(cx,ts(mn(x,y),z),mn(ts(x,z),ts(y,z)),disttm1):is(mn(ts(x,z),ts(y,z)),ts(mn(x,y),z))
+distmt2:=symis(cx,ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)),disttm2):is(mn(ts(x,y),ts(x,z)),ts(x,mn(y,z)))
+y@[n:nis(y,0c)][u1:complex][u2:complex][i:is(ts(y,u1),x)][j:is(ts(y,u2),x)]
++3229
+t1:=tris2(cx,ts(y,u1),ts(y,u2),x,i,j):is(ts(y,u1),ts(y,u2))
+t2:=tris(cx,ts(y,mn(u1,u2)),mn(ts(y,u1),ts(y,u2)),0c,disttm2(y,u1,u2),satz213b(ts(y,u1),ts(y,u2),t1)):is(ts(y,mn(u1,u2)),0c)
+t3:=ore2(is(y,0c),is(mn(u1,u2),0c),satz221c(y,mn(u1,u2),t2),n):is(mn(u1,u2),0c)
+-3229
+satz229b:=satz213a(u1,u2,t3".3229"):is(u1,u2)
++*3229
+n@t4:=pnot0(mod2(y),lemma4(y,n)):nis"r"(mod2(y),0)
+u:=ts(pli(ov(re(y),mod2(y),t4),m0"r"(ov(im(y),mod2(y),t4))),x):complex
+[v:real]
+dd:=ov(v,mod2(y),t4):real
+n@t5:=tr3is(real,m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),m0"r"(m0"r"(ts"r"(im(y),dd(im(y))))),ts"r"(im(y),dd(im(y))),dd(ts"r"(im(y),im(y))),ism0"r"(ts"r"(im(y),m0"r"(dd(im(y)))),m0"r"(ts"r"(im(y),dd(im(y)))),satz197b(im(y),dd(im(y)))),satz177(ts"r"(im(y),dd(im(y)))),lemma6(im(y),im(y),mod2(y),t4)):is"r"(m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))))
+t6:=tr3is(real,mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(dd(ts"r"(re(y),re(y))),dd(ts"r"(im(y),im(y)))),dd(mod2(y)),1rl,ispl12"r"(ts"r"(re(y),dd(re(y))),dd(ts"r"(re(y),re(y))),m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))),lemma6(re(y),re(y),mod2(y),t4),t5),lemma7(ts"r"(re(y),re(y)),ts"r"(im(y),im(y)),mod2(y),t4),lemma8(mod2(y),t4)):is"r"(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl)
+t7:=tris(real,ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(m0"r"(re(y)),dd(im(y))),dd(ts"r"(m0"r"(re(y)),im(y))),satz197d(re(y),dd(im(y))),lemma6(m0"r"(re(y)),im(y),mod2(y),t4)):is"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))))
+t8:=tris(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),pl"r"(dd(ts"r"(m0"r"(re(y)),im(y))),dd(ts"r"(im(y),re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),ispl12"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))),ts"r"(im(y),dd(re(y))),dd(ts"r"(im(y),re(y))),t7,lemma6(im(y),re(y),mod2(y),t4)),lemma7(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)),mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))))
+t9:=tr3is(real,pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),pl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),mn"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y))),0,ispl1"r"(ts"r"(m0"r"(re(y)),im(y)),m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y)),satz197a(re(y),im(y))),compl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),satz182e(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),comts"r"(im(y),re(y)))):is"r"(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0)
+t10:=tr3is(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),dd(0),0,t8,isf(real,real,[t:real]dd(t),pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0,t9),lemma9(mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0)
+t11:=tris(cx,ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),pli(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y))))),1c,tsis2a(y,dd(re(y)),m0"r"(dd(im(y)))),isrecx12(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0,t6,t10)):is(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c)
+t12:=tr3is(cx,ts(y,u),ts(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),x),ts(1c,x),x,assts2(y,pli(dd(re(y)),m0"r"(dd(im(y)))),x),ists1(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c,x,t11),satz222b(x)):is(ts(y,u),x)
+-3229
+n@satz229a:=somei(cx,[t:cx]is(ts(y,t),x),u".3229",t12".3229"):some([t:cx]is(ts(y,t),x))
+satz229:=onei(cx,[t:cx]is(ts(y,t),x),[t:cx][u:cx][v:is(ts(y,t),x)][w:is(ts(y,u),x)]satz229b(t,u,v,w),satz229a):one([t:cx]is(ts(y,t),x))
+ov:=ind(cx,[t:cx]is(ts(y,t),x),satz229):complex
+satz229c:=oneax(cx,[t:cx]is(ts(y,t),x),satz229):is(ts(y,ov(x,y,n)),x)
+satz229d:=symis(cx,ts(y,ov(x,y,n)),x,satz229c):is(x,ts(y,ov(x,y,n)))
+satz229e:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c):is(ts(ov(x,y,n),y),x)
+satz229f:=symis(cx,ts(ov(x,y,n),y),x,satz229e):is(x,ts(ov(x,y,n),y))
+y@[u:complex][n:nis(y,0c)][i:is(ts(y,u),x)]
+satz229g:=satz229b(n,u,ov(x,y,n),i,satz229c(n)):is(u,ov(x,y,n))
+satz229h:=symis(cx,u,ov(x,y,n),satz229g):is(ov(x,y,n),u)
+n@[i:is(ts(u,y),x)]
+satz229j:=satz229g(tris(cx,ts(y,u),ts(u,y),x,comts(y,u),i)):is(u,ov(x,y,n))
+satz229k:=symis(cx,u,ov(x,y,n),satz229j):is(ov(x,y,n),u)
+z@[i:is(x,y)][n:nis(z,0c)]
+isov1:=isf(cx,cx,[t:cx]ov(t,z,n),x,y,i):is(ov(x,z,n),ov(y,z,n))
+i@[n:nis(x,0c)][o:nis(y,0c)]
+isov2:=satz229h(z,x,ov(z,y,o),n,tris(cx,ts(x,ov(z,y,o)),ts(y,ov(z,y,o)),z,ists1(x,y,ov(z,y,o),i),satz229c(z,y,o))):is(ov(z,x,n),ov(z,y,o))
+z@[u:complex][i:is(x,y)][j:is(z,u)][n:nis(z,0c)][o:nis(u,0c)]
+isov12:=tris(cx,ov(x,z,n),ov(y,z,n),ov(y,u,o),isov1(x,y,z,i,n),isov2(z,u,y,j,n,o)):is(ov(x,z,n),ov(y,u,o))
+y@satz230:=tris(cx,pl(mn(x,y),y),pl(y,mn(x,y)),x,compl(mn(x,y),y),satz212h(x,y)):is(pl(mn(x,y),y),x)
+satz231:=satz212e(pl(x,y),y,x,compl(y,x)):is(mn(pl(x,y),y),x)
+satz232:=satz212e(x,mn(x,y),y,satz230):is(mn(x,mn(x,y)),y)
++4233
+z@t1:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(mn(mn(x,y),z),pl(y,z)),pl(mn(mn(x,y),z),pl(z,y)),pl(pl(mn(mn(x,y),z),z),y),compl(pl(y,z),mn(mn(x,y),z)),ispl2(pl(y,z),pl(z,y),mn(mn(x,y),z),compl(y,z)),asspl2(mn(mn(x,y),z),z,y)):is(pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y))
+t2:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y),pl(mn(x,y),y),x,t1,ispl1(pl(mn(mn(x,y),z),z),mn(x,y),y,satz230(mn(x,y),z)),satz230(x,y)):is(pl(pl(y,z),mn(mn(x,y),z)),x)
+-4233
+z@satz233:=satz212d(x,pl(y,z),mn(mn(x,y),z),t2".4233"):is(mn(mn(x,y),z),mn(x,pl(y,z)))
+satz234:=satz212g(pl(x,y),z,pl(x,mn(y,z)),tris(cx,pl(pl(x,mn(y,z)),z),pl(x,pl(mn(y,z),z)),pl(x,y),asspl1(x,mn(y,z),z),ispl2(pl(mn(y,z),z),y,x,satz230(y,z)))):is(mn(pl(x,y),z),pl(x,mn(y,z)))
+satz234a:=symis(cx,mn(pl(x,y),z),pl(x,mn(y,z)),satz234):is(pl(x,mn(y,z)),mn(pl(x,y),z))
+satz234b:=tr3is(cx,mn(pl(x,y),z),mn(pl(y,x),z),pl(y,mn(x,z)),pl(mn(x,z),y),ismn1(pl(x,y),pl(y,x),z,compl(x,y)),satz234(y,x,z),compl(y,mn(x,z))):is(mn(pl(x,y),z),pl(mn(x,z),y))
+satz234c:=symis(cx,mn(pl(x,y),z),pl(mn(x,z),y),satz234b):is(pl(mn(x,z),y),mn(pl(x,y),z))
+satz235:=satz212f(x,mn(y,z),pl(mn(x,y),z),tr3is(cx,pl(pl(mn(x,y),z),mn(y,z)),pl(mn(x,y),pl(z,mn(y,z))),pl(mn(x,y),y),x,asspl1(mn(x,y),z,mn(y,z)),ispl2(pl(z,mn(y,z)),y,mn(x,y),satz212h(y,z)),satz230(x,y))):is(pl(mn(x,y),z),mn(x,mn(y,z)))
+satz235a:=symis(cx,pl(mn(x,y),z),mn(x,mn(y,z)),satz235):is(mn(x,mn(y,z)),pl(mn(x,y),z))
+satz235b:=tris(cx,mn(x,mn(y,z)),pl(mn(x,y),z),mn(pl(x,z),y),satz235a,satz234c(x,z,y)):is(mn(x,mn(y,z)),mn(pl(x,z),y))
+satz235c:=tris(cx,mn(x,mn(y,z)),mn(pl(x,z),y),mn(pl(z,x),y),satz235b,ismn1(pl(x,z),pl(z,x),y,compl(x,z))):is(mn(x,mn(y,z)),mn(pl(z,x),y))
+satz236:=satz212g(pl(x,z),pl(y,z),mn(x,y),tris(cx,pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y)))):is(mn(pl(x,z),pl(y,z)),mn(x,y))
+satz236a:=tris(cx,mn(pl(z,x),pl(z,y)),mn(pl(x,z),pl(y,z)),mn(x,y),ismn12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y)),satz236):is(mn(pl(z,x),pl(z,y)),mn(x,y))
+[u:complex]
++4237
+t1:=tr3is(cx,pl(mn(z,u),pl(u,y)),pl(pl(mn(z,u),u),y),pl(z,y),pl(y,z),asspl2(mn(z,u),u,y),ispl1(pl(mn(z,u),u),z,y,satz230(z,u)),compl(z,y)):is(pl(mn(z,u),pl(u,y)),pl(y,z))
+t2:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(pl(mn(x,y),mn(z,u)),pl(u,y)),pl(mn(x,y),pl(mn(z,u),pl(u,y))),pl(mn(x,y),pl(y,z)),ispl2(pl(y,u),pl(u,y),pl(mn(x,y),mn(z,u)),compl(y,u)),asspl1(mn(x,y),mn(z,u),pl(u,y)),ispl2(pl(mn(z,u),pl(u,y)),pl(y,z),mn(x,y),t1)):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)))
+t3:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),t2,asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y))):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(x,z))
+-4237
+satz237:=satz212f(pl(x,z),pl(y,u),pl(mn(x,y),mn(z,u)),t3".4237"):is(pl(mn(x,y),mn(z,u)),mn(pl(x,z),pl(y,u)))
++4238
+t1:=tris(cx,pl(pl(x,u),z),pl(x,pl(u,z)),pl(x,pl(z,u)),asspl1(x,u,z),ispl2(pl(u,z),pl(z,u),x,compl(u,z))):is(pl(pl(x,u),z),pl(x,pl(z,u)))
+t2:=tr3is(cx,pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(pl(pl(x,u),z),pl(pl(y,z),u)),mn(pl(x,pl(z,u)),pl(y,pl(z,u))),mn(x,y),satz237(pl(x,u),pl(y,z),z,u),ismn12(pl(pl(x,u),z),pl(x,pl(z,u)),pl(pl(y,z),u),pl(y,pl(z,u)),t1,asspl1(y,z,u)),satz236(x,y,pl(z,u))):is(pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(x,y))
+-4238
+satz238:=satz212g(mn(x,y),mn(z,u),mn(pl(x,u),pl(y,z)),t2".4238"):is(mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)))
+[i:is(mn(x,y),mn(z,u))]
++4239
+t1:=tris1(cx,mn(pl(x,u),pl(y,z)),0c,mn(mn(x,y),mn(z,u)),satz238,satz213b(mn(x,y),mn(z,u),i)):is(mn(pl(x,u),pl(y,z)),0c)
+-4239
+satz239a:=satz213a(pl(x,u),pl(y,z),t1".4239"):is(pl(x,u),pl(y,z))
+u@[i:is(pl(x,u),pl(y,z))]
++*4239
+i@t2:=tris(cx,mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)),0c,satz238,satz213b(pl(x,u),pl(y,z),i)):is(mn(mn(x,y),mn(z,u)),0c)
+-4239
+i@satz239b:=satz213a(mn(x,y),mn(z,u),t2".4239"):is(mn(x,y),mn(z,u))
+y@[n:nis(y,0c)]
+satz240:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c(x,y,n)):is(ts(ov(x,y,n),y),x)
+satz241:=satz229h(ts(x,y),y,x,n,comts(y,x)):is(ov(ts(x,y),y,n),x)
+y@[n:nis(x,0c)][o:nis(y,0c)]
+lemma6:=th3"l.imp"(is(ov(x,y,o),0c),is(x,0c),n,[t:is(ov(x,y,o),0c)]tris1(cx,x,0c,ts(y,ov(x,y,o)),satz229c(x,y,o),satz221b(y,ov(x,y,o),t))):nis(ov(x,y,o),0c)
+satz242:=satz229h(x,ov(x,y,o),y,lemma6,satz240(o)):is(ov(x,ov(x,y,o),lemma6),y)
+z@[n:nis(y,0c)][o:nis(z,0c)]
++5243
+t1:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ov(ov(x,y,n),z,o),ts(y,z)),ts(ov(ov(x,y,n),z,o),ts(z,y)),ts(ts(ov(ov(x,y,n),z,o),z),y),comts(ts(y,z),ov(ov(x,y,n),z,o)),ists2(ts(y,z),ts(z,y),ov(ov(x,y,n),z,o),comts(y,z)),assts2(ov(ov(x,y,n),z,o),z,y)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y))
+t2:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y),ts(ov(x,y,n),y),x,t1,ists1(ts(ov(ov(x,y,n),z,o),z),ov(x,y,n),y,satz240(ov(x,y,n),z,o)),satz240(x,y,n)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),x)
+-5243
+satz243:=satz229g(x,ts(y,z),ov(ov(x,y,n),z,o),satz221d(y,z,n,o),t2".5243"):is(ov(ov(x,y,n),z,o),ov(x,ts(y,z),satz221d(y,z,n,o)))
+z@[n:nis(z,0c)]
+satz244:=satz229k(ts(x,y),z,ts(x,ov(y,z,n)),n,tris(cx,ts(ts(x,ov(y,z,n)),z),ts(x,ts(ov(y,z,n),z)),ts(x,y),assts1(x,ov(y,z,n),z),ists2(ts(ov(y,z,n),z),y,x,satz240(y,z,n)))):is(ov(ts(x,y),z,n),ts(x,ov(y,z,n)))
+satz244a:=symis(cx,ov(ts(x,y),z,n),ts(x,ov(y,z,n)),satz244):is(ts(x,ov(y,z,n)),ov(ts(x,y),z,n))
+satz244b:=tr3is(cx,ov(ts(x,y),z,n),ov(ts(y,x),z,n),ts(y,ov(x,z,n)),ts(ov(x,z,n),y),isov1(ts(x,y),ts(y,x),z,comts(x,y),n),satz244(y,x,z,n),comts(y,ov(x,z,n))):is(ov(ts(x,y),z,n),ts(ov(x,z,n),y))
+satz244c:=symis(cx,ov(ts(x,y),z,n),ts(ov(x,z,n),y),satz244b):is(ts(ov(x,z,n),y),ov(ts(x,y),z,n))
+z@[n:nis(y,0c)][o:nis(z,0c)]
+satz245:=satz229j(x,ov(y,z,o),ts(ov(x,y,n),z),lemma6(y,z,n,o),tr3is(cx,ts(ts(ov(x,y,n),z),ov(y,z,o)),ts(ov(x,y,n),ts(z,ov(y,z,o))),ts(ov(x,y,n),y),x,assts1(ov(x,y,n),z,ov(y,z,o)),ists2(ts(z,ov(y,z,o)),y,ov(x,y,n),satz229c(y,z,o)),satz240(x,y,n))):is(ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)))
+satz245a:=symis(cx,ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)),satz245):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z))
+satz245b:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z),ov(ts(x,z),y,n),satz245a,satz244c(x,z,y,n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n))
+satz245c:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n),ov(ts(z,x),y,n),satz245b,isov1(ts(x,z),ts(z,x),y,comts(x,z),n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(z,x),y,n))
+satz246:=satz229k(ts(x,z),ts(y,z),ov(x,y,n),satz221d(y,z,n,o),tris(cx,ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n)))):is(ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n))
+satz246a:=tris(cx,ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n),isov12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y),satz221d(z,y,o,n),satz221d(y,z,n,o)),satz246):is(ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(x,y,n))
+z@[u:complex][n:nis(y,0c)][o:nis(u,0c)]
++5247
+t1:=tr3is(cx,ts(ov(z,u,o),ts(u,y)),ts(ts(ov(z,u,o),u),y),ts(z,y),ts(y,z),assts2(ov(z,u,o),u,y),ists1(ts(ov(z,u,o),u),z,y,satz240(z,u,o)),comts(z,y)):is(ts(ov(z,u,o),ts(u,y)),ts(y,z))
+t2:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ts(ov(x,y,n),ov(z,u,o)),ts(u,y)),ts(ov(x,y,n),ts(ov(z,u,o),ts(u,y))),ts(ov(x,y,n),ts(y,z)),ists2(ts(y,u),ts(u,y),ts(ov(x,y,n),ov(z,u,o)),comts(y,u)),assts1(ov(x,y,n),ov(z,u,o),ts(u,y)),ists2(ts(ov(z,u,o),ts(u,y)),ts(y,z),ov(x,y,n),t1)):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)))
+t3:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),t2,assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n))):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(x,z))
+-5247
+satz247:=satz229j(ts(x,z),ts(y,u),ts(ov(x,y,n),ov(z,u,o)),satz221d(y,u,n,o),t3".5247"):is(ts(ov(x,y,n),ov(z,u,o)),ov(ts(x,z),ts(y,u),satz221d(y,u,n,o)))
+u@[n:nis(y,0c)][o:nis(z,0c)][p:nis(u,0c)]
++5248
+t1:=tris(cx,ts(ts(x,u),z),ts(x,ts(u,z)),ts(x,ts(z,u)),assts1(x,u,z),ists2(ts(u,z),ts(z,u),x,comts(u,z))):is(ts(ts(x,u),z),ts(x,ts(z,u)))
+t2:=tr3is(cx,ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(ts(ts(x,u),z),ts(ts(y,z),u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p)),ov(ts(x,ts(z,u)),ts(y,ts(z,u)),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),ov(x,y,n),satz247(ts(x,u),ts(y,z),z,u,satz221d(y,z,n,o),p),isov12(ts(ts(x,u),z),ts(x,ts(z,u)),ts(ts(y,z),u),ts(y,ts(z,u)),t1,assts1(y,z,u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),satz246(x,y,ts(z,u),n,satz221d(z,u,o,p))):is(ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(x,y,n))
+-5248
+satz248:=satz229k(ov(x,y,n),ov(z,u,p),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),lemma6(z,u,o,p),t2".5248"):is(ov(ov(x,y,n),ov(z,u,p),lemma6(z,u,o,p)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)))
+x@[n:nis(x,0c)]
+satz249:=satz229h(0c,x,0c,n,satz221b(x,0c,refis(cx,0c))):is(ov(0c,x,n),0c)
+satz250:=satz229h(x,x,1c,n,satz222(x)):is(ov(x,x,n),1c)
+y@[n:nis(y,0c)][i:is(x,y)]
+satz251a:=tris(cx,ov(x,y,n),ov(x,x,th2"e.notis"(cx,y,0c,x,n,i)),1c,isov2(y,x,x,symis(cx,x,y,i),n,th2"e.notis"(cx,y,0c,x,n,i)),satz250(x,th2"e.notis"(cx,y,0c,x,n,i))):is(ov(x,y,n),1c)
+n@[i:is(ov(x,y,n),1c)]
+satz251b:=tr3is(cx,x,ts(y,ov(x,y,n)),ts(y,1c),y,satz229d(x,y,n),ists2(ov(x,y,n),1c,y,i),satz222(y)):is(x,y)
+u@[n:nis(y,0c)][o:nis(u,0c)][i:is(ov(x,y,n),ov(z,u,o))]
++5252
+[j:is(z,0c)]
+t1:=tr3is(cx,ov(x,y,n),ov(z,u,o),ov(0c,u,o),0c,i,isov1(z,0c,u,j,o),satz249(u,o)):is(ov(x,y,n),0c)
+t2:=tris(cx,x,ts(y,ov(x,y,n)),0c,satz229d(x,y,n),satz221b(y,ov(x,y,n),t1)):is(x,0c)
+t3:=tris2(cx,ts(x,u),ts(y,z),0c,satz221a(x,u,t2),satz221b(y,z,j)):is(ts(x,u),ts(y,z))
+i@[p:nis(z,0c)]
+t4:=tris1(cx,ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),satz248(x,y,z,u,n,p,o),satz251a(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),i)):is(ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c)
+t5:=satz251b(ts(x,u),ts(y,z),satz221d(y,z,n,p),t4):is(ts(x,u),ts(y,z))
+-5252
+satz252a:=th1"l.imp"(is(z,0c),is(ts(x,u),ts(y,z)),[t:is(z,0c)]t3".5252"(t),[t:nis(z,0c)]t5".5252"(t)):is(ts(x,u),ts(y,z))
+o@[i:is(ts(x,u),ts(y,z))]
++*5252
+i@[j:is(z,0c)]
+t6:=tris(cx,ts(x,u),ts(y,z),0c,i,satz221b(y,z,j)):is(ts(x,u),0c)
+t7:=ore1(is(x,0c),is(u,0c),satz221c(x,u,t6),o):is(x,0c)
+t8:=tris2(cx,ov(x,y,n),ov(z,u,o),0c,tris(cx,ov(x,y,n),ov(0c,y,n),0c,isov1(x,0c,y,t7,n),satz249(y,n)),tris(cx,ov(z,u,o),ov(0c,u,o),0c,isov1(z,0c,u,j,o),satz249(u,o))):is(ov(x,y,n),ov(z,u,o))
+i@[p:nis(z,0c)]
+t9:=tris(cx,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,satz248(x,y,z,u,n,p,o),satz251a(ts(x,u),ts(y,z),satz221d(y,z,n,p),i)):is(ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),1c)
+t10:=satz251b(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),t9):is(ov(x,y,n),ov(z,u,o))
+-5252
+i@satz252b:=th1"l.imp"(is(z,0c),is(ov(x,y,n),ov(z,u,o)),[t:is(z,0c)]t8".5252"(t),[t:nis(z,0c)]t10".5252"(t)):is(ov(x,y,n),ov(z,u,o))
+z@[n:nis(y,0c)]
+satz253:=satz229g(pl(x,z),y,pl(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,pl(ov(x,y,n),ov(z,y,n))),pl(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),pl(x,z),disttp2(y,ov(x,y,n),ov(z,y,n)),ispl12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(pl(ov(x,y,n),ov(z,y,n)),ov(pl(x,z),y,n))
+z@[n:nis(z,0c)]
+distop:=symis(cx,pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n),satz253(x,z,y,n)):is(ov(pl(x,y),z,n),pl(ov(x,z,n),ov(y,z,n)))
+distpo:=satz253(x,z,y,n):is(pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n))
+u@[n:nis(y,0c)][o:nis(u,0c)]
+satz254:=tris1(cx,pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),pl(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ispl12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz253(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
+z@[n:nis(y,0c)]
+satz255:=satz229g(mn(x,z),y,mn(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,mn(ov(x,y,n),ov(z,y,n))),mn(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),mn(x,z),disttm2(y,ov(x,y,n),ov(z,y,n)),ismn12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(mn(ov(x,y,n),ov(z,y,n)),ov(mn(x,z),y,n))
+z@[n:nis(z,0c)]
+distom:=symis(cx,mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n),satz255(x,z,y,n)):is(ov(mn(x,y),z,n),mn(ov(x,z,n),ov(y,z,n)))
+distmo:=satz255(x,z,y,n):is(mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n))
+u@[n:nis(y,0c)][o:nis(u,0c)]
+satz256:=tris1(cx,mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),mn(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ismn12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz255(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
+x@conj:=pli(re(x),m0"r"(im(x))):complex
+b@conjisa:=isrecx12(re(pli(a,b)),a,m0"r"(im(pli(a,b))),m0"r"(b),reis(a,b),ism0"r"(im(pli(a,b)),b,imis(a,b))):is(conj(pli(a,b)),pli(a,m0"r"(b)))
+conjisb:=symis(cx,conj(pli(a,b)),pli(a,m0"r"(b)),conjisa):is(pli(a,m0"r"(b)),conj(pli(a,b)))
+y@[i:is(x,y)]
+isconj:=isf(cx,cx,[t:cx]conj(t),x,y,i):is(conj(x),conj(y))
+x@satz257:=tr3is(cx,conj(conj(x)),pli(re(x),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,conjisa(re(x),m0"r"(im(x))),isrecx2(m0"r"(m0"r"(im(x))),im(x),re(x),satz177(im(x))),pliis(x)):is(conj(conj(x)),x)
+[i:is(x,0c)]
+satz258a:=tr3is(cx,conj(x),conj(0c),pli(0,m0"r"(0)),0c,isconj(x,0c,i),conjisa(0,0),isrecx2(m0"r"(0),0,0,satz176b(0,refis(real,0)))):is(conj(x),0c)
+x@[i:is(conj(x),0c)]
++6258
+t1:=tris(real,re(x),re(conj(x)),0,isre(re(x),m0"r"(im(x))),lemma1(conj(x),i)):is"r"(re(x),0)
+t2:=satz176e(im(x),tris(real,m0"r"(im(x)),im(conj(x)),0,isim(re(x),m0"r"(im(x))),lemma2(conj(x),i))):is"r"(im(x),0)
+-6258
+satz258b:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t1".6258",t2".6258")):is(x,0c)
++*6258
+i@anders:=tris1(cx,x,0c,conj(conj(x)),satz257,satz258a(conj(x),i)):is(x,0c)
+-6258
+x@[n:nis(x,0c)]
+satz258c:=th3"l.imp"(is(conj(x),0c),is(x,0c),n,[t:is(conj(x),0c)]satz258b(t)):nis(conj(x),0c)
+x@[i:is(conj(x),x)]
++6259
+t1:=tris(real,m0"r"(im(x)),im(conj(x)),im(x),isim(re(x),m0"r"(im(x))),isceim(conj(x),x,i)):is"r"(m0"r"(im(x)),im(x))
+-6259
+satz259a:=lemma10(im(x),symis(real,m0"r"(im(x)),im(x),t1".6259")):is"r"(im(x),0)
+x@[i:is"r"(im(x),0)]
+satz259b:=tris(cx,conj(x),pli(re(x),im(x)),x,isrecx2(m0"r"(im(x)),im(x),re(x),tris2(real,m0"r"(im(x)),im(x),0,satz176b(im(x),i),i)),pliis(x)):is(conj(x),x)
+x@[i:is(x,conj(x))]
+satz269c:=satz259a(x,symis(cx,x,conj(x),i)):is"r"(im(x),0)
+x@[i:is"r"(im(x),0)]
+satz269d:=symis(cx,conj(x),x,satz259b(i)):is(x,conj(x))
+y@satz260:=tr3is(cx,conj(pl(x,y)),pli(pl"r"(re(x),re(y)),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(re(x),re(y)),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(conj(x),conj(y)),conjisa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx2(m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),pl"r"(re(x),re(y)),satz180(im(x),im(y))),plis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(pl(x,y)),pl(conj(x),conj(y)))
+satz260a:=symis(cx,conj(pl(x,y)),pl(conj(x),conj(y)),satz260):is(pl(conj(x),conj(y)),conj(pl(x,y)))
++6261
+t1:=tris(real,m0"r"(imts(x,y)),pl"r"(m0"r"(ts"r"(re(x),im(y))),m0"r"(ts"r"(im(x),re(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),satz180(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(m0"r"(ts"r"(re(x),im(y))),ts"r"(re(x),m0"r"(im(y))),m0"r"(ts"r"(im(x),re(y))),ts"r"(m0"r"(im(x)),re(y)),satz197f(re(x),im(y)),satz197e(im(x),re(y)))):is"r"(m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))))
+-6261
+satz261:=tr3is(cx,conj(ts(x,y)),pli(rets(x,y),m0"r"(imts(x,y))),pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y)))),ts(conj(x),conj(y)),conjisa(rets(x,y),imts(x,y)),isrecx12(rets(x,y),mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),ismn2"r"(ts"r"(im(x),im(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y))),ts"r"(re(x),re(y)),satz198a(im(x),im(y))),t1".6261"),tsis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(ts(x,y)),ts(conj(x),conj(y)))
+satz261a:=symis(cx,conj(ts(x,y)),ts(conj(x),conj(y)),satz261):is(ts(conj(x),conj(y)),conj(ts(x,y)))
++6262
+t1:=symis(cx,pl(mn(x,y),y),x,satz230(x,y)):is(x,pl(mn(x,y),y))
+t2:=tris(cx,conj(x),conj(pl(mn(x,y),y)),pl(conj(mn(x,y)),conj(y)),isconj(x,pl(mn(x,y),y),t1),satz260(mn(x,y),y)):is(conj(x),pl(conj(mn(x,y)),conj(y)))
+-6262
+satz262:=satz212f(conj(x),conj(y),conj(mn(x,y)),symis(cx,conj(x),pl(conj(mn(x,y)),conj(y)),t2".6262")):is(conj(mn(x,y)),mn(conj(x),conj(y)))
+satz262a:=symis(cx,conj(mn(x,y)),mn(conj(x),conj(y)),satz262):is(mn(conj(x),conj(y)),conj(mn(x,y)))
+[n:nis(y,0c)]
++6263
+t1:=satz229f(x,y,n):is(x,ts(ov(x,y,n),y))
+t2:=isconj(x,ts(ov(x,y,n),y),t1):is(conj(x),conj(ts(ov(x,y,n),y)))
+t3:=satz261(ov(x,y,n),y):is(conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)))
+t4:=tris(cx,conj(x),conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)),t2,t3):is(conj(x),ts(conj(ov(x,y,n)),conj(y)))
+t5:=satz258c(y,n):nis(conj(y),0c)
+-6263
+satz263:=satz229j(conj(x),conj(y),conj(ov(x,y,n)),t5".6263",symis(cx,conj(x),ts(conj(ov(x,y,n)),conj(y)),t4".6263")):is(conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)))
+satz263a:=symis(cx,conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)),satz263):is(ov(conj(x),conj(y),satz258c(y,n)),conj(ov(x,y,n)))
+x@mod:=sqrt(mod2(x),lemma5(x)):real
+y@[i:is(x,y)]
+ismod:=isf(cx,real,[t:cx]mod(t),x,y,i):is"r"(mod(x),mod(y))
+x@[n:nis(x,0c)]
+satz264a:=sqrtnot0(mod2(x),lemma5(x),pnot0(mod2(x),lemma4(x,n))):pos(mod(x))
+x@[i:is(x,0c)]
+satz264b:=sqrt0(mod2(x),lemma5(x),lemma3(x,i)):is"r"(mod(x),0)
+x@satz264c:=thsqrt1a(mod2(x),lemma5(x)):not(neg(mod(x)))
+satz264d:=satz167f(mod(x),0,th3"l.imp"(less(mod(x),0),neg(mod(x)),satz264c,[t:less(mod(x),0)]satz169d(mod(x),t))):moreis(mod(x),0)
++7265
+t1:=symis(real,ts"r"(mod(x),mod(x)),mod2(x),thsqrt1b(mod2(x),lemma5(x))):is"r"(mod2(x),ts"r"(mod(x),mod(x)))
+t2:=tris(real,pl"r"(ts"r"(re(x),re(x)),0),ts"r"(re(x),re(x)),ts"r"(abs(re(x)),abs(re(x))),pl02(ts"r"(re(x),re(x)),0,refis(real,0)),lemma12"r"(re(x))):is"r"(pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))))
+t3:=satz191(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),ts"r"(im(x),im(x)),0,moreisi2(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),refis(real,ts"r"(re(x),re(x)))),lemma11"r"(im(x))):moreis(mod2(x),pl"r"(ts"r"(re(x),re(x)),0))
+t4:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))),t1,t2,t3):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(re(x)),abs(re(x))))
+t5:=tris(real,pl"r"(0,ts"r"(im(x),im(x))),ts"r"(im(x),im(x)),ts"r"(abs(im(x)),abs(im(x))),pl01(0,ts"r"(im(x),im(x)),refis(real,0)),lemma12"r"(im(x))):is"r"(pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))))
+t6:=satz191(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),lemma11"r"(re(x)),moreisi2(ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),refis(real,ts"r"(im(x),im(x))))):moreis(mod2(x),pl"r"(0,ts"r"(im(x),im(x))))
+t7:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))),t1,t5,t6):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(im(x)),abs(im(x))))
+@[r:real][s:real][m:moreis(ts"r"(r,r),ts"r"(s,s))][n:moreis(r,0)][l:less(r,s)]
+t8:=lemma2"r"(r,s,l):more(s,r)
+t9:=satz169b(s,satz172d(s,r,0,t8,n)):pos(s)
+[o:more(r,0)]
+t10:=trmore(ts"r"(s,s),ts"r"(r,s),ts"r"(r,r),satz203a(s,r,s,t8,t9),satz203d(s,r,r,t8,satz169b(r,o))):more(ts"r"(s,s),ts"r"(r,r))
+l@[i:is"r"(r,0)]
+t11:=ismore2(0,ts"r"(r,r),ts"r"(s,s),symis(real,ts"r"(r,r),0,ts01(r,r,i)),satz169a(ts"r"(s,s),possq(s,pnot0(s,t9)))):more(ts"r"(s,s),ts"r"(r,r))
+l@t12:=lemma1"r"(ts"r"(s,s),ts"r"(r,r),orapp(more(r,0),is"r"(r,0),more(ts"r"(s,s),ts"r"(r,r)),n,[t:more(r,0)]t10(t),[t:is"r"(r,0)]t11(t))):less(ts"r"(r,r),ts"r"(s,s))
+n@t13:=satz167f(r,s,[t:less(r,s)]<t12(t)>satz167c(ts"r"(r,r),ts"r"(s,s),m)):moreis(r,s)
+-7265
+satz265a:=t13".7265"(mod(x),abs(re(x)),t4".7265",satz264d(x)):moreis(mod(x),abs(re(x)))
+satz265b:=t13".7265"(mod(x),abs(im(x)),t7".7265",satz264d(x)):moreis(mod(x),abs(im(x)))
+@[r:real][s:real][i:is(ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)))][n:not(neg(r))][o:not(neg(s))]
++7266
+@[t:real]
+t1:=pl02(ts"r"(t,t),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t))
+t2:=tris(real,pl"r"(ts"r"(t,0),ts"r"(0,t)),ts"r"(t,0),0,pl02(ts"r"(t,0),ts"r"(0,t),ts01(0,t,refis(real,0))),ts02(t,0,refis(real,0))):is"r"(pl"r"(ts"r"(t,0),ts"r"(0,t)),0)
+t3:=tris(cx,ts(pli(t,0),pli(t,0)),pli(mn"r"(ts"r"(t,t),ts"r"(0,0)),pl"r"(ts"r"(t,0),ts"r"(0,t))),pli(ts"r"(t,t),0),tsis12a(t,0,t,0),isrecx12(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t),pl"r"(ts"r"(t,0),ts"r"(0,t)),0,t1,t2)):is(ts(pli(t,0),pli(t,0)),pli(ts"r"(t,t),0))
+o@t4:=tr3is(cx,pli(ts"r"(r,r),0),ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)),pli(ts"r"(s,s),0),symis(cx,ts(pli(r,0),pli(r,0)),pli(ts"r"(r,r),0),t3(r)),i,t3(s)):is(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0))
+t5:=tr3is(real,ts"r"(r,r),re(pli(ts"r"(r,r),0)),re(pli(ts"r"(s,s),0)),ts"r"(s,s),isre(ts"r"(r,r),0),iscere(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0),t4),reis(ts"r"(s,s),0)):is"r"(ts"r"(r,r),ts"r"(s,s))
+t6:=andi(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)),n,t5):and(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)))
+t7:=andi(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)),o,refis(real,ts"r"(s,s))):and(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)))
+-7266
+satz266:=satzr161b(ts"r"(s,s),r,s,t6".7266",t7".7266"):is"r"(r,s)
++7267
+x@t1:=tris(cx,ts(pli(mod(x),0),pli(mod(x),0)),pli(ts"r"(mod(x),mod(x)),0),pli(mod2(x),0),t3"c.7266"(mod(x)),isrecx1(ts"r"(mod(x),mod(x)),mod2(x),0,thsqrt1b(mod2(x),lemma5(x)))):is(ts(pli(mod(x),0),pli(mod(x),0)),pli(mod2(x),0))
+t2:=ispl2"r"(m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(im(x),im(x)),ts"r"(re(x),re(x)),tris(real,m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),satz197e(im(x),m0"r"(im(x))),satz198(im(x),im(x)))):is"r"(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x))
+t3:=tris(real,pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),pl"r"(m0"r"(ts"r"(re(x),im(x))),ts"r"(re(x),im(x))),0,ispl12"r"(ts"r"(re(x),m0"r"(im(x))),m0"r"(ts"r"(re(x),im(x))),ts"r"(im(x),re(x)),ts"r"(re(x),im(x)),satz197b(re(x),im(x)),comts"r"(im(x),re(x))),satz179a(ts"r"(re(x),im(x)))):is"r"(pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0)
+t4:=tris(cx,ts(x,conj(x)),pli(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x)))),pli(mod2(x),0),tsis2a(x,re(x),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0,t2,t3)):is(ts(x,conj(x)),pli(mod2(x),0))
+-7267
+x@satz267:=tris2(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),pli(mod2(x),0),t1".7267",t4".7267"):is(ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)))
+satz267a:=symis(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),satz267):is(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)))
++7268
+z@t1:=tr3is(cx,ts(x,ts(y,z)),ts(ts(x,y),z),ts(ts(y,x),z),ts(y,ts(x,z)),assts2(x,y,z),ists1(ts(x,y),ts(y,x),z,comts(x,y)),assts1(y,x,z)):is(ts(x,ts(y,z)),ts(y,ts(x,z)))
+[u:complex]
+t2:=tr3is(cx,ts(ts(x,y),ts(z,u)),ts(x,ts(y,ts(z,u))),ts(x,ts(z,ts(y,u))),ts(ts(x,z),ts(y,u)),assts1(x,y,ts(z,u)),ists2(ts(y,ts(z,u)),ts(z,ts(y,u)),x,t1(y,z,u)),assts2(x,z,ts(y,u))):is(ts(ts(x,y),ts(z,u)),ts(ts(x,z),ts(y,u)))
+y@t3:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,y),conj(ts(x,y))),ts(ts(x,y),ts(conj(x),conj(y))),ts(ts(x,conj(x)),ts(y,conj(y))),satz267(ts(x,y)),ists2(conj(ts(x,y)),ts(conj(x),conj(y)),ts(x,y),satz261(x,y)),t2(x,y,conj(x),conj(y))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))))
+t4:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))),ts(ts(pli(mod(x),0),pli(mod(x),0)),ts(pli(mod(y),0),pli(mod(y),0))),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),t3,ists12(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)),ts(y,conj(y)),ts(pli(mod(y),0),pli(mod(y),0)),satz267a(x),satz267a(y)),t2(pli(mod(x),0),pli(mod(x),0),pli(mod(y),0),pli(mod(y),0))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))))
+@[r:real][s:real]
+t5:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
+t6:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
+t7:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t5,t6)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
+y@t8:=tris(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)),t4,ists12(ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),t7(mod(x),mod(y)),t7(mod(x),mod(y)))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)))
+[n:neg(ts"r"(mod(x),mod(y)))]
+t9:=orapp(and(pos(mod(x)),neg(mod(y))),and(neg(mod(x)),pos(mod(y))),con,satz196h(mod(x),mod(y),n),[t:and(pos(mod(x)),neg(mod(y)))]<ande2(pos(mod(x)),neg(mod(y)),t)>satz264c(y),[t:and(neg(mod(x)),pos(mod(y)))]<ande1(neg(mod(x)),pos(mod(y)),t)>satz264c(x)):con
+-7268
+y@satz268:=satz266(mod(ts(x,y)),ts"r"(mod(x),mod(y)),t8".7268",satz264c(ts(x,y)),[t:neg(ts"r"(mod(x),mod(y)))]t9".7268"(t)):is"r"(mod(ts(x,y)),ts"r"(mod(x),mod(y)))
+satz268a:=symis(real,mod(ts(x,y)),ts"r"(mod(x),mod(y)),satz268):is"r"(ts"r"(mod(x),mod(y)),mod(ts(x,y)))
+[n:nis(y,0c)]
++7269
+t1:=pnot0(mod(y),satz264a(y,n)):nis"r"(mod(y),0)
+t2:=tris1(real,ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),mod(ts(ov(x,y,n),y)),satz268(ov(x,y,n),y),ismod(ts(ov(x,y,n),y),x,satz240(x,y,n))):is"r"(ts"r"(mod(ov(x,y,n)),mod(y)),mod(x))
+t3:=satz204g(mod(x),mod(y),mod(ov(x,y,n)),t1,tris(real,ts"r"(mod(y),mod(ov(x,y,n))),ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),comts"r"(mod(y),mod(ov(x,y,n))),t2)):is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),t1))
+-7269
+satz269:=t3".7269":is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),pnot0(mod(y),satz264a(y,n))))
+y@[i:is(pl(x,y),1c)]
++7270
+@[r:real]
+t1:=th1"l.imp"(neg(r),moreis(abs(r),r),[t:neg(r)]moreisi1(abs(r),r,trmore(abs(r),0,r,satz169a(abs(r),satz166b(r,t)),lemma2"r"(r,0,satz169c(r,t)))),[t:not(neg(r))]moreisi2(abs(r),r,absnn(r,t))):moreis(abs(r),r)
+x@t2:=trmoreis(mod(x),abs(re(x)),re(x),satz265a(x),t1(re(x))):moreis(mod(x),re(x))
+i@t3:=tr3is(real,pl"r"(re(x),re(y)),re(pl(x,y)),re(1c),1rl,isre(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),iscere(pl(x,y),1c,i),reis(1rl,0)):is"r"(pl"r"(re(x),re(y)),1rl)
+-7270
+satz270:=ismoreis2(pl"r"(re(x),re(y)),1rl,pl"r"(mod(x),mod(y)),t3".7270",satz191(mod(x),re(x),mod(y),re(y),t2".7270",t2".7270"(y))):moreis(pl"r"(mod(x),mod(y)),1rl)
++7271
+y@[i:is(pl(x,y),0c)]
+t1:=satz264b(pl(x,y),i):is"r"(mod(pl(x,y)),0)
+t2:=ismoreis2(pl"r"(0,0),mod(pl(x,y)),pl"r"(mod(x),mod(y)),tris2(real,pl"r"(0,0),mod(pl(x,y)),0,pl01(0,0,refis(real,0)),t1),satz191(mod(x),0,mod(y),0,satz264d(x),satz264d(y))):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
+y@[n:nis(pl(x,y),0c)]
+t3:=pnot0(mod(pl(x,y)),satz264a(pl(x,y),n)):nis"r"(mod(pl(x,y)),0)
+t4:=tris(cx,pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),ov(pl(x,y),pl(x,y),n),1c,satz253(x,pl(x,y),y,n),satz250(pl(x,y),n)):is(pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),1c)
+t5:=satz270(ov(x,pl(x,y),n),ov(y,pl(x,y),n),t4):moreis(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),1rl)
+fx:=ov"r"(mod(x),mod(pl(x,y)),t3):real
+fy:=ov"r"(mod(y),mod(pl(x,y)),t3):real
+t6:=ismoreis1(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),pl"r"(fx,fy),1rl,ispl12"r"(mod(ov(x,pl(x,y),n)),fx,mod(ov(y,pl(x,y),n)),fy,satz269(x,pl(x,y),n),satz269(y,pl(x,y),n)),t5):moreis(pl"r"(fx,fy),1rl)
+prl:=ts"r"(pl"r"(fx,fy),mod(pl(x,y))):real
+prr:=ts"r"(1rl,mod(pl(x,y))):real
+t7:=orapp(more(pl"r"(fx,fy),1rl),is"r"(pl"r"(fx,fy),1rl),moreis(prl,prr),t6,[t:more(pl"r"(fx,fy),1rl)]moreisi1(prl,prr,satz203a(pl"r"(fx,fy),1rl,mod(pl(x,y)),t,satz264a(pl(x,y),n))),[t:is"r"(pl"r"(fx,fy),1rl)]moreisi2(prl,prr,ists1"r"(pl"r"(fx,fy),1rl,mod(pl(x,y)),t))):moreis(prl,prr)
+t8:=tris(real,prl,pl"r"(ts"r"(fx,mod(pl(x,y))),ts"r"(fy,mod(pl(x,y)))),pl"r"(mod(x),mod(y)),disttp1"r"(fx,fy,mod(pl(x,y))),ispl12"r"(ts"r"(fx,mod(pl(x,y))),mod(x),ts"r"(fy,mod(pl(x,y))),mod(y),satz204e(mod(x),mod(pl(x,y)),t3),satz204e(mod(y),mod(pl(x,y)),t3))):is"r"(prl,pl"r"(mod(x),mod(y)))
+t9:=satz195b(mod(pl(x,y))):is"r"(prr,mod(pl(x,y)))
+t10:=ismoreis12(prl,pl"r"(mod(x),mod(y)),prr,mod(pl(x,y)),t8,t9,t7):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
+y@t11:=th1"l.imp"(is(pl(x,y),0c),moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y))),[t:is(pl(x,y),0c)]t2(t),[t:nis(pl(x,y),0c)]t10(t)):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
+-7271
+y@satz271:=satz168a(pl"r"(mod(x),mod(y)),mod(pl(x,y)),t11".7271"):lessis(mod(pl(x,y)),pl"r"(mod(x),mod(y)))
+satz271a:=t11".7271":moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
++7272
+x@t1:=tris(real,re(m0(x)),re(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(re(x)),iscere(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),reis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(re(m0(x)),m0"r"(re(x)))
+t2:=tris(real,ts"r"(re(m0(x)),re(m0(x))),ts"r"(m0"r"(re(x)),m0"r"(re(x))),ts"r"(re(x),re(x)),ists12"r"(re(m0(x)),m0"r"(re(x)),re(m0(x)),m0"r"(re(x)),t1,t1),satz198(re(x),re(x))):is"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)))
+t3:=tris(real,im(m0(x)),im(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(im(x)),isceim(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),imis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(im(m0(x)),m0"r"(im(x)))
+t4:=tris(real,ts"r"(im(m0(x)),im(m0(x))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),ists12"r"(im(m0(x)),m0"r"(im(x)),im(m0(x)),m0"r"(im(x)),t3,t3),satz198(im(x),im(x))):is"r"(ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)))
+t5:=ispl12"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)),ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)),t2,t4):is"r"(mod2(m0(x)),mod2(x))
+-7272
+x@satz272:=issqrt(mod2(m0(x)),mod2(x),lemma5(m0(x)),lemma5(x),t5".7272"):is"r"(mod(m0(x)),mod(x))
+satz272a:=symis(real,mod(m0(x)),mod(x),satz272):is"r"(mod(x),mod(m0(x)))
++7273
+y@sum:=pl"r"(mod(y),mod(mn(x,y))):real
+t1:=islessis1(mod(pl(y,mn(x,y))),mod(x),sum,ismod(pl(y,mn(x,y)),x,satz212h(x,y)),satz271(y,mn(x,y))):lessis(mod(x),sum)
+t2:=th9"l.or"(less(mod(x),sum),is"r"(mod(x),sum),less(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),is"r"(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),t1,[t:less(mod(x),sum)]satz188f(mod(x),sum,m0"r"(mod(y)),t),[t:is"r"(mod(x),sum)]ismn1"r"(mod(x),sum,mod(y),t)):lessis(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y)))
+t3:=tris(real,mn"r"(sum,mod(y)),mn"r"(pl"r"(mod(mn(x,y)),mod(y)),mod(y)),mod(mn(x,y)),ismn1"r"(sum,pl"r"(mod(mn(x,y)),mod(y)),mod(y),compl"r"(mod(y),mod(mn(x,y)))),mnpl(mod(mn(x,y)),mod(y))):is"r"(mn"r"(sum,mod(y)),mod(mn(x,y)))
+t4:=satz168b(mn"r"(mod(x),mod(y)),mod(mn(x,y)),islessis2(mn"r"(sum,mod(y)),mod(mn(x,y)),mn"r"(mod(x),mod(y)),t3,t2)):moreis(mod(mn(x,y)),mn"r"(mod(x),mod(y)))
+t5:=ismoreis12(mod(mn(y,x)),mod(mn(x,y)),mn"r"(mod(y),mod(x)),m0"r"(mn"r"(mod(x),mod(y))),tris1(real,mod(mn(y,x)),mod(mn(x,y)),mod(m0(mn(x,y))),ismod(m0(mn(x,y)),mn(y,x),satz219(x,y)),satz272(mn(x,y))),satz181a(mod(y),mod(x)),t4(y,x)):moreis(mod(mn(x,y)),m0"r"(mn"r"(mod(x),mod(y))))
+@[r:real][s:real][m:moreis(r,s)][n:moreis(r,m0"r"(s))]
+r@t6:=th9"l.or"(neg(r),not(neg(r)),is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r),th6"l.or"(neg(r)),[t:neg(r)]absn(r,t),[t:not(neg(r))]absnn(r,t)):or(is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r))
+n@t7:=orapp(is"r"(abs(s),m0"r"(s)),is"r"(abs(s),s),moreis(r,abs(s)),t6(s),[t:is"r"(abs(s),m0"r"(s))]ismoreis2(m0"r"(s),abs(s),r,symis(real,abs(s),m0"r"(s),t),n),[t:is"r"(abs(s),s)]ismoreis2(s,abs(s),r,symis(real,abs(s),s,t),m)):moreis(r,abs(s))
+-7273
+y@satz273:=t7".7273"(mod(mn(x,y)),mn"r"(mod(x),mod(y)),t4".7273",t5".7273"):moreis(mod(mn(x,y)),abs(mn"r"(mod(x),mod(y))))
+-c
+-r
+-rp
+-rt
+@[x:nat][y:nat]
++8274
+prop1:=some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)):'prop'
+x@prop2:=all([y:nat]imp(less(x,y),not(prop1(y)))):'prop'
+@[y:nat][l:less(1,y)][f:[t:1to(1)]1to(y)]
+1y:=1out(y):1to(y)
+yy:=xout(y):1to(y)
+[i:is"e"(1to(y),1y,yy)]
+t1:=isoutne(y,1,satz24a(y),y,lessisi3(y),i):is(1,y)
+f@t2:=ec3e31(is(1,y),more(1,y),less(1,y),satz10b(1,y),l):nis(1,y)
+t3:=th3"l.imp"(is"e"(1to(y),1y,yy),is(1,y),t2,[t:is"e"(1to(y),1y,yy)]t1(t)):not(is"e"(1to(y),1y,yy))
+[u:1to(1)]
+t4:=isf(1to(1),1to(y),f,u,1o,th1"n.singlet"(u)):is"e"(1to(y),<u>f,<1o>f)
+f@[i:is"e"(1to(y),<1o>f,1y)][u:1to(1)]
+t5:=th2"e.notis"(1to(y),1y,yy,<u>f,t3,tris(1to(y),<u>f,<1o>f,1y,t4(u),i)):not(is"e"(1to(y),<u>f,yy))
+i@t6:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),yy,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,yy,t5(u))):not(image(1to(1),1to(y),f,yy))
+t7:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),yy,t6):not(surjective(1to(1),1to(y),f))
+f@[n:not(is"e"(1to(y),<1o>f,1y))][u:1to(1)]
+t8:=th2"e.notis"(1to(y),<1o>f,1y,<u>f,n,t4(u)):not(is"e"(1to(y),<u>f,1y))
+n@t9:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),1y,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,1y,t8(u))):not(image(1to(1),1to(y),f,1y))
+t10:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),1y,t9):not(surjective(1to(1),1to(y),f))
+f@t11:=th1"l.imp"(is"e"(1to(y),<1o>f,1y),not(surjective(1to(1),1to(y),f)),[t:is"e"(1to(y),<1o>f,1y)]t7(t),[t:not(is"e"(1to(y),<1o>f,1y))]t10(t)):not(surjective(1to(1),1to(y),f))
+t12:=th2"l.and"(injective(1to(1),1to(y),f),surjective(1to(1),1to(y),f),t11):not(bijective(1to(1),1to(y),f))
+l@t13:=th5"l.some"([t:1to(1)]1to(y),[f:[t:1to(1)]1to(y)]bijective(1to(1),1to(y),f),[f:[t:1to(1)]1to(y)]t12(f)):not(prop1(1,y))
+@t14:=[y:nat][t:less(1,y)]t13(y,t):prop2(1)
+x@[p:prop2(x)][y:nat][l:less(<x>suc,y)]
+x@xs:=<x>suc:nat
+l@xxs:=xout(xs):1to(<x>suc)
+yy1:=xout(y):1to(y)
+t15:=trless(1,<x>suc,y,satz24c(x),l):less(1,y)
+ym1:=mn(y,1,t15):nat
+t16:=isless12(<x>suc,pl(x,1),y,pl(ym1,1),satz4e(x),th1c"n.mn"(y,1,t15),l):less(pl(x,1),pl(ym1,1))
+t17:=satz20c(x,ym1,1,t16):less(x,ym1)
+t18:=isless2(pl(ym1,1),y,ym1,th1d"n.mn"(y,1,t15),satz18a(ym1,1)):less(ym1,y)
+[f:[t:1to(xs)]1to(y)][b:bijective(1to(xs),1to(y),f)]
+t19:=ande1(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):injective(1to(xs),1to(y),f)
+t20:=ande2(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):surjective(1to(xs),1to(y),f)
+[i:is"e"(1to(y),<xxs>f,yy1)][u:1to(x)]
+u1:=inn(x,u):nat
+t21:=satz16a(u1,x,xs,1top(x,u),satz18c(x)):less(u1,xs)
+t22:=ec3e31(is(u1,xs),more(u1,xs),less(u1,xs),satz10b(u1,xs),t21):nis(u1,xs)
+t23:=lessisi1(u1,xs,t21):lessis(u1,xs)
+u2:=outn(xs,u1,t23):1to(xs)
+t24:=th3"l.imp"(is"e"(1to(xs),u2,xxs),is(u1,xs),t22,[t:is"e"(1to(xs),u2,xxs)]isoutne(xs,u1,t23,xs,lessisi3(xs),t)):not(is"e"(1to(xs),u2,xxs))
+[j:is"e"(1to(y),<u2>f,yy1)]
+t25:=tris2(1to(y),<u2>f,<xxs>f,yy1,j,i):is"e"(1to(y),<u2>f,<xxs>f)
+t26:=isfe(1to(xs),1to(y),f,t19,u2,xxs,t25):is"e"(1to(xs),u2,xxs)
+u@t27:=th3"l.imp"(is"e"(1to(y),<u2>f,yy1),is"e"(1to(xs),u2,xxs),t24,[t:is"e"(1to(y),<u2>f,yy1)]t26(t)):not(is"e"(1to(y),<u2>f,yy1))
+w1:=inn(y,<u2>f):nat
+[j:is(w1,y)]
+t28:=tris(1to(y),<u2>f,outn(y,w1,1top(y,<u2>f)),yy1,isoutinn(y,<u2>f),isoutni(y,w1,1top(y,<u2>f),y,lessisi3(y),j)):is"e"(1to(y),<u2>f,yy1)
+u@t29:=th3"l.imp"(is(w1,y),is"e"(1to(y),<u2>f,yy1),t27,[t:is(w1,y)]t28(t)):nis(w1,y)
+t30:=ore1(less(w1,y),is(w1,y),1top(y,<u2>f),t29):less(w1,y)
+t31:=islessis2(y,pl(ym1,1),pl(w1,1),th1c"n.mn"(y,1,t15),satz25b(y,w1,t30)):lessis(pl(w1,1),pl(ym1,1))
+t32:=th9"l.or"(less(pl(w1,1),pl(ym1,1)),is(pl(w1,1),pl(ym1,1)),less(w1,ym1),is(w1,ym1),t31,[t:less(pl(w1,1),pl(ym1,1))]satz20c(w1,ym1,1,t),[t:is(pl(w1,1),pl(ym1,1))]satz20b(w1,ym1,1,t)):lessis(w1,ym1)
+w2:=outn(ym1,w1,t32):1to(ym1)
+i@f1:=[t:1to(x)]w2(t):[t:1to(x)]1to(ym1)
+u@[v:1to(x)][j:is"e"(1to(ym1),<u>f1,<v>f1)]
+t33:=isoutne(ym1,w1(u),t32(u),w1(v),t32(v),j):is(w1(u),w1(v))
+t34:=isinne(y,<u2(u)>f,<u2(v)>f,t33):is"e"(1to(y),<u2(u)>f,<u2(v)>f)
+t35:=<t34><u2(v)><u2(u)>t19:is"e"(1to(xs),u2(u),u2(v))
+t36:=isoutne(xs,u1(u),t23(u),u1(v),t23(v),t35):is(u1(u),u1(v))
+t37:=isinne(x,u,v,t36):is"e"(1to(x),u,v)
+i@[v:1to(ym1)]
+v1:=inn(ym1,v):nat
+t38:=satz16a(v1,ym1,y,1top(ym1,v),t18):less(v1,y)
+t39:=ec3e31(is(v1,y),more(v1,y),less(v1,y),satz10b(v1,y),t38):nis(v1,y)
+t40:=lessisi1(v1,y,t38):lessis(v1,y)
+v2:=outn(y,v1,t40):1to(y)
+w3:=<v2>invf(1to(xs),1to(y),f,b):1to(xs)
+t41:=thinvf2(1to(xs),1to(y),f,b,v2):is"e"(1to(y),v2,<w3>f)
+[j:is"e"(1to(xs),w3,xxs)]
+t42:=isf(1to(xs),1to(y),f,w3,xxs,j):is"e"(1to(y),<w3>f,<xxs>f)
+t43:=tr3is(1to(y),v2,<w3>f,<xxs>f,yy1,t41,t42,i):is"e"(1to(y),v2,yy1)
+t44:=isoutne(y,v1,t40,y,lessisi3(y),t43):is(v1,y)
+v@t45:=th3"l.imp"(is"e"(1to(xs),w3,xxs),is(v1,y),t39,[t:is"e"(1to(xs),w3,xxs)]t44(t)):not(is"e"(1to(xs),w3,xxs))
+w4:=inn(xs,w3):nat
+[j:is(w4,xs)]
+t46:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),xxs,isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),xs,lessisi3(xs),j)):is"e"(1to(xs),w3,xxs)
+v@t47:=th3"l.imp"(is(w4,xs),is"e"(1to(xs),w3,xxs),t45,[t:is(w4,xs)]t46(t)):nis(w4,xs)
+t48:=ore1(less(w4,xs),is(w4,xs),1top(xs,w3),t47):less(w4,xs)
+t49:=satz26a(x,w4,t48):lessis(w4,x)
+w5:=outn(x,w4,t49):1to(x)
+t50:=isinoutn(x,w4,t49):is(w4,u1(w5))
+t51:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),u2(w5),isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),u1(w5),t23(w5),t50)):is"e"(1to(xs),w3,u2(w5))
+t52:=isf(1to(xs),1to(y),f,w3,u2(w5),t51):is"e"(1to(y),<w3>f,<u2(w5)>f)
+t53:=tris(1to(y),v2,<w3>f,<u2(w5)>f,t41,t52):is"e"(1to(y),v2,<u2(w5)>f)
+t54:=tris(nat,v1,inn(y,v2),w1(w5),isinoutn(y,v1,t40),isinni(y,v2,<u2(w5)>f,t53)):is(v1,w1(w5))
+t55:=tris(1to(ym1),v,outn(ym1,v1,1top(ym1,v)),w2(w5),isoutinn(ym1,v),isoutni(ym1,v1,1top(ym1,v),w1(w5),t32(w5),t54)):is"e"(1to(ym1),v,<w5>f1)
+t56:=somei(1to(x),[t:1to(x)]is"e"(1to(ym1),v,<t>f1),w5,t55):image(1to(x),1to(ym1),f1,v)
+i@t57:=andi(injective(1to(x),1to(ym1),f1),surjective(1to(x),1to(ym1),f1),[u:1to(x)][v:1to(x)][t:is"e"(1to(ym1),<u>f1,<v>f1)]t37(u,v,t),[u:1to(ym1)]t56(u)):bijective(1to(x),1to(ym1),f1)
+t58:=somei([t:1to(x)]1to(ym1),[g:[t:1to(x)]1to(ym1)]bijective(1to(x),1to(ym1),g),f1,t57):prop1(ym1)
+t59:=<t58><t17><ym1>p:con
+b@[n:not(is"e"(1to(y),<xxs>f,yy1))]
+m0:=<yy1>invf(1to(xs),1to(y),f,b):1to(xs)
+t60:=thinvf2(1to(xs),1to(y),f,b,yy1):is"e"(1to(y),yy1,<m0>f)
+f2:=changef(1to(xs),1to(y),f,m0,xxs):[t:1to(xs)]1to(y)
+t61:=changef2(1to(xs),1to(y),f,m0,xxs,xxs,refis(1to(xs),xxs)):is"e"(1to(y),<xxs>f2,<m0>f)
+t62:=tris2(1to(y),<xxs>f2,yy1,<m0>f,t61,t60):is"e"(1to(y),<xxs>f2,yy1)
+t63:=th6"e.wissel"(1to(xs),1to(y),f,m0,xxs,b):bijective(1to(xs),1to(y),f2)
+t64:=t59(f2,t63,t62):con
+b@t65:=th1"l.imp"(is"e"(1to(y),<xxs>f,yy1),con,[t:is"e"(1to(y),<xxs>f,yy1)]t59(t),[t:not(is"e"(1to(y),<xxs>f,yy1))]t64(t)):con
+l@t65a:=th5"l.some"([t:1to(xs)]1to(y),[f:[t:1to(xs)]1to(y)]bijective(1to(xs),1to(y),f),[f:[t:1to(xs)]1to(y)][t:bijective(1to(xs),1to(y),f)]t65(f,t)):not(prop1(xs,y))
+p@t66:=[y:nat][t:less(xs,y)]t65a(y,t):prop2(xs)
+x@t67:=induction([t:nat]prop2(t),t14,[t:nat][u:prop2(t)]t66(t,u),x):prop2(x)
+-8274
+[l:less(x,y)]
+satz274:=<l><y>t67".8274":not(some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)))
+[f:[t:1to(x)]1to(y)]
+satz274a:=th4"l.some"([t:1to(x)]1to(y),[g:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),g),satz274,f):not(bijective(1to(x),1to(y),f))
++*rt
++*rp
++*r
++*c
+@[x:nat][u:1to(x)]
+inn:=inn"n"(x,u):nat
+@[q:[t:cx][u:cx]cx][x:nat][f:[t:1to(x)]cx]
+x@[n:1to(x)][o:not(is"e"(1to(x),n,xout(x)))]
++8275
+t1:=th3"l.imp"(is"n"(inn(x,n),x),is"e"(1to(x),n,xout(x)),o,[t:is"n"(inn(x,n),x)]tris(1to(x),n,outn(x,inn(x,n),1top(x,n)),xout(x),isoutinn(x,n),isoutni(x,inn(x,n),1top(x,n),x,lessisi3(x),t))):not(is"n"(inn(x,n),x))
+t2:=ore1(less"n"(inn(x,n),x),is"n"(inn(x,n),x),1top(x,n),t1):less"n"(inn(x,n),x)
+-8275
+lemma275:=satz25c(x,inn(x,n),t2".8275"):lessis"n"(<inn(x,n)>suc,x)
+f@[g:[t:1to(x)]cx]
+recprop:=and(is(<1out(x)>g,<1out(x)>f),[t:1to(x)][u:not(is"e"(1to(x),t,xout(x)))]is(<outn(x,<inn(x,t)>suc,lemma275(t,u))>g,<<outn(x,<inn(x,t)>suc,lemma275(t,u))>f><<t>g>q)):'prop'
++*8275
+x@1o:=1out(x):1to(x)
+xo:=xout(x):1to(x)
+[u:nat][l:lessis"n"(<u>suc,x)]
+t11:=satz16b(u,<u>suc,x,satz18c(u),l):less"n"(u,x)
+t12:=lessisi1"n"(u,x,t11):lessis"n"(u,x)
+ux:=outn(x,u,t12):1to(x)
+t13:=ec3e31(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11):nis"n"(u,x)
+t14:=th3"l.imp"(is"e"(1to(x),ux,xo),is"n"(u,x),t13,[t:is"e"(1to(x),ux,xo)]isoutne(x,u,t12,x,lessisi3(x),t)):not(is"e"(1to(x),ux,xo))
+t15:=isf(nat,nat,suc,u,inn(x,ux),isinoutn(x,u,t12)):is"n"(<u>suc,<inn(x,ux)>suc)
+t16:=isoutni(x,<u>suc,l,<inn(x,ux)>suc,lemma275(ux,t14),t15):is"e"(1to(x),outn(x,<u>suc,l),outn(x,<inn(x,ux)>suc,lemma275(ux,t14)))
+x@[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
+ns:=outn(x,<inn(x,n)>suc,lemma275(n,o)):1to(x)
+f@[g:[t:1to(x)]cx]
+prop1:=is(<1o>g,<1o>f):'prop'
+prop2:=[t:1to(x)][u:not(is"e"(1to(x),t,xo))]is(<ns(t,u)>g,<<ns(t,u)>f><<t>g>q):'prop'
+[pg:recprop(g)]
+t3:=ande1(prop1,prop2,pg):prop1
+[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
+t4:=<o><n>ande2(prop1,prop2,pg):is(<ns(n,o)>g,<<ns(n,o)>f><<n>g>q)
+pg@[u:nat][l:lessis"n"(<u>suc,x)]
+t17:=isf(1to(x),cx,g,outn(x,<u>suc,l),ns(ux(u,l),t14(u,l)),t16(u,l)):is(<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g)
+t18:=tris(cx,<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,t17,t4(pg,ux(u,l),t14(u,l))):is(<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q)
+g@[h:[t:1to(x)]cx][u:nat][l:lessis"n"(u,x)]
+prop3:=is(<outn(x,u,l)>g,<outn(x,u,l)>h):'prop'
+u@prop4:=and(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(t)):'prop'
+prop5:=or(prop4,more"n"(u,x)):'prop'
+h@[pg:recprop(g)][ph:recprop(h)][l:lessis"n"(1,x)]
+t5:=isoutni(x,1,l,1,satz24a(x),refis(nat,1)):is"e"(1to(x),outn(x,1,l),1o)
+t6:=isf(1to(x),cx,g,outn(x,1,l),1o,t5):is(<outn(x,1,l)>g,<1o>g)
+t7:=tris(cx,<outn(x,1,l)>g,<1o>g,<1o>f,t6,t3(pg)):is(<outn(x,1,l)>g,<1o>f)
+t8:=tris2(cx,<outn(x,1,l)>g,<outn(x,1,l)>h,<1o>f,t7,t7(h,g,ph,pg,l)):prop3(1,l)
+ph@t9:=andi(lessis"n"(1,x),[t:lessis"n"(1,x)]prop3(1,t),satz24a(x),[t:lessis"n"(1,x)]t8(t)):prop4(1)
+t10:=ori1(prop4(1),more"n"(1,x),t9):prop5(1)
+[u:nat][p:prop5(u)][l:lessis"n"(<u>suc,x)]
+t19:=ec3e32(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11(u,l)):not(more"n"(u,x))
+t20:=ore1(prop4(u),more"n"(u,x),p,t19):prop4(u)
+t21:=<t12(u,l)>ande2(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(u,t),t20):prop3(u,t12(u,l))
+t22:=isf(cx,cx,[t:cx]<<ns(ux(u,l),t14(u,l))>f><t>q,<ux(u,l)>g,<ux(u,l)>h,t21):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q)
+t23:=symis(cx,<outn(x,<u>suc,l)>h,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,t18(h,ph,u,l)):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h)
+t24:=tr3is(cx,<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h,t18(g,pg,u,l),t22,t23):prop3(<u>suc,l)
+t25:=andi(lessis"n"(<u>suc,x),[t:lessis"n"(<u>suc,x)]prop3(<u>suc,t),l,[t:lessis"n"(<u>suc,x)]t24(t)):prop4(<u>suc)
+t26:=ori1(prop4(<u>suc),more"n"(<u>suc,x),t25):prop5(<u>suc)
+p@[n:not(lessis"n"(<u>suc,x))]
+t27:=satz10k(<u>suc,x,n):more"n"(<u>suc,x)
+t28:=ori2(prop4(<u>suc),more"n"(<u>suc,x),t27):prop5(<u>suc)
+p@t29:=th1"l.imp"(lessis"n"(<u>suc,x),prop5(<u>suc),[t:lessis"n"(<u>suc,x)]t26(t),[t:not(lessis"n"(<u>suc,x))]t28(t)):prop5(<u>suc)
+u@t30:=induction([v:nat]prop5(v),t10,[v:nat][t:prop5(v)]t29(v,t),u):prop5(u)
+ph@[n:1to(x)]
+t31:=isf(1to(x),cx,g,n,outn(x,inn(x,n),1top(x,n)),isoutinn(x,n)):is(<n>g,<outn(x,inn(x,n),1top(x,n))>g)
+t32:=satz10d(inn(x,n),x,1top(x,n)):not(more"n"(inn(x,n),x))
+t33:=ore1(prop4(inn(x,n)),more"n"(inn(x,n),x),t30(inn(x,n)),t32):prop4(inn(x,n))
+t34:=<1top(x,n)>ande2(lessis"n"(inn(x,n),x),[t:lessis"n"(inn(x,n),x)]prop3(inn(x,n),t),t33):prop3(inn(x,n),1top(x,n))
+t35:=symis(cx,<n>h,<outn(x,inn(x,n),1top(x,n))>h,t31(h,g,ph,pg,n)):is(<outn(x,inn(x,n),1top(x,n))>h,<n>h)
+t36:=tr3is(cx,<n>g,<outn(x,inn(x,n),1top(x,n))>g,<outn(x,inn(x,n),1top(x,n))>h,<n>h,t31,t34,t35):is(<n>g,<n>h)
+ph@t37:=fisi(1to(x),cx,g,h,[t:1to(x)]t36(t)):is"e"([t:1to(x)]cx,g,h)
+f@prop6:=some"l"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(g)):'prop'
+x@prop7:=all"l"([t:1to(x)]cx,[f:[t:1to(x)]cx]prop6(f)):'prop'
+q@[f:[t:1to(1)]cx]
+t38:=refis(cx,<1o(1)>f):prop1(1,f,f)
+[n:1to(1)][o:not(is"e"(1to(1),n,xo(1)))]
+t39:=<th1"n.singlet"(n)>o:con
+t40:=cone(is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q),t39):is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q)
+f@t41:=andi(prop1(1,f,f),prop2(1,f,f),t38,[t:1to(1)][u:not(is"e"(1to(1),t,xo(1)))]t40(t,u)):recprop(1,f,f)
+t42:=somei([t:1to(1)]cx,[g:[t:1to(1)]cx]recprop(1,f,g),f,t41):prop6(1,f)
+q@t43:=[f:[t:1to(1)]cx]t42(f):prop7(1)
+x@[p:prop7(x)]
+xs:=<x>suc:nat
+[f:[t:1to(xs)]cx]
+f1:=left(cx,xs,x,lessisi1"n"(x,xs,satz18c(x)),f):[t:1to(x)]cx
+t44:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f1,g)][v:recprop(x,f1,h)]t37(f1,g,h,u,v),<f1>p):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g))
+g1:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):[t:1to(x)]cx
+t45:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):recprop(x,f1,g1)
+[n:1to(xs)]
+nxs:=is"e"(1to(xs),n,xo(xs)):'prop'
+[o:not(nxs)]
+t46:=satz26a(x,inn(xs,n),t2(xs,n,o)):lessis"n"(inn(xs,n),x)
+n1:=outn(x,inn(xs,n),t46):1to(x)
+b:=<n1>g1:cx
+[o1:not(nxs)]
+t47:=isoutni(x,inn(xs,n),t46(o),inn(xs,n),t46(o1),refis(nat,inn(xs,n))):is"e"(1to(x),n1(o),n1(o1))
+t48:=isf(1to(x),cx,g1,n1(o),n1(o1),t47):is(b(o),b(o1))
+f@a:=<<xo(xs)>f><<xo(x)>g1>q:cx
+n@c:=ite"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u)):cx
+[i:nxs]
+t49:=itet"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),i):is(c,a)
+o@t50:=itef"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),o):is(c,b)
+f@g2:=[t:1to(xs)]c(t):[t:1to(xs)]cx
+t51:=th3"l.imp"(is"e"(1to(xs),1o(xs),xo(xs)),is"n"(1,xs),symnotis(nat,xs,1,<x>ax3),[t:is"e"(1to(xs),1o(xs),xo(xs))]isoutne(xs,1,satz24a(xs),xs,lessisi3(xs),t)):not(is"e"(1to(xs),1o(xs),xo(xs)))
+t52:=t50(1o(xs),t51):is(c(1o(xs)),b(1o(xs),t51))
+t53:=isinoutn(xs,1,satz24a(xs)):is"n"(1,inn(xs,1o(xs)))
+t54:=isoutni(x,1,satz24a(x),inn(xs,1o(xs)),t46(1o(xs),t51),t53):is"e"(1to(x),1o(x),n1(1o(xs),t51))
+t55:=isf(1to(x),cx,g1,1o(x),n1(1o(xs),t51),t54):is(<1o(x)>g1,b(1o(xs),t51))
+t56:=tris2(cx,c(1o(xs)),<1o(x)>g1,b(1o(xs),t51),t52,t55):is(c(1o(xs)),<1o(x)>g1)
+t57:=tris(cx,c(1o(xs)),<1o(x)>g1,<1o(x)>f1,t56,t3(x,f1,g1,t45)):is(c(1o(xs)),<1o(x)>f1)
+t58:=isinoutn(x,1,satz24a(x)):is"n"(1,inn(x,1o(x)))
+t59:=isoutni(xs,1,satz24a(xs),inn(x,1o(x)),trlessis"n"(inn(x,1o(x)),x,xs,1top(x,1o(x)),lessisi1"n"(x,xs,satz18c(x))),t58):is"e"(1to(xs),1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)))
+t60:=isf(1to(xs),cx,f,1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)),t59):is(<1o(xs)>f,<1o(x)>f1)
+t61:=tris2(cx,c(1o(xs)),<1o(xs)>f,<1o(x)>f1,t57,t60):prop1(xs,f,g2)
+o@[i:is"e"(1to(xs),ns(xs,n,o),xo(xs))]
+t62:=isoutne(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),i):is"n"(<inn(xs,n)>suc,xs)
+t63:=<t62><x><inn(xs,n)>ax4:is"n"(inn(xs,n),x)
+t64:=isoutni(x,inn(xs,n),t46,x,lessisi3(x),t63):is"e"(1to(x),n1,xo(x))
+t65:=isf(1to(x),cx,g1,xo(x),n1,symis(1to(x),n1,xo(x),t64)):is(<xo(x)>g1,b)
+t66:=tris2(cx,<xo(x)>g1,c,b,t65,t50):is(<xo(x)>g1,c)
+t67:=isf(cx,cx,[t:cx]<<xo(xs)>f><t>q,<xo(x)>g1,c,t66):is(a,<<xo(xs)>f><c>q)
+t68:=isf(1to(xs),cx,f,xo(xs),ns(xs,n,o),symis(1to(xs),ns(xs,n,o),xo(xs),i)):is(<xo(xs)>f,<ns(xs,n,o)>f)
+t69:=isf(cx,cx,<c>q,<xo(xs)>f,<ns(xs,n,o)>f,t68):is(<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q)
+t70:=tr3is(cx,c(ns(xs,n,o)),a,<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q,t49(ns(xs,n,o),i),t67,t69):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
+o@[o1:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))][i:is"e"(1to(x),n1,xo(x))]
+t71:=isoutne(x,inn(xs,n),t46,x,lessisi3(x),i):is"n"(inn(xs,n),x)
+t72:=ax2(inn(xs,n),x,t71):is"n"(<inn(xs,n)>suc,xs)
+t73:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),t72):is"e"(1to(xs),ns(xs,n,o),xo(xs))
+o1@t74:=th3"l.imp"(is"e"(1to(x),n1,xo(x)),is"e"(1to(xs),ns(xs,n,o),xo(xs)),o1,[t:is"e"(1to(x),n1,xo(x))]t73(t)):not(is"e"(1to(x),n1,xo(x)))
+t75:=isinoutn(x,inn(xs,n),t46):is"n"(inn(xs,n),inn(x,n1))
+t76:=ax2(inn(xs,n),inn(x,n1),t75):is"n"(<inn(xs,n)>suc,<inn(x,n1)>suc)
+t77:=isinoutn(xs,<inn(xs,n)>suc,lemma275(xs,n,o)):is"n"(<inn(xs,n)>suc,inn(xs,ns(xs,n,o)))
+t78:=tris1(nat,inn(xs,ns(xs,n,o)),<inn(x,n1)>suc,<inn(xs,n)>suc,t77,t76):is"n"(inn(xs,ns(xs,n,o)),<inn(x,n1)>suc)
+t79:=isoutni(x,inn(xs,ns(xs,n,o)),t46(ns(xs,n,o),o1),<inn(x,n1)>suc,lemma275(x,n1,t74),t78):is"e"(1to(x),n1(ns(xs,n,o),o1),ns(n1,t74))
+t80:=isf(1to(x),cx,g1,n1(ns(xs,n,o),o1),ns(n1,t74),t79):is(b(ns(xs,n,o),o1),<ns(n1,t74)>g1)
+t81:=isinoutn(x,<inn(x,n1)>suc,lemma275(x,n1,t74)):is"n"(<inn(x,n1)>suc,inn(x,ns(n1,t74)))
+t82:=tris(nat,<inn(xs,n)>suc,<inn(x,n1)>suc,inn(x,ns(n1,t74)),t76,t81):is"n"(<inn(xs,n)>suc,inn(x,ns(n1,t74)))
+t83:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),inn(x,ns(n1,t74)),trlessis"n"(inn(x,ns(n1,t74)),x,xs,1top(x,ns(n1,t74)),lessisi1"n"(x,xs,satz18c(x))),t82):is"e"(1to(xs),ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)))
+t84:=isf(1to(xs),cx,f,ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)),t83):is(<ns(xs,n,o)>f,<ns(n1,t74)>f1)
+t85:=isf(cx,cx,<b>q,<ns(xs,n,o)>f,<ns(n1,t74)>f1,t84):is(<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q)
+t86:=isf(cx,cx,[t:cx]<<ns(xs,n,o)>f><t>q,c,b,t50):is(<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q)
+t87:=tr3is(cx,c(ns(xs,n,o)),b(ns(xs,n,o),o1),<ns(n1,t74)>g1,<<ns(n1,t74)>f1><b>q,t50(ns(xs,n,o),o1),t80,t4(f1,g1,t45,n1,t74)):is(c(ns(xs,n,o)),<<ns(n1,t74)>f1><b>q)
+t88:=tris(cx,<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q,t86,t85):is(<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q)
+t89:=tris2(cx,c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q,t87,t88):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
+o@t90:=th1"l.imp"(is"e"(1to(xs),ns(xs,n,o),xo(xs)),is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q),[t:is"e"(1to(xs),ns(xs,n,o),xo(xs))]t70(t),[t:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))]t89(t)):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
+f@t91:=[t:1to(xs)][u:not(nxs(t))]t90(t,u):prop2(xs,f,g2)
+t92:=andi(prop1(xs,f,g2),prop2(xs,f,g2),t61,t91):recprop(xs,f,g2)
+t93:=somei([t:1to(xs)]cx,[g:[t:1to(xs)]cx]recprop(xs,f,g),g2,t92):prop6(xs,f)
+p@t94:=[f:[t:1to(xs)]cx]t93(f):prop7(xs)
+x@t95:=induction([y:nat]prop7(y),t43,[y:nat][t:prop7(y)]t94(y,t),x):prop7(x)
+[f:[t:1to(x)]cx]
+t96:=<f>t95:prop6(x,f)
+t97:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f,g)][v:recprop(x,f,h)]t37(f,g,h,u,v),t96):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
+-8275
+f@satz275:=t97".8275"(f):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
+recf:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):[t:1to(x)]cx
+satz275a:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):recprop(x,f,recf)
+[n:1to(x)]
+rec:=<n>recf:cx
+f@satz275b:=t3".8275"(x,f,recf,satz275a):is(rec(1out(x)),<1out(x)>f)
+n@[o:not(is"e"(1to(x),n,xout(x)))]
+sucx:=ns".8275"(n,o):1to(x)
+satz275c:=t4".8275"(x,f,recf,satz275a,n,o):is(rec(sucx(n,o)),<<sucx(n,o)>f><rec(n)>q)
+f@[g:[t:1to(x)]cx][r:recprop(x,f,g)]
+satz275d:=t37".8275"(x,f,g,recf,r,satz275a):is"e"([t:1to(x)]cx,g,recf)
+[n:1to(x)]
+satz275e:=fise(1to(x),cx,g,recf,satz275d,n):is(<n>g,rec(n))
+x@[y:nat]
++*8275
+y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
+fl:=left(cx,x,y,l,f):[t:1to(y)]cx
+rf:=recf(x,f):[t:1to(x)]cx
+rfl:=left(cx,x,y,l,rf):[t:1to(y)]cx
+t98:=isinoutn(y,1,satz24a(y)):is"n"(1,inn(y,1out(y)))
+t99:=isoutni(x,1,satz24a(x),inn(y,1out(y)),trlessis"n"(inn(y,1out(y)),y,x,1top(y,1out(y)),l),t98):is"e"(1to(x),1out(x),left1to(x,y,l,1out(y)))
+t100:=isp(1to(x),[t:1to(x)]is(<t>rf,<t>f),1out(x),left1to(x,y,l,1out(y)),t3(x,f,rf,satz275a(x,f)),t99):prop1(y,fl,rfl)
+[n:1to(y)][o:not(is"e"(1to(y),n,xout(y)))]
+t100a:=th3"l.imp"(is"n"(inn(y,n),y),is"e"(1to(y),n,xout(y)),o,[t:is"n"(inn(y,n),y)]tris(1to(y),n,outn(y,inn(y,n),1top(y,n)),xout(y),isoutinn(y,n),isoutni(y,inn(y,n),1top(y,n),y,lessisi3(y),t))):not(is"n"(inn(y,n),y))
+t100b:=ore1(less"n"(inn(y,n),y),is"n"(inn(y,n),y),1top(y,n),t100a):less"n"(inn(y,n),y)
+t101:=satz16b(inn(y,n),y,x,t100b,l):less"n"(inn(y,n),x)
+t102:=ec3e31(is"n"(inn(y,n),x),more"n"(inn(y,n),x),less"n"(inn(y,n),x),satz10b(inn(y,n),x),t101):nis"n"(inn(y,n),x)
+t103:=th3"l.imp"(is"e"(1to(x),left1to(x,y,l,n),xout(x)),is"n"(inn(y,n),x),t102,[t:is"e"(1to(x),left1to(x,y,l,n),xout(x))]isoutne(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l),x,lessisi3(x),t)):not(is"e"(1to(x),left1to(x,y,l,n),xout(x)))
+t104:=t4(x,f,rf,satz275a(x,f),left1to(x,y,l,n),t103):is(<ns(x,left1to(x,y,l,n),t103)>rf,<<ns(x,left1to(x,y,l,n),t103)>f><<n>rfl>q)
+t105:=isinoutn(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l)):is"n"(inn(y,n),inn(x,left1to(x,y,l,n)))
+t106:=ax2(inn(y,n),inn(x,left1to(x,y,l,n)),t105):is"n"(<inn(y,n)>suc,<inn(x,left1to(x,y,l,n))>suc)
+t107:=isinoutn(y,<inn(y,n)>suc,lemma275(y,n,o)):is"n"(<inn(y,n)>suc,inn(y,ns(y,n,o)))
+t108:=tris1(nat,<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)),<inn(y,n)>suc,t106,t107):is"n"(<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)))
+t109:=isoutni(x,<inn(x,left1to(x,y,l,n))>suc,lemma275(x,left1to(x,y,l,n),t103),inn(y,ns(y,n,o)),trlessis"n"(inn(y,ns(y,n,o)),y,x,1top(y,ns(y,n,o)),l),t108):is"e"(1to(x),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)))
+t110:=isp(1to(x),[t:1to(x)]is(<t>rf,<<t>f><<n>rfl>q),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)),t104,t109):is(<ns(y,n,o)>rfl,<<ns(y,n,o)>fl><<n>rfl>q)
+f@t111:=[t:1to(y)][u:not(is"e"(1to(y),t,xout(y)))]t110(t,u):prop2(y,fl,rfl)
+t112:=andi(prop1(y,fl,rfl),prop2(y,fl,rfl),t100,t111):recprop(y,fl,rfl)
+-8275
+y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
+satz275f:=satz275d(y,fl".8275"(l,f),rfl".8275"(l,f),t112".8275"(l,f)):is"e"([t:1to(y)]cx,left(cx,x,y,l,recf(x,f)),recf(y,left(cx,x,y,l,f)))
+x@[f:[t:1to(pl"n"(x,1))]cx]
++8276
+xs:=<x>suc:nat
+x1:=pl"n"(x,1):nat
+t1:=lessisi1"n"(x,x1,satz18a(x,1)):lessis"n"(x,x1)
+t2:=lessisi1"n"(x,xs,satz18c(x)):lessis"n"(x,xs)
+t3:=lessisi2"n"(xs,x1,satz4e(x)):lessis"n"(xs,x1)
+fx:=left(cx,x1,x,t1,f):[t:1to(x)]cx
+f1:=left(cx,x1,xs,t3,f):[t:1to(xs)]cx
+f1x:=f1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
+g1:=g2"c.8275"(x,t95"c.8275"(x),f1):[t:1to(xs)]cx
+g1x:=g1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
+g:=left(cx,x1,xs,t3,recf(x1,f)):[t:1to(xs)]cx
+t4:=t49"c.8275"(x,t95"c.8275"(x),f1,xout(xs),refis(1to(xs),xout(xs))):is(<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q)
+t5:=satz275d(xs,f1,g1,t92"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(xs)]cx,g1,recf(xs,f1))
+t6:=satz275f(x1,xs,t3,f):is"e"([t:1to(xs)]cx,g,recf(xs,f1))
+t7:=tris2([t:1to(xs)]cx,g,g1,recf(xs,f1),t6,t5):is"e"([t:1to(xs)]cx,g,g1)
+t8:=fise(1to(xs),cx,g,g1,t7,xout(xs)):is(<xout(xs)>g,<xout(xs)>g1)
+t9:=tris(cx,<xout(xs)>g,<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q,t8,t4):is(<xout(xs)>g,<<xout(xs)>f1><<xout(x)>g1x>q)
+[n:1to(x)]
+t10:=isinoutn(xs,inn(x,n),trlessis"n"(inn(x,n),x,xs,1top(x,n),t2)):is"n"(inn(x,n),inn(xs,left1to(xs,x,t2,n)))
+t11:=isoutni(x1,inn(x,n),trlessis"n"(inn(x,n),x,x1,1top(x,n),t1),inn(xs,left1to(xs,x,t2,n)),trlessis"n"(inn(xs,left1to(xs,x,t2,n)),xs,x1,1top(xs,left1to(xs,x,t2,n)),t3),t10):is"e"(1to(x1),left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)))
+t12:=isf(1to(x1),cx,f,left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)),t11):is(<n>fx,<n>f1x)
+f@t13:=fisi(1to(x),cx,fx,f1x,[t:1to(x)]t12(t)):is"e"([t:1to(x)]cx,fx,f1x)
+t14:=isf([t:1to(x)]cx,[t:1to(x)]cx,[u:[t:1to(x)]cx]recf(x,u),fx,f1x,t13):is"e"([t:1to(x)]cx,recf(x,fx),recf(x,f1x))
+t15:=satz275d(x,f1x,g1x,t45"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(x)]cx,g1x,recf(x,f1x))
+t16:=tris2([t:1to(x)]cx,g1x,recf(x,fx),recf(x,f1x),t15,t14):is"e"([t:1to(x)]cx,g1x,recf(x,fx))
+t17:=fise(1to(x),cx,g1x,recf(x,fx),t16,xout(x)):is(<xout(x)>g1x,<xout(x)>recf(x,fx))
+t18:=isinoutn(xs,xs,lessisi3(xs)):is"n"(xs,inn(xs,xout(xs)))
+t19:=tris(nat,x1,xs,inn(xs,xout(xs)),satz4a(x),t18):is"n"(x1,inn(xs,xout(xs)))
+t20:=isoutni(x1,x1,lessisi3(x1),inn(xs,xout(xs)),trlessis"n"(inn(xs,xout(xs)),xs,x1,1top(xs,xout(xs)),t3),t19):is"e"(1to(x1),xout(x1),left1to(x1,xs,t3,xout(xs)))
+t21:=isp1(1to(x1),[t:1to(x1)]is(<t>recf(x1,f),<<t>f><<xout(x)>g1x>q),left1to(x1,xs,t3,xout(xs)),xout(x1),t9,t20):is(<xout(x1)>recf(x1,f),<<xout(x1)>f><<xout(x)>g1x>q)
+t22:=isf(cx,cx,[t:cx]<<xout(x1)>f><t>q,<xout(x)>g1x,<xout(x)>recf(x,fx),t17):is(<<xout(x1)>f><<xout(x)>g1x>q,<<xout(x1)>f><<xout(x)>recf(x,fx)>q)
+-8276
+satz276:=tris(cx,<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>g1x".8276">q,<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,fx".8276")>q,t21".8276",t22".8276"):is(<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
+x@[f:[u:1to(x)]cx]
+smpr:=rec(x,f,xout(x)):cx
+@[x:nat][f:[u:1to(x)]cx]
+sum:=smpr([t:cx][u:cx]pl(t,u),x,f):cx
+prod:=smpr([t:cx][u:cx]ts(t,u),x,f):cx
+q@[f:[u:1to(1)]cx]
++8277
+t1:=isoutni(1,1,satz24a(1),1,lessisi3(1),refis(nat,1)):is"e"(1to(1),1out(1),xout(1))
+-8277
+satz277:=isp(1to(1),[t:1to(1)]is(rec(1,f,t),<t>f),1out(1),xout(1),satz275b(1,f),t1".8277"):is(smpr(1,f),<xout(1)>f)
+q@[x:nat][f:[u:1to(pl"n"(x,1))]cx]
+satz278:=satz276(x,f):is(smpr(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><smpr(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
+x@[f:[u:1to(x)]cx][y:nat][i:is"n"(y,x)]
++v8
+t1:=lessisi2"n"(y,x,i):lessis"n"(y,x)
+f0:=left(cx,x,y,t1,f):[t:1to(y)]cx
+t2:=fise(1to(y),cx,left(cx,x,y,t1,recf(x,f)),recf(y,f0),satz275f(x,y,t1,f),xout(y)):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(y,f0))
+t3:=tris1(nat,inn(y,xout(y)),x,y,isinoutn(y,y,lessisi3(y)),i):is"n"(inn(y,xout(y)),x)
+t4:=isoutni(x,inn(y,xout(y)),trlessis"n"(inn(y,xout(y)),y,x,1top(y,xout(y)),t1),x,lessisi3(x),t3):is"e"(1to(x),left1to(x,y,t1,xout(y)),xout(x))
+t5:=isf(1to(x),cx,recf(x,f),left1to(x,y,t1,xout(y)),xout(x),t4):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(x,f))
+-v8
+issmpr:=tris1(cx,smpr(y,f0".v8"),smpr(x,f),<left1to(x,y,t1".v8",xout(y))>recf(x,f),t2".v8",t5".v8"):is(smpr(y,left(cx,x,y,lessisi2"n"(y,x,i),f)),smpr(x,f))
+@[z:complex][x:nat]
++8279
+xr:=rlofnt(x):real
+prop1:=is(sum(x,[t:1to(x)]z),ts(z,pli(xr,0))):'prop'
+z@t1:=satz277([t:cx][u:cx]pl(t,u),[t:1to(1)]z):is(sum(1,[t:1to(1)]z),z)
+t2:=tris(cx,sum(1,[t:1to(1)]z),z,ts(z,1c),t1,satz222a(z)):prop1(1)
+x@[p:prop1(x)]
+t3:=satz278([t:cx][u:cx]pl(t,u),x,[t:1to(pl"n"(x,1))]z):is(sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z))
+t4:=ispl12(sum(x,[t:1to(x)]z),ts(z,pli(xr,0)),z,ts(z,1c),p,satz222a(z)):is(pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)))
+t5:=distpt2(z,pli(xr,0),1c):is(pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)))
+t6:=plis12a(xr,0,1rl,0):is(pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)))
+t7:=isrecx12(pl"r"(xr,1rl),rlofnt(pl"n"(x,1)),pl"r"(0,0),0,satzr155b(x,1),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0))
+t8:=tris(cx,pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0),t6,t7):is(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0))
+t9:=ists2(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0),z,t8):is(ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)))
+t10:=tr4is(cx,sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)),t3,t4,t5,t9):prop1(pl"n"(x,1))
+t11:=isp(nat,[t:nat]prop1(t),pl"n"(x,1),<x>suc,t10,satz4a(x)):prop1(<x>suc)
+-8279
+satz279:=induction([t:nat]prop1".8279"(t),t2".8279",[u:nat][t:prop1".8279"(u)]t11".8279"(u,t),x):is(sum(x,[t:1to(x)]z),ts(z,pli(rlofnt(x),0)))
+q@[f:[t:1to(2)]cx]
++8280
+t1:=lessisi1"n"(1,2,satz18a(1,1)):lessis"n"(1,2)
+f1:=left(cx,2,1,t1,f):[t:1to(1)]cx
+t2:=satz278(q,1,f):is(smpr(2,f),<<xout(2)>f><smpr(1,f1)>q)
+t3:=satz277(q,f1):is(smpr(1,f1),<xout(1)>f1)
+t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+t5:=isoutni(2,1,satz24a(2),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,2,1top(1,xout(1)),t1),t4):is"e"(1to(2),1out(2),left1to(2,1,t1,xout(1)))
+t6:=isf(1to(2),cx,f,1out(2),left1to(2,1,t1,xout(1)),t5):is(<1out(2)>f,<xout(1)>f1)
+t7:=tris2(cx,smpr(1,f1),<1out(2)>f,<xout(1)>f1,t3,t6):is(smpr(1,f1),<1out(2)>f)
+t8:=isf(cx,cx,[t:cx]<<xout(2)>f><t>q,smpr(1,f1),<1out(2)>f,t7):is(<<xout(2)>f><smpr(1,f1)>q,<<xout(2)>f><<1out(2)>f>q)
+-8280
+satz280:=tris(cx,smpr(2,f),<<xout(2)>f><smpr(1,f1".8280")>q,<<xout(2)>f><<1out(2)>f>q,t2".8280",t8".8280"):is(smpr(2,f),<<xout(2)>f><<1out(2)>f>q)
+q@assoc:=[x:cx][y:cx][z:cx]is(<z><<y><x>q>q,<<z><y>q><x>q):'prop'
+@assocp1:=[x:cx][y:cx][z:cx]asspl1(x,y,z):assoc([x:cx][y:cx]pl(x,y))
+assocts:=[x:cx][y:cx][z:cx]assts1(x,y,z):assoc([x:cx][y:cx]ts(x,y))
+q@[a:assoc][z:cx][u:cx][v:cx]
+assq1:=<v><u><z>a:is(<v><<u><z>q>q,<<v><u>q><z>q)
+assq2:=symis(cx,<v><<u><z>q>q,<<v><u>q><z>q,assq1):is(<<v><u>q><z>q,<v><<u><z>q>q)
+q@[a:assoc(q)][x:nat][y:nat][f:[t:1to(pl"n"(x,y))]cx]
++8281
+y@t1:=lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)):lessis"n"(x,pl"n"(x,y))
+f@f1:=left(cx,pl"n"(x,y),x,t1,f):[t:1to(x)]cx
+f2:=right(cx,x,y,f):[t:1to(y)]cx
+prop1:=is(smpr(pl"n"(x,y),f),<smpr(y,f2)><smpr(x,f1)>q):'prop'
+y@prop2:=all"l"([t:1to(pl"n"(x,y))]cx,[u:[t:1to(pl"n"(x,y))]cx]prop1(u)):'prop'
+x@[f0:[t:1to(pl"n"(x,1))]cx]
+t2:=satz278(q,x,f0):is(smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q)
+t3:=satz277(q,f2(1,f0)):is(smpr(1,f2(1,f0)),<xout(1)>f2(1,f0))
+t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+t5:=ispl2"n"(1,inn(1,xout(1)),x,t4):is"n"(pl"n"(x,1),pl"n"(x,inn(1,xout(1))))
+t6:=isoutni(pl"n"(x,1),pl"n"(x,1),lessisi3(pl"n"(x,1)),pl"n"(x,inn(1,xout(1))),satz19o(inn(1,xout(1)),1,x,1top(1,xout(1))),t5):is"e"(1to(pl"n"(x,1)),xout(pl"n"(x,1)),right1to(x,1,xout(1)))
+t7:=isf(1to(pl"n"(x,1)),cx,f0,xout(pl"n"(x,1)),right1to(x,1,xout(1)),t6):is(<xout(pl"n"(x,1))>f0,<xout(1)>f2(1,f0))
+t8:=tris2(cx,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),<xout(1)>f2(1,f0),t7,t3):is(<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)))
+t9:=isf(cx,cx,<smpr(x,f1(1,f0))>q,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),t8):is(<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q)
+t10:=tris(cx,smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q,t2,t9):prop1(1,f0)
+x@t11:=[u:[t:1to(pl"n"(x,1))]cx]t10(u):prop2(1)
+y@yp1:=pl"n"(y,1):nat
+xpy:=pl"n"(x,y):nat
+xpy1:=pl"n"(x,yp1):nat
+xyp1:=pl"n"(xpy,1):nat
+t12:=lessisi2"n"(xyp1,xpy1,asspl1"n"(x,y,1)):lessis"n"(xyp1,xpy1)
+[p:prop2(y)][f:[t:1to(xpy1)]cx]
+t13:=isinoutn(xyp1,xyp1,lessisi3(xyp1)):is"n"(xyp1,inn(xyp1,xout(xyp1)))
+t14:=tris(nat,xpy1,xyp1,inn(xyp1,xout(xyp1)),asspl2"n"(x,y,1),t13):is"n"(xpy1,inn(xyp1,xout(xyp1)))
+t15:=isoutni(xpy1,xpy1,lessisi3(xpy1),inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),t14):is"e"(1to(xpy1),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)))
+t16:=isf(1to(xpy1),cx,recf(xpy1,f),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),t15):is(smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)))
+fr:=left(cx,xpy1,xyp1,t12,f):[t:1to(xyp1)]cx
+t17:=satz275f(xpy1,xyp1,t12,f):is"e"([t:1to(xyp1)]cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr))
+t18:=fise(1to(xyp1),cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr),t17,xout(xyp1)):is(<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr))
+t19:=lessisi1"n"(xpy,xyp1,satz18a(xpy,1)):lessis"n"(xpy,xyp1)
+frr:=left(cx,xyp1,xpy,t19,fr):[t:1to(xpy)]cx
+t20:=satz278(xpy,fr):is(smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q)
+t21:=isf(cx,cx,[u:cx]<<xout(xyp1)>fr><u>q,smpr(xpy,frr),<smpr(y,f2(frr))><smpr(x,f1(frr))>q,<frr>p):is(<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
+t22:=assq1(a,smpr(x,f1(frr)),smpr(y,f2(frr)),<xout(xyp1)>fr):is(<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q)
+t23:=lessisi1"n"(y,yp1,satz18a(y,1)):lessis"n"(y,yp1)
+fy:=left(cx,yp1,y,t23,f2(yp1,f)):[t:1to(y)]cx
+t24:=satz278(y,f2(yp1,f)):is(smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
+t25:=isinoutn(yp1,yp1,lessisi3(yp1)):is"n"(yp1,inn(yp1,xout(yp1)))
+t26:=ispl2"n"(yp1,inn(yp1,xout(yp1)),x,t25):is"n"(xpy1,pl"n"(x,inn(yp1,xout(yp1))))
+t27:=tris1(nat,inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))),xpy1,t14,t26):is"n"(inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))))
+t28:=isoutni(xpy1,inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),pl"n"(x,inn(yp1,xout(yp1))),satz19o(inn(yp1,xout(yp1)),yp1,x,1top(yp1,xout(yp1))),t27):is"e"(1to(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)))
+t29:=isf(1to(xpy1),cx,f,left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)),t28):is(<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f))
+t30:=isf(cx,cx,<smpr(y,f2(frr))>q,<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f),t29):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q)
+[n:1to(y)]
+n0:=inn(y,n):nat
+nyp1:=left1to(yp1,y,t23,n):1to(yp1)
+t31:=isinoutn(yp1,n0,trlessis"n"(n0,y,yp1,1top(y,n),t23)):is"n"(n0,inn(yp1,nyp1))
+t32:=ispl2"n"(n0,inn(yp1,nyp1),x,t31):is"n"(pl"n"(x,n0),pl"n"(x,inn(yp1,nyp1)))
+nxpy:=right1to(x,y,n):1to(xpy)
+nxyp1:=left1to(xyp1,xpy,t19,nxpy):1to(xyp1)
+t33:=isinoutn(xyp1,inn(xpy,nxpy),trlessis"n"(inn(xpy,nxpy),xpy,xyp1,1top(xpy,nxpy),t19)):is"n"(inn(xpy,nxpy),inn(xyp1,nxyp1))
+t34:=isinoutn(xpy,pl"n"(x,n0),satz19o(n0,y,x,1top(y,n))):is"n"(pl"n"(x,n0),inn(xpy,nxpy))
+t35:=tris(nat,pl"n"(x,n0),inn(xpy,nxpy),inn(xyp1,nxyp1),t34,t33):is"n"(pl"n"(x,n0),inn(xyp1,nxyp1))
+t36:=tris1(nat,pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1),pl"n"(x,n0),t32,t35):is"n"(pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1))
+t37:=isoutni(xpy1,pl"n"(x,inn(yp1,nyp1)),satz19o(inn(yp1,nyp1),yp1,x,1top(yp1,nyp1)),inn(xyp1,nxyp1),trlessis"n"(inn(xyp1,nxyp1),xyp1,xpy1,1top(xyp1,nxyp1),t12),t36):is"e"(1to(xpy1),right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1))
+t38:=isf(1to(xpy1),cx,f,right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1),t37):is(<n>fy,<n>f2(frr))
+f@t39:=fisi(1to(y),cx,fy,f2(frr),[u:1to(y)]t38(u)):is"e"([u:1to(y)]cx,fy,f2(frr))
+t40:=isf([u:1to(y)]cx,cx,[t:[u:1to(y)]cx]smpr(y,t),fy,f2(frr),t39):is(smpr(y,fy),smpr(y,f2(frr)))
+t41:=isf(cx,cx,[t:cx]<<xout(yp1)>f2(yp1,f)><t>q,smpr(y,f2(frr)),smpr(y,fy),symis(cx,smpr(y,fy),smpr(y,f2(frr)),t40)):is(<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
+t41a:=tris(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t30,t41):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
+t42:=tris2(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t41a,t24):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)))
+t43:=isf(cx,cx,<smpr(x,f1(frr))>q,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),t42):is(<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q)
+[m:1to(x)]
+m0:=inn(x,m):nat
+mxpy:=left1to(xpy,x,t1,m):1to(xpy)
+mxyp1:=left1to(xyp1,xpy,t19,mxpy):1to(xyp1)
+t44:=isinoutn(xyp1,inn(xpy,mxpy),trlessis"n"(inn(xpy,mxpy),xpy,xyp1,1top(xpy,mxpy),t19)):is"n"(inn(xpy,mxpy),inn(xyp1,mxyp1))
+t45:=isinoutn(xpy,m0,trlessis"n"(m0,x,xpy,1top(x,m),t1)):is"n"(m0,inn(xpy,mxpy))
+t46:=tris(nat,m0,inn(xpy,mxpy),inn(xyp1,mxyp1),t45,t44):is"n"(m0,inn(xyp1,mxyp1))
+t47:=isoutni(xpy1,m0,trlessis"n"(m0,x,xpy1,1top(x,m),t1(yp1)),inn(xyp1,mxyp1),trlessis"n"(inn(xyp1,mxyp1),xyp1,xpy1,1top(xyp1,mxyp1),t12),t46):is"e"(1to(xpy1),left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1))
+t48:=isf(1to(xpy1),cx,f,left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1),t47):is(<m>f1(x,yp1,f),<m>f1(x,y,frr))
+f@t49:=fisi(1to(x),cx,f1(x,yp1,f),f1(x,y,frr),[u:1to(x)]t48(u)):is"e"([u:1to(x)]cx,f1(x,yp1,f),f1(x,y,frr))
+t50:=isf([u:1to(x)]cx,cx,[t:[u:1to(x)]cx]smpr(x,t),f1(yp1,f),f1(frr),t49):is(smpr(x,f1(yp1,f)),smpr(x,f1(frr)))
+t51:=isf(cx,cx,[t:cx]<smpr(yp1,f2(yp1,f))><t>q,smpr(x,f1(frr)),smpr(x,f1(yp1,f)),symis(cx,smpr(x,f1(yp1,f)),smpr(x,f1(frr)),t50)):is(<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q)
+t52:=tr4is(cx,smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,t16,t18,t20,t21):is(smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
+t53:=tr4is(cx,smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q,t52,t22,t43,t51):prop1(yp1,f)
+p@t54:=[u:[t:1to(xpy1)]cx]t53(u):prop2(yp1)
+t55:=isp(nat,[t:nat]prop2(t),yp1,<y>suc,t54,satz4a(y)):prop2(<y>suc)
+y@t56:=induction([t:nat]prop2(t),t11,[z:nat][t:prop2(z)]t55(z,t),y):prop2(y)
+-8281
+satz281:=<f>t56".8281":is(smpr(pl"n"(x,y),f),<smpr(y,right(cx,x,y,f))><smpr(x,left(cx,pl"n"(x,y),x,lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)),f))>q)
+q@commut:=[x:cx][y:cx]is(<y><x>q,<x><y>q):'prop'
+@commutpl:=[x:cx][y:cx]compl(x,y):commut([x:cx][y:cx]pl(x,y))
+commutts:=[x:cx][y:cx]comts(x,y):commut([x:cx][y:cx]ts(x,y))
+q@[c:commut][z:cx][u:cx]
+comq:=<u><z>c:is(<u><z>q,<z><u>q)
+a@[c:commut(q)][x:nat][f:[t:1to(x)]cx][g:[t:1to(x)]cx]
++8282
+prop1:=is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q):'prop'
+x@prop2:=all"l"([t:1to(x)]cx,[u:[t:1to(x)]cx]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]prop1(u,v))):'prop'
+c@[f0:[t:1to(1)]cx][g0:[t:1to(1)]cx]
+t1:=satz277([t:1to(1)]<<t>g0><<t>f0>q):is(smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<<xout(1)>g0><<xout(1)>f0>q)
+t2:=isf(cx,cx,<smpr(1,f0)>q,smpr(1,g0),<xout(1)>g0,satz277(g0)):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q)
+t3:=isf(cx,cx,[t:cx]<<xout(1)>g0><t>q,smpr(1,f0),<xout(1)>f0,satz277(f0)):is(<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
+t4:=tris(cx,<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t2,t3):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
+t5:=tris2(cx,smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t1,t4):prop1(1,f0,g0)
+c@t6:=[u:[t:1to(1)]cx][v:[t:1to(1)]cx]t5(u,v):prop2(1)
+x@xp1:=pl"n"(x,1):nat
+[p:prop2(x)][f:[t:1to(xp1)]cx][g:[t:1to(xp1)]cx]
+c@[u:cx][v:cx][w:cx][z:cx]
+t7:=assq2(a,<v><u>q,w,z):is(<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q)
+t8:=comq(c,<v><u>q,w):is(<w><<v><u>q>q,<<v><u>q><w>q)
+t9:=assq2(a,w,u,v):is(<<v><u>q><w>q,<v><<u><w>q>q)
+t10:=tris(cx,<w><<v><u>q>q,<<v><u>q><w>q,<v><<u><w>q>q,t8,t9):is(<w><<v><u>q>q,<v><<u><w>q>q)
+t11:=isf(cx,cx,[t:cx]<z><t>q,<w><<v><u>q>q,<v><<u><w>q>q,t10):is(<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q)
+t12:=assq1(a,<u><w>q,v,z):is(<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q)
+t13:=comq(c,w,u):is(<u><w>q,<w><u>q)
+t14:=isf(cx,cx,[t:cx]<<z><v>q><t>q,<u><w>q,<w><u>q,t13):is(<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q)
+t15:=tr4is(cx,<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q,t7,t11,t12,t14):is(<<z><w>q><<v><u>q>q,<<z><v>q><<w><u>q>q)
+g@t16:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
+sfx:=smpr(x,left(cx,xp1,x,t16,f)):cx
+sgx:=smpr(x,left(cx,xp1,x,t16,g)):cx
+h:=[t:1to(xp1)]<<t>g><<t>f>q:[t:1to(xp1)]cx
+shx:=smpr(x,left(cx,xp1,x,t16,h)):cx
+t17:=satz278(x,h):is(smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q)
+t18:=<left(cx,xp1,x,t16,g)><left(cx,xp1,x,t16,f)>p:is(shx,<sgx><sfx>q)
+t19:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><<xout(xp1)>f>q><t>q,shx,<sgx><sfx>q,t18):is(<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q)
+t20:=t15(sfx,sgx,<xout(xp1)>f,<xout(xp1)>g):is(<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
+t21:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><sfx>q,satz278(x,f)):is(<<xout(xp1)>f><sfx>q,smpr(xp1,f))
+t22:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><sgx>q><t>q,<<xout(xp1)>f><sfx>q,smpr(xp1,f),t21):is(<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q)
+t23:=symis(cx,smpr(xp1,g),<<xout(xp1)>g><sgx>q,satz278(x,g)):is(<<xout(xp1)>g><sgx>q,smpr(xp1,g))
+t24:=isf(cx,cx,<smpr(xp1,f)>q,<<xout(xp1)>g><sgx>q,smpr(xp1,g),t23):is(<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q)
+t25:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,t17,t19,t20):is(smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
+t26:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q,t25,t22,t24):prop1(xp1,f,g)
+p@t27:=[u:[t:1to(xp1)]cx][v:[t:1to(xp1)]cx]t26(u,v):prop2(xp1)
+t28:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t27,satz4a(x)):prop2(<x>suc)
+x@t29:=induction([t:nat]prop2(t),t6,[y:nat][t:prop2(y)]t28(y,t),x):prop2(x)
+-8282
+satz282:=<g><f>t29".8282":is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q)
+x@[s:[t:1to(x)]1to(x)][b:bijective(1to(x),1to(x),s)][f:[t:1to(x)]cx]
++8283
+s@[f:[t:1to(x)]cx]
+g:=[t:1to(x)]<<t>s>f:[t:1to(x)]cx
+prop1:=is(smpr(x,g),smpr(x,f)):'prop'
+x@prop2:=all"l"([t:1to(x)]1to(x),[u:[t:1to(x)]1to(x)]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]imp(bijective(1to(x),1to(x),u),prop1(u,v)))):'prop'
+c@[s:[t:1to(1)]1to(1)][f:[t:1to(1)]cx]
+t1:=tris2(1to(1),<xout(1)>s,xout(1),1o"n",th1"n.singlet"(<xout(1)>s),th1"n.singlet"(xout(1))):is"e"(1to(1),<xout(1)>s,xout(1))
+t2:=satz277(g(1,s,f)):is(smpr(1,g(1,s,f)),<xout(1)>g(1,s,f))
+t3:=isf(1to(1),cx,f,<xout(1)>s,xout(1),t1):is(<xout(1)>g(1,s,f),<xout(1)>f)
+t4:=symis(cx,smpr(1,f),<xout(1)>f,satz277(f)):is(<xout(1)>f,smpr(1,f))
+t5:=tr3is(cx,smpr(1,g(1,s,f)),<xout(1)>g(1,s,f),<xout(1)>f,smpr(1,f),t2,t3,t4):prop1(1,s,f)
+c@t6:=[u:[t:1to(1)]1to(1)][v:[t:1to(1)]cx][w:bijective(1to(1),1to(1),u)]t5(u,v):prop2(1)
+x@xp1:=pl"n"(x,1):nat
+t7:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
+[p:prop2(x)][s:[t:1to(xp1)]1to(xp1)][f:[t:1to(xp1)]cx][b:bijective(1to(xp1),1to(xp1),s)]
+t8:=ande1(injective(1to(xp1),1to(xp1),s),surjective(1to(xp1),1to(xp1),s),b):injective(1to(xp1),1to(xp1),s)
+[case1:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))][u:1to(x)]
+u1:=left1to(xp1,x,t7,u):1to(xp1)
+n1:=inn(xp1,<u1>s):nat
+[i:is"n"(n1,xp1)]
+t9:=tr3is(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),xout(xp1),<xout(xp1)>s,isoutinn(xp1,<u1>s),isoutni(xp1,n1,1top(xp1,<u1>s),xp1,lessisi3(xp1),i),symis(1to(xp1),<xout(xp1)>s,xout(xp1),case1)):is"e"(1to(xp1),<u1>s,<xout(xp1)>s)
+t10:=isfe(1to(xp1),1to(xp1),s,t8,u1,xout(xp1),t9):is"e"(1to(xp1),u1,xout(xp1))
+t11:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t10):is"n"(inn(x,u),xp1)
+t12:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
+t13:=<t11>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t12):con
+u@t14:=ore1(less"n"(n1,xp1),is"n"(n1,xp1),1top(xp1,<u1>s),[t:is"n"(n1,xp1)]t13(t)):less"n"(n1,xp1)
+t15:=satz26(x,n1,t14):lessis"n"(n1,x)
+w1:=outn(x,n1,t15):1to(x)
+case1@s01:=[t:1to(x)]w1(t):[t:1to(x)]1to(x)
+u@[v:1to(x)][i:is"e"(1to(x),w1(u),w1(v))]
+t16:=isoutne(x,n1(u),t15(u),n1(v),t15(v),i):is"n"(n1(u),n1(v))
+t17:=<isinne(xp1,<u1(u)>s,<u1(v)>s,t16)><u1(v)><u1(u)>t8:is"e"(1to(xp1),u1(u),u1(v))
+t18:=thleft1(xp1,x,t7,u,v,t17):is"e"(1to(x),u,v)
+u@u2:=<u1>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
+n2:=inn(xp1,u2):nat
+[i:is"n"(n2,xp1)]
+t19:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),xout(xp1),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),xp1,lessisi3(xp1),i)):is"e"(1to(xp1),u2,xout(xp1))
+t20:=tr3is(1to(xp1),u1,<u2>s,<xout(xp1)>s,xout(xp1),thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,xout(xp1),t19),case1):is"e"(1to(xp1),u1,xout(xp1))
+t21:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t20):is"n"(inn(x,u),xp1)
+t22:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
+t23:=<t21>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t22):con
+u@t24:=ore1(less"n"(n2,xp1),is"n"(n2,xp1),1top(xp1,u2),[t:is"n"(n2,xp1)]t23(t)):less"n"(n2,xp1)
+t25:=satz26(x,n2,t24):lessis"n"(n2,x)
+w2:=outn(x,n2,t25):1to(x)
+t26:=isinoutn(x,n2,t25):is"n"(n2,inn(x,w2))
+t27:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),u1(w2),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),inn(x,w2),trlessis"n"(inn(x,w2),x,xp1,1top(x,w2),t7),t26)):is"e"(1to(xp1),u2,u1(w2))
+t28:=tris(1to(xp1),u1,<u2>s,<u1(w2)>s,thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,u1(w2),t27)):is"e"(1to(xp1),u1,<u1(w2)>s)
+t29:=tris(nat,inn(x,u),inn(xp1,u1),n1(w2),isinoutn(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7)),isinni(xp1,u1,<u1(w2)>s,t28)):is"n"(inn(x,u),n1(w2))
+t30:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w1(w2),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),n1(w2),t15(w2),t29)):is"e"(1to(x),u,w1(w2))
+t31:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w1(t)),w2,t30):image(1to(x),1to(x),s01,u)
+case1@t32:=andi(injective(1to(x),1to(x),s01),surjective(1to(x),1to(x),s01),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s01,<u>s01)]t18(t,u,v),[t:1to(x)]t31(t)):bijective(1to(x),1to(x),s01)
+f01:=left(cx,xp1,x,t7,f):[t:1to(x)]cx
+t33:=<t32><f01><s01>p:prop1(s01,f01)
+g1:=left(cx,xp1,x,t7,g(xp1,s,f)):[t:1to(x)]cx
+g2:=g(x,s01,f01):[t:1to(x)]cx
+u@t33a:=isoutinn(xp1,<u1>s):is"e"(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)))
+t34:=isinoutn(x,n1,t15):is"n"(n1,inn(x,w1))
+t35:=isoutni(xp1,n1,1top(xp1,<u1>s),inn(x,w1),trlessis"n"(inn(x,w1),x,xp1,1top(x,w1),t7),t34):is"e"(1to(xp1),outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1))
+t36:=tris(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1),t33a,t35):is"e"(1to(xp1),<u1>s,left1to(xp1,x,t7,w1))
+t37:=isf(1to(xp1),cx,f,<u1>s,left1to(xp1,x,t7,w1),t36):is(<u>g1,<u>g2)
+case1@t38:=fisi(1to(x),cx,g1,g2,[t:1to(x)]t37(t)):is"e"([t:1to(x)]cx,g1,g2)
+t39:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g1,g2,t38):is(smpr(x,g1),smpr(x,g2))
+t40:=tris(cx,smpr(x,g1),smpr(x,g2),smpr(x,f01),t39,t33):is(smpr(x,g1),smpr(x,f01))
+t41:=isf(1to(xp1),cx,f,<xout(xp1)>s,xout(xp1),case1):is(<xout(xp1)>g(xp1,s,f),<xout(xp1)>f)
+t42:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q)
+t43:=isf(cx,cx,<smpr(x,g1)>q,<xout(xp1)>g(xp1,s,f),<xout(xp1)>f,t41):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q)
+t44:=isf(cx,cx,[t:cx]<<xout(xp1)>f><t>q,smpr(x,g1),smpr(x,f01),t40):is(<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q)
+t45:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><smpr(x,f01)>q,satz278(x,f)):is(<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f))
+t46:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f),t42,t43,t44,t45):prop1(xp1,s,f)
+b@1px:=pl"n"(1,x):nat
+[case2:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))][u:1to(x)]
+u3:=right1to(1,x,u):1to(1px)
+case2@t47:=lessisi2"n"(1px,xp1,compl"n"(1,x)):lessis"n"(1px,xp1)
+s02:=left(1to(xp1),xp1,1px,t47,s):[t:1to(1px)]1to(xp1)
+u@n3:=inn(xp1,<u3>s02):nat
+[i:is"n"(n3,1)]
+t48:=tr3is(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),1out(xp1),<1out(xp1)>s,isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),1,satz24a(xp1),i),symis(1to(xp1),<1out(xp1)>s,1out(xp1),case2)):is"e"(1to(xp1),<u3>s02,<1out(xp1)>s)
+t49:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3),1out(xp1),t48):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
+t50:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t49):is"n"(inn(1px,u3),1)
+t51:=isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))):is"n"(pl"n"(1,inn(x,u)),inn(1px,u3))
+t52:=ismore1"n"(pl"n"(1,inn(x,u)),inn(1px,u3),1,t51,satz18(1,inn(x,u))):more"n"(inn(1px,u3),1)
+t53:=<t50>ec3e21(is"n"(inn(1px,u3),1),more"n"(inn(1px,u3),1),less"n"(inn(1px,u3),1),satz10b(inn(1px,u3),1),t52):con
+u@t54:=ore1(more"n"(n3,1),is"n"(n3,1),satz24(n3),[t:is"n"(n3,1)]t53(t)):more"n"(n3,1)
+nm1:=mn"n"(n3,1,t54):nat
+t54a:=islessis1"n"(n3,pl"n"(nm1,1),xp1,th1c"n.mn"(n3,1,t54),1top(xp1,<u3>s02)):lessis"n"(pl"n"(nm1,1),xp1)
+t55:=th9"l.or"(less"n"(pl"n"(nm1,1),xp1),is"n"(pl"n"(nm1,1),xp1),less"n"(nm1,x),is"n"(nm1,x),t54a,[t:less"n"(pl"n"(nm1,1),xp1)]satz20c(nm1,x,1,t),[t:is"n"(pl"n"(nm1,1),xp1)]satz20b(nm1,x,1,t)):lessis"n"(nm1,x)
+w3:=outn(x,nm1,t55):1to(x)
+case2@s03:=[t:1to(x)]w3(t):[t:1to(x)]1to(x)
+u@[v:1to(x)][i:is"e"(1to(x),w3(u),w3(v))]
+t56:=isoutne(x,nm1(u),t55(u),nm1(v),t55(v),i):is"n"(nm1(u),nm1(v))
+t57:=tr3is(nat,n3(u),pl"n"(nm1(u),1),pl"n"(nm1(v),1),n3(v),th1c"n.mn"(n3(u),1,t54(u)),ispl1"n"(nm1(u),nm1(v),1,t56),th1d"n.mn"(n3(v),1,t54(v))):is"n"(n3(u),n3(v))
+t58:=isinne(xp1,<u3(u)>s02,<u3(v)>s02,t57):is"e"(1to(xp1),<u3(u)>s02,<u3(v)>s02)
+t59:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)),t58):is"e"(1to(xp1),left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)))
+t60:=thleft1(xp1,1px,t47,u3(u),u3(v),t59):is"e"(1to(1px),u3(u),u3(v))
+t61:=thright1(1,x,u,v,t60):is"e"(1to(x),u,v)
+case2@s04:=left(1to(xp1),xp1,1px,t47,invf(1to(xp1),1to(xp1),s,b)):[t:1to(1px)]1to(xp1)
+u@u4:=<u3>s04:1to(xp1)
+n4:=inn(xp1,u4):nat
+[i:is"n"(n4,1)]
+t62:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),1out(xp1),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),1,satz24a(xp1),i)):is"e"(1to(xp1),u4,1out(xp1))
+t63:=tr3is(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<1out(xp1)>s,1out(xp1),thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,1out(xp1),t62),case2):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
+t64:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t63):is"n"(inn(1px,u3),1)
+t65:=tris(nat,pl"n"(1,inn(x,u)),inn(1px,u3),1,isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),t64):is"n"(pl"n"(1,inn(x,u)),1)
+t66:=<t65>ec3e21(is"n"(pl"n"(1,inn(x,u)),1),more"n"(pl"n"(1,inn(x,u)),1),less"n"(pl"n"(1,inn(x,u)),1),satz10b(pl"n"(1,inn(x,u)),1),satz18(1,inn(x,u))):con
+u@t67:=ore1(more"n"(n4,1),is"n"(n4,1),satz24(n4),[t:is"n"(n4,1)]t66(t)):more"n"(n4,1)
+nm2:=mn"n"(n4,1,t67):nat
+t68:=islessis1"n"(n4,pl"n"(nm2,1),xp1,th1c"n.mn"(n4,1,t67),1top(xp1,u4)):lessis"n"(pl"n"(nm2,1),xp1)
+t69:=th9"l.or"(less"n"(pl"n"(nm2,1),xp1),is"n"(pl"n"(nm2,1),xp1),less"n"(nm2,x),is"n"(nm2,x),t68,[t:less"n"(pl"n"(nm2,1),xp1)]satz20c(nm2,x,1,t),[t:is"n"(pl"n"(nm2,1),xp1)]satz20b(nm2,x,1,t)):lessis"n"(nm2,x)
+w4:=outn(x,nm2,t69):1to(x)
+t70:=isinoutn(x,nm2,t69):is"n"(nm2,inn(x,w4))
+t71:=tr3is(nat,n4,pl"n"(1,nm2),pl"n"(1,inn(x,w4)),inn(1px,u3(w4)),th1a"n.mn"(n4,1,t67),ispl2"n"(nm2,inn(x,w4),1,t70),isinoutn(1px,pl"n"(1,inn(x,w4)),satz19o(inn(x,w4),x,1,1top(x,w4)))):is"n"(n4,inn(1px,u3(w4)))
+t72:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),left1to(xp1,1px,t47,u3(w4)),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),inn(1px,u3(w4)),trlessis"n"(inn(1px,u3(w4)),1px,xp1,1top(1px,u3(w4)),t47),t71)):is"e"(1to(xp1),u4,left1to(xp1,1px,t47,u3(w4)))
+t73:=tris(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<u3(w4)>s02,thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,left1to(xp1,1px,t47,u3(w4)),t72)):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),<u3(w4)>s02)
+t74:=tr3is(nat,pl"n"(1,inn(x,u)),inn(1px,u3),inn(xp1,left1to(xp1,1px,t47,u3)),n3(w4),isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),isinoutn(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47)),isinni(xp1,left1to(xp1,1px,t47,u3),<u3(w4)>s02,t73)):is"n"(pl"n"(1,inn(x,u)),n3(w4))
+t75:=th1e"n.mn"(n3(w4),1,inn(x,u),t54(w4),t74):is"n"(inn(x,u),nm1(w4))
+t76:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w3(w4),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),nm1(w4),t55(w4),t75)):is"e"(1to(x),u,w3(w4))
+t77:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w3(t)),w4,t76):image(1to(x),1to(x),s03,u)
+case2@t78:=andi(injective(1to(x),1to(x),s03),surjective(1to(x),1to(x),s03),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s03,<u>s03)]t61(t,u,v),[t:1to(x)]t77(t)):bijective(1to(x),1to(x),s03)
+f02:=left(cx,xp1,1px,t47,f):[t:1to(1px)]cx
+f03:=right(cx,1,x,f02):[t:1to(x)]cx
+t79:=<t78><f03><s03>p:prop1(s03,f03)
+g3:=left(cx,xp1,1px,t47,g(xp1,s,f)):[t:1to(1px)]cx
+g4:=right(cx,1,x,g3):[t:1to(x)]cx
+g5:=g(x,s03,f03):[t:1to(x)]cx
+u@t80:=tr3is(nat,n3,pl"n"(1,nm1),pl"n"(1,inn(x,w3)),inn(1px,right1to(1,x,w3)),th1a"n.mn"(n3,1,t54),ispl2"n"(nm1,inn(x,w3),1,isinoutn(x,nm1,t55)),isinoutn(1px,pl"n"(1,inn(x,w3)),satz19o(inn(x,w3),x,1,1top(x,w3)))):is"n"(n3,inn(1px,right1to(1,x,w3)))
+t81:=tris(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),left1to(xp1,1px,t47,right1to(1,x,w3)),isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),inn(1px,right1to(1,x,w3)),trlessis"n"(inn(1px,right1to(1,x,w3)),1px,xp1,1top(1px,right1to(1,x,w3)),t47),t80)):is"e"(1to(xp1),<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)))
+t82:=isf(1to(xp1),cx,f,<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)),t81):is(<u>g4,<u>g5)
+case2@t83:=fisi(1to(x),cx,g4,g5,[t:1to(x)]t82(t)):is"e"([t:1to(x)]cx,g4,g5)
+t85:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g4,g5,t83):is(smpr(x,g4),smpr(x,g5))
+t86:=tris(cx,smpr(x,g4),smpr(x,g5),smpr(x,f03),t85,t79):is(smpr(x,g4),smpr(x,f03))
+t87:=lessisi1"n"(1,1px,satz18a(1,x)):lessis"n"(1,1px)
+g6:=left(cx,1px,1,t87,g3):[t:1to(1)]cx
+f04:=left(cx,1px,1,t87,f02):[t:1to(1)]cx
+t87a:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+1d:=left1to(1px,1,t87,xout(1)):1to(1px)
+t87b:=isinoutn(1px,inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,1px,1top(1,xout(1)),t87)):is"n"(inn(1,xout(1)),inn(1px,1d))
+t88:=tris(nat,1,inn(1,xout(1)),inn(1px,1d),t87a,t87b):is"n"(1,inn(1px,1d))
+1e:=left1to(xp1,1px,t47,1d):1to(xp1)
+t88a:=isoutni(xp1,1,satz24a(xp1),inn(1px,1d),trlessis"n"(inn(1px,1d),1px,xp1,1top(1px,1d),t47),t88):is"e"(1to(xp1),1out(xp1),1e)
+t88b:=isf(1to(xp1),1to(xp1),s,1e,1out(xp1),symis(1to(xp1),1out(xp1),1e,t88a)):is"e"(1to(xp1),<1e>s,<1out(xp1)>s)
+t89:=tr3is(1to(xp1),<1e>s,<1out(xp1)>s,1out(xp1),1e,t88b,case2,t88a):is"e"(1to(xp1),<1e>s,1e)
+t89a:=tr3is(cx,smpr(1,g6),<xout(1)>g6,<xout(1)>f04,smpr(1,f04),satz277(g6),isf(1to(xp1),cx,f,<1e>s,1e,t89),symis(cx,smpr(1,f04),<xout(1)>f04,satz277(f04))):is(smpr(1,g6),smpr(1,f04))
+t90:=satz281(1,x,g3):is(smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q)
+t91:=isf(cx,cx,<smpr(1,g6)>q,smpr(x,g4),smpr(x,f03),t86):is(<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q)
+t92:=isf(cx,cx,[t:cx]<smpr(x,f03)><t>q,smpr(1,g6),smpr(1,f04),t89a):is(<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q)
+t93:=symis(cx,smpr(1px,f02),<smpr(x,f03)><smpr(1,f04)>q,satz281(1,x,f02)):is(<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02))
+t94:=tr4is(cx,smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02),t90,t91,t92,t93):is(smpr(1px,g3),smpr(1px,f02))
+t95:=issmpr(xp1,f,1px,compl"n"(1,x)):is(smpr(1px,f02),smpr(xp1,f))
+t96:=symis(cx,smpr(1px,g3),smpr(xp1,g(xp1,s,f)),issmpr(xp1,g(xp1,s,f),1px,compl"n"(1,x))):is(smpr(xp1,g(xp1,s,f)),smpr(1px,g3))
+t97:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(1px,g3),smpr(1px,f02),smpr(xp1,f),t96,t94,t95):prop1(xp1,s,f)
+b@[not1:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))][not2:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]
+a0:=<1out(xp1)>s:1to(xp1)
+b0:=<1out(xp1)>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
+t98:=thinvf2(1to(xp1),1to(xp1),s,b,1out(xp1)):is"e"(1to(xp1),1out(xp1),<b0>s)
+t99:=not2:not(is"e"(1to(xp1),a0,1out(xp1)))
+t100:=symnotis(1to(xp1),<1out(xp1)>s,<b0>s,th3"e.notis"(1to(xp1),<1out(xp1)>s,1out(xp1),<b0>s,not2,t98)):not(is"e"(1to(xp1),<b0>s,<1out(xp1)>s))
+t101:=th3"l.imp"(is"e"(1to(xp1),b0,1out(xp1)),is"e"(1to(xp1),<b0>s,<1out(xp1)>s),t100,[t:is"e"(1to(xp1),b0,1out(xp1))]isf(1to(xp1),1to(xp1),s,b0,1out(xp1),t)):not(is"e"(1to(xp1),b0,1out(xp1)))
+s1:=changef(1to(xp1),1to(xp1),s,1out(xp1),b0):[t:1to(xp1)]1to(xp1)
+[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
+t102:=changef1(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,<b0>s)
+t103:=tris2(1to(xp1),<u>s1,1out(xp1),<b0>s,t102,t98):is"e"(1to(xp1),<u>s1,1out(xp1))
+u@[i:is"e"(1to(xp1),u,b0)]
+t104:=changef2(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,a0)
+u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
+t105:=changef3(1to(xp1),1to(xp1),s,1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
+not2@t106:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),b0,b):bijective(1to(xp1),1to(xp1),s1)
+[alpha:not(is"e"(1to(xp1),a0,xout(xp1)))]
+s2:=wissel(1to(xp1),1out(xp1),a0):[t:1to(xp1)]1to(xp1)
+t107:=th3"e.wissel"(1to(xp1),1out(xp1),a0):bijective(1to(xp1),1to(xp1),s2)
+[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
+t108:=iswissel1(1to(xp1),1out(xp1),a0,<u>s1,t103(u,i)):is"e"(1to(xp1),<<u>s1>s2,a0)
+t109:=tris2(1to(xp1),<u>s,<<u>s1>s2,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t108):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+u@[i:is"e"(1to(xp1),u,b0)]
+t110:=iswissel2(1to(xp1),1out(xp1),a0,<u>s1,t104(u,i)):is"e"(1to(xp1),<<u>s1>s2,1out(xp1))
+t111:=tris2(1to(xp1),<u>s,<<u>s1>s2,1out(xp1),tris2(1to(xp1),<u>s,1out(xp1),<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),t98),t110):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))][i:is"e"(1to(xp1),<u>s1,1out(xp1))]
+t112:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,1out(xp1),tris2(1to(xp1),<u>s1,<1out(xp1)>s1,1out(xp1),i,t103(1out(xp1),refis(1to(xp1),1out(xp1))))):is"e"(1to(xp1),u,1out(xp1))
+o@t113:=th3"l.imp"(is"e"(1to(xp1),<u>s1,1out(xp1)),is"e"(1to(xp1),u,1out(xp1)),n,[t:is"e"(1to(xp1),<u>s1,1out(xp1))]t112(t)):not(is"e"(1to(xp1),<u>s1,1out(xp1)))
+[i:is"e"(1to(xp1),<u>s1,a0)]
+t114:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,b0,tris2(1to(xp1),<u>s1,<b0>s1,a0,i,t104(b0,refis(1to(xp1),b0)))):is"e"(1to(xp1),u,b0)
+o@t115:=th3"l.imp"(is"e"(1to(xp1),<u>s1,a0),is"e"(1to(xp1),u,b0),o,[t:is"e"(1to(xp1),<u>s1,a0)]t114(t)):not(is"e"(1to(xp1),<u>s1,a0))
+t116:=iswissel3(1to(xp1),1out(xp1),a0,<u>s1,t113,t115):is"e"(1to(xp1),<<u>s1>s2,<u>s1)
+t117:=symis(1to(xp1),<<u>s1>s2,<u>s,tris(1to(xp1),<<u>s1>s2,<u>s1,<u>s,t116,t105(u,n,o))):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+n@t118:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,b0)]t111(t),[t:not(is"e"(1to(xp1),u,b0))]t117(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+u@t119:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,1out(xp1))]t109(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t118(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
+alpha@t120:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s1>s2,[t:1to(xp1)]t119(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s1>s2)
+not2@t121:=t103(1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s1,1out(xp1))
+t121a:=ec3e21(is"n"(xp1,1),more"n"(xp1,1),less"n"(xp1,1),satz10b(xp1,1),ismore1"n"(1px,xp1,1,compl"n"(1,x),satz18(1,x))):nis"n"(xp1,1)
+t122:=th3"l.imp"(is"e"(1to(xp1),xout(xp1),1out(xp1)),is"n"(xp1,1),t121a,[t:is"e"(1to(xp1),xout(xp1),1out(xp1))]isoutne(xp1,xp1,lessisi3(xp1),1,satz24a(xp1),t)):not(is"e"(1to(xp1),xout(xp1),1out(xp1)))
+alpha@t123:=symnotis(1to(xp1),a0,xout(xp1),alpha):not(is"e"(1to(xp1),xout(xp1),a0))
+t124:=iswissel3(1to(xp1),1out(xp1),a0,xout(xp1),t122,t123):is"e"(1to(xp1),<xout(xp1)>s2,xout(xp1))
+t125:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s1>s2,t120):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))))
+t126:=t97(s1,g(xp1,s2,f),t106,t121):is(smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)))
+t127:=t46(s2,f,t107,t124):is(smpr(xp1,g(xp1,s2,f)),smpr(xp1,f))
+t128:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)),smpr(xp1,f),t125,t126,t127):prop1(xp1,s,f)
+not2@[i3:is"e"(1to(xp1),a0,xout(xp1))][beta:not(is"e"(1to(xp1),b0,xout(xp1)))]
+s3:=wissel(1to(xp1),1out(xp1),b0):[t:1to(xp1)]1to(xp1)
+t129:=th3"e.wissel"(1to(xp1),1out(xp1),b0):bijective(1to(xp1),1to(xp1),s3)
+[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
+t130:=t104(<u>s3,iswissel1(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,a0)
+t131:=tris2(1to(xp1),<u>s,<<u>s3>s1,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t130):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+u@[i:is"e"(1to(xp1),u,b0)]
+t132:=t103(<u>s3,iswissel2(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,1out(xp1))
+t133:=tris2(1to(xp1),<u>s,<<u>s3>s1,<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),tris(1to(xp1),<<u>s3>s1,1out(xp1),<b0>s,t132,t98)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
+t134:=iswissel3(1to(xp1),1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s3,u)
+t135:=isf(1to(xp1),1to(xp1),s1,<u>s3,u,t134):is"e"(1to(xp1),<<u>s3>s1,<u>s1)
+t136:=t105(u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
+t139:=symis(1to(xp1),<<u>s3>s1,<u>s,tris(1to(xp1),<<u>s3>s1,<u>s1,<u>s,t135,t136)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+n@t140:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,b0)]t133(t),[t:not(is"e"(1to(xp1),u,b0))]t139(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+u@t141:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,1out(xp1))]t131(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t140(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
+beta@t142:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s3>s1,[t:1to(xp1)]t141(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s3>s1)
+t143:=symnotis(1to(xp1),b0,xout(xp1),beta):not(is"e"(1to(xp1),xout(xp1),b0))
+t144:=iswissel3(1to(xp1),1out(xp1),b0,xout(xp1),t122,t143):is"e"(1to(xp1),<xout(xp1)>s3,xout(xp1))
+t145:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s3>s1,t142):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))))
+t146:=t46(s3,g(xp1,s1,f),t129,t144):is(smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)))
+t147:=t97(s1,f,t106,t121):is(smpr(xp1,g(xp1,s1,f)),smpr(xp1,f))
+t148:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)),smpr(xp1,f),t145,t146,t147):prop1(xp1,s,f)
+i3@[gamma:is"e"(1to(xp1),b0,xout(xp1))][i:is"n"(x,1)]
+t149:=ispl1"n"(1,x,1,symis(nat,x,1,i)):is"n"(2,xp1)
+t150:=lessisi2"n"(2,xp1,t149):lessis"n"(2,xp1)
+f05:=left(cx,xp1,2,t150,f):[t:1to(2)]cx
+s05:=left(1to(xp1),xp1,2,t150,s):[t:1to(2)]1to(xp1)
+g7:=left(cx,xp1,2,t150,g(xp1,s,f)):[t:1to(2)]cx
+t151:=issmpr(xp1,f,2,t149):is(smpr(2,f05),smpr(xp1,f))
+t152:=issmpr(xp1,g(xp1,s,f),2,t149):is(smpr(2,g7),smpr(xp1,g(xp1,s,f)))
+t153:=satz280(f05):is(smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q)
+t154:=satz280(g7):is(smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q)
+t155:=tris1(nat,inn(2,xout(2)),xp1,2,isinoutn(2,2,lessisi3(2)),t149):is"n"(inn(2,xout(2)),xp1)
+t156:=isoutni(xp1,inn(2,xout(2)),trlessis"n"(inn(2,xout(2)),2,xp1,1top(2,xout(2)),t150),xp1,lessisi3(xp1),t155):is"e"(1to(xp1),left1to(xp1,2,t150,xout(2)),xout(xp1))
+t157:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,xout(2)),xout(xp1),t156):is"e"(1to(xp1),<xout(2)>s05,<xout(xp1)>s)
+t158:=symis(nat,1,inn(2,1out(2)),isinoutn(2,1,satz24a(2))):is"n"(inn(2,1out(2)),1)
+t159:=isoutni(xp1,inn(2,1out(2)),trlessis"n"(inn(2,1out(2)),2,xp1,1top(2,1out(2)),t150),1,satz24a(xp1),t158):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1))
+t160:=tr3is(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1),<b0>s,<xout(xp1)>s,t159,t98,isf(1to(xp1),1to(xp1),s,b0,xout(xp1),gamma)):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),<xout(xp1)>s)
+t161:=tris2(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)),<xout(xp1)>s,t157,t160):is"e"(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)))
+t163:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,1out(2)),1out(xp1),t159):is"e"(1to(xp1),<1out(2)>s05,<1out(xp1)>s)
+t164:=tris(1to(xp1),<1out(2)>s05,<1out(xp1)>s,xout(xp1),t163,i3):is"e"(1to(xp1),<1out(2)>s05,xout(xp1))
+t165:=tris2(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)),xout(xp1),t164,t156):is"e"(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)))
+t166:=isf(1to(xp1),cx,f,<xout(2)>s05,left1to(xp1,2,t150,1out(2)),t161):is(<xout(2)>g7,<1out(2)>f05)
+t167:=isf(1to(xp1),cx,f,<1out(2)>s05,left1to(xp1,2,t150,xout(2)),t165):is(<1out(2)>g7,<xout(2)>f05)
+t168:=isf(cx,cx,<<1out(2)>g7>q,<xout(2)>g7,<1out(2)>f05,t166):is(<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q)
+t169:=comq(c,<1out(2)>g7,<1out(2)>f05):is(<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q)
+t170:=isf(cx,cx,<<1out(2)>f05>q,<1out(2)>g7,<xout(2)>f05,t167):is(<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q)
+t171:=tr4is(cx,smpr(xp1,g(xp1,s,f)),smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q,symis(cx,smpr(2,g7),smpr(xp1,g(xp1,s,f)),t152),t154,t168,t169):is(smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q)
+t172:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q,smpr(2,f05),smpr(xp1,f),t171,t170,symis(cx,smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q,t153),t151):prop1(xp1,s,f)
+trivial:=t172:prop1(xp1,s,f)
+gamma@[n:nis"n"(x,1)]
+t173:=ore1(more"n"(x,1),is"n"(x,1),satz24(x),n):more"n"(x,1)
+xm1:=mn"n"(x,1,t173):nat
+s4:=changef(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1)):[t:1to(xp1)]1to(xp1)
+t174:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),b):bijective(1to(xp1),1to(xp1),s4)
+t175:=changef2(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),xout(xp1),refis(1to(xp1),xout(xp1))):is"e"(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s)
+t176:=symis(1to(xp1),a0,xout(xp1),i3):is"e"(1to(xp1),xout(xp1),<1out(xp1)>s)
+t177:=tris2(1to(xp1),<xout(xp1)>s4,xout(xp1),<1out(xp1)>s,t175,t176):is"e"(1to(xp1),<xout(xp1)>s4,xout(xp1))
+t178:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
+g8:=left(cx,xp1,x,t178,g(xp1,s,f)):[t:1to(x)]cx
+t179:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q)
+t180:=th1b"n.mn"(x,1,t173):is"n"(pl"n"(1,xm1),x)
+t181:=lessisi2"n"(pl"n"(1,xm1),x,t180):lessis"n"(pl"n"(1,xm1),x)
+g9:=left(cx,x,pl"n"(1,xm1),t181,g8):[t:1to(pl"n"(1,xm1))]cx
+t182:=symis(cx,smpr(pl"n"(1,xm1),g9),smpr(x,g8),issmpr(x,g8,pl"n"(1,xm1),t180)):is(smpr(x,g8),smpr(pl"n"(1,xm1),g9))
+g10:=right(cx,1,xm1,g9):[t:1to(xm1)]cx
+t183:=lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)):lessis"n"(1,pl"n"(1,xm1))
+g11:=left(cx,pl"n"(1,xm1),1,t183,g9):[t:1to(1)]cx
+t184:=satz281(a,1,xm1,g9):is(smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q)
+t185:=satz277(g11):is(smpr(1,g11),<xout(1)>g11)
+t186:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
+1a:=left1to(pl"n"(1,xm1),1,t183,xout(1)):1to(pl"n"(1,xm1))
+t187:=isinoutn(pl"n"(1,xm1),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,pl"n"(1,xm1),1top(1,xout(1)),t183)):is"n"(inn(1,xout(1)),inn(pl"n"(1,xm1),1a))
+1b:=left1to(x,pl"n"(1,xm1),t181,1a):1to(x)
+t188:=isinoutn(x,inn(pl"n"(1,xm1),1a),trlessis"n"(inn(pl"n"(1,xm1),1a),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),1a),t181)):is"n"(inn(pl"n"(1,xm1),1a),inn(x,1b))
+t189:=tr3is(nat,1,inn(1,xout(1)),inn(pl"n"(1,xm1),1a),inn(x,1b),t186,t187,t188):is"n"(1,inn(x,1b))
+1c:=left1to(xp1,x,t178,1b):1to(xp1)
+t190:=isoutni(xp1,1,satz24a(xp1),inn(x,1b),trlessis"n"(inn(x,1b),x,xp1,1top(x,1b),t178),t189):is"e"(1to(xp1),1out(xp1),1c)
+t191:=isf(1to(xp1),cx,g(xp1,s,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s,f),<xout(1)>g11)
+t192:=tris2(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(1)>g11,t185,t191):is(smpr(1,g11),<1out(xp1)>g(xp1,s,f))
+t193:=symis(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s,t175):is"e"(1to(xp1),<1out(xp1)>s,<xout(xp1)>s4)
+t194:=isf(1to(xp1),cx,f,<1out(xp1)>s,<xout(xp1)>s4,t193):is(<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f))
+t195:=tris(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f),t192,t194):is(smpr(1,g11),<xout(xp1)>g(xp1,s4,f))
+t196:=isf(cx,cx,[t:cx]<smpr(xm1,g10)><t>q,smpr(1,g11),<xout(xp1)>g(xp1,s4,f),t195):is(<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
+t197:=tr3is(cx,smpr(x,g8),smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t182,t184,t196):is(smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
+t198:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s,f)><t>q,smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t197):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q)
+t199:=assq1(a,<xout(xp1)>g(xp1,s4,f),smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q)
+t200:=comq(c,<xout(xp1)>g(xp1,s4,f),<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q):is(<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
+g12:=left(cx,xp1,x,t178,g(xp1,s4,f)):[t:1to(x)]cx
+g13:=left(cx,x,pl"n"(1,xm1),t181,g12):[t:1to(pl"n"(1,xm1))]cx
+g14:=right(cx,1,xm1,g13):[t:1to(xm1)]cx
+g15:=left(cx,pl"n"(1,xm1),1,lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)),g13):[t:1to(1)]cx
+t201:=satz278(x,g(xp1,s4,f)):is(smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
+t202:=symis(cx,smpr(pl"n"(1,xm1),g13),smpr(x,g12),issmpr(x,g12,pl"n"(1,xm1),t180)):is(smpr(x,g12),smpr(pl"n"(1,xm1),g13))
+t203:=satz281(a,1,xm1,g13):is(smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q)
+t204:=satz277(g15):is(smpr(1,g15),<xout(1)>g15)
+t205:=isf(1to(xp1),cx,g(xp1,s4,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s4,f),<xout(1)>g15)
+t206:=tris2(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(1)>g15,t204,t205):is(smpr(1,g15),<1out(xp1)>g(xp1,s4,f))
+t207:=changef1(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s4,<xout(xp1)>s)
+t208:=isf(1to(xp1),cx,f,<1out(xp1)>s4,<xout(xp1)>s,t207):is(<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f))
+t209:=tris(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f),t206,t208):is(smpr(1,g15),<xout(xp1)>g(xp1,s,f))
+t210:=isf(cx,cx,[t:cx]<smpr(xm1,g14)><t>q,smpr(1,g15),<xout(xp1)>g(xp1,s,f),t209):is(<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+t211:=tr3is(cx,smpr(x,g12),smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t202,t203,t210):is(smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+[u:1to(xm1)]
+ua:=right1to(1,xm1,u):1to(pl"n"(1,xm1))
+ub:=left1to(x,pl"n"(1,xm1),t181,ua):1to(x)
+uc:=left1to(xp1,x,t178,ub):1to(xp1)
+[i:is"e"(1to(xp1),uc,xout(xp1))]
+t212:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),xp1,lessisi3(xp1),i):is"n"(inn(x,ub),xp1)
+t213:=satz16a(inn(x,ub),x,xp1,1top(x,ub),satz18a(x,1)):less"n"(inn(x,ub),xp1)
+t214:=<t212>ec3e31(is"n"(inn(x,ub),xp1),more"n"(inn(x,ub),xp1),less"n"(inn(x,ub),xp1),satz10b(inn(x,ub),xp1),t213):con
+u@t215:=[t:is"e"(1to(xp1),uc,xout(xp1))]t214(t):not(is"e"(1to(xp1),uc,xout(xp1)))
+[i:is"e"(1to(xp1),uc,1out(xp1))]
+t216:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),1,satz24a(xp1),i):is"n"(inn(x,ub),1)
+t217:=isinoutn(x,inn(pl"n"(1,xm1),ua),trlessis"n"(inn(pl"n"(1,xm1),ua),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),ua),t181)):is"n"(inn(pl"n"(1,xm1),ua),inn(x,ub))
+t218:=isinoutn(pl"n"(1,xm1),pl"n"(1,inn(xm1,u)),satz19o(inn(xm1,u),xm1,1,1top(xm1,u))):is"n"(pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua))
+t219:=tr3is(nat,pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua),inn(x,ub),1,t218,t217,t216):is"n"(pl"n"(1,inn(xm1,u)),1)
+t220:=satz18(1,inn(xm1,u)):more"n"(pl"n"(1,inn(xm1,u)),1)
+t221:=<t219>ec3e21(is"n"(pl"n"(1,inn(xm1,u)),1),more"n"(pl"n"(1,inn(xm1,u)),1),less"n"(pl"n"(1,inn(xm1,u)),1),satz10b(pl"n"(1,inn(xm1,u)),1),t220):con
+u@t222:=[t:is"e"(1to(xp1),uc,1out(xp1))]t221(t):not(is"e"(1to(xp1),uc,1out(xp1)))
+t223:=changef3(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),uc,t222,t215):is"e"(1to(xp1),<uc>s4,<uc>s)
+t224:=isf(1to(xp1),cx,f,<uc>s4,<uc>s,t223):is(<u>g14,<u>g10)
+n@t225:=fisi(1to(xm1),cx,g10,g14,[t:1to(xm1)]symis(cx,<t>g14,<t>g10,t224(t))):is"e"([t:1to(xm1)]cx,g10,g14)
+t226:=isf([t:1to(xm1)]cx,cx,[u:[t:1to(xm1)]cx]smpr(xm1,u),g10,g14,t225):is(smpr(xm1,g10),smpr(xm1,g14))
+t227:=comq(c,smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q)
+t228:=isf(cx,cx,<<xout(xp1)>g(xp1,s,f)>q,smpr(xm1,g10),smpr(xm1,g14),t226):is(<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+t229:=tris(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t227,t228):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
+t230:=tris2(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t229,t211):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12))
+t231:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s4,f)><t>q,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),t230):is(<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
+t232:=symis(cx,smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,t201):is(<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)))
+t233:=t46(s4,f,t174,t177):is(smpr(xp1,g(xp1,s4,f)),smpr(xp1,f))
+t234:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,t179,t198,t199,t200):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
+t235:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)),smpr(xp1,f),t234,t231,t232,t233):prop1(xp1,s,f)
+gamma@t236:=th1"l.imp"(is"n"(x,1),prop1(xp1,s,f),[t:is"n"(x,1)]t172(t),[t:not(is"n"(x,1))]t235(t)):prop1(xp1,s,f)
+i3@t237:=th1"l.imp"(is"e"(1to(xp1),b0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),b0,xout(xp1))]t236(t),[t:not(is"e"(1to(xp1),b0,xout(xp1)))]t148(t)):prop1(xp1,s,f)
+not2@t238:=th1"l.imp"(is"e"(1to(xp1),a0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),a0,xout(xp1))]t237(t),[t:not(is"e"(1to(xp1),a0,xout(xp1)))]t128(t)):prop1(xp1,s,f)
+not1@t239:=th1"l.imp"(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))]t97(t),[t:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]t238(t)):prop1(xp1,s,f)
+b@t240:=th1"l.imp"(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))]t46(t),[t:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))]t239(t)):prop1(xp1,s,f)
+p@t241:=[u:[t:1to(xp1)]1to(xp1)][v:[t:1to(xp1)]cx][w:bijective(1to(xp1),1to(xp1),u)]t240(u,v,w):prop2(xp1)
+t242:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t241,satz4a(x)):prop2(<x>suc)
+x@t243:=induction([t:nat]prop2(t),t6,[t:nat][u:prop2(t)]t242(t,u),x):prop2(x)
+-8283
+satz283:=<b><f><s>t243".8283":is(smpr(x,[t:1to(x)]<<t>s>f),smpr(x,f))
+@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
+shiftl:=shiftl"r"(x,ix,y,iy,ly):nat
+[n:1to(shiftl)]
+shiftr:=shiftr"r"(x,ix,y,iy,ly,n):real
+intshiftr:=intshiftr"r"(x,ix,y,iy,ly,n):intrl(shiftr)
+shiftrls:=shiftrls"r"(x,ix,y,iy,ly,n):lessis(shiftr,x)
+lsshiftr:=lsshiftr"r"(x,ix,y,iy,ly,n):lessis(y,shiftr)
+[m:1to(shiftl)][i:is"r"(shiftr(n),shiftr(m))]
+iseshiftr:=iseshiftr"r"(x,ix,y,iy,ly,n,m,i):is"e"(1to(shiftl),n,m)
+ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
+shiftl1:=shiftl1"r"(x,ix,y,iy,ly,u,a):1to(shiftl)
+shiftinv1:=shiftinv1"r"(x,ix,y,iy,ly,u,a):is"r"(u,shiftr(shiftl1))
+shiftinv2:=shiftinv2"r"(x,ix,y,iy,ly,u,a):is"r"(shiftr(shiftl1),u)
+ly@[f:seq(x,ix,y,iy,ly,cx)]
+shiftf:=shiftf(x,ix,y,iy,ly,cx,f):[t:1to(shiftl)]cx
+[q:[t:cx][u:cx]cx]
+smpri:=smpr(q,shiftl,shiftf):cx
+f@[pi:proofsirrelevant(x,ix,y,iy,ly,cx,f)][q:[t:cx][u:cx]cx][a:assoc(q)][u:real][iu:intrl(u)][l:lessis(y,u)][k:less(u,x)][v:real][iv:intrl(v)][lv:lessis(y,v)][kv:lessis(v,u)]
++8284
+t1:=lessisi1(v,x,satz172a(v,u,x,kv,k)):lessis(v,x)
+-8284
+k@lft:=[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]<t1".8284"(t,v,lt,kt)><lt><v><t>f:[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]cx
+iv@[lv:lessis(pl"r"(u,1rl),v)][kv:lessis(v,x)]
++*8284
+x@[y:real]
+pl:=pl"r"(x,y):real
+mn:=mn"r"(x,y):real
+x@p1:=pl"r"(x,1rl):real
+kv@t2:=satz190c(u,u,0,1rl,lessisi2(u,u,refis(real,u)),lemma1"r"(1rl,0,satz169a(1rl,natpos(1rl,natrl1)))):less(pl(u,0),p1(u))
+t3:=isless1(pl(u,0),u,p1(u),pl02"r"(u,0,refis(real,0)),t2):less(u,p1(u))
+t4:=lessisi1(y,v,satz172b(y,p1(u),v,satz172a(y,u,p1(u),l,t3),lv)):lessis(y,v)
+-8284
+k@rgt:=[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]<kt><t4".8284"(t,v,lt,kt)><v><t>f:[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]cx
++*8284
+k@t5:=intpl(u,iu,1rl,intrl1):intrl(p1(u))
+t6:=satzr25(u,iu,x,ix,k):lessis(p1(u),x)
+t7:=tr3is(real,pl(mn(p1(u),y),mn(p1(x),p1(u))),pl(mn(p1(x),p1(u)),mn(p1(u),y)),mn(pl(mn(p1(x),p1(u)),p1(u)),y),mn(p1(x),y),compl"r"(mn(p1(u),y),mn(p1(x),p1(u))),asspl2"r"(mn(p1(x),p1(u)),p1(u),m0"r"(y)),ismn1"r"(pl(mn(p1(x),p1(u)),p1(u)),p1(x),y,plmn(p1(x),p1(u)))):is"r"(pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y))
+sxy:=shiftl(x,ix,y,iy,ly):nat
+suy:=shiftl(u,iu,y,iy,l):nat
+sxu:=shiftl(x,ix,p1(u),t5,t6):nat
+t8:=tr4is(real,rlofnt(pl"n"(suy,sxu)),pl(rlofnt(suy),rlofnt(sxu)),pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y),rlofnt(sxy),satzr155a(suy,sxu),ispl12"r"(rlofnt(suy),mn(p1(u),y),rlofnt(sxu),mn(p1(x),p1(u)),isrlnt2(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l)),isrlnt2(mn(p1(x),p1(u)),t6"r.shift"(x,ix,p1(u),t5,t6))),t7,isrlnt1(mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly))):is"r"(rlofnt(pl"n"(suy,sxu)),rlofnt(sxy))
+t9:=isntirl(pl"n"(suy,sxu),sxy,t8):is"n"(pl"n"(suy,sxu),sxy)
+t10:=lessisi2"n"(pl"n"(suy,sxu),sxy,t9):lessis"n"(pl"n"(suy,sxu),sxy)
+f1:=left(cx,sxy,pl"n"(suy,sxu),t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(pl"n"(suy,sxu))]cx
+t11:=issmpr(q,sxy,shiftf(x,ix,y,iy,ly,f),pl"n"(suy,sxu),t9):is(smpr(q,pl"n"(suy,sxu),f1),smpri(x,ix,y,iy,ly,f,q))
+fr:=right(cx,suy,sxu,f1):[t:1to(sxu)]cx
+t12:=lessisi1"n"(suy,pl"n"(suy,sxu),satz18a(suy,sxu)):lessis"n"(suy,pl"n"(suy,sxu))
+fl:=left(cx,pl"n"(suy,sxu),suy,t12,f1):[t:1to(suy)]cx
+t12a:=satz281(q,a,suy,sxu,f1):is(smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q)
+[n:1to(sxu)]
+t13:=isinoutn(pl"n"(suy,sxu),pl"n"(suy,inn(sxu,n)),satz19o(inn(sxu,n),sxu,suy,1top(sxu,n))):is"n"(pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)))
+t14:=isinoutn(sxy,inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),trlessis"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),right1to(suy,sxu,n)),t10)):is"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n))))
+n1:=left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n)):1to(sxy)
+t15:=tris(nat,pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,n1),t13,t14):is"n"(pl"n"(suy,inn(sxu,n)),inn(sxy,n1))
+t16:=isnterl(pl"n"(suy,inn(sxu,n)),inn(sxy,n1),t15):is"r"(rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)))
+t17:=satzr155b(suy,inn(sxu,n)):is"r"(pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))))
+t18:=ispl1"r"(mn(p1(u),y),rlofnt(suy),rlofnt(inn(sxu,n)),isrlnt1(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l))):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))))
+t19:=tr3is(real,pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)),t18,t17,t16):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)))
+t20:=ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)),y,t19):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxy,n1)),y))
+t21:=tr3is(real,pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y),pl(rlofnt(inn(sxu,n)),pl(mn(p1(u),y),y)),pl(rlofnt(inn(sxu,n)),p1(u)),ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y,compl"r"(mn(p1(u),y),rlofnt(inn(sxu,n)))),asspl1"r"(rlofnt(inn(sxu,n)),mn(p1(u),y),y),ispl2"r"(pl(mn(p1(u),y),y),p1(u),rlofnt(inn(sxu,n)),plmn(p1(u),y))):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxu,n)),p1(u)))
+t22:=tris1(real,pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),t20,t21):is"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)))
+t23:=ismn1"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),1rl,t22):is"r"(shiftr(x,ix,y,iy,ly,n1),shiftr(x,ix,p1(u),t5,t6,n))
+t24:=intshiftr(x,ix,y,iy,ly,n1):intrl(shiftr(x,ix,y,iy,ly,n1))
+t25:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,shiftr(x,ix,y,iy,ly,n1))
+t26:=shiftrls(x,ix,y,iy,ly,n1):lessis(shiftr(x,ix,y,iy,ly,n1),x)
+t27:=intshiftr(x,ix,p1(u),t5,t6,n):intrl(shiftr(x,ix,p1(u),t5,t6,n))
+t28:=lsshiftr(x,ix,p1(u),t5,t6,n):lessis(p1(u),shiftr(x,ix,p1(u),t5,t6,n))
+t29:=shiftrls(x,ix,p1(u),t5,t6,n):lessis(shiftr(x,ix,p1(u),t5,t6,n),x)
+t30:=t4(shiftr(x,ix,p1(u),t5,t6,n),t27,t28,t29):lessis(y,shiftr(x,ix,p1(u),t5,t6,n))
+t31:=<t23><t29><t30><t27><shiftr(x,ix,p1(u),t5,t6,n)><t26><t25><t24><shiftr(x,ix,y,iy,ly,n1)>pi:is(<n>fr,<n>shiftf(x,ix,p1(u),t5,t6,rgt))
+k@t32:=fisi(1to(sxu),cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt),[t:1to(sxu)]t31(t)):is"e"([t:1to(sxu)]cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt))
+t33:=isf([t:1to(sxu)]cx,cx,[v:[t:1to(sxu)]cx]smpr(q,sxu,v),fr,shiftf(x,ix,p1(u),t5,t6,rgt),t32):is(smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q))
+t34:=isf(cx,cx,<smpr(q,suy,fl)>q,smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q),t33):is(<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q)
+[n:1to(suy)]
+t35:=isinoutn(pl"n"(suy,sxu),inn(suy,n),trlessis"n"(inn(suy,n),suy,pl"n"(suy,sxu),1top(suy,n),t12)):is"n"(inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)))
+t36:=isinoutn(sxy,inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),trlessis"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),t10)):is"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n))))
+n2:=left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n)):1to(sxy)
+t37:=tris(nat,inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,n2),t35,t36):is"n"(inn(suy,n),inn(sxy,n2))
+t38:=isnterl(inn(suy,n),inn(sxy,n2),t37):is"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)))
+t39:=ispl1"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)),y,t38):is"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y))
+t40:=ismn1"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y),1rl,t39):is"r"(shiftr(u,iu,y,iy,l,n),shiftr(x,ix,y,iy,ly,n2))
+t41:=intshiftr(u,iu,y,iy,l,n):intrl(shiftr(u,iu,y,iy,l,n))
+t42:=lsshiftr(u,iu,y,iy,l,n):lessis(y,shiftr(u,iu,y,iy,l,n))
+t43:=shiftrls(u,iu,y,iy,l,n):lessis(shiftr(u,iu,y,iy,l,n),u)
+t44:=t1(shiftr(u,iu,y,iy,l,n),t41,t42,t43):lessis(shiftr(u,iu,y,iy,l,n),x)
+t45:=intshiftr(x,ix,y,iy,ly,n2):intrl(shiftr(x,ix,y,iy,ly,n2))
+t46:=lsshiftr(x,ix,y,iy,ly,n2):lessis(y,shiftr(x,ix,y,iy,ly,n2))
+t47:=shiftrls(x,ix,y,iy,ly,n2):lessis(shiftr(x,ix,y,iy,ly,n2),x)
+t48:=<t40><t47><t46><t45><shiftr(x,ix,y,iy,ly,n2)><t44><t42><t41><shiftr(u,iu,y,iy,l,n)>pi:is(<n>shiftf(u,iu,y,iy,l,lft),<n>fl)
+t49:=symis(cx,<n>shiftf(u,iu,y,iy,l,lft),<n>fl,t48):is(<n>fl,<n>shiftf(u,iu,y,iy,l,lft))
+k@t50:=fisi(1to(suy),cx,fl,shiftf(u,iu,y,iy,l,lft),[t:1to(suy)]t49(t)):is"e"([t:1to(suy)]cx,fl,shiftf(u,iu,y,iy,l,lft))
+t51:=isf([t:1to(suy)]cx,cx,[v:[t:1to(suy)]cx]smpr(q,suy,v),fl,shiftf(u,iu,y,iy,l,lft),t50):is(smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q))
+t52:=isf(cx,cx,[t:cx]<smpri(x,ix,p1(u),t5,t6,rgt,q)><t>q,smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q),t51):is(<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
+t53:=tr3is(cx,smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,t12a,t34,t52):is(smpr(q,pl"n"(suy,sxu),f1),<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
+-8284
+k@satz284:=tris1(cx,smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,smpr(q,pl"n"(suy".8284",sxu".8284"),f1".8284"),t11".8284",t53".8284"):is(smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
+q@[v:real][iv:intrl(v)][w:real][iw:intrl(w)][lw:lessis(pl"r"(y,v),w)][kw:lessis(w,pl"r"(x,v))]
++8285
+x@[y:real]
+pl:=pl"r"(x,y):real
+mn:=mn"r"(x,y):real
+x@p1:=pl"r"(x,1rl):real
+kw@t1:=th9"l.or"(less(pl(y,v),w),is"r"(pl(y,v),w),less(mn(pl(y,v),v),mn(w,v)),is"r"(mn(pl(y,v),v),mn(w,v)),lw,[t:less(pl(y,v),w)]satz188f(pl(y,v),w,m0"r"(v),t),[t:is"r"(pl(y,v),w)]ismn1"r"(pl(y,v),w,v,t)):lessis(mn(pl(y,v),v),mn(w,v))
+t2:=islessis1(mn(pl(y,v),v),y,mn(w,v),mnpl(y,v),t1):lessis(y,mn(w,v))
+t3:=th9"l.or"(less(w,pl(x,v)),is"r"(w,pl(x,v)),less(mn(w,v),mn(pl(x,v),v)),is"r"(mn(w,v),mn(pl(x,v),v)),kw,[t:less(w,pl(x,v))]satz188f(w,pl(x,v),m0"r"(v),t),[t:is"r"(w,pl(x,v))]ismn1"r"(w,pl(x,v),v,t)):lessis(mn(w,v),mn(pl(x,v),v))
+t4:=islessis2(mn(pl(x,v),v),x,mn(w,v),mnpl(x,v),t3):lessis(mn(w,v),x)
+-8285
+iv@sft:=[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]<t4".8285"(t,w,lt,kt)><t2".8285"(t,w,lt,kt)><intmn(t,w,v,iv)><mn"r"(t,v)>f:[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]cx
++*8285
+iv@t5:=tris(real,m0"r"(pl(y,v)),m0"r"(pl(v,y)),pl(m0"r"(v),m0"r"(y)),ism0"r"(pl(y,v),pl(v,y),compl"r"(y,v)),satz180(v,y)):is"r"(m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)))
+t6:=tr3is(real,mn(pl(1rl,pl(x,v)),v),pl(1rl,mn(pl(x,v),v)),pl(1rl,x),p1(x),asspl1"r"(1rl,pl(x,v),m0"r"(v)),ispl2"r"(mn(pl(x,v),v),x,1rl,mnpl(x,v)),compl"r"(1rl,x)):is"r"(mn(pl(1rl,pl(x,v)),v),p1(x))
+t7:=tr3is(real,mn(p1(pl(x,v)),pl(y,v)),pl(pl(1rl,pl(x,v)),pl(m0"r"(v),m0"r"(y))),mn(mn(pl(1rl,pl(x,v)),v),y),mn(p1(x),y),ispl12"r"(p1(pl(x,v)),pl(1rl,pl(x,v)),m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)),compl"r"(pl(x,v),1rl),t5),asspl2"r"(pl(1rl,pl(x,v)),m0"r"(v),m0"r"(y)),ismn1"r"(mn(pl(1rl,pl(x,v)),v),p1(x),y,t6)):is"r"(mn(p1(pl(x,v)),pl(y,v)),mn(p1(x),y))
+t8:=th9"l.or"(less(y,x),is"r"(y,x),less(pl(y,v),pl(x,v)),is"r"(pl(y,v),pl(x,v)),ly,[t:less(y,x)]satz188f(y,x,v,t),[t:is"r"(y,x)]ispl1"r"(y,x,v,t)):lessis(pl(y,v),pl(x,v))
+s0:=shiftl(x,ix,y,iy,ly):nat
+sv:=shiftl(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8):nat
+t9:=isrlent(mn(p1(pl(x,v)),pl(y,v)),t6"r.shift"(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8),mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly),t7):is"n"(sv,s0)
+t10:=lessisi2"n"(sv,s0,t9):lessis"n"(sv,s0)
+f1:=left(cx,s0,sv,t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(sv)]cx
+t11:=issmpr(q,s0,shiftf(x,ix,y,iy,ly,f),sv,t9):is(smpr(q,sv,f1),smpri(x,ix,y,iy,ly,f,q))
+[n:1to(sv)]
+t12:=isinoutn(s0,inn(sv,n),trlessis"n"(inn(sv,n),sv,s0,1top(sv,n),t10)):is"n"(inn(sv,n),inn(s0,left1to(s0,sv,t10,n)))
+n1:=left1to(s0,sv,t10,n):1to(s0)
+t13:=isnterl(inn(sv,n),inn(s0,n1),t12):is"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)))
+t14:=tris(real,mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(sv,n)),mn(pl(y,v),v)),pl(rlofnt(inn(s0,n1)),y),asspl1"r"(rlofnt(inn(sv,n)),pl(y,v),m0"r"(v)),ispl12"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)),mn(pl(y,v),v),y,t13,mnpl(y,v))):is"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y))
+st0:=shiftr(x,ix,y,iy,ly,n1):real
+stv:=shiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):real
+t15:=tr4is(real,mn(stv,v),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(1rl),m0"r"(v))),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(v),m0"r"(1rl))),mn(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),1rl),st0,asspl1"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(1rl),m0"r"(v)),ispl2"r"(pl(m0"r"(1rl),m0"r"(v)),pl(m0"r"(v),m0"r"(1rl)),pl(rlofnt(inn(sv,n)),pl(y,v)),compl"r"(m0"r"(1rl),m0"r"(v))),asspl2"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(v),m0"r"(1rl)),ismn1"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y),1rl,t14)):is"r"(mn(stv,v),st0)
+t16:=intshiftr(x,ix,y,iy,ly,n1):intrl(st0)
+t17:=shiftrls(x,ix,y,iy,ly,n1):lessis(st0,x)
+t18:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,st0)
+t19:=intshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):intrl(stv)
+t20:=shiftrls(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(stv,pl(x,v))
+t21:=lsshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(pl(y,v),stv)
+t22:=intmn(stv,t19,v,iv):intrl(mn(stv,v))
+t23:=t2(stv,t19,t21,t20):lessis(y,mn(stv,v))
+t24:=t4(stv,t19,t21,t20):lessis(mn(stv,v),x)
+t25:=<t15><t17><t18><t16><st0><t24><t23><t22><mn(stv,v)>pi:is(<n>shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),<n>f1)
+iv@t26:=fisi(1to(sv),cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,[t:1to(sv)]t25(t)):is"e"([t:1to(sv)]cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1)
+t27:=isf([t:1to(sv)]cx,cx,[w:[t:1to(sv)]cx]smpr(q,sv,w),shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,t26):is(smpri(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft,q),smpr(q,sv,f1))
+-8285
+iv@lemma285:=t8".8285":lessis(pl"r"(y,v),pl"r"(x,v))
+satz285:=tris(cx,smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpr(q,sv".8285",f1".8285"),smpri(x,ix,y,iy,ly,f,q),t27".8285",t11".8285"):is(smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpri(x,ix,y,iy,ly,f,q))
+ly@[s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][f:seq(x,ix,y,iy,ly,cx)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)]
+us:=<ul><lu><iu><u>s:real
++8286
+t1:=<ul><lu><iu><u>ins:and3(intrl(us),lessis(y,us),lessis(us,x))
+-8286
+inseqe1:=t22"r.shift"(x,ix,y,iy,ly,us,t1".8286"):intrl(us)
+inseqe2:=t23"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(y,us)
+inseqe3:=t24"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(us,x)
+usf:=<inseqe3><inseqe2><inseqe1><us>f:cx
+f@permseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]usf(t,u,v,w):[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]cx
+q@[a:assoc(q)][c:commut(q)][s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][pri:proofsirrelevant(x,ix,y,iy,ly,real,s)][ps:perm(x,ix,y,iy,ly,s)]
++*8286
+ps@ss:=shiftseq(x,ix,y,iy,ly,s,ins):[t:1to(shiftl)]1to(shiftl)
+t2:=satz283(q,a,c,shiftl,ss,bijshiftseq(x,ix,y,iy,ly,s,ins,pri,ps),shiftf(f)):is(smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)),smpri(f,q))
+[n:1to(shiftl)]
+ns:=us(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):real
+t3:=shiftinv1(ns,t34"r.shift"(x,ix,y,iy,ly,s,ins,n)):is"r"(ns,shiftr(<n>ss))
+t4:=inseqe1(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):intrl(ns)
+t5:=inseqe2(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(y,ns)
+t6:=inseqe3(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(ns,x)
+t7:=intshiftr(<n>ss):intrl(shiftr(<n>ss))
+t8:=lsshiftr(<n>ss):lessis(y,shiftr(<n>ss))
+t9:=shiftrls(<n>ss):lessis(shiftr(<n>ss),x)
+t10:=<t3><t9><t8><t7><shiftr(<n>ss)><t6><t5><t4><ns>pi:is(<n>shiftf(permseq(s,ins,f)),<<n>ss>shiftf(f))
+ps@t11:=fisi(1to(shiftl),cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),[t:1to(shiftl)]t10(t)):is"e"([t:1to(shiftl)]cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f))
+t12:=isf([t:1to(shiftl)]cx,cx,[u:[t:1to(shiftl)]cx]smpr(q,shiftl,u),shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),t11):is(smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)))
+-8286
+ps@satz286:=tris(cx,smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss".8286">shiftf(f)),smpri(f,q),t12".8286",t2".8286"):is(smpri(permseq(s,ins,f),q),smpri(f,q))
+@[x:nat][f:[t:1to(x)]cx]
+modf:=[t:1to(x)]pli(mod(<t>f),0):[t:1to(x)]cx
++8287
+[r:real]
+prop1:=lessis(mod(sum(x,f)),r):'prop'
+prop2:=is(sum(x,modf(f)),pli(r,0)):'prop'
+prop3:=and(prop1,prop2):'prop'
+f@prop4:=some"r"([t:real]prop3(t)):'prop'
+x@prop5:=[u:[t:1to(x)]cx]prop4(u):'prop'
+@[f:[t:1to(1)]cx]
+t1:=satz277([t:cx][u:cx]pl(t,u),f):is(sum(1,f),<xout(1)>f)
+t2:=ismod(sum(1,f),<xout(1)>f,t1):is"r"(mod(sum(1,f)),mod(<xout(1)>f))
+t3:=lessisi2(mod(sum(1,f)),mod(<xout(1)>f),t2):prop1(1,f,mod(<xout(1)>f))
+t4:=satz277([t:cx][u:cx]pl(t,u),modf(1,f)):prop2(1,f,mod(<xout(1)>f))
+t5:=andi(prop1(1,f,mod(<xout(1)>f)),prop2(1,f,mod(<xout(1)>f)),t3,t4):prop3(1,f,mod(<xout(1)>f))
+t6:=somei(real,[t:real]prop3(1,f,t),mod(<xout(1)>f),t5):prop4(1,f)
+@t7:=[u:[t:1to(1)]cx]t6(u):prop5(1)
+x@[p:prop5(x)][f:[t:1to(pl"n"(x,1))]cx]
+t8:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
+lf:=left(cx,pl"n"(x,1),x,t8,f):[t:1to(x)]cx
+[r:real][pr:prop3(lf,r)]
+t9:=ande1(prop1(lf,r),prop2(lf,r),pr):prop1(lf,r)
+t10:=ande2(prop1(lf,r),prop2(lf,r),pr):prop2(lf,r)
+t11:=satz278([t:cx][u:cx]pl(t,u),x,f):is(sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f))
+t12:=ismod(pl(sum(x,lf),<xout(pl"n"(x,1))>f),sum(pl"n"(x,1),f),symis(cx,sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f),t11)):is"r"(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)))
+m:=mod(<xout(pl"n"(x,1))>f):real
+t13:=islessis1(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),t12,satz271(sum(x,lf),<xout(pl"n"(x,1))>f)):lessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m))
+t14:=th9"l.or"(less(mod(sum(x,lf)),r),is"r"(mod(sum(x,lf)),r),less(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),is"r"(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),t9,[t:less(mod(sum(x,lf)),r)]satz188f(mod(sum(x,lf)),r,m,t),[t:is"r"(mod(sum(x,lf)),r)]ispl1"r"(mod(sum(x,lf)),r,m,t)):lessis(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m))
+t15:=trlessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),pl"r"(r,m),t13,t14):prop1(pl"n"(x,1),f,pl"r"(r,m))
+lmf:=left(cx,pl"n"(x,1),x,t8,modf(pl"n"(x,1),f)):[t:1to(x)]cx
+t16:=satz278([t:cx][u:cx]pl(t,u),x,modf(pl"n"(x,1),f)):is(sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)))
+t17:=ispl1(sum(x,lmf),pli(r,0),pli(m,0),t10):is(pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)))
+t18:=plis12a(r,0,m,0):is(pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)))
+t19:=isrecx2(pl"r"(0,0),0,pl"r"(r,m),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0))
+t20:=tr4is(cx,sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0),t16,t17,t18,t19):prop2(pl"n"(x,1),f,pl"r"(r,m))
+t21:=andi(prop1(pl"n"(x,1),f,pl"r"(r,m)),prop2(pl"n"(x,1),f,pl"r"(r,m)),t15,t20):prop3(pl"n"(x,1),f,pl"r"(r,m))
+t22:=somei(real,[t:real]prop3(pl"n"(x,1),f,t),pl"r"(r,m),t21):prop4(pl"n"(x,1),f)
+f@t23:=someapp(real,[t:real]prop3(lf,t),<lf>p,prop4(pl"n"(x,1),f),[t:real][u:prop3(lf,t)]t22(t,u)):prop4(pl"n"(x,1),f)
+p@t25:=[u:[t:1to(pl"n"(x,1))]cx]t23(u):prop5(pl"n"(x,1))
+t26:=isp(nat,[t:nat]prop5(t),pl"n"(x,1),<x>suc,t25,satz4a(x)):prop5(<x>suc)
+-8287
+satz287:=<f>induction([t:nat]prop5".8287"(t),t7".8287",[t:nat][u:prop5".8287"(t)]t26".8287"(t,u),x):some"r"([t:real]and(lessis(mod(sum(x,f)),t),is(sum(x,modf(f)),pli(t,0))))
++8288
+prop1:=is(pli(mod(prod(x,f)),0),prod(x,modf(f))):'prop'
+x@prop2:=[u:[t:1to(x)]cx]prop1(u):'prop'
+@[f:[t:1to(1)]cx]
+t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
+t2:=ismod(prod(1,f),<xout(1)>f,t1):is"r"(mod(prod(1,f)),mod(<xout(1)>f))
+t3:=isrecx1(mod(prod(1,f)),mod(<xout(1)>f),0,t2):is(pli(mod(prod(1,f)),0),pli(mod(<xout(1)>f),0))
+t4:=satz277([t:cx][u:cx]ts(t,u),modf(1,f)):is(prod(1,modf(1,f)),pli(mod(<xout(1)>f),0))
+t5:=tris2(cx,pli(mod(prod(1,f)),0),prod(1,modf(1,f)),pli(mod(<xout(1)>f),0),t3,t4):prop1(1,f)
+@t6:=[u:[t:1to(1)]cx]t5(u):prop2(1)
+x@[p:prop2(x)][f:[t:1to(pl"n"(x,1))]cx]
+t7:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
+lf:=left(cx,pl"n"(x,1),x,t7,f):[t:1to(x)]cx
+t8:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
+m:=mod(<xout(pl"n"(x,1))>f):real
+t9:=ismod(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),t8):is"r"(mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)))
+t10:=satz268(prod(x,lf),<xout(pl"n"(x,1))>f):is"r"(mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m))
+t11:=tris(real,mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m),t9,t10):is"r"(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m))
+t12:=isrecx1(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m),0,t11):is(pli(mod(prod(pl"n"(x,1),f)),0),pli(ts"r"(mod(prod(x,lf)),m),0))
+lmf:=left(cx,pl"n"(x,1),x,t7,modf(pl"n"(x,1),f)):[t:1to(x)]cx
+t13:=satz278([t:cx][u:cx]ts(t,u),x,modf(pl"n"(x,1),f)):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)))
+t14:=symis(cx,pli(mod(prod(x,lf)),0),prod(x,lmf),<lf>p):is(prod(x,lmf),pli(mod(prod(x,lf)),0))
+t15:=ists1(prod(x,lmf),pli(mod(prod(x,lf)),0),pli(m,0),t14):is(ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)))
+t16:=tsis12a(mod(prod(x,lf)),0,m,0):is(ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))))
+t17:=tris(real,mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),mn"r"(ts"r"(mod(prod(x,lf)),m),0),ts"r"(mod(prod(x,lf)),m),ismn2"r"(ts"r"(0,0),0,ts"r"(mod(prod(x,lf)),m),ts01"r"(0,0,refis(real,0))),pl02"r"(ts"r"(mod(prod(x,lf)),m),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m))
+t18:=tris(real,pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),pl"r"(0,0),0,ispl12"r"(ts"r"(mod(prod(x,lf)),0),0,ts"r"(0,m),0,ts02"r"(mod(prod(x,lf)),0,refis(real,0)),ts01"r"(0,m,refis(real,0))),pl01"r"(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0)
+t19:=isrecx12(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0,t17,t18):is(pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0))
+t20:=tr4is(cx,prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0),t13,t15,t16,t19):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0))
+t21:=tris2(cx,pli(mod(prod(pl"n"(x,1),f)),0),prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0),t12,t20):prop1(pl"n"(x,1),f)
+p@t21a:=[u:[t:1to(pl"n"(x,1))]cx]t21(u):prop2(pl"n"(x,1))
+t22:=isp(nat,[t:nat]prop2(t),pl"n"(x,1),<x>suc,t21a,satz4a(x)):prop2(<x>suc)
+-8288
+satz288:=<f>induction([t:nat]prop2".8288"(t),t6".8288",[t:nat][u:prop2".8288"(t)]t22".8288"(t,u),x):is(pli(mod(prod(x,f)),0),prod(x,modf(f)))
++8289
+prop1:=is(prod(x,f),0c):'prop'
+prop2:=some"l"(1to(x),[t:1to(x)]is(<t>f,0c)):'prop'
+prop3:=iff(prop1,prop2):'prop'
+x@prop4:=[u:[t:1to(x)]cx]prop3(u):'prop'
+@[f:[t:1to(1)]cx]
+t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
+[p:prop1(1,f)]
+t2:=tris1(cx,<xout(1)>f,0c,prod(1,f),t1,p):is(<xout(1)>f,0c)
+t3:=somei(1to(1),[t:1to(1)]is(<t>f,0c),xout(1),t2):prop2(1,f)
+f@[p:prop2(1,f)][u:1to(1)][i:is(<u>f,0c)]
+t4:=th1"n.singlet"(u):is"e"(1to(1),u,xout(1))
+t5:=tr3is(cx,prod(1,f),<xout(1)>f,<u>f,0c,t1,isf(1to(1),cx,f,xout(1),u,symis(1to(1),u,xout(1),t4)),i):prop1(1,f)
+p@t6:=someapp(1to(1),[t:1to(1)]is(<t>f,0c),p,prop1(1,f),[t:1to(1)][u:is(<t>f,0c)]t5(t,u)):prop1(1,f)
+f@t7:=iffi(prop1(1,f),prop2(1,f),[t:prop1(1,f)]t3(t),[t:prop2(1,f)]t6(t)):prop3(1,f)
+@t8:=[u:[t:1to(1)]cx]t7(u):prop4(1)
+x@[p:prop4(x)][f:[t:1to(pl"n"(x,1))]cx]
+t9:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
+lf:=left(cx,pl"n"(x,1),x,t9,f):[t:1to(x)]cx
+t10:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
+[q:prop1(pl"n"(x,1),f)]
+t11:=tris1(cx,ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,prod(pl"n"(x,1),f),t10,q):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+t12:=satz221c(prod(x,lf),<xout(pl"n"(x,1))>f,t11):or(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c))
+[i:is(prod(x,lf),0c)]
+t13:=th3"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,i):prop2(x,lf)
+[n:1to(x)][j:is(<n>lf,0c)]
+t14:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),left1to(pl"n"(x,1),x,t9,n),j):prop2(pl"n"(x,1),f)
+i@t15:=someapp(1to(x),[t:1to(x)]is(<t>lf,0c),t13,prop2(pl"n"(x,1),f),[t:1to(x)][u:is(<t>lf,0c)]t14(t,u)):prop2(pl"n"(x,1),f)
+q@[i:is(<xout(pl"n"(x,1))>f,0c)]
+t16:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),xout(pl"n"(x,1)),i):prop2(pl"n"(x,1),f)
+q@t17:=orapp(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c),prop2(pl"n"(x,1),f),t12,[t:is(prod(x,lf),0c)]t15(t),[t:is(<xout(pl"n"(x,1))>f,0c)]t16(t)):prop2(pl"n"(x,1),f)
+f@[q:prop2(pl"n"(x,1),f)][n:1to(pl"n"(x,1))][i:is(<n>f,0c)][j:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]
+t18:=tris1(cx,<xout(pl"n"(x,1))>f,0c,<n>f,isf(1to(pl"n"(x,1)),cx,f,n,xout(pl"n"(x,1)),j),i):is(<xout(pl"n"(x,1))>f,0c)
+t20:=satz221b(prod(x,lf),<xout(pl"n"(x,1))>f,t18):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+i@[m:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]
+n1:=inn(pl"n"(x,1),n):nat
+[j:is"n"(n1,pl"n"(x,1))]
+t21:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),pl"n"(x,1),lessisi3(pl"n"(x,1)),j):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)))
+t22:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)),isoutinn(pl"n"(x,1),n),t21):is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))
+m@t23:=th3"l.imp"(is"n"(n1,pl"n"(x,1)),is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),m,[t:is"n"(n1,pl"n"(x,1))]t22(t)):nis"n"(n1,pl"n"(x,1))
+t24:=ore1(less"n"(n1,pl"n"(x,1)),is"n"(n1,pl"n"(x,1)),1top(pl"n"(x,1),n),t23):less"n"(n1,pl"n"(x,1))
+t25:=satz26(x,n1,t24):lessis"n"(n1,x)
+n2:=outn(x,n1,t25):1to(x)
+t26:=isinoutn(x,n1,t25):is"n"(n1,inn(x,n2))
+t27:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),inn(x,n2),trlessis"n"(inn(x,n2),x,pl"n"(x,1),1top(x,n2),t9),t26):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2))
+t28:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2),isoutinn(pl"n"(x,1),n),t27):is"e"(1to(pl"n"(x,1)),n,left1to(pl"n"(x,1),x,t9,n2))
+t29:=isf(1to(pl"n"(x,1)),cx,f,n,left1to(pl"n"(x,1),x,t9,n2),t28):is(<n>f,<n2>lf)
+t30:=tris1(cx,<n2>lf,0c,<n>f,t29,i):is(<n2>lf,0c)
+t31:=somei(1to(x),[t:1to(x)]is(<t>lf,0c),n2,t30):prop2(x,lf)
+t32:=th4"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,t31):prop1(x,lf)
+t34:=satz221a(prod(x,lf),<xout(pl"n"(x,1))>f,t32):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+i@t35:=th1"l.imp"(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c),[t:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]t20(t),[t:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]t34(t)):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
+t36:=tris(cx,prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,t10,t35):prop1(pl"n"(x,1),f)
+q@t37:=someapp(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),q,prop1(pl"n"(x,1),f),[t:1to(pl"n"(x,1))][u:is(<t>f,0c)]t36(t,u)):prop1(pl"n"(x,1),f)
+f@t38:=iffi(prop1(pl"n"(x,1),f),prop2(pl"n"(x,1),f),[t:prop1(pl"n"(x,1),f)]t17(t),[t:prop2(pl"n"(x,1),f)]t37(t)):prop3(pl"n"(x,1),f)
+p@t39:=[u:[t:1to(pl"n"(x,1))]cx]t38(u):prop4(pl"n"(x,1))
+t40:=isp(nat,[t:nat]prop4(t),pl"n"(x,1),<x>suc,t39,satz4a(x)):prop4(<x>suc)
+-8289
+satz289:=<f>induction([t:nat]prop4".8289"(t),t8".8289",[t:nat][u:prop4".8289"(t)]t40".8289"(t,u),x):iff(is(prod(x,f),0c),some"l"(1to(x),[t:1to(x)]is(<t>f,0c)))
+[i:is(prod(x,f),0c)]
+satz289a:=th3"l.iff"(prop1".8289",prop2".8289",satz289,i):some"l"(1to(x),[t:1to(x)]is(<t>f,0c))
+f@[n:1to(x)][i:is(<n>f,0c)]
++*8289
+i"c"@t41:=somei(1to(x),[t:1to(x)]is(<t>f,0c),n,i):prop2
+-8289
+i@satz289b:=th4"l.iff"(prop1".8289",prop2".8289",satz289,t41".8289"):is(prod(x,f),0c)
+@[x:complex][m:real][mi:intrl(m)][o:or(nis(x,0c),pos(m))]
++v9
+[p:pos(m)]
+t1:=posintnatrl(m,p,mi):natrl(m)
+m1:=ntofrl(m,t1):nat
+pw1:=prod(m1,[t:1to(m1)]x):cx
+-v9
+x@[y:complex][m:real][n:real][i:is(x,y)][j:is"r"(m,n)][mi1:intrl(m)][ni1:intrl(n)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(n))]
++*v9
+oy@[mp:pos(m)][np:pos(n)]
+m0:=m1(x,m,mi1,ox,mp):nat
+n0:=m1(y,n,ni1,oy,np):nat
+t2:=isrlent(m,t1(x,m,mi1,ox,mp),n,t1(y,n,ni1,oy,np),j):is"n"(m0,n0)
+t3:=lessisi2"n"(m0,n0,t2):lessis"n"(m0,n0)
+t4:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]y,m0,t2):is(prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np))
+t5:=fisi(1to(m0),cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),[t:1to(m0)]i):is"e"([t:1to(m0)]cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y))
+t6:=isf([t:1to(m0)]cx,cx,[u:[t:1to(m0)]cx]prod(m0,u),[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),t5):is(pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)))
+t7:=tris(cx,pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np),t6,t4):is(pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,np))
+p@[p1:pos(m)]
+t8:=t7(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,p,p1):is(pw1(p),pw1(p1))
+p@[n:nis(x,0c)]
+t9:=th5"l.some"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c),[t:1to(m1)]n):not(some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)))
+t10:=th3"l.imp"(is(pw1,0c),some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)),t9,[t:is(pw1,0c)]satz289a(m1,[u:1to(m1)]x,t)):nis(pw1,0c)
+o@[n:neg(m)]
+mi@t11:=intabs(m,mi):intrl(abs(m))
+n@t12:=satz166b(m,n):pos(abs(m))
+t13:=ori2(nis(x,0c),pos(abs(m)),t12):or(nis(x,0c),pos(abs(m)))
+t14:=ore1(nis(x,0c),pos(m),o,nnotp(m,n)):nis(x,0c)
+t15:=t10(abs(m),t11,t13,t12,t14):nis(pw1(abs(m),t11,t13,t12),0c)
+pw2:=ov(1c,pw1(abs(m),t11,t13,t12),t15):cx
+oy@[nm:neg(m)][nn:neg(n)]
+pwm:=pw1(x,abs(m),t11(x,m,mi1),t13(x,m,mi1,ox,nm),t12(x,m,mi1,ox,nm)):cx
+pwn:=pw1(y,abs(n),t11(y,n,ni1),t13(y,n,ni1,oy,nn),t12(y,n,ni1,oy,nn)):cx
+t16:=t7(abs(m),abs(n),i,isabs(m,n,j),t11(x,m,mi1),t11(y,n,ni1),t13(x,m,mi1,ox,nm),t13(y,n,ni1,oy,nn),t12(x,m,mi1,ox,nm),t12(y,n,ni1,oy,nn)):is(pwm,pwn)
+t17:=isov2(pwm,pwn,1c,t16,t15(x,m,mi1,ox,nm),t15(y,n,ni1,oy,nn)):is(pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,nn))
+n@[n1:neg(m)]
+t18:=t17(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,n,n1):is(pw2(n),pw2(n1))
+o@pw3:=ite"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c)):cx
+n@t19:=itet"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),n):is(pw3,pw2(n))
+o@[nn:not(neg(m))]
+t20:=itef"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),nn):is(pw3,1c)
+nm@t21:=isp(real,[t:real]neg(t),m,n,nm,j):neg(n)
+t22:=t19(x,m,mi1,ox,nm):is(pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm))
+t23:=symis(cx,pw3(y,n,ni1,oy),pw2(y,n,ni1,oy,t21),t19(y,n,ni1,oy,t21)):is(pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy))
+t24:=tr3is(cx,pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy),t22,t17(t21),t23):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
+oy@[nn:not(neg(m))]
+t25:=isp(real,[t:real]not(neg(t)),m,n,nn,j):not(neg(n))
+t26:=t20(x,m,mi1,ox,nn):is(pw3(x,m,mi1,ox),1c)
+t27:=t20(y,n,ni1,oy,t25):is(pw3(y,n,ni1,oy),1c)
+t28:=tris2(cx,pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),1c,t26,t27):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
+oy@t29:=th1"l.imp"(neg(m),is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy)),[t:neg(m)]t24(t),[t:not(neg(m))]t28(t)):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
+-v9
+o@pw:=ite"l.r"(pos(m),cx,[t:pos(m)]pw1".v9"(t),[t:not(pos(m))]pw3".v9",[t:pos(m)][u:pos(m)]t8".v9"(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3".v9")):cx
++*v9
+p@t30:=itet"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),p):is(pw,pw1(p))
+o@[n:not(pos(m))]
+t31:=itef"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),n):is(pw,pw3)
+o@[i:is"r"(m,0)]
+t32:=tris(cx,pw,pw3,1c,t31(0notp(m,i)),t20(0notn(m,i))):is(pw,1c)
+o@[n:neg(m)]
+t33:=tris(cx,pw,pw3,pw2(n),t31(nnotp(m,n)),t19(n)):is(pw,pw2(n))
+-v9
+o@[p:pos(m)]
+posexp:=t30".v9"(p):is(pw(x,m,mi,o),prod(ntofrl(m,posintnatrl(m,p,mi)),[t:1to(ntofrl(m,posintnatrl(m,p,mi)))]x))
+[n:nis(x,0c)]
+lemmapw1:=th2"e.notis"(cx,pw1".v9"(p),0c,pw,t10".v9"(p,n),posexp):nis(pw(x,m,mi,o),0c)
+o@[i:is"r"(m,0)]
+0exp:=t32".v9"(i):is(pw(x,m,mi,o),1c)
+o@[n:neg(m)]
+lemmapw2:=t14".v9"(n):nis(x,0c)
+lemmapw3:=t13".v9"(n):or(nis(x,0c),pos(abs(m)))
++*v9
+n@t34:=t30(abs(m),t11,t13(n),t12(n)):is(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)))
+t35:=isov2(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)),1c,t34,lemmapw1(abs(m),t11,t13(n),t12(n),t14(n)),t15(n)):is(ov(1c,pw(x,abs(m),t11,t13(n)),lemmapw1(abs(m),t11,t13(n),t12(n),t14(n))),pw2(n))
+-v9
+n@negexp:=tris2(cx,pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)),pw2".v9"(n),t33".v9"(n),t35".v9"(n)):is(pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)))
++*v9
+mp@t36:=isp(real,[t:real]pos(t),m,n,mp,j):pos(n)
+t37:=t30(x,m,mi1,ox,mp):is(pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp))
+t38:=symis(cx,pw(y,n,ni1,oy),pw1(y,n,ni1,oy,t36),t30(y,n,ni1,oy,t36)):is(pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy))
+t39:=tr3is(cx,pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy),t37,t7(t36),t38):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
+oy@[np:not(pos(m))]
+t40:=isp(real,[t:real]not(pos(t)),m,n,np,j):not(pos(n))
+t41:=t31(x,m,mi1,ox,np):is(pw(x,m,mi1,ox),pw3(x,m,mi1,ox))
+t42:=symis(cx,pw(y,n,ni1,oy),pw3(y,n,ni1,oy),t31(y,n,ni1,oy,t40)):is(pw3(y,n,ni1,oy),pw(y,n,ni1,oy))
+t43:=tr3is(cx,pw(x,m,mi1,ox),pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),pw(y,n,ni1,oy),t41,t29,t42):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
+-v9
+oy@ispw12:=th1"l.imp"(pos(m),is(pw(x,m,mi1,ox),pw(y,n,ni1,oy)),[t:pos(m)]t39".v9"(t),[t:not(pos(m))]t43".v9"(t)):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
+m@[i:is(x,y)][mi:intrl(m)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(m))]
+ispw1:=ispw12(x,y,m,m,i,refis(real,m),mi,mi,ox,oy):is(pw(x,m,mi,ox),pw(y,m,mi,oy))
+x@[m:real][n:real][i:is"r"(m,n)][mi:intrl(m)][ni:intrl(n)][om:or(nis(x,0c),pos(m))][on:or(nis(x,0c),pos(n))]
+ispw2:=ispw12(x,x,m,n,refis(cx,x),i,mi,ni,om,on):is(pw(x,m,mi,om),pw(x,n,ni,on))
+o@[n:nis(x,0c)]
++9290
+[p:pos(m)]
+t1:=lemmapw1(p,n):nis(pw(x,m,mi,o),0c)
+@[i:is(1c,0c)]
+t2:=tr3is(real,1rl,re(1c),re(0c),0,isre(1rl,0),iscere(1c,0c,i),reis(0,0)):is"r"(1rl,0)
+-9290
+@1not0:=th3"l.imp"(is(1c,0c),is"r"(1rl,0),pnot0(1rl,pos1),[t:is(1c,0c)]t2".9290"(t)):nis(1c,0c)
++*9290
+n@[i:is"r"(m,0)]
+t4:=th2"e.notis"(cx,1c,0c,pw(x,m,mi,o),1not0,0exp(i)):nis(pw(x,m,mi,o),0c)
+n@[nm:neg(m)]
+p0:=pw(x,abs(m),intabs(m,mi),lemmapw3(nm)):cx
+t5:=lemmapw1(x,abs(m),intabs(m,mi),lemmapw3(nm),satz166b(m,nm),lemmapw2(nm)):nis(p0,0c)
+t6:=tris(cx,ts(pw(x,m,mi,o),p0),ts(ov(1c,p0,t5),p0),1c,ists1(pw(x,m,mi,o),ov(1c,p0,t5),p0,negexp(nm)),satz229e(1c,p0,t5)):is(ts(pw(x,m,mi,o),p0),1c)
+t7:=th2"e.notis"(cx,1c,0c,ts(pw(x,m,mi,o),p0),1not0,t6):nis(ts(pw(x,m,mi,o),p0),0c)
+t8:=th3"l.imp"(is(pw(x,m,mi,o),0c),is(ts(pw(x,m,mi,o),p0),0c),t7,[t:is(pw(x,m,mi,o),0c)]satz221a(pw(x,m,mi,o),p0,t)):nis(pw(x,m,mi,o),0c)
+-9290
+n@satz290:=rapp(m,nis(pw(x,m,mi,o),0c),[t:pos(m)]t1".9290"(t),[t:is"r"(m,0)]t4".9290"(t),[t:neg(m)]t8".9290"(t)):nis(pw(x,m,mi,o),0c)
+x@lemma291:=ori2(nis(x,0c),pos(1rl),pos1):or(nis(x,0c),pos(1rl))
++9291
+1a:=ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)):nat
+t1:=posexp(x,1rl,intrl1,lemma291,pos1):is(pw(x,1rl,intrl1,lemma291),prod(1a,[t:1to(1a)]x))
+t2:=tris(nat,1,ntofrl(1rl,natrl1),ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)),isntrl1(1),isrlent(1rl,natrl1,1rl,posintnatrl(1rl,pos1,intrl1),refis(real,1rl))):is"n"(1,1a)
+t3:=lessisi2"n"(1,1a,t2):lessis"n"(1,1a)
+t4:=issmpr([t:cx][u:cx]ts(t,u),1a,[t:1to(1a)]x,1,t2):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),prod(1a,[t:1to(1a)]x))
+t5:=satz277([t:cx][u:cx]ts(t,u),left(cx,1a,1,t3,[t:1to(1a)]x)):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),x)
+t6:=tris1(cx,prod(1a,[t:1to(1a)]x),x,prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),t4,t5):is(prod(1a,[t:1to(1a)]x),x)
+-9291
+satz291:=tris(cx,pw(x,1rl,intrl1,lemma291),prod(1a".9291",[t:1to(1a".9291")]x),x,t1".9291",t6".9291"):is(pw(x,1rl,intrl1,lemma291),x)
+[y:cx][m:real][mi:intrl(m)][o:or(and(nis(x,0c),nis(y,0c)),pos(m))]
++9292
+[a:and(nis(x,0c),nis(y,0c))]
+t1:=ande1(nis(x,0c),nis(y,0c),a):nis(x,0c)
+t2:=ande2(nis(x,0c),nis(y,0c),a):nis(y,0c)
+t3:=satz221d(x,y,t1,t2):nis(ts(x,y),0c)
+-9292
+lemma292a:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(x,0c),o,[t:and(nis(x,0c),nis(y,0c))]t1".9292"(t)):or(nis(x,0c),pos(m))
+lemma292b:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(y,0c),o,[t:and(nis(x,0c),nis(y,0c))]t2".9292"(t)):or(nis(y,0c),pos(m))
+lemma292c:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(ts(x,y),0c),o,[t:and(nis(x,0c),nis(y,0c))]t3".9292"(t)):or(nis(ts(x,y),0c),pos(m))
++*9292
+x@[n:nat]
+nr:=rlofnt(n):real
+t4:=natintrl(nr,natrli(n)):intrl(nr)
+t5:=ori2(nis(x,0c),pos(nr),natpos(nr,natrli(n))):or(nis(x,0c),pos(nr))
+p0:=pw(x,nr,t4,t5):cx
+x@t6:=tris(cx,p0(1),pw(x,1rl,intrl1,lemma291(x)),x,ispw1(x,x,1rl,refis(cx,x),intrl1,t5(1),lemma291(x)),satz291(x)):is(p0(1),x)
+n@n0:=ntofrl(nr,posintnatrl(nr,natpos(nr,natrli(n)),t4)):nat
+t7:=tris(nat,n,ntofrl(nr,natrli(n)),n0,isntrl1(n),isrlent(nr,natrli(n),nr,posintnatrl(nr,natpos(nr,natrli(n)),t4),refis(real,nr))):is"n"(n,n0)
+t8:=lessisi2"n"(n,n0,t7):lessis"n"(n,n0)
+t9:=posexp(x,nr,t4,t5,natpos(nr,natrli(n))):is(p0,prod(n0,[t:1to(n0)]x))
+t10:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]x,n,t7):is(prod(n,left(cx,n0,n,t8,[t:1to(n0)]x)),prod(n0,[t:1to(n0)]x))
+t11:=tris2(cx,p0,prod(n,[t:1to(n)]x),prod(n0,[t:1to(n0)]x),t9,t10):is(p0,prod(n,[t:1to(n)]x))
+n1:=pl"n"(n,1):nat
+t12:=lessisi1"n"(n,n1,satz18a(n,1)):lessis"n"(n,n1)
+t13:=satz278([t:cx][u:cx]ts(t,u),n,[t:1to(n1)]x):is(prod(n1,[t:1to(n1)]x),ts(prod(n,left(cx,n1,n,t12,[t:1to(n1)]x)),x))
+t14:=ists1(p0,prod(n,[t:1to(n)]x),x,t11):is(ts(p0,x),ts(prod(n,[t:1to(n)]x),x))
+t15:=tris2(cx,prod(n1,[t:1to(n1)]x),ts(p0,x),ts(prod(n,[t:1to(n)]x),x),t13,t14):is(prod(n1,[t:1to(n1)]x),ts(p0,x))
+t16:=tris(cx,p0(n1),prod(n1,[t:1to(n1)]x),ts(p0,x),t11(n1),t15):is(p0(n1),ts(p0(n),x))
+y@[n:nat]
+prop1:=is(p0(ts(x,y),n),ts(p0(x,n),p0(y,n))):'prop'
+y@t17:=ists12(p0(x,1),x,p0(y,1),y,t6(x),t6(y)):is(ts(p0(x,1),p0(y,1)),ts(x,y))
+t18:=tris2(cx,p0(ts(x,y),1),ts(p0(x,1),p0(y,1)),ts(x,y),t6(ts(x,y)),t17):prop1(1)
+n@[p:prop1(n)]
+t19:=ists1(p0(ts(x,y),n),ts(p0(x,n),p0(y,n)),ts(x,y),p):is(ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)))
+t20:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),x),ts(p0(x,n),ts(p0(y,n),x)),ts(p0(x,n),ts(x,p0(y,n))),ts(ts(p0(x,n),x),p0(y,n)),assts1(p0(x,n),p0(y,n),x),ists2(ts(p0(y,n),x),ts(x,p0(y,n)),p0(x,n),comts(p0(y,n),x)),assts2(p0(x,n),x,p0(y,n))):is(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)))
+t21:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(ts(p0(x,n),p0(y,n)),x),y),ts(ts(ts(p0(x,n),x),p0(y,n)),y),ts(ts(p0(x,n),x),ts(p0(y,n),y)),assts2(ts(p0(x,n),p0(y,n)),x,y),ists1(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)),y,t20),assts1(ts(p0(x,n),x),p0(y,n),y)):is(ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
+t22:=tr3is(cx,p0(ts(x,y),n1(n)),ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t16(ts(x,y),n),t19,t21):is(p0(ts(x,y),n1(n)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
+t23:=ists12(p0(x,n1(n)),ts(p0(x,n),x),p0(y,n1(n)),ts(p0(y,n),y),t16(x,n),t16(y,n)):is(ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
+t24:=tris2(cx,p0(ts(x,y),n1(n)),ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t22,t23):prop1(n1(n))
+t25:=isp(nat,[t:nat]prop1(t),n1(n),<n>suc,t24,satz4a(n)):prop1(<n>suc)
+n@t26:=induction([t:nat]prop1(t),t18,[t:nat][u:prop1(t)]t25(t,u),n):prop1
+o@prop2:=is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b))):'prop'
+[p:pos(m)]
+t28:=posintnatrl(m,p,mi):natrl(m)
+m0:=ntofrl(m,t28):nat
+t29:=isrlnt1(m,t28):is"r"(m,nr(m0))
+t30:=isrlnt2(m,t28):is"r"(nr(m0),m)
+t31:=ispw2(ts(x,y),m,nr(m0),t29,mi,t4(ts(x,y),m0),lemma292c,t5(ts(x,y),m0)):is(pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0))
+t32:=ists12(p0(x,m0),pw(x,m,mi,lemma292a),p0(y,m0),pw(y,m,mi,lemma292b),ispw2(x,nr(m0),m,t30,t4(x,m0),mi,t5(x,m0),lemma292a),ispw2(y,nr(m0),m,t30,t4(y,m0),mi,t5(y,m0),lemma292b)):is(ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
+t33:=tr3is(cx,pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0),ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),t31,t26(m0),t32):prop2
+o@[i:is"r"(m,0)]
+t34:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(1c,1c),1c,ists12(pw(x,m,mi,lemma292a),1c,pw(y,m,mi,lemma292b),1c,0exp(x,m,mi,lemma292a,i),0exp(y,m,mi,lemma292b,i)),satz222(1c)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c)
+t35:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c,0exp(ts(x,y),m,mi,lemma292c,i),t34):prop2
+o@[n:neg(m)]
+t36:=intabs(m,mi):intrl(abs(m))
+t37:=ori2(and(nis(x,0c),nis(y,0c)),pos(abs(m)),satz166b(m,n)):or(and(nis(x,0c),nis(y,0c)),pos(abs(m)))
+t38:=lemma292a(abs(m),t36,t37):or(nis(x,0c),pos(abs(m)))
+t39:=lemma292b(abs(m),t36,t37):or(nis(y,0c),pos(abs(m)))
+t40:=lemma292c(abs(m),t36,t37):or(nis(ts(x,y),0c),pos(abs(m)))
+t41:=lemmapw3(x,m,mi,lemma292a,n):or(nis(x,0c),pos(abs(m)))
+t42:=lemmapw3(y,m,mi,lemma292b,n):or(nis(y,0c),pos(abs(m)))
+t43:=lemmapw3(ts(x,y),m,mi,lemma292c,n):or(nis(ts(x,y),0c),pos(abs(m)))
+t44:=ispw2(ts(x,y),abs(m),abs(m),refis(real,abs(m)),t36,t36,t43,t40):is(pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40))
+t45:=t33(abs(m),t36,t37,satz166b(m,n)):is(pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)))
+t46:=ists12(pw(x,abs(m),t36,t38),pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t39),pw(y,abs(m),t36,t42),ispw2(x,abs(m),abs(m),refis(real,abs(m)),t36,t36,t38,t41),ispw2(y,abs(m),abs(m),refis(real,abs(m)),t36,t36,t39,t42)):is(ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
+t47:=tr3is(cx,pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t44,t45,t46):is(pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
+t48:=lemmapw1(x,abs(m),t36,t41,satz166b(m,n),lemmapw2(x,m,mi,lemma292a,n)):nis(pw(x,abs(m),t36,t41),0c)
+t49:=lemmapw1(y,abs(m),t36,t42,satz166b(m,n),lemmapw2(y,m,mi,lemma292b,n)):nis(pw(y,abs(m),t36,t42),0c)
+t50:=lemmapw1(ts(x,y),abs(m),t36,t43,satz166b(m,n),lemmapw2(ts(x,y),m,mi,lemma292c,n)):nis(pw(ts(x,y),abs(m),t36,t43),0c)
+t51:=satz221d(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42),t48,t49):nis(ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),0c)
+t52:=negexp(ts(x,y),m,mi,lemma292c,n):is(pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50))
+t53:=isov12(1c,ts(1c,1c),pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),satz222a(1c),t47,t50,t51):is(ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t54:=tris(cx,pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t52,t53):is(pw(ts(x,y),m,mi,lemma292c),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t55:=ists12(pw(x,m,mi,lemma292a),ov(1c,pw(x,abs(m),t36,t41),t48),pw(y,m,mi,lemma292b),ov(1c,pw(y,abs(m),t36,t42),t49),negexp(x,m,mi,lemma292a,n),negexp(y,m,mi,lemma292b,n)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)))
+t56:=satz247(1c,pw(x,abs(m),t36,t41),1c,pw(y,abs(m),t36,t42),t48,t49):is(ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t57:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t55,t56):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
+t58:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t54,t57):prop2
+-9292
+o@satz292:=rapp(m,prop2".9292",[t:pos(m)]t33".9292"(t),[t:is"r"(m,0)]t35".9292"(t),[t:neg(m)]t58".9292"(t)):is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
+@[m:real]
+lemma293:=ori1(nis(1c,0c),pos(m),1not0):or(nis(1c,0c),pos(m))
+[mi:intrl(m)]
++9293
+t1:=ori1(and(nis(1c,0c),nis(1c,0c)),pos(m),andi(nis(1c,0c),nis(1c,0c),1not0,1not0)):or(and(nis(1c,0c),nis(1c,0c)),pos(m))
+1m:=pw(1c,m,mi,lemma293):cx
+t2:=satz222(1m):is(ts(1m,1c),1m)
+t3:=ispw1(1c,ts(1c,1c),m,satz222a(1c),mi,lemma293,lemma292c(1c,1c,m,mi,t1)):is(1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)))
+t4:=satz292(1c,1c,m,mi,t1):is(pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))))
+t5:=ists12(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),1m,pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1)),1m,ispw1(1c,1c,m,refis(cx,1c),mi,lemma292a(1c,1c,m,mi,t1),lemma293),ispw1(1c,1c,m,refis(cx,1c),mi,lemma292b(1c,1c,m,mi,t1),lemma293)):is(ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m))
+t6:=tr4is(cx,ts(1m,1c),1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m),t2,t3,t4,t5):is(ts(1m,1c),ts(1m,1m))
+t7:=tris(cx,ts(1m,mn(1m,1c)),mn(ts(1m,1m),ts(1m,1c)),0c,disttm2(1m,1m,1c),satz213b(ts(1m,1m),ts(1m,1c),symis(cx,ts(1m,1c),ts(1m,1m),t6))):is(ts(1m,mn(1m,1c)),0c)
+t8:=ore2(is(1m,0c),is(mn(1m,1c),0c),satz221c(1m,mn(1m,1c),t7),satz290(1c,m,mi,lemma293,1not0)):is(mn(1m,1c),0c)
+-9293
+satz293:=satz213a(1m".9293",1c,t8".9293"):is(pw(1c,m,mi,lemma293),1c)
+x@[m:real][n:real][mi:intrl(m)][ni:intrl(n)][o:or(nis(x,0c),and(pos(m),pos(n)))]
++9294
+[a:and(pos(m),pos(n))]
+t1:=ande1(pos(m),pos(n),a):pos(m)
+t2:=ande2(pos(m),pos(n),a):pos(n)
+t3:=pospl(m,n,t1,t2):pos(pl"r"(m,n))
+-9294
+lemma294a:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(m),o,[t:and(pos(m),pos(n))]t1".9294"(t)):or(nis(x,0c),pos(m))
+lemma294b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(n),o,[t:and(pos(m),pos(n))]t2".9294"(t)):or(nis(x,0c),pos(n))
+lemma294c:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(pl"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9294"(t)):or(nis(x,0c),pos(pl"r"(m,n)))
++*9294
+o@prop1:=is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c)):'prop'
+a@m1:=ntofrl(m,posintnatrl(m,t1,mi)):nat
+n1:=ntofrl(n,posintnatrl(n,t2,ni)):nat
+t4:=ists12(pw(x,m,mi,lemma294a),prod(m1,[t:1to(m1)]x),pw(x,n,ni,lemma294b),prod(n1,[t:1to(n1)]x),posexp(x,m,mi,lemma294a,t1),posexp(x,n,ni,lemma294b,t2)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
+p1:=ntofrl(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni))):nat
+t5:=posexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t3):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(p1,[t:1to(p1)]x))
+t6:=tris(real,pl"r"(m,n),pl"r"(rlofnt(m1),rlofnt(n1)),rlofnt(pl"n"(m1,n1)),ispl12"r"(m,rlofnt(m1),n,rlofnt(n1),isrlnt1(m,posintnatrl(m,t1,mi)),isrlnt1(n,posintnatrl(n,t2,ni))),satzr155b(m1,n1)):is"r"(pl"r"(m,n),rlofnt(pl"n"(m1,n1)))
+t7:=tris2(nat,pl"n"(m1,n1),p1,ntofrl(rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1))),isntrl1(pl"n"(m1,n1)),isrlent(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni)),rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1)),t6)):is"n"(pl"n"(m1,n1),p1)
+t8:=lessisi2"n"(pl"n"(m1,n1),p1,t7):lessis"n"(pl"n"(m1,n1),p1)
+t9:=issmpr([t:cx][u:cx]ts(t,u),p1,[t:1to(p1)]x,pl"n"(m1,n1),t7):is(prod(pl"n"(m1,n1),left(cx,p1,pl"n"(m1,n1),t8,[t:1to(p1)]x)),prod(p1,[t:1to(p1)]x))
+t10:=tris2(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),prod(p1,[t:1to(p1)]x),t5,t9):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x))
+t11:=lessisi1"n"(m1,pl"n"(m1,n1),satz18a(m1,n1)):lessis"n"(m1,pl"n"(m1,n1))
+t12:=satz281([t:cx][u:cx]ts(t,u),assocts,m1,n1,[t:1to(pl"n"(m1,n1))]x):is(prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,left(cx,pl"n"(m1,n1),m1,t11,[t:1to(pl"n"(m1,n1))]x)),prod(n1,right(cx,m1,n1,[t:1to(pl"n"(m1,n1))]x))))
+t13:=tris(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t10,t12):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
+t14:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t4,t13):prop1
+o@[na:not(and(pos(m),pos(n)))]
+t15:=ore1(nis(x,0c),and(pos(m),pos(n)),o,na):nis(x,0c)
+t16:=th15"l.or"(pos(m),pos(n),na):or(not(pos(m)),not(pos(n)))
+o@am:=abs(m):real
+an:=abs(n):real
+ap:=abs(pl"r"(m,n)):real
+t17:=intabs(m,mi):intrl(am)
+t18:=intabs(n,ni):intrl(an)
+t19:=intabs(pl"r"(m,n),intpl(m,mi,n,ni)):intrl(ap)
+na@[nm:neg(m)][nn:neg(n)]
+t20:=andi(pos(am),pos(an),satz166e(m,nnot0(m,nm)),satz166e(n,nnot0(n,nn))):and(pos(am),pos(an))
+t21:=ori2(nis(x,0c),and(pos(am),pos(an)),t20):or(nis(x,0c),and(pos(am),pos(an)))
+t22:=lemmapw3(x,m,mi,lemma294a,nm):or(nis(x,0c),pos(am))
+t23:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
+t24:=lemma294a(x,am,an,t17,t18,t21):or(nis(x,0c),pos(am))
+t25:=lemma294b(x,am,an,t17,t18,t21):or(nis(x,0c),pos(an))
+t26:=ists12(pw(x,am,t17,t22),pw(x,am,t17,t24),pw(x,an,t18,t23),pw(x,an,t18,t25),ispw1(x,x,am,refis(cx,x),t17,t22,t24),ispw1(x,x,an,refis(cx,x),t18,t23,t25)):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)))
+t27:=lemma294c(x,am,an,t17,t18,t21):or(nis(x,0c),pos(pl"r"(am,an)))
+t28:=t14(x,am,an,t17,t18,t21,t20):is(ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27))
+t29:=tr3is(real,pl"r"(am,an),pl"r"(m0"r"(m),m0"r"(n)),m0"r"(pl"r"(m,n)),ap,ispl12"r"(am,m0"r"(m),an,m0"r"(n),absn(m,nm),absn(n,nn)),satz180a(m,n),symis(real,ap,m0"r"(pl"r"(m,n)),absn(pl"r"(m,n),negpl(m,n,nm,nn)))):is"r"(pl"r"(am,an),ap)
+t30:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn)):or(nis(x,0c),pos(ap))
+t31:=ispw2(x,pl"r"(am,an),ap,t29,intpl(am,t17,an,t18),t19,t27,t30):is(pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30))
+t32:=tr3is(cx,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30),t26,t28,t31):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30))
+t33:=lemmapw1(x,am,t17,t22,satz166b(m,nm),lemmapw2(x,m,mi,lemma294a,nm)):nis(pw(x,am,t17,t22),0c)
+t34:=lemmapw1(x,an,t18,t23,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t23),0c)
+t35:=lemmapw1(x,ap,t19,t30,satz166b(pl"r"(m,n),negpl(m,n,nm,nn)),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):nis(pw(x,ap,t19,t30),0c)
+t36:=ists12(pw(x,m,mi,lemma294a),ov(1c,pw(x,am,t17,t22),t33),pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t23),t34),negexp(x,m,mi,lemma294a,nm),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)))
+t37:=satz221d(pw(x,am,t17,t22),pw(x,an,t18,t23),t33,t34):nis(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),0c)
+t38:=satz247(1c,pw(x,am,t17,t22),1c,pw(x,an,t18,t23),t33,t34):is(ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37))
+t39:=isov12(ts(1c,1c),1c,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30),satz222(1c),t32,t37,t35):is(ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35))
+t40:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t30),t35),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):is(ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t41:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t36,t38,t39,t40):prop1
+na@[pm:pos(m)][nn:neg(n)]
+t42:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
+t43:=lemmapw1(x,an,t18,t42,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t42),0c)
+t44:=ists2(pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t42),t43),pw(x,m,mi,lemma294a),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)))
+t45:=satz244a(pw(x,m,mi,lemma294a),1c,pw(x,an,t18,t42),t43):is(ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43))
+t46:=isov1(ts(pw(x,m,mi,lemma294a),1c),pw(x,m,mi,lemma294a),pw(x,an,t18,t42),satz222(pw(x,m,mi,lemma294a)),t43):is(ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+t47:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t44,t45,t46):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+[casea:more(m,an)]
+t48:=satz182d(m,an,casea):pos(mn"r"(m,an))
+t49:=satz166e(n,nnot0(n,nn)):pos(an)
+t50:=andi(pos(an),pos(mn"r"(m,an)),t49,t48):and(pos(an),pos(mn"r"(m,an)))
+t51:=ori2(nis(x,0c),and(pos(an),pos(mn"r"(m,an))),t50):or(nis(x,0c),and(pos(an),pos(mn"r"(m,an))))
+t52:=intmn(m,mi,an,t18):intrl(mn"r"(m,an))
+t53:=lemma294a(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(an))
+t54:=lemma294b(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(mn"r"(m,an)))
+t55:=lemma294c(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(pl"r"(an,mn"r"(m,an))))
+t56:=intpl(an,t18,mn"r"(m,an),t52):intrl(pl"r"(an,mn"r"(m,an)))
+t57:=t14(x,an,mn"r"(m,an),t18,t52,t51,t50):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55))
+t58:=satz187a(m,an):is"r"(pl"r"(an,mn"r"(m,an)),m)
+t59:=ispw2(x,pl"r"(an,mn"r"(m,an)),m,t58,t56,mi,t55,lemma294a):is(pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a))
+t60:=tris(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a),t57,t59):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a))
+t61:=ispw1(x,x,an,refis(cx,x),t18,t53,t42):is(pw(x,an,t18,t53),pw(x,an,t18,t42))
+t62:=isp1(cx,[t:cx]nis(t,0c),pw(x,an,t18,t42),pw(x,an,t18,t53),t43,t61):nis(pw(x,an,t18,t53),0c)
+t63:=isov12(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a),pw(x,an,t18,t53),pw(x,an,t18,t42),t60,t61,t62,t43):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+t64:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t63):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62))
+t65:=satz229h(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54),t62,refis(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)))):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54))
+t66:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
+t67:=ispw2(x,mn"r"(m,an),pl"r"(m,n),t66,t52,intpl(m,mi,n,ni),t54,lemma294c):is(pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t68:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t64,t65,t67):prop1
+nn@[caseb:is"r"(m,an)]
+t69:=ispw2(x,m,an,caseb,mi,t18,lemma294a,t42):is(pw(x,m,mi,lemma294a),pw(x,an,t18,t42))
+t70:=satz251a(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43,t69):is(ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c)
+t71:=tr3is(real,pl"r"(m,n),mn"r"(m,m0"r"(n)),mn"r"(m,an),0,ispl2"r"(n,m0"r"(m0"r"(n)),m,satz177a(n)),ismn2"r"(m0"r"(n),an,m,symis(real,an,m0"r"(n),absn(n,nn))),satz182e(m,an,caseb)):is"r"(pl"r"(m,n),0)
+t72:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),1c,0exp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t71)):is(1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t73:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t47,t70,t72):prop1
+nn@[casec:less(m,an)]
+t74:=satz182d(an,m,lemma2"r"(m,an,casec)):pos(mn"r"(an,m))
+t75:=andi(pos(m),pos(mn"r"(an,m)),pm,t74):and(pos(m),pos(mn"r"(an,m)))
+t76:=ori2(nis(x,0c),and(pos(m),pos(mn"r"(an,m))),t75):or(nis(x,0c),and(pos(m),pos(mn"r"(an,m))))
+t77:=intmn(an,t18,m,mi):intrl(mn"r"(an,m))
+t78:=lemma294a(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(m))
+t79:=lemma294b(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(mn"r"(an,m)))
+t80:=lemma294c(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(pl"r"(m,mn"r"(an,m))))
+t81:=intpl(m,mi,mn"r"(an,m),t77):intrl(pl"r"(m,mn"r"(an,m)))
+t81a:=t14(x,m,mn"r"(an,m),mi,t77,t76,t75):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80))
+t82:=satz187a(an,m):is"r"(pl"r"(m,mn"r"(an,m)),an)
+t83:=ispw2(x,pl"r"(m,mn"r"(an,m)),an,t82,t81,t18,t80,t42):is(pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42))
+t84:=tris(cx,ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42),t81a,t83):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42))
+t85:=satz290(x,m,mi,t78,t15):nis(pw(x,m,mi,t78),0c)
+t86:=satz290(x,mn"r"(an,m),t77,t79,t15):nis(pw(x,mn"r"(an,m),t77,t79),0c)
+t87:=satz221d(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79),t85,t86):nis(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),0c)
+t88:=satz222(pw(x,m,mi,t78)):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78))
+t89:=ispw1(x,x,m,refis(cx,x),mi,t78,lemma294a):is(pw(x,m,mi,t78),pw(x,m,mi,lemma294a))
+t90:=tris(cx,ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78),pw(x,m,mi,lemma294a),t88,t89):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a))
+t91:=isov12(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42),t90,t84,t87,t43):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
+t92:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t91):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87))
+t93:=satz246a(1c,pw(x,mn"r"(an,m),t77,t79),pw(x,m,mi,t78),t86,t85):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86))
+t94:=satz182f(m,an,casec):neg(mn"r"(m,an))
+t94a:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
+t95:=tr3is(real,mn"r"(an,m),m0"r"(mn"r"(m,an)),abs(mn"r"(m,an)),ap,satz181a(an,m),symis(real,abs(mn"r"(m,an)),m0"r"(mn"r"(m,an)),absn(mn"r"(m,an),t94)),isabs(mn"r"(m,an),pl"r"(m,n),t94a)):is"r"(mn"r"(an,m),ap)
+t96:=isp(real,[t:real]neg(t),mn"r"(m,an),pl"r"(m,n),t94,t94a):neg(pl"r"(m,n))
+t97:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96):or(nis(x,0c),pos(ap))
+t98:=lemmapw1(x,ap,t19,t97,satz166b(pl"r"(m,n),t96),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):nis(pw(x,ap,t19,t97),0c)
+t99:=ispw2(x,mn"r"(an,m),ap,t95,t77,t19,t79,t97):is(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97))
+t100:=isov2(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97),1c,t99,t86,t98):is(ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98))
+t101:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t97),t98),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):is(ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t102:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t92,t93,t100,t101):prop1
+nn@t103:=or3app(is"r"(m,an),more(m,an),less(m,an),prop1,satz167a(m,an),[t:is"r"(m,an)]t73(t),[t:more(m,an)]t68(t),[t:less(m,an)]t102(t)):prop1
+na@[nm:neg(m)][qn:pos(n)]
+na@t104:=ori1(nis(x,0c),and(pos(n),pos(m)),t15):or(nis(x,0c),and(pos(n),pos(m)))
+t104a:=th5"l.and"(pos(m),pos(n),na):not(and(pos(n),pos(m)))
+t105:=lemma294a(x,n,m,ni,mi,t104):or(nis(x,0c),pos(n))
+t106:=lemma294b(x,n,m,ni,mi,t104):or(nis(x,0c),pos(m))
+t107:=lemma294c(x,n,m,ni,mi,t104):or(nis(x,0c),pos(pl"r"(n,m)))
+t108:=ists12(pw(x,m,mi,lemma294a),pw(x,m,mi,t106),pw(x,n,ni,lemma294b),pw(x,n,ni,t105),ispw1(x,x,m,refis(cx,x),mi,lemma294a,t106),ispw1(x,x,n,refis(cx,x),ni,lemma294b,t105)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)))
+t109:=comts(pw(x,m,mi,t106),pw(x,n,ni,t105)):is(ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)))
+qn@t110:=t103(x,n,m,ni,mi,t104,t104a,qn,nm):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
+na@t111:=ispw2(x,pl"r"(n,m),pl"r"(m,n),compl"r"(n,m),intpl(n,ni,m,mi),intpl(m,mi,n,ni),t107,lemma294c):is(pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+qn@t112:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t110,t111):prop1
+na@[i:is"r"(m,0)]
+t113:=ists1(pw(x,m,mi,lemma294a),1c,pw(x,n,ni,lemma294b),0exp(x,m,mi,lemma294a,i)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)))
+t114:=satz222b(pw(x,n,ni,lemma294b)):is(ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b))
+t115:=symis(real,pl"r"(m,n),n,pl01"r"(m,n,i)):is"r"(n,pl"r"(m,n))
+t116:=ispw2(x,n,pl"r"(m,n),t115,ni,intpl(m,mi,n,ni),lemma294b,lemma294c):is(pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+t117:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t113,t114,t116):prop1
+na@[i:is"r"(n,0)]
+t118:=t117(x,n,m,ni,mi,t104,t104a,i):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
+t119:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t118,t111):prop1
+na@[pm:pos(m)]
+t120:=ore2(not(pos(m)),not(pos(n)),t16,weli(pos(m),pm)):not(pos(n))
+t121:=rapp(n,prop1,th2"l.imp"(pos(n),prop1,t120),[t:is"r"(n,0)]t119(t),[t:neg(n)]t103(pm,t)):prop1
+na@[nm:neg(m)]
+t122:=rapp(n,prop1,[t:pos(n)]t112(nm,t),[t:is"r"(n,0)]t119(t),[t:neg(n)]t41(nm,t)):prop1
+na@t123:=rapp(m,prop1,[t:pos(m)]t121(t),[t:is"r"(m,0)]t117(t),[t:neg(m)]t122(t)):prop1
+-9294
+o@satz294:=th1"l.imp"(and(pos(m),pos(n)),prop1".9294",[t:and(pos(m),pos(n))]t14".9294"(t),[t:not(and(pos(m),pos(n)))]t123".9294"(t)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
+ni@[o:nis(x,0c)]
+lemma295a:=ori1(nis(x,0c),pos(m),o):or(nis(x,0c),pos(m))
+lemma295b:=ori1(nis(x,0c),pos(n),o):or(nis(x,0c),pos(n))
+lemma295c:=ori1(nis(x,0c),pos(mn"r"(m,n)),o):or(nis(x,0c),pos(mn"r"(m,n)))
++9295
+t1:=ori1(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)),o):or(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)))
+t2:=intmn(m,mi,n,ni):intrl(mn"r"(m,n))
+t3:=lemma294a(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(mn"r"(m,n)))
+t4:=lemma294b(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(n))
+t5:=lemma294c(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(pl"r"(mn"r"(m,n),n)))
+t6:=ists12(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,lemma295b),pw(x,n,ni,t4),ispw1(x,x,mn"r"(m,n),refis(cx,x),t2,lemma295c,t3),ispw1(x,x,n,refis(cx,x),ni,lemma295b,t4)):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)))
+t7:=satz294(x,mn"r"(m,n),n,t2,ni,t1):is(ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5))
+t8:=plmn(m,n):is"r"(pl"r"(mn"r"(m,n),n),m)
+t9:=ispw2(x,pl"r"(mn"r"(m,n),n),m,t8,intpl(mn"r"(m,n),t2,n,ni),mi,t5,lemma295a):is(pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a))
+t10:=tr3is(cx,ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a),t6,t7,t9):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),pw(x,m,mi,lemma295a))
+t11:=satz290(x,n,ni,lemma295b,o):nis(pw(x,n,ni,lemma295b),0c)
+-9295
+satz295:=satz229k(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),pw(x,mn"r"(m,n),t2".9295",lemma295c),t11".9295",t10".9295"):is(ov(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),satz290(x,n,ni,lemma295b,o)),pw(x,mn"r"(m,n),intmn(m,mi,n,ni),lemma295c))
+m@[mi:intrl(m)][n:nis(x,0c)]
+lemma296:=ori1(nis(x,0c),pos(m),n):or(nis(x,0c),pos(m))
++9296
+t1:=intrli0(0,refis(real,0)):intrl(0)
+t2:=lemma295a(x,0,m,t1,mi,n):or(nis(x,0c),pos(0))
+t3:=lemma295b(x,0,m,t1,mi,n):or(nis(x,0c),pos(m))
+t4:=lemma295c(x,0,m,t1,mi,n):or(nis(x,0c),pos(mn"r"(0,m)))
+t5:=satz290(x,m,mi,lemma296,n):nis(pw(x,m,mi,lemma296),0c)
+t6:=satz290(x,m,mi,t3,n):nis(pw(x,m,mi,t3),0c)
+t7:=symis(cx,pw(x,0,t1,t2),1c,0exp(x,0,t1,t2,refis(real,0))):is(1c,pw(x,0,t1,t2))
+t8:=ispw1(x,x,m,refis(cx,x),mi,lemma296,t3):is(pw(x,m,mi,lemma296),pw(x,m,mi,t3))
+t9:=isov12(1c,pw(x,0,t1,t2),pw(x,m,mi,lemma296),pw(x,m,mi,t3),t7,t8,t5,t6):is(ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6))
+t10:=satz295(x,0,m,t1,mi,n):is(ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4))
+t11:=pl01(0,m0"r"(m),refis(real,0)):is"r"(mn"r"(0,m),m0"r"(m))
+t12:=lemma296(x,m0"r"(m),intm0(m,mi),n):or(nis(x,0c),pos(m0"r"(m)))
+t13:=ispw2(x,mn"r"(0,m),m0"r"(m),t11,intmn(0,t1,m,mi),intm0(m,mi),t4,t12):is(pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12))
+t14:=tr3is(cx,ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12),t9,t10,t13):is(ov(1c,pw(x,m,mi,lemma296),t5),pw(x,m0"r"(m),intm0(m,mi),t12))
+-9296
+satz296:=t14".9296":is(ov(1c,pw(x,m,mi,lemma296),satz290(x,m,mi,lemma296,n)),pw(x,m0"r"(m),intm0(m,mi),lemma296(m0"r"(m),intm0(m,mi),n)))
+ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
++9297
+[p:nis(x,0c)]
+t1:=satz290(x,m,mi,lemma294a(o),p):nis(pw(x,m,mi,lemma294a(o)),0c)
+o@[a:and(pos(m),pos(n))]
+t2:=ande2(pos(m),pos(n),a):pos(n)
+t3:=postspp(m,n,ande1(pos(m),pos(n),a),t2):pos(ts"r"(m,n))
+-9297
+lemma297a:=th9"l.or"(nis(x,0c),and(pos(m),pos(n)),nis(pw(x,m,mi,lemma294a(o)),0c),pos(n),o,[t:nis(x,0c)]t1".9297"(t),[t:and(pos(m),pos(n))]t2".9297"(t)):or(nis(pw(x,m,mi,lemma294a(o)),0c),pos(n))
+lemma297b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(ts"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9297"(t)):or(nis(x,0c),pos(ts"r"(m,n)))
+mi@[o:or(nis(x,0c),pos(m))][i:is(x,0c)]
++*9297
+i@t4:=ore2(nis(x,0c),pos(m),o,weli(is(x,0c),i)):pos(m)
+m1:=ntofrl(m,posintnatrl(m,t4,mi)):nat
+t5:=posexp(x,m,mi,o,t4):is(pw(x,m,mi,o),prod(m1,[t:1to(m1)]x))
+t6:=satz289b(m1,[t:1to(m1)]x,xout(m1),i):is(prod(m1,[t:1to(m1)]x),0c)
+t7:=tris(cx,pw(x,m,mi,o),prod(m1,[t:1to(m1)]x),0c,t5,t6):is(pw(x,m,mi,o),0c)
+-9297
+i@pw0:=t7".9297":is(pw(x,m,mi,o),0c)
+ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
++*9297
+ni@t8:=intts(m,mi,n,ni):intrl(ts"r"(m,n))
+o@prop1:=is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o))):'prop'
+[i:is(x,0c)]
+t9:=pw0(x,m,mi,lemma294a(o),i):is(pw(x,m,mi,lemma294a(o)),0c)
+t10:=pw0(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o),t9):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),0c)
+t11:=pw0(x,ts"r"(m,n),t8,lemma297b(o),i):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),0c)
+t12:=tris2(cx,pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),0c,t10,t11):prop1
+m@[mi:intrl(m)][p:nis(x,0c)]
+t13:=ori1(nis(x,0c),pos(m),p):or(nis(x,0c),pos(m))
+p0:=pw(x,m,mi,t13):cx
+[n:nat]
+nr:=rlofnt(n):real
+t14:=natintrl(nr,natrli(n)):intrl(nr)
+t15:=ori2(nis(p0,0c),pos(nr),natpos(nr,natrli(n))):or(nis(p0,0c),pos(nr))
+t16:=ori1(nis(x,0c),pos(ts"r"(m,nr)),p):or(nis(x,0c),pos(ts"r"(m,nr)))
+t17:=intts(m,mi,nr,t14):intrl(ts"r"(m,nr))
+prop2:=is(pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16)):'prop'
+p@t18:=ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t15(1),lemma291(p0)):is(pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)))
+t19:=satz291(p0):is(pw(p0,1rl,intrl1,lemma291(p0)),p0)
+t20:=ispw2(x,m,ts"r"(m,1rl),satz195a(m),mi,t17(1),t13,t16(1)):is(p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)))
+t21:=tr3is(cx,pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)),t18,t19,t20):prop2(1)
+n@[p2:prop2(n)]
+n1:=pl"n"(n,1):nat
+t22:=satz290(x,m,mi,t13,p):nis(p0,0c)
+t23:=ori1(nis(p0,0c),and(pos(nr),pos(1rl)),t22):or(nis(p0,0c),and(pos(nr),pos(1rl)))
+t24:=lemma294a(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(nr))
+t25:=lemma294b(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(1rl))
+t26:=lemma294c(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(pl"r"(nr,1rl)))
+t27:=ispw2(p0,nr(n1),pl"r"(nr,1rl),satzr155a(n,1),t14(n1),intpl(nr,t14,1rl,intrl1),t15(n1),t26):is(pw(p0,nr(n1),t14(n1),t15(n1)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
+t27a:=satz294(p0,nr,1rl,t14,intrl1,t23):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
+t28:=tris2(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26),t27,t27a):is(pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)))
+t29:=ori1(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)),p):or(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)))
+t30:=lemma294a(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(ts"r"(m,nr)))
+t31:=lemma294b(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(m))
+t32:=lemma294c(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(pl"r"(ts"r"(m,nr),m)))
+t33:=tr3is(cx,pw(p0,nr,t14,t24),pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16),pw(x,ts"r"(m,nr),t17,t30),ispw1(p0,p0,nr,refis(cx,p0),t14,t24,t15),p2,ispw1(x,x,ts"r"(m,nr),refis(cx,x),t17,t16,t30)):is(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30))
+t34:=tr3is(cx,pw(p0,1rl,intrl1,t25),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,m,mi,t31),ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t25,lemma291(p0)),t19,ispw1(x,x,m,refis(cx,x),mi,t13,t31)):is(pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31))
+t35:=ists12(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30),pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31),t33,t34):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)))
+t36:=satz294(x,ts"r"(m,nr),m,t17,mi,t29):is(ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32))
+t37:=tr3is(real,pl"r"(ts"r"(m,nr),m),pl"r"(ts"r"(m,nr),ts"r"(m,1rl)),ts"r"(m,pl"r"(nr,1rl)),ts"r"(m,nr(n1)),ispl2"r"(m,ts"r"(m,1rl),ts"r"(m,nr),satz195a(m)),distpt2"r"(m,nr,1rl),ists2"r"(pl"r"(nr,1rl),nr(n1),m,satzr155b(n,1))):is"r"(pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)))
+t38:=ispw2(x,pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)),t37,intpl(ts"r"(m,nr),t17,m,mi),t17(n1),t32,t16(n1)):is(pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)))
+t39:=tr4is(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)),t28,t35,t36,t38):prop2(n1)
+t40:=isp(nat,[t:nat]prop2(t),n1,<n>suc,t39,satz4a(n)):prop2(<n>suc)
+n@t41:=induction([t:nat]prop2(t),t21,[t:nat][u:prop2(t)]t40(t,u),n):prop2(n)
+o@[p:nis(x,0c)][q:pos(n)]
+t42:=posintnatrl(n,q,ni):natrl(n)
+n0:=ntofrl(n,t42):nat
+t43:=isrlnt1(n,t42):is"r"(n,rlofnt(n0))
+t44:=isrlnt2(n,t42):is"r"(rlofnt(n0),n)
+o@p1:=pw(x,m,mi,lemma294a(o)):cx
+q@t44a:=ispw2(x,m,m,refis(real,m),mi,mi,lemma294a(o),t13(mi,p)):is(p1,p0(mi,p))
+t45:=ispw12(p1,p0(mi,p),n,rlofnt(n0),t44a,t43,ni,t14(mi,p,n0),lemma297a(o),t15(mi,p,n0)):is(pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)))
+t46:=t41(mi,p,n0):is(pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)))
+t47:=ists2"r"(rlofnt(n0),n,m,t44):is"r"(ts"r"(m,rlofnt(n0)),ts"r"(m,n))
+t48:=ispw2(x,ts"r"(m,rlofnt(n0)),ts"r"(m,n),t47,t17(mi,p,n0),t8,t16(mi,p,n0),lemma297b(o)):is(pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)))
+t49:=tr3is(cx,pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)),t45,t46,t48):prop1
+p@[i:is"r"(n,0)]
+t50:=0exp(p1,n,ni,lemma297a(o),i):is(pw(p1,n,ni,lemma297a(o)),1c)
+t51:=ts02"r"(m,n,i):is"r"(ts"r"(m,n),0)
+t52:=0exp(x,ts"r"(m,n),t8,lemma297b(o),t51):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),1c)
+t53:=tris2(cx,pw(p1,n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),1c,t50,t52):prop1
+p@[q:neg(n)]
+an:=abs(n):real
+t54:=intabs(n,ni):intrl(an)
+t55:=ori1(nis(x,0c),and(pos(m),pos(an)),p):or(nis(x,0c),and(pos(m),pos(an)))
+p1t55:=p1(an,mi,t54,t55):cx
+t56:=satz166e(n,nnot0(n,q)):pos(an)
+t56a:=lemma294a(an,mi,t54,t55):or(nis(x,0c),pos(m))
+t57:=lemma297a(an,mi,t54,t55):or(nis(p1t55,0c),pos(an))
+t58:=lemma297b(an,mi,t54,t55):or(nis(x,0c),pos(ts"r"(m,an)))
+t59:=t49(an,mi,t54,t55,p,t56):is(pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58))
+t60:=satz177c(an,n,absn(n,q)):is"r"(n,m0"r"(an))
+t61:=intm0(an,t54):intrl(m0"r"(an))
+t62:=satz290(x,m,mi,t56a,p):nis(p1t55,0c)
+t63:=lemma296(p1t55,an,t54,t62):or(nis(p1t55,0c),pos(an))
+t64:=satz290(p1t55,an,t54,t63,t62):nis(pw(p1t55,an,t54,t63),0c)
+t65:=lemma296(p1t55,m0"r"(an),t61,t62):or(nis(p1t55,0c),pos(m0"r"(an)))
+t66:=satz296(p1t55,an,t54,t62):is(ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65))
+t67:=ispw1(x,x,m,refis(cx,x),mi,lemma294a(o),t56a):is(p1,p1t55)
+t68:=ispw12(p1,p1t55,n,m0"r"(an),t67,t60,ni,t61,lemma297a(o),t65):is(pw(p1,n,ni,lemma297a(o)),pw(p1t55,m0"r"(an),t61,t65))
+t69:=tris2(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65),t68,t66):is(pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64))
+t70:=tris(real,m0"r"(ts"r"(m,an)),ts"r"(m,m0"r"(an)),ts"r"(m,n),satz197f(m,an),ists2"r"(m0"r"(an),n,m,symis(real,n,m0"r"(an),t60))):is"r"(m0"r"(ts"r"(m,an)),ts"r"(m,n))
+t71:=intm0(ts"r"(m,an),t8(an,mi,t54)):intrl(m0"r"(ts"r"(m,an)))
+t72:=lemma296(x,ts"r"(m,an),t8(an,mi,t54),p):or(nis(x,0c),pos(ts"r"(m,an)))
+t73:=satz290(x,ts"r"(m,an),t8(an,mi,t54),t72,p):nis(pw(x,ts"r"(m,an),t8(an,mi,t54),t72),0c)
+t74:=lemma296(x,m0"r"(ts"r"(m,an)),t71,p):or(nis(x,0c),pos(m0"r"(ts"r"(m,an))))
+t75:=satz296(x,ts"r"(m,an),t8(an,mi,t54),p):is(ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74))
+t76:=ispw2(x,m0"r"(ts"r"(m,an)),ts"r"(m,n),t70,t71,t8,t74,lemma297b(o)):is(pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)))
+t77:=ispw1(p1t55,p1t55,an,refis(cx,p1t55),t54,t63,t57):is(pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57))
+t78:=ispw1(x,x,ts"r"(m,an),refis(cx,x),t8(an,mi,t54),t58,t72):is(pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
+t79:=tr3is(cx,pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t77,t59,t78):is(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
+t80:=isov2(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),1c,t79,t64,t73):is(ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73))
+t81:=tr4is(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)),t69,t80,t75,t76):prop1
+p@t82:=rapp(n,prop1,[t:pos(n)]t49(t),[t:is"r"(n,0)]t53(t),[t:neg(n)]t81(t)):prop1
+-9297
+o@satz297:=th1"l.imp"(is(x,0c),prop1".9297",[t:is(x,0c)]t12".9297"(t),[t:nis(x,0c)]t82".9297"(t)):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),intts(m,mi,n,ni),lemma297b(o)))
+@[r:real][s:real]
++10298
+t1:=tris(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),pl"r"(0,0)),pli(pl"r"(r,s),0),plis12a(r,0,s,0),isrecx2(pl"r"(0,0),0,pl"r"(r,s),pl01(0,0,refis(real,0)))):is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
+-10298
+satz298a:=symis(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0),t1".10298"):is(pli(pl"r"(r,s),0),pl(pli(r,0),pli(s,0)))
+satz298b:=t1".10298":is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
++*10298
+s@t2:=tris(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),mn"r"(0,0)),pli(mn"r"(r,s),0),mnis12a(r,0,s,0),isrecx2(mn"r"(0,0),0,mn"r"(r,s),pl02(0,m0"r"(0),satz176b(0,refis(real,0))))):is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
+-10298
+s@satz298c:=symis(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0),t2".10298"):is(pli(mn"r"(r,s),0),mn(pli(r,0),pli(s,0)))
+satz298d:=t2".10298":is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
++*10298
+s@t3:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
+t4:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
+t5:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t3,t4)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
+-10298
+s@satz298e:=symis(cx,ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0),t5".10298"):is(pli(ts"r"(r,s),0),ts(pli(r,0),pli(s,0)))
+satz298f:=t5".10298":is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
+[n:nis"r"(s,0)]
++*10298
+n@[i:is(pli(s,0),0c)]
+t6:=tr3is(real,s,re(pli(s,0)),re(0c),0,isre(s,0),iscere(pli(s,0),0c,i),reis(0,0)):is"r"(s,0)
+-10298
+n@lemma298:=th3"l.imp"(is(pli(s,0),0c),is"r"(s,0),n,[t:is(pli(s,0),0c)]t6".10298"(t)):nis(pli(s,0),0c)
++*10298
+n@t7:=tris(cx,ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(ts"r"(s,ov"r"(r,s,n)),0),pli(r,0),t5(s,ov"r"(r,s,n)),isrecx1(ts"r"(s,ov"r"(r,s,n)),r,0,satz204c(r,s,n))):is(ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(r,0))
+-10298
+n@satz298g:=satz229g(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(pli(ov"r"(r,s,n),0),ov(pli(r,0),pli(s,0),lemma298))
+satz298h:=satz229h(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(ov(pli(r,0),pli(s,0),lemma298),pli(ov"r"(r,s,n),0))
++*10298
+r@t8:=tris(cx,m0(pli(r,0)),pli(m0"r"(r),m0"r"(0)),pli(m0"r"(r),0),m0isa(r,0),isrecx2(m0"r"(0),0,m0"r"(r),satz176b(0,refis(real,0)))):is(m0(pli(r,0)),pli(m0"r"(r),0))
+-10298
+r@satz298j:=symis(cx,m0(pli(r,0)),pli(m0"r"(r),0),t8".10298"):is(pli(m0"r"(r),0),m0(pli(r,0)))
+satz298k:=t8".10298":is(m0(pli(r,0)),pli(m0"r"(r),0))
++*10298
+r@t9:=tris(real,mod2(pli(r,0)),ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(r,r),pl02(ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(im(pli(r,0)),im(pli(r,0))),ts01(im(pli(r,0)),im(pli(r,0)),imis(r,0))),ists12"r"(re(pli(r,0)),r,re(pli(r,0)),r,reis(r,0),reis(r,0))):is"r"(mod2(pli(r,0)),ts"r"(r,r))
+ar:=abs(r):real
+[p:pos(r)]
+t10:=satz196a(r,r,p,p):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+r@[i:is"r"(r,0)]
+t11:=tris2(real,ts"r"(r,r),ts"r"(ar,ar),0,ts01(r,r,i),ts01(ar,ar,abs0(r,i))):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+r@[n:neg(r)]
+t12:=satz196b(r,r,n,n):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+r@t13:=rapp(r,is"r"(ts"r"(r,r),ts"r"(ar,ar)),[t:pos(r)]t10(t),[t:is"r"(r,0)]t11(t),[t:neg(r)]t12(t)):is"r"(ts"r"(r,r),ts"r"(ar,ar))
+t14:=tris(real,mod2(pli(r,0)),ts"r"(r,r),ts"r"(ar,ar),t9,t13):is"r"(mod2(pli(r,0)),ts"r"(ar,ar))
+t15:=th1"l.imp"(is"r"(r,0),not(neg(ar)),[t:is"r"(r,0)]0notn(ar,abs0(r,t)),[t:nis"r"(r,0)]pnotn(ar,satz166e(r,t))):not(neg(ar))
+-10298
+r@satz298l:=thsqrt3(mod2(pli(r,0)),lemma5(pli(r,0)),abs(r),t15".10298",t14".10298"):is"r"(mod(pli(r,0)),abs(r))
+satz298m:=symis(real,mod(pli(r,0)),abs(r),satz298l):is"r"(abs(r),mod(pli(r,0)))
+cofrl:=pli(r,0):complex
+s@[i:is(cofrl(r),cofrl(s))]
+isrlic:=tr3is(real,r,re(cofrl(r)),re(cofrl(s)),s,isre(r,0),iscere(cofrl(r),cofrl(s),i),reis(s,0)):is"r"(r,s)
+s@[i:is"r"(r,s)]
+isrlec:=isrecx1(r,s,0,i):is(cofrl(r),cofrl(s))
++v10
+@t1:=[t:real][u:real][v:is(cofrl(t),cofrl(u))]isrlic(t,u,v):injective(real,cx,[t:real]cofrl(t))
+-v10
+@[x:cx]
+realc:=image(real,cx,[t:real]cofrl(t),x):'prop'
+r@reali:=imagei(real,cx,[t:real]cofrl(t),r):realc(cofrl(r))
+x@[rx:realc(x)]
+rlofc:=soft(real,cx,[t:real]cofrl(t),t1".v10",x,rx):real
+[y:cx][ry:realc(y)][i:is"r"(rlofc(x,rx),rlofc(y,ry))]
+iscirl:=isinve(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is(x,y)
+ry@[i:is(x,y)]
+iscerl:=isinv(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is"r"(rlofc(x,rx),rlofc(y,ry))
+r@isrlc1:=isst1(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(r,rlofc(cofrl(r),reali(r)))
+isrlc2:=isst2(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(rlofc(cofrl(r),reali(r)),r)
+rx@iscrl1:=ists1"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(x,cofrl(rlofc(x,rx)))
+iscrl2:=ists2"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(cofrl(rlofc(x,rx)),x)
+@[n:nat]
+cofn:=cofrl(rlofnt(n)):complex
+[m:nat][i:is"n"(n,m)]
+isnec:=isrlec(rlofnt(n),rlofnt(m),isnterl(n,m,i)):is(cofn(n),cofn(m))
+m@[i:is(cofn(n),cofn(m))]
+isnic:=isntirl(n,m,isrlic(rlofnt(n),rlofnt(m),i)):is"n"(n,m)
++*v10
+@t2:=[t:nat][u:nat][v:is(cofn(t),cofn(u))]isnic(t,u,v):injective(nat,cx,[t:nat]cofn(t))
+-v10
+x@natc:=image(nat,cx,[t:nat]cofn(t),x):'prop'
+n@nati:=imagei(nat,cx,[t:nat]cofn(t),n):natc(cofn(n))
+x@[nx:natc(x)]
+nofc:=soft(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):nat
+[y:cx][ny:natc(y)][i:is(x,y)]
+iscen:=isinv(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is"n"(nofc(x,nx),nofc(y,ny))
+ny@[i:is"n"(nofc(x,nx),nofc(y,ny))]
+iscin:=isinve(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is(x,y)
+n@isnc1:=isst1(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(n,nofc(cofn(n),nati(n)))
+isnc2:=isst2(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(nofc(cofn(n),nati(n)),n)
+nx@iscn1:=ists1"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(x,cofn(nofc(x,nx)))
+iscn2:=ists2"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(cofn(nofc(x,nx)),x)
+@natt:=ot(cx,[t:cx]natc(t)):'type'
+[nt:natt]
+cofnt:=in"e"(cx,[t:cx]natc(t),nt):cx
+natti:=inp(cx,[t:cx]natc(t),nt):natc(cofnt(nt))
+[mt:natt][i:is"e"(natt,nt,mt)]
+isntec:=isini(cx,[t:cx]natc(t),nt,mt,i):is(cofnt(nt),cofnt(mt))
+mt@[i:is(cofnt(nt),cofnt(mt))]
+isntic:=isine(cx,[t:cx]natc(t),nt,mt,i):is"e"(natt,nt,mt)
+nx@ntofc:=out(cx,[t:cx]natc(t),x,nx):natt
+ny@[i:is(x,y)]
+iscent:=isouti(cx,[t:cx]natc(t),x,nx,y,ny,i):is"e"(natt,ntofc(x,nx),ntofc(y,ny))
+ny@[i:is"e"(natt,ntofc(x,nx),ntofc(y,ny))]
+iscint:=isoute(cx,[t:cx]natc(t),x,nx,y,ny,i):is(x,y)
+nt@isntc1:=isoutin(cx,[t:cx]natc(t),nt):is"e"(natt,nt,ntofc(cofnt(nt),natti(nt)))
+isntc2:=symis(natt,nt,ntofc(cofnt(nt),natti(nt)),isntc1):is"e"(natt,ntofc(cofnt(nt),natti(nt)),nt)
+nx@iscnt1:=isinout(cx,[t:cx]natc(t),x,nx):is(x,cofnt(ntofc(x,nx)))
+iscnt2:=symis(cx,x,cofnt(ntofc(x,nx)),iscnt1):is(cofnt(ntofc(x,nx)),x)
+n@ntofn:=ntofc(cofn(n),nati(n)):natt
+m@[i:is"n"(n,m)]
+isnent:=iscent(cofn(n),nati(n),cofn(m),nati(m),isnec(n,m,i)):is"e"(natt,ntofn(n),ntofn(m))
+m@[i:is"e"(natt,ntofn(n),ntofn(m))]
+isnint:=isnic(n,m,iscint(cofn(n),nati(n),cofn(m),nati(m),i)):is"n"(n,m)
+nt@nofnt:=nofc(cofnt(nt),natti(nt)):nat
+mt@[i:is"e"(natt,nt,mt)]
+isnter:=iscen(cofnt(nt),natti(nt),cofnt(mt),natti(mt),isntec(nt,mt,i)):is"n"(nofnt(nt),nofnt(mt))
+mt@[i:is"n"(nofnt(nt),nofnt(mt))]
+isntin:=isntic(nt,mt,iscin(cofnt(nt),natti(nt),cofnt(mt),natti(mt),i)):is"e"(natt,nt,mt)
++*v10
+n@t3:=iscnt1(cofn(n),nati(n)):is(cofn(n),cofnt(ntofn(n)))
+-v10
+n@isnnt1:=tris(nat,n,nofc(cofn(n),nati(n)),nofnt(ntofn(n)),isnc1(n),iscen(cofn(n),nati(n),cofnt(ntofn(n)),natti(ntofn(n)),t3".v10")):is"n"(n,nofnt(ntofn(n)))
+isnnt2:=symis(nat,n,nofnt(ntofn(n)),isnnt1):is"n"(nofnt(ntofn(n)),n)
++*v10
+nt@t4:=iscn1(cofnt(nt),natti(nt)):is(cofnt(nt),cofn(nofnt(nt)))
+-v10
+nt@isntn1:=tris(natt,nt,ntofc(cofnt(nt),natti(nt)),ntofn(nofnt(nt)),isntc1(nt),iscent(cofnt(nt),natti(nt),cofn(nofnt(nt)),nati(nofnt(nt)),t4".v10")):is"e"(natt,nt,ntofn(nofnt(nt)))
+isntn2:=symis(natt,nt,ntofn(nofnt(nt)),isntn1):is"e"(natt,ntofn(nofnt(nt)),nt)
+@1t:=ntofn(1):natt
+suct:=[t:natt]ntofn(<nofnt(t)>suc):[t:natt]natt
++10299
+nt@[i:is"e"(natt,<nt>suct,1t)]
+t1:=isnint(<nofnt(nt)>suc,1,i):is"n"(<nofnt(nt)>suc,1)
+-10299
+nt@satz299a:=th3"l.imp"(is"e"(natt,<nt>suct,1t),is"n"(<nofnt(nt)>suc,1),<nofnt(nt)>ax3,[t:is"e"(natt,<nt>suct,1t)]t1".10299"(t)):not(is"e"(natt,<nt>suct,1t))
+@ax3t:=[t:natt]satz299a(t):[t:natt]not(is"e"(natt,<t>suct,1t))
+mt@[i:is"e"(natt,<nt>suct,<mt>suct)]
++*10299
+i"c"@t2:=isnint(<nofnt(nt)>suc,<nofnt(mt)>suc,i):is"n"(<nofnt(nt)>suc,<nofnt(mt)>suc)
+t3:=<t2><nofnt(mt)><nofnt(nt)>ax4:is"n"(nofnt(nt),nofnt(mt))
+-10299
+i@satz299b:=isntin(nt,mt,t3".10299"):is"e"(natt,nt,mt)
+@ax4t:=[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]satz299b(t,u,v):[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]is"e"(natt,t,u)
+[s:set(natt)]
+cond1t:=esti(natt,1t,s):'prop'
+cond2t:=all"l"(natt,[t:natt]imp(esti(natt,t,s),esti(natt,<t>suct,s))):'prop'
+[c1:cond1t][c2:cond2t]
++*10299
+c2@[n:nat]
+prop1:=esti(natt,ntofn(n),s):'prop'
+c2@t4:=c1:prop1(1)
+n@[p:prop1(n)]
+t5:=<p><ntofn(n)>c2:esti(natt,ntofn(<nofnt(ntofn(n))>suc),s)
+t6:=isp(nat,[t:nat]esti(natt,ntofn(<t>suc),s),nofnt(ntofn(n)),n,t5,isnnt2(n)):prop1(<n>suc)
+c2@[nt:natt]
+t7:=induction([t:nat]prop1(t),t4,[t:nat][u:prop1(t)]t6(t,u),nofnt(nt)):prop1(nofnt(nt))
+-10299
+c2@satz299c:=[t:natt]isp(natt,[u:natt]esti(natt,u,s),ntofn(nofnt(t)),t,t7".10299"(t),isntn2(t)):[t:natt]esti(natt,t,s)
+@ax5t:=[t:set(natt)][u:cond1t(t)][v:cond2t(t)]satz299c(t,u,v):[t:set(natt)][u:cond1t(t)][v:cond2t(t)][w:natt]esti(natt,w,t)
+ic:=pli(0,1rl):complex
++10300
+t1:=tsis12a(0,1rl,0,1rl):is(ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))))
+t2:=tris(real,mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(ts"r"(1rl,1rl)),m0"r"(1rl),pl01(ts"r"(0,0),m0"r"(ts"r"(1rl,1rl)),ts01(0,0,refis(real,0))),ism0"r"(ts"r"(1rl,1rl),1rl,satz195(1rl))):is"r"(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl))
+t3:=tris(real,pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),ts"r"(1rl,0),0,pl01(ts"r"(0,1rl),ts"r"(1rl,0),ts01(0,1rl,refis(real,0))),ts02(1rl,0,refis(real,0))):is"r"(pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0)
+t4:=isrecx12(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0,t2,t3):is(pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)))
+t5:=satz298j(1rl):is(cofrl(m0"r"(1rl)),m0(1c))
+-10300
+satz2300:=tr3is(cx,ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)),m0(1c),t1".10300",t4".10300",t5".10300"):is(ts(ic,ic),m0(1c))
+[r:real][s:real]
++10301
+t1:=tsis12a(s,0,0,1rl):is(ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))))
+t2:=tris(real,mn"r"(ts"r"(s,0),ts"r"(0,1rl)),m0"r"(ts"r"(0,1rl)),0,pl01(ts"r"(s,0),m0"r"(ts"r"(0,1rl)),ts02(s,0,refis(real,0))),satz176b(ts"r"(0,1rl),ts01(0,1rl,refis(real,0)))):is"r"(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0)
+t3:=tris(real,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),ts"r"(s,1rl),s,pl02(ts"r"(s,1rl),ts"r"(0,0),ts01(0,0,refis(real,0))),satz195(s)):is"r"(pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s)
+t4:=isrecx12(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s,t2,t3):is(pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s))
+t5:=tris(cx,ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s),t1,t4):is(ts(cofrl(s),ic),pli(0,s))
+t6:=ispl2(ts(cofrl(s),ic),pli(0,s),cofrl(r),t5):is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)))
+t7:=plis12a(r,0,0,s):is(pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)))
+t8:=isrecx12(pl"r"(r,0),r,pl"r"(0,s),s,pl02(r,0,refis(real,0)),pl01(0,s,refis(real,0))):is(pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s))
+-10301
+satz301a:=tr3is(cx,pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s),t6".10301",t7".10301",t8".10301"):is"e"(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s))
+satz301b:=symis(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s),satz301a):is(pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)))
+@[x:complex]
+satz301c:=tris(cx,x,pli(re(x),im(x)),pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),ispli(x),satz301b(re(x),im(x))):is(x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)))
+satz301d:=symis(cx,x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),satz301c):is(pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),x)
+s@[t:real][u:real][i:is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)))]
++*10301
+i@t9:=tr3is(cx,pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)),pli(t,u),satz301b(r,s),i,satz301a(t,u)):is(pli(r,s),pli(t,u))
+-10301
+i@satz301e:=tr3is(real,r,re(pli(r,s)),re(pli(t,u)),t,isre(r,s),iscere(pli(r,s),pli(t,u),t9".10301"),reis(t,u)):is"r"(r,t)
+satz301f:=tr3is(real,s,im(pli(r,s)),im(pli(t,u)),u,isim(r,s),isceim(pli(r,s),pli(t,u),t9".10301"),imis(t,u)):is"r"(s,u)
+-c
+-r
+-rp
+-rt
+-n
+-landau
+-eq
+-st
+-e
+{}
+-l
+++ /dev/null
-# Landau's "Grundlagen der Analysis", formal specification in AUTOMATH
-# Copyright (C) 1977, L.S. van Benthem Jutting
-# 1992, revised by F. Wiedijk (http://www.cs.ru.nl/~freek/aut/)
-
-+l
-@[a:'prop'][b:'prop']
-imp:=[x:a]b:'prop'
-[a1:a][i:imp(a,b)]
-mp:=<a1>i:b
-a@refimp:=[x:a]x:imp(a,a)
-b@[c:'prop'][i:imp(a,b)][j:imp(b,c)]
-trimp:=[x:a]<<x>i>j:imp(a,c)
-@con:='prim':'prop'
-a@not:=imp(con):'prop'
-wel:=not(not(a)):'prop'
-[a1:a]
-weli:=[x:not(a)]<a1>x:wel(a)
-a@[w:wel(a)]
-et:='prim':a
-a@[c1:con]
-cone:=et([x:not(a)]c1):a
-+imp
-b@[i:imp(a,b)][j:imp(not(a),b)]
-th1:=et(b,[x:not(b)]<<trimp(con,i,x)>j>x):b
-b@[n:not(a)]
-th2:=trimp(con,b,n,[x:con]cone(b,x)):imp(a,b)
-b@[n:not(b)][i:imp(a,b)]
-th3:=trimp(con,i,n):not(a)
-b@[a1:a][n:not(b)]
-th4:=[x:imp(a,b)]<a1>th3(n,x):not(imp(a,b))
-b@[n:not(imp(a,b))]
-th5:=et([x:not(a)]<th2(x)>n):a
-th6:=[x:b]<[y:a]x>n:not(b)
-b@[n:not(b)][i:imp(not(a),b)]
-th7:=et(a,th3(not(a),b,n,i)):a
--imp
-b@[i:imp(not(b),not(a))]
-cp:=[x:a]th7".imp"(b,not(a),weli(x),i):imp(a,b)
-@obvious:=imp(con,con):'prop'
-obviousi:=refimp(con):obvious
-b@ec:=imp(a,not(b)):'prop'
-[n:not(a)]
-eci1:=th2".imp"(not(b),n):ec(a,b)
-b@[n:not(b)]
-eci2:=[x:a]n:ec(a,b)
-+ec
-b@[i:imp(a,not(b))]
-th1:=i:ec(a,b)
-b@[i:imp(b,not(a))]
-th2:=[x:a][y:b]<x><y>i:ec(a,b)
--ec
-b@[e:ec(a,b)]
-comec:=th2".ec"(b,a,e):ec(b,a)
-[a1:a]
-ece1:=<a1>e:not(b)
-e@[b1:b]
-ece2:=th3".imp"(not(b),weli(b,b1),e):not(a)
-+*ec
-c@[e:ec(a,b)][i:imp(c,a)]
-th3:=trimp(c,a,not(b),i,e):ec(c,b)
-e@[i:imp(c,b)]
-th4:=comec(c,a,th3(b,a,c,comec(e),i)):ec(a,c)
--ec
-b@and:=not(ec(a,b)):'prop'
-[a1:a][b1:b]
-andi:=th4".imp"(not(b),a1,weli(b,b1)):and(a,b)
-b@[a1:and(a,b)]
-ande1:=th5".imp"(not(b),a1):a
-ande2:=et(b,th6".imp"(not(b),a1)):b
-comand:=andi(b,a,ande2,ande1):and(b,a)
-+and
-b@[n:not(a)]
-th1:=weli(ec,eci1(n)):not(and)
-b@[n:not(b)]
-th2:=weli(ec,eci2(n)):not(and)
-b@[n:not(and)][a1:a]
-th3:=ece1(et(ec,n),a1):not(b)
-n@[b1:b]
-th4:=ece2(et(ec,n),b1):not(a)
-n@th5:=th3"l.imp"(and(b,a),and(a,b),n,[x:and(b,a)]comand(b,a,x)):not(and(b,a))
-c@[a1:and(a,b)][i:imp(a,c)]
-th6:=andi(c,b,<ande1(a1)>i,ande2(a1)):and(c,b)
-a1@[i:imp(b,c)]
-th7:=andi(a,c,ande1(a1),<ande2(a1)>i):and(a,c)
--and
-b@or:=imp(not(a),b):'prop'
-[a1:a]
-ori1:=th2".imp"(not(a),b,weli(a1)):or(a,b)
-b@[b1:b]
-ori2:=[x:not(a)]b1:or(a,b)
-+or
-b@[i:imp(not(a),b)]
-th1:=i:or(a,b)
-b@[i:imp(not(b),a)]
-th2:=[x:not]et(b,th3"l.imp"(not(b),a,x,i)):or(a,b)
--or
-b@[o:or(a,b)][n:not(a)]
-ore2:=<n>o:b
-o@[n:not(b)]
-ore1:=et(th3".imp"(not(a),b,n,o)):a
-o@comor:=[x:not(b)]ore1(x):or(b,a)
-+*or
-b@[n:not(a)][m:not(b)]
-th3:=th4"l.imp"(not(a),b,n,m):not(or(a,b))
-b@[n:not(or(a,b))]
-th4:=th5"l.imp"(not(a),b,n):not(a)
-th5:=th6"l.imp"(not(a),b,n):not(b)
-a@th6:=refimp(not(a)):or(a,not(a))
--or
-c@[o:or(a,b)][i:imp(a,c)][j:imp(b,c)]
-orapp:=th1".imp"(c,i,trimp(not,b,c,o,j)):c
-c@[d:'prop']
-+*or
-o@[i:imp(a,c)]
-th7:=trimp(not(c),not,b,[x:not(c)]th3"l.imp"(a,c,x,i),o):or(c,b)
-o@[i:imp(b,c)]
-th8:=trimp(not(a),b,c,o,i):or(a,c)
-d@[o:or(a,b)][i:imp(a,c)][j:imp(b,d)]
-th9:=th7(a,d,c,th8(a,b,d,o,j),i):or(c,d)
-b@[o:or(a,b)]
-th10:=o:imp(not(a),b)
-th11:=comor(o):imp(not(b),a)
-b@[o:or(not(a),b)]
-th12:=trimp(a,wel(a),b,[x:a]weli(x),o):imp(a,b)
-b@[i:imp(a,b)]
-th13:=trimp(wel(a),a,b,[x:wel(a)]et(x),i):or(not(a),b)
-b@[o:or(not(a),not(b))]
-th14:=weli(ec,th12(not(b),o)):not(and)
-b@[n:not(and)]
-th15:=th13(not(b),et(ec,n)):or(not(a),not(b))
-b@[a1:and(not(a),not(b))]
-th16:=th3(ande1(not(a),not(b),a1),ande2(not(a),not(b),a1)):not(or(a,b))
-b@[n:not(or(a,b))]
-th17:=andi(not(a),not(b),th4(n),th5(n)):and(not(a),not(b))
--or
-b@orec:=and(or(a,b),ec(a,b)):'prop'
-[o:or(a,b)][e:ec(a,b)]
-oreci:=andi(or(a,b),ec(a,b),o,e):orec(a,b)
-+orec
-b@[a1:a][n:not(b)]
-th1:=oreci(ori1(a1),eci2(n)):orec(a,b)
-b@[n:not(a)][b1:b]
-th2:=oreci(ori2(b1),eci1(n)):orec(a,b)
--orec
-b@[o:orec(a,b)]
-orece1:=ande1(or(a,b),ec,o):or(a,b)
-orece2:=ande2(or(a,b),ec,o):ec(a,b)
-comorec:=oreci(b,a,comor(orece1),comec(orece2)):orec(b,a)
-+*orec
-o@[a1:a]
-th3:=ece1(orece2,a1):not(b)
-o@[b1:b]
-th4:=ece2(orece2,b1):not(a)
-o@[n:not(a)]
-th5:=ore2(orece1,n):b
-o@[n:not(b)]
-th6:=ore1(orece1,n):a
--orec
-b@iff:=and(imp(a,b),imp(b,a)):'prop'
-[i:imp(a,b)][j:imp(b,a)]
-iffi:=andi(imp(a,b),imp(b,a),i,j):iff(a,b)
-+iff
-b@[a1:a][b1:b]
-th1:=iffi([x:a]b1,[x:b]a1):iff(a,b)
-b@[n:not(a)][m:not(b)]
-th2:=iffi(th2"l.imp"(n),th2"l.imp"(b,a,m)):iff(a,b)
--iff
-b@[i:iff(a,b)]
-iffe1:=ande1(imp(a,b),imp(b,a),i):imp(a,b)
-iffe2:=ande2(imp(a,b),imp(b,a),i):imp(b,a)
-comiff:=iffi(b,a,iffe2,iffe1):iff(b,a)
-+*iff
-i@[a1:a]
-th3:=<a1>iffe1:b
-i@[b1:b]
-th4:=<b1>iffe2:a
-i@[n:not(a)]
-th5:=th3"l.imp"(b,a,n,iffe2):not(b)
-i@[n:not(b)]
-th6:=th3"l.imp"(n,iffe1):not(a)
-b@[a1:a][n:not(b)]
-th7:=th1"l.and"(imp(a,b),imp(b,a),th4"l.imp"(a1,n)):not(iff(a,b))
-b@[n:not(a)][b1:b]
-th8:=th2"l.and"(imp(a,b),imp(b,a),th4"l.imp"(b,a,b1,n)):not(iff(a,b))
--iff
-a@refiff:=iffi(a,refimp,refimp):iff(a,a)
-b@[i:iff(a,b)]
-symiff:=comiff(i):iff(b,a)
-c@[i:iff(a,b)][j:iff(b,c)]
-triff:=iffi(a,c,trimp(iffe1(i),iffe1(b,c,j)),trimp(c,b,a,iffe2(b,c,j),iffe2(i))):iff(a,c)
-+*iff
-b@[i:iff(a,b)]
-th9:=[x:not(a)]th5(i,x):imp(not(a),not(b))
-th10:=[x:not(b)]th6(i,x):imp(not(b),not(a))
-th11:=iffi(not(a),not(b),th9,th10):iff(not(a),not(b))
-b@[i:imp(not(a),not(b))][j:imp(not(b),not(a))]
-th12:=iffi(cp(j),cp(b,a,i)):iff(a,b)
-b@[o:orec(a,b)]
-th13:=iffi(not(b),orece2(o),comor(orece1(o))):iff(a,not(b))
-th14:=th13(b,a,comorec(o)):iff(b,not(a))
-b@[i:iff(a,not(b))]
-th15:=oreci(comor(b,a,iffe2(not(b),i)),iffe1(not(b),i)):orec(a,b)
-b@[i:iff(b,not(a))]
-th16:=comorec(b,a,th15(b,a,i)):orec(a,b)
-c@[i:iff(a,b)][j:imp(a,c)]
-thimp1:=trimp(b,a,c,iffe2(i),j):imp(b,c)
-i@[j:imp(c,a)]
-thimp2:=trimp(c,a,b,j,iffe1(i)):imp(c,b)
-i@[e:ec(a,c)]
-thec1:=th3"l.ec"(c,b,e,iffe2(i)):ec(b,c)
-i@[e:ec(c,a)]
-thec2:=th4"l.ec"(c,a,b,e,iffe2(i)):ec(c,b)
-i@[a1:and(a,c)]
-thand1:=th6"l.and"(c,b,a1,iffe1(i)):and(b,c)
-i@[a1:and(c,a)]
-thand2:=th7"l.and"(c,a,b,a1,iffe1(i)):and(c,b)
-i@[o:or(a,c)]
-thor1:=th7"l.or"(c,b,o,iffe1(i)):or(b,c)
-i@[o:or(c,a)]
-thor2:=th8"l.or"(c,a,b,o,iffe1(i)):or(c,b)
-i@[o:orec(a,c)]
-thorec1:=oreci(b,c,thor1(orece1(a,c,o)),thec1(orece2(a,c,o))):orec(b,c)
-i@[o:orec(c,a)]
-thorec2:=oreci(c,b,thor2(orece1(c,a,o)),thec2(orece2(c,a,o))):orec(c,b)
--iff
-@[sigma:'type'][p:[x:sigma]'prop']
-all:=p:'prop'
-[a1:all(sigma,p)][s:sigma]
-alle:=<s>a1:<s>p
-+all
-p@[s:sigma][n:not(<s>p)]
-th1:=[x:all(sigma,p)]<<s>x>n:not(all(sigma,p))
--all
-p@non:=[x:sigma]not(<x>p):[x:sigma]'prop'
-some:=not(non(p)):'prop'
-[s:sigma][sp:<s>p]
-somei:=th1".all"(non(p),s,weli(<s>p,sp)):some(sigma,p)
-+some
-p@[n:not(all(sigma,p))][m:non(non(p))][s:sigma]
-t1:=et(<s>p,<s>m):<s>p
-%set etared
-m@t2:=<[x:sigma]t1(x)>n:con
-%reset etared
-n@th1:=[x:non(non(p))]t2(x):some(non(p))
-p@[s:some(non(p))][a1:all(sigma,p)][t:sigma]
-t3:=weli(<t>p,<t>a1):not(not(<t>p))
-a1@t4:=<[x:sigma]t3(x)>s:con
-s@th2:=[x:all(sigma,p)]t4(x):not(all(sigma,p))
-p@[n:not(some(sigma,p))]
-th3:=et(non(p),n):non(p)
-[s:sigma]
-th4:=<s>th3:not(<s>p)
-p@[n:non(p)]
-th5:=weli(non(p),n):not(some(sigma,p))
--some
-p@[s:some(sigma,p)][x:'prop'][i:[y:sigma]imp(<y>p,x)]
-+*some
-i@[n:not(x)][t:sigma]
-t5:=th3"l.imp"(<t>p,x,n,<t>i):not(<t>p)
-n@t6:=mp(some(sigma,p),con,s,th5([y:sigma]t5(y))):con
--some
-i@someapp:=et(x,[y:not(x)]t6".some"(y)):x
-+*some
-p@[q:[x:sigma]'prop'][s:some(sigma,p)][i:[x:sigma]imp(<x>p,<x>q)]
-th6:=someapp(s,some(q),[x:sigma][y:<x>p]somei(q,x,mp(<x>p,<x>q,y,<x>i))):some(q)
--some
-c@or3:=or(a,or(b,c)):'prop'
-[o:or3(a,b,c)][n:not(a)]
-+or3
-th1:=ore2(or(b,c),o,n):or(b,c)
--or3
-[m:not(b)]
-or3e3:=ore2(b,c,th1".or3",m):c
-o@[n:not(b)]
-+*or3
-n@th2:=th2"l.or"(c,a,[x:not(a)]or3e3(x,n)):or(c,a)
--or3
-n@[m:not(c)]
-or3e1:=ore2(c,a,th2".or3",m):a
-o@[n:not(c)]
-+*or3
-n@th3:=th2"l.or"([x:not(b)]or3e1(x,n)):or(a,b)
--or3
-n@[m:not(a)]
-or3e2:=ore2(th3".or3",m):b
-+*or3
-o@th4:=th1"l.or"(b,or(c,a),[x:not(b)]th2(x)):or3(b,c,a)
-th5:=th4(b,c,a,th4):or3(c,a,b)
--or3
-c@[a1:a]
-or3i1:=ori1(a,or(b,c),a1):or3(a,b,c)
-c@[b1:b]
-or3i2:=ori2(a,or(b,c),ori1(b,c,b1)):or3(a,b,c)
-c@[c1:c]
-or3i3:=ori2(a,or(b,c),ori2(b,c,c1)):or3(a,b,c)
-+*or3
-c@[o:or(a,b)]
-th6:=th4"or3"(c,a,b,ori2(c,or(a,b),o)):or3(a,b,c)
-c@[o:or(b,c)]
-th7:=ori2(or(b,c),o):or3(a,b,c)
-c@[o:or(c,a)]
-th8:=th4"or3"(c,a,b,th6(c,a,b,o)):or3(a,b,c)
--or3
-d@[o:or3(a,b,c)][i:imp(a,d)][j:imp(b,d)][k:imp(c,d)]
-or3app:=orapp(or(b,c),d,o,i,[x:or(b,c)]orapp(b,c,d,x,j,k)):d
-c@and3:=and(a,and(b,c)):'prop'
-[a1:and3(a,b,c)]
-and3e1:=ande1(and(b,c),a1):a
-and3e2:=ande1(b,c,ande2(and(b,c),a1)):b
-and3e3:=ande2(b,c,ande2(and(b,c),a1)):c
-c@[a1:a][b1:b][c1:c]
-and3i:=andi(a,and(b,c),a1,andi(b,c,b1,c1)):and3(a,b,c)
-+and3
-c@[a1:and3(a,b,c)]
-th1:=and3i(b,c,a,and3e2(a1),and3e3(a1),and3e1(a1)):and3(b,c,a)
-th2:=th1(b,c,a,th1):and3(c,a,b)
-th3:=andi(and3e1(a1),and3e2(a1)):and(a,b)
-th4:=ande2(and(b,c),a1):and(b,c)
-th5:=th3(c,a,b,th2):and(c,a)
-th6:=and3i(c,b,a,and3e3(a1),and3e2(a1),and3e1(a1)):and3(c,b,a)
--and3
-c@ec3:=and3(ec,ec(b,c),ec(c,a)):'prop'
-[e:ec3(a,b,c)]
-+ec3
-th1:=and3e1(ec,ec(b,c),ec(c,a),e):ec(a,b)
-th2:=and3e2(ec,ec(b,c),ec(c,a),e):ec(b,c)
-th3:=and3e3(ec,ec(b,c),ec(c,a),e):ec(c,a)
-th4:=th1"l.and3"(ec,ec(b,c),ec(c,a),e):ec3(b,c,a)
-th5:=th4(b,c,a,th4):ec3(c,a,b)
-th5a:=and3i(ec(c,b),ec(b,a),ec(a,c),comec(b,c,th2(e)),comec(a,b,th1(e)),comec(c,a,th3(e))):ec3(c,b,a)
--ec3
-[a1:a]
-ec3e12:=ece1(th1".ec3",a1):not(b)
-ec3e13:=ece2(c,a,th3".ec3",a1):not(c)
-e@[b1:b]
-ec3e23:=ec3e12(b,c,a,th4".ec3",b1):not(c)
-ec3e21:=ec3e13(b,c,a,th4".ec3",b1):not(a)
-e@[c1:c]
-ec3e31:=ec3e12(c,a,b,th5".ec3",c1):not(a)
-ec3e32:=ec3e13(c,a,b,th5".ec3",c1):not(b)
-+*ec3
-c@[e:ec(a,b)][f:ec(b,c)][g:ec(c,a)]
-th6:=and3i(ec,ec(b,c),ec(c,a),e,f,g):ec3(a,b,c)
-c@[e:ec3(a,b,c)][o:or(a,b)]
-th7:=orapp(not(c),o,[x:a]ece2(c,a,th3"ec3"(e),x),[x:b]ece1(b,c,th2"ec3"(e),x)):not(c)
-e@[o:or(b,c)]
-th8:=th7(b,c,a,th4"ec3"(e),o):not(a)
-e@[o:or(c,a)]
-th9:=th7(c,a,b,th5"ec3"(e),o):not(b)
--ec3
-c@[n:not(a)][m:not(b)]
-ec3i1:=th6".ec3"(eci1(n),eci1(b,c,m),eci2(c,a,n)):ec3(a,b,c)
-c@[n:not(b)][m:not(c)]
-ec3i2:=th6".ec3"(eci2(n),eci1(b,c,n),eci1(c,a,m)):ec3(a,b,c)
-c@[n:not(c)][m:not(a)]
-ec3i3:=th6".ec3"(eci1(m),eci2(b,c,n),eci1(c,a,n)):ec3(a,b,c)
-+*ec3
-d@[e:'prop'][f:'prop'][o1:or3(a,b,c)][p1:ec3(d,e,f)][i:imp(a,d)][j:imp(b,e)][k:imp(c,f)][d1:d]
-t1:=[x:b]mp(e,con,<x>j,ec3e12(d,e,f,p1,d1)):not(b)
-t2:=[x:c]mp(f,con,<x>k,ec3e13(d,e,f,p1,d1)):not(c)
-th10:=or3e1(o1,t1,t2):a
-k@[e1:e]
-th11:=th10(b,c,a,e,f,d,th4"l.or3"(o1),th4"ec3"(d,e,f,p1),j,k,i,e1):b
-k@[f1:f]
-th12:=th10(c,a,b,f,d,e,th5"l.or3"(o1),th5"ec3"(d,e,f,p1),k,i,j,f1):c
--ec3
-c@orec3:=and(or3(a,b,c),ec3(a,b,c)):'prop'
-[o:orec3(a,b,c)]
-orec3e1:=ande1(or3(a,b,c),ec3(a,b,c),o):or3(a,b,c)
-orec3e2:=ande2(or3(a,b,c),ec3(a,b,c),o):ec3(a,b,c)
-c@[o:or3(a,b,c)][e:ec3(a,b,c)]
-orec3i:=andi(or3(a,b,c),ec3(a,b,c),o,e):orec3(a,b,c)
-+orec3
-c@[o:orec3(a,b,c)]
-th1:=orec3i(b,c,a,th4"l.or3"(orec3e1(o)),th4"l.ec3"(orec3e2(o))):orec3(b,c,a)
-th2:=orec3i(c,a,b,th5"l.or3"(orec3e1(o)),th5"l.ec3"(orec3e2(o))):orec3(c,a,b)
--orec3
-+e
-sigma@[s:sigma][t:sigma]
-is:='prim':'prop'
-s@refis:='prim':is(s,s)
-p@[s:sigma][t:sigma][sp:<s>p][i:is(s,t)]
-isp:='prim':<t>p
-sigma@[s:sigma][t:sigma][i:is(s,t)]
-symis:=isp([x:sigma]is(x,s),s,t,refis(s),i):is(t,s)
-t@[u:sigma][i:is(s,t)][j:is(t,u)]
-tris:=isp([x:sigma]is(x,u),t,s,j,symis(i)):is(s,u)
-u@[i:is(u,s)][j:is(u,t)]
-tris1:=tris(s,u,t,symis(u,s,i),j):is(s,t)
-u@[i:is(s,u)][j:is(t,u)]
-tris2:=tris(s,u,t,i,symis(t,u,j)):is(s,t)
-sp@[i:is(t,s)]
-isp1:=isp(symis(t,s,i)):<t>p
-t@[n:not(is(s,t))]
-symnotis:=th3"l.imp"(is(t,s),is(s,t),n,[x:is(t,s)]symis(t,s,x)):not(is(t,s))
-+notis
-u@[n:not(is(s,t))][i:is(s,u)]
-th1:=isp([x:sigma]not(is(x,t)),s,u,n,i):not(is(u,t))
-n@[i:is(u,s)]
-th2:=th1(symis(u,s,i)):not(is(u,t))
-n@[i:is(t,u)]
-th3:=isp([x:sigma]not(is(s,x)),t,u,n,i):not(is(s,u))
-n@[i:is(u,t)]
-th4:=th3(symis(u,t,i)):not(is(s,u))
-u@[v:sigma][n:not(is(s,t))][i:is(s,u)][j:is(t,v)]
-th5:=th3(u,t,v,th1(n,i),j):not(is(u,v))
--notis
-u@[v:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)]
-tr3is:=tris(s,u,v,tris(i,j),k):is(s,v)
-v@[w:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)][l:is(v,w)]
-tr4is:=tris(s,v,w,tr3is(i,j,k),l):is(s,w)
-p@amone:=[x:sigma][y:sigma][u:<x>p][v:<y>p]is(x,y):'prop'
-[a1:amone(sigma,p)][s:sigma][t:sigma][sp:<s>p][tp:<t>p]
-amonee:=<tp><sp><t><s>a1:is(s,t)
-p@one:=and(amone(sigma,p),some(sigma,p)):'prop'
-[a1:amone(sigma,p)][s:some(sigma,p)]
-onei:=andi(amone(sigma,p),some(sigma,p),a1,s):one(sigma,p)
-p@[o1:one(sigma,p)]
-onee1:=ande1(amone(sigma,p),some(sigma,p),o1):amone(sigma,p)
-onee2:=ande2(amone(sigma,p),some(sigma,p),o1):some(sigma,p)
-ind:='prim':sigma
-oneax:='prim':<ind>p
-+one
-[s:sigma][sp:<s>p]
-th1:=amonee(onee1,ind,s,oneax,sp):is(ind,s)
--one
-sigma@[tau:'type'][f:[x:sigma]tau][s:sigma][t:sigma][i:is(s,t)]
-isf:=isp(sigma,[x:sigma]is(tau,<s>f,<x>f),s,t,refis(tau,<s>f),i):is(tau,<s>f,<t>f)
-f@injective:=all([x:sigma]all([y:sigma]imp(is(tau,<x>f,<y>f),is(x,y)))):'prop'
-[i:injective(f)][s:sigma][t:sigma][j:is(tau,<s>f,<t>f)]
-isfe:=<j><t><s>i:is(s,t)
-f@[t0:tau]
-image:=some([x:sigma]is(tau,t0,<x>f)):'prop'
-f@[s:sigma]
-tofs:=<s>f:tau
-imagei:=somei([x:sigma]is(tau,tofs,<x>f),s,refis(tau,tofs)):image(tofs)
-+inj
-i@[ta:tau][tb:tau][j:is(tau,ta,tb)][sa:sigma][sb:sigma][ja:is(tau,ta,tofs(sa))][jb:is(tau,tb,tofs(sb))]
-t1:=tr3is(tau,tofs(sa),ta,tb,tofs(sb),symis(tau,ta,tofs(sa),ja),j,jb):is(tau,tofs(sa),tofs(sb))
-th1:=isfe(sa,sb,t1):is(sa,sb)
-i@[t0:tau]
-th2:=[x:sigma][y:sigma][u:is(tau,t0,<x>f)][v:is(tau,t0,<y>f)]th1(t0,t0,refis(tau,t0),x,y,u,v):amone([x:sigma]is(tau,t0,<x>f))
-[j:image(f,t0)]
-th3:=onei([x:sigma]is(tau,t0,<x>f),th2,j):one([x:sigma]is(tau,t0,<x>f))
--inj
-i@[t0:tau][j:image(f,t0)]
-soft:=ind([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):sigma
-i@inverse:=[x:tau][u:image(f,x)]soft(x,u):[x:tau][u:image(f,x)]sigma
-j@ists1:=oneax([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):is(tau,t0,tofs(soft(t0,j)))
-ists2:=symis(tau,t0,tofs(soft(t0,j)),ists1):is(tau,tofs(soft(t0,j)),t0)
-i@[ta:tau][ja:image(ta)][tb:tau][jb:image(tb)][j:is(tau,ta,tb)]
-isinv:=th1".inj"(ta,tb,j,soft(ta,ja),soft(tb,jb),ists1(ta,ja),ists1(tb,jb)):is(soft(ta,ja),soft(tb,jb))
-jb@[j:is(soft(ta,ja),soft(tb,jb))]
-isinve:=tr3is(tau,ta,tofs(soft(ta,ja)),tofs(soft(tb,jb)),tb,ists1(ta,ja),isf(soft(ta,ja),soft(tb,jb),j),ists2(tb,jb)):is(tau,ta,tb)
-i@[s:sigma]
-isst1:=isfe(s,soft(tofs(s),imagei(s)),ists1(tofs(s),imagei(s))):is(s,soft(tofs(s),imagei(s)))
-isst2:=symis(s,soft(tofs(s),imagei(s)),isst1):is(soft(tofs(s),imagei(s)),s)
-f@surjective:=all(tau,[x:tau]image(x)):'prop'
-bijective:=and(injective,surjective):'prop'
-[b:bijective(f)]
-+*inj
-b@t2:=ande1(injective,surjective,b):injective(f)
-t3:=ande2(injective,surjective,b):surjective(f)
-[t:tau]
-so:=soft(t2,t,<t>t3):sigma
--inj
-b@invf:=[x:tau]so".inj"(x):[x:tau]sigma
-[s:sigma]
-thinvf1:=tris(s,soft(t2".inj",tofs(s),imagei(s)),<<s>f>invf,isst1(t2".inj",s),isinv(t2".inj",tofs(s),imagei(s),tofs(s),<tofs(s)>t3".inj",refis(tau,tofs(s)))):is(s,<<s>f>invf)
-b@[t:tau]
-thinvf2:=ists1(t2".inj",t,<t>t3".inj"):is(tau,t,<<t>invf>f)
-tau@[upsilon:'type'][f:[x:sigma]tau][g:[x:tau]upsilon]
-+*inj
-g@[if:injective(sigma,tau,f)][ig:injective(tau,upsilon,g)]
-h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
-[s:sigma][t:sigma][i:is(upsilon,<s>h,<t>h)]
-t4:=isfe(tau,upsilon,g,ig,<s>f,<t>f,i):is(tau,<s>f,<t>f)
-t5:=isfe(f,if,s,t,t4):is(s,t)
-ig@th4:=[x:sigma][y:sigma][v:is(upsilon,<x>h,<y>h)]t5(x,y,v):injective(sigma,upsilon,[x:sigma]<<x>f>g)
--inj
-+surj
-g@[sf:surjective(sigma,tau,f)][sg:surjective(tau,upsilon,g)]
-h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
-[u:upsilon]
-t1:=<u>sg:image(tau,upsilon,g,u)
-[t:tau][i:is(upsilon,u,<t>g)]
-t2:=<t>sf:image(sigma,tau,f,t)
-[s:sigma][j:is(tau,t,<s>f)]
-t3:=tris(upsilon,u,<t>g,<s>h,i,isf(tau,upsilon,g,t,<s>f,j)):is(upsilon,u,<s>h)
-t4:=somei([x:sigma]is(upsilon,u,<x>h),s,t3):image(sigma,upsilon,h,u)
-i@t5:=someapp([x:sigma]is(tau,t,<x>f),t2,image(sigma,upsilon,h,u),[x:sigma][v:is(tau,t,<x>f)]t4(x,v)):image(sigma,upsilon,h,u)
-u@t6:=someapp(tau,[x:tau]is(upsilon,u,<x>g),t1,image(sigma,upsilon,h,u),[x:tau][v:is(upsilon,u,<x>g)]t5(x,v)):image(sigma,upsilon,h,u)
-sg@th1:=[x:upsilon]t6(x):surjective(sigma,upsilon,[x:sigma]<<x>f>g)
--surj
-+bij
-g@[bf:bijective(sigma,tau,f)][bg:bijective(tau,upsilon,g)]
-h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
-t1:=th4"e.inj"(f,g,ande1(injective(f),surjective(f),bf),ande1(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):injective(sigma,upsilon,h)
-t2:=th1"e.surj"(f,g,ande2(injective(f),surjective(f),bf),ande2(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):surjective(sigma,upsilon,h)
-th1:=andi(injective(sigma,upsilon,h),surjective(sigma,upsilon,h),t1,t2):bijective(sigma,upsilon,[x:sigma]<<x>f>g)
--bij
-tau@[f:[x:sigma]tau][g:[x:sigma]tau][i:is([x:sigma]tau,f,g)][s:sigma]
-fise:=isp([x:sigma]tau,[y:[x:sigma]tau]is(tau,<s>f,<s>y),f,g,refis(tau,<s>f),i):is(tau,<s>f,<s>g)
-g@[i:[x:sigma]is(tau,<x>f,<x>g)]
-fisi:='prim':is([x:sigma]tau,f,g)
-+fis
-g@[i:is([x:sigma]tau,f,g)][s:sigma][t:sigma][j:is(s,t)]
-th1:=tris(tau,<s>f,<t>f,<t>g,isf(f,s,t,j),fise(i,t)):is(tau,<s>f,<t>g)
--fis
-p@ot:='prim':'type'
-[o1:ot]
-in:='prim':sigma
-inp:='prim':<in>p
-p@otax1:='prim':injective(ot,sigma,[x:ot]in(x))
-[s:sigma][sp:<s>p]
-otax2:='prim':image(ot,sigma,[x:ot]in(x),s)
-o1@[o2:ot][i:is(ot,o1,o2)]
-isini:=isf(ot,sigma,[x:ot]in(x),o1,o2,i):is(in(o1),in(o2))
-o2@[i:is(in(o1),in(o2))]
-isine:=isfe(ot,sigma,[x:ot]in(x),otax1,o1,o2,i):is(ot,o1,o2)
-sp@out:=soft(ot,sigma,[x:ot]in(x),otax1,s,otax2):ot
-[t:sigma][tp:<t>p][i:is(s,t)]
-isouti:=isinv(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(ot,out(s,sp),out(t,tp))
-tp@[i:is(ot,out(s,sp),out(t,tp))]
-isoute:=isinve(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(s,t)
-o1@isoutin:=tris(ot,o1,soft(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1)),out(in(o1),inp(o1)),isst1(ot,sigma,[x:ot]in(x),otax1,o1),isinv(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1),in(o1),otax2(in(o1),inp(o1)),refis(sigma,in(o1)))):is(ot,o1,out(in(o1),inp(o1)))
-sp@isinout:=ists1(ot,sigma,[x:ot]in(x),otax1,s,otax2):is(s,in(out(s,sp)))
-tau@pairtype:='prim':'type'
-[s:sigma][t:tau]
-pair:='prim':pairtype
-tau@[p1:pairtype]
-first:='prim':sigma
-second:='prim':tau
-pairis1:='prim':is(pairtype,pair(first,second),p1)
-pairis2:=symis(pairtype,pair(first,second),p1,pairis1):is(pairtype,p1,pair(first,second))
-t@firstis1:='prim':is(sigma,first(pair),s)
-firstis2:=symis(sigma,first(pair),s,firstis1):is(sigma,s,first(pair))
-secondis1:='prim':is(tau,second(pair),t)
-secondis2:=symis(tau,second(pair),t,secondis1):is(tau,t,second(pair))
-a@[ksi:'type'][x:ksi][y:ksi]
-+ite
-[z:ksi]
-prop1:=and(imp(a,is(ksi,z,x)),imp(not(a),is(ksi,z,y))):'prop'
-y@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t1:=ande1(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(a,is(ksi,x1,x))
-t2:=mp(a,is(ksi,x1,x),a1,t1):is(ksi,x1,x)
-t3:=t2(y1,x1,py1,px1):is(ksi,y1,x)
-t4:=tris2(ksi,x1,y1,x,t2,t3):is(ksi,x1,y1)
-a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
-t6:=[x1:a]refis(ksi,x):imp(a,is(ksi,x,x))
-t7:=th2"l.imp"(not(a),is(ksi,x,y),weli(a,a1)):imp(not(a),is(ksi,x,y))
-t8:=andi(imp(a,is(ksi,x,x)),imp(not(a),is(ksi,x,y)),t6,t7):prop1(x)
-t9:=somei(ksi,[t:ksi]prop1(t),x,t8):some(ksi,[t:ksi]prop1(t))
-t10:=onei(ksi,[t:ksi]prop1(t),t5,t9):one(ksi,[t:ksi]prop1(t))
-y@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t11:=ande2(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(not(a),is(ksi,x1,y))
-t12:=mp(not(a),is(ksi,x1,y),n,t11):is(ksi,x1,y)
-t13:=t12(y1,x1,py1,px1):is(ksi,y1,y)
-t14:=tris2(ksi,x1,y1,y,t12,t13):is(ksi,x1,y1)
-n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
-t16:=[x1:not(a)]refis(ksi,y):imp(not(a),is(ksi,y,y))
-t17:=th2"l.imp"(a,is(ksi,y,x),n):imp(a,is(ksi,y,x))
-t18:=andi(imp(a,is(ksi,y,x)),imp(not(a),is(ksi,y,y)),t17,t16):prop1(y)
-t19:=somei(ksi,[t:ksi]prop1(t),y,t18):some(ksi,[t:ksi]prop1(t))
-t20:=onei(ksi,[t:ksi]prop1(t),t15,t19):one(ksi,[t:ksi]prop1(t))
-y@t21:=th1"l.imp"(a,one(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one(ksi,[t:ksi]prop1(t))
--ite
-ite:=ind(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
-+*ite
-y@t22:=oneax(ksi,[t:ksi]prop1(t),t21):prop1(ite)
-t23:=ande1(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(a,is(ksi,ite,x))
-t24:=ande2(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(not(a),is(ksi,ite,y))
--ite
-y@[a1:a]
-itet:=mp(a,is(ksi,ite,x),a1,t23".ite"):is(ksi,ite,x)
-y@[n:not(a)]
-itef:=mp(not(a),is(ksi,ite,y),n,t24".ite"):is(ksi,ite,y)
-sigma@[s0:sigma][t0:sigma]
-+wissel
-[s:sigma]
-wa:=ite(is(s,s0),sigma,t0,s):sigma
-[i:is(s,s0)]
-t1:=itet(is(s,s0),sigma,t0,s,i):is(wa,t0)
-s@[n:not(is(s,s0))]
-t2:=itef(is(s,s0),sigma,t0,s,n):is(wa,s)
-s@wb:=ite(is(s,t0),sigma,s0,wa):sigma
-[i:is(s,t0)]
-t3:=itet(is(s,t0),sigma,s0,wa,i):is(wb,s0)
-s@[n:not(is(s,t0))]
-t4:=itef(is(s,t0),sigma,s0,wa,n):is(wb,wa)
-s@[i:is(s,s0)][j:is(s0,t0)]
-t5:=tris(wb,s0,t0,t3(tris(s,s0,t0,i,j)),j):is(wb,t0)
-i@[n:not(is(s0,t0))]
-t6:=tris(wb,wa,t0,t4(th2"e.notis"(s0,t0,s,n,i)),t1(i)):is(wb,t0)
-i@t7:=th1"l.imp"(is(s0,t0),is(wb,t0),[t:is(s0,t0)]t5(t),[t:not(is(s0,t0))]t6(t)):is(wb,t0)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-t8:=tris(wb,wa,s,t4(o),t2(n)):is(wb,s)
--wissel
-wissel:=[x:sigma]wb".wissel"(x):[x:sigma]sigma
-[s:sigma][i:is(s,s0)]
-iswissel1:=t7".wissel"(s,i):is(<s>wissel,t0)
-s@[i:is(s,t0)]
-iswissel2:=t3".wissel"(s,i):is(<s>wissel,s0)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-iswissel3:=t8".wissel"(s,n,o):is(<s>wissel,s)
-+*wissel
-s@[t:sigma][i:is(wb(s),wb(t))][n:not(is(s,t))][j:is(s,s0)]
-t9:=symnotis(s0,t,th1"e.notis"(s,t,s0,n,j)):not(is(t,s0))
-[k:is(s0,t0)]
-t10:=th3"e.notis"(t,s0,t0,t9,k):not(is(t,t0))
-t11:=tris(wb(s),wb(t),t,i,t8(t,t9,t10)):is(wb(s),t)
-t12:=<tris1(t,t0,wb(s),t11,t7(j))>t10:con
-j@t13:=[v:is(s0,t0)]t12(v):not(is(s0,t0))
-[k:is(t,t0)]
-t14:=tris(wb(s),wb(t),s0,i,t3(t,k)):is(wb(s),s0)
-t15:=t12(tris1(s0,t0,wb(s),t14,t7(j))):con
-j@t16:=[v:is(t,t0)]t15(v):not(is(t,t0))
-t17:=tris(wb(s),wb(t),t,i,t8(t,t9,t16)):is(wb(s),t)
-t18:=t15(tris1(t,t0,wb(s),t17,t7(j))):con
-n@t19:=[v:is(s,s0)]t18(v):not(is(s,s0))
-t20:=t19(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,s0))
-[j:is(s,t0)]
-t21:=symnotis(t0,t,th1"e.notis"(s,t,t0,n,j)):not(is(t,t0))
-t22:=tris(wb(s),wb(t),t,i,t8(t,t20,t21)):is(wb(s),t)
-t23:=<tris1(t,s0,wb(s),t22,t3(j))>t20:con
-n@t24:=[v:is(s,t0)]t23(v):not(is(s,t0))
-t25:=t24(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,t0))
-t26:=tris(wb(s),wb(t),t,i,t8(t,t20,t25)):is(wb(s),t)
-t27:=<tris1(s,t,wb(s),t8(t19,t24),t26)>n:con
-i@t28:=et(is(s,t),[v:not(is(s,t))]t27(v)):is(s,t)
-t0@th1:=[x:sigma][y:sigma][v:is(wb(x),wb(y))]t28(x,y,v):injective(sigma,sigma,wissel)
-s@[i:is(s,s0)]
-t29:=tris2(s,wb(t0),s0,i,t3(t0,refis(t0))):is(s,wb(t0))
-t30:=somei(sigma,[x:sigma]is(s,wb(x)),t0,t29):image(sigma,sigma,wissel,s)
-s@[i:is(s,t0)]
-t31:=tris2(s,wb(s0),t0,i,t7(s0,refis(s0))):is(s,wb(s0))
-t32:=somei(sigma,[x:sigma]is(s,wb(x)),s0,t31):image(sigma,sigma,wissel,s)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-t33:=symis(wb(s),s,t8(n,o)):is(s,wb(s))
-t34:=somei(sigma,[x:sigma]is(s,wb(x)),s,t33):image(sigma,sigma,wissel,s)
-n@t35:=th1"l.imp"(is(s,t0),image(sigma,sigma,wissel,s),[v:is(s,t0)]t32(v),[v:not(is(s,t0))]t34(v)):image(sigma,sigma,wissel,s)
-s@t36:=th1"l.imp"(is(s,s0),image(sigma,sigma,wissel,s),[v:is(s,s0)]t30(v),[v:not(is(s,s0))]t35(v)):image(sigma,sigma,wissel,s)
-t0@th2:=[x:sigma]t36(x):surjective(sigma,sigma,wissel)
-th3:=andi(injective(sigma,sigma,wissel),surjective(sigma,sigma,wissel),th1,th2):bijective(sigma,sigma,wissel)
--wissel
-tau@[f:[x:sigma]tau][s0:sigma][t0:sigma]
-changef:=[x:sigma]<<x>wissel(s0,t0)>f:[x:sigma]tau
-[s:sigma][i:is(s,s0)]
-changef1:=isf(sigma,tau,f,<s>wissel(s0,t0),t0,iswissel1(s0,t0,s,i)):is(tau,<s>changef,<t0>f)
-s@[i:is(s,t0)]
-changef2:=isf(sigma,tau,f,<s>wissel(s0,t0),s0,iswissel2(s0,t0,s,i)):is(tau,<s>changef,<s0>f)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-changef3:=isf(sigma,tau,f,<s>wissel(s0,t0),s,iswissel3(s0,t0,s,n,o)):is(tau,<s>changef,<s>f)
-+*wissel
-t0@[i:injective(f)]
-th4:=th4"e.inj"(sigma,sigma,tau,wissel(s0,t0),f,th1(s0,t0),i):injective(changef)
-t0@[s:surjective(f)]
-th5:=th1"e.surj"(sigma,sigma,tau,wissel(s0,t0),f,th2(s0,t0),s):surjective(changef)
-t0@[b:bijective(f)]
-th6:=th1"e.bij"(sigma,sigma,tau,wissel(s0,t0),f,th3(s0,t0),b):bijective(changef)
--wissel
--e
-+r
-a@[b:[x:a]'prop']
-imp:=b:'prop'
-[a1:a][i:imp(a,b)]
-mp:=<a1>i:<a1>b
-+imp
-b@[n:not(a)]
-%set etared
-th2:=[x:a]cone(<x>b,mp"l"(a,con,x,n)):imp(a,b)
-%reset etared
--imp
-b@ec:=[x:a]not(<x>b):'prop'
-[n:not(a)]
-eci1:=[x:a]cone(not(<x>b),mp"l"(a,con,x,n)):ec(a,b)
-b@[a1:and(a,b)]
-ande2:=<ande1(a,b,a1)>ande2"l"(a,b,a1):<ande1(a,b,a1)>b
-a@[ksi:'type']
-+ite
-[x1:ksi][y1:ksi]
-is:=is"l.e"(ksi,x1,y1):'prop'
--ite
-[x:[t:a]ksi][y:[t:not(a)]ksi][i:[t:a][u:a]is".ite"(<t>x,<u>x)][j:[t:not(a)][u:not(a)]is".ite"(<t>y,<u>y)]
-+*ite
-j@[z:ksi]
-prop1:=and(imp(a,[t:a]is(z,<t>x)),imp(not(a),[t:not(a)]is(z,<t>y))):'prop'
-j@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t1:=ande1"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(a,[t:a]is(x1,<t>x))
-t2:=mp(a,[t:a]is(x1,<t>x),a1,t1):is(x1,<a1>x)
-t3:=t2(y1,x1,py1,px1):is(y1,<a1>x)
-t4:=tris2"l.e"(ksi,x1,y1,<a1>x,t2,t3):is(x1,y1)
-a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
-t6:=<a1>i:imp(a,[t:a]is(<a1>x,<t>x))
-t7:=th2"r.imp"(not(a),[t:not(a)]is(<a1>x,<t>y),weli(a,a1)):imp(not(a),[t:not(a)]is(<a1>x,<t>y))
-t8:=andi(imp(a,[t:a]is(<a1>x,<t>x)),imp(not(a),[t:not(a)]is(<a1>x,<t>y)),t6,t7):prop1(<a1>x)
-t9:=somei(ksi,[t:ksi]prop1(t),<a1>x,t8):some(ksi,[t:ksi]prop1(t))
-t10:=onei"l.e"(ksi,[t:ksi]prop1(t),t5,t9):one"l.e"(ksi,[t:ksi]prop1(t))
-j@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t11:=ande2"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(not(a),[t:not(a)]is(x1,<t>y))
-t12:=mp(not(a),[t:not(a)]is(x1,<t>y),n,t11):is(x1,<n>y)
-t13:=t12(y1,x1,py1,px1):is(y1,<n>y)
-t14:=tris2"l.e"(ksi,x1,y1,<n>y,t12,t13):is(x1,y1)
-n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
-t16:=<n>j:imp(not(a),[t:not(a)]is(<n>y,<t>y))
-t17:=th2"r.imp"(a,[t:a]is(<n>y,<t>x),n):imp(a,[t:a]is(<n>y,<t>x))
-t18:=andi"l"(imp(a,[t:a]is(<n>y,<t>x)),imp(not(a),[t:not(a)]is(<n>y,<t>y)),t17,t16):prop1(<n>y)
-t19:=somei(ksi,[t:ksi]prop1(t),<n>y,t18):some(ksi,[t:ksi]prop1(t))
-t20:=onei"l.e"(ksi,[t:ksi]prop1(t),t15,t19):one"l.e"(ksi,[t:ksi]prop1(t))
-j@t21:=th1"l.imp"(a,one"l.e"(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one"l.e"(ksi,[t:ksi]prop1(t))
--ite
-j@ite:=ind"l.e"(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
-+*ite
-j@t22:=oneax"l.e"(ksi,[t:ksi]prop1(t),t21):prop1(ite)
-t23:=ande1"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(a,[t:a]is(ite,<t>x))
-t24:=ande2"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(not(a),[t:not(a)]is(ite,<t>y))
--ite
-j@[a1:a]
-itet:=mp(a,[t:a]is".ite"(ite,<t>x),a1,t23".ite"):is".ite"(ksi,ite,<a1>x)
-j@[n:not(a)]
-itef:=mp(not(a),[t:not(a)]is".ite"(ite,<t>y),n,t24".ite"):is".ite"(ksi,ite,<n>y)
--r
-+*e
-+st
-sigma@set:='prim':'type'
-[s:sigma][s0:set]
-esti:='prim':'prop'
-p@setof:='prim':set
-[s:sigma][sp:<s>p]
-estii:='prim':esti(s,setof(p))
-s@[e:esti(s,setof(p))]
-estie:='prim':<s>p
-sigma@[s0:set]
-empty:=non([x:sigma]esti(x,s0)):'prop'
-nonempty:=some([x:sigma]esti(x,s0)):'prop'
-[n:[x:sigma]not(esti(x,s0))]
-emptyi:=n:empty(s0)
-s0@[e:empty(s0)][s:sigma]
-emptye:=<s>e:not(esti(s,s0))
-s0@[s:sigma][ses0:esti(s,s0)]
-nonemptyi:=somei([x:sigma]esti(x,s0),s,ses0):nonempty(s0)
-s0@[n:nonempty(s0)][x:'prop'][x1:[y:sigma][z:esti(y,s0)]x]
-nonemptyapp:=someapp([y:sigma]esti(y,s0),n,x,x1):x
-s0@[t0:set]
-incl:=all([x:sigma]imp(esti(x,s0),esti(x,t0))):'prop'
-[e:[x:sigma][y:esti(x,s0)]esti(x,t0)]
-incli:=e:incl(s0,t0)
-t0@[i:incl(s0,t0)][s:sigma][ses0:esti(s,s0)]
-incle:=<ses0><s>i:esti(s,t0)
-s0@refincl:=[x:sigma][y:esti(x,s0)]y:incl(s0,s0)
-t0@disj:=all([x:sigma]ec(esti(x,s0),esti(x,t0))):'prop'
-[n:[x:sigma][y:esti(x,s0)]not(esti(x,t0))]
-disji1:=n:disj(s0,t0)
-t0@[n:[x:sigma][y:esti(x,t0)]not(esti(x,s0))]
-disji2:=[x:sigma]th2"l.ec"(esti(x,s0),esti(x,t0),<x>n):disj(s0,t0)
-t0@[d:disj(s0,t0)][s:sigma][ses0:esti(s,s0)]
-disje1:=ece1(esti(s,s0),esti(s,t0),<s>d,ses0):not(esti(s,t0))
-s@[set0:esti(s,t0)]
-disje2:=ece2(esti(s,s0),esti(s,t0),<s>d,set0):not(esti(s,s0))
-t0@[d:disj(s0,t0)]
-symdisj:=[x:sigma][y:esti(x,t0)]disje2(d,x,y):disj(t0,s0)
-+disj
-t0@[s:sigma][ses0:esti(s,s0)][set0:esti(s,t0)]
-th1:=th1"l.all"([x:sigma]ec(esti(x,s0),esti(x,t0)),s,th4"l.imp"(esti(s,s0),not(esti(s,t0)),ses0,weli(esti(s,t0),set0))):not(disj(s0,t0))
-th2:=th1(t0,s0,s,set0,ses0):not(disj(t0,s0))
--disj
-t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
-issete1:=isp(set,[x:set]esti(s,x),s0,t0,ses0,i):esti(s,t0)
-s@[set0:esti(s,t0)]
-issete2:=isp1(set,[x:set]esti(s,x),t0,s0,set0,i):esti(s,s0)
-+isset
-i@th1:=[x:sigma][y:esti(x,s0)]issete1(x,y):incl(s0,t0)
-th2:=[x:sigma][y:esti(x,t0)]issete2(x,y):incl(t0,s0)
--isset
-t0@[i:incl(s0,t0)][j:incl(t0,s0)]
-isseti:='prim':is(set,s0,t0)
-+*isset
-t0@[s:sigma][ses0:esti(s,s0)][n:not(esti(s,t0))]
-th3:=th3"l.imp"(is(set,s0,t0),esti(s,t0),n,[t:is(set,s0,t0)]issete1(t,s,ses0)):not(is(set,s0,t0))
-th4:=symnotis(set,s0,t0,th3):not(is(set,t0,s0))
-s@nissetprop:=and(esti(s,s0),not(esti(s,t0))):'prop'
-[n:not(nissetprop(s0,t0,s))][e:esti(s,s0)]
-t1:=et(esti(s,t0),th3"l.and"(esti(s,s0),not(esti(s,t0)),n,e)):esti(s,t0)
-t0@[n:not(is(set,s0,t0))][m:not(some([x:sigma]nissetprop(s0,t0,x)))][l:non([x:sigma]nissetprop(t0,s0,x))][s:sigma]
-t2:=th4"l.some"([x:sigma]nissetprop(s0,t0,x),m,s):not(nissetprop(s0,t0,s))
-t3:=<s>l:not(nissetprop(t0,s0,s))
-l@t4:=isseti(s0,t0,[x:sigma][y:esti(x,s0)]t1(s0,t0,x,t2(x),y),[x:sigma][y:esti(x,t0)]t1(t0,s0,x,t3(x),y)):is(set,s0,t0)
-m@t5:=th3"l.imp"(non([x:sigma]nissetprop(t0,s0,x)),is(set,s0,t0),n,[y:non([x:sigma]nissetprop(t0,s0,x))]t4(y)):some([x:sigma]nissetprop(t0,s0,x))
-n@th5:=th1"l.or"(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)),[y:not(some([x:sigma]nissetprop(s0,t0,x)))]t5(y)):or(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)))
--isset
-sigma@[alpha:'type'][sa:[x:alpha]set]
-unmore:=setof([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa))):set
-[s:sigma][a:alpha][seasa:esti(s,<a>sa)]
-eunmore1:=estii([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa)),s,somei(alpha,[y:alpha]esti(s,<y>sa),a,seasa)):esti(s,unmore(sa))
-s@[seun:esti(s,unmore(sa))][x:'prop'][x1:[y:alpha][z:esti(s,<y>sa)]x]
-unmoreapp:=someapp(alpha,[y:alpha]esti(s,<y>sa),estie([z:sigma]some(alpha,[y:alpha]esti(z,<y>sa)),s,seun),x,x1):x
-+eq
-sigma@[r:[x:sigma][y:sigma]'prop'][refr1:[x:sigma]<x><x>r][symr1:[x:sigma][y:sigma][t:<y><x>r]<x><y>r][trr1:[x:sigma][y:sigma][z:sigma][t:<y><x>r][u:<z><y>r]<z><x>r][s:sigma]
-refr:=<s>refr1:<s><s>r
-[t:sigma][tsr:<t><s>r]
-symr:=<tsr><t><s>symr1:<s><t>r
-t@[u:sigma][tsr:<t><s>r][utr:<u><t>r]
-trr:=<utr><tsr><u><t><s>trr1:<u><s>r
-u@[sur:<s><u>r][tur:<t><u>r]
-tr1r:=trr(s,u,t,symr(u,s,sur),tur):<t><s>r
-u@[usr:<u><s>r][utr:<u><t>r]
-tr2r:=trr(s,u,t,usr,symr(t,u,utr)):<t><s>r
-s@ecelt:=setof(<s>r):set
-+1
-th1:=estii(<s>r,s,refr):esti(s,ecelt(s))
-t@[tsr:<t><s>r]
-th2:=estii(<s>r,t,tsr):esti(t,ecelt(s))
-t@[e:esti(t,ecelt(s))]
-th3:=estie(<s>r,t,e):<t><s>r
-tsr@[u:sigma][e:esti(u,ecelt(s))]
-t1:=th2(t,u,tr1r(t,u,s,tsr,th3(u,e))):esti(u,ecelt(t))
-tsr@th4:=isseti(ecelt(s),ecelt(t),[x:sigma][y:esti(x,ecelt(s))]t1(x,y),[x:sigma][y:esti(x,ecelt(t))]t1(t,s,symr(tsr),x,y)):is(set,ecelt(s),ecelt(t))
-t@[n:not(<t><s>r)][u:sigma][e:esti(u,ecelt(s))]
-t2:=th3"l.imp"(esti(u,ecelt(t)),<t><s>r,n,[x:esti(u,ecelt(t))]tr2r(s,t,u,th3(u,e),th3(t,u,x))):not(esti(u,ecelt(t)))
-n@th5:=[x:sigma][y:esti(x,ecelt(s))]t2(x,y):disj(ecelt(s),ecelt(t))
-s@th6:=nonemptyi(ecelt(s),s,th1):nonempty(ecelt(s))
--1
-trr1@[s0:set][s:sigma]
-ecp:=is(set,s0,ecelt(s)):'prop'
-s0@anec:=some([x:sigma]ecp(x)):'prop'
-+2
-trr1@[s:sigma]
-th1:=somei([x:sigma]ecp(ecelt(s),x),s,refis(set,ecelt(s))):anec(ecelt(s))
--2
-[ecs0:anec(s0)]
-+*2
-ecs0@[s:sigma][ses0:esti(s,s0)][t:sigma][e:ecp(s0,t)]
-t1:=issete1(s0,ecelt(t),e,s,ses0):esti(s,ecelt(t))
-t2:=th4"eq.1"(t,s,th3"eq.1"(t,s,t1)):is(set,ecelt(t),ecelt(s))
-t3:=tris(set,s0,ecelt(t),ecelt(s),e,t2):is(set,s0,ecelt(s))
-ses0@th2:=someapp([x:sigma]ecp(x),ecs0,is(set,s0,ecelt(s)),[x:sigma][y:ecp(x)]t3(x,y)):is(set,s0,ecelt(s))
-[t:sigma][tes0:esti(t,s0)]
-th3:=th3"eq.1"(s,t,issete1(s0,ecelt(s),th2,t,tes0)):<t><s>r
-t@[tsr:<t><s>r]
-th4:=issete2(s0,ecelt(s),th2,t,th2"eq.1"(s,t,tsr)):esti(t,s0)
-ecs0@[s:sigma][e:ecp(s0,s)]
-t4:=isp(set,[x:set]nonempty(x),ecelt(s),s0,th6"eq.1"(s),symis(set,s0,ecelt(s),e)):nonempty(s0)
-ecs0@th5:=someapp([x:sigma]ecp(x),ecs0,nonempty(s0),[x:sigma][y:ecp(x)]t4(x,y)):nonempty(s0)
--2
-+3
-ecs0@[t0:set][ect0:anec(t0)][s:sigma][ses0:esti(s,s0)][t:sigma][tet0:esti(t,t0)][tsr:<t><s>r]
-th1:=tr3is(set,s0,ecelt(s),ecelt(t),t0,th2"eq.2"(s0,ecs0,s,ses0),th4"eq.1"(s,t,tsr),symis(set,t0,ecelt(t),th2"eq.2"(t0,ect0,t,tet0))):is(set,s0,t0)
-tet0@[n:not(<t><s>r)]
-t1:=isp1(set,[x:set]disj(x,ecelt(t)),ecelt(s),s0,th5"eq.1"(s,t,n),th2"eq.2"(s0,ecs0,s,ses0)):disj(s0,ecelt(t))
-th2:=isp1(set,[x:set]disj(s0,x),ecelt(t),t0,t1,th2"eq.2"(t0,ect0,t,tet0)):disj(s0,t0)
-t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
-t2:=issete1(s0,t0,i,s,ses0):esti(s,t0)
-t3:=th1"st.disj"(s0,t0,s,ses0,t2):not(disj(s0,t0))
-i@th3:=nonemptyapp(s0,th5"eq.2"(s0,ecs0),not(disj(s0,t0)),[x:sigma][y:esti(x,s0)]t3(x,y)):not(disj(s0,t0))
--3
-trr1@ect:=ot(set,[x:set]anec(x)):'type'
-ecs0@ectset:=out(set,[x:set]anec(x),s0,ecs0):ect
-trr1@[s:sigma]
-ectelt:=ectset(ecelt(s),th1".2"(s)):ect
-trr1@[e:ect]
-ecect:=in(set,[x:set]anec(x),e):set
-+4
-th1:=inp(set,[x:set]anec(x),e):anec(ecect(e))
-th2:=th5"eq.2"(ecect(e),th1):nonempty(ecect(e))
-[x:'prop'][x1:[y:sigma][z:esti(y,ecect(e))]x]
-th3:=nonemptyapp(ecect(e),th2,x,x1):x
-s@th4:=isinout(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s)):is(set,ecelt(s),ecect(ectelt(s)))
-th5:=issete1(ecelt(s),ecect(ectelt(s)),th4,s,th1"eq.1"(s)):esti(s,ecect(ectelt(s)))
-th6:=eunmore1(ect,[x:ect]ecect(x),s,ectelt(s),th5):esti(s,unmore(ect,[x:ect]ecect(x)))
-e@[s:sigma][see:esti(s,ecect(e))][t:sigma][tee:esti(t,ecect(e))]
-th7:=th3"eq.2"(ecect(e),th1,s,see,t,tee):<t><s>r
-t@[tsr:<t><s>r]
-th8:=th4"eq.2"(ecect(e),th1,s,see,t,tsr):esti(t,ecect(e))
--4
-+5
-[f:ect][i:is(ect,e,f)]
-th1:=isini(set,[x:set]anec(x),e,f,i):is(set,ecect(e),ecect(f))
-f@[i:is(set,ecect(e),ecect(f))]
-th2:=isine(set,[x:set]anec(x),e,f,i):is(ect,e,f)
-f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))][tsr:<t><s>r]
-th3:=th2(th1"eq.3"(ecect(e),th1"eq.4"(e),ecect(f),th1"eq.4"(f),s,see,t,tef,tsr)):is(ect,e,f)
-see@[i:is(ect,e,f)]
-th4:=issete1(ecect(e),ecect(f),th1(i),s,see):esti(s,ecect(f))
-tef@[i:is(ect,e,f)]
-th5:=th3"eq.2"(ecect(f),th1"eq.4"(f),s,th4(i),t,tef):<t><s>r
-trr1@[s:sigma][t:sigma][tsr:<t><s>r]
-th6:=isouti(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s),ecelt(t),th1"eq.2"(t),th4"eq.1"(s,t,tsr)):is(ect,ectelt(s),ectelt(t))
--5
-trr1@[alpha:'type'][fu:[x:sigma]alpha]
-fixfu:=[x:sigma][y:sigma][z:<y><x>r]is(alpha,<x>fu,<y>fu):'prop'
-+10
-[ff:fixfu][e:ect][a1:alpha][s:sigma]
-prop1:=and(esti(s,ecect(e)),is(alpha,<s>fu,a1)):'prop'
-a1@prop2:=some([x:sigma]prop1(x)):'prop'
-e@[s:sigma][see:esti(s,ecect(e))]
-t1:=andi(esti(s,ecect(e)),is(alpha,<s>fu,<s>fu),see,refis(alpha,<s>fu)):prop1(<s>fu,s)
-t2:=somei([x:sigma]prop1(<s>fu,x),s,t1):prop2(<s>fu)
-t3:=somei(alpha,[x:alpha]prop2(x),<s>fu,t2):some(alpha,[x:alpha]prop2(x))
-e@t4:=th3"eq.4"(e,some(alpha,[x:alpha]prop2(x)),[x:sigma][y:esti(x,ecect(e))]t3(x,y)):some(alpha,[x:alpha]prop2(x))
-a1@[b1:alpha][pa1:prop2(a1)][pb1:prop2(b1)][s:sigma][pa1s:prop1(a1,s)][t:sigma][pb1t:prop1(b1,t)]
-t5:=ande1(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):esti(s,ecect(e))
-t6:=ande1(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):esti(t,ecect(e))
-t7:=th7"eq.4"(e,s,t5,t,t6):<t><s>r
-t8:=ande2(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):is(alpha,<s>fu,a1)
-t9:=ande2(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):is(alpha,<t>fu,b1)
-t10:=tr3is(alpha,a1,<s>fu,<t>fu,b1,symis(alpha,<s>fu,a1,t8),<t7><t><s>ff,t9):is(alpha,a1,b1)
-pa1s@t11:=someapp([x:sigma]prop1(b1,x),pb1,is(alpha,a1,b1),[x:sigma][y:prop1(b1,x)]t10(x,y)):is(alpha,a1,b1)
-pb1@t12:=someapp([x:sigma]prop1(a1,x),pa1,is(alpha,a1,b1),[x:sigma][y:prop1(a1,x)]t11(x,y)):is(alpha,a1,b1)
-e@t13:=[x:alpha][y:alpha][u:prop2(x)][v:prop2(y)]t12(x,y,u,v):amone(alpha,[x:alpha]prop2(x))
-t14:=onei(alpha,[x:alpha]prop2(x),t13,t4):one(alpha,[x:alpha]prop2(x))
--10
-e".10"@indeq:=ind(alpha,[x:alpha]prop2".10"(x),t14".10"):alpha
-+*10
-e@th1:=oneax(alpha,[x:alpha]prop2(x),t14):some([x:sigma]and(esti(x,ecect(e)),is(alpha,<x>fu,indeq)))
-[s:sigma][see:esti(s,ecect(e))]
-th2:=t12(<s>fu,indeq,t2(s,see),th1):is(alpha,<s>fu,indeq)
-ff@[s:sigma]
-th3:=th2(ectelt(s),s,th5"eq.4"(s)):is(alpha,<s>fu,indeq(ectelt(s)))
--10
-alpha@[fu2:[x:sigma][y:sigma]alpha]
-fixfu2:=[x:sigma][y:sigma][z:sigma][u:sigma][v:<y><x>r][w:<u><z>r]is(alpha,<z><x>fu2,<u><y>fu2):'prop'
-+11
-[ff2:fixfu2][s:sigma][t:sigma][tsr:<t><s>r][u:sigma]
-t1:=<refr(u)><tsr><u><u><t><s>ff2:is(alpha,<u><s>fu2,<u><t>fu2)
-tsr@t2:=fisi(sigma,alpha,<s>fu2,<t>fu2,[x:sigma]t1(x)):is([x:sigma]alpha,<s>fu2,<t>fu2)
-ff2@[e:ect]
-i:=indeq([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e):[x:sigma]alpha
-[s:sigma][t:sigma][tsr:<t><s>r][u:sigma][uee:esti(u,ecect(e))]
-t3:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,u,uee):is([x:sigma]alpha,<u>fu2,i)
-t4:=fise(alpha,<u>fu2,i,t3,s):is(alpha,<s><u>fu2,<s>i)
-t5:=fise(alpha,<u>fu2,i,t3,t):is(alpha,<t><u>fu2,<t>i)
-t6:=<tsr><refr(u)><t><s><u><u>ff2:is(alpha,<s><u>fu2,<t><u>fu2)
-t7:=tr3is(alpha,<s>i,<s><u>fu2,<t><u>fu2,<t>i,symis(alpha,<s><u>fu2,<s>i,t4),t6,t5):is(alpha,<s>i,<t>i)
-tsr@t8:=th3"eq.4"(e,is(alpha,<s>i,<t>i),[x:sigma][y:esti(x,ecect(e))]t7(x,y)):is(alpha,<s>i,<t>i)
--11
-e".11"@[f:ect]
-indeq2:=indeq(i".11",[x:sigma][y:sigma][z:<y><x>r]t8".11"(x,y,z),f):alpha
-+*11
-f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))]
-t9:=th2"eq.10"(i,[x:sigma][y:sigma][z:<y><x>r]t8(x,y,z),f,t,tef):is(alpha,<t>i,indeq2(e,f))
-t10:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,s,see):is([x:sigma]alpha,<s>fu2,i)
-t11:=fise(alpha,<s>fu2,i,t10,t):is(alpha,<t><s>fu2,<t>i)
-th1:=tris(alpha,<t><s>fu2,<t>i,indeq2,t11,t9):is(alpha,<t><s>fu2,indeq2(e,f))
-ff2@[s:sigma][t:sigma]
-th2:=th1(ectelt(s),ectelt(t),s,th5"eq.4"(s),t,th5"eq.4"(t)):is(alpha,<t><s>fu2,indeq2(ectelt(s),ectelt(t)))
--11
-+landau
-+n
-@nat:='prim':'type'
-[x:nat][y:nat]
-is:=is"e"(nat,x,y):'prop'
-nis:=not(is(x,y)):'prop'
-x@[s:set(nat)]
-in:=esti(nat,x,s):'prop'
-@[p:[x:nat]'prop']
-some:=some"l"(nat,p):'prop'
-all:=all"l"(nat,p):'prop'
-one:=one"e"(nat,p):'prop'
-@1:='prim':nat
-suc:='prim':[x:nat]nat
-[x:nat][y:nat][i:is(x,y)]
-ax2:=isf(nat,nat,suc,x,y,i):is(<x>suc,<y>suc)
-@ax3:='prim':[x:nat]nis(<x>suc,1)
-ax4:='prim':[x:nat][y:nat][u:is(<x>suc,<y>suc)]is(x,y)
-[s:set(nat)]
-cond1:=in(1,s):'prop'
-cond2:=all([x:nat]imp(in(x,s),in(<x>suc,s))):'prop'
-@ax5:='prim':[s:set(nat)][u:cond1(s)][v:cond2(s)][x:nat]in(x,s)
-[p:[x:nat]'prop'][1p:<1>p][xsp:[x:nat][y:<x>p]<<x>suc>p][x:nat]
-+i1
-s:=setof(nat,p):set(nat)
-t1:=estii(nat,p,1,1p):cond1(s)
-[y:nat][yes:in(y,s)]
-t2:=estie(nat,p,y,yes):<y>p
-t3:=estii(nat,p,<y>suc,<t2><y>xsp):in(<y>suc,s)
-x@t4:=<x><[y:nat][u:in(y,s)]t3(y,u)><t1><s>ax5:in(x,s)
--i1
-induction:=estie(nat,p,x,t4".i1"):<x>p
-@[x:nat][y:nat][n:nis(x,y)]
-+21
-[i:is(<x>suc,<y>suc)]
-t1:=<i><y><x>ax4:is(x,y)
--21
-satz1:=th3"l.imp"(is(<x>suc,<y>suc),is(x,y),n,[u:is(<x>suc,<y>suc)]t1".21"(u)):nis(<x>suc,<y>suc)
-+22
-x@prop1:=nis(<x>suc,x):'prop'
-@t1:=<1>ax3:prop1(1)
-x@[p:prop1(x)]
-t2:=satz1(<x>suc,x,p):prop1(<x>suc)
--22
-x@satz2:=induction([y:nat]prop1".22"(y),t1".22",[y:nat][u:prop1".22"(y)]t2".22"(y,u),x):nis(<x>suc,x)
-+23
-prop1:=or(is(x,1),some([u:nat]is(x,<u>suc))):'prop'
-@t1:=ori1(is(1,1),some([u:nat]is(1,<u>suc)),refis(nat,1)):prop1(1)
-x@t2:=somei(nat,[u:nat]is(<x>suc,<u>suc),x,refis(nat,<x>suc)):some([u:nat]is(<x>suc,<u>suc))
-t3:=ori2(is(<x>suc,1),some([u:nat]is(<x>suc,<u>suc)),t2):prop1(<x>suc)
-t4:=induction([y:nat]prop1(y),t1,[y:nat][u:prop1(y)]t3(y),x):prop1(x)
--23
-[n:nis(x,1)]
-satz3:=ore2(is(x,1),some([u:nat]is(x,<u>suc)),t4".23",n):some([u:nat]is(x,<u>suc))
-y@[z:nat][i:is(x,<y>suc)][j:is(x,<z>suc)]
-+*23
-j@t5:=<tris1(nat,<y>suc,<z>suc,x,i,j)><z><y>ax4:is(y,z)
-x@t6:=[y:nat][z:nat][u:is(x,<y>suc)][v:is(x,<z>suc)]t5(y,z,u,v):amone(nat,[u:nat]is(x,<u>suc))
--23
-n@satz3a:=onei(nat,[u:nat]is(x,<u>suc),t6".23",satz3):one([u:nat]is(x,<u>suc))
-+24
-x@[f:[y:nat]nat]
-prop1:=all([y:nat]is(<<y>suc>f,<<y>f>suc)):'prop'
-prop2:=and(is(<1>f,<x>suc),prop1):'prop'
-x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
-prop3:=is(<y>a,<y>b):'prop'
-pb@t1:=ande1(is(<1>a,<x>suc),prop1(a),pa):is(<1>a,<x>suc)
-t2:=ande1(is(<1>b,<x>suc),prop1(b),pb):is(<1>b,<x>suc)
-t3:=tris2(nat,<1>a,<1>b,<x>suc,t1,t2):prop3(1)
-y@[p:prop3(y)]
-t4:=ax2(<y>a,<y>b,p):is(<<y>a>suc,<<y>b>suc)
-t5:=ande2(is(<1>a,<x>suc),prop1(a),pa):prop1(a)
-t6:=ande2(is(<1>b,<x>suc),prop1(b),pb):prop1(b)
-t7:=<y>t5:is(<<y>suc>a,<<y>a>suc)
-t8:=<y>t6:is(<<y>suc>b,<<y>b>suc)
-t9:=tr3is(nat,<<y>suc>a,<<y>a>suc,<<y>b>suc,<<y>suc>b,t7,t4,symis"e"(nat,<<y>suc>b,<<y>b>suc,t8)):prop3(<y>suc)
-y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
-pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
-x@aa:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
-prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
-@t12:=[x:nat]refis(nat,<<x>suc>suc):prop1(1,suc)
-t13:=andi(is(<1>suc,<1>suc),prop1(1,suc),refis(nat,<1>suc),t12):prop2(1,suc)
-t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),suc,t13):prop4(1)
-x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
-g:=[y:nat]<<y>f>suc:[y:nat]nat
-[y:nat]
-t15:=refis(nat,<y>g):is(<y>g,<<y>f>suc)
-pf@t16:=ande1(is(<1>f,<x>suc),prop1(f),pf):is(<1>f,<x>suc)
-t17:=tris(nat,<1>g,<<1>f>suc,<<x>suc>suc,t15(1),ax2(<1>f,<x>suc,t16)):is(<1>g,<<x>suc>suc)
-y@t18:=ande2(is(<1>f,<x>suc),prop1(f),pf):prop1(f)
-t19:=<y>t18:is(<<y>suc>f,<<y>f>suc)
-t20:=tris2(nat,<<y>suc>f,<y>g,<<y>f>suc,t19,t15):is(<<y>suc>f,<y>g)
-t21:=tris(nat,<<y>suc>g,<<<y>suc>f>suc,<<y>g>suc,t15(<y>suc),ax2(<<y>suc>f,<y>g,t20)):is(<<y>suc>g,<<y>g>suc)
-pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
-t23:=andi(is(<1>g,<<x>suc>suc),prop1(<x>suc,g),t17,t22):prop2(<x>suc,g)
-t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
-p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
-x@bb:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
--24
-x@satz4:=onei([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),aa".24",bb".24"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,<x>suc),all([y:nat]is(<<y>suc>z,<<y>z>suc))))
-plus:=ind([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),satz4):[y:nat]nat
-y@pl:=<y>plus:nat
-+*24
-x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz4):prop2(plus)
--24
-x@satz4a:=ande1(is(<1>plus,<x>suc),prop1".24"(plus),t26".24"):is(pl(x,1),<x>suc)
-+*24
-x@t27:=ande2(is(<1>plus,<x>suc),prop1(plus),t26):prop1(plus)
--24
-y@satz4b:=<y>t27".24":is(pl(x,<y>suc),<pl(x,y)>suc)
-+*24
-@t28:=t11(1,plus(1),suc,t26(1),t13):is"e"([y:nat]nat,plus(1),suc)
--24
-x@satz4c:=fise(nat,nat,plus(1),suc,t28".24",x):is(pl(1,x),<x>suc)
-+*24
-x@t29:=t11(<x>suc,plus(<x>suc),[y:nat]<<y>plus>suc,t26(<x>suc),t23(bb,plus,t26)):is"e"([y:nat]nat,plus(<x>suc),[y:nat]<<y>plus>suc)
--24
-y@satz4d:=fise(nat,nat,plus(<x>suc),[z:nat]<<z>plus>suc,t29".24",y):is(pl(<x>suc,y),<pl(x,y)>suc)
-x@satz4e:=symis(nat,pl(x,1),<x>suc,satz4a):is(<x>suc,pl(x,1))
-y@satz4f:=symis(nat,pl(x,<y>suc),<pl(x,y)>suc,satz4b):is(<pl(x,y)>suc,pl(x,<y>suc))
-x@satz4g:=symis(nat,pl(1,x),<x>suc,satz4c):is(<x>suc,pl(1,x))
-y@satz4h:=symis(nat,pl(<x>suc,y),<pl(x,y)>suc,satz4d):is(<pl(x,y)>suc,pl(<x>suc,y))
-z@[i:is(x,y)]
-ispl1:=isf(nat,nat,[u:nat]pl(u,z),x,y,i):is(pl(x,z),pl(y,z))
-ispl2:=isf(nat,nat,[u:nat]pl(z,u),x,y,i):is(pl(z,x),pl(z,y))
-z@[u:nat][i:is(x,y)][j:is(z,u)]
-ispl12:=tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
-+25
-z@prop1:=is(pl(pl(x,y),z),pl(x,pl(y,z))):'prop'
-y@t1:=tr3is(nat,pl(pl(x,y),1),<pl(x,y)>suc,pl(x,<y>suc),pl(x,pl(y,1)),satz4a(pl(x,y)),satz4f,ispl2(<y>suc,pl(y,1),x,satz4e(y))):prop1(1)
-z@[p:prop1(z)]
-t2:=ax2(pl(pl(x,y),z),pl(x,pl(y,z)),p):is(<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc)
-t3:=tr4is(nat,pl(pl(x,y),<z>suc),<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc,pl(x,<pl(y,z)>suc),pl(x,pl(y,<z>suc)),satz4b(pl(x,y),z),t2,satz4f(x,pl(y,z)),ispl2(<pl(y,z)>suc,pl(y,<z>suc),x,satz4f(y,z))):prop1(<z>suc)
--25
-z@satz5:=induction([u:nat]prop1".25"(u),t1".25",[u:nat][v:prop1".25"(u)]t3".25"(u,v),z):is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl1:=satz5:is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl2:=symis(nat,pl(pl(x,y),z),pl(x,pl(y,z)),satz5):is(pl(x,pl(y,z)),pl(pl(x,y),z))
-+26
-y@prop1:=is(pl(x,y),pl(y,x)):'prop'
-t1:=satz4a(y):is(pl(y,1),<y>suc)
-t2:=satz4c(y):is(pl(1,y),<y>suc)
-t3:=tris2(nat,pl(1,y),pl(y,1),<y>suc,t2,t1):prop1(1,y)
-[p:prop1(x,y)]
-t4:=tris(nat,<pl(x,y)>suc,<pl(y,x)>suc,pl(y,<x>suc),ax2(pl(x,y),pl(y,x),p),satz4f(y,x)):is(<pl(x,y)>suc,pl(y,<x>suc))
-t5:=satz4d:is(pl(<x>suc,y),<pl(x,y)>suc)
-t6:=tris(nat,pl(<x>suc,y),<pl(x,y)>suc,pl(y,<x>suc),t5,t4):prop1(<x>suc,y)
--26
-y@satz6:=induction([z:nat]prop1".26"(z,y),t3".26",[z:nat][u:prop1".26"(z,y)]t6".26"(z,y,u),x):is(pl(x,y),pl(y,x))
-compl:=satz6:is(pl(x,y),pl(y,x))
-+*26
-x@t7:=tris(nat,pl(x,1),<x>suc,pl(1,x),satz4a,satz4g):prop1(1)
-y@[p:prop1(y)]
-t8:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,<pl(y,x)>suc,pl(<y>suc,x),satz4b,ax2(pl(x,y),pl(y,x),p),satz4h(y,x)):prop1(<y>suc)
-y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(pl(x,y),pl(y,x))
--26
-+27
-y@prop1:=nis(y,pl(x,y)):'prop'
-x@t1:=symnotis(nat,<x>suc,1,<x>ax3):nis(1,<x>suc)
-t2:=th4"e.notis"(nat,1,<x>suc,pl(x,1),t1,satz4a):prop1(1)
-y@[p:prop1(y)]
-t3:=satz1(y,pl(x,y),p):nis(<y>suc,<pl(x,y)>suc)
-t4:=th4"e.notis"(nat,<y>suc,<pl(x,y)>suc,pl(x,<y>suc),t3,satz4b):prop1(<y>suc)
--27
-y@satz7:=induction([z:nat]prop1".27"(z),t2".27",[z:nat][u:prop1".27"(z)]t4".27"(z,u),y):nis(y,pl(x,y))
-z@[n:nis(y,z)]
-+28
-prop1:=nis(pl(x,y),pl(x,z)):'prop'
-t1:=satz1(y,z,n):nis(<y>suc,<z>suc)
-t2:=th5"e.notis"(nat,<y>suc,<z>suc,pl(1,y),pl(1,z),t1,satz4g(y),satz4g(z)):prop1(1,y,z,n)
-[p:prop1(x,y,z,n)]
-t3:=satz1(pl(x,y),pl(x,z),p):nis(<pl(x,y)>suc,<pl(x,z)>suc)
-t4:=th5"e.notis"(nat,<pl(x,y)>suc,<pl(x,z)>suc,pl(<x>suc,y),pl(<x>suc,z),t3,satz4h,satz4h(z)):prop1(<x>suc,y,z,n)
--28
-satz8:=induction([u:nat]prop1".28"(u,y,z,n),t2".28",[u:nat][v:prop1".28"(u,y,z,n)]t4".28"(u,y,z,n,v),x):nis(pl(x,y),pl(x,z))
-z@[i:is(pl(x,y),pl(x,z))]
-satz8a:=th7"l.imp"(is(y,z),nis(pl(x,y),pl(x,z)),weli(is(pl(x,y),pl(x,z)),i),[u:nis(y,z)]satz8(u)):is(y,z)
-z@diffprop:=is(x,pl(y,z)):'prop'
-+*28
-y@[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]
-t5:=satz8a(y,u,v,tris1(nat,pl(y,u),pl(y,v),x,du,dv)):is(u,v)
--28
-y@satz8b:=[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]t5".28"(u,v,du,dv):amone(nat,[z:nat]is(x,pl(y,z)))
-+29
-i:=is(x,y):'prop'
-ii:=some([u:nat]diffprop(x,y,u)):'prop'
-iii:=some([v:nat]diffprop(y,x,v)):'prop'
-[one1:i][u:nat]
-t1:=tris(nat,pl(u,x),pl(x,u),pl(y,u),compl(u,x),ispl1(u,one1)):is(pl(u,x),pl(y,u))
-t2:=th3"e.notis"(nat,x,pl(u,x),pl(y,u),satz7(u,x),t1):nis(x,pl(y,u))
-one1@t3:=th5"l.some"(nat,[u:nat]diffprop(u),[u:nat]t2(u)):not(ii)
-y@t4:=th1"l.ec"(i,ii,[z:i]t3(z)):ec(i,ii)
-one1@t5:=t3(y,x,symis(nat,x,y,one1)):not(iii)
-y@t6:=th2"l.ec"(iii,i,[z:i]t5(z)):ec(iii,i)
-[two1:ii][three1:iii][u:nat][du:diffprop(x,y,u)][v:nat][dv:diffprop(y,x,v)]
-t6a:=tr4is(nat,x,pl(y,u),pl(pl(x,v),u),pl(x,pl(v,u)),pl(pl(v,u),x),du,ispl1(y,pl(x,v),u,dv),asspl1(x,v,u),compl(x,pl(v,u))):is(x,pl(pl(v,u),x))
-t7:=mp(is(x,pl(pl(v,u),x)),con,t6a,satz7(pl(v,u),x)):con
-du@t8:=someapp(nat,[v:nat]diffprop(y,x,v),three1,con,[v:nat][dv:diffprop(y,x,v)]t7(v,dv)):con
-three1@t9:=someapp(nat,[u:nat]diffprop(u),two1,con,[u:nat][du:diffprop(u)]t8(u,du)):con
-two1@t10:=[z:iii]t9(z):not(iii)
-y@t11:=th1"l.ec"(ii,iii,[z:ii]t10(z)):ec(ii,iii)
-a:=th6"l.ec3"(i,ii,iii,t4,t11,t6):ec3(i,ii,iii)
-prop1:=or3(i,ii,iii):'prop'
-x@[j:is(x,1)]
-t12:=or3i1(i(1),ii(1),iii(1),j):prop1(1)
-x@[n:nis(x,1)][u:nat][j:is(x,<u>suc)]
-t13:=tris(nat,x,<u>suc,pl(1,u),j,satz4g(u)):is(x,pl(1,u))
-t14:=somei(nat,[z:nat]diffprop(x,1,z),u,t13):ii(1)
-t15:=someapp(nat,[u1:nat]is(x,<u1>suc),satz3(x,n),ii(1),[u1:nat][z:is(x,<u1>suc)]t14(u1,z)):ii(1)
-t16:=or3i2(i(1),ii(1),iii(1),t15):prop1(1)
-n@t16a:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),prop1(1),[u:nat][v:is(x,<u>suc)]t16(u,v)):prop1(1)
-x@t17:=th1"l.imp"(is(x,1),prop1(1),[z:is(x,1)]t12(z),[z:nis(x,1)]t16a(z)):prop1(1)
-y@[p:prop1(y)][one1:i(y)]
-t18:=tris(nat,<y>suc,pl(y,1),pl(x,1),satz4e(y),ispl1(y,x,1,symis(nat,x,y,one1))):is(<y>suc,pl(x,1))
-t19:=somei(nat,[z:nat]diffprop(<y>suc,x,z),1,t18):iii(<y>suc)
-t20:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t19):prop1(<y>suc)
-p@[two1:ii(y)][u:nat][du:diffprop(x,y,u)][j:is(u,1)]
-t21:=tr3is(nat,x,pl(y,u),pl(y,1),<y>suc,du,ispl2(u,1,y,j),satz4a(y)):is(x,<y>suc)
-t22:=or3i1(i(<y>suc),ii(<y>suc),iii(<y>suc),t21):prop1(<y>suc)
-du@[n:nis(u,1)][w:nat][j:is(u,<w>suc)]
-t23:=tris(nat,u,<w>suc,pl(1,w),j,satz4g(w)):is(u,pl(1,w))
-t24:=tr4is(nat,x,pl(y,u),pl(y,pl(1,w)),pl(pl(y,1),w),pl(<y>suc,w),du,ispl2(u,pl(1,w),y,t23),asspl2(y,1,w),ispl1(pl(y,1),<y>suc,w,satz4a(y))):is(x,pl(<y>suc,w))
-t25:=somei(nat,[z:nat]diffprop(x,<y>suc,z),w,t24):ii(<y>suc)
-n@t26:=someapp(nat,[z:nat]is(u,<z>suc),satz3(u,n),ii(<y>suc),[z:nat][v:is(u,<z>suc)]t25(z,v)):ii(<y>suc)
-t27:=or3i2(i(<y>suc),ii(<y>suc),iii(<y>suc),t26):prop1(<y>suc)
-du@t28:=th1"l.imp"(is(u,1),prop1(<y>suc),[z:is(u,1)]t22(z),[z:nis(u,1)]t27(z)):prop1(<y>suc)
-two1@t28a:=someapp(nat,[u:nat]diffprop(u),two1,prop1(<y>suc),[u:nat][du:diffprop(u)]t28(u,du)):prop1(<y>suc)
-p@[three1:iii(y)][v:nat][dv:diffprop(y,x,v)]
-t29:=tris(nat,<y>suc,<pl(x,v)>suc,pl(x,<v>suc),ax2(y,pl(x,v),dv),satz4f(x,v)):is(<y>suc,pl(x,<v>suc))
-t30:=somei(nat,[z:nat]diffprop(<y>suc,x,z),<v>suc,t29):iii(<y>suc)
-three1@t31:=someapp(nat,[v:nat]diffprop(y,x,v),three1,iii(<y>suc),[v:nat][dv:diffprop(y,x,v)]t30(v,dv)):iii(<y>suc)
-t32:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t31):prop1(<y>suc)
-p@t33:=or3app(i(y),ii(y),iii(y),prop1(<y>suc),p,[z:i(y)]t20(z),[z:ii(y)]t28a(z),[z:iii(y)]t32(z)):prop1(<y>suc)
-y@b:=induction([z:nat]prop1(z),t17,[z:nat][u:prop1(z)]t33(z,u),y):or3(i,ii,iii)
--29
-satz9:=orec3i(i".29",ii".29",iii".29",b".29",a".29"):orec3(is(x,y),some([u:nat]is(x,pl(y,u))),some([v:nat]is(y,pl(x,v))))
-satz9a:=b".29":or3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
-satz9b:=a".29":ec3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
-more:=some([u:nat]diffprop(x,y,u)):'prop'
-less:=some([v:nat]diffprop(y,x,v)):'prop'
-satz10:=satz9:orec3(is(x,y),more(x,y),less(x,y))
-satz10a:=satz9a:or3(is(x,y),more(x,y),less(x,y))
-satz10b:=satz9b:ec3(is(x,y),more(x,y),less(x,y))
-[m:more(x,y)]
-satz11:=m:less(y,x)
-y@[l:less(x,y)]
-satz12:=l:more(y,x)
-y@moreis:=or(more,is(x,y)):'prop'
-lessis:=or(less,is(x,y)):'prop'
-[m:moreis(x,y)]
-satz13:=th9"l.or"(more,is(x,y),less(y,x),is(y,x),m,[z:more]satz11(z),[z:is(x,y)]symis(nat,x,y,z)):lessis(y,x)
-y@[l:lessis(x,y)]
-satz14:=th9"l.or"(less,is(x,y),more(y,x),is(y,x),l,[z:less]satz12(z),[z:is(x,y)]symis(nat,x,y,z)):moreis(y,x)
-z@[i:is(x,y)][m:more(x,z)]
-ismore1:=isp(nat,[u:nat]more(u,z),x,y,m,i):more(y,z)
-i@[m:more(z,x)]
-ismore2:=isp(nat,[u:nat]more(z,u),x,y,m,i):more(z,y)
-i@[l:less(x,z)]
-isless1:=isp(nat,[u:nat]less(u,z),x,y,l,i):less(y,z)
-i@[l:less(z,x)]
-isless2:=isp(nat,[u:nat]less(z,u),x,y,l,i):less(z,y)
-i@[m:moreis(x,z)]
-ismoreis1:=isp(nat,[u:nat]moreis(u,z),x,y,m,i):moreis(y,z)
-i@[m:moreis(z,x)]
-ismoreis2:=isp(nat,[u:nat]moreis(z,u),x,y,m,i):moreis(z,y)
-i@[l:lessis(x,z)]
-islessis1:=isp(nat,[u:nat]lessis(u,z),x,y,l,i):lessis(y,z)
-i@[l:lessis(z,x)]
-islessis2:=isp(nat,[u:nat]lessis(z,u),x,y,l,i):lessis(z,y)
-y@[i:is(x,y)]
-moreisi2:=ori2(more(x,y),is(x,y),i):moreis(x,y)
-lessisi2:=ori2(less(x,y),is(x,y),i):lessis(x,y)
-y@[m:more(x,y)]
-moreisi1:=ori1(more(x,y),is(x,y),m):moreis(x,y)
-y@[l:less(x,y)]
-lessisi1:=ori1(less(x,y),is(x,y),l):lessis(x,y)
-z@[u:nat][i:is(x,y)][j:is(z,u)][m:more(x,z)]
-ismore12:=ismore2(z,u,y,j,ismore1(x,y,z,i,m)):more(y,u)
-j@[l:less(x,z)]
-isless12:=isless2(z,u,y,j,isless1(x,y,z,i,l)):less(y,u)
-j@[m:moreis(x,z)]
-ismoreis12:=ismoreis2(z,u,y,j,ismoreis1(x,y,z,i,m)):moreis(y,u)
-j@[l:lessis(x,z)]
-islessis12:=islessis2(z,u,y,j,islessis1(x,y,z,i,l)):lessis(y,u)
-y@[m:moreis(x,y)]
-satz10c:=th7"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,comor(more(x,y),is(x,y),m)):not(less(x,y))
-y@[l:lessis(x,y)]
-satz10d:=th9"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,l):not(more(x,y))
-y@[n:not(more(x,y))]
-satz10e:=th2"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n):lessis(x,y)
-y@[n:not(less(x,y))]
-satz10f:=comor(is(x,y),more(x,y),th3"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n)):moreis(x,y)
-y@[m:more(x,y)]
-satz10g:=th3"l.or"(less(x,y),is(x,y),ec3e23(is(x,y),more(x,y),less(x,y),satz10b,m),ec3e21(is(x,y),more(x,y),less(x,y),satz10b,m)):not(lessis(x,y))
-y@[l:less(x,y)]
-satz10h:=th3"l.or"(more(x,y),is(x,y),ec3e32(is(x,y),more(x,y),less(x,y),satz10b,l),ec3e31(is(x,y),more(x,y),less(x,y),satz10b,l)):not(moreis(x,y))
-y@[n:not(moreis(x,y))]
-satz10j:=or3e3(is(x,y),more(x,y),less(x,y),satz10a,th5"l.or"(more(x,y),is(x,y),n),th4"l.or"(more(x,y),is(x,y),n)):less(x,y)
-y@[n:not(lessis(x,y))]
-satz10k:=or3e2(is(x,y),more(x,y),less(x,y),satz10a,th4"l.or"(less(x,y),is(x,y),n),th5"l.or"(less(x,y),is(x,y),n)):more(x,y)
-z@[l:less(x,y)][k:less(y,z)]
-+315
-[v:nat][dv:diffprop(y,x,v)][w:nat][dw:diffprop(z,y,w)]
-t1:=tr3is(nat,z,pl(y,w),pl(pl(x,v),w),pl(x,pl(v,w)),dw,ispl1(y,pl(x,v),w,dv),asspl1(x,v,w)):is(z,pl(x,pl(v,w)))
-t2:=somei(nat,[u:nat]diffprop(z,x,u),pl(v,w),t1):less(x,z)
-dv@t3:=someapp(nat,[w:nat]diffprop(z,y,w),k,less(x,z),[w:nat][dw:diffprop(z,y,w)]t2(w,dw)):less(x,z)
--315
-satz15:=someapp(nat,[v:nat]diffprop(y,x,v),l,less(x,z),[v:nat][dv:diffprop(y,x,v)]t3".315"(v,dv)):less(x,z)
-trless:=satz15:less(x,z)
-z@[m:more(x,y)][n:more(y,z)]
-trmore:=satz15(z,y,x,n,m):more(x,z)
-+*315
-n@anders:=satz12(z,x,satz15(z,y,x,satz11(y,z,n),satz11(m))):more(x,z)
--315
-z@[l:lessis(x,y)][k:less(y,z)]
-satz16a:=orapp(less(x,y),is(x,y),less(x,z),l,[u:less(x,y)]trless(u,k),[u:is(x,y)]isless1(y,x,z,symis(nat,x,y,u),k)):less(x,z)
-z@[l:less(x,y)][k:lessis(y,z)]
-satz16b:=orapp(less(y,z),is(y,z),less(x,z),k,[u:less(y,z)]trless(l,u),[u:is(y,z)]isless2(y,z,x,u,l)):less(x,z)
-z@[m:moreis(x,y)][n:more(y,z)]
-satz16c:=satz16b(z,y,x,n,satz13(m)):more(x,z)
-z@[m:more(x,y)][n:moreis(y,z)]
-satz16d:=satz16a(z,y,x,satz13(y,z,n),m):more(x,z)
-z@[l:lessis(x,y)][k:lessis(y,z)]
-+317
-[i:is(x,y)][j:is(y,z)]
-t1:=lessisi2(x,z,tris(nat,x,y,z,i,j)):lessis(x,z)
-i@[j:less(y,z)]
-t2:=lessisi1(x,z,satz16a(l,j)):lessis(x,z)
-i@t3:=orapp(less(y,z),is(y,z),lessis(x,z),k,[u:less(y,z)]t2(u),[u:is(y,z)]t1(u)):lessis(x,z)
-k@[j:less(x,y)]
-t4:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
--317
-satz17:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t4".317"(u),[u:is(x,y)]t3".317"(u)):lessis(x,z)
-+*317
-k@[j:less(x,y)]
-t5:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
-k@[i:is(x,y)]
-t6:=islessis1(y,x,z,symis(nat,x,y,i),k):lessis(x,z)
-k@anders:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t5(u),[u:is(x,y)]t6(u)):lessis(x,z)
--317
-k@trlessis:=satz17:lessis(x,z)
-z@[m:moreis(x,y)][n:moreis(y,z)]
-trmoreis:=satz14(z,x,satz17(z,y,x,satz13(y,z,n),satz13(m))):moreis(x,z)
-y@satz18:=somei(nat,[u:nat]diffprop(pl(x,y),x,u),y,refis(nat,pl(x,y))):more(pl(x,y),x)
-satz18a:=satz18:less(x,pl(x,y))
-x@satz18b:=ismore1(pl(x,1),<x>suc,x,satz4a,satz18(1)):more(<x>suc,x)
-satz18c:=satz18b:less(x,<x>suc)
-z@[m:more(x,y)]
-+319
-[u:nat][du:diffprop(u)]
-t1:=tris(nat,x,pl(y,u),pl(u,y),du,compl(y,u)):is(x,pl(u,y))
-t2:=tr3is(nat,pl(x,z),pl(pl(u,y),z),pl(u,pl(y,z)),pl(pl(y,z),u),ispl1(x,pl(u,y),z,t1),asspl1(u,y,z),compl(u,pl(y,z))):is(pl(x,z),pl(pl(y,z),u))
-t3:=somei(nat,[v:nat]diffprop(pl(x,z),pl(y,z),v),u,t2):more(pl(x,z),pl(y,z))
--319
-satz19a:=someapp(nat,[u:nat]diffprop(u),m,more(pl(x,z),pl(y,z)),[u:nat][v:diffprop(u)]t3".319"(u,v)):more(pl(x,z),pl(y,z))
-z@[i:is(x,y)]
-satz19b:=ispl1(x,y,z,i):is(pl(x,z),pl(y,z))
-z@[l:less(x,y)]
-satz19c:=satz11(pl(y,z),pl(x,z),satz19a(y,x,z,satz12(x,y,l))):less(pl(x,z),pl(y,z))
-+*319
-l@anders1:=satz19a(y,x,z,l):less(pl(x,z),pl(y,z))
--319
-m@satz19d:=ismore12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19a):more(pl(z,x),pl(z,y))
-i@satz19e:=ispl2(x,y,z,i):is(pl(z,x),pl(z,y))
-l@satz19f:=isless12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19c):less(pl(z,x),pl(z,y))
-+*319
-l@anders2:=satz19d(y,x,z,l):less(pl(z,x),pl(z,y))
--319
-z@[u:nat][i:is(x,y)][m:more(z,u)]
-satz19g:=ismore2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19d(z,u,x,m)):more(pl(x,z),pl(y,u))
-satz19h:=ismore12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19g):more(pl(z,x),pl(u,y))
-i@[l:less(z,u)]
-satz19j:=isless2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19f(z,u,x,l)):less(pl(x,z),pl(y,u))
-satz19k:=isless12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19j):less(pl(z,x),pl(u,y))
-z@[m:moreis(x,y)]
-+*319
-m@[n:more(x,y)]
-t4:=moreisi1(pl(x,z),pl(y,z),satz19a(n)):moreis(pl(x,z),pl(y,z))
-m@[i:is(x,y)]
-t5:=moreisi2(pl(x,z),pl(y,z),ispl1(x,y,z,i)):moreis(pl(x,z),pl(y,z))
--319
-m@satz19l:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,z)),m,[u:more(x,y)]t4".319"(u),[u:is(x,y)]t5".319"(u)):moreis(pl(x,z),pl(y,z))
-satz19m:=ismoreis12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19l):moreis(pl(z,x),pl(z,y))
-z@[l:lessis(x,y)]
-satz19n:=satz13(pl(y,z),pl(x,z),satz19l(y,x,z,satz14(l))):lessis(pl(x,z),pl(y,z))
-satz19o:=satz13(pl(z,y),pl(z,x),satz19m(y,x,z,satz14(l))):lessis(pl(z,x),pl(z,y))
-+320
-z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
-t2:=satz10b(pl(x,z),pl(y,z)):ec3(is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)))
--320
-z@[m:more(pl(x,z),pl(y,z))]
-satz20a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),m):more(x,y)
-z@[i:is(pl(x,z),pl(y,z))]
-satz20b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),i):is(x,y)
-z@[l:less(pl(x,z),pl(y,z))]
-satz20c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),l):less(x,y)
-+*320
-i@t3:=tr3is(nat,pl(z,x),pl(x,z),pl(y,z),pl(z,y),compl(z,x),i,compl(y,z)):is(pl(z,x),pl(z,y))
-andersb:=satz8a(z,x,y,t3):is(x,y)
-l@andersc:=satz20a(y,x,z,l):less(x,y)
--320
-z@[m:more(pl(z,x),pl(z,y))]
-satz20d:=satz20a(ismore12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),m)):more(x,y)
-z@[i:is(pl(z,x),pl(z,y))]
-satz20e:=satz20b(tr3is(nat,pl(x,z),pl(z,x),pl(z,y),pl(y,z),compl(x,z),i,compl(z,y))):is(x,y)
-z@[l:less(pl(z,x),pl(z,y))]
-satz20f:=satz20c(isless12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),l)):less(x,y)
-u@[m:more(x,y)][n:more(z,u)]
-+321
-t1:=satz19a(x,y,z,m):more(pl(x,z),pl(y,z))
-t2:=ismore12(pl(z,y),pl(y,z),pl(u,y),pl(y,u),compl(z,y),compl(u,y),satz19a(z,u,y,n)):more(pl(y,z),pl(y,u))
--321
-satz21:=trmore(pl(x,z),pl(y,z),pl(y,u),t1".321",t2".321"):more(pl(x,z),pl(y,u))
-+*321
-n@anders:=trmore(pl(x,z),pl(y,z),pl(y,u),satz19a(x,y,z,m),satz19d(z,u,y,n)):more(pl(x,z),pl(y,u))
--321
-u@[l:less(x,y)][k:less(z,u)]
-satz21a:=satz21(y,x,u,z,l,k):less(pl(x,z),pl(y,u))
-+*321
-k@andersa:=satz11(pl(y,u),pl(x,z),satz21(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(pl(x,z),pl(y,u))
--321
-u@[m:moreis(x,y)][n:more(z,u)]
-satz22a:=orapp(more(x,y),is(x,y),more(pl(x,z),pl(y,u)),m,[v:more(x,y)]satz21(v,n),[v:is(x,y)]satz19g(u,v,n)):more(pl(x,z),pl(y,u))
-u@[m:more(x,y)][n:moreis(z,u)]
-satz22b:=orapp(more(z,u),is(z,u),more(pl(x,z),pl(y,u)),n,[v:more(z,u)]satz21(m,v),[v:is(z,u)]satz19h(z,u,x,y,v,m)):more(pl(x,z),pl(y,u))
-u@[l:lessis(x,y)][k:less(z,u)]
-satz22c:=satz22a(y,x,u,z,satz14(x,y,l),k):less(pl(x,z),pl(y,u))
-u@[l:less(x,y)][k:lessis(z,u)]
-satz22d:=satz22b(y,x,u,z,l,satz14(z,u,k)):less(pl(x,z),pl(y,u))
-u@[m:moreis(x,y)][n:moreis(z,u)]
-+323
-[i:is(x,y)][j:is(z,u)]
-t1:=moreisi2(pl(x,z),pl(y,u),tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j))):moreis(pl(x,z),pl(y,u))
-i@[o:more(z,u)]
-t2:=moreisi1(pl(x,z),pl(y,u),satz22a(m,o)):moreis(pl(x,z),pl(y,u))
-i@t3:=orapp(more(z,u),is(z,u),moreis(pl(x,z),pl(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(pl(x,z),pl(y,u))
-n@[o:more(x,y)]
-t4:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
--323
-satz23:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t4".323"(v),[v:is(x,y)]t3".323"(v)):moreis(pl(x,z),pl(y,u))
-+*323
-n@[o:more(x,y)]
-t5:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
-n@[i:is(x,y)]
-t6:=ismoreis2(pl(x,u),pl(y,u),pl(x,z),ispl1(u,i),satz19m(z,u,x,n)):moreis(pl(x,z),pl(y,u))
-n@anders:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(pl(x,z),pl(y,u))
--323
-u@[l:lessis(x,y)][k:lessis(z,u)]
-satz23a:=satz13(pl(y,u),pl(x,z),satz23(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(pl(x,z),pl(y,u))
-+324
-x@[n:nis(x,1)][u:nat][i:is(x,<u>suc)]
-t1:=tris(nat,x,<u>suc,pl(1,u),i,satz4g(u)):is(x,pl(1,u))
-t2:=ismore1(pl(1,u),x,1,symis(nat,x,pl(1,u),t1),satz18(1,u)):more(x,1)
-n@t3:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),more(x,1),[u:nat][v:is(x,<u>suc)]t2(u,v)):more(x,1)
--324
-x@satz24:=th2"l.or"(more(x,1),is(x,1),[u:nis(x,1)]t3".324"(u)):moreis(x,1)
-satz24a:=satz13(x,1,satz24):lessis(1,x)
-satz24b:=t3".324"(<x>suc,<x>ax3):more(<x>suc,1)
-satz24c:=satz24b:less(1,<x>suc)
-y@[m:more(y,x)]
-+325
-[u:nat][du:diffprop(y,x,u)]
-t1:=satz19m(u,1,x,satz24(u)):moreis(pl(x,u),pl(x,1))
-t2:=ismoreis1(pl(x,u),y,pl(x,1),symis(nat,y,pl(x,u),du),t1):moreis(y,pl(x,1))
--325
-satz25:=someapp(nat,[u:nat]diffprop(y,x,u),m,moreis(y,pl(x,1)),[u:nat][v:diffprop(y,x,u)]t2".325"(u,v)):moreis(y,pl(x,1))
-satz25a:=ismoreis2(pl(x,1),<x>suc,y,satz4a,satz25):moreis(y,<x>suc)
-y@[l:less(y,x)]
-satz25b:=satz13(x,pl(y,1),satz25(y,x,l)):lessis(pl(y,1),x)
-satz25c:=islessis1(pl(y,1),<y>suc,x,satz4a(y),satz25b):lessis(<y>suc,x)
-y@[l:less(y,pl(x,1))]
-+326
-[m:more(y,x)]
-t1:=satz25(m):moreis(y,pl(x,1))
-l@t2:=th3"l.imp"(more(y,x),moreis(y,pl(x,1)),satz10h(y,pl(x,1),l),[v:more(y,x)]t1(v)):not(more(y,x))
--326
-satz26:=satz10e(y,x,t2".326"):lessis(y,x)
-y@[l:less(y,<x>suc)]
-satz26a:=satz26(isless2(<x>suc,pl(x,1),y,satz4e,l)):lessis(y,x)
-y@[m:more(pl(y,1),x)]
-satz26b:=satz14(x,y,satz26(y,x,m)):moreis(y,x)
-y@[m:more(<y>suc,x)]
-satz26c:=satz26b(ismore1(<y>suc,pl(y,1),x,satz4e(y),m)):moreis(y,x)
-@[p:[x:nat]'prop'][n:nat]
-+327
-[m:nat]
-lbprop:=imp(<m>p,lessis(n,m)):'prop'
--327
-lb:=all([x:nat]lbprop".327"(x)):'prop'
-min:=and(lb,<n>p):'prop'
-p@[s:some(p)]
-+*327
-s@[n:nat]
-t1:=[x:<n>p]satz24a(n):lbprop(1,n)
-s@t2:=[x:nat]t1(x):lb(1)
-[l:[x:nat]lb(x)][y:nat][yp:<y>p]
-t3:=satz18(y,1):more(pl(y,1),y)
-t4:=satz10g(pl(y,1),y,t3):not(lessis(pl(y,1),y))
-t5:=th4"l.imp"(<y>p,lessis(pl(y,1),y),yp,t4):not(lbprop(pl(y,1),y))
-t6:=th1"l.all"(nat,[x:nat]lbprop(pl(y,1),x),y,t5):not(lb(pl(y,1)))
-t7:=mp(lb(pl(y,1)),con,<pl(y,1)>l,t6):con
-l@t8:=someapp(nat,p,s,con,[x:nat][y:<x>p]t7(x,y)):con
-s@[n:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))][m:nat][l:lb(m)]
-t9:=<m>n:not(and(lb(m),not(lb(pl(m,1)))))
-t10:=et(lb(pl(m,1)),th3"l.and"(lb(m),not(lb(pl(m,1))),t9,l)):lb(pl(m,1))
-t11:=isp(nat,[x:nat]lb(x),pl(m,1),<m>suc,t10,satz4a(m)):lb(<m>suc)
-n@t12:=[x:nat]induction([y:nat]lb(y),t2,[y:nat][z:lb(y)]t11(y,z),x):[x:nat]lb(x)
-s@t13:=[x:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))]t8(t12(x)):some([x:nat]and(lb(x),not(lb(pl(x,1)))))
-[m:nat][a:and(lb(m),not(lb(pl(m,1))))]
-t14:=ande1(lb(m),not(lb(pl(m,1))),a):lb(m)
-t15:=ande2(lb(m),not(lb(pl(m,1))),a):not(lb(pl(m,1)))
-[nmp:not(<m>p)][n:nat][np:<n>p]
-t16:=mp(<n>p,lessis(m,n),np,<n>t14):lessis(m,n)
-t17:=th3"l.imp"(is(m,n),<m>p,nmp,[x:is(m,n)]isp(nat,p,n,m,np,symis(nat,m,n,x))):not(is(m,n))
-t18:=ore1(less(m,n),is(m,n),t16,t17):less(m,n)
-t19:=satz25b(n,m,t18):lessis(pl(m,1),n)
-nmp@t20:=[x:nat][y:<x>p]t19(x,y):lb(pl(m,1))
-t21:=mp(lb(pl(m,1)),con,t20,t15):con
-a@t22:=et(<m>p,[x:not(<m>p)]t21(x)):<m>p
-t23:=andi(lb(m),<m>p,t14,t22):min(m)
--327
-s@satz27:=th6"l.some"(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))),[x:nat]min(x),t13".327",[x:nat][y:and(lb(x),not(lb(pl(x,1))))]t23".327"(x,y)):some([x:nat]min(p,x))
-+*327
-p@[n:non(nat,[x:nat]min(x))][u:nat]
-t24:=[x:<u>p]satz24a(u):lbprop(1,u)
-n@t25:=[x:nat]t24(x):lb(1)
-u@[l:lb(u)]
-t26:=<u>n:not(min(u))
-t27:=th3"l.and"(lb(u),<u>p,t26,l):not(<u>p)
-[v:nat][vp:<v>p]
-t28:=th3"l.imp"(is(u,v),<u>p,t27,[x:is(u,v)]isp1(nat,p,v,u,vp,x)):nis(u,v)
-t29:=mp(<v>p,lessis(u,v),vp,<v>l):lessis(u,v)
-t30:=ore1(less(u,v),is(u,v),t29,t28):less(u,v)
-t31:=satz25c(v,u,t30):lessis(<u>suc,v)
-v@t32:=[x:<v>p]t31(x):lbprop(<u>suc,v)
-l@t33:=[x:nat]t32(x):lb(<u>suc)
-u@t34:=induction([x:nat]lb(x),t25,[x:nat][y:lb(x)]t33(x,y),u):lb(u)
-p@[s:some(p)][u:nat][up:<u>p]
-t35:=satz10g(<u>suc,u,satz18b(u)):not(lessis(<u>suc,u))
-t36:=th4"l.imp"(<u>p,lessis(<u>suc,u),up,t35):not(lbprop(<u>suc,u))
-t37:=th1"l.all"(nat,[x:nat]lbprop(<u>suc,x),u,t36):not(lb(<u>suc))
-t38:=[y:non(nat,[x:nat]min(x))]mp(lb(<u>suc),con,t34(y,<u>suc),t37):some([x:nat]min(x))
-s@anders:=someapp(nat,p,s,some([x:nat]min(x)),[x:nat][y:<x>p]t38(x,y)):some([x:nat]min(x))
--327
-+*327
-p@[n:nat][m:nat][mn:min(p,n)][mm:min(p,m)]
-t39:=ande1(lb(n),<n>p,mn):lb(n)
-t40:=ande1(lb(m),<m>p,mm):lb(m)
-t41:=ande2(lb(n),<n>p,mn):<n>p
-t42:=ande2(lb(m),<m>p,mm):<m>p
-t43:=<m>t39:lbprop(n,m)
-t44:=<n>t40:lbprop(m,n)
-t45:=mp(<m>p,lessis(n,m),t42,t43):lessis(n,m)
-t46:=mp(<n>p,lessis(m,n),t41,t44):lessis(m,n)
-t47:=ore2(more(n,m),is(n,m),satz14(m,n,t46),satz10d(n,m,t45)):is(n,m)
-p@t48:=[x:nat][y:nat][u:min(x)][v:min(y)]t47(x,y,u,v):amone(nat,[x:nat]min(p,x))
--327
-s@satz27a:=onei(nat,[x:nat]min(p,x),t48".327",satz27):one([x:nat]min(p,x))
-+428
-x@[f:[y:nat]nat]
-prop1:=all([y:nat]is(<<y>suc>f,pl(<y>f,x))):'prop'
-prop2:=and(is(<1>f,x),prop1):'prop'
-x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
-prop3:=is(<y>a,<y>b):'prop'
-pb@t1:=ande1(is(<1>a,x),prop1(a),pa):is(<1>a,x)
-t2:=ande1(is(<1>b,x),prop1(b),pb):is(<1>b,x)
-t3:=tris2(nat,<1>a,<1>b,x,t1,t2):prop3(1)
-y@[p:prop3(y)]
-t4:=ispl1(<y>a,<y>b,x,p):is(pl(<y>a,x),pl(<y>b,x))
-t5:=ande2(is(<1>a,x),prop1(a),pa):prop1(a)
-t6:=ande2(is(<1>b,x),prop1(b),pb):prop1(b)
-t7:=<y>t5:is(<<y>suc>a,pl(<y>a,x))
-t8:=<y>t6:is(<<y>suc>b,pl(<y>b,x))
-t9:=tr3is(nat,<<y>suc>a,pl(<y>a,x),pl(<y>b,x),<<y>suc>b,t7,t4,symis(nat,<<y>suc>b,pl(<y>b,x),t8)):prop3(<y>suc)
-y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
-pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
-x@a1:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
-prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
-@id:=[y:nat]y:[y:nat]nat
-t12:=[x:nat]satz4e(x):prop1(1,id)
-t13:=andi(is(<1>id,1),prop1(1,id),refis(nat,1),t12):prop2(1,id)
-t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),id,t13):prop4(1)
-x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
-g:=[y:nat]pl(<y>f,y):[y:nat]nat
-t15:=ande1(is(<1>f,x),prop1(f),pf):is(<1>f,x)
-t16:=tris(nat,<1>g,pl(x,1),<x>suc,ispl1(<1>f,x,1,t15),satz4a(x)):is(<1>g,<x>suc)
-[y:nat]
-t17:=ande2(is(<1>f,x),prop1(f),pf):prop1(f)
-t18:=<y>t17:is(<<y>suc>f,pl(<y>f,x))
-t19:=tris(nat,<<y>suc>g,pl(pl(<y>f,x),<y>suc),pl(<y>f,pl(x,<y>suc)),ispl1(<<y>suc>f,pl(<y>f,x),<y>suc,t18),asspl1(<y>f,x,<y>suc)):is(<<y>suc>g,pl(<y>f,pl(x,<y>suc)))
-t20:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,pl(<x>suc,y),pl(y,<x>suc),satz4b(x,y),satz4h(x,y),compl(<x>suc,y)):is(pl(x,<y>suc),pl(y,<x>suc))
-t21:=tr3is(nat,<<y>suc>g,pl(<y>f,pl(x,<y>suc)),pl(<y>f,pl(y,<x>suc)),pl(<y>g,<x>suc),t19,ispl2(pl(x,<y>suc),pl(y,<x>suc),<y>f,t20),asspl2(<y>f,y,<x>suc)):is(<<y>suc>g,pl(<y>g,<x>suc))
-pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
-t23:=andi(is(<1>g,<x>suc),prop1(<x>suc,g),t16,t22):prop2(<x>suc,g)
-t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
-p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
-x@b1:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
--428
-x@satz28:=onei([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),a1".428",b1".428"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,x),all([y:nat]is(<<y>suc>z,pl(<y>z,x)))))
-times:=ind([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),satz28):[y:nat]nat
-y@ts:=<y>times:nat
-+*428
-x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz28):prop2(times)
--428
-x@satz28a:=ande1(is(<1>times,x),prop1".428"(times),t26".428"):is(ts(x,1),x)
-+*428
-x@t27:=ande2(is(<1>times,x),prop1(times),t26):prop1(times)
--428
-y@satz28b:=<y>t27".428":is(ts(x,<y>suc),pl(ts(x,y),x))
-+*428
-@t28:=t11(1,times(1),id,t26(1),t13):is"e"([y:nat]nat,times(1),id)
--428
-x@satz28c:=fise(nat,nat,times(1),id".428",t28".428",x):is(ts(1,x),x)
-+*428
-x@t29:=t11(<x>suc,times(<x>suc),[y:nat]pl(<y>times,y),t26(<x>suc),t23(b1,times,t26)):is"e"([y:nat]nat,times(<x>suc),[y:nat]pl(<y>times,y))
--428
-y@satz28d:=fise(nat,nat,times(<x>suc),[z:nat]pl(<z>times,z),t29".428",y):is(ts(<x>suc,y),pl(ts(x,y),y))
-x@satz28e:=symis(nat,ts(x,1),x,satz28a):is(x,ts(x,1))
-y@satz28f:=symis(nat,ts(x,<y>suc),pl(ts(x,y),x),satz28b):is(pl(ts(x,y),x),ts(x,<y>suc))
-x@satz28g:=symis(nat,ts(1,x),x,satz28c):is(x,ts(1,x))
-y@satz28h:=symis(nat,ts(<x>suc,y),pl(ts(x,y),y),satz28d):is(pl(ts(x,y),y),ts(<x>suc,y))
-z@[i:is(x,y)]
-ists1:=isf(nat,nat,[u:nat]ts(u,z),x,y,i):is(ts(x,z),ts(y,z))
-ists2:=isf(nat,nat,[u:nat]ts(z,u),x,y,i):is(ts(z,x),ts(z,y))
-z@[u:nat][i:is(x,y)][j:is(z,u)]
-ists12:=tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
-+429
-y@prop1:=is(ts(x,y),ts(y,x)):'prop'
-t1:=satz28a(y):is(ts(y,1),y)
-t2:=satz28c(y):is(ts(1,y),y)
-t3:=tris2(nat,ts(1,y),ts(y,1),y,t2,t1):prop1(1,y)
-[p:prop1(x,y)]
-t4:=tris(nat,pl(ts(x,y),y),pl(ts(y,x),y),ts(y,<x>suc),ispl1(ts(x,y),ts(y,x),y,p),satz28f(y,x)):is(pl(ts(x,y),y),ts(y,<x>suc))
-t5:=satz28d:is(ts(<x>suc,y),pl(ts(x,y),y))
-t6:=tris(nat,ts(<x>suc,y),pl(ts(x,y),y),ts(y,<x>suc),t5,t4):prop1(<x>suc,y)
--429
-y@satz29:=induction([z:nat]prop1".429"(z,y),t3".429",[z:nat][u:prop1".429"(z,y)]t6".429"(z,y,u),x):is(ts(x,y),ts(y,x))
-comts:=satz29:is(ts(x,y),ts(y,x))
-+*429
-x@t7:=tris(nat,ts(x,1),x,ts(1,x),satz28a,satz28g):prop1(1)
-y@[p:prop1(y)]
-t8:=tr3is(nat,ts(x,<y>suc),pl(ts(x,y),x),pl(ts(y,x),x),ts(<y>suc,x),satz28b(x,y),ispl1(ts(x,y),ts(y,x),x,p),satz28h(y,x)):prop1(<y>suc)
-y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(ts(x,y),ts(y,x))
--429
-+430
-z@prop1:=is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z))):'prop'
-y@t1:=tr3is(nat,ts(x,pl(y,1)),ts(x,<y>suc),pl(ts(x,y),x),pl(ts(x,y),ts(x,1)),ists2(pl(y,1),<y>suc,x,satz4a(y)),satz28b,ispl2(x,ts(x,1),ts(x,y),satz28e(x))):prop1(1)
-z@[p:prop1(z)]
-t2:=tr3is(nat,ts(x,pl(y,<z>suc)),ts(x,<pl(y,z)>suc),pl(ts(x,pl(y,z)),x),pl(pl(ts(x,y),ts(x,z)),x),ists2(pl(y,<z>suc),<pl(y,z)>suc,x,satz4b(y,z)),satz28b(x,pl(y,z)),ispl1(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),x,p)):is(ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x))
-t3:=tr3is(nat,ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x),pl(ts(x,y),pl(ts(x,z),x)),pl(ts(x,y),ts(x,<z>suc)),t2,asspl1(ts(x,y),ts(x,z),x),ispl2(pl(ts(x,z),x),ts(x,<z>suc),ts(x,y),satz28f(x,z))):prop1(<z>suc)
--430
-z@satz30:=induction([u:nat]prop1".430"(u),t1".430",[u:nat][v:prop1".430"(u)]t3".430"(u,v),z):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-disttp1:=tr3is(nat,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz30(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
-disttp2:=satz30:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-distpt1:=symis(nat,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
-distpt2:=symis(nat,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
-+431
-prop1:=is(ts(ts(x,y),z),ts(x,ts(y,z))):'prop'
-y@t1:=tris(nat,ts(ts(x,y),1),ts(x,y),ts(x,ts(y,1)),satz28a(ts(x,y)),ists2(y,ts(y,1),x,satz28e(y))):prop1(1)
-z@[p:prop1(z)]
-t2:=tr4is(nat,ts(ts(x,y),<z>suc),pl(ts(ts(x,y),z),ts(x,y)),pl(ts(x,ts(y,z)),ts(x,y)),ts(x,pl(ts(y,z),y)),ts(x,ts(y,<z>suc)),satz28b(ts(x,y),z),ispl1(ts(ts(x,y),z),ts(x,ts(y,z)),ts(x,y),p),distpt2(x,ts(y,z),y),ists2(pl(ts(y,z),y),ts(y,<z>suc),x,satz28f(y,z))):prop1(<z>suc)
--431
-satz31:=induction([u:nat]prop1".431"(u),t1".431",[u:nat][v:prop1".431"(u)]t2".431"(u,v),z):is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts1:=satz31:is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts2:=symis(nat,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
-[m:more(x,y)]
-+432
-[u:nat][du:diffprop(u)]
-t1:=tris(nat,ts(x,z),ts(pl(y,u),z),pl(ts(y,z),ts(u,z)),ists1(x,pl(y,u),z,du),disttp1(y,u,z)):is(ts(x,z),pl(ts(y,z),ts(u,z)))
-t2:=somei(nat,[v:nat]diffprop(ts(x,z),ts(y,z),v),ts(u,z),t1):more(ts(x,z),ts(y,z))
--432
-satz32a:=someapp(nat,[u:nat]diffprop(u),m,more(ts(x,z),ts(y,z)),[u:nat][v:diffprop(u)]t2".432"(u,v)):more(ts(x,z),ts(y,z))
-z@[i:is(x,y)]
-satz32b:=ists1(x,y,z,i):is(ts(x,z),ts(y,z))
-z@[l:less(x,y)]
-satz32c:=satz11(ts(y,z),ts(x,z),satz32a(y,x,z,satz12(x,y,l))):less(ts(x,z),ts(y,z))
-+*432
-l@anders1:=satz32a(y,x,z,l):less(ts(x,z),ts(y,z))
--432
-m@satz32d:=ismore12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32a):more(ts(z,x),ts(z,y))
-i@satz32e:=ists2(x,y,z,i):is(ts(z,x),ts(z,y))
-l@satz32f:=isless12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32c):less(ts(z,x),ts(z,y))
-+*432
-l@anders2:=satz32d(y,x,z,l):less(ts(z,x),ts(z,y))
--432
-z@[u:nat][i:is(x,y)][m:more(z,u)]
-satz32g:=ismore2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32d(z,u,x,m)):more(ts(x,z),ts(y,u))
-satz32h:=ismore12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32g):more(ts(z,x),ts(u,y))
-i@[l:less(z,u)]
-satz32j:=isless2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32f(z,u,x,l)):less(ts(x,z),ts(y,u))
-satz32k:=isless12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32j):less(ts(z,x),ts(u,y))
-z@[m:moreis(x,y)]
-+*432
-m@[n:more(x,y)]
-t3:=moreisi1(ts(x,z),ts(y,z),satz32a(n)):moreis(ts(x,z),ts(y,z))
-m@[i:is(x,y)]
-t4:=moreisi2(ts(x,z),ts(y,z),ists1(x,y,z,i)):moreis(ts(x,z),ts(y,z))
--432
-m@satz32l:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,z)),m,[u:more(x,y)]t3".432"(u),[u:is(x,y)]t4".432"(u)):moreis(ts(x,z),ts(y,z))
-satz32m:=ismoreis12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32l):moreis(ts(z,x),ts(z,y))
-z@[l:lessis(x,y)]
-satz32n:=satz13(ts(y,z),ts(x,z),satz32l(y,x,z,satz14(l))):lessis(ts(x,z),ts(y,z))
-satz32o:=satz13(ts(z,y),ts(z,x),satz32m(y,x,z,satz14(l))):lessis(ts(z,x),ts(z,y))
-+433
-z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
-t2:=satz10b(ts(x,z),ts(y,z)):ec3(is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)))
--433
-z@[m:more(ts(x,z),ts(y,z))]
-satz33a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),m):more(x,y)
-z@[i:is(ts(x,z),ts(y,z))]
-satz33b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),i):is(x,y)
-z@[l:less(ts(x,z),ts(y,z))]
-satz33c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),l):less(x,y)
-+*433
-l@anders:=satz33a(y,x,z,l):less(x,y)
--433
-u@[m:more(x,y)][n:more(z,u)]
-+434
-t1:=satz32a(x,y,z,m):more(ts(x,z),ts(y,z))
-t2:=ismore12(ts(z,y),ts(y,z),ts(u,y),ts(y,u),comts(z,y),comts(u,y),satz32a(z,u,y,n)):more(ts(y,z),ts(y,u))
--434
-satz34:=trmore(ts(x,z),ts(y,z),ts(y,u),t1".434",t2".434"):more(ts(x,z),ts(y,u))
-+*434
-n@anders:=trmore(ts(x,z),ts(y,z),ts(y,u),satz32a(x,y,z,m),satz32d(z,u,y,n)):more(ts(x,z),ts(y,u))
--434
-u@[l:less(x,y)][k:less(z,u)]
-satz34a:=satz34(y,x,u,z,l,k):less(ts(x,z),ts(y,u))
-+*434
-k@andersa:=satz11(ts(y,u),ts(x,z),satz34(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(ts(x,z),ts(y,u))
--434
-u@[m:moreis(x,y)][n:more(z,u)]
-satz35a:=orapp(more(x,y),is(x,y),more(ts(x,z),ts(y,u)),m,[v:more(x,y)]satz34(v,n),[v:is(x,y)]satz32g(u,v,n)):more(ts(x,z),ts(y,u))
-u@[m:more(x,y)][n:moreis(z,u)]
-satz35b:=orapp(more(z,u),is(z,u),more(ts(x,z),ts(y,u)),n,[v:more(z,u)]satz34(m,v),[v:is(z,u)]satz32h(z,u,x,y,v,m)):more(ts(x,z),ts(y,u))
-u@[l:lessis(x,y)][k:less(z,u)]
-satz35c:=satz35a(y,x,u,z,satz14(x,y,l),k):less(ts(x,z),ts(y,u))
-u@[l:less(x,y)][k:lessis(z,u)]
-satz35d:=satz35b(y,x,u,z,l,satz14(z,u,k)):less(ts(x,z),ts(y,u))
-u@[m:moreis(x,y)][n:moreis(z,u)]
-+436
-[i:is(x,y)][j:is(z,u)]
-t1:=moreisi2(ts(x,z),ts(y,u),tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j))):moreis(ts(x,z),ts(y,u))
-i@[o:more(z,u)]
-t2:=moreisi1(ts(x,z),ts(y,u),satz35a(m,o)):moreis(ts(x,z),ts(y,u))
-i@t3:=orapp(more(z,u),is(z,u),moreis(ts(x,z),ts(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(ts(x,z),ts(y,u))
-n@[o:more(x,y)]
-t4:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
--436
-satz36:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t4".436"(v),[v:is(x,y)]t3".436"(v)):moreis(ts(x,z),ts(y,u))
-+*436
-n@[o:more(x,y)]
-t5:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
-n@[i:is(x,y)]
-t6:=ismoreis2(ts(x,u),ts(y,u),ts(x,z),ists1(u,i),satz32m(z,u,x,n)):moreis(ts(x,z),ts(y,u))
-n@anders:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(ts(x,z),ts(y,u))
--436
-u@[l:lessis(x,y)][k:lessis(z,u)]
-satz36a:=satz13(ts(y,u),ts(x,z),satz36(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(ts(x,z),ts(y,u))
-y@[m:more(x,y)]
-+mn
-t1:=onei(nat,[z:nat]diffprop(x,y,z),satz8b(x,y),m):one([z:nat]diffprop(x,y,z))
--mn
-mn:=ind(nat,[z:nat]diffprop(x,y,z),t1".mn"):nat
-+*mn
-m@th1a:=oneax(nat,[z:nat]diffprop(x,y,z),t1):is(x,pl(y,mn(x,y,m)))
-th1b:=symis(nat,x,pl(y,mn(x,y,m)),th1a):is(pl(y,mn(x,y,m)),x)
-th1c:=tris(nat,x,pl(y,mn(x,y,m)),pl(mn(x,y,m),y),th1a,compl(y,mn(x,y,m))):is(x,pl(mn(x,y,m),y))
-th1d:=symis(nat,x,pl(mn(x,y,m),y),th1c):is(pl(mn(x,y,m),y),x)
-y@[z:nat][m:more(x,y)][i:is(pl(y,z),x)]
-th1e:=<th1a(m)><symis(nat,pl(y,z),x,i)><mn(x,y,m)><z>satz8b(x,y):is(z,mn(x,y,m))
--mn
-z@[u:nat][m:more(x,z)][n:more(y,u)][i:is(x,y)][j:is(z,u)]
-+*mn
-j@t2:=tr3is(nat,pl(u,mn(x,z,m)),pl(z,mn(x,z,m)),x,y,ispl1(u,z,mn(x,z,m),symis(nat,z,u,j)),th1b(x,z,m),i):is(pl(u,mn(x,z,m)),y)
--mn
-j@ismn12:=th1e".mn"(y,u,mn(x,z,m),n,t2".mn"):is(mn(x,z,m),mn(y,u,n))
-@[n:nat]
-1to:=ot(nat,[x:nat]lessis(x,n)):'type'
-[x:nat][l:lessis(x,n)]
-outn:=out(nat,[y:nat]lessis(y,n),x,l):1to(n)
-n@[xn:1to(n)]
-inn:=in"e"(nat,[y:nat]lessis(y,n),xn):nat
-1top:=inp(nat,[y:nat]lessis(y,n),xn):lessis(inn,n)
-l@[y:nat][k:lessis(y,n)][i:is(x,y)]
-isoutni:=isouti(nat,[z:nat]lessis(z,n),x,l,y,k,i):is"e"(1to(n),outn(x,l),outn(y,k))
-k@[i:is"e"(1to(n),outn(x,l),outn(y,k))]
-isoutne:=isoute(nat,[z:nat]lessis(z,n),x,l,y,k,i):is(x,y)
-xn@[yn:1to(n)][i:is"e"(1to(n),xn,yn)]
-isinni:=isini(nat,[z:nat]lessis(z,n),xn,yn,i):is(inn(xn),inn(yn))
-yn@[i:is(inn(xn),inn(yn))]
-isinne:=isine(nat,[z:nat]lessis(z,n),xn,yn,i):is"e"(1to(n),xn,yn)
-xn@isoutinn:=isoutin(nat,[y:nat]lessis(y,n),xn):is"e"(1to(n),xn,outn(inn(xn),1top(xn)))
-l@isinoutn:=isinout(nat,[y:nat]lessis(y,n),x,l):is(x,inn(outn(x,l)))
-@1o:=outn(1,1,lessisi2(1,1,refis(nat,1))):1to(1)
-[u:1to(1)]
-+singlet
-u0:=inn(1,u):nat
-t1:=1top(1,u):lessis(u0,1)
-t2:=ore2(more(u0,1),is(u0,1),satz24(u0),satz10d(u0,1,t1)):is(u0,1)
-th1:=tris(1to(1),u,outn(1,u0,t1),1o,isoutinn(1,u),isoutni(1,u0,t1,1,lessisi2(1,1,refis(nat,1)),t2)):is"e"(1to(1),u,1o)
--singlet
-@2:=pl(1,1):nat
-[x:nat]
-+pair
-[l:lessis(x,2)][n:nis(x,2)]
-t1:=satz26(1,x,ore1(less(x,2),is(x,2),l,n)):lessis(x,1)
-t2:=ore2(more(x,1),is(x,1),satz24(x),satz10d(x,1,t1)):is(x,1)
-l@th1:=th2"l.or"(is(x,1),is(x,2),[t:nis(x,2)]t2(t)):or(is(x,1),is(x,2))
-@th2:=th1"e.notis"(nat,<1>suc,1,2,<1>ax3,satz4e(1)):nis(2,1)
--pair
-@1t:=outn(2,1,satz24a(2)):1to(2)
-2t:=outn(2,2,lessisi2(2,2,refis(nat,2))):1to(2)
-+*pair
-@[u:1to(2)]
-u0:=inn(2,u):nat
-t3:=1top(2,u):lessis(u0,2)
-[i:is(u0,1)]
-t4:=isoutni(2,u0,t3,1,satz24a(2),i):is"e"(1to(2),outn(2,u0,t3),1t)
-t5:=tris(1to(2),u,outn(2,u0,t3),1t,isoutinn(2,u),t4):is"e"(1to(2),u,1t)
-u@[i:is(u0,2)]
-t6:=isoutni(2,u0,t3,2,lessisi2(2,2,refis(nat,2)),i):is"e"(1to(2),outn(2,u0,t3),2t)
-t7:=tris(1to(2),u,outn(2,u0,t3),2t,isoutinn(2,u),t6):is"e"(1to(2),u,2t)
-u@th3:=th9"l.or"(is(u0,1),is(u0,2),is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),th1(u0,t3),[t:is(u0,1)]t5(t),[t:is(u0,2)]t7(t)):or(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t))
-@[i:is"e"(1to(2),2t,1t)]
-t9:=isini(nat,[x:nat]lessis(x,2),2t,1t,i):is(u0(2t),u0(1t))
-t10:=tr3is(nat,2,u0(2t),u0(1t),1,isinoutn(2,2,lessisi2(2,2,refis(nat,2))),t9,symis(nat,1,u0(1t),isinoutn(2,1,satz24a(2)))):is(2,1)
-@th4:=th3"l.imp"(is"e"(1to(2),2t,1t),is(2,1),th2,[t:is"e"(1to(2),2t,1t)]t10(t)):not(is"e"(1to(2),2t,1t))
--pair
-@[alpha:'type']
-pair1type:=[x:1to(2)]alpha:'type'
-[a:alpha][b:alpha]
-pair1:=[x:1to(2)]ite(is"e"(1to(2),x,1t),alpha,a,b):pair1type
-alpha@[p:pair1type]
-first1:=<1t>p:alpha
-second1:=<2t>p:alpha
-b@first1is1:=itet(is"e"(1to(2),1t,1t),alpha,a,b,refis(1to(2),1t)):is"e"(alpha,first1(pair1),a)
-first1is2:=symis(alpha,first1(pair1),a,first1is1):is"e"(alpha,a,first1(pair1))
-second1is1:=itef(is"e"(1to(2),2t,1t),alpha,a,b,th4".pair"):is"e"(alpha,second1(pair1),b)
-second1is2:=symis(alpha,second1(pair1),b,second1is1):is"e"(alpha,b,second1(pair1))
-+*pair
-p@[q:pair1type][i:is"e"(alpha,first1(p),first1(q))][j:is"e"(alpha,second1(p),second1(q))][u:1to(2)][u1:is"e"(1to(2),u,1t)]
-t11:=isf(1to(2),alpha,p,u,1t,u1):is"e"(alpha,<u>p,first1(p))
-t12:=symis(alpha,<u>q,first1(q),isf(1to(2),alpha,q,u,1t,u1)):is"e"(alpha,first1(q),<u>q)
-t13:=tr3is(alpha,<u>p,first1(p),first1(q),<u>q,t11,i,t12):is"e"(alpha,<u>p,<u>q)
-u@[u2:is"e"(1to(2),u,2t)]
-t14:=isf(1to(2),alpha,p,u,2t,u2):is"e"(alpha,<u>p,second1(p))
-t15:=symis(alpha,<u>q,second1(q),isf(1to(2),alpha,q,u,2t,u2)):is"e"(alpha,second1(q),<u>q)
-t16:=tr3is(alpha,<u>p,second1(p),second1(q),<u>q,t14,j,t15):is"e"(alpha,<u>p,<u>q)
-u@t17:=orapp(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),is"e"(alpha,<u>p,<u>q),th3(u),[t:is"e"(1to(2),u,1t)]t13(t),[t:is"e"(1to(2),u,2t)]t16(t)):is"e"(alpha,<u>p,<u>q)
-j@th5:=fisi(1to(2),alpha,p,q,[t:1to(2)]t17(t)):is"e"(pair1type,p,q)
-p@q0:=pair1(first1,second1):pair1type
-t18:=first1is1(first1(p),second1):is"e"(alpha,first1(q0),first1(p))
-t19:=second1is1(first1,second1):is"e"(alpha,second1(q0),second1(p))
--pair
-p@pair1is1:=th5".pair"(q0".pair",p,t18".pair",t19".pair"):is"e"(pair1type,pair1(first1,second1),p)
-pair1is2:=symis(pair1type,pair1(first1,second1),p,pair1is1):is"e"(pair1type,p,pair1(first1,second1))
-@[x:nat]
-lessisi3:=lessisi2(x,x,refis(nat,x)):lessis(x,x)
-1out:=outn(x,1,satz24a(x)):1to(x)
-xout:=outn(x,x,lessisi3(x)):1to(x)
-[y:nat][l:lessis(y,x)][u:1to(y)]
-+left
-ui:=inn(y,u):nat
-t1:=1top(y,u):lessis(ui,y)
-t2:=trlessis(ui,y,x,t1,l):lessis(ui,x)
--left
-left1to:=outn(x,ui".left",t2".left"):1to(x)
-[v:1to(y)][i:is"e"(1to(x),left1to(u),left1to(v))]
-+*left
-i@t3:=isoutne(x,ui,t2,ui(v),t2(v),i):is(ui,ui(v))
--left
-i@thleft1:=isinne(y,u,v,t3".left"):is"e"(1to(y),u,v)
-l@thleft2:=[u:1to(y)][v:1to(y)][t:is"e"(1to(x),left1to(u),left1to(v))]thleft1(u,v,t):injective(1to(y),1to(x),[t:1to(y)]left1to(t))
-y@[u:1to(y)]
-+right
-ui:=inn(y,u):nat
-t4:=1top(y,u):lessis(ui,y)
-t5:=satz19o(ui,y,x,t4):lessis(pl(x,ui),pl(x,y))
--right
-right1to:=outn(pl(x,y),pl(x,ui".right"),t5".right"):1to(pl(x,y))
-[v:1to(y)][i:is"e"(1to(pl(x,y)),right1to(u),right1to(v))]
-+*right
-i@t6:=isoutne(pl(x,y),pl(x,ui(u)),t5(u),pl(x,ui(v)),t5(v),i):is(pl(x,ui(u)),pl(x,ui(v)))
-t7:=satz20e(ui(u),ui(v),x,t6):is(ui(u),ui(v))
--right
-i@thright1:=isinne(y,u,v,t7".right"):is"e"(1to(y),u,v)
-@[alpha:'type'][x:nat][y:nat][l:lessis(y,x)][f:[t:1to(x)]alpha]
-left:=[t:1to(y)]<left1to(x,y,l,t)>f:[t:1to(y)]alpha
-y@[f:[t:1to(pl(x,y))]alpha]
-right:=[t:1to(y)]<right1to(x,y,t)>f:[t:1to(y)]alpha
-y@[i:is(y,x)][f:[t:1to(y)]alpha]
-+*left
-f@t4:=lessisi2(y,x,i):lessis(y,x)
-t5:=lessisi2(x,y,symis(nat,y,x,i)):lessis(x,y)
-f1:=left(y,x,t5,f):[t:1to(x)]alpha
-f2:=left(t4,f1):[t:1to(y)]alpha
-[u:1to(y)]
-t6:=isinoutn(x,inn(y,u),trlessis(inn(y,u),y,x,1top(y,u),t4)):is(inn(y,u),inn(x,left1to(x,y,t4,u)))
-t7:=tris(1to(y),u,outn(y,inn(y,u),1top(y,u)),left1to(y,x,t5,left1to(x,y,t4,u)),isoutinn(y,u),isoutni(y,inn(y,u),1top(y,u),inn(x,left1to(x,y,t4,u)),trlessis(inn(x,left1to(x,y,t4,u)),x,y,1top(x,left1to(x,y,t4,u)),t5),t6)):is"e"(1to(y),u,left1to(y,x,t5,left1to(x,y,t4,u)))
-t8:=isf(1to(y),alpha,f,u,left1to(y,x,t5,left1to(x,y,t4,u)),t7):is"e"(alpha,<u>f,<u>f2)
--left
-f@thleft:=fisi(1to(y),alpha,f,f2".left",[t:1to(y)]t8".left"(t)):is"e"([t:1to(y)]alpha,f,left(x,y,lessisi2(y,x,i),left(y,x,lessisi2(x,y,symis(nat,y,x,i)),f)))
-@frac:=pair1type(nat):'type'
-[x1:nat][x2:nat]
-fr:=pair1(nat,x1,x2):frac
-@[x:frac]
-num:=first1(nat,x):nat
-den:=second1(nat,x):nat
-x2@numis:=first1is1(nat,x1,x2):is(num(fr(x1,x2)),x1)
-isnum:=first1is2(nat,x1,x2):is(x1,num(fr(x1,x2)))
-denis:=second1is1(nat,x1,x2):is(den(fr(x1,x2)),x2)
-isden:=second1is2(nat,x1,x2):is(x2,den(fr(x1,x2)))
-x@1x:=num(x):nat
-2x:=den(x):nat
-fris:=pair1is1(nat,x):is"e"(frac,fr(1x,2x),x)
-isfr:=pair1is2(nat,x):is"e"(frac,x,fr(1x,2x))
-x2@[y1:nat][y2:nat]
-12isnd:=ists12(x1,num(fr(x1,x2)),y2,den(fr(y1,y2)),isnum(x1,x2),isden(y1,y2)):is(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))))
-ndis12:=symis(nat,ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),12isnd):is(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2))
-x@[n1:nat][n2:nat]
-1disnd:=ists1(n1,num(fr(n1,n2)),2x,isnum(n1,n2)):is(ts(n1,2x),ts(num(fr(n1,n2)),2x))
-ndis1d:=symis(nat,ts(n1,2x),ts(num(fr(n1,n2)),2x),1disnd):is(ts(num(fr(n1,n2)),2x),ts(n1,2x))
-n2isnd:=ists2(n2,den(fr(n1,n2)),1x,isden(n1,n2)):is(ts(1x,n2),ts(1x,den(fr(n1,n2))))
-ndisn2:=symis(nat,ts(1x,n2),ts(1x,den(fr(n1,n2))),n2isnd):is(ts(1x,den(fr(n1,n2))),ts(1x,n2))
-x2@[n:nat][i:is(x1,n)]
-isn:=isf(nat,frac,[t:nat]fr(t,x2),x1,n,i):is"e"(frac,fr(x1,x2),fr(n,x2))
-n@[i:is(x2,n)]
-isd:=isf(nat,frac,[t:nat]fr(x1,t),x2,n,i):is"e"(frac,fr(x1,x2),fr(x1,n))
-y2@[i:is(x1,y1)][j:is(x2,y2)]
-isnd:=tris(frac,fr(x1,x2),fr(y1,x2),fr(y1,y2),isn(x1,x2,y1,i),isd(y1,x2,y2,j)):is"e"(frac,fr(x1,x2),fr(y1,y2))
-x@[y:frac]
-1y:=num(y):nat
-2y:=den(y):nat
-eq:=is(ts(1x,2y),ts(1y,2x)):'prop'
-y2@[i:is(ts(x1,y2),ts(y1,x2))]
-eqi12:=tr3is(nat,ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ndis12(x1,x2,y1,y2),i,12isnd(y1,y2,x1,x2)):eq(fr(x1,x2),fr(y1,y2))
-n2@[i:is(ts(1x,n2),ts(n1,2x))]
-eqi1:=isp(frac,[t:frac]eq(t,fr(n1,n2)),fr(1x,2x),x,eqi12(1x,2x,n1,n2,i),fris):eq(x,fr(n1,n2))
-n2@[i:is(ts(n1,2x),ts(1x,n2))]
-eqi2:=isp(frac,[t:frac]eq(fr(n1,n2),t),fr(1x,2x),x,eqi12(n1,n2,1x,2x,i),fris):eq(fr(n1,n2),x)
-x@satz37:=refis(nat,ts(1x,2x)):eq(x,x)
-refeq:=satz37:eq(x,x)
-y@[i:is"e"(frac,x,y)]
-refeq1:=isp(frac,[t:frac]eq(x,t),x,y,refeq,i):eq(x,y)
-refeq2:=isp(frac,[t:frac]eq(t,x),x,y,refeq,i):eq(y,x)
-y2@[i:is(x1,y1)][j:is(x2,y2)]
-eqnd:=refeq1(fr(x1,x2),fr(y1,y2),isnd(i,j)):eq(fr(x1,x2),fr(y1,y2))
-x2@[n:nat][i:is(x1,n)]
-eqn:=refeq1(fr(x1,x2),fr(n,x2),isn(n,i)):eq(fr(x1,x2),fr(n,x2))
-n@[i:is(x2,n)]
-eqd:=refeq1(fr(x1,x2),fr(x1,n),isd(n,i)):eq(fr(x1,x2),fr(x1,n))
-y@[e:eq(x,y)]
-satz38:=symis(nat,ts(1x,2y),ts(1y,2x),e):eq(y,x)
-symeq:=satz38:eq(y,x)
-@[a:nat][b:nat][c:nat][d:nat]
-+ii1
-t1:=tris(nat,ts(b,ts(c,d)),ts(ts(b,c),d),ts(d,ts(b,c)),assts2(b,c,d),comts(ts(b,c),d)):is(ts(b,ts(c,d)),ts(d,ts(b,c)))
--ii1
-stets:=tr4is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(b,c))),ts(ts(a,d),ts(b,c)),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(b,c)),a,t1".ii1"),assts2(a,d,ts(b,c)),ists2(ts(b,c),ts(c,b),ts(a,d),comts(b,c))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
-+*ii1
-d@t2:=tr3is(nat,ts(b,ts(c,d)),ts(ts(c,d),b),ts(ts(d,c),b),ts(d,ts(c,b)),comts(b,ts(c,d)),ists1(ts(c,d),ts(d,c),b,comts(c,d)),assts1(d,c,b)):is(ts(b,ts(c,d)),ts(d,ts(c,b)))
-anders:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(c,b))),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(c,b)),a,t2),assts2(a,d,ts(c,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
--ii1
-y@[z:frac]
-1z:=num(z):nat
-2z:=den(z):nat
-[e:eq(x,y)][f:eq(y,z)]
-+139
-t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
-t2:=stets(1x,2y,1y,2z):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)))
-t3:=tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)))
-t4:=tr3is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),symis(nat,ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),t2),t1,t3):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
--139
-satz39:=satz33b(ts(1x,2z),ts(1z,2x),ts(1y,2y),t4".139"):eq(x,z)
-+*139
-f@anders:=tr4is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2z,1y,2y),ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
--139
-f@treq:=satz39:eq(x,z)
-z@[e:eq(z,x)][f:eq(z,y)]
-treq1:=treq(x,z,y,symeq(z,x,e),f):eq(x,y)
-z@[e:eq(x,z)][f:eq(y,z)]
-treq2:=treq(x,z,y,e,symeq(y,z,f)):eq(x,y)
-z@[u:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)]
-tr3eq:=treq(x,y,u,e,treq(y,z,u,f,g)):eq(x,u)
-u@[v:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)][h:eq(u,v)]
-tr4eq:=tr3eq(x,y,z,v,e,f,treq(z,u,v,g,h)):eq(x,v)
-x@[n:nat]
-satz40:=eqi1(ts(1x,n),ts(2x,n),tris(nat,ts(1x,ts(2x,n)),ts(1x,ts(n,2x)),ts(ts(1x,n),2x),ists2(ts(2x,n),ts(n,2x),1x,comts(2x,n)),assts2(1x,n,2x))):eq(x,fr(ts(1x,n),ts(2x,n)))
-satz40a:=symeq(x,fr(ts(1x,n),ts(2x,n)),satz40):eq(fr(ts(1x,n),ts(2x,n)),x)
-x2@[n:nat]
-satz40b:=eqi12(ts(x1,n),ts(x2,n),tris(nat,ts(x1,ts(x2,n)),ts(x1,ts(n,x2)),ts(ts(x1,n),x2),ists2(ts(x2,n),ts(n,x2),x1,comts(x2,n)),assts2(x1,n,x2))):eq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)))
-satz40c:=symeq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)),satz40b):eq(fr(ts(x1,n),ts(x2,n)),fr(x1,x2))
-y@moref:=more(ts(1x,2y),ts(1y,2x)):'prop'
-lessf:=less(ts(1x,2y),ts(1y,2x)):'prop'
-y2@[m:more(ts(x1,y2),ts(y1,x2))]
-morefi12:=ismore12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),m):moref(fr(x1,x2),fr(y1,y2))
-y2@[l:less(ts(x1,y2),ts(y1,x2))]
-lessfi12:=isless12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),l):lessf(fr(x1,x2),fr(y1,y2))
-n2@[m:more(ts(1x,n2),ts(n1,2x))]
-morefi1:=ismore12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),m):moref(x,fr(n1,n2))
-n2@[m:more(ts(n1,2x),ts(1x,n2))]
-morefi2:=ismore12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),m):moref(fr(n1,n2),x)
-n2@[l:less(ts(1x,n2),ts(n1,2x))]
-lessfi1:=isless12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),l):lessf(x,fr(n1,n2))
-n2@[l:less(ts(n1,2x),ts(1x,n2))]
-lessfi2:=isless12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),l):lessf(fr(n1,n2),x)
-y@satz41:=satz10(ts(1x,2y),ts(1y,2x)):orec3(eq(x,y),moref(x,y),lessf(x,y))
-satz41a:=satz10a(ts(1x,2y),ts(1y,2x)):or3(eq(x,y),moref(x,y),lessf(x,y))
-satz41b:=satz10b(ts(1x,2y),ts(1y,2x)):ec3(eq(x,y),moref(x,y),lessf(x,y))
-[m:moref(x,y)]
-satz42:=satz11(ts(1x,2y),ts(1y,2x),m):lessf(y,x)
-y@[l:lessf(x,y)]
-satz43:=satz12(ts(1x,2y),ts(1y,2x),l):moref(y,x)
-u@1u:=num(u):nat
-2u:=den(u):nat
-[m:moref(x,y)][e:eq(x,z)][f:eq(y,u)]
-+244
-t1:=ists12(ts(1y,2u),ts(1u,2y),ts(1z,2x),ts(1x,2z),f,symeq(x,z,e)):is(ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)))
-t2:=tr3is(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)),ts(ts(1u,2z),ts(1x,2y)),stets(1y,2x,1z,2u),t1,stets(1u,2y,1x,2z)):is(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)))
-t3:=ismore1(ts(ts(1u,2z),ts(1x,2y)),ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)),symis(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)),t2),satz32d(ts(1x,2y),ts(1y,2x),ts(1u,2z),m)):more(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)))
--244
-satz44:=satz33a(ts(1z,2u),ts(1u,2z),ts(1y,2x),ismore1(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1z,2u),ts(1y,2x)),ts(ts(1u,2z),ts(1y,2x)),comts(ts(1y,2x),ts(1z,2u)),t3".244")):moref(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][m:moref(x,z)]
-eqmoref12:=satz44(x,z,y,u,m,e,f):moref(y,u)
-z@[e:eq(x,y)][m:moref(x,z)]
-eqmoref1:=satz44(x,z,y,z,m,e,refeq(z)):moref(y,z)
-e@[m:moref(z,x)]
-eqmoref2:=satz44(z,x,z,y,m,refeq(z),e):moref(z,y)
-u@[l:lessf(x,y)][e:eq(x,z)][f:eq(y,u)]
-satz45:=satz42(u,z,satz44(y,x,u,z,satz43(x,y,l),f,e)):lessf(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][l:lessf(x,z)]
-eqlessf12:=satz45(x,z,y,u,l,e,f):lessf(y,u)
-z@[e:eq(x,y)][l:lessf(x,z)]
-eqlessf1:=satz45(x,z,y,z,l,e,refeq(z)):lessf(y,z)
-e@[l:lessf(z,x)]
-eqlessf2:=satz45(z,x,z,y,l,refeq(z),e):lessf(z,y)
-y@moreq:=or(moref(x,y),eq(x,y)):'prop'
-lesseq:=or(lessf(x,y),eq(x,y)):'prop'
-[e:eq(x,y)]
-moreqi2:=ori2(moref(x,y),eq(x,y),e):moreq(x,y)
-lesseqi2:=ori2(lessf(x,y),eq(x,y),e):lesseq(x,y)
-y@[m:moref(x,y)]
-moreqi1:=ori1(moref(x,y),eq(x,y),m):moreq(x,y)
-y@[l:lessf(x,y)]
-lesseqi1:=ori1(lessf(x,y),eq(x,y),l):lesseq(x,y)
-y@[m:moreq(x,y)]
-satz41c:=th7"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,comor(moref(x,y),eq(x,y),m)):not(lessf(x,y))
-y@[l:lesseq(x,y)]
-satz41d:=th9"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,l):not(moref(x,y))
-y@[n:not(moref(x,y))]
-satz41e:=th2"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n):lesseq(x,y)
-y@[n:not(lessf(x,y))]
-satz41f:=comor(eq(x,y),moref(x,y),th3"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n)):moreq(x,y)
-y@[m:moref(x,y)]
-satz41g:=th3"l.or"(lessf(x,y),eq(x,y),ec3e23(eq(x,y),moref(x,y),lessf(x,y),satz41b,m),ec3e21(eq(x,y),moref(x,y),lessf(x,y),satz41b,m)):not(lesseq(x,y))
-y@[l:lessf(x,y)]
-satz41h:=th3"l.or"(moref(x,y),eq(x,y),ec3e32(eq(x,y),moref(x,y),lessf(x,y),satz41b,l),ec3e31(eq(x,y),moref(x,y),lessf(x,y),satz41b,l)):not(moreq(x,y))
-y@[n:not(moreq(x,y))]
-satz41j:=or3e3(eq(x,y),moref(x,y),lessf(x,y),satz41a,th5"l.or"(moref(x,y),eq(x,y),n),th4"l.or"(moref(x,y),eq(x,y),n)):lessf(x,y)
-y@[n:not(lesseq(x,y))]
-satz41k:=or3e2(eq(x,y),moref(x,y),lessf(x,y),satz41a,th4"l.or"(lessf(x,y),eq(x,y),n),th5"l.or"(lessf(x,y),eq(x,y),n)):moref(x,y)
-u@[m:moreq(x,y)][e:eq(x,z)][f:eq(y,u)]
-+246
-[n:moref(x,y)]
-t1:=ori1(moref(z,u),eq(z,u),satz44(n,e,f)):moreq(z,u)
-f@[g:eq(x,y)]
-t2:=ori2(moref(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):moreq(z,u)
--246
-satz46:=orapp(moref(x,y),eq(x,y),moreq(z,u),m,[t:moref(x,y)]t1".246"(t),[t:eq(x,y)]t2".246"(t)):moreq(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][m:moreq(x,z)]
-eqmoreq12:=satz46(x,z,y,u,m,e,f):moreq(y,u)
-z@[e:eq(x,y)][m:moreq(x,z)]
-eqmoreq1:=satz46(x,z,y,z,m,e,refeq(z)):moreq(y,z)
-e@[m:moreq(z,x)]
-eqmoreq2:=satz46(z,x,z,y,m,refeq(z),e):moreq(z,y)
-u@[l:lesseq(x,y)][e:eq(x,z)][f:eq(y,u)]
-+247
-[k:lessf(x,y)]
-t1:=ori1(lessf(z,u),eq(z,u),satz45(k,e,f)):lesseq(z,u)
-f@[g:eq(x,y)]
-t2:=ori2(lessf(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):lesseq(z,u)
--247
-satz47:=orapp(lessf(x,y),eq(x,y),lesseq(z,u),l,[t:lessf(x,y)]t1".247"(t),[t:eq(x,y)]t2".247"(t)):lesseq(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][l:lesseq(x,z)]
-eqlesseq12:=satz47(x,z,y,u,l,e,f):lesseq(y,u)
-z@[e:eq(x,y)][l:lesseq(x,z)]
-eqlesseq1:=satz47(x,z,y,z,l,e,refeq(z)):lesseq(y,z)
-e@[l:lesseq(z,x)]
-eqlesseq2:=satz47(z,x,z,y,l,refeq(z),e):lesseq(z,y)
-y@[m:moreq(x,y)]
-satz48:=th9"l.or"(moref(x,y),eq(x,y),lessf(y,x),eq(y,x),m,[t:moref(x,y)]satz42(x,y,t),[t:eq(x,y)]satz38(x,y,t)):lesseq(y,x)
-y@[l:lesseq(x,y)]
-satz49:=th9"l.or"(lessf(x,y),eq(x,y),moref(y,x),eq(y,x),l,[t:lessf(x,y)]satz43(x,y,t),[t:eq(x,y)]satz38(x,y,t)):moreq(y,x)
-z@[l:lessf(x,y)][k:lessf(y,z)]
-+250
-t1:=satz34a(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),l,k):less(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
-t2:=isless12(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2y,1y,2z),tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))),t1):less(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
--250
-satz50:=satz33c(ts(1x,2z),ts(1z,2x),ts(1y,2y),t2".250"):lessf(x,z)
-trlessf:=satz50:lessf(x,z)
-z@[m:moref(x,y)][n:moref(y,z)]
-trmoref:=satz43(z,x,satz50(z,y,x,satz42(y,z,n),satz42(x,y,m))):moref(x,z)
-z@[l:lesseq(x,y)][k:lessf(y,z)]
-satz51a:=orapp(lessf(x,y),eq(x,y),lessf(x,z),l,[t:lessf(x,y)]satz50(t,k),[t:eq(x,y)]eqlessf1(y,x,z,symeq(x,y,t),k)):lessf(x,z)
-z@[l:lessf(x,y)][k:lesseq(y,z)]
-satz51b:=orapp(lessf(y,z),eq(y,z),lessf(x,z),k,[t:lessf(y,z)]satz50(l,t),[t:eq(y,z)]eqlessf2(y,z,x,t,l)):lessf(x,z)
-z@[m:moreq(x,y)][n:moref(y,z)]
-satz51c:=satz43(z,x,satz51b(z,y,x,satz42(y,z,n),satz48(x,y,m))):moref(x,z)
-z@[m:moref(x,y)][n:moreq(y,z)]
-satz51d:=satz43(z,x,satz51a(z,y,x,satz48(y,z,n),satz42(x,y,m))):moref(x,z)
-z@[l:lesseq(x,y)][k:lesseq(y,z)]
-+252
-[e:eq(x,y)][f:eq(y,z)]
-t1:=ori2(lessf(x,z),eq(x,z),treq(x,y,z,e,f)):lesseq(x,z)
-e@[j:lessf(y,z)]
-t2:=ori1(lessf(x,z),eq(x,z),satz51a(l,j)):lesseq(x,z)
-e@t3:=orapp(lessf(y,z),eq(y,z),lesseq(x,z),k,[t:lessf(y,z)]t2(t),[t:eq(y,z)]t1(t)):lesseq(x,z)
-k@[j:lessf(x,y)]
-t4:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
--252
-satz52:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t4".252"(t),[t:eq(x,y)]t3".252"(t)):lesseq(x,z)
-trlesseq:=satz52:lesseq(x,z)
-+*252
-k@[j:lessf(x,y)]
-t5:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
-k@[e:eq(x,y)]
-t6:=eqlesseq1(y,x,z,symeq(x,y,e),k):lesseq(x,z)
-k@anders:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t5(t),[t:eq(x,y)]t6(t)):lesseq(x,z)
--252
-z@[m:moreq(x,y)][n:moreq(y,z)]
-trmoreq:=satz49(z,x,satz52(z,y,x,satz48(y,z,n),satz48(x,y,m))):moreq(x,z)
-+253
-x@t1:=ismore1(pl(ts(1x,2x),ts(1x,2x)),ts(pl(1x,1x),2x),ts(1x,2x),distpt1(1x,1x,2x),satz18(ts(1x,2x),ts(1x,2x))):more(ts(pl(1x,1x),2x),ts(1x,2x))
-t2:=morefi2(pl(1x,1x),2x,t1):moref(fr(pl(1x,1x),2x),x)
--253
-x@satz53:=somei(frac,[t:frac]moref(t,x),fr(pl(1x,1x),2x),t2".253"):some"l"(frac,[t:frac]moref(t,x))
-+254
-t1:=isless2(pl(ts(1x,2x),ts(1x,2x)),ts(1x,pl(2x,2x)),ts(1x,2x),distpt2(1x,2x,2x),satz18a(ts(1x,2x),ts(1x,2x))):less(ts(1x,2x),ts(1x,pl(2x,2x)))
-t2:=lessfi2(1x,pl(2x,2x),t1):lessf(fr(1x,pl(2x,2x)),x)
--254
-satz54:=somei(frac,[t:frac]lessf(t,x),fr(1x,pl(2x,2x)),t2".254"):some"l"(frac,[t:frac]lessf(t,x))
-y@[l:lessf(x,y)]
-+255
-t1:=satz19f(ts(1x,2y),ts(1y,2x),ts(1x,2x),l):less(pl(ts(1x,2x),ts(1x,2y)),pl(ts(1x,2x),ts(1y,2x)))
-t2:=satz19c(ts(1x,2y),ts(1y,2x),ts(1y,2y),l):less(pl(ts(1x,2y),ts(1y,2y)),pl(ts(1y,2x),ts(1y,2y)))
-t3:=isless12(pl(ts(1x,2x),ts(1x,2y)),ts(1x,pl(2x,2y)),pl(ts(1x,2x),ts(1y,2x)),ts(pl(1x,1y),2x),distpt2(1x,2x,2y),distpt1(1x,1y,2x),t1):less(ts(1x,pl(2x,2y)),ts(pl(1x,1y),2x))
-t4:=lessfi1(pl(1x,1y),pl(2x,2y),t3):lessf(x,fr(pl(1x,1y),pl(2x,2y)))
-t5:=isless12(pl(ts(1x,2y),ts(1y,2y)),ts(pl(1x,1y),2y),pl(ts(1y,2x),ts(1y,2y)),ts(1y,pl(2x,2y)),distpt1(1x,1y,2y),distpt2(1y,2x,2y),t2):less(ts(pl(1x,1y),2y),ts(1y,pl(2x,2y)))
-t6:=lessfi2(y,pl(1x,1y),pl(2x,2y),t5):lessf(fr(pl(1x,1y),pl(2x,2y)),y)
-t7:=andi(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y),t4,t6):and(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y))
--255
-satz55:=somei(frac,[t:frac]and(lessf(x,t),lessf(t,y)),fr(pl(1x,1y),pl(2x,2y)),t7".255"):some"l"(frac,[t:frac]and(lessf(x,t),lessf(t,y)))
-y@pf:=fr(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)):frac
-+ii3
-y2@t1:=ispl12(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ts(y1,x2),ndis12(x1,x2,y1,y2),ndis12(y1,y2,x1,x2)):is(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),pl(ts(x1,y2),ts(y1,x2)))
-t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
--ii3
-y2@pf12:=isnd(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),ts(den(fr(x1,x2)),den(fr(y1,y2))),pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2),t1".ii3",t2".ii3"):is"e"(frac,pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
-+*ii3
-n2@t3:=ispl12(ts(1x,den(fr(n1,n2))),ts(1x,n2),ts(num(fr(n1,n2)),2x),ts(n1,2x),ndisn2(x,n1,n2),ndis1d(x,n1,n2)):is(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),pl(ts(1x,n2),ts(n1,2x)))
-t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
--ii3
-n2@pf1:=isnd(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),ts(2x,den(fr(n1,n2))),pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2),t3".ii3",t4".ii3"):is"e"(frac,pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
-+*ii3
-n2@t5:=ispl12(ts(num(fr(n1,n2)),2x),ts(n1,2x),ts(1x,den(fr(n1,n2))),ts(1x,n2),ndis1d(x,n1,n2),ndisn2(x,n1,n2)):is(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),pl(ts(n1,2x),ts(1x,n2)))
-t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
--ii3
-n2@pf2:=isnd(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),ts(den(fr(n1,n2)),2x),pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x),t5".ii3",t6".ii3"):is"e"(frac,pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
-y2@pfeq12a:=refeq1(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
-pfeq12b:=refeq2(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf(fr(x1,x2),fr(y1,y2)))
-n2@pfeq1a:=refeq1(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
-pfeq1b:=refeq2(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf(x,fr(n1,n2)))
-pfeq2a:=refeq1(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
-pfeq2b:=refeq2(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf(fr(n1,n2),x))
-u@[e:eq(x,y)][f:eq(z,u)]
-+356
-t1:=ists1(ts(1x,2y),ts(1y,2x),ts(2z,2u),e):is(ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)))
-t2:=t1(z,u,x,y,f,e):is(ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)))
-t3:=tr3is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2z),ts(2u,2y)),ts(ts(1x,2y),ts(2u,2z)),ts(ts(1x,2y),ts(2z,2u)),ists2(ts(2y,2u),ts(2u,2y),ts(1x,2z),comts(2y,2u)),stets(1x,2z,2u,2y),ists2(ts(2u,2z),ts(2z,2u),ts(1x,2y),comts(2u,2z))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)))
-t4:=tr4is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)),ts(ts(1y,2u),ts(2z,2x)),ts(ts(1y,2u),ts(2x,2z)),t3,t1,stets(1y,2x,2z,2u),ists2(ts(2z,2x),ts(2x,2z),ts(1y,2u),comts(2z,2x))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)))
-t5:=tr4is(nat,ts(ts(1z,2x),ts(2y,2u)),ts(ts(1z,2u),ts(2y,2x)),ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)),ts(ts(1u,2y),ts(2x,2z)),stets(1z,2x,2y,2u),ists2(ts(2y,2x),ts(2x,2y),ts(1z,2u),comts(2y,2x)),t2,stets(1u,2z,2x,2y)):is(ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)))
-t6:=ispl12(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)),ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)),t4,t5):is(pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))))
-t7:=tr3is(nat,ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)),disttp1(ts(1x,2z),ts(1z,2x),ts(2y,2u)),t6,distpt1(ts(1y,2u),ts(1u,2y),ts(2x,2z))):is(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)))
--356
-satz56:=eqi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2u),ts(1u,2y)),ts(2y,2u),t7".356"):eq(pf(x,z),pf(y,u))
-eqpf12:=satz56:eq(pf(x,z),pf(y,u))
-z@[e:eq(x,y)]
-eqpf1:=eqpf12(x,y,z,z,e,refeq(z)):eq(pf(x,z),pf(y,z))
-eqpf2:=eqpf12(z,z,x,y,refeq(z),e):eq(pf(z,x),pf(z,y))
-x2@[n:nat]
-satz57:=tr3eq(pf(fr(x1,n),fr(x2,n)),fr(pl(ts(x1,n),ts(x2,n)),ts(n,n)),fr(ts(pl(x1,x2),n),ts(n,n)),fr(pl(x1,x2),n),pfeq12a(x1,n,x2,n),eqn(pl(ts(x1,n),ts(x2,n)),ts(n,n),ts(pl(x1,x2),n),distpt1(x1,x2,n)),satz40c(pl(x1,x2),n,n)):eq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n))
-satz57a:=symeq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n),satz57):eq(fr(pl(x1,x2),n),pf(fr(x1,n),fr(x2,n)))
-y@satz58:=eqnd(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),pl(ts(1y,2x),ts(1x,2y)),ts(2y,2x),compl(ts(1x,2y),ts(1y,2x)),comts(2x,2y)):eq(pf(x,y),pf(y,x))
-compf:=satz58:eq(pf(x,y),pf(y,x))
-+359
-z@t1:=tr3is(nat,ts(ts(1y,2x),2z),ts(ts(2x,1y),2z),ts(2x,ts(1y,2z)),ts(ts(1y,2z),2x),ists1(ts(1y,2x),ts(2x,1y),2z,comts(1y,2x)),assts1(2x,1y,2z),comts(2x,ts(1y,2z))):is(ts(ts(1y,2x),2z),ts(ts(1y,2z),2x))
-t2:=ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),t1):is(pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
-t3:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),t2):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
-t4:=tris(nat,ts(1z,ts(2x,2y)),ts(1z,ts(2y,2x)),ts(ts(1z,2y),2x),ists2(ts(2x,2y),ts(2y,2x),1z,comts(2x,2y)),assts2(1z,2y,2x)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
-t5:=ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t3,t4):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)))
-t6:=ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x)):is(pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
-t7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),t5,asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),t6):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
--359
-z@satz59:=tr3eq(pf(pf(x,y),z),fr(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z)),fr(pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z))),pf(x,pf(y,z)),pfeq2a(z,pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)),eqnd(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z)),t7".359",assts1(2x,2y,2z)),pfeq1b(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z))):eq(pf(pf(x,y),z),pf(x,pf(y,z)))
-asspf1:=satz59:eq(pf(pf(x,y),z),pf(x,pf(y,z)))
-asspf2:=symeq(pf(pf(x,y),z),pf(x,pf(y,z)),asspf1):eq(pf(x,pf(y,z)),pf(pf(x,y),z))
-c@stets1:=tr3is(nat,ts(ts(a,b),c),ts(a,ts(b,c)),ts(a,ts(c,b)),ts(ts(a,c),b),assts1(a,b,c),ists2(ts(b,c),ts(c,b),a,comts(b,c)),assts2(a,c,b)):is(ts(ts(a,b),c),ts(ts(a,c),b))
-+*359
-z@t8:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),stets1(1y,2x,2z))):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
-t9:=tris(nat,ts(1z,ts(2x,2y)),ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),assts2(1z,2x,2y),stets1(1z,2x,2y)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
-anderst7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t8,t9),asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x))):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
--359
-+360
-y@t1:=satz18(ts(1x,2y),ts(1y,2x)):more(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y))
-t2:=satz32a(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y),2x,t1):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(ts(1x,2y),2x))
-t3:=tris(nat,ts(ts(1x,2y),2x),ts(1x,ts(2y,2x)),ts(1x,ts(2x,2y)),assts1(1x,2y,2x),ists2(ts(2y,2x),ts(2x,2y),1x,comts(2y,2x))):is(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)))
-t4:=ismore2(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)),ts(pl(ts(1x,2y),ts(1y,2x)),2x),t3,t2):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(1x,ts(2x,2y)))
--360
-y@satz60:=morefi2(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),t4".360"):moref(pf(x,y),x)
-satz60a:=satz42(pf(x,y),x,satz60):lessf(x,pf(x,y))
-z@[m:moref(x,y)]
-+361
-t1:=satz32a(ts(1x,2y),ts(1y,2x),2z,m):more(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z))
-t2:=ismore12(ts(ts(1x,2y),2z),ts(ts(1x,2z),2y),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),stets1(1x,2y,2z),stets1(1y,2x,2z),t1):more(ts(ts(1x,2z),2y),ts(ts(1y,2z),2x))
-t3:=stets1(1z,2x,2y):is(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x))
-t4:=satz19h(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),ts(ts(1x,2z),2y),ts(ts(1y,2z),2x),t3,t2):more(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)))
-t5:=ismore12(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),ts(pl(ts(1x,2z),ts(1z,2x)),2y),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),distpt1(ts(1x,2z),ts(1z,2x),2y),distpt1(ts(1y,2z),ts(1z,2y),2x),t4):more(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x))
-t6:=satz32a(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z,t5):more(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z))
-t7:=ismore12(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)),assts1(pl(ts(1x,2z),ts(1z,2x)),2y,2z),assts1(pl(ts(1y,2z),ts(1z,2y)),2x,2z),t6):more(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)))
--361
-satz61:=morefi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z),t7".361"):moref(pf(x,z),pf(y,z))
-z@[m:moref(x,y)]
-satz62a:=satz61(m):moref(pf(x,z),pf(y,z))
-z@[e:eq(x,y)]
-satz62b:=eqpf1(x,y,z,e):eq(pf(x,z),pf(y,z))
-z@[l:lessf(x,y)]
-satz62c:=satz42(pf(y,z),pf(x,z),satz61(y,x,z,satz43(l))):lessf(pf(x,z),pf(y,z))
-m@satz62d:=eqmoref12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62a):moref(pf(z,x),pf(z,y))
-e@satz62e:=eqpf2(x,y,z,e):eq(pf(z,x),pf(z,y))
-l@satz62f:=eqlessf12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62c):lessf(pf(z,x),pf(z,y))
-u@[e:eq(x,y)][m:moref(z,u)]
-satz62g:=eqmoref2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62d(z,u,x,m)):moref(pf(x,z),pf(y,u))
-satz62h:=eqmoref12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62g):moref(pf(z,x),pf(u,y))
-e@[l:lessf(z,u)]
-satz62j:=eqlessf2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62f(z,u,x,l)):lessf(pf(x,z),pf(y,u))
-satz62k:=eqlessf12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62j):lessf(pf(z,x),pf(u,y))
-+363
-z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
-t2:=satz41b(pf(x,z),pf(y,z)):ec3(eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)))
--363
-z@[m:moref(pf(x,z),pf(y,z))]
-satz63a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),m):moref(x,y)
-z@[e:eq(pf(x,z),pf(y,z))]
-satz63b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),e):eq(x,y)
-z@[l:lessf(pf(x,z),pf(y,z))]
-satz63c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),l):lessf(x,y)
-z@[m:moref(pf(z,x),pf(z,y))]
-satz63d:=satz63a(eqmoref12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),m)):moref(x,y)
-z@[e:eq(pf(z,x),pf(z,y))]
-satz63e:=satz63b(tr3eq(pf(x,z),pf(z,x),pf(z,y),pf(y,z),compf(x,z),e,compf(z,y))):eq(x,y)
-z@[f:lessf(pf(z,x),pf(z,y))]
-satz63f:=satz63c(eqlessf12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),f)):lessf(x,y)
-u@[m:moref(x,y)][n:moref(z,u)]
-+364
-t1:=satz61(x,y,z,m):moref(pf(x,z),pf(y,z))
-t2:=eqmoref12(pf(z,y),pf(y,z),pf(u,y),pf(y,u),compf(z,y),compf(u,y),satz61(z,u,y,n)):moref(pf(y,z),pf(y,u))
--364
-satz64:=trmoref(pf(x,z),pf(y,z),pf(y,u),t1".364",t2".364"):moref(pf(x,z),pf(y,u))
-u@[l:lessf(x,y)][k:lessf(z,u)]
-satz64a:=satz42(pf(y,u),pf(x,z),satz64(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
-u@[m:moreq(x,y)][n:moref(z,u)]
-satz65a:=orapp(moref(x,y),eq(x,y),moref(pf(x,z),pf(y,u)),m,[v:moref(x,y)]satz64(v,n),[v:eq(x,y)]satz62g(v,n)):moref(pf(x,z),pf(y,u))
-u@[m:moref(x,y)][n:moreq(z,u)]
-satz65b:=orapp(moref(z,u),eq(z,u),moref(pf(x,z),pf(y,u)),n,[v:moref(z,u)]satz64(m,v),[v:eq(z,u)]eqmoref2(pf(y,z),pf(y,u),pf(x,z),eqpf2(z,u,y,v),satz61(x,y,z,m))):moref(pf(x,z),pf(y,u))
-u@[l:lesseq(x,y)][k:lessf(z,u)]
-satz65c:=satz42(pf(y,u),pf(x,z),satz65a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
-u@[l:lessf(x,y)][k:lesseq(z,u)]
-satz65d:=satz42(pf(y,u),pf(x,z),satz65b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(pf(x,z),pf(y,u))
-u@[m:moreq(x,y)][n:moreq(z,u)]
-+366
-[e:eq(x,y)][f:eq(z,u)]
-t1:=moreqi2(pf(x,z),pf(y,u),satz56(e,f)):moreq(pf(x,z),pf(y,u))
-e@[o:moref(z,u)]
-t2:=moreqi1(pf(x,z),pf(y,u),satz65a(m,o)):moreq(pf(x,z),pf(y,u))
-e@t3:=orapp(moref(z,u),eq(z,u),moreq(pf(x,z),pf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(pf(x,z),pf(y,u))
-n@[o:moref(x,y)]
-t4:=moreqi1(pf(x,z),pf(y,u),satz65b(o,n)):moreq(pf(x,z),pf(y,u))
--366
-satz66:=orapp(moref(x,y),eq(x,y),moreq(pf(x,z),pf(y,u)),m,[v:moref(x,y)]t4".366"(v),[v:eq(x,y)]t3".366"(v)):moreq(pf(x,z),pf(y,u))
-u@[l:lesseq(x,y)][k:lesseq(z,u)]
-satz66a:=satz48(pf(y,u),pf(x,z),satz66(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(pf(x,z),pf(y,u))
-y@[l:lesseq(x,y)]
-+367
-[v:frac][e:eq(pf(y,v),x)]
-t1:=eqmoref1(pf(y,v),x,y,e,satz60(y,v)):moref(x,y)
-v@t2:=th3"l.imp"(eq(pf(y,v),x),moref(x,y),satz41d(x,y,l),[t:eq(pf(y,v),x)]t1(t)):not(eq(pf(y,v),x))
--367
-vorbemerkung67:=th5"l.some"(frac,[v:frac]eq(pf(y,v),x),[v:frac]t2".367"(v)):not(some"l"(frac,[t:frac]eq(pf(y,t),x)))
-y@[v:frac][w:frac][e:eq(pf(y,v),x)][f:eq(pf(y,w),x)]
-satz67b:=satz63e(v,w,y,treq2(pf(y,v),pf(y,w),x,e,f)):eq(v,w)
-y@[m:moref(x,y)]
-+*367
-m@t3:=onei(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),satz8b(ts(1x,2y),ts(1y,2x)),m):one([t:nat]diffprop(ts(1x,2y),ts(1y,2x),t))
-vo:=ind(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):nat
-t4:=oneax(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):is(ts(1x,2y),pl(ts(1y,2x),vo))
-w:=fr(vo,ts(2x,2y)):frac
-t5:=treq(y,fr(ts(1y,2x),ts(2y,2x)),fr(ts(1y,2x),ts(2x,2y)),satz40(y,2x),eqd(ts(1y,2x),ts(2y,2x),ts(2x,2y),comts(2y,2x))):eq(y,fr(ts(1y,2x),ts(2x,2y)))
-t6:=tr4eq(pf(y,w),pf(fr(ts(1y,2x),ts(2x,2y)),fr(vo,ts(2x,2y))),fr(pl(ts(1y,2x),vo),ts(2x,2y)),fr(ts(1x,2y),ts(2x,2y)),x,eqpf1(y,fr(ts(1y,2x),ts(2x,2y)),w,t5),satz57(ts(1y,2x),vo,ts(2x,2y)),eqn(pl(ts(1y,2x),vo),ts(2x,2y),ts(1x,2y),symis(nat,ts(1x,2y),pl(ts(1y,2x),vo),t4)),satz40a(x,2y)):eq(pf(y,w),x)
--367
-m@satz67a:=somei(frac,[t:frac]eq(pf(y,t),x),w".367",t6".367"):some"l"(frac,[t:frac]eq(pf(y,t),x))
-mf:=w".367":frac
-satz67c:=t6".367":eq(pf(y,mf(x,y,m)),x)
-satz67d:=symeq(pf(y,mf(x,y,m)),x,satz67c):eq(x,pf(y,mf(x,y,m)))
-y@[v:frac][m:moref(x,y)][e:eq(pf(y,v),x)]
-satz67e:=satz67b(v,mf(x,y,m),e,satz67c(m)):eq(v,mf(x,y,m))
-y@tf:=fr(ts(1x,1y),ts(2x,2y)):frac
-+ii4
-y2@t1:=ists12(num(fr(x1,x2)),x1,num(fr(y1,y2)),y1,numis(x1,x2),numis(y1,y2)):is(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(x1,y1))
-t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
--ii4
-y2@tf12:=isnd(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y1),ts(x2,y2),t1".ii4",t2".ii4"):is"e"(frac,tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
-+*ii4
-n2@t3:=ists2(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(1x,num(fr(n1,n2))),ts(1x,n1))
-t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
--ii4
-n2@tf1:=isnd(ts(1x,num(fr(n1,n2))),ts(2x,den(fr(n1,n2))),ts(1x,n1),ts(2x,n2),t3".ii4",t4".ii4"):is"e"(frac,tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
-+*ii4
-n2@t5:=ists1(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(num(fr(n1,n2)),1x),ts(n1,1x))
-t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
--ii4
-n2@tf2:=isnd(ts(num(fr(n1,n2)),1x),ts(den(fr(n1,n2)),2x),ts(n1,1x),ts(n2,2x),t5".ii4",t6".ii4"):is"e"(frac,tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
-y2@tfeq12a:=refeq1(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
-tfeq12b:=refeq2(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(fr(ts(x1,y1),ts(x2,y2)),tf(fr(x1,x2),fr(y1,y2)))
-n2@tfeq1a:=refeq1(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
-tfeq1b:=refeq2(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(fr(ts(1x,n1),ts(2x,n2)),tf(x,fr(n1,n2)))
-tfeq2a:=refeq1(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
-tfeq2b:=refeq2(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(fr(ts(n1,1x),ts(n2,2x)),tf(fr(n1,n2),x))
-u@[e:eq(x,y)][f:eq(z,u)]
-+468
-t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1z,2u),ts(1u,2z),e,f):is(ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)))
--468
-d@stets2:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(ts(a,b),ts(d,c)),ts(ts(a,c),ts(d,b)),ts(ts(a,c),ts(b,d)),ists2(ts(c,d),ts(d,c),ts(a,b),comts(c,d)),stets(a,b,d,c),ists2(ts(d,b),ts(b,d),ts(a,c),comts(d,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,c),ts(b,d)))
-+*468
-f@t2:=tr3is(nat,ts(ts(1x,1z),ts(2y,2u)),ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)),ts(ts(1y,1u),ts(2x,2z)),stets2(1x,1z,2y,2u),t1,stets2(1y,2x,1u,2z)):is(ts(ts(1x,1z),ts(2y,2u)),ts(ts(1y,1u),ts(2x,2z)))
--468
-f@satz68:=eqi12(ts(1x,1z),ts(2x,2z),ts(1y,1u),ts(2y,2u),t2".468"):eq(tf(x,z),tf(y,u))
-eqtf12:=satz68:eq(tf(x,z),tf(y,u))
-z@[e:eq(x,y)]
-eqtf1:=eqtf12(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
-eqtf2:=eqtf12(z,z,x,y,refeq(z),e):eq(tf(z,x),tf(z,y))
-y@satz69:=eqnd(ts(1x,1y),ts(2x,2y),ts(1y,1x),ts(2y,2x),comts(1x,1y),comts(2x,2y)):eq(tf(x,y),tf(y,x))
-comtf:=satz69:eq(tf(x,y),tf(y,x))
-z@satz70:=tr3eq(tf(tf(x,y),z),fr(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z)),fr(ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z))),tf(x,tf(y,z)),tfeq2a(z,ts(1x,1y),ts(2x,2y)),eqnd(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z),ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z)),assts1(1x,1y,1z),assts1(2x,2y,2z)),tfeq1b(x,ts(1y,1z),ts(2y,2z))):eq(tf(tf(x,y),z),tf(x,tf(y,z)))
-asstf1:=satz70:eq(tf(tf(x,y),z),tf(x,tf(y,z)))
-asstf2:=symeq(tf(tf(x,y),z),tf(x,tf(y,z)),asstf1):eq(tf(x,tf(y,z)),tf(tf(x,y),z))
-+471
-t1:=tr3eq(tf(x,pf(y,z)),fr(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z))),fr(pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),ts(2x,ts(2y,2z))),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),tfeq1a(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z)),eqn(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z)),pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),disttp2(1x,ts(1y,2z),ts(1z,2y))),satz57a(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))):eq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))))
-t2:=treq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(ts(1x,1y),2z),ts(ts(2x,2y),2z)),tf(x,y),eqnd(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z)),ts(ts(1x,1y),2z),ts(ts(2x,2y),2z),assts2(1x,1y,2z),assts2(2x,2y,2z)),satz40c(ts(1x,1y),ts(2x,2y),2z)):eq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y))
-t3:=treq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2z,2y))),tf(x,z),eqd(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)),ts(2x,ts(2z,2y)),ists2(ts(2y,2z),ts(2z,2y),2x,comts(2y,2z))),t2(x,z,y)):eq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z))
--471
-satz71:=treq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),pf(tf(x,y),tf(x,z)),t1".471",eqpf12(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z),t2".471",t3".471")):eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
-disttpf1:=tr3eq(tf(pf(x,y),z),tf(z,pf(x,y)),pf(tf(z,x),tf(z,y)),pf(tf(x,z),tf(y,z)),comtf(pf(x,y),z),satz71(z,x,y),eqpf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y))):eq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)))
-disttpf2:=satz71:eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
-distptf1:=symeq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)),disttpf1):eq(pf(tf(x,z),tf(y,z)),tf(pf(x,y),z))
-distptf2:=symeq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),disttpf2):eq(pf(tf(x,y),tf(x,z)),tf(x,pf(y,z)))
-[m:moref(x,y)]
-+472
-t1:=satz32a(ts(1x,2y),ts(1y,2x),ts(1z,2z),m):more(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1y,2x),ts(1z,2z)))
-t2:=ismore12(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,2x),ts(1z,2z)),ts(ts(1y,1z),ts(2x,2z)),stets2(1x,2y,1z,2z),stets2(1y,2x,1z,2z),t1):more(ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,1z),ts(2x,2z)))
--472
-satz72a:=morefi12(ts(1x,1z),ts(2x,2z),ts(1y,1z),ts(2y,2z),t2".472"):moref(tf(x,z),tf(y,z))
-z@[e:eq(x,y)]
-satz72b:=satz68(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
-z@[l:lessf(x,y)]
-satz72c:=satz42(tf(y,z),tf(x,z),satz72a(y,x,z,satz43(x,y,l))):lessf(tf(x,z),tf(y,z))
-m@satz72d:=eqmoref12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72a):moref(tf(z,x),tf(z,y))
-e@satz72e:=eqtf2(x,y,z,e):eq(tf(z,x),tf(z,y))
-l@satz72f:=eqlessf12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72c):lessf(tf(z,x),tf(z,y))
-u@[e:eq(x,y)][m:moref(z,u)]
-satz72g:=eqmoref2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72d(z,u,x,m)):moref(tf(x,z),tf(y,u))
-satz72h:=eqmoref12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72g):moref(tf(z,x),tf(u,y))
-e@[l:lessf(z,u)]
-satz72j:=eqlessf2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72f(z,u,x,l)):lessf(tf(x,z),tf(y,u))
-satz72k:=eqlessf12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72j):lessf(tf(z,x),tf(u,y))
-+473
-z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
-t2:=satz41b(tf(x,z),tf(y,z)):ec3(eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)))
--473
-z@[m:moref(tf(x,z),tf(y,z))]
-satz73a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),m):moref(x,y)
-z@[e:eq(tf(x,z),tf(y,z))]
-satz73b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),e):eq(x,y)
-z@[l:lessf(tf(x,z),tf(y,z))]
-satz73c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),l):lessf(x,y)
-z@[m:moref(tf(z,x),tf(z,y))]
-satz73d:=satz73a(eqmoref12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),m)):moref(x,y)
-z@[e:eq(tf(z,x),tf(z,y))]
-satz73e:=satz73b(tr3eq(tf(x,z),tf(z,x),tf(z,y),tf(y,z),comtf(x,z),e,comtf(z,y))):eq(x,y)
-z@[l:lessf(tf(z,x),tf(z,y))]
-satz73f:=satz73c(eqlessf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),l)):lessf(x,y)
-u@[m:moref(x,y)][n:moref(z,u)]
-+474
-t1:=satz72a(x,y,z,m):moref(tf(x,z),tf(y,z))
-t2:=eqmoref12(tf(z,y),tf(y,z),tf(u,y),tf(y,u),comtf(z,y),comtf(u,y),satz72a(z,u,y,n)):moref(tf(y,z),tf(y,u))
--474
-satz74:=trmoref(tf(x,z),tf(y,z),tf(y,u),t1".474",t2".474"):moref(tf(x,z),tf(y,u))
-u@[l:lessf(x,y)][k:lessf(z,u)]
-satz74a:=satz42(tf(y,u),tf(x,z),satz74(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
-u@[m:moreq(x,y)][n:moref(z,u)]
-satz75a:=orapp(moref(x,y),eq(x,y),moref(tf(x,z),tf(y,u)),m,[v:moref(x,y)]satz74(v,n),[v:eq(x,y)]satz72g(v,n)):moref(tf(x,z),tf(y,u))
-u@[m:moref(x,y)][n:moreq(z,u)]
-satz75b:=orapp(moref(z,u),eq(z,u),moref(tf(x,z),tf(y,u)),n,[v:moref(z,u)]satz74(m,v),[v:eq(z,u)]eqmoref2(tf(y,z),tf(y,u),tf(x,z),eqtf2(z,u,y,v),satz72a(m))):moref(tf(x,z),tf(y,u))
-u@[l:lesseq(x,y)][k:lessf(z,u)]
-satz75c:=satz42(tf(y,u),tf(x,z),satz75a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
-u@[l:lessf(x,y)][k:lesseq(z,u)]
-satz75d:=satz42(tf(y,u),tf(x,z),satz75b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(tf(x,z),tf(y,u))
-u@[m:moreq(x,y)][n:moreq(z,u)]
-+476
-[e:eq(x,y)][f:eq(z,u)]
-t1:=moreqi2(tf(x,z),tf(y,u),satz68(e,f)):moreq(tf(x,z),tf(y,u))
-e@[o:moref(z,u)]
-t2:=moreqi1(tf(x,z),tf(y,u),satz75a(m,o)):moreq(tf(x,z),tf(y,u))
-e@t3:=orapp(moref(z,u),eq(z,u),moreq(tf(x,z),tf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(tf(x,z),tf(y,u))
-n@[o:moref(x,y)]
-t4:=moreqi1(tf(x,z),tf(y,u),satz75b(o,n)):moreq(tf(x,z),tf(y,u))
--476
-satz76:=orapp(moref(x,y),eq(x,y),moreq(tf(x,z),tf(y,u)),m,[v:moref(x,y)]t4".476"(v),[v:eq(x,y)]t3".476"(v)):moreq(tf(x,z),tf(y,u))
-u@[l:lesseq(x,y)][k:lesseq(z,u)]
-satz76a:=satz48(tf(y,u),tf(x,z),satz76(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(tf(x,z),tf(y,u))
-y@[v:frac][w:frac][e:eq(tf(y,v),x)][f:eq(tf(y,w),x)]
-satz77b:=satz73e(v,w,y,treq2(tf(y,v),tf(y,w),x,e,f)):eq(v,w)
-+477
-y@v:=fr(ts(1x,2y),ts(2x,1y)):frac
-t1:=tr4eq(tf(y,v),tf(v,y),fr(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y)),fr(ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y))),x,comtf(y,v),tfeq2a(y,ts(1x,2y),ts(2x,1y)),eqnd(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y),ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y)),tris(nat,ts(ts(1x,2y),1y),ts(1x,ts(2y,1y)),ts(1x,ts(1y,2y)),assts1(1x,2y,1y),ists2(ts(2y,1y),ts(1y,2y),1x,comts(2y,1y))),assts1(2x,1y,2y)),satz40a(x,ts(1y,2y))):eq(tf(y,v),x)
--477
-y@satz77a:=somei(frac,[t:frac]eq(tf(y,t),x),v".477",t1".477"):some"l"(frac,[t:frac]eq(tf(y,t),x))
-+rt
-@eq:=[x:frac][y:frac]eq"n"(x,y):[x:frac][y:frac]'prop'
-refeq:=[x:frac]refeq"n"(x):[x:frac]<x><x>eq
-symeq:=[x:frac][y:frac][t:<y><x>eq]symeq"n"(x,y,t):[x:frac][y:frac][t:<y><x>eq]<x><y>eq
-treq:=[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]treq"n"(x,y,z,t,u):[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]<z><x>eq
-[x:frac][s:set(frac)]
-inf:=esti(frac,x,s):'prop'
-@rat:=ect"eq"(frac,eq,refeq,symeq,treq):'type'
-[x0:rat][y0:rat]
-is:=is"e"(rat,x0,y0):'prop'
-nis:=not(is(x0,y0)):'prop'
-@[p:[x:rat]'prop']
-some:=some"l"(rat,p):'prop'
-all:=all"l"(rat,p):'prop'
-one:=one"e"(rat,p):'prop'
-x0@[s:set(rat)]
-in:=esti(rat,x0,s):'prop'
-x@ratof:=ectelt"eq"(frac,eq,refeq,symeq,treq,x):rat
-x0@class:=ecect"eq"(frac,eq,refeq,symeq,treq,x0):set(frac)
-x@inclass:=th5"eq.4"(frac,eq,refeq,symeq,treq,x):inf(x,class(ratof(x)))
-x0@[x:frac][y:frac][xix0:inf(x,class(x0))][e:eq"n"(x,y)]
-lemmaeq1:=th8"eq.4"(frac,eq,refeq,symeq,treq,x0,x,xix0,y,e):inf(y,class(x0))
-x0@[a:'prop'][a1:[x:frac][xi:inf(x,class(x0))]a]
-ratapp1:=th3"eq.4"(frac,eq,refeq,symeq,treq,x0,a,a1):a
-y0@[a:'prop'][a1:[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]a][x:frac][xix0:inf(x,class(x0))]
-+ii5
-t1:=ratapp1(y0,a,[y:frac][yi:inf(y,class(y0))]<yi><xix0><y><x>a1):a
--ii5
-a1@ratapp2:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t1".ii5"(x,xi)):a
-y0@[z0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]a][x:frac][xix0:inf(x,class(x0))]
-+*ii5
-xix0@t2:=ratapp2(y0,z0,a,[y:frac][z:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))]<zi><yi><xix0><z><y><x>a1):a
--ii5
-a1@ratapp3:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t2".ii5"(x,xi)):a
-z0@[u0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]a][x:frac][xix0:inf(x,class(x0))]
-+*ii5
-xix0@t3:=ratapp3(y0,z0,u0,a,[y:frac][z:frac][u:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]<ui><zi><yi><xix0><u><z><y><x>a1):a
--ii5
-a1@ratapp4:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t3".ii5"(x,xi)):a
-y0@[x1:frac][y1:frac][x1ix0:inf(x1,class(x0))][y1iy0:inf(y1,class(y0))][e:eq"n"(x1,y1)]
-isi:=th3"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,e):is(x0,y0)
-y1iy0@[i:is(x0,y0)]
-ise:=th5"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,i):eq"n"(x1,y1)
-y1iy0@[n:not(eq"n"(x1,y1))]
-nisi:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),n,[t:is(x0,y0)]ise(t)):nis(x0,y0)
-y1iy0@[n:nis(x0,y0)]
-nise:=th3"l.imp"(eq"n"(x1,y1),is(x0,y0),n,[t:eq"n"(x1,y1)]isi(t)):not(eq"n"(x1,y1))
-@[alpha:'type'][f:[x:frac][y:frac]alpha]
-fixf:=fixfu2"eq"(frac,eq,refeq,symeq,treq,alpha,f):'prop'
-y0@[alpha:'type'][f:[x:frac][y:frac]alpha][ff:fixf(alpha,f)]
-indrat:=indeq2"eq"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0):alpha
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-isindrat:=th1"eq.11"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0,x,xix0,y,yiy0):is"e"(alpha,<y><x>f,indrat)
-x0@satz78:=refis(rat,x0):is(x0,x0)
-y0@[i:is(x0,y0)]
-satz79:=symis(rat,x0,y0,i):is(y0,x0)
-z0@[i:is(x0,y0)][j:is(y0,z0)]
-satz80:=tris(rat,x0,y0,z0,i,j):is(x0,z0)
-y0@more:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),moref(x,y)))):'prop'
-+*ii5
-y1@propm:=and3(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1)):'prop'
--ii5
-y0@[m:more(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propm".ii5"(t,u))][u:frac][p:propm".ii5"(t,u)]
-+*ii5
-p@t4:=and3e1(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(t,class(x0))
-t5:=and3e2(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(u,class(y0))
-t6:=and3e3(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):moref(t,u)
-t7:=satz44(t,u,x,y,t6,ise(x0,x0,t,x,t4,xix0,refis(rat,x0)),ise(y0,y0,u,y,t5,yiy0,refis(rat,y0))):moref(x,y)
-s@t8:=someapp(frac,[u:frac]propm(t,u),s,moref(x,y),[u:frac][v:propm(t,u)]t7(u,v)):moref(x,y)
--ii5
-yiy0@also18:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propm".ii5"(t,u)),m,moref(x,y),[t:frac][v:some"l"(frac,[u:frac]propm".ii5"(t,u))]t8".ii5"(t,v)):moref(x,y)
-y1iy0@[m:moref(x1,y1)]
-+*ii5
-m@t9:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1),x1ix0,y1iy0,m):propm(x1,y1)
-t10:=somei(frac,[t:frac]propm(x1,t),y1,t9):some"l"(frac,[t:frac]propm(x1,t))
--ii5
-m@morei:=somei(frac,[u:frac]some"l"(frac,[t:frac]propm".ii5"(u,t)),x1,t10".ii5"):more(x0,y0)
-y1iy0@[m:more(x0,y0)]
-moree:=also18(m,x1,y1,x1ix0,y1iy0):moref(x1,y1)
-z0@[i:is(x0,y0)][m:more(x0,z0)]
-ismore1:=isp(rat,[t:rat]more(t,z0),x0,y0,m,i):more(y0,z0)
-i@[m:more(z0,x0)]
-ismore2:=isp(rat,[t:rat]more(z0,t),x0,y0,m,i):more(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][m:more(x0,z0)]
-ismore12:=ismore2(z0,u0,y0,j,ismore1(x0,y0,z0,i,m)):more(y0,u0)
-y0@less:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),lessf(x,y)))):'prop'
-+*ii5
-y1@propl:=and3(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1)):'prop'
--ii5
-y0@[l:less(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propl".ii5"(t,u))][u:frac][p:propl".ii5"(t,u)]
-+*ii5
-p@t11:=and3e1(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(t,class(x0))
-t12:=and3e2(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(u,class(y0))
-t13:=and3e3(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):lessf(t,u)
-t14:=satz45(t,u,x,y,t13,ise(x0,x0,t,x,t11,xix0,refis(rat,x0)),ise(y0,y0,u,y,t12,yiy0,refis(rat,y0))):lessf(x,y)
-s@t15:=someapp(frac,[u:frac]propl(t,u),s,lessf(x,y),[u:frac][v:propl(t,u)]t14(u,v)):lessf(x,y)
--ii5
-yiy0@also19:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propl".ii5"(t,u)),l,lessf(x,y),[t:frac][v:some"l"(frac,[u:frac]propl".ii5"(t,u))]t15".ii5"(t,v)):lessf(x,y)
-y1iy0@[l:lessf(x1,y1)]
-+*ii5
-l@t16:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1),x1ix0,y1iy0,l):propl(x1,y1)
-t17:=somei(frac,[t:frac]propl(x1,t),y1,t16):some"l"(frac,[t:frac]propl(x1,t))
--ii5
-l@lessi:=somei(frac,[u:frac]some"l"(frac,[t:frac]propl".ii5"(u,t)),x1,t17".ii5"):less(x0,y0)
-y1iy0@[l:less(x0,y0)]
-lesse:=also19(l,x1,y1,x1ix0,y1iy0):lessf(x1,y1)
-z0@[i:is(x0,y0)][l:less(x0,z0)]
-isless1:=isp(rat,[t:rat]less(t,z0),x0,y0,l,i):less(y0,z0)
-i@[l:less(z0,x0)]
-isless2:=isp(rat,[t:rat]less(z0,t),x0,y0,l,i):less(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][l:less(x0,z0)]
-isless12:=isless2(z0,u0,y0,j,isless1(x0,y0,z0,i,l)):less(y0,u0)
-+581
-y1iy0@t1:=satz41a(x1,y1):or3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
-[e:eq"n"(x1,y1)]
-t2:=or3i1(is(x0,y0),more(x0,y0),less(x0,y0),isi(e)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-y1iy0@[m:moref(x1,y1)]
-t3:=or3i2(is(x0,y0),more(x0,y0),less(x0,y0),morei(m)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-y1iy0@[l:lessf(x1,y1)]
-t4:=or3i3(is(x0,y0),more(x0,y0),less(x0,y0),lessi(l)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-y1iy0@t5:=or3app(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),or3(is(x0,y0),more(x0,y0),less(x0,y0)),t1,[t:eq"n"(x1,y1)]t2(t),[t:moref(x1,y1)]t3(t),[t:lessf(x1,y1)]t4(t)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-t6:=satz41b(x1,y1):ec3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
-[i:is(x0,y0)]
-t7:=th3"l.imp"(more(x0,y0),moref(x1,y1),ec3e12(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,ise(i)),[t:more(x0,y0)]moree(t)):not(more(x0,y0))
-y1iy0@[m:more(x0,y0)]
-t8:=th3"l.imp"(less(x0,y0),lessf(x1,y1),ec3e23(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,moree(m)),[t:less(x0,y0)]lesse(t)):not(less(x0,y0))
-y1iy0@[l:less(x0,y0)]
-t9:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),ec3e31(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,lesse(l)),[t:is(x0,y0)]ise(t)):nis(x0,y0)
-y1iy0@t10:=th6"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),th1"l.ec"(is(x0,y0),more(x0,y0),[t:is(x0,y0)]t7(t)),th1"l.ec"(more(x0,y0),less(x0,y0),[t:more(x0,y0)]t8(t)),th1"l.ec"(less(x0,y0),is(x0,y0),[t:less(x0,y0)]t9(t))):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
-t11:=orec3i(is(x0,y0),more(x0,y0),less(x0,y0),t5,t10):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
--581
-y0@satz81:=ratapp2(orec3(is(x0,y0),more(x0,y0),less(x0,y0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t11".581"(x,y,xi,yi)):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
-satz81a:=orec3e1(is(x0,y0),more(x0,y0),less(x0,y0),satz81):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-satz81b:=orec3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
-[m:more(x0,y0)]
-+582
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=lessi(y0,x0,y,x,yiy0,xix0,satz42(x,y,moree(x0,y0,x,y,xix0,yiy0,m))):less(y0,x0)
--582
-satz82:=ratapp2(less(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".582"(x,y,xi,yi)):less(y0,x0)
-y0@[l:less(x0,y0)]
-+583
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=morei(y0,x0,y,x,yiy0,xix0,satz43(x,y,lesse(x0,y0,x,y,xix0,yiy0,l))):more(y0,x0)
--583
-satz83:=ratapp2(more(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".583"(x,y,xi,yi)):more(y0,x0)
-y0@moreis:=or(more(x0,y0),is(x0,y0)):'prop'
-[m:more(x0,y0)]
-moreisi1:=ori1(more,is,m):moreis(x0,y0)
-y0@[i:is(x0,y0)]
-moreisi2:=ori2(more,is,i):moreis(x0,y0)
-y1iy0@[m:moreq(x1,y1)]
-moreisi:=orapp(moref(x1,y1),eq"n"(x1,y1),moreis,m,[t:moref(x1,y1)]moreisi1(morei(t)),[t:eq"n"(x1,y1)]moreisi2(isi(t))):moreis(x0,y0)
-y1iy0@[m:moreis(x0,y0)]
-moreise:=orapp(more,is,moreq(x1,y1),m,[t:more]moreqi1(x1,y1,moree(t)),[t:is]moreqi2(x1,y1,ise(t))):moreq(x1,y1)
-z0@[i:is(x0,y0)][m:moreis(x0,z0)]
-ismoreis1:=isp(rat,[t:rat]moreis(t,z0),x0,y0,m,i):moreis(y0,z0)
-i@[m:moreis(z0,x0)]
-ismoreis2:=isp(rat,[t:rat]moreis(z0,t),x0,y0,m,i):moreis(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][m:moreis(x0,z0)]
-ismoreis12:=ismoreis2(z0,u0,y0,j,ismoreis1(x0,y0,z0,i,m)):moreis(y0,u0)
-y0@lessis:=or(less(x0,y0),is(x0,y0)):'prop'
-[l:less(x0,y0)]
-lessisi1:=ori1(less,is,l):lessis(x0,y0)
-y0@[i:is(x0,y0)]
-lessisi2:=ori2(less,is,i):lessis(x0,y0)
-y1iy0@[l:lesseq(x1,y1)]
-lessisi:=orapp(lessf(x1,y1),eq"n"(x1,y1),lessis,l,[t:lessf(x1,y1)]lessisi1(lessi(t)),[t:eq"n"(x1,y1)]lessisi2(isi(t))):lessis(x0,y0)
-y1iy0@[l:lessis(x0,y0)]
-lessise:=orapp(less,is,lesseq(x1,y1),l,[t:less]lesseqi1(x1,y1,lesse(t)),[t:is]lesseqi2(x1,y1,ise(t))):lesseq(x1,y1)
-z0@[i:is(x0,y0)][l:lessis(x0,z0)]
-islessis1:=isp(rat,[t:rat]lessis(t,z0),x0,y0,l,i):lessis(y0,z0)
-i@[l:lessis(z0,x0)]
-islessis2:=isp(rat,[t:rat]lessis(z0,t),x0,y0,l,i):lessis(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][l:lessis(x0,z0)]
-islessis12:=islessis2(z0,u0,y0,j,islessis1(x0,y0,z0,i,l)):lessis(y0,u0)
-y0@[m:moreis(x0,y0)]
-satz81c:=th7"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,comor(more(x0,y0),is(x0,y0),m)):not(less(x0,y0))
-y0@[l:lessis(x0,y0)]
-satz81d:=th9"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l):not(more(x0,y0))
-y0@[n:not(more(x0,y0))]
-satz81e:=th2"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n):lessis(x0,y0)
-y0@[n:not(less(x0,y0))]
-satz81f:=comor(is(x0,y0),more(x0,y0),th3"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n)):moreis(x0,y0)
-y0@[m:more(x0,y0)]
-satz81g:=th3"l.or"(less(x0,y0),is(x0,y0),ec3e23(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m),ec3e21(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m)):not(lessis(x0,y0))
-y0@[l:less(x0,y0)]
-satz81h:=th3"l.or"(more(x0,y0),is(x0,y0),ec3e32(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l),ec3e31(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l)):not(moreis(x0,y0))
-y0@[n:not(moreis(x0,y0))]
-satz81j:=or3e3(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th5"l.or"(more(x0,y0),is(x0,y0),n),th4"l.or"(more(x0,y0),is(x0,y0),n)):less(x0,y0)
-y0@[n:not(lessis(x0,y0))]
-satz81k:=or3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th4"l.or"(less(x0,y0),is(x0,y0),n),th5"l.or"(less(x0,y0),is(x0,y0),n)):more(x0,y0)
-y0@[m:moreis(x0,y0)]
-+584
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=lessisi(y0,x0,y,x,yiy0,xix0,satz48(x,y,moreise(x0,y0,x,y,xix0,yiy0,m))):lessis(y0,x0)
--584
-satz84:=ratapp2(lessis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".584"(x,y,xi,yi)):lessis(y0,x0)
-y0@[l:lessis(x0,y0)]
-+585
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=moreisi(y0,x0,y,x,yiy0,xix0,satz49(x,y,lessise(x0,y0,x,y,xix0,yiy0,l))):moreis(y0,x0)
--585
-satz85:=ratapp2(moreis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".585"(x,y,xi,yi)):moreis(y0,x0)
-z0@[l:less(x0,y0)][k:less(y0,z0)]
-+586
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=lessi(x0,z0,x,z,xix0,ziz0,satz50(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
--586
-satz86:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".586"(x,y,z,xi,yi,zi)):less(x0,z0)
-trless:=satz86:less(x0,z0)
-z0@[m:more(x0,y0)][n:more(y0,z0)]
-trmore:=satz83(z0,x0,satz86(z0,y0,x0,satz82(y0,z0,n),satz82(m))):more(x0,z0)
-z0@[l:lessis(x0,y0)][k:less(y0,z0)]
-+587
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=lessi(x0,z0,x,z,xix0,ziz0,satz51a(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
--587
-satz87a:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".587"(x,y,z,xi,yi,zi)):less(x0,z0)
-z0@[l:less(x0,y0)][k:lessis(y0,z0)]
-+*587
-k@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=lessi(x0,z0,x,z,xix0,ziz0,satz51b(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
--587
-k@satz87b:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".587"(x,y,z,xi,yi,zi)):less(x0,z0)
-z0@[m:moreis(x0,y0)][n:more(y0,z0)]
-satz87c:=satz83(z0,x0,satz87b(z0,y0,x0,satz82(y0,z0,n),satz84(m))):more(x0,z0)
-z0@[m:more(x0,y0)][n:moreis(y0,z0)]
-satz87d:=satz83(z0,x0,satz87a(z0,y0,x0,satz84(y0,z0,n),satz82(m))):more(x0,z0)
-z0@[l:lessis(x0,y0)][k:lessis(y0,z0)]
-+588
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=lessisi(x0,z0,x,z,xix0,ziz0,satz52(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):lessis(x0,z0)
--588
-satz88:=ratapp3(lessis(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".588"(x,y,z,xi,yi,zi)):lessis(x0,z0)
-trlessis:=satz88:lessis(x0,z0)
-z0@[m:moreis(x0,y0)][n:moreis(y0,z0)]
-trmoreis:=satz85(z0,x0,satz88(z0,y0,x0,satz84(y0,z0,n),satz84(m))):moreis(x0,z0)
-+589
-x0@[x:frac][xix0:inf(x,class(x0))][z:frac][m:moref(z,x)]
-t1:=somei(rat,[t:rat]more(t,x0),ratof(z),morei(ratof(z),x0,z,x,inclass(z),xix0,m)):some([t:rat]more(t,x0))
-xix0@t2:=someapp(frac,[t:frac]moref(t,x),satz53(x),some([t:rat]more(t,x0)),[t:frac][u:moref(t,x)]t1(t,u)):some([t:rat]more(t,x0))
--589
-x0@satz89:=ratapp1(some([t:rat]more(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".589"(x,xi)):some([t:rat]more(t,x0))
-+590
-z"rt.589"@[l:lessf(z,x)]
-t1:=somei(rat,[t:rat]less(t,x0),ratof(z),lessi(ratof(z),x0,z,x,inclass(z),xix0,l)):some([t:rat]less(t,x0))
-xix0"rt.589"@t2:=someapp(frac,[t:frac]lessf(t,x),satz54(x),some([t:rat]less(t,x0)),[t:frac][u:lessf(t,x)]t1(t,u)):some([t:rat]less(t,x0))
--590
-satz90:=ratapp1(some([t:rat]less(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".590"(x,xi)):some([t:rat]less(t,x0))
-y0@[l:less(x0,y0)]
-+591
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][z:frac][a:and(lessf(x,z),lessf(z,y))]
-t1:=lessi(x0,ratof(z),x,z,xix0,inclass(z),ande1(lessf(x,z),lessf(z,y),a)):less(x0,ratof(z))
-t2:=lessi(ratof(z),y0,z,y,inclass(z),yiy0,ande2(lessf(x,z),lessf(z,y),a)):less(ratof(z),y0)
-t3:=andi(less(x0,ratof(z)),less(ratof(z),y0),t1,t2):and(less(x0,ratof(z)),less(ratof(z),y0))
-t4:=somei(rat,[t:rat]and(less(x0,t),less(t,y0)),ratof(z),t3):some([t:rat]and(less(x0,t),less(t,y0)))
-yiy0@t5:=someapp(frac,[t:frac]and(lessf(x,t),lessf(t,y)),satz55(x,y,lesse(x,y,xix0,yiy0,l)),some([t:rat]and(less(x0,t),less(t,y0))),[t:frac][u:and(lessf(x,t),lessf(t,y))]t4(t,u)):some([t:rat]and(less(x0,t),less(t,y0)))
--591
-satz91:=ratapp2(some([t:rat]and(less(x0,t),less(t,y0))),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".591"(x,y,xi,yi)):some([t:rat]and(less(x0,t),less(t,y0)))
-@plusfrt:=[x:frac][y:frac]ratof(pf(x,y)):[x:frac][y:frac]rat
-[x:frac][y:frac][z:frac][u:frac][e:eq"n"(x,y)][f:eq"n"(z,u)]
-+*ii5
-f@t18:=isi(ratof(pf(x,z)),ratof(pf(y,u)),pf(x,z),pf(y,u),inclass(pf(x,z)),inclass(pf(y,u)),satz56(x,y,z,u,e,f)):is(<z><x>plusfrt,<u><y>plusfrt)
--ii5
-@fplusfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t18".ii5"(x,y,z,u,v,w):fixf(rat,plusfrt)
-y0@pl:=indrat(rat,plusfrt,fplusfrt):rat
-+*ii5
-y1iy0@t19:=isindrat(rat,plusfrt,fplusfrt,x1,y1,x1ix0,y1iy0):is(ratof(pf(x1,y1)),pl(x0,y0))
--ii5
-y1iy0@picp:=isp(rat,[t:rat]inf(pf(x1,y1),class(t)),ratof(pf(x1,y1)),pl(x0,y0),inclass(pf(x1,y1)),t19".ii5"):inf(pf(x1,y1),class(pl(x0,y0)))
-z0@[i:is(x0,y0)]
-ispl1:=isf(rat,rat,[t:rat]pl(t,z0),x0,y0,i):is(pl(x0,z0),pl(y0,z0))
-ispl2:=isf(rat,rat,[t:rat]pl(z0,t),x0,y0,i):is(pl(z0,x0),pl(z0,y0))
-u0@[i:is(x0,y0)][j:is(z0,u0)]
-ispl12:=tris(rat,pl(x0,z0),pl(y0,z0),pl(y0,u0),ispl1(i),ispl2(z0,u0,y0,j)):is(pl(x0,z0),pl(y0,u0))
-+592
-y1iy0@t1:=isi(pl(x0,y0),pl(y0,x0),pf(x1,y1),pf(y1,x1),picp,picp(y0,x0,y1,x1,y1iy0,x1ix0),satz58(x1,y1)):is(pl(x0,y0),pl(y0,x0))
--592
-y0@satz92:=ratapp2(is(pl(x0,y0),pl(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".592"(x,y,xi,yi)):is(pl(x0,y0),pl(y0,x0))
-compl:=satz92:is(pl(x0,y0),pl(y0,x0))
-+593
-z0@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=picp(pl(x0,y0),z0,pf(x,y),z,picp(x0,y0,x,y,xix0,yiy0),ziz0):inf(pf(pf(x,y),z),class(pl(pl(x0,y0),z0)))
-t2:=picp(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(pf(x,pf(y,z)),class(pl(x0,pl(y0,z0))))
-t3:=isi(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),pf(pf(x,y),z),pf(x,pf(y,z)),t1,t2,satz59(x,y,z)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
--593
-z0@satz93:=ratapp3(is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".593"(x,y,z,xi,yi,zi)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
-asspl1:=satz93:is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
-asspl2:=symis(rat,pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),satz93):is(pl(x0,pl(y0,z0)),pl(pl(x0,y0),z0))
-+594
-y1iy0@t1:=morei(pl(x0,y0),x0,pf(x1,y1),x1,picp,x1ix0,satz60(x1,y1)):more(pl(x0,y0),x0)
--594
-y0@satz94:=ratapp2(more(pl(x0,y0),x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".594"(x,y,xi,yi)):more(pl(x0,y0),x0)
-satz94a:=satz82(pl(x0,y0),x0,satz94):less(x0,pl(x0,y0))
-z0@[m:more(x0,y0)]
-+595
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz61(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
--595
-satz95:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".595"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
-z0@[m:more(x0,y0)]
-+596
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
--596
-satz96a:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".596"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
-z0@[i:is(x0,y0)]
-+*596
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(pl(x0,z0),pl(y0,z0))
--596
-i@satz96b:=ratapp3(is(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".596"(x,y,z,xi,yi,zi)):is(pl(x0,z0),pl(y0,z0))
-z0@[l:less(x0,y0)]
-+*596
-l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t3:=lessi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62c(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l))):less(pl(x0,z0),pl(y0,z0))
--596
-l@satz96c:=ratapp3(less(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".596"(x,y,z,xi,yi,zi)):less(pl(x0,z0),pl(y0,z0))
-+*596
-m@andersa:=satz95(m):more(pl(x0,z0),pl(y0,z0))
-i@andersb:=ispl1(x0,y0,z0,i):is(pl(x0,z0),pl(y0,z0))
-l@andersc:=satz82(pl(y0,z0),pl(x0,z0),satz95(y0,x0,z0,satz83(l))):less(pl(x0,z0),pl(y0,z0))
--596
-m@satz96d:=ismore12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96a):more(pl(z0,x0),pl(z0,y0))
-i@satz96e:=ispl2(x0,y0,z0,i):is(pl(z0,x0),pl(z0,y0))
-l@satz96f:=isless12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96c):less(pl(z0,x0),pl(z0,y0))
-z0@[m:more(pl(x0,z0),pl(y0,z0))]
-+597
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(x0,y0,x,y,xix0,yiy0,satz63a(x,y,z,moree(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
--597
-satz97a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".597"(x,y,z,xi,yi,zi)):more(x0,y0)
-z0@[i:is(pl(x0,z0),pl(y0,z0))]
-+*597
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(x0,y0,x,y,xix0,yiy0,satz63b(x,y,z,ise(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
--597
-i@satz97b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".597"(x,y,z,xi,yi,zi)):is(x0,y0)
-z0@[l:less(pl(x0,z0),pl(y0,z0))]
-+*597
-l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t3:=lessi(x0,y0,x,y,xix0,yiy0,satz63c(x,y,z,lesse(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
--597
-l@satz97c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".597"(x,y,z,xi,yi,zi)):less(x0,y0)
-+*597
-l@anders:=satz82(y0,x0,satz97a(y0,x0,z0,satz83(pl(x0,z0),pl(y0,z0),l))):less(x0,y0)
--597
-u0@[m:more(x0,y0)][n:more(z0,u0)]
-+598
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz64(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
--598
-satz98:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".598"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
-u0@[l:less(x0,y0)][k:less(z0,u0)]
-satz98a:=satz82(pl(y0,u0),pl(x0,z0),satz98(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
-u0@[m:moreis(x0,y0)][n:more(z0,u0)]
-+599
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
--599
-satz99a:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
-u0@[m:more(x0,y0)][n:moreis(z0,u0)]
-+*599
-n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t2:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
--599
-n@satz99b:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
-u0@[l:lessis(x0,y0)][k:less(z0,u0)]
-satz99c:=satz82(pl(y0,u0),pl(x0,z0),satz99a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
-u0@[l:less(x0,y0)][k:lessis(z0,u0)]
-satz99d:=satz82(pl(y0,u0),pl(x0,z0),satz99b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
-u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
-+5100
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=moreisi(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz66(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(pl(x0,z0),pl(y0,u0))
--5100
-satz100:=ratapp4(moreis(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5100"(x,y,z,u,xi,yi,zi,ui)):moreis(pl(x0,z0),pl(y0,u0))
-u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
-satz100a:=satz84(pl(y0,u0),pl(x0,z0),satz100(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(pl(x0,z0),pl(y0,u0))
-y0@[l:lessis(x0,y0)]
-+5101
-[v0:rat][i:is(pl(y0,v0),x0)]
-t1:=ismore1(pl(y0,v0),x0,y0,i,satz94(y0,v0)):more(x0,y0)
-v0@t2:=th3"l.imp"(is(pl(y0,v0),x0),more(x0,y0),satz81d(x0,y0,l),[t:is(pl(y0,v0),x0)]t1(t)):nis(pl(y0,v0),x0)
--5101
-vorbemerkung101:=th5"l.some"(rat,[v:rat]is(pl(y0,v),x0),[v:rat]t2".5101"(v)):not(some([t:rat]is(pl(y0,t),x0)))
-y0@[m:more(x0,y0)]
-+*5101
-m@[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][v:frac][e:eq"n"(pf(y,v),x)]
-t3:=isi(pl(y0,ratof(v)),x0,pf(y,v),x,picp(y0,ratof(v),y,v,yiy0,inclass(v)),xix0,e):is(pl(y0,ratof(v)),x0)
-t4:=somei(rat,[t:rat]is(pl(y0,t),x0),ratof(v),t3):some([t:rat]is(pl(y0,t),x0))
-yiy0@t5:=someapp(frac,[t:frac]eq"n"(pf(y,t),x),satz67a(x,y,moree(x0,y0,x,y,xix0,yiy0,m)),some([t:rat]is(pl(y0,t),x0)),[t:frac][u:eq"n"(pf(y,t),x)]t4(t,u)):some([t:rat]is(pl(y0,t),x0))
--5101
-m@satz101a:=ratapp2(some([t:rat]is(pl(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".5101"(x,y,xi,yi)):some([t:rat]is(pl(y0,t),x0))
-y0@[v0:rat][w0:rat][i:is(pl(y0,v0),x0)][j:is(pl(y0,w0),x0)]
-+*5101
-j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
-t6:=isi(v0,w0,v,w,viv0,wiw0,satz67b(x,y,v,w,ise(pl(y0,v0),x0,pf(y,v),x,picp(y0,v0,y,v,yiy0,viv0),xix0,i),ise(pl(y0,w0),x0,pf(y,w),x,picp(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
--5101
-j@satz101b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t6".5101"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
-+*5101
-y0@t7:=[t:rat][u:rat][v:is(pl(y0,t),x0)][w:is(pl(y0,u),x0)]satz101b(t,u,v,w):amone(rat,[t:rat]is(pl(y0,t),x0))
--5101
-m@satz101:=onei(rat,[t:rat]is(pl(y0,t),x0),t7".5101",satz101a):one([t:rat]is(pl(y0,t),x0))
-mn:=ind(rat,[t:rat]is(pl(y0,t),x0),satz101):rat
-satz101c:=oneax(rat,[t:rat]is(pl(y0,t),x0),satz101):is(pl(y0,mn(x0,y0,m)),x0)
-satz101d:=symis(rat,pl(y0,mn(x0,y0,m)),x0,satz101c):is(x0,pl(y0,mn(x0,y0,m)))
-satz101e:=tris(rat,pl(mn(x0,y0,m),y0),pl(y0,mn(x0,y0,m)),x0,compl(mn(x0,y0,m),y0),satz101c):is(pl(mn(x0,y0,m),y0),x0)
-satz101f:=symis(rat,pl(mn(x0,y0,m),y0),x0,satz101e):is(x0,pl(mn(x0,y0,m),y0))
-y0@[v0:rat][m:more(x0,y0)][i:is(pl(y0,v0),x0)]
-satz101g:=satz101b(v0,mn(x0,y0,m),i,satz101c(m)):is(v0,mn(x0,y0,m))
-@timesfrt:=[x:frac][y:frac]ratof(tf(x,y)):[x:frac][y:frac]rat
-+*ii5
-f@t20:=isi(ratof(tf(x,z)),ratof(tf(y,u)),tf(x,z),tf(y,u),inclass(tf(x,z)),inclass(tf(y,u)),satz68(x,y,z,u,e,f)):is(<z><x>timesfrt,<u><y>timesfrt)
--ii5
-@ftimesfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t20".ii5"(x,y,z,u,v,w):fixf(rat,timesfrt)
-y0@ts:=indrat(rat,timesfrt,ftimesfrt):rat
-+*ii5
-y1iy0@t21:=isindrat(rat,timesfrt,ftimesfrt,x1,y1,x1ix0,y1iy0):is(ratof(tf(x1,y1)),ts(x0,y0))
--ii5
-y1iy0@tict:=isp(rat,[t:rat]inf(tf(x1,y1),class(t)),ratof(tf(x1,y1)),ts(x0,y0),inclass(tf(x1,y1)),t21".ii5"):inf(tf(x1,y1),class(ts(x0,y0)))
-z0@[i:is(x0,y0)]
-ists1:=isf(rat,rat,[t:rat]ts(t,z0),x0,y0,i):is(ts(x0,z0),ts(y0,z0))
-ists2:=isf(rat,rat,[t:rat]ts(z0,t),x0,y0,i):is(ts(z0,x0),ts(z0,y0))
-u0@[i:is(x0,y0)][j:is(z0,u0)]
-ists12:=tris(rat,ts(x0,z0),ts(y0,z0),ts(y0,u0),ists1(i),ists2(z0,u0,y0,j)):is(ts(x0,z0),ts(y0,u0))
-+5102
-y1iy0@t1:=isi(ts(x0,y0),ts(y0,x0),tf(x1,y1),tf(y1,x1),tict,tict(y0,x0,y1,x1,y1iy0,x1ix0),satz69(x1,y1)):is(ts(x0,y0),ts(y0,x0))
--5102
-y0@satz102:=ratapp2(is(ts(x0,y0),ts(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".5102"(x,y,xi,yi)):is(ts(x0,y0),ts(y0,x0))
-comts:=satz102:is(ts(x0,y0),ts(y0,x0))
-+5103
-ziz0"rt.593"@t1:=tict(ts(x0,y0),z0,tf(x,y),z,tict(x0,y0,x,y,xix0,yiy0),ziz0):inf(tf(tf(x,y),z),class(ts(ts(x0,y0),z0)))
-t2:=tict(x0,ts(y0,z0),x,tf(y,z),xix0,tict(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,tf(y,z)),class(ts(x0,ts(y0,z0))))
-t3:=isi(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),tf(tf(x,y),z),tf(x,tf(y,z)),t1,t2,satz70(x,y,z)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
--5103
-z0@satz103:=ratapp3(is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5103"(x,y,z,xi,yi,zi)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
-assts1:=satz103:is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
-assts2:=symis(rat,ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),satz103):is(ts(x0,ts(y0,z0)),ts(ts(x0,y0),z0))
-+5104
-ziz0"rt.593"@t1:=tict(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,pf(y,z)),class(ts(x0,pl(y0,z0))))
-t2:=picp(ts(x0,y0),ts(x0,z0),tf(x,y),tf(x,z),tict(x0,y0,x,y,xix0,yiy0),tict(x0,z0,x,z,xix0,ziz0)):inf(pf(tf(x,y),tf(x,z)),class(pl(ts(x0,y0),ts(x0,z0))))
-t3:=isi(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),t1,t2,satz71(x,y,z)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
--5104
-satz104:=ratapp3(is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5104"(x,y,z,xi,yi,zi)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
-disttp1:=tr3is(rat,ts(pl(x0,y0),z0),ts(z0,pl(x0,y0)),pl(ts(z0,x0),ts(z0,y0)),pl(ts(x0,z0),ts(y0,z0)),comts(pl(x0,y0),z0),satz104(z0,x0,y0),ispl12(ts(z0,x0),ts(x0,z0),ts(z0,y0),ts(y0,z0),comts(z0,x0),comts(z0,y0))):is(ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)))
-disttp2:=satz104:is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
-distpt1:=symis(rat,ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)),disttp1):is(pl(ts(x0,z0),ts(y0,z0)),ts(pl(x0,y0),z0))
-distpt2:=symis(rat,ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),disttp2):is(pl(ts(x0,y0),ts(x0,z0)),ts(x0,pl(y0,z0)))
-[m:more(x0,y0)]
-+5105
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(ts(x0,z0),ts(y0,z0))
--5105
-satz105a:=ratapp3(more(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5105"(x,y,z,xi,yi,zi)):more(ts(x0,z0),ts(y0,z0))
-z0@[i:is(x0,y0)]
-+*5105
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(ts(x0,z0),ts(y0,z0))
--5105
-i@satz105b:=ratapp3(is(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5105"(x,y,z,xi,yi,zi)):is(ts(x0,z0),ts(y0,z0))
-z0@[l:less(x0,y0)]
-+*5105
-l@[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]
-t3:=lessi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xi,zi),tict(y0,z0,y,z,yi,zi),satz72c(x,y,z,lesse(x0,y0,x,y,xi,yi,l))):less(ts(x0,z0),ts(y0,z0))
--5105
-l@satz105c:=ratapp3(less(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5105"(x,y,z,xi,yi,zi)):less(ts(x0,z0),ts(y0,z0))
-+*5105
-i@andersb:=ists1(x0,y0,z0,i):is(ts(x0,z0),ts(y0,z0))
-l@andersc:=satz82(ts(y0,z0),ts(x0,z0),satz105a(y0,x0,z0,satz83(l))):less(ts(x0,z0),ts(y0,z0))
--5105
-m@satz105d:=ismore12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105a):more(ts(z0,x0),ts(z0,y0))
-i@satz105e:=ists2(x0,y0,z0,i):is(ts(z0,x0),ts(z0,y0))
-l@satz105f:=isless12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105c):less(ts(z0,x0),ts(z0,y0))
-z0@[m:more(ts(x0,z0),ts(y0,z0))]
-+5106
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(x0,y0,x,y,xix0,yiy0,satz73a(x,y,z,moree(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
--5106
-satz106a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5106"(x,y,z,xi,yi,zi)):more(x0,y0)
-z0@[i:is(ts(x0,z0),ts(y0,z0))]
-+*5106
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(x0,y0,x,y,xix0,yiy0,satz73b(x,y,z,ise(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
--5106
-i@satz106b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5106"(x,y,z,xi,yi,zi)):is(x0,y0)
-z0@[l:less(ts(x0,z0),ts(y0,z0))]
-+*5106
-l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t3:=lessi(x0,y0,x,y,xix0,yiy0,satz73c(x,y,z,lesse(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
--5106
-l@satz106c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5106"(x,y,z,xi,yi,zi)):less(x0,y0)
-+*5106
-l@anders:=satz82(y0,x0,satz106a(y0,x0,z0,satz83(ts(x0,z0),ts(y0,z0),l))):less(x0,y0)
--5106
-u0@[m:more(x0,y0)][n:more(z0,u0)]
-+5107
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz74(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
--5107
-satz107:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5107"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
-u0@[l:less(x0,y0)][k:less(z0,u0)]
-satz107a:=satz82(ts(y0,u0),ts(x0,z0),satz107(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
-u0@[m:moreis(x0,y0)][n:more(z0,u0)]
-+5108
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
--5108
-satz108a:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
-u0@[m:more(x0,y0)][n:moreis(z0,u0)]
-+*5108
-n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t2:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
--5108
-n@satz108b:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
-u0@[l:lessis(x0,y0)][k:less(z0,u0)]
-satz108c:=satz82(ts(y0,u0),ts(x0,z0),satz108a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
-u0@[l:less(x0,y0)][k:lessis(z0,u0)]
-satz108d:=satz82(ts(y0,u0),ts(x0,z0),satz108b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
-u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
-+5109
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=moreisi(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz76(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(ts(x0,z0),ts(y0,u0))
--5109
-satz109:=ratapp4(moreis(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5109"(x,y,z,u,xi,yi,zi,ui)):moreis(ts(x0,z0),ts(y0,u0))
-u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
-satz109a:=satz84(ts(y0,u0),ts(x0,z0),satz109(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(ts(x0,z0),ts(y0,u0))
-+5110
-y1iy0@[v:frac][e:eq"n"(tf(y1,v),x1)]
-t1:=isi(ts(y0,ratof(v)),x0,tf(y1,v),x1,tict(y0,ratof(v),y1,v,y1iy0,inclass(v)),x1ix0,e):is(ts(y0,ratof(v)),x0)
-t2:=somei(rat,[t:rat]is(ts(y0,t),x0),ratof(v),t1):some([t:rat]is(ts(y0,t),x0))
-y1iy0@t3:=someapp(frac,[t:frac]eq"n"(tf(y1,t),x1),satz77a(x1,y1),some([t:rat]is(ts(y0,t),x0)),[t:frac][u:eq"n"(tf(y1,t),x1)]t2(t,u)):some([t:rat]is(ts(y0,t),x0))
--5110
-y0@satz110a:=ratapp2(some([t:rat]is(ts(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t3".5110"(x,y,xi,yi)):some([t:rat]is(ts(y0,t),x0))
-[v0:rat][w0:rat][i:is(ts(y0,v0),x0)][j:is(ts(y0,w0),x0)]
-+*5110
-j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
-t4:=isi(v0,w0,v,w,viv0,wiw0,satz77b(x,y,v,w,ise(ts(y0,v0),x0,tf(y,v),x,tict(y0,v0,y,v,yiy0,viv0),xix0,i),ise(ts(y0,w0),x0,tf(y,w),x,tict(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
--5110
-j@satz110b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t4".5110"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
-+*5110
-y0@t5:=[t:rat][u:rat][v:is(ts(y0,t),x0)][w:is(ts(y0,u),x0)]satz110b(t,u,v,w):amone(rat,[t:rat]is(ts(y0,t),x0))
--5110
-y0@satz110:=onei(rat,[t:rat]is(ts(y0,t),x0),t5".5110",satz110a):one([t:rat]is(ts(y0,t),x0))
--rt
-@[x:nat][y:nat]
-+5111
-t1:=tris(nat,ts(num(fr(x,1)),den(fr(y,1))),ts(x,1),x,ndis12(x,1,y,1),satz28a(x)):is(ts(num(fr(x,1)),den(fr(y,1))),x)
-t2:=symis(nat,ts(num(fr(x,1)),den(fr(y,1))),x,t1):is(x,ts(num(fr(x,1)),den(fr(y,1))))
--5111
-[m:moref(fr(x,1),fr(y,1))]
-satz111a:=ismore12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),m):more(x,y)
-y@[e:eq(fr(x,1),fr(y,1))]
-satz111b:=tr3is(nat,x,ts(num(fr(x,1)),den(fr(y,1))),ts(num(fr(y,1)),den(fr(x,1))),y,t2".5111",e,t1".5111"(y,x)):is(x,y)
-y@[l:lessf(fr(x,1),fr(y,1))]
-satz111c:=isless12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),l):less(x,y)
-y@[m:more(x,y)]
-satz111d:=ismore12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),m):moref(fr(x,1),fr(y,1))
-y@[i:is(x,y)]
-satz111e:=tr3is(nat,ts(num(fr(x,1)),den(fr(y,1))),x,y,ts(num(fr(y,1)),den(fr(x,1))),t1".5111",i,t2".5111"(y,x)):eq(fr(x,1),fr(y,1))
-y@[l:less(x,y)]
-satz111f:=isless12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),l):lessf(fr(x,1),fr(y,1))
-+*rt
-@[x0:rat][x:nat]
-natprop:=inf(fr(x,1),class(x0)):'prop'
-x0@natrt:=some"n"([t:nat]natprop(t)):'prop'
-+*ii5
-y0@[x:nat][y:nat][npx:natprop(x0,x)][npy:natprop(y0,y)][i:is(x0,y0)]
-t22:=satz111b(x,y,ise(x0,y0,fr(x,1),fr(y,1),npx,npy,i)):is"n"(x,y)
-x0@t23:=[t:nat][u:nat][v:natprop(x0,t)][w:natprop(x0,u)]t22(x0,x0,t,u,v,w,refis(rat,x0)):amone(nat,[t:nat]natprop(x0,t))
--ii5
-x0@[nx0:natrt(x0)]
-satz111g:=onei(nat,[t:nat]natprop(t),t23".ii5",nx0):one"n"([t:nat]natprop(x0,t))
-nofrt:=ind(nat,[t:nat]natprop(t),satz111g):nat
-inclassn:=oneax(nat,[t:nat]natprop(t),satz111g):inf(fr(nofrt,1),class(x0))
-[y0:rat][ny0:natrt(y0)][i:is(x0,y0)]
-isrten:=t22".ii5"(x0,y0,nofrt(x0,nx0),nofrt(y0,ny0),inclassn(x0,nx0),inclassn(y0,ny0),i):is"n"(nofrt(x0,nx0),nofrt(y0,ny0))
-ny0@[i:is"n"(nofrt(x0,nx0),nofrt(y0,ny0))]
-isrtin:=isi(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),eqn"n"(nofrt(x0,nx0),1,nofrt(y0,ny0),i)):is(x0,y0)
-@[x:nat]
-rtofn:=ratof(fr(x,1)):rat
-natrti:=somei(nat,[t:nat]natprop(rtofn,t),x,inclass(fr(x,1))):natrt(rtofn(x))
-[y:nat][i:is"n"(x,y)]
-isnert:=isf(nat,rat,[t:nat]rtofn(t),x,y,i):is(rtofn(x),rtofn(y))
-y@[i:is(rtofn(x),rtofn(y))]
-isnirt:=t22".ii5"(rtofn(x),rtofn(y),x,y,inclass(fr(x,1)),inclass(fr(y,1)),i):is"n"(x,y)
-nx0@isrtn1:=isi(x0,rtofn(nofrt(x0,nx0)),fr(nofrt(x0,nx0),1),fr(nofrt(x0,nx0),1),inclassn(x0,nx0),inclass(fr(nofrt(x0,nx0),1)),refeq"n"(fr(nofrt(x0,nx0),1))):is(x0,rtofn(nofrt(x0,nx0)))
-x@isnrt1:=t22".ii5"(rtofn(x),rtofn(x),x,nofrt(rtofn(x),natrti(x)),inclass(fr(x,1)),inclassn(rtofn(x),natrti(x)),refis(rat,rtofn(x))):is"n"(x,nofrt(rtofn(x),natrti(x)))
--rt
-@[x:nat][y:nat]
-satz112a:=satz57(x,y,1):eq(pf(fr(x,1),fr(y,1)),fr(pl(x,y),1))
-satz112b:=treq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),ts(1,1)),fr(ts(x,y),1),tfeq12a(x,1,y,1),eqd(ts(x,y),ts(1,1),1,satz28a(1))):eq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),1))
-+*rt
-ny0@satz112c:=lemmaeq1(pl(x0,y0),pf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),picp(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112a(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(pl(x0,y0)))
-satz112d:=somei(nat,[t:nat]natprop(pl(x0,y0),t),pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112c):natrt(pl(x0,y0))
-satz112e:=lemmaeq1(ts(x0,y0),tf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),tict(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112b(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(ts(x0,y0)))
-satz112f:=somei(nat,[t:nat]natprop(ts(x0,y0),t),ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112e):natrt(ts(x0,y0))
-[m:more(x0,y0)]
-+5112
-t1:=satz111a(nofrt(x0,nx0),nofrt(y0,ny0),moree(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),m)):more"n"(nofrt(x0,nx0),nofrt(y0,ny0))
-[z:nat][d:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),z)]
-t2:=tris(nat,nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),z),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),d,ispl2"n"(z,nofrt(rtofn(z),natrti(z)),nofrt(y0,ny0),isnrt1(z))):is"n"(nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))))
-t3:=isi(x0,pl(y0,rtofn(z)),fr(nofrt(x0,nx0),1),fr(pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),1),inclassn(x0,nx0),satz112c(y0,ny0,rtofn(z),natrti(z)),eqn(nofrt(x0,nx0),1,pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),t2)):is(x0,pl(y0,rtofn(z)))
-t4:=satz101g(x0,y0,rtofn(z),m,symis(rat,x0,pl(y0,rtofn(z)),t3)):is(rtofn(z),mn(x0,y0,m))
-t5:=isp(rat,[t:rat]natrt(t),rtofn(z),mn(x0,y0,m),natrti(z),t4):natrt(mn(x0,y0,m))
--5112
-satz112g:=someapp(nat,[t:nat]diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t),t1".5112",natrt(mn(x0,y0,m)),[t:nat][u:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t)]t5".5112"(t,u)):natrt(mn(x0,y0,m))
-@[x:nat][y:nat]
-satz112h:=isi(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),pf(fr(x,1),fr(y,1)),fr(pl"n"(x,y),1),picp(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(pl"n"(x,y),1)),satz112a(x,y)):is(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)))
-satz112j:=isi(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),tf(fr(x,1),fr(y,1)),fr(ts"n"(x,y),1),tict(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(ts"n"(x,y),1)),satz112b(x,y)):is(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)))
-+nt
-@natt:=ot(rat,[t:rat]natrt(t)):'type'
-nx0@ntofrt:=out(rat,[t:rat]natrt(t),x0,nx0):natt
-@[xt:natt][yt:natt]
-is:=is"e"(natt,xt,yt):'prop'
-nis:=not(is(xt,yt)):'prop'
-@[p:[x:natt]'prop']
-all:=all"l"(natt,p):'prop'
-some:=some"l"(natt,p):'prop'
-one:=one"e"(natt,p):'prop'
-xt@[st:set(natt)]
-in:=esti(natt,xt,st):'prop'
-xt@rtofnt:=in"e"(rat,[t:rat]natrt(t),xt):rat
-natrti:=inp(rat,[t:rat]natrt(t),xt):natrt(rtofnt(xt))
-ny0@[i:is"rt"(x0,y0)]
-isrtent:=isouti(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is(ntofrt(x0,nx0),ntofrt(y0,ny0))
-ny0@[i:is(ntofrt(x0,nx0),ntofrt(y0,ny0))]
-isrtint:=isoute(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is"rt"(x0,y0)
-yt@[i:is(xt,yt)]
-isntert:=isini(rat,[t:rat]natrt(t),xt,yt,i):is"rt"(rtofnt(xt),rtofnt(yt))
-yt@[i:is"rt"(rtofnt(xt),rtofnt(yt))]
-isntirt:=isine(rat,[t:rat]natrt(t),xt,yt,i):is(xt,yt)
-nx0@isrtnt1:=isinout(rat,[t:rat]natrt(t),x0,nx0):is"rt"(x0,rtofnt(ntofrt(x0,nx0)))
-xt@isntrt1:=isoutin(rat,[t:rat]natrt(t),xt):is(xt,ntofrt(rtofnt(xt),natrti(xt)))
-x@ntofn:=ntofrt(rtofn(x),natrti"rt"(x)):natt
-y@[i:is"n"(x,y)]
-isnent:=isrtent(rtofn(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),isnert(x,y,i)):is(ntofn(x),ntofn(y))
-y@[i:is(ntofn(x),ntofn(y))]
-isnint:=isnirt(x,y,isrtint(rtofn"rt"(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),i)):is"n"(x,y)
-xt@nofnt:=nofrt(rtofnt(xt),natrti(xt)):nat
-yt@[i:is(xt,yt)]
-isnten:=isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),isntert(xt,yt,i)):is"n"(nofnt(xt),nofnt(yt))
-yt@[i:is"n"(nofnt(xt),nofnt(yt))]
-isntin:=isntirt(xt,yt,isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),i)):is(xt,yt)
-+ii5
-x@t24:=isrtnt1(rtofn(x),natrti"rt"(x)):is"rt"(rtofn(x),rtofnt(ntofn(x)))
-t25:=isrten(rtofn(x),natrti"rt"(x),rtofnt(ntofn(x)),natrti(ntofn(x)),t24):is"n"(nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)))
--ii5
-x@isnnt1:=tris(nat,x,nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)),isnrt1(x),t25".ii5"):is"n"(x,nofnt(ntofn(x)))
-+*ii5
-xt@t26:=isrtn1(rtofnt(xt),natrti(xt)):is"rt"(rtofnt(xt),rtofn(nofnt(xt)))
-t27:=isrtent(rtofnt(xt),natrti(xt),rtofn(nofnt(xt)),natrti"rt"(nofnt(xt)),t26):is(ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)))
--ii5
-xt@isntn1:=tris(natt,xt,ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)),isntrt1(xt),t27".ii5"):is(xt,ntofn(nofnt(xt)))
-x@isnnt2:=symis(nat,x,nofnt(ntofn(x)),isnnt1):is"n"(nofnt(ntofn(x)),x)
-xt@isntn2:=symis(natt,xt,ntofn(nofnt(xt)),isntn1):is(ntofn(nofnt(xt)),xt)
-@1t:=ntofn(1):natt
-suct:=[x:natt]ntofn(<nofnt(x)>suc):[x:natt]natt
-+5113
-xt@[i:is(<xt>suct,1t)]
-t1:=isnint(<nofnt(xt)>suc,1,i):is"n"(<nofnt(xt)>suc,1)
--5113
-xt@satz113a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<nofnt(xt)>suc,1),<nofnt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5113"(t)):nis(<xt>suct,1t)
-yt@[i:is(<xt>suct,<yt>suct)]
-+*5113
-i"nt"@t2:=isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,i):is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
--5113
-i@satz113b:=isntin(xt,yt,<t2".5113"><nofnt(yt)><nofnt(xt)>ax4):is(xt,yt)
-@[st:set(natt)]
-cond1:=in(1t,st):'prop'
-cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
-[c1:cond1][c2:cond2]
-+*5113
-c2@[x:nat]
-prop1:=in(ntofn(x),st):'prop'
-[p:prop1(x)]
-t3:=<ntofn(x)>c2:imp(in(ntofn(x),st),in(<ntofn(x)>suct,st))
-t4:=mp(in(ntofn(x),st),in(<ntofn(x)>suct,st),p,t3):in(<ntofn(x)>suct,st)
-t5:=isp(nat,[t:nat]in(ntofn(<t>suc),st),nofnt(ntofn(x)),x,t4,isnnt2(x)):prop1(<x>suc)
--5113
-c2@[xt:natt]
-+*5113
-xt@t6:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t5(t,u),nofnt(xt)):in(ntofn(nofnt(xt)),st)
--5113
-xt@satz113c:=isp(natt,[t:natt]in(t,st),ntofn(nofnt(xt)),xt,t6".5113",isntn2(xt)):in(xt,st)
-@ax3t:=[x:natt]satz113a(x):[x:natt]nis(<x>suct,1t)
-ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz113b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
-ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz113c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
-yt@[n:nis(xt,yt)]
-+51
-t1:=th3"l.imp"(is"n"(nofnt(xt),nofnt(yt)),is(xt,yt),n,[t:is"n"(nofnt(xt),nofnt(yt))]isntin(xt,yt,t)):nis"n"(nofnt(xt),nofnt(yt))
-t2:=satz1(nofnt(xt),nofnt(yt),t1):nis"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
--51
-satz1:=th3"l.imp"(is(<xt>suct,<yt>suct),is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc),t2".51",[t:is(<xt>suct,<yt>suct)]isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,t)):nis(<xt>suct,<yt>suct)
-+54
-xt@x:=nofnt(xt):nat
-[ft:[x:natt]natt]
-prop1t:=all([t:natt]is(<<t>suct>ft,<<t>ft>suct)):'prop'
-prop2t:=and(is(<1t>ft,<xt>suct),prop1t):'prop'
-xt@[f:[x:nat]nat]
-prop1:=all"n"([t:nat]is"n"(<<t>suc>f,<<t>f>suc)):'prop'
-prop2:=and(is"n"(<1>f,<x>suc),prop1):'prop'
-ft@g:=[t:nat]nofnt(<ntofn(t)>ft):[x:nat]nat
-[p:prop2t]
-t1:=ande1(is(<1t>ft,<xt>suct),prop1t,p):is(<1t>ft,<xt>suct)
-t2:=tris(nat,<1>g,nofnt(<xt>suct),<x>suc,isnten(<1t>ft,<xt>suct,t1),isnnt2(<x>suc)):is"n"(<1>g,<x>suc)
-t3:=ande2(is(<1t>ft,<xt>suct),prop1t,p):prop1t
-[u:nat]
-ut:=ntofn(u):natt
-t4:=isf(nat,nat,suc,u,nofnt(ut),isnnt1(u)):is"n"(<u>suc,<nofnt(ut)>suc)
-t5:=isf(nat,nat,g,<u>suc,<nofnt(ut)>suc,t4):is"n"(<<u>suc>g,nofnt(<<ut>suct>ft))
-t6:=<ut>t3:is(<<ut>suct>ft,<<ut>ft>suct)
-t7:=isnten(<<ut>suct>ft,<<ut>ft>suct,t6):is"n"(nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct))
-t8:=isnnt2(<<u>g>suc):is"n"(nofnt(<<ut>ft>suct),<<u>g>suc)
-t9:=tr3is(nat,<<u>suc>g,nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct),<<u>g>suc,t5,t7,t8):is"n"(<<u>suc>g,<<u>g>suc)
-p@t10:=[u:nat]t9(u):prop1(g)
-t11:=andi(is"n"(<1>g,<x>suc),prop1(g),t2,t10):prop2(g)
-xt@[a:[t:natt]natt][b:[t:natt]natt][pa:prop2t(a)][pb:prop2t(b)]
-t12:=onee1([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):amone([t:nat]nat,[u:[t:nat]nat]prop2(u))
-t13:=<t11(b,pb)><t11(a,pa)><g(b)><g(a)>t12:is"e"([t:nat]nat,g(a),g(b))
-[yt:natt]
-y:=nofnt(yt):nat
-t14:=fise(nat,nat,g(a),g(b),t13,y):is"n"(nofnt(<ntofn(y)>a),nofnt(<ntofn(y)>b))
-t15:=isntin(<ntofn(y)>a,<ntofn(y)>b,t14):is(<ntofn(y)>a,<ntofn(y)>b)
-t16:=tr3is(natt,<yt>a,<ntofn(y)>a,<ntofn(y)>b,<yt>b,isf(natt,natt,a,yt,ntofn(y),isntn1(yt)),t15,isf(natt,natt,b,ntofn(y),yt,isntn2(yt))):is(<yt>a,<yt>b)
-pb@t17:=fisi(natt,natt,a,b,[t:natt]t16(t)):is"e"([t:natt]natt,a,b)
-xt@t18:=[u:[t:natt]natt][v:[t:natt]natt][w:prop2t(u)][z:prop2t(v)]t17(u,v,w,z):amone([t:natt]natt,[u:[t:natt]natt]prop2t(u))
-t19:=onee2([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):some"l"([t:nat]nat,[u:[t:nat]nat]prop2(u))
-f@gt:=[t:natt]ntofn(<nofnt(t)>f):[x:natt]natt
-[p:prop2]
-t20:=ande1(is"n"(<1>f,<x>suc),prop1,p):is"n"(<1>f,<x>suc)
-t21:=isf(nat,nat,f,nofnt(1t),1,isnnt2(1)):is"n"(<nofnt(1t)>f,<1>f)
-t22:=isnent(<nofnt(1t)>f,<x>suc,tris(nat,<nofnt(1t)>f,<1>f,<x>suc,t21,t20)):is(<1t>gt,<xt>suct)
-t23:=ande2(is"n"(<1>f,<x>suc),prop1,p):prop1
-[zt:natt]
-z:=nofnt(zt):nat
-t24:=isf(nat,nat,f,nofnt(<zt>suct),<z>suc,isnnt2(<z>suc)):is"n"(<nofnt(<zt>suct)>f,<<z>suc>f)
-t25:=<z>t23:is"n"(<<z>suc>f,<<z>f>suc)
-t26:=isf(nat,nat,suc,<z>f,nofnt(<zt>gt),isnnt1(<z>f)):is"n"(<<z>f>suc,<nofnt(<zt>gt)>suc)
-t27:=isnent(<nofnt(<zt>suct)>f,<nofnt(<zt>gt)>suc,tr3is(nat,<nofnt(<zt>suct)>f,<<z>suc>f,<<z>f>suc,<nofnt(<zt>gt)>suc,t24,t25,t26)):is(<<zt>suct>gt,<<zt>gt>suct)
-p@t28:=[u:natt]t27(u):prop1t(gt)
-t29:=andi(is(<1t>gt,<xt>suct),prop1t(gt),t22,t28):prop2t(gt)
-t30:=somei([t:natt]natt,[u:[t:natt]natt]prop2t(u),gt,t29):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
-xt@t31:=someapp([t:nat]nat,[u:[t:nat]nat]prop2(u),t19,some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u)),[u:[t:nat]nat][v:prop2(u)]t30(u,v)):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
--54
-xt@satz4:=onei([t:natt]natt,[u:[t:natt]natt]prop2t".54"(u),t18".54",t31".54"):one"e"([t:natt]natt,[u:[t:natt]natt]and(is(<1t>u,<xt>suct),all([v:natt]is(<<v>suct>u,<<v>u>suct))))
-yt@pl:=ntofrt(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt))):natt
-+*ii5
-yt@t28:=satz112c(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)):inf(fr(pl"n"(nofnt(xt),nofnt(yt)),1),class(pl"rt"(rtofnt(xt),rtofnt(yt))))
-t29:=isi(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),fr(pl"n"(nofnt(xt),nofnt(yt)),1),fr(pl"n"(nofnt(xt),nofnt(yt)),1),t28,inclass(fr(pl"n"(nofnt(xt),nofnt(yt)),1)),refeq"n"(fr(pl"n"(nofnt(xt),nofnt(yt)),1))):is"rt"(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))))
--ii5
-yt@isplnt:=isrtent(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),natrti"rt"(pl"n"(nofnt(xt),nofnt(yt))),t29".ii5"):is(pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))))
-isntpl:=symis(natt,pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))),isplnt):is(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt))
-ispln:=tris(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(ntofn(pl"n"(nofnt(xt),nofnt(yt)))),nofnt(pl(xt,yt)),isnnt1(pl"n"(nofnt(xt),nofnt(yt))),isnten(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt),isntpl)):is"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)))
-isnpl:=symis(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)),ispln):is"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)))
-[zt:natt]
-+55
-t1:=ispl1"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt),isnpl(xt,yt)):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)))
-t2:=ispl2"n"(pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),nofnt(xt),ispln(yt,zt)):is"n"(pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
-t3:=tr3is(nat,pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)),pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t1,satz5(nofnt(xt),nofnt(yt),nofnt(zt)),t2):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
--55
-satz5:=tr3is(natt,pl(pl(xt,yt),zt),ntofn(pl"n"(nofnt(pl(xt,yt)),nofnt(zt))),ntofn(pl"n"(nofnt(xt),nofnt(pl(yt,zt)))),pl(xt,pl(yt,zt)),isplnt(pl(xt,yt),zt),isnent(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t3".55"),isntpl(xt,pl(yt,zt))):is(pl(pl(xt,yt),zt),pl(xt,pl(yt,zt)))
-diffprop:=is(xt,pl(yt,zt)):'prop'
-[d:diffprop]
-diffprope:=tris(nat,nofnt(xt),nofnt(pl(yt,zt)),pl"n"(nofnt(yt),nofnt(zt)),isnten(xt,pl(yt,zt),d),isnpl(yt,zt)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))
-zt@[d:diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))]
-+*ii5
-d@t30:=tris(nat,nofnt(xt),pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),d,ispln(yt,zt)):is"n"(nofnt(xt),nofnt(pl(yt,zt)))
--ii5
-d@diffpropi:=isntin(xt,pl(yt,zt),t30".ii5"):diffprop
-+59
-yt@it:=is(xt,yt):'prop'
-iit:=some([u:natt]diffprop(xt,yt,u)):'prop'
-iiit:=some([u:natt]diffprop(yt,xt,u)):'prop'
-i:=is"n"(nofnt(xt),nofnt(yt)):'prop'
-ii:=some"n"([u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u)):'prop'
-iii:=some"n"([u:nat]diffprop"n"(nofnt(yt),nofnt(xt),u)):'prop'
-[one:i]
-t1:=or3i1(it,iit,iiit,isntin(xt,yt,one)):or3(it,iit,iiit)
-yt@[two:ii][v:nat][d:diffprop"n"(nofnt(xt),nofnt(yt),v)]
-t2:=isp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),v,nofnt(ntofn(v)),d,isnnt1(v)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(ntofn(v)))
-t3:=somei(natt,[u:natt]diffprop(xt,yt,u),ntofn(v),diffpropi(xt,yt,ntofn(v),t2)):iit
-two@t4:=someapp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),two,iit,[u:nat][v:diffprop"n"(nofnt(xt),nofnt(yt),u)]t3(u,v)):iit
-t5:=or3i2(it,iit,iiit,t4):or3(it,iit,iiit)
-yt@[three:iii]
-t6:=or3i3(it,iit,iiit,t4(yt,xt,three)):or3(it,iit,iiit)
-yt@t7:=or3app(i,ii,iii,or3(it,iit,iiit),satz9a(nofnt(xt),nofnt(yt)),[u:i]t1(u),[u:ii]t5(u),[u:iii]t6(u)):or3(it,iit,iiit)
-[onet:it]
-t8:=isnten(xt,yt,onet):i
-yt@[twot:iit][vt:natt][d:diffprop(xt,yt,vt)]
-t9:=somei(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),nofnt(vt),diffprope(xt,yt,vt,d)):ii
-twot@t10:=someapp(natt,[u:natt]diffprop(xt,yt,u),twot,ii,[u:natt][v:diffprop(xt,yt,u)]t9(u,v)):ii
-yt@[threet:iiit]
-t11:=t10(yt,xt,threet):iii
-yt@t12:=satz9b(nofnt(xt),nofnt(yt)):ec3(i,ii,iii)
-onet@t13:=ec3e12(i,ii,iii,t12,t8):not(ii)
-t14:=th3"l.imp"(iit,ii,t13,[x:iit]t10(x)):not(iit)
-yt@t15:=th1"l.ec"(it,iit,[x:it]t14(x)):ec(it,iit)
-twot@t16:=ec3e23(i,ii,iii,t12,t10):not(iii)
-t17:=th3"l.imp"(iiit,iii,t16,[x:iiit]t11(x)):not(iiit)
-yt@t18:=th1"l.ec"(iit,iiit,[x:iit]t17(x)):ec(iit,iiit)
-threet@t19:=ec3e31(i,ii,iii,t12,t11):not(i)
-t20:=th3"l.imp"(it,i,t19,[x:it]t8(x)):not(it)
-yt@t21:=th1"l.ec"(iiit,it,[x:iiit]t20(x)):ec(iiit,it)
-t22:=th6"l.ec3"(it,iit,iiit,t15,t18,t21):ec3(it,iit,iiit)
--59
-yt@satz9:=orec3i(it".59",iit".59",iiit".59",t7".59",t22".59"):orec3(is(xt,yt),some([u:natt]is(xt,pl(yt,u))),some([u:natt]is(yt,pl(xt,u))))
-more:=more"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[m:more(xt,yt)]
-+*ii5
-m@t31:=moree(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-m@moree:=satz111a(nofnt(xt),nofnt(yt),t31".ii5"):more"n"(nofnt(xt),nofnt(yt))
-yt@[m:more"n"(nofnt(xt),nofnt(yt))]
-+*ii5
-m@t32:=satz111d(nofnt(xt),nofnt(yt),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-m@morei:=morei"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t32".ii5"):more(xt,yt)
-yt@less:=less"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[l:less(xt,yt)]
-+*ii5
-l@t33:=lesse(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-l@lesse:=satz111c(nofnt(xt),nofnt(yt),t33".ii5"):less"n"(nofnt(xt),nofnt(yt))
-yt@[l:less"n"(nofnt(xt),nofnt(yt))]
-+*ii5
-l@t34:=satz111f(nofnt(xt),nofnt(yt),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-l@lessi:=lessi"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t34".ii5"):less(xt,yt)
-yt@moreis:=moreis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[m:moreis(xt,yt)]
-moreise:=th9"l.or"(more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),m,[u:more"rt"(rtofnt(xt),rtofnt(yt))]moree(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis"n"(nofnt(xt),nofnt(yt))
-yt@[m:moreis"n"(nofnt(xt),nofnt(yt))]
-moreisi:=th9"l.or"(more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),m,[u:more"n"(nofnt(xt),nofnt(yt))]morei(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis(xt,yt)
-yt@lessis:=lessis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[l:lessis(xt,yt)]
-lessise:=th9"l.or"(less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),l,[u:less"rt"(rtofnt(xt),rtofnt(yt))]lesse(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis"n"(nofnt(xt),nofnt(yt))
-yt@[l:lessis"n"(nofnt(xt),nofnt(yt))]
-lessisi:=th9"l.or"(less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),l,[u:less"n"(nofnt(xt),nofnt(yt))]lessi(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis(xt,yt)
-zt@[l:less(xt,yt)][k:less(yt,zt)]
-+515
-t1:=satz15(nofnt(xt),nofnt(yt),nofnt(zt),lesse(xt,yt,l),lesse(yt,zt,k)):less"n"(nofnt(xt),nofnt(zt))
--515
-satz15:=lessi(xt,zt,t1".515"):less(xt,zt)
-zt@[ut:natt][m:more(xt,yt)][n:more(zt,ut)]
-+521
-t1:=satz21(nofnt(xt),nofnt(yt),nofnt(zt),nofnt(ut),moree(xt,yt,m),moree(zt,ut,n)):more"n"(pl"n"(nofnt(xt),nofnt(zt)),pl"n"(nofnt(yt),nofnt(ut)))
-t2:=ismore12"n"(pl"n"(nofnt(xt),nofnt(zt)),nofnt(pl(xt,zt)),pl"n"(nofnt(yt),nofnt(ut)),nofnt(pl(yt,ut)),ispln(xt,zt),ispln(yt,ut),t1):more"n"(nofnt(pl(xt,zt)),nofnt(pl(yt,ut)))
--521
-satz21:=morei(pl(xt,zt),pl(yt,ut),t2".521"):more(pl(xt,zt),pl(yt,ut))
-@[p:[x:natt]'prop'][n:natt]
-lb:=all([x:natt]imp(<x>p,lessis(n,x))):'prop'
-min:=and(lb,<n>p):'prop'
-p@[s:some(p)]
-+527
-q:=[x:nat]<ntofn(x)>p:[x:nat]'prop'
-[n:natt][np:<n>p]
-t1:=isp(natt,p,n,ntofn(nofnt(n)),np,isntn1(n)):<nofnt(n)>q
-t2:=somei(nat,q,nofnt(n),t1):some"n"(q)
-s@t3:=someapp(natt,p,s,some"n"(q),[u:natt][v:<u>p]t2(u,v)):some"n"(q)
-t4:=satz27(q,t3):some"n"([x:nat]min"n"(q,x))
-[m:nat][mqm:min"n"(q,m)]
-t5:=ande1(lb"n"(q,m),<m>q,mqm):lb"n"(q,m)
-[n:nat][nq:<n>q]
-t6:=mp(<n>q,lessis"n"(m,n),nq,<n>t5):lessis"n"(m,n)
-mqm@[n:natt][np:<n>p]
-t7:=t6(nofnt(n),t1(n,np)):lessis"n"(m,nofnt(n))
-t8:=islessis1"n"(m,nofnt(ntofn(m)),nofnt(n),isnnt1(m),t7):lessis"n"(nofnt(ntofn(m)),nofnt(n))
-t9:=lessisi(ntofn(m),n,t8):lessis(ntofn(m),n)
-n@t10:=[u:<n>p]t9(u):imp(<n>p,lessis(ntofn(m),n))
-mqm@t11:=[x:natt]t10(x):lb(ntofn(m))
-t12:=ande2(lb"n"(q,m),<m>q,mqm):<ntofn(m)>p
-t13:=andi(lb(ntofn(m)),<ntofn(m)>p,t11,t12):min(ntofn(m))
-t14:=somei(natt,[x:natt]min(x),ntofn(m),t13):some([x:natt]min(x))
--527
-satz27:=someapp(nat,[x:nat]min"n"(q".527",x),t4".527",some([x:natt]min(x)),[x:nat][y:min"n"(q".527",x)]t14".527"(x,y)):some([x:natt]min(p,x))
--nt
-@1rt:=rtofn(1):rat
-x0@[x:frac][xix0:inf(x,class(x0))]
-+*ii5
-xix0@t35:=tr3eq(tf(x,fr(1,1)),fr(ts"n"(num(x),1),ts"n"(den(x),1)),fr(num(x),den(x)),x,tfeq1a(x,1,1),eqnd(ts"n"(num(x),1),ts"n"(den(x),1),num(x),den(x),satz28a(num(x)),satz28a(den(x))),refeq1(fr(num(x),den(x)),x,fris(x))):eq"n"(tf(x,fr(1,1)),x)
-t36:=isi(ts(x0,1rt),x0,tf(x,fr(1,1)),x,tict(x0,1rt,x,fr(1,1),xix0,inclass(fr(1,1))),xix0,t35):is(ts(x0,1rt),x0)
--ii5
-x0@example1a:=ratapp1(x0,is(ts(x0,1rt),x0),[x:frac][xi:inf(x,class(x0))]t36".ii5"(x,xi)):is(ts(x0,1rt),x0)
-example1b:=symis(rat,ts(x0,1rt),x0,example1a):is(x0,ts(x0,1rt))
-example1c:=tris(rat,ts(1rt,x0),ts(x0,1rt),x0,comts(1rt,x0),example1a):is(ts(1rt,x0),x0)
-example1d:=symis(rat,ts(1rt,x0),x0,example1c):is(x0,ts(1rt,x0))
-@[x:frac]
-+5114
-t1:=tr3eq(tf(fr(den(x),1),x),fr(ts"n"(den(x),num(x)),ts"n"(1,den(x))),fr(ts"n"(num(x),den(x)),ts"n"(1,den(x))),fr(num(x),1),tfeq2a(x,den(x),1),eqn(ts"n"(den(x),num(x)),ts"n"(1,den(x)),ts"n"(num(x),den(x)),comts"n"(den(x),num(x))),satz40c(num(x),1,den(x))):eq"n"(tf(fr(den(x),1),x),fr(num(x),1))
--5114
-satz114:=isi(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)),tf(fr(den(x),1),x),fr(num(x),1),tict(rtofn(den(x)),ratof(x),fr(den(x),1),x,inclass(fr(den(x),1)),inclass(x)),inclass(fr(num(x),1)),t1".5114"):is(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)))
-@[x1:nat][x2:nat]
-satz114a:=tr3is(rat,ts(rtofn(x2),ratof(fr(x1,x2))),ts(rtofn(den(fr(x1,x2))),ratof(fr(x1,x2))),rtofn(num(fr(x1,x2))),rtofn(x1),ists1(rtofn(x2),rtofn(den(fr(x1,x2))),ratof(fr(x1,x2)),isnert(x2,den(fr(x1,x2)),isden(x1,x2))),satz114(fr(x1,x2)),isnert(num(fr(x1,x2)),x1,numis(x1,x2))):is(ts(rtofn(x2),ratof(fr(x1,x2))),rtofn(x1))
-x0@[y0:rat]
-ov:=ind(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):rat
-satz110c:=oneax(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):is(ts(y0,ov(x0,y0)),x0)
-satz110d:=symis(rat,ts(y0,ov(x0,y0)),x0,satz110c):is(x0,ts(y0,ov(x0,y0)))
-satz110e:=tris(rat,ts(ov(x0,y0),y0),ts(y0,ov(x0,y0)),x0,comts(ov(x0,y0),y0),satz110c):is(ts(ov(x0,y0),y0),x0)
-satz110f:=symis(rat,ts(ov(x0,y0),y0),x0,satz110e):is(x0,ts(ov(x0,y0),y0))
-[v0:rat][i:is(ts(y0,v0),x0)]
-satz110g:=satz110b(x0,y0,v0,ov(x0,y0),i,satz110c):is(v0,ov(x0,y0))
-x2@satz114b:=satz110b(rtofn(x1),rtofn(x2),ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114a,satz110c(rtofn(x1),rtofn(x2))):is(ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)))
-satz114c:=symis(rat,ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114b):is(ov(rtofn(x1),rtofn(x2)),ratof(fr(x1,x2)))
-+5115
-y0@t1:=satz89(ov(y0,x0)):some([t:rat]more(t,ov(y0,x0)))
-[u0:rat][m:more(u0,ov(y0,x0))][u:frac][uiu0:inf(u,class(u0))]
-z:=num(u):nat
-v:=den(u):nat
-t2:=ismore1(u0,ov(rtofn(z),rtofn(v)),ov(y0,x0),tris(rat,u0,ratof(fr(z,v)),ov(rtofn(z),rtofn(v)),isi(u0,ratof(fr(z,v)),u,fr(z,v),uiu0,inclass(fr(z,v)),refeq1(u,fr(z,v),isfr(u))),satz114b(z,v)),m):more(ov(rtofn(z),rtofn(v)),ov(y0,x0))
-t3:=moreisi(rtofn(v),1rt,fr(v,1),fr(1,1),inclass(fr(v,1)),inclass(fr(1,1)),th9"l.or"(more"n"(v,1),is"n"(v,1),moref(fr(v,1),fr(1,1)),eq"n"(fr(v,1),fr(1,1)),satz24(v),[t:more"n"(v,1)]satz111d(v,1,t),[t:is"n"(v,1)]satz111e(v,1,t))):moreis(rtofn(v),1rt)
-t4:=tr3is(rat,ts(rtofn(z),x0),ts(x0,rtofn(z)),ts(x0,ts(ov(rtofn(z),rtofn(v)),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),comts(rtofn(z),x0),ists2(rtofn(z),ts(ov(rtofn(z),rtofn(v)),rtofn(v)),x0,satz110f(rtofn(z),rtofn(v))),assts2(x0,ov(rtofn(z),rtofn(v)),rtofn(v))):is(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)))
-[n:more(rtofn(v),1rt)]
-t5:=ismore1(ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),symis(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),t4),satz105d(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),n)):more(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-t6:=moreisi1(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t5):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-uiu0@[i:is(rtofn(v),1rt)]
-t7:=moreisi2(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),tris(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t4,ists2(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),i))):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-uiu0@t8:=orapp(more(rtofn(v),1rt),is(rtofn(v),1rt),moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt)),t3,[t:more(rtofn(v),1rt)]t6(t),[t:is(rtofn(v),1rt)]t7(t)):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-t9:=ismore12(ts(x0,ov(rtofn(z),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),ts(x0,ov(y0,x0)),y0,example1b(ts(x0,ov(rtofn(z),rtofn(v)))),satz110c(y0,x0),satz105d(ov(rtofn(z),rtofn(v)),ov(y0,x0),x0,t2)):more(ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0)
-t10:=satz87c(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0,t8,t9):more(ts(rtofn(z),x0),y0)
-t11:=somei(nat,[t:nat]more(ts(rtofn(t),x0),y0),z,t10):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
-m@t12:=ratapp1(u0,some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[u:frac][ui:inf(u,class(u0))]t11(u,ui)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
--5115
-y0@satz115:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[t:rat][u:more(t,ov(y0,x0))]t12".5115"(t,u)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
-+*5115
-uiu0@t13:=andi(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0),natrti(z),t10):and(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0))
-t14:=somei(rat,[t:rat]and(natrt(t),more(ts(t,x0),y0)),rtofn(z),t13):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
-m@t15:=ratapp1(u0,some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[u:frac][ui:inf(u,class(u0))]t14(u,ui)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
--5115
-y0@satz115a:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[t:rat][u:more(t,ov(y0,x0))]t15".5115"(t,u)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
-@[s:set(rat)]
-cutprop1a:=nonempty(rat,s):'prop'
-cutprop1b:=not(all([x:rat]in(x,s))):'prop'
-cutprop1:=and(cutprop1a,cutprop1b):'prop'
-[x0:rat]
-cutprop2a:=all([x:rat]imp(not(in(x,s)),less(x0,x))):'prop'
-s@cutprop2:=all([x:rat]imp(in(x,s),cutprop2a(x))):'prop'
-x0@[y0:rat]
-+iii1
-ubprop:=imp(in(y0,s),moreis(x0,y0)):'prop'
--iii1
-x0@ub:=all([x:rat]ubprop".iii1"(x0,x)):'prop'
-max:=and(ub(x0),in(x0,s)):'prop'
-s@cutprop3:=not(some([x:rat]max(s,x))):'prop'
-cutprop:=and3(cutprop1,cutprop2,cutprop3):'prop'
-+*iii1
-y0@lbprop:=imp(in(y0,s),lessis(x0,y0)):'prop'
--iii1
-x0@lb:=all([x:rat]lbprop".iii1"(x0,x)):'prop'
-min:=and(lb(x0),in(x0,s)):'prop'
-@cut:=ot(set(rat),[x:set(rat)]cutprop(x)):'type'
-[ksi:cut]
-lcl:=in"e"(set(rat),[x:set(rat)]cutprop(x),ksi):set(rat)
-[x0:rat]
-lrt:=in(x0,lcl(ksi)):'prop'
-urt:=not(in(x0,lcl(ksi))):'prop'
-ksi@clcl:=inp(set(rat),[x:set(rat)]cutprop(x),ksi):cutprop(lcl(ksi))
-clcl1:=and3e1(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop1(lcl(ksi))
-clcl2:=and3e2(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop2(lcl(ksi))
-clcl3:=and3e3(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop3(lcl(ksi))
-clcl1a:=ande1(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1a(lcl(ksi))
-clcl1b:=ande2(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1b(lcl(ksi))
-[p:'prop'][p1:[x:rat][t:lrt(ksi,x)]p]
-cutapp1a:=nonemptyapp(rat,lcl,clcl1a,p,p1):p
-+*iii1
-ksi@t1:=th1"l.some"(rat,[x:rat]lrt(ksi,x),clcl1b):some([x:rat]urt(ksi,x))
--iii1
-p@[p1:[x:rat][t:urt(ksi,x)]p]
-cutapp1b:=someapp(rat,[x:rat]urt(ksi,x),t1".iii1",p,p1):p
-ksi@[x0:rat][lx:lrt(ksi,x0)]
-+*iii1
-lx@t2:=mp(lrt(ksi,x0),cutprop2a(lcl,x0),lx,<x0>clcl2):cutprop2a(lcl,x0)
--iii1
-lx@[y0:rat][uy:urt(ksi,y0)]
-cutapp2a:=mp(urt(ksi,y0),less(x0,y0),uy,<y0>t2".iii1"):less(x0,y0)
-cutapp2b:=satz83(x0,y0,cutapp2a):more(y0,x0)
-+*iii1
-lx@t3:=th4"l.some"(rat,[x:rat]max(lcl,x),clcl3,x0):not(max(lcl,x0))
-t4:=th4"l.and"(ub(lcl,x0),lrt(ksi,x0),t3,lx):not(ub(lcl,x0))
-t5:=th1"l.some"(rat,[x:rat]ubprop(lcl,x0,x),t4):some([x:rat]not(ubprop(lcl,x0,x)))
--iii1
-lx@[p:'prop'][p1:[y:rat][t:lrt(ksi,y)][u:less(x0,y)]p][y0:rat][n:not(ubprop".iii1"(lcl,x0,y0))]
-+*iii1
-n@t6:=th5"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):lrt(ksi,y0)
-t7:=th6"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):not(moreis(x0,y0))
-t8:=satz81j(x0,y0,t7):less(x0,y0)
-t9:=<t8><t6><y0>p1:p
--iii1
-p1@cutapp3:=someapp(rat,[y:rat]not(ubprop".iii1"(lcl,x0,y)),t5".iii1",p,[y:rat][t:not(ubprop".iii1"(lcl,x0,y))]t9".iii1"(y,t)):p
-s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))]
-+*iii1
-n@t10:=andi(cutprop1a,cutprop1b,nonemptyi(rat,s,x0,i),th1"l.all"(rat,[x:rat]in(x,s),y0,n)):cutprop1
--iii1
-s@[n:[x:rat]not(max(s,x))]
-+*iii1
-n@t11:=th5"l.some"(rat,[x:rat]max(s,x),n):cutprop3
--iii1
-s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][l:[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]less(x,y)][m:[x:rat]not(max(s,x))]
-cut1:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),l,t11".iii1"(m)):cutprop(s)
-+rp
-ksi@[eta:cut]
-is:=is"e"(cut,ksi,eta):'prop'
-nis:=not(is(ksi,eta)):'prop'
-[i:is(ksi,eta)]
-ise:=isini(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is"e"(set(rat),lcl(ksi),lcl(eta))
-[x0:rat][lx:lrt(ksi,x0)]
-ise1:=issete1(rat,lcl(ksi),lcl(eta),ise,x0,lx):lrt(eta,x0)
-eta@[i:is"e"(set(rat),lcl(ksi),lcl(eta))]
-isi:=isine(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is(ksi,eta)
-eta@[l:[x:rat][t:lrt(ksi,x)]lrt(eta,x)][k:[x:rat][t:lrt(eta,x)]lrt(ksi,x)]
-isi1:=isi(isseti(rat,lcl(ksi),lcl(eta),l,k)):is(ksi,eta)
-@[s:set(rat)][cs:cutprop(s)]
-cutof:=out(set(rat),[x:set(rat)]cutprop(x),s,cs):cut
-[x0:rat][i:in(x0,s)]
-ine:=issete1(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,i):lrt(cutof(s,cs),x0)
-x0@[lx:lrt(cutof(s,cs),x0)]
-ini:=issete2(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,lx):in(x0,s)
-s@[t:set(rat)][cs:cutprop(s)][ct:cutprop(t)][i:[x:rat][u:in(x,s)]in(x,t)][j:[x:rat][u:in(x,t)]in(x,s)]
-isi2:=isouti(set(rat),[x:set(rat)]cutprop(x),s,cs,t,ct,isseti(rat,s,t,i,j)):is(cutof(s,cs),cutof(t,ct))
-@[p:[x:cut]'prop']
-all:=all"l"(cut,p):'prop'
-some:=some"l"(cut,p):'prop'
-one:=one"e"(cut,p):'prop'
-ksi@satz116:=refis(cut,ksi):is(ksi,ksi)
-eta@[i:is(ksi,eta)]
-satz117:=symis(cut,ksi,eta,i):is(eta,ksi)
-eta@[zeta:cut][i:is(ksi,eta)][j:is(eta,zeta)]
-satz118:=tris(cut,ksi,eta,zeta,i,j):is(ksi,zeta)
-+1119
-@[x0:rat][y0:rat][m:more(x0,y0)]
-t1:=ec3e23(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),m):not(less(x0,y0))
--1119
-ksi@[x0:rat][ux:urt(ksi,x0)][y0:rat][m:more(y0,x0)]
-satz119:=th3"l.imp"(lrt(ksi,y0),less(y0,x0),t1".1119"(y0,x0,m),[t:lrt(ksi,y0)]cutapp2a(y0,t,x0,ux)):urt(ksi,y0)
-y0@[l:less(x0,y0)]
-satz119a:=satz119(satz83(x0,y0,l)):urt(ksi,y0)
-+1120
-@[x0:rat][y0:rat][l:less(x0,y0)]
-t1:=ec3e32(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),l):not(more(x0,y0))
--1120
-ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][l:less(y0,x0)]
-satz120:=th7"l.imp"(lrt(ksi,y0),more(y0,x0),t1".1120"(y0,x0,l),[t:urt(ksi,y0)]cutapp2b(x0,lx,y0,t)):lrt(ksi,y0)
-y0@[m:more(x0,y0)]
-satz120a:=satz120(satz82(x0,y0,m)):lrt(ksi,y0)
--rp
-s@[i:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][x0:rat][j:in(x0,s)][y0:rat][n:not(in(y0,s))]
-+*iii1
-n@t12:=<y0><j><x0>i:[u:less(y0,x0)]in(y0,s)
-t13:=th3"l.imp"(less(y0,x0),in(y0,s),n,t12):not(less(y0,x0))
-t14:=satz81f(y0,x0,t13):moreis(y0,x0)
--iii1
-n@[k:is(y0,x0)]
-+*iii1
-k@t15:=isp1(rat,[x:rat]in(x,s),x0,y0,j,k):in(y0,s)
-n@t16:=th3"l.imp"(is(y0,x0),in(y0,s),n,[t:is(y0,x0)]t15(t)):nis(y0,x0)
-t17:=ore1(more(y0,x0),is(y0,x0),t14,t16):more(y0,x0)
-t18:=satz82(y0,x0,t17):less(x0,y0)
-i@t19:=[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]t18(x,t,y,u):cutprop2
--iii1
-s@[s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))][x0:rat][i:in(x0,s)]
-+*iii1
-i@t20:=<i><x0>s1:some([y:rat]and(in(y,s),more(y,x0)))
--iii1
-i@[y0:rat][a:and(in(y0,s),more(y0,x0))]
-+*iii1
-a@t21:=ande1(in(y0,s),more(y0,x0),a):in(y0,s)
-t22:=ande2(in(y0,s),more(y0,x0),a):more(y0,x0)
-t23:=satz81g(y0,x0,t22):not(lessis(y0,x0))
-t24:=th3"l.imp"(moreis(x0,y0),lessis(y0,x0),t23,[t:moreis(x0,y0)]satz84(x0,y0,t)):not(moreis(x0,y0))
-t25:=th4"l.imp"(in(y0,s),moreis(x0,y0),t21,t24):not(ubprop(x0,y0))
-t26:=th1"l.all"(rat,[y:rat]ubprop(x0,y),y0,t25):not(ub(s,x0))
-t27:=th1"l.and"(ub(s,x0),in(x0,s),t26):not(max(s,x0))
-i@t28:=someapp(rat,[y:rat]and(in(y,s),more(y,x0)),t20,not(max(s,x0)),[y:rat][t:and(in(y,s),more(y,x0))]t27(y,t)):not(max(s,x0))
--iii1
-x0@[n:not(in(x0,s))]
-+*iii1
-n@t29:=th2"l.and"(ub(x0),in(x0,s),n):not(max(s,x0))
-x0@t30:=th1"l.imp"(in(x0,s),not(max(s,x0)),[u:in(x0,s)]t28(u),[u:not(in(x0,s))]t29(u)):not(max(s,x0))
-s1@t31:=t11([x:rat]t30(x)):cutprop3
--iii1
-s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][j:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))]
-cut2:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),t19".iii1"(j),t31".iii1"(s1)):cutprop(s)
-+*rp
-eta@more:=some"rt"([x:rat]and(lrt(ksi,x),urt(eta,x))):'prop'
-[m:more(ksi,eta)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]p][x0:rat][a:and(lrt(ksi,x0),urt(eta,x0))]
-+iii2
-t1:=ande1(lrt(ksi,x0),urt(eta,x0),a):lrt(ksi,x0)
-t2:=ande2(lrt(ksi,x0),urt(eta,x0),a):urt(eta,x0)
-t3:=<t2><t1><x0>p1:p
--iii2
-p1@moreapp:=someapp(rat,[x:rat]and(lrt(ksi,x),urt(eta,x)),m,p,[x:rat][t:and(lrt(ksi,x),urt(eta,x))]t3".iii2"(x,t)):p
-eta@less:=some"rt"([x:rat]and(urt(ksi,x),lrt(eta,x))):'prop'
-[l:less(ksi,eta)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]p][x0:rat][a:and(urt(ksi,x0),lrt(eta,x0))]
-+*iii2
-a@t4:=ande1(urt(ksi,x0),lrt(eta,x0),a):urt(ksi,x0)
-t5:=ande2(urt(ksi,x0),lrt(eta,x0),a):lrt(eta,x0)
-t6:=<t5><t4><x0>p1:p
--iii2
-p1@lessapp:=someapp(rat,[x:rat]and(urt(ksi,x),lrt(eta,x)),l,p,[x:rat][t:and(urt(ksi,x),lrt(eta,x))]t6".iii2"(x,t)):p
-eta@[m:more(ksi,eta)]
-+2121
-[x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
-t1:=andi(urt(eta,x0),lrt(ksi,x0),ux,lx):and(urt(eta,x0),lrt(ksi,x0))
-t2:=somei(rat,[x:rat]and(urt(eta,x),lrt(ksi,x)),x0,t1):less(eta,ksi)
--2121
-satz121:=moreapp(m,less(eta,ksi),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2".2121"(x,t,u)):less(eta,ksi)
-eta@[l:less(ksi,eta)]
-+2122
-[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
-t1:=andi(lrt(eta,x0),urt(ksi,x0),lx,ux):and(lrt(eta,x0),urt(ksi,x0))
-t2:=somei(rat,[x:rat]and(lrt(eta,x),urt(ksi,x)),x0,t1):more(eta,ksi)
--2122
-satz122:=lessapp(l,more(eta,ksi),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t2".2122"(x,t,u)):more(eta,ksi)
-+2123
-eta@[m:more(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
-t1:=th3"st.isset"(rat,lcl(ksi),lcl(eta),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
-t2:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t1,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
-m@t3:=moreapp(ksi,eta,m,not(is(ksi,eta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2(x,t,u)):not(is(ksi,eta))
-eta@t4:=th2"l.ec"(is(ksi,eta),more(ksi,eta),[t:more(ksi,eta)]t3(t)):ec(is(ksi,eta),more(ksi,eta))
-[l:less(ksi,eta)][x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
-t5:=th4"st.isset"(rat,lcl(eta),lcl(ksi),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
-t6:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t5,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
-l@t7:=lessapp(ksi,eta,l,not(is(ksi,eta)),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t6(x,t,u)):not(is(ksi,eta))
-eta@t8:=th1"l.ec"(less(ksi,eta),is(ksi,eta),[t:less(ksi,eta)]t7(t)):ec(less(ksi,eta),is(ksi,eta))
-m@[l:less(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)][y0:rat][uy:urt(ksi,y0)][ly:lrt(eta,y0)]
-t9:=cutapp2a(ksi,x0,lx,y0,uy):less"rt"(x0,y0)
-t10:=cutapp2b(eta,y0,ly,x0,ux):more"rt"(x0,y0)
-t11:=mp(less"rt"(x0,y0),con,t9,ec3e23(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),satz81b(x0,y0),t10)):con
-ux@t12:=lessapp(ksi,eta,l,con,[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t11(x,t,u)):con
-l@t13:=moreapp(ksi,eta,m,con,[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t12(x,t,u)):con
-m@t14:=[t:less(ksi,eta)]t13(t):not(less(ksi,eta))
-eta@t15:=th1"l.ec"(more(ksi,eta),less(ksi,eta),[t:more(ksi,eta)]t14(t)):ec(more(ksi,eta),less(ksi,eta))
-a:=th6"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t4,t15,t8):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-[i:is(ksi,eta)]
-t16:=or3i1(is(ksi,eta),more(ksi,eta),less(ksi,eta),i):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-eta@[n:nis(ksi,eta)]
-t17:=th3"l.imp"(is"e"(set(rat),lcl(ksi),lcl(eta)),is(ksi,eta),n,[t:is"e"(set(rat),lcl(ksi),lcl(eta))]isi(ksi,eta,t)):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
-t18:=th5"st.isset"(rat,lcl(ksi),lcl(eta),t17):or(more(ksi,eta),more(eta,ksi))
-t19:=th8"l.or"(more(ksi,eta),more(eta,ksi),less(ksi,eta),t18,[t:more(eta,ksi)]satz121(eta,ksi,t)):or(more(ksi,eta),less(ksi,eta))
-t20:=th7"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t19):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-eta@b:=th1"l.imp"(is(ksi,eta),or3(is(ksi,eta),more(ksi,eta),less(ksi,eta)),[t:is(ksi,eta)]t16(t),[t:nis(ksi,eta)]t20(t)):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
--2123
-eta@satz123:=orec3i(is(ksi,eta),more(ksi,eta),less(ksi,eta),b".2123",a".2123"):orec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-satz123a:=orec3e1(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-satz123b:=orec3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-moreis:=or(more(ksi,eta),is(ksi,eta)):'prop'
-lessis:=or(less(ksi,eta),is(ksi,eta)):'prop'
-[m:moreis(ksi,eta)]
-satz124:=th9"l.or"(more(ksi,eta),is(ksi,eta),less(eta,ksi),is(eta,ksi),m,[t:more(ksi,eta)]satz121(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):lessis(eta,ksi)
-eta@[l:lessis(ksi,eta)]
-satz125:=th9"l.or"(less(ksi,eta),is(ksi,eta),more(eta,ksi),is(eta,ksi),l,[t:less(ksi,eta)]satz122(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):moreis(eta,ksi)
-zeta@[i:is(ksi,eta)][m:more(ksi,zeta)]
-ismore1:=isp(cut,[u:cut]more(u,zeta),ksi,eta,m,i):more(eta,zeta)
-i@[m:more(zeta,ksi)]
-ismore2:=isp(cut,[u:cut]more(zeta,u),ksi,eta,m,i):more(zeta,eta)
-i@[l:less(ksi,zeta)]
-isless1:=isp(cut,[u:cut]less(u,zeta),ksi,eta,l,i):less(eta,zeta)
-i@[l:less(zeta,ksi)]
-isless2:=isp(cut,[u:cut]less(zeta,u),ksi,eta,l,i):less(zeta,eta)
-i@[m:moreis(ksi,zeta)]
-ismoreis1:=isp(cut,[u:cut]moreis(u,zeta),ksi,eta,m,i):moreis(eta,zeta)
-i@[m:moreis(zeta,ksi)]
-ismoreis2:=isp(cut,[u:cut]moreis(zeta,u),ksi,eta,m,i):moreis(zeta,eta)
-i@[l:lessis(ksi,zeta)]
-islessis1:=isp(cut,[u:cut]lessis(u,zeta),ksi,eta,l,i):lessis(eta,zeta)
-i@[l:lessis(zeta,ksi)]
-islessis2:=isp(cut,[u:cut]lessis(zeta,u),ksi,eta,l,i):lessis(zeta,eta)
-eta@[i:is(ksi,eta)]
-moreisi2:=ori2(more(ksi,eta),is(ksi,eta),i):moreis(ksi,eta)
-lessisi2:=ori2(less(ksi,eta),is(ksi,eta),i):lessis(ksi,eta)
-eta@[m:more(ksi,eta)]
-moreisi1:=ori1(more(ksi,eta),is(ksi,eta),m):moreis(ksi,eta)
-eta@[l:less(ksi,eta)]
-lessisi1:=ori1(less(ksi,eta),is(ksi,eta),l):lessis(ksi,eta)
-zeta@[upsilon:cut][i:is(ksi,eta)][j:is(zeta,upsilon)][m:more(ksi,zeta)]
-ismore12:=ismore2(zeta,upsilon,eta,j,ismore1(ksi,eta,zeta,i,m)):more(eta,upsilon)
-j@[l:less(ksi,zeta)]
-isless12:=isless2(zeta,upsilon,eta,j,isless1(ksi,eta,zeta,i,l)):less(eta,upsilon)
-j@[m:moreis(ksi,zeta)]
-ismoreis12:=ismoreis2(zeta,upsilon,eta,j,ismoreis1(ksi,eta,zeta,i,m)):moreis(eta,upsilon)
-j@[l:lessis(ksi,zeta)]
-islessis12:=islessis2(zeta,upsilon,eta,j,islessis1(ksi,eta,zeta,i,l)):lessis(eta,upsilon)
-eta@[m:moreis(ksi,eta)]
-satz123c:=th7"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,comor(more(ksi,eta),is(ksi,eta),m)):not(less(ksi,eta))
-eta@[l:lessis(ksi,eta)]
-satz123d:=th9"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l):not(more(ksi,eta))
-eta@[n:not(more(ksi,eta))]
-satz123e:=th2"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n):lessis(ksi,eta)
-eta@[n:not(less(ksi,eta))]
-satz123f:=comor(is(ksi,eta),more(ksi,eta),th3"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n)):moreis(ksi,eta)
-eta@[m:more(ksi,eta)]
-satz123g:=th3"l.or"(less(ksi,eta),is(ksi,eta),ec3e23(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m),ec3e21(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m)):not(lessis(ksi,eta))
-eta@[l:less(ksi,eta)]
-satz123h:=th3"l.or"(more(ksi,eta),is(ksi,eta),ec3e32(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l),ec3e31(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l)):not(moreis(ksi,eta))
-eta@[n:not(moreis(ksi,eta))]
-satz123j:=or3e3(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th5"l.or"(more(ksi,eta),is(ksi,eta),n),th4"l.or"(more(ksi,eta),is(ksi,eta),n)):less(ksi,eta)
-eta@[n:not(lessis(ksi,eta))]
-satz123k:=or3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th4"l.or"(less(ksi,eta),is(ksi,eta),n),th5"l.or"(less(ksi,eta),is(ksi,eta),n)):more(ksi,eta)
-zeta@[l:less(ksi,eta)][k:less(eta,zeta)]
-+2126
-[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)][y0:rat][uy:urt(eta,y0)][ly:lrt(zeta,y0)]
-t1:=cutapp2a(eta,x0,lx,y0,uy):less"rt"(x0,y0)
-t2:=satz119a(ksi,x0,ux,y0,t1):urt(ksi,y0)
-t3:=andi(urt(ksi,y0),lrt(zeta,y0),t2,ly):and(urt(ksi,y0),lrt(zeta,y0))
-t4:=somei(rat,[x:rat]and(urt(ksi,x),lrt(zeta,x)),y0,t3):less(ksi,zeta)
-lx@t5:=lessapp(eta,zeta,k,less(ksi,zeta),[x:rat][t:urt(eta,x)][u:lrt(zeta,x)]t4(x,t,u)):less(ksi,zeta)
--2126
-satz126:=lessapp(ksi,eta,l,less(ksi,zeta),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t5".2126"(x,t,u)):less(ksi,zeta)
-trless:=satz126:less(ksi,zeta)
-zeta@[m:more(ksi,eta)][n:more(eta,zeta)]
-trmore:=satz122(zeta,ksi,satz126(zeta,eta,ksi,satz121(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
-zeta@[l:lessis(ksi,eta)][k:less(eta,zeta)]
-satz127a:=orapp(less(ksi,eta),is(ksi,eta),less(ksi,zeta),l,[u:less(ksi,eta)]trless(u,k),[u:is(ksi,eta)]isless1(eta,ksi,zeta,symis(cut,ksi,eta,u),k)):less(ksi,zeta)
-zeta@[l:less(ksi,eta)][k:lessis(eta,zeta)]
-satz127b:=orapp(less(eta,zeta),is(eta,zeta),less(ksi,zeta),k,[u:less(eta,zeta)]trless(l,u),[u:is(eta,zeta)]isless2(eta,zeta,ksi,u,l)):less(ksi,zeta)
-zeta@[m:moreis(ksi,eta)][n:more(eta,zeta)]
-satz127c:=satz122(zeta,ksi,satz127b(zeta,eta,ksi,satz121(eta,zeta,n),satz124(ksi,eta,m))):more(ksi,zeta)
-zeta@[m:more(ksi,eta)][n:moreis(eta,zeta)]
-satz127d:=satz122(zeta,ksi,satz127a(zeta,eta,ksi,satz124(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
-zeta@[l:lessis(ksi,eta)][k:lessis(eta,zeta)]
-+2128
-[i:is(ksi,eta)][j:is(eta,zeta)]
-t1:=lessisi2(ksi,zeta,tris(cut,ksi,eta,zeta,i,j)):lessis(ksi,zeta)
-i@[j:less(eta,zeta)]
-t2:=lessisi1(ksi,zeta,satz127a(l,j)):lessis(ksi,zeta)
-i@t3:=orapp(less(eta,zeta),is(eta,zeta),lessis(ksi,zeta),k,[t:less(eta,zeta)]t2(t),[t:is(eta,zeta)]t1(t)):lessis(ksi,zeta)
-k@[j:less(ksi,eta)]
-t4:=lessisi1(ksi,zeta,satz127b(j,k)):lessis(ksi,zeta)
--2128
-satz128:=orapp(less(ksi,eta),is(ksi,eta),lessis(ksi,zeta),l,[t:less(ksi,eta)]t4".2128"(t),[t:is(ksi,eta)]t3".2128"(t)):lessis(ksi,zeta)
-trlessis:=satz128:lessis(ksi,zeta)
-zeta@[m:moreis(ksi,eta)][n:moreis(eta,zeta)]
-trmoreis:=satz125(zeta,ksi,satz128(zeta,eta,ksi,satz124(eta,zeta,n),satz124(ksi,eta,m))):moreis(ksi,zeta)
-eta@[z0:rat][x0:rat][y0:rat]
-sumprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0))):'prop'
-z0@sumprop:=some"rt"([x:rat]some"rt"([y:rat]sumprop1(z0,x,y))):'prop'
-eta@sum:=setof(rat,[z:rat]sumprop(z)):set(rat)
-x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl(x0,y0))]
-+iii3
-t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),lx,ly,i):sumprop1(z0,x0,y0)
-t2:=somei(rat,[y:rat]sumprop1(z0,x0,y),y0,t1):some"rt"([y:rat]sumprop1(z0,x0,y))
-t3:=somei(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),x0,t2):sumprop(z0)
--iii3
-sum1:=estii(rat,[z:rat]sumprop(z),z0,t3".iii3"):in(z0,sum)
-z0@[i:in(z0,sum)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]p]
-+*iii3
-p1@t4:=estie(rat,[z:rat]sumprop(z),z0,i):sumprop(z0)
--iii3
-p1@[x0:rat][px:some"rt"([y:rat]sumprop1(z0,x0,y))][y0:rat][py:sumprop1(z0,x0,y0)]
-+*iii3
-py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(ksi,x0)
-t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(eta,y0)
-t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):is"rt"(z0,pl(x0,y0))
-t8:=<t7><t6><y0><t5><x0>p1:p
-px@t9:=someapp(rat,[y:rat]sumprop1(z0,x0,y),px,p,[y:rat][t:sumprop1(z0,x0,y)]t8(y,t)):p
--iii3
-p1@sumapp:=someapp(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),t4".iii3",p,[x:rat][t:some"rt"([y:rat]sumprop1(z0,x,y))]t9".iii3"(x,t)):p
-eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-+3129
-[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))]
-t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
-t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
-t3:=isless1"rt"(pl(x0,y0),z0,pl(x1,y1),symis(rat,z0,pl(x0,y0),j),satz98a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,pl(x1,y1))
-t4:=ec3e31(is"rt"(z0,pl(x1,y1)),more"rt"(z0,pl(x1,y1)),less"rt"(z0,pl(x1,y1)),satz81b(z0,pl(x1,y1)),t3):nis"rt"(z0,pl(x1,y1))
-i@t5:=sumapp(ksi,eta,z0,i,nis"rt"(z0,pl(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,pl(x1,y1))
--3129
-satz129a:=th3"l.imp"(in(pl(x1,y1),sum),nis"rt"(pl(x1,y1),pl(x1,y1)),weli(is"rt"(pl(x1,y1),pl(x1,y1)),refis(rat,pl(x1,y1))),[t:in(pl(x1,y1),sum)]t5".3129"(pl(x1,y1),t)):not(in(pl(x1,y1),sum))
-+*3129
-eta@[u0:rat][i:in(u0,sum)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,pl(x0,y0))]
-t6:=isless2"rt"(u0,pl(x0,y0),z0,j,l):less"rt"(z0,pl(x0,y0))
-z1:=ov(z0,pl(x0,y0)):rat
-t7:=isless12"rt"(z0,ts(z1,pl(x0,y0)),pl(x0,y0),ts(1rt,pl(x0,y0)),satz110f(z0,pl(x0,y0)),example1d(pl(x0,y0)),t6):less"rt"(ts(z1,pl(x0,y0)),ts(1rt,pl(x0,y0)))
-t8:=satz106c(z1,1rt,pl(x0,y0),t7):less"rt"(z1,1rt)
-t9:=isless2"rt"(ts(x0,1rt),x0,ts(x0,z1),example1a(x0),satz105f(z1,1rt,x0,t8)):less"rt"(ts(x0,z1),x0)
-t10:=isless2"rt"(ts(y0,1rt),y0,ts(y0,z1),example1a(y0),satz105f(z1,1rt,y0,t8)):less"rt"(ts(y0,z1),y0)
-t11:=satz120(ksi,x0,lx,ts(x0,z1),t9):lrt(ksi,ts(x0,z1))
-t12:=satz120(eta,y0,ly,ts(y0,z1),t10):lrt(eta,ts(y0,z1))
-t13:=tris(rat,pl(ts(x0,z1),ts(y0,z1)),ts(pl(x0,y0),z1),z0,distpt1(x0,y0,z1),satz110c(z0,pl(x0,y0))):is"rt"(pl(ts(x0,z1),ts(y0,z1)),z0)
-t14:=symis(rat,pl(ts(x0,z1),ts(y0,z1)),z0,t13):is"rt"(z0,pl(ts(x0,z1),ts(y0,z1)))
-t15:=sum1(ksi,eta,z0,ts(x0,z1),t11,ts(y0,z1),t12,t14):in(z0,sum)
-l@t16:=sumapp(ksi,eta,u0,i,in(z0,sum),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,pl(x,y))]t15(x,t,y,u,v)):in(z0,sum)
-eta@[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
-t17:=sum1(ksi,eta,pl(x1,y0),x1,lx1,y0,ly,refis(rat,pl(x1,y0))):in(pl(x1,y0),sum)
-t18:=satz96a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(pl(x1,y0),pl(x0,y0))
-t19:=ismore2"rt"(pl(x0,y0),z0,pl(x1,y0),symis(rat,z0,pl(x0,y0),j),t18):more"rt"(pl(x1,y0),z0)
-t20:=andi(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0),t17,t19):and(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0))
-t21:=somei(rat,[y:rat]and(in(y,sum),more"rt"(y,z0)),pl(x1,y0),t20):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
-j@t22:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t21(x,t,u)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
-i@t23:=sumapp(ksi,eta,z0,i,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t22(x,t,y,u,v)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
-eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-t24:=cut2(sum,pl(x0,y0),sum1(ksi,eta,pl(x0,y0),x0,lx,y0,ly,refis(rat,pl(x0,y0))),pl(x1,y1),satz129a(x1,ux,y1,uy),[x:rat][t:in(x,sum)][y:rat][u:less"rt"(y,x)]t16(x,t,y,u),[x:rat][t:in(x,sum)]t23(x,t)):cutprop(sum)
-ux@t25:=cutapp1b(eta,cutprop(sum),[y:rat][t:urt(eta,y)]t24(y,t)):cutprop(sum)
-ly@t26:=cutapp1b(ksi,cutprop(sum),[x:rat][t:urt(ksi,x)]t25(x,t)):cutprop(sum)
-lx@t27:=cutapp1a(eta,cutprop(sum),[y:rat][t:lrt(eta,y)]t26(y,t)):cutprop(sum)
--3129
-eta@satz129:=cutapp1a(ksi,cutprop(sum),[x:rat][t:lrt(ksi,x)]t27".3129"(x,t)):cutprop(sum)
-pl:=cutof(sum,satz129):cut
-[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
-lrtpl:=ine(sum,satz129,z0,sum1(z0,x0,lx,y0,ly,i)):lrt(pl(ksi,eta),z0)
-eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
-+*iii3
-i@t10:=isp1(rat,[x:rat]not(in(x,sum)),pl"rt"(x0,y0),z0,satz129a(x0,ux,y0,uy),i):not(in(z0,sum))
--iii3
-i@urtpl:=th3"l.imp"(lrt(pl(ksi,eta),z0),in(z0,sum),t10".iii3",[t:lrt(pl(ksi,eta),z0)]ini(sum,satz129,z0,t)):urt(pl(ksi,eta),z0)
-eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]p]
-+*iii3
-p1@t11:=ini(sum,satz129,z0,lz):in(z0,sum)
--iii3
-p1@plapp:=sumapp(z0,t11".iii3",p,p1):p
-zeta@[i:is(ksi,eta)]
-ispl1:=isf(cut,cut,[u:cut]pl(u,zeta),ksi,eta,i):is(pl(ksi,zeta),pl(eta,zeta))
-ispl2:=isf(cut,cut,[u:cut]pl(zeta,u),ksi,eta,i):is(pl(zeta,ksi),pl(zeta,eta))
-upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
-ispl12:=tris(cut,pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),ispl1(i),ispl2(zeta,upsilon,eta,j)):is(pl(ksi,zeta),pl(eta,upsilon))
-+3130
-eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
-t1:=tris(rat,z0,pl"rt"(x0,y0),pl"rt"(y0,x0),i,compl(x0,y0)):is"rt"(z0,pl"rt"(y0,x0))
-t2:=lrtpl(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(pl(eta,ksi),z0)
-lz@t3:=plapp(ksi,eta,z0,lz,lrt(pl(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]t2(x,t,y,u,v)):lrt(pl(eta,ksi),z0)
--3130
-eta@satz130:=isi1(pl(ksi,eta),pl(eta,ksi),[x:rat][t:lrt(pl(ksi,eta),x)]t3".3130"(x,t),[x:rat][t:lrt(pl(eta,ksi),x)]t3".3130"(eta,ksi,x,t)):is(pl(ksi,eta),pl(eta,ksi))
-compl:=satz130:is(pl(ksi,eta),pl(eta,ksi))
-+3131
-zeta@[u0:rat][lu:lrt(pl(pl(ksi,eta),zeta),u0)][v0:rat][lv:lrt(pl(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,pl"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,pl"rt"(x0,y0))]
-t1:=tr3is(rat,u0,pl"rt"(v0,z0),pl"rt"(pl"rt"(x0,y0),z0),pl"rt"(x0,pl"rt"(y0,z0)),i,ispl1"rt"(v0,pl"rt"(x0,y0),z0,j),asspl1(x0,y0,z0)):is"rt"(u0,pl"rt"(x0,pl"rt"(y0,z0)))
-t2:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
-t3:=lrtpl(ksi,pl(eta,zeta),u0,x0,lx,pl"rt"(y0,z0),t2,t1):lrt(pl(ksi,pl(eta,zeta)),u0)
-i@t4:=plapp(ksi,eta,v0,lv,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,pl"rt"(x,y))]t3(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
-lu@t5:=plapp(pl(ksi,eta),zeta,u0,lu,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(pl(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
-u0@[lu:lrt(pl(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,pl"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
-t6:=tr3is(rat,u0,pl"rt"(x0,v0),pl"rt"(x0,pl"rt"(y0,z0)),pl"rt"(pl"rt"(x0,y0),z0),i,ispl2"rt"(v0,pl"rt"(y0,z0),x0,j),asspl2(x0,y0,z0)):is"rt"(u0,pl"rt"(pl"rt"(x0,y0),z0))
-t7:=lrtpl(ksi,eta,pl"rt"(x0,y0),x0,lx,y0,ly,refis(rat,pl"rt"(x0,y0))):lrt(pl(ksi,eta),pl"rt"(x0,y0))
-t8:=lrtpl(pl(ksi,eta),zeta,u0,pl"rt"(x0,y0),t7,z0,lz,t6):lrt(pl(pl(ksi,eta),zeta),u0)
-i@t9:=plapp(eta,zeta,v0,lv,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t8(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
-lu@t10:=plapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t9(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
--3131
-zeta@satz131:=isi1(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),[x:rat][t:lrt(pl(pl(ksi,eta),zeta),x)]t5".3131"(x,t),[x:rat][t:lrt(pl(ksi,pl(eta,zeta)),x)]t10".3131"(x,t)):is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
-asspl1:=satz131:is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
-asspl2:=symis(cut,pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),satz131):is(pl(ksi,pl(eta,zeta)),pl(pl(ksi,eta),zeta))
-ksi@[a0:rat]
-+3132
-[x0:rat][y0:rat]
-prop1:=and(lrt(ksi,x0),urt(ksi,y0)):'prop'
-[p:prop1]
-t1:=cutapp2b(x0,ande1(lrt(ksi,x0),urt(ksi,y0),p),y0,ande2(lrt(ksi,x0),urt(ksi,y0),p)):more"rt"(y0,x0)
-prop2:=is"rt"(mn(y0,x0,t1),a0):'prop'
-y0@prop3:=and(prop1,[t:prop1]prop2(t)):'prop'
-a0@prop4:=some"rt"([x:rat]some"rt"([y:rat]prop3(x,y))):'prop'
-x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
-t2:=cutapp2b(x0,lx,y0,uy):more"rt"(y0,x0)
-[n:nat][m:more"rt"(ts(rtofn(n),a0),mn(y0,x0,t2))]
-t3:=satz96d(ts(rtofn(n),a0),mn(y0,x0,t2),x0,m):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),pl"rt"(x0,mn(y0,x0,t2)))
-t4:=ismore2"rt"(pl"rt"(x0,mn(y0,x0,t2)),y0,pl"rt"(x0,ts(rtofn(n),a0)),satz101c(y0,x0,t2),t3):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),y0)
-t5:=satz119(y0,uy,pl"rt"(x0,ts(rtofn(n),a0)),t4):urt(pl"rt"(x0,ts(rtofn(n),a0)))
-t6:=somei(nat,[x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),n,t5):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
-uy@t7:=someapp(nat,[x:nat]more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2)),satz115(a0,mn(y0,x0,t2)),some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0)))),[x:nat][t:more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2))]t6(x,t)):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
-[u:nat][m:min"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)]
-t8:=ande1(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)
-t9:=ande2(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):urt(pl"rt"(x0,ts(rtofn(u),a0)))
-[i:is"n"(u,1)]
-u0:=pl"rt"(x0,a0):rat
-t10:=tr3is(rat,ts(rtofn(u),a0),ts(1rt,a0),ts(a0,1rt),a0,ists1(rtofn(u),1rt,a0,isnert(u,1,i)),comts(1rt,a0),example1a(a0)):is"rt"(ts(rtofn(u),a0),a0)
-t11:=isp(rat,[x:rat]urt(pl"rt"(x0,x)),ts(rtofn(u),a0),a0,t9,t10):urt(ksi,u0)
-t12:=andi(lrt(ksi,x0),urt(ksi,u0),lx,t11):prop1(x0,u0)
-[p:prop1(x0,u0)]
-t13:=symis(rat,a0,mn(u0,x0,t1(x0,u0,p)),satz101g(u0,x0,a0,t1(x0,u0,p),refis(rat,u0))):prop2(x0,u0,p)
-i@t14:=andi(prop1(x0,u0),[t:prop1(x0,u0)]prop2(x0,u0,t),t12,[t:prop1(x0,u0)]t13(t)):prop3(x0,u0)
-t15:=somei(rat,[y:rat]prop3(x0,y),u0,t14):some"rt"([y:rat]prop3(x0,y))
-t16:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),x0,t15):prop4
-m@[o:more"n"(u,1)]
-t17:=morei(rtofn(u),1rt,fr(u,1),fr(1,1),inclass(fr(u,1)),inclass(fr(1,1)),satz111d(u,1,o)):more"rt"(rtofn(u),1rt)
-um10:=mn(rtofn(u),1rt,t17):rat
-t18:=satz112g(rtofn(u),natrti(u),1rt,natrti(1),t17):natrt(um10)
-um1:=nofrt(um10,t18):nat
-v0:=pl"rt"(x0,ts(um10,a0)):rat
-w0:=pl"rt"(x0,ts(rtofn(u),a0)):rat
-t19:=isless2"rt"(pl"rt"(um10,1rt),rtofn(u),um10,satz101e(rtofn(u),1rt,t17),satz94a(um10,1rt)):less"rt"(um10,rtofn(u))
-t20:=lesse(um10,rtofn(u),fr(um1,1),fr(u,1),inclassn(um10,t18),inclass(fr(u,1)),t19):lessf(fr(um1,1),fr(u,1))
-t21:=satz111c(um1,u,t20):less"n"(um1,u)
-t22:=th3"l.imp"(lessis"n"(u,um1),moreis"n"(um1,u),satz10h(um1,u,t21),[t:lessis"n"(u,um1)]satz14(u,um1,t)):not(lessis"n"(u,um1))
-t23:=et(lrt(pl"rt"(x0,ts(rtofn(um1),a0))),th3"l.imp"(urt(pl"rt"(x0,ts(rtofn(um1),a0))),lessis"n"(u,um1),t22,<um1>t8)):lrt(pl"rt"(x0,ts(rtofn(um1),a0)))
-t24:=isp1(rat,[x:rat]lrt(pl"rt"(x0,ts(x,a0))),rtofn(um1),um10,t23,isrtn1(um10,t18)):lrt(ksi,v0)
-t25:=andi(lrt(ksi,v0),urt(ksi,w0),t24,t9):prop1(v0,w0)
-t26:=tr3is(rat,pl"rt"(ts(um10,a0),a0),pl"rt"(ts(um10,a0),ts(1rt,a0)),ts(pl"rt"(um10,1rt),a0),ts(rtofn(u),a0),ispl2"rt"(a0,ts(1rt,a0),ts(um10,a0),example1d(a0)),distpt1(um10,1rt,a0),ists1(pl"rt"(um10,1rt),rtofn(u),a0,satz101e(rtofn(u),1rt,t17))):is"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0))
-t27:=tris(rat,pl"rt"(v0,a0),pl"rt"(x0,pl"rt"(ts(um10,a0),a0)),w0,asspl1"rt"(x0,ts(um10,a0),a0),ispl2"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0),x0,t26)):is"rt"(pl"rt"(v0,a0),w0)
-[p:prop1(v0,w0)]
-t28:=symis(rat,a0,mn(w0,v0,t1(v0,w0,p)),satz101g(w0,v0,a0,t1(v0,w0,p),t27)):prop2(v0,w0,p)
-o@t29:=andi(prop1(v0,w0),[t:prop1(v0,w0)]prop2(v0,w0,t),t25,[t:prop1(v0,w0)]t28(t)):prop3(v0,w0)
-t30:=somei(rat,[y:rat]prop3(v0,y),w0,t29):some"rt"([y:rat]prop3(v0,y))
-t31:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),v0,t30):prop4
-m@t32:=orapp(more"n"(u,1),is"n"(u,1),prop4,satz24(u),[t:more"n"(u,1)]t31(t),[t:is"n"(u,1)]t16(t)):prop4
-uy@t34:=someapp(nat,[x:nat]min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x),satz27([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),t7),prop4,[x:nat][t:min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x)]t32(x,t)):prop4
-lx@t35:=cutapp1b(prop4,[y:rat][t:urt(ksi,y)]t34(y,t)):prop4
--3132
-satz132:=cutapp1a(prop4".3132",[x:rat][t:lrt(ksi,x)]t35".3132"(x,t)):some"rt"([x:rat]some"rt"([y:rat]and(and(lrt(ksi,x),urt(ksi,y)),[t:and(lrt(ksi,x),urt(ksi,y))]is"rt"(mn(y,x,cutapp2b(x,ande1(lrt(ksi,x),urt(ksi,y),t),y,ande2(lrt(ksi,x),urt(ksi,y),t))),a0))))
-ksi@[p:'prop'][a0:rat][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),a0)]p]
-+*3132
-p1@[x0:rat][s:some"rt"([y:rat]prop3(a0,x0,y))][y0:rat][p3:prop3(a0,x0,y0)]
-t36:=ande1(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop1(a0,x0,y0)
-t37:=ande2"l.r"(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop2(a0,x0,y0,t36)
-t38:=ande1(lrt(ksi,x0),urt(ksi,y0),t36):lrt(ksi,x0)
-t39:=ande2(lrt(ksi,x0),urt(ksi,y0),t36):urt(ksi,y0)
-t40:=satz101g(y0,x0,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),t1(a0,x0,y0,t36),satz101c(y0,x0,cutapp2b(x0,t38,y0,t39))):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)))
-t41:=tris(rat,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)),a0,t40,t37):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),a0)
-t42:=<t41><t39><y0><t38><x0>p1:p
-s@t43:=someapp(rat,[y:rat]prop3(a0,x0,y),s,p,[y:rat][t:prop3(a0,x0,y)]t42(y,t)):p
--3132
-p1@satz132app:=someapp(rat,[x:rat]some"rt"([y:rat]prop3".3132"(a0,x,y)),satz132(a0),p,[x:rat][t:some"rt"([y:rat]prop3".3132"(a0,x,y))]t43".3132"(x,t)):p
-+3133
-eta@[y0:rat][ly:lrt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][uu:urt(ksi,u0)][i:is"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0)]
-t1:=tris(rat,u0,pl"rt"(x0,mn(u0,x0,cutapp2b(x0,lx,u0,uu))),pl"rt"(x0,y0),satz101d(u0,x0,cutapp2b(x0,lx,u0,uu)),ispl2"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0,x0,i)):is"rt"(u0,pl"rt"(x0,y0))
-t2:=lrtpl(ksi,eta,u0,x0,lx,y0,ly,t1):lrt(pl(ksi,eta),u0)
-t3:=andi(lrt(pl(ksi,eta),u0),urt(ksi,u0),t2,uu):and(lrt(pl(ksi,eta),u0),urt(ksi,u0))
-t4:=somei(rat,[x:rat]and(lrt(pl(ksi,eta),x),urt(ksi,x)),u0,t3):more(pl(ksi,eta),ksi)
-ly@t5:=satz132app(ksi,more(pl(ksi,eta),ksi),y0,[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),y0)]t4(x,t,y,u,v)):more(pl(ksi,eta),ksi)
--3133
-eta@satz133:=cutapp1a(eta,more(pl(ksi,eta),ksi),[x:rat][t:lrt(eta,x)]t5".3133"(x,t)):more(pl(ksi,eta),ksi)
-satz133a:=satz121(pl(ksi,eta),ksi,satz133):less(ksi,pl(ksi,eta))
-zeta@[m:more(ksi,eta)]
-+3134
-[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
-t1:=satz119a(eta,y0,uy,x0,l):urt(eta,x0)
-t2:=satz83(y0,x0,l):more"rt"(x0,y0)
-[u0:rat][lu:lrt(zeta,u0)][z0:rat][uz:urt(zeta,z0)][i:is"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2))]
-t3:=tris(rat,z0,pl"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),u0),pl"rt"(mn(x0,y0,t2),u0),satz101f(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),ispl1"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2),u0,i)):is"rt"(z0,pl"rt"(mn(x0,y0,t2),u0))
-t4:=tr3is(rat,pl"rt"(y0,z0),pl"rt"(y0,pl"rt"(mn(x0,y0,t2),u0)),pl"rt"(pl"rt"(y0,mn(x0,y0,t2)),u0),pl"rt"(x0,u0),ispl2"rt"(z0,pl"rt"(mn(x0,y0,t2),u0),y0,t3),asspl2"rt"(y0,mn(x0,y0,t2),u0),ispl1"rt"(pl"rt"(y0,mn(x0,y0,t2)),x0,u0,satz101c(x0,y0,t2))):is"rt"(pl"rt"(y0,z0),pl"rt"(x0,u0))
-t5:=lrtpl(ksi,zeta,pl"rt"(y0,z0),x0,lx,u0,lu,t4):lrt(pl(ksi,zeta),pl"rt"(y0,z0))
-t6:=urtpl(eta,zeta,pl"rt"(y0,z0),y0,uy,z0,uz,refis(rat,pl"rt"(y0,z0))):urt(pl(eta,zeta),pl"rt"(y0,z0))
-t7:=andi(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)),t5,t6):and(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)))
-t8:=somei(rat,[x:rat]and(lrt(pl(ksi,zeta),x),urt(pl(eta,zeta),x)),pl"rt"(y0,z0),t7):more(pl(ksi,zeta),pl(eta,zeta))
-l@t9:=satz132app(zeta,more(pl(ksi,zeta),pl(eta,zeta)),mn(x0,y0,t2),[x:rat][t:lrt(zeta,x)][y:rat][u:urt(zeta,y)][v:is"rt"(mn(y,x,cutapp2b(zeta,x,t,y,u)),mn(x0,y0,t2))]t8(x,t,y,u,v)):more(pl(ksi,zeta),pl(eta,zeta))
-uy@t10:=cutapp3(ksi,y0,ly,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t9(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
--3134
-satz134:=moreapp(ksi,eta,m,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t10".3134"(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
-zeta@[m:more(ksi,eta)]
-satz135a:=satz134(m):more(pl(ksi,zeta),pl(eta,zeta))
-zeta@[i:is(ksi,eta)]
-satz135b:=ispl1(ksi,eta,zeta,i):is(pl(ksi,zeta),pl(eta,zeta))
-zeta@[l:less(ksi,eta)]
-satz135c:=satz121(pl(eta,zeta),pl(ksi,zeta),satz134(eta,ksi,zeta,satz122(ksi,eta,l))):less(pl(ksi,zeta),pl(eta,zeta))
-m@satz135d:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135a):more(pl(zeta,ksi),pl(zeta,eta))
-i@satz135e:=ispl2(ksi,eta,zeta,i):is(pl(zeta,ksi),pl(zeta,eta))
-l@satz135f:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135c):less(pl(zeta,ksi),pl(zeta,eta))
-upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
-satz135g:=ismore2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135d(zeta,upsilon,ksi,m)):more(pl(ksi,zeta),pl(eta,upsilon))
-satz135h:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135g):more(pl(zeta,ksi),pl(upsilon,eta))
-i@[l:less(zeta,upsilon)]
-satz135j:=isless2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135f(zeta,upsilon,ksi,l)):less(pl(ksi,zeta),pl(eta,upsilon))
-satz135k:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135j):less(pl(zeta,ksi),pl(upsilon,eta))
-+3136
-zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-t2:=satz123b(pl(ksi,zeta),pl(eta,zeta)):ec3(is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)))
--3136
-zeta@[m:more(pl(ksi,zeta),pl(eta,zeta))]
-satz136a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),m):more(ksi,eta)
-zeta@[i:is(pl(ksi,zeta),pl(eta,zeta))]
-satz136b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),i):is(ksi,eta)
-zeta@[l:less(pl(ksi,zeta),pl(eta,zeta))]
-satz136c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),l):less(ksi,eta)
-zeta@[m:more(pl(zeta,ksi),pl(zeta,eta))]
-satz136d:=satz136a(ismore12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),m)):more(ksi,eta)
-zeta@[i:is(pl(zeta,ksi),pl(zeta,eta))]
-satz136e:=satz136b(tr3is(cut,pl(ksi,zeta),pl(zeta,ksi),pl(zeta,eta),pl(eta,zeta),compl(ksi,zeta),i,compl(zeta,eta))):is(ksi,eta)
-zeta@[l:less(pl(zeta,ksi),pl(zeta,eta))]
-satz136f:=satz136c(isless12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),l)):less(ksi,eta)
-upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
-+3137
-t1:=satz134(ksi,eta,zeta,m):more(pl(ksi,zeta),pl(eta,zeta))
-t2:=ismore12(pl(zeta,eta),pl(eta,zeta),pl(upsilon,eta),pl(eta,upsilon),compl(zeta,eta),compl(upsilon,eta),satz134(zeta,upsilon,eta,n)):more(pl(eta,zeta),pl(eta,upsilon))
--3137
-satz137:=trmore(pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),t1".3137",t2".3137"):more(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
-satz137a:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz137(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
-satz138a:=orapp(more(ksi,eta),is(ksi,eta),more(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]satz137(t,n),[t:is(ksi,eta)]satz135g(t,n)):more(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
-satz138b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]satz137(m,t),[t:is(zeta,upsilon)]satz135h(zeta,upsilon,ksi,eta,t,m)):more(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
-satz138c:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
-satz138d:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
-+3139
-[i:is(ksi,eta)][j:is(zeta,upsilon)]
-t1:=moreisi2(pl(ksi,zeta),pl(eta,upsilon),ispl12(ksi,eta,zeta,upsilon,i,j)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-i@[o:more(zeta,upsilon)]
-t2:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138a(m,o)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-n@[o:more(ksi,eta)]
-t4:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138b(o,n)):moreis(pl(ksi,zeta),pl(eta,upsilon))
--3139
-satz139:=orapp(more(ksi,eta),is(ksi,eta),moreis(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]t4".3139"(t),[t:is(ksi,eta)]t3".3139"(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
-satz139a:=satz124(pl(eta,upsilon),pl(ksi,zeta),satz139(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(pl(ksi,zeta),pl(eta,upsilon))
-eta@[l:lessis(ksi,eta)]
-+3140
-[phi:cut][i:is(pl(eta,phi),ksi)]
-t1:=ismore1(pl(eta,phi),ksi,eta,i,satz133(eta,phi)):more(ksi,eta)
-phi@t2:=th3"l.imp"(is(pl(eta,phi),ksi),more(ksi,eta),satz123d(ksi,eta,l),[t:is(pl(eta,phi),ksi)]t1(t)):nis(pl(eta,phi),ksi)
--3140
-vorbemerkung140:=th5"l.some"(cut,[a:cut]is(pl(eta,a),ksi),[a:cut]t2".3140"(a)):not(some([a:cut]is(pl(eta,a),ksi)))
-eta@[phi:cut][psi:cut]
-+*3140
-psi@[m:more(phi,psi)]
-t3:=satz135d(phi,psi,eta,m):more(pl(eta,phi),pl(eta,psi))
-t4:=ec3e21(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t3):nis(pl(eta,phi),pl(eta,psi))
-psi@[l:less(phi,psi)]
-t5:=satz135f(phi,psi,eta,l):less(pl(eta,phi),pl(eta,psi))
-t6:=ec3e31(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t5):nis(pl(eta,phi),pl(eta,psi))
-psi@[n:nis(phi,psi)]
-t7:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
-t8:=orapp(more(phi,psi),less(phi,psi),nis(pl(eta,phi),pl(eta,psi)),t7,[t:more(phi,psi)]t4(t),[t:less(phi,psi)]t6(t)):nis(pl(eta,phi),pl(eta,psi))
--3140
-psi@[i:is(pl(eta,phi),ksi)][j:is(pl(eta,psi),ksi)]
-satz140b:=th7"l.imp"(is(phi,psi),nis(pl(eta,phi),pl(eta,psi)),weli(is(pl(eta,phi),pl(eta,psi)),tris2(cut,pl(eta,phi),pl(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t8".3140"(t)):is(phi,psi)
-eta@[z0:rat][x0:rat][y0:rat]
-diffprop1:=and(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t))):'prop'
-diffprop2:=and3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0)):'prop'
-z0@diffprop:=some"rt"([x:rat]some"rt"([y:rat]diffprop2(z0,x,y))):'prop'
-eta@diff:=setof(rat,[z:rat]diffprop(z)):set(rat)
-x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][m:more"rt"(x0,y0)][i:is"rt"(z0,mn(x0,y0,m))]
-+*iii3
-i@[m1:more"rt"(x0,y0)]
-t11a:=tris(rat,z0,mn(x0,y0,m),mn(x0,y0,m1),i,satz101g(x0,y0,mn(x0,y0,m),m1,satz101c(x0,y0,m))):is"rt"(z0,mn(x0,y0,m1))
-i@t12:=andi(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),m,[t:more"rt"(x0,y0)]t11a(t)):diffprop1(z0,x0,y0)
-t13:=and3i(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),lx,uy,t12):diffprop2(z0,x0,y0)
-t14:=somei(rat,[y:rat]diffprop2(z0,x0,y),y0,t13):some"rt"([y:rat]diffprop2(z0,x0,y))
-t15:=somei(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),x0,t14):diffprop(z0)
--iii3
-i@diff1:=estii(rat,[z:rat]diffprop(z),z0,t15".iii3"):in(z0,diff)
-z0@[i:in(z0,diff)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]p]
-+*iii3
-p1@t16:=estie(rat,[z:rat]diffprop(z),z0,i):diffprop(z0)
--iii3
-p1@[x0:rat][px:some"rt"([y:rat]diffprop2(z0,x0,y))][y0:rat][py:diffprop2(z0,x0,y0)]
-+*iii3
-py@t17:=and3e1(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):lrt(ksi,x0)
-t18:=and3e2(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):urt(eta,y0)
-t19:=and3e3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):diffprop1(z0,x0,y0)
-t20:=ande1(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):more"rt"(x0,y0)
-t21:=ande2"l.r"(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):is"rt"(z0,mn(x0,y0,t20))
-t22:=<t21><t20><t18><y0><t17><x0>p1:p
-px@t23:=someapp(rat,[y:rat]diffprop2(z0,x0,y),px,p,[y:rat][t:diffprop2(z0,x0,y)]t22(y,t)):p
--iii3
-p1@diffapp:=someapp(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),t16".iii3",p,[x:rat][t:some"rt"([y:rat]diffprop2(z0,x,y))]t23".iii3"(x,t)):p
-eta@[m:more(ksi,eta)]
-+*3140
-m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
-t9:=t2"rp.3134"(eta,m,y0,ly,uy,x0,lx,l):more"rt"(x0,y0)
-t10:=diff1(mn(x0,y0,t9),x0,lx,y0,uy,t9,refis(rat,mn(x0,y0,t9))):in(mn(x0,y0,t9),diff)
-m"rp"@[x1:rat][ux:urt(ksi,x1)][z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
-t11:=isless12"rt"(mn(x0,y0,n),z0,pl"rt"(mn(x0,y0,n),y0),x0,symis(rat,z0,mn(x0,y0,n),j),satz101e(x0,y0,n),satz94a(mn(x0,y0,n),y0)):less"rt"(z0,x0)
-t12:=trless"rt"(z0,x0,x1,t11,cutapp2a(ksi,x0,lx,x1,ux)):less"rt"(z0,x1)
-t13:=ec3e31(is"rt"(z0,x1),more"rt"(z0,x1),less"rt"(z0,x1),satz81b(z0,x1),t12):nis"rt"(z0,x1)
-i@t14:=diffapp(z0,i,nis"rt"(z0,x1),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t13(x,t,y,u,v,w)):nis"rt"(z0,x1)
-ux@t15:=th3"l.imp"(in(x1,diff),nis"rt"(x1,x1),weli(is"rt"(x1,x1),refis(rat,x1)),[t:in(x1,diff)]t14(x1,t)):not(in(x1,diff))
-m"rp"@[z0:rat][i:in(z0,diff)][u0:rat][l:less"rt"(u0,z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
-t16:=tris(rat,pl"rt"(z0,y0),pl"rt"(mn(x0,y0,n),y0),x0,ispl1"rt"(z0,mn(x0,y0,n),y0,j),satz101e(x0,y0,n)):is"rt"(pl"rt"(z0,y0),x0)
-x2:=pl"rt"(u0,y0):rat
-t17:=isless2"rt"(pl"rt"(z0,y0),x0,x2,t16,satz96c(u0,z0,y0,l)):less"rt"(x2,x0)
-t18:=satz120(ksi,x0,lx,x2,t17):lrt(ksi,x2)
-t19:=ismore1"rt"(pl"rt"(y0,u0),pl"rt"(u0,y0),y0,compl"rt"(y0,u0),satz94(y0,u0)):more"rt"(x2,y0)
-t20:=satz101g(x2,y0,u0,t19,compl"rt"(y0,u0)):is"rt"(u0,mn(x2,y0,t19))
-t21:=diff1(u0,x2,t18,y0,uy,t19,t20):in(u0,diff)
-l@t22:=diffapp(z0,i,in(u0,diff),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t21(x,t,y,u,v,w)):in(u0,diff)
-m"rp"@[z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))][x3:rat][lx3:lrt(ksi,x3)][l:less"rt"(x0,x3)]
-t23:=satz83(x0,x3,l):more"rt"(x3,x0)
-t24:=trmore"rt"(x3,x0,y0,t23,n):more"rt"(x3,y0)
-t25:=ismore12"rt"(x3,pl"rt"(mn(x3,y0,t24),y0),x0,pl"rt"(mn(x0,y0,n),y0),satz101f(x3,y0,t24),satz101f(x0,y0,n),t23):more"rt"(pl"rt"(mn(x3,y0,t24),y0),pl"rt"(mn(x0,y0,n),y0))
-t26:=satz97a(mn(x3,y0,t24),mn(x0,y0,n),y0,t25):more"rt"(mn(x3,y0,t24),mn(x0,y0,n))
-t27:=ismore2"rt"(mn(x0,y0,n),z0,mn(x3,y0,t24),symis(rat,z0,mn(x0,y0,n),j),t26):more"rt"(mn(x3,y0,t24),z0)
-t28:=diff1(mn(x3,y0,t24),x3,lx3,y0,uy,t24,refis(rat,mn(x3,y0,t24))):in(mn(x3,y0,t24),diff)
-t29:=andi(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0),t28,t27):and(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0))
-t30:=somei(rat,[x:rat]and(in(x,diff),more"rt"(x,z0)),mn(x3,y0,t24),t29):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
-j@t31:=cutapp3(ksi,x0,lx,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t30(y,t,u)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
-i@t32:=diffapp(z0,i,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t31(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
-m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)][x1:rat][ux1:urt(ksi,x1)]
-t33:=cut2(diff,mn(x0,y0,t9(y0,ly,uy,x0,lx,l)),t10(y0,ly,uy,x0,lx,l),x1,t15(x1,ux1),[x:rat][t:in(x,diff)][y:rat][u:less"rt"(y,x)]t22(x,t,y,u),[x:rat][t:in(x,diff)]t32(x,t)):cutprop(diff)
-l@t34:=cutapp1b(ksi,cutprop(diff),[x:rat][t:urt(ksi,x)]t33(x,t)):cutprop(diff)
-uy@t35:=cutapp3(ksi,y0,ly,cutprop(diff),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t34(x,t,u)):cutprop(diff)
--3140
-m@satz140h:=moreapp(ksi,eta,m,cutprop(diff),[x:rat][u:lrt(ksi,x)][v:urt(eta,x)]t35".3140"(x,u,v)):cutprop(diff)
-+*3140
-m"rp"@chi:=cutof(diff,satz140h):cut
-[z0:rat][lz:lrt(pl(eta,chi),z0)][y1:rat][ly:lrt(eta,y1)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,pl"rt"(y1,u0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][o:more"rt"(x0,y0)][j:is"rt"(u0,mn(x0,y0,o))]
-t36:=cutapp2b(eta,y1,ly,y0,uy):more"rt"(y0,y1)
-t37:=tr3is(rat,pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),pl"rt"(mn(x0,y0,o),pl"rt"(y1,mn(y0,y1,t36))),pl"rt"(mn(x0,y0,o),y0),x0,asspl1"rt"(mn(x0,y0,o),y1,mn(y0,y1,t36)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t36)),y0,mn(x0,y0,o),satz101c(y0,y1,t36)),satz101e(x0,y0,o)):is"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0)
-t38:=isless2"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0,pl"rt"(mn(x0,y0,o),y1),t37,satz94a(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36))):less"rt"(pl"rt"(mn(x0,y0,o),y1),x0)
-t39:=tr3is(rat,z0,pl"rt"(y1,u0),pl"rt"(u0,y1),pl"rt"(mn(x0,y0,o),y1),i,compl"rt"(y1,u0),ispl1"rt"(u0,mn(x0,y0,o),y1,j)):is"rt"(z0,pl"rt"(mn(x0,y0,o),y1))
-t40:=isless1"rt"(pl"rt"(mn(x0,y0,o),y1),z0,x0,symis(rat,z0,pl"rt"(mn(x0,y0,o),y1),t39),t38):less"rt"(z0,x0)
-t41:=satz120(ksi,x0,lx,z0,t40):lrt(ksi,z0)
-i@t42:=diffapp(u0,ini(diff,satz140h,u0,lu),lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(u0,mn(x,y,v))]t41(x,t,y,u,v,w)):lrt(ksi,z0)
-lz@a:=plapp(eta,chi,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,pl"rt"(x,y))]t42(x,t,y,u,v)):lrt(ksi,z0)
-m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
-t43:=satz83(y0,x0,l):more"rt"(x0,y0)
-[y1:rat][ly1:lrt(eta,y1)][y2:rat][uy2:urt(eta,y2)]
-t44:=cutapp2b(eta,y1,ly1,y2,uy2):more"rt"(y2,y1)
-[i:is"rt"(mn(y2,y1,t44),mn(x0,y0,t43))]
-t45:=cutapp2b(eta,y1,ly1,y0,uy):more"rt"(y0,y1)
-t46:=tris(rat,y2,pl"rt"(mn(y2,y1,t44),y1),pl"rt"(mn(x0,y0,t43),y1),satz101f(y2,y1,t44),ispl1"rt"(mn(y2,y1,t44),mn(x0,y0,t43),y1,i)):is"rt"(y2,pl"rt"(mn(x0,y0,t43),y1))
-t47:=tr4is(rat,pl"rt"(y2,mn(y0,y1,t45)),pl"rt"(pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45)),pl"rt"(mn(x0,y0,t43),pl"rt"(y1,mn(y0,y1,t45))),pl"rt"(mn(x0,y0,t43),y0),x0,ispl1"rt"(y2,pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45),t46),asspl1"rt"(mn(x0,y0,t43),y1,mn(y0,y1,t45)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t45)),y0,mn(x0,y0,t43),satz101c(y0,y1,t45)),satz101e(x0,y0,t43)):is"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0)
-t48:=ismore1"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0,y2,t47,satz94(y2,mn(y0,y1,t45))):more"rt"(x0,y2)
-t49:=satz101g(x0,y2,mn(y0,y1,t45),t48,t47):is"rt"(mn(y0,y1,t45),mn(x0,y2,t48))
-t50:=tris(rat,y0,pl"rt"(mn(y0,y1,t45),y1),pl"rt"(mn(x0,y2,t48),y1),satz101f(y0,y1,t45),ispl1"rt"(mn(y0,y1,t45),mn(x0,y2,t48),y1,t49)):is"rt"(y0,pl"rt"(mn(x0,y2,t48),y1))
-t51:=ine(diff,satz140h,mn(x0,y2,t48),diff1(mn(x0,y2,t48),x0,lx,y2,uy2,t48,refis(rat,mn(x0,y2,t48)))):lrt(chi,mn(x0,y2,t48))
-t52:=lrtpl(eta,chi,y0,y1,ly1,mn(x0,y2,t48),t51,tris(rat,y0,pl"rt"(mn(x0,y2,t48),y1),pl"rt"(y1,mn(x0,y2,t48)),t50,compl"rt"(mn(x0,y2,t48),y1))):lrt(pl(eta,chi),y0)
-l@t53:=satz132app(eta,lrt(pl(eta,chi),y0),mn(x0,y0,t43),[x:rat][t:lrt(eta,x)][y:rat][u:urt(eta,y)][v:is"rt"(mn(y,x,cutapp2b(eta,x,t,y,u)),mn(x0,y0,t43))]t52(x,t,y,u,v)):lrt(pl(eta,chi),y0)
-uy@t54:=cutapp3(ksi,y0,ly,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t53(x,t,u)):lrt(pl(eta,chi),y0)
-ly@[ly0:lrt(eta,y0)][y1:rat][ly1:lrt(ksi,y1)][uy1:urt(eta,y1)]
-t55:=t54(y1,ly1,uy1):lrt(pl(eta,chi),y1)
-t56:=satz120(pl(eta,chi),y1,t55,y0,cutapp2a(eta,y0,ly0,y1,uy1)):lrt(pl(eta,chi),y0)
-ly0@t57:=moreapp(ksi,eta,m,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t56(x,t,u)):lrt(pl(eta,chi),y0)
-ly@b:=th1"l.imp"(lrt(eta,y0),lrt(pl(eta,chi),y0),[t:lrt(eta,y0)]t57(t),[t:urt(eta,y0)]t54(t)):lrt(pl(eta,chi),y0)
-m"rp"@t58:=isi1(pl(eta,chi),ksi,[x:rat][t:lrt(pl(eta,chi),x)]a(x,t),[x:rat][t:lrt(ksi,x)]b(x,t)):is(pl(eta,chi),ksi)
--3140
-m@satz140a:=somei(cut,[a:cut]is(pl(eta,a),ksi),chi".3140",t58".3140"):some([a:cut]is(pl(eta,a),ksi))
-+*3140
-eta@t59:=[c:cut][d:cut][t:is(pl(eta,c),ksi)][u:is(pl(eta,d),ksi)]satz140b(c,d,t,u):amone(cut,[c:cut]is(pl(eta,c),ksi))
--3140
-m@satz140:=onei(cut,[a:cut]is(pl(eta,a),ksi),t59".3140",satz140a):one([a:cut]is(pl(eta,a),ksi))
-mn:=ind(cut,[a:cut]is(pl(eta,a),ksi),satz140):cut
-satz140c:=oneax(cut,[a:cut]is(pl(eta,a),ksi),satz140):is(pl(eta,mn(ksi,eta,m)),ksi)
-satz140d:=symis(cut,pl(eta,mn(ksi,eta,m)),ksi,satz140c):is(ksi,pl(eta,mn(ksi,eta,m)))
-satz140e:=tris(cut,pl(mn(ksi,eta,m),eta),pl(eta,mn(ksi,eta,m)),ksi,compl(mn(ksi,eta,m),eta),satz140c):is(pl(mn(ksi,eta,m),eta),ksi)
-satz140f:=symis(cut,pl(mn(ksi,eta,m),eta),ksi,satz140e):is(ksi,pl(mn(ksi,eta,m),eta))
-eta@[phi:cut][m:more(ksi,eta)][i:is(pl(eta,phi),ksi)]
-satz140g:=satz140b(phi,mn(ksi,eta,m),i,satz140c(m)):is(phi,mn(ksi,eta,m))
-upsilon@[m:more(ksi,zeta)][n:more(eta,upsilon)][i:is(ksi,eta)][j:is(zeta,upsilon)]
-+*3140
-j"rp"@t60:=tr3is(cut,pl(upsilon,mn(ksi,zeta,m)),pl(zeta,mn(ksi,zeta,m)),ksi,eta,ispl1(upsilon,zeta,mn(ksi,zeta,m),symis(cut,zeta,upsilon,j)),satz140c(ksi,zeta,m),i):is(pl(upsilon,mn(ksi,zeta,m)),eta)
--3140
-j@ismn12:=satz140g(eta,upsilon,mn(ksi,zeta,m),n,t60".3140"):is(mn(ksi,zeta,m),mn(eta,upsilon,n))
-zeta@[m:more(ksi,zeta)][n:more(eta,zeta)][i:is(ksi,eta)]
-ismn1:=ismn12(zeta,m,n,i,refis(cut,zeta)):is(mn(ksi,zeta,m),mn(eta,zeta,n))
-zeta@[m:more(zeta,ksi)][n:more(zeta,eta)][i:is(ksi,eta)]
-ismn2:=ismn12(zeta,zeta,ksi,eta,m,n,refis(cut,zeta),i):is(mn(zeta,ksi,m),mn(zeta,eta,n))
-eta@[z0:rat][x0:rat][y0:rat]
-prodprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0))):'prop'
-z0@prodprop:=some"rt"([x:rat]some"rt"([y:rat]prodprop1(z0,x,y))):'prop'
-eta@prod:=setof(rat,[z:rat]prodprop(z)):set(rat)
-x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts(x0,y0))]
-+iii4
-t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),lx,ly,i):prodprop1(z0,x0,y0)
-t2:=somei(rat,[y:rat]prodprop1(z0,x0,y),y0,t1):some"rt"([y:rat]prodprop1(z0,x0,y))
-t3:=somei(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),x0,t2):prodprop(z0)
--iii4
-prod1:=estii(rat,[z:rat]prodprop(z),z0,t3".iii4"):in(z0,prod)
-z0@[i:in(z0,prod)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]p]
-+*iii4
-p1@t4:=estie(rat,[z:rat]prodprop(z),z0,i):prodprop(z0)
--iii4
-p1@[x0:rat][px:some"rt"([y:rat]prodprop1(z0,x0,y))][y0:rat][py:prodprop1(z0,x0,y0)]
-+*iii4
-py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(ksi,x0)
-t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(eta,y0)
-t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):is"rt"(z0,ts(x0,y0))
-t8:=<t7><t6><y0><t5><x0>p1:p
-px@t9:=someapp(rat,[y:rat]prodprop1(z0,x0,y),px,p,[y:rat][t:prodprop1(z0,x0,y)]t8(y,t)):p
--iii4
-p1@prodapp:=someapp(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),t4".iii4",p,[x:rat][t:some"rt"([y:rat]prodprop1(z0,x,y))]t9".iii4"(x,t)):p
-eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-+4141
-[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))]
-t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
-t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
-t3:=isless1"rt"(ts(x0,y0),z0,ts(x1,y1),symis(rat,z0,ts(x0,y0),j),satz107a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,ts(x1,y1))
-t4:=ec3e31(is"rt"(z0,ts(x1,y1)),more"rt"(z0,ts(x1,y1)),less"rt"(z0,ts(x1,y1)),satz81b(z0,ts(x1,y1)),t3):nis"rt"(z0,ts(x1,y1))
-i@t5:=prodapp(ksi,eta,z0,i,nis"rt"(z0,ts(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,ts(x1,y1))
--4141
-satz141a:=th3"l.imp"(in(ts(x1,y1),prod),nis"rt"(ts(x1,y1),ts(x1,y1)),weli(is"rt"(ts(x1,y1),ts(x1,y1)),refis(rat,ts(x1,y1))),[t:in(ts(x1,y1),prod)]t5".4141"(ts(x1,y1),t)):not(in(ts(x1,y1),prod))
--rp
-@[x0:rat][y0:rat]
-+4141
-v0:=ts(ov(1rt,y0),x0):rat
-t6:=tr3is(rat,ts(y0,v0),ts(ts(y0,ov(1rt,y0)),x0),ts(1rt,x0),x0,assts2(y0,ov(1rt,y0),x0),ists1(ts(y0,ov(1rt,y0)),1rt,x0,satz110c(1rt,y0)),example1c(x0)):is(ts(y0,v0),x0)
--4141
-satz141b:=satz110g(x0,y0,v0".4141",t6".4141"):is(ts(ov(1rt,y0),x0),ov(x0,y0))
-satz141c:=symis(rat,ts(ov(1rt,y0),x0),ov(x0,y0),satz141b):is"rt"(ov(x0,y0),ts(ov(1rt,y0),x0))
-+*rp
-+*4141
-eta@[u0:rat][i:in(u0,prod)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,ts(x0,y0))]
-t7:=isless2"rt"(u0,ts(x0,y0),z0,j,l):less"rt"(z0,ts(x0,y0))
-t8:=tr3is(rat,ts(ov(1rt,x0),ts(x0,y0)),ts(ts(ov(1rt,x0),x0),y0),ts(1rt,y0),y0,assts2(ov(1rt,x0),x0,y0),ists1(ts(ov(1rt,x0),x0),1rt,y0,satz110e(1rt,x0)),example1c(y0)):is"rt"(ts(ov(1rt,x0),ts(x0,y0)),y0)
-t9:=isless12"rt"(ts(ov(1rt,x0),z0),ov(z0,x0),ts(ov(1rt,x0),ts(x0,y0)),y0,satz141b(z0,x0),t8,satz105f(z0,ts(x0,y0),ov(1rt,x0),t7)):less"rt"(ov(z0,x0),y0)
-t10:=satz120(eta,y0,ly,ov(z0,x0),t9):lrt(eta,ov(z0,x0))
-t11:=prod1(z0,x0,lx,ov(z0,x0),t10,satz110d(z0,x0)):in(z0,prod)
-l@t12:=prodapp(u0,i,in(z0,prod),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,ts(x,y))]t11(x,t,y,u,v)):in(z0,prod)
-eta@[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
-t13:=prod1(ts(x1,y0),x1,lx1,y0,ly,refis(rat,ts(x1,y0))):in(ts(x1,y0),prod)
-t14:=satz105a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(ts(x1,y0),ts(x0,y0))
-t15:=ismore2"rt"(ts(x0,y0),z0,ts(x1,y0),symis(rat,z0,ts(x0,y0),j),t14):more"rt"(ts(x1,y0),z0)
-t16:=andi(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0),t13,t15):and(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0))
-t17:=somei(rat,[y:rat]and(in(y,prod),more"rt"(y,z0)),ts(x1,y0),t16):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
-j@t18:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t17(x,t,u)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
-i@t19:=prodapp(z0,i,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t18(x,t,y,u,v)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
-eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-t20:=cut2(prod,ts(x0,y0),prod1(ts(x0,y0),x0,lx,y0,ly,refis(rat,ts(x0,y0))),ts(x1,y1),satz141a(x1,ux,y1,uy),[x:rat][t:in(x,prod)][y:rat][u:less"rt"(y,x)]t12(x,t,y,u),[x:rat][t:in(x,prod)]t19(x,t)):cutprop(prod)
-ux@t21:=cutapp1b(eta,cutprop(prod),[y:rat][t:urt(eta,y)]t20(y,t)):cutprop(prod)
-ly@t22:=cutapp1b(ksi,cutprop(prod),[x:rat][t:urt(ksi,x)]t21(x,t)):cutprop(prod)
-lx@t23:=cutapp1a(eta,cutprop(prod),[y:rat][t:lrt(eta,y)]t22(y,t)):cutprop(prod)
--4141
-eta@satz141:=cutapp1a(ksi,cutprop(prod),[x:rat][t:lrt(ksi,x)]t23".4141"(x,t)):cutprop(prod)
-ts:=cutof(prod,satz141):cut
-[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-lrtts:=ine(prod,satz141,z0,prod1(z0,x0,lx,y0,ly,i)):lrt(ts(ksi,eta),z0)
-eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-+*iii4
-i@t10:=isp1(rat,[x:rat]not(in(x,prod)),ts"rt"(x0,y0),z0,satz141a(x0,ux,y0,uy),i):not(in(z0,prod))
--iii4
-i@urtts:=th3"l.imp"(lrt(ts(ksi,eta),z0),in(z0,prod),t10".iii4",[t:lrt(ts(ksi,eta),z0)]ini(prod,satz141,z0,t)):urt(ts(ksi,eta),z0)
-eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]p]
-+*iii4
-p1@t11:=ini(prod,satz141,z0,lz):in(z0,prod)
--iii4
-p1@tsapp:=prodapp(z0,t11".iii4",p,p1):p
-zeta@[i:is(ksi,eta)]
-ists1:=isf(cut,cut,[u:cut]ts(u,zeta),ksi,eta,i):is(ts(ksi,zeta),ts(eta,zeta))
-ists2:=isf(cut,cut,[u:cut]ts(zeta,u),ksi,eta,i):is(ts(zeta,ksi),ts(zeta,eta))
-upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
-ists12:=tris(cut,ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),ists1(i),ists2(zeta,upsilon,eta,j)):is(ts(ksi,zeta),ts(eta,upsilon))
-+4142
-eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-t1:=tris(rat,z0,ts"rt"(x0,y0),ts"rt"(y0,x0),i,comts(x0,y0)):is"rt"(z0,ts"rt"(y0,x0))
-t2:=lrtts(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(ts(eta,ksi),z0)
-lz@t3:=tsapp(ksi,eta,z0,lz,lrt(ts(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]t2(x,t,y,u,v)):lrt(ts(eta,ksi),z0)
--4142
-eta@satz142:=isi1(ts(ksi,eta),ts(eta,ksi),[x:rat][t:lrt(ts(ksi,eta),x)]t3".4142"(x,t),[x:rat][t:lrt(ts(eta,ksi),x)]t3".4142"(eta,ksi,x,t)):is(ts(ksi,eta),ts(eta,ksi))
-comts:=satz142:is(ts(ksi,eta),ts(eta,ksi))
-+4143
-zeta@[u0:rat][lu:lrt(ts(ts(ksi,eta),zeta),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,ts"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))]
-t1:=tr3is(rat,u0,ts"rt"(v0,z0),ts"rt"(ts"rt"(x0,y0),z0),ts"rt"(x0,ts"rt"(y0,z0)),i,ists1"rt"(v0,ts"rt"(x0,y0),z0,j),assts1(x0,y0,z0)):is"rt"(u0,ts"rt"(x0,ts"rt"(y0,z0)))
-t2:=lrtts(eta,zeta,ts"rt"(y0,z0),y0,ly,z0,lz,refis(rat,ts"rt"(y0,z0))):lrt(ts(eta,zeta),ts"rt"(y0,z0))
-t3:=lrtts(ksi,ts(eta,zeta),u0,x0,lx,ts"rt"(y0,z0),t2,t1):lrt(ts(ksi,ts(eta,zeta)),u0)
-i@t4:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
-lu@t5:=tsapp(ts(ksi,eta),zeta,u0,lu,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,ts"rt"(x,y))]t4(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
-u0@[lu:lrt(ts(ksi,ts(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(ts(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,ts"rt"(y0,z0))]
-t6:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,ts"rt"(y0,z0)),ts"rt"(ts"rt"(x0,y0),z0),i,ists2"rt"(v0,ts"rt"(y0,z0),x0,j),assts2(x0,y0,z0)):is"rt"(u0,ts"rt"(ts"rt"(x0,y0),z0))
-t7:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
-t8:=lrtts(ts(ksi,eta),zeta,u0,ts"rt"(x0,y0),t7,z0,lz,t6):lrt(ts(ts(ksi,eta),zeta),u0)
-i@t9:=tsapp(eta,zeta,v0,lv,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,ts"rt"(x,y))]t8(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
-lu@t10:=tsapp(ksi,ts(eta,zeta),u0,lu,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(ts(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t9(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
--4143
-zeta@satz143:=isi1(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),[x:rat][t:lrt(ts(ts(ksi,eta),zeta),x)]t5".4143"(x,t),[x:rat][t:lrt(ts(ksi,ts(eta,zeta)),x)]t10".4143"(x,t)):is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
-assts1:=satz143:is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
-assts2:=symis(cut,ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),satz143):is(ts(ksi,ts(eta,zeta)),ts(ts(ksi,eta),zeta))
-+4144
-[u0:rat][lu:lrt(ts(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
-t1:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,pl"rt"(y0,z0)),pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)),i,ists2"rt"(v0,pl"rt"(y0,z0),x0,j),disttp2(x0,y0,z0)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)))
-t2:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
-t3:=lrtts(ksi,zeta,ts"rt"(x0,z0),x0,lx,z0,lz,refis(rat,ts"rt"(x0,z0))):lrt(ts(ksi,zeta),ts"rt"(x0,z0))
-t4:=lrtpl(ts(ksi,eta),ts(ksi,zeta),u0,ts"rt"(x0,y0),t2,ts"rt"(x0,z0),t3,t1):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
-i@t5:=plapp(eta,zeta,v0,lv,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
-lu@t6:=tsapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t5(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
-u0@[lu:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][w0:rat][lw:lrt(ts(ksi,zeta),w0)][i:is"rt"(u0,pl"rt"(v0,w0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][z0:rat][lz:lrt(zeta,z0)][k:is"rt"(w0,ts"rt"(x1,z0))]
-t7:=tris(rat,u0,pl"rt"(v0,w0),pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),i,ispl12"rt"(v0,ts"rt"(x0,y0),w0,ts"rt"(x1,z0),j,k)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)))
-x2:=ite(moreis"rt"(x0,x1),rat,x0,x1):rat
-[m:moreis"rt"(x0,x1)]
-t8:=itet(moreis"rt"(x0,x1),rat,x0,x1,m):is"rt"(x2,x0)
-t9:=isp1(rat,[t:rat]lrt(ksi,t),x0,x2,lx,t8):lrt(ksi,x2)
-t10:=lessisi2"rt"(x0,x2,symis(rat,x2,x0,t8)):lessis"rt"(x0,x2)
-t11:=satz88(x1,x0,x2,satz84(x0,x1,m),t10):lessis"rt"(x1,x2)
-k@[n:not(moreis"rt"(x0,x1))]
-t12:=itef(moreis"rt"(x0,x1),rat,x0,x1,n):is"rt"(x2,x1)
-t13:=isp1(rat,[t:rat]lrt(ksi,t),x1,x2,lx1,t12):lrt(ksi,x2)
-t14:=lessisi2"rt"(x1,x2,symis(rat,x2,x1,t12)):lessis"rt"(x1,x2)
-t15:=lessisi1"rt"(x0,x2,satz87b(x0,x1,x2,satz81j(x0,x1,n),t14)):lessis"rt"(x0,x2)
-k@t16:=th1"l.imp"(moreis"rt"(x0,x1),lrt(ksi,x2),[t:moreis"rt"(x0,x1)]t9(t),[t:not(moreis"rt"(x0,x1))]t13(t)):lrt(ksi,x2)
-t17:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x0,x2),[t:moreis"rt"(x0,x1)]t10(t),[t:not(moreis"rt"(x0,x1))]t15(t)):lessis"rt"(x0,x2)
-t18:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x1,x2),[t:moreis"rt"(x0,x1)]t11(t),[t:not(moreis"rt"(x0,x1))]t14(t)):lessis"rt"(x1,x2)
-t19:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
-t20:=lrtts(ksi,pl(eta,zeta),ts"rt"(x2,pl"rt"(y0,z0)),x2,t16,pl"rt"(y0,z0),t19,refis(rat,ts"rt"(x2,pl"rt"(y0,z0)))):lrt(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)))
-t21:=satz109a(x0,x2,y0,y0,t17,lessisi2"rt"(y0,y0,refis(rat,y0))):lessis"rt"(ts"rt"(x0,y0),ts"rt"(x2,y0))
-t22:=satz109a(x1,x2,z0,z0,t18,lessisi2"rt"(z0,z0,refis(rat,z0))):lessis"rt"(ts"rt"(x1,z0),ts"rt"(x2,z0))
-t23:=islessis12"rt"(pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),u0,pl"rt"(ts"rt"(x2,y0),ts"rt"(x2,z0)),ts"rt"(x2,pl"rt"(y0,z0)),symis(rat,u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),t7),distpt2(x2,y0,z0),satz100a(ts"rt"(x0,y0),ts"rt"(x2,y0),ts"rt"(x1,z0),ts"rt"(x2,z0),t21,t22)):lessis"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))
-t24:=orapp(less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),lrt(ts(ksi,pl(eta,zeta)),u0),t23,[t:less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]satz120(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)),t20,u0,t),[t:is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]isp1(rat,[u:rat]lrt(ts(ksi,pl(eta,zeta)),u),ts"rt"(x2,pl"rt"(y0,z0)),u0,t20,t)):lrt(ts(ksi,pl(eta,zeta)),u0)
-j@t25:=tsapp(ksi,zeta,w0,lw,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(w0,ts"rt"(x,y))]t24(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
-i@t26:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t25(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
-lu@t27:=plapp(ts(ksi,eta),ts(ksi,zeta),u0,lu,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(ts(ksi,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t26(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
--4144
-satz144:=isi1(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),[x:rat][t:lrt(ts(ksi,pl(eta,zeta)),x)]t6".4144"(x,t),[x:rat][t:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),x)]t27".4144"(x,t)):is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
-disttp1:=tr3is(cut,ts(pl(ksi,eta),zeta),ts(zeta,pl(ksi,eta)),pl(ts(zeta,ksi),ts(zeta,eta)),pl(ts(ksi,zeta),ts(eta,zeta)),comts(pl(ksi,eta),zeta),satz144(zeta,ksi,eta),ispl12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta))):is(ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)))
-disttp2:=satz144:is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
-distpt1:=symis(cut,ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)),disttp1):is(pl(ts(ksi,zeta),ts(eta,zeta)),ts(pl(ksi,eta),zeta))
-distpt2:=symis(cut,ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),disttp2):is(pl(ts(ksi,eta),ts(ksi,zeta)),ts(ksi,pl(eta,zeta)))
-[m:more(ksi,eta)]
-+4145
-phi:=mn(ksi,eta,m):cut
-t1:=satz140d(ksi,eta,m):is(ksi,pl(eta,phi))
-t2:=tris(cut,ts(ksi,zeta),ts(pl(eta,phi),zeta),pl(ts(eta,zeta),ts(phi,zeta)),ists1(ksi,pl(eta,phi),zeta,t1),disttp1(eta,phi,zeta)):is(ts(ksi,zeta),pl(ts(eta,zeta),ts(phi,zeta)))
--4145
-satz145a:=ismore1(pl(ts(eta,zeta),ts(phi".4145",zeta)),ts(ksi,zeta),ts(eta,zeta),symis(cut,ts(ksi,zeta),pl(ts(eta,zeta),ts(phi".4145",zeta)),t2".4145"),satz133(ts(eta,zeta),ts(phi".4145",zeta))):more(ts(ksi,zeta),ts(eta,zeta))
-zeta@[i:is(ksi,eta)]
-satz145b:=ists1(ksi,eta,zeta,i):is(ts(ksi,zeta),ts(eta,zeta))
-zeta@[l:less(ksi,eta)]
-satz145c:=satz121(ts(eta,zeta),ts(ksi,zeta),satz145a(eta,ksi,zeta,satz122(ksi,eta,l))):less(ts(ksi,zeta),ts(eta,zeta))
-m@satz145d:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145a):more(ts(zeta,ksi),ts(zeta,eta))
-i@satz145e:=ists2(ksi,eta,zeta,i):is(ts(zeta,ksi),ts(zeta,eta))
-l@satz145f:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145c):less(ts(zeta,ksi),ts(zeta,eta))
-upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
-satz145g:=ismore2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145d(zeta,upsilon,ksi,m)):more(ts(ksi,zeta),ts(eta,upsilon))
-satz145h:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145g):more(ts(zeta,ksi),ts(upsilon,eta))
-i@[l:less(zeta,upsilon)]
-satz145j:=isless2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145f(zeta,upsilon,ksi,l)):less(ts(ksi,zeta),ts(eta,upsilon))
-satz145k:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145j):less(ts(zeta,ksi),ts(upsilon,eta))
-+4146
-zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-t2:=satz123b(ts(ksi,zeta),ts(eta,zeta)):ec3(is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)))
--4146
-zeta@[m:more(ts(ksi,zeta),ts(eta,zeta))]
-satz146a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),m):more(ksi,eta)
-zeta@[i:is(ts(ksi,zeta),ts(eta,zeta))]
-satz146b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),i):is(ksi,eta)
-zeta@[l:less(ts(ksi,zeta),ts(eta,zeta))]
-satz146c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),l):less(ksi,eta)
-zeta@[m:more(ts(zeta,ksi),ts(zeta,eta))]
-satz146d:=satz146a(ismore12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),m)):more(ksi,eta)
-zeta@[i:is(ts(zeta,ksi),ts(zeta,eta))]
-satz146e:=satz146b(tr3is(cut,ts(ksi,zeta),ts(zeta,ksi),ts(zeta,eta),ts(eta,zeta),comts(ksi,zeta),i,comts(zeta,eta))):is(ksi,eta)
-zeta@[l:less(ts(zeta,ksi),ts(zeta,eta))]
-satz146f:=satz146c(isless12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),l)):less(ksi,eta)
-upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
-+4147
-t1:=satz145a(ksi,eta,zeta,m):more(ts(ksi,zeta),ts(eta,zeta))
-t2:=ismore12(ts(zeta,eta),ts(eta,zeta),ts(upsilon,eta),ts(eta,upsilon),comts(zeta,eta),comts(upsilon,eta),satz145a(zeta,upsilon,eta,n)):more(ts(eta,zeta),ts(eta,upsilon))
--4147
-satz147:=trmore(ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),t1".4147",t2".4147"):more(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
-satz147a:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz147(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
-satz148a:=orapp(more(ksi,eta),is(ksi,eta),more(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]satz147(t,n),[t:is(ksi,eta)]satz145g(t,n)):more(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
-satz148b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]satz147(m,t),[t:is(zeta,upsilon)]satz145h(zeta,upsilon,ksi,eta,t,m)):more(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
-satz148c:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
-satz148d:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
-+4149
-[i:is(ksi,eta)][j:is(zeta,upsilon)]
-t1:=moreisi2(ts(ksi,zeta),ts(eta,upsilon),ists12(ksi,eta,zeta,upsilon,i,j)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-i@[o:more(zeta,upsilon)]
-t2:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148a(m,o)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-n@[o:more(ksi,eta)]
-t4:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148b(o,n)):moreis(ts(ksi,zeta),ts(eta,upsilon))
--4149
-satz149:=orapp(more(ksi,eta),is(ksi,eta),moreis(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]t4".4149"(t),[t:is(ksi,eta)]t3".4149"(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
-satz149a:=satz124(ts(eta,upsilon),ts(ksi,zeta),satz149(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(ts(ksi,zeta),ts(eta,upsilon))
--rp
-@[r0:rat]
-ratset:=setof(rat,[x:rat]less(x,r0)):set(rat)
-+4150
-t1:=satz90(r0):some([x:rat]less(x,r0))
-[x0:rat][l:less(x0,r0)]
-t2:=estii(rat,[x:rat]less(x,r0),x0,l):in(x0,ratset)
-r0@t3:=ec3e13(is(r0,r0),more(r0,r0),less(r0,r0),satz81b(r0,r0),refis(rat,r0)):not(less(r0,r0))
-t4:=th3"l.imp"(in(r0,ratset),less(r0,r0),t3,[t:in(r0,ratset)]estie(rat,[x:rat]less(x,r0),r0,t)):not(in(r0,ratset))
-x0@[i:in(x0,ratset)]
-t5:=estie(rat,[x:rat]less(x,r0),x0,i):less(x0,r0)
-[x1:rat][k:less(x1,x0)]
-t6:=t2(x1,trless(x1,x0,r0,k,t5)):in(x1,ratset)
-i@t7:=satz91(x0,r0,t5):some([x:rat]and(less(x0,x),less(x,r0)))
-[x1:rat][a:and(less(x0,x1),less(x1,r0))]
-t8:=ande1(less(x0,x1),less(x1,r0),a):less(x0,x1)
-t9:=ande2(less(x0,x1),less(x1,r0),a):less(x1,r0)
-t10:=andi(in(x1,ratset),more(x1,x0),t2(x1,t9),satz83(x0,x1,t8)):and(in(x1,ratset),more(x1,x0))
-i@t11:=th6"l.some"(rat,[x:rat]and(less(x0,x),less(x,r0)),[x:rat]and(in(x,ratset),more(x,x0)),t7,[x:rat][t:and(less(x0,x),less(x,r0))]t10(x,t)):some([x:rat]and(in(x,ratset),more(x,x0)))
-l@t12:=cut2(ratset,x0,t2,r0,t4,[x:rat][t:in(x,ratset)][y:rat][u:less(y,x)]t6(x,t,y,u),[x:rat][t:in(x,ratset)]t11(x,t)):cutprop(ratset)
--4150
-satz150:=someapp(rat,[x:rat]less(x,r0),t1".4150",cutprop(ratset),[x:rat][t:less(x,r0)]t12".4150"(x,t)):cutprop(ratset)
-+*rp
-r0@rpofrt:=cutof(ratset,satz150):cut
-[x0:rat][l:less"rt"(x0,r0)]
-lrtrpofrt:=ine(ratset,satz150,x0,t2"rt.4150"(x0,l)):lrt(rpofrt,x0)
-r0@[x0:rat][lx:lrt(rpofrt,x0)]
-lrtrpofrte:=t5"rt.4150"(x0,ini(ratset,satz150,x0,lx)):less"rt"(x0,r0)
-r0@[x0:rat][m:moreis"rt"(x0,r0)]
-+*iii4
-m@t12:=satz81c(x0,r0,m):not(less"rt"(x0,r0))
--iii4
-m@urtrpofrt:=th3"l.imp"(lrt(rpofrt,x0),less"rt"(x0,r0),t12".iii4",[t:lrt(rpofrt,x0)]lrtrpofrte(x0,t)):urt(rpofrt,x0)
-@1rp:=rpofrt(1rt):cut
-+4151
-ksi@[z0:rat][lz:lrt(ts(ksi,1rp),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(1rp,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-t1:=lrtrpofrte(1rt,y0,ly):less"rt"(y0,1rt)
-t2:=isless12"rt"(ts"rt"(x0,y0),z0,ts"rt"(x0,1rt),x0,symis(rat,z0,ts"rt"(x0,y0),i),example1a(x0),satz105f(y0,1rt,x0,t1)):less"rt"(z0,x0)
-t3:=satz120(ksi,x0,lx,z0,t2):lrt(ksi,z0)
-lz@t4:=tsapp(ksi,1rp,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(1rp,y)][v:is"rt"(z0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ksi,z0)
-ksi@[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
-y1:=ts"rt"(ov(1rt,x1),x0):rat
-t5:=isless2"rt"(ts"rt"(ov(1rt,x1),x1),1rt,y1,satz110e(1rt,x1),satz105f(x0,x1,ov(1rt,x1),l)):less"rt"(y1,1rt)
-t6:=lrtrpofrt(1rt,y1,t5):lrt(1rp,y1)
-t7:=tr3is(rat,ts"rt"(x1,y1),ts"rt"(ts"rt"(x1,ov(1rt,x1)),x0),ts"rt"(1rt,x0),x0,assts2"rt"(x1,ov(1rt,x1),x0),ists1"rt"(ts"rt"(x1,ov(1rt,x1)),1rt,x0,satz110c(1rt,x1)),example1c(x0)):is"rt"(ts"rt"(x1,y1),x0)
-t8:=lrtts(ksi,1rp,x0,x1,lx1,y1,t6,symis(rat,ts"rt"(x1,y1),x0,t7)):lrt(ts(ksi,1rp),x0)
-lx@t9:=cutapp3(ksi,x0,lx,lrt(ts(ksi,1rp),x0),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t8(y,t,u)):lrt(ts(ksi,1rp),x0)
--4151
-ksi@satz151:=isi1(ts(ksi,1rp),ksi,[x:rat][t:lrt(ts(ksi,1rp),x)]t4".4151"(x,t),[x:rat][t:lrt(ksi,x)]t9".4151"(x,t)):is(ts(ksi,1rp),ksi)
-satz151a:=symis(cut,ts(ksi,1rp),ksi,satz151):is(ksi,ts(ksi,1rp))
-satz151b:=tris(cut,ts(1rp,ksi),ts(ksi,1rp),ksi,comts(1rp,ksi),satz151):is(ts(1rp,ksi),ksi)
-satz151c:=symis(cut,ts(1rp,ksi),ksi,satz151b):is(ksi,ts(1rp,ksi))
-+4152
-[x0:rat][y0:rat]
-invprop1:=and(urt(ksi,y0),less"rt"(y0,x0)):'prop'
-ksi@[z0:rat][x0:rat]
-invprop2:=and3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0))):'prop'
-z0@invprop:=some"rt"([x:rat]invprop2(z0,x)):'prop'
-ksi@inv:=setof(rat,[z:rat]invprop(z)):set(rat)
-x0@[ux:urt(ksi,x0)][y0:rat][uy:urt(ksi,y0)][l:less"rt"(y0,x0)][i:is"rt"(z0,ov(1rt,x0))]
-t1:=andi(urt(ksi,y0),less"rt"(y0,x0),uy,l):invprop1(x0,y0)
-t2:=somei(rat,[x:rat]invprop1(x0,x),y0,t1):some"rt"([x:rat]invprop1(x0,x))
-t3:=and3i(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),ux,t2,i):invprop2(z0,x0)
-t4:=somei(rat,[x:rat]invprop2(z0,x),x0,t3):invprop(z0)
-inv1:=estii(rat,[z:rat]invprop(z),z0,t4):in(z0,inv)
-z0@[i:in(z0,inv)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]p]
-t5:=estie(rat,[x:rat]invprop(x),z0,i):invprop(z0)
-[x0:rat][px:invprop2(z0,x0)]
-t6:=and3e1(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):urt(ksi,x0)
-t7:=and3e2(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):some"rt"([x:rat]invprop1(x0,x))
-t8:=and3e3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):is"rt"(z0,ov(1rt,x0))
-[y0:rat][py:invprop1(x0,y0)]
-t9:=ande1(urt(ksi,y0),less"rt"(y0,x0),py):urt(ksi,y0)
-t10:=ande2(urt(ksi,y0),less"rt"(y0,x0),py):less"rt"(y0,x0)
-t11:=<t8><t10><t9><y0><t6><x0>p1:p
-px@t12:=someapp(rat,[x:rat]invprop1(x0,x),t7,p,[x:rat][t:invprop1(x0,x)]t11(x,t)):p
-p1@invapp:=someapp(rat,[x:rat]invprop2(z0,x),t5,p,[x:rat][t:invprop2(z0,x)]t12(x,t)):p
-ksi@[x0:rat][ux:urt(ksi,x0)]
-2x0:=pl"rt"(x0,x0):rat
-t13:=satz94a(x0,x0):less"rt"(x0,2x0)
-t14:=satz119a(ksi,x0,ux,2x0,t13):urt(ksi,2x0)
-t15:=inv1(ov(1rt,2x0),2x0,t14,x0,ux,t13,refis(rat,ov(1rt,2x0))):in(ov(1rt,2x0),inv)
-ksi@[x1:rat][lx:lrt(ksi,x1)][x0:rat][ux:urt(ksi,x0)]
-t16:=th3"l.imp"(is"rt"(x0,x1),lrt(ksi,x0),ux,[t:is"rt"(x0,x1)]isp1(rat,[x:rat]lrt(ksi,x),x1,x0,lx,t)):nis"rt"(x0,x1)
-t17:=satz110e(1rt,x0):is"rt"(ts"rt"(ov(1rt,x0),x0),1rt)
-t18:=satz110e(1rt,x1):is"rt"(ts"rt"(ov(1rt,x1),x1),1rt)
-[i:is"rt"(ov(1rt,x0),ov(1rt,x1))]
-t19:=tris(rat,ts"rt"(ov(1rt,x0),x1),ts"rt"(ov(1rt,x1),x1),1rt,ists1"rt"(ov(1rt,x0),ov(1rt,x1),x1,i),t18):is"rt"(ts"rt"(ov(1rt,x0),x1),1rt)
-t20:=satz110b(1rt,ov(1rt,x0),x0,x1,t17,t19):is"rt"(x0,x1)
-ux@t21:=th3"l.imp"(is"rt"(ov(1rt,x0),ov(1rt,x1)),is"rt"(x0,x1),t16,[t:is"rt"(ov(1rt,x0),ov(1rt,x1))]t20(t)):nis"rt"(ov(1rt,x0),ov(1rt,x1))
-lx@[i:in(ov(1rt,x1),inv)]
-t22:=invapp(ov(1rt,x1),i,con,[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(ov(1rt,x1),ov(1rt,x))]<symis(rat,ov(1rt,x1),ov(1rt,x),w)>t21(x,t)):con
-lx@t23:=[t:in(ov(1rt,x1),inv)]t22(t):not(in(ov(1rt,x1),inv))
-ksi@[z0:rat][i:in(z0,inv)][u0:rat][l:less"rt"(u0,z0)][x0:rat][ux:urt(ksi,x0)][j:is"rt"(z0,ov(1rt,x0))]
-t24:=isless2"rt"(z0,ov(1rt,x0),u0,j,l):less"rt"(u0,ov(1rt,x0))
-t25:=tris(rat,ts"rt"(ov(1rt,x0),x0),1rt,ts"rt"(u0,ov(1rt,u0)),satz110e(1rt,x0),satz110d(1rt,u0)):is"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)))
-t26:=isless2"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(u0,x0),t25,satz105c(u0,ov(1rt,x0),x0,t24)):less"rt"(ts"rt"(u0,x0),ts"rt"(u0,ov(1rt,u0)))
-t27:=isless12"rt"(ts"rt"(u0,x0),ts"rt"(x0,u0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(ov(1rt,u0),u0),comts"rt"(u0,x0),comts"rt"(u0,ov(1rt,u0)),t26):less"rt"(ts"rt"(x0,u0),ts"rt"(ov(1rt,u0),u0))
-t28:=satz106c(x0,ov(1rt,u0),u0,t27):less"rt"(x0,ov(1rt,u0))
-t29:=satz119a(x0,ux,ov(1rt,u0),t28):urt(ksi,ov(1rt,u0))
-t30:=satz110e(1rt,u0):is"rt"(ts"rt"(ov(1rt,u0),u0),1rt)
-t31:=satz110g(1rt,ov(1rt,u0),u0,t30):is"rt"(u0,ov(1rt,ov(1rt,u0)))
-t32:=inv1(u0,ov(1rt,u0),t29,x0,ux,t28,t31):in(u0,inv)
-l@t33:=invapp(z0,i,in(u0,inv),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t32(x,t,w)):in(u0,inv)
-i@[x0:rat][ux:urt(ksi,x0)][x1:rat][ux1:urt(ksi,x1)][l:less"rt"(x1,x0)][j:is"rt"(z0,ov(1rt,x0))]
-t34:=satz91(x1,x0,l):some"rt"([x:rat]and(less"rt"(x1,x),less"rt"(x,x0)))
-[x2:rat][a:and(less"rt"(x1,x2),less"rt"(x2,x0))]
-t35:=ande1(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x1,x2)
-t36:=satz119a(ksi,x1,ux1,x2,t35):urt(ksi,x2)
-t37:=inv1(ov(1rt,x2),x2,t36,x1,ux1,t35,refis(rat,ov(1rt,x2))):in(ov(1rt,x2),inv)
-t38:=ande2(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x2,x0)
-t39:=tris(rat,ts"rt"(x0,ov(1rt,x0)),1rt,ts"rt"(x2,ov(1rt,x2)),satz110c(1rt,x0),satz110d(1rt,x2)):is"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
-t40:=isless2"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)),ts"rt"(x2,ov(1rt,x0)),t39,satz105c(x2,x0,ov(1rt,x0),t38)):less"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
-t41:=isless12"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(ov(1rt,x0),x2),ts"rt"(x2,ov(1rt,x2)),ts"rt"(ov(1rt,x2),x2),comts"rt"(x2,ov(1rt,x0)),comts"rt"(x2,ov(1rt,x2)),t40):less"rt"(ts"rt"(ov(1rt,x0),x2),ts"rt"(ov(1rt,x2),x2))
-t42:=satz106c(ov(1rt,x0),ov(1rt,x2),x2,t41):less"rt"(ov(1rt,x0),ov(1rt,x2))
-t43:=ismore2"rt"(ov(1rt,x0),z0,ov(1rt,x2),symis(rat,z0,ov(1rt,x0),j),satz83(ov(1rt,x0),ov(1rt,x2),t42)):more"rt"(ov(1rt,x2),z0)
-t44:=andi(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0),t37,t43):and(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0))
-t45:=somei(rat,[x:rat]and(in(x,inv),more"rt"(x,z0)),ov(1rt,x2),t44):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
-j@t46:=someapp(rat,[x:rat]and(less"rt"(x1,x),less"rt"(x,x0)),t34,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:and(less"rt"(x1,x),less"rt"(x,x0))]t45(x,t)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
-i@t47:=invapp(z0,i,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t46(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
-ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
-t48:=cut2(inv,ov(1rt,pl"rt"(y0,y0)),t15(y0,uy),ov(1rt,x0),t23(x0,lx),[x:rat][t:in(x,inv)][y:rat][u:less"rt"(y,x)]t33(x,t,y,u),[x:rat][t:in(x,inv)]t47(x,t)):cutprop(inv)
-lx@t49:=cutapp1b(ksi,cutprop(inv),[x:rat][t:urt(ksi,x)]t48(x,t)):cutprop(inv)
-ksi@t50:=cutapp1a(ksi,cutprop(inv),[x:rat][t:lrt(ksi,x)]t49(x,t)):cutprop(inv)
-chi:=cutof(inv,t50):cut
-[z0:rat][lz:lrt(ts(ksi,chi),z0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,ts"rt"(x0,u0))][x1:rat][ux:urt(ksi,x1)][j:is"rt"(u0,ov(1rt,x1))]
-t51:=tris(rat,z0,ts"rt"(x0,u0),ts"rt"(x0,ov(1rt,x1)),i,ists2"rt"(u0,ov(1rt,x1),x0,j)):is"rt"(z0,ts"rt"(x0,ov(1rt,x1)))
-t52:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
-t53:=isless12"rt"(ts"rt"(x0,ov(1rt,x1)),z0,ts"rt"(x1,ov(1rt,x1)),1rt,symis(rat,z0,ts"rt"(x0,ov(1rt,x1)),t51),satz110c(1rt,x1),satz105c(x0,x1,ov(1rt,x1),t52)):less"rt"(z0,1rt)
-t54:=lrtrpofrt(1rt,z0,t53):lrt(1rp,z0)
-i@r1:=ini(inv,t50,u0,lu):in(u0,inv)
-r2:=invapp(u0,r1,lrt(1rp,z0),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(u0,ov(1rt,x))]t54(x,t,w)):lrt(1rp,z0)
-lz@r3:=tsapp(ksi,chi,z0,lz,lrt(1rp,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,ts"rt"(x,y))]r2(x,t,y,u,v)):lrt(1rp,z0)
-ksi@[u0:rat][lu:lrt(1rp,u0)]
-t55:=lrtrpofrte(1rt,u0,lu):less"rt"(u0,1rt)
-t56:=satz83(u0,1rt,t55):more"rt"(1rt,u0)
-[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][x2:rat][ux2:urt(ksi,x2)]
-t57:=cutapp2b(x1,lx1,x2,ux2):more"rt"(x2,x1)
-[i:is"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0))]
-t58:=cutapp2a(x0,lx,x2,ux2):less"rt"(x0,x2)
-t59:=satz105f(x0,x2,mn"rt"(1rt,u0,t56),t58):less"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),ts"rt"(mn"rt"(1rt,u0,t56),x2))
-t60:=isless1"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),symis(rat,mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0),i),t59):less"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2))
-t61:=tr4is(rat,pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),ts"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),x2),ts"rt"(1rt,x2),x2,pl"rt"(mn"rt"(x2,x1,t57),x1),distpt1"rt"(mn"rt"(1rt,u0,t56),u0,x2),ists1"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),1rt,x2,satz101e(1rt,u0,t56)),example1c(x2),satz101f(x2,x1,t57)):is"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
-t62:=satz96c(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2),t60):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)))
-t63:=isless2"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),t61,t62):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
-t64:=isless12"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(x1,mn"rt"(x2,x1,t57)),compl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),compl"rt"(mn"rt"(x2,x1,t57),x1),t63):less"rt"(pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(x1,mn"rt"(x2,x1,t57)))
-t65:=satz97c(ts"rt"(u0,x2),x1,mn"rt"(x2,x1,t57),t64):less"rt"(ts"rt"(u0,x2),x1)
-t66:=tr3is(rat,ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),ts"rt"(ts"rt"(ov(1rt,u0),u0),x2),ts"rt"(1rt,x2),x2,assts2"rt"(ov(1rt,u0),u0,x2),ists1"rt"(ts"rt"(ov(1rt,u0),u0),1rt,x2,satz110e(1rt,u0)),example1c(x2)):is"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2)
-t67:=isless12"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2,ts"rt"(ov(1rt,u0),x1),ov(x1,u0),t66,satz141b(x1,u0),satz105f(ts"rt"(u0,x2),x1,ov(1rt,u0),t65)):less"rt"(x2,ov(x1,u0))
-t68:=satz119a(x2,ux2,ov(x1,u0),t67):urt(ksi,ov(x1,u0))
-t69:=satz110e(x1,u0):is"rt"(ts"rt"(ov(x1,u0),u0),x1)
-t70:=tr3is(rat,u0,ov(x1,ov(x1,u0)),ts"rt"(ov(1rt,ov(x1,u0)),x1),ts"rt"(x1,ov(1rt,ov(x1,u0))),satz110g(x1,ov(x1,u0),u0,t69),satz141c(x1,ov(x1,u0)),comts"rt"(ov(1rt,ov(x1,u0)),x1)):is"rt"(u0,ts"rt"(x1,ov(1rt,ov(x1,u0))))
-t71:=inv1(ov(1rt,ov(x1,u0)),ov(x1,u0),t68,x2,ux2,t67,refis(rat,ov(1rt,ov(x1,u0)))):in(ov(1rt,ov(x1,u0)),inv)
-t72:=ine(inv,t50,ov(1rt,ov(x1,u0)),t71):lrt(chi,ov(1rt,ov(x1,u0)))
-t73:=lrtts(ksi,chi,u0,x1,lx1,ov(1rt,ov(x1,u0)),t72,t70):lrt(ts(ksi,chi),u0)
-lx@t74:=satz132app(ksi,lrt(ts(ksi,chi),u0),ts"rt"(mn"rt"(1rt,u0,t56),x0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn"rt"(y,x,cutapp2b(x,t,y,u)),ts"rt"(mn"rt"(1rt,u0,t56),x0))]t73(x,t,y,u,v)):lrt(ts(ksi,chi),u0)
-lu@t75:=cutapp1a(ksi,lrt(ts(ksi,chi),u0),[x:rat][t:lrt(ksi,x)]t74(x,t)):lrt(ts(ksi,chi),u0)
-ksi@t76:=isi1(ts(ksi,chi),1rp,[x:rat][t:lrt(ts(ksi,chi),x)]r3(x,t),[x:rat][t:lrt(1rp,x)]t75(x,t)):is(ts(ksi,chi),1rp)
--4152
-satz152:=somei(cut,[t:cut]is(ts(ksi,t),1rp),chi".4152",t76".4152"):some([c:cut]is(ts(ksi,c),1rp))
-eta@[phi:cut][psi:cut]
-+4153
-[m:more(phi,psi)]
-t1:=satz145d(phi,psi,eta,m):more(ts(eta,phi),ts(eta,psi))
-t2:=ec3e21(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t1):nis(ts(eta,phi),ts(eta,psi))
-psi@[l:less(phi,psi)]
-t3:=satz145f(phi,psi,eta,l):less(ts(eta,phi),ts(eta,psi))
-t4:=ec3e31(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t3):nis(ts(eta,phi),ts(eta,psi))
-psi@[n:nis(phi,psi)]
-t5:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
-t6:=orapp(more(phi,psi),less(phi,psi),nis(ts(eta,phi),ts(eta,psi)),t5,[t:more(phi,psi)]t2(t),[t:less(phi,psi)]t4(t)):nis(ts(eta,phi),ts(eta,psi))
--4153
-[i:is(ts(eta,phi),ksi)][j:is(ts(eta,psi),ksi)]
-satz153b:=th7"l.imp"(is(phi,psi),nis(ts(eta,phi),ts(eta,psi)),weli(is(ts(eta,phi),ts(eta,psi)),tris2(cut,ts(eta,phi),ts(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t6".4153"(t)):is(phi,psi)
-+*4153
-eta@[tau:cut][i:is(ts(eta,tau),1rp)]
-chi:=ts(tau,ksi):cut
-t7:=tr3is(cut,ts(eta,chi),ts(ts(eta,tau),ksi),ts(1rp,ksi),ksi,assts2(eta,tau,ksi),ists1(ts(eta,tau),1rp,ksi,i),satz151b(ksi)):is(ts(eta,chi),ksi)
-t8:=somei(cut,[c:cut]is(ts(eta,c),ksi),chi,t7):some([c:cut]is(ts(eta,c),ksi))
--4153
-eta@satz153a:=someapp(cut,[c:cut]is(ts(eta,c),1rp),satz152(eta),some([c:cut]is(ts(eta,c),ksi)),[c:cut][t:is(ts(eta,c),1rp)]t8".4153"(c,t)):some([c:cut]is(ts(eta,c),ksi))
-+*4153
-eta@t9:=[c:cut][d:cut][t:is(ts(eta,c),ksi)][u:is(ts(eta,d),ksi)]satz153b(c,d,t,u):amone(cut,[c:cut]is(ts(eta,c),ksi))
--4153
-eta@satz153:=onei(cut,[c:cut]is(ts(eta,c),ksi),t9".4153",satz153a):one([c:cut]is(ts(eta,c),ksi))
-ov:=ind(cut,[a:cut]is(ts(eta,a),ksi),satz153):cut
-satz153c:=oneax(cut,[a:cut]is(ts(eta,a),ksi),satz153):is(ts(eta,ov(ksi,eta)),ksi)
-satz153d:=symis(cut,ts(eta,ov(ksi,eta)),ksi,satz153c):is(ksi,ts(eta,ov(ksi,eta)))
-satz153e:=tris(cut,ts(ov(ksi,eta),eta),ts(eta,ov(ksi,eta)),ksi,comts(ov(ksi,eta),eta),satz153c):is(ts(ov(ksi,eta),eta),ksi)
-satz153f:=symis(cut,ts(ov(ksi,eta),eta),ksi,satz153e):is(ksi,ts(ov(ksi,eta),eta))
-[phi:cut][i:is(ts(eta,phi),ksi)]
-satz153g:=satz153b(phi,ov(ksi,eta),i,satz153c):is(phi,ov(ksi,eta))
-@[ksi:cut]
-ratrp:=image(rat,cut,[x:rat]rpofrt(x),ksi):'prop'
-@[x0:rat]
-ratrpi:=imagei(rat,cut,[x:rat]rpofrt(x),x0):ratrp(rpofrt(x0))
-@[x:nat]
-rpofnt:=rpofrt(rtofn(x)):cut
-ksi@natrp:=image(nat,cut,[x:nat]rpofnt(x),ksi):'prop'
-x@natrpi:=imagei(nat,cut,[y:nat]rpofnt(y),x):natrp(rpofnt(x))
-ksi@[n:natrp(ksi)]
-+iii5
-[x:nat][i:is(ksi,rpofnt(x))]
-t1:=somei(rat,[y:rat]is(ksi,rpofrt(y)),rtofn(x),i):ratrp(ksi)
--iii5
-lemmaiii5:=someapp(nat,[x:nat]is(ksi,rpofnt(x)),n,ratrp(ksi),[x:nat][t:is(ksi,rpofnt(x))]t1".iii5"(x,t)):ratrp(ksi)
-@[x0:rat][y0:rat][m:more"rt"(x0,y0)]
-+5154
-t1:=lrtrpofrt(x0,y0,satz82(x0,y0,m)):lrt(rpofrt(x0),y0)
-t2:=urtrpofrt(y0,y0,moreisi2"rt"(y0,y0,refis(rat,y0))):urt(rpofrt(y0),y0)
-t3:=andi(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0),t1,t2):and(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0))
--5154
-satz154a:=somei(rat,[x:rat]and(lrt(rpofrt(x0),x),urt(rpofrt(y0),x)),y0,t3".5154"):more(rpofrt(x0),rpofrt(y0))
-y0@[i:is"rt"(x0,y0)]
-satz154b:=isf(rat,cut,[x:rat]rpofrt(x),x0,y0,i):is(rpofrt(x0),rpofrt(y0))
-y0@[l:less"rt"(x0,y0)]
-satz154c:=satz121(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,satz83(x0,y0,l))):less(rpofrt(x0),rpofrt(y0))
-+*5154
-y0@t4:=satz81a(x0,y0):or3(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0))
-t5:=satz123b(rpofrt(x0),rpofrt(y0)):ec3(is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)))
--5154
-y0@[m:more(rpofrt(x0),rpofrt(y0))]
-satz154d:=th11"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),m):more"rt"(x0,y0)
-y0@[i:is(rpofrt(x0),rpofrt(y0))]
-satz154e:=th10"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),i):is"rt"(x0,y0)
-y0@[l:less(rpofrt(x0),rpofrt(y0))]
-satz154f:=th12"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),l):less"rt"(x0,y0)
-+*iii5
-@t2:=[x:rat][y:rat][t:is(rpofrt(x),rpofrt(y))]satz154e(x,y,t):injective(rat,cut,[x:rat]rpofrt(x))
--iii5
-y0@[i:is"rt"(x0,y0)]
-isrterp:=satz154b(x0,y0,i):is(rpofrt(x0),rpofrt(y0))
-y0@[i:is(rpofrt(x0),rpofrt(y0))]
-isrtirp:=satz154e(x0,y0,i):is"rt"(x0,y0)
-ksi@[rtksi:ratrp(ksi)]
-rtofrp:=soft(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):rat
-[eta:cut][rteta:ratrp(eta)][i:is(ksi,eta)]
-isrpert:=isinv(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))
-rteta@[i:is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))]
-isrpirt:=isinve(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is(ksi,eta)
-x0@isrtrp1:=isst1(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(x0,rtofrp(rpofrt(x0),ratrpi(x0)))
-isrtrp2:=isst2(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(rtofrp(rpofrt(x0),ratrpi(x0)),x0)
-rtksi@isrprt1:=ists1"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(ksi,rpofrt(rtofrp(ksi,rtksi)))
-isrprt2:=ists2"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(rpofrt(rtofrp(ksi,rtksi)),ksi)
-@[x:nat][y:nat][i:is"n"(x,y)]
-isnterp:=isf(nat,cut,[z:nat]rpofnt(z),x,y,i):is(rpofnt(x),rpofnt(y))
-y@[i:is(rpofnt(x),rpofnt(y))]
-isntirp:=isnirt(x,y,isrtirp(rtofn(x),rtofn(y),i)):is"n"(x,y)
-+*iii5
-@t3:=[x:nat][y:nat][t:is(rpofnt(x),rpofnt(y))]isntirp(x,y,t):injective(nat,cut,[x:nat]rpofnt(x))
--iii5
-ksi@[ntksi:natrp(ksi)]
-ntofrp:=soft(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):nat
-[eta:cut][nteta:natrp(eta)][i:is(ksi,eta)]
-isrpent:=isinv(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))
-nteta@[i:is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))]
-isrpint:=isinve(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is(ksi,eta)
-x@isntrp1:=isst1(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(x,ntofrp(rpofnt(x),natrpi(x)))
-isntrp2:=isst2(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(ntofrp(rpofnt(x),natrpi(x)),x)
-ntksi@isrpnt1:=ists1"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(ksi,rpofnt(ntofrp(ksi,ntksi)))
-isrpnt2:=ists2"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(rpofnt(ntofrp(ksi,ntksi)),ksi)
-@[x0:rat][y0:rat]
-+5155
-[z0:rat][lz:lrt(pl(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,pl"rt"(u0,v0))]
-t1:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
-t2:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
-t3:=satz98a(u0,x0,v0,y0,t1,t2):less"rt"(pl"rt"(u0,v0),pl"rt"(x0,y0))
-t4:=isless1"rt"(pl"rt"(u0,v0),z0,pl"rt"(x0,y0),symis(rat,z0,pl"rt"(u0,v0),i),t3):less"rt"(z0,pl"rt"(x0,y0))
-t5:=lrtrpofrt(pl"rt"(x0,y0),z0,t4):lrt(rpofrt(pl"rt"(x0,y0)),z0)
-lz@t6:=plapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(pl"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,pl"rt"(x,y))]t5(x,t,y,u,v)):lrt(rpofrt(pl"rt"(x0,y0)),z0)
-y0@[u0:rat][lu:lrt(rpofrt(pl"rt"(x0,y0)),u0)]
-t7:=lrtrpofrte(pl"rt"(x0,y0),u0,lu):less"rt"(u0,pl"rt"(x0,y0))
-u01:=ov"rt"(u0,pl"rt"(x0,y0)):rat
-t8:=isless12"rt"(u0,ts"rt"(u01,pl"rt"(x0,y0)),pl"rt"(x0,y0),ts"rt"(1rt,pl"rt"(x0,y0)),satz110f(u0,pl"rt"(x0,y0)),example1d(pl"rt"(x0,y0)),t7):less"rt"(ts"rt"(u01,pl"rt"(x0,y0)),ts"rt"(1rt,pl"rt"(x0,y0)))
-t9:=satz106c(u01,1rt,pl"rt"(x0,y0),t8):less"rt"(u01,1rt)
-t10:=tris(rat,u0,ts"rt"(pl"rt"(x0,y0),u01),pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)),satz110d(u0,pl"rt"(x0,y0)),disttp1"rt"(x0,y0,u01)):is"rt"(u0,pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)))
-y0@[l:less"rt"(y0,1rt)]
-t11:=isless12"rt"(ts"rt"(y0,x0),ts"rt"(x0,y0),ts"rt"(1rt,x0),x0,comts"rt"(y0,x0),example1c(x0),satz105c(y0,1rt,x0,l)):less"rt"(ts"rt"(x0,y0),x0)
-t12:=lrtrpofrt(x0,ts"rt"(x0,y0),t11):lrt(rpofrt(x0),ts"rt"(x0,y0))
-lu@t13:=lrtpl(rpofrt(x0),rpofrt(y0),u0,ts"rt"(x0,u01),t12(x0,u01,t9),ts"rt"(y0,u01),t12(y0,u01,t9),t10):lrt(pl(rpofrt(x0),rpofrt(y0)),u0)
--5155
-satz155a:=isi1(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(pl"rt"(x0,y0)),x)]t13".5155"(x,t),[x:rat][t:lrt(pl(rpofrt(x0),rpofrt(y0)),x)]t6".5155"(x,t)):is(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)))
-[m:more"rt"(x0,y0)]
-+*5155
-m@t14:=satz101f(x0,y0,m):is"rt"(x0,pl"rt"(mn"rt"(x0,y0,m),y0))
-t15:=tris(cut,rpofrt(x0),rpofrt(pl"rt"(mn"rt"(x0,y0,m),y0)),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),isrterp(x0,pl"rt"(mn"rt"(x0,y0,m),y0),t14),satz155a(mn"rt"(x0,y0,m),y0)):is(rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)))
-t16:=tris2(cut,pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),compl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),t15):is(pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0))
--5155
-m@satz155b:=satz140g(rpofrt(x0),rpofrt(y0),rpofrt(mn"rt"(x0,y0,m)),satz154a(x0,y0,m),t16".5155"):is(rpofrt(mn"rt"(x0,y0,m)),mn(rpofrt(x0),rpofrt(y0),satz154a(x0,y0,m)))
-+*5155
-y0@[z0:rat][lz:lrt(ts(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,ts"rt"(u0,v0))]
-t17:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
-t18:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
-t19:=satz107a(u0,x0,v0,y0,t17,t18):less"rt"(ts"rt"(u0,v0),ts"rt"(x0,y0))
-t20:=isless1"rt"(ts"rt"(u0,v0),z0,ts"rt"(x0,y0),symis(rat,z0,ts"rt"(u0,v0),i),t19):less"rt"(z0,ts"rt"(x0,y0))
-t21:=lrtrpofrt(ts"rt"(x0,y0),z0,t20):lrt(rpofrt(ts"rt"(x0,y0)),z0)
-lz@t22:=tsapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(ts"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,ts"rt"(x,y))]t21(x,t,y,u,v)):lrt(rpofrt(ts"rt"(x0,y0)),z0)
-y0@[u0:rat][lu:lrt(rpofrt(ts"rt"(x0,y0)),u0)]
-t23:=lrtrpofrte(ts"rt"(x0,y0),u0,lu):less"rt"(u0,ts"rt"(x0,y0))
-[u1:rat][a:and(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)))]
-t24:=ande1(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u0,u1)
-t25:=ande2(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u1,ts"rt"(x0,y0))
-t26:=isless12"rt"(u0,ts"rt"(ov"rt"(u0,u1),u1),u1,ts"rt"(1rt,u1),satz110f(u0,u1),example1d(u1),t24):less"rt"(ts"rt"(ov"rt"(u0,u1),u1),ts"rt"(1rt,u1))
-t27:=satz106c(ov"rt"(u0,u1),1rt,u1,t26):less"rt"(ov"rt"(u0,u1),1rt)
-t28:=isless1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0),satz110f(u1,y0),t25):less"rt"(ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0))
-t29:=satz106c(ov"rt"(u1,y0),x0,y0,t28):less"rt"(ov"rt"(u1,y0),x0)
-t30:=tr3is(rat,u0,ts"rt"(u1,ov"rt"(u0,u1)),ts"rt"(ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1)),ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))),satz110d(u0,u1),ists1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1),satz110f(u1,y0)),assts1"rt"(ov"rt"(u1,y0),y0,ov"rt"(u0,u1))):is"rt"(u0,ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))))
-t31:=lrtts(rpofrt(x0),rpofrt(y0),u0,ov"rt"(u1,y0),lrtrpofrt(x0,ov"rt"(u1,y0),t29),ts"rt"(y0,ov"rt"(u0,u1)),t12(y0,ov"rt"(u0,u1),t27),t30):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
-lu@t32:=someapp(rat,[x:rat]and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0))),satz91(u0,ts"rt"(x0,y0),t23),lrt(ts(rpofrt(x0),rpofrt(y0)),u0),[x:rat][t:and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0)))]t31(x,t)):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
--5155
-y0@satz155c:=isi1(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(ts"rt"(x0,y0)),x)]t32".5155"(x,t),[x:rat][t:lrt(ts(rpofrt(x0),rpofrt(y0)),x)]t22".5155"(x,t)):is(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)))
-+*5155
-y0@t33:=satz110f(x0,y0):is"rt"(x0,ts"rt"(ov"rt"(x0,y0),y0))
-t34:=tris(cut,rpofrt(x0),rpofrt(ts"rt"(ov"rt"(x0,y0),y0)),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),isrterp(x0,ts"rt"(ov"rt"(x0,y0),y0),t33),satz155c(ov"rt"(x0,y0),y0)):is(rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)))
-t35:=tris2(cut,ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),comts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),t34):is(ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0))
--5155
-y0@satz155d:=satz153g(rpofrt(x0),rpofrt(y0),rpofrt(ov"rt"(x0,y0)),t35".5155"):is(rpofrt(ov"rt"(x0,y0)),ov(rpofrt(x0),rpofrt(y0)))
-@[x:nat][y:nat]
-satz155e:=tris(cut,rpofnt(pl"n"(x,y)),rpofrt(pl"rt"(rtofn(x),rtofn(y))),pl(rpofnt(x),rpofnt(y)),isrterp(rtofn(pl"n"(x,y)),pl"rt"(rtofn(x),rtofn(y)),symis(rat,pl"rt"(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),satz112h(x,y))),satz155a(rtofn(x),rtofn(y))):is(rpofnt(pl"n"(x,y)),pl(rpofnt(x),rpofnt(y)))
-satz155f:=tris(cut,rpofnt(ts"n"(x,y)),rpofrt(ts"rt"(rtofn(x),rtofn(y))),ts(rpofnt(x),rpofnt(y)),isrterp(rtofn(ts"n"(x,y)),ts"rt"(rtofn(x),rtofn(y)),symis(rat,ts"rt"(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),satz112j(x,y))),satz155c(rtofn(x),rtofn(y))):is(rpofnt(ts"n"(x,y)),ts(rpofnt(x),rpofnt(y)))
-+nt
-@natt:=ot(cut,[t:cut]natrp(t)):'type'
-[ksi:cut][nksi:natrp(ksi)]
-nttofrp:=out(cut,[t:cut]natrp(t),ksi,nksi):natt
-@[xt:natt][yt:natt]
-is:=is"e"(natt,xt,yt):'prop'
-nis:=not(is(xt,yt)):'prop'
-@[p:[x:natt]'prop']
-all:=all"l"(natt,p):'prop'
-some:=some"l"(natt,p):'prop'
-one:=one"e"(natt,p):'prop'
-xt@[st:set(natt)]
-in:=esti(natt,xt,st):'prop'
-xt@rpofntt:=in"e"(cut,[t:cut]natrp(t),xt):cut
-natrpi:=inp(cut,[t:cut]natrp(t),xt):natrp(rpofntt(xt))
-nksi@[eta:cut][neta:natrp(eta)][i:is"rp"(ksi,eta)]
-isrpentt:=isouti(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is(nttofrp(ksi,nksi),nttofrp(eta,neta))
-neta@[i:is(nttofrp(ksi,nksi),nttofrp(eta,neta))]
-isrpintt:=isoute(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is"rp"(ksi,eta)
-yt@[i:is(xt,yt)]
-isntterp:=isini(cut,[t:cut]natrp(t),xt,yt,i):is"rp"(rpofntt(xt),rpofntt(yt))
-yt@[i:is"rp"(rpofntt(xt),rpofntt(yt))]
-isnttirp:=isine(cut,[t:cut]natrp(t),xt,yt,i):is(xt,yt)
-nksi@isrpntt1:=isinout(cut,[t:cut]natrp(t),ksi,nksi):is"rp"(ksi,rpofntt(nttofrp(ksi,nksi)))
-xt@isnttrp1:=isoutin(cut,[t:cut]natrp(t),xt):is(xt,nttofrp(rpofntt(xt),natrpi(xt)))
-@[x:nat]
-nttofnt:=nttofrp(rpofnt(x),natrpi"rp"(x)):natt
-[y:nat][i:is"n"(x,y)]
-isntentt:=isrpentt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),isnterp(x,y,i)):is(nttofnt(x),nttofnt(y))
-y@[i:is(nttofnt(x),nttofnt(y))]
-isntintt:=isntirp(x,y,isrpintt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),i)):is"n"(x,y)
-xt@ntofntt:=ntofrp(rpofntt(xt),natrpi(xt)):nat
-yt@[i:is(xt,yt)]
-isnttent:=isrpent(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),isntterp(xt,yt,i)):is"n"(ntofntt(xt),ntofntt(yt))
-yt@[i:is"n"(ntofntt(xt),ntofntt(yt))]
-isnttint:=isnttirp(xt,yt,isrpint(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),i)):is(xt,yt)
-+iii5
-x@t5:=isrpntt1(rpofnt(x),natrpi"rp"(x)):is"rp"(rpofnt(x),rpofntt(nttofnt(x)))
-t6:=isrpent(rpofnt(x),natrpi"rp"(x),rpofntt(nttofnt(x)),natrpi(nttofnt(x)),t5):is"n"(ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)))
--iii5
-x@isntntt1:=tris(nat,x,ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)),isntrp1(x),t6".iii5"):is"n"(x,ntofntt(nttofnt(x)))
-+*iii5
-xt@t7:=isrpnt1(rpofntt(xt),natrpi(xt)):is"rp"(rpofntt(xt),rpofnt(ntofntt(xt)))
-t8:=isrpentt(rpofntt(xt),natrpi(xt),rpofnt(ntofntt(xt)),natrpi"rp"(ntofntt(xt)),t7):is(nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)))
--iii5
-xt@isnttnt1:=tris(natt,xt,nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)),isnttrp1(xt),t8".iii5"):is(xt,nttofnt(ntofntt(xt)))
-x@isntntt2:=symis(nat,x,ntofntt(nttofnt(x)),isntntt1):is"n"(ntofntt(nttofnt(x)),x)
-xt@isnttnt2:=symis(natt,xt,nttofnt(ntofntt(xt)),isnttnt1):is(nttofnt(ntofntt(xt)),xt)
-@1t:=nttofnt(1):natt
-suct:=[x:natt]nttofnt(<ntofntt(x)>suc):[x:natt]natt
-+5156
-xt@[j:is(<xt>suct,1t)]
-t1:=isntintt(<ntofntt(xt)>suc,1,j):is"n"(<ntofntt(xt)>suc,1)
--5156
-xt@satz156a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<ntofntt(xt)>suc,1),<ntofntt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5156"(t)):nis(<xt>suct,1t)
-yt@[i:is(<xt>suct,<yt>suct)]
-+*5156
-i@t2:=isntintt(<ntofntt(xt)>suc,<ntofntt(yt)>suc,i):is"n"(<ntofntt(xt)>suc,<ntofntt(yt)>suc)
--5156
-i@satz156b:=isnttint(xt,yt,<t2".5156"><ntofntt(yt)><ntofntt(xt)>ax4):is(xt,yt)
-@[st:set(natt)]
-cond1:=in(1t,st):'prop'
-cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
-[c1:cond1][c2:cond2]
-+*5156
-c2@[x:nat]
-prop1:=in(nttofnt(x),st):'prop'
-[p:prop1(x)]
-t3:=<p><nttofnt(x)>c2:in(<nttofnt(x)>suct,st)
-t4:=isp(nat,[t:nat]in(nttofnt(<t>suc),st),ntofntt(nttofnt(x)),x,t3,isntntt2(x)):prop1(<x>suc)
--5156
-c2@[xt:natt]
-+*5156
-xt@t5:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t4(t,u),ntofntt(xt)):in(nttofnt(ntofntt(xt)),st)
--5156
-xt@satz156c:=isp(natt,[t:natt]in(t,st),nttofnt(ntofntt(xt)),xt,t5".5156",isnttnt2(xt)):in(xt,st)
-@ax3t:=[x:natt]satz156a(x):[x:natt]nis(<x>suct,1t)
-ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz156b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
-ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz156c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
--nt
-+rtt
-@ratt:=ot(cut,[t:cut]ratrp(t)):'type'
-[ksi:cut][rtksi:ratrp(ksi)]
-rttofrp:=out(cut,[t:cut]ratrp(t),ksi,rtksi):ratt
-@[x0t:ratt][y0t:ratt]
-is:=is"e"(ratt,x0t,y0t):'prop'
-nis:=not(is(x0t,y0t)):'prop'
-@[p:[x:ratt]'prop']
-all:=all"l"(ratt,p):'prop'
-some:=some"l"(ratt,p):'prop'
-one:=one"e"(ratt,p):'prop'
-x0t@rpofrtt:=in"e"(cut,[t:cut]ratrp(t),x0t):cut
-ratrpi:=inp(cut,[t:cut]ratrp(t),x0t):ratrp(rpofrtt(x0t))
-rtksi@[eta:cut][rteta:ratrp(eta)][i:is"rp"(ksi,eta)]
-isrpertt:=isouti(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))
-rteta@[i:is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))]
-isrpirtt:=isoute(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is"rp"(ksi,eta)
-y0t@[i:is(x0t,y0t)]
-isrtterp:=isini(cut,[t:cut]ratrp(t),x0t,y0t,i):is"rp"(rpofrtt(x0t),rpofrtt(y0t))
-y0t@[i:is"rp"(rpofrtt(x0t),rpofrtt(y0t))]
-isrttirp:=isine(cut,[t:cut]ratrp(t),x0t,y0t,i):is(x0t,y0t)
-rtksi@isrprtt1:=isinout(cut,[t:cut]ratrp(t),ksi,rtksi):is"rp"(ksi,rpofrtt(rttofrp(ksi,rtksi)))
-x0t@isrttrp1:=isoutin(cut,[t:cut]ratrp(t),x0t):is(x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)))
-@[x0:rat]
-rttofrt:=rttofrp(rpofrt(x0),ratrpi"rp"(x0)):ratt
-[y0:rat][i:is"rt"(x0,y0)]
-isrtertt:=isrpertt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),isrterp(x0,y0,i)):is(rttofrt(x0),rttofrt(y0))
-y0@[i:is(rttofrt(x0),rttofrt(y0))]
-isrtirtt:=isrtirp(x0,y0,isrpirtt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),i)):is"rt"(x0,y0)
-x0t@rtofrtt:=rtofrp(rpofrtt(x0t),ratrpi(x0t)):rat
-y0t@[i:is(x0t,y0t)]
-isrttert:=isrpert(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),isrtterp(x0t,y0t,i)):is"rt"(rtofrtt(x0t),rtofrtt(y0t))
-y0t@[i:is"rt"(rtofrtt(x0t),rtofrtt(y0t))]
-isrttirt:=isrttirp(x0t,y0t,isrpirt(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),i)):is(x0t,y0t)
-+iii5
-x0@t9:=isrprtt1(rpofrt(x0),ratrpi"rp"(x0)):is"rp"(rpofrt(x0),rpofrtt(rttofrt(x0)))
-t10:=isrpert(rpofrt(x0),ratrpi"rp"(x0),rpofrtt(rttofrt(x0)),ratrpi(rttofrt(x0)),t9):is"rt"(rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)))
--iii5
-x0@isrtrtt1:=tris(rat,x0,rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)),isrtrp1(x0),t10".iii5"):is"rt"(x0,rtofrtt(rttofrt(x0)))
-+*iii5
-x0t@t11:=isrprt1(rpofrtt(x0t),ratrpi(x0t)):is"rp"(rpofrtt(x0t),rpofrt(rtofrtt(x0t)))
-t12:=isrpertt(rpofrtt(x0t),ratrpi(x0t),rpofrt(rtofrtt(x0t)),ratrpi"rp"(rtofrtt(x0t)),t11):is(rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)))
--iii5
-x0t@isrttrt1:=tris(ratt,x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)),isrttrp1(x0t),t12".iii5"):is(x0t,rttofrt(rtofrtt(x0t)))
--rtt
-@[ksi:cut]
-example2:=satz153c(1rp,ksi):is(ts(ksi,ov(1rp,ksi)),1rp)
-[rtksi:ratrp(ksi)]
-+5157
-x01:=rtofrp(ksi,rtksi):rat
-ksi@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
-rtksi@[y0:rat][i:in(y0,s1)]
-t1:=estie(rat,[x:rat]urt(ksi,x),y0,i):urt(ksi,y0)
-[m:more"rt"(x01,y0)]
-t2:=lrtrpofrt(x01,y0,satz82(x01,y0,m)):lrt(rpofrt(x01),y0)
-t3:=isp(cut,[x:cut]lrt(x,y0),rpofrt(x01),ksi,t2,isrprt2(ksi,rtksi)):lrt(ksi,y0)
-i@t4:=th3"l.imp"(more"rt"(x01,y0),lrt(ksi,y0),t1,[t:more"rt"(x01,y0)]t3(t)):not(more"rt"(x01,y0))
-t5:=satz81e(x01,y0,t4):lessis"rt"(x01,y0)
-rtksi@t6:=[x:rat][t:in(x,s1)]t5(x,t):lb(s1,x01)
-t7:=urtrpofrt(x01,x01,moreisi2"rt"(x01,x01,refis(rat,x01))):urt(rpofrt(x01),x01)
-t8:=isp(cut,[x:cut]urt(x,x01),rpofrt(x01),ksi,t7,isrprt2(ksi,rtksi)):urt(ksi,x01)
-t9:=estii(rat,[x:rat]urt(ksi,x),x01,t8):in(x01,s1)
-t10:=andi(lb(s1,x01),in(x01,s1),t6,t9):min(s1,x01)
--5157
-satz157a:=t10".5157":min(setof(rat,[x:rat]urt(ksi,x)),rtofrp(ksi,rtksi))
-satz157b:=somei(rat,[x:rat]min(s1".5157",x),x01".5157",t10".5157"):some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))
-ksi@[x0:rat][m:min(setof(rat,[x:rat]urt(ksi,x)),x0)]
-+*5157
-m"rp"@t11:=ande1(lb(s1,x0),in(x0,s1),m):lb(s1,x0)
-t12:=ande2(lb(s1,x0),in(x0,s1),m):in(x0,s1)
-t13:=estie(rat,[x:rat]urt(ksi,x),x0,t12):urt(ksi,x0)
-[y0:rat][ly:lrt(ksi,y0)]
-t14:=cutapp2a(ksi,y0,ly,x0,t13):less"rt"(y0,x0)
-t15:=lrtrpofrt(x0,y0,t14):lrt(rpofrt(x0),y0)
-y0@[uy:urt(ksi,y0)]
-t17:=estii(rat,[x:rat]urt(ksi,x),y0,uy):in(y0,s1)
-t18:=satz85(x0,y0,<t17><y0>t11):moreis"rt"(y0,x0)
-t19:=urtrpofrt(x0,y0,t18):urt(rpofrt(x0),y0)
-y0@t20:=cp(lrt(rpofrt(x0),y0),lrt(ksi,y0),[t:urt(ksi,y0)]t19(t)):imp(lrt(rpofrt(x0),y0),lrt(ksi,y0))
--5157
-m@satz157c:=isi1(ksi,rpofrt(x0),[x:rat][t:lrt(ksi,x)]t15".5157"(x,t),[x:rat]t20".5157"(x)):is(ksi,rpofrt(x0))
-ksi@[s:some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))]
-+*5157
-s@[x0:rat][m:min(s1,x0)]
-t21:=somei(rat,[x:rat]is(ksi,rpofrt(x)),x0,satz157c(x0,m)):ratrp(ksi)
--5157
-s@satz157d:=someapp(rat,[x:rat]min(s1".5157",x),s,ratrp(ksi),[x:rat][t:min(s1".5157",x)]t21".5157"(x,t)):ratrp(ksi)
-ksi@[x0:rat][lx:lrt(ksi,x0)]
-+5158
-x0@xr:=rpofrt(x0):cut
-lx@t1:=urtrpofrt(x0,x0,moreisi2"rt"(x0,x0,refis(rat,x0))):urt(xr,x0)
-t2:=andi(urt(xr,x0),lrt(ksi,x0),t1,lx):and(urt(xr,x0),lrt(ksi,x0))
--5158
-satz158a:=somei(rat,[x:rat]and(urt(rpofrt(x0),x),lrt(ksi,x)),x0,t2".5158"):less(rpofrt(x0),ksi)
-x0@[ux:urt(ksi,x0)]
-+*5158
-ux@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
-[m:min(s1,x0)]
-t3:=symis(cut,ksi,xr,satz157c(ksi,x0,m)):is(xr,ksi)
-t4:=moreisi2(xr,ksi,t3):moreis(xr,ksi)
-ux@[n:not(min(s1,x0))]
-t5:=estii(rat,[x:rat]urt(ksi,x),x0,ux):in(x0,s1)
-t6:=th4"l.and"(lb(s1,x0),in(x0,s1),n,t5):not(lb(s1,x0))
-t7:=th1"l.some"(rat,[x:rat]imp(in(x,s1),lessis"rt"(x0,x)),t6):some"rt"([x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))))
-[y0:rat][o:not(imp(in(y0,s1),lessis"rt"(x0,y0)))]
-t8:=th5"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):in(y0,s1)
-t9:=estie(rat,[x:rat]urt(ksi,x),y0,t8):urt(ksi,y0)
-t10:=th6"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):not(lessis"rt"(x0,y0))
-t11:=satz82(x0,y0,satz81k(x0,y0,t10)):less"rt"(y0,x0)
-t12:=lrtrpofrt(x0,y0,t11):lrt(xr,y0)
-t13:=andi(lrt(xr,y0),urt(ksi,y0),t12,t9):and(lrt(xr,y0),urt(ksi,y0))
-t14:=somei(rat,[x:rat]and(lrt(xr,x),urt(ksi,x)),y0,t13):more(xr,ksi)
-n@t15:=someapp(rat,[x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))),t7,more(xr,ksi),[x:rat][t:not(imp(in(x,s1),lessis"rt"(x0,x)))]t14(x,t)):more(xr,ksi)
-t16:=moreisi1(xr,ksi,t15):moreis(xr,ksi)
--5158
-ux@satz158b:=th1"l.imp"(min(s1".5158",x0),moreis(rpofrt(x0),ksi),[t:min(s1".5158",x0)]t4".5158"(t),[t:not(min(s1".5158",x0))]t16".5158"(t)):moreis(rpofrt(x0),ksi)
-x0@[l:less(rpofrt(x0),ksi)]
-+*5158
-l@t17:=satz123h(xr,ksi,l):not(moreis(xr,ksi))
-t18:=th3"l.imp"(urt(ksi,x0),moreis(xr,ksi),t17,[t:urt(ksi,x0)]satz158b(t)):not(urt(ksi,x0))
--5158
-l@satz158c:=et(lrt(ksi,x0),t18".5158"):lrt(ksi,x0)
-x0@[m:moreis(rpofrt(x0),ksi)]
-+*5158
-m"rp"@t19:=satz123c(xr,ksi,m):not(less(xr,ksi))
--5158
-m@satz158d:=th3"l.imp"(lrt(ksi,x0),less(rpofrt(x0),ksi),t19".5158",[t:lrt(ksi,x0)]satz158a(t)):urt(ksi,x0)
-ksi@[eta:cut][l:less(ksi,eta)]
-+5159
-[x0:rat]
-xr:=rpofrt(x0):cut
-[ux:urt(ksi,x0)][lx:lrt(eta,x0)][z0:rat]
-zr:=rpofrt(z0):cut
-[lz:lrt(eta,z0)][k:less"rt"(x0,z0)]
-t1:=satz127a(ksi,xr,zr,satz124(xr,ksi,satz158b(ksi,x0,ux)),satz154c(x0,z0,k)):less(ksi,zr)
-t2:=andi(less(ksi,zr),less(zr,eta),t1,satz158a(eta,z0,lz)):and(less(ksi,zr),less(zr,eta))
-t3:=somei(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),z0,t2):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
-lx@t4:=cutapp3(eta,x0,lx,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:lrt(eta,x)][u:less"rt"(x0,x)]t3(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
--5159
-satz159:=lessapp(ksi,eta,l,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t4".5159"(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
-+*5159
-x0@[a:and(less(ksi,xr),less(xr,eta))]
-t5:=andi(ratrp(xr),and(less(ksi,xr),less(xr,eta)),ratrpi(x0),a):and3(ratrp(xr),less(ksi,xr),less(xr,eta))
-t6:=somei(cut,[c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)),xr,t5):some([c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)))
--5159
-l@satz159a:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta))),[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t6".5159"(x,t)):some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta)))
-[p:'prop'][p1:[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),eta)]p]
-+*5159
-p1@[y0:rat]
-yr:=rpofrt(y0):cut
-[a:and(less(ksi,yr),less(yr,eta))]
-t7:=ande1(less(ksi,yr),less(yr,eta),a):less(ksi,yr)
-t8:=ande2(less(ksi,yr),less(yr,eta),a):less(yr,eta)
-t9:=<t8><t7><y0>p1:p
--5159
-p1@satz159app:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,p,[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t9".5159"(x,t)):p
-eta@[z0:rat][m:more(rpofrt(z0),ts(ksi,eta))]
-+5160
-zr:=rpofrt(z0):cut
-nm:=mn(zr,ts(ksi,eta),m):cut
-dn:=pl(pl(ksi,eta),1rp):cut
-fr:=ov(nm,dn):cut
-zeta:=ite(less(fr,1rp),cut,fr,1rp):cut
-[l:less(fr,1rp)]
-t1:=itet(less(fr,1rp),cut,fr,1rp,l):is(zeta,fr)
-t2:=lessisi2(zeta,fr,t1):lessis(zeta,fr)
-t3:=lessisi1(zeta,1rp,satz127a(zeta,fr,1rp,t2,l)):lessis(zeta,1rp)
-m@[n:not(less(fr,1rp))]
-t4:=itef(less(fr,1rp),cut,fr,1rp,n):is(zeta,1rp)
-t5:=lessisi2(zeta,1rp,t4):lessis(zeta,1rp)
-t6:=trlessis(zeta,1rp,fr,t5,satz124(fr,1rp,satz123f(fr,1rp,n))):lessis(zeta,fr)
-m@t7:=th1"l.imp"(less(fr,1rp),lessis(zeta,1rp),[t:less(fr,1rp)]t3(t),[t:not(less(fr,1rp))]t5(t)):lessis(zeta,1rp)
-t8:=th1"l.imp"(less(fr,1rp),lessis(zeta,fr),[t:less(fr,1rp)]t2(t),[t:not(less(fr,1rp))]t6(t)):lessis(zeta,fr)
-[z1:rat]
-zr1:=rpofrt(z1):cut
-[l1:less(ksi,zr1)][l2:less(zr1,pl(ksi,zeta))][z2:rat]
-zr2:=rpofrt(z2):cut
-[l3:less(eta,zr2)][l4:less(zr2,pl(eta,zeta))]
-t9:=isless2(ts(pl(ksi,zeta),pl(eta,zeta)),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),ts(zr1,zr2),disttp2(pl(ksi,zeta),eta,zeta),satz147a(zr1,pl(ksi,zeta),zr2,pl(eta,zeta),l2,l4)):less(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)))
-t10:=lessisi2(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),tris(cut,ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(zeta,eta)),pl(ts(ksi,eta),ts(eta,zeta)),disttp1(ksi,zeta,eta),ispl2(ts(zeta,eta),ts(eta,zeta),ts(ksi,eta),comts(zeta,eta)))):lessis(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)))
-t11:=satz149a(pl(ksi,zeta),pl(ksi,1rp),zeta,zeta,satz139a(ksi,ksi,zeta,1rp,lessisi2(ksi,ksi,refis(cut,ksi)),t7),lessisi2(zeta,zeta,refis(cut,zeta))):lessis(ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta))
-t12:=satz139a(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta),t10,t11):lessis(pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
-t13:=satz127b(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),t9,t12):less(ts(zr1,zr2),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
-t14:=tris(cut,pl(eta,pl(ksi,1rp)),pl(pl(eta,ksi),1rp),pl(pl(ksi,eta),1rp),asspl2(eta,ksi,1rp),ispl1(pl(eta,ksi),pl(ksi,eta),1rp,compl(eta,ksi))):is(pl(eta,pl(ksi,1rp)),dn)
-t15:=tris(cut,pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(pl(eta,pl(ksi,1rp)),zeta),ts(dn,zeta),distpt1(eta,pl(ksi,1rp),zeta),ists1(pl(eta,pl(ksi,1rp)),dn,zeta,t14)):is(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta))
-t16:=tris(cut,pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta))),pl(ts(ksi,eta),ts(dn,zeta)),asspl1(ts(ksi,eta),ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ispl2(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta),ts(ksi,eta),t15)):is(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)))
-t17:=isless2(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)),ts(zr1,zr2),t16,t13):less(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)))
-t18:=islessis12(ts(zeta,dn),ts(dn,zeta),ts(fr,dn),nm,comts(zeta,dn),satz153e(nm,dn),satz149a(zeta,fr,dn,dn,t8,lessisi2(dn,dn,refis(cut,dn)))):lessis(ts(dn,zeta),nm)
-t19:=satz139a(ts(ksi,eta),ts(ksi,eta),ts(dn,zeta),nm,lessisi2(ts(ksi,eta),ts(ksi,eta),refis(cut,ts(ksi,eta))),t18):lessis(pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm))
-t20:=satz127b(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm),t17,t19):less(ts(zr1,zr2),pl(ts(ksi,eta),nm))
-t21:=isless2(pl(ts(ksi,eta),nm),zr,ts(zr1,zr2),satz140c(zr,ts(ksi,eta),m),t20):less(ts(zr1,zr2),zr)
-t22:=satz154f(ts"rt"(z1,z2),z0,isless1(ts(zr1,zr2),rpofrt(ts"rt"(z1,z2)),zr,symis(cut,rpofrt(ts"rt"(z1,z2)),ts(zr1,zr2),satz155c(z1,z2)),t21)):less"rt"(ts"rt"(z1,z2),z0)
-x0:=ov"rt"(z0,z2):rat
-xr:=rpofrt(x0):cut
-y0:=z2:rat
-yr:=rpofrt(y0):cut
-t23:=satz110e(z0,z2):is"rt"(ts"rt"(x0,y0),z0)
-t24:=ismore1"rt"(z0,ts"rt"(x0,z2),ts"rt"(z1,z2),symis(rat,ts"rt"(x0,z2),z0,t23),satz83(ts"rt"(z1,z2),z0,t22)):more"rt"(ts"rt"(x0,z2),ts"rt"(z1,z2))
-t25:=satz106a(x0,z1,z2,t24):more"rt"(x0,z1)
-t26:=trmore(xr,zr1,ksi,satz154a(x0,z1,t25),satz122(ksi,zr1,l1)):more(xr,ksi)
-t27:=satz122(eta,yr,l3):more(yr,eta)
-z0@[u0:rat]
-ur:=rpofrt(u0):cut
-[v0:rat]
-vr:=rpofrt(v0):cut
-prop1:=and3(more(ur,ksi),more(vr,eta),is"rt"(ts"rt"(u0,v0),z0)):'prop'
-z0@prop2:=some"rt"([x:rat]some"rt"([y:rat]prop1(x,y))):'prop'
-l4@t28:=and3i(more(xr,ksi),more(yr,eta),is"rt"(ts"rt"(x0,y0),z0),t26,t27,t23):prop1(x0,y0)
-t29:=somei(rat,[y:rat]prop1(x0,y),y0,t28):some"rt"([y:rat]prop1(x0,y))
-t30:=somei(rat,[x:rat]some"rt"([y:rat]prop1(x,y)),x0,t29):prop2
-l2@t31:=satz159app(eta,pl(eta,zeta),satz133a(eta,zeta),prop2,[x:rat][t:less(eta,rpofrt(x))][u:less(rpofrt(x),pl(eta,zeta))]t30(x,t,u)):prop2
--5160
-satz160:=satz159app(ksi,pl(ksi,zeta".5160"),satz133a(ksi,zeta".5160"),prop2".5160",[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),pl(ksi,zeta".5160"))]t31".5160"(x,t,u)):some"rt"([x:rat]some"rt"([y:rat]and3(more(rpofrt(x),ksi),more(rpofrt(y),eta),is"rt"(ts"rt"(x,y),z0))))
-[p:'prop'][p1:[x:rat][t:more(rpofrt(x),ksi)][y:rat][u:more(rpofrt(y),eta)][v:is"rt"(ts"rt"(x,y),z0)]p]
-+*5160
-p1@[x1:rat]
-xr1:=rpofrt(x1):cut
-[px:some"rt"([y:rat]prop1(x1,y))][y1:rat]
-yr1:=rpofrt(y1):cut
-[py:prop1(x1,y1)]
-t32:=and3e1(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(xr1,ksi)
-t33:=and3e2(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(yr1,eta)
-t34:=and3e3(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):is"rt"(ts"rt"(x1,y1),z0)
-t35:=<t34><t33><y1><t32><x1>p1:p
-px@t36:=someapp(rat,[y:rat]prop1(x1,y),px,p,[y:rat][v:prop1(x1,y)]t35(y,v)):p
--5160
-p1@satz160app:=someapp(rat,[x:rat]some"rt"([y:rat]prop1".5160"(x,y)),satz160,p,[x:rat][t:some"rt"([y:rat]prop1".5160"(x,y))]t36".5160"(x,t)):p
-+5161
-@[ksi:cut][eta:cut]
-min:=ite(less(ksi,eta),cut,ksi,eta):cut
-max:=ite(more(ksi,eta),cut,ksi,eta):cut
-[u0:rat]
-ur:=rpofrt(u0):cut
-[lu:lrt(min,u0)]
-t1:=satz158a(min,u0,lu):less(ur,min)
-[l:less(ksi,eta)]
-t2:=isless2(min,ksi,ur,itet(less(ksi,eta),cut,ksi,eta,l),t1):less(ur,ksi)
-t3:=trless(ur,ksi,eta,t2,l):less(ur,eta)
-lu@[n:not(less(ksi,eta))]
-t4:=isless2(min,eta,ur,itef(less(ksi,eta),cut,ksi,eta,n),t1):less(ur,eta)
-t5:=satz127b(ur,eta,ksi,t4,satz124(ksi,eta,satz123f(ksi,eta,n))):less(ur,ksi)
-lu@t6:=th1"l.imp"(less(ksi,eta),less(ur,ksi),[t:less(ksi,eta)]t2(t),[t:not(less(ksi,eta))]t5(t)):less(ur,ksi)
-t7:=th1"l.imp"(less(ksi,eta),less(ur,eta),[t:less(ksi,eta)]t3(t),[t:not(less(ksi,eta))]t4(t)):less(ur,eta)
-u0@[uu:urt(max,u0)]
-t8:=satz158b(max,u0,uu):moreis(ur,max)
-[m:more(ksi,eta)]
-t9:=ismoreis2(max,ksi,ur,itet(more(ksi,eta),cut,ksi,eta,m),t8):moreis(ur,ksi)
-t10:=trmoreis(ur,ksi,eta,t9,moreisi1(ksi,eta,m)):moreis(ur,eta)
-uu@[n:not(more(ksi,eta))]
-t11:=ismoreis2(max,eta,ur,itef(more(ksi,eta),cut,ksi,eta,n),t8):moreis(ur,eta)
-t12:=trmoreis(ur,eta,ksi,t11,satz125(ksi,eta,satz123e(ksi,eta,n))):moreis(ur,ksi)
-uu@t13:=th1"l.imp"(more(ksi,eta),moreis(ur,ksi),[t:more(ksi,eta)]t9(t),[t:not(more(ksi,eta))]t12(t)):moreis(ur,ksi)
-t14:=th1"l.imp"(more(ksi,eta),moreis(ur,eta),[t:more(ksi,eta)]t10(t),[t:not(more(ksi,eta))]t11(t)):moreis(ur,eta)
--5161
-@[zeta:cut]
-+*5161
-zeta@[ksi1:cut][ksi2:cut][m:more(ksi1,ksi2)]
-t15:=satz147(ksi1,ksi2,ksi1,ksi2,m,m):more(ts(ksi1,ksi1),ts(ksi2,ksi2))
-ksi2@sq1:=ts(ksi1,ksi1):cut
-sq2:=ts(ksi2,ksi2):cut
-m@t16:=ec3e21(is(sq1,sq2),more(sq1,sq2),less(sq1,sq2),satz123b(sq1,sq2),t15):nis(sq1,sq2)
-ksi2@[i:is(sq1,zeta)][j:is(sq2,zeta)]
-t17:=tris2(cut,sq1,sq2,zeta,i,j):is(sq1,sq2)
-t18:=[t:more(ksi1,ksi2)]<t17>t16(t):not(more(ksi1,ksi2))
-t19:=[t:less(ksi1,ksi2)]<symis(cut,sq1,sq2,t17)>t16(ksi2,ksi1,satz122(ksi1,ksi2,t)):not(less(ksi1,ksi2))
-t20:=or3e1(is(ksi1,ksi2),more(ksi1,ksi2),less(ksi1,ksi2),satz123a(ksi1,ksi2),t18,t19):is(ksi1,ksi2)
-zeta@t21:=[a:cut][b:cut][t:is(ts(a,a),zeta)][u:is(ts(b,b),zeta)]t20(a,b,t,u):amone(cut,[a:cut]is(ts(a,a),zeta))
-sqrtset:=setof(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta)):set(rat)
-[x0:rat]
-xr:=rpofrt(x0):cut
-[lx:lrt(min(1rp,zeta),x0)]
-t22:=t6(1rp,zeta,x0,lx):less(xr,1rp)
-t23:=t7(1rp,zeta,x0,lx):less(xr,zeta)
-t24:=isless1(xr,ts(xr,1rp),zeta,satz151a(xr),t23):less(ts(xr,1rp),zeta)
-t25:=trless(ts(xr,xr),ts(xr,1rp),zeta,satz148c(xr,xr,xr,1rp,lessisi2(xr,xr,refis(cut,xr)),t22),t24):less(ts(xr,xr),zeta)
-t26:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t25):in(x0,sqrtset)
-x0@[ux:urt(max(1rp,zeta),x0)]
-t27:=t13(1rp,zeta,x0,ux):moreis(xr,1rp)
-t28:=t14(1rp,zeta,x0,ux):moreis(xr,zeta)
-t29:=ismoreis1(xr,ts(xr,1rp),zeta,satz151a(xr),t28):moreis(ts(xr,1rp),zeta)
-t30:=trmoreis(ts(xr,xr),ts(xr,1rp),zeta,satz149(xr,xr,xr,1rp,moreisi2(xr,xr,refis(cut,xr)),t27),t29):moreis(ts(xr,xr),zeta)
-t31:=satz123c(ts(xr,xr),zeta,t30):not(less(ts(xr,xr),zeta))
-t32:=th3"l.imp"(in(x0,sqrtset),less(ts(xr,xr),zeta),t31,[t:in(x0,sqrtset)]estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t)):not(in(x0,sqrtset))
-x0@[i:in(x0,sqrtset)][y0:rat]
-yr:=rpofrt(y0):cut
-[l:less"rt"(y0,x0)]
-i@t33:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,i):less(ts(xr,xr),zeta)
-l@t34:=satz154c(y0,x0,l):less(yr,xr)
-t35:=trless(ts(yr,yr),ts(xr,xr),zeta,satz147a(yr,xr,yr,xr,t34,t34),t33):less(ts(yr,yr),zeta)
-t36:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),y0,t35):in(y0,sqrtset)
-i@t37:=satz122(ts(xr,xr),zeta,t33):more(zeta,ts(xr,xr))
-nm:=mn(zeta,ts(xr,xr),t37):cut
-dn:=pl(xr,pl(xr,1rp)):cut
-fr:=ov(nm,dn):cut
-[z0:rat]
-zr:=rpofrt(z0):cut
-[lz:lrt(min(1rp,fr),z0)]
-t38:=t6(1rp,fr,z0,lz):less(zr,1rp)
-t39:=t7(1rp,fr,z0,lz):less(zr,fr)
-t40:=satz94(x0,z0):more"rt"(pl"rt"(x0,z0),x0)
-t41:=tris(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),ts(pl(xr,zr),pl(xr,zr)),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ists12(rpofrt(pl"rt"(x0,z0)),pl(xr,zr),rpofrt(pl"rt"(x0,z0)),pl(xr,zr),satz155a(x0,z0),satz155a(x0,z0)),disttp2(pl(xr,zr),xr,zr)):is(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)))
-t42:=symis(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),t41):is(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))))
-t43:=lessisi2(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),tris(cut,ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(zr,xr)),pl(ts(xr,xr),ts(xr,zr)),disttp1(xr,zr,xr),ispl2(ts(zr,xr),ts(xr,zr),ts(xr,xr),comts(zr,xr)))):lessis(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)))
-t44:=satz145c(pl(xr,zr),pl(xr,1rp),zr,satz138c(xr,xr,zr,1rp,lessisi2(xr,xr,refis(cut,xr)),t38)):less(ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr))
-t45:=satz138c(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr),t43,t44):less(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)))
-t46:=tris(cut,pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),pl(ts(xr,zr),ts(pl(xr,1rp),zr))),pl(ts(xr,xr),ts(dn,zr)),asspl1(ts(xr,xr),ts(xr,zr),ts(pl(xr,1rp),zr)),ispl2(pl(ts(xr,zr),ts(pl(xr,1rp),zr)),ts(dn,zr),ts(xr,xr),distpt1(xr,pl(xr,1rp),zr))):is(pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)))
-t47:=isless12(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)),t42,t46,t45):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)))
-t48:=isless2(ts(dn,fr),nm,ts(dn,zr),satz153c(nm,dn),satz148c(dn,dn,zr,fr,lessisi2(dn,dn,refis(cut,dn)),t39)):less(ts(dn,zr),nm)
-t49:=satz138c(ts(xr,xr),ts(xr,xr),ts(dn,zr),nm,lessisi2(ts(xr,xr),ts(xr,xr),refis(cut,ts(xr,xr))),t48):less(pl(ts(xr,xr),ts(dn,zr)),pl(ts(xr,xr),nm))
-t50:=isless2(pl(ts(xr,xr),nm),zeta,pl(ts(xr,xr),ts(dn,zr)),satz140c(zeta,ts(xr,xr),t37),t49):less(pl(ts(xr,xr),ts(dn,zr)),zeta)
-t51:=trless(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)),zeta,t47,t50):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),zeta)
-t52:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),pl"rt"(x0,z0),t51):in(pl"rt"(x0,z0),sqrtset)
-t53:=andi(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0),t52,t40):and(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0))
-t54:=somei(rat,[y:rat]and(in(y,sqrtset),more"rt"(y,x0)),pl"rt"(x0,z0),t53):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
-i@t55:=cutapp1a(min(1rp,fr),some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0))),[x:rat][t:lrt(min(1rp,fr),x)]t54(x,t)):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
-x0@[lx:lrt(min(1rp,zeta),x0)][y0:rat][uy:urt(max(1rp,zeta),y0)]
-t56:=cut2(sqrtset,x0,t26(lx),y0,t32(y0,uy),[x:rat][t:in(x,sqrtset)][y:rat][u:less"rt"(y,x)]t36(x,t,y,u),[x:rat][t:in(x,sqrtset)]t55(x,t)):cutprop(sqrtset)
-lx@t57:=cutapp1b(max(1rp,zeta),cutprop(sqrtset),[y:rat][t:urt(max(1rp,zeta),y)]t56(y,t)):cutprop(sqrtset)
-zeta@t58:=cutapp1a(min(1rp,zeta),cutprop(sqrtset),[x:rat][t:lrt(min(1rp,zeta),x)]t57(x,t)):cutprop(sqrtset)
-rtc:=cutof(sqrtset,t58):cut
-@[x0:rat][y0:rat][l:lessis"rt"(x0,y0)]
-t59:=th9"l.or"(less"rt"(x0,y0),is"rt"(x0,y0),less(rpofrt(x0),rpofrt(y0)),is(rpofrt(x0),rpofrt(y0)),l,[t:less"rt"(x0,y0)]satz154c(x0,y0,t),[t:is"rt"(x0,y0)]satz154b(x0,y0,t)):lessis(rpofrt(x0),rpofrt(y0))
-y0@[m:moreis"rt"(x0,y0)]
-t60:=satz125(rpofrt(y0),rpofrt(x0),t59(y0,x0,satz84(x0,y0,m))):moreis(rpofrt(x0),rpofrt(y0))
-zeta@[m:more(ts(rtc,rtc),zeta)]
-t61:=satz121(ts(rtc,rtc),zeta,m):less(zeta,ts(rtc,rtc))
-[z1:rat]
-zr1:=rpofrt(z1):cut
-[l1:less(zeta,zr1)][l2:less(zr1,ts(rtc,rtc))]
-t62:=satz158c(ts(rtc,rtc),z1,l2):lrt(ts(rtc,rtc),z1)
-[x1:rat]
-xr1:=rpofrt(x1):cut
-[lx1:lrt(rtc,x1)][x2:rat]
-xr2:=rpofrt(x2):cut
-[lx2:lrt(rtc,x2)][i:is"rt"(z1,ts"rt"(x1,x2))]
-xm:=ite(more"rt"(x1,x2),rat,x1,x2):rat
-xrm:=rpofrt(xm):cut
-[o:more"rt"(x1,x2)]
-t63:=symis(rat,xm,x1,itet(more"rt"(x1,x2),rat,x1,x2,o)):is"rt"(x1,xm)
-t64:=isp(rat,[x:rat]lrt(rtc,x),x1,xm,lx1,t63):lrt(rtc,xm)
-t65:=lessisi2"rt"(x1,xm,t63):lessis"rt"(x1,xm)
-t66:=lessisi1"rt"(x2,xm,satz87b(x2,x1,xm,satz82(x1,x2,o),t65)):lessis"rt"(x2,xm)
-i@[n:not(more"rt"(x1,x2))]
-t67:=symis(rat,xm,x2,itef(more"rt"(x1,x2),rat,x1,x2,n)):is"rt"(x2,xm)
-t68:=isp(rat,[x:rat]lrt(rtc,x),x2,xm,lx2,t67):lrt(rtc,xm)
-t69:=lessisi2"rt"(x2,xm,t67):lessis"rt"(x2,xm)
-t70:=satz88(x1,x2,xm,satz81e(x1,x2,n),t69):lessis"rt"(x1,xm)
-i@t71:=th1"l.imp"(more"rt"(x1,x2),lrt(rtc,xm),[t:more"rt"(x1,x2)]t64(t),[t:not(more"rt"(x1,x2))]t68(t)):lrt(rtc,xm)
-t72:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x1,xm),[t:more"rt"(x1,x2)]t65(t),[t:not(more"rt"(x1,x2))]t70(t)):lessis"rt"(x1,xm)
-t73:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x2,xm),[t:more"rt"(x1,x2)]t66(t),[t:not(more"rt"(x1,x2))]t69(t)):lessis"rt"(x2,xm)
-t74:=ini(sqrtset,t58,xm,t71):in(xm,sqrtset)
-t75:=t59(x1,xm,t72):lessis(xr1,xrm)
-t76:=t59(x2,xm,t73):lessis(xr2,xrm)
-t77:=tris(cut,zr1,rpofrt(ts"rt"(x1,x2)),ts(xr1,xr2),satz154b(z1,ts"rt"(x1,x2),i),satz155c(x1,x2)):is(zr1,ts(xr1,xr2))
-t78:=islessis1(ts(xr1,xr2),zr1,ts(xrm,xrm),symis(cut,zr1,ts(xr1,xr2),t77),satz149a(xr1,xrm,xr2,xrm,t75,t76)):lessis(zr1,ts(xrm,xrm))
-t79:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),xm,t74):less(ts(xrm,xrm),zeta)
-t80:=satz127a(zr1,ts(xrm,xrm),zeta,t78,t79):less(zr1,zeta)
-t81:=<t80>ec3e23(is(zr1,zeta),more(zr1,zeta),less(zr1,zeta),satz123b(zr1,zeta),satz122(zeta,zr1,l1)):con
-t82:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t81(x,t,y,u,v)):con
-l2@t82a:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t82(x,t,y,u,v)):con
-m@t83:=satz159app(zeta,ts(rtc,rtc),t61,con,[x:rat][t:less(zeta,rpofrt(x))][u:less(rpofrt(x),ts(rtc,rtc))]t82a(x,t,u)):con
-zeta@[l:less(ts(rtc,rtc),zeta)][z2:rat]
-zr2:=rpofrt(z2):cut
-[l3:less(ts(rtc,rtc),zr2)][l4:less(zr2,zeta)]
-t84:=satz122(ts(rtc,rtc),zr2,l3):more(zr2,ts(rtc,rtc))
-[y1:rat]
-yr1:=rpofrt(y1):cut
-[m1:more(yr1,rtc)][y2:rat]
-yr2:=rpofrt(y2):cut
-[m2:more(yr2,rtc)][i:is"rt"(ts"rt"(y1,y2),z2)]
-ym:=ite(less"rt"(y1,y2),rat,y1,y2):rat
-yrm:=rpofrt(ym):cut
-[k:less"rt"(y1,y2)]
-t85:=symis(rat,ym,y1,itet(less"rt"(y1,y2),rat,y1,y2,k)):is"rt"(y1,ym)
-t86:=satz154b(y1,ym,t85):is(yr1,yrm)
-t87:=ismore1(yr1,yrm,rtc,t86,m1):more(yrm,rtc)
-t88:=moreisi2(yr1,yrm,t86):moreis(yr1,yrm)
-t89:=moreisi1(yr2,yrm,satz127d(yr2,yr1,yrm,satz122(yr1,yr2,satz154c(y1,y2,k)),t88)):moreis(yr2,yrm)
-i@[n:not(less"rt"(y1,y2))]
-t90:=symis(rat,ym,y2,itef(less"rt"(y1,y2),rat,y1,y2,n)):is"rt"(y2,ym)
-t91:=satz154b(y2,ym,t90):is(yr2,yrm)
-t92:=ismore1(yr2,yrm,rtc,t91,m2):more(yrm,rtc)
-t93:=moreisi2(yr2,yrm,t91):moreis(yr2,yrm)
-t94:=trmoreis(yr1,yr2,yrm,t60(y1,y2,satz81f(y1,y2,n)),t93):moreis(yr1,yrm)
-i@t95:=th1"l.imp"(less"rt"(y1,y2),more(yrm,rtc),[t:less"rt"(y1,y2)]t87(t),[t:not(less"rt"(y1,y2))]t92(t)):more(yrm,rtc)
-t96:=th1"l.imp"(less"rt"(y1,y2),moreis(yr1,yrm),[t:less"rt"(y1,y2)]t88(t),[t:not(less"rt"(y1,y2))]t94(t)):moreis(yr1,yrm)
-t97:=th1"l.imp"(less"rt"(y1,y2),moreis(yr2,yrm),[t:less"rt"(y1,y2)]t89(t),[t:not(less"rt"(y1,y2))]t93(t)):moreis(yr2,yrm)
-t98:=satz158d(rtc,ym,moreisi1(yrm,rtc,t95)):urt(rtc,ym)
-t99:=th3"l.imp"(in(ym,sqrtset),lrt(rtc,ym),t98,[t:in(ym,sqrtset)]ine(sqrtset,t58,ym,t)):not(in(ym,sqrtset))
-t100:=th3"l.imp"(less(ts(yrm,yrm),zeta),in(ym,sqrtset),t99,[t:less(ts(yrm,yrm),zeta)]estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),ym,t)):not(less(ts(yrm,yrm),zeta))
-t101:=satz123f(ts(yrm,yrm),zeta,t100):moreis(ts(yrm,yrm),zeta)
-t101a:=satz149(yr1,yrm,yr2,yrm,t96,t97):moreis(ts(yr1,yr2),ts(yrm,yrm))
-t102:=ismoreis1(ts(yr1,yr2),zr2,ts(yrm,yrm),tris(cut,ts(yr1,yr2),rpofrt(ts"rt"(y1,y2)),zr2,symis(cut,rpofrt(ts"rt"(y1,y2)),ts(yr1,yr2),satz155c(y1,y2)),satz154b(ts"rt"(y1,y2),z2,i)),t101a):moreis(zr2,ts(yrm,yrm))
-t103:=trmoreis(zr2,ts(yrm,yrm),zeta,t102,t101):moreis(zr2,zeta)
-t104:=<l4>satz123c(zr2,zeta,t103):con
-l4@t105:=satz160app(rtc,rtc,z2,t84,con,[x:rat][t:more(rpofrt(x),rtc)][y:rat][u:more(rpofrt(y),rtc)][v:is"rt"(ts"rt"(x,y),z2)]t104(x,t,y,u,v)):con
-l@t106:=satz159app(ts(rtc,rtc),zeta,l,con,[x:rat][t:less(ts(rtc,rtc),rpofrt(x))][u:less(rpofrt(x),zeta)]t105(x,t,u)):con
-zeta@t107:=or3e1(is(ts(rtc,rtc),zeta),more(ts(rtc,rtc),zeta),less(ts(rtc,rtc),zeta),satz123a(ts(rtc,rtc),zeta),[t:more(ts(rtc,rtc),zeta)]t83(t),[t:less(ts(rtc,rtc),zeta)]t106(t)):is(ts(rtc,rtc),zeta)
-t108:=somei(cut,[a:cut]is(ts(a,a),zeta),rtc,t107):some([a:cut]is(ts(a,a),zeta))
--5161
-zeta@satz161:=onei(cut,[a:cut]is(ts(a,a),zeta),t21".5161",t108".5161"):one([a:cut]is(ts(a,a),zeta))
-@[ksi:cut]
-irratrp:=not(ratrp(ksi)):'prop'
--rp
--rt
-+5162
-@[v:nat]
-t1:=tris(nat,pl(v,v),pl(ts(1,v),v),ts(<1>suc,v),ispl1(v,ts(1,v),v,satz28g(v)),satz28h(1,v)):is(pl(v,v),ts(<1>suc,v))
-t2:=isless2(pl(v,v),ts(<1>suc,v),v,t1,satz18a(v,v)):less(v,ts(<1>suc,v))
-[w:nat][l:less(ts(v,v),ts(w,w))]
-t3:=satz10j(v,w,th3"l.imp"(moreis(v,w),moreis(ts(v,v),ts(w,w)),satz10h(ts(v,v),ts(w,w),l),[t:moreis(v,w)]satz36(v,w,v,w,t,t))):less(v,w)
-w@t4:=tris(nat,ts(pl(v,w),v),pl(ts(v,v),ts(w,v)),pl(ts(v,v),ts(v,w)),disttp1(v,w,v),ispl2(ts(w,v),ts(v,w),ts(v,v),comts(w,v))):is(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)))
-t5:=tr3is(nat,ts(pl(v,w),pl(v,w)),pl(ts(pl(v,w),v),ts(pl(v,w),w)),pl(pl(ts(v,v),ts(v,w)),pl(ts(v,w),ts(w,w))),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),disttp2(pl(v,w),v,w),ispl12(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)),ts(pl(v,w),w),pl(ts(v,w),ts(w,w)),t4,disttp1(v,w,w)),asspl2(pl(ts(v,v),ts(v,w)),ts(v,w),ts(w,w))):is(ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)))
-t6:=tris(nat,pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),pl(ts(v,w),ts(v,w))),pl(ts(v,v),ts(<1>suc,ts(v,w))),asspl1(ts(v,v),ts(v,w),ts(v,w)),ispl2(pl(ts(v,w),ts(v,w)),ts(<1>suc,ts(v,w)),ts(v,v),t1(ts(v,w)))):is(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))))
-nun:=tris(nat,ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),t5,ispl1(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w),t6)):is(ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)))
-nun1:=symis(nat,ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),nun):is(pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),ts(pl(v,w),pl(v,w)))
-prop1:=eq(tf(fr(w,v),fr(w,v)),fr(<1>suc,1)):'prop'
-v@prop2:=some([t:nat]prop1(t)):'prop'
-@prop3:=some([u:nat]prop2(u)):'prop'
-[p:prop3]
-y:=ind(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):nat
-t7:=oneax(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):min([u:nat]prop2(u),y)
-t8:=ande1(lb([u:nat]prop2(u),y),prop2(y),t7):lb([u:nat]prop2(u),y)
-t9:=ande2(lb([u:nat]prop2(u),y),prop2(y),t7):prop2(y)
-[x:nat][q:prop1(y,x)]
-t10:=treq1(fr(<1>suc,1),fr(ts(x,x),ts(y,y)),tf(fr(x,y),fr(x,y)),q,tfeq12a(x,y,x,y)):eq(fr(<1>suc,1),fr(ts(x,x),ts(y,y)))
-t11:=tr4is(nat,ts(<1>suc,ts(y,y)),ts(num(fr(<1>suc,1)),den(fr(ts(x,x),ts(y,y)))),ts(num(fr(ts(x,x),ts(y,y))),den(fr(<1>suc,1))),ts(ts(x,x),1),ts(x,x),12isnd(<1>suc,1,ts(x,x),ts(y,y)),t10,ndis12(ts(x,x),ts(y,y),<1>suc,1),satz28a(ts(x,x))):is(ts(<1>suc,ts(y,y)),ts(x,x))
-t12:=isless2(ts(<1>suc,ts(y,y)),ts(x,x),ts(y,y),t11,t2(ts(y,y))):less(ts(y,y),ts(x,x))
-t13:=isless1(ts(ts(<1>suc,y),y),ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)),tris(nat,ts(ts(<1>suc,y),y),ts(<1>suc,ts(y,y)),ts(x,x),assts1(<1>suc,y,y),t11),satz35c(ts(<1>suc,y),ts(<1>suc,y),y,ts(<1>suc,y),lessisi2(ts(<1>suc,y),ts(<1>suc,y),refis(nat,ts(<1>suc,y))),t2(y))):less(ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)))
-t14:=t3(y,x,t12):less(y,x)
-t15:=t3(x,ts(<1>suc,y),t13):less(x,ts(<1>suc,y))
-[u:nat][i:is(x,pl(y,u))]
-t16:=isless12(x,pl(y,u),ts(<1>suc,y),pl(y,y),i,symis(nat,pl(y,y),ts(<1>suc,y),t1(y)),t15):less(pl(y,u),pl(y,y))
-t17:=satz20f(u,y,y,t16):less(u,y)
-[t:nat][j:is(y,pl(u,t))]
-t18:=symis(nat,y,pl(u,t),j):is(pl(u,t),y)
-t19:=tris(nat,ts(x,x),ts(pl(y,u),pl(y,u)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ists12(x,pl(y,u),x,pl(y,u),i,i),nun(y,u)):is(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)))
-t20:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),ispl1(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t),t19),asspl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u),ts(t,t))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))))
-t21:=tr3is(nat,ts(y,u),ts(u,y),ts(u,pl(u,t)),pl(ts(u,u),ts(u,t)),comts(y,u),ists2(y,pl(u,t),u,j),disttp2(u,u,t)):is(ts(y,u),pl(ts(u,u),ts(u,t)))
-t22:=tris(nat,ts(<1>suc,ts(y,u)),ts(<1>suc,pl(ts(u,u),ts(u,t))),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ists2(ts(y,u),pl(ts(u,u),ts(u,t)),<1>suc,t21),disttp2(<1>suc,ts(u,u),ts(u,t))):is(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))))
-t23:=tris(nat,pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(y,y),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),ispl2(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ts(y,y),t22),asspl2(ts(y,y),ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))):is(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))))
-t24:=tr3is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),pl(pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),t20,ispl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t)),t23),asspl1(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))))
-t25:=tr4is(nat,pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),pl(pl(ts(<1>suc,ts(u,t)),ts(u,u)),ts(t,t)),pl(pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t)),ts(pl(u,t),pl(u,t)),ts(y,y),asspl2(ts(<1>suc,ts(u,t)),ts(u,u),ts(t,t)),ispl1(pl(ts(<1>suc,ts(u,t)),ts(u,u)),pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t),compl(ts(<1>suc,ts(u,t)),ts(u,u))),nun1(u,t),ists12(pl(u,t),y,pl(u,t),y,t18,t18)):is(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y))
-t26:=tr4is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),pl(ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u)))),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),t24,ispl2(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u))),t25),compl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),asspl2(ts(y,y),ts(y,y),ts(<1>suc,ts(u,u)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))))
-t27:=tris(nat,pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(y,y)),ts(x,x),t1(ts(y,y)),t11):is(pl(ts(y,y),ts(y,y)),ts(x,x))
-t28:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),pl(ts(x,x),ts(<1>suc,ts(u,u))),t26,ispl1(pl(ts(y,y),ts(y,y)),ts(x,x),ts(<1>suc,ts(u,u)),t27)):is(pl(ts(x,x),ts(t,t)),pl(ts(x,x),ts(<1>suc,ts(u,u))))
-t29:=satz20e(ts(t,t),ts(<1>suc,ts(u,u)),ts(x,x),t28):is(ts(t,t),ts(<1>suc,ts(u,u)))
-t30:=tr4is(nat,ts(num(fr(<1>suc,1)),den(fr(ts(t,t),ts(u,u)))),ts(<1>suc,ts(u,u)),ts(t,t),ts(ts(t,t),1),ts(num(fr(ts(t,t),ts(u,u))),den(fr(<1>suc,1))),ndis12(<1>suc,1,ts(t,t),ts(u,u)),symis(nat,ts(t,t),ts(<1>suc,ts(u,u)),t29),satz28e(ts(t,t)),12isnd(ts(t,t),ts(u,u),<1>suc,1)):eq(fr(<1>suc,1),fr(ts(t,t),ts(u,u)))
-t31:=treq2(tf(fr(t,u),fr(t,u)),fr(<1>suc,1),fr(ts(t,t),ts(u,u)),tfeq12a(t,u,t,u),t30):prop1(u,t)
-t32:=somei(nat,[v:nat]prop1(u,v),t,t31):prop2(u)
-t33:=<t32><u>t8:lessis(y,u)
-t34:=<t33>satz10g(y,u,satz12(u,y,t17)):con
-i@t35:=someapp(nat,[v:nat]diffprop(y,u,v),t17,con,[v:nat][w:diffprop(y,u,v)]t34(v,w)):con
-q@t36:=someapp(nat,[v:nat]diffprop(x,y,v),t14,con,[v:nat][w:diffprop(x,y,v)]t35(v,w)):con
-p@t37:=someapp(nat,[v:nat]prop1(y,v),t9,con,[v:nat][w:prop1(y,v)]t36(v,w)):con
--5162
-+*rt
-+5162
-@[x0:rat][i:is(ts(x0,x0),rtofn(<1>suc))][x:frac][xix0:inf(x,class(x0))]
-t38:=ise(ts(x0,x0),rtofn(<1>suc),tf(x,x),fr(<1>suc,1),tict(x0,x0,x,x,xix0,xix0),inclass(fr(<1>suc,1)),i):eq"n"(tf(x,x),fr(<1>suc,1))
-t39:=refeq1(fr(num(x),den(x)),x,fris(x)):eq"n"(fr(num(x),den(x)),x)
-t40:=eqtf12(fr(num(x),den(x)),x,fr(num(x),den(x)),x,t39,t39):eq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x))
-t41:=treq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x),fr(<1>suc,1),t40,t38):prop1"n.5162"(den(x),num(x))
-t42:=somei(nat,[t:nat]prop1"n.5162"(den(x),t),num(x),t41):prop2"n.5162"(den(x))
-t43:=somei(nat,[t:nat]prop2"n.5162"(t),den(x),t42):prop3"n.5162"
-t44:=t37"n.5162"(t43):con
-i@t45:=ratapp1(x0,con,[x:frac][t:inf(x,class(x0))]t44(x,t)):con
--5162
-+*rp
-+5162
-@ksi:=ind(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):cut
-t46:=oneax(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):is(ts(ksi,ksi),rpofnt(<1>suc))
-[r:ratrp(ksi)]
-x0:=rtofrp(ksi,r):rat
-t47:=tr3is(cut,rpofrt(ts"rt"(x0,x0)),ts(rpofrt(x0),rpofrt(x0)),ts(ksi,ksi),rpofnt(<1>suc),satz155c(x0,x0),ists12(rpofrt(x0),ksi,rpofrt(x0),ksi,isrprt2(ksi,r),isrprt2(ksi,r)),t46):is(rpofrt(ts"rt"(x0,x0)),rpofnt(<1>suc))
-t48:=isrtirp(ts"rt"(x0,x0),rtofn(<1>suc),t47):is"rt"(ts"rt"(x0,x0),rtofn(<1>suc))
-t49:=t45"rt.5162"(x0,t48):con
--5162
-@satz162:=somei(cut,[a:cut]irratrp(a),ksi".5162",[t:ratrp(ksi".5162")]t49".5162"(t)):some([a:cut]irratrp(a))
-[zeta:cut]
-sqrt:=ind(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):cut
-thsqrt1:=oneax(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):is(ts(sqrt(zeta),sqrt(zeta)),zeta)
-[ksi:cut][i:is(ts(ksi,ksi),zeta)]
-thsqrt2:=t20".5161"(zeta,ksi,sqrt,i,thsqrt1):is(ksi,sqrt)
-@[ksi:cut][eta:cut][i:is(ksi,eta)]
-issqrt:=isf(cut,cut,[t:cut]sqrt(t),ksi,eta,i):is(sqrt(ksi),sqrt(eta))
-@[ksi:cut][nx:natrp(ksi)][eta:cut][ny:natrp(eta)]
-+iiia
-x:=ntofrp(ksi,nx):nat
-y:=ntofrp(eta,ny):nat
-t1:=isrpnt1(ksi,nx):is(ksi,rpofnt(x))
-t2:=isrpnt1(eta,ny):is(eta,rpofnt(y))
-t3:=ispl12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(pl(ksi,eta),pl(rpofnt(x),rpofnt(y)))
-x0:=rtofn(x):rat
-y0:=rtofn(y):rat
-t4:=natrti(x):natrt(x0)
-t5:=natrti(y):natrt(y0)
-t6:=symis(cut,rpofrt(pl"rt"(x0,y0)),pl(rpofnt(x),rpofnt(y)),satz155a(x0,y0)):is(pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)))
-t7:=satz112d(x0,t4,y0,t5):natrt(pl"rt"(x0,y0))
-xpy:=nofrt(pl"rt"(x0,y0),t7):nat
-t8:=isrtn1(pl"rt"(x0,y0),t7):is"rt"(pl"rt"(x0,y0),rtofn(xpy))
-t9:=isrterp(pl"rt"(x0,y0),rtofn(xpy),t8):is(rpofrt(pl"rt"(x0,y0)),rpofnt(xpy))
-t10:=tr3is(cut,pl(ksi,eta),pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)),rpofnt(xpy),t3,t6,t9):is(pl(ksi,eta),rpofnt(xpy))
--iiia
-natpl:=somei(nat,[t:nat]is(pl(ksi,eta),rpofnt(t)),xpy".iiia",t10".iiia"):natrp(pl(ksi,eta))
-+*iiia
-ny@t11:=ists12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(ts(ksi,eta),ts(rpofnt(x),rpofnt(y)))
-t12:=symis(cut,rpofrt(ts"rt"(x0,y0)),ts(rpofnt(x),rpofnt(y)),satz155c(x0,y0)):is(ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)))
-t13:=satz112f(x0,t4,y0,t5):natrt(ts"rt"(x0,y0))
-xty:=nofrt(ts"rt"(x0,y0),t13):nat
-t14:=isrtn1(ts"rt"(x0,y0),t13):is"rt"(ts"rt"(x0,y0),rtofn(xty))
-t15:=isrterp(ts"rt"(x0,y0),rtofn(xty),t14):is(rpofrt(ts"rt"(x0,y0)),rpofnt(xty))
-t16:=tr3is(cut,ts(ksi,eta),ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)),rpofnt(xty),t11,t12,t15):is(ts(ksi,eta),rpofnt(xty))
--iiia
-ny@natts:=somei(nat,[t:nat]is(ts(ksi,eta),rpofnt(t)),xty".iiia",t16".iiia"):natrp(ts(ksi,eta))
-[m:more(ksi,eta)]
-+*iiia
-m@t17:=ismore12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2,m):more(rpofnt(x),rpofnt(y))
-t18:=satz154d(x0,y0,t17):more"rt"(x0,y0)
-t20:=ismn12(ksi,rpofnt(x),eta,rpofnt(y),m,satz154a(x0,y0,t18),t1,t2):is(mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)))
-t21:=symis(cut,rpofrt(mn"rt"(x0,y0,t18)),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),satz155b(x0,y0,t18)):is(mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)))
-t22:=satz112g(x0,t4,y0,t5,t18):natrt(mn"rt"(x0,y0,t18))
-xmy:=nofrt(mn"rt"(x0,y0,t18),t22):nat
-t23:=isrtn1(mn"rt"(x0,y0,t18),t22):is"rt"(mn"rt"(x0,y0,t18),rtofn(xmy))
-t24:=isrterp(mn"rt"(x0,y0,t18),rtofn(xmy),t23):is(rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy))
-t25:=tr3is(cut,mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy),t20,t21,t24):is(mn(ksi,eta,m),rpofnt(xmy))
--iiia
-m@natmn:=somei(nat,[t:nat]is(mn(ksi,eta,m),rpofnt(t)),xmy".iiia",t25".iiia"):natrp(mn(ksi,eta,m))
-@[p:cut][q:cut][r:cut]
-3pl13:=tr3is(cut,pl(p,pl(q,r)),pl(pl(q,r),p),pl(pl(r,q),p),pl(r,pl(q,p)),compl(p,pl(q,r)),ispl1(pl(q,r),pl(r,q),p,compl(q,r)),asspl1(r,q,p)):is(pl(p,pl(q,r)),pl(r,pl(q,p)))
-[s:cut]
-4pl24:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(s,pl(r,q))),pl(pl(p,s),pl(r,q)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(s,pl(r,q)),p,3pl13(q,r,s)),asspl2(p,s,pl(r,q))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,s),pl(r,q)))
-r@3pl12:=tr3is(cut,pl(p,pl(q,r)),pl(pl(p,q),r),pl(pl(q,p),r),pl(q,pl(p,r)),asspl2(p,q,r),ispl1(pl(p,q),pl(q,p),r,compl(p,q)),asspl1(q,p,r)):is(pl(p,pl(q,r)),pl(q,pl(p,r)))
-s@4pl23:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(r,pl(q,s))),pl(pl(p,r),pl(q,s)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(r,pl(q,s)),p,3pl12(q,r,s)),asspl2(p,r,pl(q,s))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,r),pl(q,s)))
-r@3pl23:=tr3is(cut,pl(pl(p,q),r),pl(p,pl(q,r)),pl(p,pl(r,q)),pl(pl(p,r),q),asspl1(p,q,r),ispl2(pl(q,r),pl(r,q),p,compl(q,r)),asspl2(p,r,q)):is(pl(pl(p,q),r),pl(pl(p,r),q))
-p@a2isapa:=tris(cut,ts(p,pl(1rp,1rp)),pl(ts(p,1rp),ts(p,1rp)),pl(p,p),disttp2(p,1rp,1rp),ispl12(ts(p,1rp),p,ts(p,1rp),p,satz151(p),satz151(p))):is(ts(p,pl(1rp,1rp)),pl(p,p))
-@dif:=pair1type(cut):'type'
-[a1:cut][a2:cut]
-df:=pair1(cut,a1,a2):dif
-@[a:dif]
-stm:=first1(cut,a):cut
-std:=second1(cut,a):cut
-a2@stmis:=first1is1(cut,a1,a2):is(stm(df(a1,a2)),a1)
-isstm:=first1is2(cut,a1,a2):is(a1,stm(df(a1,a2)))
-stdis:=second1is1(cut,a1,a2):is(std(df(a1,a2)),a2)
-isstd:=second1is2(cut,a1,a2):is(a2,std(df(a1,a2)))
-a@1a:=stm(a):cut
-2a:=std(a):cut
-dfis:=pair1is1(cut,a):is"e"(dif,df(1a,2a),a)
-isdf:=pair1is2(cut,a):is"e"(dif,a,df(1a,2a))
-a2@[b1:cut][b2:cut]
-12issmsd:=ispl12(a1,stm(df(a1,a2)),b2,std(df(b1,b2)),isstm(a1,a2),isstd(b1,b2)):is(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))))
-smsdis12:=symis(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),12issmsd):is(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2))
-a@[r1:cut][r2:cut]
-1sdissmsd:=ispl1(r1,stm(df(r1,r2)),2a,isstm(r1,r2)):is(pl(r1,2a),pl(stm(df(r1,r2)),2a))
-smsdis1sd:=symis(cut,pl(r1,2a),pl(stm(df(r1,r2)),2a),1sdissmsd):is(pl(stm(df(r1,r2)),2a),pl(r1,2a))
-sm2issmsd:=ispl2(r2,std(df(r1,r2)),1a,isstd(r1,r2)):is(pl(1a,r2),pl(1a,std(df(r1,r2))))
-smsdissm2:=symis(cut,pl(1a,r2),pl(1a,std(df(r1,r2))),sm2issmsd):is(pl(1a,std(df(r1,r2))),pl(1a,r2))
-a2@[r:cut][i:is(a1,r)]
-issm:=isf(cut,dif,[t:cut]df(t,a2),a1,r,i):is"e"(dif,df(a1,a2),df(r,a2))
-r@[i:is(a2,r)]
-issd:=isf(cut,dif,[t:cut]df(a1,t),a2,r,i):is"e"(dif,df(a1,a2),df(a1,r))
-b2@[i:is(a1,b1)][j:is(a2,b2)]
-issmsd:=tris(dif,df(a1,a2),df(b1,a2),df(b1,b2),issm(a1,a2,b1,i),issd(b1,a2,b2,j)):is"e"(dif,df(a1,a2),df(b1,b2))
-a@[b:dif]
-1b:=stm(b):cut
-2b:=std(b):cut
-eq:=is(pl(1a,2b),pl(1b,2a)):'prop'
-b2@[i:is(pl(a1,b2),pl(b1,a2))]
-eqi12:=tr3is(cut,pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),smsdis12(a1,a2,b1,b2),i,12issmsd(b1,b2,a1,a2)):eq(df(a1,a2),df(b1,b2))
-r2@[i:is(pl(1a,r2),pl(r1,2a))]
-eqi1:=isp(dif,[x:dif]eq(x,df(r1,r2)),df(1a,2a),a,eqi12(1a,2a,r1,r2,i),dfis):eq(a,df(r1,r2))
-r2@[i:is(pl(r1,2a),pl(1a,r2))]
-eqi2:=isp(dif,[x:dif]eq(df(r1,r2),x),df(1a,2a),a,eqi12(r1,r2,1a,2a,i),dfis):eq(df(r1,r2),a)
-b2@[e:eq(df(a1,a2),df(b1,b2))]
-eqe12:=tr3is(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),12issmsd(a1,a2,b1,b2),e,smsdis12(b1,b2,a1,a2)):is(pl(a1,b2),pl(b1,a2))
-a@satzd163:=refis(cut,pl(1a,2a)):eq(a,a)
-refeq:=satzd163:eq(a,a)
-b@[i:is"e"(dif,a,b)]
-refeq1:=isp(dif,[x:dif]eq(a,x),a,b,refeq,i):eq(a,b)
-refeq2:=isp(dif,[x:dif]eq(x,a),a,b,refeq,i):eq(b,a)
-b2@[i:is(a1,b1)][j:is(a2,b2)]
-eqsmsd:=refeq1(df(a1,a2),df(b1,b2),issmsd(i,j)):eq(df(a1,a2),df(b1,b2))
-r@[i:is(a1,r)]
-eqsm:=refeq1(df(a1,a2),df(r,a2),issm(i)):eq(df(a1,a2),df(r,a2))
-r@[i:is(a2,r)]
-eqsd:=refeq1(df(a1,a2),df(a1,r),issd(i)):eq(df(a1,a2),df(a1,r))
-b@[e:eq(a,b)]
-satzd164:=symis(cut,pl(1a,2b),pl(1b,2a),e):eq(b,a)
-symeq:=satzd164:eq(b,a)
-b@[c:dif]
-1c:=stm(c):cut
-2c:=std(c):cut
-[e:eq(a,b)][f:eq(b,c)]
-+1d165
-t1:=ispl12(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),e,f):is(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
-t2:=tr4is(cut,pl(pl(1a,2c),pl(1b,2b)),pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2b),pl(1b,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2c,1b,2b),t1,compl(pl(1b,2a),pl(1c,2b)),4pl24(1c,2b,1b,2a)):is(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
--1d165
-satzd165:=satz136b(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".1d165"):eq(a,c)
-treq:=satzd165:eq(a,c)
-c@[e:eq(c,a)][f:eq(c,b)]
-treq1:=treq(a,c,b,symeq(c,a,e),f):eq(a,b)
-c@[e:eq(a,c)][f:eq(b,c)]
-treq2:=treq(a,c,b,e,symeq(b,c,f)):eq(a,b)
-c@[d:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)]
-tr3eq:=treq(a,b,d,e1,treq(b,c,d,e2,e3)):eq(a,d)
-d@[e:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)][e4:eq(d,e)]
-tr4eq:=tr3eq(a,b,c,e,e1,e2,treq(c,d,e,e3,e4)):eq(a,e)
-a@posd:=more(1a,2a):'prop'
-zero:=is(1a,2a):'prop'
-negd:=less(1a,2a):'prop'
-a2@[m:more(a1,a2)]
-posdi:=ismore12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),m):posd(df(a1,a2))
-a2@[i:is(a1,a2)]
-zeroi:=tr3is(cut,stm(df(a1,a2)),a1,a2,std(df(a1,a2)),stmis(a1,a2),i,isstd(a1,a2)):zero(df(a1,a2))
-a2@[l:less(a1,a2)]
-negdi:=isless12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),l):negd(df(a1,a2))
-a@axrde:=satz123b(1a,2a):ec3(zero(a),posd(a),negd(a))
-axrdo:=satz123a(1a,2a):or3(zero(a),posd(a),negd(a))
-axrd:=orec3i(zero(a),posd(a),negd(a),axrdo,axrde):orec3(zero(a),posd(a),negd(a))
-[p:'prop'][p1:[t:posd(a)]p][p2:[t:zero(a)]p][p3:[t:negd(a)]p]
-rappd:=or3app(zero(a),posd(a),negd(a),p,axrdo,p2,p1,p3):p
-a@[p:posd(a)]
-pnot0d:=ec3e21(zero(a),posd(a),negd(a),axrde,p):not(zero(a))
-pnotnd:=ec3e23(zero(a),posd(a),negd(a),axrde,p):not(negd(a))
-a@[z:zero(a)]
-0notpd:=ec3e12(zero(a),posd(a),negd(a),axrde,z):not(posd(a))
-0notnd:=ec3e13(zero(a),posd(a),negd(a),axrde,z):not(negd(a))
-a@[n:negd(a)]
-nnotpd:=ec3e32(zero(a),posd(a),negd(a),axrde,n):not(posd(a))
-nnot0d:=ec3e31(zero(a),posd(a),negd(a),axrde,n):not(zero(a))
-b@[e:eq(a,b)][p:posd(a)]
-+iv1d
-t1:=ismore12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135a(1a,2a,2b,p)):more(pl(1b,2a),pl(2b,2a))
--iv1d
-eqposd:=satz136a(1b,2b,2a,t1".iv1d"):posd(b)
-e@[z:zero(a)]
-+*iv1d
-z@t2:=tr3is(cut,pl(1b,2a),pl(1a,2b),pl(2a,2b),pl(2b,2a),symeq(a,b,e),ispl1(1a,2a,2b,z),compl(2a,2b)):is(pl(1b,2a),pl(2b,2a))
--iv1d
-z@eqzero:=satz136b(1b,2b,2a,t2".iv1d"):zero(b)
-e@[n:negd(a)]
-+*iv1d
-n@t3:=isless12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135c(1a,2a,2b,n)):less(pl(1b,2a),pl(2b,2a))
--iv1d
-n@eqnegd:=satz136c(1b,2b,2a,t3".iv1d"):negd(b)
-b@[z:zero(a)][y:zero(b)]
-zeroeq:=tris(cut,pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl12(1a,2a,2b,1b,z,symis(cut,1b,2b,y)),compl(2a,1b)):eq(a,b)
-@[r:cut]
-pdofrp:=df(pl(r,1rp),1rp):dif
-ndofrp:=df(1rp,pl(r,1rp)):dif
-[s:cut][i:is(r,s)]
-isrpepd:=refeq1(pdofrp(r),pdofrp(s),isf(cut,dif,[x:cut]pdofrp(x),r,s,i)):eq(pdofrp(r),pdofrp(s))
-isrpend:=refeq1(ndofrp(r),ndofrp(s),isf(cut,dif,[x:cut]ndofrp(x),r,s,i)):eq(ndofrp(r),ndofrp(s))
-s@[e:eq(pdofrp(r),pdofrp(s))]
-+*iv1d
-e@t4:=satz136b(pl(r,1rp),pl(s,1rp),1rp,eqe12(pl(r,1rp),1rp,pl(s,1rp),1rp,e)):is(pl(r,1rp),pl(s,1rp))
--iv1d
-e@isrpipd:=satz136b(r,s,1rp,t4".iv1d"):is(r,s)
-s@[e:eq(ndofrp(r),ndofrp(s))]
-+*iv1d
-e@t5:=satz136e(pl(s,1rp),pl(r,1rp),1rp,eqe12(1rp,pl(r,1rp),1rp,pl(s,1rp),e)):is(pl(s,1rp),pl(r,1rp))
--iv1d
-e@isrpind:=symis(cut,s,r,satz136b(s,r,1rp,t5".iv1d")):is(r,s)
-r@posdirp:=posdi(pl(r,1rp),1rp,ismore1(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133(1rp,r))):posd(pdofrp(r))
-negdirp:=negdi(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):negd(ndofrp(r))
-a@[p:posd(a)]
-rpofpd:=mn(1a,2a,p):cut
-+*iv1d
-p@t6:=tr4is(cut,pl(1a,1rp),pl(pl(rpofpd,2a),1rp),pl(rpofpd,pl(2a,1rp)),pl(rpofpd,pl(1rp,2a)),pl(pl(rpofpd,1rp),2a),ispl1(1a,pl(rpofpd,2a),1rp,satz140f(1a,2a,p)),asspl1(rpofpd,2a,1rp),ispl2(pl(2a,1rp),pl(1rp,2a),rpofpd,compl(2a,1rp)),asspl2(rpofpd,1rp,2a)):is(pl(1a,1rp),pl(pl(rpofpd,1rp),2a))
--iv1d
-p@eqpdrp1:=eqi1(a,pl(rpofpd,1rp),1rp,t6".iv1d"):eq(a,pdofrp(rpofpd(a,p)))
-eqpdrp2:=symeq(a,pdofrp(rpofpd(a,p)),eqpdrp1):eq(pdofrp(rpofpd(a,p)),a)
-a@[n:negd(a)]
-rpofnd:=mn(2a,1a,satz122(1a,2a,n)):cut
-+*iv1d
-n@t7:=tr3is(cut,pl(1a,pl(rpofnd,1rp)),pl(pl(1a,rpofnd),1rp),pl(2a,1rp),pl(1rp,2a),asspl2(1a,rpofnd,1rp),ispl1(pl(1a,rpofnd),2a,1rp,satz140c(2a,1a,satz122(1a,2a,n))),compl(2a,1rp)):is(pl(1a,pl(rpofnd,1rp)),pl(1rp,2a))
--iv1d
-n@eqndrp1:=eqi1(a,1rp,pl(rpofnd,1rp),t7".iv1d"):eq(a,ndofrp(rpofnd(a,n)))
-eqndrp2:=symeq(a,ndofrp(rpofnd(a,n)),eqndrp1):eq(ndofrp(rpofnd(a,n)),a)
-@[h:dif][p:posd(h)][k:dif][q:posd(k)][e:eq(h,k)]
-+*iv1d
-e@t8:=tr3eq(pdofrp(rpofpd(h,p)),h,k,pdofrp(rpofpd(k,q)),eqpdrp2(h,p),e,eqpdrp1(k,q)):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
--iv1d
-e@eqpderp:=isrpipd(rpofpd(h,p),rpofpd(k,q),t8".iv1d"):is(rpofpd(h,p),rpofpd(k,q))
-q@[i:is(rpofpd(h,p),rpofpd(k,q))]
-+*iv1d
-i@t9:=isrpepd(rpofpd(h,p),rpofpd(k,q),i):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
--iv1d
-i@eqpdirp:=tr3eq(h,pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)),k,eqpdrp1(h,p),t9".iv1d",eqpdrp2(k,q)):eq(h,k)
-h@[n:negd(h)][k:dif][o:negd(k)][e:eq(h,k)]
-+*iv1d
-e@t10:=tr3eq(ndofrp(rpofnd(h,n)),h,k,ndofrp(rpofnd(k,o)),eqndrp2(h,n),e,eqndrp1(k,o)):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
--iv1d
-e@eqnderp:=isrpind(rpofnd(h,n),rpofnd(k,o),t10".iv1d"):is(rpofnd(h,n),rpofnd(k,o))
-o@[i:is(rpofnd(h,n),rpofnd(k,o))]
-+*iv1d
-i@t11:=isrpend(rpofnd(h,n),rpofnd(k,o),i):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
--iv1d
-i@eqndirp:=tr3eq(h,ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)),k,eqndrp1(h,n),t11".iv1d",eqndrp2(k,o)):eq(h,k)
-@[r:cut]
-+*iv1d
-r@t12:=eqpdrp1(pdofrp(r),posdirp(r)):eq(pdofrp(r),pdofrp(rpofpd(pdofrp(r),posdirp(r))))
--iv1d
-r@isrppd1:=isrpipd(r,rpofpd(pdofrp(r),posdirp(r)),t12".iv1d"):is(r,rpofpd(pdofrp(r),posdirp(r)))
-isrppd2:=symis(cut,r,rpofpd(pdofrp(r),posdirp(r)),isrppd1):is(rpofpd(pdofrp(r),posdirp(r)),r)
-+*iv1d
-r@t13:=eqndrp1(ndofrp(r),negdirp(r)):eq(ndofrp(r),ndofrp(rpofnd(ndofrp(r),negdirp(r))))
--iv1d
-r@isrpnd1:=isrpind(r,rpofnd(ndofrp(r),negdirp(r)),t13".iv1d"):is(r,rpofnd(ndofrp(r),negdirp(r)))
-isrpnd2:=symis(cut,r,rpofnd(ndofrp(r),negdirp(r)),isrpnd1):is(rpofnd(ndofrp(r),negdirp(r)),r)
-a2@[r:cut]
-lemmad1:=eqi12(a1,a2,pl(a1,r),pl(a2,r),tris(cut,pl(a1,pl(a2,r)),pl(a1,pl(r,a2)),pl(pl(a1,r),a2),ispl2(pl(a2,r),pl(r,a2),a1,compl(a2,r)),asspl2(a1,r,a2))):eq(df(a1,a2),df(pl(a1,r),pl(a2,r)))
-lemmad2:=symeq(df(a1,a2),df(pl(a1,r),pl(a2,r)),lemmad1):eq(df(pl(a1,r),pl(a2,r)),df(a1,a2))
-a@[r:cut]
-lemmad3:=treq(a,df(1a,2a),df(pl(1a,r),pl(2a,r)),refeq1(a,df(1a,2a),isdf),lemmad1(1a,2a,r)):eq(a,df(pl(1a,r),pl(2a,r)))
-lemmad4:=symeq(a,df(pl(1a,r),pl(2a,r)),lemmad3):eq(df(pl(1a,r),pl(2a,r)),a)
-a@absd:=ite(negd(a),dif,df(2a,1a),a):dif
-[n:negd(a)]
-absnd:=refeq1(absd(a),df(2a,1a),itet(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),df(2a,1a))
-a@[n:not(negd(a))]
-absnnd:=refeq1(absd(a),a,itef(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),a)
-a2@[l:less(a1,a2)]
-absdeql:=treq(absd(df(a1,a2)),df(std(df(a1,a2)),stm(df(a1,a2))),df(a2,a1),absnd(df(a1,a2),negdi(a1,a2,l)),eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2))):eq(absd(df(a1,a2)),df(a2,a1))
-a2@[m:moreis(a1,a2)]
-absdeqm:=absnnd(df(a1,a2),th3"l.imp"(negd(df(a1,a2)),less(a1,a2),satz123c(a1,a2,m),[t:negd(df(a1,a2))]isless12(stm(df(a1,a2)),a1,std(df(a1,a2)),a2,stmis(a1,a2),stdis(a1,a2),t))):eq(absd(df(a1,a2)),df(a1,a2))
-b@[e:eq(a,b)]
-+iv2d
-[n:negd(a)]
-t1:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
-t2:=tr3eq(absd(a),df(2a,1a),df(2b,1b),absd(b),absnd(a,n),eqi12(2a,1a,2b,1b,t1),symeq(absd(b),df(2b,1b),absnd(b,eqnegd(a,b,e,n)))):eq(absd(a),absd(b))
-e@[n:not(negd(a))]
-t3:=tr3eq(absd(a),a,b,absd(b),absnnd(a,n),e,symeq(absd(b),b,absnnd(b,th3"l.imp"(negd(b),negd(a),n,[t:negd(b)]eqnegd(b,a,symeq(a,b,e),t))))):eq(absd(a),absd(b))
--iv2d
-eqabsd:=th1"l.imp"(negd(a),eq(absd(a),absd(b)),[t:negd(a)]t2".iv2d"(t),[t:not(negd(a))]t3".iv2d"(t)):eq(absd(a),absd(b))
-a@[p:posd(a)]
-satzd166a:=eqposd(a,absd(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p))),p):posd(absd(a))
-a@[n:negd(a)]
-+2d166
-t1:=posdi(2a,1a,satz122(1a,2a,n)):posd(df(2a,1a))
--2d166
-satzd166b:=eqposd(df(2a,1a),absd(a),symeq(absd(a),df(2a,1a),absnd(a,n)),t1".2d166"):posd(absd(a))
-b@[p:posd(a)][q:posd(b)][e:eq(absd(a),absd(b))]
-satzd166c:=tr3eq(a,absd(a),absd(b),b,symeq(absd(a),a,absnnd(a,pnotnd(a,p))),e,absnnd(b,pnotnd(b,q))):eq(a,b)
-b@[n:negd(a)][o:negd(b)][e:eq(absd(a),absd(b))]
-+*2d166
-e@t2:=tr3eq(df(2a,1a),absd(a),absd(b),df(2b,1b),symeq(absd(a),df(2a,1a),absnd(a,n)),e,absnd(b,o)):eq(df(2a,1a),df(2b,1b))
--2d166
-e@satzd166d:=tr3is(cut,pl(1a,2b),pl(2b,1a),pl(2a,1b),pl(1b,2a),compl(1a,2b),symis(cut,pl(2a,1b),pl(2b,1a),eqe12(2a,1a,2b,1b,t2".2d166")),compl(2a,1b)):eq(a,b)
-a@[n:not(zero(a))]
-satzd166e:=rappd(a,posd(absd(a)),[t:posd(a)]satzd166a(a,t),th2"l.imp"(zero(a),posd(absd(a)),n),[t:negd(a)]satzd166b(a,t)):posd(absd(a))
-a@[z:zero(a)]
-satzd166f:=eqzero(a,absd(a),symeq(absd(a),a,absnnd(a,0notnd(a,z))),z):zero(absd(a))
-b@mored:=more(pl(1a,2b),pl(1b,2a)):'prop'
-b2@[m:more(pl(a1,b2),pl(b1,a2))]
-moredi12:=ismore12(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),12issmsd(a1,a2,b1,b2),12issmsd(b1,b2,a1,a2),m):mored(df(a1,a2),df(b1,b2))
-r2@[m:more(pl(1a,r2),pl(r1,2a))]
-moredi1:=ismore12(pl(1a,r2),pl(1a,std(df(r1,r2))),pl(r1,2a),pl(stm(df(r1,r2)),2a),sm2issmsd(a,r1,r2),1sdissmsd(a,r1,r2),m):mored(a,df(r1,r2))
-r2@[m:more(pl(r1,2a),pl(1a,r2))]
-moredi2:=ismore12(pl(r1,2a),pl(stm(df(r1,r2)),2a),pl(1a,r2),pl(1a,std(df(r1,r2))),1sdissmsd(a,r1,r2),sm2issmsd(a,r1,r2),m):mored(df(r1,r2),a)
-b2@[m:mored(df(a1,a2),df(b1,b2))]
-morede12:=ismore12(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),smsdis12(a1,a2,b1,b2),smsdis12(b1,b2,a1,a2),m):more(pl(a1,b2),pl(b1,a2))
-b@lessd:=less(pl(1a,2b),pl(1b,2a)):'prop'
-[m:mored(a,b)]
-lemmad5:=satz121(pl(1a,2b),pl(1b,2a),m):lessd(b,a)
-b@[l:lessd(a,b)]
-lemmad6:=satz122(pl(1a,2b),pl(1b,2a),l):mored(b,a)
-b2@[l:less(pl(a1,b2),pl(b1,a2))]
-lessdi12:=lemmad5(df(b1,b2),df(a1,a2),moredi12(b1,b2,a1,a2,satz122(pl(a1,b2),pl(b1,a2),l))):lessd(df(a1,a2),df(b1,b2))
-r2@[l:less(pl(1a,r2),pl(r1,2a))]
-lessdi1:=lemmad5(df(r1,r2),a,moredi2(a,r1,r2,satz122(pl(1a,r2),pl(r1,2a),l))):lessd(a,df(r1,r2))
-r2@[l:less(pl(r1,2a),pl(1a,r2))]
-lessdi2:=lemmad5(a,df(r1,r2),moredi1(a,r1,r2,satz122(pl(r1,2a),pl(1a,r2),l))):lessd(df(r1,r2),a)
-b2@[l:lessd(df(a1,a2),df(b1,b2))]
-lessde12:=satz121(pl(b1,a2),pl(a1,b2),morede12(b1,b2,a1,a2,lemmad6(df(a1,a2),df(b1,b2),l))):less(pl(a1,b2),pl(b1,a2))
-b@satzd167:=satz123(pl(1a,2b),pl(1b,2a)):orec3(eq(a,b),mored(a,b),lessd(a,b))
-satzd167a:=satz123a(pl(1a,2b),pl(1b,2a)):or3(eq(a,b),mored(a,b),lessd(a,b))
-satzd167b:=satz123b(pl(1a,2b),pl(1b,2a)):ec3(eq(a,b),mored(a,b),lessd(a,b))
-d@1d:=stm(d):cut
-2d:=std(d):cut
-[e:eq(a,b)][f:eq(c,d)][m:mored(a,c)]
-+*iv2d
-m@t4:=tr4is(cut,pl(pl(1b,2d),pl(1c,2a)),pl(pl(1b,2a),pl(1c,2d)),pl(pl(1a,2b),pl(1d,2c)),pl(pl(1a,2c),pl(1d,2b)),pl(pl(1d,2b),pl(1a,2c)),4pl24(1b,2d,1c,2a),ispl12(pl(1b,2a),pl(1a,2b),pl(1c,2d),pl(1d,2c),symeq(a,b,e),f),4pl24(1a,2b,1d,2c),compl(pl(1a,2c),pl(1d,2b))):is(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)))
-t5:=ismore2(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)),pl(pl(1b,2d),pl(1a,2c)),t4,satz135d(pl(1a,2c),pl(1c,2a),pl(1b,2d),m)):more(pl(pl(1b,2d),pl(1a,2c)),pl(pl(1d,2b),pl(1a,2c)))
--iv2d
-m@eqmored12:=satz136a(pl(1b,2d),pl(1d,2b),pl(1a,2c),t5".iv2d"):mored(b,d)
-f@[l:lessd(a,c)]
-eqlessd12:=lemmad5(d,b,eqmored12(c,d,a,b,f,e,lemmad6(a,c,l))):lessd(b,d)
-c@[e:eq(a,b)][m:mored(a,c)]
-eqmored1:=eqmored12(a,b,c,c,e,refeq(c),m):mored(b,c)
-e@[m:mored(c,a)]
-eqmored2:=eqmored12(c,c,a,b,refeq(c),e,m):mored(c,b)
-e@[l:lessd(a,c)]
-eqlessd1:=eqlessd12(a,b,c,c,e,refeq(c),l):lessd(b,c)
-e@[l:lessd(c,a)]
-eqlessd2:=eqlessd12(c,c,a,b,refeq(c),e,l):lessd(c,b)
-b@moreq:=or(mored(a,b),eq(a,b)):'prop'
-lesseq:=or(lessd(a,b),eq(a,b)):'prop'
-[m:moreq(a,b)]
-satzd168a:=th9"l.or"(mored(a,b),eq(a,b),lessd(b,a),eq(b,a),m,[t:mored(a,b)]lemmad5(a,b,t),[t:eq(a,b)]symeq(a,b,t)):lesseq(b,a)
-b@[l:lesseq(a,b)]
-satzd168b:=th9"l.or"(lessd(a,b),eq(a,b),mored(b,a),eq(b,a),l,[t:lessd(a,b)]lemmad6(a,b,t),[t:eq(a,b)]symeq(a,b,t)):moreq(b,a)
-c@[e:eq(a,b)][m:moreq(a,c)]
-eqmoreq1:=th9"l.or"(mored(a,c),eq(a,c),mored(b,c),eq(b,c),m,[t:mored(a,c)]eqmored1(a,b,c,e,t),[t:eq(a,c)]treq1(b,c,a,e,t)):moreq(b,c)
-e@[m:moreq(c,a)]
-eqmoreq2:=th9"l.or"(mored(c,a),eq(c,a),mored(c,b),eq(c,b),m,[t:mored(c,a)]eqmored2(a,b,c,e,t),[t:eq(c,a)]treq(c,a,b,t,e)):moreq(c,b)
-e@[l:lesseq(a,c)]
-eqlesseq1:=satzd168a(c,b,eqmoreq2(a,b,c,e,satzd168b(a,c,l))):lesseq(b,c)
-e@[l:lesseq(c,a)]
-eqlesseq2:=satzd168a(b,c,eqmoreq1(a,b,c,e,satzd168b(c,a,l))):lesseq(c,b)
-d@[e:eq(a,b)][f:eq(c,d)][m:moreq(a,c)]
-eqmoreq12:=eqmoreq1(a,b,d,e,eqmoreq2(c,d,a,f,m)):moreq(b,d)
-f@[l:lesseq(a,c)]
-eqlesseq12:=eqlesseq1(a,b,d,e,eqlesseq2(c,d,a,f,l)):lesseq(b,d)
-b@[m:mored(a,b)]
-moreqi1:=ori1(mored(a,b),eq(a,b),m):moreq(a,b)
-b@[l:lessd(a,b)]
-lesseqi1:=ori1(lessd(a,b),eq(a,b),l):lesseq(a,b)
-b@[e:eq(a,b)]
-moreqi2:=ori2(mored(a,b),eq(a,b),e):moreq(a,b)
-lesseqi2:=ori2(lessd(a,b),eq(a,b),e):lesseq(a,b)
-b@[m:moreq(a,b)]
-satzd167c:=th7"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,comor(mored(a,b),eq(a,b),m)):not(lessd(a,b))
-b@[l:lesseq(a,b)]
-satzd167d:=th9"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,l):not(mored(a,b))
-b@[n:not(mored(a,b))]
-satzd167e:=th2"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n):lesseq(a,b)
-b@[n:not(lessd(a,b))]
-satzd167f:=comor(eq(a,b),mored(a,b),th3"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n)):moreq(a,b)
-b@[m:mored(a,b)]
-satzd167g:=th3"l.imp"(lesseq(a,b),not(mored(a,b)),weli(mored(a,b),m),[t:lesseq(a,b)]satzd167d(t)):not(lesseq(a,b))
-b@[l:lessd(a,b)]
-satzd167h:=th3"l.imp"(moreq(a,b),not(lessd(a,b)),weli(lessd(a,b),l),[t:moreq(a,b)]satzd167c(t)):not(moreq(a,b))
-b@[n:not(moreq(a,b))]
-satzd167j:=or3e3(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th5"l.or"(mored(a,b),eq(a,b),n),th4"l.or"(mored(a,b),eq(a,b),n)):lessd(a,b)
-b@[n:not(lesseq(a,b))]
-satzd167k:=or3e2(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th4"l.or"(lessd(a,b),eq(a,b),n),th5"l.or"(lessd(a,b),eq(a,b),n)):mored(a,b)
-b@[z:zero(b)][p:posd(a)]
-satzd169a:=ismore12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135a(1a,2a,1b,p)):mored(a,b)
-z@[m:mored(a,b)]
-satzd169b:=satz136d(1a,2a,2b,ismore12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),m)):posd(a)
-z@[n:negd(a)]
-satzd169c:=isless12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135c(1a,2a,1b,n)):lessd(a,b)
-z@[l:lessd(a,b)]
-satzd169d:=satz136f(1a,2a,2b,isless12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),l)):negd(a)
-+2d170
-z@[p:posd(a)]
-t1:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166a(a,p))):moreq(absd(a),b)
-z@[y:zero(a)]
-t2:=moreqi2(absd(a),b,treq(absd(a),a,b,absnnd(a,0notnd(a,y)),zeroeq(a,b,y,z))):moreq(absd(a),b)
-z@[n:negd(a)]
-t3:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166b(a,n))):moreq(absd(a),b)
--2d170
-z@satzd170:=rappd(a,moreq(absd(a),b),[t:posd(a)]t1".2d170"(t),[t:zero(a)]t2".2d170"(t),[t:negd(a)]t3".2d170"(t)):moreq(absd(a),b)
-c@[l:lessd(a,b)][k:lessd(b,c)]
-+2d171
-t1:=satz137a(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),l,k):less(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
-t2:=isless12(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1a,2c),pl(1b,2b)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2b,1b,2c),tris(cut,pl(pl(1b,2a),pl(1c,2b)),pl(pl(1b,2b),pl(1c,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1b,2a,1c,2b),compl(pl(1b,2b),pl(1c,2a))),t1):less(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
--2d171
-satzd171:=satz136c(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".2d171"):lessd(a,c)
-trlessd:=satzd171:lessd(a,c)
-c@[m:mored(a,b)][n:mored(b,c)]
-trmored:=lemmad6(c,a,trlessd(c,b,a,lemmad5(b,c,n),lemmad5(a,b,m))):mored(a,c)
-c@[l:lesseq(a,b)][k:lessd(b,c)]
-satzd172a:=orapp(lessd(a,b),eq(a,b),lessd(a,c),l,[t:lessd(a,b)]trlessd(t,k),[t:eq(a,b)]eqlessd1(b,a,c,symeq(a,b,t),k)):lessd(a,c)
-c@[l:lessd(a,b)][k:lesseq(b,c)]
-satzd172b:=orapp(lessd(b,c),eq(b,c),lessd(a,c),k,[t:lessd(b,c)]trlessd(l,t),[t:eq(b,c)]eqlessd2(b,c,a,t,l)):lessd(a,c)
-c@[m:moreq(a,b)][n:mored(b,c)]
-satzd172c:=lemmad6(c,a,satzd172b(c,b,a,lemmad5(b,c,n),satzd168a(a,b,m))):mored(a,c)
-c@[m:mored(a,b)][n:moreq(b,c)]
-satzd172d:=lemmad6(c,a,satzd172a(c,b,a,satzd168a(b,c,n),lemmad5(a,b,m))):mored(a,c)
-c@[l:lesseq(a,b)][k:lesseq(b,c)]
-+2d173
-[j:lessd(a,b)]
-t1:=lesseqi1(a,c,satzd172b(j,k)):lesseq(a,c)
-k@[e:eq(a,b)]
-t2:=eqlesseq1(b,a,c,symeq(a,b,e),k):lesseq(a,c)
--2d173
-satzd173:=orapp(lessd(a,b),eq(a,b),lesseq(a,c),l,[t:lessd(a,b)]t1".2d173"(t),[t:eq(a,b)]t2".2d173"(t)):lesseq(a,c)
-trlesseq:=satzd173:lesseq(a,c)
-c@[m:moreq(a,b)][n:moreq(b,c)]
-trmoreq:=satzd168b(c,a,trlesseq(c,b,a,satzd168a(b,c,n),satzd168a(a,b,m))):moreq(a,c)
-a@ratd:=[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))):'prop'
-irratd:=not(ratd(a)):'prop'
-b@[e:eq(a,b)][r:ratd(a)]
-+*iv2d
-r@[n:not(zero(b))]
-t6:=th3"l.imp"(zero(a),zero(b),n,[t:zero(a)]eqzero(a,b,e,t)):not(zero(a))
-t7:=eqpderp(absd(a),satzd166e(a,t6),absd(b),satzd166e(b,n),eqabsd(a,b,e)):is(rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)))
-t8:=isp(cut,[t:cut]ratrp(t),rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)),<t6>r,t7):ratrp(rpofpd(absd(b),satzd166e(b,n)))
--iv2d
-r@eqratd:=[t:not(zero(b))]t8".iv2d"(t):ratd(b)
-e@[i:irratd(a)]
-eqirratd:=th3"l.imp"(ratd(b),ratd(a),i,[t:ratd(b)]eqratd(b,a,symeq(a,b,e),t)):irratd(b)
-a@[z:zero(a)]
-ratdi0:=th2"l.r.imp"(not(zero(a)),[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))),weli(zero(a),z)):ratd(a)
-@[r:cut][i:irratrp(r)][x0:rat]
-+*iv2d
-x0@[s:ratrp(pl(r,rpofrt(x0)))][y0:rat][j:is(pl(r,rpofrt(x0)),rpofrt(y0))]
-t9:=tris(cut,pl(rpofrt(x0),r),pl(r,rpofrt(x0)),rpofrt(y0),compl(rpofrt(x0),r),j):is(pl(rpofrt(x0),r),rpofrt(y0))
-t10:=ismore1(pl(rpofrt(x0),r),rpofrt(y0),rpofrt(x0),t9,satz133(rpofrt(x0),r)):more(rpofrt(y0),rpofrt(x0))
-t11:=satz154d(y0,x0,t10):more"rt"(y0,x0)
-t12:=satz155b(y0,x0,t11):is(rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
-t13:=satz140g(rpofrt(y0),rpofrt(x0),r,satz154a(y0,x0,t11),t9):is(r,mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
-t14:=tris2(cut,r,rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)),t13,t12):is(r,rpofrt(mn"rt"(y0,x0,t11)))
-t15:=somei(rat,[x:rat]is(r,rpofrt(x)),mn"rt"(y0,x0,t11),t14):ratrp(r)
-s@t16:=someapp(rat,[x:rat]is(pl(r,rpofrt(x0)),rpofrt(x)),s,con,[x:rat][t:is(pl(r,rpofrt(x0)),rpofrt(x))]<t15(x,t)>i):con
--iv2d
-x0@remark1:=[t:ratrp(pl(r,rpofrt(x0)))]t16".iv2d"(t):irratrp(pl(r,rpofrt(x0)))
-+*iv2d
-r@rp:=pdofrp(r):dif
-rn:=ndofrp(r):dif
-t17:=posdirp(r):posd(rp)
-t18:=pnot0d(rp,t17):not(zero(rp))
-t19:=nnot0d(rn,negdirp(r)):not(zero(rn))
-[n:not(zero(rp))]
-t20:=tris2(cut,r,rpofpd(absd(rp),satzd166e(rp,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rp),satzd166e(rp,n),rp,t17,absnnd(rp,pnotnd(rp,t17)))):is(r,rpofpd(absd(rp),satzd166e(rp,n)))
-r@t21:=treq(absd(rn),df(std(rn),stm(rn)),rp,absnd(rn,negdirp(r)),eqsmsd(std(rn),stm(rn),pl(r,1rp),1rp,stdis(1rp,pl(r,1rp)),stmis(1rp,pl(r,1rp)))):eq(absd(rn),rp)
-[n:not(zero(rn))]
-t22:=tris2(cut,r,rpofpd(absd(rn),satzd166e(rn,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rn),satzd166e(rn,n),rp,t17,t21)):is(r,rpofpd(absd(rn),satzd166e(rn,n)))
-r@[s:cut][i:is(r,s)][rr:ratrp(r)]
-t23:=isp(cut,[x:cut]ratrp(x),r,s,rr,i):ratrp(s)
-i@[rs:ratrp(s)]
-t24:=isp1(cut,[x:cut]ratrp(x),s,r,rs,i):ratrp(r)
--iv2d
-r@[rr:ratrp(r)]
-remark2a:=[t:not(zero(pdofrp(r)))]t23".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t)),t20".iv2d"(t),rr):ratd(pdofrp(r))
-remark2b:=t17".iv2d":posd(pdofrp(r))
-remark3a:=[t:not(zero(ndofrp(r)))]t23".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t)),t22".iv2d"(t),rr):ratd(ndofrp(r))
-remark3b:=negdirp(r):negd(ndofrp(r))
-r@[i:irratrp(r)]
-remark4a:=th3"l.imp"(ratd(pdofrp(r)),ratrp(r),i,[t:ratd(pdofrp(r))]t24".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t18".iv2d")),t20".iv2d"(t18".iv2d"),<t18".iv2d">t)):irratd(pdofrp(r))
-remark4b:=t17".iv2d":posd(pdofrp(r))
-remark5a:=th3"l.imp"(ratd(ndofrp(r)),ratrp(r),i,[t:ratd(ndofrp(r))]t24".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t19".iv2d")),t22".iv2d"(t19".iv2d"),<t19".iv2d">t)):irratd(ndofrp(r))
-remark5b:=negdirp(r):negd(ndofrp(r))
-a@natd:=and(posd(a),[t:posd(a)]natrp(rpofpd(a,t))):'prop'
-[n:natd(a)]
-natposd:=ande1(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):posd(a)
-natderp:=ande2"l.r"(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):natrp(rpofpd(a,natposd(a,n)))
-b@[e:eq(a,b)][n:natd(a)]
-+*iv2d
-n"rp"@t25:=eqposd(a,b,e,natposd(a,n)):posd(b)
-[p:posd(b)]
-t26:=eqpderp(a,natposd(a,n),b,p,e):is(rpofpd(a,natposd(a,n)),rpofpd(b,p))
-t27:=isp(cut,[t:cut]natrp(t),rpofpd(a,natposd(a,n)),rpofpd(b,p),natderp(a,n),t26):natrp(rpofpd(b,p))
--iv2d
-n@eqnatd:=andi(posd(b),[t:posd(b)]natrp(rpofpd(b,t)),t25".iv2d",[t:posd(b)]t27".iv2d"(t)):natd(b)
-@[x:nat]
-pdofnt:=pdofrp(rpofnt(x)):dif
-+*iv2d
-x@t28:=posdirp(rpofnt(x)):posd(pdofnt(x))
-[p:posd(pdofnt(x))]
-t29:=isrppd1(rpofnt(x)):is(rpofnt(x),rpofpd(pdofnt(x),t28))
-t30:=eqpderp(pdofnt(x),t28,pdofnt(x),p,refeq(pdofnt(x))):is(rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p))
-t31:=tris(cut,rpofnt(x),rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p),t29,t30):is(rpofnt(x),rpofpd(pdofnt(x),p))
-t32:=isp(cut,[t:cut]natrp(t),rpofnt(x),rpofpd(pdofnt(x),p),natrpi(x),t31):natrp(rpofpd(pdofnt(x),p))
--iv2d
-x@natdi:=andi(posd(pdofnt(x)),[t:posd(pdofnt(x))]natrp(rpofpd(pdofnt(x),t)),t28".iv2d",[t:posd(pdofnt(x))]t32".iv2d"(t)):natd(pdofnt(x))
-a@intd:=or(zero(a),natd(absd(a))):'prop'
-b@[e:eq(a,b)][i:intd(a)]
-+*iv2d
-i"rp"@[z:zero(a)]
-t33:=eqzero(a,b,e,z):zero(b)
-i"rp"@[n:natd(absd(a))]
-t34:=eqnatd(absd(a),absd(b),eqabsd(a,b,e),n):natd(absd(b))
--iv2d
-i@eqintd:=th9"l.or"(zero(a),natd(absd(a)),zero(b),natd(absd(b)),i,[t:zero(a)]t33".iv2d"(t),[t:natd(absd(a))]t34".iv2d"(t)):intd(b)
-a@[n:natd(a)]
-+*iv2d
-n"rp"@t34a:=symeq(absd(a),a,absnnd(a,pnotnd(a,natposd(a,n)))):eq(a,absd(a))
-t35:=eqnatd(a,absd(a),t34a,n):natd(absd(a))
--iv2d
-n@natintd:=ori2(zero(a),natd(absd(a)),t35".iv2d"):intd(a)
-a@[p:posd(a)][i:intd(a)]
-+*iv2d
-i"rp"@t36:=ore2(zero(a),natd(absd(a)),i,pnot0d(a,p)):natd(absd(a))
--iv2d
-i@posintnatd:=eqnatd(absd(a),a,absnnd(a,pnotnd(a,p)),t36".iv2d"):natd(a)
-a@[z:zero(a)]
-intdi0:=ori1(zero(a),natd(absd(a)),z):intd(a)
-r@[n:natrp(r)]
-+*iv2d
-n"rp"@t37:=posdirp(r):posd(pdofrp(r))
-[p:posd(pdofrp(r))]
-t38:=tris(cut,r,rpofpd(pdofrp(r),t37),rpofpd(pdofrp(r),p),isrppd1(r),eqpderp(pdofrp(r),t37,pdofrp(r),p,refeq(pdofrp(r)))):is(r,rpofpd(pdofrp(r),p))
-t39:=isp(cut,[t:cut]natrp(t),r,rpofpd(pdofrp(r),p),n,t38):natrp(rpofpd(pdofrp(r),p))
--iv2d
-n@remark6a:=andi(posd(pdofrp(r)),[t:posd(pdofrp(r))]natrp(rpofpd(pdofrp(r),t)),t37".iv2d",[t:posd(pdofrp(r))]t39".iv2d"(t)):natd(pdofrp(r))
-remark6:=natintd(pdofrp(r),remark6a):intd(pdofrp(r))
-+*iv2d
-n"rp"@t40:=absdeql(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):eq(absd(ndofrp(r)),pdofrp(r))
-t41:=eqnatd(pdofrp(r),absd(ndofrp(r)),symeq(absd(ndofrp(r)),pdofrp(r),t40),remark6a):natd(absd(ndofrp(r)))
--iv2d
-n@remark7:=ori2(zero(ndofrp(r)),natd(absd(ndofrp(r))),t41".iv2d"):intd(ndofrp(r))
-a@[i:intd(a)]
-+2d174
-[n:not(zero(a))]
-t1:=ore2(zero(a),natd(absd(a)),i,n):natd(absd(a))
-t2:=ande2(posd(absd(a)),[t:posd(absd(a))]natrp(rpofpd(absd(a),t)),t1):[t:posd(absd(a))]natrp(rpofpd(absd(a),t))
-t3:=lemmaiii5(rpofpd(absd(a),satzd166e(a,n)),<satzd166e(a,n)>t2):ratrp(rpofpd(absd(a),satzd166e(a,n)))
--2d174
-satzd174:=[t:not(zero(a))]t3".2d174"(t):ratd(a)
-b@pd:=df(pl(1a,1b),pl(2a,2b)):dif
-b2@pd12:=issmsd(pl(stm(df(a1,a2)),stm(df(b1,b2))),pl(std(df(a1,a2)),std(df(b1,b2))),pl(a1,b1),pl(a2,b2),ispl12(stm(df(a1,a2)),a1,stm(df(b1,b2)),b1,stmis(a1,a2),stmis(b1,b2)),ispl12(std(df(a1,a2)),a2,std(df(b1,b2)),b2,stdis(a1,a2),stdis(b1,b2))):is"e"(dif,pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
-r2@pd1:=issmsd(pl(1a,stm(df(r1,r2))),pl(2a,std(df(r1,r2))),pl(1a,r1),pl(2a,r2),ispl2(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl2(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
-pd2:=issmsd(pl(stm(df(r1,r2)),1a),pl(std(df(r1,r2)),2a),pl(r1,1a),pl(r2,2a),ispl1(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl1(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
-b2@pdeq12a:=refeq1(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
-pdeq12b:=refeq2(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(df(pl(a1,b1),pl(a2,b2)),pd(df(a1,a2),df(b1,b2)))
-r2@pdeq1a:=refeq1(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
-pdeq1b:=refeq2(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(df(pl(1a,r1),pl(2a,r2)),pd(a,df(r1,r2)))
-pdeq2a:=refeq1(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
-pdeq2b:=refeq2(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(df(pl(r1,1a),pl(r2,2a)),pd(df(r1,r2),a))
-b@satzd175:=eqsmsd(pl(1a,1b),pl(2a,2b),pl(1b,1a),pl(2b,2a),compl(1a,1b),compl(2a,2b)):eq(pd(a,b),pd(b,a))
-compd:=satzd175:eq(pd(a,b),pd(b,a))
-c@[e:eq(a,b)]
-+iv3d
-t1:=tr3is(cut,pl(pl(1a,1c),pl(2b,2c)),pl(pl(1a,2b),pl(1c,2c)),pl(pl(1b,2a),pl(1c,2c)),pl(pl(1b,1c),pl(2a,2c)),4pl23(1a,1c,2b,2c),ispl1(pl(1a,2b),pl(1b,2a),pl(1c,2c),e),4pl23(1b,2a,1c,2c)):is(pl(pl(1a,1c),pl(2b,2c)),pl(pl(1b,1c),pl(2a,2c)))
--iv3d
-eqpd1:=eqi12(pl(1a,1c),pl(2a,2c),pl(1b,1c),pl(2b,2c),t1".iv3d"):eq(pd(a,c),pd(b,c))
-eqpd2:=tr3eq(pd(c,a),pd(a,c),pd(b,c),pd(c,b),compd(c,a),eqpd1,compd(b,c)):eq(pd(c,a),pd(c,b))
-d@[e:eq(a,b)][f:eq(c,d)]
-eqpd12:=treq(pd(a,c),pd(b,c),pd(b,d),eqpd1(a,b,c,e),eqpd2(c,d,b,f)):eq(pd(a,c),pd(b,d))
-b@[z:zero(a)]
-+*iv3d
-z@t2:=tr4is(cut,pl(pl(1a,1b),2b),pl(1a,pl(1b,2b)),pl(2a,pl(2b,1b)),pl(pl(2a,2b),1b),pl(1b,pl(2a,2b)),asspl1(1a,1b,2b),ispl12(1a,2a,pl(1b,2b),pl(2b,1b),z,compl(1b,2b)),asspl2(2a,2b,1b),compl(pl(2a,2b),1b)):is(pl(pl(1a,1b),2b),pl(1b,pl(2a,2b)))
--iv3d
-z@pd01:=eqi2(b,pl(1a,1b),pl(2a,2b),t2".iv3d"):eq(pd(a,b),b)
-b@[z:zero(b)]
-pd02:=treq(pd(a,b),pd(b,a),a,compd(a,b),pd01(b,a,z)):eq(pd(a,b),a)
-b@[p:posd(a)][q:posd(b)]
-ppd:=posdi(pl(1a,1b),pl(2a,2b),satz137(1a,2a,1b,2b,p,q)):posd(pd(a,b))
-b@[n:negd(a)][o:negd(b)]
-npd:=negdi(pl(1a,1b),pl(2a,2b),satz137a(1a,2a,1b,2b,n,o)):negd(pd(a,b))
-a@m0d:=df(2a,1a):dif
-a2@m0deqa:=eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2)):eq(m0d(df(a1,a2)),df(a2,a1))
-m0deqb:=symeq(m0d(df(a1,a2)),df(a2,a1),m0deqa):eq(df(a2,a1),m0d(df(a1,a2)))
-b@[e:eq(a,b)]
-+*iv3d
-e@t3:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
--iv3d
-e@eqm0d:=eqi12(2a,1a,2b,1b,t3".iv3d"):eq(m0d(a),m0d(b))
-a@[p:posd(a)]
-satzd176a:=negdi(2a,1a,satz121(1a,2a,p)):negd(m0d(a))
-a@[z:zero(a)]
-satzd176b:=zeroi(2a,1a,symis(cut,1a,2a,z)):zero(m0d(a))
-a@[n:negd(a)]
-satzd176c:=posdi(2a,1a,satz122(1a,2a,n)):posd(m0d(a))
-a@[n:negd(m0d(a))]
-satzd176d:=satz122(2a,1a,isless12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),n)):posd(a)
-a@[z:zero(m0d(a))]
-satzd176e:=symis(cut,2a,1a,tr3is(cut,2a,stm(df(2a,1a)),std(df(2a,1a)),1a,isstm(2a,1a),z,stdis(2a,1a))):zero(a)
-a@[p:posd(m0d(a))]
-satzd176f:=satz121(2a,1a,ismore12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),p)):negd(a)
-a@[z:zero(a)]
-m0d0:=zeroeq(m0d(a),a,satzd176b(a,z),z):eq(m0d(a),a)
-+3d177
-a@t1:=tris(dif,m0d(m0d(a)),df(1a,2a),a,issmsd(std(m0d(a)),stm(m0d(a)),1a,2a,stdis(2a,1a),stmis(2a,1a)),dfis(a)):is"e"(dif,m0d(m0d(a)),a)
--3d177
-a@satzd177:=refeq1(m0d(m0d(a)),a,t1".3d177"):eq(m0d(m0d(a)),a)
-satzd177a:=symeq(m0d(m0d(a)),a,satzd177):eq(a,m0d(m0d(a)))
-b@[e:eq(a,m0d(b))]
-satzd177b:=treq(m0d(a),m0d(m0d(b)),b,eqm0d(a,m0d(b),e),satzd177(b)):eq(m0d(a),b)
-satzd177c:=symeq(m0d(a),b,satzd177b):eq(b,m0d(a))
-b@[e:eq(m0d(a),b)]
-satzd177d:=satzd177c(b,a,symeq(m0d(a),b,e)):eq(a,m0d(b))
-satzd177e:=symeq(a,m0d(b),satzd177d):eq(m0d(b),a)
-+3d178
-a@[p:posd(a)]
-t1:=tr3eq(absd(m0d(a)),m0d(m0d(a)),a,absd(a),absnd(m0d(a),satzd176a(a,p)),satzd177(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p)))):eq(absd(m0d(a)),absd(a))
-a@[z:zero(a)]
-t2:=tr3eq(absd(m0d(a)),m0d(a),a,absd(a),absnnd(m0d(a),0notnd(m0d(a),satzd176b(a,z))),m0d0(a,z),symeq(absd(a),a,absnnd(a,0notnd(a,z)))):eq(absd(m0d(a)),absd(a))
-a@[n:negd(a)]
-t3:=treq(absd(m0d(a)),m0d(a),absd(a),absnnd(m0d(a),pnotnd(m0d(a),satzd176c(a,n))),symeq(absd(a),m0d(a),absnd(a,n))):eq(absd(m0d(a)),absd(a))
--3d178
-a@satzd178:=rappd(a,eq(absd(m0d(a)),absd(a)),[t:posd(a)]t1".3d178"(t),[t:zero(a)]t2".3d178"(t),[t:negd(a)]t3".3d178"(t)):eq(absd(m0d(a)),absd(a))
-satzd178a:=symeq(absd(m0d(a)),absd(a),satzd178):eq(absd(a),absd(m0d(a)))
-+3d179
-t1:=pdeq1b(a,2a,1a):eq(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)))
-t2:=zeroi(pl(1a,2a),pl(2a,1a),compl(1a,2a)):zero(df(pl(1a,2a),pl(2a,1a)))
--3d179
-satzd179:=eqzero(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)),t1".3d179",t2".3d179"):zero(pd(a,m0d(a)))
-satzd179a:=eqzero(pd(a,m0d(a)),pd(m0d(a),a),compd(a,m0d(a)),satzd179):zero(pd(m0d(a),a))
-b@satzd180:=treq(m0d(pd(a,b)),df(pl(2a,2b),pl(1a,1b)),pd(m0d(a),m0d(b)),m0deqa(pl(1a,1b),pl(2a,2b)),pdeq12b(2a,1a,2b,1b)):eq(m0d(pd(a,b)),pd(m0d(a),m0d(b)))
-satzd180a:=symeq(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180):eq(pd(m0d(a),m0d(b)),m0d(pd(a,b)))
-md:=pd(a,m0d(b)):dif
-b2@mdeq12a:=treq(md(df(a1,a2),df(b1,b2)),pd(df(a1,a2),df(b2,b1)),df(pl(a1,b2),pl(a2,b1)),eqpd2(m0d(df(b1,b2)),df(b2,b1),df(a1,a2),m0deqa(b1,b2)),pdeq12a(a1,a2,b2,b1)):eq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)))
-mdeq12b:=symeq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)),mdeq12a):eq(df(pl(a1,b2),pl(a2,b1)),md(df(a1,a2),df(b1,b2)))
-r2@mdeq1a:=treq(md(a,df(r1,r2)),pd(a,df(r2,r1)),df(pl(1a,r2),pl(2a,r1)),eqpd2(m0d(df(r1,r2)),df(r2,r1),a,m0deqa(r1,r2)),pdeq1a(a,r2,r1)):eq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)))
-mdeq1b:=symeq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)),mdeq1a):eq(df(pl(1a,r2),pl(2a,r1)),md(a,df(r1,r2)))
-mdeq2a:=pdeq12a(r1,r2,2a,1a):eq(md(df(r1,r2),a),df(pl(r1,2a),pl(r2,1a)))
-mdeq2b:=pdeq12b(r1,r2,2a,1a):eq(df(pl(r1,2a),pl(r2,1a)),md(df(r1,r2),a))
-c@[e:eq(a,b)]
-eqmd1:=eqpd1(a,b,m0d(c),e):eq(md(a,c),md(b,c))
-eqmd2:=eqpd2(m0d(a),m0d(b),c,eqm0d(a,b,e)):eq(md(c,a),md(c,b))
-d@[e:eq(a,b)][f:eq(c,d)]
-eqmd12:=treq(md(a,c),md(b,c),md(b,d),eqmd1(a,b,c,e),eqmd2(c,d,b,f)):eq(md(a,c),md(b,d))
-b@satzd181:=tr3eq(m0d(md(a,b)),pd(m0d(a),m0d(m0d(b))),pd(m0d(a),b),md(b,a),satzd180(a,m0d(b)),eqpd2(m0d(m0d(b)),b,m0d(a),satzd177(b)),compd(m0d(a),b)):eq(m0d(md(a,b)),md(b,a))
-satzd181a:=symeq(m0d(md(b,a)),md(a,b),satzd181(b,a)):eq(md(a,b),m0d(md(b,a)))
-+3d182
-t1:=treq(md(a,b),df(pl(1a,2b),pl(2a,1b)),df(pl(1a,2b),pl(1b,2a)),pdeq1a(a,2b,1b),eqsd(pl(1a,2b),pl(2a,1b),pl(1b,2a),compl(2a,1b))):eq(md(a,b),df(pl(1a,2b),pl(1b,2a)))
-t2:=symeq(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1):eq(df(pl(1a,2b),pl(1b,2a)),md(a,b))
-t3:=stmis(pl(1a,2b),pl(1b,2a)):is(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b))
-t4:=stdis(pl(1a,2b),pl(1b,2a)):is(std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a))
--3d182
-[p:posd(md(a,b))]
-+*3d182
-p@t5:=eqposd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,p):posd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-p@satzd182a:=ismore12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t5".3d182"):mored(a,b)
-b@[z:zero(md(a,b))]
-+*3d182
-z@t6:=eqzero(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,z):zero(df(pl(1a,2b),pl(1b,2a)))
--3d182
-z@satzd182b:=tr3is(cut,pl(1a,2b),stm(df(pl(1a,2b),pl(1b,2a))),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),isstm(pl(1a,2b),pl(1b,2a)),t6".3d182",t4".3d182"):eq(a,b)
-b@[n:negd(md(a,b))]
-+*3d182
-n@t7:=eqnegd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,n):negd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-n@satzd182c:=isless12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t7".3d182"):lessd(a,b)
-b@[m:mored(a,b)]
-+*3d182
-m@t8:=posdi(pl(1a,2b),pl(1b,2a),m):posd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-m@satzd182d:=eqposd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t8".3d182"):posd(md(a,b))
-b@[e:eq(a,b)]
-+*3d182
-e@t9:=zeroi(pl(1a,2b),pl(1b,2a),e):zero(df(pl(1a,2b),pl(1b,2a)))
--3d182
-e@satzd182e:=eqzero(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t9".3d182"):zero(md(a,b))
-b@[l:lessd(a,b)]
-+*3d182
-l@t10:=negdi(pl(1a,2b),pl(1b,2a),l):negd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-l@satzd182f:=eqnegd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t10".3d182"):negd(md(a,b))
-+3d183
-b@t1:=tris(cut,pl(1a,2b),pl(2b,1a),pl(stm(m0d(b)),std(m0d(a))),compl(1a,2b),12issmsd(2b,1b,2a,1a)):is(pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))))
-t2:=t1(b,a):is(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))))
--3d183
-b@[m:mored(a,b)]
-satzd183a:=isless12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad5(a,b,m)):lessd(m0d(a),m0d(b))
-b@[e:eq(a,b)]
-staz183b:=eqm0d(a,b,e):eq(m0d(a),m0d(b))
-b@[l:lessd(a,b)]
-satzd183c:=ismore12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad6(a,b,l)):mored(m0d(a),m0d(b))
-b@[l:lessd(m0d(a),m0d(b))]
-satzd183d:=eqmored12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183c(m0d(a),m0d(b),l)):mored(a,b)
-b@[e:eq(m0d(a),m0d(b))]
-satzd183e:=tr3eq(a,m0d(m0d(a)),m0d(m0d(b)),b,satzd177a(a),eqm0d(m0d(a),m0d(b),e),satzd177(b)):eq(a,b)
-b@[m:mored(m0d(a),m0d(b))]
-satzd183f:=eqlessd12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183a(m0d(a),m0d(b),m)):lessd(a,b)
-+3d184
-a@t1:=tr3eq(a,df(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp))),df(pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp))),md(pdofrp(1a),pdofrp(2a)),lemmad3(a,pl(1rp,1rp)),eqsmsd(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp)),pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp)),asspl2(1a,1rp,1rp),3pl12(2a,1rp,1rp)),mdeq12b(pl(1a,1rp),1rp,pl(2a,1rp),1rp)):eq(a,md(pdofrp(1a),pdofrp(2a)))
-t2:=and3i(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))),posdirp(1a),posdirp(2a),t1):and3(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))))
-t3:=somei(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))),pdofrp(2a),t2):some"l"(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))))
--3d184
-a@satzd184:=somei(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))),pdofrp(1a),t3".3d184"):some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))))
-c@asspd1:=tr3eq(pd(pd(a,b),c),df(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c)),df(pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c))),pd(a,pd(b,c)),pdeq2a(c,pl(1a,1b),pl(2a,2b)),eqsmsd(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c),pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c)),asspl1(1a,1b,1c),asspl1(2a,2b,2c)),pdeq1b(a,pl(1b,1c),pl(2b,2c))):eq(pd(pd(a,b),c),pd(a,pd(b,c)))
-asspd2:=symeq(pd(pd(a,b),c),pd(a,pd(b,c)),asspd1):eq(pd(a,pd(b,c)),pd(pd(a,b),c))
-3pd23:=tr3eq(pd(pd(a,b),c),pd(a,pd(b,c)),pd(a,pd(c,b)),pd(pd(a,c),b),asspd1(a,b,c),eqpd2(pd(b,c),pd(c,b),a,compd(b,c)),asspd2(a,c,b)):eq(pd(pd(a,b),c),pd(pd(a,c),b))
-d@4pd23:=tr3eq(pd(pd(a,b),pd(c,d)),pd(pd(pd(a,b),c),d),pd(pd(pd(a,c),b),d),pd(pd(a,c),pd(b,d)),asspd2(pd(a,b),c,d),eqpd1(pd(pd(a,b),c),pd(pd(a,c),b),d,3pd23),asspd1(pd(a,c),b,d)):eq(pd(pd(a,b),pd(c,d)),pd(pd(a,c),pd(b,d)))
-b@pdmd:=treq(pd(md(a,b),b),pd(a,pd(m0d(b),b)),a,asspd1(a,m0d(b),b),pd02(a,pd(m0d(b),b),satzd179a(b))):eq(pd(md(a,b),b),a)
-mdpd:=treq(md(pd(a,b),b),pd(a,pd(b,m0d(b))),a,asspd1(a,b,m0d(b)),pd02(a,pd(b,m0d(b)),satzd179(b))):eq(md(pd(a,b),b),a)
-d@satzd185:=treq(pd(md(a,b),md(c,d)),pd(pd(a,c),pd(m0d(b),m0d(d))),md(pd(a,c),pd(b,d)),4pd23(a,m0d(b),c,m0d(d)),eqpd2(pd(m0d(b),m0d(d)),m0d(pd(b,d)),pd(a,c),satzd180a(b,d))):eq(pd(md(a,b),md(c,d)),md(pd(a,c),pd(b,d)))
-c@satzd186:=asspd1:eq(pd(pd(a,b),c),pd(a,pd(b,c)))
-b@satzd187a:=treq(pd(b,md(a,b)),pd(md(a,b),b),a,compd(b,md(a,b)),pdmd):eq(pd(b,md(a,b)),a)
-[x:dif][e:eq(pd(b,x),a)]
-satzd187c:=treq(md(a,b),md(pd(x,b),b),x,eqmd1(a,pd(x,b),b,treq1(a,pd(x,b),pd(b,x),e,compd(b,x))),mdpd(x,b)):eq(md(a,b),x)
-satzd187d:=symeq(md(a,b),x,satzd187c):eq(x,md(a,b))
-x@[e:eq(pd(x,b),a)]
-satzd187e:=satzd187c(treq(pd(b,x),pd(x,b),a,compd(b,x),e)):eq(md(a,b),x)
-satzd187f:=symeq(md(a,b),x,satzd187e):eq(x,md(a,b))
-+3d188
-c@t1:=tr3eq(md(pd(a,c),pd(b,c)),pd(pd(a,c),pd(m0d(b),m0d(c))),pd(md(a,b),md(c,c)),md(a,b),eqpd2(m0d(pd(b,c)),pd(m0d(b),m0d(c)),pd(a,c),satzd180(b,c)),4pd23(a,c,m0d(b),m0d(c)),pd02(md(a,b),md(c,c),satzd179(c))):eq(md(pd(a,c),pd(b,c)),md(a,b))
-t2:=symeq(md(pd(a,c),pd(b,c)),md(a,b),t1):eq(md(a,b),md(pd(a,c),pd(b,c)))
--3d188
-c@[m:mored(pd(a,c),pd(b,c))]
-+*3d188
-m@t3:=eqposd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182d(pd(a,c),pd(b,c),m)):posd(md(a,b))
--3d188
-m@satzd188a:=satzd182a(a,b,t3".3d188"):mored(a,b)
-c@[e:eq(pd(a,c),pd(b,c))]
-+*3d188
-e@t4:=eqzero(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182e(pd(a,c),pd(b,c),e)):zero(md(a,b))
--3d188
-e@satzd188b:=satzd182b(a,b,t4".3d188"):eq(a,b)
-c@[l:lessd(pd(a,c),pd(b,c))]
-+*3d188
-l@t5:=eqnegd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182f(pd(a,c),pd(b,c),l)):negd(md(a,b))
--3d188
-l@satzd188c:=satzd182c(a,b,t5".3d188"):lessd(a,b)
-c@[m:mored(a,b)]
-+*3d188
-m@t6:=eqposd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182d(a,b,m)):posd(md(pd(a,c),pd(b,c)))
--3d188
-m@satzd188d:=satzd182a(pd(a,c),pd(b,c),t6".3d188"):mored(pd(a,c),pd(b,c))
-c@[e:eq(a,b)]
-satzd188e:=eqpd1(a,b,c,e):eq(pd(a,c),pd(b,c))
-c@[l:lessd(a,b)]
-+*3d188
-l@t7:=eqnegd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182f(a,b,l)):negd(md(pd(a,c),pd(b,c)))
--3d188
-l@satzd188f:=satzd182c(pd(a,c),pd(b,c),t7".3d188"):lessd(pd(a,c),pd(b,c))
-c@[m:mored(pd(c,a),pd(c,b))]
-satzd188g:=satzd188a(eqmored12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),m)):mored(a,b)
-c@[e:eq(pd(c,a),pd(c,b))]
-satzd188h:=satzd188b(tr3eq(pd(a,c),pd(c,a),pd(c,b),pd(b,c),compd(a,c),e,compd(c,b))):eq(a,b)
-[l:lessd(pd(c,a),pd(c,b))]
-satzd188j:=satzd188c(eqlessd12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),l)):lessd(a,b)
-c@[m:mored(a,b)]
-satzd188k:=eqmored12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188d(m)):mored(pd(c,a),pd(c,b))
-c@[e:eq(a,b)]
-satzd188l:=eqpd2(a,b,c,e):eq(pd(c,a),pd(c,b))
-c@[l:lessd(a,b)]
-satzd188m:=eqlessd12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188f(l)):lessd(pd(c,a),pd(c,b))
-d@[e:eq(a,b)][m:mored(c,d)]
-satzd188n:=eqmored2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188k(c,d,a,m)):mored(pd(a,c),pd(b,d))
-satzd188o:=eqmored12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188n):mored(pd(c,a),pd(d,b))
-e@[l:lessd(c,d)]
-satzd188p:=eqlessd2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188m(c,d,a,l)):lessd(pd(a,c),pd(b,d))
-satzd188q:=eqlessd12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188p):lessd(pd(c,a),pd(d,b))
-d@[m:mored(a,b)][n:mored(c,d)]
-satzd189:=trmored(pd(a,c),pd(b,c),pd(b,d),satzd188d(a,b,c,m),satzd188k(c,d,b,n)):mored(pd(a,c),pd(b,d))
-d@[l:lessd(a,b)][k:lessd(c,d)]
-satzd189a:=lemmad5(pd(b,d),pd(a,c),satzd189(b,a,d,c,lemmad6(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
-d@[m:moreq(a,b)][n:mored(c,d)]
-satzd190a:=orapp(mored(a,b),eq(a,b),mored(pd(a,c),pd(b,d)),m,[t:mored(a,b)]satzd189(t,n),[t:eq(a,b)]satzd188n(t,n)):mored(pd(a,c),pd(b,d))
-d@[m:mored(a,b)][n:moreq(c,d)]
-satzd190b:=eqmored12(pd(c,a),pd(a,c),pd(d,b),pd(b,d),compd(c,a),compd(d,b),satzd190a(c,d,a,b,n,m)):mored(pd(a,c),pd(b,d))
-d@[l:lesseq(a,b)][k:lessd(c,d)]
-satzd190c:=lemmad5(pd(b,d),pd(a,c),satzd190a(b,a,d,c,satzd168b(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
-d@[l:lessd(a,b)][k:lesseq(c,d)]
-satzd190d:=lemmad5(pd(b,d),pd(a,c),satzd190b(b,a,d,c,lemmad6(a,b,l),satzd168b(c,d,k))):lessd(pd(a,c),pd(b,d))
-d@[m:moreq(a,b)][n:moreq(c,d)]
-+3d191
-[e:eq(a,b)][f:eq(c,d)]
-t1:=moreqi2(pd(a,c),pd(b,d),eqpd12(a,b,c,d,e,f)):moreq(pd(a,c),pd(b,d))
-e@[o:mored(c,d)]
-t2:=moreqi1(pd(a,c),pd(b,d),satzd190a(m,o)):moreq(pd(a,c),pd(b,d))
-e@t3:=orapp(mored(c,d),eq(c,d),moreq(pd(a,c),pd(b,d)),n,[t:mored(c,d)]t2(t),[t:eq(c,d)]t1(t)):moreq(pd(a,c),pd(b,d))
-n@[o:mored(a,b)]
-t4:=moreqi1(pd(a,c),pd(b,d),satzd190b(o,n)):moreq(pd(a,c),pd(b,d))
--3d191
-satzd191:=orapp(mored(a,b),eq(a,b),moreq(pd(a,c),pd(b,d)),m,[t:mored(a,b)]t4".3d191"(t),[t:eq(a,b)]t3".3d191"(t)):moreq(pd(a,c),pd(b,d))
-d@[l:lesseq(a,b)][k:lesseq(c,d)]
-satzd191a:=satzd168a(pd(b,d),pd(a,c),satzd191(b,a,d,c,satzd168b(a,b,l),satzd168b(c,d,k))):lesseq(pd(a,c),pd(b,d))
-b@td:=df(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))):dif
-+iv4d
-a2@[r:cut]
-t1:=ists1(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(stm(df(a1,a2)),r),ts(a1,r))
-t2:=ists2(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(r,stm(df(a1,a2))),ts(r,a1))
-t3:=ists1(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(std(df(a1,a2)),r),ts(a2,r))
-t4:=ists2(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(r,std(df(a1,a2))),ts(r,a2))
-[s:cut]
-t5:=ispl12(ts(stm(df(a1,a2)),r),ts(a1,r),ts(std(df(a1,a2)),s),ts(a2,s),t1(r),t3(s)):is(pl(ts(stm(df(a1,a2)),r),ts(std(df(a1,a2)),s)),pl(ts(a1,r),ts(a2,s)))
-t6:=ispl12(ts(r,stm(df(a1,a2))),ts(r,a1),ts(s,std(df(a1,a2))),ts(s,a2),t2(r),t4(s)):is(pl(ts(r,stm(df(a1,a2))),ts(s,std(df(a1,a2)))),pl(ts(r,a1),ts(s,a2)))
-t7:=ispl12(ts(std(df(a1,a2)),r),ts(a2,r),ts(stm(df(a1,a2)),s),ts(a1,s),t3(r),t1(s)):is(pl(ts(std(df(a1,a2)),r),ts(stm(df(a1,a2)),s)),pl(ts(a2,r),ts(a1,s)))
-t8:=ispl12(ts(r,std(df(a1,a2))),ts(r,a2),ts(s,stm(df(a1,a2))),ts(s,a1),t4(r),t2(s)):is(pl(ts(r,std(df(a1,a2))),ts(s,stm(df(a1,a2)))),pl(ts(r,a2),ts(s,a1)))
-b2@t9:=tris(cut,pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,stm(df(b1,b2))),ts(a2,std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),t5(a1,a2,stm(df(b1,b2)),std(df(b1,b2))),t6(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)))
-t10:=tris(cut,pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,std(df(b1,b2))),ts(a2,stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)),t5(a1,a2,std(df(b1,b2)),stm(df(b1,b2))),t8(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)))
--iv4d
-b2@td12:=issmsd(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1)),t9".iv4d",t10".iv4d"):is"e"(dif,td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
-r2@td1:=issmsd(pl(ts(1a,stm(df(r1,r2))),ts(2a,std(df(r1,r2)))),pl(ts(1a,std(df(r1,r2))),ts(2a,stm(df(r1,r2)))),pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1)),t6".iv4d"(r1,r2,1a,2a),t8".iv4d"(r1,r2,1a,2a)):is"e"(dif,td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
-td2:=issmsd(pl(ts(stm(df(r1,r2)),1a),ts(std(df(r1,r2)),2a)),pl(ts(stm(df(r1,r2)),2a),ts(std(df(r1,r2)),1a)),pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a)),t5".iv4d"(r1,r2,1a,2a),t5".iv4d"(r1,r2,2a,1a)):is"e"(dif,td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
-b2@tdeq12a:=refeq1(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
-tdeq12b:=refeq2(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td(df(a1,a2),df(b1,b2)))
-r2@tdeq1a:=refeq1(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
-tdeq1b:=refeq2(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td(a,df(r1,r2)))
-tdeq2a:=refeq1(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
-tdeq2b:=refeq2(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td(df(r1,r2),a))
-+4d194
-b@t1:=ispl12(ts(1a,1b),ts(1b,1a),ts(2a,2b),ts(2b,2a),comts(1a,1b),comts(2a,2b)):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1b,1a),ts(2b,2a)))
-t2:=tris(cut,pl(ts(1a,2b),ts(2a,1b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1b,2a),ts(2b,1a)),compl(ts(1a,2b),ts(2a,1b)),ispl12(ts(2a,1b),ts(1b,2a),ts(1a,2b),ts(2b,1a),comts(2a,1b),comts(1a,2b))):is(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,2a),ts(2b,1a)))
--4d194
-b@satzd194:=eqsmsd(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,1a),ts(2b,2a)),pl(ts(1b,2a),ts(2b,1a)),t1".4d194",t2".4d194"):eq(td(a,b),td(b,a))
-comtd:=satzd194:eq(td(a,b),td(b,a))
-c@[e:eq(a,b)]
-+*iv4d
-e@[r:cut]
-t11:=tr3is(cut,pl(ts(1a,r),ts(2b,r)),ts(pl(1a,2b),r),ts(pl(1b,2a),r),pl(ts(1b,r),ts(2a,r)),distpt1(1a,2b,r),ists1(pl(1a,2b),pl(1b,2a),r,e),disttp1(1b,2a,r)):is(pl(ts(1a,r),ts(2b,r)),pl(ts(1b,r),ts(2a,r)))
-e@t12:=tr3is(cut,pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,2c),ts(2a,2c))),pl(pl(ts(1b,1c),ts(2a,1c)),pl(ts(1a,2c),ts(2b,2c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))),4pl24(ts(1a,1c),ts(2a,2c),ts(1b,2c),ts(2b,1c)),ispl12(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,1c),ts(2a,1c)),pl(ts(1b,2c),ts(2a,2c)),pl(ts(1a,2c),ts(2b,2c)),t11(1c),t11(b,a,c,symeq(a,b,e),2c)),4pl24(ts(1b,1c),ts(2a,1c),ts(1a,2c),ts(2b,2c))):is(pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))))
--iv4d
-e@eqtd1:=eqi12(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)),pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)),t12".iv4d"):eq(td(a,c),td(b,c))
-eqtd2:=tr3eq(td(c,a),td(a,c),td(b,c),td(c,b),comtd(c,a),eqtd1,comtd(b,c)):eq(td(c,a),td(c,b))
-d@[e:eq(a,b)][f:eq(c,d)]
-eqtd12:=treq(td(a,c),td(b,c),td(b,d),eqtd1(a,b,c,e),eqtd2(c,d,b,f)):eq(td(a,c),td(b,d))
-b@[z:zero(a)]
-+4d192
-t1:=tris(cut,pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1a,2b),ts(2a,1b)),ispl12(ts(1a,1b),ts(2a,1b),ts(2a,2b),ts(1a,2b),ists1(1a,2a,1b,z),ists1(2a,1a,2b,symis(cut,1a,2a,z))),compl(ts(2a,1b),ts(1a,2b))):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
--4d192
-satzd192a:=zeroi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t1".4d192"):zero(td(a,b))
-b@[z:zero(b)]
-satzd192b:=eqzero(td(b,a),td(a,b),comtd(b,a),satzd192a(b,a,z)):zero(td(a,b))
-b@[z:zero(a)]
-td01:=satzd192a(z):zero(td(a,b))
-b@[z:zero(b)]
-td02:=satzd192b(z):zero(td(a,b))
-b@satzd197a:=tr3eq(td(m0d(a),b),df(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b))),df(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b))),m0d(td(a,b)),tdeq2a(b,2a,1a),eqsmsd(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b)),compl(ts(2a,1b),ts(1a,2b)),compl(ts(2a,2b),ts(1a,1b))),m0deqb(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))):eq(td(m0d(a),b),m0d(td(a,b)))
-satzd197b:=tr3eq(td(a,m0d(b)),td(m0d(b),a),m0d(td(b,a)),m0d(td(a,b)),comtd(a,m0d(b)),satzd197a(b,a),eqm0d(td(b,a),td(a,b),comtd(b,a))):eq(td(a,m0d(b)),m0d(td(a,b)))
-satzd197c:=treq2(td(m0d(a),b),td(a,m0d(b)),m0d(td(a,b)),satzd197a,satzd197b):eq(td(m0d(a),b),td(a,m0d(b)))
-satzd197d:=symeq(td(m0d(a),b),td(a,m0d(b)),satzd197c):eq(td(a,m0d(b)),td(m0d(a),b))
-satzd197e:=symeq(td(m0d(a),b),m0d(td(a,b)),satzd197a):eq(m0d(td(a,b)),td(m0d(a),b))
-satzd197f:=symeq(td(a,m0d(b)),m0d(td(a,b)),satzd197b):eq(m0d(td(a,b)),td(a,m0d(b)))
-satzd198:=treq(td(m0d(a),m0d(b)),td(a,m0d(m0d(b))),td(a,b),satzd197c(a,m0d(b)),eqtd2(m0d(m0d(b)),b,a,satzd177(b))):eq(td(m0d(a),m0d(b)),td(a,b))
-satzd198a:=symeq(td(m0d(a),m0d(b)),td(a,b),satzd198):eq(td(a,b),td(m0d(a),m0d(b)))
-[p:posd(a)][q:posd(b)]
-+*iv4d
-q@[r:cut]
-t13:=tris(cut,pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,pl(mn(1b,2b,q),2b)),ts(r,1b),distpt2(r,mn(1b,2b,q),2b),ists2(pl(mn(1b,2b,q),2b),1b,r,satz140e(1b,2b,q))):is(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b))
-[s:cut]
-t14:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),s),pl(ts(r,1b),s),asspl2(ts(r,mn(1b,2b,q)),ts(r,2b),s),ispl1(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b),s,t13)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s))
-t15:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s),pl(s,ts(r,1b)),t14,compl(ts(r,1b),s)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(s,ts(r,1b)))
-q@t16:=satz135h(pl(ts(1a,2b),ts(2a,2b)),pl(ts(2a,2b),ts(1a,2b)),ts(1a,mn(1b,2b,q)),ts(2a,mn(1b,2b,q)),compl(ts(1a,2b),ts(2a,2b)),satz145a(1a,2a,mn(1b,2b,q),p)):more(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))))
-t17:=ismore12(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))),pl(ts(1a,2b),ts(2a,1b)),t14(1a,ts(2a,2b)),t15(2a,ts(1a,2b)),t16):more(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
--iv4d
-q@ptdpp:=posdi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t17".iv4d"):posd(td(a,b))
-b@[p:posd(a)][n:negd(b)]
-+*iv4d
-n@t18:=eqposd(td(a,m0d(b)),m0d(td(a,b)),satzd197b(a,b),ptdpp(a,m0d(b),p,satzd176c(b,n))):posd(m0d(td(a,b)))
--iv4d
-n@ntdpn:=satzd176f(td(a,b),t18".iv4d"):negd(td(a,b))
-b@[n:negd(a)][p:posd(b)]
-ntdnp:=eqnegd(td(b,a),td(a,b),comtd(b,a),ntdpn(b,a,p,n)):negd(td(a,b))
-b@[n:negd(a)][o:negd(b)]
-ptdnn:=eqposd(td(m0d(a),m0d(b)),td(a,b),satzd198(a,b),ptdpp(m0d(a),m0d(b),satzd176c(a,n),satzd176c(b,o))):posd(td(a,b))
-b@[n:not(zero(a))][o:not(zero(b))]
-+*4d192
-o@[p:posd(a)][q:posd(b)]
-t2:=pnot0d(td(a,b),ptdpp(a,b,p,q)):not(zero(td(a,b)))
-p@[m:negd(b)]
-t3:=nnot0d(td(a,b),ntdpn(a,b,p,m)):not(zero(td(a,b)))
-p@t4:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t2(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t3(t)):not(zero(td(a,b)))
-o@[m:negd(a)][p:posd(b)]
-t5:=nnot0d(td(a,b),ntdnp(a,b,m,p)):not(zero(td(a,b)))
-m@[l:negd(b)]
-t6:=pnot0d(td(a,b),ptdnn(a,b,m,l)):not(zero(td(a,b)))
-m@t7:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t5(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t6(t)):not(zero(td(a,b)))
--4d192
-o@satzd192d:=rappd(a,not(zero(td(a,b))),[t:posd(a)]t4".4d192"(t),th2"l.imp"(zero(a),not(zero(td(a,b))),n),[t:negd(a)]t7".4d192"(t)):not(zero(td(a,b)))
-b@[z:zero(td(a,b))]
-+*4d192
-z@[n:not(zero(a))]
-t8:=et(zero(b),th3"l.imp"(not(zero(b)),not(zero(td(a,b))),weli(zero(td(a,b)),z),[t:not(zero(b))]satzd192d(n,t))):zero(b)
--4d192
-z@satzd192c:=[t:not(zero(a))]t8".4d192"(t):or(zero(a),zero(b))
-+4d193
-b@[p:posd(a)][q:posd(b)]
-t1:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdpp(a,b,p,q))),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-p@[n:negd(b)]
-t2:=treq(absd(td(a,b)),m0d(td(a,b)),td(a,m0d(b)),absnd(td(a,b),ntdpn(a,b,p,n)),satzd197f(a,b)):eq(absd(td(a,b)),td(a,m0d(b)))
-t3:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,m0d(b)),t2,eqtd12(absd(a),a,absd(b),m0d(b),absnnd(a,pnotnd(a,p)),absnd(b,n))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[z:zero(a)]
-t4:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td01(a,b,z)),td01(absd(a),absd(b),satzd166f(a,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[z:zero(b)]
-t5:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td02(a,b,z)),td02(absd(a),absd(b),satzd166f(b,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[n:negd(a)][p:posd(b)]
-t6:=tr3eq(absd(td(a,b)),absd(td(b,a)),td(absd(b),absd(a)),td(absd(a),absd(b)),eqabsd(td(a,b),td(b,a),comtd(a,b)),t3(b,a,p,n),comtd(absd(b),absd(a))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-n@[o:negd(b)]
-t7:=treq(td(absd(a),absd(b)),td(m0d(a),m0d(b)),td(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o)),satzd198(a,b)):eq(td(absd(a),absd(b)),td(a,b))
-t8:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdnn(a,b,n,o))),t7):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[p:posd(a)]
-t9:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t1(p,t),[t:zero(b)]t5(t),[t:negd(b)]t3(p,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[n:negd(a)]
-t10:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t6(n,t),[t:zero(b)]t5(t),[t:negd(b)]t8(n,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
--4d193
-b@satzd193:=rappd(a,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(a)]t9".4d193"(t),[t:zero(a)]t4".4d193"(t),[t:negd(a)]t10".4d193"(t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
-satzd103a:=symeq(absd(td(a,b)),td(absd(a),absd(b)),satzd193):eq(td(absd(a),absd(b)),absd(td(a,b)))
-@1df:=pdofrp(1rp):dif
-+4d195
-a@t1:=tris(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(ts(1a,pl(1rp,1rp)),pl(ts(2a,1rp),2a)),pl(pl(1a,1a),pl(2a,2a)),asspl1(ts(1a,pl(1rp,1rp)),ts(2a,1rp),2a),ispl12(ts(1a,pl(1rp,1rp)),pl(1a,1a),pl(ts(2a,1rp),2a),pl(2a,2a),a2isapa(1a),ispl1(ts(2a,1rp),2a,2a,satz151(2a)))):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(pl(1a,1a),pl(2a,2a)))
-t2:=tris(cut,pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,ts(1a,1rp)),ts(2a,pl(1rp,1rp))),pl(pl(1a,1a),pl(2a,2a)),asspl2(1a,ts(1a,1rp),ts(2a,pl(1rp,1rp))),ispl12(pl(1a,ts(1a,1rp)),pl(1a,1a),ts(2a,pl(1rp,1rp)),pl(2a,2a),ispl2(ts(1a,1rp),1a,1a,satz151(1a)),a2isapa(2a))):is(pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)))
-t3:=tris2(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)),t1,t2):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))))
--4d195
-a@satzd195:=treq(td(a,1df),df(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),a,tdeq1a(a,pl(1rp,1rp),1rp),eqi2(a,pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp))),t3".4d195")):eq(td(a,1df),a)
-satzd195a:=symeq(td(a,1df),a,satzd195):eq(a,td(a,1df))
-satzd195b:=treq(td(1df,a),td(a,1df),a,comtd(1df,a),satzd195):eq(td(1df,a),a)
-satzd195c:=symeq(td(1df,a),a,satzd195b):eq(a,td(1df,a))
-b@[p:posd(a)][q:posd(b)]
-satzd196a:=symeq(td(absd(a),absd(b)),td(a,b),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(td(a,b),td(absd(a),absd(b)))
-b@[n:negd(a)][o:negd(b)]
-satzd196b:=treq2(td(a,b),td(absd(a),absd(b)),td(m0d(a),m0d(b)),satzd198a(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o))):eq(td(a,b),td(absd(a),absd(b)))
-b@[p:posd(a)][n:negd(b)]
-satzd196c:=treq1(td(a,b),m0d(td(absd(a),absd(b))),td(absd(a),m0d(absd(b))),eqtd12(absd(a),a,m0d(absd(b)),b,absnnd(a,pnotnd(a,p)),satzd177b(absd(b),b,absnd(b,n))),satzd197b(absd(a),absd(b))):eq(td(a,b),m0d(td(absd(a),absd(b))))
-b@[n:negd(a)][p:posd(b)]
-satzd196d:=tr3eq(td(a,b),td(b,a),m0d(td(absd(b),absd(a))),m0d(td(absd(a),absd(b))),comtd(a,b),satzd196c(b,a,p,n),eqm0d(td(absd(b),absd(a)),td(absd(a),absd(b)),comtd(absd(b),absd(a)))):eq(td(a,b),m0d(td(absd(a),absd(b))))
-+4d196
-b@p1p2:=and(posd(a),posd(b)):'prop'
-p1n2:=and(posd(a),negd(b)):'prop'
-n1p2:=and(negd(a),posd(b)):'prop'
-n1n2:=and(negd(a),negd(b)):'prop'
--4d196
-b@[n:not(zero(a))][o:not(zero(b))][e:eq(td(a,b),td(absd(a),absd(b)))]
-+*4d196
-o@t1:=ptdpp(absd(a),absd(b),satzd166e(a,n),satzd166e(b,o)):posd(td(absd(a),absd(b)))
-e@t2:=pnotnd(td(a,b),eqposd(td(absd(a),absd(b)),td(a,b),symeq(td(a,b),td(absd(a),absd(b)),e),t1)):not(negd(td(a,b)))
-[p:posd(a)]
-t3:=th3"l.imp"(negd(b),negd(td(a,b)),t2,[t:negd(b)]ntdpn(a,b,p,t)):not(negd(b))
-t4:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t3,o):posd(b)
-t5:=andi(posd(a),posd(b),p,t4):p1p2
-t6:=ori1(p1p2,n1n2,t5):or(p1p2,n1n2)
-e@[m:negd(a)]
-t7:=th3"l.imp"(posd(b),negd(td(a,b)),t2,[t:posd(b)]ntdnp(a,b,m,t)):not(posd(b))
-t8:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t7):negd(b)
-t9:=andi(negd(a),negd(b),m,t8):n1n2
-t10:=ori2(p1p2,n1n2,t9):or(p1p2,n1n2)
--4d196
-e@satzd196e:=rappd(a,or(p1p2".4d196",n1n2".4d196"),[t:posd(a)]t6".4d196"(t),th2"l.imp"(zero(a),or(p1p2".4d196",n1n2".4d196"),n),[t:negd(a)]t10".4d196"(t)):or(and(posd(a),posd(b)),and(negd(a),negd(b)))
-o@[e:eq(td(a,b),m0d(td(absd(a),absd(b))))]
-+*4d196
-o@t11:=satzd176a(td(absd(a),absd(b)),t1):negd(m0d(td(absd(a),absd(b))))
-e@t12:=nnotpd(td(a,b),eqnegd(m0d(td(absd(a),absd(b))),td(a,b),symeq(td(a,b),m0d(td(absd(a),absd(b))),e),t11)):not(posd(td(a,b)))
-[p:posd(a)]
-t13:=th3"l.imp"(posd(b),posd(td(a,b)),t12,[t:posd(b)]ptdpp(a,b,p,t)):not(posd(b))
-t14:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t13):negd(b)
-t15:=andi(posd(a),negd(b),p,t14):p1n2
-t16:=ori1(p1n2,n1p2,t15):or(p1n2,n1p2)
-e@[m:negd(a)]
-t17:=th3"l.imp"(negd(b),posd(td(a,b)),t12,[t:negd(b)]ptdnn(a,b,m,t)):not(negd(b))
-t18:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t17,o):posd(b)
-t19:=andi(negd(a),posd(b),m,t18):n1p2
-t20:=ori2(p1n2,n1p2,t19):or(p1n2,n1p2)
--4d196
-e@satzd196f:=rappd(a,or(p1n2".4d196",n1p2".4d196"),[t:posd(a)]t16".4d196"(t),th2"l.imp"(zero(a),or(p1n2".4d196",n1p2".4d196"),n),[t:negd(a)]t20".4d196"(t)):or(and(posd(a),negd(b)),and(negd(a),posd(b)))
-+4d199
-@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
-t1:=tris(cut,ts(pl(ts(p,r),ts(q,s)),t),pl(ts(ts(p,r),t),ts(ts(q,s),t)),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),disttp1(ts(p,r),ts(q,s),t),ispl12(ts(ts(p,r),t),ts(p,ts(r,t)),ts(ts(q,s),t),ts(q,ts(s,t)),assts1(p,r,t),assts1(q,s,t))):is(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))))
-t2:=tris(cut,pl(ts(q,ts(s,t)),ts(q,ts(r,u))),pl(ts(q,ts(r,u)),ts(q,ts(s,t))),ts(q,pl(ts(r,u),ts(s,t))),compl(ts(q,ts(s,t)),ts(q,ts(r,u))),distpt2(q,ts(r,u),ts(s,t))):is(pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))))
-t3:=tr3is(cut,pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(pl(ts(p,ts(r,t)),ts(q,ts(s,t))),pl(ts(p,ts(s,u)),ts(q,ts(r,u)))),pl(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u)))),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))),ispl12(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),ts(pl(ts(p,s),ts(q,r)),u),pl(ts(p,ts(s,u)),ts(q,ts(r,u))),t1,t1(p,q,s,r,u,t)),4pl23(ts(p,ts(r,t)),ts(q,ts(s,t)),ts(p,ts(s,u)),ts(q,ts(r,u))),ispl12(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),ts(p,pl(ts(r,t),ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))),distpt2(p,ts(r,t),ts(s,u)),t2)):is(pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))))
--4d199
-c@satzd199:=tr3eq(td(td(a,b),c),df(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c))),df(pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c))))),td(a,td(b,c)),tdeq2a(c,pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))),eqsmsd(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c)),pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c)))),t3".4d199"(1a,2a,1b,2b,1c,2c),t3".4d199"(1a,2a,1b,2b,2c,1c)),tdeq1b(a,pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)))):eq(td(td(a,b),c),td(a,td(b,c)))
-asstd1:=satzd199:eq(td(td(a,b),c),td(a,td(b,c)))
-asstd2:=symeq(td(td(a,b),c),td(a,td(b,c)),satzd199):eq(td(a,td(b,c)),td(td(a,b),c))
-+4d201
-@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
-t1:=tris(cut,pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(p,t)),pl(ts(q,s),ts(q,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))),ispl12(ts(p,pl(r,t)),pl(ts(p,r),ts(p,t)),ts(q,pl(s,u)),pl(ts(q,s),ts(q,u)),disttp2(p,r,t),disttp2(q,s,u)),4pl23(ts(p,r),ts(p,t),ts(q,s),ts(q,u))):is(pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))))
--4d201
-satzd201:=tr3eq(td(a,pd(b,c)),df(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c)))),df(pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c)))),pd(td(a,b),td(a,c)),tdeq1a(a,pl(1b,1c),pl(2b,2c)),eqsmsd(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c))),pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c))),t1".4d201"(1a,2a,1b,2b,1c,2c),t1".4d201"(1a,2a,2b,1b,2c,1c)),pdeq12b(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)))):eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
-disttpd1:=tr3eq(td(pd(a,b),c),td(c,pd(a,b)),pd(td(c,a),td(c,b)),pd(td(a,c),td(b,c)),comtd(pd(a,b),c),satzd201(c,a,b),eqpd12(td(c,a),td(a,c),td(c,b),td(b,c),comtd(c,a),comtd(c,b))):eq(td(pd(a,b),c),pd(td(a,c),td(b,c)))
-disttpd2:=satzd201:eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
-distptd1:=symeq(td(pd(a,b),c),pd(td(a,c),td(b,c)),disttpd1):eq(pd(td(a,c),td(b,c)),td(pd(a,b),c))
-distptd2:=symeq(td(a,pd(b,c)),pd(td(a,b),td(a,c)),disttpd2):eq(pd(td(a,b),td(a,c)),td(a,pd(b,c)))
-satzd202:=treq(td(a,md(b,c)),pd(td(a,b),td(a,m0d(c))),md(td(a,b),td(a,c)),disttpd2(a,b,m0d(c)),eqpd2(td(a,m0d(c)),m0d(td(a,c)),td(a,b),satzd197b(a,c))):eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
-disttmd1:=treq(td(md(a,b),c),pd(td(a,c),td(m0d(b),c)),md(td(a,c),td(b,c)),disttpd1(a,m0d(b),c),eqpd2(td(m0d(b),c),m0d(td(b,c)),td(a,c),satzd197a(b,c))):eq(td(md(a,b),c),md(td(a,c),td(b,c)))
-disttmd2:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
-distmtd1:=symeq(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1):eq(md(td(a,c),td(b,c)),td(md(a,b),c))
-distmtd2:=symeq(td(a,md(b,c)),md(td(a,b),td(a,c)),disttmd2):eq(md(td(a,b),td(a,c)),td(a,md(b,c)))
-satzd200:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
-[m:mored(a,b)]
-+4d203
-t1:=satzd182d(a,b,m):posd(md(a,b))
--4d203
-[p:posd(c)]
-+*4d203
-p@t2:=eqposd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ptdpp(md(a,b),c,t1,p)):posd(md(td(a,c),td(b,c)))
--4d203
-p@satzd203a:=satzd182a(td(a,c),td(b,c),t2".4d203"):mored(td(a,c),td(b,c))
-m@[z:zero(c)]
-satzd203b:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
-m@[n:negd(c)]
-+*4d203
-n@t3:=eqnegd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ntdpn(md(a,b),c,t1,n)):negd(md(td(a,c),td(b,c)))
--4d203
-n@satzd203c:=satzd182c(td(a,c),td(b,c),t3".4d203"):lessd(td(a,c),td(b,c))
-p@satzd203d:=eqmored12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203a):mored(td(c,a),td(c,b))
-z@satzd203e:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
-n@satzd203f:=eqlessd12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203c):lessd(td(c,a),td(c,b))
-c@[l:lessd(a,b)][p:posd(c)]
-satzd203g:=lemmad5(td(b,c),td(a,c),satzd203a(b,a,c,lemmad6(a,b,l),p)):lessd(td(a,c),td(b,c))
-l@[z:zero(c)]
-satzd203h:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
-l@[n:negd(c)]
-satzd203j:=lemmad6(td(b,c),td(a,c),satzd203c(b,a,c,lemmad6(a,b,l),n)):mored(td(a,c),td(b,c))
-p@satzd203k:=lemmad5(td(c,b),td(c,a),satzd203d(b,a,c,lemmad6(a,b,l),p)):lessd(td(c,a),td(c,b))
-z@satzd203l:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
-n@satzd203m:=lemmad6(td(c,b),td(c,a),satzd203f(b,a,c,lemmad6(a,b,l),n)):mored(td(c,a),td(c,b))
-+*iv4d
-@[p:cut][q:cut]
-t19:=tris(cut,ts(q,pl(p,1rp)),pl(ts(q,p),ts(q,1rp)),pl(ts(q,p),q),disttp2(q,p,1rp),ispl2(ts(q,1rp),q,ts(q,p),satz151(q))):is(ts(q,pl(p,1rp)),pl(ts(q,p),q))
-[r:cut]
-t20:=tris(cut,pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(pl(ts(q,p),q),r),pl(ts(q,p),pl(q,r)),ispl12(ts(q,pl(p,1rp)),pl(ts(q,p),q),ts(r,1rp),r,t19,satz151(r)),asspl1(ts(q,p),q,r)):is(pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)))
-t21:=tr3is(cut,pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)),pl(ts(q,p),pl(r,q)),compl(ts(r,1rp),ts(q,pl(p,1rp))),t20,ispl2(pl(q,r),pl(r,q),ts(q,p),compl(q,r))):is(pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,p),pl(r,q)))
-a@[p:posd(a)]
-arp:=rpofpd(a,p):cut
-arpi:=ov(1rp,arp):cut
-ai:=pdofrp(arpi):dif
-t22:=tr3eq(td(a,ai),df(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp)))),df(pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a))),df(ts(1a,arpi),ts(2a,arpi)),tdeq1a(a,pl(arpi,1rp),1rp),eqsmsd(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp))),pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a)),t20(arpi,1a,2a),t21(arpi,2a,1a)),lemmad2(ts(1a,arpi),ts(2a,arpi),pl(1a,2a))):eq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)))
-t23:=tr3is(cut,ts(1a,arpi),ts(pl(2a,arp),arpi),pl(ts(2a,arpi),ts(arp,arpi)),pl(ts(2a,arpi),1rp),ists1(1a,pl(2a,arp),arpi,satz140d(1a,2a,p)),disttp1(2a,arp,arpi),ispl2(ts(arp,arpi),1rp,ts(2a,arpi),satz153c(1rp,arp))):is(ts(1a,arpi),pl(ts(2a,arpi),1rp))
-t24:=tr3is(cut,pl(ts(1a,arpi),1rp),pl(pl(ts(2a,arpi),1rp),1rp),pl(ts(2a,arpi),pl(1rp,1rp)),pl(pl(1rp,1rp),ts(2a,arpi)),ispl1(ts(1a,arpi),pl(ts(2a,arpi),1rp),1rp,t23),asspl1(ts(2a,arpi),1rp,1rp),compl(ts(2a,arpi),pl(1rp,1rp))):is(pl(ts(1a,arpi),1rp),pl(pl(1rp,1rp),ts(2a,arpi)))
-t25:=eqi12(ts(1a,arpi),ts(2a,arpi),pl(1rp,1rp),1rp,t24):eq(df(ts(1a,arpi),ts(2a,arpi)),1df)
-t26:=treq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)),1df,t22,t25):eq(td(a,ai),1df)
-t27:=somei(dif,[x:dif]eq(td(a,x),1df),ai,t26):some"l"(dif,[x:dif]eq(td(a,x),1df))
-a@[n:negd(a)]
-t28:=satzd176c(a,n):posd(m0d(a))
-[h:dif][e:eq(td(m0d(a),h),1df)]
-t29:=treq(td(a,m0d(h)),td(m0d(a),h),1df,satzd197d(a,h),e):eq(td(a,m0d(h)),1df)
-t30:=somei(dif,[x:dif]eq(td(a,x),1df),m0d(h),t29):some"l"(dif,[x:dif]eq(td(a,x),1df))
-n@t31:=someapp(dif,[x:dif]eq(td(m0d(a),x),1df),t27(m0d(a),t28),some"l"(dif,[x:dif]eq(td(a,x),1df)),[x:dif][t:eq(td(m0d(a),x),1df)]t30(x,t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
--iv4d
-a@[n:not(zero(a))]
-lemmad7:=rappd(a,some"l"(dif,[x:dif]eq(td(a,x),1df)),[t:posd(a)]t27".iv4d"(t),th2"l.imp"(zero(a),some"l"(dif,[x:dif]eq(td(a,x),1df)),n),[t:negd(a)]t31".iv4d"(t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
-b@[n:not(zero(b))][h:dif][k:dif][e:eq(td(b,h),a)][f:eq(td(b,k),a)]
-+4d204
-t1:=treq2(td(b,h),td(b,k),a,e,f):eq(td(b,h),td(b,k))
-t2:=eqzero(md(td(b,h),td(b,k)),td(b,md(h,k)),distmtd2(b,h,k),satzd182e(td(b,h),td(b,k),t1)):zero(td(b,md(h,k)))
-t3:=ore2(zero(b),zero(md(h,k)),satzd192c(b,md(h,k),t2),n):zero(md(h,k))
--4d204
-satzd204b:=satzd182b(h,k,t3".4d204"):eq(h,k)
-+*4d204
-n@[h:dif][e:eq(td(b,h),1df)]
-t4:=tr3eq(td(b,td(h,a)),td(td(b,h),a),td(1df,a),a,asstd2(b,h,a),eqtd1(td(b,h),1df,a,e),satzd195b(a)):eq(td(b,td(h,a)),a)
-t5:=somei(dif,[x:dif]eq(td(b,x),a),td(h,a),t4):some"l"(dif,[x:dif]eq(td(b,x),a))
--4d204
-n@satzd204a:=someapp(dif,[x:dif]eq(td(b,x),1df),lemmad7(b,n),some"l"(dif,[x:dif]eq(td(b,x),a)),[x:dif][t:eq(td(b,x),1df)]t5".4d204"(x,t)):some"l"(dif,[x:dif]eq(td(b,x),a))
-@[r:cut][s:cut][m:more(r,s)]
-+iv5d
-t1:=ismore12(pl(r,pl(1rp,1rp)),pl(pl(r,1rp),1rp),pl(s,pl(1rp,1rp)),pl(pl(s,1rp),1rp),asspl2(r,1rp,1rp),asspl2(s,1rp,1rp),satz134(r,s,pl(1rp,1rp),m)):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
--iv5d
-morerpepd:=moredi12(pl(r,1rp),1rp,pl(s,1rp),1rp,t1".iv5d"):mored(pdofrp(r),pdofrp(s))
-s@[m:mored(pdofrp(r),pdofrp(s))]
-+*iv5d
-m@t2:=morede12(pl(r,1rp),1rp,pl(s,1rp),1rp,m):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
--iv5d
-m@morerpipd:=satz136a(r,s,pl(1rp,1rp),ismore12(pl(pl(r,1rp),1rp),pl(r,pl(1rp,1rp)),pl(pl(s,1rp),1rp),pl(s,pl(1rp,1rp)),asspl1(r,1rp,1rp),asspl1(s,1rp,1rp),t2".iv5d")):more(r,s)
-s@[l:less(r,s)]
-lessrpepd:=lemmad5(pdofrp(s),pdofrp(r),morerpepd(s,r,satz122(r,s,l))):lessd(pdofrp(r),pdofrp(s))
-s@[l:lessd(pdofrp(r),pdofrp(s))]
-lessrpipd:=satz121(s,r,morerpipd(s,r,lemmad6(pdofrp(r),pdofrp(s),l))):less(r,s)
-+*iv5d
-@i:=1rp:cut
-2:=pl(i,i):cut
-r@rp1:=pl(r,i):cut
-s@sp1:=pl(s,i):cut
-rps:=pl(r,s):cut
-rs:=ts(r,s):cut
-t3:=tris(cut,pl(pl(rp1,sp1),i),pl(pl(rps,2),i),pl(pl(rps,i),2),ispl1(pl(rp1,sp1),pl(rps,2),i,4pl23(r,i,s,i)),3pl23(rps,2,i)):is(pl(pl(rp1,sp1),i),pl(pl(rps,i),2))
-t4:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(rp1,sp1),2),pdofrp(rps),pdeq12a(rp1,i,sp1,i),eqi12(pl(rp1,sp1),2,pl(rps,i),i,t3)):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(rps))
--iv5d
-s@lemmad8:=t4".iv5d":eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
-+*iv5d
-s@t5:=tris(cut,ts(r,sp1),pl(rs,ts(r,i)),pl(rs,r),disttp2(r,s,i),ispl2(ts(r,i),r,rs,satz151(r))):is(ts(r,sp1),pl(rs,r))
-t6:=tr4is(cut,ts(rp1,sp1),pl(ts(r,sp1),ts(i,sp1)),pl(pl(rs,r),sp1),pl(pl(pl(rs,r),s),i),pl(pl(rs,rps),i),disttp1(r,i,sp1),ispl12(ts(r,sp1),pl(rs,r),ts(i,sp1),sp1,t5,satz151b(sp1)),asspl2(pl(rs,r),s,i),ispl1(pl(pl(rs,r),s),pl(rs,rps),i,asspl1(rs,r,s))):is(ts(rp1,sp1),pl(pl(rs,rps),i))
-t7:=tr3is(cut,pl(ts(rp1,sp1),ts(i,i)),pl(pl(pl(rs,rps),i),i),pl(pl(rs,rps),2),pl(rs,pl(rps,2)),ispl12(ts(rp1,sp1),pl(pl(rs,rps),i),ts(i,i),i,t6,satz151(i)),asspl1(pl(rs,rps),i,i),asspl1(rs,rps,2)):is(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)))
-t8:=tris(cut,pl(ts(rp1,i),ts(i,sp1)),pl(rp1,sp1),pl(rps,2),ispl12(ts(rp1,i),rp1,ts(i,sp1),sp1,satz151(rp1),satz151b(sp1)),4pl23(r,i,s,i)):is(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2))
-t9:=tris(cut,pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,i),pl(rps,2)),pl(pl(rs,pl(rps,2)),i),ispl2(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2),pl(rs,i),t8),3pl23(rs,i,pl(rps,2))):is(pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i))
-t10:=tris2(cut,pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i),ispl1(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)),i,t7),t9):is(pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))))
-t11:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1))),pdofrp(rs),tdeq12a(rp1,i,sp1,i),eqi12(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1)),pl(rs,i),i,t10)):eq(td(pdofrp(r),pdofrp(s)),pdofrp(rs))
--iv5d
-s@lemmad9:=t11".iv5d":eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
-@[r:cut][s0:set(cut)]
-in:=esti(cut,r,s0):'prop'
-@[s0:set(cut)][t0:set(cut)][p0:all([x:cut]or(in(x,s0),in(x,t0)))][p1a:nonempty(cut,s0)][p1b:nonempty(cut,t0)][p2:all([x:cut][t:in(x,s0)]all([y:cut][u:in(y,t0)]less(x,y)))]
-+5p205
-t0@[r:cut]
-prop1:=all([x:cut][t:less(x,r)]in(x,s0)):'prop'
-prop2:=all([x:cut][t:more(x,r)]in(x,t0)):'prop'
-prop3:=and(prop1,prop2):'prop'
-p2@[r1:cut][r2:cut][pr1:prop3(r1)][pr2:prop3(r2)]
-t1:=ande2(prop1(r1),prop2(r1),pr1):prop2(r1)
-t2:=ande1(prop1(r2),prop2(r2),pr2):prop1(r2)
-[l:less(r1,r2)][x0:rat]
-rx:=rpofrt(x0):cut
-[l1:less(r1,rx)][l2:less(rx,r2)]
-t3:=<l2><rx>t2:in(rx,s0)
-t4:=<satz122(r1,rx,l1)><rx>t1:in(rx,t0)
-t5:=<refis(cut,rx)>ec3e31(is(rx,rx),more(rx,rx),less(rx,rx),satz123b(rx,rx),<t4><rx><t3><rx>p2):con
-l@t6:=satz159app(r1,r2,l,con,[x:rat][t:less(r1,rpofrt(x))][u:less(rpofrt(x),r2)]t5(x,t,u)):con
-pr2@t7:=[t:less(r1,r2)]t6(t):not(less(r1,r2))
-t8:=[t:more(r1,r2)]t6(r2,r1,pr2,pr1,satz121(r1,r2,t)):not(more(r1,r2))
-t9:=or3e1(is(r1,r2),more(r1,r2),less(r1,r2),satz123a(r1,r2),t8,t7):is(r1,r2)
-p2@t10:=[x:cut][y:cut][t:prop3(x)][u:prop3(y)]t9(x,y,t,u):amone(cut,[x:cut]prop3(x))
-[x0:rat]
-schnittprop:=some([y:cut]and(in(y,s0),lrt(y,x0))):'prop'
-p2@schnittset:=setof(rat,[x:rat]schnittprop(x)):set(rat)
-[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)]
-t11:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
-t12:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t11):schnittprop(x0)
-t13:=estii(rat,[x:rat]schnittprop(x),x0,t12):in"rt"(x0,schnittset)
-r@[i:in(r,t0)][x0:rat][ux:urt(r,x0)][s:cut][j:in(s,s0)]
-t14:=satz122(s,r,<i><r><j><s>p2):more(r,s)
-t15:=satz158b(r,x0,ux):moreis(rpofrt(x0),r)
-t16:=moreisi1(rpofrt(x0),s,satz127c(rpofrt(x0),r,s,t15,t14)):moreis(rpofrt(x0),s)
-t17:=satz158d(s,x0,t16):urt(s,x0)
-s@t18:=weli(ec(in(s,s0),lrt(s,x0)),[t:in(s,s0)]t17(t)):not(and(in(s,s0),lrt(s,x0)))
-ux@t19:=th5"l.some"(cut,[y:cut]and(in(y,s0),lrt(y,x0)),[y:cut]t18(y)):not(schnittprop(x0))
-t20:=th3"l.imp"(in"rt"(x0,schnittset),schnittprop(x0),t19,[t:in"rt"(x0,schnittset)]estie(rat,[x:rat]schnittprop(x),x0,t)):not(in"rt"(x0,schnittset))
-p2@[x0:rat][i:in"rt"(x0,schnittset)][y0:rat][l:less"rt"(y0,x0)]
-i@t21:=estie(rat,[x:rat]schnittprop(x),x0,i):schnittprop(x0)
-l@[r:cut][a:and(in(r,s0),lrt(r,x0))]
-t22:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
-t23:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
-t24:=satz120(r,x0,t23,y0,l):lrt(r,y0)
-t25:=andi(in(r,s0),lrt(r,y0),t22,t24):and(in(r,s0),lrt(r,y0))
-t26:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t25):schnittprop(y0)
-l@t27:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,schnittprop(y0),[y:cut][r:and(in(y,s0),lrt(y,x0))]t26(y,r)):schnittprop(y0)
-t28:=estii(rat,[x:rat]schnittprop(x),y0,t27):in"rt"(y0,schnittset)
-i@[r:cut][a:and(in(r,s0),lrt(r,x0))]
-t29:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
-t30:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
-[y0:rat][ly:lrt(r,y0)][l:less"rt"(x0,y0)]
-t31:=andi(in(r,s0),lrt(r,y0),t29,ly):and(in(r,s0),lrt(r,y0))
-t32:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t31):schnittprop(y0)
-t33:=estii(rat,[x:rat]schnittprop(x),y0,t32):in"rt"(y0,schnittset)
-t34:=satz83(x0,y0,l):more"rt"(y0,x0)
-t35:=andi(in"rt"(y0,schnittset),more"rt"(y0,x0),t33,t34):and(in"rt"(y0,schnittset),more"rt"(y0,x0))
-t36:=somei(rat,[y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)),y0,t35):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
-a@t37:=cutapp3(r,x0,t30,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:rat][t:lrt(r,y)][u:less"rt"(x0,y)]t36(y,t,u)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
-i@t38:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:cut][t:and(in(y,s0),lrt(y,x0))]t37(y,t)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
-p2@[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)][s:cut][j:in(s,t0)][y0:rat][uy:urt(s,y0)]
-t39:=cut2(schnittset,x0,t13(r,i,x0,lx),y0,t20(s,j,y0,uy),[x:rat][t:in"rt"(x,schnittset)][y:rat][u:less"rt"(y,x)]t28(x,t,y,u),[x:rat][t:in"rt"(x,schnittset)]t38(x,t)):cutprop(schnittset)
-j@t40:=cutapp1b(s,cutprop(schnittset),[x:rat][t:urt(s,x)]t39(x,t)):cutprop(schnittset)
-lx@t41:=nonemptyapp(cut,t0,p1b,cutprop(schnittset),[y:cut][t:in(y,t0)]t40(y,t)):cutprop(schnittset)
-i@t42:=cutapp1a(r,cutprop(schnittset),[x:rat][t:lrt(r,x)]t41(x,t)):cutprop(schnittset)
-p2@t43:=nonemptyapp(cut,s0,p1a,cutprop(schnittset),[y:cut][t:in(y,s0)]t42(y,t)):cutprop(schnittset)
-snt:=cutof(schnittset,t43):cut
-[r:cut][l:less(r,snt)][x0:rat][ux:urt(r,x0)][lx:lrt(snt,x0)]
-t44:=ini(schnittset,t43,x0,lx):in"rt"(x0,schnittset)
-t45:=estie(rat,[x:rat]schnittprop(x),x0,t44):schnittprop(x0)
-[s:cut][a:and(in(s,s0),lrt(s,x0))]
-t46:=ande1(in(s,s0),lrt(s,x0),a):in(s,s0)
-t47:=ande2(in(s,s0),lrt(s,x0),a):lrt(s,x0)
-t48:=andi(urt(r,x0),lrt(s,x0),ux,t47):and(urt(r,x0),lrt(s,x0))
-t49:=somei(rat,[x:rat]and(urt(r,x),lrt(s,x)),x0,t48):less(r,s)
-t50:=ec3e23(is(s,r),more(s,r),less(s,r),satz123b(s,r),satz122(r,s,t49)):not(less(s,r))
-t51:=th3"l.imp"(in(r,t0),less(s,r),t50,<r><t46><s>p2):not(in(r,t0))
-t52:=ore1(in(r,s0),in(r,t0),<r>p0,t51):in(r,s0)
-lx@t53:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t45,in(r,s0),[y:cut][t:and(in(y,s0),lrt(y,x0))]t52(y,t)):in(r,s0)
-l@t54:=lessapp(r,snt,l,in(r,s0),[x:rat][t:urt(r,x)][u:lrt(snt,x)]t53(x,t,u)):in(r,s0)
-r@[m:more(r,snt)][x0:rat][lx:lrt(r,x0)][ux:urt(snt,x0)][i:in(r,s0)]
-t55:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
-t56:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t55):schnittprop(x0)
-t57:=estii(rat,[x:rat]schnittprop(x),x0,t56):in"rt"(x0,schnittset)
-t58:=ine(schnittset,t43,x0,t57):lrt(snt,x0)
-ux@t59:=th3"l.imp"(in(r,s0),lrt(snt,x0),ux,[t:in(r,s0)]t58(t)):not(in(r,s0))
-t60:=ore2(in(r,s0),in(r,t0),<r>p0,t59):in(r,t0)
-m@t61:=moreapp(r,snt,m,in(r,t0),[x:rat][t:lrt(r,x)][u:urt(snt,x)]t60(x,t,u)):in(r,t0)
-p2@t62:=andi(prop1(snt),prop2(snt),[x:cut][t:less(x,snt)]t54(x,t),[x:cut][t:more(x,snt)]t61(x,t)):prop3(snt)
-t63:=somei(cut,[x:cut]prop3(x),snt,t62):some([x:cut]prop3(x))
--5p205
-satzp205:=onei(cut,[x:cut]prop3".5p205"(x),t10".5p205",t63".5p205"):one([x:cut]and(all([y:cut][t:less(y,x)]in(y,s0)),all([y:cut][t:more(y,x)]in(y,t0))))
-schnitt:=ind(cut,[x:cut]prop3".5p205"(x),satzp205):cut
-satzp205a:=ande1(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:less(x,schnitt)]in(x,s0))
-satzp205b:=ande2(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:more(x,schnitt)]in(x,t0))
-@[r:cut][s:cut]
-+ivad
-@i:=1rp:cut
-r@r1:=pl(r,i):cut
-s@s1:=pl(s,i):cut
-rps:=pl(r,s):cut
-@2:=pl(i,i):cut
-s@t1:=pdeq12a(r1,i,s1,i):eq(pd(pdofrp(r),pdofrp(s)),df(pl(r1,s1),2))
-t2:=tris(cut,pl(r1,s1),pl(rps,2),pl(pl(rps,i),i),4pl23(r,i,s,i),asspl2(rps,i,i)):is(pl(r1,s1),pl(pl(rps,i),i))
-t3:=ispl1(pl(r1,s1),pl(pl(rps,i),i),i,t2):is(pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i))
-t4:=tris(cut,pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i),pl(pl(rps,i),2),t3,asspl1(pl(rps,i),i,i)):is(pl(pl(r1,s1),i),pl(pl(rps,i),2))
-t5:=eqi12(pl(r1,s1),2,pl(rps,i),i,t4):eq(df(pl(r1,s1),2),pdofrp(rps))
--ivad
-lemmaivad1:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(pl(r,1rp),pl(s,1rp)),pl(1rp,1rp)),pdofrp(pl(r,s)),t1".ivad",t5".ivad"):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
-+*ivad
-s@rs:=ts(r,s):cut
-t6:=tdeq12a(r1,i,s1,i):eq(td(pdofrp(r),pdofrp(s)),df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))))
-t7:=tris(cut,ts(r1,s),pl(rs,ts(i,s)),pl(rs,s),disttp1(r,i,s),ispl2(ts(i,s),s,rs,satz151b(s))):is(ts(r1,s),pl(rs,s))
-t8:=tr3is(cut,ts(r1,s1),pl(ts(r1,s),ts(r1,i)),pl(pl(rs,s),r1),pl(pl(rs,i),rps),disttp2(r1,s,i),ispl12(ts(r1,s),pl(rs,s),ts(r1,i),r1,t7,satz151(r1)),4pl24(rs,s,r,i)):is(ts(r1,s1),pl(pl(rs,i),rps))
-t9:=tris(cut,pl(ts(r1,s1),ts(i,i)),pl(pl(pl(rs,i),rps),i),pl(pl(rs,i),pl(rps,i)),ispl12(ts(r1,s1),pl(pl(rs,i),rps),ts(i,i),i,t8,satz151(i)),asspl1(pl(rs,i),rps,i)):is(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)))
-t10:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(pl(rs,i),pl(rps,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),ispl1(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)),i,t9),asspl1(pl(rs,i),pl(rps,i),i)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)))
-t11:=tr3is(cut,pl(pl(rps,i),i),pl(rps,2),pl(r1,s1),pl(ts(r1,i),ts(i,s1)),asspl1(rps,i,i),4pl23(r,s,i,i),ispl12(r1,ts(r1,i),s1,ts(i,s1),satz151a(r1),satz151c(s1))):is(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)))
-t12:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))),t10,ispl2(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)),pl(rs,i),t11)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))))
-t13:=eqi12(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1)),pl(rs,i),i,t12):eq(df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))),pdofrp(rs))
--ivad
-s@lemmaivad2:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(pl(r,1rp),pl(s,1rp)),ts(1rp,1rp)),pl(ts(pl(r,1rp),1rp),ts(1rp,pl(s,1rp)))),pdofrp(ts(r,s)),t6".ivad",t13".ivad"):eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
-[m:mored(pdofrp(r),pdofrp(s))]
-+*ivad
-m@t14:=morede12(r1,i,s1,i,m):more(pl(r1,i),pl(s1,i))
-t15:=satz136a(r1,s1,i,t14):more(r1,s1)
--ivad
-m@lemmaivad3:=satz136a(r,s,1rp,t15".ivad"):more(r,s)
-@[c:dif][a:dif][b:dif][n:not(negd(a))][o:not(negd(b))][e:eq(td(a,a),c)][f:eq(td(b,b),c)]
-+d161
-t1:=treq2(td(a,a),td(b,b),c,e,f):eq(td(a,a),td(b,b))
-t2:=treq(pd(md(td(a,a),td(a,b)),td(b,a)),pd(md(td(a,a),td(a,b)),td(a,b)),td(a,a),eqpd2(td(b,a),td(a,b),md(td(a,a),td(a,b)),comtd(b,a)),pdmd(td(a,a),td(a,b))):eq(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a))
-t3:=tr4eq(td(pd(a,b),md(a,b)),pd(td(a,md(a,b)),td(b,md(a,b))),pd(md(td(a,a),td(a,b)),md(td(b,a),td(b,b))),md(pd(md(td(a,a),td(a,b)),td(b,a)),td(b,b)),md(td(a,a),td(b,b)),disttpd1(a,b,md(a,b)),eqpd12(td(a,md(a,b)),md(td(a,a),td(a,b)),td(b,md(a,b)),md(td(b,a),td(b,b)),disttmd2(a,a,b),disttmd2(b,a,b)),asspd2(md(td(a,a),td(a,b)),td(b,a),m0d(td(b,b))),eqmd1(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a),td(b,b),t2)):eq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)))
-t4:=eqzero(md(td(a,a),td(b,b)),td(pd(a,b),md(a,b)),symeq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)),t3),satzd182e(td(a,a),td(b,b),t1)):zero(td(pd(a,b),md(a,b)))
-t5:=satzd192c(pd(a,b),md(a,b),t4):or(zero(pd(a,b)),zero(md(a,b)))
-[z:zero(a)]
-t6:=eqzero(td(a,a),td(b,b),t1,td01(a,a,z)):zero(td(b,b))
-t7:=th1"l.imp"(zero(b),zero(b),refimp(zero(b)),satzd192c(b,b,t6)):zero(b)
-t8:=zeroeq(a,b,z,t7):eq(a,b)
-f@[p:not(zero(a))]
-t9:=or3e2(zero(a),posd(a),negd(a),axrdo(a),n,p):posd(a)
-t10:=th3"l.imp"(zero(b),zero(a),p,[t:zero(b)]t7(b,a,o,n,f,e,t)):not(zero(b))
-t11:=t9(b,a,o,n,f,e,t10):posd(b)
-t12:=pnot0d(pd(a,b),ppd(a,b,t9,t11)):not(zero(pd(a,b)))
-t13:=ore2(zero(pd(a,b)),zero(md(a,b)),t5,t12):zero(md(a,b))
-t14:=satzd182b(a,b,t13):eq(a,b)
--d161
-satzd161b:=th1"l.imp"(zero(a),eq(a,b),[t:zero(a)]t8".d161"(t),[t:not(zero(a))]t14".d161"(t)):eq(a,b)
-c@[n:not(negd(c))]
-+*d161
-n@[z:zero(c)]
-t15:=zeroeq(td(c,c),c,td01(c,c,z),z):eq(td(c,c),c)
-t16:=andi(not(negd(c)),eq(td(c,c),c),n,t15):and(not(negd(c)),eq(td(c,c),c))
-t17:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),c,t16):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
-n@[o:not(zero(c))]
-t18:=or3e2(zero(c),posd(c),negd(c),axrdo(c),n,o):posd(c)
-crp:=rpofpd(c,t18):cut
-srp:=sqrt(crp):cut
-s:=pdofrp(srp):dif
-t19:=tr3eq(td(s,s),pdofrp(ts(srp,srp)),pdofrp(crp),c,lemmaivad2(srp,srp),isrpepd(ts(srp,srp),crp,thsqrt1(crp)),eqpdrp2(c,t18)):eq(td(s,s),c)
-t20:=andi(not(negd(s)),eq(td(s,s),c),pnotnd(s,posdirp(srp)),t19):and(not(negd(s)),eq(td(s,s),c))
-t21:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),s,t20):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
--d161
-n@satzd161a:=th1"l.imp"(zero(c),some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c))),[t:zero(c)]t17".d161"(t),[t:not(zero(c))]t21".d161"(t)):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
-@[a:dif][i:intd(a)]
-+intd
-[z:zero(a)]
-t1:=ori1(zero(absd(a)),natd(absd(absd(a))),satzd166f(a,z)):intd(absd(a))
-i@[n:natd(absd(a))]
-t2:=natintd(absd(a),n):intd(absd(a))
--intd
-intabsd:=orapp(zero(a),natd(absd(a)),intd(absd(a)),i,[t:zero(a)]t1".intd"(t),[t:natd(absd(a))]t2".intd"(t)):intd(absd(a))
-+*intd
-n@t4:=eqnatd(absd(a),absd(m0d(a)),satzd178a(a),n):natd(absd(m0d(a)))
--intd
-i@intm0d:=th9"l.or"(zero(a),natd(absd(a)),zero(m0d(a)),natd(absd(m0d(a))),i,[t:zero(a)]satzd176b(a,t),[t:natd(absd(a))]t4".intd"(t)):intd(m0d(a))
-a@[b:dif][i:intd(a)][j:intd(b)]
-+*intd
-j@[z:zero(a)]
-t5:=symeq(pd(a,b),b,pd01(a,b,z)):eq(b,pd(a,b))
-t6:=eqintd(b,pd(a,b),t5,j):intd(pd(a,b))
-j@[z:zero(b)]
-t7:=symeq(pd(a,b),a,pd02(a,b,z)):eq(a,pd(a,b))
-t8:=eqintd(a,pd(a,b),t7,i):intd(pd(a,b))
-a@[i:intd(a)][p:posd(a)]
-t9:=<p>ande2(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),posintnatd(a,p,i)):natrp(rpofpd(a,p))
-j@[pp:posd(pd(a,b))]
-apb1:=rpofpd(pd(a,b),pp):cut
-[p:posd(a)]
-a1:=rpofpd(a,p):cut
-[q:posd(b)]
-b1:=rpofpd(b,q):cut
-t10:=natpl(a1,t9(a,i,p),b1,t9(b,j,q)):natrp(pl(a1,b1))
-t11:=eqpd12(a,pdofrp(a1),b,pdofrp(b1),eqpdrp1(a,p),eqpdrp1(b,q)):eq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)))
-t12:=treq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)),pdofrp(pl(a1,b1)),t11,lemmaivad1(a1,b1)):eq(pd(a,b),pdofrp(pl(a1,b1)))
-t13:=tris(cut,apb1,rpofpd(pdofrp(pl(a1,b1)),posdirp(pl(a1,b1))),pl(a1,b1),eqpderp(pd(a,b),pp,pdofrp(pl(a1,b1)),posdirp(pl(a1,b1)),t12),isrppd2(pl(a1,b1))):is(apb1,pl(a1,b1))
-t14:=isp1(cut,[t:cut]natrp(t),pl(a1,b1),apb1,t10,t13):natrp(apb1)
-t15:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t14(t,p,q)):natd(pd(a,b))
-t16:=natintd(pd(a,b),t15):intd(pd(a,b))
-p@[n:negd(b)]
-t17:=satzd176c(b,n):posd(m0d(b))
-b2:=rpofpd(m0d(b),t17):cut
-t18:=eqpd2(b,m0d(m0d(b)),a,satzd177a(b)):eq(pd(a,b),md(a,m0d(b)))
-t19:=eqposd(pd(a,b),md(a,m0d(b)),t18,pp):posd(md(a,m0d(b)))
-t20:=satzd182a(a,m0d(b),t19):mored(a,m0d(b))
-t21:=eqmored12(a,pdofrp(a1),m0d(b),pdofrp(b2),eqpdrp1(a,p),eqpdrp1(m0d(b),t17),t20):mored(pdofrp(a1),pdofrp(b2))
-t22:=lemmaivad3(a1,b2,t21):more(a1,b2)
-t23:=natmn(a1,t9(a,i,p),b2,t9(m0d(b),intm0d(b,j),t17),t22):natrp(mn(a1,b2,t22))
-t24:=eqpd12(m0d(b),pdofrp(b2),pd(a,b),pdofrp(apb1),eqpdrp1(m0d(b),t17),eqpdrp1(pd(a,b),pp)):eq(pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)))
-t25:=tr4eq(a,md(pd(a,b),b),pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)),pdofrp(pl(b2,apb1)),symeq(md(pd(a,b),b),a,mdpd(a,b)),compd(pd(a,b),m0d(b)),t24,lemmaivad1(b2,apb1)):eq(a,pdofrp(pl(b2,apb1)))
-t26:=tris2(cut,pl(b2,apb1),a1,rpofpd(pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1))),isrppd1(pl(b2,apb1)),eqpderp(a,p,pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1)),t25)):is(pl(b2,apb1),a1)
-t27:=satz140g(a1,b2,apb1,t22,t26):is(apb1,mn(a1,b2,t22))
-t28:=isp1(cut,[t:cut]natrp(t),mn(a1,b2,t22),apb1,t23,t27):natrp(apb1)
-t29:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t28(t,p,n)):natd(pd(a,b))
-t30:=natintd(pd(a,b),t29):intd(pd(a,b))
-p@t31:=rappd(b,intd(pd(a,b)),[t:posd(b)]t16(t),[t:zero(b)]t8(t),[t:negd(b)]t30(t)):intd(pd(a,b))
-pp@[n:negd(a)]
-t31a:=th3"l.imp"(negd(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:negd(b)]npd(a,b,n,t)):not(negd(b))
-t32:=th3"l.imp"(zero(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:zero(b)]eqnegd(a,pd(a,b),symeq(pd(a,b),a,pd02(a,b,t)),n)):not(zero(b))
-t33:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t31a,t32):posd(b)
-t34:=eqposd(pd(a,b),pd(b,a),compd(a,b),pp):posd(pd(b,a))
-t35:=t30(b,a,j,i,t34,t33,n):intd(pd(b,a))
-t36:=eqintd(pd(b,a),pd(a,b),compd(b,a),t35):intd(pd(a,b))
-pp@t37:=rappd(a,intd(pd(a,b)),[t:posd(a)]t31(t),[t:zero(a)]t6(t),[t:negd(a)]t36(t)):intd(pd(a,b))
-j@[0p:zero(pd(a,b))]
-t38:=intdi0(pd(a,b),0p):intd(pd(a,b))
-j@[np:negd(pd(a,b))]
-t39:=satzd176c(pd(a,b),np):posd(m0d(pd(a,b)))
-t40:=eqposd(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180(a,b),t39):posd(pd(m0d(a),m0d(b)))
-t41:=t37(m0d(a),m0d(b),intm0d(a,i),intm0d(b,j),t40):intd(pd(m0d(a),m0d(b)))
-t42:=eqintd(pd(m0d(a),m0d(b)),m0d(pd(a,b)),satzd180a(a,b),t41):intd(m0d(pd(a,b)))
-t43:=intm0d(m0d(pd(a,b)),t42):intd(m0d(m0d(pd(a,b))))
-t44:=eqintd(m0d(m0d(pd(a,b))),pd(a,b),satzd177(pd(a,b)),t43):intd(pd(a,b))
--intd
-j@intpd:=rappd(pd(a,b),intd(pd(a,b)),[t:posd(pd(a,b))]t37".intd"(t),[t:zero(pd(a,b))]t38".intd"(t),[t:negd(pd(a,b))]t44".intd"(t)):intd(pd(a,b))
-intmd:=intpd(a,m0d(b),i,intm0d(b,j)):intd(md(a,b))
-+*intd
-j@[n:not(zero(td(a,b)))]
-t45:=th3"l.imp"(zero(a),zero(td(a,b)),n,[t:zero(a)]td01(a,b,t)):not(zero(a))
-t46:=th3"l.imp"(zero(b),zero(td(a,b)),n,[t:zero(b)]td02(a,b,t)):not(zero(b))
-t47:=satzd166e(a,t45):posd(absd(a))
-a3:=rpofpd(absd(a),t47):cut
-t48:=satzd166e(b,t46):posd(absd(b))
-b3:=rpofpd(absd(b),t48):cut
-t49:=natts(a3,t9(absd(a),intabsd(a,i),t47),b3,t9(absd(b),intabsd(b,j),t48)):natrp(ts(a3,b3))
-t50:=satzd166e(td(a,b),n):posd(absd(td(a,b)))
-[p:posd(absd(td(a,b)))]
-atb3:=rpofpd(absd(td(a,b)),p):cut
-t51:=eqtd12(absd(a),pdofrp(a3),absd(b),pdofrp(b3),eqpdrp1(absd(a),t47),eqpdrp1(absd(b),t48)):eq(td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)))
-t52:=tr3eq(absd(td(a,b)),td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)),pdofrp(ts(a3,b3)),satzd193(a,b),t51,lemmaivad2(a3,b3)):eq(absd(td(a,b)),pdofrp(ts(a3,b3)))
-t53:=tris2(cut,atb3,ts(a3,b3),rpofpd(pdofrp(ts(a3,b3)),posdirp(ts(a3,b3))),eqpderp(absd(td(a,b)),p,pdofrp(ts(a3,b3)),posdirp(ts(a3,b3)),t52),isrppd1(ts(a3,b3))):is(atb3,ts(a3,b3))
-t54:=isp1(cut,[t:cut]natrp(t),ts(a3,b3),atb3,t49,t53):natrp(atb3)
-n@t55:=andi(posd(absd(td(a,b))),[t:posd(absd(td(a,b)))]natrp(atb3(t)),t50,[t:posd(absd(td(a,b)))]t54(t)):natd(absd(td(a,b)))
--intd
-j@inttd:=[t:not(zero(td(a,b)))]t55".intd"(t):intd(td(a,b))
-+r
-@eq:=[x:dif][y:dif]eq"rp"(x,y):[x:dif][y:dif]'prop'
-refeq:=[x:dif]refeq"rp"(x):[x:dif]<x><x>eq
-symeq:=[x:dif][y:dif][t:<y><x>eq]symeq"rp"(x,y,t):[x:dif][y:dif][t:<y><x>eq]<x><y>eq
-treq:=[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]treq"rp"(x,y,z,t,u):[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]<z><x>eq
-[a:dif][s:set(dif)]
-inn:=esti(dif,a,s):'prop'
-@real:=ect"eq"(dif,eq,refeq,symeq,treq):'type'
-[r:real][s:real]
-is:=is"e"(real,r,s):'prop'
-nis:=not(is(r,s)):'prop'
-@[p:[x:real]'prop']
-some:=some"l"(real,p):'prop'
-all:=all"l"(real,p):'prop'
-one:=one"e"(real,p):'prop'
-r@[s0:set(real)]
-in:=esti(real,r,s0):'prop'
-a@realof:=ectelt"eq"(dif,eq,refeq,symeq,treq,a):real
-r@class:=ecect"eq"(dif,eq,refeq,symeq,treq,r):set(dif)
-a@innclass:=th5"eq.4"(dif,eq,refeq,symeq,treq,a):inn(a,class(realof(a)))
-r@[a:dif][b:dif][e:eq"rp"(a,b)][air:inn(a,class(r))]
-eqinn:=th8"eq.4"(dif,eq,refeq,symeq,treq,r,a,air,b,e):inn(b,class(r))
-r@[p:'prop'][p1:[x:dif][xi:inn(x,class(r))]p]
-realapp1:=th3"eq.4"(dif,eq,refeq,symeq,treq,r,p,p1):p
-r@[s:real][p:'prop'][p1:[x:dif][y:dif][xi:inn(x,class(r))][yi:inn(y,class(s))]p]
-+ivr1
-[a:dif][air:inn(a,class(r))]
-t1:=realapp1(s,p,[y:dif]<air><y><a>p1):p
--ivr1
-realapp2:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t1".ivr1"(x,xi)):p
-s@[t:real][p:'prop'][p1:[x:dif][y:dif][z:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))]p]
-+*ivr1
-p1@[a:dif][air:inn(a,class(r))]
-t2:=realapp2(s,t,p,[y:dif][z:dif]<air><z><y><a>p1):p
--ivr1
-p1@realapp3:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t2".ivr1"(x,xi)):p
-t@[u:real][p:'prop'][p1:[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]p]
-+*ivr1
-p1@[a:dif][air:inn(a,class(r))]
-t3:=realapp3(s,t,u,p,[y:dif][z:dif][v:dif]<air><v><z><y><a>p1):p
--ivr1
-p1@realapp4:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t3".ivr1"(x,xi)):p
-s@[a1:dif][b1:dif][a1ir:inn(a1,class(r))][b1is:inn(b1,class(s))][e:eq"rp"(a1,b1)]
-isin:=th3"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,e):is(r,s)
-b1is@[i:is(r,s)]
-isex:=th5"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,i):eq"rp"(a1,b1)
-b1is@[n:not(eq"rp"(a1,b1))]
-nisin:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),n,[t:is(r,s)]isex(t)):nis(r,s)
-b1is@[n:nis(r,s)]
-nisex:=th3"l.imp"(eq"rp"(a1,b1),is(r,s),n,[t:eq"rp"(a1,b1)]isin(t)):not(eq"rp"(a1,b1))
-@[alpha:'type'][f:[x:dif]alpha]
-fixf:=fixfu"eq"(dif,eq,refeq,symeq,treq,alpha,f):'prop'
-[ff:fixf(alpha,f)][r0:real]
-indreal:=indeq"eq"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0):alpha
-[a:dif][air:inn(a,class(r0))]
-isindreal:=th2"eq.10"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0,a,air):is"e"(alpha,<a>f,indreal)
-alpha@[g:[x:dif][y:dif]alpha]
-fixf2:=fixfu2"eq"(dif,eq,refeq,symeq,treq,alpha,g):'prop'
-[ff2:fixf2(alpha,g)][r0:real][s0:real]
-indreal2:=indeq2"eq"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0):alpha
-[a:dif][b:dif][air:inn(a,class(r0))][bis:inn(b,class(s0))]
-isindreal2:=th1"eq.11"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0,a,air,b,bis):is"e"(alpha,<b><a>g,indreal2)
-@0:=realof(df(1rp,1rp)):real
-r@[a0:dif][a0ir:inn(a0,class(r))][z:zero(a0)]
-0in:=isin(r,0,a0,df(1rp,1rp),a0ir,innclass(df(1rp,1rp)),zeroeq(a0,df(1rp,1rp),z,zeroi(1rp,1rp,refis(cut,1rp)))):is(r,0)
-a0ir@[i:is(r,0)]
-0ex:=eqzero(df(1rp,1rp),a0,isex(0,r,df(1rp,1rp),a0,innclass(df(1rp,1rp)),a0ir,symis(real,r,0,i)),tris(cut,stm(df(1rp,1rp)),1rp,std(df(1rp,1rp)),stmis(1rp,1rp),isstd(1rp,1rp))):zero(a0)
-+*ivr1
-a0@propp:=and(inn(a0,class(r)),posd(a0)):'prop'
--ivr1
-r@pos:=some"l"(dif,[x:dif]propp".ivr1"(x)):'prop'
-a0ir@[p:posd(a0)]
-+*ivr1
-p@t4:=andi(inn(a0,class(r)),posd(a0),a0ir,p):propp(a0)
--ivr1
-p@posin:=somei(dif,[x:dif]propp".ivr1"(x),a0,t4".ivr1"):pos(r)
-a0ir@[p:pos(r)]
-+*ivr1
-p@[a:dif][q1:propp(a)]
-t5:=ande1(inn(a,class(r)),posd(a),q1):inn(a,class(r))
-t6:=ande2(inn(a,class(r)),posd(a),q1):posd(a)
-t7:=eqposd(a,a0,isex(r,r,a,a0,t5,a0ir,refis(real,r)),t6):posd(a0)
--ivr1
-p@posex:=someapp(dif,[x:dif]propp".ivr1"(x),p,posd(a0),[x:dif][t:propp".ivr1"(x)]t7".ivr1"(x,t)):posd(a0)
-+*ivr1
-a0@propn:=and(inn(a0,class(r)),negd(a0)):'prop'
--ivr1
-r@neg:=some"l"(dif,[x:dif]propn".ivr1"(x)):'prop'
-a0ir@[n:negd(a0)]
-+*ivr1
-n@t8:=andi(inn(a0,class(r)),negd(a0),a0ir,n):propn(a0)
--ivr1
-n@negin:=somei(dif,[x:dif]propn".ivr1"(x),a0,t8".ivr1"):neg(r)
-a0ir@[n:neg(r)]
-+*ivr1
-n@[a:dif][pl:propn(a)]
-t9:=ande1(inn(a,class(r)),negd(a),pl):inn(a,class(r))
-t10:=ande2(inn(a,class(r)),negd(a),pl):negd(a)
-t11:=eqnegd(a,a0,isex(r,r,a,a0,t9,a0ir,refis(real,r)),t10):negd(a0)
--ivr1
-n@negex:=someapp(dif,[x:dif]propn".ivr1"(x),n,negd(a0),[x:dif][t:propn".ivr1"(x)]t11".ivr1"(x,t)):negd(a0)
-+*ivr1
-a0ir@[p:posd(a0)]
-t12:=or3i2(is(r,0),pos(r),neg(r),posin(p)):or3(is(r,0),pos(r),neg(r))
-a0ir@[z:zero(a0)]
-t13:=or3i1(is(r,0),pos(r),neg(r),0in(z)):or3(is(r,0),pos(r),neg(r))
-a0ir@[n:negd(a0)]
-t14:=or3i3(is(r,0),pos(r),neg(r),negin(n)):or3(is(r,0),pos(r),neg(r))
-a0ir@t15:=rappd(a0,or3(is(r,0),pos(r),neg(r)),[t:posd(a0)]t12(t),[t:zero(a0)]t13(t),[t:negd(a0)]t14(t)):or3(is(r,0),pos(r),neg(r))
--ivr1
-r@axrlo:=realapp1(r,or3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t15".ivr1"(x,xi)):or3(is(r,0),pos(r),neg(r))
-+*ivr1
-a0ir@[i:is(r,0)]
-t16:=th3"l.imp"(pos(r),posd(a0),0notpd(a0,0ex(i)),[t:pos(r)]posex(t)):not(pos(r))
-a0ir@[p:pos(r)]
-t17:=th3"l.imp"(neg(r),negd(a0),pnotnd(a0,posex(p)),[t:neg(r)]negex(t)):not(neg(r))
-a0ir@[n:neg(r)]
-t18:=th3"l.imp"(is(r,0),zero(a0),nnot0d(a0,negex(n)),[t:is(r,0)]0ex(t)):not(is(r,0))
-a0ir@t19:=th6"l.ec3"(is(r,0),pos(r),neg(r),[t:is(r,0)]t16(t),[t:pos(r)]t17(t),[t:neg(r)]t18(t)):ec3(is(r,0),pos(r),neg(r))
--ivr1
-r@axrle:=realapp1(r,ec3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t19".ivr1"(x,xi)):ec3(is(r,0),pos(r),neg(r))
-axrl:=orec3i(is(r,0),pos(r),neg(r),axrlo,axrle):orec3(is(r,0),pos(r),neg(r))
-[p:'prop'][p1:[t:pos(r)]p][p2:[t:is(r,0)]p][p3:[t:neg(r)]p]
-rapp:=or3app(is(r,0),pos(r),neg(r),p,axrlo,p2,p1,p3):p
-r@[p:pos(r)]
-pnotn:=ec3e23(is(r,0),pos(r),neg(r),axrle,p):not(neg(r))
-pnot0:=ec3e21(is(r,0),pos(r),neg(r),axrle,p):nis(r,0)
-r@[i:is(r,0)]
-0notp:=ec3e12(is(r,0),pos(r),neg(r),axrle,i):not(pos(r))
-0notn:=ec3e13(is(r,0),pos(r),neg(r),axrle,i):not(neg(r))
-r@[n:neg(r)]
-nnotp:=ec3e32(is(r,0),pos(r),neg(r),axrle,n):not(pos(r))
-nnot0:=ec3e31(is(r,0),pos(r),neg(r),axrle,n):nis(r,0)
-s@[i:is(r,s)][p:pos(r)]
-ispos:=isp(real,[x:real]pos(x),r,s,p,i):pos(s)
-i@[n:neg(r)]
-isneg:=isp(real,[x:real]neg(x),r,s,n,i):neg(s)
-@[r0:cut]
-pofrp:=realof(pdofrp(r0)):real
-nofrp:=realof(ndofrp(r0)):real
-[s0:cut][i:is"rp"(r0,s0)]
-isrpep:=isf(cut,real,[x:cut]pofrp(x),r0,s0,i):is(pofrp(r0),pofrp(s0))
-isrpen:=isf(cut,real,[x:cut]nofrp(x),r0,s0,i):is(nofrp(r0),nofrp(s0))
-s0@[i:is(pofrp(r0),pofrp(s0))]
-+*ivr1
-i"r"@t20:=isex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),i):eq"rp"(pdofrp(r0),pdofrp(s0))
--ivr1
-i@isrpip:=isrpipd(r0,s0,t20".ivr1"):is"rp"(r0,s0)
-s0@[i:is(nofrp(r0),nofrp(s0))]
-+*ivr1
-i"r"@t21:=isex(nofrp(r0),nofrp(s0),ndofrp(r0),ndofrp(s0),innclass(ndofrp(r0)),innclass(ndofrp(s0)),i):eq"rp"(ndofrp(r0),ndofrp(s0))
--ivr1
-i@isrpin:=isrpind(r0,s0,t21".ivr1"):is"rp"(r0,s0)
-r0@posi:=posin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),posdirp(r0)):pos(pofrp(r0))
-negi:=negin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),negdirp(r0)):neg(nofrp(r0))
-s@[r0:cut][s0:cut][i:is(r,pofrp(r0))][j:is(s,pofrp(s0))][k:is(r,s)]
-+*ivr1
-k@t22:=isrpip(r0,s0,tr3is(real,pofrp(r0),r,s,pofrp(s0),symis(real,r,pofrp(r0),i),k,j)):is"rp"(r0,s0)
-r@t23:=[x:cut][y:cut][t:is(r,pofrp(x))][u:is(r,pofrp(y))]t22(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,pofrp(x)))
-a0ir@[p1:pos(r)]
-t24:=posex(p1):posd(a0)
-pr:=rpofpd(a0,t24):cut
-t25:=isin(r,pofrp(pr),a0,pdofrp(pr),a0ir,innclass(pdofrp(pr)),eqpdrp1(a0,t24)):is(r,pofrp(pr))
-t26:=somei(cut,[x:cut]is(r,pofrp(x)),pr,t25):some"rp"([x:cut]is(r,pofrp(x)))
--ivr1
-r@[p:pos(r)]
-+*ivr1
-p"r"@t27:=realapp1(some"rp"([x:cut]is(r,pofrp(x))),[x:dif][t:inn(x,class(r))]t26(x,t,p)):some"rp"([x:cut]is(r,pofrp(x)))
-t28:=onei(cut,[x:cut]is(r,pofrp(x)),t23,t27):one"rp"([x:cut]is(r,pofrp(x)))
--ivr1
-p@rpofp:=ind(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):cut
-isprp1:=oneax(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):is(r,pofrp(rpofp(r,p)))
-isprp2:=symis(real,r,pofrp(rpofp(r,p)),isprp1):is(pofrp(rpofp(r,p)),r)
-@[r1:real][p:pos(r1)][s1:real][q:pos(s1)][i:is(r1,s1)]
-isperp:=t22".ivr1"(r1,s1,rpofp(r1,p),rpofp(s1,q),isprp1(r1,p),isprp1(s1,q),i):is"rp"(rpofp(r1,p),rpofp(s1,q))
-q@[i:is"rp"(rpofp(r1,p),rpofp(s1,q))]
-ispirp:=tr3is(real,r1,pofrp(rpofp(r1,p)),pofrp(rpofp(s1,q)),s1,isprp1(r1,p),isrpep(rpofp(r1,p),rpofp(s1,q),i),isprp2(s1,q)):is(r1,s1)
-@[r0:cut]
-isrpp1:=t22".ivr1"(pofrp(r0),pofrp(r0),r0,rpofp(pofrp(r0),posi(r0)),refis(real,pofrp(r0)),isprp1(pofrp(r0),posi(r0)),refis(real,pofrp(r0))):is"rp"(r0,rpofp(pofrp(r0),posi(r0)))
-isrpp2:=symis(cut,r0,rpofp(pofrp(r0),posi(r0)),isrpp1):is"rp"(rpofp(pofrp(r0),posi(r0)),r0)
-s@[r0:cut][s0:cut][i:is(r,nofrp(r0))][j:is(s,nofrp(s0))][k:is(r,s)]
-+*ivr1
-k@t29:=isrpin(r0,s0,tr3is(real,nofrp(r0),r,s,nofrp(s0),symis(real,r,nofrp(r0),i),k,j)):is"rp"(r0,s0)
-r@t30:=[x:cut][y:cut][t:is(r,nofrp(x))][u:is(r,nofrp(y))]t29(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,nofrp(x)))
-a0ir@[n1:neg(r)]
-t31:=negex(n1):negd(a0)
-nr:=rpofnd(a0,t31):cut
-t32:=isin(r,nofrp(nr),a0,ndofrp(nr),a0ir,innclass(ndofrp(nr)),eqndrp1(a0,t31)):is(r,nofrp(nr))
-t33:=somei(cut,[x:cut]is(r,nofrp(x)),nr,t32):some"rp"([x:cut]is(r,nofrp(x)))
--ivr1
-r@[n:neg(r)]
-+*ivr1
-n"r"@t34:=realapp1(some"rp"([x:cut]is(r,nofrp(x))),[x:dif][t:inn(x,class(r))]t33(x,t,n)):some"rp"([x:cut]is(r,nofrp(x)))
-t35:=onei(cut,[x:cut]is(r,nofrp(x)),t30,t34):one"rp"([x:cut]is(r,nofrp(x)))
--ivr1
-n@rpofn:=ind(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):cut
-isnrp1:=oneax(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):is(r,nofrp(rpofn(r,n)))
-isnrp2:=symis(real,r,nofrp(rpofn(r,n)),isnrp1):is(nofrp(rpofn(r,n)),r)
-@[r1:real][n:neg(r1)][s1:real][m:neg(s1)][i:is(r1,s1)]
-isnerp:=t29".ivr1"(r1,s1,rpofn(r1,n),rpofn(s1,m),isnrp1(r1,n),isnrp1(s1,m),i):is"rp"(rpofn(r1,n),rpofn(s1,m))
-m@[i:is"rp"(rpofn(r1,n),rpofn(s1,m))]
-isnirp:=tr3is(real,r1,nofrp(rpofn(r1,n)),nofrp(rpofn(s1,m)),s1,isnrp1(r1,n),isrpen(rpofn(r1,n),rpofn(s1,m),i),isnrp2(s1,m)):is(r1,s1)
-@[r0:cut]
-isrpn1:=t29".ivr1"(nofrp(r0),nofrp(r0),r0,rpofn(nofrp(r0),negi(r0)),refis(real,nofrp(r0)),isnrp1(nofrp(r0),negi(r0)),refis(real,nofrp(r0))):is"rp"(r0,rpofn(nofrp(r0),negi(r0)))
-isrpn2:=symis(cut,r0,rpofn(nofrp(r0),negi(r0)),isrpn1):is"rp"(rpofn(nofrp(r0),negi(r0)),r0)
-r@satz163:=refis(real,r):is(r,r)
-s@[i:is(r,s)]
-satz164:=symis(real,r,s,i):is(s,r)
-t@[i:is(r,s)][j:is(s,t)]
-satz165:=tris(real,r,s,t,i,j):is(r,t)
-@absdr:=[x:dif]realof(absd(x)):[x:dif]real
-+ivr2
-[a:dif][b:dif][e:eq"rp"(a,b)]
-t1:=isin(realof(absd(a)),realof(absd(b)),absd(a),absd(b),innclass(absd(a)),innclass(absd(b)),eqabsd(a,b,e)):is(<a>absdr,<b>absdr)
--ivr2
-fabsdr:=[x:dif][y:dif][t:<y><x>eq]t1".ivr2"(x,y,t):fixf(real,absdr)
-r@abs:=indreal(real,absdr,fabsdr,r):real
-+*ivr2
-a0ir@t2:=isindreal(real,absdr,fabsdr,r,a0,a0ir):is(realof(absd(a0)),abs(r))
--ivr2
-a0ir@aica:=isp(real,[x:real]inn(absd(a0),class(x)),realof(absd(a0)),abs(r),innclass(absd(a0)),t2".ivr2"):inn(absd(a0),class(abs(r)))
-s@[i:is(r,s)]
-isabs:=isf(real,real,[x:real]abs(x),r,s,i):is(abs(r),abs(s))
-+2r166
-a0ir@[p:pos(r)]
-t1:=satzd166a(a0,posex(p)):posd(absd(a0))
-t2:=posin(abs(r),absd(a0),aica,t1):pos(abs(r))
--2r166
-r@[p:pos(r)]
-satz166a:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t2".2r166"(x,t,p)):pos(abs(r))
-+*2r166
-a0ir@[n:neg(r)]
-t3:=satzd166b(a0,negex(n)):posd(absd(a0))
-t4:=posin(abs(r),absd(a0),aica,t3):pos(abs(r))
--2r166
-r@[n:neg(r)]
-satz166b:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t4".2r166"(x,t,n)):pos(abs(r))
-+*2r166
-b1is@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
-t5:=satzd166c(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
-t6:=isin(t5):is(r,s)
--2r166
-s@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
-satz166c:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".2r166"(x,y,t,u,p,q,i)):is(r,s)
-+*2r166
-b1is@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
-t7:=satzd166d(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
-t8:=isin(t7):is(r,s)
--2r166
-s@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
-satz166d:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".2r166"(x,y,t,u,n,o,i)):is(r,s)
-r@[n:nis(r,0)]
-satz166e:=rapp(r,pos(abs(r)),[t:pos(r)]satz166a(t),th2"l.imp"(is(r,0),pos(abs(r)),n),[t:neg(r)]satz166b(t)):pos(abs(r))
-+*2r166
-a0ir@[i:is(r,0)]
-t9:=satzd166f(a0,0ex(i)):zero(absd(a0))
-t10:=0in(abs(r),absd(a0),aica,t9):is(abs(r),0)
--2r166
-r@[i:is(r,0)]
-satz166f:=realapp1(is(abs(r),0),[x:dif][t:inn(x,class(r))]t10".2r166"(x,t,i)):is(abs(r),0)
-s@more:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),mored(x,y)))):'prop'
-+*ivr2
-b1@propm:=and3(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1)):'prop'
--ivr2
-b1is@[m:mored(a1,b1)]
-+*ivr2
-m@t3:=and3i(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1),a1ir,b1is,m):propm(a1,b1)
-t4:=somei(dif,[x:dif]propm(a1,x),b1,t3):some"l"(dif,[x:dif]propm(a1,x))
--ivr2
-m@morein:=somei(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),a1,t4".ivr2"):more(r,s)
-b1is@[m:more(r,s)]
-+*ivr2
-m@[a:dif][sa:some"l"(dif,[x:dif]propm(a,x))][b:dif][p2:propm(a,b)]
-t5:=and3e1(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(a,class(r))
-t6:=and3e2(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(b,class(s))
-t7:=and3e3(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):mored(a,b)
-t8:=eqmored12(a,a1,b,b1,isex(r,r,a,a1,t5,a1ir,refis(real,r)),isex(s,s,b,b1,t6,b1is,refis(real,s)),t7):mored(a1,b1)
-sa@t9:=someapp(dif,[x:dif]propm(a,x),sa,mored(a1,b1),[x:dif][t:propm(a,x)]t8(x,t)):mored(a1,b1)
--ivr2
-m@moreex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),m,mored(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propm".ivr2"(x,y))]t9".ivr2"(x,t)):mored(a1,b1)
-s@less:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),lessd(x,y)))):'prop'
-+*ivr2
-b1@propl:=and3(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1)):'prop'
--ivr2
-b1is@[l:lessd(a1,b1)]
-+*ivr2
-l@t10:=and3i(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1),a1ir,b1is,l):propl(a1,b1)
-t11:=somei(dif,[x:dif]propl(a1,x),b1,t10):some"l"(dif,[x:dif]propl(a1,x))
--ivr2
-l@lessin:=somei(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),a1,t11".ivr2"):less(r,s)
-b1is@[l:less(r,s)]
-+*ivr2
-l@[a:dif][sa:some"l"(dif,[x:dif]propl(a,x))][b:dif][p2:propl(a,b)]
-t12:=and3e1(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(a,class(r))
-t13:=and3e2(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(b,class(s))
-t14:=and3e3(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):lessd(a,b)
-t15:=eqlessd12(a,a1,b,b1,isex(r,r,a,a1,t12,a1ir,refis(real,r)),isex(s,s,b,b1,t13,b1is,refis(real,s)),t14):lessd(a1,b1)
-sa@t16:=someapp(dif,[x:dif]propl(a,x),sa,lessd(a1,b1),[x:dif][t:propl(a,x)]t15(x,t)):lessd(a1,b1)
--ivr2
-l@lessex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),l,lessd(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propl".ivr2"(x,y))]t16".ivr2"(x,t)):lessd(a1,b1)
-t@[i:is(r,s)][m:more(r,t)]
-ismore1:=isp(real,[x:real]more(x,t),r,s,m,i):more(s,t)
-i@[m:more(t,r)]
-ismore2:=isp(real,[x:real]more(t,x),r,s,m,i):more(t,s)
-i@[l:less(r,t)]
-isless1:=isp(real,[x:real]less(x,t),r,s,l,i):less(s,t)
-i@[l:less(t,r)]
-isless2:=isp(real,[x:real]less(t,x),r,s,l,i):less(t,s)
-u@[i:is(r,s)][j:is(t,u)][m:more(r,t)]
-ismore12:=ismore2(t,u,s,j,ismore1(r,s,t,i,m)):more(s,u)
-j@[l:less(r,t)]
-isless12:=isless2(t,u,s,j,isless1(r,s,t,i,l)):less(s,u)
-+*ivr2
-b1is@[m:more(r,s)]
-t17:=lemmad5(a1,b1,moreex(m)):lessd(b1,a1)
-t18:=lessin(s,r,b1,a1,b1is,a1ir,t17):less(s,r)
--ivr2
-s@[m:more(r,s)]
-lemma1:=realapp2(less(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t18".ivr2"(x,y,t,u,m)):less(s,r)
-+*ivr2
-b1is@[l:less(r,s)]
-t19:=lemmad6(a1,b1,lessex(l)):mored(b1,a1)
-t20:=morein(s,r,b1,a1,b1is,a1ir,t19):more(s,r)
--ivr2
-s@[l:less(r,s)]
-lemma2:=realapp2(more(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t20".ivr2"(x,y,t,u,l)):more(s,r)
-+2r167
-b1is@t1:=satzd167a(a1,b1):or3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
-[e:eq"rp"(a1,b1)]
-t2:=or3i1(is(r,s),more(r,s),less(r,s),isin(e)):or3(is(r,s),more(r,s),less(r,s))
-b1is@[m:mored(a1,b1)]
-t3:=or3i2(is(r,s),more(r,s),less(r,s),morein(m)):or3(is(r,s),more(r,s),less(r,s))
-b1is@[l:lessd(a1,b1)]
-t4:=or3i3(is(r,s),more(r,s),less(r,s),lessin(l)):or3(is(r,s),more(r,s),less(r,s))
-b1is@t5:=or3app(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),or3(is(r,s),more(r,s),less(r,s)),t1,[t:eq"rp"(a1,b1)]t2(t),[t:mored(a1,b1)]t3(t),[t:lessd(a1,b1)]t4(t)):or3(is(r,s),more(r,s),less(r,s))
-t6:=satzd167b(a1,b1):ec3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
-[i:is(r,s)]
-t7:=th3"l.imp"(more(r,s),mored(a1,b1),ec3e12(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,isex(i)),[t:more(r,s)]moreex(t)):not(more(r,s))
-b1is@[m:more(r,s)]
-t8:=th3"l.imp"(less(r,s),lessd(a1,b1),ec3e23(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,moreex(m)),[t:less(r,s)]lessex(t)):not(less(r,s))
-b1is@[l:less(r,s)]
-t9:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),ec3e31(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,lessex(l)),[t:is(r,s)]isex(t)):not(is(r,s))
-b1is@t10:=th6"l.ec3"(is(r,s),more(r,s),less(r,s),th1"l.ec"(is(r,s),more(r,s),[t:is(r,s)]t7(t)),th1"l.ec"(more(r,s),less(r,s),[t:more(r,s)]t8(t)),th1"l.ec"(less(r,s),is(r,s),[t:less(r,s)]t9(t))):ec3(is(r,s),more(r,s),less(r,s))
-t11:=orec3i(is(r,s),more(r,s),less(r,s),t5,t10):orec3(is(r,s),more(r,s),less(r,s))
--2r167
-s@satz167:=realapp2(orec3(is(r,s),more(r,s),less(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".2r167"(x,y,t,u)):orec3(is(r,s),more(r,s),less(r,s))
-satz167a:=orec3e1(is(r,s),more(r,s),less(r,s),satz167):or3(is(r,s),more(r,s),less(r,s))
-satz167b:=orec3e2(is(r,s),more(r,s),less(r,s),satz167):ec3(is(r,s),more(r,s),less(r,s))
-moreis:=or(more(r,s),is(r,s)):'prop'
-lessis:=or(less(r,s),is(r,s)):'prop'
-[m:moreis(r,s)]
-satz168a:=th9"l.or"(more(r,s),is(r,s),less(s,r),is(s,r),m,[t:more(r,s)]lemma1(t),[t:is(r,s)]symis(real,r,s,t)):lessis(s,r)
-s@[l:lessis(r,s)]
-satz168b:=th9"l.or"(less(r,s),is(r,s),more(s,r),is(s,r),l,[t:less(r,s)]lemma2(t),[t:is(r,s)]symis(real,r,s,t)):moreis(s,r)
-t@[i:is(r,s)][m:moreis(r,t)]
-ismoreis1:=isp(real,[x:real]moreis(x,t),r,s,m,i):moreis(s,t)
-i@[m:moreis(t,r)]
-ismoreis2:=isp(real,[x:real]moreis(t,x),r,s,m,i):moreis(t,s)
-i@[l:lessis(r,t)]
-islessis1:=isp(real,[x:real]lessis(x,t),r,s,l,i):lessis(s,t)
-i@[l:lessis(t,r)]
-islessis2:=isp(real,[x:real]lessis(t,x),r,s,l,i):lessis(t,s)
-u@[i:is(r,s)][j:is(t,u)][m:moreis(r,t)]
-ismoreis12:=ismoreis2(t,u,s,j,ismoreis1(r,s,t,i,m)):moreis(s,u)
-j@[l:lessis(r,t)]
-islessis12:=islessis2(t,u,s,j,islessis1(r,s,t,i,l)):lessis(s,u)
-s@[m:more(r,s)]
-moreisi1:=ori1(more(r,s),is(r,s),m):moreis(r,s)
-s@[l:less(r,s)]
-lessisi1:=ori1(less(r,s),is(r,s),l):lessis(r,s)
-s@[i:is(r,s)]
-moreisi2:=ori2(more(r,s),is(r,s),i):moreis(r,s)
-lessisi2:=ori2(less(r,s),is(r,s),i):lessis(r,s)
-b1is@[m:moreq(a1,b1)]
-moreisin:=orapp(mored(a1,b1),eq"rp"(a1,b1),moreis(r,s),m,[t:mored(a1,b1)]moreisi1(morein(t)),[t:eq"rp"(a1,b1)]moreisi2(isin(t))):moreis(r,s)
-b1is@[m:moreis(r,s)]
-moreisex:=orapp(more(r,s),is(r,s),moreq(a1,b1),m,[t:more(r,s)]moreqi1(a1,b1,moreex(t)),[t:is(r,s)]moreqi2(a1,b1,isex(t))):moreq(a1,b1)
-b1is@[l:lesseq(a1,b1)]
-lessisin:=orapp(lessd(a1,b1),eq"rp"(a1,b1),lessis(r,s),l,[t:lessd(a1,b1)]lessisi1(lessin(t)),[t:eq"rp"(a1,b1)]lessisi2(isin(t))):lessis(r,s)
-b1is@[l:lessis(r,s)]
-lessisex:=orapp(less(r,s),is(r,s),lesseq(a1,b1),l,[t:less(r,s)]lesseqi1(a1,b1,lessex(t)),[t:is(r,s)]lesseqi2(a1,b1,isex(t))):lesseq(a1,b1)
-s@[m:moreis(r,s)]
-satz167c:=th7"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,comor(more(r,s),is(r,s),m)):not(less(r,s))
-s@[l:lessis(r,s)]
-satz167d:=th9"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,l):not(more(r,s))
-s@[n:not(more(r,s))]
-satz167e:=th2"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n):lessis(r,s)
-s@[n:not(less(r,s))]
-s@[n:not(less(r,s))]
-satz167f:=comor(is(r,s),more(r,s),th3"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n)):moreis(r,s)
-s@[m:more(r,s)]
-satz167g:=th3"l.imp"(lessis(r,s),not(more(r,s)),weli(more(r,s),m),[t:lessis(r,s)]satz167d(t)):not(lessis(r,s))
-s@[l:less(r,s)]
-satz167h:=th3"l.imp"(moreis(r,s),not(less(r,s)),weli(less(r,s),l),[t:moreis(r,s)]satz167c(t)):not(moreis(r,s))
-s@[n:not(moreis(r,s))]
-satz167j:=or3e3(is(r,s),more(r,s),less(r,s),satz167a,th5"l.or"(more(r,s),is(r,s),n),th4"l.or"(more(r,s),is(r,s),n)):less(r,s)
-s@[n:not(lessis(r,s))]
-satz167k:=or3e2(is(r,s),more(r,s),less(r,s),satz167a,th4"l.or"(less(r,s),is(r,s),n),th5"l.or"(less(r,s),is(r,s),n)):more(r,s)
-r@[p:pos(r)]
-+2r169
-[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t1:=satzd169a(a,b,0ex(0,b,bi0,refis(real,0)),posex(a,air,p)):mored(a,b)
-t2:=morein(r,0,a,b,air,bi0,t1):more(r,0)
--2r169
-satz169a:=realapp2(r,0,more(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r169"(x,y,t,u)):more(r,0)
-r@[m:more(r,0)]
-+*2r169
-m@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t3:=satzd169b(a,b,0ex(0,b,bi0,refis(real,0)),moreex(r,0,a,b,air,bi0,m)):posd(a)
-t4:=posin(r,a,air,t3):pos(r)
--2r169
-m@satz169b:=realapp2(r,0,pos(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t4".2r169"(x,y,t,u)):pos(r)
-r@[n:neg(r)]
-+*2r169
-n@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t5:=satzd169c(a,b,0ex(0,b,bi0,refis(real,0)),negex(a,air,n)):lessd(a,b)
-t6:=lessin(r,0,a,b,air,bi0,t5):less(r,0)
--2r169
-n@satz169c:=realapp2(r,0,less(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t6".2r169"(x,y,t,u)):less(r,0)
-r@[l:less(r,0)]
-+*2r169
-l@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t7:=satzd169d(a,b,0ex(0,b,bi0,refis(real,0)),lessex(r,0,a,b,air,bi0,l)):negd(a)
-t8:=negin(r,a,air,t7):neg(r)
--2r169
-l@satz169d:=realapp2(r,0,neg(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t8".2r169"(x,y,t,u)):neg(r)
-+2r170
-r@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t1:=satzd170(a,b,0ex(0,b,bi0,refis(real,0))):moreq(absd(a),b)
-t2:=moreisin(abs(r),0,absd(a),b,aica(r,a,air),bi0,t1):moreis(abs(r),0)
--2r170
-r@satz170:=realapp2(r,0,moreis(abs(r),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r170"(x,y,t,u)):moreis(abs(r),0)
-satz170a:=th3"l.imp"(neg(abs(r)),less(abs(r),0),satz167c(abs(r),0,satz170),[t:neg(abs(r))]satz169c(abs(r),t)):not(neg(abs(r)))
-t@[l:less(r,s)][k:less(s,t)]
-+2r171
-[a:dif][b:dif][c:dif][air:inn(a,class(r))][bis:inn(b,class(s))][cit:inn(c,class(t))]
-t1:=satzd171(a,b,c,lessex(r,s,a,b,air,bis,l),lessex(s,t,b,c,bis,cit,k)):lessd(a,c)
-t2:=lessin(r,t,a,c,air,cit,t1):less(r,t)
--2r171
-satz171:=realapp3(r,s,t,less(r,t),[x:dif][y:dif][z:dif][w:inn(x,class(r))][u:inn(y,class(s))][v:inn(z,class(t))]t2".2r171"(x,y,z,w,u,v)):less(r,t)
-trless:=satz171:less(r,t)
-t@[m:more(r,s)][n:more(s,t)]
-trmore:=lemma2(t,r,trless(t,s,r,lemma1(s,t,n),lemma1(r,s,m))):more(r,t)
-t@[a2:dif][b2:dif][c2:dif][a2ir:inn(a2,class(r))][b2is:inn(b2,class(s))][c2it:inn(c2,class(t))]
-+2r172
-[l:lessis(r,s)][k:less(s,t)]
-t1:=satzd172a(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
-t2:=lessin(r,t,a2,c2,a2ir,c2it,t1):less(r,t)
--2r172
-t@[l:lessis(r,s)][k:less(s,t)]
-satz172a:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
-+*2r172
-c2it@[l:less(r,s)][k:lessis(s,t)]
-t3:=satzd172b(a2,b2,c2,lessex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
-t4:=lessin(r,t,a2,c2,a2ir,c2it,t3):less(r,t)
--2r172
-t@[l:less(r,s)][k:lessis(s,t)]
-satz172b:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
-t@[m:moreis(r,s)][n:more(s,t)]
-satz172c:=lemma2(t,r,satz172b(t,s,r,lemma1(s,t,n),satz168a(m))):more(r,t)
-t@[m:more(r,s)][n:moreis(s,t)]
-satz172d:=lemma2(t,r,satz172a(t,s,r,satz168a(s,t,n),lemma1(m))):more(r,t)
-+2r173
-c2it@[l:lessis(r,s)][k:lessis(s,t)]
-t1:=satzd173(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lesseq(a2,c2)
-t2:=lessisin(r,t,a2,c2,a2ir,c2it,t1):lessis(r,t)
--2r173
-t@[l:lessis(r,s)][k:lessis(s,t)]
-satz173:=realapp3(lessis(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r173"(x,y,z,u,v,w,l,k)):lessis(r,t)
-trlessis:=satz173:lessis(r,t)
-t@[m:moreis(r,s)][n:moreis(s,t)]
-trmoreis:=satz168b(t,r,trlessis(t,s,r,satz168a(s,t,n),satz168a(m))):moreis(r,t)
-r@ratrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),ratd(x))):'prop'
-a0ir@[r1:ratd(a0)]
-+*ivr2
-r1@t21:=andi(inn(a0,class(r)),ratd(a0),a0ir,r1):and(inn(a0,class(r)),ratd(a0))
--ivr2
-r1@ratrlin:=somei(dif,[x:dif]and(inn(x,class(r)),ratd(x)),a0,t21".ivr2"):ratrl(r)
-a0ir@[rr:ratrl(r)]
-+*ivr2
-rr@[a:dif][b:and(inn(a,class(r)),ratd(a))]
-t22:=ande1(inn(a,class(r)),ratd(a),b):inn(a,class(r))
-t23:=ande2(inn(a,class(r)),ratd(a),b):ratd(a)
-t24:=eqratd(a,a0,isex(r,r,a,a0,t22,a0ir,refis(real,r)),t23):ratd(a0)
--ivr2
-rr@ratrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),ratd(x)),rr,ratd(a0),[x:dif][t:and(inn(x,class(r)),ratd(x))]t24".ivr2"(x,t)):ratd(a0)
-r@irratrl:=not(ratrl(r)):'prop'
-@[r0:cut][rr:ratrp(r0)]
-remark2:=ratrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark2a(r0,rr)):ratrl(pofrp(r0))
-remark3:=ratrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark3a(r0,rr)):ratrl(nofrp(r0))
-r0@[ir:irratrp(r0)]
-remark4:=th3"l.imp"(ratrl(pofrp(r0)),ratd(pdofrp(r0)),remark4a(r0,ir),[t:ratrl(pofrp(r0))]ratrlex(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),t)):irratrl(pofrp(r0))
-remark5:=th3"l.imp"(ratrl(nofrp(r0)),ratd(ndofrp(r0)),remark5a(r0,ir),[t:ratrl(nofrp(r0))]ratrlex(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),t)):irratrl(nofrp(r0))
-r@natrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),natd(x))):'prop'
-a0ir@[n:natd(a0)]
-+*ivr2
-n@t25:=andi(inn(a0,class(r)),natd(a0),a0ir,n):and(inn(a0,class(r)),natd(a0))
--ivr2
-n@natrlin:=somei(dif,[x:dif]and(inn(x,class(r)),natd(x)),a0,t25".ivr2"):natrl(r)
-a0ir@[n:natrl(r)]
-+*ivr2
-n@[a:dif][b:and(inn(a,class(r)),natd(a))]
-t26:=ande1(inn(a,class(r)),natd(a),b):inn(a,class(r))
-t27:=ande2(inn(a,class(r)),natd(a),b):natd(a)
-t28:=eqnatd(a,a0,isex(r,r,a,a0,t26,a0ir,refis(real,r)),t27):natd(a0)
--ivr2
-n@natrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),natd(x)),n,natd(a0),[x:dif][t:and(inn(x,class(r)),natd(x))]t28".ivr2"(x,t)):natd(a0)
-+*ivr2
-a0ir@[n:natrl(r)]
-t29:=natposd(a0,natrlex(n)):posd(a0)
-t30:=posin(t29):pos(r)
--ivr2
-r@[n:natrl(r)]
-natpos:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t30".ivr2"(x,t,n)):pos(r)
-@[x:nat]
-rlofnt:=realof(pdofnt(x)):real
-natrli:=natrlin(rlofnt(x),pdofnt(x),innclass(pdofnt(x)),natdi(x)):natrl(rlofnt(x))
-[y:nat][i:is"n"(x,y)]
-isnterl:=isf(nat,real,[u:nat]rlofnt(u),x,y,i):is(rlofnt(x),rlofnt(y))
-y@[i:is(rlofnt(x),rlofnt(y))]
-isntirl:=isntirp(x,y,isrpip(rpofnt(x),rpofnt(y),i)):is"n"(x,y)
-+*ivr2
-@t31:=[x:nat][y:nat][t:is(rlofnt(x),rlofnt(y))]isntirl(x,y,t):injective(nat,real,[x:nat]rlofnt(x))
-a0ir@[n:natrl(r)]
-t32:=natposd(a0,natrlex(n)):posd(a0)
-ap:=rpofpd(a0,t32):cut
-t33:=natderp(a0,natrlex(n)):natrp(ap)
-x0:=ntofrp(ap,t33):nat
-t34:=isrpepd(ap,rpofnt(x0),isrpnt1(ap,t33)):eq"rp"(pdofrp(ap),pdofnt(x0))
-t35:=treq"rp"(a0,pdofrp(ap),pdofnt(x0),eqpdrp1(a0,t32),t34):eq"rp"(a0,pdofnt(x0))
-t36:=isin(r,rlofnt(x0),a0,pdofnt(x0),a0ir,innclass(pdofnt(x0)),t35):is(r,rlofnt(x0))
-t37:=somei(nat,[x:nat]is(r,rlofnt(x)),x0,t36):image(nat,real,[x:nat]rlofnt(x),r)
--ivr2
-r@[n:natrl(r)]
-natimage:=realapp1(image(nat,real,[x:nat]rlofnt(x),r),[x:dif][t:inn(x,class(r))]t37".ivr2"(x,t,n)):image(nat,real,[x:nat]rlofnt(x),r)
-r@[i:image(nat,real,[x:nat]rlofnt(x),r)]
-+*ivr2
-i"r"@[x:nat][j:is(r,rlofnt(x))]
-t38:=isp1(real,[u:real]natrl(u),rlofnt(x),r,natrli(x),j):natrl(r)
--ivr2
-i@imagenat:=someapp(nat,[u:nat]is(r,rlofnt(u)),i,natrl(r),[u:nat][v:is(r,rlofnt(u))]t38".ivr2"(u,v)):natrl(r)
-r@[n:natrl(r)]
-ntofrl:=soft(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):nat
-@[r1:real][n:natrl(r1)][s1:real][m:natrl(s1)][i:is(r1,s1)]
-isrlent:=isinv(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is"n"(ntofrl(r1,n),ntofrl(s1,m))
-m@[i:is"n"(ntofrl(r1,n),ntofrl(s1,m))]
-isrlint:=isinve(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is(r1,s1)
-r@[n:natrl(r)]
-isrlnt1:=ists1"e"(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):is(r,rlofnt(ntofrl(r,n)))
-isrlnt2:=symis(real,r,rlofnt(ntofrl(r,n)),isrlnt1):is(rlofnt(ntofrl(r,n)),r)
-@[x:nat]
-+*ivr2
-x"r"@xn:=soft(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x)):nat
-t39:=isinv(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x),rlofnt(x),natimage(rlofnt(x),natrli(x)),refis(real,rlofnt(x))):is"n"(xn,ntofrl(rlofnt(x),natrli(x)))
--ivr2
-x@isntrl1:=tris(nat,x,xn".ivr2",ntofrl(rlofnt(x),natrli(x)),isst1(nat,real,[u:nat]rlofnt(u),t31".ivr2",x),t39".ivr2"):is"n"(x,ntofrl(rlofnt(x),natrli(x)))
-isntrl2:=symis(nat,x,ntofrl(rlofnt(x),natrli(x)),isntrl1):is"n"(ntofrl(rlofnt(x),natrli(x)),x)
-r@intrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),intd(x))):'prop'
-a0ir@[i:intd(a0)]
-+*ivr2
-i@t40:=andi(inn(a0,class(r)),intd(a0),a0ir,i):and(inn(a0,class(r)),intd(a0))
--ivr2
-i@intrlin:=somei(dif,[x:dif]and(inn(x,class(r)),intd(x)),a0,t40".ivr2"):intrl(r)
-a0ir@[i:intrl(r)]
-+*ivr2
-i@[a:dif][b:and(inn(a,class(r)),intd(a))]
-t41:=ande1(inn(a,class(r)),intd(a),b):inn(a,class(r))
-t42:=ande2(inn(a,class(r)),intd(a),b):intd(a)
-t43:=eqintd(a,a0,isex(r,r,a,a0,t41,a0ir,refis(real,r)),t42):intd(a0)
--ivr2
-i@intrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),intd(x)),i,intd(a0),[x:dif][t:and(inn(x,class(r)),intd(x))]t43".ivr2"(x,t)):intd(a0)
-+*ivr2
-a0ir@[n:natrl(r)]
-t44:=natintd(a0,natrlex(n)):intd(a0)
-t45:=intrlin(t44):intrl(r)
--ivr2
-r@[n:natrl(r)]
-natintrl:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t45".ivr2"(x,t,n)):intrl(r)
-+*ivr2
-a0ir@[p:pos(r)][i:intrl(r)]
-t46:=posintnatd(a0,posex(p),intrlex(i)):natd(a0)
-t47:=natrlin(t46):natrl(r)
--ivr2
-r@[p:pos(r)][i:intrl(r)]
-posintnatrl:=realapp1(natrl(r),[x:dif][t:inn(x,class(r))]t47".ivr2"(x,t,p,i)):natrl(r)
-+*ivr2
-a0ir@[i2:is(r,0)]
-t48:=intdi0(a0,0ex(i2)):intd(a0)
-t49:=intrlin(t48):intrl(r)
--ivr2
-r@[i:is(r,0)]
-intrli0:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t49".ivr2"(x,t,i)):intrl(r)
-r0@[n:natrp(r0)]
-remark6:=intrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark6"rp"(r0,n)):intrl(pofrp(r0))
-remark7:=intrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark7"rp"(r0,n)):intrl(nofrp(r0))
-+2r174
-a0ir@[i:intrl(r)]
-t1:=satzd174(a0,intrlex(i)):ratd(a0)
-t2:=ratrlin(t1):ratrl(r)
--2r174
-r@[i:intrl(r)]
-satz174:=realapp1(ratrl(r),[x:dif][t:inn(x,class(r))]t2".2r174"(x,t,i)):ratrl(r)
-@plusdr:=[x:dif][y:dif]realof(pd(x,y)):[x:dif][y:dif]real
-+ivr3
-[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
-t1:=isin(realof(pd(a,c)),realof(pd(b,d)),pd(a,c),pd(b,d),innclass(pd(a,c)),innclass(pd(b,d)),eqpd12(a,b,c,d,e,f)):is(<c><a>plusdr,<d><b>plusdr)
--ivr3
-fplusdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr3"(x,y,z,v,t,u):fixf2(real,plusdr)
-s@pl:=indreal2(real,plusdr,fplusdr,r,s):real
-+*ivr3
-b1is@t2:=isindreal2(real,plusdr,fplusdr,r,s,a1,b1,a1ir,b1is):is(realof(pd(a1,b1)),pl(r,s))
--ivr3
-b1is@picp:=isp(real,[x:real]inn(pd(a1,b1),class(x)),realof(pd(a1,b1)),pl(r,s),innclass(pd(a1,b1)),t2".ivr3"):inn(pd(a1,b1),class(pl(r,s)))
-t@[i:is(r,s)]
-ispl1:=isf(real,real,[x:real]pl(x,t),r,s,i):is(pl(r,t),pl(s,t))
-ispl2:=isf(real,real,[x:real]pl(t,x),r,s,i):is(pl(t,r),pl(t,s))
-u@[i:is(r,s)][j:is(t,u)]
-ispl12:=tris(real,pl(r,t),pl(s,t),pl(s,u),ispl1(i),ispl2(t,u,s,j)):is(pl(r,t),pl(s,u))
-+3r175
-b1is@t1:=satzd175(a1,b1):eq"rp"(pd(a1,b1),pd(b1,a1))
-t2:=isin(pl(r,s),pl(s,r),pd(a1,b1),pd(b1,a1),picp,picp(s,r,b1,a1,b1is,a1ir),t1):is(pl(r,s),pl(s,r))
--3r175
-s@satz175:=realapp2(is(pl(r,s),pl(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r175"(x,y,t,u)):is(pl(r,s),pl(s,r))
-compl:=satz175:is(pl(r,s),pl(s,r))
-+*ivr3
-b1is@[i:is(r,0)]
-t3:=pd01(a1,b1,0ex(r,a1,a1ir,i)):eq"rp"(pd(a1,b1),b1)
-t4:=isin(pl(r,s),s,pd(a1,b1),b1,picp,b1is,t3):is(pl(r,s),s)
--ivr3
-s@[i:is(r,0)]
-pl01:=realapp2(is(pl(r,s),s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr3"(x,y,t,u,i)):is(pl(r,s),s)
-s@[i:is(s,0)]
-pl02:=tris(real,pl(r,s),pl(s,r),r,compl,pl01(s,r,i)):is(pl(r,s),r)
-+*ivr3
-b1is@[p:pos(r)][q:pos(s)]
-t5:=ppd(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(pd(a1,b1))
-t6:=posin(pl(r,s),pd(a1,b1),picp,t5):pos(pl(r,s))
--ivr3
-s@[p:pos(r)][q:pos(s)]
-pospl:=realapp2(pos(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr3"(x,y,t,u,p,q)):pos(pl(r,s))
-+*ivr3
-b1is@[n:neg(r)][o:neg(s)]
-t7:=npd(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):negd(pd(a1,b1))
-t8:=negin(pl(r,s),pd(a1,b1),picp,t7):neg(pl(r,s))
--ivr3
-s@[n:neg(r)][o:neg(s)]
-negpl:=realapp2(neg(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".ivr3"(x,y,t,u,n,o)):neg(pl(r,s))
-@m0dr:=[x:dif]realof(m0d(x)):[x:dif]real
-+*ivr3
-@[a:dif][b:dif][e:eq"rp"(a,b)]
-t5a:=isin(realof(m0d(a)),realof(m0d(b)),m0d(a),m0d(b),innclass(m0d(a)),innclass(m0d(b)),eqm0d(a,b,e)):is(<a>m0dr,<b>m0dr)
--ivr3
-@fm0dr:=[x:dif][y:dif][t:<y><x>eq]t5a".ivr3"(x,y,t):fixf(real,m0dr)
-r@m0:=indreal(real,m0dr,fm0dr,r):real
-+*ivr3
-a0ir@t6a:=isindreal(real,m0dr,fm0dr,r,a0,a0ir):is(realof(m0d(a0)),m0(r))
--ivr3
-a0ir@micm0:=isp(real,[x:real]inn(m0d(a0),class(x)),realof(m0d(a0)),m0(r),innclass(m0d(a0)),t6a".ivr3"):inn(m0d(a0),class(m0(r)))
-s@[i:is(r,s)]
-ism0:=isf(real,real,[x:real]m0(x),r,s,i):is(m0(r),m0(s))
-+*ivr3
-a0ir@[n:neg(r)]
-t7a:=absnd(a0,negex(n)):eq"rp"(absd(a0),m0d(a0))
-t8a:=isin(abs(r),m0(r),absd(a0),m0d(a0),aica,micm0,t7a):is(abs(r),m0(r))
--ivr3
-r@[n:neg(r)]
-absn:=realapp1(is(abs(r),m0(r)),[x:dif][t:inn(x,class(r))]t8a".ivr3"(x,t,n)):is(abs(r),m0(r))
-+*ivr3
-a0ir@[nn:not(neg(r))]
-t9:=absnnd(a0,th3"l.imp"(negd(a0),neg(r),nn,[t:negd(a0)]negin(t))):eq"rp"(absd(a0),a0)
-t10:=isin(abs(r),r,absd(a0),a0,aica,a0ir,t9):is(abs(r),r)
--ivr3
-r@[nn:not(neg(r))]
-absnn:=realapp1(is(abs(r),r),[x:dif][t:inn(x,class(r))]t10".ivr3"(x,t,nn)):is(abs(r),r)
-r@[p:pos(r)]
-absp:=absnn(r,pnotn(r,p)):is(abs(r),r)
-r@[i:is(r,0)]
-abs0:=tris(real,abs(r),r,0,absnn(r,0notn(r,i)),i):is(abs(r),0)
-+3r176
-a0ir@[p:pos(r)]
-t1:=satzd176a(a0,posex(p)):negd(m0d(a0))
-t2:=negin(m0(r),m0d(a0),micm0,t1):neg(m0(r))
--3r176
-r@[p:pos(r)]
-satz176a:=realapp1(neg(m0(r)),[x:dif][t:inn(x,class(r))]t2".3r176"(x,t,p)):neg(m0(r))
-+*3r176
-a0ir@[i:is(r,0)]
-t3:=satzd176b(a0,0ex(i)):zero(m0d(a0))
-t4:=0in(m0(r),m0d(a0),micm0,t3):is(m0(r),0)
--3r176
-r@[i:is(r,0)]
-satz176b:=realapp1(is(m0(r),0),[x:dif][t:inn(x,class(r))]t4".3r176"(x,t,i)):is(m0(r),0)
-+*3r176
-a0ir@[n:neg(r)]
-t5:=satzd176c(a0,negex(n)):posd(m0d(a0))
-t6:=posin(m0(r),m0d(a0),micm0,t5):pos(m0(r))
--3r176
-r@[n:neg(r)]
-satz176c:=realapp1(pos(m0(r)),[x:dif][t:inn(x,class(r))]t6".3r176"(x,t,n)):pos(m0(r))
-+*3r176
-a0ir@[n:neg(m0(r))]
-t7:=satzd176d(a0,negex(m0(r),m0d(a0),micm0,n)):posd(a0)
-t8:=posin(t7):pos(r)
--3r176
-r@[n:neg(m0(r))]
-satz176d:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t8".3r176"(x,t,n)):pos(r)
-+*3r176
-a0ir@[i:is(m0(r),0)]
-t9:=satzd176e(a0,0ex(m0(r),m0d(a0),micm0,i)):zero(a0)
-t10:=0in(t9):is(r,0)
--3r176
-r@[i:is(m0(r),0)]
-satz176e:=realapp1(is(r,0),[x:dif][t:inn(x,class(r))]t10".3r176"(x,t,i)):is(r,0)
-+*3r176
-a0ir@[p:pos(m0(r))]
-t11:=satzd176f(a0,posex(m0(r),m0d(a0),micm0,p)):negd(a0)
-t12:=negin(t11):neg(r)
--3r176
-r@[p:pos(m0(r))]
-satz176f:=realapp1(neg(r),[x:dif][t:inn(x,class(r))]t12".3r176"(x,t,p)):neg(r)
-+3r177
-a0ir@t1:=isin(m0(m0(r)),r,m0d(m0d(a0)),a0,micm0(m0(r),m0d(a0),micm0),a0ir,satzd177(a0)):is(m0(m0(r)),r)
--3r177
-r@satz177:=realapp1(is(m0(m0(r)),r),[x:dif][t:inn(x,class(r))]t1".3r177"(x,t)):is(m0(m0(r)),r)
-satz177a:=symis(real,m0(m0(r)),r,satz177):is(r,m0(m0(r)))
-s@[i:is(r,m0(s))]
-satz177b:=tris(real,m0(r),m0(m0(s)),s,ism0(r,m0(s),i),satz177(s)):is(m0(r),s)
-satz177c:=symis(real,m0(r),s,satz177b):is(s,m0(r))
-s@[i:is(m0(r),s)]
-satz177d:=satz177c(s,r,symis(real,m0(r),s,i)):is(r,m0(s))
-satz177e:=symis(real,r,m0(s),satz177d):is(m0(s),r)
-+3r178
-a0ir@t1:=isin(abs(m0(r)),abs(r),absd(m0d(a0)),absd(a0),aica(m0(r),m0d(a0),micm0),aica,satzd178(a0)):is(abs(m0(r)),abs(r))
--3r178
-r@satz178:=realapp1(is(abs(m0(r)),abs(r)),[x:dif][t:inn(x,class(r))]t1".3r178"(x,t)):is(abs(m0(r)),abs(r))
-satz178a:=symis(real,abs(m0(r)),abs(r),satz178):is(abs(r),abs(m0(r)))
-+3r179
-a0ir@t1:=0in(pl(r,m0(r)),pd(a0,m0d(a0)),picp(r,m0(r),a0,m0d(a0),a0ir,micm0),satzd179(a0)):is(pl(r,m0(r)),0)
--3r179
-satz179:=realapp1(is(pl(r,m0(r)),0),[x:dif][t:inn(x,class(r))]t1".3r179"(x,t)):is(pl(r,m0(r)),0)
-satz179a:=tris(real,pl(m0(r),r),pl(r,m0(r)),0,compl(m0(r),r),satz179):is(pl(m0(r),r),0)
-+3r180
-b1is@t1:=isin(m0(pl(r,s)),pl(m0(r),m0(s)),m0d(pd(a1,b1)),pd(m0d(a1),m0d(b1)),micm0(pl(r,s),pd(a1,b1),picp),picp(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is)),satzd180(a1,b1)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
--3r180
-s@satz180:=realapp2(is(m0(pl(r,s)),pl(m0(r),m0(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t1".3r180"(x,y,t,u)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
-satz180a:=symis(real,m0(pl(r,s)),pl(m0(r),m0(s)),satz180):is(pl(m0(r),m0(s)),m0(pl(r,s)))
-mn:=pl(r,m0(s)):real
-b1is@micmn:=picp(r,m0(s),a1,m0d(b1),a1ir,micm0(s,b1,b1is)):inn(md(a1,b1),class(mn(r,s)))
-t@[i:is(r,s)]
-ismn1:=ispl1(r,s,m0(t),i):is(mn(r,t),mn(s,t))
-ismn2:=ispl2(m0(r),m0(s),t,ism0(r,s,i)):is(mn(t,r),mn(t,s))
-u@[i:is(r,s)][j:is(t,u)]
-ismn12:=ispl12(r,s,m0(t),m0(u),i,ism0(t,u,j)):is(mn(r,t),mn(s,u))
-s@satz181:=tr3is(real,m0(mn(r,s)),pl(m0(r),m0(m0(s))),pl(m0(r),s),mn(s,r),satz180(r,m0(s)),ispl2(m0(m0(s)),s,m0(r),satz177(s)),compl(m0(r),s)):is(m0(mn(r,s)),mn(s,r))
-satz181a:=symis(real,m0(mn(s,r)),mn(r,s),satz181(s,r)):is(mn(r,s),m0(mn(s,r)))
-+3r182
-b1is@[p:pos(mn(r,s))]
-t1:=satzd182a(a1,b1,posex(mn(r,s),md(a1,b1),micmn,p)):mored(a1,b1)
-t2:=morein(t1):more(r,s)
--3r182
-[p:pos(mn(r,s))]
-satz182a:=realapp2(more(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r182"(x,y,t,u,p)):more(r,s)
-+*3r182
-b1is@[i:is(mn(r,s),0)]
-t3:=satzd182b(a1,b1,0ex(mn(r,s),md(a1,b1),micmn,i)):eq"rp"(a1,b1)
-t4:=isin(t3):is(r,s)
--3r182
-s@[i:is(mn(r,s),0)]
-satz182b:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r182"(x,y,t,u,i)):is(r,s)
-+*3r182
-b1is@[n:neg(mn(r,s))]
-t5:=satzd182c(a1,b1,negex(mn(r,s),md(a1,b1),micmn,n)):lessd(a1,b1)
-t6:=lessin(t5):less(r,s)
--3r182
-s@[n:neg(mn(r,s))]
-satz182c:=realapp2(less(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".3r182"(x,y,t,u,n)):less(r,s)
-+*3r182
-b1is@[m:more(r,s)]
-t7:=satzd182d(a1,b1,moreex(m)):posd(md(a1,b1))
-t8:=posin(mn(r,s),md(a1,b1),micmn,t7):pos(mn(r,s))
--3r182
-s@[m:more(r,s)]
-satz182d:=realapp2(pos(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".3r182"(x,y,t,u,m)):pos(mn(r,s))
-+*3r182
-b1is@[i:is(r,s)]
-t9:=satzd182e(a1,b1,isex(i)):zero(md(a1,b1))
-t10:=0in(mn(r,s),md(a1,b1),micmn,t9):is(mn(r,s),0)
--3r182
-s@[i:is(r,s)]
-satz182e:=realapp2(is(mn(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t10".3r182"(x,y,t,u,i)):is(mn(r,s),0)
-+*3r182
-b1is@[l:less(r,s)]
-t11:=satzd182f(a1,b1,lessex(l)):negd(md(a1,b1))
-t12:=negin(mn(r,s),md(a1,b1),micmn,t11):neg(mn(r,s))
--3r182
-s@[l:less(r,s)]
-satz182f:=realapp2(neg(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t12".3r182"(x,y,t,u,l)):neg(mn(r,s))
-+3r183
-b1is@[m:more(r,s)]
-t1:=satzd183a(a1,b1,moreex(m)):lessd(m0d(a1),m0d(b1))
-t2:=lessin(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t1):less(m0(r),m0(s))
--3r183
-s@[m:more(r,s)]
-satz183a:=realapp2(less(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r183"(x,y,t,u,m)):less(m0(r),m0(s))
-s@[i:is(r,s)]
-satz183b:=ism0(r,s,i):is(m0(r),m0(s))
-+*3r183
-b1is@[l:less(r,s)]
-t3:=satzd183c(a1,b1,lessex(l)):mored(m0d(a1),m0d(b1))
-t4:=morein(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t3):more(m0(r),m0(s))
--3r183
-s@[l:less(r,s)]
-satz183c:=realapp2(more(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r183"(x,y,t,u,l)):more(m0(r),m0(s))
-s@[l:less(m0(r),m0(s))]
-satz183d:=ismore12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183c(m0(r),m0(s),l)):more(r,s)
-s@[i:is(m0(r),m0(s))]
-satz183e:=tr3is(real,r,m0(m0(r)),m0(m0(s)),s,satz177a(r),ism0(m0(r),m0(s),i),satz177(s)):is(r,s)
-s@[m:more(m0(r),m0(s))]
-satz183f:=isless12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183a(m0(r),m0(s),m)):less(r,s)
-+3r184
-t@prop1:=and3(pos(s),pos(t),is(r,mn(s,t))):'prop'
-s@prop2:=some([x:real]prop1(x)):'prop'
-r@prop3:=some([x:real]prop2(x)):'prop'
-a0ir@[a:dif][b:dif]
-prop1d:=and3(posd(a),posd(b),eq"rp"(a0,md(a,b))):'prop'
-a@prop2d:=some"l"(dif,[x:dif]prop1d(x)):'prop'
-[p2:prop2d(a)][b:dif][p1:prop1d(a,b)]
-t1:=and3e1(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(a)
-t2:=and3e2(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(b)
-t3:=and3e3(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):eq"rp"(a0,md(a,b))
-p2@ra:=realof(a):real
-p1@rb:=realof(b):real
-t4:=innclass(a):inn(a,class(ra))
-t5:=innclass(b):inn(b,class(rb))
-t6:=isin(r,mn(ra,rb),a0,md(a,b),a0ir,micmn(ra,rb,a,b,t4,t5),t3):is(r,mn(ra,rb))
-t7:=and3i(pos(ra),pos(rb),is(r,mn(ra,rb)),posin(ra,a,t4,t1),posin(rb,b,t5,t2),t6):prop1(ra,rb)
-t8:=somei(real,[x:real]prop1(ra,x),rb,t7):prop2(ra)
-p2@t9:=someapp(dif,[x:dif]prop1d(a,x),p2,prop2(ra),[x:dif][t:prop1d(a,x)]t8(x,t)):prop2(ra)
-t10:=somei(real,[x:real]prop2(x),ra,t9):prop3
-a0ir@t11:=someapp(dif,[x:dif]prop2d(x),satzd184(a0),prop3,[x:dif][t:prop2d(x)]t10(x,t)):prop3
--3r184
-r@satz184:=realapp1(prop3".3r184",[x:dif][t:inn(x,class(r))]t11".3r184"(x,t)):some([x:real]some([y:real]and3(pos(x),pos(y),is(r,mn(x,y)))))
-u@[a3:dif][b3:dif][c3:dif][d3:dif][a3ir:inn(a3,class(r))][b3is:inn(b3,class(s))][c3it:inn(c3,class(t))][d3iu:inn(d3,class(u))]
-+3r185
-t1:=satzd185(a3,b3,c3,d3):eq"rp"(pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)))
-t2:=isin(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)),pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)),picp(mn(r,s),mn(t,u),md(a3,b3),md(c3,d3),micmn(r,s,a3,b3,a3ir,b3is),micmn(t,u,c3,d3,c3it,d3iu)),micmn(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu)),t1):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
--3r185
-u@satz185:=realapp4(is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u))),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r185"(x,y,z,v,xi,yi,zi,vi)):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
-+3r186
-c2it@t1:=satzd186(a2,b2,c2):eq"rp"(pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)))
-t2:=isin(pl(pl(r,s),t),pl(r,pl(s,t)),pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)),picp(pl(r,s),t,pd(a2,b2),c2,picp(r,s,a2,b2,a2ir,b2is),c2it),picp(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),t1):is(pl(pl(r,s),t),pl(r,pl(s,t)))
--3r186
-t@satz186:=realapp3(is(pl(pl(r,s),t),pl(r,pl(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r186"(x,y,z,u,v,w)):is(pl(pl(r,s),t),pl(r,pl(s,t)))
-asspl1:=satz186:is(pl(pl(r,s),t),pl(r,pl(s,t)))
-asspl2:=symis(real,pl(pl(r,s),t),pl(r,pl(s,t)),satz186):is(pl(r,pl(s,t)),pl(pl(r,s),t))
-s@plmn:=tris(real,pl(mn(r,s),s),pl(r,pl(m0(s),s)),r,asspl1(r,m0(s),s),pl02(r,pl(m0(s),s),satz179a(s))):is(pl(mn(r,s),s),r)
-mnpl:=tris(real,mn(pl(r,s),s),pl(r,pl(s,m0(s))),r,asspl1(r,s,m0(s)),pl02(r,pl(s,m0(s)),satz179(s))):is(mn(pl(r,s),s),r)
-satz187a:=tris(real,pl(s,mn(r,s)),pl(mn(r,s),s),r,compl(s,mn(r,s)),plmn):is(pl(s,mn(r,s)),r)
-satz187b:=somei(real,[x:real]is(pl(s,x),r),mn(r,s),satz187a):some([x:real]is(pl(s,x),r))
-[x:real][i:is(pl(s,x),r)]
-satz187c:=tris(real,mn(r,s),mn(pl(x,s),s),x,ismn1(r,pl(x,s),s,tris1(real,r,pl(x,s),pl(s,x),i,compl(s,x))),mnpl(x,s)):is(mn(r,s),x)
-satz187d:=symis(real,mn(r,s),x,satz187c):is(x,mn(r,s))
-x@[i:is(pl(x,s),r)]
-satz187e:=satz187c(tris(real,pl(s,x),pl(x,s),r,compl(s,x),i)):is(mn(r,s),x)
-satz187f:=symis(real,mn(r,s),x,satz187e):is(x,mn(r,s))
-+3r187
-s@[x:real][y:real][i:is(pl(s,x),r)][j:is(pl(s,y),r)]
-t1:=tris1(real,x,y,mn(r,s),satz187c(x,i),satz187c(y,j)):is(x,y)
-s@t2:=[x:real][y:real][t:is(pl(s,x),r)][u:is(pl(s,y),r)]t1(x,y,t,u):amone(real,[x:real]is(pl(s,x),r))
--3r187
-s@satz187:=onei(real,[x:real]is(pl(s,x),r),t2".3r187",satz187b):one([x:real]is(pl(s,x),r))
-+3r188
-c2it@[m:more(pl(r,t),pl(s,t))]
-t1:=satzd188a(a2,b2,c2,moreex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),m)):mored(a2,b2)
-t2:=morein(r,s,a2,b2,a2ir,b2is,t1):more(r,s)
--3r188
-t@[m:more(pl(r,t),pl(s,t))]
-satz188a:=realapp3(more(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r188"(x,y,z,u,v,w,m)):more(r,s)
-+*3r188
-c2it@[i:is(pl(r,t),pl(s,t))]
-t3:=satzd188b(a2,b2,c2,isex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),i)):eq"rp"(a2,b2)
-t4:=isin(r,s,a2,b2,a2ir,b2is,t3):is(r,s)
--3r188
-t@[i:is(pl(r,t),pl(s,t))]
-satz188b:=realapp3(is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".3r188"(x,y,z,u,v,w,i)):is(r,s)
-+*3r188
-c2it@[l:less(pl(r,t),pl(s,t))]
-t5:=satzd188c(a2,b2,c2,lessex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),l)):lessd(a2,b2)
-t6:=lessin(r,s,a2,b2,a2ir,b2is,t5):less(r,s)
--3r188
-t@[l:less(pl(r,t),pl(s,t))]
-satz188c:=realapp3(less(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t6".3r188"(x,y,z,u,v,w,l)):less(r,s)
-+*3r188
-c2it@[m:more(r,s)]
-t7:=satzd188d(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m)):mored(pd(a2,c2),pd(b2,c2))
-t8:=morein(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t7):more(pl(r,t),pl(s,t))
--3r188
-t@[m:more(r,s)]
-satz188d:=realapp3(more(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t8".3r188"(x,y,z,u,v,w,m)):more(pl(r,t),pl(s,t))
-t@[i:is(r,s)]
-satz188e:=ispl1(r,s,t,i):is(pl(r,t),pl(s,t))
-+*3r188
-c2it@[l:less(r,s)]
-t9:=satzd188f(a2,b2,c2,lessex(r,s,a2,b2,a2ir,b2is,l)):lessd(pd(a2,c2),pd(b2,c2))
-t10:=lessin(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t9):less(pl(r,t),pl(s,t))
--3r188
-t@[l:less(r,s)]
-satz188f:=realapp3(less(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t10".3r188"(x,y,z,u,v,w,l)):less(pl(r,t),pl(s,t))
-t@[m:more(pl(t,r),pl(t,s))]
-satz188g:=satz188a(ismore12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),m)):more(r,s)
-t@[i:is(pl(t,r),pl(t,s))]
-satz188h:=satz188b(tr3is(real,pl(r,t),pl(t,r),pl(t,s),pl(s,t),compl(r,t),i,compl(t,s))):is(r,s)
-t@[l:less(pl(t,r),pl(t,s))]
-satz188j:=satz188c(isless12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),l)):less(r,s)
-t@[m:more(r,s)]
-satz188k:=ismore12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188d(m)):more(pl(t,r),pl(t,s))
-t@[i:is(r,s)]
-satz188l:=ispl2(r,s,t,i):is(pl(t,r),pl(t,s))
-t@[l:less(r,s)]
-satz188m:=isless12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188f(l)):less(pl(t,r),pl(t,s))
-u@[i:is(r,s)][m:more(t,u)]
-satz188n:=ismore2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188k(t,u,r,m)):more(pl(r,t),pl(s,u))
-satz188o:=ismore12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188n):more(pl(t,r),pl(u,s))
-i@[l:less(t,u)]
-satz188p:=isless2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188m(t,u,r,l)):less(pl(r,t),pl(s,u))
-satz188q:=isless12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188p):less(pl(t,r),pl(u,s))
-u@[m:more(r,s)][n:more(t,u)]
-satz189:=trmore(pl(r,t),pl(s,t),pl(s,u),satz188d(m),satz188k(t,u,s,n)):more(pl(r,t),pl(s,u))
-u@[l:less(r,s)][k:less(t,u)]
-satz189a:=lemma1(pl(s,u),pl(r,t),satz189(s,r,u,t,lemma2(r,s,l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
-u@[m:moreis(r,s)][n:more(t,u)]
-satz190a:=orapp(more(r,s),is(r,s),more(pl(r,t),pl(s,u)),m,[v:more(r,s)]satz189(v,n),[v:is(r,s)]satz188n(v,n)):more(pl(r,t),pl(s,u))
-u@[m:more(r,s)][n:moreis(t,u)]
-satz190b:=ismore12(pl(t,r),pl(r,t),pl(u,s),pl(s,u),compl(t,r),compl(u,s),satz190a(t,u,r,s,n,m)):more(pl(r,t),pl(s,u))
-u@[l:lessis(r,s)][k:less(t,u)]
-satz190c:=lemma1(pl(s,u),pl(r,t),satz190a(s,r,u,t,satz168b(l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
-u@[l:less(r,s)][k:lessis(t,u)]
-satz190d:=lemma1(pl(s,u),pl(r,t),satz190b(s,r,u,t,lemma2(l),satz168b(t,u,k))):less(pl(r,t),pl(s,u))
-+3r191
-d3iu@[m:moreis(r,s)][n:moreis(t,u)]
-t1:=satzd191(a3,b3,c3,d3,moreisex(r,s,a3,b3,a3ir,b3is,m),moreisex(t,u,c3,d3,c3it,d3iu,n)):moreq(pd(a3,c3),pd(b3,d3))
-t2:=moreisin(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu),t1):moreis(pl(r,t),pl(s,u))
--3r191
-u@[m:moreis(r,s)][n:moreis(t,u)]
-satz191:=realapp4(moreis(pl(r,t),pl(s,u)),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r191"(x,y,z,v,xi,yi,zi,vi,m,n)):moreis(pl(r,t),pl(s,u))
-u@[l:lessis(r,s)][k:lessis(t,u)]
-satz191a:=satz168a(pl(s,u),pl(r,t),satz191(s,r,u,t,satz168b(l),satz168b(t,u,k))):lessis(pl(r,t),pl(s,u))
-@timesdr:=[x:dif][y:dif]realof(td(x,y)):[x:dif][y:dif]real
-+ivr4
-[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
-t1:=isin(realof(td(a,c)),realof(td(b,d)),td(a,c),td(b,d),innclass(td(a,c)),innclass(td(b,d)),eqtd12(a,b,c,d,e,f)):is(<c><a>timesdr,<d><b>timesdr)
--ivr4
-ftimesdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr4"(x,y,z,v,t,u):fixf2(real,timesdr)
-s@ts:=indreal2(real,timesdr,ftimesdr,r,s):real
-+*ivr4
-b1is@t2:=isindreal2(real,timesdr,ftimesdr,r,s,a1,b1,a1ir,b1is):is(realof(td(a1,b1)),ts(r,s))
--ivr4
-b1is@tict:=isp(real,[x:real]inn(td(a1,b1),class(x)),realof(td(a1,b1)),ts(r,s),innclass(td(a1,b1)),t2".ivr4"):inn(td(a1,b1),class(ts(r,s)))
-t@[i:is(r,s)]
-ists1:=isf(real,real,[x:real]ts(x,t),r,s,i):is(ts(r,t),ts(s,t))
-ists2:=isf(real,real,[x:real]ts(t,x),r,s,i):is(ts(t,r),ts(t,s))
-u@[i:is(r,s)][j:is(t,u)]
-ists12:=tris(real,ts(r,t),ts(s,t),ts(s,u),ists1(i),ists2(t,u,s,j)):is(ts(r,t),ts(s,u))
-+4r192
-b1is@[i:is(r,0)]
-t1:=satzd192a(a1,b1,0ex(r,a1,a1ir,i)):zero(td(a1,b1))
-t2:=0in(ts(r,s),td(a1,b1),tict,t1):is(ts(r,s),0)
--4r192
-s@[i:is(r,0)]
-satz192a:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r192"(x,y,t,u,i)):is(ts(r,s),0)
-+*4r192
-b1is@[i:is(s,0)]
-t3:=satzd192b(a1,b1,0ex(s,b1,b1is,i)):zero(td(a1,b1))
-t4:=0in(ts(r,s),td(a1,b1),tict,t3):is(ts(r,s),0)
--4r192
-s@[i:is(s,0)]
-satz192b:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".4r192"(x,y,t,u,i)):is(ts(r,s),0)
-+*4r192
-b1is@[i:is(ts(r,s),0)]
-t5:=satzd192c(a1,b1,0ex(ts(r,s),td(a1,b1),tict,i)):or(zero(a1),zero(b1))
-t6:=th9"l.or"(zero(a1),zero(b1),is(r,0),is(s,0),t5,[t:zero(a1)]0in(r,a1,a1ir,t),[t:zero(b1)]0in(s,b1,b1is,t)):or(is(r,0),is(s,0))
--4r192
-s@[i:is(ts(r,s),0)]
-satz192c:=realapp2(or(is(r,0),is(s,0)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".4r192"(x,y,t,u,i)):or(is(r,0),is(s,0))
-s@[n:nis(r,0)][o:nis(s,0)]
-satz192d:=th3"l.imp"(is(ts(r,s),0),or(is(r,0),is(s,0)),th3"l.or"(is(r,0),is(s,0),n,o),[t:is(ts(r,s),0)]satz192c(t)):nis(ts(r,s),0)
-s@[i:is(r,0)]
-ts01:=satz192a(i):is(ts(r,s),0)
-s@[i:is(s,0)]
-ts02:=satz192b(i):is(ts(r,s),0)
-+4r193
-b1is@t1:=satzd193(a1,b1):eq"rp"(absd(td(a1,b1)),td(absd(a1),absd(b1)))
-t2:=isin(abs(ts(r,s)),ts(abs(r),abs(s)),absd(td(a1,b1)),td(absd(a1),absd(b1)),aica(ts(r,s),td(a1,b1),tict),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(abs(ts(r,s)),ts(abs(r),abs(s)))
--4r193
-s@satz193:=realapp2(is(abs(ts(r,s)),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r193"(x,y,t,u)):is(abs(ts(r,s)),ts(abs(r),abs(s)))
-satz193a:=symis(real,abs(ts(r,s)),ts(abs(r),abs(s)),satz193):is(ts(abs(r),abs(s)),abs(ts(r,s)))
-+4r194
-b1is@t1:=satzd194(a1,b1):eq"rp"(td(a1,b1),td(b1,a1))
-t2:=isin(ts(r,s),ts(s,r),td(a1,b1),td(b1,a1),tict,tict(s,r,b1,a1,b1is,a1ir),t1):is(ts(r,s),ts(s,r))
--4r194
-satz194:=realapp2(is(ts(r,s),ts(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r194"(x,y,t,u)):is(ts(r,s),ts(s,r))
-comts:=satz194:is(ts(r,s),ts(s,r))
-@1rl:=realof(1df):real
-pos1:=posin(1rl,1df,innclass(1df),posdirp(1rp)):pos(1rl)
-natrl1:=natrli(1):natrl(1rl)
-intrl1:=natintrl(1rl,natrl1):intrl(1rl)
-+4r195
-a0ir@t1:=satzd195(a0):eq"rp"(td(a0,1df),a0)
-t2:=isin(ts(r,1rl),r,td(a0,1df),a0,tict(r,1rl,a0,1df,a0ir,innclass(1df)),a0ir,t1):is(ts(r,1rl),r)
--4r195
-r@satz195:=realapp1(is(ts(r,1rl),r),[x:dif][t:inn(x,class(r))]t2".4r195"(x,t)):is(ts(r,1rl),r)
-satz195a:=symis(real,ts(r,1rl),r,satz195):is(r,ts(r,1rl))
-satz195b:=tris(real,ts(1rl,r),ts(r,1rl),r,comts(1rl,r),satz195):is(ts(1rl,r),r)
-satz195c:=symis(real,ts(1rl,r),r,satz195b):is(r,ts(1rl,r))
-s@[p:pos(r)][q:pos(s)]
-satz196a:=symis(real,ts(abs(r),abs(s)),ts(r,s),ists12(abs(r),r,abs(s),s,absp(r,p),absp(s,q))):is(ts(r,s),ts(abs(r),abs(s)))
-+4r196
-b1is@[n:neg(r)][o:neg(s)]
-t1:=satzd196b(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):eq"rp"(td(a1,b1),td(absd(a1),absd(b1)))
-t2:=isin(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(ts(r,s),ts(abs(r),abs(s)))
--4r196
-s@[n:neg(r)][o:neg(s)]
-satz196b:=realapp2(is(ts(r,s),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r196"(x,y,t,u,n,o)):is(ts(r,s),ts(abs(r),abs(s)))
-+*4r196
-b1is@[p:pos(r)][n:neg(s)]
-t1a:=satzd196c(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):eq"rp"(td(a1,b1),m0d(td(absd(a1),absd(b1))))
-t2a:=isin(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),t1a):is(ts(r,s),m0(ts(abs(r),abs(s))))
--4r196
-s@[p:pos(r)][n:neg(s)]
-satz196c:=realapp2(is(ts(r,s),m0(ts(abs(r),abs(s)))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2a".4r196"(x,y,t,u,p,n)):is(ts(r,s),m0(ts(abs(r),abs(s))))
-s@[n:neg(r)][p:pos(s)]
-satz196d:=tr3is(real,ts(r,s),ts(s,r),m0(ts(abs(s),abs(r))),m0(ts(abs(r),abs(s))),comts(r,s),satz196c(s,r,p,n),ism0(ts(abs(s),abs(r)),ts(abs(r),abs(s)),comts(abs(s),abs(r)))):is(ts(r,s),m0(ts(abs(r),abs(s))))
-+*4r196
-a0ir@[n:not(is(r,0))]
-t3:=th3"l.imp"(zero(a0),is(r,0),n,[t:zero(a0)]0in(t)):not(zero(a0))
-b1is@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
-t4:=satzd196e(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),i)):or(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)))
-[a:and(posd(a1),posd(b1))]
-t5:=andi(pos(r),pos(s),posin(r,a1,a1ir,ande1(posd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(posd(a1),posd(b1),a))):and(pos(r),pos(s))
-i@[a:and(negd(a1),negd(b1))]
-t6:=andi(neg(r),neg(s),negin(r,a1,a1ir,ande1(negd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(negd(a1),negd(b1),a))):and(neg(r),neg(s))
-i@t7:=th9"l.or"(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)),and(pos(r),pos(s)),and(neg(r),neg(s)),t4,[t:and(posd(a1),posd(b1))]t5(t),[t:and(negd(a1),negd(b1))]t6(t)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
--4r196
-s@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
-satz196e:=realapp2(or(and(pos(r),pos(s)),and(neg(r),neg(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
-+*4r196
-o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
-t8:=satzd196f(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),i)):or(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)))
-[a:and(posd(a1),negd(b1))]
-t9:=andi(pos(r),neg(s),posin(r,a1,a1ir,ande1(posd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(posd(a1),negd(b1),a))):and(pos(r),neg(s))
-i@[a:and(negd(a1),posd(b1))]
-t10:=andi(neg(r),pos(s),negin(r,a1,a1ir,ande1(negd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(negd(a1),posd(b1),a))):and(neg(r),pos(s))
-i@t11:=th9"l.or"(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)),and(pos(r),neg(s)),and(neg(r),pos(s)),t8,[t:and(posd(a1),negd(b1))]t9(t),[t:and(negd(a1),posd(b1))]t10(t)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
--4r196
-o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
-satz196f:=realapp2(or(and(pos(r),neg(s)),and(neg(r),pos(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
-s@[p:pos(ts(r,s))]
-+*4r196
-p"r"@t12:=th3"l.imp"(is(r,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
-t13:=th3"l.imp"(is(s,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
-t14:=tris1(real,ts(r,s),ts(abs(r),abs(s)),abs(ts(r,s)),absp(ts(r,s),p),satz193(r,s)):is(ts(r,s),ts(abs(r),abs(s)))
--4r196
-p@satz196g:=satz196e(t12".4r196",t13".4r196",t14".4r196"):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
-s@[n:neg(ts(r,s))]
-+*4r196
-n"r"@t15:=th3"l.imp"(is(r,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
-t16:=th3"l.imp"(is(s,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
-t17:=satz177c(ts(abs(r),abs(s)),ts(r,s),tris(real,ts(abs(r),abs(s)),abs(ts(r,s)),m0(ts(r,s)),satz193a(r,s),absn(ts(r,s),n))):is(ts(r,s),m0(ts(abs(r),abs(s))))
--4r196
-n@satz196h:=satz196f(t15".4r196",t16".4r196",t17".4r196"):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
-+4r197
-b1is@t1:=satzd197a(a1,b1):eq"rp"(td(m0d(a1),b1),m0d(td(a1,b1)))
-t2:=isin(ts(m0(r),s),m0(ts(r,s)),td(m0d(a1),b1),m0d(td(a1,b1)),tict(m0(r),s,m0d(a1),b1,micm0(r,a1,a1ir),b1is),micm0(ts(r,s),td(a1,b1),tict),t1):is(ts(m0(r),s),m0(ts(r,s)))
--4r197
-s@satz197a:=realapp2(is(ts(m0(r),s),m0(ts(r,s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r197"(x,y,t,u)):is(ts(m0(r),s),m0(ts(r,s)))
-satz197b:=tr3is(real,ts(r,m0(s)),ts(m0(s),r),m0(ts(s,r)),m0(ts(r,s)),comts(r,m0(s)),satz197a(s,r),ism0(ts(s,r),ts(r,s),comts(s,r))):is(ts(r,m0(s)),m0(ts(r,s)))
-satz197c:=tris2(real,ts(m0(r),s),ts(r,m0(s)),m0(ts(r,s)),satz197a,satz197b):is(ts(m0(r),s),ts(r,m0(s)))
-satz197d:=symis(real,ts(m0(r),s),ts(r,m0(s)),satz197c):is(ts(r,m0(s)),ts(m0(r),s))
-satz197e:=symis(real,ts(m0(r),s),m0(ts(r,s)),satz197a):is(m0(ts(r,s)),ts(m0(r),s))
-satz197f:=symis(real,ts(r,m0(s)),m0(ts(r,s)),satz197b):is(m0(ts(r,s)),ts(r,m0(s)))
-satz198:=tris(real,ts(m0(r),m0(s)),ts(r,m0(m0(s))),ts(r,s),satz197c(r,m0(s)),ists2(m0(m0(s)),s,r,satz177(s))):is(ts(m0(r),m0(s)),ts(r,s))
-satz198a:=symis(real,ts(m0(r),m0(s)),ts(r,s),satz198):is(ts(r,s),ts(m0(r),m0(s)))
-+*ivr4
-b1is@[p:pos(r)][q:pos(s)]
-t3:=ptdpp(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(td(a1,b1))
-t4:=posin(ts(r,s),td(a1,b1),tict,t3):pos(ts(r,s))
--ivr4
-s@[p:pos(r)][q:pos(s)]
-postspp:=realapp2(pos(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr4"(x,y,t,u,p,q)):pos(ts(r,s))
-+*ivr4
-p@[n:neg(s)]
-t5:=ntdpn(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):negd(td(a1,b1))
-t6:=negin(ts(r,s),td(a1,b1),tict,t5):neg(ts(r,s))
--ivr4
-s@[p:pos(r)][n:neg(s)]
-negtspn:=realapp2(neg(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr4"(x,y,t,u,p,n)):neg(ts(r,s))
-s@[n:neg(r)][p:pos(s)]
-negtsnp:=isneg(ts(s,r),ts(r,s),comts(s,r),negtspn(s,r,p,n)):neg(ts(r,s))
-s@[n:neg(r)][o:neg(s)]
-postsnn:=ispos(ts(m0(r),m0(s)),ts(r,s),satz198,postspp(m0(r),m0(s),satz176c(r,n),satz176c(s,o))):pos(ts(r,s))
-r@[n:nis(r,0)]
-possq:=rapp(r,pos(ts(r,r)),[t:pos(r)]postspp(r,r,t,t),th2"l.imp"(is(r,0),pos(ts(r,r)),n),[t:neg(r)]postsnn(r,r,t,t)):pos(ts(r,r))
-r@nnegsq:=th1"l.imp"(is(r,0),not(neg(ts(r,r))),[t:is(r,0)]0notn(ts(r,r),satz192a(r,r,t)),[t:nis(r,0)]pnotn(ts(r,r),possq(r,t))):not(neg(ts(r,r)))
-+4r199
-c2it@t1:=satzd199(a2,b2,c2):eq"rp"(td(td(a2,b2),c2),td(a2,td(b2,c2)))
-t2:=isin(ts(ts(r,s),t),ts(r,ts(s,t)),td(td(a2,b2),c2),td(a2,td(b2,c2)),tict(ts(r,s),t,td(a2,b2),c2,tict(r,s,a2,b2,a2ir,b2is),c2it),tict(r,ts(s,t),a2,td(b2,c2),a2ir,tict(s,t,b2,c2,b2is,c2it)),t1):is(ts(ts(r,s),t),ts(r,ts(s,t)))
--4r199
-t@satz199:=realapp3(is(ts(ts(r,s),t),ts(r,ts(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r199"(x,y,z,u,v,w)):is(ts(ts(r,s),t),ts(r,ts(s,t)))
-assts1:=satz199:is(ts(ts(r,s),t),ts(r,ts(s,t)))
-assts2:=symis(real,ts(ts(r,s),t),ts(r,ts(s,t)),satz199):is(ts(r,ts(s,t)),ts(ts(r,s),t))
-+4r201
-c2it@t1:=satzd201(a2,b2,c2):eq"rp"(td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)))
-t2:=isin(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)),tict(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),picp(ts(r,s),ts(r,t),td(a2,b2),td(a2,c2),tict(r,s,a2,b2,a2ir,b2is),tict(r,t,a2,c2,a2ir,c2it)),t1):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
--4r201
-satz201:=realapp3(is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r201"(x,y,z,u,v,w)):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
-disttp1:=tr3is(real,ts(pl(r,s),t),ts(t,pl(r,s)),pl(ts(t,r),ts(t,s)),pl(ts(r,t),ts(s,t)),comts(pl(r,s),t),satz201(t,r,s),ispl12(ts(t,r),ts(r,t),ts(t,s),ts(s,t),comts(t,r),comts(t,s))):is(ts(pl(r,s),t),pl(ts(r,t),ts(s,t)))
-disttp2:=satz201:is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
-distpt1:=symis(real,ts(pl(r,s),t),pl(ts(r,t),ts(s,t)),disttp1):is(pl(ts(r,t),ts(s,t)),ts(pl(r,s),t))
-distpt2:=symis(real,ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),disttp2):is(pl(ts(r,s),ts(r,t)),ts(r,pl(s,t)))
-satz202:=tris(real,ts(r,mn(s,t)),pl(ts(r,s),ts(r,m0(t))),mn(ts(r,s),ts(r,t)),disttp2(r,s,m0(t)),ispl2(ts(r,m0(t)),m0(ts(r,t)),ts(r,s),satz197b(r,t))):is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
-disttm1:=tris(real,ts(mn(r,s),t),pl(ts(r,t),ts(m0(s),t)),mn(ts(r,t),ts(s,t)),disttp1(r,m0(s),t),ispl2(ts(m0(s),t),m0(ts(s,t)),ts(r,t),satz197a(s,t))):is(ts(mn(r,s),t),mn(ts(r,t),ts(s,t)))
-disttm2:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
-distmt1:=symis(real,ts(mn(r,s),t),mn(ts(r,t),ts(s,t)),disttm1):is(mn(ts(r,t),ts(s,t)),ts(mn(r,s),t))
-distmt2:=symis(real,ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)),disttm2):is(mn(ts(r,s),ts(r,t)),ts(r,mn(s,t)))
-satz200:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
-+4r203
-c2it@[m:more(r,s)][p:pos(t)]
-t1:=satzd203a(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),posex(t,c2,c2it,p)):mored(td(a2,c2),td(b2,c2))
-t2:=morein(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t1):more(ts(r,t),ts(s,t))
--4r203
-[m:more(r,s)][p:pos(t)]
-satz203a:=realapp3(more(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r203"(x,y,z,u,v,w,m,p)):more(ts(r,t),ts(s,t))
-m@[i:is(t,0)]
-satz203b:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
-+*4r203
-m@[n:neg(t)]
-t3:=satzd203c(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),negex(t,c2,c2it,n)):lessd(td(a2,c2),td(b2,c2))
-t4:=lessin(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t3):less(ts(r,t),ts(s,t))
--4r203
-m@[n:neg(t)]
-satz203c:=realapp3(less(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".4r203"(x,y,z,u,v,w,m,n)):less(ts(r,t),ts(s,t))
-p@satz203d:=ismore12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203a):more(ts(t,r),ts(t,s))
-i@satz203e:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
-n@satz203f:=isless12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203c):less(ts(t,r),ts(t,s))
-t@[l:less(r,s)][p:pos(t)]
-satz203g:=lemma1(ts(s,t),ts(r,t),satz203a(s,r,t,lemma2(r,s,l),p)):less(ts(r,t),ts(s,t))
-l@[i:is(t,0)]
-satz203h:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
-l@[n:neg(t)]
-satz203j:=lemma2(ts(s,t),ts(r,t),satz203c(s,r,t,lemma2(r,s,l),n)):more(ts(r,t),ts(s,t))
-p@satz203k:=lemma1(ts(t,s),ts(t,r),satz203d(s,r,t,lemma2(r,s,l),p)):less(ts(t,r),ts(t,s))
-i@satz203l:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
-n@satz203m:=lemma2(ts(t,s),ts(t,r),satz203f(s,r,t,lemma2(r,s,l),n)):more(ts(t,r),ts(t,s))
-+4r204
-a0ir@[n1:nis(r,0)]
-t1:=th3"l.imp"(zero(a0),is(r,0),n1,[t:zero(a0)]0in(t)):not(zero(a0))
-d3iu@[n1:nis(s,0)][i:is(ts(s,t),r)][j:is(ts(s,u),r)]
-t2:=satzd204b(a3,b3,t1(s,b3,b3is,n1),c3,d3,isex(ts(s,t),r,td(b3,c3),a3,tict(s,t,b3,c3,b3is,c3it),a3ir,i),isex(ts(s,u),r,td(b3,d3),a3,tict(s,u,b3,d3,b3is,d3iu),a3ir,j)):eq"rp"(c3,d3)
-t3:=isin(t,u,c3,d3,c3it,d3iu,t2):is(t,u)
--4r204
-s@[n:nis(s,0)][x:real][y:real][i:is(ts(s,x),r)][j:is(ts(s,y),r)]
-satz204b:=realapp4(x,y,is(x,y),[z:dif][u:dif][v:dif][w:dif][zi:inn(z,class(r))][ui:inn(u,class(s))][vi:inn(v,class(x))][wi:inn(w,class(y))]t3".4r204"(x,y,z,u,v,w,zi,ui,vi,wi,n,i,j)):is(x,y)
-+*4r204
-b1is@[n1:nis(s,0)]
-t4:=satzd204a(a1,b1,t1(s,b1,b1is,n1)):some"l"(dif,[x:dif]eq"rp"(td(b1,x),a1))
-[a:dif][e:eq"rp"(td(b1,a),a1)]
-ar:=realof(a):real
-t5:=isin(ts(s,ar),r,td(b1,a),a1,tict(s,ar,b1,a,b1is,innclass(a)),a1ir,e):is(ts(s,ar),r)
-t6:=somei(real,[x:real]is(ts(s,x),r),ar,t5):some([x:real]is(ts(s,x),r))
-n1@t7:=someapp(dif,[x:dif]eq"rp"(td(b1,x),a1),t4,some([x:real]is(ts(s,x),r)),[x:dif][t:eq"rp"(td(b1,x),a1)]t6(x,t)):some([x:real]is(ts(s,x),r))
--4r204
-n@satz204a:=realapp2(some([x:real]is(ts(s,x),r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r204"(x,y,t,u,n)):some([x:real]is(ts(s,x),r))
-satz204:=onei(real,[x:real]is(ts(s,x),r),[x:real][y:real][t:is(ts(s,x),r)][u:is(ts(s,y),r)]satz204b(x,y,t,u),satz204a):one([x:real]is(ts(s,x),r))
-ov:=ind(real,[x:real]is(ts(s,x),r),satz204):real
-satz204c:=oneax(real,[x:real]is(ts(s,x),r),satz204):is(ts(s,ov(r,s,n)),r)
-satz204d:=symis(real,ts(s,ov(r,s,n)),r,satz204c):is(r,ts(s,ov(r,s,n)))
-satz204e:=tris(real,ts(ov(r,s,n),s),ts(s,ov(r,s,n)),r,comts(ov(r,s,n),s),satz204c):is(ts(ov(r,s,n),s),r)
-satz204f:=symis(real,ts(ov(r,s,n),s),r,satz204e):is(r,ts(ov(r,s,n),s))
-s@[x:real][n:nis(s,0)][i:is(ts(s,x),r)]
-satz204g:=satz204b(n,x,ov(r,s,n),i,satz204c(n)):is(x,ov(r,s,n))
-s@[n:nis(s,0)][p:pos(r)][q:pos(s)]
-+*4r204
-n@ros:=ov(r,s,n):real
-p@t8:=ispos(r,ts(s,ros),satz204d(n),p):pos(ts(s,ros))
-q@t9:=th1"l.and"(neg(s),neg(ros),pnotn(s,q)):not(and(neg(s),neg(ros)))
-t10:=ore1(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t9):and(pos(s),pos(ros))
--4r204
-q@posovpp:=ande2(pos(s),pos(ov(r,s,n)),t10".4r204"):pos(ov(r,s,n))
-p@[m:neg(s)]
-+*4r204
-m@t11:=th1"l.and"(pos(s),pos(ros),nnotp(s,m)):not(and(pos(s),pos(ros)))
-t12:=ore2(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t11):and(neg(s),neg(ros))
--4r204
-m@negovpn:=ande2(neg(s),neg(ov(r,s,n)),t12".4r204"):neg(ov(r,s,n))
-n@[m:neg(r)][p:pos(s)]
-+*4r204
-m@t13:=isneg(r,ts(s,ros),satz204d(n),m):neg(ts(s,ros))
-p@t14:=th1"l.and"(neg(s),pos(ros),pnotn(s,p)):not(and(neg(s),pos(ros)))
-t15:=ore1(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t14):and(pos(s),neg(ros))
--4r204
-p@negovnp:=ande2(pos(s),neg(ov(r,s,n)),t15".4r204"):neg(ov(r,s,n))
-m@[l:neg(s)]
-+*4r204
-l@t16:=th1"l.and"(pos(s),neg(ros),nnotp(s,l)):not(and(pos(s),neg(ros)))
-t17:=ore2(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t16):and(neg(s),pos(ros))
--4r204
-l@posovnn:=ande2(neg(s),pos(ov(r,s,n)),t17".4r204"):pos(ov(r,s,n))
-@[r0:cut][s0:cut][m:more"rp"(r0,s0)]
-morerpep:=morein(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),morerpepd(r0,s0,m)):more(pofrp(r0),pofrp(s0))
-s0@[m:more(pofrp(r0),pofrp(s0))]
-morerpip:=morerpipd(r0,s0,moreex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),m)):more"rp"(r0,s0)
-s0@[l:less"rp"(r0,s0)]
-lessrpep:=lemma1(pofrp(s0),pofrp(r0),morerpep(s0,r0,satz122(r0,s0,l))):less(pofrp(r0),pofrp(s0))
-s0@[l:less(pofrp(r0),pofrp(s0))]
-lessrpip:=satz121(s0,r0,morerpip(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
-s@[p:pos(r)][q:pos(s)][m:more(r,s)]
-q@[m:more(r,s)]
-+ivr5
-t1:=ismore12(r,pofrp(rpofp(r,p)),s,pofrp(rpofp(s,q)),isprp1(r,p),isprp1(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
--ivr5
-moreperp:=morerpip(rpofp(r,p),rpofp(s,q),t1".ivr5"):more"rp"(rpofp(r,p),rpofp(s,q))
-q@[m:more"rp"(rpofp(r,p),rpofp(s,q))]
-+*ivr5
-m@t2:=morerpep(rpofp(r,p),rpofp(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
--ivr5
-m@morepirp:=ismore12(pofrp(rpofp(r,p)),r,pofrp(rpofp(s,q)),s,isprp2(r,p),isprp2(s,q),t2".ivr5"):more(r,s)
-q@[l:less(r,s)]
-lessperp:=satz121(rpofp(s,q),rpofp(r,p),moreperp(s,r,q,p,lemma2(r,s,l))):less"rp"(rpofp(r,p),rpofp(s,q))
-q@[l:less"rp"(rpofp(r,p),rpofp(s,q))]
-lesspirp:=lemma1(s,r,morepirp(s,r,q,p,satz122(rpofp(r,p),rpofp(s,q),l))):less(r,s)
-r@s01:=setof(real,[x:real]lessis(x,r)):set(real)
-s02:=setof(real,[x:real]more(x,r)):set(real)
-+5r205
-s@[n:not(in(s,s01))]
-t1:=th3"l.imp"(lessis(s,r),in(s,s01),n,[t:lessis(s,r)]estii(real,[x:real]lessis(x,r),s,t)):not(lessis(s,r))
-t2:=estii(real,[x:real]more(x,r),s,satz167k(s,r,t1)):in(s,s02)
--5r205
-vb00:=[x:real][t:not(in(x,s01))]t2".5r205"(x,t):all([x:real]or(in(x,s01),in(x,s02)))
-+*5r205
-r@t3:=estii(real,[x:real]lessis(x,r),r,lessisi2(r,r,refis(real,r))):in(r,s01)
--5r205
-r@vb01a:=nonemptyi(real,s01,r,t3".5r205"):nonempty(real,s01)
-+*5r205
-r@t4:=ismore2(pl(r,0),r,pl(r,1rl),pl02(r,0,refis(real,0)),satz188k(1rl,0,r,satz169a(1rl,pos1))):more(pl(r,1rl),r)
-t5:=estii(real,[x:real]more(x,r),pl(r,1rl),t4):in(pl(r,1rl),s02)
--5r205
-r@vb01b:=nonemptyi(real,s02,pl(r,1rl),t5".5r205"):nonempty(real,s02)
-+*5r205
-s@[i:in(s,s01)][t:real][j:in(t,s02)]
-t6:=satz172a(s,r,t,estie(real,[x:real]lessis(x,r),s,i),lemma1(t,r,estie(real,[x:real]more(x,r),t,j))):less(s,t)
--5r205
-r@vb02:=[x:real][t:in(x,s01)][y:real][u:in(y,s02)]t6".5r205"(x,t,y,u):all([x:real][t:in(x,s01)]all([y:real][u:in(y,s02)]less(x,y)))
-s@[l:less(s,r)]
-vb03a:=estii(real,[x:real]lessis(x,r),s,lessisi1(s,r,l)):in(s,s01)
-s@[m:more(s,r)]
-vb03b:=estii(real,[x:real]more(x,r),s,m):in(s,s02)
-r@s11:=setof(real,[x:real]less(x,r)):set(real)
-s12:=setof(real,[x:real]moreis(x,r)):set(real)
-+*5r205
-s@[n:not(in(s,s11))]
-t7:=th3"l.imp"(less(s,r),in(s,s11),n,[t:less(s,r)]estii(real,[x:real]less(x,r),s,t)):not(less(s,r))
-t8:=estii(real,[x:real]moreis(x,r),s,satz167f(s,r,t7)):in(s,s12)
--5r205
-r@vb10:=[x:real][t:not(in(x,s11))]t8".5r205"(x,t):all([x:real]or(in(x,s11),in(x,s12)))
-+*5r205
-r@t9:=isless2(pl(r,0),r,mn(r,1rl),pl02(r,0,refis(real,0)),satz188m(m0(1rl),0,r,satz169c(m0(1rl),satz176a(1rl,pos1)))):less(mn(r,1rl),r)
-t10:=estii(real,[x:real]less(x,r),mn(r,1rl),t9):in(mn(r,1rl),s11)
--5r205
-r@vb11a:=nonemptyi(real,s11,mn(r,1rl),t10".5r205"):nonempty(real,s11)
-+*5r205
-r@t11:=estii(real,[x:real]moreis(x,r),r,moreisi2(r,r,refis(real,r))):in(r,s12)
--5r205
-r@vb11b:=nonemptyi(real,s12,r,t11".5r205"):nonempty(real,s12)
-+*5r205
-s@[i:in(s,s11)][t:real][j:in(t,s12)]
-t12:=satz172b(s,r,t,estie(real,[x:real]less(x,r),s,i),satz168a(t,r,estie(real,[x:real]moreis(x,r),t,j))):less(s,t)
--5r205
-r@vb12:=[x:real][t:in(x,s11)][y:real][u:in(y,s12)]t12".5r205"(x,t,y,u):all([x:real][t:in(x,s11)]all([y:real][u:in(y,s12)]less(x,y)))
-s@[l:less(s,r)]
-vb13a:=estii(real,[x:real]less(x,r),s,l):in(s,s11)
-s@[m:more(s,r)]
-vb13b:=estii(real,[x:real]moreis(x,r),s,moreisi1(s,r,m)):in(s,s12)
-@2rl:=pl(1rl,1rl):real
-pos2:=pospl(1rl,1rl,pos1,pos1):pos(2rl)
-half:=ov(1rl,2rl,pnot0(2rl,pos2)):real
-poshalf:=posovpp(1rl,2rl,pnot0(2rl,pos2),pos1,pos2):pos(half)
-+*ivr5
-r@t3:=tris(real,pl(r,r),pl(ts(1rl,r),ts(1rl,r)),ts(2rl,r),ispl12(r,ts(1rl,r),r,ts(1rl,r),satz195c(r),satz195c(r)),distpt1(1rl,1rl,r)):is(pl(r,r),ts(2rl,r))
-t4:=tr4is(real,ts(half,pl(r,r)),ts(half,ts(2rl,r)),ts(ts(half,2rl),r),ts(1rl,r),r,ists2(pl(r,r),ts(2rl,r),half,t3),assts2(half,2rl,r),ists1(ts(half,2rl),1rl,r,satz204e(1rl,2rl,pnot0(2rl,pos2))),satz195b(r)):is(ts(half,pl(r,r)),r)
--ivr5
-s@[l:less(r,s)]
-+*ivr5
-l@t5:=satz203k(pl(r,r),pl(r,s),half,satz188m(r,s,r,l),poshalf):less(ts(half,pl(r,r)),ts(half,pl(r,s)))
--ivr5
-l@lemma3:=isless1(ts(half,pl(r,r)),r,ts(half,pl(r,s)),t4".ivr5",t5".ivr5"):less(r,ts(half,pl(r,s)))
-+*ivr5
-l@t6:=satz203k(pl(r,s),pl(s,s),half,satz188f(r,s,s,l),poshalf):less(ts(half,pl(r,s)),ts(half,pl(s,s)))
--ivr5
-l@lemma4:=isless2(ts(half,pl(s,s)),s,ts(half,pl(r,s)),t4".ivr5"(s),t6".ivr5"):less(ts(half,pl(r,s)),s)
-[p:pos(r)]
-lemma5:=satz169b(s,trmore(s,r,0,lemma2(r,s,l),satz169a(r,p))):pos(s)
-@[s1:set(real)][s2:set(real)][p0:all([x:real]or(in(x,s1),in(x,s2)))][p1a:nonempty(real,s1)][p1b:nonempty(real,s2)][p2:all([x:real][t:in(x,s1)]all([y:real][u:in(y,s2)]less(x,y)))]
-+*5r205
-s2@[r:real]
-prop1:=all([x:real][t:less(x,r)]in(x,s1)):'prop'
-prop2:=all([x:real][t:more(x,r)]in(x,s2)):'prop'
-prop3:=and(prop1,prop2):'prop'
-p2@[x:real][y:real][px:prop3(x)][py:prop3(y)][l:less(x,y)]
-mxy:=ts(half,pl(x,y)):real
-t13:=lemma2(x,mxy,lemma3(x,y,l)):more(mxy,x)
-t14:=lemma4(x,y,l):less(mxy,y)
-t15:=<t14><mxy>ande1(prop1(y),prop2(y),py):in(mxy,s1)
-t16:=<t13><mxy>ande2(prop1(x),prop2(x),px):in(mxy,s2)
-t17:=<t16><mxy><t15><mxy>p2:less(mxy,mxy)
-t18:=<refis(real,mxy)>ec3e31(is(mxy,mxy),more(mxy,mxy),less(mxy,mxy),satz167b(mxy,mxy),t17):con
-py@t19:=[t:less(x,y)]t18(t):not(less(x,y))
-t20:=[t:more(x,y)]t18(y,x,py,px,lemma1(x,y,t)):not(more(x,y))
-t21:=or3e1(is(x,y),more(x,y),less(x,y),satz167a(x,y),t20,t19):is(x,y)
-p2@t22:=[x:real][y:real][t:prop3(x)][u:prop3(y)]t21(x,y,t,u):amone(real,[x:real]prop3(x))
-[case1:some([x:real]and(pos(x),in(x,s1)))][r:real][a:and(pos(r),in(r,s1))]
-t23:=ande1(pos(r),in(r,s1),a):pos(r)
-t24:=ande2(pos(r),in(r,s1),a):in(r,s1)
-sc1:=setof(cut,[x:cut]in(pofrp(x),s1)):set(cut)
-sc2:=setof(cut,[x:cut]in(pofrp(x),s2)):set(cut)
-[r0:cut][i:in(pofrp(r0),s1)]
-t25:=estii(cut,[x:cut]in(pofrp(x),s1),r0,i):in"rp"(r0,sc1)
-r0@[i:in"rp"(r0,sc1)]
-t26:=estie(cut,[x:cut]in(pofrp(x),s1),r0,i):in(pofrp(r0),s1)
-r0@[i:in(pofrp(r0),s2)]
-t27:=estii(cut,[x:cut]in(pofrp(x),s2),r0,i):in"rp"(r0,sc2)
-r0@[i:in"rp"(r0,sc2)]
-t28:=estie(cut,[x:cut]in(pofrp(x),s2),r0,i):in(pofrp(r0),s2)
-r0@t29:=th9"l.or"(in(pofrp(r0),s1),in(pofrp(r0),s2),in"rp"(r0,sc1),in"rp"(r0,sc2),<pofrp(r0)>p0,[t:in(pofrp(r0),s1)]t25(t),[t:in(pofrp(r0),s2)]t27(t)):or(in"rp"(r0,sc1),in"rp"(r0,sc2))
-a@pr1:=rpofp(r,t23):cut
-t30:=isp(real,[x:real]in(x,s1),r,pofrp(pr1),t24,isprp1(r,t23)):in(pofrp(pr1),s1)
-t31:=nonemptyi(cut,sc1,pr1,t25(pr1,t30)):nonempty(cut,sc1)
-[s:real][i:in(s,s2)]
-t32:=<i><s><t24><r>p2:less(r,s)
-t33:=lemma5(r,s,t32,t23):pos(s)
-ps1:=rpofp(s,t33):cut
-t34:=isp(real,[x:real]in(x,s2),s,pofrp(ps1),i,isprp1(s,t33)):in(pofrp(ps1),s2)
-t35:=nonemptyi(cut,sc2,ps1,t27(ps1,t34)):nonempty(cut,sc2)
-a@t36:=nonemptyapp(real,s2,p1b,nonempty(cut,sc2),[x:real][t:in(x,s2)]t35(x,t)):nonempty(cut,sc2)
-r0@[i:in"rp"(r0,sc1)][s0:cut][j:in"rp"(s0,sc2)]
-t37:=<t28(s0,j)><pofrp(s0)><t26(r0,i)><pofrp(r0)>p2:less(pofrp(r0),pofrp(s0))
-t38:=lessrpip(r0,s0,t37):less"rp"(r0,s0)
-a@stc:=schnitt(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):cut
-t39:=satzp205a(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:less"rp"(x,stc)]in"rp"(x,sc1))
-t40:=satzp205b(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:more"rp"(x,stc)]in"rp"(x,sc2))
-stp:=pofrp(stc):real
-t41:=posi(stc):pos(stp)
-[s:real][l:less(s,stp)][p:pos(s)]
-ps2:=rpofp(s,p):cut
-t42:=lessrpip(ps2,stc,isless1(s,pofrp(ps2),stp,isprp1(s,p),l)):less"rp"(ps2,stc)
-t43:=<t42><ps2>t39:in"rp"(ps2,sc1)
-t44:=isp(real,[x:real]in(x,s1),pofrp(ps2),s,t26(ps2,t43),isprp2(s,p)):in(s,s1)
-l@[n:not(pos(s))][i:in(s,s2)]
-t45:=<i><s><t24><r>p2:less(r,s)
-t46:=<lemma5(r,s,t45,t23)>n:con
-n@t47:=ore1(in(s,s1),in(s,s2),<s>p0,[t:in(s,s2)]t46(t)):in(s,s1)
-l@t48:=th1"l.imp"(pos(s),in(s,s1),[t:pos(s)]t44(t),[t:not(pos(s))]t47(t)):in(s,s1)
-s@[m:more(s,stp)]
-t49:=lemma5(stp,s,lemma1(s,stp,m),t41):pos(s)
-ps3:=rpofp(s,t49):cut
-t50:=morerpip(ps3,stc,ismore1(s,pofrp(ps3),stp,isprp1(s,t49),m)):more"rp"(ps3,stc)
-t51:=<t50><ps3>t40:in"rp"(ps3,sc2)
-t52:=isp(real,[x:real]in(x,s2),pofrp(ps3),s,t28(ps3,t51),isprp2(s,t49)):in(s,s2)
-a@t53:=andi(prop1(stp),prop2(stp),[x:real][t:less(x,stp)]t48(x,t),[x:real][t:more(x,stp)]t52(x,t)):prop3(stp)
-t54:=somei(real,[x:real]prop3(x),stp,t53):some([x:real]prop3(x))
-case1@t55:=someapp(real,[x:real]and(pos(x),in(x,s1)),case1,some([x:real]prop3(x)),[x:real][t:and(pos(x),in(x,s1))]t54(x,t)):some([x:real]prop3(x))
-p2@[case2:some([x:real]and(neg(x),in(x,s2)))]
-sp1:=setof(real,[x:real]in(m0(x),s1)):set(real)
-sp2:=setof(real,[x:real]in(m0(x),s2)):set(real)
-[r:real][i:in(m0(r),s1)]
-t56:=estii(real,[x:real]in(m0(x),s1),r,i):in(r,sp1)
-r@[i:in(r,sp1)]
-t57:=estie(real,[x:real]in(m0(x),s1),r,i):in(m0(r),s1)
-r@[i:in(m0(r),s2)]
-t58:=estii(real,[x:real]in(m0(x),s2),r,i):in(r,sp2)
-r@[i:in(r,sp2)]
-t59:=estie(real,[x:real]in(m0(x),s2),r,i):in(m0(r),s2)
-r@t60:=comor(in(r,sp1),in(r,sp2),th9"l.or"(in(m0(r),s1),in(m0(r),s2),in(r,sp1),in(r,sp2),<m0(r)>p0,[t:in(m0(r),s1)]t56(t),[t:in(m0(r),s2)]t58(t))):or(in(r,sp2),in(r,sp1))
-[i:in(r,s2)]
-t61:=t58(m0(r),isp(real,[x:real]in(x,s2),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp2)
-t62:=nonemptyi(real,sp2,m0(r),t61):nonempty(real,sp2)
-case2@t63:=nonemptyapp(real,s2,p1b,nonempty(real,sp2),[x:real][t:in(x,s2)]t62(x,t)):nonempty(real,sp2)
-r@[i:in(r,s1)]
-t64:=t56(m0(r),isp(real,[x:real]in(x,s1),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp1)
-t65:=nonemptyi(real,sp1,m0(r),t64):nonempty(real,sp1)
-case2@t66:=nonemptyapp(real,s1,p1a,nonempty(real,sp1),[x:real][t:in(x,s1)]t65(x,t)):nonempty(real,sp1)
-r@[i:in(r,sp2)][s:real][j:in(s,sp1)]
-t67:=<t59(r,i)><m0(r)><t57(s,j)><m0(s)>p2:less(m0(s),m0(r))
-t68:=lemma1(s,r,satz183d(s,r,t67)):less(r,s)
-r@[a:and(neg(r),in(r,s2))]
-t69:=satz176c(r,ande1(neg(r),in(r,s2),a)):pos(m0(r))
-t70:=isp(real,[x:real]in(x,s2),r,m0(m0(r)),ande2(neg(r),in(r,s2),a),satz177a(r)):in(m0(m0(r)),s2)
-t71:=andi(pos(m0(r)),in(m0(r),sp2),t69,t58(m0(r),t70)):and(pos(m0(r)),in(m0(r),sp2))
-t72:=somei(real,[x:real]and(pos(x),in(x,sp2)),m0(r),t71):some([x:real]and(pos(x),in(x,sp2)))
-case2@t73:=someapp(real,[x:real]and(neg(x),in(x,s2)),case2,some([x:real]and(pos(x),in(x,sp2))),[x:real][t:and(neg(x),in(x,s2))]t72(x,t)):some([x:real]and(pos(x),in(x,sp2)))
-t74:=t55(sp2,sp1,[x:real]t60(x),t63,t66,[x:real][t:in(x,sp2)][y:real][u:in(y,sp1)]t68(x,t,y,u),t73):some([x:real]prop3(sp2,sp1,x))
-[r:real][p:prop3(sp2,sp1,r)][s:real][l:less(s,m0(r))]
-t75:=ismore2(m0(m0(r)),r,m0(s),satz177(r),satz183c(s,m0(r),l)):more(m0(s),r)
-t76:=<t75><m0(s)>ande2(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp1)
-t77:=isp(real,[x:real]in(x,s1),m0(m0(s)),s,t57(m0(s),t76),satz177(s)):in(s,s1)
-s@[m:more(s,m0(r))]
-t78:=isless2(m0(m0(r)),r,m0(s),satz177(r),satz183a(s,m0(r),m)):less(m0(s),r)
-t79:=<t78><m0(s)>ande1(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp2)
-t80:=isp(real,[x:real]in(x,s2),m0(m0(s)),s,t59(m0(s),t79),satz177(s)):in(s,s2)
-p@t81:=andi(prop1(m0(r)),prop2(m0(r)),[x:real][t:less(x,m0(r))]t77(x,t),[x:real][t:more(x,m0(r))]t80(x,t)):prop3(m0(r))
-t82:=somei(real,[x:real]prop3(x),m0(r),t81):some([x:real]prop3(x))
-case2@t83:=someapp(real,[x:real]prop3(sp2,sp1,x),t74,some([x:real]prop3(x)),[x:real][t:prop3(sp2,sp1,x)]t82(x,t)):some([x:real]prop3(x))
-p2@[notcase1:not(some([x:real]and(pos(x),in(x,s1))))][notcase2:not(some([x:real]and(neg(x),in(x,s2))))][r:real][l:less(r,0)]
-t84:=th4"l.some"(real,[x:real]and(neg(x),in(x,s2)),notcase2,r):not(and(neg(r),in(r,s2)))
-t85:=th3"l.and"(neg(r),in(r,s2),t84,satz169d(r,l)):not(in(r,s2))
-t86:=ore1(in(r,s1),in(r,s2),<r>p0,t85):in(r,s1)
-r@[m:more(r,0)]
-t87:=th4"l.some"(real,[x:real]and(pos(x),in(x,s1)),notcase1,r):not(and(pos(r),in(r,s1)))
-t88:=th3"l.and"(pos(r),in(r,s1),t87,satz169b(r,m)):not(in(r,s1))
-t89:=ore2(in(r,s1),in(r,s2),<r>p0,t88):in(r,s2)
-notcase2@t90:=andi(prop1(0),prop2(0),[x:real][t:less(x,0)]t86(x,t),[x:real][t:more(x,0)]t89(x,t)):prop3(0)
-t91:=somei(real,[x:real]prop3(x),0,t90):some([x:real]prop3(x))
-notcase1@t92:=th1"l.imp"(some([x:real]and(neg(x),in(x,s2))),some([x:real]prop3(x)),[t:some([x:real]and(neg(x),in(x,s2)))]t83(t),[t:not(some([x:real]and(neg(x),in(x,s2))))]t91(t)):some([x:real]prop3(x))
-p2@t93:=th1"l.imp"(some([x:real]and(pos(x),in(x,s1))),some([x:real]prop3(x)),[t:some([x:real]and(pos(x),in(x,s1)))]t55(t),[t:not(some([x:real]and(pos(x),in(x,s1))))]t92(t)):some([x:real]prop3(x))
-t94:=onei(real,[x:real]prop3(x),t22,t93):one([x:real]prop3(x))
--5r205
-p2@satz205:=t94".5r205":one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
-dedekind:=satz205:one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
-schnitt:=ind(real,[x:real]prop3".5r205"(x),satz205):real
-[r:real][l:less(r,schnitt)]
-satz205a:=<l><r>ande1(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s1)
-r@[m:more(r,schnitt)]
-satz205b:=<m><r>ande2(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s2)
-@[r0:cut][s0:cut]
-+iva
-dr:=pdofrp(r0):dif
-ds:=pdofrp(s0):dif
-t1:=lemmaivad1(r0,s0):eq"rp"(pd(dr,ds),pdofrp(pl"rp"(r0,s0)))
--iva
-lemmaiva1:=isin(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)),pd(pdofrp(r0),pdofrp(s0)),pdofrp(pl"rp"(r0,s0)),picp(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(pl"rp"(r0,s0))),t1".iva"):is(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)))
-+*iva
-s0@t2:=lemmaivad2(r0,s0):eq"rp"(td(dr,ds),pdofrp(ts"rp"(r0,s0)))
--iva
-s0@lemmaiva2:=isin(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)),td(pdofrp(r0),pdofrp(s0)),pdofrp(ts"rp"(r0,s0)),tict(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(ts"rp"(r0,s0))),t2".iva"):is(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)))
-[m:more(pofrp(r0),pofrp(s0))]
-+*iva
-m@t3:=moreex(pofrp(r0),pofrp(s0),dr,ds,innclass(dr),innclass(ds),m):mored(dr,ds)
--iva
-m@lemmaiva3:=lemmaivad3(r0,s0,t3".iva"):more"rp"(r0,s0)
-s0@[m:more"rp"(r0,s0)]
-+*iva
-m@[l:less(pofrp(r0),pofrp(s0))]
-t4:=satz121(s0,r0,lemmaiva3(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
-m@t5:=ec3e23(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):not(less"rp"(r0,s0))
-t6:=th3"l.imp"(less(pofrp(r0),pofrp(s0)),less"rp"(r0,s0),t5,[t:less(pofrp(r0),pofrp(s0))]t4(t)):not(less(pofrp(r0),pofrp(s0)))
-t7:=ec3e21(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):nis"rp"(r0,s0)
-t8:=th3"l.imp"(is(pofrp(r0),pofrp(s0)),is"rp"(r0,s0),t7,[t:is(pofrp(r0),pofrp(s0))]isrpip(r0,s0,t)):nis(pofrp(r0),pofrp(s0))
--iva
-m@lemmaiva4:=or3e2(is(pofrp(r0),pofrp(s0)),more(pofrp(r0),pofrp(s0)),less(pofrp(r0),pofrp(s0)),satz167a(pofrp(r0),pofrp(s0)),t6".iva",t8".iva"):more(pofrp(r0),pofrp(s0))
-@[x:nat][y:nat][m:more(rlofnt(x),rlofnt(y))]
-+*iva
-m@t9:=lemmaiva3(rpofnt(x),rpofnt(y),m):more"rp"(rpofnt(x),rpofnt(y))
-t10:=satz154d(rtofn(x),rtofn(y),t9):more"rt"(rtofn(x),rtofn(y))
-t11:=moree"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t10):moref(fr(x,1),fr(y,1))
--iva
-m@lemmaiva5:=satz111a(x,y,t11".iva"):more"n"(x,y)
-y@[m:more"n"(x,y)]
-+*iva
-m@t12:=satz111d(x,y,m):moref(fr(x,1),fr(y,1))
-t13:=morei"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t12):more"rt"(rtofn(x),rtofn(y))
-t14:=satz154a(rtofn(x),rtofn(y),t13):more"rp"(rpofnt(x),rpofnt(y))
--iva
-m@lemmaiva6:=lemmaiva4(rpofnt(x),rpofnt(y),t14".iva"):more(rlofnt(x),rlofnt(y))
-@[r:real]
-+int
-a0ir@[i:intrl(r)]
-t1:=intabsd(a0,intrlex(r,a0,a0ir,i)):intd(absd(a0))
-t2:=intrlin(abs(r),absd(a0),aica,t1):intrl(abs(r))
--int
-[i:intrl(r)]
-intabs:=realapp1(r,intrl(abs(r)),[x:dif][t:inn(x,class(r))]t2".int"(r,x,t,i)):intrl(abs(r))
-+*int
-i@t3:=intm0d(a0,intrlex(r,a0,a0ir,i)):intd(m0d(a0))
-t4:=intrlin(m0(r),m0d(a0),micm0,t3):intrl(m0(r))
--int
-i@intm0:=realapp1(r,intrl(m0(r)),[x:dif][t:inn(x,class(r))]t4".int"(r,x,t,i)):intrl(m0(r))
-+*int
-b1is@[i:intrl(r)][j:intrl(s)]
-t5:=intpd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(pd(a1,b1))
-t6:=intrlin(pl(r,s),pd(a1,b1),picp,t5):intrl(pl(r,s))
--int
-i@[s:real][j:intrl(s)]
-intpl:=realapp2(r,s,intrl(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".int"(r,s,x,y,t,u,i,j)):intrl(pl(r,s))
-intmn:=intpl(r,i,m0(s),intm0(s,j)):intrl(mn(r,s))
-+*int
-j@t7:=inttd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(td(a1,b1))
-t8:=intrlin(ts(r,s),td(a1,b1),tict,t7):intrl(ts(r,s))
--int
-j@intts:=realapp2(r,s,intrl(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".int"(r,s,x,y,t,u,i,j)):intrl(ts(r,s))
-r@[n:natrl(r)]
-+ivr24
-t1:=satz24a(ntofrl(r,n)):lessis"n"(1,ntofrl(r,n))
-t2:=th3"l.imp"(more(1rl,r),more"n"(1,ntofrl(r,n)),satz10d(1,ntofrl(r,n),t1),[t:more(1rl,r)]lemmaiva5(1,ntofrl(r,n),ismore2(r,rlofnt(ntofrl(r,n)),1rl,isrlnt1(r,n),t))):not(more(1rl,r))
--ivr24
-satzr24:=satz167e(1rl,r,t2".ivr24"):lessis(1rl,r)
-r@[i:intrl(r)][s:real][j:intrl(s)][l:less(r,s)]
-+ivr25
-t1:=satz182d(s,r,lemma2(r,s,l)):pos(mn(s,r))
-t2:=intmn(s,j,r,i):intrl(mn(s,r))
-t3:=posintnatrl(mn(s,r),t1,t2):natrl(mn(s,r))
-t4:=satzr24(mn(s,r),t3):lessis(1rl,mn(s,r))
-t5:=th9"l.or"(less(1rl,mn(s,r)),is(1rl,mn(s,r)),less(pl(1rl,r),pl(mn(s,r),r)),is(pl(1rl,r),pl(mn(s,r),r)),t4,[t:less(1rl,mn(s,r))]satz188f(1rl,mn(s,r),r,t),[t:is(1rl,mn(s,r))]ispl1(1rl,mn(s,r),r,t)):lessis(pl(1rl,r),pl(mn(s,r),r))
--ivr25
-satzr25:=islessis12(pl(1rl,r),pl(r,1rl),pl(mn(s,r),r),s,compl(1rl,r),plmn(s,r),t5".ivr25"):lessis(pl(r,1rl),s)
-@[x:nat][y:nat]
-+ivr155
-t1:=lemmaiva1(rpofnt(x),rpofnt(y)):is(pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
-t2:=isrpep(rpofnt(pl"n"(x,y)),pl"rp"(rpofnt(x),rpofnt(y)),satz155e(x,y)):is(rlofnt(pl"n"(x,y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
--ivr155
-satzr155a:=tris2(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))),t2".ivr155",t1".ivr155"):is(rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)))
-satzr155b:=symis(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),satzr155a):is(pl(rlofnt(x),rlofnt(y)),rlofnt(pl"n"(x,y)))
-+*ivr155
-y@t3:=lemmaiva2(rpofnt(x),rpofnt(y)):is(ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
-t4:=isrpep(rpofnt(ts"n"(x,y)),ts"rp"(rpofnt(x),rpofnt(y)),satz155f(x,y)):is(rlofnt(ts"n"(x,y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
--ivr155
-y@satzr155c:=tris2(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))),t4".ivr155",t3".ivr155"):is(rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)))
-satzr155d:=symis(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),satzr155c):is(ts(rlofnt(x),rlofnt(y)),rlofnt(ts"n"(x,y)))
-@[t:real][r:real][s:real][a:and(not(neg(r)),is(ts(r,r),t))][b:and(not(neg(s)),is(ts(s,s),t))]
-+7r161
-[c0:dif][cit:inn(c0,class(t))][a0:dif][air:inn(a0,class(r))][b0:dif][bis:inn(b0,class(s))]
-t1:=th3"l.imp"(negd(a0),neg(r),ande1(not(neg(r)),is(ts(r,r),t),a),[u:negd(a0)]negin(r,a0,air,u)):not(negd(a0))
-t2:=th3"l.imp"(negd(b0),neg(s),ande1(not(neg(s)),is(ts(s,s),t),b),[u:negd(b0)]negin(s,b0,bis,u)):not(negd(b0))
-t3:=isex(ts(r,r),t,td(a0,a0),c0,tict(r,r,a0,a0,air,air),cit,ande2(not(neg(r)),is(ts(r,r),t),a)):eq"rp"(td(a0,a0),c0)
-t4:=isex(ts(s,s),t,td(b0,b0),c0,tict(s,s,b0,b0,bis,bis),cit,ande2(not(neg(s)),is(ts(s,s),t),b)):eq"rp"(td(b0,b0),c0)
-t5:=isin(r,s,a0,b0,air,bis,satzd161b(c0,a0,b0,t1,t2,t3,t4)):is(r,s)
--7r161
-satzr161b:=realapp3(t,r,s,is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(t))][v:inn(y,class(r))][w:inn(z,class(s))]t5".7r161"(x,u,y,v,z,w)):is(r,s)
-t@[n:not(neg(t))]
-+*7r161
-n@[c0:dif][cit:inn(c0,class(t))]
-t6:=th3"l.imp"(negd(c0),neg(t),n,[u:negd(c0)]negin(t,c0,cit,u)):not(negd(c0))
-[a0:dif][a:and(not(negd(a0)),eq"rp"(td(a0,a0),c0))]
-ar:=realof(a0):real
-t7:=th3"l.imp"(neg(ar),negd(a0),ande1(not(negd(a0)),eq"rp"(td(a0,a0),c0),a),[u:neg(ar)]negex(ar,a0,innclass(a0),u)):not(neg(ar))
-t8:=isin(ts(ar,ar),t,td(a0,a0),c0,tict(ar,ar,a0,a0,innclass(a0),innclass(a0)),cit,ande2(not(negd(a0)),eq"rp"(td(a0,a0),c0),a)):is(ts(ar,ar),t)
-t9:=andi(not(neg(ar)),is(ts(ar,ar),t),t7,t8):and(not(neg(ar)),is(ts(ar,ar),t))
-t10:=somei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),ar,t9):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
-cit@t11:=someapp(dif,[x:dif]and(not(negd(x)),eq"rp"(td(x,x),c0)),satzd161a(c0,t6),some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:and(not(negd(x)),eq"rp"(td(x,x),c0))]t10(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
--7r161
-n@satzr161a:=realapp1(t,some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:inn(x,class(t))]t11".7r161"(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
-satzr161:=onei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),[u:real][v:real][a:and(not(neg(u)),is(ts(u,u),t))][b:and(not(neg(v)),is(ts(v,v),t))]satzr161b(u,v,a,b),satzr161a):one([u:real]and(not(neg(u)),is(ts(u,u),t)))
-sqrt:=ind(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):real
-+*7r161
-n@t12:=oneax(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):and(not(neg(sqrt)),is(ts(sqrt,sqrt),t))
--7r161
-n@thsqrt1a:=ande1(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):not(neg(sqrt))
-thsqrt1b:=ande2(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):is(ts(sqrt,sqrt),t)
-[x:real][o:not(neg(x))][i:is(ts(x,x),t)]
-thsqrt2:=satzr161b(x,sqrt,andi(not(neg(x)),is(ts(x,x),t),o,i),t12".7r161"):is(x,sqrt(t,n))
-o@[i:is(t,ts(x,x))]
-thsqrt3:=symis(real,x,sqrt(t,n),thsqrt2(symis(real,t,ts(x,x),i))):is(sqrt(t,n),x)
-@[r:real][s:real][n:not(neg(r))][o:not(neg(s))][i:is(r,s)]
-issqrt:=thsqrt2(s,o,sqrt(r,n),thsqrt1a(r,n),tris(real,ts(sqrt(r,n),sqrt(r,n)),r,s,thsqrt1b(r,n),i)):is(sqrt(r,n),sqrt(s,o))
-r@[n:not(neg(r))][i:is(r,0)]
-sqrt0:=thsqrt3(r,n,0,0notn(0,refis(real,0)),tris2(real,r,ts(0,0),0,i,ts01(0,0,refis(real,0)))):is(sqrt(r,n),0)
-n@[o:nis(r,0)]
-+sqrt
-t1:=th3"l.imp"(is(sqrt(r,n),0),is(r,0),o,[t:is(sqrt(r,n),0)]tris1(real,r,0,ts(sqrt(r,n),sqrt(r,n)),thsqrt1b(r,n),ts01(sqrt(r,n),sqrt(r,n),t))):nis(sqrt(r,n),0)
--sqrt
-sqrtnot0:=or3e2(is(sqrt(r,n),0),pos(sqrt(r,n)),neg(sqrt(r,n)),axrlo(sqrt(r,n)),thsqrt1a(r,n),t1".sqrt"):pos(sqrt(r,n))
-@[r:real][s:real][t:real][n:nis(t,0)]
-+v0
-t1:=tr3is(real,ts(t,ts(r,ov(s,t,n))),ts(ts(r,ov(s,t,n)),t),ts(r,ts(ov(s,t,n),t)),ts(r,s),comts(t,ts(r,ov(s,t,n))),assts1(r,ov(s,t,n),t),ists2(ts(ov(s,t,n),t),s,r,satz204e(s,t,n))):is(ts(t,ts(r,ov(s,t,n))),ts(r,s))
--v0
-lemma6:=satz204g(ts(r,s),t,ts(r,ov(s,t,n)),n,t1".v0"):is(ts(r,ov(s,t,n)),ov(ts(r,s),t,n))
-+*v0
-n@t2:=tris(real,ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(ts(t,ov(r,t,n)),ts(t,ov(s,t,n))),pl(r,s),disttp2(t,ov(r,t,n),ov(s,t,n)),ispl12(ts(t,ov(r,t,n)),r,ts(t,ov(s,t,n)),s,satz204c(r,t,n),satz204c(s,t,n))):is(ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(r,s))
--v0
-n@lemma7:=satz204g(pl(r,s),t,pl(ov(r,t,n),ov(s,t,n)),n,t2".v0"):is(pl(ov(r,t,n),ov(s,t,n)),ov(pl(r,s),t,n))
-r@[n:nis(r,0)]
-lemma8:=satz204b(r,r,n,ov(r,r,n),1rl,satz204c(r,r,n),satz195(r)):is(ov(r,r,n),1rl)
-lemma9:=ore2(is(r,0),is(ov(0,r,n),0),satz192c(r,ov(0,r,n),satz204c(0,r,n)),n):is(ov(0,r,n),0)
-r@[i:is(r,m0(r))]
-+*v0
-i@[p:pos(m0(r))]
-t3:=<isneg(r,m0(r),i,satz176f(r,p))>pnotn(m0(r),p):con
-i@[n:neg(m0(r))]
-t4:=<ispos(r,m0(r),i,satz176d(r,n))>nnotp(m0(r),n):con
--v0
-i@lemma10:=satz176e(r,or3e1(is(m0(r),0),pos(m0(r)),neg(m0(r)),axrlo(m0(r)),[t:pos(m0(r))]t3".v0"(t),[t:neg(m0(r))]t4".v0"(t))):is(r,0)
-r@lemma11:=satz167f(ts(r,r),0,th3"l.imp"(less(ts(r,r),0),neg(ts(r,r)),nnegsq(r),[t:less(ts(r,r),0)]satz169d(ts(r,r),t))):moreis(ts(r,r),0)
-lemma12:=rapp(r,is(ts(r,r),ts(abs(r),abs(r))),[t:pos(r)]satz196a(r,r,t,t),[t:is(r,0)]tris2(real,ts(r,r),ts(abs(r),abs(r)),0,ts01(r,r,t),ts01(abs(r),abs(r),abs0(r,t))),[t:neg(r)]satz196b(r,r,t,t)):is(ts(r,r),ts(abs(r),abs(r)))
-@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
-+shift
-t1:=satz190a(x,x,1rl,0,moreisi2(x,x,refis(real,x)),satz169a(1rl,natpos(1rl,natrl1))):more(pl(x,1rl),pl(x,0))
-t2:=ismore2(pl(x,0),x,pl(x,1rl),pl02(x,0,refis(real,0)),t1):more(pl(x,1rl),x)
-t3:=satz172d(pl(x,1rl),x,y,t2,satz168b(y,x,ly)):more(pl(x,1rl),y)
-t4:=satz182d(pl(x,1rl),y,t3):pos(mn(pl(x,1rl),y))
-t5:=intmn(pl(x,1rl),intpl(x,ix,1rl,intrl1),y,iy):intrl(mn(pl(x,1rl),y))
-t6:=posintnatrl(mn(pl(x,1rl),y),t4,t5):natrl(mn(pl(x,1rl),y))
--shift
-shiftl:=ntofrl(mn(pl(x,1rl),y),t6".shift"):nat
-[n:1to(shiftl)]
-+*shift
-n@n1:=inn"n"(shiftl,n):nat
-t7:=1top(shiftl,n):lessis"n"(n1,shiftl)
-n2:=rlofnt(n1):real
-t8:=natintrl(n2,natrli(n1)):intrl(n2)
--shift
-n@shiftr:=mn(pl(n2".shift",y),1rl):real
-intshiftr:=intmn(pl(n2".shift",y),intpl(n2".shift",t8".shift",y,iy),1rl,intrl1):intrl(shiftr)
-[m:1to(shiftl)][i:is(shiftr(n),shiftr(m))]
-+*shift
-n@t8a:=tris(real,mn(pl(shiftr(n),1rl),y),mn(pl(n2,y),y),n2,ismn1(pl(mn(pl(n2,y),1rl),1rl),pl(n2,y),y,plmn(pl(n2,y),1rl)),mnpl(n2,y)):is(mn(pl(shiftr(n),1rl),y),n2)
-i@t9a:=ismn1(pl(shiftr(n),1rl),pl(shiftr(m),1rl),y,ispl1(shiftr(n),shiftr(m),1rl,i)):is(mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y))
-t10a:=tr3is(real,n2(n),mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y),n2(m),symis(real,mn(pl(shiftr(n),1rl),y),n2,t8a),t9a,t8a(m)):is(n2(n),n2(m))
-t11a:=isntirl(n1(n),n1(m),t10a):is"n"(n1(n),n1(m))
--shift
-i@iseshiftr:=isinne(shiftl,n,m,t11a".shift"):is"e"(1to(shiftl),n,m)
-+*shift
-n@[m:more(shiftr,x)]
-t9:=satz188d(shiftr,x,1rl,m):more(pl(shiftr,1rl),pl(x,1rl))
-t10:=ismore1(pl(shiftr,1rl),pl(n2,y),pl(x,1rl),plmn(pl(n2,y),1rl),t9):more(pl(n2,y),pl(x,1rl))
-t11:=satz188d(pl(n2,y),pl(x,1rl),m0(y),t10):more(mn(pl(n2,y),y),mn(pl(x,1rl),y))
-t12:=ismore1(mn(pl(n2,y),y),n2,mn(pl(x,1rl),y),mnpl(n2,y),t11):more(n2,mn(pl(x,1rl),y))
-t13:=ismore12(n2,rlofnt(ntofrl(n2,natrli(n1))),mn(pl(x,1rl),y),rlofnt(ntofrl(mn(pl(x,1rl),y),t6)),isrlnt1(n2,natrli(n1)),isrlnt1(mn(pl(x,1rl),y),t6),t12):more(rlofnt(ntofrl(n2,natrli(n1))),rlofnt(shiftl))
-t14:=lemmaiva5(ntofrl(n2,natrli(n1)),shiftl,t13):more"n"(ntofrl(n2,natrli(n1)),shiftl)
-t15:=ismore1"n"(ntofrl(n2,natrli(n1)),n1,shiftl,isntrl2(n1),t14):more"n"(n1,shiftl)
-n@t16:=th3"l.imp"(more(shiftr,x),more"n"(n1,shiftl),satz10d(n1,shiftl,t7),[t:more(shiftr,x)]t15(t)):not(more(shiftr,x))
--shift
-n@shiftrls:=satz167e(shiftr,x,t16".shift"):lessis(shiftr,x)
-+*shift
-n@[m:more(y,shiftr)]
-t17:=satz188d(y,shiftr,1rl,m):more(pl(y,1rl),pl(shiftr,1rl))
-t18:=ismore12(pl(y,1rl),pl(1rl,y),pl(shiftr,1rl),pl(n2,y),compl(y,1rl),plmn(pl(n2,y),1rl),t17):more(pl(1rl,y),pl(n2,y))
-t19:=satz188a(1rl,n2,y,t18):more(1rl,n2)
-t20:=lemmaiva5(1,n1,t19):more"n"(1,n1)
-n@t21:=th3"l.imp"(more(y,shiftr),more"n"(1,n1),satz10d(1,n1,satz24a(n1)),[t:more(y,shiftr)]t20(t)):not(more(y,shiftr))
--shift
-n@lsshiftr:=satz167e(y,shiftr,t21".shift"):lessis(y,shiftr)
-ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
-+*shift
-a@t22:=and3e1(intrl(u),lessis(y,u),lessis(u,x),a):intrl(u)
-t23:=and3e2(intrl(u),lessis(y,u),lessis(u,x),a):lessis(y,u)
-t24:=and3e3(intrl(u),lessis(y,u),lessis(u,x),a):lessis(u,x)
-[l:less(u,x)]
-t25:=satz188f(pl(u,1rl),pl(x,1rl),m0"r"(y),satz188f(u,x,1rl,l)):less(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
-a@[i:is(u,x)]
-t26:=ismn1(pl(u,1rl),pl(x,1rl),y,ispl1(u,x,1rl,i)):is(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
-a@t27:=th9"l.or"(less(u,x),is(u,x),less(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),is(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),t24,[t:less(u,x)]t25(t),[t:is(u,x)]t26(t)):lessis(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
-ul:=shiftl(u,t22,y,iy,t23):nat
-t28:=islessis12(mn(pl(u,1rl),y),rlofnt(ul),mn(pl(x,1rl),y),rlofnt(shiftl),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isrlnt1(mn(pl(x,1rl),y),t6),t27):lessis(rlofnt(ul),rlofnt(shiftl))
-t29:=th3"l.imp"(more"n"(ul,shiftl),more(rlofnt(ul),rlofnt(shiftl)),satz167d(rlofnt(ul),rlofnt(shiftl),t28),[t:more"n"(ul,shiftl)]lemmaiva6(ul,shiftl,t)):not(more"n"(ul,shiftl))
-t30:=satz10e(ul,shiftl,t29):lessis"n"(ul,shiftl)
--shift
-a@shiftl1:=outn(shiftl,ul".shift",t30".shift"):1to(shiftl)
-+*shift
-a@t31:=isinoutn(shiftl,ul,t30):is"n"(ul,n1(shiftl1))
-t32:=tris(real,mn(pl(u,1rl),y),rlofnt(ul),n2(shiftl1),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isnterl(ul,n1(shiftl1),t31)):is(mn(pl(u,1rl),y),n2(shiftl1))
-t33:=tris(real,mn(pl(mn(pl(u,1rl),y),y),1rl),mn(pl(u,1rl),1rl),u,ismn1(pl(mn(pl(u,1rl),y),y),pl(u,1rl),1rl,plmn(pl(u,1rl),y)),mnpl(u,1rl)):is(mn(pl(mn(pl(u,1rl),y),y),1rl),u)
--shift
-a@shiftinv1:=tris1(real,u,shiftr(shiftl1),mn(pl(mn(pl(u,1rl),y),y),1rl),t33".shift",ismn1(pl(mn(pl(u,1rl),y),y),pl(n2".shift"(shiftl1),y),1rl,ispl1(mn(pl(u,1rl),y),n2".shift"(shiftl1),y,t32".shift"))):is(u,shiftr(shiftl1))
-shiftinv2:=symis(real,u,shiftr(shiftl1),shiftinv1):is(shiftr(shiftl1),u)
-ly@[alpha:'type']
-seq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]alpha:'type'
-[s:seq]
-proofsirrelevant:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is(t,u)]is"e"(alpha,<tl><lt><it><t>s,<ul><lu><iu><u>s):'prop'
-alpha@[f:seq]
-shiftf:=[t:1to(shiftl)]<shiftrls(t)><lsshiftr(t)><intshiftr(t)><shiftr(t)>f:[t:1to(shiftl)]alpha
-ly@[s:seq(real)]
-inseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]and3(intrl(<w><v><u><t>s),lessis(y,<w><v><u><t>s),lessis(<w><v><u><t>s,x)):'prop'
-injseq:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is"r"(<tl><lt><it><t>s,<ul><lu><iu><u>s)]is"r"(t,u):'prop'
-[u:real][v:real][a:and3(intrl(v),lessis(y,v),lessis(v,x))]
-+*shift
-a@prop1:=is(u,<t24(v,a)><t23(v,a)><t22(v,a)><v>s):'prop'
--shift
-v@improp:=and(and3(intrl(v),lessis(y,v),lessis(v,x)),[t:and3(intrl(v),lessis(y,v),lessis(v,x))]prop1".shift"(t)):'prop'
-u@imseq:=some([t:real]improp(u,t)):'prop'
-s@surjseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]imseq(t):'prop'
-perm:=and(injseq,surjseq):'prop'
-[ins:inseq(s)]
-+*shift
-ins@[n:1to(shiftl)]
-ns:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>s:real
-t34:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ins:and3(intrl(ns),lessis(y,ns),lessis(ns,x))
--shift
-ins@shiftseq:=[t:1to(shiftl)]shiftl1(ns".shift"(t),t34".shift"(t)):[t:1to(shiftl)]1to(shiftl)
-[js:injseq(s)]
-+*shift
-js@[n:1to(shiftl)][m:1to(shiftl)][i:is"e"(1to(shiftl),<n>shiftseq,<m>shiftseq)]
-t35:=isoutne(shiftl,ul(ns(n),t34(n)),t30(ns(n),t34(n)),ul(ns(m),t34(m)),t30(ns(m),t34(m)),i):is"n"(ul(ns(n),t34(n)),ul(ns(m),t34(m)))
-t36:=isrlint(mn(pl(ns(n),1rl),y),t6(ns(n),t22(ns(n),t34(n)),y,iy,t23(ns(n),t34(n))),mn(pl(ns(m),1rl),y),t6(ns(m),t22(ns(m),t34(m)),y,iy,t23(ns(m),t34(m))),t35):is(mn(pl(ns(n),1rl),y),mn(pl(ns(m),1rl),y))
-t37:=satz188b(ns(n),ns(m),1rl,satz188b(pl(ns(n),1rl),pl(ns(m),1rl),m0"r"(y),t36)):is(ns(n),ns(m))
-t38:=<t37><shiftrls(m)><lsshiftr(m)><intshiftr(m)><shiftr(m)><shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>js:is(shiftr(n),shiftr(m))
-t39:=satz188b(n2(n),n2(m),y,satz188b(pl(n2(n),y),pl(n2(m),y),m0(1rl),t38)):is(n2(n),n2(m))
-t40:=isntirl(n1(n),n1(m),t39):is"n"(n1(n),n1(m))
-t41:=isinne(shiftl,n,m,t40):is"e"(1to(shiftl),n,m)
--shift
-js@injshiftseq:=[t:1to(shiftl)][u:1to(shiftl)][v:is"e"(1to(shiftl),<t>shiftseq,<u>shiftseq)]t41".shift"(t,u,v):injective(1to(shiftl),1to(shiftl),shiftseq)
-ins@[pri:proofsirrelevant(real,s)][ss:surjseq(s)]
-+*shift
-ss@[n:1to(shiftl)]
-t42:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ss:imseq(shiftr(n))
-[u:real][p:improp(shiftr(n),u)]
-t43:=ande1(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):and3(intrl(u),lessis(y,u),lessis(u,x))
-t44:=ande2"l.r"(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):is(shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s)
-ul1:=shiftl1(u,t43):1to(shiftl)
-t45:=<shiftinv1(u,t43)><shiftrls(ul1)><lsshiftr(ul1)><intshiftr(ul1)><shiftr(ul1)><t24(u,t43)><t23(u,t43)><t22(u,t43)><u>pri:is(<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1))
-t46:=shiftinv1(ns(ul1),t34(ul1)):is(ns(ul1),shiftr(<ul1>shiftseq))
-t47:=tr3is(real,shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1),shiftr(<ul1>shiftseq),t44,t45,t46):is(shiftr(n),shiftr(<ul1>shiftseq))
-t48:=iseshiftr(n,<ul1>shiftseq,t47):is"e"(1to(shiftl),n,<ul1>shiftseq)
-t49:=somei(1to(shiftl),[t:1to(shiftl)]is"e"(1to(shiftl),n,<t>shiftseq),ul1,t48):image(1to(shiftl),1to(shiftl),shiftseq,n)
-n@t50:=someapp(real,[t:real]improp(shiftr(n),t),t42,image(1to(shiftl),1to(shiftl),shiftseq,n),[t:real][u:improp(shiftr(n),t)]t49(t,u)):image(1to(shiftl),1to(shiftl),shiftseq,n)
--shift
-ss@surjshiftseq:=[t:1to(shiftl)]t50".shift"(t):surjective(1to(shiftl),1to(shiftl),shiftseq)
-pri@[ps:perm(s)]
-bijshiftseq:=andi(injective(1to(shiftl),1to(shiftl),shiftseq),surjective(1to(shiftl),1to(shiftl),shiftseq),injshiftseq(ande1(injseq(s),surjseq(s),ps)),surjshiftseq(ande2(injseq(s),surjseq(s),ps))):bijective(1to(shiftl),1to(shiftl),shiftseq)
-+c
-@complex:=pair1type(real):'type'
-cx:=complex:'type'
-[x:complex][y:complex]
-is:=is"e"(cx,x,y):'prop'
-nis:=not(is(x,y)):'prop'
-@[p:[t:complex]'prop']
-some:=some"l"(cx,p):'prop'
-all:=all"l"(cx,p):'prop'
-one:=one"e"(cx,p):'prop'
-@[a:real][b:real]
-pli:=pair1(real,a,b):complex
-x@re:=first1(real,x):real
-im:=second1(real,x):real
-b@reis:=first1is1(real,a,b):is"r"(re(pli(a,b)),a)
-isre:=first1is2(real,a,b):is"r"(a,re(pli(a,b)))
-imis:=second1is1(real,a,b):is"r"(im(pli(a,b)),b)
-isim:=second1is2(real,a,b):is"r"(b,im(pli(a,b)))
-x@pliis:=pair1is1(real,x):is(pli(re(x),im(x)),x)
-ispli:=pair1is2(real,x):is(x,pli(re(x),im(x)))
-y@[i:is(x,y)]
-iscere:=isf(cx,real,[t:cx]re(t),x,y,i):is"r"(re(x),re(y))
-isceim:=isf(cx,real,[t:cx]im(t),x,y,i):is"r"(im(x),im(y))
-b@[c:real][i:is"r"(a,b)]
-isrecx1:=isf(real,cx,[t:real]pli(t,c),a,b,i):is(pli(a,c),pli(b,c))
-isrecx2:=isf(real,cx,[t:real]pli(c,t),a,b,i):is(pli(c,a),pli(c,b))
-c@[d:real][i:is"r"(a,b)][j:is"r"(c,d)]
-isrecx12:=tris(cx,pli(a,c),pli(b,c),pli(b,d),isrecx1(a,b,c,i),isrecx2(c,d,b,j)):is(pli(a,c),pli(b,d))
-x@satz206:=refis(cx,x):is(x,x)
-y@[i:is(x,y)]
-satz207:=symis(cx,x,y,i):is(y,x)
-y@[z:complex][i:is(x,y)][j:is(y,z)]
-satz208:=tris(cx,x,y,z,i,j):is(x,z)
-@0c:=pli(0,0):complex
-1c:=pli(1rl,0):complex
-y@pl:=pli(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))):complex
-d@plis12a:=isrecx12(pl"r"(re(pli(a,b)),re(pli(c,d))),pl"r"(a,c),pl"r"(im(pli(a,b)),im(pli(c,d))),pl"r"(b,d),ispl12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ispl12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)))
-plis12b:=symis(cx,pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)),plis12a):is(pli(pl"r"(a,c),pl"r"(b,d)),pl(pli(a,b),pli(c,d)))
-x@[r:real][s:real]
-plis1a:=isrecx12(pl"r"(re(pli(r,s)),re(x)),pl"r"(r,re(x)),pl"r"(im(pli(r,s)),im(x)),pl"r"(s,im(x)),ispl1(re(pli(r,s)),r,re(x),reis(r,s)),ispl1(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))))
-plis1b:=symis(cx,pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))),plis1a):is(pli(pl"r"(r,re(x)),pl"r"(s,im(x))),pl(pli(r,s),x))
-plis2a:=isrecx12(pl"r"(re(x),re(pli(r,s))),pl"r"(re(x),r),pl"r"(im(x),im(pli(r,s))),pl"r"(im(x),s),ispl2(re(pli(r,s)),r,re(x),reis(r,s)),ispl2(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)))
-plis2b:=symis(cx,pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)),plis2a):is(pli(pl"r"(re(x),r),pl"r"(im(x),s)),pl(x,pli(r,s)))
-z@[i:is(x,y)]
-ispl1:=isf(cx,cx,[t:cx]pl(t,z),x,y,i):is(pl(x,z),pl(y,z))
-ispl2:=isf(cx,cx,[t:cx]pl(z,t),x,y,i):is(pl(z,x),pl(z,y))
-z@[u:complex][i:is(x,y)][j:is(z,u)]
-ispl12:=tris(cx,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
-y@satz209:=isrecx12(pl"r"(re(x),re(y)),pl"r"(re(y),re(x)),pl"r"(im(x),im(y)),pl"r"(im(y),im(x)),compl(re(x),re(y)),compl(im(x),im(y))):is(pl(x,y),pl(y,x))
-compl:=satz209:is(pl(x,y),pl(y,x))
-x@satz210:=tr3is(cx,pl(x,0c),pli(pl"r"(re(x),0),pl"r"(im(x),0)),pli(re(x),im(x)),x,plis2a(x,0,0),isrecx12(pl"r"(re(x),0),re(x),pl"r"(im(x),0),im(x),pl02(re(x),0,refis(real,0)),pl02(im(x),0,refis(real,0))),pliis(x)):is(pl(x,0c),x)
-satz210a:=symis(cx,pl(x,0c),x,satz210):is(x,pl(x,0c))
-satz210b:=tris(cx,pl(0c,x),pl(x,0c),x,compl(0c,x),satz210):is(pl(0c,x),x)
-satz210c:=symis(cx,pl(0c,x),x,satz210b):is(x,pl(0c,x))
-z@satz211:=tr3is(cx,pl(pl(x,y),z),pli(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(pl"r"(im(x),im(y)),im(z))),pli(pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(im(x),pl"r"(im(y),im(z)))),pl(x,pl(y,z)),plis1a(z,pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(pl"r"(im(x),im(y)),im(z)),pl"r"(im(x),pl"r"(im(y),im(z))),asspl1(re(x),re(y),re(z)),asspl1(im(x),im(y),im(z))),plis2b(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z)))):is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl1:=satz211:is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl2:=symis(cx,pl(pl(x,y),z),pl(x,pl(y,z)),asspl1):is(pl(x,pl(y,z)),pl(pl(x,y),z))
-y@[u:complex][i:is(pl(y,u),x)]
-+2212
-t1:=tris(real,pl"r"(re(y),re(u)),re(pl(y,u)),re(x),isre(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),iscere(pl(y,u),x,i)):is"r"(pl"r"(re(y),re(u)),re(x))
-t2:=tris(real,pl"r"(im(y),im(u)),im(pl(y,u)),im(x),isim(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),isceim(pl(y,u),x,i)):is"r"(pl"r"(im(y),im(u)),im(x))
-t3:=satz187d(re(x),re(y),re(u),t1):is"r"(re(u),mn(re(x),re(y)))
-t4:=satz187d(im(x),im(y),im(u),t2):is"r"(im(u),mn(im(x),im(y)))
--2212
-satz212a:=tris(cx,u,pli(re(u),im(u)),pli(mn(re(x),re(y)),mn(im(x),im(y))),ispli(u),isrecx12(re(u),mn(re(x),re(y)),im(u),mn(im(x),im(y)),t3".2212",t4".2212")):is(u,pli(mn(re(x),re(y)),mn(im(x),im(y))))
-y@satz212b:=tr3is(cx,pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),pli(pl"r"(re(y),mn(re(x),re(y))),pl"r"(im(y),mn(im(x),im(y)))),pli(re(x),im(x)),x,plis2a(y,mn(re(x),re(y)),mn(im(x),im(y))),isrecx12(pl"r"(re(y),mn(re(x),re(y))),re(x),pl"r"(im(y),mn(im(x),im(y))),im(x),satz187a(re(x),re(y)),satz187a(im(x),im(y))),pliis(x)):is(pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),x)
-satz212c:=somei(cx,[t:cx]is(pl(y,t),x),pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212b):some([t:complex]is(pl(y,t),x))
-satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212a(t,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
-%satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
-mn:=pli(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))):complex
-d@mnis12a:=isrecx12(mn"r"(re(pli(a,b)),re(pli(c,d))),mn"r"(a,c),mn"r"(im(pli(a,b)),im(pli(c,d))),mn"r"(b,d),ismn12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ismn12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)))
-mnis12b:=symis(cx,mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)),mnis12a):is(pli(mn"r"(a,c),mn"r"(b,d)),mn(pli(a,b),pli(c,d)))
-x@[r:real][s:real]
-mnis1a:=isrecx12(mn"r"(re(pli(r,s)),re(x)),mn"r"(r,re(x)),mn"r"(im(pli(r,s)),im(x)),mn"r"(s,im(x)),ismn1(re(pli(r,s)),r,re(x),reis(r,s)),ismn1(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))))
-mnis1b:=symis(cx,mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mnis1a):is(pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mn(pli(r,s),x))
-mnis2a:=isrecx12(mn"r"(re(x),re(pli(r,s))),mn"r"(re(x),r),mn"r"(im(x),im(pli(r,s))),mn"r"(im(x),s),ismn2(re(pli(r,s)),r,re(x),reis(r,s)),ismn2(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)))
-mnis2b:=symis(cx,mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)),mnis2a):is(pli(mn"r"(re(x),r),mn"r"(im(x),s)),mn(x,pli(r,s)))
-z@[i:is(x,y)]
-ismn1:=isf(cx,cx,[t:cx]mn(t,z),x,y,i):is(mn(x,z),mn(y,z))
-ismn2:=isf(cx,cx,[t:cx]mn(z,t),x,y,i):is(mn(z,x),mn(z,y))
-z@[u:complex][i:is(x,y)][j:is(z,u)]
-ismn12:=tris(cx,mn(x,z),mn(y,z),mn(y,u),ismn1(x,y,z,i),ismn2(z,u,y,j)):is(mn(x,z),mn(y,u))
-y@[u:complex][i:is(pl(y,u),x)]
-satz212d:=satz212a(u,i):is(u,mn(x,y))
-satz212e:=symis(cx,u,mn(x,y),satz212d):is(mn(x,y),u)
-u@[i:is(pl(u,y),x)]
-satz212f:=satz212d(tris(cx,pl(y,u),pl(u,y),x,compl(y,u),i)):is(u,mn(x,y))
-satz212g:=symis(cx,u,mn(x,y),satz212f):is(mn(x,y),u)
-y@satz212h:=satz212b:is(pl(y,mn(x,y)),x)
-[i:is(mn(x,y),0c)]
-+2213
-t1:=tr3is(real,mn"r"(re(x),re(y)),re(mn(x,y)),re(0c),0,isre(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),iscere(mn(x,y),0c,i),reis(0,0)):is"r"(mn"r"(re(x),re(y)),0)
-t2:=tr3is(real,mn"r"(im(x),im(y)),im(mn(x,y)),im(0c),0,isim(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),isceim(mn(x,y),0c,i),imis(0,0)):is"r"(mn"r"(im(x),im(y)),0)
-t3:=satz182b(re(x),re(y),t1):is"r"(re(x),re(y))
-t4:=satz182b(im(x),im(y),t2):is"r"(im(x),im(y))
--2213
-satz213a:=tr3is(cx,x,pli(re(x),im(x)),pli(re(y),im(y)),y,ispli(x),isrecx12(re(x),re(y),im(x),im(y),t3".2213",t4".2213"),pliis(y)):is(x,y)
-y@[i:is(x,y)]
-+*2213
-i@t5:=satz182e(re(x),re(y),iscere(x,y,i)):is"r"(mn"r"(re(x),re(y)),0)
-t6:=satz182e(im(x),im(y),isceim(x,y,i)):is"r"(mn"r"(im(x),im(y)),0)
--2213
-i@satz213b:=isrecx12(mn"r"(re(x),re(y)),0,mn"r"(im(x),im(y)),0,t5".2213",t6".2213"):is(mn(x,y),0c)
-x@m0:=mn(0c,x):complex
-satz214:=isrecx12(mn"r"(re(0c),re(x)),m0"r"(re(x)),mn"r"(im(0c),im(x)),m0"r"(im(x)),pl01(re(0c),m0"r"(re(x)),reis(0,0)),pl01(im(0c),m0"r"(im(x)),imis(0,0))):is(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))))
-satz214a:=symis(cx,m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214):is(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x))
-b@m0isa:=tris(cx,m0(pli(a,b)),pli(m0"r"(re(pli(a,b))),m0"r"(im(pli(a,b)))),pli(m0"r"(a),m0"r"(b)),satz214(pli(a,b)),isrecx12(m0"r"(re(pli(a,b))),m0"r"(a),m0"r"(im(pli(a,b))),m0"r"(b),ism0(re(pli(a,b)),a,reis(a,b)),ism0(im(pli(a,b)),b,imis(a,b)))):is(m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)))
-m0isb:=symis(cx,m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)),m0isa):is(pli(m0"r"(a),m0"r"(b)),m0(pli(a,b)))
-y@[i:is(x,y)]
-ism0:=isf(cx,cx,[t:cx]m0(t),x,y,i):is(m0(x),m0(y))
-x@satz215:=tr4is(cx,m0(m0(x)),m0(pli(m0"r"(re(x)),m0"r"(im(x)))),pli(m0"r"(m0"r"(re(x))),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,ism0(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214),m0isa(m0"r"(re(x)),m0"r"(im(x))),isrecx12(m0"r"(m0"r"(re(x))),re(x),m0"r"(m0"r"(im(x))),im(x),satz177(re(x)),satz177(im(x))),pliis(x)):is(m0(m0(x)),x)
-satz215a:=symis(cx,m0(m0(x)),x,satz215):is(x,m0(m0(x)))
-y@[i:is(x,m0(y))]
-satz215b:=tris(cx,m0(x),m0(m0(y)),y,ism0(x,m0(y),i),satz215(y)):is(m0(x),y)
-satz215c:=symis(cx,m0(x),y,satz215b):is(y,m0(x))
-y@[i:is(m0(x),y)]
-satz215d:=satz215c(y,x,symis(cx,m0(x),y,i)):is(x,m0(y))
-satz215e:=symis(cx,x,m0(y),satz215d):is(m0(y),x)
-x@satz216:=tr3is(cx,pl(x,m0(x)),pl(x,pli(m0"r"(re(x)),m0"r"(im(x)))),pli(pl"r"(re(x),m0"r"(re(x))),pl"r"(im(x),m0"r"(im(x)))),0c,ispl2(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),x,satz214(x)),plis2a(x,m0"r"(re(x)),m0"r"(im(x))),isrecx12(pl"r"(re(x),m0"r"(re(x))),0,pl"r"(im(x),m0"r"(im(x))),0,satz179(re(x)),satz179(im(x)))):is(pl(x,m0(x)),0c)
-+2216
-anders:=satz212h(0c,x):is(pl(x,m0(x)),0c)
--2216
-satz216a:=tris(cx,pl(m0(x),x),pl(x,m0(x)),0c,compl(m0(x),x),satz216):is(pl(m0(x),x),0c)
-y@satz217:=tr4is(cx,m0(pl(x,y)),pli(m0"r"(pl"r"(re(x),re(y))),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(m0"r"(re(x)),m0"r"(re(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(pli(m0"r"(re(x)),m0"r"(im(x))),pli(m0"r"(re(y)),m0"r"(im(y)))),pl(m0(x),m0(y)),m0isa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(m0"r"(pl"r"(re(x),re(y))),pl"r"(m0"r"(re(x)),m0"r"(re(y))),m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),satz180(re(x),re(y)),satz180(im(x),im(y))),plis12b(m0"r"(re(x)),m0"r"(im(x)),m0"r"(re(y)),m0"r"(im(y))),ispl12(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),satz214a(x),satz214a(y))):is(m0(pl(x,y)),pl(m0(x),m0(y)))
-satz217a:=symis(cx,m0(pl(x,y)),pl(m0(x),m0(y)),satz217):is(pl(m0(x),m0(y)),m0(pl(x,y)))
-satz218:=tris(cx,mn(x,y),pl(x,pli(m0"r"(re(y)),m0"r"(im(y)))),pl(x,m0(y)),plis2b(x,m0"r"(re(y)),m0"r"(im(y))),ispl2(pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),x,satz214a(y))):is(mn(x,y),pl(x,m0(y)))
-satz218a:=symis(cx,mn(x,y),pl(x,m0(y)),satz218):is(pl(x,m0(y)),mn(x,y))
-+2219
-t1:=tr3is(cx,m0(mn(x,y)),m0(pl(x,m0(y))),pl(m0(x),m0(m0(y))),pl(m0(x),y),ism0(mn(x,y),pl(x,m0(y)),satz218),satz217(x,m0(y)),ispl2(m0(m0(y)),y,m0(x),satz215(y))):is(m0(mn(x,y)),pl(m0(x),y))
--2219
-satz219:=tr3is(cx,m0(mn(x,y)),pl(m0(x),y),pl(y,m0(x)),mn(y,x),t1".2219",compl(m0(x),y),satz218a(y,x)):is(m0(mn(x,y)),mn(y,x))
-satz219a:=symis(cx,m0(mn(y,x)),mn(x,y),satz219(y,x)):is(mn(x,y),m0(mn(y,x)))
-ts:=pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))):complex
-rets:=mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))):real
-imts:=pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))):real
-+v3
-d@t1:=ismn12"r"(ts"r"(re(pli(a,b)),re(pli(c,d))),ts"r"(a,c),ts"r"(im(pli(a,b)),im(pli(c,d))),ts"r"(b,d),ists12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ists12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is"r"(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)))
-t2:=ispl12"r"(ts"r"(re(pli(a,b)),im(pli(c,d))),ts"r"(a,d),ts"r"(im(pli(a,b)),re(pli(c,d))),ts"r"(b,c),ists12(re(pli(a,b)),a,im(pli(c,d)),d,reis(a,b),imis(c,d)),ists12(im(pli(a,b)),b,re(pli(c,d)),c,imis(a,b),reis(c,d))):is"r"(imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)))
--v3
-d@tsis12a:=isrecx12(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)),imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)),t1".v3",t2".v3"):is(ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))))
-tsis12b:=symis(cx,ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),tsis12a):is(pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),ts(pli(a,b),pli(c,d)))
-x@[r:real][s:real]
-+*v3
-s@t3:=ismn12"r"(ts"r"(re(pli(r,s)),re(x)),ts"r"(r,re(x)),ts"r"(im(pli(r,s)),im(x)),ts"r"(s,im(x)),ists1(re(pli(r,s)),r,re(x),reis(r,s)),ists1(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))))
-t4:=ispl12"r"(ts"r"(re(pli(r,s)),im(x)),ts"r"(r,im(x)),ts"r"(im(pli(r,s)),re(x)),ts"r"(s,re(x)),ists1(re(pli(r,s)),r,im(x),reis(r,s)),ists1(im(pli(r,s)),s,re(x),imis(r,s))):is"r"(imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))))
--v3
-s@tsis1a:=isrecx12(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))),t3".v3",t4".v3"):is(ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))))
-tsis1b:=symis(cx,ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),tsis1a):is(pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),ts(pli(r,s),x))
-+*v3
-s@t5:=ismn12"r"(ts"r"(re(x),re(pli(r,s))),ts"r"(re(x),r),ts"r"(im(x),im(pli(r,s))),ts"r"(im(x),s),ists2(re(pli(r,s)),r,re(x),reis(r,s)),ists2(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)))
-t6:=ispl12"r"(ts"r"(re(x),im(pli(r,s))),ts"r"(re(x),s),ts"r"(im(x),re(pli(r,s))),ts"r"(im(x),r),ists2(im(pli(r,s)),s,re(x),imis(r,s)),ists2(re(pli(r,s)),r,im(x),reis(r,s))):is"r"(imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)))
--v3
-s@tsis2a:=isrecx12(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)),t5".v3",t6".v3"):is(ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))))
-tsis2b:=symis(cx,ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),tsis2a):is(pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),ts(x,pli(r,s)))
-z@[i:is(x,y)]
-ists1:=isf(cx,cx,[t:cx]ts(t,z),x,y,i):is(ts(x,z),ts(y,z))
-ists2:=isf(cx,cx,[t:cx]ts(z,t),x,y,i):is(ts(z,x),ts(z,y))
-z@[u:complex][i:is(x,y)][j:is(z,u)]
-ists12:=tris(cx,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
-+3220
-y@t1:=ismn12"r"(ts"r"(re(x),re(y)),ts"r"(re(y),re(x)),ts"r"(im(x),im(y)),ts"r"(im(y),im(x)),comts(re(x),re(y)),comts(im(x),im(y))):is"r"(rets(x,y),rets(y,x))
-t2:=tris(real,imts(x,y),pl"r"(ts"r"(im(x),re(y)),ts"r"(re(x),im(y))),imts(y,x),compl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(ts"r"(im(x),re(y)),ts"r"(re(y),im(x)),ts"r"(re(x),im(y)),ts"r"(im(y),re(x)),comts(im(x),re(y)),comts(re(x),im(y)))):is"r"(imts(x,y),imts(y,x))
--3220
-y@satz220:=isrecx12(rets(x,y),rets(y,x),imts(x,y),imts(y,x),t1".3220",t2".3220"):is(ts(x,y),ts(y,x))
-comts:=satz220:is(ts(x,y),ts(y,x))
-x@[i:is(x,0c)]
-lemma1:=tris(real,re(x),re(0c),0,iscere(x,0c,i),reis(0,0)):is"r"(re(x),0)
-lemma2:=tris(real,im(x),im(0c),0,isceim(x,0c,i),imis(0,0)):is"r"(im(x),0)
-x@mod2:=pl"r"(ts"r"(re(x),re(x)),ts"r"(im(x),im(x))):real
-i@lemma3:=tris(real,mod2,pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),0,ts01(re(x),re(x),lemma1),ts01(im(x),im(x),lemma2)),pl01(0,0,refis(real,0))):is"r"(mod2(x),0)
-x@[n:nis(x,0c)]
-+*v3
-x@re2:=ts"r"(re(x),re(x)):real
-im2:=ts"r"(im(x),im(x)):real
-n@[i:is"r"(re(x),0)]
-t7:=th3"l.imp"(is"r"(im(x),0),is(x,0c),n,[t:is"r"(im(x),0)]tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,i,t))):nis"r"(im(x),0)
-t8:=ispos(im2,mod2,symis(real,mod2,im2,pl01(re2,im2,ts01(re(x),re(x),i))),possq(im(x),t7)):pos(mod2)
-n@[o:nis"r"(re(x),0)][i:is"r"(im(x),0)]
-t9:=ispos(re2,mod2,symis(real,mod2,re2,pl02(re2,im2,ts01(im(x),im(x),i))),possq(re(x),o)):pos(mod2)
-o@[p:nis"r"(im(x),0)]
-t10:=pospl(re2,im2,possq(re(x),o),possq(im(x),p)):pos(mod2)
-o@t11:=th1"l.imp"(is"r"(im(x),0),pos(mod2),[t:is"r"(im(x),0)]t9(t),[t:nis"r"(im(x),0)]t10(t)):pos(mod2)
--v3
-n@lemma4:=th1"l.imp"(is"r"(re(x),0),pos(mod2),[t:is"r"(re(x),0)]t8".v3"(t),[t:nis"r"(re(x),0)]t11".v3"(t)):pos(mod2(x))
-x@lemma5:=th1"l.imp"(is(x,0c),not(neg(mod2)),[t:is(x,0c)]0notn(mod2,lemma3(t)),[t:nis(x,0c)]pnotn(mod2,lemma4(t))):not(neg(mod2(x)))
-y@[i:is(x,0c)]
-+3221
-t1:=lemma1(x,i):is"r"(re(x),0)
-t2:=lemma2(x,i):is"r"(im(x),0)
-t3:=tris(real,rets(x,y),mn"r"(0,0),0,ismn12"r"(ts"r"(re(x),re(y)),0,ts"r"(im(x),im(y)),0,ts01(re(x),re(y),t1),ts01(im(x),im(y),t2)),satz187c(0,0,0,pl02(0,0,refis(real,0)))):is"r"(rets(x,y),0)
-t4:=tris(real,imts(x,y),pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),im(y)),0,ts"r"(im(x),re(y)),0,ts01(re(x),im(y),t1),ts01(im(x),re(y),t2)),pl02(0,0,refis(real,0))):is"r"(imts(x,y),0)
--3221
-satz221a:=isrecx12(rets(x,y),0,imts(x,y),0,t3".3221",t4".3221"):is(ts(x,y),0c)
-y@[i:is(y,0c)]
-satz221b:=tris(cx,ts(x,y),ts(y,x),0c,comts(x,y),satz221a(y,x,i)):is(ts(x,y),0c)
-y@[i:is(ts(x,y),0c)]
-+*3221
-i@[n:nis(y,0c)]
-t5:=lemma4(y,n):pos(mod2(y))
-t6:=tris1(real,rets(x,y),0,re(ts(x,y)),reis(rets(x,y),imts(x,y)),lemma1(ts(x,y),i)):is"r"(rets(x,y),0)
-t7:=tris1(real,imts(x,y),0,im(ts(x,y)),imis(rets(x,y),imts(x,y)),lemma2(ts(x,y),i)):is"r"(imts(x,y),0)
-t8:=tris(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(0,0),0,ispl12"r"(ts"r"(rets(x,y),re(y)),0,ts"r"(imts(x,y),im(y)),0,ts01(rets(x,y),re(y),t6),ts01(imts(x,y),im(y),t7)),pl02(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),0)
-y@ii1r:=ts"r"(ts"r"(im(x),im(y)),re(y)):real
-i1ir:=ts"r"(im(x),ts"r"(im(y),re(y))):real
-ir1i:=ts"r"(ts"r"(im(x),re(y)),im(y)):real
-i1ri:=ts"r"(im(x),ts"r"(re(y),im(y))):real
-rr1r:=ts"r"(ts"r"(re(x),re(y)),re(y)):real
-r1rr:=ts"r"(re(x),ts"r"(re(y),re(y))):real
-ri1r:=ts"r"(ts"r"(re(x),im(y)),re(y)):real
-r1ir:=ts"r"(re(x),ts"r"(im(y),re(y))):real
-ri1i:=ts"r"(ts"r"(re(x),im(y)),im(y)):real
-r1ii:=ts"r"(re(x),ts"r"(im(y),im(y))):real
-n@t9:=tris(real,ii1r,i1ir,i1ri,assts1(im(x),im(y),re(y)),ists2"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),im(x),comts"r"(im(y),re(y)))):is"r"(ii1r,i1ri)
-t10:=tris(real,ts"r"(rets(x,y),re(y)),mn"r"(rr1r,ii1r),mn"r"(r1rr,i1ri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(y)),ismn12"r"(rr1r,r1rr,ii1r,i1ri,assts1(re(x),re(y),re(y)),t9)):is"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri))
-t11:=tr3is(real,ts"r"(imts(x,y),im(y)),pl"r"(ri1i,ir1i),pl"r"(r1ii,i1ri),pl"r"(i1ri,r1ii),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(y)),ispl12"r"(ri1i,r1ii,ir1i,i1ri,assts1(re(x),im(y),im(y)),assts1(im(x),re(y),im(y))),compl"r"(r1ii,i1ri)):is"r"(ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii))
-t12:=tr4is(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(mn"r"(r1rr,i1ri),pl"r"(i1ri,r1ii)),pl"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1ii),pl"r"(r1rr,r1ii),ts"r"(re(x),mod2(y)),ispl12"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri),ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii),t10,t11),asspl2"r"(mn"r"(r1rr,i1ri),i1ri,r1ii),ispl1"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1rr,r1ii,plmn(r1rr,i1ri)),distpt2(re(x),ts"r"(re(y),re(y)),ts"r"(im(y),im(y)))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),ts"r"(re(x),mod2(y)))
-t13:=tris1(real,ts"r"(re(x),mod2(y)),0,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),t12,t8):is"r"(ts"r"(re(x),mod2(y)),0)
-t14:=ore1(is"r"(re(x),0),is"r"(mod2(y),0),satz192c(re(x),mod2(y),t13),pnot0(mod2(y),t5)):is"r"(re(x),0)
-t15:=tris1(real,ts"r"(im(x),im(y)),0,ts"r"(re(x),re(y)),satz182b(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),t6),ts01(re(x),re(y),t14)):is"r"(ts"r"(im(x),im(y)),0)
-t16:=tris1(real,ts"r"(im(x),re(y)),0,imts(x,y),pl01(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),ts01(re(x),im(y),t14)),t7):is"r"(ts"r"(im(x),re(y)),0)
-[j:is"r"(re(y),0)]
-t17:=t7"c.v3"(y,n,j):nis"r"(im(y),0)
-t18:=ore1(is"r"(im(x),0),is"r"(im(y),0),satz192c(im(x),im(y),t15),t17):is"r"(im(x),0)
-n@[o:nis"r"(re(y),0)]
-t19:=ore1(is"r"(im(x),0),is"r"(re(y),0),satz192c(im(x),re(y),t16),o):is"r"(im(x),0)
-n@t20:=th1"l.imp"(is"r"(re(y),0),is"r"(im(x),0),[t:is"r"(re(y),0)]t18(t),[t:nis"r"(re(y),0)]t19(t)):is"r"(im(x),0)
-t21:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t14,t20)):is(x,0c)
--3221
-i@satz221c:=th2"l.or"(is(x,0c),is(y,0c),[t:nis(y,0c)]t21".3221"(t)):or(is(x,0c),is(y,0c))
-y@[n:nis(x,0c)][o:nis(y,0c)]
-satz221d:=th3"l.imp"(is(ts(x,y),0c),or(is(x,0c),is(y,0c)),th3"l.or"(is(x,0c),is(y,0c),n,o),[t:is(ts(x,y),0c)]satz221c(t)):nis(ts(x,y),0c)
-+3222
-x@t1:=tris(real,mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),mn"r"(re(x),0),re(x),ismn12"r"(ts"r"(re(x),1rl),re(x),ts"r"(im(x),0),0,satz195(re(x)),ts02(im(x),0,refis(real,0))),pl02(re(x),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x))
-t2:=tris(real,pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),pl"r"(0,im(x)),im(x),ispl12"r"(ts"r"(re(x),0),0,ts"r"(im(x),1rl),im(x),ts02(re(x),0,refis(real,0)),satz195(im(x))),pl01(0,im(x),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x))
--3222
-x@satz222:=tr3is(cx,ts(x,1c),pli(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl))),pli(re(x),im(x)),x,tsis2a(x,1rl,0),isrecx12(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x),t1".3222",t2".3222"),pliis(x)):is(ts(x,1c),x)
-satz222a:=symis(cx,ts(x,1c),x,satz222):is(x,ts(x,1c))
-satz222b:=tris(cx,ts(1c,x),ts(x,1c),x,comts(1c,x),satz222):is(ts(1c,x),x)
-satz222c:=symis(cx,ts(1c,x),x,satz222b):is(x,ts(1c,x))
-+3223
-t1:=tris(real,mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),mn"r"(m0"r"(re(x)),0),m0"r"(re(x)),ismn12"r"(ts"r"(re(x),m0"r"(1rl)),m0"r"(re(x)),ts"r"(im(x),m0"r"(0)),0,tris(real,ts"r"(re(x),m0"r"(1rl)),m0"r"(ts"r"(re(x),1rl)),m0"r"(re(x)),satz197b(re(x),1rl),ism0"r"(ts"r"(re(x),1rl),re(x),satz195(re(x)))),ts02(im(x),m0"r"(0),satz176b(0,refis(real,0)))),pl02(m0"r"(re(x)),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)))
-t2:=tris(real,pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),pl"r"(0,m0"r"(im(x))),m0"r"(im(x)),ispl12"r"(ts"r"(re(x),m0"r"(0)),0,ts"r"(im(x),m0"r"(1rl)),m0"r"(im(x)),ts02(re(x),m0"r"(0),satz176b(0,refis(real,0))),tris(real,ts"r"(im(x),m0"r"(1rl)),m0"r"(ts"r"(im(x),1rl)),m0"r"(im(x)),satz197b(im(x),1rl),ism0"r"(ts"r"(im(x),1rl),im(x),satz195(im(x))))),pl01(0,m0"r"(im(x)),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)))
--3223
-satz223:=tr4is(cx,ts(x,m0(1c)),ts(x,pli(m0"r"(1rl),m0"r"(0))),pli(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl)))),pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),ists2(m0(1c),pli(m0"r"(1rl),m0"r"(0)),x,m0isa(1rl,0)),tsis2a(x,m0"r"(1rl),m0"r"(0)),isrecx12(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)),t1".3223",t2".3223"),satz214a(x)):is(ts(x,m0(1c)),m0(x))
-satz223a:=symis(cx,ts(x,m0(1c)),m0(x),satz223):is(m0(x),ts(x,m0(1c)))
-satz223b:=tris(cx,ts(m0(1c),x),ts(x,m0(1c)),m0(x),comts(m0(1c),x),satz223):is(ts(m0(1c),x),m0(x))
-satz223c:=symis(cx,ts(m0(1c),x),m0(x),satz223b):is(m0(x),ts(m0(1c),x))
-+3224
-y@rxry:=ts"r"(re(x),re(y)):real
-ixiy:=ts"r"(im(x),im(y)):real
-rxiy:=ts"r"(re(x),im(y)):real
-ixry:=ts"r"(im(x),re(y)):real
-t1:=tr4is(real,mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),mn"r"(m0"r"(rxry),m0"r"(ixiy)),pl"r"(m0"r"(rxry),ixiy),mn"r"(ixiy,rxry),m0"r"(mn"r"(rxry,ixiy)),ismn12"r"(ts"r"(m0"r"(re(x)),re(y)),m0"r"(rxry),ts"r"(m0"r"(im(x)),im(y)),m0"r"(ixiy),satz197a(re(x),re(y)),satz197a(im(x),im(y))),ispl2"r"(m0"r"(m0"r"(ixiy)),ixiy,m0"r"(rxry),satz177(ixiy)),compl"r"(m0"r"(rxry),ixiy),satz181a(ixiy,rxry)):is"r"(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(rxry,ixiy)))
-t2:=tris(real,pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),mn"r"(m0"r"(rxiy),ixry),m0"r"(pl"r"(rxiy,ixry)),ispl12"r"(ts"r"(m0"r"(re(x)),im(y)),m0"r"(rxiy),ts"r"(m0"r"(im(x)),re(y)),m0"r"(ixry),satz197a(re(x),im(y)),satz197a(im(x),re(y))),satz180a(rxiy,ixry)):is"r"(pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(rxiy,ixry)))
--3224
-y@satz224a:=tr4is(cx,ts(m0(x),y),ts(pli(m0"r"(re(x)),m0"r"(im(x))),y),pli(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y)))),pli(m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))),m0(ts(x,y)),ists1(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),y,satz214(x)),tsis1a(y,m0"r"(re(x)),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))),t1".3224",t2".3224"),m0isb(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))):is(ts(m0(x),y),m0(ts(x,y)))
-satz224b:=tr3is(cx,ts(x,m0(y)),ts(m0(y),x),m0(ts(y,x)),m0(ts(x,y)),comts(x,m0(y)),satz224a(y,x),ism0(ts(y,x),ts(x,y),comts(y,x))):is(ts(x,m0(y)),m0(ts(x,y)))
-satz224c:=tris2(cx,ts(m0(x),y),ts(x,m0(y)),m0(ts(x,y)),satz224a,satz224b):is(ts(m0(x),y),ts(x,m0(y)))
-satz224d:=symis(cx,ts(m0(x),y),ts(x,m0(y)),satz224c):is(ts(x,m0(y)),ts(m0(x),y))
-satz224e:=symis(cx,ts(m0(x),y),m0(ts(x,y)),satz224a):is(m0(ts(x,y)),ts(m0(x),y))
-satz224f:=symis(cx,ts(x,m0(y)),m0(ts(x,y)),satz224b):is(m0(ts(x,y)),ts(x,m0(y)))
-satz225:=tris(cx,ts(m0(x),m0(y)),ts(x,m0(m0(y))),ts(x,y),satz224c(x,m0(y)),ists2(m0(m0(y)),y,x,satz215(y))):is(ts(m0(x),m0(y)),ts(x,y))
-satz225a:=symis(cx,ts(m0(x),m0(y)),ts(x,y),satz225):is(ts(x,y),ts(m0(x),m0(y)))
-+3226
-z@rrr:=ts"r"(ts"r"(re(x),re(y)),re(z)):real
-iir:=ts"r"(ts"r"(im(x),im(y)),re(z)):real
-rii:=ts"r"(ts"r"(re(x),im(y)),im(z)):real
-iri:=ts"r"(ts"r"(im(x),re(y)),im(z)):real
-rri:=ts"r"(ts"r"(re(x),re(y)),im(z)):real
-iii:=ts"r"(ts"r"(im(x),im(y)),im(z)):real
-rir:=ts"r"(ts"r"(re(x),im(y)),re(z)):real
-irr:=ts"r"(ts"r"(im(x),re(y)),re(z)):real
-t1:=tr3is(real,mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(mn"r"(rrr,iir),pl"r"(rii,iri)),pl"r"(rrr,pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri)))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),ismn12"r"(ts"r"(rets(x,y),re(z)),mn"r"(rrr,iir),ts"r"(imts(x,y),im(z)),pl"r"(rii,iri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(z))),asspl1"r"(rrr,m0"r"(iir),m0"r"(pl"r"(rii,iri))),ispl2"r"(pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri))),m0"r"(pl"r"(iir,pl"r"(rii,iri))),rrr,satz180a(iir,pl"r"(rii,iri)))):is"r"(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))))
-t2:=tr3is(real,pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),pl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),pl"r"(pl"r"(rir,irr),mn"r"(rri,iii)),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),ispl12"r"(ts"r"(rets(x,y),im(z)),mn"r"(rri,iii),ts"r"(imts(x,y),re(z)),pl"r"(rir,irr),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),im(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),re(z))),compl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),asspl2"r"(pl"r"(rir,irr),rri,m0"r"(iii))):is"r"(pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii))
-t3:=tris(cx,ts(ts(x,y),z),pli(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z)))),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),tsis1a(z,rets(x,y),imts(x,y)),isrecx12(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),t1,t2)):is(ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)))
-c@t4:=tris(real,ts"r"(ts"r"(a,b),c),ts"r"(a,ts"r"(b,c)),ts"r"(ts"r"(b,c),a),assts1(a,b,c),comts"r"(a,ts"r"(b,c))):is"r"(ts"r"(ts"r"(a,b),c),ts"r"(ts"r"(b,c),a))
-t5:=tris(real,pl"r"(pl"r"(a,b),c),pl"r"(c,pl"r"(a,b)),pl"r"(pl"r"(c,a),b),compl"r"(pl"r"(a,b),c),asspl2"r"(c,a,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(c,a),b))
-t6:=tris(real,pl"r"(a,pl"r"(b,c)),pl"r"(pl"r"(b,c),a),pl"r"(b,pl"r"(c,a)),compl"r"(a,pl"r"(b,c)),asspl1"r"(b,c,a)):is"r"(pl"r"(a,pl"r"(b,c)),pl"r"(b,pl"r"(c,a)))
-z@rrr1:=rrr(y,z,x):real
-iir1:=iir(y,z,x):real
-rii1:=rii(y,z,x):real
-iri1:=iri(y,z,x):real
-rri1:=rri(y,z,x):real
-iii1:=iii(y,z,x):real
-rir1:=rir(y,z,x):real
-irr1:=irr(y,z,x):real
-t7:=tris(real,pl"r"(iir,pl"r"(rii,iri)),pl"r"(rii,pl"r"(iri,iir)),pl"r"(iir1,pl"r"(rii1,iri1)),t6(iir,rii,iri),ispl12"r"(rii,iir1,pl"r"(iri,iir),pl"r"(rii1,iri1),t4(re(x),im(y),im(z)),ispl12"r"(iri,rii1,iir,iri1,t4(im(x),re(y),im(z)),t4(im(x),im(y),re(z))))):is"r"(pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)))
-t8:=tris(real,pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rri,rir),irr),pl"r"(pl"r"(rir1,irr1),rri1),t5(rir,irr,rri),ispl12"r"(pl"r"(rri,rir),pl"r"(rir1,irr1),irr,rri1,ispl12"r"(rri,rir1,rir,irr1,t4(re(x),re(y),im(z)),t4(re(x),im(y),re(z))),t4(im(x),re(y),re(z)))):is"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1))
-t9:=ismn12"r"(rrr,rrr1,pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)),t4(re(x),re(y),re(z)),t7):is"r"(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))))
-t10:=ismn12"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1),iii,iii1,t8,t4(im(x),im(y),im(z))):is"r"(mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1))
-t11:=tris(cx,ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t3,isrecx12(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1),t9,t10)):is(ts(ts(x,y),z),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
-t12:=tris(cx,ts(x,ts(y,z)),ts(ts(y,z),x),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),comts(x,ts(y,z)),t3(y,z,x)):is(ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
-t13:=tris2(cx,ts(ts(x,y),z),ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t11,t12):is(ts(ts(x,y),z),ts(x,ts(y,z)))
--3226
-z@satz226:=t13".3226":is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts1:=satz226:is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts2:=symis(cx,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
-+3227
-c@t1:=tr3is(real,pl"r"(pl"r"(a,b),c),pl"r"(a,pl"r"(b,c)),pl"r"(a,pl"r"(c,b)),pl"r"(pl"r"(a,c),b),asspl1"r"(a,b,c),ispl2"r"(pl"r"(b,c),pl"r"(c,b),a,compl"r"(b,c)),asspl2"r"(a,c,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b))
-d@t2:=tr3is(real,pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(pl"r"(a,b),c),d),pl"r"(pl"r"(pl"r"(a,c),b),d),pl"r"(pl"r"(a,c),pl"r"(b,d)),asspl2"r"(pl"r"(a,b),c,d),ispl1"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b),d,t1),asspl1"r"(pl"r"(a,c),b,d)):is"r"(pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,c),pl"r"(b,d)))
-t3:=tris(real,mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,b),pl"r"(m0"r"(c),m0"r"(d))),pl"r"(mn"r"(a,c),mn"r"(b,d)),ispl2"r"(m0"r"(pl"r"(c,d)),pl"r"(m0"r"(c),m0"r"(d)),pl"r"(a,b),satz180(c,d)),t2(a,b,m0"r"(c),m0"r"(d))):is"r"(mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(mn"r"(a,c),mn"r"(b,d)))
-z@t4:=tris(real,mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),mn"r"(pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))),pl"r"(rets(x,y),rets(x,z)),ismn12"r"(ts"r"(re(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),ts"r"(im(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z))),disttp2(re(x),re(y),re(z)),disttp2(im(x),im(y),im(z))),t3(ts"r"(re(x),re(y)),ts"r"(re(x),re(z)),ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))):is"r"(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)))
-t5:=tris(real,pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))),pl"r"(imts(x,y),imts(x,z)),ispl12"r"(ts"r"(re(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z))),disttp2(re(x),im(y),im(z)),disttp2(im(x),re(y),re(z))),t2(ts"r"(re(x),im(y)),ts"r"(re(x),im(z)),ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))):is"r"(pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)))
-t6:=tr3is(cx,ts(x,pl(y,z)),pli(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))))),pli(pl"r"(rets(x,y),rets(x,z)),pl"r"(imts(x,y),imts(x,z))),pl(ts(x,y),ts(x,z)),tsis2a(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z))),isrecx12(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)),t4,t5),plis12b(rets(x,y),imts(x,y),rets(x,z),imts(x,z))):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
--3227
-satz227:=t6".3227":is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-disttp1:=tr3is(cx,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz227(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
-disttp2:=satz227:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-distpt1:=symis(cx,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
-distpt2:=symis(cx,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
-satz228:=tr4is(cx,ts(x,mn(y,z)),ts(x,pl(y,m0(z))),pl(ts(x,y),ts(x,m0(z))),pl(ts(x,y),m0(ts(x,z))),mn(ts(x,y),ts(x,z)),ists2(mn(y,z),pl(y,m0(z)),x,satz218(y,z)),disttp2(x,y,m0(z)),ispl2(ts(x,m0(z)),m0(ts(x,z)),ts(x,y),satz224b(x,z)),satz218a(ts(x,y),ts(x,z))):is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
-disttm1:=tr3is(cx,ts(mn(x,y),z),ts(z,mn(x,y)),mn(ts(z,x),ts(z,y)),mn(ts(x,z),ts(y,z)),comts(mn(x,y),z),satz228(z,x,y),ismn12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(mn(x,y),z),mn(ts(x,z),ts(y,z)))
-disttm2:=satz228:is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
-distmt1:=symis(cx,ts(mn(x,y),z),mn(ts(x,z),ts(y,z)),disttm1):is(mn(ts(x,z),ts(y,z)),ts(mn(x,y),z))
-distmt2:=symis(cx,ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)),disttm2):is(mn(ts(x,y),ts(x,z)),ts(x,mn(y,z)))
-y@[n:nis(y,0c)][u1:complex][u2:complex][i:is(ts(y,u1),x)][j:is(ts(y,u2),x)]
-+3229
-t1:=tris2(cx,ts(y,u1),ts(y,u2),x,i,j):is(ts(y,u1),ts(y,u2))
-t2:=tris(cx,ts(y,mn(u1,u2)),mn(ts(y,u1),ts(y,u2)),0c,disttm2(y,u1,u2),satz213b(ts(y,u1),ts(y,u2),t1)):is(ts(y,mn(u1,u2)),0c)
-t3:=ore2(is(y,0c),is(mn(u1,u2),0c),satz221c(y,mn(u1,u2),t2),n):is(mn(u1,u2),0c)
--3229
-satz229b:=satz213a(u1,u2,t3".3229"):is(u1,u2)
-+*3229
-n@t4:=pnot0(mod2(y),lemma4(y,n)):nis"r"(mod2(y),0)
-u:=ts(pli(ov(re(y),mod2(y),t4),m0"r"(ov(im(y),mod2(y),t4))),x):complex
-[v:real]
-dd:=ov(v,mod2(y),t4):real
-n@t5:=tr3is(real,m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),m0"r"(m0"r"(ts"r"(im(y),dd(im(y))))),ts"r"(im(y),dd(im(y))),dd(ts"r"(im(y),im(y))),ism0"r"(ts"r"(im(y),m0"r"(dd(im(y)))),m0"r"(ts"r"(im(y),dd(im(y)))),satz197b(im(y),dd(im(y)))),satz177(ts"r"(im(y),dd(im(y)))),lemma6(im(y),im(y),mod2(y),t4)):is"r"(m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))))
-t6:=tr3is(real,mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(dd(ts"r"(re(y),re(y))),dd(ts"r"(im(y),im(y)))),dd(mod2(y)),1rl,ispl12"r"(ts"r"(re(y),dd(re(y))),dd(ts"r"(re(y),re(y))),m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))),lemma6(re(y),re(y),mod2(y),t4),t5),lemma7(ts"r"(re(y),re(y)),ts"r"(im(y),im(y)),mod2(y),t4),lemma8(mod2(y),t4)):is"r"(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl)
-t7:=tris(real,ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(m0"r"(re(y)),dd(im(y))),dd(ts"r"(m0"r"(re(y)),im(y))),satz197d(re(y),dd(im(y))),lemma6(m0"r"(re(y)),im(y),mod2(y),t4)):is"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))))
-t8:=tris(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),pl"r"(dd(ts"r"(m0"r"(re(y)),im(y))),dd(ts"r"(im(y),re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),ispl12"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))),ts"r"(im(y),dd(re(y))),dd(ts"r"(im(y),re(y))),t7,lemma6(im(y),re(y),mod2(y),t4)),lemma7(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)),mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))))
-t9:=tr3is(real,pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),pl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),mn"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y))),0,ispl1"r"(ts"r"(m0"r"(re(y)),im(y)),m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y)),satz197a(re(y),im(y))),compl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),satz182e(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),comts"r"(im(y),re(y)))):is"r"(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0)
-t10:=tr3is(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),dd(0),0,t8,isf(real,real,[t:real]dd(t),pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0,t9),lemma9(mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0)
-t11:=tris(cx,ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),pli(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y))))),1c,tsis2a(y,dd(re(y)),m0"r"(dd(im(y)))),isrecx12(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0,t6,t10)):is(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c)
-t12:=tr3is(cx,ts(y,u),ts(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),x),ts(1c,x),x,assts2(y,pli(dd(re(y)),m0"r"(dd(im(y)))),x),ists1(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c,x,t11),satz222b(x)):is(ts(y,u),x)
--3229
-n@satz229a:=somei(cx,[t:cx]is(ts(y,t),x),u".3229",t12".3229"):some([t:cx]is(ts(y,t),x))
-satz229:=onei(cx,[t:cx]is(ts(y,t),x),[t:cx][u:cx][v:is(ts(y,t),x)][w:is(ts(y,u),x)]satz229b(t,u,v,w),satz229a):one([t:cx]is(ts(y,t),x))
-ov:=ind(cx,[t:cx]is(ts(y,t),x),satz229):complex
-satz229c:=oneax(cx,[t:cx]is(ts(y,t),x),satz229):is(ts(y,ov(x,y,n)),x)
-satz229d:=symis(cx,ts(y,ov(x,y,n)),x,satz229c):is(x,ts(y,ov(x,y,n)))
-satz229e:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c):is(ts(ov(x,y,n),y),x)
-satz229f:=symis(cx,ts(ov(x,y,n),y),x,satz229e):is(x,ts(ov(x,y,n),y))
-y@[u:complex][n:nis(y,0c)][i:is(ts(y,u),x)]
-satz229g:=satz229b(n,u,ov(x,y,n),i,satz229c(n)):is(u,ov(x,y,n))
-satz229h:=symis(cx,u,ov(x,y,n),satz229g):is(ov(x,y,n),u)
-n@[i:is(ts(u,y),x)]
-satz229j:=satz229g(tris(cx,ts(y,u),ts(u,y),x,comts(y,u),i)):is(u,ov(x,y,n))
-satz229k:=symis(cx,u,ov(x,y,n),satz229j):is(ov(x,y,n),u)
-z@[i:is(x,y)][n:nis(z,0c)]
-isov1:=isf(cx,cx,[t:cx]ov(t,z,n),x,y,i):is(ov(x,z,n),ov(y,z,n))
-i@[n:nis(x,0c)][o:nis(y,0c)]
-isov2:=satz229h(z,x,ov(z,y,o),n,tris(cx,ts(x,ov(z,y,o)),ts(y,ov(z,y,o)),z,ists1(x,y,ov(z,y,o),i),satz229c(z,y,o))):is(ov(z,x,n),ov(z,y,o))
-z@[u:complex][i:is(x,y)][j:is(z,u)][n:nis(z,0c)][o:nis(u,0c)]
-isov12:=tris(cx,ov(x,z,n),ov(y,z,n),ov(y,u,o),isov1(x,y,z,i,n),isov2(z,u,y,j,n,o)):is(ov(x,z,n),ov(y,u,o))
-y@satz230:=tris(cx,pl(mn(x,y),y),pl(y,mn(x,y)),x,compl(mn(x,y),y),satz212h(x,y)):is(pl(mn(x,y),y),x)
-satz231:=satz212e(pl(x,y),y,x,compl(y,x)):is(mn(pl(x,y),y),x)
-satz232:=satz212e(x,mn(x,y),y,satz230):is(mn(x,mn(x,y)),y)
-+4233
-z@t1:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(mn(mn(x,y),z),pl(y,z)),pl(mn(mn(x,y),z),pl(z,y)),pl(pl(mn(mn(x,y),z),z),y),compl(pl(y,z),mn(mn(x,y),z)),ispl2(pl(y,z),pl(z,y),mn(mn(x,y),z),compl(y,z)),asspl2(mn(mn(x,y),z),z,y)):is(pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y))
-t2:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y),pl(mn(x,y),y),x,t1,ispl1(pl(mn(mn(x,y),z),z),mn(x,y),y,satz230(mn(x,y),z)),satz230(x,y)):is(pl(pl(y,z),mn(mn(x,y),z)),x)
--4233
-z@satz233:=satz212d(x,pl(y,z),mn(mn(x,y),z),t2".4233"):is(mn(mn(x,y),z),mn(x,pl(y,z)))
-satz234:=satz212g(pl(x,y),z,pl(x,mn(y,z)),tris(cx,pl(pl(x,mn(y,z)),z),pl(x,pl(mn(y,z),z)),pl(x,y),asspl1(x,mn(y,z),z),ispl2(pl(mn(y,z),z),y,x,satz230(y,z)))):is(mn(pl(x,y),z),pl(x,mn(y,z)))
-satz234a:=symis(cx,mn(pl(x,y),z),pl(x,mn(y,z)),satz234):is(pl(x,mn(y,z)),mn(pl(x,y),z))
-satz234b:=tr3is(cx,mn(pl(x,y),z),mn(pl(y,x),z),pl(y,mn(x,z)),pl(mn(x,z),y),ismn1(pl(x,y),pl(y,x),z,compl(x,y)),satz234(y,x,z),compl(y,mn(x,z))):is(mn(pl(x,y),z),pl(mn(x,z),y))
-satz234c:=symis(cx,mn(pl(x,y),z),pl(mn(x,z),y),satz234b):is(pl(mn(x,z),y),mn(pl(x,y),z))
-satz235:=satz212f(x,mn(y,z),pl(mn(x,y),z),tr3is(cx,pl(pl(mn(x,y),z),mn(y,z)),pl(mn(x,y),pl(z,mn(y,z))),pl(mn(x,y),y),x,asspl1(mn(x,y),z,mn(y,z)),ispl2(pl(z,mn(y,z)),y,mn(x,y),satz212h(y,z)),satz230(x,y))):is(pl(mn(x,y),z),mn(x,mn(y,z)))
-satz235a:=symis(cx,pl(mn(x,y),z),mn(x,mn(y,z)),satz235):is(mn(x,mn(y,z)),pl(mn(x,y),z))
-satz235b:=tris(cx,mn(x,mn(y,z)),pl(mn(x,y),z),mn(pl(x,z),y),satz235a,satz234c(x,z,y)):is(mn(x,mn(y,z)),mn(pl(x,z),y))
-satz235c:=tris(cx,mn(x,mn(y,z)),mn(pl(x,z),y),mn(pl(z,x),y),satz235b,ismn1(pl(x,z),pl(z,x),y,compl(x,z))):is(mn(x,mn(y,z)),mn(pl(z,x),y))
-satz236:=satz212g(pl(x,z),pl(y,z),mn(x,y),tris(cx,pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y)))):is(mn(pl(x,z),pl(y,z)),mn(x,y))
-satz236a:=tris(cx,mn(pl(z,x),pl(z,y)),mn(pl(x,z),pl(y,z)),mn(x,y),ismn12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y)),satz236):is(mn(pl(z,x),pl(z,y)),mn(x,y))
-[u:complex]
-+4237
-t1:=tr3is(cx,pl(mn(z,u),pl(u,y)),pl(pl(mn(z,u),u),y),pl(z,y),pl(y,z),asspl2(mn(z,u),u,y),ispl1(pl(mn(z,u),u),z,y,satz230(z,u)),compl(z,y)):is(pl(mn(z,u),pl(u,y)),pl(y,z))
-t2:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(pl(mn(x,y),mn(z,u)),pl(u,y)),pl(mn(x,y),pl(mn(z,u),pl(u,y))),pl(mn(x,y),pl(y,z)),ispl2(pl(y,u),pl(u,y),pl(mn(x,y),mn(z,u)),compl(y,u)),asspl1(mn(x,y),mn(z,u),pl(u,y)),ispl2(pl(mn(z,u),pl(u,y)),pl(y,z),mn(x,y),t1)):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)))
-t3:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),t2,asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y))):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(x,z))
--4237
-satz237:=satz212f(pl(x,z),pl(y,u),pl(mn(x,y),mn(z,u)),t3".4237"):is(pl(mn(x,y),mn(z,u)),mn(pl(x,z),pl(y,u)))
-+4238
-t1:=tris(cx,pl(pl(x,u),z),pl(x,pl(u,z)),pl(x,pl(z,u)),asspl1(x,u,z),ispl2(pl(u,z),pl(z,u),x,compl(u,z))):is(pl(pl(x,u),z),pl(x,pl(z,u)))
-t2:=tr3is(cx,pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(pl(pl(x,u),z),pl(pl(y,z),u)),mn(pl(x,pl(z,u)),pl(y,pl(z,u))),mn(x,y),satz237(pl(x,u),pl(y,z),z,u),ismn12(pl(pl(x,u),z),pl(x,pl(z,u)),pl(pl(y,z),u),pl(y,pl(z,u)),t1,asspl1(y,z,u)),satz236(x,y,pl(z,u))):is(pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(x,y))
--4238
-satz238:=satz212g(mn(x,y),mn(z,u),mn(pl(x,u),pl(y,z)),t2".4238"):is(mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)))
-[i:is(mn(x,y),mn(z,u))]
-+4239
-t1:=tris1(cx,mn(pl(x,u),pl(y,z)),0c,mn(mn(x,y),mn(z,u)),satz238,satz213b(mn(x,y),mn(z,u),i)):is(mn(pl(x,u),pl(y,z)),0c)
--4239
-satz239a:=satz213a(pl(x,u),pl(y,z),t1".4239"):is(pl(x,u),pl(y,z))
-u@[i:is(pl(x,u),pl(y,z))]
-+*4239
-i@t2:=tris(cx,mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)),0c,satz238,satz213b(pl(x,u),pl(y,z),i)):is(mn(mn(x,y),mn(z,u)),0c)
--4239
-i@satz239b:=satz213a(mn(x,y),mn(z,u),t2".4239"):is(mn(x,y),mn(z,u))
-y@[n:nis(y,0c)]
-satz240:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c(x,y,n)):is(ts(ov(x,y,n),y),x)
-satz241:=satz229h(ts(x,y),y,x,n,comts(y,x)):is(ov(ts(x,y),y,n),x)
-y@[n:nis(x,0c)][o:nis(y,0c)]
-lemma6:=th3"l.imp"(is(ov(x,y,o),0c),is(x,0c),n,[t:is(ov(x,y,o),0c)]tris1(cx,x,0c,ts(y,ov(x,y,o)),satz229c(x,y,o),satz221b(y,ov(x,y,o),t))):nis(ov(x,y,o),0c)
-satz242:=satz229h(x,ov(x,y,o),y,lemma6,satz240(o)):is(ov(x,ov(x,y,o),lemma6),y)
-z@[n:nis(y,0c)][o:nis(z,0c)]
-+5243
-t1:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ov(ov(x,y,n),z,o),ts(y,z)),ts(ov(ov(x,y,n),z,o),ts(z,y)),ts(ts(ov(ov(x,y,n),z,o),z),y),comts(ts(y,z),ov(ov(x,y,n),z,o)),ists2(ts(y,z),ts(z,y),ov(ov(x,y,n),z,o),comts(y,z)),assts2(ov(ov(x,y,n),z,o),z,y)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y))
-t2:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y),ts(ov(x,y,n),y),x,t1,ists1(ts(ov(ov(x,y,n),z,o),z),ov(x,y,n),y,satz240(ov(x,y,n),z,o)),satz240(x,y,n)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),x)
--5243
-satz243:=satz229g(x,ts(y,z),ov(ov(x,y,n),z,o),satz221d(y,z,n,o),t2".5243"):is(ov(ov(x,y,n),z,o),ov(x,ts(y,z),satz221d(y,z,n,o)))
-z@[n:nis(z,0c)]
-satz244:=satz229k(ts(x,y),z,ts(x,ov(y,z,n)),n,tris(cx,ts(ts(x,ov(y,z,n)),z),ts(x,ts(ov(y,z,n),z)),ts(x,y),assts1(x,ov(y,z,n),z),ists2(ts(ov(y,z,n),z),y,x,satz240(y,z,n)))):is(ov(ts(x,y),z,n),ts(x,ov(y,z,n)))
-satz244a:=symis(cx,ov(ts(x,y),z,n),ts(x,ov(y,z,n)),satz244):is(ts(x,ov(y,z,n)),ov(ts(x,y),z,n))
-satz244b:=tr3is(cx,ov(ts(x,y),z,n),ov(ts(y,x),z,n),ts(y,ov(x,z,n)),ts(ov(x,z,n),y),isov1(ts(x,y),ts(y,x),z,comts(x,y),n),satz244(y,x,z,n),comts(y,ov(x,z,n))):is(ov(ts(x,y),z,n),ts(ov(x,z,n),y))
-satz244c:=symis(cx,ov(ts(x,y),z,n),ts(ov(x,z,n),y),satz244b):is(ts(ov(x,z,n),y),ov(ts(x,y),z,n))
-z@[n:nis(y,0c)][o:nis(z,0c)]
-satz245:=satz229j(x,ov(y,z,o),ts(ov(x,y,n),z),lemma6(y,z,n,o),tr3is(cx,ts(ts(ov(x,y,n),z),ov(y,z,o)),ts(ov(x,y,n),ts(z,ov(y,z,o))),ts(ov(x,y,n),y),x,assts1(ov(x,y,n),z,ov(y,z,o)),ists2(ts(z,ov(y,z,o)),y,ov(x,y,n),satz229c(y,z,o)),satz240(x,y,n))):is(ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)))
-satz245a:=symis(cx,ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)),satz245):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z))
-satz245b:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z),ov(ts(x,z),y,n),satz245a,satz244c(x,z,y,n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n))
-satz245c:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n),ov(ts(z,x),y,n),satz245b,isov1(ts(x,z),ts(z,x),y,comts(x,z),n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(z,x),y,n))
-satz246:=satz229k(ts(x,z),ts(y,z),ov(x,y,n),satz221d(y,z,n,o),tris(cx,ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n)))):is(ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n))
-satz246a:=tris(cx,ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n),isov12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y),satz221d(z,y,o,n),satz221d(y,z,n,o)),satz246):is(ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(x,y,n))
-z@[u:complex][n:nis(y,0c)][o:nis(u,0c)]
-+5247
-t1:=tr3is(cx,ts(ov(z,u,o),ts(u,y)),ts(ts(ov(z,u,o),u),y),ts(z,y),ts(y,z),assts2(ov(z,u,o),u,y),ists1(ts(ov(z,u,o),u),z,y,satz240(z,u,o)),comts(z,y)):is(ts(ov(z,u,o),ts(u,y)),ts(y,z))
-t2:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ts(ov(x,y,n),ov(z,u,o)),ts(u,y)),ts(ov(x,y,n),ts(ov(z,u,o),ts(u,y))),ts(ov(x,y,n),ts(y,z)),ists2(ts(y,u),ts(u,y),ts(ov(x,y,n),ov(z,u,o)),comts(y,u)),assts1(ov(x,y,n),ov(z,u,o),ts(u,y)),ists2(ts(ov(z,u,o),ts(u,y)),ts(y,z),ov(x,y,n),t1)):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)))
-t3:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),t2,assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n))):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(x,z))
--5247
-satz247:=satz229j(ts(x,z),ts(y,u),ts(ov(x,y,n),ov(z,u,o)),satz221d(y,u,n,o),t3".5247"):is(ts(ov(x,y,n),ov(z,u,o)),ov(ts(x,z),ts(y,u),satz221d(y,u,n,o)))
-u@[n:nis(y,0c)][o:nis(z,0c)][p:nis(u,0c)]
-+5248
-t1:=tris(cx,ts(ts(x,u),z),ts(x,ts(u,z)),ts(x,ts(z,u)),assts1(x,u,z),ists2(ts(u,z),ts(z,u),x,comts(u,z))):is(ts(ts(x,u),z),ts(x,ts(z,u)))
-t2:=tr3is(cx,ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(ts(ts(x,u),z),ts(ts(y,z),u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p)),ov(ts(x,ts(z,u)),ts(y,ts(z,u)),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),ov(x,y,n),satz247(ts(x,u),ts(y,z),z,u,satz221d(y,z,n,o),p),isov12(ts(ts(x,u),z),ts(x,ts(z,u)),ts(ts(y,z),u),ts(y,ts(z,u)),t1,assts1(y,z,u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),satz246(x,y,ts(z,u),n,satz221d(z,u,o,p))):is(ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(x,y,n))
--5248
-satz248:=satz229k(ov(x,y,n),ov(z,u,p),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),lemma6(z,u,o,p),t2".5248"):is(ov(ov(x,y,n),ov(z,u,p),lemma6(z,u,o,p)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)))
-x@[n:nis(x,0c)]
-satz249:=satz229h(0c,x,0c,n,satz221b(x,0c,refis(cx,0c))):is(ov(0c,x,n),0c)
-satz250:=satz229h(x,x,1c,n,satz222(x)):is(ov(x,x,n),1c)
-y@[n:nis(y,0c)][i:is(x,y)]
-satz251a:=tris(cx,ov(x,y,n),ov(x,x,th2"e.notis"(cx,y,0c,x,n,i)),1c,isov2(y,x,x,symis(cx,x,y,i),n,th2"e.notis"(cx,y,0c,x,n,i)),satz250(x,th2"e.notis"(cx,y,0c,x,n,i))):is(ov(x,y,n),1c)
-n@[i:is(ov(x,y,n),1c)]
-satz251b:=tr3is(cx,x,ts(y,ov(x,y,n)),ts(y,1c),y,satz229d(x,y,n),ists2(ov(x,y,n),1c,y,i),satz222(y)):is(x,y)
-u@[n:nis(y,0c)][o:nis(u,0c)][i:is(ov(x,y,n),ov(z,u,o))]
-+5252
-[j:is(z,0c)]
-t1:=tr3is(cx,ov(x,y,n),ov(z,u,o),ov(0c,u,o),0c,i,isov1(z,0c,u,j,o),satz249(u,o)):is(ov(x,y,n),0c)
-t2:=tris(cx,x,ts(y,ov(x,y,n)),0c,satz229d(x,y,n),satz221b(y,ov(x,y,n),t1)):is(x,0c)
-t3:=tris2(cx,ts(x,u),ts(y,z),0c,satz221a(x,u,t2),satz221b(y,z,j)):is(ts(x,u),ts(y,z))
-i@[p:nis(z,0c)]
-t4:=tris1(cx,ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),satz248(x,y,z,u,n,p,o),satz251a(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),i)):is(ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c)
-t5:=satz251b(ts(x,u),ts(y,z),satz221d(y,z,n,p),t4):is(ts(x,u),ts(y,z))
--5252
-satz252a:=th1"l.imp"(is(z,0c),is(ts(x,u),ts(y,z)),[t:is(z,0c)]t3".5252"(t),[t:nis(z,0c)]t5".5252"(t)):is(ts(x,u),ts(y,z))
-o@[i:is(ts(x,u),ts(y,z))]
-+*5252
-i@[j:is(z,0c)]
-t6:=tris(cx,ts(x,u),ts(y,z),0c,i,satz221b(y,z,j)):is(ts(x,u),0c)
-t7:=ore1(is(x,0c),is(u,0c),satz221c(x,u,t6),o):is(x,0c)
-t8:=tris2(cx,ov(x,y,n),ov(z,u,o),0c,tris(cx,ov(x,y,n),ov(0c,y,n),0c,isov1(x,0c,y,t7,n),satz249(y,n)),tris(cx,ov(z,u,o),ov(0c,u,o),0c,isov1(z,0c,u,j,o),satz249(u,o))):is(ov(x,y,n),ov(z,u,o))
-i@[p:nis(z,0c)]
-t9:=tris(cx,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,satz248(x,y,z,u,n,p,o),satz251a(ts(x,u),ts(y,z),satz221d(y,z,n,p),i)):is(ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),1c)
-t10:=satz251b(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),t9):is(ov(x,y,n),ov(z,u,o))
--5252
-i@satz252b:=th1"l.imp"(is(z,0c),is(ov(x,y,n),ov(z,u,o)),[t:is(z,0c)]t8".5252"(t),[t:nis(z,0c)]t10".5252"(t)):is(ov(x,y,n),ov(z,u,o))
-z@[n:nis(y,0c)]
-satz253:=satz229g(pl(x,z),y,pl(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,pl(ov(x,y,n),ov(z,y,n))),pl(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),pl(x,z),disttp2(y,ov(x,y,n),ov(z,y,n)),ispl12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(pl(ov(x,y,n),ov(z,y,n)),ov(pl(x,z),y,n))
-z@[n:nis(z,0c)]
-distop:=symis(cx,pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n),satz253(x,z,y,n)):is(ov(pl(x,y),z,n),pl(ov(x,z,n),ov(y,z,n)))
-distpo:=satz253(x,z,y,n):is(pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n))
-u@[n:nis(y,0c)][o:nis(u,0c)]
-satz254:=tris1(cx,pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),pl(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ispl12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz253(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
-z@[n:nis(y,0c)]
-satz255:=satz229g(mn(x,z),y,mn(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,mn(ov(x,y,n),ov(z,y,n))),mn(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),mn(x,z),disttm2(y,ov(x,y,n),ov(z,y,n)),ismn12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(mn(ov(x,y,n),ov(z,y,n)),ov(mn(x,z),y,n))
-z@[n:nis(z,0c)]
-distom:=symis(cx,mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n),satz255(x,z,y,n)):is(ov(mn(x,y),z,n),mn(ov(x,z,n),ov(y,z,n)))
-distmo:=satz255(x,z,y,n):is(mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n))
-u@[n:nis(y,0c)][o:nis(u,0c)]
-satz256:=tris1(cx,mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),mn(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ismn12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz255(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
-x@conj:=pli(re(x),m0"r"(im(x))):complex
-b@conjisa:=isrecx12(re(pli(a,b)),a,m0"r"(im(pli(a,b))),m0"r"(b),reis(a,b),ism0"r"(im(pli(a,b)),b,imis(a,b))):is(conj(pli(a,b)),pli(a,m0"r"(b)))
-conjisb:=symis(cx,conj(pli(a,b)),pli(a,m0"r"(b)),conjisa):is(pli(a,m0"r"(b)),conj(pli(a,b)))
-y@[i:is(x,y)]
-isconj:=isf(cx,cx,[t:cx]conj(t),x,y,i):is(conj(x),conj(y))
-x@satz257:=tr3is(cx,conj(conj(x)),pli(re(x),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,conjisa(re(x),m0"r"(im(x))),isrecx2(m0"r"(m0"r"(im(x))),im(x),re(x),satz177(im(x))),pliis(x)):is(conj(conj(x)),x)
-[i:is(x,0c)]
-satz258a:=tr3is(cx,conj(x),conj(0c),pli(0,m0"r"(0)),0c,isconj(x,0c,i),conjisa(0,0),isrecx2(m0"r"(0),0,0,satz176b(0,refis(real,0)))):is(conj(x),0c)
-x@[i:is(conj(x),0c)]
-+6258
-t1:=tris(real,re(x),re(conj(x)),0,isre(re(x),m0"r"(im(x))),lemma1(conj(x),i)):is"r"(re(x),0)
-t2:=satz176e(im(x),tris(real,m0"r"(im(x)),im(conj(x)),0,isim(re(x),m0"r"(im(x))),lemma2(conj(x),i))):is"r"(im(x),0)
--6258
-satz258b:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t1".6258",t2".6258")):is(x,0c)
-+*6258
-i@anders:=tris1(cx,x,0c,conj(conj(x)),satz257,satz258a(conj(x),i)):is(x,0c)
--6258
-x@[n:nis(x,0c)]
-satz258c:=th3"l.imp"(is(conj(x),0c),is(x,0c),n,[t:is(conj(x),0c)]satz258b(t)):nis(conj(x),0c)
-x@[i:is(conj(x),x)]
-+6259
-t1:=tris(real,m0"r"(im(x)),im(conj(x)),im(x),isim(re(x),m0"r"(im(x))),isceim(conj(x),x,i)):is"r"(m0"r"(im(x)),im(x))
--6259
-satz259a:=lemma10(im(x),symis(real,m0"r"(im(x)),im(x),t1".6259")):is"r"(im(x),0)
-x@[i:is"r"(im(x),0)]
-satz259b:=tris(cx,conj(x),pli(re(x),im(x)),x,isrecx2(m0"r"(im(x)),im(x),re(x),tris2(real,m0"r"(im(x)),im(x),0,satz176b(im(x),i),i)),pliis(x)):is(conj(x),x)
-x@[i:is(x,conj(x))]
-satz269c:=satz259a(x,symis(cx,x,conj(x),i)):is"r"(im(x),0)
-x@[i:is"r"(im(x),0)]
-satz269d:=symis(cx,conj(x),x,satz259b(i)):is(x,conj(x))
-y@satz260:=tr3is(cx,conj(pl(x,y)),pli(pl"r"(re(x),re(y)),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(re(x),re(y)),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(conj(x),conj(y)),conjisa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx2(m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),pl"r"(re(x),re(y)),satz180(im(x),im(y))),plis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(pl(x,y)),pl(conj(x),conj(y)))
-satz260a:=symis(cx,conj(pl(x,y)),pl(conj(x),conj(y)),satz260):is(pl(conj(x),conj(y)),conj(pl(x,y)))
-+6261
-t1:=tris(real,m0"r"(imts(x,y)),pl"r"(m0"r"(ts"r"(re(x),im(y))),m0"r"(ts"r"(im(x),re(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),satz180(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(m0"r"(ts"r"(re(x),im(y))),ts"r"(re(x),m0"r"(im(y))),m0"r"(ts"r"(im(x),re(y))),ts"r"(m0"r"(im(x)),re(y)),satz197f(re(x),im(y)),satz197e(im(x),re(y)))):is"r"(m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))))
--6261
-satz261:=tr3is(cx,conj(ts(x,y)),pli(rets(x,y),m0"r"(imts(x,y))),pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y)))),ts(conj(x),conj(y)),conjisa(rets(x,y),imts(x,y)),isrecx12(rets(x,y),mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),ismn2"r"(ts"r"(im(x),im(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y))),ts"r"(re(x),re(y)),satz198a(im(x),im(y))),t1".6261"),tsis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(ts(x,y)),ts(conj(x),conj(y)))
-satz261a:=symis(cx,conj(ts(x,y)),ts(conj(x),conj(y)),satz261):is(ts(conj(x),conj(y)),conj(ts(x,y)))
-+6262
-t1:=symis(cx,pl(mn(x,y),y),x,satz230(x,y)):is(x,pl(mn(x,y),y))
-t2:=tris(cx,conj(x),conj(pl(mn(x,y),y)),pl(conj(mn(x,y)),conj(y)),isconj(x,pl(mn(x,y),y),t1),satz260(mn(x,y),y)):is(conj(x),pl(conj(mn(x,y)),conj(y)))
--6262
-satz262:=satz212f(conj(x),conj(y),conj(mn(x,y)),symis(cx,conj(x),pl(conj(mn(x,y)),conj(y)),t2".6262")):is(conj(mn(x,y)),mn(conj(x),conj(y)))
-satz262a:=symis(cx,conj(mn(x,y)),mn(conj(x),conj(y)),satz262):is(mn(conj(x),conj(y)),conj(mn(x,y)))
-[n:nis(y,0c)]
-+6263
-t1:=satz229f(x,y,n):is(x,ts(ov(x,y,n),y))
-t2:=isconj(x,ts(ov(x,y,n),y),t1):is(conj(x),conj(ts(ov(x,y,n),y)))
-t3:=satz261(ov(x,y,n),y):is(conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)))
-t4:=tris(cx,conj(x),conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)),t2,t3):is(conj(x),ts(conj(ov(x,y,n)),conj(y)))
-t5:=satz258c(y,n):nis(conj(y),0c)
--6263
-satz263:=satz229j(conj(x),conj(y),conj(ov(x,y,n)),t5".6263",symis(cx,conj(x),ts(conj(ov(x,y,n)),conj(y)),t4".6263")):is(conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)))
-satz263a:=symis(cx,conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)),satz263):is(ov(conj(x),conj(y),satz258c(y,n)),conj(ov(x,y,n)))
-x@mod:=sqrt(mod2(x),lemma5(x)):real
-y@[i:is(x,y)]
-ismod:=isf(cx,real,[t:cx]mod(t),x,y,i):is"r"(mod(x),mod(y))
-x@[n:nis(x,0c)]
-satz264a:=sqrtnot0(mod2(x),lemma5(x),pnot0(mod2(x),lemma4(x,n))):pos(mod(x))
-x@[i:is(x,0c)]
-satz264b:=sqrt0(mod2(x),lemma5(x),lemma3(x,i)):is"r"(mod(x),0)
-x@satz264c:=thsqrt1a(mod2(x),lemma5(x)):not(neg(mod(x)))
-satz264d:=satz167f(mod(x),0,th3"l.imp"(less(mod(x),0),neg(mod(x)),satz264c,[t:less(mod(x),0)]satz169d(mod(x),t))):moreis(mod(x),0)
-+7265
-t1:=symis(real,ts"r"(mod(x),mod(x)),mod2(x),thsqrt1b(mod2(x),lemma5(x))):is"r"(mod2(x),ts"r"(mod(x),mod(x)))
-t2:=tris(real,pl"r"(ts"r"(re(x),re(x)),0),ts"r"(re(x),re(x)),ts"r"(abs(re(x)),abs(re(x))),pl02(ts"r"(re(x),re(x)),0,refis(real,0)),lemma12"r"(re(x))):is"r"(pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))))
-t3:=satz191(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),ts"r"(im(x),im(x)),0,moreisi2(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),refis(real,ts"r"(re(x),re(x)))),lemma11"r"(im(x))):moreis(mod2(x),pl"r"(ts"r"(re(x),re(x)),0))
-t4:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))),t1,t2,t3):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(re(x)),abs(re(x))))
-t5:=tris(real,pl"r"(0,ts"r"(im(x),im(x))),ts"r"(im(x),im(x)),ts"r"(abs(im(x)),abs(im(x))),pl01(0,ts"r"(im(x),im(x)),refis(real,0)),lemma12"r"(im(x))):is"r"(pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))))
-t6:=satz191(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),lemma11"r"(re(x)),moreisi2(ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),refis(real,ts"r"(im(x),im(x))))):moreis(mod2(x),pl"r"(0,ts"r"(im(x),im(x))))
-t7:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))),t1,t5,t6):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(im(x)),abs(im(x))))
-@[r:real][s:real][m:moreis(ts"r"(r,r),ts"r"(s,s))][n:moreis(r,0)][l:less(r,s)]
-t8:=lemma2"r"(r,s,l):more(s,r)
-t9:=satz169b(s,satz172d(s,r,0,t8,n)):pos(s)
-[o:more(r,0)]
-t10:=trmore(ts"r"(s,s),ts"r"(r,s),ts"r"(r,r),satz203a(s,r,s,t8,t9),satz203d(s,r,r,t8,satz169b(r,o))):more(ts"r"(s,s),ts"r"(r,r))
-l@[i:is"r"(r,0)]
-t11:=ismore2(0,ts"r"(r,r),ts"r"(s,s),symis(real,ts"r"(r,r),0,ts01(r,r,i)),satz169a(ts"r"(s,s),possq(s,pnot0(s,t9)))):more(ts"r"(s,s),ts"r"(r,r))
-l@t12:=lemma1"r"(ts"r"(s,s),ts"r"(r,r),orapp(more(r,0),is"r"(r,0),more(ts"r"(s,s),ts"r"(r,r)),n,[t:more(r,0)]t10(t),[t:is"r"(r,0)]t11(t))):less(ts"r"(r,r),ts"r"(s,s))
-n@t13:=satz167f(r,s,[t:less(r,s)]<t12(t)>satz167c(ts"r"(r,r),ts"r"(s,s),m)):moreis(r,s)
--7265
-satz265a:=t13".7265"(mod(x),abs(re(x)),t4".7265",satz264d(x)):moreis(mod(x),abs(re(x)))
-satz265b:=t13".7265"(mod(x),abs(im(x)),t7".7265",satz264d(x)):moreis(mod(x),abs(im(x)))
-@[r:real][s:real][i:is(ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)))][n:not(neg(r))][o:not(neg(s))]
-+7266
-@[t:real]
-t1:=pl02(ts"r"(t,t),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t))
-t2:=tris(real,pl"r"(ts"r"(t,0),ts"r"(0,t)),ts"r"(t,0),0,pl02(ts"r"(t,0),ts"r"(0,t),ts01(0,t,refis(real,0))),ts02(t,0,refis(real,0))):is"r"(pl"r"(ts"r"(t,0),ts"r"(0,t)),0)
-t3:=tris(cx,ts(pli(t,0),pli(t,0)),pli(mn"r"(ts"r"(t,t),ts"r"(0,0)),pl"r"(ts"r"(t,0),ts"r"(0,t))),pli(ts"r"(t,t),0),tsis12a(t,0,t,0),isrecx12(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t),pl"r"(ts"r"(t,0),ts"r"(0,t)),0,t1,t2)):is(ts(pli(t,0),pli(t,0)),pli(ts"r"(t,t),0))
-o@t4:=tr3is(cx,pli(ts"r"(r,r),0),ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)),pli(ts"r"(s,s),0),symis(cx,ts(pli(r,0),pli(r,0)),pli(ts"r"(r,r),0),t3(r)),i,t3(s)):is(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0))
-t5:=tr3is(real,ts"r"(r,r),re(pli(ts"r"(r,r),0)),re(pli(ts"r"(s,s),0)),ts"r"(s,s),isre(ts"r"(r,r),0),iscere(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0),t4),reis(ts"r"(s,s),0)):is"r"(ts"r"(r,r),ts"r"(s,s))
-t6:=andi(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)),n,t5):and(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)))
-t7:=andi(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)),o,refis(real,ts"r"(s,s))):and(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)))
--7266
-satz266:=satzr161b(ts"r"(s,s),r,s,t6".7266",t7".7266"):is"r"(r,s)
-+7267
-x@t1:=tris(cx,ts(pli(mod(x),0),pli(mod(x),0)),pli(ts"r"(mod(x),mod(x)),0),pli(mod2(x),0),t3"c.7266"(mod(x)),isrecx1(ts"r"(mod(x),mod(x)),mod2(x),0,thsqrt1b(mod2(x),lemma5(x)))):is(ts(pli(mod(x),0),pli(mod(x),0)),pli(mod2(x),0))
-t2:=ispl2"r"(m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(im(x),im(x)),ts"r"(re(x),re(x)),tris(real,m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),satz197e(im(x),m0"r"(im(x))),satz198(im(x),im(x)))):is"r"(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x))
-t3:=tris(real,pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),pl"r"(m0"r"(ts"r"(re(x),im(x))),ts"r"(re(x),im(x))),0,ispl12"r"(ts"r"(re(x),m0"r"(im(x))),m0"r"(ts"r"(re(x),im(x))),ts"r"(im(x),re(x)),ts"r"(re(x),im(x)),satz197b(re(x),im(x)),comts"r"(im(x),re(x))),satz179a(ts"r"(re(x),im(x)))):is"r"(pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0)
-t4:=tris(cx,ts(x,conj(x)),pli(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x)))),pli(mod2(x),0),tsis2a(x,re(x),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0,t2,t3)):is(ts(x,conj(x)),pli(mod2(x),0))
--7267
-x@satz267:=tris2(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),pli(mod2(x),0),t1".7267",t4".7267"):is(ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)))
-satz267a:=symis(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),satz267):is(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)))
-+7268
-z@t1:=tr3is(cx,ts(x,ts(y,z)),ts(ts(x,y),z),ts(ts(y,x),z),ts(y,ts(x,z)),assts2(x,y,z),ists1(ts(x,y),ts(y,x),z,comts(x,y)),assts1(y,x,z)):is(ts(x,ts(y,z)),ts(y,ts(x,z)))
-[u:complex]
-t2:=tr3is(cx,ts(ts(x,y),ts(z,u)),ts(x,ts(y,ts(z,u))),ts(x,ts(z,ts(y,u))),ts(ts(x,z),ts(y,u)),assts1(x,y,ts(z,u)),ists2(ts(y,ts(z,u)),ts(z,ts(y,u)),x,t1(y,z,u)),assts2(x,z,ts(y,u))):is(ts(ts(x,y),ts(z,u)),ts(ts(x,z),ts(y,u)))
-y@t3:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,y),conj(ts(x,y))),ts(ts(x,y),ts(conj(x),conj(y))),ts(ts(x,conj(x)),ts(y,conj(y))),satz267(ts(x,y)),ists2(conj(ts(x,y)),ts(conj(x),conj(y)),ts(x,y),satz261(x,y)),t2(x,y,conj(x),conj(y))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))))
-t4:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))),ts(ts(pli(mod(x),0),pli(mod(x),0)),ts(pli(mod(y),0),pli(mod(y),0))),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),t3,ists12(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)),ts(y,conj(y)),ts(pli(mod(y),0),pli(mod(y),0)),satz267a(x),satz267a(y)),t2(pli(mod(x),0),pli(mod(x),0),pli(mod(y),0),pli(mod(y),0))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))))
-@[r:real][s:real]
-t5:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
-t6:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
-t7:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t5,t6)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
-y@t8:=tris(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)),t4,ists12(ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),t7(mod(x),mod(y)),t7(mod(x),mod(y)))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)))
-[n:neg(ts"r"(mod(x),mod(y)))]
-t9:=orapp(and(pos(mod(x)),neg(mod(y))),and(neg(mod(x)),pos(mod(y))),con,satz196h(mod(x),mod(y),n),[t:and(pos(mod(x)),neg(mod(y)))]<ande2(pos(mod(x)),neg(mod(y)),t)>satz264c(y),[t:and(neg(mod(x)),pos(mod(y)))]<ande1(neg(mod(x)),pos(mod(y)),t)>satz264c(x)):con
--7268
-y@satz268:=satz266(mod(ts(x,y)),ts"r"(mod(x),mod(y)),t8".7268",satz264c(ts(x,y)),[t:neg(ts"r"(mod(x),mod(y)))]t9".7268"(t)):is"r"(mod(ts(x,y)),ts"r"(mod(x),mod(y)))
-satz268a:=symis(real,mod(ts(x,y)),ts"r"(mod(x),mod(y)),satz268):is"r"(ts"r"(mod(x),mod(y)),mod(ts(x,y)))
-[n:nis(y,0c)]
-+7269
-t1:=pnot0(mod(y),satz264a(y,n)):nis"r"(mod(y),0)
-t2:=tris1(real,ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),mod(ts(ov(x,y,n),y)),satz268(ov(x,y,n),y),ismod(ts(ov(x,y,n),y),x,satz240(x,y,n))):is"r"(ts"r"(mod(ov(x,y,n)),mod(y)),mod(x))
-t3:=satz204g(mod(x),mod(y),mod(ov(x,y,n)),t1,tris(real,ts"r"(mod(y),mod(ov(x,y,n))),ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),comts"r"(mod(y),mod(ov(x,y,n))),t2)):is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),t1))
--7269
-satz269:=t3".7269":is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),pnot0(mod(y),satz264a(y,n))))
-y@[i:is(pl(x,y),1c)]
-+7270
-@[r:real]
-t1:=th1"l.imp"(neg(r),moreis(abs(r),r),[t:neg(r)]moreisi1(abs(r),r,trmore(abs(r),0,r,satz169a(abs(r),satz166b(r,t)),lemma2"r"(r,0,satz169c(r,t)))),[t:not(neg(r))]moreisi2(abs(r),r,absnn(r,t))):moreis(abs(r),r)
-x@t2:=trmoreis(mod(x),abs(re(x)),re(x),satz265a(x),t1(re(x))):moreis(mod(x),re(x))
-i@t3:=tr3is(real,pl"r"(re(x),re(y)),re(pl(x,y)),re(1c),1rl,isre(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),iscere(pl(x,y),1c,i),reis(1rl,0)):is"r"(pl"r"(re(x),re(y)),1rl)
--7270
-satz270:=ismoreis2(pl"r"(re(x),re(y)),1rl,pl"r"(mod(x),mod(y)),t3".7270",satz191(mod(x),re(x),mod(y),re(y),t2".7270",t2".7270"(y))):moreis(pl"r"(mod(x),mod(y)),1rl)
-+7271
-y@[i:is(pl(x,y),0c)]
-t1:=satz264b(pl(x,y),i):is"r"(mod(pl(x,y)),0)
-t2:=ismoreis2(pl"r"(0,0),mod(pl(x,y)),pl"r"(mod(x),mod(y)),tris2(real,pl"r"(0,0),mod(pl(x,y)),0,pl01(0,0,refis(real,0)),t1),satz191(mod(x),0,mod(y),0,satz264d(x),satz264d(y))):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
-y@[n:nis(pl(x,y),0c)]
-t3:=pnot0(mod(pl(x,y)),satz264a(pl(x,y),n)):nis"r"(mod(pl(x,y)),0)
-t4:=tris(cx,pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),ov(pl(x,y),pl(x,y),n),1c,satz253(x,pl(x,y),y,n),satz250(pl(x,y),n)):is(pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),1c)
-t5:=satz270(ov(x,pl(x,y),n),ov(y,pl(x,y),n),t4):moreis(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),1rl)
-fx:=ov"r"(mod(x),mod(pl(x,y)),t3):real
-fy:=ov"r"(mod(y),mod(pl(x,y)),t3):real
-t6:=ismoreis1(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),pl"r"(fx,fy),1rl,ispl12"r"(mod(ov(x,pl(x,y),n)),fx,mod(ov(y,pl(x,y),n)),fy,satz269(x,pl(x,y),n),satz269(y,pl(x,y),n)),t5):moreis(pl"r"(fx,fy),1rl)
-prl:=ts"r"(pl"r"(fx,fy),mod(pl(x,y))):real
-prr:=ts"r"(1rl,mod(pl(x,y))):real
-t7:=orapp(more(pl"r"(fx,fy),1rl),is"r"(pl"r"(fx,fy),1rl),moreis(prl,prr),t6,[t:more(pl"r"(fx,fy),1rl)]moreisi1(prl,prr,satz203a(pl"r"(fx,fy),1rl,mod(pl(x,y)),t,satz264a(pl(x,y),n))),[t:is"r"(pl"r"(fx,fy),1rl)]moreisi2(prl,prr,ists1"r"(pl"r"(fx,fy),1rl,mod(pl(x,y)),t))):moreis(prl,prr)
-t8:=tris(real,prl,pl"r"(ts"r"(fx,mod(pl(x,y))),ts"r"(fy,mod(pl(x,y)))),pl"r"(mod(x),mod(y)),disttp1"r"(fx,fy,mod(pl(x,y))),ispl12"r"(ts"r"(fx,mod(pl(x,y))),mod(x),ts"r"(fy,mod(pl(x,y))),mod(y),satz204e(mod(x),mod(pl(x,y)),t3),satz204e(mod(y),mod(pl(x,y)),t3))):is"r"(prl,pl"r"(mod(x),mod(y)))
-t9:=satz195b(mod(pl(x,y))):is"r"(prr,mod(pl(x,y)))
-t10:=ismoreis12(prl,pl"r"(mod(x),mod(y)),prr,mod(pl(x,y)),t8,t9,t7):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
-y@t11:=th1"l.imp"(is(pl(x,y),0c),moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y))),[t:is(pl(x,y),0c)]t2(t),[t:nis(pl(x,y),0c)]t10(t)):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
--7271
-y@satz271:=satz168a(pl"r"(mod(x),mod(y)),mod(pl(x,y)),t11".7271"):lessis(mod(pl(x,y)),pl"r"(mod(x),mod(y)))
-satz271a:=t11".7271":moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
-+7272
-x@t1:=tris(real,re(m0(x)),re(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(re(x)),iscere(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),reis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(re(m0(x)),m0"r"(re(x)))
-t2:=tris(real,ts"r"(re(m0(x)),re(m0(x))),ts"r"(m0"r"(re(x)),m0"r"(re(x))),ts"r"(re(x),re(x)),ists12"r"(re(m0(x)),m0"r"(re(x)),re(m0(x)),m0"r"(re(x)),t1,t1),satz198(re(x),re(x))):is"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)))
-t3:=tris(real,im(m0(x)),im(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(im(x)),isceim(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),imis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(im(m0(x)),m0"r"(im(x)))
-t4:=tris(real,ts"r"(im(m0(x)),im(m0(x))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),ists12"r"(im(m0(x)),m0"r"(im(x)),im(m0(x)),m0"r"(im(x)),t3,t3),satz198(im(x),im(x))):is"r"(ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)))
-t5:=ispl12"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)),ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)),t2,t4):is"r"(mod2(m0(x)),mod2(x))
--7272
-x@satz272:=issqrt(mod2(m0(x)),mod2(x),lemma5(m0(x)),lemma5(x),t5".7272"):is"r"(mod(m0(x)),mod(x))
-satz272a:=symis(real,mod(m0(x)),mod(x),satz272):is"r"(mod(x),mod(m0(x)))
-+7273
-y@sum:=pl"r"(mod(y),mod(mn(x,y))):real
-t1:=islessis1(mod(pl(y,mn(x,y))),mod(x),sum,ismod(pl(y,mn(x,y)),x,satz212h(x,y)),satz271(y,mn(x,y))):lessis(mod(x),sum)
-t2:=th9"l.or"(less(mod(x),sum),is"r"(mod(x),sum),less(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),is"r"(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),t1,[t:less(mod(x),sum)]satz188f(mod(x),sum,m0"r"(mod(y)),t),[t:is"r"(mod(x),sum)]ismn1"r"(mod(x),sum,mod(y),t)):lessis(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y)))
-t3:=tris(real,mn"r"(sum,mod(y)),mn"r"(pl"r"(mod(mn(x,y)),mod(y)),mod(y)),mod(mn(x,y)),ismn1"r"(sum,pl"r"(mod(mn(x,y)),mod(y)),mod(y),compl"r"(mod(y),mod(mn(x,y)))),mnpl(mod(mn(x,y)),mod(y))):is"r"(mn"r"(sum,mod(y)),mod(mn(x,y)))
-t4:=satz168b(mn"r"(mod(x),mod(y)),mod(mn(x,y)),islessis2(mn"r"(sum,mod(y)),mod(mn(x,y)),mn"r"(mod(x),mod(y)),t3,t2)):moreis(mod(mn(x,y)),mn"r"(mod(x),mod(y)))
-t5:=ismoreis12(mod(mn(y,x)),mod(mn(x,y)),mn"r"(mod(y),mod(x)),m0"r"(mn"r"(mod(x),mod(y))),tris1(real,mod(mn(y,x)),mod(mn(x,y)),mod(m0(mn(x,y))),ismod(m0(mn(x,y)),mn(y,x),satz219(x,y)),satz272(mn(x,y))),satz181a(mod(y),mod(x)),t4(y,x)):moreis(mod(mn(x,y)),m0"r"(mn"r"(mod(x),mod(y))))
-@[r:real][s:real][m:moreis(r,s)][n:moreis(r,m0"r"(s))]
-r@t6:=th9"l.or"(neg(r),not(neg(r)),is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r),th6"l.or"(neg(r)),[t:neg(r)]absn(r,t),[t:not(neg(r))]absnn(r,t)):or(is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r))
-n@t7:=orapp(is"r"(abs(s),m0"r"(s)),is"r"(abs(s),s),moreis(r,abs(s)),t6(s),[t:is"r"(abs(s),m0"r"(s))]ismoreis2(m0"r"(s),abs(s),r,symis(real,abs(s),m0"r"(s),t),n),[t:is"r"(abs(s),s)]ismoreis2(s,abs(s),r,symis(real,abs(s),s,t),m)):moreis(r,abs(s))
--7273
-y@satz273:=t7".7273"(mod(mn(x,y)),mn"r"(mod(x),mod(y)),t4".7273",t5".7273"):moreis(mod(mn(x,y)),abs(mn"r"(mod(x),mod(y))))
--c
--r
--rp
--rt
-@[x:nat][y:nat]
-+8274
-prop1:=some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)):'prop'
-x@prop2:=all([y:nat]imp(less(x,y),not(prop1(y)))):'prop'
-@[y:nat][l:less(1,y)][f:[t:1to(1)]1to(y)]
-1y:=1out(y):1to(y)
-yy:=xout(y):1to(y)
-[i:is"e"(1to(y),1y,yy)]
-t1:=isoutne(y,1,satz24a(y),y,lessisi3(y),i):is(1,y)
-f@t2:=ec3e31(is(1,y),more(1,y),less(1,y),satz10b(1,y),l):nis(1,y)
-t3:=th3"l.imp"(is"e"(1to(y),1y,yy),is(1,y),t2,[t:is"e"(1to(y),1y,yy)]t1(t)):not(is"e"(1to(y),1y,yy))
-[u:1to(1)]
-t4:=isf(1to(1),1to(y),f,u,1o,th1"n.singlet"(u)):is"e"(1to(y),<u>f,<1o>f)
-f@[i:is"e"(1to(y),<1o>f,1y)][u:1to(1)]
-t5:=th2"e.notis"(1to(y),1y,yy,<u>f,t3,tris(1to(y),<u>f,<1o>f,1y,t4(u),i)):not(is"e"(1to(y),<u>f,yy))
-i@t6:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),yy,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,yy,t5(u))):not(image(1to(1),1to(y),f,yy))
-t7:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),yy,t6):not(surjective(1to(1),1to(y),f))
-f@[n:not(is"e"(1to(y),<1o>f,1y))][u:1to(1)]
-t8:=th2"e.notis"(1to(y),<1o>f,1y,<u>f,n,t4(u)):not(is"e"(1to(y),<u>f,1y))
-n@t9:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),1y,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,1y,t8(u))):not(image(1to(1),1to(y),f,1y))
-t10:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),1y,t9):not(surjective(1to(1),1to(y),f))
-f@t11:=th1"l.imp"(is"e"(1to(y),<1o>f,1y),not(surjective(1to(1),1to(y),f)),[t:is"e"(1to(y),<1o>f,1y)]t7(t),[t:not(is"e"(1to(y),<1o>f,1y))]t10(t)):not(surjective(1to(1),1to(y),f))
-t12:=th2"l.and"(injective(1to(1),1to(y),f),surjective(1to(1),1to(y),f),t11):not(bijective(1to(1),1to(y),f))
-l@t13:=th5"l.some"([t:1to(1)]1to(y),[f:[t:1to(1)]1to(y)]bijective(1to(1),1to(y),f),[f:[t:1to(1)]1to(y)]t12(f)):not(prop1(1,y))
-@t14:=[y:nat][t:less(1,y)]t13(y,t):prop2(1)
-x@[p:prop2(x)][y:nat][l:less(<x>suc,y)]
-x@xs:=<x>suc:nat
-l@xxs:=xout(xs):1to(<x>suc)
-yy1:=xout(y):1to(y)
-t15:=trless(1,<x>suc,y,satz24c(x),l):less(1,y)
-ym1:=mn(y,1,t15):nat
-t16:=isless12(<x>suc,pl(x,1),y,pl(ym1,1),satz4e(x),th1c"n.mn"(y,1,t15),l):less(pl(x,1),pl(ym1,1))
-t17:=satz20c(x,ym1,1,t16):less(x,ym1)
-t18:=isless2(pl(ym1,1),y,ym1,th1d"n.mn"(y,1,t15),satz18a(ym1,1)):less(ym1,y)
-[f:[t:1to(xs)]1to(y)][b:bijective(1to(xs),1to(y),f)]
-t19:=ande1(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):injective(1to(xs),1to(y),f)
-t20:=ande2(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):surjective(1to(xs),1to(y),f)
-[i:is"e"(1to(y),<xxs>f,yy1)][u:1to(x)]
-u1:=inn(x,u):nat
-t21:=satz16a(u1,x,xs,1top(x,u),satz18c(x)):less(u1,xs)
-t22:=ec3e31(is(u1,xs),more(u1,xs),less(u1,xs),satz10b(u1,xs),t21):nis(u1,xs)
-t23:=lessisi1(u1,xs,t21):lessis(u1,xs)
-u2:=outn(xs,u1,t23):1to(xs)
-t24:=th3"l.imp"(is"e"(1to(xs),u2,xxs),is(u1,xs),t22,[t:is"e"(1to(xs),u2,xxs)]isoutne(xs,u1,t23,xs,lessisi3(xs),t)):not(is"e"(1to(xs),u2,xxs))
-[j:is"e"(1to(y),<u2>f,yy1)]
-t25:=tris2(1to(y),<u2>f,<xxs>f,yy1,j,i):is"e"(1to(y),<u2>f,<xxs>f)
-t26:=isfe(1to(xs),1to(y),f,t19,u2,xxs,t25):is"e"(1to(xs),u2,xxs)
-u@t27:=th3"l.imp"(is"e"(1to(y),<u2>f,yy1),is"e"(1to(xs),u2,xxs),t24,[t:is"e"(1to(y),<u2>f,yy1)]t26(t)):not(is"e"(1to(y),<u2>f,yy1))
-w1:=inn(y,<u2>f):nat
-[j:is(w1,y)]
-t28:=tris(1to(y),<u2>f,outn(y,w1,1top(y,<u2>f)),yy1,isoutinn(y,<u2>f),isoutni(y,w1,1top(y,<u2>f),y,lessisi3(y),j)):is"e"(1to(y),<u2>f,yy1)
-u@t29:=th3"l.imp"(is(w1,y),is"e"(1to(y),<u2>f,yy1),t27,[t:is(w1,y)]t28(t)):nis(w1,y)
-t30:=ore1(less(w1,y),is(w1,y),1top(y,<u2>f),t29):less(w1,y)
-t31:=islessis2(y,pl(ym1,1),pl(w1,1),th1c"n.mn"(y,1,t15),satz25b(y,w1,t30)):lessis(pl(w1,1),pl(ym1,1))
-t32:=th9"l.or"(less(pl(w1,1),pl(ym1,1)),is(pl(w1,1),pl(ym1,1)),less(w1,ym1),is(w1,ym1),t31,[t:less(pl(w1,1),pl(ym1,1))]satz20c(w1,ym1,1,t),[t:is(pl(w1,1),pl(ym1,1))]satz20b(w1,ym1,1,t)):lessis(w1,ym1)
-w2:=outn(ym1,w1,t32):1to(ym1)
-i@f1:=[t:1to(x)]w2(t):[t:1to(x)]1to(ym1)
-u@[v:1to(x)][j:is"e"(1to(ym1),<u>f1,<v>f1)]
-t33:=isoutne(ym1,w1(u),t32(u),w1(v),t32(v),j):is(w1(u),w1(v))
-t34:=isinne(y,<u2(u)>f,<u2(v)>f,t33):is"e"(1to(y),<u2(u)>f,<u2(v)>f)
-t35:=<t34><u2(v)><u2(u)>t19:is"e"(1to(xs),u2(u),u2(v))
-t36:=isoutne(xs,u1(u),t23(u),u1(v),t23(v),t35):is(u1(u),u1(v))
-t37:=isinne(x,u,v,t36):is"e"(1to(x),u,v)
-i@[v:1to(ym1)]
-v1:=inn(ym1,v):nat
-t38:=satz16a(v1,ym1,y,1top(ym1,v),t18):less(v1,y)
-t39:=ec3e31(is(v1,y),more(v1,y),less(v1,y),satz10b(v1,y),t38):nis(v1,y)
-t40:=lessisi1(v1,y,t38):lessis(v1,y)
-v2:=outn(y,v1,t40):1to(y)
-w3:=<v2>invf(1to(xs),1to(y),f,b):1to(xs)
-t41:=thinvf2(1to(xs),1to(y),f,b,v2):is"e"(1to(y),v2,<w3>f)
-[j:is"e"(1to(xs),w3,xxs)]
-t42:=isf(1to(xs),1to(y),f,w3,xxs,j):is"e"(1to(y),<w3>f,<xxs>f)
-t43:=tr3is(1to(y),v2,<w3>f,<xxs>f,yy1,t41,t42,i):is"e"(1to(y),v2,yy1)
-t44:=isoutne(y,v1,t40,y,lessisi3(y),t43):is(v1,y)
-v@t45:=th3"l.imp"(is"e"(1to(xs),w3,xxs),is(v1,y),t39,[t:is"e"(1to(xs),w3,xxs)]t44(t)):not(is"e"(1to(xs),w3,xxs))
-w4:=inn(xs,w3):nat
-[j:is(w4,xs)]
-t46:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),xxs,isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),xs,lessisi3(xs),j)):is"e"(1to(xs),w3,xxs)
-v@t47:=th3"l.imp"(is(w4,xs),is"e"(1to(xs),w3,xxs),t45,[t:is(w4,xs)]t46(t)):nis(w4,xs)
-t48:=ore1(less(w4,xs),is(w4,xs),1top(xs,w3),t47):less(w4,xs)
-t49:=satz26a(x,w4,t48):lessis(w4,x)
-w5:=outn(x,w4,t49):1to(x)
-t50:=isinoutn(x,w4,t49):is(w4,u1(w5))
-t51:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),u2(w5),isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),u1(w5),t23(w5),t50)):is"e"(1to(xs),w3,u2(w5))
-t52:=isf(1to(xs),1to(y),f,w3,u2(w5),t51):is"e"(1to(y),<w3>f,<u2(w5)>f)
-t53:=tris(1to(y),v2,<w3>f,<u2(w5)>f,t41,t52):is"e"(1to(y),v2,<u2(w5)>f)
-t54:=tris(nat,v1,inn(y,v2),w1(w5),isinoutn(y,v1,t40),isinni(y,v2,<u2(w5)>f,t53)):is(v1,w1(w5))
-t55:=tris(1to(ym1),v,outn(ym1,v1,1top(ym1,v)),w2(w5),isoutinn(ym1,v),isoutni(ym1,v1,1top(ym1,v),w1(w5),t32(w5),t54)):is"e"(1to(ym1),v,<w5>f1)
-t56:=somei(1to(x),[t:1to(x)]is"e"(1to(ym1),v,<t>f1),w5,t55):image(1to(x),1to(ym1),f1,v)
-i@t57:=andi(injective(1to(x),1to(ym1),f1),surjective(1to(x),1to(ym1),f1),[u:1to(x)][v:1to(x)][t:is"e"(1to(ym1),<u>f1,<v>f1)]t37(u,v,t),[u:1to(ym1)]t56(u)):bijective(1to(x),1to(ym1),f1)
-t58:=somei([t:1to(x)]1to(ym1),[g:[t:1to(x)]1to(ym1)]bijective(1to(x),1to(ym1),g),f1,t57):prop1(ym1)
-t59:=<t58><t17><ym1>p:con
-b@[n:not(is"e"(1to(y),<xxs>f,yy1))]
-m0:=<yy1>invf(1to(xs),1to(y),f,b):1to(xs)
-t60:=thinvf2(1to(xs),1to(y),f,b,yy1):is"e"(1to(y),yy1,<m0>f)
-f2:=changef(1to(xs),1to(y),f,m0,xxs):[t:1to(xs)]1to(y)
-t61:=changef2(1to(xs),1to(y),f,m0,xxs,xxs,refis(1to(xs),xxs)):is"e"(1to(y),<xxs>f2,<m0>f)
-t62:=tris2(1to(y),<xxs>f2,yy1,<m0>f,t61,t60):is"e"(1to(y),<xxs>f2,yy1)
-t63:=th6"e.wissel"(1to(xs),1to(y),f,m0,xxs,b):bijective(1to(xs),1to(y),f2)
-t64:=t59(f2,t63,t62):con
-b@t65:=th1"l.imp"(is"e"(1to(y),<xxs>f,yy1),con,[t:is"e"(1to(y),<xxs>f,yy1)]t59(t),[t:not(is"e"(1to(y),<xxs>f,yy1))]t64(t)):con
-l@t65a:=th5"l.some"([t:1to(xs)]1to(y),[f:[t:1to(xs)]1to(y)]bijective(1to(xs),1to(y),f),[f:[t:1to(xs)]1to(y)][t:bijective(1to(xs),1to(y),f)]t65(f,t)):not(prop1(xs,y))
-p@t66:=[y:nat][t:less(xs,y)]t65a(y,t):prop2(xs)
-x@t67:=induction([t:nat]prop2(t),t14,[t:nat][u:prop2(t)]t66(t,u),x):prop2(x)
--8274
-[l:less(x,y)]
-satz274:=<l><y>t67".8274":not(some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)))
-[f:[t:1to(x)]1to(y)]
-satz274a:=th4"l.some"([t:1to(x)]1to(y),[g:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),g),satz274,f):not(bijective(1to(x),1to(y),f))
-+*rt
-+*rp
-+*r
-+*c
-@[x:nat][u:1to(x)]
-inn:=inn"n"(x,u):nat
-@[q:[t:cx][u:cx]cx][x:nat][f:[t:1to(x)]cx]
-x@[n:1to(x)][o:not(is"e"(1to(x),n,xout(x)))]
-+8275
-t1:=th3"l.imp"(is"n"(inn(x,n),x),is"e"(1to(x),n,xout(x)),o,[t:is"n"(inn(x,n),x)]tris(1to(x),n,outn(x,inn(x,n),1top(x,n)),xout(x),isoutinn(x,n),isoutni(x,inn(x,n),1top(x,n),x,lessisi3(x),t))):not(is"n"(inn(x,n),x))
-t2:=ore1(less"n"(inn(x,n),x),is"n"(inn(x,n),x),1top(x,n),t1):less"n"(inn(x,n),x)
--8275
-lemma275:=satz25c(x,inn(x,n),t2".8275"):lessis"n"(<inn(x,n)>suc,x)
-f@[g:[t:1to(x)]cx]
-recprop:=and(is(<1out(x)>g,<1out(x)>f),[t:1to(x)][u:not(is"e"(1to(x),t,xout(x)))]is(<outn(x,<inn(x,t)>suc,lemma275(t,u))>g,<<outn(x,<inn(x,t)>suc,lemma275(t,u))>f><<t>g>q)):'prop'
-+*8275
-x@1o:=1out(x):1to(x)
-xo:=xout(x):1to(x)
-[u:nat][l:lessis"n"(<u>suc,x)]
-t11:=satz16b(u,<u>suc,x,satz18c(u),l):less"n"(u,x)
-t12:=lessisi1"n"(u,x,t11):lessis"n"(u,x)
-ux:=outn(x,u,t12):1to(x)
-t13:=ec3e31(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11):nis"n"(u,x)
-t14:=th3"l.imp"(is"e"(1to(x),ux,xo),is"n"(u,x),t13,[t:is"e"(1to(x),ux,xo)]isoutne(x,u,t12,x,lessisi3(x),t)):not(is"e"(1to(x),ux,xo))
-t15:=isf(nat,nat,suc,u,inn(x,ux),isinoutn(x,u,t12)):is"n"(<u>suc,<inn(x,ux)>suc)
-t16:=isoutni(x,<u>suc,l,<inn(x,ux)>suc,lemma275(ux,t14),t15):is"e"(1to(x),outn(x,<u>suc,l),outn(x,<inn(x,ux)>suc,lemma275(ux,t14)))
-x@[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
-ns:=outn(x,<inn(x,n)>suc,lemma275(n,o)):1to(x)
-f@[g:[t:1to(x)]cx]
-prop1:=is(<1o>g,<1o>f):'prop'
-prop2:=[t:1to(x)][u:not(is"e"(1to(x),t,xo))]is(<ns(t,u)>g,<<ns(t,u)>f><<t>g>q):'prop'
-[pg:recprop(g)]
-t3:=ande1(prop1,prop2,pg):prop1
-[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
-t4:=<o><n>ande2(prop1,prop2,pg):is(<ns(n,o)>g,<<ns(n,o)>f><<n>g>q)
-pg@[u:nat][l:lessis"n"(<u>suc,x)]
-t17:=isf(1to(x),cx,g,outn(x,<u>suc,l),ns(ux(u,l),t14(u,l)),t16(u,l)):is(<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g)
-t18:=tris(cx,<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,t17,t4(pg,ux(u,l),t14(u,l))):is(<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q)
-g@[h:[t:1to(x)]cx][u:nat][l:lessis"n"(u,x)]
-prop3:=is(<outn(x,u,l)>g,<outn(x,u,l)>h):'prop'
-u@prop4:=and(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(t)):'prop'
-prop5:=or(prop4,more"n"(u,x)):'prop'
-h@[pg:recprop(g)][ph:recprop(h)][l:lessis"n"(1,x)]
-t5:=isoutni(x,1,l,1,satz24a(x),refis(nat,1)):is"e"(1to(x),outn(x,1,l),1o)
-t6:=isf(1to(x),cx,g,outn(x,1,l),1o,t5):is(<outn(x,1,l)>g,<1o>g)
-t7:=tris(cx,<outn(x,1,l)>g,<1o>g,<1o>f,t6,t3(pg)):is(<outn(x,1,l)>g,<1o>f)
-t8:=tris2(cx,<outn(x,1,l)>g,<outn(x,1,l)>h,<1o>f,t7,t7(h,g,ph,pg,l)):prop3(1,l)
-ph@t9:=andi(lessis"n"(1,x),[t:lessis"n"(1,x)]prop3(1,t),satz24a(x),[t:lessis"n"(1,x)]t8(t)):prop4(1)
-t10:=ori1(prop4(1),more"n"(1,x),t9):prop5(1)
-[u:nat][p:prop5(u)][l:lessis"n"(<u>suc,x)]
-t19:=ec3e32(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11(u,l)):not(more"n"(u,x))
-t20:=ore1(prop4(u),more"n"(u,x),p,t19):prop4(u)
-t21:=<t12(u,l)>ande2(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(u,t),t20):prop3(u,t12(u,l))
-t22:=isf(cx,cx,[t:cx]<<ns(ux(u,l),t14(u,l))>f><t>q,<ux(u,l)>g,<ux(u,l)>h,t21):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q)
-t23:=symis(cx,<outn(x,<u>suc,l)>h,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,t18(h,ph,u,l)):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h)
-t24:=tr3is(cx,<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h,t18(g,pg,u,l),t22,t23):prop3(<u>suc,l)
-t25:=andi(lessis"n"(<u>suc,x),[t:lessis"n"(<u>suc,x)]prop3(<u>suc,t),l,[t:lessis"n"(<u>suc,x)]t24(t)):prop4(<u>suc)
-t26:=ori1(prop4(<u>suc),more"n"(<u>suc,x),t25):prop5(<u>suc)
-p@[n:not(lessis"n"(<u>suc,x))]
-t27:=satz10k(<u>suc,x,n):more"n"(<u>suc,x)
-t28:=ori2(prop4(<u>suc),more"n"(<u>suc,x),t27):prop5(<u>suc)
-p@t29:=th1"l.imp"(lessis"n"(<u>suc,x),prop5(<u>suc),[t:lessis"n"(<u>suc,x)]t26(t),[t:not(lessis"n"(<u>suc,x))]t28(t)):prop5(<u>suc)
-u@t30:=induction([v:nat]prop5(v),t10,[v:nat][t:prop5(v)]t29(v,t),u):prop5(u)
-ph@[n:1to(x)]
-t31:=isf(1to(x),cx,g,n,outn(x,inn(x,n),1top(x,n)),isoutinn(x,n)):is(<n>g,<outn(x,inn(x,n),1top(x,n))>g)
-t32:=satz10d(inn(x,n),x,1top(x,n)):not(more"n"(inn(x,n),x))
-t33:=ore1(prop4(inn(x,n)),more"n"(inn(x,n),x),t30(inn(x,n)),t32):prop4(inn(x,n))
-t34:=<1top(x,n)>ande2(lessis"n"(inn(x,n),x),[t:lessis"n"(inn(x,n),x)]prop3(inn(x,n),t),t33):prop3(inn(x,n),1top(x,n))
-t35:=symis(cx,<n>h,<outn(x,inn(x,n),1top(x,n))>h,t31(h,g,ph,pg,n)):is(<outn(x,inn(x,n),1top(x,n))>h,<n>h)
-t36:=tr3is(cx,<n>g,<outn(x,inn(x,n),1top(x,n))>g,<outn(x,inn(x,n),1top(x,n))>h,<n>h,t31,t34,t35):is(<n>g,<n>h)
-ph@t37:=fisi(1to(x),cx,g,h,[t:1to(x)]t36(t)):is"e"([t:1to(x)]cx,g,h)
-f@prop6:=some"l"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(g)):'prop'
-x@prop7:=all"l"([t:1to(x)]cx,[f:[t:1to(x)]cx]prop6(f)):'prop'
-q@[f:[t:1to(1)]cx]
-t38:=refis(cx,<1o(1)>f):prop1(1,f,f)
-[n:1to(1)][o:not(is"e"(1to(1),n,xo(1)))]
-t39:=<th1"n.singlet"(n)>o:con
-t40:=cone(is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q),t39):is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q)
-f@t41:=andi(prop1(1,f,f),prop2(1,f,f),t38,[t:1to(1)][u:not(is"e"(1to(1),t,xo(1)))]t40(t,u)):recprop(1,f,f)
-t42:=somei([t:1to(1)]cx,[g:[t:1to(1)]cx]recprop(1,f,g),f,t41):prop6(1,f)
-q@t43:=[f:[t:1to(1)]cx]t42(f):prop7(1)
-x@[p:prop7(x)]
-xs:=<x>suc:nat
-[f:[t:1to(xs)]cx]
-f1:=left(cx,xs,x,lessisi1"n"(x,xs,satz18c(x)),f):[t:1to(x)]cx
-t44:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f1,g)][v:recprop(x,f1,h)]t37(f1,g,h,u,v),<f1>p):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g))
-g1:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):[t:1to(x)]cx
-t45:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):recprop(x,f1,g1)
-[n:1to(xs)]
-nxs:=is"e"(1to(xs),n,xo(xs)):'prop'
-[o:not(nxs)]
-t46:=satz26a(x,inn(xs,n),t2(xs,n,o)):lessis"n"(inn(xs,n),x)
-n1:=outn(x,inn(xs,n),t46):1to(x)
-b:=<n1>g1:cx
-[o1:not(nxs)]
-t47:=isoutni(x,inn(xs,n),t46(o),inn(xs,n),t46(o1),refis(nat,inn(xs,n))):is"e"(1to(x),n1(o),n1(o1))
-t48:=isf(1to(x),cx,g1,n1(o),n1(o1),t47):is(b(o),b(o1))
-f@a:=<<xo(xs)>f><<xo(x)>g1>q:cx
-n@c:=ite"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u)):cx
-[i:nxs]
-t49:=itet"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),i):is(c,a)
-o@t50:=itef"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),o):is(c,b)
-f@g2:=[t:1to(xs)]c(t):[t:1to(xs)]cx
-t51:=th3"l.imp"(is"e"(1to(xs),1o(xs),xo(xs)),is"n"(1,xs),symnotis(nat,xs,1,<x>ax3),[t:is"e"(1to(xs),1o(xs),xo(xs))]isoutne(xs,1,satz24a(xs),xs,lessisi3(xs),t)):not(is"e"(1to(xs),1o(xs),xo(xs)))
-t52:=t50(1o(xs),t51):is(c(1o(xs)),b(1o(xs),t51))
-t53:=isinoutn(xs,1,satz24a(xs)):is"n"(1,inn(xs,1o(xs)))
-t54:=isoutni(x,1,satz24a(x),inn(xs,1o(xs)),t46(1o(xs),t51),t53):is"e"(1to(x),1o(x),n1(1o(xs),t51))
-t55:=isf(1to(x),cx,g1,1o(x),n1(1o(xs),t51),t54):is(<1o(x)>g1,b(1o(xs),t51))
-t56:=tris2(cx,c(1o(xs)),<1o(x)>g1,b(1o(xs),t51),t52,t55):is(c(1o(xs)),<1o(x)>g1)
-t57:=tris(cx,c(1o(xs)),<1o(x)>g1,<1o(x)>f1,t56,t3(x,f1,g1,t45)):is(c(1o(xs)),<1o(x)>f1)
-t58:=isinoutn(x,1,satz24a(x)):is"n"(1,inn(x,1o(x)))
-t59:=isoutni(xs,1,satz24a(xs),inn(x,1o(x)),trlessis"n"(inn(x,1o(x)),x,xs,1top(x,1o(x)),lessisi1"n"(x,xs,satz18c(x))),t58):is"e"(1to(xs),1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)))
-t60:=isf(1to(xs),cx,f,1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)),t59):is(<1o(xs)>f,<1o(x)>f1)
-t61:=tris2(cx,c(1o(xs)),<1o(xs)>f,<1o(x)>f1,t57,t60):prop1(xs,f,g2)
-o@[i:is"e"(1to(xs),ns(xs,n,o),xo(xs))]
-t62:=isoutne(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),i):is"n"(<inn(xs,n)>suc,xs)
-t63:=<t62><x><inn(xs,n)>ax4:is"n"(inn(xs,n),x)
-t64:=isoutni(x,inn(xs,n),t46,x,lessisi3(x),t63):is"e"(1to(x),n1,xo(x))
-t65:=isf(1to(x),cx,g1,xo(x),n1,symis(1to(x),n1,xo(x),t64)):is(<xo(x)>g1,b)
-t66:=tris2(cx,<xo(x)>g1,c,b,t65,t50):is(<xo(x)>g1,c)
-t67:=isf(cx,cx,[t:cx]<<xo(xs)>f><t>q,<xo(x)>g1,c,t66):is(a,<<xo(xs)>f><c>q)
-t68:=isf(1to(xs),cx,f,xo(xs),ns(xs,n,o),symis(1to(xs),ns(xs,n,o),xo(xs),i)):is(<xo(xs)>f,<ns(xs,n,o)>f)
-t69:=isf(cx,cx,<c>q,<xo(xs)>f,<ns(xs,n,o)>f,t68):is(<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q)
-t70:=tr3is(cx,c(ns(xs,n,o)),a,<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q,t49(ns(xs,n,o),i),t67,t69):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
-o@[o1:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))][i:is"e"(1to(x),n1,xo(x))]
-t71:=isoutne(x,inn(xs,n),t46,x,lessisi3(x),i):is"n"(inn(xs,n),x)
-t72:=ax2(inn(xs,n),x,t71):is"n"(<inn(xs,n)>suc,xs)
-t73:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),t72):is"e"(1to(xs),ns(xs,n,o),xo(xs))
-o1@t74:=th3"l.imp"(is"e"(1to(x),n1,xo(x)),is"e"(1to(xs),ns(xs,n,o),xo(xs)),o1,[t:is"e"(1to(x),n1,xo(x))]t73(t)):not(is"e"(1to(x),n1,xo(x)))
-t75:=isinoutn(x,inn(xs,n),t46):is"n"(inn(xs,n),inn(x,n1))
-t76:=ax2(inn(xs,n),inn(x,n1),t75):is"n"(<inn(xs,n)>suc,<inn(x,n1)>suc)
-t77:=isinoutn(xs,<inn(xs,n)>suc,lemma275(xs,n,o)):is"n"(<inn(xs,n)>suc,inn(xs,ns(xs,n,o)))
-t78:=tris1(nat,inn(xs,ns(xs,n,o)),<inn(x,n1)>suc,<inn(xs,n)>suc,t77,t76):is"n"(inn(xs,ns(xs,n,o)),<inn(x,n1)>suc)
-t79:=isoutni(x,inn(xs,ns(xs,n,o)),t46(ns(xs,n,o),o1),<inn(x,n1)>suc,lemma275(x,n1,t74),t78):is"e"(1to(x),n1(ns(xs,n,o),o1),ns(n1,t74))
-t80:=isf(1to(x),cx,g1,n1(ns(xs,n,o),o1),ns(n1,t74),t79):is(b(ns(xs,n,o),o1),<ns(n1,t74)>g1)
-t81:=isinoutn(x,<inn(x,n1)>suc,lemma275(x,n1,t74)):is"n"(<inn(x,n1)>suc,inn(x,ns(n1,t74)))
-t82:=tris(nat,<inn(xs,n)>suc,<inn(x,n1)>suc,inn(x,ns(n1,t74)),t76,t81):is"n"(<inn(xs,n)>suc,inn(x,ns(n1,t74)))
-t83:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),inn(x,ns(n1,t74)),trlessis"n"(inn(x,ns(n1,t74)),x,xs,1top(x,ns(n1,t74)),lessisi1"n"(x,xs,satz18c(x))),t82):is"e"(1to(xs),ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)))
-t84:=isf(1to(xs),cx,f,ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)),t83):is(<ns(xs,n,o)>f,<ns(n1,t74)>f1)
-t85:=isf(cx,cx,<b>q,<ns(xs,n,o)>f,<ns(n1,t74)>f1,t84):is(<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q)
-t86:=isf(cx,cx,[t:cx]<<ns(xs,n,o)>f><t>q,c,b,t50):is(<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q)
-t87:=tr3is(cx,c(ns(xs,n,o)),b(ns(xs,n,o),o1),<ns(n1,t74)>g1,<<ns(n1,t74)>f1><b>q,t50(ns(xs,n,o),o1),t80,t4(f1,g1,t45,n1,t74)):is(c(ns(xs,n,o)),<<ns(n1,t74)>f1><b>q)
-t88:=tris(cx,<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q,t86,t85):is(<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q)
-t89:=tris2(cx,c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q,t87,t88):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
-o@t90:=th1"l.imp"(is"e"(1to(xs),ns(xs,n,o),xo(xs)),is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q),[t:is"e"(1to(xs),ns(xs,n,o),xo(xs))]t70(t),[t:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))]t89(t)):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
-f@t91:=[t:1to(xs)][u:not(nxs(t))]t90(t,u):prop2(xs,f,g2)
-t92:=andi(prop1(xs,f,g2),prop2(xs,f,g2),t61,t91):recprop(xs,f,g2)
-t93:=somei([t:1to(xs)]cx,[g:[t:1to(xs)]cx]recprop(xs,f,g),g2,t92):prop6(xs,f)
-p@t94:=[f:[t:1to(xs)]cx]t93(f):prop7(xs)
-x@t95:=induction([y:nat]prop7(y),t43,[y:nat][t:prop7(y)]t94(y,t),x):prop7(x)
-[f:[t:1to(x)]cx]
-t96:=<f>t95:prop6(x,f)
-t97:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f,g)][v:recprop(x,f,h)]t37(f,g,h,u,v),t96):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
--8275
-f@satz275:=t97".8275"(f):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
-recf:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):[t:1to(x)]cx
-satz275a:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):recprop(x,f,recf)
-[n:1to(x)]
-rec:=<n>recf:cx
-f@satz275b:=t3".8275"(x,f,recf,satz275a):is(rec(1out(x)),<1out(x)>f)
-n@[o:not(is"e"(1to(x),n,xout(x)))]
-sucx:=ns".8275"(n,o):1to(x)
-satz275c:=t4".8275"(x,f,recf,satz275a,n,o):is(rec(sucx(n,o)),<<sucx(n,o)>f><rec(n)>q)
-f@[g:[t:1to(x)]cx][r:recprop(x,f,g)]
-satz275d:=t37".8275"(x,f,g,recf,r,satz275a):is"e"([t:1to(x)]cx,g,recf)
-[n:1to(x)]
-satz275e:=fise(1to(x),cx,g,recf,satz275d,n):is(<n>g,rec(n))
-x@[y:nat]
-+*8275
-y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
-fl:=left(cx,x,y,l,f):[t:1to(y)]cx
-rf:=recf(x,f):[t:1to(x)]cx
-rfl:=left(cx,x,y,l,rf):[t:1to(y)]cx
-t98:=isinoutn(y,1,satz24a(y)):is"n"(1,inn(y,1out(y)))
-t99:=isoutni(x,1,satz24a(x),inn(y,1out(y)),trlessis"n"(inn(y,1out(y)),y,x,1top(y,1out(y)),l),t98):is"e"(1to(x),1out(x),left1to(x,y,l,1out(y)))
-t100:=isp(1to(x),[t:1to(x)]is(<t>rf,<t>f),1out(x),left1to(x,y,l,1out(y)),t3(x,f,rf,satz275a(x,f)),t99):prop1(y,fl,rfl)
-[n:1to(y)][o:not(is"e"(1to(y),n,xout(y)))]
-t100a:=th3"l.imp"(is"n"(inn(y,n),y),is"e"(1to(y),n,xout(y)),o,[t:is"n"(inn(y,n),y)]tris(1to(y),n,outn(y,inn(y,n),1top(y,n)),xout(y),isoutinn(y,n),isoutni(y,inn(y,n),1top(y,n),y,lessisi3(y),t))):not(is"n"(inn(y,n),y))
-t100b:=ore1(less"n"(inn(y,n),y),is"n"(inn(y,n),y),1top(y,n),t100a):less"n"(inn(y,n),y)
-t101:=satz16b(inn(y,n),y,x,t100b,l):less"n"(inn(y,n),x)
-t102:=ec3e31(is"n"(inn(y,n),x),more"n"(inn(y,n),x),less"n"(inn(y,n),x),satz10b(inn(y,n),x),t101):nis"n"(inn(y,n),x)
-t103:=th3"l.imp"(is"e"(1to(x),left1to(x,y,l,n),xout(x)),is"n"(inn(y,n),x),t102,[t:is"e"(1to(x),left1to(x,y,l,n),xout(x))]isoutne(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l),x,lessisi3(x),t)):not(is"e"(1to(x),left1to(x,y,l,n),xout(x)))
-t104:=t4(x,f,rf,satz275a(x,f),left1to(x,y,l,n),t103):is(<ns(x,left1to(x,y,l,n),t103)>rf,<<ns(x,left1to(x,y,l,n),t103)>f><<n>rfl>q)
-t105:=isinoutn(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l)):is"n"(inn(y,n),inn(x,left1to(x,y,l,n)))
-t106:=ax2(inn(y,n),inn(x,left1to(x,y,l,n)),t105):is"n"(<inn(y,n)>suc,<inn(x,left1to(x,y,l,n))>suc)
-t107:=isinoutn(y,<inn(y,n)>suc,lemma275(y,n,o)):is"n"(<inn(y,n)>suc,inn(y,ns(y,n,o)))
-t108:=tris1(nat,<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)),<inn(y,n)>suc,t106,t107):is"n"(<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)))
-t109:=isoutni(x,<inn(x,left1to(x,y,l,n))>suc,lemma275(x,left1to(x,y,l,n),t103),inn(y,ns(y,n,o)),trlessis"n"(inn(y,ns(y,n,o)),y,x,1top(y,ns(y,n,o)),l),t108):is"e"(1to(x),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)))
-t110:=isp(1to(x),[t:1to(x)]is(<t>rf,<<t>f><<n>rfl>q),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)),t104,t109):is(<ns(y,n,o)>rfl,<<ns(y,n,o)>fl><<n>rfl>q)
-f@t111:=[t:1to(y)][u:not(is"e"(1to(y),t,xout(y)))]t110(t,u):prop2(y,fl,rfl)
-t112:=andi(prop1(y,fl,rfl),prop2(y,fl,rfl),t100,t111):recprop(y,fl,rfl)
--8275
-y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
-satz275f:=satz275d(y,fl".8275"(l,f),rfl".8275"(l,f),t112".8275"(l,f)):is"e"([t:1to(y)]cx,left(cx,x,y,l,recf(x,f)),recf(y,left(cx,x,y,l,f)))
-x@[f:[t:1to(pl"n"(x,1))]cx]
-+8276
-xs:=<x>suc:nat
-x1:=pl"n"(x,1):nat
-t1:=lessisi1"n"(x,x1,satz18a(x,1)):lessis"n"(x,x1)
-t2:=lessisi1"n"(x,xs,satz18c(x)):lessis"n"(x,xs)
-t3:=lessisi2"n"(xs,x1,satz4e(x)):lessis"n"(xs,x1)
-fx:=left(cx,x1,x,t1,f):[t:1to(x)]cx
-f1:=left(cx,x1,xs,t3,f):[t:1to(xs)]cx
-f1x:=f1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
-g1:=g2"c.8275"(x,t95"c.8275"(x),f1):[t:1to(xs)]cx
-g1x:=g1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
-g:=left(cx,x1,xs,t3,recf(x1,f)):[t:1to(xs)]cx
-t4:=t49"c.8275"(x,t95"c.8275"(x),f1,xout(xs),refis(1to(xs),xout(xs))):is(<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q)
-t5:=satz275d(xs,f1,g1,t92"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(xs)]cx,g1,recf(xs,f1))
-t6:=satz275f(x1,xs,t3,f):is"e"([t:1to(xs)]cx,g,recf(xs,f1))
-t7:=tris2([t:1to(xs)]cx,g,g1,recf(xs,f1),t6,t5):is"e"([t:1to(xs)]cx,g,g1)
-t8:=fise(1to(xs),cx,g,g1,t7,xout(xs)):is(<xout(xs)>g,<xout(xs)>g1)
-t9:=tris(cx,<xout(xs)>g,<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q,t8,t4):is(<xout(xs)>g,<<xout(xs)>f1><<xout(x)>g1x>q)
-[n:1to(x)]
-t10:=isinoutn(xs,inn(x,n),trlessis"n"(inn(x,n),x,xs,1top(x,n),t2)):is"n"(inn(x,n),inn(xs,left1to(xs,x,t2,n)))
-t11:=isoutni(x1,inn(x,n),trlessis"n"(inn(x,n),x,x1,1top(x,n),t1),inn(xs,left1to(xs,x,t2,n)),trlessis"n"(inn(xs,left1to(xs,x,t2,n)),xs,x1,1top(xs,left1to(xs,x,t2,n)),t3),t10):is"e"(1to(x1),left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)))
-t12:=isf(1to(x1),cx,f,left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)),t11):is(<n>fx,<n>f1x)
-f@t13:=fisi(1to(x),cx,fx,f1x,[t:1to(x)]t12(t)):is"e"([t:1to(x)]cx,fx,f1x)
-t14:=isf([t:1to(x)]cx,[t:1to(x)]cx,[u:[t:1to(x)]cx]recf(x,u),fx,f1x,t13):is"e"([t:1to(x)]cx,recf(x,fx),recf(x,f1x))
-t15:=satz275d(x,f1x,g1x,t45"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(x)]cx,g1x,recf(x,f1x))
-t16:=tris2([t:1to(x)]cx,g1x,recf(x,fx),recf(x,f1x),t15,t14):is"e"([t:1to(x)]cx,g1x,recf(x,fx))
-t17:=fise(1to(x),cx,g1x,recf(x,fx),t16,xout(x)):is(<xout(x)>g1x,<xout(x)>recf(x,fx))
-t18:=isinoutn(xs,xs,lessisi3(xs)):is"n"(xs,inn(xs,xout(xs)))
-t19:=tris(nat,x1,xs,inn(xs,xout(xs)),satz4a(x),t18):is"n"(x1,inn(xs,xout(xs)))
-t20:=isoutni(x1,x1,lessisi3(x1),inn(xs,xout(xs)),trlessis"n"(inn(xs,xout(xs)),xs,x1,1top(xs,xout(xs)),t3),t19):is"e"(1to(x1),xout(x1),left1to(x1,xs,t3,xout(xs)))
-t21:=isp1(1to(x1),[t:1to(x1)]is(<t>recf(x1,f),<<t>f><<xout(x)>g1x>q),left1to(x1,xs,t3,xout(xs)),xout(x1),t9,t20):is(<xout(x1)>recf(x1,f),<<xout(x1)>f><<xout(x)>g1x>q)
-t22:=isf(cx,cx,[t:cx]<<xout(x1)>f><t>q,<xout(x)>g1x,<xout(x)>recf(x,fx),t17):is(<<xout(x1)>f><<xout(x)>g1x>q,<<xout(x1)>f><<xout(x)>recf(x,fx)>q)
--8276
-satz276:=tris(cx,<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>g1x".8276">q,<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,fx".8276")>q,t21".8276",t22".8276"):is(<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
-x@[f:[u:1to(x)]cx]
-smpr:=rec(x,f,xout(x)):cx
-@[x:nat][f:[u:1to(x)]cx]
-sum:=smpr([t:cx][u:cx]pl(t,u),x,f):cx
-prod:=smpr([t:cx][u:cx]ts(t,u),x,f):cx
-q@[f:[u:1to(1)]cx]
-+8277
-t1:=isoutni(1,1,satz24a(1),1,lessisi3(1),refis(nat,1)):is"e"(1to(1),1out(1),xout(1))
--8277
-satz277:=isp(1to(1),[t:1to(1)]is(rec(1,f,t),<t>f),1out(1),xout(1),satz275b(1,f),t1".8277"):is(smpr(1,f),<xout(1)>f)
-q@[x:nat][f:[u:1to(pl"n"(x,1))]cx]
-satz278:=satz276(x,f):is(smpr(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><smpr(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
-x@[f:[u:1to(x)]cx][y:nat][i:is"n"(y,x)]
-+v8
-t1:=lessisi2"n"(y,x,i):lessis"n"(y,x)
-f0:=left(cx,x,y,t1,f):[t:1to(y)]cx
-t2:=fise(1to(y),cx,left(cx,x,y,t1,recf(x,f)),recf(y,f0),satz275f(x,y,t1,f),xout(y)):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(y,f0))
-t3:=tris1(nat,inn(y,xout(y)),x,y,isinoutn(y,y,lessisi3(y)),i):is"n"(inn(y,xout(y)),x)
-t4:=isoutni(x,inn(y,xout(y)),trlessis"n"(inn(y,xout(y)),y,x,1top(y,xout(y)),t1),x,lessisi3(x),t3):is"e"(1to(x),left1to(x,y,t1,xout(y)),xout(x))
-t5:=isf(1to(x),cx,recf(x,f),left1to(x,y,t1,xout(y)),xout(x),t4):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(x,f))
--v8
-issmpr:=tris1(cx,smpr(y,f0".v8"),smpr(x,f),<left1to(x,y,t1".v8",xout(y))>recf(x,f),t2".v8",t5".v8"):is(smpr(y,left(cx,x,y,lessisi2"n"(y,x,i),f)),smpr(x,f))
-@[z:complex][x:nat]
-+8279
-xr:=rlofnt(x):real
-prop1:=is(sum(x,[t:1to(x)]z),ts(z,pli(xr,0))):'prop'
-z@t1:=satz277([t:cx][u:cx]pl(t,u),[t:1to(1)]z):is(sum(1,[t:1to(1)]z),z)
-t2:=tris(cx,sum(1,[t:1to(1)]z),z,ts(z,1c),t1,satz222a(z)):prop1(1)
-x@[p:prop1(x)]
-t3:=satz278([t:cx][u:cx]pl(t,u),x,[t:1to(pl"n"(x,1))]z):is(sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z))
-t4:=ispl12(sum(x,[t:1to(x)]z),ts(z,pli(xr,0)),z,ts(z,1c),p,satz222a(z)):is(pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)))
-t5:=distpt2(z,pli(xr,0),1c):is(pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)))
-t6:=plis12a(xr,0,1rl,0):is(pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)))
-t7:=isrecx12(pl"r"(xr,1rl),rlofnt(pl"n"(x,1)),pl"r"(0,0),0,satzr155b(x,1),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0))
-t8:=tris(cx,pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0),t6,t7):is(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0))
-t9:=ists2(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0),z,t8):is(ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)))
-t10:=tr4is(cx,sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)),t3,t4,t5,t9):prop1(pl"n"(x,1))
-t11:=isp(nat,[t:nat]prop1(t),pl"n"(x,1),<x>suc,t10,satz4a(x)):prop1(<x>suc)
--8279
-satz279:=induction([t:nat]prop1".8279"(t),t2".8279",[u:nat][t:prop1".8279"(u)]t11".8279"(u,t),x):is(sum(x,[t:1to(x)]z),ts(z,pli(rlofnt(x),0)))
-q@[f:[t:1to(2)]cx]
-+8280
-t1:=lessisi1"n"(1,2,satz18a(1,1)):lessis"n"(1,2)
-f1:=left(cx,2,1,t1,f):[t:1to(1)]cx
-t2:=satz278(q,1,f):is(smpr(2,f),<<xout(2)>f><smpr(1,f1)>q)
-t3:=satz277(q,f1):is(smpr(1,f1),<xout(1)>f1)
-t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-t5:=isoutni(2,1,satz24a(2),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,2,1top(1,xout(1)),t1),t4):is"e"(1to(2),1out(2),left1to(2,1,t1,xout(1)))
-t6:=isf(1to(2),cx,f,1out(2),left1to(2,1,t1,xout(1)),t5):is(<1out(2)>f,<xout(1)>f1)
-t7:=tris2(cx,smpr(1,f1),<1out(2)>f,<xout(1)>f1,t3,t6):is(smpr(1,f1),<1out(2)>f)
-t8:=isf(cx,cx,[t:cx]<<xout(2)>f><t>q,smpr(1,f1),<1out(2)>f,t7):is(<<xout(2)>f><smpr(1,f1)>q,<<xout(2)>f><<1out(2)>f>q)
--8280
-satz280:=tris(cx,smpr(2,f),<<xout(2)>f><smpr(1,f1".8280")>q,<<xout(2)>f><<1out(2)>f>q,t2".8280",t8".8280"):is(smpr(2,f),<<xout(2)>f><<1out(2)>f>q)
-q@assoc:=[x:cx][y:cx][z:cx]is(<z><<y><x>q>q,<<z><y>q><x>q):'prop'
-@assocp1:=[x:cx][y:cx][z:cx]asspl1(x,y,z):assoc([x:cx][y:cx]pl(x,y))
-assocts:=[x:cx][y:cx][z:cx]assts1(x,y,z):assoc([x:cx][y:cx]ts(x,y))
-q@[a:assoc][z:cx][u:cx][v:cx]
-assq1:=<v><u><z>a:is(<v><<u><z>q>q,<<v><u>q><z>q)
-assq2:=symis(cx,<v><<u><z>q>q,<<v><u>q><z>q,assq1):is(<<v><u>q><z>q,<v><<u><z>q>q)
-q@[a:assoc(q)][x:nat][y:nat][f:[t:1to(pl"n"(x,y))]cx]
-+8281
-y@t1:=lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)):lessis"n"(x,pl"n"(x,y))
-f@f1:=left(cx,pl"n"(x,y),x,t1,f):[t:1to(x)]cx
-f2:=right(cx,x,y,f):[t:1to(y)]cx
-prop1:=is(smpr(pl"n"(x,y),f),<smpr(y,f2)><smpr(x,f1)>q):'prop'
-y@prop2:=all"l"([t:1to(pl"n"(x,y))]cx,[u:[t:1to(pl"n"(x,y))]cx]prop1(u)):'prop'
-x@[f0:[t:1to(pl"n"(x,1))]cx]
-t2:=satz278(q,x,f0):is(smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q)
-t3:=satz277(q,f2(1,f0)):is(smpr(1,f2(1,f0)),<xout(1)>f2(1,f0))
-t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-t5:=ispl2"n"(1,inn(1,xout(1)),x,t4):is"n"(pl"n"(x,1),pl"n"(x,inn(1,xout(1))))
-t6:=isoutni(pl"n"(x,1),pl"n"(x,1),lessisi3(pl"n"(x,1)),pl"n"(x,inn(1,xout(1))),satz19o(inn(1,xout(1)),1,x,1top(1,xout(1))),t5):is"e"(1to(pl"n"(x,1)),xout(pl"n"(x,1)),right1to(x,1,xout(1)))
-t7:=isf(1to(pl"n"(x,1)),cx,f0,xout(pl"n"(x,1)),right1to(x,1,xout(1)),t6):is(<xout(pl"n"(x,1))>f0,<xout(1)>f2(1,f0))
-t8:=tris2(cx,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),<xout(1)>f2(1,f0),t7,t3):is(<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)))
-t9:=isf(cx,cx,<smpr(x,f1(1,f0))>q,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),t8):is(<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q)
-t10:=tris(cx,smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q,t2,t9):prop1(1,f0)
-x@t11:=[u:[t:1to(pl"n"(x,1))]cx]t10(u):prop2(1)
-y@yp1:=pl"n"(y,1):nat
-xpy:=pl"n"(x,y):nat
-xpy1:=pl"n"(x,yp1):nat
-xyp1:=pl"n"(xpy,1):nat
-t12:=lessisi2"n"(xyp1,xpy1,asspl1"n"(x,y,1)):lessis"n"(xyp1,xpy1)
-[p:prop2(y)][f:[t:1to(xpy1)]cx]
-t13:=isinoutn(xyp1,xyp1,lessisi3(xyp1)):is"n"(xyp1,inn(xyp1,xout(xyp1)))
-t14:=tris(nat,xpy1,xyp1,inn(xyp1,xout(xyp1)),asspl2"n"(x,y,1),t13):is"n"(xpy1,inn(xyp1,xout(xyp1)))
-t15:=isoutni(xpy1,xpy1,lessisi3(xpy1),inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),t14):is"e"(1to(xpy1),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)))
-t16:=isf(1to(xpy1),cx,recf(xpy1,f),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),t15):is(smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)))
-fr:=left(cx,xpy1,xyp1,t12,f):[t:1to(xyp1)]cx
-t17:=satz275f(xpy1,xyp1,t12,f):is"e"([t:1to(xyp1)]cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr))
-t18:=fise(1to(xyp1),cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr),t17,xout(xyp1)):is(<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr))
-t19:=lessisi1"n"(xpy,xyp1,satz18a(xpy,1)):lessis"n"(xpy,xyp1)
-frr:=left(cx,xyp1,xpy,t19,fr):[t:1to(xpy)]cx
-t20:=satz278(xpy,fr):is(smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q)
-t21:=isf(cx,cx,[u:cx]<<xout(xyp1)>fr><u>q,smpr(xpy,frr),<smpr(y,f2(frr))><smpr(x,f1(frr))>q,<frr>p):is(<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
-t22:=assq1(a,smpr(x,f1(frr)),smpr(y,f2(frr)),<xout(xyp1)>fr):is(<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q)
-t23:=lessisi1"n"(y,yp1,satz18a(y,1)):lessis"n"(y,yp1)
-fy:=left(cx,yp1,y,t23,f2(yp1,f)):[t:1to(y)]cx
-t24:=satz278(y,f2(yp1,f)):is(smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
-t25:=isinoutn(yp1,yp1,lessisi3(yp1)):is"n"(yp1,inn(yp1,xout(yp1)))
-t26:=ispl2"n"(yp1,inn(yp1,xout(yp1)),x,t25):is"n"(xpy1,pl"n"(x,inn(yp1,xout(yp1))))
-t27:=tris1(nat,inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))),xpy1,t14,t26):is"n"(inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))))
-t28:=isoutni(xpy1,inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),pl"n"(x,inn(yp1,xout(yp1))),satz19o(inn(yp1,xout(yp1)),yp1,x,1top(yp1,xout(yp1))),t27):is"e"(1to(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)))
-t29:=isf(1to(xpy1),cx,f,left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)),t28):is(<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f))
-t30:=isf(cx,cx,<smpr(y,f2(frr))>q,<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f),t29):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q)
-[n:1to(y)]
-n0:=inn(y,n):nat
-nyp1:=left1to(yp1,y,t23,n):1to(yp1)
-t31:=isinoutn(yp1,n0,trlessis"n"(n0,y,yp1,1top(y,n),t23)):is"n"(n0,inn(yp1,nyp1))
-t32:=ispl2"n"(n0,inn(yp1,nyp1),x,t31):is"n"(pl"n"(x,n0),pl"n"(x,inn(yp1,nyp1)))
-nxpy:=right1to(x,y,n):1to(xpy)
-nxyp1:=left1to(xyp1,xpy,t19,nxpy):1to(xyp1)
-t33:=isinoutn(xyp1,inn(xpy,nxpy),trlessis"n"(inn(xpy,nxpy),xpy,xyp1,1top(xpy,nxpy),t19)):is"n"(inn(xpy,nxpy),inn(xyp1,nxyp1))
-t34:=isinoutn(xpy,pl"n"(x,n0),satz19o(n0,y,x,1top(y,n))):is"n"(pl"n"(x,n0),inn(xpy,nxpy))
-t35:=tris(nat,pl"n"(x,n0),inn(xpy,nxpy),inn(xyp1,nxyp1),t34,t33):is"n"(pl"n"(x,n0),inn(xyp1,nxyp1))
-t36:=tris1(nat,pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1),pl"n"(x,n0),t32,t35):is"n"(pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1))
-t37:=isoutni(xpy1,pl"n"(x,inn(yp1,nyp1)),satz19o(inn(yp1,nyp1),yp1,x,1top(yp1,nyp1)),inn(xyp1,nxyp1),trlessis"n"(inn(xyp1,nxyp1),xyp1,xpy1,1top(xyp1,nxyp1),t12),t36):is"e"(1to(xpy1),right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1))
-t38:=isf(1to(xpy1),cx,f,right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1),t37):is(<n>fy,<n>f2(frr))
-f@t39:=fisi(1to(y),cx,fy,f2(frr),[u:1to(y)]t38(u)):is"e"([u:1to(y)]cx,fy,f2(frr))
-t40:=isf([u:1to(y)]cx,cx,[t:[u:1to(y)]cx]smpr(y,t),fy,f2(frr),t39):is(smpr(y,fy),smpr(y,f2(frr)))
-t41:=isf(cx,cx,[t:cx]<<xout(yp1)>f2(yp1,f)><t>q,smpr(y,f2(frr)),smpr(y,fy),symis(cx,smpr(y,fy),smpr(y,f2(frr)),t40)):is(<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
-t41a:=tris(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t30,t41):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
-t42:=tris2(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t41a,t24):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)))
-t43:=isf(cx,cx,<smpr(x,f1(frr))>q,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),t42):is(<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q)
-[m:1to(x)]
-m0:=inn(x,m):nat
-mxpy:=left1to(xpy,x,t1,m):1to(xpy)
-mxyp1:=left1to(xyp1,xpy,t19,mxpy):1to(xyp1)
-t44:=isinoutn(xyp1,inn(xpy,mxpy),trlessis"n"(inn(xpy,mxpy),xpy,xyp1,1top(xpy,mxpy),t19)):is"n"(inn(xpy,mxpy),inn(xyp1,mxyp1))
-t45:=isinoutn(xpy,m0,trlessis"n"(m0,x,xpy,1top(x,m),t1)):is"n"(m0,inn(xpy,mxpy))
-t46:=tris(nat,m0,inn(xpy,mxpy),inn(xyp1,mxyp1),t45,t44):is"n"(m0,inn(xyp1,mxyp1))
-t47:=isoutni(xpy1,m0,trlessis"n"(m0,x,xpy1,1top(x,m),t1(yp1)),inn(xyp1,mxyp1),trlessis"n"(inn(xyp1,mxyp1),xyp1,xpy1,1top(xyp1,mxyp1),t12),t46):is"e"(1to(xpy1),left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1))
-t48:=isf(1to(xpy1),cx,f,left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1),t47):is(<m>f1(x,yp1,f),<m>f1(x,y,frr))
-f@t49:=fisi(1to(x),cx,f1(x,yp1,f),f1(x,y,frr),[u:1to(x)]t48(u)):is"e"([u:1to(x)]cx,f1(x,yp1,f),f1(x,y,frr))
-t50:=isf([u:1to(x)]cx,cx,[t:[u:1to(x)]cx]smpr(x,t),f1(yp1,f),f1(frr),t49):is(smpr(x,f1(yp1,f)),smpr(x,f1(frr)))
-t51:=isf(cx,cx,[t:cx]<smpr(yp1,f2(yp1,f))><t>q,smpr(x,f1(frr)),smpr(x,f1(yp1,f)),symis(cx,smpr(x,f1(yp1,f)),smpr(x,f1(frr)),t50)):is(<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q)
-t52:=tr4is(cx,smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,t16,t18,t20,t21):is(smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
-t53:=tr4is(cx,smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q,t52,t22,t43,t51):prop1(yp1,f)
-p@t54:=[u:[t:1to(xpy1)]cx]t53(u):prop2(yp1)
-t55:=isp(nat,[t:nat]prop2(t),yp1,<y>suc,t54,satz4a(y)):prop2(<y>suc)
-y@t56:=induction([t:nat]prop2(t),t11,[z:nat][t:prop2(z)]t55(z,t),y):prop2(y)
--8281
-satz281:=<f>t56".8281":is(smpr(pl"n"(x,y),f),<smpr(y,right(cx,x,y,f))><smpr(x,left(cx,pl"n"(x,y),x,lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)),f))>q)
-q@commut:=[x:cx][y:cx]is(<y><x>q,<x><y>q):'prop'
-@commutpl:=[x:cx][y:cx]compl(x,y):commut([x:cx][y:cx]pl(x,y))
-commutts:=[x:cx][y:cx]comts(x,y):commut([x:cx][y:cx]ts(x,y))
-q@[c:commut][z:cx][u:cx]
-comq:=<u><z>c:is(<u><z>q,<z><u>q)
-a@[c:commut(q)][x:nat][f:[t:1to(x)]cx][g:[t:1to(x)]cx]
-+8282
-prop1:=is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q):'prop'
-x@prop2:=all"l"([t:1to(x)]cx,[u:[t:1to(x)]cx]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]prop1(u,v))):'prop'
-c@[f0:[t:1to(1)]cx][g0:[t:1to(1)]cx]
-t1:=satz277([t:1to(1)]<<t>g0><<t>f0>q):is(smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<<xout(1)>g0><<xout(1)>f0>q)
-t2:=isf(cx,cx,<smpr(1,f0)>q,smpr(1,g0),<xout(1)>g0,satz277(g0)):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q)
-t3:=isf(cx,cx,[t:cx]<<xout(1)>g0><t>q,smpr(1,f0),<xout(1)>f0,satz277(f0)):is(<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
-t4:=tris(cx,<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t2,t3):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
-t5:=tris2(cx,smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t1,t4):prop1(1,f0,g0)
-c@t6:=[u:[t:1to(1)]cx][v:[t:1to(1)]cx]t5(u,v):prop2(1)
-x@xp1:=pl"n"(x,1):nat
-[p:prop2(x)][f:[t:1to(xp1)]cx][g:[t:1to(xp1)]cx]
-c@[u:cx][v:cx][w:cx][z:cx]
-t7:=assq2(a,<v><u>q,w,z):is(<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q)
-t8:=comq(c,<v><u>q,w):is(<w><<v><u>q>q,<<v><u>q><w>q)
-t9:=assq2(a,w,u,v):is(<<v><u>q><w>q,<v><<u><w>q>q)
-t10:=tris(cx,<w><<v><u>q>q,<<v><u>q><w>q,<v><<u><w>q>q,t8,t9):is(<w><<v><u>q>q,<v><<u><w>q>q)
-t11:=isf(cx,cx,[t:cx]<z><t>q,<w><<v><u>q>q,<v><<u><w>q>q,t10):is(<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q)
-t12:=assq1(a,<u><w>q,v,z):is(<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q)
-t13:=comq(c,w,u):is(<u><w>q,<w><u>q)
-t14:=isf(cx,cx,[t:cx]<<z><v>q><t>q,<u><w>q,<w><u>q,t13):is(<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q)
-t15:=tr4is(cx,<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q,t7,t11,t12,t14):is(<<z><w>q><<v><u>q>q,<<z><v>q><<w><u>q>q)
-g@t16:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
-sfx:=smpr(x,left(cx,xp1,x,t16,f)):cx
-sgx:=smpr(x,left(cx,xp1,x,t16,g)):cx
-h:=[t:1to(xp1)]<<t>g><<t>f>q:[t:1to(xp1)]cx
-shx:=smpr(x,left(cx,xp1,x,t16,h)):cx
-t17:=satz278(x,h):is(smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q)
-t18:=<left(cx,xp1,x,t16,g)><left(cx,xp1,x,t16,f)>p:is(shx,<sgx><sfx>q)
-t19:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><<xout(xp1)>f>q><t>q,shx,<sgx><sfx>q,t18):is(<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q)
-t20:=t15(sfx,sgx,<xout(xp1)>f,<xout(xp1)>g):is(<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
-t21:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><sfx>q,satz278(x,f)):is(<<xout(xp1)>f><sfx>q,smpr(xp1,f))
-t22:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><sgx>q><t>q,<<xout(xp1)>f><sfx>q,smpr(xp1,f),t21):is(<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q)
-t23:=symis(cx,smpr(xp1,g),<<xout(xp1)>g><sgx>q,satz278(x,g)):is(<<xout(xp1)>g><sgx>q,smpr(xp1,g))
-t24:=isf(cx,cx,<smpr(xp1,f)>q,<<xout(xp1)>g><sgx>q,smpr(xp1,g),t23):is(<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q)
-t25:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,t17,t19,t20):is(smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
-t26:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q,t25,t22,t24):prop1(xp1,f,g)
-p@t27:=[u:[t:1to(xp1)]cx][v:[t:1to(xp1)]cx]t26(u,v):prop2(xp1)
-t28:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t27,satz4a(x)):prop2(<x>suc)
-x@t29:=induction([t:nat]prop2(t),t6,[y:nat][t:prop2(y)]t28(y,t),x):prop2(x)
--8282
-satz282:=<g><f>t29".8282":is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q)
-x@[s:[t:1to(x)]1to(x)][b:bijective(1to(x),1to(x),s)][f:[t:1to(x)]cx]
-+8283
-s@[f:[t:1to(x)]cx]
-g:=[t:1to(x)]<<t>s>f:[t:1to(x)]cx
-prop1:=is(smpr(x,g),smpr(x,f)):'prop'
-x@prop2:=all"l"([t:1to(x)]1to(x),[u:[t:1to(x)]1to(x)]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]imp(bijective(1to(x),1to(x),u),prop1(u,v)))):'prop'
-c@[s:[t:1to(1)]1to(1)][f:[t:1to(1)]cx]
-t1:=tris2(1to(1),<xout(1)>s,xout(1),1o"n",th1"n.singlet"(<xout(1)>s),th1"n.singlet"(xout(1))):is"e"(1to(1),<xout(1)>s,xout(1))
-t2:=satz277(g(1,s,f)):is(smpr(1,g(1,s,f)),<xout(1)>g(1,s,f))
-t3:=isf(1to(1),cx,f,<xout(1)>s,xout(1),t1):is(<xout(1)>g(1,s,f),<xout(1)>f)
-t4:=symis(cx,smpr(1,f),<xout(1)>f,satz277(f)):is(<xout(1)>f,smpr(1,f))
-t5:=tr3is(cx,smpr(1,g(1,s,f)),<xout(1)>g(1,s,f),<xout(1)>f,smpr(1,f),t2,t3,t4):prop1(1,s,f)
-c@t6:=[u:[t:1to(1)]1to(1)][v:[t:1to(1)]cx][w:bijective(1to(1),1to(1),u)]t5(u,v):prop2(1)
-x@xp1:=pl"n"(x,1):nat
-t7:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
-[p:prop2(x)][s:[t:1to(xp1)]1to(xp1)][f:[t:1to(xp1)]cx][b:bijective(1to(xp1),1to(xp1),s)]
-t8:=ande1(injective(1to(xp1),1to(xp1),s),surjective(1to(xp1),1to(xp1),s),b):injective(1to(xp1),1to(xp1),s)
-[case1:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))][u:1to(x)]
-u1:=left1to(xp1,x,t7,u):1to(xp1)
-n1:=inn(xp1,<u1>s):nat
-[i:is"n"(n1,xp1)]
-t9:=tr3is(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),xout(xp1),<xout(xp1)>s,isoutinn(xp1,<u1>s),isoutni(xp1,n1,1top(xp1,<u1>s),xp1,lessisi3(xp1),i),symis(1to(xp1),<xout(xp1)>s,xout(xp1),case1)):is"e"(1to(xp1),<u1>s,<xout(xp1)>s)
-t10:=isfe(1to(xp1),1to(xp1),s,t8,u1,xout(xp1),t9):is"e"(1to(xp1),u1,xout(xp1))
-t11:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t10):is"n"(inn(x,u),xp1)
-t12:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
-t13:=<t11>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t12):con
-u@t14:=ore1(less"n"(n1,xp1),is"n"(n1,xp1),1top(xp1,<u1>s),[t:is"n"(n1,xp1)]t13(t)):less"n"(n1,xp1)
-t15:=satz26(x,n1,t14):lessis"n"(n1,x)
-w1:=outn(x,n1,t15):1to(x)
-case1@s01:=[t:1to(x)]w1(t):[t:1to(x)]1to(x)
-u@[v:1to(x)][i:is"e"(1to(x),w1(u),w1(v))]
-t16:=isoutne(x,n1(u),t15(u),n1(v),t15(v),i):is"n"(n1(u),n1(v))
-t17:=<isinne(xp1,<u1(u)>s,<u1(v)>s,t16)><u1(v)><u1(u)>t8:is"e"(1to(xp1),u1(u),u1(v))
-t18:=thleft1(xp1,x,t7,u,v,t17):is"e"(1to(x),u,v)
-u@u2:=<u1>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
-n2:=inn(xp1,u2):nat
-[i:is"n"(n2,xp1)]
-t19:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),xout(xp1),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),xp1,lessisi3(xp1),i)):is"e"(1to(xp1),u2,xout(xp1))
-t20:=tr3is(1to(xp1),u1,<u2>s,<xout(xp1)>s,xout(xp1),thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,xout(xp1),t19),case1):is"e"(1to(xp1),u1,xout(xp1))
-t21:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t20):is"n"(inn(x,u),xp1)
-t22:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
-t23:=<t21>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t22):con
-u@t24:=ore1(less"n"(n2,xp1),is"n"(n2,xp1),1top(xp1,u2),[t:is"n"(n2,xp1)]t23(t)):less"n"(n2,xp1)
-t25:=satz26(x,n2,t24):lessis"n"(n2,x)
-w2:=outn(x,n2,t25):1to(x)
-t26:=isinoutn(x,n2,t25):is"n"(n2,inn(x,w2))
-t27:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),u1(w2),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),inn(x,w2),trlessis"n"(inn(x,w2),x,xp1,1top(x,w2),t7),t26)):is"e"(1to(xp1),u2,u1(w2))
-t28:=tris(1to(xp1),u1,<u2>s,<u1(w2)>s,thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,u1(w2),t27)):is"e"(1to(xp1),u1,<u1(w2)>s)
-t29:=tris(nat,inn(x,u),inn(xp1,u1),n1(w2),isinoutn(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7)),isinni(xp1,u1,<u1(w2)>s,t28)):is"n"(inn(x,u),n1(w2))
-t30:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w1(w2),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),n1(w2),t15(w2),t29)):is"e"(1to(x),u,w1(w2))
-t31:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w1(t)),w2,t30):image(1to(x),1to(x),s01,u)
-case1@t32:=andi(injective(1to(x),1to(x),s01),surjective(1to(x),1to(x),s01),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s01,<u>s01)]t18(t,u,v),[t:1to(x)]t31(t)):bijective(1to(x),1to(x),s01)
-f01:=left(cx,xp1,x,t7,f):[t:1to(x)]cx
-t33:=<t32><f01><s01>p:prop1(s01,f01)
-g1:=left(cx,xp1,x,t7,g(xp1,s,f)):[t:1to(x)]cx
-g2:=g(x,s01,f01):[t:1to(x)]cx
-u@t33a:=isoutinn(xp1,<u1>s):is"e"(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)))
-t34:=isinoutn(x,n1,t15):is"n"(n1,inn(x,w1))
-t35:=isoutni(xp1,n1,1top(xp1,<u1>s),inn(x,w1),trlessis"n"(inn(x,w1),x,xp1,1top(x,w1),t7),t34):is"e"(1to(xp1),outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1))
-t36:=tris(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1),t33a,t35):is"e"(1to(xp1),<u1>s,left1to(xp1,x,t7,w1))
-t37:=isf(1to(xp1),cx,f,<u1>s,left1to(xp1,x,t7,w1),t36):is(<u>g1,<u>g2)
-case1@t38:=fisi(1to(x),cx,g1,g2,[t:1to(x)]t37(t)):is"e"([t:1to(x)]cx,g1,g2)
-t39:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g1,g2,t38):is(smpr(x,g1),smpr(x,g2))
-t40:=tris(cx,smpr(x,g1),smpr(x,g2),smpr(x,f01),t39,t33):is(smpr(x,g1),smpr(x,f01))
-t41:=isf(1to(xp1),cx,f,<xout(xp1)>s,xout(xp1),case1):is(<xout(xp1)>g(xp1,s,f),<xout(xp1)>f)
-t42:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q)
-t43:=isf(cx,cx,<smpr(x,g1)>q,<xout(xp1)>g(xp1,s,f),<xout(xp1)>f,t41):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q)
-t44:=isf(cx,cx,[t:cx]<<xout(xp1)>f><t>q,smpr(x,g1),smpr(x,f01),t40):is(<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q)
-t45:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><smpr(x,f01)>q,satz278(x,f)):is(<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f))
-t46:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f),t42,t43,t44,t45):prop1(xp1,s,f)
-b@1px:=pl"n"(1,x):nat
-[case2:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))][u:1to(x)]
-u3:=right1to(1,x,u):1to(1px)
-case2@t47:=lessisi2"n"(1px,xp1,compl"n"(1,x)):lessis"n"(1px,xp1)
-s02:=left(1to(xp1),xp1,1px,t47,s):[t:1to(1px)]1to(xp1)
-u@n3:=inn(xp1,<u3>s02):nat
-[i:is"n"(n3,1)]
-t48:=tr3is(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),1out(xp1),<1out(xp1)>s,isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),1,satz24a(xp1),i),symis(1to(xp1),<1out(xp1)>s,1out(xp1),case2)):is"e"(1to(xp1),<u3>s02,<1out(xp1)>s)
-t49:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3),1out(xp1),t48):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
-t50:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t49):is"n"(inn(1px,u3),1)
-t51:=isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))):is"n"(pl"n"(1,inn(x,u)),inn(1px,u3))
-t52:=ismore1"n"(pl"n"(1,inn(x,u)),inn(1px,u3),1,t51,satz18(1,inn(x,u))):more"n"(inn(1px,u3),1)
-t53:=<t50>ec3e21(is"n"(inn(1px,u3),1),more"n"(inn(1px,u3),1),less"n"(inn(1px,u3),1),satz10b(inn(1px,u3),1),t52):con
-u@t54:=ore1(more"n"(n3,1),is"n"(n3,1),satz24(n3),[t:is"n"(n3,1)]t53(t)):more"n"(n3,1)
-nm1:=mn"n"(n3,1,t54):nat
-t54a:=islessis1"n"(n3,pl"n"(nm1,1),xp1,th1c"n.mn"(n3,1,t54),1top(xp1,<u3>s02)):lessis"n"(pl"n"(nm1,1),xp1)
-t55:=th9"l.or"(less"n"(pl"n"(nm1,1),xp1),is"n"(pl"n"(nm1,1),xp1),less"n"(nm1,x),is"n"(nm1,x),t54a,[t:less"n"(pl"n"(nm1,1),xp1)]satz20c(nm1,x,1,t),[t:is"n"(pl"n"(nm1,1),xp1)]satz20b(nm1,x,1,t)):lessis"n"(nm1,x)
-w3:=outn(x,nm1,t55):1to(x)
-case2@s03:=[t:1to(x)]w3(t):[t:1to(x)]1to(x)
-u@[v:1to(x)][i:is"e"(1to(x),w3(u),w3(v))]
-t56:=isoutne(x,nm1(u),t55(u),nm1(v),t55(v),i):is"n"(nm1(u),nm1(v))
-t57:=tr3is(nat,n3(u),pl"n"(nm1(u),1),pl"n"(nm1(v),1),n3(v),th1c"n.mn"(n3(u),1,t54(u)),ispl1"n"(nm1(u),nm1(v),1,t56),th1d"n.mn"(n3(v),1,t54(v))):is"n"(n3(u),n3(v))
-t58:=isinne(xp1,<u3(u)>s02,<u3(v)>s02,t57):is"e"(1to(xp1),<u3(u)>s02,<u3(v)>s02)
-t59:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)),t58):is"e"(1to(xp1),left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)))
-t60:=thleft1(xp1,1px,t47,u3(u),u3(v),t59):is"e"(1to(1px),u3(u),u3(v))
-t61:=thright1(1,x,u,v,t60):is"e"(1to(x),u,v)
-case2@s04:=left(1to(xp1),xp1,1px,t47,invf(1to(xp1),1to(xp1),s,b)):[t:1to(1px)]1to(xp1)
-u@u4:=<u3>s04:1to(xp1)
-n4:=inn(xp1,u4):nat
-[i:is"n"(n4,1)]
-t62:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),1out(xp1),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),1,satz24a(xp1),i)):is"e"(1to(xp1),u4,1out(xp1))
-t63:=tr3is(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<1out(xp1)>s,1out(xp1),thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,1out(xp1),t62),case2):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
-t64:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t63):is"n"(inn(1px,u3),1)
-t65:=tris(nat,pl"n"(1,inn(x,u)),inn(1px,u3),1,isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),t64):is"n"(pl"n"(1,inn(x,u)),1)
-t66:=<t65>ec3e21(is"n"(pl"n"(1,inn(x,u)),1),more"n"(pl"n"(1,inn(x,u)),1),less"n"(pl"n"(1,inn(x,u)),1),satz10b(pl"n"(1,inn(x,u)),1),satz18(1,inn(x,u))):con
-u@t67:=ore1(more"n"(n4,1),is"n"(n4,1),satz24(n4),[t:is"n"(n4,1)]t66(t)):more"n"(n4,1)
-nm2:=mn"n"(n4,1,t67):nat
-t68:=islessis1"n"(n4,pl"n"(nm2,1),xp1,th1c"n.mn"(n4,1,t67),1top(xp1,u4)):lessis"n"(pl"n"(nm2,1),xp1)
-t69:=th9"l.or"(less"n"(pl"n"(nm2,1),xp1),is"n"(pl"n"(nm2,1),xp1),less"n"(nm2,x),is"n"(nm2,x),t68,[t:less"n"(pl"n"(nm2,1),xp1)]satz20c(nm2,x,1,t),[t:is"n"(pl"n"(nm2,1),xp1)]satz20b(nm2,x,1,t)):lessis"n"(nm2,x)
-w4:=outn(x,nm2,t69):1to(x)
-t70:=isinoutn(x,nm2,t69):is"n"(nm2,inn(x,w4))
-t71:=tr3is(nat,n4,pl"n"(1,nm2),pl"n"(1,inn(x,w4)),inn(1px,u3(w4)),th1a"n.mn"(n4,1,t67),ispl2"n"(nm2,inn(x,w4),1,t70),isinoutn(1px,pl"n"(1,inn(x,w4)),satz19o(inn(x,w4),x,1,1top(x,w4)))):is"n"(n4,inn(1px,u3(w4)))
-t72:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),left1to(xp1,1px,t47,u3(w4)),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),inn(1px,u3(w4)),trlessis"n"(inn(1px,u3(w4)),1px,xp1,1top(1px,u3(w4)),t47),t71)):is"e"(1to(xp1),u4,left1to(xp1,1px,t47,u3(w4)))
-t73:=tris(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<u3(w4)>s02,thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,left1to(xp1,1px,t47,u3(w4)),t72)):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),<u3(w4)>s02)
-t74:=tr3is(nat,pl"n"(1,inn(x,u)),inn(1px,u3),inn(xp1,left1to(xp1,1px,t47,u3)),n3(w4),isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),isinoutn(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47)),isinni(xp1,left1to(xp1,1px,t47,u3),<u3(w4)>s02,t73)):is"n"(pl"n"(1,inn(x,u)),n3(w4))
-t75:=th1e"n.mn"(n3(w4),1,inn(x,u),t54(w4),t74):is"n"(inn(x,u),nm1(w4))
-t76:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w3(w4),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),nm1(w4),t55(w4),t75)):is"e"(1to(x),u,w3(w4))
-t77:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w3(t)),w4,t76):image(1to(x),1to(x),s03,u)
-case2@t78:=andi(injective(1to(x),1to(x),s03),surjective(1to(x),1to(x),s03),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s03,<u>s03)]t61(t,u,v),[t:1to(x)]t77(t)):bijective(1to(x),1to(x),s03)
-f02:=left(cx,xp1,1px,t47,f):[t:1to(1px)]cx
-f03:=right(cx,1,x,f02):[t:1to(x)]cx
-t79:=<t78><f03><s03>p:prop1(s03,f03)
-g3:=left(cx,xp1,1px,t47,g(xp1,s,f)):[t:1to(1px)]cx
-g4:=right(cx,1,x,g3):[t:1to(x)]cx
-g5:=g(x,s03,f03):[t:1to(x)]cx
-u@t80:=tr3is(nat,n3,pl"n"(1,nm1),pl"n"(1,inn(x,w3)),inn(1px,right1to(1,x,w3)),th1a"n.mn"(n3,1,t54),ispl2"n"(nm1,inn(x,w3),1,isinoutn(x,nm1,t55)),isinoutn(1px,pl"n"(1,inn(x,w3)),satz19o(inn(x,w3),x,1,1top(x,w3)))):is"n"(n3,inn(1px,right1to(1,x,w3)))
-t81:=tris(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),left1to(xp1,1px,t47,right1to(1,x,w3)),isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),inn(1px,right1to(1,x,w3)),trlessis"n"(inn(1px,right1to(1,x,w3)),1px,xp1,1top(1px,right1to(1,x,w3)),t47),t80)):is"e"(1to(xp1),<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)))
-t82:=isf(1to(xp1),cx,f,<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)),t81):is(<u>g4,<u>g5)
-case2@t83:=fisi(1to(x),cx,g4,g5,[t:1to(x)]t82(t)):is"e"([t:1to(x)]cx,g4,g5)
-t85:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g4,g5,t83):is(smpr(x,g4),smpr(x,g5))
-t86:=tris(cx,smpr(x,g4),smpr(x,g5),smpr(x,f03),t85,t79):is(smpr(x,g4),smpr(x,f03))
-t87:=lessisi1"n"(1,1px,satz18a(1,x)):lessis"n"(1,1px)
-g6:=left(cx,1px,1,t87,g3):[t:1to(1)]cx
-f04:=left(cx,1px,1,t87,f02):[t:1to(1)]cx
-t87a:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-1d:=left1to(1px,1,t87,xout(1)):1to(1px)
-t87b:=isinoutn(1px,inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,1px,1top(1,xout(1)),t87)):is"n"(inn(1,xout(1)),inn(1px,1d))
-t88:=tris(nat,1,inn(1,xout(1)),inn(1px,1d),t87a,t87b):is"n"(1,inn(1px,1d))
-1e:=left1to(xp1,1px,t47,1d):1to(xp1)
-t88a:=isoutni(xp1,1,satz24a(xp1),inn(1px,1d),trlessis"n"(inn(1px,1d),1px,xp1,1top(1px,1d),t47),t88):is"e"(1to(xp1),1out(xp1),1e)
-t88b:=isf(1to(xp1),1to(xp1),s,1e,1out(xp1),symis(1to(xp1),1out(xp1),1e,t88a)):is"e"(1to(xp1),<1e>s,<1out(xp1)>s)
-t89:=tr3is(1to(xp1),<1e>s,<1out(xp1)>s,1out(xp1),1e,t88b,case2,t88a):is"e"(1to(xp1),<1e>s,1e)
-t89a:=tr3is(cx,smpr(1,g6),<xout(1)>g6,<xout(1)>f04,smpr(1,f04),satz277(g6),isf(1to(xp1),cx,f,<1e>s,1e,t89),symis(cx,smpr(1,f04),<xout(1)>f04,satz277(f04))):is(smpr(1,g6),smpr(1,f04))
-t90:=satz281(1,x,g3):is(smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q)
-t91:=isf(cx,cx,<smpr(1,g6)>q,smpr(x,g4),smpr(x,f03),t86):is(<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q)
-t92:=isf(cx,cx,[t:cx]<smpr(x,f03)><t>q,smpr(1,g6),smpr(1,f04),t89a):is(<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q)
-t93:=symis(cx,smpr(1px,f02),<smpr(x,f03)><smpr(1,f04)>q,satz281(1,x,f02)):is(<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02))
-t94:=tr4is(cx,smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02),t90,t91,t92,t93):is(smpr(1px,g3),smpr(1px,f02))
-t95:=issmpr(xp1,f,1px,compl"n"(1,x)):is(smpr(1px,f02),smpr(xp1,f))
-t96:=symis(cx,smpr(1px,g3),smpr(xp1,g(xp1,s,f)),issmpr(xp1,g(xp1,s,f),1px,compl"n"(1,x))):is(smpr(xp1,g(xp1,s,f)),smpr(1px,g3))
-t97:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(1px,g3),smpr(1px,f02),smpr(xp1,f),t96,t94,t95):prop1(xp1,s,f)
-b@[not1:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))][not2:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]
-a0:=<1out(xp1)>s:1to(xp1)
-b0:=<1out(xp1)>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
-t98:=thinvf2(1to(xp1),1to(xp1),s,b,1out(xp1)):is"e"(1to(xp1),1out(xp1),<b0>s)
-t99:=not2:not(is"e"(1to(xp1),a0,1out(xp1)))
-t100:=symnotis(1to(xp1),<1out(xp1)>s,<b0>s,th3"e.notis"(1to(xp1),<1out(xp1)>s,1out(xp1),<b0>s,not2,t98)):not(is"e"(1to(xp1),<b0>s,<1out(xp1)>s))
-t101:=th3"l.imp"(is"e"(1to(xp1),b0,1out(xp1)),is"e"(1to(xp1),<b0>s,<1out(xp1)>s),t100,[t:is"e"(1to(xp1),b0,1out(xp1))]isf(1to(xp1),1to(xp1),s,b0,1out(xp1),t)):not(is"e"(1to(xp1),b0,1out(xp1)))
-s1:=changef(1to(xp1),1to(xp1),s,1out(xp1),b0):[t:1to(xp1)]1to(xp1)
-[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
-t102:=changef1(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,<b0>s)
-t103:=tris2(1to(xp1),<u>s1,1out(xp1),<b0>s,t102,t98):is"e"(1to(xp1),<u>s1,1out(xp1))
-u@[i:is"e"(1to(xp1),u,b0)]
-t104:=changef2(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,a0)
-u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
-t105:=changef3(1to(xp1),1to(xp1),s,1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
-not2@t106:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),b0,b):bijective(1to(xp1),1to(xp1),s1)
-[alpha:not(is"e"(1to(xp1),a0,xout(xp1)))]
-s2:=wissel(1to(xp1),1out(xp1),a0):[t:1to(xp1)]1to(xp1)
-t107:=th3"e.wissel"(1to(xp1),1out(xp1),a0):bijective(1to(xp1),1to(xp1),s2)
-[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
-t108:=iswissel1(1to(xp1),1out(xp1),a0,<u>s1,t103(u,i)):is"e"(1to(xp1),<<u>s1>s2,a0)
-t109:=tris2(1to(xp1),<u>s,<<u>s1>s2,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t108):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-u@[i:is"e"(1to(xp1),u,b0)]
-t110:=iswissel2(1to(xp1),1out(xp1),a0,<u>s1,t104(u,i)):is"e"(1to(xp1),<<u>s1>s2,1out(xp1))
-t111:=tris2(1to(xp1),<u>s,<<u>s1>s2,1out(xp1),tris2(1to(xp1),<u>s,1out(xp1),<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),t98),t110):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))][i:is"e"(1to(xp1),<u>s1,1out(xp1))]
-t112:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,1out(xp1),tris2(1to(xp1),<u>s1,<1out(xp1)>s1,1out(xp1),i,t103(1out(xp1),refis(1to(xp1),1out(xp1))))):is"e"(1to(xp1),u,1out(xp1))
-o@t113:=th3"l.imp"(is"e"(1to(xp1),<u>s1,1out(xp1)),is"e"(1to(xp1),u,1out(xp1)),n,[t:is"e"(1to(xp1),<u>s1,1out(xp1))]t112(t)):not(is"e"(1to(xp1),<u>s1,1out(xp1)))
-[i:is"e"(1to(xp1),<u>s1,a0)]
-t114:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,b0,tris2(1to(xp1),<u>s1,<b0>s1,a0,i,t104(b0,refis(1to(xp1),b0)))):is"e"(1to(xp1),u,b0)
-o@t115:=th3"l.imp"(is"e"(1to(xp1),<u>s1,a0),is"e"(1to(xp1),u,b0),o,[t:is"e"(1to(xp1),<u>s1,a0)]t114(t)):not(is"e"(1to(xp1),<u>s1,a0))
-t116:=iswissel3(1to(xp1),1out(xp1),a0,<u>s1,t113,t115):is"e"(1to(xp1),<<u>s1>s2,<u>s1)
-t117:=symis(1to(xp1),<<u>s1>s2,<u>s,tris(1to(xp1),<<u>s1>s2,<u>s1,<u>s,t116,t105(u,n,o))):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-n@t118:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,b0)]t111(t),[t:not(is"e"(1to(xp1),u,b0))]t117(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-u@t119:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,1out(xp1))]t109(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t118(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-alpha@t120:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s1>s2,[t:1to(xp1)]t119(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s1>s2)
-not2@t121:=t103(1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s1,1out(xp1))
-t121a:=ec3e21(is"n"(xp1,1),more"n"(xp1,1),less"n"(xp1,1),satz10b(xp1,1),ismore1"n"(1px,xp1,1,compl"n"(1,x),satz18(1,x))):nis"n"(xp1,1)
-t122:=th3"l.imp"(is"e"(1to(xp1),xout(xp1),1out(xp1)),is"n"(xp1,1),t121a,[t:is"e"(1to(xp1),xout(xp1),1out(xp1))]isoutne(xp1,xp1,lessisi3(xp1),1,satz24a(xp1),t)):not(is"e"(1to(xp1),xout(xp1),1out(xp1)))
-alpha@t123:=symnotis(1to(xp1),a0,xout(xp1),alpha):not(is"e"(1to(xp1),xout(xp1),a0))
-t124:=iswissel3(1to(xp1),1out(xp1),a0,xout(xp1),t122,t123):is"e"(1to(xp1),<xout(xp1)>s2,xout(xp1))
-t125:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s1>s2,t120):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))))
-t126:=t97(s1,g(xp1,s2,f),t106,t121):is(smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)))
-t127:=t46(s2,f,t107,t124):is(smpr(xp1,g(xp1,s2,f)),smpr(xp1,f))
-t128:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)),smpr(xp1,f),t125,t126,t127):prop1(xp1,s,f)
-not2@[i3:is"e"(1to(xp1),a0,xout(xp1))][beta:not(is"e"(1to(xp1),b0,xout(xp1)))]
-s3:=wissel(1to(xp1),1out(xp1),b0):[t:1to(xp1)]1to(xp1)
-t129:=th3"e.wissel"(1to(xp1),1out(xp1),b0):bijective(1to(xp1),1to(xp1),s3)
-[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
-t130:=t104(<u>s3,iswissel1(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,a0)
-t131:=tris2(1to(xp1),<u>s,<<u>s3>s1,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t130):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-u@[i:is"e"(1to(xp1),u,b0)]
-t132:=t103(<u>s3,iswissel2(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,1out(xp1))
-t133:=tris2(1to(xp1),<u>s,<<u>s3>s1,<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),tris(1to(xp1),<<u>s3>s1,1out(xp1),<b0>s,t132,t98)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
-t134:=iswissel3(1to(xp1),1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s3,u)
-t135:=isf(1to(xp1),1to(xp1),s1,<u>s3,u,t134):is"e"(1to(xp1),<<u>s3>s1,<u>s1)
-t136:=t105(u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
-t139:=symis(1to(xp1),<<u>s3>s1,<u>s,tris(1to(xp1),<<u>s3>s1,<u>s1,<u>s,t135,t136)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-n@t140:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,b0)]t133(t),[t:not(is"e"(1to(xp1),u,b0))]t139(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-u@t141:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,1out(xp1))]t131(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t140(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-beta@t142:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s3>s1,[t:1to(xp1)]t141(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s3>s1)
-t143:=symnotis(1to(xp1),b0,xout(xp1),beta):not(is"e"(1to(xp1),xout(xp1),b0))
-t144:=iswissel3(1to(xp1),1out(xp1),b0,xout(xp1),t122,t143):is"e"(1to(xp1),<xout(xp1)>s3,xout(xp1))
-t145:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s3>s1,t142):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))))
-t146:=t46(s3,g(xp1,s1,f),t129,t144):is(smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)))
-t147:=t97(s1,f,t106,t121):is(smpr(xp1,g(xp1,s1,f)),smpr(xp1,f))
-t148:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)),smpr(xp1,f),t145,t146,t147):prop1(xp1,s,f)
-i3@[gamma:is"e"(1to(xp1),b0,xout(xp1))][i:is"n"(x,1)]
-t149:=ispl1"n"(1,x,1,symis(nat,x,1,i)):is"n"(2,xp1)
-t150:=lessisi2"n"(2,xp1,t149):lessis"n"(2,xp1)
-f05:=left(cx,xp1,2,t150,f):[t:1to(2)]cx
-s05:=left(1to(xp1),xp1,2,t150,s):[t:1to(2)]1to(xp1)
-g7:=left(cx,xp1,2,t150,g(xp1,s,f)):[t:1to(2)]cx
-t151:=issmpr(xp1,f,2,t149):is(smpr(2,f05),smpr(xp1,f))
-t152:=issmpr(xp1,g(xp1,s,f),2,t149):is(smpr(2,g7),smpr(xp1,g(xp1,s,f)))
-t153:=satz280(f05):is(smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q)
-t154:=satz280(g7):is(smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q)
-t155:=tris1(nat,inn(2,xout(2)),xp1,2,isinoutn(2,2,lessisi3(2)),t149):is"n"(inn(2,xout(2)),xp1)
-t156:=isoutni(xp1,inn(2,xout(2)),trlessis"n"(inn(2,xout(2)),2,xp1,1top(2,xout(2)),t150),xp1,lessisi3(xp1),t155):is"e"(1to(xp1),left1to(xp1,2,t150,xout(2)),xout(xp1))
-t157:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,xout(2)),xout(xp1),t156):is"e"(1to(xp1),<xout(2)>s05,<xout(xp1)>s)
-t158:=symis(nat,1,inn(2,1out(2)),isinoutn(2,1,satz24a(2))):is"n"(inn(2,1out(2)),1)
-t159:=isoutni(xp1,inn(2,1out(2)),trlessis"n"(inn(2,1out(2)),2,xp1,1top(2,1out(2)),t150),1,satz24a(xp1),t158):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1))
-t160:=tr3is(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1),<b0>s,<xout(xp1)>s,t159,t98,isf(1to(xp1),1to(xp1),s,b0,xout(xp1),gamma)):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),<xout(xp1)>s)
-t161:=tris2(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)),<xout(xp1)>s,t157,t160):is"e"(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)))
-t163:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,1out(2)),1out(xp1),t159):is"e"(1to(xp1),<1out(2)>s05,<1out(xp1)>s)
-t164:=tris(1to(xp1),<1out(2)>s05,<1out(xp1)>s,xout(xp1),t163,i3):is"e"(1to(xp1),<1out(2)>s05,xout(xp1))
-t165:=tris2(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)),xout(xp1),t164,t156):is"e"(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)))
-t166:=isf(1to(xp1),cx,f,<xout(2)>s05,left1to(xp1,2,t150,1out(2)),t161):is(<xout(2)>g7,<1out(2)>f05)
-t167:=isf(1to(xp1),cx,f,<1out(2)>s05,left1to(xp1,2,t150,xout(2)),t165):is(<1out(2)>g7,<xout(2)>f05)
-t168:=isf(cx,cx,<<1out(2)>g7>q,<xout(2)>g7,<1out(2)>f05,t166):is(<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q)
-t169:=comq(c,<1out(2)>g7,<1out(2)>f05):is(<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q)
-t170:=isf(cx,cx,<<1out(2)>f05>q,<1out(2)>g7,<xout(2)>f05,t167):is(<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q)
-t171:=tr4is(cx,smpr(xp1,g(xp1,s,f)),smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q,symis(cx,smpr(2,g7),smpr(xp1,g(xp1,s,f)),t152),t154,t168,t169):is(smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q)
-t172:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q,smpr(2,f05),smpr(xp1,f),t171,t170,symis(cx,smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q,t153),t151):prop1(xp1,s,f)
-trivial:=t172:prop1(xp1,s,f)
-gamma@[n:nis"n"(x,1)]
-t173:=ore1(more"n"(x,1),is"n"(x,1),satz24(x),n):more"n"(x,1)
-xm1:=mn"n"(x,1,t173):nat
-s4:=changef(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1)):[t:1to(xp1)]1to(xp1)
-t174:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),b):bijective(1to(xp1),1to(xp1),s4)
-t175:=changef2(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),xout(xp1),refis(1to(xp1),xout(xp1))):is"e"(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s)
-t176:=symis(1to(xp1),a0,xout(xp1),i3):is"e"(1to(xp1),xout(xp1),<1out(xp1)>s)
-t177:=tris2(1to(xp1),<xout(xp1)>s4,xout(xp1),<1out(xp1)>s,t175,t176):is"e"(1to(xp1),<xout(xp1)>s4,xout(xp1))
-t178:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
-g8:=left(cx,xp1,x,t178,g(xp1,s,f)):[t:1to(x)]cx
-t179:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q)
-t180:=th1b"n.mn"(x,1,t173):is"n"(pl"n"(1,xm1),x)
-t181:=lessisi2"n"(pl"n"(1,xm1),x,t180):lessis"n"(pl"n"(1,xm1),x)
-g9:=left(cx,x,pl"n"(1,xm1),t181,g8):[t:1to(pl"n"(1,xm1))]cx
-t182:=symis(cx,smpr(pl"n"(1,xm1),g9),smpr(x,g8),issmpr(x,g8,pl"n"(1,xm1),t180)):is(smpr(x,g8),smpr(pl"n"(1,xm1),g9))
-g10:=right(cx,1,xm1,g9):[t:1to(xm1)]cx
-t183:=lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)):lessis"n"(1,pl"n"(1,xm1))
-g11:=left(cx,pl"n"(1,xm1),1,t183,g9):[t:1to(1)]cx
-t184:=satz281(a,1,xm1,g9):is(smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q)
-t185:=satz277(g11):is(smpr(1,g11),<xout(1)>g11)
-t186:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-1a:=left1to(pl"n"(1,xm1),1,t183,xout(1)):1to(pl"n"(1,xm1))
-t187:=isinoutn(pl"n"(1,xm1),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,pl"n"(1,xm1),1top(1,xout(1)),t183)):is"n"(inn(1,xout(1)),inn(pl"n"(1,xm1),1a))
-1b:=left1to(x,pl"n"(1,xm1),t181,1a):1to(x)
-t188:=isinoutn(x,inn(pl"n"(1,xm1),1a),trlessis"n"(inn(pl"n"(1,xm1),1a),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),1a),t181)):is"n"(inn(pl"n"(1,xm1),1a),inn(x,1b))
-t189:=tr3is(nat,1,inn(1,xout(1)),inn(pl"n"(1,xm1),1a),inn(x,1b),t186,t187,t188):is"n"(1,inn(x,1b))
-1c:=left1to(xp1,x,t178,1b):1to(xp1)
-t190:=isoutni(xp1,1,satz24a(xp1),inn(x,1b),trlessis"n"(inn(x,1b),x,xp1,1top(x,1b),t178),t189):is"e"(1to(xp1),1out(xp1),1c)
-t191:=isf(1to(xp1),cx,g(xp1,s,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s,f),<xout(1)>g11)
-t192:=tris2(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(1)>g11,t185,t191):is(smpr(1,g11),<1out(xp1)>g(xp1,s,f))
-t193:=symis(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s,t175):is"e"(1to(xp1),<1out(xp1)>s,<xout(xp1)>s4)
-t194:=isf(1to(xp1),cx,f,<1out(xp1)>s,<xout(xp1)>s4,t193):is(<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f))
-t195:=tris(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f),t192,t194):is(smpr(1,g11),<xout(xp1)>g(xp1,s4,f))
-t196:=isf(cx,cx,[t:cx]<smpr(xm1,g10)><t>q,smpr(1,g11),<xout(xp1)>g(xp1,s4,f),t195):is(<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
-t197:=tr3is(cx,smpr(x,g8),smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t182,t184,t196):is(smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
-t198:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s,f)><t>q,smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t197):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q)
-t199:=assq1(a,<xout(xp1)>g(xp1,s4,f),smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q)
-t200:=comq(c,<xout(xp1)>g(xp1,s4,f),<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q):is(<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
-g12:=left(cx,xp1,x,t178,g(xp1,s4,f)):[t:1to(x)]cx
-g13:=left(cx,x,pl"n"(1,xm1),t181,g12):[t:1to(pl"n"(1,xm1))]cx
-g14:=right(cx,1,xm1,g13):[t:1to(xm1)]cx
-g15:=left(cx,pl"n"(1,xm1),1,lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)),g13):[t:1to(1)]cx
-t201:=satz278(x,g(xp1,s4,f)):is(smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
-t202:=symis(cx,smpr(pl"n"(1,xm1),g13),smpr(x,g12),issmpr(x,g12,pl"n"(1,xm1),t180)):is(smpr(x,g12),smpr(pl"n"(1,xm1),g13))
-t203:=satz281(a,1,xm1,g13):is(smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q)
-t204:=satz277(g15):is(smpr(1,g15),<xout(1)>g15)
-t205:=isf(1to(xp1),cx,g(xp1,s4,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s4,f),<xout(1)>g15)
-t206:=tris2(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(1)>g15,t204,t205):is(smpr(1,g15),<1out(xp1)>g(xp1,s4,f))
-t207:=changef1(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s4,<xout(xp1)>s)
-t208:=isf(1to(xp1),cx,f,<1out(xp1)>s4,<xout(xp1)>s,t207):is(<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f))
-t209:=tris(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f),t206,t208):is(smpr(1,g15),<xout(xp1)>g(xp1,s,f))
-t210:=isf(cx,cx,[t:cx]<smpr(xm1,g14)><t>q,smpr(1,g15),<xout(xp1)>g(xp1,s,f),t209):is(<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-t211:=tr3is(cx,smpr(x,g12),smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t202,t203,t210):is(smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-[u:1to(xm1)]
-ua:=right1to(1,xm1,u):1to(pl"n"(1,xm1))
-ub:=left1to(x,pl"n"(1,xm1),t181,ua):1to(x)
-uc:=left1to(xp1,x,t178,ub):1to(xp1)
-[i:is"e"(1to(xp1),uc,xout(xp1))]
-t212:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),xp1,lessisi3(xp1),i):is"n"(inn(x,ub),xp1)
-t213:=satz16a(inn(x,ub),x,xp1,1top(x,ub),satz18a(x,1)):less"n"(inn(x,ub),xp1)
-t214:=<t212>ec3e31(is"n"(inn(x,ub),xp1),more"n"(inn(x,ub),xp1),less"n"(inn(x,ub),xp1),satz10b(inn(x,ub),xp1),t213):con
-u@t215:=[t:is"e"(1to(xp1),uc,xout(xp1))]t214(t):not(is"e"(1to(xp1),uc,xout(xp1)))
-[i:is"e"(1to(xp1),uc,1out(xp1))]
-t216:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),1,satz24a(xp1),i):is"n"(inn(x,ub),1)
-t217:=isinoutn(x,inn(pl"n"(1,xm1),ua),trlessis"n"(inn(pl"n"(1,xm1),ua),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),ua),t181)):is"n"(inn(pl"n"(1,xm1),ua),inn(x,ub))
-t218:=isinoutn(pl"n"(1,xm1),pl"n"(1,inn(xm1,u)),satz19o(inn(xm1,u),xm1,1,1top(xm1,u))):is"n"(pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua))
-t219:=tr3is(nat,pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua),inn(x,ub),1,t218,t217,t216):is"n"(pl"n"(1,inn(xm1,u)),1)
-t220:=satz18(1,inn(xm1,u)):more"n"(pl"n"(1,inn(xm1,u)),1)
-t221:=<t219>ec3e21(is"n"(pl"n"(1,inn(xm1,u)),1),more"n"(pl"n"(1,inn(xm1,u)),1),less"n"(pl"n"(1,inn(xm1,u)),1),satz10b(pl"n"(1,inn(xm1,u)),1),t220):con
-u@t222:=[t:is"e"(1to(xp1),uc,1out(xp1))]t221(t):not(is"e"(1to(xp1),uc,1out(xp1)))
-t223:=changef3(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),uc,t222,t215):is"e"(1to(xp1),<uc>s4,<uc>s)
-t224:=isf(1to(xp1),cx,f,<uc>s4,<uc>s,t223):is(<u>g14,<u>g10)
-n@t225:=fisi(1to(xm1),cx,g10,g14,[t:1to(xm1)]symis(cx,<t>g14,<t>g10,t224(t))):is"e"([t:1to(xm1)]cx,g10,g14)
-t226:=isf([t:1to(xm1)]cx,cx,[u:[t:1to(xm1)]cx]smpr(xm1,u),g10,g14,t225):is(smpr(xm1,g10),smpr(xm1,g14))
-t227:=comq(c,smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q)
-t228:=isf(cx,cx,<<xout(xp1)>g(xp1,s,f)>q,smpr(xm1,g10),smpr(xm1,g14),t226):is(<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-t229:=tris(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t227,t228):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-t230:=tris2(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t229,t211):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12))
-t231:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s4,f)><t>q,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),t230):is(<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
-t232:=symis(cx,smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,t201):is(<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)))
-t233:=t46(s4,f,t174,t177):is(smpr(xp1,g(xp1,s4,f)),smpr(xp1,f))
-t234:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,t179,t198,t199,t200):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
-t235:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)),smpr(xp1,f),t234,t231,t232,t233):prop1(xp1,s,f)
-gamma@t236:=th1"l.imp"(is"n"(x,1),prop1(xp1,s,f),[t:is"n"(x,1)]t172(t),[t:not(is"n"(x,1))]t235(t)):prop1(xp1,s,f)
-i3@t237:=th1"l.imp"(is"e"(1to(xp1),b0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),b0,xout(xp1))]t236(t),[t:not(is"e"(1to(xp1),b0,xout(xp1)))]t148(t)):prop1(xp1,s,f)
-not2@t238:=th1"l.imp"(is"e"(1to(xp1),a0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),a0,xout(xp1))]t237(t),[t:not(is"e"(1to(xp1),a0,xout(xp1)))]t128(t)):prop1(xp1,s,f)
-not1@t239:=th1"l.imp"(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))]t97(t),[t:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]t238(t)):prop1(xp1,s,f)
-b@t240:=th1"l.imp"(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))]t46(t),[t:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))]t239(t)):prop1(xp1,s,f)
-p@t241:=[u:[t:1to(xp1)]1to(xp1)][v:[t:1to(xp1)]cx][w:bijective(1to(xp1),1to(xp1),u)]t240(u,v,w):prop2(xp1)
-t242:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t241,satz4a(x)):prop2(<x>suc)
-x@t243:=induction([t:nat]prop2(t),t6,[t:nat][u:prop2(t)]t242(t,u),x):prop2(x)
--8283
-satz283:=<b><f><s>t243".8283":is(smpr(x,[t:1to(x)]<<t>s>f),smpr(x,f))
-@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
-shiftl:=shiftl"r"(x,ix,y,iy,ly):nat
-[n:1to(shiftl)]
-shiftr:=shiftr"r"(x,ix,y,iy,ly,n):real
-intshiftr:=intshiftr"r"(x,ix,y,iy,ly,n):intrl(shiftr)
-shiftrls:=shiftrls"r"(x,ix,y,iy,ly,n):lessis(shiftr,x)
-lsshiftr:=lsshiftr"r"(x,ix,y,iy,ly,n):lessis(y,shiftr)
-[m:1to(shiftl)][i:is"r"(shiftr(n),shiftr(m))]
-iseshiftr:=iseshiftr"r"(x,ix,y,iy,ly,n,m,i):is"e"(1to(shiftl),n,m)
-ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
-shiftl1:=shiftl1"r"(x,ix,y,iy,ly,u,a):1to(shiftl)
-shiftinv1:=shiftinv1"r"(x,ix,y,iy,ly,u,a):is"r"(u,shiftr(shiftl1))
-shiftinv2:=shiftinv2"r"(x,ix,y,iy,ly,u,a):is"r"(shiftr(shiftl1),u)
-ly@[f:seq(x,ix,y,iy,ly,cx)]
-shiftf:=shiftf(x,ix,y,iy,ly,cx,f):[t:1to(shiftl)]cx
-[q:[t:cx][u:cx]cx]
-smpri:=smpr(q,shiftl,shiftf):cx
-f@[pi:proofsirrelevant(x,ix,y,iy,ly,cx,f)][q:[t:cx][u:cx]cx][a:assoc(q)][u:real][iu:intrl(u)][l:lessis(y,u)][k:less(u,x)][v:real][iv:intrl(v)][lv:lessis(y,v)][kv:lessis(v,u)]
-+8284
-t1:=lessisi1(v,x,satz172a(v,u,x,kv,k)):lessis(v,x)
--8284
-k@lft:=[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]<t1".8284"(t,v,lt,kt)><lt><v><t>f:[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]cx
-iv@[lv:lessis(pl"r"(u,1rl),v)][kv:lessis(v,x)]
-+*8284
-x@[y:real]
-pl:=pl"r"(x,y):real
-mn:=mn"r"(x,y):real
-x@p1:=pl"r"(x,1rl):real
-kv@t2:=satz190c(u,u,0,1rl,lessisi2(u,u,refis(real,u)),lemma1"r"(1rl,0,satz169a(1rl,natpos(1rl,natrl1)))):less(pl(u,0),p1(u))
-t3:=isless1(pl(u,0),u,p1(u),pl02"r"(u,0,refis(real,0)),t2):less(u,p1(u))
-t4:=lessisi1(y,v,satz172b(y,p1(u),v,satz172a(y,u,p1(u),l,t3),lv)):lessis(y,v)
--8284
-k@rgt:=[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]<kt><t4".8284"(t,v,lt,kt)><v><t>f:[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]cx
-+*8284
-k@t5:=intpl(u,iu,1rl,intrl1):intrl(p1(u))
-t6:=satzr25(u,iu,x,ix,k):lessis(p1(u),x)
-t7:=tr3is(real,pl(mn(p1(u),y),mn(p1(x),p1(u))),pl(mn(p1(x),p1(u)),mn(p1(u),y)),mn(pl(mn(p1(x),p1(u)),p1(u)),y),mn(p1(x),y),compl"r"(mn(p1(u),y),mn(p1(x),p1(u))),asspl2"r"(mn(p1(x),p1(u)),p1(u),m0"r"(y)),ismn1"r"(pl(mn(p1(x),p1(u)),p1(u)),p1(x),y,plmn(p1(x),p1(u)))):is"r"(pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y))
-sxy:=shiftl(x,ix,y,iy,ly):nat
-suy:=shiftl(u,iu,y,iy,l):nat
-sxu:=shiftl(x,ix,p1(u),t5,t6):nat
-t8:=tr4is(real,rlofnt(pl"n"(suy,sxu)),pl(rlofnt(suy),rlofnt(sxu)),pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y),rlofnt(sxy),satzr155a(suy,sxu),ispl12"r"(rlofnt(suy),mn(p1(u),y),rlofnt(sxu),mn(p1(x),p1(u)),isrlnt2(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l)),isrlnt2(mn(p1(x),p1(u)),t6"r.shift"(x,ix,p1(u),t5,t6))),t7,isrlnt1(mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly))):is"r"(rlofnt(pl"n"(suy,sxu)),rlofnt(sxy))
-t9:=isntirl(pl"n"(suy,sxu),sxy,t8):is"n"(pl"n"(suy,sxu),sxy)
-t10:=lessisi2"n"(pl"n"(suy,sxu),sxy,t9):lessis"n"(pl"n"(suy,sxu),sxy)
-f1:=left(cx,sxy,pl"n"(suy,sxu),t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(pl"n"(suy,sxu))]cx
-t11:=issmpr(q,sxy,shiftf(x,ix,y,iy,ly,f),pl"n"(suy,sxu),t9):is(smpr(q,pl"n"(suy,sxu),f1),smpri(x,ix,y,iy,ly,f,q))
-fr:=right(cx,suy,sxu,f1):[t:1to(sxu)]cx
-t12:=lessisi1"n"(suy,pl"n"(suy,sxu),satz18a(suy,sxu)):lessis"n"(suy,pl"n"(suy,sxu))
-fl:=left(cx,pl"n"(suy,sxu),suy,t12,f1):[t:1to(suy)]cx
-t12a:=satz281(q,a,suy,sxu,f1):is(smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q)
-[n:1to(sxu)]
-t13:=isinoutn(pl"n"(suy,sxu),pl"n"(suy,inn(sxu,n)),satz19o(inn(sxu,n),sxu,suy,1top(sxu,n))):is"n"(pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)))
-t14:=isinoutn(sxy,inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),trlessis"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),right1to(suy,sxu,n)),t10)):is"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n))))
-n1:=left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n)):1to(sxy)
-t15:=tris(nat,pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,n1),t13,t14):is"n"(pl"n"(suy,inn(sxu,n)),inn(sxy,n1))
-t16:=isnterl(pl"n"(suy,inn(sxu,n)),inn(sxy,n1),t15):is"r"(rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)))
-t17:=satzr155b(suy,inn(sxu,n)):is"r"(pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))))
-t18:=ispl1"r"(mn(p1(u),y),rlofnt(suy),rlofnt(inn(sxu,n)),isrlnt1(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l))):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))))
-t19:=tr3is(real,pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)),t18,t17,t16):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)))
-t20:=ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)),y,t19):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxy,n1)),y))
-t21:=tr3is(real,pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y),pl(rlofnt(inn(sxu,n)),pl(mn(p1(u),y),y)),pl(rlofnt(inn(sxu,n)),p1(u)),ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y,compl"r"(mn(p1(u),y),rlofnt(inn(sxu,n)))),asspl1"r"(rlofnt(inn(sxu,n)),mn(p1(u),y),y),ispl2"r"(pl(mn(p1(u),y),y),p1(u),rlofnt(inn(sxu,n)),plmn(p1(u),y))):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxu,n)),p1(u)))
-t22:=tris1(real,pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),t20,t21):is"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)))
-t23:=ismn1"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),1rl,t22):is"r"(shiftr(x,ix,y,iy,ly,n1),shiftr(x,ix,p1(u),t5,t6,n))
-t24:=intshiftr(x,ix,y,iy,ly,n1):intrl(shiftr(x,ix,y,iy,ly,n1))
-t25:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,shiftr(x,ix,y,iy,ly,n1))
-t26:=shiftrls(x,ix,y,iy,ly,n1):lessis(shiftr(x,ix,y,iy,ly,n1),x)
-t27:=intshiftr(x,ix,p1(u),t5,t6,n):intrl(shiftr(x,ix,p1(u),t5,t6,n))
-t28:=lsshiftr(x,ix,p1(u),t5,t6,n):lessis(p1(u),shiftr(x,ix,p1(u),t5,t6,n))
-t29:=shiftrls(x,ix,p1(u),t5,t6,n):lessis(shiftr(x,ix,p1(u),t5,t6,n),x)
-t30:=t4(shiftr(x,ix,p1(u),t5,t6,n),t27,t28,t29):lessis(y,shiftr(x,ix,p1(u),t5,t6,n))
-t31:=<t23><t29><t30><t27><shiftr(x,ix,p1(u),t5,t6,n)><t26><t25><t24><shiftr(x,ix,y,iy,ly,n1)>pi:is(<n>fr,<n>shiftf(x,ix,p1(u),t5,t6,rgt))
-k@t32:=fisi(1to(sxu),cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt),[t:1to(sxu)]t31(t)):is"e"([t:1to(sxu)]cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt))
-t33:=isf([t:1to(sxu)]cx,cx,[v:[t:1to(sxu)]cx]smpr(q,sxu,v),fr,shiftf(x,ix,p1(u),t5,t6,rgt),t32):is(smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q))
-t34:=isf(cx,cx,<smpr(q,suy,fl)>q,smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q),t33):is(<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q)
-[n:1to(suy)]
-t35:=isinoutn(pl"n"(suy,sxu),inn(suy,n),trlessis"n"(inn(suy,n),suy,pl"n"(suy,sxu),1top(suy,n),t12)):is"n"(inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)))
-t36:=isinoutn(sxy,inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),trlessis"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),t10)):is"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n))))
-n2:=left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n)):1to(sxy)
-t37:=tris(nat,inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,n2),t35,t36):is"n"(inn(suy,n),inn(sxy,n2))
-t38:=isnterl(inn(suy,n),inn(sxy,n2),t37):is"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)))
-t39:=ispl1"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)),y,t38):is"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y))
-t40:=ismn1"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y),1rl,t39):is"r"(shiftr(u,iu,y,iy,l,n),shiftr(x,ix,y,iy,ly,n2))
-t41:=intshiftr(u,iu,y,iy,l,n):intrl(shiftr(u,iu,y,iy,l,n))
-t42:=lsshiftr(u,iu,y,iy,l,n):lessis(y,shiftr(u,iu,y,iy,l,n))
-t43:=shiftrls(u,iu,y,iy,l,n):lessis(shiftr(u,iu,y,iy,l,n),u)
-t44:=t1(shiftr(u,iu,y,iy,l,n),t41,t42,t43):lessis(shiftr(u,iu,y,iy,l,n),x)
-t45:=intshiftr(x,ix,y,iy,ly,n2):intrl(shiftr(x,ix,y,iy,ly,n2))
-t46:=lsshiftr(x,ix,y,iy,ly,n2):lessis(y,shiftr(x,ix,y,iy,ly,n2))
-t47:=shiftrls(x,ix,y,iy,ly,n2):lessis(shiftr(x,ix,y,iy,ly,n2),x)
-t48:=<t40><t47><t46><t45><shiftr(x,ix,y,iy,ly,n2)><t44><t42><t41><shiftr(u,iu,y,iy,l,n)>pi:is(<n>shiftf(u,iu,y,iy,l,lft),<n>fl)
-t49:=symis(cx,<n>shiftf(u,iu,y,iy,l,lft),<n>fl,t48):is(<n>fl,<n>shiftf(u,iu,y,iy,l,lft))
-k@t50:=fisi(1to(suy),cx,fl,shiftf(u,iu,y,iy,l,lft),[t:1to(suy)]t49(t)):is"e"([t:1to(suy)]cx,fl,shiftf(u,iu,y,iy,l,lft))
-t51:=isf([t:1to(suy)]cx,cx,[v:[t:1to(suy)]cx]smpr(q,suy,v),fl,shiftf(u,iu,y,iy,l,lft),t50):is(smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q))
-t52:=isf(cx,cx,[t:cx]<smpri(x,ix,p1(u),t5,t6,rgt,q)><t>q,smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q),t51):is(<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
-t53:=tr3is(cx,smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,t12a,t34,t52):is(smpr(q,pl"n"(suy,sxu),f1),<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
--8284
-k@satz284:=tris1(cx,smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,smpr(q,pl"n"(suy".8284",sxu".8284"),f1".8284"),t11".8284",t53".8284"):is(smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
-q@[v:real][iv:intrl(v)][w:real][iw:intrl(w)][lw:lessis(pl"r"(y,v),w)][kw:lessis(w,pl"r"(x,v))]
-+8285
-x@[y:real]
-pl:=pl"r"(x,y):real
-mn:=mn"r"(x,y):real
-x@p1:=pl"r"(x,1rl):real
-kw@t1:=th9"l.or"(less(pl(y,v),w),is"r"(pl(y,v),w),less(mn(pl(y,v),v),mn(w,v)),is"r"(mn(pl(y,v),v),mn(w,v)),lw,[t:less(pl(y,v),w)]satz188f(pl(y,v),w,m0"r"(v),t),[t:is"r"(pl(y,v),w)]ismn1"r"(pl(y,v),w,v,t)):lessis(mn(pl(y,v),v),mn(w,v))
-t2:=islessis1(mn(pl(y,v),v),y,mn(w,v),mnpl(y,v),t1):lessis(y,mn(w,v))
-t3:=th9"l.or"(less(w,pl(x,v)),is"r"(w,pl(x,v)),less(mn(w,v),mn(pl(x,v),v)),is"r"(mn(w,v),mn(pl(x,v),v)),kw,[t:less(w,pl(x,v))]satz188f(w,pl(x,v),m0"r"(v),t),[t:is"r"(w,pl(x,v))]ismn1"r"(w,pl(x,v),v,t)):lessis(mn(w,v),mn(pl(x,v),v))
-t4:=islessis2(mn(pl(x,v),v),x,mn(w,v),mnpl(x,v),t3):lessis(mn(w,v),x)
--8285
-iv@sft:=[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]<t4".8285"(t,w,lt,kt)><t2".8285"(t,w,lt,kt)><intmn(t,w,v,iv)><mn"r"(t,v)>f:[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]cx
-+*8285
-iv@t5:=tris(real,m0"r"(pl(y,v)),m0"r"(pl(v,y)),pl(m0"r"(v),m0"r"(y)),ism0"r"(pl(y,v),pl(v,y),compl"r"(y,v)),satz180(v,y)):is"r"(m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)))
-t6:=tr3is(real,mn(pl(1rl,pl(x,v)),v),pl(1rl,mn(pl(x,v),v)),pl(1rl,x),p1(x),asspl1"r"(1rl,pl(x,v),m0"r"(v)),ispl2"r"(mn(pl(x,v),v),x,1rl,mnpl(x,v)),compl"r"(1rl,x)):is"r"(mn(pl(1rl,pl(x,v)),v),p1(x))
-t7:=tr3is(real,mn(p1(pl(x,v)),pl(y,v)),pl(pl(1rl,pl(x,v)),pl(m0"r"(v),m0"r"(y))),mn(mn(pl(1rl,pl(x,v)),v),y),mn(p1(x),y),ispl12"r"(p1(pl(x,v)),pl(1rl,pl(x,v)),m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)),compl"r"(pl(x,v),1rl),t5),asspl2"r"(pl(1rl,pl(x,v)),m0"r"(v),m0"r"(y)),ismn1"r"(mn(pl(1rl,pl(x,v)),v),p1(x),y,t6)):is"r"(mn(p1(pl(x,v)),pl(y,v)),mn(p1(x),y))
-t8:=th9"l.or"(less(y,x),is"r"(y,x),less(pl(y,v),pl(x,v)),is"r"(pl(y,v),pl(x,v)),ly,[t:less(y,x)]satz188f(y,x,v,t),[t:is"r"(y,x)]ispl1"r"(y,x,v,t)):lessis(pl(y,v),pl(x,v))
-s0:=shiftl(x,ix,y,iy,ly):nat
-sv:=shiftl(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8):nat
-t9:=isrlent(mn(p1(pl(x,v)),pl(y,v)),t6"r.shift"(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8),mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly),t7):is"n"(sv,s0)
-t10:=lessisi2"n"(sv,s0,t9):lessis"n"(sv,s0)
-f1:=left(cx,s0,sv,t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(sv)]cx
-t11:=issmpr(q,s0,shiftf(x,ix,y,iy,ly,f),sv,t9):is(smpr(q,sv,f1),smpri(x,ix,y,iy,ly,f,q))
-[n:1to(sv)]
-t12:=isinoutn(s0,inn(sv,n),trlessis"n"(inn(sv,n),sv,s0,1top(sv,n),t10)):is"n"(inn(sv,n),inn(s0,left1to(s0,sv,t10,n)))
-n1:=left1to(s0,sv,t10,n):1to(s0)
-t13:=isnterl(inn(sv,n),inn(s0,n1),t12):is"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)))
-t14:=tris(real,mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(sv,n)),mn(pl(y,v),v)),pl(rlofnt(inn(s0,n1)),y),asspl1"r"(rlofnt(inn(sv,n)),pl(y,v),m0"r"(v)),ispl12"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)),mn(pl(y,v),v),y,t13,mnpl(y,v))):is"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y))
-st0:=shiftr(x,ix,y,iy,ly,n1):real
-stv:=shiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):real
-t15:=tr4is(real,mn(stv,v),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(1rl),m0"r"(v))),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(v),m0"r"(1rl))),mn(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),1rl),st0,asspl1"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(1rl),m0"r"(v)),ispl2"r"(pl(m0"r"(1rl),m0"r"(v)),pl(m0"r"(v),m0"r"(1rl)),pl(rlofnt(inn(sv,n)),pl(y,v)),compl"r"(m0"r"(1rl),m0"r"(v))),asspl2"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(v),m0"r"(1rl)),ismn1"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y),1rl,t14)):is"r"(mn(stv,v),st0)
-t16:=intshiftr(x,ix,y,iy,ly,n1):intrl(st0)
-t17:=shiftrls(x,ix,y,iy,ly,n1):lessis(st0,x)
-t18:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,st0)
-t19:=intshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):intrl(stv)
-t20:=shiftrls(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(stv,pl(x,v))
-t21:=lsshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(pl(y,v),stv)
-t22:=intmn(stv,t19,v,iv):intrl(mn(stv,v))
-t23:=t2(stv,t19,t21,t20):lessis(y,mn(stv,v))
-t24:=t4(stv,t19,t21,t20):lessis(mn(stv,v),x)
-t25:=<t15><t17><t18><t16><st0><t24><t23><t22><mn(stv,v)>pi:is(<n>shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),<n>f1)
-iv@t26:=fisi(1to(sv),cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,[t:1to(sv)]t25(t)):is"e"([t:1to(sv)]cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1)
-t27:=isf([t:1to(sv)]cx,cx,[w:[t:1to(sv)]cx]smpr(q,sv,w),shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,t26):is(smpri(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft,q),smpr(q,sv,f1))
--8285
-iv@lemma285:=t8".8285":lessis(pl"r"(y,v),pl"r"(x,v))
-satz285:=tris(cx,smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpr(q,sv".8285",f1".8285"),smpri(x,ix,y,iy,ly,f,q),t27".8285",t11".8285"):is(smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpri(x,ix,y,iy,ly,f,q))
-ly@[s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][f:seq(x,ix,y,iy,ly,cx)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)]
-us:=<ul><lu><iu><u>s:real
-+8286
-t1:=<ul><lu><iu><u>ins:and3(intrl(us),lessis(y,us),lessis(us,x))
--8286
-inseqe1:=t22"r.shift"(x,ix,y,iy,ly,us,t1".8286"):intrl(us)
-inseqe2:=t23"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(y,us)
-inseqe3:=t24"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(us,x)
-usf:=<inseqe3><inseqe2><inseqe1><us>f:cx
-f@permseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]usf(t,u,v,w):[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]cx
-q@[a:assoc(q)][c:commut(q)][s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][pri:proofsirrelevant(x,ix,y,iy,ly,real,s)][ps:perm(x,ix,y,iy,ly,s)]
-+*8286
-ps@ss:=shiftseq(x,ix,y,iy,ly,s,ins):[t:1to(shiftl)]1to(shiftl)
-t2:=satz283(q,a,c,shiftl,ss,bijshiftseq(x,ix,y,iy,ly,s,ins,pri,ps),shiftf(f)):is(smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)),smpri(f,q))
-[n:1to(shiftl)]
-ns:=us(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):real
-t3:=shiftinv1(ns,t34"r.shift"(x,ix,y,iy,ly,s,ins,n)):is"r"(ns,shiftr(<n>ss))
-t4:=inseqe1(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):intrl(ns)
-t5:=inseqe2(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(y,ns)
-t6:=inseqe3(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(ns,x)
-t7:=intshiftr(<n>ss):intrl(shiftr(<n>ss))
-t8:=lsshiftr(<n>ss):lessis(y,shiftr(<n>ss))
-t9:=shiftrls(<n>ss):lessis(shiftr(<n>ss),x)
-t10:=<t3><t9><t8><t7><shiftr(<n>ss)><t6><t5><t4><ns>pi:is(<n>shiftf(permseq(s,ins,f)),<<n>ss>shiftf(f))
-ps@t11:=fisi(1to(shiftl),cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),[t:1to(shiftl)]t10(t)):is"e"([t:1to(shiftl)]cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f))
-t12:=isf([t:1to(shiftl)]cx,cx,[u:[t:1to(shiftl)]cx]smpr(q,shiftl,u),shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),t11):is(smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)))
--8286
-ps@satz286:=tris(cx,smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss".8286">shiftf(f)),smpri(f,q),t12".8286",t2".8286"):is(smpri(permseq(s,ins,f),q),smpri(f,q))
-@[x:nat][f:[t:1to(x)]cx]
-modf:=[t:1to(x)]pli(mod(<t>f),0):[t:1to(x)]cx
-+8287
-[r:real]
-prop1:=lessis(mod(sum(x,f)),r):'prop'
-prop2:=is(sum(x,modf(f)),pli(r,0)):'prop'
-prop3:=and(prop1,prop2):'prop'
-f@prop4:=some"r"([t:real]prop3(t)):'prop'
-x@prop5:=[u:[t:1to(x)]cx]prop4(u):'prop'
-@[f:[t:1to(1)]cx]
-t1:=satz277([t:cx][u:cx]pl(t,u),f):is(sum(1,f),<xout(1)>f)
-t2:=ismod(sum(1,f),<xout(1)>f,t1):is"r"(mod(sum(1,f)),mod(<xout(1)>f))
-t3:=lessisi2(mod(sum(1,f)),mod(<xout(1)>f),t2):prop1(1,f,mod(<xout(1)>f))
-t4:=satz277([t:cx][u:cx]pl(t,u),modf(1,f)):prop2(1,f,mod(<xout(1)>f))
-t5:=andi(prop1(1,f,mod(<xout(1)>f)),prop2(1,f,mod(<xout(1)>f)),t3,t4):prop3(1,f,mod(<xout(1)>f))
-t6:=somei(real,[t:real]prop3(1,f,t),mod(<xout(1)>f),t5):prop4(1,f)
-@t7:=[u:[t:1to(1)]cx]t6(u):prop5(1)
-x@[p:prop5(x)][f:[t:1to(pl"n"(x,1))]cx]
-t8:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
-lf:=left(cx,pl"n"(x,1),x,t8,f):[t:1to(x)]cx
-[r:real][pr:prop3(lf,r)]
-t9:=ande1(prop1(lf,r),prop2(lf,r),pr):prop1(lf,r)
-t10:=ande2(prop1(lf,r),prop2(lf,r),pr):prop2(lf,r)
-t11:=satz278([t:cx][u:cx]pl(t,u),x,f):is(sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f))
-t12:=ismod(pl(sum(x,lf),<xout(pl"n"(x,1))>f),sum(pl"n"(x,1),f),symis(cx,sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f),t11)):is"r"(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)))
-m:=mod(<xout(pl"n"(x,1))>f):real
-t13:=islessis1(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),t12,satz271(sum(x,lf),<xout(pl"n"(x,1))>f)):lessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m))
-t14:=th9"l.or"(less(mod(sum(x,lf)),r),is"r"(mod(sum(x,lf)),r),less(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),is"r"(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),t9,[t:less(mod(sum(x,lf)),r)]satz188f(mod(sum(x,lf)),r,m,t),[t:is"r"(mod(sum(x,lf)),r)]ispl1"r"(mod(sum(x,lf)),r,m,t)):lessis(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m))
-t15:=trlessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),pl"r"(r,m),t13,t14):prop1(pl"n"(x,1),f,pl"r"(r,m))
-lmf:=left(cx,pl"n"(x,1),x,t8,modf(pl"n"(x,1),f)):[t:1to(x)]cx
-t16:=satz278([t:cx][u:cx]pl(t,u),x,modf(pl"n"(x,1),f)):is(sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)))
-t17:=ispl1(sum(x,lmf),pli(r,0),pli(m,0),t10):is(pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)))
-t18:=plis12a(r,0,m,0):is(pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)))
-t19:=isrecx2(pl"r"(0,0),0,pl"r"(r,m),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0))
-t20:=tr4is(cx,sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0),t16,t17,t18,t19):prop2(pl"n"(x,1),f,pl"r"(r,m))
-t21:=andi(prop1(pl"n"(x,1),f,pl"r"(r,m)),prop2(pl"n"(x,1),f,pl"r"(r,m)),t15,t20):prop3(pl"n"(x,1),f,pl"r"(r,m))
-t22:=somei(real,[t:real]prop3(pl"n"(x,1),f,t),pl"r"(r,m),t21):prop4(pl"n"(x,1),f)
-f@t23:=someapp(real,[t:real]prop3(lf,t),<lf>p,prop4(pl"n"(x,1),f),[t:real][u:prop3(lf,t)]t22(t,u)):prop4(pl"n"(x,1),f)
-p@t25:=[u:[t:1to(pl"n"(x,1))]cx]t23(u):prop5(pl"n"(x,1))
-t26:=isp(nat,[t:nat]prop5(t),pl"n"(x,1),<x>suc,t25,satz4a(x)):prop5(<x>suc)
--8287
-satz287:=<f>induction([t:nat]prop5".8287"(t),t7".8287",[t:nat][u:prop5".8287"(t)]t26".8287"(t,u),x):some"r"([t:real]and(lessis(mod(sum(x,f)),t),is(sum(x,modf(f)),pli(t,0))))
-+8288
-prop1:=is(pli(mod(prod(x,f)),0),prod(x,modf(f))):'prop'
-x@prop2:=[u:[t:1to(x)]cx]prop1(u):'prop'
-@[f:[t:1to(1)]cx]
-t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
-t2:=ismod(prod(1,f),<xout(1)>f,t1):is"r"(mod(prod(1,f)),mod(<xout(1)>f))
-t3:=isrecx1(mod(prod(1,f)),mod(<xout(1)>f),0,t2):is(pli(mod(prod(1,f)),0),pli(mod(<xout(1)>f),0))
-t4:=satz277([t:cx][u:cx]ts(t,u),modf(1,f)):is(prod(1,modf(1,f)),pli(mod(<xout(1)>f),0))
-t5:=tris2(cx,pli(mod(prod(1,f)),0),prod(1,modf(1,f)),pli(mod(<xout(1)>f),0),t3,t4):prop1(1,f)
-@t6:=[u:[t:1to(1)]cx]t5(u):prop2(1)
-x@[p:prop2(x)][f:[t:1to(pl"n"(x,1))]cx]
-t7:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
-lf:=left(cx,pl"n"(x,1),x,t7,f):[t:1to(x)]cx
-t8:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
-m:=mod(<xout(pl"n"(x,1))>f):real
-t9:=ismod(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),t8):is"r"(mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)))
-t10:=satz268(prod(x,lf),<xout(pl"n"(x,1))>f):is"r"(mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m))
-t11:=tris(real,mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m),t9,t10):is"r"(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m))
-t12:=isrecx1(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m),0,t11):is(pli(mod(prod(pl"n"(x,1),f)),0),pli(ts"r"(mod(prod(x,lf)),m),0))
-lmf:=left(cx,pl"n"(x,1),x,t7,modf(pl"n"(x,1),f)):[t:1to(x)]cx
-t13:=satz278([t:cx][u:cx]ts(t,u),x,modf(pl"n"(x,1),f)):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)))
-t14:=symis(cx,pli(mod(prod(x,lf)),0),prod(x,lmf),<lf>p):is(prod(x,lmf),pli(mod(prod(x,lf)),0))
-t15:=ists1(prod(x,lmf),pli(mod(prod(x,lf)),0),pli(m,0),t14):is(ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)))
-t16:=tsis12a(mod(prod(x,lf)),0,m,0):is(ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))))
-t17:=tris(real,mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),mn"r"(ts"r"(mod(prod(x,lf)),m),0),ts"r"(mod(prod(x,lf)),m),ismn2"r"(ts"r"(0,0),0,ts"r"(mod(prod(x,lf)),m),ts01"r"(0,0,refis(real,0))),pl02"r"(ts"r"(mod(prod(x,lf)),m),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m))
-t18:=tris(real,pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),pl"r"(0,0),0,ispl12"r"(ts"r"(mod(prod(x,lf)),0),0,ts"r"(0,m),0,ts02"r"(mod(prod(x,lf)),0,refis(real,0)),ts01"r"(0,m,refis(real,0))),pl01"r"(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0)
-t19:=isrecx12(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0,t17,t18):is(pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0))
-t20:=tr4is(cx,prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0),t13,t15,t16,t19):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0))
-t21:=tris2(cx,pli(mod(prod(pl"n"(x,1),f)),0),prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0),t12,t20):prop1(pl"n"(x,1),f)
-p@t21a:=[u:[t:1to(pl"n"(x,1))]cx]t21(u):prop2(pl"n"(x,1))
-t22:=isp(nat,[t:nat]prop2(t),pl"n"(x,1),<x>suc,t21a,satz4a(x)):prop2(<x>suc)
--8288
-satz288:=<f>induction([t:nat]prop2".8288"(t),t6".8288",[t:nat][u:prop2".8288"(t)]t22".8288"(t,u),x):is(pli(mod(prod(x,f)),0),prod(x,modf(f)))
-+8289
-prop1:=is(prod(x,f),0c):'prop'
-prop2:=some"l"(1to(x),[t:1to(x)]is(<t>f,0c)):'prop'
-prop3:=iff(prop1,prop2):'prop'
-x@prop4:=[u:[t:1to(x)]cx]prop3(u):'prop'
-@[f:[t:1to(1)]cx]
-t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
-[p:prop1(1,f)]
-t2:=tris1(cx,<xout(1)>f,0c,prod(1,f),t1,p):is(<xout(1)>f,0c)
-t3:=somei(1to(1),[t:1to(1)]is(<t>f,0c),xout(1),t2):prop2(1,f)
-f@[p:prop2(1,f)][u:1to(1)][i:is(<u>f,0c)]
-t4:=th1"n.singlet"(u):is"e"(1to(1),u,xout(1))
-t5:=tr3is(cx,prod(1,f),<xout(1)>f,<u>f,0c,t1,isf(1to(1),cx,f,xout(1),u,symis(1to(1),u,xout(1),t4)),i):prop1(1,f)
-p@t6:=someapp(1to(1),[t:1to(1)]is(<t>f,0c),p,prop1(1,f),[t:1to(1)][u:is(<t>f,0c)]t5(t,u)):prop1(1,f)
-f@t7:=iffi(prop1(1,f),prop2(1,f),[t:prop1(1,f)]t3(t),[t:prop2(1,f)]t6(t)):prop3(1,f)
-@t8:=[u:[t:1to(1)]cx]t7(u):prop4(1)
-x@[p:prop4(x)][f:[t:1to(pl"n"(x,1))]cx]
-t9:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
-lf:=left(cx,pl"n"(x,1),x,t9,f):[t:1to(x)]cx
-t10:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
-[q:prop1(pl"n"(x,1),f)]
-t11:=tris1(cx,ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,prod(pl"n"(x,1),f),t10,q):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-t12:=satz221c(prod(x,lf),<xout(pl"n"(x,1))>f,t11):or(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c))
-[i:is(prod(x,lf),0c)]
-t13:=th3"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,i):prop2(x,lf)
-[n:1to(x)][j:is(<n>lf,0c)]
-t14:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),left1to(pl"n"(x,1),x,t9,n),j):prop2(pl"n"(x,1),f)
-i@t15:=someapp(1to(x),[t:1to(x)]is(<t>lf,0c),t13,prop2(pl"n"(x,1),f),[t:1to(x)][u:is(<t>lf,0c)]t14(t,u)):prop2(pl"n"(x,1),f)
-q@[i:is(<xout(pl"n"(x,1))>f,0c)]
-t16:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),xout(pl"n"(x,1)),i):prop2(pl"n"(x,1),f)
-q@t17:=orapp(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c),prop2(pl"n"(x,1),f),t12,[t:is(prod(x,lf),0c)]t15(t),[t:is(<xout(pl"n"(x,1))>f,0c)]t16(t)):prop2(pl"n"(x,1),f)
-f@[q:prop2(pl"n"(x,1),f)][n:1to(pl"n"(x,1))][i:is(<n>f,0c)][j:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]
-t18:=tris1(cx,<xout(pl"n"(x,1))>f,0c,<n>f,isf(1to(pl"n"(x,1)),cx,f,n,xout(pl"n"(x,1)),j),i):is(<xout(pl"n"(x,1))>f,0c)
-t20:=satz221b(prod(x,lf),<xout(pl"n"(x,1))>f,t18):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-i@[m:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]
-n1:=inn(pl"n"(x,1),n):nat
-[j:is"n"(n1,pl"n"(x,1))]
-t21:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),pl"n"(x,1),lessisi3(pl"n"(x,1)),j):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)))
-t22:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)),isoutinn(pl"n"(x,1),n),t21):is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))
-m@t23:=th3"l.imp"(is"n"(n1,pl"n"(x,1)),is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),m,[t:is"n"(n1,pl"n"(x,1))]t22(t)):nis"n"(n1,pl"n"(x,1))
-t24:=ore1(less"n"(n1,pl"n"(x,1)),is"n"(n1,pl"n"(x,1)),1top(pl"n"(x,1),n),t23):less"n"(n1,pl"n"(x,1))
-t25:=satz26(x,n1,t24):lessis"n"(n1,x)
-n2:=outn(x,n1,t25):1to(x)
-t26:=isinoutn(x,n1,t25):is"n"(n1,inn(x,n2))
-t27:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),inn(x,n2),trlessis"n"(inn(x,n2),x,pl"n"(x,1),1top(x,n2),t9),t26):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2))
-t28:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2),isoutinn(pl"n"(x,1),n),t27):is"e"(1to(pl"n"(x,1)),n,left1to(pl"n"(x,1),x,t9,n2))
-t29:=isf(1to(pl"n"(x,1)),cx,f,n,left1to(pl"n"(x,1),x,t9,n2),t28):is(<n>f,<n2>lf)
-t30:=tris1(cx,<n2>lf,0c,<n>f,t29,i):is(<n2>lf,0c)
-t31:=somei(1to(x),[t:1to(x)]is(<t>lf,0c),n2,t30):prop2(x,lf)
-t32:=th4"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,t31):prop1(x,lf)
-t34:=satz221a(prod(x,lf),<xout(pl"n"(x,1))>f,t32):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-i@t35:=th1"l.imp"(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c),[t:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]t20(t),[t:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]t34(t)):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-t36:=tris(cx,prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,t10,t35):prop1(pl"n"(x,1),f)
-q@t37:=someapp(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),q,prop1(pl"n"(x,1),f),[t:1to(pl"n"(x,1))][u:is(<t>f,0c)]t36(t,u)):prop1(pl"n"(x,1),f)
-f@t38:=iffi(prop1(pl"n"(x,1),f),prop2(pl"n"(x,1),f),[t:prop1(pl"n"(x,1),f)]t17(t),[t:prop2(pl"n"(x,1),f)]t37(t)):prop3(pl"n"(x,1),f)
-p@t39:=[u:[t:1to(pl"n"(x,1))]cx]t38(u):prop4(pl"n"(x,1))
-t40:=isp(nat,[t:nat]prop4(t),pl"n"(x,1),<x>suc,t39,satz4a(x)):prop4(<x>suc)
--8289
-satz289:=<f>induction([t:nat]prop4".8289"(t),t8".8289",[t:nat][u:prop4".8289"(t)]t40".8289"(t,u),x):iff(is(prod(x,f),0c),some"l"(1to(x),[t:1to(x)]is(<t>f,0c)))
-[i:is(prod(x,f),0c)]
-satz289a:=th3"l.iff"(prop1".8289",prop2".8289",satz289,i):some"l"(1to(x),[t:1to(x)]is(<t>f,0c))
-f@[n:1to(x)][i:is(<n>f,0c)]
-+*8289
-i"c"@t41:=somei(1to(x),[t:1to(x)]is(<t>f,0c),n,i):prop2
--8289
-i@satz289b:=th4"l.iff"(prop1".8289",prop2".8289",satz289,t41".8289"):is(prod(x,f),0c)
-@[x:complex][m:real][mi:intrl(m)][o:or(nis(x,0c),pos(m))]
-+v9
-[p:pos(m)]
-t1:=posintnatrl(m,p,mi):natrl(m)
-m1:=ntofrl(m,t1):nat
-pw1:=prod(m1,[t:1to(m1)]x):cx
--v9
-x@[y:complex][m:real][n:real][i:is(x,y)][j:is"r"(m,n)][mi1:intrl(m)][ni1:intrl(n)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(n))]
-+*v9
-oy@[mp:pos(m)][np:pos(n)]
-m0:=m1(x,m,mi1,ox,mp):nat
-n0:=m1(y,n,ni1,oy,np):nat
-t2:=isrlent(m,t1(x,m,mi1,ox,mp),n,t1(y,n,ni1,oy,np),j):is"n"(m0,n0)
-t3:=lessisi2"n"(m0,n0,t2):lessis"n"(m0,n0)
-t4:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]y,m0,t2):is(prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np))
-t5:=fisi(1to(m0),cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),[t:1to(m0)]i):is"e"([t:1to(m0)]cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y))
-t6:=isf([t:1to(m0)]cx,cx,[u:[t:1to(m0)]cx]prod(m0,u),[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),t5):is(pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)))
-t7:=tris(cx,pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np),t6,t4):is(pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,np))
-p@[p1:pos(m)]
-t8:=t7(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,p,p1):is(pw1(p),pw1(p1))
-p@[n:nis(x,0c)]
-t9:=th5"l.some"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c),[t:1to(m1)]n):not(some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)))
-t10:=th3"l.imp"(is(pw1,0c),some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)),t9,[t:is(pw1,0c)]satz289a(m1,[u:1to(m1)]x,t)):nis(pw1,0c)
-o@[n:neg(m)]
-mi@t11:=intabs(m,mi):intrl(abs(m))
-n@t12:=satz166b(m,n):pos(abs(m))
-t13:=ori2(nis(x,0c),pos(abs(m)),t12):or(nis(x,0c),pos(abs(m)))
-t14:=ore1(nis(x,0c),pos(m),o,nnotp(m,n)):nis(x,0c)
-t15:=t10(abs(m),t11,t13,t12,t14):nis(pw1(abs(m),t11,t13,t12),0c)
-pw2:=ov(1c,pw1(abs(m),t11,t13,t12),t15):cx
-oy@[nm:neg(m)][nn:neg(n)]
-pwm:=pw1(x,abs(m),t11(x,m,mi1),t13(x,m,mi1,ox,nm),t12(x,m,mi1,ox,nm)):cx
-pwn:=pw1(y,abs(n),t11(y,n,ni1),t13(y,n,ni1,oy,nn),t12(y,n,ni1,oy,nn)):cx
-t16:=t7(abs(m),abs(n),i,isabs(m,n,j),t11(x,m,mi1),t11(y,n,ni1),t13(x,m,mi1,ox,nm),t13(y,n,ni1,oy,nn),t12(x,m,mi1,ox,nm),t12(y,n,ni1,oy,nn)):is(pwm,pwn)
-t17:=isov2(pwm,pwn,1c,t16,t15(x,m,mi1,ox,nm),t15(y,n,ni1,oy,nn)):is(pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,nn))
-n@[n1:neg(m)]
-t18:=t17(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,n,n1):is(pw2(n),pw2(n1))
-o@pw3:=ite"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c)):cx
-n@t19:=itet"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),n):is(pw3,pw2(n))
-o@[nn:not(neg(m))]
-t20:=itef"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),nn):is(pw3,1c)
-nm@t21:=isp(real,[t:real]neg(t),m,n,nm,j):neg(n)
-t22:=t19(x,m,mi1,ox,nm):is(pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm))
-t23:=symis(cx,pw3(y,n,ni1,oy),pw2(y,n,ni1,oy,t21),t19(y,n,ni1,oy,t21)):is(pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy))
-t24:=tr3is(cx,pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy),t22,t17(t21),t23):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
-oy@[nn:not(neg(m))]
-t25:=isp(real,[t:real]not(neg(t)),m,n,nn,j):not(neg(n))
-t26:=t20(x,m,mi1,ox,nn):is(pw3(x,m,mi1,ox),1c)
-t27:=t20(y,n,ni1,oy,t25):is(pw3(y,n,ni1,oy),1c)
-t28:=tris2(cx,pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),1c,t26,t27):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
-oy@t29:=th1"l.imp"(neg(m),is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy)),[t:neg(m)]t24(t),[t:not(neg(m))]t28(t)):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
--v9
-o@pw:=ite"l.r"(pos(m),cx,[t:pos(m)]pw1".v9"(t),[t:not(pos(m))]pw3".v9",[t:pos(m)][u:pos(m)]t8".v9"(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3".v9")):cx
-+*v9
-p@t30:=itet"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),p):is(pw,pw1(p))
-o@[n:not(pos(m))]
-t31:=itef"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),n):is(pw,pw3)
-o@[i:is"r"(m,0)]
-t32:=tris(cx,pw,pw3,1c,t31(0notp(m,i)),t20(0notn(m,i))):is(pw,1c)
-o@[n:neg(m)]
-t33:=tris(cx,pw,pw3,pw2(n),t31(nnotp(m,n)),t19(n)):is(pw,pw2(n))
--v9
-o@[p:pos(m)]
-posexp:=t30".v9"(p):is(pw(x,m,mi,o),prod(ntofrl(m,posintnatrl(m,p,mi)),[t:1to(ntofrl(m,posintnatrl(m,p,mi)))]x))
-[n:nis(x,0c)]
-lemmapw1:=th2"e.notis"(cx,pw1".v9"(p),0c,pw,t10".v9"(p,n),posexp):nis(pw(x,m,mi,o),0c)
-o@[i:is"r"(m,0)]
-0exp:=t32".v9"(i):is(pw(x,m,mi,o),1c)
-o@[n:neg(m)]
-lemmapw2:=t14".v9"(n):nis(x,0c)
-lemmapw3:=t13".v9"(n):or(nis(x,0c),pos(abs(m)))
-+*v9
-n@t34:=t30(abs(m),t11,t13(n),t12(n)):is(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)))
-t35:=isov2(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)),1c,t34,lemmapw1(abs(m),t11,t13(n),t12(n),t14(n)),t15(n)):is(ov(1c,pw(x,abs(m),t11,t13(n)),lemmapw1(abs(m),t11,t13(n),t12(n),t14(n))),pw2(n))
--v9
-n@negexp:=tris2(cx,pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)),pw2".v9"(n),t33".v9"(n),t35".v9"(n)):is(pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)))
-+*v9
-mp@t36:=isp(real,[t:real]pos(t),m,n,mp,j):pos(n)
-t37:=t30(x,m,mi1,ox,mp):is(pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp))
-t38:=symis(cx,pw(y,n,ni1,oy),pw1(y,n,ni1,oy,t36),t30(y,n,ni1,oy,t36)):is(pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy))
-t39:=tr3is(cx,pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy),t37,t7(t36),t38):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
-oy@[np:not(pos(m))]
-t40:=isp(real,[t:real]not(pos(t)),m,n,np,j):not(pos(n))
-t41:=t31(x,m,mi1,ox,np):is(pw(x,m,mi1,ox),pw3(x,m,mi1,ox))
-t42:=symis(cx,pw(y,n,ni1,oy),pw3(y,n,ni1,oy),t31(y,n,ni1,oy,t40)):is(pw3(y,n,ni1,oy),pw(y,n,ni1,oy))
-t43:=tr3is(cx,pw(x,m,mi1,ox),pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),pw(y,n,ni1,oy),t41,t29,t42):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
--v9
-oy@ispw12:=th1"l.imp"(pos(m),is(pw(x,m,mi1,ox),pw(y,n,ni1,oy)),[t:pos(m)]t39".v9"(t),[t:not(pos(m))]t43".v9"(t)):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
-m@[i:is(x,y)][mi:intrl(m)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(m))]
-ispw1:=ispw12(x,y,m,m,i,refis(real,m),mi,mi,ox,oy):is(pw(x,m,mi,ox),pw(y,m,mi,oy))
-x@[m:real][n:real][i:is"r"(m,n)][mi:intrl(m)][ni:intrl(n)][om:or(nis(x,0c),pos(m))][on:or(nis(x,0c),pos(n))]
-ispw2:=ispw12(x,x,m,n,refis(cx,x),i,mi,ni,om,on):is(pw(x,m,mi,om),pw(x,n,ni,on))
-o@[n:nis(x,0c)]
-+9290
-[p:pos(m)]
-t1:=lemmapw1(p,n):nis(pw(x,m,mi,o),0c)
-@[i:is(1c,0c)]
-t2:=tr3is(real,1rl,re(1c),re(0c),0,isre(1rl,0),iscere(1c,0c,i),reis(0,0)):is"r"(1rl,0)
--9290
-@1not0:=th3"l.imp"(is(1c,0c),is"r"(1rl,0),pnot0(1rl,pos1),[t:is(1c,0c)]t2".9290"(t)):nis(1c,0c)
-+*9290
-n@[i:is"r"(m,0)]
-t4:=th2"e.notis"(cx,1c,0c,pw(x,m,mi,o),1not0,0exp(i)):nis(pw(x,m,mi,o),0c)
-n@[nm:neg(m)]
-p0:=pw(x,abs(m),intabs(m,mi),lemmapw3(nm)):cx
-t5:=lemmapw1(x,abs(m),intabs(m,mi),lemmapw3(nm),satz166b(m,nm),lemmapw2(nm)):nis(p0,0c)
-t6:=tris(cx,ts(pw(x,m,mi,o),p0),ts(ov(1c,p0,t5),p0),1c,ists1(pw(x,m,mi,o),ov(1c,p0,t5),p0,negexp(nm)),satz229e(1c,p0,t5)):is(ts(pw(x,m,mi,o),p0),1c)
-t7:=th2"e.notis"(cx,1c,0c,ts(pw(x,m,mi,o),p0),1not0,t6):nis(ts(pw(x,m,mi,o),p0),0c)
-t8:=th3"l.imp"(is(pw(x,m,mi,o),0c),is(ts(pw(x,m,mi,o),p0),0c),t7,[t:is(pw(x,m,mi,o),0c)]satz221a(pw(x,m,mi,o),p0,t)):nis(pw(x,m,mi,o),0c)
--9290
-n@satz290:=rapp(m,nis(pw(x,m,mi,o),0c),[t:pos(m)]t1".9290"(t),[t:is"r"(m,0)]t4".9290"(t),[t:neg(m)]t8".9290"(t)):nis(pw(x,m,mi,o),0c)
-x@lemma291:=ori2(nis(x,0c),pos(1rl),pos1):or(nis(x,0c),pos(1rl))
-+9291
-1a:=ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)):nat
-t1:=posexp(x,1rl,intrl1,lemma291,pos1):is(pw(x,1rl,intrl1,lemma291),prod(1a,[t:1to(1a)]x))
-t2:=tris(nat,1,ntofrl(1rl,natrl1),ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)),isntrl1(1),isrlent(1rl,natrl1,1rl,posintnatrl(1rl,pos1,intrl1),refis(real,1rl))):is"n"(1,1a)
-t3:=lessisi2"n"(1,1a,t2):lessis"n"(1,1a)
-t4:=issmpr([t:cx][u:cx]ts(t,u),1a,[t:1to(1a)]x,1,t2):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),prod(1a,[t:1to(1a)]x))
-t5:=satz277([t:cx][u:cx]ts(t,u),left(cx,1a,1,t3,[t:1to(1a)]x)):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),x)
-t6:=tris1(cx,prod(1a,[t:1to(1a)]x),x,prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),t4,t5):is(prod(1a,[t:1to(1a)]x),x)
--9291
-satz291:=tris(cx,pw(x,1rl,intrl1,lemma291),prod(1a".9291",[t:1to(1a".9291")]x),x,t1".9291",t6".9291"):is(pw(x,1rl,intrl1,lemma291),x)
-[y:cx][m:real][mi:intrl(m)][o:or(and(nis(x,0c),nis(y,0c)),pos(m))]
-+9292
-[a:and(nis(x,0c),nis(y,0c))]
-t1:=ande1(nis(x,0c),nis(y,0c),a):nis(x,0c)
-t2:=ande2(nis(x,0c),nis(y,0c),a):nis(y,0c)
-t3:=satz221d(x,y,t1,t2):nis(ts(x,y),0c)
--9292
-lemma292a:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(x,0c),o,[t:and(nis(x,0c),nis(y,0c))]t1".9292"(t)):or(nis(x,0c),pos(m))
-lemma292b:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(y,0c),o,[t:and(nis(x,0c),nis(y,0c))]t2".9292"(t)):or(nis(y,0c),pos(m))
-lemma292c:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(ts(x,y),0c),o,[t:and(nis(x,0c),nis(y,0c))]t3".9292"(t)):or(nis(ts(x,y),0c),pos(m))
-+*9292
-x@[n:nat]
-nr:=rlofnt(n):real
-t4:=natintrl(nr,natrli(n)):intrl(nr)
-t5:=ori2(nis(x,0c),pos(nr),natpos(nr,natrli(n))):or(nis(x,0c),pos(nr))
-p0:=pw(x,nr,t4,t5):cx
-x@t6:=tris(cx,p0(1),pw(x,1rl,intrl1,lemma291(x)),x,ispw1(x,x,1rl,refis(cx,x),intrl1,t5(1),lemma291(x)),satz291(x)):is(p0(1),x)
-n@n0:=ntofrl(nr,posintnatrl(nr,natpos(nr,natrli(n)),t4)):nat
-t7:=tris(nat,n,ntofrl(nr,natrli(n)),n0,isntrl1(n),isrlent(nr,natrli(n),nr,posintnatrl(nr,natpos(nr,natrli(n)),t4),refis(real,nr))):is"n"(n,n0)
-t8:=lessisi2"n"(n,n0,t7):lessis"n"(n,n0)
-t9:=posexp(x,nr,t4,t5,natpos(nr,natrli(n))):is(p0,prod(n0,[t:1to(n0)]x))
-t10:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]x,n,t7):is(prod(n,left(cx,n0,n,t8,[t:1to(n0)]x)),prod(n0,[t:1to(n0)]x))
-t11:=tris2(cx,p0,prod(n,[t:1to(n)]x),prod(n0,[t:1to(n0)]x),t9,t10):is(p0,prod(n,[t:1to(n)]x))
-n1:=pl"n"(n,1):nat
-t12:=lessisi1"n"(n,n1,satz18a(n,1)):lessis"n"(n,n1)
-t13:=satz278([t:cx][u:cx]ts(t,u),n,[t:1to(n1)]x):is(prod(n1,[t:1to(n1)]x),ts(prod(n,left(cx,n1,n,t12,[t:1to(n1)]x)),x))
-t14:=ists1(p0,prod(n,[t:1to(n)]x),x,t11):is(ts(p0,x),ts(prod(n,[t:1to(n)]x),x))
-t15:=tris2(cx,prod(n1,[t:1to(n1)]x),ts(p0,x),ts(prod(n,[t:1to(n)]x),x),t13,t14):is(prod(n1,[t:1to(n1)]x),ts(p0,x))
-t16:=tris(cx,p0(n1),prod(n1,[t:1to(n1)]x),ts(p0,x),t11(n1),t15):is(p0(n1),ts(p0(n),x))
-y@[n:nat]
-prop1:=is(p0(ts(x,y),n),ts(p0(x,n),p0(y,n))):'prop'
-y@t17:=ists12(p0(x,1),x,p0(y,1),y,t6(x),t6(y)):is(ts(p0(x,1),p0(y,1)),ts(x,y))
-t18:=tris2(cx,p0(ts(x,y),1),ts(p0(x,1),p0(y,1)),ts(x,y),t6(ts(x,y)),t17):prop1(1)
-n@[p:prop1(n)]
-t19:=ists1(p0(ts(x,y),n),ts(p0(x,n),p0(y,n)),ts(x,y),p):is(ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)))
-t20:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),x),ts(p0(x,n),ts(p0(y,n),x)),ts(p0(x,n),ts(x,p0(y,n))),ts(ts(p0(x,n),x),p0(y,n)),assts1(p0(x,n),p0(y,n),x),ists2(ts(p0(y,n),x),ts(x,p0(y,n)),p0(x,n),comts(p0(y,n),x)),assts2(p0(x,n),x,p0(y,n))):is(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)))
-t21:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(ts(p0(x,n),p0(y,n)),x),y),ts(ts(ts(p0(x,n),x),p0(y,n)),y),ts(ts(p0(x,n),x),ts(p0(y,n),y)),assts2(ts(p0(x,n),p0(y,n)),x,y),ists1(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)),y,t20),assts1(ts(p0(x,n),x),p0(y,n),y)):is(ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
-t22:=tr3is(cx,p0(ts(x,y),n1(n)),ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t16(ts(x,y),n),t19,t21):is(p0(ts(x,y),n1(n)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
-t23:=ists12(p0(x,n1(n)),ts(p0(x,n),x),p0(y,n1(n)),ts(p0(y,n),y),t16(x,n),t16(y,n)):is(ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
-t24:=tris2(cx,p0(ts(x,y),n1(n)),ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t22,t23):prop1(n1(n))
-t25:=isp(nat,[t:nat]prop1(t),n1(n),<n>suc,t24,satz4a(n)):prop1(<n>suc)
-n@t26:=induction([t:nat]prop1(t),t18,[t:nat][u:prop1(t)]t25(t,u),n):prop1
-o@prop2:=is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b))):'prop'
-[p:pos(m)]
-t28:=posintnatrl(m,p,mi):natrl(m)
-m0:=ntofrl(m,t28):nat
-t29:=isrlnt1(m,t28):is"r"(m,nr(m0))
-t30:=isrlnt2(m,t28):is"r"(nr(m0),m)
-t31:=ispw2(ts(x,y),m,nr(m0),t29,mi,t4(ts(x,y),m0),lemma292c,t5(ts(x,y),m0)):is(pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0))
-t32:=ists12(p0(x,m0),pw(x,m,mi,lemma292a),p0(y,m0),pw(y,m,mi,lemma292b),ispw2(x,nr(m0),m,t30,t4(x,m0),mi,t5(x,m0),lemma292a),ispw2(y,nr(m0),m,t30,t4(y,m0),mi,t5(y,m0),lemma292b)):is(ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
-t33:=tr3is(cx,pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0),ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),t31,t26(m0),t32):prop2
-o@[i:is"r"(m,0)]
-t34:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(1c,1c),1c,ists12(pw(x,m,mi,lemma292a),1c,pw(y,m,mi,lemma292b),1c,0exp(x,m,mi,lemma292a,i),0exp(y,m,mi,lemma292b,i)),satz222(1c)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c)
-t35:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c,0exp(ts(x,y),m,mi,lemma292c,i),t34):prop2
-o@[n:neg(m)]
-t36:=intabs(m,mi):intrl(abs(m))
-t37:=ori2(and(nis(x,0c),nis(y,0c)),pos(abs(m)),satz166b(m,n)):or(and(nis(x,0c),nis(y,0c)),pos(abs(m)))
-t38:=lemma292a(abs(m),t36,t37):or(nis(x,0c),pos(abs(m)))
-t39:=lemma292b(abs(m),t36,t37):or(nis(y,0c),pos(abs(m)))
-t40:=lemma292c(abs(m),t36,t37):or(nis(ts(x,y),0c),pos(abs(m)))
-t41:=lemmapw3(x,m,mi,lemma292a,n):or(nis(x,0c),pos(abs(m)))
-t42:=lemmapw3(y,m,mi,lemma292b,n):or(nis(y,0c),pos(abs(m)))
-t43:=lemmapw3(ts(x,y),m,mi,lemma292c,n):or(nis(ts(x,y),0c),pos(abs(m)))
-t44:=ispw2(ts(x,y),abs(m),abs(m),refis(real,abs(m)),t36,t36,t43,t40):is(pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40))
-t45:=t33(abs(m),t36,t37,satz166b(m,n)):is(pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)))
-t46:=ists12(pw(x,abs(m),t36,t38),pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t39),pw(y,abs(m),t36,t42),ispw2(x,abs(m),abs(m),refis(real,abs(m)),t36,t36,t38,t41),ispw2(y,abs(m),abs(m),refis(real,abs(m)),t36,t36,t39,t42)):is(ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
-t47:=tr3is(cx,pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t44,t45,t46):is(pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
-t48:=lemmapw1(x,abs(m),t36,t41,satz166b(m,n),lemmapw2(x,m,mi,lemma292a,n)):nis(pw(x,abs(m),t36,t41),0c)
-t49:=lemmapw1(y,abs(m),t36,t42,satz166b(m,n),lemmapw2(y,m,mi,lemma292b,n)):nis(pw(y,abs(m),t36,t42),0c)
-t50:=lemmapw1(ts(x,y),abs(m),t36,t43,satz166b(m,n),lemmapw2(ts(x,y),m,mi,lemma292c,n)):nis(pw(ts(x,y),abs(m),t36,t43),0c)
-t51:=satz221d(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42),t48,t49):nis(ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),0c)
-t52:=negexp(ts(x,y),m,mi,lemma292c,n):is(pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50))
-t53:=isov12(1c,ts(1c,1c),pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),satz222a(1c),t47,t50,t51):is(ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t54:=tris(cx,pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t52,t53):is(pw(ts(x,y),m,mi,lemma292c),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t55:=ists12(pw(x,m,mi,lemma292a),ov(1c,pw(x,abs(m),t36,t41),t48),pw(y,m,mi,lemma292b),ov(1c,pw(y,abs(m),t36,t42),t49),negexp(x,m,mi,lemma292a,n),negexp(y,m,mi,lemma292b,n)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)))
-t56:=satz247(1c,pw(x,abs(m),t36,t41),1c,pw(y,abs(m),t36,t42),t48,t49):is(ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t57:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t55,t56):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t58:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t54,t57):prop2
--9292
-o@satz292:=rapp(m,prop2".9292",[t:pos(m)]t33".9292"(t),[t:is"r"(m,0)]t35".9292"(t),[t:neg(m)]t58".9292"(t)):is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
-@[m:real]
-lemma293:=ori1(nis(1c,0c),pos(m),1not0):or(nis(1c,0c),pos(m))
-[mi:intrl(m)]
-+9293
-t1:=ori1(and(nis(1c,0c),nis(1c,0c)),pos(m),andi(nis(1c,0c),nis(1c,0c),1not0,1not0)):or(and(nis(1c,0c),nis(1c,0c)),pos(m))
-1m:=pw(1c,m,mi,lemma293):cx
-t2:=satz222(1m):is(ts(1m,1c),1m)
-t3:=ispw1(1c,ts(1c,1c),m,satz222a(1c),mi,lemma293,lemma292c(1c,1c,m,mi,t1)):is(1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)))
-t4:=satz292(1c,1c,m,mi,t1):is(pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))))
-t5:=ists12(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),1m,pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1)),1m,ispw1(1c,1c,m,refis(cx,1c),mi,lemma292a(1c,1c,m,mi,t1),lemma293),ispw1(1c,1c,m,refis(cx,1c),mi,lemma292b(1c,1c,m,mi,t1),lemma293)):is(ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m))
-t6:=tr4is(cx,ts(1m,1c),1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m),t2,t3,t4,t5):is(ts(1m,1c),ts(1m,1m))
-t7:=tris(cx,ts(1m,mn(1m,1c)),mn(ts(1m,1m),ts(1m,1c)),0c,disttm2(1m,1m,1c),satz213b(ts(1m,1m),ts(1m,1c),symis(cx,ts(1m,1c),ts(1m,1m),t6))):is(ts(1m,mn(1m,1c)),0c)
-t8:=ore2(is(1m,0c),is(mn(1m,1c),0c),satz221c(1m,mn(1m,1c),t7),satz290(1c,m,mi,lemma293,1not0)):is(mn(1m,1c),0c)
--9293
-satz293:=satz213a(1m".9293",1c,t8".9293"):is(pw(1c,m,mi,lemma293),1c)
-x@[m:real][n:real][mi:intrl(m)][ni:intrl(n)][o:or(nis(x,0c),and(pos(m),pos(n)))]
-+9294
-[a:and(pos(m),pos(n))]
-t1:=ande1(pos(m),pos(n),a):pos(m)
-t2:=ande2(pos(m),pos(n),a):pos(n)
-t3:=pospl(m,n,t1,t2):pos(pl"r"(m,n))
--9294
-lemma294a:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(m),o,[t:and(pos(m),pos(n))]t1".9294"(t)):or(nis(x,0c),pos(m))
-lemma294b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(n),o,[t:and(pos(m),pos(n))]t2".9294"(t)):or(nis(x,0c),pos(n))
-lemma294c:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(pl"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9294"(t)):or(nis(x,0c),pos(pl"r"(m,n)))
-+*9294
-o@prop1:=is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c)):'prop'
-a@m1:=ntofrl(m,posintnatrl(m,t1,mi)):nat
-n1:=ntofrl(n,posintnatrl(n,t2,ni)):nat
-t4:=ists12(pw(x,m,mi,lemma294a),prod(m1,[t:1to(m1)]x),pw(x,n,ni,lemma294b),prod(n1,[t:1to(n1)]x),posexp(x,m,mi,lemma294a,t1),posexp(x,n,ni,lemma294b,t2)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
-p1:=ntofrl(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni))):nat
-t5:=posexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t3):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(p1,[t:1to(p1)]x))
-t6:=tris(real,pl"r"(m,n),pl"r"(rlofnt(m1),rlofnt(n1)),rlofnt(pl"n"(m1,n1)),ispl12"r"(m,rlofnt(m1),n,rlofnt(n1),isrlnt1(m,posintnatrl(m,t1,mi)),isrlnt1(n,posintnatrl(n,t2,ni))),satzr155b(m1,n1)):is"r"(pl"r"(m,n),rlofnt(pl"n"(m1,n1)))
-t7:=tris2(nat,pl"n"(m1,n1),p1,ntofrl(rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1))),isntrl1(pl"n"(m1,n1)),isrlent(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni)),rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1)),t6)):is"n"(pl"n"(m1,n1),p1)
-t8:=lessisi2"n"(pl"n"(m1,n1),p1,t7):lessis"n"(pl"n"(m1,n1),p1)
-t9:=issmpr([t:cx][u:cx]ts(t,u),p1,[t:1to(p1)]x,pl"n"(m1,n1),t7):is(prod(pl"n"(m1,n1),left(cx,p1,pl"n"(m1,n1),t8,[t:1to(p1)]x)),prod(p1,[t:1to(p1)]x))
-t10:=tris2(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),prod(p1,[t:1to(p1)]x),t5,t9):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x))
-t11:=lessisi1"n"(m1,pl"n"(m1,n1),satz18a(m1,n1)):lessis"n"(m1,pl"n"(m1,n1))
-t12:=satz281([t:cx][u:cx]ts(t,u),assocts,m1,n1,[t:1to(pl"n"(m1,n1))]x):is(prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,left(cx,pl"n"(m1,n1),m1,t11,[t:1to(pl"n"(m1,n1))]x)),prod(n1,right(cx,m1,n1,[t:1to(pl"n"(m1,n1))]x))))
-t13:=tris(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t10,t12):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
-t14:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t4,t13):prop1
-o@[na:not(and(pos(m),pos(n)))]
-t15:=ore1(nis(x,0c),and(pos(m),pos(n)),o,na):nis(x,0c)
-t16:=th15"l.or"(pos(m),pos(n),na):or(not(pos(m)),not(pos(n)))
-o@am:=abs(m):real
-an:=abs(n):real
-ap:=abs(pl"r"(m,n)):real
-t17:=intabs(m,mi):intrl(am)
-t18:=intabs(n,ni):intrl(an)
-t19:=intabs(pl"r"(m,n),intpl(m,mi,n,ni)):intrl(ap)
-na@[nm:neg(m)][nn:neg(n)]
-t20:=andi(pos(am),pos(an),satz166e(m,nnot0(m,nm)),satz166e(n,nnot0(n,nn))):and(pos(am),pos(an))
-t21:=ori2(nis(x,0c),and(pos(am),pos(an)),t20):or(nis(x,0c),and(pos(am),pos(an)))
-t22:=lemmapw3(x,m,mi,lemma294a,nm):or(nis(x,0c),pos(am))
-t23:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
-t24:=lemma294a(x,am,an,t17,t18,t21):or(nis(x,0c),pos(am))
-t25:=lemma294b(x,am,an,t17,t18,t21):or(nis(x,0c),pos(an))
-t26:=ists12(pw(x,am,t17,t22),pw(x,am,t17,t24),pw(x,an,t18,t23),pw(x,an,t18,t25),ispw1(x,x,am,refis(cx,x),t17,t22,t24),ispw1(x,x,an,refis(cx,x),t18,t23,t25)):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)))
-t27:=lemma294c(x,am,an,t17,t18,t21):or(nis(x,0c),pos(pl"r"(am,an)))
-t28:=t14(x,am,an,t17,t18,t21,t20):is(ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27))
-t29:=tr3is(real,pl"r"(am,an),pl"r"(m0"r"(m),m0"r"(n)),m0"r"(pl"r"(m,n)),ap,ispl12"r"(am,m0"r"(m),an,m0"r"(n),absn(m,nm),absn(n,nn)),satz180a(m,n),symis(real,ap,m0"r"(pl"r"(m,n)),absn(pl"r"(m,n),negpl(m,n,nm,nn)))):is"r"(pl"r"(am,an),ap)
-t30:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn)):or(nis(x,0c),pos(ap))
-t31:=ispw2(x,pl"r"(am,an),ap,t29,intpl(am,t17,an,t18),t19,t27,t30):is(pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30))
-t32:=tr3is(cx,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30),t26,t28,t31):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30))
-t33:=lemmapw1(x,am,t17,t22,satz166b(m,nm),lemmapw2(x,m,mi,lemma294a,nm)):nis(pw(x,am,t17,t22),0c)
-t34:=lemmapw1(x,an,t18,t23,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t23),0c)
-t35:=lemmapw1(x,ap,t19,t30,satz166b(pl"r"(m,n),negpl(m,n,nm,nn)),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):nis(pw(x,ap,t19,t30),0c)
-t36:=ists12(pw(x,m,mi,lemma294a),ov(1c,pw(x,am,t17,t22),t33),pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t23),t34),negexp(x,m,mi,lemma294a,nm),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)))
-t37:=satz221d(pw(x,am,t17,t22),pw(x,an,t18,t23),t33,t34):nis(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),0c)
-t38:=satz247(1c,pw(x,am,t17,t22),1c,pw(x,an,t18,t23),t33,t34):is(ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37))
-t39:=isov12(ts(1c,1c),1c,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30),satz222(1c),t32,t37,t35):is(ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35))
-t40:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t30),t35),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):is(ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t41:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t36,t38,t39,t40):prop1
-na@[pm:pos(m)][nn:neg(n)]
-t42:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
-t43:=lemmapw1(x,an,t18,t42,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t42),0c)
-t44:=ists2(pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t42),t43),pw(x,m,mi,lemma294a),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)))
-t45:=satz244a(pw(x,m,mi,lemma294a),1c,pw(x,an,t18,t42),t43):is(ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43))
-t46:=isov1(ts(pw(x,m,mi,lemma294a),1c),pw(x,m,mi,lemma294a),pw(x,an,t18,t42),satz222(pw(x,m,mi,lemma294a)),t43):is(ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-t47:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t44,t45,t46):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-[casea:more(m,an)]
-t48:=satz182d(m,an,casea):pos(mn"r"(m,an))
-t49:=satz166e(n,nnot0(n,nn)):pos(an)
-t50:=andi(pos(an),pos(mn"r"(m,an)),t49,t48):and(pos(an),pos(mn"r"(m,an)))
-t51:=ori2(nis(x,0c),and(pos(an),pos(mn"r"(m,an))),t50):or(nis(x,0c),and(pos(an),pos(mn"r"(m,an))))
-t52:=intmn(m,mi,an,t18):intrl(mn"r"(m,an))
-t53:=lemma294a(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(an))
-t54:=lemma294b(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(mn"r"(m,an)))
-t55:=lemma294c(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(pl"r"(an,mn"r"(m,an))))
-t56:=intpl(an,t18,mn"r"(m,an),t52):intrl(pl"r"(an,mn"r"(m,an)))
-t57:=t14(x,an,mn"r"(m,an),t18,t52,t51,t50):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55))
-t58:=satz187a(m,an):is"r"(pl"r"(an,mn"r"(m,an)),m)
-t59:=ispw2(x,pl"r"(an,mn"r"(m,an)),m,t58,t56,mi,t55,lemma294a):is(pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a))
-t60:=tris(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a),t57,t59):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a))
-t61:=ispw1(x,x,an,refis(cx,x),t18,t53,t42):is(pw(x,an,t18,t53),pw(x,an,t18,t42))
-t62:=isp1(cx,[t:cx]nis(t,0c),pw(x,an,t18,t42),pw(x,an,t18,t53),t43,t61):nis(pw(x,an,t18,t53),0c)
-t63:=isov12(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a),pw(x,an,t18,t53),pw(x,an,t18,t42),t60,t61,t62,t43):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-t64:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t63):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62))
-t65:=satz229h(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54),t62,refis(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)))):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54))
-t66:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
-t67:=ispw2(x,mn"r"(m,an),pl"r"(m,n),t66,t52,intpl(m,mi,n,ni),t54,lemma294c):is(pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t68:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t64,t65,t67):prop1
-nn@[caseb:is"r"(m,an)]
-t69:=ispw2(x,m,an,caseb,mi,t18,lemma294a,t42):is(pw(x,m,mi,lemma294a),pw(x,an,t18,t42))
-t70:=satz251a(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43,t69):is(ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c)
-t71:=tr3is(real,pl"r"(m,n),mn"r"(m,m0"r"(n)),mn"r"(m,an),0,ispl2"r"(n,m0"r"(m0"r"(n)),m,satz177a(n)),ismn2"r"(m0"r"(n),an,m,symis(real,an,m0"r"(n),absn(n,nn))),satz182e(m,an,caseb)):is"r"(pl"r"(m,n),0)
-t72:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),1c,0exp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t71)):is(1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t73:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t47,t70,t72):prop1
-nn@[casec:less(m,an)]
-t74:=satz182d(an,m,lemma2"r"(m,an,casec)):pos(mn"r"(an,m))
-t75:=andi(pos(m),pos(mn"r"(an,m)),pm,t74):and(pos(m),pos(mn"r"(an,m)))
-t76:=ori2(nis(x,0c),and(pos(m),pos(mn"r"(an,m))),t75):or(nis(x,0c),and(pos(m),pos(mn"r"(an,m))))
-t77:=intmn(an,t18,m,mi):intrl(mn"r"(an,m))
-t78:=lemma294a(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(m))
-t79:=lemma294b(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(mn"r"(an,m)))
-t80:=lemma294c(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(pl"r"(m,mn"r"(an,m))))
-t81:=intpl(m,mi,mn"r"(an,m),t77):intrl(pl"r"(m,mn"r"(an,m)))
-t81a:=t14(x,m,mn"r"(an,m),mi,t77,t76,t75):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80))
-t82:=satz187a(an,m):is"r"(pl"r"(m,mn"r"(an,m)),an)
-t83:=ispw2(x,pl"r"(m,mn"r"(an,m)),an,t82,t81,t18,t80,t42):is(pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42))
-t84:=tris(cx,ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42),t81a,t83):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42))
-t85:=satz290(x,m,mi,t78,t15):nis(pw(x,m,mi,t78),0c)
-t86:=satz290(x,mn"r"(an,m),t77,t79,t15):nis(pw(x,mn"r"(an,m),t77,t79),0c)
-t87:=satz221d(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79),t85,t86):nis(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),0c)
-t88:=satz222(pw(x,m,mi,t78)):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78))
-t89:=ispw1(x,x,m,refis(cx,x),mi,t78,lemma294a):is(pw(x,m,mi,t78),pw(x,m,mi,lemma294a))
-t90:=tris(cx,ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78),pw(x,m,mi,lemma294a),t88,t89):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a))
-t91:=isov12(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42),t90,t84,t87,t43):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-t92:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t91):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87))
-t93:=satz246a(1c,pw(x,mn"r"(an,m),t77,t79),pw(x,m,mi,t78),t86,t85):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86))
-t94:=satz182f(m,an,casec):neg(mn"r"(m,an))
-t94a:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
-t95:=tr3is(real,mn"r"(an,m),m0"r"(mn"r"(m,an)),abs(mn"r"(m,an)),ap,satz181a(an,m),symis(real,abs(mn"r"(m,an)),m0"r"(mn"r"(m,an)),absn(mn"r"(m,an),t94)),isabs(mn"r"(m,an),pl"r"(m,n),t94a)):is"r"(mn"r"(an,m),ap)
-t96:=isp(real,[t:real]neg(t),mn"r"(m,an),pl"r"(m,n),t94,t94a):neg(pl"r"(m,n))
-t97:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96):or(nis(x,0c),pos(ap))
-t98:=lemmapw1(x,ap,t19,t97,satz166b(pl"r"(m,n),t96),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):nis(pw(x,ap,t19,t97),0c)
-t99:=ispw2(x,mn"r"(an,m),ap,t95,t77,t19,t79,t97):is(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97))
-t100:=isov2(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97),1c,t99,t86,t98):is(ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98))
-t101:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t97),t98),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):is(ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t102:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t92,t93,t100,t101):prop1
-nn@t103:=or3app(is"r"(m,an),more(m,an),less(m,an),prop1,satz167a(m,an),[t:is"r"(m,an)]t73(t),[t:more(m,an)]t68(t),[t:less(m,an)]t102(t)):prop1
-na@[nm:neg(m)][qn:pos(n)]
-na@t104:=ori1(nis(x,0c),and(pos(n),pos(m)),t15):or(nis(x,0c),and(pos(n),pos(m)))
-t104a:=th5"l.and"(pos(m),pos(n),na):not(and(pos(n),pos(m)))
-t105:=lemma294a(x,n,m,ni,mi,t104):or(nis(x,0c),pos(n))
-t106:=lemma294b(x,n,m,ni,mi,t104):or(nis(x,0c),pos(m))
-t107:=lemma294c(x,n,m,ni,mi,t104):or(nis(x,0c),pos(pl"r"(n,m)))
-t108:=ists12(pw(x,m,mi,lemma294a),pw(x,m,mi,t106),pw(x,n,ni,lemma294b),pw(x,n,ni,t105),ispw1(x,x,m,refis(cx,x),mi,lemma294a,t106),ispw1(x,x,n,refis(cx,x),ni,lemma294b,t105)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)))
-t109:=comts(pw(x,m,mi,t106),pw(x,n,ni,t105)):is(ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)))
-qn@t110:=t103(x,n,m,ni,mi,t104,t104a,qn,nm):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
-na@t111:=ispw2(x,pl"r"(n,m),pl"r"(m,n),compl"r"(n,m),intpl(n,ni,m,mi),intpl(m,mi,n,ni),t107,lemma294c):is(pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-qn@t112:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t110,t111):prop1
-na@[i:is"r"(m,0)]
-t113:=ists1(pw(x,m,mi,lemma294a),1c,pw(x,n,ni,lemma294b),0exp(x,m,mi,lemma294a,i)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)))
-t114:=satz222b(pw(x,n,ni,lemma294b)):is(ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b))
-t115:=symis(real,pl"r"(m,n),n,pl01"r"(m,n,i)):is"r"(n,pl"r"(m,n))
-t116:=ispw2(x,n,pl"r"(m,n),t115,ni,intpl(m,mi,n,ni),lemma294b,lemma294c):is(pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t117:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t113,t114,t116):prop1
-na@[i:is"r"(n,0)]
-t118:=t117(x,n,m,ni,mi,t104,t104a,i):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
-t119:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t118,t111):prop1
-na@[pm:pos(m)]
-t120:=ore2(not(pos(m)),not(pos(n)),t16,weli(pos(m),pm)):not(pos(n))
-t121:=rapp(n,prop1,th2"l.imp"(pos(n),prop1,t120),[t:is"r"(n,0)]t119(t),[t:neg(n)]t103(pm,t)):prop1
-na@[nm:neg(m)]
-t122:=rapp(n,prop1,[t:pos(n)]t112(nm,t),[t:is"r"(n,0)]t119(t),[t:neg(n)]t41(nm,t)):prop1
-na@t123:=rapp(m,prop1,[t:pos(m)]t121(t),[t:is"r"(m,0)]t117(t),[t:neg(m)]t122(t)):prop1
--9294
-o@satz294:=th1"l.imp"(and(pos(m),pos(n)),prop1".9294",[t:and(pos(m),pos(n))]t14".9294"(t),[t:not(and(pos(m),pos(n)))]t123".9294"(t)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-ni@[o:nis(x,0c)]
-lemma295a:=ori1(nis(x,0c),pos(m),o):or(nis(x,0c),pos(m))
-lemma295b:=ori1(nis(x,0c),pos(n),o):or(nis(x,0c),pos(n))
-lemma295c:=ori1(nis(x,0c),pos(mn"r"(m,n)),o):or(nis(x,0c),pos(mn"r"(m,n)))
-+9295
-t1:=ori1(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)),o):or(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)))
-t2:=intmn(m,mi,n,ni):intrl(mn"r"(m,n))
-t3:=lemma294a(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(mn"r"(m,n)))
-t4:=lemma294b(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(n))
-t5:=lemma294c(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(pl"r"(mn"r"(m,n),n)))
-t6:=ists12(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,lemma295b),pw(x,n,ni,t4),ispw1(x,x,mn"r"(m,n),refis(cx,x),t2,lemma295c,t3),ispw1(x,x,n,refis(cx,x),ni,lemma295b,t4)):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)))
-t7:=satz294(x,mn"r"(m,n),n,t2,ni,t1):is(ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5))
-t8:=plmn(m,n):is"r"(pl"r"(mn"r"(m,n),n),m)
-t9:=ispw2(x,pl"r"(mn"r"(m,n),n),m,t8,intpl(mn"r"(m,n),t2,n,ni),mi,t5,lemma295a):is(pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a))
-t10:=tr3is(cx,ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a),t6,t7,t9):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),pw(x,m,mi,lemma295a))
-t11:=satz290(x,n,ni,lemma295b,o):nis(pw(x,n,ni,lemma295b),0c)
--9295
-satz295:=satz229k(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),pw(x,mn"r"(m,n),t2".9295",lemma295c),t11".9295",t10".9295"):is(ov(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),satz290(x,n,ni,lemma295b,o)),pw(x,mn"r"(m,n),intmn(m,mi,n,ni),lemma295c))
-m@[mi:intrl(m)][n:nis(x,0c)]
-lemma296:=ori1(nis(x,0c),pos(m),n):or(nis(x,0c),pos(m))
-+9296
-t1:=intrli0(0,refis(real,0)):intrl(0)
-t2:=lemma295a(x,0,m,t1,mi,n):or(nis(x,0c),pos(0))
-t3:=lemma295b(x,0,m,t1,mi,n):or(nis(x,0c),pos(m))
-t4:=lemma295c(x,0,m,t1,mi,n):or(nis(x,0c),pos(mn"r"(0,m)))
-t5:=satz290(x,m,mi,lemma296,n):nis(pw(x,m,mi,lemma296),0c)
-t6:=satz290(x,m,mi,t3,n):nis(pw(x,m,mi,t3),0c)
-t7:=symis(cx,pw(x,0,t1,t2),1c,0exp(x,0,t1,t2,refis(real,0))):is(1c,pw(x,0,t1,t2))
-t8:=ispw1(x,x,m,refis(cx,x),mi,lemma296,t3):is(pw(x,m,mi,lemma296),pw(x,m,mi,t3))
-t9:=isov12(1c,pw(x,0,t1,t2),pw(x,m,mi,lemma296),pw(x,m,mi,t3),t7,t8,t5,t6):is(ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6))
-t10:=satz295(x,0,m,t1,mi,n):is(ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4))
-t11:=pl01(0,m0"r"(m),refis(real,0)):is"r"(mn"r"(0,m),m0"r"(m))
-t12:=lemma296(x,m0"r"(m),intm0(m,mi),n):or(nis(x,0c),pos(m0"r"(m)))
-t13:=ispw2(x,mn"r"(0,m),m0"r"(m),t11,intmn(0,t1,m,mi),intm0(m,mi),t4,t12):is(pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12))
-t14:=tr3is(cx,ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12),t9,t10,t13):is(ov(1c,pw(x,m,mi,lemma296),t5),pw(x,m0"r"(m),intm0(m,mi),t12))
--9296
-satz296:=t14".9296":is(ov(1c,pw(x,m,mi,lemma296),satz290(x,m,mi,lemma296,n)),pw(x,m0"r"(m),intm0(m,mi),lemma296(m0"r"(m),intm0(m,mi),n)))
-ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
-+9297
-[p:nis(x,0c)]
-t1:=satz290(x,m,mi,lemma294a(o),p):nis(pw(x,m,mi,lemma294a(o)),0c)
-o@[a:and(pos(m),pos(n))]
-t2:=ande2(pos(m),pos(n),a):pos(n)
-t3:=postspp(m,n,ande1(pos(m),pos(n),a),t2):pos(ts"r"(m,n))
--9297
-lemma297a:=th9"l.or"(nis(x,0c),and(pos(m),pos(n)),nis(pw(x,m,mi,lemma294a(o)),0c),pos(n),o,[t:nis(x,0c)]t1".9297"(t),[t:and(pos(m),pos(n))]t2".9297"(t)):or(nis(pw(x,m,mi,lemma294a(o)),0c),pos(n))
-lemma297b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(ts"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9297"(t)):or(nis(x,0c),pos(ts"r"(m,n)))
-mi@[o:or(nis(x,0c),pos(m))][i:is(x,0c)]
-+*9297
-i@t4:=ore2(nis(x,0c),pos(m),o,weli(is(x,0c),i)):pos(m)
-m1:=ntofrl(m,posintnatrl(m,t4,mi)):nat
-t5:=posexp(x,m,mi,o,t4):is(pw(x,m,mi,o),prod(m1,[t:1to(m1)]x))
-t6:=satz289b(m1,[t:1to(m1)]x,xout(m1),i):is(prod(m1,[t:1to(m1)]x),0c)
-t7:=tris(cx,pw(x,m,mi,o),prod(m1,[t:1to(m1)]x),0c,t5,t6):is(pw(x,m,mi,o),0c)
--9297
-i@pw0:=t7".9297":is(pw(x,m,mi,o),0c)
-ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
-+*9297
-ni@t8:=intts(m,mi,n,ni):intrl(ts"r"(m,n))
-o@prop1:=is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o))):'prop'
-[i:is(x,0c)]
-t9:=pw0(x,m,mi,lemma294a(o),i):is(pw(x,m,mi,lemma294a(o)),0c)
-t10:=pw0(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o),t9):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),0c)
-t11:=pw0(x,ts"r"(m,n),t8,lemma297b(o),i):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),0c)
-t12:=tris2(cx,pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),0c,t10,t11):prop1
-m@[mi:intrl(m)][p:nis(x,0c)]
-t13:=ori1(nis(x,0c),pos(m),p):or(nis(x,0c),pos(m))
-p0:=pw(x,m,mi,t13):cx
-[n:nat]
-nr:=rlofnt(n):real
-t14:=natintrl(nr,natrli(n)):intrl(nr)
-t15:=ori2(nis(p0,0c),pos(nr),natpos(nr,natrli(n))):or(nis(p0,0c),pos(nr))
-t16:=ori1(nis(x,0c),pos(ts"r"(m,nr)),p):or(nis(x,0c),pos(ts"r"(m,nr)))
-t17:=intts(m,mi,nr,t14):intrl(ts"r"(m,nr))
-prop2:=is(pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16)):'prop'
-p@t18:=ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t15(1),lemma291(p0)):is(pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)))
-t19:=satz291(p0):is(pw(p0,1rl,intrl1,lemma291(p0)),p0)
-t20:=ispw2(x,m,ts"r"(m,1rl),satz195a(m),mi,t17(1),t13,t16(1)):is(p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)))
-t21:=tr3is(cx,pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)),t18,t19,t20):prop2(1)
-n@[p2:prop2(n)]
-n1:=pl"n"(n,1):nat
-t22:=satz290(x,m,mi,t13,p):nis(p0,0c)
-t23:=ori1(nis(p0,0c),and(pos(nr),pos(1rl)),t22):or(nis(p0,0c),and(pos(nr),pos(1rl)))
-t24:=lemma294a(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(nr))
-t25:=lemma294b(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(1rl))
-t26:=lemma294c(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(pl"r"(nr,1rl)))
-t27:=ispw2(p0,nr(n1),pl"r"(nr,1rl),satzr155a(n,1),t14(n1),intpl(nr,t14,1rl,intrl1),t15(n1),t26):is(pw(p0,nr(n1),t14(n1),t15(n1)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
-t27a:=satz294(p0,nr,1rl,t14,intrl1,t23):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
-t28:=tris2(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26),t27,t27a):is(pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)))
-t29:=ori1(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)),p):or(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)))
-t30:=lemma294a(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(ts"r"(m,nr)))
-t31:=lemma294b(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(m))
-t32:=lemma294c(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(pl"r"(ts"r"(m,nr),m)))
-t33:=tr3is(cx,pw(p0,nr,t14,t24),pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16),pw(x,ts"r"(m,nr),t17,t30),ispw1(p0,p0,nr,refis(cx,p0),t14,t24,t15),p2,ispw1(x,x,ts"r"(m,nr),refis(cx,x),t17,t16,t30)):is(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30))
-t34:=tr3is(cx,pw(p0,1rl,intrl1,t25),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,m,mi,t31),ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t25,lemma291(p0)),t19,ispw1(x,x,m,refis(cx,x),mi,t13,t31)):is(pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31))
-t35:=ists12(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30),pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31),t33,t34):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)))
-t36:=satz294(x,ts"r"(m,nr),m,t17,mi,t29):is(ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32))
-t37:=tr3is(real,pl"r"(ts"r"(m,nr),m),pl"r"(ts"r"(m,nr),ts"r"(m,1rl)),ts"r"(m,pl"r"(nr,1rl)),ts"r"(m,nr(n1)),ispl2"r"(m,ts"r"(m,1rl),ts"r"(m,nr),satz195a(m)),distpt2"r"(m,nr,1rl),ists2"r"(pl"r"(nr,1rl),nr(n1),m,satzr155b(n,1))):is"r"(pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)))
-t38:=ispw2(x,pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)),t37,intpl(ts"r"(m,nr),t17,m,mi),t17(n1),t32,t16(n1)):is(pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)))
-t39:=tr4is(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)),t28,t35,t36,t38):prop2(n1)
-t40:=isp(nat,[t:nat]prop2(t),n1,<n>suc,t39,satz4a(n)):prop2(<n>suc)
-n@t41:=induction([t:nat]prop2(t),t21,[t:nat][u:prop2(t)]t40(t,u),n):prop2(n)
-o@[p:nis(x,0c)][q:pos(n)]
-t42:=posintnatrl(n,q,ni):natrl(n)
-n0:=ntofrl(n,t42):nat
-t43:=isrlnt1(n,t42):is"r"(n,rlofnt(n0))
-t44:=isrlnt2(n,t42):is"r"(rlofnt(n0),n)
-o@p1:=pw(x,m,mi,lemma294a(o)):cx
-q@t44a:=ispw2(x,m,m,refis(real,m),mi,mi,lemma294a(o),t13(mi,p)):is(p1,p0(mi,p))
-t45:=ispw12(p1,p0(mi,p),n,rlofnt(n0),t44a,t43,ni,t14(mi,p,n0),lemma297a(o),t15(mi,p,n0)):is(pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)))
-t46:=t41(mi,p,n0):is(pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)))
-t47:=ists2"r"(rlofnt(n0),n,m,t44):is"r"(ts"r"(m,rlofnt(n0)),ts"r"(m,n))
-t48:=ispw2(x,ts"r"(m,rlofnt(n0)),ts"r"(m,n),t47,t17(mi,p,n0),t8,t16(mi,p,n0),lemma297b(o)):is(pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)))
-t49:=tr3is(cx,pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)),t45,t46,t48):prop1
-p@[i:is"r"(n,0)]
-t50:=0exp(p1,n,ni,lemma297a(o),i):is(pw(p1,n,ni,lemma297a(o)),1c)
-t51:=ts02"r"(m,n,i):is"r"(ts"r"(m,n),0)
-t52:=0exp(x,ts"r"(m,n),t8,lemma297b(o),t51):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),1c)
-t53:=tris2(cx,pw(p1,n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),1c,t50,t52):prop1
-p@[q:neg(n)]
-an:=abs(n):real
-t54:=intabs(n,ni):intrl(an)
-t55:=ori1(nis(x,0c),and(pos(m),pos(an)),p):or(nis(x,0c),and(pos(m),pos(an)))
-p1t55:=p1(an,mi,t54,t55):cx
-t56:=satz166e(n,nnot0(n,q)):pos(an)
-t56a:=lemma294a(an,mi,t54,t55):or(nis(x,0c),pos(m))
-t57:=lemma297a(an,mi,t54,t55):or(nis(p1t55,0c),pos(an))
-t58:=lemma297b(an,mi,t54,t55):or(nis(x,0c),pos(ts"r"(m,an)))
-t59:=t49(an,mi,t54,t55,p,t56):is(pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58))
-t60:=satz177c(an,n,absn(n,q)):is"r"(n,m0"r"(an))
-t61:=intm0(an,t54):intrl(m0"r"(an))
-t62:=satz290(x,m,mi,t56a,p):nis(p1t55,0c)
-t63:=lemma296(p1t55,an,t54,t62):or(nis(p1t55,0c),pos(an))
-t64:=satz290(p1t55,an,t54,t63,t62):nis(pw(p1t55,an,t54,t63),0c)
-t65:=lemma296(p1t55,m0"r"(an),t61,t62):or(nis(p1t55,0c),pos(m0"r"(an)))
-t66:=satz296(p1t55,an,t54,t62):is(ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65))
-t67:=ispw1(x,x,m,refis(cx,x),mi,lemma294a(o),t56a):is(p1,p1t55)
-t68:=ispw12(p1,p1t55,n,m0"r"(an),t67,t60,ni,t61,lemma297a(o),t65):is(pw(p1,n,ni,lemma297a(o)),pw(p1t55,m0"r"(an),t61,t65))
-t69:=tris2(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65),t68,t66):is(pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64))
-t70:=tris(real,m0"r"(ts"r"(m,an)),ts"r"(m,m0"r"(an)),ts"r"(m,n),satz197f(m,an),ists2"r"(m0"r"(an),n,m,symis(real,n,m0"r"(an),t60))):is"r"(m0"r"(ts"r"(m,an)),ts"r"(m,n))
-t71:=intm0(ts"r"(m,an),t8(an,mi,t54)):intrl(m0"r"(ts"r"(m,an)))
-t72:=lemma296(x,ts"r"(m,an),t8(an,mi,t54),p):or(nis(x,0c),pos(ts"r"(m,an)))
-t73:=satz290(x,ts"r"(m,an),t8(an,mi,t54),t72,p):nis(pw(x,ts"r"(m,an),t8(an,mi,t54),t72),0c)
-t74:=lemma296(x,m0"r"(ts"r"(m,an)),t71,p):or(nis(x,0c),pos(m0"r"(ts"r"(m,an))))
-t75:=satz296(x,ts"r"(m,an),t8(an,mi,t54),p):is(ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74))
-t76:=ispw2(x,m0"r"(ts"r"(m,an)),ts"r"(m,n),t70,t71,t8,t74,lemma297b(o)):is(pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)))
-t77:=ispw1(p1t55,p1t55,an,refis(cx,p1t55),t54,t63,t57):is(pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57))
-t78:=ispw1(x,x,ts"r"(m,an),refis(cx,x),t8(an,mi,t54),t58,t72):is(pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
-t79:=tr3is(cx,pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t77,t59,t78):is(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
-t80:=isov2(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),1c,t79,t64,t73):is(ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73))
-t81:=tr4is(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)),t69,t80,t75,t76):prop1
-p@t82:=rapp(n,prop1,[t:pos(n)]t49(t),[t:is"r"(n,0)]t53(t),[t:neg(n)]t81(t)):prop1
--9297
-o@satz297:=th1"l.imp"(is(x,0c),prop1".9297",[t:is(x,0c)]t12".9297"(t),[t:nis(x,0c)]t82".9297"(t)):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),intts(m,mi,n,ni),lemma297b(o)))
-@[r:real][s:real]
-+10298
-t1:=tris(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),pl"r"(0,0)),pli(pl"r"(r,s),0),plis12a(r,0,s,0),isrecx2(pl"r"(0,0),0,pl"r"(r,s),pl01(0,0,refis(real,0)))):is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
--10298
-satz298a:=symis(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0),t1".10298"):is(pli(pl"r"(r,s),0),pl(pli(r,0),pli(s,0)))
-satz298b:=t1".10298":is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
-+*10298
-s@t2:=tris(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),mn"r"(0,0)),pli(mn"r"(r,s),0),mnis12a(r,0,s,0),isrecx2(mn"r"(0,0),0,mn"r"(r,s),pl02(0,m0"r"(0),satz176b(0,refis(real,0))))):is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
--10298
-s@satz298c:=symis(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0),t2".10298"):is(pli(mn"r"(r,s),0),mn(pli(r,0),pli(s,0)))
-satz298d:=t2".10298":is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
-+*10298
-s@t3:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
-t4:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
-t5:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t3,t4)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
--10298
-s@satz298e:=symis(cx,ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0),t5".10298"):is(pli(ts"r"(r,s),0),ts(pli(r,0),pli(s,0)))
-satz298f:=t5".10298":is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
-[n:nis"r"(s,0)]
-+*10298
-n@[i:is(pli(s,0),0c)]
-t6:=tr3is(real,s,re(pli(s,0)),re(0c),0,isre(s,0),iscere(pli(s,0),0c,i),reis(0,0)):is"r"(s,0)
--10298
-n@lemma298:=th3"l.imp"(is(pli(s,0),0c),is"r"(s,0),n,[t:is(pli(s,0),0c)]t6".10298"(t)):nis(pli(s,0),0c)
-+*10298
-n@t7:=tris(cx,ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(ts"r"(s,ov"r"(r,s,n)),0),pli(r,0),t5(s,ov"r"(r,s,n)),isrecx1(ts"r"(s,ov"r"(r,s,n)),r,0,satz204c(r,s,n))):is(ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(r,0))
--10298
-n@satz298g:=satz229g(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(pli(ov"r"(r,s,n),0),ov(pli(r,0),pli(s,0),lemma298))
-satz298h:=satz229h(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(ov(pli(r,0),pli(s,0),lemma298),pli(ov"r"(r,s,n),0))
-+*10298
-r@t8:=tris(cx,m0(pli(r,0)),pli(m0"r"(r),m0"r"(0)),pli(m0"r"(r),0),m0isa(r,0),isrecx2(m0"r"(0),0,m0"r"(r),satz176b(0,refis(real,0)))):is(m0(pli(r,0)),pli(m0"r"(r),0))
--10298
-r@satz298j:=symis(cx,m0(pli(r,0)),pli(m0"r"(r),0),t8".10298"):is(pli(m0"r"(r),0),m0(pli(r,0)))
-satz298k:=t8".10298":is(m0(pli(r,0)),pli(m0"r"(r),0))
-+*10298
-r@t9:=tris(real,mod2(pli(r,0)),ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(r,r),pl02(ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(im(pli(r,0)),im(pli(r,0))),ts01(im(pli(r,0)),im(pli(r,0)),imis(r,0))),ists12"r"(re(pli(r,0)),r,re(pli(r,0)),r,reis(r,0),reis(r,0))):is"r"(mod2(pli(r,0)),ts"r"(r,r))
-ar:=abs(r):real
-[p:pos(r)]
-t10:=satz196a(r,r,p,p):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-r@[i:is"r"(r,0)]
-t11:=tris2(real,ts"r"(r,r),ts"r"(ar,ar),0,ts01(r,r,i),ts01(ar,ar,abs0(r,i))):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-r@[n:neg(r)]
-t12:=satz196b(r,r,n,n):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-r@t13:=rapp(r,is"r"(ts"r"(r,r),ts"r"(ar,ar)),[t:pos(r)]t10(t),[t:is"r"(r,0)]t11(t),[t:neg(r)]t12(t)):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-t14:=tris(real,mod2(pli(r,0)),ts"r"(r,r),ts"r"(ar,ar),t9,t13):is"r"(mod2(pli(r,0)),ts"r"(ar,ar))
-t15:=th1"l.imp"(is"r"(r,0),not(neg(ar)),[t:is"r"(r,0)]0notn(ar,abs0(r,t)),[t:nis"r"(r,0)]pnotn(ar,satz166e(r,t))):not(neg(ar))
--10298
-r@satz298l:=thsqrt3(mod2(pli(r,0)),lemma5(pli(r,0)),abs(r),t15".10298",t14".10298"):is"r"(mod(pli(r,0)),abs(r))
-satz298m:=symis(real,mod(pli(r,0)),abs(r),satz298l):is"r"(abs(r),mod(pli(r,0)))
-cofrl:=pli(r,0):complex
-s@[i:is(cofrl(r),cofrl(s))]
-isrlic:=tr3is(real,r,re(cofrl(r)),re(cofrl(s)),s,isre(r,0),iscere(cofrl(r),cofrl(s),i),reis(s,0)):is"r"(r,s)
-s@[i:is"r"(r,s)]
-isrlec:=isrecx1(r,s,0,i):is(cofrl(r),cofrl(s))
-+v10
-@t1:=[t:real][u:real][v:is(cofrl(t),cofrl(u))]isrlic(t,u,v):injective(real,cx,[t:real]cofrl(t))
--v10
-@[x:cx]
-realc:=image(real,cx,[t:real]cofrl(t),x):'prop'
-r@reali:=imagei(real,cx,[t:real]cofrl(t),r):realc(cofrl(r))
-x@[rx:realc(x)]
-rlofc:=soft(real,cx,[t:real]cofrl(t),t1".v10",x,rx):real
-[y:cx][ry:realc(y)][i:is"r"(rlofc(x,rx),rlofc(y,ry))]
-iscirl:=isinve(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is(x,y)
-ry@[i:is(x,y)]
-iscerl:=isinv(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is"r"(rlofc(x,rx),rlofc(y,ry))
-r@isrlc1:=isst1(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(r,rlofc(cofrl(r),reali(r)))
-isrlc2:=isst2(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(rlofc(cofrl(r),reali(r)),r)
-rx@iscrl1:=ists1"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(x,cofrl(rlofc(x,rx)))
-iscrl2:=ists2"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(cofrl(rlofc(x,rx)),x)
-@[n:nat]
-cofn:=cofrl(rlofnt(n)):complex
-[m:nat][i:is"n"(n,m)]
-isnec:=isrlec(rlofnt(n),rlofnt(m),isnterl(n,m,i)):is(cofn(n),cofn(m))
-m@[i:is(cofn(n),cofn(m))]
-isnic:=isntirl(n,m,isrlic(rlofnt(n),rlofnt(m),i)):is"n"(n,m)
-+*v10
-@t2:=[t:nat][u:nat][v:is(cofn(t),cofn(u))]isnic(t,u,v):injective(nat,cx,[t:nat]cofn(t))
--v10
-x@natc:=image(nat,cx,[t:nat]cofn(t),x):'prop'
-n@nati:=imagei(nat,cx,[t:nat]cofn(t),n):natc(cofn(n))
-x@[nx:natc(x)]
-nofc:=soft(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):nat
-[y:cx][ny:natc(y)][i:is(x,y)]
-iscen:=isinv(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is"n"(nofc(x,nx),nofc(y,ny))
-ny@[i:is"n"(nofc(x,nx),nofc(y,ny))]
-iscin:=isinve(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is(x,y)
-n@isnc1:=isst1(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(n,nofc(cofn(n),nati(n)))
-isnc2:=isst2(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(nofc(cofn(n),nati(n)),n)
-nx@iscn1:=ists1"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(x,cofn(nofc(x,nx)))
-iscn2:=ists2"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(cofn(nofc(x,nx)),x)
-@natt:=ot(cx,[t:cx]natc(t)):'type'
-[nt:natt]
-cofnt:=in"e"(cx,[t:cx]natc(t),nt):cx
-natti:=inp(cx,[t:cx]natc(t),nt):natc(cofnt(nt))
-[mt:natt][i:is"e"(natt,nt,mt)]
-isntec:=isini(cx,[t:cx]natc(t),nt,mt,i):is(cofnt(nt),cofnt(mt))
-mt@[i:is(cofnt(nt),cofnt(mt))]
-isntic:=isine(cx,[t:cx]natc(t),nt,mt,i):is"e"(natt,nt,mt)
-nx@ntofc:=out(cx,[t:cx]natc(t),x,nx):natt
-ny@[i:is(x,y)]
-iscent:=isouti(cx,[t:cx]natc(t),x,nx,y,ny,i):is"e"(natt,ntofc(x,nx),ntofc(y,ny))
-ny@[i:is"e"(natt,ntofc(x,nx),ntofc(y,ny))]
-iscint:=isoute(cx,[t:cx]natc(t),x,nx,y,ny,i):is(x,y)
-nt@isntc1:=isoutin(cx,[t:cx]natc(t),nt):is"e"(natt,nt,ntofc(cofnt(nt),natti(nt)))
-isntc2:=symis(natt,nt,ntofc(cofnt(nt),natti(nt)),isntc1):is"e"(natt,ntofc(cofnt(nt),natti(nt)),nt)
-nx@iscnt1:=isinout(cx,[t:cx]natc(t),x,nx):is(x,cofnt(ntofc(x,nx)))
-iscnt2:=symis(cx,x,cofnt(ntofc(x,nx)),iscnt1):is(cofnt(ntofc(x,nx)),x)
-n@ntofn:=ntofc(cofn(n),nati(n)):natt
-m@[i:is"n"(n,m)]
-isnent:=iscent(cofn(n),nati(n),cofn(m),nati(m),isnec(n,m,i)):is"e"(natt,ntofn(n),ntofn(m))
-m@[i:is"e"(natt,ntofn(n),ntofn(m))]
-isnint:=isnic(n,m,iscint(cofn(n),nati(n),cofn(m),nati(m),i)):is"n"(n,m)
-nt@nofnt:=nofc(cofnt(nt),natti(nt)):nat
-mt@[i:is"e"(natt,nt,mt)]
-isnter:=iscen(cofnt(nt),natti(nt),cofnt(mt),natti(mt),isntec(nt,mt,i)):is"n"(nofnt(nt),nofnt(mt))
-mt@[i:is"n"(nofnt(nt),nofnt(mt))]
-isntin:=isntic(nt,mt,iscin(cofnt(nt),natti(nt),cofnt(mt),natti(mt),i)):is"e"(natt,nt,mt)
-+*v10
-n@t3:=iscnt1(cofn(n),nati(n)):is(cofn(n),cofnt(ntofn(n)))
--v10
-n@isnnt1:=tris(nat,n,nofc(cofn(n),nati(n)),nofnt(ntofn(n)),isnc1(n),iscen(cofn(n),nati(n),cofnt(ntofn(n)),natti(ntofn(n)),t3".v10")):is"n"(n,nofnt(ntofn(n)))
-isnnt2:=symis(nat,n,nofnt(ntofn(n)),isnnt1):is"n"(nofnt(ntofn(n)),n)
-+*v10
-nt@t4:=iscn1(cofnt(nt),natti(nt)):is(cofnt(nt),cofn(nofnt(nt)))
--v10
-nt@isntn1:=tris(natt,nt,ntofc(cofnt(nt),natti(nt)),ntofn(nofnt(nt)),isntc1(nt),iscent(cofnt(nt),natti(nt),cofn(nofnt(nt)),nati(nofnt(nt)),t4".v10")):is"e"(natt,nt,ntofn(nofnt(nt)))
-isntn2:=symis(natt,nt,ntofn(nofnt(nt)),isntn1):is"e"(natt,ntofn(nofnt(nt)),nt)
-@1t:=ntofn(1):natt
-suct:=[t:natt]ntofn(<nofnt(t)>suc):[t:natt]natt
-+10299
-nt@[i:is"e"(natt,<nt>suct,1t)]
-t1:=isnint(<nofnt(nt)>suc,1,i):is"n"(<nofnt(nt)>suc,1)
--10299
-nt@satz299a:=th3"l.imp"(is"e"(natt,<nt>suct,1t),is"n"(<nofnt(nt)>suc,1),<nofnt(nt)>ax3,[t:is"e"(natt,<nt>suct,1t)]t1".10299"(t)):not(is"e"(natt,<nt>suct,1t))
-@ax3t:=[t:natt]satz299a(t):[t:natt]not(is"e"(natt,<t>suct,1t))
-mt@[i:is"e"(natt,<nt>suct,<mt>suct)]
-+*10299
-i"c"@t2:=isnint(<nofnt(nt)>suc,<nofnt(mt)>suc,i):is"n"(<nofnt(nt)>suc,<nofnt(mt)>suc)
-t3:=<t2><nofnt(mt)><nofnt(nt)>ax4:is"n"(nofnt(nt),nofnt(mt))
--10299
-i@satz299b:=isntin(nt,mt,t3".10299"):is"e"(natt,nt,mt)
-@ax4t:=[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]satz299b(t,u,v):[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]is"e"(natt,t,u)
-[s:set(natt)]
-cond1t:=esti(natt,1t,s):'prop'
-cond2t:=all"l"(natt,[t:natt]imp(esti(natt,t,s),esti(natt,<t>suct,s))):'prop'
-[c1:cond1t][c2:cond2t]
-+*10299
-c2@[n:nat]
-prop1:=esti(natt,ntofn(n),s):'prop'
-c2@t4:=c1:prop1(1)
-n@[p:prop1(n)]
-t5:=<p><ntofn(n)>c2:esti(natt,ntofn(<nofnt(ntofn(n))>suc),s)
-t6:=isp(nat,[t:nat]esti(natt,ntofn(<t>suc),s),nofnt(ntofn(n)),n,t5,isnnt2(n)):prop1(<n>suc)
-c2@[nt:natt]
-t7:=induction([t:nat]prop1(t),t4,[t:nat][u:prop1(t)]t6(t,u),nofnt(nt)):prop1(nofnt(nt))
--10299
-c2@satz299c:=[t:natt]isp(natt,[u:natt]esti(natt,u,s),ntofn(nofnt(t)),t,t7".10299"(t),isntn2(t)):[t:natt]esti(natt,t,s)
-@ax5t:=[t:set(natt)][u:cond1t(t)][v:cond2t(t)]satz299c(t,u,v):[t:set(natt)][u:cond1t(t)][v:cond2t(t)][w:natt]esti(natt,w,t)
-ic:=pli(0,1rl):complex
-+10300
-t1:=tsis12a(0,1rl,0,1rl):is(ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))))
-t2:=tris(real,mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(ts"r"(1rl,1rl)),m0"r"(1rl),pl01(ts"r"(0,0),m0"r"(ts"r"(1rl,1rl)),ts01(0,0,refis(real,0))),ism0"r"(ts"r"(1rl,1rl),1rl,satz195(1rl))):is"r"(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl))
-t3:=tris(real,pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),ts"r"(1rl,0),0,pl01(ts"r"(0,1rl),ts"r"(1rl,0),ts01(0,1rl,refis(real,0))),ts02(1rl,0,refis(real,0))):is"r"(pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0)
-t4:=isrecx12(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0,t2,t3):is(pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)))
-t5:=satz298j(1rl):is(cofrl(m0"r"(1rl)),m0(1c))
--10300
-satz2300:=tr3is(cx,ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)),m0(1c),t1".10300",t4".10300",t5".10300"):is(ts(ic,ic),m0(1c))
-[r:real][s:real]
-+10301
-t1:=tsis12a(s,0,0,1rl):is(ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))))
-t2:=tris(real,mn"r"(ts"r"(s,0),ts"r"(0,1rl)),m0"r"(ts"r"(0,1rl)),0,pl01(ts"r"(s,0),m0"r"(ts"r"(0,1rl)),ts02(s,0,refis(real,0))),satz176b(ts"r"(0,1rl),ts01(0,1rl,refis(real,0)))):is"r"(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0)
-t3:=tris(real,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),ts"r"(s,1rl),s,pl02(ts"r"(s,1rl),ts"r"(0,0),ts01(0,0,refis(real,0))),satz195(s)):is"r"(pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s)
-t4:=isrecx12(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s,t2,t3):is(pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s))
-t5:=tris(cx,ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s),t1,t4):is(ts(cofrl(s),ic),pli(0,s))
-t6:=ispl2(ts(cofrl(s),ic),pli(0,s),cofrl(r),t5):is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)))
-t7:=plis12a(r,0,0,s):is(pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)))
-t8:=isrecx12(pl"r"(r,0),r,pl"r"(0,s),s,pl02(r,0,refis(real,0)),pl01(0,s,refis(real,0))):is(pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s))
--10301
-satz301a:=tr3is(cx,pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s),t6".10301",t7".10301",t8".10301"):is"e"(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s))
-satz301b:=symis(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s),satz301a):is(pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)))
-@[x:complex]
-satz301c:=tris(cx,x,pli(re(x),im(x)),pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),ispli(x),satz301b(re(x),im(x))):is(x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)))
-satz301d:=symis(cx,x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),satz301c):is(pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),x)
-s@[t:real][u:real][i:is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)))]
-+*10301
-i@t9:=tr3is(cx,pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)),pli(t,u),satz301b(r,s),i,satz301a(t,u)):is(pli(r,s),pli(t,u))
--10301
-i@satz301e:=tr3is(real,r,re(pli(r,s)),re(pli(t,u)),t,isre(r,s),iscere(pli(r,s),pli(t,u),t9".10301"),reis(t,u)):is"r"(r,t)
-satz301f:=tr3is(real,s,im(pli(r,s)),im(pli(t,u)),u,isim(r,s),isceim(pli(r,s),pli(t,u),t9".10301"),imis(t,u)):is"r"(s,u)
--c
--r
--rp
--rt
--n
--landau
--eq
--st
--e
--l
+++ /dev/null
-# Landau's "Grundlagen der Analysis", formal specification in AUTOMATH
-# Copyright (C) 1977, L.S. van Benthem Jutting
-# 1992, revised by F. Wiedijk (http://www.cs.ru.nl/~freek/aut/)
-# 2008, revised by F. Guidi to remove the eta-reductions
-
-+l
-@[a:'prop'][b:'prop']
-imp:=[x:a]b:'prop'
-[a1:a][i:imp(a,b)]
-mp:=<a1>i:b
-a@refimp:=[x:a]x:imp(a,a)
-b@[c:'prop'][i:imp(a,b)][j:imp(b,c)]
-trimp:=[x:a]<<x>i>j:imp(a,c)
-@con:='prim':'prop'
-a@not:=imp(con):'prop'
-wel:=not(not(a)):'prop'
-[a1:a]
-weli:=[x:not(a)]<a1>x:wel(a)
-a@[w:wel(a)]
-et:='prim':a
-a@[c1:con]
-cone:=et([x:not(a)]c1):a
-+imp
-b@[i:imp(a,b)][j:imp(not(a),b)]
-th1:=et(b,[x:not(b)]<<trimp(con,i,x)>j>x):b
-b@[n:not(a)]
-th2:=trimp(con,b,n,[x:con]cone(b,x)):imp(a,b)
-b@[n:not(b)][i:imp(a,b)]
-th3:=trimp(con,i,n):not(a)
-b@[a1:a][n:not(b)]
-th4:=[x:imp(a,b)]<a1>th3(n,x):not(imp(a,b))
-b@[n:not(imp(a,b))]
-th5:=et([x:not(a)]<th2(x)>n):a
-th6:=[x:b]<[y:a]x>n:not(b)
-b@[n:not(b)][i:imp(not(a),b)]
-th7:=et(a,th3(not(a),b,n,i)):a
--imp
-b@[i:imp(not(b),not(a))]
-cp:=[x:a]th7".imp"(b,not(a),weli(x),i):imp(a,b)
-@obvious:=imp(con,con):'prop'
-obviousi:=refimp(con):obvious
-b@ec:=imp(a,not(b)):'prop'
-[n:not(a)]
-eci1:=th2".imp"(not(b),n):ec(a,b)
-b@[n:not(b)]
-eci2:=[x:a]n:ec(a,b)
-+ec
-b@[i:imp(a,not(b))]
-th1:=i:ec(a,b)
-b@[i:imp(b,not(a))]
-th2:=[x:a][y:b]<x><y>i:ec(a,b)
--ec
-b@[e:ec(a,b)]
-comec:=th2".ec"(b,a,e):ec(b,a)
-[a1:a]
-ece1:=<a1>e:not(b)
-e@[b1:b]
-ece2:=th3".imp"(not(b),weli(b,b1),e):not(a)
-+*ec
-c@[e:ec(a,b)][i:imp(c,a)]
-th3:=trimp(c,a,not(b),i,e):ec(c,b)
-e@[i:imp(c,b)]
-th4:=comec(c,a,th3(b,a,c,comec(e),i)):ec(a,c)
--ec
-b@and:=not(ec(a,b)):'prop'
-[a1:a][b1:b]
-andi:=th4".imp"(not(b),a1,weli(b,b1)):and(a,b)
-b@[a1:and(a,b)]
-ande1:=th5".imp"(not(b),a1):a
-ande2:=et(b,th6".imp"(not(b),a1)):b
-comand:=andi(b,a,ande2,ande1):and(b,a)
-+and
-b@[n:not(a)]
-th1:=weli(ec,eci1(n)):not(and)
-b@[n:not(b)]
-th2:=weli(ec,eci2(n)):not(and)
-b@[n:not(and)][a1:a]
-th3:=ece1(et(ec,n),a1):not(b)
-n@[b1:b]
-th4:=ece2(et(ec,n),b1):not(a)
-n@th5:=th3"l.imp"(and(b,a),and(a,b),n,[x:and(b,a)]comand(b,a,x)):not(and(b,a))
-c@[a1:and(a,b)][i:imp(a,c)]
-th6:=andi(c,b,<ande1(a1)>i,ande2(a1)):and(c,b)
-a1@[i:imp(b,c)]
-th7:=andi(a,c,ande1(a1),<ande2(a1)>i):and(a,c)
--and
-b@or:=imp(not(a),b):'prop'
-[a1:a]
-ori1:=th2".imp"(not(a),b,weli(a1)):or(a,b)
-b@[b1:b]
-ori2:=[x:not(a)]b1:or(a,b)
-+or
-b@[i:imp(not(a),b)]
-th1:=i:or(a,b)
-b@[i:imp(not(b),a)]
-th2:=[x:not]et(b,th3"l.imp"(not(b),a,x,i)):or(a,b)
--or
-b@[o:or(a,b)][n:not(a)]
-ore2:=<n>o:b
-o@[n:not(b)]
-ore1:=et(th3".imp"(not(a),b,n,o)):a
-o@comor:=[x:not(b)]ore1(x):or(b,a)
-+*or
-b@[n:not(a)][m:not(b)]
-th3:=th4"l.imp"(not(a),b,n,m):not(or(a,b))
-b@[n:not(or(a,b))]
-th4:=th5"l.imp"(not(a),b,n):not(a)
-th5:=th6"l.imp"(not(a),b,n):not(b)
-a@th6:=refimp(not(a)):or(a,not(a))
--or
-c@[o:or(a,b)][i:imp(a,c)][j:imp(b,c)]
-orapp:=th1".imp"(c,i,trimp(not,b,c,o,j)):c
-c@[d:'prop']
-+*or
-o@[i:imp(a,c)]
-th7:=trimp(not(c),not,b,[x:not(c)]th3"l.imp"(a,c,x,i),o):or(c,b)
-o@[i:imp(b,c)]
-th8:=trimp(not(a),b,c,o,i):or(a,c)
-d@[o:or(a,b)][i:imp(a,c)][j:imp(b,d)]
-th9:=th7(a,d,c,th8(a,b,d,o,j),i):or(c,d)
-b@[o:or(a,b)]
-th10:=o:imp(not(a),b)
-th11:=comor(o):imp(not(b),a)
-b@[o:or(not(a),b)]
-th12:=trimp(a,wel(a),b,[x:a]weli(x),o):imp(a,b)
-b@[i:imp(a,b)]
-th13:=trimp(wel(a),a,b,[x:wel(a)]et(x),i):or(not(a),b)
-b@[o:or(not(a),not(b))]
-th14:=weli(ec,th12(not(b),o)):not(and)
-b@[n:not(and)]
-th15:=th13(not(b),et(ec,n)):or(not(a),not(b))
-b@[a1:and(not(a),not(b))]
-th16:=th3(ande1(not(a),not(b),a1),ande2(not(a),not(b),a1)):not(or(a,b))
-b@[n:not(or(a,b))]
-th17:=andi(not(a),not(b),th4(n),th5(n)):and(not(a),not(b))
--or
-b@orec:=and(or(a,b),ec(a,b)):'prop'
-[o:or(a,b)][e:ec(a,b)]
-oreci:=andi(or(a,b),ec(a,b),o,e):orec(a,b)
-+orec
-b@[a1:a][n:not(b)]
-th1:=oreci(ori1(a1),eci2(n)):orec(a,b)
-b@[n:not(a)][b1:b]
-th2:=oreci(ori2(b1),eci1(n)):orec(a,b)
--orec
-b@[o:orec(a,b)]
-orece1:=ande1(or(a,b),ec,o):or(a,b)
-orece2:=ande2(or(a,b),ec,o):ec(a,b)
-comorec:=oreci(b,a,comor(orece1),comec(orece2)):orec(b,a)
-+*orec
-o@[a1:a]
-th3:=ece1(orece2,a1):not(b)
-o@[b1:b]
-th4:=ece2(orece2,b1):not(a)
-o@[n:not(a)]
-th5:=ore2(orece1,n):b
-o@[n:not(b)]
-th6:=ore1(orece1,n):a
--orec
-b@iff:=and(imp(a,b),imp(b,a)):'prop'
-[i:imp(a,b)][j:imp(b,a)]
-iffi:=andi(imp(a,b),imp(b,a),i,j):iff(a,b)
-+iff
-b@[a1:a][b1:b]
-th1:=iffi([x:a]b1,[x:b]a1):iff(a,b)
-b@[n:not(a)][m:not(b)]
-th2:=iffi(th2"l.imp"(n),th2"l.imp"(b,a,m)):iff(a,b)
--iff
-b@[i:iff(a,b)]
-iffe1:=ande1(imp(a,b),imp(b,a),i):imp(a,b)
-iffe2:=ande2(imp(a,b),imp(b,a),i):imp(b,a)
-comiff:=iffi(b,a,iffe2,iffe1):iff(b,a)
-+*iff
-i@[a1:a]
-th3:=<a1>iffe1:b
-i@[b1:b]
-th4:=<b1>iffe2:a
-i@[n:not(a)]
-th5:=th3"l.imp"(b,a,n,iffe2):not(b)
-i@[n:not(b)]
-th6:=th3"l.imp"(n,iffe1):not(a)
-b@[a1:a][n:not(b)]
-th7:=th1"l.and"(imp(a,b),imp(b,a),th4"l.imp"(a1,n)):not(iff(a,b))
-b@[n:not(a)][b1:b]
-th8:=th2"l.and"(imp(a,b),imp(b,a),th4"l.imp"(b,a,b1,n)):not(iff(a,b))
--iff
-a@refiff:=iffi(a,refimp,refimp):iff(a,a)
-b@[i:iff(a,b)]
-symiff:=comiff(i):iff(b,a)
-c@[i:iff(a,b)][j:iff(b,c)]
-triff:=iffi(a,c,trimp(iffe1(i),iffe1(b,c,j)),trimp(c,b,a,iffe2(b,c,j),iffe2(i))):iff(a,c)
-+*iff
-b@[i:iff(a,b)]
-th9:=[x:not(a)]th5(i,x):imp(not(a),not(b))
-th10:=[x:not(b)]th6(i,x):imp(not(b),not(a))
-th11:=iffi(not(a),not(b),th9,th10):iff(not(a),not(b))
-b@[i:imp(not(a),not(b))][j:imp(not(b),not(a))]
-th12:=iffi(cp(j),cp(b,a,i)):iff(a,b)
-b@[o:orec(a,b)]
-th13:=iffi(not(b),orece2(o),comor(orece1(o))):iff(a,not(b))
-th14:=th13(b,a,comorec(o)):iff(b,not(a))
-b@[i:iff(a,not(b))]
-th15:=oreci(comor(b,a,iffe2(not(b),i)),iffe1(not(b),i)):orec(a,b)
-b@[i:iff(b,not(a))]
-th16:=comorec(b,a,th15(b,a,i)):orec(a,b)
-c@[i:iff(a,b)][j:imp(a,c)]
-thimp1:=trimp(b,a,c,iffe2(i),j):imp(b,c)
-i@[j:imp(c,a)]
-thimp2:=trimp(c,a,b,j,iffe1(i)):imp(c,b)
-i@[e:ec(a,c)]
-thec1:=th3"l.ec"(c,b,e,iffe2(i)):ec(b,c)
-i@[e:ec(c,a)]
-thec2:=th4"l.ec"(c,a,b,e,iffe2(i)):ec(c,b)
-i@[a1:and(a,c)]
-thand1:=th6"l.and"(c,b,a1,iffe1(i)):and(b,c)
-i@[a1:and(c,a)]
-thand2:=th7"l.and"(c,a,b,a1,iffe1(i)):and(c,b)
-i@[o:or(a,c)]
-thor1:=th7"l.or"(c,b,o,iffe1(i)):or(b,c)
-i@[o:or(c,a)]
-thor2:=th8"l.or"(c,a,b,o,iffe1(i)):or(c,b)
-i@[o:orec(a,c)]
-thorec1:=oreci(b,c,thor1(orece1(a,c,o)),thec1(orece2(a,c,o))):orec(b,c)
-i@[o:orec(c,a)]
-thorec2:=oreci(c,b,thor2(orece1(c,a,o)),thec2(orece2(c,a,o))):orec(c,b)
--iff
-@[sigma:'type'][p:[x:sigma]'prop']
-%suggestion by van Daalen to remove the first eta-reduction
-%all:=p:'prop' %original line
-all:=[x:sigma]<x>p:'prop'
-%end of suggestion
-[a1:all(sigma,p)][s:sigma]
-alle:=<s>a1:<s>p
-+all
-p@[s:sigma][n:not(<s>p)]
-th1:=[x:all(sigma,p)]<<s>x>n:not(all(sigma,p))
--all
-p@non:=[x:sigma]not(<x>p):[x:sigma]'prop'
-some:=not(non(p)):'prop'
-[s:sigma][sp:<s>p]
-somei:=th1".all"(non(p),s,weli(<s>p,sp)):some(sigma,p)
-+some
-p@[n:not(all(sigma,p))][m:non(non(p))][s:sigma]
-t1:=et(<s>p,<s>m):<s>p
-%set etared
-m@t2:=<[x:sigma]t1(x)>n:con
-%reset etared
-n@th1:=[x:non(non(p))]t2(x):some(non(p))
-p@[s:some(non(p))][a1:all(sigma,p)][t:sigma]
-t3:=weli(<t>p,<t>a1):not(not(<t>p))
-a1@t4:=<[x:sigma]t3(x)>s:con
-s@th2:=[x:all(sigma,p)]t4(x):not(all(sigma,p))
-p@[n:not(some(sigma,p))]
-th3:=et(non(p),n):non(p)
-[s:sigma]
-th4:=<s>th3:not(<s>p)
-p@[n:non(p)]
-th5:=weli(non(p),n):not(some(sigma,p))
--some
-p@[s:some(sigma,p)][x:'prop'][i:[y:sigma]imp(<y>p,x)]
-+*some
-i@[n:not(x)][t:sigma]
-t5:=th3"l.imp"(<t>p,x,n,<t>i):not(<t>p)
-n@t6:=mp(some(sigma,p),con,s,th5([y:sigma]t5(y))):con
--some
-i@someapp:=et(x,[y:not(x)]t6".some"(y)):x
-+*some
-p@[q:[x:sigma]'prop'][s:some(sigma,p)][i:[x:sigma]imp(<x>p,<x>q)]
-th6:=someapp(s,some(q),[x:sigma][y:<x>p]somei(q,x,mp(<x>p,<x>q,y,<x>i))):some(q)
--some
-c@or3:=or(a,or(b,c)):'prop'
-[o:or3(a,b,c)][n:not(a)]
-+or3
-th1:=ore2(or(b,c),o,n):or(b,c)
--or3
-[m:not(b)]
-or3e3:=ore2(b,c,th1".or3",m):c
-o@[n:not(b)]
-+*or3
-n@th2:=th2"l.or"(c,a,[x:not(a)]or3e3(x,n)):or(c,a)
--or3
-n@[m:not(c)]
-or3e1:=ore2(c,a,th2".or3",m):a
-o@[n:not(c)]
-+*or3
-n@th3:=th2"l.or"([x:not(b)]or3e1(x,n)):or(a,b)
--or3
-n@[m:not(a)]
-or3e2:=ore2(th3".or3",m):b
-+*or3
-o@th4:=th1"l.or"(b,or(c,a),[x:not(b)]th2(x)):or3(b,c,a)
-th5:=th4(b,c,a,th4):or3(c,a,b)
--or3
-c@[a1:a]
-or3i1:=ori1(a,or(b,c),a1):or3(a,b,c)
-c@[b1:b]
-or3i2:=ori2(a,or(b,c),ori1(b,c,b1)):or3(a,b,c)
-c@[c1:c]
-or3i3:=ori2(a,or(b,c),ori2(b,c,c1)):or3(a,b,c)
-+*or3
-c@[o:or(a,b)]
-th6:=th4"or3"(c,a,b,ori2(c,or(a,b),o)):or3(a,b,c)
-c@[o:or(b,c)]
-th7:=ori2(or(b,c),o):or3(a,b,c)
-c@[o:or(c,a)]
-th8:=th4"or3"(c,a,b,th6(c,a,b,o)):or3(a,b,c)
--or3
-d@[o:or3(a,b,c)][i:imp(a,d)][j:imp(b,d)][k:imp(c,d)]
-or3app:=orapp(or(b,c),d,o,i,[x:or(b,c)]orapp(b,c,d,x,j,k)):d
-c@and3:=and(a,and(b,c)):'prop'
-[a1:and3(a,b,c)]
-and3e1:=ande1(and(b,c),a1):a
-and3e2:=ande1(b,c,ande2(and(b,c),a1)):b
-and3e3:=ande2(b,c,ande2(and(b,c),a1)):c
-c@[a1:a][b1:b][c1:c]
-and3i:=andi(a,and(b,c),a1,andi(b,c,b1,c1)):and3(a,b,c)
-+and3
-c@[a1:and3(a,b,c)]
-th1:=and3i(b,c,a,and3e2(a1),and3e3(a1),and3e1(a1)):and3(b,c,a)
-th2:=th1(b,c,a,th1):and3(c,a,b)
-th3:=andi(and3e1(a1),and3e2(a1)):and(a,b)
-th4:=ande2(and(b,c),a1):and(b,c)
-th5:=th3(c,a,b,th2):and(c,a)
-th6:=and3i(c,b,a,and3e3(a1),and3e2(a1),and3e1(a1)):and3(c,b,a)
--and3
-c@ec3:=and3(ec,ec(b,c),ec(c,a)):'prop'
-[e:ec3(a,b,c)]
-+ec3
-th1:=and3e1(ec,ec(b,c),ec(c,a),e):ec(a,b)
-th2:=and3e2(ec,ec(b,c),ec(c,a),e):ec(b,c)
-th3:=and3e3(ec,ec(b,c),ec(c,a),e):ec(c,a)
-th4:=th1"l.and3"(ec,ec(b,c),ec(c,a),e):ec3(b,c,a)
-th5:=th4(b,c,a,th4):ec3(c,a,b)
-th5a:=and3i(ec(c,b),ec(b,a),ec(a,c),comec(b,c,th2(e)),comec(a,b,th1(e)),comec(c,a,th3(e))):ec3(c,b,a)
--ec3
-[a1:a]
-ec3e12:=ece1(th1".ec3",a1):not(b)
-ec3e13:=ece2(c,a,th3".ec3",a1):not(c)
-e@[b1:b]
-ec3e23:=ec3e12(b,c,a,th4".ec3",b1):not(c)
-ec3e21:=ec3e13(b,c,a,th4".ec3",b1):not(a)
-e@[c1:c]
-ec3e31:=ec3e12(c,a,b,th5".ec3",c1):not(a)
-ec3e32:=ec3e13(c,a,b,th5".ec3",c1):not(b)
-+*ec3
-c@[e:ec(a,b)][f:ec(b,c)][g:ec(c,a)]
-th6:=and3i(ec,ec(b,c),ec(c,a),e,f,g):ec3(a,b,c)
-c@[e:ec3(a,b,c)][o:or(a,b)]
-th7:=orapp(not(c),o,[x:a]ece2(c,a,th3"ec3"(e),x),[x:b]ece1(b,c,th2"ec3"(e),x)):not(c)
-e@[o:or(b,c)]
-th8:=th7(b,c,a,th4"ec3"(e),o):not(a)
-e@[o:or(c,a)]
-th9:=th7(c,a,b,th5"ec3"(e),o):not(b)
--ec3
-c@[n:not(a)][m:not(b)]
-ec3i1:=th6".ec3"(eci1(n),eci1(b,c,m),eci2(c,a,n)):ec3(a,b,c)
-c@[n:not(b)][m:not(c)]
-ec3i2:=th6".ec3"(eci2(n),eci1(b,c,n),eci1(c,a,m)):ec3(a,b,c)
-c@[n:not(c)][m:not(a)]
-ec3i3:=th6".ec3"(eci1(m),eci2(b,c,n),eci1(c,a,n)):ec3(a,b,c)
-+*ec3
-d@[e:'prop'][f:'prop'][o1:or3(a,b,c)][p1:ec3(d,e,f)][i:imp(a,d)][j:imp(b,e)][k:imp(c,f)][d1:d]
-t1:=[x:b]mp(e,con,<x>j,ec3e12(d,e,f,p1,d1)):not(b)
-t2:=[x:c]mp(f,con,<x>k,ec3e13(d,e,f,p1,d1)):not(c)
-th10:=or3e1(o1,t1,t2):a
-k@[e1:e]
-th11:=th10(b,c,a,e,f,d,th4"l.or3"(o1),th4"ec3"(d,e,f,p1),j,k,i,e1):b
-k@[f1:f]
-th12:=th10(c,a,b,f,d,e,th5"l.or3"(o1),th5"ec3"(d,e,f,p1),k,i,j,f1):c
--ec3
-c@orec3:=and(or3(a,b,c),ec3(a,b,c)):'prop'
-[o:orec3(a,b,c)]
-orec3e1:=ande1(or3(a,b,c),ec3(a,b,c),o):or3(a,b,c)
-orec3e2:=ande2(or3(a,b,c),ec3(a,b,c),o):ec3(a,b,c)
-c@[o:or3(a,b,c)][e:ec3(a,b,c)]
-orec3i:=andi(or3(a,b,c),ec3(a,b,c),o,e):orec3(a,b,c)
-+orec3
-c@[o:orec3(a,b,c)]
-th1:=orec3i(b,c,a,th4"l.or3"(orec3e1(o)),th4"l.ec3"(orec3e2(o))):orec3(b,c,a)
-th2:=orec3i(c,a,b,th5"l.or3"(orec3e1(o)),th5"l.ec3"(orec3e2(o))):orec3(c,a,b)
--orec3
-+e
-sigma@[s:sigma][t:sigma]
-is:='prim':'prop'
-s@refis:='prim':is(s,s)
-p@[s:sigma][t:sigma][sp:<s>p][i:is(s,t)]
-isp:='prim':<t>p
-sigma@[s:sigma][t:sigma][i:is(s,t)]
-symis:=isp([x:sigma]is(x,s),s,t,refis(s),i):is(t,s)
-t@[u:sigma][i:is(s,t)][j:is(t,u)]
-tris:=isp([x:sigma]is(x,u),t,s,j,symis(i)):is(s,u)
-u@[i:is(u,s)][j:is(u,t)]
-tris1:=tris(s,u,t,symis(u,s,i),j):is(s,t)
-u@[i:is(s,u)][j:is(t,u)]
-tris2:=tris(s,u,t,i,symis(t,u,j)):is(s,t)
-sp@[i:is(t,s)]
-isp1:=isp(symis(t,s,i)):<t>p
-t@[n:not(is(s,t))]
-symnotis:=th3"l.imp"(is(t,s),is(s,t),n,[x:is(t,s)]symis(t,s,x)):not(is(t,s))
-+notis
-u@[n:not(is(s,t))][i:is(s,u)]
-th1:=isp([x:sigma]not(is(x,t)),s,u,n,i):not(is(u,t))
-n@[i:is(u,s)]
-th2:=th1(symis(u,s,i)):not(is(u,t))
-n@[i:is(t,u)]
-th3:=isp([x:sigma]not(is(s,x)),t,u,n,i):not(is(s,u))
-n@[i:is(u,t)]
-th4:=th3(symis(u,t,i)):not(is(s,u))
-u@[v:sigma][n:not(is(s,t))][i:is(s,u)][j:is(t,v)]
-th5:=th3(u,t,v,th1(n,i),j):not(is(u,v))
--notis
-u@[v:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)]
-tr3is:=tris(s,u,v,tris(i,j),k):is(s,v)
-v@[w:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)][l:is(v,w)]
-tr4is:=tris(s,v,w,tr3is(i,j,k),l):is(s,w)
-p@amone:=[x:sigma][y:sigma][u:<x>p][v:<y>p]is(x,y):'prop'
-[a1:amone(sigma,p)][s:sigma][t:sigma][sp:<s>p][tp:<t>p]
-amonee:=<tp><sp><t><s>a1:is(s,t)
-p@one:=and(amone(sigma,p),some(sigma,p)):'prop'
-[a1:amone(sigma,p)][s:some(sigma,p)]
-onei:=andi(amone(sigma,p),some(sigma,p),a1,s):one(sigma,p)
-p@[o1:one(sigma,p)]
-onee1:=ande1(amone(sigma,p),some(sigma,p),o1):amone(sigma,p)
-onee2:=ande2(amone(sigma,p),some(sigma,p),o1):some(sigma,p)
-ind:='prim':sigma
-oneax:='prim':<ind>p
-+one
-[s:sigma][sp:<s>p]
-th1:=amonee(onee1,ind,s,oneax,sp):is(ind,s)
--one
-sigma@[tau:'type'][f:[x:sigma]tau][s:sigma][t:sigma][i:is(s,t)]
-isf:=isp(sigma,[x:sigma]is(tau,<s>f,<x>f),s,t,refis(tau,<s>f),i):is(tau,<s>f,<t>f)
-f@injective:=all([x:sigma]all([y:sigma]imp(is(tau,<x>f,<y>f),is(x,y)))):'prop'
-[i:injective(f)][s:sigma][t:sigma][j:is(tau,<s>f,<t>f)]
-isfe:=<j><t><s>i:is(s,t)
-f@[t0:tau]
-image:=some([x:sigma]is(tau,t0,<x>f)):'prop'
-f@[s:sigma]
-tofs:=<s>f:tau
-imagei:=somei([x:sigma]is(tau,tofs,<x>f),s,refis(tau,tofs)):image(tofs)
-+inj
-i@[ta:tau][tb:tau][j:is(tau,ta,tb)][sa:sigma][sb:sigma][ja:is(tau,ta,tofs(sa))][jb:is(tau,tb,tofs(sb))]
-t1:=tr3is(tau,tofs(sa),ta,tb,tofs(sb),symis(tau,ta,tofs(sa),ja),j,jb):is(tau,tofs(sa),tofs(sb))
-th1:=isfe(sa,sb,t1):is(sa,sb)
-i@[t0:tau]
-th2:=[x:sigma][y:sigma][u:is(tau,t0,<x>f)][v:is(tau,t0,<y>f)]th1(t0,t0,refis(tau,t0),x,y,u,v):amone([x:sigma]is(tau,t0,<x>f))
-[j:image(f,t0)]
-th3:=onei([x:sigma]is(tau,t0,<x>f),th2,j):one([x:sigma]is(tau,t0,<x>f))
--inj
-i@[t0:tau][j:image(f,t0)]
-soft:=ind([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):sigma
-i@inverse:=[x:tau][u:image(f,x)]soft(x,u):[x:tau][u:image(f,x)]sigma
-j@ists1:=oneax([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):is(tau,t0,tofs(soft(t0,j)))
-ists2:=symis(tau,t0,tofs(soft(t0,j)),ists1):is(tau,tofs(soft(t0,j)),t0)
-i@[ta:tau][ja:image(ta)][tb:tau][jb:image(tb)][j:is(tau,ta,tb)]
-isinv:=th1".inj"(ta,tb,j,soft(ta,ja),soft(tb,jb),ists1(ta,ja),ists1(tb,jb)):is(soft(ta,ja),soft(tb,jb))
-jb@[j:is(soft(ta,ja),soft(tb,jb))]
-isinve:=tr3is(tau,ta,tofs(soft(ta,ja)),tofs(soft(tb,jb)),tb,ists1(ta,ja),isf(soft(ta,ja),soft(tb,jb),j),ists2(tb,jb)):is(tau,ta,tb)
-i@[s:sigma]
-isst1:=isfe(s,soft(tofs(s),imagei(s)),ists1(tofs(s),imagei(s))):is(s,soft(tofs(s),imagei(s)))
-isst2:=symis(s,soft(tofs(s),imagei(s)),isst1):is(soft(tofs(s),imagei(s)),s)
-f@surjective:=all(tau,[x:tau]image(x)):'prop'
-bijective:=and(injective,surjective):'prop'
-[b:bijective(f)]
-+*inj
-b@t2:=ande1(injective,surjective,b):injective(f)
-t3:=ande2(injective,surjective,b):surjective(f)
-[t:tau]
-so:=soft(t2,t,<t>t3):sigma
--inj
-b@invf:=[x:tau]so".inj"(x):[x:tau]sigma
-[s:sigma]
-thinvf1:=tris(s,soft(t2".inj",tofs(s),imagei(s)),<<s>f>invf,isst1(t2".inj",s),isinv(t2".inj",tofs(s),imagei(s),tofs(s),<tofs(s)>t3".inj",refis(tau,tofs(s)))):is(s,<<s>f>invf)
-b@[t:tau]
-thinvf2:=ists1(t2".inj",t,<t>t3".inj"):is(tau,t,<<t>invf>f)
-tau@[upsilon:'type'][f:[x:sigma]tau][g:[x:tau]upsilon]
-+*inj
-g@[if:injective(sigma,tau,f)][ig:injective(tau,upsilon,g)]
-h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
-[s:sigma][t:sigma][i:is(upsilon,<s>h,<t>h)]
-t4:=isfe(tau,upsilon,g,ig,<s>f,<t>f,i):is(tau,<s>f,<t>f)
-t5:=isfe(f,if,s,t,t4):is(s,t)
-ig@th4:=[x:sigma][y:sigma][v:is(upsilon,<x>h,<y>h)]t5(x,y,v):injective(sigma,upsilon,[x:sigma]<<x>f>g)
--inj
-+surj
-g@[sf:surjective(sigma,tau,f)][sg:surjective(tau,upsilon,g)]
-h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
-[u:upsilon]
-t1:=<u>sg:image(tau,upsilon,g,u)
-[t:tau][i:is(upsilon,u,<t>g)]
-t2:=<t>sf:image(sigma,tau,f,t)
-[s:sigma][j:is(tau,t,<s>f)]
-t3:=tris(upsilon,u,<t>g,<s>h,i,isf(tau,upsilon,g,t,<s>f,j)):is(upsilon,u,<s>h)
-t4:=somei([x:sigma]is(upsilon,u,<x>h),s,t3):image(sigma,upsilon,h,u)
-i@t5:=someapp([x:sigma]is(tau,t,<x>f),t2,image(sigma,upsilon,h,u),[x:sigma][v:is(tau,t,<x>f)]t4(x,v)):image(sigma,upsilon,h,u)
-u@t6:=someapp(tau,[x:tau]is(upsilon,u,<x>g),t1,image(sigma,upsilon,h,u),[x:tau][v:is(upsilon,u,<x>g)]t5(x,v)):image(sigma,upsilon,h,u)
-sg@th1:=[x:upsilon]t6(x):surjective(sigma,upsilon,[x:sigma]<<x>f>g)
--surj
-+bij
-g@[bf:bijective(sigma,tau,f)][bg:bijective(tau,upsilon,g)]
-h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
-t1:=th4"e.inj"(f,g,ande1(injective(f),surjective(f),bf),ande1(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):injective(sigma,upsilon,h)
-t2:=th1"e.surj"(f,g,ande2(injective(f),surjective(f),bf),ande2(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):surjective(sigma,upsilon,h)
-th1:=andi(injective(sigma,upsilon,h),surjective(sigma,upsilon,h),t1,t2):bijective(sigma,upsilon,[x:sigma]<<x>f>g)
--bij
-tau@[f:[x:sigma]tau][g:[x:sigma]tau][i:is([x:sigma]tau,f,g)][s:sigma]
-fise:=isp([x:sigma]tau,[y:[x:sigma]tau]is(tau,<s>f,<s>y),f,g,refis(tau,<s>f),i):is(tau,<s>f,<s>g)
-g@[i:[x:sigma]is(tau,<x>f,<x>g)]
-fisi:='prim':is([x:sigma]tau,f,g)
-+fis
-g@[i:is([x:sigma]tau,f,g)][s:sigma][t:sigma][j:is(s,t)]
-th1:=tris(tau,<s>f,<t>f,<t>g,isf(f,s,t,j),fise(i,t)):is(tau,<s>f,<t>g)
--fis
-p@ot:='prim':'type'
-[o1:ot]
-in:='prim':sigma
-inp:='prim':<in>p
-p@otax1:='prim':injective(ot,sigma,[x:ot]in(x))
-[s:sigma][sp:<s>p]
-otax2:='prim':image(ot,sigma,[x:ot]in(x),s)
-o1@[o2:ot][i:is(ot,o1,o2)]
-isini:=isf(ot,sigma,[x:ot]in(x),o1,o2,i):is(in(o1),in(o2))
-o2@[i:is(in(o1),in(o2))]
-isine:=isfe(ot,sigma,[x:ot]in(x),otax1,o1,o2,i):is(ot,o1,o2)
-sp@out:=soft(ot,sigma,[x:ot]in(x),otax1,s,otax2):ot
-[t:sigma][tp:<t>p][i:is(s,t)]
-isouti:=isinv(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(ot,out(s,sp),out(t,tp))
-tp@[i:is(ot,out(s,sp),out(t,tp))]
-isoute:=isinve(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(s,t)
-o1@isoutin:=tris(ot,o1,soft(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1)),out(in(o1),inp(o1)),isst1(ot,sigma,[x:ot]in(x),otax1,o1),isinv(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1),in(o1),otax2(in(o1),inp(o1)),refis(sigma,in(o1)))):is(ot,o1,out(in(o1),inp(o1)))
-sp@isinout:=ists1(ot,sigma,[x:ot]in(x),otax1,s,otax2):is(s,in(out(s,sp)))
-tau@pairtype:='prim':'type'
-[s:sigma][t:tau]
-pair:='prim':pairtype
-tau@[p1:pairtype]
-first:='prim':sigma
-second:='prim':tau
-pairis1:='prim':is(pairtype,pair(first,second),p1)
-pairis2:=symis(pairtype,pair(first,second),p1,pairis1):is(pairtype,p1,pair(first,second))
-t@firstis1:='prim':is(sigma,first(pair),s)
-firstis2:=symis(sigma,first(pair),s,firstis1):is(sigma,s,first(pair))
-secondis1:='prim':is(tau,second(pair),t)
-secondis2:=symis(tau,second(pair),t,secondis1):is(tau,t,second(pair))
-a@[ksi:'type'][x:ksi][y:ksi]
-+ite
-[z:ksi]
-prop1:=and(imp(a,is(ksi,z,x)),imp(not(a),is(ksi,z,y))):'prop'
-y@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t1:=ande1(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(a,is(ksi,x1,x))
-t2:=mp(a,is(ksi,x1,x),a1,t1):is(ksi,x1,x)
-t3:=t2(y1,x1,py1,px1):is(ksi,y1,x)
-t4:=tris2(ksi,x1,y1,x,t2,t3):is(ksi,x1,y1)
-a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
-t6:=[x1:a]refis(ksi,x):imp(a,is(ksi,x,x))
-t7:=th2"l.imp"(not(a),is(ksi,x,y),weli(a,a1)):imp(not(a),is(ksi,x,y))
-t8:=andi(imp(a,is(ksi,x,x)),imp(not(a),is(ksi,x,y)),t6,t7):prop1(x)
-t9:=somei(ksi,[t:ksi]prop1(t),x,t8):some(ksi,[t:ksi]prop1(t))
-t10:=onei(ksi,[t:ksi]prop1(t),t5,t9):one(ksi,[t:ksi]prop1(t))
-y@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t11:=ande2(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(not(a),is(ksi,x1,y))
-t12:=mp(not(a),is(ksi,x1,y),n,t11):is(ksi,x1,y)
-t13:=t12(y1,x1,py1,px1):is(ksi,y1,y)
-t14:=tris2(ksi,x1,y1,y,t12,t13):is(ksi,x1,y1)
-n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
-t16:=[x1:not(a)]refis(ksi,y):imp(not(a),is(ksi,y,y))
-t17:=th2"l.imp"(a,is(ksi,y,x),n):imp(a,is(ksi,y,x))
-t18:=andi(imp(a,is(ksi,y,x)),imp(not(a),is(ksi,y,y)),t17,t16):prop1(y)
-t19:=somei(ksi,[t:ksi]prop1(t),y,t18):some(ksi,[t:ksi]prop1(t))
-t20:=onei(ksi,[t:ksi]prop1(t),t15,t19):one(ksi,[t:ksi]prop1(t))
-y@t21:=th1"l.imp"(a,one(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one(ksi,[t:ksi]prop1(t))
--ite
-ite:=ind(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
-+*ite
-y@t22:=oneax(ksi,[t:ksi]prop1(t),t21):prop1(ite)
-t23:=ande1(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(a,is(ksi,ite,x))
-t24:=ande2(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(not(a),is(ksi,ite,y))
--ite
-y@[a1:a]
-itet:=mp(a,is(ksi,ite,x),a1,t23".ite"):is(ksi,ite,x)
-y@[n:not(a)]
-itef:=mp(not(a),is(ksi,ite,y),n,t24".ite"):is(ksi,ite,y)
-sigma@[s0:sigma][t0:sigma]
-+wissel
-[s:sigma]
-wa:=ite(is(s,s0),sigma,t0,s):sigma
-[i:is(s,s0)]
-t1:=itet(is(s,s0),sigma,t0,s,i):is(wa,t0)
-s@[n:not(is(s,s0))]
-t2:=itef(is(s,s0),sigma,t0,s,n):is(wa,s)
-s@wb:=ite(is(s,t0),sigma,s0,wa):sigma
-[i:is(s,t0)]
-t3:=itet(is(s,t0),sigma,s0,wa,i):is(wb,s0)
-s@[n:not(is(s,t0))]
-t4:=itef(is(s,t0),sigma,s0,wa,n):is(wb,wa)
-s@[i:is(s,s0)][j:is(s0,t0)]
-t5:=tris(wb,s0,t0,t3(tris(s,s0,t0,i,j)),j):is(wb,t0)
-i@[n:not(is(s0,t0))]
-t6:=tris(wb,wa,t0,t4(th2"e.notis"(s0,t0,s,n,i)),t1(i)):is(wb,t0)
-i@t7:=th1"l.imp"(is(s0,t0),is(wb,t0),[t:is(s0,t0)]t5(t),[t:not(is(s0,t0))]t6(t)):is(wb,t0)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-t8:=tris(wb,wa,s,t4(o),t2(n)):is(wb,s)
--wissel
-wissel:=[x:sigma]wb".wissel"(x):[x:sigma]sigma
-[s:sigma][i:is(s,s0)]
-iswissel1:=t7".wissel"(s,i):is(<s>wissel,t0)
-s@[i:is(s,t0)]
-iswissel2:=t3".wissel"(s,i):is(<s>wissel,s0)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-iswissel3:=t8".wissel"(s,n,o):is(<s>wissel,s)
-+*wissel
-s@[t:sigma][i:is(wb(s),wb(t))][n:not(is(s,t))][j:is(s,s0)]
-t9:=symnotis(s0,t,th1"e.notis"(s,t,s0,n,j)):not(is(t,s0))
-[k:is(s0,t0)]
-t10:=th3"e.notis"(t,s0,t0,t9,k):not(is(t,t0))
-t11:=tris(wb(s),wb(t),t,i,t8(t,t9,t10)):is(wb(s),t)
-t12:=<tris1(t,t0,wb(s),t11,t7(j))>t10:con
-j@t13:=[v:is(s0,t0)]t12(v):not(is(s0,t0))
-[k:is(t,t0)]
-t14:=tris(wb(s),wb(t),s0,i,t3(t,k)):is(wb(s),s0)
-t15:=t12(tris1(s0,t0,wb(s),t14,t7(j))):con
-j@t16:=[v:is(t,t0)]t15(v):not(is(t,t0))
-t17:=tris(wb(s),wb(t),t,i,t8(t,t9,t16)):is(wb(s),t)
-t18:=t15(tris1(t,t0,wb(s),t17,t7(j))):con
-n@t19:=[v:is(s,s0)]t18(v):not(is(s,s0))
-t20:=t19(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,s0))
-[j:is(s,t0)]
-t21:=symnotis(t0,t,th1"e.notis"(s,t,t0,n,j)):not(is(t,t0))
-t22:=tris(wb(s),wb(t),t,i,t8(t,t20,t21)):is(wb(s),t)
-t23:=<tris1(t,s0,wb(s),t22,t3(j))>t20:con
-n@t24:=[v:is(s,t0)]t23(v):not(is(s,t0))
-t25:=t24(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,t0))
-t26:=tris(wb(s),wb(t),t,i,t8(t,t20,t25)):is(wb(s),t)
-t27:=<tris1(s,t,wb(s),t8(t19,t24),t26)>n:con
-i@t28:=et(is(s,t),[v:not(is(s,t))]t27(v)):is(s,t)
-t0@th1:=[x:sigma][y:sigma][v:is(wb(x),wb(y))]t28(x,y,v):injective(sigma,sigma,wissel)
-s@[i:is(s,s0)]
-t29:=tris2(s,wb(t0),s0,i,t3(t0,refis(t0))):is(s,wb(t0))
-t30:=somei(sigma,[x:sigma]is(s,wb(x)),t0,t29):image(sigma,sigma,wissel,s)
-s@[i:is(s,t0)]
-t31:=tris2(s,wb(s0),t0,i,t7(s0,refis(s0))):is(s,wb(s0))
-t32:=somei(sigma,[x:sigma]is(s,wb(x)),s0,t31):image(sigma,sigma,wissel,s)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-t33:=symis(wb(s),s,t8(n,o)):is(s,wb(s))
-t34:=somei(sigma,[x:sigma]is(s,wb(x)),s,t33):image(sigma,sigma,wissel,s)
-n@t35:=th1"l.imp"(is(s,t0),image(sigma,sigma,wissel,s),[v:is(s,t0)]t32(v),[v:not(is(s,t0))]t34(v)):image(sigma,sigma,wissel,s)
-s@t36:=th1"l.imp"(is(s,s0),image(sigma,sigma,wissel,s),[v:is(s,s0)]t30(v),[v:not(is(s,s0))]t35(v)):image(sigma,sigma,wissel,s)
-t0@th2:=[x:sigma]t36(x):surjective(sigma,sigma,wissel)
-th3:=andi(injective(sigma,sigma,wissel),surjective(sigma,sigma,wissel),th1,th2):bijective(sigma,sigma,wissel)
--wissel
-tau@[f:[x:sigma]tau][s0:sigma][t0:sigma]
-changef:=[x:sigma]<<x>wissel(s0,t0)>f:[x:sigma]tau
-[s:sigma][i:is(s,s0)]
-changef1:=isf(sigma,tau,f,<s>wissel(s0,t0),t0,iswissel1(s0,t0,s,i)):is(tau,<s>changef,<t0>f)
-s@[i:is(s,t0)]
-changef2:=isf(sigma,tau,f,<s>wissel(s0,t0),s0,iswissel2(s0,t0,s,i)):is(tau,<s>changef,<s0>f)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-changef3:=isf(sigma,tau,f,<s>wissel(s0,t0),s,iswissel3(s0,t0,s,n,o)):is(tau,<s>changef,<s>f)
-+*wissel
-t0@[i:injective(f)]
-th4:=th4"e.inj"(sigma,sigma,tau,wissel(s0,t0),f,th1(s0,t0),i):injective(changef)
-t0@[s:surjective(f)]
-th5:=th1"e.surj"(sigma,sigma,tau,wissel(s0,t0),f,th2(s0,t0),s):surjective(changef)
-t0@[b:bijective(f)]
-th6:=th1"e.bij"(sigma,sigma,tau,wissel(s0,t0),f,th3(s0,t0),b):bijective(changef)
--wissel
--e
-+r
-a@[b:[x:a]'prop']
-%suggestion by van Daalen to remove the second eta-reduction
-%imp:=b:'prop' %original line
-imp:=[x:a]<x>b:'prop'
-%end of suggestion
-[a1:a][i:imp(a,b)]
-mp:=<a1>i:<a1>b
-+imp
-b@[n:not(a)]
-%set etared
-th2:=[x:a]cone(<x>b,mp"l"(a,con,x,n)):imp(a,b)
-%reset etared
--imp
-b@ec:=[x:a]not(<x>b):'prop'
-[n:not(a)]
-eci1:=[x:a]cone(not(<x>b),mp"l"(a,con,x,n)):ec(a,b)
-b@[a1:and(a,b)]
-ande2:=<ande1(a,b,a1)>ande2"l"(a,b,a1):<ande1(a,b,a1)>b
-a@[ksi:'type']
-+ite
-[x1:ksi][y1:ksi]
-is:=is"l.e"(ksi,x1,y1):'prop'
--ite
-[x:[t:a]ksi][y:[t:not(a)]ksi][i:[t:a][u:a]is".ite"(<t>x,<u>x)][j:[t:not(a)][u:not(a)]is".ite"(<t>y,<u>y)]
-+*ite
-j@[z:ksi]
-prop1:=and(imp(a,[t:a]is(z,<t>x)),imp(not(a),[t:not(a)]is(z,<t>y))):'prop'
-j@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t1:=ande1"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(a,[t:a]is(x1,<t>x))
-t2:=mp(a,[t:a]is(x1,<t>x),a1,t1):is(x1,<a1>x)
-t3:=t2(y1,x1,py1,px1):is(y1,<a1>x)
-t4:=tris2"l.e"(ksi,x1,y1,<a1>x,t2,t3):is(x1,y1)
-a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
-t6:=<a1>i:imp(a,[t:a]is(<a1>x,<t>x))
-t7:=th2"r.imp"(not(a),[t:not(a)]is(<a1>x,<t>y),weli(a,a1)):imp(not(a),[t:not(a)]is(<a1>x,<t>y))
-t8:=andi(imp(a,[t:a]is(<a1>x,<t>x)),imp(not(a),[t:not(a)]is(<a1>x,<t>y)),t6,t7):prop1(<a1>x)
-t9:=somei(ksi,[t:ksi]prop1(t),<a1>x,t8):some(ksi,[t:ksi]prop1(t))
-t10:=onei"l.e"(ksi,[t:ksi]prop1(t),t5,t9):one"l.e"(ksi,[t:ksi]prop1(t))
-j@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t11:=ande2"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(not(a),[t:not(a)]is(x1,<t>y))
-t12:=mp(not(a),[t:not(a)]is(x1,<t>y),n,t11):is(x1,<n>y)
-t13:=t12(y1,x1,py1,px1):is(y1,<n>y)
-t14:=tris2"l.e"(ksi,x1,y1,<n>y,t12,t13):is(x1,y1)
-n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
-t16:=<n>j:imp(not(a),[t:not(a)]is(<n>y,<t>y))
-t17:=th2"r.imp"(a,[t:a]is(<n>y,<t>x),n):imp(a,[t:a]is(<n>y,<t>x))
-t18:=andi"l"(imp(a,[t:a]is(<n>y,<t>x)),imp(not(a),[t:not(a)]is(<n>y,<t>y)),t17,t16):prop1(<n>y)
-t19:=somei(ksi,[t:ksi]prop1(t),<n>y,t18):some(ksi,[t:ksi]prop1(t))
-t20:=onei"l.e"(ksi,[t:ksi]prop1(t),t15,t19):one"l.e"(ksi,[t:ksi]prop1(t))
-j@t21:=th1"l.imp"(a,one"l.e"(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one"l.e"(ksi,[t:ksi]prop1(t))
--ite
-j@ite:=ind"l.e"(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
-+*ite
-j@t22:=oneax"l.e"(ksi,[t:ksi]prop1(t),t21):prop1(ite)
-t23:=ande1"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(a,[t:a]is(ite,<t>x))
-t24:=ande2"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(not(a),[t:not(a)]is(ite,<t>y))
--ite
-j@[a1:a]
-itet:=mp(a,[t:a]is".ite"(ite,<t>x),a1,t23".ite"):is".ite"(ksi,ite,<a1>x)
-j@[n:not(a)]
-itef:=mp(not(a),[t:not(a)]is".ite"(ite,<t>y),n,t24".ite"):is".ite"(ksi,ite,<n>y)
--r
-+*e
-+st
-sigma@set:='prim':'type'
-[s:sigma][s0:set]
-esti:='prim':'prop'
-p@setof:='prim':set
-[s:sigma][sp:<s>p]
-estii:='prim':esti(s,setof(p))
-s@[e:esti(s,setof(p))]
-estie:='prim':<s>p
-sigma@[s0:set]
-empty:=non([x:sigma]esti(x,s0)):'prop'
-nonempty:=some([x:sigma]esti(x,s0)):'prop'
-[n:[x:sigma]not(esti(x,s0))]
-emptyi:=n:empty(s0)
-s0@[e:empty(s0)][s:sigma]
-emptye:=<s>e:not(esti(s,s0))
-s0@[s:sigma][ses0:esti(s,s0)]
-nonemptyi:=somei([x:sigma]esti(x,s0),s,ses0):nonempty(s0)
-s0@[n:nonempty(s0)][x:'prop'][x1:[y:sigma][z:esti(y,s0)]x]
-nonemptyapp:=someapp([y:sigma]esti(y,s0),n,x,x1):x
-s0@[t0:set]
-incl:=all([x:sigma]imp(esti(x,s0),esti(x,t0))):'prop'
-[e:[x:sigma][y:esti(x,s0)]esti(x,t0)]
-incli:=e:incl(s0,t0)
-t0@[i:incl(s0,t0)][s:sigma][ses0:esti(s,s0)]
-incle:=<ses0><s>i:esti(s,t0)
-s0@refincl:=[x:sigma][y:esti(x,s0)]y:incl(s0,s0)
-t0@disj:=all([x:sigma]ec(esti(x,s0),esti(x,t0))):'prop'
-[n:[x:sigma][y:esti(x,s0)]not(esti(x,t0))]
-disji1:=n:disj(s0,t0)
-t0@[n:[x:sigma][y:esti(x,t0)]not(esti(x,s0))]
-disji2:=[x:sigma]th2"l.ec"(esti(x,s0),esti(x,t0),<x>n):disj(s0,t0)
-t0@[d:disj(s0,t0)][s:sigma][ses0:esti(s,s0)]
-disje1:=ece1(esti(s,s0),esti(s,t0),<s>d,ses0):not(esti(s,t0))
-s@[set0:esti(s,t0)]
-disje2:=ece2(esti(s,s0),esti(s,t0),<s>d,set0):not(esti(s,s0))
-t0@[d:disj(s0,t0)]
-symdisj:=[x:sigma][y:esti(x,t0)]disje2(d,x,y):disj(t0,s0)
-+disj
-t0@[s:sigma][ses0:esti(s,s0)][set0:esti(s,t0)]
-th1:=th1"l.all"([x:sigma]ec(esti(x,s0),esti(x,t0)),s,th4"l.imp"(esti(s,s0),not(esti(s,t0)),ses0,weli(esti(s,t0),set0))):not(disj(s0,t0))
-th2:=th1(t0,s0,s,set0,ses0):not(disj(t0,s0))
--disj
-t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
-issete1:=isp(set,[x:set]esti(s,x),s0,t0,ses0,i):esti(s,t0)
-s@[set0:esti(s,t0)]
-issete2:=isp1(set,[x:set]esti(s,x),t0,s0,set0,i):esti(s,s0)
-+isset
-i@th1:=[x:sigma][y:esti(x,s0)]issete1(x,y):incl(s0,t0)
-th2:=[x:sigma][y:esti(x,t0)]issete2(x,y):incl(t0,s0)
--isset
-t0@[i:incl(s0,t0)][j:incl(t0,s0)]
-isseti:='prim':is(set,s0,t0)
-+*isset
-t0@[s:sigma][ses0:esti(s,s0)][n:not(esti(s,t0))]
-th3:=th3"l.imp"(is(set,s0,t0),esti(s,t0),n,[t:is(set,s0,t0)]issete1(t,s,ses0)):not(is(set,s0,t0))
-th4:=symnotis(set,s0,t0,th3):not(is(set,t0,s0))
-s@nissetprop:=and(esti(s,s0),not(esti(s,t0))):'prop'
-[n:not(nissetprop(s0,t0,s))][e:esti(s,s0)]
-t1:=et(esti(s,t0),th3"l.and"(esti(s,s0),not(esti(s,t0)),n,e)):esti(s,t0)
-t0@[n:not(is(set,s0,t0))][m:not(some([x:sigma]nissetprop(s0,t0,x)))][l:non([x:sigma]nissetprop(t0,s0,x))][s:sigma]
-t2:=th4"l.some"([x:sigma]nissetprop(s0,t0,x),m,s):not(nissetprop(s0,t0,s))
-t3:=<s>l:not(nissetprop(t0,s0,s))
-l@t4:=isseti(s0,t0,[x:sigma][y:esti(x,s0)]t1(s0,t0,x,t2(x),y),[x:sigma][y:esti(x,t0)]t1(t0,s0,x,t3(x),y)):is(set,s0,t0)
-m@t5:=th3"l.imp"(non([x:sigma]nissetprop(t0,s0,x)),is(set,s0,t0),n,[y:non([x:sigma]nissetprop(t0,s0,x))]t4(y)):some([x:sigma]nissetprop(t0,s0,x))
-n@th5:=th1"l.or"(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)),[y:not(some([x:sigma]nissetprop(s0,t0,x)))]t5(y)):or(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)))
--isset
-sigma@[alpha:'type'][sa:[x:alpha]set]
-unmore:=setof([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa))):set
-[s:sigma][a:alpha][seasa:esti(s,<a>sa)]
-eunmore1:=estii([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa)),s,somei(alpha,[y:alpha]esti(s,<y>sa),a,seasa)):esti(s,unmore(sa))
-s@[seun:esti(s,unmore(sa))][x:'prop'][x1:[y:alpha][z:esti(s,<y>sa)]x]
-unmoreapp:=someapp(alpha,[y:alpha]esti(s,<y>sa),estie([z:sigma]some(alpha,[y:alpha]esti(z,<y>sa)),s,seun),x,x1):x
-+eq
-sigma@[r:[x:sigma][y:sigma]'prop'][refr1:[x:sigma]<x><x>r][symr1:[x:sigma][y:sigma][t:<y><x>r]<x><y>r][trr1:[x:sigma][y:sigma][z:sigma][t:<y><x>r][u:<z><y>r]<z><x>r][s:sigma]
-refr:=<s>refr1:<s><s>r
-[t:sigma][tsr:<t><s>r]
-symr:=<tsr><t><s>symr1:<s><t>r
-t@[u:sigma][tsr:<t><s>r][utr:<u><t>r]
-trr:=<utr><tsr><u><t><s>trr1:<u><s>r
-u@[sur:<s><u>r][tur:<t><u>r]
-tr1r:=trr(s,u,t,symr(u,s,sur),tur):<t><s>r
-u@[usr:<u><s>r][utr:<u><t>r]
-tr2r:=trr(s,u,t,usr,symr(t,u,utr)):<t><s>r
-s@ecelt:=setof(<s>r):set
-+1
-th1:=estii(<s>r,s,refr):esti(s,ecelt(s))
-t@[tsr:<t><s>r]
-th2:=estii(<s>r,t,tsr):esti(t,ecelt(s))
-t@[e:esti(t,ecelt(s))]
-th3:=estie(<s>r,t,e):<t><s>r
-tsr@[u:sigma][e:esti(u,ecelt(s))]
-t1:=th2(t,u,tr1r(t,u,s,tsr,th3(u,e))):esti(u,ecelt(t))
-tsr@th4:=isseti(ecelt(s),ecelt(t),[x:sigma][y:esti(x,ecelt(s))]t1(x,y),[x:sigma][y:esti(x,ecelt(t))]t1(t,s,symr(tsr),x,y)):is(set,ecelt(s),ecelt(t))
-t@[n:not(<t><s>r)][u:sigma][e:esti(u,ecelt(s))]
-t2:=th3"l.imp"(esti(u,ecelt(t)),<t><s>r,n,[x:esti(u,ecelt(t))]tr2r(s,t,u,th3(u,e),th3(t,u,x))):not(esti(u,ecelt(t)))
-n@th5:=[x:sigma][y:esti(x,ecelt(s))]t2(x,y):disj(ecelt(s),ecelt(t))
-s@th6:=nonemptyi(ecelt(s),s,th1):nonempty(ecelt(s))
--1
-trr1@[s0:set][s:sigma]
-ecp:=is(set,s0,ecelt(s)):'prop'
-s0@anec:=some([x:sigma]ecp(x)):'prop'
-+2
-trr1@[s:sigma]
-th1:=somei([x:sigma]ecp(ecelt(s),x),s,refis(set,ecelt(s))):anec(ecelt(s))
--2
-[ecs0:anec(s0)]
-+*2
-ecs0@[s:sigma][ses0:esti(s,s0)][t:sigma][e:ecp(s0,t)]
-t1:=issete1(s0,ecelt(t),e,s,ses0):esti(s,ecelt(t))
-t2:=th4"eq.1"(t,s,th3"eq.1"(t,s,t1)):is(set,ecelt(t),ecelt(s))
-t3:=tris(set,s0,ecelt(t),ecelt(s),e,t2):is(set,s0,ecelt(s))
-ses0@th2:=someapp([x:sigma]ecp(x),ecs0,is(set,s0,ecelt(s)),[x:sigma][y:ecp(x)]t3(x,y)):is(set,s0,ecelt(s))
-[t:sigma][tes0:esti(t,s0)]
-th3:=th3"eq.1"(s,t,issete1(s0,ecelt(s),th2,t,tes0)):<t><s>r
-t@[tsr:<t><s>r]
-th4:=issete2(s0,ecelt(s),th2,t,th2"eq.1"(s,t,tsr)):esti(t,s0)
-ecs0@[s:sigma][e:ecp(s0,s)]
-t4:=isp(set,[x:set]nonempty(x),ecelt(s),s0,th6"eq.1"(s),symis(set,s0,ecelt(s),e)):nonempty(s0)
-ecs0@th5:=someapp([x:sigma]ecp(x),ecs0,nonempty(s0),[x:sigma][y:ecp(x)]t4(x,y)):nonempty(s0)
--2
-+3
-ecs0@[t0:set][ect0:anec(t0)][s:sigma][ses0:esti(s,s0)][t:sigma][tet0:esti(t,t0)][tsr:<t><s>r]
-th1:=tr3is(set,s0,ecelt(s),ecelt(t),t0,th2"eq.2"(s0,ecs0,s,ses0),th4"eq.1"(s,t,tsr),symis(set,t0,ecelt(t),th2"eq.2"(t0,ect0,t,tet0))):is(set,s0,t0)
-tet0@[n:not(<t><s>r)]
-t1:=isp1(set,[x:set]disj(x,ecelt(t)),ecelt(s),s0,th5"eq.1"(s,t,n),th2"eq.2"(s0,ecs0,s,ses0)):disj(s0,ecelt(t))
-th2:=isp1(set,[x:set]disj(s0,x),ecelt(t),t0,t1,th2"eq.2"(t0,ect0,t,tet0)):disj(s0,t0)
-t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
-t2:=issete1(s0,t0,i,s,ses0):esti(s,t0)
-t3:=th1"st.disj"(s0,t0,s,ses0,t2):not(disj(s0,t0))
-i@th3:=nonemptyapp(s0,th5"eq.2"(s0,ecs0),not(disj(s0,t0)),[x:sigma][y:esti(x,s0)]t3(x,y)):not(disj(s0,t0))
--3
-trr1@ect:=ot(set,[x:set]anec(x)):'type'
-ecs0@ectset:=out(set,[x:set]anec(x),s0,ecs0):ect
-trr1@[s:sigma]
-ectelt:=ectset(ecelt(s),th1".2"(s)):ect
-trr1@[e:ect]
-ecect:=in(set,[x:set]anec(x),e):set
-+4
-th1:=inp(set,[x:set]anec(x),e):anec(ecect(e))
-th2:=th5"eq.2"(ecect(e),th1):nonempty(ecect(e))
-[x:'prop'][x1:[y:sigma][z:esti(y,ecect(e))]x]
-th3:=nonemptyapp(ecect(e),th2,x,x1):x
-s@th4:=isinout(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s)):is(set,ecelt(s),ecect(ectelt(s)))
-th5:=issete1(ecelt(s),ecect(ectelt(s)),th4,s,th1"eq.1"(s)):esti(s,ecect(ectelt(s)))
-th6:=eunmore1(ect,[x:ect]ecect(x),s,ectelt(s),th5):esti(s,unmore(ect,[x:ect]ecect(x)))
-e@[s:sigma][see:esti(s,ecect(e))][t:sigma][tee:esti(t,ecect(e))]
-th7:=th3"eq.2"(ecect(e),th1,s,see,t,tee):<t><s>r
-t@[tsr:<t><s>r]
-th8:=th4"eq.2"(ecect(e),th1,s,see,t,tsr):esti(t,ecect(e))
--4
-+5
-[f:ect][i:is(ect,e,f)]
-th1:=isini(set,[x:set]anec(x),e,f,i):is(set,ecect(e),ecect(f))
-f@[i:is(set,ecect(e),ecect(f))]
-th2:=isine(set,[x:set]anec(x),e,f,i):is(ect,e,f)
-f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))][tsr:<t><s>r]
-th3:=th2(th1"eq.3"(ecect(e),th1"eq.4"(e),ecect(f),th1"eq.4"(f),s,see,t,tef,tsr)):is(ect,e,f)
-see@[i:is(ect,e,f)]
-th4:=issete1(ecect(e),ecect(f),th1(i),s,see):esti(s,ecect(f))
-tef@[i:is(ect,e,f)]
-th5:=th3"eq.2"(ecect(f),th1"eq.4"(f),s,th4(i),t,tef):<t><s>r
-trr1@[s:sigma][t:sigma][tsr:<t><s>r]
-th6:=isouti(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s),ecelt(t),th1"eq.2"(t),th4"eq.1"(s,t,tsr)):is(ect,ectelt(s),ectelt(t))
--5
-trr1@[alpha:'type'][fu:[x:sigma]alpha]
-fixfu:=[x:sigma][y:sigma][z:<y><x>r]is(alpha,<x>fu,<y>fu):'prop'
-+10
-[ff:fixfu][e:ect][a1:alpha][s:sigma]
-prop1:=and(esti(s,ecect(e)),is(alpha,<s>fu,a1)):'prop'
-a1@prop2:=some([x:sigma]prop1(x)):'prop'
-e@[s:sigma][see:esti(s,ecect(e))]
-t1:=andi(esti(s,ecect(e)),is(alpha,<s>fu,<s>fu),see,refis(alpha,<s>fu)):prop1(<s>fu,s)
-t2:=somei([x:sigma]prop1(<s>fu,x),s,t1):prop2(<s>fu)
-t3:=somei(alpha,[x:alpha]prop2(x),<s>fu,t2):some(alpha,[x:alpha]prop2(x))
-e@t4:=th3"eq.4"(e,some(alpha,[x:alpha]prop2(x)),[x:sigma][y:esti(x,ecect(e))]t3(x,y)):some(alpha,[x:alpha]prop2(x))
-a1@[b1:alpha][pa1:prop2(a1)][pb1:prop2(b1)][s:sigma][pa1s:prop1(a1,s)][t:sigma][pb1t:prop1(b1,t)]
-t5:=ande1(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):esti(s,ecect(e))
-t6:=ande1(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):esti(t,ecect(e))
-t7:=th7"eq.4"(e,s,t5,t,t6):<t><s>r
-t8:=ande2(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):is(alpha,<s>fu,a1)
-t9:=ande2(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):is(alpha,<t>fu,b1)
-t10:=tr3is(alpha,a1,<s>fu,<t>fu,b1,symis(alpha,<s>fu,a1,t8),<t7><t><s>ff,t9):is(alpha,a1,b1)
-pa1s@t11:=someapp([x:sigma]prop1(b1,x),pb1,is(alpha,a1,b1),[x:sigma][y:prop1(b1,x)]t10(x,y)):is(alpha,a1,b1)
-pb1@t12:=someapp([x:sigma]prop1(a1,x),pa1,is(alpha,a1,b1),[x:sigma][y:prop1(a1,x)]t11(x,y)):is(alpha,a1,b1)
-e@t13:=[x:alpha][y:alpha][u:prop2(x)][v:prop2(y)]t12(x,y,u,v):amone(alpha,[x:alpha]prop2(x))
-t14:=onei(alpha,[x:alpha]prop2(x),t13,t4):one(alpha,[x:alpha]prop2(x))
--10
-e".10"@indeq:=ind(alpha,[x:alpha]prop2".10"(x),t14".10"):alpha
-+*10
-e@th1:=oneax(alpha,[x:alpha]prop2(x),t14):some([x:sigma]and(esti(x,ecect(e)),is(alpha,<x>fu,indeq)))
-[s:sigma][see:esti(s,ecect(e))]
-th2:=t12(<s>fu,indeq,t2(s,see),th1):is(alpha,<s>fu,indeq)
-ff@[s:sigma]
-th3:=th2(ectelt(s),s,th5"eq.4"(s)):is(alpha,<s>fu,indeq(ectelt(s)))
--10
-alpha@[fu2:[x:sigma][y:sigma]alpha]
-fixfu2:=[x:sigma][y:sigma][z:sigma][u:sigma][v:<y><x>r][w:<u><z>r]is(alpha,<z><x>fu2,<u><y>fu2):'prop'
-+11
-[ff2:fixfu2][s:sigma][t:sigma][tsr:<t><s>r][u:sigma]
-t1:=<refr(u)><tsr><u><u><t><s>ff2:is(alpha,<u><s>fu2,<u><t>fu2)
-tsr@t2:=fisi(sigma,alpha,<s>fu2,<t>fu2,[x:sigma]t1(x)):is([x:sigma]alpha,<s>fu2,<t>fu2)
-ff2@[e:ect]
-i:=indeq([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e):[x:sigma]alpha
-[s:sigma][t:sigma][tsr:<t><s>r][u:sigma][uee:esti(u,ecect(e))]
-t3:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,u,uee):is([x:sigma]alpha,<u>fu2,i)
-t4:=fise(alpha,<u>fu2,i,t3,s):is(alpha,<s><u>fu2,<s>i)
-t5:=fise(alpha,<u>fu2,i,t3,t):is(alpha,<t><u>fu2,<t>i)
-t6:=<tsr><refr(u)><t><s><u><u>ff2:is(alpha,<s><u>fu2,<t><u>fu2)
-t7:=tr3is(alpha,<s>i,<s><u>fu2,<t><u>fu2,<t>i,symis(alpha,<s><u>fu2,<s>i,t4),t6,t5):is(alpha,<s>i,<t>i)
-tsr@t8:=th3"eq.4"(e,is(alpha,<s>i,<t>i),[x:sigma][y:esti(x,ecect(e))]t7(x,y)):is(alpha,<s>i,<t>i)
--11
-e".11"@[f:ect]
-indeq2:=indeq(i".11",[x:sigma][y:sigma][z:<y><x>r]t8".11"(x,y,z),f):alpha
-+*11
-f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))]
-t9:=th2"eq.10"(i,[x:sigma][y:sigma][z:<y><x>r]t8(x,y,z),f,t,tef):is(alpha,<t>i,indeq2(e,f))
-t10:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,s,see):is([x:sigma]alpha,<s>fu2,i)
-t11:=fise(alpha,<s>fu2,i,t10,t):is(alpha,<t><s>fu2,<t>i)
-th1:=tris(alpha,<t><s>fu2,<t>i,indeq2,t11,t9):is(alpha,<t><s>fu2,indeq2(e,f))
-ff2@[s:sigma][t:sigma]
-th2:=th1(ectelt(s),ectelt(t),s,th5"eq.4"(s),t,th5"eq.4"(t)):is(alpha,<t><s>fu2,indeq2(ectelt(s),ectelt(t)))
--11
-+landau
-+n
-@nat:='prim':'type'
-[x:nat][y:nat]
-is:=is"e"(nat,x,y):'prop'
-nis:=not(is(x,y)):'prop'
-x@[s:set(nat)]
-in:=esti(nat,x,s):'prop'
-@[p:[x:nat]'prop']
-some:=some"l"(nat,p):'prop'
-all:=all"l"(nat,p):'prop'
-one:=one"e"(nat,p):'prop'
-@1:='prim':nat
-suc:='prim':[x:nat]nat
-[x:nat][y:nat][i:is(x,y)]
-ax2:=isf(nat,nat,suc,x,y,i):is(<x>suc,<y>suc)
-@ax3:='prim':[x:nat]nis(<x>suc,1)
-ax4:='prim':[x:nat][y:nat][u:is(<x>suc,<y>suc)]is(x,y)
-[s:set(nat)]
-cond1:=in(1,s):'prop'
-cond2:=all([x:nat]imp(in(x,s),in(<x>suc,s))):'prop'
-@ax5:='prim':[s:set(nat)][u:cond1(s)][v:cond2(s)][x:nat]in(x,s)
-[p:[x:nat]'prop'][1p:<1>p][xsp:[x:nat][y:<x>p]<<x>suc>p][x:nat]
-+i1
-s:=setof(nat,p):set(nat)
-t1:=estii(nat,p,1,1p):cond1(s)
-[y:nat][yes:in(y,s)]
-t2:=estie(nat,p,y,yes):<y>p
-t3:=estii(nat,p,<y>suc,<t2><y>xsp):in(<y>suc,s)
-x@t4:=<x><[y:nat][u:in(y,s)]t3(y,u)><t1><s>ax5:in(x,s)
--i1
-induction:=estie(nat,p,x,t4".i1"):<x>p
-@[x:nat][y:nat][n:nis(x,y)]
-+21
-[i:is(<x>suc,<y>suc)]
-t1:=<i><y><x>ax4:is(x,y)
--21
-satz1:=th3"l.imp"(is(<x>suc,<y>suc),is(x,y),n,[u:is(<x>suc,<y>suc)]t1".21"(u)):nis(<x>suc,<y>suc)
-+22
-x@prop1:=nis(<x>suc,x):'prop'
-@t1:=<1>ax3:prop1(1)
-x@[p:prop1(x)]
-t2:=satz1(<x>suc,x,p):prop1(<x>suc)
--22
-x@satz2:=induction([y:nat]prop1".22"(y),t1".22",[y:nat][u:prop1".22"(y)]t2".22"(y,u),x):nis(<x>suc,x)
-+23
-prop1:=or(is(x,1),some([u:nat]is(x,<u>suc))):'prop'
-@t1:=ori1(is(1,1),some([u:nat]is(1,<u>suc)),refis(nat,1)):prop1(1)
-x@t2:=somei(nat,[u:nat]is(<x>suc,<u>suc),x,refis(nat,<x>suc)):some([u:nat]is(<x>suc,<u>suc))
-t3:=ori2(is(<x>suc,1),some([u:nat]is(<x>suc,<u>suc)),t2):prop1(<x>suc)
-t4:=induction([y:nat]prop1(y),t1,[y:nat][u:prop1(y)]t3(y),x):prop1(x)
--23
-[n:nis(x,1)]
-satz3:=ore2(is(x,1),some([u:nat]is(x,<u>suc)),t4".23",n):some([u:nat]is(x,<u>suc))
-y@[z:nat][i:is(x,<y>suc)][j:is(x,<z>suc)]
-+*23
-j@t5:=<tris1(nat,<y>suc,<z>suc,x,i,j)><z><y>ax4:is(y,z)
-x@t6:=[y:nat][z:nat][u:is(x,<y>suc)][v:is(x,<z>suc)]t5(y,z,u,v):amone(nat,[u:nat]is(x,<u>suc))
--23
-n@satz3a:=onei(nat,[u:nat]is(x,<u>suc),t6".23",satz3):one([u:nat]is(x,<u>suc))
-+24
-x@[f:[y:nat]nat]
-prop1:=all([y:nat]is(<<y>suc>f,<<y>f>suc)):'prop'
-prop2:=and(is(<1>f,<x>suc),prop1):'prop'
-x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
-prop3:=is(<y>a,<y>b):'prop'
-pb@t1:=ande1(is(<1>a,<x>suc),prop1(a),pa):is(<1>a,<x>suc)
-t2:=ande1(is(<1>b,<x>suc),prop1(b),pb):is(<1>b,<x>suc)
-t3:=tris2(nat,<1>a,<1>b,<x>suc,t1,t2):prop3(1)
-y@[p:prop3(y)]
-t4:=ax2(<y>a,<y>b,p):is(<<y>a>suc,<<y>b>suc)
-t5:=ande2(is(<1>a,<x>suc),prop1(a),pa):prop1(a)
-t6:=ande2(is(<1>b,<x>suc),prop1(b),pb):prop1(b)
-t7:=<y>t5:is(<<y>suc>a,<<y>a>suc)
-t8:=<y>t6:is(<<y>suc>b,<<y>b>suc)
-t9:=tr3is(nat,<<y>suc>a,<<y>a>suc,<<y>b>suc,<<y>suc>b,t7,t4,symis"e"(nat,<<y>suc>b,<<y>b>suc,t8)):prop3(<y>suc)
-y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
-pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
-x@aa:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
-prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
-@t12:=[x:nat]refis(nat,<<x>suc>suc):prop1(1,suc)
-t13:=andi(is(<1>suc,<1>suc),prop1(1,suc),refis(nat,<1>suc),t12):prop2(1,suc)
-t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),suc,t13):prop4(1)
-x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
-g:=[y:nat]<<y>f>suc:[y:nat]nat
-[y:nat]
-t15:=refis(nat,<y>g):is(<y>g,<<y>f>suc)
-pf@t16:=ande1(is(<1>f,<x>suc),prop1(f),pf):is(<1>f,<x>suc)
-t17:=tris(nat,<1>g,<<1>f>suc,<<x>suc>suc,t15(1),ax2(<1>f,<x>suc,t16)):is(<1>g,<<x>suc>suc)
-y@t18:=ande2(is(<1>f,<x>suc),prop1(f),pf):prop1(f)
-t19:=<y>t18:is(<<y>suc>f,<<y>f>suc)
-t20:=tris2(nat,<<y>suc>f,<y>g,<<y>f>suc,t19,t15):is(<<y>suc>f,<y>g)
-t21:=tris(nat,<<y>suc>g,<<<y>suc>f>suc,<<y>g>suc,t15(<y>suc),ax2(<<y>suc>f,<y>g,t20)):is(<<y>suc>g,<<y>g>suc)
-pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
-t23:=andi(is(<1>g,<<x>suc>suc),prop1(<x>suc,g),t17,t22):prop2(<x>suc,g)
-t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
-p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
-x@bb:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
--24
-x@satz4:=onei([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),aa".24",bb".24"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,<x>suc),all([y:nat]is(<<y>suc>z,<<y>z>suc))))
-plus:=ind([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),satz4):[y:nat]nat
-y@pl:=<y>plus:nat
-+*24
-x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz4):prop2(plus)
--24
-x@satz4a:=ande1(is(<1>plus,<x>suc),prop1".24"(plus),t26".24"):is(pl(x,1),<x>suc)
-+*24
-x@t27:=ande2(is(<1>plus,<x>suc),prop1(plus),t26):prop1(plus)
--24
-y@satz4b:=<y>t27".24":is(pl(x,<y>suc),<pl(x,y)>suc)
-+*24
-@t28:=t11(1,plus(1),suc,t26(1),t13):is"e"([y:nat]nat,plus(1),suc)
--24
-x@satz4c:=fise(nat,nat,plus(1),suc,t28".24",x):is(pl(1,x),<x>suc)
-+*24
-x@t29:=t11(<x>suc,plus(<x>suc),[y:nat]<<y>plus>suc,t26(<x>suc),t23(bb,plus,t26)):is"e"([y:nat]nat,plus(<x>suc),[y:nat]<<y>plus>suc)
--24
-y@satz4d:=fise(nat,nat,plus(<x>suc),[z:nat]<<z>plus>suc,t29".24",y):is(pl(<x>suc,y),<pl(x,y)>suc)
-x@satz4e:=symis(nat,pl(x,1),<x>suc,satz4a):is(<x>suc,pl(x,1))
-y@satz4f:=symis(nat,pl(x,<y>suc),<pl(x,y)>suc,satz4b):is(<pl(x,y)>suc,pl(x,<y>suc))
-x@satz4g:=symis(nat,pl(1,x),<x>suc,satz4c):is(<x>suc,pl(1,x))
-y@satz4h:=symis(nat,pl(<x>suc,y),<pl(x,y)>suc,satz4d):is(<pl(x,y)>suc,pl(<x>suc,y))
-z@[i:is(x,y)]
-ispl1:=isf(nat,nat,[u:nat]pl(u,z),x,y,i):is(pl(x,z),pl(y,z))
-ispl2:=isf(nat,nat,[u:nat]pl(z,u),x,y,i):is(pl(z,x),pl(z,y))
-z@[u:nat][i:is(x,y)][j:is(z,u)]
-ispl12:=tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
-+25
-z@prop1:=is(pl(pl(x,y),z),pl(x,pl(y,z))):'prop'
-y@t1:=tr3is(nat,pl(pl(x,y),1),<pl(x,y)>suc,pl(x,<y>suc),pl(x,pl(y,1)),satz4a(pl(x,y)),satz4f,ispl2(<y>suc,pl(y,1),x,satz4e(y))):prop1(1)
-z@[p:prop1(z)]
-t2:=ax2(pl(pl(x,y),z),pl(x,pl(y,z)),p):is(<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc)
-t3:=tr4is(nat,pl(pl(x,y),<z>suc),<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc,pl(x,<pl(y,z)>suc),pl(x,pl(y,<z>suc)),satz4b(pl(x,y),z),t2,satz4f(x,pl(y,z)),ispl2(<pl(y,z)>suc,pl(y,<z>suc),x,satz4f(y,z))):prop1(<z>suc)
--25
-z@satz5:=induction([u:nat]prop1".25"(u),t1".25",[u:nat][v:prop1".25"(u)]t3".25"(u,v),z):is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl1:=satz5:is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl2:=symis(nat,pl(pl(x,y),z),pl(x,pl(y,z)),satz5):is(pl(x,pl(y,z)),pl(pl(x,y),z))
-+26
-y@prop1:=is(pl(x,y),pl(y,x)):'prop'
-t1:=satz4a(y):is(pl(y,1),<y>suc)
-t2:=satz4c(y):is(pl(1,y),<y>suc)
-t3:=tris2(nat,pl(1,y),pl(y,1),<y>suc,t2,t1):prop1(1,y)
-[p:prop1(x,y)]
-t4:=tris(nat,<pl(x,y)>suc,<pl(y,x)>suc,pl(y,<x>suc),ax2(pl(x,y),pl(y,x),p),satz4f(y,x)):is(<pl(x,y)>suc,pl(y,<x>suc))
-t5:=satz4d:is(pl(<x>suc,y),<pl(x,y)>suc)
-t6:=tris(nat,pl(<x>suc,y),<pl(x,y)>suc,pl(y,<x>suc),t5,t4):prop1(<x>suc,y)
--26
-y@satz6:=induction([z:nat]prop1".26"(z,y),t3".26",[z:nat][u:prop1".26"(z,y)]t6".26"(z,y,u),x):is(pl(x,y),pl(y,x))
-compl:=satz6:is(pl(x,y),pl(y,x))
-+*26
-x@t7:=tris(nat,pl(x,1),<x>suc,pl(1,x),satz4a,satz4g):prop1(1)
-y@[p:prop1(y)]
-t8:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,<pl(y,x)>suc,pl(<y>suc,x),satz4b,ax2(pl(x,y),pl(y,x),p),satz4h(y,x)):prop1(<y>suc)
-y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(pl(x,y),pl(y,x))
--26
-+27
-y@prop1:=nis(y,pl(x,y)):'prop'
-x@t1:=symnotis(nat,<x>suc,1,<x>ax3):nis(1,<x>suc)
-t2:=th4"e.notis"(nat,1,<x>suc,pl(x,1),t1,satz4a):prop1(1)
-y@[p:prop1(y)]
-t3:=satz1(y,pl(x,y),p):nis(<y>suc,<pl(x,y)>suc)
-t4:=th4"e.notis"(nat,<y>suc,<pl(x,y)>suc,pl(x,<y>suc),t3,satz4b):prop1(<y>suc)
--27
-y@satz7:=induction([z:nat]prop1".27"(z),t2".27",[z:nat][u:prop1".27"(z)]t4".27"(z,u),y):nis(y,pl(x,y))
-z@[n:nis(y,z)]
-+28
-prop1:=nis(pl(x,y),pl(x,z)):'prop'
-t1:=satz1(y,z,n):nis(<y>suc,<z>suc)
-t2:=th5"e.notis"(nat,<y>suc,<z>suc,pl(1,y),pl(1,z),t1,satz4g(y),satz4g(z)):prop1(1,y,z,n)
-[p:prop1(x,y,z,n)]
-t3:=satz1(pl(x,y),pl(x,z),p):nis(<pl(x,y)>suc,<pl(x,z)>suc)
-t4:=th5"e.notis"(nat,<pl(x,y)>suc,<pl(x,z)>suc,pl(<x>suc,y),pl(<x>suc,z),t3,satz4h,satz4h(z)):prop1(<x>suc,y,z,n)
--28
-satz8:=induction([u:nat]prop1".28"(u,y,z,n),t2".28",[u:nat][v:prop1".28"(u,y,z,n)]t4".28"(u,y,z,n,v),x):nis(pl(x,y),pl(x,z))
-z@[i:is(pl(x,y),pl(x,z))]
-satz8a:=th7"l.imp"(is(y,z),nis(pl(x,y),pl(x,z)),weli(is(pl(x,y),pl(x,z)),i),[u:nis(y,z)]satz8(u)):is(y,z)
-z@diffprop:=is(x,pl(y,z)):'prop'
-+*28
-y@[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]
-t5:=satz8a(y,u,v,tris1(nat,pl(y,u),pl(y,v),x,du,dv)):is(u,v)
--28
-y@satz8b:=[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]t5".28"(u,v,du,dv):amone(nat,[z:nat]is(x,pl(y,z)))
-+29
-i:=is(x,y):'prop'
-ii:=some([u:nat]diffprop(x,y,u)):'prop'
-iii:=some([v:nat]diffprop(y,x,v)):'prop'
-[one1:i][u:nat]
-t1:=tris(nat,pl(u,x),pl(x,u),pl(y,u),compl(u,x),ispl1(u,one1)):is(pl(u,x),pl(y,u))
-t2:=th3"e.notis"(nat,x,pl(u,x),pl(y,u),satz7(u,x),t1):nis(x,pl(y,u))
-one1@t3:=th5"l.some"(nat,[u:nat]diffprop(u),[u:nat]t2(u)):not(ii)
-y@t4:=th1"l.ec"(i,ii,[z:i]t3(z)):ec(i,ii)
-one1@t5:=t3(y,x,symis(nat,x,y,one1)):not(iii)
-y@t6:=th2"l.ec"(iii,i,[z:i]t5(z)):ec(iii,i)
-[two1:ii][three1:iii][u:nat][du:diffprop(x,y,u)][v:nat][dv:diffprop(y,x,v)]
-t6a:=tr4is(nat,x,pl(y,u),pl(pl(x,v),u),pl(x,pl(v,u)),pl(pl(v,u),x),du,ispl1(y,pl(x,v),u,dv),asspl1(x,v,u),compl(x,pl(v,u))):is(x,pl(pl(v,u),x))
-t7:=mp(is(x,pl(pl(v,u),x)),con,t6a,satz7(pl(v,u),x)):con
-du@t8:=someapp(nat,[v:nat]diffprop(y,x,v),three1,con,[v:nat][dv:diffprop(y,x,v)]t7(v,dv)):con
-three1@t9:=someapp(nat,[u:nat]diffprop(u),two1,con,[u:nat][du:diffprop(u)]t8(u,du)):con
-two1@t10:=[z:iii]t9(z):not(iii)
-y@t11:=th1"l.ec"(ii,iii,[z:ii]t10(z)):ec(ii,iii)
-a:=th6"l.ec3"(i,ii,iii,t4,t11,t6):ec3(i,ii,iii)
-prop1:=or3(i,ii,iii):'prop'
-x@[j:is(x,1)]
-t12:=or3i1(i(1),ii(1),iii(1),j):prop1(1)
-x@[n:nis(x,1)][u:nat][j:is(x,<u>suc)]
-t13:=tris(nat,x,<u>suc,pl(1,u),j,satz4g(u)):is(x,pl(1,u))
-t14:=somei(nat,[z:nat]diffprop(x,1,z),u,t13):ii(1)
-t15:=someapp(nat,[u1:nat]is(x,<u1>suc),satz3(x,n),ii(1),[u1:nat][z:is(x,<u1>suc)]t14(u1,z)):ii(1)
-t16:=or3i2(i(1),ii(1),iii(1),t15):prop1(1)
-n@t16a:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),prop1(1),[u:nat][v:is(x,<u>suc)]t16(u,v)):prop1(1)
-x@t17:=th1"l.imp"(is(x,1),prop1(1),[z:is(x,1)]t12(z),[z:nis(x,1)]t16a(z)):prop1(1)
-y@[p:prop1(y)][one1:i(y)]
-t18:=tris(nat,<y>suc,pl(y,1),pl(x,1),satz4e(y),ispl1(y,x,1,symis(nat,x,y,one1))):is(<y>suc,pl(x,1))
-t19:=somei(nat,[z:nat]diffprop(<y>suc,x,z),1,t18):iii(<y>suc)
-t20:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t19):prop1(<y>suc)
-p@[two1:ii(y)][u:nat][du:diffprop(x,y,u)][j:is(u,1)]
-t21:=tr3is(nat,x,pl(y,u),pl(y,1),<y>suc,du,ispl2(u,1,y,j),satz4a(y)):is(x,<y>suc)
-t22:=or3i1(i(<y>suc),ii(<y>suc),iii(<y>suc),t21):prop1(<y>suc)
-du@[n:nis(u,1)][w:nat][j:is(u,<w>suc)]
-t23:=tris(nat,u,<w>suc,pl(1,w),j,satz4g(w)):is(u,pl(1,w))
-t24:=tr4is(nat,x,pl(y,u),pl(y,pl(1,w)),pl(pl(y,1),w),pl(<y>suc,w),du,ispl2(u,pl(1,w),y,t23),asspl2(y,1,w),ispl1(pl(y,1),<y>suc,w,satz4a(y))):is(x,pl(<y>suc,w))
-t25:=somei(nat,[z:nat]diffprop(x,<y>suc,z),w,t24):ii(<y>suc)
-n@t26:=someapp(nat,[z:nat]is(u,<z>suc),satz3(u,n),ii(<y>suc),[z:nat][v:is(u,<z>suc)]t25(z,v)):ii(<y>suc)
-t27:=or3i2(i(<y>suc),ii(<y>suc),iii(<y>suc),t26):prop1(<y>suc)
-du@t28:=th1"l.imp"(is(u,1),prop1(<y>suc),[z:is(u,1)]t22(z),[z:nis(u,1)]t27(z)):prop1(<y>suc)
-two1@t28a:=someapp(nat,[u:nat]diffprop(u),two1,prop1(<y>suc),[u:nat][du:diffprop(u)]t28(u,du)):prop1(<y>suc)
-p@[three1:iii(y)][v:nat][dv:diffprop(y,x,v)]
-t29:=tris(nat,<y>suc,<pl(x,v)>suc,pl(x,<v>suc),ax2(y,pl(x,v),dv),satz4f(x,v)):is(<y>suc,pl(x,<v>suc))
-t30:=somei(nat,[z:nat]diffprop(<y>suc,x,z),<v>suc,t29):iii(<y>suc)
-three1@t31:=someapp(nat,[v:nat]diffprop(y,x,v),three1,iii(<y>suc),[v:nat][dv:diffprop(y,x,v)]t30(v,dv)):iii(<y>suc)
-t32:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t31):prop1(<y>suc)
-p@t33:=or3app(i(y),ii(y),iii(y),prop1(<y>suc),p,[z:i(y)]t20(z),[z:ii(y)]t28a(z),[z:iii(y)]t32(z)):prop1(<y>suc)
-y@b:=induction([z:nat]prop1(z),t17,[z:nat][u:prop1(z)]t33(z,u),y):or3(i,ii,iii)
--29
-satz9:=orec3i(i".29",ii".29",iii".29",b".29",a".29"):orec3(is(x,y),some([u:nat]is(x,pl(y,u))),some([v:nat]is(y,pl(x,v))))
-satz9a:=b".29":or3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
-satz9b:=a".29":ec3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
-more:=some([u:nat]diffprop(x,y,u)):'prop'
-less:=some([v:nat]diffprop(y,x,v)):'prop'
-satz10:=satz9:orec3(is(x,y),more(x,y),less(x,y))
-satz10a:=satz9a:or3(is(x,y),more(x,y),less(x,y))
-satz10b:=satz9b:ec3(is(x,y),more(x,y),less(x,y))
-[m:more(x,y)]
-satz11:=m:less(y,x)
-y@[l:less(x,y)]
-satz12:=l:more(y,x)
-y@moreis:=or(more,is(x,y)):'prop'
-lessis:=or(less,is(x,y)):'prop'
-[m:moreis(x,y)]
-satz13:=th9"l.or"(more,is(x,y),less(y,x),is(y,x),m,[z:more]satz11(z),[z:is(x,y)]symis(nat,x,y,z)):lessis(y,x)
-y@[l:lessis(x,y)]
-satz14:=th9"l.or"(less,is(x,y),more(y,x),is(y,x),l,[z:less]satz12(z),[z:is(x,y)]symis(nat,x,y,z)):moreis(y,x)
-z@[i:is(x,y)][m:more(x,z)]
-ismore1:=isp(nat,[u:nat]more(u,z),x,y,m,i):more(y,z)
-i@[m:more(z,x)]
-ismore2:=isp(nat,[u:nat]more(z,u),x,y,m,i):more(z,y)
-i@[l:less(x,z)]
-isless1:=isp(nat,[u:nat]less(u,z),x,y,l,i):less(y,z)
-i@[l:less(z,x)]
-isless2:=isp(nat,[u:nat]less(z,u),x,y,l,i):less(z,y)
-i@[m:moreis(x,z)]
-ismoreis1:=isp(nat,[u:nat]moreis(u,z),x,y,m,i):moreis(y,z)
-i@[m:moreis(z,x)]
-ismoreis2:=isp(nat,[u:nat]moreis(z,u),x,y,m,i):moreis(z,y)
-i@[l:lessis(x,z)]
-islessis1:=isp(nat,[u:nat]lessis(u,z),x,y,l,i):lessis(y,z)
-i@[l:lessis(z,x)]
-islessis2:=isp(nat,[u:nat]lessis(z,u),x,y,l,i):lessis(z,y)
-y@[i:is(x,y)]
-moreisi2:=ori2(more(x,y),is(x,y),i):moreis(x,y)
-lessisi2:=ori2(less(x,y),is(x,y),i):lessis(x,y)
-y@[m:more(x,y)]
-moreisi1:=ori1(more(x,y),is(x,y),m):moreis(x,y)
-y@[l:less(x,y)]
-lessisi1:=ori1(less(x,y),is(x,y),l):lessis(x,y)
-z@[u:nat][i:is(x,y)][j:is(z,u)][m:more(x,z)]
-ismore12:=ismore2(z,u,y,j,ismore1(x,y,z,i,m)):more(y,u)
-j@[l:less(x,z)]
-isless12:=isless2(z,u,y,j,isless1(x,y,z,i,l)):less(y,u)
-j@[m:moreis(x,z)]
-ismoreis12:=ismoreis2(z,u,y,j,ismoreis1(x,y,z,i,m)):moreis(y,u)
-j@[l:lessis(x,z)]
-islessis12:=islessis2(z,u,y,j,islessis1(x,y,z,i,l)):lessis(y,u)
-y@[m:moreis(x,y)]
-satz10c:=th7"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,comor(more(x,y),is(x,y),m)):not(less(x,y))
-y@[l:lessis(x,y)]
-satz10d:=th9"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,l):not(more(x,y))
-y@[n:not(more(x,y))]
-satz10e:=th2"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n):lessis(x,y)
-y@[n:not(less(x,y))]
-satz10f:=comor(is(x,y),more(x,y),th3"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n)):moreis(x,y)
-y@[m:more(x,y)]
-satz10g:=th3"l.or"(less(x,y),is(x,y),ec3e23(is(x,y),more(x,y),less(x,y),satz10b,m),ec3e21(is(x,y),more(x,y),less(x,y),satz10b,m)):not(lessis(x,y))
-y@[l:less(x,y)]
-satz10h:=th3"l.or"(more(x,y),is(x,y),ec3e32(is(x,y),more(x,y),less(x,y),satz10b,l),ec3e31(is(x,y),more(x,y),less(x,y),satz10b,l)):not(moreis(x,y))
-y@[n:not(moreis(x,y))]
-satz10j:=or3e3(is(x,y),more(x,y),less(x,y),satz10a,th5"l.or"(more(x,y),is(x,y),n),th4"l.or"(more(x,y),is(x,y),n)):less(x,y)
-y@[n:not(lessis(x,y))]
-satz10k:=or3e2(is(x,y),more(x,y),less(x,y),satz10a,th4"l.or"(less(x,y),is(x,y),n),th5"l.or"(less(x,y),is(x,y),n)):more(x,y)
-z@[l:less(x,y)][k:less(y,z)]
-+315
-[v:nat][dv:diffprop(y,x,v)][w:nat][dw:diffprop(z,y,w)]
-t1:=tr3is(nat,z,pl(y,w),pl(pl(x,v),w),pl(x,pl(v,w)),dw,ispl1(y,pl(x,v),w,dv),asspl1(x,v,w)):is(z,pl(x,pl(v,w)))
-t2:=somei(nat,[u:nat]diffprop(z,x,u),pl(v,w),t1):less(x,z)
-dv@t3:=someapp(nat,[w:nat]diffprop(z,y,w),k,less(x,z),[w:nat][dw:diffprop(z,y,w)]t2(w,dw)):less(x,z)
--315
-satz15:=someapp(nat,[v:nat]diffprop(y,x,v),l,less(x,z),[v:nat][dv:diffprop(y,x,v)]t3".315"(v,dv)):less(x,z)
-trless:=satz15:less(x,z)
-z@[m:more(x,y)][n:more(y,z)]
-trmore:=satz15(z,y,x,n,m):more(x,z)
-+*315
-n@anders:=satz12(z,x,satz15(z,y,x,satz11(y,z,n),satz11(m))):more(x,z)
--315
-z@[l:lessis(x,y)][k:less(y,z)]
-satz16a:=orapp(less(x,y),is(x,y),less(x,z),l,[u:less(x,y)]trless(u,k),[u:is(x,y)]isless1(y,x,z,symis(nat,x,y,u),k)):less(x,z)
-z@[l:less(x,y)][k:lessis(y,z)]
-satz16b:=orapp(less(y,z),is(y,z),less(x,z),k,[u:less(y,z)]trless(l,u),[u:is(y,z)]isless2(y,z,x,u,l)):less(x,z)
-z@[m:moreis(x,y)][n:more(y,z)]
-satz16c:=satz16b(z,y,x,n,satz13(m)):more(x,z)
-z@[m:more(x,y)][n:moreis(y,z)]
-satz16d:=satz16a(z,y,x,satz13(y,z,n),m):more(x,z)
-z@[l:lessis(x,y)][k:lessis(y,z)]
-+317
-[i:is(x,y)][j:is(y,z)]
-t1:=lessisi2(x,z,tris(nat,x,y,z,i,j)):lessis(x,z)
-i@[j:less(y,z)]
-t2:=lessisi1(x,z,satz16a(l,j)):lessis(x,z)
-i@t3:=orapp(less(y,z),is(y,z),lessis(x,z),k,[u:less(y,z)]t2(u),[u:is(y,z)]t1(u)):lessis(x,z)
-k@[j:less(x,y)]
-t4:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
--317
-satz17:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t4".317"(u),[u:is(x,y)]t3".317"(u)):lessis(x,z)
-+*317
-k@[j:less(x,y)]
-t5:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
-k@[i:is(x,y)]
-t6:=islessis1(y,x,z,symis(nat,x,y,i),k):lessis(x,z)
-k@anders:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t5(u),[u:is(x,y)]t6(u)):lessis(x,z)
--317
-k@trlessis:=satz17:lessis(x,z)
-z@[m:moreis(x,y)][n:moreis(y,z)]
-trmoreis:=satz14(z,x,satz17(z,y,x,satz13(y,z,n),satz13(m))):moreis(x,z)
-y@satz18:=somei(nat,[u:nat]diffprop(pl(x,y),x,u),y,refis(nat,pl(x,y))):more(pl(x,y),x)
-satz18a:=satz18:less(x,pl(x,y))
-x@satz18b:=ismore1(pl(x,1),<x>suc,x,satz4a,satz18(1)):more(<x>suc,x)
-satz18c:=satz18b:less(x,<x>suc)
-z@[m:more(x,y)]
-+319
-[u:nat][du:diffprop(u)]
-t1:=tris(nat,x,pl(y,u),pl(u,y),du,compl(y,u)):is(x,pl(u,y))
-t2:=tr3is(nat,pl(x,z),pl(pl(u,y),z),pl(u,pl(y,z)),pl(pl(y,z),u),ispl1(x,pl(u,y),z,t1),asspl1(u,y,z),compl(u,pl(y,z))):is(pl(x,z),pl(pl(y,z),u))
-t3:=somei(nat,[v:nat]diffprop(pl(x,z),pl(y,z),v),u,t2):more(pl(x,z),pl(y,z))
--319
-satz19a:=someapp(nat,[u:nat]diffprop(u),m,more(pl(x,z),pl(y,z)),[u:nat][v:diffprop(u)]t3".319"(u,v)):more(pl(x,z),pl(y,z))
-z@[i:is(x,y)]
-satz19b:=ispl1(x,y,z,i):is(pl(x,z),pl(y,z))
-z@[l:less(x,y)]
-satz19c:=satz11(pl(y,z),pl(x,z),satz19a(y,x,z,satz12(x,y,l))):less(pl(x,z),pl(y,z))
-+*319
-l@anders1:=satz19a(y,x,z,l):less(pl(x,z),pl(y,z))
--319
-m@satz19d:=ismore12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19a):more(pl(z,x),pl(z,y))
-i@satz19e:=ispl2(x,y,z,i):is(pl(z,x),pl(z,y))
-l@satz19f:=isless12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19c):less(pl(z,x),pl(z,y))
-+*319
-l@anders2:=satz19d(y,x,z,l):less(pl(z,x),pl(z,y))
--319
-z@[u:nat][i:is(x,y)][m:more(z,u)]
-satz19g:=ismore2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19d(z,u,x,m)):more(pl(x,z),pl(y,u))
-satz19h:=ismore12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19g):more(pl(z,x),pl(u,y))
-i@[l:less(z,u)]
-satz19j:=isless2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19f(z,u,x,l)):less(pl(x,z),pl(y,u))
-satz19k:=isless12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19j):less(pl(z,x),pl(u,y))
-z@[m:moreis(x,y)]
-+*319
-m@[n:more(x,y)]
-t4:=moreisi1(pl(x,z),pl(y,z),satz19a(n)):moreis(pl(x,z),pl(y,z))
-m@[i:is(x,y)]
-t5:=moreisi2(pl(x,z),pl(y,z),ispl1(x,y,z,i)):moreis(pl(x,z),pl(y,z))
--319
-m@satz19l:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,z)),m,[u:more(x,y)]t4".319"(u),[u:is(x,y)]t5".319"(u)):moreis(pl(x,z),pl(y,z))
-satz19m:=ismoreis12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19l):moreis(pl(z,x),pl(z,y))
-z@[l:lessis(x,y)]
-satz19n:=satz13(pl(y,z),pl(x,z),satz19l(y,x,z,satz14(l))):lessis(pl(x,z),pl(y,z))
-satz19o:=satz13(pl(z,y),pl(z,x),satz19m(y,x,z,satz14(l))):lessis(pl(z,x),pl(z,y))
-+320
-z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
-t2:=satz10b(pl(x,z),pl(y,z)):ec3(is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)))
--320
-z@[m:more(pl(x,z),pl(y,z))]
-satz20a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),m):more(x,y)
-z@[i:is(pl(x,z),pl(y,z))]
-satz20b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),i):is(x,y)
-z@[l:less(pl(x,z),pl(y,z))]
-satz20c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),l):less(x,y)
-+*320
-i@t3:=tr3is(nat,pl(z,x),pl(x,z),pl(y,z),pl(z,y),compl(z,x),i,compl(y,z)):is(pl(z,x),pl(z,y))
-andersb:=satz8a(z,x,y,t3):is(x,y)
-l@andersc:=satz20a(y,x,z,l):less(x,y)
--320
-z@[m:more(pl(z,x),pl(z,y))]
-satz20d:=satz20a(ismore12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),m)):more(x,y)
-z@[i:is(pl(z,x),pl(z,y))]
-satz20e:=satz20b(tr3is(nat,pl(x,z),pl(z,x),pl(z,y),pl(y,z),compl(x,z),i,compl(z,y))):is(x,y)
-z@[l:less(pl(z,x),pl(z,y))]
-satz20f:=satz20c(isless12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),l)):less(x,y)
-u@[m:more(x,y)][n:more(z,u)]
-+321
-t1:=satz19a(x,y,z,m):more(pl(x,z),pl(y,z))
-t2:=ismore12(pl(z,y),pl(y,z),pl(u,y),pl(y,u),compl(z,y),compl(u,y),satz19a(z,u,y,n)):more(pl(y,z),pl(y,u))
--321
-satz21:=trmore(pl(x,z),pl(y,z),pl(y,u),t1".321",t2".321"):more(pl(x,z),pl(y,u))
-+*321
-n@anders:=trmore(pl(x,z),pl(y,z),pl(y,u),satz19a(x,y,z,m),satz19d(z,u,y,n)):more(pl(x,z),pl(y,u))
--321
-u@[l:less(x,y)][k:less(z,u)]
-satz21a:=satz21(y,x,u,z,l,k):less(pl(x,z),pl(y,u))
-+*321
-k@andersa:=satz11(pl(y,u),pl(x,z),satz21(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(pl(x,z),pl(y,u))
--321
-u@[m:moreis(x,y)][n:more(z,u)]
-satz22a:=orapp(more(x,y),is(x,y),more(pl(x,z),pl(y,u)),m,[v:more(x,y)]satz21(v,n),[v:is(x,y)]satz19g(u,v,n)):more(pl(x,z),pl(y,u))
-u@[m:more(x,y)][n:moreis(z,u)]
-satz22b:=orapp(more(z,u),is(z,u),more(pl(x,z),pl(y,u)),n,[v:more(z,u)]satz21(m,v),[v:is(z,u)]satz19h(z,u,x,y,v,m)):more(pl(x,z),pl(y,u))
-u@[l:lessis(x,y)][k:less(z,u)]
-satz22c:=satz22a(y,x,u,z,satz14(x,y,l),k):less(pl(x,z),pl(y,u))
-u@[l:less(x,y)][k:lessis(z,u)]
-satz22d:=satz22b(y,x,u,z,l,satz14(z,u,k)):less(pl(x,z),pl(y,u))
-u@[m:moreis(x,y)][n:moreis(z,u)]
-+323
-[i:is(x,y)][j:is(z,u)]
-t1:=moreisi2(pl(x,z),pl(y,u),tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j))):moreis(pl(x,z),pl(y,u))
-i@[o:more(z,u)]
-t2:=moreisi1(pl(x,z),pl(y,u),satz22a(m,o)):moreis(pl(x,z),pl(y,u))
-i@t3:=orapp(more(z,u),is(z,u),moreis(pl(x,z),pl(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(pl(x,z),pl(y,u))
-n@[o:more(x,y)]
-t4:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
--323
-satz23:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t4".323"(v),[v:is(x,y)]t3".323"(v)):moreis(pl(x,z),pl(y,u))
-+*323
-n@[o:more(x,y)]
-t5:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
-n@[i:is(x,y)]
-t6:=ismoreis2(pl(x,u),pl(y,u),pl(x,z),ispl1(u,i),satz19m(z,u,x,n)):moreis(pl(x,z),pl(y,u))
-n@anders:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(pl(x,z),pl(y,u))
--323
-u@[l:lessis(x,y)][k:lessis(z,u)]
-satz23a:=satz13(pl(y,u),pl(x,z),satz23(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(pl(x,z),pl(y,u))
-+324
-x@[n:nis(x,1)][u:nat][i:is(x,<u>suc)]
-t1:=tris(nat,x,<u>suc,pl(1,u),i,satz4g(u)):is(x,pl(1,u))
-t2:=ismore1(pl(1,u),x,1,symis(nat,x,pl(1,u),t1),satz18(1,u)):more(x,1)
-n@t3:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),more(x,1),[u:nat][v:is(x,<u>suc)]t2(u,v)):more(x,1)
--324
-x@satz24:=th2"l.or"(more(x,1),is(x,1),[u:nis(x,1)]t3".324"(u)):moreis(x,1)
-satz24a:=satz13(x,1,satz24):lessis(1,x)
-satz24b:=t3".324"(<x>suc,<x>ax3):more(<x>suc,1)
-satz24c:=satz24b:less(1,<x>suc)
-y@[m:more(y,x)]
-+325
-[u:nat][du:diffprop(y,x,u)]
-t1:=satz19m(u,1,x,satz24(u)):moreis(pl(x,u),pl(x,1))
-t2:=ismoreis1(pl(x,u),y,pl(x,1),symis(nat,y,pl(x,u),du),t1):moreis(y,pl(x,1))
--325
-satz25:=someapp(nat,[u:nat]diffprop(y,x,u),m,moreis(y,pl(x,1)),[u:nat][v:diffprop(y,x,u)]t2".325"(u,v)):moreis(y,pl(x,1))
-satz25a:=ismoreis2(pl(x,1),<x>suc,y,satz4a,satz25):moreis(y,<x>suc)
-y@[l:less(y,x)]
-satz25b:=satz13(x,pl(y,1),satz25(y,x,l)):lessis(pl(y,1),x)
-satz25c:=islessis1(pl(y,1),<y>suc,x,satz4a(y),satz25b):lessis(<y>suc,x)
-y@[l:less(y,pl(x,1))]
-+326
-[m:more(y,x)]
-t1:=satz25(m):moreis(y,pl(x,1))
-l@t2:=th3"l.imp"(more(y,x),moreis(y,pl(x,1)),satz10h(y,pl(x,1),l),[v:more(y,x)]t1(v)):not(more(y,x))
--326
-satz26:=satz10e(y,x,t2".326"):lessis(y,x)
-y@[l:less(y,<x>suc)]
-satz26a:=satz26(isless2(<x>suc,pl(x,1),y,satz4e,l)):lessis(y,x)
-y@[m:more(pl(y,1),x)]
-satz26b:=satz14(x,y,satz26(y,x,m)):moreis(y,x)
-y@[m:more(<y>suc,x)]
-satz26c:=satz26b(ismore1(<y>suc,pl(y,1),x,satz4e(y),m)):moreis(y,x)
-@[p:[x:nat]'prop'][n:nat]
-+327
-[m:nat]
-lbprop:=imp(<m>p,lessis(n,m)):'prop'
--327
-lb:=all([x:nat]lbprop".327"(x)):'prop'
-min:=and(lb,<n>p):'prop'
-p@[s:some(p)]
-+*327
-s@[n:nat]
-t1:=[x:<n>p]satz24a(n):lbprop(1,n)
-s@t2:=[x:nat]t1(x):lb(1)
-[l:[x:nat]lb(x)][y:nat][yp:<y>p]
-t3:=satz18(y,1):more(pl(y,1),y)
-t4:=satz10g(pl(y,1),y,t3):not(lessis(pl(y,1),y))
-t5:=th4"l.imp"(<y>p,lessis(pl(y,1),y),yp,t4):not(lbprop(pl(y,1),y))
-t6:=th1"l.all"(nat,[x:nat]lbprop(pl(y,1),x),y,t5):not(lb(pl(y,1)))
-t7:=mp(lb(pl(y,1)),con,<pl(y,1)>l,t6):con
-l@t8:=someapp(nat,p,s,con,[x:nat][y:<x>p]t7(x,y)):con
-s@[n:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))][m:nat][l:lb(m)]
-t9:=<m>n:not(and(lb(m),not(lb(pl(m,1)))))
-t10:=et(lb(pl(m,1)),th3"l.and"(lb(m),not(lb(pl(m,1))),t9,l)):lb(pl(m,1))
-t11:=isp(nat,[x:nat]lb(x),pl(m,1),<m>suc,t10,satz4a(m)):lb(<m>suc)
-n@t12:=[x:nat]induction([y:nat]lb(y),t2,[y:nat][z:lb(y)]t11(y,z),x):[x:nat]lb(x)
-s@t13:=[x:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))]t8(t12(x)):some([x:nat]and(lb(x),not(lb(pl(x,1)))))
-[m:nat][a:and(lb(m),not(lb(pl(m,1))))]
-t14:=ande1(lb(m),not(lb(pl(m,1))),a):lb(m)
-t15:=ande2(lb(m),not(lb(pl(m,1))),a):not(lb(pl(m,1)))
-[nmp:not(<m>p)][n:nat][np:<n>p]
-t16:=mp(<n>p,lessis(m,n),np,<n>t14):lessis(m,n)
-t17:=th3"l.imp"(is(m,n),<m>p,nmp,[x:is(m,n)]isp(nat,p,n,m,np,symis(nat,m,n,x))):not(is(m,n))
-t18:=ore1(less(m,n),is(m,n),t16,t17):less(m,n)
-t19:=satz25b(n,m,t18):lessis(pl(m,1),n)
-nmp@t20:=[x:nat][y:<x>p]t19(x,y):lb(pl(m,1))
-t21:=mp(lb(pl(m,1)),con,t20,t15):con
-a@t22:=et(<m>p,[x:not(<m>p)]t21(x)):<m>p
-t23:=andi(lb(m),<m>p,t14,t22):min(m)
--327
-s@satz27:=th6"l.some"(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))),[x:nat]min(x),t13".327",[x:nat][y:and(lb(x),not(lb(pl(x,1))))]t23".327"(x,y)):some([x:nat]min(p,x))
-+*327
-p@[n:non(nat,[x:nat]min(x))][u:nat]
-t24:=[x:<u>p]satz24a(u):lbprop(1,u)
-n@t25:=[x:nat]t24(x):lb(1)
-u@[l:lb(u)]
-t26:=<u>n:not(min(u))
-t27:=th3"l.and"(lb(u),<u>p,t26,l):not(<u>p)
-[v:nat][vp:<v>p]
-t28:=th3"l.imp"(is(u,v),<u>p,t27,[x:is(u,v)]isp1(nat,p,v,u,vp,x)):nis(u,v)
-t29:=mp(<v>p,lessis(u,v),vp,<v>l):lessis(u,v)
-t30:=ore1(less(u,v),is(u,v),t29,t28):less(u,v)
-t31:=satz25c(v,u,t30):lessis(<u>suc,v)
-v@t32:=[x:<v>p]t31(x):lbprop(<u>suc,v)
-l@t33:=[x:nat]t32(x):lb(<u>suc)
-u@t34:=induction([x:nat]lb(x),t25,[x:nat][y:lb(x)]t33(x,y),u):lb(u)
-p@[s:some(p)][u:nat][up:<u>p]
-t35:=satz10g(<u>suc,u,satz18b(u)):not(lessis(<u>suc,u))
-t36:=th4"l.imp"(<u>p,lessis(<u>suc,u),up,t35):not(lbprop(<u>suc,u))
-t37:=th1"l.all"(nat,[x:nat]lbprop(<u>suc,x),u,t36):not(lb(<u>suc))
-t38:=[y:non(nat,[x:nat]min(x))]mp(lb(<u>suc),con,t34(y,<u>suc),t37):some([x:nat]min(x))
-s@anders:=someapp(nat,p,s,some([x:nat]min(x)),[x:nat][y:<x>p]t38(x,y)):some([x:nat]min(x))
--327
-+*327
-p@[n:nat][m:nat][mn:min(p,n)][mm:min(p,m)]
-t39:=ande1(lb(n),<n>p,mn):lb(n)
-t40:=ande1(lb(m),<m>p,mm):lb(m)
-t41:=ande2(lb(n),<n>p,mn):<n>p
-t42:=ande2(lb(m),<m>p,mm):<m>p
-t43:=<m>t39:lbprop(n,m)
-t44:=<n>t40:lbprop(m,n)
-t45:=mp(<m>p,lessis(n,m),t42,t43):lessis(n,m)
-t46:=mp(<n>p,lessis(m,n),t41,t44):lessis(m,n)
-t47:=ore2(more(n,m),is(n,m),satz14(m,n,t46),satz10d(n,m,t45)):is(n,m)
-p@t48:=[x:nat][y:nat][u:min(x)][v:min(y)]t47(x,y,u,v):amone(nat,[x:nat]min(p,x))
--327
-s@satz27a:=onei(nat,[x:nat]min(p,x),t48".327",satz27):one([x:nat]min(p,x))
-+428
-x@[f:[y:nat]nat]
-prop1:=all([y:nat]is(<<y>suc>f,pl(<y>f,x))):'prop'
-prop2:=and(is(<1>f,x),prop1):'prop'
-x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
-prop3:=is(<y>a,<y>b):'prop'
-pb@t1:=ande1(is(<1>a,x),prop1(a),pa):is(<1>a,x)
-t2:=ande1(is(<1>b,x),prop1(b),pb):is(<1>b,x)
-t3:=tris2(nat,<1>a,<1>b,x,t1,t2):prop3(1)
-y@[p:prop3(y)]
-t4:=ispl1(<y>a,<y>b,x,p):is(pl(<y>a,x),pl(<y>b,x))
-t5:=ande2(is(<1>a,x),prop1(a),pa):prop1(a)
-t6:=ande2(is(<1>b,x),prop1(b),pb):prop1(b)
-t7:=<y>t5:is(<<y>suc>a,pl(<y>a,x))
-t8:=<y>t6:is(<<y>suc>b,pl(<y>b,x))
-t9:=tr3is(nat,<<y>suc>a,pl(<y>a,x),pl(<y>b,x),<<y>suc>b,t7,t4,symis(nat,<<y>suc>b,pl(<y>b,x),t8)):prop3(<y>suc)
-y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
-pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
-x@a1:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
-prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
-@id:=[y:nat]y:[y:nat]nat
-t12:=[x:nat]satz4e(x):prop1(1,id)
-t13:=andi(is(<1>id,1),prop1(1,id),refis(nat,1),t12):prop2(1,id)
-t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),id,t13):prop4(1)
-x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
-g:=[y:nat]pl(<y>f,y):[y:nat]nat
-t15:=ande1(is(<1>f,x),prop1(f),pf):is(<1>f,x)
-t16:=tris(nat,<1>g,pl(x,1),<x>suc,ispl1(<1>f,x,1,t15),satz4a(x)):is(<1>g,<x>suc)
-[y:nat]
-t17:=ande2(is(<1>f,x),prop1(f),pf):prop1(f)
-t18:=<y>t17:is(<<y>suc>f,pl(<y>f,x))
-t19:=tris(nat,<<y>suc>g,pl(pl(<y>f,x),<y>suc),pl(<y>f,pl(x,<y>suc)),ispl1(<<y>suc>f,pl(<y>f,x),<y>suc,t18),asspl1(<y>f,x,<y>suc)):is(<<y>suc>g,pl(<y>f,pl(x,<y>suc)))
-t20:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,pl(<x>suc,y),pl(y,<x>suc),satz4b(x,y),satz4h(x,y),compl(<x>suc,y)):is(pl(x,<y>suc),pl(y,<x>suc))
-t21:=tr3is(nat,<<y>suc>g,pl(<y>f,pl(x,<y>suc)),pl(<y>f,pl(y,<x>suc)),pl(<y>g,<x>suc),t19,ispl2(pl(x,<y>suc),pl(y,<x>suc),<y>f,t20),asspl2(<y>f,y,<x>suc)):is(<<y>suc>g,pl(<y>g,<x>suc))
-pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
-t23:=andi(is(<1>g,<x>suc),prop1(<x>suc,g),t16,t22):prop2(<x>suc,g)
-t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
-p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
-x@b1:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
--428
-x@satz28:=onei([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),a1".428",b1".428"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,x),all([y:nat]is(<<y>suc>z,pl(<y>z,x)))))
-times:=ind([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),satz28):[y:nat]nat
-y@ts:=<y>times:nat
-+*428
-x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz28):prop2(times)
--428
-x@satz28a:=ande1(is(<1>times,x),prop1".428"(times),t26".428"):is(ts(x,1),x)
-+*428
-x@t27:=ande2(is(<1>times,x),prop1(times),t26):prop1(times)
--428
-y@satz28b:=<y>t27".428":is(ts(x,<y>suc),pl(ts(x,y),x))
-+*428
-@t28:=t11(1,times(1),id,t26(1),t13):is"e"([y:nat]nat,times(1),id)
--428
-x@satz28c:=fise(nat,nat,times(1),id".428",t28".428",x):is(ts(1,x),x)
-+*428
-x@t29:=t11(<x>suc,times(<x>suc),[y:nat]pl(<y>times,y),t26(<x>suc),t23(b1,times,t26)):is"e"([y:nat]nat,times(<x>suc),[y:nat]pl(<y>times,y))
--428
-y@satz28d:=fise(nat,nat,times(<x>suc),[z:nat]pl(<z>times,z),t29".428",y):is(ts(<x>suc,y),pl(ts(x,y),y))
-x@satz28e:=symis(nat,ts(x,1),x,satz28a):is(x,ts(x,1))
-y@satz28f:=symis(nat,ts(x,<y>suc),pl(ts(x,y),x),satz28b):is(pl(ts(x,y),x),ts(x,<y>suc))
-x@satz28g:=symis(nat,ts(1,x),x,satz28c):is(x,ts(1,x))
-y@satz28h:=symis(nat,ts(<x>suc,y),pl(ts(x,y),y),satz28d):is(pl(ts(x,y),y),ts(<x>suc,y))
-z@[i:is(x,y)]
-ists1:=isf(nat,nat,[u:nat]ts(u,z),x,y,i):is(ts(x,z),ts(y,z))
-ists2:=isf(nat,nat,[u:nat]ts(z,u),x,y,i):is(ts(z,x),ts(z,y))
-z@[u:nat][i:is(x,y)][j:is(z,u)]
-ists12:=tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
-+429
-y@prop1:=is(ts(x,y),ts(y,x)):'prop'
-t1:=satz28a(y):is(ts(y,1),y)
-t2:=satz28c(y):is(ts(1,y),y)
-t3:=tris2(nat,ts(1,y),ts(y,1),y,t2,t1):prop1(1,y)
-[p:prop1(x,y)]
-t4:=tris(nat,pl(ts(x,y),y),pl(ts(y,x),y),ts(y,<x>suc),ispl1(ts(x,y),ts(y,x),y,p),satz28f(y,x)):is(pl(ts(x,y),y),ts(y,<x>suc))
-t5:=satz28d:is(ts(<x>suc,y),pl(ts(x,y),y))
-t6:=tris(nat,ts(<x>suc,y),pl(ts(x,y),y),ts(y,<x>suc),t5,t4):prop1(<x>suc,y)
--429
-y@satz29:=induction([z:nat]prop1".429"(z,y),t3".429",[z:nat][u:prop1".429"(z,y)]t6".429"(z,y,u),x):is(ts(x,y),ts(y,x))
-comts:=satz29:is(ts(x,y),ts(y,x))
-+*429
-x@t7:=tris(nat,ts(x,1),x,ts(1,x),satz28a,satz28g):prop1(1)
-y@[p:prop1(y)]
-t8:=tr3is(nat,ts(x,<y>suc),pl(ts(x,y),x),pl(ts(y,x),x),ts(<y>suc,x),satz28b(x,y),ispl1(ts(x,y),ts(y,x),x,p),satz28h(y,x)):prop1(<y>suc)
-y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(ts(x,y),ts(y,x))
--429
-+430
-z@prop1:=is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z))):'prop'
-y@t1:=tr3is(nat,ts(x,pl(y,1)),ts(x,<y>suc),pl(ts(x,y),x),pl(ts(x,y),ts(x,1)),ists2(pl(y,1),<y>suc,x,satz4a(y)),satz28b,ispl2(x,ts(x,1),ts(x,y),satz28e(x))):prop1(1)
-z@[p:prop1(z)]
-t2:=tr3is(nat,ts(x,pl(y,<z>suc)),ts(x,<pl(y,z)>suc),pl(ts(x,pl(y,z)),x),pl(pl(ts(x,y),ts(x,z)),x),ists2(pl(y,<z>suc),<pl(y,z)>suc,x,satz4b(y,z)),satz28b(x,pl(y,z)),ispl1(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),x,p)):is(ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x))
-t3:=tr3is(nat,ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x),pl(ts(x,y),pl(ts(x,z),x)),pl(ts(x,y),ts(x,<z>suc)),t2,asspl1(ts(x,y),ts(x,z),x),ispl2(pl(ts(x,z),x),ts(x,<z>suc),ts(x,y),satz28f(x,z))):prop1(<z>suc)
--430
-z@satz30:=induction([u:nat]prop1".430"(u),t1".430",[u:nat][v:prop1".430"(u)]t3".430"(u,v),z):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-disttp1:=tr3is(nat,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz30(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
-disttp2:=satz30:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-distpt1:=symis(nat,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
-distpt2:=symis(nat,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
-+431
-prop1:=is(ts(ts(x,y),z),ts(x,ts(y,z))):'prop'
-y@t1:=tris(nat,ts(ts(x,y),1),ts(x,y),ts(x,ts(y,1)),satz28a(ts(x,y)),ists2(y,ts(y,1),x,satz28e(y))):prop1(1)
-z@[p:prop1(z)]
-t2:=tr4is(nat,ts(ts(x,y),<z>suc),pl(ts(ts(x,y),z),ts(x,y)),pl(ts(x,ts(y,z)),ts(x,y)),ts(x,pl(ts(y,z),y)),ts(x,ts(y,<z>suc)),satz28b(ts(x,y),z),ispl1(ts(ts(x,y),z),ts(x,ts(y,z)),ts(x,y),p),distpt2(x,ts(y,z),y),ists2(pl(ts(y,z),y),ts(y,<z>suc),x,satz28f(y,z))):prop1(<z>suc)
--431
-satz31:=induction([u:nat]prop1".431"(u),t1".431",[u:nat][v:prop1".431"(u)]t2".431"(u,v),z):is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts1:=satz31:is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts2:=symis(nat,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
-[m:more(x,y)]
-+432
-[u:nat][du:diffprop(u)]
-t1:=tris(nat,ts(x,z),ts(pl(y,u),z),pl(ts(y,z),ts(u,z)),ists1(x,pl(y,u),z,du),disttp1(y,u,z)):is(ts(x,z),pl(ts(y,z),ts(u,z)))
-t2:=somei(nat,[v:nat]diffprop(ts(x,z),ts(y,z),v),ts(u,z),t1):more(ts(x,z),ts(y,z))
--432
-satz32a:=someapp(nat,[u:nat]diffprop(u),m,more(ts(x,z),ts(y,z)),[u:nat][v:diffprop(u)]t2".432"(u,v)):more(ts(x,z),ts(y,z))
-z@[i:is(x,y)]
-satz32b:=ists1(x,y,z,i):is(ts(x,z),ts(y,z))
-z@[l:less(x,y)]
-satz32c:=satz11(ts(y,z),ts(x,z),satz32a(y,x,z,satz12(x,y,l))):less(ts(x,z),ts(y,z))
-+*432
-l@anders1:=satz32a(y,x,z,l):less(ts(x,z),ts(y,z))
--432
-m@satz32d:=ismore12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32a):more(ts(z,x),ts(z,y))
-i@satz32e:=ists2(x,y,z,i):is(ts(z,x),ts(z,y))
-l@satz32f:=isless12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32c):less(ts(z,x),ts(z,y))
-+*432
-l@anders2:=satz32d(y,x,z,l):less(ts(z,x),ts(z,y))
--432
-z@[u:nat][i:is(x,y)][m:more(z,u)]
-satz32g:=ismore2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32d(z,u,x,m)):more(ts(x,z),ts(y,u))
-satz32h:=ismore12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32g):more(ts(z,x),ts(u,y))
-i@[l:less(z,u)]
-satz32j:=isless2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32f(z,u,x,l)):less(ts(x,z),ts(y,u))
-satz32k:=isless12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32j):less(ts(z,x),ts(u,y))
-z@[m:moreis(x,y)]
-+*432
-m@[n:more(x,y)]
-t3:=moreisi1(ts(x,z),ts(y,z),satz32a(n)):moreis(ts(x,z),ts(y,z))
-m@[i:is(x,y)]
-t4:=moreisi2(ts(x,z),ts(y,z),ists1(x,y,z,i)):moreis(ts(x,z),ts(y,z))
--432
-m@satz32l:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,z)),m,[u:more(x,y)]t3".432"(u),[u:is(x,y)]t4".432"(u)):moreis(ts(x,z),ts(y,z))
-satz32m:=ismoreis12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32l):moreis(ts(z,x),ts(z,y))
-z@[l:lessis(x,y)]
-satz32n:=satz13(ts(y,z),ts(x,z),satz32l(y,x,z,satz14(l))):lessis(ts(x,z),ts(y,z))
-satz32o:=satz13(ts(z,y),ts(z,x),satz32m(y,x,z,satz14(l))):lessis(ts(z,x),ts(z,y))
-+433
-z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
-t2:=satz10b(ts(x,z),ts(y,z)):ec3(is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)))
--433
-z@[m:more(ts(x,z),ts(y,z))]
-satz33a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),m):more(x,y)
-z@[i:is(ts(x,z),ts(y,z))]
-satz33b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),i):is(x,y)
-z@[l:less(ts(x,z),ts(y,z))]
-satz33c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),l):less(x,y)
-+*433
-l@anders:=satz33a(y,x,z,l):less(x,y)
--433
-u@[m:more(x,y)][n:more(z,u)]
-+434
-t1:=satz32a(x,y,z,m):more(ts(x,z),ts(y,z))
-t2:=ismore12(ts(z,y),ts(y,z),ts(u,y),ts(y,u),comts(z,y),comts(u,y),satz32a(z,u,y,n)):more(ts(y,z),ts(y,u))
--434
-satz34:=trmore(ts(x,z),ts(y,z),ts(y,u),t1".434",t2".434"):more(ts(x,z),ts(y,u))
-+*434
-n@anders:=trmore(ts(x,z),ts(y,z),ts(y,u),satz32a(x,y,z,m),satz32d(z,u,y,n)):more(ts(x,z),ts(y,u))
--434
-u@[l:less(x,y)][k:less(z,u)]
-satz34a:=satz34(y,x,u,z,l,k):less(ts(x,z),ts(y,u))
-+*434
-k@andersa:=satz11(ts(y,u),ts(x,z),satz34(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(ts(x,z),ts(y,u))
--434
-u@[m:moreis(x,y)][n:more(z,u)]
-satz35a:=orapp(more(x,y),is(x,y),more(ts(x,z),ts(y,u)),m,[v:more(x,y)]satz34(v,n),[v:is(x,y)]satz32g(u,v,n)):more(ts(x,z),ts(y,u))
-u@[m:more(x,y)][n:moreis(z,u)]
-satz35b:=orapp(more(z,u),is(z,u),more(ts(x,z),ts(y,u)),n,[v:more(z,u)]satz34(m,v),[v:is(z,u)]satz32h(z,u,x,y,v,m)):more(ts(x,z),ts(y,u))
-u@[l:lessis(x,y)][k:less(z,u)]
-satz35c:=satz35a(y,x,u,z,satz14(x,y,l),k):less(ts(x,z),ts(y,u))
-u@[l:less(x,y)][k:lessis(z,u)]
-satz35d:=satz35b(y,x,u,z,l,satz14(z,u,k)):less(ts(x,z),ts(y,u))
-u@[m:moreis(x,y)][n:moreis(z,u)]
-+436
-[i:is(x,y)][j:is(z,u)]
-t1:=moreisi2(ts(x,z),ts(y,u),tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j))):moreis(ts(x,z),ts(y,u))
-i@[o:more(z,u)]
-t2:=moreisi1(ts(x,z),ts(y,u),satz35a(m,o)):moreis(ts(x,z),ts(y,u))
-i@t3:=orapp(more(z,u),is(z,u),moreis(ts(x,z),ts(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(ts(x,z),ts(y,u))
-n@[o:more(x,y)]
-t4:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
--436
-satz36:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t4".436"(v),[v:is(x,y)]t3".436"(v)):moreis(ts(x,z),ts(y,u))
-+*436
-n@[o:more(x,y)]
-t5:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
-n@[i:is(x,y)]
-t6:=ismoreis2(ts(x,u),ts(y,u),ts(x,z),ists1(u,i),satz32m(z,u,x,n)):moreis(ts(x,z),ts(y,u))
-n@anders:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(ts(x,z),ts(y,u))
--436
-u@[l:lessis(x,y)][k:lessis(z,u)]
-satz36a:=satz13(ts(y,u),ts(x,z),satz36(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(ts(x,z),ts(y,u))
-y@[m:more(x,y)]
-+mn
-t1:=onei(nat,[z:nat]diffprop(x,y,z),satz8b(x,y),m):one([z:nat]diffprop(x,y,z))
--mn
-mn:=ind(nat,[z:nat]diffprop(x,y,z),t1".mn"):nat
-+*mn
-m@th1a:=oneax(nat,[z:nat]diffprop(x,y,z),t1):is(x,pl(y,mn(x,y,m)))
-th1b:=symis(nat,x,pl(y,mn(x,y,m)),th1a):is(pl(y,mn(x,y,m)),x)
-th1c:=tris(nat,x,pl(y,mn(x,y,m)),pl(mn(x,y,m),y),th1a,compl(y,mn(x,y,m))):is(x,pl(mn(x,y,m),y))
-th1d:=symis(nat,x,pl(mn(x,y,m),y),th1c):is(pl(mn(x,y,m),y),x)
-y@[z:nat][m:more(x,y)][i:is(pl(y,z),x)]
-th1e:=<th1a(m)><symis(nat,pl(y,z),x,i)><mn(x,y,m)><z>satz8b(x,y):is(z,mn(x,y,m))
--mn
-z@[u:nat][m:more(x,z)][n:more(y,u)][i:is(x,y)][j:is(z,u)]
-+*mn
-j@t2:=tr3is(nat,pl(u,mn(x,z,m)),pl(z,mn(x,z,m)),x,y,ispl1(u,z,mn(x,z,m),symis(nat,z,u,j)),th1b(x,z,m),i):is(pl(u,mn(x,z,m)),y)
--mn
-j@ismn12:=th1e".mn"(y,u,mn(x,z,m),n,t2".mn"):is(mn(x,z,m),mn(y,u,n))
-@[n:nat]
-1to:=ot(nat,[x:nat]lessis(x,n)):'type'
-[x:nat][l:lessis(x,n)]
-outn:=out(nat,[y:nat]lessis(y,n),x,l):1to(n)
-n@[xn:1to(n)]
-inn:=in"e"(nat,[y:nat]lessis(y,n),xn):nat
-1top:=inp(nat,[y:nat]lessis(y,n),xn):lessis(inn,n)
-l@[y:nat][k:lessis(y,n)][i:is(x,y)]
-isoutni:=isouti(nat,[z:nat]lessis(z,n),x,l,y,k,i):is"e"(1to(n),outn(x,l),outn(y,k))
-k@[i:is"e"(1to(n),outn(x,l),outn(y,k))]
-isoutne:=isoute(nat,[z:nat]lessis(z,n),x,l,y,k,i):is(x,y)
-xn@[yn:1to(n)][i:is"e"(1to(n),xn,yn)]
-isinni:=isini(nat,[z:nat]lessis(z,n),xn,yn,i):is(inn(xn),inn(yn))
-yn@[i:is(inn(xn),inn(yn))]
-isinne:=isine(nat,[z:nat]lessis(z,n),xn,yn,i):is"e"(1to(n),xn,yn)
-xn@isoutinn:=isoutin(nat,[y:nat]lessis(y,n),xn):is"e"(1to(n),xn,outn(inn(xn),1top(xn)))
-l@isinoutn:=isinout(nat,[y:nat]lessis(y,n),x,l):is(x,inn(outn(x,l)))
-@1o:=outn(1,1,lessisi2(1,1,refis(nat,1))):1to(1)
-[u:1to(1)]
-+singlet
-u0:=inn(1,u):nat
-t1:=1top(1,u):lessis(u0,1)
-t2:=ore2(more(u0,1),is(u0,1),satz24(u0),satz10d(u0,1,t1)):is(u0,1)
-th1:=tris(1to(1),u,outn(1,u0,t1),1o,isoutinn(1,u),isoutni(1,u0,t1,1,lessisi2(1,1,refis(nat,1)),t2)):is"e"(1to(1),u,1o)
--singlet
-@2:=pl(1,1):nat
-[x:nat]
-+pair
-[l:lessis(x,2)][n:nis(x,2)]
-t1:=satz26(1,x,ore1(less(x,2),is(x,2),l,n)):lessis(x,1)
-t2:=ore2(more(x,1),is(x,1),satz24(x),satz10d(x,1,t1)):is(x,1)
-l@th1:=th2"l.or"(is(x,1),is(x,2),[t:nis(x,2)]t2(t)):or(is(x,1),is(x,2))
-@th2:=th1"e.notis"(nat,<1>suc,1,2,<1>ax3,satz4e(1)):nis(2,1)
--pair
-@1t:=outn(2,1,satz24a(2)):1to(2)
-2t:=outn(2,2,lessisi2(2,2,refis(nat,2))):1to(2)
-+*pair
-@[u:1to(2)]
-u0:=inn(2,u):nat
-t3:=1top(2,u):lessis(u0,2)
-[i:is(u0,1)]
-t4:=isoutni(2,u0,t3,1,satz24a(2),i):is"e"(1to(2),outn(2,u0,t3),1t)
-t5:=tris(1to(2),u,outn(2,u0,t3),1t,isoutinn(2,u),t4):is"e"(1to(2),u,1t)
-u@[i:is(u0,2)]
-t6:=isoutni(2,u0,t3,2,lessisi2(2,2,refis(nat,2)),i):is"e"(1to(2),outn(2,u0,t3),2t)
-t7:=tris(1to(2),u,outn(2,u0,t3),2t,isoutinn(2,u),t6):is"e"(1to(2),u,2t)
-u@th3:=th9"l.or"(is(u0,1),is(u0,2),is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),th1(u0,t3),[t:is(u0,1)]t5(t),[t:is(u0,2)]t7(t)):or(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t))
-@[i:is"e"(1to(2),2t,1t)]
-t9:=isini(nat,[x:nat]lessis(x,2),2t,1t,i):is(u0(2t),u0(1t))
-t10:=tr3is(nat,2,u0(2t),u0(1t),1,isinoutn(2,2,lessisi2(2,2,refis(nat,2))),t9,symis(nat,1,u0(1t),isinoutn(2,1,satz24a(2)))):is(2,1)
-@th4:=th3"l.imp"(is"e"(1to(2),2t,1t),is(2,1),th2,[t:is"e"(1to(2),2t,1t)]t10(t)):not(is"e"(1to(2),2t,1t))
--pair
-@[alpha:'type']
-pair1type:=[x:1to(2)]alpha:'type'
-[a:alpha][b:alpha]
-pair1:=[x:1to(2)]ite(is"e"(1to(2),x,1t),alpha,a,b):pair1type
-alpha@[p:pair1type]
-first1:=<1t>p:alpha
-second1:=<2t>p:alpha
-b@first1is1:=itet(is"e"(1to(2),1t,1t),alpha,a,b,refis(1to(2),1t)):is"e"(alpha,first1(pair1),a)
-first1is2:=symis(alpha,first1(pair1),a,first1is1):is"e"(alpha,a,first1(pair1))
-second1is1:=itef(is"e"(1to(2),2t,1t),alpha,a,b,th4".pair"):is"e"(alpha,second1(pair1),b)
-second1is2:=symis(alpha,second1(pair1),b,second1is1):is"e"(alpha,b,second1(pair1))
-+*pair
-p@[q:pair1type][i:is"e"(alpha,first1(p),first1(q))][j:is"e"(alpha,second1(p),second1(q))][u:1to(2)][u1:is"e"(1to(2),u,1t)]
-t11:=isf(1to(2),alpha,p,u,1t,u1):is"e"(alpha,<u>p,first1(p))
-t12:=symis(alpha,<u>q,first1(q),isf(1to(2),alpha,q,u,1t,u1)):is"e"(alpha,first1(q),<u>q)
-t13:=tr3is(alpha,<u>p,first1(p),first1(q),<u>q,t11,i,t12):is"e"(alpha,<u>p,<u>q)
-u@[u2:is"e"(1to(2),u,2t)]
-t14:=isf(1to(2),alpha,p,u,2t,u2):is"e"(alpha,<u>p,second1(p))
-t15:=symis(alpha,<u>q,second1(q),isf(1to(2),alpha,q,u,2t,u2)):is"e"(alpha,second1(q),<u>q)
-t16:=tr3is(alpha,<u>p,second1(p),second1(q),<u>q,t14,j,t15):is"e"(alpha,<u>p,<u>q)
-u@t17:=orapp(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),is"e"(alpha,<u>p,<u>q),th3(u),[t:is"e"(1to(2),u,1t)]t13(t),[t:is"e"(1to(2),u,2t)]t16(t)):is"e"(alpha,<u>p,<u>q)
-j@th5:=fisi(1to(2),alpha,p,q,[t:1to(2)]t17(t)):is"e"(pair1type,p,q)
-p@q0:=pair1(first1,second1):pair1type
-t18:=first1is1(first1(p),second1):is"e"(alpha,first1(q0),first1(p))
-t19:=second1is1(first1,second1):is"e"(alpha,second1(q0),second1(p))
--pair
-p@pair1is1:=th5".pair"(q0".pair",p,t18".pair",t19".pair"):is"e"(pair1type,pair1(first1,second1),p)
-pair1is2:=symis(pair1type,pair1(first1,second1),p,pair1is1):is"e"(pair1type,p,pair1(first1,second1))
-@[x:nat]
-lessisi3:=lessisi2(x,x,refis(nat,x)):lessis(x,x)
-1out:=outn(x,1,satz24a(x)):1to(x)
-xout:=outn(x,x,lessisi3(x)):1to(x)
-[y:nat][l:lessis(y,x)][u:1to(y)]
-+left
-ui:=inn(y,u):nat
-t1:=1top(y,u):lessis(ui,y)
-t2:=trlessis(ui,y,x,t1,l):lessis(ui,x)
--left
-left1to:=outn(x,ui".left",t2".left"):1to(x)
-[v:1to(y)][i:is"e"(1to(x),left1to(u),left1to(v))]
-+*left
-i@t3:=isoutne(x,ui,t2,ui(v),t2(v),i):is(ui,ui(v))
--left
-i@thleft1:=isinne(y,u,v,t3".left"):is"e"(1to(y),u,v)
-l@thleft2:=[u:1to(y)][v:1to(y)][t:is"e"(1to(x),left1to(u),left1to(v))]thleft1(u,v,t):injective(1to(y),1to(x),[t:1to(y)]left1to(t))
-y@[u:1to(y)]
-+right
-ui:=inn(y,u):nat
-t4:=1top(y,u):lessis(ui,y)
-t5:=satz19o(ui,y,x,t4):lessis(pl(x,ui),pl(x,y))
--right
-right1to:=outn(pl(x,y),pl(x,ui".right"),t5".right"):1to(pl(x,y))
-[v:1to(y)][i:is"e"(1to(pl(x,y)),right1to(u),right1to(v))]
-+*right
-i@t6:=isoutne(pl(x,y),pl(x,ui(u)),t5(u),pl(x,ui(v)),t5(v),i):is(pl(x,ui(u)),pl(x,ui(v)))
-t7:=satz20e(ui(u),ui(v),x,t6):is(ui(u),ui(v))
--right
-i@thright1:=isinne(y,u,v,t7".right"):is"e"(1to(y),u,v)
-@[alpha:'type'][x:nat][y:nat][l:lessis(y,x)][f:[t:1to(x)]alpha]
-left:=[t:1to(y)]<left1to(x,y,l,t)>f:[t:1to(y)]alpha
-y@[f:[t:1to(pl(x,y))]alpha]
-right:=[t:1to(y)]<right1to(x,y,t)>f:[t:1to(y)]alpha
-y@[i:is(y,x)][f:[t:1to(y)]alpha]
-+*left
-f@t4:=lessisi2(y,x,i):lessis(y,x)
-t5:=lessisi2(x,y,symis(nat,y,x,i)):lessis(x,y)
-f1:=left(y,x,t5,f):[t:1to(x)]alpha
-f2:=left(t4,f1):[t:1to(y)]alpha
-[u:1to(y)]
-t6:=isinoutn(x,inn(y,u),trlessis(inn(y,u),y,x,1top(y,u),t4)):is(inn(y,u),inn(x,left1to(x,y,t4,u)))
-t7:=tris(1to(y),u,outn(y,inn(y,u),1top(y,u)),left1to(y,x,t5,left1to(x,y,t4,u)),isoutinn(y,u),isoutni(y,inn(y,u),1top(y,u),inn(x,left1to(x,y,t4,u)),trlessis(inn(x,left1to(x,y,t4,u)),x,y,1top(x,left1to(x,y,t4,u)),t5),t6)):is"e"(1to(y),u,left1to(y,x,t5,left1to(x,y,t4,u)))
-t8:=isf(1to(y),alpha,f,u,left1to(y,x,t5,left1to(x,y,t4,u)),t7):is"e"(alpha,<u>f,<u>f2)
--left
-f@thleft:=fisi(1to(y),alpha,f,f2".left",[t:1to(y)]t8".left"(t)):is"e"([t:1to(y)]alpha,f,left(x,y,lessisi2(y,x,i),left(y,x,lessisi2(x,y,symis(nat,y,x,i)),f)))
-@frac:=pair1type(nat):'type'
-[x1:nat][x2:nat]
-fr:=pair1(nat,x1,x2):frac
-@[x:frac]
-num:=first1(nat,x):nat
-den:=second1(nat,x):nat
-x2@numis:=first1is1(nat,x1,x2):is(num(fr(x1,x2)),x1)
-isnum:=first1is2(nat,x1,x2):is(x1,num(fr(x1,x2)))
-denis:=second1is1(nat,x1,x2):is(den(fr(x1,x2)),x2)
-isden:=second1is2(nat,x1,x2):is(x2,den(fr(x1,x2)))
-x@1x:=num(x):nat
-2x:=den(x):nat
-fris:=pair1is1(nat,x):is"e"(frac,fr(1x,2x),x)
-isfr:=pair1is2(nat,x):is"e"(frac,x,fr(1x,2x))
-x2@[y1:nat][y2:nat]
-12isnd:=ists12(x1,num(fr(x1,x2)),y2,den(fr(y1,y2)),isnum(x1,x2),isden(y1,y2)):is(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))))
-ndis12:=symis(nat,ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),12isnd):is(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2))
-x@[n1:nat][n2:nat]
-1disnd:=ists1(n1,num(fr(n1,n2)),2x,isnum(n1,n2)):is(ts(n1,2x),ts(num(fr(n1,n2)),2x))
-ndis1d:=symis(nat,ts(n1,2x),ts(num(fr(n1,n2)),2x),1disnd):is(ts(num(fr(n1,n2)),2x),ts(n1,2x))
-n2isnd:=ists2(n2,den(fr(n1,n2)),1x,isden(n1,n2)):is(ts(1x,n2),ts(1x,den(fr(n1,n2))))
-ndisn2:=symis(nat,ts(1x,n2),ts(1x,den(fr(n1,n2))),n2isnd):is(ts(1x,den(fr(n1,n2))),ts(1x,n2))
-x2@[n:nat][i:is(x1,n)]
-isn:=isf(nat,frac,[t:nat]fr(t,x2),x1,n,i):is"e"(frac,fr(x1,x2),fr(n,x2))
-n@[i:is(x2,n)]
-isd:=isf(nat,frac,[t:nat]fr(x1,t),x2,n,i):is"e"(frac,fr(x1,x2),fr(x1,n))
-y2@[i:is(x1,y1)][j:is(x2,y2)]
-isnd:=tris(frac,fr(x1,x2),fr(y1,x2),fr(y1,y2),isn(x1,x2,y1,i),isd(y1,x2,y2,j)):is"e"(frac,fr(x1,x2),fr(y1,y2))
-x@[y:frac]
-1y:=num(y):nat
-2y:=den(y):nat
-eq:=is(ts(1x,2y),ts(1y,2x)):'prop'
-y2@[i:is(ts(x1,y2),ts(y1,x2))]
-eqi12:=tr3is(nat,ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ndis12(x1,x2,y1,y2),i,12isnd(y1,y2,x1,x2)):eq(fr(x1,x2),fr(y1,y2))
-n2@[i:is(ts(1x,n2),ts(n1,2x))]
-eqi1:=isp(frac,[t:frac]eq(t,fr(n1,n2)),fr(1x,2x),x,eqi12(1x,2x,n1,n2,i),fris):eq(x,fr(n1,n2))
-n2@[i:is(ts(n1,2x),ts(1x,n2))]
-eqi2:=isp(frac,[t:frac]eq(fr(n1,n2),t),fr(1x,2x),x,eqi12(n1,n2,1x,2x,i),fris):eq(fr(n1,n2),x)
-x@satz37:=refis(nat,ts(1x,2x)):eq(x,x)
-refeq:=satz37:eq(x,x)
-y@[i:is"e"(frac,x,y)]
-refeq1:=isp(frac,[t:frac]eq(x,t),x,y,refeq,i):eq(x,y)
-refeq2:=isp(frac,[t:frac]eq(t,x),x,y,refeq,i):eq(y,x)
-y2@[i:is(x1,y1)][j:is(x2,y2)]
-eqnd:=refeq1(fr(x1,x2),fr(y1,y2),isnd(i,j)):eq(fr(x1,x2),fr(y1,y2))
-x2@[n:nat][i:is(x1,n)]
-eqn:=refeq1(fr(x1,x2),fr(n,x2),isn(n,i)):eq(fr(x1,x2),fr(n,x2))
-n@[i:is(x2,n)]
-eqd:=refeq1(fr(x1,x2),fr(x1,n),isd(n,i)):eq(fr(x1,x2),fr(x1,n))
-y@[e:eq(x,y)]
-satz38:=symis(nat,ts(1x,2y),ts(1y,2x),e):eq(y,x)
-symeq:=satz38:eq(y,x)
-@[a:nat][b:nat][c:nat][d:nat]
-+ii1
-t1:=tris(nat,ts(b,ts(c,d)),ts(ts(b,c),d),ts(d,ts(b,c)),assts2(b,c,d),comts(ts(b,c),d)):is(ts(b,ts(c,d)),ts(d,ts(b,c)))
--ii1
-stets:=tr4is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(b,c))),ts(ts(a,d),ts(b,c)),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(b,c)),a,t1".ii1"),assts2(a,d,ts(b,c)),ists2(ts(b,c),ts(c,b),ts(a,d),comts(b,c))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
-+*ii1
-d@t2:=tr3is(nat,ts(b,ts(c,d)),ts(ts(c,d),b),ts(ts(d,c),b),ts(d,ts(c,b)),comts(b,ts(c,d)),ists1(ts(c,d),ts(d,c),b,comts(c,d)),assts1(d,c,b)):is(ts(b,ts(c,d)),ts(d,ts(c,b)))
-anders:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(c,b))),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(c,b)),a,t2),assts2(a,d,ts(c,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
--ii1
-y@[z:frac]
-1z:=num(z):nat
-2z:=den(z):nat
-[e:eq(x,y)][f:eq(y,z)]
-+139
-t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
-t2:=stets(1x,2y,1y,2z):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)))
-t3:=tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)))
-t4:=tr3is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),symis(nat,ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),t2),t1,t3):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
--139
-satz39:=satz33b(ts(1x,2z),ts(1z,2x),ts(1y,2y),t4".139"):eq(x,z)
-+*139
-f@anders:=tr4is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2z,1y,2y),ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
--139
-f@treq:=satz39:eq(x,z)
-z@[e:eq(z,x)][f:eq(z,y)]
-treq1:=treq(x,z,y,symeq(z,x,e),f):eq(x,y)
-z@[e:eq(x,z)][f:eq(y,z)]
-treq2:=treq(x,z,y,e,symeq(y,z,f)):eq(x,y)
-z@[u:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)]
-tr3eq:=treq(x,y,u,e,treq(y,z,u,f,g)):eq(x,u)
-u@[v:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)][h:eq(u,v)]
-tr4eq:=tr3eq(x,y,z,v,e,f,treq(z,u,v,g,h)):eq(x,v)
-x@[n:nat]
-satz40:=eqi1(ts(1x,n),ts(2x,n),tris(nat,ts(1x,ts(2x,n)),ts(1x,ts(n,2x)),ts(ts(1x,n),2x),ists2(ts(2x,n),ts(n,2x),1x,comts(2x,n)),assts2(1x,n,2x))):eq(x,fr(ts(1x,n),ts(2x,n)))
-satz40a:=symeq(x,fr(ts(1x,n),ts(2x,n)),satz40):eq(fr(ts(1x,n),ts(2x,n)),x)
-x2@[n:nat]
-satz40b:=eqi12(ts(x1,n),ts(x2,n),tris(nat,ts(x1,ts(x2,n)),ts(x1,ts(n,x2)),ts(ts(x1,n),x2),ists2(ts(x2,n),ts(n,x2),x1,comts(x2,n)),assts2(x1,n,x2))):eq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)))
-satz40c:=symeq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)),satz40b):eq(fr(ts(x1,n),ts(x2,n)),fr(x1,x2))
-y@moref:=more(ts(1x,2y),ts(1y,2x)):'prop'
-lessf:=less(ts(1x,2y),ts(1y,2x)):'prop'
-y2@[m:more(ts(x1,y2),ts(y1,x2))]
-morefi12:=ismore12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),m):moref(fr(x1,x2),fr(y1,y2))
-y2@[l:less(ts(x1,y2),ts(y1,x2))]
-lessfi12:=isless12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),l):lessf(fr(x1,x2),fr(y1,y2))
-n2@[m:more(ts(1x,n2),ts(n1,2x))]
-morefi1:=ismore12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),m):moref(x,fr(n1,n2))
-n2@[m:more(ts(n1,2x),ts(1x,n2))]
-morefi2:=ismore12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),m):moref(fr(n1,n2),x)
-n2@[l:less(ts(1x,n2),ts(n1,2x))]
-lessfi1:=isless12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),l):lessf(x,fr(n1,n2))
-n2@[l:less(ts(n1,2x),ts(1x,n2))]
-lessfi2:=isless12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),l):lessf(fr(n1,n2),x)
-y@satz41:=satz10(ts(1x,2y),ts(1y,2x)):orec3(eq(x,y),moref(x,y),lessf(x,y))
-satz41a:=satz10a(ts(1x,2y),ts(1y,2x)):or3(eq(x,y),moref(x,y),lessf(x,y))
-satz41b:=satz10b(ts(1x,2y),ts(1y,2x)):ec3(eq(x,y),moref(x,y),lessf(x,y))
-[m:moref(x,y)]
-satz42:=satz11(ts(1x,2y),ts(1y,2x),m):lessf(y,x)
-y@[l:lessf(x,y)]
-satz43:=satz12(ts(1x,2y),ts(1y,2x),l):moref(y,x)
-u@1u:=num(u):nat
-2u:=den(u):nat
-[m:moref(x,y)][e:eq(x,z)][f:eq(y,u)]
-+244
-t1:=ists12(ts(1y,2u),ts(1u,2y),ts(1z,2x),ts(1x,2z),f,symeq(x,z,e)):is(ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)))
-t2:=tr3is(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)),ts(ts(1u,2z),ts(1x,2y)),stets(1y,2x,1z,2u),t1,stets(1u,2y,1x,2z)):is(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)))
-t3:=ismore1(ts(ts(1u,2z),ts(1x,2y)),ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)),symis(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)),t2),satz32d(ts(1x,2y),ts(1y,2x),ts(1u,2z),m)):more(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)))
--244
-satz44:=satz33a(ts(1z,2u),ts(1u,2z),ts(1y,2x),ismore1(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1z,2u),ts(1y,2x)),ts(ts(1u,2z),ts(1y,2x)),comts(ts(1y,2x),ts(1z,2u)),t3".244")):moref(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][m:moref(x,z)]
-eqmoref12:=satz44(x,z,y,u,m,e,f):moref(y,u)
-z@[e:eq(x,y)][m:moref(x,z)]
-eqmoref1:=satz44(x,z,y,z,m,e,refeq(z)):moref(y,z)
-e@[m:moref(z,x)]
-eqmoref2:=satz44(z,x,z,y,m,refeq(z),e):moref(z,y)
-u@[l:lessf(x,y)][e:eq(x,z)][f:eq(y,u)]
-satz45:=satz42(u,z,satz44(y,x,u,z,satz43(x,y,l),f,e)):lessf(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][l:lessf(x,z)]
-eqlessf12:=satz45(x,z,y,u,l,e,f):lessf(y,u)
-z@[e:eq(x,y)][l:lessf(x,z)]
-eqlessf1:=satz45(x,z,y,z,l,e,refeq(z)):lessf(y,z)
-e@[l:lessf(z,x)]
-eqlessf2:=satz45(z,x,z,y,l,refeq(z),e):lessf(z,y)
-y@moreq:=or(moref(x,y),eq(x,y)):'prop'
-lesseq:=or(lessf(x,y),eq(x,y)):'prop'
-[e:eq(x,y)]
-moreqi2:=ori2(moref(x,y),eq(x,y),e):moreq(x,y)
-lesseqi2:=ori2(lessf(x,y),eq(x,y),e):lesseq(x,y)
-y@[m:moref(x,y)]
-moreqi1:=ori1(moref(x,y),eq(x,y),m):moreq(x,y)
-y@[l:lessf(x,y)]
-lesseqi1:=ori1(lessf(x,y),eq(x,y),l):lesseq(x,y)
-y@[m:moreq(x,y)]
-satz41c:=th7"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,comor(moref(x,y),eq(x,y),m)):not(lessf(x,y))
-y@[l:lesseq(x,y)]
-satz41d:=th9"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,l):not(moref(x,y))
-y@[n:not(moref(x,y))]
-satz41e:=th2"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n):lesseq(x,y)
-y@[n:not(lessf(x,y))]
-satz41f:=comor(eq(x,y),moref(x,y),th3"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n)):moreq(x,y)
-y@[m:moref(x,y)]
-satz41g:=th3"l.or"(lessf(x,y),eq(x,y),ec3e23(eq(x,y),moref(x,y),lessf(x,y),satz41b,m),ec3e21(eq(x,y),moref(x,y),lessf(x,y),satz41b,m)):not(lesseq(x,y))
-y@[l:lessf(x,y)]
-satz41h:=th3"l.or"(moref(x,y),eq(x,y),ec3e32(eq(x,y),moref(x,y),lessf(x,y),satz41b,l),ec3e31(eq(x,y),moref(x,y),lessf(x,y),satz41b,l)):not(moreq(x,y))
-y@[n:not(moreq(x,y))]
-satz41j:=or3e3(eq(x,y),moref(x,y),lessf(x,y),satz41a,th5"l.or"(moref(x,y),eq(x,y),n),th4"l.or"(moref(x,y),eq(x,y),n)):lessf(x,y)
-y@[n:not(lesseq(x,y))]
-satz41k:=or3e2(eq(x,y),moref(x,y),lessf(x,y),satz41a,th4"l.or"(lessf(x,y),eq(x,y),n),th5"l.or"(lessf(x,y),eq(x,y),n)):moref(x,y)
-u@[m:moreq(x,y)][e:eq(x,z)][f:eq(y,u)]
-+246
-[n:moref(x,y)]
-t1:=ori1(moref(z,u),eq(z,u),satz44(n,e,f)):moreq(z,u)
-f@[g:eq(x,y)]
-t2:=ori2(moref(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):moreq(z,u)
--246
-satz46:=orapp(moref(x,y),eq(x,y),moreq(z,u),m,[t:moref(x,y)]t1".246"(t),[t:eq(x,y)]t2".246"(t)):moreq(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][m:moreq(x,z)]
-eqmoreq12:=satz46(x,z,y,u,m,e,f):moreq(y,u)
-z@[e:eq(x,y)][m:moreq(x,z)]
-eqmoreq1:=satz46(x,z,y,z,m,e,refeq(z)):moreq(y,z)
-e@[m:moreq(z,x)]
-eqmoreq2:=satz46(z,x,z,y,m,refeq(z),e):moreq(z,y)
-u@[l:lesseq(x,y)][e:eq(x,z)][f:eq(y,u)]
-+247
-[k:lessf(x,y)]
-t1:=ori1(lessf(z,u),eq(z,u),satz45(k,e,f)):lesseq(z,u)
-f@[g:eq(x,y)]
-t2:=ori2(lessf(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):lesseq(z,u)
--247
-satz47:=orapp(lessf(x,y),eq(x,y),lesseq(z,u),l,[t:lessf(x,y)]t1".247"(t),[t:eq(x,y)]t2".247"(t)):lesseq(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][l:lesseq(x,z)]
-eqlesseq12:=satz47(x,z,y,u,l,e,f):lesseq(y,u)
-z@[e:eq(x,y)][l:lesseq(x,z)]
-eqlesseq1:=satz47(x,z,y,z,l,e,refeq(z)):lesseq(y,z)
-e@[l:lesseq(z,x)]
-eqlesseq2:=satz47(z,x,z,y,l,refeq(z),e):lesseq(z,y)
-y@[m:moreq(x,y)]
-satz48:=th9"l.or"(moref(x,y),eq(x,y),lessf(y,x),eq(y,x),m,[t:moref(x,y)]satz42(x,y,t),[t:eq(x,y)]satz38(x,y,t)):lesseq(y,x)
-y@[l:lesseq(x,y)]
-satz49:=th9"l.or"(lessf(x,y),eq(x,y),moref(y,x),eq(y,x),l,[t:lessf(x,y)]satz43(x,y,t),[t:eq(x,y)]satz38(x,y,t)):moreq(y,x)
-z@[l:lessf(x,y)][k:lessf(y,z)]
-+250
-t1:=satz34a(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),l,k):less(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
-t2:=isless12(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2y,1y,2z),tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))),t1):less(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
--250
-satz50:=satz33c(ts(1x,2z),ts(1z,2x),ts(1y,2y),t2".250"):lessf(x,z)
-trlessf:=satz50:lessf(x,z)
-z@[m:moref(x,y)][n:moref(y,z)]
-trmoref:=satz43(z,x,satz50(z,y,x,satz42(y,z,n),satz42(x,y,m))):moref(x,z)
-z@[l:lesseq(x,y)][k:lessf(y,z)]
-satz51a:=orapp(lessf(x,y),eq(x,y),lessf(x,z),l,[t:lessf(x,y)]satz50(t,k),[t:eq(x,y)]eqlessf1(y,x,z,symeq(x,y,t),k)):lessf(x,z)
-z@[l:lessf(x,y)][k:lesseq(y,z)]
-satz51b:=orapp(lessf(y,z),eq(y,z),lessf(x,z),k,[t:lessf(y,z)]satz50(l,t),[t:eq(y,z)]eqlessf2(y,z,x,t,l)):lessf(x,z)
-z@[m:moreq(x,y)][n:moref(y,z)]
-satz51c:=satz43(z,x,satz51b(z,y,x,satz42(y,z,n),satz48(x,y,m))):moref(x,z)
-z@[m:moref(x,y)][n:moreq(y,z)]
-satz51d:=satz43(z,x,satz51a(z,y,x,satz48(y,z,n),satz42(x,y,m))):moref(x,z)
-z@[l:lesseq(x,y)][k:lesseq(y,z)]
-+252
-[e:eq(x,y)][f:eq(y,z)]
-t1:=ori2(lessf(x,z),eq(x,z),treq(x,y,z,e,f)):lesseq(x,z)
-e@[j:lessf(y,z)]
-t2:=ori1(lessf(x,z),eq(x,z),satz51a(l,j)):lesseq(x,z)
-e@t3:=orapp(lessf(y,z),eq(y,z),lesseq(x,z),k,[t:lessf(y,z)]t2(t),[t:eq(y,z)]t1(t)):lesseq(x,z)
-k@[j:lessf(x,y)]
-t4:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
--252
-satz52:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t4".252"(t),[t:eq(x,y)]t3".252"(t)):lesseq(x,z)
-trlesseq:=satz52:lesseq(x,z)
-+*252
-k@[j:lessf(x,y)]
-t5:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
-k@[e:eq(x,y)]
-t6:=eqlesseq1(y,x,z,symeq(x,y,e),k):lesseq(x,z)
-k@anders:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t5(t),[t:eq(x,y)]t6(t)):lesseq(x,z)
--252
-z@[m:moreq(x,y)][n:moreq(y,z)]
-trmoreq:=satz49(z,x,satz52(z,y,x,satz48(y,z,n),satz48(x,y,m))):moreq(x,z)
-+253
-x@t1:=ismore1(pl(ts(1x,2x),ts(1x,2x)),ts(pl(1x,1x),2x),ts(1x,2x),distpt1(1x,1x,2x),satz18(ts(1x,2x),ts(1x,2x))):more(ts(pl(1x,1x),2x),ts(1x,2x))
-t2:=morefi2(pl(1x,1x),2x,t1):moref(fr(pl(1x,1x),2x),x)
--253
-x@satz53:=somei(frac,[t:frac]moref(t,x),fr(pl(1x,1x),2x),t2".253"):some"l"(frac,[t:frac]moref(t,x))
-+254
-t1:=isless2(pl(ts(1x,2x),ts(1x,2x)),ts(1x,pl(2x,2x)),ts(1x,2x),distpt2(1x,2x,2x),satz18a(ts(1x,2x),ts(1x,2x))):less(ts(1x,2x),ts(1x,pl(2x,2x)))
-t2:=lessfi2(1x,pl(2x,2x),t1):lessf(fr(1x,pl(2x,2x)),x)
--254
-satz54:=somei(frac,[t:frac]lessf(t,x),fr(1x,pl(2x,2x)),t2".254"):some"l"(frac,[t:frac]lessf(t,x))
-y@[l:lessf(x,y)]
-+255
-t1:=satz19f(ts(1x,2y),ts(1y,2x),ts(1x,2x),l):less(pl(ts(1x,2x),ts(1x,2y)),pl(ts(1x,2x),ts(1y,2x)))
-t2:=satz19c(ts(1x,2y),ts(1y,2x),ts(1y,2y),l):less(pl(ts(1x,2y),ts(1y,2y)),pl(ts(1y,2x),ts(1y,2y)))
-t3:=isless12(pl(ts(1x,2x),ts(1x,2y)),ts(1x,pl(2x,2y)),pl(ts(1x,2x),ts(1y,2x)),ts(pl(1x,1y),2x),distpt2(1x,2x,2y),distpt1(1x,1y,2x),t1):less(ts(1x,pl(2x,2y)),ts(pl(1x,1y),2x))
-t4:=lessfi1(pl(1x,1y),pl(2x,2y),t3):lessf(x,fr(pl(1x,1y),pl(2x,2y)))
-t5:=isless12(pl(ts(1x,2y),ts(1y,2y)),ts(pl(1x,1y),2y),pl(ts(1y,2x),ts(1y,2y)),ts(1y,pl(2x,2y)),distpt1(1x,1y,2y),distpt2(1y,2x,2y),t2):less(ts(pl(1x,1y),2y),ts(1y,pl(2x,2y)))
-t6:=lessfi2(y,pl(1x,1y),pl(2x,2y),t5):lessf(fr(pl(1x,1y),pl(2x,2y)),y)
-t7:=andi(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y),t4,t6):and(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y))
--255
-satz55:=somei(frac,[t:frac]and(lessf(x,t),lessf(t,y)),fr(pl(1x,1y),pl(2x,2y)),t7".255"):some"l"(frac,[t:frac]and(lessf(x,t),lessf(t,y)))
-y@pf:=fr(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)):frac
-+ii3
-y2@t1:=ispl12(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ts(y1,x2),ndis12(x1,x2,y1,y2),ndis12(y1,y2,x1,x2)):is(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),pl(ts(x1,y2),ts(y1,x2)))
-t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
--ii3
-y2@pf12:=isnd(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),ts(den(fr(x1,x2)),den(fr(y1,y2))),pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2),t1".ii3",t2".ii3"):is"e"(frac,pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
-+*ii3
-n2@t3:=ispl12(ts(1x,den(fr(n1,n2))),ts(1x,n2),ts(num(fr(n1,n2)),2x),ts(n1,2x),ndisn2(x,n1,n2),ndis1d(x,n1,n2)):is(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),pl(ts(1x,n2),ts(n1,2x)))
-t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
--ii3
-n2@pf1:=isnd(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),ts(2x,den(fr(n1,n2))),pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2),t3".ii3",t4".ii3"):is"e"(frac,pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
-+*ii3
-n2@t5:=ispl12(ts(num(fr(n1,n2)),2x),ts(n1,2x),ts(1x,den(fr(n1,n2))),ts(1x,n2),ndis1d(x,n1,n2),ndisn2(x,n1,n2)):is(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),pl(ts(n1,2x),ts(1x,n2)))
-t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
--ii3
-n2@pf2:=isnd(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),ts(den(fr(n1,n2)),2x),pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x),t5".ii3",t6".ii3"):is"e"(frac,pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
-y2@pfeq12a:=refeq1(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
-pfeq12b:=refeq2(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf(fr(x1,x2),fr(y1,y2)))
-n2@pfeq1a:=refeq1(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
-pfeq1b:=refeq2(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf(x,fr(n1,n2)))
-pfeq2a:=refeq1(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
-pfeq2b:=refeq2(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf(fr(n1,n2),x))
-u@[e:eq(x,y)][f:eq(z,u)]
-+356
-t1:=ists1(ts(1x,2y),ts(1y,2x),ts(2z,2u),e):is(ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)))
-t2:=t1(z,u,x,y,f,e):is(ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)))
-t3:=tr3is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2z),ts(2u,2y)),ts(ts(1x,2y),ts(2u,2z)),ts(ts(1x,2y),ts(2z,2u)),ists2(ts(2y,2u),ts(2u,2y),ts(1x,2z),comts(2y,2u)),stets(1x,2z,2u,2y),ists2(ts(2u,2z),ts(2z,2u),ts(1x,2y),comts(2u,2z))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)))
-t4:=tr4is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)),ts(ts(1y,2u),ts(2z,2x)),ts(ts(1y,2u),ts(2x,2z)),t3,t1,stets(1y,2x,2z,2u),ists2(ts(2z,2x),ts(2x,2z),ts(1y,2u),comts(2z,2x))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)))
-t5:=tr4is(nat,ts(ts(1z,2x),ts(2y,2u)),ts(ts(1z,2u),ts(2y,2x)),ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)),ts(ts(1u,2y),ts(2x,2z)),stets(1z,2x,2y,2u),ists2(ts(2y,2x),ts(2x,2y),ts(1z,2u),comts(2y,2x)),t2,stets(1u,2z,2x,2y)):is(ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)))
-t6:=ispl12(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)),ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)),t4,t5):is(pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))))
-t7:=tr3is(nat,ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)),disttp1(ts(1x,2z),ts(1z,2x),ts(2y,2u)),t6,distpt1(ts(1y,2u),ts(1u,2y),ts(2x,2z))):is(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)))
--356
-satz56:=eqi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2u),ts(1u,2y)),ts(2y,2u),t7".356"):eq(pf(x,z),pf(y,u))
-eqpf12:=satz56:eq(pf(x,z),pf(y,u))
-z@[e:eq(x,y)]
-eqpf1:=eqpf12(x,y,z,z,e,refeq(z)):eq(pf(x,z),pf(y,z))
-eqpf2:=eqpf12(z,z,x,y,refeq(z),e):eq(pf(z,x),pf(z,y))
-x2@[n:nat]
-satz57:=tr3eq(pf(fr(x1,n),fr(x2,n)),fr(pl(ts(x1,n),ts(x2,n)),ts(n,n)),fr(ts(pl(x1,x2),n),ts(n,n)),fr(pl(x1,x2),n),pfeq12a(x1,n,x2,n),eqn(pl(ts(x1,n),ts(x2,n)),ts(n,n),ts(pl(x1,x2),n),distpt1(x1,x2,n)),satz40c(pl(x1,x2),n,n)):eq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n))
-satz57a:=symeq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n),satz57):eq(fr(pl(x1,x2),n),pf(fr(x1,n),fr(x2,n)))
-y@satz58:=eqnd(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),pl(ts(1y,2x),ts(1x,2y)),ts(2y,2x),compl(ts(1x,2y),ts(1y,2x)),comts(2x,2y)):eq(pf(x,y),pf(y,x))
-compf:=satz58:eq(pf(x,y),pf(y,x))
-+359
-z@t1:=tr3is(nat,ts(ts(1y,2x),2z),ts(ts(2x,1y),2z),ts(2x,ts(1y,2z)),ts(ts(1y,2z),2x),ists1(ts(1y,2x),ts(2x,1y),2z,comts(1y,2x)),assts1(2x,1y,2z),comts(2x,ts(1y,2z))):is(ts(ts(1y,2x),2z),ts(ts(1y,2z),2x))
-t2:=ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),t1):is(pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
-t3:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),t2):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
-t4:=tris(nat,ts(1z,ts(2x,2y)),ts(1z,ts(2y,2x)),ts(ts(1z,2y),2x),ists2(ts(2x,2y),ts(2y,2x),1z,comts(2x,2y)),assts2(1z,2y,2x)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
-t5:=ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t3,t4):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)))
-t6:=ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x)):is(pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
-t7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),t5,asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),t6):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
--359
-z@satz59:=tr3eq(pf(pf(x,y),z),fr(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z)),fr(pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z))),pf(x,pf(y,z)),pfeq2a(z,pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)),eqnd(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z)),t7".359",assts1(2x,2y,2z)),pfeq1b(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z))):eq(pf(pf(x,y),z),pf(x,pf(y,z)))
-asspf1:=satz59:eq(pf(pf(x,y),z),pf(x,pf(y,z)))
-asspf2:=symeq(pf(pf(x,y),z),pf(x,pf(y,z)),asspf1):eq(pf(x,pf(y,z)),pf(pf(x,y),z))
-c@stets1:=tr3is(nat,ts(ts(a,b),c),ts(a,ts(b,c)),ts(a,ts(c,b)),ts(ts(a,c),b),assts1(a,b,c),ists2(ts(b,c),ts(c,b),a,comts(b,c)),assts2(a,c,b)):is(ts(ts(a,b),c),ts(ts(a,c),b))
-+*359
-z@t8:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),stets1(1y,2x,2z))):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
-t9:=tris(nat,ts(1z,ts(2x,2y)),ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),assts2(1z,2x,2y),stets1(1z,2x,2y)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
-anderst7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t8,t9),asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x))):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
--359
-+360
-y@t1:=satz18(ts(1x,2y),ts(1y,2x)):more(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y))
-t2:=satz32a(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y),2x,t1):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(ts(1x,2y),2x))
-t3:=tris(nat,ts(ts(1x,2y),2x),ts(1x,ts(2y,2x)),ts(1x,ts(2x,2y)),assts1(1x,2y,2x),ists2(ts(2y,2x),ts(2x,2y),1x,comts(2y,2x))):is(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)))
-t4:=ismore2(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)),ts(pl(ts(1x,2y),ts(1y,2x)),2x),t3,t2):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(1x,ts(2x,2y)))
--360
-y@satz60:=morefi2(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),t4".360"):moref(pf(x,y),x)
-satz60a:=satz42(pf(x,y),x,satz60):lessf(x,pf(x,y))
-z@[m:moref(x,y)]
-+361
-t1:=satz32a(ts(1x,2y),ts(1y,2x),2z,m):more(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z))
-t2:=ismore12(ts(ts(1x,2y),2z),ts(ts(1x,2z),2y),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),stets1(1x,2y,2z),stets1(1y,2x,2z),t1):more(ts(ts(1x,2z),2y),ts(ts(1y,2z),2x))
-t3:=stets1(1z,2x,2y):is(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x))
-t4:=satz19h(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),ts(ts(1x,2z),2y),ts(ts(1y,2z),2x),t3,t2):more(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)))
-t5:=ismore12(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),ts(pl(ts(1x,2z),ts(1z,2x)),2y),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),distpt1(ts(1x,2z),ts(1z,2x),2y),distpt1(ts(1y,2z),ts(1z,2y),2x),t4):more(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x))
-t6:=satz32a(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z,t5):more(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z))
-t7:=ismore12(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)),assts1(pl(ts(1x,2z),ts(1z,2x)),2y,2z),assts1(pl(ts(1y,2z),ts(1z,2y)),2x,2z),t6):more(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)))
--361
-satz61:=morefi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z),t7".361"):moref(pf(x,z),pf(y,z))
-z@[m:moref(x,y)]
-satz62a:=satz61(m):moref(pf(x,z),pf(y,z))
-z@[e:eq(x,y)]
-satz62b:=eqpf1(x,y,z,e):eq(pf(x,z),pf(y,z))
-z@[l:lessf(x,y)]
-satz62c:=satz42(pf(y,z),pf(x,z),satz61(y,x,z,satz43(l))):lessf(pf(x,z),pf(y,z))
-m@satz62d:=eqmoref12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62a):moref(pf(z,x),pf(z,y))
-e@satz62e:=eqpf2(x,y,z,e):eq(pf(z,x),pf(z,y))
-l@satz62f:=eqlessf12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62c):lessf(pf(z,x),pf(z,y))
-u@[e:eq(x,y)][m:moref(z,u)]
-satz62g:=eqmoref2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62d(z,u,x,m)):moref(pf(x,z),pf(y,u))
-satz62h:=eqmoref12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62g):moref(pf(z,x),pf(u,y))
-e@[l:lessf(z,u)]
-satz62j:=eqlessf2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62f(z,u,x,l)):lessf(pf(x,z),pf(y,u))
-satz62k:=eqlessf12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62j):lessf(pf(z,x),pf(u,y))
-+363
-z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
-t2:=satz41b(pf(x,z),pf(y,z)):ec3(eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)))
--363
-z@[m:moref(pf(x,z),pf(y,z))]
-satz63a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),m):moref(x,y)
-z@[e:eq(pf(x,z),pf(y,z))]
-satz63b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),e):eq(x,y)
-z@[l:lessf(pf(x,z),pf(y,z))]
-satz63c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),l):lessf(x,y)
-z@[m:moref(pf(z,x),pf(z,y))]
-satz63d:=satz63a(eqmoref12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),m)):moref(x,y)
-z@[e:eq(pf(z,x),pf(z,y))]
-satz63e:=satz63b(tr3eq(pf(x,z),pf(z,x),pf(z,y),pf(y,z),compf(x,z),e,compf(z,y))):eq(x,y)
-z@[f:lessf(pf(z,x),pf(z,y))]
-satz63f:=satz63c(eqlessf12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),f)):lessf(x,y)
-u@[m:moref(x,y)][n:moref(z,u)]
-+364
-t1:=satz61(x,y,z,m):moref(pf(x,z),pf(y,z))
-t2:=eqmoref12(pf(z,y),pf(y,z),pf(u,y),pf(y,u),compf(z,y),compf(u,y),satz61(z,u,y,n)):moref(pf(y,z),pf(y,u))
--364
-satz64:=trmoref(pf(x,z),pf(y,z),pf(y,u),t1".364",t2".364"):moref(pf(x,z),pf(y,u))
-u@[l:lessf(x,y)][k:lessf(z,u)]
-satz64a:=satz42(pf(y,u),pf(x,z),satz64(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
-u@[m:moreq(x,y)][n:moref(z,u)]
-satz65a:=orapp(moref(x,y),eq(x,y),moref(pf(x,z),pf(y,u)),m,[v:moref(x,y)]satz64(v,n),[v:eq(x,y)]satz62g(v,n)):moref(pf(x,z),pf(y,u))
-u@[m:moref(x,y)][n:moreq(z,u)]
-satz65b:=orapp(moref(z,u),eq(z,u),moref(pf(x,z),pf(y,u)),n,[v:moref(z,u)]satz64(m,v),[v:eq(z,u)]eqmoref2(pf(y,z),pf(y,u),pf(x,z),eqpf2(z,u,y,v),satz61(x,y,z,m))):moref(pf(x,z),pf(y,u))
-u@[l:lesseq(x,y)][k:lessf(z,u)]
-satz65c:=satz42(pf(y,u),pf(x,z),satz65a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
-u@[l:lessf(x,y)][k:lesseq(z,u)]
-satz65d:=satz42(pf(y,u),pf(x,z),satz65b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(pf(x,z),pf(y,u))
-u@[m:moreq(x,y)][n:moreq(z,u)]
-+366
-[e:eq(x,y)][f:eq(z,u)]
-t1:=moreqi2(pf(x,z),pf(y,u),satz56(e,f)):moreq(pf(x,z),pf(y,u))
-e@[o:moref(z,u)]
-t2:=moreqi1(pf(x,z),pf(y,u),satz65a(m,o)):moreq(pf(x,z),pf(y,u))
-e@t3:=orapp(moref(z,u),eq(z,u),moreq(pf(x,z),pf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(pf(x,z),pf(y,u))
-n@[o:moref(x,y)]
-t4:=moreqi1(pf(x,z),pf(y,u),satz65b(o,n)):moreq(pf(x,z),pf(y,u))
--366
-satz66:=orapp(moref(x,y),eq(x,y),moreq(pf(x,z),pf(y,u)),m,[v:moref(x,y)]t4".366"(v),[v:eq(x,y)]t3".366"(v)):moreq(pf(x,z),pf(y,u))
-u@[l:lesseq(x,y)][k:lesseq(z,u)]
-satz66a:=satz48(pf(y,u),pf(x,z),satz66(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(pf(x,z),pf(y,u))
-y@[l:lesseq(x,y)]
-+367
-[v:frac][e:eq(pf(y,v),x)]
-t1:=eqmoref1(pf(y,v),x,y,e,satz60(y,v)):moref(x,y)
-v@t2:=th3"l.imp"(eq(pf(y,v),x),moref(x,y),satz41d(x,y,l),[t:eq(pf(y,v),x)]t1(t)):not(eq(pf(y,v),x))
--367
-vorbemerkung67:=th5"l.some"(frac,[v:frac]eq(pf(y,v),x),[v:frac]t2".367"(v)):not(some"l"(frac,[t:frac]eq(pf(y,t),x)))
-y@[v:frac][w:frac][e:eq(pf(y,v),x)][f:eq(pf(y,w),x)]
-satz67b:=satz63e(v,w,y,treq2(pf(y,v),pf(y,w),x,e,f)):eq(v,w)
-y@[m:moref(x,y)]
-+*367
-m@t3:=onei(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),satz8b(ts(1x,2y),ts(1y,2x)),m):one([t:nat]diffprop(ts(1x,2y),ts(1y,2x),t))
-vo:=ind(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):nat
-t4:=oneax(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):is(ts(1x,2y),pl(ts(1y,2x),vo))
-w:=fr(vo,ts(2x,2y)):frac
-t5:=treq(y,fr(ts(1y,2x),ts(2y,2x)),fr(ts(1y,2x),ts(2x,2y)),satz40(y,2x),eqd(ts(1y,2x),ts(2y,2x),ts(2x,2y),comts(2y,2x))):eq(y,fr(ts(1y,2x),ts(2x,2y)))
-t6:=tr4eq(pf(y,w),pf(fr(ts(1y,2x),ts(2x,2y)),fr(vo,ts(2x,2y))),fr(pl(ts(1y,2x),vo),ts(2x,2y)),fr(ts(1x,2y),ts(2x,2y)),x,eqpf1(y,fr(ts(1y,2x),ts(2x,2y)),w,t5),satz57(ts(1y,2x),vo,ts(2x,2y)),eqn(pl(ts(1y,2x),vo),ts(2x,2y),ts(1x,2y),symis(nat,ts(1x,2y),pl(ts(1y,2x),vo),t4)),satz40a(x,2y)):eq(pf(y,w),x)
--367
-m@satz67a:=somei(frac,[t:frac]eq(pf(y,t),x),w".367",t6".367"):some"l"(frac,[t:frac]eq(pf(y,t),x))
-mf:=w".367":frac
-satz67c:=t6".367":eq(pf(y,mf(x,y,m)),x)
-satz67d:=symeq(pf(y,mf(x,y,m)),x,satz67c):eq(x,pf(y,mf(x,y,m)))
-y@[v:frac][m:moref(x,y)][e:eq(pf(y,v),x)]
-satz67e:=satz67b(v,mf(x,y,m),e,satz67c(m)):eq(v,mf(x,y,m))
-y@tf:=fr(ts(1x,1y),ts(2x,2y)):frac
-+ii4
-y2@t1:=ists12(num(fr(x1,x2)),x1,num(fr(y1,y2)),y1,numis(x1,x2),numis(y1,y2)):is(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(x1,y1))
-t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
--ii4
-y2@tf12:=isnd(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y1),ts(x2,y2),t1".ii4",t2".ii4"):is"e"(frac,tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
-+*ii4
-n2@t3:=ists2(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(1x,num(fr(n1,n2))),ts(1x,n1))
-t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
--ii4
-n2@tf1:=isnd(ts(1x,num(fr(n1,n2))),ts(2x,den(fr(n1,n2))),ts(1x,n1),ts(2x,n2),t3".ii4",t4".ii4"):is"e"(frac,tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
-+*ii4
-n2@t5:=ists1(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(num(fr(n1,n2)),1x),ts(n1,1x))
-t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
--ii4
-n2@tf2:=isnd(ts(num(fr(n1,n2)),1x),ts(den(fr(n1,n2)),2x),ts(n1,1x),ts(n2,2x),t5".ii4",t6".ii4"):is"e"(frac,tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
-y2@tfeq12a:=refeq1(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
-tfeq12b:=refeq2(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(fr(ts(x1,y1),ts(x2,y2)),tf(fr(x1,x2),fr(y1,y2)))
-n2@tfeq1a:=refeq1(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
-tfeq1b:=refeq2(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(fr(ts(1x,n1),ts(2x,n2)),tf(x,fr(n1,n2)))
-tfeq2a:=refeq1(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
-tfeq2b:=refeq2(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(fr(ts(n1,1x),ts(n2,2x)),tf(fr(n1,n2),x))
-u@[e:eq(x,y)][f:eq(z,u)]
-+468
-t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1z,2u),ts(1u,2z),e,f):is(ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)))
--468
-d@stets2:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(ts(a,b),ts(d,c)),ts(ts(a,c),ts(d,b)),ts(ts(a,c),ts(b,d)),ists2(ts(c,d),ts(d,c),ts(a,b),comts(c,d)),stets(a,b,d,c),ists2(ts(d,b),ts(b,d),ts(a,c),comts(d,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,c),ts(b,d)))
-+*468
-f@t2:=tr3is(nat,ts(ts(1x,1z),ts(2y,2u)),ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)),ts(ts(1y,1u),ts(2x,2z)),stets2(1x,1z,2y,2u),t1,stets2(1y,2x,1u,2z)):is(ts(ts(1x,1z),ts(2y,2u)),ts(ts(1y,1u),ts(2x,2z)))
--468
-f@satz68:=eqi12(ts(1x,1z),ts(2x,2z),ts(1y,1u),ts(2y,2u),t2".468"):eq(tf(x,z),tf(y,u))
-eqtf12:=satz68:eq(tf(x,z),tf(y,u))
-z@[e:eq(x,y)]
-eqtf1:=eqtf12(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
-eqtf2:=eqtf12(z,z,x,y,refeq(z),e):eq(tf(z,x),tf(z,y))
-y@satz69:=eqnd(ts(1x,1y),ts(2x,2y),ts(1y,1x),ts(2y,2x),comts(1x,1y),comts(2x,2y)):eq(tf(x,y),tf(y,x))
-comtf:=satz69:eq(tf(x,y),tf(y,x))
-z@satz70:=tr3eq(tf(tf(x,y),z),fr(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z)),fr(ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z))),tf(x,tf(y,z)),tfeq2a(z,ts(1x,1y),ts(2x,2y)),eqnd(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z),ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z)),assts1(1x,1y,1z),assts1(2x,2y,2z)),tfeq1b(x,ts(1y,1z),ts(2y,2z))):eq(tf(tf(x,y),z),tf(x,tf(y,z)))
-asstf1:=satz70:eq(tf(tf(x,y),z),tf(x,tf(y,z)))
-asstf2:=symeq(tf(tf(x,y),z),tf(x,tf(y,z)),asstf1):eq(tf(x,tf(y,z)),tf(tf(x,y),z))
-+471
-t1:=tr3eq(tf(x,pf(y,z)),fr(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z))),fr(pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),ts(2x,ts(2y,2z))),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),tfeq1a(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z)),eqn(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z)),pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),disttp2(1x,ts(1y,2z),ts(1z,2y))),satz57a(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))):eq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))))
-t2:=treq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(ts(1x,1y),2z),ts(ts(2x,2y),2z)),tf(x,y),eqnd(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z)),ts(ts(1x,1y),2z),ts(ts(2x,2y),2z),assts2(1x,1y,2z),assts2(2x,2y,2z)),satz40c(ts(1x,1y),ts(2x,2y),2z)):eq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y))
-t3:=treq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2z,2y))),tf(x,z),eqd(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)),ts(2x,ts(2z,2y)),ists2(ts(2y,2z),ts(2z,2y),2x,comts(2y,2z))),t2(x,z,y)):eq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z))
--471
-satz71:=treq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),pf(tf(x,y),tf(x,z)),t1".471",eqpf12(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z),t2".471",t3".471")):eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
-disttpf1:=tr3eq(tf(pf(x,y),z),tf(z,pf(x,y)),pf(tf(z,x),tf(z,y)),pf(tf(x,z),tf(y,z)),comtf(pf(x,y),z),satz71(z,x,y),eqpf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y))):eq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)))
-disttpf2:=satz71:eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
-distptf1:=symeq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)),disttpf1):eq(pf(tf(x,z),tf(y,z)),tf(pf(x,y),z))
-distptf2:=symeq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),disttpf2):eq(pf(tf(x,y),tf(x,z)),tf(x,pf(y,z)))
-[m:moref(x,y)]
-+472
-t1:=satz32a(ts(1x,2y),ts(1y,2x),ts(1z,2z),m):more(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1y,2x),ts(1z,2z)))
-t2:=ismore12(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,2x),ts(1z,2z)),ts(ts(1y,1z),ts(2x,2z)),stets2(1x,2y,1z,2z),stets2(1y,2x,1z,2z),t1):more(ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,1z),ts(2x,2z)))
--472
-satz72a:=morefi12(ts(1x,1z),ts(2x,2z),ts(1y,1z),ts(2y,2z),t2".472"):moref(tf(x,z),tf(y,z))
-z@[e:eq(x,y)]
-satz72b:=satz68(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
-z@[l:lessf(x,y)]
-satz72c:=satz42(tf(y,z),tf(x,z),satz72a(y,x,z,satz43(x,y,l))):lessf(tf(x,z),tf(y,z))
-m@satz72d:=eqmoref12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72a):moref(tf(z,x),tf(z,y))
-e@satz72e:=eqtf2(x,y,z,e):eq(tf(z,x),tf(z,y))
-l@satz72f:=eqlessf12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72c):lessf(tf(z,x),tf(z,y))
-u@[e:eq(x,y)][m:moref(z,u)]
-satz72g:=eqmoref2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72d(z,u,x,m)):moref(tf(x,z),tf(y,u))
-satz72h:=eqmoref12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72g):moref(tf(z,x),tf(u,y))
-e@[l:lessf(z,u)]
-satz72j:=eqlessf2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72f(z,u,x,l)):lessf(tf(x,z),tf(y,u))
-satz72k:=eqlessf12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72j):lessf(tf(z,x),tf(u,y))
-+473
-z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
-t2:=satz41b(tf(x,z),tf(y,z)):ec3(eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)))
--473
-z@[m:moref(tf(x,z),tf(y,z))]
-satz73a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),m):moref(x,y)
-z@[e:eq(tf(x,z),tf(y,z))]
-satz73b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),e):eq(x,y)
-z@[l:lessf(tf(x,z),tf(y,z))]
-satz73c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),l):lessf(x,y)
-z@[m:moref(tf(z,x),tf(z,y))]
-satz73d:=satz73a(eqmoref12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),m)):moref(x,y)
-z@[e:eq(tf(z,x),tf(z,y))]
-satz73e:=satz73b(tr3eq(tf(x,z),tf(z,x),tf(z,y),tf(y,z),comtf(x,z),e,comtf(z,y))):eq(x,y)
-z@[l:lessf(tf(z,x),tf(z,y))]
-satz73f:=satz73c(eqlessf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),l)):lessf(x,y)
-u@[m:moref(x,y)][n:moref(z,u)]
-+474
-t1:=satz72a(x,y,z,m):moref(tf(x,z),tf(y,z))
-t2:=eqmoref12(tf(z,y),tf(y,z),tf(u,y),tf(y,u),comtf(z,y),comtf(u,y),satz72a(z,u,y,n)):moref(tf(y,z),tf(y,u))
--474
-satz74:=trmoref(tf(x,z),tf(y,z),tf(y,u),t1".474",t2".474"):moref(tf(x,z),tf(y,u))
-u@[l:lessf(x,y)][k:lessf(z,u)]
-satz74a:=satz42(tf(y,u),tf(x,z),satz74(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
-u@[m:moreq(x,y)][n:moref(z,u)]
-satz75a:=orapp(moref(x,y),eq(x,y),moref(tf(x,z),tf(y,u)),m,[v:moref(x,y)]satz74(v,n),[v:eq(x,y)]satz72g(v,n)):moref(tf(x,z),tf(y,u))
-u@[m:moref(x,y)][n:moreq(z,u)]
-satz75b:=orapp(moref(z,u),eq(z,u),moref(tf(x,z),tf(y,u)),n,[v:moref(z,u)]satz74(m,v),[v:eq(z,u)]eqmoref2(tf(y,z),tf(y,u),tf(x,z),eqtf2(z,u,y,v),satz72a(m))):moref(tf(x,z),tf(y,u))
-u@[l:lesseq(x,y)][k:lessf(z,u)]
-satz75c:=satz42(tf(y,u),tf(x,z),satz75a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
-u@[l:lessf(x,y)][k:lesseq(z,u)]
-satz75d:=satz42(tf(y,u),tf(x,z),satz75b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(tf(x,z),tf(y,u))
-u@[m:moreq(x,y)][n:moreq(z,u)]
-+476
-[e:eq(x,y)][f:eq(z,u)]
-t1:=moreqi2(tf(x,z),tf(y,u),satz68(e,f)):moreq(tf(x,z),tf(y,u))
-e@[o:moref(z,u)]
-t2:=moreqi1(tf(x,z),tf(y,u),satz75a(m,o)):moreq(tf(x,z),tf(y,u))
-e@t3:=orapp(moref(z,u),eq(z,u),moreq(tf(x,z),tf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(tf(x,z),tf(y,u))
-n@[o:moref(x,y)]
-t4:=moreqi1(tf(x,z),tf(y,u),satz75b(o,n)):moreq(tf(x,z),tf(y,u))
--476
-satz76:=orapp(moref(x,y),eq(x,y),moreq(tf(x,z),tf(y,u)),m,[v:moref(x,y)]t4".476"(v),[v:eq(x,y)]t3".476"(v)):moreq(tf(x,z),tf(y,u))
-u@[l:lesseq(x,y)][k:lesseq(z,u)]
-satz76a:=satz48(tf(y,u),tf(x,z),satz76(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(tf(x,z),tf(y,u))
-y@[v:frac][w:frac][e:eq(tf(y,v),x)][f:eq(tf(y,w),x)]
-satz77b:=satz73e(v,w,y,treq2(tf(y,v),tf(y,w),x,e,f)):eq(v,w)
-+477
-y@v:=fr(ts(1x,2y),ts(2x,1y)):frac
-t1:=tr4eq(tf(y,v),tf(v,y),fr(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y)),fr(ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y))),x,comtf(y,v),tfeq2a(y,ts(1x,2y),ts(2x,1y)),eqnd(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y),ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y)),tris(nat,ts(ts(1x,2y),1y),ts(1x,ts(2y,1y)),ts(1x,ts(1y,2y)),assts1(1x,2y,1y),ists2(ts(2y,1y),ts(1y,2y),1x,comts(2y,1y))),assts1(2x,1y,2y)),satz40a(x,ts(1y,2y))):eq(tf(y,v),x)
--477
-y@satz77a:=somei(frac,[t:frac]eq(tf(y,t),x),v".477",t1".477"):some"l"(frac,[t:frac]eq(tf(y,t),x))
-+rt
-@eq:=[x:frac][y:frac]eq"n"(x,y):[x:frac][y:frac]'prop'
-refeq:=[x:frac]refeq"n"(x):[x:frac]<x><x>eq
-symeq:=[x:frac][y:frac][t:<y><x>eq]symeq"n"(x,y,t):[x:frac][y:frac][t:<y><x>eq]<x><y>eq
-treq:=[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]treq"n"(x,y,z,t,u):[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]<z><x>eq
-[x:frac][s:set(frac)]
-inf:=esti(frac,x,s):'prop'
-@rat:=ect"eq"(frac,eq,refeq,symeq,treq):'type'
-[x0:rat][y0:rat]
-is:=is"e"(rat,x0,y0):'prop'
-nis:=not(is(x0,y0)):'prop'
-@[p:[x:rat]'prop']
-some:=some"l"(rat,p):'prop'
-all:=all"l"(rat,p):'prop'
-one:=one"e"(rat,p):'prop'
-x0@[s:set(rat)]
-in:=esti(rat,x0,s):'prop'
-x@ratof:=ectelt"eq"(frac,eq,refeq,symeq,treq,x):rat
-x0@class:=ecect"eq"(frac,eq,refeq,symeq,treq,x0):set(frac)
-x@inclass:=th5"eq.4"(frac,eq,refeq,symeq,treq,x):inf(x,class(ratof(x)))
-x0@[x:frac][y:frac][xix0:inf(x,class(x0))][e:eq"n"(x,y)]
-lemmaeq1:=th8"eq.4"(frac,eq,refeq,symeq,treq,x0,x,xix0,y,e):inf(y,class(x0))
-x0@[a:'prop'][a1:[x:frac][xi:inf(x,class(x0))]a]
-ratapp1:=th3"eq.4"(frac,eq,refeq,symeq,treq,x0,a,a1):a
-y0@[a:'prop'][a1:[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]a][x:frac][xix0:inf(x,class(x0))]
-+ii5
-t1:=ratapp1(y0,a,[y:frac][yi:inf(y,class(y0))]<yi><xix0><y><x>a1):a
--ii5
-a1@ratapp2:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t1".ii5"(x,xi)):a
-y0@[z0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]a][x:frac][xix0:inf(x,class(x0))]
-+*ii5
-xix0@t2:=ratapp2(y0,z0,a,[y:frac][z:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))]<zi><yi><xix0><z><y><x>a1):a
--ii5
-a1@ratapp3:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t2".ii5"(x,xi)):a
-z0@[u0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]a][x:frac][xix0:inf(x,class(x0))]
-+*ii5
-xix0@t3:=ratapp3(y0,z0,u0,a,[y:frac][z:frac][u:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]<ui><zi><yi><xix0><u><z><y><x>a1):a
--ii5
-a1@ratapp4:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t3".ii5"(x,xi)):a
-y0@[x1:frac][y1:frac][x1ix0:inf(x1,class(x0))][y1iy0:inf(y1,class(y0))][e:eq"n"(x1,y1)]
-isi:=th3"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,e):is(x0,y0)
-y1iy0@[i:is(x0,y0)]
-ise:=th5"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,i):eq"n"(x1,y1)
-y1iy0@[n:not(eq"n"(x1,y1))]
-nisi:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),n,[t:is(x0,y0)]ise(t)):nis(x0,y0)
-y1iy0@[n:nis(x0,y0)]
-nise:=th3"l.imp"(eq"n"(x1,y1),is(x0,y0),n,[t:eq"n"(x1,y1)]isi(t)):not(eq"n"(x1,y1))
-@[alpha:'type'][f:[x:frac][y:frac]alpha]
-fixf:=fixfu2"eq"(frac,eq,refeq,symeq,treq,alpha,f):'prop'
-y0@[alpha:'type'][f:[x:frac][y:frac]alpha][ff:fixf(alpha,f)]
-indrat:=indeq2"eq"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0):alpha
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-isindrat:=th1"eq.11"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0,x,xix0,y,yiy0):is"e"(alpha,<y><x>f,indrat)
-x0@satz78:=refis(rat,x0):is(x0,x0)
-y0@[i:is(x0,y0)]
-satz79:=symis(rat,x0,y0,i):is(y0,x0)
-z0@[i:is(x0,y0)][j:is(y0,z0)]
-satz80:=tris(rat,x0,y0,z0,i,j):is(x0,z0)
-y0@more:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),moref(x,y)))):'prop'
-+*ii5
-y1@propm:=and3(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1)):'prop'
--ii5
-y0@[m:more(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propm".ii5"(t,u))][u:frac][p:propm".ii5"(t,u)]
-+*ii5
-p@t4:=and3e1(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(t,class(x0))
-t5:=and3e2(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(u,class(y0))
-t6:=and3e3(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):moref(t,u)
-t7:=satz44(t,u,x,y,t6,ise(x0,x0,t,x,t4,xix0,refis(rat,x0)),ise(y0,y0,u,y,t5,yiy0,refis(rat,y0))):moref(x,y)
-s@t8:=someapp(frac,[u:frac]propm(t,u),s,moref(x,y),[u:frac][v:propm(t,u)]t7(u,v)):moref(x,y)
--ii5
-yiy0@also18:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propm".ii5"(t,u)),m,moref(x,y),[t:frac][v:some"l"(frac,[u:frac]propm".ii5"(t,u))]t8".ii5"(t,v)):moref(x,y)
-y1iy0@[m:moref(x1,y1)]
-+*ii5
-m@t9:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1),x1ix0,y1iy0,m):propm(x1,y1)
-t10:=somei(frac,[t:frac]propm(x1,t),y1,t9):some"l"(frac,[t:frac]propm(x1,t))
--ii5
-m@morei:=somei(frac,[u:frac]some"l"(frac,[t:frac]propm".ii5"(u,t)),x1,t10".ii5"):more(x0,y0)
-y1iy0@[m:more(x0,y0)]
-moree:=also18(m,x1,y1,x1ix0,y1iy0):moref(x1,y1)
-z0@[i:is(x0,y0)][m:more(x0,z0)]
-ismore1:=isp(rat,[t:rat]more(t,z0),x0,y0,m,i):more(y0,z0)
-i@[m:more(z0,x0)]
-ismore2:=isp(rat,[t:rat]more(z0,t),x0,y0,m,i):more(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][m:more(x0,z0)]
-ismore12:=ismore2(z0,u0,y0,j,ismore1(x0,y0,z0,i,m)):more(y0,u0)
-y0@less:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),lessf(x,y)))):'prop'
-+*ii5
-y1@propl:=and3(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1)):'prop'
--ii5
-y0@[l:less(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propl".ii5"(t,u))][u:frac][p:propl".ii5"(t,u)]
-+*ii5
-p@t11:=and3e1(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(t,class(x0))
-t12:=and3e2(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(u,class(y0))
-t13:=and3e3(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):lessf(t,u)
-t14:=satz45(t,u,x,y,t13,ise(x0,x0,t,x,t11,xix0,refis(rat,x0)),ise(y0,y0,u,y,t12,yiy0,refis(rat,y0))):lessf(x,y)
-s@t15:=someapp(frac,[u:frac]propl(t,u),s,lessf(x,y),[u:frac][v:propl(t,u)]t14(u,v)):lessf(x,y)
--ii5
-yiy0@also19:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propl".ii5"(t,u)),l,lessf(x,y),[t:frac][v:some"l"(frac,[u:frac]propl".ii5"(t,u))]t15".ii5"(t,v)):lessf(x,y)
-y1iy0@[l:lessf(x1,y1)]
-+*ii5
-l@t16:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1),x1ix0,y1iy0,l):propl(x1,y1)
-t17:=somei(frac,[t:frac]propl(x1,t),y1,t16):some"l"(frac,[t:frac]propl(x1,t))
--ii5
-l@lessi:=somei(frac,[u:frac]some"l"(frac,[t:frac]propl".ii5"(u,t)),x1,t17".ii5"):less(x0,y0)
-y1iy0@[l:less(x0,y0)]
-lesse:=also19(l,x1,y1,x1ix0,y1iy0):lessf(x1,y1)
-z0@[i:is(x0,y0)][l:less(x0,z0)]
-isless1:=isp(rat,[t:rat]less(t,z0),x0,y0,l,i):less(y0,z0)
-i@[l:less(z0,x0)]
-isless2:=isp(rat,[t:rat]less(z0,t),x0,y0,l,i):less(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][l:less(x0,z0)]
-isless12:=isless2(z0,u0,y0,j,isless1(x0,y0,z0,i,l)):less(y0,u0)
-+581
-y1iy0@t1:=satz41a(x1,y1):or3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
-[e:eq"n"(x1,y1)]
-t2:=or3i1(is(x0,y0),more(x0,y0),less(x0,y0),isi(e)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-y1iy0@[m:moref(x1,y1)]
-t3:=or3i2(is(x0,y0),more(x0,y0),less(x0,y0),morei(m)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-y1iy0@[l:lessf(x1,y1)]
-t4:=or3i3(is(x0,y0),more(x0,y0),less(x0,y0),lessi(l)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-y1iy0@t5:=or3app(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),or3(is(x0,y0),more(x0,y0),less(x0,y0)),t1,[t:eq"n"(x1,y1)]t2(t),[t:moref(x1,y1)]t3(t),[t:lessf(x1,y1)]t4(t)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-t6:=satz41b(x1,y1):ec3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
-[i:is(x0,y0)]
-t7:=th3"l.imp"(more(x0,y0),moref(x1,y1),ec3e12(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,ise(i)),[t:more(x0,y0)]moree(t)):not(more(x0,y0))
-y1iy0@[m:more(x0,y0)]
-t8:=th3"l.imp"(less(x0,y0),lessf(x1,y1),ec3e23(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,moree(m)),[t:less(x0,y0)]lesse(t)):not(less(x0,y0))
-y1iy0@[l:less(x0,y0)]
-t9:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),ec3e31(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,lesse(l)),[t:is(x0,y0)]ise(t)):nis(x0,y0)
-y1iy0@t10:=th6"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),th1"l.ec"(is(x0,y0),more(x0,y0),[t:is(x0,y0)]t7(t)),th1"l.ec"(more(x0,y0),less(x0,y0),[t:more(x0,y0)]t8(t)),th1"l.ec"(less(x0,y0),is(x0,y0),[t:less(x0,y0)]t9(t))):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
-t11:=orec3i(is(x0,y0),more(x0,y0),less(x0,y0),t5,t10):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
--581
-y0@satz81:=ratapp2(orec3(is(x0,y0),more(x0,y0),less(x0,y0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t11".581"(x,y,xi,yi)):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
-satz81a:=orec3e1(is(x0,y0),more(x0,y0),less(x0,y0),satz81):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-satz81b:=orec3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
-[m:more(x0,y0)]
-+582
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=lessi(y0,x0,y,x,yiy0,xix0,satz42(x,y,moree(x0,y0,x,y,xix0,yiy0,m))):less(y0,x0)
--582
-satz82:=ratapp2(less(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".582"(x,y,xi,yi)):less(y0,x0)
-y0@[l:less(x0,y0)]
-+583
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=morei(y0,x0,y,x,yiy0,xix0,satz43(x,y,lesse(x0,y0,x,y,xix0,yiy0,l))):more(y0,x0)
--583
-satz83:=ratapp2(more(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".583"(x,y,xi,yi)):more(y0,x0)
-y0@moreis:=or(more(x0,y0),is(x0,y0)):'prop'
-[m:more(x0,y0)]
-moreisi1:=ori1(more,is,m):moreis(x0,y0)
-y0@[i:is(x0,y0)]
-moreisi2:=ori2(more,is,i):moreis(x0,y0)
-y1iy0@[m:moreq(x1,y1)]
-moreisi:=orapp(moref(x1,y1),eq"n"(x1,y1),moreis,m,[t:moref(x1,y1)]moreisi1(morei(t)),[t:eq"n"(x1,y1)]moreisi2(isi(t))):moreis(x0,y0)
-y1iy0@[m:moreis(x0,y0)]
-moreise:=orapp(more,is,moreq(x1,y1),m,[t:more]moreqi1(x1,y1,moree(t)),[t:is]moreqi2(x1,y1,ise(t))):moreq(x1,y1)
-z0@[i:is(x0,y0)][m:moreis(x0,z0)]
-ismoreis1:=isp(rat,[t:rat]moreis(t,z0),x0,y0,m,i):moreis(y0,z0)
-i@[m:moreis(z0,x0)]
-ismoreis2:=isp(rat,[t:rat]moreis(z0,t),x0,y0,m,i):moreis(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][m:moreis(x0,z0)]
-ismoreis12:=ismoreis2(z0,u0,y0,j,ismoreis1(x0,y0,z0,i,m)):moreis(y0,u0)
-y0@lessis:=or(less(x0,y0),is(x0,y0)):'prop'
-[l:less(x0,y0)]
-lessisi1:=ori1(less,is,l):lessis(x0,y0)
-y0@[i:is(x0,y0)]
-lessisi2:=ori2(less,is,i):lessis(x0,y0)
-y1iy0@[l:lesseq(x1,y1)]
-lessisi:=orapp(lessf(x1,y1),eq"n"(x1,y1),lessis,l,[t:lessf(x1,y1)]lessisi1(lessi(t)),[t:eq"n"(x1,y1)]lessisi2(isi(t))):lessis(x0,y0)
-y1iy0@[l:lessis(x0,y0)]
-lessise:=orapp(less,is,lesseq(x1,y1),l,[t:less]lesseqi1(x1,y1,lesse(t)),[t:is]lesseqi2(x1,y1,ise(t))):lesseq(x1,y1)
-z0@[i:is(x0,y0)][l:lessis(x0,z0)]
-islessis1:=isp(rat,[t:rat]lessis(t,z0),x0,y0,l,i):lessis(y0,z0)
-i@[l:lessis(z0,x0)]
-islessis2:=isp(rat,[t:rat]lessis(z0,t),x0,y0,l,i):lessis(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][l:lessis(x0,z0)]
-islessis12:=islessis2(z0,u0,y0,j,islessis1(x0,y0,z0,i,l)):lessis(y0,u0)
-y0@[m:moreis(x0,y0)]
-satz81c:=th7"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,comor(more(x0,y0),is(x0,y0),m)):not(less(x0,y0))
-y0@[l:lessis(x0,y0)]
-satz81d:=th9"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l):not(more(x0,y0))
-y0@[n:not(more(x0,y0))]
-satz81e:=th2"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n):lessis(x0,y0)
-y0@[n:not(less(x0,y0))]
-satz81f:=comor(is(x0,y0),more(x0,y0),th3"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n)):moreis(x0,y0)
-y0@[m:more(x0,y0)]
-satz81g:=th3"l.or"(less(x0,y0),is(x0,y0),ec3e23(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m),ec3e21(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m)):not(lessis(x0,y0))
-y0@[l:less(x0,y0)]
-satz81h:=th3"l.or"(more(x0,y0),is(x0,y0),ec3e32(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l),ec3e31(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l)):not(moreis(x0,y0))
-y0@[n:not(moreis(x0,y0))]
-satz81j:=or3e3(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th5"l.or"(more(x0,y0),is(x0,y0),n),th4"l.or"(more(x0,y0),is(x0,y0),n)):less(x0,y0)
-y0@[n:not(lessis(x0,y0))]
-satz81k:=or3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th4"l.or"(less(x0,y0),is(x0,y0),n),th5"l.or"(less(x0,y0),is(x0,y0),n)):more(x0,y0)
-y0@[m:moreis(x0,y0)]
-+584
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=lessisi(y0,x0,y,x,yiy0,xix0,satz48(x,y,moreise(x0,y0,x,y,xix0,yiy0,m))):lessis(y0,x0)
--584
-satz84:=ratapp2(lessis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".584"(x,y,xi,yi)):lessis(y0,x0)
-y0@[l:lessis(x0,y0)]
-+585
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=moreisi(y0,x0,y,x,yiy0,xix0,satz49(x,y,lessise(x0,y0,x,y,xix0,yiy0,l))):moreis(y0,x0)
--585
-satz85:=ratapp2(moreis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".585"(x,y,xi,yi)):moreis(y0,x0)
-z0@[l:less(x0,y0)][k:less(y0,z0)]
-+586
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=lessi(x0,z0,x,z,xix0,ziz0,satz50(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
--586
-satz86:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".586"(x,y,z,xi,yi,zi)):less(x0,z0)
-trless:=satz86:less(x0,z0)
-z0@[m:more(x0,y0)][n:more(y0,z0)]
-trmore:=satz83(z0,x0,satz86(z0,y0,x0,satz82(y0,z0,n),satz82(m))):more(x0,z0)
-z0@[l:lessis(x0,y0)][k:less(y0,z0)]
-+587
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=lessi(x0,z0,x,z,xix0,ziz0,satz51a(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
--587
-satz87a:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".587"(x,y,z,xi,yi,zi)):less(x0,z0)
-z0@[l:less(x0,y0)][k:lessis(y0,z0)]
-+*587
-k@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=lessi(x0,z0,x,z,xix0,ziz0,satz51b(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
--587
-k@satz87b:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".587"(x,y,z,xi,yi,zi)):less(x0,z0)
-z0@[m:moreis(x0,y0)][n:more(y0,z0)]
-satz87c:=satz83(z0,x0,satz87b(z0,y0,x0,satz82(y0,z0,n),satz84(m))):more(x0,z0)
-z0@[m:more(x0,y0)][n:moreis(y0,z0)]
-satz87d:=satz83(z0,x0,satz87a(z0,y0,x0,satz84(y0,z0,n),satz82(m))):more(x0,z0)
-z0@[l:lessis(x0,y0)][k:lessis(y0,z0)]
-+588
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=lessisi(x0,z0,x,z,xix0,ziz0,satz52(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):lessis(x0,z0)
--588
-satz88:=ratapp3(lessis(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".588"(x,y,z,xi,yi,zi)):lessis(x0,z0)
-trlessis:=satz88:lessis(x0,z0)
-z0@[m:moreis(x0,y0)][n:moreis(y0,z0)]
-trmoreis:=satz85(z0,x0,satz88(z0,y0,x0,satz84(y0,z0,n),satz84(m))):moreis(x0,z0)
-+589
-x0@[x:frac][xix0:inf(x,class(x0))][z:frac][m:moref(z,x)]
-t1:=somei(rat,[t:rat]more(t,x0),ratof(z),morei(ratof(z),x0,z,x,inclass(z),xix0,m)):some([t:rat]more(t,x0))
-xix0@t2:=someapp(frac,[t:frac]moref(t,x),satz53(x),some([t:rat]more(t,x0)),[t:frac][u:moref(t,x)]t1(t,u)):some([t:rat]more(t,x0))
--589
-x0@satz89:=ratapp1(some([t:rat]more(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".589"(x,xi)):some([t:rat]more(t,x0))
-+590
-z"rt.589"@[l:lessf(z,x)]
-t1:=somei(rat,[t:rat]less(t,x0),ratof(z),lessi(ratof(z),x0,z,x,inclass(z),xix0,l)):some([t:rat]less(t,x0))
-xix0"rt.589"@t2:=someapp(frac,[t:frac]lessf(t,x),satz54(x),some([t:rat]less(t,x0)),[t:frac][u:lessf(t,x)]t1(t,u)):some([t:rat]less(t,x0))
--590
-satz90:=ratapp1(some([t:rat]less(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".590"(x,xi)):some([t:rat]less(t,x0))
-y0@[l:less(x0,y0)]
-+591
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][z:frac][a:and(lessf(x,z),lessf(z,y))]
-t1:=lessi(x0,ratof(z),x,z,xix0,inclass(z),ande1(lessf(x,z),lessf(z,y),a)):less(x0,ratof(z))
-t2:=lessi(ratof(z),y0,z,y,inclass(z),yiy0,ande2(lessf(x,z),lessf(z,y),a)):less(ratof(z),y0)
-t3:=andi(less(x0,ratof(z)),less(ratof(z),y0),t1,t2):and(less(x0,ratof(z)),less(ratof(z),y0))
-t4:=somei(rat,[t:rat]and(less(x0,t),less(t,y0)),ratof(z),t3):some([t:rat]and(less(x0,t),less(t,y0)))
-yiy0@t5:=someapp(frac,[t:frac]and(lessf(x,t),lessf(t,y)),satz55(x,y,lesse(x,y,xix0,yiy0,l)),some([t:rat]and(less(x0,t),less(t,y0))),[t:frac][u:and(lessf(x,t),lessf(t,y))]t4(t,u)):some([t:rat]and(less(x0,t),less(t,y0)))
--591
-satz91:=ratapp2(some([t:rat]and(less(x0,t),less(t,y0))),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".591"(x,y,xi,yi)):some([t:rat]and(less(x0,t),less(t,y0)))
-@plusfrt:=[x:frac][y:frac]ratof(pf(x,y)):[x:frac][y:frac]rat
-[x:frac][y:frac][z:frac][u:frac][e:eq"n"(x,y)][f:eq"n"(z,u)]
-+*ii5
-f@t18:=isi(ratof(pf(x,z)),ratof(pf(y,u)),pf(x,z),pf(y,u),inclass(pf(x,z)),inclass(pf(y,u)),satz56(x,y,z,u,e,f)):is(<z><x>plusfrt,<u><y>plusfrt)
--ii5
-@fplusfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t18".ii5"(x,y,z,u,v,w):fixf(rat,plusfrt)
-y0@pl:=indrat(rat,plusfrt,fplusfrt):rat
-+*ii5
-y1iy0@t19:=isindrat(rat,plusfrt,fplusfrt,x1,y1,x1ix0,y1iy0):is(ratof(pf(x1,y1)),pl(x0,y0))
--ii5
-y1iy0@picp:=isp(rat,[t:rat]inf(pf(x1,y1),class(t)),ratof(pf(x1,y1)),pl(x0,y0),inclass(pf(x1,y1)),t19".ii5"):inf(pf(x1,y1),class(pl(x0,y0)))
-z0@[i:is(x0,y0)]
-ispl1:=isf(rat,rat,[t:rat]pl(t,z0),x0,y0,i):is(pl(x0,z0),pl(y0,z0))
-ispl2:=isf(rat,rat,[t:rat]pl(z0,t),x0,y0,i):is(pl(z0,x0),pl(z0,y0))
-u0@[i:is(x0,y0)][j:is(z0,u0)]
-ispl12:=tris(rat,pl(x0,z0),pl(y0,z0),pl(y0,u0),ispl1(i),ispl2(z0,u0,y0,j)):is(pl(x0,z0),pl(y0,u0))
-+592
-y1iy0@t1:=isi(pl(x0,y0),pl(y0,x0),pf(x1,y1),pf(y1,x1),picp,picp(y0,x0,y1,x1,y1iy0,x1ix0),satz58(x1,y1)):is(pl(x0,y0),pl(y0,x0))
--592
-y0@satz92:=ratapp2(is(pl(x0,y0),pl(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".592"(x,y,xi,yi)):is(pl(x0,y0),pl(y0,x0))
-compl:=satz92:is(pl(x0,y0),pl(y0,x0))
-+593
-z0@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=picp(pl(x0,y0),z0,pf(x,y),z,picp(x0,y0,x,y,xix0,yiy0),ziz0):inf(pf(pf(x,y),z),class(pl(pl(x0,y0),z0)))
-t2:=picp(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(pf(x,pf(y,z)),class(pl(x0,pl(y0,z0))))
-t3:=isi(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),pf(pf(x,y),z),pf(x,pf(y,z)),t1,t2,satz59(x,y,z)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
--593
-z0@satz93:=ratapp3(is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".593"(x,y,z,xi,yi,zi)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
-asspl1:=satz93:is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
-asspl2:=symis(rat,pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),satz93):is(pl(x0,pl(y0,z0)),pl(pl(x0,y0),z0))
-+594
-y1iy0@t1:=morei(pl(x0,y0),x0,pf(x1,y1),x1,picp,x1ix0,satz60(x1,y1)):more(pl(x0,y0),x0)
--594
-y0@satz94:=ratapp2(more(pl(x0,y0),x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".594"(x,y,xi,yi)):more(pl(x0,y0),x0)
-satz94a:=satz82(pl(x0,y0),x0,satz94):less(x0,pl(x0,y0))
-z0@[m:more(x0,y0)]
-+595
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz61(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
--595
-satz95:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".595"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
-z0@[m:more(x0,y0)]
-+596
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
--596
-satz96a:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".596"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
-z0@[i:is(x0,y0)]
-+*596
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(pl(x0,z0),pl(y0,z0))
--596
-i@satz96b:=ratapp3(is(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".596"(x,y,z,xi,yi,zi)):is(pl(x0,z0),pl(y0,z0))
-z0@[l:less(x0,y0)]
-+*596
-l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t3:=lessi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62c(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l))):less(pl(x0,z0),pl(y0,z0))
--596
-l@satz96c:=ratapp3(less(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".596"(x,y,z,xi,yi,zi)):less(pl(x0,z0),pl(y0,z0))
-+*596
-m@andersa:=satz95(m):more(pl(x0,z0),pl(y0,z0))
-i@andersb:=ispl1(x0,y0,z0,i):is(pl(x0,z0),pl(y0,z0))
-l@andersc:=satz82(pl(y0,z0),pl(x0,z0),satz95(y0,x0,z0,satz83(l))):less(pl(x0,z0),pl(y0,z0))
--596
-m@satz96d:=ismore12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96a):more(pl(z0,x0),pl(z0,y0))
-i@satz96e:=ispl2(x0,y0,z0,i):is(pl(z0,x0),pl(z0,y0))
-l@satz96f:=isless12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96c):less(pl(z0,x0),pl(z0,y0))
-z0@[m:more(pl(x0,z0),pl(y0,z0))]
-+597
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(x0,y0,x,y,xix0,yiy0,satz63a(x,y,z,moree(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
--597
-satz97a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".597"(x,y,z,xi,yi,zi)):more(x0,y0)
-z0@[i:is(pl(x0,z0),pl(y0,z0))]
-+*597
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(x0,y0,x,y,xix0,yiy0,satz63b(x,y,z,ise(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
--597
-i@satz97b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".597"(x,y,z,xi,yi,zi)):is(x0,y0)
-z0@[l:less(pl(x0,z0),pl(y0,z0))]
-+*597
-l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t3:=lessi(x0,y0,x,y,xix0,yiy0,satz63c(x,y,z,lesse(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
--597
-l@satz97c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".597"(x,y,z,xi,yi,zi)):less(x0,y0)
-+*597
-l@anders:=satz82(y0,x0,satz97a(y0,x0,z0,satz83(pl(x0,z0),pl(y0,z0),l))):less(x0,y0)
--597
-u0@[m:more(x0,y0)][n:more(z0,u0)]
-+598
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz64(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
--598
-satz98:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".598"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
-u0@[l:less(x0,y0)][k:less(z0,u0)]
-satz98a:=satz82(pl(y0,u0),pl(x0,z0),satz98(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
-u0@[m:moreis(x0,y0)][n:more(z0,u0)]
-+599
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
--599
-satz99a:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
-u0@[m:more(x0,y0)][n:moreis(z0,u0)]
-+*599
-n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t2:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
--599
-n@satz99b:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
-u0@[l:lessis(x0,y0)][k:less(z0,u0)]
-satz99c:=satz82(pl(y0,u0),pl(x0,z0),satz99a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
-u0@[l:less(x0,y0)][k:lessis(z0,u0)]
-satz99d:=satz82(pl(y0,u0),pl(x0,z0),satz99b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
-u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
-+5100
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=moreisi(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz66(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(pl(x0,z0),pl(y0,u0))
--5100
-satz100:=ratapp4(moreis(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5100"(x,y,z,u,xi,yi,zi,ui)):moreis(pl(x0,z0),pl(y0,u0))
-u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
-satz100a:=satz84(pl(y0,u0),pl(x0,z0),satz100(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(pl(x0,z0),pl(y0,u0))
-y0@[l:lessis(x0,y0)]
-+5101
-[v0:rat][i:is(pl(y0,v0),x0)]
-t1:=ismore1(pl(y0,v0),x0,y0,i,satz94(y0,v0)):more(x0,y0)
-v0@t2:=th3"l.imp"(is(pl(y0,v0),x0),more(x0,y0),satz81d(x0,y0,l),[t:is(pl(y0,v0),x0)]t1(t)):nis(pl(y0,v0),x0)
--5101
-vorbemerkung101:=th5"l.some"(rat,[v:rat]is(pl(y0,v),x0),[v:rat]t2".5101"(v)):not(some([t:rat]is(pl(y0,t),x0)))
-y0@[m:more(x0,y0)]
-+*5101
-m@[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][v:frac][e:eq"n"(pf(y,v),x)]
-t3:=isi(pl(y0,ratof(v)),x0,pf(y,v),x,picp(y0,ratof(v),y,v,yiy0,inclass(v)),xix0,e):is(pl(y0,ratof(v)),x0)
-t4:=somei(rat,[t:rat]is(pl(y0,t),x0),ratof(v),t3):some([t:rat]is(pl(y0,t),x0))
-yiy0@t5:=someapp(frac,[t:frac]eq"n"(pf(y,t),x),satz67a(x,y,moree(x0,y0,x,y,xix0,yiy0,m)),some([t:rat]is(pl(y0,t),x0)),[t:frac][u:eq"n"(pf(y,t),x)]t4(t,u)):some([t:rat]is(pl(y0,t),x0))
--5101
-m@satz101a:=ratapp2(some([t:rat]is(pl(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".5101"(x,y,xi,yi)):some([t:rat]is(pl(y0,t),x0))
-y0@[v0:rat][w0:rat][i:is(pl(y0,v0),x0)][j:is(pl(y0,w0),x0)]
-+*5101
-j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
-t6:=isi(v0,w0,v,w,viv0,wiw0,satz67b(x,y,v,w,ise(pl(y0,v0),x0,pf(y,v),x,picp(y0,v0,y,v,yiy0,viv0),xix0,i),ise(pl(y0,w0),x0,pf(y,w),x,picp(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
--5101
-j@satz101b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t6".5101"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
-+*5101
-y0@t7:=[t:rat][u:rat][v:is(pl(y0,t),x0)][w:is(pl(y0,u),x0)]satz101b(t,u,v,w):amone(rat,[t:rat]is(pl(y0,t),x0))
--5101
-m@satz101:=onei(rat,[t:rat]is(pl(y0,t),x0),t7".5101",satz101a):one([t:rat]is(pl(y0,t),x0))
-mn:=ind(rat,[t:rat]is(pl(y0,t),x0),satz101):rat
-satz101c:=oneax(rat,[t:rat]is(pl(y0,t),x0),satz101):is(pl(y0,mn(x0,y0,m)),x0)
-satz101d:=symis(rat,pl(y0,mn(x0,y0,m)),x0,satz101c):is(x0,pl(y0,mn(x0,y0,m)))
-satz101e:=tris(rat,pl(mn(x0,y0,m),y0),pl(y0,mn(x0,y0,m)),x0,compl(mn(x0,y0,m),y0),satz101c):is(pl(mn(x0,y0,m),y0),x0)
-satz101f:=symis(rat,pl(mn(x0,y0,m),y0),x0,satz101e):is(x0,pl(mn(x0,y0,m),y0))
-y0@[v0:rat][m:more(x0,y0)][i:is(pl(y0,v0),x0)]
-satz101g:=satz101b(v0,mn(x0,y0,m),i,satz101c(m)):is(v0,mn(x0,y0,m))
-@timesfrt:=[x:frac][y:frac]ratof(tf(x,y)):[x:frac][y:frac]rat
-+*ii5
-f@t20:=isi(ratof(tf(x,z)),ratof(tf(y,u)),tf(x,z),tf(y,u),inclass(tf(x,z)),inclass(tf(y,u)),satz68(x,y,z,u,e,f)):is(<z><x>timesfrt,<u><y>timesfrt)
--ii5
-@ftimesfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t20".ii5"(x,y,z,u,v,w):fixf(rat,timesfrt)
-y0@ts:=indrat(rat,timesfrt,ftimesfrt):rat
-+*ii5
-y1iy0@t21:=isindrat(rat,timesfrt,ftimesfrt,x1,y1,x1ix0,y1iy0):is(ratof(tf(x1,y1)),ts(x0,y0))
--ii5
-y1iy0@tict:=isp(rat,[t:rat]inf(tf(x1,y1),class(t)),ratof(tf(x1,y1)),ts(x0,y0),inclass(tf(x1,y1)),t21".ii5"):inf(tf(x1,y1),class(ts(x0,y0)))
-z0@[i:is(x0,y0)]
-ists1:=isf(rat,rat,[t:rat]ts(t,z0),x0,y0,i):is(ts(x0,z0),ts(y0,z0))
-ists2:=isf(rat,rat,[t:rat]ts(z0,t),x0,y0,i):is(ts(z0,x0),ts(z0,y0))
-u0@[i:is(x0,y0)][j:is(z0,u0)]
-ists12:=tris(rat,ts(x0,z0),ts(y0,z0),ts(y0,u0),ists1(i),ists2(z0,u0,y0,j)):is(ts(x0,z0),ts(y0,u0))
-+5102
-y1iy0@t1:=isi(ts(x0,y0),ts(y0,x0),tf(x1,y1),tf(y1,x1),tict,tict(y0,x0,y1,x1,y1iy0,x1ix0),satz69(x1,y1)):is(ts(x0,y0),ts(y0,x0))
--5102
-y0@satz102:=ratapp2(is(ts(x0,y0),ts(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".5102"(x,y,xi,yi)):is(ts(x0,y0),ts(y0,x0))
-comts:=satz102:is(ts(x0,y0),ts(y0,x0))
-+5103
-ziz0"rt.593"@t1:=tict(ts(x0,y0),z0,tf(x,y),z,tict(x0,y0,x,y,xix0,yiy0),ziz0):inf(tf(tf(x,y),z),class(ts(ts(x0,y0),z0)))
-t2:=tict(x0,ts(y0,z0),x,tf(y,z),xix0,tict(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,tf(y,z)),class(ts(x0,ts(y0,z0))))
-t3:=isi(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),tf(tf(x,y),z),tf(x,tf(y,z)),t1,t2,satz70(x,y,z)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
--5103
-z0@satz103:=ratapp3(is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5103"(x,y,z,xi,yi,zi)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
-assts1:=satz103:is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
-assts2:=symis(rat,ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),satz103):is(ts(x0,ts(y0,z0)),ts(ts(x0,y0),z0))
-+5104
-ziz0"rt.593"@t1:=tict(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,pf(y,z)),class(ts(x0,pl(y0,z0))))
-t2:=picp(ts(x0,y0),ts(x0,z0),tf(x,y),tf(x,z),tict(x0,y0,x,y,xix0,yiy0),tict(x0,z0,x,z,xix0,ziz0)):inf(pf(tf(x,y),tf(x,z)),class(pl(ts(x0,y0),ts(x0,z0))))
-t3:=isi(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),t1,t2,satz71(x,y,z)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
--5104
-satz104:=ratapp3(is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5104"(x,y,z,xi,yi,zi)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
-disttp1:=tr3is(rat,ts(pl(x0,y0),z0),ts(z0,pl(x0,y0)),pl(ts(z0,x0),ts(z0,y0)),pl(ts(x0,z0),ts(y0,z0)),comts(pl(x0,y0),z0),satz104(z0,x0,y0),ispl12(ts(z0,x0),ts(x0,z0),ts(z0,y0),ts(y0,z0),comts(z0,x0),comts(z0,y0))):is(ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)))
-disttp2:=satz104:is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
-distpt1:=symis(rat,ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)),disttp1):is(pl(ts(x0,z0),ts(y0,z0)),ts(pl(x0,y0),z0))
-distpt2:=symis(rat,ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),disttp2):is(pl(ts(x0,y0),ts(x0,z0)),ts(x0,pl(y0,z0)))
-[m:more(x0,y0)]
-+5105
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(ts(x0,z0),ts(y0,z0))
--5105
-satz105a:=ratapp3(more(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5105"(x,y,z,xi,yi,zi)):more(ts(x0,z0),ts(y0,z0))
-z0@[i:is(x0,y0)]
-+*5105
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(ts(x0,z0),ts(y0,z0))
--5105
-i@satz105b:=ratapp3(is(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5105"(x,y,z,xi,yi,zi)):is(ts(x0,z0),ts(y0,z0))
-z0@[l:less(x0,y0)]
-+*5105
-l@[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]
-t3:=lessi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xi,zi),tict(y0,z0,y,z,yi,zi),satz72c(x,y,z,lesse(x0,y0,x,y,xi,yi,l))):less(ts(x0,z0),ts(y0,z0))
--5105
-l@satz105c:=ratapp3(less(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5105"(x,y,z,xi,yi,zi)):less(ts(x0,z0),ts(y0,z0))
-+*5105
-i@andersb:=ists1(x0,y0,z0,i):is(ts(x0,z0),ts(y0,z0))
-l@andersc:=satz82(ts(y0,z0),ts(x0,z0),satz105a(y0,x0,z0,satz83(l))):less(ts(x0,z0),ts(y0,z0))
--5105
-m@satz105d:=ismore12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105a):more(ts(z0,x0),ts(z0,y0))
-i@satz105e:=ists2(x0,y0,z0,i):is(ts(z0,x0),ts(z0,y0))
-l@satz105f:=isless12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105c):less(ts(z0,x0),ts(z0,y0))
-z0@[m:more(ts(x0,z0),ts(y0,z0))]
-+5106
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(x0,y0,x,y,xix0,yiy0,satz73a(x,y,z,moree(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
--5106
-satz106a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5106"(x,y,z,xi,yi,zi)):more(x0,y0)
-z0@[i:is(ts(x0,z0),ts(y0,z0))]
-+*5106
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(x0,y0,x,y,xix0,yiy0,satz73b(x,y,z,ise(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
--5106
-i@satz106b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5106"(x,y,z,xi,yi,zi)):is(x0,y0)
-z0@[l:less(ts(x0,z0),ts(y0,z0))]
-+*5106
-l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t3:=lessi(x0,y0,x,y,xix0,yiy0,satz73c(x,y,z,lesse(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
--5106
-l@satz106c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5106"(x,y,z,xi,yi,zi)):less(x0,y0)
-+*5106
-l@anders:=satz82(y0,x0,satz106a(y0,x0,z0,satz83(ts(x0,z0),ts(y0,z0),l))):less(x0,y0)
--5106
-u0@[m:more(x0,y0)][n:more(z0,u0)]
-+5107
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz74(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
--5107
-satz107:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5107"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
-u0@[l:less(x0,y0)][k:less(z0,u0)]
-satz107a:=satz82(ts(y0,u0),ts(x0,z0),satz107(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
-u0@[m:moreis(x0,y0)][n:more(z0,u0)]
-+5108
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
--5108
-satz108a:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
-u0@[m:more(x0,y0)][n:moreis(z0,u0)]
-+*5108
-n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t2:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
--5108
-n@satz108b:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
-u0@[l:lessis(x0,y0)][k:less(z0,u0)]
-satz108c:=satz82(ts(y0,u0),ts(x0,z0),satz108a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
-u0@[l:less(x0,y0)][k:lessis(z0,u0)]
-satz108d:=satz82(ts(y0,u0),ts(x0,z0),satz108b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
-u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
-+5109
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=moreisi(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz76(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(ts(x0,z0),ts(y0,u0))
--5109
-satz109:=ratapp4(moreis(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5109"(x,y,z,u,xi,yi,zi,ui)):moreis(ts(x0,z0),ts(y0,u0))
-u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
-satz109a:=satz84(ts(y0,u0),ts(x0,z0),satz109(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(ts(x0,z0),ts(y0,u0))
-+5110
-y1iy0@[v:frac][e:eq"n"(tf(y1,v),x1)]
-t1:=isi(ts(y0,ratof(v)),x0,tf(y1,v),x1,tict(y0,ratof(v),y1,v,y1iy0,inclass(v)),x1ix0,e):is(ts(y0,ratof(v)),x0)
-t2:=somei(rat,[t:rat]is(ts(y0,t),x0),ratof(v),t1):some([t:rat]is(ts(y0,t),x0))
-y1iy0@t3:=someapp(frac,[t:frac]eq"n"(tf(y1,t),x1),satz77a(x1,y1),some([t:rat]is(ts(y0,t),x0)),[t:frac][u:eq"n"(tf(y1,t),x1)]t2(t,u)):some([t:rat]is(ts(y0,t),x0))
--5110
-y0@satz110a:=ratapp2(some([t:rat]is(ts(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t3".5110"(x,y,xi,yi)):some([t:rat]is(ts(y0,t),x0))
-[v0:rat][w0:rat][i:is(ts(y0,v0),x0)][j:is(ts(y0,w0),x0)]
-+*5110
-j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
-t4:=isi(v0,w0,v,w,viv0,wiw0,satz77b(x,y,v,w,ise(ts(y0,v0),x0,tf(y,v),x,tict(y0,v0,y,v,yiy0,viv0),xix0,i),ise(ts(y0,w0),x0,tf(y,w),x,tict(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
--5110
-j@satz110b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t4".5110"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
-+*5110
-y0@t5:=[t:rat][u:rat][v:is(ts(y0,t),x0)][w:is(ts(y0,u),x0)]satz110b(t,u,v,w):amone(rat,[t:rat]is(ts(y0,t),x0))
--5110
-y0@satz110:=onei(rat,[t:rat]is(ts(y0,t),x0),t5".5110",satz110a):one([t:rat]is(ts(y0,t),x0))
--rt
-@[x:nat][y:nat]
-+5111
-t1:=tris(nat,ts(num(fr(x,1)),den(fr(y,1))),ts(x,1),x,ndis12(x,1,y,1),satz28a(x)):is(ts(num(fr(x,1)),den(fr(y,1))),x)
-t2:=symis(nat,ts(num(fr(x,1)),den(fr(y,1))),x,t1):is(x,ts(num(fr(x,1)),den(fr(y,1))))
--5111
-[m:moref(fr(x,1),fr(y,1))]
-satz111a:=ismore12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),m):more(x,y)
-y@[e:eq(fr(x,1),fr(y,1))]
-satz111b:=tr3is(nat,x,ts(num(fr(x,1)),den(fr(y,1))),ts(num(fr(y,1)),den(fr(x,1))),y,t2".5111",e,t1".5111"(y,x)):is(x,y)
-y@[l:lessf(fr(x,1),fr(y,1))]
-satz111c:=isless12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),l):less(x,y)
-y@[m:more(x,y)]
-satz111d:=ismore12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),m):moref(fr(x,1),fr(y,1))
-y@[i:is(x,y)]
-satz111e:=tr3is(nat,ts(num(fr(x,1)),den(fr(y,1))),x,y,ts(num(fr(y,1)),den(fr(x,1))),t1".5111",i,t2".5111"(y,x)):eq(fr(x,1),fr(y,1))
-y@[l:less(x,y)]
-satz111f:=isless12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),l):lessf(fr(x,1),fr(y,1))
-+*rt
-@[x0:rat][x:nat]
-natprop:=inf(fr(x,1),class(x0)):'prop'
-x0@natrt:=some"n"([t:nat]natprop(t)):'prop'
-+*ii5
-y0@[x:nat][y:nat][npx:natprop(x0,x)][npy:natprop(y0,y)][i:is(x0,y0)]
-t22:=satz111b(x,y,ise(x0,y0,fr(x,1),fr(y,1),npx,npy,i)):is"n"(x,y)
-x0@t23:=[t:nat][u:nat][v:natprop(x0,t)][w:natprop(x0,u)]t22(x0,x0,t,u,v,w,refis(rat,x0)):amone(nat,[t:nat]natprop(x0,t))
--ii5
-x0@[nx0:natrt(x0)]
-satz111g:=onei(nat,[t:nat]natprop(t),t23".ii5",nx0):one"n"([t:nat]natprop(x0,t))
-nofrt:=ind(nat,[t:nat]natprop(t),satz111g):nat
-inclassn:=oneax(nat,[t:nat]natprop(t),satz111g):inf(fr(nofrt,1),class(x0))
-[y0:rat][ny0:natrt(y0)][i:is(x0,y0)]
-isrten:=t22".ii5"(x0,y0,nofrt(x0,nx0),nofrt(y0,ny0),inclassn(x0,nx0),inclassn(y0,ny0),i):is"n"(nofrt(x0,nx0),nofrt(y0,ny0))
-ny0@[i:is"n"(nofrt(x0,nx0),nofrt(y0,ny0))]
-isrtin:=isi(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),eqn"n"(nofrt(x0,nx0),1,nofrt(y0,ny0),i)):is(x0,y0)
-@[x:nat]
-rtofn:=ratof(fr(x,1)):rat
-natrti:=somei(nat,[t:nat]natprop(rtofn,t),x,inclass(fr(x,1))):natrt(rtofn(x))
-[y:nat][i:is"n"(x,y)]
-isnert:=isf(nat,rat,[t:nat]rtofn(t),x,y,i):is(rtofn(x),rtofn(y))
-y@[i:is(rtofn(x),rtofn(y))]
-isnirt:=t22".ii5"(rtofn(x),rtofn(y),x,y,inclass(fr(x,1)),inclass(fr(y,1)),i):is"n"(x,y)
-nx0@isrtn1:=isi(x0,rtofn(nofrt(x0,nx0)),fr(nofrt(x0,nx0),1),fr(nofrt(x0,nx0),1),inclassn(x0,nx0),inclass(fr(nofrt(x0,nx0),1)),refeq"n"(fr(nofrt(x0,nx0),1))):is(x0,rtofn(nofrt(x0,nx0)))
-x@isnrt1:=t22".ii5"(rtofn(x),rtofn(x),x,nofrt(rtofn(x),natrti(x)),inclass(fr(x,1)),inclassn(rtofn(x),natrti(x)),refis(rat,rtofn(x))):is"n"(x,nofrt(rtofn(x),natrti(x)))
--rt
-@[x:nat][y:nat]
-satz112a:=satz57(x,y,1):eq(pf(fr(x,1),fr(y,1)),fr(pl(x,y),1))
-satz112b:=treq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),ts(1,1)),fr(ts(x,y),1),tfeq12a(x,1,y,1),eqd(ts(x,y),ts(1,1),1,satz28a(1))):eq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),1))
-+*rt
-ny0@satz112c:=lemmaeq1(pl(x0,y0),pf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),picp(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112a(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(pl(x0,y0)))
-satz112d:=somei(nat,[t:nat]natprop(pl(x0,y0),t),pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112c):natrt(pl(x0,y0))
-satz112e:=lemmaeq1(ts(x0,y0),tf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),tict(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112b(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(ts(x0,y0)))
-satz112f:=somei(nat,[t:nat]natprop(ts(x0,y0),t),ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112e):natrt(ts(x0,y0))
-[m:more(x0,y0)]
-+5112
-t1:=satz111a(nofrt(x0,nx0),nofrt(y0,ny0),moree(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),m)):more"n"(nofrt(x0,nx0),nofrt(y0,ny0))
-[z:nat][d:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),z)]
-t2:=tris(nat,nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),z),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),d,ispl2"n"(z,nofrt(rtofn(z),natrti(z)),nofrt(y0,ny0),isnrt1(z))):is"n"(nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))))
-t3:=isi(x0,pl(y0,rtofn(z)),fr(nofrt(x0,nx0),1),fr(pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),1),inclassn(x0,nx0),satz112c(y0,ny0,rtofn(z),natrti(z)),eqn(nofrt(x0,nx0),1,pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),t2)):is(x0,pl(y0,rtofn(z)))
-t4:=satz101g(x0,y0,rtofn(z),m,symis(rat,x0,pl(y0,rtofn(z)),t3)):is(rtofn(z),mn(x0,y0,m))
-t5:=isp(rat,[t:rat]natrt(t),rtofn(z),mn(x0,y0,m),natrti(z),t4):natrt(mn(x0,y0,m))
--5112
-satz112g:=someapp(nat,[t:nat]diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t),t1".5112",natrt(mn(x0,y0,m)),[t:nat][u:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t)]t5".5112"(t,u)):natrt(mn(x0,y0,m))
-@[x:nat][y:nat]
-satz112h:=isi(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),pf(fr(x,1),fr(y,1)),fr(pl"n"(x,y),1),picp(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(pl"n"(x,y),1)),satz112a(x,y)):is(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)))
-satz112j:=isi(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),tf(fr(x,1),fr(y,1)),fr(ts"n"(x,y),1),tict(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(ts"n"(x,y),1)),satz112b(x,y)):is(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)))
-+nt
-@natt:=ot(rat,[t:rat]natrt(t)):'type'
-nx0@ntofrt:=out(rat,[t:rat]natrt(t),x0,nx0):natt
-@[xt:natt][yt:natt]
-is:=is"e"(natt,xt,yt):'prop'
-nis:=not(is(xt,yt)):'prop'
-@[p:[x:natt]'prop']
-all:=all"l"(natt,p):'prop'
-some:=some"l"(natt,p):'prop'
-one:=one"e"(natt,p):'prop'
-xt@[st:set(natt)]
-in:=esti(natt,xt,st):'prop'
-xt@rtofnt:=in"e"(rat,[t:rat]natrt(t),xt):rat
-natrti:=inp(rat,[t:rat]natrt(t),xt):natrt(rtofnt(xt))
-ny0@[i:is"rt"(x0,y0)]
-isrtent:=isouti(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is(ntofrt(x0,nx0),ntofrt(y0,ny0))
-ny0@[i:is(ntofrt(x0,nx0),ntofrt(y0,ny0))]
-isrtint:=isoute(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is"rt"(x0,y0)
-yt@[i:is(xt,yt)]
-isntert:=isini(rat,[t:rat]natrt(t),xt,yt,i):is"rt"(rtofnt(xt),rtofnt(yt))
-yt@[i:is"rt"(rtofnt(xt),rtofnt(yt))]
-isntirt:=isine(rat,[t:rat]natrt(t),xt,yt,i):is(xt,yt)
-nx0@isrtnt1:=isinout(rat,[t:rat]natrt(t),x0,nx0):is"rt"(x0,rtofnt(ntofrt(x0,nx0)))
-xt@isntrt1:=isoutin(rat,[t:rat]natrt(t),xt):is(xt,ntofrt(rtofnt(xt),natrti(xt)))
-x@ntofn:=ntofrt(rtofn(x),natrti"rt"(x)):natt
-y@[i:is"n"(x,y)]
-isnent:=isrtent(rtofn(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),isnert(x,y,i)):is(ntofn(x),ntofn(y))
-y@[i:is(ntofn(x),ntofn(y))]
-isnint:=isnirt(x,y,isrtint(rtofn"rt"(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),i)):is"n"(x,y)
-xt@nofnt:=nofrt(rtofnt(xt),natrti(xt)):nat
-yt@[i:is(xt,yt)]
-isnten:=isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),isntert(xt,yt,i)):is"n"(nofnt(xt),nofnt(yt))
-yt@[i:is"n"(nofnt(xt),nofnt(yt))]
-isntin:=isntirt(xt,yt,isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),i)):is(xt,yt)
-+ii5
-x@t24:=isrtnt1(rtofn(x),natrti"rt"(x)):is"rt"(rtofn(x),rtofnt(ntofn(x)))
-t25:=isrten(rtofn(x),natrti"rt"(x),rtofnt(ntofn(x)),natrti(ntofn(x)),t24):is"n"(nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)))
--ii5
-x@isnnt1:=tris(nat,x,nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)),isnrt1(x),t25".ii5"):is"n"(x,nofnt(ntofn(x)))
-+*ii5
-xt@t26:=isrtn1(rtofnt(xt),natrti(xt)):is"rt"(rtofnt(xt),rtofn(nofnt(xt)))
-t27:=isrtent(rtofnt(xt),natrti(xt),rtofn(nofnt(xt)),natrti"rt"(nofnt(xt)),t26):is(ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)))
--ii5
-xt@isntn1:=tris(natt,xt,ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)),isntrt1(xt),t27".ii5"):is(xt,ntofn(nofnt(xt)))
-x@isnnt2:=symis(nat,x,nofnt(ntofn(x)),isnnt1):is"n"(nofnt(ntofn(x)),x)
-xt@isntn2:=symis(natt,xt,ntofn(nofnt(xt)),isntn1):is(ntofn(nofnt(xt)),xt)
-@1t:=ntofn(1):natt
-suct:=[x:natt]ntofn(<nofnt(x)>suc):[x:natt]natt
-+5113
-xt@[i:is(<xt>suct,1t)]
-t1:=isnint(<nofnt(xt)>suc,1,i):is"n"(<nofnt(xt)>suc,1)
--5113
-xt@satz113a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<nofnt(xt)>suc,1),<nofnt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5113"(t)):nis(<xt>suct,1t)
-yt@[i:is(<xt>suct,<yt>suct)]
-+*5113
-i"nt"@t2:=isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,i):is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
--5113
-i@satz113b:=isntin(xt,yt,<t2".5113"><nofnt(yt)><nofnt(xt)>ax4):is(xt,yt)
-@[st:set(natt)]
-cond1:=in(1t,st):'prop'
-cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
-[c1:cond1][c2:cond2]
-+*5113
-c2@[x:nat]
-prop1:=in(ntofn(x),st):'prop'
-[p:prop1(x)]
-t3:=<ntofn(x)>c2:imp(in(ntofn(x),st),in(<ntofn(x)>suct,st))
-t4:=mp(in(ntofn(x),st),in(<ntofn(x)>suct,st),p,t3):in(<ntofn(x)>suct,st)
-t5:=isp(nat,[t:nat]in(ntofn(<t>suc),st),nofnt(ntofn(x)),x,t4,isnnt2(x)):prop1(<x>suc)
--5113
-c2@[xt:natt]
-+*5113
-xt@t6:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t5(t,u),nofnt(xt)):in(ntofn(nofnt(xt)),st)
--5113
-xt@satz113c:=isp(natt,[t:natt]in(t,st),ntofn(nofnt(xt)),xt,t6".5113",isntn2(xt)):in(xt,st)
-@ax3t:=[x:natt]satz113a(x):[x:natt]nis(<x>suct,1t)
-ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz113b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
-ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz113c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
-yt@[n:nis(xt,yt)]
-+51
-t1:=th3"l.imp"(is"n"(nofnt(xt),nofnt(yt)),is(xt,yt),n,[t:is"n"(nofnt(xt),nofnt(yt))]isntin(xt,yt,t)):nis"n"(nofnt(xt),nofnt(yt))
-t2:=satz1(nofnt(xt),nofnt(yt),t1):nis"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
--51
-satz1:=th3"l.imp"(is(<xt>suct,<yt>suct),is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc),t2".51",[t:is(<xt>suct,<yt>suct)]isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,t)):nis(<xt>suct,<yt>suct)
-+54
-xt@x:=nofnt(xt):nat
-[ft:[x:natt]natt]
-prop1t:=all([t:natt]is(<<t>suct>ft,<<t>ft>suct)):'prop'
-prop2t:=and(is(<1t>ft,<xt>suct),prop1t):'prop'
-xt@[f:[x:nat]nat]
-prop1:=all"n"([t:nat]is"n"(<<t>suc>f,<<t>f>suc)):'prop'
-prop2:=and(is"n"(<1>f,<x>suc),prop1):'prop'
-ft@g:=[t:nat]nofnt(<ntofn(t)>ft):[x:nat]nat
-[p:prop2t]
-t1:=ande1(is(<1t>ft,<xt>suct),prop1t,p):is(<1t>ft,<xt>suct)
-t2:=tris(nat,<1>g,nofnt(<xt>suct),<x>suc,isnten(<1t>ft,<xt>suct,t1),isnnt2(<x>suc)):is"n"(<1>g,<x>suc)
-t3:=ande2(is(<1t>ft,<xt>suct),prop1t,p):prop1t
-[u:nat]
-ut:=ntofn(u):natt
-t4:=isf(nat,nat,suc,u,nofnt(ut),isnnt1(u)):is"n"(<u>suc,<nofnt(ut)>suc)
-t5:=isf(nat,nat,g,<u>suc,<nofnt(ut)>suc,t4):is"n"(<<u>suc>g,nofnt(<<ut>suct>ft))
-t6:=<ut>t3:is(<<ut>suct>ft,<<ut>ft>suct)
-t7:=isnten(<<ut>suct>ft,<<ut>ft>suct,t6):is"n"(nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct))
-t8:=isnnt2(<<u>g>suc):is"n"(nofnt(<<ut>ft>suct),<<u>g>suc)
-t9:=tr3is(nat,<<u>suc>g,nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct),<<u>g>suc,t5,t7,t8):is"n"(<<u>suc>g,<<u>g>suc)
-p@t10:=[u:nat]t9(u):prop1(g)
-t11:=andi(is"n"(<1>g,<x>suc),prop1(g),t2,t10):prop2(g)
-xt@[a:[t:natt]natt][b:[t:natt]natt][pa:prop2t(a)][pb:prop2t(b)]
-t12:=onee1([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):amone([t:nat]nat,[u:[t:nat]nat]prop2(u))
-t13:=<t11(b,pb)><t11(a,pa)><g(b)><g(a)>t12:is"e"([t:nat]nat,g(a),g(b))
-[yt:natt]
-y:=nofnt(yt):nat
-t14:=fise(nat,nat,g(a),g(b),t13,y):is"n"(nofnt(<ntofn(y)>a),nofnt(<ntofn(y)>b))
-t15:=isntin(<ntofn(y)>a,<ntofn(y)>b,t14):is(<ntofn(y)>a,<ntofn(y)>b)
-t16:=tr3is(natt,<yt>a,<ntofn(y)>a,<ntofn(y)>b,<yt>b,isf(natt,natt,a,yt,ntofn(y),isntn1(yt)),t15,isf(natt,natt,b,ntofn(y),yt,isntn2(yt))):is(<yt>a,<yt>b)
-pb@t17:=fisi(natt,natt,a,b,[t:natt]t16(t)):is"e"([t:natt]natt,a,b)
-xt@t18:=[u:[t:natt]natt][v:[t:natt]natt][w:prop2t(u)][z:prop2t(v)]t17(u,v,w,z):amone([t:natt]natt,[u:[t:natt]natt]prop2t(u))
-t19:=onee2([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):some"l"([t:nat]nat,[u:[t:nat]nat]prop2(u))
-f@gt:=[t:natt]ntofn(<nofnt(t)>f):[x:natt]natt
-[p:prop2]
-t20:=ande1(is"n"(<1>f,<x>suc),prop1,p):is"n"(<1>f,<x>suc)
-t21:=isf(nat,nat,f,nofnt(1t),1,isnnt2(1)):is"n"(<nofnt(1t)>f,<1>f)
-t22:=isnent(<nofnt(1t)>f,<x>suc,tris(nat,<nofnt(1t)>f,<1>f,<x>suc,t21,t20)):is(<1t>gt,<xt>suct)
-t23:=ande2(is"n"(<1>f,<x>suc),prop1,p):prop1
-[zt:natt]
-z:=nofnt(zt):nat
-t24:=isf(nat,nat,f,nofnt(<zt>suct),<z>suc,isnnt2(<z>suc)):is"n"(<nofnt(<zt>suct)>f,<<z>suc>f)
-t25:=<z>t23:is"n"(<<z>suc>f,<<z>f>suc)
-t26:=isf(nat,nat,suc,<z>f,nofnt(<zt>gt),isnnt1(<z>f)):is"n"(<<z>f>suc,<nofnt(<zt>gt)>suc)
-t27:=isnent(<nofnt(<zt>suct)>f,<nofnt(<zt>gt)>suc,tr3is(nat,<nofnt(<zt>suct)>f,<<z>suc>f,<<z>f>suc,<nofnt(<zt>gt)>suc,t24,t25,t26)):is(<<zt>suct>gt,<<zt>gt>suct)
-p@t28:=[u:natt]t27(u):prop1t(gt)
-t29:=andi(is(<1t>gt,<xt>suct),prop1t(gt),t22,t28):prop2t(gt)
-t30:=somei([t:natt]natt,[u:[t:natt]natt]prop2t(u),gt,t29):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
-xt@t31:=someapp([t:nat]nat,[u:[t:nat]nat]prop2(u),t19,some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u)),[u:[t:nat]nat][v:prop2(u)]t30(u,v)):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
--54
-xt@satz4:=onei([t:natt]natt,[u:[t:natt]natt]prop2t".54"(u),t18".54",t31".54"):one"e"([t:natt]natt,[u:[t:natt]natt]and(is(<1t>u,<xt>suct),all([v:natt]is(<<v>suct>u,<<v>u>suct))))
-yt@pl:=ntofrt(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt))):natt
-+*ii5
-yt@t28:=satz112c(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)):inf(fr(pl"n"(nofnt(xt),nofnt(yt)),1),class(pl"rt"(rtofnt(xt),rtofnt(yt))))
-t29:=isi(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),fr(pl"n"(nofnt(xt),nofnt(yt)),1),fr(pl"n"(nofnt(xt),nofnt(yt)),1),t28,inclass(fr(pl"n"(nofnt(xt),nofnt(yt)),1)),refeq"n"(fr(pl"n"(nofnt(xt),nofnt(yt)),1))):is"rt"(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))))
--ii5
-yt@isplnt:=isrtent(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),natrti"rt"(pl"n"(nofnt(xt),nofnt(yt))),t29".ii5"):is(pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))))
-isntpl:=symis(natt,pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))),isplnt):is(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt))
-ispln:=tris(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(ntofn(pl"n"(nofnt(xt),nofnt(yt)))),nofnt(pl(xt,yt)),isnnt1(pl"n"(nofnt(xt),nofnt(yt))),isnten(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt),isntpl)):is"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)))
-isnpl:=symis(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)),ispln):is"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)))
-[zt:natt]
-+55
-t1:=ispl1"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt),isnpl(xt,yt)):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)))
-t2:=ispl2"n"(pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),nofnt(xt),ispln(yt,zt)):is"n"(pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
-t3:=tr3is(nat,pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)),pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t1,satz5(nofnt(xt),nofnt(yt),nofnt(zt)),t2):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
--55
-satz5:=tr3is(natt,pl(pl(xt,yt),zt),ntofn(pl"n"(nofnt(pl(xt,yt)),nofnt(zt))),ntofn(pl"n"(nofnt(xt),nofnt(pl(yt,zt)))),pl(xt,pl(yt,zt)),isplnt(pl(xt,yt),zt),isnent(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t3".55"),isntpl(xt,pl(yt,zt))):is(pl(pl(xt,yt),zt),pl(xt,pl(yt,zt)))
-diffprop:=is(xt,pl(yt,zt)):'prop'
-[d:diffprop]
-diffprope:=tris(nat,nofnt(xt),nofnt(pl(yt,zt)),pl"n"(nofnt(yt),nofnt(zt)),isnten(xt,pl(yt,zt),d),isnpl(yt,zt)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))
-zt@[d:diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))]
-+*ii5
-d@t30:=tris(nat,nofnt(xt),pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),d,ispln(yt,zt)):is"n"(nofnt(xt),nofnt(pl(yt,zt)))
--ii5
-d@diffpropi:=isntin(xt,pl(yt,zt),t30".ii5"):diffprop
-+59
-yt@it:=is(xt,yt):'prop'
-iit:=some([u:natt]diffprop(xt,yt,u)):'prop'
-iiit:=some([u:natt]diffprop(yt,xt,u)):'prop'
-i:=is"n"(nofnt(xt),nofnt(yt)):'prop'
-ii:=some"n"([u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u)):'prop'
-iii:=some"n"([u:nat]diffprop"n"(nofnt(yt),nofnt(xt),u)):'prop'
-[one:i]
-t1:=or3i1(it,iit,iiit,isntin(xt,yt,one)):or3(it,iit,iiit)
-yt@[two:ii][v:nat][d:diffprop"n"(nofnt(xt),nofnt(yt),v)]
-t2:=isp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),v,nofnt(ntofn(v)),d,isnnt1(v)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(ntofn(v)))
-t3:=somei(natt,[u:natt]diffprop(xt,yt,u),ntofn(v),diffpropi(xt,yt,ntofn(v),t2)):iit
-two@t4:=someapp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),two,iit,[u:nat][v:diffprop"n"(nofnt(xt),nofnt(yt),u)]t3(u,v)):iit
-t5:=or3i2(it,iit,iiit,t4):or3(it,iit,iiit)
-yt@[three:iii]
-t6:=or3i3(it,iit,iiit,t4(yt,xt,three)):or3(it,iit,iiit)
-yt@t7:=or3app(i,ii,iii,or3(it,iit,iiit),satz9a(nofnt(xt),nofnt(yt)),[u:i]t1(u),[u:ii]t5(u),[u:iii]t6(u)):or3(it,iit,iiit)
-[onet:it]
-t8:=isnten(xt,yt,onet):i
-yt@[twot:iit][vt:natt][d:diffprop(xt,yt,vt)]
-t9:=somei(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),nofnt(vt),diffprope(xt,yt,vt,d)):ii
-twot@t10:=someapp(natt,[u:natt]diffprop(xt,yt,u),twot,ii,[u:natt][v:diffprop(xt,yt,u)]t9(u,v)):ii
-yt@[threet:iiit]
-t11:=t10(yt,xt,threet):iii
-yt@t12:=satz9b(nofnt(xt),nofnt(yt)):ec3(i,ii,iii)
-onet@t13:=ec3e12(i,ii,iii,t12,t8):not(ii)
-t14:=th3"l.imp"(iit,ii,t13,[x:iit]t10(x)):not(iit)
-yt@t15:=th1"l.ec"(it,iit,[x:it]t14(x)):ec(it,iit)
-twot@t16:=ec3e23(i,ii,iii,t12,t10):not(iii)
-t17:=th3"l.imp"(iiit,iii,t16,[x:iiit]t11(x)):not(iiit)
-yt@t18:=th1"l.ec"(iit,iiit,[x:iit]t17(x)):ec(iit,iiit)
-threet@t19:=ec3e31(i,ii,iii,t12,t11):not(i)
-t20:=th3"l.imp"(it,i,t19,[x:it]t8(x)):not(it)
-yt@t21:=th1"l.ec"(iiit,it,[x:iiit]t20(x)):ec(iiit,it)
-t22:=th6"l.ec3"(it,iit,iiit,t15,t18,t21):ec3(it,iit,iiit)
--59
-yt@satz9:=orec3i(it".59",iit".59",iiit".59",t7".59",t22".59"):orec3(is(xt,yt),some([u:natt]is(xt,pl(yt,u))),some([u:natt]is(yt,pl(xt,u))))
-more:=more"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[m:more(xt,yt)]
-+*ii5
-m@t31:=moree(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-m@moree:=satz111a(nofnt(xt),nofnt(yt),t31".ii5"):more"n"(nofnt(xt),nofnt(yt))
-yt@[m:more"n"(nofnt(xt),nofnt(yt))]
-+*ii5
-m@t32:=satz111d(nofnt(xt),nofnt(yt),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-m@morei:=morei"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t32".ii5"):more(xt,yt)
-yt@less:=less"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[l:less(xt,yt)]
-+*ii5
-l@t33:=lesse(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-l@lesse:=satz111c(nofnt(xt),nofnt(yt),t33".ii5"):less"n"(nofnt(xt),nofnt(yt))
-yt@[l:less"n"(nofnt(xt),nofnt(yt))]
-+*ii5
-l@t34:=satz111f(nofnt(xt),nofnt(yt),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-l@lessi:=lessi"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t34".ii5"):less(xt,yt)
-yt@moreis:=moreis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[m:moreis(xt,yt)]
-moreise:=th9"l.or"(more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),m,[u:more"rt"(rtofnt(xt),rtofnt(yt))]moree(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis"n"(nofnt(xt),nofnt(yt))
-yt@[m:moreis"n"(nofnt(xt),nofnt(yt))]
-moreisi:=th9"l.or"(more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),m,[u:more"n"(nofnt(xt),nofnt(yt))]morei(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis(xt,yt)
-yt@lessis:=lessis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[l:lessis(xt,yt)]
-lessise:=th9"l.or"(less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),l,[u:less"rt"(rtofnt(xt),rtofnt(yt))]lesse(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis"n"(nofnt(xt),nofnt(yt))
-yt@[l:lessis"n"(nofnt(xt),nofnt(yt))]
-lessisi:=th9"l.or"(less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),l,[u:less"n"(nofnt(xt),nofnt(yt))]lessi(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis(xt,yt)
-zt@[l:less(xt,yt)][k:less(yt,zt)]
-+515
-t1:=satz15(nofnt(xt),nofnt(yt),nofnt(zt),lesse(xt,yt,l),lesse(yt,zt,k)):less"n"(nofnt(xt),nofnt(zt))
--515
-satz15:=lessi(xt,zt,t1".515"):less(xt,zt)
-zt@[ut:natt][m:more(xt,yt)][n:more(zt,ut)]
-+521
-t1:=satz21(nofnt(xt),nofnt(yt),nofnt(zt),nofnt(ut),moree(xt,yt,m),moree(zt,ut,n)):more"n"(pl"n"(nofnt(xt),nofnt(zt)),pl"n"(nofnt(yt),nofnt(ut)))
-t2:=ismore12"n"(pl"n"(nofnt(xt),nofnt(zt)),nofnt(pl(xt,zt)),pl"n"(nofnt(yt),nofnt(ut)),nofnt(pl(yt,ut)),ispln(xt,zt),ispln(yt,ut),t1):more"n"(nofnt(pl(xt,zt)),nofnt(pl(yt,ut)))
--521
-satz21:=morei(pl(xt,zt),pl(yt,ut),t2".521"):more(pl(xt,zt),pl(yt,ut))
-@[p:[x:natt]'prop'][n:natt]
-lb:=all([x:natt]imp(<x>p,lessis(n,x))):'prop'
-min:=and(lb,<n>p):'prop'
-p@[s:some(p)]
-+527
-q:=[x:nat]<ntofn(x)>p:[x:nat]'prop'
-[n:natt][np:<n>p]
-t1:=isp(natt,p,n,ntofn(nofnt(n)),np,isntn1(n)):<nofnt(n)>q
-t2:=somei(nat,q,nofnt(n),t1):some"n"(q)
-s@t3:=someapp(natt,p,s,some"n"(q),[u:natt][v:<u>p]t2(u,v)):some"n"(q)
-t4:=satz27(q,t3):some"n"([x:nat]min"n"(q,x))
-[m:nat][mqm:min"n"(q,m)]
-t5:=ande1(lb"n"(q,m),<m>q,mqm):lb"n"(q,m)
-[n:nat][nq:<n>q]
-t6:=mp(<n>q,lessis"n"(m,n),nq,<n>t5):lessis"n"(m,n)
-mqm@[n:natt][np:<n>p]
-t7:=t6(nofnt(n),t1(n,np)):lessis"n"(m,nofnt(n))
-t8:=islessis1"n"(m,nofnt(ntofn(m)),nofnt(n),isnnt1(m),t7):lessis"n"(nofnt(ntofn(m)),nofnt(n))
-t9:=lessisi(ntofn(m),n,t8):lessis(ntofn(m),n)
-n@t10:=[u:<n>p]t9(u):imp(<n>p,lessis(ntofn(m),n))
-mqm@t11:=[x:natt]t10(x):lb(ntofn(m))
-t12:=ande2(lb"n"(q,m),<m>q,mqm):<ntofn(m)>p
-t13:=andi(lb(ntofn(m)),<ntofn(m)>p,t11,t12):min(ntofn(m))
-t14:=somei(natt,[x:natt]min(x),ntofn(m),t13):some([x:natt]min(x))
--527
-satz27:=someapp(nat,[x:nat]min"n"(q".527",x),t4".527",some([x:natt]min(x)),[x:nat][y:min"n"(q".527",x)]t14".527"(x,y)):some([x:natt]min(p,x))
--nt
-@1rt:=rtofn(1):rat
-x0@[x:frac][xix0:inf(x,class(x0))]
-+*ii5
-xix0@t35:=tr3eq(tf(x,fr(1,1)),fr(ts"n"(num(x),1),ts"n"(den(x),1)),fr(num(x),den(x)),x,tfeq1a(x,1,1),eqnd(ts"n"(num(x),1),ts"n"(den(x),1),num(x),den(x),satz28a(num(x)),satz28a(den(x))),refeq1(fr(num(x),den(x)),x,fris(x))):eq"n"(tf(x,fr(1,1)),x)
-t36:=isi(ts(x0,1rt),x0,tf(x,fr(1,1)),x,tict(x0,1rt,x,fr(1,1),xix0,inclass(fr(1,1))),xix0,t35):is(ts(x0,1rt),x0)
--ii5
-x0@example1a:=ratapp1(x0,is(ts(x0,1rt),x0),[x:frac][xi:inf(x,class(x0))]t36".ii5"(x,xi)):is(ts(x0,1rt),x0)
-example1b:=symis(rat,ts(x0,1rt),x0,example1a):is(x0,ts(x0,1rt))
-example1c:=tris(rat,ts(1rt,x0),ts(x0,1rt),x0,comts(1rt,x0),example1a):is(ts(1rt,x0),x0)
-example1d:=symis(rat,ts(1rt,x0),x0,example1c):is(x0,ts(1rt,x0))
-@[x:frac]
-+5114
-t1:=tr3eq(tf(fr(den(x),1),x),fr(ts"n"(den(x),num(x)),ts"n"(1,den(x))),fr(ts"n"(num(x),den(x)),ts"n"(1,den(x))),fr(num(x),1),tfeq2a(x,den(x),1),eqn(ts"n"(den(x),num(x)),ts"n"(1,den(x)),ts"n"(num(x),den(x)),comts"n"(den(x),num(x))),satz40c(num(x),1,den(x))):eq"n"(tf(fr(den(x),1),x),fr(num(x),1))
--5114
-satz114:=isi(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)),tf(fr(den(x),1),x),fr(num(x),1),tict(rtofn(den(x)),ratof(x),fr(den(x),1),x,inclass(fr(den(x),1)),inclass(x)),inclass(fr(num(x),1)),t1".5114"):is(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)))
-@[x1:nat][x2:nat]
-satz114a:=tr3is(rat,ts(rtofn(x2),ratof(fr(x1,x2))),ts(rtofn(den(fr(x1,x2))),ratof(fr(x1,x2))),rtofn(num(fr(x1,x2))),rtofn(x1),ists1(rtofn(x2),rtofn(den(fr(x1,x2))),ratof(fr(x1,x2)),isnert(x2,den(fr(x1,x2)),isden(x1,x2))),satz114(fr(x1,x2)),isnert(num(fr(x1,x2)),x1,numis(x1,x2))):is(ts(rtofn(x2),ratof(fr(x1,x2))),rtofn(x1))
-x0@[y0:rat]
-ov:=ind(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):rat
-satz110c:=oneax(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):is(ts(y0,ov(x0,y0)),x0)
-satz110d:=symis(rat,ts(y0,ov(x0,y0)),x0,satz110c):is(x0,ts(y0,ov(x0,y0)))
-satz110e:=tris(rat,ts(ov(x0,y0),y0),ts(y0,ov(x0,y0)),x0,comts(ov(x0,y0),y0),satz110c):is(ts(ov(x0,y0),y0),x0)
-satz110f:=symis(rat,ts(ov(x0,y0),y0),x0,satz110e):is(x0,ts(ov(x0,y0),y0))
-[v0:rat][i:is(ts(y0,v0),x0)]
-satz110g:=satz110b(x0,y0,v0,ov(x0,y0),i,satz110c):is(v0,ov(x0,y0))
-x2@satz114b:=satz110b(rtofn(x1),rtofn(x2),ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114a,satz110c(rtofn(x1),rtofn(x2))):is(ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)))
-satz114c:=symis(rat,ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114b):is(ov(rtofn(x1),rtofn(x2)),ratof(fr(x1,x2)))
-+5115
-y0@t1:=satz89(ov(y0,x0)):some([t:rat]more(t,ov(y0,x0)))
-[u0:rat][m:more(u0,ov(y0,x0))][u:frac][uiu0:inf(u,class(u0))]
-z:=num(u):nat
-v:=den(u):nat
-t2:=ismore1(u0,ov(rtofn(z),rtofn(v)),ov(y0,x0),tris(rat,u0,ratof(fr(z,v)),ov(rtofn(z),rtofn(v)),isi(u0,ratof(fr(z,v)),u,fr(z,v),uiu0,inclass(fr(z,v)),refeq1(u,fr(z,v),isfr(u))),satz114b(z,v)),m):more(ov(rtofn(z),rtofn(v)),ov(y0,x0))
-t3:=moreisi(rtofn(v),1rt,fr(v,1),fr(1,1),inclass(fr(v,1)),inclass(fr(1,1)),th9"l.or"(more"n"(v,1),is"n"(v,1),moref(fr(v,1),fr(1,1)),eq"n"(fr(v,1),fr(1,1)),satz24(v),[t:more"n"(v,1)]satz111d(v,1,t),[t:is"n"(v,1)]satz111e(v,1,t))):moreis(rtofn(v),1rt)
-t4:=tr3is(rat,ts(rtofn(z),x0),ts(x0,rtofn(z)),ts(x0,ts(ov(rtofn(z),rtofn(v)),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),comts(rtofn(z),x0),ists2(rtofn(z),ts(ov(rtofn(z),rtofn(v)),rtofn(v)),x0,satz110f(rtofn(z),rtofn(v))),assts2(x0,ov(rtofn(z),rtofn(v)),rtofn(v))):is(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)))
-[n:more(rtofn(v),1rt)]
-t5:=ismore1(ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),symis(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),t4),satz105d(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),n)):more(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-t6:=moreisi1(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t5):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-uiu0@[i:is(rtofn(v),1rt)]
-t7:=moreisi2(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),tris(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t4,ists2(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),i))):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-uiu0@t8:=orapp(more(rtofn(v),1rt),is(rtofn(v),1rt),moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt)),t3,[t:more(rtofn(v),1rt)]t6(t),[t:is(rtofn(v),1rt)]t7(t)):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-t9:=ismore12(ts(x0,ov(rtofn(z),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),ts(x0,ov(y0,x0)),y0,example1b(ts(x0,ov(rtofn(z),rtofn(v)))),satz110c(y0,x0),satz105d(ov(rtofn(z),rtofn(v)),ov(y0,x0),x0,t2)):more(ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0)
-t10:=satz87c(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0,t8,t9):more(ts(rtofn(z),x0),y0)
-t11:=somei(nat,[t:nat]more(ts(rtofn(t),x0),y0),z,t10):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
-m@t12:=ratapp1(u0,some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[u:frac][ui:inf(u,class(u0))]t11(u,ui)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
--5115
-y0@satz115:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[t:rat][u:more(t,ov(y0,x0))]t12".5115"(t,u)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
-+*5115
-uiu0@t13:=andi(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0),natrti(z),t10):and(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0))
-t14:=somei(rat,[t:rat]and(natrt(t),more(ts(t,x0),y0)),rtofn(z),t13):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
-m@t15:=ratapp1(u0,some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[u:frac][ui:inf(u,class(u0))]t14(u,ui)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
--5115
-y0@satz115a:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[t:rat][u:more(t,ov(y0,x0))]t15".5115"(t,u)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
-@[s:set(rat)]
-cutprop1a:=nonempty(rat,s):'prop'
-cutprop1b:=not(all([x:rat]in(x,s))):'prop'
-cutprop1:=and(cutprop1a,cutprop1b):'prop'
-[x0:rat]
-cutprop2a:=all([x:rat]imp(not(in(x,s)),less(x0,x))):'prop'
-s@cutprop2:=all([x:rat]imp(in(x,s),cutprop2a(x))):'prop'
-x0@[y0:rat]
-+iii1
-ubprop:=imp(in(y0,s),moreis(x0,y0)):'prop'
--iii1
-x0@ub:=all([x:rat]ubprop".iii1"(x0,x)):'prop'
-max:=and(ub(x0),in(x0,s)):'prop'
-s@cutprop3:=not(some([x:rat]max(s,x))):'prop'
-cutprop:=and3(cutprop1,cutprop2,cutprop3):'prop'
-+*iii1
-y0@lbprop:=imp(in(y0,s),lessis(x0,y0)):'prop'
--iii1
-x0@lb:=all([x:rat]lbprop".iii1"(x0,x)):'prop'
-min:=and(lb(x0),in(x0,s)):'prop'
-@cut:=ot(set(rat),[x:set(rat)]cutprop(x)):'type'
-[ksi:cut]
-lcl:=in"e"(set(rat),[x:set(rat)]cutprop(x),ksi):set(rat)
-[x0:rat]
-lrt:=in(x0,lcl(ksi)):'prop'
-urt:=not(in(x0,lcl(ksi))):'prop'
-ksi@clcl:=inp(set(rat),[x:set(rat)]cutprop(x),ksi):cutprop(lcl(ksi))
-clcl1:=and3e1(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop1(lcl(ksi))
-clcl2:=and3e2(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop2(lcl(ksi))
-clcl3:=and3e3(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop3(lcl(ksi))
-clcl1a:=ande1(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1a(lcl(ksi))
-clcl1b:=ande2(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1b(lcl(ksi))
-[p:'prop'][p1:[x:rat][t:lrt(ksi,x)]p]
-cutapp1a:=nonemptyapp(rat,lcl,clcl1a,p,p1):p
-+*iii1
-ksi@t1:=th1"l.some"(rat,[x:rat]lrt(ksi,x),clcl1b):some([x:rat]urt(ksi,x))
--iii1
-p@[p1:[x:rat][t:urt(ksi,x)]p]
-cutapp1b:=someapp(rat,[x:rat]urt(ksi,x),t1".iii1",p,p1):p
-ksi@[x0:rat][lx:lrt(ksi,x0)]
-+*iii1
-lx@t2:=mp(lrt(ksi,x0),cutprop2a(lcl,x0),lx,<x0>clcl2):cutprop2a(lcl,x0)
--iii1
-lx@[y0:rat][uy:urt(ksi,y0)]
-cutapp2a:=mp(urt(ksi,y0),less(x0,y0),uy,<y0>t2".iii1"):less(x0,y0)
-cutapp2b:=satz83(x0,y0,cutapp2a):more(y0,x0)
-+*iii1
-lx@t3:=th4"l.some"(rat,[x:rat]max(lcl,x),clcl3,x0):not(max(lcl,x0))
-t4:=th4"l.and"(ub(lcl,x0),lrt(ksi,x0),t3,lx):not(ub(lcl,x0))
-t5:=th1"l.some"(rat,[x:rat]ubprop(lcl,x0,x),t4):some([x:rat]not(ubprop(lcl,x0,x)))
--iii1
-lx@[p:'prop'][p1:[y:rat][t:lrt(ksi,y)][u:less(x0,y)]p][y0:rat][n:not(ubprop".iii1"(lcl,x0,y0))]
-+*iii1
-n@t6:=th5"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):lrt(ksi,y0)
-t7:=th6"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):not(moreis(x0,y0))
-t8:=satz81j(x0,y0,t7):less(x0,y0)
-t9:=<t8><t6><y0>p1:p
--iii1
-p1@cutapp3:=someapp(rat,[y:rat]not(ubprop".iii1"(lcl,x0,y)),t5".iii1",p,[y:rat][t:not(ubprop".iii1"(lcl,x0,y))]t9".iii1"(y,t)):p
-s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))]
-+*iii1
-n@t10:=andi(cutprop1a,cutprop1b,nonemptyi(rat,s,x0,i),th1"l.all"(rat,[x:rat]in(x,s),y0,n)):cutprop1
--iii1
-s@[n:[x:rat]not(max(s,x))]
-+*iii1
-n@t11:=th5"l.some"(rat,[x:rat]max(s,x),n):cutprop3
--iii1
-s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][l:[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]less(x,y)][m:[x:rat]not(max(s,x))]
-cut1:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),l,t11".iii1"(m)):cutprop(s)
-+rp
-ksi@[eta:cut]
-is:=is"e"(cut,ksi,eta):'prop'
-nis:=not(is(ksi,eta)):'prop'
-[i:is(ksi,eta)]
-ise:=isini(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is"e"(set(rat),lcl(ksi),lcl(eta))
-[x0:rat][lx:lrt(ksi,x0)]
-ise1:=issete1(rat,lcl(ksi),lcl(eta),ise,x0,lx):lrt(eta,x0)
-eta@[i:is"e"(set(rat),lcl(ksi),lcl(eta))]
-isi:=isine(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is(ksi,eta)
-eta@[l:[x:rat][t:lrt(ksi,x)]lrt(eta,x)][k:[x:rat][t:lrt(eta,x)]lrt(ksi,x)]
-isi1:=isi(isseti(rat,lcl(ksi),lcl(eta),l,k)):is(ksi,eta)
-@[s:set(rat)][cs:cutprop(s)]
-cutof:=out(set(rat),[x:set(rat)]cutprop(x),s,cs):cut
-[x0:rat][i:in(x0,s)]
-ine:=issete1(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,i):lrt(cutof(s,cs),x0)
-x0@[lx:lrt(cutof(s,cs),x0)]
-ini:=issete2(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,lx):in(x0,s)
-s@[t:set(rat)][cs:cutprop(s)][ct:cutprop(t)][i:[x:rat][u:in(x,s)]in(x,t)][j:[x:rat][u:in(x,t)]in(x,s)]
-isi2:=isouti(set(rat),[x:set(rat)]cutprop(x),s,cs,t,ct,isseti(rat,s,t,i,j)):is(cutof(s,cs),cutof(t,ct))
-@[p:[x:cut]'prop']
-all:=all"l"(cut,p):'prop'
-some:=some"l"(cut,p):'prop'
-one:=one"e"(cut,p):'prop'
-ksi@satz116:=refis(cut,ksi):is(ksi,ksi)
-eta@[i:is(ksi,eta)]
-satz117:=symis(cut,ksi,eta,i):is(eta,ksi)
-eta@[zeta:cut][i:is(ksi,eta)][j:is(eta,zeta)]
-satz118:=tris(cut,ksi,eta,zeta,i,j):is(ksi,zeta)
-+1119
-@[x0:rat][y0:rat][m:more(x0,y0)]
-t1:=ec3e23(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),m):not(less(x0,y0))
--1119
-ksi@[x0:rat][ux:urt(ksi,x0)][y0:rat][m:more(y0,x0)]
-satz119:=th3"l.imp"(lrt(ksi,y0),less(y0,x0),t1".1119"(y0,x0,m),[t:lrt(ksi,y0)]cutapp2a(y0,t,x0,ux)):urt(ksi,y0)
-y0@[l:less(x0,y0)]
-satz119a:=satz119(satz83(x0,y0,l)):urt(ksi,y0)
-+1120
-@[x0:rat][y0:rat][l:less(x0,y0)]
-t1:=ec3e32(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),l):not(more(x0,y0))
--1120
-ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][l:less(y0,x0)]
-satz120:=th7"l.imp"(lrt(ksi,y0),more(y0,x0),t1".1120"(y0,x0,l),[t:urt(ksi,y0)]cutapp2b(x0,lx,y0,t)):lrt(ksi,y0)
-y0@[m:more(x0,y0)]
-satz120a:=satz120(satz82(x0,y0,m)):lrt(ksi,y0)
--rp
-s@[i:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][x0:rat][j:in(x0,s)][y0:rat][n:not(in(y0,s))]
-+*iii1
-n@t12:=<y0><j><x0>i:[u:less(y0,x0)]in(y0,s)
-t13:=th3"l.imp"(less(y0,x0),in(y0,s),n,t12):not(less(y0,x0))
-t14:=satz81f(y0,x0,t13):moreis(y0,x0)
--iii1
-n@[k:is(y0,x0)]
-+*iii1
-k@t15:=isp1(rat,[x:rat]in(x,s),x0,y0,j,k):in(y0,s)
-n@t16:=th3"l.imp"(is(y0,x0),in(y0,s),n,[t:is(y0,x0)]t15(t)):nis(y0,x0)
-t17:=ore1(more(y0,x0),is(y0,x0),t14,t16):more(y0,x0)
-t18:=satz82(y0,x0,t17):less(x0,y0)
-i@t19:=[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]t18(x,t,y,u):cutprop2
--iii1
-s@[s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))][x0:rat][i:in(x0,s)]
-+*iii1
-i@t20:=<i><x0>s1:some([y:rat]and(in(y,s),more(y,x0)))
--iii1
-i@[y0:rat][a:and(in(y0,s),more(y0,x0))]
-+*iii1
-a@t21:=ande1(in(y0,s),more(y0,x0),a):in(y0,s)
-t22:=ande2(in(y0,s),more(y0,x0),a):more(y0,x0)
-t23:=satz81g(y0,x0,t22):not(lessis(y0,x0))
-t24:=th3"l.imp"(moreis(x0,y0),lessis(y0,x0),t23,[t:moreis(x0,y0)]satz84(x0,y0,t)):not(moreis(x0,y0))
-t25:=th4"l.imp"(in(y0,s),moreis(x0,y0),t21,t24):not(ubprop(x0,y0))
-t26:=th1"l.all"(rat,[y:rat]ubprop(x0,y),y0,t25):not(ub(s,x0))
-t27:=th1"l.and"(ub(s,x0),in(x0,s),t26):not(max(s,x0))
-i@t28:=someapp(rat,[y:rat]and(in(y,s),more(y,x0)),t20,not(max(s,x0)),[y:rat][t:and(in(y,s),more(y,x0))]t27(y,t)):not(max(s,x0))
--iii1
-x0@[n:not(in(x0,s))]
-+*iii1
-n@t29:=th2"l.and"(ub(x0),in(x0,s),n):not(max(s,x0))
-x0@t30:=th1"l.imp"(in(x0,s),not(max(s,x0)),[u:in(x0,s)]t28(u),[u:not(in(x0,s))]t29(u)):not(max(s,x0))
-s1@t31:=t11([x:rat]t30(x)):cutprop3
--iii1
-s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][j:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))]
-cut2:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),t19".iii1"(j),t31".iii1"(s1)):cutprop(s)
-+*rp
-eta@more:=some"rt"([x:rat]and(lrt(ksi,x),urt(eta,x))):'prop'
-[m:more(ksi,eta)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]p][x0:rat][a:and(lrt(ksi,x0),urt(eta,x0))]
-+iii2
-t1:=ande1(lrt(ksi,x0),urt(eta,x0),a):lrt(ksi,x0)
-t2:=ande2(lrt(ksi,x0),urt(eta,x0),a):urt(eta,x0)
-t3:=<t2><t1><x0>p1:p
--iii2
-p1@moreapp:=someapp(rat,[x:rat]and(lrt(ksi,x),urt(eta,x)),m,p,[x:rat][t:and(lrt(ksi,x),urt(eta,x))]t3".iii2"(x,t)):p
-eta@less:=some"rt"([x:rat]and(urt(ksi,x),lrt(eta,x))):'prop'
-[l:less(ksi,eta)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]p][x0:rat][a:and(urt(ksi,x0),lrt(eta,x0))]
-+*iii2
-a@t4:=ande1(urt(ksi,x0),lrt(eta,x0),a):urt(ksi,x0)
-t5:=ande2(urt(ksi,x0),lrt(eta,x0),a):lrt(eta,x0)
-t6:=<t5><t4><x0>p1:p
--iii2
-p1@lessapp:=someapp(rat,[x:rat]and(urt(ksi,x),lrt(eta,x)),l,p,[x:rat][t:and(urt(ksi,x),lrt(eta,x))]t6".iii2"(x,t)):p
-eta@[m:more(ksi,eta)]
-+2121
-[x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
-t1:=andi(urt(eta,x0),lrt(ksi,x0),ux,lx):and(urt(eta,x0),lrt(ksi,x0))
-t2:=somei(rat,[x:rat]and(urt(eta,x),lrt(ksi,x)),x0,t1):less(eta,ksi)
--2121
-satz121:=moreapp(m,less(eta,ksi),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2".2121"(x,t,u)):less(eta,ksi)
-eta@[l:less(ksi,eta)]
-+2122
-[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
-t1:=andi(lrt(eta,x0),urt(ksi,x0),lx,ux):and(lrt(eta,x0),urt(ksi,x0))
-t2:=somei(rat,[x:rat]and(lrt(eta,x),urt(ksi,x)),x0,t1):more(eta,ksi)
--2122
-satz122:=lessapp(l,more(eta,ksi),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t2".2122"(x,t,u)):more(eta,ksi)
-+2123
-eta@[m:more(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
-t1:=th3"st.isset"(rat,lcl(ksi),lcl(eta),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
-t2:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t1,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
-m@t3:=moreapp(ksi,eta,m,not(is(ksi,eta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2(x,t,u)):not(is(ksi,eta))
-eta@t4:=th2"l.ec"(is(ksi,eta),more(ksi,eta),[t:more(ksi,eta)]t3(t)):ec(is(ksi,eta),more(ksi,eta))
-[l:less(ksi,eta)][x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
-t5:=th4"st.isset"(rat,lcl(eta),lcl(ksi),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
-t6:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t5,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
-l@t7:=lessapp(ksi,eta,l,not(is(ksi,eta)),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t6(x,t,u)):not(is(ksi,eta))
-eta@t8:=th1"l.ec"(less(ksi,eta),is(ksi,eta),[t:less(ksi,eta)]t7(t)):ec(less(ksi,eta),is(ksi,eta))
-m@[l:less(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)][y0:rat][uy:urt(ksi,y0)][ly:lrt(eta,y0)]
-t9:=cutapp2a(ksi,x0,lx,y0,uy):less"rt"(x0,y0)
-t10:=cutapp2b(eta,y0,ly,x0,ux):more"rt"(x0,y0)
-t11:=mp(less"rt"(x0,y0),con,t9,ec3e23(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),satz81b(x0,y0),t10)):con
-ux@t12:=lessapp(ksi,eta,l,con,[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t11(x,t,u)):con
-l@t13:=moreapp(ksi,eta,m,con,[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t12(x,t,u)):con
-m@t14:=[t:less(ksi,eta)]t13(t):not(less(ksi,eta))
-eta@t15:=th1"l.ec"(more(ksi,eta),less(ksi,eta),[t:more(ksi,eta)]t14(t)):ec(more(ksi,eta),less(ksi,eta))
-a:=th6"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t4,t15,t8):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-[i:is(ksi,eta)]
-t16:=or3i1(is(ksi,eta),more(ksi,eta),less(ksi,eta),i):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-eta@[n:nis(ksi,eta)]
-t17:=th3"l.imp"(is"e"(set(rat),lcl(ksi),lcl(eta)),is(ksi,eta),n,[t:is"e"(set(rat),lcl(ksi),lcl(eta))]isi(ksi,eta,t)):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
-t18:=th5"st.isset"(rat,lcl(ksi),lcl(eta),t17):or(more(ksi,eta),more(eta,ksi))
-t19:=th8"l.or"(more(ksi,eta),more(eta,ksi),less(ksi,eta),t18,[t:more(eta,ksi)]satz121(eta,ksi,t)):or(more(ksi,eta),less(ksi,eta))
-t20:=th7"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t19):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-eta@b:=th1"l.imp"(is(ksi,eta),or3(is(ksi,eta),more(ksi,eta),less(ksi,eta)),[t:is(ksi,eta)]t16(t),[t:nis(ksi,eta)]t20(t)):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
--2123
-eta@satz123:=orec3i(is(ksi,eta),more(ksi,eta),less(ksi,eta),b".2123",a".2123"):orec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-satz123a:=orec3e1(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-satz123b:=orec3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-moreis:=or(more(ksi,eta),is(ksi,eta)):'prop'
-lessis:=or(less(ksi,eta),is(ksi,eta)):'prop'
-[m:moreis(ksi,eta)]
-satz124:=th9"l.or"(more(ksi,eta),is(ksi,eta),less(eta,ksi),is(eta,ksi),m,[t:more(ksi,eta)]satz121(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):lessis(eta,ksi)
-eta@[l:lessis(ksi,eta)]
-satz125:=th9"l.or"(less(ksi,eta),is(ksi,eta),more(eta,ksi),is(eta,ksi),l,[t:less(ksi,eta)]satz122(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):moreis(eta,ksi)
-zeta@[i:is(ksi,eta)][m:more(ksi,zeta)]
-ismore1:=isp(cut,[u:cut]more(u,zeta),ksi,eta,m,i):more(eta,zeta)
-i@[m:more(zeta,ksi)]
-ismore2:=isp(cut,[u:cut]more(zeta,u),ksi,eta,m,i):more(zeta,eta)
-i@[l:less(ksi,zeta)]
-isless1:=isp(cut,[u:cut]less(u,zeta),ksi,eta,l,i):less(eta,zeta)
-i@[l:less(zeta,ksi)]
-isless2:=isp(cut,[u:cut]less(zeta,u),ksi,eta,l,i):less(zeta,eta)
-i@[m:moreis(ksi,zeta)]
-ismoreis1:=isp(cut,[u:cut]moreis(u,zeta),ksi,eta,m,i):moreis(eta,zeta)
-i@[m:moreis(zeta,ksi)]
-ismoreis2:=isp(cut,[u:cut]moreis(zeta,u),ksi,eta,m,i):moreis(zeta,eta)
-i@[l:lessis(ksi,zeta)]
-islessis1:=isp(cut,[u:cut]lessis(u,zeta),ksi,eta,l,i):lessis(eta,zeta)
-i@[l:lessis(zeta,ksi)]
-islessis2:=isp(cut,[u:cut]lessis(zeta,u),ksi,eta,l,i):lessis(zeta,eta)
-eta@[i:is(ksi,eta)]
-moreisi2:=ori2(more(ksi,eta),is(ksi,eta),i):moreis(ksi,eta)
-lessisi2:=ori2(less(ksi,eta),is(ksi,eta),i):lessis(ksi,eta)
-eta@[m:more(ksi,eta)]
-moreisi1:=ori1(more(ksi,eta),is(ksi,eta),m):moreis(ksi,eta)
-eta@[l:less(ksi,eta)]
-lessisi1:=ori1(less(ksi,eta),is(ksi,eta),l):lessis(ksi,eta)
-zeta@[upsilon:cut][i:is(ksi,eta)][j:is(zeta,upsilon)][m:more(ksi,zeta)]
-ismore12:=ismore2(zeta,upsilon,eta,j,ismore1(ksi,eta,zeta,i,m)):more(eta,upsilon)
-j@[l:less(ksi,zeta)]
-isless12:=isless2(zeta,upsilon,eta,j,isless1(ksi,eta,zeta,i,l)):less(eta,upsilon)
-j@[m:moreis(ksi,zeta)]
-ismoreis12:=ismoreis2(zeta,upsilon,eta,j,ismoreis1(ksi,eta,zeta,i,m)):moreis(eta,upsilon)
-j@[l:lessis(ksi,zeta)]
-islessis12:=islessis2(zeta,upsilon,eta,j,islessis1(ksi,eta,zeta,i,l)):lessis(eta,upsilon)
-eta@[m:moreis(ksi,eta)]
-satz123c:=th7"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,comor(more(ksi,eta),is(ksi,eta),m)):not(less(ksi,eta))
-eta@[l:lessis(ksi,eta)]
-satz123d:=th9"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l):not(more(ksi,eta))
-eta@[n:not(more(ksi,eta))]
-satz123e:=th2"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n):lessis(ksi,eta)
-eta@[n:not(less(ksi,eta))]
-satz123f:=comor(is(ksi,eta),more(ksi,eta),th3"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n)):moreis(ksi,eta)
-eta@[m:more(ksi,eta)]
-satz123g:=th3"l.or"(less(ksi,eta),is(ksi,eta),ec3e23(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m),ec3e21(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m)):not(lessis(ksi,eta))
-eta@[l:less(ksi,eta)]
-satz123h:=th3"l.or"(more(ksi,eta),is(ksi,eta),ec3e32(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l),ec3e31(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l)):not(moreis(ksi,eta))
-eta@[n:not(moreis(ksi,eta))]
-satz123j:=or3e3(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th5"l.or"(more(ksi,eta),is(ksi,eta),n),th4"l.or"(more(ksi,eta),is(ksi,eta),n)):less(ksi,eta)
-eta@[n:not(lessis(ksi,eta))]
-satz123k:=or3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th4"l.or"(less(ksi,eta),is(ksi,eta),n),th5"l.or"(less(ksi,eta),is(ksi,eta),n)):more(ksi,eta)
-zeta@[l:less(ksi,eta)][k:less(eta,zeta)]
-+2126
-[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)][y0:rat][uy:urt(eta,y0)][ly:lrt(zeta,y0)]
-t1:=cutapp2a(eta,x0,lx,y0,uy):less"rt"(x0,y0)
-t2:=satz119a(ksi,x0,ux,y0,t1):urt(ksi,y0)
-t3:=andi(urt(ksi,y0),lrt(zeta,y0),t2,ly):and(urt(ksi,y0),lrt(zeta,y0))
-t4:=somei(rat,[x:rat]and(urt(ksi,x),lrt(zeta,x)),y0,t3):less(ksi,zeta)
-lx@t5:=lessapp(eta,zeta,k,less(ksi,zeta),[x:rat][t:urt(eta,x)][u:lrt(zeta,x)]t4(x,t,u)):less(ksi,zeta)
--2126
-satz126:=lessapp(ksi,eta,l,less(ksi,zeta),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t5".2126"(x,t,u)):less(ksi,zeta)
-trless:=satz126:less(ksi,zeta)
-zeta@[m:more(ksi,eta)][n:more(eta,zeta)]
-trmore:=satz122(zeta,ksi,satz126(zeta,eta,ksi,satz121(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
-zeta@[l:lessis(ksi,eta)][k:less(eta,zeta)]
-satz127a:=orapp(less(ksi,eta),is(ksi,eta),less(ksi,zeta),l,[u:less(ksi,eta)]trless(u,k),[u:is(ksi,eta)]isless1(eta,ksi,zeta,symis(cut,ksi,eta,u),k)):less(ksi,zeta)
-zeta@[l:less(ksi,eta)][k:lessis(eta,zeta)]
-satz127b:=orapp(less(eta,zeta),is(eta,zeta),less(ksi,zeta),k,[u:less(eta,zeta)]trless(l,u),[u:is(eta,zeta)]isless2(eta,zeta,ksi,u,l)):less(ksi,zeta)
-zeta@[m:moreis(ksi,eta)][n:more(eta,zeta)]
-satz127c:=satz122(zeta,ksi,satz127b(zeta,eta,ksi,satz121(eta,zeta,n),satz124(ksi,eta,m))):more(ksi,zeta)
-zeta@[m:more(ksi,eta)][n:moreis(eta,zeta)]
-satz127d:=satz122(zeta,ksi,satz127a(zeta,eta,ksi,satz124(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
-zeta@[l:lessis(ksi,eta)][k:lessis(eta,zeta)]
-+2128
-[i:is(ksi,eta)][j:is(eta,zeta)]
-t1:=lessisi2(ksi,zeta,tris(cut,ksi,eta,zeta,i,j)):lessis(ksi,zeta)
-i@[j:less(eta,zeta)]
-t2:=lessisi1(ksi,zeta,satz127a(l,j)):lessis(ksi,zeta)
-i@t3:=orapp(less(eta,zeta),is(eta,zeta),lessis(ksi,zeta),k,[t:less(eta,zeta)]t2(t),[t:is(eta,zeta)]t1(t)):lessis(ksi,zeta)
-k@[j:less(ksi,eta)]
-t4:=lessisi1(ksi,zeta,satz127b(j,k)):lessis(ksi,zeta)
--2128
-satz128:=orapp(less(ksi,eta),is(ksi,eta),lessis(ksi,zeta),l,[t:less(ksi,eta)]t4".2128"(t),[t:is(ksi,eta)]t3".2128"(t)):lessis(ksi,zeta)
-trlessis:=satz128:lessis(ksi,zeta)
-zeta@[m:moreis(ksi,eta)][n:moreis(eta,zeta)]
-trmoreis:=satz125(zeta,ksi,satz128(zeta,eta,ksi,satz124(eta,zeta,n),satz124(ksi,eta,m))):moreis(ksi,zeta)
-eta@[z0:rat][x0:rat][y0:rat]
-sumprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0))):'prop'
-z0@sumprop:=some"rt"([x:rat]some"rt"([y:rat]sumprop1(z0,x,y))):'prop'
-eta@sum:=setof(rat,[z:rat]sumprop(z)):set(rat)
-x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl(x0,y0))]
-+iii3
-t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),lx,ly,i):sumprop1(z0,x0,y0)
-t2:=somei(rat,[y:rat]sumprop1(z0,x0,y),y0,t1):some"rt"([y:rat]sumprop1(z0,x0,y))
-t3:=somei(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),x0,t2):sumprop(z0)
--iii3
-sum1:=estii(rat,[z:rat]sumprop(z),z0,t3".iii3"):in(z0,sum)
-z0@[i:in(z0,sum)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]p]
-+*iii3
-p1@t4:=estie(rat,[z:rat]sumprop(z),z0,i):sumprop(z0)
--iii3
-p1@[x0:rat][px:some"rt"([y:rat]sumprop1(z0,x0,y))][y0:rat][py:sumprop1(z0,x0,y0)]
-+*iii3
-py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(ksi,x0)
-t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(eta,y0)
-t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):is"rt"(z0,pl(x0,y0))
-t8:=<t7><t6><y0><t5><x0>p1:p
-px@t9:=someapp(rat,[y:rat]sumprop1(z0,x0,y),px,p,[y:rat][t:sumprop1(z0,x0,y)]t8(y,t)):p
--iii3
-p1@sumapp:=someapp(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),t4".iii3",p,[x:rat][t:some"rt"([y:rat]sumprop1(z0,x,y))]t9".iii3"(x,t)):p
-eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-+3129
-[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))]
-t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
-t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
-t3:=isless1"rt"(pl(x0,y0),z0,pl(x1,y1),symis(rat,z0,pl(x0,y0),j),satz98a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,pl(x1,y1))
-t4:=ec3e31(is"rt"(z0,pl(x1,y1)),more"rt"(z0,pl(x1,y1)),less"rt"(z0,pl(x1,y1)),satz81b(z0,pl(x1,y1)),t3):nis"rt"(z0,pl(x1,y1))
-i@t5:=sumapp(ksi,eta,z0,i,nis"rt"(z0,pl(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,pl(x1,y1))
--3129
-satz129a:=th3"l.imp"(in(pl(x1,y1),sum),nis"rt"(pl(x1,y1),pl(x1,y1)),weli(is"rt"(pl(x1,y1),pl(x1,y1)),refis(rat,pl(x1,y1))),[t:in(pl(x1,y1),sum)]t5".3129"(pl(x1,y1),t)):not(in(pl(x1,y1),sum))
-+*3129
-eta@[u0:rat][i:in(u0,sum)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,pl(x0,y0))]
-t6:=isless2"rt"(u0,pl(x0,y0),z0,j,l):less"rt"(z0,pl(x0,y0))
-z1:=ov(z0,pl(x0,y0)):rat
-t7:=isless12"rt"(z0,ts(z1,pl(x0,y0)),pl(x0,y0),ts(1rt,pl(x0,y0)),satz110f(z0,pl(x0,y0)),example1d(pl(x0,y0)),t6):less"rt"(ts(z1,pl(x0,y0)),ts(1rt,pl(x0,y0)))
-t8:=satz106c(z1,1rt,pl(x0,y0),t7):less"rt"(z1,1rt)
-t9:=isless2"rt"(ts(x0,1rt),x0,ts(x0,z1),example1a(x0),satz105f(z1,1rt,x0,t8)):less"rt"(ts(x0,z1),x0)
-t10:=isless2"rt"(ts(y0,1rt),y0,ts(y0,z1),example1a(y0),satz105f(z1,1rt,y0,t8)):less"rt"(ts(y0,z1),y0)
-t11:=satz120(ksi,x0,lx,ts(x0,z1),t9):lrt(ksi,ts(x0,z1))
-t12:=satz120(eta,y0,ly,ts(y0,z1),t10):lrt(eta,ts(y0,z1))
-t13:=tris(rat,pl(ts(x0,z1),ts(y0,z1)),ts(pl(x0,y0),z1),z0,distpt1(x0,y0,z1),satz110c(z0,pl(x0,y0))):is"rt"(pl(ts(x0,z1),ts(y0,z1)),z0)
-t14:=symis(rat,pl(ts(x0,z1),ts(y0,z1)),z0,t13):is"rt"(z0,pl(ts(x0,z1),ts(y0,z1)))
-t15:=sum1(ksi,eta,z0,ts(x0,z1),t11,ts(y0,z1),t12,t14):in(z0,sum)
-l@t16:=sumapp(ksi,eta,u0,i,in(z0,sum),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,pl(x,y))]t15(x,t,y,u,v)):in(z0,sum)
-eta@[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
-t17:=sum1(ksi,eta,pl(x1,y0),x1,lx1,y0,ly,refis(rat,pl(x1,y0))):in(pl(x1,y0),sum)
-t18:=satz96a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(pl(x1,y0),pl(x0,y0))
-t19:=ismore2"rt"(pl(x0,y0),z0,pl(x1,y0),symis(rat,z0,pl(x0,y0),j),t18):more"rt"(pl(x1,y0),z0)
-t20:=andi(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0),t17,t19):and(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0))
-t21:=somei(rat,[y:rat]and(in(y,sum),more"rt"(y,z0)),pl(x1,y0),t20):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
-j@t22:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t21(x,t,u)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
-i@t23:=sumapp(ksi,eta,z0,i,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t22(x,t,y,u,v)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
-eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-t24:=cut2(sum,pl(x0,y0),sum1(ksi,eta,pl(x0,y0),x0,lx,y0,ly,refis(rat,pl(x0,y0))),pl(x1,y1),satz129a(x1,ux,y1,uy),[x:rat][t:in(x,sum)][y:rat][u:less"rt"(y,x)]t16(x,t,y,u),[x:rat][t:in(x,sum)]t23(x,t)):cutprop(sum)
-ux@t25:=cutapp1b(eta,cutprop(sum),[y:rat][t:urt(eta,y)]t24(y,t)):cutprop(sum)
-ly@t26:=cutapp1b(ksi,cutprop(sum),[x:rat][t:urt(ksi,x)]t25(x,t)):cutprop(sum)
-lx@t27:=cutapp1a(eta,cutprop(sum),[y:rat][t:lrt(eta,y)]t26(y,t)):cutprop(sum)
--3129
-eta@satz129:=cutapp1a(ksi,cutprop(sum),[x:rat][t:lrt(ksi,x)]t27".3129"(x,t)):cutprop(sum)
-pl:=cutof(sum,satz129):cut
-[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
-lrtpl:=ine(sum,satz129,z0,sum1(z0,x0,lx,y0,ly,i)):lrt(pl(ksi,eta),z0)
-eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
-+*iii3
-i@t10:=isp1(rat,[x:rat]not(in(x,sum)),pl"rt"(x0,y0),z0,satz129a(x0,ux,y0,uy),i):not(in(z0,sum))
--iii3
-i@urtpl:=th3"l.imp"(lrt(pl(ksi,eta),z0),in(z0,sum),t10".iii3",[t:lrt(pl(ksi,eta),z0)]ini(sum,satz129,z0,t)):urt(pl(ksi,eta),z0)
-eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]p]
-+*iii3
-p1@t11:=ini(sum,satz129,z0,lz):in(z0,sum)
--iii3
-p1@plapp:=sumapp(z0,t11".iii3",p,p1):p
-zeta@[i:is(ksi,eta)]
-ispl1:=isf(cut,cut,[u:cut]pl(u,zeta),ksi,eta,i):is(pl(ksi,zeta),pl(eta,zeta))
-ispl2:=isf(cut,cut,[u:cut]pl(zeta,u),ksi,eta,i):is(pl(zeta,ksi),pl(zeta,eta))
-upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
-ispl12:=tris(cut,pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),ispl1(i),ispl2(zeta,upsilon,eta,j)):is(pl(ksi,zeta),pl(eta,upsilon))
-+3130
-eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
-t1:=tris(rat,z0,pl"rt"(x0,y0),pl"rt"(y0,x0),i,compl(x0,y0)):is"rt"(z0,pl"rt"(y0,x0))
-t2:=lrtpl(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(pl(eta,ksi),z0)
-lz@t3:=plapp(ksi,eta,z0,lz,lrt(pl(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]t2(x,t,y,u,v)):lrt(pl(eta,ksi),z0)
--3130
-eta@satz130:=isi1(pl(ksi,eta),pl(eta,ksi),[x:rat][t:lrt(pl(ksi,eta),x)]t3".3130"(x,t),[x:rat][t:lrt(pl(eta,ksi),x)]t3".3130"(eta,ksi,x,t)):is(pl(ksi,eta),pl(eta,ksi))
-compl:=satz130:is(pl(ksi,eta),pl(eta,ksi))
-+3131
-zeta@[u0:rat][lu:lrt(pl(pl(ksi,eta),zeta),u0)][v0:rat][lv:lrt(pl(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,pl"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,pl"rt"(x0,y0))]
-t1:=tr3is(rat,u0,pl"rt"(v0,z0),pl"rt"(pl"rt"(x0,y0),z0),pl"rt"(x0,pl"rt"(y0,z0)),i,ispl1"rt"(v0,pl"rt"(x0,y0),z0,j),asspl1(x0,y0,z0)):is"rt"(u0,pl"rt"(x0,pl"rt"(y0,z0)))
-t2:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
-t3:=lrtpl(ksi,pl(eta,zeta),u0,x0,lx,pl"rt"(y0,z0),t2,t1):lrt(pl(ksi,pl(eta,zeta)),u0)
-i@t4:=plapp(ksi,eta,v0,lv,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,pl"rt"(x,y))]t3(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
-lu@t5:=plapp(pl(ksi,eta),zeta,u0,lu,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(pl(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
-u0@[lu:lrt(pl(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,pl"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
-t6:=tr3is(rat,u0,pl"rt"(x0,v0),pl"rt"(x0,pl"rt"(y0,z0)),pl"rt"(pl"rt"(x0,y0),z0),i,ispl2"rt"(v0,pl"rt"(y0,z0),x0,j),asspl2(x0,y0,z0)):is"rt"(u0,pl"rt"(pl"rt"(x0,y0),z0))
-t7:=lrtpl(ksi,eta,pl"rt"(x0,y0),x0,lx,y0,ly,refis(rat,pl"rt"(x0,y0))):lrt(pl(ksi,eta),pl"rt"(x0,y0))
-t8:=lrtpl(pl(ksi,eta),zeta,u0,pl"rt"(x0,y0),t7,z0,lz,t6):lrt(pl(pl(ksi,eta),zeta),u0)
-i@t9:=plapp(eta,zeta,v0,lv,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t8(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
-lu@t10:=plapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t9(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
--3131
-zeta@satz131:=isi1(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),[x:rat][t:lrt(pl(pl(ksi,eta),zeta),x)]t5".3131"(x,t),[x:rat][t:lrt(pl(ksi,pl(eta,zeta)),x)]t10".3131"(x,t)):is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
-asspl1:=satz131:is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
-asspl2:=symis(cut,pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),satz131):is(pl(ksi,pl(eta,zeta)),pl(pl(ksi,eta),zeta))
-ksi@[a0:rat]
-+3132
-[x0:rat][y0:rat]
-prop1:=and(lrt(ksi,x0),urt(ksi,y0)):'prop'
-[p:prop1]
-t1:=cutapp2b(x0,ande1(lrt(ksi,x0),urt(ksi,y0),p),y0,ande2(lrt(ksi,x0),urt(ksi,y0),p)):more"rt"(y0,x0)
-prop2:=is"rt"(mn(y0,x0,t1),a0):'prop'
-y0@prop3:=and(prop1,[t:prop1]prop2(t)):'prop'
-a0@prop4:=some"rt"([x:rat]some"rt"([y:rat]prop3(x,y))):'prop'
-x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
-t2:=cutapp2b(x0,lx,y0,uy):more"rt"(y0,x0)
-[n:nat][m:more"rt"(ts(rtofn(n),a0),mn(y0,x0,t2))]
-t3:=satz96d(ts(rtofn(n),a0),mn(y0,x0,t2),x0,m):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),pl"rt"(x0,mn(y0,x0,t2)))
-t4:=ismore2"rt"(pl"rt"(x0,mn(y0,x0,t2)),y0,pl"rt"(x0,ts(rtofn(n),a0)),satz101c(y0,x0,t2),t3):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),y0)
-t5:=satz119(y0,uy,pl"rt"(x0,ts(rtofn(n),a0)),t4):urt(pl"rt"(x0,ts(rtofn(n),a0)))
-t6:=somei(nat,[x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),n,t5):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
-uy@t7:=someapp(nat,[x:nat]more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2)),satz115(a0,mn(y0,x0,t2)),some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0)))),[x:nat][t:more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2))]t6(x,t)):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
-[u:nat][m:min"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)]
-t8:=ande1(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)
-t9:=ande2(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):urt(pl"rt"(x0,ts(rtofn(u),a0)))
-[i:is"n"(u,1)]
-u0:=pl"rt"(x0,a0):rat
-t10:=tr3is(rat,ts(rtofn(u),a0),ts(1rt,a0),ts(a0,1rt),a0,ists1(rtofn(u),1rt,a0,isnert(u,1,i)),comts(1rt,a0),example1a(a0)):is"rt"(ts(rtofn(u),a0),a0)
-t11:=isp(rat,[x:rat]urt(pl"rt"(x0,x)),ts(rtofn(u),a0),a0,t9,t10):urt(ksi,u0)
-t12:=andi(lrt(ksi,x0),urt(ksi,u0),lx,t11):prop1(x0,u0)
-[p:prop1(x0,u0)]
-t13:=symis(rat,a0,mn(u0,x0,t1(x0,u0,p)),satz101g(u0,x0,a0,t1(x0,u0,p),refis(rat,u0))):prop2(x0,u0,p)
-i@t14:=andi(prop1(x0,u0),[t:prop1(x0,u0)]prop2(x0,u0,t),t12,[t:prop1(x0,u0)]t13(t)):prop3(x0,u0)
-t15:=somei(rat,[y:rat]prop3(x0,y),u0,t14):some"rt"([y:rat]prop3(x0,y))
-t16:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),x0,t15):prop4
-m@[o:more"n"(u,1)]
-t17:=morei(rtofn(u),1rt,fr(u,1),fr(1,1),inclass(fr(u,1)),inclass(fr(1,1)),satz111d(u,1,o)):more"rt"(rtofn(u),1rt)
-um10:=mn(rtofn(u),1rt,t17):rat
-t18:=satz112g(rtofn(u),natrti(u),1rt,natrti(1),t17):natrt(um10)
-um1:=nofrt(um10,t18):nat
-v0:=pl"rt"(x0,ts(um10,a0)):rat
-w0:=pl"rt"(x0,ts(rtofn(u),a0)):rat
-t19:=isless2"rt"(pl"rt"(um10,1rt),rtofn(u),um10,satz101e(rtofn(u),1rt,t17),satz94a(um10,1rt)):less"rt"(um10,rtofn(u))
-t20:=lesse(um10,rtofn(u),fr(um1,1),fr(u,1),inclassn(um10,t18),inclass(fr(u,1)),t19):lessf(fr(um1,1),fr(u,1))
-t21:=satz111c(um1,u,t20):less"n"(um1,u)
-t22:=th3"l.imp"(lessis"n"(u,um1),moreis"n"(um1,u),satz10h(um1,u,t21),[t:lessis"n"(u,um1)]satz14(u,um1,t)):not(lessis"n"(u,um1))
-t23:=et(lrt(pl"rt"(x0,ts(rtofn(um1),a0))),th3"l.imp"(urt(pl"rt"(x0,ts(rtofn(um1),a0))),lessis"n"(u,um1),t22,<um1>t8)):lrt(pl"rt"(x0,ts(rtofn(um1),a0)))
-t24:=isp1(rat,[x:rat]lrt(pl"rt"(x0,ts(x,a0))),rtofn(um1),um10,t23,isrtn1(um10,t18)):lrt(ksi,v0)
-t25:=andi(lrt(ksi,v0),urt(ksi,w0),t24,t9):prop1(v0,w0)
-t26:=tr3is(rat,pl"rt"(ts(um10,a0),a0),pl"rt"(ts(um10,a0),ts(1rt,a0)),ts(pl"rt"(um10,1rt),a0),ts(rtofn(u),a0),ispl2"rt"(a0,ts(1rt,a0),ts(um10,a0),example1d(a0)),distpt1(um10,1rt,a0),ists1(pl"rt"(um10,1rt),rtofn(u),a0,satz101e(rtofn(u),1rt,t17))):is"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0))
-t27:=tris(rat,pl"rt"(v0,a0),pl"rt"(x0,pl"rt"(ts(um10,a0),a0)),w0,asspl1"rt"(x0,ts(um10,a0),a0),ispl2"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0),x0,t26)):is"rt"(pl"rt"(v0,a0),w0)
-[p:prop1(v0,w0)]
-t28:=symis(rat,a0,mn(w0,v0,t1(v0,w0,p)),satz101g(w0,v0,a0,t1(v0,w0,p),t27)):prop2(v0,w0,p)
-o@t29:=andi(prop1(v0,w0),[t:prop1(v0,w0)]prop2(v0,w0,t),t25,[t:prop1(v0,w0)]t28(t)):prop3(v0,w0)
-t30:=somei(rat,[y:rat]prop3(v0,y),w0,t29):some"rt"([y:rat]prop3(v0,y))
-t31:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),v0,t30):prop4
-m@t32:=orapp(more"n"(u,1),is"n"(u,1),prop4,satz24(u),[t:more"n"(u,1)]t31(t),[t:is"n"(u,1)]t16(t)):prop4
-uy@t34:=someapp(nat,[x:nat]min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x),satz27([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),t7),prop4,[x:nat][t:min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x)]t32(x,t)):prop4
-lx@t35:=cutapp1b(prop4,[y:rat][t:urt(ksi,y)]t34(y,t)):prop4
--3132
-satz132:=cutapp1a(prop4".3132",[x:rat][t:lrt(ksi,x)]t35".3132"(x,t)):some"rt"([x:rat]some"rt"([y:rat]and(and(lrt(ksi,x),urt(ksi,y)),[t:and(lrt(ksi,x),urt(ksi,y))]is"rt"(mn(y,x,cutapp2b(x,ande1(lrt(ksi,x),urt(ksi,y),t),y,ande2(lrt(ksi,x),urt(ksi,y),t))),a0))))
-ksi@[p:'prop'][a0:rat][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),a0)]p]
-+*3132
-p1@[x0:rat][s:some"rt"([y:rat]prop3(a0,x0,y))][y0:rat][p3:prop3(a0,x0,y0)]
-t36:=ande1(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop1(a0,x0,y0)
-t37:=ande2"l.r"(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop2(a0,x0,y0,t36)
-t38:=ande1(lrt(ksi,x0),urt(ksi,y0),t36):lrt(ksi,x0)
-t39:=ande2(lrt(ksi,x0),urt(ksi,y0),t36):urt(ksi,y0)
-t40:=satz101g(y0,x0,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),t1(a0,x0,y0,t36),satz101c(y0,x0,cutapp2b(x0,t38,y0,t39))):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)))
-t41:=tris(rat,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)),a0,t40,t37):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),a0)
-t42:=<t41><t39><y0><t38><x0>p1:p
-s@t43:=someapp(rat,[y:rat]prop3(a0,x0,y),s,p,[y:rat][t:prop3(a0,x0,y)]t42(y,t)):p
--3132
-p1@satz132app:=someapp(rat,[x:rat]some"rt"([y:rat]prop3".3132"(a0,x,y)),satz132(a0),p,[x:rat][t:some"rt"([y:rat]prop3".3132"(a0,x,y))]t43".3132"(x,t)):p
-+3133
-eta@[y0:rat][ly:lrt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][uu:urt(ksi,u0)][i:is"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0)]
-t1:=tris(rat,u0,pl"rt"(x0,mn(u0,x0,cutapp2b(x0,lx,u0,uu))),pl"rt"(x0,y0),satz101d(u0,x0,cutapp2b(x0,lx,u0,uu)),ispl2"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0,x0,i)):is"rt"(u0,pl"rt"(x0,y0))
-t2:=lrtpl(ksi,eta,u0,x0,lx,y0,ly,t1):lrt(pl(ksi,eta),u0)
-t3:=andi(lrt(pl(ksi,eta),u0),urt(ksi,u0),t2,uu):and(lrt(pl(ksi,eta),u0),urt(ksi,u0))
-t4:=somei(rat,[x:rat]and(lrt(pl(ksi,eta),x),urt(ksi,x)),u0,t3):more(pl(ksi,eta),ksi)
-ly@t5:=satz132app(ksi,more(pl(ksi,eta),ksi),y0,[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),y0)]t4(x,t,y,u,v)):more(pl(ksi,eta),ksi)
--3133
-eta@satz133:=cutapp1a(eta,more(pl(ksi,eta),ksi),[x:rat][t:lrt(eta,x)]t5".3133"(x,t)):more(pl(ksi,eta),ksi)
-satz133a:=satz121(pl(ksi,eta),ksi,satz133):less(ksi,pl(ksi,eta))
-zeta@[m:more(ksi,eta)]
-+3134
-[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
-t1:=satz119a(eta,y0,uy,x0,l):urt(eta,x0)
-t2:=satz83(y0,x0,l):more"rt"(x0,y0)
-[u0:rat][lu:lrt(zeta,u0)][z0:rat][uz:urt(zeta,z0)][i:is"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2))]
-t3:=tris(rat,z0,pl"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),u0),pl"rt"(mn(x0,y0,t2),u0),satz101f(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),ispl1"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2),u0,i)):is"rt"(z0,pl"rt"(mn(x0,y0,t2),u0))
-t4:=tr3is(rat,pl"rt"(y0,z0),pl"rt"(y0,pl"rt"(mn(x0,y0,t2),u0)),pl"rt"(pl"rt"(y0,mn(x0,y0,t2)),u0),pl"rt"(x0,u0),ispl2"rt"(z0,pl"rt"(mn(x0,y0,t2),u0),y0,t3),asspl2"rt"(y0,mn(x0,y0,t2),u0),ispl1"rt"(pl"rt"(y0,mn(x0,y0,t2)),x0,u0,satz101c(x0,y0,t2))):is"rt"(pl"rt"(y0,z0),pl"rt"(x0,u0))
-t5:=lrtpl(ksi,zeta,pl"rt"(y0,z0),x0,lx,u0,lu,t4):lrt(pl(ksi,zeta),pl"rt"(y0,z0))
-t6:=urtpl(eta,zeta,pl"rt"(y0,z0),y0,uy,z0,uz,refis(rat,pl"rt"(y0,z0))):urt(pl(eta,zeta),pl"rt"(y0,z0))
-t7:=andi(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)),t5,t6):and(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)))
-t8:=somei(rat,[x:rat]and(lrt(pl(ksi,zeta),x),urt(pl(eta,zeta),x)),pl"rt"(y0,z0),t7):more(pl(ksi,zeta),pl(eta,zeta))
-l@t9:=satz132app(zeta,more(pl(ksi,zeta),pl(eta,zeta)),mn(x0,y0,t2),[x:rat][t:lrt(zeta,x)][y:rat][u:urt(zeta,y)][v:is"rt"(mn(y,x,cutapp2b(zeta,x,t,y,u)),mn(x0,y0,t2))]t8(x,t,y,u,v)):more(pl(ksi,zeta),pl(eta,zeta))
-uy@t10:=cutapp3(ksi,y0,ly,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t9(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
--3134
-satz134:=moreapp(ksi,eta,m,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t10".3134"(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
-zeta@[m:more(ksi,eta)]
-satz135a:=satz134(m):more(pl(ksi,zeta),pl(eta,zeta))
-zeta@[i:is(ksi,eta)]
-satz135b:=ispl1(ksi,eta,zeta,i):is(pl(ksi,zeta),pl(eta,zeta))
-zeta@[l:less(ksi,eta)]
-satz135c:=satz121(pl(eta,zeta),pl(ksi,zeta),satz134(eta,ksi,zeta,satz122(ksi,eta,l))):less(pl(ksi,zeta),pl(eta,zeta))
-m@satz135d:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135a):more(pl(zeta,ksi),pl(zeta,eta))
-i@satz135e:=ispl2(ksi,eta,zeta,i):is(pl(zeta,ksi),pl(zeta,eta))
-l@satz135f:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135c):less(pl(zeta,ksi),pl(zeta,eta))
-upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
-satz135g:=ismore2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135d(zeta,upsilon,ksi,m)):more(pl(ksi,zeta),pl(eta,upsilon))
-satz135h:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135g):more(pl(zeta,ksi),pl(upsilon,eta))
-i@[l:less(zeta,upsilon)]
-satz135j:=isless2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135f(zeta,upsilon,ksi,l)):less(pl(ksi,zeta),pl(eta,upsilon))
-satz135k:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135j):less(pl(zeta,ksi),pl(upsilon,eta))
-+3136
-zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-t2:=satz123b(pl(ksi,zeta),pl(eta,zeta)):ec3(is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)))
--3136
-zeta@[m:more(pl(ksi,zeta),pl(eta,zeta))]
-satz136a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),m):more(ksi,eta)
-zeta@[i:is(pl(ksi,zeta),pl(eta,zeta))]
-satz136b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),i):is(ksi,eta)
-zeta@[l:less(pl(ksi,zeta),pl(eta,zeta))]
-satz136c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),l):less(ksi,eta)
-zeta@[m:more(pl(zeta,ksi),pl(zeta,eta))]
-satz136d:=satz136a(ismore12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),m)):more(ksi,eta)
-zeta@[i:is(pl(zeta,ksi),pl(zeta,eta))]
-satz136e:=satz136b(tr3is(cut,pl(ksi,zeta),pl(zeta,ksi),pl(zeta,eta),pl(eta,zeta),compl(ksi,zeta),i,compl(zeta,eta))):is(ksi,eta)
-zeta@[l:less(pl(zeta,ksi),pl(zeta,eta))]
-satz136f:=satz136c(isless12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),l)):less(ksi,eta)
-upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
-+3137
-t1:=satz134(ksi,eta,zeta,m):more(pl(ksi,zeta),pl(eta,zeta))
-t2:=ismore12(pl(zeta,eta),pl(eta,zeta),pl(upsilon,eta),pl(eta,upsilon),compl(zeta,eta),compl(upsilon,eta),satz134(zeta,upsilon,eta,n)):more(pl(eta,zeta),pl(eta,upsilon))
--3137
-satz137:=trmore(pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),t1".3137",t2".3137"):more(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
-satz137a:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz137(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
-satz138a:=orapp(more(ksi,eta),is(ksi,eta),more(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]satz137(t,n),[t:is(ksi,eta)]satz135g(t,n)):more(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
-satz138b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]satz137(m,t),[t:is(zeta,upsilon)]satz135h(zeta,upsilon,ksi,eta,t,m)):more(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
-satz138c:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
-satz138d:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
-+3139
-[i:is(ksi,eta)][j:is(zeta,upsilon)]
-t1:=moreisi2(pl(ksi,zeta),pl(eta,upsilon),ispl12(ksi,eta,zeta,upsilon,i,j)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-i@[o:more(zeta,upsilon)]
-t2:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138a(m,o)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-n@[o:more(ksi,eta)]
-t4:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138b(o,n)):moreis(pl(ksi,zeta),pl(eta,upsilon))
--3139
-satz139:=orapp(more(ksi,eta),is(ksi,eta),moreis(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]t4".3139"(t),[t:is(ksi,eta)]t3".3139"(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
-satz139a:=satz124(pl(eta,upsilon),pl(ksi,zeta),satz139(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(pl(ksi,zeta),pl(eta,upsilon))
-eta@[l:lessis(ksi,eta)]
-+3140
-[phi:cut][i:is(pl(eta,phi),ksi)]
-t1:=ismore1(pl(eta,phi),ksi,eta,i,satz133(eta,phi)):more(ksi,eta)
-phi@t2:=th3"l.imp"(is(pl(eta,phi),ksi),more(ksi,eta),satz123d(ksi,eta,l),[t:is(pl(eta,phi),ksi)]t1(t)):nis(pl(eta,phi),ksi)
--3140
-vorbemerkung140:=th5"l.some"(cut,[a:cut]is(pl(eta,a),ksi),[a:cut]t2".3140"(a)):not(some([a:cut]is(pl(eta,a),ksi)))
-eta@[phi:cut][psi:cut]
-+*3140
-psi@[m:more(phi,psi)]
-t3:=satz135d(phi,psi,eta,m):more(pl(eta,phi),pl(eta,psi))
-t4:=ec3e21(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t3):nis(pl(eta,phi),pl(eta,psi))
-psi@[l:less(phi,psi)]
-t5:=satz135f(phi,psi,eta,l):less(pl(eta,phi),pl(eta,psi))
-t6:=ec3e31(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t5):nis(pl(eta,phi),pl(eta,psi))
-psi@[n:nis(phi,psi)]
-t7:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
-t8:=orapp(more(phi,psi),less(phi,psi),nis(pl(eta,phi),pl(eta,psi)),t7,[t:more(phi,psi)]t4(t),[t:less(phi,psi)]t6(t)):nis(pl(eta,phi),pl(eta,psi))
--3140
-psi@[i:is(pl(eta,phi),ksi)][j:is(pl(eta,psi),ksi)]
-satz140b:=th7"l.imp"(is(phi,psi),nis(pl(eta,phi),pl(eta,psi)),weli(is(pl(eta,phi),pl(eta,psi)),tris2(cut,pl(eta,phi),pl(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t8".3140"(t)):is(phi,psi)
-eta@[z0:rat][x0:rat][y0:rat]
-diffprop1:=and(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t))):'prop'
-diffprop2:=and3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0)):'prop'
-z0@diffprop:=some"rt"([x:rat]some"rt"([y:rat]diffprop2(z0,x,y))):'prop'
-eta@diff:=setof(rat,[z:rat]diffprop(z)):set(rat)
-x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][m:more"rt"(x0,y0)][i:is"rt"(z0,mn(x0,y0,m))]
-+*iii3
-i@[m1:more"rt"(x0,y0)]
-t11a:=tris(rat,z0,mn(x0,y0,m),mn(x0,y0,m1),i,satz101g(x0,y0,mn(x0,y0,m),m1,satz101c(x0,y0,m))):is"rt"(z0,mn(x0,y0,m1))
-i@t12:=andi(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),m,[t:more"rt"(x0,y0)]t11a(t)):diffprop1(z0,x0,y0)
-t13:=and3i(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),lx,uy,t12):diffprop2(z0,x0,y0)
-t14:=somei(rat,[y:rat]diffprop2(z0,x0,y),y0,t13):some"rt"([y:rat]diffprop2(z0,x0,y))
-t15:=somei(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),x0,t14):diffprop(z0)
--iii3
-i@diff1:=estii(rat,[z:rat]diffprop(z),z0,t15".iii3"):in(z0,diff)
-z0@[i:in(z0,diff)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]p]
-+*iii3
-p1@t16:=estie(rat,[z:rat]diffprop(z),z0,i):diffprop(z0)
--iii3
-p1@[x0:rat][px:some"rt"([y:rat]diffprop2(z0,x0,y))][y0:rat][py:diffprop2(z0,x0,y0)]
-+*iii3
-py@t17:=and3e1(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):lrt(ksi,x0)
-t18:=and3e2(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):urt(eta,y0)
-t19:=and3e3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):diffprop1(z0,x0,y0)
-t20:=ande1(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):more"rt"(x0,y0)
-t21:=ande2"l.r"(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):is"rt"(z0,mn(x0,y0,t20))
-t22:=<t21><t20><t18><y0><t17><x0>p1:p
-px@t23:=someapp(rat,[y:rat]diffprop2(z0,x0,y),px,p,[y:rat][t:diffprop2(z0,x0,y)]t22(y,t)):p
--iii3
-p1@diffapp:=someapp(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),t16".iii3",p,[x:rat][t:some"rt"([y:rat]diffprop2(z0,x,y))]t23".iii3"(x,t)):p
-eta@[m:more(ksi,eta)]
-+*3140
-m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
-t9:=t2"rp.3134"(eta,m,y0,ly,uy,x0,lx,l):more"rt"(x0,y0)
-t10:=diff1(mn(x0,y0,t9),x0,lx,y0,uy,t9,refis(rat,mn(x0,y0,t9))):in(mn(x0,y0,t9),diff)
-m"rp"@[x1:rat][ux:urt(ksi,x1)][z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
-t11:=isless12"rt"(mn(x0,y0,n),z0,pl"rt"(mn(x0,y0,n),y0),x0,symis(rat,z0,mn(x0,y0,n),j),satz101e(x0,y0,n),satz94a(mn(x0,y0,n),y0)):less"rt"(z0,x0)
-t12:=trless"rt"(z0,x0,x1,t11,cutapp2a(ksi,x0,lx,x1,ux)):less"rt"(z0,x1)
-t13:=ec3e31(is"rt"(z0,x1),more"rt"(z0,x1),less"rt"(z0,x1),satz81b(z0,x1),t12):nis"rt"(z0,x1)
-i@t14:=diffapp(z0,i,nis"rt"(z0,x1),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t13(x,t,y,u,v,w)):nis"rt"(z0,x1)
-ux@t15:=th3"l.imp"(in(x1,diff),nis"rt"(x1,x1),weli(is"rt"(x1,x1),refis(rat,x1)),[t:in(x1,diff)]t14(x1,t)):not(in(x1,diff))
-m"rp"@[z0:rat][i:in(z0,diff)][u0:rat][l:less"rt"(u0,z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
-t16:=tris(rat,pl"rt"(z0,y0),pl"rt"(mn(x0,y0,n),y0),x0,ispl1"rt"(z0,mn(x0,y0,n),y0,j),satz101e(x0,y0,n)):is"rt"(pl"rt"(z0,y0),x0)
-x2:=pl"rt"(u0,y0):rat
-t17:=isless2"rt"(pl"rt"(z0,y0),x0,x2,t16,satz96c(u0,z0,y0,l)):less"rt"(x2,x0)
-t18:=satz120(ksi,x0,lx,x2,t17):lrt(ksi,x2)
-t19:=ismore1"rt"(pl"rt"(y0,u0),pl"rt"(u0,y0),y0,compl"rt"(y0,u0),satz94(y0,u0)):more"rt"(x2,y0)
-t20:=satz101g(x2,y0,u0,t19,compl"rt"(y0,u0)):is"rt"(u0,mn(x2,y0,t19))
-t21:=diff1(u0,x2,t18,y0,uy,t19,t20):in(u0,diff)
-l@t22:=diffapp(z0,i,in(u0,diff),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t21(x,t,y,u,v,w)):in(u0,diff)
-m"rp"@[z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))][x3:rat][lx3:lrt(ksi,x3)][l:less"rt"(x0,x3)]
-t23:=satz83(x0,x3,l):more"rt"(x3,x0)
-t24:=trmore"rt"(x3,x0,y0,t23,n):more"rt"(x3,y0)
-t25:=ismore12"rt"(x3,pl"rt"(mn(x3,y0,t24),y0),x0,pl"rt"(mn(x0,y0,n),y0),satz101f(x3,y0,t24),satz101f(x0,y0,n),t23):more"rt"(pl"rt"(mn(x3,y0,t24),y0),pl"rt"(mn(x0,y0,n),y0))
-t26:=satz97a(mn(x3,y0,t24),mn(x0,y0,n),y0,t25):more"rt"(mn(x3,y0,t24),mn(x0,y0,n))
-t27:=ismore2"rt"(mn(x0,y0,n),z0,mn(x3,y0,t24),symis(rat,z0,mn(x0,y0,n),j),t26):more"rt"(mn(x3,y0,t24),z0)
-t28:=diff1(mn(x3,y0,t24),x3,lx3,y0,uy,t24,refis(rat,mn(x3,y0,t24))):in(mn(x3,y0,t24),diff)
-t29:=andi(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0),t28,t27):and(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0))
-t30:=somei(rat,[x:rat]and(in(x,diff),more"rt"(x,z0)),mn(x3,y0,t24),t29):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
-j@t31:=cutapp3(ksi,x0,lx,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t30(y,t,u)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
-i@t32:=diffapp(z0,i,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t31(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
-m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)][x1:rat][ux1:urt(ksi,x1)]
-t33:=cut2(diff,mn(x0,y0,t9(y0,ly,uy,x0,lx,l)),t10(y0,ly,uy,x0,lx,l),x1,t15(x1,ux1),[x:rat][t:in(x,diff)][y:rat][u:less"rt"(y,x)]t22(x,t,y,u),[x:rat][t:in(x,diff)]t32(x,t)):cutprop(diff)
-l@t34:=cutapp1b(ksi,cutprop(diff),[x:rat][t:urt(ksi,x)]t33(x,t)):cutprop(diff)
-uy@t35:=cutapp3(ksi,y0,ly,cutprop(diff),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t34(x,t,u)):cutprop(diff)
--3140
-m@satz140h:=moreapp(ksi,eta,m,cutprop(diff),[x:rat][u:lrt(ksi,x)][v:urt(eta,x)]t35".3140"(x,u,v)):cutprop(diff)
-+*3140
-m"rp"@chi:=cutof(diff,satz140h):cut
-[z0:rat][lz:lrt(pl(eta,chi),z0)][y1:rat][ly:lrt(eta,y1)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,pl"rt"(y1,u0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][o:more"rt"(x0,y0)][j:is"rt"(u0,mn(x0,y0,o))]
-t36:=cutapp2b(eta,y1,ly,y0,uy):more"rt"(y0,y1)
-t37:=tr3is(rat,pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),pl"rt"(mn(x0,y0,o),pl"rt"(y1,mn(y0,y1,t36))),pl"rt"(mn(x0,y0,o),y0),x0,asspl1"rt"(mn(x0,y0,o),y1,mn(y0,y1,t36)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t36)),y0,mn(x0,y0,o),satz101c(y0,y1,t36)),satz101e(x0,y0,o)):is"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0)
-t38:=isless2"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0,pl"rt"(mn(x0,y0,o),y1),t37,satz94a(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36))):less"rt"(pl"rt"(mn(x0,y0,o),y1),x0)
-t39:=tr3is(rat,z0,pl"rt"(y1,u0),pl"rt"(u0,y1),pl"rt"(mn(x0,y0,o),y1),i,compl"rt"(y1,u0),ispl1"rt"(u0,mn(x0,y0,o),y1,j)):is"rt"(z0,pl"rt"(mn(x0,y0,o),y1))
-t40:=isless1"rt"(pl"rt"(mn(x0,y0,o),y1),z0,x0,symis(rat,z0,pl"rt"(mn(x0,y0,o),y1),t39),t38):less"rt"(z0,x0)
-t41:=satz120(ksi,x0,lx,z0,t40):lrt(ksi,z0)
-i@t42:=diffapp(u0,ini(diff,satz140h,u0,lu),lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(u0,mn(x,y,v))]t41(x,t,y,u,v,w)):lrt(ksi,z0)
-lz@a:=plapp(eta,chi,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,pl"rt"(x,y))]t42(x,t,y,u,v)):lrt(ksi,z0)
-m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
-t43:=satz83(y0,x0,l):more"rt"(x0,y0)
-[y1:rat][ly1:lrt(eta,y1)][y2:rat][uy2:urt(eta,y2)]
-t44:=cutapp2b(eta,y1,ly1,y2,uy2):more"rt"(y2,y1)
-[i:is"rt"(mn(y2,y1,t44),mn(x0,y0,t43))]
-t45:=cutapp2b(eta,y1,ly1,y0,uy):more"rt"(y0,y1)
-t46:=tris(rat,y2,pl"rt"(mn(y2,y1,t44),y1),pl"rt"(mn(x0,y0,t43),y1),satz101f(y2,y1,t44),ispl1"rt"(mn(y2,y1,t44),mn(x0,y0,t43),y1,i)):is"rt"(y2,pl"rt"(mn(x0,y0,t43),y1))
-t47:=tr4is(rat,pl"rt"(y2,mn(y0,y1,t45)),pl"rt"(pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45)),pl"rt"(mn(x0,y0,t43),pl"rt"(y1,mn(y0,y1,t45))),pl"rt"(mn(x0,y0,t43),y0),x0,ispl1"rt"(y2,pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45),t46),asspl1"rt"(mn(x0,y0,t43),y1,mn(y0,y1,t45)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t45)),y0,mn(x0,y0,t43),satz101c(y0,y1,t45)),satz101e(x0,y0,t43)):is"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0)
-t48:=ismore1"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0,y2,t47,satz94(y2,mn(y0,y1,t45))):more"rt"(x0,y2)
-t49:=satz101g(x0,y2,mn(y0,y1,t45),t48,t47):is"rt"(mn(y0,y1,t45),mn(x0,y2,t48))
-t50:=tris(rat,y0,pl"rt"(mn(y0,y1,t45),y1),pl"rt"(mn(x0,y2,t48),y1),satz101f(y0,y1,t45),ispl1"rt"(mn(y0,y1,t45),mn(x0,y2,t48),y1,t49)):is"rt"(y0,pl"rt"(mn(x0,y2,t48),y1))
-t51:=ine(diff,satz140h,mn(x0,y2,t48),diff1(mn(x0,y2,t48),x0,lx,y2,uy2,t48,refis(rat,mn(x0,y2,t48)))):lrt(chi,mn(x0,y2,t48))
-t52:=lrtpl(eta,chi,y0,y1,ly1,mn(x0,y2,t48),t51,tris(rat,y0,pl"rt"(mn(x0,y2,t48),y1),pl"rt"(y1,mn(x0,y2,t48)),t50,compl"rt"(mn(x0,y2,t48),y1))):lrt(pl(eta,chi),y0)
-l@t53:=satz132app(eta,lrt(pl(eta,chi),y0),mn(x0,y0,t43),[x:rat][t:lrt(eta,x)][y:rat][u:urt(eta,y)][v:is"rt"(mn(y,x,cutapp2b(eta,x,t,y,u)),mn(x0,y0,t43))]t52(x,t,y,u,v)):lrt(pl(eta,chi),y0)
-uy@t54:=cutapp3(ksi,y0,ly,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t53(x,t,u)):lrt(pl(eta,chi),y0)
-ly@[ly0:lrt(eta,y0)][y1:rat][ly1:lrt(ksi,y1)][uy1:urt(eta,y1)]
-t55:=t54(y1,ly1,uy1):lrt(pl(eta,chi),y1)
-t56:=satz120(pl(eta,chi),y1,t55,y0,cutapp2a(eta,y0,ly0,y1,uy1)):lrt(pl(eta,chi),y0)
-ly0@t57:=moreapp(ksi,eta,m,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t56(x,t,u)):lrt(pl(eta,chi),y0)
-ly@b:=th1"l.imp"(lrt(eta,y0),lrt(pl(eta,chi),y0),[t:lrt(eta,y0)]t57(t),[t:urt(eta,y0)]t54(t)):lrt(pl(eta,chi),y0)
-m"rp"@t58:=isi1(pl(eta,chi),ksi,[x:rat][t:lrt(pl(eta,chi),x)]a(x,t),[x:rat][t:lrt(ksi,x)]b(x,t)):is(pl(eta,chi),ksi)
--3140
-m@satz140a:=somei(cut,[a:cut]is(pl(eta,a),ksi),chi".3140",t58".3140"):some([a:cut]is(pl(eta,a),ksi))
-+*3140
-eta@t59:=[c:cut][d:cut][t:is(pl(eta,c),ksi)][u:is(pl(eta,d),ksi)]satz140b(c,d,t,u):amone(cut,[c:cut]is(pl(eta,c),ksi))
--3140
-m@satz140:=onei(cut,[a:cut]is(pl(eta,a),ksi),t59".3140",satz140a):one([a:cut]is(pl(eta,a),ksi))
-mn:=ind(cut,[a:cut]is(pl(eta,a),ksi),satz140):cut
-satz140c:=oneax(cut,[a:cut]is(pl(eta,a),ksi),satz140):is(pl(eta,mn(ksi,eta,m)),ksi)
-satz140d:=symis(cut,pl(eta,mn(ksi,eta,m)),ksi,satz140c):is(ksi,pl(eta,mn(ksi,eta,m)))
-satz140e:=tris(cut,pl(mn(ksi,eta,m),eta),pl(eta,mn(ksi,eta,m)),ksi,compl(mn(ksi,eta,m),eta),satz140c):is(pl(mn(ksi,eta,m),eta),ksi)
-satz140f:=symis(cut,pl(mn(ksi,eta,m),eta),ksi,satz140e):is(ksi,pl(mn(ksi,eta,m),eta))
-eta@[phi:cut][m:more(ksi,eta)][i:is(pl(eta,phi),ksi)]
-satz140g:=satz140b(phi,mn(ksi,eta,m),i,satz140c(m)):is(phi,mn(ksi,eta,m))
-upsilon@[m:more(ksi,zeta)][n:more(eta,upsilon)][i:is(ksi,eta)][j:is(zeta,upsilon)]
-+*3140
-j"rp"@t60:=tr3is(cut,pl(upsilon,mn(ksi,zeta,m)),pl(zeta,mn(ksi,zeta,m)),ksi,eta,ispl1(upsilon,zeta,mn(ksi,zeta,m),symis(cut,zeta,upsilon,j)),satz140c(ksi,zeta,m),i):is(pl(upsilon,mn(ksi,zeta,m)),eta)
--3140
-j@ismn12:=satz140g(eta,upsilon,mn(ksi,zeta,m),n,t60".3140"):is(mn(ksi,zeta,m),mn(eta,upsilon,n))
-zeta@[m:more(ksi,zeta)][n:more(eta,zeta)][i:is(ksi,eta)]
-ismn1:=ismn12(zeta,m,n,i,refis(cut,zeta)):is(mn(ksi,zeta,m),mn(eta,zeta,n))
-zeta@[m:more(zeta,ksi)][n:more(zeta,eta)][i:is(ksi,eta)]
-ismn2:=ismn12(zeta,zeta,ksi,eta,m,n,refis(cut,zeta),i):is(mn(zeta,ksi,m),mn(zeta,eta,n))
-eta@[z0:rat][x0:rat][y0:rat]
-prodprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0))):'prop'
-z0@prodprop:=some"rt"([x:rat]some"rt"([y:rat]prodprop1(z0,x,y))):'prop'
-eta@prod:=setof(rat,[z:rat]prodprop(z)):set(rat)
-x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts(x0,y0))]
-+iii4
-t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),lx,ly,i):prodprop1(z0,x0,y0)
-t2:=somei(rat,[y:rat]prodprop1(z0,x0,y),y0,t1):some"rt"([y:rat]prodprop1(z0,x0,y))
-t3:=somei(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),x0,t2):prodprop(z0)
--iii4
-prod1:=estii(rat,[z:rat]prodprop(z),z0,t3".iii4"):in(z0,prod)
-z0@[i:in(z0,prod)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]p]
-+*iii4
-p1@t4:=estie(rat,[z:rat]prodprop(z),z0,i):prodprop(z0)
--iii4
-p1@[x0:rat][px:some"rt"([y:rat]prodprop1(z0,x0,y))][y0:rat][py:prodprop1(z0,x0,y0)]
-+*iii4
-py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(ksi,x0)
-t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(eta,y0)
-t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):is"rt"(z0,ts(x0,y0))
-t8:=<t7><t6><y0><t5><x0>p1:p
-px@t9:=someapp(rat,[y:rat]prodprop1(z0,x0,y),px,p,[y:rat][t:prodprop1(z0,x0,y)]t8(y,t)):p
--iii4
-p1@prodapp:=someapp(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),t4".iii4",p,[x:rat][t:some"rt"([y:rat]prodprop1(z0,x,y))]t9".iii4"(x,t)):p
-eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-+4141
-[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))]
-t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
-t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
-t3:=isless1"rt"(ts(x0,y0),z0,ts(x1,y1),symis(rat,z0,ts(x0,y0),j),satz107a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,ts(x1,y1))
-t4:=ec3e31(is"rt"(z0,ts(x1,y1)),more"rt"(z0,ts(x1,y1)),less"rt"(z0,ts(x1,y1)),satz81b(z0,ts(x1,y1)),t3):nis"rt"(z0,ts(x1,y1))
-i@t5:=prodapp(ksi,eta,z0,i,nis"rt"(z0,ts(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,ts(x1,y1))
--4141
-satz141a:=th3"l.imp"(in(ts(x1,y1),prod),nis"rt"(ts(x1,y1),ts(x1,y1)),weli(is"rt"(ts(x1,y1),ts(x1,y1)),refis(rat,ts(x1,y1))),[t:in(ts(x1,y1),prod)]t5".4141"(ts(x1,y1),t)):not(in(ts(x1,y1),prod))
--rp
-@[x0:rat][y0:rat]
-+4141
-v0:=ts(ov(1rt,y0),x0):rat
-t6:=tr3is(rat,ts(y0,v0),ts(ts(y0,ov(1rt,y0)),x0),ts(1rt,x0),x0,assts2(y0,ov(1rt,y0),x0),ists1(ts(y0,ov(1rt,y0)),1rt,x0,satz110c(1rt,y0)),example1c(x0)):is(ts(y0,v0),x0)
--4141
-satz141b:=satz110g(x0,y0,v0".4141",t6".4141"):is(ts(ov(1rt,y0),x0),ov(x0,y0))
-satz141c:=symis(rat,ts(ov(1rt,y0),x0),ov(x0,y0),satz141b):is"rt"(ov(x0,y0),ts(ov(1rt,y0),x0))
-+*rp
-+*4141
-eta@[u0:rat][i:in(u0,prod)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,ts(x0,y0))]
-t7:=isless2"rt"(u0,ts(x0,y0),z0,j,l):less"rt"(z0,ts(x0,y0))
-t8:=tr3is(rat,ts(ov(1rt,x0),ts(x0,y0)),ts(ts(ov(1rt,x0),x0),y0),ts(1rt,y0),y0,assts2(ov(1rt,x0),x0,y0),ists1(ts(ov(1rt,x0),x0),1rt,y0,satz110e(1rt,x0)),example1c(y0)):is"rt"(ts(ov(1rt,x0),ts(x0,y0)),y0)
-t9:=isless12"rt"(ts(ov(1rt,x0),z0),ov(z0,x0),ts(ov(1rt,x0),ts(x0,y0)),y0,satz141b(z0,x0),t8,satz105f(z0,ts(x0,y0),ov(1rt,x0),t7)):less"rt"(ov(z0,x0),y0)
-t10:=satz120(eta,y0,ly,ov(z0,x0),t9):lrt(eta,ov(z0,x0))
-t11:=prod1(z0,x0,lx,ov(z0,x0),t10,satz110d(z0,x0)):in(z0,prod)
-l@t12:=prodapp(u0,i,in(z0,prod),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,ts(x,y))]t11(x,t,y,u,v)):in(z0,prod)
-eta@[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
-t13:=prod1(ts(x1,y0),x1,lx1,y0,ly,refis(rat,ts(x1,y0))):in(ts(x1,y0),prod)
-t14:=satz105a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(ts(x1,y0),ts(x0,y0))
-t15:=ismore2"rt"(ts(x0,y0),z0,ts(x1,y0),symis(rat,z0,ts(x0,y0),j),t14):more"rt"(ts(x1,y0),z0)
-t16:=andi(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0),t13,t15):and(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0))
-t17:=somei(rat,[y:rat]and(in(y,prod),more"rt"(y,z0)),ts(x1,y0),t16):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
-j@t18:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t17(x,t,u)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
-i@t19:=prodapp(z0,i,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t18(x,t,y,u,v)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
-eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-t20:=cut2(prod,ts(x0,y0),prod1(ts(x0,y0),x0,lx,y0,ly,refis(rat,ts(x0,y0))),ts(x1,y1),satz141a(x1,ux,y1,uy),[x:rat][t:in(x,prod)][y:rat][u:less"rt"(y,x)]t12(x,t,y,u),[x:rat][t:in(x,prod)]t19(x,t)):cutprop(prod)
-ux@t21:=cutapp1b(eta,cutprop(prod),[y:rat][t:urt(eta,y)]t20(y,t)):cutprop(prod)
-ly@t22:=cutapp1b(ksi,cutprop(prod),[x:rat][t:urt(ksi,x)]t21(x,t)):cutprop(prod)
-lx@t23:=cutapp1a(eta,cutprop(prod),[y:rat][t:lrt(eta,y)]t22(y,t)):cutprop(prod)
--4141
-eta@satz141:=cutapp1a(ksi,cutprop(prod),[x:rat][t:lrt(ksi,x)]t23".4141"(x,t)):cutprop(prod)
-ts:=cutof(prod,satz141):cut
-[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-lrtts:=ine(prod,satz141,z0,prod1(z0,x0,lx,y0,ly,i)):lrt(ts(ksi,eta),z0)
-eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-+*iii4
-i@t10:=isp1(rat,[x:rat]not(in(x,prod)),ts"rt"(x0,y0),z0,satz141a(x0,ux,y0,uy),i):not(in(z0,prod))
--iii4
-i@urtts:=th3"l.imp"(lrt(ts(ksi,eta),z0),in(z0,prod),t10".iii4",[t:lrt(ts(ksi,eta),z0)]ini(prod,satz141,z0,t)):urt(ts(ksi,eta),z0)
-eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]p]
-+*iii4
-p1@t11:=ini(prod,satz141,z0,lz):in(z0,prod)
--iii4
-p1@tsapp:=prodapp(z0,t11".iii4",p,p1):p
-zeta@[i:is(ksi,eta)]
-ists1:=isf(cut,cut,[u:cut]ts(u,zeta),ksi,eta,i):is(ts(ksi,zeta),ts(eta,zeta))
-ists2:=isf(cut,cut,[u:cut]ts(zeta,u),ksi,eta,i):is(ts(zeta,ksi),ts(zeta,eta))
-upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
-ists12:=tris(cut,ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),ists1(i),ists2(zeta,upsilon,eta,j)):is(ts(ksi,zeta),ts(eta,upsilon))
-+4142
-eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-t1:=tris(rat,z0,ts"rt"(x0,y0),ts"rt"(y0,x0),i,comts(x0,y0)):is"rt"(z0,ts"rt"(y0,x0))
-t2:=lrtts(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(ts(eta,ksi),z0)
-lz@t3:=tsapp(ksi,eta,z0,lz,lrt(ts(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]t2(x,t,y,u,v)):lrt(ts(eta,ksi),z0)
--4142
-eta@satz142:=isi1(ts(ksi,eta),ts(eta,ksi),[x:rat][t:lrt(ts(ksi,eta),x)]t3".4142"(x,t),[x:rat][t:lrt(ts(eta,ksi),x)]t3".4142"(eta,ksi,x,t)):is(ts(ksi,eta),ts(eta,ksi))
-comts:=satz142:is(ts(ksi,eta),ts(eta,ksi))
-+4143
-zeta@[u0:rat][lu:lrt(ts(ts(ksi,eta),zeta),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,ts"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))]
-t1:=tr3is(rat,u0,ts"rt"(v0,z0),ts"rt"(ts"rt"(x0,y0),z0),ts"rt"(x0,ts"rt"(y0,z0)),i,ists1"rt"(v0,ts"rt"(x0,y0),z0,j),assts1(x0,y0,z0)):is"rt"(u0,ts"rt"(x0,ts"rt"(y0,z0)))
-t2:=lrtts(eta,zeta,ts"rt"(y0,z0),y0,ly,z0,lz,refis(rat,ts"rt"(y0,z0))):lrt(ts(eta,zeta),ts"rt"(y0,z0))
-t3:=lrtts(ksi,ts(eta,zeta),u0,x0,lx,ts"rt"(y0,z0),t2,t1):lrt(ts(ksi,ts(eta,zeta)),u0)
-i@t4:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
-lu@t5:=tsapp(ts(ksi,eta),zeta,u0,lu,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,ts"rt"(x,y))]t4(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
-u0@[lu:lrt(ts(ksi,ts(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(ts(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,ts"rt"(y0,z0))]
-t6:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,ts"rt"(y0,z0)),ts"rt"(ts"rt"(x0,y0),z0),i,ists2"rt"(v0,ts"rt"(y0,z0),x0,j),assts2(x0,y0,z0)):is"rt"(u0,ts"rt"(ts"rt"(x0,y0),z0))
-t7:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
-t8:=lrtts(ts(ksi,eta),zeta,u0,ts"rt"(x0,y0),t7,z0,lz,t6):lrt(ts(ts(ksi,eta),zeta),u0)
-i@t9:=tsapp(eta,zeta,v0,lv,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,ts"rt"(x,y))]t8(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
-lu@t10:=tsapp(ksi,ts(eta,zeta),u0,lu,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(ts(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t9(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
--4143
-zeta@satz143:=isi1(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),[x:rat][t:lrt(ts(ts(ksi,eta),zeta),x)]t5".4143"(x,t),[x:rat][t:lrt(ts(ksi,ts(eta,zeta)),x)]t10".4143"(x,t)):is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
-assts1:=satz143:is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
-assts2:=symis(cut,ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),satz143):is(ts(ksi,ts(eta,zeta)),ts(ts(ksi,eta),zeta))
-+4144
-[u0:rat][lu:lrt(ts(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
-t1:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,pl"rt"(y0,z0)),pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)),i,ists2"rt"(v0,pl"rt"(y0,z0),x0,j),disttp2(x0,y0,z0)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)))
-t2:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
-t3:=lrtts(ksi,zeta,ts"rt"(x0,z0),x0,lx,z0,lz,refis(rat,ts"rt"(x0,z0))):lrt(ts(ksi,zeta),ts"rt"(x0,z0))
-t4:=lrtpl(ts(ksi,eta),ts(ksi,zeta),u0,ts"rt"(x0,y0),t2,ts"rt"(x0,z0),t3,t1):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
-i@t5:=plapp(eta,zeta,v0,lv,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
-lu@t6:=tsapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t5(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
-u0@[lu:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][w0:rat][lw:lrt(ts(ksi,zeta),w0)][i:is"rt"(u0,pl"rt"(v0,w0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][z0:rat][lz:lrt(zeta,z0)][k:is"rt"(w0,ts"rt"(x1,z0))]
-t7:=tris(rat,u0,pl"rt"(v0,w0),pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),i,ispl12"rt"(v0,ts"rt"(x0,y0),w0,ts"rt"(x1,z0),j,k)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)))
-x2:=ite(moreis"rt"(x0,x1),rat,x0,x1):rat
-[m:moreis"rt"(x0,x1)]
-t8:=itet(moreis"rt"(x0,x1),rat,x0,x1,m):is"rt"(x2,x0)
-t9:=isp1(rat,[t:rat]lrt(ksi,t),x0,x2,lx,t8):lrt(ksi,x2)
-t10:=lessisi2"rt"(x0,x2,symis(rat,x2,x0,t8)):lessis"rt"(x0,x2)
-t11:=satz88(x1,x0,x2,satz84(x0,x1,m),t10):lessis"rt"(x1,x2)
-k@[n:not(moreis"rt"(x0,x1))]
-t12:=itef(moreis"rt"(x0,x1),rat,x0,x1,n):is"rt"(x2,x1)
-t13:=isp1(rat,[t:rat]lrt(ksi,t),x1,x2,lx1,t12):lrt(ksi,x2)
-t14:=lessisi2"rt"(x1,x2,symis(rat,x2,x1,t12)):lessis"rt"(x1,x2)
-t15:=lessisi1"rt"(x0,x2,satz87b(x0,x1,x2,satz81j(x0,x1,n),t14)):lessis"rt"(x0,x2)
-k@t16:=th1"l.imp"(moreis"rt"(x0,x1),lrt(ksi,x2),[t:moreis"rt"(x0,x1)]t9(t),[t:not(moreis"rt"(x0,x1))]t13(t)):lrt(ksi,x2)
-t17:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x0,x2),[t:moreis"rt"(x0,x1)]t10(t),[t:not(moreis"rt"(x0,x1))]t15(t)):lessis"rt"(x0,x2)
-t18:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x1,x2),[t:moreis"rt"(x0,x1)]t11(t),[t:not(moreis"rt"(x0,x1))]t14(t)):lessis"rt"(x1,x2)
-t19:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
-t20:=lrtts(ksi,pl(eta,zeta),ts"rt"(x2,pl"rt"(y0,z0)),x2,t16,pl"rt"(y0,z0),t19,refis(rat,ts"rt"(x2,pl"rt"(y0,z0)))):lrt(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)))
-t21:=satz109a(x0,x2,y0,y0,t17,lessisi2"rt"(y0,y0,refis(rat,y0))):lessis"rt"(ts"rt"(x0,y0),ts"rt"(x2,y0))
-t22:=satz109a(x1,x2,z0,z0,t18,lessisi2"rt"(z0,z0,refis(rat,z0))):lessis"rt"(ts"rt"(x1,z0),ts"rt"(x2,z0))
-t23:=islessis12"rt"(pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),u0,pl"rt"(ts"rt"(x2,y0),ts"rt"(x2,z0)),ts"rt"(x2,pl"rt"(y0,z0)),symis(rat,u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),t7),distpt2(x2,y0,z0),satz100a(ts"rt"(x0,y0),ts"rt"(x2,y0),ts"rt"(x1,z0),ts"rt"(x2,z0),t21,t22)):lessis"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))
-t24:=orapp(less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),lrt(ts(ksi,pl(eta,zeta)),u0),t23,[t:less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]satz120(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)),t20,u0,t),[t:is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]isp1(rat,[u:rat]lrt(ts(ksi,pl(eta,zeta)),u),ts"rt"(x2,pl"rt"(y0,z0)),u0,t20,t)):lrt(ts(ksi,pl(eta,zeta)),u0)
-j@t25:=tsapp(ksi,zeta,w0,lw,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(w0,ts"rt"(x,y))]t24(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
-i@t26:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t25(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
-lu@t27:=plapp(ts(ksi,eta),ts(ksi,zeta),u0,lu,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(ts(ksi,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t26(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
--4144
-satz144:=isi1(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),[x:rat][t:lrt(ts(ksi,pl(eta,zeta)),x)]t6".4144"(x,t),[x:rat][t:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),x)]t27".4144"(x,t)):is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
-disttp1:=tr3is(cut,ts(pl(ksi,eta),zeta),ts(zeta,pl(ksi,eta)),pl(ts(zeta,ksi),ts(zeta,eta)),pl(ts(ksi,zeta),ts(eta,zeta)),comts(pl(ksi,eta),zeta),satz144(zeta,ksi,eta),ispl12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta))):is(ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)))
-disttp2:=satz144:is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
-distpt1:=symis(cut,ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)),disttp1):is(pl(ts(ksi,zeta),ts(eta,zeta)),ts(pl(ksi,eta),zeta))
-distpt2:=symis(cut,ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),disttp2):is(pl(ts(ksi,eta),ts(ksi,zeta)),ts(ksi,pl(eta,zeta)))
-[m:more(ksi,eta)]
-+4145
-phi:=mn(ksi,eta,m):cut
-t1:=satz140d(ksi,eta,m):is(ksi,pl(eta,phi))
-t2:=tris(cut,ts(ksi,zeta),ts(pl(eta,phi),zeta),pl(ts(eta,zeta),ts(phi,zeta)),ists1(ksi,pl(eta,phi),zeta,t1),disttp1(eta,phi,zeta)):is(ts(ksi,zeta),pl(ts(eta,zeta),ts(phi,zeta)))
--4145
-satz145a:=ismore1(pl(ts(eta,zeta),ts(phi".4145",zeta)),ts(ksi,zeta),ts(eta,zeta),symis(cut,ts(ksi,zeta),pl(ts(eta,zeta),ts(phi".4145",zeta)),t2".4145"),satz133(ts(eta,zeta),ts(phi".4145",zeta))):more(ts(ksi,zeta),ts(eta,zeta))
-zeta@[i:is(ksi,eta)]
-satz145b:=ists1(ksi,eta,zeta,i):is(ts(ksi,zeta),ts(eta,zeta))
-zeta@[l:less(ksi,eta)]
-satz145c:=satz121(ts(eta,zeta),ts(ksi,zeta),satz145a(eta,ksi,zeta,satz122(ksi,eta,l))):less(ts(ksi,zeta),ts(eta,zeta))
-m@satz145d:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145a):more(ts(zeta,ksi),ts(zeta,eta))
-i@satz145e:=ists2(ksi,eta,zeta,i):is(ts(zeta,ksi),ts(zeta,eta))
-l@satz145f:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145c):less(ts(zeta,ksi),ts(zeta,eta))
-upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
-satz145g:=ismore2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145d(zeta,upsilon,ksi,m)):more(ts(ksi,zeta),ts(eta,upsilon))
-satz145h:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145g):more(ts(zeta,ksi),ts(upsilon,eta))
-i@[l:less(zeta,upsilon)]
-satz145j:=isless2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145f(zeta,upsilon,ksi,l)):less(ts(ksi,zeta),ts(eta,upsilon))
-satz145k:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145j):less(ts(zeta,ksi),ts(upsilon,eta))
-+4146
-zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-t2:=satz123b(ts(ksi,zeta),ts(eta,zeta)):ec3(is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)))
--4146
-zeta@[m:more(ts(ksi,zeta),ts(eta,zeta))]
-satz146a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),m):more(ksi,eta)
-zeta@[i:is(ts(ksi,zeta),ts(eta,zeta))]
-satz146b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),i):is(ksi,eta)
-zeta@[l:less(ts(ksi,zeta),ts(eta,zeta))]
-satz146c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),l):less(ksi,eta)
-zeta@[m:more(ts(zeta,ksi),ts(zeta,eta))]
-satz146d:=satz146a(ismore12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),m)):more(ksi,eta)
-zeta@[i:is(ts(zeta,ksi),ts(zeta,eta))]
-satz146e:=satz146b(tr3is(cut,ts(ksi,zeta),ts(zeta,ksi),ts(zeta,eta),ts(eta,zeta),comts(ksi,zeta),i,comts(zeta,eta))):is(ksi,eta)
-zeta@[l:less(ts(zeta,ksi),ts(zeta,eta))]
-satz146f:=satz146c(isless12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),l)):less(ksi,eta)
-upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
-+4147
-t1:=satz145a(ksi,eta,zeta,m):more(ts(ksi,zeta),ts(eta,zeta))
-t2:=ismore12(ts(zeta,eta),ts(eta,zeta),ts(upsilon,eta),ts(eta,upsilon),comts(zeta,eta),comts(upsilon,eta),satz145a(zeta,upsilon,eta,n)):more(ts(eta,zeta),ts(eta,upsilon))
--4147
-satz147:=trmore(ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),t1".4147",t2".4147"):more(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
-satz147a:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz147(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
-satz148a:=orapp(more(ksi,eta),is(ksi,eta),more(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]satz147(t,n),[t:is(ksi,eta)]satz145g(t,n)):more(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
-satz148b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]satz147(m,t),[t:is(zeta,upsilon)]satz145h(zeta,upsilon,ksi,eta,t,m)):more(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
-satz148c:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
-satz148d:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
-+4149
-[i:is(ksi,eta)][j:is(zeta,upsilon)]
-t1:=moreisi2(ts(ksi,zeta),ts(eta,upsilon),ists12(ksi,eta,zeta,upsilon,i,j)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-i@[o:more(zeta,upsilon)]
-t2:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148a(m,o)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-n@[o:more(ksi,eta)]
-t4:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148b(o,n)):moreis(ts(ksi,zeta),ts(eta,upsilon))
--4149
-satz149:=orapp(more(ksi,eta),is(ksi,eta),moreis(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]t4".4149"(t),[t:is(ksi,eta)]t3".4149"(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
-satz149a:=satz124(ts(eta,upsilon),ts(ksi,zeta),satz149(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(ts(ksi,zeta),ts(eta,upsilon))
--rp
-@[r0:rat]
-ratset:=setof(rat,[x:rat]less(x,r0)):set(rat)
-+4150
-t1:=satz90(r0):some([x:rat]less(x,r0))
-[x0:rat][l:less(x0,r0)]
-t2:=estii(rat,[x:rat]less(x,r0),x0,l):in(x0,ratset)
-r0@t3:=ec3e13(is(r0,r0),more(r0,r0),less(r0,r0),satz81b(r0,r0),refis(rat,r0)):not(less(r0,r0))
-t4:=th3"l.imp"(in(r0,ratset),less(r0,r0),t3,[t:in(r0,ratset)]estie(rat,[x:rat]less(x,r0),r0,t)):not(in(r0,ratset))
-x0@[i:in(x0,ratset)]
-t5:=estie(rat,[x:rat]less(x,r0),x0,i):less(x0,r0)
-[x1:rat][k:less(x1,x0)]
-t6:=t2(x1,trless(x1,x0,r0,k,t5)):in(x1,ratset)
-i@t7:=satz91(x0,r0,t5):some([x:rat]and(less(x0,x),less(x,r0)))
-[x1:rat][a:and(less(x0,x1),less(x1,r0))]
-t8:=ande1(less(x0,x1),less(x1,r0),a):less(x0,x1)
-t9:=ande2(less(x0,x1),less(x1,r0),a):less(x1,r0)
-t10:=andi(in(x1,ratset),more(x1,x0),t2(x1,t9),satz83(x0,x1,t8)):and(in(x1,ratset),more(x1,x0))
-i@t11:=th6"l.some"(rat,[x:rat]and(less(x0,x),less(x,r0)),[x:rat]and(in(x,ratset),more(x,x0)),t7,[x:rat][t:and(less(x0,x),less(x,r0))]t10(x,t)):some([x:rat]and(in(x,ratset),more(x,x0)))
-l@t12:=cut2(ratset,x0,t2,r0,t4,[x:rat][t:in(x,ratset)][y:rat][u:less(y,x)]t6(x,t,y,u),[x:rat][t:in(x,ratset)]t11(x,t)):cutprop(ratset)
--4150
-satz150:=someapp(rat,[x:rat]less(x,r0),t1".4150",cutprop(ratset),[x:rat][t:less(x,r0)]t12".4150"(x,t)):cutprop(ratset)
-+*rp
-r0@rpofrt:=cutof(ratset,satz150):cut
-[x0:rat][l:less"rt"(x0,r0)]
-lrtrpofrt:=ine(ratset,satz150,x0,t2"rt.4150"(x0,l)):lrt(rpofrt,x0)
-r0@[x0:rat][lx:lrt(rpofrt,x0)]
-lrtrpofrte:=t5"rt.4150"(x0,ini(ratset,satz150,x0,lx)):less"rt"(x0,r0)
-r0@[x0:rat][m:moreis"rt"(x0,r0)]
-+*iii4
-m@t12:=satz81c(x0,r0,m):not(less"rt"(x0,r0))
--iii4
-m@urtrpofrt:=th3"l.imp"(lrt(rpofrt,x0),less"rt"(x0,r0),t12".iii4",[t:lrt(rpofrt,x0)]lrtrpofrte(x0,t)):urt(rpofrt,x0)
-@1rp:=rpofrt(1rt):cut
-+4151
-ksi@[z0:rat][lz:lrt(ts(ksi,1rp),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(1rp,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-t1:=lrtrpofrte(1rt,y0,ly):less"rt"(y0,1rt)
-t2:=isless12"rt"(ts"rt"(x0,y0),z0,ts"rt"(x0,1rt),x0,symis(rat,z0,ts"rt"(x0,y0),i),example1a(x0),satz105f(y0,1rt,x0,t1)):less"rt"(z0,x0)
-t3:=satz120(ksi,x0,lx,z0,t2):lrt(ksi,z0)
-lz@t4:=tsapp(ksi,1rp,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(1rp,y)][v:is"rt"(z0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ksi,z0)
-ksi@[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
-y1:=ts"rt"(ov(1rt,x1),x0):rat
-t5:=isless2"rt"(ts"rt"(ov(1rt,x1),x1),1rt,y1,satz110e(1rt,x1),satz105f(x0,x1,ov(1rt,x1),l)):less"rt"(y1,1rt)
-t6:=lrtrpofrt(1rt,y1,t5):lrt(1rp,y1)
-t7:=tr3is(rat,ts"rt"(x1,y1),ts"rt"(ts"rt"(x1,ov(1rt,x1)),x0),ts"rt"(1rt,x0),x0,assts2"rt"(x1,ov(1rt,x1),x0),ists1"rt"(ts"rt"(x1,ov(1rt,x1)),1rt,x0,satz110c(1rt,x1)),example1c(x0)):is"rt"(ts"rt"(x1,y1),x0)
-t8:=lrtts(ksi,1rp,x0,x1,lx1,y1,t6,symis(rat,ts"rt"(x1,y1),x0,t7)):lrt(ts(ksi,1rp),x0)
-lx@t9:=cutapp3(ksi,x0,lx,lrt(ts(ksi,1rp),x0),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t8(y,t,u)):lrt(ts(ksi,1rp),x0)
--4151
-ksi@satz151:=isi1(ts(ksi,1rp),ksi,[x:rat][t:lrt(ts(ksi,1rp),x)]t4".4151"(x,t),[x:rat][t:lrt(ksi,x)]t9".4151"(x,t)):is(ts(ksi,1rp),ksi)
-satz151a:=symis(cut,ts(ksi,1rp),ksi,satz151):is(ksi,ts(ksi,1rp))
-satz151b:=tris(cut,ts(1rp,ksi),ts(ksi,1rp),ksi,comts(1rp,ksi),satz151):is(ts(1rp,ksi),ksi)
-satz151c:=symis(cut,ts(1rp,ksi),ksi,satz151b):is(ksi,ts(1rp,ksi))
-+4152
-[x0:rat][y0:rat]
-invprop1:=and(urt(ksi,y0),less"rt"(y0,x0)):'prop'
-ksi@[z0:rat][x0:rat]
-invprop2:=and3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0))):'prop'
-z0@invprop:=some"rt"([x:rat]invprop2(z0,x)):'prop'
-ksi@inv:=setof(rat,[z:rat]invprop(z)):set(rat)
-x0@[ux:urt(ksi,x0)][y0:rat][uy:urt(ksi,y0)][l:less"rt"(y0,x0)][i:is"rt"(z0,ov(1rt,x0))]
-t1:=andi(urt(ksi,y0),less"rt"(y0,x0),uy,l):invprop1(x0,y0)
-t2:=somei(rat,[x:rat]invprop1(x0,x),y0,t1):some"rt"([x:rat]invprop1(x0,x))
-t3:=and3i(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),ux,t2,i):invprop2(z0,x0)
-t4:=somei(rat,[x:rat]invprop2(z0,x),x0,t3):invprop(z0)
-inv1:=estii(rat,[z:rat]invprop(z),z0,t4):in(z0,inv)
-z0@[i:in(z0,inv)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]p]
-t5:=estie(rat,[x:rat]invprop(x),z0,i):invprop(z0)
-[x0:rat][px:invprop2(z0,x0)]
-t6:=and3e1(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):urt(ksi,x0)
-t7:=and3e2(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):some"rt"([x:rat]invprop1(x0,x))
-t8:=and3e3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):is"rt"(z0,ov(1rt,x0))
-[y0:rat][py:invprop1(x0,y0)]
-t9:=ande1(urt(ksi,y0),less"rt"(y0,x0),py):urt(ksi,y0)
-t10:=ande2(urt(ksi,y0),less"rt"(y0,x0),py):less"rt"(y0,x0)
-t11:=<t8><t10><t9><y0><t6><x0>p1:p
-px@t12:=someapp(rat,[x:rat]invprop1(x0,x),t7,p,[x:rat][t:invprop1(x0,x)]t11(x,t)):p
-p1@invapp:=someapp(rat,[x:rat]invprop2(z0,x),t5,p,[x:rat][t:invprop2(z0,x)]t12(x,t)):p
-ksi@[x0:rat][ux:urt(ksi,x0)]
-2x0:=pl"rt"(x0,x0):rat
-t13:=satz94a(x0,x0):less"rt"(x0,2x0)
-t14:=satz119a(ksi,x0,ux,2x0,t13):urt(ksi,2x0)
-t15:=inv1(ov(1rt,2x0),2x0,t14,x0,ux,t13,refis(rat,ov(1rt,2x0))):in(ov(1rt,2x0),inv)
-ksi@[x1:rat][lx:lrt(ksi,x1)][x0:rat][ux:urt(ksi,x0)]
-t16:=th3"l.imp"(is"rt"(x0,x1),lrt(ksi,x0),ux,[t:is"rt"(x0,x1)]isp1(rat,[x:rat]lrt(ksi,x),x1,x0,lx,t)):nis"rt"(x0,x1)
-t17:=satz110e(1rt,x0):is"rt"(ts"rt"(ov(1rt,x0),x0),1rt)
-t18:=satz110e(1rt,x1):is"rt"(ts"rt"(ov(1rt,x1),x1),1rt)
-[i:is"rt"(ov(1rt,x0),ov(1rt,x1))]
-t19:=tris(rat,ts"rt"(ov(1rt,x0),x1),ts"rt"(ov(1rt,x1),x1),1rt,ists1"rt"(ov(1rt,x0),ov(1rt,x1),x1,i),t18):is"rt"(ts"rt"(ov(1rt,x0),x1),1rt)
-t20:=satz110b(1rt,ov(1rt,x0),x0,x1,t17,t19):is"rt"(x0,x1)
-ux@t21:=th3"l.imp"(is"rt"(ov(1rt,x0),ov(1rt,x1)),is"rt"(x0,x1),t16,[t:is"rt"(ov(1rt,x0),ov(1rt,x1))]t20(t)):nis"rt"(ov(1rt,x0),ov(1rt,x1))
-lx@[i:in(ov(1rt,x1),inv)]
-t22:=invapp(ov(1rt,x1),i,con,[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(ov(1rt,x1),ov(1rt,x))]<symis(rat,ov(1rt,x1),ov(1rt,x),w)>t21(x,t)):con
-lx@t23:=[t:in(ov(1rt,x1),inv)]t22(t):not(in(ov(1rt,x1),inv))
-ksi@[z0:rat][i:in(z0,inv)][u0:rat][l:less"rt"(u0,z0)][x0:rat][ux:urt(ksi,x0)][j:is"rt"(z0,ov(1rt,x0))]
-t24:=isless2"rt"(z0,ov(1rt,x0),u0,j,l):less"rt"(u0,ov(1rt,x0))
-t25:=tris(rat,ts"rt"(ov(1rt,x0),x0),1rt,ts"rt"(u0,ov(1rt,u0)),satz110e(1rt,x0),satz110d(1rt,u0)):is"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)))
-t26:=isless2"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(u0,x0),t25,satz105c(u0,ov(1rt,x0),x0,t24)):less"rt"(ts"rt"(u0,x0),ts"rt"(u0,ov(1rt,u0)))
-t27:=isless12"rt"(ts"rt"(u0,x0),ts"rt"(x0,u0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(ov(1rt,u0),u0),comts"rt"(u0,x0),comts"rt"(u0,ov(1rt,u0)),t26):less"rt"(ts"rt"(x0,u0),ts"rt"(ov(1rt,u0),u0))
-t28:=satz106c(x0,ov(1rt,u0),u0,t27):less"rt"(x0,ov(1rt,u0))
-t29:=satz119a(x0,ux,ov(1rt,u0),t28):urt(ksi,ov(1rt,u0))
-t30:=satz110e(1rt,u0):is"rt"(ts"rt"(ov(1rt,u0),u0),1rt)
-t31:=satz110g(1rt,ov(1rt,u0),u0,t30):is"rt"(u0,ov(1rt,ov(1rt,u0)))
-t32:=inv1(u0,ov(1rt,u0),t29,x0,ux,t28,t31):in(u0,inv)
-l@t33:=invapp(z0,i,in(u0,inv),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t32(x,t,w)):in(u0,inv)
-i@[x0:rat][ux:urt(ksi,x0)][x1:rat][ux1:urt(ksi,x1)][l:less"rt"(x1,x0)][j:is"rt"(z0,ov(1rt,x0))]
-t34:=satz91(x1,x0,l):some"rt"([x:rat]and(less"rt"(x1,x),less"rt"(x,x0)))
-[x2:rat][a:and(less"rt"(x1,x2),less"rt"(x2,x0))]
-t35:=ande1(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x1,x2)
-t36:=satz119a(ksi,x1,ux1,x2,t35):urt(ksi,x2)
-t37:=inv1(ov(1rt,x2),x2,t36,x1,ux1,t35,refis(rat,ov(1rt,x2))):in(ov(1rt,x2),inv)
-t38:=ande2(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x2,x0)
-t39:=tris(rat,ts"rt"(x0,ov(1rt,x0)),1rt,ts"rt"(x2,ov(1rt,x2)),satz110c(1rt,x0),satz110d(1rt,x2)):is"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
-t40:=isless2"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)),ts"rt"(x2,ov(1rt,x0)),t39,satz105c(x2,x0,ov(1rt,x0),t38)):less"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
-t41:=isless12"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(ov(1rt,x0),x2),ts"rt"(x2,ov(1rt,x2)),ts"rt"(ov(1rt,x2),x2),comts"rt"(x2,ov(1rt,x0)),comts"rt"(x2,ov(1rt,x2)),t40):less"rt"(ts"rt"(ov(1rt,x0),x2),ts"rt"(ov(1rt,x2),x2))
-t42:=satz106c(ov(1rt,x0),ov(1rt,x2),x2,t41):less"rt"(ov(1rt,x0),ov(1rt,x2))
-t43:=ismore2"rt"(ov(1rt,x0),z0,ov(1rt,x2),symis(rat,z0,ov(1rt,x0),j),satz83(ov(1rt,x0),ov(1rt,x2),t42)):more"rt"(ov(1rt,x2),z0)
-t44:=andi(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0),t37,t43):and(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0))
-t45:=somei(rat,[x:rat]and(in(x,inv),more"rt"(x,z0)),ov(1rt,x2),t44):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
-j@t46:=someapp(rat,[x:rat]and(less"rt"(x1,x),less"rt"(x,x0)),t34,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:and(less"rt"(x1,x),less"rt"(x,x0))]t45(x,t)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
-i@t47:=invapp(z0,i,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t46(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
-ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
-t48:=cut2(inv,ov(1rt,pl"rt"(y0,y0)),t15(y0,uy),ov(1rt,x0),t23(x0,lx),[x:rat][t:in(x,inv)][y:rat][u:less"rt"(y,x)]t33(x,t,y,u),[x:rat][t:in(x,inv)]t47(x,t)):cutprop(inv)
-lx@t49:=cutapp1b(ksi,cutprop(inv),[x:rat][t:urt(ksi,x)]t48(x,t)):cutprop(inv)
-ksi@t50:=cutapp1a(ksi,cutprop(inv),[x:rat][t:lrt(ksi,x)]t49(x,t)):cutprop(inv)
-chi:=cutof(inv,t50):cut
-[z0:rat][lz:lrt(ts(ksi,chi),z0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,ts"rt"(x0,u0))][x1:rat][ux:urt(ksi,x1)][j:is"rt"(u0,ov(1rt,x1))]
-t51:=tris(rat,z0,ts"rt"(x0,u0),ts"rt"(x0,ov(1rt,x1)),i,ists2"rt"(u0,ov(1rt,x1),x0,j)):is"rt"(z0,ts"rt"(x0,ov(1rt,x1)))
-t52:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
-t53:=isless12"rt"(ts"rt"(x0,ov(1rt,x1)),z0,ts"rt"(x1,ov(1rt,x1)),1rt,symis(rat,z0,ts"rt"(x0,ov(1rt,x1)),t51),satz110c(1rt,x1),satz105c(x0,x1,ov(1rt,x1),t52)):less"rt"(z0,1rt)
-t54:=lrtrpofrt(1rt,z0,t53):lrt(1rp,z0)
-i@r1:=ini(inv,t50,u0,lu):in(u0,inv)
-r2:=invapp(u0,r1,lrt(1rp,z0),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(u0,ov(1rt,x))]t54(x,t,w)):lrt(1rp,z0)
-lz@r3:=tsapp(ksi,chi,z0,lz,lrt(1rp,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,ts"rt"(x,y))]r2(x,t,y,u,v)):lrt(1rp,z0)
-ksi@[u0:rat][lu:lrt(1rp,u0)]
-t55:=lrtrpofrte(1rt,u0,lu):less"rt"(u0,1rt)
-t56:=satz83(u0,1rt,t55):more"rt"(1rt,u0)
-[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][x2:rat][ux2:urt(ksi,x2)]
-t57:=cutapp2b(x1,lx1,x2,ux2):more"rt"(x2,x1)
-[i:is"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0))]
-t58:=cutapp2a(x0,lx,x2,ux2):less"rt"(x0,x2)
-t59:=satz105f(x0,x2,mn"rt"(1rt,u0,t56),t58):less"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),ts"rt"(mn"rt"(1rt,u0,t56),x2))
-t60:=isless1"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),symis(rat,mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0),i),t59):less"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2))
-t61:=tr4is(rat,pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),ts"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),x2),ts"rt"(1rt,x2),x2,pl"rt"(mn"rt"(x2,x1,t57),x1),distpt1"rt"(mn"rt"(1rt,u0,t56),u0,x2),ists1"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),1rt,x2,satz101e(1rt,u0,t56)),example1c(x2),satz101f(x2,x1,t57)):is"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
-t62:=satz96c(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2),t60):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)))
-t63:=isless2"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),t61,t62):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
-t64:=isless12"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(x1,mn"rt"(x2,x1,t57)),compl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),compl"rt"(mn"rt"(x2,x1,t57),x1),t63):less"rt"(pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(x1,mn"rt"(x2,x1,t57)))
-t65:=satz97c(ts"rt"(u0,x2),x1,mn"rt"(x2,x1,t57),t64):less"rt"(ts"rt"(u0,x2),x1)
-t66:=tr3is(rat,ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),ts"rt"(ts"rt"(ov(1rt,u0),u0),x2),ts"rt"(1rt,x2),x2,assts2"rt"(ov(1rt,u0),u0,x2),ists1"rt"(ts"rt"(ov(1rt,u0),u0),1rt,x2,satz110e(1rt,u0)),example1c(x2)):is"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2)
-t67:=isless12"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2,ts"rt"(ov(1rt,u0),x1),ov(x1,u0),t66,satz141b(x1,u0),satz105f(ts"rt"(u0,x2),x1,ov(1rt,u0),t65)):less"rt"(x2,ov(x1,u0))
-t68:=satz119a(x2,ux2,ov(x1,u0),t67):urt(ksi,ov(x1,u0))
-t69:=satz110e(x1,u0):is"rt"(ts"rt"(ov(x1,u0),u0),x1)
-t70:=tr3is(rat,u0,ov(x1,ov(x1,u0)),ts"rt"(ov(1rt,ov(x1,u0)),x1),ts"rt"(x1,ov(1rt,ov(x1,u0))),satz110g(x1,ov(x1,u0),u0,t69),satz141c(x1,ov(x1,u0)),comts"rt"(ov(1rt,ov(x1,u0)),x1)):is"rt"(u0,ts"rt"(x1,ov(1rt,ov(x1,u0))))
-t71:=inv1(ov(1rt,ov(x1,u0)),ov(x1,u0),t68,x2,ux2,t67,refis(rat,ov(1rt,ov(x1,u0)))):in(ov(1rt,ov(x1,u0)),inv)
-t72:=ine(inv,t50,ov(1rt,ov(x1,u0)),t71):lrt(chi,ov(1rt,ov(x1,u0)))
-t73:=lrtts(ksi,chi,u0,x1,lx1,ov(1rt,ov(x1,u0)),t72,t70):lrt(ts(ksi,chi),u0)
-lx@t74:=satz132app(ksi,lrt(ts(ksi,chi),u0),ts"rt"(mn"rt"(1rt,u0,t56),x0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn"rt"(y,x,cutapp2b(x,t,y,u)),ts"rt"(mn"rt"(1rt,u0,t56),x0))]t73(x,t,y,u,v)):lrt(ts(ksi,chi),u0)
-lu@t75:=cutapp1a(ksi,lrt(ts(ksi,chi),u0),[x:rat][t:lrt(ksi,x)]t74(x,t)):lrt(ts(ksi,chi),u0)
-ksi@t76:=isi1(ts(ksi,chi),1rp,[x:rat][t:lrt(ts(ksi,chi),x)]r3(x,t),[x:rat][t:lrt(1rp,x)]t75(x,t)):is(ts(ksi,chi),1rp)
--4152
-satz152:=somei(cut,[t:cut]is(ts(ksi,t),1rp),chi".4152",t76".4152"):some([c:cut]is(ts(ksi,c),1rp))
-eta@[phi:cut][psi:cut]
-+4153
-[m:more(phi,psi)]
-t1:=satz145d(phi,psi,eta,m):more(ts(eta,phi),ts(eta,psi))
-t2:=ec3e21(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t1):nis(ts(eta,phi),ts(eta,psi))
-psi@[l:less(phi,psi)]
-t3:=satz145f(phi,psi,eta,l):less(ts(eta,phi),ts(eta,psi))
-t4:=ec3e31(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t3):nis(ts(eta,phi),ts(eta,psi))
-psi@[n:nis(phi,psi)]
-t5:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
-t6:=orapp(more(phi,psi),less(phi,psi),nis(ts(eta,phi),ts(eta,psi)),t5,[t:more(phi,psi)]t2(t),[t:less(phi,psi)]t4(t)):nis(ts(eta,phi),ts(eta,psi))
--4153
-[i:is(ts(eta,phi),ksi)][j:is(ts(eta,psi),ksi)]
-satz153b:=th7"l.imp"(is(phi,psi),nis(ts(eta,phi),ts(eta,psi)),weli(is(ts(eta,phi),ts(eta,psi)),tris2(cut,ts(eta,phi),ts(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t6".4153"(t)):is(phi,psi)
-+*4153
-eta@[tau:cut][i:is(ts(eta,tau),1rp)]
-chi:=ts(tau,ksi):cut
-t7:=tr3is(cut,ts(eta,chi),ts(ts(eta,tau),ksi),ts(1rp,ksi),ksi,assts2(eta,tau,ksi),ists1(ts(eta,tau),1rp,ksi,i),satz151b(ksi)):is(ts(eta,chi),ksi)
-t8:=somei(cut,[c:cut]is(ts(eta,c),ksi),chi,t7):some([c:cut]is(ts(eta,c),ksi))
--4153
-eta@satz153a:=someapp(cut,[c:cut]is(ts(eta,c),1rp),satz152(eta),some([c:cut]is(ts(eta,c),ksi)),[c:cut][t:is(ts(eta,c),1rp)]t8".4153"(c,t)):some([c:cut]is(ts(eta,c),ksi))
-+*4153
-eta@t9:=[c:cut][d:cut][t:is(ts(eta,c),ksi)][u:is(ts(eta,d),ksi)]satz153b(c,d,t,u):amone(cut,[c:cut]is(ts(eta,c),ksi))
--4153
-eta@satz153:=onei(cut,[c:cut]is(ts(eta,c),ksi),t9".4153",satz153a):one([c:cut]is(ts(eta,c),ksi))
-ov:=ind(cut,[a:cut]is(ts(eta,a),ksi),satz153):cut
-satz153c:=oneax(cut,[a:cut]is(ts(eta,a),ksi),satz153):is(ts(eta,ov(ksi,eta)),ksi)
-satz153d:=symis(cut,ts(eta,ov(ksi,eta)),ksi,satz153c):is(ksi,ts(eta,ov(ksi,eta)))
-satz153e:=tris(cut,ts(ov(ksi,eta),eta),ts(eta,ov(ksi,eta)),ksi,comts(ov(ksi,eta),eta),satz153c):is(ts(ov(ksi,eta),eta),ksi)
-satz153f:=symis(cut,ts(ov(ksi,eta),eta),ksi,satz153e):is(ksi,ts(ov(ksi,eta),eta))
-[phi:cut][i:is(ts(eta,phi),ksi)]
-satz153g:=satz153b(phi,ov(ksi,eta),i,satz153c):is(phi,ov(ksi,eta))
-@[ksi:cut]
-ratrp:=image(rat,cut,[x:rat]rpofrt(x),ksi):'prop'
-@[x0:rat]
-ratrpi:=imagei(rat,cut,[x:rat]rpofrt(x),x0):ratrp(rpofrt(x0))
-@[x:nat]
-rpofnt:=rpofrt(rtofn(x)):cut
-ksi@natrp:=image(nat,cut,[x:nat]rpofnt(x),ksi):'prop'
-x@natrpi:=imagei(nat,cut,[y:nat]rpofnt(y),x):natrp(rpofnt(x))
-ksi@[n:natrp(ksi)]
-+iii5
-[x:nat][i:is(ksi,rpofnt(x))]
-t1:=somei(rat,[y:rat]is(ksi,rpofrt(y)),rtofn(x),i):ratrp(ksi)
--iii5
-lemmaiii5:=someapp(nat,[x:nat]is(ksi,rpofnt(x)),n,ratrp(ksi),[x:nat][t:is(ksi,rpofnt(x))]t1".iii5"(x,t)):ratrp(ksi)
-@[x0:rat][y0:rat][m:more"rt"(x0,y0)]
-+5154
-t1:=lrtrpofrt(x0,y0,satz82(x0,y0,m)):lrt(rpofrt(x0),y0)
-t2:=urtrpofrt(y0,y0,moreisi2"rt"(y0,y0,refis(rat,y0))):urt(rpofrt(y0),y0)
-t3:=andi(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0),t1,t2):and(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0))
--5154
-satz154a:=somei(rat,[x:rat]and(lrt(rpofrt(x0),x),urt(rpofrt(y0),x)),y0,t3".5154"):more(rpofrt(x0),rpofrt(y0))
-y0@[i:is"rt"(x0,y0)]
-satz154b:=isf(rat,cut,[x:rat]rpofrt(x),x0,y0,i):is(rpofrt(x0),rpofrt(y0))
-y0@[l:less"rt"(x0,y0)]
-satz154c:=satz121(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,satz83(x0,y0,l))):less(rpofrt(x0),rpofrt(y0))
-+*5154
-y0@t4:=satz81a(x0,y0):or3(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0))
-t5:=satz123b(rpofrt(x0),rpofrt(y0)):ec3(is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)))
--5154
-y0@[m:more(rpofrt(x0),rpofrt(y0))]
-satz154d:=th11"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),m):more"rt"(x0,y0)
-y0@[i:is(rpofrt(x0),rpofrt(y0))]
-satz154e:=th10"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),i):is"rt"(x0,y0)
-y0@[l:less(rpofrt(x0),rpofrt(y0))]
-satz154f:=th12"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),l):less"rt"(x0,y0)
-+*iii5
-@t2:=[x:rat][y:rat][t:is(rpofrt(x),rpofrt(y))]satz154e(x,y,t):injective(rat,cut,[x:rat]rpofrt(x))
--iii5
-y0@[i:is"rt"(x0,y0)]
-isrterp:=satz154b(x0,y0,i):is(rpofrt(x0),rpofrt(y0))
-y0@[i:is(rpofrt(x0),rpofrt(y0))]
-isrtirp:=satz154e(x0,y0,i):is"rt"(x0,y0)
-ksi@[rtksi:ratrp(ksi)]
-rtofrp:=soft(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):rat
-[eta:cut][rteta:ratrp(eta)][i:is(ksi,eta)]
-isrpert:=isinv(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))
-rteta@[i:is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))]
-isrpirt:=isinve(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is(ksi,eta)
-x0@isrtrp1:=isst1(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(x0,rtofrp(rpofrt(x0),ratrpi(x0)))
-isrtrp2:=isst2(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(rtofrp(rpofrt(x0),ratrpi(x0)),x0)
-rtksi@isrprt1:=ists1"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(ksi,rpofrt(rtofrp(ksi,rtksi)))
-isrprt2:=ists2"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(rpofrt(rtofrp(ksi,rtksi)),ksi)
-@[x:nat][y:nat][i:is"n"(x,y)]
-isnterp:=isf(nat,cut,[z:nat]rpofnt(z),x,y,i):is(rpofnt(x),rpofnt(y))
-y@[i:is(rpofnt(x),rpofnt(y))]
-isntirp:=isnirt(x,y,isrtirp(rtofn(x),rtofn(y),i)):is"n"(x,y)
-+*iii5
-@t3:=[x:nat][y:nat][t:is(rpofnt(x),rpofnt(y))]isntirp(x,y,t):injective(nat,cut,[x:nat]rpofnt(x))
--iii5
-ksi@[ntksi:natrp(ksi)]
-ntofrp:=soft(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):nat
-[eta:cut][nteta:natrp(eta)][i:is(ksi,eta)]
-isrpent:=isinv(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))
-nteta@[i:is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))]
-isrpint:=isinve(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is(ksi,eta)
-x@isntrp1:=isst1(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(x,ntofrp(rpofnt(x),natrpi(x)))
-isntrp2:=isst2(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(ntofrp(rpofnt(x),natrpi(x)),x)
-ntksi@isrpnt1:=ists1"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(ksi,rpofnt(ntofrp(ksi,ntksi)))
-isrpnt2:=ists2"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(rpofnt(ntofrp(ksi,ntksi)),ksi)
-@[x0:rat][y0:rat]
-+5155
-[z0:rat][lz:lrt(pl(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,pl"rt"(u0,v0))]
-t1:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
-t2:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
-t3:=satz98a(u0,x0,v0,y0,t1,t2):less"rt"(pl"rt"(u0,v0),pl"rt"(x0,y0))
-t4:=isless1"rt"(pl"rt"(u0,v0),z0,pl"rt"(x0,y0),symis(rat,z0,pl"rt"(u0,v0),i),t3):less"rt"(z0,pl"rt"(x0,y0))
-t5:=lrtrpofrt(pl"rt"(x0,y0),z0,t4):lrt(rpofrt(pl"rt"(x0,y0)),z0)
-lz@t6:=plapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(pl"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,pl"rt"(x,y))]t5(x,t,y,u,v)):lrt(rpofrt(pl"rt"(x0,y0)),z0)
-y0@[u0:rat][lu:lrt(rpofrt(pl"rt"(x0,y0)),u0)]
-t7:=lrtrpofrte(pl"rt"(x0,y0),u0,lu):less"rt"(u0,pl"rt"(x0,y0))
-u01:=ov"rt"(u0,pl"rt"(x0,y0)):rat
-t8:=isless12"rt"(u0,ts"rt"(u01,pl"rt"(x0,y0)),pl"rt"(x0,y0),ts"rt"(1rt,pl"rt"(x0,y0)),satz110f(u0,pl"rt"(x0,y0)),example1d(pl"rt"(x0,y0)),t7):less"rt"(ts"rt"(u01,pl"rt"(x0,y0)),ts"rt"(1rt,pl"rt"(x0,y0)))
-t9:=satz106c(u01,1rt,pl"rt"(x0,y0),t8):less"rt"(u01,1rt)
-t10:=tris(rat,u0,ts"rt"(pl"rt"(x0,y0),u01),pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)),satz110d(u0,pl"rt"(x0,y0)),disttp1"rt"(x0,y0,u01)):is"rt"(u0,pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)))
-y0@[l:less"rt"(y0,1rt)]
-t11:=isless12"rt"(ts"rt"(y0,x0),ts"rt"(x0,y0),ts"rt"(1rt,x0),x0,comts"rt"(y0,x0),example1c(x0),satz105c(y0,1rt,x0,l)):less"rt"(ts"rt"(x0,y0),x0)
-t12:=lrtrpofrt(x0,ts"rt"(x0,y0),t11):lrt(rpofrt(x0),ts"rt"(x0,y0))
-lu@t13:=lrtpl(rpofrt(x0),rpofrt(y0),u0,ts"rt"(x0,u01),t12(x0,u01,t9),ts"rt"(y0,u01),t12(y0,u01,t9),t10):lrt(pl(rpofrt(x0),rpofrt(y0)),u0)
--5155
-satz155a:=isi1(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(pl"rt"(x0,y0)),x)]t13".5155"(x,t),[x:rat][t:lrt(pl(rpofrt(x0),rpofrt(y0)),x)]t6".5155"(x,t)):is(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)))
-[m:more"rt"(x0,y0)]
-+*5155
-m@t14:=satz101f(x0,y0,m):is"rt"(x0,pl"rt"(mn"rt"(x0,y0,m),y0))
-t15:=tris(cut,rpofrt(x0),rpofrt(pl"rt"(mn"rt"(x0,y0,m),y0)),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),isrterp(x0,pl"rt"(mn"rt"(x0,y0,m),y0),t14),satz155a(mn"rt"(x0,y0,m),y0)):is(rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)))
-t16:=tris2(cut,pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),compl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),t15):is(pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0))
--5155
-m@satz155b:=satz140g(rpofrt(x0),rpofrt(y0),rpofrt(mn"rt"(x0,y0,m)),satz154a(x0,y0,m),t16".5155"):is(rpofrt(mn"rt"(x0,y0,m)),mn(rpofrt(x0),rpofrt(y0),satz154a(x0,y0,m)))
-+*5155
-y0@[z0:rat][lz:lrt(ts(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,ts"rt"(u0,v0))]
-t17:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
-t18:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
-t19:=satz107a(u0,x0,v0,y0,t17,t18):less"rt"(ts"rt"(u0,v0),ts"rt"(x0,y0))
-t20:=isless1"rt"(ts"rt"(u0,v0),z0,ts"rt"(x0,y0),symis(rat,z0,ts"rt"(u0,v0),i),t19):less"rt"(z0,ts"rt"(x0,y0))
-t21:=lrtrpofrt(ts"rt"(x0,y0),z0,t20):lrt(rpofrt(ts"rt"(x0,y0)),z0)
-lz@t22:=tsapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(ts"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,ts"rt"(x,y))]t21(x,t,y,u,v)):lrt(rpofrt(ts"rt"(x0,y0)),z0)
-y0@[u0:rat][lu:lrt(rpofrt(ts"rt"(x0,y0)),u0)]
-t23:=lrtrpofrte(ts"rt"(x0,y0),u0,lu):less"rt"(u0,ts"rt"(x0,y0))
-[u1:rat][a:and(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)))]
-t24:=ande1(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u0,u1)
-t25:=ande2(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u1,ts"rt"(x0,y0))
-t26:=isless12"rt"(u0,ts"rt"(ov"rt"(u0,u1),u1),u1,ts"rt"(1rt,u1),satz110f(u0,u1),example1d(u1),t24):less"rt"(ts"rt"(ov"rt"(u0,u1),u1),ts"rt"(1rt,u1))
-t27:=satz106c(ov"rt"(u0,u1),1rt,u1,t26):less"rt"(ov"rt"(u0,u1),1rt)
-t28:=isless1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0),satz110f(u1,y0),t25):less"rt"(ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0))
-t29:=satz106c(ov"rt"(u1,y0),x0,y0,t28):less"rt"(ov"rt"(u1,y0),x0)
-t30:=tr3is(rat,u0,ts"rt"(u1,ov"rt"(u0,u1)),ts"rt"(ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1)),ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))),satz110d(u0,u1),ists1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1),satz110f(u1,y0)),assts1"rt"(ov"rt"(u1,y0),y0,ov"rt"(u0,u1))):is"rt"(u0,ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))))
-t31:=lrtts(rpofrt(x0),rpofrt(y0),u0,ov"rt"(u1,y0),lrtrpofrt(x0,ov"rt"(u1,y0),t29),ts"rt"(y0,ov"rt"(u0,u1)),t12(y0,ov"rt"(u0,u1),t27),t30):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
-lu@t32:=someapp(rat,[x:rat]and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0))),satz91(u0,ts"rt"(x0,y0),t23),lrt(ts(rpofrt(x0),rpofrt(y0)),u0),[x:rat][t:and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0)))]t31(x,t)):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
--5155
-y0@satz155c:=isi1(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(ts"rt"(x0,y0)),x)]t32".5155"(x,t),[x:rat][t:lrt(ts(rpofrt(x0),rpofrt(y0)),x)]t22".5155"(x,t)):is(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)))
-+*5155
-y0@t33:=satz110f(x0,y0):is"rt"(x0,ts"rt"(ov"rt"(x0,y0),y0))
-t34:=tris(cut,rpofrt(x0),rpofrt(ts"rt"(ov"rt"(x0,y0),y0)),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),isrterp(x0,ts"rt"(ov"rt"(x0,y0),y0),t33),satz155c(ov"rt"(x0,y0),y0)):is(rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)))
-t35:=tris2(cut,ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),comts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),t34):is(ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0))
--5155
-y0@satz155d:=satz153g(rpofrt(x0),rpofrt(y0),rpofrt(ov"rt"(x0,y0)),t35".5155"):is(rpofrt(ov"rt"(x0,y0)),ov(rpofrt(x0),rpofrt(y0)))
-@[x:nat][y:nat]
-satz155e:=tris(cut,rpofnt(pl"n"(x,y)),rpofrt(pl"rt"(rtofn(x),rtofn(y))),pl(rpofnt(x),rpofnt(y)),isrterp(rtofn(pl"n"(x,y)),pl"rt"(rtofn(x),rtofn(y)),symis(rat,pl"rt"(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),satz112h(x,y))),satz155a(rtofn(x),rtofn(y))):is(rpofnt(pl"n"(x,y)),pl(rpofnt(x),rpofnt(y)))
-satz155f:=tris(cut,rpofnt(ts"n"(x,y)),rpofrt(ts"rt"(rtofn(x),rtofn(y))),ts(rpofnt(x),rpofnt(y)),isrterp(rtofn(ts"n"(x,y)),ts"rt"(rtofn(x),rtofn(y)),symis(rat,ts"rt"(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),satz112j(x,y))),satz155c(rtofn(x),rtofn(y))):is(rpofnt(ts"n"(x,y)),ts(rpofnt(x),rpofnt(y)))
-+nt
-@natt:=ot(cut,[t:cut]natrp(t)):'type'
-[ksi:cut][nksi:natrp(ksi)]
-nttofrp:=out(cut,[t:cut]natrp(t),ksi,nksi):natt
-@[xt:natt][yt:natt]
-is:=is"e"(natt,xt,yt):'prop'
-nis:=not(is(xt,yt)):'prop'
-@[p:[x:natt]'prop']
-all:=all"l"(natt,p):'prop'
-some:=some"l"(natt,p):'prop'
-one:=one"e"(natt,p):'prop'
-xt@[st:set(natt)]
-in:=esti(natt,xt,st):'prop'
-xt@rpofntt:=in"e"(cut,[t:cut]natrp(t),xt):cut
-natrpi:=inp(cut,[t:cut]natrp(t),xt):natrp(rpofntt(xt))
-nksi@[eta:cut][neta:natrp(eta)][i:is"rp"(ksi,eta)]
-isrpentt:=isouti(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is(nttofrp(ksi,nksi),nttofrp(eta,neta))
-neta@[i:is(nttofrp(ksi,nksi),nttofrp(eta,neta))]
-isrpintt:=isoute(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is"rp"(ksi,eta)
-yt@[i:is(xt,yt)]
-isntterp:=isini(cut,[t:cut]natrp(t),xt,yt,i):is"rp"(rpofntt(xt),rpofntt(yt))
-yt@[i:is"rp"(rpofntt(xt),rpofntt(yt))]
-isnttirp:=isine(cut,[t:cut]natrp(t),xt,yt,i):is(xt,yt)
-nksi@isrpntt1:=isinout(cut,[t:cut]natrp(t),ksi,nksi):is"rp"(ksi,rpofntt(nttofrp(ksi,nksi)))
-xt@isnttrp1:=isoutin(cut,[t:cut]natrp(t),xt):is(xt,nttofrp(rpofntt(xt),natrpi(xt)))
-@[x:nat]
-nttofnt:=nttofrp(rpofnt(x),natrpi"rp"(x)):natt
-[y:nat][i:is"n"(x,y)]
-isntentt:=isrpentt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),isnterp(x,y,i)):is(nttofnt(x),nttofnt(y))
-y@[i:is(nttofnt(x),nttofnt(y))]
-isntintt:=isntirp(x,y,isrpintt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),i)):is"n"(x,y)
-xt@ntofntt:=ntofrp(rpofntt(xt),natrpi(xt)):nat
-yt@[i:is(xt,yt)]
-isnttent:=isrpent(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),isntterp(xt,yt,i)):is"n"(ntofntt(xt),ntofntt(yt))
-yt@[i:is"n"(ntofntt(xt),ntofntt(yt))]
-isnttint:=isnttirp(xt,yt,isrpint(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),i)):is(xt,yt)
-+iii5
-x@t5:=isrpntt1(rpofnt(x),natrpi"rp"(x)):is"rp"(rpofnt(x),rpofntt(nttofnt(x)))
-t6:=isrpent(rpofnt(x),natrpi"rp"(x),rpofntt(nttofnt(x)),natrpi(nttofnt(x)),t5):is"n"(ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)))
--iii5
-x@isntntt1:=tris(nat,x,ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)),isntrp1(x),t6".iii5"):is"n"(x,ntofntt(nttofnt(x)))
-+*iii5
-xt@t7:=isrpnt1(rpofntt(xt),natrpi(xt)):is"rp"(rpofntt(xt),rpofnt(ntofntt(xt)))
-t8:=isrpentt(rpofntt(xt),natrpi(xt),rpofnt(ntofntt(xt)),natrpi"rp"(ntofntt(xt)),t7):is(nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)))
--iii5
-xt@isnttnt1:=tris(natt,xt,nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)),isnttrp1(xt),t8".iii5"):is(xt,nttofnt(ntofntt(xt)))
-x@isntntt2:=symis(nat,x,ntofntt(nttofnt(x)),isntntt1):is"n"(ntofntt(nttofnt(x)),x)
-xt@isnttnt2:=symis(natt,xt,nttofnt(ntofntt(xt)),isnttnt1):is(nttofnt(ntofntt(xt)),xt)
-@1t:=nttofnt(1):natt
-suct:=[x:natt]nttofnt(<ntofntt(x)>suc):[x:natt]natt
-+5156
-xt@[j:is(<xt>suct,1t)]
-t1:=isntintt(<ntofntt(xt)>suc,1,j):is"n"(<ntofntt(xt)>suc,1)
--5156
-xt@satz156a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<ntofntt(xt)>suc,1),<ntofntt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5156"(t)):nis(<xt>suct,1t)
-yt@[i:is(<xt>suct,<yt>suct)]
-+*5156
-i@t2:=isntintt(<ntofntt(xt)>suc,<ntofntt(yt)>suc,i):is"n"(<ntofntt(xt)>suc,<ntofntt(yt)>suc)
--5156
-i@satz156b:=isnttint(xt,yt,<t2".5156"><ntofntt(yt)><ntofntt(xt)>ax4):is(xt,yt)
-@[st:set(natt)]
-cond1:=in(1t,st):'prop'
-cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
-[c1:cond1][c2:cond2]
-+*5156
-c2@[x:nat]
-prop1:=in(nttofnt(x),st):'prop'
-[p:prop1(x)]
-t3:=<p><nttofnt(x)>c2:in(<nttofnt(x)>suct,st)
-t4:=isp(nat,[t:nat]in(nttofnt(<t>suc),st),ntofntt(nttofnt(x)),x,t3,isntntt2(x)):prop1(<x>suc)
--5156
-c2@[xt:natt]
-+*5156
-xt@t5:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t4(t,u),ntofntt(xt)):in(nttofnt(ntofntt(xt)),st)
--5156
-xt@satz156c:=isp(natt,[t:natt]in(t,st),nttofnt(ntofntt(xt)),xt,t5".5156",isnttnt2(xt)):in(xt,st)
-@ax3t:=[x:natt]satz156a(x):[x:natt]nis(<x>suct,1t)
-ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz156b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
-ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz156c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
--nt
-+rtt
-@ratt:=ot(cut,[t:cut]ratrp(t)):'type'
-[ksi:cut][rtksi:ratrp(ksi)]
-rttofrp:=out(cut,[t:cut]ratrp(t),ksi,rtksi):ratt
-@[x0t:ratt][y0t:ratt]
-is:=is"e"(ratt,x0t,y0t):'prop'
-nis:=not(is(x0t,y0t)):'prop'
-@[p:[x:ratt]'prop']
-all:=all"l"(ratt,p):'prop'
-some:=some"l"(ratt,p):'prop'
-one:=one"e"(ratt,p):'prop'
-x0t@rpofrtt:=in"e"(cut,[t:cut]ratrp(t),x0t):cut
-ratrpi:=inp(cut,[t:cut]ratrp(t),x0t):ratrp(rpofrtt(x0t))
-rtksi@[eta:cut][rteta:ratrp(eta)][i:is"rp"(ksi,eta)]
-isrpertt:=isouti(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))
-rteta@[i:is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))]
-isrpirtt:=isoute(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is"rp"(ksi,eta)
-y0t@[i:is(x0t,y0t)]
-isrtterp:=isini(cut,[t:cut]ratrp(t),x0t,y0t,i):is"rp"(rpofrtt(x0t),rpofrtt(y0t))
-y0t@[i:is"rp"(rpofrtt(x0t),rpofrtt(y0t))]
-isrttirp:=isine(cut,[t:cut]ratrp(t),x0t,y0t,i):is(x0t,y0t)
-rtksi@isrprtt1:=isinout(cut,[t:cut]ratrp(t),ksi,rtksi):is"rp"(ksi,rpofrtt(rttofrp(ksi,rtksi)))
-x0t@isrttrp1:=isoutin(cut,[t:cut]ratrp(t),x0t):is(x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)))
-@[x0:rat]
-rttofrt:=rttofrp(rpofrt(x0),ratrpi"rp"(x0)):ratt
-[y0:rat][i:is"rt"(x0,y0)]
-isrtertt:=isrpertt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),isrterp(x0,y0,i)):is(rttofrt(x0),rttofrt(y0))
-y0@[i:is(rttofrt(x0),rttofrt(y0))]
-isrtirtt:=isrtirp(x0,y0,isrpirtt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),i)):is"rt"(x0,y0)
-x0t@rtofrtt:=rtofrp(rpofrtt(x0t),ratrpi(x0t)):rat
-y0t@[i:is(x0t,y0t)]
-isrttert:=isrpert(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),isrtterp(x0t,y0t,i)):is"rt"(rtofrtt(x0t),rtofrtt(y0t))
-y0t@[i:is"rt"(rtofrtt(x0t),rtofrtt(y0t))]
-isrttirt:=isrttirp(x0t,y0t,isrpirt(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),i)):is(x0t,y0t)
-+iii5
-x0@t9:=isrprtt1(rpofrt(x0),ratrpi"rp"(x0)):is"rp"(rpofrt(x0),rpofrtt(rttofrt(x0)))
-t10:=isrpert(rpofrt(x0),ratrpi"rp"(x0),rpofrtt(rttofrt(x0)),ratrpi(rttofrt(x0)),t9):is"rt"(rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)))
--iii5
-x0@isrtrtt1:=tris(rat,x0,rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)),isrtrp1(x0),t10".iii5"):is"rt"(x0,rtofrtt(rttofrt(x0)))
-+*iii5
-x0t@t11:=isrprt1(rpofrtt(x0t),ratrpi(x0t)):is"rp"(rpofrtt(x0t),rpofrt(rtofrtt(x0t)))
-t12:=isrpertt(rpofrtt(x0t),ratrpi(x0t),rpofrt(rtofrtt(x0t)),ratrpi"rp"(rtofrtt(x0t)),t11):is(rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)))
--iii5
-x0t@isrttrt1:=tris(ratt,x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)),isrttrp1(x0t),t12".iii5"):is(x0t,rttofrt(rtofrtt(x0t)))
--rtt
-@[ksi:cut]
-example2:=satz153c(1rp,ksi):is(ts(ksi,ov(1rp,ksi)),1rp)
-[rtksi:ratrp(ksi)]
-+5157
-x01:=rtofrp(ksi,rtksi):rat
-ksi@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
-rtksi@[y0:rat][i:in(y0,s1)]
-t1:=estie(rat,[x:rat]urt(ksi,x),y0,i):urt(ksi,y0)
-[m:more"rt"(x01,y0)]
-t2:=lrtrpofrt(x01,y0,satz82(x01,y0,m)):lrt(rpofrt(x01),y0)
-t3:=isp(cut,[x:cut]lrt(x,y0),rpofrt(x01),ksi,t2,isrprt2(ksi,rtksi)):lrt(ksi,y0)
-i@t4:=th3"l.imp"(more"rt"(x01,y0),lrt(ksi,y0),t1,[t:more"rt"(x01,y0)]t3(t)):not(more"rt"(x01,y0))
-t5:=satz81e(x01,y0,t4):lessis"rt"(x01,y0)
-rtksi@t6:=[x:rat][t:in(x,s1)]t5(x,t):lb(s1,x01)
-t7:=urtrpofrt(x01,x01,moreisi2"rt"(x01,x01,refis(rat,x01))):urt(rpofrt(x01),x01)
-t8:=isp(cut,[x:cut]urt(x,x01),rpofrt(x01),ksi,t7,isrprt2(ksi,rtksi)):urt(ksi,x01)
-t9:=estii(rat,[x:rat]urt(ksi,x),x01,t8):in(x01,s1)
-t10:=andi(lb(s1,x01),in(x01,s1),t6,t9):min(s1,x01)
--5157
-satz157a:=t10".5157":min(setof(rat,[x:rat]urt(ksi,x)),rtofrp(ksi,rtksi))
-satz157b:=somei(rat,[x:rat]min(s1".5157",x),x01".5157",t10".5157"):some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))
-ksi@[x0:rat][m:min(setof(rat,[x:rat]urt(ksi,x)),x0)]
-+*5157
-m"rp"@t11:=ande1(lb(s1,x0),in(x0,s1),m):lb(s1,x0)
-t12:=ande2(lb(s1,x0),in(x0,s1),m):in(x0,s1)
-t13:=estie(rat,[x:rat]urt(ksi,x),x0,t12):urt(ksi,x0)
-[y0:rat][ly:lrt(ksi,y0)]
-t14:=cutapp2a(ksi,y0,ly,x0,t13):less"rt"(y0,x0)
-t15:=lrtrpofrt(x0,y0,t14):lrt(rpofrt(x0),y0)
-y0@[uy:urt(ksi,y0)]
-t17:=estii(rat,[x:rat]urt(ksi,x),y0,uy):in(y0,s1)
-t18:=satz85(x0,y0,<t17><y0>t11):moreis"rt"(y0,x0)
-t19:=urtrpofrt(x0,y0,t18):urt(rpofrt(x0),y0)
-y0@t20:=cp(lrt(rpofrt(x0),y0),lrt(ksi,y0),[t:urt(ksi,y0)]t19(t)):imp(lrt(rpofrt(x0),y0),lrt(ksi,y0))
--5157
-m@satz157c:=isi1(ksi,rpofrt(x0),[x:rat][t:lrt(ksi,x)]t15".5157"(x,t),[x:rat]t20".5157"(x)):is(ksi,rpofrt(x0))
-ksi@[s:some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))]
-+*5157
-s@[x0:rat][m:min(s1,x0)]
-t21:=somei(rat,[x:rat]is(ksi,rpofrt(x)),x0,satz157c(x0,m)):ratrp(ksi)
--5157
-s@satz157d:=someapp(rat,[x:rat]min(s1".5157",x),s,ratrp(ksi),[x:rat][t:min(s1".5157",x)]t21".5157"(x,t)):ratrp(ksi)
-ksi@[x0:rat][lx:lrt(ksi,x0)]
-+5158
-x0@xr:=rpofrt(x0):cut
-lx@t1:=urtrpofrt(x0,x0,moreisi2"rt"(x0,x0,refis(rat,x0))):urt(xr,x0)
-t2:=andi(urt(xr,x0),lrt(ksi,x0),t1,lx):and(urt(xr,x0),lrt(ksi,x0))
--5158
-satz158a:=somei(rat,[x:rat]and(urt(rpofrt(x0),x),lrt(ksi,x)),x0,t2".5158"):less(rpofrt(x0),ksi)
-x0@[ux:urt(ksi,x0)]
-+*5158
-ux@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
-[m:min(s1,x0)]
-t3:=symis(cut,ksi,xr,satz157c(ksi,x0,m)):is(xr,ksi)
-t4:=moreisi2(xr,ksi,t3):moreis(xr,ksi)
-ux@[n:not(min(s1,x0))]
-t5:=estii(rat,[x:rat]urt(ksi,x),x0,ux):in(x0,s1)
-t6:=th4"l.and"(lb(s1,x0),in(x0,s1),n,t5):not(lb(s1,x0))
-t7:=th1"l.some"(rat,[x:rat]imp(in(x,s1),lessis"rt"(x0,x)),t6):some"rt"([x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))))
-[y0:rat][o:not(imp(in(y0,s1),lessis"rt"(x0,y0)))]
-t8:=th5"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):in(y0,s1)
-t9:=estie(rat,[x:rat]urt(ksi,x),y0,t8):urt(ksi,y0)
-t10:=th6"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):not(lessis"rt"(x0,y0))
-t11:=satz82(x0,y0,satz81k(x0,y0,t10)):less"rt"(y0,x0)
-t12:=lrtrpofrt(x0,y0,t11):lrt(xr,y0)
-t13:=andi(lrt(xr,y0),urt(ksi,y0),t12,t9):and(lrt(xr,y0),urt(ksi,y0))
-t14:=somei(rat,[x:rat]and(lrt(xr,x),urt(ksi,x)),y0,t13):more(xr,ksi)
-n@t15:=someapp(rat,[x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))),t7,more(xr,ksi),[x:rat][t:not(imp(in(x,s1),lessis"rt"(x0,x)))]t14(x,t)):more(xr,ksi)
-t16:=moreisi1(xr,ksi,t15):moreis(xr,ksi)
--5158
-ux@satz158b:=th1"l.imp"(min(s1".5158",x0),moreis(rpofrt(x0),ksi),[t:min(s1".5158",x0)]t4".5158"(t),[t:not(min(s1".5158",x0))]t16".5158"(t)):moreis(rpofrt(x0),ksi)
-x0@[l:less(rpofrt(x0),ksi)]
-+*5158
-l@t17:=satz123h(xr,ksi,l):not(moreis(xr,ksi))
-t18:=th3"l.imp"(urt(ksi,x0),moreis(xr,ksi),t17,[t:urt(ksi,x0)]satz158b(t)):not(urt(ksi,x0))
--5158
-l@satz158c:=et(lrt(ksi,x0),t18".5158"):lrt(ksi,x0)
-x0@[m:moreis(rpofrt(x0),ksi)]
-+*5158
-m"rp"@t19:=satz123c(xr,ksi,m):not(less(xr,ksi))
--5158
-m@satz158d:=th3"l.imp"(lrt(ksi,x0),less(rpofrt(x0),ksi),t19".5158",[t:lrt(ksi,x0)]satz158a(t)):urt(ksi,x0)
-ksi@[eta:cut][l:less(ksi,eta)]
-+5159
-[x0:rat]
-xr:=rpofrt(x0):cut
-[ux:urt(ksi,x0)][lx:lrt(eta,x0)][z0:rat]
-zr:=rpofrt(z0):cut
-[lz:lrt(eta,z0)][k:less"rt"(x0,z0)]
-t1:=satz127a(ksi,xr,zr,satz124(xr,ksi,satz158b(ksi,x0,ux)),satz154c(x0,z0,k)):less(ksi,zr)
-t2:=andi(less(ksi,zr),less(zr,eta),t1,satz158a(eta,z0,lz)):and(less(ksi,zr),less(zr,eta))
-t3:=somei(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),z0,t2):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
-lx@t4:=cutapp3(eta,x0,lx,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:lrt(eta,x)][u:less"rt"(x0,x)]t3(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
--5159
-satz159:=lessapp(ksi,eta,l,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t4".5159"(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
-+*5159
-x0@[a:and(less(ksi,xr),less(xr,eta))]
-t5:=andi(ratrp(xr),and(less(ksi,xr),less(xr,eta)),ratrpi(x0),a):and3(ratrp(xr),less(ksi,xr),less(xr,eta))
-t6:=somei(cut,[c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)),xr,t5):some([c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)))
--5159
-l@satz159a:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta))),[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t6".5159"(x,t)):some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta)))
-[p:'prop'][p1:[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),eta)]p]
-+*5159
-p1@[y0:rat]
-yr:=rpofrt(y0):cut
-[a:and(less(ksi,yr),less(yr,eta))]
-t7:=ande1(less(ksi,yr),less(yr,eta),a):less(ksi,yr)
-t8:=ande2(less(ksi,yr),less(yr,eta),a):less(yr,eta)
-t9:=<t8><t7><y0>p1:p
--5159
-p1@satz159app:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,p,[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t9".5159"(x,t)):p
-eta@[z0:rat][m:more(rpofrt(z0),ts(ksi,eta))]
-+5160
-zr:=rpofrt(z0):cut
-nm:=mn(zr,ts(ksi,eta),m):cut
-dn:=pl(pl(ksi,eta),1rp):cut
-fr:=ov(nm,dn):cut
-zeta:=ite(less(fr,1rp),cut,fr,1rp):cut
-[l:less(fr,1rp)]
-t1:=itet(less(fr,1rp),cut,fr,1rp,l):is(zeta,fr)
-t2:=lessisi2(zeta,fr,t1):lessis(zeta,fr)
-t3:=lessisi1(zeta,1rp,satz127a(zeta,fr,1rp,t2,l)):lessis(zeta,1rp)
-m@[n:not(less(fr,1rp))]
-t4:=itef(less(fr,1rp),cut,fr,1rp,n):is(zeta,1rp)
-t5:=lessisi2(zeta,1rp,t4):lessis(zeta,1rp)
-t6:=trlessis(zeta,1rp,fr,t5,satz124(fr,1rp,satz123f(fr,1rp,n))):lessis(zeta,fr)
-m@t7:=th1"l.imp"(less(fr,1rp),lessis(zeta,1rp),[t:less(fr,1rp)]t3(t),[t:not(less(fr,1rp))]t5(t)):lessis(zeta,1rp)
-t8:=th1"l.imp"(less(fr,1rp),lessis(zeta,fr),[t:less(fr,1rp)]t2(t),[t:not(less(fr,1rp))]t6(t)):lessis(zeta,fr)
-[z1:rat]
-zr1:=rpofrt(z1):cut
-[l1:less(ksi,zr1)][l2:less(zr1,pl(ksi,zeta))][z2:rat]
-zr2:=rpofrt(z2):cut
-[l3:less(eta,zr2)][l4:less(zr2,pl(eta,zeta))]
-t9:=isless2(ts(pl(ksi,zeta),pl(eta,zeta)),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),ts(zr1,zr2),disttp2(pl(ksi,zeta),eta,zeta),satz147a(zr1,pl(ksi,zeta),zr2,pl(eta,zeta),l2,l4)):less(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)))
-t10:=lessisi2(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),tris(cut,ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(zeta,eta)),pl(ts(ksi,eta),ts(eta,zeta)),disttp1(ksi,zeta,eta),ispl2(ts(zeta,eta),ts(eta,zeta),ts(ksi,eta),comts(zeta,eta)))):lessis(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)))
-t11:=satz149a(pl(ksi,zeta),pl(ksi,1rp),zeta,zeta,satz139a(ksi,ksi,zeta,1rp,lessisi2(ksi,ksi,refis(cut,ksi)),t7),lessisi2(zeta,zeta,refis(cut,zeta))):lessis(ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta))
-t12:=satz139a(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta),t10,t11):lessis(pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
-t13:=satz127b(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),t9,t12):less(ts(zr1,zr2),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
-t14:=tris(cut,pl(eta,pl(ksi,1rp)),pl(pl(eta,ksi),1rp),pl(pl(ksi,eta),1rp),asspl2(eta,ksi,1rp),ispl1(pl(eta,ksi),pl(ksi,eta),1rp,compl(eta,ksi))):is(pl(eta,pl(ksi,1rp)),dn)
-t15:=tris(cut,pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(pl(eta,pl(ksi,1rp)),zeta),ts(dn,zeta),distpt1(eta,pl(ksi,1rp),zeta),ists1(pl(eta,pl(ksi,1rp)),dn,zeta,t14)):is(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta))
-t16:=tris(cut,pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta))),pl(ts(ksi,eta),ts(dn,zeta)),asspl1(ts(ksi,eta),ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ispl2(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta),ts(ksi,eta),t15)):is(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)))
-t17:=isless2(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)),ts(zr1,zr2),t16,t13):less(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)))
-t18:=islessis12(ts(zeta,dn),ts(dn,zeta),ts(fr,dn),nm,comts(zeta,dn),satz153e(nm,dn),satz149a(zeta,fr,dn,dn,t8,lessisi2(dn,dn,refis(cut,dn)))):lessis(ts(dn,zeta),nm)
-t19:=satz139a(ts(ksi,eta),ts(ksi,eta),ts(dn,zeta),nm,lessisi2(ts(ksi,eta),ts(ksi,eta),refis(cut,ts(ksi,eta))),t18):lessis(pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm))
-t20:=satz127b(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm),t17,t19):less(ts(zr1,zr2),pl(ts(ksi,eta),nm))
-t21:=isless2(pl(ts(ksi,eta),nm),zr,ts(zr1,zr2),satz140c(zr,ts(ksi,eta),m),t20):less(ts(zr1,zr2),zr)
-t22:=satz154f(ts"rt"(z1,z2),z0,isless1(ts(zr1,zr2),rpofrt(ts"rt"(z1,z2)),zr,symis(cut,rpofrt(ts"rt"(z1,z2)),ts(zr1,zr2),satz155c(z1,z2)),t21)):less"rt"(ts"rt"(z1,z2),z0)
-x0:=ov"rt"(z0,z2):rat
-xr:=rpofrt(x0):cut
-y0:=z2:rat
-yr:=rpofrt(y0):cut
-t23:=satz110e(z0,z2):is"rt"(ts"rt"(x0,y0),z0)
-t24:=ismore1"rt"(z0,ts"rt"(x0,z2),ts"rt"(z1,z2),symis(rat,ts"rt"(x0,z2),z0,t23),satz83(ts"rt"(z1,z2),z0,t22)):more"rt"(ts"rt"(x0,z2),ts"rt"(z1,z2))
-t25:=satz106a(x0,z1,z2,t24):more"rt"(x0,z1)
-t26:=trmore(xr,zr1,ksi,satz154a(x0,z1,t25),satz122(ksi,zr1,l1)):more(xr,ksi)
-t27:=satz122(eta,yr,l3):more(yr,eta)
-z0@[u0:rat]
-ur:=rpofrt(u0):cut
-[v0:rat]
-vr:=rpofrt(v0):cut
-prop1:=and3(more(ur,ksi),more(vr,eta),is"rt"(ts"rt"(u0,v0),z0)):'prop'
-z0@prop2:=some"rt"([x:rat]some"rt"([y:rat]prop1(x,y))):'prop'
-l4@t28:=and3i(more(xr,ksi),more(yr,eta),is"rt"(ts"rt"(x0,y0),z0),t26,t27,t23):prop1(x0,y0)
-t29:=somei(rat,[y:rat]prop1(x0,y),y0,t28):some"rt"([y:rat]prop1(x0,y))
-t30:=somei(rat,[x:rat]some"rt"([y:rat]prop1(x,y)),x0,t29):prop2
-l2@t31:=satz159app(eta,pl(eta,zeta),satz133a(eta,zeta),prop2,[x:rat][t:less(eta,rpofrt(x))][u:less(rpofrt(x),pl(eta,zeta))]t30(x,t,u)):prop2
--5160
-satz160:=satz159app(ksi,pl(ksi,zeta".5160"),satz133a(ksi,zeta".5160"),prop2".5160",[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),pl(ksi,zeta".5160"))]t31".5160"(x,t,u)):some"rt"([x:rat]some"rt"([y:rat]and3(more(rpofrt(x),ksi),more(rpofrt(y),eta),is"rt"(ts"rt"(x,y),z0))))
-[p:'prop'][p1:[x:rat][t:more(rpofrt(x),ksi)][y:rat][u:more(rpofrt(y),eta)][v:is"rt"(ts"rt"(x,y),z0)]p]
-+*5160
-p1@[x1:rat]
-xr1:=rpofrt(x1):cut
-[px:some"rt"([y:rat]prop1(x1,y))][y1:rat]
-yr1:=rpofrt(y1):cut
-[py:prop1(x1,y1)]
-t32:=and3e1(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(xr1,ksi)
-t33:=and3e2(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(yr1,eta)
-t34:=and3e3(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):is"rt"(ts"rt"(x1,y1),z0)
-t35:=<t34><t33><y1><t32><x1>p1:p
-px@t36:=someapp(rat,[y:rat]prop1(x1,y),px,p,[y:rat][v:prop1(x1,y)]t35(y,v)):p
--5160
-p1@satz160app:=someapp(rat,[x:rat]some"rt"([y:rat]prop1".5160"(x,y)),satz160,p,[x:rat][t:some"rt"([y:rat]prop1".5160"(x,y))]t36".5160"(x,t)):p
-+5161
-@[ksi:cut][eta:cut]
-min:=ite(less(ksi,eta),cut,ksi,eta):cut
-max:=ite(more(ksi,eta),cut,ksi,eta):cut
-[u0:rat]
-ur:=rpofrt(u0):cut
-[lu:lrt(min,u0)]
-t1:=satz158a(min,u0,lu):less(ur,min)
-[l:less(ksi,eta)]
-t2:=isless2(min,ksi,ur,itet(less(ksi,eta),cut,ksi,eta,l),t1):less(ur,ksi)
-t3:=trless(ur,ksi,eta,t2,l):less(ur,eta)
-lu@[n:not(less(ksi,eta))]
-t4:=isless2(min,eta,ur,itef(less(ksi,eta),cut,ksi,eta,n),t1):less(ur,eta)
-t5:=satz127b(ur,eta,ksi,t4,satz124(ksi,eta,satz123f(ksi,eta,n))):less(ur,ksi)
-lu@t6:=th1"l.imp"(less(ksi,eta),less(ur,ksi),[t:less(ksi,eta)]t2(t),[t:not(less(ksi,eta))]t5(t)):less(ur,ksi)
-t7:=th1"l.imp"(less(ksi,eta),less(ur,eta),[t:less(ksi,eta)]t3(t),[t:not(less(ksi,eta))]t4(t)):less(ur,eta)
-u0@[uu:urt(max,u0)]
-t8:=satz158b(max,u0,uu):moreis(ur,max)
-[m:more(ksi,eta)]
-t9:=ismoreis2(max,ksi,ur,itet(more(ksi,eta),cut,ksi,eta,m),t8):moreis(ur,ksi)
-t10:=trmoreis(ur,ksi,eta,t9,moreisi1(ksi,eta,m)):moreis(ur,eta)
-uu@[n:not(more(ksi,eta))]
-t11:=ismoreis2(max,eta,ur,itef(more(ksi,eta),cut,ksi,eta,n),t8):moreis(ur,eta)
-t12:=trmoreis(ur,eta,ksi,t11,satz125(ksi,eta,satz123e(ksi,eta,n))):moreis(ur,ksi)
-uu@t13:=th1"l.imp"(more(ksi,eta),moreis(ur,ksi),[t:more(ksi,eta)]t9(t),[t:not(more(ksi,eta))]t12(t)):moreis(ur,ksi)
-t14:=th1"l.imp"(more(ksi,eta),moreis(ur,eta),[t:more(ksi,eta)]t10(t),[t:not(more(ksi,eta))]t11(t)):moreis(ur,eta)
--5161
-@[zeta:cut]
-+*5161
-zeta@[ksi1:cut][ksi2:cut][m:more(ksi1,ksi2)]
-t15:=satz147(ksi1,ksi2,ksi1,ksi2,m,m):more(ts(ksi1,ksi1),ts(ksi2,ksi2))
-ksi2@sq1:=ts(ksi1,ksi1):cut
-sq2:=ts(ksi2,ksi2):cut
-m@t16:=ec3e21(is(sq1,sq2),more(sq1,sq2),less(sq1,sq2),satz123b(sq1,sq2),t15):nis(sq1,sq2)
-ksi2@[i:is(sq1,zeta)][j:is(sq2,zeta)]
-t17:=tris2(cut,sq1,sq2,zeta,i,j):is(sq1,sq2)
-t18:=[t:more(ksi1,ksi2)]<t17>t16(t):not(more(ksi1,ksi2))
-t19:=[t:less(ksi1,ksi2)]<symis(cut,sq1,sq2,t17)>t16(ksi2,ksi1,satz122(ksi1,ksi2,t)):not(less(ksi1,ksi2))
-t20:=or3e1(is(ksi1,ksi2),more(ksi1,ksi2),less(ksi1,ksi2),satz123a(ksi1,ksi2),t18,t19):is(ksi1,ksi2)
-zeta@t21:=[a:cut][b:cut][t:is(ts(a,a),zeta)][u:is(ts(b,b),zeta)]t20(a,b,t,u):amone(cut,[a:cut]is(ts(a,a),zeta))
-sqrtset:=setof(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta)):set(rat)
-[x0:rat]
-xr:=rpofrt(x0):cut
-[lx:lrt(min(1rp,zeta),x0)]
-t22:=t6(1rp,zeta,x0,lx):less(xr,1rp)
-t23:=t7(1rp,zeta,x0,lx):less(xr,zeta)
-t24:=isless1(xr,ts(xr,1rp),zeta,satz151a(xr),t23):less(ts(xr,1rp),zeta)
-t25:=trless(ts(xr,xr),ts(xr,1rp),zeta,satz148c(xr,xr,xr,1rp,lessisi2(xr,xr,refis(cut,xr)),t22),t24):less(ts(xr,xr),zeta)
-t26:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t25):in(x0,sqrtset)
-x0@[ux:urt(max(1rp,zeta),x0)]
-t27:=t13(1rp,zeta,x0,ux):moreis(xr,1rp)
-t28:=t14(1rp,zeta,x0,ux):moreis(xr,zeta)
-t29:=ismoreis1(xr,ts(xr,1rp),zeta,satz151a(xr),t28):moreis(ts(xr,1rp),zeta)
-t30:=trmoreis(ts(xr,xr),ts(xr,1rp),zeta,satz149(xr,xr,xr,1rp,moreisi2(xr,xr,refis(cut,xr)),t27),t29):moreis(ts(xr,xr),zeta)
-t31:=satz123c(ts(xr,xr),zeta,t30):not(less(ts(xr,xr),zeta))
-t32:=th3"l.imp"(in(x0,sqrtset),less(ts(xr,xr),zeta),t31,[t:in(x0,sqrtset)]estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t)):not(in(x0,sqrtset))
-x0@[i:in(x0,sqrtset)][y0:rat]
-yr:=rpofrt(y0):cut
-[l:less"rt"(y0,x0)]
-i@t33:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,i):less(ts(xr,xr),zeta)
-l@t34:=satz154c(y0,x0,l):less(yr,xr)
-t35:=trless(ts(yr,yr),ts(xr,xr),zeta,satz147a(yr,xr,yr,xr,t34,t34),t33):less(ts(yr,yr),zeta)
-t36:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),y0,t35):in(y0,sqrtset)
-i@t37:=satz122(ts(xr,xr),zeta,t33):more(zeta,ts(xr,xr))
-nm:=mn(zeta,ts(xr,xr),t37):cut
-dn:=pl(xr,pl(xr,1rp)):cut
-fr:=ov(nm,dn):cut
-[z0:rat]
-zr:=rpofrt(z0):cut
-[lz:lrt(min(1rp,fr),z0)]
-t38:=t6(1rp,fr,z0,lz):less(zr,1rp)
-t39:=t7(1rp,fr,z0,lz):less(zr,fr)
-t40:=satz94(x0,z0):more"rt"(pl"rt"(x0,z0),x0)
-t41:=tris(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),ts(pl(xr,zr),pl(xr,zr)),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ists12(rpofrt(pl"rt"(x0,z0)),pl(xr,zr),rpofrt(pl"rt"(x0,z0)),pl(xr,zr),satz155a(x0,z0),satz155a(x0,z0)),disttp2(pl(xr,zr),xr,zr)):is(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)))
-t42:=symis(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),t41):is(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))))
-t43:=lessisi2(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),tris(cut,ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(zr,xr)),pl(ts(xr,xr),ts(xr,zr)),disttp1(xr,zr,xr),ispl2(ts(zr,xr),ts(xr,zr),ts(xr,xr),comts(zr,xr)))):lessis(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)))
-t44:=satz145c(pl(xr,zr),pl(xr,1rp),zr,satz138c(xr,xr,zr,1rp,lessisi2(xr,xr,refis(cut,xr)),t38)):less(ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr))
-t45:=satz138c(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr),t43,t44):less(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)))
-t46:=tris(cut,pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),pl(ts(xr,zr),ts(pl(xr,1rp),zr))),pl(ts(xr,xr),ts(dn,zr)),asspl1(ts(xr,xr),ts(xr,zr),ts(pl(xr,1rp),zr)),ispl2(pl(ts(xr,zr),ts(pl(xr,1rp),zr)),ts(dn,zr),ts(xr,xr),distpt1(xr,pl(xr,1rp),zr))):is(pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)))
-t47:=isless12(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)),t42,t46,t45):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)))
-t48:=isless2(ts(dn,fr),nm,ts(dn,zr),satz153c(nm,dn),satz148c(dn,dn,zr,fr,lessisi2(dn,dn,refis(cut,dn)),t39)):less(ts(dn,zr),nm)
-t49:=satz138c(ts(xr,xr),ts(xr,xr),ts(dn,zr),nm,lessisi2(ts(xr,xr),ts(xr,xr),refis(cut,ts(xr,xr))),t48):less(pl(ts(xr,xr),ts(dn,zr)),pl(ts(xr,xr),nm))
-t50:=isless2(pl(ts(xr,xr),nm),zeta,pl(ts(xr,xr),ts(dn,zr)),satz140c(zeta,ts(xr,xr),t37),t49):less(pl(ts(xr,xr),ts(dn,zr)),zeta)
-t51:=trless(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)),zeta,t47,t50):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),zeta)
-t52:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),pl"rt"(x0,z0),t51):in(pl"rt"(x0,z0),sqrtset)
-t53:=andi(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0),t52,t40):and(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0))
-t54:=somei(rat,[y:rat]and(in(y,sqrtset),more"rt"(y,x0)),pl"rt"(x0,z0),t53):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
-i@t55:=cutapp1a(min(1rp,fr),some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0))),[x:rat][t:lrt(min(1rp,fr),x)]t54(x,t)):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
-x0@[lx:lrt(min(1rp,zeta),x0)][y0:rat][uy:urt(max(1rp,zeta),y0)]
-t56:=cut2(sqrtset,x0,t26(lx),y0,t32(y0,uy),[x:rat][t:in(x,sqrtset)][y:rat][u:less"rt"(y,x)]t36(x,t,y,u),[x:rat][t:in(x,sqrtset)]t55(x,t)):cutprop(sqrtset)
-lx@t57:=cutapp1b(max(1rp,zeta),cutprop(sqrtset),[y:rat][t:urt(max(1rp,zeta),y)]t56(y,t)):cutprop(sqrtset)
-zeta@t58:=cutapp1a(min(1rp,zeta),cutprop(sqrtset),[x:rat][t:lrt(min(1rp,zeta),x)]t57(x,t)):cutprop(sqrtset)
-rtc:=cutof(sqrtset,t58):cut
-@[x0:rat][y0:rat][l:lessis"rt"(x0,y0)]
-t59:=th9"l.or"(less"rt"(x0,y0),is"rt"(x0,y0),less(rpofrt(x0),rpofrt(y0)),is(rpofrt(x0),rpofrt(y0)),l,[t:less"rt"(x0,y0)]satz154c(x0,y0,t),[t:is"rt"(x0,y0)]satz154b(x0,y0,t)):lessis(rpofrt(x0),rpofrt(y0))
-y0@[m:moreis"rt"(x0,y0)]
-t60:=satz125(rpofrt(y0),rpofrt(x0),t59(y0,x0,satz84(x0,y0,m))):moreis(rpofrt(x0),rpofrt(y0))
-zeta@[m:more(ts(rtc,rtc),zeta)]
-t61:=satz121(ts(rtc,rtc),zeta,m):less(zeta,ts(rtc,rtc))
-[z1:rat]
-zr1:=rpofrt(z1):cut
-[l1:less(zeta,zr1)][l2:less(zr1,ts(rtc,rtc))]
-t62:=satz158c(ts(rtc,rtc),z1,l2):lrt(ts(rtc,rtc),z1)
-[x1:rat]
-xr1:=rpofrt(x1):cut
-[lx1:lrt(rtc,x1)][x2:rat]
-xr2:=rpofrt(x2):cut
-[lx2:lrt(rtc,x2)][i:is"rt"(z1,ts"rt"(x1,x2))]
-xm:=ite(more"rt"(x1,x2),rat,x1,x2):rat
-xrm:=rpofrt(xm):cut
-[o:more"rt"(x1,x2)]
-t63:=symis(rat,xm,x1,itet(more"rt"(x1,x2),rat,x1,x2,o)):is"rt"(x1,xm)
-t64:=isp(rat,[x:rat]lrt(rtc,x),x1,xm,lx1,t63):lrt(rtc,xm)
-t65:=lessisi2"rt"(x1,xm,t63):lessis"rt"(x1,xm)
-t66:=lessisi1"rt"(x2,xm,satz87b(x2,x1,xm,satz82(x1,x2,o),t65)):lessis"rt"(x2,xm)
-i@[n:not(more"rt"(x1,x2))]
-t67:=symis(rat,xm,x2,itef(more"rt"(x1,x2),rat,x1,x2,n)):is"rt"(x2,xm)
-t68:=isp(rat,[x:rat]lrt(rtc,x),x2,xm,lx2,t67):lrt(rtc,xm)
-t69:=lessisi2"rt"(x2,xm,t67):lessis"rt"(x2,xm)
-t70:=satz88(x1,x2,xm,satz81e(x1,x2,n),t69):lessis"rt"(x1,xm)
-i@t71:=th1"l.imp"(more"rt"(x1,x2),lrt(rtc,xm),[t:more"rt"(x1,x2)]t64(t),[t:not(more"rt"(x1,x2))]t68(t)):lrt(rtc,xm)
-t72:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x1,xm),[t:more"rt"(x1,x2)]t65(t),[t:not(more"rt"(x1,x2))]t70(t)):lessis"rt"(x1,xm)
-t73:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x2,xm),[t:more"rt"(x1,x2)]t66(t),[t:not(more"rt"(x1,x2))]t69(t)):lessis"rt"(x2,xm)
-t74:=ini(sqrtset,t58,xm,t71):in(xm,sqrtset)
-t75:=t59(x1,xm,t72):lessis(xr1,xrm)
-t76:=t59(x2,xm,t73):lessis(xr2,xrm)
-t77:=tris(cut,zr1,rpofrt(ts"rt"(x1,x2)),ts(xr1,xr2),satz154b(z1,ts"rt"(x1,x2),i),satz155c(x1,x2)):is(zr1,ts(xr1,xr2))
-t78:=islessis1(ts(xr1,xr2),zr1,ts(xrm,xrm),symis(cut,zr1,ts(xr1,xr2),t77),satz149a(xr1,xrm,xr2,xrm,t75,t76)):lessis(zr1,ts(xrm,xrm))
-t79:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),xm,t74):less(ts(xrm,xrm),zeta)
-t80:=satz127a(zr1,ts(xrm,xrm),zeta,t78,t79):less(zr1,zeta)
-t81:=<t80>ec3e23(is(zr1,zeta),more(zr1,zeta),less(zr1,zeta),satz123b(zr1,zeta),satz122(zeta,zr1,l1)):con
-t82:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t81(x,t,y,u,v)):con
-l2@t82a:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t82(x,t,y,u,v)):con
-m@t83:=satz159app(zeta,ts(rtc,rtc),t61,con,[x:rat][t:less(zeta,rpofrt(x))][u:less(rpofrt(x),ts(rtc,rtc))]t82a(x,t,u)):con
-zeta@[l:less(ts(rtc,rtc),zeta)][z2:rat]
-zr2:=rpofrt(z2):cut
-[l3:less(ts(rtc,rtc),zr2)][l4:less(zr2,zeta)]
-t84:=satz122(ts(rtc,rtc),zr2,l3):more(zr2,ts(rtc,rtc))
-[y1:rat]
-yr1:=rpofrt(y1):cut
-[m1:more(yr1,rtc)][y2:rat]
-yr2:=rpofrt(y2):cut
-[m2:more(yr2,rtc)][i:is"rt"(ts"rt"(y1,y2),z2)]
-ym:=ite(less"rt"(y1,y2),rat,y1,y2):rat
-yrm:=rpofrt(ym):cut
-[k:less"rt"(y1,y2)]
-t85:=symis(rat,ym,y1,itet(less"rt"(y1,y2),rat,y1,y2,k)):is"rt"(y1,ym)
-t86:=satz154b(y1,ym,t85):is(yr1,yrm)
-t87:=ismore1(yr1,yrm,rtc,t86,m1):more(yrm,rtc)
-t88:=moreisi2(yr1,yrm,t86):moreis(yr1,yrm)
-t89:=moreisi1(yr2,yrm,satz127d(yr2,yr1,yrm,satz122(yr1,yr2,satz154c(y1,y2,k)),t88)):moreis(yr2,yrm)
-i@[n:not(less"rt"(y1,y2))]
-t90:=symis(rat,ym,y2,itef(less"rt"(y1,y2),rat,y1,y2,n)):is"rt"(y2,ym)
-t91:=satz154b(y2,ym,t90):is(yr2,yrm)
-t92:=ismore1(yr2,yrm,rtc,t91,m2):more(yrm,rtc)
-t93:=moreisi2(yr2,yrm,t91):moreis(yr2,yrm)
-t94:=trmoreis(yr1,yr2,yrm,t60(y1,y2,satz81f(y1,y2,n)),t93):moreis(yr1,yrm)
-i@t95:=th1"l.imp"(less"rt"(y1,y2),more(yrm,rtc),[t:less"rt"(y1,y2)]t87(t),[t:not(less"rt"(y1,y2))]t92(t)):more(yrm,rtc)
-t96:=th1"l.imp"(less"rt"(y1,y2),moreis(yr1,yrm),[t:less"rt"(y1,y2)]t88(t),[t:not(less"rt"(y1,y2))]t94(t)):moreis(yr1,yrm)
-t97:=th1"l.imp"(less"rt"(y1,y2),moreis(yr2,yrm),[t:less"rt"(y1,y2)]t89(t),[t:not(less"rt"(y1,y2))]t93(t)):moreis(yr2,yrm)
-t98:=satz158d(rtc,ym,moreisi1(yrm,rtc,t95)):urt(rtc,ym)
-t99:=th3"l.imp"(in(ym,sqrtset),lrt(rtc,ym),t98,[t:in(ym,sqrtset)]ine(sqrtset,t58,ym,t)):not(in(ym,sqrtset))
-t100:=th3"l.imp"(less(ts(yrm,yrm),zeta),in(ym,sqrtset),t99,[t:less(ts(yrm,yrm),zeta)]estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),ym,t)):not(less(ts(yrm,yrm),zeta))
-t101:=satz123f(ts(yrm,yrm),zeta,t100):moreis(ts(yrm,yrm),zeta)
-t101a:=satz149(yr1,yrm,yr2,yrm,t96,t97):moreis(ts(yr1,yr2),ts(yrm,yrm))
-t102:=ismoreis1(ts(yr1,yr2),zr2,ts(yrm,yrm),tris(cut,ts(yr1,yr2),rpofrt(ts"rt"(y1,y2)),zr2,symis(cut,rpofrt(ts"rt"(y1,y2)),ts(yr1,yr2),satz155c(y1,y2)),satz154b(ts"rt"(y1,y2),z2,i)),t101a):moreis(zr2,ts(yrm,yrm))
-t103:=trmoreis(zr2,ts(yrm,yrm),zeta,t102,t101):moreis(zr2,zeta)
-t104:=<l4>satz123c(zr2,zeta,t103):con
-l4@t105:=satz160app(rtc,rtc,z2,t84,con,[x:rat][t:more(rpofrt(x),rtc)][y:rat][u:more(rpofrt(y),rtc)][v:is"rt"(ts"rt"(x,y),z2)]t104(x,t,y,u,v)):con
-l@t106:=satz159app(ts(rtc,rtc),zeta,l,con,[x:rat][t:less(ts(rtc,rtc),rpofrt(x))][u:less(rpofrt(x),zeta)]t105(x,t,u)):con
-zeta@t107:=or3e1(is(ts(rtc,rtc),zeta),more(ts(rtc,rtc),zeta),less(ts(rtc,rtc),zeta),satz123a(ts(rtc,rtc),zeta),[t:more(ts(rtc,rtc),zeta)]t83(t),[t:less(ts(rtc,rtc),zeta)]t106(t)):is(ts(rtc,rtc),zeta)
-t108:=somei(cut,[a:cut]is(ts(a,a),zeta),rtc,t107):some([a:cut]is(ts(a,a),zeta))
--5161
-zeta@satz161:=onei(cut,[a:cut]is(ts(a,a),zeta),t21".5161",t108".5161"):one([a:cut]is(ts(a,a),zeta))
-@[ksi:cut]
-irratrp:=not(ratrp(ksi)):'prop'
--rp
--rt
-+5162
-@[v:nat]
-t1:=tris(nat,pl(v,v),pl(ts(1,v),v),ts(<1>suc,v),ispl1(v,ts(1,v),v,satz28g(v)),satz28h(1,v)):is(pl(v,v),ts(<1>suc,v))
-t2:=isless2(pl(v,v),ts(<1>suc,v),v,t1,satz18a(v,v)):less(v,ts(<1>suc,v))
-[w:nat][l:less(ts(v,v),ts(w,w))]
-t3:=satz10j(v,w,th3"l.imp"(moreis(v,w),moreis(ts(v,v),ts(w,w)),satz10h(ts(v,v),ts(w,w),l),[t:moreis(v,w)]satz36(v,w,v,w,t,t))):less(v,w)
-w@t4:=tris(nat,ts(pl(v,w),v),pl(ts(v,v),ts(w,v)),pl(ts(v,v),ts(v,w)),disttp1(v,w,v),ispl2(ts(w,v),ts(v,w),ts(v,v),comts(w,v))):is(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)))
-t5:=tr3is(nat,ts(pl(v,w),pl(v,w)),pl(ts(pl(v,w),v),ts(pl(v,w),w)),pl(pl(ts(v,v),ts(v,w)),pl(ts(v,w),ts(w,w))),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),disttp2(pl(v,w),v,w),ispl12(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)),ts(pl(v,w),w),pl(ts(v,w),ts(w,w)),t4,disttp1(v,w,w)),asspl2(pl(ts(v,v),ts(v,w)),ts(v,w),ts(w,w))):is(ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)))
-t6:=tris(nat,pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),pl(ts(v,w),ts(v,w))),pl(ts(v,v),ts(<1>suc,ts(v,w))),asspl1(ts(v,v),ts(v,w),ts(v,w)),ispl2(pl(ts(v,w),ts(v,w)),ts(<1>suc,ts(v,w)),ts(v,v),t1(ts(v,w)))):is(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))))
-nun:=tris(nat,ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),t5,ispl1(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w),t6)):is(ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)))
-nun1:=symis(nat,ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),nun):is(pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),ts(pl(v,w),pl(v,w)))
-prop1:=eq(tf(fr(w,v),fr(w,v)),fr(<1>suc,1)):'prop'
-v@prop2:=some([t:nat]prop1(t)):'prop'
-@prop3:=some([u:nat]prop2(u)):'prop'
-[p:prop3]
-y:=ind(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):nat
-t7:=oneax(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):min([u:nat]prop2(u),y)
-t8:=ande1(lb([u:nat]prop2(u),y),prop2(y),t7):lb([u:nat]prop2(u),y)
-t9:=ande2(lb([u:nat]prop2(u),y),prop2(y),t7):prop2(y)
-[x:nat][q:prop1(y,x)]
-t10:=treq1(fr(<1>suc,1),fr(ts(x,x),ts(y,y)),tf(fr(x,y),fr(x,y)),q,tfeq12a(x,y,x,y)):eq(fr(<1>suc,1),fr(ts(x,x),ts(y,y)))
-t11:=tr4is(nat,ts(<1>suc,ts(y,y)),ts(num(fr(<1>suc,1)),den(fr(ts(x,x),ts(y,y)))),ts(num(fr(ts(x,x),ts(y,y))),den(fr(<1>suc,1))),ts(ts(x,x),1),ts(x,x),12isnd(<1>suc,1,ts(x,x),ts(y,y)),t10,ndis12(ts(x,x),ts(y,y),<1>suc,1),satz28a(ts(x,x))):is(ts(<1>suc,ts(y,y)),ts(x,x))
-t12:=isless2(ts(<1>suc,ts(y,y)),ts(x,x),ts(y,y),t11,t2(ts(y,y))):less(ts(y,y),ts(x,x))
-t13:=isless1(ts(ts(<1>suc,y),y),ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)),tris(nat,ts(ts(<1>suc,y),y),ts(<1>suc,ts(y,y)),ts(x,x),assts1(<1>suc,y,y),t11),satz35c(ts(<1>suc,y),ts(<1>suc,y),y,ts(<1>suc,y),lessisi2(ts(<1>suc,y),ts(<1>suc,y),refis(nat,ts(<1>suc,y))),t2(y))):less(ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)))
-t14:=t3(y,x,t12):less(y,x)
-t15:=t3(x,ts(<1>suc,y),t13):less(x,ts(<1>suc,y))
-[u:nat][i:is(x,pl(y,u))]
-t16:=isless12(x,pl(y,u),ts(<1>suc,y),pl(y,y),i,symis(nat,pl(y,y),ts(<1>suc,y),t1(y)),t15):less(pl(y,u),pl(y,y))
-t17:=satz20f(u,y,y,t16):less(u,y)
-[t:nat][j:is(y,pl(u,t))]
-t18:=symis(nat,y,pl(u,t),j):is(pl(u,t),y)
-t19:=tris(nat,ts(x,x),ts(pl(y,u),pl(y,u)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ists12(x,pl(y,u),x,pl(y,u),i,i),nun(y,u)):is(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)))
-t20:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),ispl1(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t),t19),asspl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u),ts(t,t))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))))
-t21:=tr3is(nat,ts(y,u),ts(u,y),ts(u,pl(u,t)),pl(ts(u,u),ts(u,t)),comts(y,u),ists2(y,pl(u,t),u,j),disttp2(u,u,t)):is(ts(y,u),pl(ts(u,u),ts(u,t)))
-t22:=tris(nat,ts(<1>suc,ts(y,u)),ts(<1>suc,pl(ts(u,u),ts(u,t))),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ists2(ts(y,u),pl(ts(u,u),ts(u,t)),<1>suc,t21),disttp2(<1>suc,ts(u,u),ts(u,t))):is(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))))
-t23:=tris(nat,pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(y,y),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),ispl2(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ts(y,y),t22),asspl2(ts(y,y),ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))):is(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))))
-t24:=tr3is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),pl(pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),t20,ispl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t)),t23),asspl1(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))))
-t25:=tr4is(nat,pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),pl(pl(ts(<1>suc,ts(u,t)),ts(u,u)),ts(t,t)),pl(pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t)),ts(pl(u,t),pl(u,t)),ts(y,y),asspl2(ts(<1>suc,ts(u,t)),ts(u,u),ts(t,t)),ispl1(pl(ts(<1>suc,ts(u,t)),ts(u,u)),pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t),compl(ts(<1>suc,ts(u,t)),ts(u,u))),nun1(u,t),ists12(pl(u,t),y,pl(u,t),y,t18,t18)):is(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y))
-t26:=tr4is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),pl(ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u)))),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),t24,ispl2(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u))),t25),compl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),asspl2(ts(y,y),ts(y,y),ts(<1>suc,ts(u,u)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))))
-t27:=tris(nat,pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(y,y)),ts(x,x),t1(ts(y,y)),t11):is(pl(ts(y,y),ts(y,y)),ts(x,x))
-t28:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),pl(ts(x,x),ts(<1>suc,ts(u,u))),t26,ispl1(pl(ts(y,y),ts(y,y)),ts(x,x),ts(<1>suc,ts(u,u)),t27)):is(pl(ts(x,x),ts(t,t)),pl(ts(x,x),ts(<1>suc,ts(u,u))))
-t29:=satz20e(ts(t,t),ts(<1>suc,ts(u,u)),ts(x,x),t28):is(ts(t,t),ts(<1>suc,ts(u,u)))
-t30:=tr4is(nat,ts(num(fr(<1>suc,1)),den(fr(ts(t,t),ts(u,u)))),ts(<1>suc,ts(u,u)),ts(t,t),ts(ts(t,t),1),ts(num(fr(ts(t,t),ts(u,u))),den(fr(<1>suc,1))),ndis12(<1>suc,1,ts(t,t),ts(u,u)),symis(nat,ts(t,t),ts(<1>suc,ts(u,u)),t29),satz28e(ts(t,t)),12isnd(ts(t,t),ts(u,u),<1>suc,1)):eq(fr(<1>suc,1),fr(ts(t,t),ts(u,u)))
-t31:=treq2(tf(fr(t,u),fr(t,u)),fr(<1>suc,1),fr(ts(t,t),ts(u,u)),tfeq12a(t,u,t,u),t30):prop1(u,t)
-t32:=somei(nat,[v:nat]prop1(u,v),t,t31):prop2(u)
-t33:=<t32><u>t8:lessis(y,u)
-t34:=<t33>satz10g(y,u,satz12(u,y,t17)):con
-i@t35:=someapp(nat,[v:nat]diffprop(y,u,v),t17,con,[v:nat][w:diffprop(y,u,v)]t34(v,w)):con
-q@t36:=someapp(nat,[v:nat]diffprop(x,y,v),t14,con,[v:nat][w:diffprop(x,y,v)]t35(v,w)):con
-p@t37:=someapp(nat,[v:nat]prop1(y,v),t9,con,[v:nat][w:prop1(y,v)]t36(v,w)):con
--5162
-+*rt
-+5162
-@[x0:rat][i:is(ts(x0,x0),rtofn(<1>suc))][x:frac][xix0:inf(x,class(x0))]
-t38:=ise(ts(x0,x0),rtofn(<1>suc),tf(x,x),fr(<1>suc,1),tict(x0,x0,x,x,xix0,xix0),inclass(fr(<1>suc,1)),i):eq"n"(tf(x,x),fr(<1>suc,1))
-t39:=refeq1(fr(num(x),den(x)),x,fris(x)):eq"n"(fr(num(x),den(x)),x)
-t40:=eqtf12(fr(num(x),den(x)),x,fr(num(x),den(x)),x,t39,t39):eq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x))
-t41:=treq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x),fr(<1>suc,1),t40,t38):prop1"n.5162"(den(x),num(x))
-t42:=somei(nat,[t:nat]prop1"n.5162"(den(x),t),num(x),t41):prop2"n.5162"(den(x))
-t43:=somei(nat,[t:nat]prop2"n.5162"(t),den(x),t42):prop3"n.5162"
-t44:=t37"n.5162"(t43):con
-i@t45:=ratapp1(x0,con,[x:frac][t:inf(x,class(x0))]t44(x,t)):con
--5162
-+*rp
-+5162
-@ksi:=ind(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):cut
-t46:=oneax(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):is(ts(ksi,ksi),rpofnt(<1>suc))
-[r:ratrp(ksi)]
-x0:=rtofrp(ksi,r):rat
-t47:=tr3is(cut,rpofrt(ts"rt"(x0,x0)),ts(rpofrt(x0),rpofrt(x0)),ts(ksi,ksi),rpofnt(<1>suc),satz155c(x0,x0),ists12(rpofrt(x0),ksi,rpofrt(x0),ksi,isrprt2(ksi,r),isrprt2(ksi,r)),t46):is(rpofrt(ts"rt"(x0,x0)),rpofnt(<1>suc))
-t48:=isrtirp(ts"rt"(x0,x0),rtofn(<1>suc),t47):is"rt"(ts"rt"(x0,x0),rtofn(<1>suc))
-t49:=t45"rt.5162"(x0,t48):con
--5162
-@satz162:=somei(cut,[a:cut]irratrp(a),ksi".5162",[t:ratrp(ksi".5162")]t49".5162"(t)):some([a:cut]irratrp(a))
-[zeta:cut]
-sqrt:=ind(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):cut
-thsqrt1:=oneax(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):is(ts(sqrt(zeta),sqrt(zeta)),zeta)
-[ksi:cut][i:is(ts(ksi,ksi),zeta)]
-thsqrt2:=t20".5161"(zeta,ksi,sqrt,i,thsqrt1):is(ksi,sqrt)
-@[ksi:cut][eta:cut][i:is(ksi,eta)]
-issqrt:=isf(cut,cut,[t:cut]sqrt(t),ksi,eta,i):is(sqrt(ksi),sqrt(eta))
-@[ksi:cut][nx:natrp(ksi)][eta:cut][ny:natrp(eta)]
-+iiia
-x:=ntofrp(ksi,nx):nat
-y:=ntofrp(eta,ny):nat
-t1:=isrpnt1(ksi,nx):is(ksi,rpofnt(x))
-t2:=isrpnt1(eta,ny):is(eta,rpofnt(y))
-t3:=ispl12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(pl(ksi,eta),pl(rpofnt(x),rpofnt(y)))
-x0:=rtofn(x):rat
-y0:=rtofn(y):rat
-t4:=natrti(x):natrt(x0)
-t5:=natrti(y):natrt(y0)
-t6:=symis(cut,rpofrt(pl"rt"(x0,y0)),pl(rpofnt(x),rpofnt(y)),satz155a(x0,y0)):is(pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)))
-t7:=satz112d(x0,t4,y0,t5):natrt(pl"rt"(x0,y0))
-xpy:=nofrt(pl"rt"(x0,y0),t7):nat
-t8:=isrtn1(pl"rt"(x0,y0),t7):is"rt"(pl"rt"(x0,y0),rtofn(xpy))
-t9:=isrterp(pl"rt"(x0,y0),rtofn(xpy),t8):is(rpofrt(pl"rt"(x0,y0)),rpofnt(xpy))
-t10:=tr3is(cut,pl(ksi,eta),pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)),rpofnt(xpy),t3,t6,t9):is(pl(ksi,eta),rpofnt(xpy))
--iiia
-natpl:=somei(nat,[t:nat]is(pl(ksi,eta),rpofnt(t)),xpy".iiia",t10".iiia"):natrp(pl(ksi,eta))
-+*iiia
-ny@t11:=ists12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(ts(ksi,eta),ts(rpofnt(x),rpofnt(y)))
-t12:=symis(cut,rpofrt(ts"rt"(x0,y0)),ts(rpofnt(x),rpofnt(y)),satz155c(x0,y0)):is(ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)))
-t13:=satz112f(x0,t4,y0,t5):natrt(ts"rt"(x0,y0))
-xty:=nofrt(ts"rt"(x0,y0),t13):nat
-t14:=isrtn1(ts"rt"(x0,y0),t13):is"rt"(ts"rt"(x0,y0),rtofn(xty))
-t15:=isrterp(ts"rt"(x0,y0),rtofn(xty),t14):is(rpofrt(ts"rt"(x0,y0)),rpofnt(xty))
-t16:=tr3is(cut,ts(ksi,eta),ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)),rpofnt(xty),t11,t12,t15):is(ts(ksi,eta),rpofnt(xty))
--iiia
-ny@natts:=somei(nat,[t:nat]is(ts(ksi,eta),rpofnt(t)),xty".iiia",t16".iiia"):natrp(ts(ksi,eta))
-[m:more(ksi,eta)]
-+*iiia
-m@t17:=ismore12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2,m):more(rpofnt(x),rpofnt(y))
-t18:=satz154d(x0,y0,t17):more"rt"(x0,y0)
-t20:=ismn12(ksi,rpofnt(x),eta,rpofnt(y),m,satz154a(x0,y0,t18),t1,t2):is(mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)))
-t21:=symis(cut,rpofrt(mn"rt"(x0,y0,t18)),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),satz155b(x0,y0,t18)):is(mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)))
-t22:=satz112g(x0,t4,y0,t5,t18):natrt(mn"rt"(x0,y0,t18))
-xmy:=nofrt(mn"rt"(x0,y0,t18),t22):nat
-t23:=isrtn1(mn"rt"(x0,y0,t18),t22):is"rt"(mn"rt"(x0,y0,t18),rtofn(xmy))
-t24:=isrterp(mn"rt"(x0,y0,t18),rtofn(xmy),t23):is(rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy))
-t25:=tr3is(cut,mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy),t20,t21,t24):is(mn(ksi,eta,m),rpofnt(xmy))
--iiia
-m@natmn:=somei(nat,[t:nat]is(mn(ksi,eta,m),rpofnt(t)),xmy".iiia",t25".iiia"):natrp(mn(ksi,eta,m))
-@[p:cut][q:cut][r:cut]
-3pl13:=tr3is(cut,pl(p,pl(q,r)),pl(pl(q,r),p),pl(pl(r,q),p),pl(r,pl(q,p)),compl(p,pl(q,r)),ispl1(pl(q,r),pl(r,q),p,compl(q,r)),asspl1(r,q,p)):is(pl(p,pl(q,r)),pl(r,pl(q,p)))
-[s:cut]
-4pl24:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(s,pl(r,q))),pl(pl(p,s),pl(r,q)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(s,pl(r,q)),p,3pl13(q,r,s)),asspl2(p,s,pl(r,q))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,s),pl(r,q)))
-r@3pl12:=tr3is(cut,pl(p,pl(q,r)),pl(pl(p,q),r),pl(pl(q,p),r),pl(q,pl(p,r)),asspl2(p,q,r),ispl1(pl(p,q),pl(q,p),r,compl(p,q)),asspl1(q,p,r)):is(pl(p,pl(q,r)),pl(q,pl(p,r)))
-s@4pl23:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(r,pl(q,s))),pl(pl(p,r),pl(q,s)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(r,pl(q,s)),p,3pl12(q,r,s)),asspl2(p,r,pl(q,s))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,r),pl(q,s)))
-r@3pl23:=tr3is(cut,pl(pl(p,q),r),pl(p,pl(q,r)),pl(p,pl(r,q)),pl(pl(p,r),q),asspl1(p,q,r),ispl2(pl(q,r),pl(r,q),p,compl(q,r)),asspl2(p,r,q)):is(pl(pl(p,q),r),pl(pl(p,r),q))
-p@a2isapa:=tris(cut,ts(p,pl(1rp,1rp)),pl(ts(p,1rp),ts(p,1rp)),pl(p,p),disttp2(p,1rp,1rp),ispl12(ts(p,1rp),p,ts(p,1rp),p,satz151(p),satz151(p))):is(ts(p,pl(1rp,1rp)),pl(p,p))
-@dif:=pair1type(cut):'type'
-[a1:cut][a2:cut]
-df:=pair1(cut,a1,a2):dif
-@[a:dif]
-stm:=first1(cut,a):cut
-std:=second1(cut,a):cut
-a2@stmis:=first1is1(cut,a1,a2):is(stm(df(a1,a2)),a1)
-isstm:=first1is2(cut,a1,a2):is(a1,stm(df(a1,a2)))
-stdis:=second1is1(cut,a1,a2):is(std(df(a1,a2)),a2)
-isstd:=second1is2(cut,a1,a2):is(a2,std(df(a1,a2)))
-a@1a:=stm(a):cut
-2a:=std(a):cut
-dfis:=pair1is1(cut,a):is"e"(dif,df(1a,2a),a)
-isdf:=pair1is2(cut,a):is"e"(dif,a,df(1a,2a))
-a2@[b1:cut][b2:cut]
-12issmsd:=ispl12(a1,stm(df(a1,a2)),b2,std(df(b1,b2)),isstm(a1,a2),isstd(b1,b2)):is(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))))
-smsdis12:=symis(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),12issmsd):is(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2))
-a@[r1:cut][r2:cut]
-1sdissmsd:=ispl1(r1,stm(df(r1,r2)),2a,isstm(r1,r2)):is(pl(r1,2a),pl(stm(df(r1,r2)),2a))
-smsdis1sd:=symis(cut,pl(r1,2a),pl(stm(df(r1,r2)),2a),1sdissmsd):is(pl(stm(df(r1,r2)),2a),pl(r1,2a))
-sm2issmsd:=ispl2(r2,std(df(r1,r2)),1a,isstd(r1,r2)):is(pl(1a,r2),pl(1a,std(df(r1,r2))))
-smsdissm2:=symis(cut,pl(1a,r2),pl(1a,std(df(r1,r2))),sm2issmsd):is(pl(1a,std(df(r1,r2))),pl(1a,r2))
-a2@[r:cut][i:is(a1,r)]
-issm:=isf(cut,dif,[t:cut]df(t,a2),a1,r,i):is"e"(dif,df(a1,a2),df(r,a2))
-r@[i:is(a2,r)]
-issd:=isf(cut,dif,[t:cut]df(a1,t),a2,r,i):is"e"(dif,df(a1,a2),df(a1,r))
-b2@[i:is(a1,b1)][j:is(a2,b2)]
-issmsd:=tris(dif,df(a1,a2),df(b1,a2),df(b1,b2),issm(a1,a2,b1,i),issd(b1,a2,b2,j)):is"e"(dif,df(a1,a2),df(b1,b2))
-a@[b:dif]
-1b:=stm(b):cut
-2b:=std(b):cut
-eq:=is(pl(1a,2b),pl(1b,2a)):'prop'
-b2@[i:is(pl(a1,b2),pl(b1,a2))]
-eqi12:=tr3is(cut,pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),smsdis12(a1,a2,b1,b2),i,12issmsd(b1,b2,a1,a2)):eq(df(a1,a2),df(b1,b2))
-r2@[i:is(pl(1a,r2),pl(r1,2a))]
-eqi1:=isp(dif,[x:dif]eq(x,df(r1,r2)),df(1a,2a),a,eqi12(1a,2a,r1,r2,i),dfis):eq(a,df(r1,r2))
-r2@[i:is(pl(r1,2a),pl(1a,r2))]
-eqi2:=isp(dif,[x:dif]eq(df(r1,r2),x),df(1a,2a),a,eqi12(r1,r2,1a,2a,i),dfis):eq(df(r1,r2),a)
-b2@[e:eq(df(a1,a2),df(b1,b2))]
-eqe12:=tr3is(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),12issmsd(a1,a2,b1,b2),e,smsdis12(b1,b2,a1,a2)):is(pl(a1,b2),pl(b1,a2))
-a@satzd163:=refis(cut,pl(1a,2a)):eq(a,a)
-refeq:=satzd163:eq(a,a)
-b@[i:is"e"(dif,a,b)]
-refeq1:=isp(dif,[x:dif]eq(a,x),a,b,refeq,i):eq(a,b)
-refeq2:=isp(dif,[x:dif]eq(x,a),a,b,refeq,i):eq(b,a)
-b2@[i:is(a1,b1)][j:is(a2,b2)]
-eqsmsd:=refeq1(df(a1,a2),df(b1,b2),issmsd(i,j)):eq(df(a1,a2),df(b1,b2))
-r@[i:is(a1,r)]
-eqsm:=refeq1(df(a1,a2),df(r,a2),issm(i)):eq(df(a1,a2),df(r,a2))
-r@[i:is(a2,r)]
-eqsd:=refeq1(df(a1,a2),df(a1,r),issd(i)):eq(df(a1,a2),df(a1,r))
-b@[e:eq(a,b)]
-satzd164:=symis(cut,pl(1a,2b),pl(1b,2a),e):eq(b,a)
-symeq:=satzd164:eq(b,a)
-b@[c:dif]
-1c:=stm(c):cut
-2c:=std(c):cut
-[e:eq(a,b)][f:eq(b,c)]
-+1d165
-t1:=ispl12(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),e,f):is(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
-t2:=tr4is(cut,pl(pl(1a,2c),pl(1b,2b)),pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2b),pl(1b,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2c,1b,2b),t1,compl(pl(1b,2a),pl(1c,2b)),4pl24(1c,2b,1b,2a)):is(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
--1d165
-satzd165:=satz136b(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".1d165"):eq(a,c)
-treq:=satzd165:eq(a,c)
-c@[e:eq(c,a)][f:eq(c,b)]
-treq1:=treq(a,c,b,symeq(c,a,e),f):eq(a,b)
-c@[e:eq(a,c)][f:eq(b,c)]
-treq2:=treq(a,c,b,e,symeq(b,c,f)):eq(a,b)
-c@[d:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)]
-tr3eq:=treq(a,b,d,e1,treq(b,c,d,e2,e3)):eq(a,d)
-d@[e:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)][e4:eq(d,e)]
-tr4eq:=tr3eq(a,b,c,e,e1,e2,treq(c,d,e,e3,e4)):eq(a,e)
-a@posd:=more(1a,2a):'prop'
-zero:=is(1a,2a):'prop'
-negd:=less(1a,2a):'prop'
-a2@[m:more(a1,a2)]
-posdi:=ismore12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),m):posd(df(a1,a2))
-a2@[i:is(a1,a2)]
-zeroi:=tr3is(cut,stm(df(a1,a2)),a1,a2,std(df(a1,a2)),stmis(a1,a2),i,isstd(a1,a2)):zero(df(a1,a2))
-a2@[l:less(a1,a2)]
-negdi:=isless12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),l):negd(df(a1,a2))
-a@axrde:=satz123b(1a,2a):ec3(zero(a),posd(a),negd(a))
-axrdo:=satz123a(1a,2a):or3(zero(a),posd(a),negd(a))
-axrd:=orec3i(zero(a),posd(a),negd(a),axrdo,axrde):orec3(zero(a),posd(a),negd(a))
-[p:'prop'][p1:[t:posd(a)]p][p2:[t:zero(a)]p][p3:[t:negd(a)]p]
-rappd:=or3app(zero(a),posd(a),negd(a),p,axrdo,p2,p1,p3):p
-a@[p:posd(a)]
-pnot0d:=ec3e21(zero(a),posd(a),negd(a),axrde,p):not(zero(a))
-pnotnd:=ec3e23(zero(a),posd(a),negd(a),axrde,p):not(negd(a))
-a@[z:zero(a)]
-0notpd:=ec3e12(zero(a),posd(a),negd(a),axrde,z):not(posd(a))
-0notnd:=ec3e13(zero(a),posd(a),negd(a),axrde,z):not(negd(a))
-a@[n:negd(a)]
-nnotpd:=ec3e32(zero(a),posd(a),negd(a),axrde,n):not(posd(a))
-nnot0d:=ec3e31(zero(a),posd(a),negd(a),axrde,n):not(zero(a))
-b@[e:eq(a,b)][p:posd(a)]
-+iv1d
-t1:=ismore12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135a(1a,2a,2b,p)):more(pl(1b,2a),pl(2b,2a))
--iv1d
-eqposd:=satz136a(1b,2b,2a,t1".iv1d"):posd(b)
-e@[z:zero(a)]
-+*iv1d
-z@t2:=tr3is(cut,pl(1b,2a),pl(1a,2b),pl(2a,2b),pl(2b,2a),symeq(a,b,e),ispl1(1a,2a,2b,z),compl(2a,2b)):is(pl(1b,2a),pl(2b,2a))
--iv1d
-z@eqzero:=satz136b(1b,2b,2a,t2".iv1d"):zero(b)
-e@[n:negd(a)]
-+*iv1d
-n@t3:=isless12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135c(1a,2a,2b,n)):less(pl(1b,2a),pl(2b,2a))
--iv1d
-n@eqnegd:=satz136c(1b,2b,2a,t3".iv1d"):negd(b)
-b@[z:zero(a)][y:zero(b)]
-zeroeq:=tris(cut,pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl12(1a,2a,2b,1b,z,symis(cut,1b,2b,y)),compl(2a,1b)):eq(a,b)
-@[r:cut]
-pdofrp:=df(pl(r,1rp),1rp):dif
-ndofrp:=df(1rp,pl(r,1rp)):dif
-[s:cut][i:is(r,s)]
-isrpepd:=refeq1(pdofrp(r),pdofrp(s),isf(cut,dif,[x:cut]pdofrp(x),r,s,i)):eq(pdofrp(r),pdofrp(s))
-isrpend:=refeq1(ndofrp(r),ndofrp(s),isf(cut,dif,[x:cut]ndofrp(x),r,s,i)):eq(ndofrp(r),ndofrp(s))
-s@[e:eq(pdofrp(r),pdofrp(s))]
-+*iv1d
-e@t4:=satz136b(pl(r,1rp),pl(s,1rp),1rp,eqe12(pl(r,1rp),1rp,pl(s,1rp),1rp,e)):is(pl(r,1rp),pl(s,1rp))
--iv1d
-e@isrpipd:=satz136b(r,s,1rp,t4".iv1d"):is(r,s)
-s@[e:eq(ndofrp(r),ndofrp(s))]
-+*iv1d
-e@t5:=satz136e(pl(s,1rp),pl(r,1rp),1rp,eqe12(1rp,pl(r,1rp),1rp,pl(s,1rp),e)):is(pl(s,1rp),pl(r,1rp))
--iv1d
-e@isrpind:=symis(cut,s,r,satz136b(s,r,1rp,t5".iv1d")):is(r,s)
-r@posdirp:=posdi(pl(r,1rp),1rp,ismore1(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133(1rp,r))):posd(pdofrp(r))
-negdirp:=negdi(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):negd(ndofrp(r))
-a@[p:posd(a)]
-rpofpd:=mn(1a,2a,p):cut
-+*iv1d
-p@t6:=tr4is(cut,pl(1a,1rp),pl(pl(rpofpd,2a),1rp),pl(rpofpd,pl(2a,1rp)),pl(rpofpd,pl(1rp,2a)),pl(pl(rpofpd,1rp),2a),ispl1(1a,pl(rpofpd,2a),1rp,satz140f(1a,2a,p)),asspl1(rpofpd,2a,1rp),ispl2(pl(2a,1rp),pl(1rp,2a),rpofpd,compl(2a,1rp)),asspl2(rpofpd,1rp,2a)):is(pl(1a,1rp),pl(pl(rpofpd,1rp),2a))
--iv1d
-p@eqpdrp1:=eqi1(a,pl(rpofpd,1rp),1rp,t6".iv1d"):eq(a,pdofrp(rpofpd(a,p)))
-eqpdrp2:=symeq(a,pdofrp(rpofpd(a,p)),eqpdrp1):eq(pdofrp(rpofpd(a,p)),a)
-a@[n:negd(a)]
-rpofnd:=mn(2a,1a,satz122(1a,2a,n)):cut
-+*iv1d
-n@t7:=tr3is(cut,pl(1a,pl(rpofnd,1rp)),pl(pl(1a,rpofnd),1rp),pl(2a,1rp),pl(1rp,2a),asspl2(1a,rpofnd,1rp),ispl1(pl(1a,rpofnd),2a,1rp,satz140c(2a,1a,satz122(1a,2a,n))),compl(2a,1rp)):is(pl(1a,pl(rpofnd,1rp)),pl(1rp,2a))
--iv1d
-n@eqndrp1:=eqi1(a,1rp,pl(rpofnd,1rp),t7".iv1d"):eq(a,ndofrp(rpofnd(a,n)))
-eqndrp2:=symeq(a,ndofrp(rpofnd(a,n)),eqndrp1):eq(ndofrp(rpofnd(a,n)),a)
-@[h:dif][p:posd(h)][k:dif][q:posd(k)][e:eq(h,k)]
-+*iv1d
-e@t8:=tr3eq(pdofrp(rpofpd(h,p)),h,k,pdofrp(rpofpd(k,q)),eqpdrp2(h,p),e,eqpdrp1(k,q)):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
--iv1d
-e@eqpderp:=isrpipd(rpofpd(h,p),rpofpd(k,q),t8".iv1d"):is(rpofpd(h,p),rpofpd(k,q))
-q@[i:is(rpofpd(h,p),rpofpd(k,q))]
-+*iv1d
-i@t9:=isrpepd(rpofpd(h,p),rpofpd(k,q),i):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
--iv1d
-i@eqpdirp:=tr3eq(h,pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)),k,eqpdrp1(h,p),t9".iv1d",eqpdrp2(k,q)):eq(h,k)
-h@[n:negd(h)][k:dif][o:negd(k)][e:eq(h,k)]
-+*iv1d
-e@t10:=tr3eq(ndofrp(rpofnd(h,n)),h,k,ndofrp(rpofnd(k,o)),eqndrp2(h,n),e,eqndrp1(k,o)):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
--iv1d
-e@eqnderp:=isrpind(rpofnd(h,n),rpofnd(k,o),t10".iv1d"):is(rpofnd(h,n),rpofnd(k,o))
-o@[i:is(rpofnd(h,n),rpofnd(k,o))]
-+*iv1d
-i@t11:=isrpend(rpofnd(h,n),rpofnd(k,o),i):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
--iv1d
-i@eqndirp:=tr3eq(h,ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)),k,eqndrp1(h,n),t11".iv1d",eqndrp2(k,o)):eq(h,k)
-@[r:cut]
-+*iv1d
-r@t12:=eqpdrp1(pdofrp(r),posdirp(r)):eq(pdofrp(r),pdofrp(rpofpd(pdofrp(r),posdirp(r))))
--iv1d
-r@isrppd1:=isrpipd(r,rpofpd(pdofrp(r),posdirp(r)),t12".iv1d"):is(r,rpofpd(pdofrp(r),posdirp(r)))
-isrppd2:=symis(cut,r,rpofpd(pdofrp(r),posdirp(r)),isrppd1):is(rpofpd(pdofrp(r),posdirp(r)),r)
-+*iv1d
-r@t13:=eqndrp1(ndofrp(r),negdirp(r)):eq(ndofrp(r),ndofrp(rpofnd(ndofrp(r),negdirp(r))))
--iv1d
-r@isrpnd1:=isrpind(r,rpofnd(ndofrp(r),negdirp(r)),t13".iv1d"):is(r,rpofnd(ndofrp(r),negdirp(r)))
-isrpnd2:=symis(cut,r,rpofnd(ndofrp(r),negdirp(r)),isrpnd1):is(rpofnd(ndofrp(r),negdirp(r)),r)
-a2@[r:cut]
-lemmad1:=eqi12(a1,a2,pl(a1,r),pl(a2,r),tris(cut,pl(a1,pl(a2,r)),pl(a1,pl(r,a2)),pl(pl(a1,r),a2),ispl2(pl(a2,r),pl(r,a2),a1,compl(a2,r)),asspl2(a1,r,a2))):eq(df(a1,a2),df(pl(a1,r),pl(a2,r)))
-lemmad2:=symeq(df(a1,a2),df(pl(a1,r),pl(a2,r)),lemmad1):eq(df(pl(a1,r),pl(a2,r)),df(a1,a2))
-a@[r:cut]
-lemmad3:=treq(a,df(1a,2a),df(pl(1a,r),pl(2a,r)),refeq1(a,df(1a,2a),isdf),lemmad1(1a,2a,r)):eq(a,df(pl(1a,r),pl(2a,r)))
-lemmad4:=symeq(a,df(pl(1a,r),pl(2a,r)),lemmad3):eq(df(pl(1a,r),pl(2a,r)),a)
-a@absd:=ite(negd(a),dif,df(2a,1a),a):dif
-[n:negd(a)]
-absnd:=refeq1(absd(a),df(2a,1a),itet(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),df(2a,1a))
-a@[n:not(negd(a))]
-absnnd:=refeq1(absd(a),a,itef(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),a)
-a2@[l:less(a1,a2)]
-absdeql:=treq(absd(df(a1,a2)),df(std(df(a1,a2)),stm(df(a1,a2))),df(a2,a1),absnd(df(a1,a2),negdi(a1,a2,l)),eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2))):eq(absd(df(a1,a2)),df(a2,a1))
-a2@[m:moreis(a1,a2)]
-absdeqm:=absnnd(df(a1,a2),th3"l.imp"(negd(df(a1,a2)),less(a1,a2),satz123c(a1,a2,m),[t:negd(df(a1,a2))]isless12(stm(df(a1,a2)),a1,std(df(a1,a2)),a2,stmis(a1,a2),stdis(a1,a2),t))):eq(absd(df(a1,a2)),df(a1,a2))
-b@[e:eq(a,b)]
-+iv2d
-[n:negd(a)]
-t1:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
-t2:=tr3eq(absd(a),df(2a,1a),df(2b,1b),absd(b),absnd(a,n),eqi12(2a,1a,2b,1b,t1),symeq(absd(b),df(2b,1b),absnd(b,eqnegd(a,b,e,n)))):eq(absd(a),absd(b))
-e@[n:not(negd(a))]
-t3:=tr3eq(absd(a),a,b,absd(b),absnnd(a,n),e,symeq(absd(b),b,absnnd(b,th3"l.imp"(negd(b),negd(a),n,[t:negd(b)]eqnegd(b,a,symeq(a,b,e),t))))):eq(absd(a),absd(b))
--iv2d
-eqabsd:=th1"l.imp"(negd(a),eq(absd(a),absd(b)),[t:negd(a)]t2".iv2d"(t),[t:not(negd(a))]t3".iv2d"(t)):eq(absd(a),absd(b))
-a@[p:posd(a)]
-satzd166a:=eqposd(a,absd(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p))),p):posd(absd(a))
-a@[n:negd(a)]
-+2d166
-t1:=posdi(2a,1a,satz122(1a,2a,n)):posd(df(2a,1a))
--2d166
-satzd166b:=eqposd(df(2a,1a),absd(a),symeq(absd(a),df(2a,1a),absnd(a,n)),t1".2d166"):posd(absd(a))
-b@[p:posd(a)][q:posd(b)][e:eq(absd(a),absd(b))]
-satzd166c:=tr3eq(a,absd(a),absd(b),b,symeq(absd(a),a,absnnd(a,pnotnd(a,p))),e,absnnd(b,pnotnd(b,q))):eq(a,b)
-b@[n:negd(a)][o:negd(b)][e:eq(absd(a),absd(b))]
-+*2d166
-e@t2:=tr3eq(df(2a,1a),absd(a),absd(b),df(2b,1b),symeq(absd(a),df(2a,1a),absnd(a,n)),e,absnd(b,o)):eq(df(2a,1a),df(2b,1b))
--2d166
-e@satzd166d:=tr3is(cut,pl(1a,2b),pl(2b,1a),pl(2a,1b),pl(1b,2a),compl(1a,2b),symis(cut,pl(2a,1b),pl(2b,1a),eqe12(2a,1a,2b,1b,t2".2d166")),compl(2a,1b)):eq(a,b)
-a@[n:not(zero(a))]
-satzd166e:=rappd(a,posd(absd(a)),[t:posd(a)]satzd166a(a,t),th2"l.imp"(zero(a),posd(absd(a)),n),[t:negd(a)]satzd166b(a,t)):posd(absd(a))
-a@[z:zero(a)]
-satzd166f:=eqzero(a,absd(a),symeq(absd(a),a,absnnd(a,0notnd(a,z))),z):zero(absd(a))
-b@mored:=more(pl(1a,2b),pl(1b,2a)):'prop'
-b2@[m:more(pl(a1,b2),pl(b1,a2))]
-moredi12:=ismore12(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),12issmsd(a1,a2,b1,b2),12issmsd(b1,b2,a1,a2),m):mored(df(a1,a2),df(b1,b2))
-r2@[m:more(pl(1a,r2),pl(r1,2a))]
-moredi1:=ismore12(pl(1a,r2),pl(1a,std(df(r1,r2))),pl(r1,2a),pl(stm(df(r1,r2)),2a),sm2issmsd(a,r1,r2),1sdissmsd(a,r1,r2),m):mored(a,df(r1,r2))
-r2@[m:more(pl(r1,2a),pl(1a,r2))]
-moredi2:=ismore12(pl(r1,2a),pl(stm(df(r1,r2)),2a),pl(1a,r2),pl(1a,std(df(r1,r2))),1sdissmsd(a,r1,r2),sm2issmsd(a,r1,r2),m):mored(df(r1,r2),a)
-b2@[m:mored(df(a1,a2),df(b1,b2))]
-morede12:=ismore12(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),smsdis12(a1,a2,b1,b2),smsdis12(b1,b2,a1,a2),m):more(pl(a1,b2),pl(b1,a2))
-b@lessd:=less(pl(1a,2b),pl(1b,2a)):'prop'
-[m:mored(a,b)]
-lemmad5:=satz121(pl(1a,2b),pl(1b,2a),m):lessd(b,a)
-b@[l:lessd(a,b)]
-lemmad6:=satz122(pl(1a,2b),pl(1b,2a),l):mored(b,a)
-b2@[l:less(pl(a1,b2),pl(b1,a2))]
-lessdi12:=lemmad5(df(b1,b2),df(a1,a2),moredi12(b1,b2,a1,a2,satz122(pl(a1,b2),pl(b1,a2),l))):lessd(df(a1,a2),df(b1,b2))
-r2@[l:less(pl(1a,r2),pl(r1,2a))]
-lessdi1:=lemmad5(df(r1,r2),a,moredi2(a,r1,r2,satz122(pl(1a,r2),pl(r1,2a),l))):lessd(a,df(r1,r2))
-r2@[l:less(pl(r1,2a),pl(1a,r2))]
-lessdi2:=lemmad5(a,df(r1,r2),moredi1(a,r1,r2,satz122(pl(r1,2a),pl(1a,r2),l))):lessd(df(r1,r2),a)
-b2@[l:lessd(df(a1,a2),df(b1,b2))]
-lessde12:=satz121(pl(b1,a2),pl(a1,b2),morede12(b1,b2,a1,a2,lemmad6(df(a1,a2),df(b1,b2),l))):less(pl(a1,b2),pl(b1,a2))
-b@satzd167:=satz123(pl(1a,2b),pl(1b,2a)):orec3(eq(a,b),mored(a,b),lessd(a,b))
-satzd167a:=satz123a(pl(1a,2b),pl(1b,2a)):or3(eq(a,b),mored(a,b),lessd(a,b))
-satzd167b:=satz123b(pl(1a,2b),pl(1b,2a)):ec3(eq(a,b),mored(a,b),lessd(a,b))
-d@1d:=stm(d):cut
-2d:=std(d):cut
-[e:eq(a,b)][f:eq(c,d)][m:mored(a,c)]
-+*iv2d
-m@t4:=tr4is(cut,pl(pl(1b,2d),pl(1c,2a)),pl(pl(1b,2a),pl(1c,2d)),pl(pl(1a,2b),pl(1d,2c)),pl(pl(1a,2c),pl(1d,2b)),pl(pl(1d,2b),pl(1a,2c)),4pl24(1b,2d,1c,2a),ispl12(pl(1b,2a),pl(1a,2b),pl(1c,2d),pl(1d,2c),symeq(a,b,e),f),4pl24(1a,2b,1d,2c),compl(pl(1a,2c),pl(1d,2b))):is(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)))
-t5:=ismore2(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)),pl(pl(1b,2d),pl(1a,2c)),t4,satz135d(pl(1a,2c),pl(1c,2a),pl(1b,2d),m)):more(pl(pl(1b,2d),pl(1a,2c)),pl(pl(1d,2b),pl(1a,2c)))
--iv2d
-m@eqmored12:=satz136a(pl(1b,2d),pl(1d,2b),pl(1a,2c),t5".iv2d"):mored(b,d)
-f@[l:lessd(a,c)]
-eqlessd12:=lemmad5(d,b,eqmored12(c,d,a,b,f,e,lemmad6(a,c,l))):lessd(b,d)
-c@[e:eq(a,b)][m:mored(a,c)]
-eqmored1:=eqmored12(a,b,c,c,e,refeq(c),m):mored(b,c)
-e@[m:mored(c,a)]
-eqmored2:=eqmored12(c,c,a,b,refeq(c),e,m):mored(c,b)
-e@[l:lessd(a,c)]
-eqlessd1:=eqlessd12(a,b,c,c,e,refeq(c),l):lessd(b,c)
-e@[l:lessd(c,a)]
-eqlessd2:=eqlessd12(c,c,a,b,refeq(c),e,l):lessd(c,b)
-b@moreq:=or(mored(a,b),eq(a,b)):'prop'
-lesseq:=or(lessd(a,b),eq(a,b)):'prop'
-[m:moreq(a,b)]
-satzd168a:=th9"l.or"(mored(a,b),eq(a,b),lessd(b,a),eq(b,a),m,[t:mored(a,b)]lemmad5(a,b,t),[t:eq(a,b)]symeq(a,b,t)):lesseq(b,a)
-b@[l:lesseq(a,b)]
-satzd168b:=th9"l.or"(lessd(a,b),eq(a,b),mored(b,a),eq(b,a),l,[t:lessd(a,b)]lemmad6(a,b,t),[t:eq(a,b)]symeq(a,b,t)):moreq(b,a)
-c@[e:eq(a,b)][m:moreq(a,c)]
-eqmoreq1:=th9"l.or"(mored(a,c),eq(a,c),mored(b,c),eq(b,c),m,[t:mored(a,c)]eqmored1(a,b,c,e,t),[t:eq(a,c)]treq1(b,c,a,e,t)):moreq(b,c)
-e@[m:moreq(c,a)]
-eqmoreq2:=th9"l.or"(mored(c,a),eq(c,a),mored(c,b),eq(c,b),m,[t:mored(c,a)]eqmored2(a,b,c,e,t),[t:eq(c,a)]treq(c,a,b,t,e)):moreq(c,b)
-e@[l:lesseq(a,c)]
-eqlesseq1:=satzd168a(c,b,eqmoreq2(a,b,c,e,satzd168b(a,c,l))):lesseq(b,c)
-e@[l:lesseq(c,a)]
-eqlesseq2:=satzd168a(b,c,eqmoreq1(a,b,c,e,satzd168b(c,a,l))):lesseq(c,b)
-d@[e:eq(a,b)][f:eq(c,d)][m:moreq(a,c)]
-eqmoreq12:=eqmoreq1(a,b,d,e,eqmoreq2(c,d,a,f,m)):moreq(b,d)
-f@[l:lesseq(a,c)]
-eqlesseq12:=eqlesseq1(a,b,d,e,eqlesseq2(c,d,a,f,l)):lesseq(b,d)
-b@[m:mored(a,b)]
-moreqi1:=ori1(mored(a,b),eq(a,b),m):moreq(a,b)
-b@[l:lessd(a,b)]
-lesseqi1:=ori1(lessd(a,b),eq(a,b),l):lesseq(a,b)
-b@[e:eq(a,b)]
-moreqi2:=ori2(mored(a,b),eq(a,b),e):moreq(a,b)
-lesseqi2:=ori2(lessd(a,b),eq(a,b),e):lesseq(a,b)
-b@[m:moreq(a,b)]
-satzd167c:=th7"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,comor(mored(a,b),eq(a,b),m)):not(lessd(a,b))
-b@[l:lesseq(a,b)]
-satzd167d:=th9"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,l):not(mored(a,b))
-b@[n:not(mored(a,b))]
-satzd167e:=th2"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n):lesseq(a,b)
-b@[n:not(lessd(a,b))]
-satzd167f:=comor(eq(a,b),mored(a,b),th3"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n)):moreq(a,b)
-b@[m:mored(a,b)]
-satzd167g:=th3"l.imp"(lesseq(a,b),not(mored(a,b)),weli(mored(a,b),m),[t:lesseq(a,b)]satzd167d(t)):not(lesseq(a,b))
-b@[l:lessd(a,b)]
-satzd167h:=th3"l.imp"(moreq(a,b),not(lessd(a,b)),weli(lessd(a,b),l),[t:moreq(a,b)]satzd167c(t)):not(moreq(a,b))
-b@[n:not(moreq(a,b))]
-satzd167j:=or3e3(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th5"l.or"(mored(a,b),eq(a,b),n),th4"l.or"(mored(a,b),eq(a,b),n)):lessd(a,b)
-b@[n:not(lesseq(a,b))]
-satzd167k:=or3e2(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th4"l.or"(lessd(a,b),eq(a,b),n),th5"l.or"(lessd(a,b),eq(a,b),n)):mored(a,b)
-b@[z:zero(b)][p:posd(a)]
-satzd169a:=ismore12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135a(1a,2a,1b,p)):mored(a,b)
-z@[m:mored(a,b)]
-satzd169b:=satz136d(1a,2a,2b,ismore12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),m)):posd(a)
-z@[n:negd(a)]
-satzd169c:=isless12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135c(1a,2a,1b,n)):lessd(a,b)
-z@[l:lessd(a,b)]
-satzd169d:=satz136f(1a,2a,2b,isless12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),l)):negd(a)
-+2d170
-z@[p:posd(a)]
-t1:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166a(a,p))):moreq(absd(a),b)
-z@[y:zero(a)]
-t2:=moreqi2(absd(a),b,treq(absd(a),a,b,absnnd(a,0notnd(a,y)),zeroeq(a,b,y,z))):moreq(absd(a),b)
-z@[n:negd(a)]
-t3:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166b(a,n))):moreq(absd(a),b)
--2d170
-z@satzd170:=rappd(a,moreq(absd(a),b),[t:posd(a)]t1".2d170"(t),[t:zero(a)]t2".2d170"(t),[t:negd(a)]t3".2d170"(t)):moreq(absd(a),b)
-c@[l:lessd(a,b)][k:lessd(b,c)]
-+2d171
-t1:=satz137a(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),l,k):less(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
-t2:=isless12(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1a,2c),pl(1b,2b)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2b,1b,2c),tris(cut,pl(pl(1b,2a),pl(1c,2b)),pl(pl(1b,2b),pl(1c,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1b,2a,1c,2b),compl(pl(1b,2b),pl(1c,2a))),t1):less(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
--2d171
-satzd171:=satz136c(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".2d171"):lessd(a,c)
-trlessd:=satzd171:lessd(a,c)
-c@[m:mored(a,b)][n:mored(b,c)]
-trmored:=lemmad6(c,a,trlessd(c,b,a,lemmad5(b,c,n),lemmad5(a,b,m))):mored(a,c)
-c@[l:lesseq(a,b)][k:lessd(b,c)]
-satzd172a:=orapp(lessd(a,b),eq(a,b),lessd(a,c),l,[t:lessd(a,b)]trlessd(t,k),[t:eq(a,b)]eqlessd1(b,a,c,symeq(a,b,t),k)):lessd(a,c)
-c@[l:lessd(a,b)][k:lesseq(b,c)]
-satzd172b:=orapp(lessd(b,c),eq(b,c),lessd(a,c),k,[t:lessd(b,c)]trlessd(l,t),[t:eq(b,c)]eqlessd2(b,c,a,t,l)):lessd(a,c)
-c@[m:moreq(a,b)][n:mored(b,c)]
-satzd172c:=lemmad6(c,a,satzd172b(c,b,a,lemmad5(b,c,n),satzd168a(a,b,m))):mored(a,c)
-c@[m:mored(a,b)][n:moreq(b,c)]
-satzd172d:=lemmad6(c,a,satzd172a(c,b,a,satzd168a(b,c,n),lemmad5(a,b,m))):mored(a,c)
-c@[l:lesseq(a,b)][k:lesseq(b,c)]
-+2d173
-[j:lessd(a,b)]
-t1:=lesseqi1(a,c,satzd172b(j,k)):lesseq(a,c)
-k@[e:eq(a,b)]
-t2:=eqlesseq1(b,a,c,symeq(a,b,e),k):lesseq(a,c)
--2d173
-satzd173:=orapp(lessd(a,b),eq(a,b),lesseq(a,c),l,[t:lessd(a,b)]t1".2d173"(t),[t:eq(a,b)]t2".2d173"(t)):lesseq(a,c)
-trlesseq:=satzd173:lesseq(a,c)
-c@[m:moreq(a,b)][n:moreq(b,c)]
-trmoreq:=satzd168b(c,a,trlesseq(c,b,a,satzd168a(b,c,n),satzd168a(a,b,m))):moreq(a,c)
-a@ratd:=[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))):'prop'
-irratd:=not(ratd(a)):'prop'
-b@[e:eq(a,b)][r:ratd(a)]
-+*iv2d
-r@[n:not(zero(b))]
-t6:=th3"l.imp"(zero(a),zero(b),n,[t:zero(a)]eqzero(a,b,e,t)):not(zero(a))
-t7:=eqpderp(absd(a),satzd166e(a,t6),absd(b),satzd166e(b,n),eqabsd(a,b,e)):is(rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)))
-t8:=isp(cut,[t:cut]ratrp(t),rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)),<t6>r,t7):ratrp(rpofpd(absd(b),satzd166e(b,n)))
--iv2d
-r@eqratd:=[t:not(zero(b))]t8".iv2d"(t):ratd(b)
-e@[i:irratd(a)]
-eqirratd:=th3"l.imp"(ratd(b),ratd(a),i,[t:ratd(b)]eqratd(b,a,symeq(a,b,e),t)):irratd(b)
-a@[z:zero(a)]
-ratdi0:=th2"l.r.imp"(not(zero(a)),[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))),weli(zero(a),z)):ratd(a)
-@[r:cut][i:irratrp(r)][x0:rat]
-+*iv2d
-x0@[s:ratrp(pl(r,rpofrt(x0)))][y0:rat][j:is(pl(r,rpofrt(x0)),rpofrt(y0))]
-t9:=tris(cut,pl(rpofrt(x0),r),pl(r,rpofrt(x0)),rpofrt(y0),compl(rpofrt(x0),r),j):is(pl(rpofrt(x0),r),rpofrt(y0))
-t10:=ismore1(pl(rpofrt(x0),r),rpofrt(y0),rpofrt(x0),t9,satz133(rpofrt(x0),r)):more(rpofrt(y0),rpofrt(x0))
-t11:=satz154d(y0,x0,t10):more"rt"(y0,x0)
-t12:=satz155b(y0,x0,t11):is(rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
-t13:=satz140g(rpofrt(y0),rpofrt(x0),r,satz154a(y0,x0,t11),t9):is(r,mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
-t14:=tris2(cut,r,rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)),t13,t12):is(r,rpofrt(mn"rt"(y0,x0,t11)))
-t15:=somei(rat,[x:rat]is(r,rpofrt(x)),mn"rt"(y0,x0,t11),t14):ratrp(r)
-s@t16:=someapp(rat,[x:rat]is(pl(r,rpofrt(x0)),rpofrt(x)),s,con,[x:rat][t:is(pl(r,rpofrt(x0)),rpofrt(x))]<t15(x,t)>i):con
--iv2d
-x0@remark1:=[t:ratrp(pl(r,rpofrt(x0)))]t16".iv2d"(t):irratrp(pl(r,rpofrt(x0)))
-+*iv2d
-r@rp:=pdofrp(r):dif
-rn:=ndofrp(r):dif
-t17:=posdirp(r):posd(rp)
-t18:=pnot0d(rp,t17):not(zero(rp))
-t19:=nnot0d(rn,negdirp(r)):not(zero(rn))
-[n:not(zero(rp))]
-t20:=tris2(cut,r,rpofpd(absd(rp),satzd166e(rp,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rp),satzd166e(rp,n),rp,t17,absnnd(rp,pnotnd(rp,t17)))):is(r,rpofpd(absd(rp),satzd166e(rp,n)))
-r@t21:=treq(absd(rn),df(std(rn),stm(rn)),rp,absnd(rn,negdirp(r)),eqsmsd(std(rn),stm(rn),pl(r,1rp),1rp,stdis(1rp,pl(r,1rp)),stmis(1rp,pl(r,1rp)))):eq(absd(rn),rp)
-[n:not(zero(rn))]
-t22:=tris2(cut,r,rpofpd(absd(rn),satzd166e(rn,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rn),satzd166e(rn,n),rp,t17,t21)):is(r,rpofpd(absd(rn),satzd166e(rn,n)))
-r@[s:cut][i:is(r,s)][rr:ratrp(r)]
-t23:=isp(cut,[x:cut]ratrp(x),r,s,rr,i):ratrp(s)
-i@[rs:ratrp(s)]
-t24:=isp1(cut,[x:cut]ratrp(x),s,r,rs,i):ratrp(r)
--iv2d
-r@[rr:ratrp(r)]
-remark2a:=[t:not(zero(pdofrp(r)))]t23".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t)),t20".iv2d"(t),rr):ratd(pdofrp(r))
-remark2b:=t17".iv2d":posd(pdofrp(r))
-remark3a:=[t:not(zero(ndofrp(r)))]t23".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t)),t22".iv2d"(t),rr):ratd(ndofrp(r))
-remark3b:=negdirp(r):negd(ndofrp(r))
-r@[i:irratrp(r)]
-remark4a:=th3"l.imp"(ratd(pdofrp(r)),ratrp(r),i,[t:ratd(pdofrp(r))]t24".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t18".iv2d")),t20".iv2d"(t18".iv2d"),<t18".iv2d">t)):irratd(pdofrp(r))
-remark4b:=t17".iv2d":posd(pdofrp(r))
-remark5a:=th3"l.imp"(ratd(ndofrp(r)),ratrp(r),i,[t:ratd(ndofrp(r))]t24".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t19".iv2d")),t22".iv2d"(t19".iv2d"),<t19".iv2d">t)):irratd(ndofrp(r))
-remark5b:=negdirp(r):negd(ndofrp(r))
-a@natd:=and(posd(a),[t:posd(a)]natrp(rpofpd(a,t))):'prop'
-[n:natd(a)]
-natposd:=ande1(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):posd(a)
-natderp:=ande2"l.r"(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):natrp(rpofpd(a,natposd(a,n)))
-b@[e:eq(a,b)][n:natd(a)]
-+*iv2d
-n"rp"@t25:=eqposd(a,b,e,natposd(a,n)):posd(b)
-[p:posd(b)]
-t26:=eqpderp(a,natposd(a,n),b,p,e):is(rpofpd(a,natposd(a,n)),rpofpd(b,p))
-t27:=isp(cut,[t:cut]natrp(t),rpofpd(a,natposd(a,n)),rpofpd(b,p),natderp(a,n),t26):natrp(rpofpd(b,p))
--iv2d
-n@eqnatd:=andi(posd(b),[t:posd(b)]natrp(rpofpd(b,t)),t25".iv2d",[t:posd(b)]t27".iv2d"(t)):natd(b)
-@[x:nat]
-pdofnt:=pdofrp(rpofnt(x)):dif
-+*iv2d
-x@t28:=posdirp(rpofnt(x)):posd(pdofnt(x))
-[p:posd(pdofnt(x))]
-t29:=isrppd1(rpofnt(x)):is(rpofnt(x),rpofpd(pdofnt(x),t28))
-t30:=eqpderp(pdofnt(x),t28,pdofnt(x),p,refeq(pdofnt(x))):is(rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p))
-t31:=tris(cut,rpofnt(x),rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p),t29,t30):is(rpofnt(x),rpofpd(pdofnt(x),p))
-t32:=isp(cut,[t:cut]natrp(t),rpofnt(x),rpofpd(pdofnt(x),p),natrpi(x),t31):natrp(rpofpd(pdofnt(x),p))
--iv2d
-x@natdi:=andi(posd(pdofnt(x)),[t:posd(pdofnt(x))]natrp(rpofpd(pdofnt(x),t)),t28".iv2d",[t:posd(pdofnt(x))]t32".iv2d"(t)):natd(pdofnt(x))
-a@intd:=or(zero(a),natd(absd(a))):'prop'
-b@[e:eq(a,b)][i:intd(a)]
-+*iv2d
-i"rp"@[z:zero(a)]
-t33:=eqzero(a,b,e,z):zero(b)
-i"rp"@[n:natd(absd(a))]
-t34:=eqnatd(absd(a),absd(b),eqabsd(a,b,e),n):natd(absd(b))
--iv2d
-i@eqintd:=th9"l.or"(zero(a),natd(absd(a)),zero(b),natd(absd(b)),i,[t:zero(a)]t33".iv2d"(t),[t:natd(absd(a))]t34".iv2d"(t)):intd(b)
-a@[n:natd(a)]
-+*iv2d
-n"rp"@t34a:=symeq(absd(a),a,absnnd(a,pnotnd(a,natposd(a,n)))):eq(a,absd(a))
-t35:=eqnatd(a,absd(a),t34a,n):natd(absd(a))
--iv2d
-n@natintd:=ori2(zero(a),natd(absd(a)),t35".iv2d"):intd(a)
-a@[p:posd(a)][i:intd(a)]
-+*iv2d
-i"rp"@t36:=ore2(zero(a),natd(absd(a)),i,pnot0d(a,p)):natd(absd(a))
--iv2d
-i@posintnatd:=eqnatd(absd(a),a,absnnd(a,pnotnd(a,p)),t36".iv2d"):natd(a)
-a@[z:zero(a)]
-intdi0:=ori1(zero(a),natd(absd(a)),z):intd(a)
-r@[n:natrp(r)]
-+*iv2d
-n"rp"@t37:=posdirp(r):posd(pdofrp(r))
-[p:posd(pdofrp(r))]
-t38:=tris(cut,r,rpofpd(pdofrp(r),t37),rpofpd(pdofrp(r),p),isrppd1(r),eqpderp(pdofrp(r),t37,pdofrp(r),p,refeq(pdofrp(r)))):is(r,rpofpd(pdofrp(r),p))
-t39:=isp(cut,[t:cut]natrp(t),r,rpofpd(pdofrp(r),p),n,t38):natrp(rpofpd(pdofrp(r),p))
--iv2d
-n@remark6a:=andi(posd(pdofrp(r)),[t:posd(pdofrp(r))]natrp(rpofpd(pdofrp(r),t)),t37".iv2d",[t:posd(pdofrp(r))]t39".iv2d"(t)):natd(pdofrp(r))
-remark6:=natintd(pdofrp(r),remark6a):intd(pdofrp(r))
-+*iv2d
-n"rp"@t40:=absdeql(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):eq(absd(ndofrp(r)),pdofrp(r))
-t41:=eqnatd(pdofrp(r),absd(ndofrp(r)),symeq(absd(ndofrp(r)),pdofrp(r),t40),remark6a):natd(absd(ndofrp(r)))
--iv2d
-n@remark7:=ori2(zero(ndofrp(r)),natd(absd(ndofrp(r))),t41".iv2d"):intd(ndofrp(r))
-a@[i:intd(a)]
-+2d174
-[n:not(zero(a))]
-t1:=ore2(zero(a),natd(absd(a)),i,n):natd(absd(a))
-t2:=ande2(posd(absd(a)),[t:posd(absd(a))]natrp(rpofpd(absd(a),t)),t1):[t:posd(absd(a))]natrp(rpofpd(absd(a),t))
-t3:=lemmaiii5(rpofpd(absd(a),satzd166e(a,n)),<satzd166e(a,n)>t2):ratrp(rpofpd(absd(a),satzd166e(a,n)))
--2d174
-satzd174:=[t:not(zero(a))]t3".2d174"(t):ratd(a)
-b@pd:=df(pl(1a,1b),pl(2a,2b)):dif
-b2@pd12:=issmsd(pl(stm(df(a1,a2)),stm(df(b1,b2))),pl(std(df(a1,a2)),std(df(b1,b2))),pl(a1,b1),pl(a2,b2),ispl12(stm(df(a1,a2)),a1,stm(df(b1,b2)),b1,stmis(a1,a2),stmis(b1,b2)),ispl12(std(df(a1,a2)),a2,std(df(b1,b2)),b2,stdis(a1,a2),stdis(b1,b2))):is"e"(dif,pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
-r2@pd1:=issmsd(pl(1a,stm(df(r1,r2))),pl(2a,std(df(r1,r2))),pl(1a,r1),pl(2a,r2),ispl2(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl2(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
-pd2:=issmsd(pl(stm(df(r1,r2)),1a),pl(std(df(r1,r2)),2a),pl(r1,1a),pl(r2,2a),ispl1(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl1(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
-b2@pdeq12a:=refeq1(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
-pdeq12b:=refeq2(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(df(pl(a1,b1),pl(a2,b2)),pd(df(a1,a2),df(b1,b2)))
-r2@pdeq1a:=refeq1(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
-pdeq1b:=refeq2(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(df(pl(1a,r1),pl(2a,r2)),pd(a,df(r1,r2)))
-pdeq2a:=refeq1(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
-pdeq2b:=refeq2(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(df(pl(r1,1a),pl(r2,2a)),pd(df(r1,r2),a))
-b@satzd175:=eqsmsd(pl(1a,1b),pl(2a,2b),pl(1b,1a),pl(2b,2a),compl(1a,1b),compl(2a,2b)):eq(pd(a,b),pd(b,a))
-compd:=satzd175:eq(pd(a,b),pd(b,a))
-c@[e:eq(a,b)]
-+iv3d
-t1:=tr3is(cut,pl(pl(1a,1c),pl(2b,2c)),pl(pl(1a,2b),pl(1c,2c)),pl(pl(1b,2a),pl(1c,2c)),pl(pl(1b,1c),pl(2a,2c)),4pl23(1a,1c,2b,2c),ispl1(pl(1a,2b),pl(1b,2a),pl(1c,2c),e),4pl23(1b,2a,1c,2c)):is(pl(pl(1a,1c),pl(2b,2c)),pl(pl(1b,1c),pl(2a,2c)))
--iv3d
-eqpd1:=eqi12(pl(1a,1c),pl(2a,2c),pl(1b,1c),pl(2b,2c),t1".iv3d"):eq(pd(a,c),pd(b,c))
-eqpd2:=tr3eq(pd(c,a),pd(a,c),pd(b,c),pd(c,b),compd(c,a),eqpd1,compd(b,c)):eq(pd(c,a),pd(c,b))
-d@[e:eq(a,b)][f:eq(c,d)]
-eqpd12:=treq(pd(a,c),pd(b,c),pd(b,d),eqpd1(a,b,c,e),eqpd2(c,d,b,f)):eq(pd(a,c),pd(b,d))
-b@[z:zero(a)]
-+*iv3d
-z@t2:=tr4is(cut,pl(pl(1a,1b),2b),pl(1a,pl(1b,2b)),pl(2a,pl(2b,1b)),pl(pl(2a,2b),1b),pl(1b,pl(2a,2b)),asspl1(1a,1b,2b),ispl12(1a,2a,pl(1b,2b),pl(2b,1b),z,compl(1b,2b)),asspl2(2a,2b,1b),compl(pl(2a,2b),1b)):is(pl(pl(1a,1b),2b),pl(1b,pl(2a,2b)))
--iv3d
-z@pd01:=eqi2(b,pl(1a,1b),pl(2a,2b),t2".iv3d"):eq(pd(a,b),b)
-b@[z:zero(b)]
-pd02:=treq(pd(a,b),pd(b,a),a,compd(a,b),pd01(b,a,z)):eq(pd(a,b),a)
-b@[p:posd(a)][q:posd(b)]
-ppd:=posdi(pl(1a,1b),pl(2a,2b),satz137(1a,2a,1b,2b,p,q)):posd(pd(a,b))
-b@[n:negd(a)][o:negd(b)]
-npd:=negdi(pl(1a,1b),pl(2a,2b),satz137a(1a,2a,1b,2b,n,o)):negd(pd(a,b))
-a@m0d:=df(2a,1a):dif
-a2@m0deqa:=eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2)):eq(m0d(df(a1,a2)),df(a2,a1))
-m0deqb:=symeq(m0d(df(a1,a2)),df(a2,a1),m0deqa):eq(df(a2,a1),m0d(df(a1,a2)))
-b@[e:eq(a,b)]
-+*iv3d
-e@t3:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
--iv3d
-e@eqm0d:=eqi12(2a,1a,2b,1b,t3".iv3d"):eq(m0d(a),m0d(b))
-a@[p:posd(a)]
-satzd176a:=negdi(2a,1a,satz121(1a,2a,p)):negd(m0d(a))
-a@[z:zero(a)]
-satzd176b:=zeroi(2a,1a,symis(cut,1a,2a,z)):zero(m0d(a))
-a@[n:negd(a)]
-satzd176c:=posdi(2a,1a,satz122(1a,2a,n)):posd(m0d(a))
-a@[n:negd(m0d(a))]
-satzd176d:=satz122(2a,1a,isless12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),n)):posd(a)
-a@[z:zero(m0d(a))]
-satzd176e:=symis(cut,2a,1a,tr3is(cut,2a,stm(df(2a,1a)),std(df(2a,1a)),1a,isstm(2a,1a),z,stdis(2a,1a))):zero(a)
-a@[p:posd(m0d(a))]
-satzd176f:=satz121(2a,1a,ismore12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),p)):negd(a)
-a@[z:zero(a)]
-m0d0:=zeroeq(m0d(a),a,satzd176b(a,z),z):eq(m0d(a),a)
-+3d177
-a@t1:=tris(dif,m0d(m0d(a)),df(1a,2a),a,issmsd(std(m0d(a)),stm(m0d(a)),1a,2a,stdis(2a,1a),stmis(2a,1a)),dfis(a)):is"e"(dif,m0d(m0d(a)),a)
--3d177
-a@satzd177:=refeq1(m0d(m0d(a)),a,t1".3d177"):eq(m0d(m0d(a)),a)
-satzd177a:=symeq(m0d(m0d(a)),a,satzd177):eq(a,m0d(m0d(a)))
-b@[e:eq(a,m0d(b))]
-satzd177b:=treq(m0d(a),m0d(m0d(b)),b,eqm0d(a,m0d(b),e),satzd177(b)):eq(m0d(a),b)
-satzd177c:=symeq(m0d(a),b,satzd177b):eq(b,m0d(a))
-b@[e:eq(m0d(a),b)]
-satzd177d:=satzd177c(b,a,symeq(m0d(a),b,e)):eq(a,m0d(b))
-satzd177e:=symeq(a,m0d(b),satzd177d):eq(m0d(b),a)
-+3d178
-a@[p:posd(a)]
-t1:=tr3eq(absd(m0d(a)),m0d(m0d(a)),a,absd(a),absnd(m0d(a),satzd176a(a,p)),satzd177(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p)))):eq(absd(m0d(a)),absd(a))
-a@[z:zero(a)]
-t2:=tr3eq(absd(m0d(a)),m0d(a),a,absd(a),absnnd(m0d(a),0notnd(m0d(a),satzd176b(a,z))),m0d0(a,z),symeq(absd(a),a,absnnd(a,0notnd(a,z)))):eq(absd(m0d(a)),absd(a))
-a@[n:negd(a)]
-t3:=treq(absd(m0d(a)),m0d(a),absd(a),absnnd(m0d(a),pnotnd(m0d(a),satzd176c(a,n))),symeq(absd(a),m0d(a),absnd(a,n))):eq(absd(m0d(a)),absd(a))
--3d178
-a@satzd178:=rappd(a,eq(absd(m0d(a)),absd(a)),[t:posd(a)]t1".3d178"(t),[t:zero(a)]t2".3d178"(t),[t:negd(a)]t3".3d178"(t)):eq(absd(m0d(a)),absd(a))
-satzd178a:=symeq(absd(m0d(a)),absd(a),satzd178):eq(absd(a),absd(m0d(a)))
-+3d179
-t1:=pdeq1b(a,2a,1a):eq(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)))
-t2:=zeroi(pl(1a,2a),pl(2a,1a),compl(1a,2a)):zero(df(pl(1a,2a),pl(2a,1a)))
--3d179
-satzd179:=eqzero(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)),t1".3d179",t2".3d179"):zero(pd(a,m0d(a)))
-satzd179a:=eqzero(pd(a,m0d(a)),pd(m0d(a),a),compd(a,m0d(a)),satzd179):zero(pd(m0d(a),a))
-b@satzd180:=treq(m0d(pd(a,b)),df(pl(2a,2b),pl(1a,1b)),pd(m0d(a),m0d(b)),m0deqa(pl(1a,1b),pl(2a,2b)),pdeq12b(2a,1a,2b,1b)):eq(m0d(pd(a,b)),pd(m0d(a),m0d(b)))
-satzd180a:=symeq(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180):eq(pd(m0d(a),m0d(b)),m0d(pd(a,b)))
-md:=pd(a,m0d(b)):dif
-b2@mdeq12a:=treq(md(df(a1,a2),df(b1,b2)),pd(df(a1,a2),df(b2,b1)),df(pl(a1,b2),pl(a2,b1)),eqpd2(m0d(df(b1,b2)),df(b2,b1),df(a1,a2),m0deqa(b1,b2)),pdeq12a(a1,a2,b2,b1)):eq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)))
-mdeq12b:=symeq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)),mdeq12a):eq(df(pl(a1,b2),pl(a2,b1)),md(df(a1,a2),df(b1,b2)))
-r2@mdeq1a:=treq(md(a,df(r1,r2)),pd(a,df(r2,r1)),df(pl(1a,r2),pl(2a,r1)),eqpd2(m0d(df(r1,r2)),df(r2,r1),a,m0deqa(r1,r2)),pdeq1a(a,r2,r1)):eq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)))
-mdeq1b:=symeq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)),mdeq1a):eq(df(pl(1a,r2),pl(2a,r1)),md(a,df(r1,r2)))
-mdeq2a:=pdeq12a(r1,r2,2a,1a):eq(md(df(r1,r2),a),df(pl(r1,2a),pl(r2,1a)))
-mdeq2b:=pdeq12b(r1,r2,2a,1a):eq(df(pl(r1,2a),pl(r2,1a)),md(df(r1,r2),a))
-c@[e:eq(a,b)]
-eqmd1:=eqpd1(a,b,m0d(c),e):eq(md(a,c),md(b,c))
-eqmd2:=eqpd2(m0d(a),m0d(b),c,eqm0d(a,b,e)):eq(md(c,a),md(c,b))
-d@[e:eq(a,b)][f:eq(c,d)]
-eqmd12:=treq(md(a,c),md(b,c),md(b,d),eqmd1(a,b,c,e),eqmd2(c,d,b,f)):eq(md(a,c),md(b,d))
-b@satzd181:=tr3eq(m0d(md(a,b)),pd(m0d(a),m0d(m0d(b))),pd(m0d(a),b),md(b,a),satzd180(a,m0d(b)),eqpd2(m0d(m0d(b)),b,m0d(a),satzd177(b)),compd(m0d(a),b)):eq(m0d(md(a,b)),md(b,a))
-satzd181a:=symeq(m0d(md(b,a)),md(a,b),satzd181(b,a)):eq(md(a,b),m0d(md(b,a)))
-+3d182
-t1:=treq(md(a,b),df(pl(1a,2b),pl(2a,1b)),df(pl(1a,2b),pl(1b,2a)),pdeq1a(a,2b,1b),eqsd(pl(1a,2b),pl(2a,1b),pl(1b,2a),compl(2a,1b))):eq(md(a,b),df(pl(1a,2b),pl(1b,2a)))
-t2:=symeq(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1):eq(df(pl(1a,2b),pl(1b,2a)),md(a,b))
-t3:=stmis(pl(1a,2b),pl(1b,2a)):is(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b))
-t4:=stdis(pl(1a,2b),pl(1b,2a)):is(std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a))
--3d182
-[p:posd(md(a,b))]
-+*3d182
-p@t5:=eqposd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,p):posd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-p@satzd182a:=ismore12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t5".3d182"):mored(a,b)
-b@[z:zero(md(a,b))]
-+*3d182
-z@t6:=eqzero(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,z):zero(df(pl(1a,2b),pl(1b,2a)))
--3d182
-z@satzd182b:=tr3is(cut,pl(1a,2b),stm(df(pl(1a,2b),pl(1b,2a))),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),isstm(pl(1a,2b),pl(1b,2a)),t6".3d182",t4".3d182"):eq(a,b)
-b@[n:negd(md(a,b))]
-+*3d182
-n@t7:=eqnegd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,n):negd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-n@satzd182c:=isless12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t7".3d182"):lessd(a,b)
-b@[m:mored(a,b)]
-+*3d182
-m@t8:=posdi(pl(1a,2b),pl(1b,2a),m):posd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-m@satzd182d:=eqposd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t8".3d182"):posd(md(a,b))
-b@[e:eq(a,b)]
-+*3d182
-e@t9:=zeroi(pl(1a,2b),pl(1b,2a),e):zero(df(pl(1a,2b),pl(1b,2a)))
--3d182
-e@satzd182e:=eqzero(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t9".3d182"):zero(md(a,b))
-b@[l:lessd(a,b)]
-+*3d182
-l@t10:=negdi(pl(1a,2b),pl(1b,2a),l):negd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-l@satzd182f:=eqnegd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t10".3d182"):negd(md(a,b))
-+3d183
-b@t1:=tris(cut,pl(1a,2b),pl(2b,1a),pl(stm(m0d(b)),std(m0d(a))),compl(1a,2b),12issmsd(2b,1b,2a,1a)):is(pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))))
-t2:=t1(b,a):is(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))))
--3d183
-b@[m:mored(a,b)]
-satzd183a:=isless12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad5(a,b,m)):lessd(m0d(a),m0d(b))
-b@[e:eq(a,b)]
-staz183b:=eqm0d(a,b,e):eq(m0d(a),m0d(b))
-b@[l:lessd(a,b)]
-satzd183c:=ismore12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad6(a,b,l)):mored(m0d(a),m0d(b))
-b@[l:lessd(m0d(a),m0d(b))]
-satzd183d:=eqmored12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183c(m0d(a),m0d(b),l)):mored(a,b)
-b@[e:eq(m0d(a),m0d(b))]
-satzd183e:=tr3eq(a,m0d(m0d(a)),m0d(m0d(b)),b,satzd177a(a),eqm0d(m0d(a),m0d(b),e),satzd177(b)):eq(a,b)
-b@[m:mored(m0d(a),m0d(b))]
-satzd183f:=eqlessd12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183a(m0d(a),m0d(b),m)):lessd(a,b)
-+3d184
-a@t1:=tr3eq(a,df(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp))),df(pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp))),md(pdofrp(1a),pdofrp(2a)),lemmad3(a,pl(1rp,1rp)),eqsmsd(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp)),pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp)),asspl2(1a,1rp,1rp),3pl12(2a,1rp,1rp)),mdeq12b(pl(1a,1rp),1rp,pl(2a,1rp),1rp)):eq(a,md(pdofrp(1a),pdofrp(2a)))
-t2:=and3i(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))),posdirp(1a),posdirp(2a),t1):and3(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))))
-t3:=somei(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))),pdofrp(2a),t2):some"l"(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))))
--3d184
-a@satzd184:=somei(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))),pdofrp(1a),t3".3d184"):some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))))
-c@asspd1:=tr3eq(pd(pd(a,b),c),df(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c)),df(pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c))),pd(a,pd(b,c)),pdeq2a(c,pl(1a,1b),pl(2a,2b)),eqsmsd(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c),pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c)),asspl1(1a,1b,1c),asspl1(2a,2b,2c)),pdeq1b(a,pl(1b,1c),pl(2b,2c))):eq(pd(pd(a,b),c),pd(a,pd(b,c)))
-asspd2:=symeq(pd(pd(a,b),c),pd(a,pd(b,c)),asspd1):eq(pd(a,pd(b,c)),pd(pd(a,b),c))
-3pd23:=tr3eq(pd(pd(a,b),c),pd(a,pd(b,c)),pd(a,pd(c,b)),pd(pd(a,c),b),asspd1(a,b,c),eqpd2(pd(b,c),pd(c,b),a,compd(b,c)),asspd2(a,c,b)):eq(pd(pd(a,b),c),pd(pd(a,c),b))
-d@4pd23:=tr3eq(pd(pd(a,b),pd(c,d)),pd(pd(pd(a,b),c),d),pd(pd(pd(a,c),b),d),pd(pd(a,c),pd(b,d)),asspd2(pd(a,b),c,d),eqpd1(pd(pd(a,b),c),pd(pd(a,c),b),d,3pd23),asspd1(pd(a,c),b,d)):eq(pd(pd(a,b),pd(c,d)),pd(pd(a,c),pd(b,d)))
-b@pdmd:=treq(pd(md(a,b),b),pd(a,pd(m0d(b),b)),a,asspd1(a,m0d(b),b),pd02(a,pd(m0d(b),b),satzd179a(b))):eq(pd(md(a,b),b),a)
-mdpd:=treq(md(pd(a,b),b),pd(a,pd(b,m0d(b))),a,asspd1(a,b,m0d(b)),pd02(a,pd(b,m0d(b)),satzd179(b))):eq(md(pd(a,b),b),a)
-d@satzd185:=treq(pd(md(a,b),md(c,d)),pd(pd(a,c),pd(m0d(b),m0d(d))),md(pd(a,c),pd(b,d)),4pd23(a,m0d(b),c,m0d(d)),eqpd2(pd(m0d(b),m0d(d)),m0d(pd(b,d)),pd(a,c),satzd180a(b,d))):eq(pd(md(a,b),md(c,d)),md(pd(a,c),pd(b,d)))
-c@satzd186:=asspd1:eq(pd(pd(a,b),c),pd(a,pd(b,c)))
-b@satzd187a:=treq(pd(b,md(a,b)),pd(md(a,b),b),a,compd(b,md(a,b)),pdmd):eq(pd(b,md(a,b)),a)
-[x:dif][e:eq(pd(b,x),a)]
-satzd187c:=treq(md(a,b),md(pd(x,b),b),x,eqmd1(a,pd(x,b),b,treq1(a,pd(x,b),pd(b,x),e,compd(b,x))),mdpd(x,b)):eq(md(a,b),x)
-satzd187d:=symeq(md(a,b),x,satzd187c):eq(x,md(a,b))
-x@[e:eq(pd(x,b),a)]
-satzd187e:=satzd187c(treq(pd(b,x),pd(x,b),a,compd(b,x),e)):eq(md(a,b),x)
-satzd187f:=symeq(md(a,b),x,satzd187e):eq(x,md(a,b))
-+3d188
-c@t1:=tr3eq(md(pd(a,c),pd(b,c)),pd(pd(a,c),pd(m0d(b),m0d(c))),pd(md(a,b),md(c,c)),md(a,b),eqpd2(m0d(pd(b,c)),pd(m0d(b),m0d(c)),pd(a,c),satzd180(b,c)),4pd23(a,c,m0d(b),m0d(c)),pd02(md(a,b),md(c,c),satzd179(c))):eq(md(pd(a,c),pd(b,c)),md(a,b))
-t2:=symeq(md(pd(a,c),pd(b,c)),md(a,b),t1):eq(md(a,b),md(pd(a,c),pd(b,c)))
--3d188
-c@[m:mored(pd(a,c),pd(b,c))]
-+*3d188
-m@t3:=eqposd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182d(pd(a,c),pd(b,c),m)):posd(md(a,b))
--3d188
-m@satzd188a:=satzd182a(a,b,t3".3d188"):mored(a,b)
-c@[e:eq(pd(a,c),pd(b,c))]
-+*3d188
-e@t4:=eqzero(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182e(pd(a,c),pd(b,c),e)):zero(md(a,b))
--3d188
-e@satzd188b:=satzd182b(a,b,t4".3d188"):eq(a,b)
-c@[l:lessd(pd(a,c),pd(b,c))]
-+*3d188
-l@t5:=eqnegd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182f(pd(a,c),pd(b,c),l)):negd(md(a,b))
--3d188
-l@satzd188c:=satzd182c(a,b,t5".3d188"):lessd(a,b)
-c@[m:mored(a,b)]
-+*3d188
-m@t6:=eqposd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182d(a,b,m)):posd(md(pd(a,c),pd(b,c)))
--3d188
-m@satzd188d:=satzd182a(pd(a,c),pd(b,c),t6".3d188"):mored(pd(a,c),pd(b,c))
-c@[e:eq(a,b)]
-satzd188e:=eqpd1(a,b,c,e):eq(pd(a,c),pd(b,c))
-c@[l:lessd(a,b)]
-+*3d188
-l@t7:=eqnegd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182f(a,b,l)):negd(md(pd(a,c),pd(b,c)))
--3d188
-l@satzd188f:=satzd182c(pd(a,c),pd(b,c),t7".3d188"):lessd(pd(a,c),pd(b,c))
-c@[m:mored(pd(c,a),pd(c,b))]
-satzd188g:=satzd188a(eqmored12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),m)):mored(a,b)
-c@[e:eq(pd(c,a),pd(c,b))]
-satzd188h:=satzd188b(tr3eq(pd(a,c),pd(c,a),pd(c,b),pd(b,c),compd(a,c),e,compd(c,b))):eq(a,b)
-[l:lessd(pd(c,a),pd(c,b))]
-satzd188j:=satzd188c(eqlessd12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),l)):lessd(a,b)
-c@[m:mored(a,b)]
-satzd188k:=eqmored12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188d(m)):mored(pd(c,a),pd(c,b))
-c@[e:eq(a,b)]
-satzd188l:=eqpd2(a,b,c,e):eq(pd(c,a),pd(c,b))
-c@[l:lessd(a,b)]
-satzd188m:=eqlessd12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188f(l)):lessd(pd(c,a),pd(c,b))
-d@[e:eq(a,b)][m:mored(c,d)]
-satzd188n:=eqmored2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188k(c,d,a,m)):mored(pd(a,c),pd(b,d))
-satzd188o:=eqmored12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188n):mored(pd(c,a),pd(d,b))
-e@[l:lessd(c,d)]
-satzd188p:=eqlessd2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188m(c,d,a,l)):lessd(pd(a,c),pd(b,d))
-satzd188q:=eqlessd12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188p):lessd(pd(c,a),pd(d,b))
-d@[m:mored(a,b)][n:mored(c,d)]
-satzd189:=trmored(pd(a,c),pd(b,c),pd(b,d),satzd188d(a,b,c,m),satzd188k(c,d,b,n)):mored(pd(a,c),pd(b,d))
-d@[l:lessd(a,b)][k:lessd(c,d)]
-satzd189a:=lemmad5(pd(b,d),pd(a,c),satzd189(b,a,d,c,lemmad6(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
-d@[m:moreq(a,b)][n:mored(c,d)]
-satzd190a:=orapp(mored(a,b),eq(a,b),mored(pd(a,c),pd(b,d)),m,[t:mored(a,b)]satzd189(t,n),[t:eq(a,b)]satzd188n(t,n)):mored(pd(a,c),pd(b,d))
-d@[m:mored(a,b)][n:moreq(c,d)]
-satzd190b:=eqmored12(pd(c,a),pd(a,c),pd(d,b),pd(b,d),compd(c,a),compd(d,b),satzd190a(c,d,a,b,n,m)):mored(pd(a,c),pd(b,d))
-d@[l:lesseq(a,b)][k:lessd(c,d)]
-satzd190c:=lemmad5(pd(b,d),pd(a,c),satzd190a(b,a,d,c,satzd168b(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
-d@[l:lessd(a,b)][k:lesseq(c,d)]
-satzd190d:=lemmad5(pd(b,d),pd(a,c),satzd190b(b,a,d,c,lemmad6(a,b,l),satzd168b(c,d,k))):lessd(pd(a,c),pd(b,d))
-d@[m:moreq(a,b)][n:moreq(c,d)]
-+3d191
-[e:eq(a,b)][f:eq(c,d)]
-t1:=moreqi2(pd(a,c),pd(b,d),eqpd12(a,b,c,d,e,f)):moreq(pd(a,c),pd(b,d))
-e@[o:mored(c,d)]
-t2:=moreqi1(pd(a,c),pd(b,d),satzd190a(m,o)):moreq(pd(a,c),pd(b,d))
-e@t3:=orapp(mored(c,d),eq(c,d),moreq(pd(a,c),pd(b,d)),n,[t:mored(c,d)]t2(t),[t:eq(c,d)]t1(t)):moreq(pd(a,c),pd(b,d))
-n@[o:mored(a,b)]
-t4:=moreqi1(pd(a,c),pd(b,d),satzd190b(o,n)):moreq(pd(a,c),pd(b,d))
--3d191
-satzd191:=orapp(mored(a,b),eq(a,b),moreq(pd(a,c),pd(b,d)),m,[t:mored(a,b)]t4".3d191"(t),[t:eq(a,b)]t3".3d191"(t)):moreq(pd(a,c),pd(b,d))
-d@[l:lesseq(a,b)][k:lesseq(c,d)]
-satzd191a:=satzd168a(pd(b,d),pd(a,c),satzd191(b,a,d,c,satzd168b(a,b,l),satzd168b(c,d,k))):lesseq(pd(a,c),pd(b,d))
-b@td:=df(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))):dif
-+iv4d
-a2@[r:cut]
-t1:=ists1(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(stm(df(a1,a2)),r),ts(a1,r))
-t2:=ists2(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(r,stm(df(a1,a2))),ts(r,a1))
-t3:=ists1(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(std(df(a1,a2)),r),ts(a2,r))
-t4:=ists2(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(r,std(df(a1,a2))),ts(r,a2))
-[s:cut]
-t5:=ispl12(ts(stm(df(a1,a2)),r),ts(a1,r),ts(std(df(a1,a2)),s),ts(a2,s),t1(r),t3(s)):is(pl(ts(stm(df(a1,a2)),r),ts(std(df(a1,a2)),s)),pl(ts(a1,r),ts(a2,s)))
-t6:=ispl12(ts(r,stm(df(a1,a2))),ts(r,a1),ts(s,std(df(a1,a2))),ts(s,a2),t2(r),t4(s)):is(pl(ts(r,stm(df(a1,a2))),ts(s,std(df(a1,a2)))),pl(ts(r,a1),ts(s,a2)))
-t7:=ispl12(ts(std(df(a1,a2)),r),ts(a2,r),ts(stm(df(a1,a2)),s),ts(a1,s),t3(r),t1(s)):is(pl(ts(std(df(a1,a2)),r),ts(stm(df(a1,a2)),s)),pl(ts(a2,r),ts(a1,s)))
-t8:=ispl12(ts(r,std(df(a1,a2))),ts(r,a2),ts(s,stm(df(a1,a2))),ts(s,a1),t4(r),t2(s)):is(pl(ts(r,std(df(a1,a2))),ts(s,stm(df(a1,a2)))),pl(ts(r,a2),ts(s,a1)))
-b2@t9:=tris(cut,pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,stm(df(b1,b2))),ts(a2,std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),t5(a1,a2,stm(df(b1,b2)),std(df(b1,b2))),t6(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)))
-t10:=tris(cut,pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,std(df(b1,b2))),ts(a2,stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)),t5(a1,a2,std(df(b1,b2)),stm(df(b1,b2))),t8(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)))
--iv4d
-b2@td12:=issmsd(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1)),t9".iv4d",t10".iv4d"):is"e"(dif,td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
-r2@td1:=issmsd(pl(ts(1a,stm(df(r1,r2))),ts(2a,std(df(r1,r2)))),pl(ts(1a,std(df(r1,r2))),ts(2a,stm(df(r1,r2)))),pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1)),t6".iv4d"(r1,r2,1a,2a),t8".iv4d"(r1,r2,1a,2a)):is"e"(dif,td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
-td2:=issmsd(pl(ts(stm(df(r1,r2)),1a),ts(std(df(r1,r2)),2a)),pl(ts(stm(df(r1,r2)),2a),ts(std(df(r1,r2)),1a)),pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a)),t5".iv4d"(r1,r2,1a,2a),t5".iv4d"(r1,r2,2a,1a)):is"e"(dif,td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
-b2@tdeq12a:=refeq1(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
-tdeq12b:=refeq2(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td(df(a1,a2),df(b1,b2)))
-r2@tdeq1a:=refeq1(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
-tdeq1b:=refeq2(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td(a,df(r1,r2)))
-tdeq2a:=refeq1(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
-tdeq2b:=refeq2(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td(df(r1,r2),a))
-+4d194
-b@t1:=ispl12(ts(1a,1b),ts(1b,1a),ts(2a,2b),ts(2b,2a),comts(1a,1b),comts(2a,2b)):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1b,1a),ts(2b,2a)))
-t2:=tris(cut,pl(ts(1a,2b),ts(2a,1b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1b,2a),ts(2b,1a)),compl(ts(1a,2b),ts(2a,1b)),ispl12(ts(2a,1b),ts(1b,2a),ts(1a,2b),ts(2b,1a),comts(2a,1b),comts(1a,2b))):is(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,2a),ts(2b,1a)))
--4d194
-b@satzd194:=eqsmsd(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,1a),ts(2b,2a)),pl(ts(1b,2a),ts(2b,1a)),t1".4d194",t2".4d194"):eq(td(a,b),td(b,a))
-comtd:=satzd194:eq(td(a,b),td(b,a))
-c@[e:eq(a,b)]
-+*iv4d
-e@[r:cut]
-t11:=tr3is(cut,pl(ts(1a,r),ts(2b,r)),ts(pl(1a,2b),r),ts(pl(1b,2a),r),pl(ts(1b,r),ts(2a,r)),distpt1(1a,2b,r),ists1(pl(1a,2b),pl(1b,2a),r,e),disttp1(1b,2a,r)):is(pl(ts(1a,r),ts(2b,r)),pl(ts(1b,r),ts(2a,r)))
-e@t12:=tr3is(cut,pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,2c),ts(2a,2c))),pl(pl(ts(1b,1c),ts(2a,1c)),pl(ts(1a,2c),ts(2b,2c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))),4pl24(ts(1a,1c),ts(2a,2c),ts(1b,2c),ts(2b,1c)),ispl12(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,1c),ts(2a,1c)),pl(ts(1b,2c),ts(2a,2c)),pl(ts(1a,2c),ts(2b,2c)),t11(1c),t11(b,a,c,symeq(a,b,e),2c)),4pl24(ts(1b,1c),ts(2a,1c),ts(1a,2c),ts(2b,2c))):is(pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))))
--iv4d
-e@eqtd1:=eqi12(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)),pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)),t12".iv4d"):eq(td(a,c),td(b,c))
-eqtd2:=tr3eq(td(c,a),td(a,c),td(b,c),td(c,b),comtd(c,a),eqtd1,comtd(b,c)):eq(td(c,a),td(c,b))
-d@[e:eq(a,b)][f:eq(c,d)]
-eqtd12:=treq(td(a,c),td(b,c),td(b,d),eqtd1(a,b,c,e),eqtd2(c,d,b,f)):eq(td(a,c),td(b,d))
-b@[z:zero(a)]
-+4d192
-t1:=tris(cut,pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1a,2b),ts(2a,1b)),ispl12(ts(1a,1b),ts(2a,1b),ts(2a,2b),ts(1a,2b),ists1(1a,2a,1b,z),ists1(2a,1a,2b,symis(cut,1a,2a,z))),compl(ts(2a,1b),ts(1a,2b))):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
--4d192
-satzd192a:=zeroi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t1".4d192"):zero(td(a,b))
-b@[z:zero(b)]
-satzd192b:=eqzero(td(b,a),td(a,b),comtd(b,a),satzd192a(b,a,z)):zero(td(a,b))
-b@[z:zero(a)]
-td01:=satzd192a(z):zero(td(a,b))
-b@[z:zero(b)]
-td02:=satzd192b(z):zero(td(a,b))
-b@satzd197a:=tr3eq(td(m0d(a),b),df(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b))),df(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b))),m0d(td(a,b)),tdeq2a(b,2a,1a),eqsmsd(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b)),compl(ts(2a,1b),ts(1a,2b)),compl(ts(2a,2b),ts(1a,1b))),m0deqb(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))):eq(td(m0d(a),b),m0d(td(a,b)))
-satzd197b:=tr3eq(td(a,m0d(b)),td(m0d(b),a),m0d(td(b,a)),m0d(td(a,b)),comtd(a,m0d(b)),satzd197a(b,a),eqm0d(td(b,a),td(a,b),comtd(b,a))):eq(td(a,m0d(b)),m0d(td(a,b)))
-satzd197c:=treq2(td(m0d(a),b),td(a,m0d(b)),m0d(td(a,b)),satzd197a,satzd197b):eq(td(m0d(a),b),td(a,m0d(b)))
-satzd197d:=symeq(td(m0d(a),b),td(a,m0d(b)),satzd197c):eq(td(a,m0d(b)),td(m0d(a),b))
-satzd197e:=symeq(td(m0d(a),b),m0d(td(a,b)),satzd197a):eq(m0d(td(a,b)),td(m0d(a),b))
-satzd197f:=symeq(td(a,m0d(b)),m0d(td(a,b)),satzd197b):eq(m0d(td(a,b)),td(a,m0d(b)))
-satzd198:=treq(td(m0d(a),m0d(b)),td(a,m0d(m0d(b))),td(a,b),satzd197c(a,m0d(b)),eqtd2(m0d(m0d(b)),b,a,satzd177(b))):eq(td(m0d(a),m0d(b)),td(a,b))
-satzd198a:=symeq(td(m0d(a),m0d(b)),td(a,b),satzd198):eq(td(a,b),td(m0d(a),m0d(b)))
-[p:posd(a)][q:posd(b)]
-+*iv4d
-q@[r:cut]
-t13:=tris(cut,pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,pl(mn(1b,2b,q),2b)),ts(r,1b),distpt2(r,mn(1b,2b,q),2b),ists2(pl(mn(1b,2b,q),2b),1b,r,satz140e(1b,2b,q))):is(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b))
-[s:cut]
-t14:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),s),pl(ts(r,1b),s),asspl2(ts(r,mn(1b,2b,q)),ts(r,2b),s),ispl1(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b),s,t13)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s))
-t15:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s),pl(s,ts(r,1b)),t14,compl(ts(r,1b),s)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(s,ts(r,1b)))
-q@t16:=satz135h(pl(ts(1a,2b),ts(2a,2b)),pl(ts(2a,2b),ts(1a,2b)),ts(1a,mn(1b,2b,q)),ts(2a,mn(1b,2b,q)),compl(ts(1a,2b),ts(2a,2b)),satz145a(1a,2a,mn(1b,2b,q),p)):more(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))))
-t17:=ismore12(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))),pl(ts(1a,2b),ts(2a,1b)),t14(1a,ts(2a,2b)),t15(2a,ts(1a,2b)),t16):more(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
--iv4d
-q@ptdpp:=posdi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t17".iv4d"):posd(td(a,b))
-b@[p:posd(a)][n:negd(b)]
-+*iv4d
-n@t18:=eqposd(td(a,m0d(b)),m0d(td(a,b)),satzd197b(a,b),ptdpp(a,m0d(b),p,satzd176c(b,n))):posd(m0d(td(a,b)))
--iv4d
-n@ntdpn:=satzd176f(td(a,b),t18".iv4d"):negd(td(a,b))
-b@[n:negd(a)][p:posd(b)]
-ntdnp:=eqnegd(td(b,a),td(a,b),comtd(b,a),ntdpn(b,a,p,n)):negd(td(a,b))
-b@[n:negd(a)][o:negd(b)]
-ptdnn:=eqposd(td(m0d(a),m0d(b)),td(a,b),satzd198(a,b),ptdpp(m0d(a),m0d(b),satzd176c(a,n),satzd176c(b,o))):posd(td(a,b))
-b@[n:not(zero(a))][o:not(zero(b))]
-+*4d192
-o@[p:posd(a)][q:posd(b)]
-t2:=pnot0d(td(a,b),ptdpp(a,b,p,q)):not(zero(td(a,b)))
-p@[m:negd(b)]
-t3:=nnot0d(td(a,b),ntdpn(a,b,p,m)):not(zero(td(a,b)))
-p@t4:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t2(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t3(t)):not(zero(td(a,b)))
-o@[m:negd(a)][p:posd(b)]
-t5:=nnot0d(td(a,b),ntdnp(a,b,m,p)):not(zero(td(a,b)))
-m@[l:negd(b)]
-t6:=pnot0d(td(a,b),ptdnn(a,b,m,l)):not(zero(td(a,b)))
-m@t7:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t5(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t6(t)):not(zero(td(a,b)))
--4d192
-o@satzd192d:=rappd(a,not(zero(td(a,b))),[t:posd(a)]t4".4d192"(t),th2"l.imp"(zero(a),not(zero(td(a,b))),n),[t:negd(a)]t7".4d192"(t)):not(zero(td(a,b)))
-b@[z:zero(td(a,b))]
-+*4d192
-z@[n:not(zero(a))]
-t8:=et(zero(b),th3"l.imp"(not(zero(b)),not(zero(td(a,b))),weli(zero(td(a,b)),z),[t:not(zero(b))]satzd192d(n,t))):zero(b)
--4d192
-z@satzd192c:=[t:not(zero(a))]t8".4d192"(t):or(zero(a),zero(b))
-+4d193
-b@[p:posd(a)][q:posd(b)]
-t1:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdpp(a,b,p,q))),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-p@[n:negd(b)]
-t2:=treq(absd(td(a,b)),m0d(td(a,b)),td(a,m0d(b)),absnd(td(a,b),ntdpn(a,b,p,n)),satzd197f(a,b)):eq(absd(td(a,b)),td(a,m0d(b)))
-t3:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,m0d(b)),t2,eqtd12(absd(a),a,absd(b),m0d(b),absnnd(a,pnotnd(a,p)),absnd(b,n))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[z:zero(a)]
-t4:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td01(a,b,z)),td01(absd(a),absd(b),satzd166f(a,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[z:zero(b)]
-t5:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td02(a,b,z)),td02(absd(a),absd(b),satzd166f(b,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[n:negd(a)][p:posd(b)]
-t6:=tr3eq(absd(td(a,b)),absd(td(b,a)),td(absd(b),absd(a)),td(absd(a),absd(b)),eqabsd(td(a,b),td(b,a),comtd(a,b)),t3(b,a,p,n),comtd(absd(b),absd(a))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-n@[o:negd(b)]
-t7:=treq(td(absd(a),absd(b)),td(m0d(a),m0d(b)),td(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o)),satzd198(a,b)):eq(td(absd(a),absd(b)),td(a,b))
-t8:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdnn(a,b,n,o))),t7):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[p:posd(a)]
-t9:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t1(p,t),[t:zero(b)]t5(t),[t:negd(b)]t3(p,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[n:negd(a)]
-t10:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t6(n,t),[t:zero(b)]t5(t),[t:negd(b)]t8(n,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
--4d193
-b@satzd193:=rappd(a,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(a)]t9".4d193"(t),[t:zero(a)]t4".4d193"(t),[t:negd(a)]t10".4d193"(t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
-satzd103a:=symeq(absd(td(a,b)),td(absd(a),absd(b)),satzd193):eq(td(absd(a),absd(b)),absd(td(a,b)))
-@1df:=pdofrp(1rp):dif
-+4d195
-a@t1:=tris(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(ts(1a,pl(1rp,1rp)),pl(ts(2a,1rp),2a)),pl(pl(1a,1a),pl(2a,2a)),asspl1(ts(1a,pl(1rp,1rp)),ts(2a,1rp),2a),ispl12(ts(1a,pl(1rp,1rp)),pl(1a,1a),pl(ts(2a,1rp),2a),pl(2a,2a),a2isapa(1a),ispl1(ts(2a,1rp),2a,2a,satz151(2a)))):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(pl(1a,1a),pl(2a,2a)))
-t2:=tris(cut,pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,ts(1a,1rp)),ts(2a,pl(1rp,1rp))),pl(pl(1a,1a),pl(2a,2a)),asspl2(1a,ts(1a,1rp),ts(2a,pl(1rp,1rp))),ispl12(pl(1a,ts(1a,1rp)),pl(1a,1a),ts(2a,pl(1rp,1rp)),pl(2a,2a),ispl2(ts(1a,1rp),1a,1a,satz151(1a)),a2isapa(2a))):is(pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)))
-t3:=tris2(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)),t1,t2):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))))
--4d195
-a@satzd195:=treq(td(a,1df),df(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),a,tdeq1a(a,pl(1rp,1rp),1rp),eqi2(a,pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp))),t3".4d195")):eq(td(a,1df),a)
-satzd195a:=symeq(td(a,1df),a,satzd195):eq(a,td(a,1df))
-satzd195b:=treq(td(1df,a),td(a,1df),a,comtd(1df,a),satzd195):eq(td(1df,a),a)
-satzd195c:=symeq(td(1df,a),a,satzd195b):eq(a,td(1df,a))
-b@[p:posd(a)][q:posd(b)]
-satzd196a:=symeq(td(absd(a),absd(b)),td(a,b),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(td(a,b),td(absd(a),absd(b)))
-b@[n:negd(a)][o:negd(b)]
-satzd196b:=treq2(td(a,b),td(absd(a),absd(b)),td(m0d(a),m0d(b)),satzd198a(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o))):eq(td(a,b),td(absd(a),absd(b)))
-b@[p:posd(a)][n:negd(b)]
-satzd196c:=treq1(td(a,b),m0d(td(absd(a),absd(b))),td(absd(a),m0d(absd(b))),eqtd12(absd(a),a,m0d(absd(b)),b,absnnd(a,pnotnd(a,p)),satzd177b(absd(b),b,absnd(b,n))),satzd197b(absd(a),absd(b))):eq(td(a,b),m0d(td(absd(a),absd(b))))
-b@[n:negd(a)][p:posd(b)]
-satzd196d:=tr3eq(td(a,b),td(b,a),m0d(td(absd(b),absd(a))),m0d(td(absd(a),absd(b))),comtd(a,b),satzd196c(b,a,p,n),eqm0d(td(absd(b),absd(a)),td(absd(a),absd(b)),comtd(absd(b),absd(a)))):eq(td(a,b),m0d(td(absd(a),absd(b))))
-+4d196
-b@p1p2:=and(posd(a),posd(b)):'prop'
-p1n2:=and(posd(a),negd(b)):'prop'
-n1p2:=and(negd(a),posd(b)):'prop'
-n1n2:=and(negd(a),negd(b)):'prop'
--4d196
-b@[n:not(zero(a))][o:not(zero(b))][e:eq(td(a,b),td(absd(a),absd(b)))]
-+*4d196
-o@t1:=ptdpp(absd(a),absd(b),satzd166e(a,n),satzd166e(b,o)):posd(td(absd(a),absd(b)))
-e@t2:=pnotnd(td(a,b),eqposd(td(absd(a),absd(b)),td(a,b),symeq(td(a,b),td(absd(a),absd(b)),e),t1)):not(negd(td(a,b)))
-[p:posd(a)]
-t3:=th3"l.imp"(negd(b),negd(td(a,b)),t2,[t:negd(b)]ntdpn(a,b,p,t)):not(negd(b))
-t4:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t3,o):posd(b)
-t5:=andi(posd(a),posd(b),p,t4):p1p2
-t6:=ori1(p1p2,n1n2,t5):or(p1p2,n1n2)
-e@[m:negd(a)]
-t7:=th3"l.imp"(posd(b),negd(td(a,b)),t2,[t:posd(b)]ntdnp(a,b,m,t)):not(posd(b))
-t8:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t7):negd(b)
-t9:=andi(negd(a),negd(b),m,t8):n1n2
-t10:=ori2(p1p2,n1n2,t9):or(p1p2,n1n2)
--4d196
-e@satzd196e:=rappd(a,or(p1p2".4d196",n1n2".4d196"),[t:posd(a)]t6".4d196"(t),th2"l.imp"(zero(a),or(p1p2".4d196",n1n2".4d196"),n),[t:negd(a)]t10".4d196"(t)):or(and(posd(a),posd(b)),and(negd(a),negd(b)))
-o@[e:eq(td(a,b),m0d(td(absd(a),absd(b))))]
-+*4d196
-o@t11:=satzd176a(td(absd(a),absd(b)),t1):negd(m0d(td(absd(a),absd(b))))
-e@t12:=nnotpd(td(a,b),eqnegd(m0d(td(absd(a),absd(b))),td(a,b),symeq(td(a,b),m0d(td(absd(a),absd(b))),e),t11)):not(posd(td(a,b)))
-[p:posd(a)]
-t13:=th3"l.imp"(posd(b),posd(td(a,b)),t12,[t:posd(b)]ptdpp(a,b,p,t)):not(posd(b))
-t14:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t13):negd(b)
-t15:=andi(posd(a),negd(b),p,t14):p1n2
-t16:=ori1(p1n2,n1p2,t15):or(p1n2,n1p2)
-e@[m:negd(a)]
-t17:=th3"l.imp"(negd(b),posd(td(a,b)),t12,[t:negd(b)]ptdnn(a,b,m,t)):not(negd(b))
-t18:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t17,o):posd(b)
-t19:=andi(negd(a),posd(b),m,t18):n1p2
-t20:=ori2(p1n2,n1p2,t19):or(p1n2,n1p2)
--4d196
-e@satzd196f:=rappd(a,or(p1n2".4d196",n1p2".4d196"),[t:posd(a)]t16".4d196"(t),th2"l.imp"(zero(a),or(p1n2".4d196",n1p2".4d196"),n),[t:negd(a)]t20".4d196"(t)):or(and(posd(a),negd(b)),and(negd(a),posd(b)))
-+4d199
-@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
-t1:=tris(cut,ts(pl(ts(p,r),ts(q,s)),t),pl(ts(ts(p,r),t),ts(ts(q,s),t)),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),disttp1(ts(p,r),ts(q,s),t),ispl12(ts(ts(p,r),t),ts(p,ts(r,t)),ts(ts(q,s),t),ts(q,ts(s,t)),assts1(p,r,t),assts1(q,s,t))):is(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))))
-t2:=tris(cut,pl(ts(q,ts(s,t)),ts(q,ts(r,u))),pl(ts(q,ts(r,u)),ts(q,ts(s,t))),ts(q,pl(ts(r,u),ts(s,t))),compl(ts(q,ts(s,t)),ts(q,ts(r,u))),distpt2(q,ts(r,u),ts(s,t))):is(pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))))
-t3:=tr3is(cut,pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(pl(ts(p,ts(r,t)),ts(q,ts(s,t))),pl(ts(p,ts(s,u)),ts(q,ts(r,u)))),pl(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u)))),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))),ispl12(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),ts(pl(ts(p,s),ts(q,r)),u),pl(ts(p,ts(s,u)),ts(q,ts(r,u))),t1,t1(p,q,s,r,u,t)),4pl23(ts(p,ts(r,t)),ts(q,ts(s,t)),ts(p,ts(s,u)),ts(q,ts(r,u))),ispl12(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),ts(p,pl(ts(r,t),ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))),distpt2(p,ts(r,t),ts(s,u)),t2)):is(pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))))
--4d199
-c@satzd199:=tr3eq(td(td(a,b),c),df(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c))),df(pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c))))),td(a,td(b,c)),tdeq2a(c,pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))),eqsmsd(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c)),pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c)))),t3".4d199"(1a,2a,1b,2b,1c,2c),t3".4d199"(1a,2a,1b,2b,2c,1c)),tdeq1b(a,pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)))):eq(td(td(a,b),c),td(a,td(b,c)))
-asstd1:=satzd199:eq(td(td(a,b),c),td(a,td(b,c)))
-asstd2:=symeq(td(td(a,b),c),td(a,td(b,c)),satzd199):eq(td(a,td(b,c)),td(td(a,b),c))
-+4d201
-@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
-t1:=tris(cut,pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(p,t)),pl(ts(q,s),ts(q,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))),ispl12(ts(p,pl(r,t)),pl(ts(p,r),ts(p,t)),ts(q,pl(s,u)),pl(ts(q,s),ts(q,u)),disttp2(p,r,t),disttp2(q,s,u)),4pl23(ts(p,r),ts(p,t),ts(q,s),ts(q,u))):is(pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))))
--4d201
-satzd201:=tr3eq(td(a,pd(b,c)),df(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c)))),df(pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c)))),pd(td(a,b),td(a,c)),tdeq1a(a,pl(1b,1c),pl(2b,2c)),eqsmsd(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c))),pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c))),t1".4d201"(1a,2a,1b,2b,1c,2c),t1".4d201"(1a,2a,2b,1b,2c,1c)),pdeq12b(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)))):eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
-disttpd1:=tr3eq(td(pd(a,b),c),td(c,pd(a,b)),pd(td(c,a),td(c,b)),pd(td(a,c),td(b,c)),comtd(pd(a,b),c),satzd201(c,a,b),eqpd12(td(c,a),td(a,c),td(c,b),td(b,c),comtd(c,a),comtd(c,b))):eq(td(pd(a,b),c),pd(td(a,c),td(b,c)))
-disttpd2:=satzd201:eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
-distptd1:=symeq(td(pd(a,b),c),pd(td(a,c),td(b,c)),disttpd1):eq(pd(td(a,c),td(b,c)),td(pd(a,b),c))
-distptd2:=symeq(td(a,pd(b,c)),pd(td(a,b),td(a,c)),disttpd2):eq(pd(td(a,b),td(a,c)),td(a,pd(b,c)))
-satzd202:=treq(td(a,md(b,c)),pd(td(a,b),td(a,m0d(c))),md(td(a,b),td(a,c)),disttpd2(a,b,m0d(c)),eqpd2(td(a,m0d(c)),m0d(td(a,c)),td(a,b),satzd197b(a,c))):eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
-disttmd1:=treq(td(md(a,b),c),pd(td(a,c),td(m0d(b),c)),md(td(a,c),td(b,c)),disttpd1(a,m0d(b),c),eqpd2(td(m0d(b),c),m0d(td(b,c)),td(a,c),satzd197a(b,c))):eq(td(md(a,b),c),md(td(a,c),td(b,c)))
-disttmd2:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
-distmtd1:=symeq(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1):eq(md(td(a,c),td(b,c)),td(md(a,b),c))
-distmtd2:=symeq(td(a,md(b,c)),md(td(a,b),td(a,c)),disttmd2):eq(md(td(a,b),td(a,c)),td(a,md(b,c)))
-satzd200:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
-[m:mored(a,b)]
-+4d203
-t1:=satzd182d(a,b,m):posd(md(a,b))
--4d203
-[p:posd(c)]
-+*4d203
-p@t2:=eqposd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ptdpp(md(a,b),c,t1,p)):posd(md(td(a,c),td(b,c)))
--4d203
-p@satzd203a:=satzd182a(td(a,c),td(b,c),t2".4d203"):mored(td(a,c),td(b,c))
-m@[z:zero(c)]
-satzd203b:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
-m@[n:negd(c)]
-+*4d203
-n@t3:=eqnegd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ntdpn(md(a,b),c,t1,n)):negd(md(td(a,c),td(b,c)))
--4d203
-n@satzd203c:=satzd182c(td(a,c),td(b,c),t3".4d203"):lessd(td(a,c),td(b,c))
-p@satzd203d:=eqmored12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203a):mored(td(c,a),td(c,b))
-z@satzd203e:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
-n@satzd203f:=eqlessd12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203c):lessd(td(c,a),td(c,b))
-c@[l:lessd(a,b)][p:posd(c)]
-satzd203g:=lemmad5(td(b,c),td(a,c),satzd203a(b,a,c,lemmad6(a,b,l),p)):lessd(td(a,c),td(b,c))
-l@[z:zero(c)]
-satzd203h:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
-l@[n:negd(c)]
-satzd203j:=lemmad6(td(b,c),td(a,c),satzd203c(b,a,c,lemmad6(a,b,l),n)):mored(td(a,c),td(b,c))
-p@satzd203k:=lemmad5(td(c,b),td(c,a),satzd203d(b,a,c,lemmad6(a,b,l),p)):lessd(td(c,a),td(c,b))
-z@satzd203l:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
-n@satzd203m:=lemmad6(td(c,b),td(c,a),satzd203f(b,a,c,lemmad6(a,b,l),n)):mored(td(c,a),td(c,b))
-+*iv4d
-@[p:cut][q:cut]
-t19:=tris(cut,ts(q,pl(p,1rp)),pl(ts(q,p),ts(q,1rp)),pl(ts(q,p),q),disttp2(q,p,1rp),ispl2(ts(q,1rp),q,ts(q,p),satz151(q))):is(ts(q,pl(p,1rp)),pl(ts(q,p),q))
-[r:cut]
-t20:=tris(cut,pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(pl(ts(q,p),q),r),pl(ts(q,p),pl(q,r)),ispl12(ts(q,pl(p,1rp)),pl(ts(q,p),q),ts(r,1rp),r,t19,satz151(r)),asspl1(ts(q,p),q,r)):is(pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)))
-t21:=tr3is(cut,pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)),pl(ts(q,p),pl(r,q)),compl(ts(r,1rp),ts(q,pl(p,1rp))),t20,ispl2(pl(q,r),pl(r,q),ts(q,p),compl(q,r))):is(pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,p),pl(r,q)))
-a@[p:posd(a)]
-arp:=rpofpd(a,p):cut
-arpi:=ov(1rp,arp):cut
-ai:=pdofrp(arpi):dif
-t22:=tr3eq(td(a,ai),df(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp)))),df(pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a))),df(ts(1a,arpi),ts(2a,arpi)),tdeq1a(a,pl(arpi,1rp),1rp),eqsmsd(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp))),pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a)),t20(arpi,1a,2a),t21(arpi,2a,1a)),lemmad2(ts(1a,arpi),ts(2a,arpi),pl(1a,2a))):eq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)))
-t23:=tr3is(cut,ts(1a,arpi),ts(pl(2a,arp),arpi),pl(ts(2a,arpi),ts(arp,arpi)),pl(ts(2a,arpi),1rp),ists1(1a,pl(2a,arp),arpi,satz140d(1a,2a,p)),disttp1(2a,arp,arpi),ispl2(ts(arp,arpi),1rp,ts(2a,arpi),satz153c(1rp,arp))):is(ts(1a,arpi),pl(ts(2a,arpi),1rp))
-t24:=tr3is(cut,pl(ts(1a,arpi),1rp),pl(pl(ts(2a,arpi),1rp),1rp),pl(ts(2a,arpi),pl(1rp,1rp)),pl(pl(1rp,1rp),ts(2a,arpi)),ispl1(ts(1a,arpi),pl(ts(2a,arpi),1rp),1rp,t23),asspl1(ts(2a,arpi),1rp,1rp),compl(ts(2a,arpi),pl(1rp,1rp))):is(pl(ts(1a,arpi),1rp),pl(pl(1rp,1rp),ts(2a,arpi)))
-t25:=eqi12(ts(1a,arpi),ts(2a,arpi),pl(1rp,1rp),1rp,t24):eq(df(ts(1a,arpi),ts(2a,arpi)),1df)
-t26:=treq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)),1df,t22,t25):eq(td(a,ai),1df)
-t27:=somei(dif,[x:dif]eq(td(a,x),1df),ai,t26):some"l"(dif,[x:dif]eq(td(a,x),1df))
-a@[n:negd(a)]
-t28:=satzd176c(a,n):posd(m0d(a))
-[h:dif][e:eq(td(m0d(a),h),1df)]
-t29:=treq(td(a,m0d(h)),td(m0d(a),h),1df,satzd197d(a,h),e):eq(td(a,m0d(h)),1df)
-t30:=somei(dif,[x:dif]eq(td(a,x),1df),m0d(h),t29):some"l"(dif,[x:dif]eq(td(a,x),1df))
-n@t31:=someapp(dif,[x:dif]eq(td(m0d(a),x),1df),t27(m0d(a),t28),some"l"(dif,[x:dif]eq(td(a,x),1df)),[x:dif][t:eq(td(m0d(a),x),1df)]t30(x,t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
--iv4d
-a@[n:not(zero(a))]
-lemmad7:=rappd(a,some"l"(dif,[x:dif]eq(td(a,x),1df)),[t:posd(a)]t27".iv4d"(t),th2"l.imp"(zero(a),some"l"(dif,[x:dif]eq(td(a,x),1df)),n),[t:negd(a)]t31".iv4d"(t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
-b@[n:not(zero(b))][h:dif][k:dif][e:eq(td(b,h),a)][f:eq(td(b,k),a)]
-+4d204
-t1:=treq2(td(b,h),td(b,k),a,e,f):eq(td(b,h),td(b,k))
-t2:=eqzero(md(td(b,h),td(b,k)),td(b,md(h,k)),distmtd2(b,h,k),satzd182e(td(b,h),td(b,k),t1)):zero(td(b,md(h,k)))
-t3:=ore2(zero(b),zero(md(h,k)),satzd192c(b,md(h,k),t2),n):zero(md(h,k))
--4d204
-satzd204b:=satzd182b(h,k,t3".4d204"):eq(h,k)
-+*4d204
-n@[h:dif][e:eq(td(b,h),1df)]
-t4:=tr3eq(td(b,td(h,a)),td(td(b,h),a),td(1df,a),a,asstd2(b,h,a),eqtd1(td(b,h),1df,a,e),satzd195b(a)):eq(td(b,td(h,a)),a)
-t5:=somei(dif,[x:dif]eq(td(b,x),a),td(h,a),t4):some"l"(dif,[x:dif]eq(td(b,x),a))
--4d204
-n@satzd204a:=someapp(dif,[x:dif]eq(td(b,x),1df),lemmad7(b,n),some"l"(dif,[x:dif]eq(td(b,x),a)),[x:dif][t:eq(td(b,x),1df)]t5".4d204"(x,t)):some"l"(dif,[x:dif]eq(td(b,x),a))
-@[r:cut][s:cut][m:more(r,s)]
-+iv5d
-t1:=ismore12(pl(r,pl(1rp,1rp)),pl(pl(r,1rp),1rp),pl(s,pl(1rp,1rp)),pl(pl(s,1rp),1rp),asspl2(r,1rp,1rp),asspl2(s,1rp,1rp),satz134(r,s,pl(1rp,1rp),m)):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
--iv5d
-morerpepd:=moredi12(pl(r,1rp),1rp,pl(s,1rp),1rp,t1".iv5d"):mored(pdofrp(r),pdofrp(s))
-s@[m:mored(pdofrp(r),pdofrp(s))]
-+*iv5d
-m@t2:=morede12(pl(r,1rp),1rp,pl(s,1rp),1rp,m):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
--iv5d
-m@morerpipd:=satz136a(r,s,pl(1rp,1rp),ismore12(pl(pl(r,1rp),1rp),pl(r,pl(1rp,1rp)),pl(pl(s,1rp),1rp),pl(s,pl(1rp,1rp)),asspl1(r,1rp,1rp),asspl1(s,1rp,1rp),t2".iv5d")):more(r,s)
-s@[l:less(r,s)]
-lessrpepd:=lemmad5(pdofrp(s),pdofrp(r),morerpepd(s,r,satz122(r,s,l))):lessd(pdofrp(r),pdofrp(s))
-s@[l:lessd(pdofrp(r),pdofrp(s))]
-lessrpipd:=satz121(s,r,morerpipd(s,r,lemmad6(pdofrp(r),pdofrp(s),l))):less(r,s)
-+*iv5d
-@i:=1rp:cut
-2:=pl(i,i):cut
-r@rp1:=pl(r,i):cut
-s@sp1:=pl(s,i):cut
-rps:=pl(r,s):cut
-rs:=ts(r,s):cut
-t3:=tris(cut,pl(pl(rp1,sp1),i),pl(pl(rps,2),i),pl(pl(rps,i),2),ispl1(pl(rp1,sp1),pl(rps,2),i,4pl23(r,i,s,i)),3pl23(rps,2,i)):is(pl(pl(rp1,sp1),i),pl(pl(rps,i),2))
-t4:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(rp1,sp1),2),pdofrp(rps),pdeq12a(rp1,i,sp1,i),eqi12(pl(rp1,sp1),2,pl(rps,i),i,t3)):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(rps))
--iv5d
-s@lemmad8:=t4".iv5d":eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
-+*iv5d
-s@t5:=tris(cut,ts(r,sp1),pl(rs,ts(r,i)),pl(rs,r),disttp2(r,s,i),ispl2(ts(r,i),r,rs,satz151(r))):is(ts(r,sp1),pl(rs,r))
-t6:=tr4is(cut,ts(rp1,sp1),pl(ts(r,sp1),ts(i,sp1)),pl(pl(rs,r),sp1),pl(pl(pl(rs,r),s),i),pl(pl(rs,rps),i),disttp1(r,i,sp1),ispl12(ts(r,sp1),pl(rs,r),ts(i,sp1),sp1,t5,satz151b(sp1)),asspl2(pl(rs,r),s,i),ispl1(pl(pl(rs,r),s),pl(rs,rps),i,asspl1(rs,r,s))):is(ts(rp1,sp1),pl(pl(rs,rps),i))
-t7:=tr3is(cut,pl(ts(rp1,sp1),ts(i,i)),pl(pl(pl(rs,rps),i),i),pl(pl(rs,rps),2),pl(rs,pl(rps,2)),ispl12(ts(rp1,sp1),pl(pl(rs,rps),i),ts(i,i),i,t6,satz151(i)),asspl1(pl(rs,rps),i,i),asspl1(rs,rps,2)):is(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)))
-t8:=tris(cut,pl(ts(rp1,i),ts(i,sp1)),pl(rp1,sp1),pl(rps,2),ispl12(ts(rp1,i),rp1,ts(i,sp1),sp1,satz151(rp1),satz151b(sp1)),4pl23(r,i,s,i)):is(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2))
-t9:=tris(cut,pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,i),pl(rps,2)),pl(pl(rs,pl(rps,2)),i),ispl2(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2),pl(rs,i),t8),3pl23(rs,i,pl(rps,2))):is(pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i))
-t10:=tris2(cut,pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i),ispl1(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)),i,t7),t9):is(pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))))
-t11:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1))),pdofrp(rs),tdeq12a(rp1,i,sp1,i),eqi12(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1)),pl(rs,i),i,t10)):eq(td(pdofrp(r),pdofrp(s)),pdofrp(rs))
--iv5d
-s@lemmad9:=t11".iv5d":eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
-@[r:cut][s0:set(cut)]
-in:=esti(cut,r,s0):'prop'
-@[s0:set(cut)][t0:set(cut)][p0:all([x:cut]or(in(x,s0),in(x,t0)))][p1a:nonempty(cut,s0)][p1b:nonempty(cut,t0)][p2:all([x:cut][t:in(x,s0)]all([y:cut][u:in(y,t0)]less(x,y)))]
-+5p205
-t0@[r:cut]
-prop1:=all([x:cut][t:less(x,r)]in(x,s0)):'prop'
-prop2:=all([x:cut][t:more(x,r)]in(x,t0)):'prop'
-prop3:=and(prop1,prop2):'prop'
-p2@[r1:cut][r2:cut][pr1:prop3(r1)][pr2:prop3(r2)]
-t1:=ande2(prop1(r1),prop2(r1),pr1):prop2(r1)
-t2:=ande1(prop1(r2),prop2(r2),pr2):prop1(r2)
-[l:less(r1,r2)][x0:rat]
-rx:=rpofrt(x0):cut
-[l1:less(r1,rx)][l2:less(rx,r2)]
-t3:=<l2><rx>t2:in(rx,s0)
-t4:=<satz122(r1,rx,l1)><rx>t1:in(rx,t0)
-t5:=<refis(cut,rx)>ec3e31(is(rx,rx),more(rx,rx),less(rx,rx),satz123b(rx,rx),<t4><rx><t3><rx>p2):con
-l@t6:=satz159app(r1,r2,l,con,[x:rat][t:less(r1,rpofrt(x))][u:less(rpofrt(x),r2)]t5(x,t,u)):con
-pr2@t7:=[t:less(r1,r2)]t6(t):not(less(r1,r2))
-t8:=[t:more(r1,r2)]t6(r2,r1,pr2,pr1,satz121(r1,r2,t)):not(more(r1,r2))
-t9:=or3e1(is(r1,r2),more(r1,r2),less(r1,r2),satz123a(r1,r2),t8,t7):is(r1,r2)
-p2@t10:=[x:cut][y:cut][t:prop3(x)][u:prop3(y)]t9(x,y,t,u):amone(cut,[x:cut]prop3(x))
-[x0:rat]
-schnittprop:=some([y:cut]and(in(y,s0),lrt(y,x0))):'prop'
-p2@schnittset:=setof(rat,[x:rat]schnittprop(x)):set(rat)
-[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)]
-t11:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
-t12:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t11):schnittprop(x0)
-t13:=estii(rat,[x:rat]schnittprop(x),x0,t12):in"rt"(x0,schnittset)
-r@[i:in(r,t0)][x0:rat][ux:urt(r,x0)][s:cut][j:in(s,s0)]
-t14:=satz122(s,r,<i><r><j><s>p2):more(r,s)
-t15:=satz158b(r,x0,ux):moreis(rpofrt(x0),r)
-t16:=moreisi1(rpofrt(x0),s,satz127c(rpofrt(x0),r,s,t15,t14)):moreis(rpofrt(x0),s)
-t17:=satz158d(s,x0,t16):urt(s,x0)
-s@t18:=weli(ec(in(s,s0),lrt(s,x0)),[t:in(s,s0)]t17(t)):not(and(in(s,s0),lrt(s,x0)))
-ux@t19:=th5"l.some"(cut,[y:cut]and(in(y,s0),lrt(y,x0)),[y:cut]t18(y)):not(schnittprop(x0))
-t20:=th3"l.imp"(in"rt"(x0,schnittset),schnittprop(x0),t19,[t:in"rt"(x0,schnittset)]estie(rat,[x:rat]schnittprop(x),x0,t)):not(in"rt"(x0,schnittset))
-p2@[x0:rat][i:in"rt"(x0,schnittset)][y0:rat][l:less"rt"(y0,x0)]
-i@t21:=estie(rat,[x:rat]schnittprop(x),x0,i):schnittprop(x0)
-l@[r:cut][a:and(in(r,s0),lrt(r,x0))]
-t22:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
-t23:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
-t24:=satz120(r,x0,t23,y0,l):lrt(r,y0)
-t25:=andi(in(r,s0),lrt(r,y0),t22,t24):and(in(r,s0),lrt(r,y0))
-t26:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t25):schnittprop(y0)
-l@t27:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,schnittprop(y0),[y:cut][r:and(in(y,s0),lrt(y,x0))]t26(y,r)):schnittprop(y0)
-t28:=estii(rat,[x:rat]schnittprop(x),y0,t27):in"rt"(y0,schnittset)
-i@[r:cut][a:and(in(r,s0),lrt(r,x0))]
-t29:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
-t30:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
-[y0:rat][ly:lrt(r,y0)][l:less"rt"(x0,y0)]
-t31:=andi(in(r,s0),lrt(r,y0),t29,ly):and(in(r,s0),lrt(r,y0))
-t32:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t31):schnittprop(y0)
-t33:=estii(rat,[x:rat]schnittprop(x),y0,t32):in"rt"(y0,schnittset)
-t34:=satz83(x0,y0,l):more"rt"(y0,x0)
-t35:=andi(in"rt"(y0,schnittset),more"rt"(y0,x0),t33,t34):and(in"rt"(y0,schnittset),more"rt"(y0,x0))
-t36:=somei(rat,[y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)),y0,t35):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
-a@t37:=cutapp3(r,x0,t30,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:rat][t:lrt(r,y)][u:less"rt"(x0,y)]t36(y,t,u)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
-i@t38:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:cut][t:and(in(y,s0),lrt(y,x0))]t37(y,t)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
-p2@[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)][s:cut][j:in(s,t0)][y0:rat][uy:urt(s,y0)]
-t39:=cut2(schnittset,x0,t13(r,i,x0,lx),y0,t20(s,j,y0,uy),[x:rat][t:in"rt"(x,schnittset)][y:rat][u:less"rt"(y,x)]t28(x,t,y,u),[x:rat][t:in"rt"(x,schnittset)]t38(x,t)):cutprop(schnittset)
-j@t40:=cutapp1b(s,cutprop(schnittset),[x:rat][t:urt(s,x)]t39(x,t)):cutprop(schnittset)
-lx@t41:=nonemptyapp(cut,t0,p1b,cutprop(schnittset),[y:cut][t:in(y,t0)]t40(y,t)):cutprop(schnittset)
-i@t42:=cutapp1a(r,cutprop(schnittset),[x:rat][t:lrt(r,x)]t41(x,t)):cutprop(schnittset)
-p2@t43:=nonemptyapp(cut,s0,p1a,cutprop(schnittset),[y:cut][t:in(y,s0)]t42(y,t)):cutprop(schnittset)
-snt:=cutof(schnittset,t43):cut
-[r:cut][l:less(r,snt)][x0:rat][ux:urt(r,x0)][lx:lrt(snt,x0)]
-t44:=ini(schnittset,t43,x0,lx):in"rt"(x0,schnittset)
-t45:=estie(rat,[x:rat]schnittprop(x),x0,t44):schnittprop(x0)
-[s:cut][a:and(in(s,s0),lrt(s,x0))]
-t46:=ande1(in(s,s0),lrt(s,x0),a):in(s,s0)
-t47:=ande2(in(s,s0),lrt(s,x0),a):lrt(s,x0)
-t48:=andi(urt(r,x0),lrt(s,x0),ux,t47):and(urt(r,x0),lrt(s,x0))
-t49:=somei(rat,[x:rat]and(urt(r,x),lrt(s,x)),x0,t48):less(r,s)
-t50:=ec3e23(is(s,r),more(s,r),less(s,r),satz123b(s,r),satz122(r,s,t49)):not(less(s,r))
-t51:=th3"l.imp"(in(r,t0),less(s,r),t50,<r><t46><s>p2):not(in(r,t0))
-t52:=ore1(in(r,s0),in(r,t0),<r>p0,t51):in(r,s0)
-lx@t53:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t45,in(r,s0),[y:cut][t:and(in(y,s0),lrt(y,x0))]t52(y,t)):in(r,s0)
-l@t54:=lessapp(r,snt,l,in(r,s0),[x:rat][t:urt(r,x)][u:lrt(snt,x)]t53(x,t,u)):in(r,s0)
-r@[m:more(r,snt)][x0:rat][lx:lrt(r,x0)][ux:urt(snt,x0)][i:in(r,s0)]
-t55:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
-t56:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t55):schnittprop(x0)
-t57:=estii(rat,[x:rat]schnittprop(x),x0,t56):in"rt"(x0,schnittset)
-t58:=ine(schnittset,t43,x0,t57):lrt(snt,x0)
-ux@t59:=th3"l.imp"(in(r,s0),lrt(snt,x0),ux,[t:in(r,s0)]t58(t)):not(in(r,s0))
-t60:=ore2(in(r,s0),in(r,t0),<r>p0,t59):in(r,t0)
-m@t61:=moreapp(r,snt,m,in(r,t0),[x:rat][t:lrt(r,x)][u:urt(snt,x)]t60(x,t,u)):in(r,t0)
-p2@t62:=andi(prop1(snt),prop2(snt),[x:cut][t:less(x,snt)]t54(x,t),[x:cut][t:more(x,snt)]t61(x,t)):prop3(snt)
-t63:=somei(cut,[x:cut]prop3(x),snt,t62):some([x:cut]prop3(x))
--5p205
-satzp205:=onei(cut,[x:cut]prop3".5p205"(x),t10".5p205",t63".5p205"):one([x:cut]and(all([y:cut][t:less(y,x)]in(y,s0)),all([y:cut][t:more(y,x)]in(y,t0))))
-schnitt:=ind(cut,[x:cut]prop3".5p205"(x),satzp205):cut
-satzp205a:=ande1(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:less(x,schnitt)]in(x,s0))
-satzp205b:=ande2(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:more(x,schnitt)]in(x,t0))
-@[r:cut][s:cut]
-+ivad
-@i:=1rp:cut
-r@r1:=pl(r,i):cut
-s@s1:=pl(s,i):cut
-rps:=pl(r,s):cut
-@2:=pl(i,i):cut
-s@t1:=pdeq12a(r1,i,s1,i):eq(pd(pdofrp(r),pdofrp(s)),df(pl(r1,s1),2))
-t2:=tris(cut,pl(r1,s1),pl(rps,2),pl(pl(rps,i),i),4pl23(r,i,s,i),asspl2(rps,i,i)):is(pl(r1,s1),pl(pl(rps,i),i))
-t3:=ispl1(pl(r1,s1),pl(pl(rps,i),i),i,t2):is(pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i))
-t4:=tris(cut,pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i),pl(pl(rps,i),2),t3,asspl1(pl(rps,i),i,i)):is(pl(pl(r1,s1),i),pl(pl(rps,i),2))
-t5:=eqi12(pl(r1,s1),2,pl(rps,i),i,t4):eq(df(pl(r1,s1),2),pdofrp(rps))
--ivad
-lemmaivad1:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(pl(r,1rp),pl(s,1rp)),pl(1rp,1rp)),pdofrp(pl(r,s)),t1".ivad",t5".ivad"):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
-+*ivad
-s@rs:=ts(r,s):cut
-t6:=tdeq12a(r1,i,s1,i):eq(td(pdofrp(r),pdofrp(s)),df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))))
-t7:=tris(cut,ts(r1,s),pl(rs,ts(i,s)),pl(rs,s),disttp1(r,i,s),ispl2(ts(i,s),s,rs,satz151b(s))):is(ts(r1,s),pl(rs,s))
-t8:=tr3is(cut,ts(r1,s1),pl(ts(r1,s),ts(r1,i)),pl(pl(rs,s),r1),pl(pl(rs,i),rps),disttp2(r1,s,i),ispl12(ts(r1,s),pl(rs,s),ts(r1,i),r1,t7,satz151(r1)),4pl24(rs,s,r,i)):is(ts(r1,s1),pl(pl(rs,i),rps))
-t9:=tris(cut,pl(ts(r1,s1),ts(i,i)),pl(pl(pl(rs,i),rps),i),pl(pl(rs,i),pl(rps,i)),ispl12(ts(r1,s1),pl(pl(rs,i),rps),ts(i,i),i,t8,satz151(i)),asspl1(pl(rs,i),rps,i)):is(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)))
-t10:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(pl(rs,i),pl(rps,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),ispl1(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)),i,t9),asspl1(pl(rs,i),pl(rps,i),i)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)))
-t11:=tr3is(cut,pl(pl(rps,i),i),pl(rps,2),pl(r1,s1),pl(ts(r1,i),ts(i,s1)),asspl1(rps,i,i),4pl23(r,s,i,i),ispl12(r1,ts(r1,i),s1,ts(i,s1),satz151a(r1),satz151c(s1))):is(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)))
-t12:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))),t10,ispl2(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)),pl(rs,i),t11)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))))
-t13:=eqi12(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1)),pl(rs,i),i,t12):eq(df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))),pdofrp(rs))
--ivad
-s@lemmaivad2:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(pl(r,1rp),pl(s,1rp)),ts(1rp,1rp)),pl(ts(pl(r,1rp),1rp),ts(1rp,pl(s,1rp)))),pdofrp(ts(r,s)),t6".ivad",t13".ivad"):eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
-[m:mored(pdofrp(r),pdofrp(s))]
-+*ivad
-m@t14:=morede12(r1,i,s1,i,m):more(pl(r1,i),pl(s1,i))
-t15:=satz136a(r1,s1,i,t14):more(r1,s1)
--ivad
-m@lemmaivad3:=satz136a(r,s,1rp,t15".ivad"):more(r,s)
-@[c:dif][a:dif][b:dif][n:not(negd(a))][o:not(negd(b))][e:eq(td(a,a),c)][f:eq(td(b,b),c)]
-+d161
-t1:=treq2(td(a,a),td(b,b),c,e,f):eq(td(a,a),td(b,b))
-t2:=treq(pd(md(td(a,a),td(a,b)),td(b,a)),pd(md(td(a,a),td(a,b)),td(a,b)),td(a,a),eqpd2(td(b,a),td(a,b),md(td(a,a),td(a,b)),comtd(b,a)),pdmd(td(a,a),td(a,b))):eq(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a))
-t3:=tr4eq(td(pd(a,b),md(a,b)),pd(td(a,md(a,b)),td(b,md(a,b))),pd(md(td(a,a),td(a,b)),md(td(b,a),td(b,b))),md(pd(md(td(a,a),td(a,b)),td(b,a)),td(b,b)),md(td(a,a),td(b,b)),disttpd1(a,b,md(a,b)),eqpd12(td(a,md(a,b)),md(td(a,a),td(a,b)),td(b,md(a,b)),md(td(b,a),td(b,b)),disttmd2(a,a,b),disttmd2(b,a,b)),asspd2(md(td(a,a),td(a,b)),td(b,a),m0d(td(b,b))),eqmd1(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a),td(b,b),t2)):eq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)))
-t4:=eqzero(md(td(a,a),td(b,b)),td(pd(a,b),md(a,b)),symeq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)),t3),satzd182e(td(a,a),td(b,b),t1)):zero(td(pd(a,b),md(a,b)))
-t5:=satzd192c(pd(a,b),md(a,b),t4):or(zero(pd(a,b)),zero(md(a,b)))
-[z:zero(a)]
-t6:=eqzero(td(a,a),td(b,b),t1,td01(a,a,z)):zero(td(b,b))
-t7:=th1"l.imp"(zero(b),zero(b),refimp(zero(b)),satzd192c(b,b,t6)):zero(b)
-t8:=zeroeq(a,b,z,t7):eq(a,b)
-f@[p:not(zero(a))]
-t9:=or3e2(zero(a),posd(a),negd(a),axrdo(a),n,p):posd(a)
-t10:=th3"l.imp"(zero(b),zero(a),p,[t:zero(b)]t7(b,a,o,n,f,e,t)):not(zero(b))
-t11:=t9(b,a,o,n,f,e,t10):posd(b)
-t12:=pnot0d(pd(a,b),ppd(a,b,t9,t11)):not(zero(pd(a,b)))
-t13:=ore2(zero(pd(a,b)),zero(md(a,b)),t5,t12):zero(md(a,b))
-t14:=satzd182b(a,b,t13):eq(a,b)
--d161
-satzd161b:=th1"l.imp"(zero(a),eq(a,b),[t:zero(a)]t8".d161"(t),[t:not(zero(a))]t14".d161"(t)):eq(a,b)
-c@[n:not(negd(c))]
-+*d161
-n@[z:zero(c)]
-t15:=zeroeq(td(c,c),c,td01(c,c,z),z):eq(td(c,c),c)
-t16:=andi(not(negd(c)),eq(td(c,c),c),n,t15):and(not(negd(c)),eq(td(c,c),c))
-t17:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),c,t16):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
-n@[o:not(zero(c))]
-t18:=or3e2(zero(c),posd(c),negd(c),axrdo(c),n,o):posd(c)
-crp:=rpofpd(c,t18):cut
-srp:=sqrt(crp):cut
-s:=pdofrp(srp):dif
-t19:=tr3eq(td(s,s),pdofrp(ts(srp,srp)),pdofrp(crp),c,lemmaivad2(srp,srp),isrpepd(ts(srp,srp),crp,thsqrt1(crp)),eqpdrp2(c,t18)):eq(td(s,s),c)
-t20:=andi(not(negd(s)),eq(td(s,s),c),pnotnd(s,posdirp(srp)),t19):and(not(negd(s)),eq(td(s,s),c))
-t21:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),s,t20):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
--d161
-n@satzd161a:=th1"l.imp"(zero(c),some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c))),[t:zero(c)]t17".d161"(t),[t:not(zero(c))]t21".d161"(t)):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
-@[a:dif][i:intd(a)]
-+intd
-[z:zero(a)]
-t1:=ori1(zero(absd(a)),natd(absd(absd(a))),satzd166f(a,z)):intd(absd(a))
-i@[n:natd(absd(a))]
-t2:=natintd(absd(a),n):intd(absd(a))
--intd
-intabsd:=orapp(zero(a),natd(absd(a)),intd(absd(a)),i,[t:zero(a)]t1".intd"(t),[t:natd(absd(a))]t2".intd"(t)):intd(absd(a))
-+*intd
-n@t4:=eqnatd(absd(a),absd(m0d(a)),satzd178a(a),n):natd(absd(m0d(a)))
--intd
-i@intm0d:=th9"l.or"(zero(a),natd(absd(a)),zero(m0d(a)),natd(absd(m0d(a))),i,[t:zero(a)]satzd176b(a,t),[t:natd(absd(a))]t4".intd"(t)):intd(m0d(a))
-a@[b:dif][i:intd(a)][j:intd(b)]
-+*intd
-j@[z:zero(a)]
-t5:=symeq(pd(a,b),b,pd01(a,b,z)):eq(b,pd(a,b))
-t6:=eqintd(b,pd(a,b),t5,j):intd(pd(a,b))
-j@[z:zero(b)]
-t7:=symeq(pd(a,b),a,pd02(a,b,z)):eq(a,pd(a,b))
-t8:=eqintd(a,pd(a,b),t7,i):intd(pd(a,b))
-a@[i:intd(a)][p:posd(a)]
-t9:=<p>ande2(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),posintnatd(a,p,i)):natrp(rpofpd(a,p))
-j@[pp:posd(pd(a,b))]
-apb1:=rpofpd(pd(a,b),pp):cut
-[p:posd(a)]
-a1:=rpofpd(a,p):cut
-[q:posd(b)]
-b1:=rpofpd(b,q):cut
-t10:=natpl(a1,t9(a,i,p),b1,t9(b,j,q)):natrp(pl(a1,b1))
-t11:=eqpd12(a,pdofrp(a1),b,pdofrp(b1),eqpdrp1(a,p),eqpdrp1(b,q)):eq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)))
-t12:=treq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)),pdofrp(pl(a1,b1)),t11,lemmaivad1(a1,b1)):eq(pd(a,b),pdofrp(pl(a1,b1)))
-t13:=tris(cut,apb1,rpofpd(pdofrp(pl(a1,b1)),posdirp(pl(a1,b1))),pl(a1,b1),eqpderp(pd(a,b),pp,pdofrp(pl(a1,b1)),posdirp(pl(a1,b1)),t12),isrppd2(pl(a1,b1))):is(apb1,pl(a1,b1))
-t14:=isp1(cut,[t:cut]natrp(t),pl(a1,b1),apb1,t10,t13):natrp(apb1)
-t15:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t14(t,p,q)):natd(pd(a,b))
-t16:=natintd(pd(a,b),t15):intd(pd(a,b))
-p@[n:negd(b)]
-t17:=satzd176c(b,n):posd(m0d(b))
-b2:=rpofpd(m0d(b),t17):cut
-t18:=eqpd2(b,m0d(m0d(b)),a,satzd177a(b)):eq(pd(a,b),md(a,m0d(b)))
-t19:=eqposd(pd(a,b),md(a,m0d(b)),t18,pp):posd(md(a,m0d(b)))
-t20:=satzd182a(a,m0d(b),t19):mored(a,m0d(b))
-t21:=eqmored12(a,pdofrp(a1),m0d(b),pdofrp(b2),eqpdrp1(a,p),eqpdrp1(m0d(b),t17),t20):mored(pdofrp(a1),pdofrp(b2))
-t22:=lemmaivad3(a1,b2,t21):more(a1,b2)
-t23:=natmn(a1,t9(a,i,p),b2,t9(m0d(b),intm0d(b,j),t17),t22):natrp(mn(a1,b2,t22))
-t24:=eqpd12(m0d(b),pdofrp(b2),pd(a,b),pdofrp(apb1),eqpdrp1(m0d(b),t17),eqpdrp1(pd(a,b),pp)):eq(pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)))
-t25:=tr4eq(a,md(pd(a,b),b),pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)),pdofrp(pl(b2,apb1)),symeq(md(pd(a,b),b),a,mdpd(a,b)),compd(pd(a,b),m0d(b)),t24,lemmaivad1(b2,apb1)):eq(a,pdofrp(pl(b2,apb1)))
-t26:=tris2(cut,pl(b2,apb1),a1,rpofpd(pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1))),isrppd1(pl(b2,apb1)),eqpderp(a,p,pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1)),t25)):is(pl(b2,apb1),a1)
-t27:=satz140g(a1,b2,apb1,t22,t26):is(apb1,mn(a1,b2,t22))
-t28:=isp1(cut,[t:cut]natrp(t),mn(a1,b2,t22),apb1,t23,t27):natrp(apb1)
-t29:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t28(t,p,n)):natd(pd(a,b))
-t30:=natintd(pd(a,b),t29):intd(pd(a,b))
-p@t31:=rappd(b,intd(pd(a,b)),[t:posd(b)]t16(t),[t:zero(b)]t8(t),[t:negd(b)]t30(t)):intd(pd(a,b))
-pp@[n:negd(a)]
-t31a:=th3"l.imp"(negd(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:negd(b)]npd(a,b,n,t)):not(negd(b))
-t32:=th3"l.imp"(zero(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:zero(b)]eqnegd(a,pd(a,b),symeq(pd(a,b),a,pd02(a,b,t)),n)):not(zero(b))
-t33:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t31a,t32):posd(b)
-t34:=eqposd(pd(a,b),pd(b,a),compd(a,b),pp):posd(pd(b,a))
-t35:=t30(b,a,j,i,t34,t33,n):intd(pd(b,a))
-t36:=eqintd(pd(b,a),pd(a,b),compd(b,a),t35):intd(pd(a,b))
-pp@t37:=rappd(a,intd(pd(a,b)),[t:posd(a)]t31(t),[t:zero(a)]t6(t),[t:negd(a)]t36(t)):intd(pd(a,b))
-j@[0p:zero(pd(a,b))]
-t38:=intdi0(pd(a,b),0p):intd(pd(a,b))
-j@[np:negd(pd(a,b))]
-t39:=satzd176c(pd(a,b),np):posd(m0d(pd(a,b)))
-t40:=eqposd(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180(a,b),t39):posd(pd(m0d(a),m0d(b)))
-t41:=t37(m0d(a),m0d(b),intm0d(a,i),intm0d(b,j),t40):intd(pd(m0d(a),m0d(b)))
-t42:=eqintd(pd(m0d(a),m0d(b)),m0d(pd(a,b)),satzd180a(a,b),t41):intd(m0d(pd(a,b)))
-t43:=intm0d(m0d(pd(a,b)),t42):intd(m0d(m0d(pd(a,b))))
-t44:=eqintd(m0d(m0d(pd(a,b))),pd(a,b),satzd177(pd(a,b)),t43):intd(pd(a,b))
--intd
-j@intpd:=rappd(pd(a,b),intd(pd(a,b)),[t:posd(pd(a,b))]t37".intd"(t),[t:zero(pd(a,b))]t38".intd"(t),[t:negd(pd(a,b))]t44".intd"(t)):intd(pd(a,b))
-intmd:=intpd(a,m0d(b),i,intm0d(b,j)):intd(md(a,b))
-+*intd
-j@[n:not(zero(td(a,b)))]
-t45:=th3"l.imp"(zero(a),zero(td(a,b)),n,[t:zero(a)]td01(a,b,t)):not(zero(a))
-t46:=th3"l.imp"(zero(b),zero(td(a,b)),n,[t:zero(b)]td02(a,b,t)):not(zero(b))
-t47:=satzd166e(a,t45):posd(absd(a))
-a3:=rpofpd(absd(a),t47):cut
-t48:=satzd166e(b,t46):posd(absd(b))
-b3:=rpofpd(absd(b),t48):cut
-t49:=natts(a3,t9(absd(a),intabsd(a,i),t47),b3,t9(absd(b),intabsd(b,j),t48)):natrp(ts(a3,b3))
-t50:=satzd166e(td(a,b),n):posd(absd(td(a,b)))
-[p:posd(absd(td(a,b)))]
-atb3:=rpofpd(absd(td(a,b)),p):cut
-t51:=eqtd12(absd(a),pdofrp(a3),absd(b),pdofrp(b3),eqpdrp1(absd(a),t47),eqpdrp1(absd(b),t48)):eq(td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)))
-t52:=tr3eq(absd(td(a,b)),td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)),pdofrp(ts(a3,b3)),satzd193(a,b),t51,lemmaivad2(a3,b3)):eq(absd(td(a,b)),pdofrp(ts(a3,b3)))
-t53:=tris2(cut,atb3,ts(a3,b3),rpofpd(pdofrp(ts(a3,b3)),posdirp(ts(a3,b3))),eqpderp(absd(td(a,b)),p,pdofrp(ts(a3,b3)),posdirp(ts(a3,b3)),t52),isrppd1(ts(a3,b3))):is(atb3,ts(a3,b3))
-t54:=isp1(cut,[t:cut]natrp(t),ts(a3,b3),atb3,t49,t53):natrp(atb3)
-n@t55:=andi(posd(absd(td(a,b))),[t:posd(absd(td(a,b)))]natrp(atb3(t)),t50,[t:posd(absd(td(a,b)))]t54(t)):natd(absd(td(a,b)))
--intd
-j@inttd:=[t:not(zero(td(a,b)))]t55".intd"(t):intd(td(a,b))
-+r
-@eq:=[x:dif][y:dif]eq"rp"(x,y):[x:dif][y:dif]'prop'
-refeq:=[x:dif]refeq"rp"(x):[x:dif]<x><x>eq
-symeq:=[x:dif][y:dif][t:<y><x>eq]symeq"rp"(x,y,t):[x:dif][y:dif][t:<y><x>eq]<x><y>eq
-treq:=[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]treq"rp"(x,y,z,t,u):[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]<z><x>eq
-[a:dif][s:set(dif)]
-inn:=esti(dif,a,s):'prop'
-@real:=ect"eq"(dif,eq,refeq,symeq,treq):'type'
-[r:real][s:real]
-is:=is"e"(real,r,s):'prop'
-nis:=not(is(r,s)):'prop'
-@[p:[x:real]'prop']
-some:=some"l"(real,p):'prop'
-all:=all"l"(real,p):'prop'
-one:=one"e"(real,p):'prop'
-r@[s0:set(real)]
-in:=esti(real,r,s0):'prop'
-a@realof:=ectelt"eq"(dif,eq,refeq,symeq,treq,a):real
-r@class:=ecect"eq"(dif,eq,refeq,symeq,treq,r):set(dif)
-a@innclass:=th5"eq.4"(dif,eq,refeq,symeq,treq,a):inn(a,class(realof(a)))
-r@[a:dif][b:dif][e:eq"rp"(a,b)][air:inn(a,class(r))]
-eqinn:=th8"eq.4"(dif,eq,refeq,symeq,treq,r,a,air,b,e):inn(b,class(r))
-r@[p:'prop'][p1:[x:dif][xi:inn(x,class(r))]p]
-realapp1:=th3"eq.4"(dif,eq,refeq,symeq,treq,r,p,p1):p
-r@[s:real][p:'prop'][p1:[x:dif][y:dif][xi:inn(x,class(r))][yi:inn(y,class(s))]p]
-+ivr1
-[a:dif][air:inn(a,class(r))]
-t1:=realapp1(s,p,[y:dif]<air><y><a>p1):p
--ivr1
-realapp2:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t1".ivr1"(x,xi)):p
-s@[t:real][p:'prop'][p1:[x:dif][y:dif][z:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))]p]
-+*ivr1
-p1@[a:dif][air:inn(a,class(r))]
-t2:=realapp2(s,t,p,[y:dif][z:dif]<air><z><y><a>p1):p
--ivr1
-p1@realapp3:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t2".ivr1"(x,xi)):p
-t@[u:real][p:'prop'][p1:[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]p]
-+*ivr1
-p1@[a:dif][air:inn(a,class(r))]
-t3:=realapp3(s,t,u,p,[y:dif][z:dif][v:dif]<air><v><z><y><a>p1):p
--ivr1
-p1@realapp4:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t3".ivr1"(x,xi)):p
-s@[a1:dif][b1:dif][a1ir:inn(a1,class(r))][b1is:inn(b1,class(s))][e:eq"rp"(a1,b1)]
-isin:=th3"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,e):is(r,s)
-b1is@[i:is(r,s)]
-isex:=th5"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,i):eq"rp"(a1,b1)
-b1is@[n:not(eq"rp"(a1,b1))]
-nisin:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),n,[t:is(r,s)]isex(t)):nis(r,s)
-b1is@[n:nis(r,s)]
-nisex:=th3"l.imp"(eq"rp"(a1,b1),is(r,s),n,[t:eq"rp"(a1,b1)]isin(t)):not(eq"rp"(a1,b1))
-@[alpha:'type'][f:[x:dif]alpha]
-fixf:=fixfu"eq"(dif,eq,refeq,symeq,treq,alpha,f):'prop'
-[ff:fixf(alpha,f)][r0:real]
-indreal:=indeq"eq"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0):alpha
-[a:dif][air:inn(a,class(r0))]
-isindreal:=th2"eq.10"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0,a,air):is"e"(alpha,<a>f,indreal)
-alpha@[g:[x:dif][y:dif]alpha]
-fixf2:=fixfu2"eq"(dif,eq,refeq,symeq,treq,alpha,g):'prop'
-[ff2:fixf2(alpha,g)][r0:real][s0:real]
-indreal2:=indeq2"eq"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0):alpha
-[a:dif][b:dif][air:inn(a,class(r0))][bis:inn(b,class(s0))]
-isindreal2:=th1"eq.11"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0,a,air,b,bis):is"e"(alpha,<b><a>g,indreal2)
-@0:=realof(df(1rp,1rp)):real
-r@[a0:dif][a0ir:inn(a0,class(r))][z:zero(a0)]
-0in:=isin(r,0,a0,df(1rp,1rp),a0ir,innclass(df(1rp,1rp)),zeroeq(a0,df(1rp,1rp),z,zeroi(1rp,1rp,refis(cut,1rp)))):is(r,0)
-a0ir@[i:is(r,0)]
-0ex:=eqzero(df(1rp,1rp),a0,isex(0,r,df(1rp,1rp),a0,innclass(df(1rp,1rp)),a0ir,symis(real,r,0,i)),tris(cut,stm(df(1rp,1rp)),1rp,std(df(1rp,1rp)),stmis(1rp,1rp),isstd(1rp,1rp))):zero(a0)
-+*ivr1
-a0@propp:=and(inn(a0,class(r)),posd(a0)):'prop'
--ivr1
-r@pos:=some"l"(dif,[x:dif]propp".ivr1"(x)):'prop'
-a0ir@[p:posd(a0)]
-+*ivr1
-p@t4:=andi(inn(a0,class(r)),posd(a0),a0ir,p):propp(a0)
--ivr1
-p@posin:=somei(dif,[x:dif]propp".ivr1"(x),a0,t4".ivr1"):pos(r)
-a0ir@[p:pos(r)]
-+*ivr1
-p@[a:dif][q1:propp(a)]
-t5:=ande1(inn(a,class(r)),posd(a),q1):inn(a,class(r))
-t6:=ande2(inn(a,class(r)),posd(a),q1):posd(a)
-t7:=eqposd(a,a0,isex(r,r,a,a0,t5,a0ir,refis(real,r)),t6):posd(a0)
--ivr1
-p@posex:=someapp(dif,[x:dif]propp".ivr1"(x),p,posd(a0),[x:dif][t:propp".ivr1"(x)]t7".ivr1"(x,t)):posd(a0)
-+*ivr1
-a0@propn:=and(inn(a0,class(r)),negd(a0)):'prop'
--ivr1
-r@neg:=some"l"(dif,[x:dif]propn".ivr1"(x)):'prop'
-a0ir@[n:negd(a0)]
-+*ivr1
-n@t8:=andi(inn(a0,class(r)),negd(a0),a0ir,n):propn(a0)
--ivr1
-n@negin:=somei(dif,[x:dif]propn".ivr1"(x),a0,t8".ivr1"):neg(r)
-a0ir@[n:neg(r)]
-+*ivr1
-n@[a:dif][pl:propn(a)]
-t9:=ande1(inn(a,class(r)),negd(a),pl):inn(a,class(r))
-t10:=ande2(inn(a,class(r)),negd(a),pl):negd(a)
-t11:=eqnegd(a,a0,isex(r,r,a,a0,t9,a0ir,refis(real,r)),t10):negd(a0)
--ivr1
-n@negex:=someapp(dif,[x:dif]propn".ivr1"(x),n,negd(a0),[x:dif][t:propn".ivr1"(x)]t11".ivr1"(x,t)):negd(a0)
-+*ivr1
-a0ir@[p:posd(a0)]
-t12:=or3i2(is(r,0),pos(r),neg(r),posin(p)):or3(is(r,0),pos(r),neg(r))
-a0ir@[z:zero(a0)]
-t13:=or3i1(is(r,0),pos(r),neg(r),0in(z)):or3(is(r,0),pos(r),neg(r))
-a0ir@[n:negd(a0)]
-t14:=or3i3(is(r,0),pos(r),neg(r),negin(n)):or3(is(r,0),pos(r),neg(r))
-a0ir@t15:=rappd(a0,or3(is(r,0),pos(r),neg(r)),[t:posd(a0)]t12(t),[t:zero(a0)]t13(t),[t:negd(a0)]t14(t)):or3(is(r,0),pos(r),neg(r))
--ivr1
-r@axrlo:=realapp1(r,or3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t15".ivr1"(x,xi)):or3(is(r,0),pos(r),neg(r))
-+*ivr1
-a0ir@[i:is(r,0)]
-t16:=th3"l.imp"(pos(r),posd(a0),0notpd(a0,0ex(i)),[t:pos(r)]posex(t)):not(pos(r))
-a0ir@[p:pos(r)]
-t17:=th3"l.imp"(neg(r),negd(a0),pnotnd(a0,posex(p)),[t:neg(r)]negex(t)):not(neg(r))
-a0ir@[n:neg(r)]
-t18:=th3"l.imp"(is(r,0),zero(a0),nnot0d(a0,negex(n)),[t:is(r,0)]0ex(t)):not(is(r,0))
-a0ir@t19:=th6"l.ec3"(is(r,0),pos(r),neg(r),[t:is(r,0)]t16(t),[t:pos(r)]t17(t),[t:neg(r)]t18(t)):ec3(is(r,0),pos(r),neg(r))
--ivr1
-r@axrle:=realapp1(r,ec3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t19".ivr1"(x,xi)):ec3(is(r,0),pos(r),neg(r))
-axrl:=orec3i(is(r,0),pos(r),neg(r),axrlo,axrle):orec3(is(r,0),pos(r),neg(r))
-[p:'prop'][p1:[t:pos(r)]p][p2:[t:is(r,0)]p][p3:[t:neg(r)]p]
-rapp:=or3app(is(r,0),pos(r),neg(r),p,axrlo,p2,p1,p3):p
-r@[p:pos(r)]
-pnotn:=ec3e23(is(r,0),pos(r),neg(r),axrle,p):not(neg(r))
-pnot0:=ec3e21(is(r,0),pos(r),neg(r),axrle,p):nis(r,0)
-r@[i:is(r,0)]
-0notp:=ec3e12(is(r,0),pos(r),neg(r),axrle,i):not(pos(r))
-0notn:=ec3e13(is(r,0),pos(r),neg(r),axrle,i):not(neg(r))
-r@[n:neg(r)]
-nnotp:=ec3e32(is(r,0),pos(r),neg(r),axrle,n):not(pos(r))
-nnot0:=ec3e31(is(r,0),pos(r),neg(r),axrle,n):nis(r,0)
-s@[i:is(r,s)][p:pos(r)]
-ispos:=isp(real,[x:real]pos(x),r,s,p,i):pos(s)
-i@[n:neg(r)]
-isneg:=isp(real,[x:real]neg(x),r,s,n,i):neg(s)
-@[r0:cut]
-pofrp:=realof(pdofrp(r0)):real
-nofrp:=realof(ndofrp(r0)):real
-[s0:cut][i:is"rp"(r0,s0)]
-isrpep:=isf(cut,real,[x:cut]pofrp(x),r0,s0,i):is(pofrp(r0),pofrp(s0))
-isrpen:=isf(cut,real,[x:cut]nofrp(x),r0,s0,i):is(nofrp(r0),nofrp(s0))
-s0@[i:is(pofrp(r0),pofrp(s0))]
-+*ivr1
-i"r"@t20:=isex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),i):eq"rp"(pdofrp(r0),pdofrp(s0))
--ivr1
-i@isrpip:=isrpipd(r0,s0,t20".ivr1"):is"rp"(r0,s0)
-s0@[i:is(nofrp(r0),nofrp(s0))]
-+*ivr1
-i"r"@t21:=isex(nofrp(r0),nofrp(s0),ndofrp(r0),ndofrp(s0),innclass(ndofrp(r0)),innclass(ndofrp(s0)),i):eq"rp"(ndofrp(r0),ndofrp(s0))
--ivr1
-i@isrpin:=isrpind(r0,s0,t21".ivr1"):is"rp"(r0,s0)
-r0@posi:=posin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),posdirp(r0)):pos(pofrp(r0))
-negi:=negin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),negdirp(r0)):neg(nofrp(r0))
-s@[r0:cut][s0:cut][i:is(r,pofrp(r0))][j:is(s,pofrp(s0))][k:is(r,s)]
-+*ivr1
-k@t22:=isrpip(r0,s0,tr3is(real,pofrp(r0),r,s,pofrp(s0),symis(real,r,pofrp(r0),i),k,j)):is"rp"(r0,s0)
-r@t23:=[x:cut][y:cut][t:is(r,pofrp(x))][u:is(r,pofrp(y))]t22(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,pofrp(x)))
-a0ir@[p1:pos(r)]
-t24:=posex(p1):posd(a0)
-pr:=rpofpd(a0,t24):cut
-t25:=isin(r,pofrp(pr),a0,pdofrp(pr),a0ir,innclass(pdofrp(pr)),eqpdrp1(a0,t24)):is(r,pofrp(pr))
-t26:=somei(cut,[x:cut]is(r,pofrp(x)),pr,t25):some"rp"([x:cut]is(r,pofrp(x)))
--ivr1
-r@[p:pos(r)]
-+*ivr1
-p"r"@t27:=realapp1(some"rp"([x:cut]is(r,pofrp(x))),[x:dif][t:inn(x,class(r))]t26(x,t,p)):some"rp"([x:cut]is(r,pofrp(x)))
-t28:=onei(cut,[x:cut]is(r,pofrp(x)),t23,t27):one"rp"([x:cut]is(r,pofrp(x)))
--ivr1
-p@rpofp:=ind(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):cut
-isprp1:=oneax(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):is(r,pofrp(rpofp(r,p)))
-isprp2:=symis(real,r,pofrp(rpofp(r,p)),isprp1):is(pofrp(rpofp(r,p)),r)
-@[r1:real][p:pos(r1)][s1:real][q:pos(s1)][i:is(r1,s1)]
-isperp:=t22".ivr1"(r1,s1,rpofp(r1,p),rpofp(s1,q),isprp1(r1,p),isprp1(s1,q),i):is"rp"(rpofp(r1,p),rpofp(s1,q))
-q@[i:is"rp"(rpofp(r1,p),rpofp(s1,q))]
-ispirp:=tr3is(real,r1,pofrp(rpofp(r1,p)),pofrp(rpofp(s1,q)),s1,isprp1(r1,p),isrpep(rpofp(r1,p),rpofp(s1,q),i),isprp2(s1,q)):is(r1,s1)
-@[r0:cut]
-isrpp1:=t22".ivr1"(pofrp(r0),pofrp(r0),r0,rpofp(pofrp(r0),posi(r0)),refis(real,pofrp(r0)),isprp1(pofrp(r0),posi(r0)),refis(real,pofrp(r0))):is"rp"(r0,rpofp(pofrp(r0),posi(r0)))
-isrpp2:=symis(cut,r0,rpofp(pofrp(r0),posi(r0)),isrpp1):is"rp"(rpofp(pofrp(r0),posi(r0)),r0)
-s@[r0:cut][s0:cut][i:is(r,nofrp(r0))][j:is(s,nofrp(s0))][k:is(r,s)]
-+*ivr1
-k@t29:=isrpin(r0,s0,tr3is(real,nofrp(r0),r,s,nofrp(s0),symis(real,r,nofrp(r0),i),k,j)):is"rp"(r0,s0)
-r@t30:=[x:cut][y:cut][t:is(r,nofrp(x))][u:is(r,nofrp(y))]t29(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,nofrp(x)))
-a0ir@[n1:neg(r)]
-t31:=negex(n1):negd(a0)
-nr:=rpofnd(a0,t31):cut
-t32:=isin(r,nofrp(nr),a0,ndofrp(nr),a0ir,innclass(ndofrp(nr)),eqndrp1(a0,t31)):is(r,nofrp(nr))
-t33:=somei(cut,[x:cut]is(r,nofrp(x)),nr,t32):some"rp"([x:cut]is(r,nofrp(x)))
--ivr1
-r@[n:neg(r)]
-+*ivr1
-n"r"@t34:=realapp1(some"rp"([x:cut]is(r,nofrp(x))),[x:dif][t:inn(x,class(r))]t33(x,t,n)):some"rp"([x:cut]is(r,nofrp(x)))
-t35:=onei(cut,[x:cut]is(r,nofrp(x)),t30,t34):one"rp"([x:cut]is(r,nofrp(x)))
--ivr1
-n@rpofn:=ind(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):cut
-isnrp1:=oneax(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):is(r,nofrp(rpofn(r,n)))
-isnrp2:=symis(real,r,nofrp(rpofn(r,n)),isnrp1):is(nofrp(rpofn(r,n)),r)
-@[r1:real][n:neg(r1)][s1:real][m:neg(s1)][i:is(r1,s1)]
-isnerp:=t29".ivr1"(r1,s1,rpofn(r1,n),rpofn(s1,m),isnrp1(r1,n),isnrp1(s1,m),i):is"rp"(rpofn(r1,n),rpofn(s1,m))
-m@[i:is"rp"(rpofn(r1,n),rpofn(s1,m))]
-isnirp:=tr3is(real,r1,nofrp(rpofn(r1,n)),nofrp(rpofn(s1,m)),s1,isnrp1(r1,n),isrpen(rpofn(r1,n),rpofn(s1,m),i),isnrp2(s1,m)):is(r1,s1)
-@[r0:cut]
-isrpn1:=t29".ivr1"(nofrp(r0),nofrp(r0),r0,rpofn(nofrp(r0),negi(r0)),refis(real,nofrp(r0)),isnrp1(nofrp(r0),negi(r0)),refis(real,nofrp(r0))):is"rp"(r0,rpofn(nofrp(r0),negi(r0)))
-isrpn2:=symis(cut,r0,rpofn(nofrp(r0),negi(r0)),isrpn1):is"rp"(rpofn(nofrp(r0),negi(r0)),r0)
-r@satz163:=refis(real,r):is(r,r)
-s@[i:is(r,s)]
-satz164:=symis(real,r,s,i):is(s,r)
-t@[i:is(r,s)][j:is(s,t)]
-satz165:=tris(real,r,s,t,i,j):is(r,t)
-@absdr:=[x:dif]realof(absd(x)):[x:dif]real
-+ivr2
-[a:dif][b:dif][e:eq"rp"(a,b)]
-t1:=isin(realof(absd(a)),realof(absd(b)),absd(a),absd(b),innclass(absd(a)),innclass(absd(b)),eqabsd(a,b,e)):is(<a>absdr,<b>absdr)
--ivr2
-fabsdr:=[x:dif][y:dif][t:<y><x>eq]t1".ivr2"(x,y,t):fixf(real,absdr)
-r@abs:=indreal(real,absdr,fabsdr,r):real
-+*ivr2
-a0ir@t2:=isindreal(real,absdr,fabsdr,r,a0,a0ir):is(realof(absd(a0)),abs(r))
--ivr2
-a0ir@aica:=isp(real,[x:real]inn(absd(a0),class(x)),realof(absd(a0)),abs(r),innclass(absd(a0)),t2".ivr2"):inn(absd(a0),class(abs(r)))
-s@[i:is(r,s)]
-isabs:=isf(real,real,[x:real]abs(x),r,s,i):is(abs(r),abs(s))
-+2r166
-a0ir@[p:pos(r)]
-t1:=satzd166a(a0,posex(p)):posd(absd(a0))
-t2:=posin(abs(r),absd(a0),aica,t1):pos(abs(r))
--2r166
-r@[p:pos(r)]
-satz166a:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t2".2r166"(x,t,p)):pos(abs(r))
-+*2r166
-a0ir@[n:neg(r)]
-t3:=satzd166b(a0,negex(n)):posd(absd(a0))
-t4:=posin(abs(r),absd(a0),aica,t3):pos(abs(r))
--2r166
-r@[n:neg(r)]
-satz166b:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t4".2r166"(x,t,n)):pos(abs(r))
-+*2r166
-b1is@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
-t5:=satzd166c(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
-t6:=isin(t5):is(r,s)
--2r166
-s@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
-satz166c:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".2r166"(x,y,t,u,p,q,i)):is(r,s)
-+*2r166
-b1is@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
-t7:=satzd166d(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
-t8:=isin(t7):is(r,s)
--2r166
-s@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
-satz166d:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".2r166"(x,y,t,u,n,o,i)):is(r,s)
-r@[n:nis(r,0)]
-satz166e:=rapp(r,pos(abs(r)),[t:pos(r)]satz166a(t),th2"l.imp"(is(r,0),pos(abs(r)),n),[t:neg(r)]satz166b(t)):pos(abs(r))
-+*2r166
-a0ir@[i:is(r,0)]
-t9:=satzd166f(a0,0ex(i)):zero(absd(a0))
-t10:=0in(abs(r),absd(a0),aica,t9):is(abs(r),0)
--2r166
-r@[i:is(r,0)]
-satz166f:=realapp1(is(abs(r),0),[x:dif][t:inn(x,class(r))]t10".2r166"(x,t,i)):is(abs(r),0)
-s@more:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),mored(x,y)))):'prop'
-+*ivr2
-b1@propm:=and3(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1)):'prop'
--ivr2
-b1is@[m:mored(a1,b1)]
-+*ivr2
-m@t3:=and3i(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1),a1ir,b1is,m):propm(a1,b1)
-t4:=somei(dif,[x:dif]propm(a1,x),b1,t3):some"l"(dif,[x:dif]propm(a1,x))
--ivr2
-m@morein:=somei(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),a1,t4".ivr2"):more(r,s)
-b1is@[m:more(r,s)]
-+*ivr2
-m@[a:dif][sa:some"l"(dif,[x:dif]propm(a,x))][b:dif][p2:propm(a,b)]
-t5:=and3e1(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(a,class(r))
-t6:=and3e2(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(b,class(s))
-t7:=and3e3(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):mored(a,b)
-t8:=eqmored12(a,a1,b,b1,isex(r,r,a,a1,t5,a1ir,refis(real,r)),isex(s,s,b,b1,t6,b1is,refis(real,s)),t7):mored(a1,b1)
-sa@t9:=someapp(dif,[x:dif]propm(a,x),sa,mored(a1,b1),[x:dif][t:propm(a,x)]t8(x,t)):mored(a1,b1)
--ivr2
-m@moreex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),m,mored(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propm".ivr2"(x,y))]t9".ivr2"(x,t)):mored(a1,b1)
-s@less:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),lessd(x,y)))):'prop'
-+*ivr2
-b1@propl:=and3(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1)):'prop'
--ivr2
-b1is@[l:lessd(a1,b1)]
-+*ivr2
-l@t10:=and3i(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1),a1ir,b1is,l):propl(a1,b1)
-t11:=somei(dif,[x:dif]propl(a1,x),b1,t10):some"l"(dif,[x:dif]propl(a1,x))
--ivr2
-l@lessin:=somei(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),a1,t11".ivr2"):less(r,s)
-b1is@[l:less(r,s)]
-+*ivr2
-l@[a:dif][sa:some"l"(dif,[x:dif]propl(a,x))][b:dif][p2:propl(a,b)]
-t12:=and3e1(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(a,class(r))
-t13:=and3e2(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(b,class(s))
-t14:=and3e3(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):lessd(a,b)
-t15:=eqlessd12(a,a1,b,b1,isex(r,r,a,a1,t12,a1ir,refis(real,r)),isex(s,s,b,b1,t13,b1is,refis(real,s)),t14):lessd(a1,b1)
-sa@t16:=someapp(dif,[x:dif]propl(a,x),sa,lessd(a1,b1),[x:dif][t:propl(a,x)]t15(x,t)):lessd(a1,b1)
--ivr2
-l@lessex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),l,lessd(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propl".ivr2"(x,y))]t16".ivr2"(x,t)):lessd(a1,b1)
-t@[i:is(r,s)][m:more(r,t)]
-ismore1:=isp(real,[x:real]more(x,t),r,s,m,i):more(s,t)
-i@[m:more(t,r)]
-ismore2:=isp(real,[x:real]more(t,x),r,s,m,i):more(t,s)
-i@[l:less(r,t)]
-isless1:=isp(real,[x:real]less(x,t),r,s,l,i):less(s,t)
-i@[l:less(t,r)]
-isless2:=isp(real,[x:real]less(t,x),r,s,l,i):less(t,s)
-u@[i:is(r,s)][j:is(t,u)][m:more(r,t)]
-ismore12:=ismore2(t,u,s,j,ismore1(r,s,t,i,m)):more(s,u)
-j@[l:less(r,t)]
-isless12:=isless2(t,u,s,j,isless1(r,s,t,i,l)):less(s,u)
-+*ivr2
-b1is@[m:more(r,s)]
-t17:=lemmad5(a1,b1,moreex(m)):lessd(b1,a1)
-t18:=lessin(s,r,b1,a1,b1is,a1ir,t17):less(s,r)
--ivr2
-s@[m:more(r,s)]
-lemma1:=realapp2(less(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t18".ivr2"(x,y,t,u,m)):less(s,r)
-+*ivr2
-b1is@[l:less(r,s)]
-t19:=lemmad6(a1,b1,lessex(l)):mored(b1,a1)
-t20:=morein(s,r,b1,a1,b1is,a1ir,t19):more(s,r)
--ivr2
-s@[l:less(r,s)]
-lemma2:=realapp2(more(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t20".ivr2"(x,y,t,u,l)):more(s,r)
-+2r167
-b1is@t1:=satzd167a(a1,b1):or3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
-[e:eq"rp"(a1,b1)]
-t2:=or3i1(is(r,s),more(r,s),less(r,s),isin(e)):or3(is(r,s),more(r,s),less(r,s))
-b1is@[m:mored(a1,b1)]
-t3:=or3i2(is(r,s),more(r,s),less(r,s),morein(m)):or3(is(r,s),more(r,s),less(r,s))
-b1is@[l:lessd(a1,b1)]
-t4:=or3i3(is(r,s),more(r,s),less(r,s),lessin(l)):or3(is(r,s),more(r,s),less(r,s))
-b1is@t5:=or3app(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),or3(is(r,s),more(r,s),less(r,s)),t1,[t:eq"rp"(a1,b1)]t2(t),[t:mored(a1,b1)]t3(t),[t:lessd(a1,b1)]t4(t)):or3(is(r,s),more(r,s),less(r,s))
-t6:=satzd167b(a1,b1):ec3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
-[i:is(r,s)]
-t7:=th3"l.imp"(more(r,s),mored(a1,b1),ec3e12(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,isex(i)),[t:more(r,s)]moreex(t)):not(more(r,s))
-b1is@[m:more(r,s)]
-t8:=th3"l.imp"(less(r,s),lessd(a1,b1),ec3e23(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,moreex(m)),[t:less(r,s)]lessex(t)):not(less(r,s))
-b1is@[l:less(r,s)]
-t9:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),ec3e31(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,lessex(l)),[t:is(r,s)]isex(t)):not(is(r,s))
-b1is@t10:=th6"l.ec3"(is(r,s),more(r,s),less(r,s),th1"l.ec"(is(r,s),more(r,s),[t:is(r,s)]t7(t)),th1"l.ec"(more(r,s),less(r,s),[t:more(r,s)]t8(t)),th1"l.ec"(less(r,s),is(r,s),[t:less(r,s)]t9(t))):ec3(is(r,s),more(r,s),less(r,s))
-t11:=orec3i(is(r,s),more(r,s),less(r,s),t5,t10):orec3(is(r,s),more(r,s),less(r,s))
--2r167
-s@satz167:=realapp2(orec3(is(r,s),more(r,s),less(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".2r167"(x,y,t,u)):orec3(is(r,s),more(r,s),less(r,s))
-satz167a:=orec3e1(is(r,s),more(r,s),less(r,s),satz167):or3(is(r,s),more(r,s),less(r,s))
-satz167b:=orec3e2(is(r,s),more(r,s),less(r,s),satz167):ec3(is(r,s),more(r,s),less(r,s))
-moreis:=or(more(r,s),is(r,s)):'prop'
-lessis:=or(less(r,s),is(r,s)):'prop'
-[m:moreis(r,s)]
-satz168a:=th9"l.or"(more(r,s),is(r,s),less(s,r),is(s,r),m,[t:more(r,s)]lemma1(t),[t:is(r,s)]symis(real,r,s,t)):lessis(s,r)
-s@[l:lessis(r,s)]
-satz168b:=th9"l.or"(less(r,s),is(r,s),more(s,r),is(s,r),l,[t:less(r,s)]lemma2(t),[t:is(r,s)]symis(real,r,s,t)):moreis(s,r)
-t@[i:is(r,s)][m:moreis(r,t)]
-ismoreis1:=isp(real,[x:real]moreis(x,t),r,s,m,i):moreis(s,t)
-i@[m:moreis(t,r)]
-ismoreis2:=isp(real,[x:real]moreis(t,x),r,s,m,i):moreis(t,s)
-i@[l:lessis(r,t)]
-islessis1:=isp(real,[x:real]lessis(x,t),r,s,l,i):lessis(s,t)
-i@[l:lessis(t,r)]
-islessis2:=isp(real,[x:real]lessis(t,x),r,s,l,i):lessis(t,s)
-u@[i:is(r,s)][j:is(t,u)][m:moreis(r,t)]
-ismoreis12:=ismoreis2(t,u,s,j,ismoreis1(r,s,t,i,m)):moreis(s,u)
-j@[l:lessis(r,t)]
-islessis12:=islessis2(t,u,s,j,islessis1(r,s,t,i,l)):lessis(s,u)
-s@[m:more(r,s)]
-moreisi1:=ori1(more(r,s),is(r,s),m):moreis(r,s)
-s@[l:less(r,s)]
-lessisi1:=ori1(less(r,s),is(r,s),l):lessis(r,s)
-s@[i:is(r,s)]
-moreisi2:=ori2(more(r,s),is(r,s),i):moreis(r,s)
-lessisi2:=ori2(less(r,s),is(r,s),i):lessis(r,s)
-b1is@[m:moreq(a1,b1)]
-moreisin:=orapp(mored(a1,b1),eq"rp"(a1,b1),moreis(r,s),m,[t:mored(a1,b1)]moreisi1(morein(t)),[t:eq"rp"(a1,b1)]moreisi2(isin(t))):moreis(r,s)
-b1is@[m:moreis(r,s)]
-moreisex:=orapp(more(r,s),is(r,s),moreq(a1,b1),m,[t:more(r,s)]moreqi1(a1,b1,moreex(t)),[t:is(r,s)]moreqi2(a1,b1,isex(t))):moreq(a1,b1)
-b1is@[l:lesseq(a1,b1)]
-lessisin:=orapp(lessd(a1,b1),eq"rp"(a1,b1),lessis(r,s),l,[t:lessd(a1,b1)]lessisi1(lessin(t)),[t:eq"rp"(a1,b1)]lessisi2(isin(t))):lessis(r,s)
-b1is@[l:lessis(r,s)]
-lessisex:=orapp(less(r,s),is(r,s),lesseq(a1,b1),l,[t:less(r,s)]lesseqi1(a1,b1,lessex(t)),[t:is(r,s)]lesseqi2(a1,b1,isex(t))):lesseq(a1,b1)
-s@[m:moreis(r,s)]
-satz167c:=th7"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,comor(more(r,s),is(r,s),m)):not(less(r,s))
-s@[l:lessis(r,s)]
-satz167d:=th9"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,l):not(more(r,s))
-s@[n:not(more(r,s))]
-satz167e:=th2"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n):lessis(r,s)
-s@[n:not(less(r,s))]
-s@[n:not(less(r,s))]
-satz167f:=comor(is(r,s),more(r,s),th3"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n)):moreis(r,s)
-s@[m:more(r,s)]
-satz167g:=th3"l.imp"(lessis(r,s),not(more(r,s)),weli(more(r,s),m),[t:lessis(r,s)]satz167d(t)):not(lessis(r,s))
-s@[l:less(r,s)]
-satz167h:=th3"l.imp"(moreis(r,s),not(less(r,s)),weli(less(r,s),l),[t:moreis(r,s)]satz167c(t)):not(moreis(r,s))
-s@[n:not(moreis(r,s))]
-satz167j:=or3e3(is(r,s),more(r,s),less(r,s),satz167a,th5"l.or"(more(r,s),is(r,s),n),th4"l.or"(more(r,s),is(r,s),n)):less(r,s)
-s@[n:not(lessis(r,s))]
-satz167k:=or3e2(is(r,s),more(r,s),less(r,s),satz167a,th4"l.or"(less(r,s),is(r,s),n),th5"l.or"(less(r,s),is(r,s),n)):more(r,s)
-r@[p:pos(r)]
-+2r169
-[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t1:=satzd169a(a,b,0ex(0,b,bi0,refis(real,0)),posex(a,air,p)):mored(a,b)
-t2:=morein(r,0,a,b,air,bi0,t1):more(r,0)
--2r169
-satz169a:=realapp2(r,0,more(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r169"(x,y,t,u)):more(r,0)
-r@[m:more(r,0)]
-+*2r169
-m@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t3:=satzd169b(a,b,0ex(0,b,bi0,refis(real,0)),moreex(r,0,a,b,air,bi0,m)):posd(a)
-t4:=posin(r,a,air,t3):pos(r)
--2r169
-m@satz169b:=realapp2(r,0,pos(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t4".2r169"(x,y,t,u)):pos(r)
-r@[n:neg(r)]
-+*2r169
-n@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t5:=satzd169c(a,b,0ex(0,b,bi0,refis(real,0)),negex(a,air,n)):lessd(a,b)
-t6:=lessin(r,0,a,b,air,bi0,t5):less(r,0)
--2r169
-n@satz169c:=realapp2(r,0,less(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t6".2r169"(x,y,t,u)):less(r,0)
-r@[l:less(r,0)]
-+*2r169
-l@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t7:=satzd169d(a,b,0ex(0,b,bi0,refis(real,0)),lessex(r,0,a,b,air,bi0,l)):negd(a)
-t8:=negin(r,a,air,t7):neg(r)
--2r169
-l@satz169d:=realapp2(r,0,neg(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t8".2r169"(x,y,t,u)):neg(r)
-+2r170
-r@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t1:=satzd170(a,b,0ex(0,b,bi0,refis(real,0))):moreq(absd(a),b)
-t2:=moreisin(abs(r),0,absd(a),b,aica(r,a,air),bi0,t1):moreis(abs(r),0)
--2r170
-r@satz170:=realapp2(r,0,moreis(abs(r),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r170"(x,y,t,u)):moreis(abs(r),0)
-satz170a:=th3"l.imp"(neg(abs(r)),less(abs(r),0),satz167c(abs(r),0,satz170),[t:neg(abs(r))]satz169c(abs(r),t)):not(neg(abs(r)))
-t@[l:less(r,s)][k:less(s,t)]
-+2r171
-[a:dif][b:dif][c:dif][air:inn(a,class(r))][bis:inn(b,class(s))][cit:inn(c,class(t))]
-t1:=satzd171(a,b,c,lessex(r,s,a,b,air,bis,l),lessex(s,t,b,c,bis,cit,k)):lessd(a,c)
-t2:=lessin(r,t,a,c,air,cit,t1):less(r,t)
--2r171
-satz171:=realapp3(r,s,t,less(r,t),[x:dif][y:dif][z:dif][w:inn(x,class(r))][u:inn(y,class(s))][v:inn(z,class(t))]t2".2r171"(x,y,z,w,u,v)):less(r,t)
-trless:=satz171:less(r,t)
-t@[m:more(r,s)][n:more(s,t)]
-trmore:=lemma2(t,r,trless(t,s,r,lemma1(s,t,n),lemma1(r,s,m))):more(r,t)
-t@[a2:dif][b2:dif][c2:dif][a2ir:inn(a2,class(r))][b2is:inn(b2,class(s))][c2it:inn(c2,class(t))]
-+2r172
-[l:lessis(r,s)][k:less(s,t)]
-t1:=satzd172a(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
-t2:=lessin(r,t,a2,c2,a2ir,c2it,t1):less(r,t)
--2r172
-t@[l:lessis(r,s)][k:less(s,t)]
-satz172a:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
-+*2r172
-c2it@[l:less(r,s)][k:lessis(s,t)]
-t3:=satzd172b(a2,b2,c2,lessex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
-t4:=lessin(r,t,a2,c2,a2ir,c2it,t3):less(r,t)
--2r172
-t@[l:less(r,s)][k:lessis(s,t)]
-satz172b:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
-t@[m:moreis(r,s)][n:more(s,t)]
-satz172c:=lemma2(t,r,satz172b(t,s,r,lemma1(s,t,n),satz168a(m))):more(r,t)
-t@[m:more(r,s)][n:moreis(s,t)]
-satz172d:=lemma2(t,r,satz172a(t,s,r,satz168a(s,t,n),lemma1(m))):more(r,t)
-+2r173
-c2it@[l:lessis(r,s)][k:lessis(s,t)]
-t1:=satzd173(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lesseq(a2,c2)
-t2:=lessisin(r,t,a2,c2,a2ir,c2it,t1):lessis(r,t)
--2r173
-t@[l:lessis(r,s)][k:lessis(s,t)]
-satz173:=realapp3(lessis(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r173"(x,y,z,u,v,w,l,k)):lessis(r,t)
-trlessis:=satz173:lessis(r,t)
-t@[m:moreis(r,s)][n:moreis(s,t)]
-trmoreis:=satz168b(t,r,trlessis(t,s,r,satz168a(s,t,n),satz168a(m))):moreis(r,t)
-r@ratrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),ratd(x))):'prop'
-a0ir@[r1:ratd(a0)]
-+*ivr2
-r1@t21:=andi(inn(a0,class(r)),ratd(a0),a0ir,r1):and(inn(a0,class(r)),ratd(a0))
--ivr2
-r1@ratrlin:=somei(dif,[x:dif]and(inn(x,class(r)),ratd(x)),a0,t21".ivr2"):ratrl(r)
-a0ir@[rr:ratrl(r)]
-+*ivr2
-rr@[a:dif][b:and(inn(a,class(r)),ratd(a))]
-t22:=ande1(inn(a,class(r)),ratd(a),b):inn(a,class(r))
-t23:=ande2(inn(a,class(r)),ratd(a),b):ratd(a)
-t24:=eqratd(a,a0,isex(r,r,a,a0,t22,a0ir,refis(real,r)),t23):ratd(a0)
--ivr2
-rr@ratrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),ratd(x)),rr,ratd(a0),[x:dif][t:and(inn(x,class(r)),ratd(x))]t24".ivr2"(x,t)):ratd(a0)
-r@irratrl:=not(ratrl(r)):'prop'
-@[r0:cut][rr:ratrp(r0)]
-remark2:=ratrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark2a(r0,rr)):ratrl(pofrp(r0))
-remark3:=ratrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark3a(r0,rr)):ratrl(nofrp(r0))
-r0@[ir:irratrp(r0)]
-remark4:=th3"l.imp"(ratrl(pofrp(r0)),ratd(pdofrp(r0)),remark4a(r0,ir),[t:ratrl(pofrp(r0))]ratrlex(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),t)):irratrl(pofrp(r0))
-remark5:=th3"l.imp"(ratrl(nofrp(r0)),ratd(ndofrp(r0)),remark5a(r0,ir),[t:ratrl(nofrp(r0))]ratrlex(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),t)):irratrl(nofrp(r0))
-r@natrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),natd(x))):'prop'
-a0ir@[n:natd(a0)]
-+*ivr2
-n@t25:=andi(inn(a0,class(r)),natd(a0),a0ir,n):and(inn(a0,class(r)),natd(a0))
--ivr2
-n@natrlin:=somei(dif,[x:dif]and(inn(x,class(r)),natd(x)),a0,t25".ivr2"):natrl(r)
-a0ir@[n:natrl(r)]
-+*ivr2
-n@[a:dif][b:and(inn(a,class(r)),natd(a))]
-t26:=ande1(inn(a,class(r)),natd(a),b):inn(a,class(r))
-t27:=ande2(inn(a,class(r)),natd(a),b):natd(a)
-t28:=eqnatd(a,a0,isex(r,r,a,a0,t26,a0ir,refis(real,r)),t27):natd(a0)
--ivr2
-n@natrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),natd(x)),n,natd(a0),[x:dif][t:and(inn(x,class(r)),natd(x))]t28".ivr2"(x,t)):natd(a0)
-+*ivr2
-a0ir@[n:natrl(r)]
-t29:=natposd(a0,natrlex(n)):posd(a0)
-t30:=posin(t29):pos(r)
--ivr2
-r@[n:natrl(r)]
-natpos:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t30".ivr2"(x,t,n)):pos(r)
-@[x:nat]
-rlofnt:=realof(pdofnt(x)):real
-natrli:=natrlin(rlofnt(x),pdofnt(x),innclass(pdofnt(x)),natdi(x)):natrl(rlofnt(x))
-[y:nat][i:is"n"(x,y)]
-isnterl:=isf(nat,real,[u:nat]rlofnt(u),x,y,i):is(rlofnt(x),rlofnt(y))
-y@[i:is(rlofnt(x),rlofnt(y))]
-isntirl:=isntirp(x,y,isrpip(rpofnt(x),rpofnt(y),i)):is"n"(x,y)
-+*ivr2
-@t31:=[x:nat][y:nat][t:is(rlofnt(x),rlofnt(y))]isntirl(x,y,t):injective(nat,real,[x:nat]rlofnt(x))
-a0ir@[n:natrl(r)]
-t32:=natposd(a0,natrlex(n)):posd(a0)
-ap:=rpofpd(a0,t32):cut
-t33:=natderp(a0,natrlex(n)):natrp(ap)
-x0:=ntofrp(ap,t33):nat
-t34:=isrpepd(ap,rpofnt(x0),isrpnt1(ap,t33)):eq"rp"(pdofrp(ap),pdofnt(x0))
-t35:=treq"rp"(a0,pdofrp(ap),pdofnt(x0),eqpdrp1(a0,t32),t34):eq"rp"(a0,pdofnt(x0))
-t36:=isin(r,rlofnt(x0),a0,pdofnt(x0),a0ir,innclass(pdofnt(x0)),t35):is(r,rlofnt(x0))
-t37:=somei(nat,[x:nat]is(r,rlofnt(x)),x0,t36):image(nat,real,[x:nat]rlofnt(x),r)
--ivr2
-r@[n:natrl(r)]
-natimage:=realapp1(image(nat,real,[x:nat]rlofnt(x),r),[x:dif][t:inn(x,class(r))]t37".ivr2"(x,t,n)):image(nat,real,[x:nat]rlofnt(x),r)
-r@[i:image(nat,real,[x:nat]rlofnt(x),r)]
-+*ivr2
-i"r"@[x:nat][j:is(r,rlofnt(x))]
-t38:=isp1(real,[u:real]natrl(u),rlofnt(x),r,natrli(x),j):natrl(r)
--ivr2
-i@imagenat:=someapp(nat,[u:nat]is(r,rlofnt(u)),i,natrl(r),[u:nat][v:is(r,rlofnt(u))]t38".ivr2"(u,v)):natrl(r)
-r@[n:natrl(r)]
-ntofrl:=soft(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):nat
-@[r1:real][n:natrl(r1)][s1:real][m:natrl(s1)][i:is(r1,s1)]
-isrlent:=isinv(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is"n"(ntofrl(r1,n),ntofrl(s1,m))
-m@[i:is"n"(ntofrl(r1,n),ntofrl(s1,m))]
-isrlint:=isinve(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is(r1,s1)
-r@[n:natrl(r)]
-isrlnt1:=ists1"e"(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):is(r,rlofnt(ntofrl(r,n)))
-isrlnt2:=symis(real,r,rlofnt(ntofrl(r,n)),isrlnt1):is(rlofnt(ntofrl(r,n)),r)
-@[x:nat]
-+*ivr2
-x"r"@xn:=soft(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x)):nat
-t39:=isinv(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x),rlofnt(x),natimage(rlofnt(x),natrli(x)),refis(real,rlofnt(x))):is"n"(xn,ntofrl(rlofnt(x),natrli(x)))
--ivr2
-x@isntrl1:=tris(nat,x,xn".ivr2",ntofrl(rlofnt(x),natrli(x)),isst1(nat,real,[u:nat]rlofnt(u),t31".ivr2",x),t39".ivr2"):is"n"(x,ntofrl(rlofnt(x),natrli(x)))
-isntrl2:=symis(nat,x,ntofrl(rlofnt(x),natrli(x)),isntrl1):is"n"(ntofrl(rlofnt(x),natrli(x)),x)
-r@intrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),intd(x))):'prop'
-a0ir@[i:intd(a0)]
-+*ivr2
-i@t40:=andi(inn(a0,class(r)),intd(a0),a0ir,i):and(inn(a0,class(r)),intd(a0))
--ivr2
-i@intrlin:=somei(dif,[x:dif]and(inn(x,class(r)),intd(x)),a0,t40".ivr2"):intrl(r)
-a0ir@[i:intrl(r)]
-+*ivr2
-i@[a:dif][b:and(inn(a,class(r)),intd(a))]
-t41:=ande1(inn(a,class(r)),intd(a),b):inn(a,class(r))
-t42:=ande2(inn(a,class(r)),intd(a),b):intd(a)
-t43:=eqintd(a,a0,isex(r,r,a,a0,t41,a0ir,refis(real,r)),t42):intd(a0)
--ivr2
-i@intrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),intd(x)),i,intd(a0),[x:dif][t:and(inn(x,class(r)),intd(x))]t43".ivr2"(x,t)):intd(a0)
-+*ivr2
-a0ir@[n:natrl(r)]
-t44:=natintd(a0,natrlex(n)):intd(a0)
-t45:=intrlin(t44):intrl(r)
--ivr2
-r@[n:natrl(r)]
-natintrl:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t45".ivr2"(x,t,n)):intrl(r)
-+*ivr2
-a0ir@[p:pos(r)][i:intrl(r)]
-t46:=posintnatd(a0,posex(p),intrlex(i)):natd(a0)
-t47:=natrlin(t46):natrl(r)
--ivr2
-r@[p:pos(r)][i:intrl(r)]
-posintnatrl:=realapp1(natrl(r),[x:dif][t:inn(x,class(r))]t47".ivr2"(x,t,p,i)):natrl(r)
-+*ivr2
-a0ir@[i2:is(r,0)]
-t48:=intdi0(a0,0ex(i2)):intd(a0)
-t49:=intrlin(t48):intrl(r)
--ivr2
-r@[i:is(r,0)]
-intrli0:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t49".ivr2"(x,t,i)):intrl(r)
-r0@[n:natrp(r0)]
-remark6:=intrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark6"rp"(r0,n)):intrl(pofrp(r0))
-remark7:=intrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark7"rp"(r0,n)):intrl(nofrp(r0))
-+2r174
-a0ir@[i:intrl(r)]
-t1:=satzd174(a0,intrlex(i)):ratd(a0)
-t2:=ratrlin(t1):ratrl(r)
--2r174
-r@[i:intrl(r)]
-satz174:=realapp1(ratrl(r),[x:dif][t:inn(x,class(r))]t2".2r174"(x,t,i)):ratrl(r)
-@plusdr:=[x:dif][y:dif]realof(pd(x,y)):[x:dif][y:dif]real
-+ivr3
-[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
-t1:=isin(realof(pd(a,c)),realof(pd(b,d)),pd(a,c),pd(b,d),innclass(pd(a,c)),innclass(pd(b,d)),eqpd12(a,b,c,d,e,f)):is(<c><a>plusdr,<d><b>plusdr)
--ivr3
-fplusdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr3"(x,y,z,v,t,u):fixf2(real,plusdr)
-s@pl:=indreal2(real,plusdr,fplusdr,r,s):real
-+*ivr3
-b1is@t2:=isindreal2(real,plusdr,fplusdr,r,s,a1,b1,a1ir,b1is):is(realof(pd(a1,b1)),pl(r,s))
--ivr3
-b1is@picp:=isp(real,[x:real]inn(pd(a1,b1),class(x)),realof(pd(a1,b1)),pl(r,s),innclass(pd(a1,b1)),t2".ivr3"):inn(pd(a1,b1),class(pl(r,s)))
-t@[i:is(r,s)]
-ispl1:=isf(real,real,[x:real]pl(x,t),r,s,i):is(pl(r,t),pl(s,t))
-ispl2:=isf(real,real,[x:real]pl(t,x),r,s,i):is(pl(t,r),pl(t,s))
-u@[i:is(r,s)][j:is(t,u)]
-ispl12:=tris(real,pl(r,t),pl(s,t),pl(s,u),ispl1(i),ispl2(t,u,s,j)):is(pl(r,t),pl(s,u))
-+3r175
-b1is@t1:=satzd175(a1,b1):eq"rp"(pd(a1,b1),pd(b1,a1))
-t2:=isin(pl(r,s),pl(s,r),pd(a1,b1),pd(b1,a1),picp,picp(s,r,b1,a1,b1is,a1ir),t1):is(pl(r,s),pl(s,r))
--3r175
-s@satz175:=realapp2(is(pl(r,s),pl(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r175"(x,y,t,u)):is(pl(r,s),pl(s,r))
-compl:=satz175:is(pl(r,s),pl(s,r))
-+*ivr3
-b1is@[i:is(r,0)]
-t3:=pd01(a1,b1,0ex(r,a1,a1ir,i)):eq"rp"(pd(a1,b1),b1)
-t4:=isin(pl(r,s),s,pd(a1,b1),b1,picp,b1is,t3):is(pl(r,s),s)
--ivr3
-s@[i:is(r,0)]
-pl01:=realapp2(is(pl(r,s),s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr3"(x,y,t,u,i)):is(pl(r,s),s)
-s@[i:is(s,0)]
-pl02:=tris(real,pl(r,s),pl(s,r),r,compl,pl01(s,r,i)):is(pl(r,s),r)
-+*ivr3
-b1is@[p:pos(r)][q:pos(s)]
-t5:=ppd(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(pd(a1,b1))
-t6:=posin(pl(r,s),pd(a1,b1),picp,t5):pos(pl(r,s))
--ivr3
-s@[p:pos(r)][q:pos(s)]
-pospl:=realapp2(pos(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr3"(x,y,t,u,p,q)):pos(pl(r,s))
-+*ivr3
-b1is@[n:neg(r)][o:neg(s)]
-t7:=npd(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):negd(pd(a1,b1))
-t8:=negin(pl(r,s),pd(a1,b1),picp,t7):neg(pl(r,s))
--ivr3
-s@[n:neg(r)][o:neg(s)]
-negpl:=realapp2(neg(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".ivr3"(x,y,t,u,n,o)):neg(pl(r,s))
-@m0dr:=[x:dif]realof(m0d(x)):[x:dif]real
-+*ivr3
-@[a:dif][b:dif][e:eq"rp"(a,b)]
-t5a:=isin(realof(m0d(a)),realof(m0d(b)),m0d(a),m0d(b),innclass(m0d(a)),innclass(m0d(b)),eqm0d(a,b,e)):is(<a>m0dr,<b>m0dr)
--ivr3
-@fm0dr:=[x:dif][y:dif][t:<y><x>eq]t5a".ivr3"(x,y,t):fixf(real,m0dr)
-r@m0:=indreal(real,m0dr,fm0dr,r):real
-+*ivr3
-a0ir@t6a:=isindreal(real,m0dr,fm0dr,r,a0,a0ir):is(realof(m0d(a0)),m0(r))
--ivr3
-a0ir@micm0:=isp(real,[x:real]inn(m0d(a0),class(x)),realof(m0d(a0)),m0(r),innclass(m0d(a0)),t6a".ivr3"):inn(m0d(a0),class(m0(r)))
-s@[i:is(r,s)]
-ism0:=isf(real,real,[x:real]m0(x),r,s,i):is(m0(r),m0(s))
-+*ivr3
-a0ir@[n:neg(r)]
-t7a:=absnd(a0,negex(n)):eq"rp"(absd(a0),m0d(a0))
-t8a:=isin(abs(r),m0(r),absd(a0),m0d(a0),aica,micm0,t7a):is(abs(r),m0(r))
--ivr3
-r@[n:neg(r)]
-absn:=realapp1(is(abs(r),m0(r)),[x:dif][t:inn(x,class(r))]t8a".ivr3"(x,t,n)):is(abs(r),m0(r))
-+*ivr3
-a0ir@[nn:not(neg(r))]
-t9:=absnnd(a0,th3"l.imp"(negd(a0),neg(r),nn,[t:negd(a0)]negin(t))):eq"rp"(absd(a0),a0)
-t10:=isin(abs(r),r,absd(a0),a0,aica,a0ir,t9):is(abs(r),r)
--ivr3
-r@[nn:not(neg(r))]
-absnn:=realapp1(is(abs(r),r),[x:dif][t:inn(x,class(r))]t10".ivr3"(x,t,nn)):is(abs(r),r)
-r@[p:pos(r)]
-absp:=absnn(r,pnotn(r,p)):is(abs(r),r)
-r@[i:is(r,0)]
-abs0:=tris(real,abs(r),r,0,absnn(r,0notn(r,i)),i):is(abs(r),0)
-+3r176
-a0ir@[p:pos(r)]
-t1:=satzd176a(a0,posex(p)):negd(m0d(a0))
-t2:=negin(m0(r),m0d(a0),micm0,t1):neg(m0(r))
--3r176
-r@[p:pos(r)]
-satz176a:=realapp1(neg(m0(r)),[x:dif][t:inn(x,class(r))]t2".3r176"(x,t,p)):neg(m0(r))
-+*3r176
-a0ir@[i:is(r,0)]
-t3:=satzd176b(a0,0ex(i)):zero(m0d(a0))
-t4:=0in(m0(r),m0d(a0),micm0,t3):is(m0(r),0)
--3r176
-r@[i:is(r,0)]
-satz176b:=realapp1(is(m0(r),0),[x:dif][t:inn(x,class(r))]t4".3r176"(x,t,i)):is(m0(r),0)
-+*3r176
-a0ir@[n:neg(r)]
-t5:=satzd176c(a0,negex(n)):posd(m0d(a0))
-t6:=posin(m0(r),m0d(a0),micm0,t5):pos(m0(r))
--3r176
-r@[n:neg(r)]
-satz176c:=realapp1(pos(m0(r)),[x:dif][t:inn(x,class(r))]t6".3r176"(x,t,n)):pos(m0(r))
-+*3r176
-a0ir@[n:neg(m0(r))]
-t7:=satzd176d(a0,negex(m0(r),m0d(a0),micm0,n)):posd(a0)
-t8:=posin(t7):pos(r)
--3r176
-r@[n:neg(m0(r))]
-satz176d:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t8".3r176"(x,t,n)):pos(r)
-+*3r176
-a0ir@[i:is(m0(r),0)]
-t9:=satzd176e(a0,0ex(m0(r),m0d(a0),micm0,i)):zero(a0)
-t10:=0in(t9):is(r,0)
--3r176
-r@[i:is(m0(r),0)]
-satz176e:=realapp1(is(r,0),[x:dif][t:inn(x,class(r))]t10".3r176"(x,t,i)):is(r,0)
-+*3r176
-a0ir@[p:pos(m0(r))]
-t11:=satzd176f(a0,posex(m0(r),m0d(a0),micm0,p)):negd(a0)
-t12:=negin(t11):neg(r)
--3r176
-r@[p:pos(m0(r))]
-satz176f:=realapp1(neg(r),[x:dif][t:inn(x,class(r))]t12".3r176"(x,t,p)):neg(r)
-+3r177
-a0ir@t1:=isin(m0(m0(r)),r,m0d(m0d(a0)),a0,micm0(m0(r),m0d(a0),micm0),a0ir,satzd177(a0)):is(m0(m0(r)),r)
--3r177
-r@satz177:=realapp1(is(m0(m0(r)),r),[x:dif][t:inn(x,class(r))]t1".3r177"(x,t)):is(m0(m0(r)),r)
-satz177a:=symis(real,m0(m0(r)),r,satz177):is(r,m0(m0(r)))
-s@[i:is(r,m0(s))]
-satz177b:=tris(real,m0(r),m0(m0(s)),s,ism0(r,m0(s),i),satz177(s)):is(m0(r),s)
-satz177c:=symis(real,m0(r),s,satz177b):is(s,m0(r))
-s@[i:is(m0(r),s)]
-satz177d:=satz177c(s,r,symis(real,m0(r),s,i)):is(r,m0(s))
-satz177e:=symis(real,r,m0(s),satz177d):is(m0(s),r)
-+3r178
-a0ir@t1:=isin(abs(m0(r)),abs(r),absd(m0d(a0)),absd(a0),aica(m0(r),m0d(a0),micm0),aica,satzd178(a0)):is(abs(m0(r)),abs(r))
--3r178
-r@satz178:=realapp1(is(abs(m0(r)),abs(r)),[x:dif][t:inn(x,class(r))]t1".3r178"(x,t)):is(abs(m0(r)),abs(r))
-satz178a:=symis(real,abs(m0(r)),abs(r),satz178):is(abs(r),abs(m0(r)))
-+3r179
-a0ir@t1:=0in(pl(r,m0(r)),pd(a0,m0d(a0)),picp(r,m0(r),a0,m0d(a0),a0ir,micm0),satzd179(a0)):is(pl(r,m0(r)),0)
--3r179
-satz179:=realapp1(is(pl(r,m0(r)),0),[x:dif][t:inn(x,class(r))]t1".3r179"(x,t)):is(pl(r,m0(r)),0)
-satz179a:=tris(real,pl(m0(r),r),pl(r,m0(r)),0,compl(m0(r),r),satz179):is(pl(m0(r),r),0)
-+3r180
-b1is@t1:=isin(m0(pl(r,s)),pl(m0(r),m0(s)),m0d(pd(a1,b1)),pd(m0d(a1),m0d(b1)),micm0(pl(r,s),pd(a1,b1),picp),picp(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is)),satzd180(a1,b1)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
--3r180
-s@satz180:=realapp2(is(m0(pl(r,s)),pl(m0(r),m0(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t1".3r180"(x,y,t,u)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
-satz180a:=symis(real,m0(pl(r,s)),pl(m0(r),m0(s)),satz180):is(pl(m0(r),m0(s)),m0(pl(r,s)))
-mn:=pl(r,m0(s)):real
-b1is@micmn:=picp(r,m0(s),a1,m0d(b1),a1ir,micm0(s,b1,b1is)):inn(md(a1,b1),class(mn(r,s)))
-t@[i:is(r,s)]
-ismn1:=ispl1(r,s,m0(t),i):is(mn(r,t),mn(s,t))
-ismn2:=ispl2(m0(r),m0(s),t,ism0(r,s,i)):is(mn(t,r),mn(t,s))
-u@[i:is(r,s)][j:is(t,u)]
-ismn12:=ispl12(r,s,m0(t),m0(u),i,ism0(t,u,j)):is(mn(r,t),mn(s,u))
-s@satz181:=tr3is(real,m0(mn(r,s)),pl(m0(r),m0(m0(s))),pl(m0(r),s),mn(s,r),satz180(r,m0(s)),ispl2(m0(m0(s)),s,m0(r),satz177(s)),compl(m0(r),s)):is(m0(mn(r,s)),mn(s,r))
-satz181a:=symis(real,m0(mn(s,r)),mn(r,s),satz181(s,r)):is(mn(r,s),m0(mn(s,r)))
-+3r182
-b1is@[p:pos(mn(r,s))]
-t1:=satzd182a(a1,b1,posex(mn(r,s),md(a1,b1),micmn,p)):mored(a1,b1)
-t2:=morein(t1):more(r,s)
--3r182
-[p:pos(mn(r,s))]
-satz182a:=realapp2(more(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r182"(x,y,t,u,p)):more(r,s)
-+*3r182
-b1is@[i:is(mn(r,s),0)]
-t3:=satzd182b(a1,b1,0ex(mn(r,s),md(a1,b1),micmn,i)):eq"rp"(a1,b1)
-t4:=isin(t3):is(r,s)
--3r182
-s@[i:is(mn(r,s),0)]
-satz182b:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r182"(x,y,t,u,i)):is(r,s)
-+*3r182
-b1is@[n:neg(mn(r,s))]
-t5:=satzd182c(a1,b1,negex(mn(r,s),md(a1,b1),micmn,n)):lessd(a1,b1)
-t6:=lessin(t5):less(r,s)
--3r182
-s@[n:neg(mn(r,s))]
-satz182c:=realapp2(less(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".3r182"(x,y,t,u,n)):less(r,s)
-+*3r182
-b1is@[m:more(r,s)]
-t7:=satzd182d(a1,b1,moreex(m)):posd(md(a1,b1))
-t8:=posin(mn(r,s),md(a1,b1),micmn,t7):pos(mn(r,s))
--3r182
-s@[m:more(r,s)]
-satz182d:=realapp2(pos(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".3r182"(x,y,t,u,m)):pos(mn(r,s))
-+*3r182
-b1is@[i:is(r,s)]
-t9:=satzd182e(a1,b1,isex(i)):zero(md(a1,b1))
-t10:=0in(mn(r,s),md(a1,b1),micmn,t9):is(mn(r,s),0)
--3r182
-s@[i:is(r,s)]
-satz182e:=realapp2(is(mn(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t10".3r182"(x,y,t,u,i)):is(mn(r,s),0)
-+*3r182
-b1is@[l:less(r,s)]
-t11:=satzd182f(a1,b1,lessex(l)):negd(md(a1,b1))
-t12:=negin(mn(r,s),md(a1,b1),micmn,t11):neg(mn(r,s))
--3r182
-s@[l:less(r,s)]
-satz182f:=realapp2(neg(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t12".3r182"(x,y,t,u,l)):neg(mn(r,s))
-+3r183
-b1is@[m:more(r,s)]
-t1:=satzd183a(a1,b1,moreex(m)):lessd(m0d(a1),m0d(b1))
-t2:=lessin(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t1):less(m0(r),m0(s))
--3r183
-s@[m:more(r,s)]
-satz183a:=realapp2(less(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r183"(x,y,t,u,m)):less(m0(r),m0(s))
-s@[i:is(r,s)]
-satz183b:=ism0(r,s,i):is(m0(r),m0(s))
-+*3r183
-b1is@[l:less(r,s)]
-t3:=satzd183c(a1,b1,lessex(l)):mored(m0d(a1),m0d(b1))
-t4:=morein(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t3):more(m0(r),m0(s))
--3r183
-s@[l:less(r,s)]
-satz183c:=realapp2(more(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r183"(x,y,t,u,l)):more(m0(r),m0(s))
-s@[l:less(m0(r),m0(s))]
-satz183d:=ismore12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183c(m0(r),m0(s),l)):more(r,s)
-s@[i:is(m0(r),m0(s))]
-satz183e:=tr3is(real,r,m0(m0(r)),m0(m0(s)),s,satz177a(r),ism0(m0(r),m0(s),i),satz177(s)):is(r,s)
-s@[m:more(m0(r),m0(s))]
-satz183f:=isless12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183a(m0(r),m0(s),m)):less(r,s)
-+3r184
-t@prop1:=and3(pos(s),pos(t),is(r,mn(s,t))):'prop'
-s@prop2:=some([x:real]prop1(x)):'prop'
-r@prop3:=some([x:real]prop2(x)):'prop'
-a0ir@[a:dif][b:dif]
-prop1d:=and3(posd(a),posd(b),eq"rp"(a0,md(a,b))):'prop'
-a@prop2d:=some"l"(dif,[x:dif]prop1d(x)):'prop'
-[p2:prop2d(a)][b:dif][p1:prop1d(a,b)]
-t1:=and3e1(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(a)
-t2:=and3e2(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(b)
-t3:=and3e3(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):eq"rp"(a0,md(a,b))
-p2@ra:=realof(a):real
-p1@rb:=realof(b):real
-t4:=innclass(a):inn(a,class(ra))
-t5:=innclass(b):inn(b,class(rb))
-t6:=isin(r,mn(ra,rb),a0,md(a,b),a0ir,micmn(ra,rb,a,b,t4,t5),t3):is(r,mn(ra,rb))
-t7:=and3i(pos(ra),pos(rb),is(r,mn(ra,rb)),posin(ra,a,t4,t1),posin(rb,b,t5,t2),t6):prop1(ra,rb)
-t8:=somei(real,[x:real]prop1(ra,x),rb,t7):prop2(ra)
-p2@t9:=someapp(dif,[x:dif]prop1d(a,x),p2,prop2(ra),[x:dif][t:prop1d(a,x)]t8(x,t)):prop2(ra)
-t10:=somei(real,[x:real]prop2(x),ra,t9):prop3
-a0ir@t11:=someapp(dif,[x:dif]prop2d(x),satzd184(a0),prop3,[x:dif][t:prop2d(x)]t10(x,t)):prop3
--3r184
-r@satz184:=realapp1(prop3".3r184",[x:dif][t:inn(x,class(r))]t11".3r184"(x,t)):some([x:real]some([y:real]and3(pos(x),pos(y),is(r,mn(x,y)))))
-u@[a3:dif][b3:dif][c3:dif][d3:dif][a3ir:inn(a3,class(r))][b3is:inn(b3,class(s))][c3it:inn(c3,class(t))][d3iu:inn(d3,class(u))]
-+3r185
-t1:=satzd185(a3,b3,c3,d3):eq"rp"(pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)))
-t2:=isin(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)),pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)),picp(mn(r,s),mn(t,u),md(a3,b3),md(c3,d3),micmn(r,s,a3,b3,a3ir,b3is),micmn(t,u,c3,d3,c3it,d3iu)),micmn(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu)),t1):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
--3r185
-u@satz185:=realapp4(is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u))),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r185"(x,y,z,v,xi,yi,zi,vi)):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
-+3r186
-c2it@t1:=satzd186(a2,b2,c2):eq"rp"(pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)))
-t2:=isin(pl(pl(r,s),t),pl(r,pl(s,t)),pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)),picp(pl(r,s),t,pd(a2,b2),c2,picp(r,s,a2,b2,a2ir,b2is),c2it),picp(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),t1):is(pl(pl(r,s),t),pl(r,pl(s,t)))
--3r186
-t@satz186:=realapp3(is(pl(pl(r,s),t),pl(r,pl(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r186"(x,y,z,u,v,w)):is(pl(pl(r,s),t),pl(r,pl(s,t)))
-asspl1:=satz186:is(pl(pl(r,s),t),pl(r,pl(s,t)))
-asspl2:=symis(real,pl(pl(r,s),t),pl(r,pl(s,t)),satz186):is(pl(r,pl(s,t)),pl(pl(r,s),t))
-s@plmn:=tris(real,pl(mn(r,s),s),pl(r,pl(m0(s),s)),r,asspl1(r,m0(s),s),pl02(r,pl(m0(s),s),satz179a(s))):is(pl(mn(r,s),s),r)
-mnpl:=tris(real,mn(pl(r,s),s),pl(r,pl(s,m0(s))),r,asspl1(r,s,m0(s)),pl02(r,pl(s,m0(s)),satz179(s))):is(mn(pl(r,s),s),r)
-satz187a:=tris(real,pl(s,mn(r,s)),pl(mn(r,s),s),r,compl(s,mn(r,s)),plmn):is(pl(s,mn(r,s)),r)
-satz187b:=somei(real,[x:real]is(pl(s,x),r),mn(r,s),satz187a):some([x:real]is(pl(s,x),r))
-[x:real][i:is(pl(s,x),r)]
-satz187c:=tris(real,mn(r,s),mn(pl(x,s),s),x,ismn1(r,pl(x,s),s,tris1(real,r,pl(x,s),pl(s,x),i,compl(s,x))),mnpl(x,s)):is(mn(r,s),x)
-satz187d:=symis(real,mn(r,s),x,satz187c):is(x,mn(r,s))
-x@[i:is(pl(x,s),r)]
-satz187e:=satz187c(tris(real,pl(s,x),pl(x,s),r,compl(s,x),i)):is(mn(r,s),x)
-satz187f:=symis(real,mn(r,s),x,satz187e):is(x,mn(r,s))
-+3r187
-s@[x:real][y:real][i:is(pl(s,x),r)][j:is(pl(s,y),r)]
-t1:=tris1(real,x,y,mn(r,s),satz187c(x,i),satz187c(y,j)):is(x,y)
-s@t2:=[x:real][y:real][t:is(pl(s,x),r)][u:is(pl(s,y),r)]t1(x,y,t,u):amone(real,[x:real]is(pl(s,x),r))
--3r187
-s@satz187:=onei(real,[x:real]is(pl(s,x),r),t2".3r187",satz187b):one([x:real]is(pl(s,x),r))
-+3r188
-c2it@[m:more(pl(r,t),pl(s,t))]
-t1:=satzd188a(a2,b2,c2,moreex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),m)):mored(a2,b2)
-t2:=morein(r,s,a2,b2,a2ir,b2is,t1):more(r,s)
--3r188
-t@[m:more(pl(r,t),pl(s,t))]
-satz188a:=realapp3(more(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r188"(x,y,z,u,v,w,m)):more(r,s)
-+*3r188
-c2it@[i:is(pl(r,t),pl(s,t))]
-t3:=satzd188b(a2,b2,c2,isex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),i)):eq"rp"(a2,b2)
-t4:=isin(r,s,a2,b2,a2ir,b2is,t3):is(r,s)
--3r188
-t@[i:is(pl(r,t),pl(s,t))]
-satz188b:=realapp3(is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".3r188"(x,y,z,u,v,w,i)):is(r,s)
-+*3r188
-c2it@[l:less(pl(r,t),pl(s,t))]
-t5:=satzd188c(a2,b2,c2,lessex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),l)):lessd(a2,b2)
-t6:=lessin(r,s,a2,b2,a2ir,b2is,t5):less(r,s)
--3r188
-t@[l:less(pl(r,t),pl(s,t))]
-satz188c:=realapp3(less(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t6".3r188"(x,y,z,u,v,w,l)):less(r,s)
-+*3r188
-c2it@[m:more(r,s)]
-t7:=satzd188d(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m)):mored(pd(a2,c2),pd(b2,c2))
-t8:=morein(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t7):more(pl(r,t),pl(s,t))
--3r188
-t@[m:more(r,s)]
-satz188d:=realapp3(more(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t8".3r188"(x,y,z,u,v,w,m)):more(pl(r,t),pl(s,t))
-t@[i:is(r,s)]
-satz188e:=ispl1(r,s,t,i):is(pl(r,t),pl(s,t))
-+*3r188
-c2it@[l:less(r,s)]
-t9:=satzd188f(a2,b2,c2,lessex(r,s,a2,b2,a2ir,b2is,l)):lessd(pd(a2,c2),pd(b2,c2))
-t10:=lessin(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t9):less(pl(r,t),pl(s,t))
--3r188
-t@[l:less(r,s)]
-satz188f:=realapp3(less(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t10".3r188"(x,y,z,u,v,w,l)):less(pl(r,t),pl(s,t))
-t@[m:more(pl(t,r),pl(t,s))]
-satz188g:=satz188a(ismore12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),m)):more(r,s)
-t@[i:is(pl(t,r),pl(t,s))]
-satz188h:=satz188b(tr3is(real,pl(r,t),pl(t,r),pl(t,s),pl(s,t),compl(r,t),i,compl(t,s))):is(r,s)
-t@[l:less(pl(t,r),pl(t,s))]
-satz188j:=satz188c(isless12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),l)):less(r,s)
-t@[m:more(r,s)]
-satz188k:=ismore12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188d(m)):more(pl(t,r),pl(t,s))
-t@[i:is(r,s)]
-satz188l:=ispl2(r,s,t,i):is(pl(t,r),pl(t,s))
-t@[l:less(r,s)]
-satz188m:=isless12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188f(l)):less(pl(t,r),pl(t,s))
-u@[i:is(r,s)][m:more(t,u)]
-satz188n:=ismore2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188k(t,u,r,m)):more(pl(r,t),pl(s,u))
-satz188o:=ismore12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188n):more(pl(t,r),pl(u,s))
-i@[l:less(t,u)]
-satz188p:=isless2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188m(t,u,r,l)):less(pl(r,t),pl(s,u))
-satz188q:=isless12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188p):less(pl(t,r),pl(u,s))
-u@[m:more(r,s)][n:more(t,u)]
-satz189:=trmore(pl(r,t),pl(s,t),pl(s,u),satz188d(m),satz188k(t,u,s,n)):more(pl(r,t),pl(s,u))
-u@[l:less(r,s)][k:less(t,u)]
-satz189a:=lemma1(pl(s,u),pl(r,t),satz189(s,r,u,t,lemma2(r,s,l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
-u@[m:moreis(r,s)][n:more(t,u)]
-satz190a:=orapp(more(r,s),is(r,s),more(pl(r,t),pl(s,u)),m,[v:more(r,s)]satz189(v,n),[v:is(r,s)]satz188n(v,n)):more(pl(r,t),pl(s,u))
-u@[m:more(r,s)][n:moreis(t,u)]
-satz190b:=ismore12(pl(t,r),pl(r,t),pl(u,s),pl(s,u),compl(t,r),compl(u,s),satz190a(t,u,r,s,n,m)):more(pl(r,t),pl(s,u))
-u@[l:lessis(r,s)][k:less(t,u)]
-satz190c:=lemma1(pl(s,u),pl(r,t),satz190a(s,r,u,t,satz168b(l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
-u@[l:less(r,s)][k:lessis(t,u)]
-satz190d:=lemma1(pl(s,u),pl(r,t),satz190b(s,r,u,t,lemma2(l),satz168b(t,u,k))):less(pl(r,t),pl(s,u))
-+3r191
-d3iu@[m:moreis(r,s)][n:moreis(t,u)]
-t1:=satzd191(a3,b3,c3,d3,moreisex(r,s,a3,b3,a3ir,b3is,m),moreisex(t,u,c3,d3,c3it,d3iu,n)):moreq(pd(a3,c3),pd(b3,d3))
-t2:=moreisin(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu),t1):moreis(pl(r,t),pl(s,u))
--3r191
-u@[m:moreis(r,s)][n:moreis(t,u)]
-satz191:=realapp4(moreis(pl(r,t),pl(s,u)),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r191"(x,y,z,v,xi,yi,zi,vi,m,n)):moreis(pl(r,t),pl(s,u))
-u@[l:lessis(r,s)][k:lessis(t,u)]
-satz191a:=satz168a(pl(s,u),pl(r,t),satz191(s,r,u,t,satz168b(l),satz168b(t,u,k))):lessis(pl(r,t),pl(s,u))
-@timesdr:=[x:dif][y:dif]realof(td(x,y)):[x:dif][y:dif]real
-+ivr4
-[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
-t1:=isin(realof(td(a,c)),realof(td(b,d)),td(a,c),td(b,d),innclass(td(a,c)),innclass(td(b,d)),eqtd12(a,b,c,d,e,f)):is(<c><a>timesdr,<d><b>timesdr)
--ivr4
-ftimesdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr4"(x,y,z,v,t,u):fixf2(real,timesdr)
-s@ts:=indreal2(real,timesdr,ftimesdr,r,s):real
-+*ivr4
-b1is@t2:=isindreal2(real,timesdr,ftimesdr,r,s,a1,b1,a1ir,b1is):is(realof(td(a1,b1)),ts(r,s))
--ivr4
-b1is@tict:=isp(real,[x:real]inn(td(a1,b1),class(x)),realof(td(a1,b1)),ts(r,s),innclass(td(a1,b1)),t2".ivr4"):inn(td(a1,b1),class(ts(r,s)))
-t@[i:is(r,s)]
-ists1:=isf(real,real,[x:real]ts(x,t),r,s,i):is(ts(r,t),ts(s,t))
-ists2:=isf(real,real,[x:real]ts(t,x),r,s,i):is(ts(t,r),ts(t,s))
-u@[i:is(r,s)][j:is(t,u)]
-ists12:=tris(real,ts(r,t),ts(s,t),ts(s,u),ists1(i),ists2(t,u,s,j)):is(ts(r,t),ts(s,u))
-+4r192
-b1is@[i:is(r,0)]
-t1:=satzd192a(a1,b1,0ex(r,a1,a1ir,i)):zero(td(a1,b1))
-t2:=0in(ts(r,s),td(a1,b1),tict,t1):is(ts(r,s),0)
--4r192
-s@[i:is(r,0)]
-satz192a:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r192"(x,y,t,u,i)):is(ts(r,s),0)
-+*4r192
-b1is@[i:is(s,0)]
-t3:=satzd192b(a1,b1,0ex(s,b1,b1is,i)):zero(td(a1,b1))
-t4:=0in(ts(r,s),td(a1,b1),tict,t3):is(ts(r,s),0)
--4r192
-s@[i:is(s,0)]
-satz192b:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".4r192"(x,y,t,u,i)):is(ts(r,s),0)
-+*4r192
-b1is@[i:is(ts(r,s),0)]
-t5:=satzd192c(a1,b1,0ex(ts(r,s),td(a1,b1),tict,i)):or(zero(a1),zero(b1))
-t6:=th9"l.or"(zero(a1),zero(b1),is(r,0),is(s,0),t5,[t:zero(a1)]0in(r,a1,a1ir,t),[t:zero(b1)]0in(s,b1,b1is,t)):or(is(r,0),is(s,0))
--4r192
-s@[i:is(ts(r,s),0)]
-satz192c:=realapp2(or(is(r,0),is(s,0)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".4r192"(x,y,t,u,i)):or(is(r,0),is(s,0))
-s@[n:nis(r,0)][o:nis(s,0)]
-satz192d:=th3"l.imp"(is(ts(r,s),0),or(is(r,0),is(s,0)),th3"l.or"(is(r,0),is(s,0),n,o),[t:is(ts(r,s),0)]satz192c(t)):nis(ts(r,s),0)
-s@[i:is(r,0)]
-ts01:=satz192a(i):is(ts(r,s),0)
-s@[i:is(s,0)]
-ts02:=satz192b(i):is(ts(r,s),0)
-+4r193
-b1is@t1:=satzd193(a1,b1):eq"rp"(absd(td(a1,b1)),td(absd(a1),absd(b1)))
-t2:=isin(abs(ts(r,s)),ts(abs(r),abs(s)),absd(td(a1,b1)),td(absd(a1),absd(b1)),aica(ts(r,s),td(a1,b1),tict),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(abs(ts(r,s)),ts(abs(r),abs(s)))
--4r193
-s@satz193:=realapp2(is(abs(ts(r,s)),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r193"(x,y,t,u)):is(abs(ts(r,s)),ts(abs(r),abs(s)))
-satz193a:=symis(real,abs(ts(r,s)),ts(abs(r),abs(s)),satz193):is(ts(abs(r),abs(s)),abs(ts(r,s)))
-+4r194
-b1is@t1:=satzd194(a1,b1):eq"rp"(td(a1,b1),td(b1,a1))
-t2:=isin(ts(r,s),ts(s,r),td(a1,b1),td(b1,a1),tict,tict(s,r,b1,a1,b1is,a1ir),t1):is(ts(r,s),ts(s,r))
--4r194
-satz194:=realapp2(is(ts(r,s),ts(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r194"(x,y,t,u)):is(ts(r,s),ts(s,r))
-comts:=satz194:is(ts(r,s),ts(s,r))
-@1rl:=realof(1df):real
-pos1:=posin(1rl,1df,innclass(1df),posdirp(1rp)):pos(1rl)
-natrl1:=natrli(1):natrl(1rl)
-intrl1:=natintrl(1rl,natrl1):intrl(1rl)
-+4r195
-a0ir@t1:=satzd195(a0):eq"rp"(td(a0,1df),a0)
-t2:=isin(ts(r,1rl),r,td(a0,1df),a0,tict(r,1rl,a0,1df,a0ir,innclass(1df)),a0ir,t1):is(ts(r,1rl),r)
--4r195
-r@satz195:=realapp1(is(ts(r,1rl),r),[x:dif][t:inn(x,class(r))]t2".4r195"(x,t)):is(ts(r,1rl),r)
-satz195a:=symis(real,ts(r,1rl),r,satz195):is(r,ts(r,1rl))
-satz195b:=tris(real,ts(1rl,r),ts(r,1rl),r,comts(1rl,r),satz195):is(ts(1rl,r),r)
-satz195c:=symis(real,ts(1rl,r),r,satz195b):is(r,ts(1rl,r))
-s@[p:pos(r)][q:pos(s)]
-satz196a:=symis(real,ts(abs(r),abs(s)),ts(r,s),ists12(abs(r),r,abs(s),s,absp(r,p),absp(s,q))):is(ts(r,s),ts(abs(r),abs(s)))
-+4r196
-b1is@[n:neg(r)][o:neg(s)]
-t1:=satzd196b(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):eq"rp"(td(a1,b1),td(absd(a1),absd(b1)))
-t2:=isin(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(ts(r,s),ts(abs(r),abs(s)))
--4r196
-s@[n:neg(r)][o:neg(s)]
-satz196b:=realapp2(is(ts(r,s),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r196"(x,y,t,u,n,o)):is(ts(r,s),ts(abs(r),abs(s)))
-+*4r196
-b1is@[p:pos(r)][n:neg(s)]
-t1a:=satzd196c(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):eq"rp"(td(a1,b1),m0d(td(absd(a1),absd(b1))))
-t2a:=isin(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),t1a):is(ts(r,s),m0(ts(abs(r),abs(s))))
--4r196
-s@[p:pos(r)][n:neg(s)]
-satz196c:=realapp2(is(ts(r,s),m0(ts(abs(r),abs(s)))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2a".4r196"(x,y,t,u,p,n)):is(ts(r,s),m0(ts(abs(r),abs(s))))
-s@[n:neg(r)][p:pos(s)]
-satz196d:=tr3is(real,ts(r,s),ts(s,r),m0(ts(abs(s),abs(r))),m0(ts(abs(r),abs(s))),comts(r,s),satz196c(s,r,p,n),ism0(ts(abs(s),abs(r)),ts(abs(r),abs(s)),comts(abs(s),abs(r)))):is(ts(r,s),m0(ts(abs(r),abs(s))))
-+*4r196
-a0ir@[n:not(is(r,0))]
-t3:=th3"l.imp"(zero(a0),is(r,0),n,[t:zero(a0)]0in(t)):not(zero(a0))
-b1is@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
-t4:=satzd196e(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),i)):or(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)))
-[a:and(posd(a1),posd(b1))]
-t5:=andi(pos(r),pos(s),posin(r,a1,a1ir,ande1(posd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(posd(a1),posd(b1),a))):and(pos(r),pos(s))
-i@[a:and(negd(a1),negd(b1))]
-t6:=andi(neg(r),neg(s),negin(r,a1,a1ir,ande1(negd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(negd(a1),negd(b1),a))):and(neg(r),neg(s))
-i@t7:=th9"l.or"(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)),and(pos(r),pos(s)),and(neg(r),neg(s)),t4,[t:and(posd(a1),posd(b1))]t5(t),[t:and(negd(a1),negd(b1))]t6(t)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
--4r196
-s@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
-satz196e:=realapp2(or(and(pos(r),pos(s)),and(neg(r),neg(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
-+*4r196
-o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
-t8:=satzd196f(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),i)):or(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)))
-[a:and(posd(a1),negd(b1))]
-t9:=andi(pos(r),neg(s),posin(r,a1,a1ir,ande1(posd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(posd(a1),negd(b1),a))):and(pos(r),neg(s))
-i@[a:and(negd(a1),posd(b1))]
-t10:=andi(neg(r),pos(s),negin(r,a1,a1ir,ande1(negd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(negd(a1),posd(b1),a))):and(neg(r),pos(s))
-i@t11:=th9"l.or"(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)),and(pos(r),neg(s)),and(neg(r),pos(s)),t8,[t:and(posd(a1),negd(b1))]t9(t),[t:and(negd(a1),posd(b1))]t10(t)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
--4r196
-o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
-satz196f:=realapp2(or(and(pos(r),neg(s)),and(neg(r),pos(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
-s@[p:pos(ts(r,s))]
-+*4r196
-p"r"@t12:=th3"l.imp"(is(r,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
-t13:=th3"l.imp"(is(s,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
-t14:=tris1(real,ts(r,s),ts(abs(r),abs(s)),abs(ts(r,s)),absp(ts(r,s),p),satz193(r,s)):is(ts(r,s),ts(abs(r),abs(s)))
--4r196
-p@satz196g:=satz196e(t12".4r196",t13".4r196",t14".4r196"):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
-s@[n:neg(ts(r,s))]
-+*4r196
-n"r"@t15:=th3"l.imp"(is(r,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
-t16:=th3"l.imp"(is(s,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
-t17:=satz177c(ts(abs(r),abs(s)),ts(r,s),tris(real,ts(abs(r),abs(s)),abs(ts(r,s)),m0(ts(r,s)),satz193a(r,s),absn(ts(r,s),n))):is(ts(r,s),m0(ts(abs(r),abs(s))))
--4r196
-n@satz196h:=satz196f(t15".4r196",t16".4r196",t17".4r196"):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
-+4r197
-b1is@t1:=satzd197a(a1,b1):eq"rp"(td(m0d(a1),b1),m0d(td(a1,b1)))
-t2:=isin(ts(m0(r),s),m0(ts(r,s)),td(m0d(a1),b1),m0d(td(a1,b1)),tict(m0(r),s,m0d(a1),b1,micm0(r,a1,a1ir),b1is),micm0(ts(r,s),td(a1,b1),tict),t1):is(ts(m0(r),s),m0(ts(r,s)))
--4r197
-s@satz197a:=realapp2(is(ts(m0(r),s),m0(ts(r,s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r197"(x,y,t,u)):is(ts(m0(r),s),m0(ts(r,s)))
-satz197b:=tr3is(real,ts(r,m0(s)),ts(m0(s),r),m0(ts(s,r)),m0(ts(r,s)),comts(r,m0(s)),satz197a(s,r),ism0(ts(s,r),ts(r,s),comts(s,r))):is(ts(r,m0(s)),m0(ts(r,s)))
-satz197c:=tris2(real,ts(m0(r),s),ts(r,m0(s)),m0(ts(r,s)),satz197a,satz197b):is(ts(m0(r),s),ts(r,m0(s)))
-satz197d:=symis(real,ts(m0(r),s),ts(r,m0(s)),satz197c):is(ts(r,m0(s)),ts(m0(r),s))
-satz197e:=symis(real,ts(m0(r),s),m0(ts(r,s)),satz197a):is(m0(ts(r,s)),ts(m0(r),s))
-satz197f:=symis(real,ts(r,m0(s)),m0(ts(r,s)),satz197b):is(m0(ts(r,s)),ts(r,m0(s)))
-satz198:=tris(real,ts(m0(r),m0(s)),ts(r,m0(m0(s))),ts(r,s),satz197c(r,m0(s)),ists2(m0(m0(s)),s,r,satz177(s))):is(ts(m0(r),m0(s)),ts(r,s))
-satz198a:=symis(real,ts(m0(r),m0(s)),ts(r,s),satz198):is(ts(r,s),ts(m0(r),m0(s)))
-+*ivr4
-b1is@[p:pos(r)][q:pos(s)]
-t3:=ptdpp(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(td(a1,b1))
-t4:=posin(ts(r,s),td(a1,b1),tict,t3):pos(ts(r,s))
--ivr4
-s@[p:pos(r)][q:pos(s)]
-postspp:=realapp2(pos(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr4"(x,y,t,u,p,q)):pos(ts(r,s))
-+*ivr4
-p@[n:neg(s)]
-t5:=ntdpn(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):negd(td(a1,b1))
-t6:=negin(ts(r,s),td(a1,b1),tict,t5):neg(ts(r,s))
--ivr4
-s@[p:pos(r)][n:neg(s)]
-negtspn:=realapp2(neg(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr4"(x,y,t,u,p,n)):neg(ts(r,s))
-s@[n:neg(r)][p:pos(s)]
-negtsnp:=isneg(ts(s,r),ts(r,s),comts(s,r),negtspn(s,r,p,n)):neg(ts(r,s))
-s@[n:neg(r)][o:neg(s)]
-postsnn:=ispos(ts(m0(r),m0(s)),ts(r,s),satz198,postspp(m0(r),m0(s),satz176c(r,n),satz176c(s,o))):pos(ts(r,s))
-r@[n:nis(r,0)]
-possq:=rapp(r,pos(ts(r,r)),[t:pos(r)]postspp(r,r,t,t),th2"l.imp"(is(r,0),pos(ts(r,r)),n),[t:neg(r)]postsnn(r,r,t,t)):pos(ts(r,r))
-r@nnegsq:=th1"l.imp"(is(r,0),not(neg(ts(r,r))),[t:is(r,0)]0notn(ts(r,r),satz192a(r,r,t)),[t:nis(r,0)]pnotn(ts(r,r),possq(r,t))):not(neg(ts(r,r)))
-+4r199
-c2it@t1:=satzd199(a2,b2,c2):eq"rp"(td(td(a2,b2),c2),td(a2,td(b2,c2)))
-t2:=isin(ts(ts(r,s),t),ts(r,ts(s,t)),td(td(a2,b2),c2),td(a2,td(b2,c2)),tict(ts(r,s),t,td(a2,b2),c2,tict(r,s,a2,b2,a2ir,b2is),c2it),tict(r,ts(s,t),a2,td(b2,c2),a2ir,tict(s,t,b2,c2,b2is,c2it)),t1):is(ts(ts(r,s),t),ts(r,ts(s,t)))
--4r199
-t@satz199:=realapp3(is(ts(ts(r,s),t),ts(r,ts(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r199"(x,y,z,u,v,w)):is(ts(ts(r,s),t),ts(r,ts(s,t)))
-assts1:=satz199:is(ts(ts(r,s),t),ts(r,ts(s,t)))
-assts2:=symis(real,ts(ts(r,s),t),ts(r,ts(s,t)),satz199):is(ts(r,ts(s,t)),ts(ts(r,s),t))
-+4r201
-c2it@t1:=satzd201(a2,b2,c2):eq"rp"(td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)))
-t2:=isin(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)),tict(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),picp(ts(r,s),ts(r,t),td(a2,b2),td(a2,c2),tict(r,s,a2,b2,a2ir,b2is),tict(r,t,a2,c2,a2ir,c2it)),t1):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
--4r201
-satz201:=realapp3(is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r201"(x,y,z,u,v,w)):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
-disttp1:=tr3is(real,ts(pl(r,s),t),ts(t,pl(r,s)),pl(ts(t,r),ts(t,s)),pl(ts(r,t),ts(s,t)),comts(pl(r,s),t),satz201(t,r,s),ispl12(ts(t,r),ts(r,t),ts(t,s),ts(s,t),comts(t,r),comts(t,s))):is(ts(pl(r,s),t),pl(ts(r,t),ts(s,t)))
-disttp2:=satz201:is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
-distpt1:=symis(real,ts(pl(r,s),t),pl(ts(r,t),ts(s,t)),disttp1):is(pl(ts(r,t),ts(s,t)),ts(pl(r,s),t))
-distpt2:=symis(real,ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),disttp2):is(pl(ts(r,s),ts(r,t)),ts(r,pl(s,t)))
-satz202:=tris(real,ts(r,mn(s,t)),pl(ts(r,s),ts(r,m0(t))),mn(ts(r,s),ts(r,t)),disttp2(r,s,m0(t)),ispl2(ts(r,m0(t)),m0(ts(r,t)),ts(r,s),satz197b(r,t))):is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
-disttm1:=tris(real,ts(mn(r,s),t),pl(ts(r,t),ts(m0(s),t)),mn(ts(r,t),ts(s,t)),disttp1(r,m0(s),t),ispl2(ts(m0(s),t),m0(ts(s,t)),ts(r,t),satz197a(s,t))):is(ts(mn(r,s),t),mn(ts(r,t),ts(s,t)))
-disttm2:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
-distmt1:=symis(real,ts(mn(r,s),t),mn(ts(r,t),ts(s,t)),disttm1):is(mn(ts(r,t),ts(s,t)),ts(mn(r,s),t))
-distmt2:=symis(real,ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)),disttm2):is(mn(ts(r,s),ts(r,t)),ts(r,mn(s,t)))
-satz200:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
-+4r203
-c2it@[m:more(r,s)][p:pos(t)]
-t1:=satzd203a(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),posex(t,c2,c2it,p)):mored(td(a2,c2),td(b2,c2))
-t2:=morein(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t1):more(ts(r,t),ts(s,t))
--4r203
-[m:more(r,s)][p:pos(t)]
-satz203a:=realapp3(more(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r203"(x,y,z,u,v,w,m,p)):more(ts(r,t),ts(s,t))
-m@[i:is(t,0)]
-satz203b:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
-+*4r203
-m@[n:neg(t)]
-t3:=satzd203c(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),negex(t,c2,c2it,n)):lessd(td(a2,c2),td(b2,c2))
-t4:=lessin(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t3):less(ts(r,t),ts(s,t))
--4r203
-m@[n:neg(t)]
-satz203c:=realapp3(less(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".4r203"(x,y,z,u,v,w,m,n)):less(ts(r,t),ts(s,t))
-p@satz203d:=ismore12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203a):more(ts(t,r),ts(t,s))
-i@satz203e:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
-n@satz203f:=isless12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203c):less(ts(t,r),ts(t,s))
-t@[l:less(r,s)][p:pos(t)]
-satz203g:=lemma1(ts(s,t),ts(r,t),satz203a(s,r,t,lemma2(r,s,l),p)):less(ts(r,t),ts(s,t))
-l@[i:is(t,0)]
-satz203h:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
-l@[n:neg(t)]
-satz203j:=lemma2(ts(s,t),ts(r,t),satz203c(s,r,t,lemma2(r,s,l),n)):more(ts(r,t),ts(s,t))
-p@satz203k:=lemma1(ts(t,s),ts(t,r),satz203d(s,r,t,lemma2(r,s,l),p)):less(ts(t,r),ts(t,s))
-i@satz203l:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
-n@satz203m:=lemma2(ts(t,s),ts(t,r),satz203f(s,r,t,lemma2(r,s,l),n)):more(ts(t,r),ts(t,s))
-+4r204
-a0ir@[n1:nis(r,0)]
-t1:=th3"l.imp"(zero(a0),is(r,0),n1,[t:zero(a0)]0in(t)):not(zero(a0))
-d3iu@[n1:nis(s,0)][i:is(ts(s,t),r)][j:is(ts(s,u),r)]
-t2:=satzd204b(a3,b3,t1(s,b3,b3is,n1),c3,d3,isex(ts(s,t),r,td(b3,c3),a3,tict(s,t,b3,c3,b3is,c3it),a3ir,i),isex(ts(s,u),r,td(b3,d3),a3,tict(s,u,b3,d3,b3is,d3iu),a3ir,j)):eq"rp"(c3,d3)
-t3:=isin(t,u,c3,d3,c3it,d3iu,t2):is(t,u)
--4r204
-s@[n:nis(s,0)][x:real][y:real][i:is(ts(s,x),r)][j:is(ts(s,y),r)]
-satz204b:=realapp4(x,y,is(x,y),[z:dif][u:dif][v:dif][w:dif][zi:inn(z,class(r))][ui:inn(u,class(s))][vi:inn(v,class(x))][wi:inn(w,class(y))]t3".4r204"(x,y,z,u,v,w,zi,ui,vi,wi,n,i,j)):is(x,y)
-+*4r204
-b1is@[n1:nis(s,0)]
-t4:=satzd204a(a1,b1,t1(s,b1,b1is,n1)):some"l"(dif,[x:dif]eq"rp"(td(b1,x),a1))
-[a:dif][e:eq"rp"(td(b1,a),a1)]
-ar:=realof(a):real
-t5:=isin(ts(s,ar),r,td(b1,a),a1,tict(s,ar,b1,a,b1is,innclass(a)),a1ir,e):is(ts(s,ar),r)
-t6:=somei(real,[x:real]is(ts(s,x),r),ar,t5):some([x:real]is(ts(s,x),r))
-n1@t7:=someapp(dif,[x:dif]eq"rp"(td(b1,x),a1),t4,some([x:real]is(ts(s,x),r)),[x:dif][t:eq"rp"(td(b1,x),a1)]t6(x,t)):some([x:real]is(ts(s,x),r))
--4r204
-n@satz204a:=realapp2(some([x:real]is(ts(s,x),r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r204"(x,y,t,u,n)):some([x:real]is(ts(s,x),r))
-satz204:=onei(real,[x:real]is(ts(s,x),r),[x:real][y:real][t:is(ts(s,x),r)][u:is(ts(s,y),r)]satz204b(x,y,t,u),satz204a):one([x:real]is(ts(s,x),r))
-ov:=ind(real,[x:real]is(ts(s,x),r),satz204):real
-satz204c:=oneax(real,[x:real]is(ts(s,x),r),satz204):is(ts(s,ov(r,s,n)),r)
-satz204d:=symis(real,ts(s,ov(r,s,n)),r,satz204c):is(r,ts(s,ov(r,s,n)))
-satz204e:=tris(real,ts(ov(r,s,n),s),ts(s,ov(r,s,n)),r,comts(ov(r,s,n),s),satz204c):is(ts(ov(r,s,n),s),r)
-satz204f:=symis(real,ts(ov(r,s,n),s),r,satz204e):is(r,ts(ov(r,s,n),s))
-s@[x:real][n:nis(s,0)][i:is(ts(s,x),r)]
-satz204g:=satz204b(n,x,ov(r,s,n),i,satz204c(n)):is(x,ov(r,s,n))
-s@[n:nis(s,0)][p:pos(r)][q:pos(s)]
-+*4r204
-n@ros:=ov(r,s,n):real
-p@t8:=ispos(r,ts(s,ros),satz204d(n),p):pos(ts(s,ros))
-q@t9:=th1"l.and"(neg(s),neg(ros),pnotn(s,q)):not(and(neg(s),neg(ros)))
-t10:=ore1(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t9):and(pos(s),pos(ros))
--4r204
-q@posovpp:=ande2(pos(s),pos(ov(r,s,n)),t10".4r204"):pos(ov(r,s,n))
-p@[m:neg(s)]
-+*4r204
-m@t11:=th1"l.and"(pos(s),pos(ros),nnotp(s,m)):not(and(pos(s),pos(ros)))
-t12:=ore2(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t11):and(neg(s),neg(ros))
--4r204
-m@negovpn:=ande2(neg(s),neg(ov(r,s,n)),t12".4r204"):neg(ov(r,s,n))
-n@[m:neg(r)][p:pos(s)]
-+*4r204
-m@t13:=isneg(r,ts(s,ros),satz204d(n),m):neg(ts(s,ros))
-p@t14:=th1"l.and"(neg(s),pos(ros),pnotn(s,p)):not(and(neg(s),pos(ros)))
-t15:=ore1(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t14):and(pos(s),neg(ros))
--4r204
-p@negovnp:=ande2(pos(s),neg(ov(r,s,n)),t15".4r204"):neg(ov(r,s,n))
-m@[l:neg(s)]
-+*4r204
-l@t16:=th1"l.and"(pos(s),neg(ros),nnotp(s,l)):not(and(pos(s),neg(ros)))
-t17:=ore2(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t16):and(neg(s),pos(ros))
--4r204
-l@posovnn:=ande2(neg(s),pos(ov(r,s,n)),t17".4r204"):pos(ov(r,s,n))
-@[r0:cut][s0:cut][m:more"rp"(r0,s0)]
-morerpep:=morein(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),morerpepd(r0,s0,m)):more(pofrp(r0),pofrp(s0))
-s0@[m:more(pofrp(r0),pofrp(s0))]
-morerpip:=morerpipd(r0,s0,moreex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),m)):more"rp"(r0,s0)
-s0@[l:less"rp"(r0,s0)]
-lessrpep:=lemma1(pofrp(s0),pofrp(r0),morerpep(s0,r0,satz122(r0,s0,l))):less(pofrp(r0),pofrp(s0))
-s0@[l:less(pofrp(r0),pofrp(s0))]
-lessrpip:=satz121(s0,r0,morerpip(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
-s@[p:pos(r)][q:pos(s)][m:more(r,s)]
-q@[m:more(r,s)]
-+ivr5
-t1:=ismore12(r,pofrp(rpofp(r,p)),s,pofrp(rpofp(s,q)),isprp1(r,p),isprp1(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
--ivr5
-moreperp:=morerpip(rpofp(r,p),rpofp(s,q),t1".ivr5"):more"rp"(rpofp(r,p),rpofp(s,q))
-q@[m:more"rp"(rpofp(r,p),rpofp(s,q))]
-+*ivr5
-m@t2:=morerpep(rpofp(r,p),rpofp(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
--ivr5
-m@morepirp:=ismore12(pofrp(rpofp(r,p)),r,pofrp(rpofp(s,q)),s,isprp2(r,p),isprp2(s,q),t2".ivr5"):more(r,s)
-q@[l:less(r,s)]
-lessperp:=satz121(rpofp(s,q),rpofp(r,p),moreperp(s,r,q,p,lemma2(r,s,l))):less"rp"(rpofp(r,p),rpofp(s,q))
-q@[l:less"rp"(rpofp(r,p),rpofp(s,q))]
-lesspirp:=lemma1(s,r,morepirp(s,r,q,p,satz122(rpofp(r,p),rpofp(s,q),l))):less(r,s)
-r@s01:=setof(real,[x:real]lessis(x,r)):set(real)
-s02:=setof(real,[x:real]more(x,r)):set(real)
-+5r205
-s@[n:not(in(s,s01))]
-t1:=th3"l.imp"(lessis(s,r),in(s,s01),n,[t:lessis(s,r)]estii(real,[x:real]lessis(x,r),s,t)):not(lessis(s,r))
-t2:=estii(real,[x:real]more(x,r),s,satz167k(s,r,t1)):in(s,s02)
--5r205
-vb00:=[x:real][t:not(in(x,s01))]t2".5r205"(x,t):all([x:real]or(in(x,s01),in(x,s02)))
-+*5r205
-r@t3:=estii(real,[x:real]lessis(x,r),r,lessisi2(r,r,refis(real,r))):in(r,s01)
--5r205
-r@vb01a:=nonemptyi(real,s01,r,t3".5r205"):nonempty(real,s01)
-+*5r205
-r@t4:=ismore2(pl(r,0),r,pl(r,1rl),pl02(r,0,refis(real,0)),satz188k(1rl,0,r,satz169a(1rl,pos1))):more(pl(r,1rl),r)
-t5:=estii(real,[x:real]more(x,r),pl(r,1rl),t4):in(pl(r,1rl),s02)
--5r205
-r@vb01b:=nonemptyi(real,s02,pl(r,1rl),t5".5r205"):nonempty(real,s02)
-+*5r205
-s@[i:in(s,s01)][t:real][j:in(t,s02)]
-t6:=satz172a(s,r,t,estie(real,[x:real]lessis(x,r),s,i),lemma1(t,r,estie(real,[x:real]more(x,r),t,j))):less(s,t)
--5r205
-r@vb02:=[x:real][t:in(x,s01)][y:real][u:in(y,s02)]t6".5r205"(x,t,y,u):all([x:real][t:in(x,s01)]all([y:real][u:in(y,s02)]less(x,y)))
-s@[l:less(s,r)]
-vb03a:=estii(real,[x:real]lessis(x,r),s,lessisi1(s,r,l)):in(s,s01)
-s@[m:more(s,r)]
-vb03b:=estii(real,[x:real]more(x,r),s,m):in(s,s02)
-r@s11:=setof(real,[x:real]less(x,r)):set(real)
-s12:=setof(real,[x:real]moreis(x,r)):set(real)
-+*5r205
-s@[n:not(in(s,s11))]
-t7:=th3"l.imp"(less(s,r),in(s,s11),n,[t:less(s,r)]estii(real,[x:real]less(x,r),s,t)):not(less(s,r))
-t8:=estii(real,[x:real]moreis(x,r),s,satz167f(s,r,t7)):in(s,s12)
--5r205
-r@vb10:=[x:real][t:not(in(x,s11))]t8".5r205"(x,t):all([x:real]or(in(x,s11),in(x,s12)))
-+*5r205
-r@t9:=isless2(pl(r,0),r,mn(r,1rl),pl02(r,0,refis(real,0)),satz188m(m0(1rl),0,r,satz169c(m0(1rl),satz176a(1rl,pos1)))):less(mn(r,1rl),r)
-t10:=estii(real,[x:real]less(x,r),mn(r,1rl),t9):in(mn(r,1rl),s11)
--5r205
-r@vb11a:=nonemptyi(real,s11,mn(r,1rl),t10".5r205"):nonempty(real,s11)
-+*5r205
-r@t11:=estii(real,[x:real]moreis(x,r),r,moreisi2(r,r,refis(real,r))):in(r,s12)
--5r205
-r@vb11b:=nonemptyi(real,s12,r,t11".5r205"):nonempty(real,s12)
-+*5r205
-s@[i:in(s,s11)][t:real][j:in(t,s12)]
-t12:=satz172b(s,r,t,estie(real,[x:real]less(x,r),s,i),satz168a(t,r,estie(real,[x:real]moreis(x,r),t,j))):less(s,t)
--5r205
-r@vb12:=[x:real][t:in(x,s11)][y:real][u:in(y,s12)]t12".5r205"(x,t,y,u):all([x:real][t:in(x,s11)]all([y:real][u:in(y,s12)]less(x,y)))
-s@[l:less(s,r)]
-vb13a:=estii(real,[x:real]less(x,r),s,l):in(s,s11)
-s@[m:more(s,r)]
-vb13b:=estii(real,[x:real]moreis(x,r),s,moreisi1(s,r,m)):in(s,s12)
-@2rl:=pl(1rl,1rl):real
-pos2:=pospl(1rl,1rl,pos1,pos1):pos(2rl)
-half:=ov(1rl,2rl,pnot0(2rl,pos2)):real
-poshalf:=posovpp(1rl,2rl,pnot0(2rl,pos2),pos1,pos2):pos(half)
-+*ivr5
-r@t3:=tris(real,pl(r,r),pl(ts(1rl,r),ts(1rl,r)),ts(2rl,r),ispl12(r,ts(1rl,r),r,ts(1rl,r),satz195c(r),satz195c(r)),distpt1(1rl,1rl,r)):is(pl(r,r),ts(2rl,r))
-t4:=tr4is(real,ts(half,pl(r,r)),ts(half,ts(2rl,r)),ts(ts(half,2rl),r),ts(1rl,r),r,ists2(pl(r,r),ts(2rl,r),half,t3),assts2(half,2rl,r),ists1(ts(half,2rl),1rl,r,satz204e(1rl,2rl,pnot0(2rl,pos2))),satz195b(r)):is(ts(half,pl(r,r)),r)
--ivr5
-s@[l:less(r,s)]
-+*ivr5
-l@t5:=satz203k(pl(r,r),pl(r,s),half,satz188m(r,s,r,l),poshalf):less(ts(half,pl(r,r)),ts(half,pl(r,s)))
--ivr5
-l@lemma3:=isless1(ts(half,pl(r,r)),r,ts(half,pl(r,s)),t4".ivr5",t5".ivr5"):less(r,ts(half,pl(r,s)))
-+*ivr5
-l@t6:=satz203k(pl(r,s),pl(s,s),half,satz188f(r,s,s,l),poshalf):less(ts(half,pl(r,s)),ts(half,pl(s,s)))
--ivr5
-l@lemma4:=isless2(ts(half,pl(s,s)),s,ts(half,pl(r,s)),t4".ivr5"(s),t6".ivr5"):less(ts(half,pl(r,s)),s)
-[p:pos(r)]
-lemma5:=satz169b(s,trmore(s,r,0,lemma2(r,s,l),satz169a(r,p))):pos(s)
-@[s1:set(real)][s2:set(real)][p0:all([x:real]or(in(x,s1),in(x,s2)))][p1a:nonempty(real,s1)][p1b:nonempty(real,s2)][p2:all([x:real][t:in(x,s1)]all([y:real][u:in(y,s2)]less(x,y)))]
-+*5r205
-s2@[r:real]
-prop1:=all([x:real][t:less(x,r)]in(x,s1)):'prop'
-prop2:=all([x:real][t:more(x,r)]in(x,s2)):'prop'
-prop3:=and(prop1,prop2):'prop'
-p2@[x:real][y:real][px:prop3(x)][py:prop3(y)][l:less(x,y)]
-mxy:=ts(half,pl(x,y)):real
-t13:=lemma2(x,mxy,lemma3(x,y,l)):more(mxy,x)
-t14:=lemma4(x,y,l):less(mxy,y)
-t15:=<t14><mxy>ande1(prop1(y),prop2(y),py):in(mxy,s1)
-t16:=<t13><mxy>ande2(prop1(x),prop2(x),px):in(mxy,s2)
-t17:=<t16><mxy><t15><mxy>p2:less(mxy,mxy)
-t18:=<refis(real,mxy)>ec3e31(is(mxy,mxy),more(mxy,mxy),less(mxy,mxy),satz167b(mxy,mxy),t17):con
-py@t19:=[t:less(x,y)]t18(t):not(less(x,y))
-t20:=[t:more(x,y)]t18(y,x,py,px,lemma1(x,y,t)):not(more(x,y))
-t21:=or3e1(is(x,y),more(x,y),less(x,y),satz167a(x,y),t20,t19):is(x,y)
-p2@t22:=[x:real][y:real][t:prop3(x)][u:prop3(y)]t21(x,y,t,u):amone(real,[x:real]prop3(x))
-[case1:some([x:real]and(pos(x),in(x,s1)))][r:real][a:and(pos(r),in(r,s1))]
-t23:=ande1(pos(r),in(r,s1),a):pos(r)
-t24:=ande2(pos(r),in(r,s1),a):in(r,s1)
-sc1:=setof(cut,[x:cut]in(pofrp(x),s1)):set(cut)
-sc2:=setof(cut,[x:cut]in(pofrp(x),s2)):set(cut)
-[r0:cut][i:in(pofrp(r0),s1)]
-t25:=estii(cut,[x:cut]in(pofrp(x),s1),r0,i):in"rp"(r0,sc1)
-r0@[i:in"rp"(r0,sc1)]
-t26:=estie(cut,[x:cut]in(pofrp(x),s1),r0,i):in(pofrp(r0),s1)
-r0@[i:in(pofrp(r0),s2)]
-t27:=estii(cut,[x:cut]in(pofrp(x),s2),r0,i):in"rp"(r0,sc2)
-r0@[i:in"rp"(r0,sc2)]
-t28:=estie(cut,[x:cut]in(pofrp(x),s2),r0,i):in(pofrp(r0),s2)
-r0@t29:=th9"l.or"(in(pofrp(r0),s1),in(pofrp(r0),s2),in"rp"(r0,sc1),in"rp"(r0,sc2),<pofrp(r0)>p0,[t:in(pofrp(r0),s1)]t25(t),[t:in(pofrp(r0),s2)]t27(t)):or(in"rp"(r0,sc1),in"rp"(r0,sc2))
-a@pr1:=rpofp(r,t23):cut
-t30:=isp(real,[x:real]in(x,s1),r,pofrp(pr1),t24,isprp1(r,t23)):in(pofrp(pr1),s1)
-t31:=nonemptyi(cut,sc1,pr1,t25(pr1,t30)):nonempty(cut,sc1)
-[s:real][i:in(s,s2)]
-t32:=<i><s><t24><r>p2:less(r,s)
-t33:=lemma5(r,s,t32,t23):pos(s)
-ps1:=rpofp(s,t33):cut
-t34:=isp(real,[x:real]in(x,s2),s,pofrp(ps1),i,isprp1(s,t33)):in(pofrp(ps1),s2)
-t35:=nonemptyi(cut,sc2,ps1,t27(ps1,t34)):nonempty(cut,sc2)
-a@t36:=nonemptyapp(real,s2,p1b,nonempty(cut,sc2),[x:real][t:in(x,s2)]t35(x,t)):nonempty(cut,sc2)
-r0@[i:in"rp"(r0,sc1)][s0:cut][j:in"rp"(s0,sc2)]
-t37:=<t28(s0,j)><pofrp(s0)><t26(r0,i)><pofrp(r0)>p2:less(pofrp(r0),pofrp(s0))
-t38:=lessrpip(r0,s0,t37):less"rp"(r0,s0)
-a@stc:=schnitt(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):cut
-t39:=satzp205a(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:less"rp"(x,stc)]in"rp"(x,sc1))
-t40:=satzp205b(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:more"rp"(x,stc)]in"rp"(x,sc2))
-stp:=pofrp(stc):real
-t41:=posi(stc):pos(stp)
-[s:real][l:less(s,stp)][p:pos(s)]
-ps2:=rpofp(s,p):cut
-t42:=lessrpip(ps2,stc,isless1(s,pofrp(ps2),stp,isprp1(s,p),l)):less"rp"(ps2,stc)
-t43:=<t42><ps2>t39:in"rp"(ps2,sc1)
-t44:=isp(real,[x:real]in(x,s1),pofrp(ps2),s,t26(ps2,t43),isprp2(s,p)):in(s,s1)
-l@[n:not(pos(s))][i:in(s,s2)]
-t45:=<i><s><t24><r>p2:less(r,s)
-t46:=<lemma5(r,s,t45,t23)>n:con
-n@t47:=ore1(in(s,s1),in(s,s2),<s>p0,[t:in(s,s2)]t46(t)):in(s,s1)
-l@t48:=th1"l.imp"(pos(s),in(s,s1),[t:pos(s)]t44(t),[t:not(pos(s))]t47(t)):in(s,s1)
-s@[m:more(s,stp)]
-t49:=lemma5(stp,s,lemma1(s,stp,m),t41):pos(s)
-ps3:=rpofp(s,t49):cut
-t50:=morerpip(ps3,stc,ismore1(s,pofrp(ps3),stp,isprp1(s,t49),m)):more"rp"(ps3,stc)
-t51:=<t50><ps3>t40:in"rp"(ps3,sc2)
-t52:=isp(real,[x:real]in(x,s2),pofrp(ps3),s,t28(ps3,t51),isprp2(s,t49)):in(s,s2)
-a@t53:=andi(prop1(stp),prop2(stp),[x:real][t:less(x,stp)]t48(x,t),[x:real][t:more(x,stp)]t52(x,t)):prop3(stp)
-t54:=somei(real,[x:real]prop3(x),stp,t53):some([x:real]prop3(x))
-case1@t55:=someapp(real,[x:real]and(pos(x),in(x,s1)),case1,some([x:real]prop3(x)),[x:real][t:and(pos(x),in(x,s1))]t54(x,t)):some([x:real]prop3(x))
-p2@[case2:some([x:real]and(neg(x),in(x,s2)))]
-sp1:=setof(real,[x:real]in(m0(x),s1)):set(real)
-sp2:=setof(real,[x:real]in(m0(x),s2)):set(real)
-[r:real][i:in(m0(r),s1)]
-t56:=estii(real,[x:real]in(m0(x),s1),r,i):in(r,sp1)
-r@[i:in(r,sp1)]
-t57:=estie(real,[x:real]in(m0(x),s1),r,i):in(m0(r),s1)
-r@[i:in(m0(r),s2)]
-t58:=estii(real,[x:real]in(m0(x),s2),r,i):in(r,sp2)
-r@[i:in(r,sp2)]
-t59:=estie(real,[x:real]in(m0(x),s2),r,i):in(m0(r),s2)
-r@t60:=comor(in(r,sp1),in(r,sp2),th9"l.or"(in(m0(r),s1),in(m0(r),s2),in(r,sp1),in(r,sp2),<m0(r)>p0,[t:in(m0(r),s1)]t56(t),[t:in(m0(r),s2)]t58(t))):or(in(r,sp2),in(r,sp1))
-[i:in(r,s2)]
-t61:=t58(m0(r),isp(real,[x:real]in(x,s2),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp2)
-t62:=nonemptyi(real,sp2,m0(r),t61):nonempty(real,sp2)
-case2@t63:=nonemptyapp(real,s2,p1b,nonempty(real,sp2),[x:real][t:in(x,s2)]t62(x,t)):nonempty(real,sp2)
-r@[i:in(r,s1)]
-t64:=t56(m0(r),isp(real,[x:real]in(x,s1),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp1)
-t65:=nonemptyi(real,sp1,m0(r),t64):nonempty(real,sp1)
-case2@t66:=nonemptyapp(real,s1,p1a,nonempty(real,sp1),[x:real][t:in(x,s1)]t65(x,t)):nonempty(real,sp1)
-r@[i:in(r,sp2)][s:real][j:in(s,sp1)]
-t67:=<t59(r,i)><m0(r)><t57(s,j)><m0(s)>p2:less(m0(s),m0(r))
-t68:=lemma1(s,r,satz183d(s,r,t67)):less(r,s)
-r@[a:and(neg(r),in(r,s2))]
-t69:=satz176c(r,ande1(neg(r),in(r,s2),a)):pos(m0(r))
-t70:=isp(real,[x:real]in(x,s2),r,m0(m0(r)),ande2(neg(r),in(r,s2),a),satz177a(r)):in(m0(m0(r)),s2)
-t71:=andi(pos(m0(r)),in(m0(r),sp2),t69,t58(m0(r),t70)):and(pos(m0(r)),in(m0(r),sp2))
-t72:=somei(real,[x:real]and(pos(x),in(x,sp2)),m0(r),t71):some([x:real]and(pos(x),in(x,sp2)))
-case2@t73:=someapp(real,[x:real]and(neg(x),in(x,s2)),case2,some([x:real]and(pos(x),in(x,sp2))),[x:real][t:and(neg(x),in(x,s2))]t72(x,t)):some([x:real]and(pos(x),in(x,sp2)))
-t74:=t55(sp2,sp1,[x:real]t60(x),t63,t66,[x:real][t:in(x,sp2)][y:real][u:in(y,sp1)]t68(x,t,y,u),t73):some([x:real]prop3(sp2,sp1,x))
-[r:real][p:prop3(sp2,sp1,r)][s:real][l:less(s,m0(r))]
-t75:=ismore2(m0(m0(r)),r,m0(s),satz177(r),satz183c(s,m0(r),l)):more(m0(s),r)
-t76:=<t75><m0(s)>ande2(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp1)
-t77:=isp(real,[x:real]in(x,s1),m0(m0(s)),s,t57(m0(s),t76),satz177(s)):in(s,s1)
-s@[m:more(s,m0(r))]
-t78:=isless2(m0(m0(r)),r,m0(s),satz177(r),satz183a(s,m0(r),m)):less(m0(s),r)
-t79:=<t78><m0(s)>ande1(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp2)
-t80:=isp(real,[x:real]in(x,s2),m0(m0(s)),s,t59(m0(s),t79),satz177(s)):in(s,s2)
-p@t81:=andi(prop1(m0(r)),prop2(m0(r)),[x:real][t:less(x,m0(r))]t77(x,t),[x:real][t:more(x,m0(r))]t80(x,t)):prop3(m0(r))
-t82:=somei(real,[x:real]prop3(x),m0(r),t81):some([x:real]prop3(x))
-case2@t83:=someapp(real,[x:real]prop3(sp2,sp1,x),t74,some([x:real]prop3(x)),[x:real][t:prop3(sp2,sp1,x)]t82(x,t)):some([x:real]prop3(x))
-p2@[notcase1:not(some([x:real]and(pos(x),in(x,s1))))][notcase2:not(some([x:real]and(neg(x),in(x,s2))))][r:real][l:less(r,0)]
-t84:=th4"l.some"(real,[x:real]and(neg(x),in(x,s2)),notcase2,r):not(and(neg(r),in(r,s2)))
-t85:=th3"l.and"(neg(r),in(r,s2),t84,satz169d(r,l)):not(in(r,s2))
-t86:=ore1(in(r,s1),in(r,s2),<r>p0,t85):in(r,s1)
-r@[m:more(r,0)]
-t87:=th4"l.some"(real,[x:real]and(pos(x),in(x,s1)),notcase1,r):not(and(pos(r),in(r,s1)))
-t88:=th3"l.and"(pos(r),in(r,s1),t87,satz169b(r,m)):not(in(r,s1))
-t89:=ore2(in(r,s1),in(r,s2),<r>p0,t88):in(r,s2)
-notcase2@t90:=andi(prop1(0),prop2(0),[x:real][t:less(x,0)]t86(x,t),[x:real][t:more(x,0)]t89(x,t)):prop3(0)
-t91:=somei(real,[x:real]prop3(x),0,t90):some([x:real]prop3(x))
-notcase1@t92:=th1"l.imp"(some([x:real]and(neg(x),in(x,s2))),some([x:real]prop3(x)),[t:some([x:real]and(neg(x),in(x,s2)))]t83(t),[t:not(some([x:real]and(neg(x),in(x,s2))))]t91(t)):some([x:real]prop3(x))
-p2@t93:=th1"l.imp"(some([x:real]and(pos(x),in(x,s1))),some([x:real]prop3(x)),[t:some([x:real]and(pos(x),in(x,s1)))]t55(t),[t:not(some([x:real]and(pos(x),in(x,s1))))]t92(t)):some([x:real]prop3(x))
-t94:=onei(real,[x:real]prop3(x),t22,t93):one([x:real]prop3(x))
--5r205
-p2@satz205:=t94".5r205":one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
-dedekind:=satz205:one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
-schnitt:=ind(real,[x:real]prop3".5r205"(x),satz205):real
-[r:real][l:less(r,schnitt)]
-satz205a:=<l><r>ande1(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s1)
-r@[m:more(r,schnitt)]
-satz205b:=<m><r>ande2(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s2)
-@[r0:cut][s0:cut]
-+iva
-dr:=pdofrp(r0):dif
-ds:=pdofrp(s0):dif
-t1:=lemmaivad1(r0,s0):eq"rp"(pd(dr,ds),pdofrp(pl"rp"(r0,s0)))
--iva
-lemmaiva1:=isin(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)),pd(pdofrp(r0),pdofrp(s0)),pdofrp(pl"rp"(r0,s0)),picp(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(pl"rp"(r0,s0))),t1".iva"):is(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)))
-+*iva
-s0@t2:=lemmaivad2(r0,s0):eq"rp"(td(dr,ds),pdofrp(ts"rp"(r0,s0)))
--iva
-s0@lemmaiva2:=isin(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)),td(pdofrp(r0),pdofrp(s0)),pdofrp(ts"rp"(r0,s0)),tict(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(ts"rp"(r0,s0))),t2".iva"):is(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)))
-[m:more(pofrp(r0),pofrp(s0))]
-+*iva
-m@t3:=moreex(pofrp(r0),pofrp(s0),dr,ds,innclass(dr),innclass(ds),m):mored(dr,ds)
--iva
-m@lemmaiva3:=lemmaivad3(r0,s0,t3".iva"):more"rp"(r0,s0)
-s0@[m:more"rp"(r0,s0)]
-+*iva
-m@[l:less(pofrp(r0),pofrp(s0))]
-t4:=satz121(s0,r0,lemmaiva3(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
-m@t5:=ec3e23(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):not(less"rp"(r0,s0))
-t6:=th3"l.imp"(less(pofrp(r0),pofrp(s0)),less"rp"(r0,s0),t5,[t:less(pofrp(r0),pofrp(s0))]t4(t)):not(less(pofrp(r0),pofrp(s0)))
-t7:=ec3e21(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):nis"rp"(r0,s0)
-t8:=th3"l.imp"(is(pofrp(r0),pofrp(s0)),is"rp"(r0,s0),t7,[t:is(pofrp(r0),pofrp(s0))]isrpip(r0,s0,t)):nis(pofrp(r0),pofrp(s0))
--iva
-m@lemmaiva4:=or3e2(is(pofrp(r0),pofrp(s0)),more(pofrp(r0),pofrp(s0)),less(pofrp(r0),pofrp(s0)),satz167a(pofrp(r0),pofrp(s0)),t6".iva",t8".iva"):more(pofrp(r0),pofrp(s0))
-@[x:nat][y:nat][m:more(rlofnt(x),rlofnt(y))]
-+*iva
-m@t9:=lemmaiva3(rpofnt(x),rpofnt(y),m):more"rp"(rpofnt(x),rpofnt(y))
-t10:=satz154d(rtofn(x),rtofn(y),t9):more"rt"(rtofn(x),rtofn(y))
-t11:=moree"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t10):moref(fr(x,1),fr(y,1))
--iva
-m@lemmaiva5:=satz111a(x,y,t11".iva"):more"n"(x,y)
-y@[m:more"n"(x,y)]
-+*iva
-m@t12:=satz111d(x,y,m):moref(fr(x,1),fr(y,1))
-t13:=morei"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t12):more"rt"(rtofn(x),rtofn(y))
-t14:=satz154a(rtofn(x),rtofn(y),t13):more"rp"(rpofnt(x),rpofnt(y))
--iva
-m@lemmaiva6:=lemmaiva4(rpofnt(x),rpofnt(y),t14".iva"):more(rlofnt(x),rlofnt(y))
-@[r:real]
-+int
-a0ir@[i:intrl(r)]
-t1:=intabsd(a0,intrlex(r,a0,a0ir,i)):intd(absd(a0))
-t2:=intrlin(abs(r),absd(a0),aica,t1):intrl(abs(r))
--int
-[i:intrl(r)]
-intabs:=realapp1(r,intrl(abs(r)),[x:dif][t:inn(x,class(r))]t2".int"(r,x,t,i)):intrl(abs(r))
-+*int
-i@t3:=intm0d(a0,intrlex(r,a0,a0ir,i)):intd(m0d(a0))
-t4:=intrlin(m0(r),m0d(a0),micm0,t3):intrl(m0(r))
--int
-i@intm0:=realapp1(r,intrl(m0(r)),[x:dif][t:inn(x,class(r))]t4".int"(r,x,t,i)):intrl(m0(r))
-+*int
-b1is@[i:intrl(r)][j:intrl(s)]
-t5:=intpd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(pd(a1,b1))
-t6:=intrlin(pl(r,s),pd(a1,b1),picp,t5):intrl(pl(r,s))
--int
-i@[s:real][j:intrl(s)]
-intpl:=realapp2(r,s,intrl(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".int"(r,s,x,y,t,u,i,j)):intrl(pl(r,s))
-intmn:=intpl(r,i,m0(s),intm0(s,j)):intrl(mn(r,s))
-+*int
-j@t7:=inttd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(td(a1,b1))
-t8:=intrlin(ts(r,s),td(a1,b1),tict,t7):intrl(ts(r,s))
--int
-j@intts:=realapp2(r,s,intrl(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".int"(r,s,x,y,t,u,i,j)):intrl(ts(r,s))
-r@[n:natrl(r)]
-+ivr24
-t1:=satz24a(ntofrl(r,n)):lessis"n"(1,ntofrl(r,n))
-t2:=th3"l.imp"(more(1rl,r),more"n"(1,ntofrl(r,n)),satz10d(1,ntofrl(r,n),t1),[t:more(1rl,r)]lemmaiva5(1,ntofrl(r,n),ismore2(r,rlofnt(ntofrl(r,n)),1rl,isrlnt1(r,n),t))):not(more(1rl,r))
--ivr24
-satzr24:=satz167e(1rl,r,t2".ivr24"):lessis(1rl,r)
-r@[i:intrl(r)][s:real][j:intrl(s)][l:less(r,s)]
-+ivr25
-t1:=satz182d(s,r,lemma2(r,s,l)):pos(mn(s,r))
-t2:=intmn(s,j,r,i):intrl(mn(s,r))
-t3:=posintnatrl(mn(s,r),t1,t2):natrl(mn(s,r))
-t4:=satzr24(mn(s,r),t3):lessis(1rl,mn(s,r))
-t5:=th9"l.or"(less(1rl,mn(s,r)),is(1rl,mn(s,r)),less(pl(1rl,r),pl(mn(s,r),r)),is(pl(1rl,r),pl(mn(s,r),r)),t4,[t:less(1rl,mn(s,r))]satz188f(1rl,mn(s,r),r,t),[t:is(1rl,mn(s,r))]ispl1(1rl,mn(s,r),r,t)):lessis(pl(1rl,r),pl(mn(s,r),r))
--ivr25
-satzr25:=islessis12(pl(1rl,r),pl(r,1rl),pl(mn(s,r),r),s,compl(1rl,r),plmn(s,r),t5".ivr25"):lessis(pl(r,1rl),s)
-@[x:nat][y:nat]
-+ivr155
-t1:=lemmaiva1(rpofnt(x),rpofnt(y)):is(pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
-t2:=isrpep(rpofnt(pl"n"(x,y)),pl"rp"(rpofnt(x),rpofnt(y)),satz155e(x,y)):is(rlofnt(pl"n"(x,y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
--ivr155
-satzr155a:=tris2(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))),t2".ivr155",t1".ivr155"):is(rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)))
-satzr155b:=symis(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),satzr155a):is(pl(rlofnt(x),rlofnt(y)),rlofnt(pl"n"(x,y)))
-+*ivr155
-y@t3:=lemmaiva2(rpofnt(x),rpofnt(y)):is(ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
-t4:=isrpep(rpofnt(ts"n"(x,y)),ts"rp"(rpofnt(x),rpofnt(y)),satz155f(x,y)):is(rlofnt(ts"n"(x,y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
--ivr155
-y@satzr155c:=tris2(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))),t4".ivr155",t3".ivr155"):is(rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)))
-satzr155d:=symis(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),satzr155c):is(ts(rlofnt(x),rlofnt(y)),rlofnt(ts"n"(x,y)))
-@[t:real][r:real][s:real][a:and(not(neg(r)),is(ts(r,r),t))][b:and(not(neg(s)),is(ts(s,s),t))]
-+7r161
-[c0:dif][cit:inn(c0,class(t))][a0:dif][air:inn(a0,class(r))][b0:dif][bis:inn(b0,class(s))]
-t1:=th3"l.imp"(negd(a0),neg(r),ande1(not(neg(r)),is(ts(r,r),t),a),[u:negd(a0)]negin(r,a0,air,u)):not(negd(a0))
-t2:=th3"l.imp"(negd(b0),neg(s),ande1(not(neg(s)),is(ts(s,s),t),b),[u:negd(b0)]negin(s,b0,bis,u)):not(negd(b0))
-t3:=isex(ts(r,r),t,td(a0,a0),c0,tict(r,r,a0,a0,air,air),cit,ande2(not(neg(r)),is(ts(r,r),t),a)):eq"rp"(td(a0,a0),c0)
-t4:=isex(ts(s,s),t,td(b0,b0),c0,tict(s,s,b0,b0,bis,bis),cit,ande2(not(neg(s)),is(ts(s,s),t),b)):eq"rp"(td(b0,b0),c0)
-t5:=isin(r,s,a0,b0,air,bis,satzd161b(c0,a0,b0,t1,t2,t3,t4)):is(r,s)
--7r161
-satzr161b:=realapp3(t,r,s,is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(t))][v:inn(y,class(r))][w:inn(z,class(s))]t5".7r161"(x,u,y,v,z,w)):is(r,s)
-t@[n:not(neg(t))]
-+*7r161
-n@[c0:dif][cit:inn(c0,class(t))]
-t6:=th3"l.imp"(negd(c0),neg(t),n,[u:negd(c0)]negin(t,c0,cit,u)):not(negd(c0))
-[a0:dif][a:and(not(negd(a0)),eq"rp"(td(a0,a0),c0))]
-ar:=realof(a0):real
-t7:=th3"l.imp"(neg(ar),negd(a0),ande1(not(negd(a0)),eq"rp"(td(a0,a0),c0),a),[u:neg(ar)]negex(ar,a0,innclass(a0),u)):not(neg(ar))
-t8:=isin(ts(ar,ar),t,td(a0,a0),c0,tict(ar,ar,a0,a0,innclass(a0),innclass(a0)),cit,ande2(not(negd(a0)),eq"rp"(td(a0,a0),c0),a)):is(ts(ar,ar),t)
-t9:=andi(not(neg(ar)),is(ts(ar,ar),t),t7,t8):and(not(neg(ar)),is(ts(ar,ar),t))
-t10:=somei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),ar,t9):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
-cit@t11:=someapp(dif,[x:dif]and(not(negd(x)),eq"rp"(td(x,x),c0)),satzd161a(c0,t6),some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:and(not(negd(x)),eq"rp"(td(x,x),c0))]t10(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
--7r161
-n@satzr161a:=realapp1(t,some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:inn(x,class(t))]t11".7r161"(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
-satzr161:=onei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),[u:real][v:real][a:and(not(neg(u)),is(ts(u,u),t))][b:and(not(neg(v)),is(ts(v,v),t))]satzr161b(u,v,a,b),satzr161a):one([u:real]and(not(neg(u)),is(ts(u,u),t)))
-sqrt:=ind(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):real
-+*7r161
-n@t12:=oneax(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):and(not(neg(sqrt)),is(ts(sqrt,sqrt),t))
--7r161
-n@thsqrt1a:=ande1(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):not(neg(sqrt))
-thsqrt1b:=ande2(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):is(ts(sqrt,sqrt),t)
-[x:real][o:not(neg(x))][i:is(ts(x,x),t)]
-thsqrt2:=satzr161b(x,sqrt,andi(not(neg(x)),is(ts(x,x),t),o,i),t12".7r161"):is(x,sqrt(t,n))
-o@[i:is(t,ts(x,x))]
-thsqrt3:=symis(real,x,sqrt(t,n),thsqrt2(symis(real,t,ts(x,x),i))):is(sqrt(t,n),x)
-@[r:real][s:real][n:not(neg(r))][o:not(neg(s))][i:is(r,s)]
-issqrt:=thsqrt2(s,o,sqrt(r,n),thsqrt1a(r,n),tris(real,ts(sqrt(r,n),sqrt(r,n)),r,s,thsqrt1b(r,n),i)):is(sqrt(r,n),sqrt(s,o))
-r@[n:not(neg(r))][i:is(r,0)]
-sqrt0:=thsqrt3(r,n,0,0notn(0,refis(real,0)),tris2(real,r,ts(0,0),0,i,ts01(0,0,refis(real,0)))):is(sqrt(r,n),0)
-n@[o:nis(r,0)]
-+sqrt
-t1:=th3"l.imp"(is(sqrt(r,n),0),is(r,0),o,[t:is(sqrt(r,n),0)]tris1(real,r,0,ts(sqrt(r,n),sqrt(r,n)),thsqrt1b(r,n),ts01(sqrt(r,n),sqrt(r,n),t))):nis(sqrt(r,n),0)
--sqrt
-sqrtnot0:=or3e2(is(sqrt(r,n),0),pos(sqrt(r,n)),neg(sqrt(r,n)),axrlo(sqrt(r,n)),thsqrt1a(r,n),t1".sqrt"):pos(sqrt(r,n))
-@[r:real][s:real][t:real][n:nis(t,0)]
-+v0
-t1:=tr3is(real,ts(t,ts(r,ov(s,t,n))),ts(ts(r,ov(s,t,n)),t),ts(r,ts(ov(s,t,n),t)),ts(r,s),comts(t,ts(r,ov(s,t,n))),assts1(r,ov(s,t,n),t),ists2(ts(ov(s,t,n),t),s,r,satz204e(s,t,n))):is(ts(t,ts(r,ov(s,t,n))),ts(r,s))
--v0
-lemma6:=satz204g(ts(r,s),t,ts(r,ov(s,t,n)),n,t1".v0"):is(ts(r,ov(s,t,n)),ov(ts(r,s),t,n))
-+*v0
-n@t2:=tris(real,ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(ts(t,ov(r,t,n)),ts(t,ov(s,t,n))),pl(r,s),disttp2(t,ov(r,t,n),ov(s,t,n)),ispl12(ts(t,ov(r,t,n)),r,ts(t,ov(s,t,n)),s,satz204c(r,t,n),satz204c(s,t,n))):is(ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(r,s))
--v0
-n@lemma7:=satz204g(pl(r,s),t,pl(ov(r,t,n),ov(s,t,n)),n,t2".v0"):is(pl(ov(r,t,n),ov(s,t,n)),ov(pl(r,s),t,n))
-r@[n:nis(r,0)]
-lemma8:=satz204b(r,r,n,ov(r,r,n),1rl,satz204c(r,r,n),satz195(r)):is(ov(r,r,n),1rl)
-lemma9:=ore2(is(r,0),is(ov(0,r,n),0),satz192c(r,ov(0,r,n),satz204c(0,r,n)),n):is(ov(0,r,n),0)
-r@[i:is(r,m0(r))]
-+*v0
-i@[p:pos(m0(r))]
-t3:=<isneg(r,m0(r),i,satz176f(r,p))>pnotn(m0(r),p):con
-i@[n:neg(m0(r))]
-t4:=<ispos(r,m0(r),i,satz176d(r,n))>nnotp(m0(r),n):con
--v0
-i@lemma10:=satz176e(r,or3e1(is(m0(r),0),pos(m0(r)),neg(m0(r)),axrlo(m0(r)),[t:pos(m0(r))]t3".v0"(t),[t:neg(m0(r))]t4".v0"(t))):is(r,0)
-r@lemma11:=satz167f(ts(r,r),0,th3"l.imp"(less(ts(r,r),0),neg(ts(r,r)),nnegsq(r),[t:less(ts(r,r),0)]satz169d(ts(r,r),t))):moreis(ts(r,r),0)
-lemma12:=rapp(r,is(ts(r,r),ts(abs(r),abs(r))),[t:pos(r)]satz196a(r,r,t,t),[t:is(r,0)]tris2(real,ts(r,r),ts(abs(r),abs(r)),0,ts01(r,r,t),ts01(abs(r),abs(r),abs0(r,t))),[t:neg(r)]satz196b(r,r,t,t)):is(ts(r,r),ts(abs(r),abs(r)))
-@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
-+shift
-t1:=satz190a(x,x,1rl,0,moreisi2(x,x,refis(real,x)),satz169a(1rl,natpos(1rl,natrl1))):more(pl(x,1rl),pl(x,0))
-t2:=ismore2(pl(x,0),x,pl(x,1rl),pl02(x,0,refis(real,0)),t1):more(pl(x,1rl),x)
-t3:=satz172d(pl(x,1rl),x,y,t2,satz168b(y,x,ly)):more(pl(x,1rl),y)
-t4:=satz182d(pl(x,1rl),y,t3):pos(mn(pl(x,1rl),y))
-t5:=intmn(pl(x,1rl),intpl(x,ix,1rl,intrl1),y,iy):intrl(mn(pl(x,1rl),y))
-t6:=posintnatrl(mn(pl(x,1rl),y),t4,t5):natrl(mn(pl(x,1rl),y))
--shift
-shiftl:=ntofrl(mn(pl(x,1rl),y),t6".shift"):nat
-[n:1to(shiftl)]
-+*shift
-n@n1:=inn"n"(shiftl,n):nat
-t7:=1top(shiftl,n):lessis"n"(n1,shiftl)
-n2:=rlofnt(n1):real
-t8:=natintrl(n2,natrli(n1)):intrl(n2)
--shift
-n@shiftr:=mn(pl(n2".shift",y),1rl):real
-intshiftr:=intmn(pl(n2".shift",y),intpl(n2".shift",t8".shift",y,iy),1rl,intrl1):intrl(shiftr)
-[m:1to(shiftl)][i:is(shiftr(n),shiftr(m))]
-+*shift
-n@t8a:=tris(real,mn(pl(shiftr(n),1rl),y),mn(pl(n2,y),y),n2,ismn1(pl(mn(pl(n2,y),1rl),1rl),pl(n2,y),y,plmn(pl(n2,y),1rl)),mnpl(n2,y)):is(mn(pl(shiftr(n),1rl),y),n2)
-i@t9a:=ismn1(pl(shiftr(n),1rl),pl(shiftr(m),1rl),y,ispl1(shiftr(n),shiftr(m),1rl,i)):is(mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y))
-t10a:=tr3is(real,n2(n),mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y),n2(m),symis(real,mn(pl(shiftr(n),1rl),y),n2,t8a),t9a,t8a(m)):is(n2(n),n2(m))
-t11a:=isntirl(n1(n),n1(m),t10a):is"n"(n1(n),n1(m))
--shift
-i@iseshiftr:=isinne(shiftl,n,m,t11a".shift"):is"e"(1to(shiftl),n,m)
-+*shift
-n@[m:more(shiftr,x)]
-t9:=satz188d(shiftr,x,1rl,m):more(pl(shiftr,1rl),pl(x,1rl))
-t10:=ismore1(pl(shiftr,1rl),pl(n2,y),pl(x,1rl),plmn(pl(n2,y),1rl),t9):more(pl(n2,y),pl(x,1rl))
-t11:=satz188d(pl(n2,y),pl(x,1rl),m0(y),t10):more(mn(pl(n2,y),y),mn(pl(x,1rl),y))
-t12:=ismore1(mn(pl(n2,y),y),n2,mn(pl(x,1rl),y),mnpl(n2,y),t11):more(n2,mn(pl(x,1rl),y))
-t13:=ismore12(n2,rlofnt(ntofrl(n2,natrli(n1))),mn(pl(x,1rl),y),rlofnt(ntofrl(mn(pl(x,1rl),y),t6)),isrlnt1(n2,natrli(n1)),isrlnt1(mn(pl(x,1rl),y),t6),t12):more(rlofnt(ntofrl(n2,natrli(n1))),rlofnt(shiftl))
-t14:=lemmaiva5(ntofrl(n2,natrli(n1)),shiftl,t13):more"n"(ntofrl(n2,natrli(n1)),shiftl)
-t15:=ismore1"n"(ntofrl(n2,natrli(n1)),n1,shiftl,isntrl2(n1),t14):more"n"(n1,shiftl)
-n@t16:=th3"l.imp"(more(shiftr,x),more"n"(n1,shiftl),satz10d(n1,shiftl,t7),[t:more(shiftr,x)]t15(t)):not(more(shiftr,x))
--shift
-n@shiftrls:=satz167e(shiftr,x,t16".shift"):lessis(shiftr,x)
-+*shift
-n@[m:more(y,shiftr)]
-t17:=satz188d(y,shiftr,1rl,m):more(pl(y,1rl),pl(shiftr,1rl))
-t18:=ismore12(pl(y,1rl),pl(1rl,y),pl(shiftr,1rl),pl(n2,y),compl(y,1rl),plmn(pl(n2,y),1rl),t17):more(pl(1rl,y),pl(n2,y))
-t19:=satz188a(1rl,n2,y,t18):more(1rl,n2)
-t20:=lemmaiva5(1,n1,t19):more"n"(1,n1)
-n@t21:=th3"l.imp"(more(y,shiftr),more"n"(1,n1),satz10d(1,n1,satz24a(n1)),[t:more(y,shiftr)]t20(t)):not(more(y,shiftr))
--shift
-n@lsshiftr:=satz167e(y,shiftr,t21".shift"):lessis(y,shiftr)
-ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
-+*shift
-a@t22:=and3e1(intrl(u),lessis(y,u),lessis(u,x),a):intrl(u)
-t23:=and3e2(intrl(u),lessis(y,u),lessis(u,x),a):lessis(y,u)
-t24:=and3e3(intrl(u),lessis(y,u),lessis(u,x),a):lessis(u,x)
-[l:less(u,x)]
-t25:=satz188f(pl(u,1rl),pl(x,1rl),m0"r"(y),satz188f(u,x,1rl,l)):less(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
-a@[i:is(u,x)]
-t26:=ismn1(pl(u,1rl),pl(x,1rl),y,ispl1(u,x,1rl,i)):is(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
-a@t27:=th9"l.or"(less(u,x),is(u,x),less(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),is(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),t24,[t:less(u,x)]t25(t),[t:is(u,x)]t26(t)):lessis(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
-ul:=shiftl(u,t22,y,iy,t23):nat
-t28:=islessis12(mn(pl(u,1rl),y),rlofnt(ul),mn(pl(x,1rl),y),rlofnt(shiftl),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isrlnt1(mn(pl(x,1rl),y),t6),t27):lessis(rlofnt(ul),rlofnt(shiftl))
-t29:=th3"l.imp"(more"n"(ul,shiftl),more(rlofnt(ul),rlofnt(shiftl)),satz167d(rlofnt(ul),rlofnt(shiftl),t28),[t:more"n"(ul,shiftl)]lemmaiva6(ul,shiftl,t)):not(more"n"(ul,shiftl))
-t30:=satz10e(ul,shiftl,t29):lessis"n"(ul,shiftl)
--shift
-a@shiftl1:=outn(shiftl,ul".shift",t30".shift"):1to(shiftl)
-+*shift
-a@t31:=isinoutn(shiftl,ul,t30):is"n"(ul,n1(shiftl1))
-t32:=tris(real,mn(pl(u,1rl),y),rlofnt(ul),n2(shiftl1),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isnterl(ul,n1(shiftl1),t31)):is(mn(pl(u,1rl),y),n2(shiftl1))
-t33:=tris(real,mn(pl(mn(pl(u,1rl),y),y),1rl),mn(pl(u,1rl),1rl),u,ismn1(pl(mn(pl(u,1rl),y),y),pl(u,1rl),1rl,plmn(pl(u,1rl),y)),mnpl(u,1rl)):is(mn(pl(mn(pl(u,1rl),y),y),1rl),u)
--shift
-a@shiftinv1:=tris1(real,u,shiftr(shiftl1),mn(pl(mn(pl(u,1rl),y),y),1rl),t33".shift",ismn1(pl(mn(pl(u,1rl),y),y),pl(n2".shift"(shiftl1),y),1rl,ispl1(mn(pl(u,1rl),y),n2".shift"(shiftl1),y,t32".shift"))):is(u,shiftr(shiftl1))
-shiftinv2:=symis(real,u,shiftr(shiftl1),shiftinv1):is(shiftr(shiftl1),u)
-ly@[alpha:'type']
-seq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]alpha:'type'
-[s:seq]
-proofsirrelevant:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is(t,u)]is"e"(alpha,<tl><lt><it><t>s,<ul><lu><iu><u>s):'prop'
-alpha@[f:seq]
-shiftf:=[t:1to(shiftl)]<shiftrls(t)><lsshiftr(t)><intshiftr(t)><shiftr(t)>f:[t:1to(shiftl)]alpha
-ly@[s:seq(real)]
-inseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]and3(intrl(<w><v><u><t>s),lessis(y,<w><v><u><t>s),lessis(<w><v><u><t>s,x)):'prop'
-injseq:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is"r"(<tl><lt><it><t>s,<ul><lu><iu><u>s)]is"r"(t,u):'prop'
-[u:real][v:real][a:and3(intrl(v),lessis(y,v),lessis(v,x))]
-+*shift
-a@prop1:=is(u,<t24(v,a)><t23(v,a)><t22(v,a)><v>s):'prop'
--shift
-v@improp:=and(and3(intrl(v),lessis(y,v),lessis(v,x)),[t:and3(intrl(v),lessis(y,v),lessis(v,x))]prop1".shift"(t)):'prop'
-u@imseq:=some([t:real]improp(u,t)):'prop'
-s@surjseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]imseq(t):'prop'
-perm:=and(injseq,surjseq):'prop'
-[ins:inseq(s)]
-+*shift
-ins@[n:1to(shiftl)]
-ns:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>s:real
-t34:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ins:and3(intrl(ns),lessis(y,ns),lessis(ns,x))
--shift
-ins@shiftseq:=[t:1to(shiftl)]shiftl1(ns".shift"(t),t34".shift"(t)):[t:1to(shiftl)]1to(shiftl)
-[js:injseq(s)]
-+*shift
-js@[n:1to(shiftl)][m:1to(shiftl)][i:is"e"(1to(shiftl),<n>shiftseq,<m>shiftseq)]
-t35:=isoutne(shiftl,ul(ns(n),t34(n)),t30(ns(n),t34(n)),ul(ns(m),t34(m)),t30(ns(m),t34(m)),i):is"n"(ul(ns(n),t34(n)),ul(ns(m),t34(m)))
-t36:=isrlint(mn(pl(ns(n),1rl),y),t6(ns(n),t22(ns(n),t34(n)),y,iy,t23(ns(n),t34(n))),mn(pl(ns(m),1rl),y),t6(ns(m),t22(ns(m),t34(m)),y,iy,t23(ns(m),t34(m))),t35):is(mn(pl(ns(n),1rl),y),mn(pl(ns(m),1rl),y))
-t37:=satz188b(ns(n),ns(m),1rl,satz188b(pl(ns(n),1rl),pl(ns(m),1rl),m0"r"(y),t36)):is(ns(n),ns(m))
-t38:=<t37><shiftrls(m)><lsshiftr(m)><intshiftr(m)><shiftr(m)><shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>js:is(shiftr(n),shiftr(m))
-t39:=satz188b(n2(n),n2(m),y,satz188b(pl(n2(n),y),pl(n2(m),y),m0(1rl),t38)):is(n2(n),n2(m))
-t40:=isntirl(n1(n),n1(m),t39):is"n"(n1(n),n1(m))
-t41:=isinne(shiftl,n,m,t40):is"e"(1to(shiftl),n,m)
--shift
-js@injshiftseq:=[t:1to(shiftl)][u:1to(shiftl)][v:is"e"(1to(shiftl),<t>shiftseq,<u>shiftseq)]t41".shift"(t,u,v):injective(1to(shiftl),1to(shiftl),shiftseq)
-ins@[pri:proofsirrelevant(real,s)][ss:surjseq(s)]
-+*shift
-ss@[n:1to(shiftl)]
-t42:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ss:imseq(shiftr(n))
-[u:real][p:improp(shiftr(n),u)]
-t43:=ande1(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):and3(intrl(u),lessis(y,u),lessis(u,x))
-t44:=ande2"l.r"(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):is(shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s)
-ul1:=shiftl1(u,t43):1to(shiftl)
-t45:=<shiftinv1(u,t43)><shiftrls(ul1)><lsshiftr(ul1)><intshiftr(ul1)><shiftr(ul1)><t24(u,t43)><t23(u,t43)><t22(u,t43)><u>pri:is(<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1))
-t46:=shiftinv1(ns(ul1),t34(ul1)):is(ns(ul1),shiftr(<ul1>shiftseq))
-t47:=tr3is(real,shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1),shiftr(<ul1>shiftseq),t44,t45,t46):is(shiftr(n),shiftr(<ul1>shiftseq))
-t48:=iseshiftr(n,<ul1>shiftseq,t47):is"e"(1to(shiftl),n,<ul1>shiftseq)
-t49:=somei(1to(shiftl),[t:1to(shiftl)]is"e"(1to(shiftl),n,<t>shiftseq),ul1,t48):image(1to(shiftl),1to(shiftl),shiftseq,n)
-n@t50:=someapp(real,[t:real]improp(shiftr(n),t),t42,image(1to(shiftl),1to(shiftl),shiftseq,n),[t:real][u:improp(shiftr(n),t)]t49(t,u)):image(1to(shiftl),1to(shiftl),shiftseq,n)
--shift
-ss@surjshiftseq:=[t:1to(shiftl)]t50".shift"(t):surjective(1to(shiftl),1to(shiftl),shiftseq)
-pri@[ps:perm(s)]
-bijshiftseq:=andi(injective(1to(shiftl),1to(shiftl),shiftseq),surjective(1to(shiftl),1to(shiftl),shiftseq),injshiftseq(ande1(injseq(s),surjseq(s),ps)),surjshiftseq(ande2(injseq(s),surjseq(s),ps))):bijective(1to(shiftl),1to(shiftl),shiftseq)
-+c
-@complex:=pair1type(real):'type'
-cx:=complex:'type'
-[x:complex][y:complex]
-is:=is"e"(cx,x,y):'prop'
-nis:=not(is(x,y)):'prop'
-@[p:[t:complex]'prop']
-some:=some"l"(cx,p):'prop'
-all:=all"l"(cx,p):'prop'
-one:=one"e"(cx,p):'prop'
-@[a:real][b:real]
-pli:=pair1(real,a,b):complex
-x@re:=first1(real,x):real
-im:=second1(real,x):real
-b@reis:=first1is1(real,a,b):is"r"(re(pli(a,b)),a)
-isre:=first1is2(real,a,b):is"r"(a,re(pli(a,b)))
-imis:=second1is1(real,a,b):is"r"(im(pli(a,b)),b)
-isim:=second1is2(real,a,b):is"r"(b,im(pli(a,b)))
-x@pliis:=pair1is1(real,x):is(pli(re(x),im(x)),x)
-ispli:=pair1is2(real,x):is(x,pli(re(x),im(x)))
-y@[i:is(x,y)]
-iscere:=isf(cx,real,[t:cx]re(t),x,y,i):is"r"(re(x),re(y))
-isceim:=isf(cx,real,[t:cx]im(t),x,y,i):is"r"(im(x),im(y))
-b@[c:real][i:is"r"(a,b)]
-isrecx1:=isf(real,cx,[t:real]pli(t,c),a,b,i):is(pli(a,c),pli(b,c))
-isrecx2:=isf(real,cx,[t:real]pli(c,t),a,b,i):is(pli(c,a),pli(c,b))
-c@[d:real][i:is"r"(a,b)][j:is"r"(c,d)]
-isrecx12:=tris(cx,pli(a,c),pli(b,c),pli(b,d),isrecx1(a,b,c,i),isrecx2(c,d,b,j)):is(pli(a,c),pli(b,d))
-x@satz206:=refis(cx,x):is(x,x)
-y@[i:is(x,y)]
-satz207:=symis(cx,x,y,i):is(y,x)
-y@[z:complex][i:is(x,y)][j:is(y,z)]
-satz208:=tris(cx,x,y,z,i,j):is(x,z)
-@0c:=pli(0,0):complex
-1c:=pli(1rl,0):complex
-y@pl:=pli(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))):complex
-d@plis12a:=isrecx12(pl"r"(re(pli(a,b)),re(pli(c,d))),pl"r"(a,c),pl"r"(im(pli(a,b)),im(pli(c,d))),pl"r"(b,d),ispl12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ispl12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)))
-plis12b:=symis(cx,pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)),plis12a):is(pli(pl"r"(a,c),pl"r"(b,d)),pl(pli(a,b),pli(c,d)))
-x@[r:real][s:real]
-plis1a:=isrecx12(pl"r"(re(pli(r,s)),re(x)),pl"r"(r,re(x)),pl"r"(im(pli(r,s)),im(x)),pl"r"(s,im(x)),ispl1(re(pli(r,s)),r,re(x),reis(r,s)),ispl1(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))))
-plis1b:=symis(cx,pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))),plis1a):is(pli(pl"r"(r,re(x)),pl"r"(s,im(x))),pl(pli(r,s),x))
-plis2a:=isrecx12(pl"r"(re(x),re(pli(r,s))),pl"r"(re(x),r),pl"r"(im(x),im(pli(r,s))),pl"r"(im(x),s),ispl2(re(pli(r,s)),r,re(x),reis(r,s)),ispl2(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)))
-plis2b:=symis(cx,pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)),plis2a):is(pli(pl"r"(re(x),r),pl"r"(im(x),s)),pl(x,pli(r,s)))
-z@[i:is(x,y)]
-ispl1:=isf(cx,cx,[t:cx]pl(t,z),x,y,i):is(pl(x,z),pl(y,z))
-ispl2:=isf(cx,cx,[t:cx]pl(z,t),x,y,i):is(pl(z,x),pl(z,y))
-z@[u:complex][i:is(x,y)][j:is(z,u)]
-ispl12:=tris(cx,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
-y@satz209:=isrecx12(pl"r"(re(x),re(y)),pl"r"(re(y),re(x)),pl"r"(im(x),im(y)),pl"r"(im(y),im(x)),compl(re(x),re(y)),compl(im(x),im(y))):is(pl(x,y),pl(y,x))
-compl:=satz209:is(pl(x,y),pl(y,x))
-x@satz210:=tr3is(cx,pl(x,0c),pli(pl"r"(re(x),0),pl"r"(im(x),0)),pli(re(x),im(x)),x,plis2a(x,0,0),isrecx12(pl"r"(re(x),0),re(x),pl"r"(im(x),0),im(x),pl02(re(x),0,refis(real,0)),pl02(im(x),0,refis(real,0))),pliis(x)):is(pl(x,0c),x)
-satz210a:=symis(cx,pl(x,0c),x,satz210):is(x,pl(x,0c))
-satz210b:=tris(cx,pl(0c,x),pl(x,0c),x,compl(0c,x),satz210):is(pl(0c,x),x)
-satz210c:=symis(cx,pl(0c,x),x,satz210b):is(x,pl(0c,x))
-z@satz211:=tr3is(cx,pl(pl(x,y),z),pli(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(pl"r"(im(x),im(y)),im(z))),pli(pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(im(x),pl"r"(im(y),im(z)))),pl(x,pl(y,z)),plis1a(z,pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(pl"r"(im(x),im(y)),im(z)),pl"r"(im(x),pl"r"(im(y),im(z))),asspl1(re(x),re(y),re(z)),asspl1(im(x),im(y),im(z))),plis2b(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z)))):is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl1:=satz211:is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl2:=symis(cx,pl(pl(x,y),z),pl(x,pl(y,z)),asspl1):is(pl(x,pl(y,z)),pl(pl(x,y),z))
-y@[u:complex][i:is(pl(y,u),x)]
-+2212
-t1:=tris(real,pl"r"(re(y),re(u)),re(pl(y,u)),re(x),isre(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),iscere(pl(y,u),x,i)):is"r"(pl"r"(re(y),re(u)),re(x))
-t2:=tris(real,pl"r"(im(y),im(u)),im(pl(y,u)),im(x),isim(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),isceim(pl(y,u),x,i)):is"r"(pl"r"(im(y),im(u)),im(x))
-t3:=satz187d(re(x),re(y),re(u),t1):is"r"(re(u),mn(re(x),re(y)))
-t4:=satz187d(im(x),im(y),im(u),t2):is"r"(im(u),mn(im(x),im(y)))
--2212
-satz212a:=tris(cx,u,pli(re(u),im(u)),pli(mn(re(x),re(y)),mn(im(x),im(y))),ispli(u),isrecx12(re(u),mn(re(x),re(y)),im(u),mn(im(x),im(y)),t3".2212",t4".2212")):is(u,pli(mn(re(x),re(y)),mn(im(x),im(y))))
-y@satz212b:=tr3is(cx,pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),pli(pl"r"(re(y),mn(re(x),re(y))),pl"r"(im(y),mn(im(x),im(y)))),pli(re(x),im(x)),x,plis2a(y,mn(re(x),re(y)),mn(im(x),im(y))),isrecx12(pl"r"(re(y),mn(re(x),re(y))),re(x),pl"r"(im(y),mn(im(x),im(y))),im(x),satz187a(re(x),re(y)),satz187a(im(x),im(y))),pliis(x)):is(pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),x)
-satz212c:=somei(cx,[t:cx]is(pl(y,t),x),pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212b):some([t:complex]is(pl(y,t),x))
-satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212a(t,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
-%satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
-mn:=pli(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))):complex
-d@mnis12a:=isrecx12(mn"r"(re(pli(a,b)),re(pli(c,d))),mn"r"(a,c),mn"r"(im(pli(a,b)),im(pli(c,d))),mn"r"(b,d),ismn12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ismn12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)))
-mnis12b:=symis(cx,mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)),mnis12a):is(pli(mn"r"(a,c),mn"r"(b,d)),mn(pli(a,b),pli(c,d)))
-x@[r:real][s:real]
-mnis1a:=isrecx12(mn"r"(re(pli(r,s)),re(x)),mn"r"(r,re(x)),mn"r"(im(pli(r,s)),im(x)),mn"r"(s,im(x)),ismn1(re(pli(r,s)),r,re(x),reis(r,s)),ismn1(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))))
-mnis1b:=symis(cx,mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mnis1a):is(pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mn(pli(r,s),x))
-mnis2a:=isrecx12(mn"r"(re(x),re(pli(r,s))),mn"r"(re(x),r),mn"r"(im(x),im(pli(r,s))),mn"r"(im(x),s),ismn2(re(pli(r,s)),r,re(x),reis(r,s)),ismn2(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)))
-mnis2b:=symis(cx,mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)),mnis2a):is(pli(mn"r"(re(x),r),mn"r"(im(x),s)),mn(x,pli(r,s)))
-z@[i:is(x,y)]
-ismn1:=isf(cx,cx,[t:cx]mn(t,z),x,y,i):is(mn(x,z),mn(y,z))
-ismn2:=isf(cx,cx,[t:cx]mn(z,t),x,y,i):is(mn(z,x),mn(z,y))
-z@[u:complex][i:is(x,y)][j:is(z,u)]
-ismn12:=tris(cx,mn(x,z),mn(y,z),mn(y,u),ismn1(x,y,z,i),ismn2(z,u,y,j)):is(mn(x,z),mn(y,u))
-y@[u:complex][i:is(pl(y,u),x)]
-satz212d:=satz212a(u,i):is(u,mn(x,y))
-satz212e:=symis(cx,u,mn(x,y),satz212d):is(mn(x,y),u)
-u@[i:is(pl(u,y),x)]
-satz212f:=satz212d(tris(cx,pl(y,u),pl(u,y),x,compl(y,u),i)):is(u,mn(x,y))
-satz212g:=symis(cx,u,mn(x,y),satz212f):is(mn(x,y),u)
-y@satz212h:=satz212b:is(pl(y,mn(x,y)),x)
-[i:is(mn(x,y),0c)]
-+2213
-t1:=tr3is(real,mn"r"(re(x),re(y)),re(mn(x,y)),re(0c),0,isre(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),iscere(mn(x,y),0c,i),reis(0,0)):is"r"(mn"r"(re(x),re(y)),0)
-t2:=tr3is(real,mn"r"(im(x),im(y)),im(mn(x,y)),im(0c),0,isim(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),isceim(mn(x,y),0c,i),imis(0,0)):is"r"(mn"r"(im(x),im(y)),0)
-t3:=satz182b(re(x),re(y),t1):is"r"(re(x),re(y))
-t4:=satz182b(im(x),im(y),t2):is"r"(im(x),im(y))
--2213
-satz213a:=tr3is(cx,x,pli(re(x),im(x)),pli(re(y),im(y)),y,ispli(x),isrecx12(re(x),re(y),im(x),im(y),t3".2213",t4".2213"),pliis(y)):is(x,y)
-y@[i:is(x,y)]
-+*2213
-i@t5:=satz182e(re(x),re(y),iscere(x,y,i)):is"r"(mn"r"(re(x),re(y)),0)
-t6:=satz182e(im(x),im(y),isceim(x,y,i)):is"r"(mn"r"(im(x),im(y)),0)
--2213
-i@satz213b:=isrecx12(mn"r"(re(x),re(y)),0,mn"r"(im(x),im(y)),0,t5".2213",t6".2213"):is(mn(x,y),0c)
-x@m0:=mn(0c,x):complex
-satz214:=isrecx12(mn"r"(re(0c),re(x)),m0"r"(re(x)),mn"r"(im(0c),im(x)),m0"r"(im(x)),pl01(re(0c),m0"r"(re(x)),reis(0,0)),pl01(im(0c),m0"r"(im(x)),imis(0,0))):is(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))))
-satz214a:=symis(cx,m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214):is(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x))
-b@m0isa:=tris(cx,m0(pli(a,b)),pli(m0"r"(re(pli(a,b))),m0"r"(im(pli(a,b)))),pli(m0"r"(a),m0"r"(b)),satz214(pli(a,b)),isrecx12(m0"r"(re(pli(a,b))),m0"r"(a),m0"r"(im(pli(a,b))),m0"r"(b),ism0(re(pli(a,b)),a,reis(a,b)),ism0(im(pli(a,b)),b,imis(a,b)))):is(m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)))
-m0isb:=symis(cx,m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)),m0isa):is(pli(m0"r"(a),m0"r"(b)),m0(pli(a,b)))
-y@[i:is(x,y)]
-ism0:=isf(cx,cx,[t:cx]m0(t),x,y,i):is(m0(x),m0(y))
-x@satz215:=tr4is(cx,m0(m0(x)),m0(pli(m0"r"(re(x)),m0"r"(im(x)))),pli(m0"r"(m0"r"(re(x))),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,ism0(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214),m0isa(m0"r"(re(x)),m0"r"(im(x))),isrecx12(m0"r"(m0"r"(re(x))),re(x),m0"r"(m0"r"(im(x))),im(x),satz177(re(x)),satz177(im(x))),pliis(x)):is(m0(m0(x)),x)
-satz215a:=symis(cx,m0(m0(x)),x,satz215):is(x,m0(m0(x)))
-y@[i:is(x,m0(y))]
-satz215b:=tris(cx,m0(x),m0(m0(y)),y,ism0(x,m0(y),i),satz215(y)):is(m0(x),y)
-satz215c:=symis(cx,m0(x),y,satz215b):is(y,m0(x))
-y@[i:is(m0(x),y)]
-satz215d:=satz215c(y,x,symis(cx,m0(x),y,i)):is(x,m0(y))
-satz215e:=symis(cx,x,m0(y),satz215d):is(m0(y),x)
-x@satz216:=tr3is(cx,pl(x,m0(x)),pl(x,pli(m0"r"(re(x)),m0"r"(im(x)))),pli(pl"r"(re(x),m0"r"(re(x))),pl"r"(im(x),m0"r"(im(x)))),0c,ispl2(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),x,satz214(x)),plis2a(x,m0"r"(re(x)),m0"r"(im(x))),isrecx12(pl"r"(re(x),m0"r"(re(x))),0,pl"r"(im(x),m0"r"(im(x))),0,satz179(re(x)),satz179(im(x)))):is(pl(x,m0(x)),0c)
-+2216
-anders:=satz212h(0c,x):is(pl(x,m0(x)),0c)
--2216
-satz216a:=tris(cx,pl(m0(x),x),pl(x,m0(x)),0c,compl(m0(x),x),satz216):is(pl(m0(x),x),0c)
-y@satz217:=tr4is(cx,m0(pl(x,y)),pli(m0"r"(pl"r"(re(x),re(y))),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(m0"r"(re(x)),m0"r"(re(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(pli(m0"r"(re(x)),m0"r"(im(x))),pli(m0"r"(re(y)),m0"r"(im(y)))),pl(m0(x),m0(y)),m0isa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(m0"r"(pl"r"(re(x),re(y))),pl"r"(m0"r"(re(x)),m0"r"(re(y))),m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),satz180(re(x),re(y)),satz180(im(x),im(y))),plis12b(m0"r"(re(x)),m0"r"(im(x)),m0"r"(re(y)),m0"r"(im(y))),ispl12(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),satz214a(x),satz214a(y))):is(m0(pl(x,y)),pl(m0(x),m0(y)))
-satz217a:=symis(cx,m0(pl(x,y)),pl(m0(x),m0(y)),satz217):is(pl(m0(x),m0(y)),m0(pl(x,y)))
-satz218:=tris(cx,mn(x,y),pl(x,pli(m0"r"(re(y)),m0"r"(im(y)))),pl(x,m0(y)),plis2b(x,m0"r"(re(y)),m0"r"(im(y))),ispl2(pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),x,satz214a(y))):is(mn(x,y),pl(x,m0(y)))
-satz218a:=symis(cx,mn(x,y),pl(x,m0(y)),satz218):is(pl(x,m0(y)),mn(x,y))
-+2219
-t1:=tr3is(cx,m0(mn(x,y)),m0(pl(x,m0(y))),pl(m0(x),m0(m0(y))),pl(m0(x),y),ism0(mn(x,y),pl(x,m0(y)),satz218),satz217(x,m0(y)),ispl2(m0(m0(y)),y,m0(x),satz215(y))):is(m0(mn(x,y)),pl(m0(x),y))
--2219
-satz219:=tr3is(cx,m0(mn(x,y)),pl(m0(x),y),pl(y,m0(x)),mn(y,x),t1".2219",compl(m0(x),y),satz218a(y,x)):is(m0(mn(x,y)),mn(y,x))
-satz219a:=symis(cx,m0(mn(y,x)),mn(x,y),satz219(y,x)):is(mn(x,y),m0(mn(y,x)))
-ts:=pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))):complex
-rets:=mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))):real
-imts:=pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))):real
-+v3
-d@t1:=ismn12"r"(ts"r"(re(pli(a,b)),re(pli(c,d))),ts"r"(a,c),ts"r"(im(pli(a,b)),im(pli(c,d))),ts"r"(b,d),ists12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ists12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is"r"(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)))
-t2:=ispl12"r"(ts"r"(re(pli(a,b)),im(pli(c,d))),ts"r"(a,d),ts"r"(im(pli(a,b)),re(pli(c,d))),ts"r"(b,c),ists12(re(pli(a,b)),a,im(pli(c,d)),d,reis(a,b),imis(c,d)),ists12(im(pli(a,b)),b,re(pli(c,d)),c,imis(a,b),reis(c,d))):is"r"(imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)))
--v3
-d@tsis12a:=isrecx12(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)),imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)),t1".v3",t2".v3"):is(ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))))
-tsis12b:=symis(cx,ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),tsis12a):is(pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),ts(pli(a,b),pli(c,d)))
-x@[r:real][s:real]
-+*v3
-s@t3:=ismn12"r"(ts"r"(re(pli(r,s)),re(x)),ts"r"(r,re(x)),ts"r"(im(pli(r,s)),im(x)),ts"r"(s,im(x)),ists1(re(pli(r,s)),r,re(x),reis(r,s)),ists1(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))))
-t4:=ispl12"r"(ts"r"(re(pli(r,s)),im(x)),ts"r"(r,im(x)),ts"r"(im(pli(r,s)),re(x)),ts"r"(s,re(x)),ists1(re(pli(r,s)),r,im(x),reis(r,s)),ists1(im(pli(r,s)),s,re(x),imis(r,s))):is"r"(imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))))
--v3
-s@tsis1a:=isrecx12(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))),t3".v3",t4".v3"):is(ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))))
-tsis1b:=symis(cx,ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),tsis1a):is(pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),ts(pli(r,s),x))
-+*v3
-s@t5:=ismn12"r"(ts"r"(re(x),re(pli(r,s))),ts"r"(re(x),r),ts"r"(im(x),im(pli(r,s))),ts"r"(im(x),s),ists2(re(pli(r,s)),r,re(x),reis(r,s)),ists2(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)))
-t6:=ispl12"r"(ts"r"(re(x),im(pli(r,s))),ts"r"(re(x),s),ts"r"(im(x),re(pli(r,s))),ts"r"(im(x),r),ists2(im(pli(r,s)),s,re(x),imis(r,s)),ists2(re(pli(r,s)),r,im(x),reis(r,s))):is"r"(imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)))
--v3
-s@tsis2a:=isrecx12(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)),t5".v3",t6".v3"):is(ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))))
-tsis2b:=symis(cx,ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),tsis2a):is(pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),ts(x,pli(r,s)))
-z@[i:is(x,y)]
-ists1:=isf(cx,cx,[t:cx]ts(t,z),x,y,i):is(ts(x,z),ts(y,z))
-ists2:=isf(cx,cx,[t:cx]ts(z,t),x,y,i):is(ts(z,x),ts(z,y))
-z@[u:complex][i:is(x,y)][j:is(z,u)]
-ists12:=tris(cx,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
-+3220
-y@t1:=ismn12"r"(ts"r"(re(x),re(y)),ts"r"(re(y),re(x)),ts"r"(im(x),im(y)),ts"r"(im(y),im(x)),comts(re(x),re(y)),comts(im(x),im(y))):is"r"(rets(x,y),rets(y,x))
-t2:=tris(real,imts(x,y),pl"r"(ts"r"(im(x),re(y)),ts"r"(re(x),im(y))),imts(y,x),compl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(ts"r"(im(x),re(y)),ts"r"(re(y),im(x)),ts"r"(re(x),im(y)),ts"r"(im(y),re(x)),comts(im(x),re(y)),comts(re(x),im(y)))):is"r"(imts(x,y),imts(y,x))
--3220
-y@satz220:=isrecx12(rets(x,y),rets(y,x),imts(x,y),imts(y,x),t1".3220",t2".3220"):is(ts(x,y),ts(y,x))
-comts:=satz220:is(ts(x,y),ts(y,x))
-x@[i:is(x,0c)]
-lemma1:=tris(real,re(x),re(0c),0,iscere(x,0c,i),reis(0,0)):is"r"(re(x),0)
-lemma2:=tris(real,im(x),im(0c),0,isceim(x,0c,i),imis(0,0)):is"r"(im(x),0)
-x@mod2:=pl"r"(ts"r"(re(x),re(x)),ts"r"(im(x),im(x))):real
-i@lemma3:=tris(real,mod2,pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),0,ts01(re(x),re(x),lemma1),ts01(im(x),im(x),lemma2)),pl01(0,0,refis(real,0))):is"r"(mod2(x),0)
-x@[n:nis(x,0c)]
-+*v3
-x@re2:=ts"r"(re(x),re(x)):real
-im2:=ts"r"(im(x),im(x)):real
-n@[i:is"r"(re(x),0)]
-t7:=th3"l.imp"(is"r"(im(x),0),is(x,0c),n,[t:is"r"(im(x),0)]tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,i,t))):nis"r"(im(x),0)
-t8:=ispos(im2,mod2,symis(real,mod2,im2,pl01(re2,im2,ts01(re(x),re(x),i))),possq(im(x),t7)):pos(mod2)
-n@[o:nis"r"(re(x),0)][i:is"r"(im(x),0)]
-t9:=ispos(re2,mod2,symis(real,mod2,re2,pl02(re2,im2,ts01(im(x),im(x),i))),possq(re(x),o)):pos(mod2)
-o@[p:nis"r"(im(x),0)]
-t10:=pospl(re2,im2,possq(re(x),o),possq(im(x),p)):pos(mod2)
-o@t11:=th1"l.imp"(is"r"(im(x),0),pos(mod2),[t:is"r"(im(x),0)]t9(t),[t:nis"r"(im(x),0)]t10(t)):pos(mod2)
--v3
-n@lemma4:=th1"l.imp"(is"r"(re(x),0),pos(mod2),[t:is"r"(re(x),0)]t8".v3"(t),[t:nis"r"(re(x),0)]t11".v3"(t)):pos(mod2(x))
-x@lemma5:=th1"l.imp"(is(x,0c),not(neg(mod2)),[t:is(x,0c)]0notn(mod2,lemma3(t)),[t:nis(x,0c)]pnotn(mod2,lemma4(t))):not(neg(mod2(x)))
-y@[i:is(x,0c)]
-+3221
-t1:=lemma1(x,i):is"r"(re(x),0)
-t2:=lemma2(x,i):is"r"(im(x),0)
-t3:=tris(real,rets(x,y),mn"r"(0,0),0,ismn12"r"(ts"r"(re(x),re(y)),0,ts"r"(im(x),im(y)),0,ts01(re(x),re(y),t1),ts01(im(x),im(y),t2)),satz187c(0,0,0,pl02(0,0,refis(real,0)))):is"r"(rets(x,y),0)
-t4:=tris(real,imts(x,y),pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),im(y)),0,ts"r"(im(x),re(y)),0,ts01(re(x),im(y),t1),ts01(im(x),re(y),t2)),pl02(0,0,refis(real,0))):is"r"(imts(x,y),0)
--3221
-satz221a:=isrecx12(rets(x,y),0,imts(x,y),0,t3".3221",t4".3221"):is(ts(x,y),0c)
-y@[i:is(y,0c)]
-satz221b:=tris(cx,ts(x,y),ts(y,x),0c,comts(x,y),satz221a(y,x,i)):is(ts(x,y),0c)
-y@[i:is(ts(x,y),0c)]
-+*3221
-i@[n:nis(y,0c)]
-t5:=lemma4(y,n):pos(mod2(y))
-t6:=tris1(real,rets(x,y),0,re(ts(x,y)),reis(rets(x,y),imts(x,y)),lemma1(ts(x,y),i)):is"r"(rets(x,y),0)
-t7:=tris1(real,imts(x,y),0,im(ts(x,y)),imis(rets(x,y),imts(x,y)),lemma2(ts(x,y),i)):is"r"(imts(x,y),0)
-t8:=tris(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(0,0),0,ispl12"r"(ts"r"(rets(x,y),re(y)),0,ts"r"(imts(x,y),im(y)),0,ts01(rets(x,y),re(y),t6),ts01(imts(x,y),im(y),t7)),pl02(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),0)
-y@ii1r:=ts"r"(ts"r"(im(x),im(y)),re(y)):real
-i1ir:=ts"r"(im(x),ts"r"(im(y),re(y))):real
-ir1i:=ts"r"(ts"r"(im(x),re(y)),im(y)):real
-i1ri:=ts"r"(im(x),ts"r"(re(y),im(y))):real
-rr1r:=ts"r"(ts"r"(re(x),re(y)),re(y)):real
-r1rr:=ts"r"(re(x),ts"r"(re(y),re(y))):real
-ri1r:=ts"r"(ts"r"(re(x),im(y)),re(y)):real
-r1ir:=ts"r"(re(x),ts"r"(im(y),re(y))):real
-ri1i:=ts"r"(ts"r"(re(x),im(y)),im(y)):real
-r1ii:=ts"r"(re(x),ts"r"(im(y),im(y))):real
-n@t9:=tris(real,ii1r,i1ir,i1ri,assts1(im(x),im(y),re(y)),ists2"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),im(x),comts"r"(im(y),re(y)))):is"r"(ii1r,i1ri)
-t10:=tris(real,ts"r"(rets(x,y),re(y)),mn"r"(rr1r,ii1r),mn"r"(r1rr,i1ri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(y)),ismn12"r"(rr1r,r1rr,ii1r,i1ri,assts1(re(x),re(y),re(y)),t9)):is"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri))
-t11:=tr3is(real,ts"r"(imts(x,y),im(y)),pl"r"(ri1i,ir1i),pl"r"(r1ii,i1ri),pl"r"(i1ri,r1ii),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(y)),ispl12"r"(ri1i,r1ii,ir1i,i1ri,assts1(re(x),im(y),im(y)),assts1(im(x),re(y),im(y))),compl"r"(r1ii,i1ri)):is"r"(ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii))
-t12:=tr4is(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(mn"r"(r1rr,i1ri),pl"r"(i1ri,r1ii)),pl"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1ii),pl"r"(r1rr,r1ii),ts"r"(re(x),mod2(y)),ispl12"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri),ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii),t10,t11),asspl2"r"(mn"r"(r1rr,i1ri),i1ri,r1ii),ispl1"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1rr,r1ii,plmn(r1rr,i1ri)),distpt2(re(x),ts"r"(re(y),re(y)),ts"r"(im(y),im(y)))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),ts"r"(re(x),mod2(y)))
-t13:=tris1(real,ts"r"(re(x),mod2(y)),0,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),t12,t8):is"r"(ts"r"(re(x),mod2(y)),0)
-t14:=ore1(is"r"(re(x),0),is"r"(mod2(y),0),satz192c(re(x),mod2(y),t13),pnot0(mod2(y),t5)):is"r"(re(x),0)
-t15:=tris1(real,ts"r"(im(x),im(y)),0,ts"r"(re(x),re(y)),satz182b(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),t6),ts01(re(x),re(y),t14)):is"r"(ts"r"(im(x),im(y)),0)
-t16:=tris1(real,ts"r"(im(x),re(y)),0,imts(x,y),pl01(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),ts01(re(x),im(y),t14)),t7):is"r"(ts"r"(im(x),re(y)),0)
-[j:is"r"(re(y),0)]
-t17:=t7"c.v3"(y,n,j):nis"r"(im(y),0)
-t18:=ore1(is"r"(im(x),0),is"r"(im(y),0),satz192c(im(x),im(y),t15),t17):is"r"(im(x),0)
-n@[o:nis"r"(re(y),0)]
-t19:=ore1(is"r"(im(x),0),is"r"(re(y),0),satz192c(im(x),re(y),t16),o):is"r"(im(x),0)
-n@t20:=th1"l.imp"(is"r"(re(y),0),is"r"(im(x),0),[t:is"r"(re(y),0)]t18(t),[t:nis"r"(re(y),0)]t19(t)):is"r"(im(x),0)
-t21:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t14,t20)):is(x,0c)
--3221
-i@satz221c:=th2"l.or"(is(x,0c),is(y,0c),[t:nis(y,0c)]t21".3221"(t)):or(is(x,0c),is(y,0c))
-y@[n:nis(x,0c)][o:nis(y,0c)]
-satz221d:=th3"l.imp"(is(ts(x,y),0c),or(is(x,0c),is(y,0c)),th3"l.or"(is(x,0c),is(y,0c),n,o),[t:is(ts(x,y),0c)]satz221c(t)):nis(ts(x,y),0c)
-+3222
-x@t1:=tris(real,mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),mn"r"(re(x),0),re(x),ismn12"r"(ts"r"(re(x),1rl),re(x),ts"r"(im(x),0),0,satz195(re(x)),ts02(im(x),0,refis(real,0))),pl02(re(x),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x))
-t2:=tris(real,pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),pl"r"(0,im(x)),im(x),ispl12"r"(ts"r"(re(x),0),0,ts"r"(im(x),1rl),im(x),ts02(re(x),0,refis(real,0)),satz195(im(x))),pl01(0,im(x),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x))
--3222
-x@satz222:=tr3is(cx,ts(x,1c),pli(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl))),pli(re(x),im(x)),x,tsis2a(x,1rl,0),isrecx12(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x),t1".3222",t2".3222"),pliis(x)):is(ts(x,1c),x)
-satz222a:=symis(cx,ts(x,1c),x,satz222):is(x,ts(x,1c))
-satz222b:=tris(cx,ts(1c,x),ts(x,1c),x,comts(1c,x),satz222):is(ts(1c,x),x)
-satz222c:=symis(cx,ts(1c,x),x,satz222b):is(x,ts(1c,x))
-+3223
-t1:=tris(real,mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),mn"r"(m0"r"(re(x)),0),m0"r"(re(x)),ismn12"r"(ts"r"(re(x),m0"r"(1rl)),m0"r"(re(x)),ts"r"(im(x),m0"r"(0)),0,tris(real,ts"r"(re(x),m0"r"(1rl)),m0"r"(ts"r"(re(x),1rl)),m0"r"(re(x)),satz197b(re(x),1rl),ism0"r"(ts"r"(re(x),1rl),re(x),satz195(re(x)))),ts02(im(x),m0"r"(0),satz176b(0,refis(real,0)))),pl02(m0"r"(re(x)),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)))
-t2:=tris(real,pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),pl"r"(0,m0"r"(im(x))),m0"r"(im(x)),ispl12"r"(ts"r"(re(x),m0"r"(0)),0,ts"r"(im(x),m0"r"(1rl)),m0"r"(im(x)),ts02(re(x),m0"r"(0),satz176b(0,refis(real,0))),tris(real,ts"r"(im(x),m0"r"(1rl)),m0"r"(ts"r"(im(x),1rl)),m0"r"(im(x)),satz197b(im(x),1rl),ism0"r"(ts"r"(im(x),1rl),im(x),satz195(im(x))))),pl01(0,m0"r"(im(x)),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)))
--3223
-satz223:=tr4is(cx,ts(x,m0(1c)),ts(x,pli(m0"r"(1rl),m0"r"(0))),pli(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl)))),pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),ists2(m0(1c),pli(m0"r"(1rl),m0"r"(0)),x,m0isa(1rl,0)),tsis2a(x,m0"r"(1rl),m0"r"(0)),isrecx12(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)),t1".3223",t2".3223"),satz214a(x)):is(ts(x,m0(1c)),m0(x))
-satz223a:=symis(cx,ts(x,m0(1c)),m0(x),satz223):is(m0(x),ts(x,m0(1c)))
-satz223b:=tris(cx,ts(m0(1c),x),ts(x,m0(1c)),m0(x),comts(m0(1c),x),satz223):is(ts(m0(1c),x),m0(x))
-satz223c:=symis(cx,ts(m0(1c),x),m0(x),satz223b):is(m0(x),ts(m0(1c),x))
-+3224
-y@rxry:=ts"r"(re(x),re(y)):real
-ixiy:=ts"r"(im(x),im(y)):real
-rxiy:=ts"r"(re(x),im(y)):real
-ixry:=ts"r"(im(x),re(y)):real
-t1:=tr4is(real,mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),mn"r"(m0"r"(rxry),m0"r"(ixiy)),pl"r"(m0"r"(rxry),ixiy),mn"r"(ixiy,rxry),m0"r"(mn"r"(rxry,ixiy)),ismn12"r"(ts"r"(m0"r"(re(x)),re(y)),m0"r"(rxry),ts"r"(m0"r"(im(x)),im(y)),m0"r"(ixiy),satz197a(re(x),re(y)),satz197a(im(x),im(y))),ispl2"r"(m0"r"(m0"r"(ixiy)),ixiy,m0"r"(rxry),satz177(ixiy)),compl"r"(m0"r"(rxry),ixiy),satz181a(ixiy,rxry)):is"r"(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(rxry,ixiy)))
-t2:=tris(real,pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),mn"r"(m0"r"(rxiy),ixry),m0"r"(pl"r"(rxiy,ixry)),ispl12"r"(ts"r"(m0"r"(re(x)),im(y)),m0"r"(rxiy),ts"r"(m0"r"(im(x)),re(y)),m0"r"(ixry),satz197a(re(x),im(y)),satz197a(im(x),re(y))),satz180a(rxiy,ixry)):is"r"(pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(rxiy,ixry)))
--3224
-y@satz224a:=tr4is(cx,ts(m0(x),y),ts(pli(m0"r"(re(x)),m0"r"(im(x))),y),pli(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y)))),pli(m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))),m0(ts(x,y)),ists1(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),y,satz214(x)),tsis1a(y,m0"r"(re(x)),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))),t1".3224",t2".3224"),m0isb(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))):is(ts(m0(x),y),m0(ts(x,y)))
-satz224b:=tr3is(cx,ts(x,m0(y)),ts(m0(y),x),m0(ts(y,x)),m0(ts(x,y)),comts(x,m0(y)),satz224a(y,x),ism0(ts(y,x),ts(x,y),comts(y,x))):is(ts(x,m0(y)),m0(ts(x,y)))
-satz224c:=tris2(cx,ts(m0(x),y),ts(x,m0(y)),m0(ts(x,y)),satz224a,satz224b):is(ts(m0(x),y),ts(x,m0(y)))
-satz224d:=symis(cx,ts(m0(x),y),ts(x,m0(y)),satz224c):is(ts(x,m0(y)),ts(m0(x),y))
-satz224e:=symis(cx,ts(m0(x),y),m0(ts(x,y)),satz224a):is(m0(ts(x,y)),ts(m0(x),y))
-satz224f:=symis(cx,ts(x,m0(y)),m0(ts(x,y)),satz224b):is(m0(ts(x,y)),ts(x,m0(y)))
-satz225:=tris(cx,ts(m0(x),m0(y)),ts(x,m0(m0(y))),ts(x,y),satz224c(x,m0(y)),ists2(m0(m0(y)),y,x,satz215(y))):is(ts(m0(x),m0(y)),ts(x,y))
-satz225a:=symis(cx,ts(m0(x),m0(y)),ts(x,y),satz225):is(ts(x,y),ts(m0(x),m0(y)))
-+3226
-z@rrr:=ts"r"(ts"r"(re(x),re(y)),re(z)):real
-iir:=ts"r"(ts"r"(im(x),im(y)),re(z)):real
-rii:=ts"r"(ts"r"(re(x),im(y)),im(z)):real
-iri:=ts"r"(ts"r"(im(x),re(y)),im(z)):real
-rri:=ts"r"(ts"r"(re(x),re(y)),im(z)):real
-iii:=ts"r"(ts"r"(im(x),im(y)),im(z)):real
-rir:=ts"r"(ts"r"(re(x),im(y)),re(z)):real
-irr:=ts"r"(ts"r"(im(x),re(y)),re(z)):real
-t1:=tr3is(real,mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(mn"r"(rrr,iir),pl"r"(rii,iri)),pl"r"(rrr,pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri)))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),ismn12"r"(ts"r"(rets(x,y),re(z)),mn"r"(rrr,iir),ts"r"(imts(x,y),im(z)),pl"r"(rii,iri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(z))),asspl1"r"(rrr,m0"r"(iir),m0"r"(pl"r"(rii,iri))),ispl2"r"(pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri))),m0"r"(pl"r"(iir,pl"r"(rii,iri))),rrr,satz180a(iir,pl"r"(rii,iri)))):is"r"(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))))
-t2:=tr3is(real,pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),pl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),pl"r"(pl"r"(rir,irr),mn"r"(rri,iii)),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),ispl12"r"(ts"r"(rets(x,y),im(z)),mn"r"(rri,iii),ts"r"(imts(x,y),re(z)),pl"r"(rir,irr),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),im(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),re(z))),compl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),asspl2"r"(pl"r"(rir,irr),rri,m0"r"(iii))):is"r"(pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii))
-t3:=tris(cx,ts(ts(x,y),z),pli(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z)))),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),tsis1a(z,rets(x,y),imts(x,y)),isrecx12(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),t1,t2)):is(ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)))
-c@t4:=tris(real,ts"r"(ts"r"(a,b),c),ts"r"(a,ts"r"(b,c)),ts"r"(ts"r"(b,c),a),assts1(a,b,c),comts"r"(a,ts"r"(b,c))):is"r"(ts"r"(ts"r"(a,b),c),ts"r"(ts"r"(b,c),a))
-t5:=tris(real,pl"r"(pl"r"(a,b),c),pl"r"(c,pl"r"(a,b)),pl"r"(pl"r"(c,a),b),compl"r"(pl"r"(a,b),c),asspl2"r"(c,a,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(c,a),b))
-t6:=tris(real,pl"r"(a,pl"r"(b,c)),pl"r"(pl"r"(b,c),a),pl"r"(b,pl"r"(c,a)),compl"r"(a,pl"r"(b,c)),asspl1"r"(b,c,a)):is"r"(pl"r"(a,pl"r"(b,c)),pl"r"(b,pl"r"(c,a)))
-z@rrr1:=rrr(y,z,x):real
-iir1:=iir(y,z,x):real
-rii1:=rii(y,z,x):real
-iri1:=iri(y,z,x):real
-rri1:=rri(y,z,x):real
-iii1:=iii(y,z,x):real
-rir1:=rir(y,z,x):real
-irr1:=irr(y,z,x):real
-t7:=tris(real,pl"r"(iir,pl"r"(rii,iri)),pl"r"(rii,pl"r"(iri,iir)),pl"r"(iir1,pl"r"(rii1,iri1)),t6(iir,rii,iri),ispl12"r"(rii,iir1,pl"r"(iri,iir),pl"r"(rii1,iri1),t4(re(x),im(y),im(z)),ispl12"r"(iri,rii1,iir,iri1,t4(im(x),re(y),im(z)),t4(im(x),im(y),re(z))))):is"r"(pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)))
-t8:=tris(real,pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rri,rir),irr),pl"r"(pl"r"(rir1,irr1),rri1),t5(rir,irr,rri),ispl12"r"(pl"r"(rri,rir),pl"r"(rir1,irr1),irr,rri1,ispl12"r"(rri,rir1,rir,irr1,t4(re(x),re(y),im(z)),t4(re(x),im(y),re(z))),t4(im(x),re(y),re(z)))):is"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1))
-t9:=ismn12"r"(rrr,rrr1,pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)),t4(re(x),re(y),re(z)),t7):is"r"(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))))
-t10:=ismn12"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1),iii,iii1,t8,t4(im(x),im(y),im(z))):is"r"(mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1))
-t11:=tris(cx,ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t3,isrecx12(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1),t9,t10)):is(ts(ts(x,y),z),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
-t12:=tris(cx,ts(x,ts(y,z)),ts(ts(y,z),x),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),comts(x,ts(y,z)),t3(y,z,x)):is(ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
-t13:=tris2(cx,ts(ts(x,y),z),ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t11,t12):is(ts(ts(x,y),z),ts(x,ts(y,z)))
--3226
-z@satz226:=t13".3226":is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts1:=satz226:is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts2:=symis(cx,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
-+3227
-c@t1:=tr3is(real,pl"r"(pl"r"(a,b),c),pl"r"(a,pl"r"(b,c)),pl"r"(a,pl"r"(c,b)),pl"r"(pl"r"(a,c),b),asspl1"r"(a,b,c),ispl2"r"(pl"r"(b,c),pl"r"(c,b),a,compl"r"(b,c)),asspl2"r"(a,c,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b))
-d@t2:=tr3is(real,pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(pl"r"(a,b),c),d),pl"r"(pl"r"(pl"r"(a,c),b),d),pl"r"(pl"r"(a,c),pl"r"(b,d)),asspl2"r"(pl"r"(a,b),c,d),ispl1"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b),d,t1),asspl1"r"(pl"r"(a,c),b,d)):is"r"(pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,c),pl"r"(b,d)))
-t3:=tris(real,mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,b),pl"r"(m0"r"(c),m0"r"(d))),pl"r"(mn"r"(a,c),mn"r"(b,d)),ispl2"r"(m0"r"(pl"r"(c,d)),pl"r"(m0"r"(c),m0"r"(d)),pl"r"(a,b),satz180(c,d)),t2(a,b,m0"r"(c),m0"r"(d))):is"r"(mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(mn"r"(a,c),mn"r"(b,d)))
-z@t4:=tris(real,mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),mn"r"(pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))),pl"r"(rets(x,y),rets(x,z)),ismn12"r"(ts"r"(re(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),ts"r"(im(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z))),disttp2(re(x),re(y),re(z)),disttp2(im(x),im(y),im(z))),t3(ts"r"(re(x),re(y)),ts"r"(re(x),re(z)),ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))):is"r"(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)))
-t5:=tris(real,pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))),pl"r"(imts(x,y),imts(x,z)),ispl12"r"(ts"r"(re(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z))),disttp2(re(x),im(y),im(z)),disttp2(im(x),re(y),re(z))),t2(ts"r"(re(x),im(y)),ts"r"(re(x),im(z)),ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))):is"r"(pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)))
-t6:=tr3is(cx,ts(x,pl(y,z)),pli(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))))),pli(pl"r"(rets(x,y),rets(x,z)),pl"r"(imts(x,y),imts(x,z))),pl(ts(x,y),ts(x,z)),tsis2a(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z))),isrecx12(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)),t4,t5),plis12b(rets(x,y),imts(x,y),rets(x,z),imts(x,z))):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
--3227
-satz227:=t6".3227":is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-disttp1:=tr3is(cx,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz227(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
-disttp2:=satz227:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-distpt1:=symis(cx,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
-distpt2:=symis(cx,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
-satz228:=tr4is(cx,ts(x,mn(y,z)),ts(x,pl(y,m0(z))),pl(ts(x,y),ts(x,m0(z))),pl(ts(x,y),m0(ts(x,z))),mn(ts(x,y),ts(x,z)),ists2(mn(y,z),pl(y,m0(z)),x,satz218(y,z)),disttp2(x,y,m0(z)),ispl2(ts(x,m0(z)),m0(ts(x,z)),ts(x,y),satz224b(x,z)),satz218a(ts(x,y),ts(x,z))):is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
-disttm1:=tr3is(cx,ts(mn(x,y),z),ts(z,mn(x,y)),mn(ts(z,x),ts(z,y)),mn(ts(x,z),ts(y,z)),comts(mn(x,y),z),satz228(z,x,y),ismn12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(mn(x,y),z),mn(ts(x,z),ts(y,z)))
-disttm2:=satz228:is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
-distmt1:=symis(cx,ts(mn(x,y),z),mn(ts(x,z),ts(y,z)),disttm1):is(mn(ts(x,z),ts(y,z)),ts(mn(x,y),z))
-distmt2:=symis(cx,ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)),disttm2):is(mn(ts(x,y),ts(x,z)),ts(x,mn(y,z)))
-y@[n:nis(y,0c)][u1:complex][u2:complex][i:is(ts(y,u1),x)][j:is(ts(y,u2),x)]
-+3229
-t1:=tris2(cx,ts(y,u1),ts(y,u2),x,i,j):is(ts(y,u1),ts(y,u2))
-t2:=tris(cx,ts(y,mn(u1,u2)),mn(ts(y,u1),ts(y,u2)),0c,disttm2(y,u1,u2),satz213b(ts(y,u1),ts(y,u2),t1)):is(ts(y,mn(u1,u2)),0c)
-t3:=ore2(is(y,0c),is(mn(u1,u2),0c),satz221c(y,mn(u1,u2),t2),n):is(mn(u1,u2),0c)
--3229
-satz229b:=satz213a(u1,u2,t3".3229"):is(u1,u2)
-+*3229
-n@t4:=pnot0(mod2(y),lemma4(y,n)):nis"r"(mod2(y),0)
-u:=ts(pli(ov(re(y),mod2(y),t4),m0"r"(ov(im(y),mod2(y),t4))),x):complex
-[v:real]
-dd:=ov(v,mod2(y),t4):real
-n@t5:=tr3is(real,m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),m0"r"(m0"r"(ts"r"(im(y),dd(im(y))))),ts"r"(im(y),dd(im(y))),dd(ts"r"(im(y),im(y))),ism0"r"(ts"r"(im(y),m0"r"(dd(im(y)))),m0"r"(ts"r"(im(y),dd(im(y)))),satz197b(im(y),dd(im(y)))),satz177(ts"r"(im(y),dd(im(y)))),lemma6(im(y),im(y),mod2(y),t4)):is"r"(m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))))
-t6:=tr3is(real,mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(dd(ts"r"(re(y),re(y))),dd(ts"r"(im(y),im(y)))),dd(mod2(y)),1rl,ispl12"r"(ts"r"(re(y),dd(re(y))),dd(ts"r"(re(y),re(y))),m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))),lemma6(re(y),re(y),mod2(y),t4),t5),lemma7(ts"r"(re(y),re(y)),ts"r"(im(y),im(y)),mod2(y),t4),lemma8(mod2(y),t4)):is"r"(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl)
-t7:=tris(real,ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(m0"r"(re(y)),dd(im(y))),dd(ts"r"(m0"r"(re(y)),im(y))),satz197d(re(y),dd(im(y))),lemma6(m0"r"(re(y)),im(y),mod2(y),t4)):is"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))))
-t8:=tris(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),pl"r"(dd(ts"r"(m0"r"(re(y)),im(y))),dd(ts"r"(im(y),re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),ispl12"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))),ts"r"(im(y),dd(re(y))),dd(ts"r"(im(y),re(y))),t7,lemma6(im(y),re(y),mod2(y),t4)),lemma7(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)),mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))))
-t9:=tr3is(real,pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),pl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),mn"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y))),0,ispl1"r"(ts"r"(m0"r"(re(y)),im(y)),m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y)),satz197a(re(y),im(y))),compl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),satz182e(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),comts"r"(im(y),re(y)))):is"r"(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0)
-t10:=tr3is(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),dd(0),0,t8,isf(real,real,[t:real]dd(t),pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0,t9),lemma9(mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0)
-t11:=tris(cx,ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),pli(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y))))),1c,tsis2a(y,dd(re(y)),m0"r"(dd(im(y)))),isrecx12(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0,t6,t10)):is(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c)
-t12:=tr3is(cx,ts(y,u),ts(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),x),ts(1c,x),x,assts2(y,pli(dd(re(y)),m0"r"(dd(im(y)))),x),ists1(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c,x,t11),satz222b(x)):is(ts(y,u),x)
--3229
-n@satz229a:=somei(cx,[t:cx]is(ts(y,t),x),u".3229",t12".3229"):some([t:cx]is(ts(y,t),x))
-satz229:=onei(cx,[t:cx]is(ts(y,t),x),[t:cx][u:cx][v:is(ts(y,t),x)][w:is(ts(y,u),x)]satz229b(t,u,v,w),satz229a):one([t:cx]is(ts(y,t),x))
-ov:=ind(cx,[t:cx]is(ts(y,t),x),satz229):complex
-satz229c:=oneax(cx,[t:cx]is(ts(y,t),x),satz229):is(ts(y,ov(x,y,n)),x)
-satz229d:=symis(cx,ts(y,ov(x,y,n)),x,satz229c):is(x,ts(y,ov(x,y,n)))
-satz229e:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c):is(ts(ov(x,y,n),y),x)
-satz229f:=symis(cx,ts(ov(x,y,n),y),x,satz229e):is(x,ts(ov(x,y,n),y))
-y@[u:complex][n:nis(y,0c)][i:is(ts(y,u),x)]
-satz229g:=satz229b(n,u,ov(x,y,n),i,satz229c(n)):is(u,ov(x,y,n))
-satz229h:=symis(cx,u,ov(x,y,n),satz229g):is(ov(x,y,n),u)
-n@[i:is(ts(u,y),x)]
-satz229j:=satz229g(tris(cx,ts(y,u),ts(u,y),x,comts(y,u),i)):is(u,ov(x,y,n))
-satz229k:=symis(cx,u,ov(x,y,n),satz229j):is(ov(x,y,n),u)
-z@[i:is(x,y)][n:nis(z,0c)]
-isov1:=isf(cx,cx,[t:cx]ov(t,z,n),x,y,i):is(ov(x,z,n),ov(y,z,n))
-i@[n:nis(x,0c)][o:nis(y,0c)]
-isov2:=satz229h(z,x,ov(z,y,o),n,tris(cx,ts(x,ov(z,y,o)),ts(y,ov(z,y,o)),z,ists1(x,y,ov(z,y,o),i),satz229c(z,y,o))):is(ov(z,x,n),ov(z,y,o))
-z@[u:complex][i:is(x,y)][j:is(z,u)][n:nis(z,0c)][o:nis(u,0c)]
-isov12:=tris(cx,ov(x,z,n),ov(y,z,n),ov(y,u,o),isov1(x,y,z,i,n),isov2(z,u,y,j,n,o)):is(ov(x,z,n),ov(y,u,o))
-y@satz230:=tris(cx,pl(mn(x,y),y),pl(y,mn(x,y)),x,compl(mn(x,y),y),satz212h(x,y)):is(pl(mn(x,y),y),x)
-satz231:=satz212e(pl(x,y),y,x,compl(y,x)):is(mn(pl(x,y),y),x)
-satz232:=satz212e(x,mn(x,y),y,satz230):is(mn(x,mn(x,y)),y)
-+4233
-z@t1:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(mn(mn(x,y),z),pl(y,z)),pl(mn(mn(x,y),z),pl(z,y)),pl(pl(mn(mn(x,y),z),z),y),compl(pl(y,z),mn(mn(x,y),z)),ispl2(pl(y,z),pl(z,y),mn(mn(x,y),z),compl(y,z)),asspl2(mn(mn(x,y),z),z,y)):is(pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y))
-t2:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y),pl(mn(x,y),y),x,t1,ispl1(pl(mn(mn(x,y),z),z),mn(x,y),y,satz230(mn(x,y),z)),satz230(x,y)):is(pl(pl(y,z),mn(mn(x,y),z)),x)
--4233
-z@satz233:=satz212d(x,pl(y,z),mn(mn(x,y),z),t2".4233"):is(mn(mn(x,y),z),mn(x,pl(y,z)))
-satz234:=satz212g(pl(x,y),z,pl(x,mn(y,z)),tris(cx,pl(pl(x,mn(y,z)),z),pl(x,pl(mn(y,z),z)),pl(x,y),asspl1(x,mn(y,z),z),ispl2(pl(mn(y,z),z),y,x,satz230(y,z)))):is(mn(pl(x,y),z),pl(x,mn(y,z)))
-satz234a:=symis(cx,mn(pl(x,y),z),pl(x,mn(y,z)),satz234):is(pl(x,mn(y,z)),mn(pl(x,y),z))
-satz234b:=tr3is(cx,mn(pl(x,y),z),mn(pl(y,x),z),pl(y,mn(x,z)),pl(mn(x,z),y),ismn1(pl(x,y),pl(y,x),z,compl(x,y)),satz234(y,x,z),compl(y,mn(x,z))):is(mn(pl(x,y),z),pl(mn(x,z),y))
-satz234c:=symis(cx,mn(pl(x,y),z),pl(mn(x,z),y),satz234b):is(pl(mn(x,z),y),mn(pl(x,y),z))
-satz235:=satz212f(x,mn(y,z),pl(mn(x,y),z),tr3is(cx,pl(pl(mn(x,y),z),mn(y,z)),pl(mn(x,y),pl(z,mn(y,z))),pl(mn(x,y),y),x,asspl1(mn(x,y),z,mn(y,z)),ispl2(pl(z,mn(y,z)),y,mn(x,y),satz212h(y,z)),satz230(x,y))):is(pl(mn(x,y),z),mn(x,mn(y,z)))
-satz235a:=symis(cx,pl(mn(x,y),z),mn(x,mn(y,z)),satz235):is(mn(x,mn(y,z)),pl(mn(x,y),z))
-satz235b:=tris(cx,mn(x,mn(y,z)),pl(mn(x,y),z),mn(pl(x,z),y),satz235a,satz234c(x,z,y)):is(mn(x,mn(y,z)),mn(pl(x,z),y))
-satz235c:=tris(cx,mn(x,mn(y,z)),mn(pl(x,z),y),mn(pl(z,x),y),satz235b,ismn1(pl(x,z),pl(z,x),y,compl(x,z))):is(mn(x,mn(y,z)),mn(pl(z,x),y))
-satz236:=satz212g(pl(x,z),pl(y,z),mn(x,y),tris(cx,pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y)))):is(mn(pl(x,z),pl(y,z)),mn(x,y))
-satz236a:=tris(cx,mn(pl(z,x),pl(z,y)),mn(pl(x,z),pl(y,z)),mn(x,y),ismn12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y)),satz236):is(mn(pl(z,x),pl(z,y)),mn(x,y))
-[u:complex]
-+4237
-t1:=tr3is(cx,pl(mn(z,u),pl(u,y)),pl(pl(mn(z,u),u),y),pl(z,y),pl(y,z),asspl2(mn(z,u),u,y),ispl1(pl(mn(z,u),u),z,y,satz230(z,u)),compl(z,y)):is(pl(mn(z,u),pl(u,y)),pl(y,z))
-t2:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(pl(mn(x,y),mn(z,u)),pl(u,y)),pl(mn(x,y),pl(mn(z,u),pl(u,y))),pl(mn(x,y),pl(y,z)),ispl2(pl(y,u),pl(u,y),pl(mn(x,y),mn(z,u)),compl(y,u)),asspl1(mn(x,y),mn(z,u),pl(u,y)),ispl2(pl(mn(z,u),pl(u,y)),pl(y,z),mn(x,y),t1)):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)))
-t3:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),t2,asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y))):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(x,z))
--4237
-satz237:=satz212f(pl(x,z),pl(y,u),pl(mn(x,y),mn(z,u)),t3".4237"):is(pl(mn(x,y),mn(z,u)),mn(pl(x,z),pl(y,u)))
-+4238
-t1:=tris(cx,pl(pl(x,u),z),pl(x,pl(u,z)),pl(x,pl(z,u)),asspl1(x,u,z),ispl2(pl(u,z),pl(z,u),x,compl(u,z))):is(pl(pl(x,u),z),pl(x,pl(z,u)))
-t2:=tr3is(cx,pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(pl(pl(x,u),z),pl(pl(y,z),u)),mn(pl(x,pl(z,u)),pl(y,pl(z,u))),mn(x,y),satz237(pl(x,u),pl(y,z),z,u),ismn12(pl(pl(x,u),z),pl(x,pl(z,u)),pl(pl(y,z),u),pl(y,pl(z,u)),t1,asspl1(y,z,u)),satz236(x,y,pl(z,u))):is(pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(x,y))
--4238
-satz238:=satz212g(mn(x,y),mn(z,u),mn(pl(x,u),pl(y,z)),t2".4238"):is(mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)))
-[i:is(mn(x,y),mn(z,u))]
-+4239
-t1:=tris1(cx,mn(pl(x,u),pl(y,z)),0c,mn(mn(x,y),mn(z,u)),satz238,satz213b(mn(x,y),mn(z,u),i)):is(mn(pl(x,u),pl(y,z)),0c)
--4239
-satz239a:=satz213a(pl(x,u),pl(y,z),t1".4239"):is(pl(x,u),pl(y,z))
-u@[i:is(pl(x,u),pl(y,z))]
-+*4239
-i@t2:=tris(cx,mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)),0c,satz238,satz213b(pl(x,u),pl(y,z),i)):is(mn(mn(x,y),mn(z,u)),0c)
--4239
-i@satz239b:=satz213a(mn(x,y),mn(z,u),t2".4239"):is(mn(x,y),mn(z,u))
-y@[n:nis(y,0c)]
-satz240:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c(x,y,n)):is(ts(ov(x,y,n),y),x)
-satz241:=satz229h(ts(x,y),y,x,n,comts(y,x)):is(ov(ts(x,y),y,n),x)
-y@[n:nis(x,0c)][o:nis(y,0c)]
-lemma6:=th3"l.imp"(is(ov(x,y,o),0c),is(x,0c),n,[t:is(ov(x,y,o),0c)]tris1(cx,x,0c,ts(y,ov(x,y,o)),satz229c(x,y,o),satz221b(y,ov(x,y,o),t))):nis(ov(x,y,o),0c)
-satz242:=satz229h(x,ov(x,y,o),y,lemma6,satz240(o)):is(ov(x,ov(x,y,o),lemma6),y)
-z@[n:nis(y,0c)][o:nis(z,0c)]
-+5243
-t1:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ov(ov(x,y,n),z,o),ts(y,z)),ts(ov(ov(x,y,n),z,o),ts(z,y)),ts(ts(ov(ov(x,y,n),z,o),z),y),comts(ts(y,z),ov(ov(x,y,n),z,o)),ists2(ts(y,z),ts(z,y),ov(ov(x,y,n),z,o),comts(y,z)),assts2(ov(ov(x,y,n),z,o),z,y)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y))
-t2:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y),ts(ov(x,y,n),y),x,t1,ists1(ts(ov(ov(x,y,n),z,o),z),ov(x,y,n),y,satz240(ov(x,y,n),z,o)),satz240(x,y,n)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),x)
--5243
-satz243:=satz229g(x,ts(y,z),ov(ov(x,y,n),z,o),satz221d(y,z,n,o),t2".5243"):is(ov(ov(x,y,n),z,o),ov(x,ts(y,z),satz221d(y,z,n,o)))
-z@[n:nis(z,0c)]
-satz244:=satz229k(ts(x,y),z,ts(x,ov(y,z,n)),n,tris(cx,ts(ts(x,ov(y,z,n)),z),ts(x,ts(ov(y,z,n),z)),ts(x,y),assts1(x,ov(y,z,n),z),ists2(ts(ov(y,z,n),z),y,x,satz240(y,z,n)))):is(ov(ts(x,y),z,n),ts(x,ov(y,z,n)))
-satz244a:=symis(cx,ov(ts(x,y),z,n),ts(x,ov(y,z,n)),satz244):is(ts(x,ov(y,z,n)),ov(ts(x,y),z,n))
-satz244b:=tr3is(cx,ov(ts(x,y),z,n),ov(ts(y,x),z,n),ts(y,ov(x,z,n)),ts(ov(x,z,n),y),isov1(ts(x,y),ts(y,x),z,comts(x,y),n),satz244(y,x,z,n),comts(y,ov(x,z,n))):is(ov(ts(x,y),z,n),ts(ov(x,z,n),y))
-satz244c:=symis(cx,ov(ts(x,y),z,n),ts(ov(x,z,n),y),satz244b):is(ts(ov(x,z,n),y),ov(ts(x,y),z,n))
-z@[n:nis(y,0c)][o:nis(z,0c)]
-satz245:=satz229j(x,ov(y,z,o),ts(ov(x,y,n),z),lemma6(y,z,n,o),tr3is(cx,ts(ts(ov(x,y,n),z),ov(y,z,o)),ts(ov(x,y,n),ts(z,ov(y,z,o))),ts(ov(x,y,n),y),x,assts1(ov(x,y,n),z,ov(y,z,o)),ists2(ts(z,ov(y,z,o)),y,ov(x,y,n),satz229c(y,z,o)),satz240(x,y,n))):is(ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)))
-satz245a:=symis(cx,ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)),satz245):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z))
-satz245b:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z),ov(ts(x,z),y,n),satz245a,satz244c(x,z,y,n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n))
-satz245c:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n),ov(ts(z,x),y,n),satz245b,isov1(ts(x,z),ts(z,x),y,comts(x,z),n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(z,x),y,n))
-satz246:=satz229k(ts(x,z),ts(y,z),ov(x,y,n),satz221d(y,z,n,o),tris(cx,ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n)))):is(ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n))
-satz246a:=tris(cx,ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n),isov12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y),satz221d(z,y,o,n),satz221d(y,z,n,o)),satz246):is(ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(x,y,n))
-z@[u:complex][n:nis(y,0c)][o:nis(u,0c)]
-+5247
-t1:=tr3is(cx,ts(ov(z,u,o),ts(u,y)),ts(ts(ov(z,u,o),u),y),ts(z,y),ts(y,z),assts2(ov(z,u,o),u,y),ists1(ts(ov(z,u,o),u),z,y,satz240(z,u,o)),comts(z,y)):is(ts(ov(z,u,o),ts(u,y)),ts(y,z))
-t2:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ts(ov(x,y,n),ov(z,u,o)),ts(u,y)),ts(ov(x,y,n),ts(ov(z,u,o),ts(u,y))),ts(ov(x,y,n),ts(y,z)),ists2(ts(y,u),ts(u,y),ts(ov(x,y,n),ov(z,u,o)),comts(y,u)),assts1(ov(x,y,n),ov(z,u,o),ts(u,y)),ists2(ts(ov(z,u,o),ts(u,y)),ts(y,z),ov(x,y,n),t1)):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)))
-t3:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),t2,assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n))):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(x,z))
--5247
-satz247:=satz229j(ts(x,z),ts(y,u),ts(ov(x,y,n),ov(z,u,o)),satz221d(y,u,n,o),t3".5247"):is(ts(ov(x,y,n),ov(z,u,o)),ov(ts(x,z),ts(y,u),satz221d(y,u,n,o)))
-u@[n:nis(y,0c)][o:nis(z,0c)][p:nis(u,0c)]
-+5248
-t1:=tris(cx,ts(ts(x,u),z),ts(x,ts(u,z)),ts(x,ts(z,u)),assts1(x,u,z),ists2(ts(u,z),ts(z,u),x,comts(u,z))):is(ts(ts(x,u),z),ts(x,ts(z,u)))
-t2:=tr3is(cx,ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(ts(ts(x,u),z),ts(ts(y,z),u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p)),ov(ts(x,ts(z,u)),ts(y,ts(z,u)),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),ov(x,y,n),satz247(ts(x,u),ts(y,z),z,u,satz221d(y,z,n,o),p),isov12(ts(ts(x,u),z),ts(x,ts(z,u)),ts(ts(y,z),u),ts(y,ts(z,u)),t1,assts1(y,z,u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),satz246(x,y,ts(z,u),n,satz221d(z,u,o,p))):is(ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(x,y,n))
--5248
-satz248:=satz229k(ov(x,y,n),ov(z,u,p),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),lemma6(z,u,o,p),t2".5248"):is(ov(ov(x,y,n),ov(z,u,p),lemma6(z,u,o,p)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)))
-x@[n:nis(x,0c)]
-satz249:=satz229h(0c,x,0c,n,satz221b(x,0c,refis(cx,0c))):is(ov(0c,x,n),0c)
-satz250:=satz229h(x,x,1c,n,satz222(x)):is(ov(x,x,n),1c)
-y@[n:nis(y,0c)][i:is(x,y)]
-satz251a:=tris(cx,ov(x,y,n),ov(x,x,th2"e.notis"(cx,y,0c,x,n,i)),1c,isov2(y,x,x,symis(cx,x,y,i),n,th2"e.notis"(cx,y,0c,x,n,i)),satz250(x,th2"e.notis"(cx,y,0c,x,n,i))):is(ov(x,y,n),1c)
-n@[i:is(ov(x,y,n),1c)]
-satz251b:=tr3is(cx,x,ts(y,ov(x,y,n)),ts(y,1c),y,satz229d(x,y,n),ists2(ov(x,y,n),1c,y,i),satz222(y)):is(x,y)
-u@[n:nis(y,0c)][o:nis(u,0c)][i:is(ov(x,y,n),ov(z,u,o))]
-+5252
-[j:is(z,0c)]
-t1:=tr3is(cx,ov(x,y,n),ov(z,u,o),ov(0c,u,o),0c,i,isov1(z,0c,u,j,o),satz249(u,o)):is(ov(x,y,n),0c)
-t2:=tris(cx,x,ts(y,ov(x,y,n)),0c,satz229d(x,y,n),satz221b(y,ov(x,y,n),t1)):is(x,0c)
-t3:=tris2(cx,ts(x,u),ts(y,z),0c,satz221a(x,u,t2),satz221b(y,z,j)):is(ts(x,u),ts(y,z))
-i@[p:nis(z,0c)]
-t4:=tris1(cx,ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),satz248(x,y,z,u,n,p,o),satz251a(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),i)):is(ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c)
-t5:=satz251b(ts(x,u),ts(y,z),satz221d(y,z,n,p),t4):is(ts(x,u),ts(y,z))
--5252
-satz252a:=th1"l.imp"(is(z,0c),is(ts(x,u),ts(y,z)),[t:is(z,0c)]t3".5252"(t),[t:nis(z,0c)]t5".5252"(t)):is(ts(x,u),ts(y,z))
-o@[i:is(ts(x,u),ts(y,z))]
-+*5252
-i@[j:is(z,0c)]
-t6:=tris(cx,ts(x,u),ts(y,z),0c,i,satz221b(y,z,j)):is(ts(x,u),0c)
-t7:=ore1(is(x,0c),is(u,0c),satz221c(x,u,t6),o):is(x,0c)
-t8:=tris2(cx,ov(x,y,n),ov(z,u,o),0c,tris(cx,ov(x,y,n),ov(0c,y,n),0c,isov1(x,0c,y,t7,n),satz249(y,n)),tris(cx,ov(z,u,o),ov(0c,u,o),0c,isov1(z,0c,u,j,o),satz249(u,o))):is(ov(x,y,n),ov(z,u,o))
-i@[p:nis(z,0c)]
-t9:=tris(cx,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,satz248(x,y,z,u,n,p,o),satz251a(ts(x,u),ts(y,z),satz221d(y,z,n,p),i)):is(ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),1c)
-t10:=satz251b(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),t9):is(ov(x,y,n),ov(z,u,o))
--5252
-i@satz252b:=th1"l.imp"(is(z,0c),is(ov(x,y,n),ov(z,u,o)),[t:is(z,0c)]t8".5252"(t),[t:nis(z,0c)]t10".5252"(t)):is(ov(x,y,n),ov(z,u,o))
-z@[n:nis(y,0c)]
-satz253:=satz229g(pl(x,z),y,pl(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,pl(ov(x,y,n),ov(z,y,n))),pl(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),pl(x,z),disttp2(y,ov(x,y,n),ov(z,y,n)),ispl12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(pl(ov(x,y,n),ov(z,y,n)),ov(pl(x,z),y,n))
-z@[n:nis(z,0c)]
-distop:=symis(cx,pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n),satz253(x,z,y,n)):is(ov(pl(x,y),z,n),pl(ov(x,z,n),ov(y,z,n)))
-distpo:=satz253(x,z,y,n):is(pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n))
-u@[n:nis(y,0c)][o:nis(u,0c)]
-satz254:=tris1(cx,pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),pl(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ispl12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz253(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
-z@[n:nis(y,0c)]
-satz255:=satz229g(mn(x,z),y,mn(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,mn(ov(x,y,n),ov(z,y,n))),mn(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),mn(x,z),disttm2(y,ov(x,y,n),ov(z,y,n)),ismn12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(mn(ov(x,y,n),ov(z,y,n)),ov(mn(x,z),y,n))
-z@[n:nis(z,0c)]
-distom:=symis(cx,mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n),satz255(x,z,y,n)):is(ov(mn(x,y),z,n),mn(ov(x,z,n),ov(y,z,n)))
-distmo:=satz255(x,z,y,n):is(mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n))
-u@[n:nis(y,0c)][o:nis(u,0c)]
-satz256:=tris1(cx,mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),mn(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ismn12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz255(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
-x@conj:=pli(re(x),m0"r"(im(x))):complex
-b@conjisa:=isrecx12(re(pli(a,b)),a,m0"r"(im(pli(a,b))),m0"r"(b),reis(a,b),ism0"r"(im(pli(a,b)),b,imis(a,b))):is(conj(pli(a,b)),pli(a,m0"r"(b)))
-conjisb:=symis(cx,conj(pli(a,b)),pli(a,m0"r"(b)),conjisa):is(pli(a,m0"r"(b)),conj(pli(a,b)))
-y@[i:is(x,y)]
-isconj:=isf(cx,cx,[t:cx]conj(t),x,y,i):is(conj(x),conj(y))
-x@satz257:=tr3is(cx,conj(conj(x)),pli(re(x),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,conjisa(re(x),m0"r"(im(x))),isrecx2(m0"r"(m0"r"(im(x))),im(x),re(x),satz177(im(x))),pliis(x)):is(conj(conj(x)),x)
-[i:is(x,0c)]
-satz258a:=tr3is(cx,conj(x),conj(0c),pli(0,m0"r"(0)),0c,isconj(x,0c,i),conjisa(0,0),isrecx2(m0"r"(0),0,0,satz176b(0,refis(real,0)))):is(conj(x),0c)
-x@[i:is(conj(x),0c)]
-+6258
-t1:=tris(real,re(x),re(conj(x)),0,isre(re(x),m0"r"(im(x))),lemma1(conj(x),i)):is"r"(re(x),0)
-t2:=satz176e(im(x),tris(real,m0"r"(im(x)),im(conj(x)),0,isim(re(x),m0"r"(im(x))),lemma2(conj(x),i))):is"r"(im(x),0)
--6258
-satz258b:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t1".6258",t2".6258")):is(x,0c)
-+*6258
-i@anders:=tris1(cx,x,0c,conj(conj(x)),satz257,satz258a(conj(x),i)):is(x,0c)
--6258
-x@[n:nis(x,0c)]
-satz258c:=th3"l.imp"(is(conj(x),0c),is(x,0c),n,[t:is(conj(x),0c)]satz258b(t)):nis(conj(x),0c)
-x@[i:is(conj(x),x)]
-+6259
-t1:=tris(real,m0"r"(im(x)),im(conj(x)),im(x),isim(re(x),m0"r"(im(x))),isceim(conj(x),x,i)):is"r"(m0"r"(im(x)),im(x))
--6259
-satz259a:=lemma10(im(x),symis(real,m0"r"(im(x)),im(x),t1".6259")):is"r"(im(x),0)
-x@[i:is"r"(im(x),0)]
-satz259b:=tris(cx,conj(x),pli(re(x),im(x)),x,isrecx2(m0"r"(im(x)),im(x),re(x),tris2(real,m0"r"(im(x)),im(x),0,satz176b(im(x),i),i)),pliis(x)):is(conj(x),x)
-x@[i:is(x,conj(x))]
-satz269c:=satz259a(x,symis(cx,x,conj(x),i)):is"r"(im(x),0)
-x@[i:is"r"(im(x),0)]
-satz269d:=symis(cx,conj(x),x,satz259b(i)):is(x,conj(x))
-y@satz260:=tr3is(cx,conj(pl(x,y)),pli(pl"r"(re(x),re(y)),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(re(x),re(y)),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(conj(x),conj(y)),conjisa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx2(m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),pl"r"(re(x),re(y)),satz180(im(x),im(y))),plis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(pl(x,y)),pl(conj(x),conj(y)))
-satz260a:=symis(cx,conj(pl(x,y)),pl(conj(x),conj(y)),satz260):is(pl(conj(x),conj(y)),conj(pl(x,y)))
-+6261
-t1:=tris(real,m0"r"(imts(x,y)),pl"r"(m0"r"(ts"r"(re(x),im(y))),m0"r"(ts"r"(im(x),re(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),satz180(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(m0"r"(ts"r"(re(x),im(y))),ts"r"(re(x),m0"r"(im(y))),m0"r"(ts"r"(im(x),re(y))),ts"r"(m0"r"(im(x)),re(y)),satz197f(re(x),im(y)),satz197e(im(x),re(y)))):is"r"(m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))))
--6261
-satz261:=tr3is(cx,conj(ts(x,y)),pli(rets(x,y),m0"r"(imts(x,y))),pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y)))),ts(conj(x),conj(y)),conjisa(rets(x,y),imts(x,y)),isrecx12(rets(x,y),mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),ismn2"r"(ts"r"(im(x),im(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y))),ts"r"(re(x),re(y)),satz198a(im(x),im(y))),t1".6261"),tsis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(ts(x,y)),ts(conj(x),conj(y)))
-satz261a:=symis(cx,conj(ts(x,y)),ts(conj(x),conj(y)),satz261):is(ts(conj(x),conj(y)),conj(ts(x,y)))
-+6262
-t1:=symis(cx,pl(mn(x,y),y),x,satz230(x,y)):is(x,pl(mn(x,y),y))
-t2:=tris(cx,conj(x),conj(pl(mn(x,y),y)),pl(conj(mn(x,y)),conj(y)),isconj(x,pl(mn(x,y),y),t1),satz260(mn(x,y),y)):is(conj(x),pl(conj(mn(x,y)),conj(y)))
--6262
-satz262:=satz212f(conj(x),conj(y),conj(mn(x,y)),symis(cx,conj(x),pl(conj(mn(x,y)),conj(y)),t2".6262")):is(conj(mn(x,y)),mn(conj(x),conj(y)))
-satz262a:=symis(cx,conj(mn(x,y)),mn(conj(x),conj(y)),satz262):is(mn(conj(x),conj(y)),conj(mn(x,y)))
-[n:nis(y,0c)]
-+6263
-t1:=satz229f(x,y,n):is(x,ts(ov(x,y,n),y))
-t2:=isconj(x,ts(ov(x,y,n),y),t1):is(conj(x),conj(ts(ov(x,y,n),y)))
-t3:=satz261(ov(x,y,n),y):is(conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)))
-t4:=tris(cx,conj(x),conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)),t2,t3):is(conj(x),ts(conj(ov(x,y,n)),conj(y)))
-t5:=satz258c(y,n):nis(conj(y),0c)
--6263
-satz263:=satz229j(conj(x),conj(y),conj(ov(x,y,n)),t5".6263",symis(cx,conj(x),ts(conj(ov(x,y,n)),conj(y)),t4".6263")):is(conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)))
-satz263a:=symis(cx,conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)),satz263):is(ov(conj(x),conj(y),satz258c(y,n)),conj(ov(x,y,n)))
-x@mod:=sqrt(mod2(x),lemma5(x)):real
-y@[i:is(x,y)]
-ismod:=isf(cx,real,[t:cx]mod(t),x,y,i):is"r"(mod(x),mod(y))
-x@[n:nis(x,0c)]
-satz264a:=sqrtnot0(mod2(x),lemma5(x),pnot0(mod2(x),lemma4(x,n))):pos(mod(x))
-x@[i:is(x,0c)]
-satz264b:=sqrt0(mod2(x),lemma5(x),lemma3(x,i)):is"r"(mod(x),0)
-x@satz264c:=thsqrt1a(mod2(x),lemma5(x)):not(neg(mod(x)))
-satz264d:=satz167f(mod(x),0,th3"l.imp"(less(mod(x),0),neg(mod(x)),satz264c,[t:less(mod(x),0)]satz169d(mod(x),t))):moreis(mod(x),0)
-+7265
-t1:=symis(real,ts"r"(mod(x),mod(x)),mod2(x),thsqrt1b(mod2(x),lemma5(x))):is"r"(mod2(x),ts"r"(mod(x),mod(x)))
-t2:=tris(real,pl"r"(ts"r"(re(x),re(x)),0),ts"r"(re(x),re(x)),ts"r"(abs(re(x)),abs(re(x))),pl02(ts"r"(re(x),re(x)),0,refis(real,0)),lemma12"r"(re(x))):is"r"(pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))))
-t3:=satz191(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),ts"r"(im(x),im(x)),0,moreisi2(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),refis(real,ts"r"(re(x),re(x)))),lemma11"r"(im(x))):moreis(mod2(x),pl"r"(ts"r"(re(x),re(x)),0))
-t4:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))),t1,t2,t3):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(re(x)),abs(re(x))))
-t5:=tris(real,pl"r"(0,ts"r"(im(x),im(x))),ts"r"(im(x),im(x)),ts"r"(abs(im(x)),abs(im(x))),pl01(0,ts"r"(im(x),im(x)),refis(real,0)),lemma12"r"(im(x))):is"r"(pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))))
-t6:=satz191(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),lemma11"r"(re(x)),moreisi2(ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),refis(real,ts"r"(im(x),im(x))))):moreis(mod2(x),pl"r"(0,ts"r"(im(x),im(x))))
-t7:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))),t1,t5,t6):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(im(x)),abs(im(x))))
-@[r:real][s:real][m:moreis(ts"r"(r,r),ts"r"(s,s))][n:moreis(r,0)][l:less(r,s)]
-t8:=lemma2"r"(r,s,l):more(s,r)
-t9:=satz169b(s,satz172d(s,r,0,t8,n)):pos(s)
-[o:more(r,0)]
-t10:=trmore(ts"r"(s,s),ts"r"(r,s),ts"r"(r,r),satz203a(s,r,s,t8,t9),satz203d(s,r,r,t8,satz169b(r,o))):more(ts"r"(s,s),ts"r"(r,r))
-l@[i:is"r"(r,0)]
-t11:=ismore2(0,ts"r"(r,r),ts"r"(s,s),symis(real,ts"r"(r,r),0,ts01(r,r,i)),satz169a(ts"r"(s,s),possq(s,pnot0(s,t9)))):more(ts"r"(s,s),ts"r"(r,r))
-l@t12:=lemma1"r"(ts"r"(s,s),ts"r"(r,r),orapp(more(r,0),is"r"(r,0),more(ts"r"(s,s),ts"r"(r,r)),n,[t:more(r,0)]t10(t),[t:is"r"(r,0)]t11(t))):less(ts"r"(r,r),ts"r"(s,s))
-n@t13:=satz167f(r,s,[t:less(r,s)]<t12(t)>satz167c(ts"r"(r,r),ts"r"(s,s),m)):moreis(r,s)
--7265
-satz265a:=t13".7265"(mod(x),abs(re(x)),t4".7265",satz264d(x)):moreis(mod(x),abs(re(x)))
-satz265b:=t13".7265"(mod(x),abs(im(x)),t7".7265",satz264d(x)):moreis(mod(x),abs(im(x)))
-@[r:real][s:real][i:is(ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)))][n:not(neg(r))][o:not(neg(s))]
-+7266
-@[t:real]
-t1:=pl02(ts"r"(t,t),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t))
-t2:=tris(real,pl"r"(ts"r"(t,0),ts"r"(0,t)),ts"r"(t,0),0,pl02(ts"r"(t,0),ts"r"(0,t),ts01(0,t,refis(real,0))),ts02(t,0,refis(real,0))):is"r"(pl"r"(ts"r"(t,0),ts"r"(0,t)),0)
-t3:=tris(cx,ts(pli(t,0),pli(t,0)),pli(mn"r"(ts"r"(t,t),ts"r"(0,0)),pl"r"(ts"r"(t,0),ts"r"(0,t))),pli(ts"r"(t,t),0),tsis12a(t,0,t,0),isrecx12(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t),pl"r"(ts"r"(t,0),ts"r"(0,t)),0,t1,t2)):is(ts(pli(t,0),pli(t,0)),pli(ts"r"(t,t),0))
-o@t4:=tr3is(cx,pli(ts"r"(r,r),0),ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)),pli(ts"r"(s,s),0),symis(cx,ts(pli(r,0),pli(r,0)),pli(ts"r"(r,r),0),t3(r)),i,t3(s)):is(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0))
-t5:=tr3is(real,ts"r"(r,r),re(pli(ts"r"(r,r),0)),re(pli(ts"r"(s,s),0)),ts"r"(s,s),isre(ts"r"(r,r),0),iscere(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0),t4),reis(ts"r"(s,s),0)):is"r"(ts"r"(r,r),ts"r"(s,s))
-t6:=andi(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)),n,t5):and(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)))
-t7:=andi(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)),o,refis(real,ts"r"(s,s))):and(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)))
--7266
-satz266:=satzr161b(ts"r"(s,s),r,s,t6".7266",t7".7266"):is"r"(r,s)
-+7267
-x@t1:=tris(cx,ts(pli(mod(x),0),pli(mod(x),0)),pli(ts"r"(mod(x),mod(x)),0),pli(mod2(x),0),t3"c.7266"(mod(x)),isrecx1(ts"r"(mod(x),mod(x)),mod2(x),0,thsqrt1b(mod2(x),lemma5(x)))):is(ts(pli(mod(x),0),pli(mod(x),0)),pli(mod2(x),0))
-t2:=ispl2"r"(m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(im(x),im(x)),ts"r"(re(x),re(x)),tris(real,m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),satz197e(im(x),m0"r"(im(x))),satz198(im(x),im(x)))):is"r"(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x))
-t3:=tris(real,pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),pl"r"(m0"r"(ts"r"(re(x),im(x))),ts"r"(re(x),im(x))),0,ispl12"r"(ts"r"(re(x),m0"r"(im(x))),m0"r"(ts"r"(re(x),im(x))),ts"r"(im(x),re(x)),ts"r"(re(x),im(x)),satz197b(re(x),im(x)),comts"r"(im(x),re(x))),satz179a(ts"r"(re(x),im(x)))):is"r"(pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0)
-t4:=tris(cx,ts(x,conj(x)),pli(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x)))),pli(mod2(x),0),tsis2a(x,re(x),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0,t2,t3)):is(ts(x,conj(x)),pli(mod2(x),0))
--7267
-x@satz267:=tris2(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),pli(mod2(x),0),t1".7267",t4".7267"):is(ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)))
-satz267a:=symis(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),satz267):is(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)))
-+7268
-z@t1:=tr3is(cx,ts(x,ts(y,z)),ts(ts(x,y),z),ts(ts(y,x),z),ts(y,ts(x,z)),assts2(x,y,z),ists1(ts(x,y),ts(y,x),z,comts(x,y)),assts1(y,x,z)):is(ts(x,ts(y,z)),ts(y,ts(x,z)))
-[u:complex]
-t2:=tr3is(cx,ts(ts(x,y),ts(z,u)),ts(x,ts(y,ts(z,u))),ts(x,ts(z,ts(y,u))),ts(ts(x,z),ts(y,u)),assts1(x,y,ts(z,u)),ists2(ts(y,ts(z,u)),ts(z,ts(y,u)),x,t1(y,z,u)),assts2(x,z,ts(y,u))):is(ts(ts(x,y),ts(z,u)),ts(ts(x,z),ts(y,u)))
-y@t3:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,y),conj(ts(x,y))),ts(ts(x,y),ts(conj(x),conj(y))),ts(ts(x,conj(x)),ts(y,conj(y))),satz267(ts(x,y)),ists2(conj(ts(x,y)),ts(conj(x),conj(y)),ts(x,y),satz261(x,y)),t2(x,y,conj(x),conj(y))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))))
-t4:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))),ts(ts(pli(mod(x),0),pli(mod(x),0)),ts(pli(mod(y),0),pli(mod(y),0))),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),t3,ists12(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)),ts(y,conj(y)),ts(pli(mod(y),0),pli(mod(y),0)),satz267a(x),satz267a(y)),t2(pli(mod(x),0),pli(mod(x),0),pli(mod(y),0),pli(mod(y),0))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))))
-@[r:real][s:real]
-t5:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
-t6:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
-t7:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t5,t6)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
-y@t8:=tris(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)),t4,ists12(ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),t7(mod(x),mod(y)),t7(mod(x),mod(y)))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)))
-[n:neg(ts"r"(mod(x),mod(y)))]
-t9:=orapp(and(pos(mod(x)),neg(mod(y))),and(neg(mod(x)),pos(mod(y))),con,satz196h(mod(x),mod(y),n),[t:and(pos(mod(x)),neg(mod(y)))]<ande2(pos(mod(x)),neg(mod(y)),t)>satz264c(y),[t:and(neg(mod(x)),pos(mod(y)))]<ande1(neg(mod(x)),pos(mod(y)),t)>satz264c(x)):con
--7268
-y@satz268:=satz266(mod(ts(x,y)),ts"r"(mod(x),mod(y)),t8".7268",satz264c(ts(x,y)),[t:neg(ts"r"(mod(x),mod(y)))]t9".7268"(t)):is"r"(mod(ts(x,y)),ts"r"(mod(x),mod(y)))
-satz268a:=symis(real,mod(ts(x,y)),ts"r"(mod(x),mod(y)),satz268):is"r"(ts"r"(mod(x),mod(y)),mod(ts(x,y)))
-[n:nis(y,0c)]
-+7269
-t1:=pnot0(mod(y),satz264a(y,n)):nis"r"(mod(y),0)
-t2:=tris1(real,ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),mod(ts(ov(x,y,n),y)),satz268(ov(x,y,n),y),ismod(ts(ov(x,y,n),y),x,satz240(x,y,n))):is"r"(ts"r"(mod(ov(x,y,n)),mod(y)),mod(x))
-t3:=satz204g(mod(x),mod(y),mod(ov(x,y,n)),t1,tris(real,ts"r"(mod(y),mod(ov(x,y,n))),ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),comts"r"(mod(y),mod(ov(x,y,n))),t2)):is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),t1))
--7269
-satz269:=t3".7269":is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),pnot0(mod(y),satz264a(y,n))))
-y@[i:is(pl(x,y),1c)]
-+7270
-@[r:real]
-t1:=th1"l.imp"(neg(r),moreis(abs(r),r),[t:neg(r)]moreisi1(abs(r),r,trmore(abs(r),0,r,satz169a(abs(r),satz166b(r,t)),lemma2"r"(r,0,satz169c(r,t)))),[t:not(neg(r))]moreisi2(abs(r),r,absnn(r,t))):moreis(abs(r),r)
-x@t2:=trmoreis(mod(x),abs(re(x)),re(x),satz265a(x),t1(re(x))):moreis(mod(x),re(x))
-i@t3:=tr3is(real,pl"r"(re(x),re(y)),re(pl(x,y)),re(1c),1rl,isre(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),iscere(pl(x,y),1c,i),reis(1rl,0)):is"r"(pl"r"(re(x),re(y)),1rl)
--7270
-satz270:=ismoreis2(pl"r"(re(x),re(y)),1rl,pl"r"(mod(x),mod(y)),t3".7270",satz191(mod(x),re(x),mod(y),re(y),t2".7270",t2".7270"(y))):moreis(pl"r"(mod(x),mod(y)),1rl)
-+7271
-y@[i:is(pl(x,y),0c)]
-t1:=satz264b(pl(x,y),i):is"r"(mod(pl(x,y)),0)
-t2:=ismoreis2(pl"r"(0,0),mod(pl(x,y)),pl"r"(mod(x),mod(y)),tris2(real,pl"r"(0,0),mod(pl(x,y)),0,pl01(0,0,refis(real,0)),t1),satz191(mod(x),0,mod(y),0,satz264d(x),satz264d(y))):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
-y@[n:nis(pl(x,y),0c)]
-t3:=pnot0(mod(pl(x,y)),satz264a(pl(x,y),n)):nis"r"(mod(pl(x,y)),0)
-t4:=tris(cx,pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),ov(pl(x,y),pl(x,y),n),1c,satz253(x,pl(x,y),y,n),satz250(pl(x,y),n)):is(pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),1c)
-t5:=satz270(ov(x,pl(x,y),n),ov(y,pl(x,y),n),t4):moreis(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),1rl)
-fx:=ov"r"(mod(x),mod(pl(x,y)),t3):real
-fy:=ov"r"(mod(y),mod(pl(x,y)),t3):real
-t6:=ismoreis1(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),pl"r"(fx,fy),1rl,ispl12"r"(mod(ov(x,pl(x,y),n)),fx,mod(ov(y,pl(x,y),n)),fy,satz269(x,pl(x,y),n),satz269(y,pl(x,y),n)),t5):moreis(pl"r"(fx,fy),1rl)
-prl:=ts"r"(pl"r"(fx,fy),mod(pl(x,y))):real
-prr:=ts"r"(1rl,mod(pl(x,y))):real
-t7:=orapp(more(pl"r"(fx,fy),1rl),is"r"(pl"r"(fx,fy),1rl),moreis(prl,prr),t6,[t:more(pl"r"(fx,fy),1rl)]moreisi1(prl,prr,satz203a(pl"r"(fx,fy),1rl,mod(pl(x,y)),t,satz264a(pl(x,y),n))),[t:is"r"(pl"r"(fx,fy),1rl)]moreisi2(prl,prr,ists1"r"(pl"r"(fx,fy),1rl,mod(pl(x,y)),t))):moreis(prl,prr)
-t8:=tris(real,prl,pl"r"(ts"r"(fx,mod(pl(x,y))),ts"r"(fy,mod(pl(x,y)))),pl"r"(mod(x),mod(y)),disttp1"r"(fx,fy,mod(pl(x,y))),ispl12"r"(ts"r"(fx,mod(pl(x,y))),mod(x),ts"r"(fy,mod(pl(x,y))),mod(y),satz204e(mod(x),mod(pl(x,y)),t3),satz204e(mod(y),mod(pl(x,y)),t3))):is"r"(prl,pl"r"(mod(x),mod(y)))
-t9:=satz195b(mod(pl(x,y))):is"r"(prr,mod(pl(x,y)))
-t10:=ismoreis12(prl,pl"r"(mod(x),mod(y)),prr,mod(pl(x,y)),t8,t9,t7):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
-y@t11:=th1"l.imp"(is(pl(x,y),0c),moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y))),[t:is(pl(x,y),0c)]t2(t),[t:nis(pl(x,y),0c)]t10(t)):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
--7271
-y@satz271:=satz168a(pl"r"(mod(x),mod(y)),mod(pl(x,y)),t11".7271"):lessis(mod(pl(x,y)),pl"r"(mod(x),mod(y)))
-satz271a:=t11".7271":moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
-+7272
-x@t1:=tris(real,re(m0(x)),re(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(re(x)),iscere(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),reis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(re(m0(x)),m0"r"(re(x)))
-t2:=tris(real,ts"r"(re(m0(x)),re(m0(x))),ts"r"(m0"r"(re(x)),m0"r"(re(x))),ts"r"(re(x),re(x)),ists12"r"(re(m0(x)),m0"r"(re(x)),re(m0(x)),m0"r"(re(x)),t1,t1),satz198(re(x),re(x))):is"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)))
-t3:=tris(real,im(m0(x)),im(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(im(x)),isceim(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),imis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(im(m0(x)),m0"r"(im(x)))
-t4:=tris(real,ts"r"(im(m0(x)),im(m0(x))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),ists12"r"(im(m0(x)),m0"r"(im(x)),im(m0(x)),m0"r"(im(x)),t3,t3),satz198(im(x),im(x))):is"r"(ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)))
-t5:=ispl12"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)),ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)),t2,t4):is"r"(mod2(m0(x)),mod2(x))
--7272
-x@satz272:=issqrt(mod2(m0(x)),mod2(x),lemma5(m0(x)),lemma5(x),t5".7272"):is"r"(mod(m0(x)),mod(x))
-satz272a:=symis(real,mod(m0(x)),mod(x),satz272):is"r"(mod(x),mod(m0(x)))
-+7273
-y@sum:=pl"r"(mod(y),mod(mn(x,y))):real
-t1:=islessis1(mod(pl(y,mn(x,y))),mod(x),sum,ismod(pl(y,mn(x,y)),x,satz212h(x,y)),satz271(y,mn(x,y))):lessis(mod(x),sum)
-t2:=th9"l.or"(less(mod(x),sum),is"r"(mod(x),sum),less(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),is"r"(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),t1,[t:less(mod(x),sum)]satz188f(mod(x),sum,m0"r"(mod(y)),t),[t:is"r"(mod(x),sum)]ismn1"r"(mod(x),sum,mod(y),t)):lessis(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y)))
-t3:=tris(real,mn"r"(sum,mod(y)),mn"r"(pl"r"(mod(mn(x,y)),mod(y)),mod(y)),mod(mn(x,y)),ismn1"r"(sum,pl"r"(mod(mn(x,y)),mod(y)),mod(y),compl"r"(mod(y),mod(mn(x,y)))),mnpl(mod(mn(x,y)),mod(y))):is"r"(mn"r"(sum,mod(y)),mod(mn(x,y)))
-t4:=satz168b(mn"r"(mod(x),mod(y)),mod(mn(x,y)),islessis2(mn"r"(sum,mod(y)),mod(mn(x,y)),mn"r"(mod(x),mod(y)),t3,t2)):moreis(mod(mn(x,y)),mn"r"(mod(x),mod(y)))
-t5:=ismoreis12(mod(mn(y,x)),mod(mn(x,y)),mn"r"(mod(y),mod(x)),m0"r"(mn"r"(mod(x),mod(y))),tris1(real,mod(mn(y,x)),mod(mn(x,y)),mod(m0(mn(x,y))),ismod(m0(mn(x,y)),mn(y,x),satz219(x,y)),satz272(mn(x,y))),satz181a(mod(y),mod(x)),t4(y,x)):moreis(mod(mn(x,y)),m0"r"(mn"r"(mod(x),mod(y))))
-@[r:real][s:real][m:moreis(r,s)][n:moreis(r,m0"r"(s))]
-r@t6:=th9"l.or"(neg(r),not(neg(r)),is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r),th6"l.or"(neg(r)),[t:neg(r)]absn(r,t),[t:not(neg(r))]absnn(r,t)):or(is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r))
-n@t7:=orapp(is"r"(abs(s),m0"r"(s)),is"r"(abs(s),s),moreis(r,abs(s)),t6(s),[t:is"r"(abs(s),m0"r"(s))]ismoreis2(m0"r"(s),abs(s),r,symis(real,abs(s),m0"r"(s),t),n),[t:is"r"(abs(s),s)]ismoreis2(s,abs(s),r,symis(real,abs(s),s,t),m)):moreis(r,abs(s))
--7273
-y@satz273:=t7".7273"(mod(mn(x,y)),mn"r"(mod(x),mod(y)),t4".7273",t5".7273"):moreis(mod(mn(x,y)),abs(mn"r"(mod(x),mod(y))))
--c
--r
--rp
--rt
-@[x:nat][y:nat]
-+8274
-prop1:=some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)):'prop'
-x@prop2:=all([y:nat]imp(less(x,y),not(prop1(y)))):'prop'
-@[y:nat][l:less(1,y)][f:[t:1to(1)]1to(y)]
-1y:=1out(y):1to(y)
-yy:=xout(y):1to(y)
-[i:is"e"(1to(y),1y,yy)]
-t1:=isoutne(y,1,satz24a(y),y,lessisi3(y),i):is(1,y)
-f@t2:=ec3e31(is(1,y),more(1,y),less(1,y),satz10b(1,y),l):nis(1,y)
-t3:=th3"l.imp"(is"e"(1to(y),1y,yy),is(1,y),t2,[t:is"e"(1to(y),1y,yy)]t1(t)):not(is"e"(1to(y),1y,yy))
-[u:1to(1)]
-t4:=isf(1to(1),1to(y),f,u,1o,th1"n.singlet"(u)):is"e"(1to(y),<u>f,<1o>f)
-f@[i:is"e"(1to(y),<1o>f,1y)][u:1to(1)]
-t5:=th2"e.notis"(1to(y),1y,yy,<u>f,t3,tris(1to(y),<u>f,<1o>f,1y,t4(u),i)):not(is"e"(1to(y),<u>f,yy))
-i@t6:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),yy,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,yy,t5(u))):not(image(1to(1),1to(y),f,yy))
-t7:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),yy,t6):not(surjective(1to(1),1to(y),f))
-f@[n:not(is"e"(1to(y),<1o>f,1y))][u:1to(1)]
-t8:=th2"e.notis"(1to(y),<1o>f,1y,<u>f,n,t4(u)):not(is"e"(1to(y),<u>f,1y))
-n@t9:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),1y,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,1y,t8(u))):not(image(1to(1),1to(y),f,1y))
-t10:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),1y,t9):not(surjective(1to(1),1to(y),f))
-f@t11:=th1"l.imp"(is"e"(1to(y),<1o>f,1y),not(surjective(1to(1),1to(y),f)),[t:is"e"(1to(y),<1o>f,1y)]t7(t),[t:not(is"e"(1to(y),<1o>f,1y))]t10(t)):not(surjective(1to(1),1to(y),f))
-t12:=th2"l.and"(injective(1to(1),1to(y),f),surjective(1to(1),1to(y),f),t11):not(bijective(1to(1),1to(y),f))
-l@t13:=th5"l.some"([t:1to(1)]1to(y),[f:[t:1to(1)]1to(y)]bijective(1to(1),1to(y),f),[f:[t:1to(1)]1to(y)]t12(f)):not(prop1(1,y))
-@t14:=[y:nat][t:less(1,y)]t13(y,t):prop2(1)
-x@[p:prop2(x)][y:nat][l:less(<x>suc,y)]
-x@xs:=<x>suc:nat
-l@xxs:=xout(xs):1to(<x>suc)
-yy1:=xout(y):1to(y)
-t15:=trless(1,<x>suc,y,satz24c(x),l):less(1,y)
-ym1:=mn(y,1,t15):nat
-t16:=isless12(<x>suc,pl(x,1),y,pl(ym1,1),satz4e(x),th1c"n.mn"(y,1,t15),l):less(pl(x,1),pl(ym1,1))
-t17:=satz20c(x,ym1,1,t16):less(x,ym1)
-t18:=isless2(pl(ym1,1),y,ym1,th1d"n.mn"(y,1,t15),satz18a(ym1,1)):less(ym1,y)
-[f:[t:1to(xs)]1to(y)][b:bijective(1to(xs),1to(y),f)]
-t19:=ande1(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):injective(1to(xs),1to(y),f)
-t20:=ande2(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):surjective(1to(xs),1to(y),f)
-[i:is"e"(1to(y),<xxs>f,yy1)][u:1to(x)]
-u1:=inn(x,u):nat
-t21:=satz16a(u1,x,xs,1top(x,u),satz18c(x)):less(u1,xs)
-t22:=ec3e31(is(u1,xs),more(u1,xs),less(u1,xs),satz10b(u1,xs),t21):nis(u1,xs)
-t23:=lessisi1(u1,xs,t21):lessis(u1,xs)
-u2:=outn(xs,u1,t23):1to(xs)
-t24:=th3"l.imp"(is"e"(1to(xs),u2,xxs),is(u1,xs),t22,[t:is"e"(1to(xs),u2,xxs)]isoutne(xs,u1,t23,xs,lessisi3(xs),t)):not(is"e"(1to(xs),u2,xxs))
-[j:is"e"(1to(y),<u2>f,yy1)]
-t25:=tris2(1to(y),<u2>f,<xxs>f,yy1,j,i):is"e"(1to(y),<u2>f,<xxs>f)
-t26:=isfe(1to(xs),1to(y),f,t19,u2,xxs,t25):is"e"(1to(xs),u2,xxs)
-u@t27:=th3"l.imp"(is"e"(1to(y),<u2>f,yy1),is"e"(1to(xs),u2,xxs),t24,[t:is"e"(1to(y),<u2>f,yy1)]t26(t)):not(is"e"(1to(y),<u2>f,yy1))
-w1:=inn(y,<u2>f):nat
-[j:is(w1,y)]
-t28:=tris(1to(y),<u2>f,outn(y,w1,1top(y,<u2>f)),yy1,isoutinn(y,<u2>f),isoutni(y,w1,1top(y,<u2>f),y,lessisi3(y),j)):is"e"(1to(y),<u2>f,yy1)
-u@t29:=th3"l.imp"(is(w1,y),is"e"(1to(y),<u2>f,yy1),t27,[t:is(w1,y)]t28(t)):nis(w1,y)
-t30:=ore1(less(w1,y),is(w1,y),1top(y,<u2>f),t29):less(w1,y)
-t31:=islessis2(y,pl(ym1,1),pl(w1,1),th1c"n.mn"(y,1,t15),satz25b(y,w1,t30)):lessis(pl(w1,1),pl(ym1,1))
-t32:=th9"l.or"(less(pl(w1,1),pl(ym1,1)),is(pl(w1,1),pl(ym1,1)),less(w1,ym1),is(w1,ym1),t31,[t:less(pl(w1,1),pl(ym1,1))]satz20c(w1,ym1,1,t),[t:is(pl(w1,1),pl(ym1,1))]satz20b(w1,ym1,1,t)):lessis(w1,ym1)
-w2:=outn(ym1,w1,t32):1to(ym1)
-i@f1:=[t:1to(x)]w2(t):[t:1to(x)]1to(ym1)
-u@[v:1to(x)][j:is"e"(1to(ym1),<u>f1,<v>f1)]
-t33:=isoutne(ym1,w1(u),t32(u),w1(v),t32(v),j):is(w1(u),w1(v))
-t34:=isinne(y,<u2(u)>f,<u2(v)>f,t33):is"e"(1to(y),<u2(u)>f,<u2(v)>f)
-t35:=<t34><u2(v)><u2(u)>t19:is"e"(1to(xs),u2(u),u2(v))
-t36:=isoutne(xs,u1(u),t23(u),u1(v),t23(v),t35):is(u1(u),u1(v))
-t37:=isinne(x,u,v,t36):is"e"(1to(x),u,v)
-i@[v:1to(ym1)]
-v1:=inn(ym1,v):nat
-t38:=satz16a(v1,ym1,y,1top(ym1,v),t18):less(v1,y)
-t39:=ec3e31(is(v1,y),more(v1,y),less(v1,y),satz10b(v1,y),t38):nis(v1,y)
-t40:=lessisi1(v1,y,t38):lessis(v1,y)
-v2:=outn(y,v1,t40):1to(y)
-w3:=<v2>invf(1to(xs),1to(y),f,b):1to(xs)
-t41:=thinvf2(1to(xs),1to(y),f,b,v2):is"e"(1to(y),v2,<w3>f)
-[j:is"e"(1to(xs),w3,xxs)]
-t42:=isf(1to(xs),1to(y),f,w3,xxs,j):is"e"(1to(y),<w3>f,<xxs>f)
-t43:=tr3is(1to(y),v2,<w3>f,<xxs>f,yy1,t41,t42,i):is"e"(1to(y),v2,yy1)
-t44:=isoutne(y,v1,t40,y,lessisi3(y),t43):is(v1,y)
-v@t45:=th3"l.imp"(is"e"(1to(xs),w3,xxs),is(v1,y),t39,[t:is"e"(1to(xs),w3,xxs)]t44(t)):not(is"e"(1to(xs),w3,xxs))
-w4:=inn(xs,w3):nat
-[j:is(w4,xs)]
-t46:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),xxs,isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),xs,lessisi3(xs),j)):is"e"(1to(xs),w3,xxs)
-v@t47:=th3"l.imp"(is(w4,xs),is"e"(1to(xs),w3,xxs),t45,[t:is(w4,xs)]t46(t)):nis(w4,xs)
-t48:=ore1(less(w4,xs),is(w4,xs),1top(xs,w3),t47):less(w4,xs)
-t49:=satz26a(x,w4,t48):lessis(w4,x)
-w5:=outn(x,w4,t49):1to(x)
-t50:=isinoutn(x,w4,t49):is(w4,u1(w5))
-t51:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),u2(w5),isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),u1(w5),t23(w5),t50)):is"e"(1to(xs),w3,u2(w5))
-t52:=isf(1to(xs),1to(y),f,w3,u2(w5),t51):is"e"(1to(y),<w3>f,<u2(w5)>f)
-t53:=tris(1to(y),v2,<w3>f,<u2(w5)>f,t41,t52):is"e"(1to(y),v2,<u2(w5)>f)
-t54:=tris(nat,v1,inn(y,v2),w1(w5),isinoutn(y,v1,t40),isinni(y,v2,<u2(w5)>f,t53)):is(v1,w1(w5))
-t55:=tris(1to(ym1),v,outn(ym1,v1,1top(ym1,v)),w2(w5),isoutinn(ym1,v),isoutni(ym1,v1,1top(ym1,v),w1(w5),t32(w5),t54)):is"e"(1to(ym1),v,<w5>f1)
-t56:=somei(1to(x),[t:1to(x)]is"e"(1to(ym1),v,<t>f1),w5,t55):image(1to(x),1to(ym1),f1,v)
-i@t57:=andi(injective(1to(x),1to(ym1),f1),surjective(1to(x),1to(ym1),f1),[u:1to(x)][v:1to(x)][t:is"e"(1to(ym1),<u>f1,<v>f1)]t37(u,v,t),[u:1to(ym1)]t56(u)):bijective(1to(x),1to(ym1),f1)
-t58:=somei([t:1to(x)]1to(ym1),[g:[t:1to(x)]1to(ym1)]bijective(1to(x),1to(ym1),g),f1,t57):prop1(ym1)
-t59:=<t58><t17><ym1>p:con
-b@[n:not(is"e"(1to(y),<xxs>f,yy1))]
-m0:=<yy1>invf(1to(xs),1to(y),f,b):1to(xs)
-t60:=thinvf2(1to(xs),1to(y),f,b,yy1):is"e"(1to(y),yy1,<m0>f)
-f2:=changef(1to(xs),1to(y),f,m0,xxs):[t:1to(xs)]1to(y)
-t61:=changef2(1to(xs),1to(y),f,m0,xxs,xxs,refis(1to(xs),xxs)):is"e"(1to(y),<xxs>f2,<m0>f)
-t62:=tris2(1to(y),<xxs>f2,yy1,<m0>f,t61,t60):is"e"(1to(y),<xxs>f2,yy1)
-t63:=th6"e.wissel"(1to(xs),1to(y),f,m0,xxs,b):bijective(1to(xs),1to(y),f2)
-t64:=t59(f2,t63,t62):con
-b@t65:=th1"l.imp"(is"e"(1to(y),<xxs>f,yy1),con,[t:is"e"(1to(y),<xxs>f,yy1)]t59(t),[t:not(is"e"(1to(y),<xxs>f,yy1))]t64(t)):con
-l@t65a:=th5"l.some"([t:1to(xs)]1to(y),[f:[t:1to(xs)]1to(y)]bijective(1to(xs),1to(y),f),[f:[t:1to(xs)]1to(y)][t:bijective(1to(xs),1to(y),f)]t65(f,t)):not(prop1(xs,y))
-p@t66:=[y:nat][t:less(xs,y)]t65a(y,t):prop2(xs)
-x@t67:=induction([t:nat]prop2(t),t14,[t:nat][u:prop2(t)]t66(t,u),x):prop2(x)
--8274
-[l:less(x,y)]
-satz274:=<l><y>t67".8274":not(some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)))
-[f:[t:1to(x)]1to(y)]
-satz274a:=th4"l.some"([t:1to(x)]1to(y),[g:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),g),satz274,f):not(bijective(1to(x),1to(y),f))
-+*rt
-+*rp
-+*r
-+*c
-@[x:nat][u:1to(x)]
-inn:=inn"n"(x,u):nat
-@[q:[t:cx][u:cx]cx][x:nat][f:[t:1to(x)]cx]
-x@[n:1to(x)][o:not(is"e"(1to(x),n,xout(x)))]
-+8275
-t1:=th3"l.imp"(is"n"(inn(x,n),x),is"e"(1to(x),n,xout(x)),o,[t:is"n"(inn(x,n),x)]tris(1to(x),n,outn(x,inn(x,n),1top(x,n)),xout(x),isoutinn(x,n),isoutni(x,inn(x,n),1top(x,n),x,lessisi3(x),t))):not(is"n"(inn(x,n),x))
-t2:=ore1(less"n"(inn(x,n),x),is"n"(inn(x,n),x),1top(x,n),t1):less"n"(inn(x,n),x)
--8275
-lemma275:=satz25c(x,inn(x,n),t2".8275"):lessis"n"(<inn(x,n)>suc,x)
-f@[g:[t:1to(x)]cx]
-recprop:=and(is(<1out(x)>g,<1out(x)>f),[t:1to(x)][u:not(is"e"(1to(x),t,xout(x)))]is(<outn(x,<inn(x,t)>suc,lemma275(t,u))>g,<<outn(x,<inn(x,t)>suc,lemma275(t,u))>f><<t>g>q)):'prop'
-+*8275
-x@1o:=1out(x):1to(x)
-xo:=xout(x):1to(x)
-[u:nat][l:lessis"n"(<u>suc,x)]
-t11:=satz16b(u,<u>suc,x,satz18c(u),l):less"n"(u,x)
-t12:=lessisi1"n"(u,x,t11):lessis"n"(u,x)
-ux:=outn(x,u,t12):1to(x)
-t13:=ec3e31(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11):nis"n"(u,x)
-t14:=th3"l.imp"(is"e"(1to(x),ux,xo),is"n"(u,x),t13,[t:is"e"(1to(x),ux,xo)]isoutne(x,u,t12,x,lessisi3(x),t)):not(is"e"(1to(x),ux,xo))
-t15:=isf(nat,nat,suc,u,inn(x,ux),isinoutn(x,u,t12)):is"n"(<u>suc,<inn(x,ux)>suc)
-t16:=isoutni(x,<u>suc,l,<inn(x,ux)>suc,lemma275(ux,t14),t15):is"e"(1to(x),outn(x,<u>suc,l),outn(x,<inn(x,ux)>suc,lemma275(ux,t14)))
-x@[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
-ns:=outn(x,<inn(x,n)>suc,lemma275(n,o)):1to(x)
-f@[g:[t:1to(x)]cx]
-prop1:=is(<1o>g,<1o>f):'prop'
-prop2:=[t:1to(x)][u:not(is"e"(1to(x),t,xo))]is(<ns(t,u)>g,<<ns(t,u)>f><<t>g>q):'prop'
-[pg:recprop(g)]
-t3:=ande1(prop1,prop2,pg):prop1
-[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
-t4:=<o><n>ande2(prop1,prop2,pg):is(<ns(n,o)>g,<<ns(n,o)>f><<n>g>q)
-pg@[u:nat][l:lessis"n"(<u>suc,x)]
-t17:=isf(1to(x),cx,g,outn(x,<u>suc,l),ns(ux(u,l),t14(u,l)),t16(u,l)):is(<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g)
-t18:=tris(cx,<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,t17,t4(pg,ux(u,l),t14(u,l))):is(<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q)
-g@[h:[t:1to(x)]cx][u:nat][l:lessis"n"(u,x)]
-prop3:=is(<outn(x,u,l)>g,<outn(x,u,l)>h):'prop'
-u@prop4:=and(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(t)):'prop'
-prop5:=or(prop4,more"n"(u,x)):'prop'
-h@[pg:recprop(g)][ph:recprop(h)][l:lessis"n"(1,x)]
-t5:=isoutni(x,1,l,1,satz24a(x),refis(nat,1)):is"e"(1to(x),outn(x,1,l),1o)
-t6:=isf(1to(x),cx,g,outn(x,1,l),1o,t5):is(<outn(x,1,l)>g,<1o>g)
-t7:=tris(cx,<outn(x,1,l)>g,<1o>g,<1o>f,t6,t3(pg)):is(<outn(x,1,l)>g,<1o>f)
-t8:=tris2(cx,<outn(x,1,l)>g,<outn(x,1,l)>h,<1o>f,t7,t7(h,g,ph,pg,l)):prop3(1,l)
-ph@t9:=andi(lessis"n"(1,x),[t:lessis"n"(1,x)]prop3(1,t),satz24a(x),[t:lessis"n"(1,x)]t8(t)):prop4(1)
-t10:=ori1(prop4(1),more"n"(1,x),t9):prop5(1)
-[u:nat][p:prop5(u)][l:lessis"n"(<u>suc,x)]
-t19:=ec3e32(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11(u,l)):not(more"n"(u,x))
-t20:=ore1(prop4(u),more"n"(u,x),p,t19):prop4(u)
-t21:=<t12(u,l)>ande2(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(u,t),t20):prop3(u,t12(u,l))
-t22:=isf(cx,cx,[t:cx]<<ns(ux(u,l),t14(u,l))>f><t>q,<ux(u,l)>g,<ux(u,l)>h,t21):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q)
-t23:=symis(cx,<outn(x,<u>suc,l)>h,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,t18(h,ph,u,l)):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h)
-t24:=tr3is(cx,<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h,t18(g,pg,u,l),t22,t23):prop3(<u>suc,l)
-t25:=andi(lessis"n"(<u>suc,x),[t:lessis"n"(<u>suc,x)]prop3(<u>suc,t),l,[t:lessis"n"(<u>suc,x)]t24(t)):prop4(<u>suc)
-t26:=ori1(prop4(<u>suc),more"n"(<u>suc,x),t25):prop5(<u>suc)
-p@[n:not(lessis"n"(<u>suc,x))]
-t27:=satz10k(<u>suc,x,n):more"n"(<u>suc,x)
-t28:=ori2(prop4(<u>suc),more"n"(<u>suc,x),t27):prop5(<u>suc)
-p@t29:=th1"l.imp"(lessis"n"(<u>suc,x),prop5(<u>suc),[t:lessis"n"(<u>suc,x)]t26(t),[t:not(lessis"n"(<u>suc,x))]t28(t)):prop5(<u>suc)
-u@t30:=induction([v:nat]prop5(v),t10,[v:nat][t:prop5(v)]t29(v,t),u):prop5(u)
-ph@[n:1to(x)]
-t31:=isf(1to(x),cx,g,n,outn(x,inn(x,n),1top(x,n)),isoutinn(x,n)):is(<n>g,<outn(x,inn(x,n),1top(x,n))>g)
-t32:=satz10d(inn(x,n),x,1top(x,n)):not(more"n"(inn(x,n),x))
-t33:=ore1(prop4(inn(x,n)),more"n"(inn(x,n),x),t30(inn(x,n)),t32):prop4(inn(x,n))
-t34:=<1top(x,n)>ande2(lessis"n"(inn(x,n),x),[t:lessis"n"(inn(x,n),x)]prop3(inn(x,n),t),t33):prop3(inn(x,n),1top(x,n))
-t35:=symis(cx,<n>h,<outn(x,inn(x,n),1top(x,n))>h,t31(h,g,ph,pg,n)):is(<outn(x,inn(x,n),1top(x,n))>h,<n>h)
-t36:=tr3is(cx,<n>g,<outn(x,inn(x,n),1top(x,n))>g,<outn(x,inn(x,n),1top(x,n))>h,<n>h,t31,t34,t35):is(<n>g,<n>h)
-ph@t37:=fisi(1to(x),cx,g,h,[t:1to(x)]t36(t)):is"e"([t:1to(x)]cx,g,h)
-f@prop6:=some"l"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(g)):'prop'
-x@prop7:=all"l"([t:1to(x)]cx,[f:[t:1to(x)]cx]prop6(f)):'prop'
-q@[f:[t:1to(1)]cx]
-t38:=refis(cx,<1o(1)>f):prop1(1,f,f)
-[n:1to(1)][o:not(is"e"(1to(1),n,xo(1)))]
-t39:=<th1"n.singlet"(n)>o:con
-t40:=cone(is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q),t39):is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q)
-f@t41:=andi(prop1(1,f,f),prop2(1,f,f),t38,[t:1to(1)][u:not(is"e"(1to(1),t,xo(1)))]t40(t,u)):recprop(1,f,f)
-t42:=somei([t:1to(1)]cx,[g:[t:1to(1)]cx]recprop(1,f,g),f,t41):prop6(1,f)
-q@t43:=[f:[t:1to(1)]cx]t42(f):prop7(1)
-x@[p:prop7(x)]
-xs:=<x>suc:nat
-[f:[t:1to(xs)]cx]
-f1:=left(cx,xs,x,lessisi1"n"(x,xs,satz18c(x)),f):[t:1to(x)]cx
-t44:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f1,g)][v:recprop(x,f1,h)]t37(f1,g,h,u,v),<f1>p):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g))
-g1:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):[t:1to(x)]cx
-t45:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):recprop(x,f1,g1)
-[n:1to(xs)]
-nxs:=is"e"(1to(xs),n,xo(xs)):'prop'
-[o:not(nxs)]
-t46:=satz26a(x,inn(xs,n),t2(xs,n,o)):lessis"n"(inn(xs,n),x)
-n1:=outn(x,inn(xs,n),t46):1to(x)
-b:=<n1>g1:cx
-[o1:not(nxs)]
-t47:=isoutni(x,inn(xs,n),t46(o),inn(xs,n),t46(o1),refis(nat,inn(xs,n))):is"e"(1to(x),n1(o),n1(o1))
-t48:=isf(1to(x),cx,g1,n1(o),n1(o1),t47):is(b(o),b(o1))
-f@a:=<<xo(xs)>f><<xo(x)>g1>q:cx
-n@c:=ite"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u)):cx
-[i:nxs]
-t49:=itet"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),i):is(c,a)
-o@t50:=itef"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),o):is(c,b)
-f@g2:=[t:1to(xs)]c(t):[t:1to(xs)]cx
-t51:=th3"l.imp"(is"e"(1to(xs),1o(xs),xo(xs)),is"n"(1,xs),symnotis(nat,xs,1,<x>ax3),[t:is"e"(1to(xs),1o(xs),xo(xs))]isoutne(xs,1,satz24a(xs),xs,lessisi3(xs),t)):not(is"e"(1to(xs),1o(xs),xo(xs)))
-t52:=t50(1o(xs),t51):is(c(1o(xs)),b(1o(xs),t51))
-t53:=isinoutn(xs,1,satz24a(xs)):is"n"(1,inn(xs,1o(xs)))
-t54:=isoutni(x,1,satz24a(x),inn(xs,1o(xs)),t46(1o(xs),t51),t53):is"e"(1to(x),1o(x),n1(1o(xs),t51))
-t55:=isf(1to(x),cx,g1,1o(x),n1(1o(xs),t51),t54):is(<1o(x)>g1,b(1o(xs),t51))
-t56:=tris2(cx,c(1o(xs)),<1o(x)>g1,b(1o(xs),t51),t52,t55):is(c(1o(xs)),<1o(x)>g1)
-t57:=tris(cx,c(1o(xs)),<1o(x)>g1,<1o(x)>f1,t56,t3(x,f1,g1,t45)):is(c(1o(xs)),<1o(x)>f1)
-t58:=isinoutn(x,1,satz24a(x)):is"n"(1,inn(x,1o(x)))
-t59:=isoutni(xs,1,satz24a(xs),inn(x,1o(x)),trlessis"n"(inn(x,1o(x)),x,xs,1top(x,1o(x)),lessisi1"n"(x,xs,satz18c(x))),t58):is"e"(1to(xs),1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)))
-t60:=isf(1to(xs),cx,f,1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)),t59):is(<1o(xs)>f,<1o(x)>f1)
-t61:=tris2(cx,c(1o(xs)),<1o(xs)>f,<1o(x)>f1,t57,t60):prop1(xs,f,g2)
-o@[i:is"e"(1to(xs),ns(xs,n,o),xo(xs))]
-t62:=isoutne(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),i):is"n"(<inn(xs,n)>suc,xs)
-t63:=<t62><x><inn(xs,n)>ax4:is"n"(inn(xs,n),x)
-t64:=isoutni(x,inn(xs,n),t46,x,lessisi3(x),t63):is"e"(1to(x),n1,xo(x))
-t65:=isf(1to(x),cx,g1,xo(x),n1,symis(1to(x),n1,xo(x),t64)):is(<xo(x)>g1,b)
-t66:=tris2(cx,<xo(x)>g1,c,b,t65,t50):is(<xo(x)>g1,c)
-t67:=isf(cx,cx,[t:cx]<<xo(xs)>f><t>q,<xo(x)>g1,c,t66):is(a,<<xo(xs)>f><c>q)
-t68:=isf(1to(xs),cx,f,xo(xs),ns(xs,n,o),symis(1to(xs),ns(xs,n,o),xo(xs),i)):is(<xo(xs)>f,<ns(xs,n,o)>f)
-t69:=isf(cx,cx,<c>q,<xo(xs)>f,<ns(xs,n,o)>f,t68):is(<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q)
-t70:=tr3is(cx,c(ns(xs,n,o)),a,<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q,t49(ns(xs,n,o),i),t67,t69):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
-o@[o1:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))][i:is"e"(1to(x),n1,xo(x))]
-t71:=isoutne(x,inn(xs,n),t46,x,lessisi3(x),i):is"n"(inn(xs,n),x)
-t72:=ax2(inn(xs,n),x,t71):is"n"(<inn(xs,n)>suc,xs)
-t73:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),t72):is"e"(1to(xs),ns(xs,n,o),xo(xs))
-o1@t74:=th3"l.imp"(is"e"(1to(x),n1,xo(x)),is"e"(1to(xs),ns(xs,n,o),xo(xs)),o1,[t:is"e"(1to(x),n1,xo(x))]t73(t)):not(is"e"(1to(x),n1,xo(x)))
-t75:=isinoutn(x,inn(xs,n),t46):is"n"(inn(xs,n),inn(x,n1))
-t76:=ax2(inn(xs,n),inn(x,n1),t75):is"n"(<inn(xs,n)>suc,<inn(x,n1)>suc)
-t77:=isinoutn(xs,<inn(xs,n)>suc,lemma275(xs,n,o)):is"n"(<inn(xs,n)>suc,inn(xs,ns(xs,n,o)))
-t78:=tris1(nat,inn(xs,ns(xs,n,o)),<inn(x,n1)>suc,<inn(xs,n)>suc,t77,t76):is"n"(inn(xs,ns(xs,n,o)),<inn(x,n1)>suc)
-t79:=isoutni(x,inn(xs,ns(xs,n,o)),t46(ns(xs,n,o),o1),<inn(x,n1)>suc,lemma275(x,n1,t74),t78):is"e"(1to(x),n1(ns(xs,n,o),o1),ns(n1,t74))
-t80:=isf(1to(x),cx,g1,n1(ns(xs,n,o),o1),ns(n1,t74),t79):is(b(ns(xs,n,o),o1),<ns(n1,t74)>g1)
-t81:=isinoutn(x,<inn(x,n1)>suc,lemma275(x,n1,t74)):is"n"(<inn(x,n1)>suc,inn(x,ns(n1,t74)))
-t82:=tris(nat,<inn(xs,n)>suc,<inn(x,n1)>suc,inn(x,ns(n1,t74)),t76,t81):is"n"(<inn(xs,n)>suc,inn(x,ns(n1,t74)))
-t83:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),inn(x,ns(n1,t74)),trlessis"n"(inn(x,ns(n1,t74)),x,xs,1top(x,ns(n1,t74)),lessisi1"n"(x,xs,satz18c(x))),t82):is"e"(1to(xs),ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)))
-t84:=isf(1to(xs),cx,f,ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)),t83):is(<ns(xs,n,o)>f,<ns(n1,t74)>f1)
-t85:=isf(cx,cx,<b>q,<ns(xs,n,o)>f,<ns(n1,t74)>f1,t84):is(<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q)
-t86:=isf(cx,cx,[t:cx]<<ns(xs,n,o)>f><t>q,c,b,t50):is(<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q)
-t87:=tr3is(cx,c(ns(xs,n,o)),b(ns(xs,n,o),o1),<ns(n1,t74)>g1,<<ns(n1,t74)>f1><b>q,t50(ns(xs,n,o),o1),t80,t4(f1,g1,t45,n1,t74)):is(c(ns(xs,n,o)),<<ns(n1,t74)>f1><b>q)
-t88:=tris(cx,<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q,t86,t85):is(<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q)
-t89:=tris2(cx,c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q,t87,t88):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
-o@t90:=th1"l.imp"(is"e"(1to(xs),ns(xs,n,o),xo(xs)),is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q),[t:is"e"(1to(xs),ns(xs,n,o),xo(xs))]t70(t),[t:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))]t89(t)):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
-f@t91:=[t:1to(xs)][u:not(nxs(t))]t90(t,u):prop2(xs,f,g2)
-t92:=andi(prop1(xs,f,g2),prop2(xs,f,g2),t61,t91):recprop(xs,f,g2)
-t93:=somei([t:1to(xs)]cx,[g:[t:1to(xs)]cx]recprop(xs,f,g),g2,t92):prop6(xs,f)
-p@t94:=[f:[t:1to(xs)]cx]t93(f):prop7(xs)
-x@t95:=induction([y:nat]prop7(y),t43,[y:nat][t:prop7(y)]t94(y,t),x):prop7(x)
-[f:[t:1to(x)]cx]
-t96:=<f>t95:prop6(x,f)
-t97:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f,g)][v:recprop(x,f,h)]t37(f,g,h,u,v),t96):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
--8275
-f@satz275:=t97".8275"(f):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
-recf:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):[t:1to(x)]cx
-satz275a:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):recprop(x,f,recf)
-[n:1to(x)]
-rec:=<n>recf:cx
-f@satz275b:=t3".8275"(x,f,recf,satz275a):is(rec(1out(x)),<1out(x)>f)
-n@[o:not(is"e"(1to(x),n,xout(x)))]
-sucx:=ns".8275"(n,o):1to(x)
-satz275c:=t4".8275"(x,f,recf,satz275a,n,o):is(rec(sucx(n,o)),<<sucx(n,o)>f><rec(n)>q)
-f@[g:[t:1to(x)]cx][r:recprop(x,f,g)]
-satz275d:=t37".8275"(x,f,g,recf,r,satz275a):is"e"([t:1to(x)]cx,g,recf)
-[n:1to(x)]
-satz275e:=fise(1to(x),cx,g,recf,satz275d,n):is(<n>g,rec(n))
-x@[y:nat]
-+*8275
-y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
-fl:=left(cx,x,y,l,f):[t:1to(y)]cx
-rf:=recf(x,f):[t:1to(x)]cx
-rfl:=left(cx,x,y,l,rf):[t:1to(y)]cx
-t98:=isinoutn(y,1,satz24a(y)):is"n"(1,inn(y,1out(y)))
-t99:=isoutni(x,1,satz24a(x),inn(y,1out(y)),trlessis"n"(inn(y,1out(y)),y,x,1top(y,1out(y)),l),t98):is"e"(1to(x),1out(x),left1to(x,y,l,1out(y)))
-t100:=isp(1to(x),[t:1to(x)]is(<t>rf,<t>f),1out(x),left1to(x,y,l,1out(y)),t3(x,f,rf,satz275a(x,f)),t99):prop1(y,fl,rfl)
-[n:1to(y)][o:not(is"e"(1to(y),n,xout(y)))]
-t100a:=th3"l.imp"(is"n"(inn(y,n),y),is"e"(1to(y),n,xout(y)),o,[t:is"n"(inn(y,n),y)]tris(1to(y),n,outn(y,inn(y,n),1top(y,n)),xout(y),isoutinn(y,n),isoutni(y,inn(y,n),1top(y,n),y,lessisi3(y),t))):not(is"n"(inn(y,n),y))
-t100b:=ore1(less"n"(inn(y,n),y),is"n"(inn(y,n),y),1top(y,n),t100a):less"n"(inn(y,n),y)
-t101:=satz16b(inn(y,n),y,x,t100b,l):less"n"(inn(y,n),x)
-t102:=ec3e31(is"n"(inn(y,n),x),more"n"(inn(y,n),x),less"n"(inn(y,n),x),satz10b(inn(y,n),x),t101):nis"n"(inn(y,n),x)
-t103:=th3"l.imp"(is"e"(1to(x),left1to(x,y,l,n),xout(x)),is"n"(inn(y,n),x),t102,[t:is"e"(1to(x),left1to(x,y,l,n),xout(x))]isoutne(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l),x,lessisi3(x),t)):not(is"e"(1to(x),left1to(x,y,l,n),xout(x)))
-t104:=t4(x,f,rf,satz275a(x,f),left1to(x,y,l,n),t103):is(<ns(x,left1to(x,y,l,n),t103)>rf,<<ns(x,left1to(x,y,l,n),t103)>f><<n>rfl>q)
-t105:=isinoutn(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l)):is"n"(inn(y,n),inn(x,left1to(x,y,l,n)))
-t106:=ax2(inn(y,n),inn(x,left1to(x,y,l,n)),t105):is"n"(<inn(y,n)>suc,<inn(x,left1to(x,y,l,n))>suc)
-t107:=isinoutn(y,<inn(y,n)>suc,lemma275(y,n,o)):is"n"(<inn(y,n)>suc,inn(y,ns(y,n,o)))
-t108:=tris1(nat,<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)),<inn(y,n)>suc,t106,t107):is"n"(<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)))
-t109:=isoutni(x,<inn(x,left1to(x,y,l,n))>suc,lemma275(x,left1to(x,y,l,n),t103),inn(y,ns(y,n,o)),trlessis"n"(inn(y,ns(y,n,o)),y,x,1top(y,ns(y,n,o)),l),t108):is"e"(1to(x),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)))
-t110:=isp(1to(x),[t:1to(x)]is(<t>rf,<<t>f><<n>rfl>q),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)),t104,t109):is(<ns(y,n,o)>rfl,<<ns(y,n,o)>fl><<n>rfl>q)
-f@t111:=[t:1to(y)][u:not(is"e"(1to(y),t,xout(y)))]t110(t,u):prop2(y,fl,rfl)
-t112:=andi(prop1(y,fl,rfl),prop2(y,fl,rfl),t100,t111):recprop(y,fl,rfl)
--8275
-y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
-satz275f:=satz275d(y,fl".8275"(l,f),rfl".8275"(l,f),t112".8275"(l,f)):is"e"([t:1to(y)]cx,left(cx,x,y,l,recf(x,f)),recf(y,left(cx,x,y,l,f)))
-x@[f:[t:1to(pl"n"(x,1))]cx]
-+8276
-xs:=<x>suc:nat
-x1:=pl"n"(x,1):nat
-t1:=lessisi1"n"(x,x1,satz18a(x,1)):lessis"n"(x,x1)
-t2:=lessisi1"n"(x,xs,satz18c(x)):lessis"n"(x,xs)
-t3:=lessisi2"n"(xs,x1,satz4e(x)):lessis"n"(xs,x1)
-fx:=left(cx,x1,x,t1,f):[t:1to(x)]cx
-f1:=left(cx,x1,xs,t3,f):[t:1to(xs)]cx
-f1x:=f1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
-g1:=g2"c.8275"(x,t95"c.8275"(x),f1):[t:1to(xs)]cx
-g1x:=g1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
-g:=left(cx,x1,xs,t3,recf(x1,f)):[t:1to(xs)]cx
-t4:=t49"c.8275"(x,t95"c.8275"(x),f1,xout(xs),refis(1to(xs),xout(xs))):is(<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q)
-t5:=satz275d(xs,f1,g1,t92"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(xs)]cx,g1,recf(xs,f1))
-t6:=satz275f(x1,xs,t3,f):is"e"([t:1to(xs)]cx,g,recf(xs,f1))
-t7:=tris2([t:1to(xs)]cx,g,g1,recf(xs,f1),t6,t5):is"e"([t:1to(xs)]cx,g,g1)
-t8:=fise(1to(xs),cx,g,g1,t7,xout(xs)):is(<xout(xs)>g,<xout(xs)>g1)
-t9:=tris(cx,<xout(xs)>g,<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q,t8,t4):is(<xout(xs)>g,<<xout(xs)>f1><<xout(x)>g1x>q)
-[n:1to(x)]
-t10:=isinoutn(xs,inn(x,n),trlessis"n"(inn(x,n),x,xs,1top(x,n),t2)):is"n"(inn(x,n),inn(xs,left1to(xs,x,t2,n)))
-t11:=isoutni(x1,inn(x,n),trlessis"n"(inn(x,n),x,x1,1top(x,n),t1),inn(xs,left1to(xs,x,t2,n)),trlessis"n"(inn(xs,left1to(xs,x,t2,n)),xs,x1,1top(xs,left1to(xs,x,t2,n)),t3),t10):is"e"(1to(x1),left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)))
-t12:=isf(1to(x1),cx,f,left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)),t11):is(<n>fx,<n>f1x)
-f@t13:=fisi(1to(x),cx,fx,f1x,[t:1to(x)]t12(t)):is"e"([t:1to(x)]cx,fx,f1x)
-t14:=isf([t:1to(x)]cx,[t:1to(x)]cx,[u:[t:1to(x)]cx]recf(x,u),fx,f1x,t13):is"e"([t:1to(x)]cx,recf(x,fx),recf(x,f1x))
-t15:=satz275d(x,f1x,g1x,t45"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(x)]cx,g1x,recf(x,f1x))
-t16:=tris2([t:1to(x)]cx,g1x,recf(x,fx),recf(x,f1x),t15,t14):is"e"([t:1to(x)]cx,g1x,recf(x,fx))
-t17:=fise(1to(x),cx,g1x,recf(x,fx),t16,xout(x)):is(<xout(x)>g1x,<xout(x)>recf(x,fx))
-t18:=isinoutn(xs,xs,lessisi3(xs)):is"n"(xs,inn(xs,xout(xs)))
-t19:=tris(nat,x1,xs,inn(xs,xout(xs)),satz4a(x),t18):is"n"(x1,inn(xs,xout(xs)))
-t20:=isoutni(x1,x1,lessisi3(x1),inn(xs,xout(xs)),trlessis"n"(inn(xs,xout(xs)),xs,x1,1top(xs,xout(xs)),t3),t19):is"e"(1to(x1),xout(x1),left1to(x1,xs,t3,xout(xs)))
-t21:=isp1(1to(x1),[t:1to(x1)]is(<t>recf(x1,f),<<t>f><<xout(x)>g1x>q),left1to(x1,xs,t3,xout(xs)),xout(x1),t9,t20):is(<xout(x1)>recf(x1,f),<<xout(x1)>f><<xout(x)>g1x>q)
-t22:=isf(cx,cx,[t:cx]<<xout(x1)>f><t>q,<xout(x)>g1x,<xout(x)>recf(x,fx),t17):is(<<xout(x1)>f><<xout(x)>g1x>q,<<xout(x1)>f><<xout(x)>recf(x,fx)>q)
--8276
-satz276:=tris(cx,<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>g1x".8276">q,<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,fx".8276")>q,t21".8276",t22".8276"):is(<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
-x@[f:[u:1to(x)]cx]
-smpr:=rec(x,f,xout(x)):cx
-@[x:nat][f:[u:1to(x)]cx]
-sum:=smpr([t:cx][u:cx]pl(t,u),x,f):cx
-prod:=smpr([t:cx][u:cx]ts(t,u),x,f):cx
-q@[f:[u:1to(1)]cx]
-+8277
-t1:=isoutni(1,1,satz24a(1),1,lessisi3(1),refis(nat,1)):is"e"(1to(1),1out(1),xout(1))
--8277
-satz277:=isp(1to(1),[t:1to(1)]is(rec(1,f,t),<t>f),1out(1),xout(1),satz275b(1,f),t1".8277"):is(smpr(1,f),<xout(1)>f)
-q@[x:nat][f:[u:1to(pl"n"(x,1))]cx]
-satz278:=satz276(x,f):is(smpr(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><smpr(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
-x@[f:[u:1to(x)]cx][y:nat][i:is"n"(y,x)]
-+v8
-t1:=lessisi2"n"(y,x,i):lessis"n"(y,x)
-f0:=left(cx,x,y,t1,f):[t:1to(y)]cx
-t2:=fise(1to(y),cx,left(cx,x,y,t1,recf(x,f)),recf(y,f0),satz275f(x,y,t1,f),xout(y)):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(y,f0))
-t3:=tris1(nat,inn(y,xout(y)),x,y,isinoutn(y,y,lessisi3(y)),i):is"n"(inn(y,xout(y)),x)
-t4:=isoutni(x,inn(y,xout(y)),trlessis"n"(inn(y,xout(y)),y,x,1top(y,xout(y)),t1),x,lessisi3(x),t3):is"e"(1to(x),left1to(x,y,t1,xout(y)),xout(x))
-t5:=isf(1to(x),cx,recf(x,f),left1to(x,y,t1,xout(y)),xout(x),t4):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(x,f))
--v8
-issmpr:=tris1(cx,smpr(y,f0".v8"),smpr(x,f),<left1to(x,y,t1".v8",xout(y))>recf(x,f),t2".v8",t5".v8"):is(smpr(y,left(cx,x,y,lessisi2"n"(y,x,i),f)),smpr(x,f))
-@[z:complex][x:nat]
-+8279
-xr:=rlofnt(x):real
-prop1:=is(sum(x,[t:1to(x)]z),ts(z,pli(xr,0))):'prop'
-z@t1:=satz277([t:cx][u:cx]pl(t,u),[t:1to(1)]z):is(sum(1,[t:1to(1)]z),z)
-t2:=tris(cx,sum(1,[t:1to(1)]z),z,ts(z,1c),t1,satz222a(z)):prop1(1)
-x@[p:prop1(x)]
-t3:=satz278([t:cx][u:cx]pl(t,u),x,[t:1to(pl"n"(x,1))]z):is(sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z))
-t4:=ispl12(sum(x,[t:1to(x)]z),ts(z,pli(xr,0)),z,ts(z,1c),p,satz222a(z)):is(pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)))
-t5:=distpt2(z,pli(xr,0),1c):is(pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)))
-t6:=plis12a(xr,0,1rl,0):is(pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)))
-t7:=isrecx12(pl"r"(xr,1rl),rlofnt(pl"n"(x,1)),pl"r"(0,0),0,satzr155b(x,1),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0))
-t8:=tris(cx,pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0),t6,t7):is(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0))
-t9:=ists2(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0),z,t8):is(ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)))
-t10:=tr4is(cx,sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)),t3,t4,t5,t9):prop1(pl"n"(x,1))
-t11:=isp(nat,[t:nat]prop1(t),pl"n"(x,1),<x>suc,t10,satz4a(x)):prop1(<x>suc)
--8279
-satz279:=induction([t:nat]prop1".8279"(t),t2".8279",[u:nat][t:prop1".8279"(u)]t11".8279"(u,t),x):is(sum(x,[t:1to(x)]z),ts(z,pli(rlofnt(x),0)))
-q@[f:[t:1to(2)]cx]
-+8280
-t1:=lessisi1"n"(1,2,satz18a(1,1)):lessis"n"(1,2)
-f1:=left(cx,2,1,t1,f):[t:1to(1)]cx
-t2:=satz278(q,1,f):is(smpr(2,f),<<xout(2)>f><smpr(1,f1)>q)
-t3:=satz277(q,f1):is(smpr(1,f1),<xout(1)>f1)
-t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-t5:=isoutni(2,1,satz24a(2),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,2,1top(1,xout(1)),t1),t4):is"e"(1to(2),1out(2),left1to(2,1,t1,xout(1)))
-t6:=isf(1to(2),cx,f,1out(2),left1to(2,1,t1,xout(1)),t5):is(<1out(2)>f,<xout(1)>f1)
-t7:=tris2(cx,smpr(1,f1),<1out(2)>f,<xout(1)>f1,t3,t6):is(smpr(1,f1),<1out(2)>f)
-t8:=isf(cx,cx,[t:cx]<<xout(2)>f><t>q,smpr(1,f1),<1out(2)>f,t7):is(<<xout(2)>f><smpr(1,f1)>q,<<xout(2)>f><<1out(2)>f>q)
--8280
-satz280:=tris(cx,smpr(2,f),<<xout(2)>f><smpr(1,f1".8280")>q,<<xout(2)>f><<1out(2)>f>q,t2".8280",t8".8280"):is(smpr(2,f),<<xout(2)>f><<1out(2)>f>q)
-q@assoc:=[x:cx][y:cx][z:cx]is(<z><<y><x>q>q,<<z><y>q><x>q):'prop'
-@assocp1:=[x:cx][y:cx][z:cx]asspl1(x,y,z):assoc([x:cx][y:cx]pl(x,y))
-assocts:=[x:cx][y:cx][z:cx]assts1(x,y,z):assoc([x:cx][y:cx]ts(x,y))
-q@[a:assoc][z:cx][u:cx][v:cx]
-assq1:=<v><u><z>a:is(<v><<u><z>q>q,<<v><u>q><z>q)
-assq2:=symis(cx,<v><<u><z>q>q,<<v><u>q><z>q,assq1):is(<<v><u>q><z>q,<v><<u><z>q>q)
-q@[a:assoc(q)][x:nat][y:nat][f:[t:1to(pl"n"(x,y))]cx]
-+8281
-y@t1:=lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)):lessis"n"(x,pl"n"(x,y))
-f@f1:=left(cx,pl"n"(x,y),x,t1,f):[t:1to(x)]cx
-f2:=right(cx,x,y,f):[t:1to(y)]cx
-prop1:=is(smpr(pl"n"(x,y),f),<smpr(y,f2)><smpr(x,f1)>q):'prop'
-y@prop2:=all"l"([t:1to(pl"n"(x,y))]cx,[u:[t:1to(pl"n"(x,y))]cx]prop1(u)):'prop'
-x@[f0:[t:1to(pl"n"(x,1))]cx]
-t2:=satz278(q,x,f0):is(smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q)
-t3:=satz277(q,f2(1,f0)):is(smpr(1,f2(1,f0)),<xout(1)>f2(1,f0))
-t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-t5:=ispl2"n"(1,inn(1,xout(1)),x,t4):is"n"(pl"n"(x,1),pl"n"(x,inn(1,xout(1))))
-t6:=isoutni(pl"n"(x,1),pl"n"(x,1),lessisi3(pl"n"(x,1)),pl"n"(x,inn(1,xout(1))),satz19o(inn(1,xout(1)),1,x,1top(1,xout(1))),t5):is"e"(1to(pl"n"(x,1)),xout(pl"n"(x,1)),right1to(x,1,xout(1)))
-t7:=isf(1to(pl"n"(x,1)),cx,f0,xout(pl"n"(x,1)),right1to(x,1,xout(1)),t6):is(<xout(pl"n"(x,1))>f0,<xout(1)>f2(1,f0))
-t8:=tris2(cx,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),<xout(1)>f2(1,f0),t7,t3):is(<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)))
-t9:=isf(cx,cx,<smpr(x,f1(1,f0))>q,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),t8):is(<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q)
-t10:=tris(cx,smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q,t2,t9):prop1(1,f0)
-x@t11:=[u:[t:1to(pl"n"(x,1))]cx]t10(u):prop2(1)
-y@yp1:=pl"n"(y,1):nat
-xpy:=pl"n"(x,y):nat
-xpy1:=pl"n"(x,yp1):nat
-xyp1:=pl"n"(xpy,1):nat
-t12:=lessisi2"n"(xyp1,xpy1,asspl1"n"(x,y,1)):lessis"n"(xyp1,xpy1)
-[p:prop2(y)][f:[t:1to(xpy1)]cx]
-t13:=isinoutn(xyp1,xyp1,lessisi3(xyp1)):is"n"(xyp1,inn(xyp1,xout(xyp1)))
-t14:=tris(nat,xpy1,xyp1,inn(xyp1,xout(xyp1)),asspl2"n"(x,y,1),t13):is"n"(xpy1,inn(xyp1,xout(xyp1)))
-t15:=isoutni(xpy1,xpy1,lessisi3(xpy1),inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),t14):is"e"(1to(xpy1),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)))
-t16:=isf(1to(xpy1),cx,recf(xpy1,f),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),t15):is(smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)))
-fr:=left(cx,xpy1,xyp1,t12,f):[t:1to(xyp1)]cx
-t17:=satz275f(xpy1,xyp1,t12,f):is"e"([t:1to(xyp1)]cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr))
-t18:=fise(1to(xyp1),cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr),t17,xout(xyp1)):is(<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr))
-t19:=lessisi1"n"(xpy,xyp1,satz18a(xpy,1)):lessis"n"(xpy,xyp1)
-frr:=left(cx,xyp1,xpy,t19,fr):[t:1to(xpy)]cx
-t20:=satz278(xpy,fr):is(smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q)
-t21:=isf(cx,cx,[u:cx]<<xout(xyp1)>fr><u>q,smpr(xpy,frr),<smpr(y,f2(frr))><smpr(x,f1(frr))>q,<frr>p):is(<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
-t22:=assq1(a,smpr(x,f1(frr)),smpr(y,f2(frr)),<xout(xyp1)>fr):is(<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q)
-t23:=lessisi1"n"(y,yp1,satz18a(y,1)):lessis"n"(y,yp1)
-fy:=left(cx,yp1,y,t23,f2(yp1,f)):[t:1to(y)]cx
-t24:=satz278(y,f2(yp1,f)):is(smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
-t25:=isinoutn(yp1,yp1,lessisi3(yp1)):is"n"(yp1,inn(yp1,xout(yp1)))
-t26:=ispl2"n"(yp1,inn(yp1,xout(yp1)),x,t25):is"n"(xpy1,pl"n"(x,inn(yp1,xout(yp1))))
-t27:=tris1(nat,inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))),xpy1,t14,t26):is"n"(inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))))
-t28:=isoutni(xpy1,inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),pl"n"(x,inn(yp1,xout(yp1))),satz19o(inn(yp1,xout(yp1)),yp1,x,1top(yp1,xout(yp1))),t27):is"e"(1to(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)))
-t29:=isf(1to(xpy1),cx,f,left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)),t28):is(<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f))
-t30:=isf(cx,cx,<smpr(y,f2(frr))>q,<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f),t29):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q)
-[n:1to(y)]
-n0:=inn(y,n):nat
-nyp1:=left1to(yp1,y,t23,n):1to(yp1)
-t31:=isinoutn(yp1,n0,trlessis"n"(n0,y,yp1,1top(y,n),t23)):is"n"(n0,inn(yp1,nyp1))
-t32:=ispl2"n"(n0,inn(yp1,nyp1),x,t31):is"n"(pl"n"(x,n0),pl"n"(x,inn(yp1,nyp1)))
-nxpy:=right1to(x,y,n):1to(xpy)
-nxyp1:=left1to(xyp1,xpy,t19,nxpy):1to(xyp1)
-t33:=isinoutn(xyp1,inn(xpy,nxpy),trlessis"n"(inn(xpy,nxpy),xpy,xyp1,1top(xpy,nxpy),t19)):is"n"(inn(xpy,nxpy),inn(xyp1,nxyp1))
-t34:=isinoutn(xpy,pl"n"(x,n0),satz19o(n0,y,x,1top(y,n))):is"n"(pl"n"(x,n0),inn(xpy,nxpy))
-t35:=tris(nat,pl"n"(x,n0),inn(xpy,nxpy),inn(xyp1,nxyp1),t34,t33):is"n"(pl"n"(x,n0),inn(xyp1,nxyp1))
-t36:=tris1(nat,pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1),pl"n"(x,n0),t32,t35):is"n"(pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1))
-t37:=isoutni(xpy1,pl"n"(x,inn(yp1,nyp1)),satz19o(inn(yp1,nyp1),yp1,x,1top(yp1,nyp1)),inn(xyp1,nxyp1),trlessis"n"(inn(xyp1,nxyp1),xyp1,xpy1,1top(xyp1,nxyp1),t12),t36):is"e"(1to(xpy1),right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1))
-t38:=isf(1to(xpy1),cx,f,right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1),t37):is(<n>fy,<n>f2(frr))
-f@t39:=fisi(1to(y),cx,fy,f2(frr),[u:1to(y)]t38(u)):is"e"([u:1to(y)]cx,fy,f2(frr))
-t40:=isf([u:1to(y)]cx,cx,[t:[u:1to(y)]cx]smpr(y,t),fy,f2(frr),t39):is(smpr(y,fy),smpr(y,f2(frr)))
-t41:=isf(cx,cx,[t:cx]<<xout(yp1)>f2(yp1,f)><t>q,smpr(y,f2(frr)),smpr(y,fy),symis(cx,smpr(y,fy),smpr(y,f2(frr)),t40)):is(<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
-t41a:=tris(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t30,t41):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
-t42:=tris2(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t41a,t24):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)))
-t43:=isf(cx,cx,<smpr(x,f1(frr))>q,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),t42):is(<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q)
-[m:1to(x)]
-m0:=inn(x,m):nat
-mxpy:=left1to(xpy,x,t1,m):1to(xpy)
-mxyp1:=left1to(xyp1,xpy,t19,mxpy):1to(xyp1)
-t44:=isinoutn(xyp1,inn(xpy,mxpy),trlessis"n"(inn(xpy,mxpy),xpy,xyp1,1top(xpy,mxpy),t19)):is"n"(inn(xpy,mxpy),inn(xyp1,mxyp1))
-t45:=isinoutn(xpy,m0,trlessis"n"(m0,x,xpy,1top(x,m),t1)):is"n"(m0,inn(xpy,mxpy))
-t46:=tris(nat,m0,inn(xpy,mxpy),inn(xyp1,mxyp1),t45,t44):is"n"(m0,inn(xyp1,mxyp1))
-t47:=isoutni(xpy1,m0,trlessis"n"(m0,x,xpy1,1top(x,m),t1(yp1)),inn(xyp1,mxyp1),trlessis"n"(inn(xyp1,mxyp1),xyp1,xpy1,1top(xyp1,mxyp1),t12),t46):is"e"(1to(xpy1),left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1))
-t48:=isf(1to(xpy1),cx,f,left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1),t47):is(<m>f1(x,yp1,f),<m>f1(x,y,frr))
-f@t49:=fisi(1to(x),cx,f1(x,yp1,f),f1(x,y,frr),[u:1to(x)]t48(u)):is"e"([u:1to(x)]cx,f1(x,yp1,f),f1(x,y,frr))
-t50:=isf([u:1to(x)]cx,cx,[t:[u:1to(x)]cx]smpr(x,t),f1(yp1,f),f1(frr),t49):is(smpr(x,f1(yp1,f)),smpr(x,f1(frr)))
-t51:=isf(cx,cx,[t:cx]<smpr(yp1,f2(yp1,f))><t>q,smpr(x,f1(frr)),smpr(x,f1(yp1,f)),symis(cx,smpr(x,f1(yp1,f)),smpr(x,f1(frr)),t50)):is(<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q)
-t52:=tr4is(cx,smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,t16,t18,t20,t21):is(smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
-t53:=tr4is(cx,smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q,t52,t22,t43,t51):prop1(yp1,f)
-p@t54:=[u:[t:1to(xpy1)]cx]t53(u):prop2(yp1)
-t55:=isp(nat,[t:nat]prop2(t),yp1,<y>suc,t54,satz4a(y)):prop2(<y>suc)
-y@t56:=induction([t:nat]prop2(t),t11,[z:nat][t:prop2(z)]t55(z,t),y):prop2(y)
--8281
-satz281:=<f>t56".8281":is(smpr(pl"n"(x,y),f),<smpr(y,right(cx,x,y,f))><smpr(x,left(cx,pl"n"(x,y),x,lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)),f))>q)
-q@commut:=[x:cx][y:cx]is(<y><x>q,<x><y>q):'prop'
-@commutpl:=[x:cx][y:cx]compl(x,y):commut([x:cx][y:cx]pl(x,y))
-commutts:=[x:cx][y:cx]comts(x,y):commut([x:cx][y:cx]ts(x,y))
-q@[c:commut][z:cx][u:cx]
-comq:=<u><z>c:is(<u><z>q,<z><u>q)
-a@[c:commut(q)][x:nat][f:[t:1to(x)]cx][g:[t:1to(x)]cx]
-+8282
-prop1:=is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q):'prop'
-x@prop2:=all"l"([t:1to(x)]cx,[u:[t:1to(x)]cx]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]prop1(u,v))):'prop'
-c@[f0:[t:1to(1)]cx][g0:[t:1to(1)]cx]
-t1:=satz277([t:1to(1)]<<t>g0><<t>f0>q):is(smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<<xout(1)>g0><<xout(1)>f0>q)
-t2:=isf(cx,cx,<smpr(1,f0)>q,smpr(1,g0),<xout(1)>g0,satz277(g0)):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q)
-t3:=isf(cx,cx,[t:cx]<<xout(1)>g0><t>q,smpr(1,f0),<xout(1)>f0,satz277(f0)):is(<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
-t4:=tris(cx,<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t2,t3):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
-t5:=tris2(cx,smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t1,t4):prop1(1,f0,g0)
-c@t6:=[u:[t:1to(1)]cx][v:[t:1to(1)]cx]t5(u,v):prop2(1)
-x@xp1:=pl"n"(x,1):nat
-[p:prop2(x)][f:[t:1to(xp1)]cx][g:[t:1to(xp1)]cx]
-c@[u:cx][v:cx][w:cx][z:cx]
-t7:=assq2(a,<v><u>q,w,z):is(<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q)
-t8:=comq(c,<v><u>q,w):is(<w><<v><u>q>q,<<v><u>q><w>q)
-t9:=assq2(a,w,u,v):is(<<v><u>q><w>q,<v><<u><w>q>q)
-t10:=tris(cx,<w><<v><u>q>q,<<v><u>q><w>q,<v><<u><w>q>q,t8,t9):is(<w><<v><u>q>q,<v><<u><w>q>q)
-t11:=isf(cx,cx,[t:cx]<z><t>q,<w><<v><u>q>q,<v><<u><w>q>q,t10):is(<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q)
-t12:=assq1(a,<u><w>q,v,z):is(<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q)
-t13:=comq(c,w,u):is(<u><w>q,<w><u>q)
-t14:=isf(cx,cx,[t:cx]<<z><v>q><t>q,<u><w>q,<w><u>q,t13):is(<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q)
-t15:=tr4is(cx,<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q,t7,t11,t12,t14):is(<<z><w>q><<v><u>q>q,<<z><v>q><<w><u>q>q)
-g@t16:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
-sfx:=smpr(x,left(cx,xp1,x,t16,f)):cx
-sgx:=smpr(x,left(cx,xp1,x,t16,g)):cx
-h:=[t:1to(xp1)]<<t>g><<t>f>q:[t:1to(xp1)]cx
-shx:=smpr(x,left(cx,xp1,x,t16,h)):cx
-t17:=satz278(x,h):is(smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q)
-t18:=<left(cx,xp1,x,t16,g)><left(cx,xp1,x,t16,f)>p:is(shx,<sgx><sfx>q)
-t19:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><<xout(xp1)>f>q><t>q,shx,<sgx><sfx>q,t18):is(<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q)
-t20:=t15(sfx,sgx,<xout(xp1)>f,<xout(xp1)>g):is(<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
-t21:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><sfx>q,satz278(x,f)):is(<<xout(xp1)>f><sfx>q,smpr(xp1,f))
-t22:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><sgx>q><t>q,<<xout(xp1)>f><sfx>q,smpr(xp1,f),t21):is(<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q)
-t23:=symis(cx,smpr(xp1,g),<<xout(xp1)>g><sgx>q,satz278(x,g)):is(<<xout(xp1)>g><sgx>q,smpr(xp1,g))
-t24:=isf(cx,cx,<smpr(xp1,f)>q,<<xout(xp1)>g><sgx>q,smpr(xp1,g),t23):is(<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q)
-t25:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,t17,t19,t20):is(smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
-t26:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q,t25,t22,t24):prop1(xp1,f,g)
-p@t27:=[u:[t:1to(xp1)]cx][v:[t:1to(xp1)]cx]t26(u,v):prop2(xp1)
-t28:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t27,satz4a(x)):prop2(<x>suc)
-x@t29:=induction([t:nat]prop2(t),t6,[y:nat][t:prop2(y)]t28(y,t),x):prop2(x)
--8282
-satz282:=<g><f>t29".8282":is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q)
-x@[s:[t:1to(x)]1to(x)][b:bijective(1to(x),1to(x),s)][f:[t:1to(x)]cx]
-+8283
-s@[f:[t:1to(x)]cx]
-g:=[t:1to(x)]<<t>s>f:[t:1to(x)]cx
-prop1:=is(smpr(x,g),smpr(x,f)):'prop'
-x@prop2:=all"l"([t:1to(x)]1to(x),[u:[t:1to(x)]1to(x)]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]imp(bijective(1to(x),1to(x),u),prop1(u,v)))):'prop'
-c@[s:[t:1to(1)]1to(1)][f:[t:1to(1)]cx]
-t1:=tris2(1to(1),<xout(1)>s,xout(1),1o"n",th1"n.singlet"(<xout(1)>s),th1"n.singlet"(xout(1))):is"e"(1to(1),<xout(1)>s,xout(1))
-t2:=satz277(g(1,s,f)):is(smpr(1,g(1,s,f)),<xout(1)>g(1,s,f))
-t3:=isf(1to(1),cx,f,<xout(1)>s,xout(1),t1):is(<xout(1)>g(1,s,f),<xout(1)>f)
-t4:=symis(cx,smpr(1,f),<xout(1)>f,satz277(f)):is(<xout(1)>f,smpr(1,f))
-t5:=tr3is(cx,smpr(1,g(1,s,f)),<xout(1)>g(1,s,f),<xout(1)>f,smpr(1,f),t2,t3,t4):prop1(1,s,f)
-c@t6:=[u:[t:1to(1)]1to(1)][v:[t:1to(1)]cx][w:bijective(1to(1),1to(1),u)]t5(u,v):prop2(1)
-x@xp1:=pl"n"(x,1):nat
-t7:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
-[p:prop2(x)][s:[t:1to(xp1)]1to(xp1)][f:[t:1to(xp1)]cx][b:bijective(1to(xp1),1to(xp1),s)]
-t8:=ande1(injective(1to(xp1),1to(xp1),s),surjective(1to(xp1),1to(xp1),s),b):injective(1to(xp1),1to(xp1),s)
-[case1:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))][u:1to(x)]
-u1:=left1to(xp1,x,t7,u):1to(xp1)
-n1:=inn(xp1,<u1>s):nat
-[i:is"n"(n1,xp1)]
-t9:=tr3is(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),xout(xp1),<xout(xp1)>s,isoutinn(xp1,<u1>s),isoutni(xp1,n1,1top(xp1,<u1>s),xp1,lessisi3(xp1),i),symis(1to(xp1),<xout(xp1)>s,xout(xp1),case1)):is"e"(1to(xp1),<u1>s,<xout(xp1)>s)
-t10:=isfe(1to(xp1),1to(xp1),s,t8,u1,xout(xp1),t9):is"e"(1to(xp1),u1,xout(xp1))
-t11:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t10):is"n"(inn(x,u),xp1)
-t12:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
-t13:=<t11>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t12):con
-u@t14:=ore1(less"n"(n1,xp1),is"n"(n1,xp1),1top(xp1,<u1>s),[t:is"n"(n1,xp1)]t13(t)):less"n"(n1,xp1)
-t15:=satz26(x,n1,t14):lessis"n"(n1,x)
-w1:=outn(x,n1,t15):1to(x)
-case1@s01:=[t:1to(x)]w1(t):[t:1to(x)]1to(x)
-u@[v:1to(x)][i:is"e"(1to(x),w1(u),w1(v))]
-t16:=isoutne(x,n1(u),t15(u),n1(v),t15(v),i):is"n"(n1(u),n1(v))
-t17:=<isinne(xp1,<u1(u)>s,<u1(v)>s,t16)><u1(v)><u1(u)>t8:is"e"(1to(xp1),u1(u),u1(v))
-t18:=thleft1(xp1,x,t7,u,v,t17):is"e"(1to(x),u,v)
-u@u2:=<u1>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
-n2:=inn(xp1,u2):nat
-[i:is"n"(n2,xp1)]
-t19:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),xout(xp1),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),xp1,lessisi3(xp1),i)):is"e"(1to(xp1),u2,xout(xp1))
-t20:=tr3is(1to(xp1),u1,<u2>s,<xout(xp1)>s,xout(xp1),thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,xout(xp1),t19),case1):is"e"(1to(xp1),u1,xout(xp1))
-t21:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t20):is"n"(inn(x,u),xp1)
-t22:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
-t23:=<t21>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t22):con
-u@t24:=ore1(less"n"(n2,xp1),is"n"(n2,xp1),1top(xp1,u2),[t:is"n"(n2,xp1)]t23(t)):less"n"(n2,xp1)
-t25:=satz26(x,n2,t24):lessis"n"(n2,x)
-w2:=outn(x,n2,t25):1to(x)
-t26:=isinoutn(x,n2,t25):is"n"(n2,inn(x,w2))
-t27:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),u1(w2),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),inn(x,w2),trlessis"n"(inn(x,w2),x,xp1,1top(x,w2),t7),t26)):is"e"(1to(xp1),u2,u1(w2))
-t28:=tris(1to(xp1),u1,<u2>s,<u1(w2)>s,thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,u1(w2),t27)):is"e"(1to(xp1),u1,<u1(w2)>s)
-t29:=tris(nat,inn(x,u),inn(xp1,u1),n1(w2),isinoutn(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7)),isinni(xp1,u1,<u1(w2)>s,t28)):is"n"(inn(x,u),n1(w2))
-t30:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w1(w2),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),n1(w2),t15(w2),t29)):is"e"(1to(x),u,w1(w2))
-t31:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w1(t)),w2,t30):image(1to(x),1to(x),s01,u)
-case1@t32:=andi(injective(1to(x),1to(x),s01),surjective(1to(x),1to(x),s01),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s01,<u>s01)]t18(t,u,v),[t:1to(x)]t31(t)):bijective(1to(x),1to(x),s01)
-f01:=left(cx,xp1,x,t7,f):[t:1to(x)]cx
-t33:=<t32><f01><s01>p:prop1(s01,f01)
-g1:=left(cx,xp1,x,t7,g(xp1,s,f)):[t:1to(x)]cx
-g2:=g(x,s01,f01):[t:1to(x)]cx
-u@t33a:=isoutinn(xp1,<u1>s):is"e"(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)))
-t34:=isinoutn(x,n1,t15):is"n"(n1,inn(x,w1))
-t35:=isoutni(xp1,n1,1top(xp1,<u1>s),inn(x,w1),trlessis"n"(inn(x,w1),x,xp1,1top(x,w1),t7),t34):is"e"(1to(xp1),outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1))
-t36:=tris(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1),t33a,t35):is"e"(1to(xp1),<u1>s,left1to(xp1,x,t7,w1))
-t37:=isf(1to(xp1),cx,f,<u1>s,left1to(xp1,x,t7,w1),t36):is(<u>g1,<u>g2)
-case1@t38:=fisi(1to(x),cx,g1,g2,[t:1to(x)]t37(t)):is"e"([t:1to(x)]cx,g1,g2)
-t39:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g1,g2,t38):is(smpr(x,g1),smpr(x,g2))
-t40:=tris(cx,smpr(x,g1),smpr(x,g2),smpr(x,f01),t39,t33):is(smpr(x,g1),smpr(x,f01))
-t41:=isf(1to(xp1),cx,f,<xout(xp1)>s,xout(xp1),case1):is(<xout(xp1)>g(xp1,s,f),<xout(xp1)>f)
-t42:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q)
-t43:=isf(cx,cx,<smpr(x,g1)>q,<xout(xp1)>g(xp1,s,f),<xout(xp1)>f,t41):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q)
-t44:=isf(cx,cx,[t:cx]<<xout(xp1)>f><t>q,smpr(x,g1),smpr(x,f01),t40):is(<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q)
-t45:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><smpr(x,f01)>q,satz278(x,f)):is(<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f))
-t46:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f),t42,t43,t44,t45):prop1(xp1,s,f)
-b@1px:=pl"n"(1,x):nat
-[case2:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))][u:1to(x)]
-u3:=right1to(1,x,u):1to(1px)
-case2@t47:=lessisi2"n"(1px,xp1,compl"n"(1,x)):lessis"n"(1px,xp1)
-s02:=left(1to(xp1),xp1,1px,t47,s):[t:1to(1px)]1to(xp1)
-u@n3:=inn(xp1,<u3>s02):nat
-[i:is"n"(n3,1)]
-t48:=tr3is(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),1out(xp1),<1out(xp1)>s,isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),1,satz24a(xp1),i),symis(1to(xp1),<1out(xp1)>s,1out(xp1),case2)):is"e"(1to(xp1),<u3>s02,<1out(xp1)>s)
-t49:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3),1out(xp1),t48):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
-t50:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t49):is"n"(inn(1px,u3),1)
-t51:=isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))):is"n"(pl"n"(1,inn(x,u)),inn(1px,u3))
-t52:=ismore1"n"(pl"n"(1,inn(x,u)),inn(1px,u3),1,t51,satz18(1,inn(x,u))):more"n"(inn(1px,u3),1)
-t53:=<t50>ec3e21(is"n"(inn(1px,u3),1),more"n"(inn(1px,u3),1),less"n"(inn(1px,u3),1),satz10b(inn(1px,u3),1),t52):con
-u@t54:=ore1(more"n"(n3,1),is"n"(n3,1),satz24(n3),[t:is"n"(n3,1)]t53(t)):more"n"(n3,1)
-nm1:=mn"n"(n3,1,t54):nat
-t54a:=islessis1"n"(n3,pl"n"(nm1,1),xp1,th1c"n.mn"(n3,1,t54),1top(xp1,<u3>s02)):lessis"n"(pl"n"(nm1,1),xp1)
-t55:=th9"l.or"(less"n"(pl"n"(nm1,1),xp1),is"n"(pl"n"(nm1,1),xp1),less"n"(nm1,x),is"n"(nm1,x),t54a,[t:less"n"(pl"n"(nm1,1),xp1)]satz20c(nm1,x,1,t),[t:is"n"(pl"n"(nm1,1),xp1)]satz20b(nm1,x,1,t)):lessis"n"(nm1,x)
-w3:=outn(x,nm1,t55):1to(x)
-case2@s03:=[t:1to(x)]w3(t):[t:1to(x)]1to(x)
-u@[v:1to(x)][i:is"e"(1to(x),w3(u),w3(v))]
-t56:=isoutne(x,nm1(u),t55(u),nm1(v),t55(v),i):is"n"(nm1(u),nm1(v))
-t57:=tr3is(nat,n3(u),pl"n"(nm1(u),1),pl"n"(nm1(v),1),n3(v),th1c"n.mn"(n3(u),1,t54(u)),ispl1"n"(nm1(u),nm1(v),1,t56),th1d"n.mn"(n3(v),1,t54(v))):is"n"(n3(u),n3(v))
-t58:=isinne(xp1,<u3(u)>s02,<u3(v)>s02,t57):is"e"(1to(xp1),<u3(u)>s02,<u3(v)>s02)
-t59:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)),t58):is"e"(1to(xp1),left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)))
-t60:=thleft1(xp1,1px,t47,u3(u),u3(v),t59):is"e"(1to(1px),u3(u),u3(v))
-t61:=thright1(1,x,u,v,t60):is"e"(1to(x),u,v)
-case2@s04:=left(1to(xp1),xp1,1px,t47,invf(1to(xp1),1to(xp1),s,b)):[t:1to(1px)]1to(xp1)
-u@u4:=<u3>s04:1to(xp1)
-n4:=inn(xp1,u4):nat
-[i:is"n"(n4,1)]
-t62:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),1out(xp1),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),1,satz24a(xp1),i)):is"e"(1to(xp1),u4,1out(xp1))
-t63:=tr3is(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<1out(xp1)>s,1out(xp1),thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,1out(xp1),t62),case2):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
-t64:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t63):is"n"(inn(1px,u3),1)
-t65:=tris(nat,pl"n"(1,inn(x,u)),inn(1px,u3),1,isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),t64):is"n"(pl"n"(1,inn(x,u)),1)
-t66:=<t65>ec3e21(is"n"(pl"n"(1,inn(x,u)),1),more"n"(pl"n"(1,inn(x,u)),1),less"n"(pl"n"(1,inn(x,u)),1),satz10b(pl"n"(1,inn(x,u)),1),satz18(1,inn(x,u))):con
-u@t67:=ore1(more"n"(n4,1),is"n"(n4,1),satz24(n4),[t:is"n"(n4,1)]t66(t)):more"n"(n4,1)
-nm2:=mn"n"(n4,1,t67):nat
-t68:=islessis1"n"(n4,pl"n"(nm2,1),xp1,th1c"n.mn"(n4,1,t67),1top(xp1,u4)):lessis"n"(pl"n"(nm2,1),xp1)
-t69:=th9"l.or"(less"n"(pl"n"(nm2,1),xp1),is"n"(pl"n"(nm2,1),xp1),less"n"(nm2,x),is"n"(nm2,x),t68,[t:less"n"(pl"n"(nm2,1),xp1)]satz20c(nm2,x,1,t),[t:is"n"(pl"n"(nm2,1),xp1)]satz20b(nm2,x,1,t)):lessis"n"(nm2,x)
-w4:=outn(x,nm2,t69):1to(x)
-t70:=isinoutn(x,nm2,t69):is"n"(nm2,inn(x,w4))
-t71:=tr3is(nat,n4,pl"n"(1,nm2),pl"n"(1,inn(x,w4)),inn(1px,u3(w4)),th1a"n.mn"(n4,1,t67),ispl2"n"(nm2,inn(x,w4),1,t70),isinoutn(1px,pl"n"(1,inn(x,w4)),satz19o(inn(x,w4),x,1,1top(x,w4)))):is"n"(n4,inn(1px,u3(w4)))
-t72:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),left1to(xp1,1px,t47,u3(w4)),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),inn(1px,u3(w4)),trlessis"n"(inn(1px,u3(w4)),1px,xp1,1top(1px,u3(w4)),t47),t71)):is"e"(1to(xp1),u4,left1to(xp1,1px,t47,u3(w4)))
-t73:=tris(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<u3(w4)>s02,thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,left1to(xp1,1px,t47,u3(w4)),t72)):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),<u3(w4)>s02)
-t74:=tr3is(nat,pl"n"(1,inn(x,u)),inn(1px,u3),inn(xp1,left1to(xp1,1px,t47,u3)),n3(w4),isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),isinoutn(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47)),isinni(xp1,left1to(xp1,1px,t47,u3),<u3(w4)>s02,t73)):is"n"(pl"n"(1,inn(x,u)),n3(w4))
-t75:=th1e"n.mn"(n3(w4),1,inn(x,u),t54(w4),t74):is"n"(inn(x,u),nm1(w4))
-t76:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w3(w4),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),nm1(w4),t55(w4),t75)):is"e"(1to(x),u,w3(w4))
-t77:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w3(t)),w4,t76):image(1to(x),1to(x),s03,u)
-case2@t78:=andi(injective(1to(x),1to(x),s03),surjective(1to(x),1to(x),s03),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s03,<u>s03)]t61(t,u,v),[t:1to(x)]t77(t)):bijective(1to(x),1to(x),s03)
-f02:=left(cx,xp1,1px,t47,f):[t:1to(1px)]cx
-f03:=right(cx,1,x,f02):[t:1to(x)]cx
-t79:=<t78><f03><s03>p:prop1(s03,f03)
-g3:=left(cx,xp1,1px,t47,g(xp1,s,f)):[t:1to(1px)]cx
-g4:=right(cx,1,x,g3):[t:1to(x)]cx
-g5:=g(x,s03,f03):[t:1to(x)]cx
-u@t80:=tr3is(nat,n3,pl"n"(1,nm1),pl"n"(1,inn(x,w3)),inn(1px,right1to(1,x,w3)),th1a"n.mn"(n3,1,t54),ispl2"n"(nm1,inn(x,w3),1,isinoutn(x,nm1,t55)),isinoutn(1px,pl"n"(1,inn(x,w3)),satz19o(inn(x,w3),x,1,1top(x,w3)))):is"n"(n3,inn(1px,right1to(1,x,w3)))
-t81:=tris(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),left1to(xp1,1px,t47,right1to(1,x,w3)),isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),inn(1px,right1to(1,x,w3)),trlessis"n"(inn(1px,right1to(1,x,w3)),1px,xp1,1top(1px,right1to(1,x,w3)),t47),t80)):is"e"(1to(xp1),<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)))
-t82:=isf(1to(xp1),cx,f,<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)),t81):is(<u>g4,<u>g5)
-case2@t83:=fisi(1to(x),cx,g4,g5,[t:1to(x)]t82(t)):is"e"([t:1to(x)]cx,g4,g5)
-t85:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g4,g5,t83):is(smpr(x,g4),smpr(x,g5))
-t86:=tris(cx,smpr(x,g4),smpr(x,g5),smpr(x,f03),t85,t79):is(smpr(x,g4),smpr(x,f03))
-t87:=lessisi1"n"(1,1px,satz18a(1,x)):lessis"n"(1,1px)
-g6:=left(cx,1px,1,t87,g3):[t:1to(1)]cx
-f04:=left(cx,1px,1,t87,f02):[t:1to(1)]cx
-t87a:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-1d:=left1to(1px,1,t87,xout(1)):1to(1px)
-t87b:=isinoutn(1px,inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,1px,1top(1,xout(1)),t87)):is"n"(inn(1,xout(1)),inn(1px,1d))
-t88:=tris(nat,1,inn(1,xout(1)),inn(1px,1d),t87a,t87b):is"n"(1,inn(1px,1d))
-1e:=left1to(xp1,1px,t47,1d):1to(xp1)
-t88a:=isoutni(xp1,1,satz24a(xp1),inn(1px,1d),trlessis"n"(inn(1px,1d),1px,xp1,1top(1px,1d),t47),t88):is"e"(1to(xp1),1out(xp1),1e)
-t88b:=isf(1to(xp1),1to(xp1),s,1e,1out(xp1),symis(1to(xp1),1out(xp1),1e,t88a)):is"e"(1to(xp1),<1e>s,<1out(xp1)>s)
-t89:=tr3is(1to(xp1),<1e>s,<1out(xp1)>s,1out(xp1),1e,t88b,case2,t88a):is"e"(1to(xp1),<1e>s,1e)
-t89a:=tr3is(cx,smpr(1,g6),<xout(1)>g6,<xout(1)>f04,smpr(1,f04),satz277(g6),isf(1to(xp1),cx,f,<1e>s,1e,t89),symis(cx,smpr(1,f04),<xout(1)>f04,satz277(f04))):is(smpr(1,g6),smpr(1,f04))
-t90:=satz281(1,x,g3):is(smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q)
-t91:=isf(cx,cx,<smpr(1,g6)>q,smpr(x,g4),smpr(x,f03),t86):is(<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q)
-t92:=isf(cx,cx,[t:cx]<smpr(x,f03)><t>q,smpr(1,g6),smpr(1,f04),t89a):is(<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q)
-t93:=symis(cx,smpr(1px,f02),<smpr(x,f03)><smpr(1,f04)>q,satz281(1,x,f02)):is(<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02))
-t94:=tr4is(cx,smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02),t90,t91,t92,t93):is(smpr(1px,g3),smpr(1px,f02))
-t95:=issmpr(xp1,f,1px,compl"n"(1,x)):is(smpr(1px,f02),smpr(xp1,f))
-t96:=symis(cx,smpr(1px,g3),smpr(xp1,g(xp1,s,f)),issmpr(xp1,g(xp1,s,f),1px,compl"n"(1,x))):is(smpr(xp1,g(xp1,s,f)),smpr(1px,g3))
-t97:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(1px,g3),smpr(1px,f02),smpr(xp1,f),t96,t94,t95):prop1(xp1,s,f)
-b@[not1:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))][not2:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]
-a0:=<1out(xp1)>s:1to(xp1)
-b0:=<1out(xp1)>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
-t98:=thinvf2(1to(xp1),1to(xp1),s,b,1out(xp1)):is"e"(1to(xp1),1out(xp1),<b0>s)
-t99:=not2:not(is"e"(1to(xp1),a0,1out(xp1)))
-t100:=symnotis(1to(xp1),<1out(xp1)>s,<b0>s,th3"e.notis"(1to(xp1),<1out(xp1)>s,1out(xp1),<b0>s,not2,t98)):not(is"e"(1to(xp1),<b0>s,<1out(xp1)>s))
-t101:=th3"l.imp"(is"e"(1to(xp1),b0,1out(xp1)),is"e"(1to(xp1),<b0>s,<1out(xp1)>s),t100,[t:is"e"(1to(xp1),b0,1out(xp1))]isf(1to(xp1),1to(xp1),s,b0,1out(xp1),t)):not(is"e"(1to(xp1),b0,1out(xp1)))
-s1:=changef(1to(xp1),1to(xp1),s,1out(xp1),b0):[t:1to(xp1)]1to(xp1)
-[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
-t102:=changef1(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,<b0>s)
-t103:=tris2(1to(xp1),<u>s1,1out(xp1),<b0>s,t102,t98):is"e"(1to(xp1),<u>s1,1out(xp1))
-u@[i:is"e"(1to(xp1),u,b0)]
-t104:=changef2(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,a0)
-u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
-t105:=changef3(1to(xp1),1to(xp1),s,1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
-not2@t106:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),b0,b):bijective(1to(xp1),1to(xp1),s1)
-[alpha:not(is"e"(1to(xp1),a0,xout(xp1)))]
-s2:=wissel(1to(xp1),1out(xp1),a0):[t:1to(xp1)]1to(xp1)
-t107:=th3"e.wissel"(1to(xp1),1out(xp1),a0):bijective(1to(xp1),1to(xp1),s2)
-[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
-t108:=iswissel1(1to(xp1),1out(xp1),a0,<u>s1,t103(u,i)):is"e"(1to(xp1),<<u>s1>s2,a0)
-t109:=tris2(1to(xp1),<u>s,<<u>s1>s2,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t108):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-u@[i:is"e"(1to(xp1),u,b0)]
-t110:=iswissel2(1to(xp1),1out(xp1),a0,<u>s1,t104(u,i)):is"e"(1to(xp1),<<u>s1>s2,1out(xp1))
-t111:=tris2(1to(xp1),<u>s,<<u>s1>s2,1out(xp1),tris2(1to(xp1),<u>s,1out(xp1),<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),t98),t110):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))][i:is"e"(1to(xp1),<u>s1,1out(xp1))]
-t112:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,1out(xp1),tris2(1to(xp1),<u>s1,<1out(xp1)>s1,1out(xp1),i,t103(1out(xp1),refis(1to(xp1),1out(xp1))))):is"e"(1to(xp1),u,1out(xp1))
-o@t113:=th3"l.imp"(is"e"(1to(xp1),<u>s1,1out(xp1)),is"e"(1to(xp1),u,1out(xp1)),n,[t:is"e"(1to(xp1),<u>s1,1out(xp1))]t112(t)):not(is"e"(1to(xp1),<u>s1,1out(xp1)))
-[i:is"e"(1to(xp1),<u>s1,a0)]
-t114:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,b0,tris2(1to(xp1),<u>s1,<b0>s1,a0,i,t104(b0,refis(1to(xp1),b0)))):is"e"(1to(xp1),u,b0)
-o@t115:=th3"l.imp"(is"e"(1to(xp1),<u>s1,a0),is"e"(1to(xp1),u,b0),o,[t:is"e"(1to(xp1),<u>s1,a0)]t114(t)):not(is"e"(1to(xp1),<u>s1,a0))
-t116:=iswissel3(1to(xp1),1out(xp1),a0,<u>s1,t113,t115):is"e"(1to(xp1),<<u>s1>s2,<u>s1)
-t117:=symis(1to(xp1),<<u>s1>s2,<u>s,tris(1to(xp1),<<u>s1>s2,<u>s1,<u>s,t116,t105(u,n,o))):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-n@t118:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,b0)]t111(t),[t:not(is"e"(1to(xp1),u,b0))]t117(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-u@t119:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,1out(xp1))]t109(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t118(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-alpha@t120:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s1>s2,[t:1to(xp1)]t119(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s1>s2)
-not2@t121:=t103(1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s1,1out(xp1))
-t121a:=ec3e21(is"n"(xp1,1),more"n"(xp1,1),less"n"(xp1,1),satz10b(xp1,1),ismore1"n"(1px,xp1,1,compl"n"(1,x),satz18(1,x))):nis"n"(xp1,1)
-t122:=th3"l.imp"(is"e"(1to(xp1),xout(xp1),1out(xp1)),is"n"(xp1,1),t121a,[t:is"e"(1to(xp1),xout(xp1),1out(xp1))]isoutne(xp1,xp1,lessisi3(xp1),1,satz24a(xp1),t)):not(is"e"(1to(xp1),xout(xp1),1out(xp1)))
-alpha@t123:=symnotis(1to(xp1),a0,xout(xp1),alpha):not(is"e"(1to(xp1),xout(xp1),a0))
-t124:=iswissel3(1to(xp1),1out(xp1),a0,xout(xp1),t122,t123):is"e"(1to(xp1),<xout(xp1)>s2,xout(xp1))
-t125:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s1>s2,t120):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))))
-t126:=t97(s1,g(xp1,s2,f),t106,t121):is(smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)))
-t127:=t46(s2,f,t107,t124):is(smpr(xp1,g(xp1,s2,f)),smpr(xp1,f))
-t128:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)),smpr(xp1,f),t125,t126,t127):prop1(xp1,s,f)
-not2@[i3:is"e"(1to(xp1),a0,xout(xp1))][beta:not(is"e"(1to(xp1),b0,xout(xp1)))]
-s3:=wissel(1to(xp1),1out(xp1),b0):[t:1to(xp1)]1to(xp1)
-t129:=th3"e.wissel"(1to(xp1),1out(xp1),b0):bijective(1to(xp1),1to(xp1),s3)
-[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
-t130:=t104(<u>s3,iswissel1(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,a0)
-t131:=tris2(1to(xp1),<u>s,<<u>s3>s1,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t130):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-u@[i:is"e"(1to(xp1),u,b0)]
-t132:=t103(<u>s3,iswissel2(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,1out(xp1))
-t133:=tris2(1to(xp1),<u>s,<<u>s3>s1,<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),tris(1to(xp1),<<u>s3>s1,1out(xp1),<b0>s,t132,t98)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
-t134:=iswissel3(1to(xp1),1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s3,u)
-t135:=isf(1to(xp1),1to(xp1),s1,<u>s3,u,t134):is"e"(1to(xp1),<<u>s3>s1,<u>s1)
-t136:=t105(u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
-t139:=symis(1to(xp1),<<u>s3>s1,<u>s,tris(1to(xp1),<<u>s3>s1,<u>s1,<u>s,t135,t136)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-n@t140:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,b0)]t133(t),[t:not(is"e"(1to(xp1),u,b0))]t139(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-u@t141:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,1out(xp1))]t131(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t140(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-beta@t142:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s3>s1,[t:1to(xp1)]t141(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s3>s1)
-t143:=symnotis(1to(xp1),b0,xout(xp1),beta):not(is"e"(1to(xp1),xout(xp1),b0))
-t144:=iswissel3(1to(xp1),1out(xp1),b0,xout(xp1),t122,t143):is"e"(1to(xp1),<xout(xp1)>s3,xout(xp1))
-t145:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s3>s1,t142):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))))
-t146:=t46(s3,g(xp1,s1,f),t129,t144):is(smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)))
-t147:=t97(s1,f,t106,t121):is(smpr(xp1,g(xp1,s1,f)),smpr(xp1,f))
-t148:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)),smpr(xp1,f),t145,t146,t147):prop1(xp1,s,f)
-i3@[gamma:is"e"(1to(xp1),b0,xout(xp1))][i:is"n"(x,1)]
-t149:=ispl1"n"(1,x,1,symis(nat,x,1,i)):is"n"(2,xp1)
-t150:=lessisi2"n"(2,xp1,t149):lessis"n"(2,xp1)
-f05:=left(cx,xp1,2,t150,f):[t:1to(2)]cx
-s05:=left(1to(xp1),xp1,2,t150,s):[t:1to(2)]1to(xp1)
-g7:=left(cx,xp1,2,t150,g(xp1,s,f)):[t:1to(2)]cx
-t151:=issmpr(xp1,f,2,t149):is(smpr(2,f05),smpr(xp1,f))
-t152:=issmpr(xp1,g(xp1,s,f),2,t149):is(smpr(2,g7),smpr(xp1,g(xp1,s,f)))
-t153:=satz280(f05):is(smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q)
-t154:=satz280(g7):is(smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q)
-t155:=tris1(nat,inn(2,xout(2)),xp1,2,isinoutn(2,2,lessisi3(2)),t149):is"n"(inn(2,xout(2)),xp1)
-t156:=isoutni(xp1,inn(2,xout(2)),trlessis"n"(inn(2,xout(2)),2,xp1,1top(2,xout(2)),t150),xp1,lessisi3(xp1),t155):is"e"(1to(xp1),left1to(xp1,2,t150,xout(2)),xout(xp1))
-t157:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,xout(2)),xout(xp1),t156):is"e"(1to(xp1),<xout(2)>s05,<xout(xp1)>s)
-t158:=symis(nat,1,inn(2,1out(2)),isinoutn(2,1,satz24a(2))):is"n"(inn(2,1out(2)),1)
-t159:=isoutni(xp1,inn(2,1out(2)),trlessis"n"(inn(2,1out(2)),2,xp1,1top(2,1out(2)),t150),1,satz24a(xp1),t158):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1))
-t160:=tr3is(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1),<b0>s,<xout(xp1)>s,t159,t98,isf(1to(xp1),1to(xp1),s,b0,xout(xp1),gamma)):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),<xout(xp1)>s)
-t161:=tris2(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)),<xout(xp1)>s,t157,t160):is"e"(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)))
-t163:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,1out(2)),1out(xp1),t159):is"e"(1to(xp1),<1out(2)>s05,<1out(xp1)>s)
-t164:=tris(1to(xp1),<1out(2)>s05,<1out(xp1)>s,xout(xp1),t163,i3):is"e"(1to(xp1),<1out(2)>s05,xout(xp1))
-t165:=tris2(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)),xout(xp1),t164,t156):is"e"(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)))
-t166:=isf(1to(xp1),cx,f,<xout(2)>s05,left1to(xp1,2,t150,1out(2)),t161):is(<xout(2)>g7,<1out(2)>f05)
-t167:=isf(1to(xp1),cx,f,<1out(2)>s05,left1to(xp1,2,t150,xout(2)),t165):is(<1out(2)>g7,<xout(2)>f05)
-t168:=isf(cx,cx,<<1out(2)>g7>q,<xout(2)>g7,<1out(2)>f05,t166):is(<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q)
-t169:=comq(c,<1out(2)>g7,<1out(2)>f05):is(<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q)
-t170:=isf(cx,cx,<<1out(2)>f05>q,<1out(2)>g7,<xout(2)>f05,t167):is(<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q)
-t171:=tr4is(cx,smpr(xp1,g(xp1,s,f)),smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q,symis(cx,smpr(2,g7),smpr(xp1,g(xp1,s,f)),t152),t154,t168,t169):is(smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q)
-t172:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q,smpr(2,f05),smpr(xp1,f),t171,t170,symis(cx,smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q,t153),t151):prop1(xp1,s,f)
-trivial:=t172:prop1(xp1,s,f)
-gamma@[n:nis"n"(x,1)]
-t173:=ore1(more"n"(x,1),is"n"(x,1),satz24(x),n):more"n"(x,1)
-xm1:=mn"n"(x,1,t173):nat
-s4:=changef(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1)):[t:1to(xp1)]1to(xp1)
-t174:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),b):bijective(1to(xp1),1to(xp1),s4)
-t175:=changef2(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),xout(xp1),refis(1to(xp1),xout(xp1))):is"e"(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s)
-t176:=symis(1to(xp1),a0,xout(xp1),i3):is"e"(1to(xp1),xout(xp1),<1out(xp1)>s)
-t177:=tris2(1to(xp1),<xout(xp1)>s4,xout(xp1),<1out(xp1)>s,t175,t176):is"e"(1to(xp1),<xout(xp1)>s4,xout(xp1))
-t178:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
-g8:=left(cx,xp1,x,t178,g(xp1,s,f)):[t:1to(x)]cx
-t179:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q)
-t180:=th1b"n.mn"(x,1,t173):is"n"(pl"n"(1,xm1),x)
-t181:=lessisi2"n"(pl"n"(1,xm1),x,t180):lessis"n"(pl"n"(1,xm1),x)
-g9:=left(cx,x,pl"n"(1,xm1),t181,g8):[t:1to(pl"n"(1,xm1))]cx
-t182:=symis(cx,smpr(pl"n"(1,xm1),g9),smpr(x,g8),issmpr(x,g8,pl"n"(1,xm1),t180)):is(smpr(x,g8),smpr(pl"n"(1,xm1),g9))
-g10:=right(cx,1,xm1,g9):[t:1to(xm1)]cx
-t183:=lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)):lessis"n"(1,pl"n"(1,xm1))
-g11:=left(cx,pl"n"(1,xm1),1,t183,g9):[t:1to(1)]cx
-t184:=satz281(a,1,xm1,g9):is(smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q)
-t185:=satz277(g11):is(smpr(1,g11),<xout(1)>g11)
-t186:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-1a:=left1to(pl"n"(1,xm1),1,t183,xout(1)):1to(pl"n"(1,xm1))
-t187:=isinoutn(pl"n"(1,xm1),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,pl"n"(1,xm1),1top(1,xout(1)),t183)):is"n"(inn(1,xout(1)),inn(pl"n"(1,xm1),1a))
-1b:=left1to(x,pl"n"(1,xm1),t181,1a):1to(x)
-t188:=isinoutn(x,inn(pl"n"(1,xm1),1a),trlessis"n"(inn(pl"n"(1,xm1),1a),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),1a),t181)):is"n"(inn(pl"n"(1,xm1),1a),inn(x,1b))
-t189:=tr3is(nat,1,inn(1,xout(1)),inn(pl"n"(1,xm1),1a),inn(x,1b),t186,t187,t188):is"n"(1,inn(x,1b))
-1c:=left1to(xp1,x,t178,1b):1to(xp1)
-t190:=isoutni(xp1,1,satz24a(xp1),inn(x,1b),trlessis"n"(inn(x,1b),x,xp1,1top(x,1b),t178),t189):is"e"(1to(xp1),1out(xp1),1c)
-t191:=isf(1to(xp1),cx,g(xp1,s,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s,f),<xout(1)>g11)
-t192:=tris2(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(1)>g11,t185,t191):is(smpr(1,g11),<1out(xp1)>g(xp1,s,f))
-t193:=symis(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s,t175):is"e"(1to(xp1),<1out(xp1)>s,<xout(xp1)>s4)
-t194:=isf(1to(xp1),cx,f,<1out(xp1)>s,<xout(xp1)>s4,t193):is(<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f))
-t195:=tris(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f),t192,t194):is(smpr(1,g11),<xout(xp1)>g(xp1,s4,f))
-t196:=isf(cx,cx,[t:cx]<smpr(xm1,g10)><t>q,smpr(1,g11),<xout(xp1)>g(xp1,s4,f),t195):is(<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
-t197:=tr3is(cx,smpr(x,g8),smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t182,t184,t196):is(smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
-t198:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s,f)><t>q,smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t197):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q)
-t199:=assq1(a,<xout(xp1)>g(xp1,s4,f),smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q)
-t200:=comq(c,<xout(xp1)>g(xp1,s4,f),<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q):is(<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
-g12:=left(cx,xp1,x,t178,g(xp1,s4,f)):[t:1to(x)]cx
-g13:=left(cx,x,pl"n"(1,xm1),t181,g12):[t:1to(pl"n"(1,xm1))]cx
-g14:=right(cx,1,xm1,g13):[t:1to(xm1)]cx
-g15:=left(cx,pl"n"(1,xm1),1,lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)),g13):[t:1to(1)]cx
-t201:=satz278(x,g(xp1,s4,f)):is(smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
-t202:=symis(cx,smpr(pl"n"(1,xm1),g13),smpr(x,g12),issmpr(x,g12,pl"n"(1,xm1),t180)):is(smpr(x,g12),smpr(pl"n"(1,xm1),g13))
-t203:=satz281(a,1,xm1,g13):is(smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q)
-t204:=satz277(g15):is(smpr(1,g15),<xout(1)>g15)
-t205:=isf(1to(xp1),cx,g(xp1,s4,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s4,f),<xout(1)>g15)
-t206:=tris2(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(1)>g15,t204,t205):is(smpr(1,g15),<1out(xp1)>g(xp1,s4,f))
-t207:=changef1(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s4,<xout(xp1)>s)
-t208:=isf(1to(xp1),cx,f,<1out(xp1)>s4,<xout(xp1)>s,t207):is(<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f))
-t209:=tris(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f),t206,t208):is(smpr(1,g15),<xout(xp1)>g(xp1,s,f))
-t210:=isf(cx,cx,[t:cx]<smpr(xm1,g14)><t>q,smpr(1,g15),<xout(xp1)>g(xp1,s,f),t209):is(<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-t211:=tr3is(cx,smpr(x,g12),smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t202,t203,t210):is(smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-[u:1to(xm1)]
-ua:=right1to(1,xm1,u):1to(pl"n"(1,xm1))
-ub:=left1to(x,pl"n"(1,xm1),t181,ua):1to(x)
-uc:=left1to(xp1,x,t178,ub):1to(xp1)
-[i:is"e"(1to(xp1),uc,xout(xp1))]
-t212:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),xp1,lessisi3(xp1),i):is"n"(inn(x,ub),xp1)
-t213:=satz16a(inn(x,ub),x,xp1,1top(x,ub),satz18a(x,1)):less"n"(inn(x,ub),xp1)
-t214:=<t212>ec3e31(is"n"(inn(x,ub),xp1),more"n"(inn(x,ub),xp1),less"n"(inn(x,ub),xp1),satz10b(inn(x,ub),xp1),t213):con
-u@t215:=[t:is"e"(1to(xp1),uc,xout(xp1))]t214(t):not(is"e"(1to(xp1),uc,xout(xp1)))
-[i:is"e"(1to(xp1),uc,1out(xp1))]
-t216:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),1,satz24a(xp1),i):is"n"(inn(x,ub),1)
-t217:=isinoutn(x,inn(pl"n"(1,xm1),ua),trlessis"n"(inn(pl"n"(1,xm1),ua),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),ua),t181)):is"n"(inn(pl"n"(1,xm1),ua),inn(x,ub))
-t218:=isinoutn(pl"n"(1,xm1),pl"n"(1,inn(xm1,u)),satz19o(inn(xm1,u),xm1,1,1top(xm1,u))):is"n"(pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua))
-t219:=tr3is(nat,pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua),inn(x,ub),1,t218,t217,t216):is"n"(pl"n"(1,inn(xm1,u)),1)
-t220:=satz18(1,inn(xm1,u)):more"n"(pl"n"(1,inn(xm1,u)),1)
-t221:=<t219>ec3e21(is"n"(pl"n"(1,inn(xm1,u)),1),more"n"(pl"n"(1,inn(xm1,u)),1),less"n"(pl"n"(1,inn(xm1,u)),1),satz10b(pl"n"(1,inn(xm1,u)),1),t220):con
-u@t222:=[t:is"e"(1to(xp1),uc,1out(xp1))]t221(t):not(is"e"(1to(xp1),uc,1out(xp1)))
-t223:=changef3(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),uc,t222,t215):is"e"(1to(xp1),<uc>s4,<uc>s)
-t224:=isf(1to(xp1),cx,f,<uc>s4,<uc>s,t223):is(<u>g14,<u>g10)
-n@t225:=fisi(1to(xm1),cx,g10,g14,[t:1to(xm1)]symis(cx,<t>g14,<t>g10,t224(t))):is"e"([t:1to(xm1)]cx,g10,g14)
-t226:=isf([t:1to(xm1)]cx,cx,[u:[t:1to(xm1)]cx]smpr(xm1,u),g10,g14,t225):is(smpr(xm1,g10),smpr(xm1,g14))
-t227:=comq(c,smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q)
-t228:=isf(cx,cx,<<xout(xp1)>g(xp1,s,f)>q,smpr(xm1,g10),smpr(xm1,g14),t226):is(<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-t229:=tris(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t227,t228):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-t230:=tris2(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t229,t211):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12))
-t231:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s4,f)><t>q,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),t230):is(<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
-t232:=symis(cx,smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,t201):is(<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)))
-t233:=t46(s4,f,t174,t177):is(smpr(xp1,g(xp1,s4,f)),smpr(xp1,f))
-t234:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,t179,t198,t199,t200):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
-t235:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)),smpr(xp1,f),t234,t231,t232,t233):prop1(xp1,s,f)
-gamma@t236:=th1"l.imp"(is"n"(x,1),prop1(xp1,s,f),[t:is"n"(x,1)]t172(t),[t:not(is"n"(x,1))]t235(t)):prop1(xp1,s,f)
-i3@t237:=th1"l.imp"(is"e"(1to(xp1),b0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),b0,xout(xp1))]t236(t),[t:not(is"e"(1to(xp1),b0,xout(xp1)))]t148(t)):prop1(xp1,s,f)
-not2@t238:=th1"l.imp"(is"e"(1to(xp1),a0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),a0,xout(xp1))]t237(t),[t:not(is"e"(1to(xp1),a0,xout(xp1)))]t128(t)):prop1(xp1,s,f)
-not1@t239:=th1"l.imp"(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))]t97(t),[t:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]t238(t)):prop1(xp1,s,f)
-b@t240:=th1"l.imp"(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))]t46(t),[t:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))]t239(t)):prop1(xp1,s,f)
-p@t241:=[u:[t:1to(xp1)]1to(xp1)][v:[t:1to(xp1)]cx][w:bijective(1to(xp1),1to(xp1),u)]t240(u,v,w):prop2(xp1)
-t242:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t241,satz4a(x)):prop2(<x>suc)
-x@t243:=induction([t:nat]prop2(t),t6,[t:nat][u:prop2(t)]t242(t,u),x):prop2(x)
--8283
-satz283:=<b><f><s>t243".8283":is(smpr(x,[t:1to(x)]<<t>s>f),smpr(x,f))
-@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
-shiftl:=shiftl"r"(x,ix,y,iy,ly):nat
-[n:1to(shiftl)]
-shiftr:=shiftr"r"(x,ix,y,iy,ly,n):real
-intshiftr:=intshiftr"r"(x,ix,y,iy,ly,n):intrl(shiftr)
-shiftrls:=shiftrls"r"(x,ix,y,iy,ly,n):lessis(shiftr,x)
-lsshiftr:=lsshiftr"r"(x,ix,y,iy,ly,n):lessis(y,shiftr)
-[m:1to(shiftl)][i:is"r"(shiftr(n),shiftr(m))]
-iseshiftr:=iseshiftr"r"(x,ix,y,iy,ly,n,m,i):is"e"(1to(shiftl),n,m)
-ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
-shiftl1:=shiftl1"r"(x,ix,y,iy,ly,u,a):1to(shiftl)
-shiftinv1:=shiftinv1"r"(x,ix,y,iy,ly,u,a):is"r"(u,shiftr(shiftl1))
-shiftinv2:=shiftinv2"r"(x,ix,y,iy,ly,u,a):is"r"(shiftr(shiftl1),u)
-ly@[f:seq(x,ix,y,iy,ly,cx)]
-shiftf:=shiftf(x,ix,y,iy,ly,cx,f):[t:1to(shiftl)]cx
-[q:[t:cx][u:cx]cx]
-smpri:=smpr(q,shiftl,shiftf):cx
-f@[pi:proofsirrelevant(x,ix,y,iy,ly,cx,f)][q:[t:cx][u:cx]cx][a:assoc(q)][u:real][iu:intrl(u)][l:lessis(y,u)][k:less(u,x)][v:real][iv:intrl(v)][lv:lessis(y,v)][kv:lessis(v,u)]
-+8284
-t1:=lessisi1(v,x,satz172a(v,u,x,kv,k)):lessis(v,x)
--8284
-k@lft:=[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]<t1".8284"(t,v,lt,kt)><lt><v><t>f:[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]cx
-iv@[lv:lessis(pl"r"(u,1rl),v)][kv:lessis(v,x)]
-+*8284
-x@[y:real]
-pl:=pl"r"(x,y):real
-mn:=mn"r"(x,y):real
-x@p1:=pl"r"(x,1rl):real
-kv@t2:=satz190c(u,u,0,1rl,lessisi2(u,u,refis(real,u)),lemma1"r"(1rl,0,satz169a(1rl,natpos(1rl,natrl1)))):less(pl(u,0),p1(u))
-t3:=isless1(pl(u,0),u,p1(u),pl02"r"(u,0,refis(real,0)),t2):less(u,p1(u))
-t4:=lessisi1(y,v,satz172b(y,p1(u),v,satz172a(y,u,p1(u),l,t3),lv)):lessis(y,v)
--8284
-k@rgt:=[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]<kt><t4".8284"(t,v,lt,kt)><v><t>f:[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]cx
-+*8284
-k@t5:=intpl(u,iu,1rl,intrl1):intrl(p1(u))
-t6:=satzr25(u,iu,x,ix,k):lessis(p1(u),x)
-t7:=tr3is(real,pl(mn(p1(u),y),mn(p1(x),p1(u))),pl(mn(p1(x),p1(u)),mn(p1(u),y)),mn(pl(mn(p1(x),p1(u)),p1(u)),y),mn(p1(x),y),compl"r"(mn(p1(u),y),mn(p1(x),p1(u))),asspl2"r"(mn(p1(x),p1(u)),p1(u),m0"r"(y)),ismn1"r"(pl(mn(p1(x),p1(u)),p1(u)),p1(x),y,plmn(p1(x),p1(u)))):is"r"(pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y))
-sxy:=shiftl(x,ix,y,iy,ly):nat
-suy:=shiftl(u,iu,y,iy,l):nat
-sxu:=shiftl(x,ix,p1(u),t5,t6):nat
-t8:=tr4is(real,rlofnt(pl"n"(suy,sxu)),pl(rlofnt(suy),rlofnt(sxu)),pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y),rlofnt(sxy),satzr155a(suy,sxu),ispl12"r"(rlofnt(suy),mn(p1(u),y),rlofnt(sxu),mn(p1(x),p1(u)),isrlnt2(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l)),isrlnt2(mn(p1(x),p1(u)),t6"r.shift"(x,ix,p1(u),t5,t6))),t7,isrlnt1(mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly))):is"r"(rlofnt(pl"n"(suy,sxu)),rlofnt(sxy))
-t9:=isntirl(pl"n"(suy,sxu),sxy,t8):is"n"(pl"n"(suy,sxu),sxy)
-t10:=lessisi2"n"(pl"n"(suy,sxu),sxy,t9):lessis"n"(pl"n"(suy,sxu),sxy)
-f1:=left(cx,sxy,pl"n"(suy,sxu),t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(pl"n"(suy,sxu))]cx
-t11:=issmpr(q,sxy,shiftf(x,ix,y,iy,ly,f),pl"n"(suy,sxu),t9):is(smpr(q,pl"n"(suy,sxu),f1),smpri(x,ix,y,iy,ly,f,q))
-fr:=right(cx,suy,sxu,f1):[t:1to(sxu)]cx
-t12:=lessisi1"n"(suy,pl"n"(suy,sxu),satz18a(suy,sxu)):lessis"n"(suy,pl"n"(suy,sxu))
-fl:=left(cx,pl"n"(suy,sxu),suy,t12,f1):[t:1to(suy)]cx
-t12a:=satz281(q,a,suy,sxu,f1):is(smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q)
-[n:1to(sxu)]
-t13:=isinoutn(pl"n"(suy,sxu),pl"n"(suy,inn(sxu,n)),satz19o(inn(sxu,n),sxu,suy,1top(sxu,n))):is"n"(pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)))
-t14:=isinoutn(sxy,inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),trlessis"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),right1to(suy,sxu,n)),t10)):is"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n))))
-n1:=left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n)):1to(sxy)
-t15:=tris(nat,pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,n1),t13,t14):is"n"(pl"n"(suy,inn(sxu,n)),inn(sxy,n1))
-t16:=isnterl(pl"n"(suy,inn(sxu,n)),inn(sxy,n1),t15):is"r"(rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)))
-t17:=satzr155b(suy,inn(sxu,n)):is"r"(pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))))
-t18:=ispl1"r"(mn(p1(u),y),rlofnt(suy),rlofnt(inn(sxu,n)),isrlnt1(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l))):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))))
-t19:=tr3is(real,pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)),t18,t17,t16):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)))
-t20:=ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)),y,t19):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxy,n1)),y))
-t21:=tr3is(real,pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y),pl(rlofnt(inn(sxu,n)),pl(mn(p1(u),y),y)),pl(rlofnt(inn(sxu,n)),p1(u)),ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y,compl"r"(mn(p1(u),y),rlofnt(inn(sxu,n)))),asspl1"r"(rlofnt(inn(sxu,n)),mn(p1(u),y),y),ispl2"r"(pl(mn(p1(u),y),y),p1(u),rlofnt(inn(sxu,n)),plmn(p1(u),y))):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxu,n)),p1(u)))
-t22:=tris1(real,pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),t20,t21):is"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)))
-t23:=ismn1"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),1rl,t22):is"r"(shiftr(x,ix,y,iy,ly,n1),shiftr(x,ix,p1(u),t5,t6,n))
-t24:=intshiftr(x,ix,y,iy,ly,n1):intrl(shiftr(x,ix,y,iy,ly,n1))
-t25:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,shiftr(x,ix,y,iy,ly,n1))
-t26:=shiftrls(x,ix,y,iy,ly,n1):lessis(shiftr(x,ix,y,iy,ly,n1),x)
-t27:=intshiftr(x,ix,p1(u),t5,t6,n):intrl(shiftr(x,ix,p1(u),t5,t6,n))
-t28:=lsshiftr(x,ix,p1(u),t5,t6,n):lessis(p1(u),shiftr(x,ix,p1(u),t5,t6,n))
-t29:=shiftrls(x,ix,p1(u),t5,t6,n):lessis(shiftr(x,ix,p1(u),t5,t6,n),x)
-t30:=t4(shiftr(x,ix,p1(u),t5,t6,n),t27,t28,t29):lessis(y,shiftr(x,ix,p1(u),t5,t6,n))
-t31:=<t23><t29><t30><t27><shiftr(x,ix,p1(u),t5,t6,n)><t26><t25><t24><shiftr(x,ix,y,iy,ly,n1)>pi:is(<n>fr,<n>shiftf(x,ix,p1(u),t5,t6,rgt))
-k@t32:=fisi(1to(sxu),cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt),[t:1to(sxu)]t31(t)):is"e"([t:1to(sxu)]cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt))
-t33:=isf([t:1to(sxu)]cx,cx,[v:[t:1to(sxu)]cx]smpr(q,sxu,v),fr,shiftf(x,ix,p1(u),t5,t6,rgt),t32):is(smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q))
-t34:=isf(cx,cx,<smpr(q,suy,fl)>q,smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q),t33):is(<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q)
-[n:1to(suy)]
-t35:=isinoutn(pl"n"(suy,sxu),inn(suy,n),trlessis"n"(inn(suy,n),suy,pl"n"(suy,sxu),1top(suy,n),t12)):is"n"(inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)))
-t36:=isinoutn(sxy,inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),trlessis"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),t10)):is"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n))))
-n2:=left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n)):1to(sxy)
-t37:=tris(nat,inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,n2),t35,t36):is"n"(inn(suy,n),inn(sxy,n2))
-t38:=isnterl(inn(suy,n),inn(sxy,n2),t37):is"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)))
-t39:=ispl1"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)),y,t38):is"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y))
-t40:=ismn1"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y),1rl,t39):is"r"(shiftr(u,iu,y,iy,l,n),shiftr(x,ix,y,iy,ly,n2))
-t41:=intshiftr(u,iu,y,iy,l,n):intrl(shiftr(u,iu,y,iy,l,n))
-t42:=lsshiftr(u,iu,y,iy,l,n):lessis(y,shiftr(u,iu,y,iy,l,n))
-t43:=shiftrls(u,iu,y,iy,l,n):lessis(shiftr(u,iu,y,iy,l,n),u)
-t44:=t1(shiftr(u,iu,y,iy,l,n),t41,t42,t43):lessis(shiftr(u,iu,y,iy,l,n),x)
-t45:=intshiftr(x,ix,y,iy,ly,n2):intrl(shiftr(x,ix,y,iy,ly,n2))
-t46:=lsshiftr(x,ix,y,iy,ly,n2):lessis(y,shiftr(x,ix,y,iy,ly,n2))
-t47:=shiftrls(x,ix,y,iy,ly,n2):lessis(shiftr(x,ix,y,iy,ly,n2),x)
-t48:=<t40><t47><t46><t45><shiftr(x,ix,y,iy,ly,n2)><t44><t42><t41><shiftr(u,iu,y,iy,l,n)>pi:is(<n>shiftf(u,iu,y,iy,l,lft),<n>fl)
-t49:=symis(cx,<n>shiftf(u,iu,y,iy,l,lft),<n>fl,t48):is(<n>fl,<n>shiftf(u,iu,y,iy,l,lft))
-k@t50:=fisi(1to(suy),cx,fl,shiftf(u,iu,y,iy,l,lft),[t:1to(suy)]t49(t)):is"e"([t:1to(suy)]cx,fl,shiftf(u,iu,y,iy,l,lft))
-t51:=isf([t:1to(suy)]cx,cx,[v:[t:1to(suy)]cx]smpr(q,suy,v),fl,shiftf(u,iu,y,iy,l,lft),t50):is(smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q))
-t52:=isf(cx,cx,[t:cx]<smpri(x,ix,p1(u),t5,t6,rgt,q)><t>q,smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q),t51):is(<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
-t53:=tr3is(cx,smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,t12a,t34,t52):is(smpr(q,pl"n"(suy,sxu),f1),<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
--8284
-k@satz284:=tris1(cx,smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,smpr(q,pl"n"(suy".8284",sxu".8284"),f1".8284"),t11".8284",t53".8284"):is(smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
-q@[v:real][iv:intrl(v)][w:real][iw:intrl(w)][lw:lessis(pl"r"(y,v),w)][kw:lessis(w,pl"r"(x,v))]
-+8285
-x@[y:real]
-pl:=pl"r"(x,y):real
-mn:=mn"r"(x,y):real
-x@p1:=pl"r"(x,1rl):real
-kw@t1:=th9"l.or"(less(pl(y,v),w),is"r"(pl(y,v),w),less(mn(pl(y,v),v),mn(w,v)),is"r"(mn(pl(y,v),v),mn(w,v)),lw,[t:less(pl(y,v),w)]satz188f(pl(y,v),w,m0"r"(v),t),[t:is"r"(pl(y,v),w)]ismn1"r"(pl(y,v),w,v,t)):lessis(mn(pl(y,v),v),mn(w,v))
-t2:=islessis1(mn(pl(y,v),v),y,mn(w,v),mnpl(y,v),t1):lessis(y,mn(w,v))
-t3:=th9"l.or"(less(w,pl(x,v)),is"r"(w,pl(x,v)),less(mn(w,v),mn(pl(x,v),v)),is"r"(mn(w,v),mn(pl(x,v),v)),kw,[t:less(w,pl(x,v))]satz188f(w,pl(x,v),m0"r"(v),t),[t:is"r"(w,pl(x,v))]ismn1"r"(w,pl(x,v),v,t)):lessis(mn(w,v),mn(pl(x,v),v))
-t4:=islessis2(mn(pl(x,v),v),x,mn(w,v),mnpl(x,v),t3):lessis(mn(w,v),x)
--8285
-iv@sft:=[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]<t4".8285"(t,w,lt,kt)><t2".8285"(t,w,lt,kt)><intmn(t,w,v,iv)><mn"r"(t,v)>f:[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]cx
-+*8285
-iv@t5:=tris(real,m0"r"(pl(y,v)),m0"r"(pl(v,y)),pl(m0"r"(v),m0"r"(y)),ism0"r"(pl(y,v),pl(v,y),compl"r"(y,v)),satz180(v,y)):is"r"(m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)))
-t6:=tr3is(real,mn(pl(1rl,pl(x,v)),v),pl(1rl,mn(pl(x,v),v)),pl(1rl,x),p1(x),asspl1"r"(1rl,pl(x,v),m0"r"(v)),ispl2"r"(mn(pl(x,v),v),x,1rl,mnpl(x,v)),compl"r"(1rl,x)):is"r"(mn(pl(1rl,pl(x,v)),v),p1(x))
-t7:=tr3is(real,mn(p1(pl(x,v)),pl(y,v)),pl(pl(1rl,pl(x,v)),pl(m0"r"(v),m0"r"(y))),mn(mn(pl(1rl,pl(x,v)),v),y),mn(p1(x),y),ispl12"r"(p1(pl(x,v)),pl(1rl,pl(x,v)),m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)),compl"r"(pl(x,v),1rl),t5),asspl2"r"(pl(1rl,pl(x,v)),m0"r"(v),m0"r"(y)),ismn1"r"(mn(pl(1rl,pl(x,v)),v),p1(x),y,t6)):is"r"(mn(p1(pl(x,v)),pl(y,v)),mn(p1(x),y))
-t8:=th9"l.or"(less(y,x),is"r"(y,x),less(pl(y,v),pl(x,v)),is"r"(pl(y,v),pl(x,v)),ly,[t:less(y,x)]satz188f(y,x,v,t),[t:is"r"(y,x)]ispl1"r"(y,x,v,t)):lessis(pl(y,v),pl(x,v))
-s0:=shiftl(x,ix,y,iy,ly):nat
-sv:=shiftl(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8):nat
-t9:=isrlent(mn(p1(pl(x,v)),pl(y,v)),t6"r.shift"(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8),mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly),t7):is"n"(sv,s0)
-t10:=lessisi2"n"(sv,s0,t9):lessis"n"(sv,s0)
-f1:=left(cx,s0,sv,t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(sv)]cx
-t11:=issmpr(q,s0,shiftf(x,ix,y,iy,ly,f),sv,t9):is(smpr(q,sv,f1),smpri(x,ix,y,iy,ly,f,q))
-[n:1to(sv)]
-t12:=isinoutn(s0,inn(sv,n),trlessis"n"(inn(sv,n),sv,s0,1top(sv,n),t10)):is"n"(inn(sv,n),inn(s0,left1to(s0,sv,t10,n)))
-n1:=left1to(s0,sv,t10,n):1to(s0)
-t13:=isnterl(inn(sv,n),inn(s0,n1),t12):is"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)))
-t14:=tris(real,mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(sv,n)),mn(pl(y,v),v)),pl(rlofnt(inn(s0,n1)),y),asspl1"r"(rlofnt(inn(sv,n)),pl(y,v),m0"r"(v)),ispl12"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)),mn(pl(y,v),v),y,t13,mnpl(y,v))):is"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y))
-st0:=shiftr(x,ix,y,iy,ly,n1):real
-stv:=shiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):real
-t15:=tr4is(real,mn(stv,v),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(1rl),m0"r"(v))),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(v),m0"r"(1rl))),mn(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),1rl),st0,asspl1"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(1rl),m0"r"(v)),ispl2"r"(pl(m0"r"(1rl),m0"r"(v)),pl(m0"r"(v),m0"r"(1rl)),pl(rlofnt(inn(sv,n)),pl(y,v)),compl"r"(m0"r"(1rl),m0"r"(v))),asspl2"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(v),m0"r"(1rl)),ismn1"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y),1rl,t14)):is"r"(mn(stv,v),st0)
-t16:=intshiftr(x,ix,y,iy,ly,n1):intrl(st0)
-t17:=shiftrls(x,ix,y,iy,ly,n1):lessis(st0,x)
-t18:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,st0)
-t19:=intshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):intrl(stv)
-t20:=shiftrls(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(stv,pl(x,v))
-t21:=lsshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(pl(y,v),stv)
-t22:=intmn(stv,t19,v,iv):intrl(mn(stv,v))
-t23:=t2(stv,t19,t21,t20):lessis(y,mn(stv,v))
-t24:=t4(stv,t19,t21,t20):lessis(mn(stv,v),x)
-t25:=<t15><t17><t18><t16><st0><t24><t23><t22><mn(stv,v)>pi:is(<n>shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),<n>f1)
-iv@t26:=fisi(1to(sv),cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,[t:1to(sv)]t25(t)):is"e"([t:1to(sv)]cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1)
-t27:=isf([t:1to(sv)]cx,cx,[w:[t:1to(sv)]cx]smpr(q,sv,w),shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,t26):is(smpri(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft,q),smpr(q,sv,f1))
--8285
-iv@lemma285:=t8".8285":lessis(pl"r"(y,v),pl"r"(x,v))
-satz285:=tris(cx,smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpr(q,sv".8285",f1".8285"),smpri(x,ix,y,iy,ly,f,q),t27".8285",t11".8285"):is(smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpri(x,ix,y,iy,ly,f,q))
-ly@[s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][f:seq(x,ix,y,iy,ly,cx)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)]
-us:=<ul><lu><iu><u>s:real
-+8286
-t1:=<ul><lu><iu><u>ins:and3(intrl(us),lessis(y,us),lessis(us,x))
--8286
-inseqe1:=t22"r.shift"(x,ix,y,iy,ly,us,t1".8286"):intrl(us)
-inseqe2:=t23"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(y,us)
-inseqe3:=t24"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(us,x)
-usf:=<inseqe3><inseqe2><inseqe1><us>f:cx
-f@permseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]usf(t,u,v,w):[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]cx
-q@[a:assoc(q)][c:commut(q)][s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][pri:proofsirrelevant(x,ix,y,iy,ly,real,s)][ps:perm(x,ix,y,iy,ly,s)]
-+*8286
-ps@ss:=shiftseq(x,ix,y,iy,ly,s,ins):[t:1to(shiftl)]1to(shiftl)
-t2:=satz283(q,a,c,shiftl,ss,bijshiftseq(x,ix,y,iy,ly,s,ins,pri,ps),shiftf(f)):is(smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)),smpri(f,q))
-[n:1to(shiftl)]
-ns:=us(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):real
-t3:=shiftinv1(ns,t34"r.shift"(x,ix,y,iy,ly,s,ins,n)):is"r"(ns,shiftr(<n>ss))
-t4:=inseqe1(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):intrl(ns)
-t5:=inseqe2(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(y,ns)
-t6:=inseqe3(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(ns,x)
-t7:=intshiftr(<n>ss):intrl(shiftr(<n>ss))
-t8:=lsshiftr(<n>ss):lessis(y,shiftr(<n>ss))
-t9:=shiftrls(<n>ss):lessis(shiftr(<n>ss),x)
-t10:=<t3><t9><t8><t7><shiftr(<n>ss)><t6><t5><t4><ns>pi:is(<n>shiftf(permseq(s,ins,f)),<<n>ss>shiftf(f))
-ps@t11:=fisi(1to(shiftl),cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),[t:1to(shiftl)]t10(t)):is"e"([t:1to(shiftl)]cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f))
-t12:=isf([t:1to(shiftl)]cx,cx,[u:[t:1to(shiftl)]cx]smpr(q,shiftl,u),shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),t11):is(smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)))
--8286
-ps@satz286:=tris(cx,smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss".8286">shiftf(f)),smpri(f,q),t12".8286",t2".8286"):is(smpri(permseq(s,ins,f),q),smpri(f,q))
-@[x:nat][f:[t:1to(x)]cx]
-modf:=[t:1to(x)]pli(mod(<t>f),0):[t:1to(x)]cx
-+8287
-[r:real]
-prop1:=lessis(mod(sum(x,f)),r):'prop'
-prop2:=is(sum(x,modf(f)),pli(r,0)):'prop'
-prop3:=and(prop1,prop2):'prop'
-f@prop4:=some"r"([t:real]prop3(t)):'prop'
-x@prop5:=[u:[t:1to(x)]cx]prop4(u):'prop'
-@[f:[t:1to(1)]cx]
-t1:=satz277([t:cx][u:cx]pl(t,u),f):is(sum(1,f),<xout(1)>f)
-t2:=ismod(sum(1,f),<xout(1)>f,t1):is"r"(mod(sum(1,f)),mod(<xout(1)>f))
-t3:=lessisi2(mod(sum(1,f)),mod(<xout(1)>f),t2):prop1(1,f,mod(<xout(1)>f))
-t4:=satz277([t:cx][u:cx]pl(t,u),modf(1,f)):prop2(1,f,mod(<xout(1)>f))
-t5:=andi(prop1(1,f,mod(<xout(1)>f)),prop2(1,f,mod(<xout(1)>f)),t3,t4):prop3(1,f,mod(<xout(1)>f))
-t6:=somei(real,[t:real]prop3(1,f,t),mod(<xout(1)>f),t5):prop4(1,f)
-@t7:=[u:[t:1to(1)]cx]t6(u):prop5(1)
-x@[p:prop5(x)][f:[t:1to(pl"n"(x,1))]cx]
-t8:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
-lf:=left(cx,pl"n"(x,1),x,t8,f):[t:1to(x)]cx
-[r:real][pr:prop3(lf,r)]
-t9:=ande1(prop1(lf,r),prop2(lf,r),pr):prop1(lf,r)
-t10:=ande2(prop1(lf,r),prop2(lf,r),pr):prop2(lf,r)
-t11:=satz278([t:cx][u:cx]pl(t,u),x,f):is(sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f))
-t12:=ismod(pl(sum(x,lf),<xout(pl"n"(x,1))>f),sum(pl"n"(x,1),f),symis(cx,sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f),t11)):is"r"(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)))
-m:=mod(<xout(pl"n"(x,1))>f):real
-t13:=islessis1(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),t12,satz271(sum(x,lf),<xout(pl"n"(x,1))>f)):lessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m))
-t14:=th9"l.or"(less(mod(sum(x,lf)),r),is"r"(mod(sum(x,lf)),r),less(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),is"r"(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),t9,[t:less(mod(sum(x,lf)),r)]satz188f(mod(sum(x,lf)),r,m,t),[t:is"r"(mod(sum(x,lf)),r)]ispl1"r"(mod(sum(x,lf)),r,m,t)):lessis(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m))
-t15:=trlessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),pl"r"(r,m),t13,t14):prop1(pl"n"(x,1),f,pl"r"(r,m))
-lmf:=left(cx,pl"n"(x,1),x,t8,modf(pl"n"(x,1),f)):[t:1to(x)]cx
-t16:=satz278([t:cx][u:cx]pl(t,u),x,modf(pl"n"(x,1),f)):is(sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)))
-t17:=ispl1(sum(x,lmf),pli(r,0),pli(m,0),t10):is(pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)))
-t18:=plis12a(r,0,m,0):is(pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)))
-t19:=isrecx2(pl"r"(0,0),0,pl"r"(r,m),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0))
-t20:=tr4is(cx,sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0),t16,t17,t18,t19):prop2(pl"n"(x,1),f,pl"r"(r,m))
-t21:=andi(prop1(pl"n"(x,1),f,pl"r"(r,m)),prop2(pl"n"(x,1),f,pl"r"(r,m)),t15,t20):prop3(pl"n"(x,1),f,pl"r"(r,m))
-t22:=somei(real,[t:real]prop3(pl"n"(x,1),f,t),pl"r"(r,m),t21):prop4(pl"n"(x,1),f)
-f@t23:=someapp(real,[t:real]prop3(lf,t),<lf>p,prop4(pl"n"(x,1),f),[t:real][u:prop3(lf,t)]t22(t,u)):prop4(pl"n"(x,1),f)
-p@t25:=[u:[t:1to(pl"n"(x,1))]cx]t23(u):prop5(pl"n"(x,1))
-t26:=isp(nat,[t:nat]prop5(t),pl"n"(x,1),<x>suc,t25,satz4a(x)):prop5(<x>suc)
--8287
-satz287:=<f>induction([t:nat]prop5".8287"(t),t7".8287",[t:nat][u:prop5".8287"(t)]t26".8287"(t,u),x):some"r"([t:real]and(lessis(mod(sum(x,f)),t),is(sum(x,modf(f)),pli(t,0))))
-+8288
-prop1:=is(pli(mod(prod(x,f)),0),prod(x,modf(f))):'prop'
-x@prop2:=[u:[t:1to(x)]cx]prop1(u):'prop'
-@[f:[t:1to(1)]cx]
-t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
-t2:=ismod(prod(1,f),<xout(1)>f,t1):is"r"(mod(prod(1,f)),mod(<xout(1)>f))
-t3:=isrecx1(mod(prod(1,f)),mod(<xout(1)>f),0,t2):is(pli(mod(prod(1,f)),0),pli(mod(<xout(1)>f),0))
-t4:=satz277([t:cx][u:cx]ts(t,u),modf(1,f)):is(prod(1,modf(1,f)),pli(mod(<xout(1)>f),0))
-t5:=tris2(cx,pli(mod(prod(1,f)),0),prod(1,modf(1,f)),pli(mod(<xout(1)>f),0),t3,t4):prop1(1,f)
-@t6:=[u:[t:1to(1)]cx]t5(u):prop2(1)
-x@[p:prop2(x)][f:[t:1to(pl"n"(x,1))]cx]
-t7:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
-lf:=left(cx,pl"n"(x,1),x,t7,f):[t:1to(x)]cx
-t8:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
-m:=mod(<xout(pl"n"(x,1))>f):real
-t9:=ismod(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),t8):is"r"(mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)))
-t10:=satz268(prod(x,lf),<xout(pl"n"(x,1))>f):is"r"(mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m))
-t11:=tris(real,mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m),t9,t10):is"r"(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m))
-t12:=isrecx1(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m),0,t11):is(pli(mod(prod(pl"n"(x,1),f)),0),pli(ts"r"(mod(prod(x,lf)),m),0))
-lmf:=left(cx,pl"n"(x,1),x,t7,modf(pl"n"(x,1),f)):[t:1to(x)]cx
-t13:=satz278([t:cx][u:cx]ts(t,u),x,modf(pl"n"(x,1),f)):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)))
-t14:=symis(cx,pli(mod(prod(x,lf)),0),prod(x,lmf),<lf>p):is(prod(x,lmf),pli(mod(prod(x,lf)),0))
-t15:=ists1(prod(x,lmf),pli(mod(prod(x,lf)),0),pli(m,0),t14):is(ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)))
-t16:=tsis12a(mod(prod(x,lf)),0,m,0):is(ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))))
-t17:=tris(real,mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),mn"r"(ts"r"(mod(prod(x,lf)),m),0),ts"r"(mod(prod(x,lf)),m),ismn2"r"(ts"r"(0,0),0,ts"r"(mod(prod(x,lf)),m),ts01"r"(0,0,refis(real,0))),pl02"r"(ts"r"(mod(prod(x,lf)),m),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m))
-t18:=tris(real,pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),pl"r"(0,0),0,ispl12"r"(ts"r"(mod(prod(x,lf)),0),0,ts"r"(0,m),0,ts02"r"(mod(prod(x,lf)),0,refis(real,0)),ts01"r"(0,m,refis(real,0))),pl01"r"(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0)
-t19:=isrecx12(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0,t17,t18):is(pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0))
-t20:=tr4is(cx,prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0),t13,t15,t16,t19):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0))
-t21:=tris2(cx,pli(mod(prod(pl"n"(x,1),f)),0),prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0),t12,t20):prop1(pl"n"(x,1),f)
-p@t21a:=[u:[t:1to(pl"n"(x,1))]cx]t21(u):prop2(pl"n"(x,1))
-t22:=isp(nat,[t:nat]prop2(t),pl"n"(x,1),<x>suc,t21a,satz4a(x)):prop2(<x>suc)
--8288
-satz288:=<f>induction([t:nat]prop2".8288"(t),t6".8288",[t:nat][u:prop2".8288"(t)]t22".8288"(t,u),x):is(pli(mod(prod(x,f)),0),prod(x,modf(f)))
-+8289
-prop1:=is(prod(x,f),0c):'prop'
-prop2:=some"l"(1to(x),[t:1to(x)]is(<t>f,0c)):'prop'
-prop3:=iff(prop1,prop2):'prop'
-x@prop4:=[u:[t:1to(x)]cx]prop3(u):'prop'
-@[f:[t:1to(1)]cx]
-t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
-[p:prop1(1,f)]
-t2:=tris1(cx,<xout(1)>f,0c,prod(1,f),t1,p):is(<xout(1)>f,0c)
-t3:=somei(1to(1),[t:1to(1)]is(<t>f,0c),xout(1),t2):prop2(1,f)
-f@[p:prop2(1,f)][u:1to(1)][i:is(<u>f,0c)]
-t4:=th1"n.singlet"(u):is"e"(1to(1),u,xout(1))
-t5:=tr3is(cx,prod(1,f),<xout(1)>f,<u>f,0c,t1,isf(1to(1),cx,f,xout(1),u,symis(1to(1),u,xout(1),t4)),i):prop1(1,f)
-p@t6:=someapp(1to(1),[t:1to(1)]is(<t>f,0c),p,prop1(1,f),[t:1to(1)][u:is(<t>f,0c)]t5(t,u)):prop1(1,f)
-f@t7:=iffi(prop1(1,f),prop2(1,f),[t:prop1(1,f)]t3(t),[t:prop2(1,f)]t6(t)):prop3(1,f)
-@t8:=[u:[t:1to(1)]cx]t7(u):prop4(1)
-x@[p:prop4(x)][f:[t:1to(pl"n"(x,1))]cx]
-t9:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
-lf:=left(cx,pl"n"(x,1),x,t9,f):[t:1to(x)]cx
-t10:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
-[q:prop1(pl"n"(x,1),f)]
-t11:=tris1(cx,ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,prod(pl"n"(x,1),f),t10,q):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-t12:=satz221c(prod(x,lf),<xout(pl"n"(x,1))>f,t11):or(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c))
-[i:is(prod(x,lf),0c)]
-t13:=th3"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,i):prop2(x,lf)
-[n:1to(x)][j:is(<n>lf,0c)]
-t14:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),left1to(pl"n"(x,1),x,t9,n),j):prop2(pl"n"(x,1),f)
-i@t15:=someapp(1to(x),[t:1to(x)]is(<t>lf,0c),t13,prop2(pl"n"(x,1),f),[t:1to(x)][u:is(<t>lf,0c)]t14(t,u)):prop2(pl"n"(x,1),f)
-q@[i:is(<xout(pl"n"(x,1))>f,0c)]
-t16:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),xout(pl"n"(x,1)),i):prop2(pl"n"(x,1),f)
-q@t17:=orapp(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c),prop2(pl"n"(x,1),f),t12,[t:is(prod(x,lf),0c)]t15(t),[t:is(<xout(pl"n"(x,1))>f,0c)]t16(t)):prop2(pl"n"(x,1),f)
-f@[q:prop2(pl"n"(x,1),f)][n:1to(pl"n"(x,1))][i:is(<n>f,0c)][j:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]
-t18:=tris1(cx,<xout(pl"n"(x,1))>f,0c,<n>f,isf(1to(pl"n"(x,1)),cx,f,n,xout(pl"n"(x,1)),j),i):is(<xout(pl"n"(x,1))>f,0c)
-t20:=satz221b(prod(x,lf),<xout(pl"n"(x,1))>f,t18):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-i@[m:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]
-n1:=inn(pl"n"(x,1),n):nat
-[j:is"n"(n1,pl"n"(x,1))]
-t21:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),pl"n"(x,1),lessisi3(pl"n"(x,1)),j):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)))
-t22:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)),isoutinn(pl"n"(x,1),n),t21):is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))
-m@t23:=th3"l.imp"(is"n"(n1,pl"n"(x,1)),is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),m,[t:is"n"(n1,pl"n"(x,1))]t22(t)):nis"n"(n1,pl"n"(x,1))
-t24:=ore1(less"n"(n1,pl"n"(x,1)),is"n"(n1,pl"n"(x,1)),1top(pl"n"(x,1),n),t23):less"n"(n1,pl"n"(x,1))
-t25:=satz26(x,n1,t24):lessis"n"(n1,x)
-n2:=outn(x,n1,t25):1to(x)
-t26:=isinoutn(x,n1,t25):is"n"(n1,inn(x,n2))
-t27:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),inn(x,n2),trlessis"n"(inn(x,n2),x,pl"n"(x,1),1top(x,n2),t9),t26):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2))
-t28:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2),isoutinn(pl"n"(x,1),n),t27):is"e"(1to(pl"n"(x,1)),n,left1to(pl"n"(x,1),x,t9,n2))
-t29:=isf(1to(pl"n"(x,1)),cx,f,n,left1to(pl"n"(x,1),x,t9,n2),t28):is(<n>f,<n2>lf)
-t30:=tris1(cx,<n2>lf,0c,<n>f,t29,i):is(<n2>lf,0c)
-t31:=somei(1to(x),[t:1to(x)]is(<t>lf,0c),n2,t30):prop2(x,lf)
-t32:=th4"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,t31):prop1(x,lf)
-t34:=satz221a(prod(x,lf),<xout(pl"n"(x,1))>f,t32):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-i@t35:=th1"l.imp"(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c),[t:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]t20(t),[t:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]t34(t)):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-t36:=tris(cx,prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,t10,t35):prop1(pl"n"(x,1),f)
-q@t37:=someapp(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),q,prop1(pl"n"(x,1),f),[t:1to(pl"n"(x,1))][u:is(<t>f,0c)]t36(t,u)):prop1(pl"n"(x,1),f)
-f@t38:=iffi(prop1(pl"n"(x,1),f),prop2(pl"n"(x,1),f),[t:prop1(pl"n"(x,1),f)]t17(t),[t:prop2(pl"n"(x,1),f)]t37(t)):prop3(pl"n"(x,1),f)
-p@t39:=[u:[t:1to(pl"n"(x,1))]cx]t38(u):prop4(pl"n"(x,1))
-t40:=isp(nat,[t:nat]prop4(t),pl"n"(x,1),<x>suc,t39,satz4a(x)):prop4(<x>suc)
--8289
-satz289:=<f>induction([t:nat]prop4".8289"(t),t8".8289",[t:nat][u:prop4".8289"(t)]t40".8289"(t,u),x):iff(is(prod(x,f),0c),some"l"(1to(x),[t:1to(x)]is(<t>f,0c)))
-[i:is(prod(x,f),0c)]
-satz289a:=th3"l.iff"(prop1".8289",prop2".8289",satz289,i):some"l"(1to(x),[t:1to(x)]is(<t>f,0c))
-f@[n:1to(x)][i:is(<n>f,0c)]
-+*8289
-i"c"@t41:=somei(1to(x),[t:1to(x)]is(<t>f,0c),n,i):prop2
--8289
-i@satz289b:=th4"l.iff"(prop1".8289",prop2".8289",satz289,t41".8289"):is(prod(x,f),0c)
-@[x:complex][m:real][mi:intrl(m)][o:or(nis(x,0c),pos(m))]
-+v9
-[p:pos(m)]
-t1:=posintnatrl(m,p,mi):natrl(m)
-m1:=ntofrl(m,t1):nat
-pw1:=prod(m1,[t:1to(m1)]x):cx
--v9
-x@[y:complex][m:real][n:real][i:is(x,y)][j:is"r"(m,n)][mi1:intrl(m)][ni1:intrl(n)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(n))]
-+*v9
-oy@[mp:pos(m)][np:pos(n)]
-m0:=m1(x,m,mi1,ox,mp):nat
-n0:=m1(y,n,ni1,oy,np):nat
-t2:=isrlent(m,t1(x,m,mi1,ox,mp),n,t1(y,n,ni1,oy,np),j):is"n"(m0,n0)
-t3:=lessisi2"n"(m0,n0,t2):lessis"n"(m0,n0)
-t4:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]y,m0,t2):is(prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np))
-t5:=fisi(1to(m0),cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),[t:1to(m0)]i):is"e"([t:1to(m0)]cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y))
-t6:=isf([t:1to(m0)]cx,cx,[u:[t:1to(m0)]cx]prod(m0,u),[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),t5):is(pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)))
-t7:=tris(cx,pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np),t6,t4):is(pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,np))
-p@[p1:pos(m)]
-t8:=t7(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,p,p1):is(pw1(p),pw1(p1))
-p@[n:nis(x,0c)]
-t9:=th5"l.some"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c),[t:1to(m1)]n):not(some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)))
-t10:=th3"l.imp"(is(pw1,0c),some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)),t9,[t:is(pw1,0c)]satz289a(m1,[u:1to(m1)]x,t)):nis(pw1,0c)
-o@[n:neg(m)]
-mi@t11:=intabs(m,mi):intrl(abs(m))
-n@t12:=satz166b(m,n):pos(abs(m))
-t13:=ori2(nis(x,0c),pos(abs(m)),t12):or(nis(x,0c),pos(abs(m)))
-t14:=ore1(nis(x,0c),pos(m),o,nnotp(m,n)):nis(x,0c)
-t15:=t10(abs(m),t11,t13,t12,t14):nis(pw1(abs(m),t11,t13,t12),0c)
-pw2:=ov(1c,pw1(abs(m),t11,t13,t12),t15):cx
-oy@[nm:neg(m)][nn:neg(n)]
-pwm:=pw1(x,abs(m),t11(x,m,mi1),t13(x,m,mi1,ox,nm),t12(x,m,mi1,ox,nm)):cx
-pwn:=pw1(y,abs(n),t11(y,n,ni1),t13(y,n,ni1,oy,nn),t12(y,n,ni1,oy,nn)):cx
-t16:=t7(abs(m),abs(n),i,isabs(m,n,j),t11(x,m,mi1),t11(y,n,ni1),t13(x,m,mi1,ox,nm),t13(y,n,ni1,oy,nn),t12(x,m,mi1,ox,nm),t12(y,n,ni1,oy,nn)):is(pwm,pwn)
-t17:=isov2(pwm,pwn,1c,t16,t15(x,m,mi1,ox,nm),t15(y,n,ni1,oy,nn)):is(pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,nn))
-n@[n1:neg(m)]
-t18:=t17(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,n,n1):is(pw2(n),pw2(n1))
-o@pw3:=ite"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c)):cx
-n@t19:=itet"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),n):is(pw3,pw2(n))
-o@[nn:not(neg(m))]
-t20:=itef"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),nn):is(pw3,1c)
-nm@t21:=isp(real,[t:real]neg(t),m,n,nm,j):neg(n)
-t22:=t19(x,m,mi1,ox,nm):is(pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm))
-t23:=symis(cx,pw3(y,n,ni1,oy),pw2(y,n,ni1,oy,t21),t19(y,n,ni1,oy,t21)):is(pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy))
-t24:=tr3is(cx,pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy),t22,t17(t21),t23):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
-oy@[nn:not(neg(m))]
-t25:=isp(real,[t:real]not(neg(t)),m,n,nn,j):not(neg(n))
-t26:=t20(x,m,mi1,ox,nn):is(pw3(x,m,mi1,ox),1c)
-t27:=t20(y,n,ni1,oy,t25):is(pw3(y,n,ni1,oy),1c)
-t28:=tris2(cx,pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),1c,t26,t27):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
-oy@t29:=th1"l.imp"(neg(m),is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy)),[t:neg(m)]t24(t),[t:not(neg(m))]t28(t)):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
--v9
-o@pw:=ite"l.r"(pos(m),cx,[t:pos(m)]pw1".v9"(t),[t:not(pos(m))]pw3".v9",[t:pos(m)][u:pos(m)]t8".v9"(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3".v9")):cx
-+*v9
-p@t30:=itet"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),p):is(pw,pw1(p))
-o@[n:not(pos(m))]
-t31:=itef"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),n):is(pw,pw3)
-o@[i:is"r"(m,0)]
-t32:=tris(cx,pw,pw3,1c,t31(0notp(m,i)),t20(0notn(m,i))):is(pw,1c)
-o@[n:neg(m)]
-t33:=tris(cx,pw,pw3,pw2(n),t31(nnotp(m,n)),t19(n)):is(pw,pw2(n))
--v9
-o@[p:pos(m)]
-posexp:=t30".v9"(p):is(pw(x,m,mi,o),prod(ntofrl(m,posintnatrl(m,p,mi)),[t:1to(ntofrl(m,posintnatrl(m,p,mi)))]x))
-[n:nis(x,0c)]
-lemmapw1:=th2"e.notis"(cx,pw1".v9"(p),0c,pw,t10".v9"(p,n),posexp):nis(pw(x,m,mi,o),0c)
-o@[i:is"r"(m,0)]
-0exp:=t32".v9"(i):is(pw(x,m,mi,o),1c)
-o@[n:neg(m)]
-lemmapw2:=t14".v9"(n):nis(x,0c)
-lemmapw3:=t13".v9"(n):or(nis(x,0c),pos(abs(m)))
-+*v9
-n@t34:=t30(abs(m),t11,t13(n),t12(n)):is(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)))
-t35:=isov2(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)),1c,t34,lemmapw1(abs(m),t11,t13(n),t12(n),t14(n)),t15(n)):is(ov(1c,pw(x,abs(m),t11,t13(n)),lemmapw1(abs(m),t11,t13(n),t12(n),t14(n))),pw2(n))
--v9
-n@negexp:=tris2(cx,pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)),pw2".v9"(n),t33".v9"(n),t35".v9"(n)):is(pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)))
-+*v9
-mp@t36:=isp(real,[t:real]pos(t),m,n,mp,j):pos(n)
-t37:=t30(x,m,mi1,ox,mp):is(pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp))
-t38:=symis(cx,pw(y,n,ni1,oy),pw1(y,n,ni1,oy,t36),t30(y,n,ni1,oy,t36)):is(pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy))
-t39:=tr3is(cx,pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy),t37,t7(t36),t38):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
-oy@[np:not(pos(m))]
-t40:=isp(real,[t:real]not(pos(t)),m,n,np,j):not(pos(n))
-t41:=t31(x,m,mi1,ox,np):is(pw(x,m,mi1,ox),pw3(x,m,mi1,ox))
-t42:=symis(cx,pw(y,n,ni1,oy),pw3(y,n,ni1,oy),t31(y,n,ni1,oy,t40)):is(pw3(y,n,ni1,oy),pw(y,n,ni1,oy))
-t43:=tr3is(cx,pw(x,m,mi1,ox),pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),pw(y,n,ni1,oy),t41,t29,t42):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
--v9
-oy@ispw12:=th1"l.imp"(pos(m),is(pw(x,m,mi1,ox),pw(y,n,ni1,oy)),[t:pos(m)]t39".v9"(t),[t:not(pos(m))]t43".v9"(t)):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
-m@[i:is(x,y)][mi:intrl(m)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(m))]
-ispw1:=ispw12(x,y,m,m,i,refis(real,m),mi,mi,ox,oy):is(pw(x,m,mi,ox),pw(y,m,mi,oy))
-x@[m:real][n:real][i:is"r"(m,n)][mi:intrl(m)][ni:intrl(n)][om:or(nis(x,0c),pos(m))][on:or(nis(x,0c),pos(n))]
-ispw2:=ispw12(x,x,m,n,refis(cx,x),i,mi,ni,om,on):is(pw(x,m,mi,om),pw(x,n,ni,on))
-o@[n:nis(x,0c)]
-+9290
-[p:pos(m)]
-t1:=lemmapw1(p,n):nis(pw(x,m,mi,o),0c)
-@[i:is(1c,0c)]
-t2:=tr3is(real,1rl,re(1c),re(0c),0,isre(1rl,0),iscere(1c,0c,i),reis(0,0)):is"r"(1rl,0)
--9290
-@1not0:=th3"l.imp"(is(1c,0c),is"r"(1rl,0),pnot0(1rl,pos1),[t:is(1c,0c)]t2".9290"(t)):nis(1c,0c)
-+*9290
-n@[i:is"r"(m,0)]
-t4:=th2"e.notis"(cx,1c,0c,pw(x,m,mi,o),1not0,0exp(i)):nis(pw(x,m,mi,o),0c)
-n@[nm:neg(m)]
-p0:=pw(x,abs(m),intabs(m,mi),lemmapw3(nm)):cx
-t5:=lemmapw1(x,abs(m),intabs(m,mi),lemmapw3(nm),satz166b(m,nm),lemmapw2(nm)):nis(p0,0c)
-t6:=tris(cx,ts(pw(x,m,mi,o),p0),ts(ov(1c,p0,t5),p0),1c,ists1(pw(x,m,mi,o),ov(1c,p0,t5),p0,negexp(nm)),satz229e(1c,p0,t5)):is(ts(pw(x,m,mi,o),p0),1c)
-t7:=th2"e.notis"(cx,1c,0c,ts(pw(x,m,mi,o),p0),1not0,t6):nis(ts(pw(x,m,mi,o),p0),0c)
-t8:=th3"l.imp"(is(pw(x,m,mi,o),0c),is(ts(pw(x,m,mi,o),p0),0c),t7,[t:is(pw(x,m,mi,o),0c)]satz221a(pw(x,m,mi,o),p0,t)):nis(pw(x,m,mi,o),0c)
--9290
-n@satz290:=rapp(m,nis(pw(x,m,mi,o),0c),[t:pos(m)]t1".9290"(t),[t:is"r"(m,0)]t4".9290"(t),[t:neg(m)]t8".9290"(t)):nis(pw(x,m,mi,o),0c)
-x@lemma291:=ori2(nis(x,0c),pos(1rl),pos1):or(nis(x,0c),pos(1rl))
-+9291
-1a:=ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)):nat
-t1:=posexp(x,1rl,intrl1,lemma291,pos1):is(pw(x,1rl,intrl1,lemma291),prod(1a,[t:1to(1a)]x))
-t2:=tris(nat,1,ntofrl(1rl,natrl1),ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)),isntrl1(1),isrlent(1rl,natrl1,1rl,posintnatrl(1rl,pos1,intrl1),refis(real,1rl))):is"n"(1,1a)
-t3:=lessisi2"n"(1,1a,t2):lessis"n"(1,1a)
-t4:=issmpr([t:cx][u:cx]ts(t,u),1a,[t:1to(1a)]x,1,t2):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),prod(1a,[t:1to(1a)]x))
-t5:=satz277([t:cx][u:cx]ts(t,u),left(cx,1a,1,t3,[t:1to(1a)]x)):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),x)
-t6:=tris1(cx,prod(1a,[t:1to(1a)]x),x,prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),t4,t5):is(prod(1a,[t:1to(1a)]x),x)
--9291
-satz291:=tris(cx,pw(x,1rl,intrl1,lemma291),prod(1a".9291",[t:1to(1a".9291")]x),x,t1".9291",t6".9291"):is(pw(x,1rl,intrl1,lemma291),x)
-[y:cx][m:real][mi:intrl(m)][o:or(and(nis(x,0c),nis(y,0c)),pos(m))]
-+9292
-[a:and(nis(x,0c),nis(y,0c))]
-t1:=ande1(nis(x,0c),nis(y,0c),a):nis(x,0c)
-t2:=ande2(nis(x,0c),nis(y,0c),a):nis(y,0c)
-t3:=satz221d(x,y,t1,t2):nis(ts(x,y),0c)
--9292
-lemma292a:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(x,0c),o,[t:and(nis(x,0c),nis(y,0c))]t1".9292"(t)):or(nis(x,0c),pos(m))
-lemma292b:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(y,0c),o,[t:and(nis(x,0c),nis(y,0c))]t2".9292"(t)):or(nis(y,0c),pos(m))
-lemma292c:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(ts(x,y),0c),o,[t:and(nis(x,0c),nis(y,0c))]t3".9292"(t)):or(nis(ts(x,y),0c),pos(m))
-+*9292
-x@[n:nat]
-nr:=rlofnt(n):real
-t4:=natintrl(nr,natrli(n)):intrl(nr)
-t5:=ori2(nis(x,0c),pos(nr),natpos(nr,natrli(n))):or(nis(x,0c),pos(nr))
-p0:=pw(x,nr,t4,t5):cx
-x@t6:=tris(cx,p0(1),pw(x,1rl,intrl1,lemma291(x)),x,ispw1(x,x,1rl,refis(cx,x),intrl1,t5(1),lemma291(x)),satz291(x)):is(p0(1),x)
-n@n0:=ntofrl(nr,posintnatrl(nr,natpos(nr,natrli(n)),t4)):nat
-t7:=tris(nat,n,ntofrl(nr,natrli(n)),n0,isntrl1(n),isrlent(nr,natrli(n),nr,posintnatrl(nr,natpos(nr,natrli(n)),t4),refis(real,nr))):is"n"(n,n0)
-t8:=lessisi2"n"(n,n0,t7):lessis"n"(n,n0)
-t9:=posexp(x,nr,t4,t5,natpos(nr,natrli(n))):is(p0,prod(n0,[t:1to(n0)]x))
-t10:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]x,n,t7):is(prod(n,left(cx,n0,n,t8,[t:1to(n0)]x)),prod(n0,[t:1to(n0)]x))
-t11:=tris2(cx,p0,prod(n,[t:1to(n)]x),prod(n0,[t:1to(n0)]x),t9,t10):is(p0,prod(n,[t:1to(n)]x))
-n1:=pl"n"(n,1):nat
-t12:=lessisi1"n"(n,n1,satz18a(n,1)):lessis"n"(n,n1)
-t13:=satz278([t:cx][u:cx]ts(t,u),n,[t:1to(n1)]x):is(prod(n1,[t:1to(n1)]x),ts(prod(n,left(cx,n1,n,t12,[t:1to(n1)]x)),x))
-t14:=ists1(p0,prod(n,[t:1to(n)]x),x,t11):is(ts(p0,x),ts(prod(n,[t:1to(n)]x),x))
-t15:=tris2(cx,prod(n1,[t:1to(n1)]x),ts(p0,x),ts(prod(n,[t:1to(n)]x),x),t13,t14):is(prod(n1,[t:1to(n1)]x),ts(p0,x))
-t16:=tris(cx,p0(n1),prod(n1,[t:1to(n1)]x),ts(p0,x),t11(n1),t15):is(p0(n1),ts(p0(n),x))
-y@[n:nat]
-prop1:=is(p0(ts(x,y),n),ts(p0(x,n),p0(y,n))):'prop'
-y@t17:=ists12(p0(x,1),x,p0(y,1),y,t6(x),t6(y)):is(ts(p0(x,1),p0(y,1)),ts(x,y))
-t18:=tris2(cx,p0(ts(x,y),1),ts(p0(x,1),p0(y,1)),ts(x,y),t6(ts(x,y)),t17):prop1(1)
-n@[p:prop1(n)]
-t19:=ists1(p0(ts(x,y),n),ts(p0(x,n),p0(y,n)),ts(x,y),p):is(ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)))
-t20:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),x),ts(p0(x,n),ts(p0(y,n),x)),ts(p0(x,n),ts(x,p0(y,n))),ts(ts(p0(x,n),x),p0(y,n)),assts1(p0(x,n),p0(y,n),x),ists2(ts(p0(y,n),x),ts(x,p0(y,n)),p0(x,n),comts(p0(y,n),x)),assts2(p0(x,n),x,p0(y,n))):is(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)))
-t21:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(ts(p0(x,n),p0(y,n)),x),y),ts(ts(ts(p0(x,n),x),p0(y,n)),y),ts(ts(p0(x,n),x),ts(p0(y,n),y)),assts2(ts(p0(x,n),p0(y,n)),x,y),ists1(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)),y,t20),assts1(ts(p0(x,n),x),p0(y,n),y)):is(ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
-t22:=tr3is(cx,p0(ts(x,y),n1(n)),ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t16(ts(x,y),n),t19,t21):is(p0(ts(x,y),n1(n)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
-t23:=ists12(p0(x,n1(n)),ts(p0(x,n),x),p0(y,n1(n)),ts(p0(y,n),y),t16(x,n),t16(y,n)):is(ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
-t24:=tris2(cx,p0(ts(x,y),n1(n)),ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t22,t23):prop1(n1(n))
-t25:=isp(nat,[t:nat]prop1(t),n1(n),<n>suc,t24,satz4a(n)):prop1(<n>suc)
-n@t26:=induction([t:nat]prop1(t),t18,[t:nat][u:prop1(t)]t25(t,u),n):prop1
-o@prop2:=is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b))):'prop'
-[p:pos(m)]
-t28:=posintnatrl(m,p,mi):natrl(m)
-m0:=ntofrl(m,t28):nat
-t29:=isrlnt1(m,t28):is"r"(m,nr(m0))
-t30:=isrlnt2(m,t28):is"r"(nr(m0),m)
-t31:=ispw2(ts(x,y),m,nr(m0),t29,mi,t4(ts(x,y),m0),lemma292c,t5(ts(x,y),m0)):is(pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0))
-t32:=ists12(p0(x,m0),pw(x,m,mi,lemma292a),p0(y,m0),pw(y,m,mi,lemma292b),ispw2(x,nr(m0),m,t30,t4(x,m0),mi,t5(x,m0),lemma292a),ispw2(y,nr(m0),m,t30,t4(y,m0),mi,t5(y,m0),lemma292b)):is(ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
-t33:=tr3is(cx,pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0),ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),t31,t26(m0),t32):prop2
-o@[i:is"r"(m,0)]
-t34:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(1c,1c),1c,ists12(pw(x,m,mi,lemma292a),1c,pw(y,m,mi,lemma292b),1c,0exp(x,m,mi,lemma292a,i),0exp(y,m,mi,lemma292b,i)),satz222(1c)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c)
-t35:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c,0exp(ts(x,y),m,mi,lemma292c,i),t34):prop2
-o@[n:neg(m)]
-t36:=intabs(m,mi):intrl(abs(m))
-t37:=ori2(and(nis(x,0c),nis(y,0c)),pos(abs(m)),satz166b(m,n)):or(and(nis(x,0c),nis(y,0c)),pos(abs(m)))
-t38:=lemma292a(abs(m),t36,t37):or(nis(x,0c),pos(abs(m)))
-t39:=lemma292b(abs(m),t36,t37):or(nis(y,0c),pos(abs(m)))
-t40:=lemma292c(abs(m),t36,t37):or(nis(ts(x,y),0c),pos(abs(m)))
-t41:=lemmapw3(x,m,mi,lemma292a,n):or(nis(x,0c),pos(abs(m)))
-t42:=lemmapw3(y,m,mi,lemma292b,n):or(nis(y,0c),pos(abs(m)))
-t43:=lemmapw3(ts(x,y),m,mi,lemma292c,n):or(nis(ts(x,y),0c),pos(abs(m)))
-t44:=ispw2(ts(x,y),abs(m),abs(m),refis(real,abs(m)),t36,t36,t43,t40):is(pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40))
-t45:=t33(abs(m),t36,t37,satz166b(m,n)):is(pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)))
-t46:=ists12(pw(x,abs(m),t36,t38),pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t39),pw(y,abs(m),t36,t42),ispw2(x,abs(m),abs(m),refis(real,abs(m)),t36,t36,t38,t41),ispw2(y,abs(m),abs(m),refis(real,abs(m)),t36,t36,t39,t42)):is(ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
-t47:=tr3is(cx,pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t44,t45,t46):is(pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
-t48:=lemmapw1(x,abs(m),t36,t41,satz166b(m,n),lemmapw2(x,m,mi,lemma292a,n)):nis(pw(x,abs(m),t36,t41),0c)
-t49:=lemmapw1(y,abs(m),t36,t42,satz166b(m,n),lemmapw2(y,m,mi,lemma292b,n)):nis(pw(y,abs(m),t36,t42),0c)
-t50:=lemmapw1(ts(x,y),abs(m),t36,t43,satz166b(m,n),lemmapw2(ts(x,y),m,mi,lemma292c,n)):nis(pw(ts(x,y),abs(m),t36,t43),0c)
-t51:=satz221d(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42),t48,t49):nis(ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),0c)
-t52:=negexp(ts(x,y),m,mi,lemma292c,n):is(pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50))
-t53:=isov12(1c,ts(1c,1c),pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),satz222a(1c),t47,t50,t51):is(ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t54:=tris(cx,pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t52,t53):is(pw(ts(x,y),m,mi,lemma292c),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t55:=ists12(pw(x,m,mi,lemma292a),ov(1c,pw(x,abs(m),t36,t41),t48),pw(y,m,mi,lemma292b),ov(1c,pw(y,abs(m),t36,t42),t49),negexp(x,m,mi,lemma292a,n),negexp(y,m,mi,lemma292b,n)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)))
-t56:=satz247(1c,pw(x,abs(m),t36,t41),1c,pw(y,abs(m),t36,t42),t48,t49):is(ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t57:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t55,t56):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t58:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t54,t57):prop2
--9292
-o@satz292:=rapp(m,prop2".9292",[t:pos(m)]t33".9292"(t),[t:is"r"(m,0)]t35".9292"(t),[t:neg(m)]t58".9292"(t)):is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
-@[m:real]
-lemma293:=ori1(nis(1c,0c),pos(m),1not0):or(nis(1c,0c),pos(m))
-[mi:intrl(m)]
-+9293
-t1:=ori1(and(nis(1c,0c),nis(1c,0c)),pos(m),andi(nis(1c,0c),nis(1c,0c),1not0,1not0)):or(and(nis(1c,0c),nis(1c,0c)),pos(m))
-1m:=pw(1c,m,mi,lemma293):cx
-t2:=satz222(1m):is(ts(1m,1c),1m)
-t3:=ispw1(1c,ts(1c,1c),m,satz222a(1c),mi,lemma293,lemma292c(1c,1c,m,mi,t1)):is(1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)))
-t4:=satz292(1c,1c,m,mi,t1):is(pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))))
-t5:=ists12(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),1m,pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1)),1m,ispw1(1c,1c,m,refis(cx,1c),mi,lemma292a(1c,1c,m,mi,t1),lemma293),ispw1(1c,1c,m,refis(cx,1c),mi,lemma292b(1c,1c,m,mi,t1),lemma293)):is(ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m))
-t6:=tr4is(cx,ts(1m,1c),1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m),t2,t3,t4,t5):is(ts(1m,1c),ts(1m,1m))
-t7:=tris(cx,ts(1m,mn(1m,1c)),mn(ts(1m,1m),ts(1m,1c)),0c,disttm2(1m,1m,1c),satz213b(ts(1m,1m),ts(1m,1c),symis(cx,ts(1m,1c),ts(1m,1m),t6))):is(ts(1m,mn(1m,1c)),0c)
-t8:=ore2(is(1m,0c),is(mn(1m,1c),0c),satz221c(1m,mn(1m,1c),t7),satz290(1c,m,mi,lemma293,1not0)):is(mn(1m,1c),0c)
--9293
-satz293:=satz213a(1m".9293",1c,t8".9293"):is(pw(1c,m,mi,lemma293),1c)
-x@[m:real][n:real][mi:intrl(m)][ni:intrl(n)][o:or(nis(x,0c),and(pos(m),pos(n)))]
-+9294
-[a:and(pos(m),pos(n))]
-t1:=ande1(pos(m),pos(n),a):pos(m)
-t2:=ande2(pos(m),pos(n),a):pos(n)
-t3:=pospl(m,n,t1,t2):pos(pl"r"(m,n))
--9294
-lemma294a:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(m),o,[t:and(pos(m),pos(n))]t1".9294"(t)):or(nis(x,0c),pos(m))
-lemma294b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(n),o,[t:and(pos(m),pos(n))]t2".9294"(t)):or(nis(x,0c),pos(n))
-lemma294c:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(pl"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9294"(t)):or(nis(x,0c),pos(pl"r"(m,n)))
-+*9294
-o@prop1:=is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c)):'prop'
-a@m1:=ntofrl(m,posintnatrl(m,t1,mi)):nat
-n1:=ntofrl(n,posintnatrl(n,t2,ni)):nat
-t4:=ists12(pw(x,m,mi,lemma294a),prod(m1,[t:1to(m1)]x),pw(x,n,ni,lemma294b),prod(n1,[t:1to(n1)]x),posexp(x,m,mi,lemma294a,t1),posexp(x,n,ni,lemma294b,t2)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
-p1:=ntofrl(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni))):nat
-t5:=posexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t3):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(p1,[t:1to(p1)]x))
-t6:=tris(real,pl"r"(m,n),pl"r"(rlofnt(m1),rlofnt(n1)),rlofnt(pl"n"(m1,n1)),ispl12"r"(m,rlofnt(m1),n,rlofnt(n1),isrlnt1(m,posintnatrl(m,t1,mi)),isrlnt1(n,posintnatrl(n,t2,ni))),satzr155b(m1,n1)):is"r"(pl"r"(m,n),rlofnt(pl"n"(m1,n1)))
-t7:=tris2(nat,pl"n"(m1,n1),p1,ntofrl(rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1))),isntrl1(pl"n"(m1,n1)),isrlent(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni)),rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1)),t6)):is"n"(pl"n"(m1,n1),p1)
-t8:=lessisi2"n"(pl"n"(m1,n1),p1,t7):lessis"n"(pl"n"(m1,n1),p1)
-t9:=issmpr([t:cx][u:cx]ts(t,u),p1,[t:1to(p1)]x,pl"n"(m1,n1),t7):is(prod(pl"n"(m1,n1),left(cx,p1,pl"n"(m1,n1),t8,[t:1to(p1)]x)),prod(p1,[t:1to(p1)]x))
-t10:=tris2(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),prod(p1,[t:1to(p1)]x),t5,t9):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x))
-t11:=lessisi1"n"(m1,pl"n"(m1,n1),satz18a(m1,n1)):lessis"n"(m1,pl"n"(m1,n1))
-t12:=satz281([t:cx][u:cx]ts(t,u),assocts,m1,n1,[t:1to(pl"n"(m1,n1))]x):is(prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,left(cx,pl"n"(m1,n1),m1,t11,[t:1to(pl"n"(m1,n1))]x)),prod(n1,right(cx,m1,n1,[t:1to(pl"n"(m1,n1))]x))))
-t13:=tris(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t10,t12):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
-t14:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t4,t13):prop1
-o@[na:not(and(pos(m),pos(n)))]
-t15:=ore1(nis(x,0c),and(pos(m),pos(n)),o,na):nis(x,0c)
-t16:=th15"l.or"(pos(m),pos(n),na):or(not(pos(m)),not(pos(n)))
-o@am:=abs(m):real
-an:=abs(n):real
-ap:=abs(pl"r"(m,n)):real
-t17:=intabs(m,mi):intrl(am)
-t18:=intabs(n,ni):intrl(an)
-t19:=intabs(pl"r"(m,n),intpl(m,mi,n,ni)):intrl(ap)
-na@[nm:neg(m)][nn:neg(n)]
-t20:=andi(pos(am),pos(an),satz166e(m,nnot0(m,nm)),satz166e(n,nnot0(n,nn))):and(pos(am),pos(an))
-t21:=ori2(nis(x,0c),and(pos(am),pos(an)),t20):or(nis(x,0c),and(pos(am),pos(an)))
-t22:=lemmapw3(x,m,mi,lemma294a,nm):or(nis(x,0c),pos(am))
-t23:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
-t24:=lemma294a(x,am,an,t17,t18,t21):or(nis(x,0c),pos(am))
-t25:=lemma294b(x,am,an,t17,t18,t21):or(nis(x,0c),pos(an))
-t26:=ists12(pw(x,am,t17,t22),pw(x,am,t17,t24),pw(x,an,t18,t23),pw(x,an,t18,t25),ispw1(x,x,am,refis(cx,x),t17,t22,t24),ispw1(x,x,an,refis(cx,x),t18,t23,t25)):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)))
-t27:=lemma294c(x,am,an,t17,t18,t21):or(nis(x,0c),pos(pl"r"(am,an)))
-t28:=t14(x,am,an,t17,t18,t21,t20):is(ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27))
-t29:=tr3is(real,pl"r"(am,an),pl"r"(m0"r"(m),m0"r"(n)),m0"r"(pl"r"(m,n)),ap,ispl12"r"(am,m0"r"(m),an,m0"r"(n),absn(m,nm),absn(n,nn)),satz180a(m,n),symis(real,ap,m0"r"(pl"r"(m,n)),absn(pl"r"(m,n),negpl(m,n,nm,nn)))):is"r"(pl"r"(am,an),ap)
-t30:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn)):or(nis(x,0c),pos(ap))
-t31:=ispw2(x,pl"r"(am,an),ap,t29,intpl(am,t17,an,t18),t19,t27,t30):is(pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30))
-t32:=tr3is(cx,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30),t26,t28,t31):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30))
-t33:=lemmapw1(x,am,t17,t22,satz166b(m,nm),lemmapw2(x,m,mi,lemma294a,nm)):nis(pw(x,am,t17,t22),0c)
-t34:=lemmapw1(x,an,t18,t23,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t23),0c)
-t35:=lemmapw1(x,ap,t19,t30,satz166b(pl"r"(m,n),negpl(m,n,nm,nn)),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):nis(pw(x,ap,t19,t30),0c)
-t36:=ists12(pw(x,m,mi,lemma294a),ov(1c,pw(x,am,t17,t22),t33),pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t23),t34),negexp(x,m,mi,lemma294a,nm),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)))
-t37:=satz221d(pw(x,am,t17,t22),pw(x,an,t18,t23),t33,t34):nis(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),0c)
-t38:=satz247(1c,pw(x,am,t17,t22),1c,pw(x,an,t18,t23),t33,t34):is(ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37))
-t39:=isov12(ts(1c,1c),1c,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30),satz222(1c),t32,t37,t35):is(ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35))
-t40:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t30),t35),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):is(ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t41:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t36,t38,t39,t40):prop1
-na@[pm:pos(m)][nn:neg(n)]
-t42:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
-t43:=lemmapw1(x,an,t18,t42,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t42),0c)
-t44:=ists2(pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t42),t43),pw(x,m,mi,lemma294a),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)))
-t45:=satz244a(pw(x,m,mi,lemma294a),1c,pw(x,an,t18,t42),t43):is(ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43))
-t46:=isov1(ts(pw(x,m,mi,lemma294a),1c),pw(x,m,mi,lemma294a),pw(x,an,t18,t42),satz222(pw(x,m,mi,lemma294a)),t43):is(ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-t47:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t44,t45,t46):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-[casea:more(m,an)]
-t48:=satz182d(m,an,casea):pos(mn"r"(m,an))
-t49:=satz166e(n,nnot0(n,nn)):pos(an)
-t50:=andi(pos(an),pos(mn"r"(m,an)),t49,t48):and(pos(an),pos(mn"r"(m,an)))
-t51:=ori2(nis(x,0c),and(pos(an),pos(mn"r"(m,an))),t50):or(nis(x,0c),and(pos(an),pos(mn"r"(m,an))))
-t52:=intmn(m,mi,an,t18):intrl(mn"r"(m,an))
-t53:=lemma294a(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(an))
-t54:=lemma294b(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(mn"r"(m,an)))
-t55:=lemma294c(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(pl"r"(an,mn"r"(m,an))))
-t56:=intpl(an,t18,mn"r"(m,an),t52):intrl(pl"r"(an,mn"r"(m,an)))
-t57:=t14(x,an,mn"r"(m,an),t18,t52,t51,t50):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55))
-t58:=satz187a(m,an):is"r"(pl"r"(an,mn"r"(m,an)),m)
-t59:=ispw2(x,pl"r"(an,mn"r"(m,an)),m,t58,t56,mi,t55,lemma294a):is(pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a))
-t60:=tris(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a),t57,t59):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a))
-t61:=ispw1(x,x,an,refis(cx,x),t18,t53,t42):is(pw(x,an,t18,t53),pw(x,an,t18,t42))
-t62:=isp1(cx,[t:cx]nis(t,0c),pw(x,an,t18,t42),pw(x,an,t18,t53),t43,t61):nis(pw(x,an,t18,t53),0c)
-t63:=isov12(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a),pw(x,an,t18,t53),pw(x,an,t18,t42),t60,t61,t62,t43):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-t64:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t63):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62))
-t65:=satz229h(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54),t62,refis(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)))):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54))
-t66:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
-t67:=ispw2(x,mn"r"(m,an),pl"r"(m,n),t66,t52,intpl(m,mi,n,ni),t54,lemma294c):is(pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t68:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t64,t65,t67):prop1
-nn@[caseb:is"r"(m,an)]
-t69:=ispw2(x,m,an,caseb,mi,t18,lemma294a,t42):is(pw(x,m,mi,lemma294a),pw(x,an,t18,t42))
-t70:=satz251a(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43,t69):is(ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c)
-t71:=tr3is(real,pl"r"(m,n),mn"r"(m,m0"r"(n)),mn"r"(m,an),0,ispl2"r"(n,m0"r"(m0"r"(n)),m,satz177a(n)),ismn2"r"(m0"r"(n),an,m,symis(real,an,m0"r"(n),absn(n,nn))),satz182e(m,an,caseb)):is"r"(pl"r"(m,n),0)
-t72:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),1c,0exp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t71)):is(1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t73:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t47,t70,t72):prop1
-nn@[casec:less(m,an)]
-t74:=satz182d(an,m,lemma2"r"(m,an,casec)):pos(mn"r"(an,m))
-t75:=andi(pos(m),pos(mn"r"(an,m)),pm,t74):and(pos(m),pos(mn"r"(an,m)))
-t76:=ori2(nis(x,0c),and(pos(m),pos(mn"r"(an,m))),t75):or(nis(x,0c),and(pos(m),pos(mn"r"(an,m))))
-t77:=intmn(an,t18,m,mi):intrl(mn"r"(an,m))
-t78:=lemma294a(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(m))
-t79:=lemma294b(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(mn"r"(an,m)))
-t80:=lemma294c(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(pl"r"(m,mn"r"(an,m))))
-t81:=intpl(m,mi,mn"r"(an,m),t77):intrl(pl"r"(m,mn"r"(an,m)))
-t81a:=t14(x,m,mn"r"(an,m),mi,t77,t76,t75):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80))
-t82:=satz187a(an,m):is"r"(pl"r"(m,mn"r"(an,m)),an)
-t83:=ispw2(x,pl"r"(m,mn"r"(an,m)),an,t82,t81,t18,t80,t42):is(pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42))
-t84:=tris(cx,ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42),t81a,t83):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42))
-t85:=satz290(x,m,mi,t78,t15):nis(pw(x,m,mi,t78),0c)
-t86:=satz290(x,mn"r"(an,m),t77,t79,t15):nis(pw(x,mn"r"(an,m),t77,t79),0c)
-t87:=satz221d(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79),t85,t86):nis(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),0c)
-t88:=satz222(pw(x,m,mi,t78)):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78))
-t89:=ispw1(x,x,m,refis(cx,x),mi,t78,lemma294a):is(pw(x,m,mi,t78),pw(x,m,mi,lemma294a))
-t90:=tris(cx,ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78),pw(x,m,mi,lemma294a),t88,t89):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a))
-t91:=isov12(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42),t90,t84,t87,t43):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-t92:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t91):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87))
-t93:=satz246a(1c,pw(x,mn"r"(an,m),t77,t79),pw(x,m,mi,t78),t86,t85):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86))
-t94:=satz182f(m,an,casec):neg(mn"r"(m,an))
-t94a:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
-t95:=tr3is(real,mn"r"(an,m),m0"r"(mn"r"(m,an)),abs(mn"r"(m,an)),ap,satz181a(an,m),symis(real,abs(mn"r"(m,an)),m0"r"(mn"r"(m,an)),absn(mn"r"(m,an),t94)),isabs(mn"r"(m,an),pl"r"(m,n),t94a)):is"r"(mn"r"(an,m),ap)
-t96:=isp(real,[t:real]neg(t),mn"r"(m,an),pl"r"(m,n),t94,t94a):neg(pl"r"(m,n))
-t97:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96):or(nis(x,0c),pos(ap))
-t98:=lemmapw1(x,ap,t19,t97,satz166b(pl"r"(m,n),t96),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):nis(pw(x,ap,t19,t97),0c)
-t99:=ispw2(x,mn"r"(an,m),ap,t95,t77,t19,t79,t97):is(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97))
-t100:=isov2(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97),1c,t99,t86,t98):is(ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98))
-t101:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t97),t98),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):is(ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t102:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t92,t93,t100,t101):prop1
-nn@t103:=or3app(is"r"(m,an),more(m,an),less(m,an),prop1,satz167a(m,an),[t:is"r"(m,an)]t73(t),[t:more(m,an)]t68(t),[t:less(m,an)]t102(t)):prop1
-na@[nm:neg(m)][qn:pos(n)]
-na@t104:=ori1(nis(x,0c),and(pos(n),pos(m)),t15):or(nis(x,0c),and(pos(n),pos(m)))
-t104a:=th5"l.and"(pos(m),pos(n),na):not(and(pos(n),pos(m)))
-t105:=lemma294a(x,n,m,ni,mi,t104):or(nis(x,0c),pos(n))
-t106:=lemma294b(x,n,m,ni,mi,t104):or(nis(x,0c),pos(m))
-t107:=lemma294c(x,n,m,ni,mi,t104):or(nis(x,0c),pos(pl"r"(n,m)))
-t108:=ists12(pw(x,m,mi,lemma294a),pw(x,m,mi,t106),pw(x,n,ni,lemma294b),pw(x,n,ni,t105),ispw1(x,x,m,refis(cx,x),mi,lemma294a,t106),ispw1(x,x,n,refis(cx,x),ni,lemma294b,t105)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)))
-t109:=comts(pw(x,m,mi,t106),pw(x,n,ni,t105)):is(ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)))
-qn@t110:=t103(x,n,m,ni,mi,t104,t104a,qn,nm):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
-na@t111:=ispw2(x,pl"r"(n,m),pl"r"(m,n),compl"r"(n,m),intpl(n,ni,m,mi),intpl(m,mi,n,ni),t107,lemma294c):is(pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-qn@t112:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t110,t111):prop1
-na@[i:is"r"(m,0)]
-t113:=ists1(pw(x,m,mi,lemma294a),1c,pw(x,n,ni,lemma294b),0exp(x,m,mi,lemma294a,i)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)))
-t114:=satz222b(pw(x,n,ni,lemma294b)):is(ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b))
-t115:=symis(real,pl"r"(m,n),n,pl01"r"(m,n,i)):is"r"(n,pl"r"(m,n))
-t116:=ispw2(x,n,pl"r"(m,n),t115,ni,intpl(m,mi,n,ni),lemma294b,lemma294c):is(pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t117:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t113,t114,t116):prop1
-na@[i:is"r"(n,0)]
-t118:=t117(x,n,m,ni,mi,t104,t104a,i):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
-t119:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t118,t111):prop1
-na@[pm:pos(m)]
-t120:=ore2(not(pos(m)),not(pos(n)),t16,weli(pos(m),pm)):not(pos(n))
-t121:=rapp(n,prop1,th2"l.imp"(pos(n),prop1,t120),[t:is"r"(n,0)]t119(t),[t:neg(n)]t103(pm,t)):prop1
-na@[nm:neg(m)]
-t122:=rapp(n,prop1,[t:pos(n)]t112(nm,t),[t:is"r"(n,0)]t119(t),[t:neg(n)]t41(nm,t)):prop1
-na@t123:=rapp(m,prop1,[t:pos(m)]t121(t),[t:is"r"(m,0)]t117(t),[t:neg(m)]t122(t)):prop1
--9294
-o@satz294:=th1"l.imp"(and(pos(m),pos(n)),prop1".9294",[t:and(pos(m),pos(n))]t14".9294"(t),[t:not(and(pos(m),pos(n)))]t123".9294"(t)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-ni@[o:nis(x,0c)]
-lemma295a:=ori1(nis(x,0c),pos(m),o):or(nis(x,0c),pos(m))
-lemma295b:=ori1(nis(x,0c),pos(n),o):or(nis(x,0c),pos(n))
-lemma295c:=ori1(nis(x,0c),pos(mn"r"(m,n)),o):or(nis(x,0c),pos(mn"r"(m,n)))
-+9295
-t1:=ori1(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)),o):or(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)))
-t2:=intmn(m,mi,n,ni):intrl(mn"r"(m,n))
-t3:=lemma294a(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(mn"r"(m,n)))
-t4:=lemma294b(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(n))
-t5:=lemma294c(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(pl"r"(mn"r"(m,n),n)))
-t6:=ists12(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,lemma295b),pw(x,n,ni,t4),ispw1(x,x,mn"r"(m,n),refis(cx,x),t2,lemma295c,t3),ispw1(x,x,n,refis(cx,x),ni,lemma295b,t4)):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)))
-t7:=satz294(x,mn"r"(m,n),n,t2,ni,t1):is(ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5))
-t8:=plmn(m,n):is"r"(pl"r"(mn"r"(m,n),n),m)
-t9:=ispw2(x,pl"r"(mn"r"(m,n),n),m,t8,intpl(mn"r"(m,n),t2,n,ni),mi,t5,lemma295a):is(pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a))
-t10:=tr3is(cx,ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a),t6,t7,t9):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),pw(x,m,mi,lemma295a))
-t11:=satz290(x,n,ni,lemma295b,o):nis(pw(x,n,ni,lemma295b),0c)
--9295
-satz295:=satz229k(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),pw(x,mn"r"(m,n),t2".9295",lemma295c),t11".9295",t10".9295"):is(ov(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),satz290(x,n,ni,lemma295b,o)),pw(x,mn"r"(m,n),intmn(m,mi,n,ni),lemma295c))
-m@[mi:intrl(m)][n:nis(x,0c)]
-lemma296:=ori1(nis(x,0c),pos(m),n):or(nis(x,0c),pos(m))
-+9296
-t1:=intrli0(0,refis(real,0)):intrl(0)
-t2:=lemma295a(x,0,m,t1,mi,n):or(nis(x,0c),pos(0))
-t3:=lemma295b(x,0,m,t1,mi,n):or(nis(x,0c),pos(m))
-t4:=lemma295c(x,0,m,t1,mi,n):or(nis(x,0c),pos(mn"r"(0,m)))
-t5:=satz290(x,m,mi,lemma296,n):nis(pw(x,m,mi,lemma296),0c)
-t6:=satz290(x,m,mi,t3,n):nis(pw(x,m,mi,t3),0c)
-t7:=symis(cx,pw(x,0,t1,t2),1c,0exp(x,0,t1,t2,refis(real,0))):is(1c,pw(x,0,t1,t2))
-t8:=ispw1(x,x,m,refis(cx,x),mi,lemma296,t3):is(pw(x,m,mi,lemma296),pw(x,m,mi,t3))
-t9:=isov12(1c,pw(x,0,t1,t2),pw(x,m,mi,lemma296),pw(x,m,mi,t3),t7,t8,t5,t6):is(ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6))
-t10:=satz295(x,0,m,t1,mi,n):is(ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4))
-t11:=pl01(0,m0"r"(m),refis(real,0)):is"r"(mn"r"(0,m),m0"r"(m))
-t12:=lemma296(x,m0"r"(m),intm0(m,mi),n):or(nis(x,0c),pos(m0"r"(m)))
-t13:=ispw2(x,mn"r"(0,m),m0"r"(m),t11,intmn(0,t1,m,mi),intm0(m,mi),t4,t12):is(pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12))
-t14:=tr3is(cx,ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12),t9,t10,t13):is(ov(1c,pw(x,m,mi,lemma296),t5),pw(x,m0"r"(m),intm0(m,mi),t12))
--9296
-satz296:=t14".9296":is(ov(1c,pw(x,m,mi,lemma296),satz290(x,m,mi,lemma296,n)),pw(x,m0"r"(m),intm0(m,mi),lemma296(m0"r"(m),intm0(m,mi),n)))
-ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
-+9297
-[p:nis(x,0c)]
-t1:=satz290(x,m,mi,lemma294a(o),p):nis(pw(x,m,mi,lemma294a(o)),0c)
-o@[a:and(pos(m),pos(n))]
-t2:=ande2(pos(m),pos(n),a):pos(n)
-t3:=postspp(m,n,ande1(pos(m),pos(n),a),t2):pos(ts"r"(m,n))
--9297
-lemma297a:=th9"l.or"(nis(x,0c),and(pos(m),pos(n)),nis(pw(x,m,mi,lemma294a(o)),0c),pos(n),o,[t:nis(x,0c)]t1".9297"(t),[t:and(pos(m),pos(n))]t2".9297"(t)):or(nis(pw(x,m,mi,lemma294a(o)),0c),pos(n))
-lemma297b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(ts"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9297"(t)):or(nis(x,0c),pos(ts"r"(m,n)))
-mi@[o:or(nis(x,0c),pos(m))][i:is(x,0c)]
-+*9297
-i@t4:=ore2(nis(x,0c),pos(m),o,weli(is(x,0c),i)):pos(m)
-m1:=ntofrl(m,posintnatrl(m,t4,mi)):nat
-t5:=posexp(x,m,mi,o,t4):is(pw(x,m,mi,o),prod(m1,[t:1to(m1)]x))
-t6:=satz289b(m1,[t:1to(m1)]x,xout(m1),i):is(prod(m1,[t:1to(m1)]x),0c)
-t7:=tris(cx,pw(x,m,mi,o),prod(m1,[t:1to(m1)]x),0c,t5,t6):is(pw(x,m,mi,o),0c)
--9297
-i@pw0:=t7".9297":is(pw(x,m,mi,o),0c)
-ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
-+*9297
-ni@t8:=intts(m,mi,n,ni):intrl(ts"r"(m,n))
-o@prop1:=is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o))):'prop'
-[i:is(x,0c)]
-t9:=pw0(x,m,mi,lemma294a(o),i):is(pw(x,m,mi,lemma294a(o)),0c)
-t10:=pw0(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o),t9):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),0c)
-t11:=pw0(x,ts"r"(m,n),t8,lemma297b(o),i):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),0c)
-t12:=tris2(cx,pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),0c,t10,t11):prop1
-m@[mi:intrl(m)][p:nis(x,0c)]
-t13:=ori1(nis(x,0c),pos(m),p):or(nis(x,0c),pos(m))
-p0:=pw(x,m,mi,t13):cx
-[n:nat]
-nr:=rlofnt(n):real
-t14:=natintrl(nr,natrli(n)):intrl(nr)
-t15:=ori2(nis(p0,0c),pos(nr),natpos(nr,natrli(n))):or(nis(p0,0c),pos(nr))
-t16:=ori1(nis(x,0c),pos(ts"r"(m,nr)),p):or(nis(x,0c),pos(ts"r"(m,nr)))
-t17:=intts(m,mi,nr,t14):intrl(ts"r"(m,nr))
-prop2:=is(pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16)):'prop'
-p@t18:=ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t15(1),lemma291(p0)):is(pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)))
-t19:=satz291(p0):is(pw(p0,1rl,intrl1,lemma291(p0)),p0)
-t20:=ispw2(x,m,ts"r"(m,1rl),satz195a(m),mi,t17(1),t13,t16(1)):is(p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)))
-t21:=tr3is(cx,pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)),t18,t19,t20):prop2(1)
-n@[p2:prop2(n)]
-n1:=pl"n"(n,1):nat
-t22:=satz290(x,m,mi,t13,p):nis(p0,0c)
-t23:=ori1(nis(p0,0c),and(pos(nr),pos(1rl)),t22):or(nis(p0,0c),and(pos(nr),pos(1rl)))
-t24:=lemma294a(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(nr))
-t25:=lemma294b(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(1rl))
-t26:=lemma294c(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(pl"r"(nr,1rl)))
-t27:=ispw2(p0,nr(n1),pl"r"(nr,1rl),satzr155a(n,1),t14(n1),intpl(nr,t14,1rl,intrl1),t15(n1),t26):is(pw(p0,nr(n1),t14(n1),t15(n1)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
-t27a:=satz294(p0,nr,1rl,t14,intrl1,t23):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
-t28:=tris2(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26),t27,t27a):is(pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)))
-t29:=ori1(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)),p):or(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)))
-t30:=lemma294a(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(ts"r"(m,nr)))
-t31:=lemma294b(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(m))
-t32:=lemma294c(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(pl"r"(ts"r"(m,nr),m)))
-t33:=tr3is(cx,pw(p0,nr,t14,t24),pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16),pw(x,ts"r"(m,nr),t17,t30),ispw1(p0,p0,nr,refis(cx,p0),t14,t24,t15),p2,ispw1(x,x,ts"r"(m,nr),refis(cx,x),t17,t16,t30)):is(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30))
-t34:=tr3is(cx,pw(p0,1rl,intrl1,t25),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,m,mi,t31),ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t25,lemma291(p0)),t19,ispw1(x,x,m,refis(cx,x),mi,t13,t31)):is(pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31))
-t35:=ists12(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30),pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31),t33,t34):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)))
-t36:=satz294(x,ts"r"(m,nr),m,t17,mi,t29):is(ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32))
-t37:=tr3is(real,pl"r"(ts"r"(m,nr),m),pl"r"(ts"r"(m,nr),ts"r"(m,1rl)),ts"r"(m,pl"r"(nr,1rl)),ts"r"(m,nr(n1)),ispl2"r"(m,ts"r"(m,1rl),ts"r"(m,nr),satz195a(m)),distpt2"r"(m,nr,1rl),ists2"r"(pl"r"(nr,1rl),nr(n1),m,satzr155b(n,1))):is"r"(pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)))
-t38:=ispw2(x,pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)),t37,intpl(ts"r"(m,nr),t17,m,mi),t17(n1),t32,t16(n1)):is(pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)))
-t39:=tr4is(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)),t28,t35,t36,t38):prop2(n1)
-t40:=isp(nat,[t:nat]prop2(t),n1,<n>suc,t39,satz4a(n)):prop2(<n>suc)
-n@t41:=induction([t:nat]prop2(t),t21,[t:nat][u:prop2(t)]t40(t,u),n):prop2(n)
-o@[p:nis(x,0c)][q:pos(n)]
-t42:=posintnatrl(n,q,ni):natrl(n)
-n0:=ntofrl(n,t42):nat
-t43:=isrlnt1(n,t42):is"r"(n,rlofnt(n0))
-t44:=isrlnt2(n,t42):is"r"(rlofnt(n0),n)
-o@p1:=pw(x,m,mi,lemma294a(o)):cx
-q@t44a:=ispw2(x,m,m,refis(real,m),mi,mi,lemma294a(o),t13(mi,p)):is(p1,p0(mi,p))
-t45:=ispw12(p1,p0(mi,p),n,rlofnt(n0),t44a,t43,ni,t14(mi,p,n0),lemma297a(o),t15(mi,p,n0)):is(pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)))
-t46:=t41(mi,p,n0):is(pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)))
-t47:=ists2"r"(rlofnt(n0),n,m,t44):is"r"(ts"r"(m,rlofnt(n0)),ts"r"(m,n))
-t48:=ispw2(x,ts"r"(m,rlofnt(n0)),ts"r"(m,n),t47,t17(mi,p,n0),t8,t16(mi,p,n0),lemma297b(o)):is(pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)))
-t49:=tr3is(cx,pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)),t45,t46,t48):prop1
-p@[i:is"r"(n,0)]
-t50:=0exp(p1,n,ni,lemma297a(o),i):is(pw(p1,n,ni,lemma297a(o)),1c)
-t51:=ts02"r"(m,n,i):is"r"(ts"r"(m,n),0)
-t52:=0exp(x,ts"r"(m,n),t8,lemma297b(o),t51):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),1c)
-t53:=tris2(cx,pw(p1,n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),1c,t50,t52):prop1
-p@[q:neg(n)]
-an:=abs(n):real
-t54:=intabs(n,ni):intrl(an)
-t55:=ori1(nis(x,0c),and(pos(m),pos(an)),p):or(nis(x,0c),and(pos(m),pos(an)))
-p1t55:=p1(an,mi,t54,t55):cx
-t56:=satz166e(n,nnot0(n,q)):pos(an)
-t56a:=lemma294a(an,mi,t54,t55):or(nis(x,0c),pos(m))
-t57:=lemma297a(an,mi,t54,t55):or(nis(p1t55,0c),pos(an))
-t58:=lemma297b(an,mi,t54,t55):or(nis(x,0c),pos(ts"r"(m,an)))
-t59:=t49(an,mi,t54,t55,p,t56):is(pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58))
-t60:=satz177c(an,n,absn(n,q)):is"r"(n,m0"r"(an))
-t61:=intm0(an,t54):intrl(m0"r"(an))
-t62:=satz290(x,m,mi,t56a,p):nis(p1t55,0c)
-t63:=lemma296(p1t55,an,t54,t62):or(nis(p1t55,0c),pos(an))
-t64:=satz290(p1t55,an,t54,t63,t62):nis(pw(p1t55,an,t54,t63),0c)
-t65:=lemma296(p1t55,m0"r"(an),t61,t62):or(nis(p1t55,0c),pos(m0"r"(an)))
-t66:=satz296(p1t55,an,t54,t62):is(ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65))
-t67:=ispw1(x,x,m,refis(cx,x),mi,lemma294a(o),t56a):is(p1,p1t55)
-t68:=ispw12(p1,p1t55,n,m0"r"(an),t67,t60,ni,t61,lemma297a(o),t65):is(pw(p1,n,ni,lemma297a(o)),pw(p1t55,m0"r"(an),t61,t65))
-t69:=tris2(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65),t68,t66):is(pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64))
-t70:=tris(real,m0"r"(ts"r"(m,an)),ts"r"(m,m0"r"(an)),ts"r"(m,n),satz197f(m,an),ists2"r"(m0"r"(an),n,m,symis(real,n,m0"r"(an),t60))):is"r"(m0"r"(ts"r"(m,an)),ts"r"(m,n))
-t71:=intm0(ts"r"(m,an),t8(an,mi,t54)):intrl(m0"r"(ts"r"(m,an)))
-t72:=lemma296(x,ts"r"(m,an),t8(an,mi,t54),p):or(nis(x,0c),pos(ts"r"(m,an)))
-t73:=satz290(x,ts"r"(m,an),t8(an,mi,t54),t72,p):nis(pw(x,ts"r"(m,an),t8(an,mi,t54),t72),0c)
-t74:=lemma296(x,m0"r"(ts"r"(m,an)),t71,p):or(nis(x,0c),pos(m0"r"(ts"r"(m,an))))
-t75:=satz296(x,ts"r"(m,an),t8(an,mi,t54),p):is(ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74))
-t76:=ispw2(x,m0"r"(ts"r"(m,an)),ts"r"(m,n),t70,t71,t8,t74,lemma297b(o)):is(pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)))
-t77:=ispw1(p1t55,p1t55,an,refis(cx,p1t55),t54,t63,t57):is(pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57))
-t78:=ispw1(x,x,ts"r"(m,an),refis(cx,x),t8(an,mi,t54),t58,t72):is(pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
-t79:=tr3is(cx,pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t77,t59,t78):is(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
-t80:=isov2(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),1c,t79,t64,t73):is(ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73))
-t81:=tr4is(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)),t69,t80,t75,t76):prop1
-p@t82:=rapp(n,prop1,[t:pos(n)]t49(t),[t:is"r"(n,0)]t53(t),[t:neg(n)]t81(t)):prop1
--9297
-o@satz297:=th1"l.imp"(is(x,0c),prop1".9297",[t:is(x,0c)]t12".9297"(t),[t:nis(x,0c)]t82".9297"(t)):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),intts(m,mi,n,ni),lemma297b(o)))
-@[r:real][s:real]
-+10298
-t1:=tris(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),pl"r"(0,0)),pli(pl"r"(r,s),0),plis12a(r,0,s,0),isrecx2(pl"r"(0,0),0,pl"r"(r,s),pl01(0,0,refis(real,0)))):is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
--10298
-satz298a:=symis(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0),t1".10298"):is(pli(pl"r"(r,s),0),pl(pli(r,0),pli(s,0)))
-satz298b:=t1".10298":is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
-+*10298
-s@t2:=tris(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),mn"r"(0,0)),pli(mn"r"(r,s),0),mnis12a(r,0,s,0),isrecx2(mn"r"(0,0),0,mn"r"(r,s),pl02(0,m0"r"(0),satz176b(0,refis(real,0))))):is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
--10298
-s@satz298c:=symis(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0),t2".10298"):is(pli(mn"r"(r,s),0),mn(pli(r,0),pli(s,0)))
-satz298d:=t2".10298":is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
-+*10298
-s@t3:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
-t4:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
-t5:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t3,t4)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
--10298
-s@satz298e:=symis(cx,ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0),t5".10298"):is(pli(ts"r"(r,s),0),ts(pli(r,0),pli(s,0)))
-satz298f:=t5".10298":is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
-[n:nis"r"(s,0)]
-+*10298
-n@[i:is(pli(s,0),0c)]
-t6:=tr3is(real,s,re(pli(s,0)),re(0c),0,isre(s,0),iscere(pli(s,0),0c,i),reis(0,0)):is"r"(s,0)
--10298
-n@lemma298:=th3"l.imp"(is(pli(s,0),0c),is"r"(s,0),n,[t:is(pli(s,0),0c)]t6".10298"(t)):nis(pli(s,0),0c)
-+*10298
-n@t7:=tris(cx,ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(ts"r"(s,ov"r"(r,s,n)),0),pli(r,0),t5(s,ov"r"(r,s,n)),isrecx1(ts"r"(s,ov"r"(r,s,n)),r,0,satz204c(r,s,n))):is(ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(r,0))
--10298
-n@satz298g:=satz229g(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(pli(ov"r"(r,s,n),0),ov(pli(r,0),pli(s,0),lemma298))
-satz298h:=satz229h(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(ov(pli(r,0),pli(s,0),lemma298),pli(ov"r"(r,s,n),0))
-+*10298
-r@t8:=tris(cx,m0(pli(r,0)),pli(m0"r"(r),m0"r"(0)),pli(m0"r"(r),0),m0isa(r,0),isrecx2(m0"r"(0),0,m0"r"(r),satz176b(0,refis(real,0)))):is(m0(pli(r,0)),pli(m0"r"(r),0))
--10298
-r@satz298j:=symis(cx,m0(pli(r,0)),pli(m0"r"(r),0),t8".10298"):is(pli(m0"r"(r),0),m0(pli(r,0)))
-satz298k:=t8".10298":is(m0(pli(r,0)),pli(m0"r"(r),0))
-+*10298
-r@t9:=tris(real,mod2(pli(r,0)),ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(r,r),pl02(ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(im(pli(r,0)),im(pli(r,0))),ts01(im(pli(r,0)),im(pli(r,0)),imis(r,0))),ists12"r"(re(pli(r,0)),r,re(pli(r,0)),r,reis(r,0),reis(r,0))):is"r"(mod2(pli(r,0)),ts"r"(r,r))
-ar:=abs(r):real
-[p:pos(r)]
-t10:=satz196a(r,r,p,p):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-r@[i:is"r"(r,0)]
-t11:=tris2(real,ts"r"(r,r),ts"r"(ar,ar),0,ts01(r,r,i),ts01(ar,ar,abs0(r,i))):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-r@[n:neg(r)]
-t12:=satz196b(r,r,n,n):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-r@t13:=rapp(r,is"r"(ts"r"(r,r),ts"r"(ar,ar)),[t:pos(r)]t10(t),[t:is"r"(r,0)]t11(t),[t:neg(r)]t12(t)):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-t14:=tris(real,mod2(pli(r,0)),ts"r"(r,r),ts"r"(ar,ar),t9,t13):is"r"(mod2(pli(r,0)),ts"r"(ar,ar))
-t15:=th1"l.imp"(is"r"(r,0),not(neg(ar)),[t:is"r"(r,0)]0notn(ar,abs0(r,t)),[t:nis"r"(r,0)]pnotn(ar,satz166e(r,t))):not(neg(ar))
--10298
-r@satz298l:=thsqrt3(mod2(pli(r,0)),lemma5(pli(r,0)),abs(r),t15".10298",t14".10298"):is"r"(mod(pli(r,0)),abs(r))
-satz298m:=symis(real,mod(pli(r,0)),abs(r),satz298l):is"r"(abs(r),mod(pli(r,0)))
-cofrl:=pli(r,0):complex
-s@[i:is(cofrl(r),cofrl(s))]
-isrlic:=tr3is(real,r,re(cofrl(r)),re(cofrl(s)),s,isre(r,0),iscere(cofrl(r),cofrl(s),i),reis(s,0)):is"r"(r,s)
-s@[i:is"r"(r,s)]
-isrlec:=isrecx1(r,s,0,i):is(cofrl(r),cofrl(s))
-+v10
-@t1:=[t:real][u:real][v:is(cofrl(t),cofrl(u))]isrlic(t,u,v):injective(real,cx,[t:real]cofrl(t))
--v10
-@[x:cx]
-realc:=image(real,cx,[t:real]cofrl(t),x):'prop'
-r@reali:=imagei(real,cx,[t:real]cofrl(t),r):realc(cofrl(r))
-x@[rx:realc(x)]
-rlofc:=soft(real,cx,[t:real]cofrl(t),t1".v10",x,rx):real
-[y:cx][ry:realc(y)][i:is"r"(rlofc(x,rx),rlofc(y,ry))]
-iscirl:=isinve(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is(x,y)
-ry@[i:is(x,y)]
-iscerl:=isinv(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is"r"(rlofc(x,rx),rlofc(y,ry))
-r@isrlc1:=isst1(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(r,rlofc(cofrl(r),reali(r)))
-isrlc2:=isst2(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(rlofc(cofrl(r),reali(r)),r)
-rx@iscrl1:=ists1"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(x,cofrl(rlofc(x,rx)))
-iscrl2:=ists2"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(cofrl(rlofc(x,rx)),x)
-@[n:nat]
-cofn:=cofrl(rlofnt(n)):complex
-[m:nat][i:is"n"(n,m)]
-isnec:=isrlec(rlofnt(n),rlofnt(m),isnterl(n,m,i)):is(cofn(n),cofn(m))
-m@[i:is(cofn(n),cofn(m))]
-isnic:=isntirl(n,m,isrlic(rlofnt(n),rlofnt(m),i)):is"n"(n,m)
-+*v10
-@t2:=[t:nat][u:nat][v:is(cofn(t),cofn(u))]isnic(t,u,v):injective(nat,cx,[t:nat]cofn(t))
--v10
-x@natc:=image(nat,cx,[t:nat]cofn(t),x):'prop'
-n@nati:=imagei(nat,cx,[t:nat]cofn(t),n):natc(cofn(n))
-x@[nx:natc(x)]
-nofc:=soft(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):nat
-[y:cx][ny:natc(y)][i:is(x,y)]
-iscen:=isinv(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is"n"(nofc(x,nx),nofc(y,ny))
-ny@[i:is"n"(nofc(x,nx),nofc(y,ny))]
-iscin:=isinve(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is(x,y)
-n@isnc1:=isst1(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(n,nofc(cofn(n),nati(n)))
-isnc2:=isst2(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(nofc(cofn(n),nati(n)),n)
-nx@iscn1:=ists1"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(x,cofn(nofc(x,nx)))
-iscn2:=ists2"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(cofn(nofc(x,nx)),x)
-@natt:=ot(cx,[t:cx]natc(t)):'type'
-[nt:natt]
-cofnt:=in"e"(cx,[t:cx]natc(t),nt):cx
-natti:=inp(cx,[t:cx]natc(t),nt):natc(cofnt(nt))
-[mt:natt][i:is"e"(natt,nt,mt)]
-isntec:=isini(cx,[t:cx]natc(t),nt,mt,i):is(cofnt(nt),cofnt(mt))
-mt@[i:is(cofnt(nt),cofnt(mt))]
-isntic:=isine(cx,[t:cx]natc(t),nt,mt,i):is"e"(natt,nt,mt)
-nx@ntofc:=out(cx,[t:cx]natc(t),x,nx):natt
-ny@[i:is(x,y)]
-iscent:=isouti(cx,[t:cx]natc(t),x,nx,y,ny,i):is"e"(natt,ntofc(x,nx),ntofc(y,ny))
-ny@[i:is"e"(natt,ntofc(x,nx),ntofc(y,ny))]
-iscint:=isoute(cx,[t:cx]natc(t),x,nx,y,ny,i):is(x,y)
-nt@isntc1:=isoutin(cx,[t:cx]natc(t),nt):is"e"(natt,nt,ntofc(cofnt(nt),natti(nt)))
-isntc2:=symis(natt,nt,ntofc(cofnt(nt),natti(nt)),isntc1):is"e"(natt,ntofc(cofnt(nt),natti(nt)),nt)
-nx@iscnt1:=isinout(cx,[t:cx]natc(t),x,nx):is(x,cofnt(ntofc(x,nx)))
-iscnt2:=symis(cx,x,cofnt(ntofc(x,nx)),iscnt1):is(cofnt(ntofc(x,nx)),x)
-n@ntofn:=ntofc(cofn(n),nati(n)):natt
-m@[i:is"n"(n,m)]
-isnent:=iscent(cofn(n),nati(n),cofn(m),nati(m),isnec(n,m,i)):is"e"(natt,ntofn(n),ntofn(m))
-m@[i:is"e"(natt,ntofn(n),ntofn(m))]
-isnint:=isnic(n,m,iscint(cofn(n),nati(n),cofn(m),nati(m),i)):is"n"(n,m)
-nt@nofnt:=nofc(cofnt(nt),natti(nt)):nat
-mt@[i:is"e"(natt,nt,mt)]
-isnter:=iscen(cofnt(nt),natti(nt),cofnt(mt),natti(mt),isntec(nt,mt,i)):is"n"(nofnt(nt),nofnt(mt))
-mt@[i:is"n"(nofnt(nt),nofnt(mt))]
-isntin:=isntic(nt,mt,iscin(cofnt(nt),natti(nt),cofnt(mt),natti(mt),i)):is"e"(natt,nt,mt)
-+*v10
-n@t3:=iscnt1(cofn(n),nati(n)):is(cofn(n),cofnt(ntofn(n)))
--v10
-n@isnnt1:=tris(nat,n,nofc(cofn(n),nati(n)),nofnt(ntofn(n)),isnc1(n),iscen(cofn(n),nati(n),cofnt(ntofn(n)),natti(ntofn(n)),t3".v10")):is"n"(n,nofnt(ntofn(n)))
-isnnt2:=symis(nat,n,nofnt(ntofn(n)),isnnt1):is"n"(nofnt(ntofn(n)),n)
-+*v10
-nt@t4:=iscn1(cofnt(nt),natti(nt)):is(cofnt(nt),cofn(nofnt(nt)))
--v10
-nt@isntn1:=tris(natt,nt,ntofc(cofnt(nt),natti(nt)),ntofn(nofnt(nt)),isntc1(nt),iscent(cofnt(nt),natti(nt),cofn(nofnt(nt)),nati(nofnt(nt)),t4".v10")):is"e"(natt,nt,ntofn(nofnt(nt)))
-isntn2:=symis(natt,nt,ntofn(nofnt(nt)),isntn1):is"e"(natt,ntofn(nofnt(nt)),nt)
-@1t:=ntofn(1):natt
-suct:=[t:natt]ntofn(<nofnt(t)>suc):[t:natt]natt
-+10299
-nt@[i:is"e"(natt,<nt>suct,1t)]
-t1:=isnint(<nofnt(nt)>suc,1,i):is"n"(<nofnt(nt)>suc,1)
--10299
-nt@satz299a:=th3"l.imp"(is"e"(natt,<nt>suct,1t),is"n"(<nofnt(nt)>suc,1),<nofnt(nt)>ax3,[t:is"e"(natt,<nt>suct,1t)]t1".10299"(t)):not(is"e"(natt,<nt>suct,1t))
-@ax3t:=[t:natt]satz299a(t):[t:natt]not(is"e"(natt,<t>suct,1t))
-mt@[i:is"e"(natt,<nt>suct,<mt>suct)]
-+*10299
-i"c"@t2:=isnint(<nofnt(nt)>suc,<nofnt(mt)>suc,i):is"n"(<nofnt(nt)>suc,<nofnt(mt)>suc)
-t3:=<t2><nofnt(mt)><nofnt(nt)>ax4:is"n"(nofnt(nt),nofnt(mt))
--10299
-i@satz299b:=isntin(nt,mt,t3".10299"):is"e"(natt,nt,mt)
-@ax4t:=[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]satz299b(t,u,v):[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]is"e"(natt,t,u)
-[s:set(natt)]
-cond1t:=esti(natt,1t,s):'prop'
-cond2t:=all"l"(natt,[t:natt]imp(esti(natt,t,s),esti(natt,<t>suct,s))):'prop'
-[c1:cond1t][c2:cond2t]
-+*10299
-c2@[n:nat]
-prop1:=esti(natt,ntofn(n),s):'prop'
-c2@t4:=c1:prop1(1)
-n@[p:prop1(n)]
-t5:=<p><ntofn(n)>c2:esti(natt,ntofn(<nofnt(ntofn(n))>suc),s)
-t6:=isp(nat,[t:nat]esti(natt,ntofn(<t>suc),s),nofnt(ntofn(n)),n,t5,isnnt2(n)):prop1(<n>suc)
-c2@[nt:natt]
-t7:=induction([t:nat]prop1(t),t4,[t:nat][u:prop1(t)]t6(t,u),nofnt(nt)):prop1(nofnt(nt))
--10299
-c2@satz299c:=[t:natt]isp(natt,[u:natt]esti(natt,u,s),ntofn(nofnt(t)),t,t7".10299"(t),isntn2(t)):[t:natt]esti(natt,t,s)
-@ax5t:=[t:set(natt)][u:cond1t(t)][v:cond2t(t)]satz299c(t,u,v):[t:set(natt)][u:cond1t(t)][v:cond2t(t)][w:natt]esti(natt,w,t)
-ic:=pli(0,1rl):complex
-+10300
-t1:=tsis12a(0,1rl,0,1rl):is(ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))))
-t2:=tris(real,mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(ts"r"(1rl,1rl)),m0"r"(1rl),pl01(ts"r"(0,0),m0"r"(ts"r"(1rl,1rl)),ts01(0,0,refis(real,0))),ism0"r"(ts"r"(1rl,1rl),1rl,satz195(1rl))):is"r"(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl))
-t3:=tris(real,pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),ts"r"(1rl,0),0,pl01(ts"r"(0,1rl),ts"r"(1rl,0),ts01(0,1rl,refis(real,0))),ts02(1rl,0,refis(real,0))):is"r"(pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0)
-t4:=isrecx12(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0,t2,t3):is(pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)))
-t5:=satz298j(1rl):is(cofrl(m0"r"(1rl)),m0(1c))
--10300
-satz2300:=tr3is(cx,ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)),m0(1c),t1".10300",t4".10300",t5".10300"):is(ts(ic,ic),m0(1c))
-[r:real][s:real]
-+10301
-t1:=tsis12a(s,0,0,1rl):is(ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))))
-t2:=tris(real,mn"r"(ts"r"(s,0),ts"r"(0,1rl)),m0"r"(ts"r"(0,1rl)),0,pl01(ts"r"(s,0),m0"r"(ts"r"(0,1rl)),ts02(s,0,refis(real,0))),satz176b(ts"r"(0,1rl),ts01(0,1rl,refis(real,0)))):is"r"(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0)
-t3:=tris(real,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),ts"r"(s,1rl),s,pl02(ts"r"(s,1rl),ts"r"(0,0),ts01(0,0,refis(real,0))),satz195(s)):is"r"(pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s)
-t4:=isrecx12(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s,t2,t3):is(pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s))
-t5:=tris(cx,ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s),t1,t4):is(ts(cofrl(s),ic),pli(0,s))
-t6:=ispl2(ts(cofrl(s),ic),pli(0,s),cofrl(r),t5):is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)))
-t7:=plis12a(r,0,0,s):is(pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)))
-t8:=isrecx12(pl"r"(r,0),r,pl"r"(0,s),s,pl02(r,0,refis(real,0)),pl01(0,s,refis(real,0))):is(pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s))
--10301
-satz301a:=tr3is(cx,pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s),t6".10301",t7".10301",t8".10301"):is"e"(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s))
-satz301b:=symis(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s),satz301a):is(pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)))
-@[x:complex]
-satz301c:=tris(cx,x,pli(re(x),im(x)),pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),ispli(x),satz301b(re(x),im(x))):is(x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)))
-satz301d:=symis(cx,x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),satz301c):is(pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),x)
-s@[t:real][u:real][i:is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)))]
-+*10301
-i@t9:=tr3is(cx,pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)),pli(t,u),satz301b(r,s),i,satz301a(t,u)):is(pli(r,s),pli(t,u))
--10301
-i@satz301e:=tr3is(real,r,re(pli(r,s)),re(pli(t,u)),t,isre(r,s),iscere(pli(r,s),pli(t,u),t9".10301"),reis(t,u)):is"r"(r,t)
-satz301f:=tr3is(real,s,im(pli(r,s)),im(pli(t,u)),u,isim(r,s),isceim(pli(r,s),pli(t,u),t9".10301"),imis(t,u)):is"r"(s,u)
--c
--r
--rp
--rt
--n
--landau
--eq
--st
--e
--l
+++ /dev/null
-# Landau's "Grundlagen der Analysis", formal specification in AUTOMATH
-# Copyright (C) 1977, L.S. van Benthem Jutting
-# 1992, revised by F. Wiedijk (http://www.cs.ru.nl/~freek/aut/)
-# 2008, revised by F. Guidi to remove the eta-reductions
-# 2014, revised by F. Guidi to suggest @-typing removal
-
-+l
-@[a:'prop'][b:'prop']
-imp:=[x:a]b:'prop'
-[a1:a][i:imp(a,b)]
-mp:=<a1>i:b
-a@refimp:=[x:a]x:imp(a,a)
-b@[c:'prop'][i:imp(a,b)][j:imp(b,c)]
-trimp:=[x:a]<<x>i>j:imp(a,c)
-@con:='prim':'prop'
-a@not:=imp(con):'prop'
-wel:=not(not(a)):'prop'
-[a1:a]
-weli:=[x:not(a)]<a1>x:wel(a)
-a@[w:wel(a)]
-et:='prim':a
-a@[c1:con]
-cone:=et([x:not(a)]c1):a
-+imp
-b@[i:imp(a,b)][j:imp(not(a),b)]
-th1:=et(b,[x:not(b)]<<trimp(con,i,x)>j>x):b
-b@[n:not(a)]
-th2:=trimp(con,b,n,[x:con]cone(b,x)):imp(a,b)
-b@[n:not(b)][i:imp(a,b)]
-th3:=trimp(con,i,n):not(a)
-b@[a1:a][n:not(b)]
-th4:=[x:imp(a,b)]<a1>th3(n,x):not(imp(a,b))
-b@[n:not(imp(a,b))]
-th5:=et([x:not(a)]<th2(x)>n):a
-th6:=[x:b]<[y:a]x>n:not(b)
-b@[n:not(b)][i:imp(not(a),b)]
-th7:=et(a,th3(not(a),b,n,i)):a
--imp
-b@[i:imp(not(b),not(a))]
-cp:=[x:a]th7".imp"(b,not(a),weli(x),i):imp(a,b)
-@obvious:=imp(con,con):'prop'
-obviousi:=refimp(con):obvious
-b@ec:=imp(a,not(b)):'prop'
-[n:not(a)]
-eci1:=th2".imp"(not(b),n):ec(a,b)
-b@[n:not(b)]
-eci2:=[x:a]n:ec(a,b)
-+ec
-b@[i:imp(a,not(b))]
-th1:=i:ec(a,b)
-b@[i:imp(b,not(a))]
-th2:=[x:a][y:b]<x><y>i:ec(a,b)
--ec
-b@[e:ec(a,b)]
-comec:=th2".ec"(b,a,e):ec(b,a)
-[a1:a]
-ece1:=<a1>e:not(b)
-e@[b1:b]
-ece2:=th3".imp"(not(b),weli(b,b1),e):not(a)
-+*ec
-c@[e:ec(a,b)][i:imp(c,a)]
-th3:=trimp(c,a,not(b),i,e):ec(c,b)
-e@[i:imp(c,b)]
-th4:=comec(c,a,th3(b,a,c,comec(e),i)):ec(a,c)
--ec
-b@and:=not(ec(a,b)):'prop'
-[a1:a][b1:b]
-andi:=th4".imp"(not(b),a1,weli(b,b1)):and(a,b)
-b@[a1:and(a,b)]
-ande1:=th5".imp"(not(b),a1):a
-ande2:=et(b,th6".imp"(not(b),a1)):b
-comand:=andi(b,a,ande2,ande1):and(b,a)
-+and
-b@[n:not(a)]
-th1:=weli(ec,eci1(n)):not(and)
-b@[n:not(b)]
-th2:=weli(ec,eci2(n)):not(and)
-b@[n:not(and)][a1:a]
-th3:=ece1(et(ec,n),a1):not(b)
-n@[b1:b]
-th4:=ece2(et(ec,n),b1):not(a)
-n@th5:=th3"l.imp"(and(b,a),and(a,b),n,[x:and(b,a)]comand(b,a,x)):not(and(b,a))
-c@[a1:and(a,b)][i:imp(a,c)]
-th6:=andi(c,b,<ande1(a1)>i,ande2(a1)):and(c,b)
-a1@[i:imp(b,c)]
-th7:=andi(a,c,ande1(a1),<ande2(a1)>i):and(a,c)
--and
-b@or:=imp(not(a),b):'prop'
-[a1:a]
-ori1:=th2".imp"(not(a),b,weli(a1)):or(a,b)
-b@[b1:b]
-ori2:=[x:not(a)]b1:or(a,b)
-+or
-b@[i:imp(not(a),b)]
-th1:=i:or(a,b)
-b@[i:imp(not(b),a)]
-th2:=[x:not]et(b,th3"l.imp"(not(b),a,x,i)):or(a,b)
--or
-b@[o:or(a,b)][n:not(a)]
-ore2:=<n>o:b
-o@[n:not(b)]
-ore1:=et(th3".imp"(not(a),b,n,o)):a
-o@comor:=[x:not(b)]ore1(x):or(b,a)
-+*or
-b@[n:not(a)][m:not(b)]
-th3:=th4"l.imp"(not(a),b,n,m):not(or(a,b))
-b@[n:not(or(a,b))]
-th4:=th5"l.imp"(not(a),b,n):not(a)
-th5:=th6"l.imp"(not(a),b,n):not(b)
-a@th6:=refimp(not(a)):or(a,not(a))
--or
-c@[o:or(a,b)][i:imp(a,c)][j:imp(b,c)]
-orapp:=th1".imp"(c,i,trimp(not,b,c,o,j)):c
-c@[d:'prop']
-+*or
-o@[i:imp(a,c)]
-th7:=trimp(not(c),not,b,[x:not(c)]th3"l.imp"(a,c,x,i),o):or(c,b)
-o@[i:imp(b,c)]
-th8:=trimp(not(a),b,c,o,i):or(a,c)
-d@[o:or(a,b)][i:imp(a,c)][j:imp(b,d)]
-th9:=th7(a,d,c,th8(a,b,d,o,j),i):or(c,d)
-b@[o:or(a,b)]
-th10:=o:imp(not(a),b)
-th11:=comor(o):imp(not(b),a)
-b@[o:or(not(a),b)]
-th12:=trimp(a,wel(a),b,[x:a]weli(x),o):imp(a,b)
-b@[i:imp(a,b)]
-th13:=trimp(wel(a),a,b,[x:wel(a)]et(x),i):or(not(a),b)
-b@[o:or(not(a),not(b))]
-th14:=weli(ec,th12(not(b),o)):not(and)
-b@[n:not(and)]
-th15:=th13(not(b),et(ec,n)):or(not(a),not(b))
-b@[a1:and(not(a),not(b))]
-th16:=th3(ande1(not(a),not(b),a1),ande2(not(a),not(b),a1)):not(or(a,b))
-b@[n:not(or(a,b))]
-th17:=andi(not(a),not(b),th4(n),th5(n)):and(not(a),not(b))
--or
-b@orec:=and(or(a,b),ec(a,b)):'prop'
-[o:or(a,b)][e:ec(a,b)]
-oreci:=andi(or(a,b),ec(a,b),o,e):orec(a,b)
-+orec
-b@[a1:a][n:not(b)]
-th1:=oreci(ori1(a1),eci2(n)):orec(a,b)
-b@[n:not(a)][b1:b]
-th2:=oreci(ori2(b1),eci1(n)):orec(a,b)
--orec
-b@[o:orec(a,b)]
-orece1:=ande1(or(a,b),ec,o):or(a,b)
-orece2:=ande2(or(a,b),ec,o):ec(a,b)
-comorec:=oreci(b,a,comor(orece1),comec(orece2)):orec(b,a)
-+*orec
-o@[a1:a]
-th3:=ece1(orece2,a1):not(b)
-o@[b1:b]
-th4:=ece2(orece2,b1):not(a)
-o@[n:not(a)]
-th5:=ore2(orece1,n):b
-o@[n:not(b)]
-th6:=ore1(orece1,n):a
--orec
-b@iff:=and(imp(a,b),imp(b,a)):'prop'
-[i:imp(a,b)][j:imp(b,a)]
-iffi:=andi(imp(a,b),imp(b,a),i,j):iff(a,b)
-+iff
-b@[a1:a][b1:b]
-th1:=iffi([x:a]b1,[x:b]a1):iff(a,b)
-b@[n:not(a)][m:not(b)]
-th2:=iffi(th2"l.imp"(n),th2"l.imp"(b,a,m)):iff(a,b)
--iff
-b@[i:iff(a,b)]
-iffe1:=ande1(imp(a,b),imp(b,a),i):imp(a,b)
-iffe2:=ande2(imp(a,b),imp(b,a),i):imp(b,a)
-comiff:=iffi(b,a,iffe2,iffe1):iff(b,a)
-+*iff
-i@[a1:a]
-th3:=<a1>iffe1:b
-i@[b1:b]
-th4:=<b1>iffe2:a
-i@[n:not(a)]
-th5:=th3"l.imp"(b,a,n,iffe2):not(b)
-i@[n:not(b)]
-th6:=th3"l.imp"(n,iffe1):not(a)
-b@[a1:a][n:not(b)]
-th7:=th1"l.and"(imp(a,b),imp(b,a),th4"l.imp"(a1,n)):not(iff(a,b))
-b@[n:not(a)][b1:b]
-th8:=th2"l.and"(imp(a,b),imp(b,a),th4"l.imp"(b,a,b1,n)):not(iff(a,b))
--iff
-a@refiff:=iffi(a,refimp,refimp):iff(a,a)
-b@[i:iff(a,b)]
-symiff:=comiff(i):iff(b,a)
-c@[i:iff(a,b)][j:iff(b,c)]
-triff:=iffi(a,c,trimp(iffe1(i),iffe1(b,c,j)),trimp(c,b,a,iffe2(b,c,j),iffe2(i))):iff(a,c)
-+*iff
-b@[i:iff(a,b)]
-th9:=[x:not(a)]th5(i,x):imp(not(a),not(b))
-th10:=[x:not(b)]th6(i,x):imp(not(b),not(a))
-th11:=iffi(not(a),not(b),th9,th10):iff(not(a),not(b))
-b@[i:imp(not(a),not(b))][j:imp(not(b),not(a))]
-th12:=iffi(cp(j),cp(b,a,i)):iff(a,b)
-b@[o:orec(a,b)]
-th13:=iffi(not(b),orece2(o),comor(orece1(o))):iff(a,not(b))
-th14:=th13(b,a,comorec(o)):iff(b,not(a))
-b@[i:iff(a,not(b))]
-th15:=oreci(comor(b,a,iffe2(not(b),i)),iffe1(not(b),i)):orec(a,b)
-b@[i:iff(b,not(a))]
-th16:=comorec(b,a,th15(b,a,i)):orec(a,b)
-c@[i:iff(a,b)][j:imp(a,c)]
-thimp1:=trimp(b,a,c,iffe2(i),j):imp(b,c)
-i@[j:imp(c,a)]
-thimp2:=trimp(c,a,b,j,iffe1(i)):imp(c,b)
-i@[e:ec(a,c)]
-thec1:=th3"l.ec"(c,b,e,iffe2(i)):ec(b,c)
-i@[e:ec(c,a)]
-thec2:=th4"l.ec"(c,a,b,e,iffe2(i)):ec(c,b)
-i@[a1:and(a,c)]
-thand1:=th6"l.and"(c,b,a1,iffe1(i)):and(b,c)
-i@[a1:and(c,a)]
-thand2:=th7"l.and"(c,a,b,a1,iffe1(i)):and(c,b)
-i@[o:or(a,c)]
-thor1:=th7"l.or"(c,b,o,iffe1(i)):or(b,c)
-i@[o:or(c,a)]
-thor2:=th8"l.or"(c,a,b,o,iffe1(i)):or(c,b)
-i@[o:orec(a,c)]
-thorec1:=oreci(b,c,thor1(orece1(a,c,o)),thec1(orece2(a,c,o))):orec(b,c)
-i@[o:orec(c,a)]
-thorec2:=oreci(c,b,thor2(orece1(c,a,o)),thec2(orece2(c,a,o))):orec(c,b)
--iff
-@[sigma:'type'][p:[x:sigma]'prop']
-%suggestion by van Daalen to remove the first eta-reduction
-%all:=p:'prop' %original line
-all:=[x:sigma]<x>p:'prop'
-%end of suggestion
-[a1:all(sigma,p)][s:sigma]
-alle:=<s>a1:<s>p
-+all
-p@[s:sigma][n:not(<s>p)]
-th1:=[x:all(sigma,p)]<<s>x>n:not(all(sigma,p))
--all
-p@non:=[x:sigma]not(<x>p):[x:sigma]'prop'
-{ to validate }
-some:=not(non(p)):'prop'
-[s:sigma][sp:<s>p]
-somei:=th1".all"(non(p),s,weli(<s>p,sp)):some(sigma,p)
-+some
-p@[n:not(all(sigma,p))][m:non(non(p))][s:sigma]
-t1:=et(<s>p,<s>m):<s>p
-%set etared
-m@t2:=<[x:sigma]t1(x)>n:con
-%reset etared
-n@th1:=[x:non(non(p))]t2(x):some(non(p))
-p@[s:some(non(p))][a1:all(sigma,p)][t:sigma]
-t3:=weli(<t>p,<t>a1):not(not(<t>p))
-a1@t4:=<[x:sigma]t3(x)>s:con
-s@th2:=[x:all(sigma,p)]t4(x):not(all(sigma,p))
-p@[n:not(some(sigma,p))]
-th3:=et(non(p),n):non(p)
-[s:sigma]
-th4:=<s>th3:not(<s>p)
-p@[n:non(p)]
-th5:=weli(non(p),n):not(some(sigma,p))
--some
-p@[s:some(sigma,p)][x:'prop'][i:[y:sigma]imp(<y>p,x)]
-+*some
-i@[n:not(x)][t:sigma]
-t5:=th3"l.imp"(<t>p,x,n,<t>i):not(<t>p)
-n@t6:=mp(some(sigma,p),con,s,th5([y:sigma]t5(y))):con
--some
-i@someapp:=et(x,[y:not(x)]t6".some"(y)):x
-+*some
-p@[q:[x:sigma]'prop'][s:some(sigma,p)][i:[x:sigma]imp(<x>p,<x>q)]
-th6:=someapp(s,some(q),[x:sigma][y:<x>p]somei(q,x,mp(<x>p,<x>q,y,<x>i))):some(q)
--some
-c@or3:=or(a,or(b,c)):'prop'
-[o:or3(a,b,c)][n:not(a)]
-+or3
-th1:=ore2(or(b,c),o,n):or(b,c)
--or3
-[m:not(b)]
-or3e3:=ore2(b,c,th1".or3",m):c
-o@[n:not(b)]
-+*or3
-n@th2:=th2"l.or"(c,a,[x:not(a)]or3e3(x,n)):or(c,a)
--or3
-n@[m:not(c)]
-or3e1:=ore2(c,a,th2".or3",m):a
-o@[n:not(c)]
-+*or3
-n@th3:=th2"l.or"([x:not(b)]or3e1(x,n)):or(a,b)
--or3
-n@[m:not(a)]
-or3e2:=ore2(th3".or3",m):b
-+*or3
-o@th4:=th1"l.or"(b,or(c,a),[x:not(b)]th2(x)):or3(b,c,a)
-th5:=th4(b,c,a,th4):or3(c,a,b)
--or3
-c@[a1:a]
-or3i1:=ori1(a,or(b,c),a1):or3(a,b,c)
-c@[b1:b]
-or3i2:=ori2(a,or(b,c),ori1(b,c,b1)):or3(a,b,c)
-c@[c1:c]
-or3i3:=ori2(a,or(b,c),ori2(b,c,c1)):or3(a,b,c)
-+*or3
-c@[o:or(a,b)]
-th6:=th4"or3"(c,a,b,ori2(c,or(a,b),o)):or3(a,b,c)
-c@[o:or(b,c)]
-th7:=ori2(or(b,c),o):or3(a,b,c)
-c@[o:or(c,a)]
-th8:=th4"or3"(c,a,b,th6(c,a,b,o)):or3(a,b,c)
--or3
-d@[o:or3(a,b,c)][i:imp(a,d)][j:imp(b,d)][k:imp(c,d)]
-or3app:=orapp(or(b,c),d,o,i,[x:or(b,c)]orapp(b,c,d,x,j,k)):d
-c@and3:=and(a,and(b,c)):'prop'
-[a1:and3(a,b,c)]
-and3e1:=ande1(and(b,c),a1):a
-and3e2:=ande1(b,c,ande2(and(b,c),a1)):b
-and3e3:=ande2(b,c,ande2(and(b,c),a1)):c
-c@[a1:a][b1:b][c1:c]
-and3i:=andi(a,and(b,c),a1,andi(b,c,b1,c1)):and3(a,b,c)
-+and3
-c@[a1:and3(a,b,c)]
-th1:=and3i(b,c,a,and3e2(a1),and3e3(a1),and3e1(a1)):and3(b,c,a)
-th2:=th1(b,c,a,th1):and3(c,a,b)
-th3:=andi(and3e1(a1),and3e2(a1)):and(a,b)
-th4:=ande2(and(b,c),a1):and(b,c)
-th5:=th3(c,a,b,th2):and(c,a)
-th6:=and3i(c,b,a,and3e3(a1),and3e2(a1),and3e1(a1)):and3(c,b,a)
--and3
-c@ec3:=and3(ec,ec(b,c),ec(c,a)):'prop'
-[e:ec3(a,b,c)]
-+ec3
-th1:=and3e1(ec,ec(b,c),ec(c,a),e):ec(a,b)
-th2:=and3e2(ec,ec(b,c),ec(c,a),e):ec(b,c)
-th3:=and3e3(ec,ec(b,c),ec(c,a),e):ec(c,a)
-th4:=th1"l.and3"(ec,ec(b,c),ec(c,a),e):ec3(b,c,a)
-th5:=th4(b,c,a,th4):ec3(c,a,b)
-th5a:=and3i(ec(c,b),ec(b,a),ec(a,c),comec(b,c,th2(e)),comec(a,b,th1(e)),comec(c,a,th3(e))):ec3(c,b,a)
--ec3
-[a1:a]
-ec3e12:=ece1(th1".ec3",a1):not(b)
-ec3e13:=ece2(c,a,th3".ec3",a1):not(c)
-e@[b1:b]
-ec3e23:=ec3e12(b,c,a,th4".ec3",b1):not(c)
-ec3e21:=ec3e13(b,c,a,th4".ec3",b1):not(a)
-e@[c1:c]
-ec3e31:=ec3e12(c,a,b,th5".ec3",c1):not(a)
-ec3e32:=ec3e13(c,a,b,th5".ec3",c1):not(b)
-+*ec3
-c@[e:ec(a,b)][f:ec(b,c)][g:ec(c,a)]
-th6:=and3i(ec,ec(b,c),ec(c,a),e,f,g):ec3(a,b,c)
-c@[e:ec3(a,b,c)][o:or(a,b)]
-th7:=orapp(not(c),o,[x:a]ece2(c,a,th3"ec3"(e),x),[x:b]ece1(b,c,th2"ec3"(e),x)):not(c)
-e@[o:or(b,c)]
-th8:=th7(b,c,a,th4"ec3"(e),o):not(a)
-e@[o:or(c,a)]
-th9:=th7(c,a,b,th5"ec3"(e),o):not(b)
--ec3
-c@[n:not(a)][m:not(b)]
-ec3i1:=th6".ec3"(eci1(n),eci1(b,c,m),eci2(c,a,n)):ec3(a,b,c)
-c@[n:not(b)][m:not(c)]
-ec3i2:=th6".ec3"(eci2(n),eci1(b,c,n),eci1(c,a,m)):ec3(a,b,c)
-c@[n:not(c)][m:not(a)]
-ec3i3:=th6".ec3"(eci1(m),eci2(b,c,n),eci1(c,a,n)):ec3(a,b,c)
-+*ec3
-d@[e:'prop'][f:'prop'][o1:or3(a,b,c)][p1:ec3(d,e,f)][i:imp(a,d)][j:imp(b,e)][k:imp(c,f)][d1:d]
-t1:=[x:b]mp(e,con,<x>j,ec3e12(d,e,f,p1,d1)):not(b)
-t2:=[x:c]mp(f,con,<x>k,ec3e13(d,e,f,p1,d1)):not(c)
-th10:=or3e1(o1,t1,t2):a
-k@[e1:e]
-th11:=th10(b,c,a,e,f,d,th4"l.or3"(o1),th4"ec3"(d,e,f,p1),j,k,i,e1):b
-k@[f1:f]
-th12:=th10(c,a,b,f,d,e,th5"l.or3"(o1),th5"ec3"(d,e,f,p1),k,i,j,f1):c
--ec3
-c@orec3:=and(or3(a,b,c),ec3(a,b,c)):'prop'
-[o:orec3(a,b,c)]
-orec3e1:=ande1(or3(a,b,c),ec3(a,b,c),o):or3(a,b,c)
-orec3e2:=ande2(or3(a,b,c),ec3(a,b,c),o):ec3(a,b,c)
-c@[o:or3(a,b,c)][e:ec3(a,b,c)]
-orec3i:=andi(or3(a,b,c),ec3(a,b,c),o,e):orec3(a,b,c)
-+orec3
-c@[o:orec3(a,b,c)]
-th1:=orec3i(b,c,a,th4"l.or3"(orec3e1(o)),th4"l.ec3"(orec3e2(o))):orec3(b,c,a)
-th2:=orec3i(c,a,b,th5"l.or3"(orec3e1(o)),th5"l.ec3"(orec3e2(o))):orec3(c,a,b)
--orec3
-+e
-sigma@[s:sigma][t:sigma]
-is:='prim':'prop'
-s@refis:='prim':is(s,s)
-p@[s:sigma][t:sigma][sp:<s>p][i:is(s,t)]
-isp:='prim':<t>p
-sigma@[s:sigma][t:sigma][i:is(s,t)]
-symis:=isp([x:sigma]is(x,s),s,t,refis(s),i):is(t,s)
-t@[u:sigma][i:is(s,t)][j:is(t,u)]
-tris:=isp([x:sigma]is(x,u),t,s,j,symis(i)):is(s,u)
-u@[i:is(u,s)][j:is(u,t)]
-tris1:=tris(s,u,t,symis(u,s,i),j):is(s,t)
-u@[i:is(s,u)][j:is(t,u)]
-tris2:=tris(s,u,t,i,symis(t,u,j)):is(s,t)
-sp@[i:is(t,s)]
-isp1:=isp(symis(t,s,i)):<t>p
-t@[n:not(is(s,t))]
-symnotis:=th3"l.imp"(is(t,s),is(s,t),n,[x:is(t,s)]symis(t,s,x)):not(is(t,s))
-+notis
-u@[n:not(is(s,t))][i:is(s,u)]
-th1:=isp([x:sigma]not(is(x,t)),s,u,n,i):not(is(u,t))
-n@[i:is(u,s)]
-th2:=th1(symis(u,s,i)):not(is(u,t))
-n@[i:is(t,u)]
-th3:=isp([x:sigma]not(is(s,x)),t,u,n,i):not(is(s,u))
-n@[i:is(u,t)]
-th4:=th3(symis(u,t,i)):not(is(s,u))
-u@[v:sigma][n:not(is(s,t))][i:is(s,u)][j:is(t,v)]
-th5:=th3(u,t,v,th1(n,i),j):not(is(u,v))
--notis
-u@[v:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)]
-tr3is:=tris(s,u,v,tris(i,j),k):is(s,v)
-v@[w:sigma][i:is(s,t)][j:is(t,u)][k:is(u,v)][l:is(v,w)]
-tr4is:=tris(s,v,w,tr3is(i,j,k),l):is(s,w)
-p@amone:=[x:sigma][y:sigma][u:<x>p][v:<y>p]is(x,y):'prop'
-[a1:amone(sigma,p)][s:sigma][t:sigma][sp:<s>p][tp:<t>p]
-amonee:=<tp><sp><t><s>a1:is(s,t)
-p@one:=and(amone(sigma,p),some(sigma,p)):'prop'
-[a1:amone(sigma,p)][s:some(sigma,p)]
-onei:=andi(amone(sigma,p),some(sigma,p),a1,s):one(sigma,p)
-p@[o1:one(sigma,p)]
-onee1:=ande1(amone(sigma,p),some(sigma,p),o1):amone(sigma,p)
-onee2:=ande2(amone(sigma,p),some(sigma,p),o1):some(sigma,p)
-ind:='prim':sigma
-oneax:='prim':<ind>p
-+one
-[s:sigma][sp:<s>p]
-th1:=amonee(onee1,ind,s,oneax,sp):is(ind,s)
--one
-sigma@[tau:'type'][f:[x:sigma]tau][s:sigma][t:sigma][i:is(s,t)]
-isf:=isp(sigma,[x:sigma]is(tau,<s>f,<x>f),s,t,refis(tau,<s>f),i):is(tau,<s>f,<t>f)
-f@injective:=all([x:sigma]all([y:sigma]imp(is(tau,<x>f,<y>f),is(x,y)))):'prop'
-[i:injective(f)][s:sigma][t:sigma][j:is(tau,<s>f,<t>f)]
-isfe:=<j><t><s>i:is(s,t)
-f@[t0:tau]
-image:=some([x:sigma]is(tau,t0,<x>f)):'prop'
-f@[s:sigma]
-tofs:=<s>f:tau
-imagei:=somei([x:sigma]is(tau,tofs,<x>f),s,refis(tau,tofs)):image(tofs)
-+inj
-i@[ta:tau][tb:tau][j:is(tau,ta,tb)][sa:sigma][sb:sigma][ja:is(tau,ta,tofs(sa))][jb:is(tau,tb,tofs(sb))]
-t1:=tr3is(tau,tofs(sa),ta,tb,tofs(sb),symis(tau,ta,tofs(sa),ja),j,jb):is(tau,tofs(sa),tofs(sb))
-th1:=isfe(sa,sb,t1):is(sa,sb)
-i@[t0:tau]
-th2:=[x:sigma][y:sigma][u:is(tau,t0,<x>f)][v:is(tau,t0,<y>f)]th1(t0,t0,refis(tau,t0),x,y,u,v):amone([x:sigma]is(tau,t0,<x>f))
-[j:image(f,t0)]
-th3:=onei([x:sigma]is(tau,t0,<x>f),th2,j):one([x:sigma]is(tau,t0,<x>f))
--inj
-i@[t0:tau][j:image(f,t0)]
-soft:=ind([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):sigma
-i@inverse:=[x:tau][u:image(f,x)]soft(x,u):[x:tau][u:image(f,x)]sigma
-j@ists1:=oneax([x:sigma]is(tau,t0,<x>f),th3".inj"(t0,j)):is(tau,t0,tofs(soft(t0,j)))
-ists2:=symis(tau,t0,tofs(soft(t0,j)),ists1):is(tau,tofs(soft(t0,j)),t0)
-i@[ta:tau][ja:image(ta)][tb:tau][jb:image(tb)][j:is(tau,ta,tb)]
-isinv:=th1".inj"(ta,tb,j,soft(ta,ja),soft(tb,jb),ists1(ta,ja),ists1(tb,jb)):is(soft(ta,ja),soft(tb,jb))
-jb@[j:is(soft(ta,ja),soft(tb,jb))]
-isinve:=tr3is(tau,ta,tofs(soft(ta,ja)),tofs(soft(tb,jb)),tb,ists1(ta,ja),isf(soft(ta,ja),soft(tb,jb),j),ists2(tb,jb)):is(tau,ta,tb)
-i@[s:sigma]
-isst1:=isfe(s,soft(tofs(s),imagei(s)),ists1(tofs(s),imagei(s))):is(s,soft(tofs(s),imagei(s)))
-isst2:=symis(s,soft(tofs(s),imagei(s)),isst1):is(soft(tofs(s),imagei(s)),s)
-f@surjective:=all(tau,[x:tau]image(x)):'prop'
-bijective:=and(injective,surjective):'prop'
-[b:bijective(f)]
-+*inj
-b@t2:=ande1(injective,surjective,b):injective(f)
-t3:=ande2(injective,surjective,b):surjective(f)
-[t:tau]
-so:=soft(t2,t,<t>t3):sigma
--inj
-b@invf:=[x:tau]so".inj"(x):[x:tau]sigma
-[s:sigma]
-thinvf1:=tris(s,soft(t2".inj",tofs(s),imagei(s)),<<s>f>invf,isst1(t2".inj",s),isinv(t2".inj",tofs(s),imagei(s),tofs(s),<tofs(s)>t3".inj",refis(tau,tofs(s)))):is(s,<<s>f>invf)
-b@[t:tau]
-thinvf2:=ists1(t2".inj",t,<t>t3".inj"):is(tau,t,<<t>invf>f)
-tau@[upsilon:'type'][f:[x:sigma]tau][g:[x:tau]upsilon]
-+*inj
-g@[if:injective(sigma,tau,f)][ig:injective(tau,upsilon,g)]
-h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
-[s:sigma][t:sigma][i:is(upsilon,<s>h,<t>h)]
-t4:=isfe(tau,upsilon,g,ig,<s>f,<t>f,i):is(tau,<s>f,<t>f)
-t5:=isfe(f,if,s,t,t4):is(s,t)
-ig@th4:=[x:sigma][y:sigma][v:is(upsilon,<x>h,<y>h)]t5(x,y,v):injective(sigma,upsilon,[x:sigma]<<x>f>g)
--inj
-+surj
-g@[sf:surjective(sigma,tau,f)][sg:surjective(tau,upsilon,g)]
-h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
-[u:upsilon]
-t1:=<u>sg:image(tau,upsilon,g,u)
-[t:tau][i:is(upsilon,u,<t>g)]
-t2:=<t>sf:image(sigma,tau,f,t)
-[s:sigma][j:is(tau,t,<s>f)]
-t3:=tris(upsilon,u,<t>g,<s>h,i,isf(tau,upsilon,g,t,<s>f,j)):is(upsilon,u,<s>h)
-t4:=somei([x:sigma]is(upsilon,u,<x>h),s,t3):image(sigma,upsilon,h,u)
-i@t5:=someapp([x:sigma]is(tau,t,<x>f),t2,image(sigma,upsilon,h,u),[x:sigma][v:is(tau,t,<x>f)]t4(x,v)):image(sigma,upsilon,h,u)
-u@t6:=someapp(tau,[x:tau]is(upsilon,u,<x>g),t1,image(sigma,upsilon,h,u),[x:tau][v:is(upsilon,u,<x>g)]t5(x,v)):image(sigma,upsilon,h,u)
-sg@th1:=[x:upsilon]t6(x):surjective(sigma,upsilon,[x:sigma]<<x>f>g)
--surj
-+bij
-g@[bf:bijective(sigma,tau,f)][bg:bijective(tau,upsilon,g)]
-h:=[x:sigma]<<x>f>g:[x:sigma]upsilon
-t1:=th4"e.inj"(f,g,ande1(injective(f),surjective(f),bf),ande1(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):injective(sigma,upsilon,h)
-t2:=th1"e.surj"(f,g,ande2(injective(f),surjective(f),bf),ande2(injective(tau,upsilon,g),surjective(tau,upsilon,g),bg)):surjective(sigma,upsilon,h)
-th1:=andi(injective(sigma,upsilon,h),surjective(sigma,upsilon,h),t1,t2):bijective(sigma,upsilon,[x:sigma]<<x>f>g)
--bij
-tau@[f:[x:sigma]tau][g:[x:sigma]tau][i:is([x:sigma]tau,f,g)][s:sigma]
-fise:=isp([x:sigma]tau,[y:[x:sigma]tau]is(tau,<s>f,<s>y),f,g,refis(tau,<s>f),i):is(tau,<s>f,<s>g)
-g@[i:[x:sigma]is(tau,<x>f,<x>g)]
-fisi:='prim':is([x:sigma]tau,f,g)
-+fis
-g@[i:is([x:sigma]tau,f,g)][s:sigma][t:sigma][j:is(s,t)]
-th1:=tris(tau,<s>f,<t>f,<t>g,isf(f,s,t,j),fise(i,t)):is(tau,<s>f,<t>g)
--fis
-p@ot:='prim':'type'
-[o1:ot]
-in:='prim':sigma
-inp:='prim':<in>p
-p@otax1:='prim':injective(ot,sigma,[x:ot]in(x))
-[s:sigma][sp:<s>p]
-otax2:='prim':image(ot,sigma,[x:ot]in(x),s)
-o1@[o2:ot][i:is(ot,o1,o2)]
-isini:=isf(ot,sigma,[x:ot]in(x),o1,o2,i):is(in(o1),in(o2))
-o2@[i:is(in(o1),in(o2))]
-isine:=isfe(ot,sigma,[x:ot]in(x),otax1,o1,o2,i):is(ot,o1,o2)
-sp@out:=soft(ot,sigma,[x:ot]in(x),otax1,s,otax2):ot
-[t:sigma][tp:<t>p][i:is(s,t)]
-isouti:=isinv(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(ot,out(s,sp),out(t,tp))
-tp@[i:is(ot,out(s,sp),out(t,tp))]
-isoute:=isinve(ot,sigma,[x:ot]in(x),otax1,s,otax2,t,otax2(t,tp),i):is(s,t)
-o1@isoutin:=tris(ot,o1,soft(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1)),out(in(o1),inp(o1)),isst1(ot,sigma,[x:ot]in(x),otax1,o1),isinv(ot,sigma,[x:ot]in(x),otax1,in(o1),imagei(ot,sigma,[x:ot]in(x),o1),in(o1),otax2(in(o1),inp(o1)),refis(sigma,in(o1)))):is(ot,o1,out(in(o1),inp(o1)))
-sp@isinout:=ists1(ot,sigma,[x:ot]in(x),otax1,s,otax2):is(s,in(out(s,sp)))
-tau@pairtype:='prim':'type'
-[s:sigma][t:tau]
-pair:='prim':pairtype
-tau@[p1:pairtype]
-first:='prim':sigma
-second:='prim':tau
-pairis1:='prim':is(pairtype,pair(first,second),p1)
-pairis2:=symis(pairtype,pair(first,second),p1,pairis1):is(pairtype,p1,pair(first,second))
-t@firstis1:='prim':is(sigma,first(pair),s)
-firstis2:=symis(sigma,first(pair),s,firstis1):is(sigma,s,first(pair))
-secondis1:='prim':is(tau,second(pair),t)
-secondis2:=symis(tau,second(pair),t,secondis1):is(tau,t,second(pair))
-a@[ksi:'type'][x:ksi][y:ksi]
-+ite
-[z:ksi]
-prop1:=and(imp(a,is(ksi,z,x)),imp(not(a),is(ksi,z,y))):'prop'
-y@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t1:=ande1(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(a,is(ksi,x1,x))
-t2:=mp(a,is(ksi,x1,x),a1,t1):is(ksi,x1,x)
-t3:=t2(y1,x1,py1,px1):is(ksi,y1,x)
-t4:=tris2(ksi,x1,y1,x,t2,t3):is(ksi,x1,y1)
-a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
-t6:=[x1:a]refis(ksi,x):imp(a,is(ksi,x,x))
-t7:=th2"l.imp"(not(a),is(ksi,x,y),weli(a,a1)):imp(not(a),is(ksi,x,y))
-t8:=andi(imp(a,is(ksi,x,x)),imp(not(a),is(ksi,x,y)),t6,t7):prop1(x)
-t9:=somei(ksi,[t:ksi]prop1(t),x,t8):some(ksi,[t:ksi]prop1(t))
-t10:=onei(ksi,[t:ksi]prop1(t),t5,t9):one(ksi,[t:ksi]prop1(t))
-y@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t11:=ande2(imp(a,is(ksi,x1,x)),imp(not(a),is(ksi,x1,y)),px1):imp(not(a),is(ksi,x1,y))
-t12:=mp(not(a),is(ksi,x1,y),n,t11):is(ksi,x1,y)
-t13:=t12(y1,x1,py1,px1):is(ksi,y1,y)
-t14:=tris2(ksi,x1,y1,y,t12,t13):is(ksi,x1,y1)
-n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone(ksi,[t:ksi]prop1(t))
-t16:=[x1:not(a)]refis(ksi,y):imp(not(a),is(ksi,y,y))
-t17:=th2"l.imp"(a,is(ksi,y,x),n):imp(a,is(ksi,y,x))
-t18:=andi(imp(a,is(ksi,y,x)),imp(not(a),is(ksi,y,y)),t17,t16):prop1(y)
-t19:=somei(ksi,[t:ksi]prop1(t),y,t18):some(ksi,[t:ksi]prop1(t))
-t20:=onei(ksi,[t:ksi]prop1(t),t15,t19):one(ksi,[t:ksi]prop1(t))
-y@t21:=th1"l.imp"(a,one(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one(ksi,[t:ksi]prop1(t))
--ite
-ite:=ind(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
-+*ite
-y@t22:=oneax(ksi,[t:ksi]prop1(t),t21):prop1(ite)
-t23:=ande1(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(a,is(ksi,ite,x))
-t24:=ande2(imp(a,is(ksi,ite,x)),imp(not(a),is(ksi,ite,y)),t22):imp(not(a),is(ksi,ite,y))
--ite
-y@[a1:a]
-itet:=mp(a,is(ksi,ite,x),a1,t23".ite"):is(ksi,ite,x)
-y@[n:not(a)]
-itef:=mp(not(a),is(ksi,ite,y),n,t24".ite"):is(ksi,ite,y)
-sigma@[s0:sigma][t0:sigma]
-+wissel
-[s:sigma]
-wa:=ite(is(s,s0),sigma,t0,s):sigma
-[i:is(s,s0)]
-t1:=itet(is(s,s0),sigma,t0,s,i):is(wa,t0)
-s@[n:not(is(s,s0))]
-t2:=itef(is(s,s0),sigma,t0,s,n):is(wa,s)
-s@wb:=ite(is(s,t0),sigma,s0,wa):sigma
-[i:is(s,t0)]
-t3:=itet(is(s,t0),sigma,s0,wa,i):is(wb,s0)
-s@[n:not(is(s,t0))]
-t4:=itef(is(s,t0),sigma,s0,wa,n):is(wb,wa)
-s@[i:is(s,s0)][j:is(s0,t0)]
-t5:=tris(wb,s0,t0,t3(tris(s,s0,t0,i,j)),j):is(wb,t0)
-i@[n:not(is(s0,t0))]
-t6:=tris(wb,wa,t0,t4(th2"e.notis"(s0,t0,s,n,i)),t1(i)):is(wb,t0)
-i@t7:=th1"l.imp"(is(s0,t0),is(wb,t0),[t:is(s0,t0)]t5(t),[t:not(is(s0,t0))]t6(t)):is(wb,t0)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-t8:=tris(wb,wa,s,t4(o),t2(n)):is(wb,s)
--wissel
-wissel:=[x:sigma]wb".wissel"(x):[x:sigma]sigma
-[s:sigma][i:is(s,s0)]
-iswissel1:=t7".wissel"(s,i):is(<s>wissel,t0)
-s@[i:is(s,t0)]
-iswissel2:=t3".wissel"(s,i):is(<s>wissel,s0)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-iswissel3:=t8".wissel"(s,n,o):is(<s>wissel,s)
-+*wissel
-s@[t:sigma][i:is(wb(s),wb(t))][n:not(is(s,t))][j:is(s,s0)]
-t9:=symnotis(s0,t,th1"e.notis"(s,t,s0,n,j)):not(is(t,s0))
-[k:is(s0,t0)]
-t10:=th3"e.notis"(t,s0,t0,t9,k):not(is(t,t0))
-t11:=tris(wb(s),wb(t),t,i,t8(t,t9,t10)):is(wb(s),t)
-t12:=<tris1(t,t0,wb(s),t11,t7(j))>t10:con
-j@t13:=[v:is(s0,t0)]t12(v):not(is(s0,t0))
-[k:is(t,t0)]
-t14:=tris(wb(s),wb(t),s0,i,t3(t,k)):is(wb(s),s0)
-t15:=t12(tris1(s0,t0,wb(s),t14,t7(j))):con
-j@t16:=[v:is(t,t0)]t15(v):not(is(t,t0))
-t17:=tris(wb(s),wb(t),t,i,t8(t,t9,t16)):is(wb(s),t)
-t18:=t15(tris1(t,t0,wb(s),t17,t7(j))):con
-n@t19:=[v:is(s,s0)]t18(v):not(is(s,s0))
-t20:=t19(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,s0))
-[j:is(s,t0)]
-t21:=symnotis(t0,t,th1"e.notis"(s,t,t0,n,j)):not(is(t,t0))
-t22:=tris(wb(s),wb(t),t,i,t8(t,t20,t21)):is(wb(s),t)
-t23:=<tris1(t,s0,wb(s),t22,t3(j))>t20:con
-n@t24:=[v:is(s,t0)]t23(v):not(is(s,t0))
-t25:=t24(t,s,symis(wb(s),wb(t),i),symnotis(s,t,n)):not(is(t,t0))
-t26:=tris(wb(s),wb(t),t,i,t8(t,t20,t25)):is(wb(s),t)
-t27:=<tris1(s,t,wb(s),t8(t19,t24),t26)>n:con
-i@t28:=et(is(s,t),[v:not(is(s,t))]t27(v)):is(s,t)
-t0@th1:=[x:sigma][y:sigma][v:is(wb(x),wb(y))]t28(x,y,v):injective(sigma,sigma,wissel)
-s@[i:is(s,s0)]
-t29:=tris2(s,wb(t0),s0,i,t3(t0,refis(t0))):is(s,wb(t0))
-t30:=somei(sigma,[x:sigma]is(s,wb(x)),t0,t29):image(sigma,sigma,wissel,s)
-s@[i:is(s,t0)]
-t31:=tris2(s,wb(s0),t0,i,t7(s0,refis(s0))):is(s,wb(s0))
-t32:=somei(sigma,[x:sigma]is(s,wb(x)),s0,t31):image(sigma,sigma,wissel,s)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-t33:=symis(wb(s),s,t8(n,o)):is(s,wb(s))
-t34:=somei(sigma,[x:sigma]is(s,wb(x)),s,t33):image(sigma,sigma,wissel,s)
-n@t35:=th1"l.imp"(is(s,t0),image(sigma,sigma,wissel,s),[v:is(s,t0)]t32(v),[v:not(is(s,t0))]t34(v)):image(sigma,sigma,wissel,s)
-s@t36:=th1"l.imp"(is(s,s0),image(sigma,sigma,wissel,s),[v:is(s,s0)]t30(v),[v:not(is(s,s0))]t35(v)):image(sigma,sigma,wissel,s)
-t0@th2:=[x:sigma]t36(x):surjective(sigma,sigma,wissel)
-th3:=andi(injective(sigma,sigma,wissel),surjective(sigma,sigma,wissel),th1,th2):bijective(sigma,sigma,wissel)
--wissel
-tau@[f:[x:sigma]tau][s0:sigma][t0:sigma]
-changef:=[x:sigma]<<x>wissel(s0,t0)>f:[x:sigma]tau
-[s:sigma][i:is(s,s0)]
-changef1:=isf(sigma,tau,f,<s>wissel(s0,t0),t0,iswissel1(s0,t0,s,i)):is(tau,<s>changef,<t0>f)
-s@[i:is(s,t0)]
-changef2:=isf(sigma,tau,f,<s>wissel(s0,t0),s0,iswissel2(s0,t0,s,i)):is(tau,<s>changef,<s0>f)
-s@[n:not(is(s,s0))][o:not(is(s,t0))]
-changef3:=isf(sigma,tau,f,<s>wissel(s0,t0),s,iswissel3(s0,t0,s,n,o)):is(tau,<s>changef,<s>f)
-+*wissel
-t0@[i:injective(f)]
-th4:=th4"e.inj"(sigma,sigma,tau,wissel(s0,t0),f,th1(s0,t0),i):injective(changef)
-t0@[s:surjective(f)]
-th5:=th1"e.surj"(sigma,sigma,tau,wissel(s0,t0),f,th2(s0,t0),s):surjective(changef)
-t0@[b:bijective(f)]
-th6:=th1"e.bij"(sigma,sigma,tau,wissel(s0,t0),f,th3(s0,t0),b):bijective(changef)
--wissel
--e
-+r
-a@[b:[x:a]'prop']
-%suggestion by van Daalen to remove the second eta-reduction
-%imp:=b:'prop' %original line
-imp:=[x:a]<x>b:'prop'
-%end of suggestion
-[a1:a][i:imp(a,b)]
-mp:=<a1>i:<a1>b
-+imp
-b@[n:not(a)]
-%set etared
-th2:=[x:a]cone(<x>b,mp"l"(a,con,x,n)):imp(a,b)
-%reset etared
--imp
-b@ec:=[x:a]not(<x>b):'prop'
-[n:not(a)]
-eci1:=[x:a]cone(not(<x>b),mp"l"(a,con,x,n)):ec(a,b)
-%suggestion by Guidi to remove @-typing by adding imp-introduction
-b@[a1:and(a,b)] %original line
-ande2:=<ande1(a,b,a1)>ande2"l"(a,b,a1):<ande1(a,b,a1)>b %original line
-%b@[a1:and(a,imp(a,b))]
-%ande2:=<ande1(a,imp(a,b),a1)>ande2"l"(a,imp(a,b),a1):<ande1(a,imp(a,b),a1)>b
-%end of suggestion
-a@[ksi:'type']
-+ite
-[x1:ksi][y1:ksi]
-is:=is"l.e"(ksi,x1,y1):'prop'
--ite
-[x:[t:a]ksi][y:[t:not(a)]ksi][i:[t:a][u:a]is".ite"(<t>x,<u>x)][j:[t:not(a)][u:not(a)]is".ite"(<t>y,<u>y)]
-+*ite
-j@[z:ksi]
-prop1:=and(imp(a,[t:a]is(z,<t>x)),imp(not(a),[t:not(a)]is(z,<t>y))):'prop'
-j@[a1:a][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t1:=ande1"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(a,[t:a]is(x1,<t>x))
-t2:=mp(a,[t:a]is(x1,<t>x),a1,t1):is(x1,<a1>x)
-t3:=t2(y1,x1,py1,px1):is(y1,<a1>x)
-t4:=tris2"l.e"(ksi,x1,y1,<a1>x,t2,t3):is(x1,y1)
-a1@t5:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t4(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
-t6:=<a1>i:imp(a,[t:a]is(<a1>x,<t>x))
-t7:=th2"r.imp"(not(a),[t:not(a)]is(<a1>x,<t>y),weli(a,a1)):imp(not(a),[t:not(a)]is(<a1>x,<t>y))
-t8:=andi(imp(a,[t:a]is(<a1>x,<t>x)),imp(not(a),[t:not(a)]is(<a1>x,<t>y)),t6,t7):prop1(<a1>x)
-t9:=somei(ksi,[t:ksi]prop1(t),<a1>x,t8):some(ksi,[t:ksi]prop1(t))
-t10:=onei"l.e"(ksi,[t:ksi]prop1(t),t5,t9):one"l.e"(ksi,[t:ksi]prop1(t))
-j@[n:not(a)][x1:ksi][y1:ksi][px1:prop1(x1)][py1:prop1(y1)]
-t11:=ande2"l"(imp(a,[t:a]is(x1,<t>x)),imp(not(a),[t:not(a)]is(x1,<t>y)),px1):imp(not(a),[t:not(a)]is(x1,<t>y))
-t12:=mp(not(a),[t:not(a)]is(x1,<t>y),n,t11):is(x1,<n>y)
-t13:=t12(y1,x1,py1,px1):is(y1,<n>y)
-t14:=tris2"l.e"(ksi,x1,y1,<n>y,t12,t13):is(x1,y1)
-n@t15:=[s:ksi][t:ksi][ps:prop1(s)][pt:prop1(t)]t14(s,t,ps,pt):amone"l.e"(ksi,[t:ksi]prop1(t))
-t16:=<n>j:imp(not(a),[t:not(a)]is(<n>y,<t>y))
-t17:=th2"r.imp"(a,[t:a]is(<n>y,<t>x),n):imp(a,[t:a]is(<n>y,<t>x))
-t18:=andi"l"(imp(a,[t:a]is(<n>y,<t>x)),imp(not(a),[t:not(a)]is(<n>y,<t>y)),t17,t16):prop1(<n>y)
-t19:=somei(ksi,[t:ksi]prop1(t),<n>y,t18):some(ksi,[t:ksi]prop1(t))
-t20:=onei"l.e"(ksi,[t:ksi]prop1(t),t15,t19):one"l.e"(ksi,[t:ksi]prop1(t))
-j@t21:=th1"l.imp"(a,one"l.e"(ksi,[t:ksi]prop1(t)),[t:a]t10(t),[t:not(a)]t20(t)):one"l.e"(ksi,[t:ksi]prop1(t))
--ite
-j@ite:=ind"l.e"(ksi,[t:ksi]prop1".ite"(t),t21".ite"):ksi
-+*ite
-j@t22:=oneax"l.e"(ksi,[t:ksi]prop1(t),t21):prop1(ite)
-t23:=ande1"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(a,[t:a]is(ite,<t>x))
-t24:=ande2"l"(imp(a,[t:a]is(ite,<t>x)),imp(not(a),[t:not(a)]is(ite,<t>y)),t22):imp(not(a),[t:not(a)]is(ite,<t>y))
--ite
-j@[a1:a]
-itet:=mp(a,[t:a]is".ite"(ite,<t>x),a1,t23".ite"):is".ite"(ksi,ite,<a1>x)
-j@[n:not(a)]
-itef:=mp(not(a),[t:not(a)]is".ite"(ite,<t>y),n,t24".ite"):is".ite"(ksi,ite,<n>y)
--r
-+*e
-+st
-sigma@set:='prim':'type'
-[s:sigma][s0:set]
-esti:='prim':'prop'
-p@setof:='prim':set
-[s:sigma][sp:<s>p]
-estii:='prim':esti(s,setof(p))
-s@[e:esti(s,setof(p))]
-estie:='prim':<s>p
-sigma@[s0:set]
-empty:=non([x:sigma]esti(x,s0)):'prop'
-nonempty:=some([x:sigma]esti(x,s0)):'prop'
-[n:[x:sigma]not(esti(x,s0))]
-emptyi:=n:empty(s0)
-s0@[e:empty(s0)][s:sigma]
-emptye:=<s>e:not(esti(s,s0))
-s0@[s:sigma][ses0:esti(s,s0)]
-nonemptyi:=somei([x:sigma]esti(x,s0),s,ses0):nonempty(s0)
-s0@[n:nonempty(s0)][x:'prop'][x1:[y:sigma][z:esti(y,s0)]x]
-nonemptyapp:=someapp([y:sigma]esti(y,s0),n,x,x1):x
-s0@[t0:set]
-incl:=all([x:sigma]imp(esti(x,s0),esti(x,t0))):'prop'
-[e:[x:sigma][y:esti(x,s0)]esti(x,t0)]
-incli:=e:incl(s0,t0)
-t0@[i:incl(s0,t0)][s:sigma][ses0:esti(s,s0)]
-incle:=<ses0><s>i:esti(s,t0)
-s0@refincl:=[x:sigma][y:esti(x,s0)]y:incl(s0,s0)
-t0@disj:=all([x:sigma]ec(esti(x,s0),esti(x,t0))):'prop'
-[n:[x:sigma][y:esti(x,s0)]not(esti(x,t0))]
-disji1:=n:disj(s0,t0)
-t0@[n:[x:sigma][y:esti(x,t0)]not(esti(x,s0))]
-disji2:=[x:sigma]th2"l.ec"(esti(x,s0),esti(x,t0),<x>n):disj(s0,t0)
-t0@[d:disj(s0,t0)][s:sigma][ses0:esti(s,s0)]
-disje1:=ece1(esti(s,s0),esti(s,t0),<s>d,ses0):not(esti(s,t0))
-s@[set0:esti(s,t0)]
-disje2:=ece2(esti(s,s0),esti(s,t0),<s>d,set0):not(esti(s,s0))
-t0@[d:disj(s0,t0)]
-symdisj:=[x:sigma][y:esti(x,t0)]disje2(d,x,y):disj(t0,s0)
-+disj
-t0@[s:sigma][ses0:esti(s,s0)][set0:esti(s,t0)]
-th1:=th1"l.all"([x:sigma]ec(esti(x,s0),esti(x,t0)),s,th4"l.imp"(esti(s,s0),not(esti(s,t0)),ses0,weli(esti(s,t0),set0))):not(disj(s0,t0))
-th2:=th1(t0,s0,s,set0,ses0):not(disj(t0,s0))
--disj
-t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
-issete1:=isp(set,[x:set]esti(s,x),s0,t0,ses0,i):esti(s,t0)
-s@[set0:esti(s,t0)]
-issete2:=isp1(set,[x:set]esti(s,x),t0,s0,set0,i):esti(s,s0)
-+isset
-i@th1:=[x:sigma][y:esti(x,s0)]issete1(x,y):incl(s0,t0)
-th2:=[x:sigma][y:esti(x,t0)]issete2(x,y):incl(t0,s0)
--isset
-t0@[i:incl(s0,t0)][j:incl(t0,s0)]
-isseti:='prim':is(set,s0,t0)
-+*isset
-t0@[s:sigma][ses0:esti(s,s0)][n:not(esti(s,t0))]
-th3:=th3"l.imp"(is(set,s0,t0),esti(s,t0),n,[t:is(set,s0,t0)]issete1(t,s,ses0)):not(is(set,s0,t0))
-th4:=symnotis(set,s0,t0,th3):not(is(set,t0,s0))
-s@nissetprop:=and(esti(s,s0),not(esti(s,t0))):'prop'
-[n:not(nissetprop(s0,t0,s))][e:esti(s,s0)]
-t1:=et(esti(s,t0),th3"l.and"(esti(s,s0),not(esti(s,t0)),n,e)):esti(s,t0)
-t0@[n:not(is(set,s0,t0))][m:not(some([x:sigma]nissetprop(s0,t0,x)))][l:non([x:sigma]nissetprop(t0,s0,x))][s:sigma]
-t2:=th4"l.some"([x:sigma]nissetprop(s0,t0,x),m,s):not(nissetprop(s0,t0,s))
-t3:=<s>l:not(nissetprop(t0,s0,s))
-l@t4:=isseti(s0,t0,[x:sigma][y:esti(x,s0)]t1(s0,t0,x,t2(x),y),[x:sigma][y:esti(x,t0)]t1(t0,s0,x,t3(x),y)):is(set,s0,t0)
-m@t5:=th3"l.imp"(non([x:sigma]nissetprop(t0,s0,x)),is(set,s0,t0),n,[y:non([x:sigma]nissetprop(t0,s0,x))]t4(y)):some([x:sigma]nissetprop(t0,s0,x))
-n@th5:=th1"l.or"(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)),[y:not(some([x:sigma]nissetprop(s0,t0,x)))]t5(y)):or(some([x:sigma]nissetprop(s0,t0,x)),some([x:sigma]nissetprop(t0,s0,x)))
--isset
-sigma@[alpha:'type'][sa:[x:alpha]set]
-unmore:=setof([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa))):set
-[s:sigma][a:alpha][seasa:esti(s,<a>sa)]
-eunmore1:=estii([x:sigma]some(alpha,[y:alpha]esti(x,<y>sa)),s,somei(alpha,[y:alpha]esti(s,<y>sa),a,seasa)):esti(s,unmore(sa))
-s@[seun:esti(s,unmore(sa))][x:'prop'][x1:[y:alpha][z:esti(s,<y>sa)]x]
-unmoreapp:=someapp(alpha,[y:alpha]esti(s,<y>sa),estie([z:sigma]some(alpha,[y:alpha]esti(z,<y>sa)),s,seun),x,x1):x
-+eq
-sigma@[r:[x:sigma][y:sigma]'prop'][refr1:[x:sigma]<x><x>r][symr1:[x:sigma][y:sigma][t:<y><x>r]<x><y>r][trr1:[x:sigma][y:sigma][z:sigma][t:<y><x>r][u:<z><y>r]<z><x>r][s:sigma]
-refr:=<s>refr1:<s><s>r
-[t:sigma][tsr:<t><s>r]
-symr:=<tsr><t><s>symr1:<s><t>r
-t@[u:sigma][tsr:<t><s>r][utr:<u><t>r]
-trr:=<utr><tsr><u><t><s>trr1:<u><s>r
-u@[sur:<s><u>r][tur:<t><u>r]
-tr1r:=trr(s,u,t,symr(u,s,sur),tur):<t><s>r
-u@[usr:<u><s>r][utr:<u><t>r]
-tr2r:=trr(s,u,t,usr,symr(t,u,utr)):<t><s>r
-s@ecelt:=setof(<s>r):set
-+1
-th1:=estii(<s>r,s,refr):esti(s,ecelt(s))
-t@[tsr:<t><s>r]
-th2:=estii(<s>r,t,tsr):esti(t,ecelt(s))
-t@[e:esti(t,ecelt(s))]
-th3:=estie(<s>r,t,e):<t><s>r
-tsr@[u:sigma][e:esti(u,ecelt(s))]
-t1:=th2(t,u,tr1r(t,u,s,tsr,th3(u,e))):esti(u,ecelt(t))
-tsr@th4:=isseti(ecelt(s),ecelt(t),[x:sigma][y:esti(x,ecelt(s))]t1(x,y),[x:sigma][y:esti(x,ecelt(t))]t1(t,s,symr(tsr),x,y)):is(set,ecelt(s),ecelt(t))
-t@[n:not(<t><s>r)][u:sigma][e:esti(u,ecelt(s))]
-t2:=th3"l.imp"(esti(u,ecelt(t)),<t><s>r,n,[x:esti(u,ecelt(t))]tr2r(s,t,u,th3(u,e),th3(t,u,x))):not(esti(u,ecelt(t)))
-n@th5:=[x:sigma][y:esti(x,ecelt(s))]t2(x,y):disj(ecelt(s),ecelt(t))
-s@th6:=nonemptyi(ecelt(s),s,th1):nonempty(ecelt(s))
--1
-trr1@[s0:set][s:sigma]
-ecp:=is(set,s0,ecelt(s)):'prop'
-s0@anec:=some([x:sigma]ecp(x)):'prop'
-+2
-trr1@[s:sigma]
-th1:=somei([x:sigma]ecp(ecelt(s),x),s,refis(set,ecelt(s))):anec(ecelt(s))
--2
-[ecs0:anec(s0)]
-+*2
-ecs0@[s:sigma][ses0:esti(s,s0)][t:sigma][e:ecp(s0,t)]
-t1:=issete1(s0,ecelt(t),e,s,ses0):esti(s,ecelt(t))
-t2:=th4"eq.1"(t,s,th3"eq.1"(t,s,t1)):is(set,ecelt(t),ecelt(s))
-t3:=tris(set,s0,ecelt(t),ecelt(s),e,t2):is(set,s0,ecelt(s))
-ses0@th2:=someapp([x:sigma]ecp(x),ecs0,is(set,s0,ecelt(s)),[x:sigma][y:ecp(x)]t3(x,y)):is(set,s0,ecelt(s))
-[t:sigma][tes0:esti(t,s0)]
-th3:=th3"eq.1"(s,t,issete1(s0,ecelt(s),th2,t,tes0)):<t><s>r
-t@[tsr:<t><s>r]
-th4:=issete2(s0,ecelt(s),th2,t,th2"eq.1"(s,t,tsr)):esti(t,s0)
-ecs0@[s:sigma][e:ecp(s0,s)]
-t4:=isp(set,[x:set]nonempty(x),ecelt(s),s0,th6"eq.1"(s),symis(set,s0,ecelt(s),e)):nonempty(s0)
-ecs0@th5:=someapp([x:sigma]ecp(x),ecs0,nonempty(s0),[x:sigma][y:ecp(x)]t4(x,y)):nonempty(s0)
--2
-+3
-ecs0@[t0:set][ect0:anec(t0)][s:sigma][ses0:esti(s,s0)][t:sigma][tet0:esti(t,t0)][tsr:<t><s>r]
-th1:=tr3is(set,s0,ecelt(s),ecelt(t),t0,th2"eq.2"(s0,ecs0,s,ses0),th4"eq.1"(s,t,tsr),symis(set,t0,ecelt(t),th2"eq.2"(t0,ect0,t,tet0))):is(set,s0,t0)
-tet0@[n:not(<t><s>r)]
-t1:=isp1(set,[x:set]disj(x,ecelt(t)),ecelt(s),s0,th5"eq.1"(s,t,n),th2"eq.2"(s0,ecs0,s,ses0)):disj(s0,ecelt(t))
-th2:=isp1(set,[x:set]disj(s0,x),ecelt(t),t0,t1,th2"eq.2"(t0,ect0,t,tet0)):disj(s0,t0)
-t0@[i:is(set,s0,t0)][s:sigma][ses0:esti(s,s0)]
-t2:=issete1(s0,t0,i,s,ses0):esti(s,t0)
-t3:=th1"st.disj"(s0,t0,s,ses0,t2):not(disj(s0,t0))
-i@th3:=nonemptyapp(s0,th5"eq.2"(s0,ecs0),not(disj(s0,t0)),[x:sigma][y:esti(x,s0)]t3(x,y)):not(disj(s0,t0))
--3
-trr1@ect:=ot(set,[x:set]anec(x)):'type'
-ecs0@ectset:=out(set,[x:set]anec(x),s0,ecs0):ect
-trr1@[s:sigma]
-ectelt:=ectset(ecelt(s),th1".2"(s)):ect
-trr1@[e:ect]
-ecect:=in(set,[x:set]anec(x),e):set
-+4
-th1:=inp(set,[x:set]anec(x),e):anec(ecect(e))
-th2:=th5"eq.2"(ecect(e),th1):nonempty(ecect(e))
-[x:'prop'][x1:[y:sigma][z:esti(y,ecect(e))]x]
-th3:=nonemptyapp(ecect(e),th2,x,x1):x
-s@th4:=isinout(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s)):is(set,ecelt(s),ecect(ectelt(s)))
-th5:=issete1(ecelt(s),ecect(ectelt(s)),th4,s,th1"eq.1"(s)):esti(s,ecect(ectelt(s)))
-th6:=eunmore1(ect,[x:ect]ecect(x),s,ectelt(s),th5):esti(s,unmore(ect,[x:ect]ecect(x)))
-e@[s:sigma][see:esti(s,ecect(e))][t:sigma][tee:esti(t,ecect(e))]
-th7:=th3"eq.2"(ecect(e),th1,s,see,t,tee):<t><s>r
-t@[tsr:<t><s>r]
-th8:=th4"eq.2"(ecect(e),th1,s,see,t,tsr):esti(t,ecect(e))
--4
-+5
-[f:ect][i:is(ect,e,f)]
-th1:=isini(set,[x:set]anec(x),e,f,i):is(set,ecect(e),ecect(f))
-f@[i:is(set,ecect(e),ecect(f))]
-th2:=isine(set,[x:set]anec(x),e,f,i):is(ect,e,f)
-f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))][tsr:<t><s>r]
-th3:=th2(th1"eq.3"(ecect(e),th1"eq.4"(e),ecect(f),th1"eq.4"(f),s,see,t,tef,tsr)):is(ect,e,f)
-see@[i:is(ect,e,f)]
-th4:=issete1(ecect(e),ecect(f),th1(i),s,see):esti(s,ecect(f))
-tef@[i:is(ect,e,f)]
-th5:=th3"eq.2"(ecect(f),th1"eq.4"(f),s,th4(i),t,tef):<t><s>r
-trr1@[s:sigma][t:sigma][tsr:<t><s>r]
-th6:=isouti(set,[x:set]anec(x),ecelt(s),th1"eq.2"(s),ecelt(t),th1"eq.2"(t),th4"eq.1"(s,t,tsr)):is(ect,ectelt(s),ectelt(t))
--5
-trr1@[alpha:'type'][fu:[x:sigma]alpha]
-fixfu:=[x:sigma][y:sigma][z:<y><x>r]is(alpha,<x>fu,<y>fu):'prop'
-+10
-[ff:fixfu][e:ect][a1:alpha][s:sigma]
-prop1:=and(esti(s,ecect(e)),is(alpha,<s>fu,a1)):'prop'
-a1@prop2:=some([x:sigma]prop1(x)):'prop'
-e@[s:sigma][see:esti(s,ecect(e))]
-t1:=andi(esti(s,ecect(e)),is(alpha,<s>fu,<s>fu),see,refis(alpha,<s>fu)):prop1(<s>fu,s)
-t2:=somei([x:sigma]prop1(<s>fu,x),s,t1):prop2(<s>fu)
-t3:=somei(alpha,[x:alpha]prop2(x),<s>fu,t2):some(alpha,[x:alpha]prop2(x))
-e@t4:=th3"eq.4"(e,some(alpha,[x:alpha]prop2(x)),[x:sigma][y:esti(x,ecect(e))]t3(x,y)):some(alpha,[x:alpha]prop2(x))
-a1@[b1:alpha][pa1:prop2(a1)][pb1:prop2(b1)][s:sigma][pa1s:prop1(a1,s)][t:sigma][pb1t:prop1(b1,t)]
-t5:=ande1(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):esti(s,ecect(e))
-t6:=ande1(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):esti(t,ecect(e))
-t7:=th7"eq.4"(e,s,t5,t,t6):<t><s>r
-t8:=ande2(esti(s,ecect(e)),is(alpha,<s>fu,a1),pa1s):is(alpha,<s>fu,a1)
-t9:=ande2(esti(t,ecect(e)),is(alpha,<t>fu,b1),pb1t):is(alpha,<t>fu,b1)
-t10:=tr3is(alpha,a1,<s>fu,<t>fu,b1,symis(alpha,<s>fu,a1,t8),<t7><t><s>ff,t9):is(alpha,a1,b1)
-pa1s@t11:=someapp([x:sigma]prop1(b1,x),pb1,is(alpha,a1,b1),[x:sigma][y:prop1(b1,x)]t10(x,y)):is(alpha,a1,b1)
-pb1@t12:=someapp([x:sigma]prop1(a1,x),pa1,is(alpha,a1,b1),[x:sigma][y:prop1(a1,x)]t11(x,y)):is(alpha,a1,b1)
-e@t13:=[x:alpha][y:alpha][u:prop2(x)][v:prop2(y)]t12(x,y,u,v):amone(alpha,[x:alpha]prop2(x))
-t14:=onei(alpha,[x:alpha]prop2(x),t13,t4):one(alpha,[x:alpha]prop2(x))
--10
-e".10"@indeq:=ind(alpha,[x:alpha]prop2".10"(x),t14".10"):alpha
-+*10
-e@th1:=oneax(alpha,[x:alpha]prop2(x),t14):some([x:sigma]and(esti(x,ecect(e)),is(alpha,<x>fu,indeq)))
-[s:sigma][see:esti(s,ecect(e))]
-th2:=t12(<s>fu,indeq,t2(s,see),th1):is(alpha,<s>fu,indeq)
-ff@[s:sigma]
-th3:=th2(ectelt(s),s,th5"eq.4"(s)):is(alpha,<s>fu,indeq(ectelt(s)))
--10
-alpha@[fu2:[x:sigma][y:sigma]alpha]
-fixfu2:=[x:sigma][y:sigma][z:sigma][u:sigma][v:<y><x>r][w:<u><z>r]is(alpha,<z><x>fu2,<u><y>fu2):'prop'
-+11
-[ff2:fixfu2][s:sigma][t:sigma][tsr:<t><s>r][u:sigma]
-t1:=<refr(u)><tsr><u><u><t><s>ff2:is(alpha,<u><s>fu2,<u><t>fu2)
-tsr@t2:=fisi(sigma,alpha,<s>fu2,<t>fu2,[x:sigma]t1(x)):is([x:sigma]alpha,<s>fu2,<t>fu2)
-ff2@[e:ect]
-i:=indeq([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e):[x:sigma]alpha
-[s:sigma][t:sigma][tsr:<t><s>r][u:sigma][uee:esti(u,ecect(e))]
-t3:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,u,uee):is([x:sigma]alpha,<u>fu2,i)
-t4:=fise(alpha,<u>fu2,i,t3,s):is(alpha,<s><u>fu2,<s>i)
-t5:=fise(alpha,<u>fu2,i,t3,t):is(alpha,<t><u>fu2,<t>i)
-t6:=<tsr><refr(u)><t><s><u><u>ff2:is(alpha,<s><u>fu2,<t><u>fu2)
-t7:=tr3is(alpha,<s>i,<s><u>fu2,<t><u>fu2,<t>i,symis(alpha,<s><u>fu2,<s>i,t4),t6,t5):is(alpha,<s>i,<t>i)
-tsr@t8:=th3"eq.4"(e,is(alpha,<s>i,<t>i),[x:sigma][y:esti(x,ecect(e))]t7(x,y)):is(alpha,<s>i,<t>i)
--11
-e".11"@[f:ect]
-indeq2:=indeq(i".11",[x:sigma][y:sigma][z:<y><x>r]t8".11"(x,y,z),f):alpha
-+*11
-f@[s:sigma][see:esti(s,ecect(e))][t:sigma][tef:esti(t,ecect(f))]
-t9:=th2"eq.10"(i,[x:sigma][y:sigma][z:<y><x>r]t8(x,y,z),f,t,tef):is(alpha,<t>i,indeq2(e,f))
-t10:=th2"eq.10"([x:sigma]alpha,fu2,[x:sigma][y:sigma][z:<y><x>r]t2(x,y,z),e,s,see):is([x:sigma]alpha,<s>fu2,i)
-t11:=fise(alpha,<s>fu2,i,t10,t):is(alpha,<t><s>fu2,<t>i)
-th1:=tris(alpha,<t><s>fu2,<t>i,indeq2,t11,t9):is(alpha,<t><s>fu2,indeq2(e,f))
-ff2@[s:sigma][t:sigma]
-th2:=th1(ectelt(s),ectelt(t),s,th5"eq.4"(s),t,th5"eq.4"(t)):is(alpha,<t><s>fu2,indeq2(ectelt(s),ectelt(t)))
--11
-+landau
-+n
-@nat:='prim':'type'
-[x:nat][y:nat]
-is:=is"e"(nat,x,y):'prop'
-nis:=not(is(x,y)):'prop'
-x@[s:set(nat)]
-in:=esti(nat,x,s):'prop'
-@[p:[x:nat]'prop']
-some:=some"l"(nat,p):'prop'
-all:=all"l"(nat,p):'prop'
-one:=one"e"(nat,p):'prop'
-@1:='prim':nat
-suc:='prim':[x:nat]nat
-[x:nat][y:nat][i:is(x,y)]
-ax2:=isf(nat,nat,suc,x,y,i):is(<x>suc,<y>suc)
-@ax3:='prim':[x:nat]nis(<x>suc,1)
-ax4:='prim':[x:nat][y:nat][u:is(<x>suc,<y>suc)]is(x,y)
-[s:set(nat)]
-cond1:=in(1,s):'prop'
-cond2:=all([x:nat]imp(in(x,s),in(<x>suc,s))):'prop'
-@ax5:='prim':[s:set(nat)][u:cond1(s)][v:cond2(s)][x:nat]in(x,s)
-[p:[x:nat]'prop'][1p:<1>p][xsp:[x:nat][y:<x>p]<<x>suc>p][x:nat]
-+i1
-s:=setof(nat,p):set(nat)
-t1:=estii(nat,p,1,1p):cond1(s)
-[y:nat][yes:in(y,s)]
-t2:=estie(nat,p,y,yes):<y>p
-t3:=estii(nat,p,<y>suc,<t2><y>xsp):in(<y>suc,s)
-x@t4:=<x><[y:nat][u:in(y,s)]t3(y,u)><t1><s>ax5:in(x,s)
--i1
-induction:=estie(nat,p,x,t4".i1"):<x>p
-@[x:nat][y:nat][n:nis(x,y)]
-+21
-[i:is(<x>suc,<y>suc)]
-t1:=<i><y><x>ax4:is(x,y)
--21
-satz1:=th3"l.imp"(is(<x>suc,<y>suc),is(x,y),n,[u:is(<x>suc,<y>suc)]t1".21"(u)):nis(<x>suc,<y>suc)
-+22
-x@prop1:=nis(<x>suc,x):'prop'
-@t1:=<1>ax3:prop1(1)
-x@[p:prop1(x)]
-t2:=satz1(<x>suc,x,p):prop1(<x>suc)
--22
-x@satz2:=induction([y:nat]prop1".22"(y),t1".22",[y:nat][u:prop1".22"(y)]t2".22"(y,u),x):nis(<x>suc,x)
-+23
-prop1:=or(is(x,1),some([u:nat]is(x,<u>suc))):'prop'
-@t1:=ori1(is(1,1),some([u:nat]is(1,<u>suc)),refis(nat,1)):prop1(1)
-x@t2:=somei(nat,[u:nat]is(<x>suc,<u>suc),x,refis(nat,<x>suc)):some([u:nat]is(<x>suc,<u>suc))
-t3:=ori2(is(<x>suc,1),some([u:nat]is(<x>suc,<u>suc)),t2):prop1(<x>suc)
-t4:=induction([y:nat]prop1(y),t1,[y:nat][u:prop1(y)]t3(y),x):prop1(x)
--23
-[n:nis(x,1)]
-satz3:=ore2(is(x,1),some([u:nat]is(x,<u>suc)),t4".23",n):some([u:nat]is(x,<u>suc))
-y@[z:nat][i:is(x,<y>suc)][j:is(x,<z>suc)]
-+*23
-j@t5:=<tris1(nat,<y>suc,<z>suc,x,i,j)><z><y>ax4:is(y,z)
-x@t6:=[y:nat][z:nat][u:is(x,<y>suc)][v:is(x,<z>suc)]t5(y,z,u,v):amone(nat,[u:nat]is(x,<u>suc))
--23
-n@satz3a:=onei(nat,[u:nat]is(x,<u>suc),t6".23",satz3):one([u:nat]is(x,<u>suc))
-+24
-x@[f:[y:nat]nat]
-prop1:=all([y:nat]is(<<y>suc>f,<<y>f>suc)):'prop'
-prop2:=and(is(<1>f,<x>suc),prop1):'prop'
-x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
-prop3:=is(<y>a,<y>b):'prop'
-pb@t1:=ande1(is(<1>a,<x>suc),prop1(a),pa):is(<1>a,<x>suc)
-t2:=ande1(is(<1>b,<x>suc),prop1(b),pb):is(<1>b,<x>suc)
-t3:=tris2(nat,<1>a,<1>b,<x>suc,t1,t2):prop3(1)
-y@[p:prop3(y)]
-t4:=ax2(<y>a,<y>b,p):is(<<y>a>suc,<<y>b>suc)
-t5:=ande2(is(<1>a,<x>suc),prop1(a),pa):prop1(a)
-t6:=ande2(is(<1>b,<x>suc),prop1(b),pb):prop1(b)
-t7:=<y>t5:is(<<y>suc>a,<<y>a>suc)
-t8:=<y>t6:is(<<y>suc>b,<<y>b>suc)
-t9:=tr3is(nat,<<y>suc>a,<<y>a>suc,<<y>b>suc,<<y>suc>b,t7,t4,symis"e"(nat,<<y>suc>b,<<y>b>suc,t8)):prop3(<y>suc)
-y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
-pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
-x@aa:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
-prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
-@t12:=[x:nat]refis(nat,<<x>suc>suc):prop1(1,suc)
-t13:=andi(is(<1>suc,<1>suc),prop1(1,suc),refis(nat,<1>suc),t12):prop2(1,suc)
-t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),suc,t13):prop4(1)
-x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
-g:=[y:nat]<<y>f>suc:[y:nat]nat
-[y:nat]
-t15:=refis(nat,<y>g):is(<y>g,<<y>f>suc)
-pf@t16:=ande1(is(<1>f,<x>suc),prop1(f),pf):is(<1>f,<x>suc)
-t17:=tris(nat,<1>g,<<1>f>suc,<<x>suc>suc,t15(1),ax2(<1>f,<x>suc,t16)):is(<1>g,<<x>suc>suc)
-y@t18:=ande2(is(<1>f,<x>suc),prop1(f),pf):prop1(f)
-t19:=<y>t18:is(<<y>suc>f,<<y>f>suc)
-t20:=tris2(nat,<<y>suc>f,<y>g,<<y>f>suc,t19,t15):is(<<y>suc>f,<y>g)
-t21:=tris(nat,<<y>suc>g,<<<y>suc>f>suc,<<y>g>suc,t15(<y>suc),ax2(<<y>suc>f,<y>g,t20)):is(<<y>suc>g,<<y>g>suc)
-pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
-t23:=andi(is(<1>g,<<x>suc>suc),prop1(<x>suc,g),t17,t22):prop2(<x>suc,g)
-t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
-p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
-x@bb:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
--24
-x@satz4:=onei([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),aa".24",bb".24"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,<x>suc),all([y:nat]is(<<y>suc>z,<<y>z>suc))))
-plus:=ind([y:nat]nat,[z:[y:nat]nat]prop2".24"(z),satz4):[y:nat]nat
-y@pl:=<y>plus:nat
-+*24
-x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz4):prop2(plus)
--24
-x@satz4a:=ande1(is(<1>plus,<x>suc),prop1".24"(plus),t26".24"):is(pl(x,1),<x>suc)
-+*24
-x@t27:=ande2(is(<1>plus,<x>suc),prop1(plus),t26):prop1(plus)
--24
-y@satz4b:=<y>t27".24":is(pl(x,<y>suc),<pl(x,y)>suc)
-+*24
-@t28:=t11(1,plus(1),suc,t26(1),t13):is"e"([y:nat]nat,plus(1),suc)
--24
-x@satz4c:=fise(nat,nat,plus(1),suc,t28".24",x):is(pl(1,x),<x>suc)
-+*24
-x@t29:=t11(<x>suc,plus(<x>suc),[y:nat]<<y>plus>suc,t26(<x>suc),t23(bb,plus,t26)):is"e"([y:nat]nat,plus(<x>suc),[y:nat]<<y>plus>suc)
--24
-y@satz4d:=fise(nat,nat,plus(<x>suc),[z:nat]<<z>plus>suc,t29".24",y):is(pl(<x>suc,y),<pl(x,y)>suc)
-x@satz4e:=symis(nat,pl(x,1),<x>suc,satz4a):is(<x>suc,pl(x,1))
-y@satz4f:=symis(nat,pl(x,<y>suc),<pl(x,y)>suc,satz4b):is(<pl(x,y)>suc,pl(x,<y>suc))
-x@satz4g:=symis(nat,pl(1,x),<x>suc,satz4c):is(<x>suc,pl(1,x))
-y@satz4h:=symis(nat,pl(<x>suc,y),<pl(x,y)>suc,satz4d):is(<pl(x,y)>suc,pl(<x>suc,y))
-z@[i:is(x,y)]
-ispl1:=isf(nat,nat,[u:nat]pl(u,z),x,y,i):is(pl(x,z),pl(y,z))
-ispl2:=isf(nat,nat,[u:nat]pl(z,u),x,y,i):is(pl(z,x),pl(z,y))
-z@[u:nat][i:is(x,y)][j:is(z,u)]
-ispl12:=tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
-+25
-z@prop1:=is(pl(pl(x,y),z),pl(x,pl(y,z))):'prop'
-y@t1:=tr3is(nat,pl(pl(x,y),1),<pl(x,y)>suc,pl(x,<y>suc),pl(x,pl(y,1)),satz4a(pl(x,y)),satz4f,ispl2(<y>suc,pl(y,1),x,satz4e(y))):prop1(1)
-z@[p:prop1(z)]
-t2:=ax2(pl(pl(x,y),z),pl(x,pl(y,z)),p):is(<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc)
-t3:=tr4is(nat,pl(pl(x,y),<z>suc),<pl(pl(x,y),z)>suc,<pl(x,pl(y,z))>suc,pl(x,<pl(y,z)>suc),pl(x,pl(y,<z>suc)),satz4b(pl(x,y),z),t2,satz4f(x,pl(y,z)),ispl2(<pl(y,z)>suc,pl(y,<z>suc),x,satz4f(y,z))):prop1(<z>suc)
--25
-z@satz5:=induction([u:nat]prop1".25"(u),t1".25",[u:nat][v:prop1".25"(u)]t3".25"(u,v),z):is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl1:=satz5:is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl2:=symis(nat,pl(pl(x,y),z),pl(x,pl(y,z)),satz5):is(pl(x,pl(y,z)),pl(pl(x,y),z))
-+26
-y@prop1:=is(pl(x,y),pl(y,x)):'prop'
-t1:=satz4a(y):is(pl(y,1),<y>suc)
-t2:=satz4c(y):is(pl(1,y),<y>suc)
-t3:=tris2(nat,pl(1,y),pl(y,1),<y>suc,t2,t1):prop1(1,y)
-[p:prop1(x,y)]
-t4:=tris(nat,<pl(x,y)>suc,<pl(y,x)>suc,pl(y,<x>suc),ax2(pl(x,y),pl(y,x),p),satz4f(y,x)):is(<pl(x,y)>suc,pl(y,<x>suc))
-t5:=satz4d:is(pl(<x>suc,y),<pl(x,y)>suc)
-t6:=tris(nat,pl(<x>suc,y),<pl(x,y)>suc,pl(y,<x>suc),t5,t4):prop1(<x>suc,y)
--26
-y@satz6:=induction([z:nat]prop1".26"(z,y),t3".26",[z:nat][u:prop1".26"(z,y)]t6".26"(z,y,u),x):is(pl(x,y),pl(y,x))
-compl:=satz6:is(pl(x,y),pl(y,x))
-+*26
-x@t7:=tris(nat,pl(x,1),<x>suc,pl(1,x),satz4a,satz4g):prop1(1)
-y@[p:prop1(y)]
-t8:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,<pl(y,x)>suc,pl(<y>suc,x),satz4b,ax2(pl(x,y),pl(y,x),p),satz4h(y,x)):prop1(<y>suc)
-y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(pl(x,y),pl(y,x))
--26
-+27
-y@prop1:=nis(y,pl(x,y)):'prop'
-x@t1:=symnotis(nat,<x>suc,1,<x>ax3):nis(1,<x>suc)
-t2:=th4"e.notis"(nat,1,<x>suc,pl(x,1),t1,satz4a):prop1(1)
-y@[p:prop1(y)]
-t3:=satz1(y,pl(x,y),p):nis(<y>suc,<pl(x,y)>suc)
-t4:=th4"e.notis"(nat,<y>suc,<pl(x,y)>suc,pl(x,<y>suc),t3,satz4b):prop1(<y>suc)
--27
-y@satz7:=induction([z:nat]prop1".27"(z),t2".27",[z:nat][u:prop1".27"(z)]t4".27"(z,u),y):nis(y,pl(x,y))
-z@[n:nis(y,z)]
-+28
-prop1:=nis(pl(x,y),pl(x,z)):'prop'
-t1:=satz1(y,z,n):nis(<y>suc,<z>suc)
-t2:=th5"e.notis"(nat,<y>suc,<z>suc,pl(1,y),pl(1,z),t1,satz4g(y),satz4g(z)):prop1(1,y,z,n)
-[p:prop1(x,y,z,n)]
-t3:=satz1(pl(x,y),pl(x,z),p):nis(<pl(x,y)>suc,<pl(x,z)>suc)
-t4:=th5"e.notis"(nat,<pl(x,y)>suc,<pl(x,z)>suc,pl(<x>suc,y),pl(<x>suc,z),t3,satz4h,satz4h(z)):prop1(<x>suc,y,z,n)
--28
-satz8:=induction([u:nat]prop1".28"(u,y,z,n),t2".28",[u:nat][v:prop1".28"(u,y,z,n)]t4".28"(u,y,z,n,v),x):nis(pl(x,y),pl(x,z))
-z@[i:is(pl(x,y),pl(x,z))]
-satz8a:=th7"l.imp"(is(y,z),nis(pl(x,y),pl(x,z)),weli(is(pl(x,y),pl(x,z)),i),[u:nis(y,z)]satz8(u)):is(y,z)
-z@diffprop:=is(x,pl(y,z)):'prop'
-+*28
-y@[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]
-t5:=satz8a(y,u,v,tris1(nat,pl(y,u),pl(y,v),x,du,dv)):is(u,v)
--28
-y@satz8b:=[u:nat][v:nat][du:diffprop(u)][dv:diffprop(v)]t5".28"(u,v,du,dv):amone(nat,[z:nat]is(x,pl(y,z)))
-+29
-i:=is(x,y):'prop'
-ii:=some([u:nat]diffprop(x,y,u)):'prop'
-iii:=some([v:nat]diffprop(y,x,v)):'prop'
-[one1:i][u:nat]
-t1:=tris(nat,pl(u,x),pl(x,u),pl(y,u),compl(u,x),ispl1(u,one1)):is(pl(u,x),pl(y,u))
-t2:=th3"e.notis"(nat,x,pl(u,x),pl(y,u),satz7(u,x),t1):nis(x,pl(y,u))
-one1@t3:=th5"l.some"(nat,[u:nat]diffprop(u),[u:nat]t2(u)):not(ii)
-y@t4:=th1"l.ec"(i,ii,[z:i]t3(z)):ec(i,ii)
-one1@t5:=t3(y,x,symis(nat,x,y,one1)):not(iii)
-y@t6:=th2"l.ec"(iii,i,[z:i]t5(z)):ec(iii,i)
-[two1:ii][three1:iii][u:nat][du:diffprop(x,y,u)][v:nat][dv:diffprop(y,x,v)]
-t6a:=tr4is(nat,x,pl(y,u),pl(pl(x,v),u),pl(x,pl(v,u)),pl(pl(v,u),x),du,ispl1(y,pl(x,v),u,dv),asspl1(x,v,u),compl(x,pl(v,u))):is(x,pl(pl(v,u),x))
-t7:=mp(is(x,pl(pl(v,u),x)),con,t6a,satz7(pl(v,u),x)):con
-du@t8:=someapp(nat,[v:nat]diffprop(y,x,v),three1,con,[v:nat][dv:diffprop(y,x,v)]t7(v,dv)):con
-three1@t9:=someapp(nat,[u:nat]diffprop(u),two1,con,[u:nat][du:diffprop(u)]t8(u,du)):con
-two1@t10:=[z:iii]t9(z):not(iii)
-y@t11:=th1"l.ec"(ii,iii,[z:ii]t10(z)):ec(ii,iii)
-a:=th6"l.ec3"(i,ii,iii,t4,t11,t6):ec3(i,ii,iii)
-prop1:=or3(i,ii,iii):'prop'
-x@[j:is(x,1)]
-t12:=or3i1(i(1),ii(1),iii(1),j):prop1(1)
-x@[n:nis(x,1)][u:nat][j:is(x,<u>suc)]
-t13:=tris(nat,x,<u>suc,pl(1,u),j,satz4g(u)):is(x,pl(1,u))
-t14:=somei(nat,[z:nat]diffprop(x,1,z),u,t13):ii(1)
-t15:=someapp(nat,[u1:nat]is(x,<u1>suc),satz3(x,n),ii(1),[u1:nat][z:is(x,<u1>suc)]t14(u1,z)):ii(1)
-t16:=or3i2(i(1),ii(1),iii(1),t15):prop1(1)
-n@t16a:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),prop1(1),[u:nat][v:is(x,<u>suc)]t16(u,v)):prop1(1)
-x@t17:=th1"l.imp"(is(x,1),prop1(1),[z:is(x,1)]t12(z),[z:nis(x,1)]t16a(z)):prop1(1)
-y@[p:prop1(y)][one1:i(y)]
-t18:=tris(nat,<y>suc,pl(y,1),pl(x,1),satz4e(y),ispl1(y,x,1,symis(nat,x,y,one1))):is(<y>suc,pl(x,1))
-t19:=somei(nat,[z:nat]diffprop(<y>suc,x,z),1,t18):iii(<y>suc)
-t20:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t19):prop1(<y>suc)
-p@[two1:ii(y)][u:nat][du:diffprop(x,y,u)][j:is(u,1)]
-t21:=tr3is(nat,x,pl(y,u),pl(y,1),<y>suc,du,ispl2(u,1,y,j),satz4a(y)):is(x,<y>suc)
-t22:=or3i1(i(<y>suc),ii(<y>suc),iii(<y>suc),t21):prop1(<y>suc)
-du@[n:nis(u,1)][w:nat][j:is(u,<w>suc)]
-t23:=tris(nat,u,<w>suc,pl(1,w),j,satz4g(w)):is(u,pl(1,w))
-t24:=tr4is(nat,x,pl(y,u),pl(y,pl(1,w)),pl(pl(y,1),w),pl(<y>suc,w),du,ispl2(u,pl(1,w),y,t23),asspl2(y,1,w),ispl1(pl(y,1),<y>suc,w,satz4a(y))):is(x,pl(<y>suc,w))
-t25:=somei(nat,[z:nat]diffprop(x,<y>suc,z),w,t24):ii(<y>suc)
-n@t26:=someapp(nat,[z:nat]is(u,<z>suc),satz3(u,n),ii(<y>suc),[z:nat][v:is(u,<z>suc)]t25(z,v)):ii(<y>suc)
-t27:=or3i2(i(<y>suc),ii(<y>suc),iii(<y>suc),t26):prop1(<y>suc)
-du@t28:=th1"l.imp"(is(u,1),prop1(<y>suc),[z:is(u,1)]t22(z),[z:nis(u,1)]t27(z)):prop1(<y>suc)
-two1@t28a:=someapp(nat,[u:nat]diffprop(u),two1,prop1(<y>suc),[u:nat][du:diffprop(u)]t28(u,du)):prop1(<y>suc)
-p@[three1:iii(y)][v:nat][dv:diffprop(y,x,v)]
-t29:=tris(nat,<y>suc,<pl(x,v)>suc,pl(x,<v>suc),ax2(y,pl(x,v),dv),satz4f(x,v)):is(<y>suc,pl(x,<v>suc))
-t30:=somei(nat,[z:nat]diffprop(<y>suc,x,z),<v>suc,t29):iii(<y>suc)
-three1@t31:=someapp(nat,[v:nat]diffprop(y,x,v),three1,iii(<y>suc),[v:nat][dv:diffprop(y,x,v)]t30(v,dv)):iii(<y>suc)
-t32:=or3i3(i(<y>suc),ii(<y>suc),iii(<y>suc),t31):prop1(<y>suc)
-p@t33:=or3app(i(y),ii(y),iii(y),prop1(<y>suc),p,[z:i(y)]t20(z),[z:ii(y)]t28a(z),[z:iii(y)]t32(z)):prop1(<y>suc)
-y@b:=induction([z:nat]prop1(z),t17,[z:nat][u:prop1(z)]t33(z,u),y):or3(i,ii,iii)
--29
-satz9:=orec3i(i".29",ii".29",iii".29",b".29",a".29"):orec3(is(x,y),some([u:nat]is(x,pl(y,u))),some([v:nat]is(y,pl(x,v))))
-satz9a:=b".29":or3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
-satz9b:=a".29":ec3(is(x,y),some([u:nat]diffprop(x,y,u)),some([v:nat]diffprop(y,x,v)))
-more:=some([u:nat]diffprop(x,y,u)):'prop'
-less:=some([v:nat]diffprop(y,x,v)):'prop'
-satz10:=satz9:orec3(is(x,y),more(x,y),less(x,y))
-satz10a:=satz9a:or3(is(x,y),more(x,y),less(x,y))
-satz10b:=satz9b:ec3(is(x,y),more(x,y),less(x,y))
-[m:more(x,y)]
-satz11:=m:less(y,x)
-y@[l:less(x,y)]
-satz12:=l:more(y,x)
-y@moreis:=or(more,is(x,y)):'prop'
-lessis:=or(less,is(x,y)):'prop'
-[m:moreis(x,y)]
-satz13:=th9"l.or"(more,is(x,y),less(y,x),is(y,x),m,[z:more]satz11(z),[z:is(x,y)]symis(nat,x,y,z)):lessis(y,x)
-y@[l:lessis(x,y)]
-satz14:=th9"l.or"(less,is(x,y),more(y,x),is(y,x),l,[z:less]satz12(z),[z:is(x,y)]symis(nat,x,y,z)):moreis(y,x)
-z@[i:is(x,y)][m:more(x,z)]
-ismore1:=isp(nat,[u:nat]more(u,z),x,y,m,i):more(y,z)
-i@[m:more(z,x)]
-ismore2:=isp(nat,[u:nat]more(z,u),x,y,m,i):more(z,y)
-i@[l:less(x,z)]
-isless1:=isp(nat,[u:nat]less(u,z),x,y,l,i):less(y,z)
-i@[l:less(z,x)]
-isless2:=isp(nat,[u:nat]less(z,u),x,y,l,i):less(z,y)
-i@[m:moreis(x,z)]
-ismoreis1:=isp(nat,[u:nat]moreis(u,z),x,y,m,i):moreis(y,z)
-i@[m:moreis(z,x)]
-ismoreis2:=isp(nat,[u:nat]moreis(z,u),x,y,m,i):moreis(z,y)
-i@[l:lessis(x,z)]
-islessis1:=isp(nat,[u:nat]lessis(u,z),x,y,l,i):lessis(y,z)
-i@[l:lessis(z,x)]
-islessis2:=isp(nat,[u:nat]lessis(z,u),x,y,l,i):lessis(z,y)
-y@[i:is(x,y)]
-moreisi2:=ori2(more(x,y),is(x,y),i):moreis(x,y)
-lessisi2:=ori2(less(x,y),is(x,y),i):lessis(x,y)
-y@[m:more(x,y)]
-moreisi1:=ori1(more(x,y),is(x,y),m):moreis(x,y)
-y@[l:less(x,y)]
-lessisi1:=ori1(less(x,y),is(x,y),l):lessis(x,y)
-z@[u:nat][i:is(x,y)][j:is(z,u)][m:more(x,z)]
-ismore12:=ismore2(z,u,y,j,ismore1(x,y,z,i,m)):more(y,u)
-j@[l:less(x,z)]
-isless12:=isless2(z,u,y,j,isless1(x,y,z,i,l)):less(y,u)
-j@[m:moreis(x,z)]
-ismoreis12:=ismoreis2(z,u,y,j,ismoreis1(x,y,z,i,m)):moreis(y,u)
-j@[l:lessis(x,z)]
-islessis12:=islessis2(z,u,y,j,islessis1(x,y,z,i,l)):lessis(y,u)
-y@[m:moreis(x,y)]
-satz10c:=th7"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,comor(more(x,y),is(x,y),m)):not(less(x,y))
-y@[l:lessis(x,y)]
-satz10d:=th9"l.ec3"(is(x,y),more(x,y),less(x,y),satz10b,l):not(more(x,y))
-y@[n:not(more(x,y))]
-satz10e:=th2"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n):lessis(x,y)
-y@[n:not(less(x,y))]
-satz10f:=comor(is(x,y),more(x,y),th3"l.or3"(is(x,y),more(x,y),less(x,y),satz10a,n)):moreis(x,y)
-y@[m:more(x,y)]
-satz10g:=th3"l.or"(less(x,y),is(x,y),ec3e23(is(x,y),more(x,y),less(x,y),satz10b,m),ec3e21(is(x,y),more(x,y),less(x,y),satz10b,m)):not(lessis(x,y))
-y@[l:less(x,y)]
-satz10h:=th3"l.or"(more(x,y),is(x,y),ec3e32(is(x,y),more(x,y),less(x,y),satz10b,l),ec3e31(is(x,y),more(x,y),less(x,y),satz10b,l)):not(moreis(x,y))
-y@[n:not(moreis(x,y))]
-satz10j:=or3e3(is(x,y),more(x,y),less(x,y),satz10a,th5"l.or"(more(x,y),is(x,y),n),th4"l.or"(more(x,y),is(x,y),n)):less(x,y)
-y@[n:not(lessis(x,y))]
-satz10k:=or3e2(is(x,y),more(x,y),less(x,y),satz10a,th4"l.or"(less(x,y),is(x,y),n),th5"l.or"(less(x,y),is(x,y),n)):more(x,y)
-z@[l:less(x,y)][k:less(y,z)]
-+315
-[v:nat][dv:diffprop(y,x,v)][w:nat][dw:diffprop(z,y,w)]
-t1:=tr3is(nat,z,pl(y,w),pl(pl(x,v),w),pl(x,pl(v,w)),dw,ispl1(y,pl(x,v),w,dv),asspl1(x,v,w)):is(z,pl(x,pl(v,w)))
-t2:=somei(nat,[u:nat]diffprop(z,x,u),pl(v,w),t1):less(x,z)
-dv@t3:=someapp(nat,[w:nat]diffprop(z,y,w),k,less(x,z),[w:nat][dw:diffprop(z,y,w)]t2(w,dw)):less(x,z)
--315
-satz15:=someapp(nat,[v:nat]diffprop(y,x,v),l,less(x,z),[v:nat][dv:diffprop(y,x,v)]t3".315"(v,dv)):less(x,z)
-trless:=satz15:less(x,z)
-z@[m:more(x,y)][n:more(y,z)]
-trmore:=satz15(z,y,x,n,m):more(x,z)
-+*315
-n@anders:=satz12(z,x,satz15(z,y,x,satz11(y,z,n),satz11(m))):more(x,z)
--315
-z@[l:lessis(x,y)][k:less(y,z)]
-satz16a:=orapp(less(x,y),is(x,y),less(x,z),l,[u:less(x,y)]trless(u,k),[u:is(x,y)]isless1(y,x,z,symis(nat,x,y,u),k)):less(x,z)
-z@[l:less(x,y)][k:lessis(y,z)]
-satz16b:=orapp(less(y,z),is(y,z),less(x,z),k,[u:less(y,z)]trless(l,u),[u:is(y,z)]isless2(y,z,x,u,l)):less(x,z)
-z@[m:moreis(x,y)][n:more(y,z)]
-satz16c:=satz16b(z,y,x,n,satz13(m)):more(x,z)
-z@[m:more(x,y)][n:moreis(y,z)]
-satz16d:=satz16a(z,y,x,satz13(y,z,n),m):more(x,z)
-z@[l:lessis(x,y)][k:lessis(y,z)]
-+317
-[i:is(x,y)][j:is(y,z)]
-t1:=lessisi2(x,z,tris(nat,x,y,z,i,j)):lessis(x,z)
-i@[j:less(y,z)]
-t2:=lessisi1(x,z,satz16a(l,j)):lessis(x,z)
-i@t3:=orapp(less(y,z),is(y,z),lessis(x,z),k,[u:less(y,z)]t2(u),[u:is(y,z)]t1(u)):lessis(x,z)
-k@[j:less(x,y)]
-t4:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
--317
-satz17:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t4".317"(u),[u:is(x,y)]t3".317"(u)):lessis(x,z)
-+*317
-k@[j:less(x,y)]
-t5:=lessisi1(x,z,satz16b(j,k)):lessis(x,z)
-k@[i:is(x,y)]
-t6:=islessis1(y,x,z,symis(nat,x,y,i),k):lessis(x,z)
-k@anders:=orapp(less(x,y),is(x,y),lessis(x,z),l,[u:less(x,y)]t5(u),[u:is(x,y)]t6(u)):lessis(x,z)
--317
-k@trlessis:=satz17:lessis(x,z)
-z@[m:moreis(x,y)][n:moreis(y,z)]
-trmoreis:=satz14(z,x,satz17(z,y,x,satz13(y,z,n),satz13(m))):moreis(x,z)
-y@satz18:=somei(nat,[u:nat]diffprop(pl(x,y),x,u),y,refis(nat,pl(x,y))):more(pl(x,y),x)
-satz18a:=satz18:less(x,pl(x,y))
-x@satz18b:=ismore1(pl(x,1),<x>suc,x,satz4a,satz18(1)):more(<x>suc,x)
-satz18c:=satz18b:less(x,<x>suc)
-z@[m:more(x,y)]
-+319
-[u:nat][du:diffprop(u)]
-t1:=tris(nat,x,pl(y,u),pl(u,y),du,compl(y,u)):is(x,pl(u,y))
-t2:=tr3is(nat,pl(x,z),pl(pl(u,y),z),pl(u,pl(y,z)),pl(pl(y,z),u),ispl1(x,pl(u,y),z,t1),asspl1(u,y,z),compl(u,pl(y,z))):is(pl(x,z),pl(pl(y,z),u))
-t3:=somei(nat,[v:nat]diffprop(pl(x,z),pl(y,z),v),u,t2):more(pl(x,z),pl(y,z))
--319
-satz19a:=someapp(nat,[u:nat]diffprop(u),m,more(pl(x,z),pl(y,z)),[u:nat][v:diffprop(u)]t3".319"(u,v)):more(pl(x,z),pl(y,z))
-z@[i:is(x,y)]
-satz19b:=ispl1(x,y,z,i):is(pl(x,z),pl(y,z))
-z@[l:less(x,y)]
-satz19c:=satz11(pl(y,z),pl(x,z),satz19a(y,x,z,satz12(x,y,l))):less(pl(x,z),pl(y,z))
-+*319
-l@anders1:=satz19a(y,x,z,l):less(pl(x,z),pl(y,z))
--319
-m@satz19d:=ismore12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19a):more(pl(z,x),pl(z,y))
-i@satz19e:=ispl2(x,y,z,i):is(pl(z,x),pl(z,y))
-l@satz19f:=isless12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19c):less(pl(z,x),pl(z,y))
-+*319
-l@anders2:=satz19d(y,x,z,l):less(pl(z,x),pl(z,y))
--319
-z@[u:nat][i:is(x,y)][m:more(z,u)]
-satz19g:=ismore2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19d(z,u,x,m)):more(pl(x,z),pl(y,u))
-satz19h:=ismore12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19g):more(pl(z,x),pl(u,y))
-i@[l:less(z,u)]
-satz19j:=isless2(pl(x,u),pl(y,u),pl(x,z),ispl1(x,y,u,i),satz19f(z,u,x,l)):less(pl(x,z),pl(y,u))
-satz19k:=isless12(pl(x,z),pl(z,x),pl(y,u),pl(u,y),compl(x,z),compl(y,u),satz19j):less(pl(z,x),pl(u,y))
-z@[m:moreis(x,y)]
-+*319
-m@[n:more(x,y)]
-t4:=moreisi1(pl(x,z),pl(y,z),satz19a(n)):moreis(pl(x,z),pl(y,z))
-m@[i:is(x,y)]
-t5:=moreisi2(pl(x,z),pl(y,z),ispl1(x,y,z,i)):moreis(pl(x,z),pl(y,z))
--319
-m@satz19l:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,z)),m,[u:more(x,y)]t4".319"(u),[u:is(x,y)]t5".319"(u)):moreis(pl(x,z),pl(y,z))
-satz19m:=ismoreis12(pl(x,z),pl(z,x),pl(y,z),pl(z,y),compl(x,z),compl(y,z),satz19l):moreis(pl(z,x),pl(z,y))
-z@[l:lessis(x,y)]
-satz19n:=satz13(pl(y,z),pl(x,z),satz19l(y,x,z,satz14(l))):lessis(pl(x,z),pl(y,z))
-satz19o:=satz13(pl(z,y),pl(z,x),satz19m(y,x,z,satz14(l))):lessis(pl(z,x),pl(z,y))
-+320
-z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
-t2:=satz10b(pl(x,z),pl(y,z)):ec3(is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)))
--320
-z@[m:more(pl(x,z),pl(y,z))]
-satz20a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),m):more(x,y)
-z@[i:is(pl(x,z),pl(y,z))]
-satz20b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),i):is(x,y)
-z@[l:less(pl(x,z),pl(y,z))]
-satz20c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(pl(x,z),pl(y,z)),more(pl(x,z),pl(y,z)),less(pl(x,z),pl(y,z)),t1".320",t2".320",[u:is(x,y)]satz19b(x,y,z,u),[u:more(x,y)]satz19a(x,y,z,u),[u:less(x,y)]satz19c(x,y,z,u),l):less(x,y)
-+*320
-i@t3:=tr3is(nat,pl(z,x),pl(x,z),pl(y,z),pl(z,y),compl(z,x),i,compl(y,z)):is(pl(z,x),pl(z,y))
-andersb:=satz8a(z,x,y,t3):is(x,y)
-l@andersc:=satz20a(y,x,z,l):less(x,y)
--320
-z@[m:more(pl(z,x),pl(z,y))]
-satz20d:=satz20a(ismore12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),m)):more(x,y)
-z@[i:is(pl(z,x),pl(z,y))]
-satz20e:=satz20b(tr3is(nat,pl(x,z),pl(z,x),pl(z,y),pl(y,z),compl(x,z),i,compl(z,y))):is(x,y)
-z@[l:less(pl(z,x),pl(z,y))]
-satz20f:=satz20c(isless12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y),l)):less(x,y)
-u@[m:more(x,y)][n:more(z,u)]
-+321
-t1:=satz19a(x,y,z,m):more(pl(x,z),pl(y,z))
-t2:=ismore12(pl(z,y),pl(y,z),pl(u,y),pl(y,u),compl(z,y),compl(u,y),satz19a(z,u,y,n)):more(pl(y,z),pl(y,u))
--321
-satz21:=trmore(pl(x,z),pl(y,z),pl(y,u),t1".321",t2".321"):more(pl(x,z),pl(y,u))
-+*321
-n@anders:=trmore(pl(x,z),pl(y,z),pl(y,u),satz19a(x,y,z,m),satz19d(z,u,y,n)):more(pl(x,z),pl(y,u))
--321
-u@[l:less(x,y)][k:less(z,u)]
-satz21a:=satz21(y,x,u,z,l,k):less(pl(x,z),pl(y,u))
-+*321
-k@andersa:=satz11(pl(y,u),pl(x,z),satz21(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(pl(x,z),pl(y,u))
--321
-u@[m:moreis(x,y)][n:more(z,u)]
-satz22a:=orapp(more(x,y),is(x,y),more(pl(x,z),pl(y,u)),m,[v:more(x,y)]satz21(v,n),[v:is(x,y)]satz19g(u,v,n)):more(pl(x,z),pl(y,u))
-u@[m:more(x,y)][n:moreis(z,u)]
-satz22b:=orapp(more(z,u),is(z,u),more(pl(x,z),pl(y,u)),n,[v:more(z,u)]satz21(m,v),[v:is(z,u)]satz19h(z,u,x,y,v,m)):more(pl(x,z),pl(y,u))
-u@[l:lessis(x,y)][k:less(z,u)]
-satz22c:=satz22a(y,x,u,z,satz14(x,y,l),k):less(pl(x,z),pl(y,u))
-u@[l:less(x,y)][k:lessis(z,u)]
-satz22d:=satz22b(y,x,u,z,l,satz14(z,u,k)):less(pl(x,z),pl(y,u))
-u@[m:moreis(x,y)][n:moreis(z,u)]
-+323
-[i:is(x,y)][j:is(z,u)]
-t1:=moreisi2(pl(x,z),pl(y,u),tris(nat,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j))):moreis(pl(x,z),pl(y,u))
-i@[o:more(z,u)]
-t2:=moreisi1(pl(x,z),pl(y,u),satz22a(m,o)):moreis(pl(x,z),pl(y,u))
-i@t3:=orapp(more(z,u),is(z,u),moreis(pl(x,z),pl(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(pl(x,z),pl(y,u))
-n@[o:more(x,y)]
-t4:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
--323
-satz23:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t4".323"(v),[v:is(x,y)]t3".323"(v)):moreis(pl(x,z),pl(y,u))
-+*323
-n@[o:more(x,y)]
-t5:=moreisi1(pl(x,z),pl(y,u),satz22b(o,n)):moreis(pl(x,z),pl(y,u))
-n@[i:is(x,y)]
-t6:=ismoreis2(pl(x,u),pl(y,u),pl(x,z),ispl1(u,i),satz19m(z,u,x,n)):moreis(pl(x,z),pl(y,u))
-n@anders:=orapp(more(x,y),is(x,y),moreis(pl(x,z),pl(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(pl(x,z),pl(y,u))
--323
-u@[l:lessis(x,y)][k:lessis(z,u)]
-satz23a:=satz13(pl(y,u),pl(x,z),satz23(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(pl(x,z),pl(y,u))
-+324
-x@[n:nis(x,1)][u:nat][i:is(x,<u>suc)]
-t1:=tris(nat,x,<u>suc,pl(1,u),i,satz4g(u)):is(x,pl(1,u))
-t2:=ismore1(pl(1,u),x,1,symis(nat,x,pl(1,u),t1),satz18(1,u)):more(x,1)
-n@t3:=someapp(nat,[u:nat]is(x,<u>suc),satz3(x,n),more(x,1),[u:nat][v:is(x,<u>suc)]t2(u,v)):more(x,1)
--324
-x@satz24:=th2"l.or"(more(x,1),is(x,1),[u:nis(x,1)]t3".324"(u)):moreis(x,1)
-satz24a:=satz13(x,1,satz24):lessis(1,x)
-satz24b:=t3".324"(<x>suc,<x>ax3):more(<x>suc,1)
-satz24c:=satz24b:less(1,<x>suc)
-y@[m:more(y,x)]
-+325
-[u:nat][du:diffprop(y,x,u)]
-t1:=satz19m(u,1,x,satz24(u)):moreis(pl(x,u),pl(x,1))
-t2:=ismoreis1(pl(x,u),y,pl(x,1),symis(nat,y,pl(x,u),du),t1):moreis(y,pl(x,1))
--325
-satz25:=someapp(nat,[u:nat]diffprop(y,x,u),m,moreis(y,pl(x,1)),[u:nat][v:diffprop(y,x,u)]t2".325"(u,v)):moreis(y,pl(x,1))
-satz25a:=ismoreis2(pl(x,1),<x>suc,y,satz4a,satz25):moreis(y,<x>suc)
-y@[l:less(y,x)]
-satz25b:=satz13(x,pl(y,1),satz25(y,x,l)):lessis(pl(y,1),x)
-satz25c:=islessis1(pl(y,1),<y>suc,x,satz4a(y),satz25b):lessis(<y>suc,x)
-y@[l:less(y,pl(x,1))]
-+326
-[m:more(y,x)]
-t1:=satz25(m):moreis(y,pl(x,1))
-l@t2:=th3"l.imp"(more(y,x),moreis(y,pl(x,1)),satz10h(y,pl(x,1),l),[v:more(y,x)]t1(v)):not(more(y,x))
--326
-satz26:=satz10e(y,x,t2".326"):lessis(y,x)
-y@[l:less(y,<x>suc)]
-satz26a:=satz26(isless2(<x>suc,pl(x,1),y,satz4e,l)):lessis(y,x)
-y@[m:more(pl(y,1),x)]
-satz26b:=satz14(x,y,satz26(y,x,m)):moreis(y,x)
-y@[m:more(<y>suc,x)]
-satz26c:=satz26b(ismore1(<y>suc,pl(y,1),x,satz4e(y),m)):moreis(y,x)
-@[p:[x:nat]'prop'][n:nat]
-+327
-[m:nat]
-lbprop:=imp(<m>p,lessis(n,m)):'prop'
--327
-lb:=all([x:nat]lbprop".327"(x)):'prop'
-min:=and(lb,<n>p):'prop'
-p@[s:some(p)]
-+*327
-s@[n:nat]
-t1:=[x:<n>p]satz24a(n):lbprop(1,n)
-s@t2:=[x:nat]t1(x):lb(1)
-[l:[x:nat]lb(x)][y:nat][yp:<y>p]
-t3:=satz18(y,1):more(pl(y,1),y)
-t4:=satz10g(pl(y,1),y,t3):not(lessis(pl(y,1),y))
-t5:=th4"l.imp"(<y>p,lessis(pl(y,1),y),yp,t4):not(lbprop(pl(y,1),y))
-t6:=th1"l.all"(nat,[x:nat]lbprop(pl(y,1),x),y,t5):not(lb(pl(y,1)))
-t7:=mp(lb(pl(y,1)),con,<pl(y,1)>l,t6):con
-l@t8:=someapp(nat,p,s,con,[x:nat][y:<x>p]t7(x,y)):con
-s@[n:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))][m:nat][l:lb(m)]
-t9:=<m>n:not(and(lb(m),not(lb(pl(m,1)))))
-t10:=et(lb(pl(m,1)),th3"l.and"(lb(m),not(lb(pl(m,1))),t9,l)):lb(pl(m,1))
-t11:=isp(nat,[x:nat]lb(x),pl(m,1),<m>suc,t10,satz4a(m)):lb(<m>suc)
-n@t12:=[x:nat]induction([y:nat]lb(y),t2,[y:nat][z:lb(y)]t11(y,z),x):[x:nat]lb(x)
-s@t13:=[x:non(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))))]t8(t12(x)):some([x:nat]and(lb(x),not(lb(pl(x,1)))))
-[m:nat][a:and(lb(m),not(lb(pl(m,1))))]
-t14:=ande1(lb(m),not(lb(pl(m,1))),a):lb(m)
-t15:=ande2(lb(m),not(lb(pl(m,1))),a):not(lb(pl(m,1)))
-[nmp:not(<m>p)][n:nat][np:<n>p]
-t16:=mp(<n>p,lessis(m,n),np,<n>t14):lessis(m,n)
-t17:=th3"l.imp"(is(m,n),<m>p,nmp,[x:is(m,n)]isp(nat,p,n,m,np,symis(nat,m,n,x))):not(is(m,n))
-t18:=ore1(less(m,n),is(m,n),t16,t17):less(m,n)
-t19:=satz25b(n,m,t18):lessis(pl(m,1),n)
-nmp@t20:=[x:nat][y:<x>p]t19(x,y):lb(pl(m,1))
-t21:=mp(lb(pl(m,1)),con,t20,t15):con
-a@t22:=et(<m>p,[x:not(<m>p)]t21(x)):<m>p
-t23:=andi(lb(m),<m>p,t14,t22):min(m)
--327
-s@satz27:=th6"l.some"(nat,[x:nat]and(lb(x),not(lb(pl(x,1)))),[x:nat]min(x),t13".327",[x:nat][y:and(lb(x),not(lb(pl(x,1))))]t23".327"(x,y)):some([x:nat]min(p,x))
-+*327
-p@[n:non(nat,[x:nat]min(x))][u:nat]
-t24:=[x:<u>p]satz24a(u):lbprop(1,u)
-n@t25:=[x:nat]t24(x):lb(1)
-u@[l:lb(u)]
-t26:=<u>n:not(min(u))
-t27:=th3"l.and"(lb(u),<u>p,t26,l):not(<u>p)
-[v:nat][vp:<v>p]
-t28:=th3"l.imp"(is(u,v),<u>p,t27,[x:is(u,v)]isp1(nat,p,v,u,vp,x)):nis(u,v)
-t29:=mp(<v>p,lessis(u,v),vp,<v>l):lessis(u,v)
-t30:=ore1(less(u,v),is(u,v),t29,t28):less(u,v)
-t31:=satz25c(v,u,t30):lessis(<u>suc,v)
-v@t32:=[x:<v>p]t31(x):lbprop(<u>suc,v)
-l@t33:=[x:nat]t32(x):lb(<u>suc)
-u@t34:=induction([x:nat]lb(x),t25,[x:nat][y:lb(x)]t33(x,y),u):lb(u)
-p@[s:some(p)][u:nat][up:<u>p]
-t35:=satz10g(<u>suc,u,satz18b(u)):not(lessis(<u>suc,u))
-t36:=th4"l.imp"(<u>p,lessis(<u>suc,u),up,t35):not(lbprop(<u>suc,u))
-t37:=th1"l.all"(nat,[x:nat]lbprop(<u>suc,x),u,t36):not(lb(<u>suc))
-t38:=[y:non(nat,[x:nat]min(x))]mp(lb(<u>suc),con,t34(y,<u>suc),t37):some([x:nat]min(x))
-s@anders:=someapp(nat,p,s,some([x:nat]min(x)),[x:nat][y:<x>p]t38(x,y)):some([x:nat]min(x))
--327
-+*327
-p@[n:nat][m:nat][mn:min(p,n)][mm:min(p,m)]
-t39:=ande1(lb(n),<n>p,mn):lb(n)
-t40:=ande1(lb(m),<m>p,mm):lb(m)
-t41:=ande2(lb(n),<n>p,mn):<n>p
-t42:=ande2(lb(m),<m>p,mm):<m>p
-t43:=<m>t39:lbprop(n,m)
-t44:=<n>t40:lbprop(m,n)
-t45:=mp(<m>p,lessis(n,m),t42,t43):lessis(n,m)
-t46:=mp(<n>p,lessis(m,n),t41,t44):lessis(m,n)
-t47:=ore2(more(n,m),is(n,m),satz14(m,n,t46),satz10d(n,m,t45)):is(n,m)
-p@t48:=[x:nat][y:nat][u:min(x)][v:min(y)]t47(x,y,u,v):amone(nat,[x:nat]min(p,x))
--327
-s@satz27a:=onei(nat,[x:nat]min(p,x),t48".327",satz27):one([x:nat]min(p,x))
-+428
-x@[f:[y:nat]nat]
-prop1:=all([y:nat]is(<<y>suc>f,pl(<y>f,x))):'prop'
-prop2:=and(is(<1>f,x),prop1):'prop'
-x@[a:[y:nat]nat][b:[y:nat]nat][pa:prop2(a)][pb:prop2(b)][y:nat]
-prop3:=is(<y>a,<y>b):'prop'
-pb@t1:=ande1(is(<1>a,x),prop1(a),pa):is(<1>a,x)
-t2:=ande1(is(<1>b,x),prop1(b),pb):is(<1>b,x)
-t3:=tris2(nat,<1>a,<1>b,x,t1,t2):prop3(1)
-y@[p:prop3(y)]
-t4:=ispl1(<y>a,<y>b,x,p):is(pl(<y>a,x),pl(<y>b,x))
-t5:=ande2(is(<1>a,x),prop1(a),pa):prop1(a)
-t6:=ande2(is(<1>b,x),prop1(b),pb):prop1(b)
-t7:=<y>t5:is(<<y>suc>a,pl(<y>a,x))
-t8:=<y>t6:is(<<y>suc>b,pl(<y>b,x))
-t9:=tr3is(nat,<<y>suc>a,pl(<y>a,x),pl(<y>b,x),<<y>suc>b,t7,t4,symis(nat,<<y>suc>b,pl(<y>b,x),t8)):prop3(<y>suc)
-y@t10:=induction([z:nat]prop3(z),t3,[z:nat][u:prop3(z)]t9(z,u),y):prop3(y)
-pb@t11:=fisi(nat,nat,a,b,[y:nat]t10(y)):is"e"([y:nat]nat,a,b)
-x@a1:=[z:[y:nat]nat][u:[y:nat]nat][v:prop2(z)][w:prop2(u)]t11(z,u,v,w):amone([y:nat]nat,[z:[y:nat]nat]prop2(z))
-prop4:=some"l"([y:nat]nat,[z:[y:nat]nat]prop2(z)):'prop'
-@id:=[y:nat]y:[y:nat]nat
-t12:=[x:nat]satz4e(x):prop1(1,id)
-t13:=andi(is(<1>id,1),prop1(1,id),refis(nat,1),t12):prop2(1,id)
-t14:=somei([y:nat]nat,[z:[y:nat]nat]prop2(1,z),id,t13):prop4(1)
-x@[p:prop4(x)][f:[y:nat]nat][pf:prop2(f)]
-g:=[y:nat]pl(<y>f,y):[y:nat]nat
-t15:=ande1(is(<1>f,x),prop1(f),pf):is(<1>f,x)
-t16:=tris(nat,<1>g,pl(x,1),<x>suc,ispl1(<1>f,x,1,t15),satz4a(x)):is(<1>g,<x>suc)
-[y:nat]
-t17:=ande2(is(<1>f,x),prop1(f),pf):prop1(f)
-t18:=<y>t17:is(<<y>suc>f,pl(<y>f,x))
-t19:=tris(nat,<<y>suc>g,pl(pl(<y>f,x),<y>suc),pl(<y>f,pl(x,<y>suc)),ispl1(<<y>suc>f,pl(<y>f,x),<y>suc,t18),asspl1(<y>f,x,<y>suc)):is(<<y>suc>g,pl(<y>f,pl(x,<y>suc)))
-t20:=tr3is(nat,pl(x,<y>suc),<pl(x,y)>suc,pl(<x>suc,y),pl(y,<x>suc),satz4b(x,y),satz4h(x,y),compl(<x>suc,y)):is(pl(x,<y>suc),pl(y,<x>suc))
-t21:=tr3is(nat,<<y>suc>g,pl(<y>f,pl(x,<y>suc)),pl(<y>f,pl(y,<x>suc)),pl(<y>g,<x>suc),t19,ispl2(pl(x,<y>suc),pl(y,<x>suc),<y>f,t20),asspl2(<y>f,y,<x>suc)):is(<<y>suc>g,pl(<y>g,<x>suc))
-pf@t22:=[y:nat]t21(y):prop1(<x>suc,g)
-t23:=andi(is(<1>g,<x>suc),prop1(<x>suc,g),t16,t22):prop2(<x>suc,g)
-t24:=somei([y:nat]nat,[z:[y:nat]nat]prop2(<x>suc,z),g,t23):prop4(<x>suc)
-p@t25:=someapp([y:nat]nat,[z:[y:nat]nat]prop2(z),p,prop4(<x>suc),[z:[y:nat]nat][u:prop2(z)]t24(z,u)):prop4(<x>suc)
-x@b1:=induction([y:nat]prop4(y),t14,[y:nat][u:prop4(y)]t25(y,u),x):prop4(x)
--428
-x@satz28:=onei([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),a1".428",b1".428"):one"e"([y:nat]nat,[z:[y:nat]nat]and(is(<1>z,x),all([y:nat]is(<<y>suc>z,pl(<y>z,x)))))
-times:=ind([y:nat]nat,[z:[y:nat]nat]prop2".428"(z),satz28):[y:nat]nat
-y@ts:=<y>times:nat
-+*428
-x@t26:=oneax([y:nat]nat,[z:[y:nat]nat]prop2(z),satz28):prop2(times)
--428
-x@satz28a:=ande1(is(<1>times,x),prop1".428"(times),t26".428"):is(ts(x,1),x)
-+*428
-x@t27:=ande2(is(<1>times,x),prop1(times),t26):prop1(times)
--428
-y@satz28b:=<y>t27".428":is(ts(x,<y>suc),pl(ts(x,y),x))
-+*428
-@t28:=t11(1,times(1),id,t26(1),t13):is"e"([y:nat]nat,times(1),id)
--428
-x@satz28c:=fise(nat,nat,times(1),id".428",t28".428",x):is(ts(1,x),x)
-+*428
-x@t29:=t11(<x>suc,times(<x>suc),[y:nat]pl(<y>times,y),t26(<x>suc),t23(b1,times,t26)):is"e"([y:nat]nat,times(<x>suc),[y:nat]pl(<y>times,y))
--428
-y@satz28d:=fise(nat,nat,times(<x>suc),[z:nat]pl(<z>times,z),t29".428",y):is(ts(<x>suc,y),pl(ts(x,y),y))
-x@satz28e:=symis(nat,ts(x,1),x,satz28a):is(x,ts(x,1))
-y@satz28f:=symis(nat,ts(x,<y>suc),pl(ts(x,y),x),satz28b):is(pl(ts(x,y),x),ts(x,<y>suc))
-x@satz28g:=symis(nat,ts(1,x),x,satz28c):is(x,ts(1,x))
-y@satz28h:=symis(nat,ts(<x>suc,y),pl(ts(x,y),y),satz28d):is(pl(ts(x,y),y),ts(<x>suc,y))
-z@[i:is(x,y)]
-ists1:=isf(nat,nat,[u:nat]ts(u,z),x,y,i):is(ts(x,z),ts(y,z))
-ists2:=isf(nat,nat,[u:nat]ts(z,u),x,y,i):is(ts(z,x),ts(z,y))
-z@[u:nat][i:is(x,y)][j:is(z,u)]
-ists12:=tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
-+429
-y@prop1:=is(ts(x,y),ts(y,x)):'prop'
-t1:=satz28a(y):is(ts(y,1),y)
-t2:=satz28c(y):is(ts(1,y),y)
-t3:=tris2(nat,ts(1,y),ts(y,1),y,t2,t1):prop1(1,y)
-[p:prop1(x,y)]
-t4:=tris(nat,pl(ts(x,y),y),pl(ts(y,x),y),ts(y,<x>suc),ispl1(ts(x,y),ts(y,x),y,p),satz28f(y,x)):is(pl(ts(x,y),y),ts(y,<x>suc))
-t5:=satz28d:is(ts(<x>suc,y),pl(ts(x,y),y))
-t6:=tris(nat,ts(<x>suc,y),pl(ts(x,y),y),ts(y,<x>suc),t5,t4):prop1(<x>suc,y)
--429
-y@satz29:=induction([z:nat]prop1".429"(z,y),t3".429",[z:nat][u:prop1".429"(z,y)]t6".429"(z,y,u),x):is(ts(x,y),ts(y,x))
-comts:=satz29:is(ts(x,y),ts(y,x))
-+*429
-x@t7:=tris(nat,ts(x,1),x,ts(1,x),satz28a,satz28g):prop1(1)
-y@[p:prop1(y)]
-t8:=tr3is(nat,ts(x,<y>suc),pl(ts(x,y),x),pl(ts(y,x),x),ts(<y>suc,x),satz28b(x,y),ispl1(ts(x,y),ts(y,x),x,p),satz28h(y,x)):prop1(<y>suc)
-y@anders:=induction([z:nat]prop1(z),t7,[z:nat][u:prop1(z)]t8(z,u),y):is(ts(x,y),ts(y,x))
--429
-+430
-z@prop1:=is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z))):'prop'
-y@t1:=tr3is(nat,ts(x,pl(y,1)),ts(x,<y>suc),pl(ts(x,y),x),pl(ts(x,y),ts(x,1)),ists2(pl(y,1),<y>suc,x,satz4a(y)),satz28b,ispl2(x,ts(x,1),ts(x,y),satz28e(x))):prop1(1)
-z@[p:prop1(z)]
-t2:=tr3is(nat,ts(x,pl(y,<z>suc)),ts(x,<pl(y,z)>suc),pl(ts(x,pl(y,z)),x),pl(pl(ts(x,y),ts(x,z)),x),ists2(pl(y,<z>suc),<pl(y,z)>suc,x,satz4b(y,z)),satz28b(x,pl(y,z)),ispl1(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),x,p)):is(ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x))
-t3:=tr3is(nat,ts(x,pl(y,<z>suc)),pl(pl(ts(x,y),ts(x,z)),x),pl(ts(x,y),pl(ts(x,z),x)),pl(ts(x,y),ts(x,<z>suc)),t2,asspl1(ts(x,y),ts(x,z),x),ispl2(pl(ts(x,z),x),ts(x,<z>suc),ts(x,y),satz28f(x,z))):prop1(<z>suc)
--430
-z@satz30:=induction([u:nat]prop1".430"(u),t1".430",[u:nat][v:prop1".430"(u)]t3".430"(u,v),z):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-disttp1:=tr3is(nat,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz30(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
-disttp2:=satz30:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-distpt1:=symis(nat,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
-distpt2:=symis(nat,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
-+431
-prop1:=is(ts(ts(x,y),z),ts(x,ts(y,z))):'prop'
-y@t1:=tris(nat,ts(ts(x,y),1),ts(x,y),ts(x,ts(y,1)),satz28a(ts(x,y)),ists2(y,ts(y,1),x,satz28e(y))):prop1(1)
-z@[p:prop1(z)]
-t2:=tr4is(nat,ts(ts(x,y),<z>suc),pl(ts(ts(x,y),z),ts(x,y)),pl(ts(x,ts(y,z)),ts(x,y)),ts(x,pl(ts(y,z),y)),ts(x,ts(y,<z>suc)),satz28b(ts(x,y),z),ispl1(ts(ts(x,y),z),ts(x,ts(y,z)),ts(x,y),p),distpt2(x,ts(y,z),y),ists2(pl(ts(y,z),y),ts(y,<z>suc),x,satz28f(y,z))):prop1(<z>suc)
--431
-satz31:=induction([u:nat]prop1".431"(u),t1".431",[u:nat][v:prop1".431"(u)]t2".431"(u,v),z):is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts1:=satz31:is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts2:=symis(nat,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
-[m:more(x,y)]
-+432
-[u:nat][du:diffprop(u)]
-t1:=tris(nat,ts(x,z),ts(pl(y,u),z),pl(ts(y,z),ts(u,z)),ists1(x,pl(y,u),z,du),disttp1(y,u,z)):is(ts(x,z),pl(ts(y,z),ts(u,z)))
-t2:=somei(nat,[v:nat]diffprop(ts(x,z),ts(y,z),v),ts(u,z),t1):more(ts(x,z),ts(y,z))
--432
-satz32a:=someapp(nat,[u:nat]diffprop(u),m,more(ts(x,z),ts(y,z)),[u:nat][v:diffprop(u)]t2".432"(u,v)):more(ts(x,z),ts(y,z))
-z@[i:is(x,y)]
-satz32b:=ists1(x,y,z,i):is(ts(x,z),ts(y,z))
-z@[l:less(x,y)]
-satz32c:=satz11(ts(y,z),ts(x,z),satz32a(y,x,z,satz12(x,y,l))):less(ts(x,z),ts(y,z))
-+*432
-l@anders1:=satz32a(y,x,z,l):less(ts(x,z),ts(y,z))
--432
-m@satz32d:=ismore12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32a):more(ts(z,x),ts(z,y))
-i@satz32e:=ists2(x,y,z,i):is(ts(z,x),ts(z,y))
-l@satz32f:=isless12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32c):less(ts(z,x),ts(z,y))
-+*432
-l@anders2:=satz32d(y,x,z,l):less(ts(z,x),ts(z,y))
--432
-z@[u:nat][i:is(x,y)][m:more(z,u)]
-satz32g:=ismore2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32d(z,u,x,m)):more(ts(x,z),ts(y,u))
-satz32h:=ismore12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32g):more(ts(z,x),ts(u,y))
-i@[l:less(z,u)]
-satz32j:=isless2(ts(x,u),ts(y,u),ts(x,z),ists1(x,y,u,i),satz32f(z,u,x,l)):less(ts(x,z),ts(y,u))
-satz32k:=isless12(ts(x,z),ts(z,x),ts(y,u),ts(u,y),comts(x,z),comts(y,u),satz32j):less(ts(z,x),ts(u,y))
-z@[m:moreis(x,y)]
-+*432
-m@[n:more(x,y)]
-t3:=moreisi1(ts(x,z),ts(y,z),satz32a(n)):moreis(ts(x,z),ts(y,z))
-m@[i:is(x,y)]
-t4:=moreisi2(ts(x,z),ts(y,z),ists1(x,y,z,i)):moreis(ts(x,z),ts(y,z))
--432
-m@satz32l:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,z)),m,[u:more(x,y)]t3".432"(u),[u:is(x,y)]t4".432"(u)):moreis(ts(x,z),ts(y,z))
-satz32m:=ismoreis12(ts(x,z),ts(z,x),ts(y,z),ts(z,y),comts(x,z),comts(y,z),satz32l):moreis(ts(z,x),ts(z,y))
-z@[l:lessis(x,y)]
-satz32n:=satz13(ts(y,z),ts(x,z),satz32l(y,x,z,satz14(l))):lessis(ts(x,z),ts(y,z))
-satz32o:=satz13(ts(z,y),ts(z,x),satz32m(y,x,z,satz14(l))):lessis(ts(z,x),ts(z,y))
-+433
-z@t1:=satz10a(x,y):or3(is(x,y),more(x,y),less(x,y))
-t2:=satz10b(ts(x,z),ts(y,z)):ec3(is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)))
--433
-z@[m:more(ts(x,z),ts(y,z))]
-satz33a:=th11"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),m):more(x,y)
-z@[i:is(ts(x,z),ts(y,z))]
-satz33b:=th10"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),i):is(x,y)
-z@[l:less(ts(x,z),ts(y,z))]
-satz33c:=th12"l.ec3"(is(x,y),more(x,y),less(x,y),is(ts(x,z),ts(y,z)),more(ts(x,z),ts(y,z)),less(ts(x,z),ts(y,z)),t1".433",t2".433",[u:is(x,y)]satz32b(x,y,z,u),[u:more(x,y)]satz32a(x,y,z,u),[u:less(x,y)]satz32c(x,y,z,u),l):less(x,y)
-+*433
-l@anders:=satz33a(y,x,z,l):less(x,y)
--433
-u@[m:more(x,y)][n:more(z,u)]
-+434
-t1:=satz32a(x,y,z,m):more(ts(x,z),ts(y,z))
-t2:=ismore12(ts(z,y),ts(y,z),ts(u,y),ts(y,u),comts(z,y),comts(u,y),satz32a(z,u,y,n)):more(ts(y,z),ts(y,u))
--434
-satz34:=trmore(ts(x,z),ts(y,z),ts(y,u),t1".434",t2".434"):more(ts(x,z),ts(y,u))
-+*434
-n@anders:=trmore(ts(x,z),ts(y,z),ts(y,u),satz32a(x,y,z,m),satz32d(z,u,y,n)):more(ts(x,z),ts(y,u))
--434
-u@[l:less(x,y)][k:less(z,u)]
-satz34a:=satz34(y,x,u,z,l,k):less(ts(x,z),ts(y,u))
-+*434
-k@andersa:=satz11(ts(y,u),ts(x,z),satz34(y,x,u,z,satz12(x,y,l),satz12(z,u,k))):less(ts(x,z),ts(y,u))
--434
-u@[m:moreis(x,y)][n:more(z,u)]
-satz35a:=orapp(more(x,y),is(x,y),more(ts(x,z),ts(y,u)),m,[v:more(x,y)]satz34(v,n),[v:is(x,y)]satz32g(u,v,n)):more(ts(x,z),ts(y,u))
-u@[m:more(x,y)][n:moreis(z,u)]
-satz35b:=orapp(more(z,u),is(z,u),more(ts(x,z),ts(y,u)),n,[v:more(z,u)]satz34(m,v),[v:is(z,u)]satz32h(z,u,x,y,v,m)):more(ts(x,z),ts(y,u))
-u@[l:lessis(x,y)][k:less(z,u)]
-satz35c:=satz35a(y,x,u,z,satz14(x,y,l),k):less(ts(x,z),ts(y,u))
-u@[l:less(x,y)][k:lessis(z,u)]
-satz35d:=satz35b(y,x,u,z,l,satz14(z,u,k)):less(ts(x,z),ts(y,u))
-u@[m:moreis(x,y)][n:moreis(z,u)]
-+436
-[i:is(x,y)][j:is(z,u)]
-t1:=moreisi2(ts(x,z),ts(y,u),tris(nat,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j))):moreis(ts(x,z),ts(y,u))
-i@[o:more(z,u)]
-t2:=moreisi1(ts(x,z),ts(y,u),satz35a(m,o)):moreis(ts(x,z),ts(y,u))
-i@t3:=orapp(more(z,u),is(z,u),moreis(ts(x,z),ts(y,u)),n,[v:more(z,u)]t2(v),[v:is(z,u)]t1(v)):moreis(ts(x,z),ts(y,u))
-n@[o:more(x,y)]
-t4:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
--436
-satz36:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t4".436"(v),[v:is(x,y)]t3".436"(v)):moreis(ts(x,z),ts(y,u))
-+*436
-n@[o:more(x,y)]
-t5:=moreisi1(ts(x,z),ts(y,u),satz35b(o,n)):moreis(ts(x,z),ts(y,u))
-n@[i:is(x,y)]
-t6:=ismoreis2(ts(x,u),ts(y,u),ts(x,z),ists1(u,i),satz32m(z,u,x,n)):moreis(ts(x,z),ts(y,u))
-n@anders:=orapp(more(x,y),is(x,y),moreis(ts(x,z),ts(y,u)),m,[v:more(x,y)]t5(v),[v:is(x,y)]t6(v)):moreis(ts(x,z),ts(y,u))
--436
-u@[l:lessis(x,y)][k:lessis(z,u)]
-satz36a:=satz13(ts(y,u),ts(x,z),satz36(y,x,u,z,satz14(l),satz14(z,u,k))):lessis(ts(x,z),ts(y,u))
-y@[m:more(x,y)]
-+mn
-t1:=onei(nat,[z:nat]diffprop(x,y,z),satz8b(x,y),m):one([z:nat]diffprop(x,y,z))
--mn
-mn:=ind(nat,[z:nat]diffprop(x,y,z),t1".mn"):nat
-+*mn
-m@th1a:=oneax(nat,[z:nat]diffprop(x,y,z),t1):is(x,pl(y,mn(x,y,m)))
-th1b:=symis(nat,x,pl(y,mn(x,y,m)),th1a):is(pl(y,mn(x,y,m)),x)
-th1c:=tris(nat,x,pl(y,mn(x,y,m)),pl(mn(x,y,m),y),th1a,compl(y,mn(x,y,m))):is(x,pl(mn(x,y,m),y))
-th1d:=symis(nat,x,pl(mn(x,y,m),y),th1c):is(pl(mn(x,y,m),y),x)
-y@[z:nat][m:more(x,y)][i:is(pl(y,z),x)]
-th1e:=<th1a(m)><symis(nat,pl(y,z),x,i)><mn(x,y,m)><z>satz8b(x,y):is(z,mn(x,y,m))
--mn
-z@[u:nat][m:more(x,z)][n:more(y,u)][i:is(x,y)][j:is(z,u)]
-+*mn
-j@t2:=tr3is(nat,pl(u,mn(x,z,m)),pl(z,mn(x,z,m)),x,y,ispl1(u,z,mn(x,z,m),symis(nat,z,u,j)),th1b(x,z,m),i):is(pl(u,mn(x,z,m)),y)
--mn
-j@ismn12:=th1e".mn"(y,u,mn(x,z,m),n,t2".mn"):is(mn(x,z,m),mn(y,u,n))
-@[n:nat]
-1to:=ot(nat,[x:nat]lessis(x,n)):'type'
-[x:nat][l:lessis(x,n)]
-outn:=out(nat,[y:nat]lessis(y,n),x,l):1to(n)
-n@[xn:1to(n)]
-inn:=in"e"(nat,[y:nat]lessis(y,n),xn):nat
-1top:=inp(nat,[y:nat]lessis(y,n),xn):lessis(inn,n)
-l@[y:nat][k:lessis(y,n)][i:is(x,y)]
-isoutni:=isouti(nat,[z:nat]lessis(z,n),x,l,y,k,i):is"e"(1to(n),outn(x,l),outn(y,k))
-k@[i:is"e"(1to(n),outn(x,l),outn(y,k))]
-isoutne:=isoute(nat,[z:nat]lessis(z,n),x,l,y,k,i):is(x,y)
-xn@[yn:1to(n)][i:is"e"(1to(n),xn,yn)]
-isinni:=isini(nat,[z:nat]lessis(z,n),xn,yn,i):is(inn(xn),inn(yn))
-yn@[i:is(inn(xn),inn(yn))]
-isinne:=isine(nat,[z:nat]lessis(z,n),xn,yn,i):is"e"(1to(n),xn,yn)
-xn@isoutinn:=isoutin(nat,[y:nat]lessis(y,n),xn):is"e"(1to(n),xn,outn(inn(xn),1top(xn)))
-l@isinoutn:=isinout(nat,[y:nat]lessis(y,n),x,l):is(x,inn(outn(x,l)))
-@1o:=outn(1,1,lessisi2(1,1,refis(nat,1))):1to(1)
-[u:1to(1)]
-+singlet
-u0:=inn(1,u):nat
-t1:=1top(1,u):lessis(u0,1)
-t2:=ore2(more(u0,1),is(u0,1),satz24(u0),satz10d(u0,1,t1)):is(u0,1)
-th1:=tris(1to(1),u,outn(1,u0,t1),1o,isoutinn(1,u),isoutni(1,u0,t1,1,lessisi2(1,1,refis(nat,1)),t2)):is"e"(1to(1),u,1o)
--singlet
-@2:=pl(1,1):nat
-[x:nat]
-+pair
-[l:lessis(x,2)][n:nis(x,2)]
-t1:=satz26(1,x,ore1(less(x,2),is(x,2),l,n)):lessis(x,1)
-t2:=ore2(more(x,1),is(x,1),satz24(x),satz10d(x,1,t1)):is(x,1)
-l@th1:=th2"l.or"(is(x,1),is(x,2),[t:nis(x,2)]t2(t)):or(is(x,1),is(x,2))
-@th2:=th1"e.notis"(nat,<1>suc,1,2,<1>ax3,satz4e(1)):nis(2,1)
--pair
-@1t:=outn(2,1,satz24a(2)):1to(2)
-2t:=outn(2,2,lessisi2(2,2,refis(nat,2))):1to(2)
-+*pair
-@[u:1to(2)]
-u0:=inn(2,u):nat
-t3:=1top(2,u):lessis(u0,2)
-[i:is(u0,1)]
-t4:=isoutni(2,u0,t3,1,satz24a(2),i):is"e"(1to(2),outn(2,u0,t3),1t)
-t5:=tris(1to(2),u,outn(2,u0,t3),1t,isoutinn(2,u),t4):is"e"(1to(2),u,1t)
-u@[i:is(u0,2)]
-t6:=isoutni(2,u0,t3,2,lessisi2(2,2,refis(nat,2)),i):is"e"(1to(2),outn(2,u0,t3),2t)
-t7:=tris(1to(2),u,outn(2,u0,t3),2t,isoutinn(2,u),t6):is"e"(1to(2),u,2t)
-u@th3:=th9"l.or"(is(u0,1),is(u0,2),is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),th1(u0,t3),[t:is(u0,1)]t5(t),[t:is(u0,2)]t7(t)):or(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t))
-@[i:is"e"(1to(2),2t,1t)]
-t9:=isini(nat,[x:nat]lessis(x,2),2t,1t,i):is(u0(2t),u0(1t))
-t10:=tr3is(nat,2,u0(2t),u0(1t),1,isinoutn(2,2,lessisi2(2,2,refis(nat,2))),t9,symis(nat,1,u0(1t),isinoutn(2,1,satz24a(2)))):is(2,1)
-@th4:=th3"l.imp"(is"e"(1to(2),2t,1t),is(2,1),th2,[t:is"e"(1to(2),2t,1t)]t10(t)):not(is"e"(1to(2),2t,1t))
--pair
-@[alpha:'type']
-pair1type:=[x:1to(2)]alpha:'type'
-[a:alpha][b:alpha]
-pair1:=[x:1to(2)]ite(is"e"(1to(2),x,1t),alpha,a,b):pair1type
-alpha@[p:pair1type]
-first1:=<1t>p:alpha
-second1:=<2t>p:alpha
-b@first1is1:=itet(is"e"(1to(2),1t,1t),alpha,a,b,refis(1to(2),1t)):is"e"(alpha,first1(pair1),a)
-first1is2:=symis(alpha,first1(pair1),a,first1is1):is"e"(alpha,a,first1(pair1))
-second1is1:=itef(is"e"(1to(2),2t,1t),alpha,a,b,th4".pair"):is"e"(alpha,second1(pair1),b)
-second1is2:=symis(alpha,second1(pair1),b,second1is1):is"e"(alpha,b,second1(pair1))
-+*pair
-p@[q:pair1type][i:is"e"(alpha,first1(p),first1(q))][j:is"e"(alpha,second1(p),second1(q))][u:1to(2)][u1:is"e"(1to(2),u,1t)]
-t11:=isf(1to(2),alpha,p,u,1t,u1):is"e"(alpha,<u>p,first1(p))
-t12:=symis(alpha,<u>q,first1(q),isf(1to(2),alpha,q,u,1t,u1)):is"e"(alpha,first1(q),<u>q)
-t13:=tr3is(alpha,<u>p,first1(p),first1(q),<u>q,t11,i,t12):is"e"(alpha,<u>p,<u>q)
-u@[u2:is"e"(1to(2),u,2t)]
-t14:=isf(1to(2),alpha,p,u,2t,u2):is"e"(alpha,<u>p,second1(p))
-t15:=symis(alpha,<u>q,second1(q),isf(1to(2),alpha,q,u,2t,u2)):is"e"(alpha,second1(q),<u>q)
-t16:=tr3is(alpha,<u>p,second1(p),second1(q),<u>q,t14,j,t15):is"e"(alpha,<u>p,<u>q)
-u@t17:=orapp(is"e"(1to(2),u,1t),is"e"(1to(2),u,2t),is"e"(alpha,<u>p,<u>q),th3(u),[t:is"e"(1to(2),u,1t)]t13(t),[t:is"e"(1to(2),u,2t)]t16(t)):is"e"(alpha,<u>p,<u>q)
-j@th5:=fisi(1to(2),alpha,p,q,[t:1to(2)]t17(t)):is"e"(pair1type,p,q)
-p@q0:=pair1(first1,second1):pair1type
-t18:=first1is1(first1(p),second1):is"e"(alpha,first1(q0),first1(p))
-t19:=second1is1(first1,second1):is"e"(alpha,second1(q0),second1(p))
--pair
-p@pair1is1:=th5".pair"(q0".pair",p,t18".pair",t19".pair"):is"e"(pair1type,pair1(first1,second1),p)
-pair1is2:=symis(pair1type,pair1(first1,second1),p,pair1is1):is"e"(pair1type,p,pair1(first1,second1))
-@[x:nat]
-lessisi3:=lessisi2(x,x,refis(nat,x)):lessis(x,x)
-1out:=outn(x,1,satz24a(x)):1to(x)
-xout:=outn(x,x,lessisi3(x)):1to(x)
-[y:nat][l:lessis(y,x)][u:1to(y)]
-+left
-ui:=inn(y,u):nat
-t1:=1top(y,u):lessis(ui,y)
-t2:=trlessis(ui,y,x,t1,l):lessis(ui,x)
--left
-left1to:=outn(x,ui".left",t2".left"):1to(x)
-[v:1to(y)][i:is"e"(1to(x),left1to(u),left1to(v))]
-+*left
-i@t3:=isoutne(x,ui,t2,ui(v),t2(v),i):is(ui,ui(v))
--left
-i@thleft1:=isinne(y,u,v,t3".left"):is"e"(1to(y),u,v)
-l@thleft2:=[u:1to(y)][v:1to(y)][t:is"e"(1to(x),left1to(u),left1to(v))]thleft1(u,v,t):injective(1to(y),1to(x),[t:1to(y)]left1to(t))
-y@[u:1to(y)]
-+right
-ui:=inn(y,u):nat
-t4:=1top(y,u):lessis(ui,y)
-t5:=satz19o(ui,y,x,t4):lessis(pl(x,ui),pl(x,y))
--right
-right1to:=outn(pl(x,y),pl(x,ui".right"),t5".right"):1to(pl(x,y))
-[v:1to(y)][i:is"e"(1to(pl(x,y)),right1to(u),right1to(v))]
-+*right
-i@t6:=isoutne(pl(x,y),pl(x,ui(u)),t5(u),pl(x,ui(v)),t5(v),i):is(pl(x,ui(u)),pl(x,ui(v)))
-t7:=satz20e(ui(u),ui(v),x,t6):is(ui(u),ui(v))
--right
-i@thright1:=isinne(y,u,v,t7".right"):is"e"(1to(y),u,v)
-@[alpha:'type'][x:nat][y:nat][l:lessis(y,x)][f:[t:1to(x)]alpha]
-left:=[t:1to(y)]<left1to(x,y,l,t)>f:[t:1to(y)]alpha
-y@[f:[t:1to(pl(x,y))]alpha]
-right:=[t:1to(y)]<right1to(x,y,t)>f:[t:1to(y)]alpha
-y@[i:is(y,x)][f:[t:1to(y)]alpha]
-+*left
-f@t4:=lessisi2(y,x,i):lessis(y,x)
-t5:=lessisi2(x,y,symis(nat,y,x,i)):lessis(x,y)
-f1:=left(y,x,t5,f):[t:1to(x)]alpha
-f2:=left(t4,f1):[t:1to(y)]alpha
-[u:1to(y)]
-t6:=isinoutn(x,inn(y,u),trlessis(inn(y,u),y,x,1top(y,u),t4)):is(inn(y,u),inn(x,left1to(x,y,t4,u)))
-t7:=tris(1to(y),u,outn(y,inn(y,u),1top(y,u)),left1to(y,x,t5,left1to(x,y,t4,u)),isoutinn(y,u),isoutni(y,inn(y,u),1top(y,u),inn(x,left1to(x,y,t4,u)),trlessis(inn(x,left1to(x,y,t4,u)),x,y,1top(x,left1to(x,y,t4,u)),t5),t6)):is"e"(1to(y),u,left1to(y,x,t5,left1to(x,y,t4,u)))
-t8:=isf(1to(y),alpha,f,u,left1to(y,x,t5,left1to(x,y,t4,u)),t7):is"e"(alpha,<u>f,<u>f2)
--left
-f@thleft:=fisi(1to(y),alpha,f,f2".left",[t:1to(y)]t8".left"(t)):is"e"([t:1to(y)]alpha,f,left(x,y,lessisi2(y,x,i),left(y,x,lessisi2(x,y,symis(nat,y,x,i)),f)))
-@frac:=pair1type(nat):'type'
-[x1:nat][x2:nat]
-fr:=pair1(nat,x1,x2):frac
-@[x:frac]
-num:=first1(nat,x):nat
-den:=second1(nat,x):nat
-x2@numis:=first1is1(nat,x1,x2):is(num(fr(x1,x2)),x1)
-isnum:=first1is2(nat,x1,x2):is(x1,num(fr(x1,x2)))
-denis:=second1is1(nat,x1,x2):is(den(fr(x1,x2)),x2)
-isden:=second1is2(nat,x1,x2):is(x2,den(fr(x1,x2)))
-x@1x:=num(x):nat
-2x:=den(x):nat
-fris:=pair1is1(nat,x):is"e"(frac,fr(1x,2x),x)
-isfr:=pair1is2(nat,x):is"e"(frac,x,fr(1x,2x))
-x2@[y1:nat][y2:nat]
-12isnd:=ists12(x1,num(fr(x1,x2)),y2,den(fr(y1,y2)),isnum(x1,x2),isden(y1,y2)):is(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))))
-ndis12:=symis(nat,ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),12isnd):is(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2))
-x@[n1:nat][n2:nat]
-1disnd:=ists1(n1,num(fr(n1,n2)),2x,isnum(n1,n2)):is(ts(n1,2x),ts(num(fr(n1,n2)),2x))
-ndis1d:=symis(nat,ts(n1,2x),ts(num(fr(n1,n2)),2x),1disnd):is(ts(num(fr(n1,n2)),2x),ts(n1,2x))
-n2isnd:=ists2(n2,den(fr(n1,n2)),1x,isden(n1,n2)):is(ts(1x,n2),ts(1x,den(fr(n1,n2))))
-ndisn2:=symis(nat,ts(1x,n2),ts(1x,den(fr(n1,n2))),n2isnd):is(ts(1x,den(fr(n1,n2))),ts(1x,n2))
-x2@[n:nat][i:is(x1,n)]
-isn:=isf(nat,frac,[t:nat]fr(t,x2),x1,n,i):is"e"(frac,fr(x1,x2),fr(n,x2))
-n@[i:is(x2,n)]
-isd:=isf(nat,frac,[t:nat]fr(x1,t),x2,n,i):is"e"(frac,fr(x1,x2),fr(x1,n))
-y2@[i:is(x1,y1)][j:is(x2,y2)]
-isnd:=tris(frac,fr(x1,x2),fr(y1,x2),fr(y1,y2),isn(x1,x2,y1,i),isd(y1,x2,y2,j)):is"e"(frac,fr(x1,x2),fr(y1,y2))
-x@[y:frac]
-1y:=num(y):nat
-2y:=den(y):nat
-eq:=is(ts(1x,2y),ts(1y,2x)):'prop'
-y2@[i:is(ts(x1,y2),ts(y1,x2))]
-eqi12:=tr3is(nat,ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ndis12(x1,x2,y1,y2),i,12isnd(y1,y2,x1,x2)):eq(fr(x1,x2),fr(y1,y2))
-n2@[i:is(ts(1x,n2),ts(n1,2x))]
-eqi1:=isp(frac,[t:frac]eq(t,fr(n1,n2)),fr(1x,2x),x,eqi12(1x,2x,n1,n2,i),fris):eq(x,fr(n1,n2))
-n2@[i:is(ts(n1,2x),ts(1x,n2))]
-eqi2:=isp(frac,[t:frac]eq(fr(n1,n2),t),fr(1x,2x),x,eqi12(n1,n2,1x,2x,i),fris):eq(fr(n1,n2),x)
-x@satz37:=refis(nat,ts(1x,2x)):eq(x,x)
-refeq:=satz37:eq(x,x)
-y@[i:is"e"(frac,x,y)]
-refeq1:=isp(frac,[t:frac]eq(x,t),x,y,refeq,i):eq(x,y)
-refeq2:=isp(frac,[t:frac]eq(t,x),x,y,refeq,i):eq(y,x)
-y2@[i:is(x1,y1)][j:is(x2,y2)]
-eqnd:=refeq1(fr(x1,x2),fr(y1,y2),isnd(i,j)):eq(fr(x1,x2),fr(y1,y2))
-x2@[n:nat][i:is(x1,n)]
-eqn:=refeq1(fr(x1,x2),fr(n,x2),isn(n,i)):eq(fr(x1,x2),fr(n,x2))
-n@[i:is(x2,n)]
-eqd:=refeq1(fr(x1,x2),fr(x1,n),isd(n,i)):eq(fr(x1,x2),fr(x1,n))
-y@[e:eq(x,y)]
-satz38:=symis(nat,ts(1x,2y),ts(1y,2x),e):eq(y,x)
-symeq:=satz38:eq(y,x)
-@[a:nat][b:nat][c:nat][d:nat]
-+ii1
-t1:=tris(nat,ts(b,ts(c,d)),ts(ts(b,c),d),ts(d,ts(b,c)),assts2(b,c,d),comts(ts(b,c),d)):is(ts(b,ts(c,d)),ts(d,ts(b,c)))
--ii1
-stets:=tr4is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(b,c))),ts(ts(a,d),ts(b,c)),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(b,c)),a,t1".ii1"),assts2(a,d,ts(b,c)),ists2(ts(b,c),ts(c,b),ts(a,d),comts(b,c))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
-+*ii1
-d@t2:=tr3is(nat,ts(b,ts(c,d)),ts(ts(c,d),b),ts(ts(d,c),b),ts(d,ts(c,b)),comts(b,ts(c,d)),ists1(ts(c,d),ts(d,c),b,comts(c,d)),assts1(d,c,b)):is(ts(b,ts(c,d)),ts(d,ts(c,b)))
-anders:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(a,ts(b,ts(c,d))),ts(a,ts(d,ts(c,b))),ts(ts(a,d),ts(c,b)),assts1(a,b,ts(c,d)),ists2(ts(b,ts(c,d)),ts(d,ts(c,b)),a,t2),assts2(a,d,ts(c,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,d),ts(c,b)))
--ii1
-y@[z:frac]
-1z:=num(z):nat
-2z:=den(z):nat
-[e:eq(x,y)][f:eq(y,z)]
-+139
-t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
-t2:=stets(1x,2y,1y,2z):is(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)))
-t3:=tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)))
-t4:=tr3is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),symis(nat,ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),t2),t1,t3):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
--139
-satz39:=satz33b(ts(1x,2z),ts(1z,2x),ts(1y,2y),t4".139"):eq(x,z)
-+*139
-f@anders:=tr4is(nat,ts(ts(1x,2z),ts(1y,2y)),ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2z,1y,2y),ists12(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),e,f),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))):is(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
--139
-f@treq:=satz39:eq(x,z)
-z@[e:eq(z,x)][f:eq(z,y)]
-treq1:=treq(x,z,y,symeq(z,x,e),f):eq(x,y)
-z@[e:eq(x,z)][f:eq(y,z)]
-treq2:=treq(x,z,y,e,symeq(y,z,f)):eq(x,y)
-z@[u:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)]
-tr3eq:=treq(x,y,u,e,treq(y,z,u,f,g)):eq(x,u)
-u@[v:frac][e:eq(x,y)][f:eq(y,z)][g:eq(z,u)][h:eq(u,v)]
-tr4eq:=tr3eq(x,y,z,v,e,f,treq(z,u,v,g,h)):eq(x,v)
-x@[n:nat]
-satz40:=eqi1(ts(1x,n),ts(2x,n),tris(nat,ts(1x,ts(2x,n)),ts(1x,ts(n,2x)),ts(ts(1x,n),2x),ists2(ts(2x,n),ts(n,2x),1x,comts(2x,n)),assts2(1x,n,2x))):eq(x,fr(ts(1x,n),ts(2x,n)))
-satz40a:=symeq(x,fr(ts(1x,n),ts(2x,n)),satz40):eq(fr(ts(1x,n),ts(2x,n)),x)
-x2@[n:nat]
-satz40b:=eqi12(ts(x1,n),ts(x2,n),tris(nat,ts(x1,ts(x2,n)),ts(x1,ts(n,x2)),ts(ts(x1,n),x2),ists2(ts(x2,n),ts(n,x2),x1,comts(x2,n)),assts2(x1,n,x2))):eq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)))
-satz40c:=symeq(fr(x1,x2),fr(ts(x1,n),ts(x2,n)),satz40b):eq(fr(ts(x1,n),ts(x2,n)),fr(x1,x2))
-y@moref:=more(ts(1x,2y),ts(1y,2x)):'prop'
-lessf:=less(ts(1x,2y),ts(1y,2x)):'prop'
-y2@[m:more(ts(x1,y2),ts(y1,x2))]
-morefi12:=ismore12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),m):moref(fr(x1,x2),fr(y1,y2))
-y2@[l:less(ts(x1,y2),ts(y1,x2))]
-lessfi12:=isless12(ts(x1,y2),ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(y1,x2),ts(num(fr(y1,y2)),den(fr(x1,x2))),12isnd(x1,x2,y1,y2),12isnd(y1,y2,x1,x2),l):lessf(fr(x1,x2),fr(y1,y2))
-n2@[m:more(ts(1x,n2),ts(n1,2x))]
-morefi1:=ismore12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),m):moref(x,fr(n1,n2))
-n2@[m:more(ts(n1,2x),ts(1x,n2))]
-morefi2:=ismore12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),m):moref(fr(n1,n2),x)
-n2@[l:less(ts(1x,n2),ts(n1,2x))]
-lessfi1:=isless12(ts(1x,n2),ts(1x,den(fr(n1,n2))),ts(n1,2x),ts(num(fr(n1,n2)),2x),n2isnd(x,n1,n2),1disnd(x,n1,n2),l):lessf(x,fr(n1,n2))
-n2@[l:less(ts(n1,2x),ts(1x,n2))]
-lessfi2:=isless12(ts(n1,2x),ts(num(fr(n1,n2)),2x),ts(1x,n2),ts(1x,den(fr(n1,n2))),1disnd(x,n1,n2),n2isnd(x,n1,n2),l):lessf(fr(n1,n2),x)
-y@satz41:=satz10(ts(1x,2y),ts(1y,2x)):orec3(eq(x,y),moref(x,y),lessf(x,y))
-satz41a:=satz10a(ts(1x,2y),ts(1y,2x)):or3(eq(x,y),moref(x,y),lessf(x,y))
-satz41b:=satz10b(ts(1x,2y),ts(1y,2x)):ec3(eq(x,y),moref(x,y),lessf(x,y))
-[m:moref(x,y)]
-satz42:=satz11(ts(1x,2y),ts(1y,2x),m):lessf(y,x)
-y@[l:lessf(x,y)]
-satz43:=satz12(ts(1x,2y),ts(1y,2x),l):moref(y,x)
-u@1u:=num(u):nat
-2u:=den(u):nat
-[m:moref(x,y)][e:eq(x,z)][f:eq(y,u)]
-+244
-t1:=ists12(ts(1y,2u),ts(1u,2y),ts(1z,2x),ts(1x,2z),f,symeq(x,z,e)):is(ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)))
-t2:=tr3is(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1y,2u),ts(1z,2x)),ts(ts(1u,2y),ts(1x,2z)),ts(ts(1u,2z),ts(1x,2y)),stets(1y,2x,1z,2u),t1,stets(1u,2y,1x,2z)):is(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)))
-t3:=ismore1(ts(ts(1u,2z),ts(1x,2y)),ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)),symis(nat,ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1x,2y)),t2),satz32d(ts(1x,2y),ts(1y,2x),ts(1u,2z),m)):more(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1u,2z),ts(1y,2x)))
--244
-satz44:=satz33a(ts(1z,2u),ts(1u,2z),ts(1y,2x),ismore1(ts(ts(1y,2x),ts(1z,2u)),ts(ts(1z,2u),ts(1y,2x)),ts(ts(1u,2z),ts(1y,2x)),comts(ts(1y,2x),ts(1z,2u)),t3".244")):moref(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][m:moref(x,z)]
-eqmoref12:=satz44(x,z,y,u,m,e,f):moref(y,u)
-z@[e:eq(x,y)][m:moref(x,z)]
-eqmoref1:=satz44(x,z,y,z,m,e,refeq(z)):moref(y,z)
-e@[m:moref(z,x)]
-eqmoref2:=satz44(z,x,z,y,m,refeq(z),e):moref(z,y)
-u@[l:lessf(x,y)][e:eq(x,z)][f:eq(y,u)]
-satz45:=satz42(u,z,satz44(y,x,u,z,satz43(x,y,l),f,e)):lessf(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][l:lessf(x,z)]
-eqlessf12:=satz45(x,z,y,u,l,e,f):lessf(y,u)
-z@[e:eq(x,y)][l:lessf(x,z)]
-eqlessf1:=satz45(x,z,y,z,l,e,refeq(z)):lessf(y,z)
-e@[l:lessf(z,x)]
-eqlessf2:=satz45(z,x,z,y,l,refeq(z),e):lessf(z,y)
-y@moreq:=or(moref(x,y),eq(x,y)):'prop'
-lesseq:=or(lessf(x,y),eq(x,y)):'prop'
-[e:eq(x,y)]
-moreqi2:=ori2(moref(x,y),eq(x,y),e):moreq(x,y)
-lesseqi2:=ori2(lessf(x,y),eq(x,y),e):lesseq(x,y)
-y@[m:moref(x,y)]
-moreqi1:=ori1(moref(x,y),eq(x,y),m):moreq(x,y)
-y@[l:lessf(x,y)]
-lesseqi1:=ori1(lessf(x,y),eq(x,y),l):lesseq(x,y)
-y@[m:moreq(x,y)]
-satz41c:=th7"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,comor(moref(x,y),eq(x,y),m)):not(lessf(x,y))
-y@[l:lesseq(x,y)]
-satz41d:=th9"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),satz41b,l):not(moref(x,y))
-y@[n:not(moref(x,y))]
-satz41e:=th2"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n):lesseq(x,y)
-y@[n:not(lessf(x,y))]
-satz41f:=comor(eq(x,y),moref(x,y),th3"l.or3"(eq(x,y),moref(x,y),lessf(x,y),satz41a,n)):moreq(x,y)
-y@[m:moref(x,y)]
-satz41g:=th3"l.or"(lessf(x,y),eq(x,y),ec3e23(eq(x,y),moref(x,y),lessf(x,y),satz41b,m),ec3e21(eq(x,y),moref(x,y),lessf(x,y),satz41b,m)):not(lesseq(x,y))
-y@[l:lessf(x,y)]
-satz41h:=th3"l.or"(moref(x,y),eq(x,y),ec3e32(eq(x,y),moref(x,y),lessf(x,y),satz41b,l),ec3e31(eq(x,y),moref(x,y),lessf(x,y),satz41b,l)):not(moreq(x,y))
-y@[n:not(moreq(x,y))]
-satz41j:=or3e3(eq(x,y),moref(x,y),lessf(x,y),satz41a,th5"l.or"(moref(x,y),eq(x,y),n),th4"l.or"(moref(x,y),eq(x,y),n)):lessf(x,y)
-y@[n:not(lesseq(x,y))]
-satz41k:=or3e2(eq(x,y),moref(x,y),lessf(x,y),satz41a,th4"l.or"(lessf(x,y),eq(x,y),n),th5"l.or"(lessf(x,y),eq(x,y),n)):moref(x,y)
-u@[m:moreq(x,y)][e:eq(x,z)][f:eq(y,u)]
-+246
-[n:moref(x,y)]
-t1:=ori1(moref(z,u),eq(z,u),satz44(n,e,f)):moreq(z,u)
-f@[g:eq(x,y)]
-t2:=ori2(moref(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):moreq(z,u)
--246
-satz46:=orapp(moref(x,y),eq(x,y),moreq(z,u),m,[t:moref(x,y)]t1".246"(t),[t:eq(x,y)]t2".246"(t)):moreq(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][m:moreq(x,z)]
-eqmoreq12:=satz46(x,z,y,u,m,e,f):moreq(y,u)
-z@[e:eq(x,y)][m:moreq(x,z)]
-eqmoreq1:=satz46(x,z,y,z,m,e,refeq(z)):moreq(y,z)
-e@[m:moreq(z,x)]
-eqmoreq2:=satz46(z,x,z,y,m,refeq(z),e):moreq(z,y)
-u@[l:lesseq(x,y)][e:eq(x,z)][f:eq(y,u)]
-+247
-[k:lessf(x,y)]
-t1:=ori1(lessf(z,u),eq(z,u),satz45(k,e,f)):lesseq(z,u)
-f@[g:eq(x,y)]
-t2:=ori2(lessf(z,u),eq(z,u),tr3eq(z,x,y,u,symeq(x,z,e),g,f)):lesseq(z,u)
--247
-satz47:=orapp(lessf(x,y),eq(x,y),lesseq(z,u),l,[t:lessf(x,y)]t1".247"(t),[t:eq(x,y)]t2".247"(t)):lesseq(z,u)
-u@[e:eq(x,y)][f:eq(z,u)][l:lesseq(x,z)]
-eqlesseq12:=satz47(x,z,y,u,l,e,f):lesseq(y,u)
-z@[e:eq(x,y)][l:lesseq(x,z)]
-eqlesseq1:=satz47(x,z,y,z,l,e,refeq(z)):lesseq(y,z)
-e@[l:lesseq(z,x)]
-eqlesseq2:=satz47(z,x,z,y,l,refeq(z),e):lesseq(z,y)
-y@[m:moreq(x,y)]
-satz48:=th9"l.or"(moref(x,y),eq(x,y),lessf(y,x),eq(y,x),m,[t:moref(x,y)]satz42(x,y,t),[t:eq(x,y)]satz38(x,y,t)):lesseq(y,x)
-y@[l:lesseq(x,y)]
-satz49:=th9"l.or"(lessf(x,y),eq(x,y),moref(y,x),eq(y,x),l,[t:lessf(x,y)]satz43(x,y,t),[t:eq(x,y)]satz38(x,y,t)):moreq(y,x)
-z@[l:lessf(x,y)][k:lessf(y,z)]
-+250
-t1:=satz34a(ts(1x,2y),ts(1y,2x),ts(1y,2z),ts(1z,2y),l,k):less(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1y,2x),ts(1z,2y)))
-t2:=isless12(ts(ts(1x,2y),ts(1y,2z)),ts(ts(1x,2z),ts(1y,2y)),ts(ts(1y,2x),ts(1z,2y)),ts(ts(1z,2x),ts(1y,2y)),stets(1x,2y,1y,2z),tris(nat,ts(ts(1y,2x),ts(1z,2y)),ts(ts(1y,2y),ts(1z,2x)),ts(ts(1z,2x),ts(1y,2y)),stets(1y,2x,1z,2y),comts(ts(1y,2y),ts(1z,2x))),t1):less(ts(ts(1x,2z),ts(1y,2y)),ts(ts(1z,2x),ts(1y,2y)))
--250
-satz50:=satz33c(ts(1x,2z),ts(1z,2x),ts(1y,2y),t2".250"):lessf(x,z)
-trlessf:=satz50:lessf(x,z)
-z@[m:moref(x,y)][n:moref(y,z)]
-trmoref:=satz43(z,x,satz50(z,y,x,satz42(y,z,n),satz42(x,y,m))):moref(x,z)
-z@[l:lesseq(x,y)][k:lessf(y,z)]
-satz51a:=orapp(lessf(x,y),eq(x,y),lessf(x,z),l,[t:lessf(x,y)]satz50(t,k),[t:eq(x,y)]eqlessf1(y,x,z,symeq(x,y,t),k)):lessf(x,z)
-z@[l:lessf(x,y)][k:lesseq(y,z)]
-satz51b:=orapp(lessf(y,z),eq(y,z),lessf(x,z),k,[t:lessf(y,z)]satz50(l,t),[t:eq(y,z)]eqlessf2(y,z,x,t,l)):lessf(x,z)
-z@[m:moreq(x,y)][n:moref(y,z)]
-satz51c:=satz43(z,x,satz51b(z,y,x,satz42(y,z,n),satz48(x,y,m))):moref(x,z)
-z@[m:moref(x,y)][n:moreq(y,z)]
-satz51d:=satz43(z,x,satz51a(z,y,x,satz48(y,z,n),satz42(x,y,m))):moref(x,z)
-z@[l:lesseq(x,y)][k:lesseq(y,z)]
-+252
-[e:eq(x,y)][f:eq(y,z)]
-t1:=ori2(lessf(x,z),eq(x,z),treq(x,y,z,e,f)):lesseq(x,z)
-e@[j:lessf(y,z)]
-t2:=ori1(lessf(x,z),eq(x,z),satz51a(l,j)):lesseq(x,z)
-e@t3:=orapp(lessf(y,z),eq(y,z),lesseq(x,z),k,[t:lessf(y,z)]t2(t),[t:eq(y,z)]t1(t)):lesseq(x,z)
-k@[j:lessf(x,y)]
-t4:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
--252
-satz52:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t4".252"(t),[t:eq(x,y)]t3".252"(t)):lesseq(x,z)
-trlesseq:=satz52:lesseq(x,z)
-+*252
-k@[j:lessf(x,y)]
-t5:=ori1(lessf(x,z),eq(x,z),satz51b(j,k)):lesseq(x,z)
-k@[e:eq(x,y)]
-t6:=eqlesseq1(y,x,z,symeq(x,y,e),k):lesseq(x,z)
-k@anders:=orapp(lessf(x,y),eq(x,y),lesseq(x,z),l,[t:lessf(x,y)]t5(t),[t:eq(x,y)]t6(t)):lesseq(x,z)
--252
-z@[m:moreq(x,y)][n:moreq(y,z)]
-trmoreq:=satz49(z,x,satz52(z,y,x,satz48(y,z,n),satz48(x,y,m))):moreq(x,z)
-+253
-x@t1:=ismore1(pl(ts(1x,2x),ts(1x,2x)),ts(pl(1x,1x),2x),ts(1x,2x),distpt1(1x,1x,2x),satz18(ts(1x,2x),ts(1x,2x))):more(ts(pl(1x,1x),2x),ts(1x,2x))
-t2:=morefi2(pl(1x,1x),2x,t1):moref(fr(pl(1x,1x),2x),x)
--253
-x@satz53:=somei(frac,[t:frac]moref(t,x),fr(pl(1x,1x),2x),t2".253"):some"l"(frac,[t:frac]moref(t,x))
-+254
-t1:=isless2(pl(ts(1x,2x),ts(1x,2x)),ts(1x,pl(2x,2x)),ts(1x,2x),distpt2(1x,2x,2x),satz18a(ts(1x,2x),ts(1x,2x))):less(ts(1x,2x),ts(1x,pl(2x,2x)))
-t2:=lessfi2(1x,pl(2x,2x),t1):lessf(fr(1x,pl(2x,2x)),x)
--254
-satz54:=somei(frac,[t:frac]lessf(t,x),fr(1x,pl(2x,2x)),t2".254"):some"l"(frac,[t:frac]lessf(t,x))
-y@[l:lessf(x,y)]
-+255
-t1:=satz19f(ts(1x,2y),ts(1y,2x),ts(1x,2x),l):less(pl(ts(1x,2x),ts(1x,2y)),pl(ts(1x,2x),ts(1y,2x)))
-t2:=satz19c(ts(1x,2y),ts(1y,2x),ts(1y,2y),l):less(pl(ts(1x,2y),ts(1y,2y)),pl(ts(1y,2x),ts(1y,2y)))
-t3:=isless12(pl(ts(1x,2x),ts(1x,2y)),ts(1x,pl(2x,2y)),pl(ts(1x,2x),ts(1y,2x)),ts(pl(1x,1y),2x),distpt2(1x,2x,2y),distpt1(1x,1y,2x),t1):less(ts(1x,pl(2x,2y)),ts(pl(1x,1y),2x))
-t4:=lessfi1(pl(1x,1y),pl(2x,2y),t3):lessf(x,fr(pl(1x,1y),pl(2x,2y)))
-t5:=isless12(pl(ts(1x,2y),ts(1y,2y)),ts(pl(1x,1y),2y),pl(ts(1y,2x),ts(1y,2y)),ts(1y,pl(2x,2y)),distpt1(1x,1y,2y),distpt2(1y,2x,2y),t2):less(ts(pl(1x,1y),2y),ts(1y,pl(2x,2y)))
-t6:=lessfi2(y,pl(1x,1y),pl(2x,2y),t5):lessf(fr(pl(1x,1y),pl(2x,2y)),y)
-t7:=andi(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y),t4,t6):and(lessf(x,fr(pl(1x,1y),pl(2x,2y))),lessf(fr(pl(1x,1y),pl(2x,2y)),y))
--255
-satz55:=somei(frac,[t:frac]and(lessf(x,t),lessf(t,y)),fr(pl(1x,1y),pl(2x,2y)),t7".255"):some"l"(frac,[t:frac]and(lessf(x,t),lessf(t,y)))
-y@pf:=fr(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)):frac
-+ii3
-y2@t1:=ispl12(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y2),ts(num(fr(y1,y2)),den(fr(x1,x2))),ts(y1,x2),ndis12(x1,x2,y1,y2),ndis12(y1,y2,x1,x2)):is(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),pl(ts(x1,y2),ts(y1,x2)))
-t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
--ii3
-y2@pf12:=isnd(pl(ts(num(fr(x1,x2)),den(fr(y1,y2))),ts(num(fr(y1,y2)),den(fr(x1,x2)))),ts(den(fr(x1,x2)),den(fr(y1,y2))),pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2),t1".ii3",t2".ii3"):is"e"(frac,pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
-+*ii3
-n2@t3:=ispl12(ts(1x,den(fr(n1,n2))),ts(1x,n2),ts(num(fr(n1,n2)),2x),ts(n1,2x),ndisn2(x,n1,n2),ndis1d(x,n1,n2)):is(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),pl(ts(1x,n2),ts(n1,2x)))
-t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
--ii3
-n2@pf1:=isnd(pl(ts(1x,den(fr(n1,n2))),ts(num(fr(n1,n2)),2x)),ts(2x,den(fr(n1,n2))),pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2),t3".ii3",t4".ii3"):is"e"(frac,pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
-+*ii3
-n2@t5:=ispl12(ts(num(fr(n1,n2)),2x),ts(n1,2x),ts(1x,den(fr(n1,n2))),ts(1x,n2),ndis1d(x,n1,n2),ndisn2(x,n1,n2)):is(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),pl(ts(n1,2x),ts(1x,n2)))
-t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
--ii3
-n2@pf2:=isnd(pl(ts(num(fr(n1,n2)),2x),ts(1x,den(fr(n1,n2)))),ts(den(fr(n1,n2)),2x),pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x),t5".ii3",t6".ii3"):is"e"(frac,pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
-y2@pfeq12a:=refeq1(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)))
-pfeq12b:=refeq2(pf(fr(x1,x2),fr(y1,y2)),fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf12):eq(fr(pl(ts(x1,y2),ts(y1,x2)),ts(x2,y2)),pf(fr(x1,x2),fr(y1,y2)))
-n2@pfeq1a:=refeq1(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)))
-pfeq1b:=refeq2(pf(x,fr(n1,n2)),fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf1):eq(fr(pl(ts(1x,n2),ts(n1,2x)),ts(2x,n2)),pf(x,fr(n1,n2)))
-pfeq2a:=refeq1(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)))
-pfeq2b:=refeq2(pf(fr(n1,n2),x),fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf2):eq(fr(pl(ts(n1,2x),ts(1x,n2)),ts(n2,2x)),pf(fr(n1,n2),x))
-u@[e:eq(x,y)][f:eq(z,u)]
-+356
-t1:=ists1(ts(1x,2y),ts(1y,2x),ts(2z,2u),e):is(ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)))
-t2:=t1(z,u,x,y,f,e):is(ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)))
-t3:=tr3is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2z),ts(2u,2y)),ts(ts(1x,2y),ts(2u,2z)),ts(ts(1x,2y),ts(2z,2u)),ists2(ts(2y,2u),ts(2u,2y),ts(1x,2z),comts(2y,2u)),stets(1x,2z,2u,2y),ists2(ts(2u,2z),ts(2z,2u),ts(1x,2y),comts(2u,2z))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)))
-t4:=tr4is(nat,ts(ts(1x,2z),ts(2y,2u)),ts(ts(1x,2y),ts(2z,2u)),ts(ts(1y,2x),ts(2z,2u)),ts(ts(1y,2u),ts(2z,2x)),ts(ts(1y,2u),ts(2x,2z)),t3,t1,stets(1y,2x,2z,2u),ists2(ts(2z,2x),ts(2x,2z),ts(1y,2u),comts(2z,2x))):is(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)))
-t5:=tr4is(nat,ts(ts(1z,2x),ts(2y,2u)),ts(ts(1z,2u),ts(2y,2x)),ts(ts(1z,2u),ts(2x,2y)),ts(ts(1u,2z),ts(2x,2y)),ts(ts(1u,2y),ts(2x,2z)),stets(1z,2x,2y,2u),ists2(ts(2y,2x),ts(2x,2y),ts(1z,2u),comts(2y,2x)),t2,stets(1u,2z,2x,2y)):is(ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)))
-t6:=ispl12(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1y,2u),ts(2x,2z)),ts(ts(1z,2x),ts(2y,2u)),ts(ts(1u,2y),ts(2x,2z)),t4,t5):is(pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))))
-t7:=tr3is(nat,ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),pl(ts(ts(1x,2z),ts(2y,2u)),ts(ts(1z,2x),ts(2y,2u))),pl(ts(ts(1y,2u),ts(2x,2z)),ts(ts(1u,2y),ts(2x,2z))),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)),disttp1(ts(1x,2z),ts(1z,2x),ts(2y,2u)),t6,distpt1(ts(1y,2u),ts(1u,2y),ts(2x,2z))):is(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2u)),ts(pl(ts(1y,2u),ts(1u,2y)),ts(2x,2z)))
--356
-satz56:=eqi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2u),ts(1u,2y)),ts(2y,2u),t7".356"):eq(pf(x,z),pf(y,u))
-eqpf12:=satz56:eq(pf(x,z),pf(y,u))
-z@[e:eq(x,y)]
-eqpf1:=eqpf12(x,y,z,z,e,refeq(z)):eq(pf(x,z),pf(y,z))
-eqpf2:=eqpf12(z,z,x,y,refeq(z),e):eq(pf(z,x),pf(z,y))
-x2@[n:nat]
-satz57:=tr3eq(pf(fr(x1,n),fr(x2,n)),fr(pl(ts(x1,n),ts(x2,n)),ts(n,n)),fr(ts(pl(x1,x2),n),ts(n,n)),fr(pl(x1,x2),n),pfeq12a(x1,n,x2,n),eqn(pl(ts(x1,n),ts(x2,n)),ts(n,n),ts(pl(x1,x2),n),distpt1(x1,x2,n)),satz40c(pl(x1,x2),n,n)):eq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n))
-satz57a:=symeq(pf(fr(x1,n),fr(x2,n)),fr(pl(x1,x2),n),satz57):eq(fr(pl(x1,x2),n),pf(fr(x1,n),fr(x2,n)))
-y@satz58:=eqnd(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),pl(ts(1y,2x),ts(1x,2y)),ts(2y,2x),compl(ts(1x,2y),ts(1y,2x)),comts(2x,2y)):eq(pf(x,y),pf(y,x))
-compf:=satz58:eq(pf(x,y),pf(y,x))
-+359
-z@t1:=tr3is(nat,ts(ts(1y,2x),2z),ts(ts(2x,1y),2z),ts(2x,ts(1y,2z)),ts(ts(1y,2z),2x),ists1(ts(1y,2x),ts(2x,1y),2z,comts(1y,2x)),assts1(2x,1y,2z),comts(2x,ts(1y,2z))):is(ts(ts(1y,2x),2z),ts(ts(1y,2z),2x))
-t2:=ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),t1):is(pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
-t3:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),t2):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
-t4:=tris(nat,ts(1z,ts(2x,2y)),ts(1z,ts(2y,2x)),ts(ts(1z,2y),2x),ists2(ts(2x,2y),ts(2y,2x),1z,comts(2x,2y)),assts2(1z,2y,2x)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
-t5:=ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t3,t4):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)))
-t6:=ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x)):is(pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
-t7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),t5,asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),t6):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
--359
-z@satz59:=tr3eq(pf(pf(x,y),z),fr(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z)),fr(pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z))),pf(x,pf(y,z)),pfeq2a(z,pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y)),eqnd(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),ts(ts(2x,2y),2z),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ts(2x,ts(2y,2z)),t7".359",assts1(2x,2y,2z)),pfeq1b(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z))):eq(pf(pf(x,y),z),pf(x,pf(y,z)))
-asspf1:=satz59:eq(pf(pf(x,y),z),pf(x,pf(y,z)))
-asspf2:=symeq(pf(pf(x,y),z),pf(x,pf(y,z)),asspf1):eq(pf(x,pf(y,z)),pf(pf(x,y),z))
-c@stets1:=tr3is(nat,ts(ts(a,b),c),ts(a,ts(b,c)),ts(a,ts(c,b)),ts(ts(a,c),b),assts1(a,b,c),ists2(ts(b,c),ts(c,b),a,comts(b,c)),assts2(a,c,b)):is(ts(ts(a,b),c),ts(ts(a,c),b))
-+*359
-z@t8:=tris(nat,ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z)),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),disttp1(ts(1x,2y),ts(1y,2x),2z),ispl12(ts(ts(1x,2y),2z),ts(1x,ts(2y,2z)),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),assts1(1x,2y,2z),stets1(1y,2x,2z))):is(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)))
-t9:=tris(nat,ts(1z,ts(2x,2y)),ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),assts2(1z,2x,2y),stets1(1z,2x,2y)):is(ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x))
-anderst7:=tr3is(nat,pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(ts(1z,2y),2x)),pl(ts(1x,ts(2y,2z)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)),ispl12(ts(pl(ts(1x,2y),ts(1y,2x)),2z),pl(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x)),ts(1z,ts(2x,2y)),ts(ts(1z,2y),2x),t8,t9),asspl1(ts(1x,ts(2y,2z)),ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ispl2(pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),ts(1x,ts(2y,2z)),distpt1(ts(1y,2z),ts(1z,2y),2x))):is(pl(ts(pl(ts(1x,2y),ts(1y,2x)),2z),ts(1z,ts(2x,2y))),pl(ts(1x,ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),2x)))
--359
-+360
-y@t1:=satz18(ts(1x,2y),ts(1y,2x)):more(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y))
-t2:=satz32a(pl(ts(1x,2y),ts(1y,2x)),ts(1x,2y),2x,t1):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(ts(1x,2y),2x))
-t3:=tris(nat,ts(ts(1x,2y),2x),ts(1x,ts(2y,2x)),ts(1x,ts(2x,2y)),assts1(1x,2y,2x),ists2(ts(2y,2x),ts(2x,2y),1x,comts(2y,2x))):is(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)))
-t4:=ismore2(ts(ts(1x,2y),2x),ts(1x,ts(2x,2y)),ts(pl(ts(1x,2y),ts(1y,2x)),2x),t3,t2):more(ts(pl(ts(1x,2y),ts(1y,2x)),2x),ts(1x,ts(2x,2y)))
--360
-y@satz60:=morefi2(pl(ts(1x,2y),ts(1y,2x)),ts(2x,2y),t4".360"):moref(pf(x,y),x)
-satz60a:=satz42(pf(x,y),x,satz60):lessf(x,pf(x,y))
-z@[m:moref(x,y)]
-+361
-t1:=satz32a(ts(1x,2y),ts(1y,2x),2z,m):more(ts(ts(1x,2y),2z),ts(ts(1y,2x),2z))
-t2:=ismore12(ts(ts(1x,2y),2z),ts(ts(1x,2z),2y),ts(ts(1y,2x),2z),ts(ts(1y,2z),2x),stets1(1x,2y,2z),stets1(1y,2x,2z),t1):more(ts(ts(1x,2z),2y),ts(ts(1y,2z),2x))
-t3:=stets1(1z,2x,2y):is(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x))
-t4:=satz19h(ts(ts(1z,2x),2y),ts(ts(1z,2y),2x),ts(ts(1x,2z),2y),ts(ts(1y,2z),2x),t3,t2):more(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)))
-t5:=ismore12(pl(ts(ts(1x,2z),2y),ts(ts(1z,2x),2y)),ts(pl(ts(1x,2z),ts(1z,2x)),2y),pl(ts(ts(1y,2z),2x),ts(ts(1z,2y),2x)),ts(pl(ts(1y,2z),ts(1z,2y)),2x),distpt1(ts(1x,2z),ts(1z,2x),2y),distpt1(ts(1y,2z),ts(1z,2y),2x),t4):more(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x))
-t6:=satz32a(ts(pl(ts(1x,2z),ts(1z,2x)),2y),ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z,t5):more(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z))
-t7:=ismore12(ts(ts(pl(ts(1x,2z),ts(1z,2x)),2y),2z),ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(ts(pl(ts(1y,2z),ts(1z,2y)),2x),2z),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)),assts1(pl(ts(1x,2z),ts(1z,2x)),2y,2z),assts1(pl(ts(1y,2z),ts(1z,2y)),2x,2z),t6):more(ts(pl(ts(1x,2z),ts(1z,2x)),ts(2y,2z)),ts(pl(ts(1y,2z),ts(1z,2y)),ts(2x,2z)))
--361
-satz61:=morefi12(pl(ts(1x,2z),ts(1z,2x)),ts(2x,2z),pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z),t7".361"):moref(pf(x,z),pf(y,z))
-z@[m:moref(x,y)]
-satz62a:=satz61(m):moref(pf(x,z),pf(y,z))
-z@[e:eq(x,y)]
-satz62b:=eqpf1(x,y,z,e):eq(pf(x,z),pf(y,z))
-z@[l:lessf(x,y)]
-satz62c:=satz42(pf(y,z),pf(x,z),satz61(y,x,z,satz43(l))):lessf(pf(x,z),pf(y,z))
-m@satz62d:=eqmoref12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62a):moref(pf(z,x),pf(z,y))
-e@satz62e:=eqpf2(x,y,z,e):eq(pf(z,x),pf(z,y))
-l@satz62f:=eqlessf12(pf(x,z),pf(z,x),pf(y,z),pf(z,y),compf(x,z),compf(y,z),satz62c):lessf(pf(z,x),pf(z,y))
-u@[e:eq(x,y)][m:moref(z,u)]
-satz62g:=eqmoref2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62d(z,u,x,m)):moref(pf(x,z),pf(y,u))
-satz62h:=eqmoref12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62g):moref(pf(z,x),pf(u,y))
-e@[l:lessf(z,u)]
-satz62j:=eqlessf2(pf(x,u),pf(y,u),pf(x,z),eqpf1(x,y,u,e),satz62f(z,u,x,l)):lessf(pf(x,z),pf(y,u))
-satz62k:=eqlessf12(pf(x,z),pf(z,x),pf(y,u),pf(u,y),compf(x,z),compf(y,u),satz62j):lessf(pf(z,x),pf(u,y))
-+363
-z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
-t2:=satz41b(pf(x,z),pf(y,z)):ec3(eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)))
--363
-z@[m:moref(pf(x,z),pf(y,z))]
-satz63a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),m):moref(x,y)
-z@[e:eq(pf(x,z),pf(y,z))]
-satz63b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),e):eq(x,y)
-z@[l:lessf(pf(x,z),pf(y,z))]
-satz63c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(pf(x,z),pf(y,z)),moref(pf(x,z),pf(y,z)),lessf(pf(x,z),pf(y,z)),t1".363",t2".363",[u:eq(x,y)]satz62b(x,y,z,u),[u:moref(x,y)]satz62a(x,y,z,u),[u:lessf(x,y)]satz62c(x,y,z,u),l):lessf(x,y)
-z@[m:moref(pf(z,x),pf(z,y))]
-satz63d:=satz63a(eqmoref12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),m)):moref(x,y)
-z@[e:eq(pf(z,x),pf(z,y))]
-satz63e:=satz63b(tr3eq(pf(x,z),pf(z,x),pf(z,y),pf(y,z),compf(x,z),e,compf(z,y))):eq(x,y)
-z@[f:lessf(pf(z,x),pf(z,y))]
-satz63f:=satz63c(eqlessf12(pf(z,x),pf(x,z),pf(z,y),pf(y,z),compf(z,x),compf(z,y),f)):lessf(x,y)
-u@[m:moref(x,y)][n:moref(z,u)]
-+364
-t1:=satz61(x,y,z,m):moref(pf(x,z),pf(y,z))
-t2:=eqmoref12(pf(z,y),pf(y,z),pf(u,y),pf(y,u),compf(z,y),compf(u,y),satz61(z,u,y,n)):moref(pf(y,z),pf(y,u))
--364
-satz64:=trmoref(pf(x,z),pf(y,z),pf(y,u),t1".364",t2".364"):moref(pf(x,z),pf(y,u))
-u@[l:lessf(x,y)][k:lessf(z,u)]
-satz64a:=satz42(pf(y,u),pf(x,z),satz64(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
-u@[m:moreq(x,y)][n:moref(z,u)]
-satz65a:=orapp(moref(x,y),eq(x,y),moref(pf(x,z),pf(y,u)),m,[v:moref(x,y)]satz64(v,n),[v:eq(x,y)]satz62g(v,n)):moref(pf(x,z),pf(y,u))
-u@[m:moref(x,y)][n:moreq(z,u)]
-satz65b:=orapp(moref(z,u),eq(z,u),moref(pf(x,z),pf(y,u)),n,[v:moref(z,u)]satz64(m,v),[v:eq(z,u)]eqmoref2(pf(y,z),pf(y,u),pf(x,z),eqpf2(z,u,y,v),satz61(x,y,z,m))):moref(pf(x,z),pf(y,u))
-u@[l:lesseq(x,y)][k:lessf(z,u)]
-satz65c:=satz42(pf(y,u),pf(x,z),satz65a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(pf(x,z),pf(y,u))
-u@[l:lessf(x,y)][k:lesseq(z,u)]
-satz65d:=satz42(pf(y,u),pf(x,z),satz65b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(pf(x,z),pf(y,u))
-u@[m:moreq(x,y)][n:moreq(z,u)]
-+366
-[e:eq(x,y)][f:eq(z,u)]
-t1:=moreqi2(pf(x,z),pf(y,u),satz56(e,f)):moreq(pf(x,z),pf(y,u))
-e@[o:moref(z,u)]
-t2:=moreqi1(pf(x,z),pf(y,u),satz65a(m,o)):moreq(pf(x,z),pf(y,u))
-e@t3:=orapp(moref(z,u),eq(z,u),moreq(pf(x,z),pf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(pf(x,z),pf(y,u))
-n@[o:moref(x,y)]
-t4:=moreqi1(pf(x,z),pf(y,u),satz65b(o,n)):moreq(pf(x,z),pf(y,u))
--366
-satz66:=orapp(moref(x,y),eq(x,y),moreq(pf(x,z),pf(y,u)),m,[v:moref(x,y)]t4".366"(v),[v:eq(x,y)]t3".366"(v)):moreq(pf(x,z),pf(y,u))
-u@[l:lesseq(x,y)][k:lesseq(z,u)]
-satz66a:=satz48(pf(y,u),pf(x,z),satz66(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(pf(x,z),pf(y,u))
-y@[l:lesseq(x,y)]
-+367
-[v:frac][e:eq(pf(y,v),x)]
-t1:=eqmoref1(pf(y,v),x,y,e,satz60(y,v)):moref(x,y)
-v@t2:=th3"l.imp"(eq(pf(y,v),x),moref(x,y),satz41d(x,y,l),[t:eq(pf(y,v),x)]t1(t)):not(eq(pf(y,v),x))
--367
-vorbemerkung67:=th5"l.some"(frac,[v:frac]eq(pf(y,v),x),[v:frac]t2".367"(v)):not(some"l"(frac,[t:frac]eq(pf(y,t),x)))
-y@[v:frac][w:frac][e:eq(pf(y,v),x)][f:eq(pf(y,w),x)]
-satz67b:=satz63e(v,w,y,treq2(pf(y,v),pf(y,w),x,e,f)):eq(v,w)
-y@[m:moref(x,y)]
-+*367
-m@t3:=onei(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),satz8b(ts(1x,2y),ts(1y,2x)),m):one([t:nat]diffprop(ts(1x,2y),ts(1y,2x),t))
-vo:=ind(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):nat
-t4:=oneax(nat,[t:nat]diffprop(ts(1x,2y),ts(1y,2x),t),t3):is(ts(1x,2y),pl(ts(1y,2x),vo))
-w:=fr(vo,ts(2x,2y)):frac
-t5:=treq(y,fr(ts(1y,2x),ts(2y,2x)),fr(ts(1y,2x),ts(2x,2y)),satz40(y,2x),eqd(ts(1y,2x),ts(2y,2x),ts(2x,2y),comts(2y,2x))):eq(y,fr(ts(1y,2x),ts(2x,2y)))
-t6:=tr4eq(pf(y,w),pf(fr(ts(1y,2x),ts(2x,2y)),fr(vo,ts(2x,2y))),fr(pl(ts(1y,2x),vo),ts(2x,2y)),fr(ts(1x,2y),ts(2x,2y)),x,eqpf1(y,fr(ts(1y,2x),ts(2x,2y)),w,t5),satz57(ts(1y,2x),vo,ts(2x,2y)),eqn(pl(ts(1y,2x),vo),ts(2x,2y),ts(1x,2y),symis(nat,ts(1x,2y),pl(ts(1y,2x),vo),t4)),satz40a(x,2y)):eq(pf(y,w),x)
--367
-m@satz67a:=somei(frac,[t:frac]eq(pf(y,t),x),w".367",t6".367"):some"l"(frac,[t:frac]eq(pf(y,t),x))
-mf:=w".367":frac
-satz67c:=t6".367":eq(pf(y,mf(x,y,m)),x)
-satz67d:=symeq(pf(y,mf(x,y,m)),x,satz67c):eq(x,pf(y,mf(x,y,m)))
-y@[v:frac][m:moref(x,y)][e:eq(pf(y,v),x)]
-satz67e:=satz67b(v,mf(x,y,m),e,satz67c(m)):eq(v,mf(x,y,m))
-y@tf:=fr(ts(1x,1y),ts(2x,2y)):frac
-+ii4
-y2@t1:=ists12(num(fr(x1,x2)),x1,num(fr(y1,y2)),y1,numis(x1,x2),numis(y1,y2)):is(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(x1,y1))
-t2:=ists12(den(fr(x1,x2)),x2,den(fr(y1,y2)),y2,denis(x1,x2),denis(y1,y2)):is(ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x2,y2))
--ii4
-y2@tf12:=isnd(ts(num(fr(x1,x2)),num(fr(y1,y2))),ts(den(fr(x1,x2)),den(fr(y1,y2))),ts(x1,y1),ts(x2,y2),t1".ii4",t2".ii4"):is"e"(frac,tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
-+*ii4
-n2@t3:=ists2(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(1x,num(fr(n1,n2))),ts(1x,n1))
-t4:=ists2(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(2x,den(fr(n1,n2))),ts(2x,n2))
--ii4
-n2@tf1:=isnd(ts(1x,num(fr(n1,n2))),ts(2x,den(fr(n1,n2))),ts(1x,n1),ts(2x,n2),t3".ii4",t4".ii4"):is"e"(frac,tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
-+*ii4
-n2@t5:=ists1(num(fr(n1,n2)),n1,1x,numis(n1,n2)):is(ts(num(fr(n1,n2)),1x),ts(n1,1x))
-t6:=ists1(den(fr(n1,n2)),n2,2x,denis(n1,n2)):is(ts(den(fr(n1,n2)),2x),ts(n2,2x))
--ii4
-n2@tf2:=isnd(ts(num(fr(n1,n2)),1x),ts(den(fr(n1,n2)),2x),ts(n1,1x),ts(n2,2x),t5".ii4",t6".ii4"):is"e"(frac,tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
-y2@tfeq12a:=refeq1(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)))
-tfeq12b:=refeq2(tf(fr(x1,x2),fr(y1,y2)),fr(ts(x1,y1),ts(x2,y2)),tf12):eq(fr(ts(x1,y1),ts(x2,y2)),tf(fr(x1,x2),fr(y1,y2)))
-n2@tfeq1a:=refeq1(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)))
-tfeq1b:=refeq2(tf(x,fr(n1,n2)),fr(ts(1x,n1),ts(2x,n2)),tf1):eq(fr(ts(1x,n1),ts(2x,n2)),tf(x,fr(n1,n2)))
-tfeq2a:=refeq1(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)))
-tfeq2b:=refeq2(tf(fr(n1,n2),x),fr(ts(n1,1x),ts(n2,2x)),tf2):eq(fr(ts(n1,1x),ts(n2,2x)),tf(fr(n1,n2),x))
-u@[e:eq(x,y)][f:eq(z,u)]
-+468
-t1:=ists12(ts(1x,2y),ts(1y,2x),ts(1z,2u),ts(1u,2z),e,f):is(ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)))
--468
-d@stets2:=tr3is(nat,ts(ts(a,b),ts(c,d)),ts(ts(a,b),ts(d,c)),ts(ts(a,c),ts(d,b)),ts(ts(a,c),ts(b,d)),ists2(ts(c,d),ts(d,c),ts(a,b),comts(c,d)),stets(a,b,d,c),ists2(ts(d,b),ts(b,d),ts(a,c),comts(d,b))):is(ts(ts(a,b),ts(c,d)),ts(ts(a,c),ts(b,d)))
-+*468
-f@t2:=tr3is(nat,ts(ts(1x,1z),ts(2y,2u)),ts(ts(1x,2y),ts(1z,2u)),ts(ts(1y,2x),ts(1u,2z)),ts(ts(1y,1u),ts(2x,2z)),stets2(1x,1z,2y,2u),t1,stets2(1y,2x,1u,2z)):is(ts(ts(1x,1z),ts(2y,2u)),ts(ts(1y,1u),ts(2x,2z)))
--468
-f@satz68:=eqi12(ts(1x,1z),ts(2x,2z),ts(1y,1u),ts(2y,2u),t2".468"):eq(tf(x,z),tf(y,u))
-eqtf12:=satz68:eq(tf(x,z),tf(y,u))
-z@[e:eq(x,y)]
-eqtf1:=eqtf12(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
-eqtf2:=eqtf12(z,z,x,y,refeq(z),e):eq(tf(z,x),tf(z,y))
-y@satz69:=eqnd(ts(1x,1y),ts(2x,2y),ts(1y,1x),ts(2y,2x),comts(1x,1y),comts(2x,2y)):eq(tf(x,y),tf(y,x))
-comtf:=satz69:eq(tf(x,y),tf(y,x))
-z@satz70:=tr3eq(tf(tf(x,y),z),fr(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z)),fr(ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z))),tf(x,tf(y,z)),tfeq2a(z,ts(1x,1y),ts(2x,2y)),eqnd(ts(ts(1x,1y),1z),ts(ts(2x,2y),2z),ts(1x,ts(1y,1z)),ts(2x,ts(2y,2z)),assts1(1x,1y,1z),assts1(2x,2y,2z)),tfeq1b(x,ts(1y,1z),ts(2y,2z))):eq(tf(tf(x,y),z),tf(x,tf(y,z)))
-asstf1:=satz70:eq(tf(tf(x,y),z),tf(x,tf(y,z)))
-asstf2:=symeq(tf(tf(x,y),z),tf(x,tf(y,z)),asstf1):eq(tf(x,tf(y,z)),tf(tf(x,y),z))
-+471
-t1:=tr3eq(tf(x,pf(y,z)),fr(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z))),fr(pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),ts(2x,ts(2y,2z))),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),tfeq1a(x,pl(ts(1y,2z),ts(1z,2y)),ts(2y,2z)),eqn(ts(1x,pl(ts(1y,2z),ts(1z,2y))),ts(2x,ts(2y,2z)),pl(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y))),disttp2(1x,ts(1y,2z),ts(1z,2y))),satz57a(ts(1x,ts(1y,2z)),ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))):eq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))))
-t2:=treq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(ts(1x,1y),2z),ts(ts(2x,2y),2z)),tf(x,y),eqnd(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z)),ts(ts(1x,1y),2z),ts(ts(2x,2y),2z),assts2(1x,1y,2z),assts2(2x,2y,2z)),satz40c(ts(1x,1y),ts(2x,2y),2z)):eq(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y))
-t3:=treq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2z,2y))),tf(x,z),eqd(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)),ts(2x,ts(2z,2y)),ists2(ts(2y,2z),ts(2z,2y),2x,comts(2y,2z))),t2(x,z,y)):eq(fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z))
--471
-satz71:=treq(tf(x,pf(y,z)),pf(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z)))),pf(tf(x,y),tf(x,z)),t1".471",eqpf12(fr(ts(1x,ts(1y,2z)),ts(2x,ts(2y,2z))),tf(x,y),fr(ts(1x,ts(1z,2y)),ts(2x,ts(2y,2z))),tf(x,z),t2".471",t3".471")):eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
-disttpf1:=tr3eq(tf(pf(x,y),z),tf(z,pf(x,y)),pf(tf(z,x),tf(z,y)),pf(tf(x,z),tf(y,z)),comtf(pf(x,y),z),satz71(z,x,y),eqpf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y))):eq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)))
-disttpf2:=satz71:eq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)))
-distptf1:=symeq(tf(pf(x,y),z),pf(tf(x,z),tf(y,z)),disttpf1):eq(pf(tf(x,z),tf(y,z)),tf(pf(x,y),z))
-distptf2:=symeq(tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),disttpf2):eq(pf(tf(x,y),tf(x,z)),tf(x,pf(y,z)))
-[m:moref(x,y)]
-+472
-t1:=satz32a(ts(1x,2y),ts(1y,2x),ts(1z,2z),m):more(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1y,2x),ts(1z,2z)))
-t2:=ismore12(ts(ts(1x,2y),ts(1z,2z)),ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,2x),ts(1z,2z)),ts(ts(1y,1z),ts(2x,2z)),stets2(1x,2y,1z,2z),stets2(1y,2x,1z,2z),t1):more(ts(ts(1x,1z),ts(2y,2z)),ts(ts(1y,1z),ts(2x,2z)))
--472
-satz72a:=morefi12(ts(1x,1z),ts(2x,2z),ts(1y,1z),ts(2y,2z),t2".472"):moref(tf(x,z),tf(y,z))
-z@[e:eq(x,y)]
-satz72b:=satz68(x,y,z,z,e,refeq(z)):eq(tf(x,z),tf(y,z))
-z@[l:lessf(x,y)]
-satz72c:=satz42(tf(y,z),tf(x,z),satz72a(y,x,z,satz43(x,y,l))):lessf(tf(x,z),tf(y,z))
-m@satz72d:=eqmoref12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72a):moref(tf(z,x),tf(z,y))
-e@satz72e:=eqtf2(x,y,z,e):eq(tf(z,x),tf(z,y))
-l@satz72f:=eqlessf12(tf(x,z),tf(z,x),tf(y,z),tf(z,y),comtf(x,z),comtf(y,z),satz72c):lessf(tf(z,x),tf(z,y))
-u@[e:eq(x,y)][m:moref(z,u)]
-satz72g:=eqmoref2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72d(z,u,x,m)):moref(tf(x,z),tf(y,u))
-satz72h:=eqmoref12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72g):moref(tf(z,x),tf(u,y))
-e@[l:lessf(z,u)]
-satz72j:=eqlessf2(tf(x,u),tf(y,u),tf(x,z),eqtf1(x,y,u,e),satz72f(z,u,x,l)):lessf(tf(x,z),tf(y,u))
-satz72k:=eqlessf12(tf(x,z),tf(z,x),tf(y,u),tf(u,y),comtf(x,z),comtf(y,u),satz72j):lessf(tf(z,x),tf(u,y))
-+473
-z@t1:=satz41a(x,y):or3(eq(x,y),moref(x,y),lessf(x,y))
-t2:=satz41b(tf(x,z),tf(y,z)):ec3(eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)))
--473
-z@[m:moref(tf(x,z),tf(y,z))]
-satz73a:=th11"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),m):moref(x,y)
-z@[e:eq(tf(x,z),tf(y,z))]
-satz73b:=th10"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),e):eq(x,y)
-z@[l:lessf(tf(x,z),tf(y,z))]
-satz73c:=th12"l.ec3"(eq(x,y),moref(x,y),lessf(x,y),eq(tf(x,z),tf(y,z)),moref(tf(x,z),tf(y,z)),lessf(tf(x,z),tf(y,z)),t1".473",t2".473",[u:eq(x,y)]satz72b(x,y,z,u),[u:moref(x,y)]satz72a(x,y,z,u),[u:lessf(x,y)]satz72c(x,y,z,u),l):lessf(x,y)
-z@[m:moref(tf(z,x),tf(z,y))]
-satz73d:=satz73a(eqmoref12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),m)):moref(x,y)
-z@[e:eq(tf(z,x),tf(z,y))]
-satz73e:=satz73b(tr3eq(tf(x,z),tf(z,x),tf(z,y),tf(y,z),comtf(x,z),e,comtf(z,y))):eq(x,y)
-z@[l:lessf(tf(z,x),tf(z,y))]
-satz73f:=satz73c(eqlessf12(tf(z,x),tf(x,z),tf(z,y),tf(y,z),comtf(z,x),comtf(z,y),l)):lessf(x,y)
-u@[m:moref(x,y)][n:moref(z,u)]
-+474
-t1:=satz72a(x,y,z,m):moref(tf(x,z),tf(y,z))
-t2:=eqmoref12(tf(z,y),tf(y,z),tf(u,y),tf(y,u),comtf(z,y),comtf(u,y),satz72a(z,u,y,n)):moref(tf(y,z),tf(y,u))
--474
-satz74:=trmoref(tf(x,z),tf(y,z),tf(y,u),t1".474",t2".474"):moref(tf(x,z),tf(y,u))
-u@[l:lessf(x,y)][k:lessf(z,u)]
-satz74a:=satz42(tf(y,u),tf(x,z),satz74(y,x,u,z,satz43(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
-u@[m:moreq(x,y)][n:moref(z,u)]
-satz75a:=orapp(moref(x,y),eq(x,y),moref(tf(x,z),tf(y,u)),m,[v:moref(x,y)]satz74(v,n),[v:eq(x,y)]satz72g(v,n)):moref(tf(x,z),tf(y,u))
-u@[m:moref(x,y)][n:moreq(z,u)]
-satz75b:=orapp(moref(z,u),eq(z,u),moref(tf(x,z),tf(y,u)),n,[v:moref(z,u)]satz74(m,v),[v:eq(z,u)]eqmoref2(tf(y,z),tf(y,u),tf(x,z),eqtf2(z,u,y,v),satz72a(m))):moref(tf(x,z),tf(y,u))
-u@[l:lesseq(x,y)][k:lessf(z,u)]
-satz75c:=satz42(tf(y,u),tf(x,z),satz75a(y,x,u,z,satz49(x,y,l),satz43(z,u,k))):lessf(tf(x,z),tf(y,u))
-u@[l:lessf(x,y)][k:lesseq(z,u)]
-satz75d:=satz42(tf(y,u),tf(x,z),satz75b(y,x,u,z,satz43(x,y,l),satz49(z,u,k))):lessf(tf(x,z),tf(y,u))
-u@[m:moreq(x,y)][n:moreq(z,u)]
-+476
-[e:eq(x,y)][f:eq(z,u)]
-t1:=moreqi2(tf(x,z),tf(y,u),satz68(e,f)):moreq(tf(x,z),tf(y,u))
-e@[o:moref(z,u)]
-t2:=moreqi1(tf(x,z),tf(y,u),satz75a(m,o)):moreq(tf(x,z),tf(y,u))
-e@t3:=orapp(moref(z,u),eq(z,u),moreq(tf(x,z),tf(y,u)),n,[v:moref(z,u)]t2(v),[v:eq(z,u)]t1(v)):moreq(tf(x,z),tf(y,u))
-n@[o:moref(x,y)]
-t4:=moreqi1(tf(x,z),tf(y,u),satz75b(o,n)):moreq(tf(x,z),tf(y,u))
--476
-satz76:=orapp(moref(x,y),eq(x,y),moreq(tf(x,z),tf(y,u)),m,[v:moref(x,y)]t4".476"(v),[v:eq(x,y)]t3".476"(v)):moreq(tf(x,z),tf(y,u))
-u@[l:lesseq(x,y)][k:lesseq(z,u)]
-satz76a:=satz48(tf(y,u),tf(x,z),satz76(y,x,u,z,satz49(x,y,l),satz49(z,u,k))):lesseq(tf(x,z),tf(y,u))
-y@[v:frac][w:frac][e:eq(tf(y,v),x)][f:eq(tf(y,w),x)]
-satz77b:=satz73e(v,w,y,treq2(tf(y,v),tf(y,w),x,e,f)):eq(v,w)
-+477
-y@v:=fr(ts(1x,2y),ts(2x,1y)):frac
-t1:=tr4eq(tf(y,v),tf(v,y),fr(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y)),fr(ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y))),x,comtf(y,v),tfeq2a(y,ts(1x,2y),ts(2x,1y)),eqnd(ts(ts(1x,2y),1y),ts(ts(2x,1y),2y),ts(1x,ts(1y,2y)),ts(2x,ts(1y,2y)),tris(nat,ts(ts(1x,2y),1y),ts(1x,ts(2y,1y)),ts(1x,ts(1y,2y)),assts1(1x,2y,1y),ists2(ts(2y,1y),ts(1y,2y),1x,comts(2y,1y))),assts1(2x,1y,2y)),satz40a(x,ts(1y,2y))):eq(tf(y,v),x)
--477
-y@satz77a:=somei(frac,[t:frac]eq(tf(y,t),x),v".477",t1".477"):some"l"(frac,[t:frac]eq(tf(y,t),x))
-+rt
-@eq:=[x:frac][y:frac]eq"n"(x,y):[x:frac][y:frac]'prop'
-refeq:=[x:frac]refeq"n"(x):[x:frac]<x><x>eq
-symeq:=[x:frac][y:frac][t:<y><x>eq]symeq"n"(x,y,t):[x:frac][y:frac][t:<y><x>eq]<x><y>eq
-treq:=[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]treq"n"(x,y,z,t,u):[x:frac][y:frac][z:frac][t:<y><x>eq][u:<z><y>eq]<z><x>eq
-[x:frac][s:set(frac)]
-inf:=esti(frac,x,s):'prop'
-@rat:=ect"eq"(frac,eq,refeq,symeq,treq):'type'
-[x0:rat][y0:rat]
-is:=is"e"(rat,x0,y0):'prop'
-nis:=not(is(x0,y0)):'prop'
-@[p:[x:rat]'prop']
-some:=some"l"(rat,p):'prop'
-all:=all"l"(rat,p):'prop'
-one:=one"e"(rat,p):'prop'
-x0@[s:set(rat)]
-in:=esti(rat,x0,s):'prop'
-x@ratof:=ectelt"eq"(frac,eq,refeq,symeq,treq,x):rat
-x0@class:=ecect"eq"(frac,eq,refeq,symeq,treq,x0):set(frac)
-x@inclass:=th5"eq.4"(frac,eq,refeq,symeq,treq,x):inf(x,class(ratof(x)))
-x0@[x:frac][y:frac][xix0:inf(x,class(x0))][e:eq"n"(x,y)]
-lemmaeq1:=th8"eq.4"(frac,eq,refeq,symeq,treq,x0,x,xix0,y,e):inf(y,class(x0))
-x0@[a:'prop'][a1:[x:frac][xi:inf(x,class(x0))]a]
-ratapp1:=th3"eq.4"(frac,eq,refeq,symeq,treq,x0,a,a1):a
-y0@[a:'prop'][a1:[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]a][x:frac][xix0:inf(x,class(x0))]
-+ii5
-t1:=ratapp1(y0,a,[y:frac][yi:inf(y,class(y0))]<yi><xix0><y><x>a1):a
--ii5
-a1@ratapp2:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t1".ii5"(x,xi)):a
-y0@[z0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]a][x:frac][xix0:inf(x,class(x0))]
-+*ii5
-xix0@t2:=ratapp2(y0,z0,a,[y:frac][z:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))]<zi><yi><xix0><z><y><x>a1):a
--ii5
-a1@ratapp3:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t2".ii5"(x,xi)):a
-z0@[u0:rat][a:'prop'][a1:[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]a][x:frac][xix0:inf(x,class(x0))]
-+*ii5
-xix0@t3:=ratapp3(y0,z0,u0,a,[y:frac][z:frac][u:frac][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]<ui><zi><yi><xix0><u><z><y><x>a1):a
--ii5
-a1@ratapp4:=ratapp1(x0,a,[x:frac][xi:inf(x,class(x0))]t3".ii5"(x,xi)):a
-y0@[x1:frac][y1:frac][x1ix0:inf(x1,class(x0))][y1iy0:inf(y1,class(y0))][e:eq"n"(x1,y1)]
-isi:=th3"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,e):is(x0,y0)
-y1iy0@[i:is(x0,y0)]
-ise:=th5"eq.5"(frac,eq,refeq,symeq,treq,x0,y0,x1,x1ix0,y1,y1iy0,i):eq"n"(x1,y1)
-y1iy0@[n:not(eq"n"(x1,y1))]
-nisi:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),n,[t:is(x0,y0)]ise(t)):nis(x0,y0)
-y1iy0@[n:nis(x0,y0)]
-nise:=th3"l.imp"(eq"n"(x1,y1),is(x0,y0),n,[t:eq"n"(x1,y1)]isi(t)):not(eq"n"(x1,y1))
-@[alpha:'type'][f:[x:frac][y:frac]alpha]
-fixf:=fixfu2"eq"(frac,eq,refeq,symeq,treq,alpha,f):'prop'
-y0@[alpha:'type'][f:[x:frac][y:frac]alpha][ff:fixf(alpha,f)]
-indrat:=indeq2"eq"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0):alpha
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-isindrat:=th1"eq.11"(frac,eq,refeq,symeq,treq,alpha,f,ff,x0,y0,x,xix0,y,yiy0):is"e"(alpha,<y><x>f,indrat)
-x0@satz78:=refis(rat,x0):is(x0,x0)
-y0@[i:is(x0,y0)]
-satz79:=symis(rat,x0,y0,i):is(y0,x0)
-z0@[i:is(x0,y0)][j:is(y0,z0)]
-satz80:=tris(rat,x0,y0,z0,i,j):is(x0,z0)
-y0@more:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),moref(x,y)))):'prop'
-+*ii5
-y1@propm:=and3(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1)):'prop'
--ii5
-y0@[m:more(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propm".ii5"(t,u))][u:frac][p:propm".ii5"(t,u)]
-+*ii5
-p@t4:=and3e1(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(t,class(x0))
-t5:=and3e2(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):inf(u,class(y0))
-t6:=and3e3(inf(t,class(x0)),inf(u,class(y0)),moref(t,u),p):moref(t,u)
-t7:=satz44(t,u,x,y,t6,ise(x0,x0,t,x,t4,xix0,refis(rat,x0)),ise(y0,y0,u,y,t5,yiy0,refis(rat,y0))):moref(x,y)
-s@t8:=someapp(frac,[u:frac]propm(t,u),s,moref(x,y),[u:frac][v:propm(t,u)]t7(u,v)):moref(x,y)
--ii5
-yiy0@also18:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propm".ii5"(t,u)),m,moref(x,y),[t:frac][v:some"l"(frac,[u:frac]propm".ii5"(t,u))]t8".ii5"(t,v)):moref(x,y)
-y1iy0@[m:moref(x1,y1)]
-+*ii5
-m@t9:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),moref(x1,y1),x1ix0,y1iy0,m):propm(x1,y1)
-t10:=somei(frac,[t:frac]propm(x1,t),y1,t9):some"l"(frac,[t:frac]propm(x1,t))
--ii5
-m@morei:=somei(frac,[u:frac]some"l"(frac,[t:frac]propm".ii5"(u,t)),x1,t10".ii5"):more(x0,y0)
-y1iy0@[m:more(x0,y0)]
-moree:=also18(m,x1,y1,x1ix0,y1iy0):moref(x1,y1)
-z0@[i:is(x0,y0)][m:more(x0,z0)]
-ismore1:=isp(rat,[t:rat]more(t,z0),x0,y0,m,i):more(y0,z0)
-i@[m:more(z0,x0)]
-ismore2:=isp(rat,[t:rat]more(z0,t),x0,y0,m,i):more(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][m:more(x0,z0)]
-ismore12:=ismore2(z0,u0,y0,j,ismore1(x0,y0,z0,i,m)):more(y0,u0)
-y0@less:=some"l"(frac,[x:frac]some"l"(frac,[y:frac]and3(inf(x,class(x0)),inf(y,class(y0)),lessf(x,y)))):'prop'
-+*ii5
-y1@propl:=and3(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1)):'prop'
--ii5
-y0@[l:less(x0,y0)][x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][t:frac][s:some"l"(frac,[u:frac]propl".ii5"(t,u))][u:frac][p:propl".ii5"(t,u)]
-+*ii5
-p@t11:=and3e1(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(t,class(x0))
-t12:=and3e2(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):inf(u,class(y0))
-t13:=and3e3(inf(t,class(x0)),inf(u,class(y0)),lessf(t,u),p):lessf(t,u)
-t14:=satz45(t,u,x,y,t13,ise(x0,x0,t,x,t11,xix0,refis(rat,x0)),ise(y0,y0,u,y,t12,yiy0,refis(rat,y0))):lessf(x,y)
-s@t15:=someapp(frac,[u:frac]propl(t,u),s,lessf(x,y),[u:frac][v:propl(t,u)]t14(u,v)):lessf(x,y)
--ii5
-yiy0@also19:=someapp(frac,[t:frac]some"l"(frac,[u:frac]propl".ii5"(t,u)),l,lessf(x,y),[t:frac][v:some"l"(frac,[u:frac]propl".ii5"(t,u))]t15".ii5"(t,v)):lessf(x,y)
-y1iy0@[l:lessf(x1,y1)]
-+*ii5
-l@t16:=and3i(inf(x1,class(x0)),inf(y1,class(y0)),lessf(x1,y1),x1ix0,y1iy0,l):propl(x1,y1)
-t17:=somei(frac,[t:frac]propl(x1,t),y1,t16):some"l"(frac,[t:frac]propl(x1,t))
--ii5
-l@lessi:=somei(frac,[u:frac]some"l"(frac,[t:frac]propl".ii5"(u,t)),x1,t17".ii5"):less(x0,y0)
-y1iy0@[l:less(x0,y0)]
-lesse:=also19(l,x1,y1,x1ix0,y1iy0):lessf(x1,y1)
-z0@[i:is(x0,y0)][l:less(x0,z0)]
-isless1:=isp(rat,[t:rat]less(t,z0),x0,y0,l,i):less(y0,z0)
-i@[l:less(z0,x0)]
-isless2:=isp(rat,[t:rat]less(z0,t),x0,y0,l,i):less(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][l:less(x0,z0)]
-isless12:=isless2(z0,u0,y0,j,isless1(x0,y0,z0,i,l)):less(y0,u0)
-+581
-y1iy0@t1:=satz41a(x1,y1):or3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
-[e:eq"n"(x1,y1)]
-t2:=or3i1(is(x0,y0),more(x0,y0),less(x0,y0),isi(e)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-y1iy0@[m:moref(x1,y1)]
-t3:=or3i2(is(x0,y0),more(x0,y0),less(x0,y0),morei(m)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-y1iy0@[l:lessf(x1,y1)]
-t4:=or3i3(is(x0,y0),more(x0,y0),less(x0,y0),lessi(l)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-y1iy0@t5:=or3app(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),or3(is(x0,y0),more(x0,y0),less(x0,y0)),t1,[t:eq"n"(x1,y1)]t2(t),[t:moref(x1,y1)]t3(t),[t:lessf(x1,y1)]t4(t)):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-t6:=satz41b(x1,y1):ec3(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1))
-[i:is(x0,y0)]
-t7:=th3"l.imp"(more(x0,y0),moref(x1,y1),ec3e12(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,ise(i)),[t:more(x0,y0)]moree(t)):not(more(x0,y0))
-y1iy0@[m:more(x0,y0)]
-t8:=th3"l.imp"(less(x0,y0),lessf(x1,y1),ec3e23(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,moree(m)),[t:less(x0,y0)]lesse(t)):not(less(x0,y0))
-y1iy0@[l:less(x0,y0)]
-t9:=th3"l.imp"(is(x0,y0),eq"n"(x1,y1),ec3e31(eq"n"(x1,y1),moref(x1,y1),lessf(x1,y1),t6,lesse(l)),[t:is(x0,y0)]ise(t)):nis(x0,y0)
-y1iy0@t10:=th6"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),th1"l.ec"(is(x0,y0),more(x0,y0),[t:is(x0,y0)]t7(t)),th1"l.ec"(more(x0,y0),less(x0,y0),[t:more(x0,y0)]t8(t)),th1"l.ec"(less(x0,y0),is(x0,y0),[t:less(x0,y0)]t9(t))):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
-t11:=orec3i(is(x0,y0),more(x0,y0),less(x0,y0),t5,t10):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
--581
-y0@satz81:=ratapp2(orec3(is(x0,y0),more(x0,y0),less(x0,y0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t11".581"(x,y,xi,yi)):orec3(is(x0,y0),more(x0,y0),less(x0,y0))
-satz81a:=orec3e1(is(x0,y0),more(x0,y0),less(x0,y0),satz81):or3(is(x0,y0),more(x0,y0),less(x0,y0))
-satz81b:=orec3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81):ec3(is(x0,y0),more(x0,y0),less(x0,y0))
-[m:more(x0,y0)]
-+582
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=lessi(y0,x0,y,x,yiy0,xix0,satz42(x,y,moree(x0,y0,x,y,xix0,yiy0,m))):less(y0,x0)
--582
-satz82:=ratapp2(less(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".582"(x,y,xi,yi)):less(y0,x0)
-y0@[l:less(x0,y0)]
-+583
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=morei(y0,x0,y,x,yiy0,xix0,satz43(x,y,lesse(x0,y0,x,y,xix0,yiy0,l))):more(y0,x0)
--583
-satz83:=ratapp2(more(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".583"(x,y,xi,yi)):more(y0,x0)
-y0@moreis:=or(more(x0,y0),is(x0,y0)):'prop'
-[m:more(x0,y0)]
-moreisi1:=ori1(more,is,m):moreis(x0,y0)
-y0@[i:is(x0,y0)]
-moreisi2:=ori2(more,is,i):moreis(x0,y0)
-y1iy0@[m:moreq(x1,y1)]
-moreisi:=orapp(moref(x1,y1),eq"n"(x1,y1),moreis,m,[t:moref(x1,y1)]moreisi1(morei(t)),[t:eq"n"(x1,y1)]moreisi2(isi(t))):moreis(x0,y0)
-y1iy0@[m:moreis(x0,y0)]
-moreise:=orapp(more,is,moreq(x1,y1),m,[t:more]moreqi1(x1,y1,moree(t)),[t:is]moreqi2(x1,y1,ise(t))):moreq(x1,y1)
-z0@[i:is(x0,y0)][m:moreis(x0,z0)]
-ismoreis1:=isp(rat,[t:rat]moreis(t,z0),x0,y0,m,i):moreis(y0,z0)
-i@[m:moreis(z0,x0)]
-ismoreis2:=isp(rat,[t:rat]moreis(z0,t),x0,y0,m,i):moreis(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][m:moreis(x0,z0)]
-ismoreis12:=ismoreis2(z0,u0,y0,j,ismoreis1(x0,y0,z0,i,m)):moreis(y0,u0)
-y0@lessis:=or(less(x0,y0),is(x0,y0)):'prop'
-[l:less(x0,y0)]
-lessisi1:=ori1(less,is,l):lessis(x0,y0)
-y0@[i:is(x0,y0)]
-lessisi2:=ori2(less,is,i):lessis(x0,y0)
-y1iy0@[l:lesseq(x1,y1)]
-lessisi:=orapp(lessf(x1,y1),eq"n"(x1,y1),lessis,l,[t:lessf(x1,y1)]lessisi1(lessi(t)),[t:eq"n"(x1,y1)]lessisi2(isi(t))):lessis(x0,y0)
-y1iy0@[l:lessis(x0,y0)]
-lessise:=orapp(less,is,lesseq(x1,y1),l,[t:less]lesseqi1(x1,y1,lesse(t)),[t:is]lesseqi2(x1,y1,ise(t))):lesseq(x1,y1)
-z0@[i:is(x0,y0)][l:lessis(x0,z0)]
-islessis1:=isp(rat,[t:rat]lessis(t,z0),x0,y0,l,i):lessis(y0,z0)
-i@[l:lessis(z0,x0)]
-islessis2:=isp(rat,[t:rat]lessis(z0,t),x0,y0,l,i):lessis(z0,y0)
-u0@[i:is(x0,y0)][j:is(z0,u0)][l:lessis(x0,z0)]
-islessis12:=islessis2(z0,u0,y0,j,islessis1(x0,y0,z0,i,l)):lessis(y0,u0)
-y0@[m:moreis(x0,y0)]
-satz81c:=th7"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,comor(more(x0,y0),is(x0,y0),m)):not(less(x0,y0))
-y0@[l:lessis(x0,y0)]
-satz81d:=th9"l.ec3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l):not(more(x0,y0))
-y0@[n:not(more(x0,y0))]
-satz81e:=th2"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n):lessis(x0,y0)
-y0@[n:not(less(x0,y0))]
-satz81f:=comor(is(x0,y0),more(x0,y0),th3"l.or3"(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,n)):moreis(x0,y0)
-y0@[m:more(x0,y0)]
-satz81g:=th3"l.or"(less(x0,y0),is(x0,y0),ec3e23(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m),ec3e21(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,m)):not(lessis(x0,y0))
-y0@[l:less(x0,y0)]
-satz81h:=th3"l.or"(more(x0,y0),is(x0,y0),ec3e32(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l),ec3e31(is(x0,y0),more(x0,y0),less(x0,y0),satz81b,l)):not(moreis(x0,y0))
-y0@[n:not(moreis(x0,y0))]
-satz81j:=or3e3(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th5"l.or"(more(x0,y0),is(x0,y0),n),th4"l.or"(more(x0,y0),is(x0,y0),n)):less(x0,y0)
-y0@[n:not(lessis(x0,y0))]
-satz81k:=or3e2(is(x0,y0),more(x0,y0),less(x0,y0),satz81a,th4"l.or"(less(x0,y0),is(x0,y0),n),th5"l.or"(less(x0,y0),is(x0,y0),n)):more(x0,y0)
-y0@[m:moreis(x0,y0)]
-+584
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=lessisi(y0,x0,y,x,yiy0,xix0,satz48(x,y,moreise(x0,y0,x,y,xix0,yiy0,m))):lessis(y0,x0)
--584
-satz84:=ratapp2(lessis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".584"(x,y,xi,yi)):lessis(y0,x0)
-y0@[l:lessis(x0,y0)]
-+585
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))]
-t1:=moreisi(y0,x0,y,x,yiy0,xix0,satz49(x,y,lessise(x0,y0,x,y,xix0,yiy0,l))):moreis(y0,x0)
--585
-satz85:=ratapp2(moreis(y0,x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".585"(x,y,xi,yi)):moreis(y0,x0)
-z0@[l:less(x0,y0)][k:less(y0,z0)]
-+586
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=lessi(x0,z0,x,z,xix0,ziz0,satz50(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
--586
-satz86:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".586"(x,y,z,xi,yi,zi)):less(x0,z0)
-trless:=satz86:less(x0,z0)
-z0@[m:more(x0,y0)][n:more(y0,z0)]
-trmore:=satz83(z0,x0,satz86(z0,y0,x0,satz82(y0,z0,n),satz82(m))):more(x0,z0)
-z0@[l:lessis(x0,y0)][k:less(y0,z0)]
-+587
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=lessi(x0,z0,x,z,xix0,ziz0,satz51a(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lesse(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
--587
-satz87a:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".587"(x,y,z,xi,yi,zi)):less(x0,z0)
-z0@[l:less(x0,y0)][k:lessis(y0,z0)]
-+*587
-k@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=lessi(x0,z0,x,z,xix0,ziz0,satz51b(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):less(x0,z0)
--587
-k@satz87b:=ratapp3(less(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".587"(x,y,z,xi,yi,zi)):less(x0,z0)
-z0@[m:moreis(x0,y0)][n:more(y0,z0)]
-satz87c:=satz83(z0,x0,satz87b(z0,y0,x0,satz82(y0,z0,n),satz84(m))):more(x0,z0)
-z0@[m:more(x0,y0)][n:moreis(y0,z0)]
-satz87d:=satz83(z0,x0,satz87a(z0,y0,x0,satz84(y0,z0,n),satz82(m))):more(x0,z0)
-z0@[l:lessis(x0,y0)][k:lessis(y0,z0)]
-+588
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=lessisi(x0,z0,x,z,xix0,ziz0,satz52(x,y,z,lessise(x0,y0,x,y,xix0,yiy0,l),lessise(y0,z0,y,z,yiy0,ziz0,k))):lessis(x0,z0)
--588
-satz88:=ratapp3(lessis(x0,z0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".588"(x,y,z,xi,yi,zi)):lessis(x0,z0)
-trlessis:=satz88:lessis(x0,z0)
-z0@[m:moreis(x0,y0)][n:moreis(y0,z0)]
-trmoreis:=satz85(z0,x0,satz88(z0,y0,x0,satz84(y0,z0,n),satz84(m))):moreis(x0,z0)
-+589
-x0@[x:frac][xix0:inf(x,class(x0))][z:frac][m:moref(z,x)]
-t1:=somei(rat,[t:rat]more(t,x0),ratof(z),morei(ratof(z),x0,z,x,inclass(z),xix0,m)):some([t:rat]more(t,x0))
-xix0@t2:=someapp(frac,[t:frac]moref(t,x),satz53(x),some([t:rat]more(t,x0)),[t:frac][u:moref(t,x)]t1(t,u)):some([t:rat]more(t,x0))
--589
-x0@satz89:=ratapp1(some([t:rat]more(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".589"(x,xi)):some([t:rat]more(t,x0))
-+590
-z"rt.589"@[l:lessf(z,x)]
-t1:=somei(rat,[t:rat]less(t,x0),ratof(z),lessi(ratof(z),x0,z,x,inclass(z),xix0,l)):some([t:rat]less(t,x0))
-xix0"rt.589"@t2:=someapp(frac,[t:frac]lessf(t,x),satz54(x),some([t:rat]less(t,x0)),[t:frac][u:lessf(t,x)]t1(t,u)):some([t:rat]less(t,x0))
--590
-satz90:=ratapp1(some([t:rat]less(t,x0)),[x:frac][xi:inf(x,class(x0))]t2".590"(x,xi)):some([t:rat]less(t,x0))
-y0@[l:less(x0,y0)]
-+591
-[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][z:frac][a:and(lessf(x,z),lessf(z,y))]
-t1:=lessi(x0,ratof(z),x,z,xix0,inclass(z),ande1(lessf(x,z),lessf(z,y),a)):less(x0,ratof(z))
-t2:=lessi(ratof(z),y0,z,y,inclass(z),yiy0,ande2(lessf(x,z),lessf(z,y),a)):less(ratof(z),y0)
-t3:=andi(less(x0,ratof(z)),less(ratof(z),y0),t1,t2):and(less(x0,ratof(z)),less(ratof(z),y0))
-t4:=somei(rat,[t:rat]and(less(x0,t),less(t,y0)),ratof(z),t3):some([t:rat]and(less(x0,t),less(t,y0)))
-yiy0@t5:=someapp(frac,[t:frac]and(lessf(x,t),lessf(t,y)),satz55(x,y,lesse(x,y,xix0,yiy0,l)),some([t:rat]and(less(x0,t),less(t,y0))),[t:frac][u:and(lessf(x,t),lessf(t,y))]t4(t,u)):some([t:rat]and(less(x0,t),less(t,y0)))
--591
-satz91:=ratapp2(some([t:rat]and(less(x0,t),less(t,y0))),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".591"(x,y,xi,yi)):some([t:rat]and(less(x0,t),less(t,y0)))
-@plusfrt:=[x:frac][y:frac]ratof(pf(x,y)):[x:frac][y:frac]rat
-[x:frac][y:frac][z:frac][u:frac][e:eq"n"(x,y)][f:eq"n"(z,u)]
-+*ii5
-f@t18:=isi(ratof(pf(x,z)),ratof(pf(y,u)),pf(x,z),pf(y,u),inclass(pf(x,z)),inclass(pf(y,u)),satz56(x,y,z,u,e,f)):is(<z><x>plusfrt,<u><y>plusfrt)
--ii5
-@fplusfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t18".ii5"(x,y,z,u,v,w):fixf(rat,plusfrt)
-y0@pl:=indrat(rat,plusfrt,fplusfrt):rat
-+*ii5
-y1iy0@t19:=isindrat(rat,plusfrt,fplusfrt,x1,y1,x1ix0,y1iy0):is(ratof(pf(x1,y1)),pl(x0,y0))
--ii5
-y1iy0@picp:=isp(rat,[t:rat]inf(pf(x1,y1),class(t)),ratof(pf(x1,y1)),pl(x0,y0),inclass(pf(x1,y1)),t19".ii5"):inf(pf(x1,y1),class(pl(x0,y0)))
-z0@[i:is(x0,y0)]
-ispl1:=isf(rat,rat,[t:rat]pl(t,z0),x0,y0,i):is(pl(x0,z0),pl(y0,z0))
-ispl2:=isf(rat,rat,[t:rat]pl(z0,t),x0,y0,i):is(pl(z0,x0),pl(z0,y0))
-u0@[i:is(x0,y0)][j:is(z0,u0)]
-ispl12:=tris(rat,pl(x0,z0),pl(y0,z0),pl(y0,u0),ispl1(i),ispl2(z0,u0,y0,j)):is(pl(x0,z0),pl(y0,u0))
-+592
-y1iy0@t1:=isi(pl(x0,y0),pl(y0,x0),pf(x1,y1),pf(y1,x1),picp,picp(y0,x0,y1,x1,y1iy0,x1ix0),satz58(x1,y1)):is(pl(x0,y0),pl(y0,x0))
--592
-y0@satz92:=ratapp2(is(pl(x0,y0),pl(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".592"(x,y,xi,yi)):is(pl(x0,y0),pl(y0,x0))
-compl:=satz92:is(pl(x0,y0),pl(y0,x0))
-+593
-z0@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=picp(pl(x0,y0),z0,pf(x,y),z,picp(x0,y0,x,y,xix0,yiy0),ziz0):inf(pf(pf(x,y),z),class(pl(pl(x0,y0),z0)))
-t2:=picp(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(pf(x,pf(y,z)),class(pl(x0,pl(y0,z0))))
-t3:=isi(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),pf(pf(x,y),z),pf(x,pf(y,z)),t1,t2,satz59(x,y,z)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
--593
-z0@satz93:=ratapp3(is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".593"(x,y,z,xi,yi,zi)):is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
-asspl1:=satz93:is(pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)))
-asspl2:=symis(rat,pl(pl(x0,y0),z0),pl(x0,pl(y0,z0)),satz93):is(pl(x0,pl(y0,z0)),pl(pl(x0,y0),z0))
-+594
-y1iy0@t1:=morei(pl(x0,y0),x0,pf(x1,y1),x1,picp,x1ix0,satz60(x1,y1)):more(pl(x0,y0),x0)
--594
-y0@satz94:=ratapp2(more(pl(x0,y0),x0),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".594"(x,y,xi,yi)):more(pl(x0,y0),x0)
-satz94a:=satz82(pl(x0,y0),x0,satz94):less(x0,pl(x0,y0))
-z0@[m:more(x0,y0)]
-+595
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz61(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
--595
-satz95:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".595"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
-z0@[m:more(x0,y0)]
-+596
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(pl(x0,z0),pl(y0,z0))
--596
-satz96a:=ratapp3(more(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".596"(x,y,z,xi,yi,zi)):more(pl(x0,z0),pl(y0,z0))
-z0@[i:is(x0,y0)]
-+*596
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(pl(x0,z0),pl(y0,z0))
--596
-i@satz96b:=ratapp3(is(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".596"(x,y,z,xi,yi,zi)):is(pl(x0,z0),pl(y0,z0))
-z0@[l:less(x0,y0)]
-+*596
-l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t3:=lessi(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),satz62c(x,y,z,lesse(x0,y0,x,y,xix0,yiy0,l))):less(pl(x0,z0),pl(y0,z0))
--596
-l@satz96c:=ratapp3(less(pl(x0,z0),pl(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".596"(x,y,z,xi,yi,zi)):less(pl(x0,z0),pl(y0,z0))
-+*596
-m@andersa:=satz95(m):more(pl(x0,z0),pl(y0,z0))
-i@andersb:=ispl1(x0,y0,z0,i):is(pl(x0,z0),pl(y0,z0))
-l@andersc:=satz82(pl(y0,z0),pl(x0,z0),satz95(y0,x0,z0,satz83(l))):less(pl(x0,z0),pl(y0,z0))
--596
-m@satz96d:=ismore12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96a):more(pl(z0,x0),pl(z0,y0))
-i@satz96e:=ispl2(x0,y0,z0,i):is(pl(z0,x0),pl(z0,y0))
-l@satz96f:=isless12(pl(x0,z0),pl(z0,x0),pl(y0,z0),pl(z0,y0),compl(x0,z0),compl(y0,z0),satz96c):less(pl(z0,x0),pl(z0,y0))
-z0@[m:more(pl(x0,z0),pl(y0,z0))]
-+597
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(x0,y0,x,y,xix0,yiy0,satz63a(x,y,z,moree(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
--597
-satz97a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".597"(x,y,z,xi,yi,zi)):more(x0,y0)
-z0@[i:is(pl(x0,z0),pl(y0,z0))]
-+*597
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(x0,y0,x,y,xix0,yiy0,satz63b(x,y,z,ise(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
--597
-i@satz97b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".597"(x,y,z,xi,yi,zi)):is(x0,y0)
-z0@[l:less(pl(x0,z0),pl(y0,z0))]
-+*597
-l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t3:=lessi(x0,y0,x,y,xix0,yiy0,satz63c(x,y,z,lesse(pl(x0,z0),pl(y0,z0),pf(x,z),pf(y,z),picp(x0,z0,x,z,xix0,ziz0),picp(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
--597
-l@satz97c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".597"(x,y,z,xi,yi,zi)):less(x0,y0)
-+*597
-l@anders:=satz82(y0,x0,satz97a(y0,x0,z0,satz83(pl(x0,z0),pl(y0,z0),l))):less(x0,y0)
--597
-u0@[m:more(x0,y0)][n:more(z0,u0)]
-+598
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz64(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
--598
-satz98:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".598"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
-u0@[l:less(x0,y0)][k:less(z0,u0)]
-satz98a:=satz82(pl(y0,u0),pl(x0,z0),satz98(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
-u0@[m:moreis(x0,y0)][n:more(z0,u0)]
-+599
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
--599
-satz99a:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
-u0@[m:more(x0,y0)][n:moreis(z0,u0)]
-+*599
-n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t2:=morei(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz65b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(pl(x0,z0),pl(y0,u0))
--599
-n@satz99b:=ratapp4(more(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".599"(x,y,z,u,xi,yi,zi,ui)):more(pl(x0,z0),pl(y0,u0))
-u0@[l:lessis(x0,y0)][k:less(z0,u0)]
-satz99c:=satz82(pl(y0,u0),pl(x0,z0),satz99a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
-u0@[l:less(x0,y0)][k:lessis(z0,u0)]
-satz99d:=satz82(pl(y0,u0),pl(x0,z0),satz99b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(pl(x0,z0),pl(y0,u0))
-u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
-+5100
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=moreisi(pl(x0,z0),pl(y0,u0),pf(x,z),pf(y,u),picp(x0,z0,x,z,xix0,ziz0),picp(y0,u0,y,u,yiy0,uiu0),satz66(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(pl(x0,z0),pl(y0,u0))
--5100
-satz100:=ratapp4(moreis(pl(x0,z0),pl(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5100"(x,y,z,u,xi,yi,zi,ui)):moreis(pl(x0,z0),pl(y0,u0))
-u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
-satz100a:=satz84(pl(y0,u0),pl(x0,z0),satz100(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(pl(x0,z0),pl(y0,u0))
-y0@[l:lessis(x0,y0)]
-+5101
-[v0:rat][i:is(pl(y0,v0),x0)]
-t1:=ismore1(pl(y0,v0),x0,y0,i,satz94(y0,v0)):more(x0,y0)
-v0@t2:=th3"l.imp"(is(pl(y0,v0),x0),more(x0,y0),satz81d(x0,y0,l),[t:is(pl(y0,v0),x0)]t1(t)):nis(pl(y0,v0),x0)
--5101
-vorbemerkung101:=th5"l.some"(rat,[v:rat]is(pl(y0,v),x0),[v:rat]t2".5101"(v)):not(some([t:rat]is(pl(y0,t),x0)))
-y0@[m:more(x0,y0)]
-+*5101
-m@[x:frac][y:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][v:frac][e:eq"n"(pf(y,v),x)]
-t3:=isi(pl(y0,ratof(v)),x0,pf(y,v),x,picp(y0,ratof(v),y,v,yiy0,inclass(v)),xix0,e):is(pl(y0,ratof(v)),x0)
-t4:=somei(rat,[t:rat]is(pl(y0,t),x0),ratof(v),t3):some([t:rat]is(pl(y0,t),x0))
-yiy0@t5:=someapp(frac,[t:frac]eq"n"(pf(y,t),x),satz67a(x,y,moree(x0,y0,x,y,xix0,yiy0,m)),some([t:rat]is(pl(y0,t),x0)),[t:frac][u:eq"n"(pf(y,t),x)]t4(t,u)):some([t:rat]is(pl(y0,t),x0))
--5101
-m@satz101a:=ratapp2(some([t:rat]is(pl(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t5".5101"(x,y,xi,yi)):some([t:rat]is(pl(y0,t),x0))
-y0@[v0:rat][w0:rat][i:is(pl(y0,v0),x0)][j:is(pl(y0,w0),x0)]
-+*5101
-j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
-t6:=isi(v0,w0,v,w,viv0,wiw0,satz67b(x,y,v,w,ise(pl(y0,v0),x0,pf(y,v),x,picp(y0,v0,y,v,yiy0,viv0),xix0,i),ise(pl(y0,w0),x0,pf(y,w),x,picp(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
--5101
-j@satz101b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t6".5101"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
-+*5101
-y0@t7:=[t:rat][u:rat][v:is(pl(y0,t),x0)][w:is(pl(y0,u),x0)]satz101b(t,u,v,w):amone(rat,[t:rat]is(pl(y0,t),x0))
--5101
-m@satz101:=onei(rat,[t:rat]is(pl(y0,t),x0),t7".5101",satz101a):one([t:rat]is(pl(y0,t),x0))
-mn:=ind(rat,[t:rat]is(pl(y0,t),x0),satz101):rat
-satz101c:=oneax(rat,[t:rat]is(pl(y0,t),x0),satz101):is(pl(y0,mn(x0,y0,m)),x0)
-satz101d:=symis(rat,pl(y0,mn(x0,y0,m)),x0,satz101c):is(x0,pl(y0,mn(x0,y0,m)))
-satz101e:=tris(rat,pl(mn(x0,y0,m),y0),pl(y0,mn(x0,y0,m)),x0,compl(mn(x0,y0,m),y0),satz101c):is(pl(mn(x0,y0,m),y0),x0)
-satz101f:=symis(rat,pl(mn(x0,y0,m),y0),x0,satz101e):is(x0,pl(mn(x0,y0,m),y0))
-y0@[v0:rat][m:more(x0,y0)][i:is(pl(y0,v0),x0)]
-satz101g:=satz101b(v0,mn(x0,y0,m),i,satz101c(m)):is(v0,mn(x0,y0,m))
-@timesfrt:=[x:frac][y:frac]ratof(tf(x,y)):[x:frac][y:frac]rat
-+*ii5
-f@t20:=isi(ratof(tf(x,z)),ratof(tf(y,u)),tf(x,z),tf(y,u),inclass(tf(x,z)),inclass(tf(y,u)),satz68(x,y,z,u,e,f)):is(<z><x>timesfrt,<u><y>timesfrt)
--ii5
-@ftimesfrt:=[x:frac][y:frac][z:frac][u:frac][v:<y><x>eq][w:<u><z>eq]t20".ii5"(x,y,z,u,v,w):fixf(rat,timesfrt)
-y0@ts:=indrat(rat,timesfrt,ftimesfrt):rat
-+*ii5
-y1iy0@t21:=isindrat(rat,timesfrt,ftimesfrt,x1,y1,x1ix0,y1iy0):is(ratof(tf(x1,y1)),ts(x0,y0))
--ii5
-y1iy0@tict:=isp(rat,[t:rat]inf(tf(x1,y1),class(t)),ratof(tf(x1,y1)),ts(x0,y0),inclass(tf(x1,y1)),t21".ii5"):inf(tf(x1,y1),class(ts(x0,y0)))
-z0@[i:is(x0,y0)]
-ists1:=isf(rat,rat,[t:rat]ts(t,z0),x0,y0,i):is(ts(x0,z0),ts(y0,z0))
-ists2:=isf(rat,rat,[t:rat]ts(z0,t),x0,y0,i):is(ts(z0,x0),ts(z0,y0))
-u0@[i:is(x0,y0)][j:is(z0,u0)]
-ists12:=tris(rat,ts(x0,z0),ts(y0,z0),ts(y0,u0),ists1(i),ists2(z0,u0,y0,j)):is(ts(x0,z0),ts(y0,u0))
-+5102
-y1iy0@t1:=isi(ts(x0,y0),ts(y0,x0),tf(x1,y1),tf(y1,x1),tict,tict(y0,x0,y1,x1,y1iy0,x1ix0),satz69(x1,y1)):is(ts(x0,y0),ts(y0,x0))
--5102
-y0@satz102:=ratapp2(is(ts(x0,y0),ts(y0,x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t1".5102"(x,y,xi,yi)):is(ts(x0,y0),ts(y0,x0))
-comts:=satz102:is(ts(x0,y0),ts(y0,x0))
-+5103
-ziz0"rt.593"@t1:=tict(ts(x0,y0),z0,tf(x,y),z,tict(x0,y0,x,y,xix0,yiy0),ziz0):inf(tf(tf(x,y),z),class(ts(ts(x0,y0),z0)))
-t2:=tict(x0,ts(y0,z0),x,tf(y,z),xix0,tict(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,tf(y,z)),class(ts(x0,ts(y0,z0))))
-t3:=isi(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),tf(tf(x,y),z),tf(x,tf(y,z)),t1,t2,satz70(x,y,z)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
--5103
-z0@satz103:=ratapp3(is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5103"(x,y,z,xi,yi,zi)):is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
-assts1:=satz103:is(ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)))
-assts2:=symis(rat,ts(ts(x0,y0),z0),ts(x0,ts(y0,z0)),satz103):is(ts(x0,ts(y0,z0)),ts(ts(x0,y0),z0))
-+5104
-ziz0"rt.593"@t1:=tict(x0,pl(y0,z0),x,pf(y,z),xix0,picp(y0,z0,y,z,yiy0,ziz0)):inf(tf(x,pf(y,z)),class(ts(x0,pl(y0,z0))))
-t2:=picp(ts(x0,y0),ts(x0,z0),tf(x,y),tf(x,z),tict(x0,y0,x,y,xix0,yiy0),tict(x0,z0,x,z,xix0,ziz0)):inf(pf(tf(x,y),tf(x,z)),class(pl(ts(x0,y0),ts(x0,z0))))
-t3:=isi(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),tf(x,pf(y,z)),pf(tf(x,y),tf(x,z)),t1,t2,satz71(x,y,z)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
--5104
-satz104:=ratapp3(is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0))),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5104"(x,y,z,xi,yi,zi)):is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
-disttp1:=tr3is(rat,ts(pl(x0,y0),z0),ts(z0,pl(x0,y0)),pl(ts(z0,x0),ts(z0,y0)),pl(ts(x0,z0),ts(y0,z0)),comts(pl(x0,y0),z0),satz104(z0,x0,y0),ispl12(ts(z0,x0),ts(x0,z0),ts(z0,y0),ts(y0,z0),comts(z0,x0),comts(z0,y0))):is(ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)))
-disttp2:=satz104:is(ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)))
-distpt1:=symis(rat,ts(pl(x0,y0),z0),pl(ts(x0,z0),ts(y0,z0)),disttp1):is(pl(ts(x0,z0),ts(y0,z0)),ts(pl(x0,y0),z0))
-distpt2:=symis(rat,ts(x0,pl(y0,z0)),pl(ts(x0,y0),ts(x0,z0)),disttp2):is(pl(ts(x0,y0),ts(x0,z0)),ts(x0,pl(y0,z0)))
-[m:more(x0,y0)]
-+5105
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72a(x,y,z,moree(x0,y0,x,y,xix0,yiy0,m))):more(ts(x0,z0),ts(y0,z0))
--5105
-satz105a:=ratapp3(more(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5105"(x,y,z,xi,yi,zi)):more(ts(x0,z0),ts(y0,z0))
-z0@[i:is(x0,y0)]
-+*5105
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),satz72b(x,y,z,ise(x0,y0,x,y,xix0,yiy0,i))):is(ts(x0,z0),ts(y0,z0))
--5105
-i@satz105b:=ratapp3(is(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5105"(x,y,z,xi,yi,zi)):is(ts(x0,z0),ts(y0,z0))
-z0@[l:less(x0,y0)]
-+*5105
-l@[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]
-t3:=lessi(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xi,zi),tict(y0,z0,y,z,yi,zi),satz72c(x,y,z,lesse(x0,y0,x,y,xi,yi,l))):less(ts(x0,z0),ts(y0,z0))
--5105
-l@satz105c:=ratapp3(less(ts(x0,z0),ts(y0,z0)),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5105"(x,y,z,xi,yi,zi)):less(ts(x0,z0),ts(y0,z0))
-+*5105
-i@andersb:=ists1(x0,y0,z0,i):is(ts(x0,z0),ts(y0,z0))
-l@andersc:=satz82(ts(y0,z0),ts(x0,z0),satz105a(y0,x0,z0,satz83(l))):less(ts(x0,z0),ts(y0,z0))
--5105
-m@satz105d:=ismore12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105a):more(ts(z0,x0),ts(z0,y0))
-i@satz105e:=ists2(x0,y0,z0,i):is(ts(z0,x0),ts(z0,y0))
-l@satz105f:=isless12(ts(x0,z0),ts(z0,x0),ts(y0,z0),ts(z0,y0),comts(x0,z0),comts(y0,z0),satz105c):less(ts(z0,x0),ts(z0,y0))
-z0@[m:more(ts(x0,z0),ts(y0,z0))]
-+5106
-[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t1:=morei(x0,y0,x,y,xix0,yiy0,satz73a(x,y,z,moree(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),m))):more(x0,y0)
--5106
-satz106a:=ratapp3(more(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t1".5106"(x,y,z,xi,yi,zi)):more(x0,y0)
-z0@[i:is(ts(x0,z0),ts(y0,z0))]
-+*5106
-i@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t2:=isi(x0,y0,x,y,xix0,yiy0,satz73b(x,y,z,ise(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),i))):is(x0,y0)
--5106
-i@satz106b:=ratapp3(is(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t2".5106"(x,y,z,xi,yi,zi)):is(x0,y0)
-z0@[l:less(ts(x0,z0),ts(y0,z0))]
-+*5106
-l@[x:frac][y:frac][z:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))]
-t3:=lessi(x0,y0,x,y,xix0,yiy0,satz73c(x,y,z,lesse(ts(x0,z0),ts(y0,z0),tf(x,z),tf(y,z),tict(x0,z0,x,z,xix0,ziz0),tict(y0,z0,y,z,yiy0,ziz0),l))):less(x0,y0)
--5106
-l@satz106c:=ratapp3(less(x0,y0),[x:frac][y:frac][z:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))]t3".5106"(x,y,z,xi,yi,zi)):less(x0,y0)
-+*5106
-l@anders:=satz82(y0,x0,satz106a(y0,x0,z0,satz83(ts(x0,z0),ts(y0,z0),l))):less(x0,y0)
--5106
-u0@[m:more(x0,y0)][n:more(z0,u0)]
-+5107
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz74(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
--5107
-satz107:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5107"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
-u0@[l:less(x0,y0)][k:less(z0,u0)]
-satz107a:=satz82(ts(y0,u0),ts(x0,z0),satz107(y0,x0,u0,z0,satz83(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
-u0@[m:moreis(x0,y0)][n:more(z0,u0)]
-+5108
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75a(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moree(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
--5108
-satz108a:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
-u0@[m:more(x0,y0)][n:moreis(z0,u0)]
-+*5108
-n@[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t2:=morei(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz75b(x,y,z,u,moree(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):more(ts(x0,z0),ts(y0,u0))
--5108
-n@satz108b:=ratapp4(more(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t2".5108"(x,y,z,u,xi,yi,zi,ui)):more(ts(x0,z0),ts(y0,u0))
-u0@[l:lessis(x0,y0)][k:less(z0,u0)]
-satz108c:=satz82(ts(y0,u0),ts(x0,z0),satz108a(y0,x0,u0,z0,satz85(l),satz83(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
-u0@[l:less(x0,y0)][k:lessis(z0,u0)]
-satz108d:=satz82(ts(y0,u0),ts(x0,z0),satz108b(y0,x0,u0,z0,satz83(l),satz85(z0,u0,k))):less(ts(x0,z0),ts(y0,u0))
-u0@[m:moreis(x0,y0)][n:moreis(z0,u0)]
-+5109
-[x:frac][y:frac][z:frac][u:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][ziz0:inf(z,class(z0))][uiu0:inf(u,class(u0))]
-t1:=moreisi(ts(x0,z0),ts(y0,u0),tf(x,z),tf(y,u),tict(x0,z0,x,z,xix0,ziz0),tict(y0,u0,y,u,yiy0,uiu0),satz76(x,y,z,u,moreise(x0,y0,x,y,xix0,yiy0,m),moreise(z0,u0,z,u,ziz0,uiu0,n))):moreis(ts(x0,z0),ts(y0,u0))
--5109
-satz109:=ratapp4(moreis(ts(x0,z0),ts(y0,u0)),[x:frac][y:frac][z:frac][u:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][zi:inf(z,class(z0))][ui:inf(u,class(u0))]t1".5109"(x,y,z,u,xi,yi,zi,ui)):moreis(ts(x0,z0),ts(y0,u0))
-u0@[l:lessis(x0,y0)][k:lessis(z0,u0)]
-satz109a:=satz84(ts(y0,u0),ts(x0,z0),satz109(y0,x0,u0,z0,satz85(l),satz85(z0,u0,k))):lessis(ts(x0,z0),ts(y0,u0))
-+5110
-y1iy0@[v:frac][e:eq"n"(tf(y1,v),x1)]
-t1:=isi(ts(y0,ratof(v)),x0,tf(y1,v),x1,tict(y0,ratof(v),y1,v,y1iy0,inclass(v)),x1ix0,e):is(ts(y0,ratof(v)),x0)
-t2:=somei(rat,[t:rat]is(ts(y0,t),x0),ratof(v),t1):some([t:rat]is(ts(y0,t),x0))
-y1iy0@t3:=someapp(frac,[t:frac]eq"n"(tf(y1,t),x1),satz77a(x1,y1),some([t:rat]is(ts(y0,t),x0)),[t:frac][u:eq"n"(tf(y1,t),x1)]t2(t,u)):some([t:rat]is(ts(y0,t),x0))
--5110
-y0@satz110a:=ratapp2(some([t:rat]is(ts(y0,t),x0)),[x:frac][y:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))]t3".5110"(x,y,xi,yi)):some([t:rat]is(ts(y0,t),x0))
-[v0:rat][w0:rat][i:is(ts(y0,v0),x0)][j:is(ts(y0,w0),x0)]
-+*5110
-j@[x:frac][y:frac][v:frac][w:frac][xix0:inf(x,class(x0))][yiy0:inf(y,class(y0))][viv0:inf(v,class(v0))][wiw0:inf(w,class(w0))]
-t4:=isi(v0,w0,v,w,viv0,wiw0,satz77b(x,y,v,w,ise(ts(y0,v0),x0,tf(y,v),x,tict(y0,v0,y,v,yiy0,viv0),xix0,i),ise(ts(y0,w0),x0,tf(y,w),x,tict(y0,w0,y,w,yiy0,wiw0),xix0,j))):is(v0,w0)
--5110
-j@satz110b:=ratapp4(v0,w0,is(v0,w0),[x:frac][y:frac][v:frac][w:frac][xi:inf(x,class(x0))][yi:inf(y,class(y0))][vi:inf(v,class(v0))][wi:inf(w,class(w0))]t4".5110"(x,y,v,w,xi,yi,vi,wi)):is(v0,w0)
-+*5110
-y0@t5:=[t:rat][u:rat][v:is(ts(y0,t),x0)][w:is(ts(y0,u),x0)]satz110b(t,u,v,w):amone(rat,[t:rat]is(ts(y0,t),x0))
--5110
-y0@satz110:=onei(rat,[t:rat]is(ts(y0,t),x0),t5".5110",satz110a):one([t:rat]is(ts(y0,t),x0))
--rt
-@[x:nat][y:nat]
-+5111
-t1:=tris(nat,ts(num(fr(x,1)),den(fr(y,1))),ts(x,1),x,ndis12(x,1,y,1),satz28a(x)):is(ts(num(fr(x,1)),den(fr(y,1))),x)
-t2:=symis(nat,ts(num(fr(x,1)),den(fr(y,1))),x,t1):is(x,ts(num(fr(x,1)),den(fr(y,1))))
--5111
-[m:moref(fr(x,1),fr(y,1))]
-satz111a:=ismore12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),m):more(x,y)
-y@[e:eq(fr(x,1),fr(y,1))]
-satz111b:=tr3is(nat,x,ts(num(fr(x,1)),den(fr(y,1))),ts(num(fr(y,1)),den(fr(x,1))),y,t2".5111",e,t1".5111"(y,x)):is(x,y)
-y@[l:lessf(fr(x,1),fr(y,1))]
-satz111c:=isless12(ts(num(fr(x,1)),den(fr(y,1))),x,ts(num(fr(y,1)),den(fr(x,1))),y,t1".5111",t1".5111"(y,x),l):less(x,y)
-y@[m:more(x,y)]
-satz111d:=ismore12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),m):moref(fr(x,1),fr(y,1))
-y@[i:is(x,y)]
-satz111e:=tr3is(nat,ts(num(fr(x,1)),den(fr(y,1))),x,y,ts(num(fr(y,1)),den(fr(x,1))),t1".5111",i,t2".5111"(y,x)):eq(fr(x,1),fr(y,1))
-y@[l:less(x,y)]
-satz111f:=isless12(x,ts(num(fr(x,1)),den(fr(y,1))),y,ts(num(fr(y,1)),den(fr(x,1))),t2".5111",t2".5111"(y,x),l):lessf(fr(x,1),fr(y,1))
-+*rt
-@[x0:rat][x:nat]
-natprop:=inf(fr(x,1),class(x0)):'prop'
-x0@natrt:=some"n"([t:nat]natprop(t)):'prop'
-+*ii5
-y0@[x:nat][y:nat][npx:natprop(x0,x)][npy:natprop(y0,y)][i:is(x0,y0)]
-t22:=satz111b(x,y,ise(x0,y0,fr(x,1),fr(y,1),npx,npy,i)):is"n"(x,y)
-x0@t23:=[t:nat][u:nat][v:natprop(x0,t)][w:natprop(x0,u)]t22(x0,x0,t,u,v,w,refis(rat,x0)):amone(nat,[t:nat]natprop(x0,t))
--ii5
-x0@[nx0:natrt(x0)]
-satz111g:=onei(nat,[t:nat]natprop(t),t23".ii5",nx0):one"n"([t:nat]natprop(x0,t))
-nofrt:=ind(nat,[t:nat]natprop(t),satz111g):nat
-inclassn:=oneax(nat,[t:nat]natprop(t),satz111g):inf(fr(nofrt,1),class(x0))
-[y0:rat][ny0:natrt(y0)][i:is(x0,y0)]
-isrten:=t22".ii5"(x0,y0,nofrt(x0,nx0),nofrt(y0,ny0),inclassn(x0,nx0),inclassn(y0,ny0),i):is"n"(nofrt(x0,nx0),nofrt(y0,ny0))
-ny0@[i:is"n"(nofrt(x0,nx0),nofrt(y0,ny0))]
-isrtin:=isi(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),eqn"n"(nofrt(x0,nx0),1,nofrt(y0,ny0),i)):is(x0,y0)
-@[x:nat]
-rtofn:=ratof(fr(x,1)):rat
-natrti:=somei(nat,[t:nat]natprop(rtofn,t),x,inclass(fr(x,1))):natrt(rtofn(x))
-[y:nat][i:is"n"(x,y)]
-isnert:=isf(nat,rat,[t:nat]rtofn(t),x,y,i):is(rtofn(x),rtofn(y))
-y@[i:is(rtofn(x),rtofn(y))]
-isnirt:=t22".ii5"(rtofn(x),rtofn(y),x,y,inclass(fr(x,1)),inclass(fr(y,1)),i):is"n"(x,y)
-nx0@isrtn1:=isi(x0,rtofn(nofrt(x0,nx0)),fr(nofrt(x0,nx0),1),fr(nofrt(x0,nx0),1),inclassn(x0,nx0),inclass(fr(nofrt(x0,nx0),1)),refeq"n"(fr(nofrt(x0,nx0),1))):is(x0,rtofn(nofrt(x0,nx0)))
-x@isnrt1:=t22".ii5"(rtofn(x),rtofn(x),x,nofrt(rtofn(x),natrti(x)),inclass(fr(x,1)),inclassn(rtofn(x),natrti(x)),refis(rat,rtofn(x))):is"n"(x,nofrt(rtofn(x),natrti(x)))
--rt
-@[x:nat][y:nat]
-satz112a:=satz57(x,y,1):eq(pf(fr(x,1),fr(y,1)),fr(pl(x,y),1))
-satz112b:=treq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),ts(1,1)),fr(ts(x,y),1),tfeq12a(x,1,y,1),eqd(ts(x,y),ts(1,1),1,satz28a(1))):eq(tf(fr(x,1),fr(y,1)),fr(ts(x,y),1))
-+*rt
-ny0@satz112c:=lemmaeq1(pl(x0,y0),pf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),picp(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112a(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(pl(x0,y0)))
-satz112d:=somei(nat,[t:nat]natprop(pl(x0,y0),t),pl"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112c):natrt(pl(x0,y0))
-satz112e:=lemmaeq1(ts(x0,y0),tf(fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1)),fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),tict(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0)),satz112b(nofrt(x0,nx0),nofrt(y0,ny0))):inf(fr(ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),1),class(ts(x0,y0)))
-satz112f:=somei(nat,[t:nat]natprop(ts(x0,y0),t),ts"n"(nofrt(x0,nx0),nofrt(y0,ny0)),satz112e):natrt(ts(x0,y0))
-[m:more(x0,y0)]
-+5112
-t1:=satz111a(nofrt(x0,nx0),nofrt(y0,ny0),moree(x0,y0,fr(nofrt(x0,nx0),1),fr(nofrt(y0,ny0),1),inclassn(x0,nx0),inclassn(y0,ny0),m)):more"n"(nofrt(x0,nx0),nofrt(y0,ny0))
-[z:nat][d:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),z)]
-t2:=tris(nat,nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),z),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),d,ispl2"n"(z,nofrt(rtofn(z),natrti(z)),nofrt(y0,ny0),isnrt1(z))):is"n"(nofrt(x0,nx0),pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))))
-t3:=isi(x0,pl(y0,rtofn(z)),fr(nofrt(x0,nx0),1),fr(pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),1),inclassn(x0,nx0),satz112c(y0,ny0,rtofn(z),natrti(z)),eqn(nofrt(x0,nx0),1,pl"n"(nofrt(y0,ny0),nofrt(rtofn(z),natrti(z))),t2)):is(x0,pl(y0,rtofn(z)))
-t4:=satz101g(x0,y0,rtofn(z),m,symis(rat,x0,pl(y0,rtofn(z)),t3)):is(rtofn(z),mn(x0,y0,m))
-t5:=isp(rat,[t:rat]natrt(t),rtofn(z),mn(x0,y0,m),natrti(z),t4):natrt(mn(x0,y0,m))
--5112
-satz112g:=someapp(nat,[t:nat]diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t),t1".5112",natrt(mn(x0,y0,m)),[t:nat][u:diffprop(nofrt(x0,nx0),nofrt(y0,ny0),t)]t5".5112"(t,u)):natrt(mn(x0,y0,m))
-@[x:nat][y:nat]
-satz112h:=isi(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),pf(fr(x,1),fr(y,1)),fr(pl"n"(x,y),1),picp(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(pl"n"(x,y),1)),satz112a(x,y)):is(pl(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)))
-satz112j:=isi(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),tf(fr(x,1),fr(y,1)),fr(ts"n"(x,y),1),tict(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass(fr(x,1)),inclass(fr(y,1))),inclass(fr(ts"n"(x,y),1)),satz112b(x,y)):is(ts(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)))
-+nt
-@natt:=ot(rat,[t:rat]natrt(t)):'type'
-nx0@ntofrt:=out(rat,[t:rat]natrt(t),x0,nx0):natt
-@[xt:natt][yt:natt]
-is:=is"e"(natt,xt,yt):'prop'
-nis:=not(is(xt,yt)):'prop'
-@[p:[x:natt]'prop']
-all:=all"l"(natt,p):'prop'
-some:=some"l"(natt,p):'prop'
-one:=one"e"(natt,p):'prop'
-xt@[st:set(natt)]
-in:=esti(natt,xt,st):'prop'
-xt@rtofnt:=in"e"(rat,[t:rat]natrt(t),xt):rat
-natrti:=inp(rat,[t:rat]natrt(t),xt):natrt(rtofnt(xt))
-ny0@[i:is"rt"(x0,y0)]
-isrtent:=isouti(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is(ntofrt(x0,nx0),ntofrt(y0,ny0))
-ny0@[i:is(ntofrt(x0,nx0),ntofrt(y0,ny0))]
-isrtint:=isoute(rat,[t:rat]natrt(t),x0,nx0,y0,ny0,i):is"rt"(x0,y0)
-yt@[i:is(xt,yt)]
-isntert:=isini(rat,[t:rat]natrt(t),xt,yt,i):is"rt"(rtofnt(xt),rtofnt(yt))
-yt@[i:is"rt"(rtofnt(xt),rtofnt(yt))]
-isntirt:=isine(rat,[t:rat]natrt(t),xt,yt,i):is(xt,yt)
-nx0@isrtnt1:=isinout(rat,[t:rat]natrt(t),x0,nx0):is"rt"(x0,rtofnt(ntofrt(x0,nx0)))
-xt@isntrt1:=isoutin(rat,[t:rat]natrt(t),xt):is(xt,ntofrt(rtofnt(xt),natrti(xt)))
-x@ntofn:=ntofrt(rtofn(x),natrti"rt"(x)):natt
-y@[i:is"n"(x,y)]
-isnent:=isrtent(rtofn(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),isnert(x,y,i)):is(ntofn(x),ntofn(y))
-y@[i:is(ntofn(x),ntofn(y))]
-isnint:=isnirt(x,y,isrtint(rtofn"rt"(x),natrti"rt"(x),rtofn(y),natrti"rt"(y),i)):is"n"(x,y)
-xt@nofnt:=nofrt(rtofnt(xt),natrti(xt)):nat
-yt@[i:is(xt,yt)]
-isnten:=isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),isntert(xt,yt,i)):is"n"(nofnt(xt),nofnt(yt))
-yt@[i:is"n"(nofnt(xt),nofnt(yt))]
-isntin:=isntirt(xt,yt,isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),i)):is(xt,yt)
-+ii5
-x@t24:=isrtnt1(rtofn(x),natrti"rt"(x)):is"rt"(rtofn(x),rtofnt(ntofn(x)))
-t25:=isrten(rtofn(x),natrti"rt"(x),rtofnt(ntofn(x)),natrti(ntofn(x)),t24):is"n"(nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)))
--ii5
-x@isnnt1:=tris(nat,x,nofrt(rtofn(x),natrti"rt"(x)),nofnt(ntofn(x)),isnrt1(x),t25".ii5"):is"n"(x,nofnt(ntofn(x)))
-+*ii5
-xt@t26:=isrtn1(rtofnt(xt),natrti(xt)):is"rt"(rtofnt(xt),rtofn(nofnt(xt)))
-t27:=isrtent(rtofnt(xt),natrti(xt),rtofn(nofnt(xt)),natrti"rt"(nofnt(xt)),t26):is(ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)))
--ii5
-xt@isntn1:=tris(natt,xt,ntofrt(rtofnt(xt),natrti(xt)),ntofn(nofnt(xt)),isntrt1(xt),t27".ii5"):is(xt,ntofn(nofnt(xt)))
-x@isnnt2:=symis(nat,x,nofnt(ntofn(x)),isnnt1):is"n"(nofnt(ntofn(x)),x)
-xt@isntn2:=symis(natt,xt,ntofn(nofnt(xt)),isntn1):is(ntofn(nofnt(xt)),xt)
-@1t:=ntofn(1):natt
-suct:=[x:natt]ntofn(<nofnt(x)>suc):[x:natt]natt
-+5113
-xt@[i:is(<xt>suct,1t)]
-t1:=isnint(<nofnt(xt)>suc,1,i):is"n"(<nofnt(xt)>suc,1)
--5113
-xt@satz113a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<nofnt(xt)>suc,1),<nofnt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5113"(t)):nis(<xt>suct,1t)
-yt@[i:is(<xt>suct,<yt>suct)]
-+*5113
-i"nt"@t2:=isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,i):is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
--5113
-i@satz113b:=isntin(xt,yt,<t2".5113"><nofnt(yt)><nofnt(xt)>ax4):is(xt,yt)
-@[st:set(natt)]
-cond1:=in(1t,st):'prop'
-cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
-[c1:cond1][c2:cond2]
-+*5113
-c2@[x:nat]
-prop1:=in(ntofn(x),st):'prop'
-[p:prop1(x)]
-t3:=<ntofn(x)>c2:imp(in(ntofn(x),st),in(<ntofn(x)>suct,st))
-t4:=mp(in(ntofn(x),st),in(<ntofn(x)>suct,st),p,t3):in(<ntofn(x)>suct,st)
-t5:=isp(nat,[t:nat]in(ntofn(<t>suc),st),nofnt(ntofn(x)),x,t4,isnnt2(x)):prop1(<x>suc)
--5113
-c2@[xt:natt]
-+*5113
-xt@t6:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t5(t,u),nofnt(xt)):in(ntofn(nofnt(xt)),st)
--5113
-xt@satz113c:=isp(natt,[t:natt]in(t,st),ntofn(nofnt(xt)),xt,t6".5113",isntn2(xt)):in(xt,st)
-@ax3t:=[x:natt]satz113a(x):[x:natt]nis(<x>suct,1t)
-ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz113b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
-ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz113c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
-yt@[n:nis(xt,yt)]
-+51
-t1:=th3"l.imp"(is"n"(nofnt(xt),nofnt(yt)),is(xt,yt),n,[t:is"n"(nofnt(xt),nofnt(yt))]isntin(xt,yt,t)):nis"n"(nofnt(xt),nofnt(yt))
-t2:=satz1(nofnt(xt),nofnt(yt),t1):nis"n"(<nofnt(xt)>suc,<nofnt(yt)>suc)
--51
-satz1:=th3"l.imp"(is(<xt>suct,<yt>suct),is"n"(<nofnt(xt)>suc,<nofnt(yt)>suc),t2".51",[t:is(<xt>suct,<yt>suct)]isnint(<nofnt(xt)>suc,<nofnt(yt)>suc,t)):nis(<xt>suct,<yt>suct)
-+54
-xt@x:=nofnt(xt):nat
-[ft:[x:natt]natt]
-prop1t:=all([t:natt]is(<<t>suct>ft,<<t>ft>suct)):'prop'
-prop2t:=and(is(<1t>ft,<xt>suct),prop1t):'prop'
-xt@[f:[x:nat]nat]
-prop1:=all"n"([t:nat]is"n"(<<t>suc>f,<<t>f>suc)):'prop'
-prop2:=and(is"n"(<1>f,<x>suc),prop1):'prop'
-ft@g:=[t:nat]nofnt(<ntofn(t)>ft):[x:nat]nat
-[p:prop2t]
-t1:=ande1(is(<1t>ft,<xt>suct),prop1t,p):is(<1t>ft,<xt>suct)
-t2:=tris(nat,<1>g,nofnt(<xt>suct),<x>suc,isnten(<1t>ft,<xt>suct,t1),isnnt2(<x>suc)):is"n"(<1>g,<x>suc)
-t3:=ande2(is(<1t>ft,<xt>suct),prop1t,p):prop1t
-[u:nat]
-ut:=ntofn(u):natt
-t4:=isf(nat,nat,suc,u,nofnt(ut),isnnt1(u)):is"n"(<u>suc,<nofnt(ut)>suc)
-t5:=isf(nat,nat,g,<u>suc,<nofnt(ut)>suc,t4):is"n"(<<u>suc>g,nofnt(<<ut>suct>ft))
-t6:=<ut>t3:is(<<ut>suct>ft,<<ut>ft>suct)
-t7:=isnten(<<ut>suct>ft,<<ut>ft>suct,t6):is"n"(nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct))
-t8:=isnnt2(<<u>g>suc):is"n"(nofnt(<<ut>ft>suct),<<u>g>suc)
-t9:=tr3is(nat,<<u>suc>g,nofnt(<<ut>suct>ft),nofnt(<<ut>ft>suct),<<u>g>suc,t5,t7,t8):is"n"(<<u>suc>g,<<u>g>suc)
-p@t10:=[u:nat]t9(u):prop1(g)
-t11:=andi(is"n"(<1>g,<x>suc),prop1(g),t2,t10):prop2(g)
-xt@[a:[t:natt]natt][b:[t:natt]natt][pa:prop2t(a)][pb:prop2t(b)]
-t12:=onee1([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):amone([t:nat]nat,[u:[t:nat]nat]prop2(u))
-t13:=<t11(b,pb)><t11(a,pa)><g(b)><g(a)>t12:is"e"([t:nat]nat,g(a),g(b))
-[yt:natt]
-y:=nofnt(yt):nat
-t14:=fise(nat,nat,g(a),g(b),t13,y):is"n"(nofnt(<ntofn(y)>a),nofnt(<ntofn(y)>b))
-t15:=isntin(<ntofn(y)>a,<ntofn(y)>b,t14):is(<ntofn(y)>a,<ntofn(y)>b)
-t16:=tr3is(natt,<yt>a,<ntofn(y)>a,<ntofn(y)>b,<yt>b,isf(natt,natt,a,yt,ntofn(y),isntn1(yt)),t15,isf(natt,natt,b,ntofn(y),yt,isntn2(yt))):is(<yt>a,<yt>b)
-pb@t17:=fisi(natt,natt,a,b,[t:natt]t16(t)):is"e"([t:natt]natt,a,b)
-xt@t18:=[u:[t:natt]natt][v:[t:natt]natt][w:prop2t(u)][z:prop2t(v)]t17(u,v,w,z):amone([t:natt]natt,[u:[t:natt]natt]prop2t(u))
-t19:=onee2([t:nat]nat,[u:[t:nat]nat]prop2(u),satz4(x)):some"l"([t:nat]nat,[u:[t:nat]nat]prop2(u))
-f@gt:=[t:natt]ntofn(<nofnt(t)>f):[x:natt]natt
-[p:prop2]
-t20:=ande1(is"n"(<1>f,<x>suc),prop1,p):is"n"(<1>f,<x>suc)
-t21:=isf(nat,nat,f,nofnt(1t),1,isnnt2(1)):is"n"(<nofnt(1t)>f,<1>f)
-t22:=isnent(<nofnt(1t)>f,<x>suc,tris(nat,<nofnt(1t)>f,<1>f,<x>suc,t21,t20)):is(<1t>gt,<xt>suct)
-t23:=ande2(is"n"(<1>f,<x>suc),prop1,p):prop1
-[zt:natt]
-z:=nofnt(zt):nat
-t24:=isf(nat,nat,f,nofnt(<zt>suct),<z>suc,isnnt2(<z>suc)):is"n"(<nofnt(<zt>suct)>f,<<z>suc>f)
-t25:=<z>t23:is"n"(<<z>suc>f,<<z>f>suc)
-t26:=isf(nat,nat,suc,<z>f,nofnt(<zt>gt),isnnt1(<z>f)):is"n"(<<z>f>suc,<nofnt(<zt>gt)>suc)
-t27:=isnent(<nofnt(<zt>suct)>f,<nofnt(<zt>gt)>suc,tr3is(nat,<nofnt(<zt>suct)>f,<<z>suc>f,<<z>f>suc,<nofnt(<zt>gt)>suc,t24,t25,t26)):is(<<zt>suct>gt,<<zt>gt>suct)
-p@t28:=[u:natt]t27(u):prop1t(gt)
-t29:=andi(is(<1t>gt,<xt>suct),prop1t(gt),t22,t28):prop2t(gt)
-t30:=somei([t:natt]natt,[u:[t:natt]natt]prop2t(u),gt,t29):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
-xt@t31:=someapp([t:nat]nat,[u:[t:nat]nat]prop2(u),t19,some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u)),[u:[t:nat]nat][v:prop2(u)]t30(u,v)):some"l"([t:natt]natt,[u:[t:natt]natt]prop2t(u))
--54
-xt@satz4:=onei([t:natt]natt,[u:[t:natt]natt]prop2t".54"(u),t18".54",t31".54"):one"e"([t:natt]natt,[u:[t:natt]natt]and(is(<1t>u,<xt>suct),all([v:natt]is(<<v>suct>u,<<v>u>suct))))
-yt@pl:=ntofrt(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt))):natt
-+*ii5
-yt@t28:=satz112c(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)):inf(fr(pl"n"(nofnt(xt),nofnt(yt)),1),class(pl"rt"(rtofnt(xt),rtofnt(yt))))
-t29:=isi(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),fr(pl"n"(nofnt(xt),nofnt(yt)),1),fr(pl"n"(nofnt(xt),nofnt(yt)),1),t28,inclass(fr(pl"n"(nofnt(xt),nofnt(yt)),1)),refeq"n"(fr(pl"n"(nofnt(xt),nofnt(yt)),1))):is"rt"(pl"rt"(rtofnt(xt),rtofnt(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))))
--ii5
-yt@isplnt:=isrtent(pl"rt"(rtofnt(xt),rtofnt(yt)),satz112d(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt)),rtofn(pl"n"(nofnt(xt),nofnt(yt))),natrti"rt"(pl"n"(nofnt(xt),nofnt(yt))),t29".ii5"):is(pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))))
-isntpl:=symis(natt,pl(xt,yt),ntofn(pl"n"(nofnt(xt),nofnt(yt))),isplnt):is(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt))
-ispln:=tris(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(ntofn(pl"n"(nofnt(xt),nofnt(yt)))),nofnt(pl(xt,yt)),isnnt1(pl"n"(nofnt(xt),nofnt(yt))),isnten(ntofn(pl"n"(nofnt(xt),nofnt(yt))),pl(xt,yt),isntpl)):is"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)))
-isnpl:=symis(nat,pl"n"(nofnt(xt),nofnt(yt)),nofnt(pl(xt,yt)),ispln):is"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)))
-[zt:natt]
-+55
-t1:=ispl1"n"(nofnt(pl(xt,yt)),pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt),isnpl(xt,yt)):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)))
-t2:=ispl2"n"(pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),nofnt(xt),ispln(yt,zt)):is"n"(pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
-t3:=tr3is(nat,pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(pl"n"(nofnt(xt),nofnt(yt)),nofnt(zt)),pl"n"(nofnt(xt),pl"n"(nofnt(yt),nofnt(zt))),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t1,satz5(nofnt(xt),nofnt(yt),nofnt(zt)),t2):is"n"(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))))
--55
-satz5:=tr3is(natt,pl(pl(xt,yt),zt),ntofn(pl"n"(nofnt(pl(xt,yt)),nofnt(zt))),ntofn(pl"n"(nofnt(xt),nofnt(pl(yt,zt)))),pl(xt,pl(yt,zt)),isplnt(pl(xt,yt),zt),isnent(pl"n"(nofnt(pl(xt,yt)),nofnt(zt)),pl"n"(nofnt(xt),nofnt(pl(yt,zt))),t3".55"),isntpl(xt,pl(yt,zt))):is(pl(pl(xt,yt),zt),pl(xt,pl(yt,zt)))
-diffprop:=is(xt,pl(yt,zt)):'prop'
-[d:diffprop]
-diffprope:=tris(nat,nofnt(xt),nofnt(pl(yt,zt)),pl"n"(nofnt(yt),nofnt(zt)),isnten(xt,pl(yt,zt),d),isnpl(yt,zt)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))
-zt@[d:diffprop"n"(nofnt(xt),nofnt(yt),nofnt(zt))]
-+*ii5
-d@t30:=tris(nat,nofnt(xt),pl"n"(nofnt(yt),nofnt(zt)),nofnt(pl(yt,zt)),d,ispln(yt,zt)):is"n"(nofnt(xt),nofnt(pl(yt,zt)))
--ii5
-d@diffpropi:=isntin(xt,pl(yt,zt),t30".ii5"):diffprop
-+59
-yt@it:=is(xt,yt):'prop'
-iit:=some([u:natt]diffprop(xt,yt,u)):'prop'
-iiit:=some([u:natt]diffprop(yt,xt,u)):'prop'
-i:=is"n"(nofnt(xt),nofnt(yt)):'prop'
-ii:=some"n"([u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u)):'prop'
-iii:=some"n"([u:nat]diffprop"n"(nofnt(yt),nofnt(xt),u)):'prop'
-[one:i]
-t1:=or3i1(it,iit,iiit,isntin(xt,yt,one)):or3(it,iit,iiit)
-yt@[two:ii][v:nat][d:diffprop"n"(nofnt(xt),nofnt(yt),v)]
-t2:=isp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),v,nofnt(ntofn(v)),d,isnnt1(v)):diffprop"n"(nofnt(xt),nofnt(yt),nofnt(ntofn(v)))
-t3:=somei(natt,[u:natt]diffprop(xt,yt,u),ntofn(v),diffpropi(xt,yt,ntofn(v),t2)):iit
-two@t4:=someapp(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),two,iit,[u:nat][v:diffprop"n"(nofnt(xt),nofnt(yt),u)]t3(u,v)):iit
-t5:=or3i2(it,iit,iiit,t4):or3(it,iit,iiit)
-yt@[three:iii]
-t6:=or3i3(it,iit,iiit,t4(yt,xt,three)):or3(it,iit,iiit)
-yt@t7:=or3app(i,ii,iii,or3(it,iit,iiit),satz9a(nofnt(xt),nofnt(yt)),[u:i]t1(u),[u:ii]t5(u),[u:iii]t6(u)):or3(it,iit,iiit)
-[onet:it]
-t8:=isnten(xt,yt,onet):i
-yt@[twot:iit][vt:natt][d:diffprop(xt,yt,vt)]
-t9:=somei(nat,[u:nat]diffprop"n"(nofnt(xt),nofnt(yt),u),nofnt(vt),diffprope(xt,yt,vt,d)):ii
-twot@t10:=someapp(natt,[u:natt]diffprop(xt,yt,u),twot,ii,[u:natt][v:diffprop(xt,yt,u)]t9(u,v)):ii
-yt@[threet:iiit]
-t11:=t10(yt,xt,threet):iii
-yt@t12:=satz9b(nofnt(xt),nofnt(yt)):ec3(i,ii,iii)
-onet@t13:=ec3e12(i,ii,iii,t12,t8):not(ii)
-t14:=th3"l.imp"(iit,ii,t13,[x:iit]t10(x)):not(iit)
-yt@t15:=th1"l.ec"(it,iit,[x:it]t14(x)):ec(it,iit)
-twot@t16:=ec3e23(i,ii,iii,t12,t10):not(iii)
-t17:=th3"l.imp"(iiit,iii,t16,[x:iiit]t11(x)):not(iiit)
-yt@t18:=th1"l.ec"(iit,iiit,[x:iit]t17(x)):ec(iit,iiit)
-threet@t19:=ec3e31(i,ii,iii,t12,t11):not(i)
-t20:=th3"l.imp"(it,i,t19,[x:it]t8(x)):not(it)
-yt@t21:=th1"l.ec"(iiit,it,[x:iiit]t20(x)):ec(iiit,it)
-t22:=th6"l.ec3"(it,iit,iiit,t15,t18,t21):ec3(it,iit,iiit)
--59
-yt@satz9:=orec3i(it".59",iit".59",iiit".59",t7".59",t22".59"):orec3(is(xt,yt),some([u:natt]is(xt,pl(yt,u))),some([u:natt]is(yt,pl(xt,u))))
-more:=more"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[m:more(xt,yt)]
-+*ii5
-m@t31:=moree(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-m@moree:=satz111a(nofnt(xt),nofnt(yt),t31".ii5"):more"n"(nofnt(xt),nofnt(yt))
-yt@[m:more"n"(nofnt(xt),nofnt(yt))]
-+*ii5
-m@t32:=satz111d(nofnt(xt),nofnt(yt),m):moref(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-m@morei:=morei"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t32".ii5"):more(xt,yt)
-yt@less:=less"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[l:less(xt,yt)]
-+*ii5
-l@t33:=lesse(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-l@lesse:=satz111c(nofnt(xt),nofnt(yt),t33".ii5"):less"n"(nofnt(xt),nofnt(yt))
-yt@[l:less"n"(nofnt(xt),nofnt(yt))]
-+*ii5
-l@t34:=satz111f(nofnt(xt),nofnt(yt),l):lessf(fr(nofnt(xt),1),fr(nofnt(yt),1))
--ii5
-l@lessi:=lessi"rt"(rtofnt(xt),rtofnt(yt),fr(nofnt(xt),1),fr(nofnt(yt),1),inclassn(rtofnt(xt),natrti(xt)),inclassn(rtofnt(yt),natrti(yt)),t34".ii5"):less(xt,yt)
-yt@moreis:=moreis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[m:moreis(xt,yt)]
-moreise:=th9"l.or"(more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),m,[u:more"rt"(rtofnt(xt),rtofnt(yt))]moree(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis"n"(nofnt(xt),nofnt(yt))
-yt@[m:moreis"n"(nofnt(xt),nofnt(yt))]
-moreisi:=th9"l.or"(more"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),more"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),m,[u:more"n"(nofnt(xt),nofnt(yt))]morei(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):moreis(xt,yt)
-yt@lessis:=lessis"rt"(rtofnt(xt),rtofnt(yt)):'prop'
-[l:lessis(xt,yt)]
-lessise:=th9"l.or"(less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),l,[u:less"rt"(rtofnt(xt),rtofnt(yt))]lesse(xt,yt,u),[u:is"rt"(rtofnt(xt),rtofnt(yt))]isrten(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis"n"(nofnt(xt),nofnt(yt))
-yt@[l:lessis"n"(nofnt(xt),nofnt(yt))]
-lessisi:=th9"l.or"(less"n"(nofnt(xt),nofnt(yt)),is"n"(nofnt(xt),nofnt(yt)),less"rt"(rtofnt(xt),rtofnt(yt)),is"rt"(rtofnt(xt),rtofnt(yt)),l,[u:less"n"(nofnt(xt),nofnt(yt))]lessi(xt,yt,u),[u:is"n"(nofnt(xt),nofnt(yt))]isrtin(rtofnt(xt),natrti(xt),rtofnt(yt),natrti(yt),u)):lessis(xt,yt)
-zt@[l:less(xt,yt)][k:less(yt,zt)]
-+515
-t1:=satz15(nofnt(xt),nofnt(yt),nofnt(zt),lesse(xt,yt,l),lesse(yt,zt,k)):less"n"(nofnt(xt),nofnt(zt))
--515
-satz15:=lessi(xt,zt,t1".515"):less(xt,zt)
-zt@[ut:natt][m:more(xt,yt)][n:more(zt,ut)]
-+521
-t1:=satz21(nofnt(xt),nofnt(yt),nofnt(zt),nofnt(ut),moree(xt,yt,m),moree(zt,ut,n)):more"n"(pl"n"(nofnt(xt),nofnt(zt)),pl"n"(nofnt(yt),nofnt(ut)))
-t2:=ismore12"n"(pl"n"(nofnt(xt),nofnt(zt)),nofnt(pl(xt,zt)),pl"n"(nofnt(yt),nofnt(ut)),nofnt(pl(yt,ut)),ispln(xt,zt),ispln(yt,ut),t1):more"n"(nofnt(pl(xt,zt)),nofnt(pl(yt,ut)))
--521
-satz21:=morei(pl(xt,zt),pl(yt,ut),t2".521"):more(pl(xt,zt),pl(yt,ut))
-@[p:[x:natt]'prop'][n:natt]
-lb:=all([x:natt]imp(<x>p,lessis(n,x))):'prop'
-min:=and(lb,<n>p):'prop'
-p@[s:some(p)]
-+527
-q:=[x:nat]<ntofn(x)>p:[x:nat]'prop'
-[n:natt][np:<n>p]
-t1:=isp(natt,p,n,ntofn(nofnt(n)),np,isntn1(n)):<nofnt(n)>q
-t2:=somei(nat,q,nofnt(n),t1):some"n"(q)
-s@t3:=someapp(natt,p,s,some"n"(q),[u:natt][v:<u>p]t2(u,v)):some"n"(q)
-t4:=satz27(q,t3):some"n"([x:nat]min"n"(q,x))
-[m:nat][mqm:min"n"(q,m)]
-t5:=ande1(lb"n"(q,m),<m>q,mqm):lb"n"(q,m)
-[n:nat][nq:<n>q]
-t6:=mp(<n>q,lessis"n"(m,n),nq,<n>t5):lessis"n"(m,n)
-mqm@[n:natt][np:<n>p]
-t7:=t6(nofnt(n),t1(n,np)):lessis"n"(m,nofnt(n))
-t8:=islessis1"n"(m,nofnt(ntofn(m)),nofnt(n),isnnt1(m),t7):lessis"n"(nofnt(ntofn(m)),nofnt(n))
-t9:=lessisi(ntofn(m),n,t8):lessis(ntofn(m),n)
-n@t10:=[u:<n>p]t9(u):imp(<n>p,lessis(ntofn(m),n))
-mqm@t11:=[x:natt]t10(x):lb(ntofn(m))
-t12:=ande2(lb"n"(q,m),<m>q,mqm):<ntofn(m)>p
-t13:=andi(lb(ntofn(m)),<ntofn(m)>p,t11,t12):min(ntofn(m))
-t14:=somei(natt,[x:natt]min(x),ntofn(m),t13):some([x:natt]min(x))
--527
-satz27:=someapp(nat,[x:nat]min"n"(q".527",x),t4".527",some([x:natt]min(x)),[x:nat][y:min"n"(q".527",x)]t14".527"(x,y)):some([x:natt]min(p,x))
--nt
-@1rt:=rtofn(1):rat
-x0@[x:frac][xix0:inf(x,class(x0))]
-+*ii5
-xix0@t35:=tr3eq(tf(x,fr(1,1)),fr(ts"n"(num(x),1),ts"n"(den(x),1)),fr(num(x),den(x)),x,tfeq1a(x,1,1),eqnd(ts"n"(num(x),1),ts"n"(den(x),1),num(x),den(x),satz28a(num(x)),satz28a(den(x))),refeq1(fr(num(x),den(x)),x,fris(x))):eq"n"(tf(x,fr(1,1)),x)
-t36:=isi(ts(x0,1rt),x0,tf(x,fr(1,1)),x,tict(x0,1rt,x,fr(1,1),xix0,inclass(fr(1,1))),xix0,t35):is(ts(x0,1rt),x0)
--ii5
-x0@example1a:=ratapp1(x0,is(ts(x0,1rt),x0),[x:frac][xi:inf(x,class(x0))]t36".ii5"(x,xi)):is(ts(x0,1rt),x0)
-example1b:=symis(rat,ts(x0,1rt),x0,example1a):is(x0,ts(x0,1rt))
-example1c:=tris(rat,ts(1rt,x0),ts(x0,1rt),x0,comts(1rt,x0),example1a):is(ts(1rt,x0),x0)
-example1d:=symis(rat,ts(1rt,x0),x0,example1c):is(x0,ts(1rt,x0))
-@[x:frac]
-+5114
-t1:=tr3eq(tf(fr(den(x),1),x),fr(ts"n"(den(x),num(x)),ts"n"(1,den(x))),fr(ts"n"(num(x),den(x)),ts"n"(1,den(x))),fr(num(x),1),tfeq2a(x,den(x),1),eqn(ts"n"(den(x),num(x)),ts"n"(1,den(x)),ts"n"(num(x),den(x)),comts"n"(den(x),num(x))),satz40c(num(x),1,den(x))):eq"n"(tf(fr(den(x),1),x),fr(num(x),1))
--5114
-satz114:=isi(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)),tf(fr(den(x),1),x),fr(num(x),1),tict(rtofn(den(x)),ratof(x),fr(den(x),1),x,inclass(fr(den(x),1)),inclass(x)),inclass(fr(num(x),1)),t1".5114"):is(ts(rtofn(den(x)),ratof(x)),rtofn(num(x)))
-@[x1:nat][x2:nat]
-satz114a:=tr3is(rat,ts(rtofn(x2),ratof(fr(x1,x2))),ts(rtofn(den(fr(x1,x2))),ratof(fr(x1,x2))),rtofn(num(fr(x1,x2))),rtofn(x1),ists1(rtofn(x2),rtofn(den(fr(x1,x2))),ratof(fr(x1,x2)),isnert(x2,den(fr(x1,x2)),isden(x1,x2))),satz114(fr(x1,x2)),isnert(num(fr(x1,x2)),x1,numis(x1,x2))):is(ts(rtofn(x2),ratof(fr(x1,x2))),rtofn(x1))
-x0@[y0:rat]
-ov:=ind(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):rat
-satz110c:=oneax(rat,[t:rat]is(ts(y0,t),x0),satz110(x0,y0)):is(ts(y0,ov(x0,y0)),x0)
-satz110d:=symis(rat,ts(y0,ov(x0,y0)),x0,satz110c):is(x0,ts(y0,ov(x0,y0)))
-satz110e:=tris(rat,ts(ov(x0,y0),y0),ts(y0,ov(x0,y0)),x0,comts(ov(x0,y0),y0),satz110c):is(ts(ov(x0,y0),y0),x0)
-satz110f:=symis(rat,ts(ov(x0,y0),y0),x0,satz110e):is(x0,ts(ov(x0,y0),y0))
-[v0:rat][i:is(ts(y0,v0),x0)]
-satz110g:=satz110b(x0,y0,v0,ov(x0,y0),i,satz110c):is(v0,ov(x0,y0))
-x2@satz114b:=satz110b(rtofn(x1),rtofn(x2),ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114a,satz110c(rtofn(x1),rtofn(x2))):is(ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)))
-satz114c:=symis(rat,ratof(fr(x1,x2)),ov(rtofn(x1),rtofn(x2)),satz114b):is(ov(rtofn(x1),rtofn(x2)),ratof(fr(x1,x2)))
-+5115
-y0@t1:=satz89(ov(y0,x0)):some([t:rat]more(t,ov(y0,x0)))
-[u0:rat][m:more(u0,ov(y0,x0))][u:frac][uiu0:inf(u,class(u0))]
-z:=num(u):nat
-v:=den(u):nat
-t2:=ismore1(u0,ov(rtofn(z),rtofn(v)),ov(y0,x0),tris(rat,u0,ratof(fr(z,v)),ov(rtofn(z),rtofn(v)),isi(u0,ratof(fr(z,v)),u,fr(z,v),uiu0,inclass(fr(z,v)),refeq1(u,fr(z,v),isfr(u))),satz114b(z,v)),m):more(ov(rtofn(z),rtofn(v)),ov(y0,x0))
-t3:=moreisi(rtofn(v),1rt,fr(v,1),fr(1,1),inclass(fr(v,1)),inclass(fr(1,1)),th9"l.or"(more"n"(v,1),is"n"(v,1),moref(fr(v,1),fr(1,1)),eq"n"(fr(v,1),fr(1,1)),satz24(v),[t:more"n"(v,1)]satz111d(v,1,t),[t:is"n"(v,1)]satz111e(v,1,t))):moreis(rtofn(v),1rt)
-t4:=tr3is(rat,ts(rtofn(z),x0),ts(x0,rtofn(z)),ts(x0,ts(ov(rtofn(z),rtofn(v)),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),comts(rtofn(z),x0),ists2(rtofn(z),ts(ov(rtofn(z),rtofn(v)),rtofn(v)),x0,satz110f(rtofn(z),rtofn(v))),assts2(x0,ov(rtofn(z),rtofn(v)),rtofn(v))):is(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)))
-[n:more(rtofn(v),1rt)]
-t5:=ismore1(ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),symis(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),t4),satz105d(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),n)):more(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-t6:=moreisi1(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t5):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-uiu0@[i:is(rtofn(v),1rt)]
-t7:=moreisi2(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),tris(rat,ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),rtofn(v)),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),t4,ists2(rtofn(v),1rt,ts(x0,ov(rtofn(z),rtofn(v))),i))):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-uiu0@t8:=orapp(more(rtofn(v),1rt),is(rtofn(v),1rt),moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt)),t3,[t:more(rtofn(v),1rt)]t6(t),[t:is(rtofn(v),1rt)]t7(t)):moreis(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt))
-t9:=ismore12(ts(x0,ov(rtofn(z),rtofn(v))),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),ts(x0,ov(y0,x0)),y0,example1b(ts(x0,ov(rtofn(z),rtofn(v)))),satz110c(y0,x0),satz105d(ov(rtofn(z),rtofn(v)),ov(y0,x0),x0,t2)):more(ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0)
-t10:=satz87c(ts(rtofn(z),x0),ts(ts(x0,ov(rtofn(z),rtofn(v))),1rt),y0,t8,t9):more(ts(rtofn(z),x0),y0)
-t11:=somei(nat,[t:nat]more(ts(rtofn(t),x0),y0),z,t10):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
-m@t12:=ratapp1(u0,some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[u:frac][ui:inf(u,class(u0))]t11(u,ui)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
--5115
-y0@satz115:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some"n"([t:nat]more(ts(rtofn(t),x0),y0)),[t:rat][u:more(t,ov(y0,x0))]t12".5115"(t,u)):some"n"([t:nat]more(ts(rtofn(t),x0),y0))
-+*5115
-uiu0@t13:=andi(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0),natrti(z),t10):and(natrt(rtofn(z)),more(ts(rtofn(z),x0),y0))
-t14:=somei(rat,[t:rat]and(natrt(t),more(ts(t,x0),y0)),rtofn(z),t13):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
-m@t15:=ratapp1(u0,some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[u:frac][ui:inf(u,class(u0))]t14(u,ui)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
--5115
-y0@satz115a:=someapp(rat,[t:rat]more(t,ov(y0,x0)),t1".5115",some([t:rat]and(natrt(t),more(ts(t,x0),y0))),[t:rat][u:more(t,ov(y0,x0))]t15".5115"(t,u)):some([t:rat]and(natrt(t),more(ts(t,x0),y0)))
-@[s:set(rat)]
-cutprop1a:=nonempty(rat,s):'prop'
-cutprop1b:=not(all([x:rat]in(x,s))):'prop'
-cutprop1:=and(cutprop1a,cutprop1b):'prop'
-[x0:rat]
-cutprop2a:=all([x:rat]imp(not(in(x,s)),less(x0,x))):'prop'
-s@cutprop2:=all([x:rat]imp(in(x,s),cutprop2a(x))):'prop'
-x0@[y0:rat]
-+iii1
-ubprop:=imp(in(y0,s),moreis(x0,y0)):'prop'
--iii1
-x0@ub:=all([x:rat]ubprop".iii1"(x0,x)):'prop'
-max:=and(ub(x0),in(x0,s)):'prop'
-s@cutprop3:=not(some([x:rat]max(s,x))):'prop'
-cutprop:=and3(cutprop1,cutprop2,cutprop3):'prop'
-+*iii1
-y0@lbprop:=imp(in(y0,s),lessis(x0,y0)):'prop'
--iii1
-x0@lb:=all([x:rat]lbprop".iii1"(x0,x)):'prop'
-min:=and(lb(x0),in(x0,s)):'prop'
-@cut:=ot(set(rat),[x:set(rat)]cutprop(x)):'type'
-[ksi:cut]
-lcl:=in"e"(set(rat),[x:set(rat)]cutprop(x),ksi):set(rat)
-[x0:rat]
-lrt:=in(x0,lcl(ksi)):'prop'
-urt:=not(in(x0,lcl(ksi))):'prop'
-ksi@clcl:=inp(set(rat),[x:set(rat)]cutprop(x),ksi):cutprop(lcl(ksi))
-clcl1:=and3e1(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop1(lcl(ksi))
-clcl2:=and3e2(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop2(lcl(ksi))
-clcl3:=and3e3(cutprop1(lcl),cutprop2(lcl),cutprop3(lcl),clcl):cutprop3(lcl(ksi))
-clcl1a:=ande1(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1a(lcl(ksi))
-clcl1b:=ande2(cutprop1a(lcl),cutprop1b(lcl),clcl1):cutprop1b(lcl(ksi))
-[p:'prop'][p1:[x:rat][t:lrt(ksi,x)]p]
-cutapp1a:=nonemptyapp(rat,lcl,clcl1a,p,p1):p
-+*iii1
-ksi@t1:=th1"l.some"(rat,[x:rat]lrt(ksi,x),clcl1b):some([x:rat]urt(ksi,x))
--iii1
-p@[p1:[x:rat][t:urt(ksi,x)]p]
-cutapp1b:=someapp(rat,[x:rat]urt(ksi,x),t1".iii1",p,p1):p
-ksi@[x0:rat][lx:lrt(ksi,x0)]
-+*iii1
-lx@t2:=mp(lrt(ksi,x0),cutprop2a(lcl,x0),lx,<x0>clcl2):cutprop2a(lcl,x0)
--iii1
-lx@[y0:rat][uy:urt(ksi,y0)]
-cutapp2a:=mp(urt(ksi,y0),less(x0,y0),uy,<y0>t2".iii1"):less(x0,y0)
-cutapp2b:=satz83(x0,y0,cutapp2a):more(y0,x0)
-+*iii1
-lx@t3:=th4"l.some"(rat,[x:rat]max(lcl,x),clcl3,x0):not(max(lcl,x0))
-t4:=th4"l.and"(ub(lcl,x0),lrt(ksi,x0),t3,lx):not(ub(lcl,x0))
-t5:=th1"l.some"(rat,[x:rat]ubprop(lcl,x0,x),t4):some([x:rat]not(ubprop(lcl,x0,x)))
--iii1
-lx@[p:'prop'][p1:[y:rat][t:lrt(ksi,y)][u:less(x0,y)]p][y0:rat][n:not(ubprop".iii1"(lcl,x0,y0))]
-+*iii1
-n@t6:=th5"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):lrt(ksi,y0)
-t7:=th6"l.imp"(lrt(ksi,y0),moreis(x0,y0),n):not(moreis(x0,y0))
-t8:=satz81j(x0,y0,t7):less(x0,y0)
-t9:=<t8><t6><y0>p1:p
--iii1
-p1@cutapp3:=someapp(rat,[y:rat]not(ubprop".iii1"(lcl,x0,y)),t5".iii1",p,[y:rat][t:not(ubprop".iii1"(lcl,x0,y))]t9".iii1"(y,t)):p
-s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))]
-+*iii1
-n@t10:=andi(cutprop1a,cutprop1b,nonemptyi(rat,s,x0,i),th1"l.all"(rat,[x:rat]in(x,s),y0,n)):cutprop1
--iii1
-s@[n:[x:rat]not(max(s,x))]
-+*iii1
-n@t11:=th5"l.some"(rat,[x:rat]max(s,x),n):cutprop3
--iii1
-s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][l:[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]less(x,y)][m:[x:rat]not(max(s,x))]
-cut1:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),l,t11".iii1"(m)):cutprop(s)
-+rp
-ksi@[eta:cut]
-is:=is"e"(cut,ksi,eta):'prop'
-nis:=not(is(ksi,eta)):'prop'
-[i:is(ksi,eta)]
-ise:=isini(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is"e"(set(rat),lcl(ksi),lcl(eta))
-[x0:rat][lx:lrt(ksi,x0)]
-ise1:=issete1(rat,lcl(ksi),lcl(eta),ise,x0,lx):lrt(eta,x0)
-eta@[i:is"e"(set(rat),lcl(ksi),lcl(eta))]
-isi:=isine(set(rat),[x:set(rat)]cutprop(x),ksi,eta,i):is(ksi,eta)
-eta@[l:[x:rat][t:lrt(ksi,x)]lrt(eta,x)][k:[x:rat][t:lrt(eta,x)]lrt(ksi,x)]
-isi1:=isi(isseti(rat,lcl(ksi),lcl(eta),l,k)):is(ksi,eta)
-@[s:set(rat)][cs:cutprop(s)]
-cutof:=out(set(rat),[x:set(rat)]cutprop(x),s,cs):cut
-[x0:rat][i:in(x0,s)]
-ine:=issete1(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,i):lrt(cutof(s,cs),x0)
-x0@[lx:lrt(cutof(s,cs),x0)]
-ini:=issete2(rat,s,lcl(cutof(s,cs)),isinout(set(rat),[x:set(rat)]cutprop(x),s,cs),x0,lx):in(x0,s)
-s@[t:set(rat)][cs:cutprop(s)][ct:cutprop(t)][i:[x:rat][u:in(x,s)]in(x,t)][j:[x:rat][u:in(x,t)]in(x,s)]
-isi2:=isouti(set(rat),[x:set(rat)]cutprop(x),s,cs,t,ct,isseti(rat,s,t,i,j)):is(cutof(s,cs),cutof(t,ct))
-@[p:[x:cut]'prop']
-all:=all"l"(cut,p):'prop'
-some:=some"l"(cut,p):'prop'
-one:=one"e"(cut,p):'prop'
-ksi@satz116:=refis(cut,ksi):is(ksi,ksi)
-eta@[i:is(ksi,eta)]
-satz117:=symis(cut,ksi,eta,i):is(eta,ksi)
-eta@[zeta:cut][i:is(ksi,eta)][j:is(eta,zeta)]
-satz118:=tris(cut,ksi,eta,zeta,i,j):is(ksi,zeta)
-+1119
-@[x0:rat][y0:rat][m:more(x0,y0)]
-t1:=ec3e23(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),m):not(less(x0,y0))
--1119
-ksi@[x0:rat][ux:urt(ksi,x0)][y0:rat][m:more(y0,x0)]
-satz119:=th3"l.imp"(lrt(ksi,y0),less(y0,x0),t1".1119"(y0,x0,m),[t:lrt(ksi,y0)]cutapp2a(y0,t,x0,ux)):urt(ksi,y0)
-y0@[l:less(x0,y0)]
-satz119a:=satz119(satz83(x0,y0,l)):urt(ksi,y0)
-+1120
-@[x0:rat][y0:rat][l:less(x0,y0)]
-t1:=ec3e32(is"rt"(x0,y0),more(x0,y0),less(x0,y0),satz81b(x0,y0),l):not(more(x0,y0))
--1120
-ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][l:less(y0,x0)]
-satz120:=th7"l.imp"(lrt(ksi,y0),more(y0,x0),t1".1120"(y0,x0,l),[t:urt(ksi,y0)]cutapp2b(x0,lx,y0,t)):lrt(ksi,y0)
-y0@[m:more(x0,y0)]
-satz120a:=satz120(satz82(x0,y0,m)):lrt(ksi,y0)
--rp
-s@[i:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][x0:rat][j:in(x0,s)][y0:rat][n:not(in(y0,s))]
-+*iii1
-n@t12:=<y0><j><x0>i:[u:less(y0,x0)]in(y0,s)
-t13:=th3"l.imp"(less(y0,x0),in(y0,s),n,t12):not(less(y0,x0))
-t14:=satz81f(y0,x0,t13):moreis(y0,x0)
--iii1
-n@[k:is(y0,x0)]
-+*iii1
-k@t15:=isp1(rat,[x:rat]in(x,s),x0,y0,j,k):in(y0,s)
-n@t16:=th3"l.imp"(is(y0,x0),in(y0,s),n,[t:is(y0,x0)]t15(t)):nis(y0,x0)
-t17:=ore1(more(y0,x0),is(y0,x0),t14,t16):more(y0,x0)
-t18:=satz82(y0,x0,t17):less(x0,y0)
-i@t19:=[x:rat][t:in(x,s)][y:rat][u:not(in(y,s))]t18(x,t,y,u):cutprop2
--iii1
-s@[s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))][x0:rat][i:in(x0,s)]
-+*iii1
-i@t20:=<i><x0>s1:some([y:rat]and(in(y,s),more(y,x0)))
--iii1
-i@[y0:rat][a:and(in(y0,s),more(y0,x0))]
-+*iii1
-a@t21:=ande1(in(y0,s),more(y0,x0),a):in(y0,s)
-t22:=ande2(in(y0,s),more(y0,x0),a):more(y0,x0)
-t23:=satz81g(y0,x0,t22):not(lessis(y0,x0))
-t24:=th3"l.imp"(moreis(x0,y0),lessis(y0,x0),t23,[t:moreis(x0,y0)]satz84(x0,y0,t)):not(moreis(x0,y0))
-t25:=th4"l.imp"(in(y0,s),moreis(x0,y0),t21,t24):not(ubprop(x0,y0))
-t26:=th1"l.all"(rat,[y:rat]ubprop(x0,y),y0,t25):not(ub(s,x0))
-t27:=th1"l.and"(ub(s,x0),in(x0,s),t26):not(max(s,x0))
-i@t28:=someapp(rat,[y:rat]and(in(y,s),more(y,x0)),t20,not(max(s,x0)),[y:rat][t:and(in(y,s),more(y,x0))]t27(y,t)):not(max(s,x0))
--iii1
-x0@[n:not(in(x0,s))]
-+*iii1
-n@t29:=th2"l.and"(ub(x0),in(x0,s),n):not(max(s,x0))
-x0@t30:=th1"l.imp"(in(x0,s),not(max(s,x0)),[u:in(x0,s)]t28(u),[u:not(in(x0,s))]t29(u)):not(max(s,x0))
-s1@t31:=t11([x:rat]t30(x)):cutprop3
--iii1
-s@[x0:rat][i:in(x0,s)][y0:rat][n:not(in(y0,s))][j:[x:rat][t:in(x,s)][y:rat][u:less(y,x)]in(y,s)][s1:[x:rat][t:in(x,s)]some([y:rat]and(in(y,s),more(y,x)))]
-cut2:=and3i(cutprop1,cutprop2,cutprop3,t10".iii1"(x0,i,y0,n),t19".iii1"(j),t31".iii1"(s1)):cutprop(s)
-+*rp
-eta@more:=some"rt"([x:rat]and(lrt(ksi,x),urt(eta,x))):'prop'
-[m:more(ksi,eta)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]p][x0:rat][a:and(lrt(ksi,x0),urt(eta,x0))]
-+iii2
-t1:=ande1(lrt(ksi,x0),urt(eta,x0),a):lrt(ksi,x0)
-t2:=ande2(lrt(ksi,x0),urt(eta,x0),a):urt(eta,x0)
-t3:=<t2><t1><x0>p1:p
--iii2
-p1@moreapp:=someapp(rat,[x:rat]and(lrt(ksi,x),urt(eta,x)),m,p,[x:rat][t:and(lrt(ksi,x),urt(eta,x))]t3".iii2"(x,t)):p
-eta@less:=some"rt"([x:rat]and(urt(ksi,x),lrt(eta,x))):'prop'
-[l:less(ksi,eta)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]p][x0:rat][a:and(urt(ksi,x0),lrt(eta,x0))]
-+*iii2
-a@t4:=ande1(urt(ksi,x0),lrt(eta,x0),a):urt(ksi,x0)
-t5:=ande2(urt(ksi,x0),lrt(eta,x0),a):lrt(eta,x0)
-t6:=<t5><t4><x0>p1:p
--iii2
-p1@lessapp:=someapp(rat,[x:rat]and(urt(ksi,x),lrt(eta,x)),l,p,[x:rat][t:and(urt(ksi,x),lrt(eta,x))]t6".iii2"(x,t)):p
-eta@[m:more(ksi,eta)]
-+2121
-[x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
-t1:=andi(urt(eta,x0),lrt(ksi,x0),ux,lx):and(urt(eta,x0),lrt(ksi,x0))
-t2:=somei(rat,[x:rat]and(urt(eta,x),lrt(ksi,x)),x0,t1):less(eta,ksi)
--2121
-satz121:=moreapp(m,less(eta,ksi),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2".2121"(x,t,u)):less(eta,ksi)
-eta@[l:less(ksi,eta)]
-+2122
-[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
-t1:=andi(lrt(eta,x0),urt(ksi,x0),lx,ux):and(lrt(eta,x0),urt(ksi,x0))
-t2:=somei(rat,[x:rat]and(lrt(eta,x),urt(ksi,x)),x0,t1):more(eta,ksi)
--2122
-satz122:=lessapp(l,more(eta,ksi),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t2".2122"(x,t,u)):more(eta,ksi)
-+2123
-eta@[m:more(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)]
-t1:=th3"st.isset"(rat,lcl(ksi),lcl(eta),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
-t2:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t1,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
-m@t3:=moreapp(ksi,eta,m,not(is(ksi,eta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t2(x,t,u)):not(is(ksi,eta))
-eta@t4:=th2"l.ec"(is(ksi,eta),more(ksi,eta),[t:more(ksi,eta)]t3(t)):ec(is(ksi,eta),more(ksi,eta))
-[l:less(ksi,eta)][x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)]
-t5:=th4"st.isset"(rat,lcl(eta),lcl(ksi),x0,lx,ux):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
-t6:=th3"l.imp"(is(ksi,eta),is"e"(set(rat),lcl(ksi),lcl(eta)),t5,[t:is(ksi,eta)]ise(ksi,eta,t)):not(is(ksi,eta))
-l@t7:=lessapp(ksi,eta,l,not(is(ksi,eta)),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t6(x,t,u)):not(is(ksi,eta))
-eta@t8:=th1"l.ec"(less(ksi,eta),is(ksi,eta),[t:less(ksi,eta)]t7(t)):ec(less(ksi,eta),is(ksi,eta))
-m@[l:less(ksi,eta)][x0:rat][lx:lrt(ksi,x0)][ux:urt(eta,x0)][y0:rat][uy:urt(ksi,y0)][ly:lrt(eta,y0)]
-t9:=cutapp2a(ksi,x0,lx,y0,uy):less"rt"(x0,y0)
-t10:=cutapp2b(eta,y0,ly,x0,ux):more"rt"(x0,y0)
-t11:=mp(less"rt"(x0,y0),con,t9,ec3e23(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),satz81b(x0,y0),t10)):con
-ux@t12:=lessapp(ksi,eta,l,con,[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t11(x,t,u)):con
-l@t13:=moreapp(ksi,eta,m,con,[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t12(x,t,u)):con
-m@t14:=[t:less(ksi,eta)]t13(t):not(less(ksi,eta))
-eta@t15:=th1"l.ec"(more(ksi,eta),less(ksi,eta),[t:more(ksi,eta)]t14(t)):ec(more(ksi,eta),less(ksi,eta))
-a:=th6"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t4,t15,t8):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-[i:is(ksi,eta)]
-t16:=or3i1(is(ksi,eta),more(ksi,eta),less(ksi,eta),i):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-eta@[n:nis(ksi,eta)]
-t17:=th3"l.imp"(is"e"(set(rat),lcl(ksi),lcl(eta)),is(ksi,eta),n,[t:is"e"(set(rat),lcl(ksi),lcl(eta))]isi(ksi,eta,t)):not(is"e"(set(rat),lcl(ksi),lcl(eta)))
-t18:=th5"st.isset"(rat,lcl(ksi),lcl(eta),t17):or(more(ksi,eta),more(eta,ksi))
-t19:=th8"l.or"(more(ksi,eta),more(eta,ksi),less(ksi,eta),t18,[t:more(eta,ksi)]satz121(eta,ksi,t)):or(more(ksi,eta),less(ksi,eta))
-t20:=th7"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),t19):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-eta@b:=th1"l.imp"(is(ksi,eta),or3(is(ksi,eta),more(ksi,eta),less(ksi,eta)),[t:is(ksi,eta)]t16(t),[t:nis(ksi,eta)]t20(t)):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
--2123
-eta@satz123:=orec3i(is(ksi,eta),more(ksi,eta),less(ksi,eta),b".2123",a".2123"):orec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-satz123a:=orec3e1(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-satz123b:=orec3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123):ec3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-moreis:=or(more(ksi,eta),is(ksi,eta)):'prop'
-lessis:=or(less(ksi,eta),is(ksi,eta)):'prop'
-[m:moreis(ksi,eta)]
-satz124:=th9"l.or"(more(ksi,eta),is(ksi,eta),less(eta,ksi),is(eta,ksi),m,[t:more(ksi,eta)]satz121(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):lessis(eta,ksi)
-eta@[l:lessis(ksi,eta)]
-satz125:=th9"l.or"(less(ksi,eta),is(ksi,eta),more(eta,ksi),is(eta,ksi),l,[t:less(ksi,eta)]satz122(t),[t:is(ksi,eta)]symis(cut,ksi,eta,t)):moreis(eta,ksi)
-zeta@[i:is(ksi,eta)][m:more(ksi,zeta)]
-ismore1:=isp(cut,[u:cut]more(u,zeta),ksi,eta,m,i):more(eta,zeta)
-i@[m:more(zeta,ksi)]
-ismore2:=isp(cut,[u:cut]more(zeta,u),ksi,eta,m,i):more(zeta,eta)
-i@[l:less(ksi,zeta)]
-isless1:=isp(cut,[u:cut]less(u,zeta),ksi,eta,l,i):less(eta,zeta)
-i@[l:less(zeta,ksi)]
-isless2:=isp(cut,[u:cut]less(zeta,u),ksi,eta,l,i):less(zeta,eta)
-i@[m:moreis(ksi,zeta)]
-ismoreis1:=isp(cut,[u:cut]moreis(u,zeta),ksi,eta,m,i):moreis(eta,zeta)
-i@[m:moreis(zeta,ksi)]
-ismoreis2:=isp(cut,[u:cut]moreis(zeta,u),ksi,eta,m,i):moreis(zeta,eta)
-i@[l:lessis(ksi,zeta)]
-islessis1:=isp(cut,[u:cut]lessis(u,zeta),ksi,eta,l,i):lessis(eta,zeta)
-i@[l:lessis(zeta,ksi)]
-islessis2:=isp(cut,[u:cut]lessis(zeta,u),ksi,eta,l,i):lessis(zeta,eta)
-eta@[i:is(ksi,eta)]
-moreisi2:=ori2(more(ksi,eta),is(ksi,eta),i):moreis(ksi,eta)
-lessisi2:=ori2(less(ksi,eta),is(ksi,eta),i):lessis(ksi,eta)
-eta@[m:more(ksi,eta)]
-moreisi1:=ori1(more(ksi,eta),is(ksi,eta),m):moreis(ksi,eta)
-eta@[l:less(ksi,eta)]
-lessisi1:=ori1(less(ksi,eta),is(ksi,eta),l):lessis(ksi,eta)
-zeta@[upsilon:cut][i:is(ksi,eta)][j:is(zeta,upsilon)][m:more(ksi,zeta)]
-ismore12:=ismore2(zeta,upsilon,eta,j,ismore1(ksi,eta,zeta,i,m)):more(eta,upsilon)
-j@[l:less(ksi,zeta)]
-isless12:=isless2(zeta,upsilon,eta,j,isless1(ksi,eta,zeta,i,l)):less(eta,upsilon)
-j@[m:moreis(ksi,zeta)]
-ismoreis12:=ismoreis2(zeta,upsilon,eta,j,ismoreis1(ksi,eta,zeta,i,m)):moreis(eta,upsilon)
-j@[l:lessis(ksi,zeta)]
-islessis12:=islessis2(zeta,upsilon,eta,j,islessis1(ksi,eta,zeta,i,l)):lessis(eta,upsilon)
-eta@[m:moreis(ksi,eta)]
-satz123c:=th7"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,comor(more(ksi,eta),is(ksi,eta),m)):not(less(ksi,eta))
-eta@[l:lessis(ksi,eta)]
-satz123d:=th9"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l):not(more(ksi,eta))
-eta@[n:not(more(ksi,eta))]
-satz123e:=th2"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n):lessis(ksi,eta)
-eta@[n:not(less(ksi,eta))]
-satz123f:=comor(is(ksi,eta),more(ksi,eta),th3"l.or3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,n)):moreis(ksi,eta)
-eta@[m:more(ksi,eta)]
-satz123g:=th3"l.or"(less(ksi,eta),is(ksi,eta),ec3e23(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m),ec3e21(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,m)):not(lessis(ksi,eta))
-eta@[l:less(ksi,eta)]
-satz123h:=th3"l.or"(more(ksi,eta),is(ksi,eta),ec3e32(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l),ec3e31(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123b,l)):not(moreis(ksi,eta))
-eta@[n:not(moreis(ksi,eta))]
-satz123j:=or3e3(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th5"l.or"(more(ksi,eta),is(ksi,eta),n),th4"l.or"(more(ksi,eta),is(ksi,eta),n)):less(ksi,eta)
-eta@[n:not(lessis(ksi,eta))]
-satz123k:=or3e2(is(ksi,eta),more(ksi,eta),less(ksi,eta),satz123a,th4"l.or"(less(ksi,eta),is(ksi,eta),n),th5"l.or"(less(ksi,eta),is(ksi,eta),n)):more(ksi,eta)
-zeta@[l:less(ksi,eta)][k:less(eta,zeta)]
-+2126
-[x0:rat][ux:urt(ksi,x0)][lx:lrt(eta,x0)][y0:rat][uy:urt(eta,y0)][ly:lrt(zeta,y0)]
-t1:=cutapp2a(eta,x0,lx,y0,uy):less"rt"(x0,y0)
-t2:=satz119a(ksi,x0,ux,y0,t1):urt(ksi,y0)
-t3:=andi(urt(ksi,y0),lrt(zeta,y0),t2,ly):and(urt(ksi,y0),lrt(zeta,y0))
-t4:=somei(rat,[x:rat]and(urt(ksi,x),lrt(zeta,x)),y0,t3):less(ksi,zeta)
-lx@t5:=lessapp(eta,zeta,k,less(ksi,zeta),[x:rat][t:urt(eta,x)][u:lrt(zeta,x)]t4(x,t,u)):less(ksi,zeta)
--2126
-satz126:=lessapp(ksi,eta,l,less(ksi,zeta),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t5".2126"(x,t,u)):less(ksi,zeta)
-trless:=satz126:less(ksi,zeta)
-zeta@[m:more(ksi,eta)][n:more(eta,zeta)]
-trmore:=satz122(zeta,ksi,satz126(zeta,eta,ksi,satz121(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
-zeta@[l:lessis(ksi,eta)][k:less(eta,zeta)]
-satz127a:=orapp(less(ksi,eta),is(ksi,eta),less(ksi,zeta),l,[u:less(ksi,eta)]trless(u,k),[u:is(ksi,eta)]isless1(eta,ksi,zeta,symis(cut,ksi,eta,u),k)):less(ksi,zeta)
-zeta@[l:less(ksi,eta)][k:lessis(eta,zeta)]
-satz127b:=orapp(less(eta,zeta),is(eta,zeta),less(ksi,zeta),k,[u:less(eta,zeta)]trless(l,u),[u:is(eta,zeta)]isless2(eta,zeta,ksi,u,l)):less(ksi,zeta)
-zeta@[m:moreis(ksi,eta)][n:more(eta,zeta)]
-satz127c:=satz122(zeta,ksi,satz127b(zeta,eta,ksi,satz121(eta,zeta,n),satz124(ksi,eta,m))):more(ksi,zeta)
-zeta@[m:more(ksi,eta)][n:moreis(eta,zeta)]
-satz127d:=satz122(zeta,ksi,satz127a(zeta,eta,ksi,satz124(eta,zeta,n),satz121(ksi,eta,m))):more(ksi,zeta)
-zeta@[l:lessis(ksi,eta)][k:lessis(eta,zeta)]
-+2128
-[i:is(ksi,eta)][j:is(eta,zeta)]
-t1:=lessisi2(ksi,zeta,tris(cut,ksi,eta,zeta,i,j)):lessis(ksi,zeta)
-i@[j:less(eta,zeta)]
-t2:=lessisi1(ksi,zeta,satz127a(l,j)):lessis(ksi,zeta)
-i@t3:=orapp(less(eta,zeta),is(eta,zeta),lessis(ksi,zeta),k,[t:less(eta,zeta)]t2(t),[t:is(eta,zeta)]t1(t)):lessis(ksi,zeta)
-k@[j:less(ksi,eta)]
-t4:=lessisi1(ksi,zeta,satz127b(j,k)):lessis(ksi,zeta)
--2128
-satz128:=orapp(less(ksi,eta),is(ksi,eta),lessis(ksi,zeta),l,[t:less(ksi,eta)]t4".2128"(t),[t:is(ksi,eta)]t3".2128"(t)):lessis(ksi,zeta)
-trlessis:=satz128:lessis(ksi,zeta)
-zeta@[m:moreis(ksi,eta)][n:moreis(eta,zeta)]
-trmoreis:=satz125(zeta,ksi,satz128(zeta,eta,ksi,satz124(eta,zeta,n),satz124(ksi,eta,m))):moreis(ksi,zeta)
-eta@[z0:rat][x0:rat][y0:rat]
-sumprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0))):'prop'
-z0@sumprop:=some"rt"([x:rat]some"rt"([y:rat]sumprop1(z0,x,y))):'prop'
-eta@sum:=setof(rat,[z:rat]sumprop(z)):set(rat)
-x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl(x0,y0))]
-+iii3
-t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),lx,ly,i):sumprop1(z0,x0,y0)
-t2:=somei(rat,[y:rat]sumprop1(z0,x0,y),y0,t1):some"rt"([y:rat]sumprop1(z0,x0,y))
-t3:=somei(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),x0,t2):sumprop(z0)
--iii3
-sum1:=estii(rat,[z:rat]sumprop(z),z0,t3".iii3"):in(z0,sum)
-z0@[i:in(z0,sum)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]p]
-+*iii3
-p1@t4:=estie(rat,[z:rat]sumprop(z),z0,i):sumprop(z0)
--iii3
-p1@[x0:rat][px:some"rt"([y:rat]sumprop1(z0,x0,y))][y0:rat][py:sumprop1(z0,x0,y0)]
-+*iii3
-py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(ksi,x0)
-t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):lrt(eta,y0)
-t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,pl(x0,y0)),py):is"rt"(z0,pl(x0,y0))
-t8:=<t7><t6><y0><t5><x0>p1:p
-px@t9:=someapp(rat,[y:rat]sumprop1(z0,x0,y),px,p,[y:rat][t:sumprop1(z0,x0,y)]t8(y,t)):p
--iii3
-p1@sumapp:=someapp(rat,[x:rat]some"rt"([y:rat]sumprop1(z0,x,y)),t4".iii3",p,[x:rat][t:some"rt"([y:rat]sumprop1(z0,x,y))]t9".iii3"(x,t)):p
-eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-+3129
-[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))]
-t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
-t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
-t3:=isless1"rt"(pl(x0,y0),z0,pl(x1,y1),symis(rat,z0,pl(x0,y0),j),satz98a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,pl(x1,y1))
-t4:=ec3e31(is"rt"(z0,pl(x1,y1)),more"rt"(z0,pl(x1,y1)),less"rt"(z0,pl(x1,y1)),satz81b(z0,pl(x1,y1)),t3):nis"rt"(z0,pl(x1,y1))
-i@t5:=sumapp(ksi,eta,z0,i,nis"rt"(z0,pl(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,pl(x1,y1))
--3129
-satz129a:=th3"l.imp"(in(pl(x1,y1),sum),nis"rt"(pl(x1,y1),pl(x1,y1)),weli(is"rt"(pl(x1,y1),pl(x1,y1)),refis(rat,pl(x1,y1))),[t:in(pl(x1,y1),sum)]t5".3129"(pl(x1,y1),t)):not(in(pl(x1,y1),sum))
-+*3129
-eta@[u0:rat][i:in(u0,sum)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,pl(x0,y0))]
-t6:=isless2"rt"(u0,pl(x0,y0),z0,j,l):less"rt"(z0,pl(x0,y0))
-z1:=ov(z0,pl(x0,y0)):rat
-t7:=isless12"rt"(z0,ts(z1,pl(x0,y0)),pl(x0,y0),ts(1rt,pl(x0,y0)),satz110f(z0,pl(x0,y0)),example1d(pl(x0,y0)),t6):less"rt"(ts(z1,pl(x0,y0)),ts(1rt,pl(x0,y0)))
-t8:=satz106c(z1,1rt,pl(x0,y0),t7):less"rt"(z1,1rt)
-t9:=isless2"rt"(ts(x0,1rt),x0,ts(x0,z1),example1a(x0),satz105f(z1,1rt,x0,t8)):less"rt"(ts(x0,z1),x0)
-t10:=isless2"rt"(ts(y0,1rt),y0,ts(y0,z1),example1a(y0),satz105f(z1,1rt,y0,t8)):less"rt"(ts(y0,z1),y0)
-t11:=satz120(ksi,x0,lx,ts(x0,z1),t9):lrt(ksi,ts(x0,z1))
-t12:=satz120(eta,y0,ly,ts(y0,z1),t10):lrt(eta,ts(y0,z1))
-t13:=tris(rat,pl(ts(x0,z1),ts(y0,z1)),ts(pl(x0,y0),z1),z0,distpt1(x0,y0,z1),satz110c(z0,pl(x0,y0))):is"rt"(pl(ts(x0,z1),ts(y0,z1)),z0)
-t14:=symis(rat,pl(ts(x0,z1),ts(y0,z1)),z0,t13):is"rt"(z0,pl(ts(x0,z1),ts(y0,z1)))
-t15:=sum1(ksi,eta,z0,ts(x0,z1),t11,ts(y0,z1),t12,t14):in(z0,sum)
-l@t16:=sumapp(ksi,eta,u0,i,in(z0,sum),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,pl(x,y))]t15(x,t,y,u,v)):in(z0,sum)
-eta@[z0:rat][i:in(z0,sum)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,pl(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
-t17:=sum1(ksi,eta,pl(x1,y0),x1,lx1,y0,ly,refis(rat,pl(x1,y0))):in(pl(x1,y0),sum)
-t18:=satz96a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(pl(x1,y0),pl(x0,y0))
-t19:=ismore2"rt"(pl(x0,y0),z0,pl(x1,y0),symis(rat,z0,pl(x0,y0),j),t18):more"rt"(pl(x1,y0),z0)
-t20:=andi(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0),t17,t19):and(in(pl(x1,y0),sum),more"rt"(pl(x1,y0),z0))
-t21:=somei(rat,[y:rat]and(in(y,sum),more"rt"(y,z0)),pl(x1,y0),t20):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
-j@t22:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t21(x,t,u)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
-i@t23:=sumapp(ksi,eta,z0,i,some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl(x,y))]t22(x,t,y,u,v)):some"rt"([y:rat]and(in(y,sum),more"rt"(y,z0)))
-eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-t24:=cut2(sum,pl(x0,y0),sum1(ksi,eta,pl(x0,y0),x0,lx,y0,ly,refis(rat,pl(x0,y0))),pl(x1,y1),satz129a(x1,ux,y1,uy),[x:rat][t:in(x,sum)][y:rat][u:less"rt"(y,x)]t16(x,t,y,u),[x:rat][t:in(x,sum)]t23(x,t)):cutprop(sum)
-ux@t25:=cutapp1b(eta,cutprop(sum),[y:rat][t:urt(eta,y)]t24(y,t)):cutprop(sum)
-ly@t26:=cutapp1b(ksi,cutprop(sum),[x:rat][t:urt(ksi,x)]t25(x,t)):cutprop(sum)
-lx@t27:=cutapp1a(eta,cutprop(sum),[y:rat][t:lrt(eta,y)]t26(y,t)):cutprop(sum)
--3129
-eta@satz129:=cutapp1a(ksi,cutprop(sum),[x:rat][t:lrt(ksi,x)]t27".3129"(x,t)):cutprop(sum)
-pl:=cutof(sum,satz129):cut
-[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
-lrtpl:=ine(sum,satz129,z0,sum1(z0,x0,lx,y0,ly,i)):lrt(pl(ksi,eta),z0)
-eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
-+*iii3
-i@t10:=isp1(rat,[x:rat]not(in(x,sum)),pl"rt"(x0,y0),z0,satz129a(x0,ux,y0,uy),i):not(in(z0,sum))
--iii3
-i@urtpl:=th3"l.imp"(lrt(pl(ksi,eta),z0),in(z0,sum),t10".iii3",[t:lrt(pl(ksi,eta),z0)]ini(sum,satz129,z0,t)):urt(pl(ksi,eta),z0)
-eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]p]
-+*iii3
-p1@t11:=ini(sum,satz129,z0,lz):in(z0,sum)
--iii3
-p1@plapp:=sumapp(z0,t11".iii3",p,p1):p
-zeta@[i:is(ksi,eta)]
-ispl1:=isf(cut,cut,[u:cut]pl(u,zeta),ksi,eta,i):is(pl(ksi,zeta),pl(eta,zeta))
-ispl2:=isf(cut,cut,[u:cut]pl(zeta,u),ksi,eta,i):is(pl(zeta,ksi),pl(zeta,eta))
-upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
-ispl12:=tris(cut,pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),ispl1(i),ispl2(zeta,upsilon,eta,j)):is(pl(ksi,zeta),pl(eta,upsilon))
-+3130
-eta@[z0:rat][lz:lrt(pl(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,pl"rt"(x0,y0))]
-t1:=tris(rat,z0,pl"rt"(x0,y0),pl"rt"(y0,x0),i,compl(x0,y0)):is"rt"(z0,pl"rt"(y0,x0))
-t2:=lrtpl(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(pl(eta,ksi),z0)
-lz@t3:=plapp(ksi,eta,z0,lz,lrt(pl(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,pl"rt"(x,y))]t2(x,t,y,u,v)):lrt(pl(eta,ksi),z0)
--3130
-eta@satz130:=isi1(pl(ksi,eta),pl(eta,ksi),[x:rat][t:lrt(pl(ksi,eta),x)]t3".3130"(x,t),[x:rat][t:lrt(pl(eta,ksi),x)]t3".3130"(eta,ksi,x,t)):is(pl(ksi,eta),pl(eta,ksi))
-compl:=satz130:is(pl(ksi,eta),pl(eta,ksi))
-+3131
-zeta@[u0:rat][lu:lrt(pl(pl(ksi,eta),zeta),u0)][v0:rat][lv:lrt(pl(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,pl"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,pl"rt"(x0,y0))]
-t1:=tr3is(rat,u0,pl"rt"(v0,z0),pl"rt"(pl"rt"(x0,y0),z0),pl"rt"(x0,pl"rt"(y0,z0)),i,ispl1"rt"(v0,pl"rt"(x0,y0),z0,j),asspl1(x0,y0,z0)):is"rt"(u0,pl"rt"(x0,pl"rt"(y0,z0)))
-t2:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
-t3:=lrtpl(ksi,pl(eta,zeta),u0,x0,lx,pl"rt"(y0,z0),t2,t1):lrt(pl(ksi,pl(eta,zeta)),u0)
-i@t4:=plapp(ksi,eta,v0,lv,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,pl"rt"(x,y))]t3(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
-lu@t5:=plapp(pl(ksi,eta),zeta,u0,lu,lrt(pl(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(pl(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ksi,pl(eta,zeta)),u0)
-u0@[lu:lrt(pl(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,pl"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
-t6:=tr3is(rat,u0,pl"rt"(x0,v0),pl"rt"(x0,pl"rt"(y0,z0)),pl"rt"(pl"rt"(x0,y0),z0),i,ispl2"rt"(v0,pl"rt"(y0,z0),x0,j),asspl2(x0,y0,z0)):is"rt"(u0,pl"rt"(pl"rt"(x0,y0),z0))
-t7:=lrtpl(ksi,eta,pl"rt"(x0,y0),x0,lx,y0,ly,refis(rat,pl"rt"(x0,y0))):lrt(pl(ksi,eta),pl"rt"(x0,y0))
-t8:=lrtpl(pl(ksi,eta),zeta,u0,pl"rt"(x0,y0),t7,z0,lz,t6):lrt(pl(pl(ksi,eta),zeta),u0)
-i@t9:=plapp(eta,zeta,v0,lv,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t8(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
-lu@t10:=plapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(pl(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t9(x,t,y,u,v)):lrt(pl(pl(ksi,eta),zeta),u0)
--3131
-zeta@satz131:=isi1(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),[x:rat][t:lrt(pl(pl(ksi,eta),zeta),x)]t5".3131"(x,t),[x:rat][t:lrt(pl(ksi,pl(eta,zeta)),x)]t10".3131"(x,t)):is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
-asspl1:=satz131:is(pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)))
-asspl2:=symis(cut,pl(pl(ksi,eta),zeta),pl(ksi,pl(eta,zeta)),satz131):is(pl(ksi,pl(eta,zeta)),pl(pl(ksi,eta),zeta))
-ksi@[a0:rat]
-+3132
-[x0:rat][y0:rat]
-prop1:=and(lrt(ksi,x0),urt(ksi,y0)):'prop'
-[p:prop1]
-t1:=cutapp2b(x0,ande1(lrt(ksi,x0),urt(ksi,y0),p),y0,ande2(lrt(ksi,x0),urt(ksi,y0),p)):more"rt"(y0,x0)
-prop2:=is"rt"(mn(y0,x0,t1),a0):'prop'
-y0@prop3:=and(prop1,[t:prop1]prop2(t)):'prop'
-a0@prop4:=some"rt"([x:rat]some"rt"([y:rat]prop3(x,y))):'prop'
-x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
-t2:=cutapp2b(x0,lx,y0,uy):more"rt"(y0,x0)
-[n:nat][m:more"rt"(ts(rtofn(n),a0),mn(y0,x0,t2))]
-t3:=satz96d(ts(rtofn(n),a0),mn(y0,x0,t2),x0,m):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),pl"rt"(x0,mn(y0,x0,t2)))
-t4:=ismore2"rt"(pl"rt"(x0,mn(y0,x0,t2)),y0,pl"rt"(x0,ts(rtofn(n),a0)),satz101c(y0,x0,t2),t3):more"rt"(pl"rt"(x0,ts(rtofn(n),a0)),y0)
-t5:=satz119(y0,uy,pl"rt"(x0,ts(rtofn(n),a0)),t4):urt(pl"rt"(x0,ts(rtofn(n),a0)))
-t6:=somei(nat,[x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),n,t5):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
-uy@t7:=someapp(nat,[x:nat]more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2)),satz115(a0,mn(y0,x0,t2)),some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0)))),[x:nat][t:more"rt"(ts(rtofn(x),a0),mn(y0,x0,t2))]t6(x,t)):some"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))))
-[u:nat][m:min"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)]
-t8:=ande1(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u)
-t9:=ande2(lb"n"([x:nat]urt(pl"rt"(x0,ts(rtofn(x),a0))),u),urt(pl"rt"(x0,ts(rtofn(u),a0))),m):urt(pl"rt"(x0,ts(rtofn(u),a0)))
-[i:is"n"(u,1)]
-u0:=pl"rt"(x0,a0):rat
-t10:=tr3is(rat,ts(rtofn(u),a0),ts(1rt,a0),ts(a0,1rt),a0,ists1(rtofn(u),1rt,a0,isnert(u,1,i)),comts(1rt,a0),example1a(a0)):is"rt"(ts(rtofn(u),a0),a0)
-t11:=isp(rat,[x:rat]urt(pl"rt"(x0,x)),ts(rtofn(u),a0),a0,t9,t10):urt(ksi,u0)
-t12:=andi(lrt(ksi,x0),urt(ksi,u0),lx,t11):prop1(x0,u0)
-[p:prop1(x0,u0)]
-t13:=symis(rat,a0,mn(u0,x0,t1(x0,u0,p)),satz101g(u0,x0,a0,t1(x0,u0,p),refis(rat,u0))):prop2(x0,u0,p)
-i@t14:=andi(prop1(x0,u0),[t:prop1(x0,u0)]prop2(x0,u0,t),t12,[t:prop1(x0,u0)]t13(t)):prop3(x0,u0)
-t15:=somei(rat,[y:rat]prop3(x0,y),u0,t14):some"rt"([y:rat]prop3(x0,y))
-t16:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),x0,t15):prop4
-m@[o:more"n"(u,1)]
-t17:=morei(rtofn(u),1rt,fr(u,1),fr(1,1),inclass(fr(u,1)),inclass(fr(1,1)),satz111d(u,1,o)):more"rt"(rtofn(u),1rt)
-um10:=mn(rtofn(u),1rt,t17):rat
-t18:=satz112g(rtofn(u),natrti(u),1rt,natrti(1),t17):natrt(um10)
-um1:=nofrt(um10,t18):nat
-v0:=pl"rt"(x0,ts(um10,a0)):rat
-w0:=pl"rt"(x0,ts(rtofn(u),a0)):rat
-t19:=isless2"rt"(pl"rt"(um10,1rt),rtofn(u),um10,satz101e(rtofn(u),1rt,t17),satz94a(um10,1rt)):less"rt"(um10,rtofn(u))
-t20:=lesse(um10,rtofn(u),fr(um1,1),fr(u,1),inclassn(um10,t18),inclass(fr(u,1)),t19):lessf(fr(um1,1),fr(u,1))
-t21:=satz111c(um1,u,t20):less"n"(um1,u)
-t22:=th3"l.imp"(lessis"n"(u,um1),moreis"n"(um1,u),satz10h(um1,u,t21),[t:lessis"n"(u,um1)]satz14(u,um1,t)):not(lessis"n"(u,um1))
-t23:=et(lrt(pl"rt"(x0,ts(rtofn(um1),a0))),th3"l.imp"(urt(pl"rt"(x0,ts(rtofn(um1),a0))),lessis"n"(u,um1),t22,<um1>t8)):lrt(pl"rt"(x0,ts(rtofn(um1),a0)))
-t24:=isp1(rat,[x:rat]lrt(pl"rt"(x0,ts(x,a0))),rtofn(um1),um10,t23,isrtn1(um10,t18)):lrt(ksi,v0)
-t25:=andi(lrt(ksi,v0),urt(ksi,w0),t24,t9):prop1(v0,w0)
-t26:=tr3is(rat,pl"rt"(ts(um10,a0),a0),pl"rt"(ts(um10,a0),ts(1rt,a0)),ts(pl"rt"(um10,1rt),a0),ts(rtofn(u),a0),ispl2"rt"(a0,ts(1rt,a0),ts(um10,a0),example1d(a0)),distpt1(um10,1rt,a0),ists1(pl"rt"(um10,1rt),rtofn(u),a0,satz101e(rtofn(u),1rt,t17))):is"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0))
-t27:=tris(rat,pl"rt"(v0,a0),pl"rt"(x0,pl"rt"(ts(um10,a0),a0)),w0,asspl1"rt"(x0,ts(um10,a0),a0),ispl2"rt"(pl"rt"(ts(um10,a0),a0),ts(rtofn(u),a0),x0,t26)):is"rt"(pl"rt"(v0,a0),w0)
-[p:prop1(v0,w0)]
-t28:=symis(rat,a0,mn(w0,v0,t1(v0,w0,p)),satz101g(w0,v0,a0,t1(v0,w0,p),t27)):prop2(v0,w0,p)
-o@t29:=andi(prop1(v0,w0),[t:prop1(v0,w0)]prop2(v0,w0,t),t25,[t:prop1(v0,w0)]t28(t)):prop3(v0,w0)
-t30:=somei(rat,[y:rat]prop3(v0,y),w0,t29):some"rt"([y:rat]prop3(v0,y))
-t31:=somei(rat,[x:rat]some"rt"([y:rat]prop3(x,y)),v0,t30):prop4
-m@t32:=orapp(more"n"(u,1),is"n"(u,1),prop4,satz24(u),[t:more"n"(u,1)]t31(t),[t:is"n"(u,1)]t16(t)):prop4
-uy@t34:=someapp(nat,[x:nat]min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x),satz27([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),t7),prop4,[x:nat][t:min"n"([y:nat]urt(pl"rt"(x0,ts(rtofn(y),a0))),x)]t32(x,t)):prop4
-lx@t35:=cutapp1b(prop4,[y:rat][t:urt(ksi,y)]t34(y,t)):prop4
--3132
-satz132:=cutapp1a(prop4".3132",[x:rat][t:lrt(ksi,x)]t35".3132"(x,t)):some"rt"([x:rat]some"rt"([y:rat]and(and(lrt(ksi,x),urt(ksi,y)),[t:and(lrt(ksi,x),urt(ksi,y))]is"rt"(mn(y,x,cutapp2b(x,ande1(lrt(ksi,x),urt(ksi,y),t),y,ande2(lrt(ksi,x),urt(ksi,y),t))),a0))))
-ksi@[p:'prop'][a0:rat][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),a0)]p]
-+*3132
-p1@[x0:rat][s:some"rt"([y:rat]prop3(a0,x0,y))][y0:rat][p3:prop3(a0,x0,y0)]
-t36:=ande1(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop1(a0,x0,y0)
-t37:=ande2"l.r"(prop1(a0,x0,y0),[t:prop1(a0,x0,y0)]prop2(a0,x0,y0,t),p3):prop2(a0,x0,y0,t36)
-t38:=ande1(lrt(ksi,x0),urt(ksi,y0),t36):lrt(ksi,x0)
-t39:=ande2(lrt(ksi,x0),urt(ksi,y0),t36):urt(ksi,y0)
-t40:=satz101g(y0,x0,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),t1(a0,x0,y0,t36),satz101c(y0,x0,cutapp2b(x0,t38,y0,t39))):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)))
-t41:=tris(rat,mn(y0,x0,cutapp2b(x0,t38,y0,t39)),mn(y0,x0,t1(a0,x0,y0,t36)),a0,t40,t37):is"rt"(mn(y0,x0,cutapp2b(x0,t38,y0,t39)),a0)
-t42:=<t41><t39><y0><t38><x0>p1:p
-s@t43:=someapp(rat,[y:rat]prop3(a0,x0,y),s,p,[y:rat][t:prop3(a0,x0,y)]t42(y,t)):p
--3132
-p1@satz132app:=someapp(rat,[x:rat]some"rt"([y:rat]prop3".3132"(a0,x,y)),satz132(a0),p,[x:rat][t:some"rt"([y:rat]prop3".3132"(a0,x,y))]t43".3132"(x,t)):p
-+3133
-eta@[y0:rat][ly:lrt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][uu:urt(ksi,u0)][i:is"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0)]
-t1:=tris(rat,u0,pl"rt"(x0,mn(u0,x0,cutapp2b(x0,lx,u0,uu))),pl"rt"(x0,y0),satz101d(u0,x0,cutapp2b(x0,lx,u0,uu)),ispl2"rt"(mn(u0,x0,cutapp2b(x0,lx,u0,uu)),y0,x0,i)):is"rt"(u0,pl"rt"(x0,y0))
-t2:=lrtpl(ksi,eta,u0,x0,lx,y0,ly,t1):lrt(pl(ksi,eta),u0)
-t3:=andi(lrt(pl(ksi,eta),u0),urt(ksi,u0),t2,uu):and(lrt(pl(ksi,eta),u0),urt(ksi,u0))
-t4:=somei(rat,[x:rat]and(lrt(pl(ksi,eta),x),urt(ksi,x)),u0,t3):more(pl(ksi,eta),ksi)
-ly@t5:=satz132app(ksi,more(pl(ksi,eta),ksi),y0,[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn(y,x,cutapp2b(x,t,y,u)),y0)]t4(x,t,y,u,v)):more(pl(ksi,eta),ksi)
--3133
-eta@satz133:=cutapp1a(eta,more(pl(ksi,eta),ksi),[x:rat][t:lrt(eta,x)]t5".3133"(x,t)):more(pl(ksi,eta),ksi)
-satz133a:=satz121(pl(ksi,eta),ksi,satz133):less(ksi,pl(ksi,eta))
-zeta@[m:more(ksi,eta)]
-+3134
-[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
-t1:=satz119a(eta,y0,uy,x0,l):urt(eta,x0)
-t2:=satz83(y0,x0,l):more"rt"(x0,y0)
-[u0:rat][lu:lrt(zeta,u0)][z0:rat][uz:urt(zeta,z0)][i:is"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2))]
-t3:=tris(rat,z0,pl"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),u0),pl"rt"(mn(x0,y0,t2),u0),satz101f(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),ispl1"rt"(mn(z0,u0,cutapp2b(zeta,u0,lu,z0,uz)),mn(x0,y0,t2),u0,i)):is"rt"(z0,pl"rt"(mn(x0,y0,t2),u0))
-t4:=tr3is(rat,pl"rt"(y0,z0),pl"rt"(y0,pl"rt"(mn(x0,y0,t2),u0)),pl"rt"(pl"rt"(y0,mn(x0,y0,t2)),u0),pl"rt"(x0,u0),ispl2"rt"(z0,pl"rt"(mn(x0,y0,t2),u0),y0,t3),asspl2"rt"(y0,mn(x0,y0,t2),u0),ispl1"rt"(pl"rt"(y0,mn(x0,y0,t2)),x0,u0,satz101c(x0,y0,t2))):is"rt"(pl"rt"(y0,z0),pl"rt"(x0,u0))
-t5:=lrtpl(ksi,zeta,pl"rt"(y0,z0),x0,lx,u0,lu,t4):lrt(pl(ksi,zeta),pl"rt"(y0,z0))
-t6:=urtpl(eta,zeta,pl"rt"(y0,z0),y0,uy,z0,uz,refis(rat,pl"rt"(y0,z0))):urt(pl(eta,zeta),pl"rt"(y0,z0))
-t7:=andi(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)),t5,t6):and(lrt(pl(ksi,zeta),pl"rt"(y0,z0)),urt(pl(eta,zeta),pl"rt"(y0,z0)))
-t8:=somei(rat,[x:rat]and(lrt(pl(ksi,zeta),x),urt(pl(eta,zeta),x)),pl"rt"(y0,z0),t7):more(pl(ksi,zeta),pl(eta,zeta))
-l@t9:=satz132app(zeta,more(pl(ksi,zeta),pl(eta,zeta)),mn(x0,y0,t2),[x:rat][t:lrt(zeta,x)][y:rat][u:urt(zeta,y)][v:is"rt"(mn(y,x,cutapp2b(zeta,x,t,y,u)),mn(x0,y0,t2))]t8(x,t,y,u,v)):more(pl(ksi,zeta),pl(eta,zeta))
-uy@t10:=cutapp3(ksi,y0,ly,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t9(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
--3134
-satz134:=moreapp(ksi,eta,m,more(pl(ksi,zeta),pl(eta,zeta)),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t10".3134"(x,t,u)):more(pl(ksi,zeta),pl(eta,zeta))
-zeta@[m:more(ksi,eta)]
-satz135a:=satz134(m):more(pl(ksi,zeta),pl(eta,zeta))
-zeta@[i:is(ksi,eta)]
-satz135b:=ispl1(ksi,eta,zeta,i):is(pl(ksi,zeta),pl(eta,zeta))
-zeta@[l:less(ksi,eta)]
-satz135c:=satz121(pl(eta,zeta),pl(ksi,zeta),satz134(eta,ksi,zeta,satz122(ksi,eta,l))):less(pl(ksi,zeta),pl(eta,zeta))
-m@satz135d:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135a):more(pl(zeta,ksi),pl(zeta,eta))
-i@satz135e:=ispl2(ksi,eta,zeta,i):is(pl(zeta,ksi),pl(zeta,eta))
-l@satz135f:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,zeta),pl(zeta,eta),compl(ksi,zeta),compl(eta,zeta),satz135c):less(pl(zeta,ksi),pl(zeta,eta))
-upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
-satz135g:=ismore2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135d(zeta,upsilon,ksi,m)):more(pl(ksi,zeta),pl(eta,upsilon))
-satz135h:=ismore12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135g):more(pl(zeta,ksi),pl(upsilon,eta))
-i@[l:less(zeta,upsilon)]
-satz135j:=isless2(pl(ksi,upsilon),pl(eta,upsilon),pl(ksi,zeta),ispl1(ksi,eta,upsilon,i),satz135f(zeta,upsilon,ksi,l)):less(pl(ksi,zeta),pl(eta,upsilon))
-satz135k:=isless12(pl(ksi,zeta),pl(zeta,ksi),pl(eta,upsilon),pl(upsilon,eta),compl(ksi,zeta),compl(eta,upsilon),satz135j):less(pl(zeta,ksi),pl(upsilon,eta))
-+3136
-zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-t2:=satz123b(pl(ksi,zeta),pl(eta,zeta)):ec3(is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)))
--3136
-zeta@[m:more(pl(ksi,zeta),pl(eta,zeta))]
-satz136a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),m):more(ksi,eta)
-zeta@[i:is(pl(ksi,zeta),pl(eta,zeta))]
-satz136b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),i):is(ksi,eta)
-zeta@[l:less(pl(ksi,zeta),pl(eta,zeta))]
-satz136c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(pl(ksi,zeta),pl(eta,zeta)),more(pl(ksi,zeta),pl(eta,zeta)),less(pl(ksi,zeta),pl(eta,zeta)),t1".3136",t2".3136",[u:is(ksi,eta)]satz135b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz135a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz135c(ksi,eta,zeta,u),l):less(ksi,eta)
-zeta@[m:more(pl(zeta,ksi),pl(zeta,eta))]
-satz136d:=satz136a(ismore12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),m)):more(ksi,eta)
-zeta@[i:is(pl(zeta,ksi),pl(zeta,eta))]
-satz136e:=satz136b(tr3is(cut,pl(ksi,zeta),pl(zeta,ksi),pl(zeta,eta),pl(eta,zeta),compl(ksi,zeta),i,compl(zeta,eta))):is(ksi,eta)
-zeta@[l:less(pl(zeta,ksi),pl(zeta,eta))]
-satz136f:=satz136c(isless12(pl(zeta,ksi),pl(ksi,zeta),pl(zeta,eta),pl(eta,zeta),compl(zeta,ksi),compl(zeta,eta),l)):less(ksi,eta)
-upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
-+3137
-t1:=satz134(ksi,eta,zeta,m):more(pl(ksi,zeta),pl(eta,zeta))
-t2:=ismore12(pl(zeta,eta),pl(eta,zeta),pl(upsilon,eta),pl(eta,upsilon),compl(zeta,eta),compl(upsilon,eta),satz134(zeta,upsilon,eta,n)):more(pl(eta,zeta),pl(eta,upsilon))
--3137
-satz137:=trmore(pl(ksi,zeta),pl(eta,zeta),pl(eta,upsilon),t1".3137",t2".3137"):more(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
-satz137a:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz137(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
-satz138a:=orapp(more(ksi,eta),is(ksi,eta),more(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]satz137(t,n),[t:is(ksi,eta)]satz135g(t,n)):more(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
-satz138b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]satz137(m,t),[t:is(zeta,upsilon)]satz135h(zeta,upsilon,ksi,eta,t,m)):more(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
-satz138c:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
-satz138d:=satz121(pl(eta,upsilon),pl(ksi,zeta),satz138b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
-+3139
-[i:is(ksi,eta)][j:is(zeta,upsilon)]
-t1:=moreisi2(pl(ksi,zeta),pl(eta,upsilon),ispl12(ksi,eta,zeta,upsilon,i,j)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-i@[o:more(zeta,upsilon)]
-t2:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138a(m,o)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(pl(ksi,zeta),pl(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-n@[o:more(ksi,eta)]
-t4:=moreisi1(pl(ksi,zeta),pl(eta,upsilon),satz138b(o,n)):moreis(pl(ksi,zeta),pl(eta,upsilon))
--3139
-satz139:=orapp(more(ksi,eta),is(ksi,eta),moreis(pl(ksi,zeta),pl(eta,upsilon)),m,[t:more(ksi,eta)]t4".3139"(t),[t:is(ksi,eta)]t3".3139"(t)):moreis(pl(ksi,zeta),pl(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
-satz139a:=satz124(pl(eta,upsilon),pl(ksi,zeta),satz139(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(pl(ksi,zeta),pl(eta,upsilon))
-eta@[l:lessis(ksi,eta)]
-+3140
-[phi:cut][i:is(pl(eta,phi),ksi)]
-t1:=ismore1(pl(eta,phi),ksi,eta,i,satz133(eta,phi)):more(ksi,eta)
-phi@t2:=th3"l.imp"(is(pl(eta,phi),ksi),more(ksi,eta),satz123d(ksi,eta,l),[t:is(pl(eta,phi),ksi)]t1(t)):nis(pl(eta,phi),ksi)
--3140
-vorbemerkung140:=th5"l.some"(cut,[a:cut]is(pl(eta,a),ksi),[a:cut]t2".3140"(a)):not(some([a:cut]is(pl(eta,a),ksi)))
-eta@[phi:cut][psi:cut]
-+*3140
-psi@[m:more(phi,psi)]
-t3:=satz135d(phi,psi,eta,m):more(pl(eta,phi),pl(eta,psi))
-t4:=ec3e21(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t3):nis(pl(eta,phi),pl(eta,psi))
-psi@[l:less(phi,psi)]
-t5:=satz135f(phi,psi,eta,l):less(pl(eta,phi),pl(eta,psi))
-t6:=ec3e31(is(pl(eta,phi),pl(eta,psi)),more(pl(eta,phi),pl(eta,psi)),less(pl(eta,phi),pl(eta,psi)),satz123b(pl(eta,phi),pl(eta,psi)),t5):nis(pl(eta,phi),pl(eta,psi))
-psi@[n:nis(phi,psi)]
-t7:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
-t8:=orapp(more(phi,psi),less(phi,psi),nis(pl(eta,phi),pl(eta,psi)),t7,[t:more(phi,psi)]t4(t),[t:less(phi,psi)]t6(t)):nis(pl(eta,phi),pl(eta,psi))
--3140
-psi@[i:is(pl(eta,phi),ksi)][j:is(pl(eta,psi),ksi)]
-satz140b:=th7"l.imp"(is(phi,psi),nis(pl(eta,phi),pl(eta,psi)),weli(is(pl(eta,phi),pl(eta,psi)),tris2(cut,pl(eta,phi),pl(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t8".3140"(t)):is(phi,psi)
-eta@[z0:rat][x0:rat][y0:rat]
-diffprop1:=and(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t))):'prop'
-diffprop2:=and3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0)):'prop'
-z0@diffprop:=some"rt"([x:rat]some"rt"([y:rat]diffprop2(z0,x,y))):'prop'
-eta@diff:=setof(rat,[z:rat]diffprop(z)):set(rat)
-x0@[lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][m:more"rt"(x0,y0)][i:is"rt"(z0,mn(x0,y0,m))]
-+*iii3
-i@[m1:more"rt"(x0,y0)]
-t11a:=tris(rat,z0,mn(x0,y0,m),mn(x0,y0,m1),i,satz101g(x0,y0,mn(x0,y0,m),m1,satz101c(x0,y0,m))):is"rt"(z0,mn(x0,y0,m1))
-i@t12:=andi(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),m,[t:more"rt"(x0,y0)]t11a(t)):diffprop1(z0,x0,y0)
-t13:=and3i(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),lx,uy,t12):diffprop2(z0,x0,y0)
-t14:=somei(rat,[y:rat]diffprop2(z0,x0,y),y0,t13):some"rt"([y:rat]diffprop2(z0,x0,y))
-t15:=somei(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),x0,t14):diffprop(z0)
--iii3
-i@diff1:=estii(rat,[z:rat]diffprop(z),z0,t15".iii3"):in(z0,diff)
-z0@[i:in(z0,diff)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]p]
-+*iii3
-p1@t16:=estie(rat,[z:rat]diffprop(z),z0,i):diffprop(z0)
--iii3
-p1@[x0:rat][px:some"rt"([y:rat]diffprop2(z0,x0,y))][y0:rat][py:diffprop2(z0,x0,y0)]
-+*iii3
-py@t17:=and3e1(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):lrt(ksi,x0)
-t18:=and3e2(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):urt(eta,y0)
-t19:=and3e3(lrt(ksi,x0),urt(eta,y0),diffprop1(z0,x0,y0),py):diffprop1(z0,x0,y0)
-t20:=ande1(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):more"rt"(x0,y0)
-t21:=ande2"l.r"(more"rt"(x0,y0),[t:more"rt"(x0,y0)]is"rt"(z0,mn(x0,y0,t)),t19):is"rt"(z0,mn(x0,y0,t20))
-t22:=<t21><t20><t18><y0><t17><x0>p1:p
-px@t23:=someapp(rat,[y:rat]diffprop2(z0,x0,y),px,p,[y:rat][t:diffprop2(z0,x0,y)]t22(y,t)):p
--iii3
-p1@diffapp:=someapp(rat,[x:rat]some"rt"([y:rat]diffprop2(z0,x,y)),t16".iii3",p,[x:rat][t:some"rt"([y:rat]diffprop2(z0,x,y))]t23".iii3"(x,t)):p
-eta@[m:more(ksi,eta)]
-+*3140
-m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
-t9:=t2"rp.3134"(eta,m,y0,ly,uy,x0,lx,l):more"rt"(x0,y0)
-t10:=diff1(mn(x0,y0,t9),x0,lx,y0,uy,t9,refis(rat,mn(x0,y0,t9))):in(mn(x0,y0,t9),diff)
-m"rp"@[x1:rat][ux:urt(ksi,x1)][z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
-t11:=isless12"rt"(mn(x0,y0,n),z0,pl"rt"(mn(x0,y0,n),y0),x0,symis(rat,z0,mn(x0,y0,n),j),satz101e(x0,y0,n),satz94a(mn(x0,y0,n),y0)):less"rt"(z0,x0)
-t12:=trless"rt"(z0,x0,x1,t11,cutapp2a(ksi,x0,lx,x1,ux)):less"rt"(z0,x1)
-t13:=ec3e31(is"rt"(z0,x1),more"rt"(z0,x1),less"rt"(z0,x1),satz81b(z0,x1),t12):nis"rt"(z0,x1)
-i@t14:=diffapp(z0,i,nis"rt"(z0,x1),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t13(x,t,y,u,v,w)):nis"rt"(z0,x1)
-ux@t15:=th3"l.imp"(in(x1,diff),nis"rt"(x1,x1),weli(is"rt"(x1,x1),refis(rat,x1)),[t:in(x1,diff)]t14(x1,t)):not(in(x1,diff))
-m"rp"@[z0:rat][i:in(z0,diff)][u0:rat][l:less"rt"(u0,z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))]
-t16:=tris(rat,pl"rt"(z0,y0),pl"rt"(mn(x0,y0,n),y0),x0,ispl1"rt"(z0,mn(x0,y0,n),y0,j),satz101e(x0,y0,n)):is"rt"(pl"rt"(z0,y0),x0)
-x2:=pl"rt"(u0,y0):rat
-t17:=isless2"rt"(pl"rt"(z0,y0),x0,x2,t16,satz96c(u0,z0,y0,l)):less"rt"(x2,x0)
-t18:=satz120(ksi,x0,lx,x2,t17):lrt(ksi,x2)
-t19:=ismore1"rt"(pl"rt"(y0,u0),pl"rt"(u0,y0),y0,compl"rt"(y0,u0),satz94(y0,u0)):more"rt"(x2,y0)
-t20:=satz101g(x2,y0,u0,t19,compl"rt"(y0,u0)):is"rt"(u0,mn(x2,y0,t19))
-t21:=diff1(u0,x2,t18,y0,uy,t19,t20):in(u0,diff)
-l@t22:=diffapp(z0,i,in(u0,diff),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t21(x,t,y,u,v,w)):in(u0,diff)
-m"rp"@[z0:rat][i:in(z0,diff)][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][n:more"rt"(x0,y0)][j:is"rt"(z0,mn(x0,y0,n))][x3:rat][lx3:lrt(ksi,x3)][l:less"rt"(x0,x3)]
-t23:=satz83(x0,x3,l):more"rt"(x3,x0)
-t24:=trmore"rt"(x3,x0,y0,t23,n):more"rt"(x3,y0)
-t25:=ismore12"rt"(x3,pl"rt"(mn(x3,y0,t24),y0),x0,pl"rt"(mn(x0,y0,n),y0),satz101f(x3,y0,t24),satz101f(x0,y0,n),t23):more"rt"(pl"rt"(mn(x3,y0,t24),y0),pl"rt"(mn(x0,y0,n),y0))
-t26:=satz97a(mn(x3,y0,t24),mn(x0,y0,n),y0,t25):more"rt"(mn(x3,y0,t24),mn(x0,y0,n))
-t27:=ismore2"rt"(mn(x0,y0,n),z0,mn(x3,y0,t24),symis(rat,z0,mn(x0,y0,n),j),t26):more"rt"(mn(x3,y0,t24),z0)
-t28:=diff1(mn(x3,y0,t24),x3,lx3,y0,uy,t24,refis(rat,mn(x3,y0,t24))):in(mn(x3,y0,t24),diff)
-t29:=andi(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0),t28,t27):and(in(mn(x3,y0,t24),diff),more"rt"(mn(x3,y0,t24),z0))
-t30:=somei(rat,[x:rat]and(in(x,diff),more"rt"(x,z0)),mn(x3,y0,t24),t29):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
-j@t31:=cutapp3(ksi,x0,lx,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t30(y,t,u)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
-i@t32:=diffapp(z0,i,some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(z0,mn(x,y,v))]t31(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,diff),more"rt"(x,z0)))
-m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)][x1:rat][ux1:urt(ksi,x1)]
-t33:=cut2(diff,mn(x0,y0,t9(y0,ly,uy,x0,lx,l)),t10(y0,ly,uy,x0,lx,l),x1,t15(x1,ux1),[x:rat][t:in(x,diff)][y:rat][u:less"rt"(y,x)]t22(x,t,y,u),[x:rat][t:in(x,diff)]t32(x,t)):cutprop(diff)
-l@t34:=cutapp1b(ksi,cutprop(diff),[x:rat][t:urt(ksi,x)]t33(x,t)):cutprop(diff)
-uy@t35:=cutapp3(ksi,y0,ly,cutprop(diff),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t34(x,t,u)):cutprop(diff)
--3140
-m@satz140h:=moreapp(ksi,eta,m,cutprop(diff),[x:rat][u:lrt(ksi,x)][v:urt(eta,x)]t35".3140"(x,u,v)):cutprop(diff)
-+*3140
-m"rp"@chi:=cutof(diff,satz140h):cut
-[z0:rat][lz:lrt(pl(eta,chi),z0)][y1:rat][ly:lrt(eta,y1)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,pl"rt"(y1,u0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(eta,y0)][o:more"rt"(x0,y0)][j:is"rt"(u0,mn(x0,y0,o))]
-t36:=cutapp2b(eta,y1,ly,y0,uy):more"rt"(y0,y1)
-t37:=tr3is(rat,pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),pl"rt"(mn(x0,y0,o),pl"rt"(y1,mn(y0,y1,t36))),pl"rt"(mn(x0,y0,o),y0),x0,asspl1"rt"(mn(x0,y0,o),y1,mn(y0,y1,t36)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t36)),y0,mn(x0,y0,o),satz101c(y0,y1,t36)),satz101e(x0,y0,o)):is"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0)
-t38:=isless2"rt"(pl"rt"(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36)),x0,pl"rt"(mn(x0,y0,o),y1),t37,satz94a(pl"rt"(mn(x0,y0,o),y1),mn(y0,y1,t36))):less"rt"(pl"rt"(mn(x0,y0,o),y1),x0)
-t39:=tr3is(rat,z0,pl"rt"(y1,u0),pl"rt"(u0,y1),pl"rt"(mn(x0,y0,o),y1),i,compl"rt"(y1,u0),ispl1"rt"(u0,mn(x0,y0,o),y1,j)):is"rt"(z0,pl"rt"(mn(x0,y0,o),y1))
-t40:=isless1"rt"(pl"rt"(mn(x0,y0,o),y1),z0,x0,symis(rat,z0,pl"rt"(mn(x0,y0,o),y1),t39),t38):less"rt"(z0,x0)
-t41:=satz120(ksi,x0,lx,z0,t40):lrt(ksi,z0)
-i@t42:=diffapp(u0,ini(diff,satz140h,u0,lu),lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(eta,y)][v:more"rt"(x,y)][w:is"rt"(u0,mn(x,y,v))]t41(x,t,y,u,v,w)):lrt(ksi,z0)
-lz@a:=plapp(eta,chi,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,pl"rt"(x,y))]t42(x,t,y,u,v)):lrt(ksi,z0)
-m"rp"@[y0:rat][ly:lrt(ksi,y0)][uy:urt(eta,y0)][x0:rat][lx:lrt(ksi,x0)][l:less"rt"(y0,x0)]
-t43:=satz83(y0,x0,l):more"rt"(x0,y0)
-[y1:rat][ly1:lrt(eta,y1)][y2:rat][uy2:urt(eta,y2)]
-t44:=cutapp2b(eta,y1,ly1,y2,uy2):more"rt"(y2,y1)
-[i:is"rt"(mn(y2,y1,t44),mn(x0,y0,t43))]
-t45:=cutapp2b(eta,y1,ly1,y0,uy):more"rt"(y0,y1)
-t46:=tris(rat,y2,pl"rt"(mn(y2,y1,t44),y1),pl"rt"(mn(x0,y0,t43),y1),satz101f(y2,y1,t44),ispl1"rt"(mn(y2,y1,t44),mn(x0,y0,t43),y1,i)):is"rt"(y2,pl"rt"(mn(x0,y0,t43),y1))
-t47:=tr4is(rat,pl"rt"(y2,mn(y0,y1,t45)),pl"rt"(pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45)),pl"rt"(mn(x0,y0,t43),pl"rt"(y1,mn(y0,y1,t45))),pl"rt"(mn(x0,y0,t43),y0),x0,ispl1"rt"(y2,pl"rt"(mn(x0,y0,t43),y1),mn(y0,y1,t45),t46),asspl1"rt"(mn(x0,y0,t43),y1,mn(y0,y1,t45)),ispl2"rt"(pl"rt"(y1,mn(y0,y1,t45)),y0,mn(x0,y0,t43),satz101c(y0,y1,t45)),satz101e(x0,y0,t43)):is"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0)
-t48:=ismore1"rt"(pl"rt"(y2,mn(y0,y1,t45)),x0,y2,t47,satz94(y2,mn(y0,y1,t45))):more"rt"(x0,y2)
-t49:=satz101g(x0,y2,mn(y0,y1,t45),t48,t47):is"rt"(mn(y0,y1,t45),mn(x0,y2,t48))
-t50:=tris(rat,y0,pl"rt"(mn(y0,y1,t45),y1),pl"rt"(mn(x0,y2,t48),y1),satz101f(y0,y1,t45),ispl1"rt"(mn(y0,y1,t45),mn(x0,y2,t48),y1,t49)):is"rt"(y0,pl"rt"(mn(x0,y2,t48),y1))
-t51:=ine(diff,satz140h,mn(x0,y2,t48),diff1(mn(x0,y2,t48),x0,lx,y2,uy2,t48,refis(rat,mn(x0,y2,t48)))):lrt(chi,mn(x0,y2,t48))
-t52:=lrtpl(eta,chi,y0,y1,ly1,mn(x0,y2,t48),t51,tris(rat,y0,pl"rt"(mn(x0,y2,t48),y1),pl"rt"(y1,mn(x0,y2,t48)),t50,compl"rt"(mn(x0,y2,t48),y1))):lrt(pl(eta,chi),y0)
-l@t53:=satz132app(eta,lrt(pl(eta,chi),y0),mn(x0,y0,t43),[x:rat][t:lrt(eta,x)][y:rat][u:urt(eta,y)][v:is"rt"(mn(y,x,cutapp2b(eta,x,t,y,u)),mn(x0,y0,t43))]t52(x,t,y,u,v)):lrt(pl(eta,chi),y0)
-uy@t54:=cutapp3(ksi,y0,ly,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:less"rt"(y0,x)]t53(x,t,u)):lrt(pl(eta,chi),y0)
-ly@[ly0:lrt(eta,y0)][y1:rat][ly1:lrt(ksi,y1)][uy1:urt(eta,y1)]
-t55:=t54(y1,ly1,uy1):lrt(pl(eta,chi),y1)
-t56:=satz120(pl(eta,chi),y1,t55,y0,cutapp2a(eta,y0,ly0,y1,uy1)):lrt(pl(eta,chi),y0)
-ly0@t57:=moreapp(ksi,eta,m,lrt(pl(eta,chi),y0),[x:rat][t:lrt(ksi,x)][u:urt(eta,x)]t56(x,t,u)):lrt(pl(eta,chi),y0)
-ly@b:=th1"l.imp"(lrt(eta,y0),lrt(pl(eta,chi),y0),[t:lrt(eta,y0)]t57(t),[t:urt(eta,y0)]t54(t)):lrt(pl(eta,chi),y0)
-m"rp"@t58:=isi1(pl(eta,chi),ksi,[x:rat][t:lrt(pl(eta,chi),x)]a(x,t),[x:rat][t:lrt(ksi,x)]b(x,t)):is(pl(eta,chi),ksi)
--3140
-m@satz140a:=somei(cut,[a:cut]is(pl(eta,a),ksi),chi".3140",t58".3140"):some([a:cut]is(pl(eta,a),ksi))
-+*3140
-eta@t59:=[c:cut][d:cut][t:is(pl(eta,c),ksi)][u:is(pl(eta,d),ksi)]satz140b(c,d,t,u):amone(cut,[c:cut]is(pl(eta,c),ksi))
--3140
-m@satz140:=onei(cut,[a:cut]is(pl(eta,a),ksi),t59".3140",satz140a):one([a:cut]is(pl(eta,a),ksi))
-mn:=ind(cut,[a:cut]is(pl(eta,a),ksi),satz140):cut
-satz140c:=oneax(cut,[a:cut]is(pl(eta,a),ksi),satz140):is(pl(eta,mn(ksi,eta,m)),ksi)
-satz140d:=symis(cut,pl(eta,mn(ksi,eta,m)),ksi,satz140c):is(ksi,pl(eta,mn(ksi,eta,m)))
-satz140e:=tris(cut,pl(mn(ksi,eta,m),eta),pl(eta,mn(ksi,eta,m)),ksi,compl(mn(ksi,eta,m),eta),satz140c):is(pl(mn(ksi,eta,m),eta),ksi)
-satz140f:=symis(cut,pl(mn(ksi,eta,m),eta),ksi,satz140e):is(ksi,pl(mn(ksi,eta,m),eta))
-eta@[phi:cut][m:more(ksi,eta)][i:is(pl(eta,phi),ksi)]
-satz140g:=satz140b(phi,mn(ksi,eta,m),i,satz140c(m)):is(phi,mn(ksi,eta,m))
-upsilon@[m:more(ksi,zeta)][n:more(eta,upsilon)][i:is(ksi,eta)][j:is(zeta,upsilon)]
-+*3140
-j"rp"@t60:=tr3is(cut,pl(upsilon,mn(ksi,zeta,m)),pl(zeta,mn(ksi,zeta,m)),ksi,eta,ispl1(upsilon,zeta,mn(ksi,zeta,m),symis(cut,zeta,upsilon,j)),satz140c(ksi,zeta,m),i):is(pl(upsilon,mn(ksi,zeta,m)),eta)
--3140
-j@ismn12:=satz140g(eta,upsilon,mn(ksi,zeta,m),n,t60".3140"):is(mn(ksi,zeta,m),mn(eta,upsilon,n))
-zeta@[m:more(ksi,zeta)][n:more(eta,zeta)][i:is(ksi,eta)]
-ismn1:=ismn12(zeta,m,n,i,refis(cut,zeta)):is(mn(ksi,zeta,m),mn(eta,zeta,n))
-zeta@[m:more(zeta,ksi)][n:more(zeta,eta)][i:is(ksi,eta)]
-ismn2:=ismn12(zeta,zeta,ksi,eta,m,n,refis(cut,zeta),i):is(mn(zeta,ksi,m),mn(zeta,eta,n))
-eta@[z0:rat][x0:rat][y0:rat]
-prodprop1:=and3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0))):'prop'
-z0@prodprop:=some"rt"([x:rat]some"rt"([y:rat]prodprop1(z0,x,y))):'prop'
-eta@prod:=setof(rat,[z:rat]prodprop(z)):set(rat)
-x0@[lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts(x0,y0))]
-+iii4
-t1:=and3i(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),lx,ly,i):prodprop1(z0,x0,y0)
-t2:=somei(rat,[y:rat]prodprop1(z0,x0,y),y0,t1):some"rt"([y:rat]prodprop1(z0,x0,y))
-t3:=somei(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),x0,t2):prodprop(z0)
--iii4
-prod1:=estii(rat,[z:rat]prodprop(z),z0,t3".iii4"):in(z0,prod)
-z0@[i:in(z0,prod)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]p]
-+*iii4
-p1@t4:=estie(rat,[z:rat]prodprop(z),z0,i):prodprop(z0)
--iii4
-p1@[x0:rat][px:some"rt"([y:rat]prodprop1(z0,x0,y))][y0:rat][py:prodprop1(z0,x0,y0)]
-+*iii4
-py@t5:=and3e1(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(ksi,x0)
-t6:=and3e2(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):lrt(eta,y0)
-t7:=and3e3(lrt(ksi,x0),lrt(eta,y0),is"rt"(z0,ts(x0,y0)),py):is"rt"(z0,ts(x0,y0))
-t8:=<t7><t6><y0><t5><x0>p1:p
-px@t9:=someapp(rat,[y:rat]prodprop1(z0,x0,y),px,p,[y:rat][t:prodprop1(z0,x0,y)]t8(y,t)):p
--iii4
-p1@prodapp:=someapp(rat,[x:rat]some"rt"([y:rat]prodprop1(z0,x,y)),t4".iii4",p,[x:rat][t:some"rt"([y:rat]prodprop1(z0,x,y))]t9".iii4"(x,t)):p
-eta@[x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-+4141
-[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))]
-t1:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
-t2:=cutapp2a(eta,y0,ly,y1,uy):less"rt"(y0,y1)
-t3:=isless1"rt"(ts(x0,y0),z0,ts(x1,y1),symis(rat,z0,ts(x0,y0),j),satz107a(x0,x1,y0,y1,t1,t2)):less"rt"(z0,ts(x1,y1))
-t4:=ec3e31(is"rt"(z0,ts(x1,y1)),more"rt"(z0,ts(x1,y1)),less"rt"(z0,ts(x1,y1)),satz81b(z0,ts(x1,y1)),t3):nis"rt"(z0,ts(x1,y1))
-i@t5:=prodapp(ksi,eta,z0,i,nis"rt"(z0,ts(x1,y1)),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t4(x,t,y,u,v)):nis"rt"(z0,ts(x1,y1))
--4141
-satz141a:=th3"l.imp"(in(ts(x1,y1),prod),nis"rt"(ts(x1,y1),ts(x1,y1)),weli(is"rt"(ts(x1,y1),ts(x1,y1)),refis(rat,ts(x1,y1))),[t:in(ts(x1,y1),prod)]t5".4141"(ts(x1,y1),t)):not(in(ts(x1,y1),prod))
--rp
-@[x0:rat][y0:rat]
-+4141
-v0:=ts(ov(1rt,y0),x0):rat
-t6:=tr3is(rat,ts(y0,v0),ts(ts(y0,ov(1rt,y0)),x0),ts(1rt,x0),x0,assts2(y0,ov(1rt,y0),x0),ists1(ts(y0,ov(1rt,y0)),1rt,x0,satz110c(1rt,y0)),example1c(x0)):is(ts(y0,v0),x0)
--4141
-satz141b:=satz110g(x0,y0,v0".4141",t6".4141"):is(ts(ov(1rt,y0),x0),ov(x0,y0))
-satz141c:=symis(rat,ts(ov(1rt,y0),x0),ov(x0,y0),satz141b):is"rt"(ov(x0,y0),ts(ov(1rt,y0),x0))
-+*rp
-+*4141
-eta@[u0:rat][i:in(u0,prod)][z0:rat][l:less"rt"(z0,u0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(u0,ts(x0,y0))]
-t7:=isless2"rt"(u0,ts(x0,y0),z0,j,l):less"rt"(z0,ts(x0,y0))
-t8:=tr3is(rat,ts(ov(1rt,x0),ts(x0,y0)),ts(ts(ov(1rt,x0),x0),y0),ts(1rt,y0),y0,assts2(ov(1rt,x0),x0,y0),ists1(ts(ov(1rt,x0),x0),1rt,y0,satz110e(1rt,x0)),example1c(y0)):is"rt"(ts(ov(1rt,x0),ts(x0,y0)),y0)
-t9:=isless12"rt"(ts(ov(1rt,x0),z0),ov(z0,x0),ts(ov(1rt,x0),ts(x0,y0)),y0,satz141b(z0,x0),t8,satz105f(z0,ts(x0,y0),ov(1rt,x0),t7)):less"rt"(ov(z0,x0),y0)
-t10:=satz120(eta,y0,ly,ov(z0,x0),t9):lrt(eta,ov(z0,x0))
-t11:=prod1(z0,x0,lx,ov(z0,x0),t10,satz110d(z0,x0)):in(z0,prod)
-l@t12:=prodapp(u0,i,in(z0,prod),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(u0,ts(x,y))]t11(x,t,y,u,v)):in(z0,prod)
-eta@[z0:rat][i:in(z0,prod)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(z0,ts(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
-t13:=prod1(ts(x1,y0),x1,lx1,y0,ly,refis(rat,ts(x1,y0))):in(ts(x1,y0),prod)
-t14:=satz105a(x1,x0,y0,satz83(x0,x1,l)):more"rt"(ts(x1,y0),ts(x0,y0))
-t15:=ismore2"rt"(ts(x0,y0),z0,ts(x1,y0),symis(rat,z0,ts(x0,y0),j),t14):more"rt"(ts(x1,y0),z0)
-t16:=andi(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0),t13,t15):and(in(ts(x1,y0),prod),more"rt"(ts(x1,y0),z0))
-t17:=somei(rat,[y:rat]and(in(y,prod),more"rt"(y,z0)),ts(x1,y0),t16):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
-j@t18:=cutapp3(ksi,x0,lx,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][u:less"rt"(x0,x)]t17(x,t,u)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
-i@t19:=prodapp(z0,i,some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0))),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts(x,y))]t18(x,t,y,u,v)):some"rt"([y:rat]and(in(y,prod),more"rt"(y,z0)))
-eta@[x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][x1:rat][ux:urt(ksi,x1)][y1:rat][uy:urt(eta,y1)]
-t20:=cut2(prod,ts(x0,y0),prod1(ts(x0,y0),x0,lx,y0,ly,refis(rat,ts(x0,y0))),ts(x1,y1),satz141a(x1,ux,y1,uy),[x:rat][t:in(x,prod)][y:rat][u:less"rt"(y,x)]t12(x,t,y,u),[x:rat][t:in(x,prod)]t19(x,t)):cutprop(prod)
-ux@t21:=cutapp1b(eta,cutprop(prod),[y:rat][t:urt(eta,y)]t20(y,t)):cutprop(prod)
-ly@t22:=cutapp1b(ksi,cutprop(prod),[x:rat][t:urt(ksi,x)]t21(x,t)):cutprop(prod)
-lx@t23:=cutapp1a(eta,cutprop(prod),[y:rat][t:lrt(eta,y)]t22(y,t)):cutprop(prod)
--4141
-eta@satz141:=cutapp1a(ksi,cutprop(prod),[x:rat][t:lrt(ksi,x)]t23".4141"(x,t)):cutprop(prod)
-ts:=cutof(prod,satz141):cut
-[z0:rat][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-lrtts:=ine(prod,satz141,z0,prod1(z0,x0,lx,y0,ly,i)):lrt(ts(ksi,eta),z0)
-eta@[z0:rat][x0:rat][ux:urt(ksi,x0)][y0:rat][uy:urt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-+*iii4
-i@t10:=isp1(rat,[x:rat]not(in(x,prod)),ts"rt"(x0,y0),z0,satz141a(x0,ux,y0,uy),i):not(in(z0,prod))
--iii4
-i@urtts:=th3"l.imp"(lrt(ts(ksi,eta),z0),in(z0,prod),t10".iii4",[t:lrt(ts(ksi,eta),z0)]ini(prod,satz141,z0,t)):urt(ts(ksi,eta),z0)
-eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][p:'prop'][p1:[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]p]
-+*iii4
-p1@t11:=ini(prod,satz141,z0,lz):in(z0,prod)
--iii4
-p1@tsapp:=prodapp(z0,t11".iii4",p,p1):p
-zeta@[i:is(ksi,eta)]
-ists1:=isf(cut,cut,[u:cut]ts(u,zeta),ksi,eta,i):is(ts(ksi,zeta),ts(eta,zeta))
-ists2:=isf(cut,cut,[u:cut]ts(zeta,u),ksi,eta,i):is(ts(zeta,ksi),ts(zeta,eta))
-upsilon@[i:is(ksi,eta)][j:is(zeta,upsilon)]
-ists12:=tris(cut,ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),ists1(i),ists2(zeta,upsilon,eta,j)):is(ts(ksi,zeta),ts(eta,upsilon))
-+4142
-eta@[z0:rat][lz:lrt(ts(ksi,eta),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-t1:=tris(rat,z0,ts"rt"(x0,y0),ts"rt"(y0,x0),i,comts(x0,y0)):is"rt"(z0,ts"rt"(y0,x0))
-t2:=lrtts(eta,ksi,z0,y0,ly,x0,lx,t1):lrt(ts(eta,ksi),z0)
-lz@t3:=tsapp(ksi,eta,z0,lz,lrt(ts(eta,ksi),z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(z0,ts"rt"(x,y))]t2(x,t,y,u,v)):lrt(ts(eta,ksi),z0)
--4142
-eta@satz142:=isi1(ts(ksi,eta),ts(eta,ksi),[x:rat][t:lrt(ts(ksi,eta),x)]t3".4142"(x,t),[x:rat][t:lrt(ts(eta,ksi),x)]t3".4142"(eta,ksi,x,t)):is(ts(ksi,eta),ts(eta,ksi))
-comts:=satz142:is(ts(ksi,eta),ts(eta,ksi))
-+4143
-zeta@[u0:rat][lu:lrt(ts(ts(ksi,eta),zeta),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][z0:rat][lz:lrt(zeta,z0)][i:is"rt"(u0,ts"rt"(v0,z0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))]
-t1:=tr3is(rat,u0,ts"rt"(v0,z0),ts"rt"(ts"rt"(x0,y0),z0),ts"rt"(x0,ts"rt"(y0,z0)),i,ists1"rt"(v0,ts"rt"(x0,y0),z0,j),assts1(x0,y0,z0)):is"rt"(u0,ts"rt"(x0,ts"rt"(y0,z0)))
-t2:=lrtts(eta,zeta,ts"rt"(y0,z0),y0,ly,z0,lz,refis(rat,ts"rt"(y0,z0))):lrt(ts(eta,zeta),ts"rt"(y0,z0))
-t3:=lrtts(ksi,ts(eta,zeta),u0,x0,lx,ts"rt"(y0,z0),t2,t1):lrt(ts(ksi,ts(eta,zeta)),u0)
-i@t4:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
-lu@t5:=tsapp(ts(ksi,eta),zeta,u0,lu,lrt(ts(ksi,ts(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(zeta,y)][v:is"rt"(u0,ts"rt"(x,y))]t4(x,t,y,u,v)):lrt(ts(ksi,ts(eta,zeta)),u0)
-u0@[lu:lrt(ts(ksi,ts(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(ts(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,ts"rt"(y0,z0))]
-t6:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,ts"rt"(y0,z0)),ts"rt"(ts"rt"(x0,y0),z0),i,ists2"rt"(v0,ts"rt"(y0,z0),x0,j),assts2(x0,y0,z0)):is"rt"(u0,ts"rt"(ts"rt"(x0,y0),z0))
-t7:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
-t8:=lrtts(ts(ksi,eta),zeta,u0,ts"rt"(x0,y0),t7,z0,lz,t6):lrt(ts(ts(ksi,eta),zeta),u0)
-i@t9:=tsapp(eta,zeta,v0,lv,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,ts"rt"(x,y))]t8(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
-lu@t10:=tsapp(ksi,ts(eta,zeta),u0,lu,lrt(ts(ts(ksi,eta),zeta),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(ts(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t9(x,t,y,u,v)):lrt(ts(ts(ksi,eta),zeta),u0)
--4143
-zeta@satz143:=isi1(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),[x:rat][t:lrt(ts(ts(ksi,eta),zeta),x)]t5".4143"(x,t),[x:rat][t:lrt(ts(ksi,ts(eta,zeta)),x)]t10".4143"(x,t)):is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
-assts1:=satz143:is(ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)))
-assts2:=symis(cut,ts(ts(ksi,eta),zeta),ts(ksi,ts(eta,zeta)),satz143):is(ts(ksi,ts(eta,zeta)),ts(ts(ksi,eta),zeta))
-+4144
-[u0:rat][lu:lrt(ts(ksi,pl(eta,zeta)),u0)][x0:rat][lx:lrt(ksi,x0)][v0:rat][lv:lrt(pl(eta,zeta),v0)][i:is"rt"(u0,ts"rt"(x0,v0))][y0:rat][ly:lrt(eta,y0)][z0:rat][lz:lrt(zeta,z0)][j:is"rt"(v0,pl"rt"(y0,z0))]
-t1:=tr3is(rat,u0,ts"rt"(x0,v0),ts"rt"(x0,pl"rt"(y0,z0)),pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)),i,ists2"rt"(v0,pl"rt"(y0,z0),x0,j),disttp2(x0,y0,z0)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x0,z0)))
-t2:=lrtts(ksi,eta,ts"rt"(x0,y0),x0,lx,y0,ly,refis(rat,ts"rt"(x0,y0))):lrt(ts(ksi,eta),ts"rt"(x0,y0))
-t3:=lrtts(ksi,zeta,ts"rt"(x0,z0),x0,lx,z0,lz,refis(rat,ts"rt"(x0,z0))):lrt(ts(ksi,zeta),ts"rt"(x0,z0))
-t4:=lrtpl(ts(ksi,eta),ts(ksi,zeta),u0,ts"rt"(x0,y0),t2,ts"rt"(x0,z0),t3,t1):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
-i@t5:=plapp(eta,zeta,v0,lv,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(eta,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(v0,pl"rt"(x,y))]t4(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
-lu@t6:=tsapp(ksi,pl(eta,zeta),u0,lu,lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(pl(eta,zeta),y)][v:is"rt"(u0,ts"rt"(x,y))]t5(x,t,y,u,v)):lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)
-u0@[lu:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),u0)][v0:rat][lv:lrt(ts(ksi,eta),v0)][w0:rat][lw:lrt(ts(ksi,zeta),w0)][i:is"rt"(u0,pl"rt"(v0,w0))][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(eta,y0)][j:is"rt"(v0,ts"rt"(x0,y0))][x1:rat][lx1:lrt(ksi,x1)][z0:rat][lz:lrt(zeta,z0)][k:is"rt"(w0,ts"rt"(x1,z0))]
-t7:=tris(rat,u0,pl"rt"(v0,w0),pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),i,ispl12"rt"(v0,ts"rt"(x0,y0),w0,ts"rt"(x1,z0),j,k)):is"rt"(u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)))
-x2:=ite(moreis"rt"(x0,x1),rat,x0,x1):rat
-[m:moreis"rt"(x0,x1)]
-t8:=itet(moreis"rt"(x0,x1),rat,x0,x1,m):is"rt"(x2,x0)
-t9:=isp1(rat,[t:rat]lrt(ksi,t),x0,x2,lx,t8):lrt(ksi,x2)
-t10:=lessisi2"rt"(x0,x2,symis(rat,x2,x0,t8)):lessis"rt"(x0,x2)
-t11:=satz88(x1,x0,x2,satz84(x0,x1,m),t10):lessis"rt"(x1,x2)
-k@[n:not(moreis"rt"(x0,x1))]
-t12:=itef(moreis"rt"(x0,x1),rat,x0,x1,n):is"rt"(x2,x1)
-t13:=isp1(rat,[t:rat]lrt(ksi,t),x1,x2,lx1,t12):lrt(ksi,x2)
-t14:=lessisi2"rt"(x1,x2,symis(rat,x2,x1,t12)):lessis"rt"(x1,x2)
-t15:=lessisi1"rt"(x0,x2,satz87b(x0,x1,x2,satz81j(x0,x1,n),t14)):lessis"rt"(x0,x2)
-k@t16:=th1"l.imp"(moreis"rt"(x0,x1),lrt(ksi,x2),[t:moreis"rt"(x0,x1)]t9(t),[t:not(moreis"rt"(x0,x1))]t13(t)):lrt(ksi,x2)
-t17:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x0,x2),[t:moreis"rt"(x0,x1)]t10(t),[t:not(moreis"rt"(x0,x1))]t15(t)):lessis"rt"(x0,x2)
-t18:=th1"l.imp"(moreis"rt"(x0,x1),lessis"rt"(x1,x2),[t:moreis"rt"(x0,x1)]t11(t),[t:not(moreis"rt"(x0,x1))]t14(t)):lessis"rt"(x1,x2)
-t19:=lrtpl(eta,zeta,pl"rt"(y0,z0),y0,ly,z0,lz,refis(rat,pl"rt"(y0,z0))):lrt(pl(eta,zeta),pl"rt"(y0,z0))
-t20:=lrtts(ksi,pl(eta,zeta),ts"rt"(x2,pl"rt"(y0,z0)),x2,t16,pl"rt"(y0,z0),t19,refis(rat,ts"rt"(x2,pl"rt"(y0,z0)))):lrt(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)))
-t21:=satz109a(x0,x2,y0,y0,t17,lessisi2"rt"(y0,y0,refis(rat,y0))):lessis"rt"(ts"rt"(x0,y0),ts"rt"(x2,y0))
-t22:=satz109a(x1,x2,z0,z0,t18,lessisi2"rt"(z0,z0,refis(rat,z0))):lessis"rt"(ts"rt"(x1,z0),ts"rt"(x2,z0))
-t23:=islessis12"rt"(pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),u0,pl"rt"(ts"rt"(x2,y0),ts"rt"(x2,z0)),ts"rt"(x2,pl"rt"(y0,z0)),symis(rat,u0,pl"rt"(ts"rt"(x0,y0),ts"rt"(x1,z0)),t7),distpt2(x2,y0,z0),satz100a(ts"rt"(x0,y0),ts"rt"(x2,y0),ts"rt"(x1,z0),ts"rt"(x2,z0),t21,t22)):lessis"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))
-t24:=orapp(less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0))),lrt(ts(ksi,pl(eta,zeta)),u0),t23,[t:less"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]satz120(ts(ksi,pl(eta,zeta)),ts"rt"(x2,pl"rt"(y0,z0)),t20,u0,t),[t:is"rt"(u0,ts"rt"(x2,pl"rt"(y0,z0)))]isp1(rat,[u:rat]lrt(ts(ksi,pl(eta,zeta)),u),ts"rt"(x2,pl"rt"(y0,z0)),u0,t20,t)):lrt(ts(ksi,pl(eta,zeta)),u0)
-j@t25:=tsapp(ksi,zeta,w0,lw,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(zeta,y)][v:is"rt"(w0,ts"rt"(x,y))]t24(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
-i@t26:=tsapp(ksi,eta,v0,lv,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(eta,y)][v:is"rt"(v0,ts"rt"(x,y))]t25(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
-lu@t27:=plapp(ts(ksi,eta),ts(ksi,zeta),u0,lu,lrt(ts(ksi,pl(eta,zeta)),u0),[x:rat][t:lrt(ts(ksi,eta),x)][y:rat][u:lrt(ts(ksi,zeta),y)][v:is"rt"(u0,pl"rt"(x,y))]t26(x,t,y,u,v)):lrt(ts(ksi,pl(eta,zeta)),u0)
--4144
-satz144:=isi1(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),[x:rat][t:lrt(ts(ksi,pl(eta,zeta)),x)]t6".4144"(x,t),[x:rat][t:lrt(pl(ts(ksi,eta),ts(ksi,zeta)),x)]t27".4144"(x,t)):is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
-disttp1:=tr3is(cut,ts(pl(ksi,eta),zeta),ts(zeta,pl(ksi,eta)),pl(ts(zeta,ksi),ts(zeta,eta)),pl(ts(ksi,zeta),ts(eta,zeta)),comts(pl(ksi,eta),zeta),satz144(zeta,ksi,eta),ispl12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta))):is(ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)))
-disttp2:=satz144:is(ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)))
-distpt1:=symis(cut,ts(pl(ksi,eta),zeta),pl(ts(ksi,zeta),ts(eta,zeta)),disttp1):is(pl(ts(ksi,zeta),ts(eta,zeta)),ts(pl(ksi,eta),zeta))
-distpt2:=symis(cut,ts(ksi,pl(eta,zeta)),pl(ts(ksi,eta),ts(ksi,zeta)),disttp2):is(pl(ts(ksi,eta),ts(ksi,zeta)),ts(ksi,pl(eta,zeta)))
-[m:more(ksi,eta)]
-+4145
-phi:=mn(ksi,eta,m):cut
-t1:=satz140d(ksi,eta,m):is(ksi,pl(eta,phi))
-t2:=tris(cut,ts(ksi,zeta),ts(pl(eta,phi),zeta),pl(ts(eta,zeta),ts(phi,zeta)),ists1(ksi,pl(eta,phi),zeta,t1),disttp1(eta,phi,zeta)):is(ts(ksi,zeta),pl(ts(eta,zeta),ts(phi,zeta)))
--4145
-satz145a:=ismore1(pl(ts(eta,zeta),ts(phi".4145",zeta)),ts(ksi,zeta),ts(eta,zeta),symis(cut,ts(ksi,zeta),pl(ts(eta,zeta),ts(phi".4145",zeta)),t2".4145"),satz133(ts(eta,zeta),ts(phi".4145",zeta))):more(ts(ksi,zeta),ts(eta,zeta))
-zeta@[i:is(ksi,eta)]
-satz145b:=ists1(ksi,eta,zeta,i):is(ts(ksi,zeta),ts(eta,zeta))
-zeta@[l:less(ksi,eta)]
-satz145c:=satz121(ts(eta,zeta),ts(ksi,zeta),satz145a(eta,ksi,zeta,satz122(ksi,eta,l))):less(ts(ksi,zeta),ts(eta,zeta))
-m@satz145d:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145a):more(ts(zeta,ksi),ts(zeta,eta))
-i@satz145e:=ists2(ksi,eta,zeta,i):is(ts(zeta,ksi),ts(zeta,eta))
-l@satz145f:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,zeta),ts(zeta,eta),comts(ksi,zeta),comts(eta,zeta),satz145c):less(ts(zeta,ksi),ts(zeta,eta))
-upsilon@[i:is(ksi,eta)][m:more(zeta,upsilon)]
-satz145g:=ismore2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145d(zeta,upsilon,ksi,m)):more(ts(ksi,zeta),ts(eta,upsilon))
-satz145h:=ismore12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145g):more(ts(zeta,ksi),ts(upsilon,eta))
-i@[l:less(zeta,upsilon)]
-satz145j:=isless2(ts(ksi,upsilon),ts(eta,upsilon),ts(ksi,zeta),ists1(ksi,eta,upsilon,i),satz145f(zeta,upsilon,ksi,l)):less(ts(ksi,zeta),ts(eta,upsilon))
-satz145k:=isless12(ts(ksi,zeta),ts(zeta,ksi),ts(eta,upsilon),ts(upsilon,eta),comts(ksi,zeta),comts(eta,upsilon),satz145j):less(ts(zeta,ksi),ts(upsilon,eta))
-+4146
-zeta@t1:=satz123a(ksi,eta):or3(is(ksi,eta),more(ksi,eta),less(ksi,eta))
-t2:=satz123b(ts(ksi,zeta),ts(eta,zeta)):ec3(is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)))
--4146
-zeta@[m:more(ts(ksi,zeta),ts(eta,zeta))]
-satz146a:=th11"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),m):more(ksi,eta)
-zeta@[i:is(ts(ksi,zeta),ts(eta,zeta))]
-satz146b:=th10"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),i):is(ksi,eta)
-zeta@[l:less(ts(ksi,zeta),ts(eta,zeta))]
-satz146c:=th12"l.ec3"(is(ksi,eta),more(ksi,eta),less(ksi,eta),is(ts(ksi,zeta),ts(eta,zeta)),more(ts(ksi,zeta),ts(eta,zeta)),less(ts(ksi,zeta),ts(eta,zeta)),t1".4146",t2".4146",[u:is(ksi,eta)]satz145b(ksi,eta,zeta,u),[u:more(ksi,eta)]satz145a(ksi,eta,zeta,u),[u:less(ksi,eta)]satz145c(ksi,eta,zeta,u),l):less(ksi,eta)
-zeta@[m:more(ts(zeta,ksi),ts(zeta,eta))]
-satz146d:=satz146a(ismore12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),m)):more(ksi,eta)
-zeta@[i:is(ts(zeta,ksi),ts(zeta,eta))]
-satz146e:=satz146b(tr3is(cut,ts(ksi,zeta),ts(zeta,ksi),ts(zeta,eta),ts(eta,zeta),comts(ksi,zeta),i,comts(zeta,eta))):is(ksi,eta)
-zeta@[l:less(ts(zeta,ksi),ts(zeta,eta))]
-satz146f:=satz146c(isless12(ts(zeta,ksi),ts(ksi,zeta),ts(zeta,eta),ts(eta,zeta),comts(zeta,ksi),comts(zeta,eta),l)):less(ksi,eta)
-upsilon@[m:more(ksi,eta)][n:more(zeta,upsilon)]
-+4147
-t1:=satz145a(ksi,eta,zeta,m):more(ts(ksi,zeta),ts(eta,zeta))
-t2:=ismore12(ts(zeta,eta),ts(eta,zeta),ts(upsilon,eta),ts(eta,upsilon),comts(zeta,eta),comts(upsilon,eta),satz145a(zeta,upsilon,eta,n)):more(ts(eta,zeta),ts(eta,upsilon))
--4147
-satz147:=trmore(ts(ksi,zeta),ts(eta,zeta),ts(eta,upsilon),t1".4147",t2".4147"):more(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:less(zeta,upsilon)]
-satz147a:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz147(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:more(zeta,upsilon)]
-satz148a:=orapp(more(ksi,eta),is(ksi,eta),more(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]satz147(t,n),[t:is(ksi,eta)]satz145g(t,n)):more(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[m:more(ksi,eta)][n:moreis(zeta,upsilon)]
-satz148b:=orapp(more(zeta,upsilon),is(zeta,upsilon),more(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]satz147(m,t),[t:is(zeta,upsilon)]satz145h(zeta,upsilon,ksi,eta,t,m)):more(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:less(zeta,upsilon)]
-satz148c:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148a(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz122(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:less(ksi,eta)][k:lessis(zeta,upsilon)]
-satz148d:=satz121(ts(eta,upsilon),ts(ksi,zeta),satz148b(eta,ksi,upsilon,zeta,satz122(ksi,eta,l),satz125(zeta,upsilon,k))):less(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[m:moreis(ksi,eta)][n:moreis(zeta,upsilon)]
-+4149
-[i:is(ksi,eta)][j:is(zeta,upsilon)]
-t1:=moreisi2(ts(ksi,zeta),ts(eta,upsilon),ists12(ksi,eta,zeta,upsilon,i,j)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-i@[o:more(zeta,upsilon)]
-t2:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148a(m,o)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-i@t3:=orapp(more(zeta,upsilon),is(zeta,upsilon),moreis(ts(ksi,zeta),ts(eta,upsilon)),n,[t:more(zeta,upsilon)]t2(t),[t:is(zeta,upsilon)]t1(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-n@[o:more(ksi,eta)]
-t4:=moreisi1(ts(ksi,zeta),ts(eta,upsilon),satz148b(o,n)):moreis(ts(ksi,zeta),ts(eta,upsilon))
--4149
-satz149:=orapp(more(ksi,eta),is(ksi,eta),moreis(ts(ksi,zeta),ts(eta,upsilon)),m,[t:more(ksi,eta)]t4".4149"(t),[t:is(ksi,eta)]t3".4149"(t)):moreis(ts(ksi,zeta),ts(eta,upsilon))
-upsilon@[l:lessis(ksi,eta)][k:lessis(zeta,upsilon)]
-satz149a:=satz124(ts(eta,upsilon),ts(ksi,zeta),satz149(eta,ksi,upsilon,zeta,satz125(ksi,eta,l),satz125(zeta,upsilon,k))):lessis(ts(ksi,zeta),ts(eta,upsilon))
--rp
-@[r0:rat]
-ratset:=setof(rat,[x:rat]less(x,r0)):set(rat)
-+4150
-t1:=satz90(r0):some([x:rat]less(x,r0))
-[x0:rat][l:less(x0,r0)]
-t2:=estii(rat,[x:rat]less(x,r0),x0,l):in(x0,ratset)
-r0@t3:=ec3e13(is(r0,r0),more(r0,r0),less(r0,r0),satz81b(r0,r0),refis(rat,r0)):not(less(r0,r0))
-t4:=th3"l.imp"(in(r0,ratset),less(r0,r0),t3,[t:in(r0,ratset)]estie(rat,[x:rat]less(x,r0),r0,t)):not(in(r0,ratset))
-x0@[i:in(x0,ratset)]
-t5:=estie(rat,[x:rat]less(x,r0),x0,i):less(x0,r0)
-[x1:rat][k:less(x1,x0)]
-t6:=t2(x1,trless(x1,x0,r0,k,t5)):in(x1,ratset)
-i@t7:=satz91(x0,r0,t5):some([x:rat]and(less(x0,x),less(x,r0)))
-[x1:rat][a:and(less(x0,x1),less(x1,r0))]
-t8:=ande1(less(x0,x1),less(x1,r0),a):less(x0,x1)
-t9:=ande2(less(x0,x1),less(x1,r0),a):less(x1,r0)
-t10:=andi(in(x1,ratset),more(x1,x0),t2(x1,t9),satz83(x0,x1,t8)):and(in(x1,ratset),more(x1,x0))
-i@t11:=th6"l.some"(rat,[x:rat]and(less(x0,x),less(x,r0)),[x:rat]and(in(x,ratset),more(x,x0)),t7,[x:rat][t:and(less(x0,x),less(x,r0))]t10(x,t)):some([x:rat]and(in(x,ratset),more(x,x0)))
-l@t12:=cut2(ratset,x0,t2,r0,t4,[x:rat][t:in(x,ratset)][y:rat][u:less(y,x)]t6(x,t,y,u),[x:rat][t:in(x,ratset)]t11(x,t)):cutprop(ratset)
--4150
-satz150:=someapp(rat,[x:rat]less(x,r0),t1".4150",cutprop(ratset),[x:rat][t:less(x,r0)]t12".4150"(x,t)):cutprop(ratset)
-+*rp
-r0@rpofrt:=cutof(ratset,satz150):cut
-[x0:rat][l:less"rt"(x0,r0)]
-lrtrpofrt:=ine(ratset,satz150,x0,t2"rt.4150"(x0,l)):lrt(rpofrt,x0)
-r0@[x0:rat][lx:lrt(rpofrt,x0)]
-lrtrpofrte:=t5"rt.4150"(x0,ini(ratset,satz150,x0,lx)):less"rt"(x0,r0)
-r0@[x0:rat][m:moreis"rt"(x0,r0)]
-+*iii4
-m@t12:=satz81c(x0,r0,m):not(less"rt"(x0,r0))
--iii4
-m@urtrpofrt:=th3"l.imp"(lrt(rpofrt,x0),less"rt"(x0,r0),t12".iii4",[t:lrt(rpofrt,x0)]lrtrpofrte(x0,t)):urt(rpofrt,x0)
-@1rp:=rpofrt(1rt):cut
-+4151
-ksi@[z0:rat][lz:lrt(ts(ksi,1rp),z0)][x0:rat][lx:lrt(ksi,x0)][y0:rat][ly:lrt(1rp,y0)][i:is"rt"(z0,ts"rt"(x0,y0))]
-t1:=lrtrpofrte(1rt,y0,ly):less"rt"(y0,1rt)
-t2:=isless12"rt"(ts"rt"(x0,y0),z0,ts"rt"(x0,1rt),x0,symis(rat,z0,ts"rt"(x0,y0),i),example1a(x0),satz105f(y0,1rt,x0,t1)):less"rt"(z0,x0)
-t3:=satz120(ksi,x0,lx,z0,t2):lrt(ksi,z0)
-lz@t4:=tsapp(ksi,1rp,z0,lz,lrt(ksi,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(1rp,y)][v:is"rt"(z0,ts"rt"(x,y))]t3(x,t,y,u,v)):lrt(ksi,z0)
-ksi@[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][l:less"rt"(x0,x1)]
-y1:=ts"rt"(ov(1rt,x1),x0):rat
-t5:=isless2"rt"(ts"rt"(ov(1rt,x1),x1),1rt,y1,satz110e(1rt,x1),satz105f(x0,x1,ov(1rt,x1),l)):less"rt"(y1,1rt)
-t6:=lrtrpofrt(1rt,y1,t5):lrt(1rp,y1)
-t7:=tr3is(rat,ts"rt"(x1,y1),ts"rt"(ts"rt"(x1,ov(1rt,x1)),x0),ts"rt"(1rt,x0),x0,assts2"rt"(x1,ov(1rt,x1),x0),ists1"rt"(ts"rt"(x1,ov(1rt,x1)),1rt,x0,satz110c(1rt,x1)),example1c(x0)):is"rt"(ts"rt"(x1,y1),x0)
-t8:=lrtts(ksi,1rp,x0,x1,lx1,y1,t6,symis(rat,ts"rt"(x1,y1),x0,t7)):lrt(ts(ksi,1rp),x0)
-lx@t9:=cutapp3(ksi,x0,lx,lrt(ts(ksi,1rp),x0),[y:rat][t:lrt(ksi,y)][u:less"rt"(x0,y)]t8(y,t,u)):lrt(ts(ksi,1rp),x0)
--4151
-ksi@satz151:=isi1(ts(ksi,1rp),ksi,[x:rat][t:lrt(ts(ksi,1rp),x)]t4".4151"(x,t),[x:rat][t:lrt(ksi,x)]t9".4151"(x,t)):is(ts(ksi,1rp),ksi)
-satz151a:=symis(cut,ts(ksi,1rp),ksi,satz151):is(ksi,ts(ksi,1rp))
-satz151b:=tris(cut,ts(1rp,ksi),ts(ksi,1rp),ksi,comts(1rp,ksi),satz151):is(ts(1rp,ksi),ksi)
-satz151c:=symis(cut,ts(1rp,ksi),ksi,satz151b):is(ksi,ts(1rp,ksi))
-+4152
-[x0:rat][y0:rat]
-invprop1:=and(urt(ksi,y0),less"rt"(y0,x0)):'prop'
-ksi@[z0:rat][x0:rat]
-invprop2:=and3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0))):'prop'
-z0@invprop:=some"rt"([x:rat]invprop2(z0,x)):'prop'
-ksi@inv:=setof(rat,[z:rat]invprop(z)):set(rat)
-x0@[ux:urt(ksi,x0)][y0:rat][uy:urt(ksi,y0)][l:less"rt"(y0,x0)][i:is"rt"(z0,ov(1rt,x0))]
-t1:=andi(urt(ksi,y0),less"rt"(y0,x0),uy,l):invprop1(x0,y0)
-t2:=somei(rat,[x:rat]invprop1(x0,x),y0,t1):some"rt"([x:rat]invprop1(x0,x))
-t3:=and3i(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),ux,t2,i):invprop2(z0,x0)
-t4:=somei(rat,[x:rat]invprop2(z0,x),x0,t3):invprop(z0)
-inv1:=estii(rat,[z:rat]invprop(z),z0,t4):in(z0,inv)
-z0@[i:in(z0,inv)][p:'prop'][p1:[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]p]
-t5:=estie(rat,[x:rat]invprop(x),z0,i):invprop(z0)
-[x0:rat][px:invprop2(z0,x0)]
-t6:=and3e1(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):urt(ksi,x0)
-t7:=and3e2(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):some"rt"([x:rat]invprop1(x0,x))
-t8:=and3e3(urt(ksi,x0),some"rt"([x:rat]invprop1(x0,x)),is"rt"(z0,ov(1rt,x0)),px):is"rt"(z0,ov(1rt,x0))
-[y0:rat][py:invprop1(x0,y0)]
-t9:=ande1(urt(ksi,y0),less"rt"(y0,x0),py):urt(ksi,y0)
-t10:=ande2(urt(ksi,y0),less"rt"(y0,x0),py):less"rt"(y0,x0)
-t11:=<t8><t10><t9><y0><t6><x0>p1:p
-px@t12:=someapp(rat,[x:rat]invprop1(x0,x),t7,p,[x:rat][t:invprop1(x0,x)]t11(x,t)):p
-p1@invapp:=someapp(rat,[x:rat]invprop2(z0,x),t5,p,[x:rat][t:invprop2(z0,x)]t12(x,t)):p
-ksi@[x0:rat][ux:urt(ksi,x0)]
-2x0:=pl"rt"(x0,x0):rat
-t13:=satz94a(x0,x0):less"rt"(x0,2x0)
-t14:=satz119a(ksi,x0,ux,2x0,t13):urt(ksi,2x0)
-t15:=inv1(ov(1rt,2x0),2x0,t14,x0,ux,t13,refis(rat,ov(1rt,2x0))):in(ov(1rt,2x0),inv)
-ksi@[x1:rat][lx:lrt(ksi,x1)][x0:rat][ux:urt(ksi,x0)]
-t16:=th3"l.imp"(is"rt"(x0,x1),lrt(ksi,x0),ux,[t:is"rt"(x0,x1)]isp1(rat,[x:rat]lrt(ksi,x),x1,x0,lx,t)):nis"rt"(x0,x1)
-t17:=satz110e(1rt,x0):is"rt"(ts"rt"(ov(1rt,x0),x0),1rt)
-t18:=satz110e(1rt,x1):is"rt"(ts"rt"(ov(1rt,x1),x1),1rt)
-[i:is"rt"(ov(1rt,x0),ov(1rt,x1))]
-t19:=tris(rat,ts"rt"(ov(1rt,x0),x1),ts"rt"(ov(1rt,x1),x1),1rt,ists1"rt"(ov(1rt,x0),ov(1rt,x1),x1,i),t18):is"rt"(ts"rt"(ov(1rt,x0),x1),1rt)
-t20:=satz110b(1rt,ov(1rt,x0),x0,x1,t17,t19):is"rt"(x0,x1)
-ux@t21:=th3"l.imp"(is"rt"(ov(1rt,x0),ov(1rt,x1)),is"rt"(x0,x1),t16,[t:is"rt"(ov(1rt,x0),ov(1rt,x1))]t20(t)):nis"rt"(ov(1rt,x0),ov(1rt,x1))
-lx@[i:in(ov(1rt,x1),inv)]
-t22:=invapp(ov(1rt,x1),i,con,[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(ov(1rt,x1),ov(1rt,x))]<symis(rat,ov(1rt,x1),ov(1rt,x),w)>t21(x,t)):con
-lx@t23:=[t:in(ov(1rt,x1),inv)]t22(t):not(in(ov(1rt,x1),inv))
-ksi@[z0:rat][i:in(z0,inv)][u0:rat][l:less"rt"(u0,z0)][x0:rat][ux:urt(ksi,x0)][j:is"rt"(z0,ov(1rt,x0))]
-t24:=isless2"rt"(z0,ov(1rt,x0),u0,j,l):less"rt"(u0,ov(1rt,x0))
-t25:=tris(rat,ts"rt"(ov(1rt,x0),x0),1rt,ts"rt"(u0,ov(1rt,u0)),satz110e(1rt,x0),satz110d(1rt,u0)):is"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)))
-t26:=isless2"rt"(ts"rt"(ov(1rt,x0),x0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(u0,x0),t25,satz105c(u0,ov(1rt,x0),x0,t24)):less"rt"(ts"rt"(u0,x0),ts"rt"(u0,ov(1rt,u0)))
-t27:=isless12"rt"(ts"rt"(u0,x0),ts"rt"(x0,u0),ts"rt"(u0,ov(1rt,u0)),ts"rt"(ov(1rt,u0),u0),comts"rt"(u0,x0),comts"rt"(u0,ov(1rt,u0)),t26):less"rt"(ts"rt"(x0,u0),ts"rt"(ov(1rt,u0),u0))
-t28:=satz106c(x0,ov(1rt,u0),u0,t27):less"rt"(x0,ov(1rt,u0))
-t29:=satz119a(x0,ux,ov(1rt,u0),t28):urt(ksi,ov(1rt,u0))
-t30:=satz110e(1rt,u0):is"rt"(ts"rt"(ov(1rt,u0),u0),1rt)
-t31:=satz110g(1rt,ov(1rt,u0),u0,t30):is"rt"(u0,ov(1rt,ov(1rt,u0)))
-t32:=inv1(u0,ov(1rt,u0),t29,x0,ux,t28,t31):in(u0,inv)
-l@t33:=invapp(z0,i,in(u0,inv),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t32(x,t,w)):in(u0,inv)
-i@[x0:rat][ux:urt(ksi,x0)][x1:rat][ux1:urt(ksi,x1)][l:less"rt"(x1,x0)][j:is"rt"(z0,ov(1rt,x0))]
-t34:=satz91(x1,x0,l):some"rt"([x:rat]and(less"rt"(x1,x),less"rt"(x,x0)))
-[x2:rat][a:and(less"rt"(x1,x2),less"rt"(x2,x0))]
-t35:=ande1(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x1,x2)
-t36:=satz119a(ksi,x1,ux1,x2,t35):urt(ksi,x2)
-t37:=inv1(ov(1rt,x2),x2,t36,x1,ux1,t35,refis(rat,ov(1rt,x2))):in(ov(1rt,x2),inv)
-t38:=ande2(less"rt"(x1,x2),less"rt"(x2,x0),a):less"rt"(x2,x0)
-t39:=tris(rat,ts"rt"(x0,ov(1rt,x0)),1rt,ts"rt"(x2,ov(1rt,x2)),satz110c(1rt,x0),satz110d(1rt,x2)):is"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
-t40:=isless2"rt"(ts"rt"(x0,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)),ts"rt"(x2,ov(1rt,x0)),t39,satz105c(x2,x0,ov(1rt,x0),t38)):less"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(x2,ov(1rt,x2)))
-t41:=isless12"rt"(ts"rt"(x2,ov(1rt,x0)),ts"rt"(ov(1rt,x0),x2),ts"rt"(x2,ov(1rt,x2)),ts"rt"(ov(1rt,x2),x2),comts"rt"(x2,ov(1rt,x0)),comts"rt"(x2,ov(1rt,x2)),t40):less"rt"(ts"rt"(ov(1rt,x0),x2),ts"rt"(ov(1rt,x2),x2))
-t42:=satz106c(ov(1rt,x0),ov(1rt,x2),x2,t41):less"rt"(ov(1rt,x0),ov(1rt,x2))
-t43:=ismore2"rt"(ov(1rt,x0),z0,ov(1rt,x2),symis(rat,z0,ov(1rt,x0),j),satz83(ov(1rt,x0),ov(1rt,x2),t42)):more"rt"(ov(1rt,x2),z0)
-t44:=andi(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0),t37,t43):and(in(ov(1rt,x2),inv),more"rt"(ov(1rt,x2),z0))
-t45:=somei(rat,[x:rat]and(in(x,inv),more"rt"(x,z0)),ov(1rt,x2),t44):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
-j@t46:=someapp(rat,[x:rat]and(less"rt"(x1,x),less"rt"(x,x0)),t34,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:and(less"rt"(x1,x),less"rt"(x,x0))]t45(x,t)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
-i@t47:=invapp(z0,i,some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0))),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(z0,ov(1rt,x))]t46(x,t,y,u,v,w)):some"rt"([x:rat]and(in(x,inv),more"rt"(x,z0)))
-ksi@[x0:rat][lx:lrt(ksi,x0)][y0:rat][uy:urt(ksi,y0)]
-t48:=cut2(inv,ov(1rt,pl"rt"(y0,y0)),t15(y0,uy),ov(1rt,x0),t23(x0,lx),[x:rat][t:in(x,inv)][y:rat][u:less"rt"(y,x)]t33(x,t,y,u),[x:rat][t:in(x,inv)]t47(x,t)):cutprop(inv)
-lx@t49:=cutapp1b(ksi,cutprop(inv),[x:rat][t:urt(ksi,x)]t48(x,t)):cutprop(inv)
-ksi@t50:=cutapp1a(ksi,cutprop(inv),[x:rat][t:lrt(ksi,x)]t49(x,t)):cutprop(inv)
-chi:=cutof(inv,t50):cut
-[z0:rat][lz:lrt(ts(ksi,chi),z0)][x0:rat][lx:lrt(ksi,x0)][u0:rat][lu:lrt(chi,u0)][i:is"rt"(z0,ts"rt"(x0,u0))][x1:rat][ux:urt(ksi,x1)][j:is"rt"(u0,ov(1rt,x1))]
-t51:=tris(rat,z0,ts"rt"(x0,u0),ts"rt"(x0,ov(1rt,x1)),i,ists2"rt"(u0,ov(1rt,x1),x0,j)):is"rt"(z0,ts"rt"(x0,ov(1rt,x1)))
-t52:=cutapp2a(ksi,x0,lx,x1,ux):less"rt"(x0,x1)
-t53:=isless12"rt"(ts"rt"(x0,ov(1rt,x1)),z0,ts"rt"(x1,ov(1rt,x1)),1rt,symis(rat,z0,ts"rt"(x0,ov(1rt,x1)),t51),satz110c(1rt,x1),satz105c(x0,x1,ov(1rt,x1),t52)):less"rt"(z0,1rt)
-t54:=lrtrpofrt(1rt,z0,t53):lrt(1rp,z0)
-i@r1:=ini(inv,t50,u0,lu):in(u0,inv)
-r2:=invapp(u0,r1,lrt(1rp,z0),[x:rat][t:urt(ksi,x)][y:rat][u:urt(ksi,y)][v:less"rt"(y,x)][w:is"rt"(u0,ov(1rt,x))]t54(x,t,w)):lrt(1rp,z0)
-lz@r3:=tsapp(ksi,chi,z0,lz,lrt(1rp,z0),[x:rat][t:lrt(ksi,x)][y:rat][u:lrt(chi,y)][v:is"rt"(z0,ts"rt"(x,y))]r2(x,t,y,u,v)):lrt(1rp,z0)
-ksi@[u0:rat][lu:lrt(1rp,u0)]
-t55:=lrtrpofrte(1rt,u0,lu):less"rt"(u0,1rt)
-t56:=satz83(u0,1rt,t55):more"rt"(1rt,u0)
-[x0:rat][lx:lrt(ksi,x0)][x1:rat][lx1:lrt(ksi,x1)][x2:rat][ux2:urt(ksi,x2)]
-t57:=cutapp2b(x1,lx1,x2,ux2):more"rt"(x2,x1)
-[i:is"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0))]
-t58:=cutapp2a(x0,lx,x2,ux2):less"rt"(x0,x2)
-t59:=satz105f(x0,x2,mn"rt"(1rt,u0,t56),t58):less"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),ts"rt"(mn"rt"(1rt,u0,t56),x2))
-t60:=isless1"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x0),mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),symis(rat,mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x0),i),t59):less"rt"(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2))
-t61:=tr4is(rat,pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),ts"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),x2),ts"rt"(1rt,x2),x2,pl"rt"(mn"rt"(x2,x1,t57),x1),distpt1"rt"(mn"rt"(1rt,u0,t56),u0,x2),ists1"rt"(pl"rt"(mn"rt"(1rt,u0,t56),u0),1rt,x2,satz101e(1rt,u0,t56)),example1c(x2),satz101f(x2,x1,t57)):is"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
-t62:=satz96c(mn"rt"(x2,x1,t57),ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2),t60):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)))
-t63:=isless2"rt"(pl"rt"(ts"rt"(mn"rt"(1rt,u0,t56),x2),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),t61,t62):less"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(mn"rt"(x2,x1,t57),x1))
-t64:=isless12"rt"(pl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(mn"rt"(x2,x1,t57),x1),pl"rt"(x1,mn"rt"(x2,x1,t57)),compl"rt"(mn"rt"(x2,x1,t57),ts"rt"(u0,x2)),compl"rt"(mn"rt"(x2,x1,t57),x1),t63):less"rt"(pl"rt"(ts"rt"(u0,x2),mn"rt"(x2,x1,t57)),pl"rt"(x1,mn"rt"(x2,x1,t57)))
-t65:=satz97c(ts"rt"(u0,x2),x1,mn"rt"(x2,x1,t57),t64):less"rt"(ts"rt"(u0,x2),x1)
-t66:=tr3is(rat,ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),ts"rt"(ts"rt"(ov(1rt,u0),u0),x2),ts"rt"(1rt,x2),x2,assts2"rt"(ov(1rt,u0),u0,x2),ists1"rt"(ts"rt"(ov(1rt,u0),u0),1rt,x2,satz110e(1rt,u0)),example1c(x2)):is"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2)
-t67:=isless12"rt"(ts"rt"(ov(1rt,u0),ts"rt"(u0,x2)),x2,ts"rt"(ov(1rt,u0),x1),ov(x1,u0),t66,satz141b(x1,u0),satz105f(ts"rt"(u0,x2),x1,ov(1rt,u0),t65)):less"rt"(x2,ov(x1,u0))
-t68:=satz119a(x2,ux2,ov(x1,u0),t67):urt(ksi,ov(x1,u0))
-t69:=satz110e(x1,u0):is"rt"(ts"rt"(ov(x1,u0),u0),x1)
-t70:=tr3is(rat,u0,ov(x1,ov(x1,u0)),ts"rt"(ov(1rt,ov(x1,u0)),x1),ts"rt"(x1,ov(1rt,ov(x1,u0))),satz110g(x1,ov(x1,u0),u0,t69),satz141c(x1,ov(x1,u0)),comts"rt"(ov(1rt,ov(x1,u0)),x1)):is"rt"(u0,ts"rt"(x1,ov(1rt,ov(x1,u0))))
-t71:=inv1(ov(1rt,ov(x1,u0)),ov(x1,u0),t68,x2,ux2,t67,refis(rat,ov(1rt,ov(x1,u0)))):in(ov(1rt,ov(x1,u0)),inv)
-t72:=ine(inv,t50,ov(1rt,ov(x1,u0)),t71):lrt(chi,ov(1rt,ov(x1,u0)))
-t73:=lrtts(ksi,chi,u0,x1,lx1,ov(1rt,ov(x1,u0)),t72,t70):lrt(ts(ksi,chi),u0)
-lx@t74:=satz132app(ksi,lrt(ts(ksi,chi),u0),ts"rt"(mn"rt"(1rt,u0,t56),x0),[x:rat][t:lrt(ksi,x)][y:rat][u:urt(ksi,y)][v:is"rt"(mn"rt"(y,x,cutapp2b(x,t,y,u)),ts"rt"(mn"rt"(1rt,u0,t56),x0))]t73(x,t,y,u,v)):lrt(ts(ksi,chi),u0)
-lu@t75:=cutapp1a(ksi,lrt(ts(ksi,chi),u0),[x:rat][t:lrt(ksi,x)]t74(x,t)):lrt(ts(ksi,chi),u0)
-ksi@t76:=isi1(ts(ksi,chi),1rp,[x:rat][t:lrt(ts(ksi,chi),x)]r3(x,t),[x:rat][t:lrt(1rp,x)]t75(x,t)):is(ts(ksi,chi),1rp)
--4152
-satz152:=somei(cut,[t:cut]is(ts(ksi,t),1rp),chi".4152",t76".4152"):some([c:cut]is(ts(ksi,c),1rp))
-eta@[phi:cut][psi:cut]
-+4153
-[m:more(phi,psi)]
-t1:=satz145d(phi,psi,eta,m):more(ts(eta,phi),ts(eta,psi))
-t2:=ec3e21(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t1):nis(ts(eta,phi),ts(eta,psi))
-psi@[l:less(phi,psi)]
-t3:=satz145f(phi,psi,eta,l):less(ts(eta,phi),ts(eta,psi))
-t4:=ec3e31(is(ts(eta,phi),ts(eta,psi)),more(ts(eta,phi),ts(eta,psi)),less(ts(eta,phi),ts(eta,psi)),satz123b(ts(eta,phi),ts(eta,psi)),t3):nis(ts(eta,phi),ts(eta,psi))
-psi@[n:nis(phi,psi)]
-t5:=th1"l.or3"(is(phi,psi),more(phi,psi),less(phi,psi),satz123a(phi,psi),n):or(more(phi,psi),less(phi,psi))
-t6:=orapp(more(phi,psi),less(phi,psi),nis(ts(eta,phi),ts(eta,psi)),t5,[t:more(phi,psi)]t2(t),[t:less(phi,psi)]t4(t)):nis(ts(eta,phi),ts(eta,psi))
--4153
-[i:is(ts(eta,phi),ksi)][j:is(ts(eta,psi),ksi)]
-satz153b:=th7"l.imp"(is(phi,psi),nis(ts(eta,phi),ts(eta,psi)),weli(is(ts(eta,phi),ts(eta,psi)),tris2(cut,ts(eta,phi),ts(eta,psi),ksi,i,j)),[t:nis(phi,psi)]t6".4153"(t)):is(phi,psi)
-+*4153
-eta@[tau:cut][i:is(ts(eta,tau),1rp)]
-chi:=ts(tau,ksi):cut
-t7:=tr3is(cut,ts(eta,chi),ts(ts(eta,tau),ksi),ts(1rp,ksi),ksi,assts2(eta,tau,ksi),ists1(ts(eta,tau),1rp,ksi,i),satz151b(ksi)):is(ts(eta,chi),ksi)
-t8:=somei(cut,[c:cut]is(ts(eta,c),ksi),chi,t7):some([c:cut]is(ts(eta,c),ksi))
--4153
-eta@satz153a:=someapp(cut,[c:cut]is(ts(eta,c),1rp),satz152(eta),some([c:cut]is(ts(eta,c),ksi)),[c:cut][t:is(ts(eta,c),1rp)]t8".4153"(c,t)):some([c:cut]is(ts(eta,c),ksi))
-+*4153
-eta@t9:=[c:cut][d:cut][t:is(ts(eta,c),ksi)][u:is(ts(eta,d),ksi)]satz153b(c,d,t,u):amone(cut,[c:cut]is(ts(eta,c),ksi))
--4153
-eta@satz153:=onei(cut,[c:cut]is(ts(eta,c),ksi),t9".4153",satz153a):one([c:cut]is(ts(eta,c),ksi))
-ov:=ind(cut,[a:cut]is(ts(eta,a),ksi),satz153):cut
-satz153c:=oneax(cut,[a:cut]is(ts(eta,a),ksi),satz153):is(ts(eta,ov(ksi,eta)),ksi)
-satz153d:=symis(cut,ts(eta,ov(ksi,eta)),ksi,satz153c):is(ksi,ts(eta,ov(ksi,eta)))
-satz153e:=tris(cut,ts(ov(ksi,eta),eta),ts(eta,ov(ksi,eta)),ksi,comts(ov(ksi,eta),eta),satz153c):is(ts(ov(ksi,eta),eta),ksi)
-satz153f:=symis(cut,ts(ov(ksi,eta),eta),ksi,satz153e):is(ksi,ts(ov(ksi,eta),eta))
-[phi:cut][i:is(ts(eta,phi),ksi)]
-satz153g:=satz153b(phi,ov(ksi,eta),i,satz153c):is(phi,ov(ksi,eta))
-@[ksi:cut]
-ratrp:=image(rat,cut,[x:rat]rpofrt(x),ksi):'prop'
-@[x0:rat]
-ratrpi:=imagei(rat,cut,[x:rat]rpofrt(x),x0):ratrp(rpofrt(x0))
-@[x:nat]
-rpofnt:=rpofrt(rtofn(x)):cut
-ksi@natrp:=image(nat,cut,[x:nat]rpofnt(x),ksi):'prop'
-x@natrpi:=imagei(nat,cut,[y:nat]rpofnt(y),x):natrp(rpofnt(x))
-ksi@[n:natrp(ksi)]
-+iii5
-[x:nat][i:is(ksi,rpofnt(x))]
-t1:=somei(rat,[y:rat]is(ksi,rpofrt(y)),rtofn(x),i):ratrp(ksi)
--iii5
-lemmaiii5:=someapp(nat,[x:nat]is(ksi,rpofnt(x)),n,ratrp(ksi),[x:nat][t:is(ksi,rpofnt(x))]t1".iii5"(x,t)):ratrp(ksi)
-@[x0:rat][y0:rat][m:more"rt"(x0,y0)]
-+5154
-t1:=lrtrpofrt(x0,y0,satz82(x0,y0,m)):lrt(rpofrt(x0),y0)
-t2:=urtrpofrt(y0,y0,moreisi2"rt"(y0,y0,refis(rat,y0))):urt(rpofrt(y0),y0)
-t3:=andi(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0),t1,t2):and(lrt(rpofrt(x0),y0),urt(rpofrt(y0),y0))
--5154
-satz154a:=somei(rat,[x:rat]and(lrt(rpofrt(x0),x),urt(rpofrt(y0),x)),y0,t3".5154"):more(rpofrt(x0),rpofrt(y0))
-y0@[i:is"rt"(x0,y0)]
-satz154b:=isf(rat,cut,[x:rat]rpofrt(x),x0,y0,i):is(rpofrt(x0),rpofrt(y0))
-y0@[l:less"rt"(x0,y0)]
-satz154c:=satz121(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,satz83(x0,y0,l))):less(rpofrt(x0),rpofrt(y0))
-+*5154
-y0@t4:=satz81a(x0,y0):or3(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0))
-t5:=satz123b(rpofrt(x0),rpofrt(y0)):ec3(is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)))
--5154
-y0@[m:more(rpofrt(x0),rpofrt(y0))]
-satz154d:=th11"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),m):more"rt"(x0,y0)
-y0@[i:is(rpofrt(x0),rpofrt(y0))]
-satz154e:=th10"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),i):is"rt"(x0,y0)
-y0@[l:less(rpofrt(x0),rpofrt(y0))]
-satz154f:=th12"l.ec3"(is"rt"(x0,y0),more"rt"(x0,y0),less"rt"(x0,y0),is(rpofrt(x0),rpofrt(y0)),more(rpofrt(x0),rpofrt(y0)),less(rpofrt(x0),rpofrt(y0)),t4".5154",t5".5154",[u:is"rt"(x0,y0)]satz154b(u),[u:more"rt"(x0,y0)]satz154a(u),[u:less"rt"(x0,y0)]satz154c(u),l):less"rt"(x0,y0)
-+*iii5
-@t2:=[x:rat][y:rat][t:is(rpofrt(x),rpofrt(y))]satz154e(x,y,t):injective(rat,cut,[x:rat]rpofrt(x))
--iii5
-y0@[i:is"rt"(x0,y0)]
-isrterp:=satz154b(x0,y0,i):is(rpofrt(x0),rpofrt(y0))
-y0@[i:is(rpofrt(x0),rpofrt(y0))]
-isrtirp:=satz154e(x0,y0,i):is"rt"(x0,y0)
-ksi@[rtksi:ratrp(ksi)]
-rtofrp:=soft(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):rat
-[eta:cut][rteta:ratrp(eta)][i:is(ksi,eta)]
-isrpert:=isinv(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))
-rteta@[i:is"rt"(rtofrp(ksi,rtksi),rtofrp(eta,rteta))]
-isrpirt:=isinve(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi,eta,rteta,i):is(ksi,eta)
-x0@isrtrp1:=isst1(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(x0,rtofrp(rpofrt(x0),ratrpi(x0)))
-isrtrp2:=isst2(rat,cut,[x:rat]rpofrt(x),t2".iii5",x0):is"rt"(rtofrp(rpofrt(x0),ratrpi(x0)),x0)
-rtksi@isrprt1:=ists1"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(ksi,rpofrt(rtofrp(ksi,rtksi)))
-isrprt2:=ists2"e"(rat,cut,[x:rat]rpofrt(x),t2".iii5",ksi,rtksi):is(rpofrt(rtofrp(ksi,rtksi)),ksi)
-@[x:nat][y:nat][i:is"n"(x,y)]
-isnterp:=isf(nat,cut,[z:nat]rpofnt(z),x,y,i):is(rpofnt(x),rpofnt(y))
-y@[i:is(rpofnt(x),rpofnt(y))]
-isntirp:=isnirt(x,y,isrtirp(rtofn(x),rtofn(y),i)):is"n"(x,y)
-+*iii5
-@t3:=[x:nat][y:nat][t:is(rpofnt(x),rpofnt(y))]isntirp(x,y,t):injective(nat,cut,[x:nat]rpofnt(x))
--iii5
-ksi@[ntksi:natrp(ksi)]
-ntofrp:=soft(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):nat
-[eta:cut][nteta:natrp(eta)][i:is(ksi,eta)]
-isrpent:=isinv(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))
-nteta@[i:is"n"(ntofrp(ksi,ntksi),ntofrp(eta,nteta))]
-isrpint:=isinve(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi,eta,nteta,i):is(ksi,eta)
-x@isntrp1:=isst1(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(x,ntofrp(rpofnt(x),natrpi(x)))
-isntrp2:=isst2(nat,cut,[y:nat]rpofnt(y),t3".iii5",x):is"n"(ntofrp(rpofnt(x),natrpi(x)),x)
-ntksi@isrpnt1:=ists1"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(ksi,rpofnt(ntofrp(ksi,ntksi)))
-isrpnt2:=ists2"e"(nat,cut,[x:nat]rpofnt(x),t3".iii5",ksi,ntksi):is(rpofnt(ntofrp(ksi,ntksi)),ksi)
-@[x0:rat][y0:rat]
-+5155
-[z0:rat][lz:lrt(pl(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,pl"rt"(u0,v0))]
-t1:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
-t2:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
-t3:=satz98a(u0,x0,v0,y0,t1,t2):less"rt"(pl"rt"(u0,v0),pl"rt"(x0,y0))
-t4:=isless1"rt"(pl"rt"(u0,v0),z0,pl"rt"(x0,y0),symis(rat,z0,pl"rt"(u0,v0),i),t3):less"rt"(z0,pl"rt"(x0,y0))
-t5:=lrtrpofrt(pl"rt"(x0,y0),z0,t4):lrt(rpofrt(pl"rt"(x0,y0)),z0)
-lz@t6:=plapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(pl"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,pl"rt"(x,y))]t5(x,t,y,u,v)):lrt(rpofrt(pl"rt"(x0,y0)),z0)
-y0@[u0:rat][lu:lrt(rpofrt(pl"rt"(x0,y0)),u0)]
-t7:=lrtrpofrte(pl"rt"(x0,y0),u0,lu):less"rt"(u0,pl"rt"(x0,y0))
-u01:=ov"rt"(u0,pl"rt"(x0,y0)):rat
-t8:=isless12"rt"(u0,ts"rt"(u01,pl"rt"(x0,y0)),pl"rt"(x0,y0),ts"rt"(1rt,pl"rt"(x0,y0)),satz110f(u0,pl"rt"(x0,y0)),example1d(pl"rt"(x0,y0)),t7):less"rt"(ts"rt"(u01,pl"rt"(x0,y0)),ts"rt"(1rt,pl"rt"(x0,y0)))
-t9:=satz106c(u01,1rt,pl"rt"(x0,y0),t8):less"rt"(u01,1rt)
-t10:=tris(rat,u0,ts"rt"(pl"rt"(x0,y0),u01),pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)),satz110d(u0,pl"rt"(x0,y0)),disttp1"rt"(x0,y0,u01)):is"rt"(u0,pl"rt"(ts"rt"(x0,u01),ts"rt"(y0,u01)))
-y0@[l:less"rt"(y0,1rt)]
-t11:=isless12"rt"(ts"rt"(y0,x0),ts"rt"(x0,y0),ts"rt"(1rt,x0),x0,comts"rt"(y0,x0),example1c(x0),satz105c(y0,1rt,x0,l)):less"rt"(ts"rt"(x0,y0),x0)
-t12:=lrtrpofrt(x0,ts"rt"(x0,y0),t11):lrt(rpofrt(x0),ts"rt"(x0,y0))
-lu@t13:=lrtpl(rpofrt(x0),rpofrt(y0),u0,ts"rt"(x0,u01),t12(x0,u01,t9),ts"rt"(y0,u01),t12(y0,u01,t9),t10):lrt(pl(rpofrt(x0),rpofrt(y0)),u0)
--5155
-satz155a:=isi1(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(pl"rt"(x0,y0)),x)]t13".5155"(x,t),[x:rat][t:lrt(pl(rpofrt(x0),rpofrt(y0)),x)]t6".5155"(x,t)):is(rpofrt(pl"rt"(x0,y0)),pl(rpofrt(x0),rpofrt(y0)))
-[m:more"rt"(x0,y0)]
-+*5155
-m@t14:=satz101f(x0,y0,m):is"rt"(x0,pl"rt"(mn"rt"(x0,y0,m),y0))
-t15:=tris(cut,rpofrt(x0),rpofrt(pl"rt"(mn"rt"(x0,y0,m),y0)),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),isrterp(x0,pl"rt"(mn"rt"(x0,y0,m),y0),t14),satz155a(mn"rt"(x0,y0,m),y0)):is(rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)))
-t16:=tris2(cut,pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0),pl(rpofrt(mn"rt"(x0,y0,m)),rpofrt(y0)),compl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),t15):is(pl(rpofrt(y0),rpofrt(mn"rt"(x0,y0,m))),rpofrt(x0))
--5155
-m@satz155b:=satz140g(rpofrt(x0),rpofrt(y0),rpofrt(mn"rt"(x0,y0,m)),satz154a(x0,y0,m),t16".5155"):is(rpofrt(mn"rt"(x0,y0,m)),mn(rpofrt(x0),rpofrt(y0),satz154a(x0,y0,m)))
-+*5155
-y0@[z0:rat][lz:lrt(ts(rpofrt(x0),rpofrt(y0)),z0)][u0:rat][lu:lrt(rpofrt(x0),u0)][v0:rat][lv:lrt(rpofrt(y0),v0)][i:is"rt"(z0,ts"rt"(u0,v0))]
-t17:=lrtrpofrte(x0,u0,lu):less"rt"(u0,x0)
-t18:=lrtrpofrte(y0,v0,lv):less"rt"(v0,y0)
-t19:=satz107a(u0,x0,v0,y0,t17,t18):less"rt"(ts"rt"(u0,v0),ts"rt"(x0,y0))
-t20:=isless1"rt"(ts"rt"(u0,v0),z0,ts"rt"(x0,y0),symis(rat,z0,ts"rt"(u0,v0),i),t19):less"rt"(z0,ts"rt"(x0,y0))
-t21:=lrtrpofrt(ts"rt"(x0,y0),z0,t20):lrt(rpofrt(ts"rt"(x0,y0)),z0)
-lz@t22:=tsapp(rpofrt(x0),rpofrt(y0),z0,lz,lrt(rpofrt(ts"rt"(x0,y0)),z0),[x:rat][t:lrt(rpofrt(x0),x)][y:rat][u:lrt(rpofrt(y0),y)][v:is"rt"(z0,ts"rt"(x,y))]t21(x,t,y,u,v)):lrt(rpofrt(ts"rt"(x0,y0)),z0)
-y0@[u0:rat][lu:lrt(rpofrt(ts"rt"(x0,y0)),u0)]
-t23:=lrtrpofrte(ts"rt"(x0,y0),u0,lu):less"rt"(u0,ts"rt"(x0,y0))
-[u1:rat][a:and(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)))]
-t24:=ande1(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u0,u1)
-t25:=ande2(less"rt"(u0,u1),less"rt"(u1,ts"rt"(x0,y0)),a):less"rt"(u1,ts"rt"(x0,y0))
-t26:=isless12"rt"(u0,ts"rt"(ov"rt"(u0,u1),u1),u1,ts"rt"(1rt,u1),satz110f(u0,u1),example1d(u1),t24):less"rt"(ts"rt"(ov"rt"(u0,u1),u1),ts"rt"(1rt,u1))
-t27:=satz106c(ov"rt"(u0,u1),1rt,u1,t26):less"rt"(ov"rt"(u0,u1),1rt)
-t28:=isless1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0),satz110f(u1,y0),t25):less"rt"(ts"rt"(ov"rt"(u1,y0),y0),ts"rt"(x0,y0))
-t29:=satz106c(ov"rt"(u1,y0),x0,y0,t28):less"rt"(ov"rt"(u1,y0),x0)
-t30:=tr3is(rat,u0,ts"rt"(u1,ov"rt"(u0,u1)),ts"rt"(ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1)),ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))),satz110d(u0,u1),ists1"rt"(u1,ts"rt"(ov"rt"(u1,y0),y0),ov"rt"(u0,u1),satz110f(u1,y0)),assts1"rt"(ov"rt"(u1,y0),y0,ov"rt"(u0,u1))):is"rt"(u0,ts"rt"(ov"rt"(u1,y0),ts"rt"(y0,ov"rt"(u0,u1))))
-t31:=lrtts(rpofrt(x0),rpofrt(y0),u0,ov"rt"(u1,y0),lrtrpofrt(x0,ov"rt"(u1,y0),t29),ts"rt"(y0,ov"rt"(u0,u1)),t12(y0,ov"rt"(u0,u1),t27),t30):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
-lu@t32:=someapp(rat,[x:rat]and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0))),satz91(u0,ts"rt"(x0,y0),t23),lrt(ts(rpofrt(x0),rpofrt(y0)),u0),[x:rat][t:and(less"rt"(u0,x),less"rt"(x,ts"rt"(x0,y0)))]t31(x,t)):lrt(ts(rpofrt(x0),rpofrt(y0)),u0)
--5155
-y0@satz155c:=isi1(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)),[x:rat][t:lrt(rpofrt(ts"rt"(x0,y0)),x)]t32".5155"(x,t),[x:rat][t:lrt(ts(rpofrt(x0),rpofrt(y0)),x)]t22".5155"(x,t)):is(rpofrt(ts"rt"(x0,y0)),ts(rpofrt(x0),rpofrt(y0)))
-+*5155
-y0@t33:=satz110f(x0,y0):is"rt"(x0,ts"rt"(ov"rt"(x0,y0),y0))
-t34:=tris(cut,rpofrt(x0),rpofrt(ts"rt"(ov"rt"(x0,y0),y0)),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),isrterp(x0,ts"rt"(ov"rt"(x0,y0),y0),t33),satz155c(ov"rt"(x0,y0),y0)):is(rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)))
-t35:=tris2(cut,ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0),ts(rpofrt(ov"rt"(x0,y0)),rpofrt(y0)),comts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),t34):is(ts(rpofrt(y0),rpofrt(ov"rt"(x0,y0))),rpofrt(x0))
--5155
-y0@satz155d:=satz153g(rpofrt(x0),rpofrt(y0),rpofrt(ov"rt"(x0,y0)),t35".5155"):is(rpofrt(ov"rt"(x0,y0)),ov(rpofrt(x0),rpofrt(y0)))
-@[x:nat][y:nat]
-satz155e:=tris(cut,rpofnt(pl"n"(x,y)),rpofrt(pl"rt"(rtofn(x),rtofn(y))),pl(rpofnt(x),rpofnt(y)),isrterp(rtofn(pl"n"(x,y)),pl"rt"(rtofn(x),rtofn(y)),symis(rat,pl"rt"(rtofn(x),rtofn(y)),rtofn(pl"n"(x,y)),satz112h(x,y))),satz155a(rtofn(x),rtofn(y))):is(rpofnt(pl"n"(x,y)),pl(rpofnt(x),rpofnt(y)))
-satz155f:=tris(cut,rpofnt(ts"n"(x,y)),rpofrt(ts"rt"(rtofn(x),rtofn(y))),ts(rpofnt(x),rpofnt(y)),isrterp(rtofn(ts"n"(x,y)),ts"rt"(rtofn(x),rtofn(y)),symis(rat,ts"rt"(rtofn(x),rtofn(y)),rtofn(ts"n"(x,y)),satz112j(x,y))),satz155c(rtofn(x),rtofn(y))):is(rpofnt(ts"n"(x,y)),ts(rpofnt(x),rpofnt(y)))
-+nt
-@natt:=ot(cut,[t:cut]natrp(t)):'type'
-[ksi:cut][nksi:natrp(ksi)]
-nttofrp:=out(cut,[t:cut]natrp(t),ksi,nksi):natt
-@[xt:natt][yt:natt]
-is:=is"e"(natt,xt,yt):'prop'
-nis:=not(is(xt,yt)):'prop'
-@[p:[x:natt]'prop']
-all:=all"l"(natt,p):'prop'
-some:=some"l"(natt,p):'prop'
-one:=one"e"(natt,p):'prop'
-xt@[st:set(natt)]
-in:=esti(natt,xt,st):'prop'
-xt@rpofntt:=in"e"(cut,[t:cut]natrp(t),xt):cut
-natrpi:=inp(cut,[t:cut]natrp(t),xt):natrp(rpofntt(xt))
-nksi@[eta:cut][neta:natrp(eta)][i:is"rp"(ksi,eta)]
-isrpentt:=isouti(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is(nttofrp(ksi,nksi),nttofrp(eta,neta))
-neta@[i:is(nttofrp(ksi,nksi),nttofrp(eta,neta))]
-isrpintt:=isoute(cut,[t:cut]natrp(t),ksi,nksi,eta,neta,i):is"rp"(ksi,eta)
-yt@[i:is(xt,yt)]
-isntterp:=isini(cut,[t:cut]natrp(t),xt,yt,i):is"rp"(rpofntt(xt),rpofntt(yt))
-yt@[i:is"rp"(rpofntt(xt),rpofntt(yt))]
-isnttirp:=isine(cut,[t:cut]natrp(t),xt,yt,i):is(xt,yt)
-nksi@isrpntt1:=isinout(cut,[t:cut]natrp(t),ksi,nksi):is"rp"(ksi,rpofntt(nttofrp(ksi,nksi)))
-xt@isnttrp1:=isoutin(cut,[t:cut]natrp(t),xt):is(xt,nttofrp(rpofntt(xt),natrpi(xt)))
-@[x:nat]
-nttofnt:=nttofrp(rpofnt(x),natrpi"rp"(x)):natt
-[y:nat][i:is"n"(x,y)]
-isntentt:=isrpentt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),isnterp(x,y,i)):is(nttofnt(x),nttofnt(y))
-y@[i:is(nttofnt(x),nttofnt(y))]
-isntintt:=isntirp(x,y,isrpintt(rpofnt(x),natrpi"rp"(x),rpofnt(y),natrpi"rp"(y),i)):is"n"(x,y)
-xt@ntofntt:=ntofrp(rpofntt(xt),natrpi(xt)):nat
-yt@[i:is(xt,yt)]
-isnttent:=isrpent(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),isntterp(xt,yt,i)):is"n"(ntofntt(xt),ntofntt(yt))
-yt@[i:is"n"(ntofntt(xt),ntofntt(yt))]
-isnttint:=isnttirp(xt,yt,isrpint(rpofntt(xt),natrpi(xt),rpofntt(yt),natrpi(yt),i)):is(xt,yt)
-+iii5
-x@t5:=isrpntt1(rpofnt(x),natrpi"rp"(x)):is"rp"(rpofnt(x),rpofntt(nttofnt(x)))
-t6:=isrpent(rpofnt(x),natrpi"rp"(x),rpofntt(nttofnt(x)),natrpi(nttofnt(x)),t5):is"n"(ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)))
--iii5
-x@isntntt1:=tris(nat,x,ntofrp(rpofnt(x),natrpi"rp"(x)),ntofntt(nttofnt(x)),isntrp1(x),t6".iii5"):is"n"(x,ntofntt(nttofnt(x)))
-+*iii5
-xt@t7:=isrpnt1(rpofntt(xt),natrpi(xt)):is"rp"(rpofntt(xt),rpofnt(ntofntt(xt)))
-t8:=isrpentt(rpofntt(xt),natrpi(xt),rpofnt(ntofntt(xt)),natrpi"rp"(ntofntt(xt)),t7):is(nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)))
--iii5
-xt@isnttnt1:=tris(natt,xt,nttofrp(rpofntt(xt),natrpi(xt)),nttofnt(ntofntt(xt)),isnttrp1(xt),t8".iii5"):is(xt,nttofnt(ntofntt(xt)))
-x@isntntt2:=symis(nat,x,ntofntt(nttofnt(x)),isntntt1):is"n"(ntofntt(nttofnt(x)),x)
-xt@isnttnt2:=symis(natt,xt,nttofnt(ntofntt(xt)),isnttnt1):is(nttofnt(ntofntt(xt)),xt)
-@1t:=nttofnt(1):natt
-suct:=[x:natt]nttofnt(<ntofntt(x)>suc):[x:natt]natt
-+5156
-xt@[j:is(<xt>suct,1t)]
-t1:=isntintt(<ntofntt(xt)>suc,1,j):is"n"(<ntofntt(xt)>suc,1)
--5156
-xt@satz156a:=th3"l.imp"(is(<xt>suct,1t),is"n"(<ntofntt(xt)>suc,1),<ntofntt(xt)>ax3,[t:is(<xt>suct,1t)]t1".5156"(t)):nis(<xt>suct,1t)
-yt@[i:is(<xt>suct,<yt>suct)]
-+*5156
-i@t2:=isntintt(<ntofntt(xt)>suc,<ntofntt(yt)>suc,i):is"n"(<ntofntt(xt)>suc,<ntofntt(yt)>suc)
--5156
-i@satz156b:=isnttint(xt,yt,<t2".5156"><ntofntt(yt)><ntofntt(xt)>ax4):is(xt,yt)
-@[st:set(natt)]
-cond1:=in(1t,st):'prop'
-cond2:=all([x:natt]imp(in(x,st),in(<x>suct,st))):'prop'
-[c1:cond1][c2:cond2]
-+*5156
-c2@[x:nat]
-prop1:=in(nttofnt(x),st):'prop'
-[p:prop1(x)]
-t3:=<p><nttofnt(x)>c2:in(<nttofnt(x)>suct,st)
-t4:=isp(nat,[t:nat]in(nttofnt(<t>suc),st),ntofntt(nttofnt(x)),x,t3,isntntt2(x)):prop1(<x>suc)
--5156
-c2@[xt:natt]
-+*5156
-xt@t5:=induction([t:nat]prop1(t),c1,[t:nat][u:prop1(t)]t4(t,u),ntofntt(xt)):in(nttofnt(ntofntt(xt)),st)
--5156
-xt@satz156c:=isp(natt,[t:natt]in(t,st),nttofnt(ntofntt(xt)),xt,t5".5156",isnttnt2(xt)):in(xt,st)
-@ax3t:=[x:natt]satz156a(x):[x:natt]nis(<x>suct,1t)
-ax4t:=[x:natt][y:natt][u:is(<x>suct,<y>suct)]satz156b(x,y,u):[x:natt][y:natt][u:is(<x>suct,<y>suct)]is(x,y)
-ax5t:=[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]satz156c(s,u,v,x):[s:set(natt)][u:cond1(s)][v:cond2(s)][x:natt]in(x,s)
--nt
-+rtt
-@ratt:=ot(cut,[t:cut]ratrp(t)):'type'
-[ksi:cut][rtksi:ratrp(ksi)]
-rttofrp:=out(cut,[t:cut]ratrp(t),ksi,rtksi):ratt
-@[x0t:ratt][y0t:ratt]
-is:=is"e"(ratt,x0t,y0t):'prop'
-nis:=not(is(x0t,y0t)):'prop'
-@[p:[x:ratt]'prop']
-all:=all"l"(ratt,p):'prop'
-some:=some"l"(ratt,p):'prop'
-one:=one"e"(ratt,p):'prop'
-x0t@rpofrtt:=in"e"(cut,[t:cut]ratrp(t),x0t):cut
-ratrpi:=inp(cut,[t:cut]ratrp(t),x0t):ratrp(rpofrtt(x0t))
-rtksi@[eta:cut][rteta:ratrp(eta)][i:is"rp"(ksi,eta)]
-isrpertt:=isouti(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))
-rteta@[i:is(rttofrp(ksi,rtksi),rttofrp(eta,rteta))]
-isrpirtt:=isoute(cut,[t:cut]ratrp(t),ksi,rtksi,eta,rteta,i):is"rp"(ksi,eta)
-y0t@[i:is(x0t,y0t)]
-isrtterp:=isini(cut,[t:cut]ratrp(t),x0t,y0t,i):is"rp"(rpofrtt(x0t),rpofrtt(y0t))
-y0t@[i:is"rp"(rpofrtt(x0t),rpofrtt(y0t))]
-isrttirp:=isine(cut,[t:cut]ratrp(t),x0t,y0t,i):is(x0t,y0t)
-rtksi@isrprtt1:=isinout(cut,[t:cut]ratrp(t),ksi,rtksi):is"rp"(ksi,rpofrtt(rttofrp(ksi,rtksi)))
-x0t@isrttrp1:=isoutin(cut,[t:cut]ratrp(t),x0t):is(x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)))
-@[x0:rat]
-rttofrt:=rttofrp(rpofrt(x0),ratrpi"rp"(x0)):ratt
-[y0:rat][i:is"rt"(x0,y0)]
-isrtertt:=isrpertt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),isrterp(x0,y0,i)):is(rttofrt(x0),rttofrt(y0))
-y0@[i:is(rttofrt(x0),rttofrt(y0))]
-isrtirtt:=isrtirp(x0,y0,isrpirtt(rpofrt(x0),ratrpi"rp"(x0),rpofrt(y0),ratrpi"rp"(y0),i)):is"rt"(x0,y0)
-x0t@rtofrtt:=rtofrp(rpofrtt(x0t),ratrpi(x0t)):rat
-y0t@[i:is(x0t,y0t)]
-isrttert:=isrpert(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),isrtterp(x0t,y0t,i)):is"rt"(rtofrtt(x0t),rtofrtt(y0t))
-y0t@[i:is"rt"(rtofrtt(x0t),rtofrtt(y0t))]
-isrttirt:=isrttirp(x0t,y0t,isrpirt(rpofrtt(x0t),ratrpi(x0t),rpofrtt(y0t),ratrpi(y0t),i)):is(x0t,y0t)
-+iii5
-x0@t9:=isrprtt1(rpofrt(x0),ratrpi"rp"(x0)):is"rp"(rpofrt(x0),rpofrtt(rttofrt(x0)))
-t10:=isrpert(rpofrt(x0),ratrpi"rp"(x0),rpofrtt(rttofrt(x0)),ratrpi(rttofrt(x0)),t9):is"rt"(rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)))
--iii5
-x0@isrtrtt1:=tris(rat,x0,rtofrp(rpofrt(x0),ratrpi"rp"(x0)),rtofrtt(rttofrt(x0)),isrtrp1(x0),t10".iii5"):is"rt"(x0,rtofrtt(rttofrt(x0)))
-+*iii5
-x0t@t11:=isrprt1(rpofrtt(x0t),ratrpi(x0t)):is"rp"(rpofrtt(x0t),rpofrt(rtofrtt(x0t)))
-t12:=isrpertt(rpofrtt(x0t),ratrpi(x0t),rpofrt(rtofrtt(x0t)),ratrpi"rp"(rtofrtt(x0t)),t11):is(rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)))
--iii5
-x0t@isrttrt1:=tris(ratt,x0t,rttofrp(rpofrtt(x0t),ratrpi(x0t)),rttofrt(rtofrtt(x0t)),isrttrp1(x0t),t12".iii5"):is(x0t,rttofrt(rtofrtt(x0t)))
--rtt
-@[ksi:cut]
-example2:=satz153c(1rp,ksi):is(ts(ksi,ov(1rp,ksi)),1rp)
-[rtksi:ratrp(ksi)]
-+5157
-x01:=rtofrp(ksi,rtksi):rat
-ksi@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
-rtksi@[y0:rat][i:in(y0,s1)]
-t1:=estie(rat,[x:rat]urt(ksi,x),y0,i):urt(ksi,y0)
-[m:more"rt"(x01,y0)]
-t2:=lrtrpofrt(x01,y0,satz82(x01,y0,m)):lrt(rpofrt(x01),y0)
-t3:=isp(cut,[x:cut]lrt(x,y0),rpofrt(x01),ksi,t2,isrprt2(ksi,rtksi)):lrt(ksi,y0)
-i@t4:=th3"l.imp"(more"rt"(x01,y0),lrt(ksi,y0),t1,[t:more"rt"(x01,y0)]t3(t)):not(more"rt"(x01,y0))
-t5:=satz81e(x01,y0,t4):lessis"rt"(x01,y0)
-rtksi@t6:=[x:rat][t:in(x,s1)]t5(x,t):lb(s1,x01)
-t7:=urtrpofrt(x01,x01,moreisi2"rt"(x01,x01,refis(rat,x01))):urt(rpofrt(x01),x01)
-t8:=isp(cut,[x:cut]urt(x,x01),rpofrt(x01),ksi,t7,isrprt2(ksi,rtksi)):urt(ksi,x01)
-t9:=estii(rat,[x:rat]urt(ksi,x),x01,t8):in(x01,s1)
-t10:=andi(lb(s1,x01),in(x01,s1),t6,t9):min(s1,x01)
--5157
-satz157a:=t10".5157":min(setof(rat,[x:rat]urt(ksi,x)),rtofrp(ksi,rtksi))
-satz157b:=somei(rat,[x:rat]min(s1".5157",x),x01".5157",t10".5157"):some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))
-ksi@[x0:rat][m:min(setof(rat,[x:rat]urt(ksi,x)),x0)]
-+*5157
-m"rp"@t11:=ande1(lb(s1,x0),in(x0,s1),m):lb(s1,x0)
-t12:=ande2(lb(s1,x0),in(x0,s1),m):in(x0,s1)
-t13:=estie(rat,[x:rat]urt(ksi,x),x0,t12):urt(ksi,x0)
-[y0:rat][ly:lrt(ksi,y0)]
-t14:=cutapp2a(ksi,y0,ly,x0,t13):less"rt"(y0,x0)
-t15:=lrtrpofrt(x0,y0,t14):lrt(rpofrt(x0),y0)
-y0@[uy:urt(ksi,y0)]
-t17:=estii(rat,[x:rat]urt(ksi,x),y0,uy):in(y0,s1)
-t18:=satz85(x0,y0,<t17><y0>t11):moreis"rt"(y0,x0)
-t19:=urtrpofrt(x0,y0,t18):urt(rpofrt(x0),y0)
-y0@t20:=cp(lrt(rpofrt(x0),y0),lrt(ksi,y0),[t:urt(ksi,y0)]t19(t)):imp(lrt(rpofrt(x0),y0),lrt(ksi,y0))
--5157
-m@satz157c:=isi1(ksi,rpofrt(x0),[x:rat][t:lrt(ksi,x)]t15".5157"(x,t),[x:rat]t20".5157"(x)):is(ksi,rpofrt(x0))
-ksi@[s:some"rt"([x:rat]min(setof(rat,[y:rat]urt(ksi,y)),x))]
-+*5157
-s@[x0:rat][m:min(s1,x0)]
-t21:=somei(rat,[x:rat]is(ksi,rpofrt(x)),x0,satz157c(x0,m)):ratrp(ksi)
--5157
-s@satz157d:=someapp(rat,[x:rat]min(s1".5157",x),s,ratrp(ksi),[x:rat][t:min(s1".5157",x)]t21".5157"(x,t)):ratrp(ksi)
-ksi@[x0:rat][lx:lrt(ksi,x0)]
-+5158
-x0@xr:=rpofrt(x0):cut
-lx@t1:=urtrpofrt(x0,x0,moreisi2"rt"(x0,x0,refis(rat,x0))):urt(xr,x0)
-t2:=andi(urt(xr,x0),lrt(ksi,x0),t1,lx):and(urt(xr,x0),lrt(ksi,x0))
--5158
-satz158a:=somei(rat,[x:rat]and(urt(rpofrt(x0),x),lrt(ksi,x)),x0,t2".5158"):less(rpofrt(x0),ksi)
-x0@[ux:urt(ksi,x0)]
-+*5158
-ux@s1:=setof(rat,[x:rat]urt(ksi,x)):set(rat)
-[m:min(s1,x0)]
-t3:=symis(cut,ksi,xr,satz157c(ksi,x0,m)):is(xr,ksi)
-t4:=moreisi2(xr,ksi,t3):moreis(xr,ksi)
-ux@[n:not(min(s1,x0))]
-t5:=estii(rat,[x:rat]urt(ksi,x),x0,ux):in(x0,s1)
-t6:=th4"l.and"(lb(s1,x0),in(x0,s1),n,t5):not(lb(s1,x0))
-t7:=th1"l.some"(rat,[x:rat]imp(in(x,s1),lessis"rt"(x0,x)),t6):some"rt"([x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))))
-[y0:rat][o:not(imp(in(y0,s1),lessis"rt"(x0,y0)))]
-t8:=th5"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):in(y0,s1)
-t9:=estie(rat,[x:rat]urt(ksi,x),y0,t8):urt(ksi,y0)
-t10:=th6"l.imp"(in(y0,s1),lessis"rt"(x0,y0),o):not(lessis"rt"(x0,y0))
-t11:=satz82(x0,y0,satz81k(x0,y0,t10)):less"rt"(y0,x0)
-t12:=lrtrpofrt(x0,y0,t11):lrt(xr,y0)
-t13:=andi(lrt(xr,y0),urt(ksi,y0),t12,t9):and(lrt(xr,y0),urt(ksi,y0))
-t14:=somei(rat,[x:rat]and(lrt(xr,x),urt(ksi,x)),y0,t13):more(xr,ksi)
-n@t15:=someapp(rat,[x:rat]not(imp(in(x,s1),lessis"rt"(x0,x))),t7,more(xr,ksi),[x:rat][t:not(imp(in(x,s1),lessis"rt"(x0,x)))]t14(x,t)):more(xr,ksi)
-t16:=moreisi1(xr,ksi,t15):moreis(xr,ksi)
--5158
-ux@satz158b:=th1"l.imp"(min(s1".5158",x0),moreis(rpofrt(x0),ksi),[t:min(s1".5158",x0)]t4".5158"(t),[t:not(min(s1".5158",x0))]t16".5158"(t)):moreis(rpofrt(x0),ksi)
-x0@[l:less(rpofrt(x0),ksi)]
-+*5158
-l@t17:=satz123h(xr,ksi,l):not(moreis(xr,ksi))
-t18:=th3"l.imp"(urt(ksi,x0),moreis(xr,ksi),t17,[t:urt(ksi,x0)]satz158b(t)):not(urt(ksi,x0))
--5158
-l@satz158c:=et(lrt(ksi,x0),t18".5158"):lrt(ksi,x0)
-x0@[m:moreis(rpofrt(x0),ksi)]
-+*5158
-m"rp"@t19:=satz123c(xr,ksi,m):not(less(xr,ksi))
--5158
-m@satz158d:=th3"l.imp"(lrt(ksi,x0),less(rpofrt(x0),ksi),t19".5158",[t:lrt(ksi,x0)]satz158a(t)):urt(ksi,x0)
-ksi@[eta:cut][l:less(ksi,eta)]
-+5159
-[x0:rat]
-xr:=rpofrt(x0):cut
-[ux:urt(ksi,x0)][lx:lrt(eta,x0)][z0:rat]
-zr:=rpofrt(z0):cut
-[lz:lrt(eta,z0)][k:less"rt"(x0,z0)]
-t1:=satz127a(ksi,xr,zr,satz124(xr,ksi,satz158b(ksi,x0,ux)),satz154c(x0,z0,k)):less(ksi,zr)
-t2:=andi(less(ksi,zr),less(zr,eta),t1,satz158a(eta,z0,lz)):and(less(ksi,zr),less(zr,eta))
-t3:=somei(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),z0,t2):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
-lx@t4:=cutapp3(eta,x0,lx,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:lrt(eta,x)][u:less"rt"(x0,x)]t3(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
--5159
-satz159:=lessapp(ksi,eta,l,some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))),[x:rat][t:urt(ksi,x)][u:lrt(eta,x)]t4".5159"(x,t,u)):some"rt"([x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)))
-+*5159
-x0@[a:and(less(ksi,xr),less(xr,eta))]
-t5:=andi(ratrp(xr),and(less(ksi,xr),less(xr,eta)),ratrpi(x0),a):and3(ratrp(xr),less(ksi,xr),less(xr,eta))
-t6:=somei(cut,[c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)),xr,t5):some([c:cut]and3(ratrp(c),less(ksi,c),less(c,eta)))
--5159
-l@satz159a:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta))),[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t6".5159"(x,t)):some([a:cut]and3(ratrp(a),less(ksi,a),less(a,eta)))
-[p:'prop'][p1:[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),eta)]p]
-+*5159
-p1@[y0:rat]
-yr:=rpofrt(y0):cut
-[a:and(less(ksi,yr),less(yr,eta))]
-t7:=ande1(less(ksi,yr),less(yr,eta),a):less(ksi,yr)
-t8:=ande2(less(ksi,yr),less(yr,eta),a):less(yr,eta)
-t9:=<t8><t7><y0>p1:p
--5159
-p1@satz159app:=someapp(rat,[x:rat]and(less(ksi,rpofrt(x)),less(rpofrt(x),eta)),satz159,p,[x:rat][t:and(less(ksi,rpofrt(x)),less(rpofrt(x),eta))]t9".5159"(x,t)):p
-eta@[z0:rat][m:more(rpofrt(z0),ts(ksi,eta))]
-+5160
-zr:=rpofrt(z0):cut
-nm:=mn(zr,ts(ksi,eta),m):cut
-dn:=pl(pl(ksi,eta),1rp):cut
-fr:=ov(nm,dn):cut
-zeta:=ite(less(fr,1rp),cut,fr,1rp):cut
-[l:less(fr,1rp)]
-t1:=itet(less(fr,1rp),cut,fr,1rp,l):is(zeta,fr)
-t2:=lessisi2(zeta,fr,t1):lessis(zeta,fr)
-t3:=lessisi1(zeta,1rp,satz127a(zeta,fr,1rp,t2,l)):lessis(zeta,1rp)
-m@[n:not(less(fr,1rp))]
-t4:=itef(less(fr,1rp),cut,fr,1rp,n):is(zeta,1rp)
-t5:=lessisi2(zeta,1rp,t4):lessis(zeta,1rp)
-t6:=trlessis(zeta,1rp,fr,t5,satz124(fr,1rp,satz123f(fr,1rp,n))):lessis(zeta,fr)
-m@t7:=th1"l.imp"(less(fr,1rp),lessis(zeta,1rp),[t:less(fr,1rp)]t3(t),[t:not(less(fr,1rp))]t5(t)):lessis(zeta,1rp)
-t8:=th1"l.imp"(less(fr,1rp),lessis(zeta,fr),[t:less(fr,1rp)]t2(t),[t:not(less(fr,1rp))]t6(t)):lessis(zeta,fr)
-[z1:rat]
-zr1:=rpofrt(z1):cut
-[l1:less(ksi,zr1)][l2:less(zr1,pl(ksi,zeta))][z2:rat]
-zr2:=rpofrt(z2):cut
-[l3:less(eta,zr2)][l4:less(zr2,pl(eta,zeta))]
-t9:=isless2(ts(pl(ksi,zeta),pl(eta,zeta)),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),ts(zr1,zr2),disttp2(pl(ksi,zeta),eta,zeta),satz147a(zr1,pl(ksi,zeta),zr2,pl(eta,zeta),l2,l4)):less(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)))
-t10:=lessisi2(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),tris(cut,ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(zeta,eta)),pl(ts(ksi,eta),ts(eta,zeta)),disttp1(ksi,zeta,eta),ispl2(ts(zeta,eta),ts(eta,zeta),ts(ksi,eta),comts(zeta,eta)))):lessis(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)))
-t11:=satz149a(pl(ksi,zeta),pl(ksi,1rp),zeta,zeta,satz139a(ksi,ksi,zeta,1rp,lessisi2(ksi,ksi,refis(cut,ksi)),t7),lessisi2(zeta,zeta,refis(cut,zeta))):lessis(ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta))
-t12:=satz139a(ts(pl(ksi,zeta),eta),pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,zeta),zeta),ts(pl(ksi,1rp),zeta),t10,t11):lessis(pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
-t13:=satz127b(ts(zr1,zr2),pl(ts(pl(ksi,zeta),eta),ts(pl(ksi,zeta),zeta)),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),t9,t12):less(ts(zr1,zr2),pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)))
-t14:=tris(cut,pl(eta,pl(ksi,1rp)),pl(pl(eta,ksi),1rp),pl(pl(ksi,eta),1rp),asspl2(eta,ksi,1rp),ispl1(pl(eta,ksi),pl(ksi,eta),1rp,compl(eta,ksi))):is(pl(eta,pl(ksi,1rp)),dn)
-t15:=tris(cut,pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(pl(eta,pl(ksi,1rp)),zeta),ts(dn,zeta),distpt1(eta,pl(ksi,1rp),zeta),ists1(pl(eta,pl(ksi,1rp)),dn,zeta,t14)):is(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta))
-t16:=tris(cut,pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta))),pl(ts(ksi,eta),ts(dn,zeta)),asspl1(ts(ksi,eta),ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ispl2(pl(ts(eta,zeta),ts(pl(ksi,1rp),zeta)),ts(dn,zeta),ts(ksi,eta),t15)):is(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)))
-t17:=isless2(pl(pl(ts(ksi,eta),ts(eta,zeta)),ts(pl(ksi,1rp),zeta)),pl(ts(ksi,eta),ts(dn,zeta)),ts(zr1,zr2),t16,t13):less(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)))
-t18:=islessis12(ts(zeta,dn),ts(dn,zeta),ts(fr,dn),nm,comts(zeta,dn),satz153e(nm,dn),satz149a(zeta,fr,dn,dn,t8,lessisi2(dn,dn,refis(cut,dn)))):lessis(ts(dn,zeta),nm)
-t19:=satz139a(ts(ksi,eta),ts(ksi,eta),ts(dn,zeta),nm,lessisi2(ts(ksi,eta),ts(ksi,eta),refis(cut,ts(ksi,eta))),t18):lessis(pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm))
-t20:=satz127b(ts(zr1,zr2),pl(ts(ksi,eta),ts(dn,zeta)),pl(ts(ksi,eta),nm),t17,t19):less(ts(zr1,zr2),pl(ts(ksi,eta),nm))
-t21:=isless2(pl(ts(ksi,eta),nm),zr,ts(zr1,zr2),satz140c(zr,ts(ksi,eta),m),t20):less(ts(zr1,zr2),zr)
-t22:=satz154f(ts"rt"(z1,z2),z0,isless1(ts(zr1,zr2),rpofrt(ts"rt"(z1,z2)),zr,symis(cut,rpofrt(ts"rt"(z1,z2)),ts(zr1,zr2),satz155c(z1,z2)),t21)):less"rt"(ts"rt"(z1,z2),z0)
-x0:=ov"rt"(z0,z2):rat
-xr:=rpofrt(x0):cut
-y0:=z2:rat
-yr:=rpofrt(y0):cut
-t23:=satz110e(z0,z2):is"rt"(ts"rt"(x0,y0),z0)
-t24:=ismore1"rt"(z0,ts"rt"(x0,z2),ts"rt"(z1,z2),symis(rat,ts"rt"(x0,z2),z0,t23),satz83(ts"rt"(z1,z2),z0,t22)):more"rt"(ts"rt"(x0,z2),ts"rt"(z1,z2))
-t25:=satz106a(x0,z1,z2,t24):more"rt"(x0,z1)
-t26:=trmore(xr,zr1,ksi,satz154a(x0,z1,t25),satz122(ksi,zr1,l1)):more(xr,ksi)
-t27:=satz122(eta,yr,l3):more(yr,eta)
-z0@[u0:rat]
-ur:=rpofrt(u0):cut
-[v0:rat]
-vr:=rpofrt(v0):cut
-prop1:=and3(more(ur,ksi),more(vr,eta),is"rt"(ts"rt"(u0,v0),z0)):'prop'
-z0@prop2:=some"rt"([x:rat]some"rt"([y:rat]prop1(x,y))):'prop'
-l4@t28:=and3i(more(xr,ksi),more(yr,eta),is"rt"(ts"rt"(x0,y0),z0),t26,t27,t23):prop1(x0,y0)
-t29:=somei(rat,[y:rat]prop1(x0,y),y0,t28):some"rt"([y:rat]prop1(x0,y))
-t30:=somei(rat,[x:rat]some"rt"([y:rat]prop1(x,y)),x0,t29):prop2
-l2@t31:=satz159app(eta,pl(eta,zeta),satz133a(eta,zeta),prop2,[x:rat][t:less(eta,rpofrt(x))][u:less(rpofrt(x),pl(eta,zeta))]t30(x,t,u)):prop2
--5160
-satz160:=satz159app(ksi,pl(ksi,zeta".5160"),satz133a(ksi,zeta".5160"),prop2".5160",[x:rat][t:less(ksi,rpofrt(x))][u:less(rpofrt(x),pl(ksi,zeta".5160"))]t31".5160"(x,t,u)):some"rt"([x:rat]some"rt"([y:rat]and3(more(rpofrt(x),ksi),more(rpofrt(y),eta),is"rt"(ts"rt"(x,y),z0))))
-[p:'prop'][p1:[x:rat][t:more(rpofrt(x),ksi)][y:rat][u:more(rpofrt(y),eta)][v:is"rt"(ts"rt"(x,y),z0)]p]
-+*5160
-p1@[x1:rat]
-xr1:=rpofrt(x1):cut
-[px:some"rt"([y:rat]prop1(x1,y))][y1:rat]
-yr1:=rpofrt(y1):cut
-[py:prop1(x1,y1)]
-t32:=and3e1(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(xr1,ksi)
-t33:=and3e2(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):more(yr1,eta)
-t34:=and3e3(more(xr1,ksi),more(yr1,eta),is"rt"(ts"rt"(x1,y1),z0),py):is"rt"(ts"rt"(x1,y1),z0)
-t35:=<t34><t33><y1><t32><x1>p1:p
-px@t36:=someapp(rat,[y:rat]prop1(x1,y),px,p,[y:rat][v:prop1(x1,y)]t35(y,v)):p
--5160
-p1@satz160app:=someapp(rat,[x:rat]some"rt"([y:rat]prop1".5160"(x,y)),satz160,p,[x:rat][t:some"rt"([y:rat]prop1".5160"(x,y))]t36".5160"(x,t)):p
-+5161
-@[ksi:cut][eta:cut]
-min:=ite(less(ksi,eta),cut,ksi,eta):cut
-max:=ite(more(ksi,eta),cut,ksi,eta):cut
-[u0:rat]
-ur:=rpofrt(u0):cut
-[lu:lrt(min,u0)]
-t1:=satz158a(min,u0,lu):less(ur,min)
-[l:less(ksi,eta)]
-t2:=isless2(min,ksi,ur,itet(less(ksi,eta),cut,ksi,eta,l),t1):less(ur,ksi)
-t3:=trless(ur,ksi,eta,t2,l):less(ur,eta)
-lu@[n:not(less(ksi,eta))]
-t4:=isless2(min,eta,ur,itef(less(ksi,eta),cut,ksi,eta,n),t1):less(ur,eta)
-t5:=satz127b(ur,eta,ksi,t4,satz124(ksi,eta,satz123f(ksi,eta,n))):less(ur,ksi)
-lu@t6:=th1"l.imp"(less(ksi,eta),less(ur,ksi),[t:less(ksi,eta)]t2(t),[t:not(less(ksi,eta))]t5(t)):less(ur,ksi)
-t7:=th1"l.imp"(less(ksi,eta),less(ur,eta),[t:less(ksi,eta)]t3(t),[t:not(less(ksi,eta))]t4(t)):less(ur,eta)
-u0@[uu:urt(max,u0)]
-t8:=satz158b(max,u0,uu):moreis(ur,max)
-[m:more(ksi,eta)]
-t9:=ismoreis2(max,ksi,ur,itet(more(ksi,eta),cut,ksi,eta,m),t8):moreis(ur,ksi)
-t10:=trmoreis(ur,ksi,eta,t9,moreisi1(ksi,eta,m)):moreis(ur,eta)
-uu@[n:not(more(ksi,eta))]
-t11:=ismoreis2(max,eta,ur,itef(more(ksi,eta),cut,ksi,eta,n),t8):moreis(ur,eta)
-t12:=trmoreis(ur,eta,ksi,t11,satz125(ksi,eta,satz123e(ksi,eta,n))):moreis(ur,ksi)
-uu@t13:=th1"l.imp"(more(ksi,eta),moreis(ur,ksi),[t:more(ksi,eta)]t9(t),[t:not(more(ksi,eta))]t12(t)):moreis(ur,ksi)
-t14:=th1"l.imp"(more(ksi,eta),moreis(ur,eta),[t:more(ksi,eta)]t10(t),[t:not(more(ksi,eta))]t11(t)):moreis(ur,eta)
--5161
-@[zeta:cut]
-+*5161
-zeta@[ksi1:cut][ksi2:cut][m:more(ksi1,ksi2)]
-t15:=satz147(ksi1,ksi2,ksi1,ksi2,m,m):more(ts(ksi1,ksi1),ts(ksi2,ksi2))
-ksi2@sq1:=ts(ksi1,ksi1):cut
-sq2:=ts(ksi2,ksi2):cut
-m@t16:=ec3e21(is(sq1,sq2),more(sq1,sq2),less(sq1,sq2),satz123b(sq1,sq2),t15):nis(sq1,sq2)
-ksi2@[i:is(sq1,zeta)][j:is(sq2,zeta)]
-t17:=tris2(cut,sq1,sq2,zeta,i,j):is(sq1,sq2)
-t18:=[t:more(ksi1,ksi2)]<t17>t16(t):not(more(ksi1,ksi2))
-t19:=[t:less(ksi1,ksi2)]<symis(cut,sq1,sq2,t17)>t16(ksi2,ksi1,satz122(ksi1,ksi2,t)):not(less(ksi1,ksi2))
-t20:=or3e1(is(ksi1,ksi2),more(ksi1,ksi2),less(ksi1,ksi2),satz123a(ksi1,ksi2),t18,t19):is(ksi1,ksi2)
-zeta@t21:=[a:cut][b:cut][t:is(ts(a,a),zeta)][u:is(ts(b,b),zeta)]t20(a,b,t,u):amone(cut,[a:cut]is(ts(a,a),zeta))
-sqrtset:=setof(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta)):set(rat)
-[x0:rat]
-xr:=rpofrt(x0):cut
-[lx:lrt(min(1rp,zeta),x0)]
-t22:=t6(1rp,zeta,x0,lx):less(xr,1rp)
-t23:=t7(1rp,zeta,x0,lx):less(xr,zeta)
-t24:=isless1(xr,ts(xr,1rp),zeta,satz151a(xr),t23):less(ts(xr,1rp),zeta)
-t25:=trless(ts(xr,xr),ts(xr,1rp),zeta,satz148c(xr,xr,xr,1rp,lessisi2(xr,xr,refis(cut,xr)),t22),t24):less(ts(xr,xr),zeta)
-t26:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t25):in(x0,sqrtset)
-x0@[ux:urt(max(1rp,zeta),x0)]
-t27:=t13(1rp,zeta,x0,ux):moreis(xr,1rp)
-t28:=t14(1rp,zeta,x0,ux):moreis(xr,zeta)
-t29:=ismoreis1(xr,ts(xr,1rp),zeta,satz151a(xr),t28):moreis(ts(xr,1rp),zeta)
-t30:=trmoreis(ts(xr,xr),ts(xr,1rp),zeta,satz149(xr,xr,xr,1rp,moreisi2(xr,xr,refis(cut,xr)),t27),t29):moreis(ts(xr,xr),zeta)
-t31:=satz123c(ts(xr,xr),zeta,t30):not(less(ts(xr,xr),zeta))
-t32:=th3"l.imp"(in(x0,sqrtset),less(ts(xr,xr),zeta),t31,[t:in(x0,sqrtset)]estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,t)):not(in(x0,sqrtset))
-x0@[i:in(x0,sqrtset)][y0:rat]
-yr:=rpofrt(y0):cut
-[l:less"rt"(y0,x0)]
-i@t33:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),x0,i):less(ts(xr,xr),zeta)
-l@t34:=satz154c(y0,x0,l):less(yr,xr)
-t35:=trless(ts(yr,yr),ts(xr,xr),zeta,satz147a(yr,xr,yr,xr,t34,t34),t33):less(ts(yr,yr),zeta)
-t36:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),y0,t35):in(y0,sqrtset)
-i@t37:=satz122(ts(xr,xr),zeta,t33):more(zeta,ts(xr,xr))
-nm:=mn(zeta,ts(xr,xr),t37):cut
-dn:=pl(xr,pl(xr,1rp)):cut
-fr:=ov(nm,dn):cut
-[z0:rat]
-zr:=rpofrt(z0):cut
-[lz:lrt(min(1rp,fr),z0)]
-t38:=t6(1rp,fr,z0,lz):less(zr,1rp)
-t39:=t7(1rp,fr,z0,lz):less(zr,fr)
-t40:=satz94(x0,z0):more"rt"(pl"rt"(x0,z0),x0)
-t41:=tris(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),ts(pl(xr,zr),pl(xr,zr)),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ists12(rpofrt(pl"rt"(x0,z0)),pl(xr,zr),rpofrt(pl"rt"(x0,z0)),pl(xr,zr),satz155a(x0,z0),satz155a(x0,z0)),disttp2(pl(xr,zr),xr,zr)):is(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)))
-t42:=symis(cut,ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),t41):is(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))))
-t43:=lessisi2(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),tris(cut,ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(zr,xr)),pl(ts(xr,xr),ts(xr,zr)),disttp1(xr,zr,xr),ispl2(ts(zr,xr),ts(xr,zr),ts(xr,xr),comts(zr,xr)))):lessis(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)))
-t44:=satz145c(pl(xr,zr),pl(xr,1rp),zr,satz138c(xr,xr,zr,1rp,lessisi2(xr,xr,refis(cut,xr)),t38)):less(ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr))
-t45:=satz138c(ts(pl(xr,zr),xr),pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,zr),zr),ts(pl(xr,1rp),zr),t43,t44):less(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)))
-t46:=tris(cut,pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),pl(ts(xr,zr),ts(pl(xr,1rp),zr))),pl(ts(xr,xr),ts(dn,zr)),asspl1(ts(xr,xr),ts(xr,zr),ts(pl(xr,1rp),zr)),ispl2(pl(ts(xr,zr),ts(pl(xr,1rp),zr)),ts(dn,zr),ts(xr,xr),distpt1(xr,pl(xr,1rp),zr))):is(pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)))
-t47:=isless12(pl(ts(pl(xr,zr),xr),ts(pl(xr,zr),zr)),ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(pl(ts(xr,xr),ts(xr,zr)),ts(pl(xr,1rp),zr)),pl(ts(xr,xr),ts(dn,zr)),t42,t46,t45):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)))
-t48:=isless2(ts(dn,fr),nm,ts(dn,zr),satz153c(nm,dn),satz148c(dn,dn,zr,fr,lessisi2(dn,dn,refis(cut,dn)),t39)):less(ts(dn,zr),nm)
-t49:=satz138c(ts(xr,xr),ts(xr,xr),ts(dn,zr),nm,lessisi2(ts(xr,xr),ts(xr,xr),refis(cut,ts(xr,xr))),t48):less(pl(ts(xr,xr),ts(dn,zr)),pl(ts(xr,xr),nm))
-t50:=isless2(pl(ts(xr,xr),nm),zeta,pl(ts(xr,xr),ts(dn,zr)),satz140c(zeta,ts(xr,xr),t37),t49):less(pl(ts(xr,xr),ts(dn,zr)),zeta)
-t51:=trless(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),pl(ts(xr,xr),ts(dn,zr)),zeta,t47,t50):less(ts(rpofrt(pl"rt"(x0,z0)),rpofrt(pl"rt"(x0,z0))),zeta)
-t52:=estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),pl"rt"(x0,z0),t51):in(pl"rt"(x0,z0),sqrtset)
-t53:=andi(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0),t52,t40):and(in(pl"rt"(x0,z0),sqrtset),more"rt"(pl"rt"(x0,z0),x0))
-t54:=somei(rat,[y:rat]and(in(y,sqrtset),more"rt"(y,x0)),pl"rt"(x0,z0),t53):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
-i@t55:=cutapp1a(min(1rp,fr),some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0))),[x:rat][t:lrt(min(1rp,fr),x)]t54(x,t)):some"rt"([y:rat]and(in(y,sqrtset),more"rt"(y,x0)))
-x0@[lx:lrt(min(1rp,zeta),x0)][y0:rat][uy:urt(max(1rp,zeta),y0)]
-t56:=cut2(sqrtset,x0,t26(lx),y0,t32(y0,uy),[x:rat][t:in(x,sqrtset)][y:rat][u:less"rt"(y,x)]t36(x,t,y,u),[x:rat][t:in(x,sqrtset)]t55(x,t)):cutprop(sqrtset)
-lx@t57:=cutapp1b(max(1rp,zeta),cutprop(sqrtset),[y:rat][t:urt(max(1rp,zeta),y)]t56(y,t)):cutprop(sqrtset)
-zeta@t58:=cutapp1a(min(1rp,zeta),cutprop(sqrtset),[x:rat][t:lrt(min(1rp,zeta),x)]t57(x,t)):cutprop(sqrtset)
-rtc:=cutof(sqrtset,t58):cut
-@[x0:rat][y0:rat][l:lessis"rt"(x0,y0)]
-t59:=th9"l.or"(less"rt"(x0,y0),is"rt"(x0,y0),less(rpofrt(x0),rpofrt(y0)),is(rpofrt(x0),rpofrt(y0)),l,[t:less"rt"(x0,y0)]satz154c(x0,y0,t),[t:is"rt"(x0,y0)]satz154b(x0,y0,t)):lessis(rpofrt(x0),rpofrt(y0))
-y0@[m:moreis"rt"(x0,y0)]
-t60:=satz125(rpofrt(y0),rpofrt(x0),t59(y0,x0,satz84(x0,y0,m))):moreis(rpofrt(x0),rpofrt(y0))
-zeta@[m:more(ts(rtc,rtc),zeta)]
-t61:=satz121(ts(rtc,rtc),zeta,m):less(zeta,ts(rtc,rtc))
-[z1:rat]
-zr1:=rpofrt(z1):cut
-[l1:less(zeta,zr1)][l2:less(zr1,ts(rtc,rtc))]
-t62:=satz158c(ts(rtc,rtc),z1,l2):lrt(ts(rtc,rtc),z1)
-[x1:rat]
-xr1:=rpofrt(x1):cut
-[lx1:lrt(rtc,x1)][x2:rat]
-xr2:=rpofrt(x2):cut
-[lx2:lrt(rtc,x2)][i:is"rt"(z1,ts"rt"(x1,x2))]
-xm:=ite(more"rt"(x1,x2),rat,x1,x2):rat
-xrm:=rpofrt(xm):cut
-[o:more"rt"(x1,x2)]
-t63:=symis(rat,xm,x1,itet(more"rt"(x1,x2),rat,x1,x2,o)):is"rt"(x1,xm)
-t64:=isp(rat,[x:rat]lrt(rtc,x),x1,xm,lx1,t63):lrt(rtc,xm)
-t65:=lessisi2"rt"(x1,xm,t63):lessis"rt"(x1,xm)
-t66:=lessisi1"rt"(x2,xm,satz87b(x2,x1,xm,satz82(x1,x2,o),t65)):lessis"rt"(x2,xm)
-i@[n:not(more"rt"(x1,x2))]
-t67:=symis(rat,xm,x2,itef(more"rt"(x1,x2),rat,x1,x2,n)):is"rt"(x2,xm)
-t68:=isp(rat,[x:rat]lrt(rtc,x),x2,xm,lx2,t67):lrt(rtc,xm)
-t69:=lessisi2"rt"(x2,xm,t67):lessis"rt"(x2,xm)
-t70:=satz88(x1,x2,xm,satz81e(x1,x2,n),t69):lessis"rt"(x1,xm)
-i@t71:=th1"l.imp"(more"rt"(x1,x2),lrt(rtc,xm),[t:more"rt"(x1,x2)]t64(t),[t:not(more"rt"(x1,x2))]t68(t)):lrt(rtc,xm)
-t72:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x1,xm),[t:more"rt"(x1,x2)]t65(t),[t:not(more"rt"(x1,x2))]t70(t)):lessis"rt"(x1,xm)
-t73:=th1"l.imp"(more"rt"(x1,x2),lessis"rt"(x2,xm),[t:more"rt"(x1,x2)]t66(t),[t:not(more"rt"(x1,x2))]t69(t)):lessis"rt"(x2,xm)
-t74:=ini(sqrtset,t58,xm,t71):in(xm,sqrtset)
-t75:=t59(x1,xm,t72):lessis(xr1,xrm)
-t76:=t59(x2,xm,t73):lessis(xr2,xrm)
-t77:=tris(cut,zr1,rpofrt(ts"rt"(x1,x2)),ts(xr1,xr2),satz154b(z1,ts"rt"(x1,x2),i),satz155c(x1,x2)):is(zr1,ts(xr1,xr2))
-t78:=islessis1(ts(xr1,xr2),zr1,ts(xrm,xrm),symis(cut,zr1,ts(xr1,xr2),t77),satz149a(xr1,xrm,xr2,xrm,t75,t76)):lessis(zr1,ts(xrm,xrm))
-t79:=estie(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),xm,t74):less(ts(xrm,xrm),zeta)
-t80:=satz127a(zr1,ts(xrm,xrm),zeta,t78,t79):less(zr1,zeta)
-t81:=<t80>ec3e23(is(zr1,zeta),more(zr1,zeta),less(zr1,zeta),satz123b(zr1,zeta),satz122(zeta,zr1,l1)):con
-t82:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t81(x,t,y,u,v)):con
-l2@t82a:=tsapp(rtc,rtc,z1,t62,con,[x:rat][t:lrt(rtc,x)][y:rat][u:lrt(rtc,y)][v:is"rt"(z1,ts"rt"(x,y))]t82(x,t,y,u,v)):con
-m@t83:=satz159app(zeta,ts(rtc,rtc),t61,con,[x:rat][t:less(zeta,rpofrt(x))][u:less(rpofrt(x),ts(rtc,rtc))]t82a(x,t,u)):con
-zeta@[l:less(ts(rtc,rtc),zeta)][z2:rat]
-zr2:=rpofrt(z2):cut
-[l3:less(ts(rtc,rtc),zr2)][l4:less(zr2,zeta)]
-t84:=satz122(ts(rtc,rtc),zr2,l3):more(zr2,ts(rtc,rtc))
-[y1:rat]
-yr1:=rpofrt(y1):cut
-[m1:more(yr1,rtc)][y2:rat]
-yr2:=rpofrt(y2):cut
-[m2:more(yr2,rtc)][i:is"rt"(ts"rt"(y1,y2),z2)]
-ym:=ite(less"rt"(y1,y2),rat,y1,y2):rat
-yrm:=rpofrt(ym):cut
-[k:less"rt"(y1,y2)]
-t85:=symis(rat,ym,y1,itet(less"rt"(y1,y2),rat,y1,y2,k)):is"rt"(y1,ym)
-t86:=satz154b(y1,ym,t85):is(yr1,yrm)
-t87:=ismore1(yr1,yrm,rtc,t86,m1):more(yrm,rtc)
-t88:=moreisi2(yr1,yrm,t86):moreis(yr1,yrm)
-t89:=moreisi1(yr2,yrm,satz127d(yr2,yr1,yrm,satz122(yr1,yr2,satz154c(y1,y2,k)),t88)):moreis(yr2,yrm)
-i@[n:not(less"rt"(y1,y2))]
-t90:=symis(rat,ym,y2,itef(less"rt"(y1,y2),rat,y1,y2,n)):is"rt"(y2,ym)
-t91:=satz154b(y2,ym,t90):is(yr2,yrm)
-t92:=ismore1(yr2,yrm,rtc,t91,m2):more(yrm,rtc)
-t93:=moreisi2(yr2,yrm,t91):moreis(yr2,yrm)
-t94:=trmoreis(yr1,yr2,yrm,t60(y1,y2,satz81f(y1,y2,n)),t93):moreis(yr1,yrm)
-i@t95:=th1"l.imp"(less"rt"(y1,y2),more(yrm,rtc),[t:less"rt"(y1,y2)]t87(t),[t:not(less"rt"(y1,y2))]t92(t)):more(yrm,rtc)
-t96:=th1"l.imp"(less"rt"(y1,y2),moreis(yr1,yrm),[t:less"rt"(y1,y2)]t88(t),[t:not(less"rt"(y1,y2))]t94(t)):moreis(yr1,yrm)
-t97:=th1"l.imp"(less"rt"(y1,y2),moreis(yr2,yrm),[t:less"rt"(y1,y2)]t89(t),[t:not(less"rt"(y1,y2))]t93(t)):moreis(yr2,yrm)
-t98:=satz158d(rtc,ym,moreisi1(yrm,rtc,t95)):urt(rtc,ym)
-t99:=th3"l.imp"(in(ym,sqrtset),lrt(rtc,ym),t98,[t:in(ym,sqrtset)]ine(sqrtset,t58,ym,t)):not(in(ym,sqrtset))
-t100:=th3"l.imp"(less(ts(yrm,yrm),zeta),in(ym,sqrtset),t99,[t:less(ts(yrm,yrm),zeta)]estii(rat,[x:rat]less(ts(rpofrt(x),rpofrt(x)),zeta),ym,t)):not(less(ts(yrm,yrm),zeta))
-t101:=satz123f(ts(yrm,yrm),zeta,t100):moreis(ts(yrm,yrm),zeta)
-t101a:=satz149(yr1,yrm,yr2,yrm,t96,t97):moreis(ts(yr1,yr2),ts(yrm,yrm))
-t102:=ismoreis1(ts(yr1,yr2),zr2,ts(yrm,yrm),tris(cut,ts(yr1,yr2),rpofrt(ts"rt"(y1,y2)),zr2,symis(cut,rpofrt(ts"rt"(y1,y2)),ts(yr1,yr2),satz155c(y1,y2)),satz154b(ts"rt"(y1,y2),z2,i)),t101a):moreis(zr2,ts(yrm,yrm))
-t103:=trmoreis(zr2,ts(yrm,yrm),zeta,t102,t101):moreis(zr2,zeta)
-t104:=<l4>satz123c(zr2,zeta,t103):con
-l4@t105:=satz160app(rtc,rtc,z2,t84,con,[x:rat][t:more(rpofrt(x),rtc)][y:rat][u:more(rpofrt(y),rtc)][v:is"rt"(ts"rt"(x,y),z2)]t104(x,t,y,u,v)):con
-l@t106:=satz159app(ts(rtc,rtc),zeta,l,con,[x:rat][t:less(ts(rtc,rtc),rpofrt(x))][u:less(rpofrt(x),zeta)]t105(x,t,u)):con
-zeta@t107:=or3e1(is(ts(rtc,rtc),zeta),more(ts(rtc,rtc),zeta),less(ts(rtc,rtc),zeta),satz123a(ts(rtc,rtc),zeta),[t:more(ts(rtc,rtc),zeta)]t83(t),[t:less(ts(rtc,rtc),zeta)]t106(t)):is(ts(rtc,rtc),zeta)
-t108:=somei(cut,[a:cut]is(ts(a,a),zeta),rtc,t107):some([a:cut]is(ts(a,a),zeta))
--5161
-zeta@satz161:=onei(cut,[a:cut]is(ts(a,a),zeta),t21".5161",t108".5161"):one([a:cut]is(ts(a,a),zeta))
-@[ksi:cut]
-irratrp:=not(ratrp(ksi)):'prop'
--rp
--rt
-+5162
-@[v:nat]
-t1:=tris(nat,pl(v,v),pl(ts(1,v),v),ts(<1>suc,v),ispl1(v,ts(1,v),v,satz28g(v)),satz28h(1,v)):is(pl(v,v),ts(<1>suc,v))
-t2:=isless2(pl(v,v),ts(<1>suc,v),v,t1,satz18a(v,v)):less(v,ts(<1>suc,v))
-[w:nat][l:less(ts(v,v),ts(w,w))]
-t3:=satz10j(v,w,th3"l.imp"(moreis(v,w),moreis(ts(v,v),ts(w,w)),satz10h(ts(v,v),ts(w,w),l),[t:moreis(v,w)]satz36(v,w,v,w,t,t))):less(v,w)
-w@t4:=tris(nat,ts(pl(v,w),v),pl(ts(v,v),ts(w,v)),pl(ts(v,v),ts(v,w)),disttp1(v,w,v),ispl2(ts(w,v),ts(v,w),ts(v,v),comts(w,v))):is(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)))
-t5:=tr3is(nat,ts(pl(v,w),pl(v,w)),pl(ts(pl(v,w),v),ts(pl(v,w),w)),pl(pl(ts(v,v),ts(v,w)),pl(ts(v,w),ts(w,w))),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),disttp2(pl(v,w),v,w),ispl12(ts(pl(v,w),v),pl(ts(v,v),ts(v,w)),ts(pl(v,w),w),pl(ts(v,w),ts(w,w)),t4,disttp1(v,w,w)),asspl2(pl(ts(v,v),ts(v,w)),ts(v,w),ts(w,w))):is(ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)))
-t6:=tris(nat,pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),pl(ts(v,w),ts(v,w))),pl(ts(v,v),ts(<1>suc,ts(v,w))),asspl1(ts(v,v),ts(v,w),ts(v,w)),ispl2(pl(ts(v,w),ts(v,w)),ts(<1>suc,ts(v,w)),ts(v,v),t1(ts(v,w)))):is(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))))
-nun:=tris(nat,ts(pl(v,w),pl(v,w)),pl(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),ts(w,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),t5,ispl1(pl(pl(ts(v,v),ts(v,w)),ts(v,w)),pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w),t6)):is(ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)))
-nun1:=symis(nat,ts(pl(v,w),pl(v,w)),pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),nun):is(pl(pl(ts(v,v),ts(<1>suc,ts(v,w))),ts(w,w)),ts(pl(v,w),pl(v,w)))
-prop1:=eq(tf(fr(w,v),fr(w,v)),fr(<1>suc,1)):'prop'
-v@prop2:=some([t:nat]prop1(t)):'prop'
-@prop3:=some([u:nat]prop2(u)):'prop'
-[p:prop3]
-y:=ind(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):nat
-t7:=oneax(nat,[t:nat]min([u:nat]prop2(u),t),satz27a([u:nat]prop2(u),p)):min([u:nat]prop2(u),y)
-t8:=ande1(lb([u:nat]prop2(u),y),prop2(y),t7):lb([u:nat]prop2(u),y)
-t9:=ande2(lb([u:nat]prop2(u),y),prop2(y),t7):prop2(y)
-[x:nat][q:prop1(y,x)]
-t10:=treq1(fr(<1>suc,1),fr(ts(x,x),ts(y,y)),tf(fr(x,y),fr(x,y)),q,tfeq12a(x,y,x,y)):eq(fr(<1>suc,1),fr(ts(x,x),ts(y,y)))
-t11:=tr4is(nat,ts(<1>suc,ts(y,y)),ts(num(fr(<1>suc,1)),den(fr(ts(x,x),ts(y,y)))),ts(num(fr(ts(x,x),ts(y,y))),den(fr(<1>suc,1))),ts(ts(x,x),1),ts(x,x),12isnd(<1>suc,1,ts(x,x),ts(y,y)),t10,ndis12(ts(x,x),ts(y,y),<1>suc,1),satz28a(ts(x,x))):is(ts(<1>suc,ts(y,y)),ts(x,x))
-t12:=isless2(ts(<1>suc,ts(y,y)),ts(x,x),ts(y,y),t11,t2(ts(y,y))):less(ts(y,y),ts(x,x))
-t13:=isless1(ts(ts(<1>suc,y),y),ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)),tris(nat,ts(ts(<1>suc,y),y),ts(<1>suc,ts(y,y)),ts(x,x),assts1(<1>suc,y,y),t11),satz35c(ts(<1>suc,y),ts(<1>suc,y),y,ts(<1>suc,y),lessisi2(ts(<1>suc,y),ts(<1>suc,y),refis(nat,ts(<1>suc,y))),t2(y))):less(ts(x,x),ts(ts(<1>suc,y),ts(<1>suc,y)))
-t14:=t3(y,x,t12):less(y,x)
-t15:=t3(x,ts(<1>suc,y),t13):less(x,ts(<1>suc,y))
-[u:nat][i:is(x,pl(y,u))]
-t16:=isless12(x,pl(y,u),ts(<1>suc,y),pl(y,y),i,symis(nat,pl(y,y),ts(<1>suc,y),t1(y)),t15):less(pl(y,u),pl(y,y))
-t17:=satz20f(u,y,y,t16):less(u,y)
-[t:nat][j:is(y,pl(u,t))]
-t18:=symis(nat,y,pl(u,t),j):is(pl(u,t),y)
-t19:=tris(nat,ts(x,x),ts(pl(y,u),pl(y,u)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ists12(x,pl(y,u),x,pl(y,u),i,i),nun(y,u)):is(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)))
-t20:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),ispl1(ts(x,x),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u)),ts(t,t),t19),asspl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),ts(u,u),ts(t,t))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))))
-t21:=tr3is(nat,ts(y,u),ts(u,y),ts(u,pl(u,t)),pl(ts(u,u),ts(u,t)),comts(y,u),ists2(y,pl(u,t),u,j),disttp2(u,u,t)):is(ts(y,u),pl(ts(u,u),ts(u,t)))
-t22:=tris(nat,ts(<1>suc,ts(y,u)),ts(<1>suc,pl(ts(u,u),ts(u,t))),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ists2(ts(y,u),pl(ts(u,u),ts(u,t)),<1>suc,t21),disttp2(<1>suc,ts(u,u),ts(u,t))):is(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))))
-t23:=tris(nat,pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(y,y),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),ispl2(ts(<1>suc,ts(y,u)),pl(ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t))),ts(y,y),t22),asspl2(ts(y,y),ts(<1>suc,ts(u,u)),ts(<1>suc,ts(u,t)))):is(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))))
-t24:=tr3is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(ts(u,u),ts(t,t))),pl(pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),t20,ispl1(pl(ts(y,y),ts(<1>suc,ts(y,u))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t))),pl(ts(u,u),ts(t,t)),t23),asspl1(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))))
-t25:=tr4is(nat,pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),pl(pl(ts(<1>suc,ts(u,t)),ts(u,u)),ts(t,t)),pl(pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t)),ts(pl(u,t),pl(u,t)),ts(y,y),asspl2(ts(<1>suc,ts(u,t)),ts(u,u),ts(t,t)),ispl1(pl(ts(<1>suc,ts(u,t)),ts(u,u)),pl(ts(u,u),ts(<1>suc,ts(u,t))),ts(t,t),compl(ts(<1>suc,ts(u,t)),ts(u,u))),nun1(u,t),ists12(pl(u,t),y,pl(u,t),y,t18,t18)):is(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y))
-t26:=tr4is(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t)))),pl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),pl(ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u)))),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),t24,ispl2(pl(ts(<1>suc,ts(u,t)),pl(ts(u,u),ts(t,t))),ts(y,y),pl(ts(y,y),ts(<1>suc,ts(u,u))),t25),compl(pl(ts(y,y),ts(<1>suc,ts(u,u))),ts(y,y)),asspl2(ts(y,y),ts(y,y),ts(<1>suc,ts(u,u)))):is(pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))))
-t27:=tris(nat,pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(y,y)),ts(x,x),t1(ts(y,y)),t11):is(pl(ts(y,y),ts(y,y)),ts(x,x))
-t28:=tris(nat,pl(ts(x,x),ts(t,t)),pl(pl(ts(y,y),ts(y,y)),ts(<1>suc,ts(u,u))),pl(ts(x,x),ts(<1>suc,ts(u,u))),t26,ispl1(pl(ts(y,y),ts(y,y)),ts(x,x),ts(<1>suc,ts(u,u)),t27)):is(pl(ts(x,x),ts(t,t)),pl(ts(x,x),ts(<1>suc,ts(u,u))))
-t29:=satz20e(ts(t,t),ts(<1>suc,ts(u,u)),ts(x,x),t28):is(ts(t,t),ts(<1>suc,ts(u,u)))
-t30:=tr4is(nat,ts(num(fr(<1>suc,1)),den(fr(ts(t,t),ts(u,u)))),ts(<1>suc,ts(u,u)),ts(t,t),ts(ts(t,t),1),ts(num(fr(ts(t,t),ts(u,u))),den(fr(<1>suc,1))),ndis12(<1>suc,1,ts(t,t),ts(u,u)),symis(nat,ts(t,t),ts(<1>suc,ts(u,u)),t29),satz28e(ts(t,t)),12isnd(ts(t,t),ts(u,u),<1>suc,1)):eq(fr(<1>suc,1),fr(ts(t,t),ts(u,u)))
-t31:=treq2(tf(fr(t,u),fr(t,u)),fr(<1>suc,1),fr(ts(t,t),ts(u,u)),tfeq12a(t,u,t,u),t30):prop1(u,t)
-t32:=somei(nat,[v:nat]prop1(u,v),t,t31):prop2(u)
-t33:=<t32><u>t8:lessis(y,u)
-t34:=<t33>satz10g(y,u,satz12(u,y,t17)):con
-i@t35:=someapp(nat,[v:nat]diffprop(y,u,v),t17,con,[v:nat][w:diffprop(y,u,v)]t34(v,w)):con
-q@t36:=someapp(nat,[v:nat]diffprop(x,y,v),t14,con,[v:nat][w:diffprop(x,y,v)]t35(v,w)):con
-p@t37:=someapp(nat,[v:nat]prop1(y,v),t9,con,[v:nat][w:prop1(y,v)]t36(v,w)):con
--5162
-+*rt
-+5162
-@[x0:rat][i:is(ts(x0,x0),rtofn(<1>suc))][x:frac][xix0:inf(x,class(x0))]
-t38:=ise(ts(x0,x0),rtofn(<1>suc),tf(x,x),fr(<1>suc,1),tict(x0,x0,x,x,xix0,xix0),inclass(fr(<1>suc,1)),i):eq"n"(tf(x,x),fr(<1>suc,1))
-t39:=refeq1(fr(num(x),den(x)),x,fris(x)):eq"n"(fr(num(x),den(x)),x)
-t40:=eqtf12(fr(num(x),den(x)),x,fr(num(x),den(x)),x,t39,t39):eq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x))
-t41:=treq"n"(tf(fr(num(x),den(x)),fr(num(x),den(x))),tf(x,x),fr(<1>suc,1),t40,t38):prop1"n.5162"(den(x),num(x))
-t42:=somei(nat,[t:nat]prop1"n.5162"(den(x),t),num(x),t41):prop2"n.5162"(den(x))
-t43:=somei(nat,[t:nat]prop2"n.5162"(t),den(x),t42):prop3"n.5162"
-t44:=t37"n.5162"(t43):con
-i@t45:=ratapp1(x0,con,[x:frac][t:inf(x,class(x0))]t44(x,t)):con
--5162
-+*rp
-+5162
-@ksi:=ind(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):cut
-t46:=oneax(cut,[a:cut]is(ts(a,a),rpofnt(<1>suc)),satz161(rpofnt(<1>suc))):is(ts(ksi,ksi),rpofnt(<1>suc))
-[r:ratrp(ksi)]
-x0:=rtofrp(ksi,r):rat
-t47:=tr3is(cut,rpofrt(ts"rt"(x0,x0)),ts(rpofrt(x0),rpofrt(x0)),ts(ksi,ksi),rpofnt(<1>suc),satz155c(x0,x0),ists12(rpofrt(x0),ksi,rpofrt(x0),ksi,isrprt2(ksi,r),isrprt2(ksi,r)),t46):is(rpofrt(ts"rt"(x0,x0)),rpofnt(<1>suc))
-t48:=isrtirp(ts"rt"(x0,x0),rtofn(<1>suc),t47):is"rt"(ts"rt"(x0,x0),rtofn(<1>suc))
-t49:=t45"rt.5162"(x0,t48):con
--5162
-@satz162:=somei(cut,[a:cut]irratrp(a),ksi".5162",[t:ratrp(ksi".5162")]t49".5162"(t)):some([a:cut]irratrp(a))
-[zeta:cut]
-sqrt:=ind(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):cut
-thsqrt1:=oneax(cut,[a:cut]is(ts(a,a),zeta),satz161(zeta)):is(ts(sqrt(zeta),sqrt(zeta)),zeta)
-[ksi:cut][i:is(ts(ksi,ksi),zeta)]
-thsqrt2:=t20".5161"(zeta,ksi,sqrt,i,thsqrt1):is(ksi,sqrt)
-@[ksi:cut][eta:cut][i:is(ksi,eta)]
-issqrt:=isf(cut,cut,[t:cut]sqrt(t),ksi,eta,i):is(sqrt(ksi),sqrt(eta))
-@[ksi:cut][nx:natrp(ksi)][eta:cut][ny:natrp(eta)]
-+iiia
-x:=ntofrp(ksi,nx):nat
-y:=ntofrp(eta,ny):nat
-t1:=isrpnt1(ksi,nx):is(ksi,rpofnt(x))
-t2:=isrpnt1(eta,ny):is(eta,rpofnt(y))
-t3:=ispl12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(pl(ksi,eta),pl(rpofnt(x),rpofnt(y)))
-x0:=rtofn(x):rat
-y0:=rtofn(y):rat
-t4:=natrti(x):natrt(x0)
-t5:=natrti(y):natrt(y0)
-t6:=symis(cut,rpofrt(pl"rt"(x0,y0)),pl(rpofnt(x),rpofnt(y)),satz155a(x0,y0)):is(pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)))
-t7:=satz112d(x0,t4,y0,t5):natrt(pl"rt"(x0,y0))
-xpy:=nofrt(pl"rt"(x0,y0),t7):nat
-t8:=isrtn1(pl"rt"(x0,y0),t7):is"rt"(pl"rt"(x0,y0),rtofn(xpy))
-t9:=isrterp(pl"rt"(x0,y0),rtofn(xpy),t8):is(rpofrt(pl"rt"(x0,y0)),rpofnt(xpy))
-t10:=tr3is(cut,pl(ksi,eta),pl(rpofnt(x),rpofnt(y)),rpofrt(pl"rt"(x0,y0)),rpofnt(xpy),t3,t6,t9):is(pl(ksi,eta),rpofnt(xpy))
--iiia
-natpl:=somei(nat,[t:nat]is(pl(ksi,eta),rpofnt(t)),xpy".iiia",t10".iiia"):natrp(pl(ksi,eta))
-+*iiia
-ny@t11:=ists12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2):is(ts(ksi,eta),ts(rpofnt(x),rpofnt(y)))
-t12:=symis(cut,rpofrt(ts"rt"(x0,y0)),ts(rpofnt(x),rpofnt(y)),satz155c(x0,y0)):is(ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)))
-t13:=satz112f(x0,t4,y0,t5):natrt(ts"rt"(x0,y0))
-xty:=nofrt(ts"rt"(x0,y0),t13):nat
-t14:=isrtn1(ts"rt"(x0,y0),t13):is"rt"(ts"rt"(x0,y0),rtofn(xty))
-t15:=isrterp(ts"rt"(x0,y0),rtofn(xty),t14):is(rpofrt(ts"rt"(x0,y0)),rpofnt(xty))
-t16:=tr3is(cut,ts(ksi,eta),ts(rpofnt(x),rpofnt(y)),rpofrt(ts"rt"(x0,y0)),rpofnt(xty),t11,t12,t15):is(ts(ksi,eta),rpofnt(xty))
--iiia
-ny@natts:=somei(nat,[t:nat]is(ts(ksi,eta),rpofnt(t)),xty".iiia",t16".iiia"):natrp(ts(ksi,eta))
-[m:more(ksi,eta)]
-+*iiia
-m@t17:=ismore12(ksi,rpofnt(x),eta,rpofnt(y),t1,t2,m):more(rpofnt(x),rpofnt(y))
-t18:=satz154d(x0,y0,t17):more"rt"(x0,y0)
-t20:=ismn12(ksi,rpofnt(x),eta,rpofnt(y),m,satz154a(x0,y0,t18),t1,t2):is(mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)))
-t21:=symis(cut,rpofrt(mn"rt"(x0,y0,t18)),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),satz155b(x0,y0,t18)):is(mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)))
-t22:=satz112g(x0,t4,y0,t5,t18):natrt(mn"rt"(x0,y0,t18))
-xmy:=nofrt(mn"rt"(x0,y0,t18),t22):nat
-t23:=isrtn1(mn"rt"(x0,y0,t18),t22):is"rt"(mn"rt"(x0,y0,t18),rtofn(xmy))
-t24:=isrterp(mn"rt"(x0,y0,t18),rtofn(xmy),t23):is(rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy))
-t25:=tr3is(cut,mn(ksi,eta,m),mn(rpofnt(x),rpofnt(y),satz154a(x0,y0,t18)),rpofrt(mn"rt"(x0,y0,t18)),rpofnt(xmy),t20,t21,t24):is(mn(ksi,eta,m),rpofnt(xmy))
--iiia
-m@natmn:=somei(nat,[t:nat]is(mn(ksi,eta,m),rpofnt(t)),xmy".iiia",t25".iiia"):natrp(mn(ksi,eta,m))
-@[p:cut][q:cut][r:cut]
-3pl13:=tr3is(cut,pl(p,pl(q,r)),pl(pl(q,r),p),pl(pl(r,q),p),pl(r,pl(q,p)),compl(p,pl(q,r)),ispl1(pl(q,r),pl(r,q),p,compl(q,r)),asspl1(r,q,p)):is(pl(p,pl(q,r)),pl(r,pl(q,p)))
-[s:cut]
-4pl24:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(s,pl(r,q))),pl(pl(p,s),pl(r,q)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(s,pl(r,q)),p,3pl13(q,r,s)),asspl2(p,s,pl(r,q))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,s),pl(r,q)))
-r@3pl12:=tr3is(cut,pl(p,pl(q,r)),pl(pl(p,q),r),pl(pl(q,p),r),pl(q,pl(p,r)),asspl2(p,q,r),ispl1(pl(p,q),pl(q,p),r,compl(p,q)),asspl1(q,p,r)):is(pl(p,pl(q,r)),pl(q,pl(p,r)))
-s@4pl23:=tr3is(cut,pl(pl(p,q),pl(r,s)),pl(p,pl(q,pl(r,s))),pl(p,pl(r,pl(q,s))),pl(pl(p,r),pl(q,s)),asspl1(p,q,pl(r,s)),ispl2(pl(q,pl(r,s)),pl(r,pl(q,s)),p,3pl12(q,r,s)),asspl2(p,r,pl(q,s))):is(pl(pl(p,q),pl(r,s)),pl(pl(p,r),pl(q,s)))
-r@3pl23:=tr3is(cut,pl(pl(p,q),r),pl(p,pl(q,r)),pl(p,pl(r,q)),pl(pl(p,r),q),asspl1(p,q,r),ispl2(pl(q,r),pl(r,q),p,compl(q,r)),asspl2(p,r,q)):is(pl(pl(p,q),r),pl(pl(p,r),q))
-p@a2isapa:=tris(cut,ts(p,pl(1rp,1rp)),pl(ts(p,1rp),ts(p,1rp)),pl(p,p),disttp2(p,1rp,1rp),ispl12(ts(p,1rp),p,ts(p,1rp),p,satz151(p),satz151(p))):is(ts(p,pl(1rp,1rp)),pl(p,p))
-@dif:=pair1type(cut):'type'
-[a1:cut][a2:cut]
-df:=pair1(cut,a1,a2):dif
-@[a:dif]
-stm:=first1(cut,a):cut
-std:=second1(cut,a):cut
-a2@stmis:=first1is1(cut,a1,a2):is(stm(df(a1,a2)),a1)
-isstm:=first1is2(cut,a1,a2):is(a1,stm(df(a1,a2)))
-stdis:=second1is1(cut,a1,a2):is(std(df(a1,a2)),a2)
-isstd:=second1is2(cut,a1,a2):is(a2,std(df(a1,a2)))
-a@1a:=stm(a):cut
-2a:=std(a):cut
-dfis:=pair1is1(cut,a):is"e"(dif,df(1a,2a),a)
-isdf:=pair1is2(cut,a):is"e"(dif,a,df(1a,2a))
-a2@[b1:cut][b2:cut]
-12issmsd:=ispl12(a1,stm(df(a1,a2)),b2,std(df(b1,b2)),isstm(a1,a2),isstd(b1,b2)):is(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))))
-smsdis12:=symis(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),12issmsd):is(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2))
-a@[r1:cut][r2:cut]
-1sdissmsd:=ispl1(r1,stm(df(r1,r2)),2a,isstm(r1,r2)):is(pl(r1,2a),pl(stm(df(r1,r2)),2a))
-smsdis1sd:=symis(cut,pl(r1,2a),pl(stm(df(r1,r2)),2a),1sdissmsd):is(pl(stm(df(r1,r2)),2a),pl(r1,2a))
-sm2issmsd:=ispl2(r2,std(df(r1,r2)),1a,isstd(r1,r2)):is(pl(1a,r2),pl(1a,std(df(r1,r2))))
-smsdissm2:=symis(cut,pl(1a,r2),pl(1a,std(df(r1,r2))),sm2issmsd):is(pl(1a,std(df(r1,r2))),pl(1a,r2))
-a2@[r:cut][i:is(a1,r)]
-issm:=isf(cut,dif,[t:cut]df(t,a2),a1,r,i):is"e"(dif,df(a1,a2),df(r,a2))
-r@[i:is(a2,r)]
-issd:=isf(cut,dif,[t:cut]df(a1,t),a2,r,i):is"e"(dif,df(a1,a2),df(a1,r))
-b2@[i:is(a1,b1)][j:is(a2,b2)]
-issmsd:=tris(dif,df(a1,a2),df(b1,a2),df(b1,b2),issm(a1,a2,b1,i),issd(b1,a2,b2,j)):is"e"(dif,df(a1,a2),df(b1,b2))
-a@[b:dif]
-1b:=stm(b):cut
-2b:=std(b):cut
-eq:=is(pl(1a,2b),pl(1b,2a)):'prop'
-b2@[i:is(pl(a1,b2),pl(b1,a2))]
-eqi12:=tr3is(cut,pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),smsdis12(a1,a2,b1,b2),i,12issmsd(b1,b2,a1,a2)):eq(df(a1,a2),df(b1,b2))
-r2@[i:is(pl(1a,r2),pl(r1,2a))]
-eqi1:=isp(dif,[x:dif]eq(x,df(r1,r2)),df(1a,2a),a,eqi12(1a,2a,r1,r2,i),dfis):eq(a,df(r1,r2))
-r2@[i:is(pl(r1,2a),pl(1a,r2))]
-eqi2:=isp(dif,[x:dif]eq(df(r1,r2),x),df(1a,2a),a,eqi12(r1,r2,1a,2a,i),dfis):eq(df(r1,r2),a)
-b2@[e:eq(df(a1,a2),df(b1,b2))]
-eqe12:=tr3is(cut,pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),12issmsd(a1,a2,b1,b2),e,smsdis12(b1,b2,a1,a2)):is(pl(a1,b2),pl(b1,a2))
-a@satzd163:=refis(cut,pl(1a,2a)):eq(a,a)
-refeq:=satzd163:eq(a,a)
-b@[i:is"e"(dif,a,b)]
-refeq1:=isp(dif,[x:dif]eq(a,x),a,b,refeq,i):eq(a,b)
-refeq2:=isp(dif,[x:dif]eq(x,a),a,b,refeq,i):eq(b,a)
-b2@[i:is(a1,b1)][j:is(a2,b2)]
-eqsmsd:=refeq1(df(a1,a2),df(b1,b2),issmsd(i,j)):eq(df(a1,a2),df(b1,b2))
-r@[i:is(a1,r)]
-eqsm:=refeq1(df(a1,a2),df(r,a2),issm(i)):eq(df(a1,a2),df(r,a2))
-r@[i:is(a2,r)]
-eqsd:=refeq1(df(a1,a2),df(a1,r),issd(i)):eq(df(a1,a2),df(a1,r))
-b@[e:eq(a,b)]
-satzd164:=symis(cut,pl(1a,2b),pl(1b,2a),e):eq(b,a)
-symeq:=satzd164:eq(b,a)
-b@[c:dif]
-1c:=stm(c):cut
-2c:=std(c):cut
-[e:eq(a,b)][f:eq(b,c)]
-+1d165
-t1:=ispl12(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),e,f):is(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
-t2:=tr4is(cut,pl(pl(1a,2c),pl(1b,2b)),pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2b),pl(1b,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2c,1b,2b),t1,compl(pl(1b,2a),pl(1c,2b)),4pl24(1c,2b,1b,2a)):is(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
--1d165
-satzd165:=satz136b(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".1d165"):eq(a,c)
-treq:=satzd165:eq(a,c)
-c@[e:eq(c,a)][f:eq(c,b)]
-treq1:=treq(a,c,b,symeq(c,a,e),f):eq(a,b)
-c@[e:eq(a,c)][f:eq(b,c)]
-treq2:=treq(a,c,b,e,symeq(b,c,f)):eq(a,b)
-c@[d:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)]
-tr3eq:=treq(a,b,d,e1,treq(b,c,d,e2,e3)):eq(a,d)
-d@[e:dif][e1:eq(a,b)][e2:eq(b,c)][e3:eq(c,d)][e4:eq(d,e)]
-tr4eq:=tr3eq(a,b,c,e,e1,e2,treq(c,d,e,e3,e4)):eq(a,e)
-a@posd:=more(1a,2a):'prop'
-zero:=is(1a,2a):'prop'
-negd:=less(1a,2a):'prop'
-a2@[m:more(a1,a2)]
-posdi:=ismore12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),m):posd(df(a1,a2))
-a2@[i:is(a1,a2)]
-zeroi:=tr3is(cut,stm(df(a1,a2)),a1,a2,std(df(a1,a2)),stmis(a1,a2),i,isstd(a1,a2)):zero(df(a1,a2))
-a2@[l:less(a1,a2)]
-negdi:=isless12(a1,stm(df(a1,a2)),a2,std(df(a1,a2)),isstm(a1,a2),isstd(a1,a2),l):negd(df(a1,a2))
-a@axrde:=satz123b(1a,2a):ec3(zero(a),posd(a),negd(a))
-axrdo:=satz123a(1a,2a):or3(zero(a),posd(a),negd(a))
-axrd:=orec3i(zero(a),posd(a),negd(a),axrdo,axrde):orec3(zero(a),posd(a),negd(a))
-[p:'prop'][p1:[t:posd(a)]p][p2:[t:zero(a)]p][p3:[t:negd(a)]p]
-rappd:=or3app(zero(a),posd(a),negd(a),p,axrdo,p2,p1,p3):p
-a@[p:posd(a)]
-pnot0d:=ec3e21(zero(a),posd(a),negd(a),axrde,p):not(zero(a))
-pnotnd:=ec3e23(zero(a),posd(a),negd(a),axrde,p):not(negd(a))
-a@[z:zero(a)]
-0notpd:=ec3e12(zero(a),posd(a),negd(a),axrde,z):not(posd(a))
-0notnd:=ec3e13(zero(a),posd(a),negd(a),axrde,z):not(negd(a))
-a@[n:negd(a)]
-nnotpd:=ec3e32(zero(a),posd(a),negd(a),axrde,n):not(posd(a))
-nnot0d:=ec3e31(zero(a),posd(a),negd(a),axrde,n):not(zero(a))
-b@[e:eq(a,b)][p:posd(a)]
-+iv1d
-t1:=ismore12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135a(1a,2a,2b,p)):more(pl(1b,2a),pl(2b,2a))
--iv1d
-eqposd:=satz136a(1b,2b,2a,t1".iv1d"):posd(b)
-e@[z:zero(a)]
-+*iv1d
-z@t2:=tr3is(cut,pl(1b,2a),pl(1a,2b),pl(2a,2b),pl(2b,2a),symeq(a,b,e),ispl1(1a,2a,2b,z),compl(2a,2b)):is(pl(1b,2a),pl(2b,2a))
--iv1d
-z@eqzero:=satz136b(1b,2b,2a,t2".iv1d"):zero(b)
-e@[n:negd(a)]
-+*iv1d
-n@t3:=isless12(pl(1a,2b),pl(1b,2a),pl(2a,2b),pl(2b,2a),e,compl(2a,2b),satz135c(1a,2a,2b,n)):less(pl(1b,2a),pl(2b,2a))
--iv1d
-n@eqnegd:=satz136c(1b,2b,2a,t3".iv1d"):negd(b)
-b@[z:zero(a)][y:zero(b)]
-zeroeq:=tris(cut,pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl12(1a,2a,2b,1b,z,symis(cut,1b,2b,y)),compl(2a,1b)):eq(a,b)
-@[r:cut]
-pdofrp:=df(pl(r,1rp),1rp):dif
-ndofrp:=df(1rp,pl(r,1rp)):dif
-[s:cut][i:is(r,s)]
-isrpepd:=refeq1(pdofrp(r),pdofrp(s),isf(cut,dif,[x:cut]pdofrp(x),r,s,i)):eq(pdofrp(r),pdofrp(s))
-isrpend:=refeq1(ndofrp(r),ndofrp(s),isf(cut,dif,[x:cut]ndofrp(x),r,s,i)):eq(ndofrp(r),ndofrp(s))
-s@[e:eq(pdofrp(r),pdofrp(s))]
-+*iv1d
-e@t4:=satz136b(pl(r,1rp),pl(s,1rp),1rp,eqe12(pl(r,1rp),1rp,pl(s,1rp),1rp,e)):is(pl(r,1rp),pl(s,1rp))
--iv1d
-e@isrpipd:=satz136b(r,s,1rp,t4".iv1d"):is(r,s)
-s@[e:eq(ndofrp(r),ndofrp(s))]
-+*iv1d
-e@t5:=satz136e(pl(s,1rp),pl(r,1rp),1rp,eqe12(1rp,pl(r,1rp),1rp,pl(s,1rp),e)):is(pl(s,1rp),pl(r,1rp))
--iv1d
-e@isrpind:=symis(cut,s,r,satz136b(s,r,1rp,t5".iv1d")):is(r,s)
-r@posdirp:=posdi(pl(r,1rp),1rp,ismore1(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133(1rp,r))):posd(pdofrp(r))
-negdirp:=negdi(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):negd(ndofrp(r))
-a@[p:posd(a)]
-rpofpd:=mn(1a,2a,p):cut
-+*iv1d
-p@t6:=tr4is(cut,pl(1a,1rp),pl(pl(rpofpd,2a),1rp),pl(rpofpd,pl(2a,1rp)),pl(rpofpd,pl(1rp,2a)),pl(pl(rpofpd,1rp),2a),ispl1(1a,pl(rpofpd,2a),1rp,satz140f(1a,2a,p)),asspl1(rpofpd,2a,1rp),ispl2(pl(2a,1rp),pl(1rp,2a),rpofpd,compl(2a,1rp)),asspl2(rpofpd,1rp,2a)):is(pl(1a,1rp),pl(pl(rpofpd,1rp),2a))
--iv1d
-p@eqpdrp1:=eqi1(a,pl(rpofpd,1rp),1rp,t6".iv1d"):eq(a,pdofrp(rpofpd(a,p)))
-eqpdrp2:=symeq(a,pdofrp(rpofpd(a,p)),eqpdrp1):eq(pdofrp(rpofpd(a,p)),a)
-a@[n:negd(a)]
-rpofnd:=mn(2a,1a,satz122(1a,2a,n)):cut
-+*iv1d
-n@t7:=tr3is(cut,pl(1a,pl(rpofnd,1rp)),pl(pl(1a,rpofnd),1rp),pl(2a,1rp),pl(1rp,2a),asspl2(1a,rpofnd,1rp),ispl1(pl(1a,rpofnd),2a,1rp,satz140c(2a,1a,satz122(1a,2a,n))),compl(2a,1rp)):is(pl(1a,pl(rpofnd,1rp)),pl(1rp,2a))
--iv1d
-n@eqndrp1:=eqi1(a,1rp,pl(rpofnd,1rp),t7".iv1d"):eq(a,ndofrp(rpofnd(a,n)))
-eqndrp2:=symeq(a,ndofrp(rpofnd(a,n)),eqndrp1):eq(ndofrp(rpofnd(a,n)),a)
-@[h:dif][p:posd(h)][k:dif][q:posd(k)][e:eq(h,k)]
-+*iv1d
-e@t8:=tr3eq(pdofrp(rpofpd(h,p)),h,k,pdofrp(rpofpd(k,q)),eqpdrp2(h,p),e,eqpdrp1(k,q)):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
--iv1d
-e@eqpderp:=isrpipd(rpofpd(h,p),rpofpd(k,q),t8".iv1d"):is(rpofpd(h,p),rpofpd(k,q))
-q@[i:is(rpofpd(h,p),rpofpd(k,q))]
-+*iv1d
-i@t9:=isrpepd(rpofpd(h,p),rpofpd(k,q),i):eq(pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)))
--iv1d
-i@eqpdirp:=tr3eq(h,pdofrp(rpofpd(h,p)),pdofrp(rpofpd(k,q)),k,eqpdrp1(h,p),t9".iv1d",eqpdrp2(k,q)):eq(h,k)
-h@[n:negd(h)][k:dif][o:negd(k)][e:eq(h,k)]
-+*iv1d
-e@t10:=tr3eq(ndofrp(rpofnd(h,n)),h,k,ndofrp(rpofnd(k,o)),eqndrp2(h,n),e,eqndrp1(k,o)):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
--iv1d
-e@eqnderp:=isrpind(rpofnd(h,n),rpofnd(k,o),t10".iv1d"):is(rpofnd(h,n),rpofnd(k,o))
-o@[i:is(rpofnd(h,n),rpofnd(k,o))]
-+*iv1d
-i@t11:=isrpend(rpofnd(h,n),rpofnd(k,o),i):eq(ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)))
--iv1d
-i@eqndirp:=tr3eq(h,ndofrp(rpofnd(h,n)),ndofrp(rpofnd(k,o)),k,eqndrp1(h,n),t11".iv1d",eqndrp2(k,o)):eq(h,k)
-@[r:cut]
-+*iv1d
-r@t12:=eqpdrp1(pdofrp(r),posdirp(r)):eq(pdofrp(r),pdofrp(rpofpd(pdofrp(r),posdirp(r))))
--iv1d
-r@isrppd1:=isrpipd(r,rpofpd(pdofrp(r),posdirp(r)),t12".iv1d"):is(r,rpofpd(pdofrp(r),posdirp(r)))
-isrppd2:=symis(cut,r,rpofpd(pdofrp(r),posdirp(r)),isrppd1):is(rpofpd(pdofrp(r),posdirp(r)),r)
-+*iv1d
-r@t13:=eqndrp1(ndofrp(r),negdirp(r)):eq(ndofrp(r),ndofrp(rpofnd(ndofrp(r),negdirp(r))))
--iv1d
-r@isrpnd1:=isrpind(r,rpofnd(ndofrp(r),negdirp(r)),t13".iv1d"):is(r,rpofnd(ndofrp(r),negdirp(r)))
-isrpnd2:=symis(cut,r,rpofnd(ndofrp(r),negdirp(r)),isrpnd1):is(rpofnd(ndofrp(r),negdirp(r)),r)
-a2@[r:cut]
-lemmad1:=eqi12(a1,a2,pl(a1,r),pl(a2,r),tris(cut,pl(a1,pl(a2,r)),pl(a1,pl(r,a2)),pl(pl(a1,r),a2),ispl2(pl(a2,r),pl(r,a2),a1,compl(a2,r)),asspl2(a1,r,a2))):eq(df(a1,a2),df(pl(a1,r),pl(a2,r)))
-lemmad2:=symeq(df(a1,a2),df(pl(a1,r),pl(a2,r)),lemmad1):eq(df(pl(a1,r),pl(a2,r)),df(a1,a2))
-a@[r:cut]
-lemmad3:=treq(a,df(1a,2a),df(pl(1a,r),pl(2a,r)),refeq1(a,df(1a,2a),isdf),lemmad1(1a,2a,r)):eq(a,df(pl(1a,r),pl(2a,r)))
-lemmad4:=symeq(a,df(pl(1a,r),pl(2a,r)),lemmad3):eq(df(pl(1a,r),pl(2a,r)),a)
-a@absd:=ite(negd(a),dif,df(2a,1a),a):dif
-[n:negd(a)]
-absnd:=refeq1(absd(a),df(2a,1a),itet(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),df(2a,1a))
-a@[n:not(negd(a))]
-absnnd:=refeq1(absd(a),a,itef(negd(a),dif,df(2a,1a),a,n)):eq(absd(a),a)
-a2@[l:less(a1,a2)]
-absdeql:=treq(absd(df(a1,a2)),df(std(df(a1,a2)),stm(df(a1,a2))),df(a2,a1),absnd(df(a1,a2),negdi(a1,a2,l)),eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2))):eq(absd(df(a1,a2)),df(a2,a1))
-a2@[m:moreis(a1,a2)]
-absdeqm:=absnnd(df(a1,a2),th3"l.imp"(negd(df(a1,a2)),less(a1,a2),satz123c(a1,a2,m),[t:negd(df(a1,a2))]isless12(stm(df(a1,a2)),a1,std(df(a1,a2)),a2,stmis(a1,a2),stdis(a1,a2),t))):eq(absd(df(a1,a2)),df(a1,a2))
-b@[e:eq(a,b)]
-+iv2d
-[n:negd(a)]
-t1:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
-t2:=tr3eq(absd(a),df(2a,1a),df(2b,1b),absd(b),absnd(a,n),eqi12(2a,1a,2b,1b,t1),symeq(absd(b),df(2b,1b),absnd(b,eqnegd(a,b,e,n)))):eq(absd(a),absd(b))
-e@[n:not(negd(a))]
-t3:=tr3eq(absd(a),a,b,absd(b),absnnd(a,n),e,symeq(absd(b),b,absnnd(b,th3"l.imp"(negd(b),negd(a),n,[t:negd(b)]eqnegd(b,a,symeq(a,b,e),t))))):eq(absd(a),absd(b))
--iv2d
-eqabsd:=th1"l.imp"(negd(a),eq(absd(a),absd(b)),[t:negd(a)]t2".iv2d"(t),[t:not(negd(a))]t3".iv2d"(t)):eq(absd(a),absd(b))
-a@[p:posd(a)]
-satzd166a:=eqposd(a,absd(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p))),p):posd(absd(a))
-a@[n:negd(a)]
-+2d166
-t1:=posdi(2a,1a,satz122(1a,2a,n)):posd(df(2a,1a))
--2d166
-satzd166b:=eqposd(df(2a,1a),absd(a),symeq(absd(a),df(2a,1a),absnd(a,n)),t1".2d166"):posd(absd(a))
-b@[p:posd(a)][q:posd(b)][e:eq(absd(a),absd(b))]
-satzd166c:=tr3eq(a,absd(a),absd(b),b,symeq(absd(a),a,absnnd(a,pnotnd(a,p))),e,absnnd(b,pnotnd(b,q))):eq(a,b)
-b@[n:negd(a)][o:negd(b)][e:eq(absd(a),absd(b))]
-+*2d166
-e@t2:=tr3eq(df(2a,1a),absd(a),absd(b),df(2b,1b),symeq(absd(a),df(2a,1a),absnd(a,n)),e,absnd(b,o)):eq(df(2a,1a),df(2b,1b))
--2d166
-e@satzd166d:=tr3is(cut,pl(1a,2b),pl(2b,1a),pl(2a,1b),pl(1b,2a),compl(1a,2b),symis(cut,pl(2a,1b),pl(2b,1a),eqe12(2a,1a,2b,1b,t2".2d166")),compl(2a,1b)):eq(a,b)
-a@[n:not(zero(a))]
-satzd166e:=rappd(a,posd(absd(a)),[t:posd(a)]satzd166a(a,t),th2"l.imp"(zero(a),posd(absd(a)),n),[t:negd(a)]satzd166b(a,t)):posd(absd(a))
-a@[z:zero(a)]
-satzd166f:=eqzero(a,absd(a),symeq(absd(a),a,absnnd(a,0notnd(a,z))),z):zero(absd(a))
-b@mored:=more(pl(1a,2b),pl(1b,2a)):'prop'
-b2@[m:more(pl(a1,b2),pl(b1,a2))]
-moredi12:=ismore12(pl(a1,b2),pl(stm(df(a1,a2)),std(df(b1,b2))),pl(b1,a2),pl(stm(df(b1,b2)),std(df(a1,a2))),12issmsd(a1,a2,b1,b2),12issmsd(b1,b2,a1,a2),m):mored(df(a1,a2),df(b1,b2))
-r2@[m:more(pl(1a,r2),pl(r1,2a))]
-moredi1:=ismore12(pl(1a,r2),pl(1a,std(df(r1,r2))),pl(r1,2a),pl(stm(df(r1,r2)),2a),sm2issmsd(a,r1,r2),1sdissmsd(a,r1,r2),m):mored(a,df(r1,r2))
-r2@[m:more(pl(r1,2a),pl(1a,r2))]
-moredi2:=ismore12(pl(r1,2a),pl(stm(df(r1,r2)),2a),pl(1a,r2),pl(1a,std(df(r1,r2))),1sdissmsd(a,r1,r2),sm2issmsd(a,r1,r2),m):mored(df(r1,r2),a)
-b2@[m:mored(df(a1,a2),df(b1,b2))]
-morede12:=ismore12(pl(stm(df(a1,a2)),std(df(b1,b2))),pl(a1,b2),pl(stm(df(b1,b2)),std(df(a1,a2))),pl(b1,a2),smsdis12(a1,a2,b1,b2),smsdis12(b1,b2,a1,a2),m):more(pl(a1,b2),pl(b1,a2))
-b@lessd:=less(pl(1a,2b),pl(1b,2a)):'prop'
-[m:mored(a,b)]
-lemmad5:=satz121(pl(1a,2b),pl(1b,2a),m):lessd(b,a)
-b@[l:lessd(a,b)]
-lemmad6:=satz122(pl(1a,2b),pl(1b,2a),l):mored(b,a)
-b2@[l:less(pl(a1,b2),pl(b1,a2))]
-lessdi12:=lemmad5(df(b1,b2),df(a1,a2),moredi12(b1,b2,a1,a2,satz122(pl(a1,b2),pl(b1,a2),l))):lessd(df(a1,a2),df(b1,b2))
-r2@[l:less(pl(1a,r2),pl(r1,2a))]
-lessdi1:=lemmad5(df(r1,r2),a,moredi2(a,r1,r2,satz122(pl(1a,r2),pl(r1,2a),l))):lessd(a,df(r1,r2))
-r2@[l:less(pl(r1,2a),pl(1a,r2))]
-lessdi2:=lemmad5(a,df(r1,r2),moredi1(a,r1,r2,satz122(pl(r1,2a),pl(1a,r2),l))):lessd(df(r1,r2),a)
-b2@[l:lessd(df(a1,a2),df(b1,b2))]
-lessde12:=satz121(pl(b1,a2),pl(a1,b2),morede12(b1,b2,a1,a2,lemmad6(df(a1,a2),df(b1,b2),l))):less(pl(a1,b2),pl(b1,a2))
-b@satzd167:=satz123(pl(1a,2b),pl(1b,2a)):orec3(eq(a,b),mored(a,b),lessd(a,b))
-satzd167a:=satz123a(pl(1a,2b),pl(1b,2a)):or3(eq(a,b),mored(a,b),lessd(a,b))
-satzd167b:=satz123b(pl(1a,2b),pl(1b,2a)):ec3(eq(a,b),mored(a,b),lessd(a,b))
-d@1d:=stm(d):cut
-2d:=std(d):cut
-[e:eq(a,b)][f:eq(c,d)][m:mored(a,c)]
-+*iv2d
-m@t4:=tr4is(cut,pl(pl(1b,2d),pl(1c,2a)),pl(pl(1b,2a),pl(1c,2d)),pl(pl(1a,2b),pl(1d,2c)),pl(pl(1a,2c),pl(1d,2b)),pl(pl(1d,2b),pl(1a,2c)),4pl24(1b,2d,1c,2a),ispl12(pl(1b,2a),pl(1a,2b),pl(1c,2d),pl(1d,2c),symeq(a,b,e),f),4pl24(1a,2b,1d,2c),compl(pl(1a,2c),pl(1d,2b))):is(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)))
-t5:=ismore2(pl(pl(1b,2d),pl(1c,2a)),pl(pl(1d,2b),pl(1a,2c)),pl(pl(1b,2d),pl(1a,2c)),t4,satz135d(pl(1a,2c),pl(1c,2a),pl(1b,2d),m)):more(pl(pl(1b,2d),pl(1a,2c)),pl(pl(1d,2b),pl(1a,2c)))
--iv2d
-m@eqmored12:=satz136a(pl(1b,2d),pl(1d,2b),pl(1a,2c),t5".iv2d"):mored(b,d)
-f@[l:lessd(a,c)]
-eqlessd12:=lemmad5(d,b,eqmored12(c,d,a,b,f,e,lemmad6(a,c,l))):lessd(b,d)
-c@[e:eq(a,b)][m:mored(a,c)]
-eqmored1:=eqmored12(a,b,c,c,e,refeq(c),m):mored(b,c)
-e@[m:mored(c,a)]
-eqmored2:=eqmored12(c,c,a,b,refeq(c),e,m):mored(c,b)
-e@[l:lessd(a,c)]
-eqlessd1:=eqlessd12(a,b,c,c,e,refeq(c),l):lessd(b,c)
-e@[l:lessd(c,a)]
-eqlessd2:=eqlessd12(c,c,a,b,refeq(c),e,l):lessd(c,b)
-b@moreq:=or(mored(a,b),eq(a,b)):'prop'
-lesseq:=or(lessd(a,b),eq(a,b)):'prop'
-[m:moreq(a,b)]
-satzd168a:=th9"l.or"(mored(a,b),eq(a,b),lessd(b,a),eq(b,a),m,[t:mored(a,b)]lemmad5(a,b,t),[t:eq(a,b)]symeq(a,b,t)):lesseq(b,a)
-b@[l:lesseq(a,b)]
-satzd168b:=th9"l.or"(lessd(a,b),eq(a,b),mored(b,a),eq(b,a),l,[t:lessd(a,b)]lemmad6(a,b,t),[t:eq(a,b)]symeq(a,b,t)):moreq(b,a)
-c@[e:eq(a,b)][m:moreq(a,c)]
-eqmoreq1:=th9"l.or"(mored(a,c),eq(a,c),mored(b,c),eq(b,c),m,[t:mored(a,c)]eqmored1(a,b,c,e,t),[t:eq(a,c)]treq1(b,c,a,e,t)):moreq(b,c)
-e@[m:moreq(c,a)]
-eqmoreq2:=th9"l.or"(mored(c,a),eq(c,a),mored(c,b),eq(c,b),m,[t:mored(c,a)]eqmored2(a,b,c,e,t),[t:eq(c,a)]treq(c,a,b,t,e)):moreq(c,b)
-e@[l:lesseq(a,c)]
-eqlesseq1:=satzd168a(c,b,eqmoreq2(a,b,c,e,satzd168b(a,c,l))):lesseq(b,c)
-e@[l:lesseq(c,a)]
-eqlesseq2:=satzd168a(b,c,eqmoreq1(a,b,c,e,satzd168b(c,a,l))):lesseq(c,b)
-d@[e:eq(a,b)][f:eq(c,d)][m:moreq(a,c)]
-eqmoreq12:=eqmoreq1(a,b,d,e,eqmoreq2(c,d,a,f,m)):moreq(b,d)
-f@[l:lesseq(a,c)]
-eqlesseq12:=eqlesseq1(a,b,d,e,eqlesseq2(c,d,a,f,l)):lesseq(b,d)
-b@[m:mored(a,b)]
-moreqi1:=ori1(mored(a,b),eq(a,b),m):moreq(a,b)
-b@[l:lessd(a,b)]
-lesseqi1:=ori1(lessd(a,b),eq(a,b),l):lesseq(a,b)
-b@[e:eq(a,b)]
-moreqi2:=ori2(mored(a,b),eq(a,b),e):moreq(a,b)
-lesseqi2:=ori2(lessd(a,b),eq(a,b),e):lesseq(a,b)
-b@[m:moreq(a,b)]
-satzd167c:=th7"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,comor(mored(a,b),eq(a,b),m)):not(lessd(a,b))
-b@[l:lesseq(a,b)]
-satzd167d:=th9"l.ec3"(eq(a,b),mored(a,b),lessd(a,b),satzd167b,l):not(mored(a,b))
-b@[n:not(mored(a,b))]
-satzd167e:=th2"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n):lesseq(a,b)
-b@[n:not(lessd(a,b))]
-satzd167f:=comor(eq(a,b),mored(a,b),th3"l.or3"(eq(a,b),mored(a,b),lessd(a,b),satzd167a,n)):moreq(a,b)
-b@[m:mored(a,b)]
-satzd167g:=th3"l.imp"(lesseq(a,b),not(mored(a,b)),weli(mored(a,b),m),[t:lesseq(a,b)]satzd167d(t)):not(lesseq(a,b))
-b@[l:lessd(a,b)]
-satzd167h:=th3"l.imp"(moreq(a,b),not(lessd(a,b)),weli(lessd(a,b),l),[t:moreq(a,b)]satzd167c(t)):not(moreq(a,b))
-b@[n:not(moreq(a,b))]
-satzd167j:=or3e3(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th5"l.or"(mored(a,b),eq(a,b),n),th4"l.or"(mored(a,b),eq(a,b),n)):lessd(a,b)
-b@[n:not(lesseq(a,b))]
-satzd167k:=or3e2(eq(a,b),mored(a,b),lessd(a,b),satzd167a,th4"l.or"(lessd(a,b),eq(a,b),n),th5"l.or"(lessd(a,b),eq(a,b),n)):mored(a,b)
-b@[z:zero(b)][p:posd(a)]
-satzd169a:=ismore12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135a(1a,2a,1b,p)):mored(a,b)
-z@[m:mored(a,b)]
-satzd169b:=satz136d(1a,2a,2b,ismore12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),m)):posd(a)
-z@[n:negd(a)]
-satzd169c:=isless12(pl(1a,1b),pl(1a,2b),pl(2a,1b),pl(1b,2a),ispl2(1b,2b,1a,z),compl(2a,1b),satz135c(1a,2a,1b,n)):lessd(a,b)
-z@[l:lessd(a,b)]
-satzd169d:=satz136f(1a,2a,2b,isless12(pl(1a,2b),pl(2b,1a),pl(1b,2a),pl(2b,2a),compl(1a,2b),ispl1(1b,2b,2a,z),l)):negd(a)
-+2d170
-z@[p:posd(a)]
-t1:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166a(a,p))):moreq(absd(a),b)
-z@[y:zero(a)]
-t2:=moreqi2(absd(a),b,treq(absd(a),a,b,absnnd(a,0notnd(a,y)),zeroeq(a,b,y,z))):moreq(absd(a),b)
-z@[n:negd(a)]
-t3:=moreqi1(absd(a),b,satzd169a(absd(a),b,z,satzd166b(a,n))):moreq(absd(a),b)
--2d170
-z@satzd170:=rappd(a,moreq(absd(a),b),[t:posd(a)]t1".2d170"(t),[t:zero(a)]t2".2d170"(t),[t:negd(a)]t3".2d170"(t)):moreq(absd(a),b)
-c@[l:lessd(a,b)][k:lessd(b,c)]
-+2d171
-t1:=satz137a(pl(1a,2b),pl(1b,2a),pl(1b,2c),pl(1c,2b),l,k):less(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1b,2a),pl(1c,2b)))
-t2:=isless12(pl(pl(1a,2b),pl(1b,2c)),pl(pl(1a,2c),pl(1b,2b)),pl(pl(1b,2a),pl(1c,2b)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1a,2b,1b,2c),tris(cut,pl(pl(1b,2a),pl(1c,2b)),pl(pl(1b,2b),pl(1c,2a)),pl(pl(1c,2a),pl(1b,2b)),4pl24(1b,2a,1c,2b),compl(pl(1b,2b),pl(1c,2a))),t1):less(pl(pl(1a,2c),pl(1b,2b)),pl(pl(1c,2a),pl(1b,2b)))
--2d171
-satzd171:=satz136c(pl(1a,2c),pl(1c,2a),pl(1b,2b),t2".2d171"):lessd(a,c)
-trlessd:=satzd171:lessd(a,c)
-c@[m:mored(a,b)][n:mored(b,c)]
-trmored:=lemmad6(c,a,trlessd(c,b,a,lemmad5(b,c,n),lemmad5(a,b,m))):mored(a,c)
-c@[l:lesseq(a,b)][k:lessd(b,c)]
-satzd172a:=orapp(lessd(a,b),eq(a,b),lessd(a,c),l,[t:lessd(a,b)]trlessd(t,k),[t:eq(a,b)]eqlessd1(b,a,c,symeq(a,b,t),k)):lessd(a,c)
-c@[l:lessd(a,b)][k:lesseq(b,c)]
-satzd172b:=orapp(lessd(b,c),eq(b,c),lessd(a,c),k,[t:lessd(b,c)]trlessd(l,t),[t:eq(b,c)]eqlessd2(b,c,a,t,l)):lessd(a,c)
-c@[m:moreq(a,b)][n:mored(b,c)]
-satzd172c:=lemmad6(c,a,satzd172b(c,b,a,lemmad5(b,c,n),satzd168a(a,b,m))):mored(a,c)
-c@[m:mored(a,b)][n:moreq(b,c)]
-satzd172d:=lemmad6(c,a,satzd172a(c,b,a,satzd168a(b,c,n),lemmad5(a,b,m))):mored(a,c)
-c@[l:lesseq(a,b)][k:lesseq(b,c)]
-+2d173
-[j:lessd(a,b)]
-t1:=lesseqi1(a,c,satzd172b(j,k)):lesseq(a,c)
-k@[e:eq(a,b)]
-t2:=eqlesseq1(b,a,c,symeq(a,b,e),k):lesseq(a,c)
--2d173
-satzd173:=orapp(lessd(a,b),eq(a,b),lesseq(a,c),l,[t:lessd(a,b)]t1".2d173"(t),[t:eq(a,b)]t2".2d173"(t)):lesseq(a,c)
-trlesseq:=satzd173:lesseq(a,c)
-c@[m:moreq(a,b)][n:moreq(b,c)]
-trmoreq:=satzd168b(c,a,trlesseq(c,b,a,satzd168a(b,c,n),satzd168a(a,b,m))):moreq(a,c)
-a@ratd:=[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))):'prop'
-irratd:=not(ratd(a)):'prop'
-b@[e:eq(a,b)][r:ratd(a)]
-+*iv2d
-r@[n:not(zero(b))]
-t6:=th3"l.imp"(zero(a),zero(b),n,[t:zero(a)]eqzero(a,b,e,t)):not(zero(a))
-t7:=eqpderp(absd(a),satzd166e(a,t6),absd(b),satzd166e(b,n),eqabsd(a,b,e)):is(rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)))
-t8:=isp(cut,[t:cut]ratrp(t),rpofpd(absd(a),satzd166e(a,t6)),rpofpd(absd(b),satzd166e(b,n)),<t6>r,t7):ratrp(rpofpd(absd(b),satzd166e(b,n)))
--iv2d
-r@eqratd:=[t:not(zero(b))]t8".iv2d"(t):ratd(b)
-e@[i:irratd(a)]
-eqirratd:=th3"l.imp"(ratd(b),ratd(a),i,[t:ratd(b)]eqratd(b,a,symeq(a,b,e),t)):irratd(b)
-a@[z:zero(a)]
-ratdi0:=th2"l.r.imp"(not(zero(a)),[t:not(zero(a))]ratrp(rpofpd(absd(a),satzd166e(a,t))),weli(zero(a),z)):ratd(a)
-@[r:cut][i:irratrp(r)][x0:rat]
-+*iv2d
-x0@[s:ratrp(pl(r,rpofrt(x0)))][y0:rat][j:is(pl(r,rpofrt(x0)),rpofrt(y0))]
-t9:=tris(cut,pl(rpofrt(x0),r),pl(r,rpofrt(x0)),rpofrt(y0),compl(rpofrt(x0),r),j):is(pl(rpofrt(x0),r),rpofrt(y0))
-t10:=ismore1(pl(rpofrt(x0),r),rpofrt(y0),rpofrt(x0),t9,satz133(rpofrt(x0),r)):more(rpofrt(y0),rpofrt(x0))
-t11:=satz154d(y0,x0,t10):more"rt"(y0,x0)
-t12:=satz155b(y0,x0,t11):is(rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
-t13:=satz140g(rpofrt(y0),rpofrt(x0),r,satz154a(y0,x0,t11),t9):is(r,mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)))
-t14:=tris2(cut,r,rpofrt(mn"rt"(y0,x0,t11)),mn(rpofrt(y0),rpofrt(x0),satz154a(y0,x0,t11)),t13,t12):is(r,rpofrt(mn"rt"(y0,x0,t11)))
-t15:=somei(rat,[x:rat]is(r,rpofrt(x)),mn"rt"(y0,x0,t11),t14):ratrp(r)
-s@t16:=someapp(rat,[x:rat]is(pl(r,rpofrt(x0)),rpofrt(x)),s,con,[x:rat][t:is(pl(r,rpofrt(x0)),rpofrt(x))]<t15(x,t)>i):con
--iv2d
-x0@remark1:=[t:ratrp(pl(r,rpofrt(x0)))]t16".iv2d"(t):irratrp(pl(r,rpofrt(x0)))
-+*iv2d
-r@rp:=pdofrp(r):dif
-rn:=ndofrp(r):dif
-t17:=posdirp(r):posd(rp)
-t18:=pnot0d(rp,t17):not(zero(rp))
-t19:=nnot0d(rn,negdirp(r)):not(zero(rn))
-[n:not(zero(rp))]
-t20:=tris2(cut,r,rpofpd(absd(rp),satzd166e(rp,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rp),satzd166e(rp,n),rp,t17,absnnd(rp,pnotnd(rp,t17)))):is(r,rpofpd(absd(rp),satzd166e(rp,n)))
-r@t21:=treq(absd(rn),df(std(rn),stm(rn)),rp,absnd(rn,negdirp(r)),eqsmsd(std(rn),stm(rn),pl(r,1rp),1rp,stdis(1rp,pl(r,1rp)),stmis(1rp,pl(r,1rp)))):eq(absd(rn),rp)
-[n:not(zero(rn))]
-t22:=tris2(cut,r,rpofpd(absd(rn),satzd166e(rn,n)),rpofpd(rp,t17),isrppd1(r),eqpderp(absd(rn),satzd166e(rn,n),rp,t17,t21)):is(r,rpofpd(absd(rn),satzd166e(rn,n)))
-r@[s:cut][i:is(r,s)][rr:ratrp(r)]
-t23:=isp(cut,[x:cut]ratrp(x),r,s,rr,i):ratrp(s)
-i@[rs:ratrp(s)]
-t24:=isp1(cut,[x:cut]ratrp(x),s,r,rs,i):ratrp(r)
--iv2d
-r@[rr:ratrp(r)]
-remark2a:=[t:not(zero(pdofrp(r)))]t23".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t)),t20".iv2d"(t),rr):ratd(pdofrp(r))
-remark2b:=t17".iv2d":posd(pdofrp(r))
-remark3a:=[t:not(zero(ndofrp(r)))]t23".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t)),t22".iv2d"(t),rr):ratd(ndofrp(r))
-remark3b:=negdirp(r):negd(ndofrp(r))
-r@[i:irratrp(r)]
-remark4a:=th3"l.imp"(ratd(pdofrp(r)),ratrp(r),i,[t:ratd(pdofrp(r))]t24".iv2d"(rpofpd(absd(pdofrp(r)),satzd166e(pdofrp(r),t18".iv2d")),t20".iv2d"(t18".iv2d"),<t18".iv2d">t)):irratd(pdofrp(r))
-remark4b:=t17".iv2d":posd(pdofrp(r))
-remark5a:=th3"l.imp"(ratd(ndofrp(r)),ratrp(r),i,[t:ratd(ndofrp(r))]t24".iv2d"(rpofpd(absd(ndofrp(r)),satzd166e(ndofrp(r),t19".iv2d")),t22".iv2d"(t19".iv2d"),<t19".iv2d">t)):irratd(ndofrp(r))
-remark5b:=negdirp(r):negd(ndofrp(r))
-a@natd:=and(posd(a),[t:posd(a)]natrp(rpofpd(a,t))):'prop'
-[n:natd(a)]
-natposd:=ande1(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):posd(a)
-natderp:=ande2"l.r"(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),n):natrp(rpofpd(a,natposd(a,n)))
-b@[e:eq(a,b)][n:natd(a)]
-+*iv2d
-n"rp"@t25:=eqposd(a,b,e,natposd(a,n)):posd(b)
-[p:posd(b)]
-t26:=eqpderp(a,natposd(a,n),b,p,e):is(rpofpd(a,natposd(a,n)),rpofpd(b,p))
-t27:=isp(cut,[t:cut]natrp(t),rpofpd(a,natposd(a,n)),rpofpd(b,p),natderp(a,n),t26):natrp(rpofpd(b,p))
--iv2d
-n@eqnatd:=andi(posd(b),[t:posd(b)]natrp(rpofpd(b,t)),t25".iv2d",[t:posd(b)]t27".iv2d"(t)):natd(b)
-@[x:nat]
-pdofnt:=pdofrp(rpofnt(x)):dif
-+*iv2d
-x@t28:=posdirp(rpofnt(x)):posd(pdofnt(x))
-[p:posd(pdofnt(x))]
-t29:=isrppd1(rpofnt(x)):is(rpofnt(x),rpofpd(pdofnt(x),t28))
-t30:=eqpderp(pdofnt(x),t28,pdofnt(x),p,refeq(pdofnt(x))):is(rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p))
-t31:=tris(cut,rpofnt(x),rpofpd(pdofnt(x),t28),rpofpd(pdofnt(x),p),t29,t30):is(rpofnt(x),rpofpd(pdofnt(x),p))
-t32:=isp(cut,[t:cut]natrp(t),rpofnt(x),rpofpd(pdofnt(x),p),natrpi(x),t31):natrp(rpofpd(pdofnt(x),p))
--iv2d
-x@natdi:=andi(posd(pdofnt(x)),[t:posd(pdofnt(x))]natrp(rpofpd(pdofnt(x),t)),t28".iv2d",[t:posd(pdofnt(x))]t32".iv2d"(t)):natd(pdofnt(x))
-a@intd:=or(zero(a),natd(absd(a))):'prop'
-b@[e:eq(a,b)][i:intd(a)]
-+*iv2d
-i"rp"@[z:zero(a)]
-t33:=eqzero(a,b,e,z):zero(b)
-i"rp"@[n:natd(absd(a))]
-t34:=eqnatd(absd(a),absd(b),eqabsd(a,b,e),n):natd(absd(b))
--iv2d
-i@eqintd:=th9"l.or"(zero(a),natd(absd(a)),zero(b),natd(absd(b)),i,[t:zero(a)]t33".iv2d"(t),[t:natd(absd(a))]t34".iv2d"(t)):intd(b)
-a@[n:natd(a)]
-+*iv2d
-n"rp"@t34a:=symeq(absd(a),a,absnnd(a,pnotnd(a,natposd(a,n)))):eq(a,absd(a))
-t35:=eqnatd(a,absd(a),t34a,n):natd(absd(a))
--iv2d
-n@natintd:=ori2(zero(a),natd(absd(a)),t35".iv2d"):intd(a)
-a@[p:posd(a)][i:intd(a)]
-+*iv2d
-i"rp"@t36:=ore2(zero(a),natd(absd(a)),i,pnot0d(a,p)):natd(absd(a))
--iv2d
-i@posintnatd:=eqnatd(absd(a),a,absnnd(a,pnotnd(a,p)),t36".iv2d"):natd(a)
-a@[z:zero(a)]
-intdi0:=ori1(zero(a),natd(absd(a)),z):intd(a)
-r@[n:natrp(r)]
-+*iv2d
-n"rp"@t37:=posdirp(r):posd(pdofrp(r))
-[p:posd(pdofrp(r))]
-t38:=tris(cut,r,rpofpd(pdofrp(r),t37),rpofpd(pdofrp(r),p),isrppd1(r),eqpderp(pdofrp(r),t37,pdofrp(r),p,refeq(pdofrp(r)))):is(r,rpofpd(pdofrp(r),p))
-t39:=isp(cut,[t:cut]natrp(t),r,rpofpd(pdofrp(r),p),n,t38):natrp(rpofpd(pdofrp(r),p))
--iv2d
-n@remark6a:=andi(posd(pdofrp(r)),[t:posd(pdofrp(r))]natrp(rpofpd(pdofrp(r),t)),t37".iv2d",[t:posd(pdofrp(r))]t39".iv2d"(t)):natd(pdofrp(r))
-remark6:=natintd(pdofrp(r),remark6a):intd(pdofrp(r))
-+*iv2d
-n"rp"@t40:=absdeql(1rp,pl(r,1rp),isless2(pl(1rp,r),pl(r,1rp),1rp,compl(1rp,r),satz133a(1rp,r))):eq(absd(ndofrp(r)),pdofrp(r))
-t41:=eqnatd(pdofrp(r),absd(ndofrp(r)),symeq(absd(ndofrp(r)),pdofrp(r),t40),remark6a):natd(absd(ndofrp(r)))
--iv2d
-n@remark7:=ori2(zero(ndofrp(r)),natd(absd(ndofrp(r))),t41".iv2d"):intd(ndofrp(r))
-a@[i:intd(a)]
-+2d174
-[n:not(zero(a))]
-t1:=ore2(zero(a),natd(absd(a)),i,n):natd(absd(a))
-t2:=ande2(posd(absd(a)),[t:posd(absd(a))]natrp(rpofpd(absd(a),t)),t1):[t:posd(absd(a))]natrp(rpofpd(absd(a),t))
-t3:=lemmaiii5(rpofpd(absd(a),satzd166e(a,n)),<satzd166e(a,n)>t2):ratrp(rpofpd(absd(a),satzd166e(a,n)))
--2d174
-satzd174:=[t:not(zero(a))]t3".2d174"(t):ratd(a)
-b@pd:=df(pl(1a,1b),pl(2a,2b)):dif
-b2@pd12:=issmsd(pl(stm(df(a1,a2)),stm(df(b1,b2))),pl(std(df(a1,a2)),std(df(b1,b2))),pl(a1,b1),pl(a2,b2),ispl12(stm(df(a1,a2)),a1,stm(df(b1,b2)),b1,stmis(a1,a2),stmis(b1,b2)),ispl12(std(df(a1,a2)),a2,std(df(b1,b2)),b2,stdis(a1,a2),stdis(b1,b2))):is"e"(dif,pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
-r2@pd1:=issmsd(pl(1a,stm(df(r1,r2))),pl(2a,std(df(r1,r2))),pl(1a,r1),pl(2a,r2),ispl2(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl2(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
-pd2:=issmsd(pl(stm(df(r1,r2)),1a),pl(std(df(r1,r2)),2a),pl(r1,1a),pl(r2,2a),ispl1(stm(df(r1,r2)),r1,1a,stmis(r1,r2)),ispl1(std(df(r1,r2)),r2,2a,stdis(r1,r2))):is"e"(dif,pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
-b2@pdeq12a:=refeq1(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)))
-pdeq12b:=refeq2(pd(df(a1,a2),df(b1,b2)),df(pl(a1,b1),pl(a2,b2)),pd12):eq(df(pl(a1,b1),pl(a2,b2)),pd(df(a1,a2),df(b1,b2)))
-r2@pdeq1a:=refeq1(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)))
-pdeq1b:=refeq2(pd(a,df(r1,r2)),df(pl(1a,r1),pl(2a,r2)),pd1):eq(df(pl(1a,r1),pl(2a,r2)),pd(a,df(r1,r2)))
-pdeq2a:=refeq1(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)))
-pdeq2b:=refeq2(pd(df(r1,r2),a),df(pl(r1,1a),pl(r2,2a)),pd2):eq(df(pl(r1,1a),pl(r2,2a)),pd(df(r1,r2),a))
-b@satzd175:=eqsmsd(pl(1a,1b),pl(2a,2b),pl(1b,1a),pl(2b,2a),compl(1a,1b),compl(2a,2b)):eq(pd(a,b),pd(b,a))
-compd:=satzd175:eq(pd(a,b),pd(b,a))
-c@[e:eq(a,b)]
-+iv3d
-t1:=tr3is(cut,pl(pl(1a,1c),pl(2b,2c)),pl(pl(1a,2b),pl(1c,2c)),pl(pl(1b,2a),pl(1c,2c)),pl(pl(1b,1c),pl(2a,2c)),4pl23(1a,1c,2b,2c),ispl1(pl(1a,2b),pl(1b,2a),pl(1c,2c),e),4pl23(1b,2a,1c,2c)):is(pl(pl(1a,1c),pl(2b,2c)),pl(pl(1b,1c),pl(2a,2c)))
--iv3d
-eqpd1:=eqi12(pl(1a,1c),pl(2a,2c),pl(1b,1c),pl(2b,2c),t1".iv3d"):eq(pd(a,c),pd(b,c))
-eqpd2:=tr3eq(pd(c,a),pd(a,c),pd(b,c),pd(c,b),compd(c,a),eqpd1,compd(b,c)):eq(pd(c,a),pd(c,b))
-d@[e:eq(a,b)][f:eq(c,d)]
-eqpd12:=treq(pd(a,c),pd(b,c),pd(b,d),eqpd1(a,b,c,e),eqpd2(c,d,b,f)):eq(pd(a,c),pd(b,d))
-b@[z:zero(a)]
-+*iv3d
-z@t2:=tr4is(cut,pl(pl(1a,1b),2b),pl(1a,pl(1b,2b)),pl(2a,pl(2b,1b)),pl(pl(2a,2b),1b),pl(1b,pl(2a,2b)),asspl1(1a,1b,2b),ispl12(1a,2a,pl(1b,2b),pl(2b,1b),z,compl(1b,2b)),asspl2(2a,2b,1b),compl(pl(2a,2b),1b)):is(pl(pl(1a,1b),2b),pl(1b,pl(2a,2b)))
--iv3d
-z@pd01:=eqi2(b,pl(1a,1b),pl(2a,2b),t2".iv3d"):eq(pd(a,b),b)
-b@[z:zero(b)]
-pd02:=treq(pd(a,b),pd(b,a),a,compd(a,b),pd01(b,a,z)):eq(pd(a,b),a)
-b@[p:posd(a)][q:posd(b)]
-ppd:=posdi(pl(1a,1b),pl(2a,2b),satz137(1a,2a,1b,2b,p,q)):posd(pd(a,b))
-b@[n:negd(a)][o:negd(b)]
-npd:=negdi(pl(1a,1b),pl(2a,2b),satz137a(1a,2a,1b,2b,n,o)):negd(pd(a,b))
-a@m0d:=df(2a,1a):dif
-a2@m0deqa:=eqsmsd(std(df(a1,a2)),stm(df(a1,a2)),a2,a1,stdis(a1,a2),stmis(a1,a2)):eq(m0d(df(a1,a2)),df(a2,a1))
-m0deqb:=symeq(m0d(df(a1,a2)),df(a2,a1),m0deqa):eq(df(a2,a1),m0d(df(a1,a2)))
-b@[e:eq(a,b)]
-+*iv3d
-e@t3:=tr3is(cut,pl(2a,1b),pl(1b,2a),pl(1a,2b),pl(2b,1a),compl(2a,1b),symeq(a,b,e),compl(1a,2b)):is(pl(2a,1b),pl(2b,1a))
--iv3d
-e@eqm0d:=eqi12(2a,1a,2b,1b,t3".iv3d"):eq(m0d(a),m0d(b))
-a@[p:posd(a)]
-satzd176a:=negdi(2a,1a,satz121(1a,2a,p)):negd(m0d(a))
-a@[z:zero(a)]
-satzd176b:=zeroi(2a,1a,symis(cut,1a,2a,z)):zero(m0d(a))
-a@[n:negd(a)]
-satzd176c:=posdi(2a,1a,satz122(1a,2a,n)):posd(m0d(a))
-a@[n:negd(m0d(a))]
-satzd176d:=satz122(2a,1a,isless12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),n)):posd(a)
-a@[z:zero(m0d(a))]
-satzd176e:=symis(cut,2a,1a,tr3is(cut,2a,stm(df(2a,1a)),std(df(2a,1a)),1a,isstm(2a,1a),z,stdis(2a,1a))):zero(a)
-a@[p:posd(m0d(a))]
-satzd176f:=satz121(2a,1a,ismore12(stm(m0d(a)),2a,std(m0d(a)),1a,stmis(2a,1a),stdis(2a,1a),p)):negd(a)
-a@[z:zero(a)]
-m0d0:=zeroeq(m0d(a),a,satzd176b(a,z),z):eq(m0d(a),a)
-+3d177
-a@t1:=tris(dif,m0d(m0d(a)),df(1a,2a),a,issmsd(std(m0d(a)),stm(m0d(a)),1a,2a,stdis(2a,1a),stmis(2a,1a)),dfis(a)):is"e"(dif,m0d(m0d(a)),a)
--3d177
-a@satzd177:=refeq1(m0d(m0d(a)),a,t1".3d177"):eq(m0d(m0d(a)),a)
-satzd177a:=symeq(m0d(m0d(a)),a,satzd177):eq(a,m0d(m0d(a)))
-b@[e:eq(a,m0d(b))]
-satzd177b:=treq(m0d(a),m0d(m0d(b)),b,eqm0d(a,m0d(b),e),satzd177(b)):eq(m0d(a),b)
-satzd177c:=symeq(m0d(a),b,satzd177b):eq(b,m0d(a))
-b@[e:eq(m0d(a),b)]
-satzd177d:=satzd177c(b,a,symeq(m0d(a),b,e)):eq(a,m0d(b))
-satzd177e:=symeq(a,m0d(b),satzd177d):eq(m0d(b),a)
-+3d178
-a@[p:posd(a)]
-t1:=tr3eq(absd(m0d(a)),m0d(m0d(a)),a,absd(a),absnd(m0d(a),satzd176a(a,p)),satzd177(a),symeq(absd(a),a,absnnd(a,pnotnd(a,p)))):eq(absd(m0d(a)),absd(a))
-a@[z:zero(a)]
-t2:=tr3eq(absd(m0d(a)),m0d(a),a,absd(a),absnnd(m0d(a),0notnd(m0d(a),satzd176b(a,z))),m0d0(a,z),symeq(absd(a),a,absnnd(a,0notnd(a,z)))):eq(absd(m0d(a)),absd(a))
-a@[n:negd(a)]
-t3:=treq(absd(m0d(a)),m0d(a),absd(a),absnnd(m0d(a),pnotnd(m0d(a),satzd176c(a,n))),symeq(absd(a),m0d(a),absnd(a,n))):eq(absd(m0d(a)),absd(a))
--3d178
-a@satzd178:=rappd(a,eq(absd(m0d(a)),absd(a)),[t:posd(a)]t1".3d178"(t),[t:zero(a)]t2".3d178"(t),[t:negd(a)]t3".3d178"(t)):eq(absd(m0d(a)),absd(a))
-satzd178a:=symeq(absd(m0d(a)),absd(a),satzd178):eq(absd(a),absd(m0d(a)))
-+3d179
-t1:=pdeq1b(a,2a,1a):eq(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)))
-t2:=zeroi(pl(1a,2a),pl(2a,1a),compl(1a,2a)):zero(df(pl(1a,2a),pl(2a,1a)))
--3d179
-satzd179:=eqzero(df(pl(1a,2a),pl(2a,1a)),pd(a,m0d(a)),t1".3d179",t2".3d179"):zero(pd(a,m0d(a)))
-satzd179a:=eqzero(pd(a,m0d(a)),pd(m0d(a),a),compd(a,m0d(a)),satzd179):zero(pd(m0d(a),a))
-b@satzd180:=treq(m0d(pd(a,b)),df(pl(2a,2b),pl(1a,1b)),pd(m0d(a),m0d(b)),m0deqa(pl(1a,1b),pl(2a,2b)),pdeq12b(2a,1a,2b,1b)):eq(m0d(pd(a,b)),pd(m0d(a),m0d(b)))
-satzd180a:=symeq(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180):eq(pd(m0d(a),m0d(b)),m0d(pd(a,b)))
-md:=pd(a,m0d(b)):dif
-b2@mdeq12a:=treq(md(df(a1,a2),df(b1,b2)),pd(df(a1,a2),df(b2,b1)),df(pl(a1,b2),pl(a2,b1)),eqpd2(m0d(df(b1,b2)),df(b2,b1),df(a1,a2),m0deqa(b1,b2)),pdeq12a(a1,a2,b2,b1)):eq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)))
-mdeq12b:=symeq(md(df(a1,a2),df(b1,b2)),df(pl(a1,b2),pl(a2,b1)),mdeq12a):eq(df(pl(a1,b2),pl(a2,b1)),md(df(a1,a2),df(b1,b2)))
-r2@mdeq1a:=treq(md(a,df(r1,r2)),pd(a,df(r2,r1)),df(pl(1a,r2),pl(2a,r1)),eqpd2(m0d(df(r1,r2)),df(r2,r1),a,m0deqa(r1,r2)),pdeq1a(a,r2,r1)):eq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)))
-mdeq1b:=symeq(md(a,df(r1,r2)),df(pl(1a,r2),pl(2a,r1)),mdeq1a):eq(df(pl(1a,r2),pl(2a,r1)),md(a,df(r1,r2)))
-mdeq2a:=pdeq12a(r1,r2,2a,1a):eq(md(df(r1,r2),a),df(pl(r1,2a),pl(r2,1a)))
-mdeq2b:=pdeq12b(r1,r2,2a,1a):eq(df(pl(r1,2a),pl(r2,1a)),md(df(r1,r2),a))
-c@[e:eq(a,b)]
-eqmd1:=eqpd1(a,b,m0d(c),e):eq(md(a,c),md(b,c))
-eqmd2:=eqpd2(m0d(a),m0d(b),c,eqm0d(a,b,e)):eq(md(c,a),md(c,b))
-d@[e:eq(a,b)][f:eq(c,d)]
-eqmd12:=treq(md(a,c),md(b,c),md(b,d),eqmd1(a,b,c,e),eqmd2(c,d,b,f)):eq(md(a,c),md(b,d))
-b@satzd181:=tr3eq(m0d(md(a,b)),pd(m0d(a),m0d(m0d(b))),pd(m0d(a),b),md(b,a),satzd180(a,m0d(b)),eqpd2(m0d(m0d(b)),b,m0d(a),satzd177(b)),compd(m0d(a),b)):eq(m0d(md(a,b)),md(b,a))
-satzd181a:=symeq(m0d(md(b,a)),md(a,b),satzd181(b,a)):eq(md(a,b),m0d(md(b,a)))
-+3d182
-t1:=treq(md(a,b),df(pl(1a,2b),pl(2a,1b)),df(pl(1a,2b),pl(1b,2a)),pdeq1a(a,2b,1b),eqsd(pl(1a,2b),pl(2a,1b),pl(1b,2a),compl(2a,1b))):eq(md(a,b),df(pl(1a,2b),pl(1b,2a)))
-t2:=symeq(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1):eq(df(pl(1a,2b),pl(1b,2a)),md(a,b))
-t3:=stmis(pl(1a,2b),pl(1b,2a)):is(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b))
-t4:=stdis(pl(1a,2b),pl(1b,2a)):is(std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a))
--3d182
-[p:posd(md(a,b))]
-+*3d182
-p@t5:=eqposd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,p):posd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-p@satzd182a:=ismore12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t5".3d182"):mored(a,b)
-b@[z:zero(md(a,b))]
-+*3d182
-z@t6:=eqzero(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,z):zero(df(pl(1a,2b),pl(1b,2a)))
--3d182
-z@satzd182b:=tr3is(cut,pl(1a,2b),stm(df(pl(1a,2b),pl(1b,2a))),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),isstm(pl(1a,2b),pl(1b,2a)),t6".3d182",t4".3d182"):eq(a,b)
-b@[n:negd(md(a,b))]
-+*3d182
-n@t7:=eqnegd(md(a,b),df(pl(1a,2b),pl(1b,2a)),t1,n):negd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-n@satzd182c:=isless12(stm(df(pl(1a,2b),pl(1b,2a))),pl(1a,2b),std(df(pl(1a,2b),pl(1b,2a))),pl(1b,2a),t3".3d182",t4".3d182",t7".3d182"):lessd(a,b)
-b@[m:mored(a,b)]
-+*3d182
-m@t8:=posdi(pl(1a,2b),pl(1b,2a),m):posd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-m@satzd182d:=eqposd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t8".3d182"):posd(md(a,b))
-b@[e:eq(a,b)]
-+*3d182
-e@t9:=zeroi(pl(1a,2b),pl(1b,2a),e):zero(df(pl(1a,2b),pl(1b,2a)))
--3d182
-e@satzd182e:=eqzero(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t9".3d182"):zero(md(a,b))
-b@[l:lessd(a,b)]
-+*3d182
-l@t10:=negdi(pl(1a,2b),pl(1b,2a),l):negd(df(pl(1a,2b),pl(1b,2a)))
--3d182
-l@satzd182f:=eqnegd(df(pl(1a,2b),pl(1b,2a)),md(a,b),t2".3d182",t10".3d182"):negd(md(a,b))
-+3d183
-b@t1:=tris(cut,pl(1a,2b),pl(2b,1a),pl(stm(m0d(b)),std(m0d(a))),compl(1a,2b),12issmsd(2b,1b,2a,1a)):is(pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))))
-t2:=t1(b,a):is(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))))
--3d183
-b@[m:mored(a,b)]
-satzd183a:=isless12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad5(a,b,m)):lessd(m0d(a),m0d(b))
-b@[e:eq(a,b)]
-staz183b:=eqm0d(a,b,e):eq(m0d(a),m0d(b))
-b@[l:lessd(a,b)]
-satzd183c:=ismore12(pl(1b,2a),pl(stm(m0d(a)),std(m0d(b))),pl(1a,2b),pl(stm(m0d(b)),std(m0d(a))),t2".3d183",t1".3d183",lemmad6(a,b,l)):mored(m0d(a),m0d(b))
-b@[l:lessd(m0d(a),m0d(b))]
-satzd183d:=eqmored12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183c(m0d(a),m0d(b),l)):mored(a,b)
-b@[e:eq(m0d(a),m0d(b))]
-satzd183e:=tr3eq(a,m0d(m0d(a)),m0d(m0d(b)),b,satzd177a(a),eqm0d(m0d(a),m0d(b),e),satzd177(b)):eq(a,b)
-b@[m:mored(m0d(a),m0d(b))]
-satzd183f:=eqlessd12(m0d(m0d(a)),a,m0d(m0d(b)),b,satzd177(a),satzd177(b),satzd183a(m0d(a),m0d(b),m)):lessd(a,b)
-+3d184
-a@t1:=tr3eq(a,df(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp))),df(pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp))),md(pdofrp(1a),pdofrp(2a)),lemmad3(a,pl(1rp,1rp)),eqsmsd(pl(1a,pl(1rp,1rp)),pl(2a,pl(1rp,1rp)),pl(pl(1a,1rp),1rp),pl(1rp,pl(2a,1rp)),asspl2(1a,1rp,1rp),3pl12(2a,1rp,1rp)),mdeq12b(pl(1a,1rp),1rp,pl(2a,1rp),1rp)):eq(a,md(pdofrp(1a),pdofrp(2a)))
-t2:=and3i(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))),posdirp(1a),posdirp(2a),t1):and3(posd(pdofrp(1a)),posd(pdofrp(2a)),eq(a,md(pdofrp(1a),pdofrp(2a))))
-t3:=somei(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))),pdofrp(2a),t2):some"l"(dif,[x:dif]and3(posd(pdofrp(1a)),posd(x),eq(a,md(pdofrp(1a),x))))
--3d184
-a@satzd184:=somei(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))),pdofrp(1a),t3".3d184"):some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(posd(x),posd(y),eq(a,md(x,y)))))
-c@asspd1:=tr3eq(pd(pd(a,b),c),df(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c)),df(pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c))),pd(a,pd(b,c)),pdeq2a(c,pl(1a,1b),pl(2a,2b)),eqsmsd(pl(pl(1a,1b),1c),pl(pl(2a,2b),2c),pl(1a,pl(1b,1c)),pl(2a,pl(2b,2c)),asspl1(1a,1b,1c),asspl1(2a,2b,2c)),pdeq1b(a,pl(1b,1c),pl(2b,2c))):eq(pd(pd(a,b),c),pd(a,pd(b,c)))
-asspd2:=symeq(pd(pd(a,b),c),pd(a,pd(b,c)),asspd1):eq(pd(a,pd(b,c)),pd(pd(a,b),c))
-3pd23:=tr3eq(pd(pd(a,b),c),pd(a,pd(b,c)),pd(a,pd(c,b)),pd(pd(a,c),b),asspd1(a,b,c),eqpd2(pd(b,c),pd(c,b),a,compd(b,c)),asspd2(a,c,b)):eq(pd(pd(a,b),c),pd(pd(a,c),b))
-d@4pd23:=tr3eq(pd(pd(a,b),pd(c,d)),pd(pd(pd(a,b),c),d),pd(pd(pd(a,c),b),d),pd(pd(a,c),pd(b,d)),asspd2(pd(a,b),c,d),eqpd1(pd(pd(a,b),c),pd(pd(a,c),b),d,3pd23),asspd1(pd(a,c),b,d)):eq(pd(pd(a,b),pd(c,d)),pd(pd(a,c),pd(b,d)))
-b@pdmd:=treq(pd(md(a,b),b),pd(a,pd(m0d(b),b)),a,asspd1(a,m0d(b),b),pd02(a,pd(m0d(b),b),satzd179a(b))):eq(pd(md(a,b),b),a)
-mdpd:=treq(md(pd(a,b),b),pd(a,pd(b,m0d(b))),a,asspd1(a,b,m0d(b)),pd02(a,pd(b,m0d(b)),satzd179(b))):eq(md(pd(a,b),b),a)
-d@satzd185:=treq(pd(md(a,b),md(c,d)),pd(pd(a,c),pd(m0d(b),m0d(d))),md(pd(a,c),pd(b,d)),4pd23(a,m0d(b),c,m0d(d)),eqpd2(pd(m0d(b),m0d(d)),m0d(pd(b,d)),pd(a,c),satzd180a(b,d))):eq(pd(md(a,b),md(c,d)),md(pd(a,c),pd(b,d)))
-c@satzd186:=asspd1:eq(pd(pd(a,b),c),pd(a,pd(b,c)))
-b@satzd187a:=treq(pd(b,md(a,b)),pd(md(a,b),b),a,compd(b,md(a,b)),pdmd):eq(pd(b,md(a,b)),a)
-[x:dif][e:eq(pd(b,x),a)]
-satzd187c:=treq(md(a,b),md(pd(x,b),b),x,eqmd1(a,pd(x,b),b,treq1(a,pd(x,b),pd(b,x),e,compd(b,x))),mdpd(x,b)):eq(md(a,b),x)
-satzd187d:=symeq(md(a,b),x,satzd187c):eq(x,md(a,b))
-x@[e:eq(pd(x,b),a)]
-satzd187e:=satzd187c(treq(pd(b,x),pd(x,b),a,compd(b,x),e)):eq(md(a,b),x)
-satzd187f:=symeq(md(a,b),x,satzd187e):eq(x,md(a,b))
-+3d188
-c@t1:=tr3eq(md(pd(a,c),pd(b,c)),pd(pd(a,c),pd(m0d(b),m0d(c))),pd(md(a,b),md(c,c)),md(a,b),eqpd2(m0d(pd(b,c)),pd(m0d(b),m0d(c)),pd(a,c),satzd180(b,c)),4pd23(a,c,m0d(b),m0d(c)),pd02(md(a,b),md(c,c),satzd179(c))):eq(md(pd(a,c),pd(b,c)),md(a,b))
-t2:=symeq(md(pd(a,c),pd(b,c)),md(a,b),t1):eq(md(a,b),md(pd(a,c),pd(b,c)))
--3d188
-c@[m:mored(pd(a,c),pd(b,c))]
-+*3d188
-m@t3:=eqposd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182d(pd(a,c),pd(b,c),m)):posd(md(a,b))
--3d188
-m@satzd188a:=satzd182a(a,b,t3".3d188"):mored(a,b)
-c@[e:eq(pd(a,c),pd(b,c))]
-+*3d188
-e@t4:=eqzero(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182e(pd(a,c),pd(b,c),e)):zero(md(a,b))
--3d188
-e@satzd188b:=satzd182b(a,b,t4".3d188"):eq(a,b)
-c@[l:lessd(pd(a,c),pd(b,c))]
-+*3d188
-l@t5:=eqnegd(md(pd(a,c),pd(b,c)),md(a,b),t1,satzd182f(pd(a,c),pd(b,c),l)):negd(md(a,b))
--3d188
-l@satzd188c:=satzd182c(a,b,t5".3d188"):lessd(a,b)
-c@[m:mored(a,b)]
-+*3d188
-m@t6:=eqposd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182d(a,b,m)):posd(md(pd(a,c),pd(b,c)))
--3d188
-m@satzd188d:=satzd182a(pd(a,c),pd(b,c),t6".3d188"):mored(pd(a,c),pd(b,c))
-c@[e:eq(a,b)]
-satzd188e:=eqpd1(a,b,c,e):eq(pd(a,c),pd(b,c))
-c@[l:lessd(a,b)]
-+*3d188
-l@t7:=eqnegd(md(a,b),md(pd(a,c),pd(b,c)),t2,satzd182f(a,b,l)):negd(md(pd(a,c),pd(b,c)))
--3d188
-l@satzd188f:=satzd182c(pd(a,c),pd(b,c),t7".3d188"):lessd(pd(a,c),pd(b,c))
-c@[m:mored(pd(c,a),pd(c,b))]
-satzd188g:=satzd188a(eqmored12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),m)):mored(a,b)
-c@[e:eq(pd(c,a),pd(c,b))]
-satzd188h:=satzd188b(tr3eq(pd(a,c),pd(c,a),pd(c,b),pd(b,c),compd(a,c),e,compd(c,b))):eq(a,b)
-[l:lessd(pd(c,a),pd(c,b))]
-satzd188j:=satzd188c(eqlessd12(pd(c,a),pd(a,c),pd(c,b),pd(b,c),compd(c,a),compd(c,b),l)):lessd(a,b)
-c@[m:mored(a,b)]
-satzd188k:=eqmored12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188d(m)):mored(pd(c,a),pd(c,b))
-c@[e:eq(a,b)]
-satzd188l:=eqpd2(a,b,c,e):eq(pd(c,a),pd(c,b))
-c@[l:lessd(a,b)]
-satzd188m:=eqlessd12(pd(a,c),pd(c,a),pd(b,c),pd(c,b),compd(a,c),compd(b,c),satzd188f(l)):lessd(pd(c,a),pd(c,b))
-d@[e:eq(a,b)][m:mored(c,d)]
-satzd188n:=eqmored2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188k(c,d,a,m)):mored(pd(a,c),pd(b,d))
-satzd188o:=eqmored12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188n):mored(pd(c,a),pd(d,b))
-e@[l:lessd(c,d)]
-satzd188p:=eqlessd2(pd(a,d),pd(b,d),pd(a,c),eqpd1(a,b,d,e),satzd188m(c,d,a,l)):lessd(pd(a,c),pd(b,d))
-satzd188q:=eqlessd12(pd(a,c),pd(c,a),pd(b,d),pd(d,b),compd(a,c),compd(b,d),satzd188p):lessd(pd(c,a),pd(d,b))
-d@[m:mored(a,b)][n:mored(c,d)]
-satzd189:=trmored(pd(a,c),pd(b,c),pd(b,d),satzd188d(a,b,c,m),satzd188k(c,d,b,n)):mored(pd(a,c),pd(b,d))
-d@[l:lessd(a,b)][k:lessd(c,d)]
-satzd189a:=lemmad5(pd(b,d),pd(a,c),satzd189(b,a,d,c,lemmad6(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
-d@[m:moreq(a,b)][n:mored(c,d)]
-satzd190a:=orapp(mored(a,b),eq(a,b),mored(pd(a,c),pd(b,d)),m,[t:mored(a,b)]satzd189(t,n),[t:eq(a,b)]satzd188n(t,n)):mored(pd(a,c),pd(b,d))
-d@[m:mored(a,b)][n:moreq(c,d)]
-satzd190b:=eqmored12(pd(c,a),pd(a,c),pd(d,b),pd(b,d),compd(c,a),compd(d,b),satzd190a(c,d,a,b,n,m)):mored(pd(a,c),pd(b,d))
-d@[l:lesseq(a,b)][k:lessd(c,d)]
-satzd190c:=lemmad5(pd(b,d),pd(a,c),satzd190a(b,a,d,c,satzd168b(a,b,l),lemmad6(c,d,k))):lessd(pd(a,c),pd(b,d))
-d@[l:lessd(a,b)][k:lesseq(c,d)]
-satzd190d:=lemmad5(pd(b,d),pd(a,c),satzd190b(b,a,d,c,lemmad6(a,b,l),satzd168b(c,d,k))):lessd(pd(a,c),pd(b,d))
-d@[m:moreq(a,b)][n:moreq(c,d)]
-+3d191
-[e:eq(a,b)][f:eq(c,d)]
-t1:=moreqi2(pd(a,c),pd(b,d),eqpd12(a,b,c,d,e,f)):moreq(pd(a,c),pd(b,d))
-e@[o:mored(c,d)]
-t2:=moreqi1(pd(a,c),pd(b,d),satzd190a(m,o)):moreq(pd(a,c),pd(b,d))
-e@t3:=orapp(mored(c,d),eq(c,d),moreq(pd(a,c),pd(b,d)),n,[t:mored(c,d)]t2(t),[t:eq(c,d)]t1(t)):moreq(pd(a,c),pd(b,d))
-n@[o:mored(a,b)]
-t4:=moreqi1(pd(a,c),pd(b,d),satzd190b(o,n)):moreq(pd(a,c),pd(b,d))
--3d191
-satzd191:=orapp(mored(a,b),eq(a,b),moreq(pd(a,c),pd(b,d)),m,[t:mored(a,b)]t4".3d191"(t),[t:eq(a,b)]t3".3d191"(t)):moreq(pd(a,c),pd(b,d))
-d@[l:lesseq(a,b)][k:lesseq(c,d)]
-satzd191a:=satzd168a(pd(b,d),pd(a,c),satzd191(b,a,d,c,satzd168b(a,b,l),satzd168b(c,d,k))):lesseq(pd(a,c),pd(b,d))
-b@td:=df(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))):dif
-+iv4d
-a2@[r:cut]
-t1:=ists1(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(stm(df(a1,a2)),r),ts(a1,r))
-t2:=ists2(stm(df(a1,a2)),a1,r,stmis(a1,a2)):is(ts(r,stm(df(a1,a2))),ts(r,a1))
-t3:=ists1(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(std(df(a1,a2)),r),ts(a2,r))
-t4:=ists2(std(df(a1,a2)),a2,r,stdis(a1,a2)):is(ts(r,std(df(a1,a2))),ts(r,a2))
-[s:cut]
-t5:=ispl12(ts(stm(df(a1,a2)),r),ts(a1,r),ts(std(df(a1,a2)),s),ts(a2,s),t1(r),t3(s)):is(pl(ts(stm(df(a1,a2)),r),ts(std(df(a1,a2)),s)),pl(ts(a1,r),ts(a2,s)))
-t6:=ispl12(ts(r,stm(df(a1,a2))),ts(r,a1),ts(s,std(df(a1,a2))),ts(s,a2),t2(r),t4(s)):is(pl(ts(r,stm(df(a1,a2))),ts(s,std(df(a1,a2)))),pl(ts(r,a1),ts(s,a2)))
-t7:=ispl12(ts(std(df(a1,a2)),r),ts(a2,r),ts(stm(df(a1,a2)),s),ts(a1,s),t3(r),t1(s)):is(pl(ts(std(df(a1,a2)),r),ts(stm(df(a1,a2)),s)),pl(ts(a2,r),ts(a1,s)))
-t8:=ispl12(ts(r,std(df(a1,a2))),ts(r,a2),ts(s,stm(df(a1,a2))),ts(s,a1),t4(r),t2(s)):is(pl(ts(r,std(df(a1,a2))),ts(s,stm(df(a1,a2)))),pl(ts(r,a2),ts(s,a1)))
-b2@t9:=tris(cut,pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,stm(df(b1,b2))),ts(a2,std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),t5(a1,a2,stm(df(b1,b2)),std(df(b1,b2))),t6(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)))
-t10:=tris(cut,pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,std(df(b1,b2))),ts(a2,stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)),t5(a1,a2,std(df(b1,b2)),stm(df(b1,b2))),t8(b1,b2,a1,a2)):is(pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b2),ts(a2,b1)))
--iv4d
-b2@td12:=issmsd(pl(ts(stm(df(a1,a2)),stm(df(b1,b2))),ts(std(df(a1,a2)),std(df(b1,b2)))),pl(ts(stm(df(a1,a2)),std(df(b1,b2))),ts(std(df(a1,a2)),stm(df(b1,b2)))),pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1)),t9".iv4d",t10".iv4d"):is"e"(dif,td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
-r2@td1:=issmsd(pl(ts(1a,stm(df(r1,r2))),ts(2a,std(df(r1,r2)))),pl(ts(1a,std(df(r1,r2))),ts(2a,stm(df(r1,r2)))),pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1)),t6".iv4d"(r1,r2,1a,2a),t8".iv4d"(r1,r2,1a,2a)):is"e"(dif,td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
-td2:=issmsd(pl(ts(stm(df(r1,r2)),1a),ts(std(df(r1,r2)),2a)),pl(ts(stm(df(r1,r2)),2a),ts(std(df(r1,r2)),1a)),pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a)),t5".iv4d"(r1,r2,1a,2a),t5".iv4d"(r1,r2,2a,1a)):is"e"(dif,td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
-b2@tdeq12a:=refeq1(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))))
-tdeq12b:=refeq2(td(df(a1,a2),df(b1,b2)),df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td12):eq(df(pl(ts(a1,b1),ts(a2,b2)),pl(ts(a1,b2),ts(a2,b1))),td(df(a1,a2),df(b1,b2)))
-r2@tdeq1a:=refeq1(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))))
-tdeq1b:=refeq2(td(a,df(r1,r2)),df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td1):eq(df(pl(ts(1a,r1),ts(2a,r2)),pl(ts(1a,r2),ts(2a,r1))),td(a,df(r1,r2)))
-tdeq2a:=refeq1(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))))
-tdeq2b:=refeq2(td(df(r1,r2),a),df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td2):eq(df(pl(ts(r1,1a),ts(r2,2a)),pl(ts(r1,2a),ts(r2,1a))),td(df(r1,r2),a))
-+4d194
-b@t1:=ispl12(ts(1a,1b),ts(1b,1a),ts(2a,2b),ts(2b,2a),comts(1a,1b),comts(2a,2b)):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1b,1a),ts(2b,2a)))
-t2:=tris(cut,pl(ts(1a,2b),ts(2a,1b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1b,2a),ts(2b,1a)),compl(ts(1a,2b),ts(2a,1b)),ispl12(ts(2a,1b),ts(1b,2a),ts(1a,2b),ts(2b,1a),comts(2a,1b),comts(1a,2b))):is(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,2a),ts(2b,1a)))
--4d194
-b@satzd194:=eqsmsd(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1b,1a),ts(2b,2a)),pl(ts(1b,2a),ts(2b,1a)),t1".4d194",t2".4d194"):eq(td(a,b),td(b,a))
-comtd:=satzd194:eq(td(a,b),td(b,a))
-c@[e:eq(a,b)]
-+*iv4d
-e@[r:cut]
-t11:=tr3is(cut,pl(ts(1a,r),ts(2b,r)),ts(pl(1a,2b),r),ts(pl(1b,2a),r),pl(ts(1b,r),ts(2a,r)),distpt1(1a,2b,r),ists1(pl(1a,2b),pl(1b,2a),r,e),disttp1(1b,2a,r)):is(pl(ts(1a,r),ts(2b,r)),pl(ts(1b,r),ts(2a,r)))
-e@t12:=tr3is(cut,pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,2c),ts(2a,2c))),pl(pl(ts(1b,1c),ts(2a,1c)),pl(ts(1a,2c),ts(2b,2c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))),4pl24(ts(1a,1c),ts(2a,2c),ts(1b,2c),ts(2b,1c)),ispl12(pl(ts(1a,1c),ts(2b,1c)),pl(ts(1b,1c),ts(2a,1c)),pl(ts(1b,2c),ts(2a,2c)),pl(ts(1a,2c),ts(2b,2c)),t11(1c),t11(b,a,c,symeq(a,b,e),2c)),4pl24(ts(1b,1c),ts(2a,1c),ts(1a,2c),ts(2b,2c))):is(pl(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1b,2c),ts(2b,1c))),pl(pl(ts(1b,1c),ts(2b,2c)),pl(ts(1a,2c),ts(2a,1c))))
--iv4d
-e@eqtd1:=eqi12(pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)),pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)),t12".iv4d"):eq(td(a,c),td(b,c))
-eqtd2:=tr3eq(td(c,a),td(a,c),td(b,c),td(c,b),comtd(c,a),eqtd1,comtd(b,c)):eq(td(c,a),td(c,b))
-d@[e:eq(a,b)][f:eq(c,d)]
-eqtd12:=treq(td(a,c),td(b,c),td(b,d),eqtd1(a,b,c,e),eqtd2(c,d,b,f)):eq(td(a,c),td(b,d))
-b@[z:zero(a)]
-+4d192
-t1:=tris(cut,pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,1b),ts(1a,2b)),pl(ts(1a,2b),ts(2a,1b)),ispl12(ts(1a,1b),ts(2a,1b),ts(2a,2b),ts(1a,2b),ists1(1a,2a,1b,z),ists1(2a,1a,2b,symis(cut,1a,2a,z))),compl(ts(2a,1b),ts(1a,2b))):is(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
--4d192
-satzd192a:=zeroi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t1".4d192"):zero(td(a,b))
-b@[z:zero(b)]
-satzd192b:=eqzero(td(b,a),td(a,b),comtd(b,a),satzd192a(b,a,z)):zero(td(a,b))
-b@[z:zero(a)]
-td01:=satzd192a(z):zero(td(a,b))
-b@[z:zero(b)]
-td02:=satzd192b(z):zero(td(a,b))
-b@satzd197a:=tr3eq(td(m0d(a),b),df(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b))),df(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b))),m0d(td(a,b)),tdeq2a(b,2a,1a),eqsmsd(pl(ts(2a,1b),ts(1a,2b)),pl(ts(2a,2b),ts(1a,1b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1b),ts(2a,2b)),compl(ts(2a,1b),ts(1a,2b)),compl(ts(2a,2b),ts(1a,1b))),m0deqb(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))):eq(td(m0d(a),b),m0d(td(a,b)))
-satzd197b:=tr3eq(td(a,m0d(b)),td(m0d(b),a),m0d(td(b,a)),m0d(td(a,b)),comtd(a,m0d(b)),satzd197a(b,a),eqm0d(td(b,a),td(a,b),comtd(b,a))):eq(td(a,m0d(b)),m0d(td(a,b)))
-satzd197c:=treq2(td(m0d(a),b),td(a,m0d(b)),m0d(td(a,b)),satzd197a,satzd197b):eq(td(m0d(a),b),td(a,m0d(b)))
-satzd197d:=symeq(td(m0d(a),b),td(a,m0d(b)),satzd197c):eq(td(a,m0d(b)),td(m0d(a),b))
-satzd197e:=symeq(td(m0d(a),b),m0d(td(a,b)),satzd197a):eq(m0d(td(a,b)),td(m0d(a),b))
-satzd197f:=symeq(td(a,m0d(b)),m0d(td(a,b)),satzd197b):eq(m0d(td(a,b)),td(a,m0d(b)))
-satzd198:=treq(td(m0d(a),m0d(b)),td(a,m0d(m0d(b))),td(a,b),satzd197c(a,m0d(b)),eqtd2(m0d(m0d(b)),b,a,satzd177(b))):eq(td(m0d(a),m0d(b)),td(a,b))
-satzd198a:=symeq(td(m0d(a),m0d(b)),td(a,b),satzd198):eq(td(a,b),td(m0d(a),m0d(b)))
-[p:posd(a)][q:posd(b)]
-+*iv4d
-q@[r:cut]
-t13:=tris(cut,pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,pl(mn(1b,2b,q),2b)),ts(r,1b),distpt2(r,mn(1b,2b,q),2b),ists2(pl(mn(1b,2b,q),2b),1b,r,satz140e(1b,2b,q))):is(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b))
-[s:cut]
-t14:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),s),pl(ts(r,1b),s),asspl2(ts(r,mn(1b,2b,q)),ts(r,2b),s),ispl1(pl(ts(r,mn(1b,2b,q)),ts(r,2b)),ts(r,1b),s,t13)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s))
-t15:=tris(cut,pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(ts(r,1b),s),pl(s,ts(r,1b)),t14,compl(ts(r,1b),s)):is(pl(ts(r,mn(1b,2b,q)),pl(ts(r,2b),s)),pl(s,ts(r,1b)))
-q@t16:=satz135h(pl(ts(1a,2b),ts(2a,2b)),pl(ts(2a,2b),ts(1a,2b)),ts(1a,mn(1b,2b,q)),ts(2a,mn(1b,2b,q)),compl(ts(1a,2b),ts(2a,2b)),satz145a(1a,2a,mn(1b,2b,q),p)):more(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))))
-t17:=ismore12(pl(ts(1a,mn(1b,2b,q)),pl(ts(1a,2b),ts(2a,2b))),pl(ts(1a,1b),ts(2a,2b)),pl(ts(2a,mn(1b,2b,q)),pl(ts(2a,2b),ts(1a,2b))),pl(ts(1a,2b),ts(2a,1b)),t14(1a,ts(2a,2b)),t15(2a,ts(1a,2b)),t16):more(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)))
--iv4d
-q@ptdpp:=posdi(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),t17".iv4d"):posd(td(a,b))
-b@[p:posd(a)][n:negd(b)]
-+*iv4d
-n@t18:=eqposd(td(a,m0d(b)),m0d(td(a,b)),satzd197b(a,b),ptdpp(a,m0d(b),p,satzd176c(b,n))):posd(m0d(td(a,b)))
--iv4d
-n@ntdpn:=satzd176f(td(a,b),t18".iv4d"):negd(td(a,b))
-b@[n:negd(a)][p:posd(b)]
-ntdnp:=eqnegd(td(b,a),td(a,b),comtd(b,a),ntdpn(b,a,p,n)):negd(td(a,b))
-b@[n:negd(a)][o:negd(b)]
-ptdnn:=eqposd(td(m0d(a),m0d(b)),td(a,b),satzd198(a,b),ptdpp(m0d(a),m0d(b),satzd176c(a,n),satzd176c(b,o))):posd(td(a,b))
-b@[n:not(zero(a))][o:not(zero(b))]
-+*4d192
-o@[p:posd(a)][q:posd(b)]
-t2:=pnot0d(td(a,b),ptdpp(a,b,p,q)):not(zero(td(a,b)))
-p@[m:negd(b)]
-t3:=nnot0d(td(a,b),ntdpn(a,b,p,m)):not(zero(td(a,b)))
-p@t4:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t2(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t3(t)):not(zero(td(a,b)))
-o@[m:negd(a)][p:posd(b)]
-t5:=nnot0d(td(a,b),ntdnp(a,b,m,p)):not(zero(td(a,b)))
-m@[l:negd(b)]
-t6:=pnot0d(td(a,b),ptdnn(a,b,m,l)):not(zero(td(a,b)))
-m@t7:=rappd(b,not(zero(td(a,b))),[t:posd(b)]t5(t),th2"l.imp"(zero(b),not(zero(td(a,b))),o),[t:negd(b)]t6(t)):not(zero(td(a,b)))
--4d192
-o@satzd192d:=rappd(a,not(zero(td(a,b))),[t:posd(a)]t4".4d192"(t),th2"l.imp"(zero(a),not(zero(td(a,b))),n),[t:negd(a)]t7".4d192"(t)):not(zero(td(a,b)))
-b@[z:zero(td(a,b))]
-+*4d192
-z@[n:not(zero(a))]
-t8:=et(zero(b),th3"l.imp"(not(zero(b)),not(zero(td(a,b))),weli(zero(td(a,b)),z),[t:not(zero(b))]satzd192d(n,t))):zero(b)
--4d192
-z@satzd192c:=[t:not(zero(a))]t8".4d192"(t):or(zero(a),zero(b))
-+4d193
-b@[p:posd(a)][q:posd(b)]
-t1:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdpp(a,b,p,q))),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-p@[n:negd(b)]
-t2:=treq(absd(td(a,b)),m0d(td(a,b)),td(a,m0d(b)),absnd(td(a,b),ntdpn(a,b,p,n)),satzd197f(a,b)):eq(absd(td(a,b)),td(a,m0d(b)))
-t3:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,m0d(b)),t2,eqtd12(absd(a),a,absd(b),m0d(b),absnnd(a,pnotnd(a,p)),absnd(b,n))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[z:zero(a)]
-t4:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td01(a,b,z)),td01(absd(a),absd(b),satzd166f(a,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[z:zero(b)]
-t5:=zeroeq(absd(td(a,b)),td(absd(a),absd(b)),satzd166f(td(a,b),td02(a,b,z)),td02(absd(a),absd(b),satzd166f(b,z))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[n:negd(a)][p:posd(b)]
-t6:=tr3eq(absd(td(a,b)),absd(td(b,a)),td(absd(b),absd(a)),td(absd(a),absd(b)),eqabsd(td(a,b),td(b,a),comtd(a,b)),t3(b,a,p,n),comtd(absd(b),absd(a))):eq(absd(td(a,b)),td(absd(a),absd(b)))
-n@[o:negd(b)]
-t7:=treq(td(absd(a),absd(b)),td(m0d(a),m0d(b)),td(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o)),satzd198(a,b)):eq(td(absd(a),absd(b)),td(a,b))
-t8:=treq2(absd(td(a,b)),td(absd(a),absd(b)),td(a,b),absnnd(td(a,b),pnotnd(td(a,b),ptdnn(a,b,n,o))),t7):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[p:posd(a)]
-t9:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t1(p,t),[t:zero(b)]t5(t),[t:negd(b)]t3(p,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
-b@[n:negd(a)]
-t10:=rappd(b,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(b)]t6(n,t),[t:zero(b)]t5(t),[t:negd(b)]t8(n,t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
--4d193
-b@satzd193:=rappd(a,eq(absd(td(a,b)),td(absd(a),absd(b))),[t:posd(a)]t9".4d193"(t),[t:zero(a)]t4".4d193"(t),[t:negd(a)]t10".4d193"(t)):eq(absd(td(a,b)),td(absd(a),absd(b)))
-satzd103a:=symeq(absd(td(a,b)),td(absd(a),absd(b)),satzd193):eq(td(absd(a),absd(b)),absd(td(a,b)))
-@1df:=pdofrp(1rp):dif
-+4d195
-a@t1:=tris(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(ts(1a,pl(1rp,1rp)),pl(ts(2a,1rp),2a)),pl(pl(1a,1a),pl(2a,2a)),asspl1(ts(1a,pl(1rp,1rp)),ts(2a,1rp),2a),ispl12(ts(1a,pl(1rp,1rp)),pl(1a,1a),pl(ts(2a,1rp),2a),pl(2a,2a),a2isapa(1a),ispl1(ts(2a,1rp),2a,2a,satz151(2a)))):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(pl(1a,1a),pl(2a,2a)))
-t2:=tris(cut,pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,ts(1a,1rp)),ts(2a,pl(1rp,1rp))),pl(pl(1a,1a),pl(2a,2a)),asspl2(1a,ts(1a,1rp),ts(2a,pl(1rp,1rp))),ispl12(pl(1a,ts(1a,1rp)),pl(1a,1a),ts(2a,pl(1rp,1rp)),pl(2a,2a),ispl2(ts(1a,1rp),1a,1a,satz151(1a)),a2isapa(2a))):is(pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)))
-t3:=tris2(cut,pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),pl(pl(1a,1a),pl(2a,2a)),t1,t2):is(pl(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),2a),pl(1a,pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))))
--4d195
-a@satzd195:=treq(td(a,1df),df(pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp)))),a,tdeq1a(a,pl(1rp,1rp),1rp),eqi2(a,pl(ts(1a,pl(1rp,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(1rp,1rp))),t3".4d195")):eq(td(a,1df),a)
-satzd195a:=symeq(td(a,1df),a,satzd195):eq(a,td(a,1df))
-satzd195b:=treq(td(1df,a),td(a,1df),a,comtd(1df,a),satzd195):eq(td(1df,a),a)
-satzd195c:=symeq(td(1df,a),a,satzd195b):eq(a,td(1df,a))
-b@[p:posd(a)][q:posd(b)]
-satzd196a:=symeq(td(absd(a),absd(b)),td(a,b),eqtd12(absd(a),a,absd(b),b,absnnd(a,pnotnd(a,p)),absnnd(b,pnotnd(b,q)))):eq(td(a,b),td(absd(a),absd(b)))
-b@[n:negd(a)][o:negd(b)]
-satzd196b:=treq2(td(a,b),td(absd(a),absd(b)),td(m0d(a),m0d(b)),satzd198a(a,b),eqtd12(absd(a),m0d(a),absd(b),m0d(b),absnd(a,n),absnd(b,o))):eq(td(a,b),td(absd(a),absd(b)))
-b@[p:posd(a)][n:negd(b)]
-satzd196c:=treq1(td(a,b),m0d(td(absd(a),absd(b))),td(absd(a),m0d(absd(b))),eqtd12(absd(a),a,m0d(absd(b)),b,absnnd(a,pnotnd(a,p)),satzd177b(absd(b),b,absnd(b,n))),satzd197b(absd(a),absd(b))):eq(td(a,b),m0d(td(absd(a),absd(b))))
-b@[n:negd(a)][p:posd(b)]
-satzd196d:=tr3eq(td(a,b),td(b,a),m0d(td(absd(b),absd(a))),m0d(td(absd(a),absd(b))),comtd(a,b),satzd196c(b,a,p,n),eqm0d(td(absd(b),absd(a)),td(absd(a),absd(b)),comtd(absd(b),absd(a)))):eq(td(a,b),m0d(td(absd(a),absd(b))))
-+4d196
-b@p1p2:=and(posd(a),posd(b)):'prop'
-p1n2:=and(posd(a),negd(b)):'prop'
-n1p2:=and(negd(a),posd(b)):'prop'
-n1n2:=and(negd(a),negd(b)):'prop'
--4d196
-b@[n:not(zero(a))][o:not(zero(b))][e:eq(td(a,b),td(absd(a),absd(b)))]
-+*4d196
-o@t1:=ptdpp(absd(a),absd(b),satzd166e(a,n),satzd166e(b,o)):posd(td(absd(a),absd(b)))
-e@t2:=pnotnd(td(a,b),eqposd(td(absd(a),absd(b)),td(a,b),symeq(td(a,b),td(absd(a),absd(b)),e),t1)):not(negd(td(a,b)))
-[p:posd(a)]
-t3:=th3"l.imp"(negd(b),negd(td(a,b)),t2,[t:negd(b)]ntdpn(a,b,p,t)):not(negd(b))
-t4:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t3,o):posd(b)
-t5:=andi(posd(a),posd(b),p,t4):p1p2
-t6:=ori1(p1p2,n1n2,t5):or(p1p2,n1n2)
-e@[m:negd(a)]
-t7:=th3"l.imp"(posd(b),negd(td(a,b)),t2,[t:posd(b)]ntdnp(a,b,m,t)):not(posd(b))
-t8:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t7):negd(b)
-t9:=andi(negd(a),negd(b),m,t8):n1n2
-t10:=ori2(p1p2,n1n2,t9):or(p1p2,n1n2)
--4d196
-e@satzd196e:=rappd(a,or(p1p2".4d196",n1n2".4d196"),[t:posd(a)]t6".4d196"(t),th2"l.imp"(zero(a),or(p1p2".4d196",n1n2".4d196"),n),[t:negd(a)]t10".4d196"(t)):or(and(posd(a),posd(b)),and(negd(a),negd(b)))
-o@[e:eq(td(a,b),m0d(td(absd(a),absd(b))))]
-+*4d196
-o@t11:=satzd176a(td(absd(a),absd(b)),t1):negd(m0d(td(absd(a),absd(b))))
-e@t12:=nnotpd(td(a,b),eqnegd(m0d(td(absd(a),absd(b))),td(a,b),symeq(td(a,b),m0d(td(absd(a),absd(b))),e),t11)):not(posd(td(a,b)))
-[p:posd(a)]
-t13:=th3"l.imp"(posd(b),posd(td(a,b)),t12,[t:posd(b)]ptdpp(a,b,p,t)):not(posd(b))
-t14:=or3e3(zero(b),posd(b),negd(b),axrdo(b),o,t13):negd(b)
-t15:=andi(posd(a),negd(b),p,t14):p1n2
-t16:=ori1(p1n2,n1p2,t15):or(p1n2,n1p2)
-e@[m:negd(a)]
-t17:=th3"l.imp"(negd(b),posd(td(a,b)),t12,[t:negd(b)]ptdnn(a,b,m,t)):not(negd(b))
-t18:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t17,o):posd(b)
-t19:=andi(negd(a),posd(b),m,t18):n1p2
-t20:=ori2(p1n2,n1p2,t19):or(p1n2,n1p2)
--4d196
-e@satzd196f:=rappd(a,or(p1n2".4d196",n1p2".4d196"),[t:posd(a)]t16".4d196"(t),th2"l.imp"(zero(a),or(p1n2".4d196",n1p2".4d196"),n),[t:negd(a)]t20".4d196"(t)):or(and(posd(a),negd(b)),and(negd(a),posd(b)))
-+4d199
-@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
-t1:=tris(cut,ts(pl(ts(p,r),ts(q,s)),t),pl(ts(ts(p,r),t),ts(ts(q,s),t)),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),disttp1(ts(p,r),ts(q,s),t),ispl12(ts(ts(p,r),t),ts(p,ts(r,t)),ts(ts(q,s),t),ts(q,ts(s,t)),assts1(p,r,t),assts1(q,s,t))):is(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))))
-t2:=tris(cut,pl(ts(q,ts(s,t)),ts(q,ts(r,u))),pl(ts(q,ts(r,u)),ts(q,ts(s,t))),ts(q,pl(ts(r,u),ts(s,t))),compl(ts(q,ts(s,t)),ts(q,ts(r,u))),distpt2(q,ts(r,u),ts(s,t))):is(pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))))
-t3:=tr3is(cut,pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(pl(ts(p,ts(r,t)),ts(q,ts(s,t))),pl(ts(p,ts(s,u)),ts(q,ts(r,u)))),pl(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u)))),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))),ispl12(ts(pl(ts(p,r),ts(q,s)),t),pl(ts(p,ts(r,t)),ts(q,ts(s,t))),ts(pl(ts(p,s),ts(q,r)),u),pl(ts(p,ts(s,u)),ts(q,ts(r,u))),t1,t1(p,q,s,r,u,t)),4pl23(ts(p,ts(r,t)),ts(q,ts(s,t)),ts(p,ts(s,u)),ts(q,ts(r,u))),ispl12(pl(ts(p,ts(r,t)),ts(p,ts(s,u))),ts(p,pl(ts(r,t),ts(s,u))),pl(ts(q,ts(s,t)),ts(q,ts(r,u))),ts(q,pl(ts(r,u),ts(s,t))),distpt2(p,ts(r,t),ts(s,u)),t2)):is(pl(ts(pl(ts(p,r),ts(q,s)),t),ts(pl(ts(p,s),ts(q,r)),u)),pl(ts(p,pl(ts(r,t),ts(s,u))),ts(q,pl(ts(r,u),ts(s,t)))))
--4d199
-c@satzd199:=tr3eq(td(td(a,b),c),df(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c))),df(pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c))))),td(a,td(b,c)),tdeq2a(c,pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b))),eqsmsd(pl(ts(pl(ts(1a,1b),ts(2a,2b)),1c),ts(pl(ts(1a,2b),ts(2a,1b)),2c)),pl(ts(pl(ts(1a,1b),ts(2a,2b)),2c),ts(pl(ts(1a,2b),ts(2a,1b)),1c)),pl(ts(1a,pl(ts(1b,1c),ts(2b,2c))),ts(2a,pl(ts(1b,2c),ts(2b,1c)))),pl(ts(1a,pl(ts(1b,2c),ts(2b,1c))),ts(2a,pl(ts(1b,1c),ts(2b,2c)))),t3".4d199"(1a,2a,1b,2b,1c,2c),t3".4d199"(1a,2a,1b,2b,2c,1c)),tdeq1b(a,pl(ts(1b,1c),ts(2b,2c)),pl(ts(1b,2c),ts(2b,1c)))):eq(td(td(a,b),c),td(a,td(b,c)))
-asstd1:=satzd199:eq(td(td(a,b),c),td(a,td(b,c)))
-asstd2:=symeq(td(td(a,b),c),td(a,td(b,c)),satzd199):eq(td(a,td(b,c)),td(td(a,b),c))
-+4d201
-@[p:cut][q:cut][r:cut][s:cut][t:cut][u:cut]
-t1:=tris(cut,pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(p,t)),pl(ts(q,s),ts(q,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))),ispl12(ts(p,pl(r,t)),pl(ts(p,r),ts(p,t)),ts(q,pl(s,u)),pl(ts(q,s),ts(q,u)),disttp2(p,r,t),disttp2(q,s,u)),4pl23(ts(p,r),ts(p,t),ts(q,s),ts(q,u))):is(pl(ts(p,pl(r,t)),ts(q,pl(s,u))),pl(pl(ts(p,r),ts(q,s)),pl(ts(p,t),ts(q,u))))
--4d201
-satzd201:=tr3eq(td(a,pd(b,c)),df(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c)))),df(pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c)))),pd(td(a,b),td(a,c)),tdeq1a(a,pl(1b,1c),pl(2b,2c)),eqsmsd(pl(ts(1a,pl(1b,1c)),ts(2a,pl(2b,2c))),pl(ts(1a,pl(2b,2c)),ts(2a,pl(1b,1c))),pl(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,1c),ts(2a,2c))),pl(pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,2c),ts(2a,1c))),t1".4d201"(1a,2a,1b,2b,1c,2c),t1".4d201"(1a,2a,2b,1b,2c,1c)),pdeq12b(pl(ts(1a,1b),ts(2a,2b)),pl(ts(1a,2b),ts(2a,1b)),pl(ts(1a,1c),ts(2a,2c)),pl(ts(1a,2c),ts(2a,1c)))):eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
-disttpd1:=tr3eq(td(pd(a,b),c),td(c,pd(a,b)),pd(td(c,a),td(c,b)),pd(td(a,c),td(b,c)),comtd(pd(a,b),c),satzd201(c,a,b),eqpd12(td(c,a),td(a,c),td(c,b),td(b,c),comtd(c,a),comtd(c,b))):eq(td(pd(a,b),c),pd(td(a,c),td(b,c)))
-disttpd2:=satzd201:eq(td(a,pd(b,c)),pd(td(a,b),td(a,c)))
-distptd1:=symeq(td(pd(a,b),c),pd(td(a,c),td(b,c)),disttpd1):eq(pd(td(a,c),td(b,c)),td(pd(a,b),c))
-distptd2:=symeq(td(a,pd(b,c)),pd(td(a,b),td(a,c)),disttpd2):eq(pd(td(a,b),td(a,c)),td(a,pd(b,c)))
-satzd202:=treq(td(a,md(b,c)),pd(td(a,b),td(a,m0d(c))),md(td(a,b),td(a,c)),disttpd2(a,b,m0d(c)),eqpd2(td(a,m0d(c)),m0d(td(a,c)),td(a,b),satzd197b(a,c))):eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
-disttmd1:=treq(td(md(a,b),c),pd(td(a,c),td(m0d(b),c)),md(td(a,c),td(b,c)),disttpd1(a,m0d(b),c),eqpd2(td(m0d(b),c),m0d(td(b,c)),td(a,c),satzd197a(b,c))):eq(td(md(a,b),c),md(td(a,c),td(b,c)))
-disttmd2:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
-distmtd1:=symeq(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1):eq(md(td(a,c),td(b,c)),td(md(a,b),c))
-distmtd2:=symeq(td(a,md(b,c)),md(td(a,b),td(a,c)),disttmd2):eq(md(td(a,b),td(a,c)),td(a,md(b,c)))
-satzd200:=satzd202:eq(td(a,md(b,c)),md(td(a,b),td(a,c)))
-[m:mored(a,b)]
-+4d203
-t1:=satzd182d(a,b,m):posd(md(a,b))
--4d203
-[p:posd(c)]
-+*4d203
-p@t2:=eqposd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ptdpp(md(a,b),c,t1,p)):posd(md(td(a,c),td(b,c)))
--4d203
-p@satzd203a:=satzd182a(td(a,c),td(b,c),t2".4d203"):mored(td(a,c),td(b,c))
-m@[z:zero(c)]
-satzd203b:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
-m@[n:negd(c)]
-+*4d203
-n@t3:=eqnegd(td(md(a,b),c),md(td(a,c),td(b,c)),disttmd1(a,b,c),ntdpn(md(a,b),c,t1,n)):negd(md(td(a,c),td(b,c)))
--4d203
-n@satzd203c:=satzd182c(td(a,c),td(b,c),t3".4d203"):lessd(td(a,c),td(b,c))
-p@satzd203d:=eqmored12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203a):mored(td(c,a),td(c,b))
-z@satzd203e:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
-n@satzd203f:=eqlessd12(td(a,c),td(c,a),td(b,c),td(c,b),comtd(a,c),comtd(b,c),satzd203c):lessd(td(c,a),td(c,b))
-c@[l:lessd(a,b)][p:posd(c)]
-satzd203g:=lemmad5(td(b,c),td(a,c),satzd203a(b,a,c,lemmad6(a,b,l),p)):lessd(td(a,c),td(b,c))
-l@[z:zero(c)]
-satzd203h:=zeroeq(td(a,c),td(b,c),td02(a,c,z),td02(b,c,z)):eq(td(a,c),td(b,c))
-l@[n:negd(c)]
-satzd203j:=lemmad6(td(b,c),td(a,c),satzd203c(b,a,c,lemmad6(a,b,l),n)):mored(td(a,c),td(b,c))
-p@satzd203k:=lemmad5(td(c,b),td(c,a),satzd203d(b,a,c,lemmad6(a,b,l),p)):lessd(td(c,a),td(c,b))
-z@satzd203l:=zeroeq(td(c,a),td(c,b),td01(c,a,z),td01(c,b,z)):eq(td(c,a),td(c,b))
-n@satzd203m:=lemmad6(td(c,b),td(c,a),satzd203f(b,a,c,lemmad6(a,b,l),n)):mored(td(c,a),td(c,b))
-+*iv4d
-@[p:cut][q:cut]
-t19:=tris(cut,ts(q,pl(p,1rp)),pl(ts(q,p),ts(q,1rp)),pl(ts(q,p),q),disttp2(q,p,1rp),ispl2(ts(q,1rp),q,ts(q,p),satz151(q))):is(ts(q,pl(p,1rp)),pl(ts(q,p),q))
-[r:cut]
-t20:=tris(cut,pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(pl(ts(q,p),q),r),pl(ts(q,p),pl(q,r)),ispl12(ts(q,pl(p,1rp)),pl(ts(q,p),q),ts(r,1rp),r,t19,satz151(r)),asspl1(ts(q,p),q,r)):is(pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)))
-t21:=tr3is(cut,pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,pl(p,1rp)),ts(r,1rp)),pl(ts(q,p),pl(q,r)),pl(ts(q,p),pl(r,q)),compl(ts(r,1rp),ts(q,pl(p,1rp))),t20,ispl2(pl(q,r),pl(r,q),ts(q,p),compl(q,r))):is(pl(ts(r,1rp),ts(q,pl(p,1rp))),pl(ts(q,p),pl(r,q)))
-a@[p:posd(a)]
-arp:=rpofpd(a,p):cut
-arpi:=ov(1rp,arp):cut
-ai:=pdofrp(arpi):dif
-t22:=tr3eq(td(a,ai),df(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp)))),df(pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a))),df(ts(1a,arpi),ts(2a,arpi)),tdeq1a(a,pl(arpi,1rp),1rp),eqsmsd(pl(ts(1a,pl(arpi,1rp)),ts(2a,1rp)),pl(ts(1a,1rp),ts(2a,pl(arpi,1rp))),pl(ts(1a,arpi),pl(1a,2a)),pl(ts(2a,arpi),pl(1a,2a)),t20(arpi,1a,2a),t21(arpi,2a,1a)),lemmad2(ts(1a,arpi),ts(2a,arpi),pl(1a,2a))):eq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)))
-t23:=tr3is(cut,ts(1a,arpi),ts(pl(2a,arp),arpi),pl(ts(2a,arpi),ts(arp,arpi)),pl(ts(2a,arpi),1rp),ists1(1a,pl(2a,arp),arpi,satz140d(1a,2a,p)),disttp1(2a,arp,arpi),ispl2(ts(arp,arpi),1rp,ts(2a,arpi),satz153c(1rp,arp))):is(ts(1a,arpi),pl(ts(2a,arpi),1rp))
-t24:=tr3is(cut,pl(ts(1a,arpi),1rp),pl(pl(ts(2a,arpi),1rp),1rp),pl(ts(2a,arpi),pl(1rp,1rp)),pl(pl(1rp,1rp),ts(2a,arpi)),ispl1(ts(1a,arpi),pl(ts(2a,arpi),1rp),1rp,t23),asspl1(ts(2a,arpi),1rp,1rp),compl(ts(2a,arpi),pl(1rp,1rp))):is(pl(ts(1a,arpi),1rp),pl(pl(1rp,1rp),ts(2a,arpi)))
-t25:=eqi12(ts(1a,arpi),ts(2a,arpi),pl(1rp,1rp),1rp,t24):eq(df(ts(1a,arpi),ts(2a,arpi)),1df)
-t26:=treq(td(a,ai),df(ts(1a,arpi),ts(2a,arpi)),1df,t22,t25):eq(td(a,ai),1df)
-t27:=somei(dif,[x:dif]eq(td(a,x),1df),ai,t26):some"l"(dif,[x:dif]eq(td(a,x),1df))
-a@[n:negd(a)]
-t28:=satzd176c(a,n):posd(m0d(a))
-[h:dif][e:eq(td(m0d(a),h),1df)]
-t29:=treq(td(a,m0d(h)),td(m0d(a),h),1df,satzd197d(a,h),e):eq(td(a,m0d(h)),1df)
-t30:=somei(dif,[x:dif]eq(td(a,x),1df),m0d(h),t29):some"l"(dif,[x:dif]eq(td(a,x),1df))
-n@t31:=someapp(dif,[x:dif]eq(td(m0d(a),x),1df),t27(m0d(a),t28),some"l"(dif,[x:dif]eq(td(a,x),1df)),[x:dif][t:eq(td(m0d(a),x),1df)]t30(x,t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
--iv4d
-a@[n:not(zero(a))]
-lemmad7:=rappd(a,some"l"(dif,[x:dif]eq(td(a,x),1df)),[t:posd(a)]t27".iv4d"(t),th2"l.imp"(zero(a),some"l"(dif,[x:dif]eq(td(a,x),1df)),n),[t:negd(a)]t31".iv4d"(t)):some"l"(dif,[x:dif]eq(td(a,x),1df))
-b@[n:not(zero(b))][h:dif][k:dif][e:eq(td(b,h),a)][f:eq(td(b,k),a)]
-+4d204
-t1:=treq2(td(b,h),td(b,k),a,e,f):eq(td(b,h),td(b,k))
-t2:=eqzero(md(td(b,h),td(b,k)),td(b,md(h,k)),distmtd2(b,h,k),satzd182e(td(b,h),td(b,k),t1)):zero(td(b,md(h,k)))
-t3:=ore2(zero(b),zero(md(h,k)),satzd192c(b,md(h,k),t2),n):zero(md(h,k))
--4d204
-satzd204b:=satzd182b(h,k,t3".4d204"):eq(h,k)
-+*4d204
-n@[h:dif][e:eq(td(b,h),1df)]
-t4:=tr3eq(td(b,td(h,a)),td(td(b,h),a),td(1df,a),a,asstd2(b,h,a),eqtd1(td(b,h),1df,a,e),satzd195b(a)):eq(td(b,td(h,a)),a)
-t5:=somei(dif,[x:dif]eq(td(b,x),a),td(h,a),t4):some"l"(dif,[x:dif]eq(td(b,x),a))
--4d204
-n@satzd204a:=someapp(dif,[x:dif]eq(td(b,x),1df),lemmad7(b,n),some"l"(dif,[x:dif]eq(td(b,x),a)),[x:dif][t:eq(td(b,x),1df)]t5".4d204"(x,t)):some"l"(dif,[x:dif]eq(td(b,x),a))
-@[r:cut][s:cut][m:more(r,s)]
-+iv5d
-t1:=ismore12(pl(r,pl(1rp,1rp)),pl(pl(r,1rp),1rp),pl(s,pl(1rp,1rp)),pl(pl(s,1rp),1rp),asspl2(r,1rp,1rp),asspl2(s,1rp,1rp),satz134(r,s,pl(1rp,1rp),m)):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
--iv5d
-morerpepd:=moredi12(pl(r,1rp),1rp,pl(s,1rp),1rp,t1".iv5d"):mored(pdofrp(r),pdofrp(s))
-s@[m:mored(pdofrp(r),pdofrp(s))]
-+*iv5d
-m@t2:=morede12(pl(r,1rp),1rp,pl(s,1rp),1rp,m):more(pl(pl(r,1rp),1rp),pl(pl(s,1rp),1rp))
--iv5d
-m@morerpipd:=satz136a(r,s,pl(1rp,1rp),ismore12(pl(pl(r,1rp),1rp),pl(r,pl(1rp,1rp)),pl(pl(s,1rp),1rp),pl(s,pl(1rp,1rp)),asspl1(r,1rp,1rp),asspl1(s,1rp,1rp),t2".iv5d")):more(r,s)
-s@[l:less(r,s)]
-lessrpepd:=lemmad5(pdofrp(s),pdofrp(r),morerpepd(s,r,satz122(r,s,l))):lessd(pdofrp(r),pdofrp(s))
-s@[l:lessd(pdofrp(r),pdofrp(s))]
-lessrpipd:=satz121(s,r,morerpipd(s,r,lemmad6(pdofrp(r),pdofrp(s),l))):less(r,s)
-+*iv5d
-@i:=1rp:cut
-2:=pl(i,i):cut
-r@rp1:=pl(r,i):cut
-s@sp1:=pl(s,i):cut
-rps:=pl(r,s):cut
-rs:=ts(r,s):cut
-t3:=tris(cut,pl(pl(rp1,sp1),i),pl(pl(rps,2),i),pl(pl(rps,i),2),ispl1(pl(rp1,sp1),pl(rps,2),i,4pl23(r,i,s,i)),3pl23(rps,2,i)):is(pl(pl(rp1,sp1),i),pl(pl(rps,i),2))
-t4:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(rp1,sp1),2),pdofrp(rps),pdeq12a(rp1,i,sp1,i),eqi12(pl(rp1,sp1),2,pl(rps,i),i,t3)):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(rps))
--iv5d
-s@lemmad8:=t4".iv5d":eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
-+*iv5d
-s@t5:=tris(cut,ts(r,sp1),pl(rs,ts(r,i)),pl(rs,r),disttp2(r,s,i),ispl2(ts(r,i),r,rs,satz151(r))):is(ts(r,sp1),pl(rs,r))
-t6:=tr4is(cut,ts(rp1,sp1),pl(ts(r,sp1),ts(i,sp1)),pl(pl(rs,r),sp1),pl(pl(pl(rs,r),s),i),pl(pl(rs,rps),i),disttp1(r,i,sp1),ispl12(ts(r,sp1),pl(rs,r),ts(i,sp1),sp1,t5,satz151b(sp1)),asspl2(pl(rs,r),s,i),ispl1(pl(pl(rs,r),s),pl(rs,rps),i,asspl1(rs,r,s))):is(ts(rp1,sp1),pl(pl(rs,rps),i))
-t7:=tr3is(cut,pl(ts(rp1,sp1),ts(i,i)),pl(pl(pl(rs,rps),i),i),pl(pl(rs,rps),2),pl(rs,pl(rps,2)),ispl12(ts(rp1,sp1),pl(pl(rs,rps),i),ts(i,i),i,t6,satz151(i)),asspl1(pl(rs,rps),i,i),asspl1(rs,rps,2)):is(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)))
-t8:=tris(cut,pl(ts(rp1,i),ts(i,sp1)),pl(rp1,sp1),pl(rps,2),ispl12(ts(rp1,i),rp1,ts(i,sp1),sp1,satz151(rp1),satz151b(sp1)),4pl23(r,i,s,i)):is(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2))
-t9:=tris(cut,pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,i),pl(rps,2)),pl(pl(rs,pl(rps,2)),i),ispl2(pl(ts(rp1,i),ts(i,sp1)),pl(rps,2),pl(rs,i),t8),3pl23(rs,i,pl(rps,2))):is(pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i))
-t10:=tris2(cut,pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))),pl(pl(rs,pl(rps,2)),i),ispl1(pl(ts(rp1,sp1),ts(i,i)),pl(rs,pl(rps,2)),i,t7),t9):is(pl(pl(ts(rp1,sp1),ts(i,i)),i),pl(pl(rs,i),pl(ts(rp1,i),ts(i,sp1))))
-t11:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1))),pdofrp(rs),tdeq12a(rp1,i,sp1,i),eqi12(pl(ts(rp1,sp1),ts(i,i)),pl(ts(rp1,i),ts(i,sp1)),pl(rs,i),i,t10)):eq(td(pdofrp(r),pdofrp(s)),pdofrp(rs))
--iv5d
-s@lemmad9:=t11".iv5d":eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
-@[r:cut][s0:set(cut)]
-in:=esti(cut,r,s0):'prop'
-@[s0:set(cut)][t0:set(cut)][p0:all([x:cut]or(in(x,s0),in(x,t0)))][p1a:nonempty(cut,s0)][p1b:nonempty(cut,t0)][p2:all([x:cut][t:in(x,s0)]all([y:cut][u:in(y,t0)]less(x,y)))]
-+5p205
-t0@[r:cut]
-prop1:=all([x:cut][t:less(x,r)]in(x,s0)):'prop'
-prop2:=all([x:cut][t:more(x,r)]in(x,t0)):'prop'
-prop3:=and(prop1,prop2):'prop'
-p2@[r1:cut][r2:cut][pr1:prop3(r1)][pr2:prop3(r2)]
-t1:=ande2(prop1(r1),prop2(r1),pr1):prop2(r1)
-t2:=ande1(prop1(r2),prop2(r2),pr2):prop1(r2)
-[l:less(r1,r2)][x0:rat]
-rx:=rpofrt(x0):cut
-[l1:less(r1,rx)][l2:less(rx,r2)]
-t3:=<l2><rx>t2:in(rx,s0)
-t4:=<satz122(r1,rx,l1)><rx>t1:in(rx,t0)
-t5:=<refis(cut,rx)>ec3e31(is(rx,rx),more(rx,rx),less(rx,rx),satz123b(rx,rx),<t4><rx><t3><rx>p2):con
-l@t6:=satz159app(r1,r2,l,con,[x:rat][t:less(r1,rpofrt(x))][u:less(rpofrt(x),r2)]t5(x,t,u)):con
-pr2@t7:=[t:less(r1,r2)]t6(t):not(less(r1,r2))
-t8:=[t:more(r1,r2)]t6(r2,r1,pr2,pr1,satz121(r1,r2,t)):not(more(r1,r2))
-t9:=or3e1(is(r1,r2),more(r1,r2),less(r1,r2),satz123a(r1,r2),t8,t7):is(r1,r2)
-p2@t10:=[x:cut][y:cut][t:prop3(x)][u:prop3(y)]t9(x,y,t,u):amone(cut,[x:cut]prop3(x))
-[x0:rat]
-schnittprop:=some([y:cut]and(in(y,s0),lrt(y,x0))):'prop'
-p2@schnittset:=setof(rat,[x:rat]schnittprop(x)):set(rat)
-[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)]
-t11:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
-t12:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t11):schnittprop(x0)
-t13:=estii(rat,[x:rat]schnittprop(x),x0,t12):in"rt"(x0,schnittset)
-r@[i:in(r,t0)][x0:rat][ux:urt(r,x0)][s:cut][j:in(s,s0)]
-t14:=satz122(s,r,<i><r><j><s>p2):more(r,s)
-t15:=satz158b(r,x0,ux):moreis(rpofrt(x0),r)
-t16:=moreisi1(rpofrt(x0),s,satz127c(rpofrt(x0),r,s,t15,t14)):moreis(rpofrt(x0),s)
-t17:=satz158d(s,x0,t16):urt(s,x0)
-s@t18:=weli(ec(in(s,s0),lrt(s,x0)),[t:in(s,s0)]t17(t)):not(and(in(s,s0),lrt(s,x0)))
-ux@t19:=th5"l.some"(cut,[y:cut]and(in(y,s0),lrt(y,x0)),[y:cut]t18(y)):not(schnittprop(x0))
-t20:=th3"l.imp"(in"rt"(x0,schnittset),schnittprop(x0),t19,[t:in"rt"(x0,schnittset)]estie(rat,[x:rat]schnittprop(x),x0,t)):not(in"rt"(x0,schnittset))
-p2@[x0:rat][i:in"rt"(x0,schnittset)][y0:rat][l:less"rt"(y0,x0)]
-i@t21:=estie(rat,[x:rat]schnittprop(x),x0,i):schnittprop(x0)
-l@[r:cut][a:and(in(r,s0),lrt(r,x0))]
-t22:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
-t23:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
-t24:=satz120(r,x0,t23,y0,l):lrt(r,y0)
-t25:=andi(in(r,s0),lrt(r,y0),t22,t24):and(in(r,s0),lrt(r,y0))
-t26:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t25):schnittprop(y0)
-l@t27:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,schnittprop(y0),[y:cut][r:and(in(y,s0),lrt(y,x0))]t26(y,r)):schnittprop(y0)
-t28:=estii(rat,[x:rat]schnittprop(x),y0,t27):in"rt"(y0,schnittset)
-i@[r:cut][a:and(in(r,s0),lrt(r,x0))]
-t29:=ande1(in(r,s0),lrt(r,x0),a):in(r,s0)
-t30:=ande2(in(r,s0),lrt(r,x0),a):lrt(r,x0)
-[y0:rat][ly:lrt(r,y0)][l:less"rt"(x0,y0)]
-t31:=andi(in(r,s0),lrt(r,y0),t29,ly):and(in(r,s0),lrt(r,y0))
-t32:=somei(cut,[y:cut]and(in(y,s0),lrt(y,y0)),r,t31):schnittprop(y0)
-t33:=estii(rat,[x:rat]schnittprop(x),y0,t32):in"rt"(y0,schnittset)
-t34:=satz83(x0,y0,l):more"rt"(y0,x0)
-t35:=andi(in"rt"(y0,schnittset),more"rt"(y0,x0),t33,t34):and(in"rt"(y0,schnittset),more"rt"(y0,x0))
-t36:=somei(rat,[y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)),y0,t35):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
-a@t37:=cutapp3(r,x0,t30,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:rat][t:lrt(r,y)][u:less"rt"(x0,y)]t36(y,t,u)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
-i@t38:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t21,some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0))),[y:cut][t:and(in(y,s0),lrt(y,x0))]t37(y,t)):some"rt"([y:rat]and(in"rt"(y,schnittset),more"rt"(y,x0)))
-p2@[r:cut][i:in(r,s0)][x0:rat][lx:lrt(r,x0)][s:cut][j:in(s,t0)][y0:rat][uy:urt(s,y0)]
-t39:=cut2(schnittset,x0,t13(r,i,x0,lx),y0,t20(s,j,y0,uy),[x:rat][t:in"rt"(x,schnittset)][y:rat][u:less"rt"(y,x)]t28(x,t,y,u),[x:rat][t:in"rt"(x,schnittset)]t38(x,t)):cutprop(schnittset)
-j@t40:=cutapp1b(s,cutprop(schnittset),[x:rat][t:urt(s,x)]t39(x,t)):cutprop(schnittset)
-lx@t41:=nonemptyapp(cut,t0,p1b,cutprop(schnittset),[y:cut][t:in(y,t0)]t40(y,t)):cutprop(schnittset)
-i@t42:=cutapp1a(r,cutprop(schnittset),[x:rat][t:lrt(r,x)]t41(x,t)):cutprop(schnittset)
-p2@t43:=nonemptyapp(cut,s0,p1a,cutprop(schnittset),[y:cut][t:in(y,s0)]t42(y,t)):cutprop(schnittset)
-snt:=cutof(schnittset,t43):cut
-[r:cut][l:less(r,snt)][x0:rat][ux:urt(r,x0)][lx:lrt(snt,x0)]
-t44:=ini(schnittset,t43,x0,lx):in"rt"(x0,schnittset)
-t45:=estie(rat,[x:rat]schnittprop(x),x0,t44):schnittprop(x0)
-[s:cut][a:and(in(s,s0),lrt(s,x0))]
-t46:=ande1(in(s,s0),lrt(s,x0),a):in(s,s0)
-t47:=ande2(in(s,s0),lrt(s,x0),a):lrt(s,x0)
-t48:=andi(urt(r,x0),lrt(s,x0),ux,t47):and(urt(r,x0),lrt(s,x0))
-t49:=somei(rat,[x:rat]and(urt(r,x),lrt(s,x)),x0,t48):less(r,s)
-t50:=ec3e23(is(s,r),more(s,r),less(s,r),satz123b(s,r),satz122(r,s,t49)):not(less(s,r))
-t51:=th3"l.imp"(in(r,t0),less(s,r),t50,<r><t46><s>p2):not(in(r,t0))
-t52:=ore1(in(r,s0),in(r,t0),<r>p0,t51):in(r,s0)
-lx@t53:=someapp(cut,[y:cut]and(in(y,s0),lrt(y,x0)),t45,in(r,s0),[y:cut][t:and(in(y,s0),lrt(y,x0))]t52(y,t)):in(r,s0)
-l@t54:=lessapp(r,snt,l,in(r,s0),[x:rat][t:urt(r,x)][u:lrt(snt,x)]t53(x,t,u)):in(r,s0)
-r@[m:more(r,snt)][x0:rat][lx:lrt(r,x0)][ux:urt(snt,x0)][i:in(r,s0)]
-t55:=andi(in(r,s0),lrt(r,x0),i,lx):and(in(r,s0),lrt(r,x0))
-t56:=somei(cut,[y:cut]and(in(y,s0),lrt(y,x0)),r,t55):schnittprop(x0)
-t57:=estii(rat,[x:rat]schnittprop(x),x0,t56):in"rt"(x0,schnittset)
-t58:=ine(schnittset,t43,x0,t57):lrt(snt,x0)
-ux@t59:=th3"l.imp"(in(r,s0),lrt(snt,x0),ux,[t:in(r,s0)]t58(t)):not(in(r,s0))
-t60:=ore2(in(r,s0),in(r,t0),<r>p0,t59):in(r,t0)
-m@t61:=moreapp(r,snt,m,in(r,t0),[x:rat][t:lrt(r,x)][u:urt(snt,x)]t60(x,t,u)):in(r,t0)
-p2@t62:=andi(prop1(snt),prop2(snt),[x:cut][t:less(x,snt)]t54(x,t),[x:cut][t:more(x,snt)]t61(x,t)):prop3(snt)
-t63:=somei(cut,[x:cut]prop3(x),snt,t62):some([x:cut]prop3(x))
--5p205
-satzp205:=onei(cut,[x:cut]prop3".5p205"(x),t10".5p205",t63".5p205"):one([x:cut]and(all([y:cut][t:less(y,x)]in(y,s0)),all([y:cut][t:more(y,x)]in(y,t0))))
-schnitt:=ind(cut,[x:cut]prop3".5p205"(x),satzp205):cut
-satzp205a:=ande1(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:less(x,schnitt)]in(x,s0))
-satzp205b:=ande2(prop1".5p205"(schnitt),prop2".5p205"(schnitt),oneax(cut,[x:cut]prop3".5p205"(x),satzp205)):all([x:cut][t:more(x,schnitt)]in(x,t0))
-@[r:cut][s:cut]
-+ivad
-@i:=1rp:cut
-r@r1:=pl(r,i):cut
-s@s1:=pl(s,i):cut
-rps:=pl(r,s):cut
-@2:=pl(i,i):cut
-s@t1:=pdeq12a(r1,i,s1,i):eq(pd(pdofrp(r),pdofrp(s)),df(pl(r1,s1),2))
-t2:=tris(cut,pl(r1,s1),pl(rps,2),pl(pl(rps,i),i),4pl23(r,i,s,i),asspl2(rps,i,i)):is(pl(r1,s1),pl(pl(rps,i),i))
-t3:=ispl1(pl(r1,s1),pl(pl(rps,i),i),i,t2):is(pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i))
-t4:=tris(cut,pl(pl(r1,s1),i),pl(pl(pl(rps,i),i),i),pl(pl(rps,i),2),t3,asspl1(pl(rps,i),i,i)):is(pl(pl(r1,s1),i),pl(pl(rps,i),2))
-t5:=eqi12(pl(r1,s1),2,pl(rps,i),i,t4):eq(df(pl(r1,s1),2),pdofrp(rps))
--ivad
-lemmaivad1:=treq(pd(pdofrp(r),pdofrp(s)),df(pl(pl(r,1rp),pl(s,1rp)),pl(1rp,1rp)),pdofrp(pl(r,s)),t1".ivad",t5".ivad"):eq(pd(pdofrp(r),pdofrp(s)),pdofrp(pl(r,s)))
-+*ivad
-s@rs:=ts(r,s):cut
-t6:=tdeq12a(r1,i,s1,i):eq(td(pdofrp(r),pdofrp(s)),df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))))
-t7:=tris(cut,ts(r1,s),pl(rs,ts(i,s)),pl(rs,s),disttp1(r,i,s),ispl2(ts(i,s),s,rs,satz151b(s))):is(ts(r1,s),pl(rs,s))
-t8:=tr3is(cut,ts(r1,s1),pl(ts(r1,s),ts(r1,i)),pl(pl(rs,s),r1),pl(pl(rs,i),rps),disttp2(r1,s,i),ispl12(ts(r1,s),pl(rs,s),ts(r1,i),r1,t7,satz151(r1)),4pl24(rs,s,r,i)):is(ts(r1,s1),pl(pl(rs,i),rps))
-t9:=tris(cut,pl(ts(r1,s1),ts(i,i)),pl(pl(pl(rs,i),rps),i),pl(pl(rs,i),pl(rps,i)),ispl12(ts(r1,s1),pl(pl(rs,i),rps),ts(i,i),i,t8,satz151(i)),asspl1(pl(rs,i),rps,i)):is(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)))
-t10:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(pl(rs,i),pl(rps,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),ispl1(pl(ts(r1,s1),ts(i,i)),pl(pl(rs,i),pl(rps,i)),i,t9),asspl1(pl(rs,i),pl(rps,i),i)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)))
-t11:=tr3is(cut,pl(pl(rps,i),i),pl(rps,2),pl(r1,s1),pl(ts(r1,i),ts(i,s1)),asspl1(rps,i,i),4pl23(r,s,i,i),ispl12(r1,ts(r1,i),s1,ts(i,s1),satz151a(r1),satz151c(s1))):is(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)))
-t12:=tris(cut,pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(pl(rps,i),i)),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))),t10,ispl2(pl(pl(rps,i),i),pl(ts(r1,i),ts(i,s1)),pl(rs,i),t11)):is(pl(pl(ts(r1,s1),ts(i,i)),i),pl(pl(rs,i),pl(ts(r1,i),ts(i,s1))))
-t13:=eqi12(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1)),pl(rs,i),i,t12):eq(df(pl(ts(r1,s1),ts(i,i)),pl(ts(r1,i),ts(i,s1))),pdofrp(rs))
--ivad
-s@lemmaivad2:=treq(td(pdofrp(r),pdofrp(s)),df(pl(ts(pl(r,1rp),pl(s,1rp)),ts(1rp,1rp)),pl(ts(pl(r,1rp),1rp),ts(1rp,pl(s,1rp)))),pdofrp(ts(r,s)),t6".ivad",t13".ivad"):eq(td(pdofrp(r),pdofrp(s)),pdofrp(ts(r,s)))
-[m:mored(pdofrp(r),pdofrp(s))]
-+*ivad
-m@t14:=morede12(r1,i,s1,i,m):more(pl(r1,i),pl(s1,i))
-t15:=satz136a(r1,s1,i,t14):more(r1,s1)
--ivad
-m@lemmaivad3:=satz136a(r,s,1rp,t15".ivad"):more(r,s)
-@[c:dif][a:dif][b:dif][n:not(negd(a))][o:not(negd(b))][e:eq(td(a,a),c)][f:eq(td(b,b),c)]
-+d161
-t1:=treq2(td(a,a),td(b,b),c,e,f):eq(td(a,a),td(b,b))
-t2:=treq(pd(md(td(a,a),td(a,b)),td(b,a)),pd(md(td(a,a),td(a,b)),td(a,b)),td(a,a),eqpd2(td(b,a),td(a,b),md(td(a,a),td(a,b)),comtd(b,a)),pdmd(td(a,a),td(a,b))):eq(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a))
-t3:=tr4eq(td(pd(a,b),md(a,b)),pd(td(a,md(a,b)),td(b,md(a,b))),pd(md(td(a,a),td(a,b)),md(td(b,a),td(b,b))),md(pd(md(td(a,a),td(a,b)),td(b,a)),td(b,b)),md(td(a,a),td(b,b)),disttpd1(a,b,md(a,b)),eqpd12(td(a,md(a,b)),md(td(a,a),td(a,b)),td(b,md(a,b)),md(td(b,a),td(b,b)),disttmd2(a,a,b),disttmd2(b,a,b)),asspd2(md(td(a,a),td(a,b)),td(b,a),m0d(td(b,b))),eqmd1(pd(md(td(a,a),td(a,b)),td(b,a)),td(a,a),td(b,b),t2)):eq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)))
-t4:=eqzero(md(td(a,a),td(b,b)),td(pd(a,b),md(a,b)),symeq(td(pd(a,b),md(a,b)),md(td(a,a),td(b,b)),t3),satzd182e(td(a,a),td(b,b),t1)):zero(td(pd(a,b),md(a,b)))
-t5:=satzd192c(pd(a,b),md(a,b),t4):or(zero(pd(a,b)),zero(md(a,b)))
-[z:zero(a)]
-t6:=eqzero(td(a,a),td(b,b),t1,td01(a,a,z)):zero(td(b,b))
-t7:=th1"l.imp"(zero(b),zero(b),refimp(zero(b)),satzd192c(b,b,t6)):zero(b)
-t8:=zeroeq(a,b,z,t7):eq(a,b)
-f@[p:not(zero(a))]
-t9:=or3e2(zero(a),posd(a),negd(a),axrdo(a),n,p):posd(a)
-t10:=th3"l.imp"(zero(b),zero(a),p,[t:zero(b)]t7(b,a,o,n,f,e,t)):not(zero(b))
-t11:=t9(b,a,o,n,f,e,t10):posd(b)
-t12:=pnot0d(pd(a,b),ppd(a,b,t9,t11)):not(zero(pd(a,b)))
-t13:=ore2(zero(pd(a,b)),zero(md(a,b)),t5,t12):zero(md(a,b))
-t14:=satzd182b(a,b,t13):eq(a,b)
--d161
-satzd161b:=th1"l.imp"(zero(a),eq(a,b),[t:zero(a)]t8".d161"(t),[t:not(zero(a))]t14".d161"(t)):eq(a,b)
-c@[n:not(negd(c))]
-+*d161
-n@[z:zero(c)]
-t15:=zeroeq(td(c,c),c,td01(c,c,z),z):eq(td(c,c),c)
-t16:=andi(not(negd(c)),eq(td(c,c),c),n,t15):and(not(negd(c)),eq(td(c,c),c))
-t17:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),c,t16):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
-n@[o:not(zero(c))]
-t18:=or3e2(zero(c),posd(c),negd(c),axrdo(c),n,o):posd(c)
-crp:=rpofpd(c,t18):cut
-srp:=sqrt(crp):cut
-s:=pdofrp(srp):dif
-t19:=tr3eq(td(s,s),pdofrp(ts(srp,srp)),pdofrp(crp),c,lemmaivad2(srp,srp),isrpepd(ts(srp,srp),crp,thsqrt1(crp)),eqpdrp2(c,t18)):eq(td(s,s),c)
-t20:=andi(not(negd(s)),eq(td(s,s),c),pnotnd(s,posdirp(srp)),t19):and(not(negd(s)),eq(td(s,s),c))
-t21:=somei(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)),s,t20):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
--d161
-n@satzd161a:=th1"l.imp"(zero(c),some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c))),[t:zero(c)]t17".d161"(t),[t:not(zero(c))]t21".d161"(t)):some"l"(dif,[x:dif]and(not(negd(x)),eq(td(x,x),c)))
-@[a:dif][i:intd(a)]
-+intd
-[z:zero(a)]
-t1:=ori1(zero(absd(a)),natd(absd(absd(a))),satzd166f(a,z)):intd(absd(a))
-i@[n:natd(absd(a))]
-t2:=natintd(absd(a),n):intd(absd(a))
--intd
-intabsd:=orapp(zero(a),natd(absd(a)),intd(absd(a)),i,[t:zero(a)]t1".intd"(t),[t:natd(absd(a))]t2".intd"(t)):intd(absd(a))
-+*intd
-n@t4:=eqnatd(absd(a),absd(m0d(a)),satzd178a(a),n):natd(absd(m0d(a)))
--intd
-i@intm0d:=th9"l.or"(zero(a),natd(absd(a)),zero(m0d(a)),natd(absd(m0d(a))),i,[t:zero(a)]satzd176b(a,t),[t:natd(absd(a))]t4".intd"(t)):intd(m0d(a))
-a@[b:dif][i:intd(a)][j:intd(b)]
-+*intd
-j@[z:zero(a)]
-t5:=symeq(pd(a,b),b,pd01(a,b,z)):eq(b,pd(a,b))
-t6:=eqintd(b,pd(a,b),t5,j):intd(pd(a,b))
-j@[z:zero(b)]
-t7:=symeq(pd(a,b),a,pd02(a,b,z)):eq(a,pd(a,b))
-t8:=eqintd(a,pd(a,b),t7,i):intd(pd(a,b))
-a@[i:intd(a)][p:posd(a)]
-t9:=<p>ande2(posd(a),[t:posd(a)]natrp(rpofpd(a,t)),posintnatd(a,p,i)):natrp(rpofpd(a,p))
-j@[pp:posd(pd(a,b))]
-apb1:=rpofpd(pd(a,b),pp):cut
-[p:posd(a)]
-a1:=rpofpd(a,p):cut
-[q:posd(b)]
-b1:=rpofpd(b,q):cut
-t10:=natpl(a1,t9(a,i,p),b1,t9(b,j,q)):natrp(pl(a1,b1))
-t11:=eqpd12(a,pdofrp(a1),b,pdofrp(b1),eqpdrp1(a,p),eqpdrp1(b,q)):eq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)))
-t12:=treq(pd(a,b),pd(pdofrp(a1),pdofrp(b1)),pdofrp(pl(a1,b1)),t11,lemmaivad1(a1,b1)):eq(pd(a,b),pdofrp(pl(a1,b1)))
-t13:=tris(cut,apb1,rpofpd(pdofrp(pl(a1,b1)),posdirp(pl(a1,b1))),pl(a1,b1),eqpderp(pd(a,b),pp,pdofrp(pl(a1,b1)),posdirp(pl(a1,b1)),t12),isrppd2(pl(a1,b1))):is(apb1,pl(a1,b1))
-t14:=isp1(cut,[t:cut]natrp(t),pl(a1,b1),apb1,t10,t13):natrp(apb1)
-t15:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t14(t,p,q)):natd(pd(a,b))
-t16:=natintd(pd(a,b),t15):intd(pd(a,b))
-p@[n:negd(b)]
-t17:=satzd176c(b,n):posd(m0d(b))
-b2:=rpofpd(m0d(b),t17):cut
-t18:=eqpd2(b,m0d(m0d(b)),a,satzd177a(b)):eq(pd(a,b),md(a,m0d(b)))
-t19:=eqposd(pd(a,b),md(a,m0d(b)),t18,pp):posd(md(a,m0d(b)))
-t20:=satzd182a(a,m0d(b),t19):mored(a,m0d(b))
-t21:=eqmored12(a,pdofrp(a1),m0d(b),pdofrp(b2),eqpdrp1(a,p),eqpdrp1(m0d(b),t17),t20):mored(pdofrp(a1),pdofrp(b2))
-t22:=lemmaivad3(a1,b2,t21):more(a1,b2)
-t23:=natmn(a1,t9(a,i,p),b2,t9(m0d(b),intm0d(b,j),t17),t22):natrp(mn(a1,b2,t22))
-t24:=eqpd12(m0d(b),pdofrp(b2),pd(a,b),pdofrp(apb1),eqpdrp1(m0d(b),t17),eqpdrp1(pd(a,b),pp)):eq(pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)))
-t25:=tr4eq(a,md(pd(a,b),b),pd(m0d(b),pd(a,b)),pd(pdofrp(b2),pdofrp(apb1)),pdofrp(pl(b2,apb1)),symeq(md(pd(a,b),b),a,mdpd(a,b)),compd(pd(a,b),m0d(b)),t24,lemmaivad1(b2,apb1)):eq(a,pdofrp(pl(b2,apb1)))
-t26:=tris2(cut,pl(b2,apb1),a1,rpofpd(pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1))),isrppd1(pl(b2,apb1)),eqpderp(a,p,pdofrp(pl(b2,apb1)),posdirp(pl(b2,apb1)),t25)):is(pl(b2,apb1),a1)
-t27:=satz140g(a1,b2,apb1,t22,t26):is(apb1,mn(a1,b2,t22))
-t28:=isp1(cut,[t:cut]natrp(t),mn(a1,b2,t22),apb1,t23,t27):natrp(apb1)
-t29:=andi(posd(pd(a,b)),[t:posd(pd(a,b))]natrp(apb1(t)),pp,[t:posd(pd(a,b))]t28(t,p,n)):natd(pd(a,b))
-t30:=natintd(pd(a,b),t29):intd(pd(a,b))
-p@t31:=rappd(b,intd(pd(a,b)),[t:posd(b)]t16(t),[t:zero(b)]t8(t),[t:negd(b)]t30(t)):intd(pd(a,b))
-pp@[n:negd(a)]
-t31a:=th3"l.imp"(negd(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:negd(b)]npd(a,b,n,t)):not(negd(b))
-t32:=th3"l.imp"(zero(b),negd(pd(a,b)),pnotnd(pd(a,b),pp),[t:zero(b)]eqnegd(a,pd(a,b),symeq(pd(a,b),a,pd02(a,b,t)),n)):not(zero(b))
-t33:=or3e2(zero(b),posd(b),negd(b),axrdo(b),t31a,t32):posd(b)
-t34:=eqposd(pd(a,b),pd(b,a),compd(a,b),pp):posd(pd(b,a))
-t35:=t30(b,a,j,i,t34,t33,n):intd(pd(b,a))
-t36:=eqintd(pd(b,a),pd(a,b),compd(b,a),t35):intd(pd(a,b))
-pp@t37:=rappd(a,intd(pd(a,b)),[t:posd(a)]t31(t),[t:zero(a)]t6(t),[t:negd(a)]t36(t)):intd(pd(a,b))
-j@[0p:zero(pd(a,b))]
-t38:=intdi0(pd(a,b),0p):intd(pd(a,b))
-j@[np:negd(pd(a,b))]
-t39:=satzd176c(pd(a,b),np):posd(m0d(pd(a,b)))
-t40:=eqposd(m0d(pd(a,b)),pd(m0d(a),m0d(b)),satzd180(a,b),t39):posd(pd(m0d(a),m0d(b)))
-t41:=t37(m0d(a),m0d(b),intm0d(a,i),intm0d(b,j),t40):intd(pd(m0d(a),m0d(b)))
-t42:=eqintd(pd(m0d(a),m0d(b)),m0d(pd(a,b)),satzd180a(a,b),t41):intd(m0d(pd(a,b)))
-t43:=intm0d(m0d(pd(a,b)),t42):intd(m0d(m0d(pd(a,b))))
-t44:=eqintd(m0d(m0d(pd(a,b))),pd(a,b),satzd177(pd(a,b)),t43):intd(pd(a,b))
--intd
-j@intpd:=rappd(pd(a,b),intd(pd(a,b)),[t:posd(pd(a,b))]t37".intd"(t),[t:zero(pd(a,b))]t38".intd"(t),[t:negd(pd(a,b))]t44".intd"(t)):intd(pd(a,b))
-intmd:=intpd(a,m0d(b),i,intm0d(b,j)):intd(md(a,b))
-+*intd
-j@[n:not(zero(td(a,b)))]
-t45:=th3"l.imp"(zero(a),zero(td(a,b)),n,[t:zero(a)]td01(a,b,t)):not(zero(a))
-t46:=th3"l.imp"(zero(b),zero(td(a,b)),n,[t:zero(b)]td02(a,b,t)):not(zero(b))
-t47:=satzd166e(a,t45):posd(absd(a))
-a3:=rpofpd(absd(a),t47):cut
-t48:=satzd166e(b,t46):posd(absd(b))
-b3:=rpofpd(absd(b),t48):cut
-t49:=natts(a3,t9(absd(a),intabsd(a,i),t47),b3,t9(absd(b),intabsd(b,j),t48)):natrp(ts(a3,b3))
-t50:=satzd166e(td(a,b),n):posd(absd(td(a,b)))
-[p:posd(absd(td(a,b)))]
-atb3:=rpofpd(absd(td(a,b)),p):cut
-t51:=eqtd12(absd(a),pdofrp(a3),absd(b),pdofrp(b3),eqpdrp1(absd(a),t47),eqpdrp1(absd(b),t48)):eq(td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)))
-t52:=tr3eq(absd(td(a,b)),td(absd(a),absd(b)),td(pdofrp(a3),pdofrp(b3)),pdofrp(ts(a3,b3)),satzd193(a,b),t51,lemmaivad2(a3,b3)):eq(absd(td(a,b)),pdofrp(ts(a3,b3)))
-t53:=tris2(cut,atb3,ts(a3,b3),rpofpd(pdofrp(ts(a3,b3)),posdirp(ts(a3,b3))),eqpderp(absd(td(a,b)),p,pdofrp(ts(a3,b3)),posdirp(ts(a3,b3)),t52),isrppd1(ts(a3,b3))):is(atb3,ts(a3,b3))
-t54:=isp1(cut,[t:cut]natrp(t),ts(a3,b3),atb3,t49,t53):natrp(atb3)
-n@t55:=andi(posd(absd(td(a,b))),[t:posd(absd(td(a,b)))]natrp(atb3(t)),t50,[t:posd(absd(td(a,b)))]t54(t)):natd(absd(td(a,b)))
--intd
-j@inttd:=[t:not(zero(td(a,b)))]t55".intd"(t):intd(td(a,b))
-+r
-@eq:=[x:dif][y:dif]eq"rp"(x,y):[x:dif][y:dif]'prop'
-refeq:=[x:dif]refeq"rp"(x):[x:dif]<x><x>eq
-symeq:=[x:dif][y:dif][t:<y><x>eq]symeq"rp"(x,y,t):[x:dif][y:dif][t:<y><x>eq]<x><y>eq
-treq:=[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]treq"rp"(x,y,z,t,u):[x:dif][y:dif][z:dif][t:<y><x>eq][u:<z><y>eq]<z><x>eq
-[a:dif][s:set(dif)]
-inn:=esti(dif,a,s):'prop'
-@real:=ect"eq"(dif,eq,refeq,symeq,treq):'type'
-[r:real][s:real]
-is:=is"e"(real,r,s):'prop'
-nis:=not(is(r,s)):'prop'
-@[p:[x:real]'prop']
-some:=some"l"(real,p):'prop'
-all:=all"l"(real,p):'prop'
-one:=one"e"(real,p):'prop'
-r@[s0:set(real)]
-in:=esti(real,r,s0):'prop'
-a@realof:=ectelt"eq"(dif,eq,refeq,symeq,treq,a):real
-r@class:=ecect"eq"(dif,eq,refeq,symeq,treq,r):set(dif)
-a@innclass:=th5"eq.4"(dif,eq,refeq,symeq,treq,a):inn(a,class(realof(a)))
-r@[a:dif][b:dif][e:eq"rp"(a,b)][air:inn(a,class(r))]
-eqinn:=th8"eq.4"(dif,eq,refeq,symeq,treq,r,a,air,b,e):inn(b,class(r))
-r@[p:'prop'][p1:[x:dif][xi:inn(x,class(r))]p]
-realapp1:=th3"eq.4"(dif,eq,refeq,symeq,treq,r,p,p1):p
-r@[s:real][p:'prop'][p1:[x:dif][y:dif][xi:inn(x,class(r))][yi:inn(y,class(s))]p]
-+ivr1
-[a:dif][air:inn(a,class(r))]
-t1:=realapp1(s,p,[y:dif]<air><y><a>p1):p
--ivr1
-realapp2:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t1".ivr1"(x,xi)):p
-s@[t:real][p:'prop'][p1:[x:dif][y:dif][z:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))]p]
-+*ivr1
-p1@[a:dif][air:inn(a,class(r))]
-t2:=realapp2(s,t,p,[y:dif][z:dif]<air><z><y><a>p1):p
--ivr1
-p1@realapp3:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t2".ivr1"(x,xi)):p
-t@[u:real][p:'prop'][p1:[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]p]
-+*ivr1
-p1@[a:dif][air:inn(a,class(r))]
-t3:=realapp3(s,t,u,p,[y:dif][z:dif][v:dif]<air><v><z><y><a>p1):p
--ivr1
-p1@realapp4:=realapp1(r,p,[x:dif][xi:inn(x,class(r))]t3".ivr1"(x,xi)):p
-s@[a1:dif][b1:dif][a1ir:inn(a1,class(r))][b1is:inn(b1,class(s))][e:eq"rp"(a1,b1)]
-isin:=th3"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,e):is(r,s)
-b1is@[i:is(r,s)]
-isex:=th5"eq.5"(dif,eq,refeq,symeq,treq,r,s,a1,a1ir,b1,b1is,i):eq"rp"(a1,b1)
-b1is@[n:not(eq"rp"(a1,b1))]
-nisin:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),n,[t:is(r,s)]isex(t)):nis(r,s)
-b1is@[n:nis(r,s)]
-nisex:=th3"l.imp"(eq"rp"(a1,b1),is(r,s),n,[t:eq"rp"(a1,b1)]isin(t)):not(eq"rp"(a1,b1))
-@[alpha:'type'][f:[x:dif]alpha]
-fixf:=fixfu"eq"(dif,eq,refeq,symeq,treq,alpha,f):'prop'
-[ff:fixf(alpha,f)][r0:real]
-indreal:=indeq"eq"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0):alpha
-[a:dif][air:inn(a,class(r0))]
-isindreal:=th2"eq.10"(dif,eq,refeq,symeq,treq,alpha,f,ff,r0,a,air):is"e"(alpha,<a>f,indreal)
-alpha@[g:[x:dif][y:dif]alpha]
-fixf2:=fixfu2"eq"(dif,eq,refeq,symeq,treq,alpha,g):'prop'
-[ff2:fixf2(alpha,g)][r0:real][s0:real]
-indreal2:=indeq2"eq"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0):alpha
-[a:dif][b:dif][air:inn(a,class(r0))][bis:inn(b,class(s0))]
-isindreal2:=th1"eq.11"(dif,eq,refeq,symeq,treq,alpha,g,ff2,r0,s0,a,air,b,bis):is"e"(alpha,<b><a>g,indreal2)
-@0:=realof(df(1rp,1rp)):real
-r@[a0:dif][a0ir:inn(a0,class(r))][z:zero(a0)]
-0in:=isin(r,0,a0,df(1rp,1rp),a0ir,innclass(df(1rp,1rp)),zeroeq(a0,df(1rp,1rp),z,zeroi(1rp,1rp,refis(cut,1rp)))):is(r,0)
-a0ir@[i:is(r,0)]
-0ex:=eqzero(df(1rp,1rp),a0,isex(0,r,df(1rp,1rp),a0,innclass(df(1rp,1rp)),a0ir,symis(real,r,0,i)),tris(cut,stm(df(1rp,1rp)),1rp,std(df(1rp,1rp)),stmis(1rp,1rp),isstd(1rp,1rp))):zero(a0)
-+*ivr1
-a0@propp:=and(inn(a0,class(r)),posd(a0)):'prop'
--ivr1
-r@pos:=some"l"(dif,[x:dif]propp".ivr1"(x)):'prop'
-a0ir@[p:posd(a0)]
-+*ivr1
-p@t4:=andi(inn(a0,class(r)),posd(a0),a0ir,p):propp(a0)
--ivr1
-p@posin:=somei(dif,[x:dif]propp".ivr1"(x),a0,t4".ivr1"):pos(r)
-a0ir@[p:pos(r)]
-+*ivr1
-p@[a:dif][q1:propp(a)]
-t5:=ande1(inn(a,class(r)),posd(a),q1):inn(a,class(r))
-t6:=ande2(inn(a,class(r)),posd(a),q1):posd(a)
-t7:=eqposd(a,a0,isex(r,r,a,a0,t5,a0ir,refis(real,r)),t6):posd(a0)
--ivr1
-p@posex:=someapp(dif,[x:dif]propp".ivr1"(x),p,posd(a0),[x:dif][t:propp".ivr1"(x)]t7".ivr1"(x,t)):posd(a0)
-+*ivr1
-a0@propn:=and(inn(a0,class(r)),negd(a0)):'prop'
--ivr1
-r@neg:=some"l"(dif,[x:dif]propn".ivr1"(x)):'prop'
-a0ir@[n:negd(a0)]
-+*ivr1
-n@t8:=andi(inn(a0,class(r)),negd(a0),a0ir,n):propn(a0)
--ivr1
-n@negin:=somei(dif,[x:dif]propn".ivr1"(x),a0,t8".ivr1"):neg(r)
-a0ir@[n:neg(r)]
-+*ivr1
-n@[a:dif][pl:propn(a)]
-t9:=ande1(inn(a,class(r)),negd(a),pl):inn(a,class(r))
-t10:=ande2(inn(a,class(r)),negd(a),pl):negd(a)
-t11:=eqnegd(a,a0,isex(r,r,a,a0,t9,a0ir,refis(real,r)),t10):negd(a0)
--ivr1
-n@negex:=someapp(dif,[x:dif]propn".ivr1"(x),n,negd(a0),[x:dif][t:propn".ivr1"(x)]t11".ivr1"(x,t)):negd(a0)
-+*ivr1
-a0ir@[p:posd(a0)]
-t12:=or3i2(is(r,0),pos(r),neg(r),posin(p)):or3(is(r,0),pos(r),neg(r))
-a0ir@[z:zero(a0)]
-t13:=or3i1(is(r,0),pos(r),neg(r),0in(z)):or3(is(r,0),pos(r),neg(r))
-a0ir@[n:negd(a0)]
-t14:=or3i3(is(r,0),pos(r),neg(r),negin(n)):or3(is(r,0),pos(r),neg(r))
-a0ir@t15:=rappd(a0,or3(is(r,0),pos(r),neg(r)),[t:posd(a0)]t12(t),[t:zero(a0)]t13(t),[t:negd(a0)]t14(t)):or3(is(r,0),pos(r),neg(r))
--ivr1
-r@axrlo:=realapp1(r,or3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t15".ivr1"(x,xi)):or3(is(r,0),pos(r),neg(r))
-+*ivr1
-a0ir@[i:is(r,0)]
-t16:=th3"l.imp"(pos(r),posd(a0),0notpd(a0,0ex(i)),[t:pos(r)]posex(t)):not(pos(r))
-a0ir@[p:pos(r)]
-t17:=th3"l.imp"(neg(r),negd(a0),pnotnd(a0,posex(p)),[t:neg(r)]negex(t)):not(neg(r))
-a0ir@[n:neg(r)]
-t18:=th3"l.imp"(is(r,0),zero(a0),nnot0d(a0,negex(n)),[t:is(r,0)]0ex(t)):not(is(r,0))
-a0ir@t19:=th6"l.ec3"(is(r,0),pos(r),neg(r),[t:is(r,0)]t16(t),[t:pos(r)]t17(t),[t:neg(r)]t18(t)):ec3(is(r,0),pos(r),neg(r))
--ivr1
-r@axrle:=realapp1(r,ec3(is(r,0),pos(r),neg(r)),[x:dif][xi:inn(x,class(r))]t19".ivr1"(x,xi)):ec3(is(r,0),pos(r),neg(r))
-axrl:=orec3i(is(r,0),pos(r),neg(r),axrlo,axrle):orec3(is(r,0),pos(r),neg(r))
-[p:'prop'][p1:[t:pos(r)]p][p2:[t:is(r,0)]p][p3:[t:neg(r)]p]
-rapp:=or3app(is(r,0),pos(r),neg(r),p,axrlo,p2,p1,p3):p
-r@[p:pos(r)]
-pnotn:=ec3e23(is(r,0),pos(r),neg(r),axrle,p):not(neg(r))
-pnot0:=ec3e21(is(r,0),pos(r),neg(r),axrle,p):nis(r,0)
-r@[i:is(r,0)]
-0notp:=ec3e12(is(r,0),pos(r),neg(r),axrle,i):not(pos(r))
-0notn:=ec3e13(is(r,0),pos(r),neg(r),axrle,i):not(neg(r))
-r@[n:neg(r)]
-nnotp:=ec3e32(is(r,0),pos(r),neg(r),axrle,n):not(pos(r))
-nnot0:=ec3e31(is(r,0),pos(r),neg(r),axrle,n):nis(r,0)
-s@[i:is(r,s)][p:pos(r)]
-ispos:=isp(real,[x:real]pos(x),r,s,p,i):pos(s)
-i@[n:neg(r)]
-isneg:=isp(real,[x:real]neg(x),r,s,n,i):neg(s)
-@[r0:cut]
-pofrp:=realof(pdofrp(r0)):real
-nofrp:=realof(ndofrp(r0)):real
-[s0:cut][i:is"rp"(r0,s0)]
-isrpep:=isf(cut,real,[x:cut]pofrp(x),r0,s0,i):is(pofrp(r0),pofrp(s0))
-isrpen:=isf(cut,real,[x:cut]nofrp(x),r0,s0,i):is(nofrp(r0),nofrp(s0))
-s0@[i:is(pofrp(r0),pofrp(s0))]
-+*ivr1
-i"r"@t20:=isex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),i):eq"rp"(pdofrp(r0),pdofrp(s0))
--ivr1
-i@isrpip:=isrpipd(r0,s0,t20".ivr1"):is"rp"(r0,s0)
-s0@[i:is(nofrp(r0),nofrp(s0))]
-+*ivr1
-i"r"@t21:=isex(nofrp(r0),nofrp(s0),ndofrp(r0),ndofrp(s0),innclass(ndofrp(r0)),innclass(ndofrp(s0)),i):eq"rp"(ndofrp(r0),ndofrp(s0))
--ivr1
-i@isrpin:=isrpind(r0,s0,t21".ivr1"):is"rp"(r0,s0)
-r0@posi:=posin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),posdirp(r0)):pos(pofrp(r0))
-negi:=negin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),negdirp(r0)):neg(nofrp(r0))
-s@[r0:cut][s0:cut][i:is(r,pofrp(r0))][j:is(s,pofrp(s0))][k:is(r,s)]
-+*ivr1
-k@t22:=isrpip(r0,s0,tr3is(real,pofrp(r0),r,s,pofrp(s0),symis(real,r,pofrp(r0),i),k,j)):is"rp"(r0,s0)
-r@t23:=[x:cut][y:cut][t:is(r,pofrp(x))][u:is(r,pofrp(y))]t22(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,pofrp(x)))
-a0ir@[p1:pos(r)]
-t24:=posex(p1):posd(a0)
-pr:=rpofpd(a0,t24):cut
-t25:=isin(r,pofrp(pr),a0,pdofrp(pr),a0ir,innclass(pdofrp(pr)),eqpdrp1(a0,t24)):is(r,pofrp(pr))
-t26:=somei(cut,[x:cut]is(r,pofrp(x)),pr,t25):some"rp"([x:cut]is(r,pofrp(x)))
--ivr1
-r@[p:pos(r)]
-+*ivr1
-p"r"@t27:=realapp1(some"rp"([x:cut]is(r,pofrp(x))),[x:dif][t:inn(x,class(r))]t26(x,t,p)):some"rp"([x:cut]is(r,pofrp(x)))
-t28:=onei(cut,[x:cut]is(r,pofrp(x)),t23,t27):one"rp"([x:cut]is(r,pofrp(x)))
--ivr1
-p@rpofp:=ind(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):cut
-isprp1:=oneax(cut,[x:cut]is(r,pofrp(x)),t28".ivr1"):is(r,pofrp(rpofp(r,p)))
-isprp2:=symis(real,r,pofrp(rpofp(r,p)),isprp1):is(pofrp(rpofp(r,p)),r)
-@[r1:real][p:pos(r1)][s1:real][q:pos(s1)][i:is(r1,s1)]
-isperp:=t22".ivr1"(r1,s1,rpofp(r1,p),rpofp(s1,q),isprp1(r1,p),isprp1(s1,q),i):is"rp"(rpofp(r1,p),rpofp(s1,q))
-q@[i:is"rp"(rpofp(r1,p),rpofp(s1,q))]
-ispirp:=tr3is(real,r1,pofrp(rpofp(r1,p)),pofrp(rpofp(s1,q)),s1,isprp1(r1,p),isrpep(rpofp(r1,p),rpofp(s1,q),i),isprp2(s1,q)):is(r1,s1)
-@[r0:cut]
-isrpp1:=t22".ivr1"(pofrp(r0),pofrp(r0),r0,rpofp(pofrp(r0),posi(r0)),refis(real,pofrp(r0)),isprp1(pofrp(r0),posi(r0)),refis(real,pofrp(r0))):is"rp"(r0,rpofp(pofrp(r0),posi(r0)))
-isrpp2:=symis(cut,r0,rpofp(pofrp(r0),posi(r0)),isrpp1):is"rp"(rpofp(pofrp(r0),posi(r0)),r0)
-s@[r0:cut][s0:cut][i:is(r,nofrp(r0))][j:is(s,nofrp(s0))][k:is(r,s)]
-+*ivr1
-k@t29:=isrpin(r0,s0,tr3is(real,nofrp(r0),r,s,nofrp(s0),symis(real,r,nofrp(r0),i),k,j)):is"rp"(r0,s0)
-r@t30:=[x:cut][y:cut][t:is(r,nofrp(x))][u:is(r,nofrp(y))]t29(r,r,x,y,t,u,refis(real,r)):amone(cut,[x:cut]is(r,nofrp(x)))
-a0ir@[n1:neg(r)]
-t31:=negex(n1):negd(a0)
-nr:=rpofnd(a0,t31):cut
-t32:=isin(r,nofrp(nr),a0,ndofrp(nr),a0ir,innclass(ndofrp(nr)),eqndrp1(a0,t31)):is(r,nofrp(nr))
-t33:=somei(cut,[x:cut]is(r,nofrp(x)),nr,t32):some"rp"([x:cut]is(r,nofrp(x)))
--ivr1
-r@[n:neg(r)]
-+*ivr1
-n"r"@t34:=realapp1(some"rp"([x:cut]is(r,nofrp(x))),[x:dif][t:inn(x,class(r))]t33(x,t,n)):some"rp"([x:cut]is(r,nofrp(x)))
-t35:=onei(cut,[x:cut]is(r,nofrp(x)),t30,t34):one"rp"([x:cut]is(r,nofrp(x)))
--ivr1
-n@rpofn:=ind(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):cut
-isnrp1:=oneax(cut,[x:cut]is(r,nofrp(x)),t35".ivr1"):is(r,nofrp(rpofn(r,n)))
-isnrp2:=symis(real,r,nofrp(rpofn(r,n)),isnrp1):is(nofrp(rpofn(r,n)),r)
-@[r1:real][n:neg(r1)][s1:real][m:neg(s1)][i:is(r1,s1)]
-isnerp:=t29".ivr1"(r1,s1,rpofn(r1,n),rpofn(s1,m),isnrp1(r1,n),isnrp1(s1,m),i):is"rp"(rpofn(r1,n),rpofn(s1,m))
-m@[i:is"rp"(rpofn(r1,n),rpofn(s1,m))]
-isnirp:=tr3is(real,r1,nofrp(rpofn(r1,n)),nofrp(rpofn(s1,m)),s1,isnrp1(r1,n),isrpen(rpofn(r1,n),rpofn(s1,m),i),isnrp2(s1,m)):is(r1,s1)
-@[r0:cut]
-isrpn1:=t29".ivr1"(nofrp(r0),nofrp(r0),r0,rpofn(nofrp(r0),negi(r0)),refis(real,nofrp(r0)),isnrp1(nofrp(r0),negi(r0)),refis(real,nofrp(r0))):is"rp"(r0,rpofn(nofrp(r0),negi(r0)))
-isrpn2:=symis(cut,r0,rpofn(nofrp(r0),negi(r0)),isrpn1):is"rp"(rpofn(nofrp(r0),negi(r0)),r0)
-r@satz163:=refis(real,r):is(r,r)
-s@[i:is(r,s)]
-satz164:=symis(real,r,s,i):is(s,r)
-t@[i:is(r,s)][j:is(s,t)]
-satz165:=tris(real,r,s,t,i,j):is(r,t)
-@absdr:=[x:dif]realof(absd(x)):[x:dif]real
-+ivr2
-[a:dif][b:dif][e:eq"rp"(a,b)]
-t1:=isin(realof(absd(a)),realof(absd(b)),absd(a),absd(b),innclass(absd(a)),innclass(absd(b)),eqabsd(a,b,e)):is(<a>absdr,<b>absdr)
--ivr2
-fabsdr:=[x:dif][y:dif][t:<y><x>eq]t1".ivr2"(x,y,t):fixf(real,absdr)
-r@abs:=indreal(real,absdr,fabsdr,r):real
-+*ivr2
-a0ir@t2:=isindreal(real,absdr,fabsdr,r,a0,a0ir):is(realof(absd(a0)),abs(r))
--ivr2
-a0ir@aica:=isp(real,[x:real]inn(absd(a0),class(x)),realof(absd(a0)),abs(r),innclass(absd(a0)),t2".ivr2"):inn(absd(a0),class(abs(r)))
-s@[i:is(r,s)]
-isabs:=isf(real,real,[x:real]abs(x),r,s,i):is(abs(r),abs(s))
-+2r166
-a0ir@[p:pos(r)]
-t1:=satzd166a(a0,posex(p)):posd(absd(a0))
-t2:=posin(abs(r),absd(a0),aica,t1):pos(abs(r))
--2r166
-r@[p:pos(r)]
-satz166a:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t2".2r166"(x,t,p)):pos(abs(r))
-+*2r166
-a0ir@[n:neg(r)]
-t3:=satzd166b(a0,negex(n)):posd(absd(a0))
-t4:=posin(abs(r),absd(a0),aica,t3):pos(abs(r))
--2r166
-r@[n:neg(r)]
-satz166b:=realapp1(pos(abs(r)),[x:dif][t:inn(x,class(r))]t4".2r166"(x,t,n)):pos(abs(r))
-+*2r166
-b1is@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
-t5:=satzd166c(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
-t6:=isin(t5):is(r,s)
--2r166
-s@[p:pos(r)][q:pos(s)][i:is(abs(r),abs(s))]
-satz166c:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".2r166"(x,y,t,u,p,q,i)):is(r,s)
-+*2r166
-b1is@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
-t7:=satzd166d(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o),isex(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is),i)):eq"rp"(a1,b1)
-t8:=isin(t7):is(r,s)
--2r166
-s@[n:neg(r)][o:neg(s)][i:is(abs(r),abs(s))]
-satz166d:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".2r166"(x,y,t,u,n,o,i)):is(r,s)
-r@[n:nis(r,0)]
-satz166e:=rapp(r,pos(abs(r)),[t:pos(r)]satz166a(t),th2"l.imp"(is(r,0),pos(abs(r)),n),[t:neg(r)]satz166b(t)):pos(abs(r))
-+*2r166
-a0ir@[i:is(r,0)]
-t9:=satzd166f(a0,0ex(i)):zero(absd(a0))
-t10:=0in(abs(r),absd(a0),aica,t9):is(abs(r),0)
--2r166
-r@[i:is(r,0)]
-satz166f:=realapp1(is(abs(r),0),[x:dif][t:inn(x,class(r))]t10".2r166"(x,t,i)):is(abs(r),0)
-s@more:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),mored(x,y)))):'prop'
-+*ivr2
-b1@propm:=and3(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1)):'prop'
--ivr2
-b1is@[m:mored(a1,b1)]
-+*ivr2
-m@t3:=and3i(inn(a1,class(r)),inn(b1,class(s)),mored(a1,b1),a1ir,b1is,m):propm(a1,b1)
-t4:=somei(dif,[x:dif]propm(a1,x),b1,t3):some"l"(dif,[x:dif]propm(a1,x))
--ivr2
-m@morein:=somei(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),a1,t4".ivr2"):more(r,s)
-b1is@[m:more(r,s)]
-+*ivr2
-m@[a:dif][sa:some"l"(dif,[x:dif]propm(a,x))][b:dif][p2:propm(a,b)]
-t5:=and3e1(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(a,class(r))
-t6:=and3e2(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):inn(b,class(s))
-t7:=and3e3(inn(a,class(r)),inn(b,class(s)),mored(a,b),p2):mored(a,b)
-t8:=eqmored12(a,a1,b,b1,isex(r,r,a,a1,t5,a1ir,refis(real,r)),isex(s,s,b,b1,t6,b1is,refis(real,s)),t7):mored(a1,b1)
-sa@t9:=someapp(dif,[x:dif]propm(a,x),sa,mored(a1,b1),[x:dif][t:propm(a,x)]t8(x,t)):mored(a1,b1)
--ivr2
-m@moreex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propm".ivr2"(x,y)),m,mored(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propm".ivr2"(x,y))]t9".ivr2"(x,t)):mored(a1,b1)
-s@less:=some"l"(dif,[x:dif]some"l"(dif,[y:dif]and3(inn(x,class(r)),inn(y,class(s)),lessd(x,y)))):'prop'
-+*ivr2
-b1@propl:=and3(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1)):'prop'
--ivr2
-b1is@[l:lessd(a1,b1)]
-+*ivr2
-l@t10:=and3i(inn(a1,class(r)),inn(b1,class(s)),lessd(a1,b1),a1ir,b1is,l):propl(a1,b1)
-t11:=somei(dif,[x:dif]propl(a1,x),b1,t10):some"l"(dif,[x:dif]propl(a1,x))
--ivr2
-l@lessin:=somei(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),a1,t11".ivr2"):less(r,s)
-b1is@[l:less(r,s)]
-+*ivr2
-l@[a:dif][sa:some"l"(dif,[x:dif]propl(a,x))][b:dif][p2:propl(a,b)]
-t12:=and3e1(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(a,class(r))
-t13:=and3e2(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):inn(b,class(s))
-t14:=and3e3(inn(a,class(r)),inn(b,class(s)),lessd(a,b),p2):lessd(a,b)
-t15:=eqlessd12(a,a1,b,b1,isex(r,r,a,a1,t12,a1ir,refis(real,r)),isex(s,s,b,b1,t13,b1is,refis(real,s)),t14):lessd(a1,b1)
-sa@t16:=someapp(dif,[x:dif]propl(a,x),sa,lessd(a1,b1),[x:dif][t:propl(a,x)]t15(x,t)):lessd(a1,b1)
--ivr2
-l@lessex:=someapp(dif,[x:dif]some"l"(dif,[y:dif]propl".ivr2"(x,y)),l,lessd(a1,b1),[x:dif][t:some"l"(dif,[y:dif]propl".ivr2"(x,y))]t16".ivr2"(x,t)):lessd(a1,b1)
-t@[i:is(r,s)][m:more(r,t)]
-ismore1:=isp(real,[x:real]more(x,t),r,s,m,i):more(s,t)
-i@[m:more(t,r)]
-ismore2:=isp(real,[x:real]more(t,x),r,s,m,i):more(t,s)
-i@[l:less(r,t)]
-isless1:=isp(real,[x:real]less(x,t),r,s,l,i):less(s,t)
-i@[l:less(t,r)]
-isless2:=isp(real,[x:real]less(t,x),r,s,l,i):less(t,s)
-u@[i:is(r,s)][j:is(t,u)][m:more(r,t)]
-ismore12:=ismore2(t,u,s,j,ismore1(r,s,t,i,m)):more(s,u)
-j@[l:less(r,t)]
-isless12:=isless2(t,u,s,j,isless1(r,s,t,i,l)):less(s,u)
-+*ivr2
-b1is@[m:more(r,s)]
-t17:=lemmad5(a1,b1,moreex(m)):lessd(b1,a1)
-t18:=lessin(s,r,b1,a1,b1is,a1ir,t17):less(s,r)
--ivr2
-s@[m:more(r,s)]
-lemma1:=realapp2(less(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t18".ivr2"(x,y,t,u,m)):less(s,r)
-+*ivr2
-b1is@[l:less(r,s)]
-t19:=lemmad6(a1,b1,lessex(l)):mored(b1,a1)
-t20:=morein(s,r,b1,a1,b1is,a1ir,t19):more(s,r)
--ivr2
-s@[l:less(r,s)]
-lemma2:=realapp2(more(s,r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t20".ivr2"(x,y,t,u,l)):more(s,r)
-+2r167
-b1is@t1:=satzd167a(a1,b1):or3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
-[e:eq"rp"(a1,b1)]
-t2:=or3i1(is(r,s),more(r,s),less(r,s),isin(e)):or3(is(r,s),more(r,s),less(r,s))
-b1is@[m:mored(a1,b1)]
-t3:=or3i2(is(r,s),more(r,s),less(r,s),morein(m)):or3(is(r,s),more(r,s),less(r,s))
-b1is@[l:lessd(a1,b1)]
-t4:=or3i3(is(r,s),more(r,s),less(r,s),lessin(l)):or3(is(r,s),more(r,s),less(r,s))
-b1is@t5:=or3app(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),or3(is(r,s),more(r,s),less(r,s)),t1,[t:eq"rp"(a1,b1)]t2(t),[t:mored(a1,b1)]t3(t),[t:lessd(a1,b1)]t4(t)):or3(is(r,s),more(r,s),less(r,s))
-t6:=satzd167b(a1,b1):ec3(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1))
-[i:is(r,s)]
-t7:=th3"l.imp"(more(r,s),mored(a1,b1),ec3e12(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,isex(i)),[t:more(r,s)]moreex(t)):not(more(r,s))
-b1is@[m:more(r,s)]
-t8:=th3"l.imp"(less(r,s),lessd(a1,b1),ec3e23(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,moreex(m)),[t:less(r,s)]lessex(t)):not(less(r,s))
-b1is@[l:less(r,s)]
-t9:=th3"l.imp"(is(r,s),eq"rp"(a1,b1),ec3e31(eq"rp"(a1,b1),mored(a1,b1),lessd(a1,b1),t6,lessex(l)),[t:is(r,s)]isex(t)):not(is(r,s))
-b1is@t10:=th6"l.ec3"(is(r,s),more(r,s),less(r,s),th1"l.ec"(is(r,s),more(r,s),[t:is(r,s)]t7(t)),th1"l.ec"(more(r,s),less(r,s),[t:more(r,s)]t8(t)),th1"l.ec"(less(r,s),is(r,s),[t:less(r,s)]t9(t))):ec3(is(r,s),more(r,s),less(r,s))
-t11:=orec3i(is(r,s),more(r,s),less(r,s),t5,t10):orec3(is(r,s),more(r,s),less(r,s))
--2r167
-s@satz167:=realapp2(orec3(is(r,s),more(r,s),less(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".2r167"(x,y,t,u)):orec3(is(r,s),more(r,s),less(r,s))
-satz167a:=orec3e1(is(r,s),more(r,s),less(r,s),satz167):or3(is(r,s),more(r,s),less(r,s))
-satz167b:=orec3e2(is(r,s),more(r,s),less(r,s),satz167):ec3(is(r,s),more(r,s),less(r,s))
-moreis:=or(more(r,s),is(r,s)):'prop'
-lessis:=or(less(r,s),is(r,s)):'prop'
-[m:moreis(r,s)]
-satz168a:=th9"l.or"(more(r,s),is(r,s),less(s,r),is(s,r),m,[t:more(r,s)]lemma1(t),[t:is(r,s)]symis(real,r,s,t)):lessis(s,r)
-s@[l:lessis(r,s)]
-satz168b:=th9"l.or"(less(r,s),is(r,s),more(s,r),is(s,r),l,[t:less(r,s)]lemma2(t),[t:is(r,s)]symis(real,r,s,t)):moreis(s,r)
-t@[i:is(r,s)][m:moreis(r,t)]
-ismoreis1:=isp(real,[x:real]moreis(x,t),r,s,m,i):moreis(s,t)
-i@[m:moreis(t,r)]
-ismoreis2:=isp(real,[x:real]moreis(t,x),r,s,m,i):moreis(t,s)
-i@[l:lessis(r,t)]
-islessis1:=isp(real,[x:real]lessis(x,t),r,s,l,i):lessis(s,t)
-i@[l:lessis(t,r)]
-islessis2:=isp(real,[x:real]lessis(t,x),r,s,l,i):lessis(t,s)
-u@[i:is(r,s)][j:is(t,u)][m:moreis(r,t)]
-ismoreis12:=ismoreis2(t,u,s,j,ismoreis1(r,s,t,i,m)):moreis(s,u)
-j@[l:lessis(r,t)]
-islessis12:=islessis2(t,u,s,j,islessis1(r,s,t,i,l)):lessis(s,u)
-s@[m:more(r,s)]
-moreisi1:=ori1(more(r,s),is(r,s),m):moreis(r,s)
-s@[l:less(r,s)]
-lessisi1:=ori1(less(r,s),is(r,s),l):lessis(r,s)
-s@[i:is(r,s)]
-moreisi2:=ori2(more(r,s),is(r,s),i):moreis(r,s)
-lessisi2:=ori2(less(r,s),is(r,s),i):lessis(r,s)
-b1is@[m:moreq(a1,b1)]
-moreisin:=orapp(mored(a1,b1),eq"rp"(a1,b1),moreis(r,s),m,[t:mored(a1,b1)]moreisi1(morein(t)),[t:eq"rp"(a1,b1)]moreisi2(isin(t))):moreis(r,s)
-b1is@[m:moreis(r,s)]
-moreisex:=orapp(more(r,s),is(r,s),moreq(a1,b1),m,[t:more(r,s)]moreqi1(a1,b1,moreex(t)),[t:is(r,s)]moreqi2(a1,b1,isex(t))):moreq(a1,b1)
-b1is@[l:lesseq(a1,b1)]
-lessisin:=orapp(lessd(a1,b1),eq"rp"(a1,b1),lessis(r,s),l,[t:lessd(a1,b1)]lessisi1(lessin(t)),[t:eq"rp"(a1,b1)]lessisi2(isin(t))):lessis(r,s)
-b1is@[l:lessis(r,s)]
-lessisex:=orapp(less(r,s),is(r,s),lesseq(a1,b1),l,[t:less(r,s)]lesseqi1(a1,b1,lessex(t)),[t:is(r,s)]lesseqi2(a1,b1,isex(t))):lesseq(a1,b1)
-s@[m:moreis(r,s)]
-satz167c:=th7"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,comor(more(r,s),is(r,s),m)):not(less(r,s))
-s@[l:lessis(r,s)]
-satz167d:=th9"l.ec3"(is(r,s),more(r,s),less(r,s),satz167b,l):not(more(r,s))
-s@[n:not(more(r,s))]
-satz167e:=th2"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n):lessis(r,s)
-s@[n:not(less(r,s))]
-s@[n:not(less(r,s))]
-satz167f:=comor(is(r,s),more(r,s),th3"l.or3"(is(r,s),more(r,s),less(r,s),satz167a,n)):moreis(r,s)
-s@[m:more(r,s)]
-satz167g:=th3"l.imp"(lessis(r,s),not(more(r,s)),weli(more(r,s),m),[t:lessis(r,s)]satz167d(t)):not(lessis(r,s))
-s@[l:less(r,s)]
-satz167h:=th3"l.imp"(moreis(r,s),not(less(r,s)),weli(less(r,s),l),[t:moreis(r,s)]satz167c(t)):not(moreis(r,s))
-s@[n:not(moreis(r,s))]
-satz167j:=or3e3(is(r,s),more(r,s),less(r,s),satz167a,th5"l.or"(more(r,s),is(r,s),n),th4"l.or"(more(r,s),is(r,s),n)):less(r,s)
-s@[n:not(lessis(r,s))]
-satz167k:=or3e2(is(r,s),more(r,s),less(r,s),satz167a,th4"l.or"(less(r,s),is(r,s),n),th5"l.or"(less(r,s),is(r,s),n)):more(r,s)
-r@[p:pos(r)]
-+2r169
-[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t1:=satzd169a(a,b,0ex(0,b,bi0,refis(real,0)),posex(a,air,p)):mored(a,b)
-t2:=morein(r,0,a,b,air,bi0,t1):more(r,0)
--2r169
-satz169a:=realapp2(r,0,more(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r169"(x,y,t,u)):more(r,0)
-r@[m:more(r,0)]
-+*2r169
-m@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t3:=satzd169b(a,b,0ex(0,b,bi0,refis(real,0)),moreex(r,0,a,b,air,bi0,m)):posd(a)
-t4:=posin(r,a,air,t3):pos(r)
--2r169
-m@satz169b:=realapp2(r,0,pos(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t4".2r169"(x,y,t,u)):pos(r)
-r@[n:neg(r)]
-+*2r169
-n@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t5:=satzd169c(a,b,0ex(0,b,bi0,refis(real,0)),negex(a,air,n)):lessd(a,b)
-t6:=lessin(r,0,a,b,air,bi0,t5):less(r,0)
--2r169
-n@satz169c:=realapp2(r,0,less(r,0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t6".2r169"(x,y,t,u)):less(r,0)
-r@[l:less(r,0)]
-+*2r169
-l@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t7:=satzd169d(a,b,0ex(0,b,bi0,refis(real,0)),lessex(r,0,a,b,air,bi0,l)):negd(a)
-t8:=negin(r,a,air,t7):neg(r)
--2r169
-l@satz169d:=realapp2(r,0,neg(r),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t8".2r169"(x,y,t,u)):neg(r)
-+2r170
-r@[a:dif][b:dif][air:inn(a,class(r))][bi0:inn(b,class(0))]
-t1:=satzd170(a,b,0ex(0,b,bi0,refis(real,0))):moreq(absd(a),b)
-t2:=moreisin(abs(r),0,absd(a),b,aica(r,a,air),bi0,t1):moreis(abs(r),0)
--2r170
-r@satz170:=realapp2(r,0,moreis(abs(r),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(0))]t2".2r170"(x,y,t,u)):moreis(abs(r),0)
-satz170a:=th3"l.imp"(neg(abs(r)),less(abs(r),0),satz167c(abs(r),0,satz170),[t:neg(abs(r))]satz169c(abs(r),t)):not(neg(abs(r)))
-t@[l:less(r,s)][k:less(s,t)]
-+2r171
-[a:dif][b:dif][c:dif][air:inn(a,class(r))][bis:inn(b,class(s))][cit:inn(c,class(t))]
-t1:=satzd171(a,b,c,lessex(r,s,a,b,air,bis,l),lessex(s,t,b,c,bis,cit,k)):lessd(a,c)
-t2:=lessin(r,t,a,c,air,cit,t1):less(r,t)
--2r171
-satz171:=realapp3(r,s,t,less(r,t),[x:dif][y:dif][z:dif][w:inn(x,class(r))][u:inn(y,class(s))][v:inn(z,class(t))]t2".2r171"(x,y,z,w,u,v)):less(r,t)
-trless:=satz171:less(r,t)
-t@[m:more(r,s)][n:more(s,t)]
-trmore:=lemma2(t,r,trless(t,s,r,lemma1(s,t,n),lemma1(r,s,m))):more(r,t)
-t@[a2:dif][b2:dif][c2:dif][a2ir:inn(a2,class(r))][b2is:inn(b2,class(s))][c2it:inn(c2,class(t))]
-+2r172
-[l:lessis(r,s)][k:less(s,t)]
-t1:=satzd172a(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
-t2:=lessin(r,t,a2,c2,a2ir,c2it,t1):less(r,t)
--2r172
-t@[l:lessis(r,s)][k:less(s,t)]
-satz172a:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
-+*2r172
-c2it@[l:less(r,s)][k:lessis(s,t)]
-t3:=satzd172b(a2,b2,c2,lessex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lessd(a2,c2)
-t4:=lessin(r,t,a2,c2,a2ir,c2it,t3):less(r,t)
--2r172
-t@[l:less(r,s)][k:lessis(s,t)]
-satz172b:=realapp3(less(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".2r172"(x,y,z,u,v,w,l,k)):less(r,t)
-t@[m:moreis(r,s)][n:more(s,t)]
-satz172c:=lemma2(t,r,satz172b(t,s,r,lemma1(s,t,n),satz168a(m))):more(r,t)
-t@[m:more(r,s)][n:moreis(s,t)]
-satz172d:=lemma2(t,r,satz172a(t,s,r,satz168a(s,t,n),lemma1(m))):more(r,t)
-+2r173
-c2it@[l:lessis(r,s)][k:lessis(s,t)]
-t1:=satzd173(a2,b2,c2,lessisex(a2,b2,a2ir,b2is,l),lessisex(s,t,b2,c2,b2is,c2it,k)):lesseq(a2,c2)
-t2:=lessisin(r,t,a2,c2,a2ir,c2it,t1):lessis(r,t)
--2r173
-t@[l:lessis(r,s)][k:lessis(s,t)]
-satz173:=realapp3(lessis(r,t),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".2r173"(x,y,z,u,v,w,l,k)):lessis(r,t)
-trlessis:=satz173:lessis(r,t)
-t@[m:moreis(r,s)][n:moreis(s,t)]
-trmoreis:=satz168b(t,r,trlessis(t,s,r,satz168a(s,t,n),satz168a(m))):moreis(r,t)
-r@ratrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),ratd(x))):'prop'
-a0ir@[r1:ratd(a0)]
-+*ivr2
-r1@t21:=andi(inn(a0,class(r)),ratd(a0),a0ir,r1):and(inn(a0,class(r)),ratd(a0))
--ivr2
-r1@ratrlin:=somei(dif,[x:dif]and(inn(x,class(r)),ratd(x)),a0,t21".ivr2"):ratrl(r)
-a0ir@[rr:ratrl(r)]
-+*ivr2
-rr@[a:dif][b:and(inn(a,class(r)),ratd(a))]
-t22:=ande1(inn(a,class(r)),ratd(a),b):inn(a,class(r))
-t23:=ande2(inn(a,class(r)),ratd(a),b):ratd(a)
-t24:=eqratd(a,a0,isex(r,r,a,a0,t22,a0ir,refis(real,r)),t23):ratd(a0)
--ivr2
-rr@ratrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),ratd(x)),rr,ratd(a0),[x:dif][t:and(inn(x,class(r)),ratd(x))]t24".ivr2"(x,t)):ratd(a0)
-r@irratrl:=not(ratrl(r)):'prop'
-@[r0:cut][rr:ratrp(r0)]
-remark2:=ratrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark2a(r0,rr)):ratrl(pofrp(r0))
-remark3:=ratrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark3a(r0,rr)):ratrl(nofrp(r0))
-r0@[ir:irratrp(r0)]
-remark4:=th3"l.imp"(ratrl(pofrp(r0)),ratd(pdofrp(r0)),remark4a(r0,ir),[t:ratrl(pofrp(r0))]ratrlex(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),t)):irratrl(pofrp(r0))
-remark5:=th3"l.imp"(ratrl(nofrp(r0)),ratd(ndofrp(r0)),remark5a(r0,ir),[t:ratrl(nofrp(r0))]ratrlex(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),t)):irratrl(nofrp(r0))
-r@natrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),natd(x))):'prop'
-a0ir@[n:natd(a0)]
-+*ivr2
-n@t25:=andi(inn(a0,class(r)),natd(a0),a0ir,n):and(inn(a0,class(r)),natd(a0))
--ivr2
-n@natrlin:=somei(dif,[x:dif]and(inn(x,class(r)),natd(x)),a0,t25".ivr2"):natrl(r)
-a0ir@[n:natrl(r)]
-+*ivr2
-n@[a:dif][b:and(inn(a,class(r)),natd(a))]
-t26:=ande1(inn(a,class(r)),natd(a),b):inn(a,class(r))
-t27:=ande2(inn(a,class(r)),natd(a),b):natd(a)
-t28:=eqnatd(a,a0,isex(r,r,a,a0,t26,a0ir,refis(real,r)),t27):natd(a0)
--ivr2
-n@natrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),natd(x)),n,natd(a0),[x:dif][t:and(inn(x,class(r)),natd(x))]t28".ivr2"(x,t)):natd(a0)
-+*ivr2
-a0ir@[n:natrl(r)]
-t29:=natposd(a0,natrlex(n)):posd(a0)
-t30:=posin(t29):pos(r)
--ivr2
-r@[n:natrl(r)]
-natpos:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t30".ivr2"(x,t,n)):pos(r)
-@[x:nat]
-rlofnt:=realof(pdofnt(x)):real
-natrli:=natrlin(rlofnt(x),pdofnt(x),innclass(pdofnt(x)),natdi(x)):natrl(rlofnt(x))
-[y:nat][i:is"n"(x,y)]
-isnterl:=isf(nat,real,[u:nat]rlofnt(u),x,y,i):is(rlofnt(x),rlofnt(y))
-y@[i:is(rlofnt(x),rlofnt(y))]
-isntirl:=isntirp(x,y,isrpip(rpofnt(x),rpofnt(y),i)):is"n"(x,y)
-+*ivr2
-@t31:=[x:nat][y:nat][t:is(rlofnt(x),rlofnt(y))]isntirl(x,y,t):injective(nat,real,[x:nat]rlofnt(x))
-a0ir@[n:natrl(r)]
-t32:=natposd(a0,natrlex(n)):posd(a0)
-ap:=rpofpd(a0,t32):cut
-t33:=natderp(a0,natrlex(n)):natrp(ap)
-x0:=ntofrp(ap,t33):nat
-t34:=isrpepd(ap,rpofnt(x0),isrpnt1(ap,t33)):eq"rp"(pdofrp(ap),pdofnt(x0))
-t35:=treq"rp"(a0,pdofrp(ap),pdofnt(x0),eqpdrp1(a0,t32),t34):eq"rp"(a0,pdofnt(x0))
-t36:=isin(r,rlofnt(x0),a0,pdofnt(x0),a0ir,innclass(pdofnt(x0)),t35):is(r,rlofnt(x0))
-t37:=somei(nat,[x:nat]is(r,rlofnt(x)),x0,t36):image(nat,real,[x:nat]rlofnt(x),r)
--ivr2
-r@[n:natrl(r)]
-natimage:=realapp1(image(nat,real,[x:nat]rlofnt(x),r),[x:dif][t:inn(x,class(r))]t37".ivr2"(x,t,n)):image(nat,real,[x:nat]rlofnt(x),r)
-r@[i:image(nat,real,[x:nat]rlofnt(x),r)]
-+*ivr2
-i"r"@[x:nat][j:is(r,rlofnt(x))]
-t38:=isp1(real,[u:real]natrl(u),rlofnt(x),r,natrli(x),j):natrl(r)
--ivr2
-i@imagenat:=someapp(nat,[u:nat]is(r,rlofnt(u)),i,natrl(r),[u:nat][v:is(r,rlofnt(u))]t38".ivr2"(u,v)):natrl(r)
-r@[n:natrl(r)]
-ntofrl:=soft(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):nat
-@[r1:real][n:natrl(r1)][s1:real][m:natrl(s1)][i:is(r1,s1)]
-isrlent:=isinv(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is"n"(ntofrl(r1,n),ntofrl(s1,m))
-m@[i:is"n"(ntofrl(r1,n),ntofrl(s1,m))]
-isrlint:=isinve(nat,real,[x:nat]rlofnt(x),t31".ivr2",r1,natimage(r1,n),s1,natimage(s1,m),i):is(r1,s1)
-r@[n:natrl(r)]
-isrlnt1:=ists1"e"(nat,real,[x:nat]rlofnt(x),t31".ivr2",r,natimage(r,n)):is(r,rlofnt(ntofrl(r,n)))
-isrlnt2:=symis(real,r,rlofnt(ntofrl(r,n)),isrlnt1):is(rlofnt(ntofrl(r,n)),r)
-@[x:nat]
-+*ivr2
-x"r"@xn:=soft(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x)):nat
-t39:=isinv(nat,real,[u:nat]rlofnt(u),t31,rlofnt(x),imagei(nat,real,[u:nat]rlofnt(u),x),rlofnt(x),natimage(rlofnt(x),natrli(x)),refis(real,rlofnt(x))):is"n"(xn,ntofrl(rlofnt(x),natrli(x)))
--ivr2
-x@isntrl1:=tris(nat,x,xn".ivr2",ntofrl(rlofnt(x),natrli(x)),isst1(nat,real,[u:nat]rlofnt(u),t31".ivr2",x),t39".ivr2"):is"n"(x,ntofrl(rlofnt(x),natrli(x)))
-isntrl2:=symis(nat,x,ntofrl(rlofnt(x),natrli(x)),isntrl1):is"n"(ntofrl(rlofnt(x),natrli(x)),x)
-r@intrl:=some"l"(dif,[x:dif]and(inn(x,class(r)),intd(x))):'prop'
-a0ir@[i:intd(a0)]
-+*ivr2
-i@t40:=andi(inn(a0,class(r)),intd(a0),a0ir,i):and(inn(a0,class(r)),intd(a0))
--ivr2
-i@intrlin:=somei(dif,[x:dif]and(inn(x,class(r)),intd(x)),a0,t40".ivr2"):intrl(r)
-a0ir@[i:intrl(r)]
-+*ivr2
-i@[a:dif][b:and(inn(a,class(r)),intd(a))]
-t41:=ande1(inn(a,class(r)),intd(a),b):inn(a,class(r))
-t42:=ande2(inn(a,class(r)),intd(a),b):intd(a)
-t43:=eqintd(a,a0,isex(r,r,a,a0,t41,a0ir,refis(real,r)),t42):intd(a0)
--ivr2
-i@intrlex:=someapp(dif,[x:dif]and(inn(x,class(r)),intd(x)),i,intd(a0),[x:dif][t:and(inn(x,class(r)),intd(x))]t43".ivr2"(x,t)):intd(a0)
-+*ivr2
-a0ir@[n:natrl(r)]
-t44:=natintd(a0,natrlex(n)):intd(a0)
-t45:=intrlin(t44):intrl(r)
--ivr2
-r@[n:natrl(r)]
-natintrl:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t45".ivr2"(x,t,n)):intrl(r)
-+*ivr2
-a0ir@[p:pos(r)][i:intrl(r)]
-t46:=posintnatd(a0,posex(p),intrlex(i)):natd(a0)
-t47:=natrlin(t46):natrl(r)
--ivr2
-r@[p:pos(r)][i:intrl(r)]
-posintnatrl:=realapp1(natrl(r),[x:dif][t:inn(x,class(r))]t47".ivr2"(x,t,p,i)):natrl(r)
-+*ivr2
-a0ir@[i2:is(r,0)]
-t48:=intdi0(a0,0ex(i2)):intd(a0)
-t49:=intrlin(t48):intrl(r)
--ivr2
-r@[i:is(r,0)]
-intrli0:=realapp1(intrl(r),[x:dif][t:inn(x,class(r))]t49".ivr2"(x,t,i)):intrl(r)
-r0@[n:natrp(r0)]
-remark6:=intrlin(pofrp(r0),pdofrp(r0),innclass(pdofrp(r0)),remark6"rp"(r0,n)):intrl(pofrp(r0))
-remark7:=intrlin(nofrp(r0),ndofrp(r0),innclass(ndofrp(r0)),remark7"rp"(r0,n)):intrl(nofrp(r0))
-+2r174
-a0ir@[i:intrl(r)]
-t1:=satzd174(a0,intrlex(i)):ratd(a0)
-t2:=ratrlin(t1):ratrl(r)
--2r174
-r@[i:intrl(r)]
-satz174:=realapp1(ratrl(r),[x:dif][t:inn(x,class(r))]t2".2r174"(x,t,i)):ratrl(r)
-@plusdr:=[x:dif][y:dif]realof(pd(x,y)):[x:dif][y:dif]real
-+ivr3
-[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
-t1:=isin(realof(pd(a,c)),realof(pd(b,d)),pd(a,c),pd(b,d),innclass(pd(a,c)),innclass(pd(b,d)),eqpd12(a,b,c,d,e,f)):is(<c><a>plusdr,<d><b>plusdr)
--ivr3
-fplusdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr3"(x,y,z,v,t,u):fixf2(real,plusdr)
-s@pl:=indreal2(real,plusdr,fplusdr,r,s):real
-+*ivr3
-b1is@t2:=isindreal2(real,plusdr,fplusdr,r,s,a1,b1,a1ir,b1is):is(realof(pd(a1,b1)),pl(r,s))
--ivr3
-b1is@picp:=isp(real,[x:real]inn(pd(a1,b1),class(x)),realof(pd(a1,b1)),pl(r,s),innclass(pd(a1,b1)),t2".ivr3"):inn(pd(a1,b1),class(pl(r,s)))
-t@[i:is(r,s)]
-ispl1:=isf(real,real,[x:real]pl(x,t),r,s,i):is(pl(r,t),pl(s,t))
-ispl2:=isf(real,real,[x:real]pl(t,x),r,s,i):is(pl(t,r),pl(t,s))
-u@[i:is(r,s)][j:is(t,u)]
-ispl12:=tris(real,pl(r,t),pl(s,t),pl(s,u),ispl1(i),ispl2(t,u,s,j)):is(pl(r,t),pl(s,u))
-+3r175
-b1is@t1:=satzd175(a1,b1):eq"rp"(pd(a1,b1),pd(b1,a1))
-t2:=isin(pl(r,s),pl(s,r),pd(a1,b1),pd(b1,a1),picp,picp(s,r,b1,a1,b1is,a1ir),t1):is(pl(r,s),pl(s,r))
--3r175
-s@satz175:=realapp2(is(pl(r,s),pl(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r175"(x,y,t,u)):is(pl(r,s),pl(s,r))
-compl:=satz175:is(pl(r,s),pl(s,r))
-+*ivr3
-b1is@[i:is(r,0)]
-t3:=pd01(a1,b1,0ex(r,a1,a1ir,i)):eq"rp"(pd(a1,b1),b1)
-t4:=isin(pl(r,s),s,pd(a1,b1),b1,picp,b1is,t3):is(pl(r,s),s)
--ivr3
-s@[i:is(r,0)]
-pl01:=realapp2(is(pl(r,s),s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr3"(x,y,t,u,i)):is(pl(r,s),s)
-s@[i:is(s,0)]
-pl02:=tris(real,pl(r,s),pl(s,r),r,compl,pl01(s,r,i)):is(pl(r,s),r)
-+*ivr3
-b1is@[p:pos(r)][q:pos(s)]
-t5:=ppd(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(pd(a1,b1))
-t6:=posin(pl(r,s),pd(a1,b1),picp,t5):pos(pl(r,s))
--ivr3
-s@[p:pos(r)][q:pos(s)]
-pospl:=realapp2(pos(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr3"(x,y,t,u,p,q)):pos(pl(r,s))
-+*ivr3
-b1is@[n:neg(r)][o:neg(s)]
-t7:=npd(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):negd(pd(a1,b1))
-t8:=negin(pl(r,s),pd(a1,b1),picp,t7):neg(pl(r,s))
--ivr3
-s@[n:neg(r)][o:neg(s)]
-negpl:=realapp2(neg(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".ivr3"(x,y,t,u,n,o)):neg(pl(r,s))
-@m0dr:=[x:dif]realof(m0d(x)):[x:dif]real
-+*ivr3
-@[a:dif][b:dif][e:eq"rp"(a,b)]
-t5a:=isin(realof(m0d(a)),realof(m0d(b)),m0d(a),m0d(b),innclass(m0d(a)),innclass(m0d(b)),eqm0d(a,b,e)):is(<a>m0dr,<b>m0dr)
--ivr3
-@fm0dr:=[x:dif][y:dif][t:<y><x>eq]t5a".ivr3"(x,y,t):fixf(real,m0dr)
-r@m0:=indreal(real,m0dr,fm0dr,r):real
-+*ivr3
-a0ir@t6a:=isindreal(real,m0dr,fm0dr,r,a0,a0ir):is(realof(m0d(a0)),m0(r))
--ivr3
-a0ir@micm0:=isp(real,[x:real]inn(m0d(a0),class(x)),realof(m0d(a0)),m0(r),innclass(m0d(a0)),t6a".ivr3"):inn(m0d(a0),class(m0(r)))
-s@[i:is(r,s)]
-ism0:=isf(real,real,[x:real]m0(x),r,s,i):is(m0(r),m0(s))
-+*ivr3
-a0ir@[n:neg(r)]
-t7a:=absnd(a0,negex(n)):eq"rp"(absd(a0),m0d(a0))
-t8a:=isin(abs(r),m0(r),absd(a0),m0d(a0),aica,micm0,t7a):is(abs(r),m0(r))
--ivr3
-r@[n:neg(r)]
-absn:=realapp1(is(abs(r),m0(r)),[x:dif][t:inn(x,class(r))]t8a".ivr3"(x,t,n)):is(abs(r),m0(r))
-+*ivr3
-a0ir@[nn:not(neg(r))]
-t9:=absnnd(a0,th3"l.imp"(negd(a0),neg(r),nn,[t:negd(a0)]negin(t))):eq"rp"(absd(a0),a0)
-t10:=isin(abs(r),r,absd(a0),a0,aica,a0ir,t9):is(abs(r),r)
--ivr3
-r@[nn:not(neg(r))]
-absnn:=realapp1(is(abs(r),r),[x:dif][t:inn(x,class(r))]t10".ivr3"(x,t,nn)):is(abs(r),r)
-r@[p:pos(r)]
-absp:=absnn(r,pnotn(r,p)):is(abs(r),r)
-r@[i:is(r,0)]
-abs0:=tris(real,abs(r),r,0,absnn(r,0notn(r,i)),i):is(abs(r),0)
-+3r176
-a0ir@[p:pos(r)]
-t1:=satzd176a(a0,posex(p)):negd(m0d(a0))
-t2:=negin(m0(r),m0d(a0),micm0,t1):neg(m0(r))
--3r176
-r@[p:pos(r)]
-satz176a:=realapp1(neg(m0(r)),[x:dif][t:inn(x,class(r))]t2".3r176"(x,t,p)):neg(m0(r))
-+*3r176
-a0ir@[i:is(r,0)]
-t3:=satzd176b(a0,0ex(i)):zero(m0d(a0))
-t4:=0in(m0(r),m0d(a0),micm0,t3):is(m0(r),0)
--3r176
-r@[i:is(r,0)]
-satz176b:=realapp1(is(m0(r),0),[x:dif][t:inn(x,class(r))]t4".3r176"(x,t,i)):is(m0(r),0)
-+*3r176
-a0ir@[n:neg(r)]
-t5:=satzd176c(a0,negex(n)):posd(m0d(a0))
-t6:=posin(m0(r),m0d(a0),micm0,t5):pos(m0(r))
--3r176
-r@[n:neg(r)]
-satz176c:=realapp1(pos(m0(r)),[x:dif][t:inn(x,class(r))]t6".3r176"(x,t,n)):pos(m0(r))
-+*3r176
-a0ir@[n:neg(m0(r))]
-t7:=satzd176d(a0,negex(m0(r),m0d(a0),micm0,n)):posd(a0)
-t8:=posin(t7):pos(r)
--3r176
-r@[n:neg(m0(r))]
-satz176d:=realapp1(pos(r),[x:dif][t:inn(x,class(r))]t8".3r176"(x,t,n)):pos(r)
-+*3r176
-a0ir@[i:is(m0(r),0)]
-t9:=satzd176e(a0,0ex(m0(r),m0d(a0),micm0,i)):zero(a0)
-t10:=0in(t9):is(r,0)
--3r176
-r@[i:is(m0(r),0)]
-satz176e:=realapp1(is(r,0),[x:dif][t:inn(x,class(r))]t10".3r176"(x,t,i)):is(r,0)
-+*3r176
-a0ir@[p:pos(m0(r))]
-t11:=satzd176f(a0,posex(m0(r),m0d(a0),micm0,p)):negd(a0)
-t12:=negin(t11):neg(r)
--3r176
-r@[p:pos(m0(r))]
-satz176f:=realapp1(neg(r),[x:dif][t:inn(x,class(r))]t12".3r176"(x,t,p)):neg(r)
-+3r177
-a0ir@t1:=isin(m0(m0(r)),r,m0d(m0d(a0)),a0,micm0(m0(r),m0d(a0),micm0),a0ir,satzd177(a0)):is(m0(m0(r)),r)
--3r177
-r@satz177:=realapp1(is(m0(m0(r)),r),[x:dif][t:inn(x,class(r))]t1".3r177"(x,t)):is(m0(m0(r)),r)
-satz177a:=symis(real,m0(m0(r)),r,satz177):is(r,m0(m0(r)))
-s@[i:is(r,m0(s))]
-satz177b:=tris(real,m0(r),m0(m0(s)),s,ism0(r,m0(s),i),satz177(s)):is(m0(r),s)
-satz177c:=symis(real,m0(r),s,satz177b):is(s,m0(r))
-s@[i:is(m0(r),s)]
-satz177d:=satz177c(s,r,symis(real,m0(r),s,i)):is(r,m0(s))
-satz177e:=symis(real,r,m0(s),satz177d):is(m0(s),r)
-+3r178
-a0ir@t1:=isin(abs(m0(r)),abs(r),absd(m0d(a0)),absd(a0),aica(m0(r),m0d(a0),micm0),aica,satzd178(a0)):is(abs(m0(r)),abs(r))
--3r178
-r@satz178:=realapp1(is(abs(m0(r)),abs(r)),[x:dif][t:inn(x,class(r))]t1".3r178"(x,t)):is(abs(m0(r)),abs(r))
-satz178a:=symis(real,abs(m0(r)),abs(r),satz178):is(abs(r),abs(m0(r)))
-+3r179
-a0ir@t1:=0in(pl(r,m0(r)),pd(a0,m0d(a0)),picp(r,m0(r),a0,m0d(a0),a0ir,micm0),satzd179(a0)):is(pl(r,m0(r)),0)
--3r179
-satz179:=realapp1(is(pl(r,m0(r)),0),[x:dif][t:inn(x,class(r))]t1".3r179"(x,t)):is(pl(r,m0(r)),0)
-satz179a:=tris(real,pl(m0(r),r),pl(r,m0(r)),0,compl(m0(r),r),satz179):is(pl(m0(r),r),0)
-+3r180
-b1is@t1:=isin(m0(pl(r,s)),pl(m0(r),m0(s)),m0d(pd(a1,b1)),pd(m0d(a1),m0d(b1)),micm0(pl(r,s),pd(a1,b1),picp),picp(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is)),satzd180(a1,b1)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
--3r180
-s@satz180:=realapp2(is(m0(pl(r,s)),pl(m0(r),m0(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t1".3r180"(x,y,t,u)):is(m0(pl(r,s)),pl(m0(r),m0(s)))
-satz180a:=symis(real,m0(pl(r,s)),pl(m0(r),m0(s)),satz180):is(pl(m0(r),m0(s)),m0(pl(r,s)))
-mn:=pl(r,m0(s)):real
-b1is@micmn:=picp(r,m0(s),a1,m0d(b1),a1ir,micm0(s,b1,b1is)):inn(md(a1,b1),class(mn(r,s)))
-t@[i:is(r,s)]
-ismn1:=ispl1(r,s,m0(t),i):is(mn(r,t),mn(s,t))
-ismn2:=ispl2(m0(r),m0(s),t,ism0(r,s,i)):is(mn(t,r),mn(t,s))
-u@[i:is(r,s)][j:is(t,u)]
-ismn12:=ispl12(r,s,m0(t),m0(u),i,ism0(t,u,j)):is(mn(r,t),mn(s,u))
-s@satz181:=tr3is(real,m0(mn(r,s)),pl(m0(r),m0(m0(s))),pl(m0(r),s),mn(s,r),satz180(r,m0(s)),ispl2(m0(m0(s)),s,m0(r),satz177(s)),compl(m0(r),s)):is(m0(mn(r,s)),mn(s,r))
-satz181a:=symis(real,m0(mn(s,r)),mn(r,s),satz181(s,r)):is(mn(r,s),m0(mn(s,r)))
-+3r182
-b1is@[p:pos(mn(r,s))]
-t1:=satzd182a(a1,b1,posex(mn(r,s),md(a1,b1),micmn,p)):mored(a1,b1)
-t2:=morein(t1):more(r,s)
--3r182
-[p:pos(mn(r,s))]
-satz182a:=realapp2(more(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r182"(x,y,t,u,p)):more(r,s)
-+*3r182
-b1is@[i:is(mn(r,s),0)]
-t3:=satzd182b(a1,b1,0ex(mn(r,s),md(a1,b1),micmn,i)):eq"rp"(a1,b1)
-t4:=isin(t3):is(r,s)
--3r182
-s@[i:is(mn(r,s),0)]
-satz182b:=realapp2(is(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r182"(x,y,t,u,i)):is(r,s)
-+*3r182
-b1is@[n:neg(mn(r,s))]
-t5:=satzd182c(a1,b1,negex(mn(r,s),md(a1,b1),micmn,n)):lessd(a1,b1)
-t6:=lessin(t5):less(r,s)
--3r182
-s@[n:neg(mn(r,s))]
-satz182c:=realapp2(less(r,s),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".3r182"(x,y,t,u,n)):less(r,s)
-+*3r182
-b1is@[m:more(r,s)]
-t7:=satzd182d(a1,b1,moreex(m)):posd(md(a1,b1))
-t8:=posin(mn(r,s),md(a1,b1),micmn,t7):pos(mn(r,s))
--3r182
-s@[m:more(r,s)]
-satz182d:=realapp2(pos(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".3r182"(x,y,t,u,m)):pos(mn(r,s))
-+*3r182
-b1is@[i:is(r,s)]
-t9:=satzd182e(a1,b1,isex(i)):zero(md(a1,b1))
-t10:=0in(mn(r,s),md(a1,b1),micmn,t9):is(mn(r,s),0)
--3r182
-s@[i:is(r,s)]
-satz182e:=realapp2(is(mn(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t10".3r182"(x,y,t,u,i)):is(mn(r,s),0)
-+*3r182
-b1is@[l:less(r,s)]
-t11:=satzd182f(a1,b1,lessex(l)):negd(md(a1,b1))
-t12:=negin(mn(r,s),md(a1,b1),micmn,t11):neg(mn(r,s))
--3r182
-s@[l:less(r,s)]
-satz182f:=realapp2(neg(mn(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t12".3r182"(x,y,t,u,l)):neg(mn(r,s))
-+3r183
-b1is@[m:more(r,s)]
-t1:=satzd183a(a1,b1,moreex(m)):lessd(m0d(a1),m0d(b1))
-t2:=lessin(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t1):less(m0(r),m0(s))
--3r183
-s@[m:more(r,s)]
-satz183a:=realapp2(less(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".3r183"(x,y,t,u,m)):less(m0(r),m0(s))
-s@[i:is(r,s)]
-satz183b:=ism0(r,s,i):is(m0(r),m0(s))
-+*3r183
-b1is@[l:less(r,s)]
-t3:=satzd183c(a1,b1,lessex(l)):mored(m0d(a1),m0d(b1))
-t4:=morein(m0(r),m0(s),m0d(a1),m0d(b1),micm0(r,a1,a1ir),micm0(s,b1,b1is),t3):more(m0(r),m0(s))
--3r183
-s@[l:less(r,s)]
-satz183c:=realapp2(more(m0(r),m0(s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".3r183"(x,y,t,u,l)):more(m0(r),m0(s))
-s@[l:less(m0(r),m0(s))]
-satz183d:=ismore12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183c(m0(r),m0(s),l)):more(r,s)
-s@[i:is(m0(r),m0(s))]
-satz183e:=tr3is(real,r,m0(m0(r)),m0(m0(s)),s,satz177a(r),ism0(m0(r),m0(s),i),satz177(s)):is(r,s)
-s@[m:more(m0(r),m0(s))]
-satz183f:=isless12(m0(m0(r)),r,m0(m0(s)),s,satz177(r),satz177(s),satz183a(m0(r),m0(s),m)):less(r,s)
-+3r184
-t@prop1:=and3(pos(s),pos(t),is(r,mn(s,t))):'prop'
-s@prop2:=some([x:real]prop1(x)):'prop'
-r@prop3:=some([x:real]prop2(x)):'prop'
-a0ir@[a:dif][b:dif]
-prop1d:=and3(posd(a),posd(b),eq"rp"(a0,md(a,b))):'prop'
-a@prop2d:=some"l"(dif,[x:dif]prop1d(x)):'prop'
-[p2:prop2d(a)][b:dif][p1:prop1d(a,b)]
-t1:=and3e1(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(a)
-t2:=and3e2(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):posd(b)
-t3:=and3e3(posd(a),posd(b),eq"rp"(a0,md(a,b)),p1):eq"rp"(a0,md(a,b))
-p2@ra:=realof(a):real
-p1@rb:=realof(b):real
-t4:=innclass(a):inn(a,class(ra))
-t5:=innclass(b):inn(b,class(rb))
-t6:=isin(r,mn(ra,rb),a0,md(a,b),a0ir,micmn(ra,rb,a,b,t4,t5),t3):is(r,mn(ra,rb))
-t7:=and3i(pos(ra),pos(rb),is(r,mn(ra,rb)),posin(ra,a,t4,t1),posin(rb,b,t5,t2),t6):prop1(ra,rb)
-t8:=somei(real,[x:real]prop1(ra,x),rb,t7):prop2(ra)
-p2@t9:=someapp(dif,[x:dif]prop1d(a,x),p2,prop2(ra),[x:dif][t:prop1d(a,x)]t8(x,t)):prop2(ra)
-t10:=somei(real,[x:real]prop2(x),ra,t9):prop3
-a0ir@t11:=someapp(dif,[x:dif]prop2d(x),satzd184(a0),prop3,[x:dif][t:prop2d(x)]t10(x,t)):prop3
--3r184
-r@satz184:=realapp1(prop3".3r184",[x:dif][t:inn(x,class(r))]t11".3r184"(x,t)):some([x:real]some([y:real]and3(pos(x),pos(y),is(r,mn(x,y)))))
-u@[a3:dif][b3:dif][c3:dif][d3:dif][a3ir:inn(a3,class(r))][b3is:inn(b3,class(s))][c3it:inn(c3,class(t))][d3iu:inn(d3,class(u))]
-+3r185
-t1:=satzd185(a3,b3,c3,d3):eq"rp"(pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)))
-t2:=isin(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)),pd(md(a3,b3),md(c3,d3)),md(pd(a3,c3),pd(b3,d3)),picp(mn(r,s),mn(t,u),md(a3,b3),md(c3,d3),micmn(r,s,a3,b3,a3ir,b3is),micmn(t,u,c3,d3,c3it,d3iu)),micmn(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu)),t1):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
--3r185
-u@satz185:=realapp4(is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u))),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r185"(x,y,z,v,xi,yi,zi,vi)):is(pl(mn(r,s),mn(t,u)),mn(pl(r,t),pl(s,u)))
-+3r186
-c2it@t1:=satzd186(a2,b2,c2):eq"rp"(pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)))
-t2:=isin(pl(pl(r,s),t),pl(r,pl(s,t)),pd(pd(a2,b2),c2),pd(a2,pd(b2,c2)),picp(pl(r,s),t,pd(a2,b2),c2,picp(r,s,a2,b2,a2ir,b2is),c2it),picp(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),t1):is(pl(pl(r,s),t),pl(r,pl(s,t)))
--3r186
-t@satz186:=realapp3(is(pl(pl(r,s),t),pl(r,pl(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r186"(x,y,z,u,v,w)):is(pl(pl(r,s),t),pl(r,pl(s,t)))
-asspl1:=satz186:is(pl(pl(r,s),t),pl(r,pl(s,t)))
-asspl2:=symis(real,pl(pl(r,s),t),pl(r,pl(s,t)),satz186):is(pl(r,pl(s,t)),pl(pl(r,s),t))
-s@plmn:=tris(real,pl(mn(r,s),s),pl(r,pl(m0(s),s)),r,asspl1(r,m0(s),s),pl02(r,pl(m0(s),s),satz179a(s))):is(pl(mn(r,s),s),r)
-mnpl:=tris(real,mn(pl(r,s),s),pl(r,pl(s,m0(s))),r,asspl1(r,s,m0(s)),pl02(r,pl(s,m0(s)),satz179(s))):is(mn(pl(r,s),s),r)
-satz187a:=tris(real,pl(s,mn(r,s)),pl(mn(r,s),s),r,compl(s,mn(r,s)),plmn):is(pl(s,mn(r,s)),r)
-satz187b:=somei(real,[x:real]is(pl(s,x),r),mn(r,s),satz187a):some([x:real]is(pl(s,x),r))
-[x:real][i:is(pl(s,x),r)]
-satz187c:=tris(real,mn(r,s),mn(pl(x,s),s),x,ismn1(r,pl(x,s),s,tris1(real,r,pl(x,s),pl(s,x),i,compl(s,x))),mnpl(x,s)):is(mn(r,s),x)
-satz187d:=symis(real,mn(r,s),x,satz187c):is(x,mn(r,s))
-x@[i:is(pl(x,s),r)]
-satz187e:=satz187c(tris(real,pl(s,x),pl(x,s),r,compl(s,x),i)):is(mn(r,s),x)
-satz187f:=symis(real,mn(r,s),x,satz187e):is(x,mn(r,s))
-+3r187
-s@[x:real][y:real][i:is(pl(s,x),r)][j:is(pl(s,y),r)]
-t1:=tris1(real,x,y,mn(r,s),satz187c(x,i),satz187c(y,j)):is(x,y)
-s@t2:=[x:real][y:real][t:is(pl(s,x),r)][u:is(pl(s,y),r)]t1(x,y,t,u):amone(real,[x:real]is(pl(s,x),r))
--3r187
-s@satz187:=onei(real,[x:real]is(pl(s,x),r),t2".3r187",satz187b):one([x:real]is(pl(s,x),r))
-+3r188
-c2it@[m:more(pl(r,t),pl(s,t))]
-t1:=satzd188a(a2,b2,c2,moreex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),m)):mored(a2,b2)
-t2:=morein(r,s,a2,b2,a2ir,b2is,t1):more(r,s)
--3r188
-t@[m:more(pl(r,t),pl(s,t))]
-satz188a:=realapp3(more(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".3r188"(x,y,z,u,v,w,m)):more(r,s)
-+*3r188
-c2it@[i:is(pl(r,t),pl(s,t))]
-t3:=satzd188b(a2,b2,c2,isex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),i)):eq"rp"(a2,b2)
-t4:=isin(r,s,a2,b2,a2ir,b2is,t3):is(r,s)
--3r188
-t@[i:is(pl(r,t),pl(s,t))]
-satz188b:=realapp3(is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".3r188"(x,y,z,u,v,w,i)):is(r,s)
-+*3r188
-c2it@[l:less(pl(r,t),pl(s,t))]
-t5:=satzd188c(a2,b2,c2,lessex(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),l)):lessd(a2,b2)
-t6:=lessin(r,s,a2,b2,a2ir,b2is,t5):less(r,s)
--3r188
-t@[l:less(pl(r,t),pl(s,t))]
-satz188c:=realapp3(less(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t6".3r188"(x,y,z,u,v,w,l)):less(r,s)
-+*3r188
-c2it@[m:more(r,s)]
-t7:=satzd188d(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m)):mored(pd(a2,c2),pd(b2,c2))
-t8:=morein(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t7):more(pl(r,t),pl(s,t))
--3r188
-t@[m:more(r,s)]
-satz188d:=realapp3(more(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t8".3r188"(x,y,z,u,v,w,m)):more(pl(r,t),pl(s,t))
-t@[i:is(r,s)]
-satz188e:=ispl1(r,s,t,i):is(pl(r,t),pl(s,t))
-+*3r188
-c2it@[l:less(r,s)]
-t9:=satzd188f(a2,b2,c2,lessex(r,s,a2,b2,a2ir,b2is,l)):lessd(pd(a2,c2),pd(b2,c2))
-t10:=lessin(pl(r,t),pl(s,t),pd(a2,c2),pd(b2,c2),picp(r,t,a2,c2,a2ir,c2it),picp(s,t,b2,c2,b2is,c2it),t9):less(pl(r,t),pl(s,t))
--3r188
-t@[l:less(r,s)]
-satz188f:=realapp3(less(pl(r,t),pl(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t10".3r188"(x,y,z,u,v,w,l)):less(pl(r,t),pl(s,t))
-t@[m:more(pl(t,r),pl(t,s))]
-satz188g:=satz188a(ismore12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),m)):more(r,s)
-t@[i:is(pl(t,r),pl(t,s))]
-satz188h:=satz188b(tr3is(real,pl(r,t),pl(t,r),pl(t,s),pl(s,t),compl(r,t),i,compl(t,s))):is(r,s)
-t@[l:less(pl(t,r),pl(t,s))]
-satz188j:=satz188c(isless12(pl(t,r),pl(r,t),pl(t,s),pl(s,t),compl(t,r),compl(t,s),l)):less(r,s)
-t@[m:more(r,s)]
-satz188k:=ismore12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188d(m)):more(pl(t,r),pl(t,s))
-t@[i:is(r,s)]
-satz188l:=ispl2(r,s,t,i):is(pl(t,r),pl(t,s))
-t@[l:less(r,s)]
-satz188m:=isless12(pl(r,t),pl(t,r),pl(s,t),pl(t,s),compl(r,t),compl(s,t),satz188f(l)):less(pl(t,r),pl(t,s))
-u@[i:is(r,s)][m:more(t,u)]
-satz188n:=ismore2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188k(t,u,r,m)):more(pl(r,t),pl(s,u))
-satz188o:=ismore12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188n):more(pl(t,r),pl(u,s))
-i@[l:less(t,u)]
-satz188p:=isless2(pl(r,u),pl(s,u),pl(r,t),ispl1(r,s,u,i),satz188m(t,u,r,l)):less(pl(r,t),pl(s,u))
-satz188q:=isless12(pl(r,t),pl(t,r),pl(s,u),pl(u,s),compl(r,t),compl(s,u),satz188p):less(pl(t,r),pl(u,s))
-u@[m:more(r,s)][n:more(t,u)]
-satz189:=trmore(pl(r,t),pl(s,t),pl(s,u),satz188d(m),satz188k(t,u,s,n)):more(pl(r,t),pl(s,u))
-u@[l:less(r,s)][k:less(t,u)]
-satz189a:=lemma1(pl(s,u),pl(r,t),satz189(s,r,u,t,lemma2(r,s,l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
-u@[m:moreis(r,s)][n:more(t,u)]
-satz190a:=orapp(more(r,s),is(r,s),more(pl(r,t),pl(s,u)),m,[v:more(r,s)]satz189(v,n),[v:is(r,s)]satz188n(v,n)):more(pl(r,t),pl(s,u))
-u@[m:more(r,s)][n:moreis(t,u)]
-satz190b:=ismore12(pl(t,r),pl(r,t),pl(u,s),pl(s,u),compl(t,r),compl(u,s),satz190a(t,u,r,s,n,m)):more(pl(r,t),pl(s,u))
-u@[l:lessis(r,s)][k:less(t,u)]
-satz190c:=lemma1(pl(s,u),pl(r,t),satz190a(s,r,u,t,satz168b(l),lemma2(t,u,k))):less(pl(r,t),pl(s,u))
-u@[l:less(r,s)][k:lessis(t,u)]
-satz190d:=lemma1(pl(s,u),pl(r,t),satz190b(s,r,u,t,lemma2(l),satz168b(t,u,k))):less(pl(r,t),pl(s,u))
-+3r191
-d3iu@[m:moreis(r,s)][n:moreis(t,u)]
-t1:=satzd191(a3,b3,c3,d3,moreisex(r,s,a3,b3,a3ir,b3is,m),moreisex(t,u,c3,d3,c3it,d3iu,n)):moreq(pd(a3,c3),pd(b3,d3))
-t2:=moreisin(pl(r,t),pl(s,u),pd(a3,c3),pd(b3,d3),picp(r,t,a3,c3,a3ir,c3it),picp(s,u,b3,d3,b3is,d3iu),t1):moreis(pl(r,t),pl(s,u))
--3r191
-u@[m:moreis(r,s)][n:moreis(t,u)]
-satz191:=realapp4(moreis(pl(r,t),pl(s,u)),[x:dif][y:dif][z:dif][v:dif][xi:inn(x,class(r))][yi:inn(y,class(s))][zi:inn(z,class(t))][vi:inn(v,class(u))]t2".3r191"(x,y,z,v,xi,yi,zi,vi,m,n)):moreis(pl(r,t),pl(s,u))
-u@[l:lessis(r,s)][k:lessis(t,u)]
-satz191a:=satz168a(pl(s,u),pl(r,t),satz191(s,r,u,t,satz168b(l),satz168b(t,u,k))):lessis(pl(r,t),pl(s,u))
-@timesdr:=[x:dif][y:dif]realof(td(x,y)):[x:dif][y:dif]real
-+ivr4
-[a:dif][b:dif][c:dif][d:dif][e:eq"rp"(a,b)][f:eq"rp"(c,d)]
-t1:=isin(realof(td(a,c)),realof(td(b,d)),td(a,c),td(b,d),innclass(td(a,c)),innclass(td(b,d)),eqtd12(a,b,c,d,e,f)):is(<c><a>timesdr,<d><b>timesdr)
--ivr4
-ftimesdr:=[x:dif][y:dif][z:dif][v:dif][t:<y><x>eq][u:<v><z>eq]t1".ivr4"(x,y,z,v,t,u):fixf2(real,timesdr)
-s@ts:=indreal2(real,timesdr,ftimesdr,r,s):real
-+*ivr4
-b1is@t2:=isindreal2(real,timesdr,ftimesdr,r,s,a1,b1,a1ir,b1is):is(realof(td(a1,b1)),ts(r,s))
--ivr4
-b1is@tict:=isp(real,[x:real]inn(td(a1,b1),class(x)),realof(td(a1,b1)),ts(r,s),innclass(td(a1,b1)),t2".ivr4"):inn(td(a1,b1),class(ts(r,s)))
-t@[i:is(r,s)]
-ists1:=isf(real,real,[x:real]ts(x,t),r,s,i):is(ts(r,t),ts(s,t))
-ists2:=isf(real,real,[x:real]ts(t,x),r,s,i):is(ts(t,r),ts(t,s))
-u@[i:is(r,s)][j:is(t,u)]
-ists12:=tris(real,ts(r,t),ts(s,t),ts(s,u),ists1(i),ists2(t,u,s,j)):is(ts(r,t),ts(s,u))
-+4r192
-b1is@[i:is(r,0)]
-t1:=satzd192a(a1,b1,0ex(r,a1,a1ir,i)):zero(td(a1,b1))
-t2:=0in(ts(r,s),td(a1,b1),tict,t1):is(ts(r,s),0)
--4r192
-s@[i:is(r,0)]
-satz192a:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r192"(x,y,t,u,i)):is(ts(r,s),0)
-+*4r192
-b1is@[i:is(s,0)]
-t3:=satzd192b(a1,b1,0ex(s,b1,b1is,i)):zero(td(a1,b1))
-t4:=0in(ts(r,s),td(a1,b1),tict,t3):is(ts(r,s),0)
--4r192
-s@[i:is(s,0)]
-satz192b:=realapp2(is(ts(r,s),0),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".4r192"(x,y,t,u,i)):is(ts(r,s),0)
-+*4r192
-b1is@[i:is(ts(r,s),0)]
-t5:=satzd192c(a1,b1,0ex(ts(r,s),td(a1,b1),tict,i)):or(zero(a1),zero(b1))
-t6:=th9"l.or"(zero(a1),zero(b1),is(r,0),is(s,0),t5,[t:zero(a1)]0in(r,a1,a1ir,t),[t:zero(b1)]0in(s,b1,b1is,t)):or(is(r,0),is(s,0))
--4r192
-s@[i:is(ts(r,s),0)]
-satz192c:=realapp2(or(is(r,0),is(s,0)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".4r192"(x,y,t,u,i)):or(is(r,0),is(s,0))
-s@[n:nis(r,0)][o:nis(s,0)]
-satz192d:=th3"l.imp"(is(ts(r,s),0),or(is(r,0),is(s,0)),th3"l.or"(is(r,0),is(s,0),n,o),[t:is(ts(r,s),0)]satz192c(t)):nis(ts(r,s),0)
-s@[i:is(r,0)]
-ts01:=satz192a(i):is(ts(r,s),0)
-s@[i:is(s,0)]
-ts02:=satz192b(i):is(ts(r,s),0)
-+4r193
-b1is@t1:=satzd193(a1,b1):eq"rp"(absd(td(a1,b1)),td(absd(a1),absd(b1)))
-t2:=isin(abs(ts(r,s)),ts(abs(r),abs(s)),absd(td(a1,b1)),td(absd(a1),absd(b1)),aica(ts(r,s),td(a1,b1),tict),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(abs(ts(r,s)),ts(abs(r),abs(s)))
--4r193
-s@satz193:=realapp2(is(abs(ts(r,s)),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r193"(x,y,t,u)):is(abs(ts(r,s)),ts(abs(r),abs(s)))
-satz193a:=symis(real,abs(ts(r,s)),ts(abs(r),abs(s)),satz193):is(ts(abs(r),abs(s)),abs(ts(r,s)))
-+4r194
-b1is@t1:=satzd194(a1,b1):eq"rp"(td(a1,b1),td(b1,a1))
-t2:=isin(ts(r,s),ts(s,r),td(a1,b1),td(b1,a1),tict,tict(s,r,b1,a1,b1is,a1ir),t1):is(ts(r,s),ts(s,r))
--4r194
-satz194:=realapp2(is(ts(r,s),ts(s,r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r194"(x,y,t,u)):is(ts(r,s),ts(s,r))
-comts:=satz194:is(ts(r,s),ts(s,r))
-@1rl:=realof(1df):real
-pos1:=posin(1rl,1df,innclass(1df),posdirp(1rp)):pos(1rl)
-natrl1:=natrli(1):natrl(1rl)
-intrl1:=natintrl(1rl,natrl1):intrl(1rl)
-+4r195
-a0ir@t1:=satzd195(a0):eq"rp"(td(a0,1df),a0)
-t2:=isin(ts(r,1rl),r,td(a0,1df),a0,tict(r,1rl,a0,1df,a0ir,innclass(1df)),a0ir,t1):is(ts(r,1rl),r)
--4r195
-r@satz195:=realapp1(is(ts(r,1rl),r),[x:dif][t:inn(x,class(r))]t2".4r195"(x,t)):is(ts(r,1rl),r)
-satz195a:=symis(real,ts(r,1rl),r,satz195):is(r,ts(r,1rl))
-satz195b:=tris(real,ts(1rl,r),ts(r,1rl),r,comts(1rl,r),satz195):is(ts(1rl,r),r)
-satz195c:=symis(real,ts(1rl,r),r,satz195b):is(r,ts(1rl,r))
-s@[p:pos(r)][q:pos(s)]
-satz196a:=symis(real,ts(abs(r),abs(s)),ts(r,s),ists12(abs(r),r,abs(s),s,absp(r,p),absp(s,q))):is(ts(r,s),ts(abs(r),abs(s)))
-+4r196
-b1is@[n:neg(r)][o:neg(s)]
-t1:=satzd196b(a1,b1,negex(r,a1,a1ir,n),negex(s,b1,b1is,o)):eq"rp"(td(a1,b1),td(absd(a1),absd(b1)))
-t2:=isin(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),t1):is(ts(r,s),ts(abs(r),abs(s)))
--4r196
-s@[n:neg(r)][o:neg(s)]
-satz196b:=realapp2(is(ts(r,s),ts(abs(r),abs(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r196"(x,y,t,u,n,o)):is(ts(r,s),ts(abs(r),abs(s)))
-+*4r196
-b1is@[p:pos(r)][n:neg(s)]
-t1a:=satzd196c(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):eq"rp"(td(a1,b1),m0d(td(absd(a1),absd(b1))))
-t2a:=isin(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),t1a):is(ts(r,s),m0(ts(abs(r),abs(s))))
--4r196
-s@[p:pos(r)][n:neg(s)]
-satz196c:=realapp2(is(ts(r,s),m0(ts(abs(r),abs(s)))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2a".4r196"(x,y,t,u,p,n)):is(ts(r,s),m0(ts(abs(r),abs(s))))
-s@[n:neg(r)][p:pos(s)]
-satz196d:=tr3is(real,ts(r,s),ts(s,r),m0(ts(abs(s),abs(r))),m0(ts(abs(r),abs(s))),comts(r,s),satz196c(s,r,p,n),ism0(ts(abs(s),abs(r)),ts(abs(r),abs(s)),comts(abs(s),abs(r)))):is(ts(r,s),m0(ts(abs(r),abs(s))))
-+*4r196
-a0ir@[n:not(is(r,0))]
-t3:=th3"l.imp"(zero(a0),is(r,0),n,[t:zero(a0)]0in(t)):not(zero(a0))
-b1is@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
-t4:=satzd196e(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),ts(abs(r),abs(s)),td(a1,b1),td(absd(a1),absd(b1)),tict,tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is)),i)):or(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)))
-[a:and(posd(a1),posd(b1))]
-t5:=andi(pos(r),pos(s),posin(r,a1,a1ir,ande1(posd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(posd(a1),posd(b1),a))):and(pos(r),pos(s))
-i@[a:and(negd(a1),negd(b1))]
-t6:=andi(neg(r),neg(s),negin(r,a1,a1ir,ande1(negd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(negd(a1),negd(b1),a))):and(neg(r),neg(s))
-i@t7:=th9"l.or"(and(posd(a1),posd(b1)),and(negd(a1),negd(b1)),and(pos(r),pos(s)),and(neg(r),neg(s)),t4,[t:and(posd(a1),posd(b1))]t5(t),[t:and(negd(a1),negd(b1))]t6(t)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
--4r196
-s@[n:not(is(r,0))][o:not(is(s,0))][i:is(ts(r,s),ts(abs(r),abs(s)))]
-satz196e:=realapp2(or(and(pos(r),pos(s)),and(neg(r),neg(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
-+*4r196
-o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
-t8:=satzd196f(a1,b1,t3(r,a1,a1ir,n),t3(s,b1,b1is,o),isex(ts(r,s),m0(ts(abs(r),abs(s))),td(a1,b1),m0d(td(absd(a1),absd(b1))),tict,micm0(ts(abs(r),abs(s)),td(absd(a1),absd(b1)),tict(abs(r),abs(s),absd(a1),absd(b1),aica(r,a1,a1ir),aica(s,b1,b1is))),i)):or(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)))
-[a:and(posd(a1),negd(b1))]
-t9:=andi(pos(r),neg(s),posin(r,a1,a1ir,ande1(posd(a1),negd(b1),a)),negin(s,b1,b1is,ande2(posd(a1),negd(b1),a))):and(pos(r),neg(s))
-i@[a:and(negd(a1),posd(b1))]
-t10:=andi(neg(r),pos(s),negin(r,a1,a1ir,ande1(negd(a1),posd(b1),a)),posin(s,b1,b1is,ande2(negd(a1),posd(b1),a))):and(neg(r),pos(s))
-i@t11:=th9"l.or"(and(posd(a1),negd(b1)),and(negd(a1),posd(b1)),and(pos(r),neg(s)),and(neg(r),pos(s)),t8,[t:and(posd(a1),negd(b1))]t9(t),[t:and(negd(a1),posd(b1))]t10(t)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
--4r196
-o@[i:is(ts(r,s),m0(ts(abs(r),abs(s))))]
-satz196f:=realapp2(or(and(pos(r),neg(s)),and(neg(r),pos(s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t11".4r196"(x,y,t,u,n,o,i)):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
-s@[p:pos(ts(r,s))]
-+*4r196
-p"r"@t12:=th3"l.imp"(is(r,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
-t13:=th3"l.imp"(is(s,0),is(ts(r,s),0),pnot0(ts(r,s),p),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
-t14:=tris1(real,ts(r,s),ts(abs(r),abs(s)),abs(ts(r,s)),absp(ts(r,s),p),satz193(r,s)):is(ts(r,s),ts(abs(r),abs(s)))
--4r196
-p@satz196g:=satz196e(t12".4r196",t13".4r196",t14".4r196"):or(and(pos(r),pos(s)),and(neg(r),neg(s)))
-s@[n:neg(ts(r,s))]
-+*4r196
-n"r"@t15:=th3"l.imp"(is(r,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(r,0)]ts01(r,s,t)):nis(r,0)
-t16:=th3"l.imp"(is(s,0),is(ts(r,s),0),nnot0(ts(r,s),n),[t:is(s,0)]ts02(r,s,t)):nis(s,0)
-t17:=satz177c(ts(abs(r),abs(s)),ts(r,s),tris(real,ts(abs(r),abs(s)),abs(ts(r,s)),m0(ts(r,s)),satz193a(r,s),absn(ts(r,s),n))):is(ts(r,s),m0(ts(abs(r),abs(s))))
--4r196
-n@satz196h:=satz196f(t15".4r196",t16".4r196",t17".4r196"):or(and(pos(r),neg(s)),and(neg(r),pos(s)))
-+4r197
-b1is@t1:=satzd197a(a1,b1):eq"rp"(td(m0d(a1),b1),m0d(td(a1,b1)))
-t2:=isin(ts(m0(r),s),m0(ts(r,s)),td(m0d(a1),b1),m0d(td(a1,b1)),tict(m0(r),s,m0d(a1),b1,micm0(r,a1,a1ir),b1is),micm0(ts(r,s),td(a1,b1),tict),t1):is(ts(m0(r),s),m0(ts(r,s)))
--4r197
-s@satz197a:=realapp2(is(ts(m0(r),s),m0(ts(r,s))),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t2".4r197"(x,y,t,u)):is(ts(m0(r),s),m0(ts(r,s)))
-satz197b:=tr3is(real,ts(r,m0(s)),ts(m0(s),r),m0(ts(s,r)),m0(ts(r,s)),comts(r,m0(s)),satz197a(s,r),ism0(ts(s,r),ts(r,s),comts(s,r))):is(ts(r,m0(s)),m0(ts(r,s)))
-satz197c:=tris2(real,ts(m0(r),s),ts(r,m0(s)),m0(ts(r,s)),satz197a,satz197b):is(ts(m0(r),s),ts(r,m0(s)))
-satz197d:=symis(real,ts(m0(r),s),ts(r,m0(s)),satz197c):is(ts(r,m0(s)),ts(m0(r),s))
-satz197e:=symis(real,ts(m0(r),s),m0(ts(r,s)),satz197a):is(m0(ts(r,s)),ts(m0(r),s))
-satz197f:=symis(real,ts(r,m0(s)),m0(ts(r,s)),satz197b):is(m0(ts(r,s)),ts(r,m0(s)))
-satz198:=tris(real,ts(m0(r),m0(s)),ts(r,m0(m0(s))),ts(r,s),satz197c(r,m0(s)),ists2(m0(m0(s)),s,r,satz177(s))):is(ts(m0(r),m0(s)),ts(r,s))
-satz198a:=symis(real,ts(m0(r),m0(s)),ts(r,s),satz198):is(ts(r,s),ts(m0(r),m0(s)))
-+*ivr4
-b1is@[p:pos(r)][q:pos(s)]
-t3:=ptdpp(a1,b1,posex(r,a1,a1ir,p),posex(s,b1,b1is,q)):posd(td(a1,b1))
-t4:=posin(ts(r,s),td(a1,b1),tict,t3):pos(ts(r,s))
--ivr4
-s@[p:pos(r)][q:pos(s)]
-postspp:=realapp2(pos(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t4".ivr4"(x,y,t,u,p,q)):pos(ts(r,s))
-+*ivr4
-p@[n:neg(s)]
-t5:=ntdpn(a1,b1,posex(r,a1,a1ir,p),negex(s,b1,b1is,n)):negd(td(a1,b1))
-t6:=negin(ts(r,s),td(a1,b1),tict,t5):neg(ts(r,s))
--ivr4
-s@[p:pos(r)][n:neg(s)]
-negtspn:=realapp2(neg(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".ivr4"(x,y,t,u,p,n)):neg(ts(r,s))
-s@[n:neg(r)][p:pos(s)]
-negtsnp:=isneg(ts(s,r),ts(r,s),comts(s,r),negtspn(s,r,p,n)):neg(ts(r,s))
-s@[n:neg(r)][o:neg(s)]
-postsnn:=ispos(ts(m0(r),m0(s)),ts(r,s),satz198,postspp(m0(r),m0(s),satz176c(r,n),satz176c(s,o))):pos(ts(r,s))
-r@[n:nis(r,0)]
-possq:=rapp(r,pos(ts(r,r)),[t:pos(r)]postspp(r,r,t,t),th2"l.imp"(is(r,0),pos(ts(r,r)),n),[t:neg(r)]postsnn(r,r,t,t)):pos(ts(r,r))
-r@nnegsq:=th1"l.imp"(is(r,0),not(neg(ts(r,r))),[t:is(r,0)]0notn(ts(r,r),satz192a(r,r,t)),[t:nis(r,0)]pnotn(ts(r,r),possq(r,t))):not(neg(ts(r,r)))
-+4r199
-c2it@t1:=satzd199(a2,b2,c2):eq"rp"(td(td(a2,b2),c2),td(a2,td(b2,c2)))
-t2:=isin(ts(ts(r,s),t),ts(r,ts(s,t)),td(td(a2,b2),c2),td(a2,td(b2,c2)),tict(ts(r,s),t,td(a2,b2),c2,tict(r,s,a2,b2,a2ir,b2is),c2it),tict(r,ts(s,t),a2,td(b2,c2),a2ir,tict(s,t,b2,c2,b2is,c2it)),t1):is(ts(ts(r,s),t),ts(r,ts(s,t)))
--4r199
-t@satz199:=realapp3(is(ts(ts(r,s),t),ts(r,ts(s,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r199"(x,y,z,u,v,w)):is(ts(ts(r,s),t),ts(r,ts(s,t)))
-assts1:=satz199:is(ts(ts(r,s),t),ts(r,ts(s,t)))
-assts2:=symis(real,ts(ts(r,s),t),ts(r,ts(s,t)),satz199):is(ts(r,ts(s,t)),ts(ts(r,s),t))
-+4r201
-c2it@t1:=satzd201(a2,b2,c2):eq"rp"(td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)))
-t2:=isin(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),td(a2,pd(b2,c2)),pd(td(a2,b2),td(a2,c2)),tict(r,pl(s,t),a2,pd(b2,c2),a2ir,picp(s,t,b2,c2,b2is,c2it)),picp(ts(r,s),ts(r,t),td(a2,b2),td(a2,c2),tict(r,s,a2,b2,a2ir,b2is),tict(r,t,a2,c2,a2ir,c2it)),t1):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
--4r201
-satz201:=realapp3(is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t))),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r201"(x,y,z,u,v,w)):is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
-disttp1:=tr3is(real,ts(pl(r,s),t),ts(t,pl(r,s)),pl(ts(t,r),ts(t,s)),pl(ts(r,t),ts(s,t)),comts(pl(r,s),t),satz201(t,r,s),ispl12(ts(t,r),ts(r,t),ts(t,s),ts(s,t),comts(t,r),comts(t,s))):is(ts(pl(r,s),t),pl(ts(r,t),ts(s,t)))
-disttp2:=satz201:is(ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)))
-distpt1:=symis(real,ts(pl(r,s),t),pl(ts(r,t),ts(s,t)),disttp1):is(pl(ts(r,t),ts(s,t)),ts(pl(r,s),t))
-distpt2:=symis(real,ts(r,pl(s,t)),pl(ts(r,s),ts(r,t)),disttp2):is(pl(ts(r,s),ts(r,t)),ts(r,pl(s,t)))
-satz202:=tris(real,ts(r,mn(s,t)),pl(ts(r,s),ts(r,m0(t))),mn(ts(r,s),ts(r,t)),disttp2(r,s,m0(t)),ispl2(ts(r,m0(t)),m0(ts(r,t)),ts(r,s),satz197b(r,t))):is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
-disttm1:=tris(real,ts(mn(r,s),t),pl(ts(r,t),ts(m0(s),t)),mn(ts(r,t),ts(s,t)),disttp1(r,m0(s),t),ispl2(ts(m0(s),t),m0(ts(s,t)),ts(r,t),satz197a(s,t))):is(ts(mn(r,s),t),mn(ts(r,t),ts(s,t)))
-disttm2:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
-distmt1:=symis(real,ts(mn(r,s),t),mn(ts(r,t),ts(s,t)),disttm1):is(mn(ts(r,t),ts(s,t)),ts(mn(r,s),t))
-distmt2:=symis(real,ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)),disttm2):is(mn(ts(r,s),ts(r,t)),ts(r,mn(s,t)))
-satz200:=satz202:is(ts(r,mn(s,t)),mn(ts(r,s),ts(r,t)))
-+4r203
-c2it@[m:more(r,s)][p:pos(t)]
-t1:=satzd203a(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),posex(t,c2,c2it,p)):mored(td(a2,c2),td(b2,c2))
-t2:=morein(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t1):more(ts(r,t),ts(s,t))
--4r203
-[m:more(r,s)][p:pos(t)]
-satz203a:=realapp3(more(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t2".4r203"(x,y,z,u,v,w,m,p)):more(ts(r,t),ts(s,t))
-m@[i:is(t,0)]
-satz203b:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
-+*4r203
-m@[n:neg(t)]
-t3:=satzd203c(a2,b2,c2,moreex(r,s,a2,b2,a2ir,b2is,m),negex(t,c2,c2it,n)):lessd(td(a2,c2),td(b2,c2))
-t4:=lessin(ts(r,t),ts(s,t),td(a2,c2),td(b2,c2),tict(r,t,a2,c2,a2ir,c2it),tict(s,t,b2,c2,b2is,c2it),t3):less(ts(r,t),ts(s,t))
--4r203
-m@[n:neg(t)]
-satz203c:=realapp3(less(ts(r,t),ts(s,t)),[x:dif][y:dif][z:dif][u:inn(x,class(r))][v:inn(y,class(s))][w:inn(z,class(t))]t4".4r203"(x,y,z,u,v,w,m,n)):less(ts(r,t),ts(s,t))
-p@satz203d:=ismore12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203a):more(ts(t,r),ts(t,s))
-i@satz203e:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
-n@satz203f:=isless12(ts(r,t),ts(t,r),ts(s,t),ts(t,s),comts(r,t),comts(s,t),satz203c):less(ts(t,r),ts(t,s))
-t@[l:less(r,s)][p:pos(t)]
-satz203g:=lemma1(ts(s,t),ts(r,t),satz203a(s,r,t,lemma2(r,s,l),p)):less(ts(r,t),ts(s,t))
-l@[i:is(t,0)]
-satz203h:=tris2(real,ts(r,t),ts(s,t),0,ts02(r,t,i),ts02(s,t,i)):is(ts(r,t),ts(s,t))
-l@[n:neg(t)]
-satz203j:=lemma2(ts(s,t),ts(r,t),satz203c(s,r,t,lemma2(r,s,l),n)):more(ts(r,t),ts(s,t))
-p@satz203k:=lemma1(ts(t,s),ts(t,r),satz203d(s,r,t,lemma2(r,s,l),p)):less(ts(t,r),ts(t,s))
-i@satz203l:=tris2(real,ts(t,r),ts(t,s),0,ts01(t,r,i),ts01(t,s,i)):is(ts(t,r),ts(t,s))
-n@satz203m:=lemma2(ts(t,s),ts(t,r),satz203f(s,r,t,lemma2(r,s,l),n)):more(ts(t,r),ts(t,s))
-+4r204
-a0ir@[n1:nis(r,0)]
-t1:=th3"l.imp"(zero(a0),is(r,0),n1,[t:zero(a0)]0in(t)):not(zero(a0))
-d3iu@[n1:nis(s,0)][i:is(ts(s,t),r)][j:is(ts(s,u),r)]
-t2:=satzd204b(a3,b3,t1(s,b3,b3is,n1),c3,d3,isex(ts(s,t),r,td(b3,c3),a3,tict(s,t,b3,c3,b3is,c3it),a3ir,i),isex(ts(s,u),r,td(b3,d3),a3,tict(s,u,b3,d3,b3is,d3iu),a3ir,j)):eq"rp"(c3,d3)
-t3:=isin(t,u,c3,d3,c3it,d3iu,t2):is(t,u)
--4r204
-s@[n:nis(s,0)][x:real][y:real][i:is(ts(s,x),r)][j:is(ts(s,y),r)]
-satz204b:=realapp4(x,y,is(x,y),[z:dif][u:dif][v:dif][w:dif][zi:inn(z,class(r))][ui:inn(u,class(s))][vi:inn(v,class(x))][wi:inn(w,class(y))]t3".4r204"(x,y,z,u,v,w,zi,ui,vi,wi,n,i,j)):is(x,y)
-+*4r204
-b1is@[n1:nis(s,0)]
-t4:=satzd204a(a1,b1,t1(s,b1,b1is,n1)):some"l"(dif,[x:dif]eq"rp"(td(b1,x),a1))
-[a:dif][e:eq"rp"(td(b1,a),a1)]
-ar:=realof(a):real
-t5:=isin(ts(s,ar),r,td(b1,a),a1,tict(s,ar,b1,a,b1is,innclass(a)),a1ir,e):is(ts(s,ar),r)
-t6:=somei(real,[x:real]is(ts(s,x),r),ar,t5):some([x:real]is(ts(s,x),r))
-n1@t7:=someapp(dif,[x:dif]eq"rp"(td(b1,x),a1),t4,some([x:real]is(ts(s,x),r)),[x:dif][t:eq"rp"(td(b1,x),a1)]t6(x,t)):some([x:real]is(ts(s,x),r))
--4r204
-n@satz204a:=realapp2(some([x:real]is(ts(s,x),r)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t7".4r204"(x,y,t,u,n)):some([x:real]is(ts(s,x),r))
-satz204:=onei(real,[x:real]is(ts(s,x),r),[x:real][y:real][t:is(ts(s,x),r)][u:is(ts(s,y),r)]satz204b(x,y,t,u),satz204a):one([x:real]is(ts(s,x),r))
-ov:=ind(real,[x:real]is(ts(s,x),r),satz204):real
-satz204c:=oneax(real,[x:real]is(ts(s,x),r),satz204):is(ts(s,ov(r,s,n)),r)
-satz204d:=symis(real,ts(s,ov(r,s,n)),r,satz204c):is(r,ts(s,ov(r,s,n)))
-satz204e:=tris(real,ts(ov(r,s,n),s),ts(s,ov(r,s,n)),r,comts(ov(r,s,n),s),satz204c):is(ts(ov(r,s,n),s),r)
-satz204f:=symis(real,ts(ov(r,s,n),s),r,satz204e):is(r,ts(ov(r,s,n),s))
-s@[x:real][n:nis(s,0)][i:is(ts(s,x),r)]
-satz204g:=satz204b(n,x,ov(r,s,n),i,satz204c(n)):is(x,ov(r,s,n))
-s@[n:nis(s,0)][p:pos(r)][q:pos(s)]
-+*4r204
-n@ros:=ov(r,s,n):real
-p@t8:=ispos(r,ts(s,ros),satz204d(n),p):pos(ts(s,ros))
-q@t9:=th1"l.and"(neg(s),neg(ros),pnotn(s,q)):not(and(neg(s),neg(ros)))
-t10:=ore1(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t9):and(pos(s),pos(ros))
--4r204
-q@posovpp:=ande2(pos(s),pos(ov(r,s,n)),t10".4r204"):pos(ov(r,s,n))
-p@[m:neg(s)]
-+*4r204
-m@t11:=th1"l.and"(pos(s),pos(ros),nnotp(s,m)):not(and(pos(s),pos(ros)))
-t12:=ore2(and(pos(s),pos(ros)),and(neg(s),neg(ros)),satz196g(s,ros,t8),t11):and(neg(s),neg(ros))
--4r204
-m@negovpn:=ande2(neg(s),neg(ov(r,s,n)),t12".4r204"):neg(ov(r,s,n))
-n@[m:neg(r)][p:pos(s)]
-+*4r204
-m@t13:=isneg(r,ts(s,ros),satz204d(n),m):neg(ts(s,ros))
-p@t14:=th1"l.and"(neg(s),pos(ros),pnotn(s,p)):not(and(neg(s),pos(ros)))
-t15:=ore1(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t14):and(pos(s),neg(ros))
--4r204
-p@negovnp:=ande2(pos(s),neg(ov(r,s,n)),t15".4r204"):neg(ov(r,s,n))
-m@[l:neg(s)]
-+*4r204
-l@t16:=th1"l.and"(pos(s),neg(ros),nnotp(s,l)):not(and(pos(s),neg(ros)))
-t17:=ore2(and(pos(s),neg(ros)),and(neg(s),pos(ros)),satz196h(s,ros,t13),t16):and(neg(s),pos(ros))
--4r204
-l@posovnn:=ande2(neg(s),pos(ov(r,s,n)),t17".4r204"):pos(ov(r,s,n))
-@[r0:cut][s0:cut][m:more"rp"(r0,s0)]
-morerpep:=morein(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),morerpepd(r0,s0,m)):more(pofrp(r0),pofrp(s0))
-s0@[m:more(pofrp(r0),pofrp(s0))]
-morerpip:=morerpipd(r0,s0,moreex(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0)),m)):more"rp"(r0,s0)
-s0@[l:less"rp"(r0,s0)]
-lessrpep:=lemma1(pofrp(s0),pofrp(r0),morerpep(s0,r0,satz122(r0,s0,l))):less(pofrp(r0),pofrp(s0))
-s0@[l:less(pofrp(r0),pofrp(s0))]
-lessrpip:=satz121(s0,r0,morerpip(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
-s@[p:pos(r)][q:pos(s)][m:more(r,s)]
-q@[m:more(r,s)]
-+ivr5
-t1:=ismore12(r,pofrp(rpofp(r,p)),s,pofrp(rpofp(s,q)),isprp1(r,p),isprp1(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
--ivr5
-moreperp:=morerpip(rpofp(r,p),rpofp(s,q),t1".ivr5"):more"rp"(rpofp(r,p),rpofp(s,q))
-q@[m:more"rp"(rpofp(r,p),rpofp(s,q))]
-+*ivr5
-m@t2:=morerpep(rpofp(r,p),rpofp(s,q),m):more(pofrp(rpofp(r,p)),pofrp(rpofp(s,q)))
--ivr5
-m@morepirp:=ismore12(pofrp(rpofp(r,p)),r,pofrp(rpofp(s,q)),s,isprp2(r,p),isprp2(s,q),t2".ivr5"):more(r,s)
-q@[l:less(r,s)]
-lessperp:=satz121(rpofp(s,q),rpofp(r,p),moreperp(s,r,q,p,lemma2(r,s,l))):less"rp"(rpofp(r,p),rpofp(s,q))
-q@[l:less"rp"(rpofp(r,p),rpofp(s,q))]
-lesspirp:=lemma1(s,r,morepirp(s,r,q,p,satz122(rpofp(r,p),rpofp(s,q),l))):less(r,s)
-r@s01:=setof(real,[x:real]lessis(x,r)):set(real)
-s02:=setof(real,[x:real]more(x,r)):set(real)
-+5r205
-s@[n:not(in(s,s01))]
-t1:=th3"l.imp"(lessis(s,r),in(s,s01),n,[t:lessis(s,r)]estii(real,[x:real]lessis(x,r),s,t)):not(lessis(s,r))
-t2:=estii(real,[x:real]more(x,r),s,satz167k(s,r,t1)):in(s,s02)
--5r205
-vb00:=[x:real][t:not(in(x,s01))]t2".5r205"(x,t):all([x:real]or(in(x,s01),in(x,s02)))
-+*5r205
-r@t3:=estii(real,[x:real]lessis(x,r),r,lessisi2(r,r,refis(real,r))):in(r,s01)
--5r205
-r@vb01a:=nonemptyi(real,s01,r,t3".5r205"):nonempty(real,s01)
-+*5r205
-r@t4:=ismore2(pl(r,0),r,pl(r,1rl),pl02(r,0,refis(real,0)),satz188k(1rl,0,r,satz169a(1rl,pos1))):more(pl(r,1rl),r)
-t5:=estii(real,[x:real]more(x,r),pl(r,1rl),t4):in(pl(r,1rl),s02)
--5r205
-r@vb01b:=nonemptyi(real,s02,pl(r,1rl),t5".5r205"):nonempty(real,s02)
-+*5r205
-s@[i:in(s,s01)][t:real][j:in(t,s02)]
-t6:=satz172a(s,r,t,estie(real,[x:real]lessis(x,r),s,i),lemma1(t,r,estie(real,[x:real]more(x,r),t,j))):less(s,t)
--5r205
-r@vb02:=[x:real][t:in(x,s01)][y:real][u:in(y,s02)]t6".5r205"(x,t,y,u):all([x:real][t:in(x,s01)]all([y:real][u:in(y,s02)]less(x,y)))
-s@[l:less(s,r)]
-vb03a:=estii(real,[x:real]lessis(x,r),s,lessisi1(s,r,l)):in(s,s01)
-s@[m:more(s,r)]
-vb03b:=estii(real,[x:real]more(x,r),s,m):in(s,s02)
-r@s11:=setof(real,[x:real]less(x,r)):set(real)
-s12:=setof(real,[x:real]moreis(x,r)):set(real)
-+*5r205
-s@[n:not(in(s,s11))]
-t7:=th3"l.imp"(less(s,r),in(s,s11),n,[t:less(s,r)]estii(real,[x:real]less(x,r),s,t)):not(less(s,r))
-t8:=estii(real,[x:real]moreis(x,r),s,satz167f(s,r,t7)):in(s,s12)
--5r205
-r@vb10:=[x:real][t:not(in(x,s11))]t8".5r205"(x,t):all([x:real]or(in(x,s11),in(x,s12)))
-+*5r205
-r@t9:=isless2(pl(r,0),r,mn(r,1rl),pl02(r,0,refis(real,0)),satz188m(m0(1rl),0,r,satz169c(m0(1rl),satz176a(1rl,pos1)))):less(mn(r,1rl),r)
-t10:=estii(real,[x:real]less(x,r),mn(r,1rl),t9):in(mn(r,1rl),s11)
--5r205
-r@vb11a:=nonemptyi(real,s11,mn(r,1rl),t10".5r205"):nonempty(real,s11)
-+*5r205
-r@t11:=estii(real,[x:real]moreis(x,r),r,moreisi2(r,r,refis(real,r))):in(r,s12)
--5r205
-r@vb11b:=nonemptyi(real,s12,r,t11".5r205"):nonempty(real,s12)
-+*5r205
-s@[i:in(s,s11)][t:real][j:in(t,s12)]
-t12:=satz172b(s,r,t,estie(real,[x:real]less(x,r),s,i),satz168a(t,r,estie(real,[x:real]moreis(x,r),t,j))):less(s,t)
--5r205
-r@vb12:=[x:real][t:in(x,s11)][y:real][u:in(y,s12)]t12".5r205"(x,t,y,u):all([x:real][t:in(x,s11)]all([y:real][u:in(y,s12)]less(x,y)))
-s@[l:less(s,r)]
-vb13a:=estii(real,[x:real]less(x,r),s,l):in(s,s11)
-s@[m:more(s,r)]
-vb13b:=estii(real,[x:real]moreis(x,r),s,moreisi1(s,r,m)):in(s,s12)
-@2rl:=pl(1rl,1rl):real
-pos2:=pospl(1rl,1rl,pos1,pos1):pos(2rl)
-half:=ov(1rl,2rl,pnot0(2rl,pos2)):real
-poshalf:=posovpp(1rl,2rl,pnot0(2rl,pos2),pos1,pos2):pos(half)
-+*ivr5
-r@t3:=tris(real,pl(r,r),pl(ts(1rl,r),ts(1rl,r)),ts(2rl,r),ispl12(r,ts(1rl,r),r,ts(1rl,r),satz195c(r),satz195c(r)),distpt1(1rl,1rl,r)):is(pl(r,r),ts(2rl,r))
-t4:=tr4is(real,ts(half,pl(r,r)),ts(half,ts(2rl,r)),ts(ts(half,2rl),r),ts(1rl,r),r,ists2(pl(r,r),ts(2rl,r),half,t3),assts2(half,2rl,r),ists1(ts(half,2rl),1rl,r,satz204e(1rl,2rl,pnot0(2rl,pos2))),satz195b(r)):is(ts(half,pl(r,r)),r)
--ivr5
-s@[l:less(r,s)]
-+*ivr5
-l@t5:=satz203k(pl(r,r),pl(r,s),half,satz188m(r,s,r,l),poshalf):less(ts(half,pl(r,r)),ts(half,pl(r,s)))
--ivr5
-l@lemma3:=isless1(ts(half,pl(r,r)),r,ts(half,pl(r,s)),t4".ivr5",t5".ivr5"):less(r,ts(half,pl(r,s)))
-+*ivr5
-l@t6:=satz203k(pl(r,s),pl(s,s),half,satz188f(r,s,s,l),poshalf):less(ts(half,pl(r,s)),ts(half,pl(s,s)))
--ivr5
-l@lemma4:=isless2(ts(half,pl(s,s)),s,ts(half,pl(r,s)),t4".ivr5"(s),t6".ivr5"):less(ts(half,pl(r,s)),s)
-[p:pos(r)]
-lemma5:=satz169b(s,trmore(s,r,0,lemma2(r,s,l),satz169a(r,p))):pos(s)
-@[s1:set(real)][s2:set(real)][p0:all([x:real]or(in(x,s1),in(x,s2)))][p1a:nonempty(real,s1)][p1b:nonempty(real,s2)][p2:all([x:real][t:in(x,s1)]all([y:real][u:in(y,s2)]less(x,y)))]
-+*5r205
-s2@[r:real]
-prop1:=all([x:real][t:less(x,r)]in(x,s1)):'prop'
-prop2:=all([x:real][t:more(x,r)]in(x,s2)):'prop'
-prop3:=and(prop1,prop2):'prop'
-p2@[x:real][y:real][px:prop3(x)][py:prop3(y)][l:less(x,y)]
-mxy:=ts(half,pl(x,y)):real
-t13:=lemma2(x,mxy,lemma3(x,y,l)):more(mxy,x)
-t14:=lemma4(x,y,l):less(mxy,y)
-t15:=<t14><mxy>ande1(prop1(y),prop2(y),py):in(mxy,s1)
-t16:=<t13><mxy>ande2(prop1(x),prop2(x),px):in(mxy,s2)
-t17:=<t16><mxy><t15><mxy>p2:less(mxy,mxy)
-t18:=<refis(real,mxy)>ec3e31(is(mxy,mxy),more(mxy,mxy),less(mxy,mxy),satz167b(mxy,mxy),t17):con
-py@t19:=[t:less(x,y)]t18(t):not(less(x,y))
-t20:=[t:more(x,y)]t18(y,x,py,px,lemma1(x,y,t)):not(more(x,y))
-t21:=or3e1(is(x,y),more(x,y),less(x,y),satz167a(x,y),t20,t19):is(x,y)
-p2@t22:=[x:real][y:real][t:prop3(x)][u:prop3(y)]t21(x,y,t,u):amone(real,[x:real]prop3(x))
-[case1:some([x:real]and(pos(x),in(x,s1)))][r:real][a:and(pos(r),in(r,s1))]
-t23:=ande1(pos(r),in(r,s1),a):pos(r)
-t24:=ande2(pos(r),in(r,s1),a):in(r,s1)
-sc1:=setof(cut,[x:cut]in(pofrp(x),s1)):set(cut)
-sc2:=setof(cut,[x:cut]in(pofrp(x),s2)):set(cut)
-[r0:cut][i:in(pofrp(r0),s1)]
-t25:=estii(cut,[x:cut]in(pofrp(x),s1),r0,i):in"rp"(r0,sc1)
-r0@[i:in"rp"(r0,sc1)]
-t26:=estie(cut,[x:cut]in(pofrp(x),s1),r0,i):in(pofrp(r0),s1)
-r0@[i:in(pofrp(r0),s2)]
-t27:=estii(cut,[x:cut]in(pofrp(x),s2),r0,i):in"rp"(r0,sc2)
-r0@[i:in"rp"(r0,sc2)]
-t28:=estie(cut,[x:cut]in(pofrp(x),s2),r0,i):in(pofrp(r0),s2)
-r0@t29:=th9"l.or"(in(pofrp(r0),s1),in(pofrp(r0),s2),in"rp"(r0,sc1),in"rp"(r0,sc2),<pofrp(r0)>p0,[t:in(pofrp(r0),s1)]t25(t),[t:in(pofrp(r0),s2)]t27(t)):or(in"rp"(r0,sc1),in"rp"(r0,sc2))
-a@pr1:=rpofp(r,t23):cut
-t30:=isp(real,[x:real]in(x,s1),r,pofrp(pr1),t24,isprp1(r,t23)):in(pofrp(pr1),s1)
-t31:=nonemptyi(cut,sc1,pr1,t25(pr1,t30)):nonempty(cut,sc1)
-[s:real][i:in(s,s2)]
-t32:=<i><s><t24><r>p2:less(r,s)
-t33:=lemma5(r,s,t32,t23):pos(s)
-ps1:=rpofp(s,t33):cut
-t34:=isp(real,[x:real]in(x,s2),s,pofrp(ps1),i,isprp1(s,t33)):in(pofrp(ps1),s2)
-t35:=nonemptyi(cut,sc2,ps1,t27(ps1,t34)):nonempty(cut,sc2)
-a@t36:=nonemptyapp(real,s2,p1b,nonempty(cut,sc2),[x:real][t:in(x,s2)]t35(x,t)):nonempty(cut,sc2)
-r0@[i:in"rp"(r0,sc1)][s0:cut][j:in"rp"(s0,sc2)]
-t37:=<t28(s0,j)><pofrp(s0)><t26(r0,i)><pofrp(r0)>p2:less(pofrp(r0),pofrp(s0))
-t38:=lessrpip(r0,s0,t37):less"rp"(r0,s0)
-a@stc:=schnitt(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):cut
-t39:=satzp205a(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:less"rp"(x,stc)]in"rp"(x,sc1))
-t40:=satzp205b(sc1,sc2,[x:cut]t29(x),t31,t36,[x:cut][t:in"rp"(x,sc1)][y:cut][u:in"rp"(y,sc2)]t38(x,t,y,u)):all"rp"([x:cut][t:more"rp"(x,stc)]in"rp"(x,sc2))
-stp:=pofrp(stc):real
-t41:=posi(stc):pos(stp)
-[s:real][l:less(s,stp)][p:pos(s)]
-ps2:=rpofp(s,p):cut
-t42:=lessrpip(ps2,stc,isless1(s,pofrp(ps2),stp,isprp1(s,p),l)):less"rp"(ps2,stc)
-t43:=<t42><ps2>t39:in"rp"(ps2,sc1)
-t44:=isp(real,[x:real]in(x,s1),pofrp(ps2),s,t26(ps2,t43),isprp2(s,p)):in(s,s1)
-l@[n:not(pos(s))][i:in(s,s2)]
-t45:=<i><s><t24><r>p2:less(r,s)
-t46:=<lemma5(r,s,t45,t23)>n:con
-n@t47:=ore1(in(s,s1),in(s,s2),<s>p0,[t:in(s,s2)]t46(t)):in(s,s1)
-l@t48:=th1"l.imp"(pos(s),in(s,s1),[t:pos(s)]t44(t),[t:not(pos(s))]t47(t)):in(s,s1)
-s@[m:more(s,stp)]
-t49:=lemma5(stp,s,lemma1(s,stp,m),t41):pos(s)
-ps3:=rpofp(s,t49):cut
-t50:=morerpip(ps3,stc,ismore1(s,pofrp(ps3),stp,isprp1(s,t49),m)):more"rp"(ps3,stc)
-t51:=<t50><ps3>t40:in"rp"(ps3,sc2)
-t52:=isp(real,[x:real]in(x,s2),pofrp(ps3),s,t28(ps3,t51),isprp2(s,t49)):in(s,s2)
-a@t53:=andi(prop1(stp),prop2(stp),[x:real][t:less(x,stp)]t48(x,t),[x:real][t:more(x,stp)]t52(x,t)):prop3(stp)
-t54:=somei(real,[x:real]prop3(x),stp,t53):some([x:real]prop3(x))
-case1@t55:=someapp(real,[x:real]and(pos(x),in(x,s1)),case1,some([x:real]prop3(x)),[x:real][t:and(pos(x),in(x,s1))]t54(x,t)):some([x:real]prop3(x))
-p2@[case2:some([x:real]and(neg(x),in(x,s2)))]
-sp1:=setof(real,[x:real]in(m0(x),s1)):set(real)
-sp2:=setof(real,[x:real]in(m0(x),s2)):set(real)
-[r:real][i:in(m0(r),s1)]
-t56:=estii(real,[x:real]in(m0(x),s1),r,i):in(r,sp1)
-r@[i:in(r,sp1)]
-t57:=estie(real,[x:real]in(m0(x),s1),r,i):in(m0(r),s1)
-r@[i:in(m0(r),s2)]
-t58:=estii(real,[x:real]in(m0(x),s2),r,i):in(r,sp2)
-r@[i:in(r,sp2)]
-t59:=estie(real,[x:real]in(m0(x),s2),r,i):in(m0(r),s2)
-r@t60:=comor(in(r,sp1),in(r,sp2),th9"l.or"(in(m0(r),s1),in(m0(r),s2),in(r,sp1),in(r,sp2),<m0(r)>p0,[t:in(m0(r),s1)]t56(t),[t:in(m0(r),s2)]t58(t))):or(in(r,sp2),in(r,sp1))
-[i:in(r,s2)]
-t61:=t58(m0(r),isp(real,[x:real]in(x,s2),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp2)
-t62:=nonemptyi(real,sp2,m0(r),t61):nonempty(real,sp2)
-case2@t63:=nonemptyapp(real,s2,p1b,nonempty(real,sp2),[x:real][t:in(x,s2)]t62(x,t)):nonempty(real,sp2)
-r@[i:in(r,s1)]
-t64:=t56(m0(r),isp(real,[x:real]in(x,s1),r,m0(m0(r)),i,satz177a(r))):in(m0(r),sp1)
-t65:=nonemptyi(real,sp1,m0(r),t64):nonempty(real,sp1)
-case2@t66:=nonemptyapp(real,s1,p1a,nonempty(real,sp1),[x:real][t:in(x,s1)]t65(x,t)):nonempty(real,sp1)
-r@[i:in(r,sp2)][s:real][j:in(s,sp1)]
-t67:=<t59(r,i)><m0(r)><t57(s,j)><m0(s)>p2:less(m0(s),m0(r))
-t68:=lemma1(s,r,satz183d(s,r,t67)):less(r,s)
-r@[a:and(neg(r),in(r,s2))]
-t69:=satz176c(r,ande1(neg(r),in(r,s2),a)):pos(m0(r))
-t70:=isp(real,[x:real]in(x,s2),r,m0(m0(r)),ande2(neg(r),in(r,s2),a),satz177a(r)):in(m0(m0(r)),s2)
-t71:=andi(pos(m0(r)),in(m0(r),sp2),t69,t58(m0(r),t70)):and(pos(m0(r)),in(m0(r),sp2))
-t72:=somei(real,[x:real]and(pos(x),in(x,sp2)),m0(r),t71):some([x:real]and(pos(x),in(x,sp2)))
-case2@t73:=someapp(real,[x:real]and(neg(x),in(x,s2)),case2,some([x:real]and(pos(x),in(x,sp2))),[x:real][t:and(neg(x),in(x,s2))]t72(x,t)):some([x:real]and(pos(x),in(x,sp2)))
-t74:=t55(sp2,sp1,[x:real]t60(x),t63,t66,[x:real][t:in(x,sp2)][y:real][u:in(y,sp1)]t68(x,t,y,u),t73):some([x:real]prop3(sp2,sp1,x))
-[r:real][p:prop3(sp2,sp1,r)][s:real][l:less(s,m0(r))]
-t75:=ismore2(m0(m0(r)),r,m0(s),satz177(r),satz183c(s,m0(r),l)):more(m0(s),r)
-t76:=<t75><m0(s)>ande2(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp1)
-t77:=isp(real,[x:real]in(x,s1),m0(m0(s)),s,t57(m0(s),t76),satz177(s)):in(s,s1)
-s@[m:more(s,m0(r))]
-t78:=isless2(m0(m0(r)),r,m0(s),satz177(r),satz183a(s,m0(r),m)):less(m0(s),r)
-t79:=<t78><m0(s)>ande1(prop1(sp2,sp1,r),prop2(sp2,sp1,r),p):in(m0(s),sp2)
-t80:=isp(real,[x:real]in(x,s2),m0(m0(s)),s,t59(m0(s),t79),satz177(s)):in(s,s2)
-p@t81:=andi(prop1(m0(r)),prop2(m0(r)),[x:real][t:less(x,m0(r))]t77(x,t),[x:real][t:more(x,m0(r))]t80(x,t)):prop3(m0(r))
-t82:=somei(real,[x:real]prop3(x),m0(r),t81):some([x:real]prop3(x))
-case2@t83:=someapp(real,[x:real]prop3(sp2,sp1,x),t74,some([x:real]prop3(x)),[x:real][t:prop3(sp2,sp1,x)]t82(x,t)):some([x:real]prop3(x))
-p2@[notcase1:not(some([x:real]and(pos(x),in(x,s1))))][notcase2:not(some([x:real]and(neg(x),in(x,s2))))][r:real][l:less(r,0)]
-t84:=th4"l.some"(real,[x:real]and(neg(x),in(x,s2)),notcase2,r):not(and(neg(r),in(r,s2)))
-t85:=th3"l.and"(neg(r),in(r,s2),t84,satz169d(r,l)):not(in(r,s2))
-t86:=ore1(in(r,s1),in(r,s2),<r>p0,t85):in(r,s1)
-r@[m:more(r,0)]
-t87:=th4"l.some"(real,[x:real]and(pos(x),in(x,s1)),notcase1,r):not(and(pos(r),in(r,s1)))
-t88:=th3"l.and"(pos(r),in(r,s1),t87,satz169b(r,m)):not(in(r,s1))
-t89:=ore2(in(r,s1),in(r,s2),<r>p0,t88):in(r,s2)
-notcase2@t90:=andi(prop1(0),prop2(0),[x:real][t:less(x,0)]t86(x,t),[x:real][t:more(x,0)]t89(x,t)):prop3(0)
-t91:=somei(real,[x:real]prop3(x),0,t90):some([x:real]prop3(x))
-notcase1@t92:=th1"l.imp"(some([x:real]and(neg(x),in(x,s2))),some([x:real]prop3(x)),[t:some([x:real]and(neg(x),in(x,s2)))]t83(t),[t:not(some([x:real]and(neg(x),in(x,s2))))]t91(t)):some([x:real]prop3(x))
-p2@t93:=th1"l.imp"(some([x:real]and(pos(x),in(x,s1))),some([x:real]prop3(x)),[t:some([x:real]and(pos(x),in(x,s1)))]t55(t),[t:not(some([x:real]and(pos(x),in(x,s1))))]t92(t)):some([x:real]prop3(x))
-t94:=onei(real,[x:real]prop3(x),t22,t93):one([x:real]prop3(x))
--5r205
-p2@satz205:=t94".5r205":one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
-dedekind:=satz205:one([x:real]and(all([y:real][t:less(y,x)]in(y,s1)),all([y:real][t:more(y,x)]in(y,s2))))
-schnitt:=ind(real,[x:real]prop3".5r205"(x),satz205):real
-[r:real][l:less(r,schnitt)]
-satz205a:=<l><r>ande1(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s1)
-r@[m:more(r,schnitt)]
-satz205b:=<m><r>ande2(prop1".5r205"(schnitt),prop2".5r205"(schnitt),oneax(real,[x:real]prop3".5r205"(x),satz205)):in(r,s2)
-@[r0:cut][s0:cut]
-+iva
-dr:=pdofrp(r0):dif
-ds:=pdofrp(s0):dif
-t1:=lemmaivad1(r0,s0):eq"rp"(pd(dr,ds),pdofrp(pl"rp"(r0,s0)))
--iva
-lemmaiva1:=isin(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)),pd(pdofrp(r0),pdofrp(s0)),pdofrp(pl"rp"(r0,s0)),picp(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(pl"rp"(r0,s0))),t1".iva"):is(pl(pofrp(r0),pofrp(s0)),pofrp(pl"rp"(r0,s0)))
-+*iva
-s0@t2:=lemmaivad2(r0,s0):eq"rp"(td(dr,ds),pdofrp(ts"rp"(r0,s0)))
--iva
-s0@lemmaiva2:=isin(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)),td(pdofrp(r0),pdofrp(s0)),pdofrp(ts"rp"(r0,s0)),tict(pofrp(r0),pofrp(s0),pdofrp(r0),pdofrp(s0),innclass(pdofrp(r0)),innclass(pdofrp(s0))),innclass(pdofrp(ts"rp"(r0,s0))),t2".iva"):is(ts(pofrp(r0),pofrp(s0)),pofrp(ts"rp"(r0,s0)))
-[m:more(pofrp(r0),pofrp(s0))]
-+*iva
-m@t3:=moreex(pofrp(r0),pofrp(s0),dr,ds,innclass(dr),innclass(ds),m):mored(dr,ds)
--iva
-m@lemmaiva3:=lemmaivad3(r0,s0,t3".iva"):more"rp"(r0,s0)
-s0@[m:more"rp"(r0,s0)]
-+*iva
-m@[l:less(pofrp(r0),pofrp(s0))]
-t4:=satz121(s0,r0,lemmaiva3(s0,r0,lemma2(pofrp(r0),pofrp(s0),l))):less"rp"(r0,s0)
-m@t5:=ec3e23(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):not(less"rp"(r0,s0))
-t6:=th3"l.imp"(less(pofrp(r0),pofrp(s0)),less"rp"(r0,s0),t5,[t:less(pofrp(r0),pofrp(s0))]t4(t)):not(less(pofrp(r0),pofrp(s0)))
-t7:=ec3e21(is"rp"(r0,s0),more"rp"(r0,s0),less"rp"(r0,s0),satz123b(r0,s0),m):nis"rp"(r0,s0)
-t8:=th3"l.imp"(is(pofrp(r0),pofrp(s0)),is"rp"(r0,s0),t7,[t:is(pofrp(r0),pofrp(s0))]isrpip(r0,s0,t)):nis(pofrp(r0),pofrp(s0))
--iva
-m@lemmaiva4:=or3e2(is(pofrp(r0),pofrp(s0)),more(pofrp(r0),pofrp(s0)),less(pofrp(r0),pofrp(s0)),satz167a(pofrp(r0),pofrp(s0)),t6".iva",t8".iva"):more(pofrp(r0),pofrp(s0))
-@[x:nat][y:nat][m:more(rlofnt(x),rlofnt(y))]
-+*iva
-m@t9:=lemmaiva3(rpofnt(x),rpofnt(y),m):more"rp"(rpofnt(x),rpofnt(y))
-t10:=satz154d(rtofn(x),rtofn(y),t9):more"rt"(rtofn(x),rtofn(y))
-t11:=moree"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t10):moref(fr(x,1),fr(y,1))
--iva
-m@lemmaiva5:=satz111a(x,y,t11".iva"):more"n"(x,y)
-y@[m:more"n"(x,y)]
-+*iva
-m@t12:=satz111d(x,y,m):moref(fr(x,1),fr(y,1))
-t13:=morei"rt"(rtofn(x),rtofn(y),fr(x,1),fr(y,1),inclass"rt"(fr(x,1)),inclass"rt"(fr(y,1)),t12):more"rt"(rtofn(x),rtofn(y))
-t14:=satz154a(rtofn(x),rtofn(y),t13):more"rp"(rpofnt(x),rpofnt(y))
--iva
-m@lemmaiva6:=lemmaiva4(rpofnt(x),rpofnt(y),t14".iva"):more(rlofnt(x),rlofnt(y))
-@[r:real]
-+int
-a0ir@[i:intrl(r)]
-t1:=intabsd(a0,intrlex(r,a0,a0ir,i)):intd(absd(a0))
-t2:=intrlin(abs(r),absd(a0),aica,t1):intrl(abs(r))
--int
-[i:intrl(r)]
-intabs:=realapp1(r,intrl(abs(r)),[x:dif][t:inn(x,class(r))]t2".int"(r,x,t,i)):intrl(abs(r))
-+*int
-i@t3:=intm0d(a0,intrlex(r,a0,a0ir,i)):intd(m0d(a0))
-t4:=intrlin(m0(r),m0d(a0),micm0,t3):intrl(m0(r))
--int
-i@intm0:=realapp1(r,intrl(m0(r)),[x:dif][t:inn(x,class(r))]t4".int"(r,x,t,i)):intrl(m0(r))
-+*int
-b1is@[i:intrl(r)][j:intrl(s)]
-t5:=intpd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(pd(a1,b1))
-t6:=intrlin(pl(r,s),pd(a1,b1),picp,t5):intrl(pl(r,s))
--int
-i@[s:real][j:intrl(s)]
-intpl:=realapp2(r,s,intrl(pl(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t6".int"(r,s,x,y,t,u,i,j)):intrl(pl(r,s))
-intmn:=intpl(r,i,m0(s),intm0(s,j)):intrl(mn(r,s))
-+*int
-j@t7:=inttd(a1,b1,intrlex(r,a1,a1ir,i),intrlex(s,b1,b1is,j)):intd(td(a1,b1))
-t8:=intrlin(ts(r,s),td(a1,b1),tict,t7):intrl(ts(r,s))
--int
-j@intts:=realapp2(r,s,intrl(ts(r,s)),[x:dif][y:dif][t:inn(x,class(r))][u:inn(y,class(s))]t8".int"(r,s,x,y,t,u,i,j)):intrl(ts(r,s))
-r@[n:natrl(r)]
-+ivr24
-t1:=satz24a(ntofrl(r,n)):lessis"n"(1,ntofrl(r,n))
-t2:=th3"l.imp"(more(1rl,r),more"n"(1,ntofrl(r,n)),satz10d(1,ntofrl(r,n),t1),[t:more(1rl,r)]lemmaiva5(1,ntofrl(r,n),ismore2(r,rlofnt(ntofrl(r,n)),1rl,isrlnt1(r,n),t))):not(more(1rl,r))
--ivr24
-satzr24:=satz167e(1rl,r,t2".ivr24"):lessis(1rl,r)
-r@[i:intrl(r)][s:real][j:intrl(s)][l:less(r,s)]
-+ivr25
-t1:=satz182d(s,r,lemma2(r,s,l)):pos(mn(s,r))
-t2:=intmn(s,j,r,i):intrl(mn(s,r))
-t3:=posintnatrl(mn(s,r),t1,t2):natrl(mn(s,r))
-t4:=satzr24(mn(s,r),t3):lessis(1rl,mn(s,r))
-t5:=th9"l.or"(less(1rl,mn(s,r)),is(1rl,mn(s,r)),less(pl(1rl,r),pl(mn(s,r),r)),is(pl(1rl,r),pl(mn(s,r),r)),t4,[t:less(1rl,mn(s,r))]satz188f(1rl,mn(s,r),r,t),[t:is(1rl,mn(s,r))]ispl1(1rl,mn(s,r),r,t)):lessis(pl(1rl,r),pl(mn(s,r),r))
--ivr25
-satzr25:=islessis12(pl(1rl,r),pl(r,1rl),pl(mn(s,r),r),s,compl(1rl,r),plmn(s,r),t5".ivr25"):lessis(pl(r,1rl),s)
-@[x:nat][y:nat]
-+ivr155
-t1:=lemmaiva1(rpofnt(x),rpofnt(y)):is(pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
-t2:=isrpep(rpofnt(pl"n"(x,y)),pl"rp"(rpofnt(x),rpofnt(y)),satz155e(x,y)):is(rlofnt(pl"n"(x,y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))))
--ivr155
-satzr155a:=tris2(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),pofrp(pl"rp"(rpofnt(x),rpofnt(y))),t2".ivr155",t1".ivr155"):is(rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)))
-satzr155b:=symis(real,rlofnt(pl"n"(x,y)),pl(rlofnt(x),rlofnt(y)),satzr155a):is(pl(rlofnt(x),rlofnt(y)),rlofnt(pl"n"(x,y)))
-+*ivr155
-y@t3:=lemmaiva2(rpofnt(x),rpofnt(y)):is(ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
-t4:=isrpep(rpofnt(ts"n"(x,y)),ts"rp"(rpofnt(x),rpofnt(y)),satz155f(x,y)):is(rlofnt(ts"n"(x,y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))))
--ivr155
-y@satzr155c:=tris2(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),pofrp(ts"rp"(rpofnt(x),rpofnt(y))),t4".ivr155",t3".ivr155"):is(rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)))
-satzr155d:=symis(real,rlofnt(ts"n"(x,y)),ts(rlofnt(x),rlofnt(y)),satzr155c):is(ts(rlofnt(x),rlofnt(y)),rlofnt(ts"n"(x,y)))
-@[t:real][r:real][s:real][a:and(not(neg(r)),is(ts(r,r),t))][b:and(not(neg(s)),is(ts(s,s),t))]
-+7r161
-[c0:dif][cit:inn(c0,class(t))][a0:dif][air:inn(a0,class(r))][b0:dif][bis:inn(b0,class(s))]
-t1:=th3"l.imp"(negd(a0),neg(r),ande1(not(neg(r)),is(ts(r,r),t),a),[u:negd(a0)]negin(r,a0,air,u)):not(negd(a0))
-t2:=th3"l.imp"(negd(b0),neg(s),ande1(not(neg(s)),is(ts(s,s),t),b),[u:negd(b0)]negin(s,b0,bis,u)):not(negd(b0))
-t3:=isex(ts(r,r),t,td(a0,a0),c0,tict(r,r,a0,a0,air,air),cit,ande2(not(neg(r)),is(ts(r,r),t),a)):eq"rp"(td(a0,a0),c0)
-t4:=isex(ts(s,s),t,td(b0,b0),c0,tict(s,s,b0,b0,bis,bis),cit,ande2(not(neg(s)),is(ts(s,s),t),b)):eq"rp"(td(b0,b0),c0)
-t5:=isin(r,s,a0,b0,air,bis,satzd161b(c0,a0,b0,t1,t2,t3,t4)):is(r,s)
--7r161
-satzr161b:=realapp3(t,r,s,is(r,s),[x:dif][y:dif][z:dif][u:inn(x,class(t))][v:inn(y,class(r))][w:inn(z,class(s))]t5".7r161"(x,u,y,v,z,w)):is(r,s)
-t@[n:not(neg(t))]
-+*7r161
-n@[c0:dif][cit:inn(c0,class(t))]
-t6:=th3"l.imp"(negd(c0),neg(t),n,[u:negd(c0)]negin(t,c0,cit,u)):not(negd(c0))
-[a0:dif][a:and(not(negd(a0)),eq"rp"(td(a0,a0),c0))]
-ar:=realof(a0):real
-t7:=th3"l.imp"(neg(ar),negd(a0),ande1(not(negd(a0)),eq"rp"(td(a0,a0),c0),a),[u:neg(ar)]negex(ar,a0,innclass(a0),u)):not(neg(ar))
-t8:=isin(ts(ar,ar),t,td(a0,a0),c0,tict(ar,ar,a0,a0,innclass(a0),innclass(a0)),cit,ande2(not(negd(a0)),eq"rp"(td(a0,a0),c0),a)):is(ts(ar,ar),t)
-t9:=andi(not(neg(ar)),is(ts(ar,ar),t),t7,t8):and(not(neg(ar)),is(ts(ar,ar),t))
-t10:=somei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),ar,t9):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
-cit@t11:=someapp(dif,[x:dif]and(not(negd(x)),eq"rp"(td(x,x),c0)),satzd161a(c0,t6),some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:and(not(negd(x)),eq"rp"(td(x,x),c0))]t10(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
--7r161
-n@satzr161a:=realapp1(t,some([u:real]and(not(neg(u)),is(ts(u,u),t))),[x:dif][v:inn(x,class(t))]t11".7r161"(x,v)):some([u:real]and(not(neg(u)),is(ts(u,u),t)))
-satzr161:=onei(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),[u:real][v:real][a:and(not(neg(u)),is(ts(u,u),t))][b:and(not(neg(v)),is(ts(v,v),t))]satzr161b(u,v,a,b),satzr161a):one([u:real]and(not(neg(u)),is(ts(u,u),t)))
-sqrt:=ind(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):real
-+*7r161
-n@t12:=oneax(real,[u:real]and(not(neg(u)),is(ts(u,u),t)),satzr161):and(not(neg(sqrt)),is(ts(sqrt,sqrt),t))
--7r161
-n@thsqrt1a:=ande1(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):not(neg(sqrt))
-thsqrt1b:=ande2(not(neg(sqrt)),is(ts(sqrt,sqrt),t),t12".7r161"):is(ts(sqrt,sqrt),t)
-[x:real][o:not(neg(x))][i:is(ts(x,x),t)]
-thsqrt2:=satzr161b(x,sqrt,andi(not(neg(x)),is(ts(x,x),t),o,i),t12".7r161"):is(x,sqrt(t,n))
-o@[i:is(t,ts(x,x))]
-thsqrt3:=symis(real,x,sqrt(t,n),thsqrt2(symis(real,t,ts(x,x),i))):is(sqrt(t,n),x)
-@[r:real][s:real][n:not(neg(r))][o:not(neg(s))][i:is(r,s)]
-issqrt:=thsqrt2(s,o,sqrt(r,n),thsqrt1a(r,n),tris(real,ts(sqrt(r,n),sqrt(r,n)),r,s,thsqrt1b(r,n),i)):is(sqrt(r,n),sqrt(s,o))
-r@[n:not(neg(r))][i:is(r,0)]
-sqrt0:=thsqrt3(r,n,0,0notn(0,refis(real,0)),tris2(real,r,ts(0,0),0,i,ts01(0,0,refis(real,0)))):is(sqrt(r,n),0)
-n@[o:nis(r,0)]
-+sqrt
-t1:=th3"l.imp"(is(sqrt(r,n),0),is(r,0),o,[t:is(sqrt(r,n),0)]tris1(real,r,0,ts(sqrt(r,n),sqrt(r,n)),thsqrt1b(r,n),ts01(sqrt(r,n),sqrt(r,n),t))):nis(sqrt(r,n),0)
--sqrt
-sqrtnot0:=or3e2(is(sqrt(r,n),0),pos(sqrt(r,n)),neg(sqrt(r,n)),axrlo(sqrt(r,n)),thsqrt1a(r,n),t1".sqrt"):pos(sqrt(r,n))
-@[r:real][s:real][t:real][n:nis(t,0)]
-+v0
-t1:=tr3is(real,ts(t,ts(r,ov(s,t,n))),ts(ts(r,ov(s,t,n)),t),ts(r,ts(ov(s,t,n),t)),ts(r,s),comts(t,ts(r,ov(s,t,n))),assts1(r,ov(s,t,n),t),ists2(ts(ov(s,t,n),t),s,r,satz204e(s,t,n))):is(ts(t,ts(r,ov(s,t,n))),ts(r,s))
--v0
-lemma6:=satz204g(ts(r,s),t,ts(r,ov(s,t,n)),n,t1".v0"):is(ts(r,ov(s,t,n)),ov(ts(r,s),t,n))
-+*v0
-n@t2:=tris(real,ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(ts(t,ov(r,t,n)),ts(t,ov(s,t,n))),pl(r,s),disttp2(t,ov(r,t,n),ov(s,t,n)),ispl12(ts(t,ov(r,t,n)),r,ts(t,ov(s,t,n)),s,satz204c(r,t,n),satz204c(s,t,n))):is(ts(t,pl(ov(r,t,n),ov(s,t,n))),pl(r,s))
--v0
-n@lemma7:=satz204g(pl(r,s),t,pl(ov(r,t,n),ov(s,t,n)),n,t2".v0"):is(pl(ov(r,t,n),ov(s,t,n)),ov(pl(r,s),t,n))
-r@[n:nis(r,0)]
-lemma8:=satz204b(r,r,n,ov(r,r,n),1rl,satz204c(r,r,n),satz195(r)):is(ov(r,r,n),1rl)
-lemma9:=ore2(is(r,0),is(ov(0,r,n),0),satz192c(r,ov(0,r,n),satz204c(0,r,n)),n):is(ov(0,r,n),0)
-r@[i:is(r,m0(r))]
-+*v0
-i@[p:pos(m0(r))]
-t3:=<isneg(r,m0(r),i,satz176f(r,p))>pnotn(m0(r),p):con
-i@[n:neg(m0(r))]
-t4:=<ispos(r,m0(r),i,satz176d(r,n))>nnotp(m0(r),n):con
--v0
-i@lemma10:=satz176e(r,or3e1(is(m0(r),0),pos(m0(r)),neg(m0(r)),axrlo(m0(r)),[t:pos(m0(r))]t3".v0"(t),[t:neg(m0(r))]t4".v0"(t))):is(r,0)
-r@lemma11:=satz167f(ts(r,r),0,th3"l.imp"(less(ts(r,r),0),neg(ts(r,r)),nnegsq(r),[t:less(ts(r,r),0)]satz169d(ts(r,r),t))):moreis(ts(r,r),0)
-lemma12:=rapp(r,is(ts(r,r),ts(abs(r),abs(r))),[t:pos(r)]satz196a(r,r,t,t),[t:is(r,0)]tris2(real,ts(r,r),ts(abs(r),abs(r)),0,ts01(r,r,t),ts01(abs(r),abs(r),abs0(r,t))),[t:neg(r)]satz196b(r,r,t,t)):is(ts(r,r),ts(abs(r),abs(r)))
-@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
-+shift
-t1:=satz190a(x,x,1rl,0,moreisi2(x,x,refis(real,x)),satz169a(1rl,natpos(1rl,natrl1))):more(pl(x,1rl),pl(x,0))
-t2:=ismore2(pl(x,0),x,pl(x,1rl),pl02(x,0,refis(real,0)),t1):more(pl(x,1rl),x)
-t3:=satz172d(pl(x,1rl),x,y,t2,satz168b(y,x,ly)):more(pl(x,1rl),y)
-t4:=satz182d(pl(x,1rl),y,t3):pos(mn(pl(x,1rl),y))
-t5:=intmn(pl(x,1rl),intpl(x,ix,1rl,intrl1),y,iy):intrl(mn(pl(x,1rl),y))
-t6:=posintnatrl(mn(pl(x,1rl),y),t4,t5):natrl(mn(pl(x,1rl),y))
--shift
-shiftl:=ntofrl(mn(pl(x,1rl),y),t6".shift"):nat
-[n:1to(shiftl)]
-+*shift
-n@n1:=inn"n"(shiftl,n):nat
-t7:=1top(shiftl,n):lessis"n"(n1,shiftl)
-n2:=rlofnt(n1):real
-t8:=natintrl(n2,natrli(n1)):intrl(n2)
--shift
-n@shiftr:=mn(pl(n2".shift",y),1rl):real
-intshiftr:=intmn(pl(n2".shift",y),intpl(n2".shift",t8".shift",y,iy),1rl,intrl1):intrl(shiftr)
-[m:1to(shiftl)][i:is(shiftr(n),shiftr(m))]
-+*shift
-n@t8a:=tris(real,mn(pl(shiftr(n),1rl),y),mn(pl(n2,y),y),n2,ismn1(pl(mn(pl(n2,y),1rl),1rl),pl(n2,y),y,plmn(pl(n2,y),1rl)),mnpl(n2,y)):is(mn(pl(shiftr(n),1rl),y),n2)
-i@t9a:=ismn1(pl(shiftr(n),1rl),pl(shiftr(m),1rl),y,ispl1(shiftr(n),shiftr(m),1rl,i)):is(mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y))
-t10a:=tr3is(real,n2(n),mn(pl(shiftr(n),1rl),y),mn(pl(shiftr(m),1rl),y),n2(m),symis(real,mn(pl(shiftr(n),1rl),y),n2,t8a),t9a,t8a(m)):is(n2(n),n2(m))
-t11a:=isntirl(n1(n),n1(m),t10a):is"n"(n1(n),n1(m))
--shift
-i@iseshiftr:=isinne(shiftl,n,m,t11a".shift"):is"e"(1to(shiftl),n,m)
-+*shift
-n@[m:more(shiftr,x)]
-t9:=satz188d(shiftr,x,1rl,m):more(pl(shiftr,1rl),pl(x,1rl))
-t10:=ismore1(pl(shiftr,1rl),pl(n2,y),pl(x,1rl),plmn(pl(n2,y),1rl),t9):more(pl(n2,y),pl(x,1rl))
-t11:=satz188d(pl(n2,y),pl(x,1rl),m0(y),t10):more(mn(pl(n2,y),y),mn(pl(x,1rl),y))
-t12:=ismore1(mn(pl(n2,y),y),n2,mn(pl(x,1rl),y),mnpl(n2,y),t11):more(n2,mn(pl(x,1rl),y))
-t13:=ismore12(n2,rlofnt(ntofrl(n2,natrli(n1))),mn(pl(x,1rl),y),rlofnt(ntofrl(mn(pl(x,1rl),y),t6)),isrlnt1(n2,natrli(n1)),isrlnt1(mn(pl(x,1rl),y),t6),t12):more(rlofnt(ntofrl(n2,natrli(n1))),rlofnt(shiftl))
-t14:=lemmaiva5(ntofrl(n2,natrli(n1)),shiftl,t13):more"n"(ntofrl(n2,natrli(n1)),shiftl)
-t15:=ismore1"n"(ntofrl(n2,natrli(n1)),n1,shiftl,isntrl2(n1),t14):more"n"(n1,shiftl)
-n@t16:=th3"l.imp"(more(shiftr,x),more"n"(n1,shiftl),satz10d(n1,shiftl,t7),[t:more(shiftr,x)]t15(t)):not(more(shiftr,x))
--shift
-n@shiftrls:=satz167e(shiftr,x,t16".shift"):lessis(shiftr,x)
-+*shift
-n@[m:more(y,shiftr)]
-t17:=satz188d(y,shiftr,1rl,m):more(pl(y,1rl),pl(shiftr,1rl))
-t18:=ismore12(pl(y,1rl),pl(1rl,y),pl(shiftr,1rl),pl(n2,y),compl(y,1rl),plmn(pl(n2,y),1rl),t17):more(pl(1rl,y),pl(n2,y))
-t19:=satz188a(1rl,n2,y,t18):more(1rl,n2)
-t20:=lemmaiva5(1,n1,t19):more"n"(1,n1)
-n@t21:=th3"l.imp"(more(y,shiftr),more"n"(1,n1),satz10d(1,n1,satz24a(n1)),[t:more(y,shiftr)]t20(t)):not(more(y,shiftr))
--shift
-n@lsshiftr:=satz167e(y,shiftr,t21".shift"):lessis(y,shiftr)
-ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
-+*shift
-a@t22:=and3e1(intrl(u),lessis(y,u),lessis(u,x),a):intrl(u)
-t23:=and3e2(intrl(u),lessis(y,u),lessis(u,x),a):lessis(y,u)
-t24:=and3e3(intrl(u),lessis(y,u),lessis(u,x),a):lessis(u,x)
-[l:less(u,x)]
-t25:=satz188f(pl(u,1rl),pl(x,1rl),m0"r"(y),satz188f(u,x,1rl,l)):less(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
-a@[i:is(u,x)]
-t26:=ismn1(pl(u,1rl),pl(x,1rl),y,ispl1(u,x,1rl,i)):is(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
-a@t27:=th9"l.or"(less(u,x),is(u,x),less(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),is(mn(pl(u,1rl),y),mn(pl(x,1rl),y)),t24,[t:less(u,x)]t25(t),[t:is(u,x)]t26(t)):lessis(mn(pl(u,1rl),y),mn(pl(x,1rl),y))
-ul:=shiftl(u,t22,y,iy,t23):nat
-t28:=islessis12(mn(pl(u,1rl),y),rlofnt(ul),mn(pl(x,1rl),y),rlofnt(shiftl),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isrlnt1(mn(pl(x,1rl),y),t6),t27):lessis(rlofnt(ul),rlofnt(shiftl))
-t29:=th3"l.imp"(more"n"(ul,shiftl),more(rlofnt(ul),rlofnt(shiftl)),satz167d(rlofnt(ul),rlofnt(shiftl),t28),[t:more"n"(ul,shiftl)]lemmaiva6(ul,shiftl,t)):not(more"n"(ul,shiftl))
-t30:=satz10e(ul,shiftl,t29):lessis"n"(ul,shiftl)
--shift
-a@shiftl1:=outn(shiftl,ul".shift",t30".shift"):1to(shiftl)
-+*shift
-a@t31:=isinoutn(shiftl,ul,t30):is"n"(ul,n1(shiftl1))
-t32:=tris(real,mn(pl(u,1rl),y),rlofnt(ul),n2(shiftl1),isrlnt1(mn(pl(u,1rl),y),t6(u,t22,y,iy,t23)),isnterl(ul,n1(shiftl1),t31)):is(mn(pl(u,1rl),y),n2(shiftl1))
-t33:=tris(real,mn(pl(mn(pl(u,1rl),y),y),1rl),mn(pl(u,1rl),1rl),u,ismn1(pl(mn(pl(u,1rl),y),y),pl(u,1rl),1rl,plmn(pl(u,1rl),y)),mnpl(u,1rl)):is(mn(pl(mn(pl(u,1rl),y),y),1rl),u)
--shift
-a@shiftinv1:=tris1(real,u,shiftr(shiftl1),mn(pl(mn(pl(u,1rl),y),y),1rl),t33".shift",ismn1(pl(mn(pl(u,1rl),y),y),pl(n2".shift"(shiftl1),y),1rl,ispl1(mn(pl(u,1rl),y),n2".shift"(shiftl1),y,t32".shift"))):is(u,shiftr(shiftl1))
-shiftinv2:=symis(real,u,shiftr(shiftl1),shiftinv1):is(shiftr(shiftl1),u)
-ly@[alpha:'type']
-seq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]alpha:'type'
-[s:seq]
-proofsirrelevant:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is(t,u)]is"e"(alpha,<tl><lt><it><t>s,<ul><lu><iu><u>s):'prop'
-alpha@[f:seq]
-shiftf:=[t:1to(shiftl)]<shiftrls(t)><lsshiftr(t)><intshiftr(t)><shiftr(t)>f:[t:1to(shiftl)]alpha
-ly@[s:seq(real)]
-inseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]and3(intrl(<w><v><u><t>s),lessis(y,<w><v><u><t>s),lessis(<w><v><u><t>s,x)):'prop'
-injseq:=[t:real][it:intrl(t)][lt:lessis(y,t)][tl:lessis(t,x)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)][v:is"r"(<tl><lt><it><t>s,<ul><lu><iu><u>s)]is"r"(t,u):'prop'
-[u:real][v:real][a:and3(intrl(v),lessis(y,v),lessis(v,x))]
-+*shift
-a@prop1:=is(u,<t24(v,a)><t23(v,a)><t22(v,a)><v>s):'prop'
--shift
-v@improp:=and(and3(intrl(v),lessis(y,v),lessis(v,x)),[t:and3(intrl(v),lessis(y,v),lessis(v,x))]prop1".shift"(t)):'prop'
-u@imseq:=some([t:real]improp(u,t)):'prop'
-s@surjseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]imseq(t):'prop'
-perm:=and(injseq,surjseq):'prop'
-[ins:inseq(s)]
-+*shift
-ins@[n:1to(shiftl)]
-ns:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>s:real
-t34:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ins:and3(intrl(ns),lessis(y,ns),lessis(ns,x))
--shift
-ins@shiftseq:=[t:1to(shiftl)]shiftl1(ns".shift"(t),t34".shift"(t)):[t:1to(shiftl)]1to(shiftl)
-[js:injseq(s)]
-+*shift
-js@[n:1to(shiftl)][m:1to(shiftl)][i:is"e"(1to(shiftl),<n>shiftseq,<m>shiftseq)]
-t35:=isoutne(shiftl,ul(ns(n),t34(n)),t30(ns(n),t34(n)),ul(ns(m),t34(m)),t30(ns(m),t34(m)),i):is"n"(ul(ns(n),t34(n)),ul(ns(m),t34(m)))
-t36:=isrlint(mn(pl(ns(n),1rl),y),t6(ns(n),t22(ns(n),t34(n)),y,iy,t23(ns(n),t34(n))),mn(pl(ns(m),1rl),y),t6(ns(m),t22(ns(m),t34(m)),y,iy,t23(ns(m),t34(m))),t35):is(mn(pl(ns(n),1rl),y),mn(pl(ns(m),1rl),y))
-t37:=satz188b(ns(n),ns(m),1rl,satz188b(pl(ns(n),1rl),pl(ns(m),1rl),m0"r"(y),t36)):is(ns(n),ns(m))
-t38:=<t37><shiftrls(m)><lsshiftr(m)><intshiftr(m)><shiftr(m)><shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>js:is(shiftr(n),shiftr(m))
-t39:=satz188b(n2(n),n2(m),y,satz188b(pl(n2(n),y),pl(n2(m),y),m0(1rl),t38)):is(n2(n),n2(m))
-t40:=isntirl(n1(n),n1(m),t39):is"n"(n1(n),n1(m))
-t41:=isinne(shiftl,n,m,t40):is"e"(1to(shiftl),n,m)
--shift
-js@injshiftseq:=[t:1to(shiftl)][u:1to(shiftl)][v:is"e"(1to(shiftl),<t>shiftseq,<u>shiftseq)]t41".shift"(t,u,v):injective(1to(shiftl),1to(shiftl),shiftseq)
-ins@[pri:proofsirrelevant(real,s)][ss:surjseq(s)]
-+*shift
-ss@[n:1to(shiftl)]
-t42:=<shiftrls(n)><lsshiftr(n)><intshiftr(n)><shiftr(n)>ss:imseq(shiftr(n))
-[u:real][p:improp(shiftr(n),u)]
-t43:=ande1(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):and3(intrl(u),lessis(y,u),lessis(u,x))
-t44:=ande2"l.r"(and3(intrl(u),lessis(y,u),lessis(u,x)),[t:and3(intrl(u),lessis(y,u),lessis(u,x))]prop1(shiftr(n),u,t),p):is(shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s)
-ul1:=shiftl1(u,t43):1to(shiftl)
-t45:=<shiftinv1(u,t43)><shiftrls(ul1)><lsshiftr(ul1)><intshiftr(ul1)><shiftr(ul1)><t24(u,t43)><t23(u,t43)><t22(u,t43)><u>pri:is(<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1))
-t46:=shiftinv1(ns(ul1),t34(ul1)):is(ns(ul1),shiftr(<ul1>shiftseq))
-t47:=tr3is(real,shiftr(n),<t24(u,t43)><t23(u,t43)><t22(u,t43)><u>s,ns(ul1),shiftr(<ul1>shiftseq),t44,t45,t46):is(shiftr(n),shiftr(<ul1>shiftseq))
-t48:=iseshiftr(n,<ul1>shiftseq,t47):is"e"(1to(shiftl),n,<ul1>shiftseq)
-t49:=somei(1to(shiftl),[t:1to(shiftl)]is"e"(1to(shiftl),n,<t>shiftseq),ul1,t48):image(1to(shiftl),1to(shiftl),shiftseq,n)
-n@t50:=someapp(real,[t:real]improp(shiftr(n),t),t42,image(1to(shiftl),1to(shiftl),shiftseq,n),[t:real][u:improp(shiftr(n),t)]t49(t,u)):image(1to(shiftl),1to(shiftl),shiftseq,n)
--shift
-ss@surjshiftseq:=[t:1to(shiftl)]t50".shift"(t):surjective(1to(shiftl),1to(shiftl),shiftseq)
-pri@[ps:perm(s)]
-bijshiftseq:=andi(injective(1to(shiftl),1to(shiftl),shiftseq),surjective(1to(shiftl),1to(shiftl),shiftseq),injshiftseq(ande1(injseq(s),surjseq(s),ps)),surjshiftseq(ande2(injseq(s),surjseq(s),ps))):bijective(1to(shiftl),1to(shiftl),shiftseq)
-+c
-@complex:=pair1type(real):'type'
-cx:=complex:'type'
-[x:complex][y:complex]
-is:=is"e"(cx,x,y):'prop'
-nis:=not(is(x,y)):'prop'
-@[p:[t:complex]'prop']
-some:=some"l"(cx,p):'prop'
-all:=all"l"(cx,p):'prop'
-one:=one"e"(cx,p):'prop'
-@[a:real][b:real]
-pli:=pair1(real,a,b):complex
-x@re:=first1(real,x):real
-im:=second1(real,x):real
-b@reis:=first1is1(real,a,b):is"r"(re(pli(a,b)),a)
-isre:=first1is2(real,a,b):is"r"(a,re(pli(a,b)))
-imis:=second1is1(real,a,b):is"r"(im(pli(a,b)),b)
-isim:=second1is2(real,a,b):is"r"(b,im(pli(a,b)))
-x@pliis:=pair1is1(real,x):is(pli(re(x),im(x)),x)
-ispli:=pair1is2(real,x):is(x,pli(re(x),im(x)))
-y@[i:is(x,y)]
-iscere:=isf(cx,real,[t:cx]re(t),x,y,i):is"r"(re(x),re(y))
-isceim:=isf(cx,real,[t:cx]im(t),x,y,i):is"r"(im(x),im(y))
-b@[c:real][i:is"r"(a,b)]
-isrecx1:=isf(real,cx,[t:real]pli(t,c),a,b,i):is(pli(a,c),pli(b,c))
-isrecx2:=isf(real,cx,[t:real]pli(c,t),a,b,i):is(pli(c,a),pli(c,b))
-c@[d:real][i:is"r"(a,b)][j:is"r"(c,d)]
-isrecx12:=tris(cx,pli(a,c),pli(b,c),pli(b,d),isrecx1(a,b,c,i),isrecx2(c,d,b,j)):is(pli(a,c),pli(b,d))
-x@satz206:=refis(cx,x):is(x,x)
-y@[i:is(x,y)]
-satz207:=symis(cx,x,y,i):is(y,x)
-y@[z:complex][i:is(x,y)][j:is(y,z)]
-satz208:=tris(cx,x,y,z,i,j):is(x,z)
-@0c:=pli(0,0):complex
-1c:=pli(1rl,0):complex
-y@pl:=pli(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))):complex
-d@plis12a:=isrecx12(pl"r"(re(pli(a,b)),re(pli(c,d))),pl"r"(a,c),pl"r"(im(pli(a,b)),im(pli(c,d))),pl"r"(b,d),ispl12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ispl12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)))
-plis12b:=symis(cx,pl(pli(a,b),pli(c,d)),pli(pl"r"(a,c),pl"r"(b,d)),plis12a):is(pli(pl"r"(a,c),pl"r"(b,d)),pl(pli(a,b),pli(c,d)))
-x@[r:real][s:real]
-plis1a:=isrecx12(pl"r"(re(pli(r,s)),re(x)),pl"r"(r,re(x)),pl"r"(im(pli(r,s)),im(x)),pl"r"(s,im(x)),ispl1(re(pli(r,s)),r,re(x),reis(r,s)),ispl1(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))))
-plis1b:=symis(cx,pl(pli(r,s),x),pli(pl"r"(r,re(x)),pl"r"(s,im(x))),plis1a):is(pli(pl"r"(r,re(x)),pl"r"(s,im(x))),pl(pli(r,s),x))
-plis2a:=isrecx12(pl"r"(re(x),re(pli(r,s))),pl"r"(re(x),r),pl"r"(im(x),im(pli(r,s))),pl"r"(im(x),s),ispl2(re(pli(r,s)),r,re(x),reis(r,s)),ispl2(im(pli(r,s)),s,im(x),imis(r,s))):is(pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)))
-plis2b:=symis(cx,pl(x,pli(r,s)),pli(pl"r"(re(x),r),pl"r"(im(x),s)),plis2a):is(pli(pl"r"(re(x),r),pl"r"(im(x),s)),pl(x,pli(r,s)))
-z@[i:is(x,y)]
-ispl1:=isf(cx,cx,[t:cx]pl(t,z),x,y,i):is(pl(x,z),pl(y,z))
-ispl2:=isf(cx,cx,[t:cx]pl(z,t),x,y,i):is(pl(z,x),pl(z,y))
-z@[u:complex][i:is(x,y)][j:is(z,u)]
-ispl12:=tris(cx,pl(x,z),pl(y,z),pl(y,u),ispl1(x,y,z,i),ispl2(z,u,y,j)):is(pl(x,z),pl(y,u))
-y@satz209:=isrecx12(pl"r"(re(x),re(y)),pl"r"(re(y),re(x)),pl"r"(im(x),im(y)),pl"r"(im(y),im(x)),compl(re(x),re(y)),compl(im(x),im(y))):is(pl(x,y),pl(y,x))
-compl:=satz209:is(pl(x,y),pl(y,x))
-x@satz210:=tr3is(cx,pl(x,0c),pli(pl"r"(re(x),0),pl"r"(im(x),0)),pli(re(x),im(x)),x,plis2a(x,0,0),isrecx12(pl"r"(re(x),0),re(x),pl"r"(im(x),0),im(x),pl02(re(x),0,refis(real,0)),pl02(im(x),0,refis(real,0))),pliis(x)):is(pl(x,0c),x)
-satz210a:=symis(cx,pl(x,0c),x,satz210):is(x,pl(x,0c))
-satz210b:=tris(cx,pl(0c,x),pl(x,0c),x,compl(0c,x),satz210):is(pl(0c,x),x)
-satz210c:=symis(cx,pl(0c,x),x,satz210b):is(x,pl(0c,x))
-z@satz211:=tr3is(cx,pl(pl(x,y),z),pli(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(pl"r"(im(x),im(y)),im(z))),pli(pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(im(x),pl"r"(im(y),im(z)))),pl(x,pl(y,z)),plis1a(z,pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(pl"r"(pl"r"(re(x),re(y)),re(z)),pl"r"(re(x),pl"r"(re(y),re(z))),pl"r"(pl"r"(im(x),im(y)),im(z)),pl"r"(im(x),pl"r"(im(y),im(z))),asspl1(re(x),re(y),re(z)),asspl1(im(x),im(y),im(z))),plis2b(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z)))):is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl1:=satz211:is(pl(pl(x,y),z),pl(x,pl(y,z)))
-asspl2:=symis(cx,pl(pl(x,y),z),pl(x,pl(y,z)),asspl1):is(pl(x,pl(y,z)),pl(pl(x,y),z))
-y@[u:complex][i:is(pl(y,u),x)]
-+2212
-t1:=tris(real,pl"r"(re(y),re(u)),re(pl(y,u)),re(x),isre(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),iscere(pl(y,u),x,i)):is"r"(pl"r"(re(y),re(u)),re(x))
-t2:=tris(real,pl"r"(im(y),im(u)),im(pl(y,u)),im(x),isim(pl"r"(re(y),re(u)),pl"r"(im(y),im(u))),isceim(pl(y,u),x,i)):is"r"(pl"r"(im(y),im(u)),im(x))
-t3:=satz187d(re(x),re(y),re(u),t1):is"r"(re(u),mn(re(x),re(y)))
-t4:=satz187d(im(x),im(y),im(u),t2):is"r"(im(u),mn(im(x),im(y)))
--2212
-satz212a:=tris(cx,u,pli(re(u),im(u)),pli(mn(re(x),re(y)),mn(im(x),im(y))),ispli(u),isrecx12(re(u),mn(re(x),re(y)),im(u),mn(im(x),im(y)),t3".2212",t4".2212")):is(u,pli(mn(re(x),re(y)),mn(im(x),im(y))))
-y@satz212b:=tr3is(cx,pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),pli(pl"r"(re(y),mn(re(x),re(y))),pl"r"(im(y),mn(im(x),im(y)))),pli(re(x),im(x)),x,plis2a(y,mn(re(x),re(y)),mn(im(x),im(y))),isrecx12(pl"r"(re(y),mn(re(x),re(y))),re(x),pl"r"(im(y),mn(im(x),im(y))),im(x),satz187a(re(x),re(y)),satz187a(im(x),im(y))),pliis(x)):is(pl(y,pli(mn(re(x),re(y)),mn(im(x),im(y)))),x)
-satz212c:=somei(cx,[t:cx]is(pl(y,t),x),pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212b):some([t:complex]is(pl(y,t),x))
-satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,pli(mn(re(x),re(y)),mn(im(x),im(y))),satz212a(t,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
-%satz212:=onei(cx,[t:cx]is(pl(y,t),x),[t:cx][u:cx][v:is(pl(y,t),x)][w:is(pl(y,u),x)]tris2(cx,t,u,v),satz212a(u,w)),satz212c):one([t:complex]is(pl(y,t),x))
-mn:=pli(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))):complex
-d@mnis12a:=isrecx12(mn"r"(re(pli(a,b)),re(pli(c,d))),mn"r"(a,c),mn"r"(im(pli(a,b)),im(pli(c,d))),mn"r"(b,d),ismn12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ismn12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is(mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)))
-mnis12b:=symis(cx,mn(pli(a,b),pli(c,d)),pli(mn"r"(a,c),mn"r"(b,d)),mnis12a):is(pli(mn"r"(a,c),mn"r"(b,d)),mn(pli(a,b),pli(c,d)))
-x@[r:real][s:real]
-mnis1a:=isrecx12(mn"r"(re(pli(r,s)),re(x)),mn"r"(r,re(x)),mn"r"(im(pli(r,s)),im(x)),mn"r"(s,im(x)),ismn1(re(pli(r,s)),r,re(x),reis(r,s)),ismn1(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))))
-mnis1b:=symis(cx,mn(pli(r,s),x),pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mnis1a):is(pli(mn"r"(r,re(x)),mn"r"(s,im(x))),mn(pli(r,s),x))
-mnis2a:=isrecx12(mn"r"(re(x),re(pli(r,s))),mn"r"(re(x),r),mn"r"(im(x),im(pli(r,s))),mn"r"(im(x),s),ismn2(re(pli(r,s)),r,re(x),reis(r,s)),ismn2(im(pli(r,s)),s,im(x),imis(r,s))):is(mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)))
-mnis2b:=symis(cx,mn(x,pli(r,s)),pli(mn"r"(re(x),r),mn"r"(im(x),s)),mnis2a):is(pli(mn"r"(re(x),r),mn"r"(im(x),s)),mn(x,pli(r,s)))
-z@[i:is(x,y)]
-ismn1:=isf(cx,cx,[t:cx]mn(t,z),x,y,i):is(mn(x,z),mn(y,z))
-ismn2:=isf(cx,cx,[t:cx]mn(z,t),x,y,i):is(mn(z,x),mn(z,y))
-z@[u:complex][i:is(x,y)][j:is(z,u)]
-ismn12:=tris(cx,mn(x,z),mn(y,z),mn(y,u),ismn1(x,y,z,i),ismn2(z,u,y,j)):is(mn(x,z),mn(y,u))
-y@[u:complex][i:is(pl(y,u),x)]
-satz212d:=satz212a(u,i):is(u,mn(x,y))
-satz212e:=symis(cx,u,mn(x,y),satz212d):is(mn(x,y),u)
-u@[i:is(pl(u,y),x)]
-satz212f:=satz212d(tris(cx,pl(y,u),pl(u,y),x,compl(y,u),i)):is(u,mn(x,y))
-satz212g:=symis(cx,u,mn(x,y),satz212f):is(mn(x,y),u)
-y@satz212h:=satz212b:is(pl(y,mn(x,y)),x)
-[i:is(mn(x,y),0c)]
-+2213
-t1:=tr3is(real,mn"r"(re(x),re(y)),re(mn(x,y)),re(0c),0,isre(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),iscere(mn(x,y),0c,i),reis(0,0)):is"r"(mn"r"(re(x),re(y)),0)
-t2:=tr3is(real,mn"r"(im(x),im(y)),im(mn(x,y)),im(0c),0,isim(mn"r"(re(x),re(y)),mn"r"(im(x),im(y))),isceim(mn(x,y),0c,i),imis(0,0)):is"r"(mn"r"(im(x),im(y)),0)
-t3:=satz182b(re(x),re(y),t1):is"r"(re(x),re(y))
-t4:=satz182b(im(x),im(y),t2):is"r"(im(x),im(y))
--2213
-satz213a:=tr3is(cx,x,pli(re(x),im(x)),pli(re(y),im(y)),y,ispli(x),isrecx12(re(x),re(y),im(x),im(y),t3".2213",t4".2213"),pliis(y)):is(x,y)
-y@[i:is(x,y)]
-+*2213
-i@t5:=satz182e(re(x),re(y),iscere(x,y,i)):is"r"(mn"r"(re(x),re(y)),0)
-t6:=satz182e(im(x),im(y),isceim(x,y,i)):is"r"(mn"r"(im(x),im(y)),0)
--2213
-i@satz213b:=isrecx12(mn"r"(re(x),re(y)),0,mn"r"(im(x),im(y)),0,t5".2213",t6".2213"):is(mn(x,y),0c)
-x@m0:=mn(0c,x):complex
-satz214:=isrecx12(mn"r"(re(0c),re(x)),m0"r"(re(x)),mn"r"(im(0c),im(x)),m0"r"(im(x)),pl01(re(0c),m0"r"(re(x)),reis(0,0)),pl01(im(0c),m0"r"(im(x)),imis(0,0))):is(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))))
-satz214a:=symis(cx,m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214):is(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x))
-b@m0isa:=tris(cx,m0(pli(a,b)),pli(m0"r"(re(pli(a,b))),m0"r"(im(pli(a,b)))),pli(m0"r"(a),m0"r"(b)),satz214(pli(a,b)),isrecx12(m0"r"(re(pli(a,b))),m0"r"(a),m0"r"(im(pli(a,b))),m0"r"(b),ism0(re(pli(a,b)),a,reis(a,b)),ism0(im(pli(a,b)),b,imis(a,b)))):is(m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)))
-m0isb:=symis(cx,m0(pli(a,b)),pli(m0"r"(a),m0"r"(b)),m0isa):is(pli(m0"r"(a),m0"r"(b)),m0(pli(a,b)))
-y@[i:is(x,y)]
-ism0:=isf(cx,cx,[t:cx]m0(t),x,y,i):is(m0(x),m0(y))
-x@satz215:=tr4is(cx,m0(m0(x)),m0(pli(m0"r"(re(x)),m0"r"(im(x)))),pli(m0"r"(m0"r"(re(x))),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,ism0(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214),m0isa(m0"r"(re(x)),m0"r"(im(x))),isrecx12(m0"r"(m0"r"(re(x))),re(x),m0"r"(m0"r"(im(x))),im(x),satz177(re(x)),satz177(im(x))),pliis(x)):is(m0(m0(x)),x)
-satz215a:=symis(cx,m0(m0(x)),x,satz215):is(x,m0(m0(x)))
-y@[i:is(x,m0(y))]
-satz215b:=tris(cx,m0(x),m0(m0(y)),y,ism0(x,m0(y),i),satz215(y)):is(m0(x),y)
-satz215c:=symis(cx,m0(x),y,satz215b):is(y,m0(x))
-y@[i:is(m0(x),y)]
-satz215d:=satz215c(y,x,symis(cx,m0(x),y,i)):is(x,m0(y))
-satz215e:=symis(cx,x,m0(y),satz215d):is(m0(y),x)
-x@satz216:=tr3is(cx,pl(x,m0(x)),pl(x,pli(m0"r"(re(x)),m0"r"(im(x)))),pli(pl"r"(re(x),m0"r"(re(x))),pl"r"(im(x),m0"r"(im(x)))),0c,ispl2(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),x,satz214(x)),plis2a(x,m0"r"(re(x)),m0"r"(im(x))),isrecx12(pl"r"(re(x),m0"r"(re(x))),0,pl"r"(im(x),m0"r"(im(x))),0,satz179(re(x)),satz179(im(x)))):is(pl(x,m0(x)),0c)
-+2216
-anders:=satz212h(0c,x):is(pl(x,m0(x)),0c)
--2216
-satz216a:=tris(cx,pl(m0(x),x),pl(x,m0(x)),0c,compl(m0(x),x),satz216):is(pl(m0(x),x),0c)
-y@satz217:=tr4is(cx,m0(pl(x,y)),pli(m0"r"(pl"r"(re(x),re(y))),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(m0"r"(re(x)),m0"r"(re(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(pli(m0"r"(re(x)),m0"r"(im(x))),pli(m0"r"(re(y)),m0"r"(im(y)))),pl(m0(x),m0(y)),m0isa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx12(m0"r"(pl"r"(re(x),re(y))),pl"r"(m0"r"(re(x)),m0"r"(re(y))),m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),satz180(re(x),re(y)),satz180(im(x),im(y))),plis12b(m0"r"(re(x)),m0"r"(im(x)),m0"r"(re(y)),m0"r"(im(y))),ispl12(pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),satz214a(x),satz214a(y))):is(m0(pl(x,y)),pl(m0(x),m0(y)))
-satz217a:=symis(cx,m0(pl(x,y)),pl(m0(x),m0(y)),satz217):is(pl(m0(x),m0(y)),m0(pl(x,y)))
-satz218:=tris(cx,mn(x,y),pl(x,pli(m0"r"(re(y)),m0"r"(im(y)))),pl(x,m0(y)),plis2b(x,m0"r"(re(y)),m0"r"(im(y))),ispl2(pli(m0"r"(re(y)),m0"r"(im(y))),m0(y),x,satz214a(y))):is(mn(x,y),pl(x,m0(y)))
-satz218a:=symis(cx,mn(x,y),pl(x,m0(y)),satz218):is(pl(x,m0(y)),mn(x,y))
-+2219
-t1:=tr3is(cx,m0(mn(x,y)),m0(pl(x,m0(y))),pl(m0(x),m0(m0(y))),pl(m0(x),y),ism0(mn(x,y),pl(x,m0(y)),satz218),satz217(x,m0(y)),ispl2(m0(m0(y)),y,m0(x),satz215(y))):is(m0(mn(x,y)),pl(m0(x),y))
--2219
-satz219:=tr3is(cx,m0(mn(x,y)),pl(m0(x),y),pl(y,m0(x)),mn(y,x),t1".2219",compl(m0(x),y),satz218a(y,x)):is(m0(mn(x,y)),mn(y,x))
-satz219a:=symis(cx,m0(mn(y,x)),mn(x,y),satz219(y,x)):is(mn(x,y),m0(mn(y,x)))
-ts:=pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))):complex
-rets:=mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))):real
-imts:=pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))):real
-+v3
-d@t1:=ismn12"r"(ts"r"(re(pli(a,b)),re(pli(c,d))),ts"r"(a,c),ts"r"(im(pli(a,b)),im(pli(c,d))),ts"r"(b,d),ists12(re(pli(a,b)),a,re(pli(c,d)),c,reis(a,b),reis(c,d)),ists12(im(pli(a,b)),b,im(pli(c,d)),d,imis(a,b),imis(c,d))):is"r"(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)))
-t2:=ispl12"r"(ts"r"(re(pli(a,b)),im(pli(c,d))),ts"r"(a,d),ts"r"(im(pli(a,b)),re(pli(c,d))),ts"r"(b,c),ists12(re(pli(a,b)),a,im(pli(c,d)),d,reis(a,b),imis(c,d)),ists12(im(pli(a,b)),b,re(pli(c,d)),c,imis(a,b),reis(c,d))):is"r"(imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)))
--v3
-d@tsis12a:=isrecx12(rets(pli(a,b),pli(c,d)),mn"r"(ts"r"(a,c),ts"r"(b,d)),imts(pli(a,b),pli(c,d)),pl"r"(ts"r"(a,d),ts"r"(b,c)),t1".v3",t2".v3"):is(ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))))
-tsis12b:=symis(cx,ts(pli(a,b),pli(c,d)),pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),tsis12a):is(pli(mn"r"(ts"r"(a,c),ts"r"(b,d)),pl"r"(ts"r"(a,d),ts"r"(b,c))),ts(pli(a,b),pli(c,d)))
-x@[r:real][s:real]
-+*v3
-s@t3:=ismn12"r"(ts"r"(re(pli(r,s)),re(x)),ts"r"(r,re(x)),ts"r"(im(pli(r,s)),im(x)),ts"r"(s,im(x)),ists1(re(pli(r,s)),r,re(x),reis(r,s)),ists1(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))))
-t4:=ispl12"r"(ts"r"(re(pli(r,s)),im(x)),ts"r"(r,im(x)),ts"r"(im(pli(r,s)),re(x)),ts"r"(s,re(x)),ists1(re(pli(r,s)),r,im(x),reis(r,s)),ists1(im(pli(r,s)),s,re(x),imis(r,s))):is"r"(imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))))
--v3
-s@tsis1a:=isrecx12(rets(pli(r,s),x),mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),imts(pli(r,s),x),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x))),t3".v3",t4".v3"):is(ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))))
-tsis1b:=symis(cx,ts(pli(r,s),x),pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),tsis1a):is(pli(mn"r"(ts"r"(r,re(x)),ts"r"(s,im(x))),pl"r"(ts"r"(r,im(x)),ts"r"(s,re(x)))),ts(pli(r,s),x))
-+*v3
-s@t5:=ismn12"r"(ts"r"(re(x),re(pli(r,s))),ts"r"(re(x),r),ts"r"(im(x),im(pli(r,s))),ts"r"(im(x),s),ists2(re(pli(r,s)),r,re(x),reis(r,s)),ists2(im(pli(r,s)),s,im(x),imis(r,s))):is"r"(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)))
-t6:=ispl12"r"(ts"r"(re(x),im(pli(r,s))),ts"r"(re(x),s),ts"r"(im(x),re(pli(r,s))),ts"r"(im(x),r),ists2(im(pli(r,s)),s,re(x),imis(r,s)),ists2(re(pli(r,s)),r,im(x),reis(r,s))):is"r"(imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)))
--v3
-s@tsis2a:=isrecx12(rets(x,pli(r,s)),mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),imts(x,pli(r,s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r)),t5".v3",t6".v3"):is(ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))))
-tsis2b:=symis(cx,ts(x,pli(r,s)),pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),tsis2a):is(pli(mn"r"(ts"r"(re(x),r),ts"r"(im(x),s)),pl"r"(ts"r"(re(x),s),ts"r"(im(x),r))),ts(x,pli(r,s)))
-z@[i:is(x,y)]
-ists1:=isf(cx,cx,[t:cx]ts(t,z),x,y,i):is(ts(x,z),ts(y,z))
-ists2:=isf(cx,cx,[t:cx]ts(z,t),x,y,i):is(ts(z,x),ts(z,y))
-z@[u:complex][i:is(x,y)][j:is(z,u)]
-ists12:=tris(cx,ts(x,z),ts(y,z),ts(y,u),ists1(x,y,z,i),ists2(z,u,y,j)):is(ts(x,z),ts(y,u))
-+3220
-y@t1:=ismn12"r"(ts"r"(re(x),re(y)),ts"r"(re(y),re(x)),ts"r"(im(x),im(y)),ts"r"(im(y),im(x)),comts(re(x),re(y)),comts(im(x),im(y))):is"r"(rets(x,y),rets(y,x))
-t2:=tris(real,imts(x,y),pl"r"(ts"r"(im(x),re(y)),ts"r"(re(x),im(y))),imts(y,x),compl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(ts"r"(im(x),re(y)),ts"r"(re(y),im(x)),ts"r"(re(x),im(y)),ts"r"(im(y),re(x)),comts(im(x),re(y)),comts(re(x),im(y)))):is"r"(imts(x,y),imts(y,x))
--3220
-y@satz220:=isrecx12(rets(x,y),rets(y,x),imts(x,y),imts(y,x),t1".3220",t2".3220"):is(ts(x,y),ts(y,x))
-comts:=satz220:is(ts(x,y),ts(y,x))
-x@[i:is(x,0c)]
-lemma1:=tris(real,re(x),re(0c),0,iscere(x,0c,i),reis(0,0)):is"r"(re(x),0)
-lemma2:=tris(real,im(x),im(0c),0,isceim(x,0c,i),imis(0,0)):is"r"(im(x),0)
-x@mod2:=pl"r"(ts"r"(re(x),re(x)),ts"r"(im(x),im(x))):real
-i@lemma3:=tris(real,mod2,pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),0,ts01(re(x),re(x),lemma1),ts01(im(x),im(x),lemma2)),pl01(0,0,refis(real,0))):is"r"(mod2(x),0)
-x@[n:nis(x,0c)]
-+*v3
-x@re2:=ts"r"(re(x),re(x)):real
-im2:=ts"r"(im(x),im(x)):real
-n@[i:is"r"(re(x),0)]
-t7:=th3"l.imp"(is"r"(im(x),0),is(x,0c),n,[t:is"r"(im(x),0)]tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,i,t))):nis"r"(im(x),0)
-t8:=ispos(im2,mod2,symis(real,mod2,im2,pl01(re2,im2,ts01(re(x),re(x),i))),possq(im(x),t7)):pos(mod2)
-n@[o:nis"r"(re(x),0)][i:is"r"(im(x),0)]
-t9:=ispos(re2,mod2,symis(real,mod2,re2,pl02(re2,im2,ts01(im(x),im(x),i))),possq(re(x),o)):pos(mod2)
-o@[p:nis"r"(im(x),0)]
-t10:=pospl(re2,im2,possq(re(x),o),possq(im(x),p)):pos(mod2)
-o@t11:=th1"l.imp"(is"r"(im(x),0),pos(mod2),[t:is"r"(im(x),0)]t9(t),[t:nis"r"(im(x),0)]t10(t)):pos(mod2)
--v3
-n@lemma4:=th1"l.imp"(is"r"(re(x),0),pos(mod2),[t:is"r"(re(x),0)]t8".v3"(t),[t:nis"r"(re(x),0)]t11".v3"(t)):pos(mod2(x))
-x@lemma5:=th1"l.imp"(is(x,0c),not(neg(mod2)),[t:is(x,0c)]0notn(mod2,lemma3(t)),[t:nis(x,0c)]pnotn(mod2,lemma4(t))):not(neg(mod2(x)))
-y@[i:is(x,0c)]
-+3221
-t1:=lemma1(x,i):is"r"(re(x),0)
-t2:=lemma2(x,i):is"r"(im(x),0)
-t3:=tris(real,rets(x,y),mn"r"(0,0),0,ismn12"r"(ts"r"(re(x),re(y)),0,ts"r"(im(x),im(y)),0,ts01(re(x),re(y),t1),ts01(im(x),im(y),t2)),satz187c(0,0,0,pl02(0,0,refis(real,0)))):is"r"(rets(x,y),0)
-t4:=tris(real,imts(x,y),pl"r"(0,0),0,ispl12"r"(ts"r"(re(x),im(y)),0,ts"r"(im(x),re(y)),0,ts01(re(x),im(y),t1),ts01(im(x),re(y),t2)),pl02(0,0,refis(real,0))):is"r"(imts(x,y),0)
--3221
-satz221a:=isrecx12(rets(x,y),0,imts(x,y),0,t3".3221",t4".3221"):is(ts(x,y),0c)
-y@[i:is(y,0c)]
-satz221b:=tris(cx,ts(x,y),ts(y,x),0c,comts(x,y),satz221a(y,x,i)):is(ts(x,y),0c)
-y@[i:is(ts(x,y),0c)]
-+*3221
-i@[n:nis(y,0c)]
-t5:=lemma4(y,n):pos(mod2(y))
-t6:=tris1(real,rets(x,y),0,re(ts(x,y)),reis(rets(x,y),imts(x,y)),lemma1(ts(x,y),i)):is"r"(rets(x,y),0)
-t7:=tris1(real,imts(x,y),0,im(ts(x,y)),imis(rets(x,y),imts(x,y)),lemma2(ts(x,y),i)):is"r"(imts(x,y),0)
-t8:=tris(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(0,0),0,ispl12"r"(ts"r"(rets(x,y),re(y)),0,ts"r"(imts(x,y),im(y)),0,ts01(rets(x,y),re(y),t6),ts01(imts(x,y),im(y),t7)),pl02(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),0)
-y@ii1r:=ts"r"(ts"r"(im(x),im(y)),re(y)):real
-i1ir:=ts"r"(im(x),ts"r"(im(y),re(y))):real
-ir1i:=ts"r"(ts"r"(im(x),re(y)),im(y)):real
-i1ri:=ts"r"(im(x),ts"r"(re(y),im(y))):real
-rr1r:=ts"r"(ts"r"(re(x),re(y)),re(y)):real
-r1rr:=ts"r"(re(x),ts"r"(re(y),re(y))):real
-ri1r:=ts"r"(ts"r"(re(x),im(y)),re(y)):real
-r1ir:=ts"r"(re(x),ts"r"(im(y),re(y))):real
-ri1i:=ts"r"(ts"r"(re(x),im(y)),im(y)):real
-r1ii:=ts"r"(re(x),ts"r"(im(y),im(y))):real
-n@t9:=tris(real,ii1r,i1ir,i1ri,assts1(im(x),im(y),re(y)),ists2"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),im(x),comts"r"(im(y),re(y)))):is"r"(ii1r,i1ri)
-t10:=tris(real,ts"r"(rets(x,y),re(y)),mn"r"(rr1r,ii1r),mn"r"(r1rr,i1ri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(y)),ismn12"r"(rr1r,r1rr,ii1r,i1ri,assts1(re(x),re(y),re(y)),t9)):is"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri))
-t11:=tr3is(real,ts"r"(imts(x,y),im(y)),pl"r"(ri1i,ir1i),pl"r"(r1ii,i1ri),pl"r"(i1ri,r1ii),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(y)),ispl12"r"(ri1i,r1ii,ir1i,i1ri,assts1(re(x),im(y),im(y)),assts1(im(x),re(y),im(y))),compl"r"(r1ii,i1ri)):is"r"(ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii))
-t12:=tr4is(real,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),pl"r"(mn"r"(r1rr,i1ri),pl"r"(i1ri,r1ii)),pl"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1ii),pl"r"(r1rr,r1ii),ts"r"(re(x),mod2(y)),ispl12"r"(ts"r"(rets(x,y),re(y)),mn"r"(r1rr,i1ri),ts"r"(imts(x,y),im(y)),pl"r"(i1ri,r1ii),t10,t11),asspl2"r"(mn"r"(r1rr,i1ri),i1ri,r1ii),ispl1"r"(pl"r"(mn"r"(r1rr,i1ri),i1ri),r1rr,r1ii,plmn(r1rr,i1ri)),distpt2(re(x),ts"r"(re(y),re(y)),ts"r"(im(y),im(y)))):is"r"(pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),ts"r"(re(x),mod2(y)))
-t13:=tris1(real,ts"r"(re(x),mod2(y)),0,pl"r"(ts"r"(rets(x,y),re(y)),ts"r"(imts(x,y),im(y))),t12,t8):is"r"(ts"r"(re(x),mod2(y)),0)
-t14:=ore1(is"r"(re(x),0),is"r"(mod2(y),0),satz192c(re(x),mod2(y),t13),pnot0(mod2(y),t5)):is"r"(re(x),0)
-t15:=tris1(real,ts"r"(im(x),im(y)),0,ts"r"(re(x),re(y)),satz182b(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),t6),ts01(re(x),re(y),t14)):is"r"(ts"r"(im(x),im(y)),0)
-t16:=tris1(real,ts"r"(im(x),re(y)),0,imts(x,y),pl01(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),ts01(re(x),im(y),t14)),t7):is"r"(ts"r"(im(x),re(y)),0)
-[j:is"r"(re(y),0)]
-t17:=t7"c.v3"(y,n,j):nis"r"(im(y),0)
-t18:=ore1(is"r"(im(x),0),is"r"(im(y),0),satz192c(im(x),im(y),t15),t17):is"r"(im(x),0)
-n@[o:nis"r"(re(y),0)]
-t19:=ore1(is"r"(im(x),0),is"r"(re(y),0),satz192c(im(x),re(y),t16),o):is"r"(im(x),0)
-n@t20:=th1"l.imp"(is"r"(re(y),0),is"r"(im(x),0),[t:is"r"(re(y),0)]t18(t),[t:nis"r"(re(y),0)]t19(t)):is"r"(im(x),0)
-t21:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t14,t20)):is(x,0c)
--3221
-i@satz221c:=th2"l.or"(is(x,0c),is(y,0c),[t:nis(y,0c)]t21".3221"(t)):or(is(x,0c),is(y,0c))
-y@[n:nis(x,0c)][o:nis(y,0c)]
-satz221d:=th3"l.imp"(is(ts(x,y),0c),or(is(x,0c),is(y,0c)),th3"l.or"(is(x,0c),is(y,0c),n,o),[t:is(ts(x,y),0c)]satz221c(t)):nis(ts(x,y),0c)
-+3222
-x@t1:=tris(real,mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),mn"r"(re(x),0),re(x),ismn12"r"(ts"r"(re(x),1rl),re(x),ts"r"(im(x),0),0,satz195(re(x)),ts02(im(x),0,refis(real,0))),pl02(re(x),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x))
-t2:=tris(real,pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),pl"r"(0,im(x)),im(x),ispl12"r"(ts"r"(re(x),0),0,ts"r"(im(x),1rl),im(x),ts02(re(x),0,refis(real,0)),satz195(im(x))),pl01(0,im(x),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x))
--3222
-x@satz222:=tr3is(cx,ts(x,1c),pli(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl))),pli(re(x),im(x)),x,tsis2a(x,1rl,0),isrecx12(mn"r"(ts"r"(re(x),1rl),ts"r"(im(x),0)),re(x),pl"r"(ts"r"(re(x),0),ts"r"(im(x),1rl)),im(x),t1".3222",t2".3222"),pliis(x)):is(ts(x,1c),x)
-satz222a:=symis(cx,ts(x,1c),x,satz222):is(x,ts(x,1c))
-satz222b:=tris(cx,ts(1c,x),ts(x,1c),x,comts(1c,x),satz222):is(ts(1c,x),x)
-satz222c:=symis(cx,ts(1c,x),x,satz222b):is(x,ts(1c,x))
-+3223
-t1:=tris(real,mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),mn"r"(m0"r"(re(x)),0),m0"r"(re(x)),ismn12"r"(ts"r"(re(x),m0"r"(1rl)),m0"r"(re(x)),ts"r"(im(x),m0"r"(0)),0,tris(real,ts"r"(re(x),m0"r"(1rl)),m0"r"(ts"r"(re(x),1rl)),m0"r"(re(x)),satz197b(re(x),1rl),ism0"r"(ts"r"(re(x),1rl),re(x),satz195(re(x)))),ts02(im(x),m0"r"(0),satz176b(0,refis(real,0)))),pl02(m0"r"(re(x)),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)))
-t2:=tris(real,pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),pl"r"(0,m0"r"(im(x))),m0"r"(im(x)),ispl12"r"(ts"r"(re(x),m0"r"(0)),0,ts"r"(im(x),m0"r"(1rl)),m0"r"(im(x)),ts02(re(x),m0"r"(0),satz176b(0,refis(real,0))),tris(real,ts"r"(im(x),m0"r"(1rl)),m0"r"(ts"r"(im(x),1rl)),m0"r"(im(x)),satz197b(im(x),1rl),ism0"r"(ts"r"(im(x),1rl),im(x),satz195(im(x))))),pl01(0,m0"r"(im(x)),refis(real,0))):is"r"(pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)))
--3223
-satz223:=tr4is(cx,ts(x,m0(1c)),ts(x,pli(m0"r"(1rl),m0"r"(0))),pli(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl)))),pli(m0"r"(re(x)),m0"r"(im(x))),m0(x),ists2(m0(1c),pli(m0"r"(1rl),m0"r"(0)),x,m0isa(1rl,0)),tsis2a(x,m0"r"(1rl),m0"r"(0)),isrecx12(mn"r"(ts"r"(re(x),m0"r"(1rl)),ts"r"(im(x),m0"r"(0))),m0"r"(re(x)),pl"r"(ts"r"(re(x),m0"r"(0)),ts"r"(im(x),m0"r"(1rl))),m0"r"(im(x)),t1".3223",t2".3223"),satz214a(x)):is(ts(x,m0(1c)),m0(x))
-satz223a:=symis(cx,ts(x,m0(1c)),m0(x),satz223):is(m0(x),ts(x,m0(1c)))
-satz223b:=tris(cx,ts(m0(1c),x),ts(x,m0(1c)),m0(x),comts(m0(1c),x),satz223):is(ts(m0(1c),x),m0(x))
-satz223c:=symis(cx,ts(m0(1c),x),m0(x),satz223b):is(m0(x),ts(m0(1c),x))
-+3224
-y@rxry:=ts"r"(re(x),re(y)):real
-ixiy:=ts"r"(im(x),im(y)):real
-rxiy:=ts"r"(re(x),im(y)):real
-ixry:=ts"r"(im(x),re(y)):real
-t1:=tr4is(real,mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),mn"r"(m0"r"(rxry),m0"r"(ixiy)),pl"r"(m0"r"(rxry),ixiy),mn"r"(ixiy,rxry),m0"r"(mn"r"(rxry,ixiy)),ismn12"r"(ts"r"(m0"r"(re(x)),re(y)),m0"r"(rxry),ts"r"(m0"r"(im(x)),im(y)),m0"r"(ixiy),satz197a(re(x),re(y)),satz197a(im(x),im(y))),ispl2"r"(m0"r"(m0"r"(ixiy)),ixiy,m0"r"(rxry),satz177(ixiy)),compl"r"(m0"r"(rxry),ixiy),satz181a(ixiy,rxry)):is"r"(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(rxry,ixiy)))
-t2:=tris(real,pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),mn"r"(m0"r"(rxiy),ixry),m0"r"(pl"r"(rxiy,ixry)),ispl12"r"(ts"r"(m0"r"(re(x)),im(y)),m0"r"(rxiy),ts"r"(m0"r"(im(x)),re(y)),m0"r"(ixry),satz197a(re(x),im(y)),satz197a(im(x),re(y))),satz180a(rxiy,ixry)):is"r"(pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(rxiy,ixry)))
--3224
-y@satz224a:=tr4is(cx,ts(m0(x),y),ts(pli(m0"r"(re(x)),m0"r"(im(x))),y),pli(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y)))),pli(m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))),m0(ts(x,y)),ists1(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),y,satz214(x)),tsis1a(y,m0"r"(re(x)),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(m0"r"(re(x)),re(y)),ts"r"(m0"r"(im(x)),im(y))),m0"r"(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)))),pl"r"(ts"r"(m0"r"(re(x)),im(y)),ts"r"(m0"r"(im(x)),re(y))),m0"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)))),t1".3224",t2".3224"),m0isb(mn"r"(ts"r"(re(x),re(y)),ts"r"(im(x),im(y))),pl"r"(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))))):is(ts(m0(x),y),m0(ts(x,y)))
-satz224b:=tr3is(cx,ts(x,m0(y)),ts(m0(y),x),m0(ts(y,x)),m0(ts(x,y)),comts(x,m0(y)),satz224a(y,x),ism0(ts(y,x),ts(x,y),comts(y,x))):is(ts(x,m0(y)),m0(ts(x,y)))
-satz224c:=tris2(cx,ts(m0(x),y),ts(x,m0(y)),m0(ts(x,y)),satz224a,satz224b):is(ts(m0(x),y),ts(x,m0(y)))
-satz224d:=symis(cx,ts(m0(x),y),ts(x,m0(y)),satz224c):is(ts(x,m0(y)),ts(m0(x),y))
-satz224e:=symis(cx,ts(m0(x),y),m0(ts(x,y)),satz224a):is(m0(ts(x,y)),ts(m0(x),y))
-satz224f:=symis(cx,ts(x,m0(y)),m0(ts(x,y)),satz224b):is(m0(ts(x,y)),ts(x,m0(y)))
-satz225:=tris(cx,ts(m0(x),m0(y)),ts(x,m0(m0(y))),ts(x,y),satz224c(x,m0(y)),ists2(m0(m0(y)),y,x,satz215(y))):is(ts(m0(x),m0(y)),ts(x,y))
-satz225a:=symis(cx,ts(m0(x),m0(y)),ts(x,y),satz225):is(ts(x,y),ts(m0(x),m0(y)))
-+3226
-z@rrr:=ts"r"(ts"r"(re(x),re(y)),re(z)):real
-iir:=ts"r"(ts"r"(im(x),im(y)),re(z)):real
-rii:=ts"r"(ts"r"(re(x),im(y)),im(z)):real
-iri:=ts"r"(ts"r"(im(x),re(y)),im(z)):real
-rri:=ts"r"(ts"r"(re(x),re(y)),im(z)):real
-iii:=ts"r"(ts"r"(im(x),im(y)),im(z)):real
-rir:=ts"r"(ts"r"(re(x),im(y)),re(z)):real
-irr:=ts"r"(ts"r"(im(x),re(y)),re(z)):real
-t1:=tr3is(real,mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(mn"r"(rrr,iir),pl"r"(rii,iri)),pl"r"(rrr,pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri)))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),ismn12"r"(ts"r"(rets(x,y),re(z)),mn"r"(rrr,iir),ts"r"(imts(x,y),im(z)),pl"r"(rii,iri),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),re(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),im(z))),asspl1"r"(rrr,m0"r"(iir),m0"r"(pl"r"(rii,iri))),ispl2"r"(pl"r"(m0"r"(iir),m0"r"(pl"r"(rii,iri))),m0"r"(pl"r"(iir,pl"r"(rii,iri))),rrr,satz180a(iir,pl"r"(rii,iri)))):is"r"(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))))
-t2:=tr3is(real,pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),pl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),pl"r"(pl"r"(rir,irr),mn"r"(rri,iii)),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),ispl12"r"(ts"r"(rets(x,y),im(z)),mn"r"(rri,iii),ts"r"(imts(x,y),re(z)),pl"r"(rir,irr),disttm1(ts"r"(re(x),re(y)),ts"r"(im(x),im(y)),im(z)),disttp1(ts"r"(re(x),im(y)),ts"r"(im(x),re(y)),re(z))),compl"r"(mn"r"(rri,iii),pl"r"(rir,irr)),asspl2"r"(pl"r"(rir,irr),rri,m0"r"(iii))):is"r"(pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii))
-t3:=tris(cx,ts(ts(x,y),z),pli(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z)))),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),tsis1a(z,rets(x,y),imts(x,y)),isrecx12(mn"r"(ts"r"(rets(x,y),re(z)),ts"r"(imts(x,y),im(z))),mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),pl"r"(ts"r"(rets(x,y),im(z)),ts"r"(imts(x,y),re(z))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),t1,t2)):is(ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)))
-c@t4:=tris(real,ts"r"(ts"r"(a,b),c),ts"r"(a,ts"r"(b,c)),ts"r"(ts"r"(b,c),a),assts1(a,b,c),comts"r"(a,ts"r"(b,c))):is"r"(ts"r"(ts"r"(a,b),c),ts"r"(ts"r"(b,c),a))
-t5:=tris(real,pl"r"(pl"r"(a,b),c),pl"r"(c,pl"r"(a,b)),pl"r"(pl"r"(c,a),b),compl"r"(pl"r"(a,b),c),asspl2"r"(c,a,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(c,a),b))
-t6:=tris(real,pl"r"(a,pl"r"(b,c)),pl"r"(pl"r"(b,c),a),pl"r"(b,pl"r"(c,a)),compl"r"(a,pl"r"(b,c)),asspl1"r"(b,c,a)):is"r"(pl"r"(a,pl"r"(b,c)),pl"r"(b,pl"r"(c,a)))
-z@rrr1:=rrr(y,z,x):real
-iir1:=iir(y,z,x):real
-rii1:=rii(y,z,x):real
-iri1:=iri(y,z,x):real
-rri1:=rri(y,z,x):real
-iii1:=iii(y,z,x):real
-rir1:=rir(y,z,x):real
-irr1:=irr(y,z,x):real
-t7:=tris(real,pl"r"(iir,pl"r"(rii,iri)),pl"r"(rii,pl"r"(iri,iir)),pl"r"(iir1,pl"r"(rii1,iri1)),t6(iir,rii,iri),ispl12"r"(rii,iir1,pl"r"(iri,iir),pl"r"(rii1,iri1),t4(re(x),im(y),im(z)),ispl12"r"(iri,rii1,iir,iri1,t4(im(x),re(y),im(z)),t4(im(x),im(y),re(z))))):is"r"(pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)))
-t8:=tris(real,pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rri,rir),irr),pl"r"(pl"r"(rir1,irr1),rri1),t5(rir,irr,rri),ispl12"r"(pl"r"(rri,rir),pl"r"(rir1,irr1),irr,rri1,ispl12"r"(rri,rir1,rir,irr1,t4(re(x),re(y),im(z)),t4(re(x),im(y),re(z))),t4(im(x),re(y),re(z)))):is"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1))
-t9:=ismn12"r"(rrr,rrr1,pl"r"(iir,pl"r"(rii,iri)),pl"r"(iir1,pl"r"(rii1,iri1)),t4(re(x),re(y),re(z)),t7):is"r"(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))))
-t10:=ismn12"r"(pl"r"(pl"r"(rir,irr),rri),pl"r"(pl"r"(rir1,irr1),rri1),iii,iii1,t8,t4(im(x),im(y),im(z))):is"r"(mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1))
-t11:=tris(cx,ts(ts(x,y),z),pli(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t3,isrecx12(mn"r"(rrr,pl"r"(iir,pl"r"(rii,iri))),mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir,irr),rri),iii),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1),t9,t10)):is(ts(ts(x,y),z),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
-t12:=tris(cx,ts(x,ts(y,z)),ts(ts(y,z),x),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),comts(x,ts(y,z)),t3(y,z,x)):is(ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)))
-t13:=tris2(cx,ts(ts(x,y),z),ts(x,ts(y,z)),pli(mn"r"(rrr1,pl"r"(iir1,pl"r"(rii1,iri1))),mn"r"(pl"r"(pl"r"(rir1,irr1),rri1),iii1)),t11,t12):is(ts(ts(x,y),z),ts(x,ts(y,z)))
--3226
-z@satz226:=t13".3226":is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts1:=satz226:is(ts(ts(x,y),z),ts(x,ts(y,z)))
-assts2:=symis(cx,ts(ts(x,y),z),ts(x,ts(y,z)),assts1):is(ts(x,ts(y,z)),ts(ts(x,y),z))
-+3227
-c@t1:=tr3is(real,pl"r"(pl"r"(a,b),c),pl"r"(a,pl"r"(b,c)),pl"r"(a,pl"r"(c,b)),pl"r"(pl"r"(a,c),b),asspl1"r"(a,b,c),ispl2"r"(pl"r"(b,c),pl"r"(c,b),a,compl"r"(b,c)),asspl2"r"(a,c,b)):is"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b))
-d@t2:=tr3is(real,pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(pl"r"(a,b),c),d),pl"r"(pl"r"(pl"r"(a,c),b),d),pl"r"(pl"r"(a,c),pl"r"(b,d)),asspl2"r"(pl"r"(a,b),c,d),ispl1"r"(pl"r"(pl"r"(a,b),c),pl"r"(pl"r"(a,c),b),d,t1),asspl1"r"(pl"r"(a,c),b,d)):is"r"(pl"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,c),pl"r"(b,d)))
-t3:=tris(real,mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(pl"r"(a,b),pl"r"(m0"r"(c),m0"r"(d))),pl"r"(mn"r"(a,c),mn"r"(b,d)),ispl2"r"(m0"r"(pl"r"(c,d)),pl"r"(m0"r"(c),m0"r"(d)),pl"r"(a,b),satz180(c,d)),t2(a,b,m0"r"(c),m0"r"(d))):is"r"(mn"r"(pl"r"(a,b),pl"r"(c,d)),pl"r"(mn"r"(a,c),mn"r"(b,d)))
-z@t4:=tris(real,mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),mn"r"(pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))),pl"r"(rets(x,y),rets(x,z)),ismn12"r"(ts"r"(re(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(re(x),re(y)),ts"r"(re(x),re(z))),ts"r"(im(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(im(x),im(y)),ts"r"(im(x),im(z))),disttp2(re(x),re(y),re(z)),disttp2(im(x),im(y),im(z))),t3(ts"r"(re(x),re(y)),ts"r"(re(x),re(z)),ts"r"(im(x),im(y)),ts"r"(im(x),im(z)))):is"r"(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)))
-t5:=tris(real,pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))),pl"r"(imts(x,y),imts(x,z)),ispl12"r"(ts"r"(re(x),pl"r"(im(y),im(z))),pl"r"(ts"r"(re(x),im(y)),ts"r"(re(x),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))),pl"r"(ts"r"(im(x),re(y)),ts"r"(im(x),re(z))),disttp2(re(x),im(y),im(z)),disttp2(im(x),re(y),re(z))),t2(ts"r"(re(x),im(y)),ts"r"(re(x),im(z)),ts"r"(im(x),re(y)),ts"r"(im(x),re(z)))):is"r"(pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)))
-t6:=tr3is(cx,ts(x,pl(y,z)),pli(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z))))),pli(pl"r"(rets(x,y),rets(x,z)),pl"r"(imts(x,y),imts(x,z))),pl(ts(x,y),ts(x,z)),tsis2a(x,pl"r"(re(y),re(z)),pl"r"(im(y),im(z))),isrecx12(mn"r"(ts"r"(re(x),pl"r"(re(y),re(z))),ts"r"(im(x),pl"r"(im(y),im(z)))),pl"r"(rets(x,y),rets(x,z)),pl"r"(ts"r"(re(x),pl"r"(im(y),im(z))),ts"r"(im(x),pl"r"(re(y),re(z)))),pl"r"(imts(x,y),imts(x,z)),t4,t5),plis12b(rets(x,y),imts(x,y),rets(x,z),imts(x,z))):is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
--3227
-satz227:=t6".3227":is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-disttp1:=tr3is(cx,ts(pl(x,y),z),ts(z,pl(x,y)),pl(ts(z,x),ts(z,y)),pl(ts(x,z),ts(y,z)),comts(pl(x,y),z),satz227(z,x,y),ispl12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(pl(x,y),z),pl(ts(x,z),ts(y,z)))
-disttp2:=satz227:is(ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)))
-distpt1:=symis(cx,ts(pl(x,y),z),pl(ts(x,z),ts(y,z)),disttp1):is(pl(ts(x,z),ts(y,z)),ts(pl(x,y),z))
-distpt2:=symis(cx,ts(x,pl(y,z)),pl(ts(x,y),ts(x,z)),disttp2):is(pl(ts(x,y),ts(x,z)),ts(x,pl(y,z)))
-satz228:=tr4is(cx,ts(x,mn(y,z)),ts(x,pl(y,m0(z))),pl(ts(x,y),ts(x,m0(z))),pl(ts(x,y),m0(ts(x,z))),mn(ts(x,y),ts(x,z)),ists2(mn(y,z),pl(y,m0(z)),x,satz218(y,z)),disttp2(x,y,m0(z)),ispl2(ts(x,m0(z)),m0(ts(x,z)),ts(x,y),satz224b(x,z)),satz218a(ts(x,y),ts(x,z))):is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
-disttm1:=tr3is(cx,ts(mn(x,y),z),ts(z,mn(x,y)),mn(ts(z,x),ts(z,y)),mn(ts(x,z),ts(y,z)),comts(mn(x,y),z),satz228(z,x,y),ismn12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y))):is(ts(mn(x,y),z),mn(ts(x,z),ts(y,z)))
-disttm2:=satz228:is(ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)))
-distmt1:=symis(cx,ts(mn(x,y),z),mn(ts(x,z),ts(y,z)),disttm1):is(mn(ts(x,z),ts(y,z)),ts(mn(x,y),z))
-distmt2:=symis(cx,ts(x,mn(y,z)),mn(ts(x,y),ts(x,z)),disttm2):is(mn(ts(x,y),ts(x,z)),ts(x,mn(y,z)))
-y@[n:nis(y,0c)][u1:complex][u2:complex][i:is(ts(y,u1),x)][j:is(ts(y,u2),x)]
-+3229
-t1:=tris2(cx,ts(y,u1),ts(y,u2),x,i,j):is(ts(y,u1),ts(y,u2))
-t2:=tris(cx,ts(y,mn(u1,u2)),mn(ts(y,u1),ts(y,u2)),0c,disttm2(y,u1,u2),satz213b(ts(y,u1),ts(y,u2),t1)):is(ts(y,mn(u1,u2)),0c)
-t3:=ore2(is(y,0c),is(mn(u1,u2),0c),satz221c(y,mn(u1,u2),t2),n):is(mn(u1,u2),0c)
--3229
-satz229b:=satz213a(u1,u2,t3".3229"):is(u1,u2)
-+*3229
-n@t4:=pnot0(mod2(y),lemma4(y,n)):nis"r"(mod2(y),0)
-u:=ts(pli(ov(re(y),mod2(y),t4),m0"r"(ov(im(y),mod2(y),t4))),x):complex
-[v:real]
-dd:=ov(v,mod2(y),t4):real
-n@t5:=tr3is(real,m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),m0"r"(m0"r"(ts"r"(im(y),dd(im(y))))),ts"r"(im(y),dd(im(y))),dd(ts"r"(im(y),im(y))),ism0"r"(ts"r"(im(y),m0"r"(dd(im(y)))),m0"r"(ts"r"(im(y),dd(im(y)))),satz197b(im(y),dd(im(y)))),satz177(ts"r"(im(y),dd(im(y)))),lemma6(im(y),im(y),mod2(y),t4)):is"r"(m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))))
-t6:=tr3is(real,mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(dd(ts"r"(re(y),re(y))),dd(ts"r"(im(y),im(y)))),dd(mod2(y)),1rl,ispl12"r"(ts"r"(re(y),dd(re(y))),dd(ts"r"(re(y),re(y))),m0"r"(ts"r"(im(y),m0"r"(dd(im(y))))),dd(ts"r"(im(y),im(y))),lemma6(re(y),re(y),mod2(y),t4),t5),lemma7(ts"r"(re(y),re(y)),ts"r"(im(y),im(y)),mod2(y),t4),lemma8(mod2(y),t4)):is"r"(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl)
-t7:=tris(real,ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(m0"r"(re(y)),dd(im(y))),dd(ts"r"(m0"r"(re(y)),im(y))),satz197d(re(y),dd(im(y))),lemma6(m0"r"(re(y)),im(y),mod2(y),t4)):is"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))))
-t8:=tris(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),pl"r"(dd(ts"r"(m0"r"(re(y)),im(y))),dd(ts"r"(im(y),re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),ispl12"r"(ts"r"(re(y),m0"r"(dd(im(y)))),dd(ts"r"(m0"r"(re(y)),im(y))),ts"r"(im(y),dd(re(y))),dd(ts"r"(im(y),re(y))),t7,lemma6(im(y),re(y),mod2(y),t4)),lemma7(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)),mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))))
-t9:=tr3is(real,pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),pl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),mn"r"(ts"r"(im(y),re(y)),ts"r"(re(y),im(y))),0,ispl1"r"(ts"r"(m0"r"(re(y)),im(y)),m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y)),satz197a(re(y),im(y))),compl"r"(m0"r"(ts"r"(re(y),im(y))),ts"r"(im(y),re(y))),satz182e(ts"r"(im(y),re(y)),ts"r"(re(y),im(y)),comts"r"(im(y),re(y)))):is"r"(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0)
-t10:=tr3is(real,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),dd(pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y)))),dd(0),0,t8,isf(real,real,[t:real]dd(t),pl"r"(ts"r"(m0"r"(re(y)),im(y)),ts"r"(im(y),re(y))),0,t9),lemma9(mod2(y),t4)):is"r"(pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0)
-t11:=tris(cx,ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),pli(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y))))),1c,tsis2a(y,dd(re(y)),m0"r"(dd(im(y)))),isrecx12(mn"r"(ts"r"(re(y),dd(re(y))),ts"r"(im(y),m0"r"(dd(im(y))))),1rl,pl"r"(ts"r"(re(y),m0"r"(dd(im(y)))),ts"r"(im(y),dd(re(y)))),0,t6,t10)):is(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c)
-t12:=tr3is(cx,ts(y,u),ts(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),x),ts(1c,x),x,assts2(y,pli(dd(re(y)),m0"r"(dd(im(y)))),x),ists1(ts(y,pli(dd(re(y)),m0"r"(dd(im(y))))),1c,x,t11),satz222b(x)):is(ts(y,u),x)
--3229
-n@satz229a:=somei(cx,[t:cx]is(ts(y,t),x),u".3229",t12".3229"):some([t:cx]is(ts(y,t),x))
-satz229:=onei(cx,[t:cx]is(ts(y,t),x),[t:cx][u:cx][v:is(ts(y,t),x)][w:is(ts(y,u),x)]satz229b(t,u,v,w),satz229a):one([t:cx]is(ts(y,t),x))
-ov:=ind(cx,[t:cx]is(ts(y,t),x),satz229):complex
-satz229c:=oneax(cx,[t:cx]is(ts(y,t),x),satz229):is(ts(y,ov(x,y,n)),x)
-satz229d:=symis(cx,ts(y,ov(x,y,n)),x,satz229c):is(x,ts(y,ov(x,y,n)))
-satz229e:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c):is(ts(ov(x,y,n),y),x)
-satz229f:=symis(cx,ts(ov(x,y,n),y),x,satz229e):is(x,ts(ov(x,y,n),y))
-y@[u:complex][n:nis(y,0c)][i:is(ts(y,u),x)]
-satz229g:=satz229b(n,u,ov(x,y,n),i,satz229c(n)):is(u,ov(x,y,n))
-satz229h:=symis(cx,u,ov(x,y,n),satz229g):is(ov(x,y,n),u)
-n@[i:is(ts(u,y),x)]
-satz229j:=satz229g(tris(cx,ts(y,u),ts(u,y),x,comts(y,u),i)):is(u,ov(x,y,n))
-satz229k:=symis(cx,u,ov(x,y,n),satz229j):is(ov(x,y,n),u)
-z@[i:is(x,y)][n:nis(z,0c)]
-isov1:=isf(cx,cx,[t:cx]ov(t,z,n),x,y,i):is(ov(x,z,n),ov(y,z,n))
-i@[n:nis(x,0c)][o:nis(y,0c)]
-isov2:=satz229h(z,x,ov(z,y,o),n,tris(cx,ts(x,ov(z,y,o)),ts(y,ov(z,y,o)),z,ists1(x,y,ov(z,y,o),i),satz229c(z,y,o))):is(ov(z,x,n),ov(z,y,o))
-z@[u:complex][i:is(x,y)][j:is(z,u)][n:nis(z,0c)][o:nis(u,0c)]
-isov12:=tris(cx,ov(x,z,n),ov(y,z,n),ov(y,u,o),isov1(x,y,z,i,n),isov2(z,u,y,j,n,o)):is(ov(x,z,n),ov(y,u,o))
-y@satz230:=tris(cx,pl(mn(x,y),y),pl(y,mn(x,y)),x,compl(mn(x,y),y),satz212h(x,y)):is(pl(mn(x,y),y),x)
-satz231:=satz212e(pl(x,y),y,x,compl(y,x)):is(mn(pl(x,y),y),x)
-satz232:=satz212e(x,mn(x,y),y,satz230):is(mn(x,mn(x,y)),y)
-+4233
-z@t1:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(mn(mn(x,y),z),pl(y,z)),pl(mn(mn(x,y),z),pl(z,y)),pl(pl(mn(mn(x,y),z),z),y),compl(pl(y,z),mn(mn(x,y),z)),ispl2(pl(y,z),pl(z,y),mn(mn(x,y),z),compl(y,z)),asspl2(mn(mn(x,y),z),z,y)):is(pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y))
-t2:=tr3is(cx,pl(pl(y,z),mn(mn(x,y),z)),pl(pl(mn(mn(x,y),z),z),y),pl(mn(x,y),y),x,t1,ispl1(pl(mn(mn(x,y),z),z),mn(x,y),y,satz230(mn(x,y),z)),satz230(x,y)):is(pl(pl(y,z),mn(mn(x,y),z)),x)
--4233
-z@satz233:=satz212d(x,pl(y,z),mn(mn(x,y),z),t2".4233"):is(mn(mn(x,y),z),mn(x,pl(y,z)))
-satz234:=satz212g(pl(x,y),z,pl(x,mn(y,z)),tris(cx,pl(pl(x,mn(y,z)),z),pl(x,pl(mn(y,z),z)),pl(x,y),asspl1(x,mn(y,z),z),ispl2(pl(mn(y,z),z),y,x,satz230(y,z)))):is(mn(pl(x,y),z),pl(x,mn(y,z)))
-satz234a:=symis(cx,mn(pl(x,y),z),pl(x,mn(y,z)),satz234):is(pl(x,mn(y,z)),mn(pl(x,y),z))
-satz234b:=tr3is(cx,mn(pl(x,y),z),mn(pl(y,x),z),pl(y,mn(x,z)),pl(mn(x,z),y),ismn1(pl(x,y),pl(y,x),z,compl(x,y)),satz234(y,x,z),compl(y,mn(x,z))):is(mn(pl(x,y),z),pl(mn(x,z),y))
-satz234c:=symis(cx,mn(pl(x,y),z),pl(mn(x,z),y),satz234b):is(pl(mn(x,z),y),mn(pl(x,y),z))
-satz235:=satz212f(x,mn(y,z),pl(mn(x,y),z),tr3is(cx,pl(pl(mn(x,y),z),mn(y,z)),pl(mn(x,y),pl(z,mn(y,z))),pl(mn(x,y),y),x,asspl1(mn(x,y),z,mn(y,z)),ispl2(pl(z,mn(y,z)),y,mn(x,y),satz212h(y,z)),satz230(x,y))):is(pl(mn(x,y),z),mn(x,mn(y,z)))
-satz235a:=symis(cx,pl(mn(x,y),z),mn(x,mn(y,z)),satz235):is(mn(x,mn(y,z)),pl(mn(x,y),z))
-satz235b:=tris(cx,mn(x,mn(y,z)),pl(mn(x,y),z),mn(pl(x,z),y),satz235a,satz234c(x,z,y)):is(mn(x,mn(y,z)),mn(pl(x,z),y))
-satz235c:=tris(cx,mn(x,mn(y,z)),mn(pl(x,z),y),mn(pl(z,x),y),satz235b,ismn1(pl(x,z),pl(z,x),y,compl(x,z))):is(mn(x,mn(y,z)),mn(pl(z,x),y))
-satz236:=satz212g(pl(x,z),pl(y,z),mn(x,y),tris(cx,pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y)))):is(mn(pl(x,z),pl(y,z)),mn(x,y))
-satz236a:=tris(cx,mn(pl(z,x),pl(z,y)),mn(pl(x,z),pl(y,z)),mn(x,y),ismn12(pl(z,x),pl(x,z),pl(z,y),pl(y,z),compl(z,x),compl(z,y)),satz236):is(mn(pl(z,x),pl(z,y)),mn(x,y))
-[u:complex]
-+4237
-t1:=tr3is(cx,pl(mn(z,u),pl(u,y)),pl(pl(mn(z,u),u),y),pl(z,y),pl(y,z),asspl2(mn(z,u),u,y),ispl1(pl(mn(z,u),u),z,y,satz230(z,u)),compl(z,y)):is(pl(mn(z,u),pl(u,y)),pl(y,z))
-t2:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(pl(mn(x,y),mn(z,u)),pl(u,y)),pl(mn(x,y),pl(mn(z,u),pl(u,y))),pl(mn(x,y),pl(y,z)),ispl2(pl(y,u),pl(u,y),pl(mn(x,y),mn(z,u)),compl(y,u)),asspl1(mn(x,y),mn(z,u),pl(u,y)),ispl2(pl(mn(z,u),pl(u,y)),pl(y,z),mn(x,y),t1)):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)))
-t3:=tr3is(cx,pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(mn(x,y),pl(y,z)),pl(pl(mn(x,y),y),z),pl(x,z),t2,asspl2(mn(x,y),y,z),ispl1(pl(mn(x,y),y),x,z,satz230(x,y))):is(pl(pl(mn(x,y),mn(z,u)),pl(y,u)),pl(x,z))
--4237
-satz237:=satz212f(pl(x,z),pl(y,u),pl(mn(x,y),mn(z,u)),t3".4237"):is(pl(mn(x,y),mn(z,u)),mn(pl(x,z),pl(y,u)))
-+4238
-t1:=tris(cx,pl(pl(x,u),z),pl(x,pl(u,z)),pl(x,pl(z,u)),asspl1(x,u,z),ispl2(pl(u,z),pl(z,u),x,compl(u,z))):is(pl(pl(x,u),z),pl(x,pl(z,u)))
-t2:=tr3is(cx,pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(pl(pl(x,u),z),pl(pl(y,z),u)),mn(pl(x,pl(z,u)),pl(y,pl(z,u))),mn(x,y),satz237(pl(x,u),pl(y,z),z,u),ismn12(pl(pl(x,u),z),pl(x,pl(z,u)),pl(pl(y,z),u),pl(y,pl(z,u)),t1,asspl1(y,z,u)),satz236(x,y,pl(z,u))):is(pl(mn(pl(x,u),pl(y,z)),mn(z,u)),mn(x,y))
--4238
-satz238:=satz212g(mn(x,y),mn(z,u),mn(pl(x,u),pl(y,z)),t2".4238"):is(mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)))
-[i:is(mn(x,y),mn(z,u))]
-+4239
-t1:=tris1(cx,mn(pl(x,u),pl(y,z)),0c,mn(mn(x,y),mn(z,u)),satz238,satz213b(mn(x,y),mn(z,u),i)):is(mn(pl(x,u),pl(y,z)),0c)
--4239
-satz239a:=satz213a(pl(x,u),pl(y,z),t1".4239"):is(pl(x,u),pl(y,z))
-u@[i:is(pl(x,u),pl(y,z))]
-+*4239
-i@t2:=tris(cx,mn(mn(x,y),mn(z,u)),mn(pl(x,u),pl(y,z)),0c,satz238,satz213b(pl(x,u),pl(y,z),i)):is(mn(mn(x,y),mn(z,u)),0c)
--4239
-i@satz239b:=satz213a(mn(x,y),mn(z,u),t2".4239"):is(mn(x,y),mn(z,u))
-y@[n:nis(y,0c)]
-satz240:=tris(cx,ts(ov(x,y,n),y),ts(y,ov(x,y,n)),x,comts(ov(x,y,n),y),satz229c(x,y,n)):is(ts(ov(x,y,n),y),x)
-satz241:=satz229h(ts(x,y),y,x,n,comts(y,x)):is(ov(ts(x,y),y,n),x)
-y@[n:nis(x,0c)][o:nis(y,0c)]
-lemma6:=th3"l.imp"(is(ov(x,y,o),0c),is(x,0c),n,[t:is(ov(x,y,o),0c)]tris1(cx,x,0c,ts(y,ov(x,y,o)),satz229c(x,y,o),satz221b(y,ov(x,y,o),t))):nis(ov(x,y,o),0c)
-satz242:=satz229h(x,ov(x,y,o),y,lemma6,satz240(o)):is(ov(x,ov(x,y,o),lemma6),y)
-z@[n:nis(y,0c)][o:nis(z,0c)]
-+5243
-t1:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ov(ov(x,y,n),z,o),ts(y,z)),ts(ov(ov(x,y,n),z,o),ts(z,y)),ts(ts(ov(ov(x,y,n),z,o),z),y),comts(ts(y,z),ov(ov(x,y,n),z,o)),ists2(ts(y,z),ts(z,y),ov(ov(x,y,n),z,o),comts(y,z)),assts2(ov(ov(x,y,n),z,o),z,y)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y))
-t2:=tr3is(cx,ts(ts(y,z),ov(ov(x,y,n),z,o)),ts(ts(ov(ov(x,y,n),z,o),z),y),ts(ov(x,y,n),y),x,t1,ists1(ts(ov(ov(x,y,n),z,o),z),ov(x,y,n),y,satz240(ov(x,y,n),z,o)),satz240(x,y,n)):is(ts(ts(y,z),ov(ov(x,y,n),z,o)),x)
--5243
-satz243:=satz229g(x,ts(y,z),ov(ov(x,y,n),z,o),satz221d(y,z,n,o),t2".5243"):is(ov(ov(x,y,n),z,o),ov(x,ts(y,z),satz221d(y,z,n,o)))
-z@[n:nis(z,0c)]
-satz244:=satz229k(ts(x,y),z,ts(x,ov(y,z,n)),n,tris(cx,ts(ts(x,ov(y,z,n)),z),ts(x,ts(ov(y,z,n),z)),ts(x,y),assts1(x,ov(y,z,n),z),ists2(ts(ov(y,z,n),z),y,x,satz240(y,z,n)))):is(ov(ts(x,y),z,n),ts(x,ov(y,z,n)))
-satz244a:=symis(cx,ov(ts(x,y),z,n),ts(x,ov(y,z,n)),satz244):is(ts(x,ov(y,z,n)),ov(ts(x,y),z,n))
-satz244b:=tr3is(cx,ov(ts(x,y),z,n),ov(ts(y,x),z,n),ts(y,ov(x,z,n)),ts(ov(x,z,n),y),isov1(ts(x,y),ts(y,x),z,comts(x,y),n),satz244(y,x,z,n),comts(y,ov(x,z,n))):is(ov(ts(x,y),z,n),ts(ov(x,z,n),y))
-satz244c:=symis(cx,ov(ts(x,y),z,n),ts(ov(x,z,n),y),satz244b):is(ts(ov(x,z,n),y),ov(ts(x,y),z,n))
-z@[n:nis(y,0c)][o:nis(z,0c)]
-satz245:=satz229j(x,ov(y,z,o),ts(ov(x,y,n),z),lemma6(y,z,n,o),tr3is(cx,ts(ts(ov(x,y,n),z),ov(y,z,o)),ts(ov(x,y,n),ts(z,ov(y,z,o))),ts(ov(x,y,n),y),x,assts1(ov(x,y,n),z,ov(y,z,o)),ists2(ts(z,ov(y,z,o)),y,ov(x,y,n),satz229c(y,z,o)),satz240(x,y,n))):is(ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)))
-satz245a:=symis(cx,ts(ov(x,y,n),z),ov(x,ov(y,z,o),lemma6(y,z,n,o)),satz245):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z))
-satz245b:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ts(ov(x,y,n),z),ov(ts(x,z),y,n),satz245a,satz244c(x,z,y,n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n))
-satz245c:=tris(cx,ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(x,z),y,n),ov(ts(z,x),y,n),satz245b,isov1(ts(x,z),ts(z,x),y,comts(x,z),n)):is(ov(x,ov(y,z,o),lemma6(y,z,n,o)),ov(ts(z,x),y,n))
-satz246:=satz229k(ts(x,z),ts(y,z),ov(x,y,n),satz221d(y,z,n,o),tris(cx,ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n)))):is(ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n))
-satz246a:=tris(cx,ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(ts(x,z),ts(y,z),satz221d(y,z,n,o)),ov(x,y,n),isov12(ts(z,x),ts(x,z),ts(z,y),ts(y,z),comts(z,x),comts(z,y),satz221d(z,y,o,n),satz221d(y,z,n,o)),satz246):is(ov(ts(z,x),ts(z,y),satz221d(z,y,o,n)),ov(x,y,n))
-z@[u:complex][n:nis(y,0c)][o:nis(u,0c)]
-+5247
-t1:=tr3is(cx,ts(ov(z,u,o),ts(u,y)),ts(ts(ov(z,u,o),u),y),ts(z,y),ts(y,z),assts2(ov(z,u,o),u,y),ists1(ts(ov(z,u,o),u),z,y,satz240(z,u,o)),comts(z,y)):is(ts(ov(z,u,o),ts(u,y)),ts(y,z))
-t2:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ts(ov(x,y,n),ov(z,u,o)),ts(u,y)),ts(ov(x,y,n),ts(ov(z,u,o),ts(u,y))),ts(ov(x,y,n),ts(y,z)),ists2(ts(y,u),ts(u,y),ts(ov(x,y,n),ov(z,u,o)),comts(y,u)),assts1(ov(x,y,n),ov(z,u,o),ts(u,y)),ists2(ts(ov(z,u,o),ts(u,y)),ts(y,z),ov(x,y,n),t1)):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)))
-t3:=tr3is(cx,ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(ov(x,y,n),ts(y,z)),ts(ts(ov(x,y,n),y),z),ts(x,z),t2,assts2(ov(x,y,n),y,z),ists1(ts(ov(x,y,n),y),x,z,satz240(x,y,n))):is(ts(ts(ov(x,y,n),ov(z,u,o)),ts(y,u)),ts(x,z))
--5247
-satz247:=satz229j(ts(x,z),ts(y,u),ts(ov(x,y,n),ov(z,u,o)),satz221d(y,u,n,o),t3".5247"):is(ts(ov(x,y,n),ov(z,u,o)),ov(ts(x,z),ts(y,u),satz221d(y,u,n,o)))
-u@[n:nis(y,0c)][o:nis(z,0c)][p:nis(u,0c)]
-+5248
-t1:=tris(cx,ts(ts(x,u),z),ts(x,ts(u,z)),ts(x,ts(z,u)),assts1(x,u,z),ists2(ts(u,z),ts(z,u),x,comts(u,z))):is(ts(ts(x,u),z),ts(x,ts(z,u)))
-t2:=tr3is(cx,ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(ts(ts(x,u),z),ts(ts(y,z),u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p)),ov(ts(x,ts(z,u)),ts(y,ts(z,u)),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),ov(x,y,n),satz247(ts(x,u),ts(y,z),z,u,satz221d(y,z,n,o),p),isov12(ts(ts(x,u),z),ts(x,ts(z,u)),ts(ts(y,z),u),ts(y,ts(z,u)),t1,assts1(y,z,u),satz221d(ts(y,z),u,satz221d(y,z,n,o),p),satz221d(y,ts(z,u),n,satz221d(z,u,o,p))),satz246(x,y,ts(z,u),n,satz221d(z,u,o,p))):is(ts(ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),ov(z,u,p)),ov(x,y,n))
--5248
-satz248:=satz229k(ov(x,y,n),ov(z,u,p),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)),lemma6(z,u,o,p),t2".5248"):is(ov(ov(x,y,n),ov(z,u,p),lemma6(z,u,o,p)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,o)))
-x@[n:nis(x,0c)]
-satz249:=satz229h(0c,x,0c,n,satz221b(x,0c,refis(cx,0c))):is(ov(0c,x,n),0c)
-satz250:=satz229h(x,x,1c,n,satz222(x)):is(ov(x,x,n),1c)
-y@[n:nis(y,0c)][i:is(x,y)]
-satz251a:=tris(cx,ov(x,y,n),ov(x,x,th2"e.notis"(cx,y,0c,x,n,i)),1c,isov2(y,x,x,symis(cx,x,y,i),n,th2"e.notis"(cx,y,0c,x,n,i)),satz250(x,th2"e.notis"(cx,y,0c,x,n,i))):is(ov(x,y,n),1c)
-n@[i:is(ov(x,y,n),1c)]
-satz251b:=tr3is(cx,x,ts(y,ov(x,y,n)),ts(y,1c),y,satz229d(x,y,n),ists2(ov(x,y,n),1c,y,i),satz222(y)):is(x,y)
-u@[n:nis(y,0c)][o:nis(u,0c)][i:is(ov(x,y,n),ov(z,u,o))]
-+5252
-[j:is(z,0c)]
-t1:=tr3is(cx,ov(x,y,n),ov(z,u,o),ov(0c,u,o),0c,i,isov1(z,0c,u,j,o),satz249(u,o)):is(ov(x,y,n),0c)
-t2:=tris(cx,x,ts(y,ov(x,y,n)),0c,satz229d(x,y,n),satz221b(y,ov(x,y,n),t1)):is(x,0c)
-t3:=tris2(cx,ts(x,u),ts(y,z),0c,satz221a(x,u,t2),satz221b(y,z,j)):is(ts(x,u),ts(y,z))
-i@[p:nis(z,0c)]
-t4:=tris1(cx,ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),satz248(x,y,z,u,n,p,o),satz251a(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),i)):is(ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c)
-t5:=satz251b(ts(x,u),ts(y,z),satz221d(y,z,n,p),t4):is(ts(x,u),ts(y,z))
--5252
-satz252a:=th1"l.imp"(is(z,0c),is(ts(x,u),ts(y,z)),[t:is(z,0c)]t3".5252"(t),[t:nis(z,0c)]t5".5252"(t)):is(ts(x,u),ts(y,z))
-o@[i:is(ts(x,u),ts(y,z))]
-+*5252
-i@[j:is(z,0c)]
-t6:=tris(cx,ts(x,u),ts(y,z),0c,i,satz221b(y,z,j)):is(ts(x,u),0c)
-t7:=ore1(is(x,0c),is(u,0c),satz221c(x,u,t6),o):is(x,0c)
-t8:=tris2(cx,ov(x,y,n),ov(z,u,o),0c,tris(cx,ov(x,y,n),ov(0c,y,n),0c,isov1(x,0c,y,t7,n),satz249(y,n)),tris(cx,ov(z,u,o),ov(0c,u,o),0c,isov1(z,0c,u,j,o),satz249(u,o))):is(ov(x,y,n),ov(z,u,o))
-i@[p:nis(z,0c)]
-t9:=tris(cx,ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),ov(ts(x,u),ts(y,z),satz221d(y,z,n,p)),1c,satz248(x,y,z,u,n,p,o),satz251a(ts(x,u),ts(y,z),satz221d(y,z,n,p),i)):is(ov(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o)),1c)
-t10:=satz251b(ov(x,y,n),ov(z,u,o),lemma6(z,u,p,o),t9):is(ov(x,y,n),ov(z,u,o))
--5252
-i@satz252b:=th1"l.imp"(is(z,0c),is(ov(x,y,n),ov(z,u,o)),[t:is(z,0c)]t8".5252"(t),[t:nis(z,0c)]t10".5252"(t)):is(ov(x,y,n),ov(z,u,o))
-z@[n:nis(y,0c)]
-satz253:=satz229g(pl(x,z),y,pl(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,pl(ov(x,y,n),ov(z,y,n))),pl(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),pl(x,z),disttp2(y,ov(x,y,n),ov(z,y,n)),ispl12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(pl(ov(x,y,n),ov(z,y,n)),ov(pl(x,z),y,n))
-z@[n:nis(z,0c)]
-distop:=symis(cx,pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n),satz253(x,z,y,n)):is(ov(pl(x,y),z,n),pl(ov(x,z,n),ov(y,z,n)))
-distpo:=satz253(x,z,y,n):is(pl(ov(x,z,n),ov(y,z,n)),ov(pl(x,y),z,n))
-u@[n:nis(y,0c)][o:nis(u,0c)]
-satz254:=tris1(cx,pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),pl(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ispl12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz253(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(pl(ov(x,y,n),ov(z,u,o)),ov(pl(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
-z@[n:nis(y,0c)]
-satz255:=satz229g(mn(x,z),y,mn(ov(x,y,n),ov(z,y,n)),n,tris(cx,ts(y,mn(ov(x,y,n),ov(z,y,n))),mn(ts(y,ov(x,y,n)),ts(y,ov(z,y,n))),mn(x,z),disttm2(y,ov(x,y,n),ov(z,y,n)),ismn12(ts(y,ov(x,y,n)),x,ts(y,ov(z,y,n)),z,satz229c(x,y,n),satz229c(z,y,n)))):is(mn(ov(x,y,n),ov(z,y,n)),ov(mn(x,z),y,n))
-z@[n:nis(z,0c)]
-distom:=symis(cx,mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n),satz255(x,z,y,n)):is(ov(mn(x,y),z,n),mn(ov(x,z,n),ov(y,z,n)))
-distmo:=satz255(x,z,y,n):is(mn(ov(x,z,n),ov(y,z,n)),ov(mn(x,y),z,n))
-u@[n:nis(y,0c)][o:nis(u,0c)]
-satz256:=tris1(cx,mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)),mn(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o))),ismn12(ov(ts(x,u),ts(y,u),satz221d(y,u,n,o)),ov(x,y,n),ov(ts(y,z),ts(y,u),satz221d(y,u,n,o)),ov(z,u,o),satz246(x,y,u,n,o),satz246a(z,u,y,o,n)),satz255(ts(x,u),ts(y,u),ts(y,z),satz221d(y,u,n,o))):is(mn(ov(x,y,n),ov(z,u,o)),ov(mn(ts(x,u),ts(y,z)),ts(y,u),satz221d(y,u,n,o)))
-x@conj:=pli(re(x),m0"r"(im(x))):complex
-b@conjisa:=isrecx12(re(pli(a,b)),a,m0"r"(im(pli(a,b))),m0"r"(b),reis(a,b),ism0"r"(im(pli(a,b)),b,imis(a,b))):is(conj(pli(a,b)),pli(a,m0"r"(b)))
-conjisb:=symis(cx,conj(pli(a,b)),pli(a,m0"r"(b)),conjisa):is(pli(a,m0"r"(b)),conj(pli(a,b)))
-y@[i:is(x,y)]
-isconj:=isf(cx,cx,[t:cx]conj(t),x,y,i):is(conj(x),conj(y))
-x@satz257:=tr3is(cx,conj(conj(x)),pli(re(x),m0"r"(m0"r"(im(x)))),pli(re(x),im(x)),x,conjisa(re(x),m0"r"(im(x))),isrecx2(m0"r"(m0"r"(im(x))),im(x),re(x),satz177(im(x))),pliis(x)):is(conj(conj(x)),x)
-[i:is(x,0c)]
-satz258a:=tr3is(cx,conj(x),conj(0c),pli(0,m0"r"(0)),0c,isconj(x,0c,i),conjisa(0,0),isrecx2(m0"r"(0),0,0,satz176b(0,refis(real,0)))):is(conj(x),0c)
-x@[i:is(conj(x),0c)]
-+6258
-t1:=tris(real,re(x),re(conj(x)),0,isre(re(x),m0"r"(im(x))),lemma1(conj(x),i)):is"r"(re(x),0)
-t2:=satz176e(im(x),tris(real,m0"r"(im(x)),im(conj(x)),0,isim(re(x),m0"r"(im(x))),lemma2(conj(x),i))):is"r"(im(x),0)
--6258
-satz258b:=tris(cx,x,pli(re(x),im(x)),0c,ispli(x),isrecx12(re(x),0,im(x),0,t1".6258",t2".6258")):is(x,0c)
-+*6258
-i@anders:=tris1(cx,x,0c,conj(conj(x)),satz257,satz258a(conj(x),i)):is(x,0c)
--6258
-x@[n:nis(x,0c)]
-satz258c:=th3"l.imp"(is(conj(x),0c),is(x,0c),n,[t:is(conj(x),0c)]satz258b(t)):nis(conj(x),0c)
-x@[i:is(conj(x),x)]
-+6259
-t1:=tris(real,m0"r"(im(x)),im(conj(x)),im(x),isim(re(x),m0"r"(im(x))),isceim(conj(x),x,i)):is"r"(m0"r"(im(x)),im(x))
--6259
-satz259a:=lemma10(im(x),symis(real,m0"r"(im(x)),im(x),t1".6259")):is"r"(im(x),0)
-x@[i:is"r"(im(x),0)]
-satz259b:=tris(cx,conj(x),pli(re(x),im(x)),x,isrecx2(m0"r"(im(x)),im(x),re(x),tris2(real,m0"r"(im(x)),im(x),0,satz176b(im(x),i),i)),pliis(x)):is(conj(x),x)
-x@[i:is(x,conj(x))]
-satz269c:=satz259a(x,symis(cx,x,conj(x),i)):is"r"(im(x),0)
-x@[i:is"r"(im(x),0)]
-satz269d:=symis(cx,conj(x),x,satz259b(i)):is(x,conj(x))
-y@satz260:=tr3is(cx,conj(pl(x,y)),pli(pl"r"(re(x),re(y)),m0"r"(pl"r"(im(x),im(y)))),pli(pl"r"(re(x),re(y)),pl"r"(m0"r"(im(x)),m0"r"(im(y)))),pl(conj(x),conj(y)),conjisa(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),isrecx2(m0"r"(pl"r"(im(x),im(y))),pl"r"(m0"r"(im(x)),m0"r"(im(y))),pl"r"(re(x),re(y)),satz180(im(x),im(y))),plis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(pl(x,y)),pl(conj(x),conj(y)))
-satz260a:=symis(cx,conj(pl(x,y)),pl(conj(x),conj(y)),satz260):is(pl(conj(x),conj(y)),conj(pl(x,y)))
-+6261
-t1:=tris(real,m0"r"(imts(x,y)),pl"r"(m0"r"(ts"r"(re(x),im(y))),m0"r"(ts"r"(im(x),re(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),satz180(ts"r"(re(x),im(y)),ts"r"(im(x),re(y))),ispl12"r"(m0"r"(ts"r"(re(x),im(y))),ts"r"(re(x),m0"r"(im(y))),m0"r"(ts"r"(im(x),re(y))),ts"r"(m0"r"(im(x)),re(y)),satz197f(re(x),im(y)),satz197e(im(x),re(y)))):is"r"(m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))))
--6261
-satz261:=tr3is(cx,conj(ts(x,y)),pli(rets(x,y),m0"r"(imts(x,y))),pli(mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y)))),ts(conj(x),conj(y)),conjisa(rets(x,y),imts(x,y)),isrecx12(rets(x,y),mn"r"(ts"r"(re(x),re(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y)))),m0"r"(imts(x,y)),pl"r"(ts"r"(re(x),m0"r"(im(y))),ts"r"(m0"r"(im(x)),re(y))),ismn2"r"(ts"r"(im(x),im(y)),ts"r"(m0"r"(im(x)),m0"r"(im(y))),ts"r"(re(x),re(y)),satz198a(im(x),im(y))),t1".6261"),tsis12b(re(x),m0"r"(im(x)),re(y),m0"r"(im(y)))):is(conj(ts(x,y)),ts(conj(x),conj(y)))
-satz261a:=symis(cx,conj(ts(x,y)),ts(conj(x),conj(y)),satz261):is(ts(conj(x),conj(y)),conj(ts(x,y)))
-+6262
-t1:=symis(cx,pl(mn(x,y),y),x,satz230(x,y)):is(x,pl(mn(x,y),y))
-t2:=tris(cx,conj(x),conj(pl(mn(x,y),y)),pl(conj(mn(x,y)),conj(y)),isconj(x,pl(mn(x,y),y),t1),satz260(mn(x,y),y)):is(conj(x),pl(conj(mn(x,y)),conj(y)))
--6262
-satz262:=satz212f(conj(x),conj(y),conj(mn(x,y)),symis(cx,conj(x),pl(conj(mn(x,y)),conj(y)),t2".6262")):is(conj(mn(x,y)),mn(conj(x),conj(y)))
-satz262a:=symis(cx,conj(mn(x,y)),mn(conj(x),conj(y)),satz262):is(mn(conj(x),conj(y)),conj(mn(x,y)))
-[n:nis(y,0c)]
-+6263
-t1:=satz229f(x,y,n):is(x,ts(ov(x,y,n),y))
-t2:=isconj(x,ts(ov(x,y,n),y),t1):is(conj(x),conj(ts(ov(x,y,n),y)))
-t3:=satz261(ov(x,y,n),y):is(conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)))
-t4:=tris(cx,conj(x),conj(ts(ov(x,y,n),y)),ts(conj(ov(x,y,n)),conj(y)),t2,t3):is(conj(x),ts(conj(ov(x,y,n)),conj(y)))
-t5:=satz258c(y,n):nis(conj(y),0c)
--6263
-satz263:=satz229j(conj(x),conj(y),conj(ov(x,y,n)),t5".6263",symis(cx,conj(x),ts(conj(ov(x,y,n)),conj(y)),t4".6263")):is(conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)))
-satz263a:=symis(cx,conj(ov(x,y,n)),ov(conj(x),conj(y),satz258c(y,n)),satz263):is(ov(conj(x),conj(y),satz258c(y,n)),conj(ov(x,y,n)))
-x@mod:=sqrt(mod2(x),lemma5(x)):real
-y@[i:is(x,y)]
-ismod:=isf(cx,real,[t:cx]mod(t),x,y,i):is"r"(mod(x),mod(y))
-x@[n:nis(x,0c)]
-satz264a:=sqrtnot0(mod2(x),lemma5(x),pnot0(mod2(x),lemma4(x,n))):pos(mod(x))
-x@[i:is(x,0c)]
-satz264b:=sqrt0(mod2(x),lemma5(x),lemma3(x,i)):is"r"(mod(x),0)
-x@satz264c:=thsqrt1a(mod2(x),lemma5(x)):not(neg(mod(x)))
-satz264d:=satz167f(mod(x),0,th3"l.imp"(less(mod(x),0),neg(mod(x)),satz264c,[t:less(mod(x),0)]satz169d(mod(x),t))):moreis(mod(x),0)
-+7265
-t1:=symis(real,ts"r"(mod(x),mod(x)),mod2(x),thsqrt1b(mod2(x),lemma5(x))):is"r"(mod2(x),ts"r"(mod(x),mod(x)))
-t2:=tris(real,pl"r"(ts"r"(re(x),re(x)),0),ts"r"(re(x),re(x)),ts"r"(abs(re(x)),abs(re(x))),pl02(ts"r"(re(x),re(x)),0,refis(real,0)),lemma12"r"(re(x))):is"r"(pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))))
-t3:=satz191(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),ts"r"(im(x),im(x)),0,moreisi2(ts"r"(re(x),re(x)),ts"r"(re(x),re(x)),refis(real,ts"r"(re(x),re(x)))),lemma11"r"(im(x))):moreis(mod2(x),pl"r"(ts"r"(re(x),re(x)),0))
-t4:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(ts"r"(re(x),re(x)),0),ts"r"(abs(re(x)),abs(re(x))),t1,t2,t3):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(re(x)),abs(re(x))))
-t5:=tris(real,pl"r"(0,ts"r"(im(x),im(x))),ts"r"(im(x),im(x)),ts"r"(abs(im(x)),abs(im(x))),pl01(0,ts"r"(im(x),im(x)),refis(real,0)),lemma12"r"(im(x))):is"r"(pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))))
-t6:=satz191(ts"r"(re(x),re(x)),0,ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),lemma11"r"(re(x)),moreisi2(ts"r"(im(x),im(x)),ts"r"(im(x),im(x)),refis(real,ts"r"(im(x),im(x))))):moreis(mod2(x),pl"r"(0,ts"r"(im(x),im(x))))
-t7:=ismoreis12(mod2(x),ts"r"(mod(x),mod(x)),pl"r"(0,ts"r"(im(x),im(x))),ts"r"(abs(im(x)),abs(im(x))),t1,t5,t6):moreis(ts"r"(mod(x),mod(x)),ts"r"(abs(im(x)),abs(im(x))))
-@[r:real][s:real][m:moreis(ts"r"(r,r),ts"r"(s,s))][n:moreis(r,0)][l:less(r,s)]
-t8:=lemma2"r"(r,s,l):more(s,r)
-t9:=satz169b(s,satz172d(s,r,0,t8,n)):pos(s)
-[o:more(r,0)]
-t10:=trmore(ts"r"(s,s),ts"r"(r,s),ts"r"(r,r),satz203a(s,r,s,t8,t9),satz203d(s,r,r,t8,satz169b(r,o))):more(ts"r"(s,s),ts"r"(r,r))
-l@[i:is"r"(r,0)]
-t11:=ismore2(0,ts"r"(r,r),ts"r"(s,s),symis(real,ts"r"(r,r),0,ts01(r,r,i)),satz169a(ts"r"(s,s),possq(s,pnot0(s,t9)))):more(ts"r"(s,s),ts"r"(r,r))
-l@t12:=lemma1"r"(ts"r"(s,s),ts"r"(r,r),orapp(more(r,0),is"r"(r,0),more(ts"r"(s,s),ts"r"(r,r)),n,[t:more(r,0)]t10(t),[t:is"r"(r,0)]t11(t))):less(ts"r"(r,r),ts"r"(s,s))
-n@t13:=satz167f(r,s,[t:less(r,s)]<t12(t)>satz167c(ts"r"(r,r),ts"r"(s,s),m)):moreis(r,s)
--7265
-satz265a:=t13".7265"(mod(x),abs(re(x)),t4".7265",satz264d(x)):moreis(mod(x),abs(re(x)))
-satz265b:=t13".7265"(mod(x),abs(im(x)),t7".7265",satz264d(x)):moreis(mod(x),abs(im(x)))
-@[r:real][s:real][i:is(ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)))][n:not(neg(r))][o:not(neg(s))]
-+7266
-@[t:real]
-t1:=pl02(ts"r"(t,t),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t))
-t2:=tris(real,pl"r"(ts"r"(t,0),ts"r"(0,t)),ts"r"(t,0),0,pl02(ts"r"(t,0),ts"r"(0,t),ts01(0,t,refis(real,0))),ts02(t,0,refis(real,0))):is"r"(pl"r"(ts"r"(t,0),ts"r"(0,t)),0)
-t3:=tris(cx,ts(pli(t,0),pli(t,0)),pli(mn"r"(ts"r"(t,t),ts"r"(0,0)),pl"r"(ts"r"(t,0),ts"r"(0,t))),pli(ts"r"(t,t),0),tsis12a(t,0,t,0),isrecx12(mn"r"(ts"r"(t,t),ts"r"(0,0)),ts"r"(t,t),pl"r"(ts"r"(t,0),ts"r"(0,t)),0,t1,t2)):is(ts(pli(t,0),pli(t,0)),pli(ts"r"(t,t),0))
-o@t4:=tr3is(cx,pli(ts"r"(r,r),0),ts(pli(r,0),pli(r,0)),ts(pli(s,0),pli(s,0)),pli(ts"r"(s,s),0),symis(cx,ts(pli(r,0),pli(r,0)),pli(ts"r"(r,r),0),t3(r)),i,t3(s)):is(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0))
-t5:=tr3is(real,ts"r"(r,r),re(pli(ts"r"(r,r),0)),re(pli(ts"r"(s,s),0)),ts"r"(s,s),isre(ts"r"(r,r),0),iscere(pli(ts"r"(r,r),0),pli(ts"r"(s,s),0),t4),reis(ts"r"(s,s),0)):is"r"(ts"r"(r,r),ts"r"(s,s))
-t6:=andi(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)),n,t5):and(not(neg(r)),is"r"(ts"r"(r,r),ts"r"(s,s)))
-t7:=andi(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)),o,refis(real,ts"r"(s,s))):and(not(neg(s)),is"r"(ts"r"(s,s),ts"r"(s,s)))
--7266
-satz266:=satzr161b(ts"r"(s,s),r,s,t6".7266",t7".7266"):is"r"(r,s)
-+7267
-x@t1:=tris(cx,ts(pli(mod(x),0),pli(mod(x),0)),pli(ts"r"(mod(x),mod(x)),0),pli(mod2(x),0),t3"c.7266"(mod(x)),isrecx1(ts"r"(mod(x),mod(x)),mod2(x),0,thsqrt1b(mod2(x),lemma5(x)))):is(ts(pli(mod(x),0),pli(mod(x),0)),pli(mod2(x),0))
-t2:=ispl2"r"(m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(im(x),im(x)),ts"r"(re(x),re(x)),tris(real,m0"r"(ts"r"(im(x),m0"r"(im(x)))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),satz197e(im(x),m0"r"(im(x))),satz198(im(x),im(x)))):is"r"(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x))
-t3:=tris(real,pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),pl"r"(m0"r"(ts"r"(re(x),im(x))),ts"r"(re(x),im(x))),0,ispl12"r"(ts"r"(re(x),m0"r"(im(x))),m0"r"(ts"r"(re(x),im(x))),ts"r"(im(x),re(x)),ts"r"(re(x),im(x)),satz197b(re(x),im(x)),comts"r"(im(x),re(x))),satz179a(ts"r"(re(x),im(x)))):is"r"(pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0)
-t4:=tris(cx,ts(x,conj(x)),pli(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x)))),pli(mod2(x),0),tsis2a(x,re(x),m0"r"(im(x))),isrecx12(mn"r"(ts"r"(re(x),re(x)),ts"r"(im(x),m0"r"(im(x)))),mod2(x),pl"r"(ts"r"(re(x),m0"r"(im(x))),ts"r"(im(x),re(x))),0,t2,t3)):is(ts(x,conj(x)),pli(mod2(x),0))
--7267
-x@satz267:=tris2(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),pli(mod2(x),0),t1".7267",t4".7267"):is(ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)))
-satz267a:=symis(cx,ts(pli(mod(x),0),pli(mod(x),0)),ts(x,conj(x)),satz267):is(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)))
-+7268
-z@t1:=tr3is(cx,ts(x,ts(y,z)),ts(ts(x,y),z),ts(ts(y,x),z),ts(y,ts(x,z)),assts2(x,y,z),ists1(ts(x,y),ts(y,x),z,comts(x,y)),assts1(y,x,z)):is(ts(x,ts(y,z)),ts(y,ts(x,z)))
-[u:complex]
-t2:=tr3is(cx,ts(ts(x,y),ts(z,u)),ts(x,ts(y,ts(z,u))),ts(x,ts(z,ts(y,u))),ts(ts(x,z),ts(y,u)),assts1(x,y,ts(z,u)),ists2(ts(y,ts(z,u)),ts(z,ts(y,u)),x,t1(y,z,u)),assts2(x,z,ts(y,u))):is(ts(ts(x,y),ts(z,u)),ts(ts(x,z),ts(y,u)))
-y@t3:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,y),conj(ts(x,y))),ts(ts(x,y),ts(conj(x),conj(y))),ts(ts(x,conj(x)),ts(y,conj(y))),satz267(ts(x,y)),ists2(conj(ts(x,y)),ts(conj(x),conj(y)),ts(x,y),satz261(x,y)),t2(x,y,conj(x),conj(y))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))))
-t4:=tr3is(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(x,conj(x)),ts(y,conj(y))),ts(ts(pli(mod(x),0),pli(mod(x),0)),ts(pli(mod(y),0),pli(mod(y),0))),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),t3,ists12(ts(x,conj(x)),ts(pli(mod(x),0),pli(mod(x),0)),ts(y,conj(y)),ts(pli(mod(y),0),pli(mod(y),0)),satz267a(x),satz267a(y)),t2(pli(mod(x),0),pli(mod(x),0),pli(mod(y),0),pli(mod(y),0))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))))
-@[r:real][s:real]
-t5:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
-t6:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
-t7:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t5,t6)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
-y@t8:=tris(cx,ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(ts(pli(mod(x),0),pli(mod(y),0)),ts(pli(mod(x),0),pli(mod(y),0))),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)),t4,ists12(ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),ts(pli(mod(x),0),pli(mod(y),0)),pli(ts"r"(mod(x),mod(y)),0),t7(mod(x),mod(y)),t7(mod(x),mod(y)))):is(ts(pli(mod(ts(x,y)),0),pli(mod(ts(x,y)),0)),ts(pli(ts"r"(mod(x),mod(y)),0),pli(ts"r"(mod(x),mod(y)),0)))
-[n:neg(ts"r"(mod(x),mod(y)))]
-t9:=orapp(and(pos(mod(x)),neg(mod(y))),and(neg(mod(x)),pos(mod(y))),con,satz196h(mod(x),mod(y),n),[t:and(pos(mod(x)),neg(mod(y)))]<ande2(pos(mod(x)),neg(mod(y)),t)>satz264c(y),[t:and(neg(mod(x)),pos(mod(y)))]<ande1(neg(mod(x)),pos(mod(y)),t)>satz264c(x)):con
--7268
-y@satz268:=satz266(mod(ts(x,y)),ts"r"(mod(x),mod(y)),t8".7268",satz264c(ts(x,y)),[t:neg(ts"r"(mod(x),mod(y)))]t9".7268"(t)):is"r"(mod(ts(x,y)),ts"r"(mod(x),mod(y)))
-satz268a:=symis(real,mod(ts(x,y)),ts"r"(mod(x),mod(y)),satz268):is"r"(ts"r"(mod(x),mod(y)),mod(ts(x,y)))
-[n:nis(y,0c)]
-+7269
-t1:=pnot0(mod(y),satz264a(y,n)):nis"r"(mod(y),0)
-t2:=tris1(real,ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),mod(ts(ov(x,y,n),y)),satz268(ov(x,y,n),y),ismod(ts(ov(x,y,n),y),x,satz240(x,y,n))):is"r"(ts"r"(mod(ov(x,y,n)),mod(y)),mod(x))
-t3:=satz204g(mod(x),mod(y),mod(ov(x,y,n)),t1,tris(real,ts"r"(mod(y),mod(ov(x,y,n))),ts"r"(mod(ov(x,y,n)),mod(y)),mod(x),comts"r"(mod(y),mod(ov(x,y,n))),t2)):is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),t1))
--7269
-satz269:=t3".7269":is"r"(mod(ov(x,y,n)),ov"r"(mod(x),mod(y),pnot0(mod(y),satz264a(y,n))))
-y@[i:is(pl(x,y),1c)]
-+7270
-@[r:real]
-t1:=th1"l.imp"(neg(r),moreis(abs(r),r),[t:neg(r)]moreisi1(abs(r),r,trmore(abs(r),0,r,satz169a(abs(r),satz166b(r,t)),lemma2"r"(r,0,satz169c(r,t)))),[t:not(neg(r))]moreisi2(abs(r),r,absnn(r,t))):moreis(abs(r),r)
-x@t2:=trmoreis(mod(x),abs(re(x)),re(x),satz265a(x),t1(re(x))):moreis(mod(x),re(x))
-i@t3:=tr3is(real,pl"r"(re(x),re(y)),re(pl(x,y)),re(1c),1rl,isre(pl"r"(re(x),re(y)),pl"r"(im(x),im(y))),iscere(pl(x,y),1c,i),reis(1rl,0)):is"r"(pl"r"(re(x),re(y)),1rl)
--7270
-satz270:=ismoreis2(pl"r"(re(x),re(y)),1rl,pl"r"(mod(x),mod(y)),t3".7270",satz191(mod(x),re(x),mod(y),re(y),t2".7270",t2".7270"(y))):moreis(pl"r"(mod(x),mod(y)),1rl)
-+7271
-y@[i:is(pl(x,y),0c)]
-t1:=satz264b(pl(x,y),i):is"r"(mod(pl(x,y)),0)
-t2:=ismoreis2(pl"r"(0,0),mod(pl(x,y)),pl"r"(mod(x),mod(y)),tris2(real,pl"r"(0,0),mod(pl(x,y)),0,pl01(0,0,refis(real,0)),t1),satz191(mod(x),0,mod(y),0,satz264d(x),satz264d(y))):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
-y@[n:nis(pl(x,y),0c)]
-t3:=pnot0(mod(pl(x,y)),satz264a(pl(x,y),n)):nis"r"(mod(pl(x,y)),0)
-t4:=tris(cx,pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),ov(pl(x,y),pl(x,y),n),1c,satz253(x,pl(x,y),y,n),satz250(pl(x,y),n)):is(pl(ov(x,pl(x,y),n),ov(y,pl(x,y),n)),1c)
-t5:=satz270(ov(x,pl(x,y),n),ov(y,pl(x,y),n),t4):moreis(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),1rl)
-fx:=ov"r"(mod(x),mod(pl(x,y)),t3):real
-fy:=ov"r"(mod(y),mod(pl(x,y)),t3):real
-t6:=ismoreis1(pl"r"(mod(ov(x,pl(x,y),n)),mod(ov(y,pl(x,y),n))),pl"r"(fx,fy),1rl,ispl12"r"(mod(ov(x,pl(x,y),n)),fx,mod(ov(y,pl(x,y),n)),fy,satz269(x,pl(x,y),n),satz269(y,pl(x,y),n)),t5):moreis(pl"r"(fx,fy),1rl)
-prl:=ts"r"(pl"r"(fx,fy),mod(pl(x,y))):real
-prr:=ts"r"(1rl,mod(pl(x,y))):real
-t7:=orapp(more(pl"r"(fx,fy),1rl),is"r"(pl"r"(fx,fy),1rl),moreis(prl,prr),t6,[t:more(pl"r"(fx,fy),1rl)]moreisi1(prl,prr,satz203a(pl"r"(fx,fy),1rl,mod(pl(x,y)),t,satz264a(pl(x,y),n))),[t:is"r"(pl"r"(fx,fy),1rl)]moreisi2(prl,prr,ists1"r"(pl"r"(fx,fy),1rl,mod(pl(x,y)),t))):moreis(prl,prr)
-t8:=tris(real,prl,pl"r"(ts"r"(fx,mod(pl(x,y))),ts"r"(fy,mod(pl(x,y)))),pl"r"(mod(x),mod(y)),disttp1"r"(fx,fy,mod(pl(x,y))),ispl12"r"(ts"r"(fx,mod(pl(x,y))),mod(x),ts"r"(fy,mod(pl(x,y))),mod(y),satz204e(mod(x),mod(pl(x,y)),t3),satz204e(mod(y),mod(pl(x,y)),t3))):is"r"(prl,pl"r"(mod(x),mod(y)))
-t9:=satz195b(mod(pl(x,y))):is"r"(prr,mod(pl(x,y)))
-t10:=ismoreis12(prl,pl"r"(mod(x),mod(y)),prr,mod(pl(x,y)),t8,t9,t7):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
-y@t11:=th1"l.imp"(is(pl(x,y),0c),moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y))),[t:is(pl(x,y),0c)]t2(t),[t:nis(pl(x,y),0c)]t10(t)):moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
--7271
-y@satz271:=satz168a(pl"r"(mod(x),mod(y)),mod(pl(x,y)),t11".7271"):lessis(mod(pl(x,y)),pl"r"(mod(x),mod(y)))
-satz271a:=t11".7271":moreis(pl"r"(mod(x),mod(y)),mod(pl(x,y)))
-+7272
-x@t1:=tris(real,re(m0(x)),re(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(re(x)),iscere(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),reis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(re(m0(x)),m0"r"(re(x)))
-t2:=tris(real,ts"r"(re(m0(x)),re(m0(x))),ts"r"(m0"r"(re(x)),m0"r"(re(x))),ts"r"(re(x),re(x)),ists12"r"(re(m0(x)),m0"r"(re(x)),re(m0(x)),m0"r"(re(x)),t1,t1),satz198(re(x),re(x))):is"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)))
-t3:=tris(real,im(m0(x)),im(pli(m0"r"(re(x)),m0"r"(im(x)))),m0"r"(im(x)),isceim(m0(x),pli(m0"r"(re(x)),m0"r"(im(x))),satz214(x)),imis(m0"r"(re(x)),m0"r"(im(x)))):is"r"(im(m0(x)),m0"r"(im(x)))
-t4:=tris(real,ts"r"(im(m0(x)),im(m0(x))),ts"r"(m0"r"(im(x)),m0"r"(im(x))),ts"r"(im(x),im(x)),ists12"r"(im(m0(x)),m0"r"(im(x)),im(m0(x)),m0"r"(im(x)),t3,t3),satz198(im(x),im(x))):is"r"(ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)))
-t5:=ispl12"r"(ts"r"(re(m0(x)),re(m0(x))),ts"r"(re(x),re(x)),ts"r"(im(m0(x)),im(m0(x))),ts"r"(im(x),im(x)),t2,t4):is"r"(mod2(m0(x)),mod2(x))
--7272
-x@satz272:=issqrt(mod2(m0(x)),mod2(x),lemma5(m0(x)),lemma5(x),t5".7272"):is"r"(mod(m0(x)),mod(x))
-satz272a:=symis(real,mod(m0(x)),mod(x),satz272):is"r"(mod(x),mod(m0(x)))
-+7273
-y@sum:=pl"r"(mod(y),mod(mn(x,y))):real
-t1:=islessis1(mod(pl(y,mn(x,y))),mod(x),sum,ismod(pl(y,mn(x,y)),x,satz212h(x,y)),satz271(y,mn(x,y))):lessis(mod(x),sum)
-t2:=th9"l.or"(less(mod(x),sum),is"r"(mod(x),sum),less(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),is"r"(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y))),t1,[t:less(mod(x),sum)]satz188f(mod(x),sum,m0"r"(mod(y)),t),[t:is"r"(mod(x),sum)]ismn1"r"(mod(x),sum,mod(y),t)):lessis(mn"r"(mod(x),mod(y)),mn"r"(sum,mod(y)))
-t3:=tris(real,mn"r"(sum,mod(y)),mn"r"(pl"r"(mod(mn(x,y)),mod(y)),mod(y)),mod(mn(x,y)),ismn1"r"(sum,pl"r"(mod(mn(x,y)),mod(y)),mod(y),compl"r"(mod(y),mod(mn(x,y)))),mnpl(mod(mn(x,y)),mod(y))):is"r"(mn"r"(sum,mod(y)),mod(mn(x,y)))
-t4:=satz168b(mn"r"(mod(x),mod(y)),mod(mn(x,y)),islessis2(mn"r"(sum,mod(y)),mod(mn(x,y)),mn"r"(mod(x),mod(y)),t3,t2)):moreis(mod(mn(x,y)),mn"r"(mod(x),mod(y)))
-t5:=ismoreis12(mod(mn(y,x)),mod(mn(x,y)),mn"r"(mod(y),mod(x)),m0"r"(mn"r"(mod(x),mod(y))),tris1(real,mod(mn(y,x)),mod(mn(x,y)),mod(m0(mn(x,y))),ismod(m0(mn(x,y)),mn(y,x),satz219(x,y)),satz272(mn(x,y))),satz181a(mod(y),mod(x)),t4(y,x)):moreis(mod(mn(x,y)),m0"r"(mn"r"(mod(x),mod(y))))
-@[r:real][s:real][m:moreis(r,s)][n:moreis(r,m0"r"(s))]
-r@t6:=th9"l.or"(neg(r),not(neg(r)),is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r),th6"l.or"(neg(r)),[t:neg(r)]absn(r,t),[t:not(neg(r))]absnn(r,t)):or(is"r"(abs(r),m0"r"(r)),is"r"(abs(r),r))
-n@t7:=orapp(is"r"(abs(s),m0"r"(s)),is"r"(abs(s),s),moreis(r,abs(s)),t6(s),[t:is"r"(abs(s),m0"r"(s))]ismoreis2(m0"r"(s),abs(s),r,symis(real,abs(s),m0"r"(s),t),n),[t:is"r"(abs(s),s)]ismoreis2(s,abs(s),r,symis(real,abs(s),s,t),m)):moreis(r,abs(s))
--7273
-y@satz273:=t7".7273"(mod(mn(x,y)),mn"r"(mod(x),mod(y)),t4".7273",t5".7273"):moreis(mod(mn(x,y)),abs(mn"r"(mod(x),mod(y))))
--c
--r
--rp
--rt
-@[x:nat][y:nat]
-+8274
-prop1:=some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)):'prop'
-x@prop2:=all([y:nat]imp(less(x,y),not(prop1(y)))):'prop'
-@[y:nat][l:less(1,y)][f:[t:1to(1)]1to(y)]
-1y:=1out(y):1to(y)
-yy:=xout(y):1to(y)
-[i:is"e"(1to(y),1y,yy)]
-t1:=isoutne(y,1,satz24a(y),y,lessisi3(y),i):is(1,y)
-f@t2:=ec3e31(is(1,y),more(1,y),less(1,y),satz10b(1,y),l):nis(1,y)
-t3:=th3"l.imp"(is"e"(1to(y),1y,yy),is(1,y),t2,[t:is"e"(1to(y),1y,yy)]t1(t)):not(is"e"(1to(y),1y,yy))
-[u:1to(1)]
-t4:=isf(1to(1),1to(y),f,u,1o,th1"n.singlet"(u)):is"e"(1to(y),<u>f,<1o>f)
-f@[i:is"e"(1to(y),<1o>f,1y)][u:1to(1)]
-t5:=th2"e.notis"(1to(y),1y,yy,<u>f,t3,tris(1to(y),<u>f,<1o>f,1y,t4(u),i)):not(is"e"(1to(y),<u>f,yy))
-i@t6:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),yy,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,yy,t5(u))):not(image(1to(1),1to(y),f,yy))
-t7:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),yy,t6):not(surjective(1to(1),1to(y),f))
-f@[n:not(is"e"(1to(y),<1o>f,1y))][u:1to(1)]
-t8:=th2"e.notis"(1to(y),<1o>f,1y,<u>f,n,t4(u)):not(is"e"(1to(y),<u>f,1y))
-n@t9:=th5"l.some"(1to(1),[u:1to(1)]is"e"(1to(y),1y,<u>f),[u:1to(1)]symnotis(1to(y),<u>f,1y,t8(u))):not(image(1to(1),1to(y),f,1y))
-t10:=th1"l.all"(1to(y),[u:1to(y)]image(1to(1),1to(y),f,u),1y,t9):not(surjective(1to(1),1to(y),f))
-f@t11:=th1"l.imp"(is"e"(1to(y),<1o>f,1y),not(surjective(1to(1),1to(y),f)),[t:is"e"(1to(y),<1o>f,1y)]t7(t),[t:not(is"e"(1to(y),<1o>f,1y))]t10(t)):not(surjective(1to(1),1to(y),f))
-t12:=th2"l.and"(injective(1to(1),1to(y),f),surjective(1to(1),1to(y),f),t11):not(bijective(1to(1),1to(y),f))
-l@t13:=th5"l.some"([t:1to(1)]1to(y),[f:[t:1to(1)]1to(y)]bijective(1to(1),1to(y),f),[f:[t:1to(1)]1to(y)]t12(f)):not(prop1(1,y))
-@t14:=[y:nat][t:less(1,y)]t13(y,t):prop2(1)
-x@[p:prop2(x)][y:nat][l:less(<x>suc,y)]
-x@xs:=<x>suc:nat
-l@xxs:=xout(xs):1to(<x>suc)
-yy1:=xout(y):1to(y)
-t15:=trless(1,<x>suc,y,satz24c(x),l):less(1,y)
-ym1:=mn(y,1,t15):nat
-t16:=isless12(<x>suc,pl(x,1),y,pl(ym1,1),satz4e(x),th1c"n.mn"(y,1,t15),l):less(pl(x,1),pl(ym1,1))
-t17:=satz20c(x,ym1,1,t16):less(x,ym1)
-t18:=isless2(pl(ym1,1),y,ym1,th1d"n.mn"(y,1,t15),satz18a(ym1,1)):less(ym1,y)
-[f:[t:1to(xs)]1to(y)][b:bijective(1to(xs),1to(y),f)]
-t19:=ande1(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):injective(1to(xs),1to(y),f)
-t20:=ande2(injective(1to(xs),1to(y),f),surjective(1to(xs),1to(y),f),b):surjective(1to(xs),1to(y),f)
-[i:is"e"(1to(y),<xxs>f,yy1)][u:1to(x)]
-u1:=inn(x,u):nat
-t21:=satz16a(u1,x,xs,1top(x,u),satz18c(x)):less(u1,xs)
-t22:=ec3e31(is(u1,xs),more(u1,xs),less(u1,xs),satz10b(u1,xs),t21):nis(u1,xs)
-t23:=lessisi1(u1,xs,t21):lessis(u1,xs)
-u2:=outn(xs,u1,t23):1to(xs)
-t24:=th3"l.imp"(is"e"(1to(xs),u2,xxs),is(u1,xs),t22,[t:is"e"(1to(xs),u2,xxs)]isoutne(xs,u1,t23,xs,lessisi3(xs),t)):not(is"e"(1to(xs),u2,xxs))
-[j:is"e"(1to(y),<u2>f,yy1)]
-t25:=tris2(1to(y),<u2>f,<xxs>f,yy1,j,i):is"e"(1to(y),<u2>f,<xxs>f)
-t26:=isfe(1to(xs),1to(y),f,t19,u2,xxs,t25):is"e"(1to(xs),u2,xxs)
-u@t27:=th3"l.imp"(is"e"(1to(y),<u2>f,yy1),is"e"(1to(xs),u2,xxs),t24,[t:is"e"(1to(y),<u2>f,yy1)]t26(t)):not(is"e"(1to(y),<u2>f,yy1))
-w1:=inn(y,<u2>f):nat
-[j:is(w1,y)]
-t28:=tris(1to(y),<u2>f,outn(y,w1,1top(y,<u2>f)),yy1,isoutinn(y,<u2>f),isoutni(y,w1,1top(y,<u2>f),y,lessisi3(y),j)):is"e"(1to(y),<u2>f,yy1)
-u@t29:=th3"l.imp"(is(w1,y),is"e"(1to(y),<u2>f,yy1),t27,[t:is(w1,y)]t28(t)):nis(w1,y)
-t30:=ore1(less(w1,y),is(w1,y),1top(y,<u2>f),t29):less(w1,y)
-t31:=islessis2(y,pl(ym1,1),pl(w1,1),th1c"n.mn"(y,1,t15),satz25b(y,w1,t30)):lessis(pl(w1,1),pl(ym1,1))
-t32:=th9"l.or"(less(pl(w1,1),pl(ym1,1)),is(pl(w1,1),pl(ym1,1)),less(w1,ym1),is(w1,ym1),t31,[t:less(pl(w1,1),pl(ym1,1))]satz20c(w1,ym1,1,t),[t:is(pl(w1,1),pl(ym1,1))]satz20b(w1,ym1,1,t)):lessis(w1,ym1)
-w2:=outn(ym1,w1,t32):1to(ym1)
-i@f1:=[t:1to(x)]w2(t):[t:1to(x)]1to(ym1)
-u@[v:1to(x)][j:is"e"(1to(ym1),<u>f1,<v>f1)]
-t33:=isoutne(ym1,w1(u),t32(u),w1(v),t32(v),j):is(w1(u),w1(v))
-t34:=isinne(y,<u2(u)>f,<u2(v)>f,t33):is"e"(1to(y),<u2(u)>f,<u2(v)>f)
-t35:=<t34><u2(v)><u2(u)>t19:is"e"(1to(xs),u2(u),u2(v))
-t36:=isoutne(xs,u1(u),t23(u),u1(v),t23(v),t35):is(u1(u),u1(v))
-t37:=isinne(x,u,v,t36):is"e"(1to(x),u,v)
-i@[v:1to(ym1)]
-v1:=inn(ym1,v):nat
-t38:=satz16a(v1,ym1,y,1top(ym1,v),t18):less(v1,y)
-t39:=ec3e31(is(v1,y),more(v1,y),less(v1,y),satz10b(v1,y),t38):nis(v1,y)
-t40:=lessisi1(v1,y,t38):lessis(v1,y)
-v2:=outn(y,v1,t40):1to(y)
-w3:=<v2>invf(1to(xs),1to(y),f,b):1to(xs)
-t41:=thinvf2(1to(xs),1to(y),f,b,v2):is"e"(1to(y),v2,<w3>f)
-[j:is"e"(1to(xs),w3,xxs)]
-t42:=isf(1to(xs),1to(y),f,w3,xxs,j):is"e"(1to(y),<w3>f,<xxs>f)
-t43:=tr3is(1to(y),v2,<w3>f,<xxs>f,yy1,t41,t42,i):is"e"(1to(y),v2,yy1)
-t44:=isoutne(y,v1,t40,y,lessisi3(y),t43):is(v1,y)
-v@t45:=th3"l.imp"(is"e"(1to(xs),w3,xxs),is(v1,y),t39,[t:is"e"(1to(xs),w3,xxs)]t44(t)):not(is"e"(1to(xs),w3,xxs))
-w4:=inn(xs,w3):nat
-[j:is(w4,xs)]
-t46:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),xxs,isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),xs,lessisi3(xs),j)):is"e"(1to(xs),w3,xxs)
-v@t47:=th3"l.imp"(is(w4,xs),is"e"(1to(xs),w3,xxs),t45,[t:is(w4,xs)]t46(t)):nis(w4,xs)
-t48:=ore1(less(w4,xs),is(w4,xs),1top(xs,w3),t47):less(w4,xs)
-t49:=satz26a(x,w4,t48):lessis(w4,x)
-w5:=outn(x,w4,t49):1to(x)
-t50:=isinoutn(x,w4,t49):is(w4,u1(w5))
-t51:=tris(1to(xs),w3,outn(xs,w4,1top(xs,w3)),u2(w5),isoutinn(xs,w3),isoutni(xs,w4,1top(xs,w3),u1(w5),t23(w5),t50)):is"e"(1to(xs),w3,u2(w5))
-t52:=isf(1to(xs),1to(y),f,w3,u2(w5),t51):is"e"(1to(y),<w3>f,<u2(w5)>f)
-t53:=tris(1to(y),v2,<w3>f,<u2(w5)>f,t41,t52):is"e"(1to(y),v2,<u2(w5)>f)
-t54:=tris(nat,v1,inn(y,v2),w1(w5),isinoutn(y,v1,t40),isinni(y,v2,<u2(w5)>f,t53)):is(v1,w1(w5))
-t55:=tris(1to(ym1),v,outn(ym1,v1,1top(ym1,v)),w2(w5),isoutinn(ym1,v),isoutni(ym1,v1,1top(ym1,v),w1(w5),t32(w5),t54)):is"e"(1to(ym1),v,<w5>f1)
-t56:=somei(1to(x),[t:1to(x)]is"e"(1to(ym1),v,<t>f1),w5,t55):image(1to(x),1to(ym1),f1,v)
-i@t57:=andi(injective(1to(x),1to(ym1),f1),surjective(1to(x),1to(ym1),f1),[u:1to(x)][v:1to(x)][t:is"e"(1to(ym1),<u>f1,<v>f1)]t37(u,v,t),[u:1to(ym1)]t56(u)):bijective(1to(x),1to(ym1),f1)
-t58:=somei([t:1to(x)]1to(ym1),[g:[t:1to(x)]1to(ym1)]bijective(1to(x),1to(ym1),g),f1,t57):prop1(ym1)
-t59:=<t58><t17><ym1>p:con
-b@[n:not(is"e"(1to(y),<xxs>f,yy1))]
-m0:=<yy1>invf(1to(xs),1to(y),f,b):1to(xs)
-t60:=thinvf2(1to(xs),1to(y),f,b,yy1):is"e"(1to(y),yy1,<m0>f)
-f2:=changef(1to(xs),1to(y),f,m0,xxs):[t:1to(xs)]1to(y)
-t61:=changef2(1to(xs),1to(y),f,m0,xxs,xxs,refis(1to(xs),xxs)):is"e"(1to(y),<xxs>f2,<m0>f)
-t62:=tris2(1to(y),<xxs>f2,yy1,<m0>f,t61,t60):is"e"(1to(y),<xxs>f2,yy1)
-t63:=th6"e.wissel"(1to(xs),1to(y),f,m0,xxs,b):bijective(1to(xs),1to(y),f2)
-t64:=t59(f2,t63,t62):con
-b@t65:=th1"l.imp"(is"e"(1to(y),<xxs>f,yy1),con,[t:is"e"(1to(y),<xxs>f,yy1)]t59(t),[t:not(is"e"(1to(y),<xxs>f,yy1))]t64(t)):con
-l@t65a:=th5"l.some"([t:1to(xs)]1to(y),[f:[t:1to(xs)]1to(y)]bijective(1to(xs),1to(y),f),[f:[t:1to(xs)]1to(y)][t:bijective(1to(xs),1to(y),f)]t65(f,t)):not(prop1(xs,y))
-p@t66:=[y:nat][t:less(xs,y)]t65a(y,t):prop2(xs)
-x@t67:=induction([t:nat]prop2(t),t14,[t:nat][u:prop2(t)]t66(t,u),x):prop2(x)
--8274
-[l:less(x,y)]
-satz274:=<l><y>t67".8274":not(some"l"([t:1to(x)]1to(y),[f:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),f)))
-[f:[t:1to(x)]1to(y)]
-satz274a:=th4"l.some"([t:1to(x)]1to(y),[g:[t:1to(x)]1to(y)]bijective(1to(x),1to(y),g),satz274,f):not(bijective(1to(x),1to(y),f))
-+*rt
-+*rp
-+*r
-+*c
-@[x:nat][u:1to(x)]
-inn:=inn"n"(x,u):nat
-@[q:[t:cx][u:cx]cx][x:nat][f:[t:1to(x)]cx]
-x@[n:1to(x)][o:not(is"e"(1to(x),n,xout(x)))]
-+8275
-t1:=th3"l.imp"(is"n"(inn(x,n),x),is"e"(1to(x),n,xout(x)),o,[t:is"n"(inn(x,n),x)]tris(1to(x),n,outn(x,inn(x,n),1top(x,n)),xout(x),isoutinn(x,n),isoutni(x,inn(x,n),1top(x,n),x,lessisi3(x),t))):not(is"n"(inn(x,n),x))
-t2:=ore1(less"n"(inn(x,n),x),is"n"(inn(x,n),x),1top(x,n),t1):less"n"(inn(x,n),x)
--8275
-lemma275:=satz25c(x,inn(x,n),t2".8275"):lessis"n"(<inn(x,n)>suc,x)
-f@[g:[t:1to(x)]cx]
-recprop:=and(is(<1out(x)>g,<1out(x)>f),[t:1to(x)][u:not(is"e"(1to(x),t,xout(x)))]is(<outn(x,<inn(x,t)>suc,lemma275(t,u))>g,<<outn(x,<inn(x,t)>suc,lemma275(t,u))>f><<t>g>q)):'prop'
-+*8275
-x@1o:=1out(x):1to(x)
-xo:=xout(x):1to(x)
-[u:nat][l:lessis"n"(<u>suc,x)]
-t11:=satz16b(u,<u>suc,x,satz18c(u),l):less"n"(u,x)
-t12:=lessisi1"n"(u,x,t11):lessis"n"(u,x)
-ux:=outn(x,u,t12):1to(x)
-t13:=ec3e31(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11):nis"n"(u,x)
-t14:=th3"l.imp"(is"e"(1to(x),ux,xo),is"n"(u,x),t13,[t:is"e"(1to(x),ux,xo)]isoutne(x,u,t12,x,lessisi3(x),t)):not(is"e"(1to(x),ux,xo))
-t15:=isf(nat,nat,suc,u,inn(x,ux),isinoutn(x,u,t12)):is"n"(<u>suc,<inn(x,ux)>suc)
-t16:=isoutni(x,<u>suc,l,<inn(x,ux)>suc,lemma275(ux,t14),t15):is"e"(1to(x),outn(x,<u>suc,l),outn(x,<inn(x,ux)>suc,lemma275(ux,t14)))
-x@[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
-ns:=outn(x,<inn(x,n)>suc,lemma275(n,o)):1to(x)
-f@[g:[t:1to(x)]cx]
-prop1:=is(<1o>g,<1o>f):'prop'
-prop2:=[t:1to(x)][u:not(is"e"(1to(x),t,xo))]is(<ns(t,u)>g,<<ns(t,u)>f><<t>g>q):'prop'
-[pg:recprop(g)]
-t3:=ande1(prop1,prop2,pg):prop1
-[n:1to(x)][o:not(is"e"(1to(x),n,xo))]
-t4:=<o><n>ande2(prop1,prop2,pg):is(<ns(n,o)>g,<<ns(n,o)>f><<n>g>q)
-pg@[u:nat][l:lessis"n"(<u>suc,x)]
-t17:=isf(1to(x),cx,g,outn(x,<u>suc,l),ns(ux(u,l),t14(u,l)),t16(u,l)):is(<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g)
-t18:=tris(cx,<outn(x,<u>suc,l)>g,<ns(ux(u,l),t14(u,l))>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,t17,t4(pg,ux(u,l),t14(u,l))):is(<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q)
-g@[h:[t:1to(x)]cx][u:nat][l:lessis"n"(u,x)]
-prop3:=is(<outn(x,u,l)>g,<outn(x,u,l)>h):'prop'
-u@prop4:=and(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(t)):'prop'
-prop5:=or(prop4,more"n"(u,x)):'prop'
-h@[pg:recprop(g)][ph:recprop(h)][l:lessis"n"(1,x)]
-t5:=isoutni(x,1,l,1,satz24a(x),refis(nat,1)):is"e"(1to(x),outn(x,1,l),1o)
-t6:=isf(1to(x),cx,g,outn(x,1,l),1o,t5):is(<outn(x,1,l)>g,<1o>g)
-t7:=tris(cx,<outn(x,1,l)>g,<1o>g,<1o>f,t6,t3(pg)):is(<outn(x,1,l)>g,<1o>f)
-t8:=tris2(cx,<outn(x,1,l)>g,<outn(x,1,l)>h,<1o>f,t7,t7(h,g,ph,pg,l)):prop3(1,l)
-ph@t9:=andi(lessis"n"(1,x),[t:lessis"n"(1,x)]prop3(1,t),satz24a(x),[t:lessis"n"(1,x)]t8(t)):prop4(1)
-t10:=ori1(prop4(1),more"n"(1,x),t9):prop5(1)
-[u:nat][p:prop5(u)][l:lessis"n"(<u>suc,x)]
-t19:=ec3e32(is"n"(u,x),more"n"(u,x),less"n"(u,x),satz10b(u,x),t11(u,l)):not(more"n"(u,x))
-t20:=ore1(prop4(u),more"n"(u,x),p,t19):prop4(u)
-t21:=<t12(u,l)>ande2(lessis"n"(u,x),[t:lessis"n"(u,x)]prop3(u,t),t20):prop3(u,t12(u,l))
-t22:=isf(cx,cx,[t:cx]<<ns(ux(u,l),t14(u,l))>f><t>q,<ux(u,l)>g,<ux(u,l)>h,t21):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q)
-t23:=symis(cx,<outn(x,<u>suc,l)>h,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,t18(h,ph,u,l)):is(<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h)
-t24:=tr3is(cx,<outn(x,<u>suc,l)>g,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>g>q,<<ns(ux(u,l),t14(u,l))>f><<ux(u,l)>h>q,<outn(x,<u>suc,l)>h,t18(g,pg,u,l),t22,t23):prop3(<u>suc,l)
-t25:=andi(lessis"n"(<u>suc,x),[t:lessis"n"(<u>suc,x)]prop3(<u>suc,t),l,[t:lessis"n"(<u>suc,x)]t24(t)):prop4(<u>suc)
-t26:=ori1(prop4(<u>suc),more"n"(<u>suc,x),t25):prop5(<u>suc)
-p@[n:not(lessis"n"(<u>suc,x))]
-t27:=satz10k(<u>suc,x,n):more"n"(<u>suc,x)
-t28:=ori2(prop4(<u>suc),more"n"(<u>suc,x),t27):prop5(<u>suc)
-p@t29:=th1"l.imp"(lessis"n"(<u>suc,x),prop5(<u>suc),[t:lessis"n"(<u>suc,x)]t26(t),[t:not(lessis"n"(<u>suc,x))]t28(t)):prop5(<u>suc)
-u@t30:=induction([v:nat]prop5(v),t10,[v:nat][t:prop5(v)]t29(v,t),u):prop5(u)
-ph@[n:1to(x)]
-t31:=isf(1to(x),cx,g,n,outn(x,inn(x,n),1top(x,n)),isoutinn(x,n)):is(<n>g,<outn(x,inn(x,n),1top(x,n))>g)
-t32:=satz10d(inn(x,n),x,1top(x,n)):not(more"n"(inn(x,n),x))
-t33:=ore1(prop4(inn(x,n)),more"n"(inn(x,n),x),t30(inn(x,n)),t32):prop4(inn(x,n))
-t34:=<1top(x,n)>ande2(lessis"n"(inn(x,n),x),[t:lessis"n"(inn(x,n),x)]prop3(inn(x,n),t),t33):prop3(inn(x,n),1top(x,n))
-t35:=symis(cx,<n>h,<outn(x,inn(x,n),1top(x,n))>h,t31(h,g,ph,pg,n)):is(<outn(x,inn(x,n),1top(x,n))>h,<n>h)
-t36:=tr3is(cx,<n>g,<outn(x,inn(x,n),1top(x,n))>g,<outn(x,inn(x,n),1top(x,n))>h,<n>h,t31,t34,t35):is(<n>g,<n>h)
-ph@t37:=fisi(1to(x),cx,g,h,[t:1to(x)]t36(t)):is"e"([t:1to(x)]cx,g,h)
-f@prop6:=some"l"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(g)):'prop'
-x@prop7:=all"l"([t:1to(x)]cx,[f:[t:1to(x)]cx]prop6(f)):'prop'
-q@[f:[t:1to(1)]cx]
-t38:=refis(cx,<1o(1)>f):prop1(1,f,f)
-[n:1to(1)][o:not(is"e"(1to(1),n,xo(1)))]
-t39:=<th1"n.singlet"(n)>o:con
-t40:=cone(is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q),t39):is(<ns(1,n,o)>f,<<ns(1,n,o)>f><<n>f>q)
-f@t41:=andi(prop1(1,f,f),prop2(1,f,f),t38,[t:1to(1)][u:not(is"e"(1to(1),t,xo(1)))]t40(t,u)):recprop(1,f,f)
-t42:=somei([t:1to(1)]cx,[g:[t:1to(1)]cx]recprop(1,f,g),f,t41):prop6(1,f)
-q@t43:=[f:[t:1to(1)]cx]t42(f):prop7(1)
-x@[p:prop7(x)]
-xs:=<x>suc:nat
-[f:[t:1to(xs)]cx]
-f1:=left(cx,xs,x,lessisi1"n"(x,xs,satz18c(x)),f):[t:1to(x)]cx
-t44:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f1,g)][v:recprop(x,f1,h)]t37(f1,g,h,u,v),<f1>p):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g))
-g1:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):[t:1to(x)]cx
-t45:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f1,g),t44):recprop(x,f1,g1)
-[n:1to(xs)]
-nxs:=is"e"(1to(xs),n,xo(xs)):'prop'
-[o:not(nxs)]
-t46:=satz26a(x,inn(xs,n),t2(xs,n,o)):lessis"n"(inn(xs,n),x)
-n1:=outn(x,inn(xs,n),t46):1to(x)
-b:=<n1>g1:cx
-[o1:not(nxs)]
-t47:=isoutni(x,inn(xs,n),t46(o),inn(xs,n),t46(o1),refis(nat,inn(xs,n))):is"e"(1to(x),n1(o),n1(o1))
-t48:=isf(1to(x),cx,g1,n1(o),n1(o1),t47):is(b(o),b(o1))
-f@a:=<<xo(xs)>f><<xo(x)>g1>q:cx
-n@c:=ite"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u)):cx
-[i:nxs]
-t49:=itet"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),i):is(c,a)
-o@t50:=itef"l.r"(nxs,cx,[t:nxs]a,[t:not(nxs)]b(t),[t:nxs][u:nxs]refis(cx,a),[t:not(nxs)][u:not(nxs)]t48(t,u),o):is(c,b)
-f@g2:=[t:1to(xs)]c(t):[t:1to(xs)]cx
-t51:=th3"l.imp"(is"e"(1to(xs),1o(xs),xo(xs)),is"n"(1,xs),symnotis(nat,xs,1,<x>ax3),[t:is"e"(1to(xs),1o(xs),xo(xs))]isoutne(xs,1,satz24a(xs),xs,lessisi3(xs),t)):not(is"e"(1to(xs),1o(xs),xo(xs)))
-t52:=t50(1o(xs),t51):is(c(1o(xs)),b(1o(xs),t51))
-t53:=isinoutn(xs,1,satz24a(xs)):is"n"(1,inn(xs,1o(xs)))
-t54:=isoutni(x,1,satz24a(x),inn(xs,1o(xs)),t46(1o(xs),t51),t53):is"e"(1to(x),1o(x),n1(1o(xs),t51))
-t55:=isf(1to(x),cx,g1,1o(x),n1(1o(xs),t51),t54):is(<1o(x)>g1,b(1o(xs),t51))
-t56:=tris2(cx,c(1o(xs)),<1o(x)>g1,b(1o(xs),t51),t52,t55):is(c(1o(xs)),<1o(x)>g1)
-t57:=tris(cx,c(1o(xs)),<1o(x)>g1,<1o(x)>f1,t56,t3(x,f1,g1,t45)):is(c(1o(xs)),<1o(x)>f1)
-t58:=isinoutn(x,1,satz24a(x)):is"n"(1,inn(x,1o(x)))
-t59:=isoutni(xs,1,satz24a(xs),inn(x,1o(x)),trlessis"n"(inn(x,1o(x)),x,xs,1top(x,1o(x)),lessisi1"n"(x,xs,satz18c(x))),t58):is"e"(1to(xs),1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)))
-t60:=isf(1to(xs),cx,f,1o(xs),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),1o(x)),t59):is(<1o(xs)>f,<1o(x)>f1)
-t61:=tris2(cx,c(1o(xs)),<1o(xs)>f,<1o(x)>f1,t57,t60):prop1(xs,f,g2)
-o@[i:is"e"(1to(xs),ns(xs,n,o),xo(xs))]
-t62:=isoutne(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),i):is"n"(<inn(xs,n)>suc,xs)
-t63:=<t62><x><inn(xs,n)>ax4:is"n"(inn(xs,n),x)
-t64:=isoutni(x,inn(xs,n),t46,x,lessisi3(x),t63):is"e"(1to(x),n1,xo(x))
-t65:=isf(1to(x),cx,g1,xo(x),n1,symis(1to(x),n1,xo(x),t64)):is(<xo(x)>g1,b)
-t66:=tris2(cx,<xo(x)>g1,c,b,t65,t50):is(<xo(x)>g1,c)
-t67:=isf(cx,cx,[t:cx]<<xo(xs)>f><t>q,<xo(x)>g1,c,t66):is(a,<<xo(xs)>f><c>q)
-t68:=isf(1to(xs),cx,f,xo(xs),ns(xs,n,o),symis(1to(xs),ns(xs,n,o),xo(xs),i)):is(<xo(xs)>f,<ns(xs,n,o)>f)
-t69:=isf(cx,cx,<c>q,<xo(xs)>f,<ns(xs,n,o)>f,t68):is(<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q)
-t70:=tr3is(cx,c(ns(xs,n,o)),a,<<xo(xs)>f><c>q,<<ns(xs,n,o)>f><c>q,t49(ns(xs,n,o),i),t67,t69):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
-o@[o1:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))][i:is"e"(1to(x),n1,xo(x))]
-t71:=isoutne(x,inn(xs,n),t46,x,lessisi3(x),i):is"n"(inn(xs,n),x)
-t72:=ax2(inn(xs,n),x,t71):is"n"(<inn(xs,n)>suc,xs)
-t73:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),xs,lessisi3(xs),t72):is"e"(1to(xs),ns(xs,n,o),xo(xs))
-o1@t74:=th3"l.imp"(is"e"(1to(x),n1,xo(x)),is"e"(1to(xs),ns(xs,n,o),xo(xs)),o1,[t:is"e"(1to(x),n1,xo(x))]t73(t)):not(is"e"(1to(x),n1,xo(x)))
-t75:=isinoutn(x,inn(xs,n),t46):is"n"(inn(xs,n),inn(x,n1))
-t76:=ax2(inn(xs,n),inn(x,n1),t75):is"n"(<inn(xs,n)>suc,<inn(x,n1)>suc)
-t77:=isinoutn(xs,<inn(xs,n)>suc,lemma275(xs,n,o)):is"n"(<inn(xs,n)>suc,inn(xs,ns(xs,n,o)))
-t78:=tris1(nat,inn(xs,ns(xs,n,o)),<inn(x,n1)>suc,<inn(xs,n)>suc,t77,t76):is"n"(inn(xs,ns(xs,n,o)),<inn(x,n1)>suc)
-t79:=isoutni(x,inn(xs,ns(xs,n,o)),t46(ns(xs,n,o),o1),<inn(x,n1)>suc,lemma275(x,n1,t74),t78):is"e"(1to(x),n1(ns(xs,n,o),o1),ns(n1,t74))
-t80:=isf(1to(x),cx,g1,n1(ns(xs,n,o),o1),ns(n1,t74),t79):is(b(ns(xs,n,o),o1),<ns(n1,t74)>g1)
-t81:=isinoutn(x,<inn(x,n1)>suc,lemma275(x,n1,t74)):is"n"(<inn(x,n1)>suc,inn(x,ns(n1,t74)))
-t82:=tris(nat,<inn(xs,n)>suc,<inn(x,n1)>suc,inn(x,ns(n1,t74)),t76,t81):is"n"(<inn(xs,n)>suc,inn(x,ns(n1,t74)))
-t83:=isoutni(xs,<inn(xs,n)>suc,lemma275(xs,n,o),inn(x,ns(n1,t74)),trlessis"n"(inn(x,ns(n1,t74)),x,xs,1top(x,ns(n1,t74)),lessisi1"n"(x,xs,satz18c(x))),t82):is"e"(1to(xs),ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)))
-t84:=isf(1to(xs),cx,f,ns(xs,n,o),left1to(xs,x,lessisi1"n"(x,xs,satz18c(x)),ns(n1,t74)),t83):is(<ns(xs,n,o)>f,<ns(n1,t74)>f1)
-t85:=isf(cx,cx,<b>q,<ns(xs,n,o)>f,<ns(n1,t74)>f1,t84):is(<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q)
-t86:=isf(cx,cx,[t:cx]<<ns(xs,n,o)>f><t>q,c,b,t50):is(<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q)
-t87:=tr3is(cx,c(ns(xs,n,o)),b(ns(xs,n,o),o1),<ns(n1,t74)>g1,<<ns(n1,t74)>f1><b>q,t50(ns(xs,n,o),o1),t80,t4(f1,g1,t45,n1,t74)):is(c(ns(xs,n,o)),<<ns(n1,t74)>f1><b>q)
-t88:=tris(cx,<<ns(xs,n,o)>f><c>q,<<ns(xs,n,o)>f><b>q,<<ns(n1,t74)>f1><b>q,t86,t85):is(<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q)
-t89:=tris2(cx,c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q,<<ns(n1,t74)>f1><b>q,t87,t88):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
-o@t90:=th1"l.imp"(is"e"(1to(xs),ns(xs,n,o),xo(xs)),is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q),[t:is"e"(1to(xs),ns(xs,n,o),xo(xs))]t70(t),[t:not(is"e"(1to(xs),ns(xs,n,o),xo(xs)))]t89(t)):is(c(ns(xs,n,o)),<<ns(xs,n,o)>f><c>q)
-f@t91:=[t:1to(xs)][u:not(nxs(t))]t90(t,u):prop2(xs,f,g2)
-t92:=andi(prop1(xs,f,g2),prop2(xs,f,g2),t61,t91):recprop(xs,f,g2)
-t93:=somei([t:1to(xs)]cx,[g:[t:1to(xs)]cx]recprop(xs,f,g),g2,t92):prop6(xs,f)
-p@t94:=[f:[t:1to(xs)]cx]t93(f):prop7(xs)
-x@t95:=induction([y:nat]prop7(y),t43,[y:nat][t:prop7(y)]t94(y,t),x):prop7(x)
-[f:[t:1to(x)]cx]
-t96:=<f>t95:prop6(x,f)
-t97:=onei([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),[g:[t:1to(x)]cx][h:[t:1to(x)]cx][u:recprop(x,f,g)][v:recprop(x,f,h)]t37(f,g,h,u,v),t96):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
--8275
-f@satz275:=t97".8275"(f):one"e"([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g))
-recf:=ind([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):[t:1to(x)]cx
-satz275a:=oneax([t:1to(x)]cx,[g:[t:1to(x)]cx]recprop(x,f,g),satz275):recprop(x,f,recf)
-[n:1to(x)]
-rec:=<n>recf:cx
-f@satz275b:=t3".8275"(x,f,recf,satz275a):is(rec(1out(x)),<1out(x)>f)
-n@[o:not(is"e"(1to(x),n,xout(x)))]
-sucx:=ns".8275"(n,o):1to(x)
-satz275c:=t4".8275"(x,f,recf,satz275a,n,o):is(rec(sucx(n,o)),<<sucx(n,o)>f><rec(n)>q)
-f@[g:[t:1to(x)]cx][r:recprop(x,f,g)]
-satz275d:=t37".8275"(x,f,g,recf,r,satz275a):is"e"([t:1to(x)]cx,g,recf)
-[n:1to(x)]
-satz275e:=fise(1to(x),cx,g,recf,satz275d,n):is(<n>g,rec(n))
-x@[y:nat]
-+*8275
-y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
-fl:=left(cx,x,y,l,f):[t:1to(y)]cx
-rf:=recf(x,f):[t:1to(x)]cx
-rfl:=left(cx,x,y,l,rf):[t:1to(y)]cx
-t98:=isinoutn(y,1,satz24a(y)):is"n"(1,inn(y,1out(y)))
-t99:=isoutni(x,1,satz24a(x),inn(y,1out(y)),trlessis"n"(inn(y,1out(y)),y,x,1top(y,1out(y)),l),t98):is"e"(1to(x),1out(x),left1to(x,y,l,1out(y)))
-t100:=isp(1to(x),[t:1to(x)]is(<t>rf,<t>f),1out(x),left1to(x,y,l,1out(y)),t3(x,f,rf,satz275a(x,f)),t99):prop1(y,fl,rfl)
-[n:1to(y)][o:not(is"e"(1to(y),n,xout(y)))]
-t100a:=th3"l.imp"(is"n"(inn(y,n),y),is"e"(1to(y),n,xout(y)),o,[t:is"n"(inn(y,n),y)]tris(1to(y),n,outn(y,inn(y,n),1top(y,n)),xout(y),isoutinn(y,n),isoutni(y,inn(y,n),1top(y,n),y,lessisi3(y),t))):not(is"n"(inn(y,n),y))
-t100b:=ore1(less"n"(inn(y,n),y),is"n"(inn(y,n),y),1top(y,n),t100a):less"n"(inn(y,n),y)
-t101:=satz16b(inn(y,n),y,x,t100b,l):less"n"(inn(y,n),x)
-t102:=ec3e31(is"n"(inn(y,n),x),more"n"(inn(y,n),x),less"n"(inn(y,n),x),satz10b(inn(y,n),x),t101):nis"n"(inn(y,n),x)
-t103:=th3"l.imp"(is"e"(1to(x),left1to(x,y,l,n),xout(x)),is"n"(inn(y,n),x),t102,[t:is"e"(1to(x),left1to(x,y,l,n),xout(x))]isoutne(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l),x,lessisi3(x),t)):not(is"e"(1to(x),left1to(x,y,l,n),xout(x)))
-t104:=t4(x,f,rf,satz275a(x,f),left1to(x,y,l,n),t103):is(<ns(x,left1to(x,y,l,n),t103)>rf,<<ns(x,left1to(x,y,l,n),t103)>f><<n>rfl>q)
-t105:=isinoutn(x,inn(y,n),trlessis"n"(inn(y,n),y,x,1top(y,n),l)):is"n"(inn(y,n),inn(x,left1to(x,y,l,n)))
-t106:=ax2(inn(y,n),inn(x,left1to(x,y,l,n)),t105):is"n"(<inn(y,n)>suc,<inn(x,left1to(x,y,l,n))>suc)
-t107:=isinoutn(y,<inn(y,n)>suc,lemma275(y,n,o)):is"n"(<inn(y,n)>suc,inn(y,ns(y,n,o)))
-t108:=tris1(nat,<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)),<inn(y,n)>suc,t106,t107):is"n"(<inn(x,left1to(x,y,l,n))>suc,inn(y,ns(y,n,o)))
-t109:=isoutni(x,<inn(x,left1to(x,y,l,n))>suc,lemma275(x,left1to(x,y,l,n),t103),inn(y,ns(y,n,o)),trlessis"n"(inn(y,ns(y,n,o)),y,x,1top(y,ns(y,n,o)),l),t108):is"e"(1to(x),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)))
-t110:=isp(1to(x),[t:1to(x)]is(<t>rf,<<t>f><<n>rfl>q),ns(x,left1to(x,y,l,n),t103),left1to(x,y,l,ns(y,n,o)),t104,t109):is(<ns(y,n,o)>rfl,<<ns(y,n,o)>fl><<n>rfl>q)
-f@t111:=[t:1to(y)][u:not(is"e"(1to(y),t,xout(y)))]t110(t,u):prop2(y,fl,rfl)
-t112:=andi(prop1(y,fl,rfl),prop2(y,fl,rfl),t100,t111):recprop(y,fl,rfl)
--8275
-y@[l:lessis"n"(y,x)][f:[t:1to(x)]cx]
-satz275f:=satz275d(y,fl".8275"(l,f),rfl".8275"(l,f),t112".8275"(l,f)):is"e"([t:1to(y)]cx,left(cx,x,y,l,recf(x,f)),recf(y,left(cx,x,y,l,f)))
-x@[f:[t:1to(pl"n"(x,1))]cx]
-+8276
-xs:=<x>suc:nat
-x1:=pl"n"(x,1):nat
-t1:=lessisi1"n"(x,x1,satz18a(x,1)):lessis"n"(x,x1)
-t2:=lessisi1"n"(x,xs,satz18c(x)):lessis"n"(x,xs)
-t3:=lessisi2"n"(xs,x1,satz4e(x)):lessis"n"(xs,x1)
-fx:=left(cx,x1,x,t1,f):[t:1to(x)]cx
-f1:=left(cx,x1,xs,t3,f):[t:1to(xs)]cx
-f1x:=f1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
-g1:=g2"c.8275"(x,t95"c.8275"(x),f1):[t:1to(xs)]cx
-g1x:=g1"c.8275"(x,t95"c.8275"(x),f1):[t:1to(x)]cx
-g:=left(cx,x1,xs,t3,recf(x1,f)):[t:1to(xs)]cx
-t4:=t49"c.8275"(x,t95"c.8275"(x),f1,xout(xs),refis(1to(xs),xout(xs))):is(<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q)
-t5:=satz275d(xs,f1,g1,t92"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(xs)]cx,g1,recf(xs,f1))
-t6:=satz275f(x1,xs,t3,f):is"e"([t:1to(xs)]cx,g,recf(xs,f1))
-t7:=tris2([t:1to(xs)]cx,g,g1,recf(xs,f1),t6,t5):is"e"([t:1to(xs)]cx,g,g1)
-t8:=fise(1to(xs),cx,g,g1,t7,xout(xs)):is(<xout(xs)>g,<xout(xs)>g1)
-t9:=tris(cx,<xout(xs)>g,<xout(xs)>g1,<<xout(xs)>f1><<xout(x)>g1x>q,t8,t4):is(<xout(xs)>g,<<xout(xs)>f1><<xout(x)>g1x>q)
-[n:1to(x)]
-t10:=isinoutn(xs,inn(x,n),trlessis"n"(inn(x,n),x,xs,1top(x,n),t2)):is"n"(inn(x,n),inn(xs,left1to(xs,x,t2,n)))
-t11:=isoutni(x1,inn(x,n),trlessis"n"(inn(x,n),x,x1,1top(x,n),t1),inn(xs,left1to(xs,x,t2,n)),trlessis"n"(inn(xs,left1to(xs,x,t2,n)),xs,x1,1top(xs,left1to(xs,x,t2,n)),t3),t10):is"e"(1to(x1),left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)))
-t12:=isf(1to(x1),cx,f,left1to(x1,x,t1,n),left1to(x1,xs,t3,left1to(xs,x,t2,n)),t11):is(<n>fx,<n>f1x)
-f@t13:=fisi(1to(x),cx,fx,f1x,[t:1to(x)]t12(t)):is"e"([t:1to(x)]cx,fx,f1x)
-t14:=isf([t:1to(x)]cx,[t:1to(x)]cx,[u:[t:1to(x)]cx]recf(x,u),fx,f1x,t13):is"e"([t:1to(x)]cx,recf(x,fx),recf(x,f1x))
-t15:=satz275d(x,f1x,g1x,t45"c.8275"(x,t95"c.8275"(x),f1)):is"e"([t:1to(x)]cx,g1x,recf(x,f1x))
-t16:=tris2([t:1to(x)]cx,g1x,recf(x,fx),recf(x,f1x),t15,t14):is"e"([t:1to(x)]cx,g1x,recf(x,fx))
-t17:=fise(1to(x),cx,g1x,recf(x,fx),t16,xout(x)):is(<xout(x)>g1x,<xout(x)>recf(x,fx))
-t18:=isinoutn(xs,xs,lessisi3(xs)):is"n"(xs,inn(xs,xout(xs)))
-t19:=tris(nat,x1,xs,inn(xs,xout(xs)),satz4a(x),t18):is"n"(x1,inn(xs,xout(xs)))
-t20:=isoutni(x1,x1,lessisi3(x1),inn(xs,xout(xs)),trlessis"n"(inn(xs,xout(xs)),xs,x1,1top(xs,xout(xs)),t3),t19):is"e"(1to(x1),xout(x1),left1to(x1,xs,t3,xout(xs)))
-t21:=isp1(1to(x1),[t:1to(x1)]is(<t>recf(x1,f),<<t>f><<xout(x)>g1x>q),left1to(x1,xs,t3,xout(xs)),xout(x1),t9,t20):is(<xout(x1)>recf(x1,f),<<xout(x1)>f><<xout(x)>g1x>q)
-t22:=isf(cx,cx,[t:cx]<<xout(x1)>f><t>q,<xout(x)>g1x,<xout(x)>recf(x,fx),t17):is(<<xout(x1)>f><<xout(x)>g1x>q,<<xout(x1)>f><<xout(x)>recf(x,fx)>q)
--8276
-satz276:=tris(cx,<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>g1x".8276">q,<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,fx".8276")>q,t21".8276",t22".8276"):is(<xout(pl"n"(x,1))>recf(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><<xout(x)>recf(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
-x@[f:[u:1to(x)]cx]
-smpr:=rec(x,f,xout(x)):cx
-@[x:nat][f:[u:1to(x)]cx]
-sum:=smpr([t:cx][u:cx]pl(t,u),x,f):cx
-prod:=smpr([t:cx][u:cx]ts(t,u),x,f):cx
-q@[f:[u:1to(1)]cx]
-+8277
-t1:=isoutni(1,1,satz24a(1),1,lessisi3(1),refis(nat,1)):is"e"(1to(1),1out(1),xout(1))
--8277
-satz277:=isp(1to(1),[t:1to(1)]is(rec(1,f,t),<t>f),1out(1),xout(1),satz275b(1,f),t1".8277"):is(smpr(1,f),<xout(1)>f)
-q@[x:nat][f:[u:1to(pl"n"(x,1))]cx]
-satz278:=satz276(x,f):is(smpr(pl"n"(x,1),f),<<xout(pl"n"(x,1))>f><smpr(x,left(cx,pl"n"(x,1),x,lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)),f))>q)
-x@[f:[u:1to(x)]cx][y:nat][i:is"n"(y,x)]
-+v8
-t1:=lessisi2"n"(y,x,i):lessis"n"(y,x)
-f0:=left(cx,x,y,t1,f):[t:1to(y)]cx
-t2:=fise(1to(y),cx,left(cx,x,y,t1,recf(x,f)),recf(y,f0),satz275f(x,y,t1,f),xout(y)):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(y,f0))
-t3:=tris1(nat,inn(y,xout(y)),x,y,isinoutn(y,y,lessisi3(y)),i):is"n"(inn(y,xout(y)),x)
-t4:=isoutni(x,inn(y,xout(y)),trlessis"n"(inn(y,xout(y)),y,x,1top(y,xout(y)),t1),x,lessisi3(x),t3):is"e"(1to(x),left1to(x,y,t1,xout(y)),xout(x))
-t5:=isf(1to(x),cx,recf(x,f),left1to(x,y,t1,xout(y)),xout(x),t4):is(<left1to(x,y,t1,xout(y))>recf(x,f),smpr(x,f))
--v8
-issmpr:=tris1(cx,smpr(y,f0".v8"),smpr(x,f),<left1to(x,y,t1".v8",xout(y))>recf(x,f),t2".v8",t5".v8"):is(smpr(y,left(cx,x,y,lessisi2"n"(y,x,i),f)),smpr(x,f))
-@[z:complex][x:nat]
-+8279
-xr:=rlofnt(x):real
-prop1:=is(sum(x,[t:1to(x)]z),ts(z,pli(xr,0))):'prop'
-z@t1:=satz277([t:cx][u:cx]pl(t,u),[t:1to(1)]z):is(sum(1,[t:1to(1)]z),z)
-t2:=tris(cx,sum(1,[t:1to(1)]z),z,ts(z,1c),t1,satz222a(z)):prop1(1)
-x@[p:prop1(x)]
-t3:=satz278([t:cx][u:cx]pl(t,u),x,[t:1to(pl"n"(x,1))]z):is(sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z))
-t4:=ispl12(sum(x,[t:1to(x)]z),ts(z,pli(xr,0)),z,ts(z,1c),p,satz222a(z)):is(pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)))
-t5:=distpt2(z,pli(xr,0),1c):is(pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)))
-t6:=plis12a(xr,0,1rl,0):is(pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)))
-t7:=isrecx12(pl"r"(xr,1rl),rlofnt(pl"n"(x,1)),pl"r"(0,0),0,satzr155b(x,1),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0))
-t8:=tris(cx,pl(pli(xr,0),1c),pli(pl"r"(xr,1rl),pl"r"(0,0)),pli(rlofnt(pl"n"(x,1)),0),t6,t7):is(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0))
-t9:=ists2(pl(pli(xr,0),1c),pli(rlofnt(pl"n"(x,1)),0),z,t8):is(ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)))
-t10:=tr4is(cx,sum(pl"n"(x,1),[t:1to(pl"n"(x,1))]z),pl(sum(x,[t:1to(x)]z),z),pl(ts(z,pli(xr,0)),ts(z,1c)),ts(z,pl(pli(xr,0),1c)),ts(z,pli(rlofnt(pl"n"(x,1)),0)),t3,t4,t5,t9):prop1(pl"n"(x,1))
-t11:=isp(nat,[t:nat]prop1(t),pl"n"(x,1),<x>suc,t10,satz4a(x)):prop1(<x>suc)
--8279
-satz279:=induction([t:nat]prop1".8279"(t),t2".8279",[u:nat][t:prop1".8279"(u)]t11".8279"(u,t),x):is(sum(x,[t:1to(x)]z),ts(z,pli(rlofnt(x),0)))
-q@[f:[t:1to(2)]cx]
-+8280
-t1:=lessisi1"n"(1,2,satz18a(1,1)):lessis"n"(1,2)
-f1:=left(cx,2,1,t1,f):[t:1to(1)]cx
-t2:=satz278(q,1,f):is(smpr(2,f),<<xout(2)>f><smpr(1,f1)>q)
-t3:=satz277(q,f1):is(smpr(1,f1),<xout(1)>f1)
-t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-t5:=isoutni(2,1,satz24a(2),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,2,1top(1,xout(1)),t1),t4):is"e"(1to(2),1out(2),left1to(2,1,t1,xout(1)))
-t6:=isf(1to(2),cx,f,1out(2),left1to(2,1,t1,xout(1)),t5):is(<1out(2)>f,<xout(1)>f1)
-t7:=tris2(cx,smpr(1,f1),<1out(2)>f,<xout(1)>f1,t3,t6):is(smpr(1,f1),<1out(2)>f)
-t8:=isf(cx,cx,[t:cx]<<xout(2)>f><t>q,smpr(1,f1),<1out(2)>f,t7):is(<<xout(2)>f><smpr(1,f1)>q,<<xout(2)>f><<1out(2)>f>q)
--8280
-satz280:=tris(cx,smpr(2,f),<<xout(2)>f><smpr(1,f1".8280")>q,<<xout(2)>f><<1out(2)>f>q,t2".8280",t8".8280"):is(smpr(2,f),<<xout(2)>f><<1out(2)>f>q)
-q@assoc:=[x:cx][y:cx][z:cx]is(<z><<y><x>q>q,<<z><y>q><x>q):'prop'
-@assocp1:=[x:cx][y:cx][z:cx]asspl1(x,y,z):assoc([x:cx][y:cx]pl(x,y))
-assocts:=[x:cx][y:cx][z:cx]assts1(x,y,z):assoc([x:cx][y:cx]ts(x,y))
-q@[a:assoc][z:cx][u:cx][v:cx]
-assq1:=<v><u><z>a:is(<v><<u><z>q>q,<<v><u>q><z>q)
-assq2:=symis(cx,<v><<u><z>q>q,<<v><u>q><z>q,assq1):is(<<v><u>q><z>q,<v><<u><z>q>q)
-q@[a:assoc(q)][x:nat][y:nat][f:[t:1to(pl"n"(x,y))]cx]
-+8281
-y@t1:=lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)):lessis"n"(x,pl"n"(x,y))
-f@f1:=left(cx,pl"n"(x,y),x,t1,f):[t:1to(x)]cx
-f2:=right(cx,x,y,f):[t:1to(y)]cx
-prop1:=is(smpr(pl"n"(x,y),f),<smpr(y,f2)><smpr(x,f1)>q):'prop'
-y@prop2:=all"l"([t:1to(pl"n"(x,y))]cx,[u:[t:1to(pl"n"(x,y))]cx]prop1(u)):'prop'
-x@[f0:[t:1to(pl"n"(x,1))]cx]
-t2:=satz278(q,x,f0):is(smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q)
-t3:=satz277(q,f2(1,f0)):is(smpr(1,f2(1,f0)),<xout(1)>f2(1,f0))
-t4:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-t5:=ispl2"n"(1,inn(1,xout(1)),x,t4):is"n"(pl"n"(x,1),pl"n"(x,inn(1,xout(1))))
-t6:=isoutni(pl"n"(x,1),pl"n"(x,1),lessisi3(pl"n"(x,1)),pl"n"(x,inn(1,xout(1))),satz19o(inn(1,xout(1)),1,x,1top(1,xout(1))),t5):is"e"(1to(pl"n"(x,1)),xout(pl"n"(x,1)),right1to(x,1,xout(1)))
-t7:=isf(1to(pl"n"(x,1)),cx,f0,xout(pl"n"(x,1)),right1to(x,1,xout(1)),t6):is(<xout(pl"n"(x,1))>f0,<xout(1)>f2(1,f0))
-t8:=tris2(cx,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),<xout(1)>f2(1,f0),t7,t3):is(<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)))
-t9:=isf(cx,cx,<smpr(x,f1(1,f0))>q,<xout(pl"n"(x,1))>f0,smpr(1,f2(1,f0)),t8):is(<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q)
-t10:=tris(cx,smpr(pl"n"(x,1),f0),<<xout(pl"n"(x,1))>f0><smpr(x,f1(1,f0))>q,<smpr(1,f2(1,f0))><smpr(x,f1(1,f0))>q,t2,t9):prop1(1,f0)
-x@t11:=[u:[t:1to(pl"n"(x,1))]cx]t10(u):prop2(1)
-y@yp1:=pl"n"(y,1):nat
-xpy:=pl"n"(x,y):nat
-xpy1:=pl"n"(x,yp1):nat
-xyp1:=pl"n"(xpy,1):nat
-t12:=lessisi2"n"(xyp1,xpy1,asspl1"n"(x,y,1)):lessis"n"(xyp1,xpy1)
-[p:prop2(y)][f:[t:1to(xpy1)]cx]
-t13:=isinoutn(xyp1,xyp1,lessisi3(xyp1)):is"n"(xyp1,inn(xyp1,xout(xyp1)))
-t14:=tris(nat,xpy1,xyp1,inn(xyp1,xout(xyp1)),asspl2"n"(x,y,1),t13):is"n"(xpy1,inn(xyp1,xout(xyp1)))
-t15:=isoutni(xpy1,xpy1,lessisi3(xpy1),inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),t14):is"e"(1to(xpy1),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)))
-t16:=isf(1to(xpy1),cx,recf(xpy1,f),xout(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),t15):is(smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)))
-fr:=left(cx,xpy1,xyp1,t12,f):[t:1to(xyp1)]cx
-t17:=satz275f(xpy1,xyp1,t12,f):is"e"([t:1to(xyp1)]cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr))
-t18:=fise(1to(xyp1),cx,left(cx,xpy1,xyp1,t12,recf(xpy1,f)),recf(xyp1,fr),t17,xout(xyp1)):is(<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr))
-t19:=lessisi1"n"(xpy,xyp1,satz18a(xpy,1)):lessis"n"(xpy,xyp1)
-frr:=left(cx,xyp1,xpy,t19,fr):[t:1to(xpy)]cx
-t20:=satz278(xpy,fr):is(smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q)
-t21:=isf(cx,cx,[u:cx]<<xout(xyp1)>fr><u>q,smpr(xpy,frr),<smpr(y,f2(frr))><smpr(x,f1(frr))>q,<frr>p):is(<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
-t22:=assq1(a,smpr(x,f1(frr)),smpr(y,f2(frr)),<xout(xyp1)>fr):is(<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q)
-t23:=lessisi1"n"(y,yp1,satz18a(y,1)):lessis"n"(y,yp1)
-fy:=left(cx,yp1,y,t23,f2(yp1,f)):[t:1to(y)]cx
-t24:=satz278(y,f2(yp1,f)):is(smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
-t25:=isinoutn(yp1,yp1,lessisi3(yp1)):is"n"(yp1,inn(yp1,xout(yp1)))
-t26:=ispl2"n"(yp1,inn(yp1,xout(yp1)),x,t25):is"n"(xpy1,pl"n"(x,inn(yp1,xout(yp1))))
-t27:=tris1(nat,inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))),xpy1,t14,t26):is"n"(inn(xyp1,xout(xyp1)),pl"n"(x,inn(yp1,xout(yp1))))
-t28:=isoutni(xpy1,inn(xyp1,xout(xyp1)),trlessis"n"(inn(xyp1,xout(xyp1)),xyp1,xpy1,1top(xyp1,xout(xyp1)),t12),pl"n"(x,inn(yp1,xout(yp1))),satz19o(inn(yp1,xout(yp1)),yp1,x,1top(yp1,xout(yp1))),t27):is"e"(1to(xpy1),left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)))
-t29:=isf(1to(xpy1),cx,f,left1to(xpy1,xyp1,t12,xout(xyp1)),right1to(x,yp1,xout(yp1)),t28):is(<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f))
-t30:=isf(cx,cx,<smpr(y,f2(frr))>q,<xout(xyp1)>fr,<xout(yp1)>f2(yp1,f),t29):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q)
-[n:1to(y)]
-n0:=inn(y,n):nat
-nyp1:=left1to(yp1,y,t23,n):1to(yp1)
-t31:=isinoutn(yp1,n0,trlessis"n"(n0,y,yp1,1top(y,n),t23)):is"n"(n0,inn(yp1,nyp1))
-t32:=ispl2"n"(n0,inn(yp1,nyp1),x,t31):is"n"(pl"n"(x,n0),pl"n"(x,inn(yp1,nyp1)))
-nxpy:=right1to(x,y,n):1to(xpy)
-nxyp1:=left1to(xyp1,xpy,t19,nxpy):1to(xyp1)
-t33:=isinoutn(xyp1,inn(xpy,nxpy),trlessis"n"(inn(xpy,nxpy),xpy,xyp1,1top(xpy,nxpy),t19)):is"n"(inn(xpy,nxpy),inn(xyp1,nxyp1))
-t34:=isinoutn(xpy,pl"n"(x,n0),satz19o(n0,y,x,1top(y,n))):is"n"(pl"n"(x,n0),inn(xpy,nxpy))
-t35:=tris(nat,pl"n"(x,n0),inn(xpy,nxpy),inn(xyp1,nxyp1),t34,t33):is"n"(pl"n"(x,n0),inn(xyp1,nxyp1))
-t36:=tris1(nat,pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1),pl"n"(x,n0),t32,t35):is"n"(pl"n"(x,inn(yp1,nyp1)),inn(xyp1,nxyp1))
-t37:=isoutni(xpy1,pl"n"(x,inn(yp1,nyp1)),satz19o(inn(yp1,nyp1),yp1,x,1top(yp1,nyp1)),inn(xyp1,nxyp1),trlessis"n"(inn(xyp1,nxyp1),xyp1,xpy1,1top(xyp1,nxyp1),t12),t36):is"e"(1to(xpy1),right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1))
-t38:=isf(1to(xpy1),cx,f,right1to(x,yp1,nyp1),left1to(xpy1,xyp1,t12,nxyp1),t37):is(<n>fy,<n>f2(frr))
-f@t39:=fisi(1to(y),cx,fy,f2(frr),[u:1to(y)]t38(u)):is"e"([u:1to(y)]cx,fy,f2(frr))
-t40:=isf([u:1to(y)]cx,cx,[t:[u:1to(y)]cx]smpr(y,t),fy,f2(frr),t39):is(smpr(y,fy),smpr(y,f2(frr)))
-t41:=isf(cx,cx,[t:cx]<<xout(yp1)>f2(yp1,f)><t>q,smpr(y,f2(frr)),smpr(y,fy),symis(cx,smpr(y,fy),smpr(y,f2(frr)),t40)):is(<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
-t41a:=tris(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t30,t41):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q)
-t42:=tris2(cx,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),<<xout(yp1)>f2(yp1,f)><smpr(y,fy)>q,t41a,t24):is(<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)))
-t43:=isf(cx,cx,<smpr(x,f1(frr))>q,<<xout(xyp1)>fr><smpr(y,f2(frr))>q,smpr(yp1,f2(yp1,f)),t42):is(<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q)
-[m:1to(x)]
-m0:=inn(x,m):nat
-mxpy:=left1to(xpy,x,t1,m):1to(xpy)
-mxyp1:=left1to(xyp1,xpy,t19,mxpy):1to(xyp1)
-t44:=isinoutn(xyp1,inn(xpy,mxpy),trlessis"n"(inn(xpy,mxpy),xpy,xyp1,1top(xpy,mxpy),t19)):is"n"(inn(xpy,mxpy),inn(xyp1,mxyp1))
-t45:=isinoutn(xpy,m0,trlessis"n"(m0,x,xpy,1top(x,m),t1)):is"n"(m0,inn(xpy,mxpy))
-t46:=tris(nat,m0,inn(xpy,mxpy),inn(xyp1,mxyp1),t45,t44):is"n"(m0,inn(xyp1,mxyp1))
-t47:=isoutni(xpy1,m0,trlessis"n"(m0,x,xpy1,1top(x,m),t1(yp1)),inn(xyp1,mxyp1),trlessis"n"(inn(xyp1,mxyp1),xyp1,xpy1,1top(xyp1,mxyp1),t12),t46):is"e"(1to(xpy1),left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1))
-t48:=isf(1to(xpy1),cx,f,left1to(xpy1,x,t1(yp1),m),left1to(xpy1,xyp1,t12,mxyp1),t47):is(<m>f1(x,yp1,f),<m>f1(x,y,frr))
-f@t49:=fisi(1to(x),cx,f1(x,yp1,f),f1(x,y,frr),[u:1to(x)]t48(u)):is"e"([u:1to(x)]cx,f1(x,yp1,f),f1(x,y,frr))
-t50:=isf([u:1to(x)]cx,cx,[t:[u:1to(x)]cx]smpr(x,t),f1(yp1,f),f1(frr),t49):is(smpr(x,f1(yp1,f)),smpr(x,f1(frr)))
-t51:=isf(cx,cx,[t:cx]<smpr(yp1,f2(yp1,f))><t>q,smpr(x,f1(frr)),smpr(x,f1(yp1,f)),symis(cx,smpr(x,f1(yp1,f)),smpr(x,f1(frr)),t50)):is(<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q)
-t52:=tr4is(cx,smpr(xpy1,f),<xout(xyp1)>left(cx,xpy1,xyp1,t12,recf(xpy1,f)),smpr(xyp1,fr),<<xout(xyp1)>fr><smpr(xpy,frr)>q,<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,t16,t18,t20,t21):is(smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q)
-t53:=tr4is(cx,smpr(xpy1,f),<<xout(xyp1)>fr><<smpr(y,f2(frr))><smpr(x,f1(frr))>q>q,<<<xout(xyp1)>fr><smpr(y,f2(frr))>q><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(frr))>q,<smpr(yp1,f2(yp1,f))><smpr(x,f1(yp1,f))>q,t52,t22,t43,t51):prop1(yp1,f)
-p@t54:=[u:[t:1to(xpy1)]cx]t53(u):prop2(yp1)
-t55:=isp(nat,[t:nat]prop2(t),yp1,<y>suc,t54,satz4a(y)):prop2(<y>suc)
-y@t56:=induction([t:nat]prop2(t),t11,[z:nat][t:prop2(z)]t55(z,t),y):prop2(y)
--8281
-satz281:=<f>t56".8281":is(smpr(pl"n"(x,y),f),<smpr(y,right(cx,x,y,f))><smpr(x,left(cx,pl"n"(x,y),x,lessisi1"n"(x,pl"n"(x,y),satz18a(x,y)),f))>q)
-q@commut:=[x:cx][y:cx]is(<y><x>q,<x><y>q):'prop'
-@commutpl:=[x:cx][y:cx]compl(x,y):commut([x:cx][y:cx]pl(x,y))
-commutts:=[x:cx][y:cx]comts(x,y):commut([x:cx][y:cx]ts(x,y))
-q@[c:commut][z:cx][u:cx]
-comq:=<u><z>c:is(<u><z>q,<z><u>q)
-a@[c:commut(q)][x:nat][f:[t:1to(x)]cx][g:[t:1to(x)]cx]
-+8282
-prop1:=is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q):'prop'
-x@prop2:=all"l"([t:1to(x)]cx,[u:[t:1to(x)]cx]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]prop1(u,v))):'prop'
-c@[f0:[t:1to(1)]cx][g0:[t:1to(1)]cx]
-t1:=satz277([t:1to(1)]<<t>g0><<t>f0>q):is(smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<<xout(1)>g0><<xout(1)>f0>q)
-t2:=isf(cx,cx,<smpr(1,f0)>q,smpr(1,g0),<xout(1)>g0,satz277(g0)):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q)
-t3:=isf(cx,cx,[t:cx]<<xout(1)>g0><t>q,smpr(1,f0),<xout(1)>f0,satz277(f0)):is(<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
-t4:=tris(cx,<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t2,t3):is(<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q)
-t5:=tris2(cx,smpr(1,[t:1to(1)]<<t>g0><<t>f0>q),<smpr(1,g0)><smpr(1,f0)>q,<<xout(1)>g0><<xout(1)>f0>q,t1,t4):prop1(1,f0,g0)
-c@t6:=[u:[t:1to(1)]cx][v:[t:1to(1)]cx]t5(u,v):prop2(1)
-x@xp1:=pl"n"(x,1):nat
-[p:prop2(x)][f:[t:1to(xp1)]cx][g:[t:1to(xp1)]cx]
-c@[u:cx][v:cx][w:cx][z:cx]
-t7:=assq2(a,<v><u>q,w,z):is(<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q)
-t8:=comq(c,<v><u>q,w):is(<w><<v><u>q>q,<<v><u>q><w>q)
-t9:=assq2(a,w,u,v):is(<<v><u>q><w>q,<v><<u><w>q>q)
-t10:=tris(cx,<w><<v><u>q>q,<<v><u>q><w>q,<v><<u><w>q>q,t8,t9):is(<w><<v><u>q>q,<v><<u><w>q>q)
-t11:=isf(cx,cx,[t:cx]<z><t>q,<w><<v><u>q>q,<v><<u><w>q>q,t10):is(<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q)
-t12:=assq1(a,<u><w>q,v,z):is(<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q)
-t13:=comq(c,w,u):is(<u><w>q,<w><u>q)
-t14:=isf(cx,cx,[t:cx]<<z><v>q><t>q,<u><w>q,<w><u>q,t13):is(<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q)
-t15:=tr4is(cx,<<z><w>q><<v><u>q>q,<z><<w><<v><u>q>q>q,<z><<v><<u><w>q>q>q,<<z><v>q><<u><w>q>q,<<z><v>q><<w><u>q>q,t7,t11,t12,t14):is(<<z><w>q><<v><u>q>q,<<z><v>q><<w><u>q>q)
-g@t16:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
-sfx:=smpr(x,left(cx,xp1,x,t16,f)):cx
-sgx:=smpr(x,left(cx,xp1,x,t16,g)):cx
-h:=[t:1to(xp1)]<<t>g><<t>f>q:[t:1to(xp1)]cx
-shx:=smpr(x,left(cx,xp1,x,t16,h)):cx
-t17:=satz278(x,h):is(smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q)
-t18:=<left(cx,xp1,x,t16,g)><left(cx,xp1,x,t16,f)>p:is(shx,<sgx><sfx>q)
-t19:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><<xout(xp1)>f>q><t>q,shx,<sgx><sfx>q,t18):is(<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q)
-t20:=t15(sfx,sgx,<xout(xp1)>f,<xout(xp1)>g):is(<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
-t21:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><sfx>q,satz278(x,f)):is(<<xout(xp1)>f><sfx>q,smpr(xp1,f))
-t22:=isf(cx,cx,[t:cx]<<<xout(xp1)>g><sgx>q><t>q,<<xout(xp1)>f><sfx>q,smpr(xp1,f),t21):is(<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q)
-t23:=symis(cx,smpr(xp1,g),<<xout(xp1)>g><sgx>q,satz278(x,g)):is(<<xout(xp1)>g><sgx>q,smpr(xp1,g))
-t24:=isf(cx,cx,<smpr(xp1,f)>q,<<xout(xp1)>g><sgx>q,smpr(xp1,g),t23):is(<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q)
-t25:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><<xout(xp1)>f>q><shx>q,<<<xout(xp1)>g><<xout(xp1)>f>q><<sgx><sfx>q>q,<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,t17,t19,t20):is(smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q)
-t26:=tr3is(cx,smpr(xp1,h),<<<xout(xp1)>g><sgx>q><<<xout(xp1)>f><sfx>q>q,<<<xout(xp1)>g><sgx>q><smpr(xp1,f)>q,<smpr(xp1,g)><smpr(xp1,f)>q,t25,t22,t24):prop1(xp1,f,g)
-p@t27:=[u:[t:1to(xp1)]cx][v:[t:1to(xp1)]cx]t26(u,v):prop2(xp1)
-t28:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t27,satz4a(x)):prop2(<x>suc)
-x@t29:=induction([t:nat]prop2(t),t6,[y:nat][t:prop2(y)]t28(y,t),x):prop2(x)
--8282
-satz282:=<g><f>t29".8282":is(smpr(x,[t:1to(x)]<<t>g><<t>f>q),<smpr(x,g)><smpr(x,f)>q)
-x@[s:[t:1to(x)]1to(x)][b:bijective(1to(x),1to(x),s)][f:[t:1to(x)]cx]
-+8283
-s@[f:[t:1to(x)]cx]
-g:=[t:1to(x)]<<t>s>f:[t:1to(x)]cx
-prop1:=is(smpr(x,g),smpr(x,f)):'prop'
-x@prop2:=all"l"([t:1to(x)]1to(x),[u:[t:1to(x)]1to(x)]all"l"([t:1to(x)]cx,[v:[t:1to(x)]cx]imp(bijective(1to(x),1to(x),u),prop1(u,v)))):'prop'
-c@[s:[t:1to(1)]1to(1)][f:[t:1to(1)]cx]
-t1:=tris2(1to(1),<xout(1)>s,xout(1),1o"n",th1"n.singlet"(<xout(1)>s),th1"n.singlet"(xout(1))):is"e"(1to(1),<xout(1)>s,xout(1))
-t2:=satz277(g(1,s,f)):is(smpr(1,g(1,s,f)),<xout(1)>g(1,s,f))
-t3:=isf(1to(1),cx,f,<xout(1)>s,xout(1),t1):is(<xout(1)>g(1,s,f),<xout(1)>f)
-t4:=symis(cx,smpr(1,f),<xout(1)>f,satz277(f)):is(<xout(1)>f,smpr(1,f))
-t5:=tr3is(cx,smpr(1,g(1,s,f)),<xout(1)>g(1,s,f),<xout(1)>f,smpr(1,f),t2,t3,t4):prop1(1,s,f)
-c@t6:=[u:[t:1to(1)]1to(1)][v:[t:1to(1)]cx][w:bijective(1to(1),1to(1),u)]t5(u,v):prop2(1)
-x@xp1:=pl"n"(x,1):nat
-t7:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
-[p:prop2(x)][s:[t:1to(xp1)]1to(xp1)][f:[t:1to(xp1)]cx][b:bijective(1to(xp1),1to(xp1),s)]
-t8:=ande1(injective(1to(xp1),1to(xp1),s),surjective(1to(xp1),1to(xp1),s),b):injective(1to(xp1),1to(xp1),s)
-[case1:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))][u:1to(x)]
-u1:=left1to(xp1,x,t7,u):1to(xp1)
-n1:=inn(xp1,<u1>s):nat
-[i:is"n"(n1,xp1)]
-t9:=tr3is(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),xout(xp1),<xout(xp1)>s,isoutinn(xp1,<u1>s),isoutni(xp1,n1,1top(xp1,<u1>s),xp1,lessisi3(xp1),i),symis(1to(xp1),<xout(xp1)>s,xout(xp1),case1)):is"e"(1to(xp1),<u1>s,<xout(xp1)>s)
-t10:=isfe(1to(xp1),1to(xp1),s,t8,u1,xout(xp1),t9):is"e"(1to(xp1),u1,xout(xp1))
-t11:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t10):is"n"(inn(x,u),xp1)
-t12:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
-t13:=<t11>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t12):con
-u@t14:=ore1(less"n"(n1,xp1),is"n"(n1,xp1),1top(xp1,<u1>s),[t:is"n"(n1,xp1)]t13(t)):less"n"(n1,xp1)
-t15:=satz26(x,n1,t14):lessis"n"(n1,x)
-w1:=outn(x,n1,t15):1to(x)
-case1@s01:=[t:1to(x)]w1(t):[t:1to(x)]1to(x)
-u@[v:1to(x)][i:is"e"(1to(x),w1(u),w1(v))]
-t16:=isoutne(x,n1(u),t15(u),n1(v),t15(v),i):is"n"(n1(u),n1(v))
-t17:=<isinne(xp1,<u1(u)>s,<u1(v)>s,t16)><u1(v)><u1(u)>t8:is"e"(1to(xp1),u1(u),u1(v))
-t18:=thleft1(xp1,x,t7,u,v,t17):is"e"(1to(x),u,v)
-u@u2:=<u1>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
-n2:=inn(xp1,u2):nat
-[i:is"n"(n2,xp1)]
-t19:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),xout(xp1),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),xp1,lessisi3(xp1),i)):is"e"(1to(xp1),u2,xout(xp1))
-t20:=tr3is(1to(xp1),u1,<u2>s,<xout(xp1)>s,xout(xp1),thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,xout(xp1),t19),case1):is"e"(1to(xp1),u1,xout(xp1))
-t21:=isoutne(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7),xp1,lessisi3(xp1),t20):is"n"(inn(x,u),xp1)
-t22:=satz16a(inn(x,u),x,xp1,1top(x,u),satz18a(x,1)):less"n"(inn(x,u),xp1)
-t23:=<t21>ec3e31(is"n"(inn(x,u),xp1),more"n"(inn(x,u),xp1),less"n"(inn(x,u),xp1),satz10b(inn(x,u),xp1),t22):con
-u@t24:=ore1(less"n"(n2,xp1),is"n"(n2,xp1),1top(xp1,u2),[t:is"n"(n2,xp1)]t23(t)):less"n"(n2,xp1)
-t25:=satz26(x,n2,t24):lessis"n"(n2,x)
-w2:=outn(x,n2,t25):1to(x)
-t26:=isinoutn(x,n2,t25):is"n"(n2,inn(x,w2))
-t27:=tris(1to(xp1),u2,outn(xp1,n2,1top(xp1,u2)),u1(w2),isoutinn(xp1,u2),isoutni(xp1,n2,1top(xp1,u2),inn(x,w2),trlessis"n"(inn(x,w2),x,xp1,1top(x,w2),t7),t26)):is"e"(1to(xp1),u2,u1(w2))
-t28:=tris(1to(xp1),u1,<u2>s,<u1(w2)>s,thinvf2(1to(xp1),1to(xp1),s,b,u1),isf(1to(xp1),1to(xp1),s,u2,u1(w2),t27)):is"e"(1to(xp1),u1,<u1(w2)>s)
-t29:=tris(nat,inn(x,u),inn(xp1,u1),n1(w2),isinoutn(xp1,inn(x,u),trlessis"n"(inn(x,u),x,xp1,1top(x,u),t7)),isinni(xp1,u1,<u1(w2)>s,t28)):is"n"(inn(x,u),n1(w2))
-t30:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w1(w2),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),n1(w2),t15(w2),t29)):is"e"(1to(x),u,w1(w2))
-t31:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w1(t)),w2,t30):image(1to(x),1to(x),s01,u)
-case1@t32:=andi(injective(1to(x),1to(x),s01),surjective(1to(x),1to(x),s01),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s01,<u>s01)]t18(t,u,v),[t:1to(x)]t31(t)):bijective(1to(x),1to(x),s01)
-f01:=left(cx,xp1,x,t7,f):[t:1to(x)]cx
-t33:=<t32><f01><s01>p:prop1(s01,f01)
-g1:=left(cx,xp1,x,t7,g(xp1,s,f)):[t:1to(x)]cx
-g2:=g(x,s01,f01):[t:1to(x)]cx
-u@t33a:=isoutinn(xp1,<u1>s):is"e"(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)))
-t34:=isinoutn(x,n1,t15):is"n"(n1,inn(x,w1))
-t35:=isoutni(xp1,n1,1top(xp1,<u1>s),inn(x,w1),trlessis"n"(inn(x,w1),x,xp1,1top(x,w1),t7),t34):is"e"(1to(xp1),outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1))
-t36:=tris(1to(xp1),<u1>s,outn(xp1,n1,1top(xp1,<u1>s)),left1to(xp1,x,t7,w1),t33a,t35):is"e"(1to(xp1),<u1>s,left1to(xp1,x,t7,w1))
-t37:=isf(1to(xp1),cx,f,<u1>s,left1to(xp1,x,t7,w1),t36):is(<u>g1,<u>g2)
-case1@t38:=fisi(1to(x),cx,g1,g2,[t:1to(x)]t37(t)):is"e"([t:1to(x)]cx,g1,g2)
-t39:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g1,g2,t38):is(smpr(x,g1),smpr(x,g2))
-t40:=tris(cx,smpr(x,g1),smpr(x,g2),smpr(x,f01),t39,t33):is(smpr(x,g1),smpr(x,f01))
-t41:=isf(1to(xp1),cx,f,<xout(xp1)>s,xout(xp1),case1):is(<xout(xp1)>g(xp1,s,f),<xout(xp1)>f)
-t42:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q)
-t43:=isf(cx,cx,<smpr(x,g1)>q,<xout(xp1)>g(xp1,s,f),<xout(xp1)>f,t41):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q)
-t44:=isf(cx,cx,[t:cx]<<xout(xp1)>f><t>q,smpr(x,g1),smpr(x,f01),t40):is(<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q)
-t45:=symis(cx,smpr(xp1,f),<<xout(xp1)>f><smpr(x,f01)>q,satz278(x,f)):is(<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f))
-t46:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,g1)>q,<<xout(xp1)>f><smpr(x,f01)>q,smpr(xp1,f),t42,t43,t44,t45):prop1(xp1,s,f)
-b@1px:=pl"n"(1,x):nat
-[case2:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))][u:1to(x)]
-u3:=right1to(1,x,u):1to(1px)
-case2@t47:=lessisi2"n"(1px,xp1,compl"n"(1,x)):lessis"n"(1px,xp1)
-s02:=left(1to(xp1),xp1,1px,t47,s):[t:1to(1px)]1to(xp1)
-u@n3:=inn(xp1,<u3>s02):nat
-[i:is"n"(n3,1)]
-t48:=tr3is(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),1out(xp1),<1out(xp1)>s,isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),1,satz24a(xp1),i),symis(1to(xp1),<1out(xp1)>s,1out(xp1),case2)):is"e"(1to(xp1),<u3>s02,<1out(xp1)>s)
-t49:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3),1out(xp1),t48):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
-t50:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t49):is"n"(inn(1px,u3),1)
-t51:=isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))):is"n"(pl"n"(1,inn(x,u)),inn(1px,u3))
-t52:=ismore1"n"(pl"n"(1,inn(x,u)),inn(1px,u3),1,t51,satz18(1,inn(x,u))):more"n"(inn(1px,u3),1)
-t53:=<t50>ec3e21(is"n"(inn(1px,u3),1),more"n"(inn(1px,u3),1),less"n"(inn(1px,u3),1),satz10b(inn(1px,u3),1),t52):con
-u@t54:=ore1(more"n"(n3,1),is"n"(n3,1),satz24(n3),[t:is"n"(n3,1)]t53(t)):more"n"(n3,1)
-nm1:=mn"n"(n3,1,t54):nat
-t54a:=islessis1"n"(n3,pl"n"(nm1,1),xp1,th1c"n.mn"(n3,1,t54),1top(xp1,<u3>s02)):lessis"n"(pl"n"(nm1,1),xp1)
-t55:=th9"l.or"(less"n"(pl"n"(nm1,1),xp1),is"n"(pl"n"(nm1,1),xp1),less"n"(nm1,x),is"n"(nm1,x),t54a,[t:less"n"(pl"n"(nm1,1),xp1)]satz20c(nm1,x,1,t),[t:is"n"(pl"n"(nm1,1),xp1)]satz20b(nm1,x,1,t)):lessis"n"(nm1,x)
-w3:=outn(x,nm1,t55):1to(x)
-case2@s03:=[t:1to(x)]w3(t):[t:1to(x)]1to(x)
-u@[v:1to(x)][i:is"e"(1to(x),w3(u),w3(v))]
-t56:=isoutne(x,nm1(u),t55(u),nm1(v),t55(v),i):is"n"(nm1(u),nm1(v))
-t57:=tr3is(nat,n3(u),pl"n"(nm1(u),1),pl"n"(nm1(v),1),n3(v),th1c"n.mn"(n3(u),1,t54(u)),ispl1"n"(nm1(u),nm1(v),1,t56),th1d"n.mn"(n3(v),1,t54(v))):is"n"(n3(u),n3(v))
-t58:=isinne(xp1,<u3(u)>s02,<u3(v)>s02,t57):is"e"(1to(xp1),<u3(u)>s02,<u3(v)>s02)
-t59:=isfe(1to(xp1),1to(xp1),s,t8,left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)),t58):is"e"(1to(xp1),left1to(xp1,1px,t47,u3(u)),left1to(xp1,1px,t47,u3(v)))
-t60:=thleft1(xp1,1px,t47,u3(u),u3(v),t59):is"e"(1to(1px),u3(u),u3(v))
-t61:=thright1(1,x,u,v,t60):is"e"(1to(x),u,v)
-case2@s04:=left(1to(xp1),xp1,1px,t47,invf(1to(xp1),1to(xp1),s,b)):[t:1to(1px)]1to(xp1)
-u@u4:=<u3>s04:1to(xp1)
-n4:=inn(xp1,u4):nat
-[i:is"n"(n4,1)]
-t62:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),1out(xp1),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),1,satz24a(xp1),i)):is"e"(1to(xp1),u4,1out(xp1))
-t63:=tr3is(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<1out(xp1)>s,1out(xp1),thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,1out(xp1),t62),case2):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),1out(xp1))
-t64:=isoutne(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47),1,satz24a(xp1),t63):is"n"(inn(1px,u3),1)
-t65:=tris(nat,pl"n"(1,inn(x,u)),inn(1px,u3),1,isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),t64):is"n"(pl"n"(1,inn(x,u)),1)
-t66:=<t65>ec3e21(is"n"(pl"n"(1,inn(x,u)),1),more"n"(pl"n"(1,inn(x,u)),1),less"n"(pl"n"(1,inn(x,u)),1),satz10b(pl"n"(1,inn(x,u)),1),satz18(1,inn(x,u))):con
-u@t67:=ore1(more"n"(n4,1),is"n"(n4,1),satz24(n4),[t:is"n"(n4,1)]t66(t)):more"n"(n4,1)
-nm2:=mn"n"(n4,1,t67):nat
-t68:=islessis1"n"(n4,pl"n"(nm2,1),xp1,th1c"n.mn"(n4,1,t67),1top(xp1,u4)):lessis"n"(pl"n"(nm2,1),xp1)
-t69:=th9"l.or"(less"n"(pl"n"(nm2,1),xp1),is"n"(pl"n"(nm2,1),xp1),less"n"(nm2,x),is"n"(nm2,x),t68,[t:less"n"(pl"n"(nm2,1),xp1)]satz20c(nm2,x,1,t),[t:is"n"(pl"n"(nm2,1),xp1)]satz20b(nm2,x,1,t)):lessis"n"(nm2,x)
-w4:=outn(x,nm2,t69):1to(x)
-t70:=isinoutn(x,nm2,t69):is"n"(nm2,inn(x,w4))
-t71:=tr3is(nat,n4,pl"n"(1,nm2),pl"n"(1,inn(x,w4)),inn(1px,u3(w4)),th1a"n.mn"(n4,1,t67),ispl2"n"(nm2,inn(x,w4),1,t70),isinoutn(1px,pl"n"(1,inn(x,w4)),satz19o(inn(x,w4),x,1,1top(x,w4)))):is"n"(n4,inn(1px,u3(w4)))
-t72:=tris(1to(xp1),u4,outn(xp1,n4,1top(xp1,u4)),left1to(xp1,1px,t47,u3(w4)),isoutinn(xp1,u4),isoutni(xp1,n4,1top(xp1,u4),inn(1px,u3(w4)),trlessis"n"(inn(1px,u3(w4)),1px,xp1,1top(1px,u3(w4)),t47),t71)):is"e"(1to(xp1),u4,left1to(xp1,1px,t47,u3(w4)))
-t73:=tris(1to(xp1),left1to(xp1,1px,t47,u3),<u4>s,<u3(w4)>s02,thinvf2(1to(xp1),1to(xp1),s,b,left1to(xp1,1px,t47,u3)),isf(1to(xp1),1to(xp1),s,u4,left1to(xp1,1px,t47,u3(w4)),t72)):is"e"(1to(xp1),left1to(xp1,1px,t47,u3),<u3(w4)>s02)
-t74:=tr3is(nat,pl"n"(1,inn(x,u)),inn(1px,u3),inn(xp1,left1to(xp1,1px,t47,u3)),n3(w4),isinoutn(1px,pl"n"(1,inn(x,u)),satz19o(inn(x,u),x,1,1top(x,u))),isinoutn(xp1,inn(1px,u3),trlessis"n"(inn(1px,u3),1px,xp1,1top(1px,u3),t47)),isinni(xp1,left1to(xp1,1px,t47,u3),<u3(w4)>s02,t73)):is"n"(pl"n"(1,inn(x,u)),n3(w4))
-t75:=th1e"n.mn"(n3(w4),1,inn(x,u),t54(w4),t74):is"n"(inn(x,u),nm1(w4))
-t76:=tris(1to(x),u,outn(x,inn(x,u),1top(x,u)),w3(w4),isoutinn(x,u),isoutni(x,inn(x,u),1top(x,u),nm1(w4),t55(w4),t75)):is"e"(1to(x),u,w3(w4))
-t77:=somei(1to(x),[t:1to(x)]is"e"(1to(x),u,w3(t)),w4,t76):image(1to(x),1to(x),s03,u)
-case2@t78:=andi(injective(1to(x),1to(x),s03),surjective(1to(x),1to(x),s03),[t:1to(x)][u:1to(x)][v:is"e"(1to(x),<t>s03,<u>s03)]t61(t,u,v),[t:1to(x)]t77(t)):bijective(1to(x),1to(x),s03)
-f02:=left(cx,xp1,1px,t47,f):[t:1to(1px)]cx
-f03:=right(cx,1,x,f02):[t:1to(x)]cx
-t79:=<t78><f03><s03>p:prop1(s03,f03)
-g3:=left(cx,xp1,1px,t47,g(xp1,s,f)):[t:1to(1px)]cx
-g4:=right(cx,1,x,g3):[t:1to(x)]cx
-g5:=g(x,s03,f03):[t:1to(x)]cx
-u@t80:=tr3is(nat,n3,pl"n"(1,nm1),pl"n"(1,inn(x,w3)),inn(1px,right1to(1,x,w3)),th1a"n.mn"(n3,1,t54),ispl2"n"(nm1,inn(x,w3),1,isinoutn(x,nm1,t55)),isinoutn(1px,pl"n"(1,inn(x,w3)),satz19o(inn(x,w3),x,1,1top(x,w3)))):is"n"(n3,inn(1px,right1to(1,x,w3)))
-t81:=tris(1to(xp1),<u3>s02,outn(xp1,n3,1top(xp1,<u3>s02)),left1to(xp1,1px,t47,right1to(1,x,w3)),isoutinn(xp1,<u3>s02),isoutni(xp1,n3,1top(xp1,<u3>s02),inn(1px,right1to(1,x,w3)),trlessis"n"(inn(1px,right1to(1,x,w3)),1px,xp1,1top(1px,right1to(1,x,w3)),t47),t80)):is"e"(1to(xp1),<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)))
-t82:=isf(1to(xp1),cx,f,<u3>s02,left1to(xp1,1px,t47,right1to(1,x,w3)),t81):is(<u>g4,<u>g5)
-case2@t83:=fisi(1to(x),cx,g4,g5,[t:1to(x)]t82(t)):is"e"([t:1to(x)]cx,g4,g5)
-t85:=isf([t:1to(x)]cx,cx,[u:[t:1to(x)]cx]smpr(x,u),g4,g5,t83):is(smpr(x,g4),smpr(x,g5))
-t86:=tris(cx,smpr(x,g4),smpr(x,g5),smpr(x,f03),t85,t79):is(smpr(x,g4),smpr(x,f03))
-t87:=lessisi1"n"(1,1px,satz18a(1,x)):lessis"n"(1,1px)
-g6:=left(cx,1px,1,t87,g3):[t:1to(1)]cx
-f04:=left(cx,1px,1,t87,f02):[t:1to(1)]cx
-t87a:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-1d:=left1to(1px,1,t87,xout(1)):1to(1px)
-t87b:=isinoutn(1px,inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,1px,1top(1,xout(1)),t87)):is"n"(inn(1,xout(1)),inn(1px,1d))
-t88:=tris(nat,1,inn(1,xout(1)),inn(1px,1d),t87a,t87b):is"n"(1,inn(1px,1d))
-1e:=left1to(xp1,1px,t47,1d):1to(xp1)
-t88a:=isoutni(xp1,1,satz24a(xp1),inn(1px,1d),trlessis"n"(inn(1px,1d),1px,xp1,1top(1px,1d),t47),t88):is"e"(1to(xp1),1out(xp1),1e)
-t88b:=isf(1to(xp1),1to(xp1),s,1e,1out(xp1),symis(1to(xp1),1out(xp1),1e,t88a)):is"e"(1to(xp1),<1e>s,<1out(xp1)>s)
-t89:=tr3is(1to(xp1),<1e>s,<1out(xp1)>s,1out(xp1),1e,t88b,case2,t88a):is"e"(1to(xp1),<1e>s,1e)
-t89a:=tr3is(cx,smpr(1,g6),<xout(1)>g6,<xout(1)>f04,smpr(1,f04),satz277(g6),isf(1to(xp1),cx,f,<1e>s,1e,t89),symis(cx,smpr(1,f04),<xout(1)>f04,satz277(f04))):is(smpr(1,g6),smpr(1,f04))
-t90:=satz281(1,x,g3):is(smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q)
-t91:=isf(cx,cx,<smpr(1,g6)>q,smpr(x,g4),smpr(x,f03),t86):is(<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q)
-t92:=isf(cx,cx,[t:cx]<smpr(x,f03)><t>q,smpr(1,g6),smpr(1,f04),t89a):is(<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q)
-t93:=symis(cx,smpr(1px,f02),<smpr(x,f03)><smpr(1,f04)>q,satz281(1,x,f02)):is(<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02))
-t94:=tr4is(cx,smpr(1px,g3),<smpr(x,g4)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,g6)>q,<smpr(x,f03)><smpr(1,f04)>q,smpr(1px,f02),t90,t91,t92,t93):is(smpr(1px,g3),smpr(1px,f02))
-t95:=issmpr(xp1,f,1px,compl"n"(1,x)):is(smpr(1px,f02),smpr(xp1,f))
-t96:=symis(cx,smpr(1px,g3),smpr(xp1,g(xp1,s,f)),issmpr(xp1,g(xp1,s,f),1px,compl"n"(1,x))):is(smpr(xp1,g(xp1,s,f)),smpr(1px,g3))
-t97:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(1px,g3),smpr(1px,f02),smpr(xp1,f),t96,t94,t95):prop1(xp1,s,f)
-b@[not1:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))][not2:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]
-a0:=<1out(xp1)>s:1to(xp1)
-b0:=<1out(xp1)>invf(1to(xp1),1to(xp1),s,b):1to(xp1)
-t98:=thinvf2(1to(xp1),1to(xp1),s,b,1out(xp1)):is"e"(1to(xp1),1out(xp1),<b0>s)
-t99:=not2:not(is"e"(1to(xp1),a0,1out(xp1)))
-t100:=symnotis(1to(xp1),<1out(xp1)>s,<b0>s,th3"e.notis"(1to(xp1),<1out(xp1)>s,1out(xp1),<b0>s,not2,t98)):not(is"e"(1to(xp1),<b0>s,<1out(xp1)>s))
-t101:=th3"l.imp"(is"e"(1to(xp1),b0,1out(xp1)),is"e"(1to(xp1),<b0>s,<1out(xp1)>s),t100,[t:is"e"(1to(xp1),b0,1out(xp1))]isf(1to(xp1),1to(xp1),s,b0,1out(xp1),t)):not(is"e"(1to(xp1),b0,1out(xp1)))
-s1:=changef(1to(xp1),1to(xp1),s,1out(xp1),b0):[t:1to(xp1)]1to(xp1)
-[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
-t102:=changef1(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,<b0>s)
-t103:=tris2(1to(xp1),<u>s1,1out(xp1),<b0>s,t102,t98):is"e"(1to(xp1),<u>s1,1out(xp1))
-u@[i:is"e"(1to(xp1),u,b0)]
-t104:=changef2(1to(xp1),1to(xp1),s,1out(xp1),b0,u,i):is"e"(1to(xp1),<u>s1,a0)
-u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
-t105:=changef3(1to(xp1),1to(xp1),s,1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
-not2@t106:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),b0,b):bijective(1to(xp1),1to(xp1),s1)
-[alpha:not(is"e"(1to(xp1),a0,xout(xp1)))]
-s2:=wissel(1to(xp1),1out(xp1),a0):[t:1to(xp1)]1to(xp1)
-t107:=th3"e.wissel"(1to(xp1),1out(xp1),a0):bijective(1to(xp1),1to(xp1),s2)
-[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
-t108:=iswissel1(1to(xp1),1out(xp1),a0,<u>s1,t103(u,i)):is"e"(1to(xp1),<<u>s1>s2,a0)
-t109:=tris2(1to(xp1),<u>s,<<u>s1>s2,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t108):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-u@[i:is"e"(1to(xp1),u,b0)]
-t110:=iswissel2(1to(xp1),1out(xp1),a0,<u>s1,t104(u,i)):is"e"(1to(xp1),<<u>s1>s2,1out(xp1))
-t111:=tris2(1to(xp1),<u>s,<<u>s1>s2,1out(xp1),tris2(1to(xp1),<u>s,1out(xp1),<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),t98),t110):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))][i:is"e"(1to(xp1),<u>s1,1out(xp1))]
-t112:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,1out(xp1),tris2(1to(xp1),<u>s1,<1out(xp1)>s1,1out(xp1),i,t103(1out(xp1),refis(1to(xp1),1out(xp1))))):is"e"(1to(xp1),u,1out(xp1))
-o@t113:=th3"l.imp"(is"e"(1to(xp1),<u>s1,1out(xp1)),is"e"(1to(xp1),u,1out(xp1)),n,[t:is"e"(1to(xp1),<u>s1,1out(xp1))]t112(t)):not(is"e"(1to(xp1),<u>s1,1out(xp1)))
-[i:is"e"(1to(xp1),<u>s1,a0)]
-t114:=isfe(1to(xp1),1to(xp1),s1,t8(s1,f,t106),u,b0,tris2(1to(xp1),<u>s1,<b0>s1,a0,i,t104(b0,refis(1to(xp1),b0)))):is"e"(1to(xp1),u,b0)
-o@t115:=th3"l.imp"(is"e"(1to(xp1),<u>s1,a0),is"e"(1to(xp1),u,b0),o,[t:is"e"(1to(xp1),<u>s1,a0)]t114(t)):not(is"e"(1to(xp1),<u>s1,a0))
-t116:=iswissel3(1to(xp1),1out(xp1),a0,<u>s1,t113,t115):is"e"(1to(xp1),<<u>s1>s2,<u>s1)
-t117:=symis(1to(xp1),<<u>s1>s2,<u>s,tris(1to(xp1),<<u>s1>s2,<u>s1,<u>s,t116,t105(u,n,o))):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-n@t118:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,b0)]t111(t),[t:not(is"e"(1to(xp1),u,b0))]t117(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-u@t119:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s1>s2),[t:is"e"(1to(xp1),u,1out(xp1))]t109(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t118(t)):is"e"(1to(xp1),<u>s,<<u>s1>s2)
-alpha@t120:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s1>s2,[t:1to(xp1)]t119(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s1>s2)
-not2@t121:=t103(1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s1,1out(xp1))
-t121a:=ec3e21(is"n"(xp1,1),more"n"(xp1,1),less"n"(xp1,1),satz10b(xp1,1),ismore1"n"(1px,xp1,1,compl"n"(1,x),satz18(1,x))):nis"n"(xp1,1)
-t122:=th3"l.imp"(is"e"(1to(xp1),xout(xp1),1out(xp1)),is"n"(xp1,1),t121a,[t:is"e"(1to(xp1),xout(xp1),1out(xp1))]isoutne(xp1,xp1,lessisi3(xp1),1,satz24a(xp1),t)):not(is"e"(1to(xp1),xout(xp1),1out(xp1)))
-alpha@t123:=symnotis(1to(xp1),a0,xout(xp1),alpha):not(is"e"(1to(xp1),xout(xp1),a0))
-t124:=iswissel3(1to(xp1),1out(xp1),a0,xout(xp1),t122,t123):is"e"(1to(xp1),<xout(xp1)>s2,xout(xp1))
-t125:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s1>s2,t120):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))))
-t126:=t97(s1,g(xp1,s2,f),t106,t121):is(smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)))
-t127:=t46(s2,f,t107,t124):is(smpr(xp1,g(xp1,s2,f)),smpr(xp1,f))
-t128:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s1,g(xp1,s2,f))),smpr(xp1,g(xp1,s2,f)),smpr(xp1,f),t125,t126,t127):prop1(xp1,s,f)
-not2@[i3:is"e"(1to(xp1),a0,xout(xp1))][beta:not(is"e"(1to(xp1),b0,xout(xp1)))]
-s3:=wissel(1to(xp1),1out(xp1),b0):[t:1to(xp1)]1to(xp1)
-t129:=th3"e.wissel"(1to(xp1),1out(xp1),b0):bijective(1to(xp1),1to(xp1),s3)
-[u:1to(xp1)][i:is"e"(1to(xp1),u,1out(xp1))]
-t130:=t104(<u>s3,iswissel1(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,a0)
-t131:=tris2(1to(xp1),<u>s,<<u>s3>s1,a0,isf(1to(xp1),1to(xp1),s,u,1out(xp1),i),t130):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-u@[i:is"e"(1to(xp1),u,b0)]
-t132:=t103(<u>s3,iswissel2(1to(xp1),1out(xp1),b0,u,i)):is"e"(1to(xp1),<<u>s3>s1,1out(xp1))
-t133:=tris2(1to(xp1),<u>s,<<u>s3>s1,<b0>s,isf(1to(xp1),1to(xp1),s,u,b0,i),tris(1to(xp1),<<u>s3>s1,1out(xp1),<b0>s,t132,t98)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-u@[n:not(is"e"(1to(xp1),u,1out(xp1)))][o:not(is"e"(1to(xp1),u,b0))]
-t134:=iswissel3(1to(xp1),1out(xp1),b0,u,n,o):is"e"(1to(xp1),<u>s3,u)
-t135:=isf(1to(xp1),1to(xp1),s1,<u>s3,u,t134):is"e"(1to(xp1),<<u>s3>s1,<u>s1)
-t136:=t105(u,n,o):is"e"(1to(xp1),<u>s1,<u>s)
-t139:=symis(1to(xp1),<<u>s3>s1,<u>s,tris(1to(xp1),<<u>s3>s1,<u>s1,<u>s,t135,t136)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-n@t140:=th1"l.imp"(is"e"(1to(xp1),u,b0),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,b0)]t133(t),[t:not(is"e"(1to(xp1),u,b0))]t139(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-u@t141:=th1"l.imp"(is"e"(1to(xp1),u,1out(xp1)),is"e"(1to(xp1),<u>s,<<u>s3>s1),[t:is"e"(1to(xp1),u,1out(xp1))]t131(t),[t:not(is"e"(1to(xp1),u,1out(xp1)))]t140(t)):is"e"(1to(xp1),<u>s,<<u>s3>s1)
-beta@t142:=fisi(1to(xp1),1to(xp1),s,[t:1to(xp1)]<<t>s3>s1,[t:1to(xp1)]t141(t)):is"e"([t:1to(xp1)]1to(xp1),s,[t:1to(xp1)]<<t>s3>s1)
-t143:=symnotis(1to(xp1),b0,xout(xp1),beta):not(is"e"(1to(xp1),xout(xp1),b0))
-t144:=iswissel3(1to(xp1),1out(xp1),b0,xout(xp1),t122,t143):is"e"(1to(xp1),<xout(xp1)>s3,xout(xp1))
-t145:=isf([t:1to(xp1)]1to(xp1),cx,[u:[t:1to(xp1)]1to(xp1)]smpr(xp1,g(xp1,u,f)),s,[t:1to(xp1)]<<t>s3>s1,t142):is(smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))))
-t146:=t46(s3,g(xp1,s1,f),t129,t144):is(smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)))
-t147:=t97(s1,f,t106,t121):is(smpr(xp1,g(xp1,s1,f)),smpr(xp1,f))
-t148:=tr3is(cx,smpr(xp1,g(xp1,s,f)),smpr(xp1,g(xp1,s3,g(xp1,s1,f))),smpr(xp1,g(xp1,s1,f)),smpr(xp1,f),t145,t146,t147):prop1(xp1,s,f)
-i3@[gamma:is"e"(1to(xp1),b0,xout(xp1))][i:is"n"(x,1)]
-t149:=ispl1"n"(1,x,1,symis(nat,x,1,i)):is"n"(2,xp1)
-t150:=lessisi2"n"(2,xp1,t149):lessis"n"(2,xp1)
-f05:=left(cx,xp1,2,t150,f):[t:1to(2)]cx
-s05:=left(1to(xp1),xp1,2,t150,s):[t:1to(2)]1to(xp1)
-g7:=left(cx,xp1,2,t150,g(xp1,s,f)):[t:1to(2)]cx
-t151:=issmpr(xp1,f,2,t149):is(smpr(2,f05),smpr(xp1,f))
-t152:=issmpr(xp1,g(xp1,s,f),2,t149):is(smpr(2,g7),smpr(xp1,g(xp1,s,f)))
-t153:=satz280(f05):is(smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q)
-t154:=satz280(g7):is(smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q)
-t155:=tris1(nat,inn(2,xout(2)),xp1,2,isinoutn(2,2,lessisi3(2)),t149):is"n"(inn(2,xout(2)),xp1)
-t156:=isoutni(xp1,inn(2,xout(2)),trlessis"n"(inn(2,xout(2)),2,xp1,1top(2,xout(2)),t150),xp1,lessisi3(xp1),t155):is"e"(1to(xp1),left1to(xp1,2,t150,xout(2)),xout(xp1))
-t157:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,xout(2)),xout(xp1),t156):is"e"(1to(xp1),<xout(2)>s05,<xout(xp1)>s)
-t158:=symis(nat,1,inn(2,1out(2)),isinoutn(2,1,satz24a(2))):is"n"(inn(2,1out(2)),1)
-t159:=isoutni(xp1,inn(2,1out(2)),trlessis"n"(inn(2,1out(2)),2,xp1,1top(2,1out(2)),t150),1,satz24a(xp1),t158):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1))
-t160:=tr3is(1to(xp1),left1to(xp1,2,t150,1out(2)),1out(xp1),<b0>s,<xout(xp1)>s,t159,t98,isf(1to(xp1),1to(xp1),s,b0,xout(xp1),gamma)):is"e"(1to(xp1),left1to(xp1,2,t150,1out(2)),<xout(xp1)>s)
-t161:=tris2(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)),<xout(xp1)>s,t157,t160):is"e"(1to(xp1),<xout(2)>s05,left1to(xp1,2,t150,1out(2)))
-t163:=isf(1to(xp1),1to(xp1),s,left1to(xp1,2,t150,1out(2)),1out(xp1),t159):is"e"(1to(xp1),<1out(2)>s05,<1out(xp1)>s)
-t164:=tris(1to(xp1),<1out(2)>s05,<1out(xp1)>s,xout(xp1),t163,i3):is"e"(1to(xp1),<1out(2)>s05,xout(xp1))
-t165:=tris2(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)),xout(xp1),t164,t156):is"e"(1to(xp1),<1out(2)>s05,left1to(xp1,2,t150,xout(2)))
-t166:=isf(1to(xp1),cx,f,<xout(2)>s05,left1to(xp1,2,t150,1out(2)),t161):is(<xout(2)>g7,<1out(2)>f05)
-t167:=isf(1to(xp1),cx,f,<1out(2)>s05,left1to(xp1,2,t150,xout(2)),t165):is(<1out(2)>g7,<xout(2)>f05)
-t168:=isf(cx,cx,<<1out(2)>g7>q,<xout(2)>g7,<1out(2)>f05,t166):is(<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q)
-t169:=comq(c,<1out(2)>g7,<1out(2)>f05):is(<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q)
-t170:=isf(cx,cx,<<1out(2)>f05>q,<1out(2)>g7,<xout(2)>f05,t167):is(<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q)
-t171:=tr4is(cx,smpr(xp1,g(xp1,s,f)),smpr(2,g7),<<xout(2)>g7><<1out(2)>g7>q,<<1out(2)>f05><<1out(2)>g7>q,<<1out(2)>g7><<1out(2)>f05>q,symis(cx,smpr(2,g7),smpr(xp1,g(xp1,s,f)),t152),t154,t168,t169):is(smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q)
-t172:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<1out(2)>g7><<1out(2)>f05>q,<<xout(2)>f05><<1out(2)>f05>q,smpr(2,f05),smpr(xp1,f),t171,t170,symis(cx,smpr(2,f05),<<xout(2)>f05><<1out(2)>f05>q,t153),t151):prop1(xp1,s,f)
-trivial:=t172:prop1(xp1,s,f)
-gamma@[n:nis"n"(x,1)]
-t173:=ore1(more"n"(x,1),is"n"(x,1),satz24(x),n):more"n"(x,1)
-xm1:=mn"n"(x,1,t173):nat
-s4:=changef(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1)):[t:1to(xp1)]1to(xp1)
-t174:=th6"e.wissel"(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),b):bijective(1to(xp1),1to(xp1),s4)
-t175:=changef2(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),xout(xp1),refis(1to(xp1),xout(xp1))):is"e"(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s)
-t176:=symis(1to(xp1),a0,xout(xp1),i3):is"e"(1to(xp1),xout(xp1),<1out(xp1)>s)
-t177:=tris2(1to(xp1),<xout(xp1)>s4,xout(xp1),<1out(xp1)>s,t175,t176):is"e"(1to(xp1),<xout(xp1)>s4,xout(xp1))
-t178:=lessisi1"n"(x,xp1,satz18a(x,1)):lessis"n"(x,xp1)
-g8:=left(cx,xp1,x,t178,g(xp1,s,f)):[t:1to(x)]cx
-t179:=satz278(x,g(xp1,s,f)):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q)
-t180:=th1b"n.mn"(x,1,t173):is"n"(pl"n"(1,xm1),x)
-t181:=lessisi2"n"(pl"n"(1,xm1),x,t180):lessis"n"(pl"n"(1,xm1),x)
-g9:=left(cx,x,pl"n"(1,xm1),t181,g8):[t:1to(pl"n"(1,xm1))]cx
-t182:=symis(cx,smpr(pl"n"(1,xm1),g9),smpr(x,g8),issmpr(x,g8,pl"n"(1,xm1),t180)):is(smpr(x,g8),smpr(pl"n"(1,xm1),g9))
-g10:=right(cx,1,xm1,g9):[t:1to(xm1)]cx
-t183:=lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)):lessis"n"(1,pl"n"(1,xm1))
-g11:=left(cx,pl"n"(1,xm1),1,t183,g9):[t:1to(1)]cx
-t184:=satz281(a,1,xm1,g9):is(smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q)
-t185:=satz277(g11):is(smpr(1,g11),<xout(1)>g11)
-t186:=isinoutn(1,1,lessisi3(1)):is"n"(1,inn(1,xout(1)))
-1a:=left1to(pl"n"(1,xm1),1,t183,xout(1)):1to(pl"n"(1,xm1))
-t187:=isinoutn(pl"n"(1,xm1),inn(1,xout(1)),trlessis"n"(inn(1,xout(1)),1,pl"n"(1,xm1),1top(1,xout(1)),t183)):is"n"(inn(1,xout(1)),inn(pl"n"(1,xm1),1a))
-1b:=left1to(x,pl"n"(1,xm1),t181,1a):1to(x)
-t188:=isinoutn(x,inn(pl"n"(1,xm1),1a),trlessis"n"(inn(pl"n"(1,xm1),1a),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),1a),t181)):is"n"(inn(pl"n"(1,xm1),1a),inn(x,1b))
-t189:=tr3is(nat,1,inn(1,xout(1)),inn(pl"n"(1,xm1),1a),inn(x,1b),t186,t187,t188):is"n"(1,inn(x,1b))
-1c:=left1to(xp1,x,t178,1b):1to(xp1)
-t190:=isoutni(xp1,1,satz24a(xp1),inn(x,1b),trlessis"n"(inn(x,1b),x,xp1,1top(x,1b),t178),t189):is"e"(1to(xp1),1out(xp1),1c)
-t191:=isf(1to(xp1),cx,g(xp1,s,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s,f),<xout(1)>g11)
-t192:=tris2(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(1)>g11,t185,t191):is(smpr(1,g11),<1out(xp1)>g(xp1,s,f))
-t193:=symis(1to(xp1),<xout(xp1)>s4,<1out(xp1)>s,t175):is"e"(1to(xp1),<1out(xp1)>s,<xout(xp1)>s4)
-t194:=isf(1to(xp1),cx,f,<1out(xp1)>s,<xout(xp1)>s4,t193):is(<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f))
-t195:=tris(cx,smpr(1,g11),<1out(xp1)>g(xp1,s,f),<xout(xp1)>g(xp1,s4,f),t192,t194):is(smpr(1,g11),<xout(xp1)>g(xp1,s4,f))
-t196:=isf(cx,cx,[t:cx]<smpr(xm1,g10)><t>q,smpr(1,g11),<xout(xp1)>g(xp1,s4,f),t195):is(<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
-t197:=tr3is(cx,smpr(x,g8),smpr(pl"n"(1,xm1),g9),<smpr(xm1,g10)><smpr(1,g11)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t182,t184,t196):is(smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q)
-t198:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s,f)><t>q,smpr(x,g8),<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q,t197):is(<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q)
-t199:=assq1(a,<xout(xp1)>g(xp1,s4,f),smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q)
-t200:=comq(c,<xout(xp1)>g(xp1,s4,f),<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q):is(<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
-g12:=left(cx,xp1,x,t178,g(xp1,s4,f)):[t:1to(x)]cx
-g13:=left(cx,x,pl"n"(1,xm1),t181,g12):[t:1to(pl"n"(1,xm1))]cx
-g14:=right(cx,1,xm1,g13):[t:1to(xm1)]cx
-g15:=left(cx,pl"n"(1,xm1),1,lessisi1"n"(1,pl"n"(1,xm1),satz18a(1,xm1)),g13):[t:1to(1)]cx
-t201:=satz278(x,g(xp1,s4,f)):is(smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
-t202:=symis(cx,smpr(pl"n"(1,xm1),g13),smpr(x,g12),issmpr(x,g12,pl"n"(1,xm1),t180)):is(smpr(x,g12),smpr(pl"n"(1,xm1),g13))
-t203:=satz281(a,1,xm1,g13):is(smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q)
-t204:=satz277(g15):is(smpr(1,g15),<xout(1)>g15)
-t205:=isf(1to(xp1),cx,g(xp1,s4,f),1out(xp1),1c,t190):is(<1out(xp1)>g(xp1,s4,f),<xout(1)>g15)
-t206:=tris2(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(1)>g15,t204,t205):is(smpr(1,g15),<1out(xp1)>g(xp1,s4,f))
-t207:=changef1(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),1out(xp1),refis(1to(xp1),1out(xp1))):is"e"(1to(xp1),<1out(xp1)>s4,<xout(xp1)>s)
-t208:=isf(1to(xp1),cx,f,<1out(xp1)>s4,<xout(xp1)>s,t207):is(<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f))
-t209:=tris(cx,smpr(1,g15),<1out(xp1)>g(xp1,s4,f),<xout(xp1)>g(xp1,s,f),t206,t208):is(smpr(1,g15),<xout(xp1)>g(xp1,s,f))
-t210:=isf(cx,cx,[t:cx]<smpr(xm1,g14)><t>q,smpr(1,g15),<xout(xp1)>g(xp1,s,f),t209):is(<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-t211:=tr3is(cx,smpr(x,g12),smpr(pl"n"(1,xm1),g13),<smpr(xm1,g14)><smpr(1,g15)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t202,t203,t210):is(smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-[u:1to(xm1)]
-ua:=right1to(1,xm1,u):1to(pl"n"(1,xm1))
-ub:=left1to(x,pl"n"(1,xm1),t181,ua):1to(x)
-uc:=left1to(xp1,x,t178,ub):1to(xp1)
-[i:is"e"(1to(xp1),uc,xout(xp1))]
-t212:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),xp1,lessisi3(xp1),i):is"n"(inn(x,ub),xp1)
-t213:=satz16a(inn(x,ub),x,xp1,1top(x,ub),satz18a(x,1)):less"n"(inn(x,ub),xp1)
-t214:=<t212>ec3e31(is"n"(inn(x,ub),xp1),more"n"(inn(x,ub),xp1),less"n"(inn(x,ub),xp1),satz10b(inn(x,ub),xp1),t213):con
-u@t215:=[t:is"e"(1to(xp1),uc,xout(xp1))]t214(t):not(is"e"(1to(xp1),uc,xout(xp1)))
-[i:is"e"(1to(xp1),uc,1out(xp1))]
-t216:=isoutne(xp1,inn(x,ub),trlessis"n"(inn(x,ub),x,xp1,1top(x,ub),t178),1,satz24a(xp1),i):is"n"(inn(x,ub),1)
-t217:=isinoutn(x,inn(pl"n"(1,xm1),ua),trlessis"n"(inn(pl"n"(1,xm1),ua),pl"n"(1,xm1),x,1top(pl"n"(1,xm1),ua),t181)):is"n"(inn(pl"n"(1,xm1),ua),inn(x,ub))
-t218:=isinoutn(pl"n"(1,xm1),pl"n"(1,inn(xm1,u)),satz19o(inn(xm1,u),xm1,1,1top(xm1,u))):is"n"(pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua))
-t219:=tr3is(nat,pl"n"(1,inn(xm1,u)),inn(pl"n"(1,xm1),ua),inn(x,ub),1,t218,t217,t216):is"n"(pl"n"(1,inn(xm1,u)),1)
-t220:=satz18(1,inn(xm1,u)):more"n"(pl"n"(1,inn(xm1,u)),1)
-t221:=<t219>ec3e21(is"n"(pl"n"(1,inn(xm1,u)),1),more"n"(pl"n"(1,inn(xm1,u)),1),less"n"(pl"n"(1,inn(xm1,u)),1),satz10b(pl"n"(1,inn(xm1,u)),1),t220):con
-u@t222:=[t:is"e"(1to(xp1),uc,1out(xp1))]t221(t):not(is"e"(1to(xp1),uc,1out(xp1)))
-t223:=changef3(1to(xp1),1to(xp1),s,1out(xp1),xout(xp1),uc,t222,t215):is"e"(1to(xp1),<uc>s4,<uc>s)
-t224:=isf(1to(xp1),cx,f,<uc>s4,<uc>s,t223):is(<u>g14,<u>g10)
-n@t225:=fisi(1to(xm1),cx,g10,g14,[t:1to(xm1)]symis(cx,<t>g14,<t>g10,t224(t))):is"e"([t:1to(xm1)]cx,g10,g14)
-t226:=isf([t:1to(xm1)]cx,cx,[u:[t:1to(xm1)]cx]smpr(xm1,u),g10,g14,t225):is(smpr(xm1,g10),smpr(xm1,g14))
-t227:=comq(c,smpr(xm1,g10),<xout(xp1)>g(xp1,s,f)):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q)
-t228:=isf(cx,cx,<<xout(xp1)>g(xp1,s,f)>q,smpr(xm1,g10),smpr(xm1,g14),t226):is(<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-t229:=tris(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g10)><<xout(xp1)>g(xp1,s,f)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t227,t228):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q)
-t230:=tris2(cx,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),<smpr(xm1,g14)><<xout(xp1)>g(xp1,s,f)>q,t229,t211):is(<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12))
-t231:=isf(cx,cx,[t:cx]<<xout(xp1)>g(xp1,s4,f)><t>q,<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q,smpr(x,g12),t230):is(<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q)
-t232:=symis(cx,smpr(xp1,g(xp1,s4,f)),<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,t201):is(<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)))
-t233:=t46(s4,f,t174,t177):is(smpr(xp1,g(xp1,s4,f)),smpr(xp1,f))
-t234:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s,f)><smpr(x,g8)>q,<<xout(xp1)>g(xp1,s,f)><<smpr(xm1,g10)><<xout(xp1)>g(xp1,s4,f)>q>q,<<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q><<xout(xp1)>g(xp1,s4,f)>q,<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,t179,t198,t199,t200):is(smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q)
-t235:=tr4is(cx,smpr(xp1,g(xp1,s,f)),<<xout(xp1)>g(xp1,s4,f)><<<xout(xp1)>g(xp1,s,f)><smpr(xm1,g10)>q>q,<<xout(xp1)>g(xp1,s4,f)><smpr(x,g12)>q,smpr(xp1,g(xp1,s4,f)),smpr(xp1,f),t234,t231,t232,t233):prop1(xp1,s,f)
-gamma@t236:=th1"l.imp"(is"n"(x,1),prop1(xp1,s,f),[t:is"n"(x,1)]t172(t),[t:not(is"n"(x,1))]t235(t)):prop1(xp1,s,f)
-i3@t237:=th1"l.imp"(is"e"(1to(xp1),b0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),b0,xout(xp1))]t236(t),[t:not(is"e"(1to(xp1),b0,xout(xp1)))]t148(t)):prop1(xp1,s,f)
-not2@t238:=th1"l.imp"(is"e"(1to(xp1),a0,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),a0,xout(xp1))]t237(t),[t:not(is"e"(1to(xp1),a0,xout(xp1)))]t128(t)):prop1(xp1,s,f)
-not1@t239:=th1"l.imp"(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<1out(xp1)>s,1out(xp1))]t97(t),[t:not(is"e"(1to(xp1),<1out(xp1)>s,1out(xp1)))]t238(t)):prop1(xp1,s,f)
-b@t240:=th1"l.imp"(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)),prop1(xp1,s,f),[t:is"e"(1to(xp1),<xout(xp1)>s,xout(xp1))]t46(t),[t:not(is"e"(1to(xp1),<xout(xp1)>s,xout(xp1)))]t239(t)):prop1(xp1,s,f)
-p@t241:=[u:[t:1to(xp1)]1to(xp1)][v:[t:1to(xp1)]cx][w:bijective(1to(xp1),1to(xp1),u)]t240(u,v,w):prop2(xp1)
-t242:=isp(nat,[t:nat]prop2(t),xp1,<x>suc,t241,satz4a(x)):prop2(<x>suc)
-x@t243:=induction([t:nat]prop2(t),t6,[t:nat][u:prop2(t)]t242(t,u),x):prop2(x)
--8283
-satz283:=<b><f><s>t243".8283":is(smpr(x,[t:1to(x)]<<t>s>f),smpr(x,f))
-@[x:real][ix:intrl(x)][y:real][iy:intrl(y)][ly:lessis(y,x)]
-shiftl:=shiftl"r"(x,ix,y,iy,ly):nat
-[n:1to(shiftl)]
-shiftr:=shiftr"r"(x,ix,y,iy,ly,n):real
-intshiftr:=intshiftr"r"(x,ix,y,iy,ly,n):intrl(shiftr)
-shiftrls:=shiftrls"r"(x,ix,y,iy,ly,n):lessis(shiftr,x)
-lsshiftr:=lsshiftr"r"(x,ix,y,iy,ly,n):lessis(y,shiftr)
-[m:1to(shiftl)][i:is"r"(shiftr(n),shiftr(m))]
-iseshiftr:=iseshiftr"r"(x,ix,y,iy,ly,n,m,i):is"e"(1to(shiftl),n,m)
-ly@[u:real][a:and3(intrl(u),lessis(y,u),lessis(u,x))]
-shiftl1:=shiftl1"r"(x,ix,y,iy,ly,u,a):1to(shiftl)
-shiftinv1:=shiftinv1"r"(x,ix,y,iy,ly,u,a):is"r"(u,shiftr(shiftl1))
-shiftinv2:=shiftinv2"r"(x,ix,y,iy,ly,u,a):is"r"(shiftr(shiftl1),u)
-ly@[f:seq(x,ix,y,iy,ly,cx)]
-shiftf:=shiftf(x,ix,y,iy,ly,cx,f):[t:1to(shiftl)]cx
-[q:[t:cx][u:cx]cx]
-smpri:=smpr(q,shiftl,shiftf):cx
-f@[pi:proofsirrelevant(x,ix,y,iy,ly,cx,f)][q:[t:cx][u:cx]cx][a:assoc(q)][u:real][iu:intrl(u)][l:lessis(y,u)][k:less(u,x)][v:real][iv:intrl(v)][lv:lessis(y,v)][kv:lessis(v,u)]
-+8284
-t1:=lessisi1(v,x,satz172a(v,u,x,kv,k)):lessis(v,x)
--8284
-k@lft:=[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]<t1".8284"(t,v,lt,kt)><lt><v><t>f:[t:real][v:intrl(t)][lt:lessis(y,t)][kt:lessis(t,u)]cx
-iv@[lv:lessis(pl"r"(u,1rl),v)][kv:lessis(v,x)]
-+*8284
-x@[y:real]
-pl:=pl"r"(x,y):real
-mn:=mn"r"(x,y):real
-x@p1:=pl"r"(x,1rl):real
-kv@t2:=satz190c(u,u,0,1rl,lessisi2(u,u,refis(real,u)),lemma1"r"(1rl,0,satz169a(1rl,natpos(1rl,natrl1)))):less(pl(u,0),p1(u))
-t3:=isless1(pl(u,0),u,p1(u),pl02"r"(u,0,refis(real,0)),t2):less(u,p1(u))
-t4:=lessisi1(y,v,satz172b(y,p1(u),v,satz172a(y,u,p1(u),l,t3),lv)):lessis(y,v)
--8284
-k@rgt:=[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]<kt><t4".8284"(t,v,lt,kt)><v><t>f:[t:real][v:intrl(t)][lt:lessis(pl"r"(u,1rl),t)][kt:lessis(t,x)]cx
-+*8284
-k@t5:=intpl(u,iu,1rl,intrl1):intrl(p1(u))
-t6:=satzr25(u,iu,x,ix,k):lessis(p1(u),x)
-t7:=tr3is(real,pl(mn(p1(u),y),mn(p1(x),p1(u))),pl(mn(p1(x),p1(u)),mn(p1(u),y)),mn(pl(mn(p1(x),p1(u)),p1(u)),y),mn(p1(x),y),compl"r"(mn(p1(u),y),mn(p1(x),p1(u))),asspl2"r"(mn(p1(x),p1(u)),p1(u),m0"r"(y)),ismn1"r"(pl(mn(p1(x),p1(u)),p1(u)),p1(x),y,plmn(p1(x),p1(u)))):is"r"(pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y))
-sxy:=shiftl(x,ix,y,iy,ly):nat
-suy:=shiftl(u,iu,y,iy,l):nat
-sxu:=shiftl(x,ix,p1(u),t5,t6):nat
-t8:=tr4is(real,rlofnt(pl"n"(suy,sxu)),pl(rlofnt(suy),rlofnt(sxu)),pl(mn(p1(u),y),mn(p1(x),p1(u))),mn(p1(x),y),rlofnt(sxy),satzr155a(suy,sxu),ispl12"r"(rlofnt(suy),mn(p1(u),y),rlofnt(sxu),mn(p1(x),p1(u)),isrlnt2(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l)),isrlnt2(mn(p1(x),p1(u)),t6"r.shift"(x,ix,p1(u),t5,t6))),t7,isrlnt1(mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly))):is"r"(rlofnt(pl"n"(suy,sxu)),rlofnt(sxy))
-t9:=isntirl(pl"n"(suy,sxu),sxy,t8):is"n"(pl"n"(suy,sxu),sxy)
-t10:=lessisi2"n"(pl"n"(suy,sxu),sxy,t9):lessis"n"(pl"n"(suy,sxu),sxy)
-f1:=left(cx,sxy,pl"n"(suy,sxu),t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(pl"n"(suy,sxu))]cx
-t11:=issmpr(q,sxy,shiftf(x,ix,y,iy,ly,f),pl"n"(suy,sxu),t9):is(smpr(q,pl"n"(suy,sxu),f1),smpri(x,ix,y,iy,ly,f,q))
-fr:=right(cx,suy,sxu,f1):[t:1to(sxu)]cx
-t12:=lessisi1"n"(suy,pl"n"(suy,sxu),satz18a(suy,sxu)):lessis"n"(suy,pl"n"(suy,sxu))
-fl:=left(cx,pl"n"(suy,sxu),suy,t12,f1):[t:1to(suy)]cx
-t12a:=satz281(q,a,suy,sxu,f1):is(smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q)
-[n:1to(sxu)]
-t13:=isinoutn(pl"n"(suy,sxu),pl"n"(suy,inn(sxu,n)),satz19o(inn(sxu,n),sxu,suy,1top(sxu,n))):is"n"(pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)))
-t14:=isinoutn(sxy,inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),trlessis"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),right1to(suy,sxu,n)),t10)):is"n"(inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n))))
-n1:=left1to(sxy,pl"n"(suy,sxu),t10,right1to(suy,sxu,n)):1to(sxy)
-t15:=tris(nat,pl"n"(suy,inn(sxu,n)),inn(pl"n"(suy,sxu),right1to(suy,sxu,n)),inn(sxy,n1),t13,t14):is"n"(pl"n"(suy,inn(sxu,n)),inn(sxy,n1))
-t16:=isnterl(pl"n"(suy,inn(sxu,n)),inn(sxy,n1),t15):is"r"(rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)))
-t17:=satzr155b(suy,inn(sxu,n)):is"r"(pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))))
-t18:=ispl1"r"(mn(p1(u),y),rlofnt(suy),rlofnt(inn(sxu,n)),isrlnt1(mn(p1(u),y),t6"r.shift"(u,iu,y,iy,l))):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))))
-t19:=tr3is(real,pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(suy),rlofnt(inn(sxu,n))),rlofnt(pl"n"(suy,inn(sxu,n))),rlofnt(inn(sxy,n1)),t18,t17,t16):is"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)))
-t20:=ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),rlofnt(inn(sxy,n1)),y,t19):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxy,n1)),y))
-t21:=tr3is(real,pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y),pl(rlofnt(inn(sxu,n)),pl(mn(p1(u),y),y)),pl(rlofnt(inn(sxu,n)),p1(u)),ispl1"r"(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),pl(rlofnt(inn(sxu,n)),mn(p1(u),y)),y,compl"r"(mn(p1(u),y),rlofnt(inn(sxu,n)))),asspl1"r"(rlofnt(inn(sxu,n)),mn(p1(u),y),y),ispl2"r"(pl(mn(p1(u),y),y),p1(u),rlofnt(inn(sxu,n)),plmn(p1(u),y))):is"r"(pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),pl(rlofnt(inn(sxu,n)),p1(u)))
-t22:=tris1(real,pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),pl(pl(mn(p1(u),y),rlofnt(inn(sxu,n))),y),t20,t21):is"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)))
-t23:=ismn1"r"(pl(rlofnt(inn(sxy,n1)),y),pl(rlofnt(inn(sxu,n)),p1(u)),1rl,t22):is"r"(shiftr(x,ix,y,iy,ly,n1),shiftr(x,ix,p1(u),t5,t6,n))
-t24:=intshiftr(x,ix,y,iy,ly,n1):intrl(shiftr(x,ix,y,iy,ly,n1))
-t25:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,shiftr(x,ix,y,iy,ly,n1))
-t26:=shiftrls(x,ix,y,iy,ly,n1):lessis(shiftr(x,ix,y,iy,ly,n1),x)
-t27:=intshiftr(x,ix,p1(u),t5,t6,n):intrl(shiftr(x,ix,p1(u),t5,t6,n))
-t28:=lsshiftr(x,ix,p1(u),t5,t6,n):lessis(p1(u),shiftr(x,ix,p1(u),t5,t6,n))
-t29:=shiftrls(x,ix,p1(u),t5,t6,n):lessis(shiftr(x,ix,p1(u),t5,t6,n),x)
-t30:=t4(shiftr(x,ix,p1(u),t5,t6,n),t27,t28,t29):lessis(y,shiftr(x,ix,p1(u),t5,t6,n))
-t31:=<t23><t29><t30><t27><shiftr(x,ix,p1(u),t5,t6,n)><t26><t25><t24><shiftr(x,ix,y,iy,ly,n1)>pi:is(<n>fr,<n>shiftf(x,ix,p1(u),t5,t6,rgt))
-k@t32:=fisi(1to(sxu),cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt),[t:1to(sxu)]t31(t)):is"e"([t:1to(sxu)]cx,fr,shiftf(x,ix,p1(u),t5,t6,rgt))
-t33:=isf([t:1to(sxu)]cx,cx,[v:[t:1to(sxu)]cx]smpr(q,sxu,v),fr,shiftf(x,ix,p1(u),t5,t6,rgt),t32):is(smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q))
-t34:=isf(cx,cx,<smpr(q,suy,fl)>q,smpr(q,sxu,fr),smpri(x,ix,p1(u),t5,t6,rgt,q),t33):is(<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q)
-[n:1to(suy)]
-t35:=isinoutn(pl"n"(suy,sxu),inn(suy,n),trlessis"n"(inn(suy,n),suy,pl"n"(suy,sxu),1top(suy,n),t12)):is"n"(inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)))
-t36:=isinoutn(sxy,inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),trlessis"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),pl"n"(suy,sxu),sxy,1top(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),t10)):is"n"(inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n))))
-n2:=left1to(sxy,pl"n"(suy,sxu),t10,left1to(pl"n"(suy,sxu),suy,t12,n)):1to(sxy)
-t37:=tris(nat,inn(suy,n),inn(pl"n"(suy,sxu),left1to(pl"n"(suy,sxu),suy,t12,n)),inn(sxy,n2),t35,t36):is"n"(inn(suy,n),inn(sxy,n2))
-t38:=isnterl(inn(suy,n),inn(sxy,n2),t37):is"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)))
-t39:=ispl1"r"(rlofnt(inn(suy,n)),rlofnt(inn(sxy,n2)),y,t38):is"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y))
-t40:=ismn1"r"(pl(rlofnt(inn(suy,n)),y),pl(rlofnt(inn(sxy,n2)),y),1rl,t39):is"r"(shiftr(u,iu,y,iy,l,n),shiftr(x,ix,y,iy,ly,n2))
-t41:=intshiftr(u,iu,y,iy,l,n):intrl(shiftr(u,iu,y,iy,l,n))
-t42:=lsshiftr(u,iu,y,iy,l,n):lessis(y,shiftr(u,iu,y,iy,l,n))
-t43:=shiftrls(u,iu,y,iy,l,n):lessis(shiftr(u,iu,y,iy,l,n),u)
-t44:=t1(shiftr(u,iu,y,iy,l,n),t41,t42,t43):lessis(shiftr(u,iu,y,iy,l,n),x)
-t45:=intshiftr(x,ix,y,iy,ly,n2):intrl(shiftr(x,ix,y,iy,ly,n2))
-t46:=lsshiftr(x,ix,y,iy,ly,n2):lessis(y,shiftr(x,ix,y,iy,ly,n2))
-t47:=shiftrls(x,ix,y,iy,ly,n2):lessis(shiftr(x,ix,y,iy,ly,n2),x)
-t48:=<t40><t47><t46><t45><shiftr(x,ix,y,iy,ly,n2)><t44><t42><t41><shiftr(u,iu,y,iy,l,n)>pi:is(<n>shiftf(u,iu,y,iy,l,lft),<n>fl)
-t49:=symis(cx,<n>shiftf(u,iu,y,iy,l,lft),<n>fl,t48):is(<n>fl,<n>shiftf(u,iu,y,iy,l,lft))
-k@t50:=fisi(1to(suy),cx,fl,shiftf(u,iu,y,iy,l,lft),[t:1to(suy)]t49(t)):is"e"([t:1to(suy)]cx,fl,shiftf(u,iu,y,iy,l,lft))
-t51:=isf([t:1to(suy)]cx,cx,[v:[t:1to(suy)]cx]smpr(q,suy,v),fl,shiftf(u,iu,y,iy,l,lft),t50):is(smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q))
-t52:=isf(cx,cx,[t:cx]<smpri(x,ix,p1(u),t5,t6,rgt,q)><t>q,smpr(q,suy,fl),smpri(u,iu,y,iy,l,lft,q),t51):is(<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
-t53:=tr3is(cx,smpr(q,pl"n"(suy,sxu),f1),<smpr(q,sxu,fr)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpr(q,suy,fl)>q,<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,t12a,t34,t52):is(smpr(q,pl"n"(suy,sxu),f1),<smpri(x,ix,p1(u),t5,t6,rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
--8284
-k@satz284:=tris1(cx,smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q,smpr(q,pl"n"(suy".8284",sxu".8284"),f1".8284"),t11".8284",t53".8284"):is(smpri(x,ix,y,iy,ly,f,q),<smpri(x,ix,pl"r"(u,1rl),intpl(u,iu,1rl,intrl1),satzr25(u,iu,x,ix,k),rgt,q)><smpri(u,iu,y,iy,l,lft,q)>q)
-q@[v:real][iv:intrl(v)][w:real][iw:intrl(w)][lw:lessis(pl"r"(y,v),w)][kw:lessis(w,pl"r"(x,v))]
-+8285
-x@[y:real]
-pl:=pl"r"(x,y):real
-mn:=mn"r"(x,y):real
-x@p1:=pl"r"(x,1rl):real
-kw@t1:=th9"l.or"(less(pl(y,v),w),is"r"(pl(y,v),w),less(mn(pl(y,v),v),mn(w,v)),is"r"(mn(pl(y,v),v),mn(w,v)),lw,[t:less(pl(y,v),w)]satz188f(pl(y,v),w,m0"r"(v),t),[t:is"r"(pl(y,v),w)]ismn1"r"(pl(y,v),w,v,t)):lessis(mn(pl(y,v),v),mn(w,v))
-t2:=islessis1(mn(pl(y,v),v),y,mn(w,v),mnpl(y,v),t1):lessis(y,mn(w,v))
-t3:=th9"l.or"(less(w,pl(x,v)),is"r"(w,pl(x,v)),less(mn(w,v),mn(pl(x,v),v)),is"r"(mn(w,v),mn(pl(x,v),v)),kw,[t:less(w,pl(x,v))]satz188f(w,pl(x,v),m0"r"(v),t),[t:is"r"(w,pl(x,v))]ismn1"r"(w,pl(x,v),v,t)):lessis(mn(w,v),mn(pl(x,v),v))
-t4:=islessis2(mn(pl(x,v),v),x,mn(w,v),mnpl(x,v),t3):lessis(mn(w,v),x)
--8285
-iv@sft:=[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]<t4".8285"(t,w,lt,kt)><t2".8285"(t,w,lt,kt)><intmn(t,w,v,iv)><mn"r"(t,v)>f:[t:real][w:intrl(t)][lt:lessis(pl"r"(y,v),t)][kt:lessis(t,pl"r"(x,v))]cx
-+*8285
-iv@t5:=tris(real,m0"r"(pl(y,v)),m0"r"(pl(v,y)),pl(m0"r"(v),m0"r"(y)),ism0"r"(pl(y,v),pl(v,y),compl"r"(y,v)),satz180(v,y)):is"r"(m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)))
-t6:=tr3is(real,mn(pl(1rl,pl(x,v)),v),pl(1rl,mn(pl(x,v),v)),pl(1rl,x),p1(x),asspl1"r"(1rl,pl(x,v),m0"r"(v)),ispl2"r"(mn(pl(x,v),v),x,1rl,mnpl(x,v)),compl"r"(1rl,x)):is"r"(mn(pl(1rl,pl(x,v)),v),p1(x))
-t7:=tr3is(real,mn(p1(pl(x,v)),pl(y,v)),pl(pl(1rl,pl(x,v)),pl(m0"r"(v),m0"r"(y))),mn(mn(pl(1rl,pl(x,v)),v),y),mn(p1(x),y),ispl12"r"(p1(pl(x,v)),pl(1rl,pl(x,v)),m0"r"(pl(y,v)),pl(m0"r"(v),m0"r"(y)),compl"r"(pl(x,v),1rl),t5),asspl2"r"(pl(1rl,pl(x,v)),m0"r"(v),m0"r"(y)),ismn1"r"(mn(pl(1rl,pl(x,v)),v),p1(x),y,t6)):is"r"(mn(p1(pl(x,v)),pl(y,v)),mn(p1(x),y))
-t8:=th9"l.or"(less(y,x),is"r"(y,x),less(pl(y,v),pl(x,v)),is"r"(pl(y,v),pl(x,v)),ly,[t:less(y,x)]satz188f(y,x,v,t),[t:is"r"(y,x)]ispl1"r"(y,x,v,t)):lessis(pl(y,v),pl(x,v))
-s0:=shiftl(x,ix,y,iy,ly):nat
-sv:=shiftl(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8):nat
-t9:=isrlent(mn(p1(pl(x,v)),pl(y,v)),t6"r.shift"(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8),mn(p1(x),y),t6"r.shift"(x,ix,y,iy,ly),t7):is"n"(sv,s0)
-t10:=lessisi2"n"(sv,s0,t9):lessis"n"(sv,s0)
-f1:=left(cx,s0,sv,t10,shiftf(x,ix,y,iy,ly,f)):[t:1to(sv)]cx
-t11:=issmpr(q,s0,shiftf(x,ix,y,iy,ly,f),sv,t9):is(smpr(q,sv,f1),smpri(x,ix,y,iy,ly,f,q))
-[n:1to(sv)]
-t12:=isinoutn(s0,inn(sv,n),trlessis"n"(inn(sv,n),sv,s0,1top(sv,n),t10)):is"n"(inn(sv,n),inn(s0,left1to(s0,sv,t10,n)))
-n1:=left1to(s0,sv,t10,n):1to(s0)
-t13:=isnterl(inn(sv,n),inn(s0,n1),t12):is"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)))
-t14:=tris(real,mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(sv,n)),mn(pl(y,v),v)),pl(rlofnt(inn(s0,n1)),y),asspl1"r"(rlofnt(inn(sv,n)),pl(y,v),m0"r"(v)),ispl12"r"(rlofnt(inn(sv,n)),rlofnt(inn(s0,n1)),mn(pl(y,v),v),y,t13,mnpl(y,v))):is"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y))
-st0:=shiftr(x,ix,y,iy,ly,n1):real
-stv:=shiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):real
-t15:=tr4is(real,mn(stv,v),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(1rl),m0"r"(v))),pl(pl(rlofnt(inn(sv,n)),pl(y,v)),pl(m0"r"(v),m0"r"(1rl))),mn(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),1rl),st0,asspl1"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(1rl),m0"r"(v)),ispl2"r"(pl(m0"r"(1rl),m0"r"(v)),pl(m0"r"(v),m0"r"(1rl)),pl(rlofnt(inn(sv,n)),pl(y,v)),compl"r"(m0"r"(1rl),m0"r"(v))),asspl2"r"(pl(rlofnt(inn(sv,n)),pl(y,v)),m0"r"(v),m0"r"(1rl)),ismn1"r"(mn(pl(rlofnt(inn(sv,n)),pl(y,v)),v),pl(rlofnt(inn(s0,n1)),y),1rl,t14)):is"r"(mn(stv,v),st0)
-t16:=intshiftr(x,ix,y,iy,ly,n1):intrl(st0)
-t17:=shiftrls(x,ix,y,iy,ly,n1):lessis(st0,x)
-t18:=lsshiftr(x,ix,y,iy,ly,n1):lessis(y,st0)
-t19:=intshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):intrl(stv)
-t20:=shiftrls(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(stv,pl(x,v))
-t21:=lsshiftr(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,n):lessis(pl(y,v),stv)
-t22:=intmn(stv,t19,v,iv):intrl(mn(stv,v))
-t23:=t2(stv,t19,t21,t20):lessis(y,mn(stv,v))
-t24:=t4(stv,t19,t21,t20):lessis(mn(stv,v),x)
-t25:=<t15><t17><t18><t16><st0><t24><t23><t22><mn(stv,v)>pi:is(<n>shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),<n>f1)
-iv@t26:=fisi(1to(sv),cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,[t:1to(sv)]t25(t)):is"e"([t:1to(sv)]cx,shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1)
-t27:=isf([t:1to(sv)]cx,cx,[w:[t:1to(sv)]cx]smpr(q,sv,w),shiftf(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft),f1,t26):is(smpri(pl(x,v),intpl(x,ix,v,iv),pl(y,v),intpl(y,iy,v,iv),t8,sft,q),smpr(q,sv,f1))
--8285
-iv@lemma285:=t8".8285":lessis(pl"r"(y,v),pl"r"(x,v))
-satz285:=tris(cx,smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpr(q,sv".8285",f1".8285"),smpri(x,ix,y,iy,ly,f,q),t27".8285",t11".8285"):is(smpri(pl"r"(x,v),intpl(x,ix,v,iv),pl"r"(y,v),intpl(y,iy,v,iv),lemma285,sft,q),smpri(x,ix,y,iy,ly,f,q))
-ly@[s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][f:seq(x,ix,y,iy,ly,cx)][u:real][iu:intrl(u)][lu:lessis(y,u)][ul:lessis(u,x)]
-us:=<ul><lu><iu><u>s:real
-+8286
-t1:=<ul><lu><iu><u>ins:and3(intrl(us),lessis(y,us),lessis(us,x))
--8286
-inseqe1:=t22"r.shift"(x,ix,y,iy,ly,us,t1".8286"):intrl(us)
-inseqe2:=t23"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(y,us)
-inseqe3:=t24"r.shift"(x,ix,y,iy,ly,us,t1".8286"):lessis(us,x)
-usf:=<inseqe3><inseqe2><inseqe1><us>f:cx
-f@permseq:=[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]usf(t,u,v,w):[t:real][u:intrl(t)][v:lessis(y,t)][w:lessis(t,x)]cx
-q@[a:assoc(q)][c:commut(q)][s:seq(x,ix,y,iy,ly,real)][ins:inseq(x,ix,y,iy,ly,s)][pri:proofsirrelevant(x,ix,y,iy,ly,real,s)][ps:perm(x,ix,y,iy,ly,s)]
-+*8286
-ps@ss:=shiftseq(x,ix,y,iy,ly,s,ins):[t:1to(shiftl)]1to(shiftl)
-t2:=satz283(q,a,c,shiftl,ss,bijshiftseq(x,ix,y,iy,ly,s,ins,pri,ps),shiftf(f)):is(smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)),smpri(f,q))
-[n:1to(shiftl)]
-ns:=us(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):real
-t3:=shiftinv1(ns,t34"r.shift"(x,ix,y,iy,ly,s,ins,n)):is"r"(ns,shiftr(<n>ss))
-t4:=inseqe1(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):intrl(ns)
-t5:=inseqe2(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(y,ns)
-t6:=inseqe3(s,ins,f,shiftr(n),intshiftr(n),lsshiftr(n),shiftrls(n)):lessis(ns,x)
-t7:=intshiftr(<n>ss):intrl(shiftr(<n>ss))
-t8:=lsshiftr(<n>ss):lessis(y,shiftr(<n>ss))
-t9:=shiftrls(<n>ss):lessis(shiftr(<n>ss),x)
-t10:=<t3><t9><t8><t7><shiftr(<n>ss)><t6><t5><t4><ns>pi:is(<n>shiftf(permseq(s,ins,f)),<<n>ss>shiftf(f))
-ps@t11:=fisi(1to(shiftl),cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),[t:1to(shiftl)]t10(t)):is"e"([t:1to(shiftl)]cx,shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f))
-t12:=isf([t:1to(shiftl)]cx,cx,[u:[t:1to(shiftl)]cx]smpr(q,shiftl,u),shiftf(permseq(s,ins,f)),[t:1to(shiftl)]<<t>ss>shiftf(f),t11):is(smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss>shiftf(f)))
--8286
-ps@satz286:=tris(cx,smpri(permseq(s,ins,f),q),smpr(q,shiftl,[t:1to(shiftl)]<<t>ss".8286">shiftf(f)),smpri(f,q),t12".8286",t2".8286"):is(smpri(permseq(s,ins,f),q),smpri(f,q))
-@[x:nat][f:[t:1to(x)]cx]
-modf:=[t:1to(x)]pli(mod(<t>f),0):[t:1to(x)]cx
-+8287
-[r:real]
-prop1:=lessis(mod(sum(x,f)),r):'prop'
-prop2:=is(sum(x,modf(f)),pli(r,0)):'prop'
-prop3:=and(prop1,prop2):'prop'
-f@prop4:=some"r"([t:real]prop3(t)):'prop'
-x@prop5:=[u:[t:1to(x)]cx]prop4(u):'prop'
-@[f:[t:1to(1)]cx]
-t1:=satz277([t:cx][u:cx]pl(t,u),f):is(sum(1,f),<xout(1)>f)
-t2:=ismod(sum(1,f),<xout(1)>f,t1):is"r"(mod(sum(1,f)),mod(<xout(1)>f))
-t3:=lessisi2(mod(sum(1,f)),mod(<xout(1)>f),t2):prop1(1,f,mod(<xout(1)>f))
-t4:=satz277([t:cx][u:cx]pl(t,u),modf(1,f)):prop2(1,f,mod(<xout(1)>f))
-t5:=andi(prop1(1,f,mod(<xout(1)>f)),prop2(1,f,mod(<xout(1)>f)),t3,t4):prop3(1,f,mod(<xout(1)>f))
-t6:=somei(real,[t:real]prop3(1,f,t),mod(<xout(1)>f),t5):prop4(1,f)
-@t7:=[u:[t:1to(1)]cx]t6(u):prop5(1)
-x@[p:prop5(x)][f:[t:1to(pl"n"(x,1))]cx]
-t8:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
-lf:=left(cx,pl"n"(x,1),x,t8,f):[t:1to(x)]cx
-[r:real][pr:prop3(lf,r)]
-t9:=ande1(prop1(lf,r),prop2(lf,r),pr):prop1(lf,r)
-t10:=ande2(prop1(lf,r),prop2(lf,r),pr):prop2(lf,r)
-t11:=satz278([t:cx][u:cx]pl(t,u),x,f):is(sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f))
-t12:=ismod(pl(sum(x,lf),<xout(pl"n"(x,1))>f),sum(pl"n"(x,1),f),symis(cx,sum(pl"n"(x,1),f),pl(sum(x,lf),<xout(pl"n"(x,1))>f),t11)):is"r"(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)))
-m:=mod(<xout(pl"n"(x,1))>f):real
-t13:=islessis1(mod(pl(sum(x,lf),<xout(pl"n"(x,1))>f)),mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),t12,satz271(sum(x,lf),<xout(pl"n"(x,1))>f)):lessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m))
-t14:=th9"l.or"(less(mod(sum(x,lf)),r),is"r"(mod(sum(x,lf)),r),less(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),is"r"(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m)),t9,[t:less(mod(sum(x,lf)),r)]satz188f(mod(sum(x,lf)),r,m,t),[t:is"r"(mod(sum(x,lf)),r)]ispl1"r"(mod(sum(x,lf)),r,m,t)):lessis(pl"r"(mod(sum(x,lf)),m),pl"r"(r,m))
-t15:=trlessis(mod(sum(pl"n"(x,1),f)),pl"r"(mod(sum(x,lf)),m),pl"r"(r,m),t13,t14):prop1(pl"n"(x,1),f,pl"r"(r,m))
-lmf:=left(cx,pl"n"(x,1),x,t8,modf(pl"n"(x,1),f)):[t:1to(x)]cx
-t16:=satz278([t:cx][u:cx]pl(t,u),x,modf(pl"n"(x,1),f)):is(sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)))
-t17:=ispl1(sum(x,lmf),pli(r,0),pli(m,0),t10):is(pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)))
-t18:=plis12a(r,0,m,0):is(pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)))
-t19:=isrecx2(pl"r"(0,0),0,pl"r"(r,m),pl01"r"(0,0,refis(real,0))):is(pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0))
-t20:=tr4is(cx,sum(pl"n"(x,1),modf(pl"n"(x,1),f)),pl(sum(x,lmf),pli(m,0)),pl(pli(r,0),pli(m,0)),pli(pl"r"(r,m),pl"r"(0,0)),pli(pl"r"(r,m),0),t16,t17,t18,t19):prop2(pl"n"(x,1),f,pl"r"(r,m))
-t21:=andi(prop1(pl"n"(x,1),f,pl"r"(r,m)),prop2(pl"n"(x,1),f,pl"r"(r,m)),t15,t20):prop3(pl"n"(x,1),f,pl"r"(r,m))
-t22:=somei(real,[t:real]prop3(pl"n"(x,1),f,t),pl"r"(r,m),t21):prop4(pl"n"(x,1),f)
-f@t23:=someapp(real,[t:real]prop3(lf,t),<lf>p,prop4(pl"n"(x,1),f),[t:real][u:prop3(lf,t)]t22(t,u)):prop4(pl"n"(x,1),f)
-p@t25:=[u:[t:1to(pl"n"(x,1))]cx]t23(u):prop5(pl"n"(x,1))
-t26:=isp(nat,[t:nat]prop5(t),pl"n"(x,1),<x>suc,t25,satz4a(x)):prop5(<x>suc)
--8287
-satz287:=<f>induction([t:nat]prop5".8287"(t),t7".8287",[t:nat][u:prop5".8287"(t)]t26".8287"(t,u),x):some"r"([t:real]and(lessis(mod(sum(x,f)),t),is(sum(x,modf(f)),pli(t,0))))
-+8288
-prop1:=is(pli(mod(prod(x,f)),0),prod(x,modf(f))):'prop'
-x@prop2:=[u:[t:1to(x)]cx]prop1(u):'prop'
-@[f:[t:1to(1)]cx]
-t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
-t2:=ismod(prod(1,f),<xout(1)>f,t1):is"r"(mod(prod(1,f)),mod(<xout(1)>f))
-t3:=isrecx1(mod(prod(1,f)),mod(<xout(1)>f),0,t2):is(pli(mod(prod(1,f)),0),pli(mod(<xout(1)>f),0))
-t4:=satz277([t:cx][u:cx]ts(t,u),modf(1,f)):is(prod(1,modf(1,f)),pli(mod(<xout(1)>f),0))
-t5:=tris2(cx,pli(mod(prod(1,f)),0),prod(1,modf(1,f)),pli(mod(<xout(1)>f),0),t3,t4):prop1(1,f)
-@t6:=[u:[t:1to(1)]cx]t5(u):prop2(1)
-x@[p:prop2(x)][f:[t:1to(pl"n"(x,1))]cx]
-t7:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
-lf:=left(cx,pl"n"(x,1),x,t7,f):[t:1to(x)]cx
-t8:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
-m:=mod(<xout(pl"n"(x,1))>f):real
-t9:=ismod(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),t8):is"r"(mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)))
-t10:=satz268(prod(x,lf),<xout(pl"n"(x,1))>f):is"r"(mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m))
-t11:=tris(real,mod(prod(pl"n"(x,1),f)),mod(ts(prod(x,lf),<xout(pl"n"(x,1))>f)),ts"r"(mod(prod(x,lf)),m),t9,t10):is"r"(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m))
-t12:=isrecx1(mod(prod(pl"n"(x,1),f)),ts"r"(mod(prod(x,lf)),m),0,t11):is(pli(mod(prod(pl"n"(x,1),f)),0),pli(ts"r"(mod(prod(x,lf)),m),0))
-lmf:=left(cx,pl"n"(x,1),x,t7,modf(pl"n"(x,1),f)):[t:1to(x)]cx
-t13:=satz278([t:cx][u:cx]ts(t,u),x,modf(pl"n"(x,1),f)):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)))
-t14:=symis(cx,pli(mod(prod(x,lf)),0),prod(x,lmf),<lf>p):is(prod(x,lmf),pli(mod(prod(x,lf)),0))
-t15:=ists1(prod(x,lmf),pli(mod(prod(x,lf)),0),pli(m,0),t14):is(ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)))
-t16:=tsis12a(mod(prod(x,lf)),0,m,0):is(ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))))
-t17:=tris(real,mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),mn"r"(ts"r"(mod(prod(x,lf)),m),0),ts"r"(mod(prod(x,lf)),m),ismn2"r"(ts"r"(0,0),0,ts"r"(mod(prod(x,lf)),m),ts01"r"(0,0,refis(real,0))),pl02"r"(ts"r"(mod(prod(x,lf)),m),m0"r"(0),satz176b(0,refis(real,0)))):is"r"(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m))
-t18:=tris(real,pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),pl"r"(0,0),0,ispl12"r"(ts"r"(mod(prod(x,lf)),0),0,ts"r"(0,m),0,ts02"r"(mod(prod(x,lf)),0,refis(real,0)),ts01"r"(0,m,refis(real,0))),pl01"r"(0,0,refis(real,0))):is"r"(pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0)
-t19:=isrecx12(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),ts"r"(mod(prod(x,lf)),m),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m)),0,t17,t18):is(pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0))
-t20:=tr4is(cx,prod(pl"n"(x,1),modf(pl"n"(x,1),f)),ts(prod(x,lmf),pli(m,0)),ts(pli(mod(prod(x,lf)),0),pli(m,0)),pli(mn"r"(ts"r"(mod(prod(x,lf)),m),ts"r"(0,0)),pl"r"(ts"r"(mod(prod(x,lf)),0),ts"r"(0,m))),pli(ts"r"(mod(prod(x,lf)),m),0),t13,t15,t16,t19):is(prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0))
-t21:=tris2(cx,pli(mod(prod(pl"n"(x,1),f)),0),prod(pl"n"(x,1),modf(pl"n"(x,1),f)),pli(ts"r"(mod(prod(x,lf)),m),0),t12,t20):prop1(pl"n"(x,1),f)
-p@t21a:=[u:[t:1to(pl"n"(x,1))]cx]t21(u):prop2(pl"n"(x,1))
-t22:=isp(nat,[t:nat]prop2(t),pl"n"(x,1),<x>suc,t21a,satz4a(x)):prop2(<x>suc)
--8288
-satz288:=<f>induction([t:nat]prop2".8288"(t),t6".8288",[t:nat][u:prop2".8288"(t)]t22".8288"(t,u),x):is(pli(mod(prod(x,f)),0),prod(x,modf(f)))
-+8289
-prop1:=is(prod(x,f),0c):'prop'
-prop2:=some"l"(1to(x),[t:1to(x)]is(<t>f,0c)):'prop'
-prop3:=iff(prop1,prop2):'prop'
-x@prop4:=[u:[t:1to(x)]cx]prop3(u):'prop'
-@[f:[t:1to(1)]cx]
-t1:=satz277([t:cx][u:cx]ts(t,u),f):is(prod(1,f),<xout(1)>f)
-[p:prop1(1,f)]
-t2:=tris1(cx,<xout(1)>f,0c,prod(1,f),t1,p):is(<xout(1)>f,0c)
-t3:=somei(1to(1),[t:1to(1)]is(<t>f,0c),xout(1),t2):prop2(1,f)
-f@[p:prop2(1,f)][u:1to(1)][i:is(<u>f,0c)]
-t4:=th1"n.singlet"(u):is"e"(1to(1),u,xout(1))
-t5:=tr3is(cx,prod(1,f),<xout(1)>f,<u>f,0c,t1,isf(1to(1),cx,f,xout(1),u,symis(1to(1),u,xout(1),t4)),i):prop1(1,f)
-p@t6:=someapp(1to(1),[t:1to(1)]is(<t>f,0c),p,prop1(1,f),[t:1to(1)][u:is(<t>f,0c)]t5(t,u)):prop1(1,f)
-f@t7:=iffi(prop1(1,f),prop2(1,f),[t:prop1(1,f)]t3(t),[t:prop2(1,f)]t6(t)):prop3(1,f)
-@t8:=[u:[t:1to(1)]cx]t7(u):prop4(1)
-x@[p:prop4(x)][f:[t:1to(pl"n"(x,1))]cx]
-t9:=lessisi1"n"(x,pl"n"(x,1),satz18a(x,1)):lessis"n"(x,pl"n"(x,1))
-lf:=left(cx,pl"n"(x,1),x,t9,f):[t:1to(x)]cx
-t10:=satz278([t:cx][u:cx]ts(t,u),x,f):is(prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f))
-[q:prop1(pl"n"(x,1),f)]
-t11:=tris1(cx,ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,prod(pl"n"(x,1),f),t10,q):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-t12:=satz221c(prod(x,lf),<xout(pl"n"(x,1))>f,t11):or(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c))
-[i:is(prod(x,lf),0c)]
-t13:=th3"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,i):prop2(x,lf)
-[n:1to(x)][j:is(<n>lf,0c)]
-t14:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),left1to(pl"n"(x,1),x,t9,n),j):prop2(pl"n"(x,1),f)
-i@t15:=someapp(1to(x),[t:1to(x)]is(<t>lf,0c),t13,prop2(pl"n"(x,1),f),[t:1to(x)][u:is(<t>lf,0c)]t14(t,u)):prop2(pl"n"(x,1),f)
-q@[i:is(<xout(pl"n"(x,1))>f,0c)]
-t16:=somei(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),xout(pl"n"(x,1)),i):prop2(pl"n"(x,1),f)
-q@t17:=orapp(is(prod(x,lf),0c),is(<xout(pl"n"(x,1))>f,0c),prop2(pl"n"(x,1),f),t12,[t:is(prod(x,lf),0c)]t15(t),[t:is(<xout(pl"n"(x,1))>f,0c)]t16(t)):prop2(pl"n"(x,1),f)
-f@[q:prop2(pl"n"(x,1),f)][n:1to(pl"n"(x,1))][i:is(<n>f,0c)][j:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]
-t18:=tris1(cx,<xout(pl"n"(x,1))>f,0c,<n>f,isf(1to(pl"n"(x,1)),cx,f,n,xout(pl"n"(x,1)),j),i):is(<xout(pl"n"(x,1))>f,0c)
-t20:=satz221b(prod(x,lf),<xout(pl"n"(x,1))>f,t18):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-i@[m:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]
-n1:=inn(pl"n"(x,1),n):nat
-[j:is"n"(n1,pl"n"(x,1))]
-t21:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),pl"n"(x,1),lessisi3(pl"n"(x,1)),j):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)))
-t22:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),xout(pl"n"(x,1)),isoutinn(pl"n"(x,1),n),t21):is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))
-m@t23:=th3"l.imp"(is"n"(n1,pl"n"(x,1)),is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),m,[t:is"n"(n1,pl"n"(x,1))]t22(t)):nis"n"(n1,pl"n"(x,1))
-t24:=ore1(less"n"(n1,pl"n"(x,1)),is"n"(n1,pl"n"(x,1)),1top(pl"n"(x,1),n),t23):less"n"(n1,pl"n"(x,1))
-t25:=satz26(x,n1,t24):lessis"n"(n1,x)
-n2:=outn(x,n1,t25):1to(x)
-t26:=isinoutn(x,n1,t25):is"n"(n1,inn(x,n2))
-t27:=isoutni(pl"n"(x,1),n1,1top(pl"n"(x,1),n),inn(x,n2),trlessis"n"(inn(x,n2),x,pl"n"(x,1),1top(x,n2),t9),t26):is"e"(1to(pl"n"(x,1)),outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2))
-t28:=tris(1to(pl"n"(x,1)),n,outn(pl"n"(x,1),n1,1top(pl"n"(x,1),n)),left1to(pl"n"(x,1),x,t9,n2),isoutinn(pl"n"(x,1),n),t27):is"e"(1to(pl"n"(x,1)),n,left1to(pl"n"(x,1),x,t9,n2))
-t29:=isf(1to(pl"n"(x,1)),cx,f,n,left1to(pl"n"(x,1),x,t9,n2),t28):is(<n>f,<n2>lf)
-t30:=tris1(cx,<n2>lf,0c,<n>f,t29,i):is(<n2>lf,0c)
-t31:=somei(1to(x),[t:1to(x)]is(<t>lf,0c),n2,t30):prop2(x,lf)
-t32:=th4"l.iff"(prop1(x,lf),prop2(x,lf),<lf>p,t31):prop1(x,lf)
-t34:=satz221a(prod(x,lf),<xout(pl"n"(x,1))>f,t32):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-i@t35:=th1"l.imp"(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))),is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c),[t:is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1)))]t20(t),[t:not(is"e"(1to(pl"n"(x,1)),n,xout(pl"n"(x,1))))]t34(t)):is(ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c)
-t36:=tris(cx,prod(pl"n"(x,1),f),ts(prod(x,lf),<xout(pl"n"(x,1))>f),0c,t10,t35):prop1(pl"n"(x,1),f)
-q@t37:=someapp(1to(pl"n"(x,1)),[t:1to(pl"n"(x,1))]is(<t>f,0c),q,prop1(pl"n"(x,1),f),[t:1to(pl"n"(x,1))][u:is(<t>f,0c)]t36(t,u)):prop1(pl"n"(x,1),f)
-f@t38:=iffi(prop1(pl"n"(x,1),f),prop2(pl"n"(x,1),f),[t:prop1(pl"n"(x,1),f)]t17(t),[t:prop2(pl"n"(x,1),f)]t37(t)):prop3(pl"n"(x,1),f)
-p@t39:=[u:[t:1to(pl"n"(x,1))]cx]t38(u):prop4(pl"n"(x,1))
-t40:=isp(nat,[t:nat]prop4(t),pl"n"(x,1),<x>suc,t39,satz4a(x)):prop4(<x>suc)
--8289
-satz289:=<f>induction([t:nat]prop4".8289"(t),t8".8289",[t:nat][u:prop4".8289"(t)]t40".8289"(t,u),x):iff(is(prod(x,f),0c),some"l"(1to(x),[t:1to(x)]is(<t>f,0c)))
-[i:is(prod(x,f),0c)]
-satz289a:=th3"l.iff"(prop1".8289",prop2".8289",satz289,i):some"l"(1to(x),[t:1to(x)]is(<t>f,0c))
-f@[n:1to(x)][i:is(<n>f,0c)]
-+*8289
-i"c"@t41:=somei(1to(x),[t:1to(x)]is(<t>f,0c),n,i):prop2
--8289
-i@satz289b:=th4"l.iff"(prop1".8289",prop2".8289",satz289,t41".8289"):is(prod(x,f),0c)
-@[x:complex][m:real][mi:intrl(m)][o:or(nis(x,0c),pos(m))]
-+v9
-[p:pos(m)]
-t1:=posintnatrl(m,p,mi):natrl(m)
-m1:=ntofrl(m,t1):nat
-pw1:=prod(m1,[t:1to(m1)]x):cx
--v9
-x@[y:complex][m:real][n:real][i:is(x,y)][j:is"r"(m,n)][mi1:intrl(m)][ni1:intrl(n)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(n))]
-+*v9
-oy@[mp:pos(m)][np:pos(n)]
-m0:=m1(x,m,mi1,ox,mp):nat
-n0:=m1(y,n,ni1,oy,np):nat
-t2:=isrlent(m,t1(x,m,mi1,ox,mp),n,t1(y,n,ni1,oy,np),j):is"n"(m0,n0)
-t3:=lessisi2"n"(m0,n0,t2):lessis"n"(m0,n0)
-t4:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]y,m0,t2):is(prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np))
-t5:=fisi(1to(m0),cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),[t:1to(m0)]i):is"e"([t:1to(m0)]cx,[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y))
-t6:=isf([t:1to(m0)]cx,cx,[u:[t:1to(m0)]cx]prod(m0,u),[t:1to(m0)]x,left(cx,n0,m0,t3,[t:1to(n0)]y),t5):is(pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)))
-t7:=tris(cx,pw1(x,m,mi1,ox,mp),prod(m0,left(cx,n0,m0,t3,[t:1to(n0)]y)),pw1(y,n,ni1,oy,np),t6,t4):is(pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,np))
-p@[p1:pos(m)]
-t8:=t7(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,p,p1):is(pw1(p),pw1(p1))
-p@[n:nis(x,0c)]
-t9:=th5"l.some"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c),[t:1to(m1)]n):not(some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)))
-t10:=th3"l.imp"(is(pw1,0c),some"l"(1to(m1),[t:1to(m1)]is(<t>[u:1to(m1)]x,0c)),t9,[t:is(pw1,0c)]satz289a(m1,[u:1to(m1)]x,t)):nis(pw1,0c)
-o@[n:neg(m)]
-mi@t11:=intabs(m,mi):intrl(abs(m))
-n@t12:=satz166b(m,n):pos(abs(m))
-t13:=ori2(nis(x,0c),pos(abs(m)),t12):or(nis(x,0c),pos(abs(m)))
-t14:=ore1(nis(x,0c),pos(m),o,nnotp(m,n)):nis(x,0c)
-t15:=t10(abs(m),t11,t13,t12,t14):nis(pw1(abs(m),t11,t13,t12),0c)
-pw2:=ov(1c,pw1(abs(m),t11,t13,t12),t15):cx
-oy@[nm:neg(m)][nn:neg(n)]
-pwm:=pw1(x,abs(m),t11(x,m,mi1),t13(x,m,mi1,ox,nm),t12(x,m,mi1,ox,nm)):cx
-pwn:=pw1(y,abs(n),t11(y,n,ni1),t13(y,n,ni1,oy,nn),t12(y,n,ni1,oy,nn)):cx
-t16:=t7(abs(m),abs(n),i,isabs(m,n,j),t11(x,m,mi1),t11(y,n,ni1),t13(x,m,mi1,ox,nm),t13(y,n,ni1,oy,nn),t12(x,m,mi1,ox,nm),t12(y,n,ni1,oy,nn)):is(pwm,pwn)
-t17:=isov2(pwm,pwn,1c,t16,t15(x,m,mi1,ox,nm),t15(y,n,ni1,oy,nn)):is(pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,nn))
-n@[n1:neg(m)]
-t18:=t17(x,x,m,m,refis(cx,x),refis(real,m),mi,mi,o,o,n,n1):is(pw2(n),pw2(n1))
-o@pw3:=ite"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c)):cx
-n@t19:=itet"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),n):is(pw3,pw2(n))
-o@[nn:not(neg(m))]
-t20:=itef"l.r"(neg(m),cx,[t:neg(m)]pw2(t),[t:not(neg(m))]1c,[t:neg(m)][u:neg(m)]t18(t,u),[t:not(neg(m))][u:not(neg(m))]refis(cx,1c),nn):is(pw3,1c)
-nm@t21:=isp(real,[t:real]neg(t),m,n,nm,j):neg(n)
-t22:=t19(x,m,mi1,ox,nm):is(pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm))
-t23:=symis(cx,pw3(y,n,ni1,oy),pw2(y,n,ni1,oy,t21),t19(y,n,ni1,oy,t21)):is(pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy))
-t24:=tr3is(cx,pw3(x,m,mi1,ox),pw2(x,m,mi1,ox,nm),pw2(y,n,ni1,oy,t21),pw3(y,n,ni1,oy),t22,t17(t21),t23):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
-oy@[nn:not(neg(m))]
-t25:=isp(real,[t:real]not(neg(t)),m,n,nn,j):not(neg(n))
-t26:=t20(x,m,mi1,ox,nn):is(pw3(x,m,mi1,ox),1c)
-t27:=t20(y,n,ni1,oy,t25):is(pw3(y,n,ni1,oy),1c)
-t28:=tris2(cx,pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),1c,t26,t27):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
-oy@t29:=th1"l.imp"(neg(m),is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy)),[t:neg(m)]t24(t),[t:not(neg(m))]t28(t)):is(pw3(x,m,mi1,ox),pw3(y,n,ni1,oy))
--v9
-o@pw:=ite"l.r"(pos(m),cx,[t:pos(m)]pw1".v9"(t),[t:not(pos(m))]pw3".v9",[t:pos(m)][u:pos(m)]t8".v9"(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3".v9")):cx
-+*v9
-p@t30:=itet"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),p):is(pw,pw1(p))
-o@[n:not(pos(m))]
-t31:=itef"l.r"(pos(m),cx,[t:pos(m)]pw1(t),[t:not(pos(m))]pw3,[t:pos(m)][u:pos(m)]t8(t,u),[t:not(pos(m))][u:not(pos(m))]refis(cx,pw3),n):is(pw,pw3)
-o@[i:is"r"(m,0)]
-t32:=tris(cx,pw,pw3,1c,t31(0notp(m,i)),t20(0notn(m,i))):is(pw,1c)
-o@[n:neg(m)]
-t33:=tris(cx,pw,pw3,pw2(n),t31(nnotp(m,n)),t19(n)):is(pw,pw2(n))
--v9
-o@[p:pos(m)]
-posexp:=t30".v9"(p):is(pw(x,m,mi,o),prod(ntofrl(m,posintnatrl(m,p,mi)),[t:1to(ntofrl(m,posintnatrl(m,p,mi)))]x))
-[n:nis(x,0c)]
-lemmapw1:=th2"e.notis"(cx,pw1".v9"(p),0c,pw,t10".v9"(p,n),posexp):nis(pw(x,m,mi,o),0c)
-o@[i:is"r"(m,0)]
-0exp:=t32".v9"(i):is(pw(x,m,mi,o),1c)
-o@[n:neg(m)]
-lemmapw2:=t14".v9"(n):nis(x,0c)
-lemmapw3:=t13".v9"(n):or(nis(x,0c),pos(abs(m)))
-+*v9
-n@t34:=t30(abs(m),t11,t13(n),t12(n)):is(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)))
-t35:=isov2(pw(x,abs(m),t11,t13(n)),pw1(x,abs(m),t11,t13(n),t12(n)),1c,t34,lemmapw1(abs(m),t11,t13(n),t12(n),t14(n)),t15(n)):is(ov(1c,pw(x,abs(m),t11,t13(n)),lemmapw1(abs(m),t11,t13(n),t12(n),t14(n))),pw2(n))
--v9
-n@negexp:=tris2(cx,pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)),pw2".v9"(n),t33".v9"(n),t35".v9"(n)):is(pw(x,m,mi,o),ov(1c,pw(x,abs(m),intabs(m,mi),lemmapw3),lemmapw1(x,abs(m),intabs(m,mi),lemmapw3,satz166b(m,n),lemmapw2)))
-+*v9
-mp@t36:=isp(real,[t:real]pos(t),m,n,mp,j):pos(n)
-t37:=t30(x,m,mi1,ox,mp):is(pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp))
-t38:=symis(cx,pw(y,n,ni1,oy),pw1(y,n,ni1,oy,t36),t30(y,n,ni1,oy,t36)):is(pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy))
-t39:=tr3is(cx,pw(x,m,mi1,ox),pw1(x,m,mi1,ox,mp),pw1(y,n,ni1,oy,t36),pw(y,n,ni1,oy),t37,t7(t36),t38):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
-oy@[np:not(pos(m))]
-t40:=isp(real,[t:real]not(pos(t)),m,n,np,j):not(pos(n))
-t41:=t31(x,m,mi1,ox,np):is(pw(x,m,mi1,ox),pw3(x,m,mi1,ox))
-t42:=symis(cx,pw(y,n,ni1,oy),pw3(y,n,ni1,oy),t31(y,n,ni1,oy,t40)):is(pw3(y,n,ni1,oy),pw(y,n,ni1,oy))
-t43:=tr3is(cx,pw(x,m,mi1,ox),pw3(x,m,mi1,ox),pw3(y,n,ni1,oy),pw(y,n,ni1,oy),t41,t29,t42):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
--v9
-oy@ispw12:=th1"l.imp"(pos(m),is(pw(x,m,mi1,ox),pw(y,n,ni1,oy)),[t:pos(m)]t39".v9"(t),[t:not(pos(m))]t43".v9"(t)):is(pw(x,m,mi1,ox),pw(y,n,ni1,oy))
-m@[i:is(x,y)][mi:intrl(m)][ox:or(nis(x,0c),pos(m))][oy:or(nis(y,0c),pos(m))]
-ispw1:=ispw12(x,y,m,m,i,refis(real,m),mi,mi,ox,oy):is(pw(x,m,mi,ox),pw(y,m,mi,oy))
-x@[m:real][n:real][i:is"r"(m,n)][mi:intrl(m)][ni:intrl(n)][om:or(nis(x,0c),pos(m))][on:or(nis(x,0c),pos(n))]
-ispw2:=ispw12(x,x,m,n,refis(cx,x),i,mi,ni,om,on):is(pw(x,m,mi,om),pw(x,n,ni,on))
-o@[n:nis(x,0c)]
-+9290
-[p:pos(m)]
-t1:=lemmapw1(p,n):nis(pw(x,m,mi,o),0c)
-@[i:is(1c,0c)]
-t2:=tr3is(real,1rl,re(1c),re(0c),0,isre(1rl,0),iscere(1c,0c,i),reis(0,0)):is"r"(1rl,0)
--9290
-@1not0:=th3"l.imp"(is(1c,0c),is"r"(1rl,0),pnot0(1rl,pos1),[t:is(1c,0c)]t2".9290"(t)):nis(1c,0c)
-+*9290
-n@[i:is"r"(m,0)]
-t4:=th2"e.notis"(cx,1c,0c,pw(x,m,mi,o),1not0,0exp(i)):nis(pw(x,m,mi,o),0c)
-n@[nm:neg(m)]
-p0:=pw(x,abs(m),intabs(m,mi),lemmapw3(nm)):cx
-t5:=lemmapw1(x,abs(m),intabs(m,mi),lemmapw3(nm),satz166b(m,nm),lemmapw2(nm)):nis(p0,0c)
-t6:=tris(cx,ts(pw(x,m,mi,o),p0),ts(ov(1c,p0,t5),p0),1c,ists1(pw(x,m,mi,o),ov(1c,p0,t5),p0,negexp(nm)),satz229e(1c,p0,t5)):is(ts(pw(x,m,mi,o),p0),1c)
-t7:=th2"e.notis"(cx,1c,0c,ts(pw(x,m,mi,o),p0),1not0,t6):nis(ts(pw(x,m,mi,o),p0),0c)
-t8:=th3"l.imp"(is(pw(x,m,mi,o),0c),is(ts(pw(x,m,mi,o),p0),0c),t7,[t:is(pw(x,m,mi,o),0c)]satz221a(pw(x,m,mi,o),p0,t)):nis(pw(x,m,mi,o),0c)
--9290
-n@satz290:=rapp(m,nis(pw(x,m,mi,o),0c),[t:pos(m)]t1".9290"(t),[t:is"r"(m,0)]t4".9290"(t),[t:neg(m)]t8".9290"(t)):nis(pw(x,m,mi,o),0c)
-x@lemma291:=ori2(nis(x,0c),pos(1rl),pos1):or(nis(x,0c),pos(1rl))
-+9291
-1a:=ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)):nat
-t1:=posexp(x,1rl,intrl1,lemma291,pos1):is(pw(x,1rl,intrl1,lemma291),prod(1a,[t:1to(1a)]x))
-t2:=tris(nat,1,ntofrl(1rl,natrl1),ntofrl(1rl,posintnatrl(1rl,pos1,intrl1)),isntrl1(1),isrlent(1rl,natrl1,1rl,posintnatrl(1rl,pos1,intrl1),refis(real,1rl))):is"n"(1,1a)
-t3:=lessisi2"n"(1,1a,t2):lessis"n"(1,1a)
-t4:=issmpr([t:cx][u:cx]ts(t,u),1a,[t:1to(1a)]x,1,t2):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),prod(1a,[t:1to(1a)]x))
-t5:=satz277([t:cx][u:cx]ts(t,u),left(cx,1a,1,t3,[t:1to(1a)]x)):is(prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),x)
-t6:=tris1(cx,prod(1a,[t:1to(1a)]x),x,prod(1,left(cx,1a,1,t3,[t:1to(1a)]x)),t4,t5):is(prod(1a,[t:1to(1a)]x),x)
--9291
-satz291:=tris(cx,pw(x,1rl,intrl1,lemma291),prod(1a".9291",[t:1to(1a".9291")]x),x,t1".9291",t6".9291"):is(pw(x,1rl,intrl1,lemma291),x)
-[y:cx][m:real][mi:intrl(m)][o:or(and(nis(x,0c),nis(y,0c)),pos(m))]
-+9292
-[a:and(nis(x,0c),nis(y,0c))]
-t1:=ande1(nis(x,0c),nis(y,0c),a):nis(x,0c)
-t2:=ande2(nis(x,0c),nis(y,0c),a):nis(y,0c)
-t3:=satz221d(x,y,t1,t2):nis(ts(x,y),0c)
--9292
-lemma292a:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(x,0c),o,[t:and(nis(x,0c),nis(y,0c))]t1".9292"(t)):or(nis(x,0c),pos(m))
-lemma292b:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(y,0c),o,[t:and(nis(x,0c),nis(y,0c))]t2".9292"(t)):or(nis(y,0c),pos(m))
-lemma292c:=th7"l.or"(and(nis(x,0c),nis(y,0c)),pos(m),nis(ts(x,y),0c),o,[t:and(nis(x,0c),nis(y,0c))]t3".9292"(t)):or(nis(ts(x,y),0c),pos(m))
-+*9292
-x@[n:nat]
-nr:=rlofnt(n):real
-t4:=natintrl(nr,natrli(n)):intrl(nr)
-t5:=ori2(nis(x,0c),pos(nr),natpos(nr,natrli(n))):or(nis(x,0c),pos(nr))
-p0:=pw(x,nr,t4,t5):cx
-x@t6:=tris(cx,p0(1),pw(x,1rl,intrl1,lemma291(x)),x,ispw1(x,x,1rl,refis(cx,x),intrl1,t5(1),lemma291(x)),satz291(x)):is(p0(1),x)
-n@n0:=ntofrl(nr,posintnatrl(nr,natpos(nr,natrli(n)),t4)):nat
-t7:=tris(nat,n,ntofrl(nr,natrli(n)),n0,isntrl1(n),isrlent(nr,natrli(n),nr,posintnatrl(nr,natpos(nr,natrli(n)),t4),refis(real,nr))):is"n"(n,n0)
-t8:=lessisi2"n"(n,n0,t7):lessis"n"(n,n0)
-t9:=posexp(x,nr,t4,t5,natpos(nr,natrli(n))):is(p0,prod(n0,[t:1to(n0)]x))
-t10:=issmpr([t:cx][u:cx]ts(t,u),n0,[t:1to(n0)]x,n,t7):is(prod(n,left(cx,n0,n,t8,[t:1to(n0)]x)),prod(n0,[t:1to(n0)]x))
-t11:=tris2(cx,p0,prod(n,[t:1to(n)]x),prod(n0,[t:1to(n0)]x),t9,t10):is(p0,prod(n,[t:1to(n)]x))
-n1:=pl"n"(n,1):nat
-t12:=lessisi1"n"(n,n1,satz18a(n,1)):lessis"n"(n,n1)
-t13:=satz278([t:cx][u:cx]ts(t,u),n,[t:1to(n1)]x):is(prod(n1,[t:1to(n1)]x),ts(prod(n,left(cx,n1,n,t12,[t:1to(n1)]x)),x))
-t14:=ists1(p0,prod(n,[t:1to(n)]x),x,t11):is(ts(p0,x),ts(prod(n,[t:1to(n)]x),x))
-t15:=tris2(cx,prod(n1,[t:1to(n1)]x),ts(p0,x),ts(prod(n,[t:1to(n)]x),x),t13,t14):is(prod(n1,[t:1to(n1)]x),ts(p0,x))
-t16:=tris(cx,p0(n1),prod(n1,[t:1to(n1)]x),ts(p0,x),t11(n1),t15):is(p0(n1),ts(p0(n),x))
-y@[n:nat]
-prop1:=is(p0(ts(x,y),n),ts(p0(x,n),p0(y,n))):'prop'
-y@t17:=ists12(p0(x,1),x,p0(y,1),y,t6(x),t6(y)):is(ts(p0(x,1),p0(y,1)),ts(x,y))
-t18:=tris2(cx,p0(ts(x,y),1),ts(p0(x,1),p0(y,1)),ts(x,y),t6(ts(x,y)),t17):prop1(1)
-n@[p:prop1(n)]
-t19:=ists1(p0(ts(x,y),n),ts(p0(x,n),p0(y,n)),ts(x,y),p):is(ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)))
-t20:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),x),ts(p0(x,n),ts(p0(y,n),x)),ts(p0(x,n),ts(x,p0(y,n))),ts(ts(p0(x,n),x),p0(y,n)),assts1(p0(x,n),p0(y,n),x),ists2(ts(p0(y,n),x),ts(x,p0(y,n)),p0(x,n),comts(p0(y,n),x)),assts2(p0(x,n),x,p0(y,n))):is(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)))
-t21:=tr3is(cx,ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(ts(p0(x,n),p0(y,n)),x),y),ts(ts(ts(p0(x,n),x),p0(y,n)),y),ts(ts(p0(x,n),x),ts(p0(y,n),y)),assts2(ts(p0(x,n),p0(y,n)),x,y),ists1(ts(ts(p0(x,n),p0(y,n)),x),ts(ts(p0(x,n),x),p0(y,n)),y,t20),assts1(ts(p0(x,n),x),p0(y,n),y)):is(ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
-t22:=tr3is(cx,p0(ts(x,y),n1(n)),ts(p0(ts(x,y),n),ts(x,y)),ts(ts(p0(x,n),p0(y,n)),ts(x,y)),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t16(ts(x,y),n),t19,t21):is(p0(ts(x,y),n1(n)),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
-t23:=ists12(p0(x,n1(n)),ts(p0(x,n),x),p0(y,n1(n)),ts(p0(y,n),y),t16(x,n),t16(y,n)):is(ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)))
-t24:=tris2(cx,p0(ts(x,y),n1(n)),ts(p0(x,n1(n)),p0(y,n1(n))),ts(ts(p0(x,n),x),ts(p0(y,n),y)),t22,t23):prop1(n1(n))
-t25:=isp(nat,[t:nat]prop1(t),n1(n),<n>suc,t24,satz4a(n)):prop1(<n>suc)
-n@t26:=induction([t:nat]prop1(t),t18,[t:nat][u:prop1(t)]t25(t,u),n):prop1
-o@prop2:=is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b))):'prop'
-[p:pos(m)]
-t28:=posintnatrl(m,p,mi):natrl(m)
-m0:=ntofrl(m,t28):nat
-t29:=isrlnt1(m,t28):is"r"(m,nr(m0))
-t30:=isrlnt2(m,t28):is"r"(nr(m0),m)
-t31:=ispw2(ts(x,y),m,nr(m0),t29,mi,t4(ts(x,y),m0),lemma292c,t5(ts(x,y),m0)):is(pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0))
-t32:=ists12(p0(x,m0),pw(x,m,mi,lemma292a),p0(y,m0),pw(y,m,mi,lemma292b),ispw2(x,nr(m0),m,t30,t4(x,m0),mi,t5(x,m0),lemma292a),ispw2(y,nr(m0),m,t30,t4(y,m0),mi,t5(y,m0),lemma292b)):is(ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
-t33:=tr3is(cx,pw(ts(x,y),m,mi,lemma292c),p0(ts(x,y),m0),ts(p0(x,m0),p0(y,m0)),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),t31,t26(m0),t32):prop2
-o@[i:is"r"(m,0)]
-t34:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(1c,1c),1c,ists12(pw(x,m,mi,lemma292a),1c,pw(y,m,mi,lemma292b),1c,0exp(x,m,mi,lemma292a,i),0exp(y,m,mi,lemma292b,i)),satz222(1c)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c)
-t35:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),1c,0exp(ts(x,y),m,mi,lemma292c,i),t34):prop2
-o@[n:neg(m)]
-t36:=intabs(m,mi):intrl(abs(m))
-t37:=ori2(and(nis(x,0c),nis(y,0c)),pos(abs(m)),satz166b(m,n)):or(and(nis(x,0c),nis(y,0c)),pos(abs(m)))
-t38:=lemma292a(abs(m),t36,t37):or(nis(x,0c),pos(abs(m)))
-t39:=lemma292b(abs(m),t36,t37):or(nis(y,0c),pos(abs(m)))
-t40:=lemma292c(abs(m),t36,t37):or(nis(ts(x,y),0c),pos(abs(m)))
-t41:=lemmapw3(x,m,mi,lemma292a,n):or(nis(x,0c),pos(abs(m)))
-t42:=lemmapw3(y,m,mi,lemma292b,n):or(nis(y,0c),pos(abs(m)))
-t43:=lemmapw3(ts(x,y),m,mi,lemma292c,n):or(nis(ts(x,y),0c),pos(abs(m)))
-t44:=ispw2(ts(x,y),abs(m),abs(m),refis(real,abs(m)),t36,t36,t43,t40):is(pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40))
-t45:=t33(abs(m),t36,t37,satz166b(m,n)):is(pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)))
-t46:=ists12(pw(x,abs(m),t36,t38),pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t39),pw(y,abs(m),t36,t42),ispw2(x,abs(m),abs(m),refis(real,abs(m)),t36,t36,t38,t41),ispw2(y,abs(m),abs(m),refis(real,abs(m)),t36,t36,t39,t42)):is(ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
-t47:=tr3is(cx,pw(ts(x,y),abs(m),t36,t43),pw(ts(x,y),abs(m),t36,t40),ts(pw(x,abs(m),t36,t38),pw(y,abs(m),t36,t39)),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t44,t45,t46):is(pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)))
-t48:=lemmapw1(x,abs(m),t36,t41,satz166b(m,n),lemmapw2(x,m,mi,lemma292a,n)):nis(pw(x,abs(m),t36,t41),0c)
-t49:=lemmapw1(y,abs(m),t36,t42,satz166b(m,n),lemmapw2(y,m,mi,lemma292b,n)):nis(pw(y,abs(m),t36,t42),0c)
-t50:=lemmapw1(ts(x,y),abs(m),t36,t43,satz166b(m,n),lemmapw2(ts(x,y),m,mi,lemma292c,n)):nis(pw(ts(x,y),abs(m),t36,t43),0c)
-t51:=satz221d(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42),t48,t49):nis(ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),0c)
-t52:=negexp(ts(x,y),m,mi,lemma292c,n):is(pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50))
-t53:=isov12(1c,ts(1c,1c),pw(ts(x,y),abs(m),t36,t43),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),satz222a(1c),t47,t50,t51):is(ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t54:=tris(cx,pw(ts(x,y),m,mi,lemma292c),ov(1c,pw(ts(x,y),abs(m),t36,t43),t50),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t52,t53):is(pw(ts(x,y),m,mi,lemma292c),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t55:=ists12(pw(x,m,mi,lemma292a),ov(1c,pw(x,abs(m),t36,t41),t48),pw(y,m,mi,lemma292b),ov(1c,pw(y,abs(m),t36,t42),t49),negexp(x,m,mi,lemma292a,n),negexp(y,m,mi,lemma292b,n)):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)))
-t56:=satz247(1c,pw(x,abs(m),t36,t41),1c,pw(y,abs(m),t36,t42),t48,t49):is(ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t57:=tris(cx,ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ts(ov(1c,pw(x,abs(m),t36,t41),t48),ov(1c,pw(y,abs(m),t36,t42),t49)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t55,t56):is(ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51))
-t58:=tris2(cx,pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)),ov(ts(1c,1c),ts(pw(x,abs(m),t36,t41),pw(y,abs(m),t36,t42)),t51),t54,t57):prop2
--9292
-o@satz292:=rapp(m,prop2".9292",[t:pos(m)]t33".9292"(t),[t:is"r"(m,0)]t35".9292"(t),[t:neg(m)]t58".9292"(t)):is(pw(ts(x,y),m,mi,lemma292c),ts(pw(x,m,mi,lemma292a),pw(y,m,mi,lemma292b)))
-@[m:real]
-lemma293:=ori1(nis(1c,0c),pos(m),1not0):or(nis(1c,0c),pos(m))
-[mi:intrl(m)]
-+9293
-t1:=ori1(and(nis(1c,0c),nis(1c,0c)),pos(m),andi(nis(1c,0c),nis(1c,0c),1not0,1not0)):or(and(nis(1c,0c),nis(1c,0c)),pos(m))
-1m:=pw(1c,m,mi,lemma293):cx
-t2:=satz222(1m):is(ts(1m,1c),1m)
-t3:=ispw1(1c,ts(1c,1c),m,satz222a(1c),mi,lemma293,lemma292c(1c,1c,m,mi,t1)):is(1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)))
-t4:=satz292(1c,1c,m,mi,t1):is(pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))))
-t5:=ists12(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),1m,pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1)),1m,ispw1(1c,1c,m,refis(cx,1c),mi,lemma292a(1c,1c,m,mi,t1),lemma293),ispw1(1c,1c,m,refis(cx,1c),mi,lemma292b(1c,1c,m,mi,t1),lemma293)):is(ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m))
-t6:=tr4is(cx,ts(1m,1c),1m,pw(ts(1c,1c),m,mi,lemma292c(1c,1c,m,mi,t1)),ts(pw(1c,m,mi,lemma292a(1c,1c,m,mi,t1)),pw(1c,m,mi,lemma292b(1c,1c,m,mi,t1))),ts(1m,1m),t2,t3,t4,t5):is(ts(1m,1c),ts(1m,1m))
-t7:=tris(cx,ts(1m,mn(1m,1c)),mn(ts(1m,1m),ts(1m,1c)),0c,disttm2(1m,1m,1c),satz213b(ts(1m,1m),ts(1m,1c),symis(cx,ts(1m,1c),ts(1m,1m),t6))):is(ts(1m,mn(1m,1c)),0c)
-t8:=ore2(is(1m,0c),is(mn(1m,1c),0c),satz221c(1m,mn(1m,1c),t7),satz290(1c,m,mi,lemma293,1not0)):is(mn(1m,1c),0c)
--9293
-satz293:=satz213a(1m".9293",1c,t8".9293"):is(pw(1c,m,mi,lemma293),1c)
-x@[m:real][n:real][mi:intrl(m)][ni:intrl(n)][o:or(nis(x,0c),and(pos(m),pos(n)))]
-+9294
-[a:and(pos(m),pos(n))]
-t1:=ande1(pos(m),pos(n),a):pos(m)
-t2:=ande2(pos(m),pos(n),a):pos(n)
-t3:=pospl(m,n,t1,t2):pos(pl"r"(m,n))
--9294
-lemma294a:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(m),o,[t:and(pos(m),pos(n))]t1".9294"(t)):or(nis(x,0c),pos(m))
-lemma294b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(n),o,[t:and(pos(m),pos(n))]t2".9294"(t)):or(nis(x,0c),pos(n))
-lemma294c:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(pl"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9294"(t)):or(nis(x,0c),pos(pl"r"(m,n)))
-+*9294
-o@prop1:=is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c)):'prop'
-a@m1:=ntofrl(m,posintnatrl(m,t1,mi)):nat
-n1:=ntofrl(n,posintnatrl(n,t2,ni)):nat
-t4:=ists12(pw(x,m,mi,lemma294a),prod(m1,[t:1to(m1)]x),pw(x,n,ni,lemma294b),prod(n1,[t:1to(n1)]x),posexp(x,m,mi,lemma294a,t1),posexp(x,n,ni,lemma294b,t2)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
-p1:=ntofrl(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni))):nat
-t5:=posexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t3):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(p1,[t:1to(p1)]x))
-t6:=tris(real,pl"r"(m,n),pl"r"(rlofnt(m1),rlofnt(n1)),rlofnt(pl"n"(m1,n1)),ispl12"r"(m,rlofnt(m1),n,rlofnt(n1),isrlnt1(m,posintnatrl(m,t1,mi)),isrlnt1(n,posintnatrl(n,t2,ni))),satzr155b(m1,n1)):is"r"(pl"r"(m,n),rlofnt(pl"n"(m1,n1)))
-t7:=tris2(nat,pl"n"(m1,n1),p1,ntofrl(rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1))),isntrl1(pl"n"(m1,n1)),isrlent(pl"r"(m,n),posintnatrl(pl"r"(m,n),t3,intpl(m,mi,n,ni)),rlofnt(pl"n"(m1,n1)),natrli(pl"n"(m1,n1)),t6)):is"n"(pl"n"(m1,n1),p1)
-t8:=lessisi2"n"(pl"n"(m1,n1),p1,t7):lessis"n"(pl"n"(m1,n1),p1)
-t9:=issmpr([t:cx][u:cx]ts(t,u),p1,[t:1to(p1)]x,pl"n"(m1,n1),t7):is(prod(pl"n"(m1,n1),left(cx,p1,pl"n"(m1,n1),t8,[t:1to(p1)]x)),prod(p1,[t:1to(p1)]x))
-t10:=tris2(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),prod(p1,[t:1to(p1)]x),t5,t9):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x))
-t11:=lessisi1"n"(m1,pl"n"(m1,n1),satz18a(m1,n1)):lessis"n"(m1,pl"n"(m1,n1))
-t12:=satz281([t:cx][u:cx]ts(t,u),assocts,m1,n1,[t:1to(pl"n"(m1,n1))]x):is(prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,left(cx,pl"n"(m1,n1),m1,t11,[t:1to(pl"n"(m1,n1))]x)),prod(n1,right(cx,m1,n1,[t:1to(pl"n"(m1,n1))]x))))
-t13:=tris(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),prod(pl"n"(m1,n1),[t:1to(pl"n"(m1,n1))]x),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t10,t12):is(pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)))
-t14:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ts(prod(m1,[t:1to(m1)]x),prod(n1,[t:1to(n1)]x)),t4,t13):prop1
-o@[na:not(and(pos(m),pos(n)))]
-t15:=ore1(nis(x,0c),and(pos(m),pos(n)),o,na):nis(x,0c)
-t16:=th15"l.or"(pos(m),pos(n),na):or(not(pos(m)),not(pos(n)))
-o@am:=abs(m):real
-an:=abs(n):real
-ap:=abs(pl"r"(m,n)):real
-t17:=intabs(m,mi):intrl(am)
-t18:=intabs(n,ni):intrl(an)
-t19:=intabs(pl"r"(m,n),intpl(m,mi,n,ni)):intrl(ap)
-na@[nm:neg(m)][nn:neg(n)]
-t20:=andi(pos(am),pos(an),satz166e(m,nnot0(m,nm)),satz166e(n,nnot0(n,nn))):and(pos(am),pos(an))
-t21:=ori2(nis(x,0c),and(pos(am),pos(an)),t20):or(nis(x,0c),and(pos(am),pos(an)))
-t22:=lemmapw3(x,m,mi,lemma294a,nm):or(nis(x,0c),pos(am))
-t23:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
-t24:=lemma294a(x,am,an,t17,t18,t21):or(nis(x,0c),pos(am))
-t25:=lemma294b(x,am,an,t17,t18,t21):or(nis(x,0c),pos(an))
-t26:=ists12(pw(x,am,t17,t22),pw(x,am,t17,t24),pw(x,an,t18,t23),pw(x,an,t18,t25),ispw1(x,x,am,refis(cx,x),t17,t22,t24),ispw1(x,x,an,refis(cx,x),t18,t23,t25)):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)))
-t27:=lemma294c(x,am,an,t17,t18,t21):or(nis(x,0c),pos(pl"r"(am,an)))
-t28:=t14(x,am,an,t17,t18,t21,t20):is(ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27))
-t29:=tr3is(real,pl"r"(am,an),pl"r"(m0"r"(m),m0"r"(n)),m0"r"(pl"r"(m,n)),ap,ispl12"r"(am,m0"r"(m),an,m0"r"(n),absn(m,nm),absn(n,nn)),satz180a(m,n),symis(real,ap,m0"r"(pl"r"(m,n)),absn(pl"r"(m,n),negpl(m,n,nm,nn)))):is"r"(pl"r"(am,an),ap)
-t30:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn)):or(nis(x,0c),pos(ap))
-t31:=ispw2(x,pl"r"(am,an),ap,t29,intpl(am,t17,an,t18),t19,t27,t30):is(pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30))
-t32:=tr3is(cx,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),ts(pw(x,am,t17,t24),pw(x,an,t18,t25)),pw(x,pl"r"(am,an),intpl(am,t17,an,t18),t27),pw(x,ap,t19,t30),t26,t28,t31):is(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30))
-t33:=lemmapw1(x,am,t17,t22,satz166b(m,nm),lemmapw2(x,m,mi,lemma294a,nm)):nis(pw(x,am,t17,t22),0c)
-t34:=lemmapw1(x,an,t18,t23,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t23),0c)
-t35:=lemmapw1(x,ap,t19,t30,satz166b(pl"r"(m,n),negpl(m,n,nm,nn)),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):nis(pw(x,ap,t19,t30),0c)
-t36:=ists12(pw(x,m,mi,lemma294a),ov(1c,pw(x,am,t17,t22),t33),pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t23),t34),negexp(x,m,mi,lemma294a,nm),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)))
-t37:=satz221d(pw(x,am,t17,t22),pw(x,an,t18,t23),t33,t34):nis(ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),0c)
-t38:=satz247(1c,pw(x,am,t17,t22),1c,pw(x,an,t18,t23),t33,t34):is(ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37))
-t39:=isov12(ts(1c,1c),1c,ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),pw(x,ap,t19,t30),satz222(1c),t32,t37,t35):is(ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35))
-t40:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t30),t35),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,negpl(m,n,nm,nn))):is(ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t41:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(ov(1c,pw(x,am,t17,t22),t33),ov(1c,pw(x,an,t18,t23),t34)),ov(ts(1c,1c),ts(pw(x,am,t17,t22),pw(x,an,t18,t23)),t37),ov(1c,pw(x,ap,t19,t30),t35),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t36,t38,t39,t40):prop1
-na@[pm:pos(m)][nn:neg(n)]
-t42:=lemmapw3(x,n,ni,lemma294b,nn):or(nis(x,0c),pos(an))
-t43:=lemmapw1(x,an,t18,t42,satz166b(n,nn),lemmapw2(x,n,ni,lemma294b,nn)):nis(pw(x,an,t18,t42),0c)
-t44:=ists2(pw(x,n,ni,lemma294b),ov(1c,pw(x,an,t18,t42),t43),pw(x,m,mi,lemma294a),negexp(x,n,ni,lemma294b,nn)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)))
-t45:=satz244a(pw(x,m,mi,lemma294a),1c,pw(x,an,t18,t42),t43):is(ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43))
-t46:=isov1(ts(pw(x,m,mi,lemma294a),1c),pw(x,m,mi,lemma294a),pw(x,an,t18,t42),satz222(pw(x,m,mi,lemma294a)),t43):is(ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-t47:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,lemma294a),ov(1c,pw(x,an,t18,t42),t43)),ov(ts(pw(x,m,mi,lemma294a),1c),pw(x,an,t18,t42),t43),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t44,t45,t46):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-[casea:more(m,an)]
-t48:=satz182d(m,an,casea):pos(mn"r"(m,an))
-t49:=satz166e(n,nnot0(n,nn)):pos(an)
-t50:=andi(pos(an),pos(mn"r"(m,an)),t49,t48):and(pos(an),pos(mn"r"(m,an)))
-t51:=ori2(nis(x,0c),and(pos(an),pos(mn"r"(m,an))),t50):or(nis(x,0c),and(pos(an),pos(mn"r"(m,an))))
-t52:=intmn(m,mi,an,t18):intrl(mn"r"(m,an))
-t53:=lemma294a(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(an))
-t54:=lemma294b(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(mn"r"(m,an)))
-t55:=lemma294c(x,an,mn"r"(m,an),t18,t52,t51):or(nis(x,0c),pos(pl"r"(an,mn"r"(m,an))))
-t56:=intpl(an,t18,mn"r"(m,an),t52):intrl(pl"r"(an,mn"r"(m,an)))
-t57:=t14(x,an,mn"r"(m,an),t18,t52,t51,t50):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55))
-t58:=satz187a(m,an):is"r"(pl"r"(an,mn"r"(m,an)),m)
-t59:=ispw2(x,pl"r"(an,mn"r"(m,an)),m,t58,t56,mi,t55,lemma294a):is(pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a))
-t60:=tris(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,pl"r"(an,mn"r"(m,an)),t56,t55),pw(x,m,mi,lemma294a),t57,t59):is(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a))
-t61:=ispw1(x,x,an,refis(cx,x),t18,t53,t42):is(pw(x,an,t18,t53),pw(x,an,t18,t42))
-t62:=isp1(cx,[t:cx]nis(t,0c),pw(x,an,t18,t42),pw(x,an,t18,t53),t43,t61):nis(pw(x,an,t18,t53),0c)
-t63:=isov12(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,m,mi,lemma294a),pw(x,an,t18,t53),pw(x,an,t18,t42),t60,t61,t62,t43):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-t64:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t63):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62))
-t65:=satz229h(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54),t62,refis(cx,ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)))):is(ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54))
-t66:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
-t67:=ispw2(x,mn"r"(m,an),pl"r"(m,n),t66,t52,intpl(m,mi,n,ni),t54,lemma294c):is(pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t68:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,an,t18,t53),pw(x,mn"r"(m,an),t52,t54)),pw(x,an,t18,t53),t62),pw(x,mn"r"(m,an),t52,t54),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t64,t65,t67):prop1
-nn@[caseb:is"r"(m,an)]
-t69:=ispw2(x,m,an,caseb,mi,t18,lemma294a,t42):is(pw(x,m,mi,lemma294a),pw(x,an,t18,t42))
-t70:=satz251a(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43,t69):is(ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c)
-t71:=tr3is(real,pl"r"(m,n),mn"r"(m,m0"r"(n)),mn"r"(m,an),0,ispl2"r"(n,m0"r"(m0"r"(n)),m,satz177a(n)),ismn2"r"(m0"r"(n),an,m,symis(real,an,m0"r"(n),absn(n,nn))),satz182e(m,an,caseb)):is"r"(pl"r"(m,n),0)
-t72:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),1c,0exp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t71)):is(1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t73:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),1c,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t47,t70,t72):prop1
-nn@[casec:less(m,an)]
-t74:=satz182d(an,m,lemma2"r"(m,an,casec)):pos(mn"r"(an,m))
-t75:=andi(pos(m),pos(mn"r"(an,m)),pm,t74):and(pos(m),pos(mn"r"(an,m)))
-t76:=ori2(nis(x,0c),and(pos(m),pos(mn"r"(an,m))),t75):or(nis(x,0c),and(pos(m),pos(mn"r"(an,m))))
-t77:=intmn(an,t18,m,mi):intrl(mn"r"(an,m))
-t78:=lemma294a(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(m))
-t79:=lemma294b(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(mn"r"(an,m)))
-t80:=lemma294c(x,m,mn"r"(an,m),mi,t77,t76):or(nis(x,0c),pos(pl"r"(m,mn"r"(an,m))))
-t81:=intpl(m,mi,mn"r"(an,m),t77):intrl(pl"r"(m,mn"r"(an,m)))
-t81a:=t14(x,m,mn"r"(an,m),mi,t77,t76,t75):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80))
-t82:=satz187a(an,m):is"r"(pl"r"(m,mn"r"(an,m)),an)
-t83:=ispw2(x,pl"r"(m,mn"r"(an,m)),an,t82,t81,t18,t80,t42):is(pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42))
-t84:=tris(cx,ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,pl"r"(m,mn"r"(an,m)),t81,t80),pw(x,an,t18,t42),t81a,t83):is(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42))
-t85:=satz290(x,m,mi,t78,t15):nis(pw(x,m,mi,t78),0c)
-t86:=satz290(x,mn"r"(an,m),t77,t79,t15):nis(pw(x,mn"r"(an,m),t77,t79),0c)
-t87:=satz221d(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79),t85,t86):nis(ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),0c)
-t88:=satz222(pw(x,m,mi,t78)):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78))
-t89:=ispw1(x,x,m,refis(cx,x),mi,t78,lemma294a):is(pw(x,m,mi,t78),pw(x,m,mi,lemma294a))
-t90:=tris(cx,ts(pw(x,m,mi,t78),1c),pw(x,m,mi,t78),pw(x,m,mi,lemma294a),t88,t89):is(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a))
-t91:=isov12(ts(pw(x,m,mi,t78),1c),pw(x,m,mi,lemma294a),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),pw(x,an,t18,t42),t90,t84,t87,t43):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43))
-t92:=tris2(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(pw(x,m,mi,lemma294a),pw(x,an,t18,t42),t43),t47,t91):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87))
-t93:=satz246a(1c,pw(x,mn"r"(an,m),t77,t79),pw(x,m,mi,t78),t86,t85):is(ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86))
-t94:=satz182f(m,an,casec):neg(mn"r"(m,an))
-t94a:=tris(real,mn"r"(m,an),mn"r"(m,m0"r"(n)),pl"r"(m,n),ismn2"r"(an,m0"r"(n),m,absn(n,nn)),ispl2"r"(m0"r"(m0"r"(n)),n,m,satz177(n))):is"r"(mn"r"(m,an),pl"r"(m,n))
-t95:=tr3is(real,mn"r"(an,m),m0"r"(mn"r"(m,an)),abs(mn"r"(m,an)),ap,satz181a(an,m),symis(real,abs(mn"r"(m,an)),m0"r"(mn"r"(m,an)),absn(mn"r"(m,an),t94)),isabs(mn"r"(m,an),pl"r"(m,n),t94a)):is"r"(mn"r"(an,m),ap)
-t96:=isp(real,[t:real]neg(t),mn"r"(m,an),pl"r"(m,n),t94,t94a):neg(pl"r"(m,n))
-t97:=lemmapw3(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96):or(nis(x,0c),pos(ap))
-t98:=lemmapw1(x,ap,t19,t97,satz166b(pl"r"(m,n),t96),lemmapw2(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):nis(pw(x,ap,t19,t97),0c)
-t99:=ispw2(x,mn"r"(an,m),ap,t95,t77,t19,t79,t97):is(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97))
-t100:=isov2(pw(x,mn"r"(an,m),t77,t79),pw(x,ap,t19,t97),1c,t99,t86,t98):is(ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98))
-t101:=symis(cx,pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),ov(1c,pw(x,ap,t19,t97),t98),negexp(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c,t96)):is(ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t102:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ov(ts(pw(x,m,mi,t78),1c),ts(pw(x,m,mi,t78),pw(x,mn"r"(an,m),t77,t79)),t87),ov(1c,pw(x,mn"r"(an,m),t77,t79),t86),ov(1c,pw(x,ap,t19,t97),t98),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t92,t93,t100,t101):prop1
-nn@t103:=or3app(is"r"(m,an),more(m,an),less(m,an),prop1,satz167a(m,an),[t:is"r"(m,an)]t73(t),[t:more(m,an)]t68(t),[t:less(m,an)]t102(t)):prop1
-na@[nm:neg(m)][qn:pos(n)]
-na@t104:=ori1(nis(x,0c),and(pos(n),pos(m)),t15):or(nis(x,0c),and(pos(n),pos(m)))
-t104a:=th5"l.and"(pos(m),pos(n),na):not(and(pos(n),pos(m)))
-t105:=lemma294a(x,n,m,ni,mi,t104):or(nis(x,0c),pos(n))
-t106:=lemma294b(x,n,m,ni,mi,t104):or(nis(x,0c),pos(m))
-t107:=lemma294c(x,n,m,ni,mi,t104):or(nis(x,0c),pos(pl"r"(n,m)))
-t108:=ists12(pw(x,m,mi,lemma294a),pw(x,m,mi,t106),pw(x,n,ni,lemma294b),pw(x,n,ni,t105),ispw1(x,x,m,refis(cx,x),mi,lemma294a,t106),ispw1(x,x,n,refis(cx,x),ni,lemma294b,t105)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)))
-t109:=comts(pw(x,m,mi,t106),pw(x,n,ni,t105)):is(ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)))
-qn@t110:=t103(x,n,m,ni,mi,t104,t104a,qn,nm):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
-na@t111:=ispw2(x,pl"r"(n,m),pl"r"(m,n),compl"r"(n,m),intpl(n,ni,m,mi),intpl(m,mi,n,ni),t107,lemma294c):is(pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-qn@t112:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t110,t111):prop1
-na@[i:is"r"(m,0)]
-t113:=ists1(pw(x,m,mi,lemma294a),1c,pw(x,n,ni,lemma294b),0exp(x,m,mi,lemma294a,i)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)))
-t114:=satz222b(pw(x,n,ni,lemma294b)):is(ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b))
-t115:=symis(real,pl"r"(m,n),n,pl01"r"(m,n,i)):is"r"(n,pl"r"(m,n))
-t116:=ispw2(x,n,pl"r"(m,n),t115,ni,intpl(m,mi,n,ni),lemma294b,lemma294c):is(pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-t117:=tr3is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(1c,pw(x,n,ni,lemma294b)),pw(x,n,ni,lemma294b),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t113,t114,t116):prop1
-na@[i:is"r"(n,0)]
-t118:=t117(x,n,m,ni,mi,t104,t104a,i):is(ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107))
-t119:=tr4is(cx,ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),ts(pw(x,m,mi,t106),pw(x,n,ni,t105)),ts(pw(x,n,ni,t105),pw(x,m,mi,t106)),pw(x,pl"r"(n,m),intpl(n,ni,m,mi),t107),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c),t108,t109,t118,t111):prop1
-na@[pm:pos(m)]
-t120:=ore2(not(pos(m)),not(pos(n)),t16,weli(pos(m),pm)):not(pos(n))
-t121:=rapp(n,prop1,th2"l.imp"(pos(n),prop1,t120),[t:is"r"(n,0)]t119(t),[t:neg(n)]t103(pm,t)):prop1
-na@[nm:neg(m)]
-t122:=rapp(n,prop1,[t:pos(n)]t112(nm,t),[t:is"r"(n,0)]t119(t),[t:neg(n)]t41(nm,t)):prop1
-na@t123:=rapp(m,prop1,[t:pos(m)]t121(t),[t:is"r"(m,0)]t117(t),[t:neg(m)]t122(t)):prop1
--9294
-o@satz294:=th1"l.imp"(and(pos(m),pos(n)),prop1".9294",[t:and(pos(m),pos(n))]t14".9294"(t),[t:not(and(pos(m),pos(n)))]t123".9294"(t)):is(ts(pw(x,m,mi,lemma294a),pw(x,n,ni,lemma294b)),pw(x,pl"r"(m,n),intpl(m,mi,n,ni),lemma294c))
-ni@[o:nis(x,0c)]
-lemma295a:=ori1(nis(x,0c),pos(m),o):or(nis(x,0c),pos(m))
-lemma295b:=ori1(nis(x,0c),pos(n),o):or(nis(x,0c),pos(n))
-lemma295c:=ori1(nis(x,0c),pos(mn"r"(m,n)),o):or(nis(x,0c),pos(mn"r"(m,n)))
-+9295
-t1:=ori1(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)),o):or(nis(x,0c),and(pos(mn"r"(m,n)),pos(n)))
-t2:=intmn(m,mi,n,ni):intrl(mn"r"(m,n))
-t3:=lemma294a(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(mn"r"(m,n)))
-t4:=lemma294b(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(n))
-t5:=lemma294c(x,mn"r"(m,n),n,t2,ni,t1):or(nis(x,0c),pos(pl"r"(mn"r"(m,n),n)))
-t6:=ists12(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,lemma295b),pw(x,n,ni,t4),ispw1(x,x,mn"r"(m,n),refis(cx,x),t2,lemma295c,t3),ispw1(x,x,n,refis(cx,x),ni,lemma295b,t4)):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)))
-t7:=satz294(x,mn"r"(m,n),n,t2,ni,t1):is(ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5))
-t8:=plmn(m,n):is"r"(pl"r"(mn"r"(m,n),n),m)
-t9:=ispw2(x,pl"r"(mn"r"(m,n),n),m,t8,intpl(mn"r"(m,n),t2,n,ni),mi,t5,lemma295a):is(pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a))
-t10:=tr3is(cx,ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),ts(pw(x,mn"r"(m,n),t2,t3),pw(x,n,ni,t4)),pw(x,pl"r"(mn"r"(m,n),n),intpl(mn"r"(m,n),t2,n,ni),t5),pw(x,m,mi,lemma295a),t6,t7,t9):is(ts(pw(x,mn"r"(m,n),t2,lemma295c),pw(x,n,ni,lemma295b)),pw(x,m,mi,lemma295a))
-t11:=satz290(x,n,ni,lemma295b,o):nis(pw(x,n,ni,lemma295b),0c)
--9295
-satz295:=satz229k(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),pw(x,mn"r"(m,n),t2".9295",lemma295c),t11".9295",t10".9295"):is(ov(pw(x,m,mi,lemma295a),pw(x,n,ni,lemma295b),satz290(x,n,ni,lemma295b,o)),pw(x,mn"r"(m,n),intmn(m,mi,n,ni),lemma295c))
-m@[mi:intrl(m)][n:nis(x,0c)]
-lemma296:=ori1(nis(x,0c),pos(m),n):or(nis(x,0c),pos(m))
-+9296
-t1:=intrli0(0,refis(real,0)):intrl(0)
-t2:=lemma295a(x,0,m,t1,mi,n):or(nis(x,0c),pos(0))
-t3:=lemma295b(x,0,m,t1,mi,n):or(nis(x,0c),pos(m))
-t4:=lemma295c(x,0,m,t1,mi,n):or(nis(x,0c),pos(mn"r"(0,m)))
-t5:=satz290(x,m,mi,lemma296,n):nis(pw(x,m,mi,lemma296),0c)
-t6:=satz290(x,m,mi,t3,n):nis(pw(x,m,mi,t3),0c)
-t7:=symis(cx,pw(x,0,t1,t2),1c,0exp(x,0,t1,t2,refis(real,0))):is(1c,pw(x,0,t1,t2))
-t8:=ispw1(x,x,m,refis(cx,x),mi,lemma296,t3):is(pw(x,m,mi,lemma296),pw(x,m,mi,t3))
-t9:=isov12(1c,pw(x,0,t1,t2),pw(x,m,mi,lemma296),pw(x,m,mi,t3),t7,t8,t5,t6):is(ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6))
-t10:=satz295(x,0,m,t1,mi,n):is(ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4))
-t11:=pl01(0,m0"r"(m),refis(real,0)):is"r"(mn"r"(0,m),m0"r"(m))
-t12:=lemma296(x,m0"r"(m),intm0(m,mi),n):or(nis(x,0c),pos(m0"r"(m)))
-t13:=ispw2(x,mn"r"(0,m),m0"r"(m),t11,intmn(0,t1,m,mi),intm0(m,mi),t4,t12):is(pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12))
-t14:=tr3is(cx,ov(1c,pw(x,m,mi,lemma296),t5),ov(pw(x,0,t1,t2),pw(x,m,mi,t3),t6),pw(x,mn"r"(0,m),intmn(0,t1,m,mi),t4),pw(x,m0"r"(m),intm0(m,mi),t12),t9,t10,t13):is(ov(1c,pw(x,m,mi,lemma296),t5),pw(x,m0"r"(m),intm0(m,mi),t12))
--9296
-satz296:=t14".9296":is(ov(1c,pw(x,m,mi,lemma296),satz290(x,m,mi,lemma296,n)),pw(x,m0"r"(m),intm0(m,mi),lemma296(m0"r"(m),intm0(m,mi),n)))
-ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
-+9297
-[p:nis(x,0c)]
-t1:=satz290(x,m,mi,lemma294a(o),p):nis(pw(x,m,mi,lemma294a(o)),0c)
-o@[a:and(pos(m),pos(n))]
-t2:=ande2(pos(m),pos(n),a):pos(n)
-t3:=postspp(m,n,ande1(pos(m),pos(n),a),t2):pos(ts"r"(m,n))
--9297
-lemma297a:=th9"l.or"(nis(x,0c),and(pos(m),pos(n)),nis(pw(x,m,mi,lemma294a(o)),0c),pos(n),o,[t:nis(x,0c)]t1".9297"(t),[t:and(pos(m),pos(n))]t2".9297"(t)):or(nis(pw(x,m,mi,lemma294a(o)),0c),pos(n))
-lemma297b:=th8"l.or"(nis(x,0c),and(pos(m),pos(n)),pos(ts"r"(m,n)),o,[t:and(pos(m),pos(n))]t3".9297"(t)):or(nis(x,0c),pos(ts"r"(m,n)))
-mi@[o:or(nis(x,0c),pos(m))][i:is(x,0c)]
-+*9297
-i@t4:=ore2(nis(x,0c),pos(m),o,weli(is(x,0c),i)):pos(m)
-m1:=ntofrl(m,posintnatrl(m,t4,mi)):nat
-t5:=posexp(x,m,mi,o,t4):is(pw(x,m,mi,o),prod(m1,[t:1to(m1)]x))
-t6:=satz289b(m1,[t:1to(m1)]x,xout(m1),i):is(prod(m1,[t:1to(m1)]x),0c)
-t7:=tris(cx,pw(x,m,mi,o),prod(m1,[t:1to(m1)]x),0c,t5,t6):is(pw(x,m,mi,o),0c)
--9297
-i@pw0:=t7".9297":is(pw(x,m,mi,o),0c)
-ni@[o:or(nis(x,0c),and(pos(m),pos(n)))]
-+*9297
-ni@t8:=intts(m,mi,n,ni):intrl(ts"r"(m,n))
-o@prop1:=is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o))):'prop'
-[i:is(x,0c)]
-t9:=pw0(x,m,mi,lemma294a(o),i):is(pw(x,m,mi,lemma294a(o)),0c)
-t10:=pw0(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o),t9):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),0c)
-t11:=pw0(x,ts"r"(m,n),t8,lemma297b(o),i):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),0c)
-t12:=tris2(cx,pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),0c,t10,t11):prop1
-m@[mi:intrl(m)][p:nis(x,0c)]
-t13:=ori1(nis(x,0c),pos(m),p):or(nis(x,0c),pos(m))
-p0:=pw(x,m,mi,t13):cx
-[n:nat]
-nr:=rlofnt(n):real
-t14:=natintrl(nr,natrli(n)):intrl(nr)
-t15:=ori2(nis(p0,0c),pos(nr),natpos(nr,natrli(n))):or(nis(p0,0c),pos(nr))
-t16:=ori1(nis(x,0c),pos(ts"r"(m,nr)),p):or(nis(x,0c),pos(ts"r"(m,nr)))
-t17:=intts(m,mi,nr,t14):intrl(ts"r"(m,nr))
-prop2:=is(pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16)):'prop'
-p@t18:=ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t15(1),lemma291(p0)):is(pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)))
-t19:=satz291(p0):is(pw(p0,1rl,intrl1,lemma291(p0)),p0)
-t20:=ispw2(x,m,ts"r"(m,1rl),satz195a(m),mi,t17(1),t13,t16(1)):is(p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)))
-t21:=tr3is(cx,pw(p0,1rl,t14(1),t15(1)),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,ts"r"(m,1rl),t17(1),t16(1)),t18,t19,t20):prop2(1)
-n@[p2:prop2(n)]
-n1:=pl"n"(n,1):nat
-t22:=satz290(x,m,mi,t13,p):nis(p0,0c)
-t23:=ori1(nis(p0,0c),and(pos(nr),pos(1rl)),t22):or(nis(p0,0c),and(pos(nr),pos(1rl)))
-t24:=lemma294a(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(nr))
-t25:=lemma294b(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(1rl))
-t26:=lemma294c(p0,nr,1rl,t14,intrl1,t23):or(nis(p0,0c),pos(pl"r"(nr,1rl)))
-t27:=ispw2(p0,nr(n1),pl"r"(nr,1rl),satzr155a(n,1),t14(n1),intpl(nr,t14,1rl,intrl1),t15(n1),t26):is(pw(p0,nr(n1),t14(n1),t15(n1)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
-t27a:=satz294(p0,nr,1rl,t14,intrl1,t23):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26))
-t28:=tris2(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),pw(p0,pl"r"(nr,1rl),intpl(nr,t14,1rl,intrl1),t26),t27,t27a):is(pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)))
-t29:=ori1(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)),p):or(nis(x,0c),and(pos(ts"r"(m,nr)),pos(m)))
-t30:=lemma294a(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(ts"r"(m,nr)))
-t31:=lemma294b(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(m))
-t32:=lemma294c(x,ts"r"(m,nr),m,t17,mi,t29):or(nis(x,0c),pos(pl"r"(ts"r"(m,nr),m)))
-t33:=tr3is(cx,pw(p0,nr,t14,t24),pw(p0,nr,t14,t15),pw(x,ts"r"(m,nr),t17,t16),pw(x,ts"r"(m,nr),t17,t30),ispw1(p0,p0,nr,refis(cx,p0),t14,t24,t15),p2,ispw1(x,x,ts"r"(m,nr),refis(cx,x),t17,t16,t30)):is(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30))
-t34:=tr3is(cx,pw(p0,1rl,intrl1,t25),pw(p0,1rl,intrl1,lemma291(p0)),p0,pw(x,m,mi,t31),ispw1(p0,p0,1rl,refis(cx,p0),intrl1,t25,lemma291(p0)),t19,ispw1(x,x,m,refis(cx,x),mi,t13,t31)):is(pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31))
-t35:=ists12(pw(p0,nr,t14,t24),pw(x,ts"r"(m,nr),t17,t30),pw(p0,1rl,intrl1,t25),pw(x,m,mi,t31),t33,t34):is(ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)))
-t36:=satz294(x,ts"r"(m,nr),m,t17,mi,t29):is(ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32))
-t37:=tr3is(real,pl"r"(ts"r"(m,nr),m),pl"r"(ts"r"(m,nr),ts"r"(m,1rl)),ts"r"(m,pl"r"(nr,1rl)),ts"r"(m,nr(n1)),ispl2"r"(m,ts"r"(m,1rl),ts"r"(m,nr),satz195a(m)),distpt2"r"(m,nr,1rl),ists2"r"(pl"r"(nr,1rl),nr(n1),m,satzr155b(n,1))):is"r"(pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)))
-t38:=ispw2(x,pl"r"(ts"r"(m,nr),m),ts"r"(m,nr(n1)),t37,intpl(ts"r"(m,nr),t17,m,mi),t17(n1),t32,t16(n1)):is(pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)))
-t39:=tr4is(cx,pw(p0,nr(n1),t14(n1),t15(n1)),ts(pw(p0,nr,t14,t24),pw(p0,1rl,intrl1,t25)),ts(pw(x,ts"r"(m,nr),t17,t30),pw(x,m,mi,t31)),pw(x,pl"r"(ts"r"(m,nr),m),intpl(ts"r"(m,nr),t17,m,mi),t32),pw(x,ts"r"(m,nr(n1)),t17(n1),t16(n1)),t28,t35,t36,t38):prop2(n1)
-t40:=isp(nat,[t:nat]prop2(t),n1,<n>suc,t39,satz4a(n)):prop2(<n>suc)
-n@t41:=induction([t:nat]prop2(t),t21,[t:nat][u:prop2(t)]t40(t,u),n):prop2(n)
-o@[p:nis(x,0c)][q:pos(n)]
-t42:=posintnatrl(n,q,ni):natrl(n)
-n0:=ntofrl(n,t42):nat
-t43:=isrlnt1(n,t42):is"r"(n,rlofnt(n0))
-t44:=isrlnt2(n,t42):is"r"(rlofnt(n0),n)
-o@p1:=pw(x,m,mi,lemma294a(o)):cx
-q@t44a:=ispw2(x,m,m,refis(real,m),mi,mi,lemma294a(o),t13(mi,p)):is(p1,p0(mi,p))
-t45:=ispw12(p1,p0(mi,p),n,rlofnt(n0),t44a,t43,ni,t14(mi,p,n0),lemma297a(o),t15(mi,p,n0)):is(pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)))
-t46:=t41(mi,p,n0):is(pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)))
-t47:=ists2"r"(rlofnt(n0),n,m,t44):is"r"(ts"r"(m,rlofnt(n0)),ts"r"(m,n))
-t48:=ispw2(x,ts"r"(m,rlofnt(n0)),ts"r"(m,n),t47,t17(mi,p,n0),t8,t16(mi,p,n0),lemma297b(o)):is(pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)))
-t49:=tr3is(cx,pw(p1,n,ni,lemma297a(o)),pw(p0(mi,p),rlofnt(n0),t14(mi,p,n0),t15(mi,p,n0)),pw(x,ts"r"(m,rlofnt(n0)),t17(mi,p,n0),t16(mi,p,n0)),pw(x,ts"r"(m,n),t8,lemma297b(o)),t45,t46,t48):prop1
-p@[i:is"r"(n,0)]
-t50:=0exp(p1,n,ni,lemma297a(o),i):is(pw(p1,n,ni,lemma297a(o)),1c)
-t51:=ts02"r"(m,n,i):is"r"(ts"r"(m,n),0)
-t52:=0exp(x,ts"r"(m,n),t8,lemma297b(o),t51):is(pw(x,ts"r"(m,n),t8,lemma297b(o)),1c)
-t53:=tris2(cx,pw(p1,n,ni,lemma297a(o)),pw(x,ts"r"(m,n),t8,lemma297b(o)),1c,t50,t52):prop1
-p@[q:neg(n)]
-an:=abs(n):real
-t54:=intabs(n,ni):intrl(an)
-t55:=ori1(nis(x,0c),and(pos(m),pos(an)),p):or(nis(x,0c),and(pos(m),pos(an)))
-p1t55:=p1(an,mi,t54,t55):cx
-t56:=satz166e(n,nnot0(n,q)):pos(an)
-t56a:=lemma294a(an,mi,t54,t55):or(nis(x,0c),pos(m))
-t57:=lemma297a(an,mi,t54,t55):or(nis(p1t55,0c),pos(an))
-t58:=lemma297b(an,mi,t54,t55):or(nis(x,0c),pos(ts"r"(m,an)))
-t59:=t49(an,mi,t54,t55,p,t56):is(pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58))
-t60:=satz177c(an,n,absn(n,q)):is"r"(n,m0"r"(an))
-t61:=intm0(an,t54):intrl(m0"r"(an))
-t62:=satz290(x,m,mi,t56a,p):nis(p1t55,0c)
-t63:=lemma296(p1t55,an,t54,t62):or(nis(p1t55,0c),pos(an))
-t64:=satz290(p1t55,an,t54,t63,t62):nis(pw(p1t55,an,t54,t63),0c)
-t65:=lemma296(p1t55,m0"r"(an),t61,t62):or(nis(p1t55,0c),pos(m0"r"(an)))
-t66:=satz296(p1t55,an,t54,t62):is(ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65))
-t67:=ispw1(x,x,m,refis(cx,x),mi,lemma294a(o),t56a):is(p1,p1t55)
-t68:=ispw12(p1,p1t55,n,m0"r"(an),t67,t60,ni,t61,lemma297a(o),t65):is(pw(p1,n,ni,lemma297a(o)),pw(p1t55,m0"r"(an),t61,t65))
-t69:=tris2(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),pw(p1t55,m0"r"(an),t61,t65),t68,t66):is(pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64))
-t70:=tris(real,m0"r"(ts"r"(m,an)),ts"r"(m,m0"r"(an)),ts"r"(m,n),satz197f(m,an),ists2"r"(m0"r"(an),n,m,symis(real,n,m0"r"(an),t60))):is"r"(m0"r"(ts"r"(m,an)),ts"r"(m,n))
-t71:=intm0(ts"r"(m,an),t8(an,mi,t54)):intrl(m0"r"(ts"r"(m,an)))
-t72:=lemma296(x,ts"r"(m,an),t8(an,mi,t54),p):or(nis(x,0c),pos(ts"r"(m,an)))
-t73:=satz290(x,ts"r"(m,an),t8(an,mi,t54),t72,p):nis(pw(x,ts"r"(m,an),t8(an,mi,t54),t72),0c)
-t74:=lemma296(x,m0"r"(ts"r"(m,an)),t71,p):or(nis(x,0c),pos(m0"r"(ts"r"(m,an))))
-t75:=satz296(x,ts"r"(m,an),t8(an,mi,t54),p):is(ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74))
-t76:=ispw2(x,m0"r"(ts"r"(m,an)),ts"r"(m,n),t70,t71,t8,t74,lemma297b(o)):is(pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)))
-t77:=ispw1(p1t55,p1t55,an,refis(cx,p1t55),t54,t63,t57):is(pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57))
-t78:=ispw1(x,x,ts"r"(m,an),refis(cx,x),t8(an,mi,t54),t58,t72):is(pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
-t79:=tr3is(cx,pw(p1t55,an,t54,t63),pw(p1t55,an,t54,t57),pw(x,ts"r"(m,an),t8(an,mi,t54),t58),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t77,t59,t78):is(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72))
-t80:=isov2(pw(p1t55,an,t54,t63),pw(x,ts"r"(m,an),t8(an,mi,t54),t72),1c,t79,t64,t73):is(ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73))
-t81:=tr4is(cx,pw(p1,n,ni,lemma297a(o)),ov(1c,pw(p1t55,an,t54,t63),t64),ov(1c,pw(x,ts"r"(m,an),t8(an,mi,t54),t72),t73),pw(x,m0"r"(ts"r"(m,an)),t71,t74),pw(x,ts"r"(m,n),t8,lemma297b(o)),t69,t80,t75,t76):prop1
-p@t82:=rapp(n,prop1,[t:pos(n)]t49(t),[t:is"r"(n,0)]t53(t),[t:neg(n)]t81(t)):prop1
--9297
-o@satz297:=th1"l.imp"(is(x,0c),prop1".9297",[t:is(x,0c)]t12".9297"(t),[t:nis(x,0c)]t82".9297"(t)):is(pw(pw(x,m,mi,lemma294a(o)),n,ni,lemma297a(o)),pw(x,ts"r"(m,n),intts(m,mi,n,ni),lemma297b(o)))
-@[r:real][s:real]
-+10298
-t1:=tris(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),pl"r"(0,0)),pli(pl"r"(r,s),0),plis12a(r,0,s,0),isrecx2(pl"r"(0,0),0,pl"r"(r,s),pl01(0,0,refis(real,0)))):is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
--10298
-satz298a:=symis(cx,pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0),t1".10298"):is(pli(pl"r"(r,s),0),pl(pli(r,0),pli(s,0)))
-satz298b:=t1".10298":is(pl(pli(r,0),pli(s,0)),pli(pl"r"(r,s),0))
-+*10298
-s@t2:=tris(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),mn"r"(0,0)),pli(mn"r"(r,s),0),mnis12a(r,0,s,0),isrecx2(mn"r"(0,0),0,mn"r"(r,s),pl02(0,m0"r"(0),satz176b(0,refis(real,0))))):is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
--10298
-s@satz298c:=symis(cx,mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0),t2".10298"):is(pli(mn"r"(r,s),0),mn(pli(r,0),pli(s,0)))
-satz298d:=t2".10298":is(mn(pli(r,0),pli(s,0)),pli(mn"r"(r,s),0))
-+*10298
-s@t3:=pl02(ts"r"(r,s),m0"r"(ts"r"(0,0)),satz176b(ts"r"(0,0),ts01(0,0,refis(real,0)))):is"r"(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s))
-t4:=tris(real,pl"r"(ts"r"(r,0),ts"r"(0,s)),ts"r"(r,0),0,pl02(ts"r"(r,0),ts"r"(0,s),ts01(0,s,refis(real,0))),ts02(r,0,refis(real,0))):is"r"(pl"r"(ts"r"(r,0),ts"r"(0,s)),0)
-t5:=tris(cx,ts(pli(r,0),pli(s,0)),pli(mn"r"(ts"r"(r,s),ts"r"(0,0)),pl"r"(ts"r"(r,0),ts"r"(0,s))),pli(ts"r"(r,s),0),tsis12a(r,0,s,0),isrecx12(mn"r"(ts"r"(r,s),ts"r"(0,0)),ts"r"(r,s),pl"r"(ts"r"(r,0),ts"r"(0,s)),0,t3,t4)):is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
--10298
-s@satz298e:=symis(cx,ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0),t5".10298"):is(pli(ts"r"(r,s),0),ts(pli(r,0),pli(s,0)))
-satz298f:=t5".10298":is(ts(pli(r,0),pli(s,0)),pli(ts"r"(r,s),0))
-[n:nis"r"(s,0)]
-+*10298
-n@[i:is(pli(s,0),0c)]
-t6:=tr3is(real,s,re(pli(s,0)),re(0c),0,isre(s,0),iscere(pli(s,0),0c,i),reis(0,0)):is"r"(s,0)
--10298
-n@lemma298:=th3"l.imp"(is(pli(s,0),0c),is"r"(s,0),n,[t:is(pli(s,0),0c)]t6".10298"(t)):nis(pli(s,0),0c)
-+*10298
-n@t7:=tris(cx,ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(ts"r"(s,ov"r"(r,s,n)),0),pli(r,0),t5(s,ov"r"(r,s,n)),isrecx1(ts"r"(s,ov"r"(r,s,n)),r,0,satz204c(r,s,n))):is(ts(pli(s,0),pli(ov"r"(r,s,n),0)),pli(r,0))
--10298
-n@satz298g:=satz229g(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(pli(ov"r"(r,s,n),0),ov(pli(r,0),pli(s,0),lemma298))
-satz298h:=satz229h(pli(r,0),pli(s,0),pli(ov"r"(r,s,n),0),lemma298,t7".10298"):is(ov(pli(r,0),pli(s,0),lemma298),pli(ov"r"(r,s,n),0))
-+*10298
-r@t8:=tris(cx,m0(pli(r,0)),pli(m0"r"(r),m0"r"(0)),pli(m0"r"(r),0),m0isa(r,0),isrecx2(m0"r"(0),0,m0"r"(r),satz176b(0,refis(real,0)))):is(m0(pli(r,0)),pli(m0"r"(r),0))
--10298
-r@satz298j:=symis(cx,m0(pli(r,0)),pli(m0"r"(r),0),t8".10298"):is(pli(m0"r"(r),0),m0(pli(r,0)))
-satz298k:=t8".10298":is(m0(pli(r,0)),pli(m0"r"(r),0))
-+*10298
-r@t9:=tris(real,mod2(pli(r,0)),ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(r,r),pl02(ts"r"(re(pli(r,0)),re(pli(r,0))),ts"r"(im(pli(r,0)),im(pli(r,0))),ts01(im(pli(r,0)),im(pli(r,0)),imis(r,0))),ists12"r"(re(pli(r,0)),r,re(pli(r,0)),r,reis(r,0),reis(r,0))):is"r"(mod2(pli(r,0)),ts"r"(r,r))
-ar:=abs(r):real
-[p:pos(r)]
-t10:=satz196a(r,r,p,p):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-r@[i:is"r"(r,0)]
-t11:=tris2(real,ts"r"(r,r),ts"r"(ar,ar),0,ts01(r,r,i),ts01(ar,ar,abs0(r,i))):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-r@[n:neg(r)]
-t12:=satz196b(r,r,n,n):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-r@t13:=rapp(r,is"r"(ts"r"(r,r),ts"r"(ar,ar)),[t:pos(r)]t10(t),[t:is"r"(r,0)]t11(t),[t:neg(r)]t12(t)):is"r"(ts"r"(r,r),ts"r"(ar,ar))
-t14:=tris(real,mod2(pli(r,0)),ts"r"(r,r),ts"r"(ar,ar),t9,t13):is"r"(mod2(pli(r,0)),ts"r"(ar,ar))
-t15:=th1"l.imp"(is"r"(r,0),not(neg(ar)),[t:is"r"(r,0)]0notn(ar,abs0(r,t)),[t:nis"r"(r,0)]pnotn(ar,satz166e(r,t))):not(neg(ar))
--10298
-r@satz298l:=thsqrt3(mod2(pli(r,0)),lemma5(pli(r,0)),abs(r),t15".10298",t14".10298"):is"r"(mod(pli(r,0)),abs(r))
-satz298m:=symis(real,mod(pli(r,0)),abs(r),satz298l):is"r"(abs(r),mod(pli(r,0)))
-cofrl:=pli(r,0):complex
-s@[i:is(cofrl(r),cofrl(s))]
-isrlic:=tr3is(real,r,re(cofrl(r)),re(cofrl(s)),s,isre(r,0),iscere(cofrl(r),cofrl(s),i),reis(s,0)):is"r"(r,s)
-s@[i:is"r"(r,s)]
-isrlec:=isrecx1(r,s,0,i):is(cofrl(r),cofrl(s))
-+v10
-@t1:=[t:real][u:real][v:is(cofrl(t),cofrl(u))]isrlic(t,u,v):injective(real,cx,[t:real]cofrl(t))
--v10
-@[x:cx]
-realc:=image(real,cx,[t:real]cofrl(t),x):'prop'
-r@reali:=imagei(real,cx,[t:real]cofrl(t),r):realc(cofrl(r))
-x@[rx:realc(x)]
-rlofc:=soft(real,cx,[t:real]cofrl(t),t1".v10",x,rx):real
-[y:cx][ry:realc(y)][i:is"r"(rlofc(x,rx),rlofc(y,ry))]
-iscirl:=isinve(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is(x,y)
-ry@[i:is(x,y)]
-iscerl:=isinv(real,cx,[t:real]cofrl(t),t1".v10",x,rx,y,ry,i):is"r"(rlofc(x,rx),rlofc(y,ry))
-r@isrlc1:=isst1(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(r,rlofc(cofrl(r),reali(r)))
-isrlc2:=isst2(real,cx,[t:real]cofrl(t),t1".v10",r):is"r"(rlofc(cofrl(r),reali(r)),r)
-rx@iscrl1:=ists1"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(x,cofrl(rlofc(x,rx)))
-iscrl2:=ists2"e"(real,cx,[t:real]cofrl(t),t1".v10",x,rx):is(cofrl(rlofc(x,rx)),x)
-@[n:nat]
-cofn:=cofrl(rlofnt(n)):complex
-[m:nat][i:is"n"(n,m)]
-isnec:=isrlec(rlofnt(n),rlofnt(m),isnterl(n,m,i)):is(cofn(n),cofn(m))
-m@[i:is(cofn(n),cofn(m))]
-isnic:=isntirl(n,m,isrlic(rlofnt(n),rlofnt(m),i)):is"n"(n,m)
-+*v10
-@t2:=[t:nat][u:nat][v:is(cofn(t),cofn(u))]isnic(t,u,v):injective(nat,cx,[t:nat]cofn(t))
--v10
-x@natc:=image(nat,cx,[t:nat]cofn(t),x):'prop'
-n@nati:=imagei(nat,cx,[t:nat]cofn(t),n):natc(cofn(n))
-x@[nx:natc(x)]
-nofc:=soft(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):nat
-[y:cx][ny:natc(y)][i:is(x,y)]
-iscen:=isinv(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is"n"(nofc(x,nx),nofc(y,ny))
-ny@[i:is"n"(nofc(x,nx),nofc(y,ny))]
-iscin:=isinve(nat,cx,[t:nat]cofn(t),t2".v10",x,nx,y,ny,i):is(x,y)
-n@isnc1:=isst1(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(n,nofc(cofn(n),nati(n)))
-isnc2:=isst2(nat,cx,[t:nat]cofn(t),t2".v10",n):is"n"(nofc(cofn(n),nati(n)),n)
-nx@iscn1:=ists1"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(x,cofn(nofc(x,nx)))
-iscn2:=ists2"e"(nat,cx,[t:nat]cofn(t),t2".v10",x,nx):is(cofn(nofc(x,nx)),x)
-@natt:=ot(cx,[t:cx]natc(t)):'type'
-[nt:natt]
-cofnt:=in"e"(cx,[t:cx]natc(t),nt):cx
-natti:=inp(cx,[t:cx]natc(t),nt):natc(cofnt(nt))
-[mt:natt][i:is"e"(natt,nt,mt)]
-isntec:=isini(cx,[t:cx]natc(t),nt,mt,i):is(cofnt(nt),cofnt(mt))
-mt@[i:is(cofnt(nt),cofnt(mt))]
-isntic:=isine(cx,[t:cx]natc(t),nt,mt,i):is"e"(natt,nt,mt)
-nx@ntofc:=out(cx,[t:cx]natc(t),x,nx):natt
-ny@[i:is(x,y)]
-iscent:=isouti(cx,[t:cx]natc(t),x,nx,y,ny,i):is"e"(natt,ntofc(x,nx),ntofc(y,ny))
-ny@[i:is"e"(natt,ntofc(x,nx),ntofc(y,ny))]
-iscint:=isoute(cx,[t:cx]natc(t),x,nx,y,ny,i):is(x,y)
-nt@isntc1:=isoutin(cx,[t:cx]natc(t),nt):is"e"(natt,nt,ntofc(cofnt(nt),natti(nt)))
-isntc2:=symis(natt,nt,ntofc(cofnt(nt),natti(nt)),isntc1):is"e"(natt,ntofc(cofnt(nt),natti(nt)),nt)
-nx@iscnt1:=isinout(cx,[t:cx]natc(t),x,nx):is(x,cofnt(ntofc(x,nx)))
-iscnt2:=symis(cx,x,cofnt(ntofc(x,nx)),iscnt1):is(cofnt(ntofc(x,nx)),x)
-n@ntofn:=ntofc(cofn(n),nati(n)):natt
-m@[i:is"n"(n,m)]
-isnent:=iscent(cofn(n),nati(n),cofn(m),nati(m),isnec(n,m,i)):is"e"(natt,ntofn(n),ntofn(m))
-m@[i:is"e"(natt,ntofn(n),ntofn(m))]
-isnint:=isnic(n,m,iscint(cofn(n),nati(n),cofn(m),nati(m),i)):is"n"(n,m)
-nt@nofnt:=nofc(cofnt(nt),natti(nt)):nat
-mt@[i:is"e"(natt,nt,mt)]
-isnter:=iscen(cofnt(nt),natti(nt),cofnt(mt),natti(mt),isntec(nt,mt,i)):is"n"(nofnt(nt),nofnt(mt))
-mt@[i:is"n"(nofnt(nt),nofnt(mt))]
-isntin:=isntic(nt,mt,iscin(cofnt(nt),natti(nt),cofnt(mt),natti(mt),i)):is"e"(natt,nt,mt)
-+*v10
-n@t3:=iscnt1(cofn(n),nati(n)):is(cofn(n),cofnt(ntofn(n)))
--v10
-n@isnnt1:=tris(nat,n,nofc(cofn(n),nati(n)),nofnt(ntofn(n)),isnc1(n),iscen(cofn(n),nati(n),cofnt(ntofn(n)),natti(ntofn(n)),t3".v10")):is"n"(n,nofnt(ntofn(n)))
-isnnt2:=symis(nat,n,nofnt(ntofn(n)),isnnt1):is"n"(nofnt(ntofn(n)),n)
-+*v10
-nt@t4:=iscn1(cofnt(nt),natti(nt)):is(cofnt(nt),cofn(nofnt(nt)))
--v10
-nt@isntn1:=tris(natt,nt,ntofc(cofnt(nt),natti(nt)),ntofn(nofnt(nt)),isntc1(nt),iscent(cofnt(nt),natti(nt),cofn(nofnt(nt)),nati(nofnt(nt)),t4".v10")):is"e"(natt,nt,ntofn(nofnt(nt)))
-isntn2:=symis(natt,nt,ntofn(nofnt(nt)),isntn1):is"e"(natt,ntofn(nofnt(nt)),nt)
-@1t:=ntofn(1):natt
-suct:=[t:natt]ntofn(<nofnt(t)>suc):[t:natt]natt
-+10299
-nt@[i:is"e"(natt,<nt>suct,1t)]
-t1:=isnint(<nofnt(nt)>suc,1,i):is"n"(<nofnt(nt)>suc,1)
--10299
-nt@satz299a:=th3"l.imp"(is"e"(natt,<nt>suct,1t),is"n"(<nofnt(nt)>suc,1),<nofnt(nt)>ax3,[t:is"e"(natt,<nt>suct,1t)]t1".10299"(t)):not(is"e"(natt,<nt>suct,1t))
-@ax3t:=[t:natt]satz299a(t):[t:natt]not(is"e"(natt,<t>suct,1t))
-mt@[i:is"e"(natt,<nt>suct,<mt>suct)]
-+*10299
-i"c"@t2:=isnint(<nofnt(nt)>suc,<nofnt(mt)>suc,i):is"n"(<nofnt(nt)>suc,<nofnt(mt)>suc)
-t3:=<t2><nofnt(mt)><nofnt(nt)>ax4:is"n"(nofnt(nt),nofnt(mt))
--10299
-i@satz299b:=isntin(nt,mt,t3".10299"):is"e"(natt,nt,mt)
-@ax4t:=[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]satz299b(t,u,v):[t:natt][u:natt][v:is"e"(natt,<t>suct,<u>suct)]is"e"(natt,t,u)
-[s:set(natt)]
-cond1t:=esti(natt,1t,s):'prop'
-cond2t:=all"l"(natt,[t:natt]imp(esti(natt,t,s),esti(natt,<t>suct,s))):'prop'
-[c1:cond1t][c2:cond2t]
-+*10299
-c2@[n:nat]
-prop1:=esti(natt,ntofn(n),s):'prop'
-c2@t4:=c1:prop1(1)
-n@[p:prop1(n)]
-t5:=<p><ntofn(n)>c2:esti(natt,ntofn(<nofnt(ntofn(n))>suc),s)
-t6:=isp(nat,[t:nat]esti(natt,ntofn(<t>suc),s),nofnt(ntofn(n)),n,t5,isnnt2(n)):prop1(<n>suc)
-c2@[nt:natt]
-t7:=induction([t:nat]prop1(t),t4,[t:nat][u:prop1(t)]t6(t,u),nofnt(nt)):prop1(nofnt(nt))
--10299
-c2@satz299c:=[t:natt]isp(natt,[u:natt]esti(natt,u,s),ntofn(nofnt(t)),t,t7".10299"(t),isntn2(t)):[t:natt]esti(natt,t,s)
-@ax5t:=[t:set(natt)][u:cond1t(t)][v:cond2t(t)]satz299c(t,u,v):[t:set(natt)][u:cond1t(t)][v:cond2t(t)][w:natt]esti(natt,w,t)
-ic:=pli(0,1rl):complex
-+10300
-t1:=tsis12a(0,1rl,0,1rl):is(ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))))
-t2:=tris(real,mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(ts"r"(1rl,1rl)),m0"r"(1rl),pl01(ts"r"(0,0),m0"r"(ts"r"(1rl,1rl)),ts01(0,0,refis(real,0))),ism0"r"(ts"r"(1rl,1rl),1rl,satz195(1rl))):is"r"(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl))
-t3:=tris(real,pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),ts"r"(1rl,0),0,pl01(ts"r"(0,1rl),ts"r"(1rl,0),ts01(0,1rl,refis(real,0))),ts02(1rl,0,refis(real,0))):is"r"(pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0)
-t4:=isrecx12(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),m0"r"(1rl),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0)),0,t2,t3):is(pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)))
-t5:=satz298j(1rl):is(cofrl(m0"r"(1rl)),m0(1c))
--10300
-satz2300:=tr3is(cx,ts(ic,ic),pli(mn"r"(ts"r"(0,0),ts"r"(1rl,1rl)),pl"r"(ts"r"(0,1rl),ts"r"(1rl,0))),cofrl(m0"r"(1rl)),m0(1c),t1".10300",t4".10300",t5".10300"):is(ts(ic,ic),m0(1c))
-[r:real][s:real]
-+10301
-t1:=tsis12a(s,0,0,1rl):is(ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))))
-t2:=tris(real,mn"r"(ts"r"(s,0),ts"r"(0,1rl)),m0"r"(ts"r"(0,1rl)),0,pl01(ts"r"(s,0),m0"r"(ts"r"(0,1rl)),ts02(s,0,refis(real,0))),satz176b(ts"r"(0,1rl),ts01(0,1rl,refis(real,0)))):is"r"(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0)
-t3:=tris(real,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),ts"r"(s,1rl),s,pl02(ts"r"(s,1rl),ts"r"(0,0),ts01(0,0,refis(real,0))),satz195(s)):is"r"(pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s)
-t4:=isrecx12(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),0,pl"r"(ts"r"(s,1rl),ts"r"(0,0)),s,t2,t3):is(pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s))
-t5:=tris(cx,ts(cofrl(s),ic),pli(mn"r"(ts"r"(s,0),ts"r"(0,1rl)),pl"r"(ts"r"(s,1rl),ts"r"(0,0))),pli(0,s),t1,t4):is(ts(cofrl(s),ic),pli(0,s))
-t6:=ispl2(ts(cofrl(s),ic),pli(0,s),cofrl(r),t5):is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)))
-t7:=plis12a(r,0,0,s):is(pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)))
-t8:=isrecx12(pl"r"(r,0),r,pl"r"(0,s),s,pl02(r,0,refis(real,0)),pl01(0,s,refis(real,0))):is(pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s))
--10301
-satz301a:=tr3is(cx,pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(r),pli(0,s)),pli(pl"r"(r,0),pl"r"(0,s)),pli(r,s),t6".10301",t7".10301",t8".10301"):is"e"(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s))
-satz301b:=symis(cx,pl(cofrl(r),ts(cofrl(s),ic)),pli(r,s),satz301a):is(pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)))
-@[x:complex]
-satz301c:=tris(cx,x,pli(re(x),im(x)),pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),ispli(x),satz301b(re(x),im(x))):is(x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)))
-satz301d:=symis(cx,x,pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),satz301c):is(pl(cofrl(re(x)),ts(cofrl(im(x)),ic)),x)
-s@[t:real][u:real][i:is(pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)))]
-+*10301
-i@t9:=tr3is(cx,pli(r,s),pl(cofrl(r),ts(cofrl(s),ic)),pl(cofrl(t),ts(cofrl(u),ic)),pli(t,u),satz301b(r,s),i,satz301a(t,u)):is(pli(r,s),pli(t,u))
--10301
-i@satz301e:=tr3is(real,r,re(pli(r,s)),re(pli(t,u)),t,isre(r,s),iscere(pli(r,s),pli(t,u),t9".10301"),reis(t,u)):is"r"(r,t)
-satz301f:=tr3is(real,s,im(pli(r,s)),im(pli(t,u)),u,isim(r,s),isceim(pli(r,s),pli(t,u),t9".10301"),imis(t,u)):is"r"(s,u)
--c
--r
--rp
--rt
--n
--landau
--eq
--st
--e
-{}
--l
+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-(* This file is generated by Helena 0.8.2 M - November 2014: do not edit **)
-
-include "basics/pts.ma".
-
-(* notion 1 *)
-definition l_imp ≝ λa:Prop.λb:Prop.(Πx:a.b : Prop).
-
-(* notion 2 *)
-definition l_mp ≝ λa:Prop.λb:Prop.λa1:a.λi:l_imp a b.(i a1 : b).
-
-(* notion 3 *)
-definition l_refimp ≝ λa:Prop.(λx:a.x : l_imp a a).
-
-(* notion 4 *)
-definition l_trimp ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_imp a b.λj:l_imp b c.(λx:a.j (i x) : l_imp a c).
-
-(* notion 5 *)
-axiom l_con : Prop.
-
-(* notion 6 *)
-definition l_not ≝ λa:Prop.(l_imp a l_con : Prop).
-
-(* notion 7 *)
-definition l_wel ≝ λa:Prop.(l_not (l_not a) : Prop).
-
-(* notion 8 *)
-definition l_weli ≝ λa:Prop.λa1:a.(λx:l_not a.x a1 : l_wel a).
-
-(* notion 9 *)
-axiom l_et : Πa:Prop.Πw:l_wel a.a.
-
-(* notion 10 *)
-definition l_cone ≝ λa:Prop.λc1:l_con.(l_et a (λx:l_not a.c1) : a).
-
-(* notion 11 *)
-definition l_imp_th1 ≝ λa:Prop.λb:Prop.λi:l_imp a b.λj:l_imp (l_not a) b.(l_et b (λx:l_not b.x (j (l_trimp a b l_con i x))) : b).
-
-(* notion 12 *)
-definition l_imp_th2 ≝ λa:Prop.λb:Prop.λn:l_not a.(l_trimp a l_con b n (λx:l_con.l_cone b x) : l_imp a b).
-
-(* notion 13 *)
-definition l_imp_th3 ≝ λa:Prop.λb:Prop.λn:l_not b.λi:l_imp a b.(l_trimp a b l_con i n : l_not a).
-
-(* notion 14 *)
-definition l_imp_th4 ≝ λa:Prop.λb:Prop.λa1:a.λn:l_not b.(λx:l_imp a b.l_imp_th3 a b n x a1 : l_not (l_imp a b)).
-
-(* notion 15 *)
-definition l_imp_th5 ≝ λa:Prop.λb:Prop.λn:l_not (l_imp a b).(l_et a (λx:l_not a.n (l_imp_th2 a b x)) : a).
-
-(* notion 16 *)
-definition l_imp_th6 ≝ λa:Prop.λb:Prop.λn:l_not (l_imp a b).(λx:b.n (λy:a.x) : l_not b).
-
-(* notion 17 *)
-definition l_imp_th7 ≝ λa:Prop.λb:Prop.λn:l_not b.λi:l_imp (l_not a) b.(l_et a (l_imp_th3 (l_not a) b n i) : a).
-
-(* notion 18 *)
-definition l_cp ≝ λa:Prop.λb:Prop.λi:l_imp (l_not b) (l_not a).(λx:a.l_imp_th7 b (l_not a) (l_weli a x) i : l_imp a b).
-
-(* notion 19 *)
-definition l_obvious ≝ (l_imp l_con l_con : Prop).
-
-(* notion 20 *)
-definition l_obviousi ≝ (l_refimp l_con : l_obvious).
-
-(* notion 21 *)
-definition l_ec ≝ λa:Prop.λb:Prop.(l_imp a (l_not b) : Prop).
-
-(* notion 22 *)
-definition l_eci1 ≝ λa:Prop.λb:Prop.λn:l_not a.(l_imp_th2 a (l_not b) n : l_ec a b).
-
-(* notion 23 *)
-definition l_eci2 ≝ λa:Prop.λb:Prop.λn:l_not b.(λx:a.n : l_ec a b).
-
-(* notion 24 *)
-definition l_ec_th1 ≝ λa:Prop.λb:Prop.λi:l_imp a (l_not b).(i : l_ec a b).
-
-(* notion 25 *)
-definition l_ec_th2 ≝ λa:Prop.λb:Prop.λi:l_imp b (l_not a).(λx:a.λy:b.i y x : l_ec a b).
-
-(* notion 26 *)
-definition l_comec ≝ λa:Prop.λb:Prop.λe:l_ec a b.(l_ec_th2 b a e : l_ec b a).
-
-(* notion 27 *)
-definition l_ece1 ≝ λa:Prop.λb:Prop.λe:l_ec a b.λa1:a.(e a1 : l_not b).
-
-(* notion 28 *)
-definition l_ece2 ≝ λa:Prop.λb:Prop.λe:l_ec a b.λb1:b.(l_imp_th3 a (l_not b) (l_weli b b1) e : l_not a).
-
-(* notion 29 *)
-definition l_ec_th3 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec a b.λi:l_imp c a.(l_trimp c a (l_not b) i e : l_ec c b).
-
-(* notion 30 *)
-definition l_ec_th4 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec a b.λi:l_imp c b.(l_comec c a (l_ec_th3 b a c (l_comec a b e) i) : l_ec a c).
-
-(* notion 31 *)
-definition l_and ≝ λa:Prop.λb:Prop.(l_not (l_ec a b) : Prop).
-
-(* notion 32 *)
-definition l_andi ≝ λa:Prop.λb:Prop.λa1:a.λb1:b.(l_imp_th4 a (l_not b) a1 (l_weli b b1) : l_and a b).
-
-(* notion 33 *)
-definition l_ande1 ≝ λa:Prop.λb:Prop.λa1:l_and a b.(l_imp_th5 a (l_not b) a1 : a).
-
-(* notion 34 *)
-definition l_ande2 ≝ λa:Prop.λb:Prop.λa1:l_and a b.(l_et b (l_imp_th6 a (l_not b) a1) : b).
-
-(* notion 35 *)
-definition l_comand ≝ λa:Prop.λb:Prop.λa1:l_and a b.(l_andi b a (l_ande2 a b a1) (l_ande1 a b a1) : l_and b a).
-
-(* notion 36 *)
-definition l_and_th1 ≝ λa:Prop.λb:Prop.λn:l_not a.(l_weli (l_ec a b) (l_eci1 a b n) : l_not (l_and a b)).
-
-(* notion 37 *)
-definition l_and_th2 ≝ λa:Prop.λb:Prop.λn:l_not b.(l_weli (l_ec a b) (l_eci2 a b n) : l_not (l_and a b)).
-
-(* notion 38 *)
-definition l_and_th3 ≝ λa:Prop.λb:Prop.λn:l_not (l_and a b).λa1:a.(l_ece1 a b (l_et (l_ec a b) n) a1 : l_not b).
-
-(* notion 39 *)
-definition l_and_th4 ≝ λa:Prop.λb:Prop.λn:l_not (l_and a b).λb1:b.(l_ece2 a b (l_et (l_ec a b) n) b1 : l_not a).
-
-(* notion 40 *)
-definition l_and_th5 ≝ λa:Prop.λb:Prop.λn:l_not (l_and a b).(l_imp_th3 (l_and b a) (l_and a b) n (λx:l_and b a.l_comand b a x) : l_not (l_and b a)).
-
-(* notion 41 *)
-definition l_and_th6 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and a b.λi:l_imp a c.(l_andi c b (i (l_ande1 a b a1)) (l_ande2 a b a1) : l_and c b).
-
-(* notion 42 *)
-definition l_and_th7 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and a b.λi:l_imp b c.(l_andi a c (l_ande1 a b a1) (i (l_ande2 a b a1)) : l_and a c).
-
-(* notion 43 *)
-definition l_or ≝ λa:Prop.λb:Prop.(l_imp (l_not a) b : Prop).
-
-(* notion 44 *)
-definition l_ori1 ≝ λa:Prop.λb:Prop.λa1:a.(l_imp_th2 (l_not a) b (l_weli a a1) : l_or a b).
-
-(* notion 45 *)
-definition l_ori2 ≝ λa:Prop.λb:Prop.λb1:b.(λx:l_not a.b1 : l_or a b).
-
-(* notion 46 *)
-definition l_or_th1 ≝ λa:Prop.λb:Prop.λi:l_imp (l_not a) b.(i : l_or a b).
-
-(* notion 47 *)
-definition l_or_th2 ≝ λa:Prop.λb:Prop.λi:l_imp (l_not b) a.(λx:l_not a.l_et b (l_imp_th3 (l_not b) a x i) : l_or a b).
-
-(* notion 48 *)
-definition l_ore2 ≝ λa:Prop.λb:Prop.λo:l_or a b.λn:l_not a.(o n : b).
-
-(* notion 49 *)
-definition l_ore1 ≝ λa:Prop.λb:Prop.λo:l_or a b.λn:l_not b.(l_et a (l_imp_th3 (l_not a) b n o) : a).
-
-(* notion 50 *)
-definition l_comor ≝ λa:Prop.λb:Prop.λo:l_or a b.(λx:l_not b.l_ore1 a b o x : l_or b a).
-
-(* notion 51 *)
-definition l_or_th3 ≝ λa:Prop.λb:Prop.λn:l_not a.λm:l_not b.(l_imp_th4 (l_not a) b n m : l_not (l_or a b)).
-
-(* notion 52 *)
-definition l_or_th4 ≝ λa:Prop.λb:Prop.λn:l_not (l_or a b).(l_imp_th5 (l_not a) b n : l_not a).
-
-(* notion 53 *)
-definition l_or_th5 ≝ λa:Prop.λb:Prop.λn:l_not (l_or a b).(l_imp_th6 (l_not a) b n : l_not b).
-
-(* notion 54 *)
-definition l_or_th6 ≝ λa:Prop.(l_refimp (l_not a) : l_or a (l_not a)).
-
-(* notion 55 *)
-definition l_orapp ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or a b.λi:l_imp a c.λj:l_imp b c.(l_imp_th1 a c i (l_trimp (l_not a) b c o j) : c).
-
-(* notion 56 *)
-definition l_or_th7 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or a b.λi:l_imp a c.(l_trimp (l_not c) (l_not a) b (λx:l_not c.l_imp_th3 a c x i) o : l_or c b).
-
-(* notion 57 *)
-definition l_or_th8 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or a b.λi:l_imp b c.(l_trimp (l_not a) b c o i : l_or a c).
-
-(* notion 58 *)
-definition l_or_th9 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λo:l_or a b.λi:l_imp a c.λj:l_imp b d.(l_or_th7 a d c (l_or_th8 a b d o j) i : l_or c d).
-
-(* notion 59 *)
-definition l_or_th10 ≝ λa:Prop.λb:Prop.λo:l_or a b.(o : l_imp (l_not a) b).
-
-(* notion 60 *)
-definition l_or_th11 ≝ λa:Prop.λb:Prop.λo:l_or a b.(l_comor a b o : l_imp (l_not b) a).
-
-(* notion 61 *)
-definition l_or_th12 ≝ λa:Prop.λb:Prop.λo:l_or (l_not a) b.(l_trimp a (l_wel a) b (λx:a.l_weli a x) o : l_imp a b).
-
-(* notion 62 *)
-definition l_or_th13 ≝ λa:Prop.λb:Prop.λi:l_imp a b.(l_trimp (l_wel a) a b (λx:l_wel a.l_et a x) i : l_or (l_not a) b).
-
-(* notion 63 *)
-definition l_or_th14 ≝ λa:Prop.λb:Prop.λo:l_or (l_not a) (l_not b).(l_weli (l_ec a b) (l_or_th12 a (l_not b) o) : l_not (l_and a b)).
-
-(* notion 64 *)
-definition l_or_th15 ≝ λa:Prop.λb:Prop.λn:l_not (l_and a b).(l_or_th13 a (l_not b) (l_et (l_ec a b) n) : l_or (l_not a) (l_not b)).
-
-(* notion 65 *)
-definition l_or_th16 ≝ λa:Prop.λb:Prop.λa1:l_and (l_not a) (l_not b).(l_or_th3 a b (l_ande1 (l_not a) (l_not b) a1) (l_ande2 (l_not a) (l_not b) a1) : l_not (l_or a b)).
-
-(* notion 66 *)
-definition l_or_th17 ≝ λa:Prop.λb:Prop.λn:l_not (l_or a b).(l_andi (l_not a) (l_not b) (l_or_th4 a b n) (l_or_th5 a b n) : l_and (l_not a) (l_not b)).
-
-(* notion 67 *)
-definition l_orec ≝ λa:Prop.λb:Prop.(l_and (l_or a b) (l_ec a b) : Prop).
-
-(* notion 68 *)
-definition l_oreci ≝ λa:Prop.λb:Prop.λo:l_or a b.λe:l_ec a b.(l_andi (l_or a b) (l_ec a b) o e : l_orec a b).
-
-(* notion 69 *)
-definition l_orec_th1 ≝ λa:Prop.λb:Prop.λa1:a.λn:l_not b.(l_oreci a b (l_ori1 a b a1) (l_eci2 a b n) : l_orec a b).
-
-(* notion 70 *)
-definition l_orec_th2 ≝ λa:Prop.λb:Prop.λn:l_not a.λb1:b.(l_oreci a b (l_ori2 a b b1) (l_eci1 a b n) : l_orec a b).
-
-(* notion 71 *)
-definition l_orece1 ≝ λa:Prop.λb:Prop.λo:l_orec a b.(l_ande1 (l_or a b) (l_ec a b) o : l_or a b).
-
-(* notion 72 *)
-definition l_orece2 ≝ λa:Prop.λb:Prop.λo:l_orec a b.(l_ande2 (l_or a b) (l_ec a b) o : l_ec a b).
-
-(* notion 73 *)
-definition l_comorec ≝ λa:Prop.λb:Prop.λo:l_orec a b.(l_oreci b a (l_comor a b (l_orece1 a b o)) (l_comec a b (l_orece2 a b o)) : l_orec b a).
-
-(* notion 74 *)
-definition l_orec_th3 ≝ λa:Prop.λb:Prop.λo:l_orec a b.λa1:a.(l_ece1 a b (l_orece2 a b o) a1 : l_not b).
-
-(* notion 75 *)
-definition l_orec_th4 ≝ λa:Prop.λb:Prop.λo:l_orec a b.λb1:b.(l_ece2 a b (l_orece2 a b o) b1 : l_not a).
-
-(* notion 76 *)
-definition l_orec_th5 ≝ λa:Prop.λb:Prop.λo:l_orec a b.λn:l_not a.(l_ore2 a b (l_orece1 a b o) n : b).
-
-(* notion 77 *)
-definition l_orec_th6 ≝ λa:Prop.λb:Prop.λo:l_orec a b.λn:l_not b.(l_ore1 a b (l_orece1 a b o) n : a).
-
-(* notion 78 *)
-definition l_iff ≝ λa:Prop.λb:Prop.(l_and (l_imp a b) (l_imp b a) : Prop).
-
-(* notion 79 *)
-definition l_iffi ≝ λa:Prop.λb:Prop.λi:l_imp a b.λj:l_imp b a.(l_andi (l_imp a b) (l_imp b a) i j : l_iff a b).
-
-(* notion 80 *)
-definition l_iff_th1 ≝ λa:Prop.λb:Prop.λa1:a.λb1:b.(l_iffi a b (λx:a.b1) (λx:b.a1) : l_iff a b).
-
-(* notion 81 *)
-definition l_iff_th2 ≝ λa:Prop.λb:Prop.λn:l_not a.λm:l_not b.(l_iffi a b (l_imp_th2 a b n) (l_imp_th2 b a m) : l_iff a b).
-
-(* notion 82 *)
-definition l_iffe1 ≝ λa:Prop.λb:Prop.λi:l_iff a b.(l_ande1 (l_imp a b) (l_imp b a) i : l_imp a b).
-
-(* notion 83 *)
-definition l_iffe2 ≝ λa:Prop.λb:Prop.λi:l_iff a b.(l_ande2 (l_imp a b) (l_imp b a) i : l_imp b a).
-
-(* notion 84 *)
-definition l_comiff ≝ λa:Prop.λb:Prop.λi:l_iff a b.(l_iffi b a (l_iffe2 a b i) (l_iffe1 a b i) : l_iff b a).
-
-(* notion 85 *)
-definition l_iff_th3 ≝ λa:Prop.λb:Prop.λi:l_iff a b.λa1:a.(l_iffe1 a b i a1 : b).
-
-(* notion 86 *)
-definition l_iff_th4 ≝ λa:Prop.λb:Prop.λi:l_iff a b.λb1:b.(l_iffe2 a b i b1 : a).
-
-(* notion 87 *)
-definition l_iff_th5 ≝ λa:Prop.λb:Prop.λi:l_iff a b.λn:l_not a.(l_imp_th3 b a n (l_iffe2 a b i) : l_not b).
-
-(* notion 88 *)
-definition l_iff_th6 ≝ λa:Prop.λb:Prop.λi:l_iff a b.λn:l_not b.(l_imp_th3 a b n (l_iffe1 a b i) : l_not a).
-
-(* notion 89 *)
-definition l_iff_th7 ≝ λa:Prop.λb:Prop.λa1:a.λn:l_not b.(l_and_th1 (l_imp a b) (l_imp b a) (l_imp_th4 a b a1 n) : l_not (l_iff a b)).
-
-(* notion 90 *)
-definition l_iff_th8 ≝ λa:Prop.λb:Prop.λn:l_not a.λb1:b.(l_and_th2 (l_imp a b) (l_imp b a) (l_imp_th4 b a b1 n) : l_not (l_iff a b)).
-
-(* notion 91 *)
-definition l_refiff ≝ λa:Prop.(l_iffi a a (l_refimp a) (l_refimp a) : l_iff a a).
-
-(* notion 92 *)
-definition l_symiff ≝ λa:Prop.λb:Prop.λi:l_iff a b.(l_comiff a b i : l_iff b a).
-
-(* notion 93 *)
-definition l_triff ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λj:l_iff b c.(l_iffi a c (l_trimp a b c (l_iffe1 a b i) (l_iffe1 b c j)) (l_trimp c b a (l_iffe2 b c j) (l_iffe2 a b i)) : l_iff a c).
-
-(* notion 94 *)
-definition l_iff_th9 ≝ λa:Prop.λb:Prop.λi:l_iff a b.(λx:l_not a.l_iff_th5 a b i x : l_imp (l_not a) (l_not b)).
-
-(* notion 95 *)
-definition l_iff_th10 ≝ λa:Prop.λb:Prop.λi:l_iff a b.(λx:l_not b.l_iff_th6 a b i x : l_imp (l_not b) (l_not a)).
-
-(* notion 96 *)
-definition l_iff_th11 ≝ λa:Prop.λb:Prop.λi:l_iff a b.(l_iffi (l_not a) (l_not b) (l_iff_th9 a b i) (l_iff_th10 a b i) : l_iff (l_not a) (l_not b)).
-
-(* notion 97 *)
-definition l_iff_th12 ≝ λa:Prop.λb:Prop.λi:l_imp (l_not a) (l_not b).λj:l_imp (l_not b) (l_not a).(l_iffi a b (l_cp a b j) (l_cp b a i) : l_iff a b).
-
-(* notion 98 *)
-definition l_iff_th13 ≝ λa:Prop.λb:Prop.λo:l_orec a b.(l_iffi a (l_not b) (l_orece2 a b o) (l_comor a b (l_orece1 a b o)) : l_iff a (l_not b)).
-
-(* notion 99 *)
-definition l_iff_th14 ≝ λa:Prop.λb:Prop.λo:l_orec a b.(l_iff_th13 b a (l_comorec a b o) : l_iff b (l_not a)).
-
-(* notion 100 *)
-definition l_iff_th15 ≝ λa:Prop.λb:Prop.λi:l_iff a (l_not b).(l_oreci a b (l_comor b a (l_iffe2 a (l_not b) i)) (l_iffe1 a (l_not b) i) : l_orec a b).
-
-(* notion 101 *)
-definition l_iff_th16 ≝ λa:Prop.λb:Prop.λi:l_iff b (l_not a).(l_comorec b a (l_iff_th15 b a i) : l_orec a b).
-
-(* notion 102 *)
-definition l_iff_thimp1 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λj:l_imp a c.(l_trimp b a c (l_iffe2 a b i) j : l_imp b c).
-
-(* notion 103 *)
-definition l_iff_thimp2 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λj:l_imp c a.(l_trimp c a b j (l_iffe1 a b i) : l_imp c b).
-
-(* notion 104 *)
-definition l_iff_thec1 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λe:l_ec a c.(l_ec_th3 a c b e (l_iffe2 a b i) : l_ec b c).
-
-(* notion 105 *)
-definition l_iff_thec2 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λe:l_ec c a.(l_ec_th4 c a b e (l_iffe2 a b i) : l_ec c b).
-
-(* notion 106 *)
-definition l_iff_thand1 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λa1:l_and a c.(l_and_th6 a c b a1 (l_iffe1 a b i) : l_and b c).
-
-(* notion 107 *)
-definition l_iff_thand2 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λa1:l_and c a.(l_and_th7 c a b a1 (l_iffe1 a b i) : l_and c b).
-
-(* notion 108 *)
-definition l_iff_thor1 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λo:l_or a c.(l_or_th7 a c b o (l_iffe1 a b i) : l_or b c).
-
-(* notion 109 *)
-definition l_iff_thor2 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λo:l_or c a.(l_or_th8 c a b o (l_iffe1 a b i) : l_or c b).
-
-(* notion 110 *)
-definition l_iff_thorec1 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λo:l_orec a c.(l_oreci b c (l_iff_thor1 a b c i (l_orece1 a c o)) (l_iff_thec1 a b c i (l_orece2 a c o)) : l_orec b c).
-
-(* notion 111 *)
-definition l_iff_thorec2 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λo:l_orec c a.(l_oreci c b (l_iff_thor2 a b c i (l_orece1 c a o)) (l_iff_thec2 a b c i (l_orece2 c a o)) : l_orec c b).
-
-(* notion 112 *)
-definition l_all ≝ λsigma:Type[0].λp:Πx:sigma.Prop.(Πx:sigma.p x : Prop).
-
-(* notion 113 *)
-definition l_alle ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λa1:l_all sigma p.λs:sigma.(a1 s : p s).
-
-(* notion 114 *)
-definition l_all_th1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λn:l_not (p s).(λx:l_all sigma p.n (x s) : l_not (l_all sigma p)).
-
-(* notion 115 *)
-definition l_non ≝ λsigma:Type[0].λp:Πx:sigma.Prop.(Πx:sigma.l_not (p x) : Πx:sigma.Prop).
-
-(* notion 116 *)
-definition l_some ≝ λsigma:Type[0].λp:Πx:sigma.Prop.(l_not (l_non sigma p) : Prop).
-
-(* notion 117 *)
-definition l_somei ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λsp:p s.(l_all_th1 sigma (l_non sigma p) s (l_weli (p s) sp) : l_some sigma p).
-
-(* notion 118 *)
-definition l_some_t1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_not (l_all sigma p).λm:l_non sigma (l_non sigma p).λs:sigma.(l_et (p s) (m s) : p s).
-
-(* notion 119 *)
-definition l_some_t2 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_not (l_all sigma p).λm:l_non sigma (l_non sigma p).(n (λx:sigma.l_some_t1 sigma p n m x) : l_con).
-
-(* notion 120 *)
-definition l_some_th1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_not (l_all sigma p).(λx:l_non sigma (l_non sigma p).l_some_t2 sigma p n x : l_some sigma (l_non sigma p)).
-
-(* notion 121 *)
-definition l_some_t3 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma (l_non sigma p).λa1:l_all sigma p.λt:sigma.(l_weli (p t) (a1 t) : l_not (l_not (p t))).
-
-(* notion 122 *)
-definition l_some_t4 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma (l_non sigma p).λa1:l_all sigma p.(s (λx:sigma.l_some_t3 sigma p s a1 x) : l_con).
-
-(* notion 123 *)
-definition l_some_th2 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma (l_non sigma p).(λx:l_all sigma p.l_some_t4 sigma p s x : l_not (l_all sigma p)).
-
-(* notion 124 *)
-definition l_some_th3 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_not (l_some sigma p).(l_et (l_non sigma p) n : l_non sigma p).
-
-(* notion 125 *)
-definition l_some_th4 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_not (l_some sigma p).λs:sigma.(l_some_th3 sigma p n s : l_not (p s)).
-
-(* notion 126 *)
-definition l_some_th5 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_non sigma p.(l_weli (l_non sigma p) n : l_not (l_some sigma p)).
-
-(* notion 127 *)
-definition l_some_t5 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma p.λx:Prop.λi:Πy:sigma.l_imp (p y) x.λn:l_not x.λt:sigma.(l_imp_th3 (p t) x n (i t) : l_not (p t)).
-
-(* notion 128 *)
-definition l_some_t6 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma p.λx:Prop.λi:Πy:sigma.l_imp (p y) x.λn:l_not x.(l_mp (l_some sigma p) l_con s (l_some_th5 sigma p (λy:sigma.l_some_t5 sigma p s x i n y)) : l_con).
-
-(* notion 129 *)
-definition l_someapp ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma p.λx:Prop.λi:Πy:sigma.l_imp (p y) x.(l_et x (λy:l_not x.l_some_t6 sigma p s x i y) : x).
-
-(* notion 130 *)
-definition l_some_th6 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λq:Πx:sigma.Prop.λs:l_some sigma p.λi:Πx:sigma.l_imp (p x) (q x).(l_someapp sigma p s (l_some sigma q) (λx:sigma.λy:p x.l_somei sigma q x (l_mp (p x) (q x) y (i x))) : l_some sigma q).
-
-(* notion 131 *)
-definition l_or3 ≝ λa:Prop.λb:Prop.λc:Prop.(l_or a (l_or b c) : Prop).
-
-(* notion 132 *)
-definition l_or3_th1 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not a.(l_ore2 a (l_or b c) o n : l_or b c).
-
-(* notion 133 *)
-definition l_or3e3 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not a.λm:l_not b.(l_ore2 b c (l_or3_th1 a b c o n) m : c).
-
-(* notion 134 *)
-definition l_or3_th2 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not b.(l_or_th2 c a (λx:l_not a.l_or3e3 a b c o x n) : l_or c a).
-
-(* notion 135 *)
-definition l_or3e1 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not b.λm:l_not c.(l_ore2 c a (l_or3_th2 a b c o n) m : a).
-
-(* notion 136 *)
-definition l_or3_th3 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not c.(l_or_th2 a b (λx:l_not b.l_or3e1 a b c o x n) : l_or a b).
-
-(* notion 137 *)
-definition l_or3e2 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not c.λm:l_not a.(l_ore2 a b (l_or3_th3 a b c o n) m : b).
-
-(* notion 138 *)
-definition l_or3_th4 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.(l_or_th1 b (l_or c a) (λx:l_not b.l_or3_th2 a b c o x) : l_or3 b c a).
-
-(* notion 139 *)
-definition l_or3_th5 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.(l_or3_th4 b c a (l_or3_th4 a b c o) : l_or3 c a b).
-
-(* notion 140 *)
-definition l_or3i1 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:a.(l_ori1 a (l_or b c) a1 : l_or3 a b c).
-
-(* notion 141 *)
-definition l_or3i2 ≝ λa:Prop.λb:Prop.λc:Prop.λb1:b.(l_ori2 a (l_or b c) (l_ori1 b c b1) : l_or3 a b c).
-
-(* notion 142 *)
-definition l_or3i3 ≝ λa:Prop.λb:Prop.λc:Prop.λc1:c.(l_ori2 a (l_or b c) (l_ori2 b c c1) : l_or3 a b c).
-
-(* notion 143 *)
-definition l_or3_th6 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or a b.(l_or3_th4 c a b (l_ori2 c (l_or a b) o) : l_or3 a b c).
-
-(* notion 144 *)
-definition l_or3_th7 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or b c.(l_ori2 a (l_or b c) o : l_or3 a b c).
-
-(* notion 145 *)
-definition l_or3_th8 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or c a.(l_or3_th4 c a b (l_or3_th6 c a b o) : l_or3 a b c).
-
-(* notion 146 *)
-definition l_or3app ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λo:l_or3 a b c.λi:l_imp a d.λj:l_imp b d.λk:l_imp c d.(l_orapp a (l_or b c) d o i (λx:l_or b c.l_orapp b c d x j k) : d).
-
-(* notion 147 *)
-definition l_and3 ≝ λa:Prop.λb:Prop.λc:Prop.(l_and a (l_and b c) : Prop).
-
-(* notion 148 *)
-definition l_and3e1 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_ande1 a (l_and b c) a1 : a).
-
-(* notion 149 *)
-definition l_and3e2 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_ande1 b c (l_ande2 a (l_and b c) a1) : b).
-
-(* notion 150 *)
-definition l_and3e3 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_ande2 b c (l_ande2 a (l_and b c) a1) : c).
-
-(* notion 151 *)
-definition l_and3i ≝ λa:Prop.λb:Prop.λc:Prop.λa1:a.λb1:b.λc1:c.(l_andi a (l_and b c) a1 (l_andi b c b1 c1) : l_and3 a b c).
-
-(* notion 152 *)
-definition l_and3_th1 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_and3i b c a (l_and3e2 a b c a1) (l_and3e3 a b c a1) (l_and3e1 a b c a1) : l_and3 b c a).
-
-(* notion 153 *)
-definition l_and3_th2 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_and3_th1 b c a (l_and3_th1 a b c a1) : l_and3 c a b).
-
-(* notion 154 *)
-definition l_and3_th3 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_andi a b (l_and3e1 a b c a1) (l_and3e2 a b c a1) : l_and a b).
-
-(* notion 155 *)
-definition l_and3_th4 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_ande2 a (l_and b c) a1 : l_and b c).
-
-(* notion 156 *)
-definition l_and3_th5 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_and3_th3 c a b (l_and3_th2 a b c a1) : l_and c a).
-
-(* notion 157 *)
-definition l_and3_th6 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_and3i c b a (l_and3e3 a b c a1) (l_and3e2 a b c a1) (l_and3e1 a b c a1) : l_and3 c b a).
-
-(* notion 158 *)
-definition l_ec3 ≝ λa:Prop.λb:Prop.λc:Prop.(l_and3 (l_ec a b) (l_ec b c) (l_ec c a) : Prop).
-
-(* notion 159 *)
-definition l_ec3_th1 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_and3e1 (l_ec a b) (l_ec b c) (l_ec c a) e : l_ec a b).
-
-(* notion 160 *)
-definition l_ec3_th2 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_and3e2 (l_ec a b) (l_ec b c) (l_ec c a) e : l_ec b c).
-
-(* notion 161 *)
-definition l_ec3_th3 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_and3e3 (l_ec a b) (l_ec b c) (l_ec c a) e : l_ec c a).
-
-(* notion 162 *)
-definition l_ec3_th4 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_and3_th1 (l_ec a b) (l_ec b c) (l_ec c a) e : l_ec3 b c a).
-
-(* notion 163 *)
-definition l_ec3_th5 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_ec3_th4 b c a (l_ec3_th4 a b c e) : l_ec3 c a b).
-
-(* notion 164 *)
-definition l_ec3_th5a ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_and3i (l_ec c b) (l_ec b a) (l_ec a c) (l_comec b c (l_ec3_th2 a b c e)) (l_comec a b (l_ec3_th1 a b c e)) (l_comec c a (l_ec3_th3 a b c e)) : l_ec3 c b a).
-
-(* notion 165 *)
-definition l_ec3e12 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λa1:a.(l_ece1 a b (l_ec3_th1 a b c e) a1 : l_not b).
-
-(* notion 166 *)
-definition l_ec3e13 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λa1:a.(l_ece2 c a (l_ec3_th3 a b c e) a1 : l_not c).
-
-(* notion 167 *)
-definition l_ec3e23 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λb1:b.(l_ec3e12 b c a (l_ec3_th4 a b c e) b1 : l_not c).
-
-(* notion 168 *)
-definition l_ec3e21 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λb1:b.(l_ec3e13 b c a (l_ec3_th4 a b c e) b1 : l_not a).
-
-(* notion 169 *)
-definition l_ec3e31 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λc1:c.(l_ec3e12 c a b (l_ec3_th5 a b c e) c1 : l_not a).
-
-(* notion 170 *)
-definition l_ec3e32 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λc1:c.(l_ec3e13 c a b (l_ec3_th5 a b c e) c1 : l_not b).
-
-(* notion 171 *)
-definition l_ec3_th6 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec a b.λf:l_ec b c.λg:l_ec c a.(l_and3i (l_ec a b) (l_ec b c) (l_ec c a) e f g : l_ec3 a b c).
-
-(* notion 172 *)
-definition l_ec3_th7 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λo:l_or a b.(l_orapp a b (l_not c) o (λx:a.l_ece2 c a (l_ec3_th3 a b c e) x) (λx:b.l_ece1 b c (l_ec3_th2 a b c e) x) : l_not c).
-
-(* notion 173 *)
-definition l_ec3_th8 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λo:l_or b c.(l_ec3_th7 b c a (l_ec3_th4 a b c e) o : l_not a).
-
-(* notion 174 *)
-definition l_ec3_th9 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λo:l_or c a.(l_ec3_th7 c a b (l_ec3_th5 a b c e) o : l_not b).
-
-(* notion 175 *)
-definition l_ec3i1 ≝ λa:Prop.λb:Prop.λc:Prop.λn:l_not a.λm:l_not b.(l_ec3_th6 a b c (l_eci1 a b n) (l_eci1 b c m) (l_eci2 c a n) : l_ec3 a b c).
-
-(* notion 176 *)
-definition l_ec3i2 ≝ λa:Prop.λb:Prop.λc:Prop.λn:l_not b.λm:l_not c.(l_ec3_th6 a b c (l_eci2 a b n) (l_eci1 b c n) (l_eci1 c a m) : l_ec3 a b c).
-
-(* notion 177 *)
-definition l_ec3i3 ≝ λa:Prop.λb:Prop.λc:Prop.λn:l_not c.λm:l_not a.(l_ec3_th6 a b c (l_eci1 a b m) (l_eci2 b c n) (l_eci1 c a n) : l_ec3 a b c).
-
-(* notion 178 *)
-definition l_ec3_t1 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λe:Prop.λf:Prop.λo1:l_or3 a b c.λp1:l_ec3 d e f.λi:l_imp a d.λj:l_imp b e.λk:l_imp c f.λd1:d.(λx:b.l_mp e l_con (j x) (l_ec3e12 d e f p1 d1) : l_not b).
-
-(* notion 179 *)
-definition l_ec3_t2 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λe:Prop.λf:Prop.λo1:l_or3 a b c.λp1:l_ec3 d e f.λi:l_imp a d.λj:l_imp b e.λk:l_imp c f.λd1:d.(λx:c.l_mp f l_con (k x) (l_ec3e13 d e f p1 d1) : l_not c).
-
-(* notion 180 *)
-definition l_ec3_th10 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λe:Prop.λf:Prop.λo1:l_or3 a b c.λp1:l_ec3 d e f.λi:l_imp a d.λj:l_imp b e.λk:l_imp c f.λd1:d.(l_or3e1 a b c o1 (l_ec3_t1 a b c d e f o1 p1 i j k d1) (l_ec3_t2 a b c d e f o1 p1 i j k d1) : a).
-
-(* notion 181 *)
-definition l_ec3_th11 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λe:Prop.λf:Prop.λo1:l_or3 a b c.λp1:l_ec3 d e f.λi:l_imp a d.λj:l_imp b e.λk:l_imp c f.λe1:e.(l_ec3_th10 b c a e f d (l_or3_th4 a b c o1) (l_ec3_th4 d e f p1) j k i e1 : b).
-
-(* notion 182 *)
-definition l_ec3_th12 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λe:Prop.λf:Prop.λo1:l_or3 a b c.λp1:l_ec3 d e f.λi:l_imp a d.λj:l_imp b e.λk:l_imp c f.λf1:f.(l_ec3_th10 c a b f d e (l_or3_th5 a b c o1) (l_ec3_th5 d e f p1) k i j f1 : c).
-
-(* notion 183 *)
-definition l_orec3 ≝ λa:Prop.λb:Prop.λc:Prop.(l_and (l_or3 a b c) (l_ec3 a b c) : Prop).
-
-(* notion 184 *)
-definition l_orec3e1 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_orec3 a b c.(l_ande1 (l_or3 a b c) (l_ec3 a b c) o : l_or3 a b c).
-
-(* notion 185 *)
-definition l_orec3e2 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_orec3 a b c.(l_ande2 (l_or3 a b c) (l_ec3 a b c) o : l_ec3 a b c).
-
-(* notion 186 *)
-definition l_orec3i ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λe:l_ec3 a b c.(l_andi (l_or3 a b c) (l_ec3 a b c) o e : l_orec3 a b c).
-
-(* notion 187 *)
-definition l_orec3_th1 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_orec3 a b c.(l_orec3i b c a (l_or3_th4 a b c (l_orec3e1 a b c o)) (l_ec3_th4 a b c (l_orec3e2 a b c o)) : l_orec3 b c a).
-
-(* notion 188 *)
-definition l_orec3_th2 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_orec3 a b c.(l_orec3i c a b (l_or3_th5 a b c (l_orec3e1 a b c o)) (l_ec3_th5 a b c (l_orec3e2 a b c o)) : l_orec3 c a b).
-
-(* notion 189 *)
-axiom l_e_is : Πsigma:Type[0].Πs:sigma.Πt:sigma.Prop.
-
-(* notion 190 *)
-axiom l_e_refis : Πsigma:Type[0].Πs:sigma.l_e_is sigma s s.
-
-(* notion 191 *)
-axiom l_e_isp : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πs:sigma.Πt:sigma.Πsp:p s.Πi:l_e_is sigma s t.p t.
-
-(* notion 192 *)
-definition l_e_symis ≝ λsigma:Type[0].λs:sigma.λt:sigma.λi:l_e_is sigma s t.(l_e_isp sigma (λx:sigma.l_e_is sigma x s) s t (l_e_refis sigma s) i : l_e_is sigma t s).
-
-(* notion 193 *)
-definition l_e_tris ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λi:l_e_is sigma s t.λj:l_e_is sigma t u.(l_e_isp sigma (λx:sigma.l_e_is sigma x u) t s j (l_e_symis sigma s t i) : l_e_is sigma s u).
-
-(* notion 194 *)
-definition l_e_tris1 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λi:l_e_is sigma u s.λj:l_e_is sigma u t.(l_e_tris sigma s u t (l_e_symis sigma u s i) j : l_e_is sigma s t).
-
-(* notion 195 *)
-definition l_e_tris2 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λi:l_e_is sigma s u.λj:l_e_is sigma t u.(l_e_tris sigma s u t i (l_e_symis sigma t u j) : l_e_is sigma s t).
-
-(* notion 196 *)
-definition l_e_isp1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λt:sigma.λsp:p s.λi:l_e_is sigma t s.(l_e_isp sigma p s t sp (l_e_symis sigma t s i) : p t).
-
-(* notion 197 *)
-definition l_e_symnotis ≝ λsigma:Type[0].λs:sigma.λt:sigma.λn:l_not (l_e_is sigma s t).(l_imp_th3 (l_e_is sigma t s) (l_e_is sigma s t) n (λx:l_e_is sigma t s.l_e_symis sigma t s x) : l_not (l_e_is sigma t s)).
-
-(* notion 198 *)
-definition l_e_notis_th1 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λn:l_not (l_e_is sigma s t).λi:l_e_is sigma s u.(l_e_isp sigma (Πx:sigma.l_not (l_e_is sigma x t)) s u n i : l_not (l_e_is sigma u t)).
-
-(* notion 199 *)
-definition l_e_notis_th2 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λn:l_not (l_e_is sigma s t).λi:l_e_is sigma u s.(l_e_notis_th1 sigma s t u n (l_e_symis sigma u s i) : l_not (l_e_is sigma u t)).
-
-(* notion 200 *)
-definition l_e_notis_th3 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λn:l_not (l_e_is sigma s t).λi:l_e_is sigma t u.(l_e_isp sigma (Πx:sigma.l_not (l_e_is sigma s x)) t u n i : l_not (l_e_is sigma s u)).
-
-(* notion 201 *)
-definition l_e_notis_th4 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λn:l_not (l_e_is sigma s t).λi:l_e_is sigma u t.(l_e_notis_th3 sigma s t u n (l_e_symis sigma u t i) : l_not (l_e_is sigma s u)).
-
-(* notion 202 *)
-definition l_e_notis_th5 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λv:sigma.λn:l_not (l_e_is sigma s t).λi:l_e_is sigma s u.λj:l_e_is sigma t v.(l_e_notis_th3 sigma u t v (l_e_notis_th1 sigma s t u n i) j : l_not (l_e_is sigma u v)).
-
-(* notion 203 *)
-definition l_e_tr3is ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λv:sigma.λi:l_e_is sigma s t.λj:l_e_is sigma t u.λk:l_e_is sigma u v.(l_e_tris sigma s u v (l_e_tris sigma s t u i j) k : l_e_is sigma s v).
-
-(* notion 204 *)
-definition l_e_tr4is ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λv:sigma.λw:sigma.λi:l_e_is sigma s t.λj:l_e_is sigma t u.λk:l_e_is sigma u v.λl:l_e_is sigma v w.(l_e_tris sigma s v w (l_e_tr3is sigma s t u v i j k) l : l_e_is sigma s w).
-
-(* notion 205 *)
-definition l_e_amone ≝ λsigma:Type[0].λp:Πx:sigma.Prop.(Πx:sigma.Πy:sigma.Πu:p x.Πv:p y.l_e_is sigma x y : Prop).
-
-(* notion 206 *)
-definition l_e_amonee ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λa1:l_e_amone sigma p.λs:sigma.λt:sigma.λsp:p s.λtp:p t.(a1 s t sp tp : l_e_is sigma s t).
-
-(* notion 207 *)
-definition l_e_one ≝ λsigma:Type[0].λp:Πx:sigma.Prop.(l_and (l_e_amone sigma p) (l_some sigma p) : Prop).
-
-(* notion 208 *)
-definition l_e_onei ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λa1:l_e_amone sigma p.λs:l_some sigma p.(l_andi (l_e_amone sigma p) (l_some sigma p) a1 s : l_e_one sigma p).
-
-(* notion 209 *)
-definition l_e_onee1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_one sigma p.(l_ande1 (l_e_amone sigma p) (l_some sigma p) o1 : l_e_amone sigma p).
-
-(* notion 210 *)
-definition l_e_onee2 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_one sigma p.(l_ande2 (l_e_amone sigma p) (l_some sigma p) o1 : l_some sigma p).
-
-(* notion 211 *)
-axiom l_e_ind : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πo1:l_e_one sigma p.sigma.
-
-(* notion 212 *)
-axiom l_e_oneax : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πo1:l_e_one sigma p.p (l_e_ind sigma p o1).
-
-(* notion 213 *)
-definition l_e_one_th1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_one sigma p.λs:sigma.λsp:p s.(l_e_amonee sigma p (l_e_onee1 sigma p o1) (l_e_ind sigma p o1) s (l_e_oneax sigma p o1) sp : l_e_is sigma (l_e_ind sigma p o1) s).
-
-(* notion 214 *)
-definition l_e_isf ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs:sigma.λt:sigma.λi:l_e_is sigma s t.(l_e_isp sigma (λx:sigma.l_e_is tau (f s) (f x)) s t (l_e_refis tau (f s)) i : l_e_is tau (f s) (f t)).
-
-(* notion 215 *)
-definition l_e_injective ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.(l_all sigma (λx:sigma.l_all sigma (λy:sigma.l_imp (l_e_is tau (f x) (f y)) (l_e_is sigma x y))) : Prop).
-
-(* notion 216 *)
-definition l_e_isfe ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λs:sigma.λt:sigma.λj:l_e_is tau (f s) (f t).(i s t j : l_e_is sigma s t).
-
-(* notion 217 *)
-definition l_e_image ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λt0:tau.(l_some sigma (λx:sigma.l_e_is tau t0 (f x)) : Prop).
-
-(* notion 218 *)
-definition l_e_tofs ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs:sigma.(f s : tau).
-
-(* notion 219 *)
-definition l_e_imagei ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs:sigma.(l_somei sigma (λx:sigma.l_e_is tau (l_e_tofs sigma tau f s) (f x)) s (l_e_refis tau (l_e_tofs sigma tau f s)) : l_e_image sigma tau f (l_e_tofs sigma tau f s)).
-
-(* notion 220 *)
-definition l_e_inj_t1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λta:tau.λtb:tau.λj:l_e_is tau ta tb.λsa:sigma.λsb:sigma.λja:l_e_is tau ta (l_e_tofs sigma tau f sa).λjb:l_e_is tau tb (l_e_tofs sigma tau f sb).(l_e_tr3is tau (l_e_tofs sigma tau f sa) ta tb (l_e_tofs sigma tau f sb) (l_e_symis tau ta (l_e_tofs sigma tau f sa) ja) j jb : l_e_is tau (l_e_tofs sigma tau f sa) (l_e_tofs sigma tau f sb)).
-
-(* notion 221 *)
-definition l_e_inj_th1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λta:tau.λtb:tau.λj:l_e_is tau ta tb.λsa:sigma.λsb:sigma.λja:l_e_is tau ta (l_e_tofs sigma tau f sa).λjb:l_e_is tau tb (l_e_tofs sigma tau f sb).(l_e_isfe sigma tau f i sa sb (l_e_inj_t1 sigma tau f i ta tb j sa sb ja jb) : l_e_is sigma sa sb).
-
-(* notion 222 *)
-definition l_e_inj_th2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λt0:tau.(λx:sigma.λy:sigma.λu:l_e_is tau t0 (f x).λv:l_e_is tau t0 (f y).l_e_inj_th1 sigma tau f i t0 t0 (l_e_refis tau t0) x y u v : l_e_amone sigma (λx:sigma.l_e_is tau t0 (f x))).
-
-(* notion 223 *)
-definition l_e_inj_th3 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λt0:tau.λj:l_e_image sigma tau f t0.(l_e_onei sigma (λx:sigma.l_e_is tau t0 (f x)) (l_e_inj_th2 sigma tau f i t0) j : l_e_one sigma (λx:sigma.l_e_is tau t0 (f x))).
-
-(* notion 224 *)
-definition l_e_soft ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λt0:tau.λj:l_e_image sigma tau f t0.(l_e_ind sigma (λx:sigma.l_e_is tau t0 (f x)) (l_e_inj_th3 sigma tau f i t0 j) : sigma).
-
-(* notion 225 *)
-definition l_e_inverse ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.(λx:tau.λu:l_e_image sigma tau f x.l_e_soft sigma tau f i x u : Πx:tau.Πu:l_e_image sigma tau f x.sigma).
-
-(* notion 226 *)
-definition l_e_ists1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λt0:tau.λj:l_e_image sigma tau f t0.(l_e_oneax sigma (λx:sigma.l_e_is tau t0 (f x)) (l_e_inj_th3 sigma tau f i t0 j) : l_e_is tau t0 (l_e_tofs sigma tau f (l_e_soft sigma tau f i t0 j))).
-
-(* notion 227 *)
-definition l_e_ists2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λt0:tau.λj:l_e_image sigma tau f t0.(l_e_symis tau t0 (l_e_tofs sigma tau f (l_e_soft sigma tau f i t0 j)) (l_e_ists1 sigma tau f i t0 j) : l_e_is tau (l_e_tofs sigma tau f (l_e_soft sigma tau f i t0 j)) t0).
-
-(* notion 228 *)
-definition l_e_isinv ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λta:tau.λja:l_e_image sigma tau f ta.λtb:tau.λjb:l_e_image sigma tau f tb.λj:l_e_is tau ta tb.(l_e_inj_th1 sigma tau f i ta tb j (l_e_soft sigma tau f i ta ja) (l_e_soft sigma tau f i tb jb) (l_e_ists1 sigma tau f i ta ja) (l_e_ists1 sigma tau f i tb jb) : l_e_is sigma (l_e_soft sigma tau f i ta ja) (l_e_soft sigma tau f i tb jb)).
-
-(* notion 229 *)
-definition l_e_isinve ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λta:tau.λja:l_e_image sigma tau f ta.λtb:tau.λjb:l_e_image sigma tau f tb.λj:l_e_is sigma (l_e_soft sigma tau f i ta ja) (l_e_soft sigma tau f i tb jb).(l_e_tr3is tau ta (l_e_tofs sigma tau f (l_e_soft sigma tau f i ta ja)) (l_e_tofs sigma tau f (l_e_soft sigma tau f i tb jb)) tb (l_e_ists1 sigma tau f i ta ja) (l_e_isf sigma tau f (l_e_soft sigma tau f i ta ja) (l_e_soft sigma tau f i tb jb) j) (l_e_ists2 sigma tau f i tb jb) : l_e_is tau ta tb).
-
-(* notion 230 *)
-definition l_e_isst1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λs:sigma.(l_e_isfe sigma tau f i s (l_e_soft sigma tau f i (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s)) (l_e_ists1 sigma tau f i (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s)) : l_e_is sigma s (l_e_soft sigma tau f i (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s))).
-
-(* notion 231 *)
-definition l_e_isst2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λs:sigma.(l_e_symis sigma s (l_e_soft sigma tau f i (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s)) (l_e_isst1 sigma tau f i s) : l_e_is sigma (l_e_soft sigma tau f i (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s)) s).
-
-(* notion 232 *)
-definition l_e_surjective ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.(l_all tau (Πx:tau.l_e_image sigma tau f x) : Prop).
-
-(* notion 233 *)
-definition l_e_bijective ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.(l_and (l_e_injective sigma tau f) (l_e_surjective sigma tau f) : Prop).
-
-(* notion 234 *)
-definition l_e_inj_t2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.(l_ande1 (l_e_injective sigma tau f) (l_e_surjective sigma tau f) b : l_e_injective sigma tau f).
-
-(* notion 235 *)
-definition l_e_inj_t3 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.(l_ande2 (l_e_injective sigma tau f) (l_e_surjective sigma tau f) b : l_e_surjective sigma tau f).
-
-(* notion 236 *)
-definition l_e_inj_so ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.λt:tau.(l_e_soft sigma tau f (l_e_inj_t2 sigma tau f b) t (l_e_inj_t3 sigma tau f b t) : sigma).
-
-(* notion 237 *)
-definition l_e_invf ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.(λx:tau.l_e_inj_so sigma tau f b x : Πx:tau.sigma).
-
-(* notion 238 *)
-definition l_e_thinvf1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.λs:sigma.(l_e_tris sigma s (l_e_soft sigma tau f (l_e_inj_t2 sigma tau f b) (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s)) (l_e_invf sigma tau f b (f s)) (l_e_isst1 sigma tau f (l_e_inj_t2 sigma tau f b) s) (l_e_isinv sigma tau f (l_e_inj_t2 sigma tau f b) (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s) (l_e_tofs sigma tau f s) (l_e_inj_t3 sigma tau f b (l_e_tofs sigma tau f s)) (l_e_refis tau (l_e_tofs sigma tau f s))) : l_e_is sigma s (l_e_invf sigma tau f b (f s))).
-
-(* notion 239 *)
-definition l_e_thinvf2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.λt:tau.(l_e_ists1 sigma tau f (l_e_inj_t2 sigma tau f b) t (l_e_inj_t3 sigma tau f b t) : l_e_is tau t (f (l_e_invf sigma tau f b t))).
-
-(* notion 240 *)
-definition l_e_inj_h ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λif:l_e_injective sigma tau f.λig:l_e_injective tau upsilon g.(λx:sigma.g (f x) : Πx:sigma.upsilon).
-
-(* notion 241 *)
-definition l_e_inj_t4 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λif:l_e_injective sigma tau f.λig:l_e_injective tau upsilon g.λs:sigma.λt:sigma.λi:l_e_is upsilon (l_e_inj_h sigma tau upsilon f g if ig s) (l_e_inj_h sigma tau upsilon f g if ig t).(l_e_isfe tau upsilon g ig (f s) (f t) i : l_e_is tau (f s) (f t)).
-
-(* notion 242 *)
-definition l_e_inj_t5 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λif:l_e_injective sigma tau f.λig:l_e_injective tau upsilon g.λs:sigma.λt:sigma.λi:l_e_is upsilon (l_e_inj_h sigma tau upsilon f g if ig s) (l_e_inj_h sigma tau upsilon f g if ig t).(l_e_isfe sigma tau f if s t (l_e_inj_t4 sigma tau upsilon f g if ig s t i) : l_e_is sigma s t).
-
-(* notion 243 *)
-definition l_e_inj_th4 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λif:l_e_injective sigma tau f.λig:l_e_injective tau upsilon g.(λx:sigma.λy:sigma.λv:l_e_is upsilon (l_e_inj_h sigma tau upsilon f g if ig x) (l_e_inj_h sigma tau upsilon f g if ig y).l_e_inj_t5 sigma tau upsilon f g if ig x y v : l_e_injective sigma upsilon (λx:sigma.g (f x))).
-
-(* notion 244 *)
-definition l_e_surj_h ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.(λx:sigma.g (f x) : Πx:sigma.upsilon).
-
-(* notion 245 *)
-definition l_e_surj_t1 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.(sg u : l_e_image tau upsilon g u).
-
-(* notion 246 *)
-definition l_e_surj_t2 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.λt:tau.λi:l_e_is upsilon u (g t).(sf t : l_e_image sigma tau f t).
-
-(* notion 247 *)
-definition l_e_surj_t3 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.λt:tau.λi:l_e_is upsilon u (g t).λs:sigma.λj:l_e_is tau t (f s).(l_e_tris upsilon u (g t) (l_e_surj_h sigma tau upsilon f g sf sg s) i (l_e_isf tau upsilon g t (f s) j) : l_e_is upsilon u (l_e_surj_h sigma tau upsilon f g sf sg s)).
-
-(* notion 248 *)
-definition l_e_surj_t4 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.λt:tau.λi:l_e_is upsilon u (g t).λs:sigma.λj:l_e_is tau t (f s).(l_somei sigma (λx:sigma.l_e_is upsilon u (l_e_surj_h sigma tau upsilon f g sf sg x)) s (l_e_surj_t3 sigma tau upsilon f g sf sg u t i s j) : l_e_image sigma upsilon (l_e_surj_h sigma tau upsilon f g sf sg) u).
-
-(* notion 249 *)
-definition l_e_surj_t5 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.λt:tau.λi:l_e_is upsilon u (g t).(l_someapp sigma (λx:sigma.l_e_is tau t (f x)) (l_e_surj_t2 sigma tau upsilon f g sf sg u t i) (l_e_image sigma upsilon (l_e_surj_h sigma tau upsilon f g sf sg) u) (λx:sigma.λv:l_e_is tau t (f x).l_e_surj_t4 sigma tau upsilon f g sf sg u t i x v) : l_e_image sigma upsilon (l_e_surj_h sigma tau upsilon f g sf sg) u).
-
-(* notion 250 *)
-definition l_e_surj_t6 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.(l_someapp tau (λx:tau.l_e_is upsilon u (g x)) (l_e_surj_t1 sigma tau upsilon f g sf sg u) (l_e_image sigma upsilon (l_e_surj_h sigma tau upsilon f g sf sg) u) (λx:tau.λv:l_e_is upsilon u (g x).l_e_surj_t5 sigma tau upsilon f g sf sg u x v) : l_e_image sigma upsilon (l_e_surj_h sigma tau upsilon f g sf sg) u).
-
-(* notion 251 *)
-definition l_e_surj_th1 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.(λx:upsilon.l_e_surj_t6 sigma tau upsilon f g sf sg x : l_e_surjective sigma upsilon (λx:sigma.g (f x))).
-
-(* notion 252 *)
-definition l_e_bij_h ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λbf:l_e_bijective sigma tau f.λbg:l_e_bijective tau upsilon g.(λx:sigma.g (f x) : Πx:sigma.upsilon).
-
-(* notion 253 *)
-definition l_e_bij_t1 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λbf:l_e_bijective sigma tau f.λbg:l_e_bijective tau upsilon g.(l_e_inj_th4 sigma tau upsilon f g (l_ande1 (l_e_injective sigma tau f) (l_e_surjective sigma tau f) bf) (l_ande1 (l_e_injective tau upsilon g) (l_e_surjective tau upsilon g) bg) : l_e_injective sigma upsilon (l_e_bij_h sigma tau upsilon f g bf bg)).
-
-(* notion 254 *)
-definition l_e_bij_t2 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λbf:l_e_bijective sigma tau f.λbg:l_e_bijective tau upsilon g.(l_e_surj_th1 sigma tau upsilon f g (l_ande2 (l_e_injective sigma tau f) (l_e_surjective sigma tau f) bf) (l_ande2 (l_e_injective tau upsilon g) (l_e_surjective tau upsilon g) bg) : l_e_surjective sigma upsilon (l_e_bij_h sigma tau upsilon f g bf bg)).
-
-(* notion 255 *)
-definition l_e_bij_th1 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λbf:l_e_bijective sigma tau f.λbg:l_e_bijective tau upsilon g.(l_andi (l_e_injective sigma upsilon (l_e_bij_h sigma tau upsilon f g bf bg)) (l_e_surjective sigma upsilon (l_e_bij_h sigma tau upsilon f g bf bg)) (l_e_bij_t1 sigma tau upsilon f g bf bg) (l_e_bij_t2 sigma tau upsilon f g bf bg) : l_e_bijective sigma upsilon (λx:sigma.g (f x))).
-
-(* notion 256 *)
-definition l_e_fise ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λg:Πx:sigma.tau.λi:l_e_is (Πx:sigma.tau) f g.λs:sigma.(l_e_isp (Πx:sigma.tau) (λy:Πx:sigma.tau.l_e_is tau (f s) (y s)) f g (l_e_refis tau (f s)) i : l_e_is tau (f s) (g s)).
-
-(* notion 257 *)
-axiom l_e_fisi : Πsigma:Type[0].Πtau:Type[0].Πf:Πx:sigma.tau.Πg:Πx:sigma.tau.Πi:Πx:sigma.l_e_is tau (f x) (g x).l_e_is (Πx:sigma.tau) f g.
-
-(* notion 258 *)
-definition l_e_fis_th1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λg:Πx:sigma.tau.λi:l_e_is (Πx:sigma.tau) f g.λs:sigma.λt:sigma.λj:l_e_is sigma s t.(l_e_tris tau (f s) (f t) (g t) (l_e_isf sigma tau f s t j) (l_e_fise sigma tau f g i t) : l_e_is tau (f s) (g t)).
-
-(* notion 259 *)
-axiom l_e_ot : Πsigma:Type[0].Πp:Πx:sigma.Prop.Type[0].
-
-(* notion 260 *)
-axiom l_e_in : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πo1:l_e_ot sigma p.sigma.
-
-(* notion 261 *)
-axiom l_e_inp : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πo1:l_e_ot sigma p.p (l_e_in sigma p o1).
-
-(* notion 262 *)
-axiom l_e_otax1 : Πsigma:Type[0].Πp:Πx:sigma.Prop.l_e_injective (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x).
-
-(* notion 263 *)
-axiom l_e_otax2 : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πs:sigma.Πsp:p s.l_e_image (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) s.
-
-(* notion 264 *)
-definition l_e_isini ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_ot sigma p.λo2:l_e_ot sigma p.λi:l_e_is (l_e_ot sigma p) o1 o2.(l_e_isf (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) o1 o2 i : l_e_is sigma (l_e_in sigma p o1) (l_e_in sigma p o2)).
-
-(* notion 265 *)
-definition l_e_isine ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_ot sigma p.λo2:l_e_ot sigma p.λi:l_e_is sigma (l_e_in sigma p o1) (l_e_in sigma p o2).(l_e_isfe (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) o1 o2 i : l_e_is (l_e_ot sigma p) o1 o2).
-
-(* notion 266 *)
-definition l_e_out ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λsp:p s.(l_e_soft (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) s (l_e_otax2 sigma p s sp) : l_e_ot sigma p).
-
-(* notion 267 *)
-definition l_e_isouti ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λsp:p s.λt:sigma.λtp:p t.λi:l_e_is sigma s t.(l_e_isinv (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) s (l_e_otax2 sigma p s sp) t (l_e_otax2 sigma p t tp) i : l_e_is (l_e_ot sigma p) (l_e_out sigma p s sp) (l_e_out sigma p t tp)).
-
-(* notion 268 *)
-definition l_e_isoute ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λsp:p s.λt:sigma.λtp:p t.λi:l_e_is (l_e_ot sigma p) (l_e_out sigma p s sp) (l_e_out sigma p t tp).(l_e_isinve (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) s (l_e_otax2 sigma p s sp) t (l_e_otax2 sigma p t tp) i : l_e_is sigma s t).
-
-(* notion 269 *)
-definition l_e_isoutin ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_ot sigma p.(l_e_tris (l_e_ot sigma p) o1 (l_e_soft (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) (l_e_in sigma p o1) (l_e_imagei (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) o1)) (l_e_out sigma p (l_e_in sigma p o1) (l_e_inp sigma p o1)) (l_e_isst1 (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) o1) (l_e_isinv (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) (l_e_in sigma p o1) (l_e_imagei (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) o1) (l_e_in sigma p o1) (l_e_otax2 sigma p (l_e_in sigma p o1) (l_e_inp sigma p o1)) (l_e_refis sigma (l_e_in sigma p o1))) : l_e_is (l_e_ot sigma p) o1 (l_e_out sigma p (l_e_in sigma p o1) (l_e_inp sigma p o1))).
-
-(* notion 270 *)
-definition l_e_isinout ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λsp:p s.(l_e_ists1 (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) s (l_e_otax2 sigma p s sp) : l_e_is sigma s (l_e_in sigma p (l_e_out sigma p s sp))).
-
-(* notion 271 *)
-axiom l_e_pairtype : Πsigma:Type[0].Πtau:Type[0].Type[0].
-
-(* notion 272 *)
-axiom l_e_pair : Πsigma:Type[0].Πtau:Type[0].Πs:sigma.Πt:tau.l_e_pairtype sigma tau.
-
-(* notion 273 *)
-axiom l_e_first : Πsigma:Type[0].Πtau:Type[0].Πp1:l_e_pairtype sigma tau.sigma.
-
-(* notion 274 *)
-axiom l_e_second : Πsigma:Type[0].Πtau:Type[0].Πp1:l_e_pairtype sigma tau.tau.
-
-(* notion 275 *)
-axiom l_e_pairis1 : Πsigma:Type[0].Πtau:Type[0].Πp1:l_e_pairtype sigma tau.l_e_is (l_e_pairtype sigma tau) (l_e_pair sigma tau (l_e_first sigma tau p1) (l_e_second sigma tau p1)) p1.
-
-(* notion 276 *)
-definition l_e_pairis2 ≝ λsigma:Type[0].λtau:Type[0].λp1:l_e_pairtype sigma tau.(l_e_symis (l_e_pairtype sigma tau) (l_e_pair sigma tau (l_e_first sigma tau p1) (l_e_second sigma tau p1)) p1 (l_e_pairis1 sigma tau p1) : l_e_is (l_e_pairtype sigma tau) p1 (l_e_pair sigma tau (l_e_first sigma tau p1) (l_e_second sigma tau p1))).
-
-(* notion 277 *)
-axiom l_e_firstis1 : Πsigma:Type[0].Πtau:Type[0].Πs:sigma.Πt:tau.l_e_is sigma (l_e_first sigma tau (l_e_pair sigma tau s t)) s.
-
-(* notion 278 *)
-definition l_e_firstis2 ≝ λsigma:Type[0].λtau:Type[0].λs:sigma.λt:tau.(l_e_symis sigma (l_e_first sigma tau (l_e_pair sigma tau s t)) s (l_e_firstis1 sigma tau s t) : l_e_is sigma s (l_e_first sigma tau (l_e_pair sigma tau s t))).
-
-(* notion 279 *)
-axiom l_e_secondis1 : Πsigma:Type[0].Πtau:Type[0].Πs:sigma.Πt:tau.l_e_is tau (l_e_second sigma tau (l_e_pair sigma tau s t)) t.
-
-(* notion 280 *)
-definition l_e_secondis2 ≝ λsigma:Type[0].λtau:Type[0].λs:sigma.λt:tau.(l_e_symis tau (l_e_second sigma tau (l_e_pair sigma tau s t)) t (l_e_secondis1 sigma tau s t) : l_e_is tau t (l_e_second sigma tau (l_e_pair sigma tau s t))).
-
-(* notion 281 *)
-definition l_e_ite_prop1 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λz:ksi.(l_and (l_imp a (l_e_is ksi z x)) (l_imp (l_not a) (l_e_is ksi z y)) : Prop).
-
-(* notion 282 *)
-definition l_e_ite_t1 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_ande1 (l_imp a (l_e_is ksi x1 x)) (l_imp (l_not a) (l_e_is ksi x1 y)) px1 : l_imp a (l_e_is ksi x1 x)).
-
-(* notion 283 *)
-definition l_e_ite_t2 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_mp a (l_e_is ksi x1 x) a1 (l_e_ite_t1 a ksi x y a1 x1 y1 px1 py1) : l_e_is ksi x1 x).
-
-(* notion 284 *)
-definition l_e_ite_t3 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_e_ite_t2 a ksi x y a1 y1 x1 py1 px1 : l_e_is ksi y1 x).
-
-(* notion 285 *)
-definition l_e_ite_t4 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_e_tris2 ksi x1 y1 x (l_e_ite_t2 a ksi x y a1 x1 y1 px1 py1) (l_e_ite_t3 a ksi x y a1 x1 y1 px1 py1) : l_e_is ksi x1 y1).
-
-(* notion 286 *)
-definition l_e_ite_t5 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(λs:ksi.λt:ksi.λps:l_e_ite_prop1 a ksi x y s.λpt:l_e_ite_prop1 a ksi x y t.l_e_ite_t4 a ksi x y a1 s t ps pt : l_e_amone ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t)).
-
-(* notion 287 *)
-definition l_e_ite_t6 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(λx1:a.l_e_refis ksi x : l_imp a (l_e_is ksi x x)).
-
-(* notion 288 *)
-definition l_e_ite_t7 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(l_imp_th2 (l_not a) (l_e_is ksi x y) (l_weli a a1) : l_imp (l_not a) (l_e_is ksi x y)).
-
-(* notion 289 *)
-definition l_e_ite_t8 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(l_andi (l_imp a (l_e_is ksi x x)) (l_imp (l_not a) (l_e_is ksi x y)) (l_e_ite_t6 a ksi x y a1) (l_e_ite_t7 a ksi x y a1) : l_e_ite_prop1 a ksi x y x).
-
-(* notion 290 *)
-definition l_e_ite_t9 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(l_somei ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t) x (l_e_ite_t8 a ksi x y a1) : l_some ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t)).
-
-(* notion 291 *)
-definition l_e_ite_t10 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(l_e_onei ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t) (l_e_ite_t5 a ksi x y a1) (l_e_ite_t9 a ksi x y a1) : l_e_one ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t)).
-
-(* notion 292 *)
-definition l_e_ite_t11 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_ande2 (l_imp a (l_e_is ksi x1 x)) (l_imp (l_not a) (l_e_is ksi x1 y)) px1 : l_imp (l_not a) (l_e_is ksi x1 y)).
-
-(* notion 293 *)
-definition l_e_ite_t12 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_mp (l_not a) (l_e_is ksi x1 y) n (l_e_ite_t11 a ksi x y n x1 y1 px1 py1) : l_e_is ksi x1 y).
-
-(* notion 294 *)
-definition l_e_ite_t13 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_e_ite_t12 a ksi x y n y1 x1 py1 px1 : l_e_is ksi y1 y).
-
-(* notion 295 *)
-definition l_e_ite_t14 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_e_tris2 ksi x1 y1 y (l_e_ite_t12 a ksi x y n x1 y1 px1 py1) (l_e_ite_t13 a ksi x y n x1 y1 px1 py1) : l_e_is ksi x1 y1).
-
-(* notion 296 *)
-definition l_e_ite_t15 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(λs:ksi.λt:ksi.λps:l_e_ite_prop1 a ksi x y s.λpt:l_e_ite_prop1 a ksi x y t.l_e_ite_t14 a ksi x y n s t ps pt : l_e_amone ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t)).
-
-(* notion 297 *)
-definition l_e_ite_t16 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(λx1:l_not a.l_e_refis ksi y : l_imp (l_not a) (l_e_is ksi y y)).
-
-(* notion 298 *)
-definition l_e_ite_t17 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(l_imp_th2 a (l_e_is ksi y x) n : l_imp a (l_e_is ksi y x)).
-
-(* notion 299 *)
-definition l_e_ite_t18 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(l_andi (l_imp a (l_e_is ksi y x)) (l_imp (l_not a) (l_e_is ksi y y)) (l_e_ite_t17 a ksi x y n) (l_e_ite_t16 a ksi x y n) : l_e_ite_prop1 a ksi x y y).
-
-(* notion 300 *)
-definition l_e_ite_t19 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(l_somei ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t) y (l_e_ite_t18 a ksi x y n) : l_some ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t)).
-
-(* notion 301 *)
-definition l_e_ite_t20 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(l_e_onei ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t) (l_e_ite_t15 a ksi x y n) (l_e_ite_t19 a ksi x y n) : l_e_one ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t)).
-
-(* notion 302 *)
-definition l_e_ite_t21 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.(l_imp_th1 a (l_e_one ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t)) (λt:a.l_e_ite_t10 a ksi x y t) (λt:l_not a.l_e_ite_t20 a ksi x y t) : l_e_one ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t)).
-
-(* notion 303 *)
-definition l_e_ite ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.(l_e_ind ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t) (l_e_ite_t21 a ksi x y) : ksi).
-
-(* notion 304 *)
-definition l_e_ite_t22 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.(l_e_oneax ksi (Πt:ksi.l_e_ite_prop1 a ksi x y t) (l_e_ite_t21 a ksi x y) : l_e_ite_prop1 a ksi x y (l_e_ite a ksi x y)).
-
-(* notion 305 *)
-definition l_e_ite_t23 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.(l_ande1 (l_imp a (l_e_is ksi (l_e_ite a ksi x y) x)) (l_imp (l_not a) (l_e_is ksi (l_e_ite a ksi x y) y)) (l_e_ite_t22 a ksi x y) : l_imp a (l_e_is ksi (l_e_ite a ksi x y) x)).
-
-(* notion 306 *)
-definition l_e_ite_t24 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.(l_ande2 (l_imp a (l_e_is ksi (l_e_ite a ksi x y) x)) (l_imp (l_not a) (l_e_is ksi (l_e_ite a ksi x y) y)) (l_e_ite_t22 a ksi x y) : l_imp (l_not a) (l_e_is ksi (l_e_ite a ksi x y) y)).
-
-(* notion 307 *)
-definition l_e_itet ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(l_mp a (l_e_is ksi (l_e_ite a ksi x y) x) a1 (l_e_ite_t23 a ksi x y) : l_e_is ksi (l_e_ite a ksi x y) x).
-
-(* notion 308 *)
-definition l_e_itef ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(l_mp (l_not a) (l_e_is ksi (l_e_ite a ksi x y) y) n (l_e_ite_t24 a ksi x y) : l_e_is ksi (l_e_ite a ksi x y) y).
-
-(* notion 309 *)
-definition l_e_wissel_wa ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.(l_e_ite (l_e_is sigma s s0) sigma t0 s : sigma).
-
-(* notion 310 *)
-definition l_e_wissel_t1 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_e_itet (l_e_is sigma s s0) sigma t0 s i : l_e_is sigma (l_e_wissel_wa sigma s0 t0 s) t0).
-
-(* notion 311 *)
-definition l_e_wissel_t2 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).(l_e_itef (l_e_is sigma s s0) sigma t0 s n : l_e_is sigma (l_e_wissel_wa sigma s0 t0 s) s).
-
-(* notion 312 *)
-definition l_e_wissel_wb ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.(l_e_ite (l_e_is sigma s t0) sigma s0 (l_e_wissel_wa sigma s0 t0 s) : sigma).
-
-(* notion 313 *)
-definition l_e_wissel_t3 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s t0.(l_e_itet (l_e_is sigma s t0) sigma s0 (l_e_wissel_wa sigma s0 t0 s) i : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) s0).
-
-(* notion 314 *)
-definition l_e_wissel_t4 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s t0).(l_e_itef (l_e_is sigma s t0) sigma s0 (l_e_wissel_wa sigma s0 t0 s) n : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wa sigma s0 t0 s)).
-
-(* notion 315 *)
-definition l_e_wissel_t5 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.λj:l_e_is sigma s0 t0.(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) s0 t0 (l_e_wissel_t3 sigma s0 t0 s (l_e_tris sigma s s0 t0 i j)) j : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t0).
-
-(* notion 316 *)
-definition l_e_wissel_t6 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.λn:l_not (l_e_is sigma s0 t0).(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wa sigma s0 t0 s) t0 (l_e_wissel_t4 sigma s0 t0 s (l_e_notis_th2 sigma s0 t0 s n i)) (l_e_wissel_t1 sigma s0 t0 s i) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t0).
-
-(* notion 317 *)
-definition l_e_wissel_t7 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_imp_th1 (l_e_is sigma s0 t0) (l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t0) (λt:l_e_is sigma s0 t0.l_e_wissel_t5 sigma s0 t0 s i t) (λt:l_not (l_e_is sigma s0 t0).l_e_wissel_t6 sigma s0 t0 s i t) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t0).
-
-(* notion 318 *)
-definition l_e_wissel_t8 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).λo:l_not (l_e_is sigma s t0).(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wa sigma s0 t0 s) s (l_e_wissel_t4 sigma s0 t0 s o) (l_e_wissel_t2 sigma s0 t0 s n) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) s).
-
-(* notion 319 *)
-definition l_e_wissel ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.(λx:sigma.l_e_wissel_wb sigma s0 t0 x : Πx:sigma.sigma).
-
-(* notion 320 *)
-definition l_e_iswissel1 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_e_wissel_t7 sigma s0 t0 s i : l_e_is sigma (l_e_wissel sigma s0 t0 s) t0).
-
-(* notion 321 *)
-definition l_e_iswissel2 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s t0.(l_e_wissel_t3 sigma s0 t0 s i : l_e_is sigma (l_e_wissel sigma s0 t0 s) s0).
-
-(* notion 322 *)
-definition l_e_iswissel3 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).λo:l_not (l_e_is sigma s t0).(l_e_wissel_t8 sigma s0 t0 s n o : l_e_is sigma (l_e_wissel sigma s0 t0 s) s).
-
-(* notion 323 *)
-definition l_e_wissel_t9 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.(l_e_symnotis sigma s0 t (l_e_notis_th1 sigma s t s0 n j) : l_not (l_e_is sigma t s0)).
-
-(* notion 324 *)
-definition l_e_wissel_t10 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.λk:l_e_is sigma s0 t0.(l_e_notis_th3 sigma t s0 t0 (l_e_wissel_t9 sigma s0 t0 s t i n j) k : l_not (l_e_is sigma t t0)).
-
-(* notion 325 *)
-definition l_e_wissel_t11 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.λk:l_e_is sigma s0 t0.(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) t i (l_e_wissel_t8 sigma s0 t0 t (l_e_wissel_t9 sigma s0 t0 s t i n j) (l_e_wissel_t10 sigma s0 t0 s t i n j k)) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t).
-
-(* notion 326 *)
-definition l_e_wissel_t12 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.λk:l_e_is sigma s0 t0.(l_e_wissel_t10 sigma s0 t0 s t i n j k (l_e_tris1 sigma t t0 (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_t11 sigma s0 t0 s t i n j k) (l_e_wissel_t7 sigma s0 t0 s j)) : l_con).
-
-(* notion 327 *)
-definition l_e_wissel_t13 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.(λv:l_e_is sigma s0 t0.l_e_wissel_t12 sigma s0 t0 s t i n j v : l_not (l_e_is sigma s0 t0)).
-
-(* notion 328 *)
-definition l_e_wissel_t14 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.λk:l_e_is sigma t t0.(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) s0 i (l_e_wissel_t3 sigma s0 t0 t k) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) s0).
-
-(* notion 329 *)
-definition l_e_wissel_t15 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.λk:l_e_is sigma t t0.(l_e_wissel_t12 sigma s0 t0 s t i n j (l_e_tris1 sigma s0 t0 (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_t14 sigma s0 t0 s t i n j k) (l_e_wissel_t7 sigma s0 t0 s j)) : l_con).
-
-(* notion 330 *)
-definition l_e_wissel_t16 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.(λv:l_e_is sigma t t0.l_e_wissel_t15 sigma s0 t0 s t i n j v : l_not (l_e_is sigma t t0)).
-
-(* notion 331 *)
-definition l_e_wissel_t17 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) t i (l_e_wissel_t8 sigma s0 t0 t (l_e_wissel_t9 sigma s0 t0 s t i n j) (l_e_wissel_t16 sigma s0 t0 s t i n j)) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t).
-
-(* notion 332 *)
-definition l_e_wissel_t18 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.(l_e_wissel_t15 sigma s0 t0 s t i n j (l_e_tris1 sigma t t0 (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_t17 sigma s0 t0 s t i n j) (l_e_wissel_t7 sigma s0 t0 s j)) : l_con).
-
-(* notion 333 *)
-definition l_e_wissel_t19 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(λv:l_e_is sigma s s0.l_e_wissel_t18 sigma s0 t0 s t i n v : l_not (l_e_is sigma s s0)).
-
-(* notion 334 *)
-definition l_e_wissel_t20 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(l_e_wissel_t19 sigma s0 t0 t s (l_e_symis sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) i) (l_e_symnotis sigma s t n) : l_not (l_e_is sigma t s0)).
-
-(* notion 335 *)
-definition l_e_wissel_t21 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s t0.(l_e_symnotis sigma t0 t (l_e_notis_th1 sigma s t t0 n j) : l_not (l_e_is sigma t t0)).
-
-(* notion 336 *)
-definition l_e_wissel_t22 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s t0.(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) t i (l_e_wissel_t8 sigma s0 t0 t (l_e_wissel_t20 sigma s0 t0 s t i n) (l_e_wissel_t21 sigma s0 t0 s t i n j)) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t).
-
-(* notion 337 *)
-definition l_e_wissel_t23 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s t0.(l_e_wissel_t20 sigma s0 t0 s t i n (l_e_tris1 sigma t s0 (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_t22 sigma s0 t0 s t i n j) (l_e_wissel_t3 sigma s0 t0 s j)) : l_con).
-
-(* notion 338 *)
-definition l_e_wissel_t24 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(λv:l_e_is sigma s t0.l_e_wissel_t23 sigma s0 t0 s t i n v : l_not (l_e_is sigma s t0)).
-
-(* notion 339 *)
-definition l_e_wissel_t25 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(l_e_wissel_t24 sigma s0 t0 t s (l_e_symis sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) i) (l_e_symnotis sigma s t n) : l_not (l_e_is sigma t t0)).
-
-(* notion 340 *)
-definition l_e_wissel_t26 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) t i (l_e_wissel_t8 sigma s0 t0 t (l_e_wissel_t20 sigma s0 t0 s t i n) (l_e_wissel_t25 sigma s0 t0 s t i n)) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t).
-
-(* notion 341 *)
-definition l_e_wissel_t27 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(n (l_e_tris1 sigma s t (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_t8 sigma s0 t0 s (l_e_wissel_t19 sigma s0 t0 s t i n) (l_e_wissel_t24 sigma s0 t0 s t i n)) (l_e_wissel_t26 sigma s0 t0 s t i n)) : l_con).
-
-(* notion 342 *)
-definition l_e_wissel_t28 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).(l_et (l_e_is sigma s t) (λv:l_not (l_e_is sigma s t).l_e_wissel_t27 sigma s0 t0 s t i v) : l_e_is sigma s t).
-
-(* notion 343 *)
-definition l_e_wissel_th1 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.(λx:sigma.λy:sigma.λv:l_e_is sigma (l_e_wissel_wb sigma s0 t0 x) (l_e_wissel_wb sigma s0 t0 y).l_e_wissel_t28 sigma s0 t0 x y v : l_e_injective sigma sigma (l_e_wissel sigma s0 t0)).
-
-(* notion 344 *)
-definition l_e_wissel_t29 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_e_tris2 sigma s (l_e_wissel_wb sigma s0 t0 t0) s0 i (l_e_wissel_t3 sigma s0 t0 t0 (l_e_refis sigma t0)) : l_e_is sigma s (l_e_wissel_wb sigma s0 t0 t0)).
-
-(* notion 345 *)
-definition l_e_wissel_t30 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_somei sigma (λx:sigma.l_e_is sigma s (l_e_wissel_wb sigma s0 t0 x)) t0 (l_e_wissel_t29 sigma s0 t0 s i) : l_e_image sigma sigma (l_e_wissel sigma s0 t0) s).
-
-(* notion 346 *)
-definition l_e_wissel_t31 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s t0.(l_e_tris2 sigma s (l_e_wissel_wb sigma s0 t0 s0) t0 i (l_e_wissel_t7 sigma s0 t0 s0 (l_e_refis sigma s0)) : l_e_is sigma s (l_e_wissel_wb sigma s0 t0 s0)).
-
-(* notion 347 *)
-definition l_e_wissel_t32 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s t0.(l_somei sigma (λx:sigma.l_e_is sigma s (l_e_wissel_wb sigma s0 t0 x)) s0 (l_e_wissel_t31 sigma s0 t0 s i) : l_e_image sigma sigma (l_e_wissel sigma s0 t0) s).
-
-(* notion 348 *)
-definition l_e_wissel_t33 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).λo:l_not (l_e_is sigma s t0).(l_e_symis sigma (l_e_wissel_wb sigma s0 t0 s) s (l_e_wissel_t8 sigma s0 t0 s n o) : l_e_is sigma s (l_e_wissel_wb sigma s0 t0 s)).
-
-(* notion 349 *)
-definition l_e_wissel_t34 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).λo:l_not (l_e_is sigma s t0).(l_somei sigma (λx:sigma.l_e_is sigma s (l_e_wissel_wb sigma s0 t0 x)) s (l_e_wissel_t33 sigma s0 t0 s n o) : l_e_image sigma sigma (l_e_wissel sigma s0 t0) s).
-
-(* notion 350 *)
-definition l_e_wissel_t35 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).(l_imp_th1 (l_e_is sigma s t0) (l_e_image sigma sigma (l_e_wissel sigma s0 t0) s) (λv:l_e_is sigma s t0.l_e_wissel_t32 sigma s0 t0 s v) (λv:l_not (l_e_is sigma s t0).l_e_wissel_t34 sigma s0 t0 s n v) : l_e_image sigma sigma (l_e_wissel sigma s0 t0) s).
-
-(* notion 351 *)
-definition l_e_wissel_t36 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.(l_imp_th1 (l_e_is sigma s s0) (l_e_image sigma sigma (l_e_wissel sigma s0 t0) s) (λv:l_e_is sigma s s0.l_e_wissel_t30 sigma s0 t0 s v) (λv:l_not (l_e_is sigma s s0).l_e_wissel_t35 sigma s0 t0 s v) : l_e_image sigma sigma (l_e_wissel sigma s0 t0) s).
-
-(* notion 352 *)
-definition l_e_wissel_th2 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.(λx:sigma.l_e_wissel_t36 sigma s0 t0 x : l_e_surjective sigma sigma (l_e_wissel sigma s0 t0)).
-
-(* notion 353 *)
-definition l_e_wissel_th3 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.(l_andi (l_e_injective sigma sigma (l_e_wissel sigma s0 t0)) (l_e_surjective sigma sigma (l_e_wissel sigma s0 t0)) (l_e_wissel_th1 sigma s0 t0) (l_e_wissel_th2 sigma s0 t0) : l_e_bijective sigma sigma (l_e_wissel sigma s0 t0)).
-
-(* notion 354 *)
-definition l_e_changef ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.(λx:sigma.f (l_e_wissel sigma s0 t0 x) : Πx:sigma.tau).
-
-(* notion 355 *)
-definition l_e_changef1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_e_isf sigma tau f (l_e_wissel sigma s0 t0 s) t0 (l_e_iswissel1 sigma s0 t0 s i) : l_e_is tau (l_e_changef sigma tau f s0 t0 s) (f t0)).
-
-(* notion 356 *)
-definition l_e_changef2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s t0.(l_e_isf sigma tau f (l_e_wissel sigma s0 t0 s) s0 (l_e_iswissel2 sigma s0 t0 s i) : l_e_is tau (l_e_changef sigma tau f s0 t0 s) (f s0)).
-
-(* notion 357 *)
-definition l_e_changef3 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).λo:l_not (l_e_is sigma s t0).(l_e_isf sigma tau f (l_e_wissel sigma s0 t0 s) s (l_e_iswissel3 sigma s0 t0 s n o) : l_e_is tau (l_e_changef sigma tau f s0 t0 s) (f s)).
-
-(* notion 358 *)
-definition l_e_wissel_th4 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λi:l_e_injective sigma tau f.(l_e_inj_th4 sigma sigma tau (l_e_wissel sigma s0 t0) f (l_e_wissel_th1 sigma s0 t0) i : l_e_injective sigma tau (l_e_changef sigma tau f s0 t0)).
-
-(* notion 359 *)
-definition l_e_wissel_th5 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λs:l_e_surjective sigma tau f.(l_e_surj_th1 sigma sigma tau (l_e_wissel sigma s0 t0) f (l_e_wissel_th2 sigma s0 t0) s : l_e_surjective sigma tau (l_e_changef sigma tau f s0 t0)).
-
-(* notion 360 *)
-definition l_e_wissel_th6 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λb:l_e_bijective sigma tau f.(l_e_bij_th1 sigma sigma tau (l_e_wissel sigma s0 t0) f (l_e_wissel_th3 sigma s0 t0) b : l_e_bijective sigma tau (l_e_changef sigma tau f s0 t0)).
-
-(* notion 361 *)
-definition l_r_imp ≝ λa:Prop.λb:Πx:a.Prop.(Πx:a.b x : Prop).
-
-(* notion 362 *)
-definition l_r_mp ≝ λa:Prop.λb:Πx:a.Prop.λa1:a.λi:l_r_imp a b.(i a1 : b a1).
-
-(* notion 363 *)
-definition l_r_imp_th2 ≝ λa:Prop.λb:Πx:a.Prop.λn:l_not a.(λx:a.l_cone (b x) (l_mp a l_con x n) : l_r_imp a b).
-
-(* notion 364 *)
-definition l_r_ec ≝ λa:Prop.λb:Πx:a.Prop.(Πx:a.l_not (b x) : Prop).
-
-(* notion 365 *)
-definition l_r_eci1 ≝ λa:Prop.λb:Πx:a.Prop.λn:l_not a.(λx:a.l_cone (l_not (b x)) (l_mp a l_con x n) : l_r_ec a b).
-
-(* notion 366 *)
-definition l_r_ande2 ≝ λa:Prop.λb:Πx:a.Prop.λa1:l_and a b.(l_ande2 a b a1 (l_ande1 a b a1) : b (l_ande1 a b a1)).
-
-(* notion 367 *)
-definition l_r_ite_is ≝ λa:Prop.λksi:Type[0].λx1:ksi.λy1:ksi.(l_e_is ksi x1 y1 : Prop).
-
-(* notion 368 *)
-definition l_r_ite_prop1 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λz:ksi.(l_and (l_r_imp a (λt:a.l_r_ite_is a ksi z (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi z (y t))) : Prop).
-
-(* notion 369 *)
-definition l_r_ite_t1 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_ande1 (l_r_imp a (λt:a.l_r_ite_is a ksi x1 (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi x1 (y t))) px1 : l_r_imp a (λt:a.l_r_ite_is a ksi x1 (x t))).
-
-(* notion 370 *)
-definition l_r_ite_t2 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_r_mp a (λt:a.l_r_ite_is a ksi x1 (x t)) a1 (l_r_ite_t1 a ksi x y i j a1 x1 y1 px1 py1) : l_r_ite_is a ksi x1 (x a1)).
-
-(* notion 371 *)
-definition l_r_ite_t3 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_r_ite_t2 a ksi x y i j a1 y1 x1 py1 px1 : l_r_ite_is a ksi y1 (x a1)).
-
-(* notion 372 *)
-definition l_r_ite_t4 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_e_tris2 ksi x1 y1 (x a1) (l_r_ite_t2 a ksi x y i j a1 x1 y1 px1 py1) (l_r_ite_t3 a ksi x y i j a1 x1 y1 px1 py1) : l_r_ite_is a ksi x1 y1).
-
-(* notion 373 *)
-definition l_r_ite_t5 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(λs:ksi.λt:ksi.λps:l_r_ite_prop1 a ksi x y i j s.λpt:l_r_ite_prop1 a ksi x y i j t.l_r_ite_t4 a ksi x y i j a1 s t ps pt : l_e_amone ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t)).
-
-(* notion 374 *)
-definition l_r_ite_t6 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(i a1 : l_r_imp a (λt:a.l_r_ite_is a ksi (x a1) (x t))).
-
-(* notion 375 *)
-definition l_r_ite_t7 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(l_r_imp_th2 (l_not a) (λt:l_not a.l_r_ite_is a ksi (x a1) (y t)) (l_weli a a1) : l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (x a1) (y t))).
-
-(* notion 376 *)
-definition l_r_ite_t8 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(l_andi (l_r_imp a (λt:a.l_r_ite_is a ksi (x a1) (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (x a1) (y t))) (l_r_ite_t6 a ksi x y i j a1) (l_r_ite_t7 a ksi x y i j a1) : l_r_ite_prop1 a ksi x y i j (x a1)).
-
-(* notion 377 *)
-definition l_r_ite_t9 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(l_somei ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t) (x a1) (l_r_ite_t8 a ksi x y i j a1) : l_some ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t)).
-
-(* notion 378 *)
-definition l_r_ite_t10 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(l_e_onei ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t) (l_r_ite_t5 a ksi x y i j a1) (l_r_ite_t9 a ksi x y i j a1) : l_e_one ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t)).
-
-(* notion 379 *)
-definition l_r_ite_t11 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_ande2 (l_r_imp a (λt:a.l_r_ite_is a ksi x1 (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi x1 (y t))) px1 : l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi x1 (y t))).
-
-(* notion 380 *)
-definition l_r_ite_t12 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_r_mp (l_not a) (λt:l_not a.l_r_ite_is a ksi x1 (y t)) n (l_r_ite_t11 a ksi x y i j n x1 y1 px1 py1) : l_r_ite_is a ksi x1 (y n)).
-
-(* notion 381 *)
-definition l_r_ite_t13 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_r_ite_t12 a ksi x y i j n y1 x1 py1 px1 : l_r_ite_is a ksi y1 (y n)).
-
-(* notion 382 *)
-definition l_r_ite_t14 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_e_tris2 ksi x1 y1 (y n) (l_r_ite_t12 a ksi x y i j n x1 y1 px1 py1) (l_r_ite_t13 a ksi x y i j n x1 y1 px1 py1) : l_r_ite_is a ksi x1 y1).
-
-(* notion 383 *)
-definition l_r_ite_t15 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(λs:ksi.λt:ksi.λps:l_r_ite_prop1 a ksi x y i j s.λpt:l_r_ite_prop1 a ksi x y i j t.l_r_ite_t14 a ksi x y i j n s t ps pt : l_e_amone ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t)).
-
-(* notion 384 *)
-definition l_r_ite_t16 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(j n : l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (y n) (y t))).
-
-(* notion 385 *)
-definition l_r_ite_t17 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(l_r_imp_th2 a (λt:a.l_r_ite_is a ksi (y n) (x t)) n : l_r_imp a (λt:a.l_r_ite_is a ksi (y n) (x t))).
-
-(* notion 386 *)
-definition l_r_ite_t18 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(l_andi (l_r_imp a (λt:a.l_r_ite_is a ksi (y n) (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (y n) (y t))) (l_r_ite_t17 a ksi x y i j n) (l_r_ite_t16 a ksi x y i j n) : l_r_ite_prop1 a ksi x y i j (y n)).
-
-(* notion 387 *)
-definition l_r_ite_t19 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(l_somei ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t) (y n) (l_r_ite_t18 a ksi x y i j n) : l_some ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t)).
-
-(* notion 388 *)
-definition l_r_ite_t20 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(l_e_onei ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t) (l_r_ite_t15 a ksi x y i j n) (l_r_ite_t19 a ksi x y i j n) : l_e_one ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t)).
-
-(* notion 389 *)
-definition l_r_ite_t21 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).(l_imp_th1 a (l_e_one ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t)) (λt:a.l_r_ite_t10 a ksi x y i j t) (λt:l_not a.l_r_ite_t20 a ksi x y i j t) : l_e_one ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t)).
-
-(* notion 390 *)
-definition l_r_ite ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).(l_e_ind ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t) (l_r_ite_t21 a ksi x y i j) : ksi).
-
-(* notion 391 *)
-definition l_r_ite_t22 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).(l_e_oneax ksi (Πt:ksi.l_r_ite_prop1 a ksi x y i j t) (l_r_ite_t21 a ksi x y i j) : l_r_ite_prop1 a ksi x y i j (l_r_ite a ksi x y i j)).
-
-(* notion 392 *)
-definition l_r_ite_t23 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).(l_ande1 (l_r_imp a (λt:a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (y t))) (l_r_ite_t22 a ksi x y i j) : l_r_imp a (λt:a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (x t))).
-
-(* notion 393 *)
-definition l_r_ite_t24 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).(l_ande2 (l_r_imp a (λt:a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (y t))) (l_r_ite_t22 a ksi x y i j) : l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (y t))).
-
-(* notion 394 *)
-definition l_r_itet ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(l_r_mp a (λt:a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (x t)) a1 (l_r_ite_t23 a ksi x y i j) : l_r_ite_is a ksi (l_r_ite a ksi x y i j) (x a1)).
-
-(* notion 395 *)
-definition l_r_itef ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(l_r_mp (l_not a) (λt:l_not a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (y t)) n (l_r_ite_t24 a ksi x y i j) : l_r_ite_is a ksi (l_r_ite a ksi x y i j) (y n)).
-
-(* notion 396 *)
-axiom l_e_st_set : Πsigma:Type[0].Type[0].
-
-(* notion 397 *)
-axiom l_e_st_esti : Πsigma:Type[0].Πs:sigma.Πs0:l_e_st_set sigma.Prop.
-
-(* notion 398 *)
-axiom l_e_st_setof : Πsigma:Type[0].Πp:Πx:sigma.Prop.l_e_st_set sigma.
-
-(* notion 399 *)
-axiom l_e_st_estii : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πs:sigma.Πsp:p s.l_e_st_esti sigma s (l_e_st_setof sigma p).
-
-(* notion 400 *)
-axiom l_e_st_estie : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πs:sigma.Πe:l_e_st_esti sigma s (l_e_st_setof sigma p).p s.
-
-(* notion 401 *)
-definition l_e_st_empty ≝ λsigma:Type[0].λs0:l_e_st_set sigma.(l_non sigma (λx:sigma.l_e_st_esti sigma x s0) : Prop).
-
-(* notion 402 *)
-definition l_e_st_nonempty ≝ λsigma:Type[0].λs0:l_e_st_set sigma.(l_some sigma (λx:sigma.l_e_st_esti sigma x s0) : Prop).
-
-(* notion 403 *)
-definition l_e_st_emptyi ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λn:Πx:sigma.l_not (l_e_st_esti sigma x s0).(n : l_e_st_empty sigma s0).
-
-(* notion 404 *)
-definition l_e_st_emptye ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λe:l_e_st_empty sigma s0.λs:sigma.(e s : l_not (l_e_st_esti sigma s s0)).
-
-(* notion 405 *)
-definition l_e_st_nonemptyi ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_somei sigma (λx:sigma.l_e_st_esti sigma x s0) s ses0 : l_e_st_nonempty sigma s0).
-
-(* notion 406 *)
-definition l_e_st_nonemptyapp ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λn:l_e_st_nonempty sigma s0.λx:Prop.λx1:Πy:sigma.Πz:l_e_st_esti sigma y s0.x.(l_someapp sigma (λy:sigma.l_e_st_esti sigma y s0) n x x1 : x).
-
-(* notion 407 *)
-definition l_e_st_incl ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.(l_all sigma (λx:sigma.l_imp (l_e_st_esti sigma x s0) (l_e_st_esti sigma x t0)) : Prop).
-
-(* notion 408 *)
-definition l_e_st_incli ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λe:Πx:sigma.Πy:l_e_st_esti sigma x s0.l_e_st_esti sigma x t0.(e : l_e_st_incl sigma s0 t0).
-
-(* notion 409 *)
-definition l_e_st_incle ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λi:l_e_st_incl sigma s0 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.(i s ses0 : l_e_st_esti sigma s t0).
-
-(* notion 410 *)
-definition l_e_st_refincl ≝ λsigma:Type[0].λs0:l_e_st_set sigma.(λx:sigma.λy:l_e_st_esti sigma x s0.y : l_e_st_incl sigma s0 s0).
-
-(* notion 411 *)
-definition l_e_st_disj ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.(l_all sigma (λx:sigma.l_ec (l_e_st_esti sigma x s0) (l_e_st_esti sigma x t0)) : Prop).
-
-(* notion 412 *)
-definition l_e_st_disji1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:Πx:sigma.Πy:l_e_st_esti sigma x s0.l_not (l_e_st_esti sigma x t0).(n : l_e_st_disj sigma s0 t0).
-
-(* notion 413 *)
-definition l_e_st_disji2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:Πx:sigma.Πy:l_e_st_esti sigma x t0.l_not (l_e_st_esti sigma x s0).(λx:sigma.l_ec_th2 (l_e_st_esti sigma x s0) (l_e_st_esti sigma x t0) (n x) : l_e_st_disj sigma s0 t0).
-
-(* notion 414 *)
-definition l_e_st_disje1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λd:l_e_st_disj sigma s0 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_ece1 (l_e_st_esti sigma s s0) (l_e_st_esti sigma s t0) (d s) ses0 : l_not (l_e_st_esti sigma s t0)).
-
-(* notion 415 *)
-definition l_e_st_disje2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λd:l_e_st_disj sigma s0 t0.λs:sigma.λset0:l_e_st_esti sigma s t0.(l_ece2 (l_e_st_esti sigma s s0) (l_e_st_esti sigma s t0) (d s) set0 : l_not (l_e_st_esti sigma s s0)).
-
-(* notion 416 *)
-definition l_e_st_symdisj ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λd:l_e_st_disj sigma s0 t0.(λx:sigma.λy:l_e_st_esti sigma x t0.l_e_st_disje2 sigma s0 t0 d x y : l_e_st_disj sigma t0 s0).
-
-(* notion 417 *)
-definition l_e_st_disj_th1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.λses0:l_e_st_esti sigma s s0.λset0:l_e_st_esti sigma s t0.(l_all_th1 sigma (λx:sigma.l_ec (l_e_st_esti sigma x s0) (l_e_st_esti sigma x t0)) s (l_imp_th4 (l_e_st_esti sigma s s0) (l_not (l_e_st_esti sigma s t0)) ses0 (l_weli (l_e_st_esti sigma s t0) set0)) : l_not (l_e_st_disj sigma s0 t0)).
-
-(* notion 418 *)
-definition l_e_st_disj_th2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.λses0:l_e_st_esti sigma s s0.λset0:l_e_st_esti sigma s t0.(l_e_st_disj_th1 sigma t0 s0 s set0 ses0 : l_not (l_e_st_disj sigma t0 s0)).
-
-(* notion 419 *)
-definition l_e_st_issete1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_e_isp (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_esti sigma s x) s0 t0 ses0 i : l_e_st_esti sigma s t0).
-
-(* notion 420 *)
-definition l_e_st_issete2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.λs:sigma.λset0:l_e_st_esti sigma s t0.(l_e_isp1 (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_esti sigma s x) t0 s0 set0 i : l_e_st_esti sigma s s0).
-
-(* notion 421 *)
-definition l_e_st_isset_th1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.(λx:sigma.λy:l_e_st_esti sigma x s0.l_e_st_issete1 sigma s0 t0 i x y : l_e_st_incl sigma s0 t0).
-
-(* notion 422 *)
-definition l_e_st_isset_th2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.(λx:sigma.λy:l_e_st_esti sigma x t0.l_e_st_issete2 sigma s0 t0 i x y : l_e_st_incl sigma t0 s0).
-
-(* notion 423 *)
-axiom l_e_st_isseti : Πsigma:Type[0].Πs0:l_e_st_set sigma.Πt0:l_e_st_set sigma.Πi:l_e_st_incl sigma s0 t0.Πj:l_e_st_incl sigma t0 s0.l_e_is (l_e_st_set sigma) s0 t0.
-
-(* notion 424 *)
-definition l_e_st_isset_th3 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.λses0:l_e_st_esti sigma s s0.λn:l_not (l_e_st_esti sigma s t0).(l_imp_th3 (l_e_is (l_e_st_set sigma) s0 t0) (l_e_st_esti sigma s t0) n (λt:l_e_is (l_e_st_set sigma) s0 t0.l_e_st_issete1 sigma s0 t0 t s ses0) : l_not (l_e_is (l_e_st_set sigma) s0 t0)).
-
-(* notion 425 *)
-definition l_e_st_isset_th4 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.λses0:l_e_st_esti sigma s s0.λn:l_not (l_e_st_esti sigma s t0).(l_e_symnotis (l_e_st_set sigma) s0 t0 (l_e_st_isset_th3 sigma s0 t0 s ses0 n) : l_not (l_e_is (l_e_st_set sigma) t0 s0)).
-
-(* notion 426 *)
-definition l_e_st_isset_nissetprop ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.(l_and (l_e_st_esti sigma s s0) (l_not (l_e_st_esti sigma s t0)) : Prop).
-
-(* notion 427 *)
-definition l_e_st_isset_t1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.λn:l_not (l_e_st_isset_nissetprop sigma s0 t0 s).λe:l_e_st_esti sigma s s0.(l_et (l_e_st_esti sigma s t0) (l_and_th3 (l_e_st_esti sigma s s0) (l_not (l_e_st_esti sigma s t0)) n e) : l_e_st_esti sigma s t0).
-
-(* notion 428 *)
-definition l_e_st_isset_t2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:l_not (l_e_is (l_e_st_set sigma) s0 t0).λm:l_not (l_some sigma (Πx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)).λl:l_non sigma (Πx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x).λs:sigma.(l_some_th4 sigma (Πx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x) m s : l_not (l_e_st_isset_nissetprop sigma s0 t0 s)).
-
-(* notion 429 *)
-definition l_e_st_isset_t3 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:l_not (l_e_is (l_e_st_set sigma) s0 t0).λm:l_not (l_some sigma (Πx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)).λl:l_non sigma (Πx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x).λs:sigma.(l s : l_not (l_e_st_isset_nissetprop sigma t0 s0 s)).
-
-(* notion 430 *)
-definition l_e_st_isset_t4 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:l_not (l_e_is (l_e_st_set sigma) s0 t0).λm:l_not (l_some sigma (Πx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)).λl:l_non sigma (Πx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x).(l_e_st_isseti sigma s0 t0 (λx:sigma.λy:l_e_st_esti sigma x s0.l_e_st_isset_t1 sigma s0 t0 x (l_e_st_isset_t2 sigma s0 t0 n m l x) y) (λx:sigma.λy:l_e_st_esti sigma x t0.l_e_st_isset_t1 sigma t0 s0 x (l_e_st_isset_t3 sigma s0 t0 n m l x) y) : l_e_is (l_e_st_set sigma) s0 t0).
-
-(* notion 431 *)
-definition l_e_st_isset_t5 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:l_not (l_e_is (l_e_st_set sigma) s0 t0).λm:l_not (l_some sigma (Πx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)).(l_imp_th3 (l_non sigma (Πx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x)) (l_e_is (l_e_st_set sigma) s0 t0) n (λy:l_non sigma (Πx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x).l_e_st_isset_t4 sigma s0 t0 n m y) : l_some sigma (Πx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x)).
-
-(* notion 432 *)
-definition l_e_st_isset_th5 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:l_not (l_e_is (l_e_st_set sigma) s0 t0).(l_or_th1 (l_some sigma (Πx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)) (l_some sigma (Πx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x)) (λy:l_not (l_some sigma (Πx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)).l_e_st_isset_t5 sigma s0 t0 n y) : l_or (l_some sigma (Πx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)) (l_some sigma (Πx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x))).
-
-(* notion 433 *)
-definition l_e_st_unmore ≝ λsigma:Type[0].λalpha:Type[0].λsa:Πx:alpha.l_e_st_set sigma.(l_e_st_setof sigma (Πx:sigma.l_some alpha (λy:alpha.l_e_st_esti sigma x (sa y))) : l_e_st_set sigma).
-
-(* notion 434 *)
-definition l_e_st_eunmore1 ≝ λsigma:Type[0].λalpha:Type[0].λsa:Πx:alpha.l_e_st_set sigma.λs:sigma.λa:alpha.λseasa:l_e_st_esti sigma s (sa a).(l_e_st_estii sigma (Πx:sigma.l_some alpha (λy:alpha.l_e_st_esti sigma x (sa y))) s (l_somei alpha (λy:alpha.l_e_st_esti sigma s (sa y)) a seasa) : l_e_st_esti sigma s (l_e_st_unmore sigma alpha sa)).
-
-(* notion 435 *)
-definition l_e_st_unmoreapp ≝ λsigma:Type[0].λalpha:Type[0].λsa:Πx:alpha.l_e_st_set sigma.λs:sigma.λseun:l_e_st_esti sigma s (l_e_st_unmore sigma alpha sa).λx:Prop.λx1:Πy:alpha.Πz:l_e_st_esti sigma s (sa y).x.(l_someapp alpha (λy:alpha.l_e_st_esti sigma s (sa y)) (l_e_st_estie sigma (Πz:sigma.l_some alpha (λy:alpha.l_e_st_esti sigma z (sa y))) s seun) x x1 : x).
-
-(* notion 436 *)
-definition l_e_st_eq_refr ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(refr1 s : r s s).
-
-(* notion 437 *)
-definition l_e_st_eq_symr ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λtsr:r s t.(symr1 s t tsr : r t s).
-
-(* notion 438 *)
-definition l_e_st_eq_trr ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λu:sigma.λtsr:r s t.λutr:r t u.(trr1 s t u tsr utr : r s u).
-
-(* notion 439 *)
-definition l_e_st_eq_tr1r ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λu:sigma.λsur:r u s.λtur:r u t.(l_e_st_eq_trr sigma r refr1 symr1 trr1 s u t (l_e_st_eq_symr sigma r refr1 symr1 trr1 u s sur) tur : r s t).
-
-(* notion 440 *)
-definition l_e_st_eq_tr2r ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λu:sigma.λusr:r s u.λutr:r t u.(l_e_st_eq_trr sigma r refr1 symr1 trr1 s u t usr (l_e_st_eq_symr sigma r refr1 symr1 trr1 t u utr) : r s t).
-
-(* notion 441 *)
-definition l_e_st_eq_ecelt ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_setof sigma (r s) : l_e_st_set sigma).
-
-(* notion 442 *)
-definition l_e_st_eq_1_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_estii sigma (r s) s (l_e_st_eq_refr sigma r refr1 symr1 trr1 s) : l_e_st_esti sigma s (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
-
-(* notion 443 *)
-definition l_e_st_eq_1_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λtsr:r s t.(l_e_st_estii sigma (r s) t tsr : l_e_st_esti sigma t (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
-
-(* notion 444 *)
-definition l_e_st_eq_1_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λe:l_e_st_esti sigma t (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s).(l_e_st_estie sigma (r s) t e : r s t).
-
-(* notion 445 *)
-definition l_e_st_eq_1_t1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λe:l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s).(l_e_st_eq_1_th2 sigma r refr1 symr1 trr1 t u (l_e_st_eq_tr1r sigma r refr1 symr1 trr1 t u s tsr (l_e_st_eq_1_th3 sigma r refr1 symr1 trr1 s u e)) : l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)).
-
-(* notion 446 *)
-definition l_e_st_eq_1_th4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λtsr:r s t.(l_e_st_isseti sigma (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) (λx:sigma.λy:l_e_st_esti sigma x (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s).l_e_st_eq_1_t1 sigma r refr1 symr1 trr1 s t tsr x y) (λx:sigma.λy:l_e_st_esti sigma x (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t).l_e_st_eq_1_t1 sigma r refr1 symr1 trr1 t s (l_e_st_eq_symr sigma r refr1 symr1 trr1 s t tsr) x y) : l_e_is (l_e_st_set sigma) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)).
-
-(* notion 447 *)
-definition l_e_st_eq_1_t2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λn:l_not (r s t).λu:sigma.λe:l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s).(l_imp_th3 (l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)) (r s t) n (λx:l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t).l_e_st_eq_tr2r sigma r refr1 symr1 trr1 s t u (l_e_st_eq_1_th3 sigma r refr1 symr1 trr1 s u e) (l_e_st_eq_1_th3 sigma r refr1 symr1 trr1 t u x)) : l_not (l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t))).
-
-(* notion 448 *)
-definition l_e_st_eq_1_th5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λn:l_not (r s t).(λx:sigma.λy:l_e_st_esti sigma x (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s).l_e_st_eq_1_t2 sigma r refr1 symr1 trr1 s t n x y : l_e_st_disj sigma (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)).
-
-(* notion 449 *)
-definition l_e_st_eq_1_th6 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_nonemptyi sigma (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) s (l_e_st_eq_1_th1 sigma r refr1 symr1 trr1 s) : l_e_st_nonempty sigma (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
-
-(* notion 450 *)
-definition l_e_st_eq_ecp ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λs:sigma.(l_e_is (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) : Prop).
-
-(* notion 451 *)
-definition l_e_st_eq_anec ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.(l_some sigma (λx:sigma.l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 x) : Prop).
-
-(* notion 452 *)
-definition l_e_st_eq_2_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_somei sigma (λx:sigma.l_e_st_eq_ecp sigma r refr1 symr1 trr1 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) x) s (l_e_refis (l_e_st_set sigma) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)) : l_e_st_eq_anec sigma r refr1 symr1 trr1 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
-
-(* notion 453 *)
-definition l_e_st_eq_2_t1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λe:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 t.(l_e_st_issete1 sigma s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) e s ses0 : l_e_st_esti sigma s (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)).
-
-(* notion 454 *)
-definition l_e_st_eq_2_t2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λe:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 t.(l_e_st_eq_1_th4 sigma r refr1 symr1 trr1 t s (l_e_st_eq_1_th3 sigma r refr1 symr1 trr1 t s (l_e_st_eq_2_t1 sigma r refr1 symr1 trr1 s0 ecs0 s ses0 t e)) : l_e_is (l_e_st_set sigma) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
-
-(* notion 455 *)
-definition l_e_st_eq_2_t3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λe:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 t.(l_e_tris (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) e (l_e_st_eq_2_t2 sigma r refr1 symr1 trr1 s0 ecs0 s ses0 t e) : l_e_is (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
-
-(* notion 456 *)
-definition l_e_st_eq_2_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_someapp sigma (λx:sigma.l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 x) ecs0 (l_e_is (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)) (λx:sigma.λy:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 x.l_e_st_eq_2_t3 sigma r refr1 symr1 trr1 s0 ecs0 s ses0 x y) : l_e_is (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
-
-(* notion 457 *)
-definition l_e_st_eq_2_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λtes0:l_e_st_esti sigma t s0.(l_e_st_eq_1_th3 sigma r refr1 symr1 trr1 s t (l_e_st_issete1 sigma s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 s0 ecs0 s ses0) t tes0) : r s t).
-
-(* notion 458 *)
-definition l_e_st_eq_2_th4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λtsr:r s t.(l_e_st_issete2 sigma s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 s0 ecs0 s ses0) t (l_e_st_eq_1_th2 sigma r refr1 symr1 trr1 s t tsr) : l_e_st_esti sigma t s0).
-
-(* notion 459 *)
-definition l_e_st_eq_2_t4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λe:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 s.(l_e_isp (l_e_st_set sigma) (Πx:l_e_st_set sigma.l_e_st_nonempty sigma x) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) s0 (l_e_st_eq_1_th6 sigma r refr1 symr1 trr1 s) (l_e_symis (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) e) : l_e_st_nonempty sigma s0).
-
-(* notion 460 *)
-definition l_e_st_eq_2_th5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.(l_someapp sigma (λx:sigma.l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 x) ecs0 (l_e_st_nonempty sigma s0) (λx:sigma.λy:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 x.l_e_st_eq_2_t4 sigma r refr1 symr1 trr1 s0 ecs0 x y) : l_e_st_nonempty sigma s0).
-
-(* notion 461 *)
-definition l_e_st_eq_3_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λect0:l_e_st_eq_anec sigma r refr1 symr1 trr1 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λtet0:l_e_st_esti sigma t t0.λtsr:r s t.(l_e_tr3is (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) t0 (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 s0 ecs0 s ses0) (l_e_st_eq_1_th4 sigma r refr1 symr1 trr1 s t tsr) (l_e_symis (l_e_st_set sigma) t0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 t0 ect0 t tet0)) : l_e_is (l_e_st_set sigma) s0 t0).
-
-(* notion 462 *)
-definition l_e_st_eq_3_t1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λect0:l_e_st_eq_anec sigma r refr1 symr1 trr1 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λtet0:l_e_st_esti sigma t t0.λn:l_not (r s t).(l_e_isp1 (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_disj sigma x (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) s0 (l_e_st_eq_1_th5 sigma r refr1 symr1 trr1 s t n) (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 s0 ecs0 s ses0) : l_e_st_disj sigma s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)).
-
-(* notion 463 *)
-definition l_e_st_eq_3_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λect0:l_e_st_eq_anec sigma r refr1 symr1 trr1 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λtet0:l_e_st_esti sigma t t0.λn:l_not (r s t).(l_e_isp1 (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_disj sigma s0 x) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) t0 (l_e_st_eq_3_t1 sigma r refr1 symr1 trr1 s0 ecs0 t0 ect0 s ses0 t tet0 n) (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 t0 ect0 t tet0) : l_e_st_disj sigma s0 t0).
-
-(* notion 464 *)
-definition l_e_st_eq_3_t2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_e_st_issete1 sigma s0 t0 i s ses0 : l_e_st_esti sigma s t0).
-
-(* notion 465 *)
-definition l_e_st_eq_3_t3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_e_st_disj_th1 sigma s0 t0 s ses0 (l_e_st_eq_3_t2 sigma r refr1 symr1 trr1 s0 ecs0 t0 i s ses0) : l_not (l_e_st_disj sigma s0 t0)).
-
-(* notion 466 *)
-definition l_e_st_eq_3_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.(l_e_st_nonemptyapp sigma s0 (l_e_st_eq_2_th5 sigma r refr1 symr1 trr1 s0 ecs0) (l_not (l_e_st_disj sigma s0 t0)) (λx:sigma.λy:l_e_st_esti sigma x s0.l_e_st_eq_3_t3 sigma r refr1 symr1 trr1 s0 ecs0 t0 i x y) : l_not (l_e_st_disj sigma s0 t0)).
-
-(* notion 467 *)
-definition l_e_st_eq_ect ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.(l_e_ot (l_e_st_set sigma) (Πx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) : Type[0]).
-
-(* notion 468 *)
-definition l_e_st_eq_ectset ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.(l_e_out (l_e_st_set sigma) (Πx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) s0 ecs0 : l_e_st_eq_ect sigma r refr1 symr1 trr1).
-
-(* notion 469 *)
-definition l_e_st_eq_ectelt ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_eq_ectset sigma r refr1 symr1 trr1 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_2_th1 sigma r refr1 symr1 trr1 s) : l_e_st_eq_ect sigma r refr1 symr1 trr1).
-
-(* notion 470 *)
-definition l_e_st_eq_ecect ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_in (l_e_st_set sigma) (Πx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) e : l_e_st_set sigma).
-
-(* notion 471 *)
-definition l_e_st_eq_4_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_inp (l_e_st_set sigma) (Πx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) e : l_e_st_eq_anec sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)).
-
-(* notion 472 *)
-definition l_e_st_eq_4_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_st_eq_2_th5 sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 e) : l_e_st_nonempty sigma (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)).
-
-(* notion 473 *)
-definition l_e_st_eq_4_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λx:Prop.λx1:Πy:sigma.Πz:l_e_st_esti sigma y (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).x.(l_e_st_nonemptyapp sigma (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_4_th2 sigma r refr1 symr1 trr1 e) x x1 : x).
-
-(* notion 474 *)
-definition l_e_st_eq_4_th4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_isinout (l_e_st_set sigma) (Πx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_2_th1 sigma r refr1 symr1 trr1 s) : l_e_is (l_e_st_set sigma) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s))).
-
-(* notion 475 *)
-definition l_e_st_eq_4_th5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_issete1 sigma (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s)) (l_e_st_eq_4_th4 sigma r refr1 symr1 trr1 s) s (l_e_st_eq_1_th1 sigma r refr1 symr1 trr1 s) : l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s))).
-
-(* notion 476 *)
-definition l_e_st_eq_4_th6 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_eunmore1 sigma (l_e_st_eq_ect sigma r refr1 symr1 trr1) (λx:l_e_st_eq_ect sigma r refr1 symr1 trr1.l_e_st_eq_ecect sigma r refr1 symr1 trr1 x) s (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_4_th5 sigma r refr1 symr1 trr1 s) : l_e_st_esti sigma s (l_e_st_unmore sigma (l_e_st_eq_ect sigma r refr1 symr1 trr1) (λx:l_e_st_eq_ect sigma r refr1 symr1 trr1.l_e_st_eq_ecect sigma r refr1 symr1 trr1 x))).
-
-(* notion 477 *)
-definition l_e_st_eq_4_th7 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtee:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_st_eq_2_th3 sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 e) s see t tee : r s t).
-
-(* notion 478 *)
-definition l_e_st_eq_4_th8 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtsr:r s t.(l_e_st_eq_2_th4 sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 e) s see t tsr : l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)).
-
-(* notion 479 *)
-definition l_e_st_eq_5_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λi:l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) e f.(l_e_isini (l_e_st_set sigma) (Πx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) e f i : l_e_is (l_e_st_set sigma) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f)).
-
-(* notion 480 *)
-definition l_e_st_eq_5_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λi:l_e_is (l_e_st_set sigma) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).(l_e_isine (l_e_st_set sigma) (Πx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) e f i : l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) e f).
-
-(* notion 481 *)
-definition l_e_st_eq_5_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).λtsr:r s t.(l_e_st_eq_5_th2 sigma r refr1 symr1 trr1 e f (l_e_st_eq_3_th1 sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 e) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 f) s see t tef tsr) : l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) e f).
-
-(* notion 482 *)
-definition l_e_st_eq_5_th4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λi:l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) e f.(l_e_st_issete1 sigma (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f) (l_e_st_eq_5_th1 sigma r refr1 symr1 trr1 e f i) s see : l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f)).
-
-(* notion 483 *)
-definition l_e_st_eq_5_th5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).λi:l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) e f.(l_e_st_eq_2_th3 sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 f) s (l_e_st_eq_5_th4 sigma r refr1 symr1 trr1 e f s see i) t tef : r s t).
-
-(* notion 484 *)
-definition l_e_st_eq_5_th6 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λtsr:r s t.(l_e_isouti (l_e_st_set sigma) (Πx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_2_th1 sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) (l_e_st_eq_2_th1 sigma r refr1 symr1 trr1 t) (l_e_st_eq_1_th4 sigma r refr1 symr1 trr1 s t tsr) : l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 t)).
-
-(* notion 485 *)
-definition l_e_st_eq_fixfu ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.(Πx:sigma.Πy:sigma.Πz:r x y.l_e_is alpha (fu x) (fu y) : Prop).
-
-(* notion 486 *)
-definition l_e_st_eq_10_prop1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λs:sigma.(l_and (l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu s) a1) : Prop).
-
-(* notion 487 *)
-definition l_e_st_eq_10_prop2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.(l_some sigma (Πx:sigma.l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 x) : Prop).
-
-(* notion 488 *)
-definition l_e_st_eq_10_t1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_andi (l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu s) (fu s)) see (l_e_refis alpha (fu s)) : l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e (fu s) s).
-
-(* notion 489 *)
-definition l_e_st_eq_10_t2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_somei sigma (Πx:sigma.l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e (fu s) x) s (l_e_st_eq_10_t1 sigma r refr1 symr1 trr1 alpha fu ff e s see) : l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e (fu s)).
-
-(* notion 490 *)
-definition l_e_st_eq_10_t3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_somei alpha (Πx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x) (fu s) (l_e_st_eq_10_t2 sigma r refr1 symr1 trr1 alpha fu ff e s see) : l_some alpha (Πx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x)).
-
-(* notion 491 *)
-definition l_e_st_eq_10_t4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_st_eq_4_th3 sigma r refr1 symr1 trr1 e (l_some alpha (Πx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x)) (λx:sigma.λy:l_e_st_esti sigma x (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).l_e_st_eq_10_t3 sigma r refr1 symr1 trr1 alpha fu ff e x y) : l_some alpha (Πx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x)).
-
-(* notion 492 *)
-definition l_e_st_eq_10_t5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_ande1 (l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu s) a1) pa1s : l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)).
-
-(* notion 493 *)
-definition l_e_st_eq_10_t6 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_ande1 (l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu t) b1) pb1t : l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)).
-
-(* notion 494 *)
-definition l_e_st_eq_10_t7 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_e_st_eq_4_th7 sigma r refr1 symr1 trr1 e s (l_e_st_eq_10_t5 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s t pb1t) t (l_e_st_eq_10_t6 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s t pb1t) : r s t).
-
-(* notion 495 *)
-definition l_e_st_eq_10_t8 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_ande2 (l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu s) a1) pa1s : l_e_is alpha (fu s) a1).
-
-(* notion 496 *)
-definition l_e_st_eq_10_t9 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_ande2 (l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu t) b1) pb1t : l_e_is alpha (fu t) b1).
-
-(* notion 497 *)
-definition l_e_st_eq_10_t10 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_e_tr3is alpha a1 (fu s) (fu t) b1 (l_e_symis alpha (fu s) a1 (l_e_st_eq_10_t8 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s t pb1t)) (ff s t (l_e_st_eq_10_t7 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s t pb1t)) (l_e_st_eq_10_t9 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s t pb1t) : l_e_is alpha a1 b1).
-
-(* notion 498 *)
-definition l_e_st_eq_10_t11 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.(l_someapp sigma (Πx:sigma.l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 x) pb1 (l_e_is alpha a1 b1) (λx:sigma.λy:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 x.l_e_st_eq_10_t10 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s x y) : l_e_is alpha a1 b1).
-
-(* notion 499 *)
-definition l_e_st_eq_10_t12 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.(l_someapp sigma (Πx:sigma.l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 x) pa1 (l_e_is alpha a1 b1) (λx:sigma.λy:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 x.l_e_st_eq_10_t11 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 x y) : l_e_is alpha a1 b1).
-
-(* notion 500 *)
-definition l_e_st_eq_10_t13 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(λx:alpha.λy:alpha.λu:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x.λv:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e y.l_e_st_eq_10_t12 sigma r refr1 symr1 trr1 alpha fu ff e x y u v : l_e_amone alpha (Πx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x)).
-
-(* notion 501 *)
-definition l_e_st_eq_10_t14 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_onei alpha (Πx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x) (l_e_st_eq_10_t13 sigma r refr1 symr1 trr1 alpha fu ff e) (l_e_st_eq_10_t4 sigma r refr1 symr1 trr1 alpha fu ff e) : l_e_one alpha (Πx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x)).
-
-(* notion 502 *)
-definition l_e_st_eq_indeq ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_ind alpha (Πx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x) (l_e_st_eq_10_t14 sigma r refr1 symr1 trr1 alpha fu ff e) : alpha).
-
-(* notion 503 *)
-definition l_e_st_eq_10_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_oneax alpha (Πx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x) (l_e_st_eq_10_t14 sigma r refr1 symr1 trr1 alpha fu ff e) : l_some sigma (Πx:sigma.l_and (l_e_st_esti sigma x (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu x) (l_e_st_eq_indeq sigma r refr1 symr1 trr1 alpha fu ff e)))).
-
-(* notion 504 *)
-definition l_e_st_eq_10_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_st_eq_10_t12 sigma r refr1 symr1 trr1 alpha fu ff e (fu s) (l_e_st_eq_indeq sigma r refr1 symr1 trr1 alpha fu ff e) (l_e_st_eq_10_t2 sigma r refr1 symr1 trr1 alpha fu ff e s see) (l_e_st_eq_10_th1 sigma r refr1 symr1 trr1 alpha fu ff e) : l_e_is alpha (fu s) (l_e_st_eq_indeq sigma r refr1 symr1 trr1 alpha fu ff e)).
-
-(* notion 505 *)
-definition l_e_st_eq_10_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λs:sigma.(l_e_st_eq_10_th2 sigma r refr1 symr1 trr1 alpha fu ff (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s) s (l_e_st_eq_4_th5 sigma r refr1 symr1 trr1 s) : l_e_is alpha (fu s) (l_e_st_eq_indeq sigma r refr1 symr1 trr1 alpha fu ff (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s))).
-
-(* notion 506 *)
-definition l_e_st_eq_fixfu2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.(Πx:sigma.Πy:sigma.Πz:sigma.Πu:sigma.Πv:r x y.Πw:r z u.l_e_is alpha (fu2 x z) (fu2 y u) : Prop).
-
-(* notion 507 *)
-definition l_e_st_eq_11_t1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.(ff2 s t u u tsr (l_e_st_eq_refr sigma r refr1 symr1 trr1 u) : l_e_is alpha (fu2 s u) (fu2 t u)).
-
-(* notion 508 *)
-definition l_e_st_eq_11_t2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λs:sigma.λt:sigma.λtsr:r s t.(l_e_fisi sigma alpha (fu2 s) (fu2 t) (λx:sigma.l_e_st_eq_11_t1 sigma r refr1 symr1 trr1 alpha fu2 ff2 s t tsr x) : l_e_is (Πx:sigma.alpha) (fu2 s) (fu2 t)).
-
-(* notion 509 *)
-definition l_e_st_eq_11_i ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_st_eq_indeq sigma r refr1 symr1 trr1 (Πx:sigma.alpha) fu2 (λx:sigma.λy:sigma.λz:r x y.l_e_st_eq_11_t2 sigma r refr1 symr1 trr1 alpha fu2 ff2 x y z) e : Πx:sigma.alpha).
-
-(* notion 510 *)
-definition l_e_st_eq_11_t3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λuee:l_e_st_esti sigma u (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_st_eq_10_th2 sigma r refr1 symr1 trr1 (Πx:sigma.alpha) fu2 (λx:sigma.λy:sigma.λz:r x y.l_e_st_eq_11_t2 sigma r refr1 symr1 trr1 alpha fu2 ff2 x y z) e u uee : l_e_is (Πx:sigma.alpha) (fu2 u) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e)).
-
-(* notion 511 *)
-definition l_e_st_eq_11_t4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λuee:l_e_st_esti sigma u (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_fise sigma alpha (fu2 u) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e) (l_e_st_eq_11_t3 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr u uee) s : l_e_is alpha (fu2 u s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s)).
-
-(* notion 512 *)
-definition l_e_st_eq_11_t5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λuee:l_e_st_esti sigma u (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_fise sigma alpha (fu2 u) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e) (l_e_st_eq_11_t3 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr u uee) t : l_e_is alpha (fu2 u t) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t)).
-
-(* notion 513 *)
-definition l_e_st_eq_11_t6 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λuee:l_e_st_esti sigma u (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(ff2 u u s t (l_e_st_eq_refr sigma r refr1 symr1 trr1 u) tsr : l_e_is alpha (fu2 u s) (fu2 u t)).
-
-(* notion 514 *)
-definition l_e_st_eq_11_t7 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λuee:l_e_st_esti sigma u (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_tr3is alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s) (fu2 u s) (fu2 u t) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t) (l_e_symis alpha (fu2 u s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s) (l_e_st_eq_11_t4 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr u uee)) (l_e_st_eq_11_t6 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr u uee) (l_e_st_eq_11_t5 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr u uee) : l_e_is alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t)).
-
-(* notion 515 *)
-definition l_e_st_eq_11_t8 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.(l_e_st_eq_4_th3 sigma r refr1 symr1 trr1 e (l_e_is alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t)) (λx:sigma.λy:l_e_st_esti sigma x (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).l_e_st_eq_11_t7 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr x y) : l_e_is alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t)).
-
-(* notion 516 *)
-definition l_e_st_eq_indeq2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_st_eq_indeq sigma r refr1 symr1 trr1 alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e) (λx:sigma.λy:sigma.λz:r x y.l_e_st_eq_11_t8 sigma r refr1 symr1 trr1 alpha fu2 ff2 e x y z) f : alpha).
-
-(* notion 517 *)
-definition l_e_st_eq_11_t9 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).(l_e_st_eq_10_th2 sigma r refr1 symr1 trr1 alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e) (λx:sigma.λy:sigma.λz:r x y.l_e_st_eq_11_t8 sigma r refr1 symr1 trr1 alpha fu2 ff2 e x y z) f t tef : l_e_is alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t) (l_e_st_eq_indeq2 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f)).
-
-(* notion 518 *)
-definition l_e_st_eq_11_t10 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).(l_e_st_eq_10_th2 sigma r refr1 symr1 trr1 (Πx:sigma.alpha) fu2 (λx:sigma.λy:sigma.λz:r x y.l_e_st_eq_11_t2 sigma r refr1 symr1 trr1 alpha fu2 ff2 x y z) e s see : l_e_is (Πx:sigma.alpha) (fu2 s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e)).
-
-(* notion 519 *)
-definition l_e_st_eq_11_t11 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).(l_e_fise sigma alpha (fu2 s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e) (l_e_st_eq_11_t10 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f s see t tef) t : l_e_is alpha (fu2 s t) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t)).
-
-(* notion 520 *)
-definition l_e_st_eq_11_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).(l_e_tris alpha (fu2 s t) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t) (l_e_st_eq_indeq2 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f) (l_e_st_eq_11_t11 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f s see t tef) (l_e_st_eq_11_t9 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f s see t tef) : l_e_is alpha (fu2 s t) (l_e_st_eq_indeq2 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f)).
-
-(* notion 521 *)
-definition l_e_st_eq_11_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λs:sigma.λt:sigma.(l_e_st_eq_11_th1 sigma r refr1 symr1 trr1 alpha fu2 ff2 (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 t) s (l_e_st_eq_4_th5 sigma r refr1 symr1 trr1 s) t (l_e_st_eq_4_th5 sigma r refr1 symr1 trr1 t) : l_e_is alpha (fu2 s t) (l_e_st_eq_indeq2 sigma r refr1 symr1 trr1 alpha fu2 ff2 (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 t))).
-
-(* notion 522 *)
-axiom l_e_st_eq_landau_n_nat : Type[0].
-
-(* notion 523 *)
-definition l_e_st_eq_landau_n_is ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_is l_e_st_eq_landau_n_nat x y : Prop).
-
-(* notion 524 *)
-definition l_e_st_eq_landau_n_nis ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_not (l_e_st_eq_landau_n_is x y) : Prop).
-
-(* notion 525 *)
-definition l_e_st_eq_landau_n_in ≝ λx:l_e_st_eq_landau_n_nat.λs:l_e_st_set l_e_st_eq_landau_n_nat.(l_e_st_esti l_e_st_eq_landau_n_nat x s : Prop).
-
-(* notion 526 *)
-definition l_e_st_eq_landau_n_some ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.(l_some l_e_st_eq_landau_n_nat p : Prop).
-
-(* notion 527 *)
-definition l_e_st_eq_landau_n_all ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.(l_all l_e_st_eq_landau_n_nat p : Prop).
-
-(* notion 528 *)
-definition l_e_st_eq_landau_n_one ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.(l_e_one l_e_st_eq_landau_n_nat p : Prop).
-
-(* notion 529 *)
-axiom l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat.
-
-(* notion 530 *)
-axiom l_e_st_eq_landau_n_suc : Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.
-
-(* notion 531 *)
-definition l_e_st_eq_landau_n_ax2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_suc x y i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y)).
-
-(* notion 532 *)
-axiom l_e_st_eq_landau_n_ax3 : Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc x) l_e_st_eq_landau_n_1.
-
-(* notion 533 *)
-axiom l_e_st_eq_landau_n_ax4 : Πx:l_e_st_eq_landau_n_nat.Πy:l_e_st_eq_landau_n_nat.Πu:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y).l_e_st_eq_landau_n_is x y.
-
-(* notion 534 *)
-definition l_e_st_eq_landau_n_cond1 ≝ λs:l_e_st_set l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_in l_e_st_eq_landau_n_1 s : Prop).
-
-(* notion 535 *)
-definition l_e_st_eq_landau_n_cond2 ≝ λs:l_e_st_set l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λx:l_e_st_eq_landau_n_nat.l_imp (l_e_st_eq_landau_n_in x s) (l_e_st_eq_landau_n_in (l_e_st_eq_landau_n_suc x) s)) : Prop).
-
-(* notion 536 *)
-axiom l_e_st_eq_landau_n_ax5 : Πs:l_e_st_set l_e_st_eq_landau_n_nat.Πu:l_e_st_eq_landau_n_cond1 s.Πv:l_e_st_eq_landau_n_cond2 s.Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_in x s.
-
-(* notion 537 *)
-definition l_e_st_eq_landau_n_i1_s ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.(l_e_st_setof l_e_st_eq_landau_n_nat p : l_e_st_set l_e_st_eq_landau_n_nat).
-
-(* notion 538 *)
-definition l_e_st_eq_landau_n_i1_t1 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.(l_e_st_estii l_e_st_eq_landau_n_nat p l_e_st_eq_landau_n_1 1p : l_e_st_eq_landau_n_cond1 (l_e_st_eq_landau_n_i1_s p 1p xsp x)).
-
-(* notion 539 *)
-definition l_e_st_eq_landau_n_i1_t2 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λyes:l_e_st_eq_landau_n_in y (l_e_st_eq_landau_n_i1_s p 1p xsp x).(l_e_st_estie l_e_st_eq_landau_n_nat p y yes : p y).
-
-(* notion 540 *)
-definition l_e_st_eq_landau_n_i1_t3 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λyes:l_e_st_eq_landau_n_in y (l_e_st_eq_landau_n_i1_s p 1p xsp x).(l_e_st_estii l_e_st_eq_landau_n_nat p (l_e_st_eq_landau_n_suc y) (xsp y (l_e_st_eq_landau_n_i1_t2 p 1p xsp x y yes)) : l_e_st_eq_landau_n_in (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_i1_s p 1p xsp x)).
-
-(* notion 541 *)
-definition l_e_st_eq_landau_n_i1_t4 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ax5 (l_e_st_eq_landau_n_i1_s p 1p xsp x) (l_e_st_eq_landau_n_i1_t1 p 1p xsp x) (λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_in y (l_e_st_eq_landau_n_i1_s p 1p xsp x).l_e_st_eq_landau_n_i1_t3 p 1p xsp x y u) x : l_e_st_eq_landau_n_in x (l_e_st_eq_landau_n_i1_s p 1p xsp x)).
-
-(* notion 542 *)
-definition l_e_st_eq_landau_n_induction ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.(l_e_st_estie l_e_st_eq_landau_n_nat p x (l_e_st_eq_landau_n_i1_t4 p 1p xsp x) : p x).
-
-(* notion 543 *)
-definition l_e_st_eq_landau_n_21_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x y.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y).(l_e_st_eq_landau_n_ax4 x y i : l_e_st_eq_landau_n_is x y).
-
-(* notion 544 *)
-definition l_e_st_eq_landau_n_satz1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x y.(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_is x y) n (λu:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y).l_e_st_eq_landau_n_21_t1 x y n u) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y)).
-
-(* notion 545 *)
-definition l_e_st_eq_landau_n_22_prop1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc x) x : Prop).
-
-(* notion 546 *)
-definition l_e_st_eq_landau_n_22_t1 ≝ (l_e_st_eq_landau_n_ax3 l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_22_prop1 l_e_st_eq_landau_n_1).
-
-(* notion 547 *)
-definition l_e_st_eq_landau_n_22_t2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_22_prop1 x.(l_e_st_eq_landau_n_satz1 (l_e_st_eq_landau_n_suc x) x p : l_e_st_eq_landau_n_22_prop1 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 548 *)
-definition l_e_st_eq_landau_n_satz2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_22_prop1 y) l_e_st_eq_landau_n_22_t1 (λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_22_prop1 y.l_e_st_eq_landau_n_22_t2 y u) x : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc x) x).
-
-(* notion 549 *)
-definition l_e_st_eq_landau_n_23_prop1 ≝ λx:l_e_st_eq_landau_n_nat.(l_or (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u))) : Prop).
-
-(* notion 550 *)
-definition l_e_st_eq_landau_n_23_t1 ≝ (l_ori1 (l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_suc u))) (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_23_prop1 l_e_st_eq_landau_n_1).
-
-(* notion 551 *)
-definition l_e_st_eq_landau_n_23_t2 ≝ λx:l_e_st_eq_landau_n_nat.(l_somei l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc u)) x (l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc x)) : l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc u))).
-
-(* notion 552 *)
-definition l_e_st_eq_landau_n_23_t3 ≝ λx:l_e_st_eq_landau_n_nat.(l_ori2 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc u))) (l_e_st_eq_landau_n_23_t2 x) : l_e_st_eq_landau_n_23_prop1 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 553 *)
-definition l_e_st_eq_landau_n_23_t4 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_23_prop1 y) l_e_st_eq_landau_n_23_t1 (Πy:l_e_st_eq_landau_n_nat.Πu:l_e_st_eq_landau_n_23_prop1 y.l_e_st_eq_landau_n_23_t3 y) x : l_e_st_eq_landau_n_23_prop1 x).
-
-(* notion 554 *)
-definition l_e_st_eq_landau_n_satz3 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_ore2 (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u))) (l_e_st_eq_landau_n_23_t4 x) n : l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u))).
-
-(* notion 555 *)
-definition l_e_st_eq_landau_n_23_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc y).λj:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc z).(l_e_st_eq_landau_n_ax4 y z (l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc z) x i j) : l_e_st_eq_landau_n_is y z).
-
-(* notion 556 *)
-definition l_e_st_eq_landau_n_23_t6 ≝ λx:l_e_st_eq_landau_n_nat.(λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc y).λv:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc z).l_e_st_eq_landau_n_23_t5 x y z u v : l_e_amone l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u))).
-
-(* notion 557 *)
-definition l_e_st_eq_landau_n_satz3a ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_onei l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_23_t6 x) (l_e_st_eq_landau_n_satz3 x n) : l_e_st_eq_landau_n_one (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u))).
-
-(* notion 558 *)
-definition l_e_st_eq_landau_n_24_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (f y))) : Prop).
-
-(* notion 559 *)
-definition l_e_st_eq_landau_n_24_prop2 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_and (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x f) : Prop).
-
-(* notion 560 *)
-definition l_e_st_eq_landau_n_24_prop3 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (a y) (b y) : Prop).
-
-(* notion 561 *)
-definition l_e_st_eq_landau_n_24_t1 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.(l_ande1 (l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x a) pa : l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)).
-
-(* notion 562 *)
-definition l_e_st_eq_landau_n_24_t2 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.(l_ande1 (l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x b) pb : l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)).
-
-(* notion 563 *)
-definition l_e_st_eq_landau_n_24_t3 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.(l_e_tris2 l_e_st_eq_landau_n_nat (a l_e_st_eq_landau_n_1) (b l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_24_t1 x a b pa pb) (l_e_st_eq_landau_n_24_t2 x a b pa pb) : l_e_st_eq_landau_n_24_prop3 x a b pa pb l_e_st_eq_landau_n_1).
-
-(* notion 564 *)
-definition l_e_st_eq_landau_n_24_t4 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_e_st_eq_landau_n_ax2 (a y) (b y) p : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (a y)) (l_e_st_eq_landau_n_suc (b y))).
-
-(* notion 565 *)
-definition l_e_st_eq_landau_n_24_t5 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_ande2 (l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x a) pa : l_e_st_eq_landau_n_24_prop1 x a).
-
-(* notion 566 *)
-definition l_e_st_eq_landau_n_24_t6 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_ande2 (l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x b) pb : l_e_st_eq_landau_n_24_prop1 x b).
-
-(* notion 567 *)
-definition l_e_st_eq_landau_n_24_t7 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_e_st_eq_landau_n_24_t5 x a b pa pb y p y : l_e_st_eq_landau_n_is (a (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (a y))).
-
-(* notion 568 *)
-definition l_e_st_eq_landau_n_24_t8 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_e_st_eq_landau_n_24_t6 x a b pa pb y p y : l_e_st_eq_landau_n_is (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (b y))).
-
-(* notion 569 *)
-definition l_e_st_eq_landau_n_24_t9 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_e_tr3is l_e_st_eq_landau_n_nat (a (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (a y)) (l_e_st_eq_landau_n_suc (b y)) (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_24_t7 x a b pa pb y p) (l_e_st_eq_landau_n_24_t4 x a b pa pb y p) (l_e_symis l_e_st_eq_landau_n_nat (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (b y)) (l_e_st_eq_landau_n_24_t8 x a b pa pb y p)) : l_e_st_eq_landau_n_24_prop3 x a b pa pb (l_e_st_eq_landau_n_suc y)).
-
-(* notion 570 *)
-definition l_e_st_eq_landau_n_24_t10 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop3 x a b pa pb z) (l_e_st_eq_landau_n_24_t3 x a b pa pb) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_24_prop3 x a b pa pb z.l_e_st_eq_landau_n_24_t9 x a b pa pb z u) y : l_e_st_eq_landau_n_24_prop3 x a b pa pb y).
-
-(* notion 571 *)
-definition l_e_st_eq_landau_n_24_t11 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.(l_e_fisi l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat a b (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_t10 x a b pa pb y) : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) a b).
-
-(* notion 572 *)
-definition l_e_st_eq_landau_n_24_aa ≝ λx:l_e_st_eq_landau_n_nat.(λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λu:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_24_prop2 x z.λw:l_e_st_eq_landau_n_24_prop2 x u.l_e_st_eq_landau_n_24_t11 x z u v w : l_e_amone (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z)).
-
-(* notion 573 *)
-definition l_e_st_eq_landau_n_24_prop4 ≝ λx:l_e_st_eq_landau_n_nat.(l_some (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z) : Prop).
-
-(* notion 574 *)
-definition l_e_st_eq_landau_n_24_t12 ≝ (λx:l_e_st_eq_landau_n_nat.l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_suc x)) : l_e_st_eq_landau_n_24_prop1 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_suc).
-
-(* notion 575 *)
-definition l_e_st_eq_landau_n_24_t13 ≝ (l_andi (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_24_prop1 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_suc) (l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_24_t12 : l_e_st_eq_landau_n_24_prop2 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_suc).
-
-(* notion 576 *)
-definition l_e_st_eq_landau_n_24_t14 ≝ (l_somei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 l_e_st_eq_landau_n_1 z) l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_24_t13 : l_e_st_eq_landau_n_24_prop4 l_e_st_eq_landau_n_1).
-
-(* notion 577 *)
-definition l_e_st_eq_landau_n_24_g ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_suc (f y) : Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
-
-(* notion 578 *)
-definition l_e_st_eq_landau_n_24_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_24_g x p f pf y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_24_g x p f pf y) (l_e_st_eq_landau_n_suc (f y))).
-
-(* notion 579 *)
-definition l_e_st_eq_landau_n_24_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(l_ande1 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x f) pf : l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)).
-
-(* notion 580 *)
-definition l_e_st_eq_landau_n_24_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_24_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (f l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_t15 x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ax2 (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_24_t16 x p f pf)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_24_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_suc x))).
-
-(* notion 581 *)
-definition l_e_st_eq_landau_n_24_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_ande2 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x f) pf : l_e_st_eq_landau_n_24_prop1 x f).
-
-(* notion 582 *)
-definition l_e_st_eq_landau_n_24_t19 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_24_t18 x p f pf y y : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (f y))).
-
-(* notion 583 *)
-definition l_e_st_eq_landau_n_24_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_nat (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_24_g x p f pf y) (l_e_st_eq_landau_n_suc (f y)) (l_e_st_eq_landau_n_24_t19 x p f pf y) (l_e_st_eq_landau_n_24_t15 x p f pf y) : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_24_g x p f pf y)).
-
-(* notion 584 *)
-definition l_e_st_eq_landau_n_24_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_24_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (f (l_e_st_eq_landau_n_suc y))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_24_g x p f pf y)) (l_e_st_eq_landau_n_24_t15 x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_ax2 (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_24_g x p f pf y) (l_e_st_eq_landau_n_24_t20 x p f pf y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_24_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_24_g x p f pf y))).
-
-(* notion 585 *)
-definition l_e_st_eq_landau_n_24_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_t21 x p f pf y : l_e_st_eq_landau_n_24_prop1 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_24_g x p f pf)).
-
-(* notion 586 *)
-definition l_e_st_eq_landau_n_24_t23 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(l_andi (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_24_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_suc x))) (l_e_st_eq_landau_n_24_prop1 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_24_g x p f pf)) (l_e_st_eq_landau_n_24_t17 x p f pf) (l_e_st_eq_landau_n_24_t22 x p f pf) : l_e_st_eq_landau_n_24_prop2 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_24_g x p f pf)).
-
-(* notion 587 *)
-definition l_e_st_eq_landau_n_24_t24 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(l_somei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 (l_e_st_eq_landau_n_suc x) z) (l_e_st_eq_landau_n_24_g x p f pf) (l_e_st_eq_landau_n_24_t23 x p f pf) : l_e_st_eq_landau_n_24_prop4 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 588 *)
-definition l_e_st_eq_landau_n_24_t25 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.(l_someapp (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z) p (l_e_st_eq_landau_n_24_prop4 (l_e_st_eq_landau_n_suc x)) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_24_prop2 x z.l_e_st_eq_landau_n_24_t24 x p z u) : l_e_st_eq_landau_n_24_prop4 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 589 *)
-definition l_e_st_eq_landau_n_24_bb ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop4 y) l_e_st_eq_landau_n_24_t14 (λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_24_prop4 y.l_e_st_eq_landau_n_24_t25 y u) x : l_e_st_eq_landau_n_24_prop4 x).
-
-(* notion 590 *)
-definition l_e_st_eq_landau_n_satz4 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_onei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z) (l_e_st_eq_landau_n_24_aa x) (l_e_st_eq_landau_n_24_bb x) : l_e_one (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_is (z l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_all (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (z (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (z y)))))).
-
-(* notion 591 *)
-definition l_e_st_eq_landau_n_plus ≝ λx:l_e_st_eq_landau_n_nat.(l_e_ind (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z) (l_e_st_eq_landau_n_satz4 x) : Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
-
-(* notion 592 *)
-definition l_e_st_eq_landau_n_pl ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_plus x y : l_e_st_eq_landau_n_nat).
-
-(* notion 593 *)
-definition l_e_st_eq_landau_n_24_t26 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_oneax (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z) (l_e_st_eq_landau_n_satz4 x) : l_e_st_eq_landau_n_24_prop2 x (l_e_st_eq_landau_n_plus x)).
-
-(* notion 594 *)
-definition l_e_st_eq_landau_n_satz4a ≝ λx:l_e_st_eq_landau_n_nat.(l_ande1 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_plus x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x (l_e_st_eq_landau_n_plus x)) (l_e_st_eq_landau_n_24_t26 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)).
-
-(* notion 595 *)
-definition l_e_st_eq_landau_n_24_t27 ≝ λx:l_e_st_eq_landau_n_nat.(l_ande2 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_plus x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x (l_e_st_eq_landau_n_plus x)) (l_e_st_eq_landau_n_24_t26 x) : l_e_st_eq_landau_n_24_prop1 x (l_e_st_eq_landau_n_plus x)).
-
-(* notion 596 *)
-definition l_e_st_eq_landau_n_satz4b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_24_t27 x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y))).
-
-(* notion 597 *)
-definition l_e_st_eq_landau_n_24_t28 ≝ (l_e_st_eq_landau_n_24_t11 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_plus l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_24_t26 l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_24_t13 : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (l_e_st_eq_landau_n_plus l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_suc).
-
-(* notion 598 *)
-definition l_e_st_eq_landau_n_satz4c ≝ λx:l_e_st_eq_landau_n_nat.(l_e_fise l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_plus l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_24_t28 x : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_suc x)).
-
-(* notion 599 *)
-definition l_e_st_eq_landau_n_24_t29 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_24_t11 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_plus (l_e_st_eq_landau_n_suc x)) (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_plus x y)) (l_e_st_eq_landau_n_24_t26 (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_t23 x (l_e_st_eq_landau_n_24_bb x) (l_e_st_eq_landau_n_plus x) (l_e_st_eq_landau_n_24_t26 x)) : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (l_e_st_eq_landau_n_plus (l_e_st_eq_landau_n_suc x)) (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_plus x y))).
-
-(* notion 600 *)
-definition l_e_st_eq_landau_n_satz4d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_fise l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_plus (l_e_st_eq_landau_n_suc x)) (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_plus x z)) (l_e_st_eq_landau_n_24_t29 x) y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y))).
-
-(* notion 601 *)
-definition l_e_st_eq_landau_n_satz4e ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 602 *)
-definition l_e_st_eq_landau_n_satz4f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_satz4b x y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y))).
-
-(* notion 603 *)
-definition l_e_st_eq_landau_n_satz4g ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_satz4c x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 x)).
-
-(* notion 604 *)
-definition l_e_st_eq_landau_n_satz4h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_satz4d x y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y)).
-
-(* notion 605 *)
-definition l_e_st_eq_landau_n_ispl1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl u z) x y i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
-
-(* notion 606 *)
-definition l_e_st_eq_landau_n_ispl2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl z u) x y i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
-
-(* notion 607 *)
-definition l_e_st_eq_landau_n_ispl12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_ispl1 x y z i) (l_e_st_eq_landau_n_ispl2 z u y j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 608 *)
-definition l_e_st_eq_landau_n_25_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z)) : Prop).
-
-(* notion 609 *)
-definition l_e_st_eq_landau_n_25_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz4a (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_satz4f x y) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_satz4e y)) : l_e_st_eq_landau_n_25_prop1 x y l_e_st_eq_landau_n_1).
-
-(* notion 610 *)
-definition l_e_st_eq_landau_n_25_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_25_prop1 x y z.(l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z)) p : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z)))).
-
-(* notion 611 *)
-definition l_e_st_eq_landau_n_25_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_25_prop1 x y z.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_suc z)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z))) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y z))) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_satz4b (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_25_t2 x y z p) (l_e_st_eq_landau_n_satz4f x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z)) x (l_e_st_eq_landau_n_satz4f y z)) : l_e_st_eq_landau_n_25_prop1 x y (l_e_st_eq_landau_n_suc z)).
-
-(* notion 612 *)
-definition l_e_st_eq_landau_n_satz5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_25_prop1 x y u) (l_e_st_eq_landau_n_25_t1 x y) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_25_prop1 x y u.l_e_st_eq_landau_n_25_t3 x y u v) z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z))).
-
-(* notion 613 *)
-definition l_e_st_eq_landau_n_asspl1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz5 x y z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z))).
-
-(* notion 614 *)
-definition l_e_st_eq_landau_n_asspl2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_satz5 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z)).
-
-(* notion 615 *)
-definition l_e_st_eq_landau_n_26_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x) : Prop).
-
-(* notion 616 *)
-definition l_e_st_eq_landau_n_26_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz4a y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y)).
-
-(* notion 617 *)
-definition l_e_st_eq_landau_n_26_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz4c y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_suc y)).
-
-(* notion 618 *)
-definition l_e_st_eq_landau_n_26_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_26_t2 x y) (l_e_st_eq_landau_n_26_t1 x y) : l_e_st_eq_landau_n_26_prop1 l_e_st_eq_landau_n_1 y).
-
-(* notion 619 *)
-definition l_e_st_eq_landau_n_26_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_26_prop1 x y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y x)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x) p) (l_e_st_eq_landau_n_satz4f y x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x))).
-
-(* notion 620 *)
-definition l_e_st_eq_landau_n_26_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_26_prop1 x y.(l_e_st_eq_landau_n_satz4d x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y))).
-
-(* notion 621 *)
-definition l_e_st_eq_landau_n_26_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_26_prop1 x y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_26_t5 x y p) (l_e_st_eq_landau_n_26_t4 x y p) : l_e_st_eq_landau_n_26_prop1 (l_e_st_eq_landau_n_suc x) y).
-
-(* notion 622 *)
-definition l_e_st_eq_landau_n_satz6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_26_prop1 z y) (l_e_st_eq_landau_n_26_t3 x y) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_26_prop1 z y.l_e_st_eq_landau_n_26_t6 z y u) x : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x)).
-
-(* notion 623 *)
-definition l_e_st_eq_landau_n_compl ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz6 x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x)).
-
-(* notion 624 *)
-definition l_e_st_eq_landau_n_26_t7 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_satz4a x) (l_e_st_eq_landau_n_satz4g x) : l_e_st_eq_landau_n_26_prop1 x l_e_st_eq_landau_n_1).
-
-(* notion 625 *)
-definition l_e_st_eq_landau_n_26_t8 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_26_prop1 x y.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y x)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc y) x) (l_e_st_eq_landau_n_satz4b x y) (l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x) p) (l_e_st_eq_landau_n_satz4h y x) : l_e_st_eq_landau_n_26_prop1 x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 626 *)
-definition l_e_st_eq_landau_n_26_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_26_prop1 x z) (l_e_st_eq_landau_n_26_t7 x) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_26_prop1 x z.l_e_st_eq_landau_n_26_t8 x z u) y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x)).
-
-(* notion 627 *)
-definition l_e_st_eq_landau_n_27_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_nis y (l_e_st_eq_landau_n_pl x y) : Prop).
-
-(* notion 628 *)
-definition l_e_st_eq_landau_n_27_t1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symnotis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_ax3 x) : l_e_st_eq_landau_n_nis l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 629 *)
-definition l_e_st_eq_landau_n_27_t2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_notis_th4 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_27_t1 x) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_27_prop1 x l_e_st_eq_landau_n_1).
-
-(* notion 630 *)
-definition l_e_st_eq_landau_n_27_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_27_prop1 x y.(l_e_st_eq_landau_n_satz1 y (l_e_st_eq_landau_n_pl x y) p : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y))).
-
-(* notion 631 *)
-definition l_e_st_eq_landau_n_27_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_27_prop1 x y.(l_e_notis_th4 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_27_t3 x y p) (l_e_st_eq_landau_n_satz4b x y) : l_e_st_eq_landau_n_27_prop1 x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 632 *)
-definition l_e_st_eq_landau_n_satz7 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (Πz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_27_prop1 x z) (l_e_st_eq_landau_n_27_t2 x) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_27_prop1 x z.l_e_st_eq_landau_n_27_t4 x z u) y : l_e_st_eq_landau_n_nis y (l_e_st_eq_landau_n_pl x y)).
-
-(* notion 633 *)
-definition l_e_st_eq_landau_n_28_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.(l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z) : Prop).
-
-(* notion 634 *)
-definition l_e_st_eq_landau_n_28_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.(l_e_st_eq_landau_n_satz1 y z n : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc z)).
-
-(* notion 635 *)
-definition l_e_st_eq_landau_n_28_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.(l_e_notis_th5 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc z) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 z) (l_e_st_eq_landau_n_28_t1 x y z n) (l_e_st_eq_landau_n_satz4g y) (l_e_st_eq_landau_n_satz4g z) : l_e_st_eq_landau_n_28_prop1 l_e_st_eq_landau_n_1 y z n).
-
-(* notion 636 *)
-definition l_e_st_eq_landau_n_28_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.λp:l_e_st_eq_landau_n_28_prop1 x y z n.(l_e_st_eq_landau_n_satz1 (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z) p : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x z))).
-
-(* notion 637 *)
-definition l_e_st_eq_landau_n_28_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.λp:l_e_st_eq_landau_n_28_prop1 x y z n.(l_e_notis_th5 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) z) (l_e_st_eq_landau_n_28_t3 x y z n p) (l_e_st_eq_landau_n_satz4h x y) (l_e_st_eq_landau_n_satz4h x z) : l_e_st_eq_landau_n_28_prop1 (l_e_st_eq_landau_n_suc x) y z n).
-
-(* notion 638 *)
-definition l_e_st_eq_landau_n_satz8 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.(l_e_st_eq_landau_n_induction (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_28_prop1 u y z n) (l_e_st_eq_landau_n_28_t2 x y z n) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_28_prop1 u y z n.l_e_st_eq_landau_n_28_t4 u y z n v) x : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z)).
-
-(* notion 639 *)
-definition l_e_st_eq_landau_n_satz8a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z).(l_imp_th7 (l_e_st_eq_landau_n_is y z) (l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z)) (l_weli (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z)) i) (λu:l_e_st_eq_landau_n_nis y z.l_e_st_eq_landau_n_satz8 x y z u) : l_e_st_eq_landau_n_is y z).
-
-(* notion 640 *)
-definition l_e_st_eq_landau_n_diffprop ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl y z) : Prop).
-
-(* notion 641 *)
-definition l_e_st_eq_landau_n_28_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λdv:l_e_st_eq_landau_n_diffprop x y v.(l_e_st_eq_landau_n_satz8a y u v (l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl y v) x du dv) : l_e_st_eq_landau_n_is u v).
-
-(* notion 642 *)
-definition l_e_st_eq_landau_n_satz8b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λdv:l_e_st_eq_landau_n_diffprop x y v.l_e_st_eq_landau_n_28_t5 x y u v du dv : l_e_amone l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl y z))).
-
-(* notion 643 *)
-definition l_e_st_eq_landau_n_29_i ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is x y : Prop).
-
-(* notion 644 *)
-definition l_e_st_eq_landau_n_29_ii ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) : Prop).
-
-(* notion 645 *)
-definition l_e_st_eq_landau_n_29_iii ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_some (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v) : Prop).
-
-(* notion 646 *)
-definition l_e_st_eq_landau_n_29_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λone1:l_e_st_eq_landau_n_29_i x y.λu:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl u x) (l_e_st_eq_landau_n_pl x u) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_compl u x) (l_e_st_eq_landau_n_ispl1 x y u one1) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl u x) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 647 *)
-definition l_e_st_eq_landau_n_29_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λone1:l_e_st_eq_landau_n_29_i x y.λu:l_e_st_eq_landau_n_nat.(l_e_notis_th3 l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl u x) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_satz7 u x) (l_e_st_eq_landau_n_29_t1 x y one1 u) : l_e_st_eq_landau_n_nis x (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 648 *)
-definition l_e_st_eq_landau_n_29_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λone1:l_e_st_eq_landau_n_29_i x y.(l_some_th5 l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_29_t2 x y one1 u) : l_not (l_e_st_eq_landau_n_29_ii x y)).
-
-(* notion 649 *)
-definition l_e_st_eq_landau_n_29_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_ec_th1 (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (λz:l_e_st_eq_landau_n_29_i x y.l_e_st_eq_landau_n_29_t3 x y z) : l_ec (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y)).
-
-(* notion 650 *)
-definition l_e_st_eq_landau_n_29_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λone1:l_e_st_eq_landau_n_29_i x y.(l_e_st_eq_landau_n_29_t3 y x (l_e_symis l_e_st_eq_landau_n_nat x y one1) : l_not (l_e_st_eq_landau_n_29_iii x y)).
-
-(* notion 651 *)
-definition l_e_st_eq_landau_n_29_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_ec_th2 (l_e_st_eq_landau_n_29_iii x y) (l_e_st_eq_landau_n_29_i x y) (λz:l_e_st_eq_landau_n_29_i x y.l_e_st_eq_landau_n_29_t5 x y z) : l_ec (l_e_st_eq_landau_n_29_iii x y) (l_e_st_eq_landau_n_29_i x y)).
-
-(* notion 652 *)
-definition l_e_st_eq_landau_n_29_t6a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λtwo1:l_e_st_eq_landau_n_29_ii x y.λthree1:l_e_st_eq_landau_n_29_iii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.(l_e_tr4is l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x v) u) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl v u)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl v u) x) du (l_e_st_eq_landau_n_ispl1 y (l_e_st_eq_landau_n_pl x v) u dv) (l_e_st_eq_landau_n_asspl1 x v u) (l_e_st_eq_landau_n_compl x (l_e_st_eq_landau_n_pl v u)) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl v u) x)).
-
-(* notion 653 *)
-definition l_e_st_eq_landau_n_29_t7 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λtwo1:l_e_st_eq_landau_n_29_ii x y.λthree1:l_e_st_eq_landau_n_29_iii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.(l_mp (l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl v u) x)) l_con (l_e_st_eq_landau_n_29_t6a x y two1 three1 u du v dv) (l_e_st_eq_landau_n_satz7 (l_e_st_eq_landau_n_pl v u) x) : l_con).
-
-(* notion 654 *)
-definition l_e_st_eq_landau_n_29_t8 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λtwo1:l_e_st_eq_landau_n_29_ii x y.λthree1:l_e_st_eq_landau_n_29_iii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v) three1 l_con (λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.l_e_st_eq_landau_n_29_t7 x y two1 three1 u du v dv) : l_con).
-
-(* notion 655 *)
-definition l_e_st_eq_landau_n_29_t9 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λtwo1:l_e_st_eq_landau_n_29_ii x y.λthree1:l_e_st_eq_landau_n_29_iii x y.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) two1 l_con (λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.l_e_st_eq_landau_n_29_t8 x y two1 three1 u du) : l_con).
-
-(* notion 656 *)
-definition l_e_st_eq_landau_n_29_t10 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λtwo1:l_e_st_eq_landau_n_29_ii x y.(λz:l_e_st_eq_landau_n_29_iii x y.l_e_st_eq_landau_n_29_t9 x y two1 z : l_not (l_e_st_eq_landau_n_29_iii x y)).
-
-(* notion 657 *)
-definition l_e_st_eq_landau_n_29_t11 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_ec_th1 (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y) (λz:l_e_st_eq_landau_n_29_ii x y.l_e_st_eq_landau_n_29_t10 x y z) : l_ec (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y)).
-
-(* notion 658 *)
-definition l_e_st_eq_landau_n_29_a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_ec3_th6 (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y) (l_e_st_eq_landau_n_29_t4 x y) (l_e_st_eq_landau_n_29_t11 x y) (l_e_st_eq_landau_n_29_t6 x y) : l_ec3 (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y)).
-
-(* notion 659 *)
-definition l_e_st_eq_landau_n_29_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_or3 (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y) : Prop).
-
-(* notion 660 *)
-definition l_e_st_eq_landau_n_29_t12 ≝ λx:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_or3i1 (l_e_st_eq_landau_n_29_i x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_ii x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_iii x l_e_st_eq_landau_n_1) j : l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1).
-
-(* notion 661 *)
-definition l_e_st_eq_landau_n_29_t13 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_suc u) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u) j (l_e_st_eq_landau_n_satz4g u) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u)).
-
-(* notion 662 *)
-definition l_e_st_eq_landau_n_29_t14 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_somei l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x l_e_st_eq_landau_n_1 z) u (l_e_st_eq_landau_n_29_t13 x n u j) : l_e_st_eq_landau_n_29_ii x l_e_st_eq_landau_n_1).
-
-(* notion 663 *)
-definition l_e_st_eq_landau_n_29_t15 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_someapp l_e_st_eq_landau_n_nat (λu1:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u1)) (l_e_st_eq_landau_n_satz3 x n) (l_e_st_eq_landau_n_29_ii x l_e_st_eq_landau_n_1) (λu1:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u1).l_e_st_eq_landau_n_29_t14 x n u1 z) : l_e_st_eq_landau_n_29_ii x l_e_st_eq_landau_n_1).
-
-(* notion 664 *)
-definition l_e_st_eq_landau_n_29_t16 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_or3i2 (l_e_st_eq_landau_n_29_i x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_ii x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_iii x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_t15 x n u j) : l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1).
-
-(* notion 665 *)
-definition l_e_st_eq_landau_n_29_t16a ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_satz3 x n) (l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).l_e_st_eq_landau_n_29_t16 x n u v) : l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1).
-
-(* notion 666 *)
-definition l_e_st_eq_landau_n_29_t17 ≝ λx:l_e_st_eq_landau_n_nat.(l_imp_th1 (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1) (λz:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_29_t12 x z) (λz:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_29_t16a x z) : l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1).
-
-(* notion 667 *)
-definition l_e_st_eq_landau_n_29_t18 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λone1:l_e_st_eq_landau_n_29_i x y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz4e y) (l_e_st_eq_landau_n_ispl1 y x l_e_st_eq_landau_n_1 (l_e_symis l_e_st_eq_landau_n_nat x y one1)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 668 *)
-definition l_e_st_eq_landau_n_29_t19 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λone1:l_e_st_eq_landau_n_29_i x y.(l_somei l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_suc y) x z) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_29_t18 x y p one1) : l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 669 *)
-definition l_e_st_eq_landau_n_29_t20 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λone1:l_e_st_eq_landau_n_29_i x y.(l_or3i3 (l_e_st_eq_landau_n_29_i x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_t19 x y p one1) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 670 *)
-definition l_e_st_eq_landau_n_29_t21 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λj:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y) du (l_e_st_eq_landau_n_ispl2 u l_e_st_eq_landau_n_1 y j) (l_e_st_eq_landau_n_satz4a y) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 671 *)
-definition l_e_st_eq_landau_n_29_t22 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λj:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_or3i1 (l_e_st_eq_landau_n_29_i x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_t21 x y p two1 u du j) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 672 *)
-definition l_e_st_eq_landau_n_29_t23 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λn:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.λw:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_suc w).(l_e_tris l_e_st_eq_landau_n_nat u (l_e_st_eq_landau_n_suc w) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 w) j (l_e_st_eq_landau_n_satz4g w) : l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 w)).
-
-(* notion 673 *)
-definition l_e_st_eq_landau_n_29_t24 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λn:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.λw:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_suc w).(l_e_tr4is l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) w) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc y) w) du (l_e_st_eq_landau_n_ispl2 u (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 w) y (l_e_st_eq_landau_n_29_t23 x y p two1 u du n w j)) (l_e_st_eq_landau_n_asspl2 y l_e_st_eq_landau_n_1 w) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y) w (l_e_st_eq_landau_n_satz4a y)) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc y) w)).
-
-(* notion 674 *)
-definition l_e_st_eq_landau_n_29_t25 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λn:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.λw:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_suc w).(l_somei l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x (l_e_st_eq_landau_n_suc y) z) w (l_e_st_eq_landau_n_29_t24 x y p two1 u du n w j) : l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 675 *)
-definition l_e_st_eq_landau_n_29_t26 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λn:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.(l_someapp l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_suc z)) (l_e_st_eq_landau_n_satz3 u n) (l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)) (λz:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_suc z).l_e_st_eq_landau_n_29_t25 x y p two1 u du n z v) : l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 676 *)
-definition l_e_st_eq_landau_n_29_t27 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λn:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.(l_or3i2 (l_e_st_eq_landau_n_29_i x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_t26 x y p two1 u du n) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 677 *)
-definition l_e_st_eq_landau_n_29_t28 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_imp_th1 (l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)) (λz:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_29_t22 x y p two1 u du z) (λz:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_29_t27 x y p two1 u du z) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 678 *)
-definition l_e_st_eq_landau_n_29_t28a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) two1 (l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)) (λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.l_e_st_eq_landau_n_29_t28 x y p two1 u du) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 679 *)
-definition l_e_st_eq_landau_n_29_t29 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λthree1:l_e_st_eq_landau_n_29_iii x y.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x v)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc v)) (l_e_st_eq_landau_n_ax2 y (l_e_st_eq_landau_n_pl x v) dv) (l_e_st_eq_landau_n_satz4f x v) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc v))).
-
-(* notion 680 *)
-definition l_e_st_eq_landau_n_29_t30 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λthree1:l_e_st_eq_landau_n_29_iii x y.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.(l_somei l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_suc y) x z) (l_e_st_eq_landau_n_suc v) (l_e_st_eq_landau_n_29_t29 x y p three1 v dv) : l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 681 *)
-definition l_e_st_eq_landau_n_29_t31 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λthree1:l_e_st_eq_landau_n_29_iii x y.(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v) three1 (l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)) (λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.l_e_st_eq_landau_n_29_t30 x y p three1 v dv) : l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 682 *)
-definition l_e_st_eq_landau_n_29_t32 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λthree1:l_e_st_eq_landau_n_29_iii x y.(l_or3i3 (l_e_st_eq_landau_n_29_i x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_t31 x y p three1) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 683 *)
-definition l_e_st_eq_landau_n_29_t33 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.(l_or3app (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y) (l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)) p (λz:l_e_st_eq_landau_n_29_i x y.l_e_st_eq_landau_n_29_t20 x y p z) (λz:l_e_st_eq_landau_n_29_ii x y.l_e_st_eq_landau_n_29_t28a x y p z) (λz:l_e_st_eq_landau_n_29_iii x y.l_e_st_eq_landau_n_29_t32 x y p z) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 684 *)
-definition l_e_st_eq_landau_n_29_b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_29_prop1 x z) (l_e_st_eq_landau_n_29_t17 x) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_29_prop1 x z.l_e_st_eq_landau_n_29_t33 x z u) y : l_or3 (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y)).
-
-(* notion 685 *)
-definition l_e_st_eq_landau_n_satz9 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_orec3i (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y) (l_e_st_eq_landau_n_29_b x y) (l_e_st_eq_landau_n_29_a x y) : l_orec3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl y u))) (l_e_st_eq_landau_n_some (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is y (l_e_st_eq_landau_n_pl x v)))).
-
-(* notion 686 *)
-definition l_e_st_eq_landau_n_satz9a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_29_b x y : l_or3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u)) (l_e_st_eq_landau_n_some (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v))).
-
-(* notion 687 *)
-definition l_e_st_eq_landau_n_satz9b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_29_a x y : l_ec3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u)) (l_e_st_eq_landau_n_some (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v))).
-
-(* notion 688 *)
-definition l_e_st_eq_landau_n_more ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) : Prop).
-
-(* notion 689 *)
-definition l_e_st_eq_landau_n_less ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_some (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v) : Prop).
-
-(* notion 690 *)
-definition l_e_st_eq_landau_n_satz10 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz9 x y : l_orec3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y)).
-
-(* notion 691 *)
-definition l_e_st_eq_landau_n_satz10a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz9a x y : l_or3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y)).
-
-(* notion 692 *)
-definition l_e_st_eq_landau_n_satz10b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz9b x y : l_ec3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y)).
-
-(* notion 693 *)
-definition l_e_st_eq_landau_n_satz11 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(m : l_e_st_eq_landau_n_less y x).
-
-(* notion 694 *)
-definition l_e_st_eq_landau_n_satz12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l : l_e_st_eq_landau_n_more y x).
-
-(* notion 695 *)
-definition l_e_st_eq_landau_n_moreis ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_or (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) : Prop).
-
-(* notion 696 *)
-definition l_e_st_eq_landau_n_lessis ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_or (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) : Prop).
-
-(* notion 697 *)
-definition l_e_st_eq_landau_n_satz13 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_or_th9 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_less y x) (l_e_st_eq_landau_n_is y x) m (λz:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz11 x y z) (λz:l_e_st_eq_landau_n_is x y.l_e_symis l_e_st_eq_landau_n_nat x y z) : l_e_st_eq_landau_n_lessis y x).
-
-(* notion 698 *)
-definition l_e_st_eq_landau_n_satz14 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_or_th9 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more y x) (l_e_st_eq_landau_n_is y x) l (λz:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz12 x y z) (λz:l_e_st_eq_landau_n_is x y.l_e_symis l_e_st_eq_landau_n_nat x y z) : l_e_st_eq_landau_n_moreis y x).
-
-(* notion 699 *)
-definition l_e_st_eq_landau_n_ismore1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more x z.(l_e_isp l_e_st_eq_landau_n_nat (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_more u z) x y m i : l_e_st_eq_landau_n_more y z).
-
-(* notion 700 *)
-definition l_e_st_eq_landau_n_ismore2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more z x.(l_e_isp l_e_st_eq_landau_n_nat (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_more z u) x y m i : l_e_st_eq_landau_n_more z y).
-
-(* notion 701 *)
-definition l_e_st_eq_landau_n_isless1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less x z.(l_e_isp l_e_st_eq_landau_n_nat (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_less u z) x y l i : l_e_st_eq_landau_n_less y z).
-
-(* notion 702 *)
-definition l_e_st_eq_landau_n_isless2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less z x.(l_e_isp l_e_st_eq_landau_n_nat (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_less z u) x y l i : l_e_st_eq_landau_n_less z y).
-
-(* notion 703 *)
-definition l_e_st_eq_landau_n_ismoreis1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_moreis x z.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_moreis u z) x y m i : l_e_st_eq_landau_n_moreis y z).
-
-(* notion 704 *)
-definition l_e_st_eq_landau_n_ismoreis2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_moreis z x.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_moreis z u) x y m i : l_e_st_eq_landau_n_moreis z y).
-
-(* notion 705 *)
-definition l_e_st_eq_landau_n_islessis1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_lessis x z.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis u z) x y l i : l_e_st_eq_landau_n_lessis y z).
-
-(* notion 706 *)
-definition l_e_st_eq_landau_n_islessis2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_lessis z x.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis z u) x y l i : l_e_st_eq_landau_n_lessis z y).
-
-(* notion 707 *)
-definition l_e_st_eq_landau_n_moreisi2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_ori2 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) i : l_e_st_eq_landau_n_moreis x y).
-
-(* notion 708 *)
-definition l_e_st_eq_landau_n_lessisi2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_ori2 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) i : l_e_st_eq_landau_n_lessis x y).
-
-(* notion 709 *)
-definition l_e_st_eq_landau_n_moreisi1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_ori1 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) m : l_e_st_eq_landau_n_moreis x y).
-
-(* notion 710 *)
-definition l_e_st_eq_landau_n_lessisi1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_ori1 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) l : l_e_st_eq_landau_n_lessis x y).
-
-(* notion 711 *)
-definition l_e_st_eq_landau_n_ismore12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.λm:l_e_st_eq_landau_n_more x z.(l_e_st_eq_landau_n_ismore2 z u y j (l_e_st_eq_landau_n_ismore1 x y z i m) : l_e_st_eq_landau_n_more y u).
-
-(* notion 712 *)
-definition l_e_st_eq_landau_n_isless12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.λl:l_e_st_eq_landau_n_less x z.(l_e_st_eq_landau_n_isless2 z u y j (l_e_st_eq_landau_n_isless1 x y z i l) : l_e_st_eq_landau_n_less y u).
-
-(* notion 713 *)
-definition l_e_st_eq_landau_n_ismoreis12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.λm:l_e_st_eq_landau_n_moreis x z.(l_e_st_eq_landau_n_ismoreis2 z u y j (l_e_st_eq_landau_n_ismoreis1 x y z i m) : l_e_st_eq_landau_n_moreis y u).
-
-(* notion 714 *)
-definition l_e_st_eq_landau_n_islessis12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.λl:l_e_st_eq_landau_n_lessis x z.(l_e_st_eq_landau_n_islessis2 z u y j (l_e_st_eq_landau_n_islessis1 x y z i l) : l_e_st_eq_landau_n_lessis y u).
-
-(* notion 715 *)
-definition l_e_st_eq_landau_n_satz10c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_ec3_th7 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) (l_comor (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) m) : l_not (l_e_st_eq_landau_n_less x y)).
-
-(* notion 716 *)
-definition l_e_st_eq_landau_n_satz10d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_ec3_th9 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) l : l_not (l_e_st_eq_landau_n_more x y)).
-
-(* notion 717 *)
-definition l_e_st_eq_landau_n_satz10e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_not (l_e_st_eq_landau_n_more x y).(l_or3_th2 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10a x y) n : l_e_st_eq_landau_n_lessis x y).
-
-(* notion 718 *)
-definition l_e_st_eq_landau_n_satz10f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_not (l_e_st_eq_landau_n_less x y).(l_comor (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_or3_th3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10a x y) n) : l_e_st_eq_landau_n_moreis x y).
-
-(* notion 719 *)
-definition l_e_st_eq_landau_n_satz10g ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_or_th3 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) (l_ec3e23 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) m) (l_ec3e21 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) m) : l_not (l_e_st_eq_landau_n_lessis x y)).
-
-(* notion 720 *)
-definition l_e_st_eq_landau_n_satz10h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_or_th3 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_ec3e32 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) l) (l_ec3e31 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) l) : l_not (l_e_st_eq_landau_n_moreis x y)).
-
-(* notion 721 *)
-definition l_e_st_eq_landau_n_satz10j ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_not (l_e_st_eq_landau_n_moreis x y).(l_or3e3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10a x y) (l_or_th5 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) n) (l_or_th4 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) n) : l_e_st_eq_landau_n_less x y).
-
-(* notion 722 *)
-definition l_e_st_eq_landau_n_satz10k ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_not (l_e_st_eq_landau_n_lessis x y).(l_or3e2 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10a x y) (l_or_th4 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) n) (l_or_th5 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) n) : l_e_st_eq_landau_n_more x y).
-
-(* notion 723 *)
-definition l_e_st_eq_landau_n_315_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less y z.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.λw:l_e_st_eq_landau_n_nat.λdw:l_e_st_eq_landau_n_diffprop z y w.(l_e_tr3is l_e_st_eq_landau_n_nat z (l_e_st_eq_landau_n_pl y w) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x v) w) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl v w)) dw (l_e_st_eq_landau_n_ispl1 y (l_e_st_eq_landau_n_pl x v) w dv) (l_e_st_eq_landau_n_asspl1 x v w) : l_e_st_eq_landau_n_is z (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl v w))).
-
-(* notion 724 *)
-definition l_e_st_eq_landau_n_315_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less y z.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.λw:l_e_st_eq_landau_n_nat.λdw:l_e_st_eq_landau_n_diffprop z y w.(l_somei l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop z x u) (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_315_t1 x y z l k v dv w dw) : l_e_st_eq_landau_n_less x z).
-
-(* notion 725 *)
-definition l_e_st_eq_landau_n_315_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less y z.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.(l_someapp l_e_st_eq_landau_n_nat (λw:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop z y w) k (l_e_st_eq_landau_n_less x z) (λw:l_e_st_eq_landau_n_nat.λdw:l_e_st_eq_landau_n_diffprop z y w.l_e_st_eq_landau_n_315_t2 x y z l k v dv w dw) : l_e_st_eq_landau_n_less x z).
-
-(* notion 726 *)
-definition l_e_st_eq_landau_n_satz15 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less y z.(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v) l (l_e_st_eq_landau_n_less x z) (λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.l_e_st_eq_landau_n_315_t3 x y z l k v dv) : l_e_st_eq_landau_n_less x z).
-
-(* notion 727 *)
-definition l_e_st_eq_landau_n_trless ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less y z.(l_e_st_eq_landau_n_satz15 x y z l k : l_e_st_eq_landau_n_less x z).
-
-(* notion 728 *)
-definition l_e_st_eq_landau_n_trmore ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more y z.(l_e_st_eq_landau_n_satz15 z y x n m : l_e_st_eq_landau_n_more x z).
-
-(* notion 729 *)
-definition l_e_st_eq_landau_n_315_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more y z.(l_e_st_eq_landau_n_satz12 z x (l_e_st_eq_landau_n_satz15 z y x (l_e_st_eq_landau_n_satz11 y z n) (l_e_st_eq_landau_n_satz11 x y m)) : l_e_st_eq_landau_n_more x z).
-
-(* notion 730 *)
-definition l_e_st_eq_landau_n_satz16a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_less y z.(l_orapp (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_less x z) l (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_trless x y z u k) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_isless1 y x z (l_e_symis l_e_st_eq_landau_n_nat x y u) k) : l_e_st_eq_landau_n_less x z).
-
-(* notion 731 *)
-definition l_e_st_eq_landau_n_satz16b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_lessis y z.(l_orapp (l_e_st_eq_landau_n_less y z) (l_e_st_eq_landau_n_is y z) (l_e_st_eq_landau_n_less x z) k (λu:l_e_st_eq_landau_n_less y z.l_e_st_eq_landau_n_trless x y z l u) (λu:l_e_st_eq_landau_n_is y z.l_e_st_eq_landau_n_isless2 y z x u l) : l_e_st_eq_landau_n_less x z).
-
-(* notion 732 *)
-definition l_e_st_eq_landau_n_satz16c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_more y z.(l_e_st_eq_landau_n_satz16b z y x n (l_e_st_eq_landau_n_satz13 x y m) : l_e_st_eq_landau_n_more x z).
-
-(* notion 733 *)
-definition l_e_st_eq_landau_n_satz16d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_moreis y z.(l_e_st_eq_landau_n_satz16a z y x (l_e_st_eq_landau_n_satz13 y z n) m : l_e_st_eq_landau_n_more x z).
-
-(* notion 734 *)
-definition l_e_st_eq_landau_n_317_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is y z.(l_e_st_eq_landau_n_lessisi2 x z (l_e_tris l_e_st_eq_landau_n_nat x y z i j) : l_e_st_eq_landau_n_lessis x z).
-
-(* notion 735 *)
-definition l_e_st_eq_landau_n_317_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_less y z.(l_e_st_eq_landau_n_lessisi1 x z (l_e_st_eq_landau_n_satz16a x y z l j) : l_e_st_eq_landau_n_lessis x z).
-
-(* notion 736 *)
-definition l_e_st_eq_landau_n_317_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λi:l_e_st_eq_landau_n_is x y.(l_orapp (l_e_st_eq_landau_n_less y z) (l_e_st_eq_landau_n_is y z) (l_e_st_eq_landau_n_lessis x z) k (λu:l_e_st_eq_landau_n_less y z.l_e_st_eq_landau_n_317_t2 x y z l k i u) (λu:l_e_st_eq_landau_n_is y z.l_e_st_eq_landau_n_317_t1 x y z l k i u) : l_e_st_eq_landau_n_lessis x z).
-
-(* notion 737 *)
-definition l_e_st_eq_landau_n_317_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λj:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_lessisi1 x z (l_e_st_eq_landau_n_satz16b x y z j k) : l_e_st_eq_landau_n_lessis x z).
-
-(* notion 738 *)
-definition l_e_st_eq_landau_n_satz17 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.(l_orapp (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_lessis x z) l (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_317_t4 x y z l k u) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_317_t3 x y z l k u) : l_e_st_eq_landau_n_lessis x z).
-
-(* notion 739 *)
-definition l_e_st_eq_landau_n_317_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λj:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_lessisi1 x z (l_e_st_eq_landau_n_satz16b x y z j k) : l_e_st_eq_landau_n_lessis x z).
-
-(* notion 740 *)
-definition l_e_st_eq_landau_n_317_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_islessis1 y x z (l_e_symis l_e_st_eq_landau_n_nat x y i) k : l_e_st_eq_landau_n_lessis x z).
-
-(* notion 741 *)
-definition l_e_st_eq_landau_n_317_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.(l_orapp (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_lessis x z) l (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_317_t5 x y z l k u) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_317_t6 x y z l k u) : l_e_st_eq_landau_n_lessis x z).
-
-(* notion 742 *)
-definition l_e_st_eq_landau_n_trlessis ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.(l_e_st_eq_landau_n_satz17 x y z l k : l_e_st_eq_landau_n_lessis x z).
-
-(* notion 743 *)
-definition l_e_st_eq_landau_n_trmoreis ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis y z.(l_e_st_eq_landau_n_satz14 z x (l_e_st_eq_landau_n_satz17 z y x (l_e_st_eq_landau_n_satz13 y z n) (l_e_st_eq_landau_n_satz13 x y m)) : l_e_st_eq_landau_n_moreis x z).
-
-(* notion 744 *)
-definition l_e_st_eq_landau_n_satz18 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_somei l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_pl x y) x u) y (l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x y)) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x y) x).
-
-(* notion 745 *)
-definition l_e_st_eq_landau_n_satz18a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz18 x y : l_e_st_eq_landau_n_less x (l_e_st_eq_landau_n_pl x y)).
-
-(* notion 746 *)
-definition l_e_st_eq_landau_n_satz18b ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) x (l_e_st_eq_landau_n_satz4a x) (l_e_st_eq_landau_n_satz18 x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc x) x).
-
-(* notion 747 *)
-definition l_e_st_eq_landau_n_satz18c ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz18b x : l_e_st_eq_landau_n_less x (l_e_st_eq_landau_n_suc x)).
-
-(* notion 748 *)
-definition l_e_st_eq_landau_n_319_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl u y) du (l_e_st_eq_landau_n_compl y u) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl u y)).
-
-(* notion 749 *)
-definition l_e_st_eq_landau_n_319_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl u y) z) (l_e_st_eq_landau_n_pl u (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl y z) u) (l_e_st_eq_landau_n_ispl1 x (l_e_st_eq_landau_n_pl u y) z (l_e_st_eq_landau_n_319_t1 x y z m u du)) (l_e_st_eq_landau_n_asspl1 u y z) (l_e_st_eq_landau_n_compl u (l_e_st_eq_landau_n_pl y z)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl y z) u)).
-
-(* notion 750 *)
-definition l_e_st_eq_landau_n_319_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_somei l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) v) u (l_e_st_eq_landau_n_319_t2 x y z m u du) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
-
-(* notion 751 *)
-definition l_e_st_eq_landau_n_satz19a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) m (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_diffprop x y u.l_e_st_eq_landau_n_319_t3 x y z m u v) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
-
-(* notion 752 *)
-definition l_e_st_eq_landau_n_satz19b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ispl1 x y z i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
-
-(* notion 753 *)
-definition l_e_st_eq_landau_n_satz19c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz11 (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_satz19a y x z (l_e_st_eq_landau_n_satz12 x y l)) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
-
-(* notion 754 *)
-definition l_e_st_eq_landau_n_319_anders1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz19a y x z l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
-
-(* notion 755 *)
-definition l_e_st_eq_landau_n_satz19d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_compl x z) (l_e_st_eq_landau_n_compl y z) (l_e_st_eq_landau_n_satz19a x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
-
-(* notion 756 *)
-definition l_e_st_eq_landau_n_satz19e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ispl2 x y z i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
-
-(* notion 757 *)
-definition l_e_st_eq_landau_n_satz19f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_compl x z) (l_e_st_eq_landau_n_compl y z) (l_e_st_eq_landau_n_satz19c x y z l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
-
-(* notion 758 *)
-definition l_e_st_eq_landau_n_319_anders2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz19d y x z l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
-
-(* notion 759 *)
-definition l_e_st_eq_landau_n_satz19g ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore2 (l_e_st_eq_landau_n_pl x u) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_ispl1 x y u i) (l_e_st_eq_landau_n_satz19d z u x m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 760 *)
-definition l_e_st_eq_landau_n_satz19h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl u y) (l_e_st_eq_landau_n_compl x z) (l_e_st_eq_landau_n_compl y u) (l_e_st_eq_landau_n_satz19g x y z u i m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl u y)).
-
-(* notion 761 *)
-definition l_e_st_eq_landau_n_satz19j ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_pl x u) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_ispl1 x y u i) (l_e_st_eq_landau_n_satz19f z u x l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 762 *)
-definition l_e_st_eq_landau_n_satz19k ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl u y) (l_e_st_eq_landau_n_compl x z) (l_e_st_eq_landau_n_compl y u) (l_e_st_eq_landau_n_satz19j x y z u i l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl u y)).
-
-(* notion 763 *)
-definition l_e_st_eq_landau_n_319_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_satz19a x y z n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
-
-(* notion 764 *)
-definition l_e_st_eq_landau_n_319_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_moreisi2 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_ispl1 x y z i) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
-
-(* notion 765 *)
-definition l_e_st_eq_landau_n_satz19l ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) m (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_319_t4 x y z m u) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_319_t5 x y z m u) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
-
-(* notion 766 *)
-definition l_e_st_eq_landau_n_satz19m ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_e_st_eq_landau_n_ismoreis12 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_compl x z) (l_e_st_eq_landau_n_compl y z) (l_e_st_eq_landau_n_satz19l x y z m) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
-
-(* notion 767 *)
-definition l_e_st_eq_landau_n_satz19n ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_satz19l y x z (l_e_st_eq_landau_n_satz14 x y l)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
-
-(* notion 768 *)
-definition l_e_st_eq_landau_n_satz19o ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_satz19m y x z (l_e_st_eq_landau_n_satz14 x y l)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
-
-(* notion 769 *)
-definition l_e_st_eq_landau_n_320_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz10a x y : l_or3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y)).
-
-(* notion 770 *)
-definition l_e_st_eq_landau_n_320_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) : l_ec3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z))).
-
-(* notion 771 *)
-definition l_e_st_eq_landau_n_satz20a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_ec3_th11 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_320_t1 x y z) (l_e_st_eq_landau_n_320_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz19b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz19a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz19c x y z u) m : l_e_st_eq_landau_n_more x y).
-
-(* notion 772 *)
-definition l_e_st_eq_landau_n_satz20b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_ec3_th10 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_320_t1 x y z) (l_e_st_eq_landau_n_320_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz19b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz19a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz19c x y z u) i : l_e_st_eq_landau_n_is x y).
-
-(* notion 773 *)
-definition l_e_st_eq_landau_n_satz20c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_ec3_th12 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_320_t1 x y z) (l_e_st_eq_landau_n_320_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz19b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz19a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz19c x y z u) l : l_e_st_eq_landau_n_less x y).
-
-(* notion 774 *)
-definition l_e_st_eq_landau_n_320_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_compl z x) i (l_e_st_eq_landau_n_compl y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
-
-(* notion 775 *)
-definition l_e_st_eq_landau_n_320_andersb ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_e_st_eq_landau_n_satz8a z x y (l_e_st_eq_landau_n_320_t3 x y z i) : l_e_st_eq_landau_n_is x y).
-
-(* notion 776 *)
-definition l_e_st_eq_landau_n_320_andersc ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_e_st_eq_landau_n_satz20a y x z l : l_e_st_eq_landau_n_less x y).
-
-(* notion 777 *)
-definition l_e_st_eq_landau_n_satz20d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y).(l_e_st_eq_landau_n_satz20a x y z (l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_compl z x) (l_e_st_eq_landau_n_compl z y) m) : l_e_st_eq_landau_n_more x y).
-
-(* notion 778 *)
-definition l_e_st_eq_landau_n_satz20e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y).(l_e_st_eq_landau_n_satz20b x y z (l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_compl x z) i (l_e_st_eq_landau_n_compl z y)) : l_e_st_eq_landau_n_is x y).
-
-(* notion 779 *)
-definition l_e_st_eq_landau_n_satz20f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y).(l_e_st_eq_landau_n_satz20c x y z (l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_compl z x) (l_e_st_eq_landau_n_compl z y) l) : l_e_st_eq_landau_n_less x y).
-
-(* notion 780 *)
-definition l_e_st_eq_landau_n_321_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_satz19a x y z m : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
-
-(* notion 781 *)
-definition l_e_st_eq_landau_n_321_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl u y) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_compl z y) (l_e_st_eq_landau_n_compl u y) (l_e_st_eq_landau_n_satz19a z u y n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 782 *)
-definition l_e_st_eq_landau_n_satz21 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_trmore (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_321_t1 x y z u m n) (l_e_st_eq_landau_n_321_t2 x y z u m n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 783 *)
-definition l_e_st_eq_landau_n_321_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_trmore (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_satz19a x y z m) (l_e_st_eq_landau_n_satz19d z u y n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 784 *)
-definition l_e_st_eq_landau_n_satz21a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz21 y x u z l k : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 785 *)
-definition l_e_st_eq_landau_n_321_andersa ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz11 (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_satz21 y x u z (l_e_st_eq_landau_n_satz12 x y l) (l_e_st_eq_landau_n_satz12 z u k)) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 786 *)
-definition l_e_st_eq_landau_n_satz22a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_more z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz21 x y z u v n) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz19g x y z u v n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 787 *)
-definition l_e_st_eq_landau_n_satz22b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more z u) (l_e_st_eq_landau_n_is z u) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)) n (λv:l_e_st_eq_landau_n_more z u.l_e_st_eq_landau_n_satz21 x y z u m v) (λv:l_e_st_eq_landau_n_is z u.l_e_st_eq_landau_n_satz19h z u x y v m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 788 *)
-definition l_e_st_eq_landau_n_satz22c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz22a y x u z (l_e_st_eq_landau_n_satz14 x y l) k : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 789 *)
-definition l_e_st_eq_landau_n_satz22d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_lessis z u.(l_e_st_eq_landau_n_satz22b y x u z l (l_e_st_eq_landau_n_satz14 z u k) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 790 *)
-definition l_e_st_eq_landau_n_323_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_st_eq_landau_n_moreisi2 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_ispl1 x y z i) (l_e_st_eq_landau_n_ispl2 z u y j)) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 791 *)
-definition l_e_st_eq_landau_n_323_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.λo:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_satz22a x y z u m o) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 792 *)
-definition l_e_st_eq_landau_n_323_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.(l_orapp (l_e_st_eq_landau_n_more z u) (l_e_st_eq_landau_n_is z u) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)) n (λv:l_e_st_eq_landau_n_more z u.l_e_st_eq_landau_n_323_t2 x y z u m n i v) (λv:l_e_st_eq_landau_n_is z u.l_e_st_eq_landau_n_323_t1 x y z u m n i v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 793 *)
-definition l_e_st_eq_landau_n_323_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λo:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_satz22b x y z u o n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 794 *)
-definition l_e_st_eq_landau_n_satz23 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_323_t4 x y z u m n v) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_323_t3 x y z u m n v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 795 *)
-definition l_e_st_eq_landau_n_323_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λo:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_satz22b x y z u o n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 796 *)
-definition l_e_st_eq_landau_n_323_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ismoreis2 (l_e_st_eq_landau_n_pl x u) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_ispl1 x y u i) (l_e_st_eq_landau_n_satz19m z u x n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 797 *)
-definition l_e_st_eq_landau_n_323_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_323_t5 x y z u m n v) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_323_t6 x y z u m n v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 798 *)
-definition l_e_st_eq_landau_n_satz23a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis z u.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_satz23 y x u z (l_e_st_eq_landau_n_satz14 x y l) (l_e_st_eq_landau_n_satz14 z u k)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
-
-(* notion 799 *)
-definition l_e_st_eq_landau_n_324_t1 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_suc u) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u) i (l_e_st_eq_landau_n_satz4g u) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u)).
-
-(* notion 800 *)
-definition l_e_st_eq_landau_n_324_t2 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u) x l_e_st_eq_landau_n_1 (l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u) (l_e_st_eq_landau_n_324_t1 x n u i)) (l_e_st_eq_landau_n_satz18 l_e_st_eq_landau_n_1 u) : l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1).
-
-(* notion 801 *)
-definition l_e_st_eq_landau_n_324_t3 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_satz3 x n) (l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).l_e_st_eq_landau_n_324_t2 x n u v) : l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1).
-
-(* notion 802 *)
-definition l_e_st_eq_landau_n_satz24 ≝ λx:l_e_st_eq_landau_n_nat.(l_or_th2 (l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (λu:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_324_t3 x u) : l_e_st_eq_landau_n_moreis x l_e_st_eq_landau_n_1).
-
-(* notion 803 *)
-definition l_e_st_eq_landau_n_satz24a ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz13 x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24 x) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x).
-
-(* notion 804 *)
-definition l_e_st_eq_landau_n_satz24b ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_324_t3 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_ax3 x) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc x) l_e_st_eq_landau_n_1).
-
-(* notion 805 *)
-definition l_e_st_eq_landau_n_satz24c ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz24b x : l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 806 *)
-definition l_e_st_eq_landau_n_325_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more y x.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop y x u.(l_e_st_eq_landau_n_satz19m u l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_satz24 u) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x u) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 807 *)
-definition l_e_st_eq_landau_n_325_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more y x.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop y x u.(l_e_st_eq_landau_n_ismoreis1 (l_e_st_eq_landau_n_pl x u) y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_symis l_e_st_eq_landau_n_nat y (l_e_st_eq_landau_n_pl x u) du) (l_e_st_eq_landau_n_325_t1 x y m u du) : l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 808 *)
-definition l_e_st_eq_landau_n_satz25 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more y x.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x u) m (l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_diffprop y x u.l_e_st_eq_landau_n_325_t2 x y m u v) : l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 809 *)
-definition l_e_st_eq_landau_n_satz25a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more y x.(l_e_st_eq_landau_n_ismoreis2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) y (l_e_st_eq_landau_n_satz4a x) (l_e_st_eq_landau_n_satz25 x y m) : l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_suc x)).
-
-(* notion 810 *)
-definition l_e_st_eq_landau_n_satz25b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y x.(l_e_st_eq_landau_n_satz13 x (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz25 y x l) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) x).
-
-(* notion 811 *)
-definition l_e_st_eq_landau_n_satz25c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y x.(l_e_st_eq_landau_n_islessis1 (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y) x (l_e_st_eq_landau_n_satz4a y) (l_e_st_eq_landau_n_satz25b x y l) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc y) x).
-
-(* notion 812 *)
-definition l_e_st_eq_landau_n_326_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λm:l_e_st_eq_landau_n_more y x.(l_e_st_eq_landau_n_satz25 x y m : l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 813 *)
-definition l_e_st_eq_landau_n_326_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).(l_imp_th3 (l_e_st_eq_landau_n_more y x) (l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz10h y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) l) (λv:l_e_st_eq_landau_n_more y x.l_e_st_eq_landau_n_326_t1 x y l v) : l_not (l_e_st_eq_landau_n_more y x)).
-
-(* notion 814 *)
-definition l_e_st_eq_landau_n_satz26 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).(l_e_st_eq_landau_n_satz10e y x (l_e_st_eq_landau_n_326_t2 x y l) : l_e_st_eq_landau_n_lessis y x).
-
-(* notion 815 *)
-definition l_e_st_eq_landau_n_satz26a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y (l_e_st_eq_landau_n_suc x).(l_e_st_eq_landau_n_satz26 x y (l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) y (l_e_st_eq_landau_n_satz4e x) l) : l_e_st_eq_landau_n_lessis y x).
-
-(* notion 816 *)
-definition l_e_st_eq_landau_n_satz26b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) x.(l_e_st_eq_landau_n_satz14 x y (l_e_st_eq_landau_n_satz26 y x m) : l_e_st_eq_landau_n_moreis y x).
-
-(* notion 817 *)
-definition l_e_st_eq_landau_n_satz26c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc y) x.(l_e_st_eq_landau_n_satz26b x y (l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_satz4e y) m) : l_e_st_eq_landau_n_moreis y x).
-
-(* notion 818 *)
-definition l_e_st_eq_landau_n_327_lbprop ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.(l_imp (p m) (l_e_st_eq_landau_n_lessis n m) : Prop).
-
-(* notion 819 *)
-definition l_e_st_eq_landau_n_lb ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_lbprop p n x) : Prop).
-
-(* notion 820 *)
-definition l_e_st_eq_landau_n_min ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.(l_and (l_e_st_eq_landau_n_lb p n) (p n) : Prop).
-
-(* notion 821 *)
-definition l_e_st_eq_landau_n_327_t1 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λn:l_e_st_eq_landau_n_nat.(Πx:p n.l_e_st_eq_landau_n_satz24a n : l_e_st_eq_landau_n_327_lbprop p l_e_st_eq_landau_n_1 n).
-
-(* notion 822 *)
-definition l_e_st_eq_landau_n_327_t2 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.(Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_t1 p s x : l_e_st_eq_landau_n_lb p l_e_st_eq_landau_n_1).
-
-(* notion 823 *)
-definition l_e_st_eq_landau_n_327_t3 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.λy:l_e_st_eq_landau_n_nat.λyp:p y.(l_e_st_eq_landau_n_satz18 y l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) y).
-
-(* notion 824 *)
-definition l_e_st_eq_landau_n_327_t4 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.λy:l_e_st_eq_landau_n_nat.λyp:p y.(l_e_st_eq_landau_n_satz10g (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) y (l_e_st_eq_landau_n_327_t3 p s l y yp) : l_not (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) y)).
-
-(* notion 825 *)
-definition l_e_st_eq_landau_n_327_t5 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.λy:l_e_st_eq_landau_n_nat.λyp:p y.(l_imp_th4 (p y) (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) y) yp (l_e_st_eq_landau_n_327_t4 p s l y yp) : l_not (l_e_st_eq_landau_n_327_lbprop p (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) y)).
-
-(* notion 826 *)
-definition l_e_st_eq_landau_n_327_t6 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.λy:l_e_st_eq_landau_n_nat.λyp:p y.(l_all_th1 l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_lbprop p (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) x) y (l_e_st_eq_landau_n_327_t5 p s l y yp) : l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1))).
-
-(* notion 827 *)
-definition l_e_st_eq_landau_n_327_t7 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.λy:l_e_st_eq_landau_n_nat.λyp:p y.(l_mp (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1)) l_con (l (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_327_t6 p s l y yp) : l_con).
-
-(* notion 828 *)
-definition l_e_st_eq_landau_n_327_t8 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.(l_someapp l_e_st_eq_landau_n_nat p s l_con (λx:l_e_st_eq_landau_n_nat.λy:p x.l_e_st_eq_landau_n_327_t7 p s l x y) : l_con).
-
-(* notion 829 *)
-definition l_e_st_eq_landau_n_327_t9 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))).λm:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p m.(n m : l_not (l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))))).
-
-(* notion 830 *)
-definition l_e_st_eq_landau_n_327_t10 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))).λm:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p m.(l_et (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1)) (l_and_th3 (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_327_t9 p s n m l) l) : l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1)).
-
-(* notion 831 *)
-definition l_e_st_eq_landau_n_327_t11 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))).λm:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p m.(l_e_isp l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x) (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc m) (l_e_st_eq_landau_n_327_t10 p s n m l) (l_e_st_eq_landau_n_satz4a m) : l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_suc m)).
-
-(* notion 832 *)
-definition l_e_st_eq_landau_n_327_t12 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))).(λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_induction (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p y) (l_e_st_eq_landau_n_327_t2 p s) (λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_lb p y.l_e_st_eq_landau_n_327_t11 p s n y z) x : Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x).
-
-(* notion 833 *)
-definition l_e_st_eq_landau_n_327_t13 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.(λx:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))).l_e_st_eq_landau_n_327_t8 p s (l_e_st_eq_landau_n_327_t12 p s x) : l_e_st_eq_landau_n_some (Πx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
-
-(* notion 834 *)
-definition l_e_st_eq_landau_n_327_t14 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).(l_ande1 (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))) a : l_e_st_eq_landau_n_lb p m).
-
-(* notion 835 *)
-definition l_e_st_eq_landau_n_327_t15 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).(l_ande2 (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))) a : l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).
-
-(* notion 836 *)
-definition l_e_st_eq_landau_n_327_t16 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).λn:l_e_st_eq_landau_n_nat.λnp:p n.(l_mp (p n) (l_e_st_eq_landau_n_lessis m n) np (l_e_st_eq_landau_n_327_t14 p s m a n) : l_e_st_eq_landau_n_lessis m n).
-
-(* notion 837 *)
-definition l_e_st_eq_landau_n_327_t17 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).λn:l_e_st_eq_landau_n_nat.λnp:p n.(l_imp_th3 (l_e_st_eq_landau_n_is m n) (p m) nmp (λx:l_e_st_eq_landau_n_is m n.l_e_isp l_e_st_eq_landau_n_nat p n m np (l_e_symis l_e_st_eq_landau_n_nat m n x)) : l_not (l_e_st_eq_landau_n_is m n)).
-
-(* notion 838 *)
-definition l_e_st_eq_landau_n_327_t18 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).λn:l_e_st_eq_landau_n_nat.λnp:p n.(l_ore1 (l_e_st_eq_landau_n_less m n) (l_e_st_eq_landau_n_is m n) (l_e_st_eq_landau_n_327_t16 p s m a nmp n np) (l_e_st_eq_landau_n_327_t17 p s m a nmp n np) : l_e_st_eq_landau_n_less m n).
-
-(* notion 839 *)
-definition l_e_st_eq_landau_n_327_t19 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).λn:l_e_st_eq_landau_n_nat.λnp:p n.(l_e_st_eq_landau_n_satz25b n m (l_e_st_eq_landau_n_327_t18 p s m a nmp n np) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1) n).
-
-(* notion 840 *)
-definition l_e_st_eq_landau_n_327_t20 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).(λx:l_e_st_eq_landau_n_nat.λy:p x.l_e_st_eq_landau_n_327_t19 p s m a nmp x y : l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1)).
-
-(* notion 841 *)
-definition l_e_st_eq_landau_n_327_t21 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).(l_mp (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1)) l_con (l_e_st_eq_landau_n_327_t20 p s m a nmp) (l_e_st_eq_landau_n_327_t15 p s m a) : l_con).
-
-(* notion 842 *)
-definition l_e_st_eq_landau_n_327_t22 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).(l_et (p m) (λx:l_not (p m).l_e_st_eq_landau_n_327_t21 p s m a x) : p m).
-
-(* notion 843 *)
-definition l_e_st_eq_landau_n_327_t23 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).(l_andi (l_e_st_eq_landau_n_lb p m) (p m) (l_e_st_eq_landau_n_327_t14 p s m a) (l_e_st_eq_landau_n_327_t22 p s m a) : l_e_st_eq_landau_n_min p m).
-
-(* notion 844 *)
-definition l_e_st_eq_landau_n_satz27 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.(l_some_th6 l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x) (l_e_st_eq_landau_n_327_t13 p s) (λx:l_e_st_eq_landau_n_nat.λy:l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).l_e_st_eq_landau_n_327_t23 p s x y) : l_e_st_eq_landau_n_some (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)).
-
-(* notion 845 *)
-definition l_e_st_eq_landau_n_327_t24 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.(Πx:p u.l_e_st_eq_landau_n_satz24a u : l_e_st_eq_landau_n_327_lbprop p l_e_st_eq_landau_n_1 u).
-
-(* notion 846 *)
-definition l_e_st_eq_landau_n_327_t25 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).(Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_t24 p n x : l_e_st_eq_landau_n_lb p l_e_st_eq_landau_n_1).
-
-(* notion 847 *)
-definition l_e_st_eq_landau_n_327_t26 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.(n u : l_not (l_e_st_eq_landau_n_min p u)).
-
-(* notion 848 *)
-definition l_e_st_eq_landau_n_327_t27 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.(l_and_th3 (l_e_st_eq_landau_n_lb p u) (p u) (l_e_st_eq_landau_n_327_t26 p n u l) l : l_not (p u)).
-
-(* notion 849 *)
-definition l_e_st_eq_landau_n_327_t28 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.λv:l_e_st_eq_landau_n_nat.λvp:p v.(l_imp_th3 (l_e_st_eq_landau_n_is u v) (p u) (l_e_st_eq_landau_n_327_t27 p n u l) (λx:l_e_st_eq_landau_n_is u v.l_e_isp1 l_e_st_eq_landau_n_nat p v u vp x) : l_e_st_eq_landau_n_nis u v).
-
-(* notion 850 *)
-definition l_e_st_eq_landau_n_327_t29 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.λv:l_e_st_eq_landau_n_nat.λvp:p v.(l_mp (p v) (l_e_st_eq_landau_n_lessis u v) vp (l v) : l_e_st_eq_landau_n_lessis u v).
-
-(* notion 851 *)
-definition l_e_st_eq_landau_n_327_t30 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.λv:l_e_st_eq_landau_n_nat.λvp:p v.(l_ore1 (l_e_st_eq_landau_n_less u v) (l_e_st_eq_landau_n_is u v) (l_e_st_eq_landau_n_327_t29 p n u l v vp) (l_e_st_eq_landau_n_327_t28 p n u l v vp) : l_e_st_eq_landau_n_less u v).
-
-(* notion 852 *)
-definition l_e_st_eq_landau_n_327_t31 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.λv:l_e_st_eq_landau_n_nat.λvp:p v.(l_e_st_eq_landau_n_satz25c v u (l_e_st_eq_landau_n_327_t30 p n u l v vp) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) v).
-
-(* notion 853 *)
-definition l_e_st_eq_landau_n_327_t32 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.λv:l_e_st_eq_landau_n_nat.(λx:p v.l_e_st_eq_landau_n_327_t31 p n u l v x : l_e_st_eq_landau_n_327_lbprop p (l_e_st_eq_landau_n_suc u) v).
-
-(* notion 854 *)
-definition l_e_st_eq_landau_n_327_t33 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.(λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_t32 p n u l x : l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_suc u)).
-
-(* notion 855 *)
-definition l_e_st_eq_landau_n_327_t34 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x) (l_e_st_eq_landau_n_327_t25 p n) (λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_lb p x.l_e_st_eq_landau_n_327_t33 p n x y) u : l_e_st_eq_landau_n_lb p u).
-
-(* notion 856 *)
-definition l_e_st_eq_landau_n_327_t35 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λu:l_e_st_eq_landau_n_nat.λup:p u.(l_e_st_eq_landau_n_satz10g (l_e_st_eq_landau_n_suc u) u (l_e_st_eq_landau_n_satz18b u) : l_not (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) u)).
-
-(* notion 857 *)
-definition l_e_st_eq_landau_n_327_t36 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λu:l_e_st_eq_landau_n_nat.λup:p u.(l_imp_th4 (p u) (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) u) up (l_e_st_eq_landau_n_327_t35 p s u up) : l_not (l_e_st_eq_landau_n_327_lbprop p (l_e_st_eq_landau_n_suc u) u)).
-
-(* notion 858 *)
-definition l_e_st_eq_landau_n_327_t37 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λu:l_e_st_eq_landau_n_nat.λup:p u.(l_all_th1 l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_lbprop p (l_e_st_eq_landau_n_suc u) x) u (l_e_st_eq_landau_n_327_t36 p s u up) : l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_suc u))).
-
-(* notion 859 *)
-definition l_e_st_eq_landau_n_327_t38 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λu:l_e_st_eq_landau_n_nat.λup:p u.(λy:l_non l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).l_mp (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_suc u)) l_con (l_e_st_eq_landau_n_327_t34 p y (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_327_t37 p s u up) : l_e_st_eq_landau_n_some (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)).
-
-(* notion 860 *)
-definition l_e_st_eq_landau_n_327_anders ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.(l_someapp l_e_st_eq_landau_n_nat p s (l_e_st_eq_landau_n_some (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)) (λx:l_e_st_eq_landau_n_nat.λy:p x.l_e_st_eq_landau_n_327_t38 p s x y) : l_e_st_eq_landau_n_some (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)).
-
-(* notion 861 *)
-definition l_e_st_eq_landau_n_327_t39 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_ande1 (l_e_st_eq_landau_n_lb p n) (p n) mn : l_e_st_eq_landau_n_lb p n).
-
-(* notion 862 *)
-definition l_e_st_eq_landau_n_327_t40 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_ande1 (l_e_st_eq_landau_n_lb p m) (p m) mm : l_e_st_eq_landau_n_lb p m).
-
-(* notion 863 *)
-definition l_e_st_eq_landau_n_327_t41 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_ande2 (l_e_st_eq_landau_n_lb p n) (p n) mn : p n).
-
-(* notion 864 *)
-definition l_e_st_eq_landau_n_327_t42 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_ande2 (l_e_st_eq_landau_n_lb p m) (p m) mm : p m).
-
-(* notion 865 *)
-definition l_e_st_eq_landau_n_327_t43 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_e_st_eq_landau_n_327_t39 p n m mn mm m : l_e_st_eq_landau_n_327_lbprop p n m).
-
-(* notion 866 *)
-definition l_e_st_eq_landau_n_327_t44 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_e_st_eq_landau_n_327_t40 p n m mn mm n : l_e_st_eq_landau_n_327_lbprop p m n).
-
-(* notion 867 *)
-definition l_e_st_eq_landau_n_327_t45 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_mp (p m) (l_e_st_eq_landau_n_lessis n m) (l_e_st_eq_landau_n_327_t42 p n m mn mm) (l_e_st_eq_landau_n_327_t43 p n m mn mm) : l_e_st_eq_landau_n_lessis n m).
-
-(* notion 868 *)
-definition l_e_st_eq_landau_n_327_t46 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_mp (p n) (l_e_st_eq_landau_n_lessis m n) (l_e_st_eq_landau_n_327_t41 p n m mn mm) (l_e_st_eq_landau_n_327_t44 p n m mn mm) : l_e_st_eq_landau_n_lessis m n).
-
-(* notion 869 *)
-definition l_e_st_eq_landau_n_327_t47 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_ore2 (l_e_st_eq_landau_n_more n m) (l_e_st_eq_landau_n_is n m) (l_e_st_eq_landau_n_satz14 m n (l_e_st_eq_landau_n_327_t46 p n m mn mm)) (l_e_st_eq_landau_n_satz10d n m (l_e_st_eq_landau_n_327_t45 p n m mn mm)) : l_e_st_eq_landau_n_is n m).
-
-(* notion 870 *)
-definition l_e_st_eq_landau_n_327_t48 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.(λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_min p x.λv:l_e_st_eq_landau_n_min p y.l_e_st_eq_landau_n_327_t47 p x y u v : l_e_amone l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)).
-
-(* notion 871 *)
-definition l_e_st_eq_landau_n_satz27a ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.(l_e_onei l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x) (l_e_st_eq_landau_n_327_t48 p) (l_e_st_eq_landau_n_satz27 p s) : l_e_st_eq_landau_n_one (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)).
-
-(* notion 872 *)
-definition l_e_st_eq_landau_n_428_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) x)) : Prop).
-
-(* notion 873 *)
-definition l_e_st_eq_landau_n_428_prop2 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_and (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x f) : Prop).
-
-(* notion 874 *)
-definition l_e_st_eq_landau_n_428_prop3 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (a y) (b y) : Prop).
-
-(* notion 875 *)
-definition l_e_st_eq_landau_n_428_t1 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.(l_ande1 (l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x a) pa : l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) x).
-
-(* notion 876 *)
-definition l_e_st_eq_landau_n_428_t2 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.(l_ande1 (l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x b) pb : l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) x).
-
-(* notion 877 *)
-definition l_e_st_eq_landau_n_428_t3 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.(l_e_tris2 l_e_st_eq_landau_n_nat (a l_e_st_eq_landau_n_1) (b l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_428_t1 x a b pa pb) (l_e_st_eq_landau_n_428_t2 x a b pa pb) : l_e_st_eq_landau_n_428_prop3 x a b pa pb l_e_st_eq_landau_n_1).
-
-(* notion 878 *)
-definition l_e_st_eq_landau_n_428_t4 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_e_st_eq_landau_n_ispl1 (a y) (b y) x p : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (a y) x) (l_e_st_eq_landau_n_pl (b y) x)).
-
-(* notion 879 *)
-definition l_e_st_eq_landau_n_428_t5 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_ande2 (l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x a) pa : l_e_st_eq_landau_n_428_prop1 x a).
-
-(* notion 880 *)
-definition l_e_st_eq_landau_n_428_t6 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_ande2 (l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x b) pb : l_e_st_eq_landau_n_428_prop1 x b).
-
-(* notion 881 *)
-definition l_e_st_eq_landau_n_428_t7 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_e_st_eq_landau_n_428_t5 x a b pa pb y p y : l_e_st_eq_landau_n_is (a (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (a y) x)).
-
-(* notion 882 *)
-definition l_e_st_eq_landau_n_428_t8 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_e_st_eq_landau_n_428_t6 x a b pa pb y p y : l_e_st_eq_landau_n_is (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (b y) x)).
-
-(* notion 883 *)
-definition l_e_st_eq_landau_n_428_t9 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_e_tr3is l_e_st_eq_landau_n_nat (a (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (a y) x) (l_e_st_eq_landau_n_pl (b y) x) (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_428_t7 x a b pa pb y p) (l_e_st_eq_landau_n_428_t4 x a b pa pb y p) (l_e_symis l_e_st_eq_landau_n_nat (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (b y) x) (l_e_st_eq_landau_n_428_t8 x a b pa pb y p)) : l_e_st_eq_landau_n_428_prop3 x a b pa pb (l_e_st_eq_landau_n_suc y)).
-
-(* notion 884 *)
-definition l_e_st_eq_landau_n_428_t10 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop3 x a b pa pb z) (l_e_st_eq_landau_n_428_t3 x a b pa pb) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_428_prop3 x a b pa pb z.l_e_st_eq_landau_n_428_t9 x a b pa pb z u) y : l_e_st_eq_landau_n_428_prop3 x a b pa pb y).
-
-(* notion 885 *)
-definition l_e_st_eq_landau_n_428_t11 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.(l_e_fisi l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat a b (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_t10 x a b pa pb y) : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) a b).
-
-(* notion 886 *)
-definition l_e_st_eq_landau_n_428_a1 ≝ λx:l_e_st_eq_landau_n_nat.(λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λu:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_428_prop2 x z.λw:l_e_st_eq_landau_n_428_prop2 x u.l_e_st_eq_landau_n_428_t11 x z u v w : l_e_amone (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z)).
-
-(* notion 887 *)
-definition l_e_st_eq_landau_n_428_prop4 ≝ λx:l_e_st_eq_landau_n_nat.(l_some (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z) : Prop).
-
-(* notion 888 *)
-definition l_e_st_eq_landau_n_428_id ≝ (λy:l_e_st_eq_landau_n_nat.y : Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
-
-(* notion 889 *)
-definition l_e_st_eq_landau_n_428_t12 ≝ (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_satz4e x : l_e_st_eq_landau_n_428_prop1 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_428_id).
-
-(* notion 890 *)
-definition l_e_st_eq_landau_n_428_t13 ≝ (l_andi (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_428_id l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_428_prop1 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_428_id) (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_428_t12 : l_e_st_eq_landau_n_428_prop2 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_428_id).
-
-(* notion 891 *)
-definition l_e_st_eq_landau_n_428_t14 ≝ (l_somei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 l_e_st_eq_landau_n_1 z) l_e_st_eq_landau_n_428_id l_e_st_eq_landau_n_428_t13 : l_e_st_eq_landau_n_428_prop4 l_e_st_eq_landau_n_1).
-
-(* notion 892 *)
-definition l_e_st_eq_landau_n_428_g ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl (f y) y : Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
-
-(* notion 893 *)
-definition l_e_st_eq_landau_n_428_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(l_ande1 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x f) pf : l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) x).
-
-(* notion 894 *)
-definition l_e_st_eq_landau_n_428_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_428_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_ispl1 (f l_e_st_eq_landau_n_1) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_428_t15 x p f pf)) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_428_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)).
-
-(* notion 895 *)
-definition l_e_st_eq_landau_n_428_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_ande2 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x f) pf : l_e_st_eq_landau_n_428_prop1 x f).
-
-(* notion 896 *)
-definition l_e_st_eq_landau_n_428_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_428_t17 x p f pf y y : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) x)).
-
-(* notion 897 *)
-definition l_e_st_eq_landau_n_428_t19 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_428_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (f y) x) (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y))) (l_e_st_eq_landau_n_ispl1 (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) x) (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_428_t18 x p f pf y)) (l_e_st_eq_landau_n_asspl1 (f y) x (l_e_st_eq_landau_n_suc y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_428_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)))).
-
-(* notion 898 *)
-definition l_e_st_eq_landau_n_428_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_satz4b x y) (l_e_st_eq_landau_n_satz4h x y) (l_e_st_eq_landau_n_compl (l_e_st_eq_landau_n_suc x) y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x))).
-
-(* notion 899 *)
-definition l_e_st_eq_landau_n_428_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_428_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y))) (l_e_st_eq_landau_n_pl (f y) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_428_g x p f pf y) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_428_t19 x p f pf y) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x)) (f y) (l_e_st_eq_landau_n_428_t20 x p f pf y)) (l_e_st_eq_landau_n_asspl2 (f y) y (l_e_st_eq_landau_n_suc x)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_428_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_428_g x p f pf y) (l_e_st_eq_landau_n_suc x))).
-
-(* notion 900 *)
-definition l_e_st_eq_landau_n_428_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_t21 x p f pf y : l_e_st_eq_landau_n_428_prop1 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_428_g x p f pf)).
-
-(* notion 901 *)
-definition l_e_st_eq_landau_n_428_t23 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(l_andi (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_428_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_428_prop1 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_428_g x p f pf)) (l_e_st_eq_landau_n_428_t16 x p f pf) (l_e_st_eq_landau_n_428_t22 x p f pf) : l_e_st_eq_landau_n_428_prop2 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_428_g x p f pf)).
-
-(* notion 902 *)
-definition l_e_st_eq_landau_n_428_t24 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(l_somei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 (l_e_st_eq_landau_n_suc x) z) (l_e_st_eq_landau_n_428_g x p f pf) (l_e_st_eq_landau_n_428_t23 x p f pf) : l_e_st_eq_landau_n_428_prop4 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 903 *)
-definition l_e_st_eq_landau_n_428_t25 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.(l_someapp (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z) p (l_e_st_eq_landau_n_428_prop4 (l_e_st_eq_landau_n_suc x)) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_428_prop2 x z.l_e_st_eq_landau_n_428_t24 x p z u) : l_e_st_eq_landau_n_428_prop4 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 904 *)
-definition l_e_st_eq_landau_n_428_b1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop4 y) l_e_st_eq_landau_n_428_t14 (λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_428_prop4 y.l_e_st_eq_landau_n_428_t25 y u) x : l_e_st_eq_landau_n_428_prop4 x).
-
-(* notion 905 *)
-definition l_e_st_eq_landau_n_satz28 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_onei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z) (l_e_st_eq_landau_n_428_a1 x) (l_e_st_eq_landau_n_428_b1 x) : l_e_one (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_is (z l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_all (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (z (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (z y) x))))).
-
-(* notion 906 *)
-definition l_e_st_eq_landau_n_times ≝ λx:l_e_st_eq_landau_n_nat.(l_e_ind (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z) (l_e_st_eq_landau_n_satz28 x) : Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
-
-(* notion 907 *)
-definition l_e_st_eq_landau_n_ts ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_times x y : l_e_st_eq_landau_n_nat).
-
-(* notion 908 *)
-definition l_e_st_eq_landau_n_428_t26 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_oneax (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z) (l_e_st_eq_landau_n_satz28 x) : l_e_st_eq_landau_n_428_prop2 x (l_e_st_eq_landau_n_times x)).
-
-(* notion 909 *)
-definition l_e_st_eq_landau_n_satz28a ≝ λx:l_e_st_eq_landau_n_nat.(l_ande1 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_times x l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x (l_e_st_eq_landau_n_times x)) (l_e_st_eq_landau_n_428_t26 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1) x).
-
-(* notion 910 *)
-definition l_e_st_eq_landau_n_428_t27 ≝ λx:l_e_st_eq_landau_n_nat.(l_ande2 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_times x l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x (l_e_st_eq_landau_n_times x)) (l_e_st_eq_landau_n_428_t26 x) : l_e_st_eq_landau_n_428_prop1 x (l_e_st_eq_landau_n_times x)).
-
-(* notion 911 *)
-definition l_e_st_eq_landau_n_satz28b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_428_t27 x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) x)).
-
-(* notion 912 *)
-definition l_e_st_eq_landau_n_428_t28 ≝ (l_e_st_eq_landau_n_428_t11 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_times l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_428_id (l_e_st_eq_landau_n_428_t26 l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_428_t13 : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (l_e_st_eq_landau_n_times l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_428_id).
-
-(* notion 913 *)
-definition l_e_st_eq_landau_n_satz28c ≝ λx:l_e_st_eq_landau_n_nat.(l_e_fise l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_times l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_428_id l_e_st_eq_landau_n_428_t28 x : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 x) x).
-
-(* notion 914 *)
-definition l_e_st_eq_landau_n_428_t29 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_428_t11 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_times (l_e_st_eq_landau_n_suc x)) (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_times x y) y) (l_e_st_eq_landau_n_428_t26 (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_428_t23 x (l_e_st_eq_landau_n_428_b1 x) (l_e_st_eq_landau_n_times x) (l_e_st_eq_landau_n_428_t26 x)) : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (l_e_st_eq_landau_n_times (l_e_st_eq_landau_n_suc x)) (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_times x y) y)).
-
-(* notion 915 *)
-definition l_e_st_eq_landau_n_satz28d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_fise l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_times (l_e_st_eq_landau_n_suc x)) (Πz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_times x z) z) (l_e_st_eq_landau_n_428_t29 x) y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y)).
-
-(* notion 916 *)
-definition l_e_st_eq_landau_n_satz28e ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_satz28a x) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1)).
-
-(* notion 917 *)
-definition l_e_st_eq_landau_n_satz28f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) x) (l_e_st_eq_landau_n_satz28b x y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) x) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc y))).
-
-(* notion 918 *)
-definition l_e_st_eq_landau_n_satz28g ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 x) x (l_e_st_eq_landau_n_satz28c x) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 x)).
-
-(* notion 919 *)
-definition l_e_st_eq_landau_n_satz28h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y) (l_e_st_eq_landau_n_satz28d x y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc x) y)).
-
-(* notion 920 *)
-definition l_e_st_eq_landau_n_ists1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_ts u z) x y i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
-
-(* notion 921 *)
-definition l_e_st_eq_landau_n_ists2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_ts z u) x y i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
-
-(* notion 922 *)
-definition l_e_st_eq_landau_n_ists12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ists1 x y z i) (l_e_st_eq_landau_n_ists2 z u y j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 923 *)
-definition l_e_st_eq_landau_n_429_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x) : Prop).
-
-(* notion 924 *)
-definition l_e_st_eq_landau_n_429_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz28a y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts y l_e_st_eq_landau_n_1) y).
-
-(* notion 925 *)
-definition l_e_st_eq_landau_n_429_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz28c y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 y) y).
-
-(* notion 926 *)
-definition l_e_st_eq_landau_n_429_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_ts y l_e_st_eq_landau_n_1) y (l_e_st_eq_landau_n_429_t2 x y) (l_e_st_eq_landau_n_429_t1 x y) : l_e_st_eq_landau_n_429_prop1 l_e_st_eq_landau_n_1 y).
-
-(* notion 927 *)
-definition l_e_st_eq_landau_n_429_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_429_prop1 x y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y x) y) (l_e_st_eq_landau_n_ts y (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x) y p) (l_e_st_eq_landau_n_satz28f y x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y) (l_e_st_eq_landau_n_ts y (l_e_st_eq_landau_n_suc x))).
-
-(* notion 928 *)
-definition l_e_st_eq_landau_n_429_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_429_prop1 x y.(l_e_st_eq_landau_n_satz28d x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y)).
-
-(* notion 929 *)
-definition l_e_st_eq_landau_n_429_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_429_prop1 x y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y) (l_e_st_eq_landau_n_ts y (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_429_t5 x y p) (l_e_st_eq_landau_n_429_t4 x y p) : l_e_st_eq_landau_n_429_prop1 (l_e_st_eq_landau_n_suc x) y).
-
-(* notion 930 *)
-definition l_e_st_eq_landau_n_satz29 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_429_prop1 z y) (l_e_st_eq_landau_n_429_t3 x y) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_429_prop1 z y.l_e_st_eq_landau_n_429_t6 z y u) x : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x)).
-
-(* notion 931 *)
-definition l_e_st_eq_landau_n_comts ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz29 x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x)).
-
-(* notion 932 *)
-definition l_e_st_eq_landau_n_429_t7 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_satz28a x) (l_e_st_eq_landau_n_satz28g x) : l_e_st_eq_landau_n_429_prop1 x l_e_st_eq_landau_n_1).
-
-(* notion 933 *)
-definition l_e_st_eq_landau_n_429_t8 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_429_prop1 x y.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y x) x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc y) x) (l_e_st_eq_landau_n_satz28b x y) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x) x p) (l_e_st_eq_landau_n_satz28h y x) : l_e_st_eq_landau_n_429_prop1 x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 934 *)
-definition l_e_st_eq_landau_n_429_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_429_prop1 x z) (l_e_st_eq_landau_n_429_t7 x) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_429_prop1 x z.l_e_st_eq_landau_n_429_t8 x z u) y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x)).
-
-(* notion 935 *)
-definition l_e_st_eq_landau_n_430_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) : Prop).
-
-(* notion 936 *)
-definition l_e_st_eq_landau_n_430_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y) x (l_e_st_eq_landau_n_satz4a y)) (l_e_st_eq_landau_n_satz28b x y) (l_e_st_eq_landau_n_ispl2 x (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_satz28e x)) : l_e_st_eq_landau_n_430_prop1 x y l_e_st_eq_landau_n_1).
-
-(* notion 937 *)
-definition l_e_st_eq_landau_n_430_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_430_prop1 x y z.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) x) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y z)) x (l_e_st_eq_landau_n_satz4b y z)) (l_e_st_eq_landau_n_satz28b x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) x p) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) x)).
-
-(* notion 938 *)
-definition l_e_st_eq_landau_n_430_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_430_prop1 x y z.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) x)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_430_t2 x y z p) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z) x) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) x) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc z)) (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_satz28f x z)) : l_e_st_eq_landau_n_430_prop1 x y (l_e_st_eq_landau_n_suc z)).
-
-(* notion 939 *)
-definition l_e_st_eq_landau_n_satz30 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_430_prop1 x y u) (l_e_st_eq_landau_n_430_t1 x y) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_430_prop1 x y u.l_e_st_eq_landau_n_430_t3 x y u v) z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z))).
-
-(* notion 940 *)
-definition l_e_st_eq_landau_n_disttp1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_ts z (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_satz30 z x y) (l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_comts z x) (l_e_st_eq_landau_n_comts z y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z))).
-
-(* notion 941 *)
-definition l_e_st_eq_landau_n_disttp2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz30 x y z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z))).
-
-(* notion 942 *)
-definition l_e_st_eq_landau_n_distpt1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_disttp1 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x y) z)).
-
-(* notion 943 *)
-definition l_e_st_eq_landau_n_distpt2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) (l_e_st_eq_landau_n_disttp2 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z))).
-
-(* notion 944 *)
-definition l_e_st_eq_landau_n_431_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z)) : Prop).
-
-(* notion 945 *)
-definition l_e_st_eq_landau_n_431_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz28a (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_ists2 y (l_e_st_eq_landau_n_ts y l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_satz28e y)) : l_e_st_eq_landau_n_431_prop1 x y l_e_st_eq_landau_n_1).
-
-(* notion 946 *)
-definition l_e_st_eq_landau_n_431_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_431_prop1 x y z.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_suc z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y z) y)) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_satz28b (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_ts x y) p) (l_e_st_eq_landau_n_distpt2 x (l_e_st_eq_landau_n_ts y z) y) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y z) y) (l_e_st_eq_landau_n_ts y (l_e_st_eq_landau_n_suc z)) x (l_e_st_eq_landau_n_satz28f y z)) : l_e_st_eq_landau_n_431_prop1 x y (l_e_st_eq_landau_n_suc z)).
-
-(* notion 947 *)
-definition l_e_st_eq_landau_n_satz31 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_431_prop1 x y u) (l_e_st_eq_landau_n_431_t1 x y) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_431_prop1 x y u.l_e_st_eq_landau_n_431_t2 x y u v) z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z))).
-
-(* notion 948 *)
-definition l_e_st_eq_landau_n_assts1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz31 x y z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z))).
-
-(* notion 949 *)
-definition l_e_st_eq_landau_n_assts2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_assts1 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z)).
-
-(* notion 950 *)
-definition l_e_st_eq_landau_n_432_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl y u) z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts u z)) (l_e_st_eq_landau_n_ists1 x (l_e_st_eq_landau_n_pl y u) z du) (l_e_st_eq_landau_n_disttp1 y u z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts u z))).
-
-(* notion 951 *)
-definition l_e_st_eq_landau_n_432_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_somei l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) v) (l_e_st_eq_landau_n_ts u z) (l_e_st_eq_landau_n_432_t1 x y z m u du) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
-
-(* notion 952 *)
-definition l_e_st_eq_landau_n_satz32a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) m (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_diffprop x y u.l_e_st_eq_landau_n_432_t2 x y z m u v) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
-
-(* notion 953 *)
-definition l_e_st_eq_landau_n_satz32b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ists1 x y z i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
-
-(* notion 954 *)
-definition l_e_st_eq_landau_n_satz32c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz11 (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_satz32a y x z (l_e_st_eq_landau_n_satz12 x y l)) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
-
-(* notion 955 *)
-definition l_e_st_eq_landau_n_432_anders1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz32a y x z l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
-
-(* notion 956 *)
-definition l_e_st_eq_landau_n_satz32d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_comts x z) (l_e_st_eq_landau_n_comts y z) (l_e_st_eq_landau_n_satz32a x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
-
-(* notion 957 *)
-definition l_e_st_eq_landau_n_satz32e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ists2 x y z i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
-
-(* notion 958 *)
-definition l_e_st_eq_landau_n_satz32f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_comts x z) (l_e_st_eq_landau_n_comts y z) (l_e_st_eq_landau_n_satz32c x y z l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
-
-(* notion 959 *)
-definition l_e_st_eq_landau_n_432_anders2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz32d y x z l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
-
-(* notion 960 *)
-definition l_e_st_eq_landau_n_satz32g ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore2 (l_e_st_eq_landau_n_ts x u) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ists1 x y u i) (l_e_st_eq_landau_n_satz32d z u x m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 961 *)
-definition l_e_st_eq_landau_n_satz32h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts u y) (l_e_st_eq_landau_n_comts x z) (l_e_st_eq_landau_n_comts y u) (l_e_st_eq_landau_n_satz32g x y z u i m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts u y)).
-
-(* notion 962 *)
-definition l_e_st_eq_landau_n_satz32j ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_ts x u) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ists1 x y u i) (l_e_st_eq_landau_n_satz32f z u x l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 963 *)
-definition l_e_st_eq_landau_n_satz32k ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts u y) (l_e_st_eq_landau_n_comts x z) (l_e_st_eq_landau_n_comts y u) (l_e_st_eq_landau_n_satz32j x y z u i l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts u y)).
-
-(* notion 964 *)
-definition l_e_st_eq_landau_n_432_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_satz32a x y z n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
-
-(* notion 965 *)
-definition l_e_st_eq_landau_n_432_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_moreisi2 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ists1 x y z i) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
-
-(* notion 966 *)
-definition l_e_st_eq_landau_n_satz32l ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) m (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_432_t3 x y z m u) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_432_t4 x y z m u) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
-
-(* notion 967 *)
-definition l_e_st_eq_landau_n_satz32m ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_e_st_eq_landau_n_ismoreis12 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_comts x z) (l_e_st_eq_landau_n_comts y z) (l_e_st_eq_landau_n_satz32l x y z m) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
-
-(* notion 968 *)
-definition l_e_st_eq_landau_n_satz32n ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_satz32l y x z (l_e_st_eq_landau_n_satz14 x y l)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
-
-(* notion 969 *)
-definition l_e_st_eq_landau_n_satz32o ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_satz32m y x z (l_e_st_eq_landau_n_satz14 x y l)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
-
-(* notion 970 *)
-definition l_e_st_eq_landau_n_433_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz10a x y : l_or3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y)).
-
-(* notion 971 *)
-definition l_e_st_eq_landau_n_433_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) : l_ec3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z))).
-
-(* notion 972 *)
-definition l_e_st_eq_landau_n_satz33a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z).(l_ec3_th11 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_433_t1 x y z) (l_e_st_eq_landau_n_433_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz32b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz32a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz32c x y z u) m : l_e_st_eq_landau_n_more x y).
-
-(* notion 973 *)
-definition l_e_st_eq_landau_n_satz33b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z).(l_ec3_th10 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_433_t1 x y z) (l_e_st_eq_landau_n_433_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz32b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz32a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz32c x y z u) i : l_e_st_eq_landau_n_is x y).
-
-(* notion 974 *)
-definition l_e_st_eq_landau_n_satz33c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z).(l_ec3_th12 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_433_t1 x y z) (l_e_st_eq_landau_n_433_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz32b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz32a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz32c x y z u) l : l_e_st_eq_landau_n_less x y).
-
-(* notion 975 *)
-definition l_e_st_eq_landau_n_433_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z).(l_e_st_eq_landau_n_satz33a y x z l : l_e_st_eq_landau_n_less x y).
-
-(* notion 976 *)
-definition l_e_st_eq_landau_n_434_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_satz32a x y z m : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
-
-(* notion 977 *)
-definition l_e_st_eq_landau_n_434_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts u y) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_comts z y) (l_e_st_eq_landau_n_comts u y) (l_e_st_eq_landau_n_satz32a z u y n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 978 *)
-definition l_e_st_eq_landau_n_satz34 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_trmore (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_434_t1 x y z u m n) (l_e_st_eq_landau_n_434_t2 x y z u m n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 979 *)
-definition l_e_st_eq_landau_n_434_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_trmore (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_satz32a x y z m) (l_e_st_eq_landau_n_satz32d z u y n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 980 *)
-definition l_e_st_eq_landau_n_satz34a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz34 y x u z l k : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 981 *)
-definition l_e_st_eq_landau_n_434_andersa ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz11 (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_satz34 y x u z (l_e_st_eq_landau_n_satz12 x y l) (l_e_st_eq_landau_n_satz12 z u k)) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 982 *)
-definition l_e_st_eq_landau_n_satz35a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_more z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz34 x y z u v n) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz32g x y z u v n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 983 *)
-definition l_e_st_eq_landau_n_satz35b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more z u) (l_e_st_eq_landau_n_is z u) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)) n (λv:l_e_st_eq_landau_n_more z u.l_e_st_eq_landau_n_satz34 x y z u m v) (λv:l_e_st_eq_landau_n_is z u.l_e_st_eq_landau_n_satz32h z u x y v m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 984 *)
-definition l_e_st_eq_landau_n_satz35c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz35a y x u z (l_e_st_eq_landau_n_satz14 x y l) k : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 985 *)
-definition l_e_st_eq_landau_n_satz35d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_lessis z u.(l_e_st_eq_landau_n_satz35b y x u z l (l_e_st_eq_landau_n_satz14 z u k) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 986 *)
-definition l_e_st_eq_landau_n_436_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_st_eq_landau_n_moreisi2 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ists1 x y z i) (l_e_st_eq_landau_n_ists2 z u y j)) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 987 *)
-definition l_e_st_eq_landau_n_436_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.λo:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_satz35a x y z u m o) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 988 *)
-definition l_e_st_eq_landau_n_436_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.(l_orapp (l_e_st_eq_landau_n_more z u) (l_e_st_eq_landau_n_is z u) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)) n (λv:l_e_st_eq_landau_n_more z u.l_e_st_eq_landau_n_436_t2 x y z u m n i v) (λv:l_e_st_eq_landau_n_is z u.l_e_st_eq_landau_n_436_t1 x y z u m n i v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 989 *)
-definition l_e_st_eq_landau_n_436_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λo:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_satz35b x y z u o n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 990 *)
-definition l_e_st_eq_landau_n_satz36 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_436_t4 x y z u m n v) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_436_t3 x y z u m n v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 991 *)
-definition l_e_st_eq_landau_n_436_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λo:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_satz35b x y z u o n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 992 *)
-definition l_e_st_eq_landau_n_436_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ismoreis2 (l_e_st_eq_landau_n_ts x u) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ists1 x y u i) (l_e_st_eq_landau_n_satz32m z u x n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 993 *)
-definition l_e_st_eq_landau_n_436_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_436_t5 x y z u m n v) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_436_t6 x y z u m n v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 994 *)
-definition l_e_st_eq_landau_n_satz36a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis z u.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_satz36 y x u z (l_e_st_eq_landau_n_satz14 x y l) (l_e_st_eq_landau_n_satz14 z u k)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
-
-(* notion 995 *)
-definition l_e_st_eq_landau_n_mn_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_onei l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y z) (l_e_st_eq_landau_n_satz8b x y) m : l_e_st_eq_landau_n_one (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y z)).
-
-(* notion 996 *)
-definition l_e_st_eq_landau_n_mn ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_ind l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y z) (l_e_st_eq_landau_n_mn_t1 x y m) : l_e_st_eq_landau_n_nat).
-
-(* notion 997 *)
-definition l_e_st_eq_landau_n_mn_th1a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_oneax l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y z) (l_e_st_eq_landau_n_mn_t1 x y m) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_mn x y m))).
-
-(* notion 998 *)
-definition l_e_st_eq_landau_n_mn_th1b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_mn x y m)) (l_e_st_eq_landau_n_mn_th1a x y m) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_mn x y m)) x).
-
-(* notion 999 *)
-definition l_e_st_eq_landau_n_mn_th1c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_mn x y m)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_mn x y m) y) (l_e_st_eq_landau_n_mn_th1a x y m) (l_e_st_eq_landau_n_compl y (l_e_st_eq_landau_n_mn x y m)) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_mn x y m) y)).
-
-(* notion 1000 *)
-definition l_e_st_eq_landau_n_mn_th1d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_mn x y m) y) (l_e_st_eq_landau_n_mn_th1c x y m) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_mn x y m) y) x).
-
-(* notion 1001 *)
-definition l_e_st_eq_landau_n_mn_th1e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl y z) x.(l_e_st_eq_landau_n_satz8b x y z (l_e_st_eq_landau_n_mn x y m) (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl y z) x i) (l_e_st_eq_landau_n_mn_th1a x y m) : l_e_st_eq_landau_n_is z (l_e_st_eq_landau_n_mn x y m)).
-
-(* notion 1002 *)
-definition l_e_st_eq_landau_n_mn_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x z.λn:l_e_st_eq_landau_n_more y u.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl u (l_e_st_eq_landau_n_mn x z m)) (l_e_st_eq_landau_n_pl z (l_e_st_eq_landau_n_mn x z m)) x y (l_e_st_eq_landau_n_ispl1 u z (l_e_st_eq_landau_n_mn x z m) (l_e_symis l_e_st_eq_landau_n_nat z u j)) (l_e_st_eq_landau_n_mn_th1b x z m) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl u (l_e_st_eq_landau_n_mn x z m)) y).
-
-(* notion 1003 *)
-definition l_e_st_eq_landau_n_ismn12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x z.λn:l_e_st_eq_landau_n_more y u.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_st_eq_landau_n_mn_th1e y u (l_e_st_eq_landau_n_mn x z m) n (l_e_st_eq_landau_n_mn_t2 x y z u m n i j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_mn x z m) (l_e_st_eq_landau_n_mn y u n)).
-
-(* notion 1004 *)
-definition l_e_st_eq_landau_n_1to ≝ λn:l_e_st_eq_landau_n_nat.(l_e_ot l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis x n) : Type[0]).
-
-(* notion 1005 *)
-definition l_e_st_eq_landau_n_outn ≝ λn:l_e_st_eq_landau_n_nat.λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x n.(l_e_out l_e_st_eq_landau_n_nat (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis y n) x l : l_e_st_eq_landau_n_1to n).
-
-(* notion 1006 *)
-definition l_e_st_eq_landau_n_inn ≝ λn:l_e_st_eq_landau_n_nat.λxn:l_e_st_eq_landau_n_1to n.(l_e_in l_e_st_eq_landau_n_nat (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis y n) xn : l_e_st_eq_landau_n_nat).
-
-(* notion 1007 *)
-definition l_e_st_eq_landau_n_1top ≝ λn:l_e_st_eq_landau_n_nat.λxn:l_e_st_eq_landau_n_1to n.(l_e_inp l_e_st_eq_landau_n_nat (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis y n) xn : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_inn n xn) n).
-
-(* notion 1008 *)
-definition l_e_st_eq_landau_n_isoutni ≝ λn:l_e_st_eq_landau_n_nat.λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x n.λy:l_e_st_eq_landau_n_nat.λk:l_e_st_eq_landau_n_lessis y n.λi:l_e_st_eq_landau_n_is x y.(l_e_isouti l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis z n) x l y k i : l_e_is (l_e_st_eq_landau_n_1to n) (l_e_st_eq_landau_n_outn n x l) (l_e_st_eq_landau_n_outn n y k)).
-
-(* notion 1009 *)
-definition l_e_st_eq_landau_n_isoutne ≝ λn:l_e_st_eq_landau_n_nat.λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x n.λy:l_e_st_eq_landau_n_nat.λk:l_e_st_eq_landau_n_lessis y n.λi:l_e_is (l_e_st_eq_landau_n_1to n) (l_e_st_eq_landau_n_outn n x l) (l_e_st_eq_landau_n_outn n y k).(l_e_isoute l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis z n) x l y k i : l_e_st_eq_landau_n_is x y).
-
-(* notion 1010 *)
-definition l_e_st_eq_landau_n_isinni ≝ λn:l_e_st_eq_landau_n_nat.λxn:l_e_st_eq_landau_n_1to n.λyn:l_e_st_eq_landau_n_1to n.λi:l_e_is (l_e_st_eq_landau_n_1to n) xn yn.(l_e_isini l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis z n) xn yn i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_inn n xn) (l_e_st_eq_landau_n_inn n yn)).
-
-(* notion 1011 *)
-definition l_e_st_eq_landau_n_isinne ≝ λn:l_e_st_eq_landau_n_nat.λxn:l_e_st_eq_landau_n_1to n.λyn:l_e_st_eq_landau_n_1to n.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_inn n xn) (l_e_st_eq_landau_n_inn n yn).(l_e_isine l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis z n) xn yn i : l_e_is (l_e_st_eq_landau_n_1to n) xn yn).
-
-(* notion 1012 *)
-definition l_e_st_eq_landau_n_isoutinn ≝ λn:l_e_st_eq_landau_n_nat.λxn:l_e_st_eq_landau_n_1to n.(l_e_isoutin l_e_st_eq_landau_n_nat (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis y n) xn : l_e_is (l_e_st_eq_landau_n_1to n) xn (l_e_st_eq_landau_n_outn n (l_e_st_eq_landau_n_inn n xn) (l_e_st_eq_landau_n_1top n xn))).
-
-(* notion 1013 *)
-definition l_e_st_eq_landau_n_isinoutn ≝ λn:l_e_st_eq_landau_n_nat.λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x n.(l_e_isinout l_e_st_eq_landau_n_nat (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis y n) x l : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_inn n (l_e_st_eq_landau_n_outn n x l))).
-
-(* notion 1014 *)
-definition l_e_st_eq_landau_n_1o ≝ (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1).
-
-(* notion 1015 *)
-definition l_e_st_eq_landau_n_singlet_u0 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_inn l_e_st_eq_landau_n_1 u : l_e_st_eq_landau_n_nat).
-
-(* notion 1016 *)
-definition l_e_st_eq_landau_n_singlet_t1 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_1 u : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_singlet_u0 u) l_e_st_eq_landau_n_1).
-
-(* notion 1017 *)
-definition l_e_st_eq_landau_n_singlet_t2 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_ore2 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_singlet_u0 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_singlet_u0 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz24 (l_e_st_eq_landau_n_singlet_u0 u)) (l_e_st_eq_landau_n_satz10d (l_e_st_eq_landau_n_singlet_u0 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_singlet_t1 u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_singlet_u0 u) l_e_st_eq_landau_n_1).
-
-(* notion 1018 *)
-definition l_e_st_eq_landau_n_singlet_th1 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_tris (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) u (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_singlet_u0 u) (l_e_st_eq_landau_n_singlet_t1 u)) l_e_st_eq_landau_n_1o (l_e_st_eq_landau_n_isoutinn l_e_st_eq_landau_n_1 u) (l_e_st_eq_landau_n_isoutni l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_singlet_u0 u) (l_e_st_eq_landau_n_singlet_t1 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_singlet_t2 u)) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) u l_e_st_eq_landau_n_1o).
-
-(* notion 1019 *)
-definition l_e_st_eq_landau_n_2 ≝ (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
-
-(* notion 1020 *)
-definition l_e_st_eq_landau_n_pair_t1 ≝ λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x l_e_st_eq_landau_n_2.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_2.(l_e_st_eq_landau_n_satz26 l_e_st_eq_landau_n_1 x (l_ore1 (l_e_st_eq_landau_n_less x l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_2) l n) : l_e_st_eq_landau_n_lessis x l_e_st_eq_landau_n_1).
-
-(* notion 1021 *)
-definition l_e_st_eq_landau_n_pair_t2 ≝ λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x l_e_st_eq_landau_n_2.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_2.(l_ore2 (l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz24 x) (l_e_st_eq_landau_n_satz10d x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pair_t1 x l n)) : l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1).
-
-(* notion 1022 *)
-definition l_e_st_eq_landau_n_pair_th1 ≝ λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x l_e_st_eq_landau_n_2.(l_or_th2 (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_2) (λt:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_pair_t2 x l t) : l_or (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_2)).
-
-(* notion 1023 *)
-definition l_e_st_eq_landau_n_pair_th2 ≝ (l_e_notis_th1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_ax3 l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz4e l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_nis l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1).
-
-(* notion 1024 *)
-definition l_e_st_eq_landau_n_1t ≝ (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_2) : l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2).
-
-(* notion 1025 *)
-definition l_e_st_eq_landau_n_2t ≝ (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_2)) : l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2).
-
-(* notion 1026 *)
-definition l_e_st_eq_landau_n_pair_u0 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.(l_e_st_eq_landau_n_inn l_e_st_eq_landau_n_2 u : l_e_st_eq_landau_n_nat).
-
-(* notion 1027 *)
-definition l_e_st_eq_landau_n_pair_t3 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.(l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_2 u : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_2).
-
-(* notion 1028 *)
-definition l_e_st_eq_landau_n_pair_t4 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutni l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_2) i : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u)) l_e_st_eq_landau_n_1t).
-
-(* notion 1029 *)
-definition l_e_st_eq_landau_n_pair_t5 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_1.(l_e_tris (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u)) l_e_st_eq_landau_n_1t (l_e_st_eq_landau_n_isoutinn l_e_st_eq_landau_n_2 u) (l_e_st_eq_landau_n_pair_t4 u i) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t).
-
-(* notion 1030 *)
-definition l_e_st_eq_landau_n_pair_t6 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_2.(l_e_st_eq_landau_n_isoutni l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_2)) i : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u)) l_e_st_eq_landau_n_2t).
-
-(* notion 1031 *)
-definition l_e_st_eq_landau_n_pair_t7 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_2.(l_e_tris (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u)) l_e_st_eq_landau_n_2t (l_e_st_eq_landau_n_isoutinn l_e_st_eq_landau_n_2 u) (l_e_st_eq_landau_n_pair_t6 u i) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t).
-
-(* notion 1032 *)
-definition l_e_st_eq_landau_n_pair_th3 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.(l_or_th9 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_2) (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t) (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t) (l_e_st_eq_landau_n_pair_th1 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u)) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_pair_t5 u t) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_pair_t7 u t) : l_or (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t) (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t)).
-
-(* notion 1033 *)
-definition l_e_st_eq_landau_n_pair_t9 ≝ λi:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t.(l_e_isini l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis x l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 l_e_st_eq_landau_n_2t) (l_e_st_eq_landau_n_pair_u0 l_e_st_eq_landau_n_1t)).
-
-(* notion 1034 *)
-definition l_e_st_eq_landau_n_pair_t10 ≝ λi:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t.(l_e_tr3is l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 l_e_st_eq_landau_n_2t) (l_e_st_eq_landau_n_pair_u0 l_e_st_eq_landau_n_1t) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_pair_t9 i) (l_e_symis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pair_u0 l_e_st_eq_landau_n_1t) (l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_2))) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1).
-
-(* notion 1035 *)
-definition l_e_st_eq_landau_n_pair_th4 ≝ (l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t) (l_e_st_eq_landau_n_is l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_pair_th2 (Πt:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t.l_e_st_eq_landau_n_pair_t10 t) : l_not (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t)).
-
-(* notion 1036 *)
-definition l_e_st_eq_landau_n_pair1type ≝ λalpha:Type[0].(Πx:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.alpha : Type[0]).
-
-(* notion 1037 *)
-definition l_e_st_eq_landau_n_pair1 ≝ λalpha:Type[0].λa:alpha.λb:alpha.(λx:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_ite (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) x l_e_st_eq_landau_n_1t) alpha a b : l_e_st_eq_landau_n_pair1type alpha).
-
-(* notion 1038 *)
-definition l_e_st_eq_landau_n_first1 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(p l_e_st_eq_landau_n_1t : alpha).
-
-(* notion 1039 *)
-definition l_e_st_eq_landau_n_second1 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(p l_e_st_eq_landau_n_2t : alpha).
-
-(* notion 1040 *)
-definition l_e_st_eq_landau_n_first1is1 ≝ λalpha:Type[0].λa:alpha.λb:alpha.(l_e_itet (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_1t l_e_st_eq_landau_n_1t) alpha a b (l_e_refis (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_1t) : l_e_is alpha (l_e_st_eq_landau_n_first1 alpha (l_e_st_eq_landau_n_pair1 alpha a b)) a).
-
-(* notion 1041 *)
-definition l_e_st_eq_landau_n_first1is2 ≝ λalpha:Type[0].λa:alpha.λb:alpha.(l_e_symis alpha (l_e_st_eq_landau_n_first1 alpha (l_e_st_eq_landau_n_pair1 alpha a b)) a (l_e_st_eq_landau_n_first1is1 alpha a b) : l_e_is alpha a (l_e_st_eq_landau_n_first1 alpha (l_e_st_eq_landau_n_pair1 alpha a b))).
-
-(* notion 1042 *)
-definition l_e_st_eq_landau_n_second1is1 ≝ λalpha:Type[0].λa:alpha.λb:alpha.(l_e_itef (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t) alpha a b l_e_st_eq_landau_n_pair_th4 : l_e_is alpha (l_e_st_eq_landau_n_second1 alpha (l_e_st_eq_landau_n_pair1 alpha a b)) b).
-
-(* notion 1043 *)
-definition l_e_st_eq_landau_n_second1is2 ≝ λalpha:Type[0].λa:alpha.λb:alpha.(l_e_symis alpha (l_e_st_eq_landau_n_second1 alpha (l_e_st_eq_landau_n_pair1 alpha a b)) b (l_e_st_eq_landau_n_second1is1 alpha a b) : l_e_is alpha b (l_e_st_eq_landau_n_second1 alpha (l_e_st_eq_landau_n_pair1 alpha a b))).
-
-(* notion 1044 *)
-definition l_e_st_eq_landau_n_pair_t11 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu1:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t.(l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) alpha p u l_e_st_eq_landau_n_1t u1 : l_e_is alpha (p u) (l_e_st_eq_landau_n_first1 alpha p)).
-
-(* notion 1045 *)
-definition l_e_st_eq_landau_n_pair_t12 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu1:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t.(l_e_symis alpha (q u) (l_e_st_eq_landau_n_first1 alpha q) (l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) alpha q u l_e_st_eq_landau_n_1t u1) : l_e_is alpha (l_e_st_eq_landau_n_first1 alpha q) (q u)).
-
-(* notion 1046 *)
-definition l_e_st_eq_landau_n_pair_t13 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu1:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t.(l_e_tr3is alpha (p u) (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q) (q u) (l_e_st_eq_landau_n_pair_t11 alpha p q i j u u1) i (l_e_st_eq_landau_n_pair_t12 alpha p q i j u u1) : l_e_is alpha (p u) (q u)).
-
-(* notion 1047 *)
-definition l_e_st_eq_landau_n_pair_t14 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu2:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t.(l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) alpha p u l_e_st_eq_landau_n_2t u2 : l_e_is alpha (p u) (l_e_st_eq_landau_n_second1 alpha p)).
-
-(* notion 1048 *)
-definition l_e_st_eq_landau_n_pair_t15 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu2:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t.(l_e_symis alpha (q u) (l_e_st_eq_landau_n_second1 alpha q) (l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) alpha q u l_e_st_eq_landau_n_2t u2) : l_e_is alpha (l_e_st_eq_landau_n_second1 alpha q) (q u)).
-
-(* notion 1049 *)
-definition l_e_st_eq_landau_n_pair_t16 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu2:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t.(l_e_tr3is alpha (p u) (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q) (q u) (l_e_st_eq_landau_n_pair_t14 alpha p q i j u u2) j (l_e_st_eq_landau_n_pair_t15 alpha p q i j u u2) : l_e_is alpha (p u) (q u)).
-
-(* notion 1050 *)
-definition l_e_st_eq_landau_n_pair_t17 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.(l_orapp (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t) (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t) (l_e_is alpha (p u) (q u)) (l_e_st_eq_landau_n_pair_th3 u) (λt:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t.l_e_st_eq_landau_n_pair_t13 alpha p q i j u t) (λt:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t.l_e_st_eq_landau_n_pair_t16 alpha p q i j u t) : l_e_is alpha (p u) (q u)).
-
-(* notion 1051 *)
-definition l_e_st_eq_landau_n_pair_th5 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).(l_e_fisi (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) alpha p q (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_pair_t17 alpha p q i j t) : l_e_is (l_e_st_eq_landau_n_pair1type alpha) p q).
-
-(* notion 1052 *)
-definition l_e_st_eq_landau_n_pair_q0 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(l_e_st_eq_landau_n_pair1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p) : l_e_st_eq_landau_n_pair1type alpha).
-
-(* notion 1053 *)
-definition l_e_st_eq_landau_n_pair_t18 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(l_e_st_eq_landau_n_first1is1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p) : l_e_is alpha (l_e_st_eq_landau_n_first1 alpha (l_e_st_eq_landau_n_pair_q0 alpha p)) (l_e_st_eq_landau_n_first1 alpha p)).
-
-(* notion 1054 *)
-definition l_e_st_eq_landau_n_pair_t19 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(l_e_st_eq_landau_n_second1is1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p) : l_e_is alpha (l_e_st_eq_landau_n_second1 alpha (l_e_st_eq_landau_n_pair_q0 alpha p)) (l_e_st_eq_landau_n_second1 alpha p)).
-
-(* notion 1055 *)
-definition l_e_st_eq_landau_n_pair1is1 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(l_e_st_eq_landau_n_pair_th5 alpha (l_e_st_eq_landau_n_pair_q0 alpha p) p (l_e_st_eq_landau_n_pair_t18 alpha p) (l_e_st_eq_landau_n_pair_t19 alpha p) : l_e_is (l_e_st_eq_landau_n_pair1type alpha) (l_e_st_eq_landau_n_pair1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p)) p).
-
-(* notion 1056 *)
-definition l_e_st_eq_landau_n_pair1is2 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(l_e_symis (l_e_st_eq_landau_n_pair1type alpha) (l_e_st_eq_landau_n_pair1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p)) p (l_e_st_eq_landau_n_pair1is1 alpha p) : l_e_is (l_e_st_eq_landau_n_pair1type alpha) p (l_e_st_eq_landau_n_pair1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p))).
-
-(* notion 1057 *)
-definition l_e_st_eq_landau_n_lessisi3 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_lessisi2 x x (l_e_refis l_e_st_eq_landau_n_nat x) : l_e_st_eq_landau_n_lessis x x).
-
-(* notion 1058 *)
-definition l_e_st_eq_landau_n_1out ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a x) : l_e_st_eq_landau_n_1to x).
-
-(* notion 1059 *)
-definition l_e_st_eq_landau_n_xout ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_outn x x (l_e_st_eq_landau_n_lessisi3 x) : l_e_st_eq_landau_n_1to x).
-
-(* notion 1060 *)
-definition l_e_st_eq_landau_n_left_ui ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_inn y u : l_e_st_eq_landau_n_nat).
-
-(* notion 1061 *)
-definition l_e_st_eq_landau_n_left_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_1top y u : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_left_ui x y l u) y).
-
-(* notion 1062 *)
-definition l_e_st_eq_landau_n_left_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_left_ui x y l u) y x (l_e_st_eq_landau_n_left_t1 x y l u) l : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_left_ui x y l u) x).
-
-(* notion 1063 *)
-definition l_e_st_eq_landau_n_left1to ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_left_ui x y l u) (l_e_st_eq_landau_n_left_t2 x y l u) : l_e_st_eq_landau_n_1to x).
-
-(* notion 1064 *)
-definition l_e_st_eq_landau_n_left_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l u) (l_e_st_eq_landau_n_left1to x y l v).(l_e_st_eq_landau_n_isoutne x (l_e_st_eq_landau_n_left_ui x y l u) (l_e_st_eq_landau_n_left_t2 x y l u) (l_e_st_eq_landau_n_left_ui x y l v) (l_e_st_eq_landau_n_left_t2 x y l v) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_left_ui x y l u) (l_e_st_eq_landau_n_left_ui x y l v)).
-
-(* notion 1065 *)
-definition l_e_st_eq_landau_n_thleft1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l u) (l_e_st_eq_landau_n_left1to x y l v).(l_e_st_eq_landau_n_isinne y u v (l_e_st_eq_landau_n_left_t3 x y l u v i) : l_e_is (l_e_st_eq_landau_n_1to y) u v).
-
-(* notion 1066 *)
-definition l_e_st_eq_landau_n_thleft2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.(λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λt:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l u) (l_e_st_eq_landau_n_left1to x y l v).l_e_st_eq_landau_n_thleft1 x y l u v t : l_e_injective (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_left1to x y l t)).
-
-(* notion 1067 *)
-definition l_e_st_eq_landau_n_right_ui ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_inn y u : l_e_st_eq_landau_n_nat).
-
-(* notion 1068 *)
-definition l_e_st_eq_landau_n_right_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_1top y u : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_right_ui x y u) y).
-
-(* notion 1069 *)
-definition l_e_st_eq_landau_n_right_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_right_ui x y u) y x (l_e_st_eq_landau_n_right_t4 x y u) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y u)) (l_e_st_eq_landau_n_pl x y)).
-
-(* notion 1070 *)
-definition l_e_st_eq_landau_n_right1to ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y u)) (l_e_st_eq_landau_n_right_t5 x y u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y)).
-
-(* notion 1071 *)
-definition l_e_st_eq_landau_n_right_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_right1to x y u) (l_e_st_eq_landau_n_right1to x y v).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y u)) (l_e_st_eq_landau_n_right_t5 x y u) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y v)) (l_e_st_eq_landau_n_right_t5 x y v) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y u)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y v))).
-
-(* notion 1072 *)
-definition l_e_st_eq_landau_n_right_t7 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_right1to x y u) (l_e_st_eq_landau_n_right1to x y v).(l_e_st_eq_landau_n_satz20e (l_e_st_eq_landau_n_right_ui x y u) (l_e_st_eq_landau_n_right_ui x y v) x (l_e_st_eq_landau_n_right_t6 x y u v i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_right_ui x y u) (l_e_st_eq_landau_n_right_ui x y v)).
-
-(* notion 1073 *)
-definition l_e_st_eq_landau_n_thright1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_right1to x y u) (l_e_st_eq_landau_n_right1to x y v).(l_e_st_eq_landau_n_isinne y u v (l_e_st_eq_landau_n_right_t7 x y u v i) : l_e_is (l_e_st_eq_landau_n_1to y) u v).
-
-(* notion 1074 *)
-definition l_e_st_eq_landau_n_left ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.alpha.(λt:l_e_st_eq_landau_n_1to y.f (l_e_st_eq_landau_n_left1to x y l t) : Πt:l_e_st_eq_landau_n_1to y.alpha).
-
-(* notion 1075 *)
-definition l_e_st_eq_landau_n_right ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).alpha.(λt:l_e_st_eq_landau_n_1to y.f (l_e_st_eq_landau_n_right1to x y t) : Πt:l_e_st_eq_landau_n_1to y.alpha).
-
-(* notion 1076 *)
-definition l_e_st_eq_landau_n_left_t4 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.(l_e_st_eq_landau_n_lessisi2 y x i : l_e_st_eq_landau_n_lessis y x).
-
-(* notion 1077 *)
-definition l_e_st_eq_landau_n_left_t5 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.(l_e_st_eq_landau_n_lessisi2 x y (l_e_symis l_e_st_eq_landau_n_nat y x i) : l_e_st_eq_landau_n_lessis x y).
-
-(* notion 1078 *)
-definition l_e_st_eq_landau_n_left_f1 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.(l_e_st_eq_landau_n_left alpha y x (l_e_st_eq_landau_n_left_t5 alpha x y i f) f : Πt:l_e_st_eq_landau_n_1to x.alpha).
-
-(* notion 1079 *)
-definition l_e_st_eq_landau_n_left_f2 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.(l_e_st_eq_landau_n_left alpha x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) (l_e_st_eq_landau_n_left_f1 alpha x y i f) : Πt:l_e_st_eq_landau_n_1to y.alpha).
-
-(* notion 1080 *)
-definition l_e_st_eq_landau_n_left_t6 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_inn y u) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_inn y u) y x (l_e_st_eq_landau_n_1top y u) (l_e_st_eq_landau_n_left_t4 alpha x y i f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_inn y u) (l_e_st_eq_landau_n_inn x (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u))).
-
-(* notion 1081 *)
-definition l_e_st_eq_landau_n_left_t7 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.λu:l_e_st_eq_landau_n_1to y.(l_e_tris (l_e_st_eq_landau_n_1to y) u (l_e_st_eq_landau_n_outn y (l_e_st_eq_landau_n_inn y u) (l_e_st_eq_landau_n_1top y u)) (l_e_st_eq_landau_n_left1to y x (l_e_st_eq_landau_n_left_t5 alpha x y i f) (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u)) (l_e_st_eq_landau_n_isoutinn y u) (l_e_st_eq_landau_n_isoutni y (l_e_st_eq_landau_n_inn y u) (l_e_st_eq_landau_n_1top y u) (l_e_st_eq_landau_n_inn x (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_inn x (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u)) x y (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u)) (l_e_st_eq_landau_n_left_t5 alpha x y i f)) (l_e_st_eq_landau_n_left_t6 alpha x y i f u)) : l_e_is (l_e_st_eq_landau_n_1to y) u (l_e_st_eq_landau_n_left1to y x (l_e_st_eq_landau_n_left_t5 alpha x y i f) (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u))).
-
-(* notion 1082 *)
-definition l_e_st_eq_landau_n_left_t8 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.λu:l_e_st_eq_landau_n_1to y.(l_e_isf (l_e_st_eq_landau_n_1to y) alpha f u (l_e_st_eq_landau_n_left1to y x (l_e_st_eq_landau_n_left_t5 alpha x y i f) (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u)) (l_e_st_eq_landau_n_left_t7 alpha x y i f u) : l_e_is alpha (f u) (l_e_st_eq_landau_n_left_f2 alpha x y i f u)).
-
-(* notion 1083 *)
-definition l_e_st_eq_landau_n_thleft ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.(l_e_fisi (l_e_st_eq_landau_n_1to y) alpha f (l_e_st_eq_landau_n_left_f2 alpha x y i f) (λt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_left_t8 alpha x y i f t) : l_e_is (Πt:l_e_st_eq_landau_n_1to y.alpha) f (l_e_st_eq_landau_n_left alpha x y (l_e_st_eq_landau_n_lessisi2 y x i) (l_e_st_eq_landau_n_left alpha y x (l_e_st_eq_landau_n_lessisi2 x y (l_e_symis l_e_st_eq_landau_n_nat y x i)) f))).
-
-(* notion 1084 *)
-definition l_e_st_eq_landau_n_frac ≝ (l_e_st_eq_landau_n_pair1type l_e_st_eq_landau_n_nat : Type[0]).
-
-(* notion 1085 *)
-definition l_e_st_eq_landau_n_fr ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pair1 l_e_st_eq_landau_n_nat x1 x2 : l_e_st_eq_landau_n_frac).
-
-(* notion 1086 *)
-definition l_e_st_eq_landau_n_num ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_first1 l_e_st_eq_landau_n_nat x : l_e_st_eq_landau_n_nat).
-
-(* notion 1087 *)
-definition l_e_st_eq_landau_n_den ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_second1 l_e_st_eq_landau_n_nat x : l_e_st_eq_landau_n_nat).
-
-(* notion 1088 *)
-definition l_e_st_eq_landau_n_numis ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_first1is1 l_e_st_eq_landau_n_nat x1 x2 : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) x1).
-
-(* notion 1089 *)
-definition l_e_st_eq_landau_n_isnum ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_first1is2 l_e_st_eq_landau_n_nat x1 x2 : l_e_st_eq_landau_n_is x1 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2))).
-
-(* notion 1090 *)
-definition l_e_st_eq_landau_n_denis ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_second1is1 l_e_st_eq_landau_n_nat x1 x2 : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) x2).
-
-(* notion 1091 *)
-definition l_e_st_eq_landau_n_isden ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_second1is2 l_e_st_eq_landau_n_nat x1 x2 : l_e_st_eq_landau_n_is x2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))).
-
-(* notion 1092 *)
-definition l_e_st_eq_landau_n_1x ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_num x : l_e_st_eq_landau_n_nat).
-
-(* notion 1093 *)
-definition l_e_st_eq_landau_n_2x ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_den x : l_e_st_eq_landau_n_nat).
-
-(* notion 1094 *)
-definition l_e_st_eq_landau_n_fris ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_pair1is1 l_e_st_eq_landau_n_nat x : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) x).
-
-(* notion 1095 *)
-definition l_e_st_eq_landau_n_isfr ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_pair1is2 l_e_st_eq_landau_n_nat x : l_e_is l_e_st_eq_landau_n_frac x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1096 *)
-definition l_e_st_eq_landau_n_12isnd ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists12 x1 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) y2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_isnum x1 x2) (l_e_st_eq_landau_n_isden y1 y2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2)))).
-
-(* notion 1097 *)
-definition l_e_st_eq_landau_n_ndis12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_12isnd x1 x2 y1 y2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x1 y2)).
-
-(* notion 1098 *)
-definition l_e_st_eq_landau_n_1disnd ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists1 n1 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_isnum n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1099 *)
-definition l_e_st_eq_landau_n_ndis1d ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_1disnd x n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1100 *)
-definition l_e_st_eq_landau_n_n2isnd ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists2 n2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_isden n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)))).
-
-(* notion 1101 *)
-definition l_e_st_eq_landau_n_ndisn2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_n2isnd x n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)).
-
-(* notion 1102 *)
-definition l_e_st_eq_landau_n_isn ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x1 n.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_fr t x2) x1 n i : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr n x2)).
-
-(* notion 1103 *)
-definition l_e_st_eq_landau_n_isd ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x2 n.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_fr x1 t) x2 n i : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr x1 n)).
-
-(* notion 1104 *)
-definition l_e_st_eq_landau_n_isnd ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x1 y1.λj:l_e_st_eq_landau_n_is x2 y2.(l_e_tris l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 x2) (l_e_st_eq_landau_n_fr y1 y2) (l_e_st_eq_landau_n_isn x1 x2 y1 i) (l_e_st_eq_landau_n_isd y1 x2 y2 j) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)).
-
-(* notion 1105 *)
-definition l_e_st_eq_landau_n_1y ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_num y : l_e_st_eq_landau_n_nat).
-
-(* notion 1106 *)
-definition l_e_st_eq_landau_n_2y ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_den y : l_e_st_eq_landau_n_nat).
-
-(* notion 1107 *)
-definition l_e_st_eq_landau_n_eq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : Prop).
-
-(* notion 1108 *)
-definition l_e_st_eq_landau_n_eqi12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_ndis12 x1 x2 y1 y2) i (l_e_st_eq_landau_n_12isnd y1 y2 x1 x2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)).
-
-(* notion 1109 *)
-definition l_e_st_eq_landau_n_eqi1 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)).(l_e_isp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq t (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) x (l_e_st_eq_landau_n_eqi12 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x) n1 n2 i) (l_e_st_eq_landau_n_fris x) : l_e_st_eq_landau_n_eq x (l_e_st_eq_landau_n_fr n1 n2)).
-
-(* notion 1110 *)
-definition l_e_st_eq_landau_n_eqi2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2).(l_e_isp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr n1 n2) t) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) x (l_e_st_eq_landau_n_eqi12 n1 n2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x) i) (l_e_st_eq_landau_n_fris x) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr n1 n2) x).
-
-(* notion 1111 *)
-definition l_e_st_eq_landau_n_satz37 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) : l_e_st_eq_landau_n_eq x x).
-
-(* notion 1112 *)
-definition l_e_st_eq_landau_n_refeq ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz37 x : l_e_st_eq_landau_n_eq x x).
-
-(* notion 1113 *)
-definition l_e_st_eq_landau_n_refeq1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λi:l_e_is l_e_st_eq_landau_n_frac x y.(l_e_isp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq x t) x y (l_e_st_eq_landau_n_refeq x) i : l_e_st_eq_landau_n_eq x y).
-
-(* notion 1114 *)
-definition l_e_st_eq_landau_n_refeq2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λi:l_e_is l_e_st_eq_landau_n_frac x y.(l_e_isp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq t x) x y (l_e_st_eq_landau_n_refeq x) i : l_e_st_eq_landau_n_eq y x).
-
-(* notion 1115 *)
-definition l_e_st_eq_landau_n_eqnd ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x1 y1.λj:l_e_st_eq_landau_n_is x2 y2.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2) (l_e_st_eq_landau_n_isnd x1 x2 y1 y2 i j) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)).
-
-(* notion 1116 *)
-definition l_e_st_eq_landau_n_eqn ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x1 n.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr n x2) (l_e_st_eq_landau_n_isn x1 x2 n i) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr n x2)).
-
-(* notion 1117 *)
-definition l_e_st_eq_landau_n_eqd ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x2 n.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr x1 n) (l_e_st_eq_landau_n_isd x1 x2 n i) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr x1 n)).
-
-(* notion 1118 *)
-definition l_e_st_eq_landau_n_satz38 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) e : l_e_st_eq_landau_n_eq y x).
-
-(* notion 1119 *)
-definition l_e_st_eq_landau_n_symeq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_satz38 x y e : l_e_st_eq_landau_n_eq y x).
-
-(* notion 1120 *)
-definition l_e_st_eq_landau_n_ii1_t1 ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts b c) d) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts b c)) (l_e_st_eq_landau_n_assts2 b c d) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_ts b c) d) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts b c))).
-
-(* notion 1121 *)
-definition l_e_st_eq_landau_n_stets ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_nat.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d))) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts b c))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_ts b c)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_ts c b)) (l_e_st_eq_landau_n_assts1 a b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts b c)) a (l_e_st_eq_landau_n_ii1_t1 a b c d)) (l_e_st_eq_landau_n_assts2 a d (l_e_st_eq_landau_n_ts b c)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts b c) (l_e_st_eq_landau_n_ts c b) (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_comts b c)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_ts c b))).
-
-(* notion 1122 *)
-definition l_e_st_eq_landau_n_ii1_t2 ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts c d) b) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts d c) b) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts c b)) (l_e_st_eq_landau_n_comts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_ts c d) (l_e_st_eq_landau_n_ts d c) b (l_e_st_eq_landau_n_comts c d)) (l_e_st_eq_landau_n_assts1 d c b) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts c b))).
-
-(* notion 1123 *)
-definition l_e_st_eq_landau_n_ii1_anders ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d))) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts c b))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_ts c b)) (l_e_st_eq_landau_n_assts1 a b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts c b)) a (l_e_st_eq_landau_n_ii1_t2 a b c d)) (l_e_st_eq_landau_n_assts2 a d (l_e_st_eq_landau_n_ts c b)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_ts c b))).
-
-(* notion 1124 *)
-definition l_e_st_eq_landau_n_1z ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_num z : l_e_st_eq_landau_n_nat).
-
-(* notion 1125 *)
-definition l_e_st_eq_landau_n_2z ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_den z : l_e_st_eq_landau_n_nat).
-
-(* notion 1126 *)
-definition l_e_st_eq_landau_n_139_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) e f : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1127 *)
-definition l_e_st_eq_landau_n_139_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1128 *)
-definition l_e_st_eq_landau_n_139_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1129 *)
-definition l_e_st_eq_landau_n_139_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_139_t2 x y z e f)) (l_e_st_eq_landau_n_139_t1 x y z e f) (l_e_st_eq_landau_n_139_t3 x y z e f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1130 *)
-definition l_e_st_eq_landau_n_satz39 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_st_eq_landau_n_satz33b (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_139_t4 x y z e f) : l_e_st_eq_landau_n_eq x z).
-
-(* notion 1131 *)
-definition l_e_st_eq_landau_n_139_anders ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) e f) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1132 *)
-definition l_e_st_eq_landau_n_treq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_st_eq_landau_n_satz39 x y z e f : l_e_st_eq_landau_n_eq x z).
-
-(* notion 1133 *)
-definition l_e_st_eq_landau_n_treq1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq z x.λf:l_e_st_eq_landau_n_eq z y.(l_e_st_eq_landau_n_treq x z y (l_e_st_eq_landau_n_symeq z x e) f : l_e_st_eq_landau_n_eq x y).
-
-(* notion 1134 *)
-definition l_e_st_eq_landau_n_treq2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y z.(l_e_st_eq_landau_n_treq x z y e (l_e_st_eq_landau_n_symeq y z f) : l_e_st_eq_landau_n_eq x y).
-
-(* notion 1135 *)
-definition l_e_st_eq_landau_n_tr3eq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.λg:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_treq x y u e (l_e_st_eq_landau_n_treq y z u f g) : l_e_st_eq_landau_n_eq x u).
-
-(* notion 1136 *)
-definition l_e_st_eq_landau_n_tr4eq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.λg:l_e_st_eq_landau_n_eq z u.λh:l_e_st_eq_landau_n_eq u v.(l_e_st_eq_landau_n_tr3eq x y z v e f (l_e_st_eq_landau_n_treq z u v g h) : l_e_st_eq_landau_n_eq x v).
-
-(* notion 1137 *)
-definition l_e_st_eq_landau_n_satz40 ≝ λx:l_e_st_eq_landau_n_frac.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_eqi1 x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts n (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n) (l_e_st_eq_landau_n_ts n (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2x x) n)) (l_e_st_eq_landau_n_assts2 (l_e_st_eq_landau_n_1x x) n (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_eq x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n))).
-
-(* notion 1138 *)
-definition l_e_st_eq_landau_n_satz40a ≝ λx:l_e_st_eq_landau_n_frac.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_symeq x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n)) (l_e_st_eq_landau_n_satz40 x n) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n)) x).
-
-(* notion 1139 *)
-definition l_e_st_eq_landau_n_satz40b ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_eqi12 x1 x2 (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x1 (l_e_st_eq_landau_n_ts x2 n)) (l_e_st_eq_landau_n_ts x1 (l_e_st_eq_landau_n_ts n x2)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x1 n) x2) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts x2 n) (l_e_st_eq_landau_n_ts n x2) x1 (l_e_st_eq_landau_n_comts x2 n)) (l_e_st_eq_landau_n_assts2 x1 n x2)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n))).
-
-(* notion 1140 *)
-definition l_e_st_eq_landau_n_satz40c ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n)) (l_e_st_eq_landau_n_satz40b x1 x2 n) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n)) (l_e_st_eq_landau_n_fr x1 x2)).
-
-(* notion 1141 *)
-definition l_e_st_eq_landau_n_moref ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : Prop).
-
-(* notion 1142 *)
-definition l_e_st_eq_landau_n_lessf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : Prop).
-
-(* notion 1143 *)
-definition l_e_st_eq_landau_n_morefi12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2).(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts y1 x2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_12isnd x1 x2 y1 y2) (l_e_st_eq_landau_n_12isnd y1 y2 x1 x2) m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)).
-
-(* notion 1144 *)
-definition l_e_st_eq_landau_n_lessfi12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2).(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts y1 x2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_12isnd x1 x2 y1 y2) (l_e_st_eq_landau_n_12isnd y1 y2 x1 x2) l : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)).
-
-(* notion 1145 *)
-definition l_e_st_eq_landau_n_morefi1 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)).(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_n2isnd x n1 n2) (l_e_st_eq_landau_n_1disnd x n1 n2) m : l_e_st_eq_landau_n_moref x (l_e_st_eq_landau_n_fr n1 n2)).
-
-(* notion 1146 *)
-definition l_e_st_eq_landau_n_morefi2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2).(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_1disnd x n1 n2) (l_e_st_eq_landau_n_n2isnd x n1 n2) m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr n1 n2) x).
-
-(* notion 1147 *)
-definition l_e_st_eq_landau_n_lessfi1 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)).(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_n2isnd x n1 n2) (l_e_st_eq_landau_n_1disnd x n1 n2) l : l_e_st_eq_landau_n_lessf x (l_e_st_eq_landau_n_fr n1 n2)).
-
-(* notion 1148 *)
-definition l_e_st_eq_landau_n_lessfi2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2).(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_1disnd x n1 n2) (l_e_st_eq_landau_n_n2isnd x n1 n2) l : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr n1 n2) x).
-
-(* notion 1149 *)
-definition l_e_st_eq_landau_n_satz41 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz10 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : l_orec3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y)).
-
-(* notion 1150 *)
-definition l_e_st_eq_landau_n_satz41a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz10a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : l_or3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y)).
-
-(* notion 1151 *)
-definition l_e_st_eq_landau_n_satz41b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : l_ec3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y)).
-
-(* notion 1152 *)
-definition l_e_st_eq_landau_n_satz42 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz11 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) m : l_e_st_eq_landau_n_lessf y x).
-
-(* notion 1153 *)
-definition l_e_st_eq_landau_n_satz43 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_satz12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) l : l_e_st_eq_landau_n_moref y x).
-
-(* notion 1154 *)
-definition l_e_st_eq_landau_n_1u ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_num u : l_e_st_eq_landau_n_nat).
-
-(* notion 1155 *)
-definition l_e_st_eq_landau_n_2u ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_den u : l_e_st_eq_landau_n_nat).
-
-(* notion 1156 *)
-definition l_e_st_eq_landau_n_244_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) f (l_e_st_eq_landau_n_symeq x z e) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)))).
-
-(* notion 1157 *)
-definition l_e_st_eq_landau_n_244_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_244_t1 x y z u m e f) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1158 *)
-definition l_e_st_eq_landau_n_244_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_244_t2 x y z u m e f)) (l_e_st_eq_landau_n_satz32d (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1159 *)
-definition l_e_st_eq_landau_n_satz44 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_e_st_eq_landau_n_satz33a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_244_t3 x y z u m e f)) : l_e_st_eq_landau_n_moref z u).
-
-(* notion 1160 *)
-definition l_e_st_eq_landau_n_eqmoref12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.λm:l_e_st_eq_landau_n_moref x z.(l_e_st_eq_landau_n_satz44 x z y u m e f : l_e_st_eq_landau_n_moref y u).
-
-(* notion 1161 *)
-definition l_e_st_eq_landau_n_eqmoref1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref x z.(l_e_st_eq_landau_n_satz44 x z y z m e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_moref y z).
-
-(* notion 1162 *)
-definition l_e_st_eq_landau_n_eqmoref2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref z x.(l_e_st_eq_landau_n_satz44 z x z y m (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_moref z y).
-
-(* notion 1163 *)
-definition l_e_st_eq_landau_n_satz45 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_e_st_eq_landau_n_satz42 u z (l_e_st_eq_landau_n_satz44 y x u z (l_e_st_eq_landau_n_satz43 x y l) f e) : l_e_st_eq_landau_n_lessf z u).
-
-(* notion 1164 *)
-definition l_e_st_eq_landau_n_eqlessf12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.λl:l_e_st_eq_landau_n_lessf x z.(l_e_st_eq_landau_n_satz45 x z y u l e f : l_e_st_eq_landau_n_lessf y u).
-
-(* notion 1165 *)
-definition l_e_st_eq_landau_n_eqlessf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf x z.(l_e_st_eq_landau_n_satz45 x z y z l e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_lessf y z).
-
-(* notion 1166 *)
-definition l_e_st_eq_landau_n_eqlessf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf z x.(l_e_st_eq_landau_n_satz45 z x z y l (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_lessf z y).
-
-(* notion 1167 *)
-definition l_e_st_eq_landau_n_moreq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_or (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) : Prop).
-
-(* notion 1168 *)
-definition l_e_st_eq_landau_n_lesseq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_or (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) : Prop).
-
-(* notion 1169 *)
-definition l_e_st_eq_landau_n_moreqi2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_ori2 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) e : l_e_st_eq_landau_n_moreq x y).
-
-(* notion 1170 *)
-definition l_e_st_eq_landau_n_lesseqi2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_ori2 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) e : l_e_st_eq_landau_n_lesseq x y).
-
-(* notion 1171 *)
-definition l_e_st_eq_landau_n_moreqi1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_ori1 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) m : l_e_st_eq_landau_n_moreq x y).
-
-(* notion 1172 *)
-definition l_e_st_eq_landau_n_lesseqi1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_ori1 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) l : l_e_st_eq_landau_n_lesseq x y).
-
-(* notion 1173 *)
-definition l_e_st_eq_landau_n_satz41c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.(l_ec3_th7 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) (l_comor (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) m) : l_not (l_e_st_eq_landau_n_lessf x y)).
-
-(* notion 1174 *)
-definition l_e_st_eq_landau_n_satz41d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.(l_ec3_th9 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) l : l_not (l_e_st_eq_landau_n_moref x y)).
-
-(* notion 1175 *)
-definition l_e_st_eq_landau_n_satz41e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λn:l_not (l_e_st_eq_landau_n_moref x y).(l_or3_th2 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41a x y) n : l_e_st_eq_landau_n_lesseq x y).
-
-(* notion 1176 *)
-definition l_e_st_eq_landau_n_satz41f ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λn:l_not (l_e_st_eq_landau_n_lessf x y).(l_comor (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_or3_th3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41a x y) n) : l_e_st_eq_landau_n_moreq x y).
-
-(* notion 1177 *)
-definition l_e_st_eq_landau_n_satz41g ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_or_th3 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_ec3e23 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) m) (l_ec3e21 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) m) : l_not (l_e_st_eq_landau_n_lesseq x y)).
-
-(* notion 1178 *)
-definition l_e_st_eq_landau_n_satz41h ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_or_th3 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_ec3e32 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) l) (l_ec3e31 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) l) : l_not (l_e_st_eq_landau_n_moreq x y)).
-
-(* notion 1179 *)
-definition l_e_st_eq_landau_n_satz41j ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λn:l_not (l_e_st_eq_landau_n_moreq x y).(l_or3e3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41a x y) (l_or_th5 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) n) (l_or_th4 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) n) : l_e_st_eq_landau_n_lessf x y).
-
-(* notion 1180 *)
-definition l_e_st_eq_landau_n_satz41k ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λn:l_not (l_e_st_eq_landau_n_lesseq x y).(l_or3e2 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41a x y) (l_or_th4 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) n) (l_or_th5 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) n) : l_e_st_eq_landau_n_moref x y).
-
-(* notion 1181 *)
-definition l_e_st_eq_landau_n_246_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.λn:l_e_st_eq_landau_n_moref x y.(l_ori1 (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_satz44 x y z u n e f) : l_e_st_eq_landau_n_moreq z u).
-
-(* notion 1182 *)
-definition l_e_st_eq_landau_n_246_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.λg:l_e_st_eq_landau_n_eq x y.(l_ori2 (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_tr3eq z x y u (l_e_st_eq_landau_n_symeq x z e) g f) : l_e_st_eq_landau_n_moreq z u).
-
-(* notion 1183 *)
-definition l_e_st_eq_landau_n_satz46 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_orapp (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moreq z u) m (λt:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_246_t1 x y z u m e f t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_246_t2 x y z u m e f t) : l_e_st_eq_landau_n_moreq z u).
-
-(* notion 1184 *)
-definition l_e_st_eq_landau_n_eqmoreq12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.λm:l_e_st_eq_landau_n_moreq x z.(l_e_st_eq_landau_n_satz46 x z y u m e f : l_e_st_eq_landau_n_moreq y u).
-
-(* notion 1185 *)
-definition l_e_st_eq_landau_n_eqmoreq1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moreq x z.(l_e_st_eq_landau_n_satz46 x z y z m e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_moreq y z).
-
-(* notion 1186 *)
-definition l_e_st_eq_landau_n_eqmoreq2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moreq z x.(l_e_st_eq_landau_n_satz46 z x z y m (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_moreq z y).
-
-(* notion 1187 *)
-definition l_e_st_eq_landau_n_247_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.λk:l_e_st_eq_landau_n_lessf x y.(l_ori1 (l_e_st_eq_landau_n_lessf z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_satz45 x y z u k e f) : l_e_st_eq_landau_n_lesseq z u).
-
-(* notion 1188 *)
-definition l_e_st_eq_landau_n_247_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.λg:l_e_st_eq_landau_n_eq x y.(l_ori2 (l_e_st_eq_landau_n_lessf z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_tr3eq z x y u (l_e_st_eq_landau_n_symeq x z e) g f) : l_e_st_eq_landau_n_lesseq z u).
-
-(* notion 1189 *)
-definition l_e_st_eq_landau_n_satz47 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_orapp (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_lesseq z u) l (λt:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_247_t1 x y z u l e f t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_247_t2 x y z u l e f t) : l_e_st_eq_landau_n_lesseq z u).
-
-(* notion 1190 *)
-definition l_e_st_eq_landau_n_eqlesseq12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.λl:l_e_st_eq_landau_n_lesseq x z.(l_e_st_eq_landau_n_satz47 x z y u l e f : l_e_st_eq_landau_n_lesseq y u).
-
-(* notion 1191 *)
-definition l_e_st_eq_landau_n_eqlesseq1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lesseq x z.(l_e_st_eq_landau_n_satz47 x z y z l e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_lesseq y z).
-
-(* notion 1192 *)
-definition l_e_st_eq_landau_n_eqlesseq2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lesseq z x.(l_e_st_eq_landau_n_satz47 z x z y l (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_lesseq z y).
-
-(* notion 1193 *)
-definition l_e_st_eq_landau_n_satz48 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.(l_or_th9 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_lessf y x) (l_e_st_eq_landau_n_eq y x) m (λt:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz42 x y t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz38 x y t) : l_e_st_eq_landau_n_lesseq y x).
-
-(* notion 1194 *)
-definition l_e_st_eq_landau_n_satz49 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.(l_or_th9 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref y x) (l_e_st_eq_landau_n_eq y x) l (λt:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz43 x y t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz38 x y t) : l_e_st_eq_landau_n_moreq y x).
-
-(* notion 1195 *)
-definition l_e_st_eq_landau_n_250_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf y z.(l_e_st_eq_landau_n_satz34a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) l k : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1196 *)
-definition l_e_st_eq_landau_n_250_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf y z.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)))) (l_e_st_eq_landau_n_250_t1 x y z l k) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1197 *)
-definition l_e_st_eq_landau_n_satz50 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf y z.(l_e_st_eq_landau_n_satz33c (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_250_t2 x y z l k) : l_e_st_eq_landau_n_lessf x z).
-
-(* notion 1198 *)
-definition l_e_st_eq_landau_n_trlessf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf y z.(l_e_st_eq_landau_n_satz50 x y z l k : l_e_st_eq_landau_n_lessf x z).
-
-(* notion 1199 *)
-definition l_e_st_eq_landau_n_trmoref ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref y z.(l_e_st_eq_landau_n_satz43 z x (l_e_st_eq_landau_n_satz50 z y x (l_e_st_eq_landau_n_satz42 y z n) (l_e_st_eq_landau_n_satz42 x y m)) : l_e_st_eq_landau_n_moref x z).
-
-(* notion 1200 *)
-definition l_e_st_eq_landau_n_satz51a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lessf y z.(l_orapp (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_lessf x z) l (λt:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz50 x y z t k) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_eqlessf1 y x z (l_e_st_eq_landau_n_symeq x y t) k) : l_e_st_eq_landau_n_lessf x z).
-
-(* notion 1201 *)
-definition l_e_st_eq_landau_n_satz51b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lesseq y z.(l_orapp (l_e_st_eq_landau_n_lessf y z) (l_e_st_eq_landau_n_eq y z) (l_e_st_eq_landau_n_lessf x z) k (λt:l_e_st_eq_landau_n_lessf y z.l_e_st_eq_landau_n_satz50 x y z l t) (λt:l_e_st_eq_landau_n_eq y z.l_e_st_eq_landau_n_eqlessf2 y z x t l) : l_e_st_eq_landau_n_lessf x z).
-
-(* notion 1202 *)
-definition l_e_st_eq_landau_n_satz51c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moref y z.(l_e_st_eq_landau_n_satz43 z x (l_e_st_eq_landau_n_satz51b z y x (l_e_st_eq_landau_n_satz42 y z n) (l_e_st_eq_landau_n_satz48 x y m)) : l_e_st_eq_landau_n_moref x z).
-
-(* notion 1203 *)
-definition l_e_st_eq_landau_n_satz51d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moreq y z.(l_e_st_eq_landau_n_satz43 z x (l_e_st_eq_landau_n_satz51a z y x (l_e_st_eq_landau_n_satz48 y z n) (l_e_st_eq_landau_n_satz42 x y m)) : l_e_st_eq_landau_n_moref x z).
-
-(* notion 1204 *)
-definition l_e_st_eq_landau_n_252_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_ori2 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_eq x z) (l_e_st_eq_landau_n_treq x y z e f) : l_e_st_eq_landau_n_lesseq x z).
-
-(* notion 1205 *)
-definition l_e_st_eq_landau_n_252_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λe:l_e_st_eq_landau_n_eq x y.λj:l_e_st_eq_landau_n_lessf y z.(l_ori1 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_eq x z) (l_e_st_eq_landau_n_satz51a x y z l j) : l_e_st_eq_landau_n_lesseq x z).
-
-(* notion 1206 *)
-definition l_e_st_eq_landau_n_252_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λe:l_e_st_eq_landau_n_eq x y.(l_orapp (l_e_st_eq_landau_n_lessf y z) (l_e_st_eq_landau_n_eq y z) (l_e_st_eq_landau_n_lesseq x z) k (λt:l_e_st_eq_landau_n_lessf y z.l_e_st_eq_landau_n_252_t2 x y z l k e t) (λt:l_e_st_eq_landau_n_eq y z.l_e_st_eq_landau_n_252_t1 x y z l k e t) : l_e_st_eq_landau_n_lesseq x z).
-
-(* notion 1207 *)
-definition l_e_st_eq_landau_n_252_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λj:l_e_st_eq_landau_n_lessf x y.(l_ori1 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_eq x z) (l_e_st_eq_landau_n_satz51b x y z j k) : l_e_st_eq_landau_n_lesseq x z).
-
-(* notion 1208 *)
-definition l_e_st_eq_landau_n_satz52 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.(l_orapp (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_lesseq x z) l (λt:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_252_t4 x y z l k t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_252_t3 x y z l k t) : l_e_st_eq_landau_n_lesseq x z).
-
-(* notion 1209 *)
-definition l_e_st_eq_landau_n_trlesseq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.(l_e_st_eq_landau_n_satz52 x y z l k : l_e_st_eq_landau_n_lesseq x z).
-
-(* notion 1210 *)
-definition l_e_st_eq_landau_n_252_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λj:l_e_st_eq_landau_n_lessf x y.(l_ori1 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_eq x z) (l_e_st_eq_landau_n_satz51b x y z j k) : l_e_st_eq_landau_n_lesseq x z).
-
-(* notion 1211 *)
-definition l_e_st_eq_landau_n_252_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqlesseq1 y x z (l_e_st_eq_landau_n_symeq x y e) k : l_e_st_eq_landau_n_lesseq x z).
-
-(* notion 1212 *)
-definition l_e_st_eq_landau_n_252_anders ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.(l_orapp (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_lesseq x z) l (λt:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_252_t5 x y z l k t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_252_t6 x y z l k t) : l_e_st_eq_landau_n_lesseq x z).
-
-(* notion 1213 *)
-definition l_e_st_eq_landau_n_trmoreq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq y z.(l_e_st_eq_landau_n_satz49 z x (l_e_st_eq_landau_n_satz52 z y x (l_e_st_eq_landau_n_satz48 y z n) (l_e_st_eq_landau_n_satz48 x y m)) : l_e_st_eq_landau_n_moreq x z).
-
-(* notion 1214 *)
-definition l_e_st_eq_landau_n_253_t1 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_satz18 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1215 *)
-definition l_e_st_eq_landau_n_253_t2 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_morefi2 x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_253_t1 x) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_2x x)) x).
-
-(* notion 1216 *)
-definition l_e_st_eq_landau_n_satz53 ≝ λx:l_e_st_eq_landau_n_frac.(l_somei l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_moref t x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_253_t2 x) : l_some l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_moref t x)).
-
-(* notion 1217 *)
-definition l_e_st_eq_landau_n_254_t1 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_distpt2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_satz18a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1218 *)
-definition l_e_st_eq_landau_n_254_t2 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_lessfi2 x (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_254_t1 x) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x))) x).
-
-(* notion 1219 *)
-definition l_e_st_eq_landau_n_satz54 ≝ λx:l_e_st_eq_landau_n_frac.(l_somei l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_lessf t x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_254_t2 x) : l_some l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_lessf t x)).
-
-(* notion 1220 *)
-definition l_e_st_eq_landau_n_255_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_satz19f (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1221 *)
-definition l_e_st_eq_landau_n_255_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_satz19c (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1222 *)
-definition l_e_st_eq_landau_n_255_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_distpt2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_255_t1 x y l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1223 *)
-definition l_e_st_eq_landau_n_255_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_lessfi1 x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_255_t3 x y l) : l_e_st_eq_landau_n_lessf x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1224 *)
-definition l_e_st_eq_landau_n_255_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_distpt2 (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_255_t2 x y l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1225 *)
-definition l_e_st_eq_landau_n_255_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_lessfi2 y (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_255_t5 x y l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) y).
-
-(* notion 1226 *)
-definition l_e_st_eq_landau_n_255_t7 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_andi (l_e_st_eq_landau_n_lessf x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) y) (l_e_st_eq_landau_n_255_t4 x y l) (l_e_st_eq_landau_n_255_t6 x y l) : l_and (l_e_st_eq_landau_n_lessf x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) y)).
-
-(* notion 1227 *)
-definition l_e_st_eq_landau_n_satz55 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_somei l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_and (l_e_st_eq_landau_n_lessf x t) (l_e_st_eq_landau_n_lessf t y)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_255_t7 x y l) : l_some l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_and (l_e_st_eq_landau_n_lessf x t) (l_e_st_eq_landau_n_lessf t y))).
-
-(* notion 1228 *)
-definition l_e_st_eq_landau_n_pf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_frac).
-
-(* notion 1229 *)
-definition l_e_st_eq_landau_n_ii3_t1 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_ts y1 x2) (l_e_st_eq_landau_n_ndis12 x1 x2 y1 y2) (l_e_st_eq_landau_n_ndis12 y1 y2 x1 x2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2))).
-
-(* notion 1230 *)
-definition l_e_st_eq_landau_n_ii3_t2 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) x2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2)) y2 (l_e_st_eq_landau_n_denis x1 x2) (l_e_st_eq_landau_n_denis y1 y2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x2 y2)).
-
-(* notion 1231 *)
-definition l_e_st_eq_landau_n_pf12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2) (l_e_st_eq_landau_n_ii3_t1 x1 x2 y1 y2) (l_e_st_eq_landau_n_ii3_t2 x1 x2 y1 y2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2))).
-
-(* notion 1232 *)
-definition l_e_st_eq_landau_n_ii3_t3 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ndisn2 x n1 n2) (l_e_st_eq_landau_n_ndis1d x n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1233 *)
-definition l_e_st_eq_landau_n_ii3_t4 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) n2 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_denis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)).
-
-(* notion 1234 *)
-definition l_e_st_eq_landau_n_pf1 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2) (l_e_st_eq_landau_n_ii3_t3 x n1 n2) (l_e_st_eq_landau_n_ii3_t4 x n1 n2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2))).
-
-(* notion 1235 *)
-definition l_e_st_eq_landau_n_ii3_t5 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ndis1d x n1 n2) (l_e_st_eq_landau_n_ndisn2 x n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2))).
-
-(* notion 1236 *)
-definition l_e_st_eq_landau_n_ii3_t6 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) n2 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_denis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1237 *)
-definition l_e_st_eq_landau_n_pf2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ii3_t5 x n1 n2) (l_e_st_eq_landau_n_ii3_t6 x n1 n2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1238 *)
-definition l_e_st_eq_landau_n_pfeq12a ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_pf12 x1 x2 y1 y2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2))).
-
-(* notion 1239 *)
-definition l_e_st_eq_landau_n_pfeq12b ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_pf12 x1 x2 y1 y2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2))).
-
-(* notion 1240 *)
-definition l_e_st_eq_landau_n_pfeq1a ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_pf1 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2))).
-
-(* notion 1241 *)
-definition l_e_st_eq_landau_n_pfeq1b ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_pf1 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_fr n1 n2))).
-
-(* notion 1242 *)
-definition l_e_st_eq_landau_n_pfeq2a ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pf2 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1243 *)
-definition l_e_st_eq_landau_n_pfeq2b ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pf2 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr n1 n2) x)).
-
-(* notion 1244 *)
-definition l_e_st_eq_landau_n_356_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u)) e : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u)))).
-
-(* notion 1245 *)
-definition l_e_st_eq_landau_n_356_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_356_t1 z u x y f e : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1246 *)
-definition l_e_st_eq_landau_n_356_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u)))).
-
-(* notion 1247 *)
-definition l_e_st_eq_landau_n_356_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_356_t3 x y z u e f) (l_e_st_eq_landau_n_356_t1 x y z u e f) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
-
-(* notion 1248 *)
-definition l_e_st_eq_landau_n_356_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_356_t2 x y z u e f) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
-
-(* notion 1249 *)
-definition l_e_st_eq_landau_n_356_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_356_t4 x y z u e f) (l_e_st_eq_landau_n_356_t5 x y z u e f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))))).
-
-(* notion 1250 *)
-definition l_e_st_eq_landau_n_356_t7 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_disttp1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_356_t6 x y z u e f) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
-
-(* notion 1251 *)
-definition l_e_st_eq_landau_n_satz56 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_eqi12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_356_t7 x y z u e f) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1252 *)
-definition l_e_st_eq_landau_n_eqpf12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_satz56 x y z u e f : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1253 *)
-definition l_e_st_eq_landau_n_eqpf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqpf12 x y z z e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
-
-(* notion 1254 *)
-definition l_e_st_eq_landau_n_eqpf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqpf12 z z x y (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y)).
-
-(* notion 1255 *)
-definition l_e_st_eq_landau_n_satz57 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 n) (l_e_st_eq_landau_n_fr x2 n)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n)) (l_e_st_eq_landau_n_ts n n)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x1 x2) n) (l_e_st_eq_landau_n_ts n n)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x1 x2) n) (l_e_st_eq_landau_n_pfeq12a x1 n x2 n) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n)) (l_e_st_eq_landau_n_ts n n) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x1 x2) n) (l_e_st_eq_landau_n_distpt1 x1 x2 n)) (l_e_st_eq_landau_n_satz40c (l_e_st_eq_landau_n_pl x1 x2) n n) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 n) (l_e_st_eq_landau_n_fr x2 n)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x1 x2) n)).
-
-(* notion 1256 *)
-definition l_e_st_eq_landau_n_satz57a ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 n) (l_e_st_eq_landau_n_fr x2 n)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x1 x2) n) (l_e_st_eq_landau_n_satz57 x1 x2 n) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x1 x2) n) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 n) (l_e_st_eq_landau_n_fr x2 n))).
-
-(* notion 1257 *)
-definition l_e_st_eq_landau_n_satz58 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_compl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x y) (l_e_st_eq_landau_n_pf y x)).
-
-(* notion 1258 *)
-definition l_e_st_eq_landau_n_compf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz58 x y : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x y) (l_e_st_eq_landau_n_pf y x)).
-
-(* notion 1259 *)
-definition l_e_st_eq_landau_n_359_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1260 *)
-definition l_e_st_eq_landau_n_359_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_359_t1 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1261 *)
-definition l_e_st_eq_landau_n_359_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_disttp1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_359_t2 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1262 *)
-definition l_e_st_eq_landau_n_359_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_assts2 (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1263 *)
-definition l_e_st_eq_landau_n_359_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_359_t3 x y z) (l_e_st_eq_landau_n_359_t4 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1264 *)
-definition l_e_st_eq_landau_n_359_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1265 *)
-definition l_e_st_eq_landau_n_359_t7 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_359_t5 x y z) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_359_t6 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1266 *)
-definition l_e_st_eq_landau_n_satz59 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pfeq2a z (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_359_t7 x y z) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pfeq1b x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z))).
-
-(* notion 1267 *)
-definition l_e_st_eq_landau_n_asspf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz59 x y z : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z))).
-
-(* notion 1268 *)
-definition l_e_st_eq_landau_n_asspf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_asspf1 x y z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z)).
-
-(* notion 1269 *)
-definition l_e_st_eq_landau_n_stets1 ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) c) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts b c)) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts c b)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a c) b) (l_e_st_eq_landau_n_assts1 a b c) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts b c) (l_e_st_eq_landau_n_ts c b) a (l_e_st_eq_landau_n_comts b c)) (l_e_st_eq_landau_n_assts2 a c b) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) c) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a c) b)).
-
-(* notion 1270 *)
-definition l_e_st_eq_landau_n_359_t8 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_disttp1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_stets1 (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1271 *)
-definition l_e_st_eq_landau_n_359_t9 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_assts2 (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_stets1 (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1272 *)
-definition l_e_st_eq_landau_n_359_anderst7 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_359_t8 x y z) (l_e_st_eq_landau_n_359_t9 x y z)) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1273 *)
-definition l_e_st_eq_landau_n_360_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz18 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))).
-
-(* notion 1274 *)
-definition l_e_st_eq_landau_n_360_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz32a (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_360_t1 x y) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1275 *)
-definition l_e_st_eq_landau_n_360_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1276 *)
-definition l_e_st_eq_landau_n_360_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_ismore2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_360_t3 x y) (l_e_st_eq_landau_n_360_t2 x y) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1277 *)
-definition l_e_st_eq_landau_n_satz60 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_morefi2 x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_360_t4 x y) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x y) x).
-
-(* notion 1278 *)
-definition l_e_st_eq_landau_n_satz60a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_pf x y) x (l_e_st_eq_landau_n_satz60 x y) : l_e_st_eq_landau_n_lessf x (l_e_st_eq_landau_n_pf x y)).
-
-(* notion 1279 *)
-definition l_e_st_eq_landau_n_361_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz32a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z) m : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z))).
-
-(* notion 1280 *)
-definition l_e_st_eq_landau_n_361_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_stets1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_stets1 (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_361_t1 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1281 *)
-definition l_e_st_eq_landau_n_361_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_stets1 (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1282 *)
-definition l_e_st_eq_landau_n_361_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz19h (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_361_t3 x y z m) (l_e_st_eq_landau_n_361_t2 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1283 *)
-definition l_e_st_eq_landau_n_361_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_361_t4 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1284 *)
-definition l_e_st_eq_landau_n_361_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz32a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_361_t5 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z))).
-
-(* notion 1285 *)
-definition l_e_st_eq_landau_n_361_t7 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_361_t6 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
-
-(* notion 1286 *)
-definition l_e_st_eq_landau_n_satz61 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_morefi12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_361_t7 x y z m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
-
-(* notion 1287 *)
-definition l_e_st_eq_landau_n_satz62a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz61 x y z m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
-
-(* notion 1288 *)
-definition l_e_st_eq_landau_n_satz62b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqpf1 x y z e : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
-
-(* notion 1289 *)
-definition l_e_st_eq_landau_n_satz62c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_satz61 y x z (l_e_st_eq_landau_n_satz43 x y l)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
-
-(* notion 1290 *)
-definition l_e_st_eq_landau_n_satz62d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_compf x z) (l_e_st_eq_landau_n_compf y z) (l_e_st_eq_landau_n_satz62a x y z m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y)).
-
-(* notion 1291 *)
-definition l_e_st_eq_landau_n_satz62e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqpf2 x y z e : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y)).
-
-(* notion 1292 *)
-definition l_e_st_eq_landau_n_satz62f ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_compf x z) (l_e_st_eq_landau_n_compf y z) (l_e_st_eq_landau_n_satz62c x y z l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y)).
-
-(* notion 1293 *)
-definition l_e_st_eq_landau_n_satz62g ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref2 (l_e_st_eq_landau_n_pf x u) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_eqpf1 x y u e) (l_e_st_eq_landau_n_satz62d z u x m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1294 *)
-definition l_e_st_eq_landau_n_satz62h ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf u y) (l_e_st_eq_landau_n_compf x z) (l_e_st_eq_landau_n_compf y u) (l_e_st_eq_landau_n_satz62g x y z u e m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf u y)).
-
-(* notion 1295 *)
-definition l_e_st_eq_landau_n_satz62j ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_eqlessf2 (l_e_st_eq_landau_n_pf x u) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_eqpf1 x y u e) (l_e_st_eq_landau_n_satz62f z u x l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1296 *)
-definition l_e_st_eq_landau_n_satz62k ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf u y) (l_e_st_eq_landau_n_compf x z) (l_e_st_eq_landau_n_compf y u) (l_e_st_eq_landau_n_satz62j x y z u e l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf u y)).
-
-(* notion 1297 *)
-definition l_e_st_eq_landau_n_363_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz41a x y : l_or3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y)).
-
-(* notion 1298 *)
-definition l_e_st_eq_landau_n_363_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz41b (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) : l_ec3 (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z))).
-
-(* notion 1299 *)
-definition l_e_st_eq_landau_n_satz63a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z).(l_ec3_th11 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_363_t1 x y z) (l_e_st_eq_landau_n_363_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz62b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz62a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz62c x y z u) m : l_e_st_eq_landau_n_moref x y).
-
-(* notion 1300 *)
-definition l_e_st_eq_landau_n_satz63b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z).(l_ec3_th10 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_363_t1 x y z) (l_e_st_eq_landau_n_363_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz62b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz62a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz62c x y z u) e : l_e_st_eq_landau_n_eq x y).
-
-(* notion 1301 *)
-definition l_e_st_eq_landau_n_satz63c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z).(l_ec3_th12 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_363_t1 x y z) (l_e_st_eq_landau_n_363_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz62b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz62a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz62c x y z u) l : l_e_st_eq_landau_n_lessf x y).
-
-(* notion 1302 *)
-definition l_e_st_eq_landau_n_satz63d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y).(l_e_st_eq_landau_n_satz63a x y z (l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_compf z x) (l_e_st_eq_landau_n_compf z y) m) : l_e_st_eq_landau_n_moref x y).
-
-(* notion 1303 *)
-definition l_e_st_eq_landau_n_satz63e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y).(l_e_st_eq_landau_n_satz63b x y z (l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_compf x z) e (l_e_st_eq_landau_n_compf z y)) : l_e_st_eq_landau_n_eq x y).
-
-(* notion 1304 *)
-definition l_e_st_eq_landau_n_satz63f ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λf:l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y).(l_e_st_eq_landau_n_satz63c x y z (l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_compf z x) (l_e_st_eq_landau_n_compf z y) f) : l_e_st_eq_landau_n_lessf x y).
-
-(* notion 1305 *)
-definition l_e_st_eq_landau_n_364_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_satz61 x y z m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
-
-(* notion 1306 *)
-definition l_e_st_eq_landau_n_364_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf u y) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_compf z y) (l_e_st_eq_landau_n_compf u y) (l_e_st_eq_landau_n_satz61 z u y n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1307 *)
-definition l_e_st_eq_landau_n_satz64 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_trmoref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_364_t1 x y z u m n) (l_e_st_eq_landau_n_364_t2 x y z u m n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1308 *)
-definition l_e_st_eq_landau_n_satz64a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_satz64 y x u z (l_e_st_eq_landau_n_satz43 x y l) (l_e_st_eq_landau_n_satz43 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1309 *)
-definition l_e_st_eq_landau_n_satz65a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moref z u.(l_orapp (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)) m (λv:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz64 x y z u v n) (λv:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz62g x y z u v n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1310 *)
-definition l_e_st_eq_landau_n_satz65b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moreq z u.(l_orapp (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)) n (λv:l_e_st_eq_landau_n_moref z u.l_e_st_eq_landau_n_satz64 x y z u m v) (λv:l_e_st_eq_landau_n_eq z u.l_e_st_eq_landau_n_eqmoref2 (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_eqpf2 z u y v) (l_e_st_eq_landau_n_satz61 x y z m)) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1311 *)
-definition l_e_st_eq_landau_n_satz65c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_satz65a y x u z (l_e_st_eq_landau_n_satz49 x y l) (l_e_st_eq_landau_n_satz43 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1312 *)
-definition l_e_st_eq_landau_n_satz65d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lesseq z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_satz65b y x u z (l_e_st_eq_landau_n_satz43 x y l) (l_e_st_eq_landau_n_satz49 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1313 *)
-definition l_e_st_eq_landau_n_366_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_moreqi2 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_satz56 x y z u e f) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1314 *)
-definition l_e_st_eq_landau_n_366_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.λo:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_moreqi1 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_satz65a x y z u m o) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1315 *)
-definition l_e_st_eq_landau_n_366_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.(l_orapp (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)) n (λv:l_e_st_eq_landau_n_moref z u.l_e_st_eq_landau_n_366_t2 x y z u m n e v) (λv:l_e_st_eq_landau_n_eq z u.l_e_st_eq_landau_n_366_t1 x y z u m n e v) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1316 *)
-definition l_e_st_eq_landau_n_366_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λo:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_moreqi1 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_satz65b x y z u o n) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1317 *)
-definition l_e_st_eq_landau_n_satz66 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.(l_orapp (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)) m (λv:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_366_t4 x y z u m n v) (λv:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_366_t3 x y z u m n v) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1318 *)
-definition l_e_st_eq_landau_n_satz66a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq z u.(l_e_st_eq_landau_n_satz48 (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_satz66 y x u z (l_e_st_eq_landau_n_satz49 x y l) (l_e_st_eq_landau_n_satz49 z u k)) : l_e_st_eq_landau_n_lesseq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
-
-(* notion 1319 *)
-definition l_e_st_eq_landau_n_367_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.(l_e_st_eq_landau_n_eqmoref1 (l_e_st_eq_landau_n_pf y v) x y e (l_e_st_eq_landau_n_satz60 y v) : l_e_st_eq_landau_n_moref x y).
-
-(* notion 1320 *)
-definition l_e_st_eq_landau_n_367_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λv:l_e_st_eq_landau_n_frac.(l_imp_th3 (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_satz41d x y l) (λt:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.l_e_st_eq_landau_n_367_t1 x y l v t) : l_not (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x)).
-
-(* notion 1321 *)
-definition l_e_st_eq_landau_n_vorbemerkung67 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.(l_some_th5 l_e_st_eq_landau_n_frac (λv:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x) (λv:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_367_t2 x y l v) : l_not (l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y t) x))).
-
-(* notion 1322 *)
-definition l_e_st_eq_landau_n_satz67b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.λf:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y w) x.(l_e_st_eq_landau_n_satz63e v w y (l_e_st_eq_landau_n_treq2 (l_e_st_eq_landau_n_pf y v) (l_e_st_eq_landau_n_pf y w) x e f) : l_e_st_eq_landau_n_eq v w).
-
-(* notion 1323 *)
-definition l_e_st_eq_landau_n_367_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_onei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) t) (l_e_st_eq_landau_n_satz8b (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) m : l_e_st_eq_landau_n_one (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) t)).
-
-(* notion 1324 *)
-definition l_e_st_eq_landau_n_367_vo ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_ind l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) t) (l_e_st_eq_landau_n_367_t3 x y m) : l_e_st_eq_landau_n_nat).
-
-(* notion 1325 *)
-definition l_e_st_eq_landau_n_367_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_oneax l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) t) (l_e_st_eq_landau_n_367_t3 x y m) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_367_vo x y m))).
-
-(* notion 1326 *)
-definition l_e_st_eq_landau_n_367_w ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_367_vo x y m) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_frac).
-
-(* notion 1327 *)
-definition l_e_st_eq_landau_n_367_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_treq y (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_satz40 y (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_eqd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_eq y (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
-
-(* notion 1328 *)
-definition l_e_st_eq_landau_n_367_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_tr4eq (l_e_st_eq_landau_n_pf y (l_e_st_eq_landau_n_367_w x y m)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_367_vo x y m) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_367_vo x y m)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) x (l_e_st_eq_landau_n_eqpf1 y (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_367_w x y m) (l_e_st_eq_landau_n_367_t5 x y m)) (l_e_st_eq_landau_n_satz57 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_367_vo x y m) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_367_vo x y m)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_367_vo x y m)) (l_e_st_eq_landau_n_367_t4 x y m))) (l_e_st_eq_landau_n_satz40a x (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y (l_e_st_eq_landau_n_367_w x y m)) x).
-
-(* notion 1329 *)
-definition l_e_st_eq_landau_n_satz67a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_somei l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y t) x) (l_e_st_eq_landau_n_367_w x y m) (l_e_st_eq_landau_n_367_t6 x y m) : l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y t) x)).
-
-(* notion 1330 *)
-definition l_e_st_eq_landau_n_mf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_367_w x y m : l_e_st_eq_landau_n_frac).
-
-(* notion 1331 *)
-definition l_e_st_eq_landau_n_satz67c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_367_t6 x y m : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y (l_e_st_eq_landau_n_mf x y m)) x).
-
-(* notion 1332 *)
-definition l_e_st_eq_landau_n_satz67d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_pf y (l_e_st_eq_landau_n_mf x y m)) x (l_e_st_eq_landau_n_satz67c x y m) : l_e_st_eq_landau_n_eq x (l_e_st_eq_landau_n_pf y (l_e_st_eq_landau_n_mf x y m))).
-
-(* notion 1333 *)
-definition l_e_st_eq_landau_n_satz67e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.(l_e_st_eq_landau_n_satz67b x y v (l_e_st_eq_landau_n_mf x y m) e (l_e_st_eq_landau_n_satz67c x y m) : l_e_st_eq_landau_n_eq v (l_e_st_eq_landau_n_mf x y m)).
-
-(* notion 1334 *)
-definition l_e_st_eq_landau_n_tf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_frac).
-
-(* notion 1335 *)
-definition l_e_st_eq_landau_n_ii4_t1 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) x1 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) y1 (l_e_st_eq_landau_n_numis x1 x2) (l_e_st_eq_landau_n_numis y1 y2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x1 y1)).
-
-(* notion 1336 *)
-definition l_e_st_eq_landau_n_ii4_t2 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) x2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2)) y2 (l_e_st_eq_landau_n_denis x1 x2) (l_e_st_eq_landau_n_denis y1 y2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x2 y2)).
-
-(* notion 1337 *)
-definition l_e_st_eq_landau_n_tf12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2) (l_e_st_eq_landau_n_ii4_t1 x1 x2 y1 y2) (l_e_st_eq_landau_n_ii4_t2 x1 x2 y1 y2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2))).
-
-(* notion 1338 *)
-definition l_e_st_eq_landau_n_ii4_t3 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) n1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_numis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1)).
-
-(* notion 1339 *)
-definition l_e_st_eq_landau_n_ii4_t4 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) n2 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_denis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)).
-
-(* notion 1340 *)
-definition l_e_st_eq_landau_n_tf1 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2) (l_e_st_eq_landau_n_ii4_t3 x n1 n2) (l_e_st_eq_landau_n_ii4_t4 x n1 n2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2))).
-
-(* notion 1341 *)
-definition l_e_st_eq_landau_n_ii4_t5 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) n1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_numis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x))).
-
-(* notion 1342 *)
-definition l_e_st_eq_landau_n_ii4_t6 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) n2 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_denis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))).
-
-(* notion 1343 *)
-definition l_e_st_eq_landau_n_tf2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ii4_t5 x n1 n2) (l_e_st_eq_landau_n_ii4_t6 x n1 n2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1344 *)
-definition l_e_st_eq_landau_n_tfeq12a ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_tf12 x1 x2 y1 y2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2))).
-
-(* notion 1345 *)
-definition l_e_st_eq_landau_n_tfeq12b ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_tf12 x1 x2 y1 y2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2))).
-
-(* notion 1346 *)
-definition l_e_st_eq_landau_n_tfeq1a ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_tf1 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2))).
-
-(* notion 1347 *)
-definition l_e_st_eq_landau_n_tfeq1b ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_tf1 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr n1 n2))).
-
-(* notion 1348 *)
-definition l_e_st_eq_landau_n_tfeq2a ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_tf2 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)))).
-
-(* notion 1349 *)
-definition l_e_st_eq_landau_n_tfeq2b ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_tf2 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr n1 n2) x)).
-
-(* notion 1350 *)
-definition l_e_st_eq_landau_n_468_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) e f : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)))).
-
-(* notion 1351 *)
-definition l_e_st_eq_landau_n_stets2 ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts d c)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a c) (l_e_st_eq_landau_n_ts d b)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a c) (l_e_st_eq_landau_n_ts b d)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts c d) (l_e_st_eq_landau_n_ts d c) (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_comts c d)) (l_e_st_eq_landau_n_stets a b d c) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts d b) (l_e_st_eq_landau_n_ts b d) (l_e_st_eq_landau_n_ts a c) (l_e_st_eq_landau_n_comts d b)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a c) (l_e_st_eq_landau_n_ts b d))).
-
-(* notion 1352 *)
-definition l_e_st_eq_landau_n_468_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_stets2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_468_t1 x y z u e f) (l_e_st_eq_landau_n_stets2 (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
-
-(* notion 1353 *)
-definition l_e_st_eq_landau_n_satz68 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_eqi12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_468_t2 x y z u e f) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1354 *)
-definition l_e_st_eq_landau_n_eqtf12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_satz68 x y z u e f : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1355 *)
-definition l_e_st_eq_landau_n_eqtf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqtf12 x y z z e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)).
-
-(* notion 1356 *)
-definition l_e_st_eq_landau_n_eqtf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqtf12 z z x y (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y)).
-
-(* notion 1357 *)
-definition l_e_st_eq_landau_n_satz69 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf y x)).
-
-(* notion 1358 *)
-definition l_e_st_eq_landau_n_comtf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz69 x y : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf y x)).
-
-(* notion 1359 *)
-definition l_e_st_eq_landau_n_satz70 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_tfeq2a z (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_tfeq1b x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z))).
-
-(* notion 1360 *)
-definition l_e_st_eq_landau_n_asstf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz70 x y z : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z))).
-
-(* notion 1361 *)
-definition l_e_st_eq_landau_n_asstf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_asstf1 x y z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z)).
-
-(* notion 1362 *)
-definition l_e_st_eq_landau_n_471_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))))) (l_e_st_eq_landau_n_tfeq1a x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_disttp2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_satz57a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))))).
-
-(* notion 1363 *)
-definition l_e_st_eq_landau_n_471_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_treq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_assts2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_assts2 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_satz40c (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_tf x y)).
-
-(* notion 1364 *)
-definition l_e_st_eq_landau_n_471_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_treq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_eqd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_471_t2 x z y) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_tf x z)).
-
-(* notion 1365 *)
-definition l_e_st_eq_landau_n_satz71 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_treq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))))) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_471_t1 x y z) (l_e_st_eq_landau_n_eqpf12 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_471_t2 x y z) (l_e_st_eq_landau_n_471_t3 x y z)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z))).
-
-(* notion 1366 *)
-definition l_e_st_eq_landau_n_disttpf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_tf z (l_e_st_eq_landau_n_pf x y)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_comtf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_satz71 z x y) (l_e_st_eq_landau_n_eqpf12 (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_comtf z x) (l_e_st_eq_landau_n_comtf z y)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z))).
-
-(* notion 1367 *)
-definition l_e_st_eq_landau_n_disttpf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz71 x y z : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z))).
-
-(* notion 1368 *)
-definition l_e_st_eq_landau_n_distptf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_disttpf1 x y z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_pf x y) z)).
-
-(* notion 1369 *)
-definition l_e_st_eq_landau_n_distptf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_disttpf2 x y z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z))).
-
-(* notion 1370 *)
-definition l_e_st_eq_landau_n_472_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz32a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z)) m : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z)))).
-
-(* notion 1371 *)
-definition l_e_st_eq_landau_n_472_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_stets2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_stets2 (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_472_t1 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
-
-(* notion 1372 *)
-definition l_e_st_eq_landau_n_satz72a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_morefi12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_472_t2 x y z m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)).
-
-(* notion 1373 *)
-definition l_e_st_eq_landau_n_satz72b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_satz68 x y z z e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)).
-
-(* notion 1374 *)
-definition l_e_st_eq_landau_n_satz72c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_satz72a y x z (l_e_st_eq_landau_n_satz43 x y l)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)).
-
-(* notion 1375 *)
-definition l_e_st_eq_landau_n_satz72d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_comtf x z) (l_e_st_eq_landau_n_comtf y z) (l_e_st_eq_landau_n_satz72a x y z m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y)).
-
-(* notion 1376 *)
-definition l_e_st_eq_landau_n_satz72e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqtf2 x y z e : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y)).
-
-(* notion 1377 *)
-definition l_e_st_eq_landau_n_satz72f ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_comtf x z) (l_e_st_eq_landau_n_comtf y z) (l_e_st_eq_landau_n_satz72c x y z l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y)).
-
-(* notion 1378 *)
-definition l_e_st_eq_landau_n_satz72g ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref2 (l_e_st_eq_landau_n_tf x u) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_eqtf1 x y u e) (l_e_st_eq_landau_n_satz72d z u x m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1379 *)
-definition l_e_st_eq_landau_n_satz72h ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf u y) (l_e_st_eq_landau_n_comtf x z) (l_e_st_eq_landau_n_comtf y u) (l_e_st_eq_landau_n_satz72g x y z u e m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf u y)).
-
-(* notion 1380 *)
-definition l_e_st_eq_landau_n_satz72j ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_eqlessf2 (l_e_st_eq_landau_n_tf x u) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_eqtf1 x y u e) (l_e_st_eq_landau_n_satz72f z u x l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1381 *)
-definition l_e_st_eq_landau_n_satz72k ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf u y) (l_e_st_eq_landau_n_comtf x z) (l_e_st_eq_landau_n_comtf y u) (l_e_st_eq_landau_n_satz72j x y z u e l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf u y)).
-
-(* notion 1382 *)
-definition l_e_st_eq_landau_n_473_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz41a x y : l_or3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y)).
-
-(* notion 1383 *)
-definition l_e_st_eq_landau_n_473_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz41b (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) : l_ec3 (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z))).
-
-(* notion 1384 *)
-definition l_e_st_eq_landau_n_satz73a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z).(l_ec3_th11 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_473_t1 x y z) (l_e_st_eq_landau_n_473_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz72b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz72a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz72c x y z u) m : l_e_st_eq_landau_n_moref x y).
-
-(* notion 1385 *)
-definition l_e_st_eq_landau_n_satz73b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z).(l_ec3_th10 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_473_t1 x y z) (l_e_st_eq_landau_n_473_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz72b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz72a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz72c x y z u) e : l_e_st_eq_landau_n_eq x y).
-
-(* notion 1386 *)
-definition l_e_st_eq_landau_n_satz73c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z).(l_ec3_th12 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_473_t1 x y z) (l_e_st_eq_landau_n_473_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz72b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz72a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz72c x y z u) l : l_e_st_eq_landau_n_lessf x y).
-
-(* notion 1387 *)
-definition l_e_st_eq_landau_n_satz73d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y).(l_e_st_eq_landau_n_satz73a x y z (l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_comtf z x) (l_e_st_eq_landau_n_comtf z y) m) : l_e_st_eq_landau_n_moref x y).
-
-(* notion 1388 *)
-definition l_e_st_eq_landau_n_satz73e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y).(l_e_st_eq_landau_n_satz73b x y z (l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_comtf x z) e (l_e_st_eq_landau_n_comtf z y)) : l_e_st_eq_landau_n_eq x y).
-
-(* notion 1389 *)
-definition l_e_st_eq_landau_n_satz73f ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y).(l_e_st_eq_landau_n_satz73c x y z (l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_comtf z x) (l_e_st_eq_landau_n_comtf z y) l) : l_e_st_eq_landau_n_lessf x y).
-
-(* notion 1390 *)
-definition l_e_st_eq_landau_n_474_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_satz72a x y z m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)).
-
-(* notion 1391 *)
-definition l_e_st_eq_landau_n_474_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf u y) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_comtf z y) (l_e_st_eq_landau_n_comtf u y) (l_e_st_eq_landau_n_satz72a z u y n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1392 *)
-definition l_e_st_eq_landau_n_satz74 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_trmoref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_474_t1 x y z u m n) (l_e_st_eq_landau_n_474_t2 x y z u m n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1393 *)
-definition l_e_st_eq_landau_n_satz74a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_satz74 y x u z (l_e_st_eq_landau_n_satz43 x y l) (l_e_st_eq_landau_n_satz43 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1394 *)
-definition l_e_st_eq_landau_n_satz75a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moref z u.(l_orapp (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)) m (λv:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz74 x y z u v n) (λv:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz72g x y z u v n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1395 *)
-definition l_e_st_eq_landau_n_satz75b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moreq z u.(l_orapp (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)) n (λv:l_e_st_eq_landau_n_moref z u.l_e_st_eq_landau_n_satz74 x y z u m v) (λv:l_e_st_eq_landau_n_eq z u.l_e_st_eq_landau_n_eqmoref2 (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_eqtf2 z u y v) (l_e_st_eq_landau_n_satz72a x y z m)) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1396 *)
-definition l_e_st_eq_landau_n_satz75c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_satz75a y x u z (l_e_st_eq_landau_n_satz49 x y l) (l_e_st_eq_landau_n_satz43 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1397 *)
-definition l_e_st_eq_landau_n_satz75d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lesseq z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_satz75b y x u z (l_e_st_eq_landau_n_satz43 x y l) (l_e_st_eq_landau_n_satz49 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1398 *)
-definition l_e_st_eq_landau_n_476_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_moreqi2 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_satz68 x y z u e f) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1399 *)
-definition l_e_st_eq_landau_n_476_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.λo:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_moreqi1 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_satz75a x y z u m o) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1400 *)
-definition l_e_st_eq_landau_n_476_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.(l_orapp (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)) n (λv:l_e_st_eq_landau_n_moref z u.l_e_st_eq_landau_n_476_t2 x y z u m n e v) (λv:l_e_st_eq_landau_n_eq z u.l_e_st_eq_landau_n_476_t1 x y z u m n e v) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1401 *)
-definition l_e_st_eq_landau_n_476_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λo:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_moreqi1 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_satz75b x y z u o n) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1402 *)
-definition l_e_st_eq_landau_n_satz76 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.(l_orapp (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)) m (λv:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_476_t4 x y z u m n v) (λv:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_476_t3 x y z u m n v) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1403 *)
-definition l_e_st_eq_landau_n_satz76a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq z u.(l_e_st_eq_landau_n_satz48 (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_satz76 y x u z (l_e_st_eq_landau_n_satz49 x y l) (l_e_st_eq_landau_n_satz49 z u k)) : l_e_st_eq_landau_n_lesseq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
-
-(* notion 1404 *)
-definition l_e_st_eq_landau_n_satz77b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y v) x.λf:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y w) x.(l_e_st_eq_landau_n_satz73e v w y (l_e_st_eq_landau_n_treq2 (l_e_st_eq_landau_n_tf y v) (l_e_st_eq_landau_n_tf y w) x e f) : l_e_st_eq_landau_n_eq v w).
-
-(* notion 1405 *)
-definition l_e_st_eq_landau_n_477_v ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y)) : l_e_st_eq_landau_n_frac).
-
-(* notion 1406 *)
-definition l_e_st_eq_landau_n_477_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr4eq (l_e_st_eq_landau_n_tf y (l_e_st_eq_landau_n_477_v x y)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_477_v x y) y) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))) x (l_e_st_eq_landau_n_comtf y (l_e_st_eq_landau_n_477_v x y)) (l_e_st_eq_landau_n_tfeq2a y (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y))) (l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y)))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_satz40a x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y (l_e_st_eq_landau_n_477_v x y)) x).
-
-(* notion 1407 *)
-definition l_e_st_eq_landau_n_satz77a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_somei l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y t) x) (l_e_st_eq_landau_n_477_v x y) (l_e_st_eq_landau_n_477_t1 x y) : l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y t) x)).
-
-(* notion 1408 *)
-definition l_e_st_eq_landau_n_rt_eq ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq x y : Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Prop).
-
-(* notion 1409 *)
-definition l_e_st_eq_landau_n_rt_refeq ≝ (Πx:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_refeq x : Πx:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_eq x x).
-
-(* notion 1410 *)
-definition l_e_st_eq_landau_n_rt_symeq ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λt:l_e_st_eq_landau_n_rt_eq x y.l_e_st_eq_landau_n_symeq x y t : Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πt:l_e_st_eq_landau_n_rt_eq x y.l_e_st_eq_landau_n_rt_eq y x).
-
-(* notion 1411 *)
-definition l_e_st_eq_landau_n_rt_treq ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λt:l_e_st_eq_landau_n_rt_eq x y.λu:l_e_st_eq_landau_n_rt_eq y z.l_e_st_eq_landau_n_treq x y z t u : Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πz:l_e_st_eq_landau_n_frac.Πt:l_e_st_eq_landau_n_rt_eq x y.Πu:l_e_st_eq_landau_n_rt_eq y z.l_e_st_eq_landau_n_rt_eq x z).
-
-(* notion 1412 *)
-definition l_e_st_eq_landau_n_rt_inf ≝ λx:l_e_st_eq_landau_n_frac.λs:l_e_st_set l_e_st_eq_landau_n_frac.(l_e_st_esti l_e_st_eq_landau_n_frac x s : Prop).
-
-(* notion 1413 *)
-definition l_e_st_eq_landau_n_rt_rat ≝ (l_e_st_eq_ect l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq : Type[0]).
-
-(* notion 1414 *)
-definition l_e_st_eq_landau_n_rt_is ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_is l_e_st_eq_landau_n_rt_rat x0 y0 : Prop).
-
-(* notion 1415 *)
-definition l_e_st_eq_landau_n_rt_nis ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_not (l_e_st_eq_landau_n_rt_is x0 y0) : Prop).
-
-(* notion 1416 *)
-definition l_e_st_eq_landau_n_rt_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_rat.Prop.(l_some l_e_st_eq_landau_n_rt_rat p : Prop).
-
-(* notion 1417 *)
-definition l_e_st_eq_landau_n_rt_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_rat.Prop.(l_all l_e_st_eq_landau_n_rt_rat p : Prop).
-
-(* notion 1418 *)
-definition l_e_st_eq_landau_n_rt_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_rat.Prop.(l_e_one l_e_st_eq_landau_n_rt_rat p : Prop).
-
-(* notion 1419 *)
-definition l_e_st_eq_landau_n_rt_in ≝ λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_e_st_esti l_e_st_eq_landau_n_rt_rat x0 s : Prop).
-
-(* notion 1420 *)
-definition l_e_st_eq_landau_n_rt_ratof ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_ectelt l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 1421 *)
-definition l_e_st_eq_landau_n_rt_class ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_ecect l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x0 : l_e_st_set l_e_st_eq_landau_n_frac).
-
-(* notion 1422 *)
-definition l_e_st_eq_landau_n_rt_inclass ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_4_th5 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x : l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ratof x))).
-
-(* notion 1423 *)
-definition l_e_st_eq_landau_n_rt_lemmaeq1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_4_th8 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x0 x xix0 y e : l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class x0)).
-
-(* notion 1424 *)
-definition l_e_st_eq_landau_n_rt_ratapp1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).a.(l_e_st_eq_4_th3 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x0 a a1 : a).
-
-(* notion 1425 *)
-definition l_e_st_eq_landau_n_rt_ii5_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).a.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_rt_ratapp1 y0 a (λy:l_e_st_eq_landau_n_frac.λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).a1 x y xix0 yi) : a).
-
-(* notion 1426 *)
-definition l_e_st_eq_landau_n_rt_ratapp2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).a.(l_e_st_eq_landau_n_rt_ratapp1 x0 a (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_ii5_t1 x0 y0 a a1 x xi) : a).
-
-(* notion 1427 *)
-definition l_e_st_eq_landau_n_rt_ii5_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πz:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).Πzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).a.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_rt_ratapp2 y0 z0 a (λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).a1 x y z xix0 yi zi) : a).
-
-(* notion 1428 *)
-definition l_e_st_eq_landau_n_rt_ratapp3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πz:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).Πzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).a.(l_e_st_eq_landau_n_rt_ratapp1 x0 a (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_ii5_t2 x0 y0 z0 a a1 x xi) : a).
-
-(* notion 1429 *)
-definition l_e_st_eq_landau_n_rt_ii5_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πz:l_e_st_eq_landau_n_frac.Πu:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).Πzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).Πui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).a.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_rt_ratapp3 y0 z0 u0 a (λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).a1 x y z u xix0 yi zi ui) : a).
-
-(* notion 1430 *)
-definition l_e_st_eq_landau_n_rt_ratapp4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πz:l_e_st_eq_landau_n_frac.Πu:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).Πzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).Πui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).a.(l_e_st_eq_landau_n_rt_ratapp1 x0 a (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_ii5_t3 x0 y0 z0 u0 a a1 x xi) : a).
-
-(* notion 1431 *)
-definition l_e_st_eq_landau_n_rt_isi ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λe:l_e_st_eq_landau_n_eq x1 y1.(l_e_st_eq_5_th3 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x0 y0 x1 x1ix0 y1 y1iy0 e : l_e_st_eq_landau_n_rt_is x0 y0).
-
-(* notion 1432 *)
-definition l_e_st_eq_landau_n_rt_ise ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_5_th5 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x0 y0 x1 x1ix0 y1 y1iy0 i : l_e_st_eq_landau_n_eq x1 y1).
-
-(* notion 1433 *)
-definition l_e_st_eq_landau_n_rt_nisi ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λn:l_not (l_e_st_eq_landau_n_eq x1 y1).(l_imp_th3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_eq x1 y1) n (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_ise x0 y0 x1 y1 x1ix0 y1iy0 t) : l_e_st_eq_landau_n_rt_nis x0 y0).
-
-(* notion 1434 *)
-definition l_e_st_eq_landau_n_rt_nise ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λn:l_e_st_eq_landau_n_rt_nis x0 y0.(l_imp_th3 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_rt_is x0 y0) n (λt:l_e_st_eq_landau_n_eq x1 y1.l_e_st_eq_landau_n_rt_isi x0 y0 x1 y1 x1ix0 y1iy0 t) : l_not (l_e_st_eq_landau_n_eq x1 y1)).
-
-(* notion 1435 *)
-definition l_e_st_eq_landau_n_rt_fixf ≝ λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.alpha.(l_e_st_eq_fixfu2 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq alpha f : Prop).
-
-(* notion 1436 *)
-definition l_e_st_eq_landau_n_rt_indrat ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.alpha.λff:l_e_st_eq_landau_n_rt_fixf alpha f.(l_e_st_eq_indeq2 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq alpha f ff x0 y0 : alpha).
-
-(* notion 1437 *)
-definition l_e_st_eq_landau_n_rt_isindrat ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.alpha.λff:l_e_st_eq_landau_n_rt_fixf alpha f.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_11_th1 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq alpha f ff x0 y0 x xix0 y yiy0 : l_e_is alpha (f x y) (l_e_st_eq_landau_n_rt_indrat x0 y0 alpha f ff)).
-
-(* notion 1438 *)
-definition l_e_st_eq_landau_n_rt_satz78 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_refis l_e_st_eq_landau_n_rt_rat x0 : l_e_st_eq_landau_n_rt_is x0 x0).
-
-(* notion 1439 *)
-definition l_e_st_eq_landau_n_rt_satz79 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_symis l_e_st_eq_landau_n_rt_rat x0 y0 i : l_e_st_eq_landau_n_rt_is y0 x0).
-
-(* notion 1440 *)
-definition l_e_st_eq_landau_n_rt_satz80 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is y0 z0.(l_e_tris l_e_st_eq_landau_n_rt_rat x0 y0 z0 i j : l_e_st_eq_landau_n_rt_is x0 z0).
-
-(* notion 1441 *)
-definition l_e_st_eq_landau_n_rt_more ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_some l_e_st_eq_landau_n_frac (Πx:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (Πy:l_e_st_eq_landau_n_frac.l_and3 (l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref x y))) : Prop).
-
-(* notion 1442 *)
-definition l_e_st_eq_landau_n_rt_ii5_propm ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.(l_and3 (l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref x1 y1) : Prop).
-
-(* notion 1443 *)
-definition l_e_st_eq_landau_n_rt_ii5_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u.(l_and3e1 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref t u) p : l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)).
-
-(* notion 1444 *)
-definition l_e_st_eq_landau_n_rt_ii5_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u.(l_and3e2 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref t u) p : l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)).
-
-(* notion 1445 *)
-definition l_e_st_eq_landau_n_rt_ii5_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u.(l_and3e3 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref t u) p : l_e_st_eq_landau_n_moref t u).
-
-(* notion 1446 *)
-definition l_e_st_eq_landau_n_rt_ii5_t7 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u.(l_e_st_eq_landau_n_satz44 t u x y (l_e_st_eq_landau_n_rt_ii5_t6 x0 y0 m x y xix0 yiy0 t s u p) (l_e_st_eq_landau_n_rt_ise x0 x0 t x (l_e_st_eq_landau_n_rt_ii5_t4 x0 y0 m x y xix0 yiy0 t s u p) xix0 (l_e_refis l_e_st_eq_landau_n_rt_rat x0)) (l_e_st_eq_landau_n_rt_ise y0 y0 u y (l_e_st_eq_landau_n_rt_ii5_t5 x0 y0 m x y xix0 yiy0 t s u p) yiy0 (l_e_refis l_e_st_eq_landau_n_rt_rat y0)) : l_e_st_eq_landau_n_moref x y).
-
-(* notion 1447 *)
-definition l_e_st_eq_landau_n_rt_ii5_t8 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).(l_someapp l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u) s (l_e_st_eq_landau_n_moref x y) (λu:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u.l_e_st_eq_landau_n_rt_ii5_t7 x0 y0 m x y xix0 yiy0 t s u v) : l_e_st_eq_landau_n_moref x y).
-
-(* notion 1448 *)
-definition l_e_st_eq_landau_n_rt_also18 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_someapp l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u)) m (l_e_st_eq_landau_n_moref x y) (λt:l_e_st_eq_landau_n_frac.λv:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).l_e_st_eq_landau_n_rt_ii5_t8 x0 y0 m x y xix0 yiy0 t v) : l_e_st_eq_landau_n_moref x y).
-
-(* notion 1449 *)
-definition l_e_st_eq_landau_n_rt_ii5_t9 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_moref x1 y1.(l_and3i (l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref x1 y1) x1ix0 y1iy0 m : l_e_st_eq_landau_n_rt_ii5_propm x0 y0 x1 y1).
-
-(* notion 1450 *)
-definition l_e_st_eq_landau_n_rt_ii5_t10 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_moref x1 y1.(l_somei l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 x1 t) y1 (l_e_st_eq_landau_n_rt_ii5_t9 x0 y0 x1 y1 x1ix0 y1iy0 m) : l_some l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 x1 t)).
-
-(* notion 1451 *)
-definition l_e_st_eq_landau_n_rt_morei ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_moref x1 y1.(l_somei l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 u t)) x1 (l_e_st_eq_landau_n_rt_ii5_t10 x0 y0 x1 y1 x1ix0 y1iy0 m) : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 1452 *)
-definition l_e_st_eq_landau_n_rt_moree ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_also18 x0 y0 m x1 y1 x1ix0 y1iy0 : l_e_st_eq_landau_n_moref x1 y1).
-
-(* notion 1453 *)
-definition l_e_st_eq_landau_n_rt_ismore1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λm:l_e_st_eq_landau_n_rt_more x0 z0.(l_e_isp l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t z0) x0 y0 m i : l_e_st_eq_landau_n_rt_more y0 z0).
-
-(* notion 1454 *)
-definition l_e_st_eq_landau_n_rt_ismore2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λm:l_e_st_eq_landau_n_rt_more z0 x0.(l_e_isp l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more z0 t) x0 y0 m i : l_e_st_eq_landau_n_rt_more z0 y0).
-
-(* notion 1455 *)
-definition l_e_st_eq_landau_n_rt_ismore12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.λm:l_e_st_eq_landau_n_rt_more x0 z0.(l_e_st_eq_landau_n_rt_ismore2 z0 u0 y0 j (l_e_st_eq_landau_n_rt_ismore1 x0 y0 z0 i m) : l_e_st_eq_landau_n_rt_more y0 u0).
-
-(* notion 1456 *)
-definition l_e_st_eq_landau_n_rt_less ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_some l_e_st_eq_landau_n_frac (Πx:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (Πy:l_e_st_eq_landau_n_frac.l_and3 (l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf x y))) : Prop).
-
-(* notion 1457 *)
-definition l_e_st_eq_landau_n_rt_ii5_propl ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.(l_and3 (l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf x1 y1) : Prop).
-
-(* notion 1458 *)
-definition l_e_st_eq_landau_n_rt_ii5_t11 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u.(l_and3e1 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf t u) p : l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)).
-
-(* notion 1459 *)
-definition l_e_st_eq_landau_n_rt_ii5_t12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u.(l_and3e2 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf t u) p : l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)).
-
-(* notion 1460 *)
-definition l_e_st_eq_landau_n_rt_ii5_t13 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u.(l_and3e3 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf t u) p : l_e_st_eq_landau_n_lessf t u).
-
-(* notion 1461 *)
-definition l_e_st_eq_landau_n_rt_ii5_t14 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u.(l_e_st_eq_landau_n_satz45 t u x y (l_e_st_eq_landau_n_rt_ii5_t13 x0 y0 l x y xix0 yiy0 t s u p) (l_e_st_eq_landau_n_rt_ise x0 x0 t x (l_e_st_eq_landau_n_rt_ii5_t11 x0 y0 l x y xix0 yiy0 t s u p) xix0 (l_e_refis l_e_st_eq_landau_n_rt_rat x0)) (l_e_st_eq_landau_n_rt_ise y0 y0 u y (l_e_st_eq_landau_n_rt_ii5_t12 x0 y0 l x y xix0 yiy0 t s u p) yiy0 (l_e_refis l_e_st_eq_landau_n_rt_rat y0)) : l_e_st_eq_landau_n_lessf x y).
-
-(* notion 1462 *)
-definition l_e_st_eq_landau_n_rt_ii5_t15 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).(l_someapp l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u) s (l_e_st_eq_landau_n_lessf x y) (λu:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u.l_e_st_eq_landau_n_rt_ii5_t14 x0 y0 l x y xix0 yiy0 t s u v) : l_e_st_eq_landau_n_lessf x y).
-
-(* notion 1463 *)
-definition l_e_st_eq_landau_n_rt_also19 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_someapp l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u)) l (l_e_st_eq_landau_n_lessf x y) (λt:l_e_st_eq_landau_n_frac.λv:l_some l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).l_e_st_eq_landau_n_rt_ii5_t15 x0 y0 l x y xix0 yiy0 t v) : l_e_st_eq_landau_n_lessf x y).
-
-(* notion 1464 *)
-definition l_e_st_eq_landau_n_rt_ii5_t16 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_lessf x1 y1.(l_and3i (l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf x1 y1) x1ix0 y1iy0 l : l_e_st_eq_landau_n_rt_ii5_propl x0 y0 x1 y1).
-
-(* notion 1465 *)
-definition l_e_st_eq_landau_n_rt_ii5_t17 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_lessf x1 y1.(l_somei l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 x1 t) y1 (l_e_st_eq_landau_n_rt_ii5_t16 x0 y0 x1 y1 x1ix0 y1iy0 l) : l_some l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 x1 t)).
-
-(* notion 1466 *)
-definition l_e_st_eq_landau_n_rt_lessi ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_lessf x1 y1.(l_somei l_e_st_eq_landau_n_frac (Πu:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 u t)) x1 (l_e_st_eq_landau_n_rt_ii5_t17 x0 y0 x1 y1 x1ix0 y1iy0 l) : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 1467 *)
-definition l_e_st_eq_landau_n_rt_lesse ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_also19 x0 y0 l x1 y1 x1ix0 y1iy0 : l_e_st_eq_landau_n_lessf x1 y1).
-
-(* notion 1468 *)
-definition l_e_st_eq_landau_n_rt_isless1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λl:l_e_st_eq_landau_n_rt_less x0 z0.(l_e_isp l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t z0) x0 y0 l i : l_e_st_eq_landau_n_rt_less y0 z0).
-
-(* notion 1469 *)
-definition l_e_st_eq_landau_n_rt_isless2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λl:l_e_st_eq_landau_n_rt_less z0 x0.(l_e_isp l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less z0 t) x0 y0 l i : l_e_st_eq_landau_n_rt_less z0 y0).
-
-(* notion 1470 *)
-definition l_e_st_eq_landau_n_rt_isless12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.λl:l_e_st_eq_landau_n_rt_less x0 z0.(l_e_st_eq_landau_n_rt_isless2 z0 u0 y0 j (l_e_st_eq_landau_n_rt_isless1 x0 y0 z0 i l) : l_e_st_eq_landau_n_rt_less y0 u0).
-
-(* notion 1471 *)
-definition l_e_st_eq_landau_n_rt_581_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_satz41a x1 y1 : l_or3 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1)).
-
-(* notion 1472 *)
-definition l_e_st_eq_landau_n_rt_581_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λe:l_e_st_eq_landau_n_eq x1 y1.(l_or3i1 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_isi x0 y0 x1 y1 x1ix0 y1iy0 e) : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1473 *)
-definition l_e_st_eq_landau_n_rt_581_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_moref x1 y1.(l_or3i2 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_morei x0 y0 x1 y1 x1ix0 y1iy0 m) : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1474 *)
-definition l_e_st_eq_landau_n_rt_581_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_lessf x1 y1.(l_or3i3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_lessi x0 y0 x1 y1 x1ix0 y1iy0 l) : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1475 *)
-definition l_e_st_eq_landau_n_rt_581_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_or3app (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1) (l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)) (l_e_st_eq_landau_n_rt_581_t1 x0 y0 x1 y1 x1ix0 y1iy0) (λt:l_e_st_eq_landau_n_eq x1 y1.l_e_st_eq_landau_n_rt_581_t2 x0 y0 x1 y1 x1ix0 y1iy0 t) (λt:l_e_st_eq_landau_n_moref x1 y1.l_e_st_eq_landau_n_rt_581_t3 x0 y0 x1 y1 x1ix0 y1iy0 t) (λt:l_e_st_eq_landau_n_lessf x1 y1.l_e_st_eq_landau_n_rt_581_t4 x0 y0 x1 y1 x1ix0 y1iy0 t) : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1476 *)
-definition l_e_st_eq_landau_n_rt_581_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_satz41b x1 y1 : l_ec3 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1)).
-
-(* notion 1477 *)
-definition l_e_st_eq_landau_n_rt_581_t7 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_imp_th3 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_moref x1 y1) (l_ec3e12 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1) (l_e_st_eq_landau_n_rt_581_t6 x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_ise x0 y0 x1 y1 x1ix0 y1iy0 i)) (λt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_moree x0 y0 x1 y1 x1ix0 y1iy0 t) : l_not (l_e_st_eq_landau_n_rt_more x0 y0)).
-
-(* notion 1478 *)
-definition l_e_st_eq_landau_n_rt_581_t8 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_imp_th3 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_lessf x1 y1) (l_ec3e23 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1) (l_e_st_eq_landau_n_rt_581_t6 x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_moree x0 y0 x1 y1 x1ix0 y1iy0 m)) (λt:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_lesse x0 y0 x1 y1 x1ix0 y1iy0 t) : l_not (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1479 *)
-definition l_e_st_eq_landau_n_rt_581_t9 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_imp_th3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_eq x1 y1) (l_ec3e31 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1) (l_e_st_eq_landau_n_rt_581_t6 x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_lesse x0 y0 x1 y1 x1ix0 y1iy0 l)) (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_ise x0 y0 x1 y1 x1ix0 y1iy0 t) : l_e_st_eq_landau_n_rt_nis x0 y0).
-
-(* notion 1480 *)
-definition l_e_st_eq_landau_n_rt_581_t10 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_ec3_th6 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_ec_th1 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_581_t7 x0 y0 x1 y1 x1ix0 y1iy0 t)) (l_ec_th1 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (λt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_581_t8 x0 y0 x1 y1 x1ix0 y1iy0 t)) (l_ec_th1 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (λt:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_581_t9 x0 y0 x1 y1 x1ix0 y1iy0 t)) : l_ec3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1481 *)
-definition l_e_st_eq_landau_n_rt_581_t11 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_orec3i (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_581_t5 x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_581_t10 x0 y0 x1 y1 x1ix0 y1iy0) : l_orec3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1482 *)
-definition l_e_st_eq_landau_n_rt_satz81 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_orec3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_581_t11 x0 y0 x y xi yi) : l_orec3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1483 *)
-definition l_e_st_eq_landau_n_rt_satz81a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_orec3e1 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81 x0 y0) : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1484 *)
-definition l_e_st_eq_landau_n_rt_satz81b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_orec3e2 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81 x0 y0) : l_ec3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1485 *)
-definition l_e_st_eq_landau_n_rt_582_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_lessi y0 x0 y x yiy0 xix0 (l_e_st_eq_landau_n_satz42 x y (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m)) : l_e_st_eq_landau_n_rt_less y0 x0).
-
-(* notion 1486 *)
-definition l_e_st_eq_landau_n_rt_satz82 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_less y0 x0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_582_t1 x0 y0 m x y xi yi) : l_e_st_eq_landau_n_rt_less y0 x0).
-
-(* notion 1487 *)
-definition l_e_st_eq_landau_n_rt_583_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_morei y0 x0 y x yiy0 xix0 (l_e_st_eq_landau_n_satz43 x y (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xix0 yiy0 l)) : l_e_st_eq_landau_n_rt_more y0 x0).
-
-(* notion 1488 *)
-definition l_e_st_eq_landau_n_rt_satz83 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_more y0 x0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_583_t1 x0 y0 l x y xi yi) : l_e_st_eq_landau_n_rt_more y0 x0).
-
-(* notion 1489 *)
-definition l_e_st_eq_landau_n_rt_moreis ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_or (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) : Prop).
-
-(* notion 1490 *)
-definition l_e_st_eq_landau_n_rt_moreisi1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_ori1 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) m : l_e_st_eq_landau_n_rt_moreis x0 y0).
-
-(* notion 1491 *)
-definition l_e_st_eq_landau_n_rt_moreisi2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_ori2 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) i : l_e_st_eq_landau_n_rt_moreis x0 y0).
-
-(* notion 1492 *)
-definition l_e_st_eq_landau_n_rt_moreisi ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_moreq x1 y1.(l_orapp (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_rt_moreis x0 y0) m (λt:l_e_st_eq_landau_n_moref x1 y1.l_e_st_eq_landau_n_rt_moreisi1 x0 y0 (l_e_st_eq_landau_n_rt_morei x0 y0 x1 y1 x1ix0 y1iy0 t)) (λt:l_e_st_eq_landau_n_eq x1 y1.l_e_st_eq_landau_n_rt_moreisi2 x0 y0 (l_e_st_eq_landau_n_rt_isi x0 y0 x1 y1 x1ix0 y1iy0 t)) : l_e_st_eq_landau_n_rt_moreis x0 y0).
-
-(* notion 1493 *)
-definition l_e_st_eq_landau_n_rt_moreise ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_rt_moreis x0 y0.(l_orapp (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_moreq x1 y1) m (λt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_moreqi1 x1 y1 (l_e_st_eq_landau_n_rt_moree x0 y0 x1 y1 x1ix0 y1iy0 t)) (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_moreqi2 x1 y1 (l_e_st_eq_landau_n_rt_ise x0 y0 x1 y1 x1ix0 y1iy0 t)) : l_e_st_eq_landau_n_moreq x1 y1).
-
-(* notion 1494 *)
-definition l_e_st_eq_landau_n_rt_ismoreis1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λm:l_e_st_eq_landau_n_rt_moreis x0 z0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_moreis t z0) x0 y0 m i : l_e_st_eq_landau_n_rt_moreis y0 z0).
-
-(* notion 1495 *)
-definition l_e_st_eq_landau_n_rt_ismoreis2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λm:l_e_st_eq_landau_n_rt_moreis z0 x0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_moreis z0 t) x0 y0 m i : l_e_st_eq_landau_n_rt_moreis z0 y0).
-
-(* notion 1496 *)
-definition l_e_st_eq_landau_n_rt_ismoreis12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.λm:l_e_st_eq_landau_n_rt_moreis x0 z0.(l_e_st_eq_landau_n_rt_ismoreis2 z0 u0 y0 j (l_e_st_eq_landau_n_rt_ismoreis1 x0 y0 z0 i m) : l_e_st_eq_landau_n_rt_moreis y0 u0).
-
-(* notion 1497 *)
-definition l_e_st_eq_landau_n_rt_lessis ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_or (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) : Prop).
-
-(* notion 1498 *)
-definition l_e_st_eq_landau_n_rt_lessisi1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_ori1 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) l : l_e_st_eq_landau_n_rt_lessis x0 y0).
-
-(* notion 1499 *)
-definition l_e_st_eq_landau_n_rt_lessisi2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_ori2 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) i : l_e_st_eq_landau_n_rt_lessis x0 y0).
-
-(* notion 1500 *)
-definition l_e_st_eq_landau_n_rt_lessisi ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_lesseq x1 y1.(l_orapp (l_e_st_eq_landau_n_lessf x1 y1) (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_rt_lessis x0 y0) l (λt:l_e_st_eq_landau_n_lessf x1 y1.l_e_st_eq_landau_n_rt_lessisi1 x0 y0 (l_e_st_eq_landau_n_rt_lessi x0 y0 x1 y1 x1ix0 y1iy0 t)) (λt:l_e_st_eq_landau_n_eq x1 y1.l_e_st_eq_landau_n_rt_lessisi2 x0 y0 (l_e_st_eq_landau_n_rt_isi x0 y0 x1 y1 x1ix0 y1iy0 t)) : l_e_st_eq_landau_n_rt_lessis x0 y0).
-
-(* notion 1501 *)
-definition l_e_st_eq_landau_n_rt_lessise ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_rt_lessis x0 y0.(l_orapp (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_lesseq x1 y1) l (λt:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_lesseqi1 x1 y1 (l_e_st_eq_landau_n_rt_lesse x0 y0 x1 y1 x1ix0 y1iy0 t)) (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_lesseqi2 x1 y1 (l_e_st_eq_landau_n_rt_ise x0 y0 x1 y1 x1ix0 y1iy0 t)) : l_e_st_eq_landau_n_lesseq x1 y1).
-
-(* notion 1502 *)
-definition l_e_st_eq_landau_n_rt_islessis1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λl:l_e_st_eq_landau_n_rt_lessis x0 z0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lessis t z0) x0 y0 l i : l_e_st_eq_landau_n_rt_lessis y0 z0).
-
-(* notion 1503 *)
-definition l_e_st_eq_landau_n_rt_islessis2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λl:l_e_st_eq_landau_n_rt_lessis z0 x0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lessis z0 t) x0 y0 l i : l_e_st_eq_landau_n_rt_lessis z0 y0).
-
-(* notion 1504 *)
-definition l_e_st_eq_landau_n_rt_islessis12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.λl:l_e_st_eq_landau_n_rt_lessis x0 z0.(l_e_st_eq_landau_n_rt_islessis2 z0 u0 y0 j (l_e_st_eq_landau_n_rt_islessis1 x0 y0 z0 i l) : l_e_st_eq_landau_n_rt_lessis y0 u0).
-
-(* notion 1505 *)
-definition l_e_st_eq_landau_n_rt_satz81c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.(l_ec3_th7 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) (l_comor (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) m) : l_not (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1506 *)
-definition l_e_st_eq_landau_n_rt_satz81d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.(l_ec3_th9 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) l : l_not (l_e_st_eq_landau_n_rt_more x0 y0)).
-
-(* notion 1507 *)
-definition l_e_st_eq_landau_n_rt_satz81e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_more x0 y0).(l_or3_th2 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81a x0 y0) n : l_e_st_eq_landau_n_rt_lessis x0 y0).
-
-(* notion 1508 *)
-definition l_e_st_eq_landau_n_rt_satz81f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_less x0 y0).(l_comor (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_or3_th3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81a x0 y0) n) : l_e_st_eq_landau_n_rt_moreis x0 y0).
-
-(* notion 1509 *)
-definition l_e_st_eq_landau_n_rt_satz81g ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_or_th3 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (l_ec3e23 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) m) (l_ec3e21 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) m) : l_not (l_e_st_eq_landau_n_rt_lessis x0 y0)).
-
-(* notion 1510 *)
-definition l_e_st_eq_landau_n_rt_satz81h ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_or_th3 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (l_ec3e32 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) l) (l_ec3e31 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) l) : l_not (l_e_st_eq_landau_n_rt_moreis x0 y0)).
-
-(* notion 1511 *)
-definition l_e_st_eq_landau_n_rt_satz81j ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_moreis x0 y0).(l_or3e3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81a x0 y0) (l_or_th5 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) n) (l_or_th4 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) n) : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 1512 *)
-definition l_e_st_eq_landau_n_rt_satz81k ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_lessis x0 y0).(l_or3e2 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81a x0 y0) (l_or_th4 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) n) (l_or_th5 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) n) : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 1513 *)
-definition l_e_st_eq_landau_n_rt_584_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_lessisi y0 x0 y x yiy0 xix0 (l_e_st_eq_landau_n_satz48 x y (l_e_st_eq_landau_n_rt_moreise x0 y0 x y xix0 yiy0 m)) : l_e_st_eq_landau_n_rt_lessis y0 x0).
-
-(* notion 1514 *)
-definition l_e_st_eq_landau_n_rt_satz84 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_lessis y0 x0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_584_t1 x0 y0 m x y xi yi) : l_e_st_eq_landau_n_rt_lessis y0 x0).
-
-(* notion 1515 *)
-definition l_e_st_eq_landau_n_rt_585_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_moreisi y0 x0 y x yiy0 xix0 (l_e_st_eq_landau_n_satz49 x y (l_e_st_eq_landau_n_rt_lessise x0 y0 x y xix0 yiy0 l)) : l_e_st_eq_landau_n_rt_moreis y0 x0).
-
-(* notion 1516 *)
-definition l_e_st_eq_landau_n_rt_satz85 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_moreis y0 x0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_585_t1 x0 y0 l x y xi yi) : l_e_st_eq_landau_n_rt_moreis y0 x0).
-
-(* notion 1517 *)
-definition l_e_st_eq_landau_n_rt_586_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_less y0 z0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi x0 z0 x z xix0 ziz0 (l_e_st_eq_landau_n_satz50 x y z (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xix0 yiy0 l) (l_e_st_eq_landau_n_rt_lesse y0 z0 y z yiy0 ziz0 k)) : l_e_st_eq_landau_n_rt_less x0 z0).
-
-(* notion 1518 *)
-definition l_e_st_eq_landau_n_rt_satz86 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_less y0 z0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less x0 z0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_586_t1 x0 y0 z0 l k x y z xi yi zi) : l_e_st_eq_landau_n_rt_less x0 z0).
-
-(* notion 1519 *)
-definition l_e_st_eq_landau_n_rt_trless ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_less y0 z0.(l_e_st_eq_landau_n_rt_satz86 x0 y0 z0 l k : l_e_st_eq_landau_n_rt_less x0 z0).
-
-(* notion 1520 *)
-definition l_e_st_eq_landau_n_rt_trmore ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_more y0 z0.(l_e_st_eq_landau_n_rt_satz83 z0 x0 (l_e_st_eq_landau_n_rt_satz86 z0 y0 x0 (l_e_st_eq_landau_n_rt_satz82 y0 z0 n) (l_e_st_eq_landau_n_rt_satz82 x0 y0 m)) : l_e_st_eq_landau_n_rt_more x0 z0).
-
-(* notion 1521 *)
-definition l_e_st_eq_landau_n_rt_587_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_less y0 z0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi x0 z0 x z xix0 ziz0 (l_e_st_eq_landau_n_satz51a x y z (l_e_st_eq_landau_n_rt_lessise x0 y0 x y xix0 yiy0 l) (l_e_st_eq_landau_n_rt_lesse y0 z0 y z yiy0 ziz0 k)) : l_e_st_eq_landau_n_rt_less x0 z0).
-
-(* notion 1522 *)
-definition l_e_st_eq_landau_n_rt_satz87a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_less y0 z0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less x0 z0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_587_t1 x0 y0 z0 l k x y z xi yi zi) : l_e_st_eq_landau_n_rt_less x0 z0).
-
-(* notion 1523 *)
-definition l_e_st_eq_landau_n_rt_587_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_lessis y0 z0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi x0 z0 x z xix0 ziz0 (l_e_st_eq_landau_n_satz51b x y z (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xix0 yiy0 l) (l_e_st_eq_landau_n_rt_lessise y0 z0 y z yiy0 ziz0 k)) : l_e_st_eq_landau_n_rt_less x0 z0).
-
-(* notion 1524 *)
-definition l_e_st_eq_landau_n_rt_satz87b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_lessis y0 z0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less x0 z0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_587_t2 x0 y0 z0 l k x y z xi yi zi) : l_e_st_eq_landau_n_rt_less x0 z0).
-
-(* notion 1525 *)
-definition l_e_st_eq_landau_n_rt_satz87c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_more y0 z0.(l_e_st_eq_landau_n_rt_satz83 z0 x0 (l_e_st_eq_landau_n_rt_satz87b z0 y0 x0 (l_e_st_eq_landau_n_rt_satz82 y0 z0 n) (l_e_st_eq_landau_n_rt_satz84 x0 y0 m)) : l_e_st_eq_landau_n_rt_more x0 z0).
-
-(* notion 1526 *)
-definition l_e_st_eq_landau_n_rt_satz87d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_moreis y0 z0.(l_e_st_eq_landau_n_rt_satz83 z0 x0 (l_e_st_eq_landau_n_rt_satz87a z0 y0 x0 (l_e_st_eq_landau_n_rt_satz84 y0 z0 n) (l_e_st_eq_landau_n_rt_satz82 x0 y0 m)) : l_e_st_eq_landau_n_rt_more x0 z0).
-
-(* notion 1527 *)
-definition l_e_st_eq_landau_n_rt_588_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_lessis y0 z0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessisi x0 z0 x z xix0 ziz0 (l_e_st_eq_landau_n_satz52 x y z (l_e_st_eq_landau_n_rt_lessise x0 y0 x y xix0 yiy0 l) (l_e_st_eq_landau_n_rt_lessise y0 z0 y z yiy0 ziz0 k)) : l_e_st_eq_landau_n_rt_lessis x0 z0).
-
-(* notion 1528 *)
-definition l_e_st_eq_landau_n_rt_satz88 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_lessis y0 z0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_lessis x0 z0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_588_t1 x0 y0 z0 l k x y z xi yi zi) : l_e_st_eq_landau_n_rt_lessis x0 z0).
-
-(* notion 1529 *)
-definition l_e_st_eq_landau_n_rt_trlessis ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_lessis y0 z0.(l_e_st_eq_landau_n_rt_satz88 x0 y0 z0 l k : l_e_st_eq_landau_n_rt_lessis x0 z0).
-
-(* notion 1530 *)
-definition l_e_st_eq_landau_n_rt_trmoreis ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_moreis y0 z0.(l_e_st_eq_landau_n_rt_satz85 z0 x0 (l_e_st_eq_landau_n_rt_satz88 z0 y0 x0 (l_e_st_eq_landau_n_rt_satz84 y0 z0 n) (l_e_st_eq_landau_n_rt_satz84 x0 y0 m)) : l_e_st_eq_landau_n_rt_moreis x0 z0).
-
-(* notion 1531 *)
-definition l_e_st_eq_landau_n_rt_589_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref z x.(l_somei l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0) (l_e_st_eq_landau_n_rt_ratof z) (l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_ratof z) x0 z x (l_e_st_eq_landau_n_rt_inclass z) xix0 m) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0)).
-
-(* notion 1532 *)
-definition l_e_st_eq_landau_n_rt_589_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_someapp l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_moref t x) (l_e_st_eq_landau_n_satz53 x) (l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0)) (λt:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_moref t x.l_e_st_eq_landau_n_rt_589_t1 x0 x xix0 t u) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0)).
-
-(* notion 1533 *)
-definition l_e_st_eq_landau_n_rt_satz89 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp1 x0 (l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0)) (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_589_t2 x0 x xi) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0)).
-
-(* notion 1534 *)
-definition l_e_st_eq_landau_n_rt_590_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf z x.(l_somei l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0) (l_e_st_eq_landau_n_rt_ratof z) (l_e_st_eq_landau_n_rt_lessi (l_e_st_eq_landau_n_rt_ratof z) x0 z x (l_e_st_eq_landau_n_rt_inclass z) xix0 l) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0)).
-
-(* notion 1535 *)
-definition l_e_st_eq_landau_n_rt_590_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_someapp l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_lessf t x) (l_e_st_eq_landau_n_satz54 x) (l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0)) (λt:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_lessf t x.l_e_st_eq_landau_n_rt_590_t1 x0 x xix0 t u) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0)).
-
-(* notion 1536 *)
-definition l_e_st_eq_landau_n_rt_satz90 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp1 x0 (l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0)) (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_590_t2 x0 x xi) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0)).
-
-(* notion 1537 *)
-definition l_e_st_eq_landau_n_rt_591_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λz:l_e_st_eq_landau_n_frac.λa:l_and (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y).(l_e_st_eq_landau_n_rt_lessi x0 (l_e_st_eq_landau_n_rt_ratof z) x z xix0 (l_e_st_eq_landau_n_rt_inclass z) (l_ande1 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y) a) : l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_ratof z)).
-
-(* notion 1538 *)
-definition l_e_st_eq_landau_n_rt_591_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λz:l_e_st_eq_landau_n_frac.λa:l_and (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y).(l_e_st_eq_landau_n_rt_lessi (l_e_st_eq_landau_n_rt_ratof z) y0 z y (l_e_st_eq_landau_n_rt_inclass z) yiy0 (l_ande2 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y) a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ratof z) y0).
-
-(* notion 1539 *)
-definition l_e_st_eq_landau_n_rt_591_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λz:l_e_st_eq_landau_n_frac.λa:l_and (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y).(l_andi (l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_ratof z)) (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ratof z) y0) (l_e_st_eq_landau_n_rt_591_t1 x0 y0 l x y xix0 yiy0 z a) (l_e_st_eq_landau_n_rt_591_t2 x0 y0 l x y xix0 yiy0 z a) : l_and (l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_ratof z)) (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ratof z) y0)).
-
-(* notion 1540 *)
-definition l_e_st_eq_landau_n_rt_591_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λz:l_e_st_eq_landau_n_frac.λa:l_and (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y).(l_somei l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0)) (l_e_st_eq_landau_n_rt_ratof z) (l_e_st_eq_landau_n_rt_591_t3 x0 y0 l x y xix0 yiy0 z a) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0))).
-
-(* notion 1541 *)
-definition l_e_st_eq_landau_n_rt_591_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_someapp l_e_st_eq_landau_n_frac (Πt:l_e_st_eq_landau_n_frac.l_and (l_e_st_eq_landau_n_lessf x t) (l_e_st_eq_landau_n_lessf t y)) (l_e_st_eq_landau_n_satz55 x y (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xix0 yiy0 l)) (l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0))) (λt:l_e_st_eq_landau_n_frac.λu:l_and (l_e_st_eq_landau_n_lessf x t) (l_e_st_eq_landau_n_lessf t y).l_e_st_eq_landau_n_rt_591_t4 x0 y0 l x y xix0 yiy0 t u) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0))).
-
-(* notion 1542 *)
-definition l_e_st_eq_landau_n_rt_satz91 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0))) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_591_t5 x0 y0 l x y xi yi) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0))).
-
-(* notion 1543 *)
-definition l_e_st_eq_landau_n_rt_plusfrt ≝ (Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_pf x y) : Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_rat).
-
-(* notion 1544 *)
-definition l_e_st_eq_landau_n_rt_ii5_t18 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_pf x z)) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_pf y u)) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_pf x z)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_pf y u)) (l_e_st_eq_landau_n_satz56 x y z u e f) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_plusfrt x z) (l_e_st_eq_landau_n_rt_plusfrt y u)).
-
-(* notion 1545 *)
-definition l_e_st_eq_landau_n_rt_fplusfrt ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_rt_eq x y.λw:l_e_st_eq_landau_n_rt_eq z u.l_e_st_eq_landau_n_rt_ii5_t18 x y z u v w : l_e_st_eq_landau_n_rt_fixf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_plusfrt).
-
-(* notion 1546 *)
-definition l_e_st_eq_landau_n_rt_pl ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_indrat x0 y0 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_plusfrt l_e_st_eq_landau_n_rt_fplusfrt : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 1547 *)
-definition l_e_st_eq_landau_n_rt_ii5_t19 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_isindrat x0 y0 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_plusfrt l_e_st_eq_landau_n_rt_fplusfrt x1 y1 x1ix0 y1iy0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_pf x1 y1)) (l_e_st_eq_landau_n_rt_pl x0 y0)).
-
-(* notion 1548 *)
-definition l_e_st_eq_landau_n_rt_picp ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_pf x1 y1) (l_e_st_eq_landau_n_rt_class t)) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_pf x1 y1)) (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_pf x1 y1)) (l_e_st_eq_landau_n_rt_ii5_t19 x0 y0 x1 y1 x1ix0 y1iy0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_pf x1 y1) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl x0 y0))).
-
-(* notion 1549 *)
-definition l_e_st_eq_landau_n_rt_ispl1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_pl t z0) x0 y0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1550 *)
-definition l_e_st_eq_landau_n_rt_ispl2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_pl z0 t) x0 y0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl z0 y0)).
-
-(* notion 1551 *)
-definition l_e_st_eq_landau_n_rt_ispl12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_ispl1 x0 y0 z0 i) (l_e_st_eq_landau_n_rt_ispl2 z0 u0 y0 j) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1552 *)
-definition l_e_st_eq_landau_n_rt_592_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0) (l_e_st_eq_landau_n_pf x1 y1) (l_e_st_eq_landau_n_pf y1 x1) (l_e_st_eq_landau_n_rt_picp x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_picp y0 x0 y1 x1 y1iy0 x1ix0) (l_e_st_eq_landau_n_satz58 x1 y1) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0)).
-
-(* notion 1553 *)
-definition l_e_st_eq_landau_n_rt_satz92 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_592_t1 x0 y0 x y xi yi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0)).
-
-(* notion 1554 *)
-definition l_e_st_eq_landau_n_rt_compl ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz92 x0 y0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0)).
-
-(* notion 1555 *)
-definition l_e_st_eq_landau_n_rt_593_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_picp (l_e_st_eq_landau_n_rt_pl x0 y0) z0 (l_e_st_eq_landau_n_pf x y) z (l_e_st_eq_landau_n_rt_picp x0 y0 x y xix0 yiy0) ziz0 : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0))).
-
-(* notion 1556 *)
-definition l_e_st_eq_landau_n_rt_593_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_picp x0 (l_e_st_eq_landau_n_rt_pl y0 z0) x (l_e_st_eq_landau_n_pf y z) xix0 (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)))).
-
-(* notion 1557 *)
-definition l_e_st_eq_landau_n_rt_593_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_rt_593_t1 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_rt_593_t2 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_satz59 x y z) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0))).
-
-(* notion 1558 *)
-definition l_e_st_eq_landau_n_rt_satz93 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0))) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_593_t3 x0 y0 z0 x y z xi yi zi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0))).
-
-(* notion 1559 *)
-definition l_e_st_eq_landau_n_rt_asspl1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz93 x0 y0 z0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0))).
-
-(* notion 1560 *)
-definition l_e_st_eq_landau_n_rt_asspl2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_satz93 x0 y0 z0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0)).
-
-(* notion 1561 *)
-definition l_e_st_eq_landau_n_rt_594_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 y0) x0 (l_e_st_eq_landau_n_pf x1 y1) x1 (l_e_st_eq_landau_n_rt_picp x0 y0 x1 y1 x1ix0 y1iy0) x1ix0 (l_e_st_eq_landau_n_satz60 x1 y1) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 y0) x0).
-
-(* notion 1562 *)
-definition l_e_st_eq_landau_n_rt_satz94 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 y0) x0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_594_t1 x0 y0 x y xi yi) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 y0) x0).
-
-(* notion 1563 *)
-definition l_e_st_eq_landau_n_rt_satz94a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_pl x0 y0) x0 (l_e_st_eq_landau_n_rt_satz94 x0 y0) : l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
-
-(* notion 1564 *)
-definition l_e_st_eq_landau_n_rt_595_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz61 x y z (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1565 *)
-definition l_e_st_eq_landau_n_rt_satz95 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_595_t1 x0 y0 z0 m x y z xi yi zi) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1566 *)
-definition l_e_st_eq_landau_n_rt_596_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz62a x y z (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1567 *)
-definition l_e_st_eq_landau_n_rt_satz96a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_596_t1 x0 y0 z0 m x y z xi yi zi) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1568 *)
-definition l_e_st_eq_landau_n_rt_596_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz62b x y z (l_e_st_eq_landau_n_rt_ise x0 y0 x y xix0 yiy0 i)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1569 *)
-definition l_e_st_eq_landau_n_rt_satz96b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_596_t2 x0 y0 z0 i x y z xi yi zi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1570 *)
-definition l_e_st_eq_landau_n_rt_596_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz62c x y z (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xix0 yiy0 l)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1571 *)
-definition l_e_st_eq_landau_n_rt_satz96c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_596_t3 x0 y0 z0 l x y z xi yi zi) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1572 *)
-definition l_e_st_eq_landau_n_rt_596_andersa ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_satz95 x0 y0 z0 m : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1573 *)
-definition l_e_st_eq_landau_n_rt_596_andersb ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ispl1 x0 y0 z0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1574 *)
-definition l_e_st_eq_landau_n_rt_596_andersc ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_satz95 y0 x0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 1575 *)
-definition l_e_st_eq_landau_n_rt_satz96d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ismore12 (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl z0 y0) (l_e_st_eq_landau_n_rt_compl x0 z0) (l_e_st_eq_landau_n_rt_compl y0 z0) (l_e_st_eq_landau_n_rt_satz96a x0 y0 z0 m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl z0 y0)).
-
-(* notion 1576 *)
-definition l_e_st_eq_landau_n_rt_satz96e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ispl2 x0 y0 z0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl z0 y0)).
-
-(* notion 1577 *)
-definition l_e_st_eq_landau_n_rt_satz96f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl z0 y0) (l_e_st_eq_landau_n_rt_compl x0 z0) (l_e_st_eq_landau_n_rt_compl y0 z0) (l_e_st_eq_landau_n_rt_satz96c x0 y0 z0 l) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl z0 y0)).
-
-(* notion 1578 *)
-definition l_e_st_eq_landau_n_rt_597_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_morei x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz63a x y z (l_e_st_eq_landau_n_rt_moree (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) m)) : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 1579 *)
-definition l_e_st_eq_landau_n_rt_satz97a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_more x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_597_t1 x0 y0 z0 m x y z xi yi zi) : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 1580 *)
-definition l_e_st_eq_landau_n_rt_597_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz63b x y z (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) i)) : l_e_st_eq_landau_n_rt_is x0 y0).
-
-(* notion 1581 *)
-definition l_e_st_eq_landau_n_rt_satz97b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_597_t2 x0 y0 z0 i x y z xi yi zi) : l_e_st_eq_landau_n_rt_is x0 y0).
-
-(* notion 1582 *)
-definition l_e_st_eq_landau_n_rt_597_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz63c x y z (l_e_st_eq_landau_n_rt_lesse (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) l)) : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 1583 *)
-definition l_e_st_eq_landau_n_rt_satz97c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_597_t3 x0 y0 z0 l x y z xi yi zi) : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 1584 *)
-definition l_e_st_eq_landau_n_rt_597_anders ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_satz82 y0 x0 (l_e_st_eq_landau_n_rt_satz97a y0 x0 z0 (l_e_st_eq_landau_n_rt_satz83 (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) l)) : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 1585 *)
-definition l_e_st_eq_landau_n_rt_598_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz64 x y z u (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moree z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1586 *)
-definition l_e_st_eq_landau_n_rt_satz98 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_598_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1587 *)
-definition l_e_st_eq_landau_n_rt_satz98a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_satz98 y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l) (l_e_st_eq_landau_n_rt_satz83 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1588 *)
-definition l_e_st_eq_landau_n_rt_599_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz65a x y z u (l_e_st_eq_landau_n_rt_moreise x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moree z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1589 *)
-definition l_e_st_eq_landau_n_rt_satz99a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_599_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1590 *)
-definition l_e_st_eq_landau_n_rt_599_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz65b x y z u (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moreise z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1591 *)
-definition l_e_st_eq_landau_n_rt_satz99b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_599_t2 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1592 *)
-definition l_e_st_eq_landau_n_rt_satz99c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_satz99a y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz85 x0 y0 l) (l_e_st_eq_landau_n_rt_satz83 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1593 *)
-definition l_e_st_eq_landau_n_rt_satz99d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_lessis z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_satz99b y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l) (l_e_st_eq_landau_n_rt_satz85 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1594 *)
-definition l_e_st_eq_landau_n_rt_5100_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_moreisi (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz66 x y z u (l_e_st_eq_landau_n_rt_moreise x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moreise z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1595 *)
-definition l_e_st_eq_landau_n_rt_satz100 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5100_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1596 *)
-definition l_e_st_eq_landau_n_rt_satz100a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_lessis z0 u0.(l_e_st_eq_landau_n_rt_satz84 (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_satz100 y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz85 x0 y0 l) (l_e_st_eq_landau_n_rt_satz85 z0 u0 k)) : l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
-
-(* notion 1597 *)
-definition l_e_st_eq_landau_n_rt_5101_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λv0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0.(l_e_st_eq_landau_n_rt_ismore1 (l_e_st_eq_landau_n_rt_pl y0 v0) x0 y0 i (l_e_st_eq_landau_n_rt_satz94 y0 v0) : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 1598 *)
-definition l_e_st_eq_landau_n_rt_5101_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λv0:l_e_st_eq_landau_n_rt_rat.(l_imp_th3 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_satz81d x0 y0 l) (λt:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0.l_e_st_eq_landau_n_rt_5101_t1 x0 y0 l v0 t) : l_e_st_eq_landau_n_rt_nis (l_e_st_eq_landau_n_rt_pl y0 v0) x0).
-
-(* notion 1599 *)
-definition l_e_st_eq_landau_n_rt_vorbemerkung101 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.(l_some_th5 l_e_st_eq_landau_n_rt_rat (λv:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v) x0) (λv:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_5101_t2 x0 y0 l v) : l_not (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0))).
-
-(* notion 1600 *)
-definition l_e_st_eq_landau_n_rt_5101_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_ratof v)) x0 (l_e_st_eq_landau_n_pf y v) x (l_e_st_eq_landau_n_rt_picp y0 (l_e_st_eq_landau_n_rt_ratof v) y v yiy0 (l_e_st_eq_landau_n_rt_inclass v)) xix0 e : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_ratof v)) x0).
-
-(* notion 1601 *)
-definition l_e_st_eq_landau_n_rt_5101_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.(l_somei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0) (l_e_st_eq_landau_n_rt_ratof v) (l_e_st_eq_landau_n_rt_5101_t3 x0 y0 m x y xix0 yiy0 v e) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)).
-
-(* notion 1602 *)
-definition l_e_st_eq_landau_n_rt_5101_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_someapp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y t) x) (l_e_st_eq_landau_n_satz67a x y (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m)) (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)) (λt:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y t) x.l_e_st_eq_landau_n_rt_5101_t4 x0 y0 m x y xix0 yiy0 t u) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)).
-
-(* notion 1603 *)
-definition l_e_st_eq_landau_n_rt_satz101a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_5101_t5 x0 y0 m x y xi yi) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)).
-
-(* notion 1604 *)
-definition l_e_st_eq_landau_n_rt_5101_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λw0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0.λj:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 w0) x0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λviv0:l_e_st_eq_landau_n_rt_inf v (l_e_st_eq_landau_n_rt_class v0).λwiw0:l_e_st_eq_landau_n_rt_inf w (l_e_st_eq_landau_n_rt_class w0).(l_e_st_eq_landau_n_rt_isi v0 w0 v w viv0 wiw0 (l_e_st_eq_landau_n_satz67b x y v w (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_pl y0 v0) x0 (l_e_st_eq_landau_n_pf y v) x (l_e_st_eq_landau_n_rt_picp y0 v0 y v yiy0 viv0) xix0 i) (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_pl y0 w0) x0 (l_e_st_eq_landau_n_pf y w) x (l_e_st_eq_landau_n_rt_picp y0 w0 y w yiy0 wiw0) xix0 j)) : l_e_st_eq_landau_n_rt_is v0 w0).
-
-(* notion 1605 *)
-definition l_e_st_eq_landau_n_rt_satz101b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λw0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0.λj:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 w0) x0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 v0 w0 (l_e_st_eq_landau_n_rt_is v0 w0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λvi:l_e_st_eq_landau_n_rt_inf v (l_e_st_eq_landau_n_rt_class v0).λwi:l_e_st_eq_landau_n_rt_inf w (l_e_st_eq_landau_n_rt_class w0).l_e_st_eq_landau_n_rt_5101_t6 x0 y0 v0 w0 i j x y v w xi yi vi wi) : l_e_st_eq_landau_n_rt_is v0 w0).
-
-(* notion 1606 *)
-definition l_e_st_eq_landau_n_rt_5101_t7 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(λt:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_rat.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0.λw:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 u) x0.l_e_st_eq_landau_n_rt_satz101b x0 y0 t u v w : l_e_amone l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)).
-
-(* notion 1607 *)
-definition l_e_st_eq_landau_n_rt_satz101 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_onei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0) (l_e_st_eq_landau_n_rt_5101_t7 x0 y0) (l_e_st_eq_landau_n_rt_satz101a x0 y0 m) : l_e_st_eq_landau_n_rt_one (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)).
-
-(* notion 1608 *)
-definition l_e_st_eq_landau_n_rt_mn ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_ind l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0) (l_e_st_eq_landau_n_rt_satz101 x0 y0 m) : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 1609 *)
-definition l_e_st_eq_landau_n_rt_satz101c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_oneax l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0) (l_e_st_eq_landau_n_rt_satz101 x0 y0 m) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 m)) x0).
-
-(* notion 1610 *)
-definition l_e_st_eq_landau_n_rt_satz101d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 m)) x0 (l_e_st_eq_landau_n_rt_satz101c x0 y0 m) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 m))).
-
-(* notion 1611 *)
-definition l_e_st_eq_landau_n_rt_satz101e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 m)) x0 (l_e_st_eq_landau_n_rt_compl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) (l_e_st_eq_landau_n_rt_satz101c x0 y0 m) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) x0).
-
-(* notion 1612 *)
-definition l_e_st_eq_landau_n_rt_satz101f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) x0 (l_e_st_eq_landau_n_rt_satz101e x0 y0 m) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0)).
-
-(* notion 1613 *)
-definition l_e_st_eq_landau_n_rt_satz101g ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0.(l_e_st_eq_landau_n_rt_satz101b x0 y0 v0 (l_e_st_eq_landau_n_rt_mn x0 y0 m) i (l_e_st_eq_landau_n_rt_satz101c x0 y0 m) : l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_mn x0 y0 m)).
-
-(* notion 1614 *)
-definition l_e_st_eq_landau_n_rt_timesfrt ≝ (Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_tf x y) : Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_rat).
-
-(* notion 1615 *)
-definition l_e_st_eq_landau_n_rt_ii5_t20 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_tf y u)) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_tf y u)) (l_e_st_eq_landau_n_satz68 x y z u e f) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_timesfrt x z) (l_e_st_eq_landau_n_rt_timesfrt y u)).
-
-(* notion 1616 *)
-definition l_e_st_eq_landau_n_rt_ftimesfrt ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_rt_eq x y.λw:l_e_st_eq_landau_n_rt_eq z u.l_e_st_eq_landau_n_rt_ii5_t20 x y z u v w : l_e_st_eq_landau_n_rt_fixf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_timesfrt).
-
-(* notion 1617 *)
-definition l_e_st_eq_landau_n_rt_ts ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_indrat x0 y0 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_timesfrt l_e_st_eq_landau_n_rt_ftimesfrt : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 1618 *)
-definition l_e_st_eq_landau_n_rt_ii5_t21 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_isindrat x0 y0 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_timesfrt l_e_st_eq_landau_n_rt_ftimesfrt x1 y1 x1ix0 y1iy0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_tf x1 y1)) (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 1619 *)
-definition l_e_st_eq_landau_n_rt_tict ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_tf x1 y1) (l_e_st_eq_landau_n_rt_class t)) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_tf x1 y1)) (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_tf x1 y1)) (l_e_st_eq_landau_n_rt_ii5_t21 x0 y0 x1 y1 x1ix0 y1iy0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_tf x1 y1) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ts x0 y0))).
-
-(* notion 1620 *)
-definition l_e_st_eq_landau_n_rt_ists1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_ts t z0) x0 y0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
-
-(* notion 1621 *)
-definition l_e_st_eq_landau_n_rt_ists2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_ts z0 t) x0 y0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts z0 y0)).
-
-(* notion 1622 *)
-definition l_e_st_eq_landau_n_rt_ists12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_rt_ists1 x0 y0 z0 i) (l_e_st_eq_landau_n_rt_ists2 z0 u0 y0 j) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1623 *)
-definition l_e_st_eq_landau_n_rt_5102_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0) (l_e_st_eq_landau_n_tf x1 y1) (l_e_st_eq_landau_n_tf y1 x1) (l_e_st_eq_landau_n_rt_tict x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_tict y0 x0 y1 x1 y1iy0 x1ix0) (l_e_st_eq_landau_n_satz69 x1 y1) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0)).
-
-(* notion 1624 *)
-definition l_e_st_eq_landau_n_rt_satz102 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_5102_t1 x0 y0 x y xi yi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0)).
-
-(* notion 1625 *)
-definition l_e_st_eq_landau_n_rt_comts ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz102 x0 y0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0)).
-
-(* notion 1626 *)
-definition l_e_st_eq_landau_n_rt_5103_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_tict (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_tf x y) z (l_e_st_eq_landau_n_rt_tict x0 y0 x y xix0 yiy0) ziz0 : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0))).
-
-(* notion 1627 *)
-definition l_e_st_eq_landau_n_rt_5103_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_tict x0 (l_e_st_eq_landau_n_rt_ts y0 z0) x (l_e_st_eq_landau_n_tf y z) xix0 (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)))).
-
-(* notion 1628 *)
-definition l_e_st_eq_landau_n_rt_5103_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_rt_5103_t1 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_rt_5103_t2 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_satz70 x y z) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0))).
-
-(* notion 1629 *)
-definition l_e_st_eq_landau_n_rt_satz103 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0))) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5103_t3 x0 y0 z0 x y z xi yi zi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0))).
-
-(* notion 1630 *)
-definition l_e_st_eq_landau_n_rt_assts1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz103 x0 y0 z0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0))).
-
-(* notion 1631 *)
-definition l_e_st_eq_landau_n_rt_assts2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_satz103 x0 y0 z0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0)).
-
-(* notion 1632 *)
-definition l_e_st_eq_landau_n_rt_5104_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_tict x0 (l_e_st_eq_landau_n_rt_pl y0 z0) x (l_e_st_eq_landau_n_pf y z) xix0 (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)))).
-
-(* notion 1633 *)
-definition l_e_st_eq_landau_n_rt_5104_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_picp (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_rt_tict x0 y0 x y xix0 yiy0) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0)))).
-
-(* notion 1634 *)
-definition l_e_st_eq_landau_n_rt_5104_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0)) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_rt_5104_t1 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_rt_5104_t2 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_satz71 x y z) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0))).
-
-(* notion 1635 *)
-definition l_e_st_eq_landau_n_rt_satz104 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0))) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5104_t3 x0 y0 z0 x y z xi yi zi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0))).
-
-(* notion 1636 *)
-definition l_e_st_eq_landau_n_rt_disttp1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_ts z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts z0 y0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_comts (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_satz104 z0 x0 y0) (l_e_st_eq_landau_n_rt_ispl12 (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts z0 y0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_comts z0 x0) (l_e_st_eq_landau_n_rt_comts z0 y0)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0))).
-
-(* notion 1637 *)
-definition l_e_st_eq_landau_n_rt_disttp2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz104 x0 y0 z0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0))).
-
-(* notion 1638 *)
-definition l_e_st_eq_landau_n_rt_distpt1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_disttp1 x0 y0 z0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) z0)).
-
-(* notion 1639 *)
-definition l_e_st_eq_landau_n_rt_distpt2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0)) (l_e_st_eq_landau_n_rt_disttp2 x0 y0 z0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0)) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0))).
-
-(* notion 1640 *)
-definition l_e_st_eq_landau_n_rt_5105_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz72a x y z (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
-
-(* notion 1641 *)
-definition l_e_st_eq_landau_n_rt_satz105a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5105_t1 x0 y0 z0 m x y z xi yi zi) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
-
-(* notion 1642 *)
-definition l_e_st_eq_landau_n_rt_5105_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz72b x y z (l_e_st_eq_landau_n_rt_ise x0 y0 x y xix0 yiy0 i)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
-
-(* notion 1643 *)
-definition l_e_st_eq_landau_n_rt_satz105b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5105_t2 x0 y0 z0 i x y z xi yi zi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
-
-(* notion 1644 *)
-definition l_e_st_eq_landau_n_rt_5105_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xi zi) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yi zi) (l_e_st_eq_landau_n_satz72c x y z (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xi yi l)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
-
-(* notion 1645 *)
-definition l_e_st_eq_landau_n_rt_satz105c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5105_t3 x0 y0 z0 l x y z xi yi zi) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
-
-(* notion 1646 *)
-definition l_e_st_eq_landau_n_rt_5105_andersb ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ists1 x0 y0 z0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
-
-(* notion 1647 *)
-definition l_e_st_eq_landau_n_rt_5105_andersc ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_satz105a y0 x0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
-
-(* notion 1648 *)
-definition l_e_st_eq_landau_n_rt_satz105d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ismore12 (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_ts z0 y0) (l_e_st_eq_landau_n_rt_comts x0 z0) (l_e_st_eq_landau_n_rt_comts y0 z0) (l_e_st_eq_landau_n_rt_satz105a x0 y0 z0 m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts z0 y0)).
-
-(* notion 1649 *)
-definition l_e_st_eq_landau_n_rt_satz105e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ists2 x0 y0 z0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts z0 y0)).
-
-(* notion 1650 *)
-definition l_e_st_eq_landau_n_rt_satz105f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_ts z0 y0) (l_e_st_eq_landau_n_rt_comts x0 z0) (l_e_st_eq_landau_n_rt_comts y0 z0) (l_e_st_eq_landau_n_rt_satz105c x0 y0 z0 l) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts z0 y0)).
-
-(* notion 1651 *)
-definition l_e_st_eq_landau_n_rt_5106_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_morei x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz73a x y z (l_e_st_eq_landau_n_rt_moree (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) m)) : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 1652 *)
-definition l_e_st_eq_landau_n_rt_satz106a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_more x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5106_t1 x0 y0 z0 m x y z xi yi zi) : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 1653 *)
-definition l_e_st_eq_landau_n_rt_5106_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz73b x y z (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) i)) : l_e_st_eq_landau_n_rt_is x0 y0).
-
-(* notion 1654 *)
-definition l_e_st_eq_landau_n_rt_satz106b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5106_t2 x0 y0 z0 i x y z xi yi zi) : l_e_st_eq_landau_n_rt_is x0 y0).
-
-(* notion 1655 *)
-definition l_e_st_eq_landau_n_rt_5106_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz73c x y z (l_e_st_eq_landau_n_rt_lesse (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) l)) : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 1656 *)
-definition l_e_st_eq_landau_n_rt_satz106c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5106_t3 x0 y0 z0 l x y z xi yi zi) : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 1657 *)
-definition l_e_st_eq_landau_n_rt_5106_anders ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_satz82 y0 x0 (l_e_st_eq_landau_n_rt_satz106a y0 x0 z0 (l_e_st_eq_landau_n_rt_satz83 (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) l)) : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 1658 *)
-definition l_e_st_eq_landau_n_rt_5107_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz74 x y z u (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moree z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1659 *)
-definition l_e_st_eq_landau_n_rt_satz107 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5107_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1660 *)
-definition l_e_st_eq_landau_n_rt_satz107a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_satz107 y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l) (l_e_st_eq_landau_n_rt_satz83 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1661 *)
-definition l_e_st_eq_landau_n_rt_5108_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz75a x y z u (l_e_st_eq_landau_n_rt_moreise x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moree z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1662 *)
-definition l_e_st_eq_landau_n_rt_satz108a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5108_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1663 *)
-definition l_e_st_eq_landau_n_rt_5108_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz75b x y z u (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moreise z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1664 *)
-definition l_e_st_eq_landau_n_rt_satz108b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5108_t2 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1665 *)
-definition l_e_st_eq_landau_n_rt_satz108c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_satz108a y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz85 x0 y0 l) (l_e_st_eq_landau_n_rt_satz83 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1666 *)
-definition l_e_st_eq_landau_n_rt_satz108d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_lessis z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_satz108b y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l) (l_e_st_eq_landau_n_rt_satz85 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1667 *)
-definition l_e_st_eq_landau_n_rt_5109_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_moreisi (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz76 x y z u (l_e_st_eq_landau_n_rt_moreise x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moreise z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1668 *)
-definition l_e_st_eq_landau_n_rt_satz109 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5109_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1669 *)
-definition l_e_st_eq_landau_n_rt_satz109a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_lessis z0 u0.(l_e_st_eq_landau_n_rt_satz84 (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_satz109 y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz85 x0 y0 l) (l_e_st_eq_landau_n_rt_satz85 z0 u0 k)) : l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
-
-(* notion 1670 *)
-definition l_e_st_eq_landau_n_rt_5110_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y1 v) x1.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ratof v)) x0 (l_e_st_eq_landau_n_tf y1 v) x1 (l_e_st_eq_landau_n_rt_tict y0 (l_e_st_eq_landau_n_rt_ratof v) y1 v y1iy0 (l_e_st_eq_landau_n_rt_inclass v)) x1ix0 e : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ratof v)) x0).
-
-(* notion 1671 *)
-definition l_e_st_eq_landau_n_rt_5110_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y1 v) x1.(l_somei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0) (l_e_st_eq_landau_n_rt_ratof v) (l_e_st_eq_landau_n_rt_5110_t1 x0 y0 x1 y1 x1ix0 y1iy0 v e) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)).
-
-(* notion 1672 *)
-definition l_e_st_eq_landau_n_rt_5110_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_someapp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y1 t) x1) (l_e_st_eq_landau_n_satz77a x1 y1) (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)) (λt:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y1 t) x1.l_e_st_eq_landau_n_rt_5110_t2 x0 y0 x1 y1 x1ix0 y1iy0 t u) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)).
-
-(* notion 1673 *)
-definition l_e_st_eq_landau_n_rt_satz110a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_5110_t3 x0 y0 x y xi yi) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)).
-
-(* notion 1674 *)
-definition l_e_st_eq_landau_n_rt_5110_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λw0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 v0) x0.λj:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 w0) x0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λviv0:l_e_st_eq_landau_n_rt_inf v (l_e_st_eq_landau_n_rt_class v0).λwiw0:l_e_st_eq_landau_n_rt_inf w (l_e_st_eq_landau_n_rt_class w0).(l_e_st_eq_landau_n_rt_isi v0 w0 v w viv0 wiw0 (l_e_st_eq_landau_n_satz77b x y v w (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_ts y0 v0) x0 (l_e_st_eq_landau_n_tf y v) x (l_e_st_eq_landau_n_rt_tict y0 v0 y v yiy0 viv0) xix0 i) (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_ts y0 w0) x0 (l_e_st_eq_landau_n_tf y w) x (l_e_st_eq_landau_n_rt_tict y0 w0 y w yiy0 wiw0) xix0 j)) : l_e_st_eq_landau_n_rt_is v0 w0).
-
-(* notion 1675 *)
-definition l_e_st_eq_landau_n_rt_satz110b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λw0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 v0) x0.λj:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 w0) x0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 v0 w0 (l_e_st_eq_landau_n_rt_is v0 w0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λvi:l_e_st_eq_landau_n_rt_inf v (l_e_st_eq_landau_n_rt_class v0).λwi:l_e_st_eq_landau_n_rt_inf w (l_e_st_eq_landau_n_rt_class w0).l_e_st_eq_landau_n_rt_5110_t4 x0 y0 v0 w0 i j x y v w xi yi vi wi) : l_e_st_eq_landau_n_rt_is v0 w0).
-
-(* notion 1676 *)
-definition l_e_st_eq_landau_n_rt_5110_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(λt:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_rat.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0.λw:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 u) x0.l_e_st_eq_landau_n_rt_satz110b x0 y0 t u v w : l_e_amone l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)).
-
-(* notion 1677 *)
-definition l_e_st_eq_landau_n_rt_satz110 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_onei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0) (l_e_st_eq_landau_n_rt_5110_t5 x0 y0) (l_e_st_eq_landau_n_rt_satz110a x0 y0) : l_e_st_eq_landau_n_rt_one (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)).
-
-(* notion 1678 *)
-definition l_e_st_eq_landau_n_5111_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_ndis12 x l_e_st_eq_landau_n_1 y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz28a x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) x).
-
-(* notion 1679 *)
-definition l_e_st_eq_landau_n_5111_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) x (l_e_st_eq_landau_n_5111_t1 x y) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)))).
-
-(* notion 1680 *)
-definition l_e_st_eq_landau_n_satz111a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1).(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) y (l_e_st_eq_landau_n_5111_t1 x y) (l_e_st_eq_landau_n_5111_t1 y x) m : l_e_st_eq_landau_n_more x y).
-
-(* notion 1681 *)
-definition l_e_st_eq_landau_n_satz111b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1).(l_e_tr3is l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) y (l_e_st_eq_landau_n_5111_t2 x y) e (l_e_st_eq_landau_n_5111_t1 y x) : l_e_st_eq_landau_n_is x y).
-
-(* notion 1682 *)
-definition l_e_st_eq_landau_n_satz111c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1).(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) y (l_e_st_eq_landau_n_5111_t1 x y) (l_e_st_eq_landau_n_5111_t1 y x) l : l_e_st_eq_landau_n_less x y).
-
-(* notion 1683 *)
-definition l_e_st_eq_landau_n_satz111d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_ismore12 x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) y (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_5111_t2 x y) (l_e_st_eq_landau_n_5111_t2 y x) m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)).
-
-(* notion 1684 *)
-definition l_e_st_eq_landau_n_satz111e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) x y (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_5111_t1 x y) i (l_e_st_eq_landau_n_5111_t2 y x) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)).
-
-(* notion 1685 *)
-definition l_e_st_eq_landau_n_satz111f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_isless12 x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) y (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_5111_t2 x y) (l_e_st_eq_landau_n_5111_t2 y x) l : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)).
-
-(* notion 1686 *)
-definition l_e_st_eq_landau_n_rt_natprop ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_class x0) : Prop).
-
-(* notion 1687 *)
-definition l_e_st_eq_landau_n_rt_natrt ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_some (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t) : Prop).
-
-(* notion 1688 *)
-definition l_e_st_eq_landau_n_rt_ii5_t22 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λnpx:l_e_st_eq_landau_n_rt_natprop x0 x.λnpy:l_e_st_eq_landau_n_rt_natprop y0 y.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_satz111b x y (l_e_st_eq_landau_n_rt_ise x0 y0 (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1) npx npy i) : l_e_st_eq_landau_n_is x y).
-
-(* notion 1689 *)
-definition l_e_st_eq_landau_n_rt_ii5_t23 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_rt_natprop x0 t.λw:l_e_st_eq_landau_n_rt_natprop x0 u.l_e_st_eq_landau_n_rt_ii5_t22 x0 x0 t u v w (l_e_refis l_e_st_eq_landau_n_rt_rat x0) : l_e_amone l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t)).
-
-(* notion 1690 *)
-definition l_e_st_eq_landau_n_rt_satz111g ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_onei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t) (l_e_st_eq_landau_n_rt_ii5_t23 x0) nx0 : l_e_st_eq_landau_n_one (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t)).
-
-(* notion 1691 *)
-definition l_e_st_eq_landau_n_rt_nofrt ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_ind l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t) (l_e_st_eq_landau_n_rt_satz111g x0 nx0) : l_e_st_eq_landau_n_nat).
-
-(* notion 1692 *)
-definition l_e_st_eq_landau_n_rt_inclassn ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_oneax l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t) (l_e_st_eq_landau_n_rt_satz111g x0 nx0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_class x0)).
-
-(* notion 1693 *)
-definition l_e_st_eq_landau_n_rt_isrten ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ii5_t22 x0 y0 (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclassn y0 ny0) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)).
-
-(* notion 1694 *)
-definition l_e_st_eq_landau_n_rt_isrtin ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0).(l_e_st_eq_landau_n_rt_isi x0 y0 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclassn y0 ny0) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_nofrt y0 ny0) i) : l_e_st_eq_landau_n_rt_is x0 y0).
-
-(* notion 1695 *)
-definition l_e_st_eq_landau_n_rt_rtofn ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 1696 *)
-definition l_e_st_eq_landau_n_rt_natrti ≝ λx:l_e_st_eq_landau_n_nat.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop (l_e_st_eq_landau_n_rt_rtofn x) t) x (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rtofn x)).
-
-(* notion 1697 *)
-definition l_e_st_eq_landau_n_rt_isnert ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rtofn t) x y i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)).
-
-(* notion 1698 *)
-definition l_e_st_eq_landau_n_rt_isnirt ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y).(l_e_st_eq_landau_n_rt_ii5_t22 (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) x y (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) i : l_e_st_eq_landau_n_is x y).
-
-(* notion 1699 *)
-definition l_e_st_eq_landau_n_rt_isrtn1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_st_eq_landau_n_rt_isi x0 (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_nofrt x0 nx0)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_refeq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_nofrt x0 nx0))).
-
-(* notion 1700 *)
-definition l_e_st_eq_landau_n_rt_isnrt1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_ii5_t22 (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn x) x (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x)) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rtofn x)) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x))).
-
-(* notion 1701 *)
-definition l_e_st_eq_landau_n_satz112a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz57 x y l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x y) l_e_st_eq_landau_n_1)).
-
-(* notion 1702 *)
-definition l_e_st_eq_landau_n_satz112b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_treq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x y) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_tfeq12a x l_e_st_eq_landau_n_1 y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_eqd (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz28a l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x y) l_e_st_eq_landau_n_1)).
-
-(* notion 1703 *)
-definition l_e_st_eq_landau_n_rt_satz112c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.(l_e_st_eq_landau_n_rt_lemmaeq1 (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_picp x0 y0 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclassn y0 ny0)) (l_e_st_eq_landau_n_satz112a (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl x0 y0))).
-
-(* notion 1704 *)
-definition l_e_st_eq_landau_n_rt_satz112d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop (l_e_st_eq_landau_n_rt_pl x0 y0) t) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) (l_e_st_eq_landau_n_rt_satz112c x0 nx0 y0 ny0) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_pl x0 y0)).
-
-(* notion 1705 *)
-definition l_e_st_eq_landau_n_rt_satz112e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.(l_e_st_eq_landau_n_rt_lemmaeq1 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_tict x0 y0 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclassn y0 ny0)) (l_e_st_eq_landau_n_satz112b (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ts x0 y0))).
-
-(* notion 1706 *)
-definition l_e_st_eq_landau_n_rt_satz112f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop (l_e_st_eq_landau_n_rt_ts x0 y0) t) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) (l_e_st_eq_landau_n_rt_satz112e x0 nx0 y0 ny0) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 1707 *)
-definition l_e_st_eq_landau_n_rt_5112_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_satz111a (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_moree x0 y0 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclassn y0 ny0) m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)).
-
-(* notion 1708 *)
-definition l_e_st_eq_landau_n_rt_5112_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λz:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) z.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt y0 ny0) z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z))) d (l_e_st_eq_landau_n_ispl2 z (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z)) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_isnrt1 z)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z)))).
-
-(* notion 1709 *)
-definition l_e_st_eq_landau_n_rt_5112_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λz:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) z.(l_e_st_eq_landau_n_rt_isi x0 (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_rtofn z)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z))) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_satz112c y0 ny0 (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z)) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z))) (l_e_st_eq_landau_n_rt_5112_t2 x0 nx0 y0 ny0 m z d)) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_rtofn z))).
-
-(* notion 1710 *)
-definition l_e_st_eq_landau_n_rt_5112_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λz:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) z.(l_e_st_eq_landau_n_rt_satz101g x0 y0 (l_e_st_eq_landau_n_rt_rtofn z) m (l_e_symis l_e_st_eq_landau_n_rt_rat x0 (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_rtofn z)) (l_e_st_eq_landau_n_rt_5112_t3 x0 nx0 y0 ny0 m z d)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_mn x0 y0 m)).
-
-(* notion 1711 *)
-definition l_e_st_eq_landau_n_rt_5112_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λz:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) z.(l_e_isp l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_mn x0 y0 m) (l_e_st_eq_landau_n_rt_natrti z) (l_e_st_eq_landau_n_rt_5112_t4 x0 nx0 y0 ny0 m z d) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)).
-
-(* notion 1712 *)
-definition l_e_st_eq_landau_n_rt_satz112g ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_someapp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) t) (l_e_st_eq_landau_n_rt_5112_t1 x0 nx0 y0 ny0 m) (l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) t.l_e_st_eq_landau_n_rt_5112_t5 x0 nx0 y0 ny0 m t u) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)).
-
-(* notion 1713 *)
-definition l_e_st_eq_landau_n_rt_satz112h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x y) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_picp (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x y) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz112a x y) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl x y))).
-
-(* notion 1714 *)
-definition l_e_st_eq_landau_n_rt_satz112j ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x y) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_tict (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x y) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz112b x y) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_ts x y))).
-
-(* notion 1715 *)
-definition l_e_st_eq_landau_n_rt_nt_natt ≝ (l_e_ot l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) : Type[0]).
-
-(* notion 1716 *)
-definition l_e_st_eq_landau_n_rt_nt_ntofrt ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_out l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) x0 nx0 : l_e_st_eq_landau_n_rt_nt_natt).
-
-(* notion 1717 *)
-definition l_e_st_eq_landau_n_rt_nt_is ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_is l_e_st_eq_landau_n_rt_nt_natt xt yt : Prop).
-
-(* notion 1718 *)
-definition l_e_st_eq_landau_n_rt_nt_nis ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_not (l_e_st_eq_landau_n_rt_nt_is xt yt) : Prop).
-
-(* notion 1719 *)
-definition l_e_st_eq_landau_n_rt_nt_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.(l_all l_e_st_eq_landau_n_rt_nt_natt p : Prop).
-
-(* notion 1720 *)
-definition l_e_st_eq_landau_n_rt_nt_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.(l_some l_e_st_eq_landau_n_rt_nt_natt p : Prop).
-
-(* notion 1721 *)
-definition l_e_st_eq_landau_n_rt_nt_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.(l_e_one l_e_st_eq_landau_n_rt_nt_natt p : Prop).
-
-(* notion 1722 *)
-definition l_e_st_eq_landau_n_rt_nt_in ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_esti l_e_st_eq_landau_n_rt_nt_natt xt st : Prop).
-
-(* notion 1723 *)
-definition l_e_st_eq_landau_n_rt_nt_rtofnt ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_in l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) xt : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 1724 *)
-definition l_e_st_eq_landau_n_rt_nt_natrti ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_inp l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) xt : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_nt_rtofnt xt)).
-
-(* notion 1725 *)
-definition l_e_st_eq_landau_n_rt_nt_isrtent ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isouti l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) x0 nx0 y0 ny0 i : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofrt x0 nx0) (l_e_st_eq_landau_n_rt_nt_ntofrt y0 ny0)).
-
-(* notion 1726 *)
-definition l_e_st_eq_landau_n_rt_nt_isrtint ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λi:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofrt x0 nx0) (l_e_st_eq_landau_n_rt_nt_ntofrt y0 ny0).(l_e_isoute l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) x0 nx0 y0 ny0 i : l_e_st_eq_landau_n_rt_is x0 y0).
-
-(* notion 1727 *)
-definition l_e_st_eq_landau_n_rt_nt_isntert ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_nt_is xt yt.(l_e_isini l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) xt yt i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)).
-
-(* notion 1728 *)
-definition l_e_st_eq_landau_n_rt_nt_isntirt ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt).(l_e_isine l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) xt yt i : l_e_st_eq_landau_n_rt_nt_is xt yt).
-
-(* notion 1729 *)
-definition l_e_st_eq_landau_n_rt_nt_isrtnt1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_isinout l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) x0 nx0 : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_nt_rtofnt (l_e_st_eq_landau_n_rt_nt_ntofrt x0 nx0))).
-
-(* notion 1730 *)
-definition l_e_st_eq_landau_n_rt_nt_isntrt1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_isoutin l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) xt : l_e_st_eq_landau_n_rt_nt_is xt (l_e_st_eq_landau_n_rt_nt_ntofrt (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt))).
-
-(* notion 1731 *)
-definition l_e_st_eq_landau_n_rt_nt_ntofn ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_ntofrt (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x) : l_e_st_eq_landau_n_rt_nt_natt).
-
-(* notion 1732 *)
-definition l_e_st_eq_landau_n_rt_nt_isnent ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_rt_nt_isrtent (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_rt_natrti y) (l_e_st_eq_landau_n_rt_isnert x y i) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofn x) (l_e_st_eq_landau_n_rt_nt_ntofn y)).
-
-(* notion 1733 *)
-definition l_e_st_eq_landau_n_rt_nt_isnint ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofn x) (l_e_st_eq_landau_n_rt_nt_ntofn y).(l_e_st_eq_landau_n_rt_isnirt x y (l_e_st_eq_landau_n_rt_nt_isrtint (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_rt_natrti y) i) : l_e_st_eq_landau_n_is x y).
-
-(* notion 1734 *)
-definition l_e_st_eq_landau_n_rt_nt_nofnt ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) : l_e_st_eq_landau_n_nat).
-
-(* notion 1735 *)
-definition l_e_st_eq_landau_n_rt_nt_isnten ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_nt_is xt yt.(l_e_st_eq_landau_n_rt_isrten (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) (l_e_st_eq_landau_n_rt_nt_isntert xt yt i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
-
-(* notion 1736 *)
-definition l_e_st_eq_landau_n_rt_nt_isntin ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_e_st_eq_landau_n_rt_nt_isntirt xt yt (l_e_st_eq_landau_n_rt_isrtin (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) i) : l_e_st_eq_landau_n_rt_nt_is xt yt).
-
-(* notion 1737 *)
-definition l_e_st_eq_landau_n_rt_nt_ii5_t24 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_isrtnt1 (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_nt_rtofnt (l_e_st_eq_landau_n_rt_nt_ntofn x))).
-
-(* notion 1738 *)
-definition l_e_st_eq_landau_n_rt_nt_ii5_t25 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_isrten (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x) (l_e_st_eq_landau_n_rt_nt_rtofnt (l_e_st_eq_landau_n_rt_nt_ntofn x)) (l_e_st_eq_landau_n_rt_nt_natrti (l_e_st_eq_landau_n_rt_nt_ntofn x)) (l_e_st_eq_landau_n_rt_nt_ii5_t24 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x))).
-
-(* notion 1739 *)
-definition l_e_st_eq_landau_n_rt_nt_isnnt1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x)) (l_e_st_eq_landau_n_rt_isnrt1 x) (l_e_st_eq_landau_n_rt_nt_ii5_t25 x) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x))).
-
-(* notion 1740 *)
-definition l_e_st_eq_landau_n_rt_nt_ii5_t26 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_isrtn1 (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_nt_nofnt xt))).
-
-(* notion 1741 *)
-definition l_e_st_eq_landau_n_rt_nt_ii5_t27 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_isrtent (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_rt_natrti (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_rt_nt_ii5_t26 xt) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofrt (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt))).
-
-(* notion 1742 *)
-definition l_e_st_eq_landau_n_rt_nt_isntn1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_tris l_e_st_eq_landau_n_rt_nt_natt xt (l_e_st_eq_landau_n_rt_nt_ntofrt (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_rt_nt_isntrt1 xt) (l_e_st_eq_landau_n_rt_nt_ii5_t27 xt) : l_e_st_eq_landau_n_rt_nt_is xt (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt))).
-
-(* notion 1743 *)
-definition l_e_st_eq_landau_n_rt_nt_isnnt2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x)) (l_e_st_eq_landau_n_rt_nt_isnnt1 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x)) x).
-
-(* notion 1744 *)
-definition l_e_st_eq_landau_n_rt_nt_isntn2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_symis l_e_st_eq_landau_n_rt_nt_natt xt (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_rt_nt_isntn1 xt) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) xt).
-
-(* notion 1745 *)
-definition l_e_st_eq_landau_n_rt_nt_1t ≝ (l_e_st_eq_landau_n_rt_nt_ntofn l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_rt_nt_natt).
-
-(* notion 1746 *)
-definition l_e_st_eq_landau_n_rt_nt_suct ≝ (Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt x)) : Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt).
-
-(* notion 1747 *)
-definition l_e_st_eq_landau_n_rt_nt_5113_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) l_e_st_eq_landau_n_rt_nt_1t.(l_e_st_eq_landau_n_rt_nt_isnint (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) l_e_st_eq_landau_n_1 i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) l_e_st_eq_landau_n_1).
-
-(* notion 1748 *)
-definition l_e_st_eq_landau_n_rt_nt_satz113a ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_imp_th3 (l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ax3 (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (λt:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) l_e_st_eq_landau_n_rt_nt_1t.l_e_st_eq_landau_n_rt_nt_5113_t1 xt t) : l_e_st_eq_landau_n_rt_nt_nis (l_e_st_eq_landau_n_rt_nt_suct xt) l_e_st_eq_landau_n_rt_nt_1t).
-
-(* notion 1749 *)
-definition l_e_st_eq_landau_n_rt_nt_5113_t2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_suct yt).(l_e_st_eq_landau_n_rt_nt_isnint (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt yt)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt yt))).
-
-(* notion 1750 *)
-definition l_e_st_eq_landau_n_rt_nt_satz113b ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_suct yt).(l_e_st_eq_landau_n_rt_nt_isntin xt yt (l_e_st_eq_landau_n_ax4 (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_5113_t2 xt yt i)) : l_e_st_eq_landau_n_rt_nt_is xt yt).
-
-(* notion 1751 *)
-definition l_e_st_eq_landau_n_rt_nt_cond1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_in l_e_st_eq_landau_n_rt_nt_1t st : Prop).
-
-(* notion 1752 *)
-definition l_e_st_eq_landau_n_rt_nt_cond2 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_all (λx:l_e_st_eq_landau_n_rt_nt_natt.l_imp (l_e_st_eq_landau_n_rt_nt_in x st) (l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_suct x) st)) : Prop).
-
-(* notion 1753 *)
-definition l_e_st_eq_landau_n_rt_nt_5113_prop1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_ntofn x) st : Prop).
-
-(* notion 1754 *)
-definition l_e_st_eq_landau_n_rt_nt_5113_t3 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 x.(c2 (l_e_st_eq_landau_n_rt_nt_ntofn x) : l_imp (l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_ntofn x) st) (l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_ntofn x)) st)).
-
-(* notion 1755 *)
-definition l_e_st_eq_landau_n_rt_nt_5113_t4 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 x.(l_mp (l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_ntofn x) st) (l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_ntofn x)) st) p (l_e_st_eq_landau_n_rt_nt_5113_t3 st c1 c2 x p) : l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_ntofn x)) st).
-
-(* notion 1756 *)
-definition l_e_st_eq_landau_n_rt_nt_5113_t5 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_suc t)) st) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x)) x (l_e_st_eq_landau_n_rt_nt_5113_t4 st c1 c2 x p) (l_e_st_eq_landau_n_rt_nt_isnnt2 x) : l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 1757 *)
-definition l_e_st_eq_landau_n_rt_nt_5113_t6 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 t) c1 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 t.l_e_st_eq_landau_n_rt_nt_5113_t5 st c1 c2 t u) (l_e_st_eq_landau_n_rt_nt_nofnt xt) : l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) st).
-
-(* notion 1758 *)
-definition l_e_st_eq_landau_n_rt_nt_satz113c ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_isp l_e_st_eq_landau_n_rt_nt_natt (λt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_in t st) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) xt (l_e_st_eq_landau_n_rt_nt_5113_t6 st c1 c2 xt) (l_e_st_eq_landau_n_rt_nt_isntn2 xt) : l_e_st_eq_landau_n_rt_nt_in xt st).
-
-(* notion 1759 *)
-definition l_e_st_eq_landau_n_rt_nt_ax3t ≝ (Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_satz113a x : Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_nis (l_e_st_eq_landau_n_rt_nt_suct x) l_e_st_eq_landau_n_rt_nt_1t).
-
-(* notion 1760 *)
-definition l_e_st_eq_landau_n_rt_nt_ax4t ≝ (λx:l_e_st_eq_landau_n_rt_nt_natt.λy:l_e_st_eq_landau_n_rt_nt_natt.λu:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct x) (l_e_st_eq_landau_n_rt_nt_suct y).l_e_st_eq_landau_n_rt_nt_satz113b x y u : Πx:l_e_st_eq_landau_n_rt_nt_natt.Πy:l_e_st_eq_landau_n_rt_nt_natt.Πu:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct x) (l_e_st_eq_landau_n_rt_nt_suct y).l_e_st_eq_landau_n_rt_nt_is x y).
-
-(* notion 1761 *)
-definition l_e_st_eq_landau_n_rt_nt_ax5t ≝ (λs:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λu:l_e_st_eq_landau_n_rt_nt_cond1 s.λv:l_e_st_eq_landau_n_rt_nt_cond2 s.λx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_satz113c s u v x : Πs:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.Πu:l_e_st_eq_landau_n_rt_nt_cond1 s.Πv:l_e_st_eq_landau_n_rt_nt_cond2 s.Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_in x s).
-
-(* notion 1762 *)
-definition l_e_st_eq_landau_n_rt_nt_51_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λn:l_e_st_eq_landau_n_rt_nt_nis xt yt.(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_is xt yt) n (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).l_e_st_eq_landau_n_rt_nt_isntin xt yt t) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
-
-(* notion 1763 *)
-definition l_e_st_eq_landau_n_rt_nt_51_t2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λn:l_e_st_eq_landau_n_rt_nt_nis xt yt.(l_e_st_eq_landau_n_satz1 (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_51_t1 xt yt n) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt yt))).
-
-(* notion 1764 *)
-definition l_e_st_eq_landau_n_rt_nt_satz1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λn:l_e_st_eq_landau_n_rt_nt_nis xt yt.(l_imp_th3 (l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_suct yt)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_51_t2 xt yt n) (λt:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_suct yt).l_e_st_eq_landau_n_rt_nt_isnint (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt yt)) t) : l_e_st_eq_landau_n_rt_nt_nis (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_suct yt)).
-
-(* notion 1765 *)
-definition l_e_st_eq_landau_n_rt_nt_54_x ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_nofnt xt : l_e_st_eq_landau_n_nat).
-
-(* notion 1766 *)
-definition l_e_st_eq_landau_n_rt_nt_54_prop1t ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_all (λt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_is (ft (l_e_st_eq_landau_n_rt_nt_suct t)) (l_e_st_eq_landau_n_rt_nt_suct (ft t))) : Prop).
-
-(* notion 1767 *)
-definition l_e_st_eq_landau_n_rt_nt_54_prop2t ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.(l_and (l_e_st_eq_landau_n_rt_nt_is (ft l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt ft) : Prop).
-
-(* notion 1768 *)
-definition l_e_st_eq_landau_n_rt_nt_54_prop1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc t)) (l_e_st_eq_landau_n_suc (f t))) : Prop).
-
-(* notion 1769 *)
-definition l_e_st_eq_landau_n_rt_nt_54_prop2 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_and (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))) (l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt f) : Prop).
-
-(* notion 1770 *)
-definition l_e_st_eq_landau_n_rt_nt_54_g ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.(Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_nofnt (ft (l_e_st_eq_landau_n_rt_nt_ntofn t)) : Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
-
-(* notion 1771 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.(l_ande1 (l_e_st_eq_landau_n_rt_nt_is (ft l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt ft) p : l_e_st_eq_landau_n_rt_nt_is (ft l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)).
-
-(* notion 1772 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t2 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt)) (l_e_st_eq_landau_n_rt_nt_isnten (ft l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_54_t1 st c1 c2 xt ft p)) (l_e_st_eq_landau_n_rt_nt_isnnt2 (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))).
-
-(* notion 1773 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t3 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.(l_ande2 (l_e_st_eq_landau_n_rt_nt_is (ft l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt ft) p : l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt ft).
-
-(* notion 1774 *)
-definition l_e_st_eq_landau_n_rt_nt_54_ut ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_ntofn u : l_e_st_eq_landau_n_rt_nt_natt).
-
-(* notion 1775 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t4 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_suc u (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)) (l_e_st_eq_landau_n_rt_nt_isnnt1 u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc u) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))).
-
-(* notion 1776 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t5 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft) (l_e_st_eq_landau_n_suc u) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))) (l_e_st_eq_landau_n_rt_nt_54_t4 st c1 c2 xt ft p u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_rt_nt_nofnt (ft (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))))).
-
-(* notion 1777 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t6 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_54_t3 st c1 c2 xt ft p (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u) : l_e_st_eq_landau_n_rt_nt_is (ft (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))) (l_e_st_eq_landau_n_rt_nt_suct (ft (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))).
-
-(* notion 1778 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t7 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_isnten (ft (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))) (l_e_st_eq_landau_n_rt_nt_suct (ft (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))) (l_e_st_eq_landau_n_rt_nt_54_t6 st c1 c2 xt ft p u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt (ft (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct (ft (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))))).
-
-(* notion 1779 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t8 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_isnnt2 (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct (ft (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft u))).
-
-(* notion 1780 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t9 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_rt_nt_nofnt (ft (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct (ft (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft u)) (l_e_st_eq_landau_n_rt_nt_54_t5 st c1 c2 xt ft p u) (l_e_st_eq_landau_n_rt_nt_54_t7 st c1 c2 xt ft p u) (l_e_st_eq_landau_n_rt_nt_54_t8 st c1 c2 xt ft p u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft u))).
-
-(* notion 1781 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t10 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.(λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_t9 st c1 c2 xt ft p u : l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft)).
-
-(* notion 1782 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t11 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.(l_andi (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))) (l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft)) (l_e_st_eq_landau_n_rt_nt_54_t2 st c1 c2 xt ft p) (l_e_st_eq_landau_n_rt_nt_54_t10 st c1 c2 xt ft p) : l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft)).
-
-(* notion 1783 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t12 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.(l_e_onee1 (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u) (l_e_st_eq_landau_n_satz4 (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt)) : l_e_amone (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u)).
-
-(* notion 1784 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t13 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.(l_e_st_eq_landau_n_rt_nt_54_t12 st c1 c2 xt a b pa pb (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt a) (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt b) (l_e_st_eq_landau_n_rt_nt_54_t11 st c1 c2 xt a pa) (l_e_st_eq_landau_n_rt_nt_54_t11 st c1 c2 xt b pb) : l_e_is (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt a) (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt b)).
-
-(* notion 1785 *)
-definition l_e_st_eq_landau_n_rt_nt_54_y ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_nofnt yt : l_e_st_eq_landau_n_nat).
-
-(* notion 1786 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t14 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_fise l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt a) (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt b) (l_e_st_eq_landau_n_rt_nt_54_t13 st c1 c2 xt a b pa pb) (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt (a (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt)))) (l_e_st_eq_landau_n_rt_nt_nofnt (b (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))))).
-
-(* notion 1787 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t15 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_isntin (a (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))) (b (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))) (l_e_st_eq_landau_n_rt_nt_54_t14 st c1 c2 xt a b pa pb yt) : l_e_st_eq_landau_n_rt_nt_is (a (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))) (b (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt)))).
-
-(* notion 1788 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t16 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_tr3is l_e_st_eq_landau_n_rt_nt_natt (a yt) (a (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))) (b (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))) (b yt) (l_e_isf l_e_st_eq_landau_n_rt_nt_natt l_e_st_eq_landau_n_rt_nt_natt a yt (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt)) (l_e_st_eq_landau_n_rt_nt_isntn1 yt)) (l_e_st_eq_landau_n_rt_nt_54_t15 st c1 c2 xt a b pa pb yt) (l_e_isf l_e_st_eq_landau_n_rt_nt_natt l_e_st_eq_landau_n_rt_nt_natt b (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt)) yt (l_e_st_eq_landau_n_rt_nt_isntn2 yt)) : l_e_st_eq_landau_n_rt_nt_is (a yt) (b yt)).
-
-(* notion 1789 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t17 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.(l_e_fisi l_e_st_eq_landau_n_rt_nt_natt l_e_st_eq_landau_n_rt_nt_natt a b (λt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_t16 st c1 c2 xt a b pa pb t) : l_e_is (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) a b).
-
-(* notion 1790 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t18 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(λu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λv:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λw:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u.λz:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt v.l_e_st_eq_landau_n_rt_nt_54_t17 st c1 c2 xt u v w z : l_e_amone (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (Πu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u)).
-
-(* notion 1791 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t19 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_onee2 (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u) (l_e_st_eq_landau_n_satz4 (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt)) : l_some (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u)).
-
-(* notion 1792 *)
-definition l_e_st_eq_landau_n_rt_nt_54_gt ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_ntofn (f (l_e_st_eq_landau_n_rt_nt_nofnt t)) : Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt).
-
-(* notion 1793 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t20 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_ande1 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))) (l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt f) p : l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))).
-
-(* notion 1794 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t21 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat f (l_e_st_eq_landau_n_rt_nt_nofnt l_e_st_eq_landau_n_rt_nt_1t) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_nt_isnnt2 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_rt_nt_nofnt l_e_st_eq_landau_n_rt_nt_1t)) (f l_e_st_eq_landau_n_1)).
-
-(* notion 1795 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t22 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_e_st_eq_landau_n_rt_nt_isnent (f (l_e_st_eq_landau_n_rt_nt_nofnt l_e_st_eq_landau_n_rt_nt_1t)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt)) (l_e_tris l_e_st_eq_landau_n_nat (f (l_e_st_eq_landau_n_rt_nt_nofnt l_e_st_eq_landau_n_rt_nt_1t)) (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt)) (l_e_st_eq_landau_n_rt_nt_54_t21 st c1 c2 xt f p) (l_e_st_eq_landau_n_rt_nt_54_t20 st c1 c2 xt f p)) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)).
-
-(* notion 1796 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t23 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_ande2 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))) (l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt f) p : l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt f).
-
-(* notion 1797 *)
-definition l_e_st_eq_landau_n_rt_nt_54_z ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_nofnt zt : l_e_st_eq_landau_n_nat).
-
-(* notion 1798 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t24 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat f (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct zt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt)) (l_e_st_eq_landau_n_rt_nt_isnnt2 (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct zt))) (f (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt)))).
-
-(* notion 1799 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t25 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_54_t23 st c1 c2 xt f p (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt) : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) (l_e_st_eq_landau_n_suc (f (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt)))).
-
-(* notion 1800 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t26 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_suc (f (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f zt)) (l_e_st_eq_landau_n_rt_nt_isnnt1 (f (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (f (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f zt)))).
-
-(* notion 1801 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t27 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_isnent (f (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct zt))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f zt))) (l_e_tr3is l_e_st_eq_landau_n_nat (f (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct zt))) (f (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) (l_e_st_eq_landau_n_suc (f (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f zt))) (l_e_st_eq_landau_n_rt_nt_54_t24 st c1 c2 xt f p zt) (l_e_st_eq_landau_n_rt_nt_54_t25 st c1 c2 xt f p zt) (l_e_st_eq_landau_n_rt_nt_54_t26 st c1 c2 xt f p zt)) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f (l_e_st_eq_landau_n_rt_nt_suct zt)) (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f zt))).
-
-(* notion 1802 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t28 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_t27 st c1 c2 xt f p u : l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f)).
-
-(* notion 1803 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t29 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_andi (l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f)) (l_e_st_eq_landau_n_rt_nt_54_t22 st c1 c2 xt f p) (l_e_st_eq_landau_n_rt_nt_54_t28 st c1 c2 xt f p) : l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f)).
-
-(* notion 1804 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t30 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_somei (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (Πu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u) (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f) (l_e_st_eq_landau_n_rt_nt_54_t29 st c1 c2 xt f p) : l_some (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (Πu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u)).
-
-(* notion 1805 *)
-definition l_e_st_eq_landau_n_rt_nt_54_t31 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_someapp (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (Πu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u) (l_e_st_eq_landau_n_rt_nt_54_t19 st c1 c2 xt) (l_some (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (Πu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u)) (λu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u.l_e_st_eq_landau_n_rt_nt_54_t30 st c1 c2 xt u v) : l_some (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (Πu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u)).
-
-(* notion 1806 *)
-definition l_e_st_eq_landau_n_rt_nt_satz4 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_onei (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (Πu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u) (l_e_st_eq_landau_n_rt_nt_54_t18 st c1 c2 xt) (l_e_st_eq_landau_n_rt_nt_54_t31 st c1 c2 xt) : l_e_one (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (Πu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_and (l_e_st_eq_landau_n_rt_nt_is (u l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_rt_nt_all (λv:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_is (u (l_e_st_eq_landau_n_rt_nt_suct v)) (l_e_st_eq_landau_n_rt_nt_suct (u v)))))).
-
-(* notion 1807 *)
-definition l_e_st_eq_landau_n_rt_nt_pl ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_ntofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_satz112d (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) : l_e_st_eq_landau_n_rt_nt_natt).
-
-(* notion 1808 *)
-definition l_e_st_eq_landau_n_rt_nt_ii5_t28 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_satz112c (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)))).
-
-(* notion 1809 *)
-definition l_e_st_eq_landau_n_rt_nt_ii5_t29 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_nt_ii5_t28 xt yt) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_refeq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)))).
-
-(* notion 1810 *)
-definition l_e_st_eq_landau_n_rt_nt_isplnt ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_isrtent (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_satz112d (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_natrti (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_ii5_t29 xt yt) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_pl xt yt) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)))).
-
-(* notion 1811 *)
-definition l_e_st_eq_landau_n_rt_nt_isntpl ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_symis l_e_st_eq_landau_n_rt_nt_natt (l_e_st_eq_landau_n_rt_nt_pl xt yt) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_isplnt xt yt) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_pl xt yt)).
-
-(* notion 1812 *)
-definition l_e_st_eq_landau_n_rt_nt_ispln ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)))) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_isnnt1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_isnten (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_pl xt yt) (l_e_st_eq_landau_n_rt_nt_isntpl xt yt)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt))).
-
-(* notion 1813 *)
-definition l_e_st_eq_landau_n_rt_nt_isnpl ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_ispln xt yt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))).
-
-(* notion 1814 *)
-definition l_e_st_eq_landau_n_rt_nt_55_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt) (l_e_st_eq_landau_n_rt_nt_isnpl xt yt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt))).
-
-(* notion 1815 *)
-definition l_e_st_eq_landau_n_rt_nt_55_t2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)) (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_ispln yt zt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)))).
-
-(* notion 1816 *)
-definition l_e_st_eq_landau_n_rt_nt_55_t3 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt))) (l_e_st_eq_landau_n_rt_nt_55_t1 xt yt zt) (l_e_st_eq_landau_n_satz5 (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_rt_nt_55_t2 xt yt zt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)))).
-
-(* notion 1817 *)
-definition l_e_st_eq_landau_n_rt_nt_satz5 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_tr3is l_e_st_eq_landau_n_rt_nt_natt (l_e_st_eq_landau_n_rt_nt_pl (l_e_st_eq_landau_n_rt_nt_pl xt yt) zt) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt))) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)))) (l_e_st_eq_landau_n_rt_nt_pl xt (l_e_st_eq_landau_n_rt_nt_pl yt zt)) (l_e_st_eq_landau_n_rt_nt_isplnt (l_e_st_eq_landau_n_rt_nt_pl xt yt) zt) (l_e_st_eq_landau_n_rt_nt_isnent (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt))) (l_e_st_eq_landau_n_rt_nt_55_t3 xt yt zt)) (l_e_st_eq_landau_n_rt_nt_isntpl xt (l_e_st_eq_landau_n_rt_nt_pl yt zt)) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_pl (l_e_st_eq_landau_n_rt_nt_pl xt yt) zt) (l_e_st_eq_landau_n_rt_nt_pl xt (l_e_st_eq_landau_n_rt_nt_pl yt zt))).
-
-(* notion 1818 *)
-definition l_e_st_eq_landau_n_rt_nt_diffprop ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_is xt (l_e_st_eq_landau_n_rt_nt_pl yt zt) : Prop).
-
-(* notion 1819 *)
-definition l_e_st_eq_landau_n_rt_nt_diffprope ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λd:l_e_st_eq_landau_n_rt_nt_diffprop xt yt zt.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_rt_nt_isnten xt (l_e_st_eq_landau_n_rt_nt_pl yt zt) d) (l_e_st_eq_landau_n_rt_nt_isnpl yt zt) : l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)).
-
-(* notion 1820 *)
-definition l_e_st_eq_landau_n_rt_nt_ii5_t30 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)) d (l_e_st_eq_landau_n_rt_nt_ispln yt zt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt))).
-
-(* notion 1821 *)
-definition l_e_st_eq_landau_n_rt_nt_diffpropi ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt).(l_e_st_eq_landau_n_rt_nt_isntin xt (l_e_st_eq_landau_n_rt_nt_pl yt zt) (l_e_st_eq_landau_n_rt_nt_ii5_t30 xt yt zt d) : l_e_st_eq_landau_n_rt_nt_diffprop xt yt zt).
-
-(* notion 1822 *)
-definition l_e_st_eq_landau_n_rt_nt_59_it ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_is xt yt : Prop).
-
-(* notion 1823 *)
-definition l_e_st_eq_landau_n_rt_nt_59_iit ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_some (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_diffprop xt yt u) : Prop).
-
-(* notion 1824 *)
-definition l_e_st_eq_landau_n_rt_nt_59_iiit ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_some (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_diffprop yt xt u) : Prop).
-
-(* notion 1825 *)
-definition l_e_st_eq_landau_n_rt_nt_59_i ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) : Prop).
-
-(* notion 1826 *)
-definition l_e_st_eq_landau_n_rt_nt_59_ii ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) u) : Prop).
-
-(* notion 1827 *)
-definition l_e_st_eq_landau_n_rt_nt_59_iii ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt xt) u) : Prop).
-
-(* notion 1828 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λone:l_e_st_eq_landau_n_rt_nt_59_i xt yt.(l_or3i1 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_isntin xt yt one) : l_or3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
-
-(* notion 1829 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwo:l_e_st_eq_landau_n_rt_nt_59_ii xt yt.λv:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) v.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) u) v (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn v)) d (l_e_st_eq_landau_n_rt_nt_isnnt1 v) : l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn v))).
-
-(* notion 1830 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t3 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwo:l_e_st_eq_landau_n_rt_nt_59_ii xt yt.λv:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) v.(l_somei l_e_st_eq_landau_n_rt_nt_natt (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_diffprop xt yt u) (l_e_st_eq_landau_n_rt_nt_ntofn v) (l_e_st_eq_landau_n_rt_nt_diffpropi xt yt (l_e_st_eq_landau_n_rt_nt_ntofn v) (l_e_st_eq_landau_n_rt_nt_59_t2 xt yt two v d)) : l_e_st_eq_landau_n_rt_nt_59_iit xt yt).
-
-(* notion 1831 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t4 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwo:l_e_st_eq_landau_n_rt_nt_59_ii xt yt.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) u) two (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) u.l_e_st_eq_landau_n_rt_nt_59_t3 xt yt two u v) : l_e_st_eq_landau_n_rt_nt_59_iit xt yt).
-
-(* notion 1832 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t5 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwo:l_e_st_eq_landau_n_rt_nt_59_ii xt yt.(l_or3i2 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_t4 xt yt two) : l_or3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
-
-(* notion 1833 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t6 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λthree:l_e_st_eq_landau_n_rt_nt_59_iii xt yt.(l_or3i3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_t4 yt xt three) : l_or3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
-
-(* notion 1834 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t7 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_or3app (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt) (l_or3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)) (l_e_st_eq_landau_n_satz9a (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (λu:l_e_st_eq_landau_n_rt_nt_59_i xt yt.l_e_st_eq_landau_n_rt_nt_59_t1 xt yt u) (λu:l_e_st_eq_landau_n_rt_nt_59_ii xt yt.l_e_st_eq_landau_n_rt_nt_59_t5 xt yt u) (λu:l_e_st_eq_landau_n_rt_nt_59_iii xt yt.l_e_st_eq_landau_n_rt_nt_59_t6 xt yt u) : l_or3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
-
-(* notion 1835 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t8 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λonet:l_e_st_eq_landau_n_rt_nt_59_it xt yt.(l_e_st_eq_landau_n_rt_nt_isnten xt yt onet : l_e_st_eq_landau_n_rt_nt_59_i xt yt).
-
-(* notion 1836 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t9 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwot:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.λvt:l_e_st_eq_landau_n_rt_nt_natt.λd:l_e_st_eq_landau_n_rt_nt_diffprop xt yt vt.(l_somei l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) u) (l_e_st_eq_landau_n_rt_nt_nofnt vt) (l_e_st_eq_landau_n_rt_nt_diffprope xt yt vt d) : l_e_st_eq_landau_n_rt_nt_59_ii xt yt).
-
-(* notion 1837 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t10 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwot:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.(l_someapp l_e_st_eq_landau_n_rt_nt_natt (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_diffprop xt yt u) twot (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (λu:l_e_st_eq_landau_n_rt_nt_natt.λv:l_e_st_eq_landau_n_rt_nt_diffprop xt yt u.l_e_st_eq_landau_n_rt_nt_59_t9 xt yt twot u v) : l_e_st_eq_landau_n_rt_nt_59_ii xt yt).
-
-(* notion 1838 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t11 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λthreet:l_e_st_eq_landau_n_rt_nt_59_iiit xt yt.(l_e_st_eq_landau_n_rt_nt_59_t10 yt xt threet : l_e_st_eq_landau_n_rt_nt_59_iii xt yt).
-
-(* notion 1839 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t12 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_satz9b (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) : l_ec3 (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt)).
-
-(* notion 1840 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t13 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λonet:l_e_st_eq_landau_n_rt_nt_59_it xt yt.(l_ec3e12 (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt) (l_e_st_eq_landau_n_rt_nt_59_t12 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t8 xt yt onet) : l_not (l_e_st_eq_landau_n_rt_nt_59_ii xt yt)).
-
-(* notion 1841 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t14 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λonet:l_e_st_eq_landau_n_rt_nt_59_it xt yt.(l_imp_th3 (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_t13 xt yt onet) (λx:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.l_e_st_eq_landau_n_rt_nt_59_t10 xt yt x) : l_not (l_e_st_eq_landau_n_rt_nt_59_iit xt yt)).
-
-(* notion 1842 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t15 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_ec_th1 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (λx:l_e_st_eq_landau_n_rt_nt_59_it xt yt.l_e_st_eq_landau_n_rt_nt_59_t14 xt yt x) : l_ec (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt)).
-
-(* notion 1843 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t16 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwot:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.(l_ec3e23 (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt) (l_e_st_eq_landau_n_rt_nt_59_t12 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t10 xt yt twot) : l_not (l_e_st_eq_landau_n_rt_nt_59_iii xt yt)).
-
-(* notion 1844 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t17 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwot:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.(l_imp_th3 (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt) (l_e_st_eq_landau_n_rt_nt_59_t16 xt yt twot) (λx:l_e_st_eq_landau_n_rt_nt_59_iiit xt yt.l_e_st_eq_landau_n_rt_nt_59_t11 xt yt x) : l_not (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
-
-(* notion 1845 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t18 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_ec_th1 (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (λx:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.l_e_st_eq_landau_n_rt_nt_59_t17 xt yt x) : l_ec (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
-
-(* notion 1846 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t19 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λthreet:l_e_st_eq_landau_n_rt_nt_59_iiit xt yt.(l_ec3e31 (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt) (l_e_st_eq_landau_n_rt_nt_59_t12 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t11 xt yt threet) : l_not (l_e_st_eq_landau_n_rt_nt_59_i xt yt)).
-
-(* notion 1847 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t20 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λthreet:l_e_st_eq_landau_n_rt_nt_59_iiit xt yt.(l_imp_th3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_t19 xt yt threet) (λx:l_e_st_eq_landau_n_rt_nt_59_it xt yt.l_e_st_eq_landau_n_rt_nt_59_t8 xt yt x) : l_not (l_e_st_eq_landau_n_rt_nt_59_it xt yt)).
-
-(* notion 1848 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t21 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_ec_th1 (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (λx:l_e_st_eq_landau_n_rt_nt_59_iiit xt yt.l_e_st_eq_landau_n_rt_nt_59_t20 xt yt x) : l_ec (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_it xt yt)).
-
-(* notion 1849 *)
-definition l_e_st_eq_landau_n_rt_nt_59_t22 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_ec3_th6 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_t15 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t18 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t21 xt yt) : l_ec3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
-
-(* notion 1850 *)
-definition l_e_st_eq_landau_n_rt_nt_satz9 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_orec3i (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_t7 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t22 xt yt) : l_orec3 (l_e_st_eq_landau_n_rt_nt_is xt yt) (l_e_st_eq_landau_n_rt_nt_some (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_is xt (l_e_st_eq_landau_n_rt_nt_pl yt u))) (l_e_st_eq_landau_n_rt_nt_some (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_is yt (l_e_st_eq_landau_n_rt_nt_pl xt u)))).
-
-(* notion 1851 *)
-definition l_e_st_eq_landau_n_rt_nt_more ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) : Prop).
-
-(* notion 1852 *)
-definition l_e_st_eq_landau_n_rt_nt_ii5_t31 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_more xt yt.(l_e_st_eq_landau_n_rt_moree (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1)).
-
-(* notion 1853 *)
-definition l_e_st_eq_landau_n_rt_nt_moree ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_more xt yt.(l_e_st_eq_landau_n_satz111a (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_ii5_t31 xt yt m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
-
-(* notion 1854 *)
-definition l_e_st_eq_landau_n_rt_nt_ii5_t32 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_e_st_eq_landau_n_satz111d (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1)).
-
-(* notion 1855 *)
-definition l_e_st_eq_landau_n_rt_nt_morei ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) (l_e_st_eq_landau_n_rt_nt_ii5_t32 xt yt m) : l_e_st_eq_landau_n_rt_nt_more xt yt).
-
-(* notion 1856 *)
-definition l_e_st_eq_landau_n_rt_nt_less ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) : Prop).
-
-(* notion 1857 *)
-definition l_e_st_eq_landau_n_rt_nt_ii5_t33 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_rt_nt_less xt yt.(l_e_st_eq_landau_n_rt_lesse (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) l : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1)).
-
-(* notion 1858 *)
-definition l_e_st_eq_landau_n_rt_nt_lesse ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_rt_nt_less xt yt.(l_e_st_eq_landau_n_satz111c (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_ii5_t33 xt yt l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
-
-(* notion 1859 *)
-definition l_e_st_eq_landau_n_rt_nt_ii5_t34 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_e_st_eq_landau_n_satz111f (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) l : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1)).
-
-(* notion 1860 *)
-definition l_e_st_eq_landau_n_rt_nt_lessi ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_e_st_eq_landau_n_rt_lessi (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) (l_e_st_eq_landau_n_rt_nt_ii5_t34 xt yt l) : l_e_st_eq_landau_n_rt_nt_less xt yt).
-
-(* notion 1861 *)
-definition l_e_st_eq_landau_n_rt_nt_moreis ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) : Prop).
-
-(* notion 1862 *)
-definition l_e_st_eq_landau_n_rt_nt_moreise ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_moreis xt yt.(l_or_th9 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) m (λu:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt).l_e_st_eq_landau_n_rt_nt_moree xt yt u) (λu:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt).l_e_st_eq_landau_n_rt_isrten (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) u) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
-
-(* notion 1863 *)
-definition l_e_st_eq_landau_n_rt_nt_moreisi ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_or_th9 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) m (λu:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).l_e_st_eq_landau_n_rt_nt_morei xt yt u) (λu:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).l_e_st_eq_landau_n_rt_isrtin (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) u) : l_e_st_eq_landau_n_rt_nt_moreis xt yt).
-
-(* notion 1864 *)
-definition l_e_st_eq_landau_n_rt_nt_lessis ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) : Prop).
-
-(* notion 1865 *)
-definition l_e_st_eq_landau_n_rt_nt_lessise ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_rt_nt_lessis xt yt.(l_or_th9 (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l (λu:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt).l_e_st_eq_landau_n_rt_nt_lesse xt yt u) (λu:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt).l_e_st_eq_landau_n_rt_isrten (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) u) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
-
-(* notion 1866 *)
-definition l_e_st_eq_landau_n_rt_nt_lessisi ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_or_th9 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) l (λu:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).l_e_st_eq_landau_n_rt_nt_lessi xt yt u) (λu:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).l_e_st_eq_landau_n_rt_isrtin (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) u) : l_e_st_eq_landau_n_rt_nt_lessis xt yt).
-
-(* notion 1867 *)
-definition l_e_st_eq_landau_n_rt_nt_515_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_rt_nt_less xt yt.λk:l_e_st_eq_landau_n_rt_nt_less yt zt.(l_e_st_eq_landau_n_satz15 (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt) (l_e_st_eq_landau_n_rt_nt_lesse xt yt l) (l_e_st_eq_landau_n_rt_nt_lesse yt zt k) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)).
-
-(* notion 1868 *)
-definition l_e_st_eq_landau_n_rt_nt_satz15 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_rt_nt_less xt yt.λk:l_e_st_eq_landau_n_rt_nt_less yt zt.(l_e_st_eq_landau_n_rt_nt_lessi xt zt (l_e_st_eq_landau_n_rt_nt_515_t1 xt yt zt l k) : l_e_st_eq_landau_n_rt_nt_less xt zt).
-
-(* notion 1869 *)
-definition l_e_st_eq_landau_n_rt_nt_521_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λut:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_more xt yt.λn:l_e_st_eq_landau_n_rt_nt_more zt ut.(l_e_st_eq_landau_n_satz21 (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt) (l_e_st_eq_landau_n_rt_nt_nofnt ut) (l_e_st_eq_landau_n_rt_nt_moree xt yt m) (l_e_st_eq_landau_n_rt_nt_moree zt ut n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt ut))).
-
-(* notion 1870 *)
-definition l_e_st_eq_landau_n_rt_nt_521_t2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λut:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_more xt yt.λn:l_e_st_eq_landau_n_rt_nt_more zt ut.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt ut)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt ut)) (l_e_st_eq_landau_n_rt_nt_ispln xt zt) (l_e_st_eq_landau_n_rt_nt_ispln yt ut) (l_e_st_eq_landau_n_rt_nt_521_t1 xt yt zt ut m n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt zt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt ut))).
-
-(* notion 1871 *)
-definition l_e_st_eq_landau_n_rt_nt_satz21 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λut:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_more xt yt.λn:l_e_st_eq_landau_n_rt_nt_more zt ut.(l_e_st_eq_landau_n_rt_nt_morei (l_e_st_eq_landau_n_rt_nt_pl xt zt) (l_e_st_eq_landau_n_rt_nt_pl yt ut) (l_e_st_eq_landau_n_rt_nt_521_t2 xt yt zt ut m n) : l_e_st_eq_landau_n_rt_nt_more (l_e_st_eq_landau_n_rt_nt_pl xt zt) (l_e_st_eq_landau_n_rt_nt_pl yt ut)).
-
-(* notion 1872 *)
-definition l_e_st_eq_landau_n_rt_nt_lb ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λn:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_all (λx:l_e_st_eq_landau_n_rt_nt_natt.l_imp (p x) (l_e_st_eq_landau_n_rt_nt_lessis n x)) : Prop).
-
-(* notion 1873 *)
-definition l_e_st_eq_landau_n_rt_nt_min ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λn:l_e_st_eq_landau_n_rt_nt_natt.(l_and (l_e_st_eq_landau_n_rt_nt_lb p n) (p n) : Prop).
-
-(* notion 1874 *)
-definition l_e_st_eq_landau_n_rt_nt_527_q ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.(λx:l_e_st_eq_landau_n_nat.p (l_e_st_eq_landau_n_rt_nt_ntofn x) : Πx:l_e_st_eq_landau_n_nat.Prop).
-
-(* notion 1875 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t1 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λn:l_e_st_eq_landau_n_rt_nt_natt.λnp:p n.(l_e_isp l_e_st_eq_landau_n_rt_nt_natt p n (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt n)) np (l_e_st_eq_landau_n_rt_nt_isntn1 n) : l_e_st_eq_landau_n_rt_nt_527_q p s (l_e_st_eq_landau_n_rt_nt_nofnt n)).
-
-(* notion 1876 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t2 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λn:l_e_st_eq_landau_n_rt_nt_natt.λnp:p n.(l_somei l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_527_q p s) (l_e_st_eq_landau_n_rt_nt_nofnt n) (l_e_st_eq_landau_n_rt_nt_527_t1 p s n np) : l_e_st_eq_landau_n_some (l_e_st_eq_landau_n_rt_nt_527_q p s)).
-
-(* notion 1877 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t3 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.(l_someapp l_e_st_eq_landau_n_rt_nt_natt p s (l_e_st_eq_landau_n_some (l_e_st_eq_landau_n_rt_nt_527_q p s)) (λu:l_e_st_eq_landau_n_rt_nt_natt.λv:p u.l_e_st_eq_landau_n_rt_nt_527_t2 p s u v) : l_e_st_eq_landau_n_some (l_e_st_eq_landau_n_rt_nt_527_q p s)).
-
-(* notion 1878 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t4 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.(l_e_st_eq_landau_n_satz27 (l_e_st_eq_landau_n_rt_nt_527_q p s) (l_e_st_eq_landau_n_rt_nt_527_t3 p s) : l_e_st_eq_landau_n_some (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) x)).
-
-(* notion 1879 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t5 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.(l_ande1 (l_e_st_eq_landau_n_lb (l_e_st_eq_landau_n_rt_nt_527_q p s) m) (l_e_st_eq_landau_n_rt_nt_527_q p s m) mqm : l_e_st_eq_landau_n_lb (l_e_st_eq_landau_n_rt_nt_527_q p s) m).
-
-(* notion 1880 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t6 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.λn:l_e_st_eq_landau_n_nat.λnq:l_e_st_eq_landau_n_rt_nt_527_q p s n.(l_mp (l_e_st_eq_landau_n_rt_nt_527_q p s n) (l_e_st_eq_landau_n_lessis m n) nq (l_e_st_eq_landau_n_rt_nt_527_t5 p s m mqm n) : l_e_st_eq_landau_n_lessis m n).
-
-(* notion 1881 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t7 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.λn:l_e_st_eq_landau_n_rt_nt_natt.λnp:p n.(l_e_st_eq_landau_n_rt_nt_527_t6 p s m mqm (l_e_st_eq_landau_n_rt_nt_nofnt n) (l_e_st_eq_landau_n_rt_nt_527_t1 p s n np) : l_e_st_eq_landau_n_lessis m (l_e_st_eq_landau_n_rt_nt_nofnt n)).
-
-(* notion 1882 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t8 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.λn:l_e_st_eq_landau_n_rt_nt_natt.λnp:p n.(l_e_st_eq_landau_n_islessis1 m (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn m)) (l_e_st_eq_landau_n_rt_nt_nofnt n) (l_e_st_eq_landau_n_rt_nt_isnnt1 m) (l_e_st_eq_landau_n_rt_nt_527_t7 p s m mqm n np) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn m)) (l_e_st_eq_landau_n_rt_nt_nofnt n)).
-
-(* notion 1883 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t9 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.λn:l_e_st_eq_landau_n_rt_nt_natt.λnp:p n.(l_e_st_eq_landau_n_rt_nt_lessisi (l_e_st_eq_landau_n_rt_nt_ntofn m) n (l_e_st_eq_landau_n_rt_nt_527_t8 p s m mqm n np) : l_e_st_eq_landau_n_rt_nt_lessis (l_e_st_eq_landau_n_rt_nt_ntofn m) n).
-
-(* notion 1884 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t10 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.λn:l_e_st_eq_landau_n_rt_nt_natt.(λu:p n.l_e_st_eq_landau_n_rt_nt_527_t9 p s m mqm n u : l_imp (p n) (l_e_st_eq_landau_n_rt_nt_lessis (l_e_st_eq_landau_n_rt_nt_ntofn m) n)).
-
-(* notion 1885 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t11 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.(λx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_527_t10 p s m mqm x : l_e_st_eq_landau_n_rt_nt_lb p (l_e_st_eq_landau_n_rt_nt_ntofn m)).
-
-(* notion 1886 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t12 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.(l_ande2 (l_e_st_eq_landau_n_lb (l_e_st_eq_landau_n_rt_nt_527_q p s) m) (l_e_st_eq_landau_n_rt_nt_527_q p s m) mqm : p (l_e_st_eq_landau_n_rt_nt_ntofn m)).
-
-(* notion 1887 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t13 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.(l_andi (l_e_st_eq_landau_n_rt_nt_lb p (l_e_st_eq_landau_n_rt_nt_ntofn m)) (p (l_e_st_eq_landau_n_rt_nt_ntofn m)) (l_e_st_eq_landau_n_rt_nt_527_t11 p s m mqm) (l_e_st_eq_landau_n_rt_nt_527_t12 p s m mqm) : l_e_st_eq_landau_n_rt_nt_min p (l_e_st_eq_landau_n_rt_nt_ntofn m)).
-
-(* notion 1888 *)
-definition l_e_st_eq_landau_n_rt_nt_527_t14 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.(l_somei l_e_st_eq_landau_n_rt_nt_natt (Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_min p x) (l_e_st_eq_landau_n_rt_nt_ntofn m) (l_e_st_eq_landau_n_rt_nt_527_t13 p s m mqm) : l_e_st_eq_landau_n_rt_nt_some (Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_min p x)).
-
-(* notion 1889 *)
-definition l_e_st_eq_landau_n_rt_nt_satz27 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.(l_someapp l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) x) (l_e_st_eq_landau_n_rt_nt_527_t4 p s) (l_e_st_eq_landau_n_rt_nt_some (Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_min p x)) (λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) x.l_e_st_eq_landau_n_rt_nt_527_t14 p s x y) : l_e_st_eq_landau_n_rt_nt_some (Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_min p x)).
-
-(* notion 1890 *)
-definition l_e_st_eq_landau_n_rt_1rt ≝ (l_e_st_eq_landau_n_rt_rtofn l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 1891 *)
-definition l_e_st_eq_landau_n_rt_ii5_t35 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x (l_e_st_eq_landau_n_tfeq1a x l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_satz28a (l_e_st_eq_landau_n_num x)) (l_e_st_eq_landau_n_satz28a (l_e_st_eq_landau_n_den x))) (l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x (l_e_st_eq_landau_n_fris x)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) x).
-
-(* notion 1892 *)
-definition l_e_st_eq_landau_n_rt_ii5_t36 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0 (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) x (l_e_st_eq_landau_n_rt_tict x0 l_e_st_eq_landau_n_rt_1rt x (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) xix0 (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1))) xix0 (l_e_st_eq_landau_n_rt_ii5_t35 x0 x xix0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0).
-
-(* notion 1893 *)
-definition l_e_st_eq_landau_n_rt_example1a ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp1 x0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0) (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_ii5_t36 x0 x xi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0).
-
-(* notion 1894 *)
-definition l_e_st_eq_landau_n_rt_example1b ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0 (l_e_st_eq_landau_n_rt_example1a x0) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt)).
-
-(* notion 1895 *)
-definition l_e_st_eq_landau_n_rt_example1c ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0 (l_e_st_eq_landau_n_rt_comts l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_example1a x0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) x0).
-
-(* notion 1896 *)
-definition l_e_st_eq_landau_n_rt_example1d ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) x0 (l_e_st_eq_landau_n_rt_example1c x0) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0)).
-
-(* notion 1897 *)
-definition l_e_st_eq_landau_n_rt_5114_t1 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_num x)) (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_den x))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_den x))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_tfeq2a x (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_num x)) (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_num x))) (l_e_st_eq_landau_n_satz40c (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_den x)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1)).
-
-(* notion 1898 *)
-definition l_e_st_eq_landau_n_rt_satz114 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_rt_ratof x)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_num x)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_tict (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_rt_ratof x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass x)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_5114_t1 x) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_rt_ratof x)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_num x))).
-
-(* notion 1899 *)
-definition l_e_st_eq_landau_n_rt_satz114a ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x2) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_rtofn x2) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_rt_isnert x2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_isden x1 x2))) (l_e_st_eq_landau_n_rt_satz114 (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_rt_isnert (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) x1 (l_e_st_eq_landau_n_numis x1 x2)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x2) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_rtofn x1)).
-
-(* notion 1900 *)
-definition l_e_st_eq_landau_n_rt_ov ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_ind l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0) (l_e_st_eq_landau_n_rt_satz110 x0 y0) : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 1901 *)
-definition l_e_st_eq_landau_n_rt_satz110c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_oneax l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0) (l_e_st_eq_landau_n_rt_satz110 x0 y0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov x0 y0)) x0).
-
-(* notion 1902 *)
-definition l_e_st_eq_landau_n_rt_satz110d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov x0 y0)) x0 (l_e_st_eq_landau_n_rt_satz110c x0 y0) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov x0 y0))).
-
-(* notion 1903 *)
-definition l_e_st_eq_landau_n_rt_satz110e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov x0 y0)) x0 (l_e_st_eq_landau_n_rt_comts (l_e_st_eq_landau_n_rt_ov x0 y0) y0) (l_e_st_eq_landau_n_rt_satz110c x0 y0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0) x0).
-
-(* notion 1904 *)
-definition l_e_st_eq_landau_n_rt_satz110f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0) x0 (l_e_st_eq_landau_n_rt_satz110e x0 y0) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0)).
-
-(* notion 1905 *)
-definition l_e_st_eq_landau_n_rt_satz110g ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 v0) x0.(l_e_st_eq_landau_n_rt_satz110b x0 y0 v0 (l_e_st_eq_landau_n_rt_ov x0 y0) i (l_e_st_eq_landau_n_rt_satz110c x0 y0) : l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ov x0 y0)).
-
-(* notion 1906 *)
-definition l_e_st_eq_landau_n_rt_satz114b ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_satz110b (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2)) (l_e_st_eq_landau_n_rt_satz114a x1 x2) (l_e_st_eq_landau_n_rt_satz110c (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2))).
-
-(* notion 1907 *)
-definition l_e_st_eq_landau_n_rt_satz114c ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2)) (l_e_st_eq_landau_n_rt_satz114b x1 x2) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2)) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2))).
-
-(* notion 1908 *)
-definition l_e_st_eq_landau_n_rt_5115_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz89 (l_e_st_eq_landau_n_rt_ov y0 x0) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t (l_e_st_eq_landau_n_rt_ov y0 x0))).
-
-(* notion 1909 *)
-definition l_e_st_eq_landau_n_rt_5115_z ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_num u : l_e_st_eq_landau_n_nat).
-
-(* notion 1910 *)
-definition l_e_st_eq_landau_n_rt_5115_v ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_den u : l_e_st_eq_landau_n_nat).
-
-(* notion 1911 *)
-definition l_e_st_eq_landau_n_rt_5115_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_ismore1 u0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ov y0 x0) (l_e_tris l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_isi u0 (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) u (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) uiu0 (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_refeq1 u (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_isfr u))) (l_e_st_eq_landau_n_rt_satz114b (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) m : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ov y0 x0)).
-
-(* notion 1912 *)
-definition l_e_st_eq_landau_n_rt_5115_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_moreisi (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_or_th9 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz24 (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) (λt:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_satz111d (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1 t) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_satz111e (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1 t)) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 1913 *)
-definition l_e_st_eq_landau_n_rt_5115_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_comts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ists2 (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) x0 (l_e_st_eq_landau_n_rt_satz110f (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_assts2 x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))).
-
-(* notion 1914 *)
-definition l_e_st_eq_landau_n_rt_5115_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).λn:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt.(l_e_st_eq_landau_n_rt_ismore1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_5115_t4 x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_satz105d (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) n) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt)).
-
-(* notion 1915 *)
-definition l_e_st_eq_landau_n_rt_5115_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).λn:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt.(l_e_st_eq_landau_n_rt_moreisi1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_5115_t5 x0 y0 u0 m u uiu0 n) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt)).
-
-(* notion 1916 *)
-definition l_e_st_eq_landau_n_rt_5115_t7 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt.(l_e_st_eq_landau_n_rt_moreisi2 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) (l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_5115_t4 x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_ists2 (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) i)) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt)).
-
-(* notion 1917 *)
-definition l_e_st_eq_landau_n_rt_5115_t8 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_orapp (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt)) (l_e_st_eq_landau_n_rt_5115_t3 x0 y0 u0 m u uiu0) (λt:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt.l_e_st_eq_landau_n_rt_5115_t6 x0 y0 u0 m u uiu0 t) (λt:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt.l_e_st_eq_landau_n_rt_5115_t7 x0 y0 u0 m u uiu0 t) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt)).
-
-(* notion 1918 *)
-definition l_e_st_eq_landau_n_rt_5115_t9 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_ismore12 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov y0 x0)) y0 (l_e_st_eq_landau_n_rt_example1b (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))))) (l_e_st_eq_landau_n_rt_satz110c y0 x0) (l_e_st_eq_landau_n_rt_satz105d (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ov y0 x0) x0 (l_e_st_eq_landau_n_rt_5115_t2 x0 y0 u0 m u uiu0)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) y0).
-
-(* notion 1919 *)
-definition l_e_st_eq_landau_n_rt_5115_t10 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_satz87c (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) y0 (l_e_st_eq_landau_n_rt_5115_t8 x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_t9 x0 y0 u0 m u uiu0) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) y0).
-
-(* notion 1920 *)
-definition l_e_st_eq_landau_n_rt_5115_t11 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_somei l_e_st_eq_landau_n_nat (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0) (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_t10 x0 y0 u0 m u uiu0) : l_e_st_eq_landau_n_some (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0)).
-
-(* notion 1921 *)
-definition l_e_st_eq_landau_n_rt_5115_t12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).(l_e_st_eq_landau_n_rt_ratapp1 u0 (l_e_st_eq_landau_n_some (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0)) (λu:l_e_st_eq_landau_n_frac.λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5115_t11 x0 y0 u0 m u ui) : l_e_st_eq_landau_n_some (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0)).
-
-(* notion 1922 *)
-definition l_e_st_eq_landau_n_rt_satz115 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_someapp l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t (l_e_st_eq_landau_n_rt_ov y0 x0)) (l_e_st_eq_landau_n_rt_5115_t1 x0 y0) (l_e_st_eq_landau_n_some (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0)) (λt:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_more t (l_e_st_eq_landau_n_rt_ov y0 x0).l_e_st_eq_landau_n_rt_5115_t12 x0 y0 t u) : l_e_st_eq_landau_n_some (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0)).
-
-(* notion 1923 *)
-definition l_e_st_eq_landau_n_rt_5115_t13 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_andi (l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) y0) (l_e_st_eq_landau_n_rt_natrti (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_5115_t10 x0 y0 u0 m u uiu0) : l_and (l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) y0)).
-
-(* notion 1924 *)
-definition l_e_st_eq_landau_n_rt_5115_t14 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_somei l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_5115_t13 x0 y0 u0 m u uiu0) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0))).
-
-(* notion 1925 *)
-definition l_e_st_eq_landau_n_rt_5115_t15 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).(l_e_st_eq_landau_n_rt_ratapp1 u0 (l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0))) (λu:l_e_st_eq_landau_n_frac.λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5115_t14 x0 y0 u0 m u ui) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0))).
-
-(* notion 1926 *)
-definition l_e_st_eq_landau_n_rt_satz115a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_someapp l_e_st_eq_landau_n_rt_rat (Πt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t (l_e_st_eq_landau_n_rt_ov y0 x0)) (l_e_st_eq_landau_n_rt_5115_t1 x0 y0) (l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0))) (λt:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_more t (l_e_st_eq_landau_n_rt_ov y0 x0).l_e_st_eq_landau_n_rt_5115_t15 x0 y0 t u) : l_e_st_eq_landau_n_rt_some (Πt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0))).
-
-(* notion 1927 *)
-definition l_e_st_eq_landau_n_rt_cutprop1a ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_e_st_nonempty l_e_st_eq_landau_n_rt_rat s : Prop).
-
-(* notion 1928 *)
-definition l_e_st_eq_landau_n_rt_cutprop1b ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_not (l_e_st_eq_landau_n_rt_all (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_in x s)) : Prop).
-
-(* notion 1929 *)
-definition l_e_st_eq_landau_n_rt_cutprop1 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_cutprop1a s) (l_e_st_eq_landau_n_rt_cutprop1b s) : Prop).
-
-(* notion 1930 *)
-definition l_e_st_eq_landau_n_rt_cutprop2a ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_all (λx:l_e_st_eq_landau_n_rt_rat.l_imp (l_not (l_e_st_eq_landau_n_rt_in x s)) (l_e_st_eq_landau_n_rt_less x0 x)) : Prop).
-
-(* notion 1931 *)
-definition l_e_st_eq_landau_n_rt_cutprop2 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_all (λx:l_e_st_eq_landau_n_rt_rat.l_imp (l_e_st_eq_landau_n_rt_in x s) (l_e_st_eq_landau_n_rt_cutprop2a s x)) : Prop).
-
-(* notion 1932 *)
-definition l_e_st_eq_landau_n_rt_iii1_ubprop ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_imp (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_moreis x0 y0) : Prop).
-
-(* notion 1933 *)
-definition l_e_st_eq_landau_n_rt_ub ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_all (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_iii1_ubprop s x0 x) : Prop).
-
-(* notion 1934 *)
-definition l_e_st_eq_landau_n_rt_max ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_ub s x0) (l_e_st_eq_landau_n_rt_in x0 s) : Prop).
-
-(* notion 1935 *)
-definition l_e_st_eq_landau_n_rt_cutprop3 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_not (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_max s x)) : Prop).
-
-(* notion 1936 *)
-definition l_e_st_eq_landau_n_rt_cutprop ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_cutprop1 s) (l_e_st_eq_landau_n_rt_cutprop2 s) (l_e_st_eq_landau_n_rt_cutprop3 s) : Prop).
-
-(* notion 1937 *)
-definition l_e_st_eq_landau_n_rt_iii1_lbprop ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_imp (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_lessis x0 y0) : Prop).
-
-(* notion 1938 *)
-definition l_e_st_eq_landau_n_rt_lb ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_all (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_iii1_lbprop s x0 x) : Prop).
-
-(* notion 1939 *)
-definition l_e_st_eq_landau_n_rt_min ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_lb s x0) (l_e_st_eq_landau_n_rt_in x0 s) : Prop).
-
-(* notion 1940 *)
-definition l_e_st_eq_landau_n_rt_cut ≝ (l_e_ot (l_e_st_set l_e_st_eq_landau_n_rt_rat) (Πx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) : Type[0]).
-
-(* notion 1941 *)
-definition l_e_st_eq_landau_n_rt_lcl ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_in (l_e_st_set l_e_st_eq_landau_n_rt_rat) (Πx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) ksi : l_e_st_set l_e_st_eq_landau_n_rt_rat).
-
-(* notion 1942 *)
-definition l_e_st_eq_landau_n_rt_lrt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_lcl ksi) : Prop).
-
-(* notion 1943 *)
-definition l_e_st_eq_landau_n_rt_urt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.(l_not (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_lcl ksi)) : Prop).
-
-(* notion 1944 *)
-definition l_e_st_eq_landau_n_rt_clcl ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_inp (l_e_st_set l_e_st_eq_landau_n_rt_rat) (Πx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) ksi : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_lcl ksi)).
-
-(* notion 1945 *)
-definition l_e_st_eq_landau_n_rt_clcl1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_and3e1 (l_e_st_eq_landau_n_rt_cutprop1 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop2 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop3 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_clcl ksi) : l_e_st_eq_landau_n_rt_cutprop1 (l_e_st_eq_landau_n_rt_lcl ksi)).
-
-(* notion 1946 *)
-definition l_e_st_eq_landau_n_rt_clcl2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_and3e2 (l_e_st_eq_landau_n_rt_cutprop1 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop2 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop3 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_clcl ksi) : l_e_st_eq_landau_n_rt_cutprop2 (l_e_st_eq_landau_n_rt_lcl ksi)).
-
-(* notion 1947 *)
-definition l_e_st_eq_landau_n_rt_clcl3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_and3e3 (l_e_st_eq_landau_n_rt_cutprop1 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop2 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop3 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_clcl ksi) : l_e_st_eq_landau_n_rt_cutprop3 (l_e_st_eq_landau_n_rt_lcl ksi)).
-
-(* notion 1948 *)
-definition l_e_st_eq_landau_n_rt_clcl1a ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_ande1 (l_e_st_eq_landau_n_rt_cutprop1a (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop1b (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_clcl1 ksi) : l_e_st_eq_landau_n_rt_cutprop1a (l_e_st_eq_landau_n_rt_lcl ksi)).
-
-(* notion 1949 *)
-definition l_e_st_eq_landau_n_rt_clcl1b ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_ande2 (l_e_st_eq_landau_n_rt_cutprop1a (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop1b (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_clcl1 ksi) : l_e_st_eq_landau_n_rt_cutprop1b (l_e_st_eq_landau_n_rt_lcl ksi)).
-
-(* notion 1950 *)
-definition l_e_st_eq_landau_n_rt_cutapp1a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.p.(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_clcl1a ksi) p p1 : p).
-
-(* notion 1951 *)
-definition l_e_st_eq_landau_n_rt_iii1_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_some_th1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_clcl1b ksi) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)).
-
-(* notion 1952 *)
-definition l_e_st_eq_landau_n_rt_cutapp1b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_iii1_t1 ksi) p p1 : p).
-
-(* notion 1953 *)
-definition l_e_st_eq_landau_n_rt_iii1_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_mp (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_cutprop2a (l_e_st_eq_landau_n_rt_lcl ksi) x0) lx (l_e_st_eq_landau_n_rt_clcl2 ksi x0) : l_e_st_eq_landau_n_rt_cutprop2a (l_e_st_eq_landau_n_rt_lcl ksi) x0).
-
-(* notion 1954 *)
-definition l_e_st_eq_landau_n_rt_cutapp2a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_mp (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_less x0 y0) uy (l_e_st_eq_landau_n_rt_iii1_t2 ksi x0 lx y0) : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 1955 *)
-definition l_e_st_eq_landau_n_rt_cutapp2b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_eq_landau_n_rt_satz83 x0 y0 (l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx y0 uy) : l_e_st_eq_landau_n_rt_more y0 x0).
-
-(* notion 1956 *)
-definition l_e_st_eq_landau_n_rt_iii1_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_some_th4 l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_max (l_e_st_eq_landau_n_rt_lcl ksi) x) (l_e_st_eq_landau_n_rt_clcl3 ksi) x0 : l_not (l_e_st_eq_landau_n_rt_max (l_e_st_eq_landau_n_rt_lcl ksi) x0)).
-
-(* notion 1957 *)
-definition l_e_st_eq_landau_n_rt_iii1_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_and_th4 (l_e_st_eq_landau_n_rt_ub (l_e_st_eq_landau_n_rt_lcl ksi) x0) (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_iii1_t3 ksi x0 lx) lx : l_not (l_e_st_eq_landau_n_rt_ub (l_e_st_eq_landau_n_rt_lcl ksi) x0)).
-
-(* notion 1958 *)
-definition l_e_st_eq_landau_n_rt_iii1_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_some_th1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 x) (l_e_st_eq_landau_n_rt_iii1_t4 ksi x0 lx) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 x))).
-
-(* notion 1959 *)
-definition l_e_st_eq_landau_n_rt_iii1_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λp:Prop.λp1:Πy:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi y.Πu:l_e_st_eq_landau_n_rt_less x0 y.p.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y0).(l_imp_th5 (l_e_st_eq_landau_n_rt_lrt ksi y0) (l_e_st_eq_landau_n_rt_moreis x0 y0) n : l_e_st_eq_landau_n_rt_lrt ksi y0).
-
-(* notion 1960 *)
-definition l_e_st_eq_landau_n_rt_iii1_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λp:Prop.λp1:Πy:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi y.Πu:l_e_st_eq_landau_n_rt_less x0 y.p.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y0).(l_imp_th6 (l_e_st_eq_landau_n_rt_lrt ksi y0) (l_e_st_eq_landau_n_rt_moreis x0 y0) n : l_not (l_e_st_eq_landau_n_rt_moreis x0 y0)).
-
-(* notion 1961 *)
-definition l_e_st_eq_landau_n_rt_iii1_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λp:Prop.λp1:Πy:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi y.Πu:l_e_st_eq_landau_n_rt_less x0 y.p.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y0).(l_e_st_eq_landau_n_rt_satz81j x0 y0 (l_e_st_eq_landau_n_rt_iii1_t7 ksi x0 lx p p1 y0 n) : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 1962 *)
-definition l_e_st_eq_landau_n_rt_iii1_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λp:Prop.λp1:Πy:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi y.Πu:l_e_st_eq_landau_n_rt_less x0 y.p.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y0).(p1 y0 (l_e_st_eq_landau_n_rt_iii1_t6 ksi x0 lx p p1 y0 n) (l_e_st_eq_landau_n_rt_iii1_t8 ksi x0 lx p p1 y0 n) : p).
-
-(* notion 1963 *)
-definition l_e_st_eq_landau_n_rt_cutapp3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λp:Prop.λp1:Πy:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi y.Πu:l_e_st_eq_landau_n_rt_less x0 y.p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y)) (l_e_st_eq_landau_n_rt_iii1_t5 ksi x0 lx) p (λy:l_e_st_eq_landau_n_rt_rat.λt:l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y).l_e_st_eq_landau_n_rt_iii1_t9 ksi x0 lx p p1 y t) : p).
-
-(* notion 1964 *)
-definition l_e_st_eq_landau_n_rt_iii1_t10 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_andi (l_e_st_eq_landau_n_rt_cutprop1a s) (l_e_st_eq_landau_n_rt_cutprop1b s) (l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rat s x0 i) (l_all_th1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_in x s) y0 n) : l_e_st_eq_landau_n_rt_cutprop1 s).
-
-(* notion 1965 *)
-definition l_e_st_eq_landau_n_rt_iii1_t11 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λn:Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_max s x).(l_some_th5 l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_max s x) n : l_e_st_eq_landau_n_rt_cutprop3 s).
-
-(* notion 1966 *)
-definition l_e_st_eq_landau_n_rt_cut1 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).λl:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_not (l_e_st_eq_landau_n_rt_in y s).l_e_st_eq_landau_n_rt_less x y.λm:Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_max s x).(l_and3i (l_e_st_eq_landau_n_rt_cutprop1 s) (l_e_st_eq_landau_n_rt_cutprop2 s) (l_e_st_eq_landau_n_rt_cutprop3 s) (l_e_st_eq_landau_n_rt_iii1_t10 s x0 i y0 n) l (l_e_st_eq_landau_n_rt_iii1_t11 s m) : l_e_st_eq_landau_n_rt_cutprop s).
-
-(* notion 1967 *)
-definition l_e_st_eq_landau_n_rt_rp_is ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_is l_e_st_eq_landau_n_rt_cut ksi eta : Prop).
-
-(* notion 1968 *)
-definition l_e_st_eq_landau_n_rt_rp_nis ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta) : Prop).
-
-(* notion 1969 *)
-definition l_e_st_eq_landau_n_rt_rp_ise ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isini (l_e_st_set l_e_st_eq_landau_n_rt_rat) (Πx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) ksi eta i : l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta)).
-
-(* notion 1970 *)
-definition l_e_st_eq_landau_n_rt_rp_ise1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_issete1 l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta) (l_e_st_eq_landau_n_rt_rp_ise ksi eta i) x0 lx : l_e_st_eq_landau_n_rt_lrt eta x0).
-
-(* notion 1971 *)
-definition l_e_st_eq_landau_n_rt_rp_isi ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta).(l_e_isine (l_e_st_set l_e_st_eq_landau_n_rt_rat) (Πx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) ksi eta i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
-
-(* notion 1972 *)
-definition l_e_st_eq_landau_n_rt_rp_isi1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_lrt eta x.λk:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_lrt ksi x.(l_e_st_eq_landau_n_rt_rp_isi ksi eta (l_e_st_isseti l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta) l k) : l_e_st_eq_landau_n_rt_rp_is ksi eta).
-
-(* notion 1973 *)
-definition l_e_st_eq_landau_n_rt_rp_cutof ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λcs:l_e_st_eq_landau_n_rt_cutprop s.(l_e_out (l_e_st_set l_e_st_eq_landau_n_rt_rat) (Πx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) s cs : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 1974 *)
-definition l_e_st_eq_landau_n_rt_rp_ine ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λcs:l_e_st_eq_landau_n_rt_cutprop s.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.(l_e_st_issete1 l_e_st_eq_landau_n_rt_rat s (l_e_st_eq_landau_n_rt_lcl (l_e_st_eq_landau_n_rt_rp_cutof s cs)) (l_e_isinout (l_e_st_set l_e_st_eq_landau_n_rt_rat) (Πx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) s cs) x0 i : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_cutof s cs) x0).
-
-(* notion 1975 *)
-definition l_e_st_eq_landau_n_rt_rp_ini ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λcs:l_e_st_eq_landau_n_rt_cutprop s.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_cutof s cs) x0.(l_e_st_issete2 l_e_st_eq_landau_n_rt_rat s (l_e_st_eq_landau_n_rt_lcl (l_e_st_eq_landau_n_rt_rp_cutof s cs)) (l_e_isinout (l_e_st_set l_e_st_eq_landau_n_rt_rat) (Πx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) s cs) x0 lx : l_e_st_eq_landau_n_rt_in x0 s).
-
-(* notion 1976 *)
-definition l_e_st_eq_landau_n_rt_rp_isi2 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λt:l_e_st_set l_e_st_eq_landau_n_rt_rat.λcs:l_e_st_eq_landau_n_rt_cutprop s.λct:l_e_st_eq_landau_n_rt_cutprop t.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_in x t.λj:Πx:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_in x t.l_e_st_eq_landau_n_rt_in x s.(l_e_isouti (l_e_st_set l_e_st_eq_landau_n_rt_rat) (Πx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) s cs t ct (l_e_st_isseti l_e_st_eq_landau_n_rt_rat s t i j) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_cutof s cs) (l_e_st_eq_landau_n_rt_rp_cutof t ct)).
-
-(* notion 1977 *)
-definition l_e_st_eq_landau_n_rt_rp_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_cut.Prop.(l_all l_e_st_eq_landau_n_rt_cut p : Prop).
-
-(* notion 1978 *)
-definition l_e_st_eq_landau_n_rt_rp_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_cut.Prop.(l_some l_e_st_eq_landau_n_rt_cut p : Prop).
-
-(* notion 1979 *)
-definition l_e_st_eq_landau_n_rt_rp_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_cut.Prop.(l_e_one l_e_st_eq_landau_n_rt_cut p : Prop).
-
-(* notion 1980 *)
-definition l_e_st_eq_landau_n_rt_rp_satz116 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_refis l_e_st_eq_landau_n_rt_cut ksi : l_e_st_eq_landau_n_rt_rp_is ksi ksi).
-
-(* notion 1981 *)
-definition l_e_st_eq_landau_n_rt_rp_satz117 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_symis l_e_st_eq_landau_n_rt_cut ksi eta i : l_e_st_eq_landau_n_rt_rp_is eta ksi).
-
-(* notion 1982 *)
-definition l_e_st_eq_landau_n_rt_rp_satz118 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is eta zeta.(l_e_tris l_e_st_eq_landau_n_rt_cut ksi eta zeta i j : l_e_st_eq_landau_n_rt_rp_is ksi zeta).
-
-(* notion 1983 *)
-definition l_e_st_eq_landau_n_rt_rp_1119_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_ec3e23 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) m : l_not (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 1984 *)
-definition l_e_st_eq_landau_n_rt_rp_satz119 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more y0 x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_lrt ksi y0) (l_e_st_eq_landau_n_rt_less y0 x0) (l_e_st_eq_landau_n_rt_rp_1119_t1 y0 x0 m) (λt:l_e_st_eq_landau_n_rt_lrt ksi y0.l_e_st_eq_landau_n_rt_cutapp2a ksi y0 t x0 ux) : l_e_st_eq_landau_n_rt_urt ksi y0).
-
-(* notion 1985 *)
-definition l_e_st_eq_landau_n_rt_rp_satz119a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_rp_satz119 ksi x0 ux y0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l) : l_e_st_eq_landau_n_rt_urt ksi y0).
-
-(* notion 1986 *)
-definition l_e_st_eq_landau_n_rt_rp_1120_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_ec3e32 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) l : l_not (l_e_st_eq_landau_n_rt_more x0 y0)).
-
-(* notion 1987 *)
-definition l_e_st_eq_landau_n_rt_rp_satz120 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_imp_th7 (l_e_st_eq_landau_n_rt_lrt ksi y0) (l_e_st_eq_landau_n_rt_more y0 x0) (l_e_st_eq_landau_n_rt_rp_1120_t1 y0 x0 l) (λt:l_e_st_eq_landau_n_rt_urt ksi y0.l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx y0 t) : l_e_st_eq_landau_n_rt_lrt ksi y0).
-
-(* notion 1988 *)
-definition l_e_st_eq_landau_n_rt_rp_satz120a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_rp_satz120 ksi x0 lx y0 (l_e_st_eq_landau_n_rt_satz82 x0 y0 m) : l_e_st_eq_landau_n_rt_lrt ksi y0).
-
-(* notion 1989 *)
-definition l_e_st_eq_landau_n_rt_iii1_t12 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(i x0 j y0 : Πu:l_e_st_eq_landau_n_rt_less y0 x0.l_e_st_eq_landau_n_rt_in y0 s).
-
-(* notion 1990 *)
-definition l_e_st_eq_landau_n_rt_iii1_t13 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_imp_th3 (l_e_st_eq_landau_n_rt_less y0 x0) (l_e_st_eq_landau_n_rt_in y0 s) n (l_e_st_eq_landau_n_rt_iii1_t12 s i x0 j y0 n) : l_not (l_e_st_eq_landau_n_rt_less y0 x0)).
-
-(* notion 1991 *)
-definition l_e_st_eq_landau_n_rt_iii1_t14 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_e_st_eq_landau_n_rt_satz81f y0 x0 (l_e_st_eq_landau_n_rt_iii1_t13 s i x0 j y0 n) : l_e_st_eq_landau_n_rt_moreis y0 x0).
-
-(* notion 1992 *)
-definition l_e_st_eq_landau_n_rt_iii1_t15 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).λk:l_e_st_eq_landau_n_rt_is y0 x0.(l_e_isp1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_in x s) x0 y0 j k : l_e_st_eq_landau_n_rt_in y0 s).
-
-(* notion 1993 *)
-definition l_e_st_eq_landau_n_rt_iii1_t16 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_imp_th3 (l_e_st_eq_landau_n_rt_is y0 x0) (l_e_st_eq_landau_n_rt_in y0 s) n (λt:l_e_st_eq_landau_n_rt_is y0 x0.l_e_st_eq_landau_n_rt_iii1_t15 s i x0 j y0 n t) : l_e_st_eq_landau_n_rt_nis y0 x0).
-
-(* notion 1994 *)
-definition l_e_st_eq_landau_n_rt_iii1_t17 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_ore1 (l_e_st_eq_landau_n_rt_more y0 x0) (l_e_st_eq_landau_n_rt_is y0 x0) (l_e_st_eq_landau_n_rt_iii1_t14 s i x0 j y0 n) (l_e_st_eq_landau_n_rt_iii1_t16 s i x0 j y0 n) : l_e_st_eq_landau_n_rt_more y0 x0).
-
-(* notion 1995 *)
-definition l_e_st_eq_landau_n_rt_iii1_t18 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_e_st_eq_landau_n_rt_satz82 y0 x0 (l_e_st_eq_landau_n_rt_iii1_t17 s i x0 j y0 n) : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 1996 *)
-definition l_e_st_eq_landau_n_rt_iii1_t19 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.(λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x s.λy:l_e_st_eq_landau_n_rt_rat.λu:l_not (l_e_st_eq_landau_n_rt_in y s).l_e_st_eq_landau_n_rt_iii1_t18 s i x t y u : l_e_st_eq_landau_n_rt_cutprop2 s).
-
-(* notion 1997 *)
-definition l_e_st_eq_landau_n_rt_iii1_t20 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.(s1 x0 i : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x0))).
-
-(* notion 1998 *)
-definition l_e_st_eq_landau_n_rt_iii1_t21 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_ande1 (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0) a : l_e_st_eq_landau_n_rt_in y0 s).
-
-(* notion 1999 *)
-definition l_e_st_eq_landau_n_rt_iii1_t22 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_ande2 (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0) a : l_e_st_eq_landau_n_rt_more y0 x0).
-
-(* notion 2000 *)
-definition l_e_st_eq_landau_n_rt_iii1_t23 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_e_st_eq_landau_n_rt_satz81g y0 x0 (l_e_st_eq_landau_n_rt_iii1_t22 s s1 x0 i y0 a) : l_not (l_e_st_eq_landau_n_rt_lessis y0 x0)).
-
-(* notion 2001 *)
-definition l_e_st_eq_landau_n_rt_iii1_t24 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_imp_th3 (l_e_st_eq_landau_n_rt_moreis x0 y0) (l_e_st_eq_landau_n_rt_lessis y0 x0) (l_e_st_eq_landau_n_rt_iii1_t23 s s1 x0 i y0 a) (λt:l_e_st_eq_landau_n_rt_moreis x0 y0.l_e_st_eq_landau_n_rt_satz84 x0 y0 t) : l_not (l_e_st_eq_landau_n_rt_moreis x0 y0)).
-
-(* notion 2002 *)
-definition l_e_st_eq_landau_n_rt_iii1_t25 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_imp_th4 (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_moreis x0 y0) (l_e_st_eq_landau_n_rt_iii1_t21 s s1 x0 i y0 a) (l_e_st_eq_landau_n_rt_iii1_t24 s s1 x0 i y0 a) : l_not (l_e_st_eq_landau_n_rt_iii1_ubprop s x0 y0)).
-
-(* notion 2003 *)
-definition l_e_st_eq_landau_n_rt_iii1_t26 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_all_th1 l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_iii1_ubprop s x0 y) y0 (l_e_st_eq_landau_n_rt_iii1_t25 s s1 x0 i y0 a) : l_not (l_e_st_eq_landau_n_rt_ub s x0)).
-
-(* notion 2004 *)
-definition l_e_st_eq_landau_n_rt_iii1_t27 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_and_th1 (l_e_st_eq_landau_n_rt_ub s x0) (l_e_st_eq_landau_n_rt_in x0 s) (l_e_st_eq_landau_n_rt_iii1_t26 s s1 x0 i y0 a) : l_not (l_e_st_eq_landau_n_rt_max s x0)).
-
-(* notion 2005 *)
-definition l_e_st_eq_landau_n_rt_iii1_t28 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.(l_someapp l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x0)) (l_e_st_eq_landau_n_rt_iii1_t20 s s1 x0 i) (l_not (l_e_st_eq_landau_n_rt_max s x0)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x0).l_e_st_eq_landau_n_rt_iii1_t27 s s1 x0 i y t) : l_not (l_e_st_eq_landau_n_rt_max s x0)).
-
-(* notion 2006 *)
-definition l_e_st_eq_landau_n_rt_iii1_t29 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in x0 s).(l_and_th2 (l_e_st_eq_landau_n_rt_ub s x0) (l_e_st_eq_landau_n_rt_in x0 s) n : l_not (l_e_st_eq_landau_n_rt_max s x0)).
-
-(* notion 2007 *)
-definition l_e_st_eq_landau_n_rt_iii1_t30 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.(l_imp_th1 (l_e_st_eq_landau_n_rt_in x0 s) (l_not (l_e_st_eq_landau_n_rt_max s x0)) (λu:l_e_st_eq_landau_n_rt_in x0 s.l_e_st_eq_landau_n_rt_iii1_t28 s s1 x0 u) (λu:l_not (l_e_st_eq_landau_n_rt_in x0 s).l_e_st_eq_landau_n_rt_iii1_t29 s s1 x0 u) : l_not (l_e_st_eq_landau_n_rt_max s x0)).
-
-(* notion 2008 *)
-definition l_e_st_eq_landau_n_rt_iii1_t31 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).(l_e_st_eq_landau_n_rt_iii1_t11 s (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_iii1_t30 s s1 x) : l_e_st_eq_landau_n_rt_cutprop3 s).
-
-(* notion 2009 *)
-definition l_e_st_eq_landau_n_rt_cut2 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).λj:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).(l_and3i (l_e_st_eq_landau_n_rt_cutprop1 s) (l_e_st_eq_landau_n_rt_cutprop2 s) (l_e_st_eq_landau_n_rt_cutprop3 s) (l_e_st_eq_landau_n_rt_iii1_t10 s x0 i y0 n) (l_e_st_eq_landau_n_rt_iii1_t19 s j) (l_e_st_eq_landau_n_rt_iii1_t31 s s1) : l_e_st_eq_landau_n_rt_cutprop s).
-
-(* notion 2010 *)
-definition l_e_st_eq_landau_n_rt_rp_more ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt eta x)) : Prop).
-
-(* notion 2011 *)
-definition l_e_st_eq_landau_n_rt_rp_iii2_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πu:l_e_st_eq_landau_n_rt_urt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta x0).(l_ande1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta x0) a : l_e_st_eq_landau_n_rt_lrt ksi x0).
-
-(* notion 2012 *)
-definition l_e_st_eq_landau_n_rt_rp_iii2_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πu:l_e_st_eq_landau_n_rt_urt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta x0).(l_ande2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta x0) a : l_e_st_eq_landau_n_rt_urt eta x0).
-
-(* notion 2013 *)
-definition l_e_st_eq_landau_n_rt_rp_iii2_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πu:l_e_st_eq_landau_n_rt_urt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta x0).(p1 x0 (l_e_st_eq_landau_n_rt_rp_iii2_t1 ksi eta m p p1 x0 a) (l_e_st_eq_landau_n_rt_rp_iii2_t2 ksi eta m p p1 x0 a) : p).
-
-(* notion 2014 *)
-definition l_e_st_eq_landau_n_rt_rp_moreapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πu:l_e_st_eq_landau_n_rt_urt eta x.p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt eta x)) m p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt eta x).l_e_st_eq_landau_n_rt_rp_iii2_t3 ksi eta m p p1 x t) : p).
-
-(* notion 2015 *)
-definition l_e_st_eq_landau_n_rt_rp_less ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_lrt eta x)) : Prop).
-
-(* notion 2016 *)
-definition l_e_st_eq_landau_n_rt_rp_iii2_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πu:l_e_st_eq_landau_n_rt_lrt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta x0).(l_ande1 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta x0) a : l_e_st_eq_landau_n_rt_urt ksi x0).
-
-(* notion 2017 *)
-definition l_e_st_eq_landau_n_rt_rp_iii2_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πu:l_e_st_eq_landau_n_rt_lrt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta x0).(l_ande2 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta x0) a : l_e_st_eq_landau_n_rt_lrt eta x0).
-
-(* notion 2018 *)
-definition l_e_st_eq_landau_n_rt_rp_iii2_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πu:l_e_st_eq_landau_n_rt_lrt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta x0).(p1 x0 (l_e_st_eq_landau_n_rt_rp_iii2_t4 ksi eta l p p1 x0 a) (l_e_st_eq_landau_n_rt_rp_iii2_t5 ksi eta l p p1 x0 a) : p).
-
-(* notion 2019 *)
-definition l_e_st_eq_landau_n_rt_rp_lessapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πu:l_e_st_eq_landau_n_rt_lrt eta x.p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_lrt eta x)) l p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_lrt eta x).l_e_st_eq_landau_n_rt_rp_iii2_t6 ksi eta l p p1 x t) : p).
-
-(* notion 2020 *)
-definition l_e_st_eq_landau_n_rt_rp_2121_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.(l_andi (l_e_st_eq_landau_n_rt_urt eta x0) (l_e_st_eq_landau_n_rt_lrt ksi x0) ux lx : l_and (l_e_st_eq_landau_n_rt_urt eta x0) (l_e_st_eq_landau_n_rt_lrt ksi x0)).
-
-(* notion 2021 *)
-definition l_e_st_eq_landau_n_rt_rp_2121_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt eta x) (l_e_st_eq_landau_n_rt_lrt ksi x)) x0 (l_e_st_eq_landau_n_rt_rp_2121_t1 ksi eta m x0 lx ux) : l_e_st_eq_landau_n_rt_rp_less eta ksi).
-
-(* notion 2022 *)
-definition l_e_st_eq_landau_n_rt_rp_satz121 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m (l_e_st_eq_landau_n_rt_rp_less eta ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_2121_t2 ksi eta m x t u) : l_e_st_eq_landau_n_rt_rp_less eta ksi).
-
-(* notion 2023 *)
-definition l_e_st_eq_landau_n_rt_rp_2122_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_andi (l_e_st_eq_landau_n_rt_lrt eta x0) (l_e_st_eq_landau_n_rt_urt ksi x0) lx ux : l_and (l_e_st_eq_landau_n_rt_lrt eta x0) (l_e_st_eq_landau_n_rt_urt ksi x0)).
-
-(* notion 2024 *)
-definition l_e_st_eq_landau_n_rt_rp_2122_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt eta x) (l_e_st_eq_landau_n_rt_urt ksi x)) x0 (l_e_st_eq_landau_n_rt_rp_2122_t1 ksi eta l x0 ux lx) : l_e_st_eq_landau_n_rt_rp_more eta ksi).
-
-(* notion 2025 *)
-definition l_e_st_eq_landau_n_rt_rp_satz122 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_lessapp ksi eta l (l_e_st_eq_landau_n_rt_rp_more eta ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λu:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_2122_t2 ksi eta l x t u) : l_e_st_eq_landau_n_rt_rp_more eta ksi).
-
-(* notion 2026 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.(l_e_st_isset_th3 l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta) x0 lx ux : l_not (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta))).
-
-(* notion 2027 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta)) (l_e_st_eq_landau_n_rt_rp_2123_t1 ksi eta m x0 lx ux) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_ise ksi eta t) : l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)).
-
-(* notion 2028 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m (l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_2123_t2 ksi eta m x t u) : l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)).
-
-(* notion 2029 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_ec_th2 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t3 ksi eta t) : l_ec (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta)).
-
-(* notion 2030 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_e_st_isset_th4 l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl eta) (l_e_st_eq_landau_n_rt_lcl ksi) x0 lx ux : l_not (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta))).
-
-(* notion 2031 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta)) (l_e_st_eq_landau_n_rt_rp_2123_t5 ksi eta l x0 ux lx) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_ise ksi eta t) : l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)).
-
-(* notion 2032 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_lessapp ksi eta l (l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λu:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_2123_t6 ksi eta l x t u) : l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)).
-
-(* notion 2033 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_ec_th1 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t7 ksi eta t) : l_ec (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta)).
-
-(* notion 2034 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx y0 uy : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 2035 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_cutapp2b eta y0 ly x0 ux : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 2036 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_mp (l_e_st_eq_landau_n_rt_less x0 y0) l_con (l_e_st_eq_landau_n_rt_rp_2123_t9 ksi eta m l x0 lx ux y0 uy ly) (l_ec3e23 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) (l_e_st_eq_landau_n_rt_rp_2123_t10 ksi eta m l x0 lx ux y0 uy ly)) : l_con).
-
-(* notion 2037 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.(l_e_st_eq_landau_n_rt_rp_lessapp ksi eta l l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λu:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_2123_t11 ksi eta m l x0 lx ux x t u) : l_con).
-
-(* notion 2038 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_2123_t12 ksi eta m l x t u) : l_con).
-
-(* notion 2039 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t13 ksi eta m t : l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2040 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_ec_th1 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t14 ksi eta t) : l_ec (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2041 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_ec3_th6 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_t4 ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_t15 ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_t8 ksi eta) : l_ec3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2042 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_or3i1 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) i : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2043 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis ksi eta.(l_imp_th3 (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta)) (l_e_st_eq_landau_n_rt_rp_is ksi eta) n (λt:l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta).l_e_st_eq_landau_n_rt_rp_isi ksi eta t) : l_not (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta))).
-
-(* notion 2044 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis ksi eta.(l_e_st_isset_th5 l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta) (l_e_st_eq_landau_n_rt_rp_2123_t17 ksi eta n) : l_or (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_more eta ksi)).
-
-(* notion 2045 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis ksi eta.(l_or_th8 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_more eta ksi) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_t18 ksi eta n) (λt:l_e_st_eq_landau_n_rt_rp_more eta ksi.l_e_st_eq_landau_n_rt_rp_satz121 eta ksi t) : l_or (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2046 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis ksi eta.(l_or3_th7 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_t19 ksi eta n) : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2047 *)
-definition l_e_st_eq_landau_n_rt_rp_2123_b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t16 ksi eta t) (λt:l_e_st_eq_landau_n_rt_rp_nis ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t20 ksi eta t) : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2048 *)
-definition l_e_st_eq_landau_n_rt_rp_satz123 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_orec3i (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_b ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_a ksi eta) : l_orec3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2049 *)
-definition l_e_st_eq_landau_n_rt_rp_satz123a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_orec3e1 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123 ksi eta) : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2050 *)
-definition l_e_st_eq_landau_n_rt_rp_satz123b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_orec3e2 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123 ksi eta) : l_ec3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2051 *)
-definition l_e_st_eq_landau_n_rt_rp_moreis ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_or (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) : Prop).
-
-(* notion 2052 *)
-definition l_e_st_eq_landau_n_rt_rp_lessis ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_or (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) : Prop).
-
-(* notion 2053 *)
-definition l_e_st_eq_landau_n_rt_rp_satz124 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_less eta ksi) (l_e_st_eq_landau_n_rt_rp_is eta ksi) m (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz121 ksi eta t) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_symis l_e_st_eq_landau_n_rt_cut ksi eta t) : l_e_st_eq_landau_n_rt_rp_lessis eta ksi).
-
-(* notion 2054 *)
-definition l_e_st_eq_landau_n_rt_rp_satz125 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more eta ksi) (l_e_st_eq_landau_n_rt_rp_is eta ksi) l (λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz122 ksi eta t) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_symis l_e_st_eq_landau_n_rt_cut ksi eta t) : l_e_st_eq_landau_n_rt_rp_moreis eta ksi).
-
-(* notion 2055 *)
-definition l_e_st_eq_landau_n_rt_rp_ismore1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi zeta.(l_e_isp l_e_st_eq_landau_n_rt_cut (Πu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_more u zeta) ksi eta m i : l_e_st_eq_landau_n_rt_rp_more eta zeta).
-
-(* notion 2056 *)
-definition l_e_st_eq_landau_n_rt_rp_ismore2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more zeta ksi.(l_e_isp l_e_st_eq_landau_n_rt_cut (Πu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_more zeta u) ksi eta m i : l_e_st_eq_landau_n_rt_rp_more zeta eta).
-
-(* notion 2057 *)
-definition l_e_st_eq_landau_n_rt_rp_isless1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi zeta.(l_e_isp l_e_st_eq_landau_n_rt_cut (Πu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_less u zeta) ksi eta l i : l_e_st_eq_landau_n_rt_rp_less eta zeta).
-
-(* notion 2058 *)
-definition l_e_st_eq_landau_n_rt_rp_isless2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less zeta ksi.(l_e_isp l_e_st_eq_landau_n_rt_cut (Πu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_less zeta u) ksi eta l i : l_e_st_eq_landau_n_rt_rp_less zeta eta).
-
-(* notion 2059 *)
-definition l_e_st_eq_landau_n_rt_rp_ismoreis1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi zeta.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_moreis u zeta) ksi eta m i : l_e_st_eq_landau_n_rt_rp_moreis eta zeta).
-
-(* notion 2060 *)
-definition l_e_st_eq_landau_n_rt_rp_ismoreis2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_moreis zeta ksi.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_moreis zeta u) ksi eta m i : l_e_st_eq_landau_n_rt_rp_moreis zeta eta).
-
-(* notion 2061 *)
-definition l_e_st_eq_landau_n_rt_rp_islessis1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi zeta.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_lessis u zeta) ksi eta l i : l_e_st_eq_landau_n_rt_rp_lessis eta zeta).
-
-(* notion 2062 *)
-definition l_e_st_eq_landau_n_rt_rp_islessis2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_lessis zeta ksi.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_lessis zeta u) ksi eta l i : l_e_st_eq_landau_n_rt_rp_lessis zeta eta).
-
-(* notion 2063 *)
-definition l_e_st_eq_landau_n_rt_rp_moreisi2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_ori2 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) i : l_e_st_eq_landau_n_rt_rp_moreis ksi eta).
-
-(* notion 2064 *)
-definition l_e_st_eq_landau_n_rt_rp_lessisi2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_ori2 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) i : l_e_st_eq_landau_n_rt_rp_lessis ksi eta).
-
-(* notion 2065 *)
-definition l_e_st_eq_landau_n_rt_rp_moreisi1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_ori1 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) m : l_e_st_eq_landau_n_rt_rp_moreis ksi eta).
-
-(* notion 2066 *)
-definition l_e_st_eq_landau_n_rt_rp_lessisi1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_ori1 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) l : l_e_st_eq_landau_n_rt_rp_lessis ksi eta).
-
-(* notion 2067 *)
-definition l_e_st_eq_landau_n_rt_rp_ismore12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.λm:l_e_st_eq_landau_n_rt_rp_more ksi zeta.(l_e_st_eq_landau_n_rt_rp_ismore2 zeta upsilon eta j (l_e_st_eq_landau_n_rt_rp_ismore1 ksi eta zeta i m) : l_e_st_eq_landau_n_rt_rp_more eta upsilon).
-
-(* notion 2068 *)
-definition l_e_st_eq_landau_n_rt_rp_isless12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.λl:l_e_st_eq_landau_n_rt_rp_less ksi zeta.(l_e_st_eq_landau_n_rt_rp_isless2 zeta upsilon eta j (l_e_st_eq_landau_n_rt_rp_isless1 ksi eta zeta i l) : l_e_st_eq_landau_n_rt_rp_less eta upsilon).
-
-(* notion 2069 *)
-definition l_e_st_eq_landau_n_rt_rp_ismoreis12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi zeta.(l_e_st_eq_landau_n_rt_rp_ismoreis2 zeta upsilon eta j (l_e_st_eq_landau_n_rt_rp_ismoreis1 ksi eta zeta i m) : l_e_st_eq_landau_n_rt_rp_moreis eta upsilon).
-
-(* notion 2070 *)
-definition l_e_st_eq_landau_n_rt_rp_islessis12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi zeta.(l_e_st_eq_landau_n_rt_rp_islessis2 zeta upsilon eta j (l_e_st_eq_landau_n_rt_rp_islessis1 ksi eta zeta i l) : l_e_st_eq_landau_n_rt_rp_lessis eta upsilon).
-
-(* notion 2071 *)
-definition l_e_st_eq_landau_n_rt_rp_satz123c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.(l_ec3_th7 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) (l_comor (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) m) : l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2072 *)
-definition l_e_st_eq_landau_n_rt_rp_satz123d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.(l_ec3_th9 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) l : l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta)).
-
-(* notion 2073 *)
-definition l_e_st_eq_landau_n_rt_rp_satz123e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta).(l_or3_th2 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123a ksi eta) n : l_e_st_eq_landau_n_rt_rp_lessis ksi eta).
-
-(* notion 2074 *)
-definition l_e_st_eq_landau_n_rt_rp_satz123f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta).(l_comor (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_or3_th3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123a ksi eta) n) : l_e_st_eq_landau_n_rt_rp_moreis ksi eta).
-
-(* notion 2075 *)
-definition l_e_st_eq_landau_n_rt_rp_satz123g ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_or_th3 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_ec3e23 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) m) (l_ec3e21 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) m) : l_not (l_e_st_eq_landau_n_rt_rp_lessis ksi eta)).
-
-(* notion 2076 *)
-definition l_e_st_eq_landau_n_rt_rp_satz123h ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_or_th3 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_ec3e32 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) l) (l_ec3e31 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) l) : l_not (l_e_st_eq_landau_n_rt_rp_moreis ksi eta)).
-
-(* notion 2077 *)
-definition l_e_st_eq_landau_n_rt_rp_satz123j ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_moreis ksi eta).(l_or3e3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123a ksi eta) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) n) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) n) : l_e_st_eq_landau_n_rt_rp_less ksi eta).
-
-(* notion 2078 *)
-definition l_e_st_eq_landau_n_rt_rp_satz123k ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_lessis ksi eta).(l_or3e2 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123a ksi eta) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) n) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) n) : l_e_st_eq_landau_n_rt_rp_more ksi eta).
-
-(* notion 2079 *)
-definition l_e_st_eq_landau_n_rt_rp_2126_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λly:l_e_st_eq_landau_n_rt_lrt zeta y0.(l_e_st_eq_landau_n_rt_cutapp2a eta x0 lx y0 uy : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 2080 *)
-definition l_e_st_eq_landau_n_rt_rp_2126_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λly:l_e_st_eq_landau_n_rt_lrt zeta y0.(l_e_st_eq_landau_n_rt_rp_satz119a ksi x0 ux y0 (l_e_st_eq_landau_n_rt_rp_2126_t1 ksi eta zeta l k x0 ux lx y0 uy ly) : l_e_st_eq_landau_n_rt_urt ksi y0).
-
-(* notion 2081 *)
-definition l_e_st_eq_landau_n_rt_rp_2126_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λly:l_e_st_eq_landau_n_rt_lrt zeta y0.(l_andi (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_lrt zeta y0) (l_e_st_eq_landau_n_rt_rp_2126_t2 ksi eta zeta l k x0 ux lx y0 uy ly) ly : l_and (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_lrt zeta y0)).
-
-(* notion 2082 *)
-definition l_e_st_eq_landau_n_rt_rp_2126_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λly:l_e_st_eq_landau_n_rt_lrt zeta y0.(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_lrt zeta x)) y0 (l_e_st_eq_landau_n_rt_rp_2126_t3 ksi eta zeta l k x0 ux lx y0 uy ly) : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
-
-(* notion 2083 *)
-definition l_e_st_eq_landau_n_rt_rp_2126_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_e_st_eq_landau_n_rt_rp_lessapp eta zeta k (l_e_st_eq_landau_n_rt_rp_less ksi zeta) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt eta x.λu:l_e_st_eq_landau_n_rt_lrt zeta x.l_e_st_eq_landau_n_rt_rp_2126_t4 ksi eta zeta l k x0 ux lx x t u) : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
-
-(* notion 2084 *)
-definition l_e_st_eq_landau_n_rt_rp_satz126 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.(l_e_st_eq_landau_n_rt_rp_lessapp ksi eta l (l_e_st_eq_landau_n_rt_rp_less ksi zeta) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λu:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_2126_t5 ksi eta zeta l k x t u) : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
-
-(* notion 2085 *)
-definition l_e_st_eq_landau_n_rt_rp_trless ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.(l_e_st_eq_landau_n_rt_rp_satz126 ksi eta zeta l k : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
-
-(* notion 2086 *)
-definition l_e_st_eq_landau_n_rt_rp_trmore ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more eta zeta.(l_e_st_eq_landau_n_rt_rp_satz122 zeta ksi (l_e_st_eq_landau_n_rt_rp_satz126 zeta eta ksi (l_e_st_eq_landau_n_rt_rp_satz121 eta zeta n) (l_e_st_eq_landau_n_rt_rp_satz121 ksi eta m)) : l_e_st_eq_landau_n_rt_rp_more ksi zeta).
-
-(* notion 2087 *)
-definition l_e_st_eq_landau_n_rt_rp_satz127a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.(l_orapp (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi zeta) l (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_trless ksi eta zeta u k) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_isless1 eta ksi zeta (l_e_symis l_e_st_eq_landau_n_rt_cut ksi eta u) k) : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
-
-(* notion 2088 *)
-definition l_e_st_eq_landau_n_rt_rp_satz127b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.(l_orapp (l_e_st_eq_landau_n_rt_rp_less eta zeta) (l_e_st_eq_landau_n_rt_rp_is eta zeta) (l_e_st_eq_landau_n_rt_rp_less ksi zeta) k (λu:l_e_st_eq_landau_n_rt_rp_less eta zeta.l_e_st_eq_landau_n_rt_rp_trless ksi eta zeta l u) (λu:l_e_st_eq_landau_n_rt_rp_is eta zeta.l_e_st_eq_landau_n_rt_rp_isless2 eta zeta ksi u l) : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
-
-(* notion 2089 *)
-definition l_e_st_eq_landau_n_rt_rp_satz127c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more eta zeta.(l_e_st_eq_landau_n_rt_rp_satz122 zeta ksi (l_e_st_eq_landau_n_rt_rp_satz127b zeta eta ksi (l_e_st_eq_landau_n_rt_rp_satz121 eta zeta n) (l_e_st_eq_landau_n_rt_rp_satz124 ksi eta m)) : l_e_st_eq_landau_n_rt_rp_more ksi zeta).
-
-(* notion 2090 *)
-definition l_e_st_eq_landau_n_rt_rp_satz127d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis eta zeta.(l_e_st_eq_landau_n_rt_rp_satz122 zeta ksi (l_e_st_eq_landau_n_rt_rp_satz127a zeta eta ksi (l_e_st_eq_landau_n_rt_rp_satz124 eta zeta n) (l_e_st_eq_landau_n_rt_rp_satz121 ksi eta m)) : l_e_st_eq_landau_n_rt_rp_more ksi zeta).
-
-(* notion 2091 *)
-definition l_e_st_eq_landau_n_rt_rp_2128_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is eta zeta.(l_e_st_eq_landau_n_rt_rp_lessisi2 ksi zeta (l_e_tris l_e_st_eq_landau_n_rt_cut ksi eta zeta i j) : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
-
-(* notion 2092 *)
-definition l_e_st_eq_landau_n_rt_rp_2128_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_less eta zeta.(l_e_st_eq_landau_n_rt_rp_lessisi1 ksi zeta (l_e_st_eq_landau_n_rt_rp_satz127a ksi eta zeta l j) : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
-
-(* notion 2093 *)
-definition l_e_st_eq_landau_n_rt_rp_2128_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_orapp (l_e_st_eq_landau_n_rt_rp_less eta zeta) (l_e_st_eq_landau_n_rt_rp_is eta zeta) (l_e_st_eq_landau_n_rt_rp_lessis ksi zeta) k (λt:l_e_st_eq_landau_n_rt_rp_less eta zeta.l_e_st_eq_landau_n_rt_rp_2128_t2 ksi eta zeta l k i t) (λt:l_e_st_eq_landau_n_rt_rp_is eta zeta.l_e_st_eq_landau_n_rt_rp_2128_t1 ksi eta zeta l k i t) : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
-
-(* notion 2094 *)
-definition l_e_st_eq_landau_n_rt_rp_2128_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.λj:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_lessisi1 ksi zeta (l_e_st_eq_landau_n_rt_rp_satz127b ksi eta zeta j k) : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
-
-(* notion 2095 *)
-definition l_e_st_eq_landau_n_rt_rp_satz128 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.(l_orapp (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_lessis ksi zeta) l (λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_2128_t4 ksi eta zeta l k t) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_2128_t3 ksi eta zeta l k t) : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
-
-(* notion 2096 *)
-definition l_e_st_eq_landau_n_rt_rp_trlessis ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.(l_e_st_eq_landau_n_rt_rp_satz128 ksi eta zeta l k : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
-
-(* notion 2097 *)
-definition l_e_st_eq_landau_n_rt_rp_trmoreis ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis eta zeta.(l_e_st_eq_landau_n_rt_rp_satz125 zeta ksi (l_e_st_eq_landau_n_rt_rp_satz128 zeta eta ksi (l_e_st_eq_landau_n_rt_rp_satz124 eta zeta n) (l_e_st_eq_landau_n_rt_rp_satz124 ksi eta m)) : l_e_st_eq_landau_n_rt_rp_moreis ksi zeta).
-
-(* notion 2098 *)
-definition l_e_st_eq_landau_n_rt_rp_sumprop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) : Prop).
-
-(* notion 2099 *)
-definition l_e_st_eq_landau_n_rt_rp_sumprop ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x y)) : Prop).
-
-(* notion 2100 *)
-definition l_e_st_eq_landau_n_rt_rp_sum ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop ksi eta z) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2101 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_and3i (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) lx ly i : l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y0).
-
-(* notion 2102 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_somei l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y) y0 (l_e_st_eq_landau_n_rt_rp_iii3_t1 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y)).
-
-(* notion 2103 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x y)) x0 (l_e_st_eq_landau_n_rt_rp_iii3_t2 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_rp_sumprop ksi eta z0).
-
-(* notion 2104 *)
-definition l_e_st_eq_landau_n_rt_rp_sum1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop ksi eta z) z0 (l_e_st_eq_landau_n_rt_rp_iii3_t3 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
-
-(* notion 2105 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop ksi eta z) z0 i : l_e_st_eq_landau_n_rt_rp_sumprop ksi eta z0).
-
-(* notion 2106 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y0.(l_and3e1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) py : l_e_st_eq_landau_n_rt_lrt ksi x0).
-
-(* notion 2107 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y0.(l_and3e2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) py : l_e_st_eq_landau_n_rt_lrt eta y0).
-
-(* notion 2108 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y0.(l_and3e3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) py : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
-
-(* notion 2109 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y0.(p1 x0 (l_e_st_eq_landau_n_rt_rp_iii3_t5 ksi eta z0 i p p1 x0 px y0 py) y0 (l_e_st_eq_landau_n_rt_rp_iii3_t6 ksi eta z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_iii3_t7 ksi eta z0 i p p1 x0 px y0 py) : p).
-
-(* notion 2110 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y).(l_someapp l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y) px p (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y.l_e_st_eq_landau_n_rt_rp_iii3_t8 ksi eta z0 i p p1 x0 px y t) : p).
-
-(* notion 2111 *)
-definition l_e_st_eq_landau_n_rt_rp_sumapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x y)) (l_e_st_eq_landau_n_rt_rp_iii3_t4 ksi eta z0 i p p1) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x y).l_e_st_eq_landau_n_rt_rp_iii3_t9 ksi eta z0 i p p1 x t) : p).
-
-(* notion 2112 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx x1 ux : l_e_st_eq_landau_n_rt_less x0 x1).
-
-(* notion 2113 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_cutapp2a eta y0 ly y1 uy : l_e_st_eq_landau_n_rt_less y0 y1).
-
-(* notion 2114 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_pl x0 y0) z0 (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl x0 y0) j) (l_e_st_eq_landau_n_rt_satz98a x0 x1 y0 y1 (l_e_st_eq_landau_n_rt_rp_3129_t1 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_rp_3129_t2 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j)) : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_pl x1 y1)).
-
-(* notion 2115 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_ec3e31 (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_e_st_eq_landau_n_rt_more z0 (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_e_st_eq_landau_n_rt_satz81b z0 (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_e_st_eq_landau_n_rt_rp_3129_t3 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_pl x1 y1)).
-
-(* notion 2116 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).(l_e_st_eq_landau_n_rt_rp_sumapp ksi eta z0 i (l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_pl x1 y1)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3129_t4 ksi eta x1 ux y1 uy z0 i x t y u v) : l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_pl x1 y1)).
-
-(* notion 2117 *)
-definition l_e_st_eq_landau_n_rt_rp_satz129a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.(l_imp_th3 (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_nis (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_weli (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl x1 y1))) (λt:l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_rp_sum ksi eta).l_e_st_eq_landau_n_rt_rp_3129_t5 ksi eta x1 ux y1 uy (l_e_st_eq_landau_n_rt_pl x1 y1) t) : l_not (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_rp_sum ksi eta))).
-
-(* notion 2118 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_isless2 u0 (l_e_st_eq_landau_n_rt_pl x0 y0) z0 j l : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
-
-(* notion 2119 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_z1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_ov z0 (l_e_st_eq_landau_n_rt_pl x0 y0) : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2120 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_isless12 z0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_satz110f z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_example1d (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_rp_3129_t6 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0))).
-
-(* notion 2121 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_satz106c (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_3129_t7 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2122 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_example1a x0) (l_e_st_eq_landau_n_rt_satz105f (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) l_e_st_eq_landau_n_rt_1rt x0 (l_e_st_eq_landau_n_rt_rp_3129_t8 ksi eta u0 i z0 l x0 lx y0 ly j)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) x0).
-
-(* notion 2123 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_ts y0 l_e_st_eq_landau_n_rt_1rt) y0 (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_example1a y0) (l_e_st_eq_landau_n_rt_satz105f (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) l_e_st_eq_landau_n_rt_1rt y0 (l_e_st_eq_landau_n_rt_rp_3129_t8 ksi eta u0 i z0 l x0 lx y0 ly j)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) y0).
-
-(* notion 2124 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_satz120 ksi x0 lx (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_rp_3129_t9 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j))).
-
-(* notion 2125 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_satz120 eta y0 ly (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_rp_3129_t10 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_lrt eta (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j))).
-
-(* notion 2126 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) z0 (l_e_st_eq_landau_n_rt_distpt1 x0 y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_satz110c z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j))) z0).
-
-(* notion 2127 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j))) z0 (l_e_st_eq_landau_n_rt_rp_3129_t13 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)))).
-
-(* notion 2128 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_sum1 ksi eta z0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_rp_3129_t11 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_rp_3129_t12 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_rp_3129_t14 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
-
-(* notion 2129 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_rp_sumapp ksi eta u0 i (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3129_t15 ksi eta u0 i z0 l x t y u v) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
-
-(* notion 2130 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_rp_sum1 ksi eta (l_e_st_eq_landau_n_rt_pl x1 y0) x1 lx1 y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl x1 y0)) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
-
-(* notion 2131 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_satz96a x1 x0 y0 (l_e_st_eq_landau_n_rt_satz83 x0 x1 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_st_eq_landau_n_rt_pl x0 y0)).
-
-(* notion 2132 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_ismore2 (l_e_st_eq_landau_n_rt_pl x0 y0) z0 (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl x0 y0) j) (l_e_st_eq_landau_n_rt_rp_3129_t18 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x1 y0) z0).
-
-(* notion 2133 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_andi (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x1 y0) z0) (l_e_st_eq_landau_n_rt_rp_3129_t17 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) (l_e_st_eq_landau_n_rt_rp_3129_t19 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_and (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x1 y0) z0)).
-
-(* notion 2134 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_somei l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0)) (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_st_eq_landau_n_rt_rp_3129_t20 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
-
-(* notion 2135 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_cutapp3 ksi x0 lx (l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_less x0 x.l_e_st_eq_landau_n_rt_rp_3129_t21 ksi eta z0 i x0 lx y0 ly j x t u) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
-
-(* notion 2136 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).(l_e_st_eq_landau_n_rt_rp_sumapp ksi eta z0 i (l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3129_t22 ksi eta z0 i x t y u v) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
-
-(* notion 2137 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_sum ksi eta) (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_sum1 ksi eta (l_e_st_eq_landau_n_rt_pl x0 y0) x0 lx y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl x0 y0))) (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_rp_satz129a ksi eta x1 ux y1 uy) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_3129_t16 ksi eta x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_sum ksi eta).l_e_st_eq_landau_n_rt_rp_3129_t23 ksi eta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
-
-(* notion 2138 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.(l_e_st_eq_landau_n_rt_cutapp1b eta (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt eta y.l_e_st_eq_landau_n_rt_rp_3129_t24 ksi eta x0 lx y0 ly x1 ux y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
-
-(* notion 2139 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_cutapp1b ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.l_e_st_eq_landau_n_rt_rp_3129_t25 ksi eta x0 lx y0 ly x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
-
-(* notion 2140 *)
-definition l_e_st_eq_landau_n_rt_rp_3129_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_cutapp1a eta (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta y.l_e_st_eq_landau_n_rt_rp_3129_t26 ksi eta x0 lx y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
-
-(* notion 2141 *)
-definition l_e_st_eq_landau_n_rt_rp_satz129 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_cutapp1a ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_3129_t27 ksi eta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
-
-(* notion 2142 *)
-definition l_e_st_eq_landau_n_rt_rp_pl ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_sum ksi eta) (l_e_st_eq_landau_n_rt_rp_satz129 ksi eta) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2143 *)
-definition l_e_st_eq_landau_n_rt_rp_lrtpl ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_sum ksi eta) (l_e_st_eq_landau_n_rt_rp_satz129 ksi eta) z0 (l_e_st_eq_landau_n_rt_rp_sum1 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0).
-
-(* notion 2144 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_isp1 l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_sum ksi eta))) (l_e_st_eq_landau_n_rt_pl x0 y0) z0 (l_e_st_eq_landau_n_rt_rp_satz129a ksi eta x0 ux y0 uy) i : l_not (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta))).
-
-(* notion 2145 *)
-definition l_e_st_eq_landau_n_rt_rp_urtpl ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_imp_th3 (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0) (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_rp_iii3_t10 ksi eta z0 x0 ux y0 uy i) (λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_sum ksi eta) (l_e_st_eq_landau_n_rt_rp_satz129 ksi eta) z0 t) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0).
-
-(* notion 2146 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.(l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_sum ksi eta) (l_e_st_eq_landau_n_rt_rp_satz129 ksi eta) z0 lz : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
-
-(* notion 2147 *)
-definition l_e_st_eq_landau_n_rt_rp_plapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.(l_e_st_eq_landau_n_rt_rp_sumapp ksi eta z0 (l_e_st_eq_landau_n_rt_rp_iii3_t11 ksi eta z0 lz p p1) p p1 : p).
-
-(* notion 2148 *)
-definition l_e_st_eq_landau_n_rt_rp_ispl1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_pl u zeta) ksi eta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
-
-(* notion 2149 *)
-definition l_e_st_eq_landau_n_rt_rp_ispl2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_pl zeta u) ksi eta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta)).
-
-(* notion 2150 *)
-definition l_e_st_eq_landau_n_rt_rp_ispl12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_ispl1 ksi eta zeta i) (l_e_st_eq_landau_n_rt_rp_ispl2 zeta upsilon eta j) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2151 *)
-definition l_e_st_eq_landau_n_rt_rp_3130_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_tris l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0) i (l_e_st_eq_landau_n_rt_compl x0 y0) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y0 x0)).
-
-(* notion 2152 *)
-definition l_e_st_eq_landau_n_rt_rp_3130_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtpl eta ksi z0 y0 ly x0 lx (l_e_st_eq_landau_n_rt_rp_3130_t1 ksi eta z0 lz x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta ksi) z0).
-
-(* notion 2153 *)
-definition l_e_st_eq_landau_n_rt_rp_3130_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.(l_e_st_eq_landau_n_rt_rp_plapp ksi eta z0 lz (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta ksi) z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3130_t2 ksi eta z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta ksi) z0).
-
-(* notion 2154 *)
-definition l_e_st_eq_landau_n_rt_rp_satz130 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_pl eta ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) x.l_e_st_eq_landau_n_rt_rp_3130_t3 ksi eta x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta ksi) x.l_e_st_eq_landau_n_rt_rp_3130_t3 eta ksi x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_pl eta ksi)).
-
-(* notion 2155 *)
-definition l_e_st_eq_landau_n_rt_rp_compl ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz130 ksi eta : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_pl eta ksi)).
-
-(* notion 2156 *)
-definition l_e_st_eq_landau_n_rt_rp_3131_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_pl v0 z0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) i (l_e_st_eq_landau_n_rt_ispl1 v0 (l_e_st_eq_landau_n_rt_pl x0 y0) z0 j) (l_e_st_eq_landau_n_rt_asspl1 x0 y0 z0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0))).
-
-(* notion 2157 *)
-definition l_e_st_eq_landau_n_rt_rp_3131_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtpl eta zeta (l_e_st_eq_landau_n_rt_pl y0 z0) y0 ly z0 lz (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y0 z0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 2158 *)
-definition l_e_st_eq_landau_n_rt_rp_3131_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtpl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta) u0 x0 lx (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_rp_3131_t2 ksi eta zeta u0 lu v0 lv z0 lz i x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_rp_3131_t1 ksi eta zeta u0 lu v0 lv z0 lz i x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
-
-(* notion 2159 *)
-definition l_e_st_eq_landau_n_rt_rp_3131_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 z0).(l_e_st_eq_landau_n_rt_rp_plapp ksi eta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3131_t3 ksi eta zeta u0 lu v0 lv z0 lz i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
-
-(* notion 2160 *)
-definition l_e_st_eq_landau_n_rt_rp_3131_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0.(l_e_st_eq_landau_n_rt_rp_plapp (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3131_t4 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
-
-(* notion 2161 *)
-definition l_e_st_eq_landau_n_rt_rp_3131_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_pl x0 v0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) i (l_e_st_eq_landau_n_rt_ispl2 v0 (l_e_st_eq_landau_n_rt_pl y0 z0) x0 j) (l_e_st_eq_landau_n_rt_asspl2 x0 y0 z0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0)).
-
-(* notion 2162 *)
-definition l_e_st_eq_landau_n_rt_rp_3131_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtpl ksi eta (l_e_st_eq_landau_n_rt_pl x0 y0) x0 lx y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl x0 y0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_pl x0 y0)).
-
-(* notion 2163 *)
-definition l_e_st_eq_landau_n_rt_rp_3131_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtpl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta u0 (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_3131_t7 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) z0 lz (l_e_st_eq_landau_n_rt_rp_3131_t6 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0).
-
-(* notion 2164 *)
-definition l_e_st_eq_landau_n_rt_rp_3131_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 v0).(l_e_st_eq_landau_n_rt_rp_plapp eta zeta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3131_t8 ksi eta zeta u0 lu x0 lx v0 lv i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0).
-
-(* notion 2165 *)
-definition l_e_st_eq_landau_n_rt_rp_3131_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.(l_e_st_eq_landau_n_rt_rp_plapp ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta) u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3131_t9 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0).
-
-(* notion 2166 *)
-definition l_e_st_eq_landau_n_rt_rp_satz131 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) x.l_e_st_eq_landau_n_rt_rp_3131_t5 ksi eta zeta x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) x.l_e_st_eq_landau_n_rt_rp_3131_t10 ksi eta zeta x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta))).
-
-(* notion 2167 *)
-definition l_e_st_eq_landau_n_rt_rp_asspl1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz131 ksi eta zeta : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta))).
-
-(* notion 2168 *)
-definition l_e_st_eq_landau_n_rt_rp_asspl2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_satz131 ksi eta zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta)).
-
-(* notion 2169 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_prop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi y0) : Prop).
-
-(* notion 2170 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λp:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0.(l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_ande1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi y0) p) y0 (l_ande2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi y0) p) : l_e_st_eq_landau_n_rt_more y0 x0).
-
-(* notion 2171 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_prop2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λp:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0.(l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 y0 p)) a0 : Prop).
-
-(* notion 2172 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_prop3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0) (Πt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0.l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 y0 t) : Prop).
-
-(* notion 2173 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_prop4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x y)) : Prop).
-
-(* notion 2174 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx y0 uy : l_e_st_eq_landau_n_rt_more y0 x0).
-
-(* notion 2175 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)).(l_e_st_eq_landau_n_rt_satz96d (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)) x0 m : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0)) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)))).
-
-(* notion 2176 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)).(l_e_st_eq_landau_n_rt_ismore2 (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy))) y0 (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0)) (l_e_st_eq_landau_n_rt_satz101c y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)) (l_e_st_eq_landau_n_rt_rp_3132_t3 ksi a0 x0 lx y0 uy n m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0)) y0).
-
-(* notion 2177 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)).(l_e_st_eq_landau_n_rt_rp_satz119 ksi y0 uy (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0)) (l_e_st_eq_landau_n_rt_rp_3132_t4 ksi a0 x0 lx y0 uy n m) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0))).
-
-(* notion 2178 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)).(l_somei l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) n (l_e_st_eq_landau_n_rt_rp_3132_t5 ksi a0 x0 lx y0 uy n m) : l_e_st_eq_landau_n_some (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0)))).
-
-(* notion 2179 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_someapp l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy))) (l_e_st_eq_landau_n_rt_satz115 a0 (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy))) (l_e_st_eq_landau_n_some (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0)))) (λx:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)).l_e_st_eq_landau_n_rt_rp_3132_t6 ksi a0 x0 lx y0 uy x t) : l_e_st_eq_landau_n_some (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0)))).
-
-(* notion 2180 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.(l_ande1 (l_e_st_eq_landau_n_lb (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u) (l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0))) m : l_e_st_eq_landau_n_lb (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u).
-
-(* notion 2181 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.(l_ande2 (l_e_st_eq_landau_n_lb (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u) (l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0))) m : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0))).
-
-(* notion 2182 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_u0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_pl x0 a0 : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2183 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt a0) (l_e_st_eq_landau_n_rt_ts a0 l_e_st_eq_landau_n_rt_1rt) a0 (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt a0 (l_e_st_eq_landau_n_rt_isnert u l_e_st_eq_landau_n_1 i)) (l_e_st_eq_landau_n_rt_comts l_e_st_eq_landau_n_rt_1rt a0) (l_e_st_eq_landau_n_rt_example1a a0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) a0).
-
-(* notion 2184 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_e_isp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 x)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) a0 (l_e_st_eq_landau_n_rt_rp_3132_t9 ksi a0 x0 lx y0 uy u m) (l_e_st_eq_landau_n_rt_rp_3132_t10 ksi a0 x0 lx y0 uy u m i) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i)).
-
-(* notion 2185 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_andi (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i)) lx (l_e_st_eq_landau_n_rt_rp_3132_t11 ksi a0 x0 lx y0 uy u m i) : l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i)).
-
-(* notion 2186 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.λp:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i).(l_e_symis l_e_st_eq_landau_n_rt_rat a0 (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) x0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) p)) (l_e_st_eq_landau_n_rt_satz101g (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) x0 a0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) p) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i))) : l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) p).
-
-(* notion 2187 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_andi (l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i)) (Πt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i).l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) t) (l_e_st_eq_landau_n_rt_rp_3132_t12 ksi a0 x0 lx y0 uy u m i) (λt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i).l_e_st_eq_landau_n_rt_rp_3132_t13 ksi a0 x0 lx y0 uy u m i t) : l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i)).
-
-(* notion 2188 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_somei l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y) (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) (l_e_st_eq_landau_n_rt_rp_3132_t14 ksi a0 x0 lx y0 uy u m i) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y)).
-
-(* notion 2189 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x y)) x0 (l_e_st_eq_landau_n_rt_rp_3132_t15 ksi a0 x0 lx y0 uy u m i) : l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0).
-
-(* notion 2190 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_fr u l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr u l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz111d u l_e_st_eq_landau_n_1 o) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2191 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_um10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_3132_t17 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2192 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_satz112g (l_e_st_eq_landau_n_rt_rtofn u) (l_e_st_eq_landau_n_rt_natrti u) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_natrti l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_3132_t17 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o)).
-
-(* notion 2193 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_um1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t18 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_nat).
-
-(* notion 2194 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_v0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2195 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_w0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2196 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_rtofn u) (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_satz101e (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_3132_t17 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_satz94a (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_rt_1rt) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rtofn u)).
-
-(* notion 2197 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_lesse (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rtofn u) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr u l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t18 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr u l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_3132_t19 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr u l_e_st_eq_landau_n_1)).
-
-(* notion 2198 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_satz111c (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) u (l_e_st_eq_landau_n_rt_rp_3132_t20 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) u).
-
-(* notion 2199 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_imp_th3 (l_e_st_eq_landau_n_lessis u (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) u) (l_e_st_eq_landau_n_satz10h (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) u (l_e_st_eq_landau_n_rt_rp_3132_t21 ksi a0 x0 lx y0 uy u m o)) (λt:l_e_st_eq_landau_n_lessis u (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o).l_e_st_eq_landau_n_satz14 u (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) t) : l_not (l_e_st_eq_landau_n_lessis u (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o))).
-
-(* notion 2200 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_et (l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) a0))) (l_imp_th3 (l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) a0))) (l_e_st_eq_landau_n_lessis u (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_rp_3132_t22 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t8 ksi a0 x0 lx y0 uy u m (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o))) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) a0))).
-
-(* notion 2201 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_isp1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts x a0))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t23 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_isrtn1 (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t18 ksi a0 x0 lx y0 uy u m o)) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o)).
-
-(* notion 2202 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_andi (l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_rp_3132_t24 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t9 ksi a0 x0 lx y0 uy u m) : l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o)).
-
-(* notion 2203 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) a0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt a0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_rt_1rt) a0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) (l_e_st_eq_landau_n_rt_ispl2 a0 (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt a0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) (l_e_st_eq_landau_n_rt_example1d a0)) (l_e_st_eq_landau_n_rt_distpt1 (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_rt_1rt a0) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_rtofn u) a0 (l_e_st_eq_landau_n_rt_satz101e (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_3132_t17 ksi a0 x0 lx y0 uy u m o))) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) a0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0)).
-
-(* notion 2204 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) a0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) a0)) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_asspl1 x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) a0) (l_e_st_eq_landau_n_rt_ispl2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) a0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) x0 (l_e_st_eq_landau_n_rt_rp_3132_t26 ksi a0 x0 lx y0 uy u m o)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) a0) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o)).
-
-(* notion 2205 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t28 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.λp:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o).(l_e_symis l_e_st_eq_landau_n_rt_rat a0 (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) p)) (l_e_st_eq_landau_n_rt_satz101g (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) a0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) p) (l_e_st_eq_landau_n_rt_rp_3132_t27 ksi a0 x0 lx y0 uy u m o)) : l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) p).
-
-(* notion 2206 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t29 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_andi (l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o)) (Πt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o).l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) t) (l_e_st_eq_landau_n_rt_rp_3132_t25 ksi a0 x0 lx y0 uy u m o) (λt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o).l_e_st_eq_landau_n_rt_rp_3132_t28 ksi a0 x0 lx y0 uy u m o t) : l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o)).
-
-(* notion 2207 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t30 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_somei l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) y) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t29 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) y)).
-
-(* notion 2208 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t31 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x y)) (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t30 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0).
-
-(* notion 2209 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t32 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.(l_orapp (l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0) (l_e_st_eq_landau_n_satz24 u) (λt:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_3132_t31 ksi a0 x0 lx y0 uy u m t) (λt:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_3132_t16 ksi a0 x0 lx y0 uy u m t) : l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0).
-
-(* notion 2210 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t34 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_someapp l_e_st_eq_landau_n_nat (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn y) a0))) x) (l_e_st_eq_landau_n_satz27 (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn y) a0))) (l_e_st_eq_landau_n_rt_rp_3132_t7 ksi a0 x0 lx y0 uy)) (l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0) (λx:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_min (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn y) a0))) x.l_e_st_eq_landau_n_rt_rp_3132_t32 ksi a0 x0 lx y0 uy x t) : l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0).
-
-(* notion 2211 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t35 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_cutapp1b ksi (l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi y.l_e_st_eq_landau_n_rt_rp_3132_t34 ksi a0 x0 lx y t) : l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0).
-
-(* notion 2212 *)
-definition l_e_st_eq_landau_n_rt_rp_satz132 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_cutapp1a ksi (l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_3132_t35 ksi a0 x t) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_and (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt ksi y)) (Πt:l_and (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt ksi y).l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x (l_ande1 (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt ksi y) t) y (l_ande2 (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt ksi y) t))) a0)))).
-
-(* notion 2213 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t36 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_ande1 (l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0) (Πt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0.l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 y0 t) p3 : l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0).
-
-(* notion 2214 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t37 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_r_ande2 (l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0) (Πt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0.l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 y0 t) p3 : l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 y0 (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3)).
-
-(* notion 2215 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t38 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_ande1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3) : l_e_st_eq_landau_n_rt_lrt ksi x0).
-
-(* notion 2216 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t39 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_ande2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3) : l_e_st_eq_landau_n_rt_urt ksi y0).
-
-(* notion 2217 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t40 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_e_st_eq_landau_n_rt_satz101g y0 x0 (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3))) (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 y0 (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3)) (l_e_st_eq_landau_n_rt_satz101c y0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3))) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3))) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 y0 (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3)))).
-
-(* notion 2218 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t41 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3))) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 y0 (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3))) a0 (l_e_st_eq_landau_n_rt_rp_3132_t40 ksi p a0 p1 x0 s y0 p3) (l_e_st_eq_landau_n_rt_rp_3132_t37 ksi p a0 p1 x0 s y0 p3) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3))) a0).
-
-(* notion 2219 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t42 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(p1 x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3) (l_e_st_eq_landau_n_rt_rp_3132_t41 ksi p a0 p1 x0 s y0 p3) : p).
-
-(* notion 2220 *)
-definition l_e_st_eq_landau_n_rt_rp_3132_t43 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).(l_someapp l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y) s p (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y.l_e_st_eq_landau_n_rt_rp_3132_t42 ksi p a0 p1 x0 s y t) : p).
-
-(* notion 2221 *)
-definition l_e_st_eq_landau_n_rt_rp_satz132app ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x y)) (l_e_st_eq_landau_n_rt_rp_satz132 ksi a0) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x y).l_e_st_eq_landau_n_rt_rp_3132_t43 ksi p a0 p1 x t) : p).
-
-(* notion 2222 *)
-definition l_e_st_eq_landau_n_rt_rp_3133_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt ksi u0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) y0.(l_e_tris l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu))) (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_satz101d u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) (l_e_st_eq_landau_n_rt_ispl2 (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) y0 x0 i) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
-
-(* notion 2223 *)
-definition l_e_st_eq_landau_n_rt_rp_3133_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt ksi u0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) y0.(l_e_st_eq_landau_n_rt_rp_lrtpl ksi eta u0 x0 lx y0 ly (l_e_st_eq_landau_n_rt_rp_3133_t1 ksi eta y0 ly x0 lx u0 uu i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) u0).
-
-(* notion 2224 *)
-definition l_e_st_eq_landau_n_rt_rp_3133_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt ksi u0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) y0.(l_andi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) u0) (l_e_st_eq_landau_n_rt_urt ksi u0) (l_e_st_eq_landau_n_rt_rp_3133_t2 ksi eta y0 ly x0 lx u0 uu i) uu : l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) u0) (l_e_st_eq_landau_n_rt_urt ksi u0)).
-
-(* notion 2225 *)
-definition l_e_st_eq_landau_n_rt_rp_3133_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt ksi u0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) y0.(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) x) (l_e_st_eq_landau_n_rt_urt ksi x)) u0 (l_e_st_eq_landau_n_rt_rp_3133_t3 ksi eta y0 ly x0 lx u0 uu i) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi).
-
-(* notion 2226 *)
-definition l_e_st_eq_landau_n_rt_rp_3133_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_rp_satz132app ksi (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi) y0 (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) y0.l_e_st_eq_landau_n_rt_rp_3133_t4 ksi eta y0 ly x t y u v) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi).
-
-(* notion 2227 *)
-definition l_e_st_eq_landau_n_rt_rp_satz133 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_cutapp1a eta (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_3133_t5 ksi eta x t) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi).
-
-(* notion 2228 *)
-definition l_e_st_eq_landau_n_rt_rp_satz133a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi (l_e_st_eq_landau_n_rt_rp_satz133 ksi eta) : l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_pl ksi eta)).
-
-(* notion 2229 *)
-definition l_e_st_eq_landau_n_rt_rp_3134_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_satz119a eta y0 uy x0 l : l_e_st_eq_landau_n_rt_urt eta x0).
-
-(* notion 2230 *)
-definition l_e_st_eq_landau_n_rt_rp_3134_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_satz83 y0 x0 l : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 2231 *)
-definition l_e_st_eq_landau_n_rt_rp_3134_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_e_tris l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) u0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0) (l_e_st_eq_landau_n_rt_satz101f z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_ispl1 (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0 i) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0)).
-
-(* notion 2232 *)
-definition l_e_st_eq_landau_n_rt_rp_3134_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l))) u0) (l_e_st_eq_landau_n_rt_pl x0 u0) (l_e_st_eq_landau_n_rt_ispl2 z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0) y0 (l_e_st_eq_landau_n_rt_rp_3134_t3 ksi eta zeta m y0 ly uy x0 lx l u0 lu z0 uz i)) (l_e_st_eq_landau_n_rt_asspl2 y0 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0) (l_e_st_eq_landau_n_rt_ispl1 (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l))) x0 u0 (l_e_st_eq_landau_n_rt_satz101c x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l))) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl x0 u0)).
-
-(* notion 2233 *)
-definition l_e_st_eq_landau_n_rt_rp_3134_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_rp_lrtpl ksi zeta (l_e_st_eq_landau_n_rt_pl y0 z0) x0 lx u0 lu (l_e_st_eq_landau_n_rt_rp_3134_t4 ksi eta zeta m y0 ly uy x0 lx l u0 lu z0 uz i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 2234 *)
-definition l_e_st_eq_landau_n_rt_rp_3134_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_rp_urtpl eta zeta (l_e_st_eq_landau_n_rt_pl y0 z0) y0 uy z0 uz (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y0 z0)) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 2235 *)
-definition l_e_st_eq_landau_n_rt_rp_3134_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_andi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_rp_3134_t5 ksi eta zeta m y0 ly uy x0 lx l u0 lu z0 uz i) (l_e_st_eq_landau_n_rt_rp_3134_t6 ksi eta zeta m y0 ly uy x0 lx l u0 lu z0 uz i) : l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_pl y0 z0))).
-
-(* notion 2236 *)
-definition l_e_st_eq_landau_n_rt_rp_3134_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) x) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) x)) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_rp_3134_t7 ksi eta zeta m y0 ly uy x0 lx l u0 lu z0 uz i) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
-
-(* notion 2237 *)
-definition l_e_st_eq_landau_n_rt_rp_3134_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_satz132app zeta (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt zeta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt zeta y.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b zeta x t y u)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).l_e_st_eq_landau_n_rt_rp_3134_t8 ksi eta zeta m y0 ly uy x0 lx l x t y u v) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
-
-(* notion 2238 *)
-definition l_e_st_eq_landau_n_rt_rp_3134_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.(l_e_st_eq_landau_n_rt_cutapp3 ksi y0 ly (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_less y0 x.l_e_st_eq_landau_n_rt_rp_3134_t9 ksi eta zeta m y0 ly uy x t u) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
-
-(* notion 2239 *)
-definition l_e_st_eq_landau_n_rt_rp_satz134 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_3134_t10 ksi eta zeta m x t u) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
-
-(* notion 2240 *)
-definition l_e_st_eq_landau_n_rt_rp_satz135a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_satz134 ksi eta zeta m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
-
-(* notion 2241 *)
-definition l_e_st_eq_landau_n_rt_rp_satz135b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ispl1 ksi eta zeta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
-
-(* notion 2242 *)
-definition l_e_st_eq_landau_n_rt_rp_satz135c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz134 eta ksi zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
-
-(* notion 2243 *)
-definition l_e_st_eq_landau_n_rt_rp_satz135d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_compl ksi zeta) (l_e_st_eq_landau_n_rt_rp_compl eta zeta) (l_e_st_eq_landau_n_rt_rp_satz135a ksi eta zeta m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta)).
-
-(* notion 2244 *)
-definition l_e_st_eq_landau_n_rt_rp_satz135e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ispl2 ksi eta zeta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta)).
-
-(* notion 2245 *)
-definition l_e_st_eq_landau_n_rt_rp_satz135f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_compl ksi zeta) (l_e_st_eq_landau_n_rt_rp_compl eta zeta) (l_e_st_eq_landau_n_rt_rp_satz135c ksi eta zeta l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta)).
-
-(* notion 2246 *)
-definition l_e_st_eq_landau_n_rt_rp_satz135g ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore2 (l_e_st_eq_landau_n_rt_rp_pl ksi upsilon) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_ispl1 ksi eta upsilon i) (l_e_st_eq_landau_n_rt_rp_satz135d zeta upsilon ksi m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2247 *)
-definition l_e_st_eq_landau_n_rt_rp_satz135h ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl upsilon eta) (l_e_st_eq_landau_n_rt_rp_compl ksi zeta) (l_e_st_eq_landau_n_rt_rp_compl eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz135g ksi eta zeta upsilon i m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl upsilon eta)).
-
-(* notion 2248 *)
-definition l_e_st_eq_landau_n_rt_rp_satz135j ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl ksi upsilon) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_ispl1 ksi eta upsilon i) (l_e_st_eq_landau_n_rt_rp_satz135f zeta upsilon ksi l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2249 *)
-definition l_e_st_eq_landau_n_rt_rp_satz135k ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl upsilon eta) (l_e_st_eq_landau_n_rt_rp_compl ksi zeta) (l_e_st_eq_landau_n_rt_rp_compl eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz135j ksi eta zeta upsilon i l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl upsilon eta)).
-
-(* notion 2250 *)
-definition l_e_st_eq_landau_n_rt_rp_3136_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz123a ksi eta : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2251 *)
-definition l_e_st_eq_landau_n_rt_rp_3136_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) : l_ec3 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta))).
-
-(* notion 2252 *)
-definition l_e_st_eq_landau_n_rt_rp_satz136a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta).(l_ec3_th11 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_3136_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_3136_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz135b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz135a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz135c ksi eta zeta u) m : l_e_st_eq_landau_n_rt_rp_more ksi eta).
-
-(* notion 2253 *)
-definition l_e_st_eq_landau_n_rt_rp_satz136b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta).(l_ec3_th10 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_3136_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_3136_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz135b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz135a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz135c ksi eta zeta u) i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
-
-(* notion 2254 *)
-definition l_e_st_eq_landau_n_rt_rp_satz136c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta).(l_ec3_th12 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_3136_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_3136_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz135b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz135a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz135c ksi eta zeta u) l : l_e_st_eq_landau_n_rt_rp_less ksi eta).
-
-(* notion 2255 *)
-definition l_e_st_eq_landau_n_rt_rp_satz136d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta).(l_e_st_eq_landau_n_rt_rp_satz136a ksi eta zeta (l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_compl zeta ksi) (l_e_st_eq_landau_n_rt_rp_compl zeta eta) m) : l_e_st_eq_landau_n_rt_rp_more ksi eta).
-
-(* notion 2256 *)
-definition l_e_st_eq_landau_n_rt_rp_satz136e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta).(l_e_st_eq_landau_n_rt_rp_satz136b ksi eta zeta (l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_compl ksi zeta) i (l_e_st_eq_landau_n_rt_rp_compl zeta eta)) : l_e_st_eq_landau_n_rt_rp_is ksi eta).
-
-(* notion 2257 *)
-definition l_e_st_eq_landau_n_rt_rp_satz136f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta).(l_e_st_eq_landau_n_rt_rp_satz136c ksi eta zeta (l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_compl zeta ksi) (l_e_st_eq_landau_n_rt_rp_compl zeta eta) l) : l_e_st_eq_landau_n_rt_rp_less ksi eta).
-
-(* notion 2258 *)
-definition l_e_st_eq_landau_n_rt_rp_3137_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz134 ksi eta zeta m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
-
-(* notion 2259 *)
-definition l_e_st_eq_landau_n_rt_rp_3137_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl upsilon eta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_compl zeta eta) (l_e_st_eq_landau_n_rt_rp_compl upsilon eta) (l_e_st_eq_landau_n_rt_rp_satz134 zeta upsilon eta n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2260 *)
-definition l_e_st_eq_landau_n_rt_rp_satz137 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_trmore (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_3137_t1 ksi eta zeta upsilon m n) (l_e_st_eq_landau_n_rt_rp_3137_t2 ksi eta zeta upsilon m n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2261 *)
-definition l_e_st_eq_landau_n_rt_rp_satz137a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz137 eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz122 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2262 *)
-definition l_e_st_eq_landau_n_rt_rp_satz138a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)) m (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz137 ksi eta zeta upsilon t n) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz135g ksi eta zeta upsilon t n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2263 *)
-definition l_e_st_eq_landau_n_rt_rp_satz138b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more zeta upsilon) (l_e_st_eq_landau_n_rt_rp_is zeta upsilon) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)) n (λt:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.l_e_st_eq_landau_n_rt_rp_satz137 ksi eta zeta upsilon m t) (λt:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.l_e_st_eq_landau_n_rt_rp_satz135h zeta upsilon ksi eta t m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2264 *)
-definition l_e_st_eq_landau_n_rt_rp_satz138c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz138a eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz125 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz122 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2265 *)
-definition l_e_st_eq_landau_n_rt_rp_satz138d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz138b eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz125 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2266 *)
-definition l_e_st_eq_landau_n_rt_rp_3139_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_ispl12 ksi eta zeta upsilon i j) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2267 *)
-definition l_e_st_eq_landau_n_rt_rp_3139_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λo:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz138a ksi eta zeta upsilon m o) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2268 *)
-definition l_e_st_eq_landau_n_rt_rp_3139_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_orapp (l_e_st_eq_landau_n_rt_rp_more zeta upsilon) (l_e_st_eq_landau_n_rt_rp_is zeta upsilon) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)) n (λt:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.l_e_st_eq_landau_n_rt_rp_3139_t2 ksi eta zeta upsilon m n i t) (λt:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.l_e_st_eq_landau_n_rt_rp_3139_t1 ksi eta zeta upsilon m n i t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2269 *)
-definition l_e_st_eq_landau_n_rt_rp_3139_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λo:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz138b ksi eta zeta upsilon o n) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2270 *)
-definition l_e_st_eq_landau_n_rt_rp_satz139 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)) m (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_3139_t4 ksi eta zeta upsilon m n t) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_3139_t3 ksi eta zeta upsilon m n t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2271 *)
-definition l_e_st_eq_landau_n_rt_rp_satz139a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz124 (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz139 eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz125 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz125 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
-
-(* notion 2272 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λphi:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi.(l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi eta i (l_e_st_eq_landau_n_rt_rp_satz133 eta phi) : l_e_st_eq_landau_n_rt_rp_more ksi eta).
-
-(* notion 2273 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λphi:l_e_st_eq_landau_n_rt_cut.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123d ksi eta l) (λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi.l_e_st_eq_landau_n_rt_rp_3140_t1 ksi eta l phi t) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi).
-
-(* notion 2274 *)
-definition l_e_st_eq_landau_n_rt_rp_vorbemerkung140 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.(l_some_th5 l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi) (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_3140_t2 ksi eta l a) : l_not (l_e_st_eq_landau_n_rt_rp_some (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi))).
-
-(* notion 2275 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more phi psi.(l_e_st_eq_landau_n_rt_rp_satz135d phi psi eta m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)).
-
-(* notion 2276 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more phi psi.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_3140_t3 ksi eta phi psi m) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)).
-
-(* notion 2277 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less phi psi.(l_e_st_eq_landau_n_rt_rp_satz135f phi psi eta l : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)).
-
-(* notion 2278 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less phi psi.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_3140_t5 ksi eta phi psi l) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)).
-
-(* notion 2279 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis phi psi.(l_or3_th1 (l_e_st_eq_landau_n_rt_rp_is phi psi) (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi) (l_e_st_eq_landau_n_rt_rp_satz123a phi psi) n : l_or (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi)).
-
-(* notion 2280 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis phi psi.(l_orapp (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi) (l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_3140_t7 ksi eta phi psi n) (λt:l_e_st_eq_landau_n_rt_rp_more phi psi.l_e_st_eq_landau_n_rt_rp_3140_t4 ksi eta phi psi t) (λt:l_e_st_eq_landau_n_rt_rp_less phi psi.l_e_st_eq_landau_n_rt_rp_3140_t6 ksi eta phi psi t) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)).
-
-(* notion 2281 *)
-definition l_e_st_eq_landau_n_rt_rp_satz140b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta psi) ksi.(l_imp_th7 (l_e_st_eq_landau_n_rt_rp_is phi psi) (l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_weli (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi) ksi i j)) (λt:l_e_st_eq_landau_n_rt_rp_nis phi psi.l_e_st_eq_landau_n_rt_rp_3140_t8 ksi eta phi psi t) : l_e_st_eq_landau_n_rt_rp_is phi psi).
-
-(* notion 2282 *)
-definition l_e_st_eq_landau_n_rt_rp_diffprop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_more x0 y0) (Πt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 t)) : Prop).
-
-(* notion 2283 *)
-definition l_e_st_eq_landau_n_rt_rp_diffprop2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta y0) (l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0) : Prop).
-
-(* notion 2284 *)
-definition l_e_st_eq_landau_n_rt_rp_diffprop ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x y)) : Prop).
-
-(* notion 2285 *)
-definition l_e_st_eq_landau_n_rt_rp_diff ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop ksi eta z) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2286 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t11a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).λm1:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_tris l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m) (l_e_st_eq_landau_n_rt_mn x0 y0 m1) i (l_e_st_eq_landau_n_rt_satz101g x0 y0 (l_e_st_eq_landau_n_rt_mn x0 y0 m) m1 (l_e_st_eq_landau_n_rt_satz101c x0 y0 m)) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m1)).
-
-(* notion 2287 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).(l_andi (l_e_st_eq_landau_n_rt_more x0 y0) (Πt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 t)) m (λt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_rp_iii3_t11a ksi eta z0 x0 lx y0 uy m i t) : l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0).
-
-(* notion 2288 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).(l_and3i (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta y0) (l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0) lx uy (l_e_st_eq_landau_n_rt_rp_iii3_t12 ksi eta z0 x0 lx y0 uy m i) : l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0).
-
-(* notion 2289 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).(l_somei l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y) y0 (l_e_st_eq_landau_n_rt_rp_iii3_t13 ksi eta z0 x0 lx y0 uy m i) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y)).
-
-(* notion 2290 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x y)) x0 (l_e_st_eq_landau_n_rt_rp_iii3_t14 ksi eta z0 x0 lx y0 uy m i) : l_e_st_eq_landau_n_rt_rp_diffprop ksi eta z0).
-
-(* notion 2291 *)
-definition l_e_st_eq_landau_n_rt_rp_diff1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop ksi eta z) z0 (l_e_st_eq_landau_n_rt_rp_iii3_t15 ksi eta z0 x0 lx y0 uy m i) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
-
-(* notion 2292 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop ksi eta z) z0 i : l_e_st_eq_landau_n_rt_rp_diffprop ksi eta z0).
-
-(* notion 2293 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(l_and3e1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta y0) (l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0) py : l_e_st_eq_landau_n_rt_lrt ksi x0).
-
-(* notion 2294 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(l_and3e2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta y0) (l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0) py : l_e_st_eq_landau_n_rt_urt eta y0).
-
-(* notion 2295 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(l_and3e3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta y0) (l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0) py : l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0).
-
-(* notion 2296 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(l_ande1 (l_e_st_eq_landau_n_rt_more x0 y0) (Πt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 t)) (l_e_st_eq_landau_n_rt_rp_iii3_t19 ksi eta z0 i p p1 x0 px y0 py) : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 2297 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(l_r_ande2 (l_e_st_eq_landau_n_rt_more x0 y0) (Πt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 t)) (l_e_st_eq_landau_n_rt_rp_iii3_t19 ksi eta z0 i p p1 x0 px y0 py) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_iii3_t20 ksi eta z0 i p p1 x0 px y0 py))).
-
-(* notion 2298 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(p1 x0 (l_e_st_eq_landau_n_rt_rp_iii3_t17 ksi eta z0 i p p1 x0 px y0 py) y0 (l_e_st_eq_landau_n_rt_rp_iii3_t18 ksi eta z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_iii3_t20 ksi eta z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_iii3_t21 ksi eta z0 i p p1 x0 px y0 py) : p).
-
-(* notion 2299 *)
-definition l_e_st_eq_landau_n_rt_rp_iii3_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).(l_someapp l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y) px p (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y.l_e_st_eq_landau_n_rt_rp_iii3_t22 ksi eta z0 i p p1 x0 px y t) : p).
-
-(* notion 2300 *)
-definition l_e_st_eq_landau_n_rt_rp_diffapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x y)) (l_e_st_eq_landau_n_rt_rp_iii3_t16 ksi eta z0 i p p1) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x y).l_e_st_eq_landau_n_rt_rp_iii3_t23 ksi eta z0 i p p1 x t) : p).
-
-(* notion 2301 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta eta m y0 ly uy x0 lx l : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 2302 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_diff1 ksi eta (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t9 ksi eta m y0 ly uy x0 lx l)) x0 lx y0 uy (l_e_st_eq_landau_n_rt_rp_3140_t9 ksi eta m y0 ly uy x0 lx l) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t9 ksi eta m y0 ly uy x0 lx l))) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t9 ksi eta m y0 ly uy x0 lx l)) (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
-
-(* notion 2303 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_mn x0 y0 n) z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0) x0 (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n) j) (l_e_st_eq_landau_n_rt_satz101e x0 y0 n) (l_e_st_eq_landau_n_rt_satz94a (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0) : l_e_st_eq_landau_n_rt_less z0 x0).
-
-(* notion 2304 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_trless z0 x0 x1 (l_e_st_eq_landau_n_rt_rp_3140_t11 ksi eta m x1 ux z0 i x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx x1 ux) : l_e_st_eq_landau_n_rt_less z0 x1).
-
-(* notion 2305 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_ec3e31 (l_e_st_eq_landau_n_rt_is z0 x1) (l_e_st_eq_landau_n_rt_more z0 x1) (l_e_st_eq_landau_n_rt_less z0 x1) (l_e_st_eq_landau_n_rt_satz81b z0 x1) (l_e_st_eq_landau_n_rt_rp_3140_t12 ksi eta m x1 ux z0 i x0 lx y0 uy n j) : l_e_st_eq_landau_n_rt_nis z0 x1).
-
-(* notion 2306 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).(l_e_st_eq_landau_n_rt_rp_diffapp ksi eta z0 i (l_e_st_eq_landau_n_rt_nis z0 x1) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt eta y.λv:l_e_st_eq_landau_n_rt_more x y.λw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).l_e_st_eq_landau_n_rt_rp_3140_t13 ksi eta m x1 ux z0 i x t y u v w) : l_e_st_eq_landau_n_rt_nis z0 x1).
-
-(* notion 2307 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.(l_imp_th3 (l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_nis x1 x1) (l_weli (l_e_st_eq_landau_n_rt_is x1 x1) (l_e_refis l_e_st_eq_landau_n_rt_rat x1)) (λt:l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).l_e_st_eq_landau_n_rt_rp_3140_t14 ksi eta m x1 ux x1 t) : l_not (l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_rp_diff ksi eta))).
-
-(* notion 2308 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl z0 y0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0) x0 (l_e_st_eq_landau_n_rt_ispl1 z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0 j) (l_e_st_eq_landau_n_rt_satz101e x0 y0 n) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl z0 y0) x0).
-
-(* notion 2309 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_x2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_pl u0 y0 : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2310 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_pl z0 y0) x0 (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_rp_3140_t16 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_satz96c u0 z0 y0 l) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) x0).
-
-(* notion 2311 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_rp_satz120 ksi x0 lx (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_rp_3140_t17 ksi eta m z0 i u0 l x0 lx y0 uy n j) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j)).
-
-(* notion 2312 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_ismore1 (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_pl u0 y0) y0 (l_e_st_eq_landau_n_rt_compl y0 u0) (l_e_st_eq_landau_n_rt_satz94 y0 u0) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) y0).
-
-(* notion 2313 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_satz101g (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) y0 u0 (l_e_st_eq_landau_n_rt_rp_3140_t19 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_compl y0 u0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) y0 (l_e_st_eq_landau_n_rt_rp_3140_t19 ksi eta m z0 i u0 l x0 lx y0 uy n j))).
-
-(* notion 2314 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_rp_diff1 ksi eta u0 (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_rp_3140_t18 ksi eta m z0 i u0 l x0 lx y0 uy n j) y0 uy (l_e_st_eq_landau_n_rt_rp_3140_t19 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_rp_3140_t20 ksi eta m z0 i u0 l x0 lx y0 uy n j) : l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
-
-(* notion 2315 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.(l_e_st_eq_landau_n_rt_rp_diffapp ksi eta z0 i (l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt eta y.λv:l_e_st_eq_landau_n_rt_more x y.λw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).l_e_st_eq_landau_n_rt_rp_3140_t21 ksi eta m z0 i u0 l x t y u v w) : l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
-
-(* notion 2316 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_satz83 x0 x3 l : l_e_st_eq_landau_n_rt_more x3 x0).
-
-(* notion 2317 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_trmore x3 x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t23 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) n : l_e_st_eq_landau_n_rt_more x3 y0).
-
-(* notion 2318 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_ismore12 x3 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) y0) x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0) (l_e_st_eq_landau_n_rt_satz101f x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_satz101f x0 y0 n) (l_e_st_eq_landau_n_rt_rp_3140_t23 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) y0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0)).
-
-(* notion 2319 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_satz97a (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0 (l_e_st_eq_landau_n_rt_rp_3140_t25 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_mn x0 y0 n)).
-
-(* notion 2320 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_ismore2 (l_e_st_eq_landau_n_rt_mn x0 y0 n) z0 (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n) j) (l_e_st_eq_landau_n_rt_rp_3140_t26 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) z0).
-
-(* notion 2321 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t28 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_rp_diff1 ksi eta (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) x3 lx3 y0 uy (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l))) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
-
-(* notion 2322 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t29 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_andi (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) z0) (l_e_st_eq_landau_n_rt_rp_3140_t28 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) (l_e_st_eq_landau_n_rt_rp_3140_t27 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) : l_and (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) z0)).
-
-(* notion 2323 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t30 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0)) (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_rp_3140_t29 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0))).
-
-(* notion 2324 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t31 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_cutapp3 ksi x0 lx (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0))) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi y.λu:l_e_st_eq_landau_n_rt_less x0 y.l_e_st_eq_landau_n_rt_rp_3140_t30 ksi eta m z0 i x0 lx y0 uy n j y t u) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0))).
-
-(* notion 2325 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t32 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).(l_e_st_eq_landau_n_rt_rp_diffapp ksi eta z0 i (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt eta y.λv:l_e_st_eq_landau_n_rt_more x y.λw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).l_e_st_eq_landau_n_rt_rp_3140_t31 ksi eta m z0 i x t y u v w) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0))).
-
-(* notion 2326 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t33 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_diff ksi eta) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t9 ksi eta m y0 ly uy x0 lx l)) (l_e_st_eq_landau_n_rt_rp_3140_t10 ksi eta m y0 ly uy x0 lx l) x1 (l_e_st_eq_landau_n_rt_rp_3140_t15 ksi eta m x1 ux1) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_3140_t22 ksi eta m x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta).l_e_st_eq_landau_n_rt_rp_3140_t32 ksi eta m x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
-
-(* notion 2327 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t34 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_cutapp1b ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.l_e_st_eq_landau_n_rt_rp_3140_t33 ksi eta m y0 ly uy x0 lx l x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
-
-(* notion 2328 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t35 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.(l_e_st_eq_landau_n_rt_cutapp3 ksi y0 ly (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_less y0 x.l_e_st_eq_landau_n_rt_rp_3140_t34 ksi eta m y0 ly uy x t u) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
-
-(* notion 2329 *)
-definition l_e_st_eq_landau_n_rt_rp_satz140h ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt ksi x.λv:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_3140_t35 ksi eta m x u v) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
-
-(* notion 2330 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_chi ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_diff ksi eta) (l_e_st_eq_landau_n_rt_rp_satz140h ksi eta m) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2331 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t36 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_st_eq_landau_n_rt_cutapp2b eta y1 ly y0 uy : l_e_st_eq_landau_n_rt_more y0 y1).
-
-(* notion 2332 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t37 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) (l_e_st_eq_landau_n_rt_pl y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j)))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y0) x0 (l_e_st_eq_landau_n_rt_asspl1 (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) (l_e_st_eq_landau_n_rt_ispl2 (l_e_st_eq_landau_n_rt_pl y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) y0 (l_e_st_eq_landau_n_rt_mn x0 y0 o) (l_e_st_eq_landau_n_rt_satz101c y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) (l_e_st_eq_landau_n_rt_satz101e x0 y0 o) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) x0).
-
-(* notion 2333 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t38 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_rp_3140_t37 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j) (l_e_st_eq_landau_n_rt_satz94a (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) x0).
-
-(* notion 2334 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t39 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_tr3is l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl y1 u0) (l_e_st_eq_landau_n_rt_pl u0 y1) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) i (l_e_st_eq_landau_n_rt_compl y1 u0) (l_e_st_eq_landau_n_rt_ispl1 u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1 j) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1)).
-
-(* notion 2335 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t40 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) z0 x0 (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_rp_3140_t39 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j)) (l_e_st_eq_landau_n_rt_rp_3140_t38 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j) : l_e_st_eq_landau_n_rt_less z0 x0).
-
-(* notion 2336 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t41 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_st_eq_landau_n_rt_rp_satz120 ksi x0 lx z0 (l_e_st_eq_landau_n_rt_rp_3140_t40 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j) : l_e_st_eq_landau_n_rt_lrt ksi z0).
-
-(* notion 2337 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t42 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).(l_e_st_eq_landau_n_rt_rp_diffapp ksi eta u0 (l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_diff ksi eta) (l_e_st_eq_landau_n_rt_rp_satz140h ksi eta m) u0 lu) (l_e_st_eq_landau_n_rt_lrt ksi z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt eta y.λv:l_e_st_eq_landau_n_rt_more x y.λw:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x y v).l_e_st_eq_landau_n_rt_rp_3140_t41 ksi eta m z0 lz y1 ly u0 lu i x t y u v w) : l_e_st_eq_landau_n_rt_lrt ksi z0).
-
-(* notion 2338 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.(l_e_st_eq_landau_n_rt_rp_plapp eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) z0 lz (l_e_st_eq_landau_n_rt_lrt ksi z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3140_t42 ksi eta m z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt ksi z0).
-
-(* notion 2339 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t43 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_satz83 y0 x0 l : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 2340 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t44 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.(l_e_st_eq_landau_n_rt_cutapp2b eta y1 ly1 y2 uy2 : l_e_st_eq_landau_n_rt_more y2 y1).
-
-(* notion 2341 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t45 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_cutapp2b eta y1 ly1 y0 uy : l_e_st_eq_landau_n_rt_more y0 y1).
-
-(* notion 2342 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t46 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_tris l_e_st_eq_landau_n_rt_rat y2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) y1) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1) (l_e_st_eq_landau_n_rt_satz101f y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_ispl1 (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1 i) : l_e_st_eq_landau_n_rt_is y2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1)).
-
-(* notion 2343 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t47 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_tr4is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y2 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) (l_e_st_eq_landau_n_rt_pl y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y0) x0 (l_e_st_eq_landau_n_rt_ispl1 y2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_rp_3140_t46 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_asspl1 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) (l_e_st_eq_landau_n_rt_ispl2 (l_e_st_eq_landau_n_rt_pl y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) y0 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) (l_e_st_eq_landau_n_rt_satz101c y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) (l_e_st_eq_landau_n_rt_satz101e x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y2 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) x0).
-
-(* notion 2344 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t48 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_ismore1 (l_e_st_eq_landau_n_rt_pl y2 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t47 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) (l_e_st_eq_landau_n_rt_satz94 y2 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) : l_e_st_eq_landau_n_rt_more x0 y2).
-
-(* notion 2345 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t49 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_satz101g x0 y2 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) (l_e_st_eq_landau_n_rt_rp_3140_t47 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))).
-
-(* notion 2346 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t50 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_tris l_e_st_eq_landau_n_rt_rat y0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1) (l_e_st_eq_landau_n_rt_satz101f y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_ispl1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1 (l_e_st_eq_landau_n_rt_rp_3140_t49 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) : l_e_st_eq_landau_n_rt_is y0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1)).
-
-(* notion 2347 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t51 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_diff ksi eta) (l_e_st_eq_landau_n_rt_rp_satz140h ksi eta m) (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_rp_diff1 ksi eta (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) x0 lx y2 uy2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)))) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))).
-
-(* notion 2348 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t52 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_rp_lrtpl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) y0 y1 ly1 (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_rp_3140_t51 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) (l_e_tris l_e_st_eq_landau_n_rt_rat y0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1) (l_e_st_eq_landau_n_rt_pl y1 (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) (l_e_st_eq_landau_n_rt_rp_3140_t50 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) (l_e_st_eq_landau_n_rt_compl (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
-
-(* notion 2349 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t53 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_satz132app eta (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt eta y.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b eta x t y u)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).l_e_st_eq_landau_n_rt_rp_3140_t52 ksi eta m y0 ly uy x0 lx l x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
-
-(* notion 2350 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t54 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.(l_e_st_eq_landau_n_rt_cutapp3 ksi y0 ly (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_less y0 x.l_e_st_eq_landau_n_rt_rp_3140_t53 ksi eta m y0 ly uy x t u) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
-
-(* notion 2351 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t55 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λly0:l_e_st_eq_landau_n_rt_lrt eta y0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt ksi y1.λuy1:l_e_st_eq_landau_n_rt_urt eta y1.(l_e_st_eq_landau_n_rt_rp_3140_t54 ksi eta m y1 ly1 uy1 : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y1).
-
-(* notion 2352 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t56 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λly0:l_e_st_eq_landau_n_rt_lrt eta y0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt ksi y1.λuy1:l_e_st_eq_landau_n_rt_urt eta y1.(l_e_st_eq_landau_n_rt_rp_satz120 (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y1 (l_e_st_eq_landau_n_rt_rp_3140_t55 ksi eta m y0 ly ly0 y1 ly1 uy1) y0 (l_e_st_eq_landau_n_rt_cutapp2a eta y0 ly0 y1 uy1) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
-
-(* notion 2353 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t57 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λly0:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_3140_t56 ksi eta m y0 ly ly0 x t u) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
-
-(* notion 2354 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.(l_imp_th1 (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0) (λt:l_e_st_eq_landau_n_rt_lrt eta y0.l_e_st_eq_landau_n_rt_rp_3140_t57 ksi eta m y0 ly t) (λt:l_e_st_eq_landau_n_rt_urt eta y0.l_e_st_eq_landau_n_rt_rp_3140_t54 ksi eta m y0 ly t) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
-
-(* notion 2355 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t58 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) ksi (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) x.l_e_st_eq_landau_n_rt_rp_3140_a ksi eta m x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_3140_b ksi eta m x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) ksi).
-
-(* notion 2356 *)
-definition l_e_st_eq_landau_n_rt_rp_satz140a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_somei l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi) (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) (l_e_st_eq_landau_n_rt_rp_3140_t58 ksi eta m) : l_e_st_eq_landau_n_rt_rp_some (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi)).
-
-(* notion 2357 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t59 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(λc:l_e_st_eq_landau_n_rt_cut.λd:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta c) ksi.λu:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta d) ksi.l_e_st_eq_landau_n_rt_rp_satz140b ksi eta c d t u : l_e_amone l_e_st_eq_landau_n_rt_cut (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta c) ksi)).
-
-(* notion 2358 *)
-definition l_e_st_eq_landau_n_rt_rp_satz140 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_onei l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi) (l_e_st_eq_landau_n_rt_rp_3140_t59 ksi eta) (l_e_st_eq_landau_n_rt_rp_satz140a ksi eta m) : l_e_st_eq_landau_n_rt_rp_one (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi)).
-
-(* notion 2359 *)
-definition l_e_st_eq_landau_n_rt_rp_mn ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_ind l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi) (l_e_st_eq_landau_n_rt_rp_satz140 ksi eta m) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2360 *)
-definition l_e_st_eq_landau_n_rt_rp_satz140c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_oneax l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi) (l_e_st_eq_landau_n_rt_rp_satz140 ksi eta m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_mn ksi eta m)) ksi).
-
-(* notion 2361 *)
-definition l_e_st_eq_landau_n_rt_rp_satz140d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_mn ksi eta m)) ksi (l_e_st_eq_landau_n_rt_rp_satz140c ksi eta m) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_mn ksi eta m))).
-
-(* notion 2362 *)
-definition l_e_st_eq_landau_n_rt_rp_satz140e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) eta) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_mn ksi eta m)) ksi (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) eta) (l_e_st_eq_landau_n_rt_rp_satz140c ksi eta m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) eta) ksi).
-
-(* notion 2363 *)
-definition l_e_st_eq_landau_n_rt_rp_satz140f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) eta) ksi (l_e_st_eq_landau_n_rt_rp_satz140e ksi eta m) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) eta)).
-
-(* notion 2364 *)
-definition l_e_st_eq_landau_n_rt_rp_satz140g ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi.(l_e_st_eq_landau_n_rt_rp_satz140b ksi eta phi (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) i (l_e_st_eq_landau_n_rt_rp_satz140c ksi eta m) : l_e_st_eq_landau_n_rt_rp_is phi (l_e_st_eq_landau_n_rt_rp_mn ksi eta m)).
-
-(* notion 2365 *)
-definition l_e_st_eq_landau_n_rt_rp_3140_t60 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi zeta.λn:l_e_st_eq_landau_n_rt_rp_more eta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl upsilon (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m)) (l_e_st_eq_landau_n_rt_rp_pl zeta (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m)) ksi eta (l_e_st_eq_landau_n_rt_rp_ispl1 upsilon zeta (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m) (l_e_symis l_e_st_eq_landau_n_rt_cut zeta upsilon j)) (l_e_st_eq_landau_n_rt_rp_satz140c ksi zeta m) i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl upsilon (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m)) eta).
-
-(* notion 2366 *)
-definition l_e_st_eq_landau_n_rt_rp_ismn12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi zeta.λn:l_e_st_eq_landau_n_rt_rp_more eta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz140g eta upsilon (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m) n (l_e_st_eq_landau_n_rt_rp_3140_t60 ksi eta zeta upsilon m n i j) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m) (l_e_st_eq_landau_n_rt_rp_mn eta upsilon n)).
-
-(* notion 2367 *)
-definition l_e_st_eq_landau_n_rt_rp_ismn1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi zeta.λn:l_e_st_eq_landau_n_rt_rp_more eta zeta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ismn12 ksi eta zeta zeta m n i (l_e_refis l_e_st_eq_landau_n_rt_cut zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m) (l_e_st_eq_landau_n_rt_rp_mn eta zeta n)).
-
-(* notion 2368 *)
-definition l_e_st_eq_landau_n_rt_rp_ismn2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more zeta ksi.λn:l_e_st_eq_landau_n_rt_rp_more zeta eta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ismn12 zeta zeta ksi eta m n (l_e_refis l_e_st_eq_landau_n_rt_cut zeta) i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn zeta ksi m) (l_e_st_eq_landau_n_rt_rp_mn zeta eta n)).
-
-(* notion 2369 *)
-definition l_e_st_eq_landau_n_rt_rp_prodprop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)) : Prop).
-
-(* notion 2370 *)
-definition l_e_st_eq_landau_n_rt_rp_prodprop ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x y)) : Prop).
-
-(* notion 2371 *)
-definition l_e_st_eq_landau_n_rt_rp_prod ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop ksi eta z) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2372 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_and3i (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)) lx ly i : l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y0).
-
-(* notion 2373 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_somei l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y) y0 (l_e_st_eq_landau_n_rt_rp_iii4_t1 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y)).
-
-(* notion 2374 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x y)) x0 (l_e_st_eq_landau_n_rt_rp_iii4_t2 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_rp_prodprop ksi eta z0).
-
-(* notion 2375 *)
-definition l_e_st_eq_landau_n_rt_rp_prod1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop ksi eta z) z0 (l_e_st_eq_landau_n_rt_rp_iii4_t3 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
-
-(* notion 2376 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop ksi eta z) z0 i : l_e_st_eq_landau_n_rt_rp_prodprop ksi eta z0).
-
-(* notion 2377 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y0.(l_and3e1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)) py : l_e_st_eq_landau_n_rt_lrt ksi x0).
-
-(* notion 2378 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y0.(l_and3e2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)) py : l_e_st_eq_landau_n_rt_lrt eta y0).
-
-(* notion 2379 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y0.(l_and3e3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)) py : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 2380 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y0.(p1 x0 (l_e_st_eq_landau_n_rt_rp_iii4_t5 ksi eta z0 i p p1 x0 px y0 py) y0 (l_e_st_eq_landau_n_rt_rp_iii4_t6 ksi eta z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_iii4_t7 ksi eta z0 i p p1 x0 px y0 py) : p).
-
-(* notion 2381 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y).(l_someapp l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y) px p (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y.l_e_st_eq_landau_n_rt_rp_iii4_t8 ksi eta z0 i p p1 x0 px y t) : p).
-
-(* notion 2382 *)
-definition l_e_st_eq_landau_n_rt_rp_prodapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x y)) (l_e_st_eq_landau_n_rt_rp_iii4_t4 ksi eta z0 i p p1) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x y).l_e_st_eq_landau_n_rt_rp_iii4_t9 ksi eta z0 i p p1 x t) : p).
-
-(* notion 2383 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx x1 ux : l_e_st_eq_landau_n_rt_less x0 x1).
-
-(* notion 2384 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_cutapp2a eta y0 ly y1 uy : l_e_st_eq_landau_n_rt_less y0 y1).
-
-(* notion 2385 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 y0) j) (l_e_st_eq_landau_n_rt_satz107a x0 x1 y0 y1 (l_e_st_eq_landau_n_rt_rp_4141_t1 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_rp_4141_t2 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j)) : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_ts x1 y1)).
-
-(* notion 2386 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_ec3e31 (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_e_st_eq_landau_n_rt_more z0 (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_e_st_eq_landau_n_rt_satz81b z0 (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_e_st_eq_landau_n_rt_rp_4141_t3 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_ts x1 y1)).
-
-(* notion 2387 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).(l_e_st_eq_landau_n_rt_rp_prodapp ksi eta z0 i (l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_ts x1 y1)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4141_t4 ksi eta x1 ux y1 uy z0 i x t y u v) : l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_ts x1 y1)).
-
-(* notion 2388 *)
-definition l_e_st_eq_landau_n_rt_rp_satz141a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.(l_imp_th3 (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_nis (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_weli (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x1 y1))) (λt:l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_rp_prod ksi eta).l_e_st_eq_landau_n_rt_rp_4141_t5 ksi eta x1 ux y1 uy (l_e_st_eq_landau_n_rt_ts x1 y1) t) : l_not (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_rp_prod ksi eta))).
-
-(* notion 2389 *)
-definition l_e_st_eq_landau_n_rt_4141_v0 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0) x0 : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2390 *)
-definition l_e_st_eq_landau_n_rt_4141_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_4141_v0 x0 y0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0)) x0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) x0 (l_e_st_eq_landau_n_rt_assts2 y0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0) x0) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0)) l_e_st_eq_landau_n_rt_1rt x0 (l_e_st_eq_landau_n_rt_satz110c l_e_st_eq_landau_n_rt_1rt y0)) (l_e_st_eq_landau_n_rt_example1c x0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_4141_v0 x0 y0)) x0).
-
-(* notion 2391 *)
-definition l_e_st_eq_landau_n_rt_satz141b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz110g x0 y0 (l_e_st_eq_landau_n_rt_4141_v0 x0 y0) (l_e_st_eq_landau_n_rt_4141_t6 x0 y0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0) x0) (l_e_st_eq_landau_n_rt_ov x0 y0)).
-
-(* notion 2392 *)
-definition l_e_st_eq_landau_n_rt_satz141c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0) x0) (l_e_st_eq_landau_n_rt_ov x0 y0) (l_e_st_eq_landau_n_rt_satz141b x0 y0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov x0 y0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0) x0)).
-
-(* notion 2393 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_isless2 u0 (l_e_st_eq_landau_n_rt_ts x0 y0) z0 j l : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 2394 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ts x0 y0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) y0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt y0) y0 (l_e_st_eq_landau_n_rt_assts2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0 y0) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) l_e_st_eq_landau_n_rt_1rt y0 (l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_example1c y0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ts x0 y0)) y0).
-
-(* notion 2395 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) z0) (l_e_st_eq_landau_n_rt_ov z0 x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ts x0 y0)) y0 (l_e_st_eq_landau_n_rt_satz141b z0 x0) (l_e_st_eq_landau_n_rt_rp_4141_t8 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_satz105f z0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_rp_4141_t7 ksi eta u0 i z0 l x0 lx y0 ly j)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ov z0 x0) y0).
-
-(* notion 2396 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_satz120 eta y0 ly (l_e_st_eq_landau_n_rt_ov z0 x0) (l_e_st_eq_landau_n_rt_rp_4141_t9 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_lrt eta (l_e_st_eq_landau_n_rt_ov z0 x0)).
-
-(* notion 2397 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_prod1 ksi eta z0 x0 lx (l_e_st_eq_landau_n_rt_ov z0 x0) (l_e_st_eq_landau_n_rt_rp_4141_t10 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_satz110d z0 x0) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
-
-(* notion 2398 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_rp_prodapp ksi eta u0 i (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4141_t11 ksi eta u0 i z0 l x t y u v) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
-
-(* notion 2399 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_rp_prod1 ksi eta (l_e_st_eq_landau_n_rt_ts x1 y0) x1 lx1 y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x1 y0)) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
-
-(* notion 2400 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_satz105a x1 x0 y0 (l_e_st_eq_landau_n_rt_satz83 x0 x1 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 2401 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_ismore2 (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 y0) j) (l_e_st_eq_landau_n_rt_rp_4141_t14 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x1 y0) z0).
-
-(* notion 2402 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_andi (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x1 y0) z0) (l_e_st_eq_landau_n_rt_rp_4141_t13 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) (l_e_st_eq_landau_n_rt_rp_4141_t15 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_and (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x1 y0) z0)).
-
-(* notion 2403 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_somei l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0)) (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_st_eq_landau_n_rt_rp_4141_t16 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
-
-(* notion 2404 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_cutapp3 ksi x0 lx (l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_less x0 x.l_e_st_eq_landau_n_rt_rp_4141_t17 ksi eta z0 i x0 lx y0 ly j x t u) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
-
-(* notion 2405 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).(l_e_st_eq_landau_n_rt_rp_prodapp ksi eta z0 i (l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4141_t18 ksi eta z0 i x t y u v) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
-
-(* notion 2406 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_prod ksi eta) (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_rp_prod1 ksi eta (l_e_st_eq_landau_n_rt_ts x0 y0) x0 lx y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 y0))) (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_rp_satz141a ksi eta x1 ux y1 uy) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_4141_t12 ksi eta x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_prod ksi eta).l_e_st_eq_landau_n_rt_rp_4141_t19 ksi eta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
-
-(* notion 2407 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.(l_e_st_eq_landau_n_rt_cutapp1b eta (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt eta y.l_e_st_eq_landau_n_rt_rp_4141_t20 ksi eta x0 lx y0 ly x1 ux y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
-
-(* notion 2408 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_cutapp1b ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.l_e_st_eq_landau_n_rt_rp_4141_t21 ksi eta x0 lx y0 ly x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
-
-(* notion 2409 *)
-definition l_e_st_eq_landau_n_rt_rp_4141_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_cutapp1a eta (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta y.l_e_st_eq_landau_n_rt_rp_4141_t22 ksi eta x0 lx y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
-
-(* notion 2410 *)
-definition l_e_st_eq_landau_n_rt_rp_satz141 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_cutapp1a ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_4141_t23 ksi eta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
-
-(* notion 2411 *)
-definition l_e_st_eq_landau_n_rt_rp_ts ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_prod ksi eta) (l_e_st_eq_landau_n_rt_rp_satz141 ksi eta) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2412 *)
-definition l_e_st_eq_landau_n_rt_rp_lrtts ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_prod ksi eta) (l_e_st_eq_landau_n_rt_rp_satz141 ksi eta) z0 (l_e_st_eq_landau_n_rt_rp_prod1 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0).
-
-(* notion 2413 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_isp1 l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_prod ksi eta))) (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_rt_rp_satz141a ksi eta x0 ux y0 uy) i : l_not (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta))).
-
-(* notion 2414 *)
-definition l_e_st_eq_landau_n_rt_rp_urtts ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_imp_th3 (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0) (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_rp_iii4_t10 ksi eta z0 x0 ux y0 uy i) (λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_prod ksi eta) (l_e_st_eq_landau_n_rt_rp_satz141 ksi eta) z0 t) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0).
-
-(* notion 2415 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.(l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_prod ksi eta) (l_e_st_eq_landau_n_rt_rp_satz141 ksi eta) z0 lz : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
-
-(* notion 2416 *)
-definition l_e_st_eq_landau_n_rt_rp_tsapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.(l_e_st_eq_landau_n_rt_rp_prodapp ksi eta z0 (l_e_st_eq_landau_n_rt_rp_iii4_t11 ksi eta z0 lz p p1) p p1 : p).
-
-(* notion 2417 *)
-definition l_e_st_eq_landau_n_rt_rp_ists1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ts u zeta) ksi eta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)).
-
-(* notion 2418 *)
-definition l_e_st_eq_landau_n_rt_rp_ists2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ts zeta u) ksi eta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta)).
-
-(* notion 2419 *)
-definition l_e_st_eq_landau_n_rt_rp_ists12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ists1 ksi eta zeta i) (l_e_st_eq_landau_n_rt_rp_ists2 zeta upsilon eta j) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2420 *)
-definition l_e_st_eq_landau_n_rt_rp_4142_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_tris l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0) i (l_e_st_eq_landau_n_rt_comts x0 y0) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts y0 x0)).
-
-(* notion 2421 *)
-definition l_e_st_eq_landau_n_rt_rp_4142_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtts eta ksi z0 y0 ly x0 lx (l_e_st_eq_landau_n_rt_rp_4142_t1 ksi eta z0 lz x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta ksi) z0).
-
-(* notion 2422 *)
-definition l_e_st_eq_landau_n_rt_rp_4142_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.(l_e_st_eq_landau_n_rt_rp_tsapp ksi eta z0 lz (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta ksi) z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4142_t2 ksi eta z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta ksi) z0).
-
-(* notion 2423 *)
-definition l_e_st_eq_landau_n_rt_rp_satz142 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) x.l_e_st_eq_landau_n_rt_rp_4142_t3 ksi eta x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta ksi) x.l_e_st_eq_landau_n_rt_rp_4142_t3 eta ksi x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta ksi)).
-
-(* notion 2424 *)
-definition l_e_st_eq_landau_n_rt_rp_comts ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz142 ksi eta : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta ksi)).
-
-(* notion 2425 *)
-definition l_e_st_eq_landau_n_rt_rp_4143_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ts v0 z0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)) i (l_e_st_eq_landau_n_rt_ists1 v0 (l_e_st_eq_landau_n_rt_ts x0 y0) z0 j) (l_e_st_eq_landau_n_rt_assts1 x0 y0 z0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0))).
-
-(* notion 2426 *)
-definition l_e_st_eq_landau_n_rt_rp_4143_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtts eta zeta (l_e_st_eq_landau_n_rt_ts y0 z0) y0 ly z0 lz (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts y0 z0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_ts y0 z0)).
-
-(* notion 2427 *)
-definition l_e_st_eq_landau_n_rt_rp_4143_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta) u0 x0 lx (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_rp_4143_t2 ksi eta zeta u0 lu v0 lv z0 lz i x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_rp_4143_t1 ksi eta zeta u0 lu v0 lv z0 lz i x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0).
-
-(* notion 2428 *)
-definition l_e_st_eq_landau_n_rt_rp_4143_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts v0 z0).(l_e_st_eq_landau_n_rt_rp_tsapp ksi eta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4143_t3 ksi eta zeta u0 lu v0 lv z0 lz i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0).
-
-(* notion 2429 *)
-definition l_e_st_eq_landau_n_rt_rp_4143_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0.(l_e_st_eq_landau_n_rt_rp_tsapp (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4143_t4 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0).
-
-(* notion 2430 *)
-definition l_e_st_eq_landau_n_rt_rp_4143_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ts x0 v0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) i (l_e_st_eq_landau_n_rt_ists2 v0 (l_e_st_eq_landau_n_rt_ts y0 z0) x0 j) (l_e_st_eq_landau_n_rt_assts2 x0 y0 z0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0)).
-
-(* notion 2431 *)
-definition l_e_st_eq_landau_n_rt_rp_4143_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi eta (l_e_st_eq_landau_n_rt_ts x0 y0) x0 lx y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 y0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 2432 *)
-definition l_e_st_eq_landau_n_rt_rp_4143_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta u0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_rp_4143_t7 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) z0 lz (l_e_st_eq_landau_n_rt_rp_4143_t6 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0).
-
-(* notion 2433 *)
-definition l_e_st_eq_landau_n_rt_rp_4143_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).(l_e_st_eq_landau_n_rt_rp_tsapp eta zeta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4143_t8 ksi eta zeta u0 lu x0 lx v0 lv i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0).
-
-(* notion 2434 *)
-definition l_e_st_eq_landau_n_rt_rp_4143_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0.(l_e_st_eq_landau_n_rt_rp_tsapp ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta) u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4143_t9 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0).
-
-(* notion 2435 *)
-definition l_e_st_eq_landau_n_rt_rp_satz143 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) x.l_e_st_eq_landau_n_rt_rp_4143_t5 ksi eta zeta x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) x.l_e_st_eq_landau_n_rt_rp_4143_t10 ksi eta zeta x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta))).
-
-(* notion 2436 *)
-definition l_e_st_eq_landau_n_rt_rp_assts1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz143 ksi eta zeta : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta))).
-
-(* notion 2437 *)
-definition l_e_st_eq_landau_n_rt_rp_assts2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_satz143 ksi eta zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta)).
-
-(* notion 2438 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ts x0 v0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0)) i (l_e_st_eq_landau_n_rt_ists2 v0 (l_e_st_eq_landau_n_rt_pl y0 z0) x0 j) (l_e_st_eq_landau_n_rt_disttp2 x0 y0 z0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0))).
-
-(* notion 2439 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi eta (l_e_st_eq_landau_n_rt_ts x0 y0) x0 lx y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 y0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 2440 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi zeta (l_e_st_eq_landau_n_rt_ts x0 z0) x0 lx z0 lz (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 z0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_ts x0 z0)).
-
-(* notion 2441 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtpl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) u0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_rp_4144_t2 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_rp_4144_t3 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) (l_e_st_eq_landau_n_rt_rp_4144_t1 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0).
-
-(* notion 2442 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).(l_e_st_eq_landau_n_rt_rp_plapp eta zeta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_4144_t4 ksi eta zeta u0 lu x0 lx v0 lv i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0).
-
-(* notion 2443 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.(l_e_st_eq_landau_n_rt_rp_tsapp ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta) u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4144_t5 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0).
-
-(* notion 2444 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_tris l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_pl v0 w0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x1 z0)) i (l_e_st_eq_landau_n_rt_ispl12 v0 (l_e_st_eq_landau_n_rt_ts x0 y0) w0 (l_e_st_eq_landau_n_rt_ts x1 z0) j k) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x1 z0))).
-
-(* notion 2445 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_x2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_ite (l_e_st_eq_landau_n_rt_moreis x0 x1) l_e_st_eq_landau_n_rt_rat x0 x1 : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2446 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λm:l_e_st_eq_landau_n_rt_moreis x0 x1.(l_e_itet (l_e_st_eq_landau_n_rt_moreis x0 x1) l_e_st_eq_landau_n_rt_rat x0 x1 m : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) x0).
-
-(* notion 2447 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λm:l_e_st_eq_landau_n_rt_moreis x0 x1.(l_e_isp1 l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt ksi t) x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) lx (l_e_st_eq_landau_n_rt_rp_4144_t8 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k m) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
-
-(* notion 2448 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λm:l_e_st_eq_landau_n_rt_moreis x0 x1.(l_e_st_eq_landau_n_rt_lessisi2 x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) x0 (l_e_st_eq_landau_n_rt_rp_4144_t8 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k m)) : l_e_st_eq_landau_n_rt_lessis x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
-
-(* notion 2449 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λm:l_e_st_eq_landau_n_rt_moreis x0 x1.(l_e_st_eq_landau_n_rt_satz88 x1 x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_satz84 x0 x1 m) (l_e_st_eq_landau_n_rt_rp_4144_t10 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k m) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
-
-(* notion 2450 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λn:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).(l_e_itef (l_e_st_eq_landau_n_rt_moreis x0 x1) l_e_st_eq_landau_n_rt_rat x0 x1 n : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) x1).
-
-(* notion 2451 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λn:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).(l_e_isp1 l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt ksi t) x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) lx1 (l_e_st_eq_landau_n_rt_rp_4144_t12 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k n) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
-
-(* notion 2452 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λn:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).(l_e_st_eq_landau_n_rt_lessisi2 x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) x1 (l_e_st_eq_landau_n_rt_rp_4144_t12 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k n)) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
-
-(* notion 2453 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λn:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).(l_e_st_eq_landau_n_rt_lessisi1 x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_satz87b x0 x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_satz81j x0 x1 n) (l_e_st_eq_landau_n_rt_rp_4144_t14 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k n)) : l_e_st_eq_landau_n_rt_lessis x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
-
-(* notion 2454 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_imp_th1 (l_e_st_eq_landau_n_rt_moreis x0 x1) (l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)) (λt:l_e_st_eq_landau_n_rt_moreis x0 x1.l_e_st_eq_landau_n_rt_rp_4144_t9 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) (λt:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).l_e_st_eq_landau_n_rt_rp_4144_t13 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
-
-(* notion 2455 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_imp_th1 (l_e_st_eq_landau_n_rt_moreis x0 x1) (l_e_st_eq_landau_n_rt_lessis x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)) (λt:l_e_st_eq_landau_n_rt_moreis x0 x1.l_e_st_eq_landau_n_rt_rp_4144_t10 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) (λt:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).l_e_st_eq_landau_n_rt_rp_4144_t15 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) : l_e_st_eq_landau_n_rt_lessis x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
-
-(* notion 2456 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_imp_th1 (l_e_st_eq_landau_n_rt_moreis x0 x1) (l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)) (λt:l_e_st_eq_landau_n_rt_moreis x0 x1.l_e_st_eq_landau_n_rt_rp_4144_t11 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) (λt:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).l_e_st_eq_landau_n_rt_rp_4144_t14 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
-
-(* notion 2457 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_st_eq_landau_n_rt_rp_lrtpl eta zeta (l_e_st_eq_landau_n_rt_pl y0 z0) y0 ly z0 lz (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y0 z0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)).
-
-(* notion 2458 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_rp_4144_t16 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_rp_4144_t19 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0))) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0))).
-
-(* notion 2459 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_st_eq_landau_n_rt_satz109a x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) y0 y0 (l_e_st_eq_landau_n_rt_rp_4144_t17 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_lessisi2 y0 y0 (l_e_refis l_e_st_eq_landau_n_rt_rat y0)) : l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) y0)).
-
-(* notion 2460 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_st_eq_landau_n_rt_satz109a x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) z0 z0 (l_e_st_eq_landau_n_rt_rp_4144_t18 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_lessisi2 z0 z0 (l_e_refis l_e_st_eq_landau_n_rt_rat z0)) : l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_ts x1 z0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) z0)).
-
-(* notion 2461 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_st_eq_landau_n_rt_islessis12 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x1 z0)) u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) y0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) z0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_symis l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x1 z0)) (l_e_st_eq_landau_n_rt_rp_4144_t7 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)) (l_e_st_eq_landau_n_rt_distpt2 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) y0 z0) (l_e_st_eq_landau_n_rt_satz100a (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) y0) (l_e_st_eq_landau_n_rt_ts x1 z0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) z0) (l_e_st_eq_landau_n_rt_rp_4144_t21 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_rp_4144_t22 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)) : l_e_st_eq_landau_n_rt_lessis u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0))).
-
-(* notion 2462 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_orapp (l_e_st_eq_landau_n_rt_less u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0))) (l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0))) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (l_e_st_eq_landau_n_rt_rp_4144_t23 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (λt:l_e_st_eq_landau_n_rt_less u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)).l_e_st_eq_landau_n_rt_rp_satz120 (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_rp_4144_t20 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) u0 t) (λt:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)).l_e_isp1 l_e_st_eq_landau_n_rt_rat (λu:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)) u0 (l_e_st_eq_landau_n_rt_rp_4144_t20 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) t) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
-
-(* notion 2463 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_tsapp ksi zeta w0 lw (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4144_t24 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
-
-(* notion 2464 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).(l_e_st_eq_landau_n_rt_rp_tsapp ksi eta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4144_t25 ksi eta zeta u0 lu v0 lv w0 lw i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
-
-(* notion 2465 *)
-definition l_e_st_eq_landau_n_rt_rp_4144_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.(l_e_st_eq_landau_n_rt_rp_plapp (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_4144_t26 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
-
-(* notion 2466 *)
-definition l_e_st_eq_landau_n_rt_rp_satz144 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) x.l_e_st_eq_landau_n_rt_rp_4144_t6 ksi eta zeta x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) x.l_e_st_eq_landau_n_rt_rp_4144_t27 ksi eta zeta x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta))).
-
-(* notion 2467 *)
-definition l_e_st_eq_landau_n_rt_rp_disttp1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta (l_e_st_eq_landau_n_rt_rp_pl ksi eta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_satz144 zeta ksi eta) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_comts zeta ksi) (l_e_st_eq_landau_n_rt_rp_comts zeta eta)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta))).
-
-(* notion 2468 *)
-definition l_e_st_eq_landau_n_rt_rp_disttp2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz144 ksi eta zeta : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta))).
-
-(* notion 2469 *)
-definition l_e_st_eq_landau_n_rt_rp_distpt1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_disttp1 ksi eta zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta)).
-
-(* notion 2470 *)
-definition l_e_st_eq_landau_n_rt_rp_distpt2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) (l_e_st_eq_landau_n_rt_rp_disttp2 ksi eta zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta))).
-
-(* notion 2471 *)
-definition l_e_st_eq_landau_n_rt_rp_4145_phi ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_mn ksi eta m : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2472 *)
-definition l_e_st_eq_landau_n_rt_rp_4145_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_satz140d ksi eta m : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m))).
-
-(* notion 2473 *)
-definition l_e_st_eq_landau_n_rt_rp_4145_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m)) zeta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta)) (l_e_st_eq_landau_n_rt_rp_ists1 ksi (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m)) zeta (l_e_st_eq_landau_n_rt_rp_4145_t1 ksi eta zeta m)) (l_e_st_eq_landau_n_rt_rp_disttp1 eta (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta))).
-
-(* notion 2474 *)
-definition l_e_st_eq_landau_n_rt_rp_satz145a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta)) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta)) (l_e_st_eq_landau_n_rt_rp_4145_t2 ksi eta zeta m)) (l_e_st_eq_landau_n_rt_rp_satz133 (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta)) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)).
-
-(* notion 2475 *)
-definition l_e_st_eq_landau_n_rt_rp_satz145b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ists1 ksi eta zeta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)).
-
-(* notion 2476 *)
-definition l_e_st_eq_landau_n_rt_rp_satz145c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz145a eta ksi zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)).
-
-(* notion 2477 *)
-definition l_e_st_eq_landau_n_rt_rp_satz145d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_comts ksi zeta) (l_e_st_eq_landau_n_rt_rp_comts eta zeta) (l_e_st_eq_landau_n_rt_rp_satz145a ksi eta zeta m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta)).
-
-(* notion 2478 *)
-definition l_e_st_eq_landau_n_rt_rp_satz145e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ists2 ksi eta zeta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta)).
-
-(* notion 2479 *)
-definition l_e_st_eq_landau_n_rt_rp_satz145f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_comts ksi zeta) (l_e_st_eq_landau_n_rt_rp_comts eta zeta) (l_e_st_eq_landau_n_rt_rp_satz145c ksi eta zeta l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta)).
-
-(* notion 2480 *)
-definition l_e_st_eq_landau_n_rt_rp_satz145g ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore2 (l_e_st_eq_landau_n_rt_rp_ts ksi upsilon) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ists1 ksi eta upsilon i) (l_e_st_eq_landau_n_rt_rp_satz145d zeta upsilon ksi m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2481 *)
-definition l_e_st_eq_landau_n_rt_rp_satz145h ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts upsilon eta) (l_e_st_eq_landau_n_rt_rp_comts ksi zeta) (l_e_st_eq_landau_n_rt_rp_comts eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz145g ksi eta zeta upsilon i m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts upsilon eta)).
-
-(* notion 2482 *)
-definition l_e_st_eq_landau_n_rt_rp_satz145j ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_ts ksi upsilon) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ists1 ksi eta upsilon i) (l_e_st_eq_landau_n_rt_rp_satz145f zeta upsilon ksi l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2483 *)
-definition l_e_st_eq_landau_n_rt_rp_satz145k ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts upsilon eta) (l_e_st_eq_landau_n_rt_rp_comts ksi zeta) (l_e_st_eq_landau_n_rt_rp_comts eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz145j ksi eta zeta upsilon i l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts upsilon eta)).
-
-(* notion 2484 *)
-definition l_e_st_eq_landau_n_rt_rp_4146_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz123a ksi eta : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
-
-(* notion 2485 *)
-definition l_e_st_eq_landau_n_rt_rp_4146_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) : l_ec3 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta))).
-
-(* notion 2486 *)
-definition l_e_st_eq_landau_n_rt_rp_satz146a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta).(l_ec3_th11 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_4146_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_4146_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz145b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz145a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz145c ksi eta zeta u) m : l_e_st_eq_landau_n_rt_rp_more ksi eta).
-
-(* notion 2487 *)
-definition l_e_st_eq_landau_n_rt_rp_satz146b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta).(l_ec3_th10 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_4146_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_4146_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz145b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz145a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz145c ksi eta zeta u) i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
-
-(* notion 2488 *)
-definition l_e_st_eq_landau_n_rt_rp_satz146c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta).(l_ec3_th12 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_4146_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_4146_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz145b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz145a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz145c ksi eta zeta u) l : l_e_st_eq_landau_n_rt_rp_less ksi eta).
-
-(* notion 2489 *)
-definition l_e_st_eq_landau_n_rt_rp_satz146d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta).(l_e_st_eq_landau_n_rt_rp_satz146a ksi eta zeta (l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_comts zeta ksi) (l_e_st_eq_landau_n_rt_rp_comts zeta eta) m) : l_e_st_eq_landau_n_rt_rp_more ksi eta).
-
-(* notion 2490 *)
-definition l_e_st_eq_landau_n_rt_rp_satz146e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta).(l_e_st_eq_landau_n_rt_rp_satz146b ksi eta zeta (l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_comts ksi zeta) i (l_e_st_eq_landau_n_rt_rp_comts zeta eta)) : l_e_st_eq_landau_n_rt_rp_is ksi eta).
-
-(* notion 2491 *)
-definition l_e_st_eq_landau_n_rt_rp_satz146f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta).(l_e_st_eq_landau_n_rt_rp_satz146c ksi eta zeta (l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_comts zeta ksi) (l_e_st_eq_landau_n_rt_rp_comts zeta eta) l) : l_e_st_eq_landau_n_rt_rp_less ksi eta).
-
-(* notion 2492 *)
-definition l_e_st_eq_landau_n_rt_rp_4147_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz145a ksi eta zeta m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)).
-
-(* notion 2493 *)
-definition l_e_st_eq_landau_n_rt_rp_4147_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts upsilon eta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_comts zeta eta) (l_e_st_eq_landau_n_rt_rp_comts upsilon eta) (l_e_st_eq_landau_n_rt_rp_satz145a zeta upsilon eta n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2494 *)
-definition l_e_st_eq_landau_n_rt_rp_satz147 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_trmore (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_4147_t1 ksi eta zeta upsilon m n) (l_e_st_eq_landau_n_rt_rp_4147_t2 ksi eta zeta upsilon m n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2495 *)
-definition l_e_st_eq_landau_n_rt_rp_satz147a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz147 eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz122 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2496 *)
-definition l_e_st_eq_landau_n_rt_rp_satz148a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)) m (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz147 ksi eta zeta upsilon t n) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz145g ksi eta zeta upsilon t n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2497 *)
-definition l_e_st_eq_landau_n_rt_rp_satz148b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more zeta upsilon) (l_e_st_eq_landau_n_rt_rp_is zeta upsilon) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)) n (λt:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.l_e_st_eq_landau_n_rt_rp_satz147 ksi eta zeta upsilon m t) (λt:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.l_e_st_eq_landau_n_rt_rp_satz145h zeta upsilon ksi eta t m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2498 *)
-definition l_e_st_eq_landau_n_rt_rp_satz148c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz148a eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz125 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz122 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2499 *)
-definition l_e_st_eq_landau_n_rt_rp_satz148d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz148b eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz125 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2500 *)
-definition l_e_st_eq_landau_n_rt_rp_4149_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ists12 ksi eta zeta upsilon i j) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2501 *)
-definition l_e_st_eq_landau_n_rt_rp_4149_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λo:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz148a ksi eta zeta upsilon m o) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2502 *)
-definition l_e_st_eq_landau_n_rt_rp_4149_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_orapp (l_e_st_eq_landau_n_rt_rp_more zeta upsilon) (l_e_st_eq_landau_n_rt_rp_is zeta upsilon) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)) n (λt:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.l_e_st_eq_landau_n_rt_rp_4149_t2 ksi eta zeta upsilon m n i t) (λt:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.l_e_st_eq_landau_n_rt_rp_4149_t1 ksi eta zeta upsilon m n i t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2503 *)
-definition l_e_st_eq_landau_n_rt_rp_4149_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λo:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz148b ksi eta zeta upsilon o n) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2504 *)
-definition l_e_st_eq_landau_n_rt_rp_satz149 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)) m (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_4149_t4 ksi eta zeta upsilon m n t) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_4149_t3 ksi eta zeta upsilon m n t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2505 *)
-definition l_e_st_eq_landau_n_rt_rp_satz149a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz124 (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz149 eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz125 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz125 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
-
-(* notion 2506 *)
-definition l_e_st_eq_landau_n_rt_ratset ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2507 *)
-definition l_e_st_eq_landau_n_rt_4150_t1 ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz90 r0 : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0)).
-
-(* notion 2508 *)
-definition l_e_st_eq_landau_n_rt_4150_t2 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 r0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0) x0 l : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0)).
-
-(* notion 2509 *)
-definition l_e_st_eq_landau_n_rt_4150_t3 ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_ec3e13 (l_e_st_eq_landau_n_rt_is r0 r0) (l_e_st_eq_landau_n_rt_more r0 r0) (l_e_st_eq_landau_n_rt_less r0 r0) (l_e_st_eq_landau_n_rt_satz81b r0 r0) (l_e_refis l_e_st_eq_landau_n_rt_rat r0) : l_not (l_e_st_eq_landau_n_rt_less r0 r0)).
-
-(* notion 2510 *)
-definition l_e_st_eq_landau_n_rt_4150_t4 ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_imp_th3 (l_e_st_eq_landau_n_rt_in r0 (l_e_st_eq_landau_n_rt_ratset r0)) (l_e_st_eq_landau_n_rt_less r0 r0) (l_e_st_eq_landau_n_rt_4150_t3 r0) (λt:l_e_st_eq_landau_n_rt_in r0 (l_e_st_eq_landau_n_rt_ratset r0).l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0) r0 t) : l_not (l_e_st_eq_landau_n_rt_in r0 (l_e_st_eq_landau_n_rt_ratset r0))).
-
-(* notion 2511 *)
-definition l_e_st_eq_landau_n_rt_4150_t5 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0) x0 i : l_e_st_eq_landau_n_rt_less x0 r0).
-
-(* notion 2512 *)
-definition l_e_st_eq_landau_n_rt_4150_t6 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).λx1:l_e_st_eq_landau_n_rt_rat.λk:l_e_st_eq_landau_n_rt_less x1 x0.(l_e_st_eq_landau_n_rt_4150_t2 r0 x1 (l_e_st_eq_landau_n_rt_trless x1 x0 r0 k (l_e_st_eq_landau_n_rt_4150_t5 r0 x0 i)) : l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_ratset r0)).
-
-(* notion 2513 *)
-definition l_e_st_eq_landau_n_rt_4150_t7 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).(l_e_st_eq_landau_n_rt_satz91 x0 r0 (l_e_st_eq_landau_n_rt_4150_t5 r0 x0 i) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 x) (l_e_st_eq_landau_n_rt_less x r0))).
-
-(* notion 2514 *)
-definition l_e_st_eq_landau_n_rt_4150_t8 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).λx1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x0 x1) (l_e_st_eq_landau_n_rt_less x1 r0).(l_ande1 (l_e_st_eq_landau_n_rt_less x0 x1) (l_e_st_eq_landau_n_rt_less x1 r0) a : l_e_st_eq_landau_n_rt_less x0 x1).
-
-(* notion 2515 *)
-definition l_e_st_eq_landau_n_rt_4150_t9 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).λx1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x0 x1) (l_e_st_eq_landau_n_rt_less x1 r0).(l_ande2 (l_e_st_eq_landau_n_rt_less x0 x1) (l_e_st_eq_landau_n_rt_less x1 r0) a : l_e_st_eq_landau_n_rt_less x1 r0).
-
-(* notion 2516 *)
-definition l_e_st_eq_landau_n_rt_4150_t10 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).λx1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x0 x1) (l_e_st_eq_landau_n_rt_less x1 r0).(l_andi (l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_ratset r0)) (l_e_st_eq_landau_n_rt_more x1 x0) (l_e_st_eq_landau_n_rt_4150_t2 r0 x1 (l_e_st_eq_landau_n_rt_4150_t9 r0 x0 i x1 a)) (l_e_st_eq_landau_n_rt_satz83 x0 x1 (l_e_st_eq_landau_n_rt_4150_t8 r0 x0 i x1 a)) : l_and (l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_ratset r0)) (l_e_st_eq_landau_n_rt_more x1 x0)).
-
-(* notion 2517 *)
-definition l_e_st_eq_landau_n_rt_4150_t11 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).(l_some_th6 l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 x) (l_e_st_eq_landau_n_rt_less x r0)) (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_ratset r0)) (l_e_st_eq_landau_n_rt_more x x0)) (l_e_st_eq_landau_n_rt_4150_t7 r0 x0 i) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_less x0 x) (l_e_st_eq_landau_n_rt_less x r0).l_e_st_eq_landau_n_rt_4150_t10 r0 x0 i x t) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_ratset r0)) (l_e_st_eq_landau_n_rt_more x x0))).
-
-(* notion 2518 *)
-definition l_e_st_eq_landau_n_rt_4150_t12 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 r0.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_ratset r0) x0 (l_e_st_eq_landau_n_rt_4150_t2 r0 x0 l) r0 (l_e_st_eq_landau_n_rt_4150_t4 r0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_ratset r0).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_4150_t6 r0 x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_ratset r0).l_e_st_eq_landau_n_rt_4150_t11 r0 x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_ratset r0)).
-
-(* notion 2519 *)
-definition l_e_st_eq_landau_n_rt_satz150 ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0) (l_e_st_eq_landau_n_rt_4150_t1 r0) (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_ratset r0)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_less x r0.l_e_st_eq_landau_n_rt_4150_t12 r0 x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_ratset r0)).
-
-(* notion 2520 *)
-definition l_e_st_eq_landau_n_rt_rp_rpofrt ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_ratset r0) (l_e_st_eq_landau_n_rt_satz150 r0) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2521 *)
-definition l_e_st_eq_landau_n_rt_rp_lrtrpofrt ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 r0.(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_ratset r0) (l_e_st_eq_landau_n_rt_satz150 r0) x0 (l_e_st_eq_landau_n_rt_4150_t2 r0 x0 l) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt r0) x0).
-
-(* notion 2522 *)
-definition l_e_st_eq_landau_n_rt_rp_lrtrpofrte ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt r0) x0.(l_e_st_eq_landau_n_rt_4150_t5 r0 x0 (l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_ratset r0) (l_e_st_eq_landau_n_rt_satz150 r0) x0 lx) : l_e_st_eq_landau_n_rt_less x0 r0).
-
-(* notion 2523 *)
-definition l_e_st_eq_landau_n_rt_rp_iii4_t12 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 r0.(l_e_st_eq_landau_n_rt_satz81c x0 r0 m : l_not (l_e_st_eq_landau_n_rt_less x0 r0)).
-
-(* notion 2524 *)
-definition l_e_st_eq_landau_n_rt_rp_urtrpofrt ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 r0.(l_imp_th3 (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt r0) x0) (l_e_st_eq_landau_n_rt_less x0 r0) (l_e_st_eq_landau_n_rt_rp_iii4_t12 r0 x0 m) (λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt r0) x0.l_e_st_eq_landau_n_rt_rp_lrtrpofrte r0 x0 t) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt r0) x0).
-
-(* notion 2525 *)
-definition l_e_st_eq_landau_n_rt_rp_1rp ≝ (l_e_st_eq_landau_n_rt_rp_rpofrt l_e_st_eq_landau_n_rt_1rt : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2526 *)
-definition l_e_st_eq_landau_n_rt_rp_4151_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrte l_e_st_eq_landau_n_rt_1rt y0 ly : l_e_st_eq_landau_n_rt_less y0 l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2527 *)
-definition l_e_st_eq_landau_n_rt_rp_4151_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0 (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 y0) i) (l_e_st_eq_landau_n_rt_example1a x0) (l_e_st_eq_landau_n_rt_satz105f y0 l_e_st_eq_landau_n_rt_1rt x0 (l_e_st_eq_landau_n_rt_rp_4151_t1 ksi z0 lz x0 lx y0 ly i)) : l_e_st_eq_landau_n_rt_less z0 x0).
-
-(* notion 2528 *)
-definition l_e_st_eq_landau_n_rt_rp_4151_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_satz120 ksi x0 lx z0 (l_e_st_eq_landau_n_rt_rp_4151_t2 ksi z0 lz x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_lrt ksi z0).
-
-(* notion 2529 *)
-definition l_e_st_eq_landau_n_rt_rp_4151_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) z0.(l_e_st_eq_landau_n_rt_rp_tsapp ksi l_e_st_eq_landau_n_rt_rp_1rp z0 lz (l_e_st_eq_landau_n_rt_lrt ksi z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4151_t3 ksi z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt ksi z0).
-
-(* notion 2530 *)
-definition l_e_st_eq_landau_n_rt_rp_4151_y1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x0 : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2531 *)
-definition l_e_st_eq_landau_n_rt_rp_4151_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x1) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l) (l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_satz105f x0 x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) l) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l) l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2532 *)
-definition l_e_st_eq_landau_n_rt_rp_4151_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_rp_lrtrpofrt l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l) (l_e_st_eq_landau_n_rt_rp_4151_t5 ksi x0 lx x1 lx1 l) : l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l)).
-
-(* notion 2533 *)
-definition l_e_st_eq_landau_n_rt_rp_4151_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) x0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) x0 (l_e_st_eq_landau_n_rt_assts2 x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x0) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) l_e_st_eq_landau_n_rt_1rt x0 (l_e_st_eq_landau_n_rt_satz110c l_e_st_eq_landau_n_rt_1rt x1)) (l_e_st_eq_landau_n_rt_example1c x0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l)) x0).
-
-(* notion 2534 *)
-definition l_e_st_eq_landau_n_rt_rp_4151_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_rp_lrtts ksi l_e_st_eq_landau_n_rt_rp_1rp x0 x1 lx1 (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l) (l_e_st_eq_landau_n_rt_rp_4151_t6 ksi x0 lx x1 lx1 l) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l)) x0 (l_e_st_eq_landau_n_rt_rp_4151_t7 ksi x0 lx x1 lx1 l)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) x0).
-
-(* notion 2535 *)
-definition l_e_st_eq_landau_n_rt_rp_4151_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_cutapp3 ksi x0 lx (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) x0) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi y.λu:l_e_st_eq_landau_n_rt_less x0 y.l_e_st_eq_landau_n_rt_rp_4151_t8 ksi x0 lx y t u) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) x0).
-
-(* notion 2536 *)
-definition l_e_st_eq_landau_n_rt_rp_satz151 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) ksi (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) x.l_e_st_eq_landau_n_rt_rp_4151_t4 ksi x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_4151_t9 ksi x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) ksi).
-
-(* notion 2537 *)
-definition l_e_st_eq_landau_n_rt_rp_satz151a ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) ksi (l_e_st_eq_landau_n_rt_rp_satz151 ksi) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp)).
-
-(* notion 2538 *)
-definition l_e_st_eq_landau_n_rt_rp_satz151b ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp ksi) (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) ksi (l_e_st_eq_landau_n_rt_rp_comts l_e_st_eq_landau_n_rt_rp_1rp ksi) (l_e_st_eq_landau_n_rt_rp_satz151 ksi) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp ksi) ksi).
-
-(* notion 2539 *)
-definition l_e_st_eq_landau_n_rt_rp_satz151c ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp ksi) ksi (l_e_st_eq_landau_n_rt_rp_satz151b ksi) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp ksi)).
-
-(* notion 2540 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_invprop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_less y0 x0) : Prop).
-
-(* notion 2541 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_invprop2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) : Prop).
-
-(* notion 2542 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_invprop ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x) : Prop).
-
-(* notion 2543 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_inv ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop ksi z) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2544 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_andi (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_less y0 x0) uy l : l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 y0).
-
-(* notion 2545 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x) y0 (l_e_st_eq_landau_n_rt_rp_4152_t1 ksi z0 x0 ux y0 uy l i) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)).
-
-(* notion 2546 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_and3i (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) ux (l_e_st_eq_landau_n_rt_rp_4152_t2 ksi z0 x0 ux y0 uy l i) i : l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0).
-
-(* notion 2547 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x) x0 (l_e_st_eq_landau_n_rt_rp_4152_t3 ksi z0 x0 ux y0 uy l i) : l_e_st_eq_landau_n_rt_rp_4152_invprop ksi z0).
-
-(* notion 2548 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_inv1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop ksi z) z0 (l_e_st_eq_landau_n_rt_rp_4152_t4 ksi z0 x0 ux y0 uy l i) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
-
-(* notion 2549 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop ksi x) z0 i : l_e_st_eq_landau_n_rt_rp_4152_invprop ksi z0).
-
-(* notion 2550 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.(l_and3e1 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) px : l_e_st_eq_landau_n_rt_urt ksi x0).
-
-(* notion 2551 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.(l_and3e2 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) px : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)).
-
-(* notion 2552 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.(l_and3e3 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) px : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)).
-
-(* notion 2553 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 y0.(l_ande1 (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_less y0 x0) py : l_e_st_eq_landau_n_rt_urt ksi y0).
-
-(* notion 2554 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 y0.(l_ande2 (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_less y0 x0) py : l_e_st_eq_landau_n_rt_less y0 x0).
-
-(* notion 2555 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 y0.(p1 x0 (l_e_st_eq_landau_n_rt_rp_4152_t6 ksi z0 i p p1 x0 px) y0 (l_e_st_eq_landau_n_rt_rp_4152_t9 ksi z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_4152_t10 ksi z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_4152_t8 ksi z0 i p p1 x0 px) : p).
-
-(* notion 2556 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x) (l_e_st_eq_landau_n_rt_rp_4152_t7 ksi z0 i p p1 x0 px) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x.l_e_st_eq_landau_n_rt_rp_4152_t11 ksi z0 i p p1 x0 px x t) : p).
-
-(* notion 2557 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_invapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x) (l_e_st_eq_landau_n_rt_rp_4152_t5 ksi z0 i p p1) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x.l_e_st_eq_landau_n_rt_rp_4152_t12 ksi z0 i p p1 x t) : p).
-
-(* notion 2558 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_2x0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_pl x0 x0 : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2559 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_satz94a x0 x0 : l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux)).
-
-(* notion 2560 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_rp_satz119a ksi x0 ux (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux) (l_e_st_eq_landau_n_rt_rp_4152_t13 ksi x0 ux) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux)).
-
-(* notion 2561 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_rp_4152_inv1 ksi (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux)) (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux) (l_e_st_eq_landau_n_rt_rp_4152_t14 ksi x0 ux) x0 ux (l_e_st_eq_landau_n_rt_rp_4152_t13 ksi x0 ux) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux))) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux)) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
-
-(* notion 2562 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_is x0 x1) (l_e_st_eq_landau_n_rt_lrt ksi x0) ux (λt:l_e_st_eq_landau_n_rt_is x0 x1.l_e_isp1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt ksi x) x1 x0 lx t) : l_e_st_eq_landau_n_rt_nis x0 x1).
-
-(* notion 2563 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt x0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2564 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt x1 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x1) l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2565 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x1) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x1) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x1 i) (l_e_st_eq_landau_n_rt_rp_4152_t18 ksi x1 lx x0 ux) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x1) l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2566 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_st_eq_landau_n_rt_satz110b l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0 x1 (l_e_st_eq_landau_n_rt_rp_4152_t17 ksi x1 lx x0 ux) (l_e_st_eq_landau_n_rt_rp_4152_t19 ksi x1 lx x0 ux i) : l_e_st_eq_landau_n_rt_is x0 x1).
-
-(* notion 2567 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) (l_e_st_eq_landau_n_rt_is x0 x1) (l_e_st_eq_landau_n_rt_rp_4152_t16 ksi x1 lx x0 ux) (λt:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).l_e_st_eq_landau_n_rt_rp_4152_t20 ksi x1 lx x0 ux t) : l_e_st_eq_landau_n_rt_nis (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)).
-
-(* notion 2568 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λi:l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).(l_e_st_eq_landau_n_rt_rp_4152_invapp ksi (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) i l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_less y x.λw:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).l_e_st_eq_landau_n_rt_rp_4152_t21 ksi x1 lx x t (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x) w)) : l_con).
-
-(* notion 2569 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.(λt:l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).l_e_st_eq_landau_n_rt_rp_4152_t22 ksi x1 lx t : l_not (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi))).
-
-(* notion 2570 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_isless2 z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) u0 j l : l_e_st_eq_landau_n_rt_less u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)).
-
-(* notion 2571 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)) (l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_satz110d l_e_st_eq_landau_n_rt_1rt u0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) (l_e_st_eq_landau_n_rt_ts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0))).
-
-(* notion 2572 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) (l_e_st_eq_landau_n_rt_ts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)) (l_e_st_eq_landau_n_rt_ts u0 x0) (l_e_st_eq_landau_n_rt_rp_4152_t25 ksi z0 i u0 l x0 ux j) (l_e_st_eq_landau_n_rt_satz105c u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0 (l_e_st_eq_landau_n_rt_rp_4152_t24 ksi z0 i u0 l x0 ux j)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts u0 x0) (l_e_st_eq_landau_n_rt_ts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0))).
-
-(* notion 2573 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts u0 x0) (l_e_st_eq_landau_n_rt_ts x0 u0) (l_e_st_eq_landau_n_rt_ts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0) (l_e_st_eq_landau_n_rt_comts u0 x0) (l_e_st_eq_landau_n_rt_comts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)) (l_e_st_eq_landau_n_rt_rp_4152_t26 ksi z0 i u0 l x0 ux j) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 u0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0)).
-
-(* notion 2574 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t28 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_satz106c x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0 (l_e_st_eq_landau_n_rt_rp_4152_t27 ksi z0 i u0 l x0 ux j) : l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)).
-
-(* notion 2575 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t29 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_rp_satz119a ksi x0 ux (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_rp_4152_t28 ksi z0 i u0 l x0 ux j) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)).
-
-(* notion 2576 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t30 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt u0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0) l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2577 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t31 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_satz110g l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0 (l_e_st_eq_landau_n_rt_rp_4152_t30 ksi z0 i u0 l x0 ux j) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0))).
-
-(* notion 2578 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t32 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_rp_4152_inv1 ksi u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_rp_4152_t29 ksi z0 i u0 l x0 ux j) x0 ux (l_e_st_eq_landau_n_rt_rp_4152_t28 ksi z0 i u0 l x0 ux j) (l_e_st_eq_landau_n_rt_rp_4152_t31 ksi z0 i u0 l x0 ux j) : l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
-
-(* notion 2579 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t33 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.(l_e_st_eq_landau_n_rt_rp_4152_invapp ksi z0 i (l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_less y x.λw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).l_e_st_eq_landau_n_rt_rp_4152_t32 ksi z0 i u0 l x t w) : l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
-
-(* notion 2580 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t34 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_satz91 x1 x0 l : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x1 x) (l_e_st_eq_landau_n_rt_less x x0))).
-
-(* notion 2581 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t35 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_ande1 (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0) a : l_e_st_eq_landau_n_rt_less x1 x2).
-
-(* notion 2582 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t36 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_rp_satz119a ksi x1 ux1 x2 (l_e_st_eq_landau_n_rt_rp_4152_t35 ksi z0 i x0 ux x1 ux1 l j x2 a) : l_e_st_eq_landau_n_rt_urt ksi x2).
-
-(* notion 2583 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t37 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_rp_4152_inv1 ksi (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) x2 (l_e_st_eq_landau_n_rt_rp_4152_t36 ksi z0 i x0 ux x1 ux1 l j x2 a) x1 ux1 (l_e_st_eq_landau_n_rt_rp_4152_t35 ksi z0 i x0 ux x1 ux1 l j x2 a) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
-
-(* notion 2584 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t38 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_ande2 (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0) a : l_e_st_eq_landau_n_rt_less x2 x0).
-
-(* notion 2585 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t39 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)) (l_e_st_eq_landau_n_rt_satz110c l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_satz110d l_e_st_eq_landau_n_rt_1rt x2) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2))).
-
-(* notion 2586 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t40 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)) (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_rp_4152_t39 ksi z0 i x0 ux x1 ux1 l j x2 a) (l_e_st_eq_landau_n_rt_satz105c x2 x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_rp_4152_t38 ksi z0 i x0 ux x1 ux1 l j x2 a)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2))).
-
-(* notion 2587 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t41 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x2) (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) x2) (l_e_st_eq_landau_n_rt_comts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_comts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)) (l_e_st_eq_landau_n_rt_rp_4152_t40 ksi z0 i x0 ux x1 ux1 l j x2 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x2) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) x2)).
-
-(* notion 2588 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t42 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_satz106c (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) x2 (l_e_st_eq_landau_n_rt_rp_4152_t41 ksi z0 i x0 ux x1 ux1 l j x2 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)).
-
-(* notion 2589 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t43 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_ismore2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) j) (l_e_st_eq_landau_n_rt_satz83 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_st_eq_landau_n_rt_rp_4152_t42 ksi z0 i x0 ux x1 ux1 l j x2 a)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) z0).
-
-(* notion 2590 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t44 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_andi (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) z0) (l_e_st_eq_landau_n_rt_rp_4152_t37 ksi z0 i x0 ux x1 ux1 l j x2 a) (l_e_st_eq_landau_n_rt_rp_4152_t43 ksi z0 i x0 ux x1 ux1 l j x2 a) : l_and (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) z0)).
-
-(* notion 2591 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t45 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0)) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_st_eq_landau_n_rt_rp_4152_t44 ksi z0 i x0 ux x1 ux1 l j x2 a) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0))).
-
-(* notion 2592 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t46 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x1 x) (l_e_st_eq_landau_n_rt_less x x0)) (l_e_st_eq_landau_n_rt_rp_4152_t34 ksi z0 i x0 ux x1 ux1 l j) (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_less x1 x) (l_e_st_eq_landau_n_rt_less x x0).l_e_st_eq_landau_n_rt_rp_4152_t45 ksi z0 i x0 ux x1 ux1 l j x t) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0))).
-
-(* notion 2593 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t47 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).(l_e_st_eq_landau_n_rt_rp_4152_invapp ksi z0 i (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_less y x.λw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).l_e_st_eq_landau_n_rt_rp_4152_t46 ksi z0 i x t y u v w) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0))).
-
-(* notion 2594 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t48 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl y0 y0)) (l_e_st_eq_landau_n_rt_rp_4152_t15 ksi y0 uy) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_rp_4152_t23 ksi x0 lx) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_4152_t33 ksi x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).l_e_st_eq_landau_n_rt_rp_4152_t47 ksi x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
-
-(* notion 2595 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t49 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_cutapp1b ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.l_e_st_eq_landau_n_rt_rp_4152_t48 ksi x0 lx x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
-
-(* notion 2596 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t50 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_cutapp1a ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_4152_t49 ksi x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
-
-(* notion 2597 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_chi ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_4152_inv ksi) (l_e_st_eq_landau_n_rt_rp_4152_t50 ksi) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2598 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t51 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_tris l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 u0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) i (l_e_st_eq_landau_n_rt_ists2 u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x0 j) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1))).
-
-(* notion 2599 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t52 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx x1 ux : l_e_st_eq_landau_n_rt_less x0 x1).
-
-(* notion 2600 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t53 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) z0 (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) l_e_st_eq_landau_n_rt_1rt (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) (l_e_st_eq_landau_n_rt_rp_4152_t51 ksi z0 lz x0 lx u0 lu i x1 ux j)) (l_e_st_eq_landau_n_rt_satz110c l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_satz105c x0 x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_rp_4152_t52 ksi z0 lz x0 lx u0 lu i x1 ux j)) : l_e_st_eq_landau_n_rt_less z0 l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2601 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t54 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_st_eq_landau_n_rt_rp_lrtrpofrt l_e_st_eq_landau_n_rt_1rt z0 (l_e_st_eq_landau_n_rt_rp_4152_t53 ksi z0 lz x0 lx u0 lu i x1 ux j) : l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp z0).
-
-(* notion 2602 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_r1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).(l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_4152_inv ksi) (l_e_st_eq_landau_n_rt_rp_4152_t50 ksi) u0 lu : l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
-
-(* notion 2603 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_r2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).(l_e_st_eq_landau_n_rt_rp_4152_invapp ksi u0 (l_e_st_eq_landau_n_rt_rp_4152_r1 ksi z0 lz x0 lx u0 lu i) (l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_less y x.λw:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).l_e_st_eq_landau_n_rt_rp_4152_t54 ksi z0 lz x0 lx u0 lu i x t w) : l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp z0).
-
-(* notion 2604 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_r3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.(l_e_st_eq_landau_n_rt_rp_tsapp ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) z0 lz (l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4152_r2 ksi z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp z0).
-
-(* notion 2605 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t55 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrte l_e_st_eq_landau_n_rt_1rt u0 lu : l_e_st_eq_landau_n_rt_less u0 l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2606 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t56 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.(l_e_st_eq_landau_n_rt_satz83 u0 l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4152_t55 ksi u0 lu) : l_e_st_eq_landau_n_rt_more l_e_st_eq_landau_n_rt_1rt u0).
-
-(* notion 2607 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t57 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.(l_e_st_eq_landau_n_rt_cutapp2b ksi x1 lx1 x2 ux2 : l_e_st_eq_landau_n_rt_more x2 x1).
-
-(* notion 2608 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t58 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx x2 ux2 : l_e_st_eq_landau_n_rt_less x0 x2).
-
-(* notion 2609 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t59 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_satz105f x0 x2 (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) (l_e_st_eq_landau_n_rt_rp_4152_t58 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2)).
-
-(* notion 2610 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t60 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0) (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0) i) (l_e_st_eq_landau_n_rt_rp_4152_t59 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2)).
-
-(* notion 2611 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t61 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_tr4is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) u0) x2) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x2) x2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1) (l_e_st_eq_landau_n_rt_distpt1 (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) u0 x2) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) u0) l_e_st_eq_landau_n_rt_1rt x2 (l_e_st_eq_landau_n_rt_satz101e l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu))) (l_e_st_eq_landau_n_rt_example1c x2) (l_e_st_eq_landau_n_rt_satz101f x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1)).
-
-(* notion 2612 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t62 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_satz96c (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_st_eq_landau_n_rt_ts u0 x2) (l_e_st_eq_landau_n_rt_rp_4152_t60 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_st_eq_landau_n_rt_ts u0 x2))).
-
-(* notion 2613 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t63 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_rp_4152_t61 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) (l_e_st_eq_landau_n_rt_rp_4152_t62 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1)).
-
-(* notion 2614 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t64 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts u0 x2) (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1) (l_e_st_eq_landau_n_rt_pl x1 (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2))) (l_e_st_eq_landau_n_rt_compl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_compl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1) (l_e_st_eq_landau_n_rt_rp_4152_t63 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts u0 x2) (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2))) (l_e_st_eq_landau_n_rt_pl x1 (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)))).
-
-(* notion 2615 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t65 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_satz97c (l_e_st_eq_landau_n_rt_ts u0 x2) x1 (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_rp_4152_t64 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts u0 x2) x1).
-
-(* notion 2616 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t66 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0) x2) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x2) x2 (l_e_st_eq_landau_n_rt_assts2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0 x2) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0) l_e_st_eq_landau_n_rt_1rt x2 (l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt u0)) (l_e_st_eq_landau_n_rt_example1c x2) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_ts u0 x2)) x2).
-
-(* notion 2617 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t67 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_ts u0 x2)) x2 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) x1) (l_e_st_eq_landau_n_rt_ov x1 u0) (l_e_st_eq_landau_n_rt_rp_4152_t66 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) (l_e_st_eq_landau_n_rt_satz141b x1 u0) (l_e_st_eq_landau_n_rt_satz105f (l_e_st_eq_landau_n_rt_ts u0 x2) x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_rp_4152_t65 ksi u0 lu x0 lx x1 lx1 x2 ux2 i)) : l_e_st_eq_landau_n_rt_less x2 (l_e_st_eq_landau_n_rt_ov x1 u0)).
-
-(* notion 2618 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t68 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_rp_satz119a ksi x2 ux2 (l_e_st_eq_landau_n_rt_ov x1 u0) (l_e_st_eq_landau_n_rt_rp_4152_t67 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_ov x1 u0)).
-
-(* notion 2619 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t69 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_satz110e x1 u0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x1 u0) u0) x1).
-
-(* notion 2620 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t70 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ov x1 (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) x1) (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0))) (l_e_st_eq_landau_n_rt_satz110g x1 (l_e_st_eq_landau_n_rt_ov x1 u0) u0 (l_e_st_eq_landau_n_rt_rp_4152_t69 ksi u0 lu x0 lx x1 lx1 x2 ux2 i)) (l_e_st_eq_landau_n_rt_satz141c x1 (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_comts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) x1) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)))).
-
-(* notion 2621 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t71 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_rp_4152_inv1 ksi (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_ov x1 u0) (l_e_st_eq_landau_n_rt_rp_4152_t68 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) x2 ux2 (l_e_st_eq_landau_n_rt_rp_4152_t67 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0))) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
-
-(* notion 2622 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t72 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_4152_inv ksi) (l_e_st_eq_landau_n_rt_rp_4152_t50 ksi) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_rp_4152_t71 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0))).
-
-(* notion 2623 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t73 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0 x1 lx1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_rp_4152_t72 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) (l_e_st_eq_landau_n_rt_rp_4152_t70 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) u0).
-
-(* notion 2624 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t74 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_rp_satz132app ksi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) u0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).l_e_st_eq_landau_n_rt_rp_4152_t73 ksi u0 lu x0 lx x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) u0).
-
-(* notion 2625 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t75 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.(l_e_st_eq_landau_n_rt_cutapp1a ksi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_4152_t74 ksi u0 lu x t) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) u0).
-
-(* notion 2626 *)
-definition l_e_st_eq_landau_n_rt_rp_4152_t76 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) l_e_st_eq_landau_n_rt_rp_1rp (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) x.l_e_st_eq_landau_n_rt_rp_4152_r3 ksi x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp x.l_e_st_eq_landau_n_rt_rp_4152_t75 ksi x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) l_e_st_eq_landau_n_rt_rp_1rp).
-
-(* notion 2627 *)
-definition l_e_st_eq_landau_n_rt_rp_satz152 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_somei l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi t) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) (l_e_st_eq_landau_n_rt_rp_4152_t76 ksi) : l_e_st_eq_landau_n_rt_rp_some (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi c) l_e_st_eq_landau_n_rt_rp_1rp)).
-
-(* notion 2628 *)
-definition l_e_st_eq_landau_n_rt_rp_4153_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more phi psi.(l_e_st_eq_landau_n_rt_rp_satz145d phi psi eta m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)).
-
-(* notion 2629 *)
-definition l_e_st_eq_landau_n_rt_rp_4153_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more phi psi.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_4153_t1 ksi eta phi psi m) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)).
-
-(* notion 2630 *)
-definition l_e_st_eq_landau_n_rt_rp_4153_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less phi psi.(l_e_st_eq_landau_n_rt_rp_satz145f phi psi eta l : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)).
-
-(* notion 2631 *)
-definition l_e_st_eq_landau_n_rt_rp_4153_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less phi psi.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_4153_t3 ksi eta phi psi l) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)).
-
-(* notion 2632 *)
-definition l_e_st_eq_landau_n_rt_rp_4153_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis phi psi.(l_or3_th1 (l_e_st_eq_landau_n_rt_rp_is phi psi) (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi) (l_e_st_eq_landau_n_rt_rp_satz123a phi psi) n : l_or (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi)).
-
-(* notion 2633 *)
-definition l_e_st_eq_landau_n_rt_rp_4153_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis phi psi.(l_orapp (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi) (l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_4153_t5 ksi eta phi psi n) (λt:l_e_st_eq_landau_n_rt_rp_more phi psi.l_e_st_eq_landau_n_rt_rp_4153_t2 ksi eta phi psi t) (λt:l_e_st_eq_landau_n_rt_rp_less phi psi.l_e_st_eq_landau_n_rt_rp_4153_t4 ksi eta phi psi t) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)).
-
-(* notion 2634 *)
-definition l_e_st_eq_landau_n_rt_rp_satz153b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta phi) ksi.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta psi) ksi.(l_imp_th7 (l_e_st_eq_landau_n_rt_rp_is phi psi) (l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_weli (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi) ksi i j)) (λt:l_e_st_eq_landau_n_rt_rp_nis phi psi.l_e_st_eq_landau_n_rt_rp_4153_t6 ksi eta phi psi t) : l_e_st_eq_landau_n_rt_rp_is phi psi).
-
-(* notion 2635 *)
-definition l_e_st_eq_landau_n_rt_rp_4153_chi ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λtau:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta tau) l_e_st_eq_landau_n_rt_rp_1rp.(l_e_st_eq_landau_n_rt_rp_ts tau ksi : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2636 *)
-definition l_e_st_eq_landau_n_rt_rp_4153_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λtau:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta tau) l_e_st_eq_landau_n_rt_rp_1rp.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_4153_chi ksi eta tau i)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts eta tau) ksi) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp ksi) ksi (l_e_st_eq_landau_n_rt_rp_assts2 eta tau ksi) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_ts eta tau) l_e_st_eq_landau_n_rt_rp_1rp ksi i) (l_e_st_eq_landau_n_rt_rp_satz151b ksi) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_4153_chi ksi eta tau i)) ksi).
-
-(* notion 2637 *)
-definition l_e_st_eq_landau_n_rt_rp_4153_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λtau:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta tau) l_e_st_eq_landau_n_rt_rp_1rp.(l_somei l_e_st_eq_landau_n_rt_cut (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi) (l_e_st_eq_landau_n_rt_rp_4153_chi ksi eta tau i) (l_e_st_eq_landau_n_rt_rp_4153_t7 ksi eta tau i) : l_e_st_eq_landau_n_rt_rp_some (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi)).
-
-(* notion 2638 *)
-definition l_e_st_eq_landau_n_rt_rp_satz153a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_someapp l_e_st_eq_landau_n_rt_cut (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_satz152 eta) (l_e_st_eq_landau_n_rt_rp_some (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi)) (λc:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) l_e_st_eq_landau_n_rt_rp_1rp.l_e_st_eq_landau_n_rt_rp_4153_t8 ksi eta c t) : l_e_st_eq_landau_n_rt_rp_some (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi)).
-
-(* notion 2639 *)
-definition l_e_st_eq_landau_n_rt_rp_4153_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(λc:l_e_st_eq_landau_n_rt_cut.λd:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi.λu:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta d) ksi.l_e_st_eq_landau_n_rt_rp_satz153b ksi eta c d t u : l_e_amone l_e_st_eq_landau_n_rt_cut (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi)).
-
-(* notion 2640 *)
-definition l_e_st_eq_landau_n_rt_rp_satz153 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_onei l_e_st_eq_landau_n_rt_cut (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi) (l_e_st_eq_landau_n_rt_rp_4153_t9 ksi eta) (l_e_st_eq_landau_n_rt_rp_satz153a ksi eta) : l_e_st_eq_landau_n_rt_rp_one (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi)).
-
-(* notion 2641 *)
-definition l_e_st_eq_landau_n_rt_rp_ov ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_ind l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta a) ksi) (l_e_st_eq_landau_n_rt_rp_satz153 ksi eta) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2642 *)
-definition l_e_st_eq_landau_n_rt_rp_satz153c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_oneax l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta a) ksi) (l_e_st_eq_landau_n_rt_rp_satz153 ksi eta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_ov ksi eta)) ksi).
-
-(* notion 2643 *)
-definition l_e_st_eq_landau_n_rt_rp_satz153d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_ov ksi eta)) ksi (l_e_st_eq_landau_n_rt_rp_satz153c ksi eta) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_ov ksi eta))).
-
-(* notion 2644 *)
-definition l_e_st_eq_landau_n_rt_rp_satz153e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ov ksi eta) eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_ov ksi eta)) ksi (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_ov ksi eta) eta) (l_e_st_eq_landau_n_rt_rp_satz153c ksi eta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ov ksi eta) eta) ksi).
-
-(* notion 2645 *)
-definition l_e_st_eq_landau_n_rt_rp_satz153f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ov ksi eta) eta) ksi (l_e_st_eq_landau_n_rt_rp_satz153e ksi eta) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ov ksi eta) eta)).
-
-(* notion 2646 *)
-definition l_e_st_eq_landau_n_rt_rp_satz153g ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta phi) ksi.(l_e_st_eq_landau_n_rt_rp_satz153b ksi eta phi (l_e_st_eq_landau_n_rt_rp_ov ksi eta) i (l_e_st_eq_landau_n_rt_rp_satz153c ksi eta) : l_e_st_eq_landau_n_rt_rp_is phi (l_e_st_eq_landau_n_rt_rp_ov ksi eta)).
-
-(* notion 2647 *)
-definition l_e_st_eq_landau_n_rt_rp_ratrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_image l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi : Prop).
-
-(* notion 2648 *)
-definition l_e_st_eq_landau_n_rt_rp_ratrpi ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_imagei l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) x0 : l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).
-
-(* notion 2649 *)
-definition l_e_st_eq_landau_n_rt_rp_rpofnt ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rtofn x) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2650 *)
-definition l_e_st_eq_landau_n_rt_rp_natrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) ksi : Prop).
-
-(* notion 2651 *)
-definition l_e_st_eq_landau_n_rt_rp_natrpi ≝ λx:l_e_st_eq_landau_n_nat.(l_e_imagei l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt y) x : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofnt x)).
-
-(* notion 2652 *)
-definition l_e_st_eq_landau_n_rt_rp_iii5_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp ksi.λx:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofnt x).(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofrt y)) (l_e_st_eq_landau_n_rt_rtofn x) i : l_e_st_eq_landau_n_rt_rp_ratrp ksi).
-
-(* notion 2653 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmaiii5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_someapp l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofnt x)) n (l_e_st_eq_landau_n_rt_rp_ratrp ksi) (λx:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofnt x).l_e_st_eq_landau_n_rt_rp_iii5_t1 ksi n x t) : l_e_st_eq_landau_n_rt_rp_ratrp ksi).
-
-(* notion 2654 *)
-definition l_e_st_eq_landau_n_rt_rp_5154_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrt x0 y0 (l_e_st_eq_landau_n_rt_satz82 x0 y0 m) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0).
-
-(* notion 2655 *)
-definition l_e_st_eq_landau_n_rt_rp_5154_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_rp_urtrpofrt y0 y0 (l_e_st_eq_landau_n_rt_moreisi2 y0 y0 (l_e_refis l_e_st_eq_landau_n_rt_rat y0)) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) y0).
-
-(* notion 2656 *)
-definition l_e_st_eq_landau_n_rt_rp_5154_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_andi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) y0) (l_e_st_eq_landau_n_rt_rp_5154_t1 x0 y0 m) (l_e_st_eq_landau_n_rt_rp_5154_t2 x0 y0 m) : l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) y0)).
-
-(* notion 2657 *)
-definition l_e_st_eq_landau_n_rt_rp_satz154a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) x) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) x)) y0 (l_e_st_eq_landau_n_rt_rp_5154_t3 x0 y0 m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
-
-(* notion 2658 *)
-definition l_e_st_eq_landau_n_rt_rp_satz154b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) x0 y0 i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
-
-(* notion 2659 *)
-definition l_e_st_eq_landau_n_rt_rp_satz154c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_satz154a y0 x0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
-
-(* notion 2660 *)
-definition l_e_st_eq_landau_n_rt_rp_5154_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz81a x0 y0 : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
-
-(* notion 2661 *)
-definition l_e_st_eq_landau_n_rt_rp_5154_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) : l_ec3 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
-
-(* notion 2662 *)
-definition l_e_st_eq_landau_n_rt_rp_satz154d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_ec3_th11 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_5154_t4 x0 y0) (l_e_st_eq_landau_n_rt_rp_5154_t5 x0 y0) (λu:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_rp_satz154b x0 y0 u) (λu:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_rp_satz154a x0 y0 u) (λu:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_rp_satz154c x0 y0 u) m : l_e_st_eq_landau_n_rt_more x0 y0).
-
-(* notion 2663 *)
-definition l_e_st_eq_landau_n_rt_rp_satz154e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_ec3_th10 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_5154_t4 x0 y0) (l_e_st_eq_landau_n_rt_rp_5154_t5 x0 y0) (λu:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_rp_satz154b x0 y0 u) (λu:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_rp_satz154a x0 y0 u) (λu:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_rp_satz154c x0 y0 u) i : l_e_st_eq_landau_n_rt_is x0 y0).
-
-(* notion 2664 *)
-definition l_e_st_eq_landau_n_rt_rp_satz154f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_ec3_th12 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_5154_t4 x0 y0) (l_e_st_eq_landau_n_rt_rp_5154_t5 x0 y0) (λu:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_rp_satz154b x0 y0 u) (λu:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_rp_satz154a x0 y0 u) (λu:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_rp_satz154c x0 y0 u) l : l_e_st_eq_landau_n_rt_less x0 y0).
-
-(* notion 2665 *)
-definition l_e_st_eq_landau_n_rt_rp_iii5_t2 ≝ (λx:l_e_st_eq_landau_n_rt_rat.λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt y).l_e_st_eq_landau_n_rt_rp_satz154e x y t : l_e_injective l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x)).
-
-(* notion 2666 *)
-definition l_e_st_eq_landau_n_rt_rp_isrterp ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_rp_satz154b x0 y0 i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
-
-(* notion 2667 *)
-definition l_e_st_eq_landau_n_rt_rp_isrtirp ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_st_eq_landau_n_rt_rp_satz154e x0 y0 i : l_e_st_eq_landau_n_rt_is x0 y0).
-
-(* notion 2668 *)
-definition l_e_st_eq_landau_n_rt_rp_rtofrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_soft l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 ksi rtksi : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2669 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpert ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λrteta:l_e_st_eq_landau_n_rt_rp_ratrp eta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isinv l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 ksi rtksi eta rteta i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi) (l_e_st_eq_landau_n_rt_rp_rtofrp eta rteta)).
-
-(* notion 2670 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpirt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λrteta:l_e_st_eq_landau_n_rt_rp_ratrp eta.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi) (l_e_st_eq_landau_n_rt_rp_rtofrp eta rteta).(l_e_isinve l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 ksi rtksi eta rteta i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
-
-(* notion 2671 *)
-definition l_e_st_eq_landau_n_rt_rp_isrtrp1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_isst1 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 x0 : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_rp_rtofrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0))).
-
-(* notion 2672 *)
-definition l_e_st_eq_landau_n_rt_rp_isrtrp2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_isst2 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 x0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtofrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0)) x0).
-
-(* notion 2673 *)
-definition l_e_st_eq_landau_n_rt_rp_isrprt1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_ists1 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 ksi rtksi : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi))).
-
-(* notion 2674 *)
-definition l_e_st_eq_landau_n_rt_rp_isrprt2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_ists2 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 ksi rtksi : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi)) ksi).
-
-(* notion 2675 *)
-definition l_e_st_eq_landau_n_rt_rp_isnterp ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (Πz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt z) x y i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)).
-
-(* notion 2676 *)
-definition l_e_st_eq_landau_n_rt_rp_isntirp ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y).(l_e_st_eq_landau_n_rt_isnirt x y (l_e_st_eq_landau_n_rt_rp_isrtirp (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) i) : l_e_st_eq_landau_n_is x y).
-
-(* notion 2677 *)
-definition l_e_st_eq_landau_n_rt_rp_iii5_t3 ≝ (λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y).l_e_st_eq_landau_n_rt_rp_isntirp x y t : l_e_injective l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x)).
-
-(* notion 2678 *)
-definition l_e_st_eq_landau_n_rt_rp_ntofrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λntksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_e_soft l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) l_e_st_eq_landau_n_rt_rp_iii5_t3 ksi ntksi : l_e_st_eq_landau_n_nat).
-
-(* notion 2679 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpent ≝ λksi:l_e_st_eq_landau_n_rt_cut.λntksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λnteta:l_e_st_eq_landau_n_rt_rp_natrp eta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isinv l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) l_e_st_eq_landau_n_rt_rp_iii5_t3 ksi ntksi eta nteta i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_ntofrp ksi ntksi) (l_e_st_eq_landau_n_rt_rp_ntofrp eta nteta)).
-
-(* notion 2680 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpint ≝ λksi:l_e_st_eq_landau_n_rt_cut.λntksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λnteta:l_e_st_eq_landau_n_rt_rp_natrp eta.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_ntofrp ksi ntksi) (l_e_st_eq_landau_n_rt_rp_ntofrp eta nteta).(l_e_isinve l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) l_e_st_eq_landau_n_rt_rp_iii5_t3 ksi ntksi eta nteta i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
-
-(* notion 2681 *)
-definition l_e_st_eq_landau_n_rt_rp_isntrp1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_isst1 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt y) l_e_st_eq_landau_n_rt_rp_iii5_t3 x : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x))).
-
-(* notion 2682 *)
-definition l_e_st_eq_landau_n_rt_rp_isntrp2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_isst2 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt y) l_e_st_eq_landau_n_rt_rp_iii5_t3 x : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x)) x).
-
-(* notion 2683 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpnt1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λntksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_e_ists1 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) l_e_st_eq_landau_n_rt_rp_iii5_t3 ksi ntksi : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_ntofrp ksi ntksi))).
-
-(* notion 2684 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpnt2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λntksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_e_ists2 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) l_e_st_eq_landau_n_rt_rp_iii5_t3 ksi ntksi : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_ntofrp ksi ntksi)) ksi).
-
-(* notion 2685 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrte x0 u0 lu : l_e_st_eq_landau_n_rt_less u0 x0).
-
-(* notion 2686 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrte y0 v0 lv : l_e_st_eq_landau_n_rt_less v0 y0).
-
-(* notion 2687 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl u0 v0).(l_e_st_eq_landau_n_rt_satz98a u0 x0 v0 y0 (l_e_st_eq_landau_n_rt_rp_5155_t1 x0 y0 z0 lz u0 lu v0 lv i) (l_e_st_eq_landau_n_rt_rp_5155_t2 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl u0 v0) (l_e_st_eq_landau_n_rt_pl x0 y0)).
-
-(* notion 2688 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl u0 v0).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_pl u0 v0) z0 (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl u0 v0) i) (l_e_st_eq_landau_n_rt_rp_5155_t3 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
-
-(* notion 2689 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrt (l_e_st_eq_landau_n_rt_pl x0 y0) z0 (l_e_st_eq_landau_n_rt_rp_5155_t4 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) z0).
-
-(* notion 2690 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.(l_e_st_eq_landau_n_rt_rp_plapp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) z0 lz (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_5155_t5 x0 y0 z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) z0).
-
-(* notion 2691 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t7 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrte (l_e_st_eq_landau_n_rt_pl x0 y0) u0 lu : l_e_st_eq_landau_n_rt_less u0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
-
-(* notion 2692 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_u01 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_st_eq_landau_n_rt_ov u0 (l_e_st_eq_landau_n_rt_pl x0 y0) : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2693 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t8 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_st_eq_landau_n_rt_isless12 u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_satz110f u0 (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_example1d (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_rp_5155_t7 x0 y0 u0 lu) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0))).
-
-(* notion 2694 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t9 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_st_eq_landau_n_rt_satz106c (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_5155_t8 x0 y0 u0 lu) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2695 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t10 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_tris l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu))) (l_e_st_eq_landau_n_rt_satz110d u0 (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_disttp1 x0 y0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)))).
-
-(* notion 2696 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t11 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 l_e_st_eq_landau_n_rt_1rt.(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts y0 x0) (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) x0 (l_e_st_eq_landau_n_rt_comts y0 x0) (l_e_st_eq_landau_n_rt_example1c x0) (l_e_st_eq_landau_n_rt_satz105c y0 l_e_st_eq_landau_n_rt_1rt x0 l) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 y0) x0).
-
-(* notion 2697 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 l_e_st_eq_landau_n_rt_1rt.(l_e_st_eq_landau_n_rt_rp_lrtrpofrt x0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_rp_5155_t11 x0 y0 l) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 2698 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t13 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_st_eq_landau_n_rt_rp_lrtpl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) u0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_rp_5155_t12 x0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) (l_e_st_eq_landau_n_rt_rp_5155_t9 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_rp_5155_t12 y0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) (l_e_st_eq_landau_n_rt_rp_5155_t9 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_rp_5155_t10 x0 y0 u0 lu) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) u0).
-
-(* notion 2699 *)
-definition l_e_st_eq_landau_n_rt_rp_satz155a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) x.l_e_st_eq_landau_n_rt_rp_5155_t13 x0 y0 x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) x.l_e_st_eq_landau_n_rt_rp_5155_t6 x0 y0 x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
-
-(* notion 2700 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t14 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_satz101f x0 y0 m : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0)).
-
-(* notion 2701 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t15 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_isrterp x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) (l_e_st_eq_landau_n_rt_rp_5155_t14 x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_satz155a (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
-
-(* notion 2702 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t16 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m))) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m))) (l_e_st_eq_landau_n_rt_rp_5155_t15 x0 y0 m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m))) (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).
-
-(* notion 2703 *)
-definition l_e_st_eq_landau_n_rt_rp_satz155b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_rp_satz140g (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_satz154a x0 y0 m) (l_e_st_eq_landau_n_rt_rp_5155_t16 x0 y0 m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_satz154a x0 y0 m))).
-
-(* notion 2704 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t17 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrte x0 u0 lu : l_e_st_eq_landau_n_rt_less u0 x0).
-
-(* notion 2705 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t18 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrte y0 v0 lv : l_e_st_eq_landau_n_rt_less v0 y0).
-
-(* notion 2706 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t19 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts u0 v0).(l_e_st_eq_landau_n_rt_satz107a u0 x0 v0 y0 (l_e_st_eq_landau_n_rt_rp_5155_t17 x0 y0 z0 lz u0 lu v0 lv i) (l_e_st_eq_landau_n_rt_rp_5155_t18 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts u0 v0) (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 2707 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t20 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts u0 v0).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_ts u0 v0) z0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts u0 v0) i) (l_e_st_eq_landau_n_rt_rp_5155_t19 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 2708 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t21 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrt (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_rt_rp_5155_t20 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) z0).
-
-(* notion 2709 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t22 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.(l_e_st_eq_landau_n_rt_rp_tsapp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) z0 lz (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_5155_t21 x0 y0 z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) z0).
-
-(* notion 2710 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t23 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrte (l_e_st_eq_landau_n_rt_ts x0 y0) u0 lu : l_e_st_eq_landau_n_rt_less u0 (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 2711 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t24 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_ande1 (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)) a : l_e_st_eq_landau_n_rt_less u0 u1).
-
-(* notion 2712 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t25 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_ande2 (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)) a : l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 2713 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t26 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_st_eq_landau_n_rt_isless12 u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u0 u1) u1) u1 (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt u1) (l_e_st_eq_landau_n_rt_satz110f u0 u1) (l_e_st_eq_landau_n_rt_example1d u1) (l_e_st_eq_landau_n_rt_rp_5155_t24 x0 y0 u0 lu u1 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u0 u1) u1) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt u1)).
-
-(* notion 2714 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t27 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_st_eq_landau_n_rt_satz106c (l_e_st_eq_landau_n_rt_ov u0 u1) l_e_st_eq_landau_n_rt_1rt u1 (l_e_st_eq_landau_n_rt_rp_5155_t26 x0 y0 u0 lu u1 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ov u0 u1) l_e_st_eq_landau_n_rt_1rt).
-
-(* notion 2715 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t28 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_st_eq_landau_n_rt_isless1 u1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) y0) (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_satz110f u1 y0) (l_e_st_eq_landau_n_rt_rp_5155_t25 x0 y0 u0 lu u1 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) y0) (l_e_st_eq_landau_n_rt_ts x0 y0)).
-
-(* notion 2716 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t29 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_st_eq_landau_n_rt_satz106c (l_e_st_eq_landau_n_rt_ov u1 y0) x0 y0 (l_e_st_eq_landau_n_rt_rp_5155_t28 x0 y0 u0 lu u1 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ov u1 y0) x0).
-
-(* notion 2717 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t30 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ts u1 (l_e_st_eq_landau_n_rt_ov u0 u1)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) y0) (l_e_st_eq_landau_n_rt_ov u0 u1)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov u0 u1))) (l_e_st_eq_landau_n_rt_satz110d u0 u1) (l_e_st_eq_landau_n_rt_ists1 u1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) y0) (l_e_st_eq_landau_n_rt_ov u0 u1) (l_e_st_eq_landau_n_rt_satz110f u1 y0)) (l_e_st_eq_landau_n_rt_assts1 (l_e_st_eq_landau_n_rt_ov u1 y0) y0 (l_e_st_eq_landau_n_rt_ov u0 u1)) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov u0 u1)))).
-
-(* notion 2718 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t31 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_st_eq_landau_n_rt_rp_lrtts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) u0 (l_e_st_eq_landau_n_rt_ov u1 y0) (l_e_st_eq_landau_n_rt_rp_lrtrpofrt x0 (l_e_st_eq_landau_n_rt_ov u1 y0) (l_e_st_eq_landau_n_rt_rp_5155_t29 x0 y0 u0 lu u1 a)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov u0 u1)) (l_e_st_eq_landau_n_rt_rp_5155_t12 y0 (l_e_st_eq_landau_n_rt_ov u0 u1) (l_e_st_eq_landau_n_rt_rp_5155_t27 x0 y0 u0 lu u1 a)) (l_e_st_eq_landau_n_rt_rp_5155_t30 x0 y0 u0 lu u1 a) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) u0).
-
-(* notion 2719 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t32 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less u0 x) (l_e_st_eq_landau_n_rt_less x (l_e_st_eq_landau_n_rt_ts x0 y0))) (l_e_st_eq_landau_n_rt_satz91 u0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_rp_5155_t23 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_less u0 x) (l_e_st_eq_landau_n_rt_less x (l_e_st_eq_landau_n_rt_ts x0 y0)).l_e_st_eq_landau_n_rt_rp_5155_t31 x0 y0 u0 lu x t) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) u0).
-
-(* notion 2720 *)
-definition l_e_st_eq_landau_n_rt_rp_satz155c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) x.l_e_st_eq_landau_n_rt_rp_5155_t32 x0 y0 x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) x.l_e_st_eq_landau_n_rt_rp_5155_t22 x0 y0 x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
-
-(* notion 2721 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t33 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz110f x0 y0 : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0)).
-
-(* notion 2722 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t34 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_isrterp x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0) (l_e_st_eq_landau_n_rt_rp_5155_t33 x0 y0)) (l_e_st_eq_landau_n_rt_rp_satz155c (l_e_st_eq_landau_n_rt_ov x0 y0) y0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
-
-(* notion 2723 *)
-definition l_e_st_eq_landau_n_rt_rp_5155_t35 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0))) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0))) (l_e_st_eq_landau_n_rt_rp_5155_t34 x0 y0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0))) (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).
-
-(* notion 2724 *)
-definition l_e_st_eq_landau_n_rt_rp_satz155d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_satz153g (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0)) (l_e_st_eq_landau_n_rt_rp_5155_t35 x0 y0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0)) (l_e_st_eq_landau_n_rt_rp_ov (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
-
-(* notion 2725 *)
-definition l_e_st_eq_landau_n_rt_rp_satz155e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)) (l_e_st_eq_landau_n_rt_rp_isrterp (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_satz112h x y))) (l_e_st_eq_landau_n_rt_rp_satz155a (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y))).
-
-(* notion 2726 *)
-definition l_e_st_eq_landau_n_rt_rp_satz155f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)) (l_e_st_eq_landau_n_rt_rp_isrterp (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_satz112j x y))) (l_e_st_eq_landau_n_rt_rp_satz155c (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y))).
-
-(* notion 2727 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_natt ≝ (l_e_ot l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) : Type[0]).
-
-(* notion 2728 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_nttofrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_e_out l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) ksi nksi : l_e_st_eq_landau_n_rt_rp_nt_natt).
-
-(* notion 2729 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_is ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_is l_e_st_eq_landau_n_rt_rp_nt_natt xt yt : Prop).
-
-(* notion 2730 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_nis ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_not (l_e_st_eq_landau_n_rt_rp_nt_is xt yt) : Prop).
-
-(* notion 2731 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.Prop.(l_all l_e_st_eq_landau_n_rt_rp_nt_natt p : Prop).
-
-(* notion 2732 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.Prop.(l_some l_e_st_eq_landau_n_rt_rp_nt_natt p : Prop).
-
-(* notion 2733 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.Prop.(l_e_one l_e_st_eq_landau_n_rt_rp_nt_natt p : Prop).
-
-(* notion 2734 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_in ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_esti l_e_st_eq_landau_n_rt_rp_nt_natt xt st : Prop).
-
-(* notion 2735 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_rpofntt ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_in l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) xt : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2736 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_natrpi ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_inp l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) xt : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt)).
-
-(* notion 2737 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isrpentt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λneta:l_e_st_eq_landau_n_rt_rp_natrp eta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isouti l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) ksi nksi eta neta i : l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofrp ksi nksi) (l_e_st_eq_landau_n_rt_rp_nt_nttofrp eta neta)).
-
-(* notion 2738 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isrpintt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λneta:l_e_st_eq_landau_n_rt_rp_natrp eta.λi:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofrp ksi nksi) (l_e_st_eq_landau_n_rt_rp_nt_nttofrp eta neta).(l_e_isoute l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) ksi nksi eta neta i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
-
-(* notion 2739 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isntterp ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_rt_rp_nt_is xt yt.(l_e_isini l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) xt yt i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt yt)).
-
-(* notion 2740 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isnttirp ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt yt).(l_e_isine l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) xt yt i : l_e_st_eq_landau_n_rt_rp_nt_is xt yt).
-
-(* notion 2741 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isrpntt1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_e_isinout l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) ksi nksi : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_nt_rpofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofrp ksi nksi))).
-
-(* notion 2742 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isnttrp1 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_isoutin l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) xt : l_e_st_eq_landau_n_rt_rp_nt_is xt (l_e_st_eq_landau_n_rt_rp_nt_nttofrp (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt))).
-
-(* notion 2743 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_nttofnt ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_nt_nttofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x) : l_e_st_eq_landau_n_rt_rp_nt_natt).
-
-(* notion 2744 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isntentt ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_rt_rp_nt_isrpentt (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) (l_e_st_eq_landau_n_rt_rp_natrpi y) (l_e_st_eq_landau_n_rt_rp_isnterp x y i) : l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x) (l_e_st_eq_landau_n_rt_rp_nt_nttofnt y)).
-
-(* notion 2745 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isntintt ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x) (l_e_st_eq_landau_n_rt_rp_nt_nttofnt y).(l_e_st_eq_landau_n_rt_rp_isntirp x y (l_e_st_eq_landau_n_rt_rp_nt_isrpintt (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) (l_e_st_eq_landau_n_rt_rp_natrpi y) i) : l_e_st_eq_landau_n_is x y).
-
-(* notion 2746 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_ntofntt ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt) : l_e_st_eq_landau_n_nat).
-
-(* notion 2747 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isnttent ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_rt_rp_nt_is xt yt.(l_e_st_eq_landau_n_rt_rp_isrpent (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt yt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi yt) (l_e_st_eq_landau_n_rt_rp_nt_isntterp xt yt i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt yt)).
-
-(* notion 2748 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isnttint ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt yt).(l_e_st_eq_landau_n_rt_rp_nt_isnttirp xt yt (l_e_st_eq_landau_n_rt_rp_isrpint (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt yt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi yt) i) : l_e_st_eq_landau_n_rt_rp_nt_is xt yt).
-
-(* notion 2749 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_iii5_t5 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_nt_isrpntt1 (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x))).
-
-(* notion 2750 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_iii5_t6 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_isrpent (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) (l_e_st_eq_landau_n_rt_rp_nt_natrpi (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) (l_e_st_eq_landau_n_rt_rp_nt_iii5_t5 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x)) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x))).
-
-(* notion 2751 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isntntt1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x)) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) (l_e_st_eq_landau_n_rt_rp_isntrp1 x) (l_e_st_eq_landau_n_rt_rp_nt_iii5_t6 x) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x))).
-
-(* notion 2752 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_iii5_t7 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_rt_rp_isrpnt1 (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt))).
-
-(* notion 2753 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_iii5_t8 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_rt_rp_nt_isrpentt (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_rt_rp_natrpi (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_rt_rp_nt_iii5_t7 xt) : l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofrp (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt)) (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt))).
-
-(* notion 2754 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isnttnt1 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_tris l_e_st_eq_landau_n_rt_rp_nt_natt xt (l_e_st_eq_landau_n_rt_rp_nt_nttofrp (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt)) (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_rt_rp_nt_isnttrp1 xt) (l_e_st_eq_landau_n_rt_rp_nt_iii5_t8 xt) : l_e_st_eq_landau_n_rt_rp_nt_is xt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt))).
-
-(* notion 2755 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isntntt2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) (l_e_st_eq_landau_n_rt_rp_nt_isntntt1 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) x).
-
-(* notion 2756 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_isnttnt2 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_symis l_e_st_eq_landau_n_rt_rp_nt_natt xt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_rt_rp_nt_isnttnt1 xt) : l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) xt).
-
-(* notion 2757 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_1t ≝ (l_e_st_eq_landau_n_rt_rp_nt_nttofnt l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_rt_rp_nt_natt).
-
-(* notion 2758 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_suct ≝ (Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt x)) : Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_natt).
-
-(* notion 2759 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_5156_t1 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λj:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct xt) l_e_st_eq_landau_n_rt_rp_nt_1t.(l_e_st_eq_landau_n_rt_rp_nt_isntintt (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) l_e_st_eq_landau_n_1 j : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) l_e_st_eq_landau_n_1).
-
-(* notion 2760 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_satz156a ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct xt) l_e_st_eq_landau_n_rt_rp_nt_1t) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ax3 (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (λt:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct xt) l_e_st_eq_landau_n_rt_rp_nt_1t.l_e_st_eq_landau_n_rt_rp_nt_5156_t1 xt t) : l_e_st_eq_landau_n_rt_rp_nt_nis (l_e_st_eq_landau_n_rt_rp_nt_suct xt) l_e_st_eq_landau_n_rt_rp_nt_1t).
-
-(* notion 2761 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_5156_t2 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct xt) (l_e_st_eq_landau_n_rt_rp_nt_suct yt).(l_e_st_eq_landau_n_rt_rp_nt_isntintt (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt yt)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt yt))).
-
-(* notion 2762 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_satz156b ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct xt) (l_e_st_eq_landau_n_rt_rp_nt_suct yt).(l_e_st_eq_landau_n_rt_rp_nt_isnttint xt yt (l_e_st_eq_landau_n_ax4 (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt yt) (l_e_st_eq_landau_n_rt_rp_nt_5156_t2 xt yt i)) : l_e_st_eq_landau_n_rt_rp_nt_is xt yt).
-
-(* notion 2763 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_cond1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_rt_rp_nt_in l_e_st_eq_landau_n_rt_rp_nt_1t st : Prop).
-
-(* notion 2764 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_cond2 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_rt_rp_nt_all (λx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_imp (l_e_st_eq_landau_n_rt_rp_nt_in x st) (l_e_st_eq_landau_n_rt_rp_nt_in (l_e_st_eq_landau_n_rt_rp_nt_suct x) st)) : Prop).
-
-(* notion 2765 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λc1:l_e_st_eq_landau_n_rt_rp_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_rp_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_nt_in (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x) st : Prop).
-
-(* notion 2766 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_5156_t3 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λc1:l_e_st_eq_landau_n_rt_rp_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_rp_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 st c1 c2 x.(c2 (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x) p : l_e_st_eq_landau_n_rt_rp_nt_in (l_e_st_eq_landau_n_rt_rp_nt_suct (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) st).
-
-(* notion 2767 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_5156_t4 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λc1:l_e_st_eq_landau_n_rt_rp_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_rp_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 st c1 c2 x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_nt_in (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_suc t)) st) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) x (l_e_st_eq_landau_n_rt_rp_nt_5156_t3 st c1 c2 x p) (l_e_st_eq_landau_n_rt_rp_nt_isntntt2 x) : l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 st c1 c2 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 2768 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_5156_t5 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λc1:l_e_st_eq_landau_n_rt_rp_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_rp_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 st c1 c2 t) c1 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 st c1 c2 t.l_e_st_eq_landau_n_rt_rp_nt_5156_t4 st c1 c2 t u) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt) : l_e_st_eq_landau_n_rt_rp_nt_in (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) st).
-
-(* notion 2769 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_satz156c ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λc1:l_e_st_eq_landau_n_rt_rp_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_rp_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_isp l_e_st_eq_landau_n_rt_rp_nt_natt (λt:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_in t st) (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) xt (l_e_st_eq_landau_n_rt_rp_nt_5156_t5 st c1 c2 xt) (l_e_st_eq_landau_n_rt_rp_nt_isnttnt2 xt) : l_e_st_eq_landau_n_rt_rp_nt_in xt st).
-
-(* notion 2770 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_ax3t ≝ (Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_satz156a x : Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_nis (l_e_st_eq_landau_n_rt_rp_nt_suct x) l_e_st_eq_landau_n_rt_rp_nt_1t).
-
-(* notion 2771 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_ax4t ≝ (λx:l_e_st_eq_landau_n_rt_rp_nt_natt.λy:l_e_st_eq_landau_n_rt_rp_nt_natt.λu:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct x) (l_e_st_eq_landau_n_rt_rp_nt_suct y).l_e_st_eq_landau_n_rt_rp_nt_satz156b x y u : Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.Πy:l_e_st_eq_landau_n_rt_rp_nt_natt.Πu:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct x) (l_e_st_eq_landau_n_rt_rp_nt_suct y).l_e_st_eq_landau_n_rt_rp_nt_is x y).
-
-(* notion 2772 *)
-definition l_e_st_eq_landau_n_rt_rp_nt_ax5t ≝ (λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λu:l_e_st_eq_landau_n_rt_rp_nt_cond1 s.λv:l_e_st_eq_landau_n_rt_rp_nt_cond2 s.λx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_satz156c s u v x : Πs:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.Πu:l_e_st_eq_landau_n_rt_rp_nt_cond1 s.Πv:l_e_st_eq_landau_n_rt_rp_nt_cond2 s.Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_in x s).
-
-(* notion 2773 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_ratt ≝ (l_e_ot l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) : Type[0]).
-
-(* notion 2774 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_rttofrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_out l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) ksi rtksi : l_e_st_eq_landau_n_rt_rp_rtt_ratt).
-
-(* notion 2775 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_is ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_is l_e_st_eq_landau_n_rt_rp_rtt_ratt x0t y0t : Prop).
-
-(* notion 2776 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_nis ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_not (l_e_st_eq_landau_n_rt_rp_rtt_is x0t y0t) : Prop).
-
-(* notion 2777 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_rtt_ratt.Prop.(l_all l_e_st_eq_landau_n_rt_rp_rtt_ratt p : Prop).
-
-(* notion 2778 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_rtt_ratt.Prop.(l_some l_e_st_eq_landau_n_rt_rp_rtt_ratt p : Prop).
-
-(* notion 2779 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_rtt_ratt.Prop.(l_e_one l_e_st_eq_landau_n_rt_rp_rtt_ratt p : Prop).
-
-(* notion 2780 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_in l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) x0t : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2781 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_ratrpi ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_inp l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) x0t : l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t)).
-
-(* notion 2782 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrpertt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λrteta:l_e_st_eq_landau_n_rt_rp_ratrp eta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isouti l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) ksi rtksi eta rteta i : l_e_st_eq_landau_n_rt_rp_rtt_is (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp ksi rtksi) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp eta rteta)).
-
-(* notion 2783 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrpirtt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λrteta:l_e_st_eq_landau_n_rt_rp_ratrp eta.λi:l_e_st_eq_landau_n_rt_rp_rtt_is (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp ksi rtksi) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp eta rteta).(l_e_isoute l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) ksi rtksi eta rteta i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
-
-(* notion 2784 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrtterp ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λi:l_e_st_eq_landau_n_rt_rp_rtt_is x0t y0t.(l_e_isini l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) x0t y0t i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt y0t)).
-
-(* notion 2785 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrttirp ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt y0t).(l_e_isine l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) x0t y0t i : l_e_st_eq_landau_n_rt_rp_rtt_is x0t y0t).
-
-(* notion 2786 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrprtt1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_isinout l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) ksi rtksi : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp ksi rtksi))).
-
-(* notion 2787 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrttrp1 ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_isoutin l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) x0t : l_e_st_eq_landau_n_rt_rp_rtt_is x0t (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t))).
-
-(* notion 2788 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_rttofrt ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rtt_rttofrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) : l_e_st_eq_landau_n_rt_rp_rtt_ratt).
-
-(* notion 2789 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrtertt ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_rp_rtt_isrpertt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_ratrpi y0) (l_e_st_eq_landau_n_rt_rp_isrterp x0 y0 i) : l_e_st_eq_landau_n_rt_rp_rtt_is (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt y0)).
-
-(* notion 2790 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrtirtt ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_rp_rtt_is (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt y0).(l_e_st_eq_landau_n_rt_rp_isrtirp x0 y0 (l_e_st_eq_landau_n_rt_rp_rtt_isrpirtt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_ratrpi y0) i) : l_e_st_eq_landau_n_rt_is x0 y0).
-
-(* notion 2791 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_st_eq_landau_n_rt_rp_rtofrp (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t) : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2792 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrttert ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λi:l_e_st_eq_landau_n_rt_rp_rtt_is x0t y0t.(l_e_st_eq_landau_n_rt_rp_isrpert (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt y0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi y0t) (l_e_st_eq_landau_n_rt_rp_rtt_isrtterp x0t y0t i) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt y0t)).
-
-(* notion 2793 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrttirt ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt y0t).(l_e_st_eq_landau_n_rt_rp_rtt_isrttirp x0t y0t (l_e_st_eq_landau_n_rt_rp_isrpirt (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt y0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi y0t) i) : l_e_st_eq_landau_n_rt_rp_rtt_is x0t y0t).
-
-(* notion 2794 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_iii5_t9 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rtt_isrprtt1 (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0))).
-
-(* notion 2795 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_iii5_t10 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_isrpert (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0)) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0)) (l_e_st_eq_landau_n_rt_rp_rtt_iii5_t9 x0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtofrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0)) (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0))).
-
-(* notion 2796 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrtrtt1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_tris l_e_st_eq_landau_n_rt_rat x0 (l_e_st_eq_landau_n_rt_rp_rtofrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0)) (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0)) (l_e_st_eq_landau_n_rt_rp_isrtrp1 x0) (l_e_st_eq_landau_n_rt_rp_rtt_iii5_t10 x0) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0))).
-
-(* notion 2797 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_iii5_t11 ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_st_eq_landau_n_rt_rp_isrprt1 (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t))).
-
-(* notion 2798 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_iii5_t12 ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_st_eq_landau_n_rt_rp_rtt_isrpertt (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t)) (l_e_st_eq_landau_n_rt_rp_ratrpi (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t)) (l_e_st_eq_landau_n_rt_rp_rtt_iii5_t11 x0t) : l_e_st_eq_landau_n_rt_rp_rtt_is (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t)) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t))).
-
-(* notion 2799 *)
-definition l_e_st_eq_landau_n_rt_rp_rtt_isrttrt1 ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_tris l_e_st_eq_landau_n_rt_rp_rtt_ratt x0t (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t)) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t)) (l_e_st_eq_landau_n_rt_rp_rtt_isrttrp1 x0t) (l_e_st_eq_landau_n_rt_rp_rtt_iii5_t12 x0t) : l_e_st_eq_landau_n_rt_rp_rtt_is x0t (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t))).
-
-(* notion 2800 *)
-definition l_e_st_eq_landau_n_rt_rp_example2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz153c l_e_st_eq_landau_n_rt_rp_1rp ksi : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ov l_e_st_eq_landau_n_rt_rp_1rp ksi)) l_e_st_eq_landau_n_rt_rp_1rp).
-
-(* notion 2801 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_x01 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2802 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_s1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2803 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) y0 i : l_e_st_eq_landau_n_rt_urt ksi y0).
-
-(* notion 2804 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0 (l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0 m) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) y0).
-
-(* notion 2805 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0.(l_e_isp l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_lrt x y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) ksi (l_e_st_eq_landau_n_rt_rp_5157_t2 ksi rtksi y0 i m) (l_e_st_eq_landau_n_rt_rp_isrprt2 ksi rtksi) : l_e_st_eq_landau_n_rt_lrt ksi y0).
-
-(* notion 2806 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).(l_imp_th3 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0) (l_e_st_eq_landau_n_rt_lrt ksi y0) (l_e_st_eq_landau_n_rt_rp_5157_t1 ksi rtksi y0 i) (λt:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0.l_e_st_eq_landau_n_rt_rp_5157_t3 ksi rtksi y0 i t) : l_not (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0)).
-
-(* notion 2807 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).(l_e_st_eq_landau_n_rt_satz81e (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0 (l_e_st_eq_landau_n_rt_rp_5157_t4 ksi rtksi y0 i) : l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0).
-
-(* notion 2808 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).l_e_st_eq_landau_n_rt_rp_5157_t5 ksi rtksi x t : l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)).
-
-(* notion 2809 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_st_eq_landau_n_rt_rp_urtrpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_moreisi2 (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi))) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)).
-
-(* notion 2810 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_isp l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_urt x (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) ksi (l_e_st_eq_landau_n_rt_rp_5157_t7 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_isrprt2 ksi rtksi) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)).
-
-(* notion 2811 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_t8 ksi rtksi) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)).
-
-(* notion 2812 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_andi (l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)) (l_e_st_eq_landau_n_rt_rp_5157_t6 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_t9 ksi rtksi) : l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)).
-
-(* notion 2813 *)
-definition l_e_st_eq_landau_n_rt_rp_satz157a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_st_eq_landau_n_rt_rp_5157_t10 ksi rtksi : l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) (l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi)).
-
-(* notion 2814 *)
-definition l_e_st_eq_landau_n_rt_rp_satz157b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_t10 ksi rtksi) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi y)) x)).
-
-(* notion 2815 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.(l_ande1 (l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x0) (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)) m : l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x0).
-
-(* notion 2816 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.(l_ande2 (l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x0) (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)) m : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)).
-
-(* notion 2817 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) x0 (l_e_st_eq_landau_n_rt_rp_5157_t12 ksi x0 m) : l_e_st_eq_landau_n_rt_urt ksi x0).
-
-(* notion 2818 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.(l_e_st_eq_landau_n_rt_cutapp2a ksi y0 ly x0 (l_e_st_eq_landau_n_rt_rp_5157_t13 ksi x0 m) : l_e_st_eq_landau_n_rt_less y0 x0).
-
-(* notion 2819 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrt x0 y0 (l_e_st_eq_landau_n_rt_rp_5157_t14 ksi x0 m y0 ly) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0).
-
-(* notion 2820 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) y0 uy : l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)).
-
-(* notion 2821 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_eq_landau_n_rt_satz85 x0 y0 (l_e_st_eq_landau_n_rt_rp_5157_t11 ksi x0 m y0 (l_e_st_eq_landau_n_rt_rp_5157_t17 ksi x0 m y0 uy)) : l_e_st_eq_landau_n_rt_moreis y0 x0).
-
-(* notion 2822 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_eq_landau_n_rt_rp_urtrpofrt x0 y0 (l_e_st_eq_landau_n_rt_rp_5157_t18 ksi x0 m y0 uy) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0).
-
-(* notion 2823 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.(l_cp (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0) (l_e_st_eq_landau_n_rt_lrt ksi y0) (λt:l_e_st_eq_landau_n_rt_urt ksi y0.l_e_st_eq_landau_n_rt_rp_5157_t19 ksi x0 m y0 t) : l_imp (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0) (l_e_st_eq_landau_n_rt_lrt ksi y0)).
-
-(* notion 2824 *)
-definition l_e_st_eq_landau_n_rt_rp_satz157c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.(l_e_st_eq_landau_n_rt_rp_isi1 ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_5157_t15 ksi x0 m x t) (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5157_t20 ksi x0 m x) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).
-
-(* notion 2825 *)
-definition l_e_st_eq_landau_n_rt_rp_5157_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi y)) x).λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x0.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) x0 (l_e_st_eq_landau_n_rt_rp_satz157c ksi x0 m) : l_e_st_eq_landau_n_rt_rp_ratrp ksi).
-
-(* notion 2826 *)
-definition l_e_st_eq_landau_n_rt_rp_satz157d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi y)) x).(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x) s (l_e_st_eq_landau_n_rt_rp_ratrp ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x.l_e_st_eq_landau_n_rt_rp_5157_t21 ksi s x t) : l_e_st_eq_landau_n_rt_rp_ratrp ksi).
-
-(* notion 2827 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_xr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2828 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_rp_urtrpofrt x0 x0 (l_e_st_eq_landau_n_rt_moreisi2 x0 x0 (l_e_refis l_e_st_eq_landau_n_rt_rat x0)) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) x0).
-
-(* notion 2829 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_andi (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) x0) (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_rp_5158_t1 ksi x0 lx) lx : l_and (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) x0) (l_e_st_eq_landau_n_rt_lrt ksi x0)).
-
-(* notion 2830 *)
-definition l_e_st_eq_landau_n_rt_rp_satz158a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) x) (l_e_st_eq_landau_n_rt_lrt ksi x)) x0 (l_e_st_eq_landau_n_rt_rp_5158_t2 ksi x0 lx) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi).
-
-(* notion 2831 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_s1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2832 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λm:l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0.(l_e_symis l_e_st_eq_landau_n_rt_cut ksi (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) (l_e_st_eq_landau_n_rt_rp_satz157c ksi x0 m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi).
-
-(* notion 2833 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λm:l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0.(l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi (l_e_st_eq_landau_n_rt_rp_5158_t3 ksi x0 ux m) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi).
-
-(* notion 2834 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) x0 ux : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)).
-
-(* notion 2835 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).(l_and_th4 (l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0) (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) n (l_e_st_eq_landau_n_rt_rp_5158_t5 ksi x0 ux n) : l_not (l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0)).
-
-(* notion 2836 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).(l_some_th1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_imp (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 x)) (l_e_st_eq_landau_n_rt_rp_5158_t6 ksi x0 ux n) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_imp (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 x)))).
-
-(* notion 2837 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_imp_th5 (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0) o : l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)).
-
-(* notion 2838 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) y0 (l_e_st_eq_landau_n_rt_rp_5158_t8 ksi x0 ux n y0 o) : l_e_st_eq_landau_n_rt_urt ksi y0).
-
-(* notion 2839 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_imp_th6 (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0) o : l_not (l_e_st_eq_landau_n_rt_lessis x0 y0)).
-
-(* notion 2840 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_e_st_eq_landau_n_rt_satz82 x0 y0 (l_e_st_eq_landau_n_rt_satz81k x0 y0 (l_e_st_eq_landau_n_rt_rp_5158_t10 ksi x0 ux n y0 o)) : l_e_st_eq_landau_n_rt_less y0 x0).
-
-(* notion 2841 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_e_st_eq_landau_n_rt_rp_lrtrpofrt x0 y0 (l_e_st_eq_landau_n_rt_rp_5158_t11 ksi x0 ux n y0 o) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) y0).
-
-(* notion 2842 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_andi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) y0) (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_rp_5158_t12 ksi x0 ux n y0 o) (l_e_st_eq_landau_n_rt_rp_5158_t9 ksi x0 ux n y0 o) : l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) y0) (l_e_st_eq_landau_n_rt_urt ksi y0)).
-
-(* notion 2843 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) x) (l_e_st_eq_landau_n_rt_urt ksi x)) y0 (l_e_st_eq_landau_n_rt_rp_5158_t13 ksi x0 ux n y0 o) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi).
-
-(* notion 2844 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_imp (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 x))) (l_e_st_eq_landau_n_rt_rp_5158_t7 ksi x0 ux n) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_not (l_imp (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 x)).l_e_st_eq_landau_n_rt_rp_5158_t14 ksi x0 ux n x t) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi).
-
-(* notion 2845 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi (l_e_st_eq_landau_n_rt_rp_5158_t15 ksi x0 ux n) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi).
-
-(* notion 2846 *)
-definition l_e_st_eq_landau_n_rt_rp_satz158b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_imp_th1 (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi) (λt:l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0.l_e_st_eq_landau_n_rt_rp_5158_t4 ksi x0 ux t) (λt:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).l_e_st_eq_landau_n_rt_rp_5158_t16 ksi x0 ux t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi).
-
-(* notion 2847 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi.(l_e_st_eq_landau_n_rt_rp_satz123h (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi l : l_not (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi)).
-
-(* notion 2848 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi.(l_imp_th3 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi) (l_e_st_eq_landau_n_rt_rp_5158_t17 ksi x0 l) (λt:l_e_st_eq_landau_n_rt_urt ksi x0.l_e_st_eq_landau_n_rt_rp_satz158b ksi x0 t) : l_not (l_e_st_eq_landau_n_rt_urt ksi x0)).
-
-(* notion 2849 *)
-definition l_e_st_eq_landau_n_rt_rp_satz158c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi.(l_et (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_rp_5158_t18 ksi x0 l) : l_e_st_eq_landau_n_rt_lrt ksi x0).
-
-(* notion 2850 *)
-definition l_e_st_eq_landau_n_rt_rp_5158_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi.(l_e_st_eq_landau_n_rt_rp_satz123c (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi m : l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi)).
-
-(* notion 2851 *)
-definition l_e_st_eq_landau_n_rt_rp_satz158d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi.(l_imp_th3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi) (l_e_st_eq_landau_n_rt_rp_5158_t19 ksi x0 m) (λt:l_e_st_eq_landau_n_rt_lrt ksi x0.l_e_st_eq_landau_n_rt_rp_satz158a ksi x0 t) : l_e_st_eq_landau_n_rt_urt ksi x0).
-
-(* notion 2852 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_xr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2853 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_zr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2854 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt eta z0.λk:l_e_st_eq_landau_n_rt_less x0 z0.(l_e_st_eq_landau_n_rt_rp_satz127a ksi (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0) (l_e_st_eq_landau_n_rt_rp_satz124 (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) ksi (l_e_st_eq_landau_n_rt_rp_satz158b ksi x0 ux)) (l_e_st_eq_landau_n_rt_rp_satz154c x0 z0 k) : l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0)).
-
-(* notion 2855 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt eta z0.λk:l_e_st_eq_landau_n_rt_less x0 z0.(l_andi (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0) eta) (l_e_st_eq_landau_n_rt_rp_5159_t1 ksi eta l x0 ux lx z0 lz k) (l_e_st_eq_landau_n_rt_rp_satz158a eta z0 lz) : l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0) eta)).
-
-(* notion 2856 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt eta z0.λk:l_e_st_eq_landau_n_rt_less x0 z0.(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta)) z0 (l_e_st_eq_landau_n_rt_rp_5159_t2 ksi eta l x0 ux lx z0 lz k) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta))).
-
-(* notion 2857 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_e_st_eq_landau_n_rt_cutapp3 eta x0 lx (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λu:l_e_st_eq_landau_n_rt_less x0 x.l_e_st_eq_landau_n_rt_rp_5159_t3 ksi eta l x0 ux lx x t u) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta))).
-
-(* notion 2858 *)
-definition l_e_st_eq_landau_n_rt_rp_satz159 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_lessapp ksi eta l (l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λu:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_5159_t4 ksi eta l x t u) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta))).
-
-(* notion 2859 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) eta).(l_andi (l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) eta)) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) a : l_and3 (l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) eta)).
-
-(* notion 2860 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) eta).(l_somei l_e_st_eq_landau_n_rt_cut (Πc:l_e_st_eq_landau_n_rt_cut.l_and3 (l_e_st_eq_landau_n_rt_rp_ratrp c) (l_e_st_eq_landau_n_rt_rp_less ksi c) (l_e_st_eq_landau_n_rt_rp_less c eta)) (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) (l_e_st_eq_landau_n_rt_rp_5159_t5 ksi eta l x0 a) : l_e_st_eq_landau_n_rt_rp_some (Πc:l_e_st_eq_landau_n_rt_cut.l_and3 (l_e_st_eq_landau_n_rt_rp_ratrp c) (l_e_st_eq_landau_n_rt_rp_less ksi c) (l_e_st_eq_landau_n_rt_rp_less c eta))).
-
-(* notion 2861 *)
-definition l_e_st_eq_landau_n_rt_rp_satz159a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta)) (l_e_st_eq_landau_n_rt_rp_satz159 ksi eta l) (l_e_st_eq_landau_n_rt_rp_some (Πa:l_e_st_eq_landau_n_rt_cut.l_and3 (l_e_st_eq_landau_n_rt_rp_ratrp a) (l_e_st_eq_landau_n_rt_rp_less ksi a) (l_e_st_eq_landau_n_rt_rp_less a eta))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta).l_e_st_eq_landau_n_rt_rp_5159_t6 ksi eta l x t) : l_e_st_eq_landau_n_rt_rp_some (Πa:l_e_st_eq_landau_n_rt_cut.l_and3 (l_e_st_eq_landau_n_rt_rp_ratrp a) (l_e_st_eq_landau_n_rt_rp_less ksi a) (l_e_st_eq_landau_n_rt_rp_less a eta))).
-
-(* notion 2862 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_yr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).Πu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta.p.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt y0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2863 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).Πu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta.p.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta).(l_ande1 (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta) a : l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)).
-
-(* notion 2864 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).Πu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta.p.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta).(l_ande2 (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta) a : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta).
-
-(* notion 2865 *)
-definition l_e_st_eq_landau_n_rt_rp_5159_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).Πu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta.p.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta).(p1 y0 (l_e_st_eq_landau_n_rt_rp_5159_t7 ksi eta l p p1 y0 a) (l_e_st_eq_landau_n_rt_rp_5159_t8 ksi eta l p p1 y0 a) : p).
-
-(* notion 2866 *)
-definition l_e_st_eq_landau_n_rt_rp_satz159app ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).Πu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta.p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta)) (l_e_st_eq_landau_n_rt_rp_satz159 ksi eta l) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta).l_e_st_eq_landau_n_rt_rp_5159_t9 ksi eta l p p1 x t) : p).
-
-(* notion 2867 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_zr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_st_eq_landau_n_rt_rp_rpofrt z0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2868 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_nm ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_5160_zr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) m : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2869 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_dn ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2870 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_fr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_st_eq_landau_n_rt_rp_ov (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2871 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_zeta ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_ite (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2872 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp.(l_e_itet (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp l : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m)).
-
-(* notion 2873 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp.(l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_t1 ksi eta z0 m l) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m)).
-
-(* notion 2874 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp.(l_e_st_eq_landau_n_rt_rp_lessisi1 (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_satz127a (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5160_t2 ksi eta z0 m l) l) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).
-
-(* notion 2875 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λn:l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).(l_e_itef (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp n : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).
-
-(* notion 2876 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λn:l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).(l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5160_t4 ksi eta z0 m n) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).
-
-(* notion 2877 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λn:l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).(l_e_st_eq_landau_n_rt_rp_trlessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_t5 ksi eta z0 m n) (l_e_st_eq_landau_n_rt_rp_satz124 (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_satz123f (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp n)) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m)).
-
-(* notion 2878 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) (λt:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp.l_e_st_eq_landau_n_rt_rp_5160_t3 ksi eta z0 m t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).l_e_st_eq_landau_n_rt_rp_5160_t5 ksi eta z0 m t) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).
-
-(* notion 2879 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m)) (λt:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp.l_e_st_eq_landau_n_rt_rp_5160_t2 ksi eta z0 m t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).l_e_st_eq_landau_n_rt_rp_5160_t6 ksi eta z0 m t) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m)).
-
-(* notion 2880 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_zr1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z1 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2881 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_zr2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z2 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2882 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_disttp2 (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_satz147a (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) l2 l4) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
-
-(* notion 2883 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) eta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_disttp1 ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) eta) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) eta))) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
-
-(* notion 2884 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz149a (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_satz139a ksi ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_lessisi2 ksi ksi (l_e_refis l_e_st_eq_landau_n_rt_cut ksi)) (l_e_st_eq_landau_n_rt_rp_5160_t7 ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))).
-
-(* notion 2885 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz139a (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_t10 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t11 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
-
-(* notion 2886 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz127b (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_5160_t9 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t12 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
-
-(* notion 2887 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl eta ksi) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_asspl2 eta ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl eta ksi) (l_e_st_eq_landau_n_rt_rp_pl ksi eta) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_compl eta ksi)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)).
-
-(* notion 2888 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_distpt1 eta (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_t14 ksi eta z0 m z1 l1 l2 z2 l3 l4)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))).
-
-(* notion 2889 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_5160_t15 ksi eta z0 m z1 l1 l2 z2 l3 l4)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
-
-(* notion 2890 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_5160_t16 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t13 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
-
-(* notion 2891 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_islessis12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_satz153e (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_satz149a (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_t8 ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)))) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m)).
-
-(* notion 2892 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz139a (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi eta))) (l_e_st_eq_landau_n_rt_rp_5160_t18 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m))).
-
-(* notion 2893 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz127b (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_t17 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t19 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m))).
-
-(* notion 2894 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_satz140c (l_e_st_eq_landau_n_rt_rp_5160_zr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) m) (l_e_st_eq_landau_n_rt_rp_5160_t20 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_5160_zr ksi eta z0 m)).
-
-(* notion 2895 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz154f (l_e_st_eq_landau_n_rt_ts z1 z2) z0 (l_e_st_eq_landau_n_rt_rp_isless1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts z1 z2)) (l_e_st_eq_landau_n_rt_rp_5160_zr ksi eta z0 m) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts z1 z2)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_satz155c z1 z2)) (l_e_st_eq_landau_n_rt_rp_5160_t21 ksi eta z0 m z1 l1 l2 z2 l3 l4)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts z1 z2) z0).
-
-(* notion 2896 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_x0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_ov z0 z2 : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2897 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_xr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2898 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_y0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(z2 : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2899 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_yr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5160_y0 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2900 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_satz110e z0 z2 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_y0 ksi eta z0 m z1 l1 l2 z2 l3 l4)) z0).
-
-(* notion 2901 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_ismore1 z0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z2) (l_e_st_eq_landau_n_rt_ts z1 z2) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z2) z0 (l_e_st_eq_landau_n_rt_rp_5160_t23 ksi eta z0 m z1 l1 l2 z2 l3 l4)) (l_e_st_eq_landau_n_rt_satz83 (l_e_st_eq_landau_n_rt_ts z1 z2) z0 (l_e_st_eq_landau_n_rt_rp_5160_t22 ksi eta z0 m z1 l1 l2 z2 l3 l4)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z2) (l_e_st_eq_landau_n_rt_ts z1 z2)).
-
-(* notion 2902 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_satz106a (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z1 z2 (l_e_st_eq_landau_n_rt_rp_5160_t24 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z1).
-
-(* notion 2903 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_trmore (l_e_st_eq_landau_n_rt_rp_5160_xr ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) ksi (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z1 (l_e_st_eq_landau_n_rt_rp_5160_t25 ksi eta z0 m z1 l1 l2 z2 l3 l4)) (l_e_st_eq_landau_n_rt_rp_satz122 ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) l1) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr ksi eta z0 m z1 l1 l2 z2 l3 l4) ksi).
-
-(* notion 2904 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz122 eta (l_e_st_eq_landau_n_rt_rp_5160_yr ksi eta z0 m z1 l1 l2 z2 l3 l4) l3 : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr ksi eta z0 m z1 l1 l2 z2 l3 l4) eta).
-
-(* notion 2905 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_ur ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt u0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2906 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_vr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt v0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2907 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_prop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_ur ksi eta z0 u0) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_vr ksi eta z0 u0 v0) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts u0 v0) z0) : Prop).
-
-(* notion 2908 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_prop2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x y)) : Prop).
-
-(* notion 2909 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t28 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_and3i (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr ksi eta z0 m z1 l1 l2 z2 l3 l4) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr ksi eta z0 m z1 l1 l2 z2 l3 l4) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_y0 ksi eta z0 m z1 l1 l2 z2 l3 l4)) z0) (l_e_st_eq_landau_n_rt_rp_5160_t26 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t27 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t23 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_y0 ksi eta z0 m z1 l1 l2 z2 l3 l4)).
-
-(* notion 2910 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t29 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_somei l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) y) (l_e_st_eq_landau_n_rt_rp_5160_y0 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t28 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) y)).
-
-(* notion 2911 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t30 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x y)) (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t29 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_5160_prop2 ksi eta z0).
-
-(* notion 2912 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t31 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz159app eta (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_satz133a eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_prop2 ksi eta z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_rpofrt x).λu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).l_e_st_eq_landau_n_rt_rp_5160_t30 ksi eta z0 m z1 l1 l2 x t u) : l_e_st_eq_landau_n_rt_rp_5160_prop2 ksi eta z0).
-
-(* notion 2913 *)
-definition l_e_st_eq_landau_n_rt_rp_satz160 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_st_eq_landau_n_rt_rp_satz159app ksi (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_satz133a ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_prop2 ksi eta z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).λu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).l_e_st_eq_landau_n_rt_rp_5160_t31 ksi eta z0 m x t u) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and3 (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0)))).
-
-(* notion 2914 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_xr1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x1 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2915 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_yr1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).λy1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt y1 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2916 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t32 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).λy1:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y1.(l_and3e1 (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr1 ksi eta z0 m p p1 x1) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr1 ksi eta z0 m p p1 x1 px y1) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 y1) z0) py : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr1 ksi eta z0 m p p1 x1) ksi).
-
-(* notion 2917 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t33 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).λy1:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y1.(l_and3e2 (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr1 ksi eta z0 m p p1 x1) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr1 ksi eta z0 m p p1 x1 px y1) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 y1) z0) py : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr1 ksi eta z0 m p p1 x1 px y1) eta).
-
-(* notion 2918 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t34 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).λy1:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y1.(l_and3e3 (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr1 ksi eta z0 m p p1 x1) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr1 ksi eta z0 m p p1 x1 px y1) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 y1) z0) py : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 y1) z0).
-
-(* notion 2919 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t35 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).λy1:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y1.(p1 x1 (l_e_st_eq_landau_n_rt_rp_5160_t32 ksi eta z0 m p p1 x1 px y1 py) y1 (l_e_st_eq_landau_n_rt_rp_5160_t33 ksi eta z0 m p p1 x1 px y1 py) (l_e_st_eq_landau_n_rt_rp_5160_t34 ksi eta z0 m p p1 x1 px y1 py) : p).
-
-(* notion 2920 *)
-definition l_e_st_eq_landau_n_rt_rp_5160_t36 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).(l_someapp l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y) px p (λy:l_e_st_eq_landau_n_rt_rat.λv:l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y.l_e_st_eq_landau_n_rt_rp_5160_t35 ksi eta z0 m p p1 x1 px y v) : p).
-
-(* notion 2921 *)
-definition l_e_st_eq_landau_n_rt_rp_satz160app ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x y)) (l_e_st_eq_landau_n_rt_rp_satz160 ksi eta z0 m) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x y).l_e_st_eq_landau_n_rt_rp_5160_t36 ksi eta z0 m p p1 x t) : p).
-
-(* notion 2922 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_min ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_ite (l_e_st_eq_landau_n_rt_rp_less ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2923 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_max ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_ite (l_e_st_eq_landau_n_rt_rp_more ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2924 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_ur ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt u0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2925 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.(l_e_st_eq_landau_n_rt_rp_satz158a (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0 lu : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta)).
-
-(* notion 2926 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) ksi (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_itet (l_e_st_eq_landau_n_rt_rp_less ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta l) (l_e_st_eq_landau_n_rt_rp_5161_t1 ksi eta u0 lu) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
-
-(* notion 2927 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_trless (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi eta (l_e_st_eq_landau_n_rt_rp_5161_t2 ksi eta u0 lu l) l : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
-
-(* notion 2928 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.λn:l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta).(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) eta (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_itef (l_e_st_eq_landau_n_rt_rp_less ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta n) (l_e_st_eq_landau_n_rt_rp_5161_t1 ksi eta u0 lu) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
-
-(* notion 2929 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.λn:l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta).(l_e_st_eq_landau_n_rt_rp_satz127b (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta ksi (l_e_st_eq_landau_n_rt_rp_5161_t4 ksi eta u0 lu n) (l_e_st_eq_landau_n_rt_rp_satz124 ksi eta (l_e_st_eq_landau_n_rt_rp_satz123f ksi eta n)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
-
-(* notion 2930 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi) (λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_5161_t2 ksi eta u0 lu t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta).l_e_st_eq_landau_n_rt_rp_5161_t5 ksi eta u0 lu t) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
-
-(* notion 2931 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta) (λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_5161_t3 ksi eta u0 lu t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta).l_e_st_eq_landau_n_rt_rp_5161_t4 ksi eta u0 lu t) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
-
-(* notion 2932 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.(l_e_st_eq_landau_n_rt_rp_satz158b (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0 uu : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta)).
-
-(* notion 2933 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismoreis2 (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) ksi (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_itet (l_e_st_eq_landau_n_rt_rp_more ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta m) (l_e_st_eq_landau_n_rt_rp_5161_t8 ksi eta u0 uu) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
-
-(* notion 2934 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_trmoreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi eta (l_e_st_eq_landau_n_rt_rp_5161_t9 ksi eta u0 uu m) (l_e_st_eq_landau_n_rt_rp_moreisi1 ksi eta m) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
-
-(* notion 2935 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.λn:l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta).(l_e_st_eq_landau_n_rt_rp_ismoreis2 (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) eta (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_itef (l_e_st_eq_landau_n_rt_rp_more ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta n) (l_e_st_eq_landau_n_rt_rp_5161_t8 ksi eta u0 uu) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
-
-(* notion 2936 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.λn:l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta).(l_e_st_eq_landau_n_rt_rp_trmoreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta ksi (l_e_st_eq_landau_n_rt_rp_5161_t11 ksi eta u0 uu n) (l_e_st_eq_landau_n_rt_rp_satz125 ksi eta (l_e_st_eq_landau_n_rt_rp_satz123e ksi eta n)) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
-
-(* notion 2937 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi) (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_5161_t9 ksi eta u0 uu t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta).l_e_st_eq_landau_n_rt_rp_5161_t12 ksi eta u0 uu t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
-
-(* notion 2938 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta) (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_5161_t10 ksi eta u0 uu t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta).l_e_st_eq_landau_n_rt_rp_5161_t11 ksi eta u0 uu t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
-
-(* notion 2939 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t15 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi1 ksi2.(l_e_st_eq_landau_n_rt_rp_satz147 ksi1 ksi2 ksi1 ksi2 m m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi1 ksi1) (l_e_st_eq_landau_n_rt_rp_ts ksi2 ksi2)).
-
-(* notion 2940 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_sq1 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ts ksi1 ksi1 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2941 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_sq2 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ts ksi2 ksi2 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2942 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t16 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi1 ksi2.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)) (l_e_st_eq_landau_n_rt_rp_5161_t15 zeta ksi1 ksi2 m) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)).
-
-(* notion 2943 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t17 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) zeta.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) zeta.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) zeta i j : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)).
-
-(* notion 2944 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t18 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) zeta.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) zeta.(λt:l_e_st_eq_landau_n_rt_rp_more ksi1 ksi2.l_e_st_eq_landau_n_rt_rp_5161_t16 zeta ksi1 ksi2 t (l_e_st_eq_landau_n_rt_rp_5161_t17 zeta ksi1 ksi2 i j) : l_not (l_e_st_eq_landau_n_rt_rp_more ksi1 ksi2)).
-
-(* notion 2945 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t19 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) zeta.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) zeta.(λt:l_e_st_eq_landau_n_rt_rp_less ksi1 ksi2.l_e_st_eq_landau_n_rt_rp_5161_t16 zeta ksi2 ksi1 (l_e_st_eq_landau_n_rt_rp_satz122 ksi1 ksi2 t) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_t17 zeta ksi1 ksi2 i j)) : l_not (l_e_st_eq_landau_n_rt_rp_less ksi1 ksi2)).
-
-(* notion 2946 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t20 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) zeta.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) zeta.(l_or3e1 (l_e_st_eq_landau_n_rt_rp_is ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_more ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_less ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_satz123a ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_t18 zeta ksi1 ksi2 i j) (l_e_st_eq_landau_n_rt_rp_5161_t19 zeta ksi1 ksi2 i j) : l_e_st_eq_landau_n_rt_rp_is ksi1 ksi2).
-
-(* notion 2947 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t21 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(λa:l_e_st_eq_landau_n_rt_cut.λb:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta.λu:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts b b) zeta.l_e_st_eq_landau_n_rt_rp_5161_t20 zeta a b t u : l_e_amone l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta)).
-
-(* notion 2948 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_sqrtset ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
-
-(* notion 2949 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_xr ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2950 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t22 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_5161_t6 l_e_st_eq_landau_n_rt_rp_1rp zeta x0 lx : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp).
-
-(* notion 2951 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t23 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_5161_t7 l_e_st_eq_landau_n_rt_rp_1rp zeta x0 lx : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) zeta).
-
-(* notion 2952 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t24 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_isless1 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta (l_e_st_eq_landau_n_rt_rp_satz151a (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_t23 zeta x0 lx) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta).
-
-(* notion 2953 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t25 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_trless (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta (l_e_st_eq_landau_n_rt_rp_satz148c (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0))) (l_e_st_eq_landau_n_rt_rp_5161_t22 zeta x0 lx)) (l_e_st_eq_landau_n_rt_rp_5161_t24 zeta x0 lx) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta).
-
-(* notion 2954 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t26 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) x0 (l_e_st_eq_landau_n_rt_rp_5161_t25 zeta x0 lx) : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
-
-(* notion 2955 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t27 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_5161_t13 l_e_st_eq_landau_n_rt_rp_1rp zeta x0 ux : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp).
-
-(* notion 2956 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t28 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_5161_t14 l_e_st_eq_landau_n_rt_rp_1rp zeta x0 ux : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) zeta).
-
-(* notion 2957 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t29 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_ismoreis1 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta (l_e_st_eq_landau_n_rt_rp_satz151a (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_t28 zeta x0 ux) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta).
-
-(* notion 2958 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t30 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_trmoreis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta (l_e_st_eq_landau_n_rt_rp_satz149 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0))) (l_e_st_eq_landau_n_rt_rp_5161_t27 zeta x0 ux)) (l_e_st_eq_landau_n_rt_rp_5161_t29 zeta x0 ux) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta).
-
-(* notion 2959 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t31 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_satz123c (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta (l_e_st_eq_landau_n_rt_rp_5161_t30 zeta x0 ux) : l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta)).
-
-(* notion 2960 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t32 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta) (l_e_st_eq_landau_n_rt_rp_5161_t31 zeta x0 ux) (λt:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) x0 t) : l_not (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta))).
-
-(* notion 2961 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_yr ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt y0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2962 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t33 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) x0 i : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta).
-
-(* notion 2963 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t34 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_satz154c y0 x0 l : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)).
-
-(* notion 2964 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t35 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_trless (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0) (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta (l_e_st_eq_landau_n_rt_rp_satz147a (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_t34 zeta x0 i y0 l) (l_e_st_eq_landau_n_rt_rp_5161_t34 zeta x0 i y0 l)) (l_e_st_eq_landau_n_rt_rp_5161_t33 zeta x0 i) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0) (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0)) zeta).
-
-(* notion 2965 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t36 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) y0 (l_e_st_eq_landau_n_rt_rp_5161_t35 zeta x0 i y0 l) : l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
-
-(* notion 2966 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t37 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta (l_e_st_eq_landau_n_rt_rp_5161_t33 zeta x0 i) : l_e_st_eq_landau_n_rt_rp_more zeta (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0))).
-
-(* notion 2967 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_nm ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_eq_landau_n_rt_rp_mn zeta (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_t37 zeta x0 i) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2968 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_dn ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2969 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_fr ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_eq_landau_n_rt_rp_ov (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2970 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_zr ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2971 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t38 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_5161_t6 l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i) z0 lz : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) l_e_st_eq_landau_n_rt_rp_1rp).
-
-(* notion 2972 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t39 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_5161_t7 l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i) z0 lz : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)).
-
-(* notion 2973 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t40 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_satz94 x0 z0 : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) x0).
-
-(* notion 2974 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t41 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ists12 (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_satz155a x0 z0) (l_e_st_eq_landau_n_rt_rp_satz155a x0 z0)) (l_e_st_eq_landau_n_rt_rp_disttp2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))).
-
-(* notion 2975 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t42 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_5161_t41 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)))).
-
-(* notion 2976 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t43 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_disttp1 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)))) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))).
-
-(* notion 2977 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t44 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_satz145c (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_satz138c (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0))) (l_e_st_eq_landau_n_rt_rp_5161_t38 zeta x0 i z0 lz)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))).
-
-(* notion 2978 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t45 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_satz138c (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_t43 zeta x0 i z0 lz) (l_e_st_eq_landau_n_rt_rp_5161_t44 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))).
-
-(* notion 2979 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t46 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_distpt1 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))).
-
-(* notion 2980 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t47 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_5161_t42 zeta x0 i z0 lz) (l_e_st_eq_landau_n_rt_rp_5161_t46 zeta x0 i z0 lz) (l_e_st_eq_landau_n_rt_rp_5161_t45 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))).
-
-(* notion 2981 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t48 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_satz153c (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i)) (l_e_st_eq_landau_n_rt_rp_satz148c (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i) (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i))) (l_e_st_eq_landau_n_rt_rp_5161_t39 zeta x0 i z0 lz)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i)).
-
-(* notion 2982 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t49 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_satz138c (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i) (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)))) (l_e_st_eq_landau_n_rt_rp_5161_t48 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i))).
-
-(* notion 2983 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t50 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i)) zeta (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_satz140c zeta (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_t37 zeta x0 i)) (l_e_st_eq_landau_n_rt_rp_5161_t49 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) zeta).
-
-(* notion 2984 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t51 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_trless (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) zeta (l_e_st_eq_landau_n_rt_rp_5161_t47 zeta x0 i z0 lz) (l_e_st_eq_landau_n_rt_rp_5161_t50 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) zeta).
-
-(* notion 2985 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t52 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_rp_5161_t51 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
-
-(* notion 2986 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t53 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_andi (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) x0) (l_e_st_eq_landau_n_rt_rp_5161_t52 zeta x0 i z0 lz) (l_e_st_eq_landau_n_rt_rp_5161_t40 zeta x0 i z0 lz) : l_and (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) x0)).
-
-(* notion 2987 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t54 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_somei l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more y x0)) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_rp_5161_t53 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more y x0))).
-
-(* notion 2988 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t55 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_eq_landau_n_rt_cutapp1a (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) (l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more y x0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) x.l_e_st_eq_landau_n_rt_rp_5161_t54 zeta x0 i x t) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more y x0))).
-
-(* notion 2989 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t56 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) y0.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta) x0 (l_e_st_eq_landau_n_rt_rp_5161_t26 zeta x0 lx) y0 (l_e_st_eq_landau_n_rt_rp_5161_t32 zeta y0 uy) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_5161_t36 zeta x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).l_e_st_eq_landau_n_rt_rp_5161_t55 zeta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
-
-(* notion 2990 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t57 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_cutapp1b (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) y.l_e_st_eq_landau_n_rt_rp_5161_t56 zeta x0 lx y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
-
-(* notion 2991 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t58 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_cutapp1a (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x.l_e_st_eq_landau_n_rt_rp_5161_t57 zeta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
-
-(* notion 2992 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_rtc ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta) (l_e_st_eq_landau_n_rt_rp_5161_t58 zeta) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2993 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t59 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.(l_or_th9 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) l (λt:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_rp_satz154c x0 y0 t) (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_rp_satz154b x0 y0 t) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
-
-(* notion 2994 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t60 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.(l_e_st_eq_landau_n_rt_rp_satz125 (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_5161_t59 y0 x0 (l_e_st_eq_landau_n_rt_satz84 x0 y0 m)) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
-
-(* notion 2995 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t61 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta m : l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta))).
-
-(* notion 2996 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_zr1 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z1 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2997 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t62 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).(l_e_st_eq_landau_n_rt_rp_satz158c (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) z1 l2 : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) z1).
-
-(* notion 2998 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_xr1 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x1 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 2999 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_xr2 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x2 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3000 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_xm ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_ite (l_e_st_eq_landau_n_rt_more x1 x2) l_e_st_eq_landau_n_rt_rat x1 x2 : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 3001 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_xrm ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3002 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t63 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λo:l_e_st_eq_landau_n_rt_more x1 x2.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) x1 (l_e_itet (l_e_st_eq_landau_n_rt_more x1 x2) l_e_st_eq_landau_n_rt_rat x1 x2 o) : l_e_st_eq_landau_n_rt_is x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3003 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t64 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λo:l_e_st_eq_landau_n_rt_more x1 x2.(l_e_isp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x) x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) lx1 (l_e_st_eq_landau_n_rt_rp_5161_t63 zeta m z1 l1 l2 x1 lx1 x2 lx2 i o) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3004 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t65 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λo:l_e_st_eq_landau_n_rt_more x1 x2.(l_e_st_eq_landau_n_rt_lessisi2 x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t63 zeta m z1 l1 l2 x1 lx1 x2 lx2 i o) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3005 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t66 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λo:l_e_st_eq_landau_n_rt_more x1 x2.(l_e_st_eq_landau_n_rt_lessisi1 x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_satz87b x2 x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_satz82 x1 x2 o) (l_e_st_eq_landau_n_rt_rp_5161_t65 zeta m z1 l1 l2 x1 lx1 x2 lx2 i o)) : l_e_st_eq_landau_n_rt_lessis x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3006 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t67 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λn:l_not (l_e_st_eq_landau_n_rt_more x1 x2).(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) x2 (l_e_itef (l_e_st_eq_landau_n_rt_more x1 x2) l_e_st_eq_landau_n_rt_rat x1 x2 n) : l_e_st_eq_landau_n_rt_is x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3007 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t68 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λn:l_not (l_e_st_eq_landau_n_rt_more x1 x2).(l_e_isp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x) x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) lx2 (l_e_st_eq_landau_n_rt_rp_5161_t67 zeta m z1 l1 l2 x1 lx1 x2 lx2 i n) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3008 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t69 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λn:l_not (l_e_st_eq_landau_n_rt_more x1 x2).(l_e_st_eq_landau_n_rt_lessisi2 x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t67 zeta m z1 l1 l2 x1 lx1 x2 lx2 i n) : l_e_st_eq_landau_n_rt_lessis x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3009 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t70 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λn:l_not (l_e_st_eq_landau_n_rt_more x1 x2).(l_e_st_eq_landau_n_rt_satz88 x1 x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_satz81e x1 x2 n) (l_e_st_eq_landau_n_rt_rp_5161_t69 zeta m z1 l1 l2 x1 lx1 x2 lx2 i n) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3010 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t71 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_imp_th1 (l_e_st_eq_landau_n_rt_more x1 x2) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) (λt:l_e_st_eq_landau_n_rt_more x1 x2.l_e_st_eq_landau_n_rt_rp_5161_t64 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_more x1 x2).l_e_st_eq_landau_n_rt_rp_5161_t68 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3011 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t72 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_imp_th1 (l_e_st_eq_landau_n_rt_more x1 x2) (l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) (λt:l_e_st_eq_landau_n_rt_more x1 x2.l_e_st_eq_landau_n_rt_rp_5161_t65 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_more x1 x2).l_e_st_eq_landau_n_rt_rp_5161_t70 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3012 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t73 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_imp_th1 (l_e_st_eq_landau_n_rt_more x1 x2) (l_e_st_eq_landau_n_rt_lessis x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) (λt:l_e_st_eq_landau_n_rt_more x1 x2.l_e_st_eq_landau_n_rt_rp_5161_t66 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_more x1 x2).l_e_st_eq_landau_n_rt_rp_5161_t69 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) : l_e_st_eq_landau_n_rt_lessis x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3013 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t74 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta) (l_e_st_eq_landau_n_rt_rp_5161_t58 zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t71 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
-
-(* notion 3014 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t75 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_5161_t59 x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t72 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3015 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t76 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_5161_t59 x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t73 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
-
-(* notion 3016 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t77 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x1 x2)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2)) (l_e_st_eq_landau_n_rt_rp_satz154b z1 (l_e_st_eq_landau_n_rt_ts x1 x2) i) (l_e_st_eq_landau_n_rt_rp_satz155c x1 x2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2))).
-
-(* notion 3017 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t78 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_islessis1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2)) (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2)) (l_e_st_eq_landau_n_rt_rp_5161_t77 zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) (l_e_st_eq_landau_n_rt_rp_satz149a (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t75 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t76 zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i))).
-
-(* notion 3018 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t79 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t74 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) zeta).
-
-(* notion 3019 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t80 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_satz127a (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) zeta (l_e_st_eq_landau_n_rt_rp_5161_t78 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t79 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) zeta).
-
-(* notion 3020 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t81 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_ec3e23 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) zeta) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) zeta) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) zeta) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) zeta) (l_e_st_eq_landau_n_rt_rp_satz122 zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) l1) (l_e_st_eq_landau_n_rt_rp_5161_t80 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_con).
-
-(* notion 3021 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t82 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_tsapp (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) z1 (l_e_st_eq_landau_n_rt_rp_5161_t62 zeta m z1 l1 l2) l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) y.λv:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_5161_t81 zeta m z1 l1 l2 x t y u v) : l_con).
-
-(* notion 3022 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t82a ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).(l_e_st_eq_landau_n_rt_rp_tsapp (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) z1 (l_e_st_eq_landau_n_rt_rp_5161_t62 zeta m z1 l1 l2) l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) y.λv:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_5161_t82 zeta m z1 l1 l2 x t y u v) : l_con).
-
-(* notion 3023 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t83 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.(l_e_st_eq_landau_n_rt_rp_satz159app zeta (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_t61 zeta m) l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_rpofrt x).λu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).l_e_st_eq_landau_n_rt_rp_5161_t82a zeta m x t u) : l_con).
-
-(* notion 3024 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_zr2 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z2 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3025 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t84 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.(l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) l3 : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta))).
-
-(* notion 3026 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_yr1 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt y1 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3027 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_yr2 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt y2 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3028 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_ym ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_ite (l_e_st_eq_landau_n_rt_less y1 y2) l_e_st_eq_landau_n_rt_rat y1 y2 : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 3029 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_yrm ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3030 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t85 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λk:l_e_st_eq_landau_n_rt_less y1 y2.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) y1 (l_e_itet (l_e_st_eq_landau_n_rt_less y1 y2) l_e_st_eq_landau_n_rt_rat y1 y2 k) : l_e_st_eq_landau_n_rt_is y1 (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i)).
-
-(* notion 3031 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t86 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λk:l_e_st_eq_landau_n_rt_less y1 y2.(l_e_st_eq_landau_n_rt_rp_satz154b y1 (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t85 zeta l z2 l3 l4 y1 m1 y2 m2 i k) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
-
-(* notion 3032 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t87 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λk:l_e_st_eq_landau_n_rt_less y1 y2.(l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_t86 zeta l z2 l3 l4 y1 m1 y2 m2 i k) m1 : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).
-
-(* notion 3033 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t88 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λk:l_e_st_eq_landau_n_rt_less y1 y2.(l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t86 zeta l z2 l3 l4 y1 m1 y2 m2 i k) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
-
-(* notion 3034 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t89 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λk:l_e_st_eq_landau_n_rt_less y1 y2.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_satz127d (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_satz154c y1 y2 k)) (l_e_st_eq_landau_n_rt_rp_5161_t88 zeta l z2 l3 l4 y1 m1 y2 m2 i k)) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
-
-(* notion 3035 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t90 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λn:l_not (l_e_st_eq_landau_n_rt_less y1 y2).(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) y2 (l_e_itef (l_e_st_eq_landau_n_rt_less y1 y2) l_e_st_eq_landau_n_rt_rat y1 y2 n) : l_e_st_eq_landau_n_rt_is y2 (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i)).
-
-(* notion 3036 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t91 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λn:l_not (l_e_st_eq_landau_n_rt_less y1 y2).(l_e_st_eq_landau_n_rt_rp_satz154b y2 (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t90 zeta l z2 l3 l4 y1 m1 y2 m2 i n) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
-
-(* notion 3037 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t92 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λn:l_not (l_e_st_eq_landau_n_rt_less y1 y2).(l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_t91 zeta l z2 l3 l4 y1 m1 y2 m2 i n) m2 : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).
-
-(* notion 3038 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t93 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λn:l_not (l_e_st_eq_landau_n_rt_less y1 y2).(l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t91 zeta l z2 l3 l4 y1 m1 y2 m2 i n) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
-
-(* notion 3039 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t94 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λn:l_not (l_e_st_eq_landau_n_rt_less y1 y2).(l_e_st_eq_landau_n_rt_rp_trmoreis (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t60 y1 y2 (l_e_st_eq_landau_n_rt_satz81f y1 y2 n)) (l_e_st_eq_landau_n_rt_rp_5161_t93 zeta l z2 l3 l4 y1 m1 y2 m2 i n) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
-
-(* notion 3040 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t95 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_imp_th1 (l_e_st_eq_landau_n_rt_less y1 y2) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (λt:l_e_st_eq_landau_n_rt_less y1 y2.l_e_st_eq_landau_n_rt_rp_5161_t87 zeta l z2 l3 l4 y1 m1 y2 m2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_less y1 y2).l_e_st_eq_landau_n_rt_rp_5161_t92 zeta l z2 l3 l4 y1 m1 y2 m2 i t) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).
-
-(* notion 3041 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t96 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_imp_th1 (l_e_st_eq_landau_n_rt_less y1 y2) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) (λt:l_e_st_eq_landau_n_rt_less y1 y2.l_e_st_eq_landau_n_rt_rp_5161_t88 zeta l z2 l3 l4 y1 m1 y2 m2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_less y1 y2).l_e_st_eq_landau_n_rt_rp_5161_t94 zeta l z2 l3 l4 y1 m1 y2 m2 i t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
-
-(* notion 3042 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t97 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_imp_th1 (l_e_st_eq_landau_n_rt_less y1 y2) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) (λt:l_e_st_eq_landau_n_rt_less y1 y2.l_e_st_eq_landau_n_rt_rp_5161_t89 zeta l z2 l3 l4 y1 m1 y2 m2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_less y1 y2).l_e_st_eq_landau_n_rt_rp_5161_t93 zeta l z2 l3 l4 y1 m1 y2 m2 i t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
-
-(* notion 3043 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t98 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_satz158d (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_t95 zeta l z2 l3 l4 y1 m1 y2 m2 i)) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i)).
-
-(* notion 3044 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t99 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_imp_th3 (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i)) (l_e_st_eq_landau_n_rt_rp_5161_t98 zeta l z2 l3 l4 y1 m1 y2 m2 i) (λt:l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta) (l_e_st_eq_landau_n_rt_rp_5161_t58 zeta) (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) t) : l_not (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta))).
-
-(* notion 3045 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t100 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta) (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_rp_5161_t99 zeta l z2 l3 l4 y1 m1 y2 m2 i) (λt:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta.l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) t) : l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta)).
-
-(* notion 3046 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t101 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_satz123f (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta (l_e_st_eq_landau_n_rt_rp_5161_t100 zeta l z2 l3 l4 y1 m1 y2 m2 i) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta).
-
-(* notion 3047 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t101a ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_satz149 (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t96 zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t97 zeta l z2 l3 l4 y1 m1 y2 m2 i) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i))).
-
-(* notion 3048 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t102 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_ismoreis1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts y1 y2)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts y1 y2)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2)) (l_e_st_eq_landau_n_rt_rp_satz155c y1 y2)) (l_e_st_eq_landau_n_rt_rp_satz154b (l_e_st_eq_landau_n_rt_ts y1 y2) z2 i)) (l_e_st_eq_landau_n_rt_rp_5161_t101a zeta l z2 l3 l4 y1 m1 y2 m2 i) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i))).
-
-(* notion 3049 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t103 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_trmoreis (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta (l_e_st_eq_landau_n_rt_rp_5161_t102 zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t101 zeta l z2 l3 l4 y1 m1 y2 m2 i) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta).
-
-(* notion 3050 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t104 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_satz123c (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta (l_e_st_eq_landau_n_rt_rp_5161_t103 zeta l z2 l3 l4 y1 m1 y2 m2 i) l4 : l_con).
-
-(* notion 3051 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t105 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.(l_e_st_eq_landau_n_rt_rp_satz160app (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) z2 (l_e_st_eq_landau_n_rt_rp_5161_t84 zeta l z2 l3 l4) l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z2.l_e_st_eq_landau_n_rt_rp_5161_t104 zeta l z2 l3 l4 x t y u v) : l_con).
-
-(* notion 3052 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t106 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.(l_e_st_eq_landau_n_rt_rp_satz159app (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta l l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_rpofrt x).λu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) zeta.l_e_st_eq_landau_n_rt_rp_5161_t105 zeta l x t u) : l_con).
-
-(* notion 3053 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t107 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_or3e1 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta) (l_e_st_eq_landau_n_rt_rp_satz123a (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta) (λt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.l_e_st_eq_landau_n_rt_rp_5161_t83 zeta t) (λt:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.l_e_st_eq_landau_n_rt_rp_5161_t106 zeta t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta).
-
-(* notion 3054 *)
-definition l_e_st_eq_landau_n_rt_rp_5161_t108 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_somei l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_t107 zeta) : l_e_st_eq_landau_n_rt_rp_some (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta)).
-
-(* notion 3055 *)
-definition l_e_st_eq_landau_n_rt_rp_satz161 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_onei l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta) (l_e_st_eq_landau_n_rt_rp_5161_t21 zeta) (l_e_st_eq_landau_n_rt_rp_5161_t108 zeta) : l_e_st_eq_landau_n_rt_rp_one (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta)).
-
-(* notion 3056 *)
-definition l_e_st_eq_landau_n_rt_rp_irratrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_not (l_e_st_eq_landau_n_rt_rp_ratrp ksi) : Prop).
-
-(* notion 3057 *)
-definition l_e_st_eq_landau_n_5162_t1 ≝ λv:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl v v) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 v) v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) v) (l_e_st_eq_landau_n_ispl1 v (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 v) v (l_e_st_eq_landau_n_satz28g v)) (l_e_st_eq_landau_n_satz28h l_e_st_eq_landau_n_1 v) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) v)).
-
-(* notion 3058 *)
-definition l_e_st_eq_landau_n_5162_t2 ≝ λv:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_pl v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) v) v (l_e_st_eq_landau_n_5162_t1 v) (l_e_st_eq_landau_n_satz18a v v) : l_e_st_eq_landau_n_less v (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) v)).
-
-(* notion 3059 *)
-definition l_e_st_eq_landau_n_5162_t3 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts w w).(l_e_st_eq_landau_n_satz10j v w (l_imp_th3 (l_e_st_eq_landau_n_moreis v w) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_satz10h (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts w w) l) (λt:l_e_st_eq_landau_n_moreis v w.l_e_st_eq_landau_n_satz36 v w v w t t)) : l_e_st_eq_landau_n_less v w).
-
-(* notion 3060 *)
-definition l_e_st_eq_landau_n_5162_t4 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) v) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts w v)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_disttp1 v w v) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_ts w v) (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_comts w v)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) v) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w))).
-
-(* notion 3061 *)
-definition l_e_st_eq_landau_n_5162_t5 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts w w))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_disttp2 (l_e_st_eq_landau_n_pl v w) v w) (l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) v) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) w) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_5162_t4 v w) (l_e_st_eq_landau_n_disttp1 v w w)) (l_e_st_eq_landau_n_asspl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts w w)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts w w))).
-
-(* notion 3062 *)
-definition l_e_st_eq_landau_n_5162_t6 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_5162_t1 (l_e_st_eq_landau_n_ts v w))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w)))).
-
-(* notion 3063 *)
-definition l_e_st_eq_landau_n_5162_nun ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_5162_t5 v w) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_ts w w) (l_e_st_eq_landau_n_5162_t6 v w)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_ts w w))).
-
-(* notion 3064 *)
-definition l_e_st_eq_landau_n_5162_nun1 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_5162_nun v w) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w))).
-
-(* notion 3065 *)
-definition l_e_st_eq_landau_n_5162_prop1 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr w v) (l_e_st_eq_landau_n_fr w v)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) : Prop).
-
-(* notion 3066 *)
-definition l_e_st_eq_landau_n_5162_prop2 ≝ λv:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_some (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop1 v t) : Prop).
-
-(* notion 3067 *)
-definition l_e_st_eq_landau_n_5162_prop3 ≝ (l_e_st_eq_landau_n_some (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) : Prop).
-
-(* notion 3068 *)
-definition l_e_st_eq_landau_n_5162_y ≝ λp:l_e_st_eq_landau_n_5162_prop3.(l_e_ind l_e_st_eq_landau_n_nat (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) t) (l_e_st_eq_landau_n_satz27a (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) p) : l_e_st_eq_landau_n_nat).
-
-(* notion 3069 *)
-definition l_e_st_eq_landau_n_5162_t7 ≝ λp:l_e_st_eq_landau_n_5162_prop3.(l_e_oneax l_e_st_eq_landau_n_nat (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) t) (l_e_st_eq_landau_n_satz27a (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) p) : l_e_st_eq_landau_n_min (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) (l_e_st_eq_landau_n_5162_y p)).
-
-(* notion 3070 *)
-definition l_e_st_eq_landau_n_5162_t8 ≝ λp:l_e_st_eq_landau_n_5162_prop3.(l_ande1 (l_e_st_eq_landau_n_lb (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_prop2 (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t7 p) : l_e_st_eq_landau_n_lb (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) (l_e_st_eq_landau_n_5162_y p)).
-
-(* notion 3071 *)
-definition l_e_st_eq_landau_n_5162_t9 ≝ λp:l_e_st_eq_landau_n_5162_prop3.(l_ande2 (l_e_st_eq_landau_n_lb (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_prop2 (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t7 p) : l_e_st_eq_landau_n_5162_prop2 (l_e_st_eq_landau_n_5162_y p)).
-
-(* notion 3072 *)
-definition l_e_st_eq_landau_n_5162_t10 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_st_eq_landau_n_treq1 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_fr x (l_e_st_eq_landau_n_5162_y p))) q (l_e_st_eq_landau_n_tfeq12a x (l_e_st_eq_landau_n_5162_y p) x (l_e_st_eq_landau_n_5162_y p)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)))).
-
-(* notion 3073 *)
-definition l_e_st_eq_landau_n_5162_t11 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)))) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_12isnd (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_5162_t10 p x q) (l_e_st_eq_landau_n_ndis12 (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz28a (l_e_st_eq_landau_n_ts x x)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x)).
-
-(* notion 3074 *)
-definition l_e_st_eq_landau_n_5162_t12 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t11 p x q) (l_e_st_eq_landau_n_5162_t2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts x x)).
-
-(* notion 3075 *)
-definition l_e_st_eq_landau_n_5162_t13 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_st_eq_landau_n_isless1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p))) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t11 p x q)) (l_e_st_eq_landau_n_satz35c (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)))) (l_e_st_eq_landau_n_5162_t2 (l_e_st_eq_landau_n_5162_y p))) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)))).
-
-(* notion 3076 *)
-definition l_e_st_eq_landau_n_5162_t14 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_st_eq_landau_n_5162_t3 (l_e_st_eq_landau_n_5162_y p) x (l_e_st_eq_landau_n_5162_t12 p x q) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_5162_y p) x).
-
-(* notion 3077 *)
-definition l_e_st_eq_landau_n_5162_t15 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_st_eq_landau_n_5162_t3 x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t13 p x q) : l_e_st_eq_landau_n_less x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p))).
-
-(* notion 3078 *)
-definition l_e_st_eq_landau_n_5162_t16 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).(l_e_st_eq_landau_n_isless12 x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) i (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t1 (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_5162_t15 p x q) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))).
-
-(* notion 3079 *)
-definition l_e_st_eq_landau_n_5162_t17 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).(l_e_st_eq_landau_n_satz20f u (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_t16 p x q u i) : l_e_st_eq_landau_n_less u (l_e_st_eq_landau_n_5162_y p)).
-
-(* notion 3080 *)
-definition l_e_st_eq_landau_n_5162_t18 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t) j : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl u t) (l_e_st_eq_landau_n_5162_y p)).
-
-(* notion 3081 *)
-definition l_e_st_eq_landau_n_5162_t19 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ists12 x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u) x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u) i i) (l_e_st_eq_landau_n_5162_nun (l_e_st_eq_landau_n_5162_y p) u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_ts u u))).
-
-(* notion 3082 *)
-definition l_e_st_eq_landau_n_5162_t20 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_5162_t19 p x q u i t j)) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)))).
-
-(* notion 3083 *)
-definition l_e_st_eq_landau_n_5162_t21 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_ts u (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts u (l_e_st_eq_landau_n_pl u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t) u j) (l_e_st_eq_landau_n_disttp2 u u t) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts u t))).
-
-(* notion 3084 *)
-definition l_e_st_eq_landau_n_5162_t22 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_t21 p x q u i t j)) (l_e_st_eq_landau_n_disttp2 (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts u t)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)))).
-
-(* notion 3085 *)
-definition l_e_st_eq_landau_n_5162_t23 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t22 p x q u i t j)) (l_e_st_eq_landau_n_asspl2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)))).
-
-(* notion 3086 *)
-definition l_e_st_eq_landau_n_5162_t24 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)))) (l_e_st_eq_landau_n_5162_t20 p x q u i t j) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_5162_t23 p x q u i t j)) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))))).
-
-(* notion 3087 *)
-definition l_e_st_eq_landau_n_5162_t25 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl u t) (l_e_st_eq_landau_n_pl u t)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_asspl2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_compl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_5162_nun1 u t) (l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_pl u t) (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t) (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_t18 p x q u i t j) (l_e_st_eq_landau_n_5162_t18 p x q u i t j)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))).
-
-(* notion 3088 *)
-definition l_e_st_eq_landau_n_5162_t26 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_5162_t24 p x q u i t j) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_5162_t25 p x q u i t j)) (l_e_st_eq_landau_n_compl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_asspl2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)))).
-
-(* notion 3089 *)
-definition l_e_st_eq_landau_n_5162_t27 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_5162_t1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_5162_t11 p x q) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x)).
-
-(* notion 3090 *)
-definition l_e_st_eq_landau_n_5162_t28 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_5162_t26 p x q u i t j) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_5162_t27 p x q u i t j)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)))).
-
-(* notion 3091 *)
-definition l_e_st_eq_landau_n_5162_t29 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_st_eq_landau_n_satz20e (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_5162_t28 p x q u i t j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))).
-
-(* notion 3092 *)
-definition l_e_st_eq_landau_n_5162_t30 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts t t) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_ndis12 (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u)) (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_5162_t29 p x q u i t j)) (l_e_st_eq_landau_n_satz28e (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_12isnd (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u))).
-
-(* notion 3093 *)
-definition l_e_st_eq_landau_n_5162_t31 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_st_eq_landau_n_treq2 (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr t u) (l_e_st_eq_landau_n_fr t u)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_tfeq12a t u t u) (l_e_st_eq_landau_n_5162_t30 p x q u i t j) : l_e_st_eq_landau_n_5162_prop1 u t).
-
-(* notion 3094 *)
-definition l_e_st_eq_landau_n_5162_t32 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_somei l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop1 u v) t (l_e_st_eq_landau_n_5162_t31 p x q u i t j) : l_e_st_eq_landau_n_5162_prop2 u).
-
-(* notion 3095 *)
-definition l_e_st_eq_landau_n_5162_t33 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_st_eq_landau_n_5162_t8 p u (l_e_st_eq_landau_n_5162_t32 p x q u i t j) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_5162_y p) u).
-
-(* notion 3096 *)
-definition l_e_st_eq_landau_n_5162_t34 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_st_eq_landau_n_satz10g (l_e_st_eq_landau_n_5162_y p) u (l_e_st_eq_landau_n_satz12 u (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_t17 p x q u i)) (l_e_st_eq_landau_n_5162_t33 p x q u i t j) : l_con).
-
-(* notion 3097 *)
-definition l_e_st_eq_landau_n_5162_t35 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_5162_y p) u v) (l_e_st_eq_landau_n_5162_t17 p x q u i) l_con (λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_5162_y p) u v.l_e_st_eq_landau_n_5162_t34 p x q u i v w) : l_con).
-
-(* notion 3098 *)
-definition l_e_st_eq_landau_n_5162_t36 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x (l_e_st_eq_landau_n_5162_y p) v) (l_e_st_eq_landau_n_5162_t14 p x q) l_con (λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_diffprop x (l_e_st_eq_landau_n_5162_y p) v.l_e_st_eq_landau_n_5162_t35 p x q v w) : l_con).
-
-(* notion 3099 *)
-definition l_e_st_eq_landau_n_5162_t37 ≝ λp:l_e_st_eq_landau_n_5162_prop3.(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) v) (l_e_st_eq_landau_n_5162_t9 p) l_con (λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) v.l_e_st_eq_landau_n_5162_t36 p v w) : l_con).
-
-(* notion 3100 *)
-definition l_e_st_eq_landau_n_rt_5162_t38 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_tf x x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_tict x0 x0 x x xix0 xix0) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1)) i : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1)).
-
-(* notion 3101 *)
-definition l_e_st_eq_landau_n_rt_5162_t39 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x (l_e_st_eq_landau_n_fris x) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x).
-
-(* notion 3102 *)
-definition l_e_st_eq_landau_n_rt_5162_t40 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_eqtf12 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x (l_e_st_eq_landau_n_rt_5162_t39 x0 i x xix0) (l_e_st_eq_landau_n_rt_5162_t39 x0 i x xix0) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x))) (l_e_st_eq_landau_n_tf x x)).
-
-(* notion 3103 *)
-definition l_e_st_eq_landau_n_rt_5162_t41 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_treq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x))) (l_e_st_eq_landau_n_tf x x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_5162_t40 x0 i x xix0) (l_e_st_eq_landau_n_rt_5162_t38 x0 i x xix0) : l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_num x)).
-
-(* notion 3104 *)
-definition l_e_st_eq_landau_n_rt_5162_t42 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_den x) t) (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_rt_5162_t41 x0 i x xix0) : l_e_st_eq_landau_n_5162_prop2 (l_e_st_eq_landau_n_den x)).
-
-(* notion 3105 *)
-definition l_e_st_eq_landau_n_rt_5162_t43 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_somei l_e_st_eq_landau_n_nat (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 t) (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_rt_5162_t42 x0 i x xix0) : l_e_st_eq_landau_n_5162_prop3).
-
-(* notion 3106 *)
-definition l_e_st_eq_landau_n_rt_5162_t44 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_5162_t37 (l_e_st_eq_landau_n_rt_5162_t43 x0 i x xix0) : l_con).
-
-(* notion 3107 *)
-definition l_e_st_eq_landau_n_rt_5162_t45 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).(l_e_st_eq_landau_n_rt_ratapp1 x0 l_con (Πx:l_e_st_eq_landau_n_frac.Πt:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_5162_t44 x0 i x t) : l_con).
-
-(* notion 3108 *)
-definition l_e_st_eq_landau_n_rt_rp_5162_ksi ≝ (l_e_ind l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_satz161 (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3109 *)
-definition l_e_st_eq_landau_n_rt_rp_5162_t46 ≝ (l_e_oneax l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_satz161 (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_5162_ksi l_e_st_eq_landau_n_rt_rp_5162_ksi) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))).
-
-(* notion 3110 *)
-definition l_e_st_eq_landau_n_rt_rp_5162_x0 ≝ λr:l_e_st_eq_landau_n_rt_rp_ratrp l_e_st_eq_landau_n_rt_rp_5162_ksi.(l_e_st_eq_landau_n_rt_rp_rtofrp l_e_st_eq_landau_n_rt_rp_5162_ksi r : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 3111 *)
-definition l_e_st_eq_landau_n_rt_rp_5162_t47 ≝ λr:l_e_st_eq_landau_n_rt_rp_ratrp l_e_st_eq_landau_n_rt_rp_5162_ksi.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_x0 r))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5162_x0 r))) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_5162_ksi l_e_st_eq_landau_n_rt_rp_5162_ksi) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_satz155c (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) (l_e_st_eq_landau_n_rt_rp_ists12 (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) l_e_st_eq_landau_n_rt_rp_5162_ksi (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) l_e_st_eq_landau_n_rt_rp_5162_ksi (l_e_st_eq_landau_n_rt_rp_isrprt2 l_e_st_eq_landau_n_rt_rp_5162_ksi r) (l_e_st_eq_landau_n_rt_rp_isrprt2 l_e_st_eq_landau_n_rt_rp_5162_ksi r)) l_e_st_eq_landau_n_rt_rp_5162_t46 : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_x0 r))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))).
-
-(* notion 3112 *)
-definition l_e_st_eq_landau_n_rt_rp_5162_t48 ≝ λr:l_e_st_eq_landau_n_rt_rp_ratrp l_e_st_eq_landau_n_rt_rp_5162_ksi.(l_e_st_eq_landau_n_rt_rp_isrtirp (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_5162_t47 r) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))).
-
-(* notion 3113 *)
-definition l_e_st_eq_landau_n_rt_rp_5162_t49 ≝ λr:l_e_st_eq_landau_n_rt_rp_ratrp l_e_st_eq_landau_n_rt_rp_5162_ksi.(l_e_st_eq_landau_n_rt_5162_t45 (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_t48 r) : l_con).
-
-(* notion 3114 *)
-definition l_e_st_eq_landau_n_rt_rp_satz162 ≝ (l_somei l_e_st_eq_landau_n_rt_cut (Πa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_irratrp a) l_e_st_eq_landau_n_rt_rp_5162_ksi (Πt:l_e_st_eq_landau_n_rt_rp_ratrp l_e_st_eq_landau_n_rt_rp_5162_ksi.l_e_st_eq_landau_n_rt_rp_5162_t49 t) : l_e_st_eq_landau_n_rt_rp_some (Πa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_irratrp a)).
-
-(* notion 3115 *)
-definition l_e_st_eq_landau_n_rt_rp_sqrt ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_ind l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta) (l_e_st_eq_landau_n_rt_rp_satz161 zeta) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3116 *)
-definition l_e_st_eq_landau_n_rt_rp_thsqrt1 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_oneax l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta) (l_e_st_eq_landau_n_rt_rp_satz161 zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_sqrt zeta) (l_e_st_eq_landau_n_rt_rp_sqrt zeta)) zeta).
-
-(* notion 3117 *)
-definition l_e_st_eq_landau_n_rt_rp_thsqrt2 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi ksi) zeta.(l_e_st_eq_landau_n_rt_rp_5161_t20 zeta ksi (l_e_st_eq_landau_n_rt_rp_sqrt zeta) i (l_e_st_eq_landau_n_rt_rp_thsqrt1 zeta) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_sqrt zeta)).
-
-(* notion 3118 *)
-definition l_e_st_eq_landau_n_rt_rp_issqrt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_sqrt t) ksi eta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_sqrt ksi) (l_e_st_eq_landau_n_rt_rp_sqrt eta)).
-
-(* notion 3119 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_x ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_ntofrp ksi nx : l_e_st_eq_landau_n_nat).
-
-(* notion 3120 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_y ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_ntofrp eta ny : l_e_st_eq_landau_n_nat).
-
-(* notion 3121 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_isrpnt1 ksi nx : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny))).
-
-(* notion 3122 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_isrpnt1 eta ny : l_e_st_eq_landau_n_rt_rp_is eta (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))).
-
-(* notion 3123 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_ispl12 ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) eta (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t1 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t2 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)))).
-
-(* notion 3124 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_x0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny) : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 3125 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_y0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny) : l_e_st_eq_landau_n_rt_rat).
-
-(* notion 3126 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_natrti (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny)).
-
-(* notion 3127 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_natrti (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)).
-
-(* notion 3128 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_satz155a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)))).
-
-(* notion 3129 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_satz112d (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t4 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t5 ksi nx eta ny) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))).
-
-(* notion 3130 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_xpy ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t7 ksi nx eta ny) : l_e_st_eq_landau_n_nat).
-
-(* notion 3131 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_isrtn1 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t7 ksi nx eta ny) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny))).
-
-(* notion 3132 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_isrterp (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t8 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny))).
-
-(* notion 3133 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t3 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t6 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t9 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny))).
-
-(* notion 3134 *)
-definition l_e_st_eq_landau_n_rt_rp_natpl ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_rpofnt t)) (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t10 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_pl ksi eta)).
-
-(* notion 3135 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_ists12 ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) eta (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t1 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t2 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)))).
-
-(* notion 3136 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_satz155c (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)))).
-
-(* notion 3137 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_satz112f (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t4 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t5 ksi nx eta ny) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))).
-
-(* notion 3138 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_xty ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t13 ksi nx eta ny) : l_e_st_eq_landau_n_nat).
-
-(* notion 3139 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_isrtn1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t13 ksi nx eta ny) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny))).
-
-(* notion 3140 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_isrterp (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t14 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny))).
-
-(* notion 3141 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t11 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t12 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t15 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny))).
-
-(* notion 3142 *)
-definition l_e_st_eq_landau_n_rt_rp_natts ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_rpofnt t)) (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t16 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_ts ksi eta)).
-
-(* notion 3143 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismore12 ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) eta (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t1 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t2 ksi nx eta ny) m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))).
-
-(* notion 3144 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_satz154d (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t17 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)).
-
-(* notion 3145 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismn12 ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) eta (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) m (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rp_iiia_t1 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t2 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)))).
-
-(* notion 3146 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_satz155b (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)))).
-
-(* notion 3147 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_satz112g (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t4 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t5 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))).
-
-(* notion 3148 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_xmy ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rp_iiia_t22 ksi nx eta ny m) : l_e_st_eq_landau_n_nat).
-
-(* notion 3149 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_isrtn1 (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rp_iiia_t22 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m))).
-
-(* notion 3150 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_isrterp (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rp_iiia_t23 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m))).
-
-(* notion 3151 *)
-definition l_e_st_eq_landau_n_rt_rp_iiia_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rp_iiia_t20 ksi nx eta ny m) (l_e_st_eq_landau_n_rt_rp_iiia_t21 ksi nx eta ny m) (l_e_st_eq_landau_n_rt_rp_iiia_t24 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m))).
-
-(* notion 3152 *)
-definition l_e_st_eq_landau_n_rt_rp_natmn ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) (l_e_st_eq_landau_n_rt_rp_rpofnt t)) (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m) (l_e_st_eq_landau_n_rt_rp_iiia_t25 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_mn ksi eta m)).
-
-(* notion 3153 *)
-definition l_e_st_eq_landau_n_rt_rp_3pl13 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl q r) p) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r q) p) (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl q p)) (l_e_st_eq_landau_n_rt_rp_compl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl q r) (l_e_st_eq_landau_n_rt_rp_pl r q) p (l_e_st_eq_landau_n_rt_rp_compl q r)) (l_e_st_eq_landau_n_rt_rp_asspl1 r q p) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl q p))).
-
-(* notion 3154 *)
-definition l_e_st_eq_landau_n_rt_rp_4pl24 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl r s))) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_pl r q))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p s) (l_e_st_eq_landau_n_rt_rp_pl r q)) (l_e_st_eq_landau_n_rt_rp_asspl1 p q (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_pl r q)) p (l_e_st_eq_landau_n_rt_rp_3pl13 q r s)) (l_e_st_eq_landau_n_rt_rp_asspl2 p s (l_e_st_eq_landau_n_rt_rp_pl r q)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p s) (l_e_st_eq_landau_n_rt_rp_pl r q))).
-
-(* notion 3155 *)
-definition l_e_st_eq_landau_n_rt_rp_3pl12 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl q p) r) (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl p r)) (l_e_st_eq_landau_n_rt_rp_asspl2 p q r) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl p q) (l_e_st_eq_landau_n_rt_rp_pl q p) r (l_e_st_eq_landau_n_rt_rp_compl p q)) (l_e_st_eq_landau_n_rt_rp_asspl1 q p r) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl p r))).
-
-(* notion 3156 *)
-definition l_e_st_eq_landau_n_rt_rp_4pl23 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl r s))) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl q s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p r) (l_e_st_eq_landau_n_rt_rp_pl q s)) (l_e_st_eq_landau_n_rt_rp_asspl1 p q (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl q s)) p (l_e_st_eq_landau_n_rt_rp_3pl12 q r s)) (l_e_st_eq_landau_n_rt_rp_asspl2 p r (l_e_st_eq_landau_n_rt_rp_pl q s)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p r) (l_e_st_eq_landau_n_rt_rp_pl q s))).
-
-(* notion 3157 *)
-definition l_e_st_eq_landau_n_rt_rp_3pl23 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) r) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl r q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p r) q) (l_e_st_eq_landau_n_rt_rp_asspl1 p q r) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl q r) (l_e_st_eq_landau_n_rt_rp_pl r q) p (l_e_st_eq_landau_n_rt_rp_compl q r)) (l_e_st_eq_landau_n_rt_rp_asspl2 p r q) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p r) q)).
-
-(* notion 3158 *)
-definition l_e_st_eq_landau_n_rt_rp_a2isapa ≝ λp:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl p p) (l_e_st_eq_landau_n_rt_rp_disttp2 p l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts p l_e_st_eq_landau_n_rt_rp_1rp) p (l_e_st_eq_landau_n_rt_rp_ts p l_e_st_eq_landau_n_rt_rp_1rp) p (l_e_st_eq_landau_n_rt_rp_satz151 p) (l_e_st_eq_landau_n_rt_rp_satz151 p)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl p p)).
-
-(* notion 3159 *)
-definition l_e_st_eq_landau_n_rt_rp_dif ≝ (l_e_st_eq_landau_n_pair1type l_e_st_eq_landau_n_rt_cut : Type[0]).
-
-(* notion 3160 *)
-definition l_e_st_eq_landau_n_rt_rp_df ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_pair1 l_e_st_eq_landau_n_rt_cut a1 a2 : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3161 *)
-definition l_e_st_eq_landau_n_rt_rp_stm ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_first1 l_e_st_eq_landau_n_rt_cut a : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3162 *)
-definition l_e_st_eq_landau_n_rt_rp_std ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_second1 l_e_st_eq_landau_n_rt_cut a : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3163 *)
-definition l_e_st_eq_landau_n_rt_rp_stmis ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_first1is1 l_e_st_eq_landau_n_rt_cut a1 a2 : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1).
-
-(* notion 3164 *)
-definition l_e_st_eq_landau_n_rt_rp_isstm ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_first1is2 l_e_st_eq_landau_n_rt_cut a1 a2 : l_e_st_eq_landau_n_rt_rp_is a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))).
-
-(* notion 3165 *)
-definition l_e_st_eq_landau_n_rt_rp_stdis ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_second1is1 l_e_st_eq_landau_n_rt_cut a1 a2 : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2).
-
-(* notion 3166 *)
-definition l_e_st_eq_landau_n_rt_rp_isstd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_second1is2 l_e_st_eq_landau_n_rt_cut a1 a2 : l_e_st_eq_landau_n_rt_rp_is a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))).
-
-(* notion 3167 *)
-definition l_e_st_eq_landau_n_rt_rp_1a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stm a : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3168 *)
-definition l_e_st_eq_landau_n_rt_rp_2a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_std a : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3169 *)
-definition l_e_st_eq_landau_n_rt_rp_dfis ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_pair1is1 l_e_st_eq_landau_n_rt_cut a : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) a).
-
-(* notion 3170 *)
-definition l_e_st_eq_landau_n_rt_rp_isdf ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_pair1is2 l_e_st_eq_landau_n_rt_cut a : l_e_is l_e_st_eq_landau_n_rt_rp_dif a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a))).
-
-(* notion 3171 *)
-definition l_e_st_eq_landau_n_rt_rp_12issmsd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl12 a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) b2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_isstm a1 a2) (l_e_st_eq_landau_n_rt_rp_isstd b1 b2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)))).
-
-(* notion 3172 *)
-definition l_e_st_eq_landau_n_rt_rp_smsdis12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_12issmsd a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl a1 b2)).
-
-(* notion 3173 *)
-definition l_e_st_eq_landau_n_rt_rp_1sdissmsd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl1 r1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_isstm r1 r2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a))).
-
-(* notion 3174 *)
-definition l_e_st_eq_landau_n_rt_rp_smsdis1sd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_1sdissmsd a r1 r2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a))).
-
-(* notion 3175 *)
-definition l_e_st_eq_landau_n_rt_rp_sm2issmsd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl2 r2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_isstd r1 r2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)))).
-
-(* notion 3176 *)
-definition l_e_st_eq_landau_n_rt_rp_smsdissm2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_sm2issmsd a r1 r2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2)).
-
-(* notion 3177 *)
-definition l_e_st_eq_landau_n_rt_rp_issm ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a1 r.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_dif (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_df t a2) a1 r i : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df r a2)).
-
-(* notion 3178 *)
-definition l_e_st_eq_landau_n_rt_rp_issd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a2 r.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_dif (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_df a1 t) a2 r i : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df a1 r)).
-
-(* notion 3179 *)
-definition l_e_st_eq_landau_n_rt_rp_issmsd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a1 b1.λj:l_e_st_eq_landau_n_rt_rp_is a2 b2.(l_e_tris l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2) (l_e_st_eq_landau_n_rt_rp_issm a1 a2 b1 i) (l_e_st_eq_landau_n_rt_rp_issd b1 a2 b2 j) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)).
-
-(* notion 3180 *)
-definition l_e_st_eq_landau_n_rt_rp_1b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stm b : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3181 *)
-definition l_e_st_eq_landau_n_rt_rp_2b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_std b : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3182 *)
-definition l_e_st_eq_landau_n_rt_rp_eq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : Prop).
-
-(* notion 3183 *)
-definition l_e_st_eq_landau_n_rt_rp_eqi12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2).(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_smsdis12 a1 a2 b1 b2) i (l_e_st_eq_landau_n_rt_rp_12issmsd b1 b2 a1 a2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)).
-
-(* notion 3184 *)
-definition l_e_st_eq_landau_n_rt_rp_eqi1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)).(l_e_isp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq x (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) a (l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) r1 r2 i) (l_e_st_eq_landau_n_rt_rp_dfis a) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_df r1 r2)).
-
-(* notion 3185 *)
-definition l_e_st_eq_landau_n_rt_rp_eqi2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2).(l_e_isp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df r1 r2) x) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) a (l_e_st_eq_landau_n_rt_rp_eqi12 r1 r2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) i) (l_e_st_eq_landau_n_rt_rp_dfis a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df r1 r2) a).
-
-(* notion 3186 *)
-definition l_e_st_eq_landau_n_rt_rp_eqe12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2).(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_pl b1 a2) (l_e_st_eq_landau_n_rt_rp_12issmsd a1 a2 b1 b2) e (l_e_st_eq_landau_n_rt_rp_smsdis12 b1 b2 a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2)).
-
-(* notion 3187 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd163 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_eq a a).
-
-(* notion 3188 *)
-definition l_e_st_eq_landau_n_rt_rp_refeq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd163 a : l_e_st_eq_landau_n_rt_rp_eq a a).
-
-(* notion 3189 *)
-definition l_e_st_eq_landau_n_rt_rp_refeq1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_is l_e_st_eq_landau_n_rt_rp_dif a b.(l_e_isp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq a x) a b (l_e_st_eq_landau_n_rt_rp_refeq a) i : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3190 *)
-definition l_e_st_eq_landau_n_rt_rp_refeq2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_is l_e_st_eq_landau_n_rt_rp_dif a b.(l_e_isp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq x a) a b (l_e_st_eq_landau_n_rt_rp_refeq a) i : l_e_st_eq_landau_n_rt_rp_eq b a).
-
-(* notion 3191 *)
-definition l_e_st_eq_landau_n_rt_rp_eqsmsd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a1 b1.λj:l_e_st_eq_landau_n_rt_rp_is a2 b2.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2) (l_e_st_eq_landau_n_rt_rp_issmsd a1 a2 b1 b2 i j) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)).
-
-(* notion 3192 *)
-definition l_e_st_eq_landau_n_rt_rp_eqsm ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a1 r.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df r a2) (l_e_st_eq_landau_n_rt_rp_issm a1 a2 r i) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df r a2)).
-
-(* notion 3193 *)
-definition l_e_st_eq_landau_n_rt_rp_eqsd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a2 r.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df a1 r) (l_e_st_eq_landau_n_rt_rp_issd a1 a2 r i) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df a1 r)).
-
-(* notion 3194 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd164 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) e : l_e_st_eq_landau_n_rt_rp_eq b a).
-
-(* notion 3195 *)
-definition l_e_st_eq_landau_n_rt_rp_symeq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_satzd164 a b e : l_e_st_eq_landau_n_rt_rp_eq b a).
-
-(* notion 3196 *)
-definition l_e_st_eq_landau_n_rt_rp_1c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stm c : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3197 *)
-definition l_e_st_eq_landau_n_rt_rp_2c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_std c : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3198 *)
-definition l_e_st_eq_landau_n_rt_rp_1d165_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq b c.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)) e f : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)))).
-
-(* notion 3199 *)
-definition l_e_st_eq_landau_n_rt_rp_1d165_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq b c.(l_e_tr4is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_1d165_t1 a b c e f) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)))).
-
-(* notion 3200 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd165 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq b c.(l_e_st_eq_landau_n_rt_rp_satz136b (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_1d165_t2 a b c e f) : l_e_st_eq_landau_n_rt_rp_eq a c).
-
-(* notion 3201 *)
-definition l_e_st_eq_landau_n_rt_rp_treq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq b c.(l_e_st_eq_landau_n_rt_rp_satzd165 a b c e f : l_e_st_eq_landau_n_rt_rp_eq a c).
-
-(* notion 3202 *)
-definition l_e_st_eq_landau_n_rt_rp_treq1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq c a.λf:l_e_st_eq_landau_n_rt_rp_eq c b.(l_e_st_eq_landau_n_rt_rp_treq a c b (l_e_st_eq_landau_n_rt_rp_symeq c a e) f : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3203 *)
-definition l_e_st_eq_landau_n_rt_rp_treq2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a c.λf:l_e_st_eq_landau_n_rt_rp_eq b c.(l_e_st_eq_landau_n_rt_rp_treq a c b e (l_e_st_eq_landau_n_rt_rp_symeq b c f) : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3204 *)
-definition l_e_st_eq_landau_n_rt_rp_tr3eq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe1:l_e_st_eq_landau_n_rt_rp_eq a b.λe2:l_e_st_eq_landau_n_rt_rp_eq b c.λe3:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_treq a b d e1 (l_e_st_eq_landau_n_rt_rp_treq b c d e2 e3) : l_e_st_eq_landau_n_rt_rp_eq a d).
-
-(* notion 3205 *)
-definition l_e_st_eq_landau_n_rt_rp_tr4eq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_dif.λe1:l_e_st_eq_landau_n_rt_rp_eq a b.λe2:l_e_st_eq_landau_n_rt_rp_eq b c.λe3:l_e_st_eq_landau_n_rt_rp_eq c d.λe4:l_e_st_eq_landau_n_rt_rp_eq d e.(l_e_st_eq_landau_n_rt_rp_tr3eq a b c e e1 e2 (l_e_st_eq_landau_n_rt_rp_treq c d e e3 e4) : l_e_st_eq_landau_n_rt_rp_eq a e).
-
-(* notion 3206 *)
-definition l_e_st_eq_landau_n_rt_rp_posd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) : Prop).
-
-(* notion 3207 *)
-definition l_e_st_eq_landau_n_rt_rp_zero ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) : Prop).
-
-(* notion 3208 *)
-definition l_e_st_eq_landau_n_rt_rp_negd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) : Prop).
-
-(* notion 3209 *)
-definition l_e_st_eq_landau_n_rt_rp_posdi ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more a1 a2.(l_e_st_eq_landau_n_rt_rp_ismore12 a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_isstm a1 a2) (l_e_st_eq_landau_n_rt_rp_isstd a1 a2) m : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_df a1 a2)).
-
-(* notion 3210 *)
-definition l_e_st_eq_landau_n_rt_rp_zeroi ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a1 a2.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1 a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) i (l_e_st_eq_landau_n_rt_rp_isstd a1 a2) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_df a1 a2)).
-
-(* notion 3211 *)
-definition l_e_st_eq_landau_n_rt_rp_negdi ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less a1 a2.(l_e_st_eq_landau_n_rt_rp_isless12 a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_isstm a1 a2) (l_e_st_eq_landau_n_rt_rp_isstd a1 a2) l : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_df a1 a2)).
-
-(* notion 3212 *)
-definition l_e_st_eq_landau_n_rt_rp_axrde ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) : l_ec3 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a)).
-
-(* notion 3213 *)
-definition l_e_st_eq_landau_n_rt_rp_axrdo ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satz123a (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) : l_or3 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a)).
-
-(* notion 3214 *)
-definition l_e_st_eq_landau_n_rt_rp_axrd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_orec3i (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrdo a) (l_e_st_eq_landau_n_rt_rp_axrde a) : l_orec3 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a)).
-
-(* notion 3215 *)
-definition l_e_st_eq_landau_n_rt_rp_rappd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:Prop.λp1:Πt:l_e_st_eq_landau_n_rt_rp_posd a.p.λp2:Πt:l_e_st_eq_landau_n_rt_rp_zero a.p.λp3:Πt:l_e_st_eq_landau_n_rt_rp_negd a.p.(l_or3app (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) p (l_e_st_eq_landau_n_rt_rp_axrdo a) p2 p1 p3 : p).
-
-(* notion 3216 *)
-definition l_e_st_eq_landau_n_rt_rp_pnot0d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) p : l_not (l_e_st_eq_landau_n_rt_rp_zero a)).
-
-(* notion 3217 *)
-definition l_e_st_eq_landau_n_rt_rp_pnotnd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_ec3e23 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) p : l_not (l_e_st_eq_landau_n_rt_rp_negd a)).
-
-(* notion 3218 *)
-definition l_e_st_eq_landau_n_rt_rp_0notpd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_ec3e12 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) z : l_not (l_e_st_eq_landau_n_rt_rp_posd a)).
-
-(* notion 3219 *)
-definition l_e_st_eq_landau_n_rt_rp_0notnd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_ec3e13 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) z : l_not (l_e_st_eq_landau_n_rt_rp_negd a)).
-
-(* notion 3220 *)
-definition l_e_st_eq_landau_n_rt_rp_nnotpd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_ec3e32 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) n : l_not (l_e_st_eq_landau_n_rt_rp_posd a)).
-
-(* notion 3221 *)
-definition l_e_st_eq_landau_n_rt_rp_nnot0d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) n : l_not (l_e_st_eq_landau_n_rt_rp_zero a)).
-
-(* notion 3222 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) e (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_satz135a (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) p) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a))).
-
-(* notion 3223 *)
-definition l_e_st_eq_landau_n_rt_rp_eqposd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_satz136a (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv1d_t1 a b e p) : l_e_st_eq_landau_n_rt_rp_posd b).
-
-(* notion 3224 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_symeq a b e) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) z) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a))).
-
-(* notion 3225 *)
-definition l_e_st_eq_landau_n_rt_rp_eqzero ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_satz136b (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv1d_t2 a b e z) : l_e_st_eq_landau_n_rt_rp_zero b).
-
-(* notion 3226 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) e (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_satz135c (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) n) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a))).
-
-(* notion 3227 *)
-definition l_e_st_eq_landau_n_rt_rp_eqnegd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_satz136c (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv1d_t3 a b e n) : l_e_st_eq_landau_n_rt_rp_negd b).
-
-(* notion 3228 *)
-definition l_e_st_eq_landau_n_rt_rp_zeroeq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.λy:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) z (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) y)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3229 *)
-definition l_e_st_eq_landau_n_rt_rp_pdofrp ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3230 *)
-definition l_e_st_eq_landau_n_rt_rp_ndofrp ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3231 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpepd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r s.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s) (l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_pdofrp x) r s i) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)).
-
-(* notion 3232 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpend ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r s.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_ndofrp s) (l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ndofrp x) r s i) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_ndofrp s)).
-
-(* notion 3233 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t4 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz136b (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_eqe12 (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp e) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp)).
-
-(* notion 3234 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpipd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz136b r s l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv1d_t4 r s e) : l_e_st_eq_landau_n_rt_rp_is r s).
-
-(* notion 3235 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t5 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_ndofrp s).(l_e_st_eq_landau_n_rt_rp_satz136e (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_eqe12 l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) e) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp)).
-
-(* notion 3236 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpind ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_ndofrp s).(l_e_symis l_e_st_eq_landau_n_rt_cut s r (l_e_st_eq_landau_n_rt_rp_satz136b s r l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv1d_t5 r s e)) : l_e_st_eq_landau_n_rt_rp_is r s).
-
-(* notion 3237 *)
-definition l_e_st_eq_landau_n_rt_rp_posdirp ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_compl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_satz133 l_e_st_eq_landau_n_rt_rp_1rp r)) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
-
-(* notion 3238 *)
-definition l_e_st_eq_landau_n_rt_rp_negdirp ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_negdi l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_compl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_satz133a l_e_st_eq_landau_n_rt_rp_1rp r)) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
-
-(* notion 3239 *)
-definition l_e_st_eq_landau_n_rt_rp_rpofpd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) p : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3240 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_tr4is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_2a a)) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_2a a)) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_satz140f (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) p)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_rpofpd a p) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a))).
-
-(* notion 3241 *)
-definition l_e_st_eq_landau_n_rt_rp_eqpdrp1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_eqi1 a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv1d_t6 a p) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd a p))).
-
-(* notion 3242 *)
-definition l_e_st_eq_landau_n_rt_rp_eqpdrp2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_symeq a (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd a p)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 a p) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd a p)) a).
-
-(* notion 3243 *)
-definition l_e_st_eq_landau_n_rt_rp_rpofnd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) n) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3244 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnd a n) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_rpofnd a n)) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_rpofnd a n) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_rpofnd a n)) (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_satz140c (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) n))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnd a n) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_2a a))).
-
-(* notion 3245 *)
-definition l_e_st_eq_landau_n_rt_rp_eqndrp1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_eqi1 a l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnd a n) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_iv1d_t7 a n) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd a n))).
-
-(* notion 3246 *)
-definition l_e_st_eq_landau_n_rt_rp_eqndrp2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_symeq a (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd a n)) (l_e_st_eq_landau_n_rt_rp_eqndrp1 a n) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd a n)) a).
-
-(* notion 3247 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t8 ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λq:l_e_st_eq_landau_n_rt_rp_posd k.λe:l_e_st_eq_landau_n_rt_rp_eq h k.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd h p)) h k (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd k q)) (l_e_st_eq_landau_n_rt_rp_eqpdrp2 h p) e (l_e_st_eq_landau_n_rt_rp_eqpdrp1 k q) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd h p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd k q))).
-
-(* notion 3248 *)
-definition l_e_st_eq_landau_n_rt_rp_eqpderp ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λq:l_e_st_eq_landau_n_rt_rp_posd k.λe:l_e_st_eq_landau_n_rt_rp_eq h k.(l_e_st_eq_landau_n_rt_rp_isrpipd (l_e_st_eq_landau_n_rt_rp_rpofpd h p) (l_e_st_eq_landau_n_rt_rp_rpofpd k q) (l_e_st_eq_landau_n_rt_rp_iv1d_t8 h p k q e) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd h p) (l_e_st_eq_landau_n_rt_rp_rpofpd k q)).
-
-(* notion 3249 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t9 ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λq:l_e_st_eq_landau_n_rt_rp_posd k.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd h p) (l_e_st_eq_landau_n_rt_rp_rpofpd k q).(l_e_st_eq_landau_n_rt_rp_isrpepd (l_e_st_eq_landau_n_rt_rp_rpofpd h p) (l_e_st_eq_landau_n_rt_rp_rpofpd k q) i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd h p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd k q))).
-
-(* notion 3250 *)
-definition l_e_st_eq_landau_n_rt_rp_eqpdirp ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λq:l_e_st_eq_landau_n_rt_rp_posd k.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd h p) (l_e_st_eq_landau_n_rt_rp_rpofpd k q).(l_e_st_eq_landau_n_rt_rp_tr3eq h (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd h p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd k q)) k (l_e_st_eq_landau_n_rt_rp_eqpdrp1 h p) (l_e_st_eq_landau_n_rt_rp_iv1d_t9 h p k q i) (l_e_st_eq_landau_n_rt_rp_eqpdrp2 k q) : l_e_st_eq_landau_n_rt_rp_eq h k).
-
-(* notion 3251 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t10 ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λo:l_e_st_eq_landau_n_rt_rp_negd k.λe:l_e_st_eq_landau_n_rt_rp_eq h k.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd h n)) h k (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd k o)) (l_e_st_eq_landau_n_rt_rp_eqndrp2 h n) e (l_e_st_eq_landau_n_rt_rp_eqndrp1 k o) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd h n)) (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd k o))).
-
-(* notion 3252 *)
-definition l_e_st_eq_landau_n_rt_rp_eqnderp ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λo:l_e_st_eq_landau_n_rt_rp_negd k.λe:l_e_st_eq_landau_n_rt_rp_eq h k.(l_e_st_eq_landau_n_rt_rp_isrpind (l_e_st_eq_landau_n_rt_rp_rpofnd h n) (l_e_st_eq_landau_n_rt_rp_rpofnd k o) (l_e_st_eq_landau_n_rt_rp_iv1d_t10 h n k o e) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnd h n) (l_e_st_eq_landau_n_rt_rp_rpofnd k o)).
-
-(* notion 3253 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t11 ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λo:l_e_st_eq_landau_n_rt_rp_negd k.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnd h n) (l_e_st_eq_landau_n_rt_rp_rpofnd k o).(l_e_st_eq_landau_n_rt_rp_isrpend (l_e_st_eq_landau_n_rt_rp_rpofnd h n) (l_e_st_eq_landau_n_rt_rp_rpofnd k o) i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd h n)) (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd k o))).
-
-(* notion 3254 *)
-definition l_e_st_eq_landau_n_rt_rp_eqndirp ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λo:l_e_st_eq_landau_n_rt_rp_negd k.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnd h n) (l_e_st_eq_landau_n_rt_rp_rpofnd k o).(l_e_st_eq_landau_n_rt_rp_tr3eq h (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd h n)) (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd k o)) k (l_e_st_eq_landau_n_rt_rp_eqndrp1 h n) (l_e_st_eq_landau_n_rt_rp_iv1d_t11 h n k o i) (l_e_st_eq_landau_n_rt_rp_eqndrp2 k o) : l_e_st_eq_landau_n_rt_rp_eq h k).
-
-(* notion 3255 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t12 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r)))).
-
-(* notion 3256 *)
-definition l_e_st_eq_landau_n_rt_rp_isrppd1 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isrpipd r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r)) (l_e_st_eq_landau_n_rt_rp_iv1d_t12 r) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r))).
-
-(* notion 3257 *)
-definition l_e_st_eq_landau_n_rt_rp_isrppd2 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r)) (l_e_st_eq_landau_n_rt_rp_isrppd1 r) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r)) r).
-
-(* notion 3258 *)
-definition l_e_st_eq_landau_n_rt_rp_iv1d_t13 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqndrp1 (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r)))).
-
-(* notion 3259 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpnd1 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isrpind r (l_e_st_eq_landau_n_rt_rp_rpofnd (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r)) (l_e_st_eq_landau_n_rt_rp_iv1d_t13 r) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofnd (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r))).
-
-(* notion 3260 *)
-definition l_e_st_eq_landau_n_rt_rp_isrpnd2 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofnd (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r)) (l_e_st_eq_landau_n_rt_rp_isrpnd1 r) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnd (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r)) r).
-
-(* notion 3261 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmad1 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqi12 a1 a2 (l_e_st_eq_landau_n_rt_rp_pl a1 r) (l_e_st_eq_landau_n_rt_rp_pl a2 r) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl a1 (l_e_st_eq_landau_n_rt_rp_pl a2 r)) (l_e_st_eq_landau_n_rt_rp_pl a1 (l_e_st_eq_landau_n_rt_rp_pl r a2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl a1 r) a2) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl a2 r) (l_e_st_eq_landau_n_rt_rp_pl r a2) a1 (l_e_st_eq_landau_n_rt_rp_compl a2 r)) (l_e_st_eq_landau_n_rt_rp_asspl2 a1 r a2)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 r) (l_e_st_eq_landau_n_rt_rp_pl a2 r))).
-
-(* notion 3262 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmad2 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 r) (l_e_st_eq_landau_n_rt_rp_pl a2 r)) (l_e_st_eq_landau_n_rt_rp_lemmad1 a1 a2 r) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 r) (l_e_st_eq_landau_n_rt_rp_pl a2 r)) (l_e_st_eq_landau_n_rt_rp_df a1 a2)).
-
-(* notion 3263 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmad3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r)) (l_e_st_eq_landau_n_rt_rp_refeq1 a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_isdf a)) (l_e_st_eq_landau_n_rt_rp_lemmad1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) r) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r))).
-
-(* notion 3264 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmad4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_symeq a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r)) (l_e_st_eq_landau_n_rt_rp_lemmad3 a r) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r)) a).
-
-(* notion 3265 *)
-definition l_e_st_eq_landau_n_rt_rp_absd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_ite (l_e_st_eq_landau_n_rt_rp_negd a) l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) a : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3266 *)
-definition l_e_st_eq_landau_n_rt_rp_absnd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_itet (l_e_st_eq_landau_n_rt_rp_negd a) l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) a n) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))).
-
-(* notion 3267 *)
-definition l_e_st_eq_landau_n_rt_rp_absnnd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_itef (l_e_st_eq_landau_n_rt_rp_negd a) l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) a n) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) a).
-
-(* notion 3268 *)
-definition l_e_st_eq_landau_n_rt_rp_absdeql ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less a1 a2.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_df a2 a1) (l_e_st_eq_landau_n_rt_rp_absnd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_negdi a1 a2 l)) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 a1 (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) (l_e_st_eq_landau_n_rt_rp_stmis a1 a2)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_df a2 a1)).
-
-(* notion 3269 *)
-definition l_e_st_eq_landau_n_rt_rp_absdeqm ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis a1 a2.(l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_less a1 a2) (l_e_st_eq_landau_n_rt_rp_satz123c a1 a2 m) (λt:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_df a1 a2).l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) t)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_df a1 a2)).
-
-(* notion 3270 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_symeq a b e) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a))).
-
-(* notion 3271 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absnd a n) (l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_iv2d_t1 a b e n)) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_absnd b (l_e_st_eq_landau_n_rt_rp_eqnegd a b e n))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).
-
-(* notion 3272 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd a) a b (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absnnd a n) e (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd b) b (l_e_st_eq_landau_n_rt_rp_absnnd b (l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_negd a) n (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_eqnegd b a (l_e_st_eq_landau_n_rt_rp_symeq a b e) t)))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).
-
-(* notion 3273 *)
-definition l_e_st_eq_landau_n_rt_rp_eqabsd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_iv2d_t2 a b e t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_negd a).l_e_st_eq_landau_n_rt_rp_iv2d_t3 a b e t) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).
-
-(* notion 3274 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd166a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_eqposd a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p))) p : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3275 *)
-definition l_e_st_eq_landau_n_rt_rp_2d166_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))).
-
-(* notion 3276 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd166b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_absnd a n)) (l_e_st_eq_landau_n_rt_rp_2d166_t1 a n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3277 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd166c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b).(l_e_st_eq_landau_n_rt_rp_tr3eq a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) b (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p))) e (l_e_st_eq_landau_n_rt_rp_absnnd b (l_e_st_eq_landau_n_rt_rp_pnotnd b q)) : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3278 *)
-definition l_e_st_eq_landau_n_rt_rp_2d166_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b).(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_absnd a n)) e (l_e_st_eq_landau_n_rt_rp_absnd b o) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b))).
-
-(* notion 3279 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd166d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b).(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_eqe12 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d166_t2 a b n o e))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3280 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd166e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_rappd a (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_satzd166a a t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)) n) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_satzd166b a t) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3281 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd166f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_eqzero a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_0notnd a z))) z : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3282 *)
-definition l_e_st_eq_landau_n_rt_rp_mored ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : Prop).
-
-(* notion 3283 *)
-definition l_e_st_eq_landau_n_rt_rp_moredi12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2).(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl b1 a2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_12issmsd a1 a2 b1 b2) (l_e_st_eq_landau_n_rt_rp_12issmsd b1 b2 a1 a2) m : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)).
-
-(* notion 3284 *)
-definition l_e_st_eq_landau_n_rt_rp_moredi1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)).(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_sm2issmsd a r1 r2) (l_e_st_eq_landau_n_rt_rp_1sdissmsd a r1 r2) m : l_e_st_eq_landau_n_rt_rp_mored a (l_e_st_eq_landau_n_rt_rp_df r1 r2)).
-
-(* notion 3285 *)
-definition l_e_st_eq_landau_n_rt_rp_moredi2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2).(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_1sdissmsd a r1 r2) (l_e_st_eq_landau_n_rt_rp_sm2issmsd a r1 r2) m : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_df r1 r2) a).
-
-(* notion 3286 *)
-definition l_e_st_eq_landau_n_rt_rp_morede12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2).(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_pl b1 a2) (l_e_st_eq_landau_n_rt_rp_smsdis12 a1 a2 b1 b2) (l_e_st_eq_landau_n_rt_rp_smsdis12 b1 b2 a1 a2) m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2)).
-
-(* notion 3287 *)
-definition l_e_st_eq_landau_n_rt_rp_lessd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : Prop).
-
-(* notion 3288 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmad5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) m : l_e_st_eq_landau_n_rt_rp_lessd b a).
-
-(* notion 3289 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmad6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) l : l_e_st_eq_landau_n_rt_rp_mored b a).
-
-(* notion 3290 *)
-definition l_e_st_eq_landau_n_rt_rp_lessdi12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2).(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_df b1 b2) (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_moredi12 b1 b2 a1 a2 (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2) l)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)).
-
-(* notion 3291 *)
-definition l_e_st_eq_landau_n_rt_rp_lessdi1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)).(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_df r1 r2) a (l_e_st_eq_landau_n_rt_rp_moredi2 a r1 r2 (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) l)) : l_e_st_eq_landau_n_rt_rp_lessd a (l_e_st_eq_landau_n_rt_rp_df r1 r2)).
-
-(* notion 3292 *)
-definition l_e_st_eq_landau_n_rt_rp_lessdi2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2).(l_e_st_eq_landau_n_rt_rp_lemmad5 a (l_e_st_eq_landau_n_rt_rp_df r1 r2) (l_e_st_eq_landau_n_rt_rp_moredi1 a r1 r2 (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) l)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a).
-
-(* notion 3293 *)
-definition l_e_st_eq_landau_n_rt_rp_lessde12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2).(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl b1 a2) (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_morede12 b1 b2 a1 a2 (l_e_st_eq_landau_n_rt_rp_lemmad6 (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2) l)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2)).
-
-(* notion 3294 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd167 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satz123 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_orec3 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b)).
-
-(* notion 3295 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd167a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satz123a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_or3 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b)).
-
-(* notion 3296 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd167b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_ec3 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b)).
-
-(* notion 3297 *)
-definition l_e_st_eq_landau_n_rt_rp_1d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stm d : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3298 *)
-definition l_e_st_eq_landau_n_rt_rp_2d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_std d : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3299 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λm:l_e_st_eq_landau_n_rt_rp_mored a c.(l_e_tr4is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2d a b c d))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_symeq a b e) f) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))).
-
-(* notion 3300 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λm:l_e_st_eq_landau_n_rt_rp_mored a c.(l_e_st_eq_landau_n_rt_rp_ismore2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_iv2d_t4 a b c d e f m) (l_e_st_eq_landau_n_rt_rp_satz135d (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))).
-
-(* notion 3301 *)
-definition l_e_st_eq_landau_n_rt_rp_eqmored12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λm:l_e_st_eq_landau_n_rt_rp_mored a c.(l_e_st_eq_landau_n_rt_rp_satz136a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_iv2d_t5 a b c d e f m) : l_e_st_eq_landau_n_rt_rp_mored b d).
-
-(* notion 3302 *)
-definition l_e_st_eq_landau_n_rt_rp_eqlessd12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λl:l_e_st_eq_landau_n_rt_rp_lessd a c.(l_e_st_eq_landau_n_rt_rp_lemmad5 d b (l_e_st_eq_landau_n_rt_rp_eqmored12 c d a b f e (l_e_st_eq_landau_n_rt_rp_lemmad6 a c l)) : l_e_st_eq_landau_n_rt_rp_lessd b d).
-
-(* notion 3303 *)
-definition l_e_st_eq_landau_n_rt_rp_eqmored1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_mored a c.(l_e_st_eq_landau_n_rt_rp_eqmored12 a b c c e (l_e_st_eq_landau_n_rt_rp_refeq c) m : l_e_st_eq_landau_n_rt_rp_mored b c).
-
-(* notion 3304 *)
-definition l_e_st_eq_landau_n_rt_rp_eqmored2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_mored c a.(l_e_st_eq_landau_n_rt_rp_eqmored12 c c a b (l_e_st_eq_landau_n_rt_rp_refeq c) e m : l_e_st_eq_landau_n_rt_rp_mored c b).
-
-(* notion 3305 *)
-definition l_e_st_eq_landau_n_rt_rp_eqlessd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lessd a c.(l_e_st_eq_landau_n_rt_rp_eqlessd12 a b c c e (l_e_st_eq_landau_n_rt_rp_refeq c) l : l_e_st_eq_landau_n_rt_rp_lessd b c).
-
-(* notion 3306 *)
-definition l_e_st_eq_landau_n_rt_rp_eqlessd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lessd c a.(l_e_st_eq_landau_n_rt_rp_eqlessd12 c c a b (l_e_st_eq_landau_n_rt_rp_refeq c) e l : l_e_st_eq_landau_n_rt_rp_lessd c b).
-
-(* notion 3307 *)
-definition l_e_st_eq_landau_n_rt_rp_moreq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_or (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) : Prop).
-
-(* notion 3308 *)
-definition l_e_st_eq_landau_n_rt_rp_lesseq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_or (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) : Prop).
-
-(* notion 3309 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd168a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_lessd b a) (l_e_st_eq_landau_n_rt_rp_eq b a) m (λt:l_e_st_eq_landau_n_rt_rp_mored a b.l_e_st_eq_landau_n_rt_rp_lemmad5 a b t) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_symeq a b t) : l_e_st_eq_landau_n_rt_rp_lesseq b a).
-
-(* notion 3310 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd168b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored b a) (l_e_st_eq_landau_n_rt_rp_eq b a) l (λt:l_e_st_eq_landau_n_rt_rp_lessd a b.l_e_st_eq_landau_n_rt_rp_lemmad6 a b t) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_symeq a b t) : l_e_st_eq_landau_n_rt_rp_moreq b a).
-
-(* notion 3311 *)
-definition l_e_st_eq_landau_n_rt_rp_eqmoreq1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_moreq a c.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_mored a c) (l_e_st_eq_landau_n_rt_rp_eq a c) (l_e_st_eq_landau_n_rt_rp_mored b c) (l_e_st_eq_landau_n_rt_rp_eq b c) m (λt:l_e_st_eq_landau_n_rt_rp_mored a c.l_e_st_eq_landau_n_rt_rp_eqmored1 a b c e t) (λt:l_e_st_eq_landau_n_rt_rp_eq a c.l_e_st_eq_landau_n_rt_rp_treq1 b c a e t) : l_e_st_eq_landau_n_rt_rp_moreq b c).
-
-(* notion 3312 *)
-definition l_e_st_eq_landau_n_rt_rp_eqmoreq2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_moreq c a.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_mored c a) (l_e_st_eq_landau_n_rt_rp_eq c a) (l_e_st_eq_landau_n_rt_rp_mored c b) (l_e_st_eq_landau_n_rt_rp_eq c b) m (λt:l_e_st_eq_landau_n_rt_rp_mored c a.l_e_st_eq_landau_n_rt_rp_eqmored2 a b c e t) (λt:l_e_st_eq_landau_n_rt_rp_eq c a.l_e_st_eq_landau_n_rt_rp_treq c a b t e) : l_e_st_eq_landau_n_rt_rp_moreq c b).
-
-(* notion 3313 *)
-definition l_e_st_eq_landau_n_rt_rp_eqlesseq1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lesseq a c.(l_e_st_eq_landau_n_rt_rp_satzd168a c b (l_e_st_eq_landau_n_rt_rp_eqmoreq2 a b c e (l_e_st_eq_landau_n_rt_rp_satzd168b a c l)) : l_e_st_eq_landau_n_rt_rp_lesseq b c).
-
-(* notion 3314 *)
-definition l_e_st_eq_landau_n_rt_rp_eqlesseq2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lesseq c a.(l_e_st_eq_landau_n_rt_rp_satzd168a b c (l_e_st_eq_landau_n_rt_rp_eqmoreq1 a b c e (l_e_st_eq_landau_n_rt_rp_satzd168b c a l)) : l_e_st_eq_landau_n_rt_rp_lesseq c b).
-
-(* notion 3315 *)
-definition l_e_st_eq_landau_n_rt_rp_eqmoreq12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λm:l_e_st_eq_landau_n_rt_rp_moreq a c.(l_e_st_eq_landau_n_rt_rp_eqmoreq1 a b d e (l_e_st_eq_landau_n_rt_rp_eqmoreq2 c d a f m) : l_e_st_eq_landau_n_rt_rp_moreq b d).
-
-(* notion 3316 *)
-definition l_e_st_eq_landau_n_rt_rp_eqlesseq12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λl:l_e_st_eq_landau_n_rt_rp_lesseq a c.(l_e_st_eq_landau_n_rt_rp_eqlesseq1 a b d e (l_e_st_eq_landau_n_rt_rp_eqlesseq2 c d a f l) : l_e_st_eq_landau_n_rt_rp_lesseq b d).
-
-(* notion 3317 *)
-definition l_e_st_eq_landau_n_rt_rp_moreqi1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_ori1 (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) m : l_e_st_eq_landau_n_rt_rp_moreq a b).
-
-(* notion 3318 *)
-definition l_e_st_eq_landau_n_rt_rp_lesseqi1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_ori1 (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) l : l_e_st_eq_landau_n_rt_rp_lesseq a b).
-
-(* notion 3319 *)
-definition l_e_st_eq_landau_n_rt_rp_moreqi2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_ori2 (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) e : l_e_st_eq_landau_n_rt_rp_moreq a b).
-
-(* notion 3320 *)
-definition l_e_st_eq_landau_n_rt_rp_lesseqi2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_ori2 (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) e : l_e_st_eq_landau_n_rt_rp_lesseq a b).
-
-(* notion 3321 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd167c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.(l_ec3_th7 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167b a b) (l_comor (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) m) : l_not (l_e_st_eq_landau_n_rt_rp_lessd a b)).
-
-(* notion 3322 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd167d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.(l_ec3_th9 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167b a b) l : l_not (l_e_st_eq_landau_n_rt_rp_mored a b)).
-
-(* notion 3323 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd167e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_mored a b).(l_or3_th2 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167a a b) n : l_e_st_eq_landau_n_rt_rp_lesseq a b).
-
-(* notion 3324 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd167f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_lessd a b).(l_comor (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_or3_th3 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167a a b) n) : l_e_st_eq_landau_n_rt_rp_moreq a b).
-
-(* notion 3325 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd167g ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_lesseq a b) (l_not (l_e_st_eq_landau_n_rt_rp_mored a b)) (l_weli (l_e_st_eq_landau_n_rt_rp_mored a b) m) (λt:l_e_st_eq_landau_n_rt_rp_lesseq a b.l_e_st_eq_landau_n_rt_rp_satzd167d a b t) : l_not (l_e_st_eq_landau_n_rt_rp_lesseq a b)).
-
-(* notion 3326 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd167h ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_moreq a b) (l_not (l_e_st_eq_landau_n_rt_rp_lessd a b)) (l_weli (l_e_st_eq_landau_n_rt_rp_lessd a b) l) (λt:l_e_st_eq_landau_n_rt_rp_moreq a b.l_e_st_eq_landau_n_rt_rp_satzd167c a b t) : l_not (l_e_st_eq_landau_n_rt_rp_moreq a b)).
-
-(* notion 3327 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd167j ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_moreq a b).(l_or3e3 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167a a b) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) n) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) n) : l_e_st_eq_landau_n_rt_rp_lessd a b).
-
-(* notion 3328 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd167k ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_lesseq a b).(l_or3e2 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167a a b) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) n) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) n) : l_e_st_eq_landau_n_rt_rp_mored a b).
-
-(* notion 3329 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd169a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a) z) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_satz135a (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) p) : l_e_st_eq_landau_n_rt_rp_mored a b).
-
-(* notion 3330 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd169b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_satz136d (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a) z) m) : l_e_st_eq_landau_n_rt_rp_posd a).
-
-(* notion 3331 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd169c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a) z) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_satz135c (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) n) : l_e_st_eq_landau_n_rt_rp_lessd a b).
-
-(* notion 3332 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd169d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_satz136f (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a) z) l) : l_e_st_eq_landau_n_rt_rp_negd a).
-
-(* notion 3333 *)
-definition l_e_st_eq_landau_n_rt_rp_2d170_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_moreqi1 (l_e_st_eq_landau_n_rt_rp_absd a) b (l_e_st_eq_landau_n_rt_rp_satzd169a (l_e_st_eq_landau_n_rt_rp_absd a) b z (l_e_st_eq_landau_n_rt_rp_satzd166a a p)) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b).
-
-(* notion 3334 *)
-definition l_e_st_eq_landau_n_rt_rp_2d170_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λy:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_moreqi2 (l_e_st_eq_landau_n_rt_rp_absd a) b (l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_absd a) a b (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_0notnd a y)) (l_e_st_eq_landau_n_rt_rp_zeroeq a b y z)) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b).
-
-(* notion 3335 *)
-definition l_e_st_eq_landau_n_rt_rp_2d170_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_moreqi1 (l_e_st_eq_landau_n_rt_rp_absd a) b (l_e_st_eq_landau_n_rt_rp_satzd169a (l_e_st_eq_landau_n_rt_rp_absd a) b z (l_e_st_eq_landau_n_rt_rp_satzd166b a n)) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b).
-
-(* notion 3336 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd170 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_rappd a (l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_2d170_t1 a b z t) (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_2d170_t2 a b z t) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_2d170_t3 a b z t) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b).
-
-(* notion 3337 *)
-definition l_e_st_eq_landau_n_rt_rp_2d171_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lessd b c.(l_e_st_eq_landau_n_rt_rp_satz137a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)) l k : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)))).
-
-(* notion 3338 *)
-definition l_e_st_eq_landau_n_rt_rp_2d171_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lessd b c.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_2d171_t1 a b c l k) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)))).
-
-(* notion 3339 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd171 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lessd b c.(l_e_st_eq_landau_n_rt_rp_satz136c (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_2d171_t2 a b c l k) : l_e_st_eq_landau_n_rt_rp_lessd a c).
-
-(* notion 3340 *)
-definition l_e_st_eq_landau_n_rt_rp_trlessd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lessd b c.(l_e_st_eq_landau_n_rt_rp_satzd171 a b c l k : l_e_st_eq_landau_n_rt_rp_lessd a c).
-
-(* notion 3341 *)
-definition l_e_st_eq_landau_n_rt_rp_trmored ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_mored b c.(l_e_st_eq_landau_n_rt_rp_lemmad6 c a (l_e_st_eq_landau_n_rt_rp_trlessd c b a (l_e_st_eq_landau_n_rt_rp_lemmad5 b c n) (l_e_st_eq_landau_n_rt_rp_lemmad5 a b m)) : l_e_st_eq_landau_n_rt_rp_mored a c).
-
-(* notion 3342 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd172a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lessd b c.(l_orapp (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_lessd a c) l (λt:l_e_st_eq_landau_n_rt_rp_lessd a b.l_e_st_eq_landau_n_rt_rp_trlessd a b c t k) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_eqlessd1 b a c (l_e_st_eq_landau_n_rt_rp_symeq a b t) k) : l_e_st_eq_landau_n_rt_rp_lessd a c).
-
-(* notion 3343 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd172b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq b c.(l_orapp (l_e_st_eq_landau_n_rt_rp_lessd b c) (l_e_st_eq_landau_n_rt_rp_eq b c) (l_e_st_eq_landau_n_rt_rp_lessd a c) k (λt:l_e_st_eq_landau_n_rt_rp_lessd b c.l_e_st_eq_landau_n_rt_rp_trlessd a b c l t) (λt:l_e_st_eq_landau_n_rt_rp_eq b c.l_e_st_eq_landau_n_rt_rp_eqlessd2 b c a t l) : l_e_st_eq_landau_n_rt_rp_lessd a c).
-
-(* notion 3344 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd172c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_mored b c.(l_e_st_eq_landau_n_rt_rp_lemmad6 c a (l_e_st_eq_landau_n_rt_rp_satzd172b c b a (l_e_st_eq_landau_n_rt_rp_lemmad5 b c n) (l_e_st_eq_landau_n_rt_rp_satzd168a a b m)) : l_e_st_eq_landau_n_rt_rp_mored a c).
-
-(* notion 3345 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd172d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_moreq b c.(l_e_st_eq_landau_n_rt_rp_lemmad6 c a (l_e_st_eq_landau_n_rt_rp_satzd172a c b a (l_e_st_eq_landau_n_rt_rp_satzd168a b c n) (l_e_st_eq_landau_n_rt_rp_lemmad5 a b m)) : l_e_st_eq_landau_n_rt_rp_mored a c).
-
-(* notion 3346 *)
-definition l_e_st_eq_landau_n_rt_rp_2d173_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq b c.λj:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_lesseqi1 a c (l_e_st_eq_landau_n_rt_rp_satzd172b a b c j k) : l_e_st_eq_landau_n_rt_rp_lesseq a c).
-
-(* notion 3347 *)
-definition l_e_st_eq_landau_n_rt_rp_2d173_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq b c.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqlesseq1 b a c (l_e_st_eq_landau_n_rt_rp_symeq a b e) k : l_e_st_eq_landau_n_rt_rp_lesseq a c).
-
-(* notion 3348 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd173 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq b c.(l_orapp (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_lesseq a c) l (λt:l_e_st_eq_landau_n_rt_rp_lessd a b.l_e_st_eq_landau_n_rt_rp_2d173_t1 a b c l k t) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_2d173_t2 a b c l k t) : l_e_st_eq_landau_n_rt_rp_lesseq a c).
-
-(* notion 3349 *)
-definition l_e_st_eq_landau_n_rt_rp_trlesseq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq b c.(l_e_st_eq_landau_n_rt_rp_satzd173 a b c l k : l_e_st_eq_landau_n_rt_rp_lesseq a c).
-
-(* notion 3350 *)
-definition l_e_st_eq_landau_n_rt_rp_trmoreq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq b c.(l_e_st_eq_landau_n_rt_rp_satzd168b c a (l_e_st_eq_landau_n_rt_rp_trlesseq c b a (l_e_st_eq_landau_n_rt_rp_satzd168a b c n) (l_e_st_eq_landau_n_rt_rp_satzd168a a b m)) : l_e_st_eq_landau_n_rt_rp_moreq a c).
-
-(* notion 3351 *)
-definition l_e_st_eq_landau_n_rt_rp_ratd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(Πt:l_not (l_e_st_eq_landau_n_rt_rp_zero a).l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a t)) : Prop).
-
-(* notion 3352 *)
-definition l_e_st_eq_landau_n_rt_rp_irratd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_not (l_e_st_eq_landau_n_rt_rp_ratd a) : Prop).
-
-(* notion 3353 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λr:l_e_st_eq_landau_n_rt_rp_ratd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_zero b) n (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_eqzero a b e t) : l_not (l_e_st_eq_landau_n_rt_rp_zero a)).
-
-(* notion 3354 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λr:l_e_st_eq_landau_n_rt_rp_ratd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a (l_e_st_eq_landau_n_rt_rp_iv2d_t6 a b e r n)) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166e b n) (l_e_st_eq_landau_n_rt_rp_eqabsd a b e) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a (l_e_st_eq_landau_n_rt_rp_iv2d_t6 a b e r n))) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166e b n))).
-
-(* notion 3355 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λr:l_e_st_eq_landau_n_rt_rp_ratd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_e_isp l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a (l_e_st_eq_landau_n_rt_rp_iv2d_t6 a b e r n))) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166e b n)) (r (l_e_st_eq_landau_n_rt_rp_iv2d_t6 a b e r n)) (l_e_st_eq_landau_n_rt_rp_iv2d_t7 a b e r n) : l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166e b n))).
-
-(* notion 3356 *)
-definition l_e_st_eq_landau_n_rt_rp_eqratd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λr:l_e_st_eq_landau_n_rt_rp_ratd a.(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero b).l_e_st_eq_landau_n_rt_rp_iv2d_t8 a b e r t : l_e_st_eq_landau_n_rt_rp_ratd b).
-
-(* notion 3357 *)
-definition l_e_st_eq_landau_n_rt_rp_eqirratd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λi:l_e_st_eq_landau_n_rt_rp_irratd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_ratd b) (l_e_st_eq_landau_n_rt_rp_ratd a) i (λt:l_e_st_eq_landau_n_rt_rp_ratd b.l_e_st_eq_landau_n_rt_rp_eqratd b a (l_e_st_eq_landau_n_rt_rp_symeq a b e) t) : l_e_st_eq_landau_n_rt_rp_irratd b).
-
-(* notion 3358 *)
-definition l_e_st_eq_landau_n_rt_rp_ratdi0 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_r_imp_th2 (l_not (l_e_st_eq_landau_n_rt_rp_zero a)) (Πt:l_not (l_e_st_eq_landau_n_rt_rp_zero a).l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a t))) (l_weli (l_e_st_eq_landau_n_rt_rp_zero a) z) : l_e_st_eq_landau_n_rt_rp_ratd a).
-
-(* notion 3359 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t9 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r) (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r) j : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
-
-(* notion 3360 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t10 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_iv2d_t9 r i x0 s y0 j) (l_e_st_eq_landau_n_rt_rp_satz133 (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).
-
-(* notion 3361 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t11 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_st_eq_landau_n_rt_rp_satz154d y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t10 r i x0 s y0 j) : l_e_st_eq_landau_n_rt_more y0 x0).
-
-(* notion 3362 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t12 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_st_eq_landau_n_rt_rp_satz155b y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j))) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_satz154a y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j)))).
-
-(* notion 3363 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t13 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_st_eq_landau_n_rt_rp_satz140g (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r (l_e_st_eq_landau_n_rt_rp_satz154a y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j)) (l_e_st_eq_landau_n_rt_rp_iv2d_t9 r i x0 s y0 j) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_satz154a y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j)))).
-
-(* notion 3364 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t14 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_tris2 l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j))) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_satz154a y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j))) (l_e_st_eq_landau_n_rt_rp_iv2d_t13 r i x0 s y0 j) (l_e_st_eq_landau_n_rt_rp_iv2d_t12 r i x0 s y0 j) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j)))).
-
-(* notion 3365 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t15 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j)) (l_e_st_eq_landau_n_rt_rp_iv2d_t14 r i x0 s y0 j) : l_e_st_eq_landau_n_rt_rp_ratrp r).
-
-(* notion 3366 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t16 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) s l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt x).i (l_e_st_eq_landau_n_rt_rp_iv2d_t15 r i x0 s x t)) : l_con).
-
-(* notion 3367 *)
-definition l_e_st_eq_landau_n_rt_rp_remark1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.(λt:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).l_e_st_eq_landau_n_rt_rp_iv2d_t16 r i x0 t : l_e_st_eq_landau_n_rt_rp_irratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0))).
-
-(* notion 3368 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_rp ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdofrp r : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3369 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_rn ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ndofrp r : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3370 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t17 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_posdirp r : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)).
-
-(* notion 3371 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t18 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pnot0d (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_iv2d_rp r))).
-
-(* notion 3372 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t19 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_nnot0d (l_e_st_eq_landau_n_rt_rp_iv2d_rn r) (l_e_st_eq_landau_n_rt_rp_negdirp r) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_iv2d_rn r))).
-
-(* notion 3373 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t20 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)).(l_e_tris2 l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) n)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r)) (l_e_st_eq_landau_n_rt_rp_isrppd1 r) (l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) n) (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r) (l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r)))) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) n))).
-
-(* notion 3374 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t21 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_iv2d_rn r))) (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_absnd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r) (l_e_st_eq_landau_n_rt_rp_negdirp r)) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_stdis l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_stmis l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)).
-
-(* notion 3375 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t22 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)).(l_e_tris2 l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rn r) n)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r)) (l_e_st_eq_landau_n_rt_rp_isrppd1 r) (l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rn r) n) (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r) (l_e_st_eq_landau_n_rt_rp_iv2d_t21 r)) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rn r) n))).
-
-(* notion 3376 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t23 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r s.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r.(l_e_isp l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp x) r s rr i : l_e_st_eq_landau_n_rt_rp_ratrp s).
-
-(* notion 3377 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t24 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r s.λrs:l_e_st_eq_landau_n_rt_rp_ratrp s.(l_e_isp1 l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp x) s r rs i : l_e_st_eq_landau_n_rt_rp_ratrp r).
-
-(* notion 3378 *)
-definition l_e_st_eq_landau_n_rt_rp_remark2a ≝ λr:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r.(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pdofrp r)).l_e_st_eq_landau_n_rt_rp_iv2d_t23 r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_pdofrp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_pdofrp r) t)) (l_e_st_eq_landau_n_rt_rp_iv2d_t20 r t) rr : l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
-
-(* notion 3379 *)
-definition l_e_st_eq_landau_n_rt_rp_remark2b ≝ λr:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r.(l_e_st_eq_landau_n_rt_rp_iv2d_t17 r : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
-
-(* notion 3380 *)
-definition l_e_st_eq_landau_n_rt_rp_remark3a ≝ λr:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r.(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_ndofrp r)).l_e_st_eq_landau_n_rt_rp_iv2d_t23 r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_ndofrp r) t)) (l_e_st_eq_landau_n_rt_rp_iv2d_t22 r t) rr : l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
-
-(* notion 3381 *)
-definition l_e_st_eq_landau_n_rt_rp_remark3b ≝ λr:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r.(l_e_st_eq_landau_n_rt_rp_negdirp r : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
-
-(* notion 3382 *)
-definition l_e_st_eq_landau_n_rt_rp_remark4a ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_pdofrp r)) (l_e_st_eq_landau_n_rt_rp_ratrp r) i (λt:l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_pdofrp r).l_e_st_eq_landau_n_rt_rp_iv2d_t24 r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_pdofrp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t18 r))) (l_e_st_eq_landau_n_rt_rp_iv2d_t20 r (l_e_st_eq_landau_n_rt_rp_iv2d_t18 r)) (t (l_e_st_eq_landau_n_rt_rp_iv2d_t18 r))) : l_e_st_eq_landau_n_rt_rp_irratd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
-
-(* notion 3383 *)
-definition l_e_st_eq_landau_n_rt_rp_remark4b ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.(l_e_st_eq_landau_n_rt_rp_iv2d_t17 r : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
-
-(* notion 3384 *)
-definition l_e_st_eq_landau_n_rt_rp_remark5a ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_ratrp r) i (λt:l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_ndofrp r).l_e_st_eq_landau_n_rt_rp_iv2d_t24 r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t19 r))) (l_e_st_eq_landau_n_rt_rp_iv2d_t22 r (l_e_st_eq_landau_n_rt_rp_iv2d_t19 r)) (t (l_e_st_eq_landau_n_rt_rp_iv2d_t19 r))) : l_e_st_eq_landau_n_rt_rp_irratd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
-
-(* notion 3385 *)
-definition l_e_st_eq_landau_n_rt_rp_remark5b ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.(l_e_st_eq_landau_n_rt_rp_negdirp r : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
-
-(* notion 3386 *)
-definition l_e_st_eq_landau_n_rt_rp_natd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_posd a) (Πt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a t)) : Prop).
-
-(* notion 3387 *)
-definition l_e_st_eq_landau_n_rt_rp_natposd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_ande1 (l_e_st_eq_landau_n_rt_rp_posd a) (Πt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a t)) n : l_e_st_eq_landau_n_rt_rp_posd a).
-
-(* notion 3388 *)
-definition l_e_st_eq_landau_n_rt_rp_natderp ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_r_ande2 (l_e_st_eq_landau_n_rt_rp_posd a) (Πt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a t)) n : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a (l_e_st_eq_landau_n_rt_rp_natposd a n))).
-
-(* notion 3389 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t25 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_e_st_eq_landau_n_rt_rp_eqposd a b e (l_e_st_eq_landau_n_rt_rp_natposd a n) : l_e_st_eq_landau_n_rt_rp_posd b).
-
-(* notion 3390 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t26 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_natd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_eqpderp a (l_e_st_eq_landau_n_rt_rp_natposd a n) b p e : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd a (l_e_st_eq_landau_n_rt_rp_natposd a n)) (l_e_st_eq_landau_n_rt_rp_rpofpd b p)).
-
-(* notion 3391 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t27 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_natd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_isp l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) (l_e_st_eq_landau_n_rt_rp_rpofpd a (l_e_st_eq_landau_n_rt_rp_natposd a n)) (l_e_st_eq_landau_n_rt_rp_rpofpd b p) (l_e_st_eq_landau_n_rt_rp_natderp a n) (l_e_st_eq_landau_n_rt_rp_iv2d_t26 a b e n p) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd b p)).
-
-(* notion 3392 *)
-definition l_e_st_eq_landau_n_rt_rp_eqnatd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_andi (l_e_st_eq_landau_n_rt_rp_posd b) (Πt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd b t)) (l_e_st_eq_landau_n_rt_rp_iv2d_t25 a b e n) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_iv2d_t27 a b e n t) : l_e_st_eq_landau_n_rt_rp_natd b).
-
-(* notion 3393 *)
-definition l_e_st_eq_landau_n_rt_rp_pdofnt ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3394 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t28 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_rpofnt x) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x)).
-
-(* notion 3395 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t29 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).(l_e_st_eq_landau_n_rt_rp_isrppd1 (l_e_st_eq_landau_n_rt_rp_rpofnt x) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) (l_e_st_eq_landau_n_rt_rp_iv2d_t28 x))).
-
-(* notion 3396 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t30 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).(l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_pdofnt x) (l_e_st_eq_landau_n_rt_rp_iv2d_t28 x) (l_e_st_eq_landau_n_rt_rp_pdofnt x) p (l_e_st_eq_landau_n_rt_rp_refeq (l_e_st_eq_landau_n_rt_rp_pdofnt x)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) (l_e_st_eq_landau_n_rt_rp_iv2d_t28 x)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) p)).
-
-(* notion 3397 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t31 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) (l_e_st_eq_landau_n_rt_rp_iv2d_t28 x)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) p) (l_e_st_eq_landau_n_rt_rp_iv2d_t29 x p) (l_e_st_eq_landau_n_rt_rp_iv2d_t30 x p) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) p)).
-
-(* notion 3398 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t32 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).(l_e_isp l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) p) (l_e_st_eq_landau_n_rt_rp_natrpi x) (l_e_st_eq_landau_n_rt_rp_iv2d_t31 x p) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) p)).
-
-(* notion 3399 *)
-definition l_e_st_eq_landau_n_rt_rp_natdi ≝ λx:l_e_st_eq_landau_n_nat.(l_andi (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x)) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) t)) (l_e_st_eq_landau_n_rt_rp_iv2d_t28 x) (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).l_e_st_eq_landau_n_rt_rp_iv2d_t32 x t) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_pdofnt x)).
-
-(* notion 3400 *)
-definition l_e_st_eq_landau_n_rt_rp_intd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_or (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) : Prop).
-
-(* notion 3401 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t33 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λi:l_e_st_eq_landau_n_rt_rp_intd a.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_eqzero a b e z : l_e_st_eq_landau_n_rt_rp_zero b).
-
-(* notion 3402 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t34 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).(l_e_st_eq_landau_n_rt_rp_eqnatd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_eqabsd a b e) n : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd b)).
-
-(* notion 3403 *)
-definition l_e_st_eq_landau_n_rt_rp_eqintd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λi:l_e_st_eq_landau_n_rt_rp_intd a.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd b)) i (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_iv2d_t33 a b e i t) (λt:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).l_e_st_eq_landau_n_rt_rp_iv2d_t34 a b e i t) : l_e_st_eq_landau_n_rt_rp_intd b).
-
-(* notion 3404 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t34a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a (l_e_st_eq_landau_n_rt_rp_natposd a n))) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3405 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t35 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_e_st_eq_landau_n_rt_rp_eqnatd a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_iv2d_t34a a n) n : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3406 *)
-definition l_e_st_eq_landau_n_rt_rp_natintd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_ori2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_iv2d_t35 a n) : l_e_st_eq_landau_n_rt_rp_intd a).
-
-(* notion 3407 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t36 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λi:l_e_st_eq_landau_n_rt_rp_intd a.(l_ore2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) i (l_e_st_eq_landau_n_rt_rp_pnot0d a p) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3408 *)
-definition l_e_st_eq_landau_n_rt_rp_posintnatd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λi:l_e_st_eq_landau_n_rt_rp_intd a.(l_e_st_eq_landau_n_rt_rp_eqnatd (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p)) (l_e_st_eq_landau_n_rt_rp_iv2d_t36 a p i) : l_e_st_eq_landau_n_rt_rp_natd a).
-
-(* notion 3409 *)
-definition l_e_st_eq_landau_n_rt_rp_intdi0 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_ori1 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) z : l_e_st_eq_landau_n_rt_rp_intd a).
-
-(* notion 3410 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t37 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_e_st_eq_landau_n_rt_rp_posdirp r : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
-
-(* notion 3411 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t38 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r).(l_e_tris l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t37 r n)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) p) (l_e_st_eq_landau_n_rt_rp_isrppd1 r) (l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t37 r n) (l_e_st_eq_landau_n_rt_rp_pdofrp r) p (l_e_st_eq_landau_n_rt_rp_refeq (l_e_st_eq_landau_n_rt_rp_pdofrp r))) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) p)).
-
-(* notion 3412 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t39 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r).(l_e_isp l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) p) n (l_e_st_eq_landau_n_rt_rp_iv2d_t38 r n p) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) p)).
-
-(* notion 3413 *)
-definition l_e_st_eq_landau_n_rt_rp_remark6a ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_andi (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r)) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) t)) (l_e_st_eq_landau_n_rt_rp_iv2d_t37 r n) (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r).l_e_st_eq_landau_n_rt_rp_iv2d_t39 r n t) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
-
-(* notion 3414 *)
-definition l_e_st_eq_landau_n_rt_rp_remark6 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_e_st_eq_landau_n_rt_rp_natintd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_remark6a r n) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
-
-(* notion 3415 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t40 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_e_st_eq_landau_n_rt_rp_absdeql l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_compl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_satz133a l_e_st_eq_landau_n_rt_rp_1rp r)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
-
-(* notion 3416 *)
-definition l_e_st_eq_landau_n_rt_rp_iv2d_t41 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_e_st_eq_landau_n_rt_rp_eqnatd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t40 r n)) (l_e_st_eq_landau_n_rt_rp_remark6a r n) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r))).
-
-(* notion 3417 *)
-definition l_e_st_eq_landau_n_rt_rp_remark7 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_ori2 (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r))) (l_e_st_eq_landau_n_rt_rp_iv2d_t41 r n) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
-
-(* notion 3418 *)
-definition l_e_st_eq_landau_n_rt_rp_2d174_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_ore2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) i n : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3419 *)
-definition l_e_st_eq_landau_n_rt_rp_2d174_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_ande2 (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) t)) (l_e_st_eq_landau_n_rt_rp_2d174_t1 a i n) : Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) t)).
-
-(* notion 3420 *)
-definition l_e_st_eq_landau_n_rt_rp_2d174_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_lemmaiii5 (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a n)) (l_e_st_eq_landau_n_rt_rp_2d174_t2 a i n (l_e_st_eq_landau_n_rt_rp_satzd166e a n)) : l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a n))).
-
-(* notion 3421 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd174 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero a).l_e_st_eq_landau_n_rt_rp_2d174_t3 a i t : l_e_st_eq_landau_n_rt_rp_ratd a).
-
-(* notion 3422 *)
-definition l_e_st_eq_landau_n_rt_rp_pd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3423 *)
-definition l_e_st_eq_landau_n_rt_rp_pd12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) b1 (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) (l_e_st_eq_landau_n_rt_rp_stmis b1 b2)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)) b2 (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) (l_e_st_eq_landau_n_rt_rp_stdis b1 b2)) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2))).
-
-(* notion 3424 *)
-definition l_e_st_eq_landau_n_rt_rp_pd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) r1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stmis r1 r2)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) r2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_stdis r1 r2)) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2))).
-
-(* notion 3425 *)
-definition l_e_st_eq_landau_n_rt_rp_pd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) r1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stmis r1 r2)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) r2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_stdis r1 r2)) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3426 *)
-definition l_e_st_eq_landau_n_rt_rp_pdeq12a ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2)) (l_e_st_eq_landau_n_rt_rp_pd12 a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2))).
-
-(* notion 3427 *)
-definition l_e_st_eq_landau_n_rt_rp_pdeq12b ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2)) (l_e_st_eq_landau_n_rt_rp_pd12 a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2))).
-
-(* notion 3428 *)
-definition l_e_st_eq_landau_n_rt_rp_pdeq1a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pd1 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2))).
-
-(* notion 3429 *)
-definition l_e_st_eq_landau_n_rt_rp_pdeq1b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pd1 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r1 r2))).
-
-(* notion 3430 *)
-definition l_e_st_eq_landau_n_rt_rp_pdeq2a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pd2 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3431 *)
-definition l_e_st_eq_landau_n_rt_rp_pdeq2b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pd2 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a)).
-
-(* notion 3432 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd175 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd b a)).
-
-(* notion 3433 *)
-definition l_e_st_eq_landau_n_rt_rp_compd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd175 a b : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd b a)).
-
-(* notion 3434 *)
-definition l_e_st_eq_landau_n_rt_rp_iv3d_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_4pl23 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c)) e) (l_e_st_eq_landau_n_rt_rp_4pl23 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))).
-
-(* notion 3435 *)
-definition l_e_st_eq_landau_n_rt_rp_eqpd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_iv3d_t1 a b c e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)).
-
-(* notion 3436 *)
-definition l_e_st_eq_landau_n_rt_rp_eqpd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_compd c a) (l_e_st_eq_landau_n_rt_rp_eqpd1 a b c e) (l_e_st_eq_landau_n_rt_rp_compd b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b)).
-
-(* notion 3437 *)
-definition l_e_st_eq_landau_n_rt_rp_eqpd12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_eqpd1 a b c e) (l_e_st_eq_landau_n_rt_rp_eqpd2 c d b f) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3438 *)
-definition l_e_st_eq_landau_n_rt_rp_iv3d_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_tr4is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) z (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_1b a b)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)))).
-
-(* notion 3439 *)
-definition l_e_st_eq_landau_n_rt_rp_pd01 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_eqi2 b (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_iv3d_t2 a b z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) b).
-
-(* notion 3440 *)
-definition l_e_st_eq_landau_n_rt_rp_pd02 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd b a) a (l_e_st_eq_landau_n_rt_rp_compd a b) (l_e_st_eq_landau_n_rt_rp_pd01 b a z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) a).
-
-(* notion 3441 *)
-definition l_e_st_eq_landau_n_rt_rp_ppd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_satz137 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) p q) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3442 *)
-definition l_e_st_eq_landau_n_rt_rp_npd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_negdi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_satz137a (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) n o) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3443 *)
-definition l_e_st_eq_landau_n_rt_rp_m0d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3444 *)
-definition l_e_st_eq_landau_n_rt_rp_m0deqa ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 a1 (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_df a2 a1)).
-
-(* notion 3445 *)
-definition l_e_st_eq_landau_n_rt_rp_m0deqb ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_df a2 a1) (l_e_st_eq_landau_n_rt_rp_m0deqa a1 a2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a2 a1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_df a1 a2))).
-
-(* notion 3446 *)
-definition l_e_st_eq_landau_n_rt_rp_iv3d_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_symeq a b e) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a))).
-
-(* notion 3447 *)
-definition l_e_st_eq_landau_n_rt_rp_eqm0d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_iv3d_t3 a b e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)).
-
-(* notion 3448 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd176a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_negdi (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) p) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_m0d a)).
-
-(* notion 3449 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd176b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_zeroi (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) z) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_m0d a)).
-
-(* notion 3450 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd176c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d a)).
-
-(* notion 3451 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd176d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_m0d a).(l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stmis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_stdis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) n) : l_e_st_eq_landau_n_rt_rp_posd a).
-
-(* notion 3452 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd176e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_m0d a).(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_isstm (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) z (l_e_st_eq_landau_n_rt_rp_stdis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) : l_e_st_eq_landau_n_rt_rp_zero a).
-
-(* notion 3453 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd176f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d a).(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stmis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_stdis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) p) : l_e_st_eq_landau_n_rt_rp_negd a).
-
-(* notion 3454 *)
-definition l_e_st_eq_landau_n_rt_rp_m0d0 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_m0d a) a (l_e_st_eq_landau_n_rt_rp_satzd176b a z) z : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) a).
-
-(* notion 3455 *)
-definition l_e_st_eq_landau_n_rt_rp_3d177_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) a (l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_stdis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_stmis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_dfis a) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a).
-
-(* notion 3456 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd177 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a (l_e_st_eq_landau_n_rt_rp_3d177_t1 a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a).
-
-(* notion 3457 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd177a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a (l_e_st_eq_landau_n_rt_rp_satzd177 a) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a))).
-
-(* notion 3458 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd177b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_m0d b).(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b (l_e_st_eq_landau_n_rt_rp_eqm0d a (l_e_st_eq_landau_n_rt_rp_m0d b) e) (l_e_st_eq_landau_n_rt_rp_satzd177 b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) b).
-
-(* notion 3459 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd177c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_m0d b).(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d a) b (l_e_st_eq_landau_n_rt_rp_satzd177b a b e) : l_e_st_eq_landau_n_rt_rp_eq b (l_e_st_eq_landau_n_rt_rp_m0d a)).
-
-(* notion 3460 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd177d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) b.(l_e_st_eq_landau_n_rt_rp_satzd177c b a (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d a) b e) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_m0d b)).
-
-(* notion 3461 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd177e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) b.(l_e_st_eq_landau_n_rt_rp_symeq a (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_satzd177d a b e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d b) a).
-
-(* notion 3462 *)
-definition l_e_st_eq_landau_n_rt_rp_3d178_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absnd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_satzd176a a p)) (l_e_st_eq_landau_n_rt_rp_satzd177 a) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3463 *)
-definition l_e_st_eq_landau_n_rt_rp_3d178_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_m0d a) a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_0notnd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_satzd176b a z))) (l_e_st_eq_landau_n_rt_rp_m0d0 a z) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_0notnd a z))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3464 *)
-definition l_e_st_eq_landau_n_rt_rp_3d178_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_satzd176c a n))) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_absnd a n)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3465 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd178 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_rappd a (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_3d178_t1 a t) (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_3d178_t2 a t) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_3d178_t3 a t) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3466 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd178a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd178 a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a))).
-
-(* notion 3467 *)
-definition l_e_st_eq_landau_n_rt_rp_3d179_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_pdeq1b a (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_m0d a))).
-
-(* notion 3468 *)
-definition l_e_st_eq_landau_n_rt_rp_3d179_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_zeroi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)))).
-
-(* notion 3469 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd179 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_3d179_t1 a) (l_e_st_eq_landau_n_rt_rp_3d179_t2 a) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_m0d a))).
-
-(* notion 3470 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd179a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) a) (l_e_st_eq_landau_n_rt_rp_compd a (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_satzd179 a) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) a)).
-
-(* notion 3471 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd180 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0deqa (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pdeq12b (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b))).
-
-(* notion 3472 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd180a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd180 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b))).
-
-(* notion 3473 *)
-definition l_e_st_eq_landau_n_rt_rp_md ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_m0d b) : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3474 *)
-definition l_e_st_eq_landau_n_rt_rp_mdeq12a ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b2 b1)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl a2 b1)) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df b2 b1) (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_m0deqa b1 b2)) (l_e_st_eq_landau_n_rt_rp_pdeq12a a1 a2 b2 b1) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl a2 b1))).
-
-(* notion 3475 *)
-definition l_e_st_eq_landau_n_rt_rp_mdeq12b ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl a2 b1)) (l_e_st_eq_landau_n_rt_rp_mdeq12a a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl a2 b1)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2))).
-
-(* notion 3476 *)
-definition l_e_st_eq_landau_n_rt_rp_mdeq1a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r2 r1)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r1)) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df r2 r1) a (l_e_st_eq_landau_n_rt_rp_m0deqa r1 r2)) (l_e_st_eq_landau_n_rt_rp_pdeq1a a r2 r1) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r1))).
-
-(* notion 3477 *)
-definition l_e_st_eq_landau_n_rt_rp_mdeq1b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r1)) (l_e_st_eq_landau_n_rt_rp_mdeq1a a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r1)) (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_df r1 r2))).
-
-(* notion 3478 *)
-definition l_e_st_eq_landau_n_rt_rp_mdeq2a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdeq12a r1 r2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_1a a)))).
-
-(* notion 3479 *)
-definition l_e_st_eq_landau_n_rt_rp_mdeq2b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdeq12b r1 r2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df r1 r2) a)).
-
-(* notion 3480 *)
-definition l_e_st_eq_landau_n_rt_rp_eqmd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqpd1 a b (l_e_st_eq_landau_n_rt_rp_m0d c) e : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a c) (l_e_st_eq_landau_n_rt_rp_md b c)).
-
-(* notion 3481 *)
-definition l_e_st_eq_landau_n_rt_rp_eqmd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) c (l_e_st_eq_landau_n_rt_rp_eqm0d a b e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md c a) (l_e_st_eq_landau_n_rt_rp_md c b)).
-
-(* notion 3482 *)
-definition l_e_st_eq_landau_n_rt_rp_eqmd12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md a c) (l_e_st_eq_landau_n_rt_rp_md b c) (l_e_st_eq_landau_n_rt_rp_md b d) (l_e_st_eq_landau_n_rt_rp_eqmd1 a b c e) (l_e_st_eq_landau_n_rt_rp_eqmd2 c d b f) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a c) (l_e_st_eq_landau_n_rt_rp_md b d)).
-
-(* notion 3483 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd181 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_md b a) (l_e_st_eq_landau_n_rt_rp_satzd180 a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_satzd177 b)) (l_e_st_eq_landau_n_rt_rp_compd (l_e_st_eq_landau_n_rt_rp_m0d a) b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_md b a)).
-
-(* notion 3484 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd181a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_md b a)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_satzd181 b a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_md b a))).
-
-(* notion 3485 *)
-definition l_e_st_eq_landau_n_rt_rp_3d182_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pdeq1a a (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_eqsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3486 *)
-definition l_e_st_eq_landau_n_rt_rp_3d182_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_3d182_t1 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3487 *)
-definition l_e_st_eq_landau_n_rt_rp_3d182_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stmis (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))).
-
-(* notion 3488 *)
-definition l_e_st_eq_landau_n_rt_rp_3d182_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stdis (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))).
-
-(* notion 3489 *)
-definition l_e_st_eq_landau_n_rt_rp_3d182_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_3d182_t1 a b) p : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3490 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd182a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_3d182_t3 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t4 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t5 a b p) : l_e_st_eq_landau_n_rt_rp_mored a b).
-
-(* notion 3491 *)
-definition l_e_st_eq_landau_n_rt_rp_3d182_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_3d182_t1 a b) z : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3492 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd182b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_isstm (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_3d182_t6 a b z) (l_e_st_eq_landau_n_rt_rp_3d182_t4 a b) : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3493 *)
-definition l_e_st_eq_landau_n_rt_rp_3d182_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_3d182_t1 a b) n : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3494 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd182c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_3d182_t3 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t4 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t7 a b n) : l_e_st_eq_landau_n_rt_rp_lessd a b).
-
-(* notion 3495 *)
-definition l_e_st_eq_landau_n_rt_rp_3d182_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) m : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3496 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd182d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d182_t2 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t8 a b m) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3497 *)
-definition l_e_st_eq_landau_n_rt_rp_3d182_t9 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_zeroi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) e : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3498 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd182e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d182_t2 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t9 a b e) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3499 *)
-definition l_e_st_eq_landau_n_rt_rp_3d182_t10 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_negdi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) l : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3500 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd182f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d182_t2 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t10 a b l) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3501 *)
-definition l_e_st_eq_landau_n_rt_rp_3d183_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_12issmsd (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a)))).
-
-(* notion 3502 *)
-definition l_e_st_eq_landau_n_rt_rp_3d183_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_3d183_t1 b a : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d b)))).
-
-(* notion 3503 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd183a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a))) (l_e_st_eq_landau_n_rt_rp_3d183_t2 a b) (l_e_st_eq_landau_n_rt_rp_3d183_t1 a b) (l_e_st_eq_landau_n_rt_rp_lemmad5 a b m) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)).
-
-(* notion 3504 *)
-definition l_e_st_eq_landau_n_rt_rp_staz183b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqm0d a b e : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)).
-
-(* notion 3505 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd183c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a))) (l_e_st_eq_landau_n_rt_rp_3d183_t2 a b) (l_e_st_eq_landau_n_rt_rp_3d183_t1 a b) (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)).
-
-(* notion 3506 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd183d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b).(l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b (l_e_st_eq_landau_n_rt_rp_satzd177 a) (l_e_st_eq_landau_n_rt_rp_satzd177 b) (l_e_st_eq_landau_n_rt_rp_satzd183c (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) l) : l_e_st_eq_landau_n_rt_rp_mored a b).
-
-(* notion 3507 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd183e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b).(l_e_st_eq_landau_n_rt_rp_tr3eq a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b (l_e_st_eq_landau_n_rt_rp_satzd177a a) (l_e_st_eq_landau_n_rt_rp_eqm0d (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) e) (l_e_st_eq_landau_n_rt_rp_satzd177 b) : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3508 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd183f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b).(l_e_st_eq_landau_n_rt_rp_eqlessd12 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b (l_e_st_eq_landau_n_rt_rp_satzd177 a) (l_e_st_eq_landau_n_rt_rp_satzd177 b) (l_e_st_eq_landau_n_rt_rp_satzd183a (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) m) : l_e_st_eq_landau_n_rt_rp_lessd a b).
-
-(* notion 3509 *)
-definition l_e_st_eq_landau_n_rt_rp_3d184_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_lemmad3 a (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_3pl12 (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_mdeq12b (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3510 *)
-definition l_e_st_eq_landau_n_rt_rp_3d184_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_and3i (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_3d184_t1 a) : l_and3 (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a))))).
-
-(* notion 3511 *)
-definition l_e_st_eq_landau_n_rt_rp_3d184_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_posd x) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) x))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_3d184_t2 a) : l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_posd x) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) x)))).
-
-(* notion 3512 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd184 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (Πy:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_posd x) (l_e_st_eq_landau_n_rt_rp_posd y) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md x y)))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_3d184_t3 a) : l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (Πy:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_posd x) (l_e_st_eq_landau_n_rt_rp_posd y) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md x y))))).
-
-(* notion 3513 *)
-definition l_e_st_eq_landau_n_rt_rp_asspd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pdeq2a c (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pdeq1b a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c))).
-
-(* notion 3514 *)
-definition l_e_st_eq_landau_n_rt_rp_asspd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_asspd1 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c)).
-
-(* notion 3515 *)
-definition l_e_st_eq_landau_n_rt_rp_3pd23 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd c b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) b) (l_e_st_eq_landau_n_rt_rp_asspd1 a b c) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd c b) a (l_e_st_eq_landau_n_rt_rp_compd b c)) (l_e_st_eq_landau_n_rt_rp_asspd2 a c b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) b)).
-
-(* notion 3516 *)
-definition l_e_st_eq_landau_n_rt_rp_4pd23 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd c d)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) d) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) b) d) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)) (l_e_st_eq_landau_n_rt_rp_asspd2 (l_e_st_eq_landau_n_rt_rp_pd a b) c d) (l_e_st_eq_landau_n_rt_rp_eqpd1 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) b) d (l_e_st_eq_landau_n_rt_rp_3pd23 a b c)) (l_e_st_eq_landau_n_rt_rp_asspd1 (l_e_st_eq_landau_n_rt_rp_pd a c) b d) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd c d)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d))).
-
-(* notion 3517 *)
-definition l_e_st_eq_landau_n_rt_rp_pdmd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) b) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) b)) a (l_e_st_eq_landau_n_rt_rp_asspd1 a (l_e_st_eq_landau_n_rt_rp_m0d b) b) (l_e_st_eq_landau_n_rt_rp_pd02 a (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) b) (l_e_st_eq_landau_n_rt_rp_satzd179a b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) b) a).
-
-(* notion 3518 *)
-definition l_e_st_eq_landau_n_rt_rp_mdpd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a b) b) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b (l_e_st_eq_landau_n_rt_rp_m0d b))) a (l_e_st_eq_landau_n_rt_rp_asspd1 a b (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_pd02 a (l_e_st_eq_landau_n_rt_rp_pd b (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd179 b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a b) b) a).
-
-(* notion 3519 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd185 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md c d)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_m0d d))) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)) (l_e_st_eq_landau_n_rt_rp_4pd23 a (l_e_st_eq_landau_n_rt_rp_m0d b) c (l_e_st_eq_landau_n_rt_rp_m0d d)) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_m0d d)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd b d)) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd180a b d)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md c d)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d))).
-
-(* notion 3520 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd186 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_asspd1 a b c : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c))).
-
-(* notion 3521 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd187a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd b (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) b) a (l_e_st_eq_landau_n_rt_rp_compd b (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_pdmd a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd b (l_e_st_eq_landau_n_rt_rp_md a b)) a).
-
-(* notion 3522 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd187c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λx:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd b x) a.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd x b) b) x (l_e_st_eq_landau_n_rt_rp_eqmd1 a (l_e_st_eq_landau_n_rt_rp_pd x b) b (l_e_st_eq_landau_n_rt_rp_treq1 a (l_e_st_eq_landau_n_rt_rp_pd x b) (l_e_st_eq_landau_n_rt_rp_pd b x) e (l_e_st_eq_landau_n_rt_rp_compd b x))) (l_e_st_eq_landau_n_rt_rp_mdpd x b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a b) x).
-
-(* notion 3523 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd187d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λx:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd b x) a.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md a b) x (l_e_st_eq_landau_n_rt_rp_satzd187c a b x e) : l_e_st_eq_landau_n_rt_rp_eq x (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3524 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd187e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λx:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd x b) a.(l_e_st_eq_landau_n_rt_rp_satzd187c a b x (l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd b x) (l_e_st_eq_landau_n_rt_rp_pd x b) a (l_e_st_eq_landau_n_rt_rp_compd b x) e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a b) x).
-
-(* notion 3525 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd187f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λx:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd x b) a.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md a b) x (l_e_st_eq_landau_n_rt_rp_satzd187e a b x e) : l_e_st_eq_landau_n_rt_rp_eq x (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3526 *)
-definition l_e_st_eq_landau_n_rt_rp_3d188_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_m0d c))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md c c)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_m0d c)) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd180 b c)) (l_e_st_eq_landau_n_rt_rp_4pd23 a c (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_m0d c)) (l_e_st_eq_landau_n_rt_rp_pd02 (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md c c) (l_e_st_eq_landau_n_rt_rp_satzd179 c)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3527 *)
-definition l_e_st_eq_landau_n_rt_rp_3d188_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d188_t1 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c))).
-
-(* notion 3528 *)
-definition l_e_st_eq_landau_n_rt_rp_3d188_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d188_t1 a b c) (l_e_st_eq_landau_n_rt_rp_satzd182d (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) m) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3529 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_satzd182a a b (l_e_st_eq_landau_n_rt_rp_3d188_t3 a b c m) : l_e_st_eq_landau_n_rt_rp_mored a b).
-
-(* notion 3530 *)
-definition l_e_st_eq_landau_n_rt_rp_3d188_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d188_t1 a b c) (l_e_st_eq_landau_n_rt_rp_satzd182e (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) e) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3531 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_satzd182b a b (l_e_st_eq_landau_n_rt_rp_3d188_t4 a b c e) : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3532 *)
-definition l_e_st_eq_landau_n_rt_rp_3d188_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d188_t1 a b c) (l_e_st_eq_landau_n_rt_rp_satzd182f (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) l) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3533 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_satzd182c a b (l_e_st_eq_landau_n_rt_rp_3d188_t5 a b c l) : l_e_st_eq_landau_n_rt_rp_lessd a b).
-
-(* notion 3534 *)
-definition l_e_st_eq_landau_n_rt_rp_3d188_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_3d188_t2 a b c) (l_e_st_eq_landau_n_rt_rp_satzd182d a b m) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c))).
-
-(* notion 3535 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_satzd182a (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_3d188_t6 a b c m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)).
-
-(* notion 3536 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqpd1 a b c e : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)).
-
-(* notion 3537 *)
-definition l_e_st_eq_landau_n_rt_rp_3d188_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_3d188_t2 a b c) (l_e_st_eq_landau_n_rt_rp_satzd182f a b l) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c))).
-
-(* notion 3538 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_satzd182c (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_3d188_t7 a b c l) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)).
-
-(* notion 3539 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188g ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b).(l_e_st_eq_landau_n_rt_rp_satzd188a a b c (l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_compd c a) (l_e_st_eq_landau_n_rt_rp_compd c b) m) : l_e_st_eq_landau_n_rt_rp_mored a b).
-
-(* notion 3540 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188h ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b).(l_e_st_eq_landau_n_rt_rp_satzd188b a b c (l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_compd a c) e (l_e_st_eq_landau_n_rt_rp_compd c b)) : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3541 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188j ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b).λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b).(l_e_st_eq_landau_n_rt_rp_satzd188c a b c (l_e_st_eq_landau_n_rt_rp_eqlessd12 (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_compd c a) (l_e_st_eq_landau_n_rt_rp_compd c b) l) : l_e_st_eq_landau_n_rt_rp_lessd a b).
-
-(* notion 3542 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188k ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_compd a c) (l_e_st_eq_landau_n_rt_rp_compd b c) (l_e_st_eq_landau_n_rt_rp_satzd188d a b c m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b)).
-
-(* notion 3543 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188l ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqpd2 a b c e : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b)).
-
-(* notion 3544 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188m ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_eqlessd12 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_compd a c) (l_e_st_eq_landau_n_rt_rp_compd b c) (l_e_st_eq_landau_n_rt_rp_satzd188f a b c l) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b)).
-
-(* notion 3545 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188n ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_mored c d.(l_e_st_eq_landau_n_rt_rp_eqmored2 (l_e_st_eq_landau_n_rt_rp_pd a d) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_eqpd1 a b d e) (l_e_st_eq_landau_n_rt_rp_satzd188k c d a m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3546 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188o ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_mored c d.(l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd d b) (l_e_st_eq_landau_n_rt_rp_compd a c) (l_e_st_eq_landau_n_rt_rp_compd b d) (l_e_st_eq_landau_n_rt_rp_satzd188n a b c d e m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd d b)).
-
-(* notion 3547 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188p ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lessd c d.(l_e_st_eq_landau_n_rt_rp_eqlessd2 (l_e_st_eq_landau_n_rt_rp_pd a d) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_eqpd1 a b d e) (l_e_st_eq_landau_n_rt_rp_satzd188m c d a l) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3548 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd188q ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lessd c d.(l_e_st_eq_landau_n_rt_rp_eqlessd12 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd d b) (l_e_st_eq_landau_n_rt_rp_compd a c) (l_e_st_eq_landau_n_rt_rp_compd b d) (l_e_st_eq_landau_n_rt_rp_satzd188p a b c d e l) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd d b)).
-
-(* notion 3549 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd189 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_mored c d.(l_e_st_eq_landau_n_rt_rp_trmored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_satzd188d a b c m) (l_e_st_eq_landau_n_rt_rp_satzd188k c d b n) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3550 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd189a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lessd c d.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd189 b a d c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) (l_e_st_eq_landau_n_rt_rp_lemmad6 c d k)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3551 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd190a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_mored c d.(l_orapp (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)) m (λt:l_e_st_eq_landau_n_rt_rp_mored a b.l_e_st_eq_landau_n_rt_rp_satzd189 a b c d t n) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_satzd188n a b c d t n) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3552 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd190b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.(l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd d b) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_compd c a) (l_e_st_eq_landau_n_rt_rp_compd d b) (l_e_st_eq_landau_n_rt_rp_satzd190a c d a b n m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3553 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd190c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lessd c d.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd190a b a d c (l_e_st_eq_landau_n_rt_rp_satzd168b a b l) (l_e_st_eq_landau_n_rt_rp_lemmad6 c d k)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3554 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd190d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq c d.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd190b b a d c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) (l_e_st_eq_landau_n_rt_rp_satzd168b c d k)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3555 *)
-definition l_e_st_eq_landau_n_rt_rp_3d191_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_moreqi2 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_eqpd12 a b c d e f) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3556 *)
-definition l_e_st_eq_landau_n_rt_rp_3d191_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λo:l_e_st_eq_landau_n_rt_rp_mored c d.(l_e_st_eq_landau_n_rt_rp_moreqi1 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_satzd190a a b c d m o) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3557 *)
-definition l_e_st_eq_landau_n_rt_rp_3d191_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_orapp (l_e_st_eq_landau_n_rt_rp_mored c d) (l_e_st_eq_landau_n_rt_rp_eq c d) (l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)) n (λt:l_e_st_eq_landau_n_rt_rp_mored c d.l_e_st_eq_landau_n_rt_rp_3d191_t2 a b c d m n e t) (λt:l_e_st_eq_landau_n_rt_rp_eq c d.l_e_st_eq_landau_n_rt_rp_3d191_t1 a b c d m n e t) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3558 *)
-definition l_e_st_eq_landau_n_rt_rp_3d191_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.λo:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_moreqi1 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_satzd190b a b c d o n) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3559 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd191 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.(l_orapp (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)) m (λt:l_e_st_eq_landau_n_rt_rp_mored a b.l_e_st_eq_landau_n_rt_rp_3d191_t4 a b c d m n t) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_3d191_t3 a b c d m n t) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3560 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd191a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq c d.(l_e_st_eq_landau_n_rt_rp_satzd168a (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd191 b a d c (l_e_st_eq_landau_n_rt_rp_satzd168b a b l) (l_e_st_eq_landau_n_rt_rp_satzd168b c d k)) : l_e_st_eq_landau_n_rt_rp_lesseq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
-
-(* notion 3561 *)
-definition l_e_st_eq_landau_n_rt_rp_td ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3562 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t1 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1 r (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts a1 r)).
-
-(* notion 3563 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t2 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ists2 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1 r (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts r a1)).
-
-(* notion 3564 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t3 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 r (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts a2 r)).
-
-(* notion 3565 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t4 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ists2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 r (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts r a2)).
-
-(* notion 3566 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t5 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts a1 r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) s) (l_e_st_eq_landau_n_rt_rp_ts a2 s) (l_e_st_eq_landau_n_rt_rp_iv4d_t1 a1 a2 r) (l_e_st_eq_landau_n_rt_rp_iv4d_t3 a1 a2 s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 r) (l_e_st_eq_landau_n_rt_rp_ts a2 s))).
-
-(* notion 3567 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t6 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts r a1) (l_e_st_eq_landau_n_rt_rp_ts s (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts s a2) (l_e_st_eq_landau_n_rt_rp_iv4d_t2 a1 a2 r) (l_e_st_eq_landau_n_rt_rp_iv4d_t4 a1 a2 s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts s (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r a1) (l_e_st_eq_landau_n_rt_rp_ts s a2))).
-
-(* notion 3568 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t7 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts a2 r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) s) (l_e_st_eq_landau_n_rt_rp_ts a1 s) (l_e_st_eq_landau_n_rt_rp_iv4d_t3 a1 a2 r) (l_e_st_eq_landau_n_rt_rp_iv4d_t1 a1 a2 s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a2 r) (l_e_st_eq_landau_n_rt_rp_ts a1 s))).
-
-(* notion 3569 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t8 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts r a2) (l_e_st_eq_landau_n_rt_rp_ts s (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts s a1) (l_e_st_eq_landau_n_rt_rp_iv4d_t4 a1 a2 r) (l_e_st_eq_landau_n_rt_rp_iv4d_t2 a1 a2 s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts s (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r a2) (l_e_st_eq_landau_n_rt_rp_ts s a1))).
-
-(* notion 3570 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t9 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_iv4d_t5 a1 a2 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_iv4d_t6 b1 b2 a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2))).
-
-(* notion 3571 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t10 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts a2 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1)) (l_e_st_eq_landau_n_rt_rp_iv4d_t5 a1 a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_iv4d_t8 b1 b2 a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1))).
-
-(* notion 3572 *)
-definition l_e_st_eq_landau_n_rt_rp_td12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1)) (l_e_st_eq_landau_n_rt_rp_iv4d_t9 a1 a2 b1 b2) (l_e_st_eq_landau_n_rt_rp_iv4d_t10 a1 a2 b1 b2) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1)))).
-
-(* notion 3573 *)
-definition l_e_st_eq_landau_n_rt_rp_td1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1)) (l_e_st_eq_landau_n_rt_rp_iv4d_t6 r1 r2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_iv4d_t8 r1 r2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1)))).
-
-(* notion 3574 *)
-definition l_e_st_eq_landau_n_rt_rp_td2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_iv4d_t5 r1 r2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_iv4d_t5 r1 r2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a))))).
-
-(* notion 3575 *)
-definition l_e_st_eq_landau_n_rt_rp_tdeq12a ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1))) (l_e_st_eq_landau_n_rt_rp_td12 a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1)))).
-
-(* notion 3576 *)
-definition l_e_st_eq_landau_n_rt_rp_tdeq12b ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1))) (l_e_st_eq_landau_n_rt_rp_td12 a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1))) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2))).
-
-(* notion 3577 *)
-definition l_e_st_eq_landau_n_rt_rp_tdeq1a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1))) (l_e_st_eq_landau_n_rt_rp_td1 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1)))).
-
-(* notion 3578 *)
-definition l_e_st_eq_landau_n_rt_rp_tdeq1b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1))) (l_e_st_eq_landau_n_rt_rp_td1 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1))) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_df r1 r2))).
-
-(* notion 3579 *)
-definition l_e_st_eq_landau_n_rt_rp_tdeq2a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a)))) (l_e_st_eq_landau_n_rt_rp_td2 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a))))).
-
-(* notion 3580 *)
-definition l_e_st_eq_landau_n_rt_rp_tdeq2b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a)))) (l_e_st_eq_landau_n_rt_rp_td2 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a)))) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df r1 r2) a)).
-
-(* notion 3581 *)
-definition l_e_st_eq_landau_n_rt_rp_4d194_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3582 *)
-definition l_e_st_eq_landau_n_rt_rp_4d194_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)))).
-
-(* notion 3583 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd194 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_4d194_t1 a b) (l_e_st_eq_landau_n_rt_rp_4d194_t2 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td b a)).
-
-(* notion 3584 *)
-definition l_e_st_eq_landau_n_rt_rp_comtd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd194 a b : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td b a)).
-
-(* notion 3585 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t11 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) r)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r)) (l_e_st_eq_landau_n_rt_rp_distpt1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) r) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) r e) (l_e_st_eq_landau_n_rt_rp_disttp1 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a) r) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) r)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r))).
-
-(* notion 3586 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_iv4d_t11 a b c e (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_iv4d_t11 b a c (l_e_st_eq_landau_n_rt_rp_symeq a b e) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c))))).
-
-(* notion 3587 *)
-definition l_e_st_eq_landau_n_rt_rp_eqtd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_iv4d_t12 a b c e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
-
-(* notion 3588 *)
-definition l_e_st_eq_landau_n_rt_rp_eqtd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_comtd c a) (l_e_st_eq_landau_n_rt_rp_eqtd1 a b c e) (l_e_st_eq_landau_n_rt_rp_comtd b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
-
-(* notion 3589 *)
-definition l_e_st_eq_landau_n_rt_rp_eqtd12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td b d) (l_e_st_eq_landau_n_rt_rp_eqtd1 a b c e) (l_e_st_eq_landau_n_rt_rp_eqtd2 c d b f) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b d)).
-
-(* notion 3590 *)
-definition l_e_st_eq_landau_n_rt_rp_4d192_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) z) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) z))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))).
-
-(* notion 3591 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd192a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_zeroi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_4d192_t1 a b z) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).
-
-(* notion 3592 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd192b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_comtd b a) (l_e_st_eq_landau_n_rt_rp_satzd192a b a z) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).
-
-(* notion 3593 *)
-definition l_e_st_eq_landau_n_rt_rp_td01 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_satzd192a a b z : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).
-
-(* notion 3594 *)
-definition l_e_st_eq_landau_n_rt_rp_td02 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_satzd192b a b z : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).
-
-(* notion 3595 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd197a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)))) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_tdeq2a b (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))) (l_e_st_eq_landau_n_rt_rp_m0deqb (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3596 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd197b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d b) a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_comtd a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd197a b a) (l_e_st_eq_landau_n_rt_rp_eqm0d (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_comtd b a)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3597 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd197c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_satzd197a a b) (l_e_st_eq_landau_n_rt_rp_satzd197b a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b))).
-
-(* notion 3598 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd197d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd197c a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b)).
-
-(* notion 3599 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd197e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_satzd197a a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b)).
-
-(* notion 3600 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd197f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_satzd197b a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b))).
-
-(* notion 3601 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd198 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b))) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_satzd197c a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_eqtd2 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b a (l_e_st_eq_landau_n_rt_rp_satzd177 b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td a b)).
-
-(* notion 3602 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd198a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_satzd198 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b))).
-
-(* notion 3603 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t13 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_distpt2 r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ists2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_1b a b) r (l_e_st_eq_landau_n_rt_rp_satz140e (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b))).
-
-(* notion 3604 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t14 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b)) s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b))) s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) s) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b)) s) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) s (l_e_st_eq_landau_n_rt_rp_iv4d_t13 a b p q r)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b)) s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) s)).
-
-(* notion 3605 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t15 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b)) s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) s) (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_iv4d_t14 a b p q r s) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b)) s)) (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)))).
-
-(* notion 3606 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t16 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_satz135h (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_satz145a (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q) p) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))))).
-
-(* notion 3607 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t17 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_iv4d_t14 a b p q (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_iv4d_t15 a b p q (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_iv4d_t16 a b p q) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))).
-
-(* notion 3608 *)
-definition l_e_st_eq_landau_n_rt_rp_ptdpp ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_iv4d_t17 a b p q) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a b)).
-
-(* notion 3609 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t18 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_satzd197b a b) (l_e_st_eq_landau_n_rt_rp_ptdpp a (l_e_st_eq_landau_n_rt_rp_m0d b) p (l_e_st_eq_landau_n_rt_rp_satzd176c b n)) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3610 *)
-definition l_e_st_eq_landau_n_rt_rp_ntdpn ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_satzd176f (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_iv4d_t18 a b p n) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a b)).
-
-(* notion 3611 *)
-definition l_e_st_eq_landau_n_rt_rp_ntdnp ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_comtd b a) (l_e_st_eq_landau_n_rt_rp_ntdpn b a p n) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a b)).
-
-(* notion 3612 *)
-definition l_e_st_eq_landau_n_rt_rp_ptdnn ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_satzd198 a b) (l_e_st_eq_landau_n_rt_rp_ptdpp (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_satzd176c a n) (l_e_st_eq_landau_n_rt_rp_satzd176c b o)) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a b)).
-
-(* notion 3613 *)
-definition l_e_st_eq_landau_n_rt_rp_4d192_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_pnot0d (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ptdpp a b p q) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3614 *)
-definition l_e_st_eq_landau_n_rt_rp_4d192_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λm:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_nnot0d (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ntdpn a b p m) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3615 *)
-definition l_e_st_eq_landau_n_rt_rp_4d192_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_rappd b (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_4d192_t2 a b n o p t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) o) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_4d192_t3 a b n o p t) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3616 *)
-definition l_e_st_eq_landau_n_rt_rp_4d192_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λm:l_e_st_eq_landau_n_rt_rp_negd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_nnot0d (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ntdnp a b m p) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3617 *)
-definition l_e_st_eq_landau_n_rt_rp_4d192_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λm:l_e_st_eq_landau_n_rt_rp_negd a.λl:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_pnot0d (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ptdnn a b m l) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3618 *)
-definition l_e_st_eq_landau_n_rt_rp_4d192_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_rappd b (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_4d192_t5 a b n o m t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) o) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_4d192_t6 a b n o m t) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3619 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd192d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_e_st_eq_landau_n_rt_rp_rappd a (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_4d192_t4 a b n o t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) n) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_4d192_t7 a b n o t) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3620 *)
-definition l_e_st_eq_landau_n_rt_rp_4d192_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b).λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_et (l_e_st_eq_landau_n_rt_rp_zero b) (l_imp_th3 (l_not (l_e_st_eq_landau_n_rt_rp_zero b)) (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) (l_weli (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)) z) (λt:l_not (l_e_st_eq_landau_n_rt_rp_zero b).l_e_st_eq_landau_n_rt_rp_satzd192d a b n t)) : l_e_st_eq_landau_n_rt_rp_zero b).
-
-(* notion 3621 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd192c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b).(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero a).l_e_st_eq_landau_n_rt_rp_4d192_t8 a b z t : l_or (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_zero b)).
-
-(* notion 3622 *)
-definition l_e_st_eq_landau_n_rt_rp_4d193_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ptdpp a b p q))) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absd b) b (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p)) (l_e_st_eq_landau_n_rt_rp_absnnd b (l_e_st_eq_landau_n_rt_rp_pnotnd b q))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3623 *)
-definition l_e_st_eq_landau_n_rt_rp_4d193_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_absnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ntdpn a b p n)) (l_e_st_eq_landau_n_rt_rp_satzd197f a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b))).
-
-(* notion 3624 *)
-definition l_e_st_eq_landau_n_rt_rp_4d193_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_4d193_t2 a b p n) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p)) (l_e_st_eq_landau_n_rt_rp_absnd b n)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3625 *)
-definition l_e_st_eq_landau_n_rt_rp_4d193_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_satzd166f (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td01 a b z)) (l_e_st_eq_landau_n_rt_rp_td01 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166f a z)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3626 *)
-definition l_e_st_eq_landau_n_rt_rp_4d193_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_satzd166f (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td02 a b z)) (l_e_st_eq_landau_n_rt_rp_td02 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166f b z)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3627 *)
-definition l_e_st_eq_landau_n_rt_rp_4d193_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_eqabsd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_comtd a b)) (l_e_st_eq_landau_n_rt_rp_4d193_t3 b a p n) (l_e_st_eq_landau_n_rt_rp_comtd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absd a)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3628 *)
-definition l_e_st_eq_landau_n_rt_rp_4d193_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_absnd a n) (l_e_st_eq_landau_n_rt_rp_absnd b o)) (l_e_st_eq_landau_n_rt_rp_satzd198 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a b)).
-
-(* notion 3629 *)
-definition l_e_st_eq_landau_n_rt_rp_4d193_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ptdnn a b n o))) (l_e_st_eq_landau_n_rt_rp_4d193_t7 a b n o) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3630 *)
-definition l_e_st_eq_landau_n_rt_rp_4d193_t9 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_rappd b (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_4d193_t1 a b p t) (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_4d193_t5 a b t) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_4d193_t3 a b p t) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3631 *)
-definition l_e_st_eq_landau_n_rt_rp_4d193_t10 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_rappd b (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_4d193_t6 a b n t) (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_4d193_t5 a b t) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_4d193_t8 a b n t) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3632 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd193 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_rappd a (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_4d193_t9 a b t) (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_4d193_t4 a b t) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_4d193_t10 a b t) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3633 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd103a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_satzd193 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3634 *)
-definition l_e_st_eq_landau_n_rt_rp_1df ≝ (l_e_st_eq_landau_n_rt_rp_pdofrp l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3635 *)
-definition l_e_st_eq_landau_n_rt_rp_4d195_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_a2isapa (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_satz151 (l_e_st_eq_landau_n_rt_rp_2a a)))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3636 *)
-definition l_e_st_eq_landau_n_rt_rp_4d195_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz151 (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_a2isapa (l_e_st_eq_landau_n_rt_rp_2a a))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a)))).
-
-(* notion 3637 *)
-definition l_e_st_eq_landau_n_rt_rp_4d195_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_4d195_t1 a) (l_e_st_eq_landau_n_rt_rp_4d195_t2 a) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp))))).
-
-(* notion 3638 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd195 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td a l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)))) a (l_e_st_eq_landau_n_rt_rp_tdeq1a a (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_eqi2 a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_4d195_t3 a)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a l_e_st_eq_landau_n_rt_rp_1df) a).
-
-(* notion 3639 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd195a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a l_e_st_eq_landau_n_rt_rp_1df) a (l_e_st_eq_landau_n_rt_rp_satzd195 a) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_td a l_e_st_eq_landau_n_rt_rp_1df)).
-
-(* notion 3640 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd195b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td l_e_st_eq_landau_n_rt_rp_1df a) (l_e_st_eq_landau_n_rt_rp_td a l_e_st_eq_landau_n_rt_rp_1df) a (l_e_st_eq_landau_n_rt_rp_comtd l_e_st_eq_landau_n_rt_rp_1df a) (l_e_st_eq_landau_n_rt_rp_satzd195 a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td l_e_st_eq_landau_n_rt_rp_1df a) a).
-
-(* notion 3641 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd195c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td l_e_st_eq_landau_n_rt_rp_1df a) a (l_e_st_eq_landau_n_rt_rp_satzd195b a) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_td l_e_st_eq_landau_n_rt_rp_1df a)).
-
-(* notion 3642 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd196a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absd b) b (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p)) (l_e_st_eq_landau_n_rt_rp_absnnd b (l_e_st_eq_landau_n_rt_rp_pnotnd b q))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3643 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd196b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd198a a b) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_absnd a n) (l_e_st_eq_landau_n_rt_rp_absnd b o)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3644 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd196c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq1 (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_absd b))) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_absd b)) b (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p)) (l_e_st_eq_landau_n_rt_rp_satzd177b (l_e_st_eq_landau_n_rt_rp_absd b) b (l_e_st_eq_landau_n_rt_rp_absnd b n))) (l_e_st_eq_landau_n_rt_rp_satzd197b (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)))).
-
-(* notion 3645 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd196d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absd a))) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (l_e_st_eq_landau_n_rt_rp_comtd a b) (l_e_st_eq_landau_n_rt_rp_satzd196c b a p n) (l_e_st_eq_landau_n_rt_rp_eqm0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_comtd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absd a))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)))).
-
-(* notion 3646 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_p1p2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) : Prop).
-
-(* notion 3647 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_p1n2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd b) : Prop).
-
-(* notion 3648 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_n1p2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_posd b) : Prop).
-
-(* notion 3649 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_n1n2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_negd b) : Prop).
-
-(* notion 3650 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_e_st_eq_landau_n_rt_rp_ptdpp (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166e a n) (l_e_st_eq_landau_n_rt_rp_satzd166e b o) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
-
-(* notion 3651 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).(l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) e) (l_e_st_eq_landau_n_rt_rp_4d196_t1 a b n o)) : l_not (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3652 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_4d196_t2 a b n o e) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_ntdpn a b p t) : l_not (l_e_st_eq_landau_n_rt_rp_negd b)).
-
-(* notion 3653 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_or3e2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_axrdo b) (l_e_st_eq_landau_n_rt_rp_4d196_t3 a b n o e p) o : l_e_st_eq_landau_n_rt_rp_posd b).
-
-(* notion 3654 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_andi (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) p (l_e_st_eq_landau_n_rt_rp_4d196_t4 a b n o e p) : l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b).
-
-(* notion 3655 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_ori1 (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_t5 a b n o e p) : l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b)).
-
-(* notion 3656 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_4d196_t2 a b n o e) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_ntdnp a b m t) : l_not (l_e_st_eq_landau_n_rt_rp_posd b)).
-
-(* notion 3657 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_or3e3 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_axrdo b) o (l_e_st_eq_landau_n_rt_rp_4d196_t7 a b n o e m) : l_e_st_eq_landau_n_rt_rp_negd b).
-
-(* notion 3658 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t9 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_andi (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_negd b) m (l_e_st_eq_landau_n_rt_rp_4d196_t8 a b n o e m) : l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b).
-
-(* notion 3659 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t10 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_ori2 (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_t9 a b n o e m) : l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b)).
-
-(* notion 3660 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd196e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).(l_e_st_eq_landau_n_rt_rp_rappd a (l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_4d196_t6 a b n o e t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b)) n) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_4d196_t10 a b n o e t) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_negd b))).
-
-(* notion 3661 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t11 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_e_st_eq_landau_n_rt_rp_satzd176a (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_4d196_t1 a b n o) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)))).
-
-(* notion 3662 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).(l_e_st_eq_landau_n_rt_rp_nnotpd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) e) (l_e_st_eq_landau_n_rt_rp_4d196_t11 a b n o)) : l_not (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3663 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t13 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_4d196_t12 a b n o e) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_ptdpp a b p t) : l_not (l_e_st_eq_landau_n_rt_rp_posd b)).
-
-(* notion 3664 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t14 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_or3e3 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_axrdo b) o (l_e_st_eq_landau_n_rt_rp_4d196_t13 a b n o e p) : l_e_st_eq_landau_n_rt_rp_negd b).
-
-(* notion 3665 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t15 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_andi (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd b) p (l_e_st_eq_landau_n_rt_rp_4d196_t14 a b n o e p) : l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b).
-
-(* notion 3666 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t16 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_ori1 (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_t15 a b n o e p) : l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b)).
-
-(* notion 3667 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t17 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_4d196_t12 a b n o e) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_ptdnn a b m t) : l_not (l_e_st_eq_landau_n_rt_rp_negd b)).
-
-(* notion 3668 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t18 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_or3e2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_axrdo b) (l_e_st_eq_landau_n_rt_rp_4d196_t17 a b n o e m) o : l_e_st_eq_landau_n_rt_rp_posd b).
-
-(* notion 3669 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t19 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_andi (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_posd b) m (l_e_st_eq_landau_n_rt_rp_4d196_t18 a b n o e m) : l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b).
-
-(* notion 3670 *)
-definition l_e_st_eq_landau_n_rt_rp_4d196_t20 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_ori2 (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_t19 a b n o e m) : l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b)).
-
-(* notion 3671 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd196f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).(l_e_st_eq_landau_n_rt_rp_rappd a (l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_4d196_t16 a b n o e t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b)) n) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_4d196_t20 a b n o e t) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd b)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_posd b))).
-
-(* notion 3672 *)
-definition l_e_st_eq_landau_n_rt_rp_4d199_t1 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) t) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts p r) t) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts q s) t)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_disttp1 (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s) t) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts p r) t) (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts q s) t) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_assts1 p r t) (l_e_st_eq_landau_n_rt_rp_assts1 q s t)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) t) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)))).
-
-(* notion 3673 *)
-definition l_e_st_eq_landau_n_rt_rp_4d199_t2 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_distpt2 q (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t)))).
-
-(* notion 3674 *)
-definition l_e_st_eq_landau_n_rt_rp_4d199_t3 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) t) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p s) (l_e_st_eq_landau_n_rt_rp_ts q r)) u)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts s u)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts s u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r t) (l_e_st_eq_landau_n_rt_rp_ts s u))) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t)))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) t) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p s) (l_e_st_eq_landau_n_rt_rp_ts q r)) u) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts s u)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_4d199_t1 p q r s t u) (l_e_st_eq_landau_n_rt_rp_4d199_t1 p q s r u t)) (l_e_st_eq_landau_n_rt_rp_4pl23 (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts s u)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts s u))) (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r t) (l_e_st_eq_landau_n_rt_rp_ts s u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_distpt2 p (l_e_st_eq_landau_n_rt_rp_ts r t) (l_e_st_eq_landau_n_rt_rp_ts s u)) (l_e_st_eq_landau_n_rt_rp_4d199_t2 p q r s t u)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) t) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p s) (l_e_st_eq_landau_n_rt_rp_ts q r)) u)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r t) (l_e_st_eq_landau_n_rt_rp_ts s u))) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t))))).
-
-(* notion 3675 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd199 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a b) c) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))))) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_tdeq2a c (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))))) (l_e_st_eq_landau_n_rt_rp_4d199_t3 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_4d199_t3 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_tdeq1b a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a b) c) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_td b c))).
-
-(* notion 3676 *)
-definition l_e_st_eq_landau_n_rt_rp_asstd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd199 a b c : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a b) c) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_td b c))).
-
-(* notion 3677 *)
-definition l_e_st_eq_landau_n_rt_rp_asstd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a b) c) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_satzd199 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a b) c)).
-
-(* notion 3678 *)
-definition l_e_st_eq_landau_n_rt_rp_4d201_t1 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl s u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts p t)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q s) (l_e_st_eq_landau_n_rt_rp_ts q u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p t) (l_e_st_eq_landau_n_rt_rp_ts q u))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl r t)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts p t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl s u)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q s) (l_e_st_eq_landau_n_rt_rp_ts q u)) (l_e_st_eq_landau_n_rt_rp_disttp2 p r t) (l_e_st_eq_landau_n_rt_rp_disttp2 q s u)) (l_e_st_eq_landau_n_rt_rp_4pl23 (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts p t) (l_e_st_eq_landau_n_rt_rp_ts q s) (l_e_st_eq_landau_n_rt_rp_ts q u)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl s u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p t) (l_e_st_eq_landau_n_rt_rp_ts q u)))).
-
-(* notion 3679 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd201 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c))))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_tdeq1a a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_4d201_t1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_4d201_t1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pdeq12b (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c))).
-
-(* notion 3680 *)
-definition l_e_st_eq_landau_n_rt_rp_disttpd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_td c (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_comtd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_satzd201 c a b) (l_e_st_eq_landau_n_rt_rp_eqpd12 (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_comtd c a) (l_e_st_eq_landau_n_rt_rp_comtd c b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c))).
-
-(* notion 3681 *)
-definition l_e_st_eq_landau_n_rt_rp_disttpd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd201 a b c : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c))).
-
-(* notion 3682 *)
-definition l_e_st_eq_landau_n_rt_rp_distptd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_disttpd1 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) c)).
-
-(* notion 3683 *)
-definition l_e_st_eq_landau_n_rt_rp_distptd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_disttpd2 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_pd b c))).
-
-(* notion 3684 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd202 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d c))) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_disttpd2 a b (l_e_st_eq_landau_n_rt_rp_m0d c)) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d c)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_satzd197b a c)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c))).
-
-(* notion 3685 *)
-definition l_e_st_eq_landau_n_rt_rp_disttmd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d b) c)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_disttpd1 a (l_e_st_eq_landau_n_rt_rp_m0d b) c) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d b) c) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_satzd197a b c)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c))).
-
-(* notion 3686 *)
-definition l_e_st_eq_landau_n_rt_rp_disttmd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd202 a b c : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c))).
-
-(* notion 3687 *)
-definition l_e_st_eq_landau_n_rt_rp_distmtd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_disttmd1 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c)).
-
-(* notion 3688 *)
-definition l_e_st_eq_landau_n_rt_rp_distmtd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_disttmd2 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c))).
-
-(* notion 3689 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd200 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd202 a b c : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c))).
-
-(* notion 3690 *)
-definition l_e_st_eq_landau_n_rt_rp_4d203_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_satzd182d a b m : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3691 *)
-definition l_e_st_eq_landau_n_rt_rp_4d203_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λp:l_e_st_eq_landau_n_rt_rp_posd c.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_disttmd1 a b c) (l_e_st_eq_landau_n_rt_rp_ptdpp (l_e_st_eq_landau_n_rt_rp_md a b) c (l_e_st_eq_landau_n_rt_rp_4d203_t1 a b c m) p) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c))).
-
-(* notion 3692 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λp:l_e_st_eq_landau_n_rt_rp_posd c.(l_e_st_eq_landau_n_rt_rp_satzd182a (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_4d203_t2 a b c m p) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
-
-(* notion 3693 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td02 a c z) (l_e_st_eq_landau_n_rt_rp_td02 b c z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
-
-(* notion 3694 *)
-definition l_e_st_eq_landau_n_rt_rp_4d203_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_negd c.(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_disttmd1 a b c) (l_e_st_eq_landau_n_rt_rp_ntdpn (l_e_st_eq_landau_n_rt_rp_md a b) c (l_e_st_eq_landau_n_rt_rp_4d203_t1 a b c m) n) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c))).
-
-(* notion 3695 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_negd c.(l_e_st_eq_landau_n_rt_rp_satzd182c (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_4d203_t3 a b c m n) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
-
-(* notion 3696 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λp:l_e_st_eq_landau_n_rt_rp_posd c.(l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_comtd a c) (l_e_st_eq_landau_n_rt_rp_comtd b c) (l_e_st_eq_landau_n_rt_rp_satzd203a a b c m p) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
-
-(* notion 3697 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_td01 c a z) (l_e_st_eq_landau_n_rt_rp_td01 c b z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
-
-(* notion 3698 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_negd c.(l_e_st_eq_landau_n_rt_rp_eqlessd12 (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_comtd a c) (l_e_st_eq_landau_n_rt_rp_comtd b c) (l_e_st_eq_landau_n_rt_rp_satzd203c a b c m n) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
-
-(* notion 3699 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203g ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λp:l_e_st_eq_landau_n_rt_rp_posd c.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_satzd203a b a c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) p) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
-
-(* notion 3700 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203h ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td02 a c z) (l_e_st_eq_landau_n_rt_rp_td02 b c z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
-
-(* notion 3701 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203j ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λn:l_e_st_eq_landau_n_rt_rp_negd c.(l_e_st_eq_landau_n_rt_rp_lemmad6 (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_satzd203c b a c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) n) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
-
-(* notion 3702 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203k ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λp:l_e_st_eq_landau_n_rt_rp_posd c.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_satzd203d b a c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) p) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
-
-(* notion 3703 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203l ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_td01 c a z) (l_e_st_eq_landau_n_rt_rp_td01 c b z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
-
-(* notion 3704 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd203m ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λn:l_e_st_eq_landau_n_rt_rp_negd c.(l_e_st_eq_landau_n_rt_rp_lemmad6 (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_satzd203f b a c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) n) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
-
-(* notion 3705 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t19 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_ts q l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) q) (l_e_st_eq_landau_n_rt_rp_disttp2 q p l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts q l_e_st_eq_landau_n_rt_rp_1rp) q (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_satz151 q)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) q)).
-
-(* notion 3706 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t20 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) q) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) q) (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp) r (l_e_st_eq_landau_n_rt_rp_iv4d_t19 p q) (l_e_st_eq_landau_n_rt_rp_satz151 r)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ts q p) q r) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_pl q r))).
-
-(* notion 3707 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t21 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_pl r q)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_iv4d_t20 p q r) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl q r) (l_e_st_eq_landau_n_rt_rp_pl r q) (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_compl q r)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_pl r q))).
-
-(* notion 3708 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_arp ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_rpofpd a p : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3709 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_arpi ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_ov l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3710 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_ai ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3711 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t22 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_iv4d_ai a p)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) l_e_st_eq_landau_n_rt_rp_1rp)))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p))) (l_e_st_eq_landau_n_rt_rp_tdeq1a a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_iv4d_t20 (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_iv4d_t21 (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_lemmad2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_iv4d_ai a p)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)))).
-
-(* notion 3712 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t23 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p)) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p)) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) (l_e_st_eq_landau_n_rt_rp_satz140d (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) p)) (l_e_st_eq_landau_n_rt_rp_disttp1 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_satz153c l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp)).
-
-(* notion 3713 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t24 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p))) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv4d_t23 a p)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)))).
-
-(* notion 3714 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t25 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv4d_t24 a p) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p))) l_e_st_eq_landau_n_rt_rp_1df).
-
-(* notion 3715 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t26 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_iv4d_ai a p)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p))) l_e_st_eq_landau_n_rt_rp_1df (l_e_st_eq_landau_n_rt_rp_iv4d_t22 a p) (l_e_st_eq_landau_n_rt_rp_iv4d_t25 a p) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_iv4d_ai a p)) l_e_st_eq_landau_n_rt_rp_1df).
-
-(* notion 3716 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t27 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_iv4d_ai a p) (l_e_st_eq_landau_n_rt_rp_iv4d_t26 a p) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)).
-
-(* notion 3717 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t28 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_satzd176c a n : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d a)).
-
-(* notion 3718 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t29 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λh:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) h) l_e_st_eq_landau_n_rt_rp_1df.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d h)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) h) l_e_st_eq_landau_n_rt_rp_1df (l_e_st_eq_landau_n_rt_rp_satzd197d a h) e : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d h)) l_e_st_eq_landau_n_rt_rp_1df).
-
-(* notion 3719 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t30 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λh:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) h) l_e_st_eq_landau_n_rt_rp_1df.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_m0d h) (l_e_st_eq_landau_n_rt_rp_iv4d_t29 a n h e) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)).
-
-(* notion 3720 *)
-definition l_e_st_eq_landau_n_rt_rp_iv4d_t31 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) x) l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_iv4d_t27 (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_iv4d_t28 a n)) (l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) x) l_e_st_eq_landau_n_rt_rp_1df.l_e_st_eq_landau_n_rt_rp_iv4d_t30 a n x t) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)).
-
-(* notion 3721 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmad7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_rappd a (l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_iv4d_t27 a t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)) n) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_iv4d_t31 a t) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)).
-
-(* notion 3722 *)
-definition l_e_st_eq_landau_n_rt_rp_4d204_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λk:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) a.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b k) a.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_td b h) (l_e_st_eq_landau_n_rt_rp_td b k) a e f : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) (l_e_st_eq_landau_n_rt_rp_td b k)).
-
-(* notion 3723 *)
-definition l_e_st_eq_landau_n_rt_rp_4d204_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λk:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) a.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b k) a.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td b h) (l_e_st_eq_landau_n_rt_rp_td b k)) (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_md h k)) (l_e_st_eq_landau_n_rt_rp_distmtd2 b h k) (l_e_st_eq_landau_n_rt_rp_satzd182e (l_e_st_eq_landau_n_rt_rp_td b h) (l_e_st_eq_landau_n_rt_rp_td b k) (l_e_st_eq_landau_n_rt_rp_4d204_t1 a b n h k e f)) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_md h k))).
-
-(* notion 3724 *)
-definition l_e_st_eq_landau_n_rt_rp_4d204_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λk:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) a.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b k) a.(l_ore2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md h k)) (l_e_st_eq_landau_n_rt_rp_satzd192c b (l_e_st_eq_landau_n_rt_rp_md h k) (l_e_st_eq_landau_n_rt_rp_4d204_t2 a b n h k e f)) n : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md h k)).
-
-(* notion 3725 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd204b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λk:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) a.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b k) a.(l_e_st_eq_landau_n_rt_rp_satzd182b h k (l_e_st_eq_landau_n_rt_rp_4d204_t3 a b n h k e f) : l_e_st_eq_landau_n_rt_rp_eq h k).
-
-(* notion 3726 *)
-definition l_e_st_eq_landau_n_rt_rp_4d204_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) l_e_st_eq_landau_n_rt_rp_1df.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_td h a)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td b h) a) (l_e_st_eq_landau_n_rt_rp_td l_e_st_eq_landau_n_rt_rp_1df a) a (l_e_st_eq_landau_n_rt_rp_asstd2 b h a) (l_e_st_eq_landau_n_rt_rp_eqtd1 (l_e_st_eq_landau_n_rt_rp_td b h) l_e_st_eq_landau_n_rt_rp_1df a e) (l_e_st_eq_landau_n_rt_rp_satzd195b a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_td h a)) a).
-
-(* notion 3727 *)
-definition l_e_st_eq_landau_n_rt_rp_4d204_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) l_e_st_eq_landau_n_rt_rp_1df.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) a) (l_e_st_eq_landau_n_rt_rp_td h a) (l_e_st_eq_landau_n_rt_rp_4d204_t4 a b n h e) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) a)).
-
-(* notion 3728 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd204a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_lemmad7 b n) (l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) a)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) l_e_st_eq_landau_n_rt_rp_1df.l_e_st_eq_landau_n_rt_rp_4d204_t5 a b n x t) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) a)).
-
-(* notion 3729 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_t1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r s.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_asspl2 r l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_asspl2 s l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_satz134 r s (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp)).
-
-(* notion 3730 *)
-definition l_e_st_eq_landau_n_rt_rp_morerpepd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r s.(l_e_st_eq_landau_n_rt_rp_moredi12 (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv5d_t1 r s m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)).
-
-(* notion 3731 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_t2 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_morede12 (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp)).
-
-(* notion 3732 *)
-definition l_e_st_eq_landau_n_rt_rp_morerpipd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz136a r s (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_asspl1 r l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_asspl1 s l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_iv5d_t2 r s m)) : l_e_st_eq_landau_n_rt_rp_more r s).
-
-(* notion 3733 *)
-definition l_e_st_eq_landau_n_rt_rp_lessrpepd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r s.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_pdofrp s) (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_morerpepd s r (l_e_st_eq_landau_n_rt_rp_satz122 r s l)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)).
-
-(* notion 3734 *)
-definition l_e_st_eq_landau_n_rt_rp_lessrpipd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz121 s r (l_e_st_eq_landau_n_rt_rp_morerpipd s r (l_e_st_eq_landau_n_rt_rp_lemmad6 (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s) l)) : l_e_st_eq_landau_n_rt_rp_less r s).
-
-(* notion 3735 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_i ≝ (l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3736 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_2 ≝ (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3737 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_rp1 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_iv5d_i : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3738 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_sp1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_iv5d_i : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3739 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_rps ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl r s : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3740 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_rs ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ts r s : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3741 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_t3 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_2) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_4pl23 r l_e_st_eq_landau_n_rt_rp_iv5d_i s l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_3pl23 (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2 l_e_st_eq_landau_n_rt_rp_iv5d_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_2)).
-
-(* notion 3742 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_t4 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) l_e_st_eq_landau_n_rt_rp_iv5d_2) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) (l_e_st_eq_landau_n_rt_rp_pdeq12a (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) l_e_st_eq_landau_n_rt_rp_iv5d_2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_t3 r s)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s))).
-
-(* notion 3743 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmad8 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_iv5d_t4 r s : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r s))).
-
-(* notion 3744 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_t5 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) (l_e_st_eq_landau_n_rt_rp_disttp2 r s l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_iv5d_i) r (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_satz151 r)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r)).
-
-(* notion 3745 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_t6 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr4is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_disttp1 r l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s) (l_e_st_eq_landau_n_rt_rp_iv5d_t5 r s) (l_e_st_eq_landau_n_rt_rp_satz151b (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) s l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r s)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i)).
-
-(* notion 3746 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_t7 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_t6 r s) (l_e_st_eq_landau_n_rt_rp_satz151 l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2))).
-
-(* notion 3747 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_t8 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s) (l_e_st_eq_landau_n_rt_rp_satz151 (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r)) (l_e_st_eq_landau_n_rt_rp_satz151b (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_4pl23 r l_e_st_eq_landau_n_rt_rp_iv5d_i s l_e_st_eq_landau_n_rt_rp_iv5d_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)).
-
-(* notion 3748 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_t9 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_iv5d_t8 r s)) (l_e_st_eq_landau_n_rt_rp_3pl23 (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) l_e_st_eq_landau_n_rt_rp_iv5d_i)).
-
-(* notion 3749 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_t10 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_t7 r s)) (l_e_st_eq_landau_n_rt_rp_iv5d_t9 r s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))))).
-
-(* notion 3750 *)
-definition l_e_st_eq_landau_n_rt_rp_iv5d_t11 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s)) (l_e_st_eq_landau_n_rt_rp_tdeq12a (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_t10 r s)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s))).
-
-(* notion 3751 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmad9 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_iv5d_t11 r s : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r s))).
-
-(* notion 3752 *)
-definition l_e_st_eq_landau_n_rt_rp_in ≝ λr:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.(l_e_st_esti l_e_st_eq_landau_n_rt_cut r s0 : Prop).
-
-(* notion 3753 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_prop1 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_less x r.l_e_st_eq_landau_n_rt_rp_in x s0) : Prop).
-
-(* notion 3754 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_prop2 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_more x r.l_e_st_eq_landau_n_rt_rp_in x t0) : Prop).
-
-(* notion 3755 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_prop3 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_and (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 r) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 r) : Prop).
-
-(* notion 3756 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t1 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.(l_ande2 (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 r1) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 r1) pr1 : l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 r1).
-
-(* notion 3757 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t2 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.(l_ande1 (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 r2) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 r2) pr2 : l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 r2).
-
-(* notion 3758 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_rx ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.λl:l_e_st_eq_landau_n_rt_rp_less r1 r2.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x0 : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3759 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t3 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.λl:l_e_st_eq_landau_n_rt_rp_less r1 r2.λx0:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less r1 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) r2.(l_e_st_eq_landau_n_rt_rp_5p205_t2 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) l2 : l_e_st_eq_landau_n_rt_rp_in (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) s0).
-
-(* notion 3760 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t4 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.λl:l_e_st_eq_landau_n_rt_rp_less r1 r2.λx0:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less r1 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) r2.(l_e_st_eq_landau_n_rt_rp_5p205_t1 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_satz122 r1 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) l1) : l_e_st_eq_landau_n_rt_rp_in (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) t0).
-
-(* notion 3761 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t5 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.λl:l_e_st_eq_landau_n_rt_rp_less r1 r2.λx0:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less r1 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) r2.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0)) (p2 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_t3 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0 l1 l2) (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_t4 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0 l1 l2)) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0)) : l_con).
-
-(* notion 3762 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t6 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.λl:l_e_st_eq_landau_n_rt_rp_less r1 r2.(l_e_st_eq_landau_n_rt_rp_satz159app r1 r2 l l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_less r1 (l_e_st_eq_landau_n_rt_rp_rpofrt x).λu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) r2.l_e_st_eq_landau_n_rt_rp_5p205_t5 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x t u) : l_con).
-
-(* notion 3763 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t7 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.(λt:l_e_st_eq_landau_n_rt_rp_less r1 r2.l_e_st_eq_landau_n_rt_rp_5p205_t6 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 t : l_not (l_e_st_eq_landau_n_rt_rp_less r1 r2)).
-
-(* notion 3764 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t8 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.(λt:l_e_st_eq_landau_n_rt_rp_more r1 r2.l_e_st_eq_landau_n_rt_rp_5p205_t6 s0 t0 p0 p1a p1b p2 r2 r1 pr2 pr1 (l_e_st_eq_landau_n_rt_rp_satz121 r1 r2 t) : l_not (l_e_st_eq_landau_n_rt_rp_more r1 r2)).
-
-(* notion 3765 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t9 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.(l_or3e1 (l_e_st_eq_landau_n_rt_rp_is r1 r2) (l_e_st_eq_landau_n_rt_rp_more r1 r2) (l_e_st_eq_landau_n_rt_rp_less r1 r2) (l_e_st_eq_landau_n_rt_rp_satz123a r1 r2) (l_e_st_eq_landau_n_rt_rp_5p205_t8 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2) (l_e_st_eq_landau_n_rt_rp_5p205_t7 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2) : l_e_st_eq_landau_n_rt_rp_is r1 r2).
-
-(* notion 3766 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t10 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(λx:l_e_st_eq_landau_n_rt_cut.λy:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x.λu:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 y.l_e_st_eq_landau_n_rt_rp_5p205_t9 s0 t0 p0 p1a p1b p2 x y t u : l_e_amone l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x)).
-
-(* notion 3767 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_schnittprop ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_some (Πy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) : Prop).
-
-(* notion 3768 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_schnittset ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_e_st_setof l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
-
-(* notion 3769 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t11 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.(l_andi (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) i lx : l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0)).
-
-(* notion 3770 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t12 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.(l_somei l_e_st_eq_landau_n_rt_cut (Πy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) r (l_e_st_eq_landau_n_rt_rp_5p205_t11 s0 t0 p0 p1a p1b p2 r i x0 lx) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0).
-
-(* notion 3771 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t13 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t12 s0 t0 p0 p1a p1b p2 r i x0 lx) : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
-
-(* notion 3772 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t14 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s s0.(l_e_st_eq_landau_n_rt_rp_satz122 s r (p2 s j r i) : l_e_st_eq_landau_n_rt_rp_more r s).
-
-(* notion 3773 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t15 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s s0.(l_e_st_eq_landau_n_rt_rp_satz158b r x0 ux : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r).
-
-(* notion 3774 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t16 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s s0.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_rpofrt x0) s (l_e_st_eq_landau_n_rt_rp_satz127c (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r s (l_e_st_eq_landau_n_rt_rp_5p205_t15 s0 t0 p0 p1a p1b p2 r i x0 ux s j) (l_e_st_eq_landau_n_rt_rp_5p205_t14 s0 t0 p0 p1a p1b p2 r i x0 ux s j)) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) s).
-
-(* notion 3775 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t17 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s s0.(l_e_st_eq_landau_n_rt_rp_satz158d s x0 (l_e_st_eq_landau_n_rt_rp_5p205_t16 s0 t0 p0 p1a p1b p2 r i x0 ux s j) : l_e_st_eq_landau_n_rt_urt s x0).
-
-(* notion 3776 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t18 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λs:l_e_st_eq_landau_n_rt_cut.(l_weli (l_ec (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0)) (λt:l_e_st_eq_landau_n_rt_rp_in s s0.l_e_st_eq_landau_n_rt_rp_5p205_t17 s0 t0 p0 p1a p1b p2 r i x0 ux s t) : l_not (l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0))).
-
-(* notion 3777 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t19 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.(l_some_th5 l_e_st_eq_landau_n_rt_cut (Πy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) (λy:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_t18 s0 t0 p0 p1a p1b p2 r i x0 ux y) : l_not (l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0)).
-
-(* notion 3778 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t20 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0) (l_e_st_eq_landau_n_rt_rp_5p205_t19 s0 t0 p0 p1a p1b p2 r i x0 ux) (λt:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) x0 t) : l_not (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2))).
-
-(* notion 3779 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t21 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) x0 i : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0).
-
-(* notion 3780 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t22 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_ande1 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) a : l_e_st_eq_landau_n_rt_rp_in r s0).
-
-(* notion 3781 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t23 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_ande2 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) a : l_e_st_eq_landau_n_rt_lrt r x0).
-
-(* notion 3782 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t24 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_e_st_eq_landau_n_rt_rp_satz120 r x0 (l_e_st_eq_landau_n_rt_rp_5p205_t23 s0 t0 p0 p1a p1b p2 x0 i y0 l r a) y0 l : l_e_st_eq_landau_n_rt_lrt r y0).
-
-(* notion 3783 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t25 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_andi (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r y0) (l_e_st_eq_landau_n_rt_rp_5p205_t22 s0 t0 p0 p1a p1b p2 x0 i y0 l r a) (l_e_st_eq_landau_n_rt_rp_5p205_t24 s0 t0 p0 p1a p1b p2 x0 i y0 l r a) : l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r y0)).
-
-(* notion 3784 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t26 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_somei l_e_st_eq_landau_n_rt_cut (Πy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y y0)) r (l_e_st_eq_landau_n_rt_rp_5p205_t25 s0 t0 p0 p1a p1b p2 x0 i y0 l r a) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 y0).
-
-(* notion 3785 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t27 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_someapp l_e_st_eq_landau_n_rt_cut (Πy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) (l_e_st_eq_landau_n_rt_rp_5p205_t21 s0 t0 p0 p1a p1b p2 x0 i) (l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 y0) (λy:l_e_st_eq_landau_n_rt_cut.λr:l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0).l_e_st_eq_landau_n_rt_rp_5p205_t26 s0 t0 p0 p1a p1b p2 x0 i y0 l y r) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 y0).
-
-(* notion 3786 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t28 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) y0 (l_e_st_eq_landau_n_rt_rp_5p205_t27 s0 t0 p0 p1a p1b p2 x0 i y0 l) : l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
-
-(* notion 3787 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t29 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_ande1 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) a : l_e_st_eq_landau_n_rt_rp_in r s0).
-
-(* notion 3788 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t30 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_ande2 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) a : l_e_st_eq_landau_n_rt_lrt r x0).
-
-(* notion 3789 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t31 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_andi (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r y0) (l_e_st_eq_landau_n_rt_rp_5p205_t29 s0 t0 p0 p1a p1b p2 x0 i r a) ly : l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r y0)).
-
-(* notion 3790 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t32 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_somei l_e_st_eq_landau_n_rt_cut (Πy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y y0)) r (l_e_st_eq_landau_n_rt_rp_5p205_t31 s0 t0 p0 p1a p1b p2 x0 i r a y0 ly l) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 y0).
-
-(* notion 3791 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t33 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) y0 (l_e_st_eq_landau_n_rt_rp_5p205_t32 s0 t0 p0 p1a p1b p2 x0 i r a y0 ly l) : l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
-
-(* notion 3792 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t34 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_satz83 x0 y0 l : l_e_st_eq_landau_n_rt_more y0 x0).
-
-(* notion 3793 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t35 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_andi (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y0 x0) (l_e_st_eq_landau_n_rt_rp_5p205_t33 s0 t0 p0 p1a p1b p2 x0 i r a y0 ly l) (l_e_st_eq_landau_n_rt_rp_5p205_t34 s0 t0 p0 p1a p1b p2 x0 i r a y0 ly l) : l_and (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y0 x0)).
-
-(* notion 3794 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t36 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_somei l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0)) y0 (l_e_st_eq_landau_n_rt_rp_5p205_t35 s0 t0 p0 p1a p1b p2 x0 i r a y0 ly l) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0))).
-
-(* notion 3795 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t37 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_e_st_eq_landau_n_rt_cutapp3 r x0 (l_e_st_eq_landau_n_rt_rp_5p205_t30 s0 t0 p0 p1a p1b p2 x0 i r a) (l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0))) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt r y.λu:l_e_st_eq_landau_n_rt_less x0 y.l_e_st_eq_landau_n_rt_rp_5p205_t36 s0 t0 p0 p1a p1b p2 x0 i r a y t u) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0))).
-
-(* notion 3796 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t38 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).(l_someapp l_e_st_eq_landau_n_rt_cut (Πy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) (l_e_st_eq_landau_n_rt_rp_5p205_t21 s0 t0 p0 p1a p1b p2 x0 i) (l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0))) (λy:l_e_st_eq_landau_n_rt_cut.λt:l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0).l_e_st_eq_landau_n_rt_rp_5p205_t37 s0 t0 p0 p1a p1b p2 x0 i y t) : l_e_st_eq_landau_n_rt_some (Πy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0))).
-
-(* notion 3797 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t39 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s t0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt s y0.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t13 s0 t0 p0 p1a p1b p2 r i x0 lx) y0 (l_e_st_eq_landau_n_rt_rp_5p205_t20 s0 t0 p0 p1a p1b p2 s j y0 uy) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_5p205_t28 s0 t0 p0 p1a p1b p2 x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).l_e_st_eq_landau_n_rt_rp_5p205_t38 s0 t0 p0 p1a p1b p2 x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
-
-(* notion 3798 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t40 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s t0.(l_e_st_eq_landau_n_rt_cutapp1b s (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt s x.l_e_st_eq_landau_n_rt_rp_5p205_t39 s0 t0 p0 p1a p1b p2 r i x0 lx s j x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
-
-(* notion 3799 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t41 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_cut t0 p1b (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (λy:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_5p205_t40 s0 t0 p0 p1a p1b p2 r i x0 lx y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
-
-(* notion 3800 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t42 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.(l_e_st_eq_landau_n_rt_cutapp1a r (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt r x.l_e_st_eq_landau_n_rt_rp_5p205_t41 s0 t0 p0 p1a p1b p2 r i x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
-
-(* notion 3801 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t43 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_cut s0 p1a (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (λy:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_in y s0.l_e_st_eq_landau_n_rt_rp_5p205_t42 s0 t0 p0 p1a p1b p2 y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
-
-(* notion 3802 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_snt ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_5p205_t43 s0 t0 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3803 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t44 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.(l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_5p205_t43 s0 t0 p0 p1a p1b p2) x0 lx : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
-
-(* notion 3804 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t45 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t44 s0 t0 p0 p1a p1b p2 r l x0 ux lx) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0).
-
-(* notion 3805 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t46 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_ande1 (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0) a : l_e_st_eq_landau_n_rt_rp_in s s0).
-
-(* notion 3806 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t47 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_ande2 (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0) a : l_e_st_eq_landau_n_rt_lrt s x0).
-
-(* notion 3807 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t48 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_andi (l_e_st_eq_landau_n_rt_urt r x0) (l_e_st_eq_landau_n_rt_lrt s x0) ux (l_e_st_eq_landau_n_rt_rp_5p205_t47 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a) : l_and (l_e_st_eq_landau_n_rt_urt r x0) (l_e_st_eq_landau_n_rt_lrt s x0)).
-
-(* notion 3808 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t49 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_somei l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt r x) (l_e_st_eq_landau_n_rt_lrt s x)) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t48 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a) : l_e_st_eq_landau_n_rt_rp_less r s).
-
-(* notion 3809 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t50 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_ec3e23 (l_e_st_eq_landau_n_rt_rp_is s r) (l_e_st_eq_landau_n_rt_rp_more s r) (l_e_st_eq_landau_n_rt_rp_less s r) (l_e_st_eq_landau_n_rt_rp_satz123b s r) (l_e_st_eq_landau_n_rt_rp_satz122 r s (l_e_st_eq_landau_n_rt_rp_5p205_t49 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a)) : l_not (l_e_st_eq_landau_n_rt_rp_less s r)).
-
-(* notion 3810 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t51 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_in r t0) (l_e_st_eq_landau_n_rt_rp_less s r) (l_e_st_eq_landau_n_rt_rp_5p205_t50 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a) (p2 s (l_e_st_eq_landau_n_rt_rp_5p205_t46 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a) r) : l_not (l_e_st_eq_landau_n_rt_rp_in r t0)).
-
-(* notion 3811 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t52 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_ore1 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_rp_in r t0) (p0 r) (l_e_st_eq_landau_n_rt_rp_5p205_t51 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a) : l_e_st_eq_landau_n_rt_rp_in r s0).
-
-(* notion 3812 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t53 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.(l_someapp l_e_st_eq_landau_n_rt_cut (Πy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) (l_e_st_eq_landau_n_rt_rp_5p205_t45 s0 t0 p0 p1a p1b p2 r l x0 ux lx) (l_e_st_eq_landau_n_rt_rp_in r s0) (λy:l_e_st_eq_landau_n_rt_cut.λt:l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0).l_e_st_eq_landau_n_rt_rp_5p205_t52 s0 t0 p0 p1a p1b p2 r l x0 ux lx y t) : l_e_st_eq_landau_n_rt_rp_in r s0).
-
-(* notion 3813 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t54 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).(l_e_st_eq_landau_n_rt_rp_lessapp r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) l (l_e_st_eq_landau_n_rt_rp_in r s0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt r x.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x.l_e_st_eq_landau_n_rt_rp_5p205_t53 s0 t0 p0 p1a p1b p2 r l x t u) : l_e_st_eq_landau_n_rt_rp_in r s0).
-
-(* notion 3814 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t55 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λi:l_e_st_eq_landau_n_rt_rp_in r s0.(l_andi (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) i lx : l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0)).
-
-(* notion 3815 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t56 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λi:l_e_st_eq_landau_n_rt_rp_in r s0.(l_somei l_e_st_eq_landau_n_rt_cut (Πy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) r (l_e_st_eq_landau_n_rt_rp_5p205_t55 s0 t0 p0 p1a p1b p2 r m x0 lx ux i) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0).
-
-(* notion 3816 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t57 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λi:l_e_st_eq_landau_n_rt_rp_in r s0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t56 s0 t0 p0 p1a p1b p2 r m x0 lx ux i) : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
-
-(* notion 3817 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t58 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λi:l_e_st_eq_landau_n_rt_rp_in r s0.(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_5p205_t43 s0 t0 p0 p1a p1b p2) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t57 s0 t0 p0 p1a p1b p2 r m x0 lx ux i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0).
-
-(* notion 3818 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t59 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0) ux (λt:l_e_st_eq_landau_n_rt_rp_in r s0.l_e_st_eq_landau_n_rt_rp_5p205_t58 s0 t0 p0 p1a p1b p2 r m x0 lx ux t) : l_not (l_e_st_eq_landau_n_rt_rp_in r s0)).
-
-(* notion 3819 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t60 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.(l_ore2 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_rp_in r t0) (p0 r) (l_e_st_eq_landau_n_rt_rp_5p205_t59 s0 t0 p0 p1a p1b p2 r m x0 lx ux) : l_e_st_eq_landau_n_rt_rp_in r t0).
-
-(* notion 3820 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t61 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).(l_e_st_eq_landau_n_rt_rp_moreapp r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) m (l_e_st_eq_landau_n_rt_rp_in r t0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt r x.λu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x.l_e_st_eq_landau_n_rt_rp_5p205_t60 s0 t0 p0 p1a p1b p2 r m x t u) : l_e_st_eq_landau_n_rt_rp_in r t0).
-
-(* notion 3821 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t62 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_andi (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2)) (λx:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_less x (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).l_e_st_eq_landau_n_rt_rp_5p205_t54 s0 t0 p0 p1a p1b p2 x t) (λx:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_more x (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).l_e_st_eq_landau_n_rt_rp_5p205_t61 s0 t0 p0 p1a p1b p2 x t) : l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2)).
-
-(* notion 3822 *)
-definition l_e_st_eq_landau_n_rt_rp_5p205_t63 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_somei l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x) (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_5p205_t62 s0 t0 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_rp_some (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x)).
-
-(* notion 3823 *)
-definition l_e_st_eq_landau_n_rt_rp_satzp205 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_e_onei l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x) (l_e_st_eq_landau_n_rt_rp_5p205_t10 s0 t0 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_5p205_t63 s0 t0 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_rp_one (Πx:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_less y x.l_e_st_eq_landau_n_rt_rp_in y s0)) (l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_more y x.l_e_st_eq_landau_n_rt_rp_in y t0)))).
-
-(* notion 3824 *)
-definition l_e_st_eq_landau_n_rt_rp_schnitt ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_e_ind l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x) (l_e_st_eq_landau_n_rt_rp_satzp205 s0 t0 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3825 *)
-definition l_e_st_eq_landau_n_rt_rp_satzp205a ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_ande1 (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2)) (l_e_oneax l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x) (l_e_st_eq_landau_n_rt_rp_satzp205 s0 t0 p0 p1a p1b p2)) : l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_less x (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2).l_e_st_eq_landau_n_rt_rp_in x s0)).
-
-(* notion 3826 *)
-definition l_e_st_eq_landau_n_rt_rp_satzp205b ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (Πx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (Πy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_ande2 (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2)) (l_e_oneax l_e_st_eq_landau_n_rt_cut (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x) (l_e_st_eq_landau_n_rt_rp_satzp205 s0 t0 p0 p1a p1b p2)) : l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_more x (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2).l_e_st_eq_landau_n_rt_rp_in x t0)).
-
-(* notion 3827 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_i ≝ (l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3828 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_r1 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_ivad_i : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3829 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_s1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_ivad_i : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3830 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_rps ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl r s : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3831 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_2 ≝ (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3832 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdeq12a (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) l_e_st_eq_landau_n_rt_rp_ivad_i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_2)).
-
-(* notion 3833 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t2 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_4pl23 r l_e_st_eq_landau_n_rt_rp_ivad_i s l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i)).
-
-(* notion 3834 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t3 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t2 r s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i)).
-
-(* notion 3835 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t4 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_2) (l_e_st_eq_landau_n_rt_rp_ivad_t3 r s) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_2)).
-
-(* notion 3836 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t5 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t4 r s) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_2) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ivad_rps r s))).
-
-(* notion 3837 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmaivad1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_ivad_t1 r s) (l_e_st_eq_landau_n_rt_rp_ivad_t5 r s) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r s))).
-
-(* notion 3838 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_rs ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ts r s : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3839 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t6 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_tdeq12a (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) l_e_st_eq_landau_n_rt_rp_ivad_i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))))).
-
-(* notion 3840 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t7 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) s) (l_e_st_eq_landau_n_rt_rp_disttp1 r l_e_st_eq_landau_n_rt_rp_ivad_i s) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i s) s (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) (l_e_st_eq_landau_n_rt_rp_satz151b s)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) s)).
-
-(* notion 3841 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t8 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) s) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) s) (l_e_st_eq_landau_n_rt_rp_ivad_r1 r)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_rps r s)) (l_e_st_eq_landau_n_rt_rp_disttp2 (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) s l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) s) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_t7 r s) (l_e_st_eq_landau_n_rt_rp_satz151 (l_e_st_eq_landau_n_rt_rp_ivad_r1 r))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) s r l_e_st_eq_landau_n_rt_rp_ivad_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_rps r s))).
-
-(* notion 3842 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t9 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_rps r s)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_rps r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t8 r s) (l_e_st_eq_landau_n_rt_rp_satz151 l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i))).
-
-(* notion 3843 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t10 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t9 r s)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i))).
-
-(* notion 3844 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t11 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_4pl23 r s l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_satz151a (l_e_st_eq_landau_n_rt_rp_ivad_r1 r)) (l_e_st_eq_landau_n_rt_rp_satz151c (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)))).
-
-(* notion 3845 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t12 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)))) (l_e_st_eq_landau_n_rt_rp_ivad_t10 r s) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_t11 r s)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))))).
-
-(* notion 3846 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t13 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t12 r s) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ivad_rs r s))).
-
-(* notion 3847 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmaivad2 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp)))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r s)) (l_e_st_eq_landau_n_rt_rp_ivad_t6 r s) (l_e_st_eq_landau_n_rt_rp_ivad_t13 r s) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r s))).
-
-(* notion 3848 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t14 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_morede12 (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) l_e_st_eq_landau_n_rt_rp_ivad_i m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) l_e_st_eq_landau_n_rt_rp_ivad_i)).
-
-(* notion 3849 *)
-definition l_e_st_eq_landau_n_rt_rp_ivad_t15 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz136a (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t14 r s m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)).
-
-(* notion 3850 *)
-definition l_e_st_eq_landau_n_rt_rp_lemmaivad3 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz136a r s l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_ivad_t15 r s m) : l_e_st_eq_landau_n_rt_rp_more r s).
-
-(* notion 3851 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t1 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b) c e f : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b)).
-
-(* notion 3852 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t2 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_comtd b a)) (l_e_st_eq_landau_n_rt_rp_pdmd (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_td a a)).
-
-(* notion 3853 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t3 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_e_st_eq_landau_n_rt_rp_tr4eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_md a b))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td b b))) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_td b b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b)) (l_e_st_eq_landau_n_rt_rp_disttpd1 a b (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_eqpd12 (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td b b)) (l_e_st_eq_landau_n_rt_rp_disttmd2 a a b) (l_e_st_eq_landau_n_rt_rp_disttmd2 b a b)) (l_e_st_eq_landau_n_rt_rp_asspd2 (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td b b))) (l_e_st_eq_landau_n_rt_rp_eqmd1 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b) (l_e_st_eq_landau_n_rt_rp_d161_t2 c a b n o e f)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b))).
-
-(* notion 3854 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t4 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b)) (l_e_st_eq_landau_n_rt_rp_d161_t3 c a b n o e f)) (l_e_st_eq_landau_n_rt_rp_satzd182e (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b) (l_e_st_eq_landau_n_rt_rp_d161_t1 c a b n o e f)) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b))).
-
-(* notion 3855 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t5 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_e_st_eq_landau_n_rt_rp_satzd192c (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_d161_t4 c a b n o e f) : l_or (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b))).
-
-(* notion 3856 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t6 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b) (l_e_st_eq_landau_n_rt_rp_d161_t1 c a b n o e f) (l_e_st_eq_landau_n_rt_rp_td01 a a z) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td b b)).
-
-(* notion 3857 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t7 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_zero b) (l_refimp (l_e_st_eq_landau_n_rt_rp_zero b)) (l_e_st_eq_landau_n_rt_rp_satzd192c b b (l_e_st_eq_landau_n_rt_rp_d161_t6 c a b n o e f z)) : l_e_st_eq_landau_n_rt_rp_zero b).
-
-(* notion 3858 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t8 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_zeroeq a b z (l_e_st_eq_landau_n_rt_rp_d161_t7 c a b n o e f z) : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3859 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t9 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_or3e2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrdo a) n p : l_e_st_eq_landau_n_rt_rp_posd a).
-
-(* notion 3860 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t10 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_zero a) p (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_d161_t7 c b a o n f e t) : l_not (l_e_st_eq_landau_n_rt_rp_zero b)).
-
-(* notion 3861 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t11 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_d161_t9 c b a o n f e (l_e_st_eq_landau_n_rt_rp_d161_t10 c a b n o e f p) : l_e_st_eq_landau_n_rt_rp_posd b).
-
-(* notion 3862 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t12 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_pnot0d (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_ppd a b (l_e_st_eq_landau_n_rt_rp_d161_t9 c a b n o e f p) (l_e_st_eq_landau_n_rt_rp_d161_t11 c a b n o e f p)) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a b))).
-
-(* notion 3863 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t13 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_ore2 (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_d161_t5 c a b n o e f) (l_e_st_eq_landau_n_rt_rp_d161_t12 c a b n o e f p) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3864 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t14 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_satzd182b a b (l_e_st_eq_landau_n_rt_rp_d161_t13 c a b n o e f p) : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3865 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd161b ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_eq a b) (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_d161_t8 c a b n o e f t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_zero a).l_e_st_eq_landau_n_rt_rp_d161_t14 c a b n o e f t) : l_e_st_eq_landau_n_rt_rp_eq a b).
-
-(* notion 3866 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t15 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_td c c) c (l_e_st_eq_landau_n_rt_rp_td01 c c z) z : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c c) c).
-
-(* notion 3867 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t16 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_andi (l_not (l_e_st_eq_landau_n_rt_rp_negd c)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c c) c) n (l_e_st_eq_landau_n_rt_rp_d161_t15 c n z) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd c)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c c) c)).
-
-(* notion 3868 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t17 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c)) c (l_e_st_eq_landau_n_rt_rp_d161_t16 c n z) : l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c))).
-
-(* notion 3869 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t18 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_or3e2 (l_e_st_eq_landau_n_rt_rp_zero c) (l_e_st_eq_landau_n_rt_rp_posd c) (l_e_st_eq_landau_n_rt_rp_negd c) (l_e_st_eq_landau_n_rt_rp_axrdo c) n o : l_e_st_eq_landau_n_rt_rp_posd c).
-
-(* notion 3870 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_crp ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_e_st_eq_landau_n_rt_rp_rpofpd c (l_e_st_eq_landau_n_rt_rp_d161_t18 c n o) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3871 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_srp ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_e_st_eq_landau_n_rt_rp_sqrt (l_e_st_eq_landau_n_rt_rp_d161_crp c n o) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3872 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_s ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_d161_srp c n o) : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3873 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t19 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_d161_s c n o)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_d161_srp c n o) (l_e_st_eq_landau_n_rt_rp_d161_srp c n o))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_d161_crp c n o)) c (l_e_st_eq_landau_n_rt_rp_lemmaivad2 (l_e_st_eq_landau_n_rt_rp_d161_srp c n o) (l_e_st_eq_landau_n_rt_rp_d161_srp c n o)) (l_e_st_eq_landau_n_rt_rp_isrpepd (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_d161_srp c n o) (l_e_st_eq_landau_n_rt_rp_d161_srp c n o)) (l_e_st_eq_landau_n_rt_rp_d161_crp c n o) (l_e_st_eq_landau_n_rt_rp_thsqrt1 (l_e_st_eq_landau_n_rt_rp_d161_crp c n o))) (l_e_st_eq_landau_n_rt_rp_eqpdrp2 c (l_e_st_eq_landau_n_rt_rp_d161_t18 c n o)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_d161_s c n o)) c).
-
-(* notion 3874 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t20 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_andi (l_not (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_d161_s c n o))) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_d161_s c n o)) c) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_d161_srp c n o))) (l_e_st_eq_landau_n_rt_rp_d161_t19 c n o) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_d161_s c n o))) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_d161_s c n o)) c)).
-
-(* notion 3875 *)
-definition l_e_st_eq_landau_n_rt_rp_d161_t21 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c)) (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_d161_t20 c n o) : l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c))).
-
-(* notion 3876 *)
-definition l_e_st_eq_landau_n_rt_rp_satzd161a ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_zero c) (l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c))) (λt:l_e_st_eq_landau_n_rt_rp_zero c.l_e_st_eq_landau_n_rt_rp_d161_t17 c n t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_zero c).l_e_st_eq_landau_n_rt_rp_d161_t21 c n t) : l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c))).
-
-(* notion 3877 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_ori1 (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_absd a))) (l_e_st_eq_landau_n_rt_rp_satzd166f a z) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3878 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).(l_e_st_eq_landau_n_rt_rp_natintd (l_e_st_eq_landau_n_rt_rp_absd a) n : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3879 *)
-definition l_e_st_eq_landau_n_rt_rp_intabsd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.(l_orapp (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_absd a)) i (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_intd_t1 a i t) (λt:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).l_e_st_eq_landau_n_rt_rp_intd_t2 a i t) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3880 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).(l_e_st_eq_landau_n_rt_rp_eqnatd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_satzd178a a) n : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a))).
-
-(* notion 3881 *)
-definition l_e_st_eq_landau_n_rt_rp_intm0d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a))) i (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_satzd176b a t) (λt:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).l_e_st_eq_landau_n_rt_rp_intd_t4 a i t) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_m0d a)).
-
-(* notion 3882 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_pd a b) b (l_e_st_eq_landau_n_rt_rp_pd01 a b z) : l_e_st_eq_landau_n_rt_rp_eq b (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3883 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_eqintd b (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_intd_t5 a b i j z) j : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3884 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_pd a b) a (l_e_st_eq_landau_n_rt_rp_pd02 a b z) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3885 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_eqintd a (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_intd_t7 a b i j z) i : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3886 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t9 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_ande2 (l_e_st_eq_landau_n_rt_rp_posd a) (Πt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a t)) (l_e_st_eq_landau_n_rt_rp_posintnatd a p i) p : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a p)).
-
-(* notion 3887 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_apb1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pd a b) pp : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3888 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_a1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_rpofpd a p : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3889 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_b1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_rpofpd b q : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3890 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t10 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_natpl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_t9 a i p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q) (l_e_st_eq_landau_n_rt_rp_intd_t9 b j q) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))).
-
-(* notion 3891 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t11 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_eqpd12 a (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)) b (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 a p) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 b q) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)))).
-
-(* notion 3892 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) (l_e_st_eq_landau_n_rt_rp_intd_t11 a b i j pp p q) (l_e_st_eq_landau_n_rt_rp_lemmaivad1 (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)))).
-
-(* notion 3893 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t13 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)) (l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_pd a b) pp (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) (l_e_st_eq_landau_n_rt_rp_intd_t12 a b i j pp p q)) (l_e_st_eq_landau_n_rt_rp_isrppd2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))).
-
-(* notion 3894 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t14 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_isp1 l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_intd_t10 a b i j pp p q) (l_e_st_eq_landau_n_rt_rp_intd_t13 a b i j pp p q) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)).
-
-(* notion 3895 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t15 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_andi (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b)) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j t)) pp (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_intd_t14 a b i j t p q) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3896 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t16 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_natintd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_intd_t15 a b i j pp p q) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3897 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t17 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_satzd176c b n : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d b)).
-
-(* notion 3898 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_b2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intd_t17 a b i j pp p n) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3899 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t18 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqpd2 b (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) a (l_e_st_eq_landau_n_rt_rp_satzd177a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_m0d b))).
-
-(* notion 3900 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t19 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_intd_t18 a b i j pp p n) pp : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_m0d b))).
-
-(* notion 3901 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t20 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_satzd182a a (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intd_t19 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_mored a (l_e_st_eq_landau_n_rt_rp_m0d b)).
-
-(* notion 3902 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t21 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqmored12 a (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 a p) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intd_t17 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_intd_t20 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n))).
-
-(* notion 3903 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t22 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_lemmaivad3 (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t21 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n)).
-
-(* notion 3904 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t23 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_natmn (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_t9 a i p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t9 (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intm0d b j) (l_e_st_eq_landau_n_rt_rp_intd_t17 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_intd_t22 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t22 a b i j pp p n))).
-
-(* notion 3905 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t24 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqpd12 (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intd_t17 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_pd a b) pp) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)))).
-
-(* notion 3906 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t25 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_tr4eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a b) b) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a b) b) a (l_e_st_eq_landau_n_rt_rp_mdpd a b)) (l_e_st_eq_landau_n_rt_rp_compd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_intd_t24 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_lemmaivad1 (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)))).
-
-(* notion 3907 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t26 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)) (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)))) (l_e_st_eq_landau_n_rt_rp_isrppd1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_eqpderp a p (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_intd_t25 a b i j pp p n)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)) (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)).
-
-(* notion 3908 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t27 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_satz140g (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_intd_t22 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t26 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t22 a b i j pp p n))).
-
-(* notion 3909 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t28 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_isp1 l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t22 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_intd_t23 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t27 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)).
-
-(* notion 3910 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t29 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_andi (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b)) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j t)) pp (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_intd_t28 a b i j t p n) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3911 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t30 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_natintd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_intd_t29 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3912 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t31 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_rappd b (l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_intd_t16 a b i j pp p t) (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_intd_t8 a b i j t) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_intd_t30 a b i j pp p t) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3913 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t31a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_pd a b) pp) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_npd a b n t) : l_not (l_e_st_eq_landau_n_rt_rp_negd b)).
-
-(* notion 3914 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t32 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_pd a b) pp) (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_eqnegd a (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_pd a b) a (l_e_st_eq_landau_n_rt_rp_pd02 a b t)) n) : l_not (l_e_st_eq_landau_n_rt_rp_zero b)).
-
-(* notion 3915 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t33 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_or3e2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_axrdo b) (l_e_st_eq_landau_n_rt_rp_intd_t31a a b i j pp n) (l_e_st_eq_landau_n_rt_rp_intd_t32 a b i j pp n) : l_e_st_eq_landau_n_rt_rp_posd b).
-
-(* notion 3916 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t34 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd b a) (l_e_st_eq_landau_n_rt_rp_compd a b) pp : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd b a)).
-
-(* notion 3917 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t35 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_intd_t30 b a j i (l_e_st_eq_landau_n_rt_rp_intd_t34 a b i j pp n) (l_e_st_eq_landau_n_rt_rp_intd_t33 a b i j pp n) n : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd b a)).
-
-(* notion 3918 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t36 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_eqintd (l_e_st_eq_landau_n_rt_rp_pd b a) (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_compd b a) (l_e_st_eq_landau_n_rt_rp_intd_t35 a b i j pp n) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3919 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t37 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_rappd a (l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_intd_t31 a b i j pp t) (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_intd_t6 a b i j t) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_intd_t36 a b i j pp t) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3920 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t38 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λ0p:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_intdi0 (l_e_st_eq_landau_n_rt_rp_pd a b) 0p : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3921 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t39 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_satzd176c (l_e_st_eq_landau_n_rt_rp_pd a b) np : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b))).
-
-(* notion 3922 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t40 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd180 a b) (l_e_st_eq_landau_n_rt_rp_intd_t39 a b i j np) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b))).
-
-(* notion 3923 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t41 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_intd_t37 (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intm0d a i) (l_e_st_eq_landau_n_rt_rp_intm0d b j) (l_e_st_eq_landau_n_rt_rp_intd_t40 a b i j np) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b))).
-
-(* notion 3924 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t42 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_eqintd (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_satzd180a a b) (l_e_st_eq_landau_n_rt_rp_intd_t41 a b i j np) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b))).
-
-(* notion 3925 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t43 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_intm0d (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_intd_t42 a b i j np) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)))).
-
-(* notion 3926 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t44 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_eqintd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b))) (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_satzd177 (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_intd_t43 a b i j np) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3927 *)
-definition l_e_st_eq_landau_n_rt_rp_intpd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.(l_e_st_eq_landau_n_rt_rp_rappd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)) (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_intd_t37 a b i j t) (λt:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_intd_t38 a b i j t) (λt:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_intd_t44 a b i j t) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
-
-(* notion 3928 *)
-definition l_e_st_eq_landau_n_rt_rp_intmd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.(l_e_st_eq_landau_n_rt_rp_intpd a (l_e_st_eq_landau_n_rt_rp_m0d b) i (l_e_st_eq_landau_n_rt_rp_intm0d b j) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 3929 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t45 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)) n (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_td01 a b t) : l_not (l_e_st_eq_landau_n_rt_rp_zero a)).
-
-(* notion 3930 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t46 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)) n (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_td02 a b t) : l_not (l_e_st_eq_landau_n_rt_rp_zero b)).
-
-(* notion 3931 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t47 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_satzd166e a (l_e_st_eq_landau_n_rt_rp_intd_t45 a b i j n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)).
-
-(* notion 3932 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_a3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_intd_t47 a b i j n) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3933 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t48 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_satzd166e b (l_e_st_eq_landau_n_rt_rp_intd_t46 a b i j n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd b)).
-
-(* notion 3934 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_b3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_intd_t48 a b i j n) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3935 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t49 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_natts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_t9 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_intabsd a i) (l_e_st_eq_landau_n_rt_rp_intd_t47 a b i j n)) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_t9 (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_intabsd b j) (l_e_st_eq_landau_n_rt_rp_intd_t48 a b i j n)) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))).
-
-(* notion 3936 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t50 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_td a b) n : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3937 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_atb3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) p : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 3938 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t51 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_intd_t47 a b i j n)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_intd_t48 a b i j n)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)))).
-
-(* notion 3939 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t52 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) (l_e_st_eq_landau_n_rt_rp_satzd193 a b) (l_e_st_eq_landau_n_rt_rp_intd_t51 a b i j n p) (l_e_st_eq_landau_n_rt_rp_lemmaivad2 (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)))).
-
-(* notion 3940 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t53 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_intd_atb3 a b i j n p) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)))) (l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) p (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) (l_e_st_eq_landau_n_rt_rp_intd_t52 a b i j n p)) (l_e_st_eq_landau_n_rt_rp_isrppd1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_intd_atb3 a b i j n p) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))).
-
-(* notion 3941 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t54 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_isp1 l_e_st_eq_landau_n_rt_cut (Πt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_intd_atb3 a b i j n p) (l_e_st_eq_landau_n_rt_rp_intd_t49 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_t53 a b i j n p) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_atb3 a b i j n p)).
-
-(* notion 3942 *)
-definition l_e_st_eq_landau_n_rt_rp_intd_t55 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_andi (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b))) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_atb3 a b i j n t)) (l_e_st_eq_landau_n_rt_rp_intd_t50 a b i j n) (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).l_e_st_eq_landau_n_rt_rp_intd_t54 a b i j n t) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b))).
-
-(* notion 3943 *)
-definition l_e_st_eq_landau_n_rt_rp_inttd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).l_e_st_eq_landau_n_rt_rp_intd_t55 a b i j t : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_td a b)).
-
-(* notion 3944 *)
-definition l_e_st_eq_landau_n_rt_rp_r_eq ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq x y : Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Prop).
-
-(* notion 3945 *)
-definition l_e_st_eq_landau_n_rt_rp_r_refeq ≝ (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_refeq x : Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_eq x x).
-
-(* notion 3946 *)
-definition l_e_st_eq_landau_n_rt_rp_r_symeq ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.l_e_st_eq_landau_n_rt_rp_symeq x y t : Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πt:l_e_st_eq_landau_n_rt_rp_r_eq x y.l_e_st_eq_landau_n_rt_rp_r_eq y x).
-
-(* notion 3947 *)
-definition l_e_st_eq_landau_n_rt_rp_r_treq ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.λu:l_e_st_eq_landau_n_rt_rp_r_eq y z.l_e_st_eq_landau_n_rt_rp_treq x y z t u : Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πz:l_e_st_eq_landau_n_rt_rp_dif.Πt:l_e_st_eq_landau_n_rt_rp_r_eq x y.Πu:l_e_st_eq_landau_n_rt_rp_r_eq y z.l_e_st_eq_landau_n_rt_rp_r_eq x z).
-
-(* notion 3948 *)
-definition l_e_st_eq_landau_n_rt_rp_r_inn ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_esti l_e_st_eq_landau_n_rt_rp_dif a s : Prop).
-
-(* notion 3949 *)
-definition l_e_st_eq_landau_n_rt_rp_r_real ≝ (l_e_st_eq_ect l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq : Type[0]).
-
-(* notion 3950 *)
-definition l_e_st_eq_landau_n_rt_rp_r_is ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_is l_e_st_eq_landau_n_rt_rp_r_real r s : Prop).
-
-(* notion 3951 *)
-definition l_e_st_eq_landau_n_rt_rp_r_nis ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_not (l_e_st_eq_landau_n_rt_rp_r_is r s) : Prop).
-
-(* notion 3952 *)
-definition l_e_st_eq_landau_n_rt_rp_r_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_r_real.Prop.(l_some l_e_st_eq_landau_n_rt_rp_r_real p : Prop).
-
-(* notion 3953 *)
-definition l_e_st_eq_landau_n_rt_rp_r_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_r_real.Prop.(l_all l_e_st_eq_landau_n_rt_rp_r_real p : Prop).
-
-(* notion 3954 *)
-definition l_e_st_eq_landau_n_rt_rp_r_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_r_real.Prop.(l_e_one l_e_st_eq_landau_n_rt_rp_r_real p : Prop).
-
-(* notion 3955 *)
-definition l_e_st_eq_landau_n_rt_rp_r_in ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs0:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_esti l_e_st_eq_landau_n_rt_rp_r_real r s0 : Prop).
-
-(* notion 3956 *)
-definition l_e_st_eq_landau_n_rt_rp_r_realof ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_ectelt l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq a : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 3957 *)
-definition l_e_st_eq_landau_n_rt_rp_r_class ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_ecect l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq r : l_e_st_set l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 3958 *)
-definition l_e_st_eq_landau_n_rt_rp_r_innclass ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_4_th5 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq a : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_realof a))).
-
-(* notion 3959 *)
-definition l_e_st_eq_landau_n_rt_rp_r_eqinn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_4_th8 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq r a air b e : l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class r)).
-
-(* notion 3960 *)
-definition l_e_st_eq_landau_n_rt_rp_r_realapp1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).p.(l_e_st_eq_4_th3 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq r p p1 : p).
-
-(* notion 3961 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).p.λa:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_realapp1 s p (λy:l_e_st_eq_landau_n_rt_rp_dif.p1 a y air) : p).
-
-(* notion 3962 *)
-definition l_e_st_eq_landau_n_rt_rp_r_realapp2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).p.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r p (λx:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t1 r s p p1 x xi) : p).
-
-(* notion 3963 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πz:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).Πzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).p.λa:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_realapp2 s t p (λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.p1 a y z air) : p).
-
-(* notion 3964 *)
-definition l_e_st_eq_landau_n_rt_rp_r_realapp3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πz:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).Πzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).p.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r p (λx:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t2 r s t p p1 x xi) : p).
-
-(* notion 3965 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πz:l_e_st_eq_landau_n_rt_rp_dif.Πv:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).Πzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).Πvi:l_e_st_eq_landau_n_rt_rp_r_inn v (l_e_st_eq_landau_n_rt_rp_r_class u).p.λa:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_realapp3 s t u p (λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.p1 a y z v air) : p).
-
-(* notion 3966 *)
-definition l_e_st_eq_landau_n_rt_rp_r_realapp4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πz:l_e_st_eq_landau_n_rt_rp_dif.Πv:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).Πzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).Πvi:l_e_st_eq_landau_n_rt_rp_r_inn v (l_e_st_eq_landau_n_rt_rp_r_class u).p.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r p (λx:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t3 r s t u p p1 x xi) : p).
-
-(* notion 3967 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λe:l_e_st_eq_landau_n_rt_rp_eq a1 b1.(l_e_st_eq_5_th3 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq r s a1 a1ir b1 b1is e : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 3968 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_5_th5 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq r s a1 a1ir b1 b1is i : l_e_st_eq_landau_n_rt_rp_eq a1 b1).
-
-(* notion 3969 *)
-definition l_e_st_eq_landau_n_rt_rp_r_nisin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_eq a1 b1).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_eq a1 b1) n (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is t) : l_e_st_eq_landau_n_rt_rp_r_nis r s).
-
-(* notion 3970 *)
-definition l_e_st_eq_landau_n_rt_rp_r_nisex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_nis r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_r_is r s) n (λt:l_e_st_eq_landau_n_rt_rp_eq a1 b1.l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is t) : l_not (l_e_st_eq_landau_n_rt_rp_eq a1 b1)).
-
-(* notion 3971 *)
-definition l_e_st_eq_landau_n_rt_rp_r_fixf ≝ λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_rt_rp_dif.alpha.(l_e_st_eq_fixfu l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha f : Prop).
-
-(* notion 3972 *)
-definition l_e_st_eq_landau_n_rt_rp_r_indreal ≝ λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_rt_rp_dif.alpha.λff:l_e_st_eq_landau_n_rt_rp_r_fixf alpha f.λr0:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_indeq l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha f ff r0 : alpha).
-
-(* notion 3973 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isindreal ≝ λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_rt_rp_dif.alpha.λff:l_e_st_eq_landau_n_rt_rp_r_fixf alpha f.λr0:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r0).(l_e_st_eq_10_th2 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha f ff r0 a air : l_e_is alpha (f a) (l_e_st_eq_landau_n_rt_rp_r_indreal alpha f ff r0)).
-
-(* notion 3974 *)
-definition l_e_st_eq_landau_n_rt_rp_r_fixf2 ≝ λalpha:Type[0].λg:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.alpha.(l_e_st_eq_fixfu2 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha g : Prop).
-
-(* notion 3975 *)
-definition l_e_st_eq_landau_n_rt_rp_r_indreal2 ≝ λalpha:Type[0].λg:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.alpha.λff2:l_e_st_eq_landau_n_rt_rp_r_fixf2 alpha g.λr0:l_e_st_eq_landau_n_rt_rp_r_real.λs0:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_indeq2 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha g ff2 r0 s0 : alpha).
-
-(* notion 3976 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isindreal2 ≝ λalpha:Type[0].λg:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.alpha.λff2:l_e_st_eq_landau_n_rt_rp_r_fixf2 alpha g.λr0:l_e_st_eq_landau_n_rt_rp_r_real.λs0:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r0).λbis:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s0).(l_e_st_eq_11_th1 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha g ff2 r0 s0 a air b bis : l_e_is alpha (g a b) (l_e_st_eq_landau_n_rt_rp_r_indreal2 alpha g ff2 r0 s0)).
-
-(* notion 3977 *)
-definition l_e_st_eq_landau_n_rt_rp_r_0 ≝ (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 3978 *)
-definition l_e_st_eq_landau_n_rt_rp_r_0in ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λz:l_e_st_eq_landau_n_rt_rp_zero a0.(l_e_st_eq_landau_n_rt_rp_r_isin r l_e_st_eq_landau_n_rt_rp_r_0 a0 (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) a0ir (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_zeroeq a0 (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) z (l_e_st_eq_landau_n_rt_rp_zeroi l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp (l_e_refis l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_1rp))) : l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 3979 *)
-definition l_e_st_eq_landau_n_rt_rp_r_0ex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) a0 (l_e_st_eq_landau_n_rt_rp_r_isex l_e_st_eq_landau_n_rt_rp_r_0 r (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) a0 (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) a0ir (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r l_e_st_eq_landau_n_rt_rp_r_0 i)) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_stmis l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_isstd l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) : l_e_st_eq_landau_n_rt_rp_zero a0).
-
-(* notion 3980 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_propp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_posd a0) : Prop).
-
-(* notion 3981 *)
-definition l_e_st_eq_landau_n_rt_rp_r_pos ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r x) : Prop).
-
-(* notion 3982 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_posd a0.(l_andi (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_posd a0) a0ir p : l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r a0).
-
-(* notion 3983 *)
-definition l_e_st_eq_landau_n_rt_rp_r_posin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_posd a0.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r x) a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t4 r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_r_pos r).
-
-(* notion 3984 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λa:l_e_st_eq_landau_n_rt_rp_dif.λq1:l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r a.(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_posd a) q1 : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
-
-(* notion 3985 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λa:l_e_st_eq_landau_n_rt_rp_dif.λq1:l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r a.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_posd a) q1 : l_e_st_eq_landau_n_rt_rp_posd a).
-
-(* notion 3986 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λa:l_e_st_eq_landau_n_rt_rp_dif.λq1:l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r a.(l_e_st_eq_landau_n_rt_rp_eqposd a a0 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t5 r a0 a0ir p a q1) a0ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t6 r a0 a0ir p a q1) : l_e_st_eq_landau_n_rt_rp_posd a0).
-
-(* notion 3987 *)
-definition l_e_st_eq_landau_n_rt_rp_r_posex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r x) p (l_e_st_eq_landau_n_rt_rp_posd a0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r x.l_e_st_eq_landau_n_rt_rp_r_ivr1_t7 r a0 a0ir p x t) : l_e_st_eq_landau_n_rt_rp_posd a0).
-
-(* notion 3988 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_propn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_negd a0) : Prop).
-
-(* notion 3989 *)
-definition l_e_st_eq_landau_n_rt_rp_r_neg ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r x) : Prop).
-
-(* notion 3990 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_negd a0.(l_andi (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_negd a0) a0ir n : l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r a0).
-
-(* notion 3991 *)
-definition l_e_st_eq_landau_n_rt_rp_r_negin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_negd a0.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r x) a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t8 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_neg r).
-
-(* notion 3992 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λa:l_e_st_eq_landau_n_rt_rp_dif.λpl:l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r a.(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_negd a) pl : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
-
-(* notion 3993 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λa:l_e_st_eq_landau_n_rt_rp_dif.λpl:l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r a.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_negd a) pl : l_e_st_eq_landau_n_rt_rp_negd a).
-
-(* notion 3994 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λa:l_e_st_eq_landau_n_rt_rp_dif.λpl:l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r a.(l_e_st_eq_landau_n_rt_rp_eqnegd a a0 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t9 r a0 a0ir n a pl) a0ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t10 r a0 a0ir n a pl) : l_e_st_eq_landau_n_rt_rp_negd a0).
-
-(* notion 3995 *)
-definition l_e_st_eq_landau_n_rt_rp_r_negex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r x) n (l_e_st_eq_landau_n_rt_rp_negd a0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r x.l_e_st_eq_landau_n_rt_rp_r_ivr1_t11 r a0 a0ir n x t) : l_e_st_eq_landau_n_rt_rp_negd a0).
-
-(* notion 3996 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_posd a0.(l_or3i2 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_posin r a0 a0ir p) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
-
-(* notion 3997 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t13 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λz:l_e_st_eq_landau_n_rt_rp_zero a0.(l_or3i1 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_0in r a0 a0ir z) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
-
-(* notion 3998 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t14 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_negd a0.(l_or3i3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_negin r a0 a0ir n) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
-
-(* notion 3999 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t15 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_rappd a0 (l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)) (λt:l_e_st_eq_landau_n_rt_rp_posd a0.l_e_st_eq_landau_n_rt_rp_r_ivr1_t12 r a0 a0ir t) (λt:l_e_st_eq_landau_n_rt_rp_zero a0.l_e_st_eq_landau_n_rt_rp_r_ivr1_t13 r a0 a0ir t) (λt:l_e_st_eq_landau_n_rt_rp_negd a0.l_e_st_eq_landau_n_rt_rp_r_ivr1_t14 r a0 a0ir t) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
-
-(* notion 4000 *)
-definition l_e_st_eq_landau_n_rt_rp_r_axrlo ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t15 r x xi) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
-
-(* notion 4001 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t16 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_posd a0) (l_e_st_eq_landau_n_rt_rp_0notpd a0 (l_e_st_eq_landau_n_rt_rp_r_0ex r a0 a0ir i)) (λt:l_e_st_eq_landau_n_rt_rp_r_pos r.l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir t) : l_not (l_e_st_eq_landau_n_rt_rp_r_pos r)).
-
-(* notion 4002 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t17 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_negd a0) (l_e_st_eq_landau_n_rt_rp_pnotnd a0 (l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir p)) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir t) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)).
-
-(* notion 4003 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t18 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_zero a0) (l_e_st_eq_landau_n_rt_rp_nnot0d a0 (l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir n)) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_0ex r a0 a0ir t) : l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 4004 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t19 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_ec3_th6 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_ivr1_t16 r a0 a0ir t) (λt:l_e_st_eq_landau_n_rt_rp_r_pos r.l_e_st_eq_landau_n_rt_rp_r_ivr1_t17 r a0 a0ir t) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_ivr1_t18 r a0 a0ir t) : l_ec3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
-
-(* notion 4005 *)
-definition l_e_st_eq_landau_n_rt_rp_r_axrle ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_ec3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t19 r x xi) : l_ec3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
-
-(* notion 4006 *)
-definition l_e_st_eq_landau_n_rt_rp_r_axrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_orec3i (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrlo r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) : l_orec3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
-
-(* notion 4007 *)
-definition l_e_st_eq_landau_n_rt_rp_r_rapp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πt:l_e_st_eq_landau_n_rt_rp_r_pos r.p.λp2:Πt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.p.λp3:Πt:l_e_st_eq_landau_n_rt_rp_r_neg r.p.(l_or3app (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) p (l_e_st_eq_landau_n_rt_rp_r_axrlo r) p2 p1 p3 : p).
-
-(* notion 4008 *)
-definition l_e_st_eq_landau_n_rt_rp_r_pnotn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_ec3e23 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) p : l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)).
-
-(* notion 4009 *)
-definition l_e_st_eq_landau_n_rt_rp_r_pnot0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) p : l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4010 *)
-definition l_e_st_eq_landau_n_rt_rp_r_0notp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_ec3e12 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) i : l_not (l_e_st_eq_landau_n_rt_rp_r_pos r)).
-
-(* notion 4011 *)
-definition l_e_st_eq_landau_n_rt_rp_r_0notn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_ec3e13 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) i : l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)).
-
-(* notion 4012 *)
-definition l_e_st_eq_landau_n_rt_rp_r_nnotp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_ec3e32 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) n : l_not (l_e_st_eq_landau_n_rt_rp_r_pos r)).
-
-(* notion 4013 *)
-definition l_e_st_eq_landau_n_rt_rp_r_nnot0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) n : l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4014 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ispos ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_pos x) r s p i : l_e_st_eq_landau_n_rt_rp_r_pos s).
-
-(* notion 4015 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isneg ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_neg x) r s n i : l_e_st_eq_landau_n_rt_rp_r_neg s).
-
-(* notion 4016 *)
-definition l_e_st_eq_landau_n_rt_rp_r_pofrp ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pdofrp r0) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4017 *)
-definition l_e_st_eq_landau_n_rt_rp_r_nofrp ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_ndofrp r0) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4018 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrpep ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r0 s0.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_pofrp x) r0 s0 i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
-
-(* notion 4019 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrpen ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r0 s0.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_nofrp x) r0 s0 i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_nofrp s0)).
-
-(* notion 4020 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t20 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp s0)) i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0)).
-
-(* notion 4021 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrpip ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_isrpipd r0 s0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t20 r0 s0 i) : l_e_st_eq_landau_n_rt_rp_is r0 s0).
-
-(* notion 4022 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t21 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_nofrp s0).(l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_nofrp s0) (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp s0)) i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp s0)).
-
-(* notion 4023 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrpin ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_nofrp s0).(l_e_st_eq_landau_n_rt_rp_isrpind r0 s0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t21 r0 s0 i) : l_e_st_eq_landau_n_rt_rp_is r0 s0).
-
-(* notion 4024 *)
-definition l_e_st_eq_landau_n_rt_rp_r_posi ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_posdirp r0) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)).
-
-(* notion 4025 *)
-definition l_e_st_eq_landau_n_rt_rp_r_negi ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_negin (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) (l_e_st_eq_landau_n_rt_rp_negdirp r0) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)).
-
-(* notion 4026 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t22 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp r0).λj:l_e_st_eq_landau_n_rt_rp_r_is s (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).λk:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_isrpip r0 s0 (l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) r s (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) i) k j) : l_e_st_eq_landau_n_rt_rp_is r0 s0).
-
-(* notion 4027 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t23 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_cut.λy:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x).λu:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp y).l_e_st_eq_landau_n_rt_rp_r_ivr1_t22 r r x y t u (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r) : l_e_amone l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x))).
-
-(* notion 4028 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t24 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp1:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir p1 : l_e_st_eq_landau_n_rt_rp_posd a0).
-
-(* notion 4029 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_pr ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp1:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_rpofpd a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t24 r a0 a0ir p1) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4030 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t25 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp1:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_isin r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_pr r a0 a0ir p1)) a0 (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_pr r a0 a0ir p1)) a0ir (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_pr r a0 a0ir p1))) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t24 r a0 a0ir p1)) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_pr r a0 a0ir p1))).
-
-(* notion 4031 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t26 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp1:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_somei l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_pr r a0 a0ir p1) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t25 r a0 a0ir p1) : l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x))).
-
-(* notion 4032 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t27 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t26 r x t p) : l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x))).
-
-(* notion 4033 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t28 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_onei l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t23 r) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t27 r p) : l_e_st_eq_landau_n_rt_rp_one (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x))).
-
-(* notion 4034 *)
-definition l_e_st_eq_landau_n_rt_rp_r_rpofp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_ind l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t28 r p) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4035 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isprp1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_oneax l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t28 r p) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p))).
-
-(* notion 4036 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isprp2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) (l_e_st_eq_landau_n_rt_rp_r_isprp1 r p) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) r).
-
-(* notion 4037 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isperp ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λq:l_e_st_eq_landau_n_rt_rp_r_pos s1.λi:l_e_st_eq_landau_n_rt_rp_r_is r1 s1.(l_e_st_eq_landau_n_rt_rp_r_ivr1_t22 r1 s1 (l_e_st_eq_landau_n_rt_rp_r_rpofp r1 p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s1 q) (l_e_st_eq_landau_n_rt_rp_r_isprp1 r1 p) (l_e_st_eq_landau_n_rt_rp_r_isprp1 s1 q) i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofp r1 p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s1 q)).
-
-(* notion 4038 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ispirp ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λq:l_e_st_eq_landau_n_rt_rp_r_pos s1.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofp r1 p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s1 q).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real r1 (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r1 p)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp s1 q)) s1 (l_e_st_eq_landau_n_rt_rp_r_isprp1 r1 p) (l_e_st_eq_landau_n_rt_rp_r_isrpep (l_e_st_eq_landau_n_rt_rp_r_rpofp r1 p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s1 q) i) (l_e_st_eq_landau_n_rt_rp_r_isprp2 s1 q) : l_e_st_eq_landau_n_rt_rp_r_is r1 s1).
-
-(* notion 4039 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrpp1 ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_ivr1_t22 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) r0 (l_e_st_eq_landau_n_rt_rp_r_rpofp (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_posi r0)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_isprp1 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_posi r0)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)) : l_e_st_eq_landau_n_rt_rp_is r0 (l_e_st_eq_landau_n_rt_rp_r_rpofp (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_posi r0))).
-
-(* notion 4040 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrpp2 ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut r0 (l_e_st_eq_landau_n_rt_rp_r_rpofp (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_posi r0)) (l_e_st_eq_landau_n_rt_rp_r_isrpp1 r0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofp (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_posi r0)) r0).
-
-(* notion 4041 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t29 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp r0).λj:l_e_st_eq_landau_n_rt_rp_r_is s (l_e_st_eq_landau_n_rt_rp_r_nofrp s0).λk:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_isrpin r0 s0 (l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) r s (l_e_st_eq_landau_n_rt_rp_r_nofrp s0) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) i) k j) : l_e_st_eq_landau_n_rt_rp_is r0 s0).
-
-(* notion 4042 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t30 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_cut.λy:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x).λu:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp y).l_e_st_eq_landau_n_rt_rp_r_ivr1_t29 r r x y t u (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r) : l_e_amone l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x))).
-
-(* notion 4043 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t31 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn1:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir n1 : l_e_st_eq_landau_n_rt_rp_negd a0).
-
-(* notion 4044 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_nr ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn1:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_rpofnd a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t31 r a0 a0ir n1) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4045 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t32 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn1:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_isin r (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_nr r a0 a0ir n1)) a0 (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_nr r a0 a0ir n1)) a0ir (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_nr r a0 a0ir n1))) (l_e_st_eq_landau_n_rt_rp_eqndrp1 a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t31 r a0 a0ir n1)) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_nr r a0 a0ir n1))).
-
-(* notion 4046 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t33 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn1:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_somei l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_nr r a0 a0ir n1) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t32 r a0 a0ir n1) : l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x))).
-
-(* notion 4047 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t34 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t33 r x t n) : l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x))).
-
-(* notion 4048 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t35 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_onei l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t30 r) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t34 r n) : l_e_st_eq_landau_n_rt_rp_one (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x))).
-
-(* notion 4049 *)
-definition l_e_st_eq_landau_n_rt_rp_r_rpofn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_ind l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t35 r n) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4050 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isnrp1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_oneax l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t35 r n) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_rpofn r n))).
-
-(* notion 4051 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isnrp2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_rpofn r n)) (l_e_st_eq_landau_n_rt_rp_r_isnrp1 r n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_rpofn r n)) r).
-
-(* notion 4052 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isnerp ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_neg s1.λi:l_e_st_eq_landau_n_rt_rp_r_is r1 s1.(l_e_st_eq_landau_n_rt_rp_r_ivr1_t29 r1 s1 (l_e_st_eq_landau_n_rt_rp_r_rpofn r1 n) (l_e_st_eq_landau_n_rt_rp_r_rpofn s1 m) (l_e_st_eq_landau_n_rt_rp_r_isnrp1 r1 n) (l_e_st_eq_landau_n_rt_rp_r_isnrp1 s1 m) i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofn r1 n) (l_e_st_eq_landau_n_rt_rp_r_rpofn s1 m)).
-
-(* notion 4053 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isnirp ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_neg s1.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofn r1 n) (l_e_st_eq_landau_n_rt_rp_r_rpofn s1 m).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real r1 (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_rpofn r1 n)) (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_rpofn s1 m)) s1 (l_e_st_eq_landau_n_rt_rp_r_isnrp1 r1 n) (l_e_st_eq_landau_n_rt_rp_r_isrpen (l_e_st_eq_landau_n_rt_rp_r_rpofn r1 n) (l_e_st_eq_landau_n_rt_rp_r_rpofn s1 m) i) (l_e_st_eq_landau_n_rt_rp_r_isnrp2 s1 m) : l_e_st_eq_landau_n_rt_rp_r_is r1 s1).
-
-(* notion 4054 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrpn1 ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_ivr1_t29 (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) r0 (l_e_st_eq_landau_n_rt_rp_r_rpofn (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_negi r0)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_isnrp1 (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_negi r0)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)) : l_e_st_eq_landau_n_rt_rp_is r0 (l_e_st_eq_landau_n_rt_rp_r_rpofn (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_negi r0))).
-
-(* notion 4055 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrpn2 ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut r0 (l_e_st_eq_landau_n_rt_rp_r_rpofn (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_negi r0)) (l_e_st_eq_landau_n_rt_rp_r_isrpn1 r0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofn (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_negi r0)) r0).
-
-(* notion 4056 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz163 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r : l_e_st_eq_landau_n_rt_rp_r_is r r).
-
-(* notion 4057 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz164 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r s i : l_e_st_eq_landau_n_rt_rp_r_is s r).
-
-(* notion 4058 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz165 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is s t.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real r s t i j : l_e_st_eq_landau_n_rt_rp_r_is r t).
-
-(* notion 4059 *)
-definition l_e_st_eq_landau_n_rt_rp_r_absdr ≝ (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_absd x) : Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4060 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_eqabsd a b e) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_absdr a) (l_e_st_eq_landau_n_rt_rp_r_absdr b)).
-
-(* notion 4061 *)
-definition l_e_st_eq_landau_n_rt_rp_r_fabsdr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.l_e_st_eq_landau_n_rt_rp_r_ivr2_t1 x y t : l_e_st_eq_landau_n_rt_rp_r_fixf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_absdr).
-
-(* notion 4062 *)
-definition l_e_st_eq_landau_n_rt_rp_r_abs ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_indreal l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_absdr l_e_st_eq_landau_n_rt_rp_r_fabsdr r : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4063 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_isindreal l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_absdr l_e_st_eq_landau_n_rt_rp_r_fabsdr r a0 a0ir : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_absd a0)) (l_e_st_eq_landau_n_rt_rp_r_abs r)).
-
-(* notion 4064 *)
-definition l_e_st_eq_landau_n_rt_rp_r_aica ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_class x)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_absd a0)) (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_absd a0)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t2 r a0 a0ir) : l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_abs r))).
-
-(* notion 4065 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isabs ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_abs x) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).
-
-(* notion 4066 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r166_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_satzd166a a0 (l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a0)).
-
-(* notion 4067 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r166_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_2r166_t1 r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)).
-
-(* notion 4068 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz166a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_2r166_t2 r x t p) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)).
-
-(* notion 4069 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r166_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_satzd166b a0 (l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a0)).
-
-(* notion 4070 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r166_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_2r166_t3 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)).
-
-(* notion 4071 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz166b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_2r166_t4 r x t n) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)).
-
-(* notion 4072 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r166_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_satzd166c a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex r a1 a1ir p) (l_e_st_eq_landau_n_rt_rp_r_posex s b1 b1is q) (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is) i) : l_e_st_eq_landau_n_rt_rp_eq a1 b1).
-
-(* notion 4073 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r166_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is (l_e_st_eq_landau_n_rt_rp_r_2r166_t5 r s a1 b1 a1ir b1is p q i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4074 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz166c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_2r166_t6 r s x y t u p q i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4075 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r166_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_satzd166d a1 b1 (l_e_st_eq_landau_n_rt_rp_r_negex r a1 a1ir n) (l_e_st_eq_landau_n_rt_rp_r_negex s b1 b1is o) (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is) i) : l_e_st_eq_landau_n_rt_rp_eq a1 b1).
-
-(* notion 4076 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r166_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is (l_e_st_eq_landau_n_rt_rp_r_2r166_t7 r s a1 b1 a1ir b1is n o i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4077 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz166d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_2r166_t8 r s x y t u n o i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4078 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz166e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_rapp r (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)) (λt:l_e_st_eq_landau_n_rt_rp_r_pos r.l_e_st_eq_landau_n_rt_rp_r_satz166a r t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)) n) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_satz166b r t) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)).
-
-(* notion 4079 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r166_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd166f a0 (l_e_st_eq_landau_n_rt_rp_r_0ex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_absd a0)).
-
-(* notion 4080 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r166_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_2r166_t9 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4081 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz166f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_2r166_t10 r x t i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4082 *)
-definition l_e_st_eq_landau_n_rt_rp_r_more ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (Πy:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored x y))) : Prop).
-
-(* notion 4083 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_propm ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.(l_and3 (l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) : Prop).
-
-(* notion 4084 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_mored a1 b1.(l_and3i (l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) a1ir b1is m : l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a1 b1).
-
-(* notion 4085 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_mored a1 b1.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a1 x) b1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t3 r s a1 b1 a1ir b1is m) : l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a1 x)).
-
-(* notion 4086 *)
-definition l_e_st_eq_landau_n_rt_rp_r_morein ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_mored a1 b1.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s x y)) a1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t4 r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_r_more r s).
-
-(* notion 4087 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a b.(l_and3e1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored a b) p2 : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
-
-(* notion 4088 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a b.(l_and3e2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored a b) p2 : l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)).
-
-(* notion 4089 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a b.(l_and3e3 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored a b) p2 : l_e_st_eq_landau_n_rt_rp_mored a b).
-
-(* notion 4090 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a b.(l_e_st_eq_landau_n_rt_rp_eqmored12 a a1 b b1 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t5 r s a1 b1 a1ir b1is m a sa b p2) a1ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_isex s s b b1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t6 r s a1 b1 a1ir b1is m a sa b p2) b1is (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real s)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t7 r s a1 b1 a1ir b1is m a sa b p2) : l_e_st_eq_landau_n_rt_rp_mored a1 b1).
-
-(* notion 4091 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x).(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x) sa (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x.l_e_st_eq_landau_n_rt_rp_r_ivr2_t8 r s a1 b1 a1ir b1is m a sa x t) : l_e_st_eq_landau_n_rt_rp_mored a1 b1).
-
-(* notion 4092 *)
-definition l_e_st_eq_landau_n_rt_rp_r_moreex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s x y)) m (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_some l_e_st_eq_landau_n_rt_rp_dif (Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s x y).l_e_st_eq_landau_n_rt_rp_r_ivr2_t9 r s a1 b1 a1ir b1is m x t) : l_e_st_eq_landau_n_rt_rp_mored a1 b1).
-
-(* notion 4093 *)
-definition l_e_st_eq_landau_n_rt_rp_r_less ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (Πy:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd x y))) : Prop).
-
-(* notion 4094 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_propl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.(l_and3 (l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) : Prop).
-
-(* notion 4095 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.(l_and3i (l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) a1ir b1is l : l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a1 b1).
-
-(* notion 4096 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a1 x) b1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t10 r s a1 b1 a1ir b1is l) : l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a1 x)).
-
-(* notion 4097 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lessin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s x y)) a1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t11 r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4098 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a b.(l_and3e1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd a b) p2 : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
-
-(* notion 4099 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t13 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a b.(l_and3e2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd a b) p2 : l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)).
-
-(* notion 4100 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t14 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a b.(l_and3e3 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd a b) p2 : l_e_st_eq_landau_n_rt_rp_lessd a b).
-
-(* notion 4101 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t15 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a b.(l_e_st_eq_landau_n_rt_rp_eqlessd12 a a1 b b1 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t12 r s a1 b1 a1ir b1is l a sa b p2) a1ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_isex s s b b1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t13 r s a1 b1 a1ir b1is l a sa b p2) b1is (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real s)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t14 r s a1 b1 a1ir b1is l a sa b p2) : l_e_st_eq_landau_n_rt_rp_lessd a1 b1).
-
-(* notion 4102 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t16 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x).(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x) sa (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x.l_e_st_eq_landau_n_rt_rp_r_ivr2_t15 r s a1 b1 a1ir b1is l a sa x t) : l_e_st_eq_landau_n_rt_rp_lessd a1 b1).
-
-(* notion 4103 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lessex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s x y)) l (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_some l_e_st_eq_landau_n_rt_rp_dif (Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s x y).l_e_st_eq_landau_n_rt_rp_r_ivr2_t16 r s a1 b1 a1ir b1is l x t) : l_e_st_eq_landau_n_rt_rp_lessd a1 b1).
-
-(* notion 4104 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ismore1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_more r t.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x t) r s m i : l_e_st_eq_landau_n_rt_rp_r_more s t).
-
-(* notion 4105 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ismore2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_more t r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more t x) r s m i : l_e_st_eq_landau_n_rt_rp_r_more t s).
-
-(* notion 4106 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isless1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_less r t.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x t) r s l i : l_e_st_eq_landau_n_rt_rp_r_less s t).
-
-(* notion 4107 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isless2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_less t r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less t x) r s l i : l_e_st_eq_landau_n_rt_rp_r_less t s).
-
-(* notion 4108 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ismore12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.λm:l_e_st_eq_landau_n_rt_rp_r_more r t.(l_e_st_eq_landau_n_rt_rp_r_ismore2 t u s j (l_e_st_eq_landau_n_rt_rp_r_ismore1 r s t i m) : l_e_st_eq_landau_n_rt_rp_r_more s u).
-
-(* notion 4109 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isless12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.λl:l_e_st_eq_landau_n_rt_rp_r_less r t.(l_e_st_eq_landau_n_rt_rp_r_isless2 t u s j (l_e_st_eq_landau_n_rt_rp_r_isless1 r s t i l) : l_e_st_eq_landau_n_rt_rp_r_less s u).
-
-(* notion 4110 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t17 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_lemmad5 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_lessd b1 a1).
-
-(* notion 4111 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t18 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_lessin s r b1 a1 b1is a1ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t17 r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_r_less s r).
-
-(* notion 4112 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_less s r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr2_t18 r s x y t u m) : l_e_st_eq_landau_n_rt_rp_r_less s r).
-
-(* notion 4113 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t19 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_lemmad6 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_mored b1 a1).
-
-(* notion 4114 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t20 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_morein s r b1 a1 b1is a1ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t19 r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_r_more s r).
-
-(* notion 4115 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_more s r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr2_t20 r s x y t u l) : l_e_st_eq_landau_n_rt_rp_r_more s r).
-
-(* notion 4116 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r167_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd167a a1 b1 : l_or3 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1)).
-
-(* notion 4117 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r167_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λe:l_e_st_eq_landau_n_rt_rp_eq a1 b1.(l_or3i1 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is e) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
-
-(* notion 4118 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r167_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_mored a1 b1.(l_or3i2 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_morein r s a1 b1 a1ir b1is m) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
-
-(* notion 4119 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r167_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.(l_or3i3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_lessin r s a1 b1 a1ir b1is l) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
-
-(* notion 4120 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r167_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_or3app (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)) (l_e_st_eq_landau_n_rt_rp_r_2r167_t1 r s a1 b1 a1ir b1is) (λt:l_e_st_eq_landau_n_rt_rp_eq a1 b1.l_e_st_eq_landau_n_rt_rp_r_2r167_t2 r s a1 b1 a1ir b1is t) (λt:l_e_st_eq_landau_n_rt_rp_mored a1 b1.l_e_st_eq_landau_n_rt_rp_r_2r167_t3 r s a1 b1 a1ir b1is t) (λt:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.l_e_st_eq_landau_n_rt_rp_r_2r167_t4 r s a1 b1 a1ir b1is t) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
-
-(* notion 4121 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r167_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd167b a1 b1 : l_ec3 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1)).
-
-(* notion 4122 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r167_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_ec3e12 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_2r167_t6 r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is i)) (λt:l_e_st_eq_landau_n_rt_rp_r_more r s.l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is t) : l_not (l_e_st_eq_landau_n_rt_rp_r_more r s)).
-
-(* notion 4123 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r167_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_ec3e23 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_2r167_t6 r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is m)) (λt:l_e_st_eq_landau_n_rt_rp_r_less r s.l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is t) : l_not (l_e_st_eq_landau_n_rt_rp_r_less r s)).
-
-(* notion 4124 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r167_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_ec3e31 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_2r167_t6 r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is l)) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is t) : l_not (l_e_st_eq_landau_n_rt_rp_r_is r s)).
-
-(* notion 4125 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r167_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_ec3_th6 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_ec_th1 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_r_2r167_t7 r s a1 b1 a1ir b1is t)) (l_ec_th1 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (λt:l_e_st_eq_landau_n_rt_rp_r_more r s.l_e_st_eq_landau_n_rt_rp_r_2r167_t8 r s a1 b1 a1ir b1is t)) (l_ec_th1 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (λt:l_e_st_eq_landau_n_rt_rp_r_less r s.l_e_st_eq_landau_n_rt_rp_r_2r167_t9 r s a1 b1 a1ir b1is t)) : l_ec3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
-
-(* notion 4126 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r167_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_orec3i (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_2r167_t5 r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_2r167_t10 r s a1 b1 a1ir b1is) : l_orec3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
-
-(* notion 4127 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz167 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_orec3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_2r167_t11 r s x y t u) : l_orec3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
-
-(* notion 4128 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz167a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_orec3e1 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167 r s) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
-
-(* notion 4129 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz167b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_orec3e2 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167 r s) : l_ec3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
-
-(* notion 4130 *)
-definition l_e_st_eq_landau_n_rt_rp_r_moreis ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_or (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) : Prop).
-
-(* notion 4131 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lessis ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_or (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) : Prop).
-
-(* notion 4132 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz168a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_less s r) (l_e_st_eq_landau_n_rt_rp_r_is s r) m (λt:l_e_st_eq_landau_n_rt_rp_r_more r s.l_e_st_eq_landau_n_rt_rp_r_lemma1 r s t) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r s t) : l_e_st_eq_landau_n_rt_rp_r_lessis s r).
-
-(* notion 4133 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz168b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more s r) (l_e_st_eq_landau_n_rt_rp_r_is s r) l (λt:l_e_st_eq_landau_n_rt_rp_r_less r s.l_e_st_eq_landau_n_rt_rp_r_lemma2 r s t) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r s t) : l_e_st_eq_landau_n_rt_rp_r_moreis s r).
-
-(* notion 4134 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ismoreis1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r t.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x t) r s m i : l_e_st_eq_landau_n_rt_rp_r_moreis s t).
-
-(* notion 4135 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ismoreis2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_moreis t r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis t x) r s m i : l_e_st_eq_landau_n_rt_rp_r_moreis t s).
-
-(* notion 4136 *)
-definition l_e_st_eq_landau_n_rt_rp_r_islessis1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r t.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x t) r s l i : l_e_st_eq_landau_n_rt_rp_r_lessis s t).
-
-(* notion 4137 *)
-definition l_e_st_eq_landau_n_rt_rp_r_islessis2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_lessis t r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis t x) r s l i : l_e_st_eq_landau_n_rt_rp_r_lessis t s).
-
-(* notion 4138 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ismoreis12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r t.(l_e_st_eq_landau_n_rt_rp_r_ismoreis2 t u s j (l_e_st_eq_landau_n_rt_rp_r_ismoreis1 r s t i m) : l_e_st_eq_landau_n_rt_rp_r_moreis s u).
-
-(* notion 4139 *)
-definition l_e_st_eq_landau_n_rt_rp_r_islessis12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r t.(l_e_st_eq_landau_n_rt_rp_r_islessis2 t u s j (l_e_st_eq_landau_n_rt_rp_r_islessis1 r s t i l) : l_e_st_eq_landau_n_rt_rp_r_lessis s u).
-
-(* notion 4140 *)
-definition l_e_st_eq_landau_n_rt_rp_r_moreisi1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) m : l_e_st_eq_landau_n_rt_rp_r_moreis r s).
-
-(* notion 4141 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lessisi1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) l : l_e_st_eq_landau_n_rt_rp_r_lessis r s).
-
-(* notion 4142 *)
-definition l_e_st_eq_landau_n_rt_rp_r_moreisi2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) i : l_e_st_eq_landau_n_rt_rp_r_moreis r s).
-
-(* notion 4143 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lessisi2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) i : l_e_st_eq_landau_n_rt_rp_r_lessis r s).
-
-(* notion 4144 *)
-definition l_e_st_eq_landau_n_rt_rp_r_moreisin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_moreq a1 b1.(l_orapp (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_r_moreis r s) m (λt:l_e_st_eq_landau_n_rt_rp_mored a1 b1.l_e_st_eq_landau_n_rt_rp_r_moreisi1 r s (l_e_st_eq_landau_n_rt_rp_r_morein r s a1 b1 a1ir b1is t)) (λt:l_e_st_eq_landau_n_rt_rp_eq a1 b1.l_e_st_eq_landau_n_rt_rp_r_moreisi2 r s (l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is t)) : l_e_st_eq_landau_n_rt_rp_r_moreis r s).
-
-(* notion 4145 *)
-definition l_e_st_eq_landau_n_rt_rp_r_moreisex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.(l_orapp (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_moreq a1 b1) m (λt:l_e_st_eq_landau_n_rt_rp_r_more r s.l_e_st_eq_landau_n_rt_rp_moreqi1 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is t)) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_moreqi2 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is t)) : l_e_st_eq_landau_n_rt_rp_moreq a1 b1).
-
-(* notion 4146 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lessisin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_lesseq a1 b1.(l_orapp (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_r_lessis r s) l (λt:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.l_e_st_eq_landau_n_rt_rp_r_lessisi1 r s (l_e_st_eq_landau_n_rt_rp_r_lessin r s a1 b1 a1ir b1is t)) (λt:l_e_st_eq_landau_n_rt_rp_eq a1 b1.l_e_st_eq_landau_n_rt_rp_r_lessisi2 r s (l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is t)) : l_e_st_eq_landau_n_rt_rp_r_lessis r s).
-
-(* notion 4147 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lessisex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.(l_orapp (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_lesseq a1 b1) l (λt:l_e_st_eq_landau_n_rt_rp_r_less r s.l_e_st_eq_landau_n_rt_rp_lesseqi1 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is t)) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_lesseqi2 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is t)) : l_e_st_eq_landau_n_rt_rp_lesseq a1 b1).
-
-(* notion 4148 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz167c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.(l_ec3_th7 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167b r s) (l_comor (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) m) : l_not (l_e_st_eq_landau_n_rt_rp_r_less r s)).
-
-(* notion 4149 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz167d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.(l_ec3_th9 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167b r s) l : l_not (l_e_st_eq_landau_n_rt_rp_r_more r s)).
-
-(* notion 4150 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz167e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_more r s).(l_or3_th2 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167a r s) n : l_e_st_eq_landau_n_rt_rp_r_lessis r s).
-
-(* notion 4151 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz167f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_less r s).(l_comor (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_or3_th3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167a r s) n) : l_e_st_eq_landau_n_rt_rp_r_moreis r s).
-
-(* notion 4152 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz167g ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_lessis r s) (l_not (l_e_st_eq_landau_n_rt_rp_r_more r s)) (l_weli (l_e_st_eq_landau_n_rt_rp_r_more r s) m) (λt:l_e_st_eq_landau_n_rt_rp_r_lessis r s.l_e_st_eq_landau_n_rt_rp_r_satz167d r s t) : l_not (l_e_st_eq_landau_n_rt_rp_r_lessis r s)).
-
-(* notion 4153 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz167h ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_moreis r s) (l_not (l_e_st_eq_landau_n_rt_rp_r_less r s)) (l_weli (l_e_st_eq_landau_n_rt_rp_r_less r s) l) (λt:l_e_st_eq_landau_n_rt_rp_r_moreis r s.l_e_st_eq_landau_n_rt_rp_r_satz167c r s t) : l_not (l_e_st_eq_landau_n_rt_rp_r_moreis r s)).
-
-(* notion 4154 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz167j ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_moreis r s).(l_or3e3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167a r s) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) n) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) n) : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4155 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz167k ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_lessis r s).(l_or3e2 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167a r s) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) n) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) n) : l_e_st_eq_landau_n_rt_rp_r_more r s).
-
-(* notion 4156 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r169_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_satzd169a a b (l_e_st_eq_landau_n_rt_rp_r_0ex l_e_st_eq_landau_n_rt_rp_r_0 b bi0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_posex r a air p) : l_e_st_eq_landau_n_rt_rp_mored a b).
-
-(* notion 4157 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r169_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_r_morein r l_e_st_eq_landau_n_rt_rp_r_0 a b air bi0 (l_e_st_eq_landau_n_rt_rp_r_2r169_t1 r p a b air bi0) : l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4158 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz169a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).l_e_st_eq_landau_n_rt_rp_r_2r169_t2 r p x y t u) : l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4159 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r169_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_satzd169b a b (l_e_st_eq_landau_n_rt_rp_r_0ex l_e_st_eq_landau_n_rt_rp_r_0 b bi0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_moreex r l_e_st_eq_landau_n_rt_rp_r_0 a b air bi0 m) : l_e_st_eq_landau_n_rt_rp_posd a).
-
-(* notion 4160 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r169_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_r_posin r a air (l_e_st_eq_landau_n_rt_rp_r_2r169_t3 r m a b air bi0) : l_e_st_eq_landau_n_rt_rp_r_pos r).
-
-(* notion 4161 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz169b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pos r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).l_e_st_eq_landau_n_rt_rp_r_2r169_t4 r m x y t u) : l_e_st_eq_landau_n_rt_rp_r_pos r).
-
-(* notion 4162 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r169_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_satzd169c a b (l_e_st_eq_landau_n_rt_rp_r_0ex l_e_st_eq_landau_n_rt_rp_r_0 b bi0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_negex r a air n) : l_e_st_eq_landau_n_rt_rp_lessd a b).
-
-(* notion 4163 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r169_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_r_lessin r l_e_st_eq_landau_n_rt_rp_r_0 a b air bi0 (l_e_st_eq_landau_n_rt_rp_r_2r169_t5 r n a b air bi0) : l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4164 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz169c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).l_e_st_eq_landau_n_rt_rp_r_2r169_t6 r n x y t u) : l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4165 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r169_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_satzd169d a b (l_e_st_eq_landau_n_rt_rp_r_0ex l_e_st_eq_landau_n_rt_rp_r_0 b bi0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_lessex r l_e_st_eq_landau_n_rt_rp_r_0 a b air bi0 l) : l_e_st_eq_landau_n_rt_rp_negd a).
-
-(* notion 4166 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r169_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_r_negin r a air (l_e_st_eq_landau_n_rt_rp_r_2r169_t7 r l a b air bi0) : l_e_st_eq_landau_n_rt_rp_r_neg r).
-
-(* notion 4167 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz169d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_neg r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).l_e_st_eq_landau_n_rt_rp_r_2r169_t8 r l x y t u) : l_e_st_eq_landau_n_rt_rp_r_neg r).
-
-(* notion 4168 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r170_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_satzd170 a b (l_e_st_eq_landau_n_rt_rp_r_0ex l_e_st_eq_landau_n_rt_rp_r_0 b bi0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b).
-
-(* notion 4169 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r170_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_r_moreisin (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_absd a) b (l_e_st_eq_landau_n_rt_rp_r_aica r a air) bi0 (l_e_st_eq_landau_n_rt_rp_r_2r170_t1 r a b air bi0) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4170 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz170 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).l_e_st_eq_landau_n_rt_rp_r_2r170_t2 r x y t u) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4171 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz170a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_abs r)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz167c (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz170 r)) (λt:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_abs r).l_e_st_eq_landau_n_rt_rp_r_satz169c (l_e_st_eq_landau_n_rt_rp_r_abs r) t) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_abs r))).
-
-(* notion 4172 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r171_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbis:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s).λcit:l_e_st_eq_landau_n_rt_rp_r_inn c (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_satzd171 a b c (l_e_st_eq_landau_n_rt_rp_r_lessex r s a b air bis l) (l_e_st_eq_landau_n_rt_rp_r_lessex s t b c bis cit k) : l_e_st_eq_landau_n_rt_rp_lessd a c).
-
-(* notion 4173 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r171_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbis:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s).λcit:l_e_st_eq_landau_n_rt_rp_r_inn c (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_r_lessin r t a c air cit (l_e_st_eq_landau_n_rt_rp_r_2r171_t1 r s t l k a b c air bis cit) : l_e_st_eq_landau_n_rt_rp_r_less r t).
-
-(* notion 4174 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz171 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less r t) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λw:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λv:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_2r171_t2 r s t l k x y z w u v) : l_e_st_eq_landau_n_rt_rp_r_less r t).
-
-(* notion 4175 *)
-definition l_e_st_eq_landau_n_rt_rp_r_trless ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.(l_e_st_eq_landau_n_rt_rp_r_satz171 r s t l k : l_e_st_eq_landau_n_rt_rp_r_less r t).
-
-(* notion 4176 *)
-definition l_e_st_eq_landau_n_rt_rp_r_trmore ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_more s t.(l_e_st_eq_landau_n_rt_rp_r_lemma2 t r (l_e_st_eq_landau_n_rt_rp_r_trless t s r (l_e_st_eq_landau_n_rt_rp_r_lemma1 s t n) (l_e_st_eq_landau_n_rt_rp_r_lemma1 r s m)) : l_e_st_eq_landau_n_rt_rp_r_more r t).
-
-(* notion 4177 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r172_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.(l_e_st_eq_landau_n_rt_rp_satzd172a a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_lessisex r s a2 b2 a2ir b2is l) (l_e_st_eq_landau_n_rt_rp_r_lessex s t b2 c2 b2is c2it k) : l_e_st_eq_landau_n_rt_rp_lessd a2 c2).
-
-(* notion 4178 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r172_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.(l_e_st_eq_landau_n_rt_rp_r_lessin r t a2 c2 a2ir c2it (l_e_st_eq_landau_n_rt_rp_r_2r172_t1 r s t a2 b2 c2 a2ir b2is c2it l k) : l_e_st_eq_landau_n_rt_rp_r_less r t).
-
-(* notion 4179 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz172a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less r t) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_2r172_t2 r s t x y z u v w l k) : l_e_st_eq_landau_n_rt_rp_r_less r t).
-
-(* notion 4180 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r172_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_satzd172b a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a2 b2 a2ir b2is l) (l_e_st_eq_landau_n_rt_rp_r_lessisex s t b2 c2 b2is c2it k) : l_e_st_eq_landau_n_rt_rp_lessd a2 c2).
-
-(* notion 4181 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r172_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_r_lessin r t a2 c2 a2ir c2it (l_e_st_eq_landau_n_rt_rp_r_2r172_t3 r s t a2 b2 c2 a2ir b2is c2it l k) : l_e_st_eq_landau_n_rt_rp_r_less r t).
-
-(* notion 4182 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz172b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less r t) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_2r172_t4 r s t x y z u v w l k) : l_e_st_eq_landau_n_rt_rp_r_less r t).
-
-(* notion 4183 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz172c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_more s t.(l_e_st_eq_landau_n_rt_rp_r_lemma2 t r (l_e_st_eq_landau_n_rt_rp_r_satz172b t s r (l_e_st_eq_landau_n_rt_rp_r_lemma1 s t n) (l_e_st_eq_landau_n_rt_rp_r_satz168a r s m)) : l_e_st_eq_landau_n_rt_rp_r_more r t).
-
-(* notion 4184 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz172d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis s t.(l_e_st_eq_landau_n_rt_rp_r_lemma2 t r (l_e_st_eq_landau_n_rt_rp_r_satz172a t s r (l_e_st_eq_landau_n_rt_rp_r_satz168a s t n) (l_e_st_eq_landau_n_rt_rp_r_lemma1 r s m)) : l_e_st_eq_landau_n_rt_rp_r_more r t).
-
-(* notion 4185 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r173_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_satzd173 a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_lessisex r s a2 b2 a2ir b2is l) (l_e_st_eq_landau_n_rt_rp_r_lessisex s t b2 c2 b2is c2it k) : l_e_st_eq_landau_n_rt_rp_lesseq a2 c2).
-
-(* notion 4186 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r173_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_r_lessisin r t a2 c2 a2ir c2it (l_e_st_eq_landau_n_rt_rp_r_2r173_t1 r s t a2 b2 c2 a2ir b2is c2it l k) : l_e_st_eq_landau_n_rt_rp_r_lessis r t).
-
-(* notion 4187 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz173 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_lessis r t) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_2r173_t2 r s t x y z u v w l k) : l_e_st_eq_landau_n_rt_rp_r_lessis r t).
-
-(* notion 4188 *)
-definition l_e_st_eq_landau_n_rt_rp_r_trlessis ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_r_satz173 r s t l k : l_e_st_eq_landau_n_rt_rp_r_lessis r t).
-
-(* notion 4189 *)
-definition l_e_st_eq_landau_n_rt_rp_r_trmoreis ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis s t.(l_e_st_eq_landau_n_rt_rp_r_satz168b t r (l_e_st_eq_landau_n_rt_rp_r_trlessis t s r (l_e_st_eq_landau_n_rt_rp_r_satz168a s t n) (l_e_st_eq_landau_n_rt_rp_r_satz168a r s m)) : l_e_st_eq_landau_n_rt_rp_r_moreis r t).
-
-(* notion 4190 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ratrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd x)) : Prop).
-
-(* notion 4191 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t21 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λr1:l_e_st_eq_landau_n_rt_rp_ratd a0.(l_andi (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a0) a0ir r1 : l_and (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a0)).
-
-(* notion 4192 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ratrlin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λr1:l_e_st_eq_landau_n_rt_rp_ratd a0.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd x)) a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t21 r a0 a0ir r1) : l_e_st_eq_landau_n_rt_rp_r_ratrl r).
-
-(* notion 4193 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t22 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λrr:l_e_st_eq_landau_n_rt_rp_r_ratrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a) b : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
-
-(* notion 4194 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t23 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λrr:l_e_st_eq_landau_n_rt_rp_r_ratrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a) b : l_e_st_eq_landau_n_rt_rp_ratd a).
-
-(* notion 4195 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t24 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λrr:l_e_st_eq_landau_n_rt_rp_r_ratrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a).(l_e_st_eq_landau_n_rt_rp_eqratd a a0 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t22 r a0 a0ir rr a b) a0ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t23 r a0 a0ir rr a b) : l_e_st_eq_landau_n_rt_rp_ratd a0).
-
-(* notion 4196 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ratrlex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λrr:l_e_st_eq_landau_n_rt_rp_r_ratrl r.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd x)) rr (l_e_st_eq_landau_n_rt_rp_ratd a0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd x).l_e_st_eq_landau_n_rt_rp_r_ivr2_t24 r a0 a0ir rr x t) : l_e_st_eq_landau_n_rt_rp_ratd a0).
-
-(* notion 4197 *)
-definition l_e_st_eq_landau_n_rt_rp_r_irratrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_not (l_e_st_eq_landau_n_rt_rp_r_ratrl r) : Prop).
-
-(* notion 4198 *)
-definition l_e_st_eq_landau_n_rt_rp_r_remark2 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r0.(l_e_st_eq_landau_n_rt_rp_r_ratrlin (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark2a r0 rr) : l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)).
-
-(* notion 4199 *)
-definition l_e_st_eq_landau_n_rt_rp_r_remark3 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r0.(l_e_st_eq_landau_n_rt_rp_r_ratrlin (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark3a r0 rr) : l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)).
-
-(* notion 4200 *)
-definition l_e_st_eq_landau_n_rt_rp_r_remark4 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λir:l_e_st_eq_landau_n_rt_rp_irratrp r0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)) (l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark4a r0 ir) (λt:l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0).l_e_st_eq_landau_n_rt_rp_r_ratrlex (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) t) : l_e_st_eq_landau_n_rt_rp_r_irratrl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)).
-
-(* notion 4201 *)
-definition l_e_st_eq_landau_n_rt_rp_r_remark5 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λir:l_e_st_eq_landau_n_rt_rp_irratrp r0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)) (l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark5a r0 ir) (λt:l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_nofrp r0).l_e_st_eq_landau_n_rt_rp_r_ratrlex (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) t) : l_e_st_eq_landau_n_rt_rp_r_irratrl (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)).
-
-(* notion 4202 *)
-definition l_e_st_eq_landau_n_rt_rp_r_natrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd x)) : Prop).
-
-(* notion 4203 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t25 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_natd a0.(l_andi (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a0) a0ir n : l_and (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a0)).
-
-(* notion 4204 *)
-definition l_e_st_eq_landau_n_rt_rp_r_natrlin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_natd a0.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd x)) a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t25 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_natrl r).
-
-(* notion 4205 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t26 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a) b : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
-
-(* notion 4206 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t27 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a) b : l_e_st_eq_landau_n_rt_rp_natd a).
-
-(* notion 4207 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t28 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a).(l_e_st_eq_landau_n_rt_rp_eqnatd a a0 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t26 r a0 a0ir n a b) a0ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t27 r a0 a0ir n a b) : l_e_st_eq_landau_n_rt_rp_natd a0).
-
-(* notion 4208 *)
-definition l_e_st_eq_landau_n_rt_rp_r_natrlex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd x)) n (l_e_st_eq_landau_n_rt_rp_natd a0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd x).l_e_st_eq_landau_n_rt_rp_r_ivr2_t28 r a0 a0ir n x t) : l_e_st_eq_landau_n_rt_rp_natd a0).
-
-(* notion 4209 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t29 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_natposd a0 (l_e_st_eq_landau_n_rt_rp_r_natrlex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_posd a0).
-
-(* notion 4210 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t30 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_posin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t29 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_pos r).
-
-(* notion 4211 *)
-definition l_e_st_eq_landau_n_rt_rp_r_natpos ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_pos r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr2_t30 r x t n) : l_e_st_eq_landau_n_rt_rp_r_pos r).
-
-(* notion 4212 *)
-definition l_e_st_eq_landau_n_rt_rp_r_rlofnt ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pdofnt x) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4213 *)
-definition l_e_st_eq_landau_n_rt_rp_r_natrli ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_natrlin (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_pdofnt x) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofnt x)) (l_e_st_eq_landau_n_rt_rp_natdi x) : l_e_st_eq_landau_n_rt_rp_r_natrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x)).
-
-(* notion 4214 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isnterl ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) x y i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)).
-
-(* notion 4215 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isntirl ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).(l_e_st_eq_landau_n_rt_rp_isntirp x y (l_e_st_eq_landau_n_rt_rp_r_isrpip (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) i) : l_e_st_eq_landau_n_is x y).
-
-(* notion 4216 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 ≝ (λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).l_e_st_eq_landau_n_rt_rp_r_isntirl x y t : l_e_injective l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x)).
-
-(* notion 4217 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t32 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_natposd a0 (l_e_st_eq_landau_n_rt_rp_r_natrlex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_posd a0).
-
-(* notion 4218 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_ap ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_rpofpd a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t32 r a0 a0ir n) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4219 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t33 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_natderp a0 (l_e_st_eq_landau_n_rt_rp_r_natrlex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n)).
-
-(* notion 4220 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t33 r a0 a0ir n) : l_e_st_eq_landau_n_nat).
-
-(* notion 4221 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t34 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_isrpepd (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n)) (l_e_st_eq_landau_n_rt_rp_isrpnt1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t33 r a0 a0ir n)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n)) (l_e_st_eq_landau_n_rt_rp_pdofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n))).
-
-(* notion 4222 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t35 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_treq a0 (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n)) (l_e_st_eq_landau_n_rt_rp_pdofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t32 r a0 a0ir n)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t34 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_pdofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n))).
-
-(* notion 4223 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t36 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_isin r (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n)) a0 (l_e_st_eq_landau_n_rt_rp_pdofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n)) a0ir (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n))) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t35 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n))).
-
-(* notion 4224 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t37 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_somei l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt x)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t36 r a0 a0ir n) : l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r).
-
-(* notion 4225 *)
-definition l_e_st_eq_landau_n_rt_rp_r_natimage ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr2_t37 r x t n) : l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r).
-
-(* notion 4226 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t38 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r.λx:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt x).(l_e_isp1 l_e_st_eq_landau_n_rt_rp_r_real (Πu:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_natrl u) (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r (l_e_st_eq_landau_n_rt_rp_r_natrli x) j : l_e_st_eq_landau_n_rt_rp_r_natrl r).
-
-(* notion 4227 *)
-definition l_e_st_eq_landau_n_rt_rp_r_imagenat ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt u)) i (l_e_st_eq_landau_n_rt_rp_r_natrl r) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt u).l_e_st_eq_landau_n_rt_rp_r_ivr2_t38 r i u v) : l_e_st_eq_landau_n_rt_rp_r_natrl r).
-
-(* notion 4228 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ntofrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_soft l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 r (l_e_st_eq_landau_n_rt_rp_r_natimage r n) : l_e_st_eq_landau_n_nat).
-
-(* notion 4229 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrlent ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_natrl s1.λi:l_e_st_eq_landau_n_rt_rp_r_is r1 s1.(l_e_isinv l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 r1 (l_e_st_eq_landau_n_rt_rp_r_natimage r1 n) s1 (l_e_st_eq_landau_n_rt_rp_r_natimage s1 m) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_ntofrl r1 n) (l_e_st_eq_landau_n_rt_rp_r_ntofrl s1 m)).
-
-(* notion 4230 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrlint ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_natrl s1.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_ntofrl r1 n) (l_e_st_eq_landau_n_rt_rp_r_ntofrl s1 m).(l_e_isinve l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 r1 (l_e_st_eq_landau_n_rt_rp_r_natimage r1 n) s1 (l_e_st_eq_landau_n_rt_rp_r_natimage s1 m) i : l_e_st_eq_landau_n_rt_rp_r_is r1 s1).
-
-(* notion 4231 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrlnt1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_ists1 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 r (l_e_st_eq_landau_n_rt_rp_r_natimage r n) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n))).
-
-(* notion 4232 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isrlnt2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 r n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n)) r).
-
-(* notion 4233 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_xn ≝ λx:l_e_st_eq_landau_n_nat.(l_e_soft l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_imagei l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) x) : l_e_st_eq_landau_n_nat).
-
-(* notion 4234 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t39 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_isinv l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_imagei l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natimage (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt x)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_ivr2_xn x) (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x))).
-
-(* notion 4235 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isntrl1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_rp_r_ivr2_xn x) (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x)) (l_e_isst1 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (Πu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 x) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t39 x) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x))).
-
-(* notion 4236 *)
-definition l_e_st_eq_landau_n_rt_rp_r_isntrl2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x)) (l_e_st_eq_landau_n_rt_rp_r_isntrl1 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x)) x).
-
-(* notion 4237 *)
-definition l_e_st_eq_landau_n_rt_rp_r_intrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd x)) : Prop).
-
-(* notion 4238 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t40 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_intd a0.(l_andi (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a0) a0ir i : l_and (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a0)).
-
-(* notion 4239 *)
-definition l_e_st_eq_landau_n_rt_rp_r_intrlin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_intd a0.(l_somei l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd x)) a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t40 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_intrl r).
-
-(* notion 4240 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t41 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a) b : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
-
-(* notion 4241 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t42 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a) b : l_e_st_eq_landau_n_rt_rp_intd a).
-
-(* notion 4242 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t43 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a).(l_e_st_eq_landau_n_rt_rp_eqintd a a0 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t41 r a0 a0ir i a b) a0ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t42 r a0 a0ir i a b) : l_e_st_eq_landau_n_rt_rp_intd a0).
-
-(* notion 4243 *)
-definition l_e_st_eq_landau_n_rt_rp_r_intrlex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd x)) i (l_e_st_eq_landau_n_rt_rp_intd a0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd x).l_e_st_eq_landau_n_rt_rp_r_ivr2_t43 r a0 a0ir i x t) : l_e_st_eq_landau_n_rt_rp_intd a0).
-
-(* notion 4244 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t44 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_natintd a0 (l_e_st_eq_landau_n_rt_rp_r_natrlex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_intd a0).
-
-(* notion 4245 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t45 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_intrlin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t44 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_intrl r).
-
-(* notion 4246 *)
-definition l_e_st_eq_landau_n_rt_rp_r_natintrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_intrl r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr2_t45 r x t n) : l_e_st_eq_landau_n_rt_rp_r_intrl r).
-
-(* notion 4247 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t46 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_posintnatd a0 (l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir p) (l_e_st_eq_landau_n_rt_rp_r_intrlex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_natd a0).
-
-(* notion 4248 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t47 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_natrlin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t46 r a0 a0ir p i) : l_e_st_eq_landau_n_rt_rp_r_natrl r).
-
-(* notion 4249 *)
-definition l_e_st_eq_landau_n_rt_rp_r_posintnatrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_natrl r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr2_t47 r x t p i) : l_e_st_eq_landau_n_rt_rp_r_natrl r).
-
-(* notion 4250 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t48 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi2:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_intdi0 a0 (l_e_st_eq_landau_n_rt_rp_r_0ex r a0 a0ir i2) : l_e_st_eq_landau_n_rt_rp_intd a0).
-
-(* notion 4251 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t49 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi2:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_intrlin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t48 r a0 a0ir i2) : l_e_st_eq_landau_n_rt_rp_r_intrl r).
-
-(* notion 4252 *)
-definition l_e_st_eq_landau_n_rt_rp_r_intrli0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_intrl r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr2_t49 r x t i) : l_e_st_eq_landau_n_rt_rp_r_intrl r).
-
-(* notion 4253 *)
-definition l_e_st_eq_landau_n_rt_rp_r_remark6 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r0.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark6 r0 n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)).
-
-(* notion 4254 *)
-definition l_e_st_eq_landau_n_rt_rp_r_remark7 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r0.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark7 r0 n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)).
-
-(* notion 4255 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r174_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_satzd174 a0 (l_e_st_eq_landau_n_rt_rp_r_intrlex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_ratd a0).
-
-(* notion 4256 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2r174_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_ratrlin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_2r174_t1 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_ratrl r).
-
-(* notion 4257 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz174 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_ratrl r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_2r174_t2 r x t i) : l_e_st_eq_landau_n_rt_rp_r_ratrl r).
-
-(* notion 4258 *)
-definition l_e_st_eq_landau_n_rt_rp_r_plusdr ≝ (Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pd x y) : Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4259 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pd a c)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pd b d)) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pd a c)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pd b d)) (l_e_st_eq_landau_n_rt_rp_eqpd12 a b c d e f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_plusdr a c) (l_e_st_eq_landau_n_rt_rp_r_plusdr b d)).
-
-(* notion 4260 *)
-definition l_e_st_eq_landau_n_rt_rp_r_fplusdr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.λu:l_e_st_eq_landau_n_rt_rp_r_eq z v.l_e_st_eq_landau_n_rt_rp_r_ivr3_t1 x y z v t u : l_e_st_eq_landau_n_rt_rp_r_fixf2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_plusdr).
-
-(* notion 4261 *)
-definition l_e_st_eq_landau_n_rt_rp_r_pl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_indreal2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_plusdr l_e_st_eq_landau_n_rt_rp_r_fplusdr r s : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4262 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isindreal2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_plusdr l_e_st_eq_landau_n_rt_rp_r_fplusdr r s a1 b1 a1ir b1is : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pd a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
-
-(* notion 4263 *)
-definition l_e_st_eq_landau_n_rt_rp_r_picp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_class x)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pd a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pd a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_ivr3_t2 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_pl r s))).
-
-(* notion 4264 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ispl1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_pl x t) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
-
-(* notion 4265 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ispl2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_pl t x) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s)).
-
-(* notion 4266 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ispl12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_ispl1 r s t i) (l_e_st_eq_landau_n_rt_rp_r_ispl2 t u s j) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4267 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r175_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd175 a1 b1 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_pd b1 a1)).
-
-(* notion 4268 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r175_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r) (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_pd b1 a1) (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_picp s r b1 a1 b1is a1ir) (l_e_st_eq_landau_n_rt_rp_r_3r175_t1 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r)).
-
-(* notion 4269 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz175 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r175_t2 r s x y t u) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r)).
-
-(* notion 4270 *)
-definition l_e_st_eq_landau_n_rt_rp_r_compl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz175 r s : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r)).
-
-(* notion 4271 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_pd01 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_0ex r a1 a1ir i) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a1 b1) b1).
-
-(* notion 4272 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_pl r s) s (l_e_st_eq_landau_n_rt_rp_pd a1 b1) b1 (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is) b1is (l_e_st_eq_landau_n_rt_rp_r_ivr3_t3 r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) s).
-
-(* notion 4273 *)
-definition l_e_st_eq_landau_n_rt_rp_r_pl01 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr3_t4 r s x y t u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) s).
-
-(* notion 4274 *)
-definition l_e_st_eq_landau_n_rt_rp_r_pl02 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r) r (l_e_st_eq_landau_n_rt_rp_r_compl r s) (l_e_st_eq_landau_n_rt_rp_r_pl01 s r i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) r).
-
-(* notion 4275 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_ppd a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex r a1 a1ir p) (l_e_st_eq_landau_n_rt_rp_r_posex s b1 b1is q) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a1 b1)).
-
-(* notion 4276 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_ivr3_t5 r s a1 b1 a1ir b1is p q) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
-
-(* notion 4277 *)
-definition l_e_st_eq_landau_n_rt_rp_r_pospl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr3_t6 r s x y t u p q) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
-
-(* notion 4278 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_npd a1 b1 (l_e_st_eq_landau_n_rt_rp_r_negex r a1 a1ir n) (l_e_st_eq_landau_n_rt_rp_r_negex s b1 b1is o) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a1 b1)).
-
-(* notion 4279 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_negin (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_ivr3_t7 r s a1 b1 a1ir b1is n o) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
-
-(* notion 4280 *)
-definition l_e_st_eq_landau_n_rt_rp_r_negpl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr3_t8 r s x y t u n o) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
-
-(* notion 4281 *)
-definition l_e_st_eq_landau_n_rt_rp_r_m0dr ≝ (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_m0d x) : Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4282 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t5a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_eqm0d a b e) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0dr a) (l_e_st_eq_landau_n_rt_rp_r_m0dr b)).
-
-(* notion 4283 *)
-definition l_e_st_eq_landau_n_rt_rp_r_fm0dr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.l_e_st_eq_landau_n_rt_rp_r_ivr3_t5a x y t : l_e_st_eq_landau_n_rt_rp_r_fixf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_m0dr).
-
-(* notion 4284 *)
-definition l_e_st_eq_landau_n_rt_rp_r_m0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_indreal l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_m0dr l_e_st_eq_landau_n_rt_rp_r_fm0dr r : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4285 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t6a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_isindreal l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_m0dr l_e_st_eq_landau_n_rt_rp_r_fm0dr r a0 a0ir : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_m0d a0)) (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4286 *)
-definition l_e_st_eq_landau_n_rt_rp_r_micm0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_class x)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_m0d a0)) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_m0d a0)) (l_e_st_eq_landau_n_rt_rp_r_ivr3_t6a r a0 a0ir) : l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_m0 r))).
-
-(* notion 4287 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ism0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_m0 x) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
-
-(* notion 4288 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t7a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_absnd a0 (l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_m0d a0)).
-
-(* notion 4289 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t8a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_ivr3_t7a r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4290 *)
-definition l_e_st_eq_landau_n_rt_rp_r_absn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr3_t8a r x t n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4291 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λnn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).(l_e_st_eq_landau_n_rt_rp_absnnd a0 (l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd a0) (l_e_st_eq_landau_n_rt_rp_r_neg r) nn (λt:l_e_st_eq_landau_n_rt_rp_negd a0.l_e_st_eq_landau_n_rt_rp_r_negin r a0 a0ir t)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a0) a0).
-
-(* notion 4292 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λnn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_abs r) r (l_e_st_eq_landau_n_rt_rp_absd a0) a0 (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) a0ir (l_e_st_eq_landau_n_rt_rp_r_ivr3_t9 r a0 a0ir nn) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r).
-
-(* notion 4293 *)
-definition l_e_st_eq_landau_n_rt_rp_r_absnn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λnn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr3_t10 r x t nn) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r).
-
-(* notion 4294 *)
-definition l_e_st_eq_landau_n_rt_rp_r_absp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_absnn r (l_e_st_eq_landau_n_rt_rp_r_pnotn r p) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r).
-
-(* notion 4295 *)
-definition l_e_st_eq_landau_n_rt_rp_r_abs0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs r) r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_absnn r (l_e_st_eq_landau_n_rt_rp_r_0notn r i)) i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4296 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_satzd176a a0 (l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_m0d a0)).
-
-(* notion 4297 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_negin (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_3r176_t1 r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4298 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz176a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t2 r x t p) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4299 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd176b a0 (l_e_st_eq_landau_n_rt_rp_r_0ex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_m0d a0)).
-
-(* notion 4300 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_3r176_t3 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4301 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz176b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t4 r x t i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4302 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_satzd176c a0 (l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d a0)).
-
-(* notion 4303 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_3r176_t5 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4304 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz176c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t6 r x t n) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4305 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_satzd176d a0 (l_e_st_eq_landau_n_rt_rp_r_negex (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) n) : l_e_st_eq_landau_n_rt_rp_posd a0).
-
-(* notion 4306 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_posin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_3r176_t7 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_pos r).
-
-(* notion 4307 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz176d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_pos r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t8 r x t n) : l_e_st_eq_landau_n_rt_rp_r_pos r).
-
-(* notion 4308 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd176e a0 (l_e_st_eq_landau_n_rt_rp_r_0ex (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) i) : l_e_st_eq_landau_n_rt_rp_zero a0).
-
-(* notion 4309 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_0in r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_3r176_t9 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4310 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz176e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t10 r x t i) : l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4311 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_satzd176f a0 (l_e_st_eq_landau_n_rt_rp_r_posex (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) p) : l_e_st_eq_landau_n_rt_rp_negd a0).
-
-(* notion 4312 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r176_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_negin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_3r176_t11 r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_r_neg r).
-
-(* notion 4313 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz176f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_neg r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t12 r x t p) : l_e_st_eq_landau_n_rt_rp_r_neg r).
-
-(* notion 4314 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r177_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a0)) a0 (l_e_st_eq_landau_n_rt_rp_r_micm0 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir)) a0ir (l_e_st_eq_landau_n_rt_rp_satzd177 a0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r).
-
-(* notion 4315 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz177 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r177_t1 r x t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r).
-
-(* notion 4316 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz177a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_r_satz177 r) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r))).
-
-(* notion 4317 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz177b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_ism0 r (l_e_st_eq_landau_n_rt_rp_r_m0 s) i) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) s).
-
-(* notion 4318 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz177c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 r) s (l_e_st_eq_landau_n_rt_rp_r_satz177b r s i) : l_e_st_eq_landau_n_rt_rp_r_is s (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4319 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz177d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) s.(l_e_st_eq_landau_n_rt_rp_r_satz177c s r (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 r) s i) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
-
-(* notion 4320 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz177e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) s.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_satz177d r s i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 s) r).
-
-(* notion 4321 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r178_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a0)) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_aica (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir)) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_satzd178 a0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_abs r)).
-
-(* notion 4322 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz178 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_abs r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r178_t1 r x t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_abs r)).
-
-(* notion 4323 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz178a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_satz178 r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r))).
-
-(* notion 4324 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r179_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_pd a0 (l_e_st_eq_landau_n_rt_rp_m0d a0)) (l_e_st_eq_landau_n_rt_rp_r_picp r (l_e_st_eq_landau_n_rt_rp_r_m0 r) a0 (l_e_st_eq_landau_n_rt_rp_m0d a0) a0ir (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir)) (l_e_st_eq_landau_n_rt_rp_satzd179 a0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 r)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4325 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz179 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 r)) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r179_t1 r x t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 r)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4326 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz179a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) r) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 r)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_m0 r) r) (l_e_st_eq_landau_n_rt_rp_r_satz179 r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) r) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4327 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r180_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a1 b1)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1)) (l_e_st_eq_landau_n_rt_rp_r_micm0 (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is)) (l_e_st_eq_landau_n_rt_rp_r_picp (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_micm0 s b1 b1is)) (l_e_st_eq_landau_n_rt_rp_satzd180 a1 b1) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s))).
-
-(* notion 4328 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz180 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r180_t1 r s x y t u) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s))).
-
-(* notion 4329 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz180a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_satz180 r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s))).
-
-(* notion 4330 *)
-definition l_e_st_eq_landau_n_rt_rp_r_mn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 s) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4331 *)
-definition l_e_st_eq_landau_n_rt_rp_r_micmn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_picp r (l_e_st_eq_landau_n_rt_rp_r_m0 s) a1 (l_e_st_eq_landau_n_rt_rp_m0d b1) a1ir (l_e_st_eq_landau_n_rt_rp_r_micm0 s b1 b1is) : l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_mn r s))).
-
-(* notion 4332 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ismn1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_ispl1 r s (l_e_st_eq_landau_n_rt_rp_r_m0 t) i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r t) (l_e_st_eq_landau_n_rt_rp_r_mn s t)).
-
-(* notion 4333 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ismn2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) t (l_e_st_eq_landau_n_rt_rp_r_ism0 r s i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn t r) (l_e_st_eq_landau_n_rt_rp_r_mn t s)).
-
-(* notion 4334 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ismn12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.(l_e_st_eq_landau_n_rt_rp_r_ispl12 r s (l_e_st_eq_landau_n_rt_rp_r_m0 t) (l_e_st_eq_landau_n_rt_rp_r_m0 u) i (l_e_st_eq_landau_n_rt_rp_r_ism0 t u j) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r t) (l_e_st_eq_landau_n_rt_rp_r_mn s u)).
-
-(* notion 4335 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz181 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_mn s r) (l_e_st_eq_landau_n_rt_rp_r_satz180 r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_satz177 s)) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (l_e_st_eq_landau_n_rt_rp_r_mn s r)).
-
-(* notion 4336 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz181a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn s r)) (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_satz181 s r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn s r))).
-
-(* notion 4337 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_satzd182a a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) p) : l_e_st_eq_landau_n_rt_rp_mored a1 b1).
-
-(* notion 4338 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_r_morein r s a1 b1 a1ir b1is (l_e_st_eq_landau_n_rt_rp_r_3r182_t1 r s a1 b1 a1ir b1is p) : l_e_st_eq_landau_n_rt_rp_r_more r s).
-
-(* notion 4339 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz182a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_more r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t2 r s x y t u p) : l_e_st_eq_landau_n_rt_rp_r_more r s).
-
-(* notion 4340 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd182b a1 b1 (l_e_st_eq_landau_n_rt_rp_r_0ex (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) i) : l_e_st_eq_landau_n_rt_rp_eq a1 b1).
-
-(* notion 4341 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is (l_e_st_eq_landau_n_rt_rp_r_3r182_t3 r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4342 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz182b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t4 r s x y t u i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4343 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_satzd182c a1 b1 (l_e_st_eq_landau_n_rt_rp_r_negex (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) n) : l_e_st_eq_landau_n_rt_rp_lessd a1 b1).
-
-(* notion 4344 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_r_lessin r s a1 b1 a1ir b1is (l_e_st_eq_landau_n_rt_rp_r_3r182_t5 r s a1 b1 a1ir b1is n) : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4345 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz182c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_less r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t6 r s x y t u n) : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4346 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_satzd182d a1 b1 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a1 b1)).
-
-(* notion 4347 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_3r182_t7 r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
-
-(* notion 4348 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz182d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t8 r s x y t u m) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
-
-(* notion 4349 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_satzd182e a1 b1 (l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a1 b1)).
-
-(* notion 4350 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_3r182_t9 r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4351 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz182e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t10 r s x y t u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4352 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_satzd182f a1 b1 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md a1 b1)).
-
-(* notion 4353 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r182_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_negin (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_3r182_t11 r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
-
-(* notion 4354 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz182f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t12 r s x y t u l) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
-
-(* notion 4355 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r183_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_satzd183a a1 b1 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1)).
-
-(* notion 4356 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r183_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_lessin (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_micm0 s b1 b1is) (l_e_st_eq_landau_n_rt_rp_r_3r183_t1 r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
-
-(* notion 4357 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz183a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r183_t2 r s x y t u m) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
-
-(* notion 4358 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz183b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_ism0 r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
-
-(* notion 4359 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r183_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_satzd183c a1 b1 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1)).
-
-(* notion 4360 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r183_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_morein (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_micm0 s b1 b1is) (l_e_st_eq_landau_n_rt_rp_r_3r183_t3 r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
-
-(* notion 4361 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz183c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r183_t4 r s x y t u l) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
-
-(* notion 4362 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz183d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_satz177 r) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) (l_e_st_eq_landau_n_rt_rp_r_satz183c (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) l) : l_e_st_eq_landau_n_rt_rp_r_more r s).
-
-(* notion 4363 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz183e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_satz177a r) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) i) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4364 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz183f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_e_st_eq_landau_n_rt_rp_r_isless12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_satz177 r) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) (l_e_st_eq_landau_n_rt_rp_r_satz183a (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) m) : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4365 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_prop1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_and3 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos t) (l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) : Prop).
-
-(* notion 4366 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_3r184_prop1 r s x) : Prop).
-
-(* notion 4367 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_prop3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 r x) : Prop).
-
-(* notion 4368 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_and3 (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_md a b)) : Prop).
-
-(* notion 4369 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.(l_some l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a x) : Prop).
-
-(* notion 4370 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_and3e1 (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_md a b)) p1 : l_e_st_eq_landau_n_rt_rp_posd a).
-
-(* notion 4371 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_and3e2 (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_md a b)) p1 : l_e_st_eq_landau_n_rt_rp_posd b).
-
-(* notion 4372 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_and3e3 (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_md a b)) p1 : l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_md a b)).
-
-(* notion 4373 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_ra ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.(l_e_st_eq_landau_n_rt_rp_r_realof a : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4374 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_rb ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_e_st_eq_landau_n_rt_rp_r_realof b : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4375 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_e_st_eq_landau_n_rt_rp_r_innclass a : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2))).
-
-(* notion 4376 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_e_st_eq_landau_n_rt_rp_r_innclass b : l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1))).
-
-(* notion 4377 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_e_st_eq_landau_n_rt_rp_r_isin r (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1)) a0 (l_e_st_eq_landau_n_rt_rp_md a b) a0ir (l_e_st_eq_landau_n_rt_rp_r_micmn (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1) a b (l_e_st_eq_landau_n_rt_rp_r_3r184_t4 r a0 a0ir a p2 b p1) (l_e_st_eq_landau_n_rt_rp_r_3r184_t5 r a0 a0ir a p2 b p1)) (l_e_st_eq_landau_n_rt_rp_r_3r184_t3 r a0 a0ir a p2 b p1) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1))).
-
-(* notion 4378 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_and3i (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1)) (l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1))) (l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) a (l_e_st_eq_landau_n_rt_rp_r_3r184_t4 r a0 a0ir a p2 b p1) (l_e_st_eq_landau_n_rt_rp_r_3r184_t1 r a0 a0ir a p2 b p1)) (l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1) b (l_e_st_eq_landau_n_rt_rp_r_3r184_t5 r a0 a0ir a p2 b p1) (l_e_st_eq_landau_n_rt_rp_r_3r184_t2 r a0 a0ir a p2 b p1)) (l_e_st_eq_landau_n_rt_rp_r_3r184_t6 r a0 a0ir a p2 b p1) : l_e_st_eq_landau_n_rt_rp_r_3r184_prop1 r (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1)).
-
-(* notion 4379 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_3r184_prop1 r (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) x) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1) (l_e_st_eq_landau_n_rt_rp_r_3r184_t7 r a0 a0ir a p2 b p1) : l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 r (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2)).
-
-(* notion 4380 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a x) p2 (l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 r (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a x.l_e_st_eq_landau_n_rt_rp_r_3r184_t8 r a0 a0ir a p2 x t) : l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 r (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2)).
-
-(* notion 4381 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 r x) (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_t9 r a0 a0ir a p2) : l_e_st_eq_landau_n_rt_rp_r_3r184_prop3 r).
-
-(* notion 4382 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r184_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir x) (l_e_st_eq_landau_n_rt_rp_satzd184 a0) (l_e_st_eq_landau_n_rt_rp_r_3r184_prop3 r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir x.l_e_st_eq_landau_n_rt_rp_r_3r184_t10 r a0 a0ir x t) : l_e_st_eq_landau_n_rt_rp_r_3r184_prop3 r).
-
-(* notion 4383 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz184 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_3r184_prop3 r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r184_t11 r x t) : l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_some (Πy:l_e_st_eq_landau_n_rt_rp_r_real.l_and3 (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_pos y) (l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_mn x y))))).
-
-(* notion 4384 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r185_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).(l_e_st_eq_landau_n_rt_rp_satzd185 a3 b3 c3 d3 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a3 b3) (l_e_st_eq_landau_n_rt_rp_md c3 d3)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a3 c3) (l_e_st_eq_landau_n_rt_rp_pd b3 d3))).
-
-(* notion 4385 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r185_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn t u)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a3 b3) (l_e_st_eq_landau_n_rt_rp_md c3 d3)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a3 c3) (l_e_st_eq_landau_n_rt_rp_pd b3 d3)) (l_e_st_eq_landau_n_rt_rp_r_picp (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn t u) (l_e_st_eq_landau_n_rt_rp_md a3 b3) (l_e_st_eq_landau_n_rt_rp_md c3 d3) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a3 b3 a3ir b3is) (l_e_st_eq_landau_n_rt_rp_r_micmn t u c3 d3 c3it d3iu)) (l_e_st_eq_landau_n_rt_rp_r_micmn (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_pd a3 c3) (l_e_st_eq_landau_n_rt_rp_pd b3 d3) (l_e_st_eq_landau_n_rt_rp_r_picp r t a3 c3 a3ir c3it) (l_e_st_eq_landau_n_rt_rp_r_picp s u b3 d3 b3is d3iu)) (l_e_st_eq_landau_n_rt_rp_r_3r185_t1 r s t u a3 b3 c3 d3 a3ir b3is c3it d3iu) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn t u)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u))).
-
-(* notion 4386 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz185 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp4 r s t u (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn t u)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).λvi:l_e_st_eq_landau_n_rt_rp_r_inn v (l_e_st_eq_landau_n_rt_rp_r_class u).l_e_st_eq_landau_n_rt_rp_r_3r185_t2 r s t u x y z v xi yi zi vi) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn t u)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u))).
-
-(* notion 4387 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r186_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_satzd186 a2 b2 c2 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a2 b2) c2) (l_e_st_eq_landau_n_rt_rp_pd a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2))).
-
-(* notion 4388 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r186_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a2 b2) c2) (l_e_st_eq_landau_n_rt_rp_pd a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2)) (l_e_st_eq_landau_n_rt_rp_r_picp (l_e_st_eq_landau_n_rt_rp_r_pl r s) t (l_e_st_eq_landau_n_rt_rp_pd a2 b2) c2 (l_e_st_eq_landau_n_rt_rp_r_picp r s a2 b2 a2ir b2is) c2it) (l_e_st_eq_landau_n_rt_rp_r_picp r (l_e_st_eq_landau_n_rt_rp_r_pl s t) a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2) a2ir (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it)) (l_e_st_eq_landau_n_rt_rp_r_3r186_t1 r s t a2 b2 c2 a2ir b2is c2it) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t))).
-
-(* notion 4389 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz186 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r186_t2 r s t x y z u v w) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t))).
-
-(* notion 4390 *)
-definition l_e_st_eq_landau_n_rt_rp_r_asspl1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz186 r s t : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t))).
-
-(* notion 4391 *)
-definition l_e_st_eq_landau_n_rt_rp_r_asspl2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_satz186 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t)).
-
-(* notion 4392 *)
-definition l_e_st_eq_landau_n_rt_rp_r_plmn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) s) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 s) s)) r (l_e_st_eq_landau_n_rt_rp_r_asspl1 r (l_e_st_eq_landau_n_rt_rp_r_m0 s) s) (l_e_st_eq_landau_n_rt_rp_r_pl02 r (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 s) s) (l_e_st_eq_landau_n_rt_rp_r_satz179a s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) s) r).
-
-(* notion 4393 *)
-definition l_e_st_eq_landau_n_rt_rp_r_mnpl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r s) s) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_m0 s))) r (l_e_st_eq_landau_n_rt_rp_r_asspl1 r s (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_pl02 r (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_satz179 s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r s) s) r).
-
-(* notion 4394 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz187a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) s) r (l_e_st_eq_landau_n_rt_rp_r_compl s (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (l_e_st_eq_landau_n_rt_rp_r_plmn r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_mn r s)) r).
-
-(* notion 4395 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz187b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r) (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_satz187a r s) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r)).
-
-(* notion 4396 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz187c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x s) s) x (l_e_st_eq_landau_n_rt_rp_r_ismn1 r (l_e_st_eq_landau_n_rt_rp_r_pl x s) s (l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_pl x s) (l_e_st_eq_landau_n_rt_rp_r_pl s x) i (l_e_st_eq_landau_n_rt_rp_r_compl s x))) (l_e_st_eq_landau_n_rt_rp_r_mnpl x s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) x).
-
-(* notion 4397 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz187d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn r s) x (l_e_st_eq_landau_n_rt_rp_r_satz187c r s x i) : l_e_st_eq_landau_n_rt_rp_r_is x (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
-
-(* notion 4398 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz187e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl x s) r.(l_e_st_eq_landau_n_rt_rp_r_satz187c r s x (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl s x) (l_e_st_eq_landau_n_rt_rp_r_pl x s) r (l_e_st_eq_landau_n_rt_rp_r_compl s x) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) x).
-
-(* notion 4399 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz187f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl x s) r.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn r s) x (l_e_st_eq_landau_n_rt_rp_r_satz187e r s x i) : l_e_st_eq_landau_n_rt_rp_r_is x (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
-
-(* notion 4400 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r187_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s y) r.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real x y (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_satz187c r s x i) (l_e_st_eq_landau_n_rt_rp_r_satz187c r s y j) : l_e_st_eq_landau_n_rt_rp_r_is x y).
-
-(* notion 4401 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r187_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r.λu:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s y) r.l_e_st_eq_landau_n_rt_rp_r_3r187_t1 r s x y t u : l_e_amone l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r)).
-
-(* notion 4402 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz187 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_onei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r) (l_e_st_eq_landau_n_rt_rp_r_3r187_t2 r s) (l_e_st_eq_landau_n_rt_rp_r_satz187b r s) : l_e_st_eq_landau_n_rt_rp_r_one (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r)).
-
-(* notion 4403 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r188_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_satzd188a a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_moreex (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2) (l_e_st_eq_landau_n_rt_rp_r_picp r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it) m) : l_e_st_eq_landau_n_rt_rp_mored a2 b2).
-
-(* notion 4404 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r188_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_morein r s a2 b2 a2ir b2is (l_e_st_eq_landau_n_rt_rp_r_3r188_t1 r s t a2 b2 c2 a2ir b2is c2it m) : l_e_st_eq_landau_n_rt_rp_r_more r s).
-
-(* notion 4405 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_more r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r188_t2 r s t x y z u v w m) : l_e_st_eq_landau_n_rt_rp_r_more r s).
-
-(* notion 4406 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r188_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_satzd188b a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2) (l_e_st_eq_landau_n_rt_rp_r_picp r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it) i) : l_e_st_eq_landau_n_rt_rp_eq a2 b2).
-
-(* notion 4407 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r188_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_isin r s a2 b2 a2ir b2is (l_e_st_eq_landau_n_rt_rp_r_3r188_t3 r s t a2 b2 c2 a2ir b2is c2it i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4408 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_is r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r188_t4 r s t x y z u v w i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4409 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r188_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_satzd188c a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_lessex (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2) (l_e_st_eq_landau_n_rt_rp_r_picp r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it) l) : l_e_st_eq_landau_n_rt_rp_lessd a2 b2).
-
-(* notion 4410 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r188_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_lessin r s a2 b2 a2ir b2is (l_e_st_eq_landau_n_rt_rp_r_3r188_t5 r s t a2 b2 c2 a2ir b2is c2it l) : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4411 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r188_t6 r s t x y z u v w l) : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4412 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r188_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_satzd188d a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a2 b2 a2ir b2is m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2)).
-
-(* notion 4413 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r188_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_morein (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2) (l_e_st_eq_landau_n_rt_rp_r_picp r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it) (l_e_st_eq_landau_n_rt_rp_r_3r188_t7 r s t a2 b2 c2 a2ir b2is c2it m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
-
-(* notion 4414 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r188_t8 r s t x y z u v w m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
-
-(* notion 4415 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_ispl1 r s t i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
-
-(* notion 4416 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r188_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_satzd188f a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a2 b2 a2ir b2is l) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2)).
-
-(* notion 4417 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r188_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_lessin (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2) (l_e_st_eq_landau_n_rt_rp_r_picp r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it) (l_e_st_eq_landau_n_rt_rp_r_3r188_t9 r s t a2 b2 c2 a2ir b2is c2it l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
-
-(* notion 4418 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r188_t10 r s t x y z u v w l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
-
-(* notion 4419 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188g ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s).(l_e_st_eq_landau_n_rt_rp_r_satz188a r s t (l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t s) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_compl t r) (l_e_st_eq_landau_n_rt_rp_r_compl t s) m) : l_e_st_eq_landau_n_rt_rp_r_more r s).
-
-(* notion 4420 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188h ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s).(l_e_st_eq_landau_n_rt_rp_r_satz188b r s t (l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_compl r t) i (l_e_st_eq_landau_n_rt_rp_r_compl t s)) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4421 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188j ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s).(l_e_st_eq_landau_n_rt_rp_r_satz188c r s t (l_e_st_eq_landau_n_rt_rp_r_isless12 (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t s) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_compl t r) (l_e_st_eq_landau_n_rt_rp_r_compl t s) l) : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4422 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188k ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_pl t s) (l_e_st_eq_landau_n_rt_rp_r_compl r t) (l_e_st_eq_landau_n_rt_rp_r_compl s t) (l_e_st_eq_landau_n_rt_rp_r_satz188d r s t m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s)).
-
-(* notion 4423 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188l ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_ispl2 r s t i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s)).
-
-(* notion 4424 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188m ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_isless12 (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_pl t s) (l_e_st_eq_landau_n_rt_rp_r_compl r t) (l_e_st_eq_landau_n_rt_rp_r_compl s t) (l_e_st_eq_landau_n_rt_rp_r_satz188f r s t l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s)).
-
-(* notion 4425 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188n ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_more t u.(l_e_st_eq_landau_n_rt_rp_r_ismore2 (l_e_st_eq_landau_n_rt_rp_r_pl r u) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_ispl1 r s u i) (l_e_st_eq_landau_n_rt_rp_r_satz188k t u r m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4426 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188o ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_more t u.(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl u s) (l_e_st_eq_landau_n_rt_rp_r_compl r t) (l_e_st_eq_landau_n_rt_rp_r_compl s u) (l_e_st_eq_landau_n_rt_rp_r_satz188n r s t u i m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl u s)).
-
-(* notion 4427 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188p ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_less t u.(l_e_st_eq_landau_n_rt_rp_r_isless2 (l_e_st_eq_landau_n_rt_rp_r_pl r u) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_ispl1 r s u i) (l_e_st_eq_landau_n_rt_rp_r_satz188m t u r l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4428 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz188q ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_less t u.(l_e_st_eq_landau_n_rt_rp_r_isless12 (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl u s) (l_e_st_eq_landau_n_rt_rp_r_compl r t) (l_e_st_eq_landau_n_rt_rp_r_compl s u) (l_e_st_eq_landau_n_rt_rp_r_satz188p r s t u i l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl u s)).
-
-(* notion 4429 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz189 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_more t u.(l_e_st_eq_landau_n_rt_rp_r_trmore (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_satz188d r s t m) (l_e_st_eq_landau_n_rt_rp_r_satz188k t u s n) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4430 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz189a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_less t u.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_satz189 s r u t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) (l_e_st_eq_landau_n_rt_rp_r_lemma2 t u k)) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4431 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz190a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_more t u.(l_orapp (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)) m (λv:l_e_st_eq_landau_n_rt_rp_r_more r s.l_e_st_eq_landau_n_rt_rp_r_satz189 r s t u v n) (λv:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_r_satz188n r s t u v n) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4432 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz190b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis t u.(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl u s) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_compl t r) (l_e_st_eq_landau_n_rt_rp_r_compl u s) (l_e_st_eq_landau_n_rt_rp_r_satz190a t u r s n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4433 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz190c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_less t u.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_satz190a s r u t (l_e_st_eq_landau_n_rt_rp_r_satz168b r s l) (l_e_st_eq_landau_n_rt_rp_r_lemma2 t u k)) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4434 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz190d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis t u.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_satz190b s r u t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) (l_e_st_eq_landau_n_rt_rp_r_satz168b t u k)) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4435 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r191_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis t u.(l_e_st_eq_landau_n_rt_rp_satzd191 a3 b3 c3 d3 (l_e_st_eq_landau_n_rt_rp_r_moreisex r s a3 b3 a3ir b3is m) (l_e_st_eq_landau_n_rt_rp_r_moreisex t u c3 d3 c3it d3iu n) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a3 c3) (l_e_st_eq_landau_n_rt_rp_pd b3 d3)).
-
-(* notion 4436 *)
-definition l_e_st_eq_landau_n_rt_rp_r_3r191_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis t u.(l_e_st_eq_landau_n_rt_rp_r_moreisin (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_pd a3 c3) (l_e_st_eq_landau_n_rt_rp_pd b3 d3) (l_e_st_eq_landau_n_rt_rp_r_picp r t a3 c3 a3ir c3it) (l_e_st_eq_landau_n_rt_rp_r_picp s u b3 d3 b3is d3iu) (l_e_st_eq_landau_n_rt_rp_r_3r191_t1 r s t u a3 b3 c3 d3 a3ir b3is c3it d3iu m n) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4437 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz191 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis t u.(l_e_st_eq_landau_n_rt_rp_r_realapp4 r s t u (l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).λvi:l_e_st_eq_landau_n_rt_rp_r_inn v (l_e_st_eq_landau_n_rt_rp_r_class u).l_e_st_eq_landau_n_rt_rp_r_3r191_t2 r s t u x y z v xi yi zi vi m n) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4438 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz191a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis t u.(l_e_st_eq_landau_n_rt_rp_r_satz168a (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_satz191 s r u t (l_e_st_eq_landau_n_rt_rp_r_satz168b r s l) (l_e_st_eq_landau_n_rt_rp_r_satz168b t u k)) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
-
-(* notion 4439 *)
-definition l_e_st_eq_landau_n_rt_rp_r_timesdr ≝ (Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_td x y) : Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4440 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_td b d)) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b d) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_td b d)) (l_e_st_eq_landau_n_rt_rp_eqtd12 a b c d e f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_timesdr a c) (l_e_st_eq_landau_n_rt_rp_r_timesdr b d)).
-
-(* notion 4441 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ftimesdr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.λu:l_e_st_eq_landau_n_rt_rp_r_eq z v.l_e_st_eq_landau_n_rt_rp_r_ivr4_t1 x y z v t u : l_e_st_eq_landau_n_rt_rp_r_fixf2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_timesdr).
-
-(* notion 4442 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ts ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_indreal2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_timesdr l_e_st_eq_landau_n_rt_rp_r_ftimesdr r s : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4443 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isindreal2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_timesdr l_e_st_eq_landau_n_rt_rp_r_ftimesdr r s a1 b1 a1ir b1is : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 4444 *)
-definition l_e_st_eq_landau_n_rt_rp_r_tict ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_class x)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_ivr4_t2 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_ts r s))).
-
-(* notion 4445 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ists1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_ts x t) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
-
-(* notion 4446 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ists2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_ts t x) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
-
-(* notion 4447 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ists12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_ts s u) (l_e_st_eq_landau_n_rt_rp_r_ists1 r s t i) (l_e_st_eq_landau_n_rt_rp_r_ists2 t u s j) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s u)).
-
-(* notion 4448 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r192_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd192a a1 b1 (l_e_st_eq_landau_n_rt_rp_r_0ex r a1 a1ir i) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a1 b1)).
-
-(* notion 4449 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r192_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_4r192_t1 r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4450 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz192a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r192_t2 r s x y t u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4451 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r192_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd192b a1 b1 (l_e_st_eq_landau_n_rt_rp_r_0ex s b1 b1is i) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a1 b1)).
-
-(* notion 4452 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r192_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_4r192_t3 r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4453 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz192b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r192_t4 r s x y t u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4454 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r192_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd192c a1 b1 (l_e_st_eq_landau_n_rt_rp_r_0ex (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) i) : l_or (l_e_st_eq_landau_n_rt_rp_zero a1) (l_e_st_eq_landau_n_rt_rp_zero b1)).
-
-(* notion 4455 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r192_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_zero a1) (l_e_st_eq_landau_n_rt_rp_zero b1) (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_4r192_t5 r s a1 b1 a1ir b1is i) (λt:l_e_st_eq_landau_n_rt_rp_zero a1.l_e_st_eq_landau_n_rt_rp_r_0in r a1 a1ir t) (λt:l_e_st_eq_landau_n_rt_rp_zero b1.l_e_st_eq_landau_n_rt_rp_r_0in s b1 b1is t) : l_or (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 4456 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz192c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_or (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r192_t6 r s x y t u i) : l_or (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 4457 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz192d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.λo:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_or (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0)) (l_or_th3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0) n o) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_satz192c r s t) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4458 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ts01 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz192a r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4459 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ts02 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz192b r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4460 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r193_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd193 a1 b1 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1))).
-
-(* notion 4461 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r193_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)) (l_e_st_eq_landau_n_rt_rp_r_aica (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is)) (l_e_st_eq_landau_n_rt_rp_r_4r193_t1 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
-
-(* notion 4462 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz193 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r193_t2 r s x y t u) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
-
-(* notion 4463 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz193a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_satz193 r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s))).
-
-(* notion 4464 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r194_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd194 a1 b1 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_td b1 a1)).
-
-(* notion 4465 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r194_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_td b1 a1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_tict s r b1 a1 b1is a1ir) (l_e_st_eq_landau_n_rt_rp_r_4r194_t1 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r)).
-
-(* notion 4466 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz194 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r194_t2 r s x y t u) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r)).
-
-(* notion 4467 *)
-definition l_e_st_eq_landau_n_rt_rp_r_comts ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz194 r s : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r)).
-
-(* notion 4468 *)
-definition l_e_st_eq_landau_n_rt_rp_r_1rl ≝ (l_e_st_eq_landau_n_rt_rp_r_realof l_e_st_eq_landau_n_rt_rp_1df : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4469 *)
-definition l_e_st_eq_landau_n_rt_rp_r_pos1 ≝ (l_e_st_eq_landau_n_rt_rp_r_posin l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_1df (l_e_st_eq_landau_n_rt_rp_r_innclass l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_posdirp l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_1rl).
-
-(* notion 4470 *)
-definition l_e_st_eq_landau_n_rt_rp_r_natrl1 ≝ (l_e_st_eq_landau_n_rt_rp_r_natrli l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_rt_rp_r_natrl l_e_st_eq_landau_n_rt_rp_r_1rl).
-
-(* notion 4471 *)
-definition l_e_st_eq_landau_n_rt_rp_r_intrl1 ≝ (l_e_st_eq_landau_n_rt_rp_r_natintrl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_natrl1 : l_e_st_eq_landau_n_rt_rp_r_intrl l_e_st_eq_landau_n_rt_rp_r_1rl).
-
-(* notion 4472 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r195_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_satzd195 a0 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 l_e_st_eq_landau_n_rt_rp_1df) a0).
-
-(* notion 4473 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r195_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r (l_e_st_eq_landau_n_rt_rp_td a0 l_e_st_eq_landau_n_rt_rp_1df) a0 (l_e_st_eq_landau_n_rt_rp_r_tict r l_e_st_eq_landau_n_rt_rp_r_1rl a0 l_e_st_eq_landau_n_rt_rp_1df a0ir (l_e_st_eq_landau_n_rt_rp_r_innclass l_e_st_eq_landau_n_rt_rp_1df)) a0ir (l_e_st_eq_landau_n_rt_rp_r_4r195_t1 r a0 a0ir) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r).
-
-(* notion 4474 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz195 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_4r195_t2 r x t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r).
-
-(* notion 4475 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz195a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r (l_e_st_eq_landau_n_rt_rp_r_satz195 r) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl)).
-
-(* notion 4476 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz195b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r (l_e_st_eq_landau_n_rt_rp_r_comts l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_satz195 r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) r).
-
-(* notion 4477 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz195c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) r (l_e_st_eq_landau_n_rt_rp_r_satz195b r) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r)).
-
-(* notion 4478 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz196a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_abs r) r (l_e_st_eq_landau_n_rt_rp_r_abs s) s (l_e_st_eq_landau_n_rt_rp_r_absp r p) (l_e_st_eq_landau_n_rt_rp_r_absp s q)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
-
-(* notion 4479 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_satzd196b a1 b1 (l_e_st_eq_landau_n_rt_rp_r_negex r a1 a1ir n) (l_e_st_eq_landau_n_rt_rp_r_negex s b1 b1is o) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1))).
-
-(* notion 4480 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is)) (l_e_st_eq_landau_n_rt_rp_r_4r196_t1 r s a1 b1 a1ir b1is n o) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
-
-(* notion 4481 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz196b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r196_t2 r s x y t u n o) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
-
-(* notion 4482 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t1a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_satzd196c a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex r a1 a1ir p) (l_e_st_eq_landau_n_rt_rp_r_negex s b1 b1is n) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)))).
-
-(* notion 4483 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t2a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1))) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_micm0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is))) (l_e_st_eq_landau_n_rt_rp_r_4r196_t1a r s a1 b1 a1ir b1is p n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)))).
-
-(* notion 4484 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz196c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r196_t2a r s x y t u p n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)))).
-
-(* notion 4485 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz196d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_abs r))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))) (l_e_st_eq_landau_n_rt_rp_r_comts r s) (l_e_st_eq_landau_n_rt_rp_r_satz196c s r p n) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_abs r)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_abs r))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)))).
-
-(* notion 4486 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero a0) (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) n (λt:l_e_st_eq_landau_n_rt_rp_zero a0.l_e_st_eq_landau_n_rt_rp_r_0in r a0 a0ir t) : l_not (l_e_st_eq_landau_n_rt_rp_zero a0)).
-
-(* notion 4487 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).(l_e_st_eq_landau_n_rt_rp_satzd196e a1 b1 (l_e_st_eq_landau_n_rt_rp_r_4r196_t3 r a1 a1ir n) (l_e_st_eq_landau_n_rt_rp_r_4r196_t3 s b1 b1is o) (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is)) i) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1))).
-
-(* notion 4488 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).λa:l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1).(l_andi (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_posin r a1 a1ir (l_ande1 (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1) a)) (l_e_st_eq_landau_n_rt_rp_r_posin s b1 b1is (l_ande2 (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1) a)) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)).
-
-(* notion 4489 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).λa:l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1).(l_andi (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_negin r a1 a1ir (l_ande1 (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1) a)) (l_e_st_eq_landau_n_rt_rp_r_negin s b1 b1is (l_ande2 (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1) a)) : l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s)).
-
-(* notion 4490 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).(l_or_th9 (l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_4r196_t4 r s a1 b1 a1ir b1is n o i) (λt:l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1).l_e_st_eq_landau_n_rt_rp_r_4r196_t5 r s a1 b1 a1ir b1is n o i t) (λt:l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1).l_e_st_eq_landau_n_rt_rp_r_4r196_t6 r s a1 b1 a1ir b1is n o i t) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s))).
-
-(* notion 4491 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz196e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r196_t7 r s x y t u n o i) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s))).
-
-(* notion 4492 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).(l_e_st_eq_landau_n_rt_rp_satzd196f a1 b1 (l_e_st_eq_landau_n_rt_rp_r_4r196_t3 r a1 a1ir n) (l_e_st_eq_landau_n_rt_rp_r_4r196_t3 s b1 b1is o) (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1))) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_micm0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is))) i) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1))).
-
-(* notion 4493 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).λa:l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1).(l_andi (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_posin r a1 a1ir (l_ande1 (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1) a)) (l_e_st_eq_landau_n_rt_rp_r_negin s b1 b1is (l_ande2 (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1) a)) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)).
-
-(* notion 4494 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).λa:l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1).(l_andi (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_negin r a1 a1ir (l_ande1 (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1) a)) (l_e_st_eq_landau_n_rt_rp_r_posin s b1 b1is (l_ande2 (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1) a)) : l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s)).
-
-(* notion 4495 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).(l_or_th9 (l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_e_st_eq_landau_n_rt_rp_r_4r196_t8 r s a1 b1 a1ir b1is n o i) (λt:l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1).l_e_st_eq_landau_n_rt_rp_r_4r196_t9 r s a1 b1 a1ir b1is n o i t) (λt:l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1).l_e_st_eq_landau_n_rt_rp_r_4r196_t10 r s a1 b1 a1ir b1is n o i t) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s))).
-
-(* notion 4496 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz196f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r196_t11 r s x y t u n o i) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s))).
-
-(* notion 4497 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_ts r s) p) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_ts01 r s t) : l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4498 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t13 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_ts r s) p) (λt:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_ts02 r s t) : l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4499 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t14 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_absp (l_e_st_eq_landau_n_rt_rp_r_ts r s) p) (l_e_st_eq_landau_n_rt_rp_r_satz193 r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
-
-(* notion 4500 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz196g ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_e_st_eq_landau_n_rt_rp_r_satz196e r s (l_e_st_eq_landau_n_rt_rp_r_4r196_t12 r s p) (l_e_st_eq_landau_n_rt_rp_r_4r196_t13 r s p) (l_e_st_eq_landau_n_rt_rp_r_4r196_t14 r s p) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s))).
-
-(* notion 4501 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t15 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_nnot0 (l_e_st_eq_landau_n_rt_rp_r_ts r s) n) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_ts01 r s t) : l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4502 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t16 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_nnot0 (l_e_st_eq_landau_n_rt_rp_r_ts r s) n) (λt:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_ts02 r s t) : l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4503 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r196_t17 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_e_st_eq_landau_n_rt_rp_r_satz177c (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_satz193a r s) (l_e_st_eq_landau_n_rt_rp_r_absn (l_e_st_eq_landau_n_rt_rp_r_ts r s) n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)))).
-
-(* notion 4504 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz196h ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_e_st_eq_landau_n_rt_rp_r_satz196f r s (l_e_st_eq_landau_n_rt_rp_r_4r196_t15 r s n) (l_e_st_eq_landau_n_rt_rp_r_4r196_t16 r s n) (l_e_st_eq_landau_n_rt_rp_r_4r196_t17 r s n) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s))).
-
-(* notion 4505 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r197_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd197a a1 b1 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a1) b1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a1 b1))).
-
-(* notion 4506 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r197_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a1) b1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_m0 r) s (l_e_st_eq_landau_n_rt_rp_m0d a1) b1 (l_e_st_eq_landau_n_rt_rp_r_micm0 r a1 a1ir) b1is) (l_e_st_eq_landau_n_rt_rp_r_micm0 (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is)) (l_e_st_eq_landau_n_rt_rp_r_4r197_t1 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s))).
-
-(* notion 4507 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz197a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r197_t2 r s x y t u) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s))).
-
-(* notion 4508 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz197b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 s) r) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts s r)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_comts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_satz197a s r) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_ts s r) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_comts s r)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s))).
-
-(* notion 4509 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz197c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_satz197a r s) (l_e_st_eq_landau_n_rt_rp_r_satz197b r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s))).
-
-(* notion 4510 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz197d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_satz197c r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s)).
-
-(* notion 4511 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz197e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_satz197a r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s)).
-
-(* notion 4512 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz197f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_satz197b r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s))).
-
-(* notion 4513 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz198 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s))) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_satz197c r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s r (l_e_st_eq_landau_n_rt_rp_r_satz177 s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 4514 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz198a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_satz198 r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s))).
-
-(* notion 4515 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_ptdpp a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex r a1 a1ir p) (l_e_st_eq_landau_n_rt_rp_r_posex s b1 b1is q) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a1 b1)).
-
-(* notion 4516 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_ivr4_t3 r s a1 b1 a1ir b1is p q) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 4517 *)
-definition l_e_st_eq_landau_n_rt_rp_r_postspp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr4_t4 r s x y t u p q) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 4518 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_ntdpn a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex r a1 a1ir p) (l_e_st_eq_landau_n_rt_rp_r_negex s b1 b1is n) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a1 b1)).
-
-(* notion 4519 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_negin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_ivr4_t5 r s a1 b1 a1ir b1is p n) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 4520 *)
-definition l_e_st_eq_landau_n_rt_rp_r_negtspn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr4_t6 r s x y t u p n) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 4521 *)
-definition l_e_st_eq_landau_n_rt_rp_r_negtsnp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_isneg (l_e_st_eq_landau_n_rt_rp_r_ts s r) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_comts s r) (l_e_st_eq_landau_n_rt_rp_r_negtspn s r p n) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 4522 *)
-definition l_e_st_eq_landau_n_rt_rp_r_postsnn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_ispos (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_satz198 r s) (l_e_st_eq_landau_n_rt_rp_r_postspp (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_satz176c r n) (l_e_st_eq_landau_n_rt_rp_r_satz176c s o)) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 4523 *)
-definition l_e_st_eq_landau_n_rt_rp_r_possq ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_rapp r (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r r)) (λt:l_e_st_eq_landau_n_rt_rp_r_pos r.l_e_st_eq_landau_n_rt_rp_r_postspp r r t t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r r)) n) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_postsnn r r t t) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r r)).
-
-(* notion 4524 *)
-definition l_e_st_eq_landau_n_rt_rp_r_nnegsq ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r r))) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_0notn (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_satz192a r r t)) (λt:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_pnotn (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_possq r t)) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r r))).
-
-(* notion 4525 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r199_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_satzd199 a2 b2 c2 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a2 b2) c2) (l_e_st_eq_landau_n_rt_rp_td a2 (l_e_st_eq_landau_n_rt_rp_td b2 c2))).
-
-(* notion 4526 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r199_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a2 b2) c2) (l_e_st_eq_landau_n_rt_rp_td a2 (l_e_st_eq_landau_n_rt_rp_td b2 c2)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_ts r s) t (l_e_st_eq_landau_n_rt_rp_td a2 b2) c2 (l_e_st_eq_landau_n_rt_rp_r_tict r s a2 b2 a2ir b2is) c2it) (l_e_st_eq_landau_n_rt_rp_r_tict r (l_e_st_eq_landau_n_rt_rp_r_ts s t) a2 (l_e_st_eq_landau_n_rt_rp_td b2 c2) a2ir (l_e_st_eq_landau_n_rt_rp_r_tict s t b2 c2 b2is c2it)) (l_e_st_eq_landau_n_rt_rp_r_4r199_t1 r s t a2 b2 c2 a2ir b2is c2it) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t))).
-
-(* notion 4527 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz199 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_4r199_t2 r s t x y z u v w) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t))).
-
-(* notion 4528 *)
-definition l_e_st_eq_landau_n_rt_rp_r_assts1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz199 r s t : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t))).
-
-(* notion 4529 *)
-definition l_e_st_eq_landau_n_rt_rp_r_assts2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_satz199 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t)).
-
-(* notion 4530 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r201_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_satzd201 a2 b2 c2 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a2 b2) (l_e_st_eq_landau_n_rt_rp_td a2 c2))).
-
-(* notion 4531 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r201_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_td a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a2 b2) (l_e_st_eq_landau_n_rt_rp_td a2 c2)) (l_e_st_eq_landau_n_rt_rp_r_tict r (l_e_st_eq_landau_n_rt_rp_r_pl s t) a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2) a2ir (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it)) (l_e_st_eq_landau_n_rt_rp_r_picp (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_td a2 b2) (l_e_st_eq_landau_n_rt_rp_td a2 c2) (l_e_st_eq_landau_n_rt_rp_r_tict r s a2 b2 a2ir b2is) (l_e_st_eq_landau_n_rt_rp_r_tict r t a2 c2 a2ir c2it)) (l_e_st_eq_landau_n_rt_rp_r_4r201_t1 r s t a2 b2 c2 a2ir b2is c2it) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
-
-(* notion 4532 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz201 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_4r201_t2 r s t x y z u v w) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
-
-(* notion 4533 *)
-definition l_e_st_eq_landau_n_rt_rp_r_disttp1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_satz201 t r s) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts t s) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_comts t r) (l_e_st_eq_landau_n_rt_rp_r_comts t s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t))).
-
-(* notion 4534 *)
-definition l_e_st_eq_landau_n_rt_rp_r_disttp2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz201 r s t : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
-
-(* notion 4535 *)
-definition l_e_st_eq_landau_n_rt_rp_r_distpt1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pl r s) t)).
-
-(* notion 4536 *)
-definition l_e_st_eq_landau_n_rt_rp_r_distpt2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_disttp2 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t))).
-
-(* notion 4537 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz202 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 t))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_disttp2 r s (l_e_st_eq_landau_n_rt_rp_r_m0 t)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 t)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_satz197b r t)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
-
-(* notion 4538 *)
-definition l_e_st_eq_landau_n_rt_rp_r_disttm1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_mn r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 s) t)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 r (l_e_st_eq_landau_n_rt_rp_r_m0 s) t) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 s) t) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_satz197a s t)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_mn r s) t) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t))).
-
-(* notion 4539 *)
-definition l_e_st_eq_landau_n_rt_rp_r_disttm2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz202 r s t : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
-
-(* notion 4540 *)
-definition l_e_st_eq_landau_n_rt_rp_r_distmt1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_mn r s) t) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_disttm1 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_mn r s) t)).
-
-(* notion 4541 *)
-definition l_e_st_eq_landau_n_rt_rp_r_distmt2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_disttm2 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t))).
-
-(* notion 4542 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz200 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz202 r s t : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
-
-(* notion 4543 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r203_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_satzd203a a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a2 b2 a2ir b2is m) (l_e_st_eq_landau_n_rt_rp_r_posex t c2 c2it p) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_td a2 c2) (l_e_st_eq_landau_n_rt_rp_td b2 c2)).
-
-(* notion 4544 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r203_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_r_morein (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_td a2 c2) (l_e_st_eq_landau_n_rt_rp_td b2 c2) (l_e_st_eq_landau_n_rt_rp_r_tict r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_tict s t b2 c2 b2is c2it) (l_e_st_eq_landau_n_rt_rp_r_4r203_t1 r s t a2 b2 c2 a2ir b2is c2it m p) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
-
-(* notion 4545 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_4r203_t2 r s t x y z u v w m p) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
-
-(* notion 4546 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λi:l_e_st_eq_landau_n_rt_rp_r_is t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts02 r t i) (l_e_st_eq_landau_n_rt_rp_r_ts02 s t i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
-
-(* notion 4547 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r203_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_satzd203c a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a2 b2 a2ir b2is m) (l_e_st_eq_landau_n_rt_rp_r_negex t c2 c2it n) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_td a2 c2) (l_e_st_eq_landau_n_rt_rp_td b2 c2)).
-
-(* notion 4548 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r203_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_r_lessin (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_td a2 c2) (l_e_st_eq_landau_n_rt_rp_td b2 c2) (l_e_st_eq_landau_n_rt_rp_r_tict r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_tict s t b2 c2 b2is c2it) (l_e_st_eq_landau_n_rt_rp_r_4r203_t3 r s t a2 b2 c2 a2ir b2is c2it m n) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
-
-(* notion 4549 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_4r203_t4 r s t x y z u v w m n) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
-
-(* notion 4550 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_ts t s) (l_e_st_eq_landau_n_rt_rp_r_comts r t) (l_e_st_eq_landau_n_rt_rp_r_comts s t) (l_e_st_eq_landau_n_rt_rp_r_satz203a r s t m p) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
-
-(* notion 4551 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λi:l_e_st_eq_landau_n_rt_rp_r_is t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 t r i) (l_e_st_eq_landau_n_rt_rp_r_ts01 t s i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
-
-(* notion 4552 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_r_isless12 (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_ts t s) (l_e_st_eq_landau_n_rt_rp_r_comts r t) (l_e_st_eq_landau_n_rt_rp_r_comts s t) (l_e_st_eq_landau_n_rt_rp_r_satz203c r s t m n) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
-
-(* notion 4553 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203g ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_satz203a s r t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) p) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
-
-(* notion 4554 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203h ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λi:l_e_st_eq_landau_n_rt_rp_r_is t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts02 r t i) (l_e_st_eq_landau_n_rt_rp_r_ts02 s t i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
-
-(* notion 4555 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203j ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_r_lemma2 (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_satz203c s r t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) n) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
-
-(* notion 4556 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203k ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_ts t s) (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_satz203d s r t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) p) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
-
-(* notion 4557 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203l ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λi:l_e_st_eq_landau_n_rt_rp_r_is t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 t r i) (l_e_st_eq_landau_n_rt_rp_r_ts01 t s i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
-
-(* notion 4558 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz203m ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_r_lemma2 (l_e_st_eq_landau_n_rt_rp_r_ts t s) (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_satz203f s r t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) n) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
-
-(* notion 4559 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn1:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero a0) (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) n1 (λt:l_e_st_eq_landau_n_rt_rp_zero a0.l_e_st_eq_landau_n_rt_rp_r_0in r a0 a0ir t) : l_not (l_e_st_eq_landau_n_rt_rp_zero a0)).
-
-(* notion 4560 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s t) r.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s u) r.(l_e_st_eq_landau_n_rt_rp_satzd204b a3 b3 (l_e_st_eq_landau_n_rt_rp_r_4r204_t1 s b3 b3is n1) c3 d3 (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts s t) r (l_e_st_eq_landau_n_rt_rp_td b3 c3) a3 (l_e_st_eq_landau_n_rt_rp_r_tict s t b3 c3 b3is c3it) a3ir i) (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts s u) r (l_e_st_eq_landau_n_rt_rp_td b3 d3) a3 (l_e_st_eq_landau_n_rt_rp_r_tict s u b3 d3 b3is d3iu) a3ir j) : l_e_st_eq_landau_n_rt_rp_eq c3 d3).
-
-(* notion 4561 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s t) r.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s u) r.(l_e_st_eq_landau_n_rt_rp_r_isin t u c3 d3 c3it d3iu (l_e_st_eq_landau_n_rt_rp_r_4r204_t2 r s t u a3 b3 c3 d3 a3ir b3is c3it d3iu n1 i j) : l_e_st_eq_landau_n_rt_rp_r_is t u).
-
-(* notion 4562 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz204b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s y) r.(l_e_st_eq_landau_n_rt_rp_r_realapp4 r s x y (l_e_st_eq_landau_n_rt_rp_r_is x y) (λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.λw:l_e_st_eq_landau_n_rt_rp_dif.λzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class r).λui:l_e_st_eq_landau_n_rt_rp_r_inn u (l_e_st_eq_landau_n_rt_rp_r_class s).λvi:l_e_st_eq_landau_n_rt_rp_r_inn v (l_e_st_eq_landau_n_rt_rp_r_class x).λwi:l_e_st_eq_landau_n_rt_rp_r_inn w (l_e_st_eq_landau_n_rt_rp_r_class y).l_e_st_eq_landau_n_rt_rp_r_4r204_t3 r s x y z u v w zi ui vi wi n i j) : l_e_st_eq_landau_n_rt_rp_r_is x y).
-
-(* notion 4563 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd204a a1 b1 (l_e_st_eq_landau_n_rt_rp_r_4r204_t1 s b1 b1is n1) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 x) a1)).
-
-(* notion 4564 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_ar ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 a) a1.(l_e_st_eq_landau_n_rt_rp_r_realof a : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4565 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 a) a1.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ar r s a1 b1 a1ir b1is n1 a e)) r (l_e_st_eq_landau_n_rt_rp_td b1 a) a1 (l_e_st_eq_landau_n_rt_rp_r_tict s (l_e_st_eq_landau_n_rt_rp_r_4r204_ar r s a1 b1 a1ir b1is n1 a e) b1 a b1is (l_e_st_eq_landau_n_rt_rp_r_innclass a)) a1ir e : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ar r s a1 b1 a1ir b1is n1 a e)) r).
-
-(* notion 4566 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 a) a1.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r) (l_e_st_eq_landau_n_rt_rp_r_4r204_ar r s a1 b1 a1ir b1is n1 a e) (l_e_st_eq_landau_n_rt_rp_r_4r204_t5 r s a1 b1 a1ir b1is n1 a e) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)).
-
-(* notion 4567 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 x) a1) (l_e_st_eq_landau_n_rt_rp_r_4r204_t4 r s a1 b1 a1ir b1is n1) (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 x) a1.l_e_st_eq_landau_n_rt_rp_r_4r204_t6 r s a1 b1 a1ir b1is n1 x t) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)).
-
-(* notion 4568 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz204a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r204_t7 r s x y t u n) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)).
-
-(* notion 4569 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz204 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_onei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r.λu:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s y) r.l_e_st_eq_landau_n_rt_rp_r_satz204b r s n x y t u) (l_e_st_eq_landau_n_rt_rp_r_satz204a r s n) : l_e_st_eq_landau_n_rt_rp_r_one (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)).
-
-(* notion 4570 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ov ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_ind l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r) (l_e_st_eq_landau_n_rt_rp_r_satz204 r s n) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4571 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz204c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_oneax l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r) (l_e_st_eq_landau_n_rt_rp_r_satz204 r s n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) r).
-
-(* notion 4572 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz204d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) r (l_e_st_eq_landau_n_rt_rp_r_satz204c r s n) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_ov r s n))).
-
-(* notion 4573 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz204e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov r s n) s) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) r (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_ov r s n) s) (l_e_st_eq_landau_n_rt_rp_r_satz204c r s n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov r s n) s) r).
-
-(* notion 4574 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz204f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov r s n) s) r (l_e_st_eq_landau_n_rt_rp_r_satz204e r s n) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov r s n) s)).
-
-(* notion 4575 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz204g ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r.(l_e_st_eq_landau_n_rt_rp_r_satz204b r s n x (l_e_st_eq_landau_n_rt_rp_r_ov r s n) i (l_e_st_eq_landau_n_rt_rp_r_satz204c r s n) : l_e_st_eq_landau_n_rt_rp_r_is x (l_e_st_eq_landau_n_rt_rp_r_ov r s n)).
-
-(* notion 4576 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_ros ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_ov r s n : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4577 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_ispos r (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_satz204d r s n) p : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
-
-(* notion 4578 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_and_th1 (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_pnotn s q) : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)))).
-
-(* notion 4579 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_ore1 (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_e_st_eq_landau_n_rt_rp_r_satz196g s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n) (l_e_st_eq_landau_n_rt_rp_r_4r204_t8 r s n p)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t9 r s n p q) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
-
-(* notion 4580 *)
-definition l_e_st_eq_landau_n_rt_rp_r_posovpp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t10 r s n p q) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ov r s n)).
-
-(* notion 4581 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λm:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_and_th1 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_nnotp s m) : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)))).
-
-(* notion 4582 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λm:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_ore2 (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_e_st_eq_landau_n_rt_rp_r_satz196g s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n) (l_e_st_eq_landau_n_rt_rp_r_4r204_t8 r s n p)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t11 r s n p m) : l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
-
-(* notion 4583 *)
-definition l_e_st_eq_landau_n_rt_rp_r_negovpn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λm:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t12 r s n p m) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ov r s n)).
-
-(* notion 4584 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t13 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_isneg r (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_satz204d r s n) m : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
-
-(* notion 4585 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t14 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_and_th1 (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_pnotn s p) : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)))).
-
-(* notion 4586 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t15 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_ore1 (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_e_st_eq_landau_n_rt_rp_r_satz196h s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n) (l_e_st_eq_landau_n_rt_rp_r_4r204_t13 r s n m)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t14 r s n m p) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
-
-(* notion 4587 *)
-definition l_e_st_eq_landau_n_rt_rp_r_negovnp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t15 r s n m p) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ov r s n)).
-
-(* notion 4588 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t16 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λl:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_and_th1 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_nnotp s l) : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)))).
-
-(* notion 4589 *)
-definition l_e_st_eq_landau_n_rt_rp_r_4r204_t17 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λl:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_ore2 (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_e_st_eq_landau_n_rt_rp_r_satz196h s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n) (l_e_st_eq_landau_n_rt_rp_r_4r204_t13 r s n m)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t16 r s n m l) : l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
-
-(* notion 4590 *)
-definition l_e_st_eq_landau_n_rt_rp_r_posovnn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λl:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t17 r s n m l) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ov r s n)).
-
-(* notion 4591 *)
-definition l_e_st_eq_landau_n_rt_rp_r_morerpep ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_e_st_eq_landau_n_rt_rp_r_morein (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp s0)) (l_e_st_eq_landau_n_rt_rp_morerpepd r0 s0 m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
-
-(* notion 4592 *)
-definition l_e_st_eq_landau_n_rt_rp_r_morerpip ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_morerpipd r0 s0 (l_e_st_eq_landau_n_rt_rp_r_moreex (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp s0)) m) : l_e_st_eq_landau_n_rt_rp_more r0 s0).
-
-(* notion 4593 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lessrpep ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r0 s0.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_morerpep s0 r0 (l_e_st_eq_landau_n_rt_rp_satz122 r0 s0 l)) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
-
-(* notion 4594 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lessrpip ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_satz121 s0 r0 (l_e_st_eq_landau_n_rt_rp_r_morerpip s0 r0 (l_e_st_eq_landau_n_rt_rp_r_lemma2 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) l)) : l_e_st_eq_landau_n_rt_rp_less r0 s0).
-
-(* notion 4595 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_ismore12 r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) s (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp s q)) (l_e_st_eq_landau_n_rt_rp_r_isprp1 r p) (l_e_st_eq_landau_n_rt_rp_r_isprp1 s q) m : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp s q))).
-
-(* notion 4596 *)
-definition l_e_st_eq_landau_n_rt_rp_r_moreperp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_morerpip (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t1 r s p q m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q)).
-
-(* notion 4597 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q).(l_e_st_eq_landau_n_rt_rp_r_morerpep (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q) m : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp s q))).
-
-(* notion 4598 *)
-definition l_e_st_eq_landau_n_rt_rp_r_morepirp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q).(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp s q)) s (l_e_st_eq_landau_n_rt_rp_r_isprp2 r p) (l_e_st_eq_landau_n_rt_rp_r_isprp2 s q) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t2 r s p q m) : l_e_st_eq_landau_n_rt_rp_r_more r s).
-
-(* notion 4599 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lessperp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_r_rpofp s q) (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_moreperp s r q p (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q)).
-
-(* notion 4600 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lesspirp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q).(l_e_st_eq_landau_n_rt_rp_r_lemma1 s r (l_e_st_eq_landau_n_rt_rp_r_morepirp s r q p (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q) l)) : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4601 *)
-definition l_e_st_eq_landau_n_rt_rp_r_s01 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x r) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4602 *)
-definition l_e_st_eq_landau_n_rt_rp_r_s02 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x r) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4603 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s01 r)).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_lessis s r) (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s01 r)) n (λt:l_e_st_eq_landau_n_rt_rp_r_lessis s r.l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x r) s t) : l_not (l_e_st_eq_landau_n_rt_rp_r_lessis s r)).
-
-(* notion 4604 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s01 r)).(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x r) s (l_e_st_eq_landau_n_rt_rp_r_satz167k s r (l_e_st_eq_landau_n_rt_rp_r_5r205_t1 r s n)) : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s02 r)).
-
-(* notion 4605 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb00 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_not (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s01 r)).l_e_st_eq_landau_n_rt_rp_r_5r205_t2 r x t : l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s01 r)) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s02 r)))).
-
-(* notion 4606 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x r) r (l_e_st_eq_landau_n_rt_rp_r_lessisi2 r r (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) : l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_s01 r)).
-
-(* notion 4607 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb01a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s01 r) r (l_e_st_eq_landau_n_rt_rp_r_5r205_t3 r) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s01 r)).
-
-(* notion 4608 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ismore2 (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_0) r (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl02 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_satz188k l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 r (l_e_st_eq_landau_n_rt_rp_r_satz169a l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_pos1)) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) r).
-
-(* notion 4609 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x r) (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_5r205_t4 r) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_s02 r)).
-
-(* notion 4610 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb01b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s02 r) (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_5r205_t5 r) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s02 r)).
-
-(* notion 4611 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s01 r).λt:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_in t (l_e_st_eq_landau_n_rt_rp_r_s02 r).(l_e_st_eq_landau_n_rt_rp_r_satz172a s r t (l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x r) s i) (l_e_st_eq_landau_n_rt_rp_r_lemma1 t r (l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x r) t j)) : l_e_st_eq_landau_n_rt_rp_r_less s t).
-
-(* notion 4612 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb02 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s01 r).λy:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_in y (l_e_st_eq_landau_n_rt_rp_r_s02 r).l_e_st_eq_landau_n_rt_rp_r_5r205_t6 r x t y u : l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s01 r).l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y (l_e_st_eq_landau_n_rt_rp_r_s02 r).l_e_st_eq_landau_n_rt_rp_r_less x y))).
-
-(* notion 4613 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb03a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s r.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x r) s (l_e_st_eq_landau_n_rt_rp_r_lessisi1 s r l) : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s01 r)).
-
-(* notion 4614 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb03b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s r.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x r) s m : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s02 r)).
-
-(* notion 4615 *)
-definition l_e_st_eq_landau_n_rt_rp_r_s11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x r) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4616 *)
-definition l_e_st_eq_landau_n_rt_rp_r_s12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x r) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4617 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s11 r)).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_less s r) (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s11 r)) n (λt:l_e_st_eq_landau_n_rt_rp_r_less s r.l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x r) s t) : l_not (l_e_st_eq_landau_n_rt_rp_r_less s r)).
-
-(* notion 4618 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s11 r)).(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x r) s (l_e_st_eq_landau_n_rt_rp_r_satz167f s r (l_e_st_eq_landau_n_rt_rp_r_5r205_t7 r s n)) : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s12 r)).
-
-(* notion 4619 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_not (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s11 r)).l_e_st_eq_landau_n_rt_rp_r_5r205_t8 r x t : l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s11 r)) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s12 r)))).
-
-(* notion 4620 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_isless2 (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_0) r (l_e_st_eq_landau_n_rt_rp_r_mn r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl02 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_satz188m (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) l_e_st_eq_landau_n_rt_rp_r_0 r (l_e_st_eq_landau_n_rt_rp_r_satz169c (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_satz176a l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_pos1))) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_mn r l_e_st_eq_landau_n_rt_rp_r_1rl) r).
-
-(* notion 4621 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x r) (l_e_st_eq_landau_n_rt_rp_r_mn r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_5r205_t9 r) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_mn r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_s11 r)).
-
-(* notion 4622 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb11a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s11 r) (l_e_st_eq_landau_n_rt_rp_r_mn r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_5r205_t10 r) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s11 r)).
-
-(* notion 4623 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x r) r (l_e_st_eq_landau_n_rt_rp_r_moreisi2 r r (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) : l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_s12 r)).
-
-(* notion 4624 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb11b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s12 r) r (l_e_st_eq_landau_n_rt_rp_r_5r205_t11 r) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s12 r)).
-
-(* notion 4625 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s11 r).λt:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_in t (l_e_st_eq_landau_n_rt_rp_r_s12 r).(l_e_st_eq_landau_n_rt_rp_r_satz172b s r t (l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x r) s i) (l_e_st_eq_landau_n_rt_rp_r_satz168a t r (l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x r) t j)) : l_e_st_eq_landau_n_rt_rp_r_less s t).
-
-(* notion 4626 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s11 r).λy:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_in y (l_e_st_eq_landau_n_rt_rp_r_s12 r).l_e_st_eq_landau_n_rt_rp_r_5r205_t12 r x t y u : l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s11 r).l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y (l_e_st_eq_landau_n_rt_rp_r_s12 r).l_e_st_eq_landau_n_rt_rp_r_less x y))).
-
-(* notion 4627 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb13a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s r.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x r) s l : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s11 r)).
-
-(* notion 4628 *)
-definition l_e_st_eq_landau_n_rt_rp_r_vb13b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s r.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x r) s (l_e_st_eq_landau_n_rt_rp_r_moreisi1 s r m) : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s12 r)).
-
-(* notion 4629 *)
-definition l_e_st_eq_landau_n_rt_rp_r_2rl ≝ (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4630 *)
-definition l_e_st_eq_landau_n_rt_rp_r_pos2 ≝ (l_e_st_eq_landau_n_rt_rp_r_pospl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_pos1 l_e_st_eq_landau_n_rt_rp_r_pos1 : l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_2rl).
-
-(* notion 4631 *)
-definition l_e_st_eq_landau_n_rt_rp_r_half ≝ (l_e_st_eq_landau_n_rt_rp_r_ov l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_2rl (l_e_st_eq_landau_n_rt_rp_r_pnot0 l_e_st_eq_landau_n_rt_rp_r_2rl l_e_st_eq_landau_n_rt_rp_r_pos2) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4632 *)
-definition l_e_st_eq_landau_n_rt_rp_r_poshalf ≝ (l_e_st_eq_landau_n_rt_rp_r_posovpp l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_2rl (l_e_st_eq_landau_n_rt_rp_r_pnot0 l_e_st_eq_landau_n_rt_rp_r_2rl l_e_st_eq_landau_n_rt_rp_r_pos2) l_e_st_eq_landau_n_rt_rp_r_pos1 l_e_st_eq_landau_n_rt_rp_r_pos2 : l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_half).
-
-(* notion 4633 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl r r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_2rl r) (l_e_st_eq_landau_n_rt_rp_r_ispl12 r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_satz195c r) (l_e_st_eq_landau_n_rt_rp_r_satz195c r)) (l_e_st_eq_landau_n_rt_rp_r_distpt1 l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r r) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_2rl r)).
-
-(* notion 4634 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r r)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_2rl r)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half l_e_st_eq_landau_n_rt_rp_r_2rl) r) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) r (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_pl r r) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_2rl r) l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_ivr5_t3 r)) (l_e_st_eq_landau_n_rt_rp_r_assts2 l_e_st_eq_landau_n_rt_rp_r_half l_e_st_eq_landau_n_rt_rp_r_2rl r) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half l_e_st_eq_landau_n_rt_rp_r_2rl) l_e_st_eq_landau_n_rt_rp_r_1rl r (l_e_st_eq_landau_n_rt_rp_r_satz204e l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_2rl (l_e_st_eq_landau_n_rt_rp_r_pnot0 l_e_st_eq_landau_n_rt_rp_r_2rl l_e_st_eq_landau_n_rt_rp_r_pos2))) (l_e_st_eq_landau_n_rt_rp_r_satz195b r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r r)) r).
-
-(* notion 4635 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_satz203k (l_e_st_eq_landau_n_rt_rp_r_pl r r) (l_e_st_eq_landau_n_rt_rp_r_pl r s) l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_satz188m r s r l) l_e_st_eq_landau_n_rt_rp_r_poshalf : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r r)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s))).
-
-(* notion 4636 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_isless1 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r r)) r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t4 r) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t5 r s l) : l_e_st_eq_landau_n_rt_rp_r_less r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s))).
-
-(* notion 4637 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_satz203k (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s s) l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_satz188f r s s l) l_e_st_eq_landau_n_rt_rp_r_poshalf : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl s s))).
-
-(* notion 4638 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_isless2 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl s s)) s (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t4 s) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t6 r s l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s)) s).
-
-(* notion 4639 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_satz169b s (l_e_st_eq_landau_n_rt_rp_r_trmore s r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) (l_e_st_eq_landau_n_rt_rp_r_satz169a r p)) : l_e_st_eq_landau_n_rt_rp_r_pos s).
-
-(* notion 4640 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_less x r.l_e_st_eq_landau_n_rt_rp_r_in x s1) : Prop).
-
-(* notion 4641 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_more x r.l_e_st_eq_landau_n_rt_rp_r_in x s2) : Prop).
-
-(* notion 4642 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_and (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 r) : Prop).
-
-(* notion 4643 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_mxy ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl x y) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4644 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t13 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_e_st_eq_landau_n_rt_rp_r_lemma2 x (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_lemma3 x y l) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) x).
-
-(* notion 4645 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t14 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_e_st_eq_landau_n_rt_rp_r_lemma4 x y l : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) y).
-
-(* notion 4646 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t15 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 y) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 y) py (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_t14 s1 s2 p0 p1a p1b p2 x y px py l) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) s1).
-
-(* notion 4647 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t16 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 x) px (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_t13 s1 s2 p0 p1a p1b p2 x y px py l) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) s2).
-
-(* notion 4648 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t17 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(p2 (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_t15 s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_t16 s1 s2 p0 p1a p1b p2 x y px py l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)).
-
-(* notion 4649 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t18 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)) (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)) (l_e_st_eq_landau_n_rt_rp_r_satz167b (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)) (l_e_st_eq_landau_n_rt_rp_r_5r205_t17 s1 s2 p0 p1a p1b p2 x y px py l) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)) : l_con).
-
-(* notion 4650 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t19 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.(λt:l_e_st_eq_landau_n_rt_rp_r_less x y.l_e_st_eq_landau_n_rt_rp_r_5r205_t18 s1 s2 p0 p1a p1b p2 x y px py t : l_not (l_e_st_eq_landau_n_rt_rp_r_less x y)).
-
-(* notion 4651 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t20 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.(λt:l_e_st_eq_landau_n_rt_rp_r_more x y.l_e_st_eq_landau_n_rt_rp_r_5r205_t18 s1 s2 p0 p1a p1b p2 y x py px (l_e_st_eq_landau_n_rt_rp_r_lemma1 x y t) : l_not (l_e_st_eq_landau_n_rt_rp_r_more x y)).
-
-(* notion 4652 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t21 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.(l_or3e1 (l_e_st_eq_landau_n_rt_rp_r_is x y) (l_e_st_eq_landau_n_rt_rp_r_more x y) (l_e_st_eq_landau_n_rt_rp_r_less x y) (l_e_st_eq_landau_n_rt_rp_r_satz167a x y) (l_e_st_eq_landau_n_rt_rp_r_5r205_t20 s1 s2 p0 p1a p1b p2 x y px py) (l_e_st_eq_landau_n_rt_rp_r_5r205_t19 s1 s2 p0 p1a p1b p2 x y px py) : l_e_st_eq_landau_n_rt_rp_r_is x y).
-
-(* notion 4653 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t22 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λu:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.l_e_st_eq_landau_n_rt_rp_r_5r205_t21 s1 s2 p0 p1a p1b p2 x y t u : l_e_amone l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
-
-(* notion 4654 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t23 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1) a : l_e_st_eq_landau_n_rt_rp_r_pos r).
-
-(* notion 4655 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t24 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1) a : l_e_st_eq_landau_n_rt_rp_r_in r s1).
-
-(* notion 4656 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_setof l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s1) : l_e_st_set l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4657 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_setof l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s2) : l_e_st_set l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4658 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t25 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s1.(l_e_st_estii l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s1) r0 i : l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a)).
-
-(* notion 4659 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t26 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_estie l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s1) r0 i : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s1).
-
-(* notion 4660 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t27 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s2.(l_e_st_estii l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s2) r0 i : l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)).
-
-(* notion 4661 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t28 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_estie l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s2) r0 i : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s2).
-
-(* notion 4662 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t29 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s1) (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s2) (l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a)) (l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)) (p0 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)) (λt:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s1.l_e_st_eq_landau_n_rt_rp_r_5r205_t25 s1 s2 p0 p1a p1b p2 case1 r a r0 t) (λt:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s2.l_e_st_eq_landau_n_rt_rp_r_5r205_t27 s1 s2 p0 p1a p1b p2 case1 r a r0 t) : l_or (l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a)) (l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a))).
-
-(* notion 4663 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_pr1 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_r_rpofp r (l_e_st_eq_landau_n_rt_rp_r_5r205_t23 s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4664 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t30 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s1) r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_pr1 s1 s2 p0 p1a p1b p2 case1 r a)) (l_e_st_eq_landau_n_rt_rp_r_5r205_t24 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_isprp1 r (l_e_st_eq_landau_n_rt_rp_r_5r205_t23 s1 s2 p0 p1a p1b p2 case1 r a)) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_pr1 s1 s2 p0 p1a p1b p2 case1 r a)) s1).
-
-(* notion 4665 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t31 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_pr1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t25 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_pr1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t30 s1 s2 p0 p1a p1b p2 case1 r a)) : l_e_st_nonempty l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a)).
-
-(* notion 4666 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t32 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(p2 r (l_e_st_eq_landau_n_rt_rp_r_5r205_t24 s1 s2 p0 p1a p1b p2 case1 r a) s i : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4667 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t33 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(l_e_st_eq_landau_n_rt_rp_r_lemma5 r s (l_e_st_eq_landau_n_rt_rp_r_5r205_t32 s1 s2 p0 p1a p1b p2 case1 r a s i) (l_e_st_eq_landau_n_rt_rp_r_5r205_t23 s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_rp_r_pos s).
-
-(* notion 4668 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_ps1 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(l_e_st_eq_landau_n_rt_rp_r_rpofp s (l_e_st_eq_landau_n_rt_rp_r_5r205_t33 s1 s2 p0 p1a p1b p2 case1 r a s i) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4669 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t34 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s2) s (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps1 s1 s2 p0 p1a p1b p2 case1 r a s i)) i (l_e_st_eq_landau_n_rt_rp_r_isprp1 s (l_e_st_eq_landau_n_rt_rp_r_5r205_t33 s1 s2 p0 p1a p1b p2 case1 r a s i)) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps1 s1 s2 p0 p1a p1b p2 case1 r a s i)) s2).
-
-(* notion 4670 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t35 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_ps1 s1 s2 p0 p1a p1b p2 case1 r a s i) (l_e_st_eq_landau_n_rt_rp_r_5r205_t27 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_ps1 s1 s2 p0 p1a p1b p2 case1 r a s i) (l_e_st_eq_landau_n_rt_rp_r_5r205_t34 s1 s2 p0 p1a p1b p2 case1 r a s i)) : l_e_st_nonempty l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)).
-
-(* notion 4671 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t36 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_rp_r_real s2 p1b (l_e_st_nonempty l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x s2.l_e_st_eq_landau_n_rt_rp_r_5r205_t35 s1 s2 p0 p1a p1b p2 case1 r a x t) : l_e_st_nonempty l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)).
-
-(* notion 4672 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t37 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).λs0:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).(p2 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_5r205_t26 s1 s2 p0 p1a p1b p2 case1 r a r0 i) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_r_5r205_t28 s1 s2 p0 p1a p1b p2 case1 r a s0 j) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
-
-(* notion 4673 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t38 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).λs0:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_eq_landau_n_rt_rp_r_lessrpip r0 s0 (l_e_st_eq_landau_n_rt_rp_r_5r205_t37 s1 s2 p0 p1a p1b p2 case1 r a r0 i s0 j) : l_e_st_eq_landau_n_rt_rp_less r0 s0).
-
-(* notion 4674 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_stc ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_schnitt (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_5r205_t29 s1 s2 p0 p1a p1b p2 case1 r a x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t31 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t36 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).λy:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_rp_in y (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_r_5r205_t38 s1 s2 p0 p1a p1b p2 case1 r a x t y u) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4675 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t39 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_satzp205a (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_5r205_t29 s1 s2 p0 p1a p1b p2 case1 r a x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t31 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t36 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).λy:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_rp_in y (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_r_5r205_t38 s1 s2 p0 p1a p1b p2 case1 r a x t y u) : l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_less x (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a))).
-
-(* notion 4676 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t40 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_satzp205b (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_5r205_t29 s1 s2 p0 p1a p1b p2 case1 r a x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t31 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t36 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).λy:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_rp_in y (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_r_5r205_t38 s1 s2 p0 p1a p1b p2 case1 r a x t y u) : l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_more x (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a))).
-
-(* notion 4677 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_stp ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4678 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t41 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_r_posi (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a)).
-
-(* notion 4679 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_rpofp s p : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4680 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t42 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_lessrpip (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p) (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_isless1 s (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p)) (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_isprp1 s p) l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p) (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a)).
-
-(* notion 4681 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t43 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_5r205_t39 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p) (l_e_st_eq_landau_n_rt_rp_r_5r205_t42 s1 s2 p0 p1a p1b p2 case1 r a s l p) : l_e_st_eq_landau_n_rt_rp_in (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p) (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a)).
-
-(* notion 4682 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t44 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p)) s (l_e_st_eq_landau_n_rt_rp_r_5r205_t26 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p) (l_e_st_eq_landau_n_rt_rp_r_5r205_t43 s1 s2 p0 p1a p1b p2 case1 r a s l p)) (l_e_st_eq_landau_n_rt_rp_r_isprp2 s p) : l_e_st_eq_landau_n_rt_rp_r_in s s1).
-
-(* notion 4683 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t45 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_pos s).λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(p2 r (l_e_st_eq_landau_n_rt_rp_r_5r205_t24 s1 s2 p0 p1a p1b p2 case1 r a) s i : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4684 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t46 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_pos s).λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(n (l_e_st_eq_landau_n_rt_rp_r_lemma5 r s (l_e_st_eq_landau_n_rt_rp_r_5r205_t45 s1 s2 p0 p1a p1b p2 case1 r a s l n i) (l_e_st_eq_landau_n_rt_rp_r_5r205_t23 s1 s2 p0 p1a p1b p2 case1 r a)) : l_con).
-
-(* notion 4685 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t47 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_pos s).(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_in s s1) (l_e_st_eq_landau_n_rt_rp_r_in s s2) (p0 s) (λt:l_e_st_eq_landau_n_rt_rp_r_in s s2.l_e_st_eq_landau_n_rt_rp_r_5r205_t46 s1 s2 p0 p1a p1b p2 case1 r a s l n t) : l_e_st_eq_landau_n_rt_rp_r_in s s1).
-
-(* notion 4686 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t48 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_in s s1) (λt:l_e_st_eq_landau_n_rt_rp_r_pos s.l_e_st_eq_landau_n_rt_rp_r_5r205_t44 s1 s2 p0 p1a p1b p2 case1 r a s l t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_pos s).l_e_st_eq_landau_n_rt_rp_r_5r205_t47 s1 s2 p0 p1a p1b p2 case1 r a s l t) : l_e_st_eq_landau_n_rt_rp_r_in s s1).
-
-(* notion 4687 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t49 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_eq_landau_n_rt_rp_r_lemma5 (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a) s (l_e_st_eq_landau_n_rt_rp_r_lemma1 s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a) m) (l_e_st_eq_landau_n_rt_rp_r_5r205_t41 s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_rp_r_pos s).
-
-(* notion 4688 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_eq_landau_n_rt_rp_r_rpofp s (l_e_st_eq_landau_n_rt_rp_r_5r205_t49 s1 s2 p0 p1a p1b p2 case1 r a s m) : l_e_st_eq_landau_n_rt_cut).
-
-(* notion 4689 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t50 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_eq_landau_n_rt_rp_r_morerpip (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m) (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_ismore1 s (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m)) (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_isprp1 s (l_e_st_eq_landau_n_rt_rp_r_5r205_t49 s1 s2 p0 p1a p1b p2 case1 r a s m)) m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m) (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a)).
-
-(* notion 4690 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t51 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_eq_landau_n_rt_rp_r_5r205_t40 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m) (l_e_st_eq_landau_n_rt_rp_r_5r205_t50 s1 s2 p0 p1a p1b p2 case1 r a s m) : l_e_st_eq_landau_n_rt_rp_in (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m) (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)).
-
-(* notion 4691 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t52 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s2) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m)) s (l_e_st_eq_landau_n_rt_rp_r_5r205_t28 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m) (l_e_st_eq_landau_n_rt_rp_r_5r205_t51 s1 s2 p0 p1a p1b p2 case1 r a s m)) (l_e_st_eq_landau_n_rt_rp_r_isprp2 s (l_e_st_eq_landau_n_rt_rp_r_5r205_t49 s1 s2 p0 p1a p1b p2 case1 r a s m)) : l_e_st_eq_landau_n_rt_rp_r_in s s2).
-
-(* notion 4692 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t53 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_andi (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a)) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_less x (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_r_5r205_t48 s1 s2 p0 p1a p1b p2 case1 r a x t) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_more x (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_r_5r205_t52 s1 s2 p0 p1a p1b p2 case1 r a x t) : l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a)).
-
-(* notion 4693 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t54 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_somei l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t53 s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
-
-(* notion 4694 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t55 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).(l_someapp l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)) case1 (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1).l_e_st_eq_landau_n_rt_rp_r_5r205_t54 s1 s2 p0 p1a p1b p2 case1 x t) : l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
-
-(* notion 4695 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s1) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4696 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s2) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4697 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t56 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s1.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s1) r i : l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)).
-
-(* notion 4698 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t57 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2).(l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s1) r i : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s1).
-
-(* notion 4699 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t58 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s2.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s2) r i : l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)).
-
-(* notion 4700 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t59 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2).(l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s2) r i : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s2).
-
-(* notion 4701 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t60 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_comor (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)) (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)) (l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s1) (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s2) (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)) (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)) (p0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λt:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s1.l_e_st_eq_landau_n_rt_rp_r_5r205_t56 s1 s2 p0 p1a p1b p2 case2 r t) (λt:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s2.l_e_st_eq_landau_n_rt_rp_r_5r205_t58 s1 s2 p0 p1a p1b p2 case2 r t)) : l_or (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)) (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2))).
-
-(* notion 4702 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t61 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r s2.(l_e_st_eq_landau_n_rt_rp_r_5r205_t58 s1 s2 p0 p1a p1b p2 case2 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s2) r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) i (l_e_st_eq_landau_n_rt_rp_r_satz177a r)) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)).
-
-(* notion 4703 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t62 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r s2.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t61 s1 s2 p0 p1a p1b p2 case2 r i) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)).
-
-(* notion 4704 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t63 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_rp_r_real s2 p1b (l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x s2.l_e_st_eq_landau_n_rt_rp_r_5r205_t62 s1 s2 p0 p1a p1b p2 case2 x t) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)).
-
-(* notion 4705 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t64 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r s1.(l_e_st_eq_landau_n_rt_rp_r_5r205_t56 s1 s2 p0 p1a p1b p2 case2 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s1) r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) i (l_e_st_eq_landau_n_rt_rp_r_satz177a r)) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)).
-
-(* notion 4706 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t65 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r s1.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t64 s1 s2 p0 p1a p1b p2 case2 r i) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)).
-
-(* notion 4707 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t66 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_rp_r_real s1 p1a (l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_5r205_t65 s1 s2 p0 p1a p1b p2 case2 x t) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)).
-
-(* notion 4708 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t67 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2).λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2).(p2 (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_t57 s1 s2 p0 p1a p1b p2 case2 s j) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t59 s1 s2 p0 p1a p1b p2 case2 r i) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4709 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t68 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2).λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2).(l_e_st_eq_landau_n_rt_rp_r_lemma1 s r (l_e_st_eq_landau_n_rt_rp_r_satz183d s r (l_e_st_eq_landau_n_rt_rp_r_5r205_t67 s1 s2 p0 p1a p1b p2 case2 r i s j)) : l_e_st_eq_landau_n_rt_rp_r_less r s).
-
-(* notion 4710 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t69 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2).(l_e_st_eq_landau_n_rt_rp_r_satz176c r (l_ande1 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2) a) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4711 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t70 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s2) r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_ande2 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2) a) (l_e_st_eq_landau_n_rt_rp_r_satz177a r) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) s2).
-
-(* notion 4712 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t71 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2).(l_andi (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)) (l_e_st_eq_landau_n_rt_rp_r_5r205_t69 s1 s2 p0 p1a p1b p2 case2 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t58 s1 s2 p0 p1a p1b p2 case2 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t70 s1 s2 p0 p1a p1b p2 case2 r a)) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2))).
-
-(* notion 4713 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t72 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2).(l_somei l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2))) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t71 s1 s2 p0 p1a p1b p2 case2 r a) : l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)))).
-
-(* notion 4714 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t73 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_someapp l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)) case2 (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)))) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2).l_e_st_eq_landau_n_rt_rp_r_5r205_t72 s1 s2 p0 p1a p1b p2 case2 x t) : l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)))).
-
-(* notion 4715 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t74 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_e_st_eq_landau_n_rt_rp_r_5r205_t55 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_t60 s1 s2 p0 p1a p1b p2 case2 x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t63 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_t66 s1 s2 p0 p1a p1b p2 case2) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2).λy:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_in y (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2).l_e_st_eq_landau_n_rt_rp_r_5r205_t68 s1 s2 p0 p1a p1b p2 case2 x t y u) (l_e_st_eq_landau_n_rt_rp_r_5r205_t73 s1 s2 p0 p1a p1b p2 case2) : l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) x)).
-
-(* notion 4716 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t75 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_ismore2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_satz177 r) (l_e_st_eq_landau_n_rt_rp_r_satz183c s (l_e_st_eq_landau_n_rt_rp_r_m0 r) l) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_m0 s) r).
-
-(* notion 4717 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t76 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r) p (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_t75 s1 s2 p0 p1a p1b p2 case2 r p s l) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)).
-
-(* notion 4718 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t77 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_5r205_t57 s1 s2 p0 p1a p1b p2 case2 (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_t76 s1 s2 p0 p1a p1b p2 case2 r p s l)) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) : l_e_st_eq_landau_n_rt_rp_r_in s s1).
-
-(* notion 4719 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t78 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_isless2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_satz177 r) (l_e_st_eq_landau_n_rt_rp_r_satz183a s (l_e_st_eq_landau_n_rt_rp_r_m0 r) m) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 s) r).
-
-(* notion 4720 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t79 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r) p (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_t78 s1 s2 p0 p1a p1b p2 case2 r p s m) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)).
-
-(* notion 4721 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t80 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s2) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_5r205_t59 s1 s2 p0 p1a p1b p2 case2 (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_t79 s1 s2 p0 p1a p1b p2 case2 r p s m)) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) : l_e_st_eq_landau_n_rt_rp_r_in s s2).
-
-(* notion 4722 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t81 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.(l_andi (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_less x (l_e_st_eq_landau_n_rt_rp_r_m0 r).l_e_st_eq_landau_n_rt_rp_r_5r205_t77 s1 s2 p0 p1a p1b p2 case2 r p x t) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_more x (l_e_st_eq_landau_n_rt_rp_r_m0 r).l_e_st_eq_landau_n_rt_rp_r_5r205_t80 s1 s2 p0 p1a p1b p2 case2 r p x t) : l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4723 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t82 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t81 s1 s2 p0 p1a p1b p2 case2 r p) : l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
-
-(* notion 4724 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t83 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_someapp l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t74 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) x.l_e_st_eq_landau_n_rt_rp_r_5r205_t82 s1 s2 p0 p1a p1b p2 case2 x t) : l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
-
-(* notion 4725 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t84 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.(l_some_th4 l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)) notcase2 r : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2))).
-
-(* notion 4726 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t85 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.(l_and_th3 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2) (l_e_st_eq_landau_n_rt_rp_r_5r205_t84 s1 s2 p0 p1a p1b p2 notcase1 notcase2 r l) (l_e_st_eq_landau_n_rt_rp_r_satz169d r l) : l_not (l_e_st_eq_landau_n_rt_rp_r_in r s2)).
-
-(* notion 4727 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t86 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_in r s1) (l_e_st_eq_landau_n_rt_rp_r_in r s2) (p0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t85 s1 s2 p0 p1a p1b p2 notcase1 notcase2 r l) : l_e_st_eq_landau_n_rt_rp_r_in r s1).
-
-(* notion 4728 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t87 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.(l_some_th4 l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)) notcase1 r : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1))).
-
-(* notion 4729 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t88 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.(l_and_th3 (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1) (l_e_st_eq_landau_n_rt_rp_r_5r205_t87 s1 s2 p0 p1a p1b p2 notcase1 notcase2 r m) (l_e_st_eq_landau_n_rt_rp_r_satz169b r m) : l_not (l_e_st_eq_landau_n_rt_rp_r_in r s1)).
-
-(* notion 4730 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t89 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.(l_ore2 (l_e_st_eq_landau_n_rt_rp_r_in r s1) (l_e_st_eq_landau_n_rt_rp_r_in r s2) (p0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t88 s1 s2 p0 p1a p1b p2 notcase1 notcase2 r m) : l_e_st_eq_landau_n_rt_rp_r_in r s2).
-
-(* notion 4731 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t90 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).(l_andi (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_less x l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_5r205_t86 s1 s2 p0 p1a p1b p2 notcase1 notcase2 x t) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_more x l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_5r205_t89 s1 s2 p0 p1a p1b p2 notcase1 notcase2 x t) : l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4732 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t91 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).(l_somei l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_5r205_t90 s1 s2 p0 p1a p1b p2 notcase1 notcase2) : l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
-
-(* notion 4733 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t92 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))) (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)) (λt:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).l_e_st_eq_landau_n_rt_rp_r_5r205_t83 s1 s2 p0 p1a p1b p2 t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).l_e_st_eq_landau_n_rt_rp_r_5r205_t91 s1 s2 p0 p1a p1b p2 notcase1 t) : l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
-
-(* notion 4734 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t93 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))) (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)) (λt:l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).l_e_st_eq_landau_n_rt_rp_r_5r205_t55 s1 s2 p0 p1a p1b p2 t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).l_e_st_eq_landau_n_rt_rp_r_5r205_t92 s1 s2 p0 p1a p1b p2 t) : l_e_st_eq_landau_n_rt_rp_r_some (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
-
-(* notion 4735 *)
-definition l_e_st_eq_landau_n_rt_rp_r_5r205_t94 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(l_e_onei l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t22 s1 s2 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_r_5r205_t93 s1 s2 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_rp_r_one (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
-
-(* notion 4736 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz205 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(l_e_st_eq_landau_n_rt_rp_r_5r205_t94 s1 s2 p0 p1a p1b p2 : l_e_st_eq_landau_n_rt_rp_r_one (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_less y x.l_e_st_eq_landau_n_rt_rp_r_in y s1)) (l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_more y x.l_e_st_eq_landau_n_rt_rp_r_in y s2)))).
-
-(* notion 4737 *)
-definition l_e_st_eq_landau_n_rt_rp_r_dedekind ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(l_e_st_eq_landau_n_rt_rp_r_satz205 s1 s2 p0 p1a p1b p2 : l_e_st_eq_landau_n_rt_rp_r_one (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_less y x.l_e_st_eq_landau_n_rt_rp_r_in y s1)) (l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_more y x.l_e_st_eq_landau_n_rt_rp_r_in y s2)))).
-
-(* notion 4738 *)
-definition l_e_st_eq_landau_n_rt_rp_r_schnitt ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(l_e_ind l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_satz205 s1 s2 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4739 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz205a ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2)) (l_e_oneax l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_satz205 s1 s2 p0 p1a p1b p2)) r l : l_e_st_eq_landau_n_rt_rp_r_in r s1).
-
-(* notion 4740 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satz205b ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (Πx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (Πy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2)) (l_e_oneax l_e_st_eq_landau_n_rt_rp_r_real (Πx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_satz205 s1 s2 p0 p1a p1b p2)) r m : l_e_st_eq_landau_n_rt_rp_r_in r s2).
-
-(* notion 4741 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_dr ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdofrp r0 : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 4742 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_ds ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdofrp s0 : l_e_st_eq_landau_n_rt_rp_dif).
-
-(* notion 4743 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t1 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_lemmaivad1 r0 s0 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_r_iva_dr r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_ds r0 s0)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r0 s0))).
-
-(* notion 4744 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva1 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_pl r0 s0)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r0 s0)) (l_e_st_eq_landau_n_rt_rp_r_picp (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp s0))) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r0 s0))) (l_e_st_eq_landau_n_rt_rp_r_iva_t1 r0 s0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_pl r0 s0))).
-
-(* notion 4745 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t2 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_lemmaivad2 r0 s0 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_r_iva_dr r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_ds r0 s0)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r0 s0))).
-
-(* notion 4746 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva2 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_ts r0 s0)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r0 s0)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp s0))) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r0 s0))) (l_e_st_eq_landau_n_rt_rp_r_iva_t2 r0 s0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_ts r0 s0))).
-
-(* notion 4747 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t3 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_r_moreex (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_r_iva_dr r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_ds r0 s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_r_iva_dr r0 s0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_r_iva_ds r0 s0)) m : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_r_iva_dr r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_ds r0 s0)).
-
-(* notion 4748 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva3 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_lemmaivad3 r0 s0 (l_e_st_eq_landau_n_rt_rp_r_iva_t3 r0 s0 m) : l_e_st_eq_landau_n_rt_rp_more r0 s0).
-
-(* notion 4749 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t4 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_satz121 s0 r0 (l_e_st_eq_landau_n_rt_rp_r_lemmaiva3 s0 r0 (l_e_st_eq_landau_n_rt_rp_r_lemma2 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) l)) : l_e_st_eq_landau_n_rt_rp_less r0 s0).
-
-(* notion 4750 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t5 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_ec3e23 (l_e_st_eq_landau_n_rt_rp_is r0 s0) (l_e_st_eq_landau_n_rt_rp_more r0 s0) (l_e_st_eq_landau_n_rt_rp_less r0 s0) (l_e_st_eq_landau_n_rt_rp_satz123b r0 s0) m : l_not (l_e_st_eq_landau_n_rt_rp_less r0 s0)).
-
-(* notion 4751 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t6 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_less r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_t5 r0 s0 m) (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).l_e_st_eq_landau_n_rt_rp_r_iva_t4 r0 s0 m t) : l_not (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0))).
-
-(* notion 4752 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t7 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_is r0 s0) (l_e_st_eq_landau_n_rt_rp_more r0 s0) (l_e_st_eq_landau_n_rt_rp_less r0 s0) (l_e_st_eq_landau_n_rt_rp_satz123b r0 s0) m : l_e_st_eq_landau_n_rt_rp_nis r0 s0).
-
-(* notion 4753 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t8 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_is r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_t7 r0 s0 m) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).l_e_st_eq_landau_n_rt_rp_r_isrpip r0 s0 t) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
-
-(* notion 4754 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva4 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_or3e2 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_satz167a (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_iva_t6 r0 s0 m) (l_e_st_eq_landau_n_rt_rp_r_iva_t8 r0 s0 m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
-
-(* notion 4755 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t9 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).(l_e_st_eq_landau_n_rt_rp_r_lemmaiva3 (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)).
-
-(* notion 4756 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t10 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).(l_e_st_eq_landau_n_rt_rp_satz154d (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_rt_rp_r_iva_t9 x y m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)).
-
-(* notion 4757 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t11 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).(l_e_st_eq_landau_n_rt_moree (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_iva_t10 x y m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)).
-
-(* notion 4758 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).(l_e_st_eq_landau_n_satz111a x y (l_e_st_eq_landau_n_rt_rp_r_iva_t11 x y m) : l_e_st_eq_landau_n_more x y).
-
-(* notion 4759 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_satz111d x y m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)).
-
-(* notion 4760 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t13 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_iva_t12 x y m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)).
-
-(* notion 4761 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iva_t14 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_rt_rp_r_iva_t13 x y m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)).
-
-(* notion 4762 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_rt_rp_r_lemmaiva4 (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) (l_e_st_eq_landau_n_rt_rp_r_iva_t14 x y m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)).
-
-(* notion 4763 *)
-definition l_e_st_eq_landau_n_rt_rp_r_int_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_intabsd a0 (l_e_st_eq_landau_n_rt_rp_r_intrlex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_absd a0)).
-
-(* notion 4764 *)
-definition l_e_st_eq_landau_n_rt_rp_r_int_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_int_t1 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_abs r)).
-
-(* notion 4765 *)
-definition l_e_st_eq_landau_n_rt_rp_r_intabs ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_abs r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_int_t2 r x t i) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_abs r)).
-
-(* notion 4766 *)
-definition l_e_st_eq_landau_n_rt_rp_r_int_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_intm0d a0 (l_e_st_eq_landau_n_rt_rp_r_intrlex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_m0d a0)).
-
-(* notion 4767 *)
-definition l_e_st_eq_landau_n_rt_rp_r_int_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_int_t3 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4768 *)
-definition l_e_st_eq_landau_n_rt_rp_r_intm0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_int_t4 r x t i) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
-
-(* notion 4769 *)
-definition l_e_st_eq_landau_n_rt_rp_r_int_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_intpd a1 b1 (l_e_st_eq_landau_n_rt_rp_r_intrlex r a1 a1ir i) (l_e_st_eq_landau_n_rt_rp_r_intrlex s b1 b1is j) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a1 b1)).
-
-(* notion 4770 *)
-definition l_e_st_eq_landau_n_rt_rp_r_int_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_int_t5 r s a1 b1 a1ir b1is i j) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
-
-(* notion 4771 *)
-definition l_e_st_eq_landau_n_rt_rp_r_intpl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_int_t6 r s x y t u i j) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
-
-(* notion 4772 *)
-definition l_e_st_eq_landau_n_rt_rp_r_intmn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_r_intpl r i (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_intm0 s j) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
-
-(* notion 4773 *)
-definition l_e_st_eq_landau_n_rt_rp_r_int_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_inttd a1 b1 (l_e_st_eq_landau_n_rt_rp_r_intrlex r a1 a1ir i) (l_e_st_eq_landau_n_rt_rp_r_intrlex s b1 b1is j) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_td a1 b1)).
-
-(* notion 4774 *)
-definition l_e_st_eq_landau_n_rt_rp_r_int_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_int_t7 r s a1 b1 a1ir b1is i j) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 4775 *)
-definition l_e_st_eq_landau_n_rt_rp_r_intts ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_int_t8 r s x y t u i j) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 4776 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr24_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n)).
-
-(* notion 4777 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr24_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_more l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_more l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n)) (l_e_st_eq_landau_n_satz10d l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n) (l_e_st_eq_landau_n_rt_rp_r_ivr24_t1 r n)) (λt:l_e_st_eq_landau_n_rt_rp_r_more l_e_st_eq_landau_n_rt_rp_r_1rl r.l_e_st_eq_landau_n_rt_rp_r_lemmaiva5 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n) (l_e_st_eq_landau_n_rt_rp_r_ismore2 r (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 r n) t)) : l_not (l_e_st_eq_landau_n_rt_rp_r_more l_e_st_eq_landau_n_rt_rp_r_1rl r)).
-
-(* notion 4778 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satzr24 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_satz167e l_e_st_eq_landau_n_rt_rp_r_1rl r (l_e_st_eq_landau_n_rt_rp_r_ivr24_t2 r n) : l_e_st_eq_landau_n_rt_rp_r_lessis l_e_st_eq_landau_n_rt_rp_r_1rl r).
-
-(* notion 4779 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr25_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_satz182d s r (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn s r)).
-
-(* notion 4780 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr25_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_intmn s j r i : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_mn s r)).
-
-(* notion 4781 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr25_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_posintnatrl (l_e_st_eq_landau_n_rt_rp_r_mn s r) (l_e_st_eq_landau_n_rt_rp_r_ivr25_t1 r i s j l) (l_e_st_eq_landau_n_rt_rp_r_ivr25_t2 r i s j l) : l_e_st_eq_landau_n_rt_rp_r_natrl (l_e_st_eq_landau_n_rt_rp_r_mn s r)).
-
-(* notion 4782 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr25_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_satzr24 (l_e_st_eq_landau_n_rt_rp_r_mn s r) (l_e_st_eq_landau_n_rt_rp_r_ivr25_t3 r i s j l) : l_e_st_eq_landau_n_rt_rp_r_lessis l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r)).
-
-(* notion 4783 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr25_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r)) (l_e_st_eq_landau_n_rt_rp_r_is l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r)) (l_e_st_eq_landau_n_rt_rp_r_ivr25_t4 r i s j l) (λt:l_e_st_eq_landau_n_rt_rp_r_less l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r).l_e_st_eq_landau_n_rt_rp_r_satz188f l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r t) (λt:l_e_st_eq_landau_n_rt_rp_r_is l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r).l_e_st_eq_landau_n_rt_rp_r_ispl1 l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r)).
-
-(* notion 4784 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satzr25 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_islessis12 (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r) s (l_e_st_eq_landau_n_rt_rp_r_compl l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_plmn s r) (l_e_st_eq_landau_n_rt_rp_r_ivr25_t5 r i s j l) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) s).
-
-(* notion 4785 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr155_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_lemmaiva1 (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)))).
-
-(* notion 4786 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr155_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_isrpep (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)) (l_e_st_eq_landau_n_rt_rp_satz155e x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)))).
-
-(* notion 4787 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satzr155a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y))) (l_e_st_eq_landau_n_rt_rp_r_ivr155_t2 x y) (l_e_st_eq_landau_n_rt_rp_r_ivr155_t1 x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y))).
-
-(* notion 4788 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satzr155b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_satzr155a x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x y))).
-
-(* notion 4789 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr155_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_lemmaiva2 (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)))).
-
-(* notion 4790 *)
-definition l_e_st_eq_landau_n_rt_rp_r_ivr155_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_isrpep (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)) (l_e_st_eq_landau_n_rt_rp_satz155f x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)))).
-
-(* notion 4791 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satzr155c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y))) (l_e_st_eq_landau_n_rt_rp_r_ivr155_t4 x y) (l_e_st_eq_landau_n_rt_rp_r_ivr155_t3 x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y))).
-
-(* notion 4792 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satzr155d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_satzr155c x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_ts x y))).
-
-(* notion 4793 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t1 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λb0:l_e_st_eq_landau_n_rt_rp_dif.λbis:l_e_st_eq_landau_n_rt_rp_r_inn b0 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd a0) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_ande1 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t) a) (λu:l_e_st_eq_landau_n_rt_rp_negd a0.l_e_st_eq_landau_n_rt_rp_r_negin r a0 air u) : l_not (l_e_st_eq_landau_n_rt_rp_negd a0)).
-
-(* notion 4794 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t2 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λb0:l_e_st_eq_landau_n_rt_rp_dif.λbis:l_e_st_eq_landau_n_rt_rp_r_inn b0 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd b0) (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_ande1 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t) b) (λu:l_e_st_eq_landau_n_rt_rp_negd b0.l_e_st_eq_landau_n_rt_rp_r_negin s b0 bis u) : l_not (l_e_st_eq_landau_n_rt_rp_negd b0)).
-
-(* notion 4795 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t3 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λb0:l_e_st_eq_landau_n_rt_rp_dif.λbis:l_e_st_eq_landau_n_rt_rp_r_inn b0 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts r r) t (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0 (l_e_st_eq_landau_n_rt_rp_r_tict r r a0 a0 air air) cit (l_ande2 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t) a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).
-
-(* notion 4796 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t4 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λb0:l_e_st_eq_landau_n_rt_rp_dif.λbis:l_e_st_eq_landau_n_rt_rp_r_inn b0 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts s s) t (l_e_st_eq_landau_n_rt_rp_td b0 b0) c0 (l_e_st_eq_landau_n_rt_rp_r_tict s s b0 b0 bis bis) cit (l_ande2 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t) b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b0 b0) c0).
-
-(* notion 4797 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t5 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λb0:l_e_st_eq_landau_n_rt_rp_dif.λbis:l_e_st_eq_landau_n_rt_rp_r_inn b0 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin r s a0 b0 air bis (l_e_st_eq_landau_n_rt_rp_satzd161b c0 a0 b0 (l_e_st_eq_landau_n_rt_rp_r_7r161_t1 t r s a b c0 cit a0 air b0 bis) (l_e_st_eq_landau_n_rt_rp_r_7r161_t2 t r s a b c0 cit a0 air b0 bis) (l_e_st_eq_landau_n_rt_rp_r_7r161_t3 t r s a b c0 cit a0 air b0 bis) (l_e_st_eq_landau_n_rt_rp_r_7r161_t4 t r s a b c0 cit a0 air b0 bis)) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4798 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satzr161b ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).(l_e_st_eq_landau_n_rt_rp_r_realapp3 t r s (l_e_st_eq_landau_n_rt_rp_r_is r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class t).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class r).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_7r161_t5 t r s a b x u y v z w) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 4799 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t6 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd c0) (l_e_st_eq_landau_n_rt_rp_r_neg t) n (λu:l_e_st_eq_landau_n_rt_rp_negd c0.l_e_st_eq_landau_n_rt_rp_r_negin t c0 cit u) : l_not (l_e_st_eq_landau_n_rt_rp_negd c0)).
-
-(* notion 4800 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_ar ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).(l_e_st_eq_landau_n_rt_rp_r_realof a0 : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4801 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t7 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a)) (l_e_st_eq_landau_n_rt_rp_negd a0) (l_ande1 (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0) a) (λu:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a).l_e_st_eq_landau_n_rt_rp_r_negex (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) a0 (l_e_st_eq_landau_n_rt_rp_r_innclass a0) u) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a))).
-
-(* notion 4802 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t8 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a)) t (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0 (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) a0 a0 (l_e_st_eq_landau_n_rt_rp_r_innclass a0) (l_e_st_eq_landau_n_rt_rp_r_innclass a0)) cit (l_ande2 (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0) a) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a)) t).
-
-(* notion 4803 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t9 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).(l_andi (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a)) t) (l_e_st_eq_landau_n_rt_rp_r_7r161_t7 t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_t8 t n c0 cit a0 a) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a)) t)).
-
-(* notion 4804 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t10 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).(l_somei l_e_st_eq_landau_n_rt_rp_r_real (Πu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t)) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_t9 t n c0 cit a0 a) : l_e_st_eq_landau_n_rt_rp_r_some (Πu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))).
-
-(* notion 4805 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t11 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_someapp l_e_st_eq_landau_n_rt_rp_dif (Πx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c0)) (l_e_st_eq_landau_n_rt_rp_satzd161a c0 (l_e_st_eq_landau_n_rt_rp_r_7r161_t6 t n c0 cit)) (l_e_st_eq_landau_n_rt_rp_r_some (Πu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λv:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c0).l_e_st_eq_landau_n_rt_rp_r_7r161_t10 t n c0 cit x v) : l_e_st_eq_landau_n_rt_rp_r_some (Πu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))).
-
-(* notion 4806 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satzr161a ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_e_st_eq_landau_n_rt_rp_r_realapp1 t (l_e_st_eq_landau_n_rt_rp_r_some (Πu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_7r161_t11 t n x v) : l_e_st_eq_landau_n_rt_rp_r_some (Πu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))).
-
-(* notion 4807 *)
-definition l_e_st_eq_landau_n_rt_rp_r_satzr161 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_e_onei l_e_st_eq_landau_n_rt_rp_r_real (Πu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t)) (λu:l_e_st_eq_landau_n_rt_rp_r_real.λv:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg v)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts v v) t).l_e_st_eq_landau_n_rt_rp_r_satzr161b t u v a b) (l_e_st_eq_landau_n_rt_rp_r_satzr161a t n) : l_e_st_eq_landau_n_rt_rp_r_one (Πu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))).
-
-(* notion 4808 *)
-definition l_e_st_eq_landau_n_rt_rp_r_sqrt ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_e_ind l_e_st_eq_landau_n_rt_rp_r_real (Πu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t)) (l_e_st_eq_landau_n_rt_rp_r_satzr161 t n) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4809 *)
-definition l_e_st_eq_landau_n_rt_rp_r_7r161_t12 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_e_oneax l_e_st_eq_landau_n_rt_rp_r_real (Πu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t)) (l_e_st_eq_landau_n_rt_rp_r_satzr161 t n) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_sqrt t n))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_e_st_eq_landau_n_rt_rp_r_sqrt t n)) t)).
-
-(* notion 4810 *)
-definition l_e_st_eq_landau_n_rt_rp_r_thsqrt1a ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_ande1 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_sqrt t n))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_e_st_eq_landau_n_rt_rp_r_sqrt t n)) t) (l_e_st_eq_landau_n_rt_rp_r_7r161_t12 t n) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_sqrt t n))).
-
-(* notion 4811 *)
-definition l_e_st_eq_landau_n_rt_rp_r_thsqrt1b ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_ande2 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_sqrt t n))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_e_st_eq_landau_n_rt_rp_r_sqrt t n)) t) (l_e_st_eq_landau_n_rt_rp_r_7r161_t12 t n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_e_st_eq_landau_n_rt_rp_r_sqrt t n)) t).
-
-(* notion 4812 *)
-definition l_e_st_eq_landau_n_rt_rp_r_thsqrt2 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λx:l_e_st_eq_landau_n_rt_rp_r_real.λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg x).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts x x) t.(l_e_st_eq_landau_n_rt_rp_r_satzr161b t x (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_andi (l_not (l_e_st_eq_landau_n_rt_rp_r_neg x)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts x x) t) o i) (l_e_st_eq_landau_n_rt_rp_r_7r161_t12 t n) : l_e_st_eq_landau_n_rt_rp_r_is x (l_e_st_eq_landau_n_rt_rp_r_sqrt t n)).
-
-(* notion 4813 *)
-definition l_e_st_eq_landau_n_rt_rp_r_thsqrt3 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λx:l_e_st_eq_landau_n_rt_rp_r_real.λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg x).λi:l_e_st_eq_landau_n_rt_rp_r_is t (l_e_st_eq_landau_n_rt_rp_r_ts x x).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real x (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_e_st_eq_landau_n_rt_rp_r_thsqrt2 t n x o (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real t (l_e_st_eq_landau_n_rt_rp_r_ts x x) i)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) x).
-
-(* notion 4814 *)
-definition l_e_st_eq_landau_n_rt_rp_r_issqrt ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_thsqrt2 s o (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) (l_e_st_eq_landau_n_rt_rp_r_thsqrt1a r n) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)) r s (l_e_st_eq_landau_n_rt_rp_r_thsqrt1b r n) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) (l_e_st_eq_landau_n_rt_rp_r_sqrt s o)).
-
-(* notion 4815 *)
-definition l_e_st_eq_landau_n_rt_rp_r_sqrt0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_thsqrt3 r n l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_0notn l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 i (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4816 *)
-definition l_e_st_eq_landau_n_rt_rp_r_sqrt_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) o (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) l_e_st_eq_landau_n_rt_rp_r_0.l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)) (l_e_st_eq_landau_n_rt_rp_r_thsqrt1b r n) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) t)) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4817 *)
-definition l_e_st_eq_landau_n_rt_rp_r_sqrtnot0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_or3e2 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)) (l_e_st_eq_landau_n_rt_rp_r_axrlo (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)) (l_e_st_eq_landau_n_rt_rp_r_thsqrt1a r n) (l_e_st_eq_landau_n_rt_rp_r_sqrt_t1 r n o) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)).
-
-(* notion 4818 *)
-definition l_e_st_eq_landau_n_rt_rp_r_v0_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov s t n) t)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_comts t (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_assts1 r (l_e_st_eq_landau_n_rt_rp_r_ov s t n) t) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov s t n) t) s r (l_e_st_eq_landau_n_rt_rp_r_satz204e s t n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 4819 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz204g (l_e_st_eq_landau_n_rt_rp_r_ts r s) t (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) n (l_e_st_eq_landau_n_rt_rp_r_v0_t1 r s t n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_ts r s) t n)).
-
-(* notion 4820 *)
-definition l_e_st_eq_landau_n_rt_rp_r_v0_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ov r t n) (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ov r t n)) (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_disttp2 t (l_e_st_eq_landau_n_rt_rp_r_ov r t n) (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ov r t n)) r (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) s (l_e_st_eq_landau_n_rt_rp_r_satz204c r t n) (l_e_st_eq_landau_n_rt_rp_r_satz204c s t n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ov r t n) (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
-
-(* notion 4821 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz204g (l_e_st_eq_landau_n_rt_rp_r_pl r s) t (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ov r t n) (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) n (l_e_st_eq_landau_n_rt_rp_r_v0_t2 r s t n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ov r t n) (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_pl r s) t n)).
-
-(* notion 4822 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz204b r r n (l_e_st_eq_landau_n_rt_rp_r_ov r r n) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_satz204c r r n) (l_e_st_eq_landau_n_rt_rp_r_satz195 r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ov r r n) l_e_st_eq_landau_n_rt_rp_r_1rl).
-
-(* notion 4823 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_ore2 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ov l_e_st_eq_landau_n_rt_rp_r_0 r n) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz192c r (l_e_st_eq_landau_n_rt_rp_r_ov l_e_st_eq_landau_n_rt_rp_r_0 r n) (l_e_st_eq_landau_n_rt_rp_r_satz204c l_e_st_eq_landau_n_rt_rp_r_0 r n)) n : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ov l_e_st_eq_landau_n_rt_rp_r_0 r n) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4824 *)
-definition l_e_st_eq_landau_n_rt_rp_r_v0_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 r).λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_pnotn (l_e_st_eq_landau_n_rt_rp_r_m0 r) p (l_e_st_eq_landau_n_rt_rp_r_isneg r (l_e_st_eq_landau_n_rt_rp_r_m0 r) i (l_e_st_eq_landau_n_rt_rp_r_satz176f r p)) : l_con).
-
-(* notion 4825 *)
-definition l_e_st_eq_landau_n_rt_rp_r_v0_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 r).λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_nnotp (l_e_st_eq_landau_n_rt_rp_r_m0 r) n (l_e_st_eq_landau_n_rt_rp_r_ispos r (l_e_st_eq_landau_n_rt_rp_r_m0 r) i (l_e_st_eq_landau_n_rt_rp_r_satz176d r n)) : l_con).
-
-(* notion 4826 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_satz176e r (l_or3e1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_axrlo (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λt:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r).l_e_st_eq_landau_n_rt_rp_r_v0_t3 r i t) (λt:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r).l_e_st_eq_landau_n_rt_rp_r_v0_t4 r i t)) : l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4827 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz167f (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0 (l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r r)) (l_e_st_eq_landau_n_rt_rp_r_nnegsq r) (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_satz169d (l_e_st_eq_landau_n_rt_rp_r_ts r r) t)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4828 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lemma12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_rapp r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs r))) (λt:l_e_st_eq_landau_n_rt_rp_r_pos r.l_e_st_eq_landau_n_rt_rp_r_satz196a r r t t) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs r)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 r r t) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs0 r t))) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_satz196b r r t t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs r))).
-
-(* notion 4829 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_satz190a x x l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_moreisi2 x x (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real x)) (l_e_st_eq_landau_n_rt_rp_r_satz169a l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_natpos l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_natrl1)) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 4830 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_ismore2 (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_0) x (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl02 x l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_shift_t1 x ix y iy ly) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) x).
-
-(* notion 4831 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_satz172d (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) x y (l_e_st_eq_landau_n_rt_rp_r_shift_t2 x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_satz168b y x ly) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y).
-
-(* notion 4832 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_satz182d (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y (l_e_st_eq_landau_n_rt_rp_r_shift_t3 x ix y iy ly) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
-
-(* notion 4833 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_intmn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1) y iy : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
-
-(* notion 4834 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_posintnatrl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t4 x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_t5 x ix y iy ly) : l_e_st_eq_landau_n_rt_rp_r_natrl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
-
-(* notion 4835 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shiftl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly) : l_e_st_eq_landau_n_nat).
-
-(* notion 4836 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_n1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_inn (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) n : l_e_st_eq_landau_n_nat).
-
-(* notion 4837 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) n : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
-
-(* notion 4838 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_n2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4839 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_natintrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n)).
-
-(* notion 4840 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4841 *)
-definition l_e_st_eq_landau_n_rt_rp_r_intshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_intmn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_t8 x ix y iy ly n) y iy) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n)).
-
-(* notion 4842 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t8a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) l_e_st_eq_landau_n_rt_rp_r_1rl) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) y (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_mnpl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n)).
-
-(* notion 4843 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t9a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m).(l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m) l_e_st_eq_landau_n_rt_rp_r_1rl) y (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m) l_e_st_eq_landau_n_rt_rp_r_1rl i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m) l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
-
-(* notion 4844 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t10a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly m) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_t8a x ix y iy ly n)) (l_e_st_eq_landau_n_rt_rp_r_shift_t9a x ix y iy ly n m i) (l_e_st_eq_landau_n_rt_rp_r_shift_t8a x ix y iy ly m) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly m)).
-
-(* notion 4845 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t11a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m).(l_e_st_eq_landau_n_rt_rp_r_isntirl (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_shift_t10a x ix y iy ly n m i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly m)).
-
-(* notion 4846 *)
-definition l_e_st_eq_landau_n_rt_rp_r_iseshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m).(l_e_st_eq_landau_n_isinne (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) n m (l_e_st_eq_landau_n_rt_rp_r_shift_t11a x ix y iy ly n m i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) n m).
-
-(* notion 4847 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_satz188d (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x l_e_st_eq_landau_n_rt_rp_r_1rl m : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl)).
-
-(* notion 4848 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_ismore1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_shift_t9 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl)).
-
-(* notion 4849 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_satz188d (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 y) (l_e_st_eq_landau_n_rt_rp_r_shift_t10 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
-
-(* notion 4850 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_ismore1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mnpl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t11 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
-
-(* notion 4851 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly))) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n))) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shift_t12 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly))).
-
-(* notion 4852 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_lemmaiva5 (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n))) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_t13 x ix y iy ly n m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n))) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
-
-(* notion 4853 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n))) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_isntrl2 (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)) (l_e_st_eq_landau_n_rt_rp_r_shift_t14 x ix y iy ly n m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
-
-(* notion 4854 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_satz10d (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_t7 x ix y iy ly n)) (λt:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.l_e_st_eq_landau_n_rt_rp_r_shift_t15 x ix y iy ly n t) : l_not (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x)).
-
-(* notion 4855 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shiftrls ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_satz167e (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x (l_e_st_eq_landau_n_rt_rp_r_shift_t16 x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x).
-
-(* notion 4856 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n).(l_e_st_eq_landau_n_rt_rp_r_satz188d y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl m : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl y l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl)).
-
-(* notion 4857 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n).(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pl y l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_compl y l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_shift_t17 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y)).
-
-(* notion 4858 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n).(l_e_st_eq_landau_n_rt_rp_r_satz188a l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y (l_e_st_eq_landau_n_rt_rp_r_shift_t18 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n)).
-
-(* notion 4859 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n).(l_e_st_eq_landau_n_rt_rp_r_lemmaiva5 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_t19 x ix y iy ly n m) : l_e_st_eq_landau_n_more l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)).
-
-(* notion 4860 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n)) (l_e_st_eq_landau_n_more l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)) (l_e_st_eq_landau_n_satz10d l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n))) (λt:l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n).l_e_st_eq_landau_n_rt_rp_r_shift_t20 x ix y iy ly n t) : l_not (l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n))).
-
-(* notion 4861 *)
-definition l_e_st_eq_landau_n_rt_rp_r_lsshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_satz167e y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_t21 x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n)).
-
-(* notion 4862 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t22 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_and3e1 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x) a : l_e_st_eq_landau_n_rt_rp_r_intrl u).
-
-(* notion 4863 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t23 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_and3e2 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x) a : l_e_st_eq_landau_n_rt_rp_r_lessis y u).
-
-(* notion 4864 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t24 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_and3e3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x) a : l_e_st_eq_landau_n_rt_rp_r_lessis u x).
-
-(* notion 4865 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t25 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).λl:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_satz188f (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 y) (l_e_st_eq_landau_n_rt_rp_r_satz188f u x l_e_st_eq_landau_n_rt_rp_r_1rl l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
-
-(* notion 4866 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t26 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).λi:l_e_st_eq_landau_n_rt_rp_r_is u x.(l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y (l_e_st_eq_landau_n_rt_rp_r_ispl1 u x l_e_st_eq_landau_n_rt_rp_r_1rl i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
-
-(* notion 4867 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t27 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less u x) (l_e_st_eq_landau_n_rt_rp_r_is u x) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly u a) (λt:l_e_st_eq_landau_n_rt_rp_r_less u x.l_e_st_eq_landau_n_rt_rp_r_shift_t25 x ix y iy ly u a t) (λt:l_e_st_eq_landau_n_rt_rp_r_is u x.l_e_st_eq_landau_n_rt_rp_r_shift_t26 x ix y iy ly u a t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
-
-(* notion 4868 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_ul ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_rt_rp_r_shiftl u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u a) y iy (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u a) : l_e_st_eq_landau_n_nat).
-
-(* notion 4869 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t28 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_rt_rp_r_islessis12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u a) y iy (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u a))) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shift_t27 x ix y iy ly u a) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly))).
-
-(* notion 4870 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t29 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_imp_th3 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly))) (l_e_st_eq_landau_n_rt_rp_r_satz167d (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shift_t28 x ix y iy ly u a)) (λt:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_lemmaiva6 (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) t) : l_not (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly))).
-
-(* notion 4871 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t30 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_satz10e (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_t29 x ix y iy ly u a) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
-
-(* notion 4872 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shiftl1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shift_t30 x ix y iy ly u a) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
-
-(* notion 4873 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t31 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shift_t30 x ix y iy ly u a) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a))).
-
-(* notion 4874 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t32 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u a) y iy (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u a))) (l_e_st_eq_landau_n_rt_rp_r_isnterl (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_shift_t31 x ix y iy ly u a)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a))).
-
-(* notion 4875 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t33 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) y) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) l_e_st_eq_landau_n_rt_rp_r_1rl) u (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) y) (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y)) (l_e_st_eq_landau_n_rt_rp_r_mnpl u l_e_st_eq_landau_n_rt_rp_r_1rl) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) y) l_e_st_eq_landau_n_rt_rp_r_1rl) u).
-
-(* notion 4876 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shiftinv1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real u (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) y) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_shift_t33 x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) y) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) y (l_e_st_eq_landau_n_rt_rp_r_shift_t32 x ix y iy ly u a))) : l_e_st_eq_landau_n_rt_rp_r_is u (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a))).
-
-(* notion 4877 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shiftinv2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real u (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_shiftinv1 x ix y iy ly u a) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) u).
-
-(* notion 4878 *)
-definition l_e_st_eq_landau_n_rt_rp_r_seq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λalpha:Type[0].(Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πv:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πw:l_e_st_eq_landau_n_rt_rp_r_lessis t x.alpha : Type[0]).
-
-(* notion 4879 *)
-definition l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λalpha:Type[0].λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly alpha.(Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πit:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πlt:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πtl:l_e_st_eq_landau_n_rt_rp_r_lessis t x.Πu:l_e_st_eq_landau_n_rt_rp_r_real.Πiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.Πlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.Πul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.Πv:l_e_st_eq_landau_n_rt_rp_r_is t u.l_e_is alpha (s t it lt tl) (s u iu lu ul) : Prop).
-
-(* notion 4880 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shiftf ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λalpha:Type[0].λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly alpha.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).f (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly t) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly t) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly t) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly t) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).alpha).
-
-(* notion 4881 *)
-definition l_e_st_eq_landau_n_rt_rp_r_inseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.(Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πv:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πw:l_e_st_eq_landau_n_rt_rp_r_lessis t x.l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl (s t u v w)) (l_e_st_eq_landau_n_rt_rp_r_lessis y (s t u v w)) (l_e_st_eq_landau_n_rt_rp_r_lessis (s t u v w) x) : Prop).
-
-(* notion 4882 *)
-definition l_e_st_eq_landau_n_rt_rp_r_injseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.(Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πit:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πlt:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πtl:l_e_st_eq_landau_n_rt_rp_r_lessis t x.Πu:l_e_st_eq_landau_n_rt_rp_r_real.Πiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.Πlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.Πul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.Πv:l_e_st_eq_landau_n_rt_rp_r_is (s t it lt tl) (s u iu lu ul).l_e_st_eq_landau_n_rt_rp_r_is t u : Prop).
-
-(* notion 4883 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_prop1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λv:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl v) (l_e_st_eq_landau_n_rt_rp_r_lessis y v) (l_e_st_eq_landau_n_rt_rp_r_lessis v x).(l_e_st_eq_landau_n_rt_rp_r_is u (s v (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly v a) (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly v a) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly v a)) : Prop).
-
-(* notion 4884 *)
-definition l_e_st_eq_landau_n_rt_rp_r_improp ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λv:l_e_st_eq_landau_n_rt_rp_r_real.(l_and (l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl v) (l_e_st_eq_landau_n_rt_rp_r_lessis y v) (l_e_st_eq_landau_n_rt_rp_r_lessis v x)) (Πt:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl v) (l_e_st_eq_landau_n_rt_rp_r_lessis y v) (l_e_st_eq_landau_n_rt_rp_r_lessis v x).l_e_st_eq_landau_n_rt_rp_r_shift_prop1 x ix y iy ly s u v t) : Prop).
-
-(* notion 4885 *)
-definition l_e_st_eq_landau_n_rt_rp_r_imseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_some (Πt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s u t) : Prop).
-
-(* notion 4886 *)
-definition l_e_st_eq_landau_n_rt_rp_r_surjseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.(Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πv:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πw:l_e_st_eq_landau_n_rt_rp_r_lessis t x.l_e_st_eq_landau_n_rt_rp_r_imseq x ix y iy ly s t : Prop).
-
-(* notion 4887 *)
-definition l_e_st_eq_landau_n_rt_rp_r_perm ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.(l_and (l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s) (l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s) : Prop).
-
-(* notion 4888 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_ns ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4889 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t34 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(ins (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly n) : l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n)) (l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n)) (l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) x)).
-
-(* notion 4890 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shiftseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins t) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins t) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
-
-(* notion 4891 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t35 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n)) (l_e_st_eq_landau_n_rt_rp_r_shift_t30 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n)) (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins m)) (l_e_st_eq_landau_n_rt_rp_r_shift_t30 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins m)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n)) (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins m))).
-
-(* notion 4892 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t36 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_rt_rp_r_isrlint (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n)) y iy (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins m)) y iy (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins m))) (l_e_st_eq_landau_n_rt_rp_r_shift_t35 x ix y iy ly s ins js n m i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
-
-(* notion 4893 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t37 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_rt_rp_r_satz188b (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_satz188b (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 y) (l_e_st_eq_landau_n_rt_rp_r_shift_t36 x ix y iy ly s ins js n m i)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m)).
-
-(* notion 4894 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t38 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(js (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_shift_t37 x ix y iy ly s ins js n m i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m)).
-
-(* notion 4895 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t39 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_rt_rp_r_satz188b (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly m) y (l_e_st_eq_landau_n_rt_rp_r_satz188b (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly m) y) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_shift_t38 x ix y iy ly s ins js n m i)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly m)).
-
-(* notion 4896 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t40 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_rt_rp_r_isntirl (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_shift_t39 x ix y iy ly s ins js n m i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly m)).
-
-(* notion 4897 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t41 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_isinne (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) n m (l_e_st_eq_landau_n_rt_rp_r_shift_t40 x ix y iy ly s ins js n m i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) n m).
-
-(* notion 4898 *)
-definition l_e_st_eq_landau_n_rt_rp_r_injshiftseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λv:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins t) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins u).l_e_st_eq_landau_n_rt_rp_r_shift_t41 x ix y iy ly s ins js t u v : l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins)).
-
-(* notion 4899 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t42 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(ss (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_imseq x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n)).
-
-(* notion 4900 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t43 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_ande1 (l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x)) (Πt:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).l_e_st_eq_landau_n_rt_rp_r_shift_prop1 x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u t) p : l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x)).
-
-(* notion 4901 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t44 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_r_ande2 (l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x)) (Πt:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).l_e_st_eq_landau_n_rt_rp_r_shift_prop1 x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u t) p : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (s u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)))).
-
-(* notion 4902 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_ul1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
-
-(* notion 4903 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t45 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(pri u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shiftinv1 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) : l_e_st_eq_landau_n_rt_rp_r_is (s u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p))) (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p))).
-
-(* notion 4904 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t46 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_e_st_eq_landau_n_rt_rp_r_shiftinv1 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)))).
-
-(* notion 4905 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t47 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (s u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p))) (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p))) (l_e_st_eq_landau_n_rt_rp_r_shift_t44 x ix y iy ly s ins pri ss n u p) (l_e_st_eq_landau_n_rt_rp_r_shift_t45 x ix y iy ly s ins pri ss n u p) (l_e_st_eq_landau_n_rt_rp_r_shift_t46 x ix y iy ly s ins pri ss n u p) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)))).
-
-(* notion 4906 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t48 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_e_st_eq_landau_n_rt_rp_r_iseshiftr x ix y iy ly n (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t47 x ix y iy ly s ins pri ss n u p) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) n (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p))).
-
-(* notion 4907 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t49 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_somei (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) n (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins t)) (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p) (l_e_st_eq_landau_n_rt_rp_r_shift_t48 x ix y iy ly s ins pri ss n u p) : l_e_image (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins) n).
-
-(* notion 4908 *)
-definition l_e_st_eq_landau_n_rt_rp_r_shift_t50 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_someapp l_e_st_eq_landau_n_rt_rp_r_real (Πt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) t) (l_e_st_eq_landau_n_rt_rp_r_shift_t42 x ix y iy ly s ins pri ss n) (l_e_image (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins) n) (λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) t.l_e_st_eq_landau_n_rt_rp_r_shift_t49 x ix y iy ly s ins pri ss n t u) : l_e_image (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins) n).
-
-(* notion 4909 *)
-definition l_e_st_eq_landau_n_rt_rp_r_surjshiftseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_shift_t50 x ix y iy ly s ins pri ss t : l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins)).
-
-(* notion 4910 *)
-definition l_e_st_eq_landau_n_rt_rp_r_bijshiftseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_andi (l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins)) (l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins)) (l_e_st_eq_landau_n_rt_rp_r_injshiftseq x ix y iy ly s ins (l_ande1 (l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s) (l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s) ps)) (l_e_st_eq_landau_n_rt_rp_r_surjshiftseq x ix y iy ly s ins pri (l_ande2 (l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s) (l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s) ps)) : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins)).
-
-(* notion 4911 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_complex ≝ (l_e_st_eq_landau_n_pair1type l_e_st_eq_landau_n_rt_rp_r_real : Type[0]).
-
-(* notion 4912 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_cx ≝ (l_e_st_eq_landau_n_rt_rp_r_c_complex : Type[0]).
-
-(* notion 4913 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_is ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_is l_e_st_eq_landau_n_rt_rp_r_c_cx x y : Prop).
-
-(* notion 4914 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_nis ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_not (l_e_st_eq_landau_n_rt_rp_r_c_is x y) : Prop).
-
-(* notion 4915 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_some ≝ λp:Πt:l_e_st_eq_landau_n_rt_rp_r_c_complex.Prop.(l_some l_e_st_eq_landau_n_rt_rp_r_c_cx p : Prop).
-
-(* notion 4916 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_all ≝ λp:Πt:l_e_st_eq_landau_n_rt_rp_r_c_complex.Prop.(l_all l_e_st_eq_landau_n_rt_rp_r_c_cx p : Prop).
-
-(* notion 4917 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_one ≝ λp:Πt:l_e_st_eq_landau_n_rt_rp_r_c_complex.Prop.(l_e_one l_e_st_eq_landau_n_rt_rp_r_c_cx p : Prop).
-
-(* notion 4918 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_pli ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_pair1 l_e_st_eq_landau_n_rt_rp_r_real a b : l_e_st_eq_landau_n_rt_rp_r_c_complex).
-
-(* notion 4919 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_re ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_first1 l_e_st_eq_landau_n_rt_rp_r_real x : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4920 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_im ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_second1 l_e_st_eq_landau_n_rt_rp_r_real x : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 4921 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_reis ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_first1is1 l_e_st_eq_landau_n_rt_rp_r_real a b : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a).
-
-(* notion 4922 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_isre ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_first1is2 l_e_st_eq_landau_n_rt_rp_r_real a b : l_e_st_eq_landau_n_rt_rp_r_is a (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))).
-
-(* notion 4923 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_imis ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_second1is1 l_e_st_eq_landau_n_rt_rp_r_real a b : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b).
-
-(* notion 4924 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_isim ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_second1is2 l_e_st_eq_landau_n_rt_rp_r_real a b : l_e_st_eq_landau_n_rt_rp_r_is b (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))).
-
-(* notion 4925 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_pliis ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_pair1is1 l_e_st_eq_landau_n_rt_rp_r_real x : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x).
-
-(* notion 4926 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ispli ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_pair1is2 l_e_st_eq_landau_n_rt_rp_r_real x : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))).
-
-(* notion 4927 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_iscere ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_real (Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_re t) x y i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)).
-
-(* notion 4928 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_isceim ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_real (Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_im t) x y i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)).
-
-(* notion 4929 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is a b.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_pli t c) a b i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli a c) (l_e_st_eq_landau_n_rt_rp_r_c_pli b c)).
-
-(* notion 4930 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is a b.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_pli c t) a b i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli c a) (l_e_st_eq_landau_n_rt_rp_r_c_pli c b)).
-
-(* notion 4931 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is a b.λj:l_e_st_eq_landau_n_rt_rp_r_is c d.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pli a c) (l_e_st_eq_landau_n_rt_rp_r_c_pli b c) (l_e_st_eq_landau_n_rt_rp_r_c_pli b d) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 a b c i) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 c d b j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli a c) (l_e_st_eq_landau_n_rt_rp_r_c_pli b d)).
-
-(* notion 4932 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz206 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x : l_e_st_eq_landau_n_rt_rp_r_c_is x x).
-
-(* notion 4933 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz207 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx x y i : l_e_st_eq_landau_n_rt_rp_r_c_is y x).
-
-(* notion 4934 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz208 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_c_is y z.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx x y z i j : l_e_st_eq_landau_n_rt_rp_r_c_is x z).
-
-(* notion 4935 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_0c ≝ (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 : l_e_st_eq_landau_n_rt_rp_r_c_complex).
-
-(* notion 4936 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_1c ≝ (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 : l_e_st_eq_landau_n_rt_rp_r_c_complex).
-
-(* notion 4937 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_pl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_c_complex).
-
-(* notion 4938 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_plis12a ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_pl b d) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) c (l_e_st_eq_landau_n_rt_rp_r_c_reis a b) (l_e_st_eq_landau_n_rt_rp_r_c_reis c d)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) d (l_e_st_eq_landau_n_rt_rp_r_c_imis a b) (l_e_st_eq_landau_n_rt_rp_r_c_imis c d)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl b d))).
-
-(* notion 4939 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_plis12b ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl b d)) (l_e_st_eq_landau_n_rt_rp_r_c_plis12a a b c d) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl b d)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))).
-
-(* notion 4940 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_plis1a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
-
-(* notion 4941 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_plis1b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_plis1a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x)).
-
-(* notion 4942 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_plis2a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) s) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) s))).
-
-(* notion 4943 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_plis2b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_c_plis2a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))).
-
-(* notion 4944 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ispl1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t z) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)).
-
-(* notion 4945 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ispl2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl z t) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y)).
-
-(* notion 4946 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ispl12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_c_is z u.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) (l_e_st_eq_landau_n_rt_rp_r_c_ispl1 x y z i) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 z u y j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)).
-
-(* notion 4947 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz209 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y x)).
-
-(* notion 4948 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_compl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz209 x y : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y x)).
-
-(* notion 4949 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz210 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_plis2a x l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x l_e_st_eq_landau_n_rt_rp_r_c_0c) x).
-
-(* notion 4950 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz210a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl x l_e_st_eq_landau_n_rt_rp_r_c_0c) x (l_e_st_eq_landau_n_rt_rp_r_c_satz210 x) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_pl x l_e_st_eq_landau_n_rt_rp_r_c_0c)).
-
-(* notion 4951 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz210b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl l_e_st_eq_landau_n_rt_rp_r_c_0c x) (l_e_st_eq_landau_n_rt_rp_r_c_pl x l_e_st_eq_landau_n_rt_rp_r_c_0c) x (l_e_st_eq_landau_n_rt_rp_r_c_compl l_e_st_eq_landau_n_rt_rp_r_c_0c x) (l_e_st_eq_landau_n_rt_rp_r_c_satz210 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl l_e_st_eq_landau_n_rt_rp_r_c_0c x) x).
-
-(* notion 4952 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz210c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl l_e_st_eq_landau_n_rt_rp_r_c_0c x) x (l_e_st_eq_landau_n_rt_rp_r_c_satz210b x) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_pl l_e_st_eq_landau_n_rt_rp_r_c_0c x)).
-
-(* notion 4953 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz211 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_plis1a z (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_c_plis2b x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
-
-(* notion 4954 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_asspl1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz211 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
-
-(* notion 4955 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_asspl2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z)).
-
-(* notion 4956 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2212_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re u)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_isre (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re u)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im u))) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re u)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)).
-
-(* notion 4957 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2212_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im u)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_isim (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re u)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im u))) (l_e_st_eq_landau_n_rt_rp_r_c_isceim (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im u)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)).
-
-(* notion 4958 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2212_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_st_eq_landau_n_rt_rp_r_satz187d (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re u) (l_e_st_eq_landau_n_rt_rp_r_c_2212_t1 x y u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re u) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))).
-
-(* notion 4959 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2212_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_st_eq_landau_n_rt_rp_r_satz187d (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im u) (l_e_st_eq_landau_n_rt_rp_r_c_2212_t2 x y u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im u) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))).
-
-(* notion 4960 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz212a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx u (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re u) (l_e_st_eq_landau_n_rt_rp_r_c_im u)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_ispli u) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re u) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im u) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_2212_t3 x y u i) (l_e_st_eq_landau_n_rt_rp_r_c_2212_t4 x y u i)) : l_e_st_eq_landau_n_rt_rp_r_c_is u (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))).
-
-(* notion 4961 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz212b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_plis2a y (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_satz187a (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz187a (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) x).
-
-(* notion 4962 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz212c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_somei l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y t) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_satz212b x y) : l_e_st_eq_landau_n_rt_rp_r_c_some (λt:l_e_st_eq_landau_n_rt_rp_r_c_complex.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y t) x)).
-
-(* notion 4963 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz212 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_onei l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y t) x) (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y t) x.λw:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx t u (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_satz212a x y t v) (l_e_st_eq_landau_n_rt_rp_r_c_satz212a x y u w)) (l_e_st_eq_landau_n_rt_rp_r_c_satz212c x y) : l_e_st_eq_landau_n_rt_rp_r_c_one (λt:l_e_st_eq_landau_n_rt_rp_r_c_complex.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y t) x)).
-
-(* notion 4964 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_mn ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_c_complex).
-
-(* notion 4965 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_mnis12a ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_mn b d) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) c (l_e_st_eq_landau_n_rt_rp_r_c_reis a b) (l_e_st_eq_landau_n_rt_rp_r_c_reis c d)) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) d (l_e_st_eq_landau_n_rt_rp_r_c_imis a b) (l_e_st_eq_landau_n_rt_rp_r_c_imis c d)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn b d))).
-
-(* notion 4966 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_mnis12b ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn b d)) (l_e_st_eq_landau_n_rt_rp_r_c_mnis12a a b c d) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn b d)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))).
-
-(* notion 4967 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_mnis1a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_mn s (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn s (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
-
-(* notion 4968 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_mnis1b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_mnis1a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x)).
-
-(* notion 4969 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_mnis2a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) s) (l_e_st_eq_landau_n_rt_rp_r_ismn2 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ismn2 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) s))).
-
-(* notion 4970 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_mnis2b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_c_mnis2a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))).
-
-(* notion 4971 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ismn1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_mn t z) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)).
-
-(* notion 4972 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ismn2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_mn z t) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn z x) (l_e_st_eq_landau_n_rt_rp_r_c_mn z y)).
-
-(* notion 4973 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ismn12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_c_is z u.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn y u) (l_e_st_eq_landau_n_rt_rp_r_c_ismn1 x y z i) (l_e_st_eq_landau_n_rt_rp_r_c_ismn2 z u y j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) (l_e_st_eq_landau_n_rt_rp_r_c_mn y u)).
-
-(* notion 4974 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz212d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_st_eq_landau_n_rt_rp_r_c_satz212a x y u i : l_e_st_eq_landau_n_rt_rp_r_c_is u (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
-
-(* notion 4975 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz212e ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx u (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz212d x y u i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) u).
-
-(* notion 4976 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz212f ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl u y) x.(l_e_st_eq_landau_n_rt_rp_r_c_satz212d x y u (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y) x (l_e_st_eq_landau_n_rt_rp_r_c_compl y u) i) : l_e_st_eq_landau_n_rt_rp_r_c_is u (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
-
-(* notion 4977 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz212g ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl u y) x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx u (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz212f x y u i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) u).
-
-(* notion 4978 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz212h ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212b x y : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) x).
-
-(* notion 4979 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_0c) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isre (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_reis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4980 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_im l_e_st_eq_landau_n_rt_rp_r_c_0c) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isim (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_isceim (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_imis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4981 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_satz182b (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_2213_t1 x y i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)).
-
-(* notion 4982 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_satz182b (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_2213_t2 x y i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)).
-
-(* notion 4983 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz213a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) y (l_e_st_eq_landau_n_rt_rp_r_c_ispli x) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_2213_t3 x y i) (l_e_st_eq_landau_n_rt_rp_r_c_2213_t4 x y i)) (l_e_st_eq_landau_n_rt_rp_r_c_pliis y) : l_e_st_eq_landau_n_rt_rp_r_c_is x y).
-
-(* notion 4984 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_st_eq_landau_n_rt_rp_r_satz182e (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_iscere x y i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4985 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_st_eq_landau_n_rt_rp_r_satz182e (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_isceim x y i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 4986 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz213b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_2213_t5 x y i) (l_e_st_eq_landau_n_rt_rp_r_c_2213_t6 x y i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 4987 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_m0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_mn l_e_st_eq_landau_n_rt_rp_r_c_0c x : l_e_st_eq_landau_n_rt_rp_r_c_complex).
-
-(* notion 4988 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz214 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_pl01 (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_reis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl01 (l_e_st_eq_landau_n_rt_rp_r_c_im l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_imis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
-
-(* notion 4989 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz214a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)).
-
-(* notion 4990 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_m0isa ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 a) (l_e_st_eq_landau_n_rt_rp_r_m0 b)) (l_e_st_eq_landau_n_rt_rp_r_c_satz214 (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))) (l_e_st_eq_landau_n_rt_rp_r_m0 a) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))) (l_e_st_eq_landau_n_rt_rp_r_m0 b) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_c_reis a b)) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_imis a b))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 a) (l_e_st_eq_landau_n_rt_rp_r_m0 b))).
-
-(* notion 4991 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_m0isb ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 a) (l_e_st_eq_landau_n_rt_rp_r_m0 b)) (l_e_st_eq_landau_n_rt_rp_r_c_m0isa a b) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 a) (l_e_st_eq_landau_n_rt_rp_r_m0 b)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))).
-
-(* notion 4992 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ism0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_m0 t) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)).
-
-(* notion 4993 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz215 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x)) (l_e_st_eq_landau_n_rt_rp_r_c_m0isa (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_satz177 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_satz177 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) x).
-
-(* notion 4994 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz215a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) x (l_e_st_eq_landau_n_rt_rp_r_c_satz215 x) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))).
-
-(* notion 4995 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz215b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) y (l_e_st_eq_landau_n_rt_rp_r_c_ism0 x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) i) (l_e_st_eq_landau_n_rt_rp_r_c_satz215 y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y).
-
-(* notion 4996 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz215c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y (l_e_st_eq_landau_n_rt_rp_r_c_satz215b x y i) : l_e_st_eq_landau_n_rt_rp_r_c_is y (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)).
-
-(* notion 4997 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz215d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y.(l_e_st_eq_landau_n_rt_rp_r_c_satz215c y x (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y i) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)).
-
-(* notion 4998 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz215e ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) (l_e_st_eq_landau_n_rt_rp_r_c_satz215d x y i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) x).
-
-(* notion 4999 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz216 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) x (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x)) (l_e_st_eq_landau_n_rt_rp_r_c_plis2a x (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz179 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_satz179 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5000 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2216_anders ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212h l_e_st_eq_landau_n_rt_rp_r_c_0c x : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5001 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz216a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) x) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_compl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) x) (l_e_st_eq_landau_n_rt_rp_r_c_satz216 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) x) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5002 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz217 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0isa (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_satz180 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz180 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_plis12b (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) (l_e_st_eq_landau_n_rt_rp_r_c_satz214a x) (l_e_st_eq_landau_n_rt_rp_r_c_satz214a y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))).
-
-(* notion 5003 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz217a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz217 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
-
-(* notion 5004 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz218 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_plis2b x (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) x (l_e_st_eq_landau_n_rt_rp_r_c_satz214a y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))).
-
-(* notion 5005 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz218a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz218 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
-
-(* notion 5006 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_2219_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz218 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz217 x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) y (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz215 y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y)).
-
-(* notion 5007 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz219 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_mn y x) (l_e_st_eq_landau_n_rt_rp_r_c_2219_t1 x y) (l_e_st_eq_landau_n_rt_rp_r_c_compl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz218a y x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn y x)).
-
-(* notion 5008 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz219a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn y x)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz219 y x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn y x))).
-
-(* notion 5009 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ts ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) : l_e_st_eq_landau_n_rt_rp_r_c_complex).
-
-(* notion 5010 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_rets ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5011 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_imts ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5012 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_ts b d) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) c (l_e_st_eq_landau_n_rt_rp_r_c_reis a b) (l_e_st_eq_landau_n_rt_rp_r_c_reis c d)) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) d (l_e_st_eq_landau_n_rt_rp_r_c_imis a b) (l_e_st_eq_landau_n_rt_rp_r_c_imis c d)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts b d))).
-
-(* notion 5013 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_ts b c) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) d (l_e_st_eq_landau_n_rt_rp_r_c_reis a b) (l_e_st_eq_landau_n_rt_rp_r_c_imis c d)) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) c (l_e_st_eq_landau_n_rt_rp_r_c_imis a b) (l_e_st_eq_landau_n_rt_rp_r_c_reis c d)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts b c))).
-
-(* notion 5014 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_tsis12a ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts b d)) (l_e_st_eq_landau_n_rt_rp_r_c_imts (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts b c)) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t1 a b c d) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t2 a b c d) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts b d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts b c)))).
-
-(* notion 5015 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_tsis12b ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts b d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts b c))) (l_e_st_eq_landau_n_rt_rp_r_c_tsis12a a b c d) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts b d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts b c))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))).
-
-(* notion 5016 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
-
-(* notion 5017 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x)))).
-
-(* notion 5018 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_tsis1a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_imts (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t3 x r s) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t4 x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x))))).
-
-(* notion 5019 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_tsis1b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x)))) (l_e_st_eq_landau_n_rt_rp_r_c_tsis1a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x)))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x)).
-
-(* notion 5020 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s))).
-
-(* notion 5021 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r))).
-
-(* notion 5022 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_tsis2a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_c_imts x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r)) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t5 x r s) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t6 x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r)))).
-
-(* notion 5023 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_tsis2b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r))) (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r))) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))).
-
-(* notion 5024 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ists1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t z) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)).
-
-(* notion 5025 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ists2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts z t) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y)).
-
-(* notion 5026 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ists12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_c_is z u.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 x y z i) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 z u y j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)).
-
-(* notion 5027 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3220_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets y x)).
-
-(* notion 5028 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3220_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_imts y x) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts y x)).
-
-(* notion 5029 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz220 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets y x) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts y x) (l_e_st_eq_landau_n_rt_rp_r_c_3220_t1 x y) (l_e_st_eq_landau_n_rt_rp_r_c_3220_t2 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y x)).
-
-(* notion 5030 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_comts ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz220 x y : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y x)).
-
-(* notion 5031 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_lemma1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_0c) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_iscere x l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_reis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5032 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_lemma2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im l_e_st_eq_landau_n_rt_rp_r_c_0c) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isceim x l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_imis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5033 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_mod2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5034 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_lemma3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma1 x i)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma2 x i))) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5035 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5036 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5037 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) n (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_ispli x) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 i t)) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5038 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_ispos (l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 x) (l_e_st_eq_landau_n_rt_rp_r_pl01 (l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 x) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) i))) (l_e_st_eq_landau_n_rt_rp_r_possq (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t7 x n i)) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
-
-(* notion 5039 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_ispos (l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 x) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 x) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x) i))) (l_e_st_eq_landau_n_rt_rp_r_possq (l_e_st_eq_landau_n_rt_rp_r_c_re x) o) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
-
-(* notion 5040 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_pospl (l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 x) (l_e_st_eq_landau_n_rt_rp_r_possq (l_e_st_eq_landau_n_rt_rp_r_c_re x) o) (l_e_st_eq_landau_n_rt_rp_r_possq (l_e_st_eq_landau_n_rt_rp_r_c_im x) p) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
-
-(* notion 5041 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_v3_t9 x n o t) (λt:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_v3_t10 x n o t) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
-
-(* notion 5042 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_lemma4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_v3_t8 x n t) (λt:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_v3_t11 x n t) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
-
-(* notion 5043 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_lemma5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x))) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_0notn (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma3 x t)) (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_pnotn (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma4 x t)) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x))).
-
-(* notion 5044 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma1 x i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5045 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma2 x i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5046 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_mn l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t1 x y i)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t2 x y i))) (l_e_st_eq_landau_n_rt_rp_r_satz187c l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl02 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5047 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t1 x y i)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t2 x y i))) (l_e_st_eq_landau_n_rt_rp_r_pl02 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5048 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz221a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_3221_t3 x y i) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t4 x y i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5049 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz221b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_comts x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz221a y x i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5050 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma4 y n : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y)).
-
-(* notion 5051 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_reis (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma1 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5052 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_imis (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma2 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5053 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t6 x y i n)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t7 x y i n))) (l_e_st_eq_landau_n_rt_rp_r_pl02 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5054 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_ii1r ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re y) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5055 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ir ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5056 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_ir1i ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5057 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5058 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_rr1r ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re y) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5059 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5060 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_ri1r ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re y) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5061 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ir ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5062 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_ri1i ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5063 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5064 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_3221_ii1r x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ir x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_3221_ii1r x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)).
-
-(* notion 5065 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_rr1r x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_ii1r x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_disttm1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_3221_rr1r x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_ii1r x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t9 x y i n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y))).
-
-(* notion 5066 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_ri1i x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_ir1i x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_3221_ri1i x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_ir1i x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y))).
-
-(* notion 5067 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t10 x y i n) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t11 x y i n)) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y)) (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y) (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y))) (l_e_st_eq_landau_n_rt_rp_r_distpt2 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y))).
-
-(* notion 5068 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t12 x y i n) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t8 x y i n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5069 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz192c (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t13 x y i n)) (l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t5 x y i n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5070 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz182b (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t6 x y i n)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t14 x y i n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5071 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_pl01 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t14 x y i n))) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t7 x y i n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5072 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_c_v3_t7 y n j : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_im y) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5073 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz192c (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t15 x y i n)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t17 x y i n j) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5074 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz192c (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t16 x y i n)) o : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5075 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_3221_t18 x y i n t) (λt:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_3221_t19 x y i n t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5076 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_ispli x) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_3221_t14 x y i n) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t20 x y i n)) : l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5077 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz221c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_or_th2 (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c) (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_3221_t21 x y i t) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c)).
-
-(* notion 5078 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz221d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_or (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_or_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c) n o) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_satz221c x y t) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5079 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3222_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz195 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts02 (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)).
-
-(* notion 5080 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3222_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_ts02 (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_satz195 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)).
-
-(* notion 5081 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz222 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a x l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_3222_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_3222_t2 x)) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x l_e_st_eq_landau_n_rt_rp_r_c_1c) x).
-
-(* notion 5082 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz222a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x l_e_st_eq_landau_n_rt_rp_r_c_1c) x (l_e_st_eq_landau_n_rt_rp_r_c_satz222 x) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_ts x l_e_st_eq_landau_n_rt_rp_r_c_1c)).
-
-(* notion 5083 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz222b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x l_e_st_eq_landau_n_rt_rp_r_c_1c) x (l_e_st_eq_landau_n_rt_rp_r_c_comts l_e_st_eq_landau_n_rt_rp_r_c_1c x) (l_e_st_eq_landau_n_rt_rp_r_c_satz222 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c x) x).
-
-(* notion 5084 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz222c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c x) x (l_e_st_eq_landau_n_rt_rp_r_c_satz222b x) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c x)).
-
-(* notion 5085 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3223_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_satz197b (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_satz195 (l_e_st_eq_landau_n_rt_rp_r_c_re x)))) (l_e_st_eq_landau_n_rt_rp_r_ts02 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)))) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))).
-
-(* notion 5086 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3223_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl))) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts02 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_satz197b (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_satz195 (l_e_st_eq_landau_n_rt_rp_r_c_im x))))) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))).
-
-(* notion 5087 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz223 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) x (l_e_st_eq_landau_n_rt_rp_r_c_m0isa l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a x (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_3223_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_3223_t2 x)) (l_e_st_eq_landau_n_rt_rp_r_c_satz214a x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)).
-
-(* notion 5088 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz223a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz223 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c))).
-
-(* notion 5089 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz223b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) x) (l_e_st_eq_landau_n_rt_rp_r_c_satz223 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)).
-
-(* notion 5090 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz223c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz223b x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) x)).
-
-(* notion 5091 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5092 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5093 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5094 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5095 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3224_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y))) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y)) (l_e_st_eq_landau_n_rt_rp_r_satz197a (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz197a (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y))) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_satz177 (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y))) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y)) (l_e_st_eq_landau_n_rt_rp_r_satz181a (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y)))).
-
-(* notion 5096 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3224_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry x y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry x y))) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry x y)) (l_e_st_eq_landau_n_rt_rp_r_satz197a (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_satz197a (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_satz180a (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry x y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry x y)))).
-
-(* notion 5097 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz224a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) y) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) y (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x)) (l_e_st_eq_landau_n_rt_rp_r_c_tsis1a y (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3224_t1 x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_t2 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0isb (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y))).
-
-(* notion 5098 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz224b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts y x)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_comts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz224a y x) (l_e_st_eq_landau_n_rt_rp_r_c_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_comts y x)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y))).
-
-(* notion 5099 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz224c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz224a x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz224b x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))).
-
-(* notion 5100 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz224d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz224c x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y)).
-
-(* notion 5101 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz224e ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz224a x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y)).
-
-(* notion 5102 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz224f ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz224b x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))).
-
-(* notion 5103 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz225 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz224c x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) y x (l_e_st_eq_landau_n_rt_rp_r_c_satz215 y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)).
-
-(* notion 5104 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz225a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz225 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))).
-
-(* notion 5105 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5106 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iir ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5107 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rii ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5108 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iri ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5109 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rri ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5110 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iii ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5111 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rir ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5112 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_irr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5113 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)) (l_e_st_eq_landau_n_rt_rp_r_disttm1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_satz180a (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))))).
-
-(* notion 5114 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_disttm1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z))) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z))).
-
-(* notion 5115 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_tsis1a z (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t2 x y z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)))).
-
-(* notion 5116 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts a b) c) (l_e_st_eq_landau_n_rt_rp_r_ts a (l_e_st_eq_landau_n_rt_rp_r_ts b c)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts b c) a) (l_e_st_eq_landau_n_rt_rp_r_assts1 a b c) (l_e_st_eq_landau_n_rt_rp_r_comts a (l_e_st_eq_landau_n_rt_rp_r_ts b c)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts a b) c) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts b c) a)).
-
-(* notion 5117 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_pl c (l_e_st_eq_landau_n_rt_rp_r_pl a b)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl c a) b) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_asspl2 c a b) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl c a) b)).
-
-(* notion 5118 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl a (l_e_st_eq_landau_n_rt_rp_r_pl b c)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl b c) a) (l_e_st_eq_landau_n_rt_rp_r_pl b (l_e_st_eq_landau_n_rt_rp_r_pl c a)) (l_e_st_eq_landau_n_rt_rp_r_compl a (l_e_st_eq_landau_n_rt_rp_r_pl b c)) (l_e_st_eq_landau_n_rt_rp_r_asspl1 b c a) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl a (l_e_st_eq_landau_n_rt_rp_r_pl b c)) (l_e_st_eq_landau_n_rt_rp_r_pl b (l_e_st_eq_landau_n_rt_rp_r_pl c a))).
-
-(* notion 5119 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr y z x : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5120 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_iir y z x : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5121 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_rii y z x : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5122 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_iri y z x : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5123 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_rri y z x : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5124 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_iii y z x : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5125 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_rir y z x : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5126 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_irr y z x : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5127 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t6 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))).
-
-(* notion 5128 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t5 (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z))).
-
-(* notion 5129 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t7 x y z) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z))))).
-
-(* notion 5130 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t8 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z))).
-
-(* notion 5131 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t3 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t9 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t10 x y z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z)))).
-
-(* notion 5132 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_comts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t3 y z x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z)))).
-
-(* notion 5133 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t11 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t12 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
-
-(* notion 5134 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz226 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_t13 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
-
-(* notion 5135 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_assts1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz226 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
-
-(* notion 5136 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_assts2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z)).
-
-(* notion 5137 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_pl a (l_e_st_eq_landau_n_rt_rp_r_pl b c)) (l_e_st_eq_landau_n_rt_rp_r_pl a (l_e_st_eq_landau_n_rt_rp_r_pl c b)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) b) (l_e_st_eq_landau_n_rt_rp_r_asspl1 a b c) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_pl b c) (l_e_st_eq_landau_n_rt_rp_r_pl c b) a (l_e_st_eq_landau_n_rt_rp_r_compl b c)) (l_e_st_eq_landau_n_rt_rp_r_asspl2 a c b) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) b)).
-
-(* notion 5138 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_pl c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) d) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) b) d) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl b d)) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_pl a b) c d) (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) b) d (l_e_st_eq_landau_n_rt_rp_r_c_3227_t1 a b c)) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_pl a c) b d) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_pl c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl b d))).
-
-(* notion 5139 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_pl c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 c) (l_e_st_eq_landau_n_rt_rp_r_m0 d))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn b d)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 c) (l_e_st_eq_landau_n_rt_rp_r_m0 d)) (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_satz180 c d)) (l_e_st_eq_landau_n_rt_rp_r_c_3227_t2 a b (l_e_st_eq_landau_n_rt_rp_r_m0 c) (l_e_st_eq_landau_n_rt_rp_r_m0 d)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_pl c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn b d))).
-
-(* notion 5140 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets x z)) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_disttp2 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_disttp2 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_c_3227_t3 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets x z))).
-
-(* notion 5141 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x z)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_disttp2 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_disttp2 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_c_3227_t2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x z))).
-
-(* notion 5142 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets x z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x z))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets x z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_3227_t4 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3227_t5 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_plis12b (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets x z) (l_e_st_eq_landau_n_rt_rp_r_c_imts x z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
-
-(* notion 5143 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz227 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3227_t6 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
-
-(* notion 5144 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_disttp1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_satz227 z x y) (l_e_st_eq_landau_n_rt_rp_r_c_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_comts z x) (l_e_st_eq_landau_n_rt_rp_r_c_comts z y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
-
-(* notion 5145 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_disttp2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz227 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
-
-(* notion 5146 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_distpt1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_disttp1 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z)).
-
-(* notion 5147 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_distpt2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_disttp2 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
-
-(* notion 5148 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz228 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_m0 z))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 z))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_m0 z)) x (l_e_st_eq_landau_n_rt_rp_r_c_satz218 y z)) (l_e_st_eq_landau_n_rt_rp_r_c_disttp2 x y (l_e_st_eq_landau_n_rt_rp_r_c_m0 z)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 z)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz224b x z)) (l_e_st_eq_landau_n_rt_rp_r_c_satz218a (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
-
-(* notion 5149 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_disttm1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_satz228 z x y) (l_e_st_eq_landau_n_rt_rp_r_c_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_comts z x) (l_e_st_eq_landau_n_rt_rp_r_c_comts z y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
-
-(* notion 5150 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_disttm2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz228 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
-
-(* notion 5151 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_distmt1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_disttm1 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)).
-
-(* notion 5152 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_distmt2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_disttm2 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z))).
-
-(* notion 5153 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λu1:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu2:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) x.λj:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) x.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) x i j : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2)).
-
-(* notion 5154 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λu1:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu2:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) x.λj:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_mn u1 u2)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_disttm2 y u1 u2) (l_e_st_eq_landau_n_rt_rp_r_c_satz213b (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t1 x y n u1 u2 i j)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_mn u1 u2)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5155 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λu1:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu2:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) x.λj:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) x.(l_ore2 (l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn u1 u2) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_satz221c y (l_e_st_eq_landau_n_rt_rp_r_c_mn u1 u2) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t2 x y n u1 u2 i j)) n : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn u1 u2) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5156 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz229b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λu1:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu2:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) x.λj:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) x.(l_e_st_eq_landau_n_rt_rp_r_c_satz213a u1 u2 (l_e_st_eq_landau_n_rt_rp_r_c_3229_t3 x y n u1 u2 i j) : l_e_st_eq_landau_n_rt_rp_r_c_is u1 u2).
-
-(* notion 5157 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_lemma4 y n) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5158 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_u ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)))) x : l_e_st_eq_landau_n_rt_rp_r_c_complex).
-
-(* notion 5159 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_dd ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λv:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ov v (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5160 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_satz197b (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_satz177 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_lemma6 (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))).
-
-(* notion 5161 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_lemma6 (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t5 x y n)) (l_e_st_eq_landau_n_rt_rp_r_lemma7 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) (l_e_st_eq_landau_n_rt_rp_r_lemma8 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) l_e_st_eq_landau_n_rt_rp_r_1rl).
-
-(* notion 5162 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_satz197d (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_lemma6 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))).
-
-(* notion 5163 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t7 x y n) (l_e_st_eq_landau_n_rt_rp_r_lemma6 (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n))) (l_e_st_eq_landau_n_rt_rp_r_lemma7 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))))).
-
-(* notion 5164 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz197a (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_satz182e (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5165 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_t8 x y n) (l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n t) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_t9 x y n)) (l_e_st_eq_landau_n_rt_rp_r_lemma9 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5166 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))))) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a y (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_t6 x y n) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t10 x y n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) l_e_st_eq_landau_n_rt_rp_r_c_1c).
-
-(* notion 5167 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_3229_u x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c x) x (l_e_st_eq_landau_n_rt_rp_r_c_assts2 y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) x) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) l_e_st_eq_landau_n_rt_rp_r_c_1c x (l_e_st_eq_landau_n_rt_rp_r_c_3229_t11 x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_satz222b x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_3229_u x y n)) x).
-
-(* notion 5168 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz229a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_somei l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x) (l_e_st_eq_landau_n_rt_rp_r_c_3229_u x y n) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t12 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_some (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x)).
-
-(* notion 5169 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz229 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_onei l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x) (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x.λw:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) x.l_e_st_eq_landau_n_rt_rp_r_c_satz229b x y n t u v w) (l_e_st_eq_landau_n_rt_rp_r_c_satz229a x y n) : l_e_st_eq_landau_n_rt_rp_r_c_one (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x)).
-
-(* notion 5170 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ov ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_ind l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x) (l_e_st_eq_landau_n_rt_rp_r_c_satz229 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_complex).
-
-(* notion 5171 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz229c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_oneax l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x) (l_e_st_eq_landau_n_rt_rp_r_c_satz229 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x).
-
-(* notion 5172 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz229d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n))).
-
-(* notion 5173 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz229e ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x).
-
-(* notion 5174 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz229f ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x (l_e_st_eq_landau_n_rt_rp_r_c_satz229e x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y)).
-
-(* notion 5175 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz229g ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) x.(l_e_st_eq_landau_n_rt_rp_r_c_satz229b x y n u (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) i (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is u (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)).
-
-(* notion 5176 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz229h ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx u (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz229g x y u n i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) u).
-
-(* notion 5177 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz229j ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts u y) x.(l_e_st_eq_landau_n_rt_rp_r_c_satz229g x y u n (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y) x (l_e_st_eq_landau_n_rt_rp_r_c_comts y u) i) : l_e_st_eq_landau_n_rt_rp_r_c_is u (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)).
-
-(* notion 5178 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz229k ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts u y) x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx u (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz229j x y u n i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) u).
-
-(* notion 5179 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_isov1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ov t z n) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)).
-
-(* notion 5180 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_isov2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229h z x (l_e_st_eq_landau_n_rt_rp_r_c_ov z y o) n (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov z y o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y o)) z (l_e_st_eq_landau_n_rt_rp_r_c_ists1 x y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y o) i) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c z y o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov z x n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y o)).
-
-(* notion 5181 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_isov12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_c_is z u.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y u o) (l_e_st_eq_landau_n_rt_rp_r_c_isov1 x y z i n) (l_e_st_eq_landau_n_rt_rp_r_c_isov2 z u y j n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y u o)).
-
-(* notion 5182 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz230 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) x (l_e_st_eq_landau_n_rt_rp_r_c_compl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz212h x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x).
-
-(* notion 5183 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz231 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212e (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) y x (l_e_st_eq_landau_n_rt_rp_r_c_compl y x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) y) x).
-
-(* notion 5184 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz232 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212e x (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) y).
-
-(* notion 5185 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_4233_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) z) y) (l_e_st_eq_landau_n_rt_rp_r_c_compl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_compl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) z y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) z) y)).
-
-(* notion 5186 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_4233_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) z) y) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x (l_e_st_eq_landau_n_rt_rp_r_c_4233_t1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y (l_e_st_eq_landau_n_rt_rp_r_c_satz230 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) x).
-
-(* notion 5187 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz233 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212d x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_4233_t2 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
-
-(* notion 5188 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz234 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212g (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) z) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) z) y x (l_e_st_eq_landau_n_rt_rp_r_c_satz230 y z))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z))).
-
-(* notion 5189 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz234a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_satz234 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z)).
-
-(* notion 5190 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz234b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl y x) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y) (l_e_st_eq_landau_n_rt_rp_r_c_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y x) z (l_e_st_eq_landau_n_rt_rp_r_c_compl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz234 y x z) (l_e_st_eq_landau_n_rt_rp_r_c_compl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y)).
-
-(* notion 5191 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz234c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz234b x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z)).
-
-(* notion 5192 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz235 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212f x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl z (l_e_st_eq_landau_n_rt_rp_r_c_mn y z))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl z (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz212h y z)) (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z))).
-
-(* notion 5193 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz235a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_satz235 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)).
-
-(* notion 5194 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz235b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz235a x y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz234c x z y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) y)).
-
-(* notion 5195 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz235c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) y) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz235b x y z) (l_e_st_eq_landau_n_rt_rp_r_c_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) y (l_e_st_eq_landau_n_rt_rp_r_c_compl x z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) y)).
-
-(* notion 5196 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz236 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212g (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y z) (l_e_st_eq_landau_n_rt_rp_r_c_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x z (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
-
-(* notion 5197 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz236a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_compl z x) (l_e_st_eq_landau_n_rt_rp_r_c_compl z y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz236 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
-
-(* notion 5198 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_4237_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) u) y) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) u y) (l_e_st_eq_landau_n_rt_rp_r_c_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) u) z y (l_e_st_eq_landau_n_rt_rp_r_c_satz230 z u)) (l_e_st_eq_landau_n_rt_rp_r_c_compl z y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)).
-
-(* notion 5199 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_4237_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_compl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_4237_t1 x y z u)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
-
-(* notion 5200 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_4237_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_4237_t2 x y z u) (l_e_st_eq_landau_n_rt_rp_r_c_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y z) (l_e_st_eq_landau_n_rt_rp_r_c_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x z (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl x z)).
-
-(* notion 5201 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz237 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212f (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_4237_t3 x y z u) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u))).
-
-(* notion 5202 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_4238_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl u z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl z u)) (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 x u z) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl u z) (l_e_st_eq_landau_n_rt_rp_r_c_pl z u) x (l_e_st_eq_landau_n_rt_rp_r_c_compl u z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl z u))).
-
-(* notion 5203 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_4238_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_pl z u))) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz237 (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) z u) (l_e_st_eq_landau_n_rt_rp_r_c_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_pl z u)) (l_e_st_eq_landau_n_rt_rp_r_c_4238_t1 x y z u) (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 y z u)) (l_e_st_eq_landau_n_rt_rp_r_c_satz236 x y (l_e_st_eq_landau_n_rt_rp_r_c_pl z u)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
-
-(* notion 5204 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz238 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212g (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_4238_t2 x y z u) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
-
-(* notion 5205 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_4239_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_satz238 x y z u) (l_e_st_eq_landau_n_rt_rp_r_c_satz213b (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5206 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz239a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u).(l_e_st_eq_landau_n_rt_rp_r_c_satz213a (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_4239_t1 x y z u i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)).
-
-(* notion 5207 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_4239_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_satz238 x y z u) (l_e_st_eq_landau_n_rt_rp_r_c_satz213b (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5208 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz239b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z).(l_e_st_eq_landau_n_rt_rp_r_c_satz213a (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_4239_t2 x y z u i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)).
-
-(* notion 5209 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz240 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x).
-
-(* notion 5210 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz241 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229h (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) y x n (l_e_st_eq_landau_n_rt_rp_r_c_comts y x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) y n) x).
-
-(* notion 5211 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_lemma6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) n (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx x l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y o) (l_e_st_eq_landau_n_rt_rp_r_c_satz221b y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) t)) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5212 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz242 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229h x (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) y (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 x y n o) (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 x y n o)) y).
-
-(* notion 5213 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5243_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) z) y) (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) (l_e_st_eq_landau_n_rt_rp_r_c_comts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) z y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) z) y)).
-
-(* notion 5214 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5243_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) z) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x (l_e_st_eq_landau_n_rt_rp_r_c_5243_t1 x y z n o) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) z) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y (l_e_st_eq_landau_n_rt_rp_r_c_satz240 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) x).
-
-(* notion 5215 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz243 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229g x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o) (l_e_st_eq_landau_n_rt_rp_r_c_5243_t2 x y z n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o))).
-
-(* notion 5216 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz244 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229k (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) n (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n) z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n) z) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n) z) y x (l_e_st_eq_landau_n_rt_rp_r_c_satz240 y z n))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n))).
-
-(* notion 5217 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz244a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_satz244 x y z n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n)).
-
-(* notion 5218 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz244b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) y) (l_e_st_eq_landau_n_rt_rp_r_c_isov1 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) z (l_e_st_eq_landau_n_rt_rp_r_c_comts x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_satz244 y x z n) (l_e_st_eq_landau_n_rt_rp_r_c_comts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) y)).
-
-(* notion 5219 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz244c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz244b x y z n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) y) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n)).
-
-(* notion 5220 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz245 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229j x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o) (l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x (l_e_st_eq_landau_n_rt_rp_r_c_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o)) y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c y z o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z) (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o))).
-
-(* notion 5221 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz245a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z) (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz245 x y z n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z)).
-
-(* notion 5222 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz245b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz245a x y z n o) (l_e_st_eq_landau_n_rt_rp_r_c_satz244c x z y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) y n)).
-
-(* notion 5223 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz245c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz245b x y z n o) (l_e_st_eq_landau_n_rt_rp_r_c_isov1 (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) y (l_e_st_eq_landau_n_rt_rp_r_c_comts x z) n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) y n)).
-
-(* notion 5224 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz246 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229k (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y z) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x z (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y n))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)).
-
-(* notion 5225 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz246a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z y o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_isov12 (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_comts z x) (l_e_st_eq_landau_n_rt_rp_r_c_comts z y) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z y o n) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz246 x y z n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z y o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)).
-
-(* notion 5226 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5247_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) u) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) u y) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) u) z y (l_e_st_eq_landau_n_rt_rp_r_c_satz240 z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_comts z y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)).
-
-(* notion 5227 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5247_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_comts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_5247_t1 x y z u n o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
-
-(* notion 5228 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5247_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_5247_t2 x y z u n o) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y z) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x z (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)).
-
-(* notion 5229 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz247 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229j (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o) (l_e_st_eq_landau_n_rt_rp_r_c_5247_t3 x y z u n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o))).
-
-(* notion 5230 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5248_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts u z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 x u z) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts u z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z u) x (l_e_st_eq_landau_n_rt_rp_r_c_comts u z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts z u))).
-
-(* notion 5231 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5248_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u p)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) u (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o) p)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u) n (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z u o p))) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz247 (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) z u (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o) p) (l_e_st_eq_landau_n_rt_rp_r_c_isov12 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_5248_t1 x y z u n o p) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 y z u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) u (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o) p) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u) n (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z u o p))) (l_e_st_eq_landau_n_rt_rp_r_c_satz246 x y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u) n (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z u o p)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u p)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)).
-
-(* notion 5232 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz248 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229k (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u p) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u o p) (l_e_st_eq_landau_n_rt_rp_r_c_5248_t2 x y z u n o p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u p) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u o p)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o))).
-
-(* notion 5233 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz249 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229h l_e_st_eq_landau_n_rt_rp_r_c_0c x l_e_st_eq_landau_n_rt_rp_r_c_0c n (l_e_st_eq_landau_n_rt_rp_r_c_satz221b x l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_0c)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_0c x n) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5234 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz250 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229h x x l_e_st_eq_landau_n_rt_rp_r_c_1c n (l_e_st_eq_landau_n_rt_rp_r_c_satz222 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x x n) l_e_st_eq_landau_n_rt_rp_r_c_1c).
-
-(* notion 5235 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz251a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov x x (l_e_notis_th2 l_e_st_eq_landau_n_rt_rp_r_c_cx y l_e_st_eq_landau_n_rt_rp_r_c_0c x n i)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_isov2 y x x (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx x y i) n (l_e_notis_th2 l_e_st_eq_landau_n_rt_rp_r_c_cx y l_e_st_eq_landau_n_rt_rp_r_c_0c x n i)) (l_e_st_eq_landau_n_rt_rp_r_c_satz250 x (l_e_notis_th2 l_e_st_eq_landau_n_rt_rp_r_c_cx y l_e_st_eq_landau_n_rt_rp_r_c_0c x n i)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) l_e_st_eq_landau_n_rt_rp_r_c_1c).
-
-(* notion 5236 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz251b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) l_e_st_eq_landau_n_rt_rp_r_c_1c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y l_e_st_eq_landau_n_rt_rp_r_c_1c) y (l_e_st_eq_landau_n_rt_rp_r_c_satz229d x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) l_e_st_eq_landau_n_rt_rp_r_c_1c y i) (l_e_st_eq_landau_n_rt_rp_r_c_satz222 y) : l_e_st_eq_landau_n_rt_rp_r_c_is x y).
-
-(* notion 5237 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_0c u o) l_e_st_eq_landau_n_rt_rp_r_c_0c i (l_e_st_eq_landau_n_rt_rp_r_c_isov1 z l_e_st_eq_landau_n_rt_rp_r_c_0c u j o) (l_e_st_eq_landau_n_rt_rp_r_c_satz249 u o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5238 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_satz229d x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz221b y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_5252_t1 x y z u n o i j)) : l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5239 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_satz221a x u (l_e_st_eq_landau_n_rt_rp_r_c_5252_t2 x y z u n o i j)) (l_e_st_eq_landau_n_rt_rp_r_c_satz221b y z j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)).
-
-(* notion 5240 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n p)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u p o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz248 x y z u n p o) (l_e_st_eq_landau_n_rt_rp_r_c_satz251a (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u p o) i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n p)) l_e_st_eq_landau_n_rt_rp_r_c_1c).
-
-(* notion 5241 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz251b (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n p) (l_e_st_eq_landau_n_rt_rp_r_c_5252_t4 x y z u n o i p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)).
-
-(* notion 5242 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz252a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_5252_t3 x y z u n o i t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_5252_t5 x y z u n o i t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)).
-
-(* notion 5243 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) l_e_st_eq_landau_n_rt_rp_r_c_0c i (l_e_st_eq_landau_n_rt_rp_r_c_satz221b y z j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5244 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is u l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_satz221c x u (l_e_st_eq_landau_n_rt_rp_r_c_5252_t6 x y z u n o i j)) o : l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5245 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_0c y n) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_isov1 x l_e_st_eq_landau_n_rt_rp_r_c_0c y (l_e_st_eq_landau_n_rt_rp_r_c_5252_t7 x y z u n o i j) n) (l_e_st_eq_landau_n_rt_rp_r_c_satz249 y n)) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_0c u o) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_isov1 z l_e_st_eq_landau_n_rt_rp_r_c_0c u j o) (l_e_st_eq_landau_n_rt_rp_r_c_satz249 u o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)).
-
-(* notion 5246 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u p o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n p)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_satz248 x y z u n p o) (l_e_st_eq_landau_n_rt_rp_r_c_satz251a (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n p) i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u p o)) l_e_st_eq_landau_n_rt_rp_r_c_1c).
-
-(* notion 5247 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz251b (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u p o) (l_e_st_eq_landau_n_rt_rp_r_c_5252_t9 x y z u n o i p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)).
-
-(* notion 5248 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz252b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_5252_t8 x y z u n o i t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_5252_t10 x y z u n o i t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)).
-
-(* notion 5249 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz253 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229g (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) y (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) n (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n))) (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_disttp2 y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) z (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c z y n))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) y n)).
-
-(* notion 5250 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_distop ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_satz253 x z y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n))).
-
-(* notion 5251 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_distpo ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz253 x z y n : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z n)).
-
-(* notion 5252 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz254 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o))) (l_e_st_eq_landau_n_rt_rp_r_c_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_satz246 x y u n o) (l_e_st_eq_landau_n_rt_rp_r_c_satz246a z u y o n)) (l_e_st_eq_landau_n_rt_rp_r_c_satz253 (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o))).
-
-(* notion 5253 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz255 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229g (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) n (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n))) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n))) (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) (l_e_st_eq_landau_n_rt_rp_r_c_disttm2 y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) z (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c z y n))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y n)).
-
-(* notion 5254 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_distom ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_satz255 x z y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n))).
-
-(* notion 5255 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_distmo ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz255 x z y n : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z n)).
-
-(* notion 5256 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz256 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o))) (l_e_st_eq_landau_n_rt_rp_r_c_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_satz246 x y u n o) (l_e_st_eq_landau_n_rt_rp_r_c_satz246a z u y o n)) (l_e_st_eq_landau_n_rt_rp_r_c_satz255 (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o))).
-
-(* notion 5257 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_conj ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) : l_e_st_eq_landau_n_rt_rp_r_c_complex).
-
-(* notion 5258 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_conjisa ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))) (l_e_st_eq_landau_n_rt_rp_r_m0 b) (l_e_st_eq_landau_n_rt_rp_r_c_reis a b) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_imis a b)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_pli a (l_e_st_eq_landau_n_rt_rp_r_m0 b))).
-
-(* notion 5259 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_conjisb ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_pli a (l_e_st_eq_landau_n_rt_rp_r_m0 b)) (l_e_st_eq_landau_n_rt_rp_r_c_conjisa a b) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli a (l_e_st_eq_landau_n_rt_rp_r_m0 b)) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))).
-
-(* notion 5260 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_isconj ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_conj t) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)).
-
-(* notion 5261 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz257 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_conjisa (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_satz177 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) x).
-
-(* notion 5262 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz258a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_isconj x l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_conjisa l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5263 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6258_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isre (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma1 (l_e_st_eq_landau_n_rt_rp_r_c_conj x) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5264 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6258_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_satz176e (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isim (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma2 (l_e_st_eq_landau_n_rt_rp_r_c_conj x) i)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5265 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz258b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_ispli x) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_6258_t1 x i) (l_e_st_eq_landau_n_rt_rp_r_c_6258_t2 x i)) : l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5266 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6258_anders ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx x l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_satz257 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz258a (l_e_st_eq_landau_n_rt_rp_r_c_conj x) i) : l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5267 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz258c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) n (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_satz258b x t) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5268 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6259_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_isim (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isceim (l_e_st_eq_landau_n_rt_rp_r_c_conj x) x i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)).
-
-(* notion 5269 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz259a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) x.(l_e_st_eq_landau_n_rt_rp_r_lemma10 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_6259_t1 x i)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5270 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz259b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz176b (l_e_st_eq_landau_n_rt_rp_r_c_im x) i) i)) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) x).
-
-(* notion 5271 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz269c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_conj x).(l_e_st_eq_landau_n_rt_rp_r_c_satz259a x (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_conj x) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5272 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz269d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) x (l_e_st_eq_landau_n_rt_rp_r_c_satz259b x i) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)).
-
-(* notion 5273 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz260 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_conjisa (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz180 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_plis12b (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
-
-(* notion 5274 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz260a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz260 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
-
-(* notion 5275 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6261_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_satz180 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz197f (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_satz197e (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))).
-
-(* notion 5276 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz261 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_conjisa (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ismn2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz198a (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_6261_t1 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_tsis12b (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
-
-(* notion 5277 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz261a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz261 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y))).
-
-(* notion 5278 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6262_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y)).
-
-(* notion 5279 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6262_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_isconj x (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) (l_e_st_eq_landau_n_rt_rp_r_c_6262_t1 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz260 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
-
-(* notion 5280 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz262 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212f (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_6262_t2 x y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
-
-(* notion 5281 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz262a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz262 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y))).
-
-(* notion 5282 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6263_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229f x y n : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y)).
-
-(* notion 5283 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6263_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_isconj x (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_6263_t1 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y))).
-
-(* notion 5284 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6263_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz261 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
-
-(* notion 5285 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6263_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_6263_t2 x y n) (l_e_st_eq_landau_n_rt_rp_r_c_6263_t3 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
-
-(* notion 5286 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_6263_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz258c y n : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_conj y) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 5287 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz263 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229j (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_6263_t5 x y n) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_6263_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y) (l_e_st_eq_landau_n_rt_rp_r_c_satz258c y n))).
-
-(* notion 5288 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz263a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y) (l_e_st_eq_landau_n_rt_rp_r_c_satz258c y n)) (l_e_st_eq_landau_n_rt_rp_r_c_satz263 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y) (l_e_st_eq_landau_n_rt_rp_r_c_satz258c y n)) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n))).
-
-(* notion 5289 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_mod ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_sqrt (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5290 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_ismod ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_real (Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_mod t) x y i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)).
-
-(* notion 5291 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz264a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_sqrtnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x) (l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma4 x n)) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod x)).
-
-(* notion 5292 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz264b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_sqrt0 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma3 x i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5293 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz264c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_thsqrt1a (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod x))).
-
-(* notion 5294 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz264d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_satz167f (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0 (l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_c_satz264c x) (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_satz169d (l_e_st_eq_landau_n_rt_rp_r_c_mod x) t)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5295 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_thsqrt1b (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x))).
-
-(* notion 5296 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_lemma12 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)))).
-
-(* notion 5297 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_satz191 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_moreisi2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)))) (l_e_st_eq_landau_n_rt_rp_r_lemma11 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 5298 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismoreis12 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t2 x) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t3 x) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)))).
-
-(* notion 5299 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_lemma12 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
-
-(* notion 5300 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_satz191 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_lemma11 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_moreisi2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
-
-(* notion 5301 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismoreis12 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t5 x) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t6 x) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
-
-(* notion 5302 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l : l_e_st_eq_landau_n_rt_rp_r_more s r).
-
-(* notion 5303 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_satz169b s (l_e_st_eq_landau_n_rt_rp_r_satz172d s r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_7265_t8 r s m n l) n) : l_e_st_eq_landau_n_rt_rp_r_pos s).
-
-(* notion 5304 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λo:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_trmore (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_satz203a s r s (l_e_st_eq_landau_n_rt_rp_r_c_7265_t8 r s m n l) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t9 r s m n l)) (l_e_st_eq_landau_n_rt_rp_r_satz203d s r r (l_e_st_eq_landau_n_rt_rp_r_c_7265_t8 r s m n l) (l_e_st_eq_landau_n_rt_rp_r_satz169b r o)) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts r r)).
-
-(* notion 5305 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_ismore2 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 r r i)) (l_e_st_eq_landau_n_rt_rp_r_satz169a (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_possq s (l_e_st_eq_landau_n_rt_rp_r_pnot0 s (l_e_st_eq_landau_n_rt_rp_r_c_7265_t9 r s m n l)))) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts r r)).
-
-(* notion 5306 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_orapp (l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts r r)) n (λt:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_7265_t10 r s m n l t) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_7265_t11 r s m n l t)) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s)).
-
-(* notion 5307 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t13 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz167f r s (λt:l_e_st_eq_landau_n_rt_rp_r_less r s.l_e_st_eq_landau_n_rt_rp_r_satz167c (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s) m (l_e_st_eq_landau_n_rt_rp_r_c_7265_t12 r s m n t)) : l_e_st_eq_landau_n_rt_rp_r_moreis r s).
-
-(* notion 5308 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz265a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_7265_t13 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t4 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz264d x) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x))).
-
-(* notion 5309 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz265b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_7265_t13 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t7 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz264d x) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x))).
-
-(* notion 5310 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t1 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts t t) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_satz176b (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts t t) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts t t)).
-
-(* notion 5311 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t2 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 t)) (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 t) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 t (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_ts02 t l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 t)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5312 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t3 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli t l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts t t) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 t))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts t t) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_tsis12a t l_e_st_eq_landau_n_rt_rp_r_0 t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts t t) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts t t) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 t)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_7266_t1 t) (l_e_st_eq_landau_n_rt_rp_r_c_7266_t2 t)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli t l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts t t) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 5313 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts s s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_7266_t3 r)) i (l_e_st_eq_landau_n_rt_rp_r_c_7266_t3 s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts s s) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 5314 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts s s) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_c_isre (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts s s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_7266_t4 r s i n o)) (l_e_st_eq_landau_n_rt_rp_r_c_reis (l_e_st_eq_landau_n_rt_rp_r_ts s s) l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s)).
-
-(* notion 5315 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).(l_andi (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s)) n (l_e_st_eq_landau_n_rt_rp_r_c_7266_t5 r s i n o) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s))).
-
-(* notion 5316 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).(l_andi (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts s s)) o (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts s s)) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts s s))).
-
-(* notion 5317 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz266 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).(l_e_st_eq_landau_n_rt_rp_r_satzr161b (l_e_st_eq_landau_n_rt_rp_r_ts s s) r s (l_e_st_eq_landau_n_rt_rp_r_c_7266_t6 r s i n o) (l_e_st_eq_landau_n_rt_rp_r_c_7266_t7 r s i n o) : l_e_st_eq_landau_n_rt_rp_r_is r s).
-
-(* notion 5318 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7267_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_7266_t3 (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_thsqrt1b (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 5319 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7267_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_satz197e (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_satz198 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
-
-(* notion 5320 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7267_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_satz197b (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_satz179a (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x))) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5321 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7267_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a x (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_7267_t2 x) (l_e_st_eq_landau_n_rt_rp_r_c_7267_t3 x)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 5322 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz267 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_7267_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_7267_t4 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x))).
-
-(* notion 5323 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz267a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_satz267 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0))).
-
-(* notion 5324 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) z (l_e_st_eq_landau_n_rt_rp_r_c_comts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 y x z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
-
-(* notion 5325 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u))) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_ts y u))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 x y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) x (l_e_st_eq_landau_n_rt_rp_r_c_7268_t1 y z u)) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 x z (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u))).
-
-(* notion 5326 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_conj y))) (l_e_st_eq_landau_n_rt_rp_r_c_satz267 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz261 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t2 x y (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_conj y)))).
-
-(* notion 5327 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_conj y))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t3 x y) (l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_satz267a x) (l_e_st_eq_landau_n_rt_rp_r_c_satz267a y)) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t2 (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)))).
-
-(* notion 5328 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_satz176b (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
-
-(* notion 5329 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 s (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_ts02 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5330 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_tsis12a r l_e_st_eq_landau_n_rt_rp_r_0 s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_7268_t5 r s) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t6 r s)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 5331 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t4 x y) (l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t7 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t7 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0))).
-
-(* notion 5332 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)).(l_orapp (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) l_con (l_e_st_eq_landau_n_rt_rp_r_satz196h (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) n) (Πt:l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod y)).l_e_st_eq_landau_n_rt_rp_r_c_satz264c y (l_ande2 (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) t)) (Πt:l_and (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod y)).l_e_st_eq_landau_n_rt_rp_r_c_satz264c x (l_ande1 (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) t)) : l_con).
-
-(* notion 5333 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz268 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz266 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t8 x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz264c (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (λt:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)).l_e_st_eq_landau_n_rt_rp_r_c_7268_t9 x y t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))).
-
-(* notion 5334 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz268a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz268 x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y))).
-
-(* notion 5335 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7269_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_satz264a y n) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5336 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7269_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz268 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)).
-
-(* notion 5337 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7269_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_satz204g (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_7269_t1 x y n) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n))) (l_e_st_eq_landau_n_rt_rp_r_c_7269_t2 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_7269_t1 x y n))).
-
-(* notion 5338 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz269 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_7269_t3 x y n : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_satz264a y n)))).
-
-(* notion 5339 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7270_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_abs r) r) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_moreisi1 (l_e_st_eq_landau_n_rt_rp_r_abs r) r (l_e_st_eq_landau_n_rt_rp_r_trmore (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0 r (l_e_st_eq_landau_n_rt_rp_r_satz169a (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_satz166b r t)) (l_e_st_eq_landau_n_rt_rp_r_lemma2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz169c r t)))) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).l_e_st_eq_landau_n_rt_rp_r_moreisi2 (l_e_st_eq_landau_n_rt_rp_r_abs r) r (l_e_st_eq_landau_n_rt_rp_r_absnn r t)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_abs r) r).
-
-(* notion 5340 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7270_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_trmoreis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_satz265a x) (l_e_st_eq_landau_n_rt_rp_r_c_7270_t1 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)).
-
-(* notion 5341 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7270_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_1c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_1c) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_isre (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_1c i) (l_e_st_eq_landau_n_rt_rp_r_c_reis l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_1rl).
-
-(* notion 5342 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz270 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_1c.(l_e_st_eq_landau_n_rt_rp_r_ismoreis2 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7270_t3 x y i) (l_e_st_eq_landau_n_rt_rp_r_satz191 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_7270_t2 x) (l_e_st_eq_landau_n_rt_rp_r_c_7270_t2 y)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_1rl).
-
-(* notion 5343 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz264b (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5344 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ismoreis2 (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t1 x y i)) (l_e_st_eq_landau_n_rt_rp_r_satz191 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_satz264d x) (l_e_st_eq_landau_n_rt_rp_r_c_satz264d y)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
-
-(* notion 5345 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz264a (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 5346 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_satz253 x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz250 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) l_e_st_eq_landau_n_rt_rp_r_c_1c).
-
-(* notion 5347 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz270 (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t4 x y n) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n))) l_e_st_eq_landau_n_rt_rp_r_1rl).
-
-(* notion 5348 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_fx ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t3 x y n) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5349 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_fy ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t3 x y n) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5350 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ismoreis1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz269 x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_satz269 y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t5 x y n) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl).
-
-(* notion 5351 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_prl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5352 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_prr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5353 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_orapp (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t6 x y n) (λt:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl.l_e_st_eq_landau_n_rt_rp_r_moreisi1 (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n) (l_e_st_eq_landau_n_rt_rp_r_satz203a (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) t (l_e_st_eq_landau_n_rt_rp_r_c_satz264a (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n))) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl.l_e_st_eq_landau_n_rt_rp_r_moreisi2 (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) t)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n)).
-
-(* notion 5354 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))) (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_satz204e (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t3 x y n)) (l_e_st_eq_landau_n_rt_rp_r_satz204e (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t3 x y n))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))).
-
-(* notion 5355 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_satz195b (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
-
-(* notion 5356 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ismoreis12 (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t8 x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t9 x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t7 x y n) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
-
-(* notion 5357 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_7271_t2 x y t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_7271_t10 x y t) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
-
-(* notion 5358 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz271 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_satz168a (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t11 x y) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))).
-
-(* notion 5359 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz271a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_7271_t11 x y : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
-
-(* notion 5360 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7272_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x)) (l_e_st_eq_landau_n_rt_rp_r_c_reis (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))).
-
-(* notion 5361 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7272_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t1 x)) (l_e_st_eq_landau_n_rt_rp_r_satz198 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x))).
-
-(* notion 5362 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7272_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_isceim (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x)) (l_e_st_eq_landau_n_rt_rp_r_c_imis (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))).
-
-(* notion 5363 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7272_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t3 x) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t3 x)) (l_e_st_eq_landau_n_rt_rp_r_satz198 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))).
-
-(* notion 5364 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7272_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t2 x) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t4 x) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
-
-(* notion 5365 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz272 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_issqrt (l_e_st_eq_landau_n_rt_rp_r_c_mod2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t5 x) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)).
-
-(* notion 5366 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz272a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_satz272 x) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))).
-
-(* notion 5367 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7273_sum ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5368 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_islessis1 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y))) (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) x (l_e_st_eq_landau_n_rt_rp_r_c_satz212h x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz271 y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y)).
-
-(* notion 5369 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t1 x y) (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y).l_e_st_eq_landau_n_rt_rp_r_satz188f (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) t) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y).l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))).
-
-(* notion 5370 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)))) (l_e_st_eq_landau_n_rt_rp_r_mnpl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y))).
-
-(* notion 5371 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_satz168b (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_islessis2 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t3 x y) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t2 x y)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))).
-
-(* notion 5372 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismoreis12 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn y x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) (l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn y x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y))) (l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn y x) (l_e_st_eq_landau_n_rt_rp_r_c_satz219 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz272 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y))) (l_e_st_eq_landau_n_rt_rp_r_satz181a (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t4 y x) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)))).
-
-(* notion 5373 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r) (l_or_th6 (l_e_st_eq_landau_n_rt_rp_r_neg r)) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_absn r t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).l_e_st_eq_landau_n_rt_rp_r_absnn r t) : l_or (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r)).
-
-(* notion 5374 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis r (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_orapp (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs s) s) (l_e_st_eq_landau_n_rt_rp_r_moreis r (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t6 s) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_m0 s).l_e_st_eq_landau_n_rt_rp_r_ismoreis2 (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_abs s) r (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_m0 s) t) n) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs s) s.l_e_st_eq_landau_n_rt_rp_r_ismoreis2 s (l_e_st_eq_landau_n_rt_rp_r_abs s) r (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs s) s t) m) : l_e_st_eq_landau_n_rt_rp_r_moreis r (l_e_st_eq_landau_n_rt_rp_r_abs s)).
-
-(* notion 5375 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz273 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_7273_t7 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t4 x y) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t5 x y) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)))).
-
-(* notion 5376 *)
-definition l_e_st_eq_landau_n_8274_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_some (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y) (Πf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y.l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to y) f) : Prop).
-
-(* notion 5377 *)
-definition l_e_st_eq_landau_n_8274_prop2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λy:l_e_st_eq_landau_n_nat.l_imp (l_e_st_eq_landau_n_less x y) (l_not (l_e_st_eq_landau_n_8274_prop1 x y))) : Prop).
-
-(* notion 5378 *)
-definition l_e_st_eq_landau_n_8274_1y ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_1out y : l_e_st_eq_landau_n_1to y).
-
-(* notion 5379 *)
-definition l_e_st_eq_landau_n_8274_yy ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_xout y : l_e_st_eq_landau_n_1to y).
-
-(* notion 5380 *)
-definition l_e_st_eq_landau_n_8274_t1 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_yy y l f).(l_e_st_eq_landau_n_isoutne y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a y) y (l_e_st_eq_landau_n_lessisi3 y) i : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 y).
-
-(* notion 5381 *)
-definition l_e_st_eq_landau_n_8274_t2 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_ec3e31 (l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_more l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_satz10b l_e_st_eq_landau_n_1 y) l : l_e_st_eq_landau_n_nis l_e_st_eq_landau_n_1 y).
-
-(* notion 5382 *)
-definition l_e_st_eq_landau_n_8274_t3 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_yy y l f)) (l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_8274_t2 y l f) (λt:l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_yy y l f).l_e_st_eq_landau_n_8274_t1 y l f t) : l_not (l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_yy y l f))).
-
-(* notion 5383 *)
-definition l_e_st_eq_landau_n_8274_t4 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f u l_e_st_eq_landau_n_1o (l_e_st_eq_landau_n_singlet_th1 u) : l_e_is (l_e_st_eq_landau_n_1to y) (f u) (f l_e_st_eq_landau_n_1o)).
-
-(* notion 5384 *)
-definition l_e_st_eq_landau_n_8274_t5 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_notis_th2 (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_yy y l f) (f u) (l_e_st_eq_landau_n_8274_t3 y l f) (l_e_tris (l_e_st_eq_landau_n_1to y) (f u) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_t4 y l f u) i) : l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f u) (l_e_st_eq_landau_n_8274_yy y l f))).
-
-(* notion 5385 *)
-definition l_e_st_eq_landau_n_8274_t6 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f).(l_some_th5 (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_yy y l f) (f u)) (λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_symnotis (l_e_st_eq_landau_n_1to y) (f u) (l_e_st_eq_landau_n_8274_yy y l f) (l_e_st_eq_landau_n_8274_t5 y l f i u)) : l_not (l_e_image (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_yy y l f))).
-
-(* notion 5386 *)
-definition l_e_st_eq_landau_n_8274_t7 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f).(l_all_th1 (l_e_st_eq_landau_n_1to y) (Πu:l_e_st_eq_landau_n_1to y.l_e_image (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f u) (l_e_st_eq_landau_n_8274_yy y l f) (l_e_st_eq_landau_n_8274_t6 y l f i) : l_not (l_e_surjective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f)).
-
-(* notion 5387 *)
-definition l_e_st_eq_landau_n_8274_t8 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f)).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_notis_th2 (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f) (f u) n (l_e_st_eq_landau_n_8274_t4 y l f u) : l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f u) (l_e_st_eq_landau_n_8274_1y y l f))).
-
-(* notion 5388 *)
-definition l_e_st_eq_landau_n_8274_t9 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f)).(l_some_th5 (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (f u)) (λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_symnotis (l_e_st_eq_landau_n_1to y) (f u) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_t8 y l f n u)) : l_not (l_e_image (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_1y y l f))).
-
-(* notion 5389 *)
-definition l_e_st_eq_landau_n_8274_t10 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f)).(l_all_th1 (l_e_st_eq_landau_n_1to y) (Πu:l_e_st_eq_landau_n_1to y.l_e_image (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f u) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_t9 y l f n) : l_not (l_e_surjective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f)).
-
-(* notion 5390 *)
-definition l_e_st_eq_landau_n_8274_t11 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f)) (l_not (l_e_surjective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f)) (λt:l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f).l_e_st_eq_landau_n_8274_t7 y l f t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f)).l_e_st_eq_landau_n_8274_t10 y l f t) : l_not (l_e_surjective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f)).
-
-(* notion 5391 *)
-definition l_e_st_eq_landau_n_8274_t12 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_and_th2 (l_e_injective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f) (l_e_surjective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f) (l_e_st_eq_landau_n_8274_t11 y l f) : l_not (l_e_bijective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f)).
-
-(* notion 5392 *)
-definition l_e_st_eq_landau_n_8274_t13 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.(l_some_th5 (Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y) (Πf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.l_e_bijective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f) (λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_8274_t12 y l f) : l_not (l_e_st_eq_landau_n_8274_prop1 l_e_st_eq_landau_n_1 y)).
-
-(* notion 5393 *)
-definition l_e_st_eq_landau_n_8274_t14 ≝ (λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.l_e_st_eq_landau_n_8274_t13 y t : l_e_st_eq_landau_n_8274_prop2 l_e_st_eq_landau_n_1).
-
-(* notion 5394 *)
-definition l_e_st_eq_landau_n_8274_xs ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_suc x : l_e_st_eq_landau_n_nat).
-
-(* notion 5395 *)
-definition l_e_st_eq_landau_n_8274_xxs ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_8274_xs x) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_suc x)).
-
-(* notion 5396 *)
-definition l_e_st_eq_landau_n_8274_yy1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_xout y : l_e_st_eq_landau_n_1to y).
-
-(* notion 5397 *)
-definition l_e_st_eq_landau_n_8274_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_trless l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_suc x) y (l_e_st_eq_landau_n_satz24c x) l : l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y).
-
-(* notion 5398 *)
-definition l_e_st_eq_landau_n_8274_ym1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_mn y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_8274_t15 x p y l) : l_e_st_eq_landau_n_nat).
-
-(* notion 5399 *)
-definition l_e_st_eq_landau_n_8274_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) y (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz4e x) (l_e_st_eq_landau_n_mn_th1c y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_8274_t15 x p y l)) l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1)).
-
-(* notion 5400 *)
-definition l_e_st_eq_landau_n_8274_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_satz20c x (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_8274_t16 x p y l) : l_e_st_eq_landau_n_less x (l_e_st_eq_landau_n_8274_ym1 x p y l)).
-
-(* notion 5401 *)
-definition l_e_st_eq_landau_n_8274_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1) y (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_mn_th1d y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_8274_t15 x p y l)) (l_e_st_eq_landau_n_satz18a (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_ym1 x p y l) y).
-
-(* notion 5402 *)
-definition l_e_st_eq_landau_n_8274_t19 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.(l_ande1 (l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f) (l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f) b : l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f).
-
-(* notion 5403 *)
-definition l_e_st_eq_landau_n_8274_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.(l_ande2 (l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f) (l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f) b : l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f).
-
-(* notion 5404 *)
-definition l_e_st_eq_landau_n_8274_u1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_inn x u : l_e_st_eq_landau_n_nat).
-
-(* notion 5405 *)
-definition l_e_st_eq_landau_n_8274_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_satz16a (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) x (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_satz18c x) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)).
-
-(* notion 5406 *)
-definition l_e_st_eq_landau_n_8274_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_t21 x p y l f b i u) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)).
-
-(* notion 5407 *)
-definition l_e_st_eq_landau_n_8274_t23 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_lessisi1 (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_t21 x p y l f b i u) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)).
-
-(* notion 5408 *)
-definition l_e_st_eq_landau_n_8274_u2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t23 x p y l f b i u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)).
-
-(* notion 5409 *)
-definition l_e_st_eq_landau_n_8274_t24 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_t22 x p y l f b i u) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l).l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t23 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_8274_xs x)) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l))).
-
-(* notion 5410 *)
-definition l_e_st_eq_landau_n_8274_t25 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(l_e_tris2 (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l) j i : l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (f (l_e_st_eq_landau_n_8274_xxs x p y l))).
-
-(* notion 5411 *)
-definition l_e_st_eq_landau_n_8274_t26 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_t19 x p y l f b) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l) (l_e_st_eq_landau_n_8274_t25 x p y l f b i u j) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l)).
-
-(* notion 5412 *)
-definition l_e_st_eq_landau_n_8274_t27 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_t24 x p y l f b i u) (λt:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l).l_e_st_eq_landau_n_8274_t26 x p y l f b i u t) : l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l))).
-
-(* notion 5413 *)
-definition l_e_st_eq_landau_n_8274_w1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_inn y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) : l_e_st_eq_landau_n_nat).
-
-(* notion 5414 *)
-definition l_e_st_eq_landau_n_8274_t28 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y.(l_e_tris (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_outn y (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_1top y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)))) (l_e_st_eq_landau_n_8274_yy1 x p y l) (l_e_st_eq_landau_n_isoutinn y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u))) (l_e_st_eq_landau_n_isoutni y (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_1top y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u))) y (l_e_st_eq_landau_n_lessisi3 y) j) : l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).
-
-(* notion 5415 *)
-definition l_e_st_eq_landau_n_8274_t29 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y) (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l)) (l_e_st_eq_landau_n_8274_t27 x p y l f b i u) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y.l_e_st_eq_landau_n_8274_t28 x p y l f b i u t) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y).
-
-(* notion 5416 *)
-definition l_e_st_eq_landau_n_8274_t30 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y) (l_e_st_eq_landau_n_1top y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u))) (l_e_st_eq_landau_n_8274_t29 x p y l f b i u) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y).
-
-(* notion 5417 *)
-definition l_e_st_eq_landau_n_8274_t31 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_islessis2 y (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_mn_th1c y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_8274_t15 x p y l)) (l_e_st_eq_landau_n_satz25b y (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t30 x p y l f b i u)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1)).
-
-(* notion 5418 *)
-definition l_e_st_eq_landau_n_8274_t32 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_or_th9 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_t31 x p y l f b i u) (λt:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_satz20c (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1 t) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_satz20b (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1 t) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_ym1 x p y l)).
-
-(* notion 5419 *)
-definition l_e_st_eq_landau_n_8274_w2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t32 x p y l f b i u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)).
-
-(* notion 5420 *)
-definition l_e_st_eq_landau_n_8274_f1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_8274_w2 x p y l f b i t : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)).
-
-(* notion 5421 *)
-definition l_e_st_eq_landau_n_8274_t33 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t32 x p y l f b i u) (l_e_st_eq_landau_n_8274_w1 x p y l f b i v) (l_e_st_eq_landau_n_8274_t32 x p y l f b i v) j : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_w1 x p y l f b i v)).
-
-(* notion 5422 *)
-definition l_e_st_eq_landau_n_8274_t34 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).(l_e_st_eq_landau_n_isinne y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t33 x p y l f b i u v j) : l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i v))).
-
-(* notion 5423 *)
-definition l_e_st_eq_landau_n_8274_t35 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).(l_e_st_eq_landau_n_8274_t19 x p y l f b (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_u2 x p y l f b i v) (l_e_st_eq_landau_n_8274_t34 x p y l f b i u v j) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_u2 x p y l f b i v)).
-
-(* notion 5424 *)
-definition l_e_st_eq_landau_n_8274_t36 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t23 x p y l f b i u) (l_e_st_eq_landau_n_8274_u1 x p y l f b i v) (l_e_st_eq_landau_n_8274_t23 x p y l f b i v) (l_e_st_eq_landau_n_8274_t35 x p y l f b i u v j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_u1 x p y l f b i v)).
-
-(* notion 5425 *)
-definition l_e_st_eq_landau_n_8274_t37 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).(l_e_st_eq_landau_n_isinne x u v (l_e_st_eq_landau_n_8274_t36 x p y l f b i u v j) : l_e_is (l_e_st_eq_landau_n_1to x) u v).
-
-(* notion 5426 *)
-definition l_e_st_eq_landau_n_8274_v1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_inn (l_e_st_eq_landau_n_8274_ym1 x p y l) v : l_e_st_eq_landau_n_nat).
-
-(* notion 5427 *)
-definition l_e_st_eq_landau_n_8274_t38 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_satz16a (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_8274_ym1 x p y l) y (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_ym1 x p y l) v) (l_e_st_eq_landau_n_8274_t18 x p y l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y).
-
-(* notion 5428 *)
-definition l_e_st_eq_landau_n_8274_t39 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y) (l_e_st_eq_landau_n_8274_t38 x p y l f b i v) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y).
-
-(* notion 5429 *)
-definition l_e_st_eq_landau_n_8274_t40 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_lessisi1 (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y (l_e_st_eq_landau_n_8274_t38 x p y l f b i v) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y).
-
-(* notion 5430 *)
-definition l_e_st_eq_landau_n_8274_v2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_outn y (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_8274_t40 x p y l f b i v) : l_e_st_eq_landau_n_1to y).
-
-(* notion 5431 *)
-definition l_e_st_eq_landau_n_8274_w3 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_invf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f b (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)).
-
-(* notion 5432 *)
-definition l_e_st_eq_landau_n_8274_t41 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f b (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v))).
-
-(* notion 5433 *)
-definition l_e_st_eq_landau_n_8274_t42 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l) j : l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (f (l_e_st_eq_landau_n_8274_xxs x p y l))).
-
-(* notion 5434 *)
-definition l_e_st_eq_landau_n_8274_t43 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l).(l_e_tr3is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l) (l_e_st_eq_landau_n_8274_t41 x p y l f b i v) (l_e_st_eq_landau_n_8274_t42 x p y l f b i v j) i : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (l_e_st_eq_landau_n_8274_yy1 x p y l)).
-
-(* notion 5435 *)
-definition l_e_st_eq_landau_n_8274_t44 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l).(l_e_st_eq_landau_n_isoutne y (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_8274_t40 x p y l f b i v) y (l_e_st_eq_landau_n_lessisi3 y) (l_e_st_eq_landau_n_8274_t43 x p y l f b i v j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y).
-
-(* notion 5436 *)
-definition l_e_st_eq_landau_n_8274_t45 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y) (l_e_st_eq_landau_n_8274_t39 x p y l f b i v) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l).l_e_st_eq_landau_n_8274_t44 x p y l f b i v t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l))).
-
-(* notion 5437 *)
-definition l_e_st_eq_landau_n_8274_w4 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_inn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) : l_e_st_eq_landau_n_nat).
-
-(* notion 5438 *)
-definition l_e_st_eq_landau_n_8274_t46 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v))) (l_e_st_eq_landau_n_8274_xxs x p y l) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_8274_xs x)) j) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l)).
-
-(* notion 5439 *)
-definition l_e_st_eq_landau_n_8274_t47 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_t45 x p y l f b i v) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_8274_t46 x p y l f b i v t) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x)).
-
-(* notion 5440 *)
-definition l_e_st_eq_landau_n_8274_t48 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t47 x p y l f b i v) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x)).
-
-(* notion 5441 *)
-definition l_e_st_eq_landau_n_8274_t49 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_satz26a x (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_t48 x p y l f b i v) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) x).
-
-(* notion 5442 *)
-definition l_e_st_eq_landau_n_8274_w5 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_t49 x p y l f b i v) : l_e_st_eq_landau_n_1to x).
-
-(* notion 5443 *)
-definition l_e_st_eq_landau_n_8274_t50 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_t49 x p y l f b i v) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_u1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))).
-
-(* notion 5444 *)
-definition l_e_st_eq_landau_n_8274_t51 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v))) (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (l_e_st_eq_landau_n_8274_u1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t23 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t50 x p y l f b i v)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))).
-
-(* notion 5445 *)
-definition l_e_st_eq_landau_n_8274_t52 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t51 x p y l f b i v) : l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)))).
-
-(* notion 5446 *)
-definition l_e_st_eq_landau_n_8274_t53 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_tris (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))) (l_e_st_eq_landau_n_8274_t41 x p y l f b i v) (l_e_st_eq_landau_n_8274_t52 x p y l f b i v) : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)))).
-
-(* notion 5447 *)
-definition l_e_st_eq_landau_n_8274_t54 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_inn y (l_e_st_eq_landau_n_8274_v2 x p y l f b i v)) (l_e_st_eq_landau_n_8274_w1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_isinoutn y (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_8274_t40 x p y l f b i v)) (l_e_st_eq_landau_n_isinni y (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))) (l_e_st_eq_landau_n_8274_t53 x p y l f b i v)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_8274_w1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))).
-
-(* notion 5448 *)
-definition l_e_st_eq_landau_n_8274_t55 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) v (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_ym1 x p y l) v)) (l_e_st_eq_landau_n_8274_w2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_8274_ym1 x p y l) v) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_ym1 x p y l) v) (l_e_st_eq_landau_n_8274_w1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t32 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t54 x p y l f b i v)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) v (l_e_st_eq_landau_n_8274_f1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))).
-
-(* notion 5449 *)
-definition l_e_st_eq_landau_n_8274_t56 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_somei (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) v (l_e_st_eq_landau_n_8274_f1 x p y l f b i t)) (l_e_st_eq_landau_n_8274_w5 x p y l f b i v) (l_e_st_eq_landau_n_8274_t55 x p y l f b i v) : l_e_image (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i) v).
-
-(* notion 5450 *)
-definition l_e_st_eq_landau_n_8274_t57 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(l_andi (l_e_injective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i)) (l_e_surjective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i)) (λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).l_e_st_eq_landau_n_8274_t37 x p y l f b i u v t) (λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).l_e_st_eq_landau_n_8274_t56 x p y l f b i u) : l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i)).
-
-(* notion 5451 *)
-definition l_e_st_eq_landau_n_8274_t58 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(l_somei (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) g) (l_e_st_eq_landau_n_8274_f1 x p y l f b i) (l_e_st_eq_landau_n_8274_t57 x p y l f b i) : l_e_st_eq_landau_n_8274_prop1 x (l_e_st_eq_landau_n_8274_ym1 x p y l)).
-
-(* notion 5452 *)
-definition l_e_st_eq_landau_n_8274_t59 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(p (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_8274_t17 x p y l) (l_e_st_eq_landau_n_8274_t58 x p y l f b i) : l_con).
-
-(* notion 5453 *)
-definition l_e_st_eq_landau_n_8274_m0 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_invf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f b (l_e_st_eq_landau_n_8274_yy1 x p y l) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)).
-
-(* notion 5454 *)
-definition l_e_st_eq_landau_n_8274_t60 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f b (l_e_st_eq_landau_n_8274_yy1 x p y l) : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_yy1 x p y l) (f (l_e_st_eq_landau_n_8274_m0 x p y l f b n))).
-
-(* notion 5455 *)
-definition l_e_st_eq_landau_n_8274_f2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_changef (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_m0 x p y l f b n) (l_e_st_eq_landau_n_8274_xxs x p y l) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y).
-
-(* notion 5456 *)
-definition l_e_st_eq_landau_n_8274_t61 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_changef2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_m0 x p y l f b n) (l_e_st_eq_landau_n_8274_xxs x p y l) (l_e_st_eq_landau_n_8274_xxs x p y l) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_xxs x p y l)) : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_f2 x p y l f b n (l_e_st_eq_landau_n_8274_xxs x p y l)) (f (l_e_st_eq_landau_n_8274_m0 x p y l f b n))).
-
-(* notion 5457 *)
-definition l_e_st_eq_landau_n_8274_t62 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_tris2 (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_f2 x p y l f b n (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l) (f (l_e_st_eq_landau_n_8274_m0 x p y l f b n)) (l_e_st_eq_landau_n_8274_t61 x p y l f b n) (l_e_st_eq_landau_n_8274_t60 x p y l f b n) : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_f2 x p y l f b n (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).
-
-(* notion 5458 *)
-definition l_e_st_eq_landau_n_8274_t63 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_wissel_th6 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_m0 x p y l f b n) (l_e_st_eq_landau_n_8274_xxs x p y l) b : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_f2 x p y l f b n)).
-
-(* notion 5459 *)
-definition l_e_st_eq_landau_n_8274_t64 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_st_eq_landau_n_8274_t59 x p y l (l_e_st_eq_landau_n_8274_f2 x p y l f b n) (l_e_st_eq_landau_n_8274_t63 x p y l f b n) (l_e_st_eq_landau_n_8274_t62 x p y l f b n) : l_con).
-
-(* notion 5460 *)
-definition l_e_st_eq_landau_n_8274_t65 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)) l_con (λt:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).l_e_st_eq_landau_n_8274_t59 x p y l f b t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).l_e_st_eq_landau_n_8274_t64 x p y l f b t) : l_con).
-
-(* notion 5461 *)
-definition l_e_st_eq_landau_n_8274_t65a ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_some_th5 (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y) (Πf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f) (λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λt:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.l_e_st_eq_landau_n_8274_t65 x p y l f t) : l_not (l_e_st_eq_landau_n_8274_prop1 (l_e_st_eq_landau_n_8274_xs x) y)).
-
-(* notion 5462 *)
-definition l_e_st_eq_landau_n_8274_t66 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.(λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_xs x) y.l_e_st_eq_landau_n_8274_t65a x p y t : l_e_st_eq_landau_n_8274_prop2 (l_e_st_eq_landau_n_8274_xs x)).
-
-(* notion 5463 *)
-definition l_e_st_eq_landau_n_8274_t67 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_8274_prop2 t) l_e_st_eq_landau_n_8274_t14 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_8274_prop2 t.l_e_st_eq_landau_n_8274_t66 t u) x : l_e_st_eq_landau_n_8274_prop2 x).
-
-(* notion 5464 *)
-definition l_e_st_eq_landau_n_satz274 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_8274_t67 x y l : l_not (l_some (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y) (Πf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y.l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to y) f))).
-
-(* notion 5465 *)
-definition l_e_st_eq_landau_n_satz274a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y.(l_some_th4 (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y.l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to y) g) (l_e_st_eq_landau_n_satz274 x y l) f : l_not (l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to y) f)).
-
-(* notion 5466 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_inn ≝ λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_inn x u : l_e_st_eq_landau_n_nat).
-
-(* notion 5467 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)).(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x) (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)) o (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x.l_e_tris (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n)) (l_e_st_eq_landau_n_xout x) (l_e_st_eq_landau_n_isoutinn x n) (l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n) x (l_e_st_eq_landau_n_lessisi3 x) t)) : l_not (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x)).
-
-(* notion 5468 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)).(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x) (l_e_st_eq_landau_n_1top x n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t1 q x n o) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x).
-
-(* notion 5469 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_lemma275 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)).(l_e_st_eq_landau_n_satz25c x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t2 q x n o) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x n)) x).
-
-(* notion 5470 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_recprop ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_and (l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_1out x)) (f (l_e_st_eq_landau_n_1out x))) (Πt:l_e_st_eq_landau_n_1to x.Πu:l_not (l_e_is (l_e_st_eq_landau_n_1to x) t (l_e_st_eq_landau_n_xout x)).l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x t)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x t u))) (q (g t) (f (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x t)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x t u))))) : Prop).
-
-(* notion 5471 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_1o ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_1out x : l_e_st_eq_landau_n_1to x).
-
-(* notion 5472 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_xo ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_xout x : l_e_st_eq_landau_n_1to x).
-
-(* notion 5473 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_st_eq_landau_n_satz16b u (l_e_st_eq_landau_n_suc u) x (l_e_st_eq_landau_n_satz18c u) l : l_e_st_eq_landau_n_less u x).
-
-(* notion 5474 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_st_eq_landau_n_lessisi1 u x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t11 q x u l) : l_e_st_eq_landau_n_lessis u x).
-
-(* notion 5475 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_ux ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_st_eq_landau_n_outn x u (l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 q x u l) : l_e_st_eq_landau_n_1to x).
-
-(* notion 5476 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_ec3e31 (l_e_st_eq_landau_n_is u x) (l_e_st_eq_landau_n_more u x) (l_e_st_eq_landau_n_less u x) (l_e_st_eq_landau_n_satz10b u x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t11 q x u l) : l_e_st_eq_landau_n_nis u x).
-
-(* notion 5477 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_st_eq_landau_n_is u x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t13 q x u l) (λt:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x).l_e_st_eq_landau_n_isoutne x u (l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 q x u l) x (l_e_st_eq_landau_n_lessisi3 x) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x))).
-
-(* notion 5478 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_suc u (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (l_e_st_eq_landau_n_isinoutn x u (l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 q x u l)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc u) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)))).
-
-(* notion 5479 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t16 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_suc u) l (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t15 q x u l) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l) (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))).
-
-(* notion 5480 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_ns ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)).(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x n o) : l_e_st_eq_landau_n_1to x).
-
-(* notion 5481 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) : Prop).
-
-(* notion 5482 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(Πt:l_e_st_eq_landau_n_1to x.Πu:l_not (l_e_is (l_e_st_eq_landau_n_1to x) t (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)).l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x t u)) (q (g t) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x t u))) : Prop).
-
-(* notion 5483 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q x f g) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q x f g) pg : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q x f g).
-
-(* notion 5484 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q x f g) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q x f g) pg n o : l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x n o)) (q (g n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x n o)))).
-
-(* notion 5485 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t17 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t16 q x u l) : l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))).
-
-(* notion 5486 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t18 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l))) (q (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t17 q x f g pg u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t4 q x f g pg (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)) : l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (q (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l))))).
-
-(* notion 5487 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis u x.(l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x u l)) (h (l_e_st_eq_landau_n_outn x u l)) : Prop).
-
-(* notion 5488 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_nat.(l_and (l_e_st_eq_landau_n_lessis u x) (Πt:l_e_st_eq_landau_n_lessis u x.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h u t) : Prop).
-
-(* notion 5489 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_nat.(l_or (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h u) (l_e_st_eq_landau_n_more u x) : Prop).
-
-(* notion 5490 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λl:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.(l_e_st_eq_landau_n_isoutni x l_e_st_eq_landau_n_1 l l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a x) (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)).
-
-(* notion 5491 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λl:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx g (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t5 q x f g h pg ph l) : l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l)) (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
-
-(* notion 5492 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λl:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (g (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l)) (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t6 q x f g h pg ph l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t3 q x f g pg) : l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
-
-(* notion 5493 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λl:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (g (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l)) (h (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t7 q x f g h pg ph l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t7 q x f h g ph pg l) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h l_e_st_eq_landau_n_1 l).
-
-(* notion 5494 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.(l_andi (l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x) (Πt:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h l_e_st_eq_landau_n_1 t) (l_e_st_eq_landau_n_satz24a x) (λt:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.l_e_st_eq_landau_n_rt_rp_r_c_8275_t8 q x f g h pg ph t) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h l_e_st_eq_landau_n_1).
-
-(* notion 5495 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_more l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t9 q x f g h pg ph) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h l_e_st_eq_landau_n_1).
-
-(* notion 5496 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t19 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_ec3e32 (l_e_st_eq_landau_n_is u x) (l_e_st_eq_landau_n_more u x) (l_e_st_eq_landau_n_less u x) (l_e_st_eq_landau_n_satz10b u x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t11 q x u l) : l_not (l_e_st_eq_landau_n_more u x)).
-
-(* notion 5497 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t20 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h u) (l_e_st_eq_landau_n_more u x) p (l_e_st_eq_landau_n_rt_rp_r_c_8275_t19 q x f g h pg ph u p l) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h u).
-
-(* notion 5498 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t21 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_ande2 (l_e_st_eq_landau_n_lessis u x) (Πt:l_e_st_eq_landau_n_lessis u x.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h u t) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t20 q x f g h pg ph u p l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 q x u l) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h u (l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 q x u l)).
-
-(* notion 5499 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t22 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (h (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t21 q x f g h pg ph u p l) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (q (h (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l))))).
-
-(* notion 5500 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t23 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (q (h (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t18 q x f h ph u l) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (h (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l))).
-
-(* notion 5501 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t24 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (q (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (q (h (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t18 q x f g pg u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t22 q x f g h pg ph u p l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t23 q x f g h pg ph u p l) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h (l_e_st_eq_landau_n_suc u) l).
-
-(* notion 5502 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t25 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_andi (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x) (Πt:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h (l_e_st_eq_landau_n_suc u) t) l (λt:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.l_e_st_eq_landau_n_rt_rp_r_c_8275_t24 q x f g h pg ph u p t) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h (l_e_st_eq_landau_n_suc u)).
-
-(* notion 5503 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t26 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc u) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t25 q x f g h pg ph u p l) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h (l_e_st_eq_landau_n_suc u)).
-
-(* notion 5504 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t27 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λn:l_not (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x).(l_e_st_eq_landau_n_satz10k (l_e_st_eq_landau_n_suc u) x n : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc u) x).
-
-(* notion 5505 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t28 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λn:l_not (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x).(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc u) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t27 q x f g h pg ph u p n) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h (l_e_st_eq_landau_n_suc u)).
-
-(* notion 5506 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t29 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.(l_imp_th1 (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h (l_e_st_eq_landau_n_suc u)) (λt:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.l_e_st_eq_landau_n_rt_rp_r_c_8275_t26 q x f g h pg ph u p t) (λt:l_not (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x).l_e_st_eq_landau_n_rt_rp_r_c_8275_t28 q x f g h pg ph u p t) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h (l_e_st_eq_landau_n_suc u)).
-
-(* notion 5507 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t30 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h v) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t10 q x f g h pg ph) (λv:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h v.l_e_st_eq_landau_n_rt_rp_r_c_8275_t29 q x f g h pg ph v t) u : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u).
-
-(* notion 5508 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t31 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx g n (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n)) (l_e_st_eq_landau_n_isoutinn x n) : l_e_st_eq_landau_n_rt_rp_r_c_is (g n) (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n)))).
-
-(* notion 5509 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t32 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_satz10d (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x (l_e_st_eq_landau_n_1top x n) : l_not (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x)).
-
-(* notion 5510 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t33 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h (l_e_st_eq_landau_n_rt_rp_r_c_inn x n)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t30 q x f g h pg ph (l_e_st_eq_landau_n_rt_rp_r_c_inn x n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t32 q x f g h pg ph n) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h (l_e_st_eq_landau_n_rt_rp_r_c_inn x n)).
-
-(* notion 5511 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t34 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_ande2 (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x) (Πt:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) t) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t33 q x f g h pg ph n) (l_e_st_eq_landau_n_1top x n) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n)).
-
-(* notion 5512 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t35 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (h n) (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t31 q x f h g ph pg n) : l_e_st_eq_landau_n_rt_rp_r_c_is (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n))) (h n)).
-
-(* notion 5513 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t36 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (g n) (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n))) (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n))) (h n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t31 q x f g h pg ph n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t34 q x f g h pg ph n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t35 q x f g h pg ph n) : l_e_st_eq_landau_n_rt_rp_r_c_is (g n) (h n)).
-
-(* notion 5514 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t37 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.(l_e_fisi (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx g h (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8275_t36 q x f g h pg ph t) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) g h).
-
-(* notion 5515 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_some (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g) : Prop).
-
-(* notion 5516 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.(l_all (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop6 q x f) : Prop).
-
-(* notion 5517 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t38 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q l_e_st_eq_landau_n_1 f f).
-
-(* notion 5518 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t39 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) n (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q l_e_st_eq_landau_n_1)).(o (l_e_st_eq_landau_n_singlet_th1 n) : l_con).
-
-(* notion 5519 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t40 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) n (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q l_e_st_eq_landau_n_1)).(l_cone (l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q l_e_st_eq_landau_n_1 n o)) (q (f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q l_e_st_eq_landau_n_1 n o)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t39 q f n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q l_e_st_eq_landau_n_1 n o)) (q (f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q l_e_st_eq_landau_n_1 n o)))).
-
-(* notion 5520 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t41 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_andi (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q l_e_st_eq_landau_n_1 f f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q l_e_st_eq_landau_n_1 f f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t38 q f) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λu:l_not (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) t (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q l_e_st_eq_landau_n_1)).l_e_st_eq_landau_n_rt_rp_r_c_8275_t40 q f t u) : l_e_st_eq_landau_n_rt_rp_r_c_recprop q l_e_st_eq_landau_n_1 f f).
-
-(* notion 5521 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t42 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_somei (Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q l_e_st_eq_landau_n_1 f g) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_t41 q f) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop6 q l_e_st_eq_landau_n_1 f).
-
-(* notion 5522 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t43 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.(λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8275_t42 q f : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q l_e_st_eq_landau_n_1).
-
-(* notion 5523 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_xs ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.(l_e_st_eq_landau_n_suc x : l_e_st_eq_landau_n_nat).
-
-(* notion 5524 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x)) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5525 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t44 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_onei (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g.λv:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) h.l_e_st_eq_landau_n_rt_rp_r_c_8275_t37 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g h u v) (p (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f)) : l_e_one (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g)).
-
-(* notion 5526 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_ind (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t44 q x p f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5527 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t45 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_oneax (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t44 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f)).
-
-(* notion 5528 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).(l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) n (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) : Prop).
-
-(* notion 5529 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_e_st_eq_landau_n_satz26a x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t2 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) x).
-
-(* notion 5530 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o) : l_e_st_eq_landau_n_1to x).
-
-(* notion 5531 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5532 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t47 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o1) (l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o1)).
-
-(* notion 5533 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t48 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t47 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o1)).
-
-(* notion 5534 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(q (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5535 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_c ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).(l_r_ite (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.λu:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f)) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_t48 q x p f n t u) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5536 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t49 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λi:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.(l_r_itet (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.λu:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f)) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_t48 q x p f n t u) i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f)).
-
-(* notion 5537 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t50 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_r_itef (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.λu:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f)) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_t48 q x p f n t u) o : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o)).
-
-(* notion 5538 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f t : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5539 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_symnotis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_ax3 x)) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)))).
-
-(* notion 5540 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t52 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t50 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f))).
-
-(* notion 5541 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t53 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)))).
-
-(* notion 5542 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t54 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a x) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t53 q x p f) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f))).
-
-(* notion 5543 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t55 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t54 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f))).
-
-(* notion 5544 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t56 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t52 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t55 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
-
-(* notion 5545 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t57 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t56 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t3 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t45 q x p f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
-
-(* notion 5546 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t58 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a x) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
-
-(* notion 5547 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t59 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t58 q x p f) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
-
-(* notion 5548 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t60 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t59 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
-
-(* notion 5549 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t61 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t57 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t60 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f)).
-
-(* notion 5550 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t62 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).
-
-(* notion 5551 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t63 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_st_eq_landau_n_ax4 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t62 q x p f n o i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) x).
-
-(* notion 5552 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t64 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o) x (l_e_st_eq_landau_n_lessisi3 x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t63 q x p f n o i) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)).
-
-(* notion 5553 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t65 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_symis (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t64 q x p f n o i)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o)).
-
-(* notion 5554 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t66 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t65 q x p f n o i) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t50 q x p f n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n)).
-
-(* notion 5555 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t67 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t66 q x p f n o i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))))).
-
-(* notion 5556 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t68 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) i) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))).
-
-(* notion 5557 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t69 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t68 q x p f n o i) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))).
-
-(* notion 5558 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t70 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t49 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) i) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t67 q x p f n o i) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t69 q x p f n o i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))).
-
-(* notion 5559 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t71 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x).(l_e_st_eq_landau_n_isoutne x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o) x (l_e_st_eq_landau_n_lessisi3 x) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) x).
-
-(* notion 5560 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t72 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x).(l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t71 q x p f n o o1 i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).
-
-(* notion 5561 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t73 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x).(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t72 q x p f n o o1 i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).
-
-(* notion 5562 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) o1 (λt:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x).l_e_st_eq_landau_n_rt_rp_r_c_8275_t73 q x p f n o o1 t) : l_not (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x))).
-
-(* notion 5563 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t75 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))).
-
-(* notion 5564 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t76 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t75 q x p f n o o1) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o)))).
-
-(* notion 5565 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t77 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))).
-
-(* notion 5566 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t78 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t77 q x p f n o o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t76 q x p f n o o1) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o)))).
-
-(* notion 5567 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t79 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t78 q x p f n o o1) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))).
-
-(* notion 5568 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t80 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t79 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))).
-
-(* notion 5569 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t81 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))).
-
-(* notion 5570 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t82 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t76 q x p f n o o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t81 q x p f n o o1) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))).
-
-(* notion 5571 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t83 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t82 q x p f n o o1) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))).
-
-(* notion 5572 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t84 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t83 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))).
-
-(* notion 5573 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t85 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t84 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))))).
-
-(* notion 5574 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t86 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t50 q x p f n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))).
-
-(* notion 5575 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t87 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t50 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t80 q x p f n o o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t4 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t45 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))))).
-
-(* notion 5576 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t88 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t86 q x p f n o o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t85 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))))).
-
-(* notion 5577 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t89 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t87 q x p f n o o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t88 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))).
-
-(* notion 5578 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t90 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).l_e_st_eq_landau_n_rt_rp_r_c_8275_t70 q x p f n o t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).l_e_st_eq_landau_n_rt_rp_r_c_8275_t89 q x p f n o t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))).
-
-(* notion 5579 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t91 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f t).l_e_st_eq_landau_n_rt_rp_r_c_8275_t90 q x p f t u : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f)).
-
-(* notion 5580 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t92 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_andi (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t61 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t91 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_recprop q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f)).
-
-(* notion 5581 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t93 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_somei (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f g) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t92 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop6 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f).
-
-(* notion 5582 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t94 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.(λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8275_t93 q x p f : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).
-
-(* notion 5583 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q y) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t43 q) (λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q y.l_e_st_eq_landau_n_rt_rp_r_c_8275_t94 q y t) x : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x).
-
-(* notion 5584 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t96 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x f : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop6 q x f).
-
-(* notion 5585 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t97 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_onei (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λv:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.l_e_st_eq_landau_n_rt_rp_r_c_8275_t37 q x f g h u v) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t96 q x f) : l_e_one (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g)).
-
-(* notion 5586 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz275 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t97 q x f : l_e_one (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g)).
-
-(* notion 5587 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_recf ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_ind (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g) (l_e_st_eq_landau_n_rt_rp_r_c_satz275 q x f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5588 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz275a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_oneax (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g) (l_e_st_eq_landau_n_rt_rp_r_c_satz275 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f)).
-
-(* notion 5589 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_rec ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_recf q x f n : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5590 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz275b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t3 q x f (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f) (l_e_st_eq_landau_n_rt_rp_r_c_satz275a q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_rec q x f (l_e_st_eq_landau_n_1out x)) (f (l_e_st_eq_landau_n_1out x))).
-
-(* notion 5591 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_sucx ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)).(l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x n o : l_e_st_eq_landau_n_1to x).
-
-(* notion 5592 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz275c ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)).(l_e_st_eq_landau_n_rt_rp_r_c_8275_t4 q x f (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f) (l_e_st_eq_landau_n_rt_rp_r_c_satz275a q x f) n o : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_rec q x f (l_e_st_eq_landau_n_rt_rp_r_c_sucx q x f n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_rec q x f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_sucx q x f n o)))).
-
-(* notion 5593 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz275d ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t37 q x f g (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f) r (l_e_st_eq_landau_n_rt_rp_r_c_satz275a q x f) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) g (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f)).
-
-(* notion 5594 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz275e ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λn:l_e_st_eq_landau_n_1to x.(l_e_fise (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx g (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f) (l_e_st_eq_landau_n_rt_rp_r_c_satz275d q x f g r) n : l_e_st_eq_landau_n_rt_rp_r_c_is (g n) (l_e_st_eq_landau_n_rt_rp_r_c_rec q x f n)).
-
-(* notion 5595 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_fl ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y l f : Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5596 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_rf ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_recf q x f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5597 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y l (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f) : Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5598 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t98 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a y) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_1out y))).
-
-(* notion 5599 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t99 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a x) (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_1out y)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_1out y)) y x (l_e_st_eq_landau_n_1top y (l_e_st_eq_landau_n_1out y)) l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t98 q x y l f) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1out x) (l_e_st_eq_landau_n_left1to x y l (l_e_st_eq_landau_n_1out y))).
-
-(* notion 5600 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t100 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isp (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f t) (f t)) (l_e_st_eq_landau_n_1out x) (l_e_st_eq_landau_n_left1to x y l (l_e_st_eq_landau_n_1out y)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t3 q x f (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_satz275a q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t99 q x y l f) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f)).
-
-(* notion 5601 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t100a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y) (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)) o (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y.l_e_tris (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_outn y (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_1top y n)) (l_e_st_eq_landau_n_xout y) (l_e_st_eq_landau_n_isoutinn y n) (l_e_st_eq_landau_n_isoutni y (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_1top y n) y (l_e_st_eq_landau_n_lessisi3 y) t)) : l_not (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y)).
-
-(* notion 5602 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t100b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y) (l_e_st_eq_landau_n_1top y n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t100a q x y l f n o) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y).
-
-(* notion 5603 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t101 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_satz16b (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t100b q x y l f n o) l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x).
-
-(* notion 5604 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t102 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t101 q x y l f n o) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x).
-
-(* notion 5605 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t102 q x y l f n o) (λt:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_xout x).l_e_st_eq_landau_n_isoutne x (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y x (l_e_st_eq_landau_n_1top y n) l) x (l_e_st_eq_landau_n_lessisi3 x) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_xout x))).
-
-(* notion 5606 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t104 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_rt_rp_r_c_8275_t4 q x f (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_satz275a q x f) (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o))))).
-
-(* notion 5607 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t105 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y x (l_e_st_eq_landau_n_1top y n) l) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n))).
-
-(* notion 5608 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t106 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t105 q x y l f n o) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn y n)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n)))).
-
-(* notion 5609 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t107 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_isinoutn y (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn y n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q y n o) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn y n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o))).
-
-(* notion 5610 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t108 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n))) (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn y n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t106 q x y l f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t107 q x y l f n o) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n))) (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o))).
-
-(* notion 5611 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t109 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o)) (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) y x (l_e_st_eq_landau_n_1top y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t108 q x y l f n o) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o)) (l_e_st_eq_landau_n_left1to x y l (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o))).
-
-(* notion 5612 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t110 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_isp (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f t) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f n) (f t))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o)) (l_e_st_eq_landau_n_left1to x y l (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t104 q x y l f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t109 q x y l f n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)))).
-
-(* notion 5613 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t111 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to y.λu:l_not (l_e_is (l_e_st_eq_landau_n_1to y) t (l_e_st_eq_landau_n_xout y)).l_e_st_eq_landau_n_rt_rp_r_c_8275_t110 q x y l f t u : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f)).
-
-(* notion 5614 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t112 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_andi (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t100 q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t111 q x y l f) : l_e_st_eq_landau_n_rt_rp_r_c_recprop q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f)).
-
-(* notion 5615 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz275f ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz275d q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t112 q x y l f) : l_e_is (Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y l (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q y (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y l f))).
-
-(* notion 5616 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_xs ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_suc x : l_e_st_eq_landau_n_nat).
-
-(* notion 5617 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
-
-(* notion 5618 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)).
-
-(* notion 5619 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_satz18c x) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)).
-
-(* notion 5620 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_satz4e x) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)).
-
-(* notion 5621 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_fx ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t1 q x f) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5622 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) f : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5623 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5624 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5625 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5626 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_g ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5627 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t49 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))))).
-
-(* notion 5628 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz275d q (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t92 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f)) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f))).
-
-(* notion 5629 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz275f q (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) f : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f))).
-
-(* notion 5630 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t6 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t5 q x f) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f)).
-
-(* notion 5631 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fise (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t7 q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)))).
-
-(* notion 5632 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t8 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t4 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))))).
-
-(* notion 5633 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_1top x n) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n))).
-
-(* notion 5634 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_1top x n) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t1 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t10 q x f n) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t1 q x f) n) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n))).
-
-(* notion 5635 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t1 q x f) n) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t11 q x f n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f n) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f n)).
-
-(* notion 5636 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fisi (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8276_t12 q x f t) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f)).
-
-(* notion 5637 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recf q x u) (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t13 q x f) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f))).
-
-(* notion 5638 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz275d q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t45 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f)) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f))).
-
-(* notion 5639 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t16 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t15 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t14 q x f) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f))).
-
-(* notion 5640 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t17 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fise (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t16 q x f) (l_e_st_eq_landau_n_xout x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_xout x))).
-
-(* notion 5641 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t18 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)))).
-
-(* notion 5642 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t19 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_satz4a x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t18 q x f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)))).
-
-(* notion 5643 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t20 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t19 q x f) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)))).
-
-(* notion 5644 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t21 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isp1 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f).l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) f t) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (f t))) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t9 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t20 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f))))).
-
-(* notion 5645 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t22 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t17 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f))))).
-
-(* notion 5646 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz276 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t21 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t22 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (q (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1)) f) (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
-
-(* notion 5647 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_smpr ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_rec q x f (l_e_st_eq_landau_n_xout x) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5648 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_sum ≝ λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5649 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_prod ≝ λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5650 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8277_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_1) (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)).
-
-(* notion 5651 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz277 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isp (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_rec q l_e_st_eq_landau_n_1 f t) (f t)) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_satz275b q l_e_st_eq_landau_n_1 f) (l_e_st_eq_landau_n_rt_rp_r_c_8277_t1 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5652 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz278 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz276 q x f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1)) f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
-
-(* notion 5653 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_st_eq_landau_n_lessisi2 y x i : l_e_st_eq_landau_n_lessis y x).
-
-(* notion 5654 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v8_f0 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) f : Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5655 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v8_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_fise (l_e_st_eq_landau_n_1to y) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q y (l_e_st_eq_landau_n_rt_rp_r_c_v8_f0 q x f y i)) (l_e_st_eq_landau_n_rt_rp_r_c_satz275f q x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) f) (l_e_st_eq_landau_n_xout y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_xout y))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_v8_f0 q x f y i))).
-
-(* notion 5656 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v8_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_xout y)) x y (l_e_st_eq_landau_n_isinoutn y y (l_e_st_eq_landau_n_lessisi3 y)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_xout y)) x).
-
-(* notion 5657 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v8_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_xout y)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_xout y)) y x (l_e_st_eq_landau_n_1top y (l_e_st_eq_landau_n_xout y)) (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i)) x (l_e_st_eq_landau_n_lessisi3 x) (l_e_st_eq_landau_n_rt_rp_r_c_v8_t3 q x f y i) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_xout y)) (l_e_st_eq_landau_n_xout x)).
-
-(* notion 5658 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v8_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f) (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_xout y)) (l_e_st_eq_landau_n_xout x) (l_e_st_eq_landau_n_rt_rp_r_c_v8_t4 q x f y i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_xout y))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f)).
-
-(* notion 5659 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_issmpr ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_v8_f0 q x f y i)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_xout y))) (l_e_st_eq_landau_n_rt_rp_r_c_v8_t2 q x f y i) (l_e_st_eq_landau_n_rt_rp_r_c_v8_t5 q x f y i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y (l_e_st_eq_landau_n_lessisi2 y x i) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f)).
-
-(* notion 5660 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_xr ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_rlofnt x : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 5661 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0)) : Prop).
-
-(* notion 5662 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t1 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.z)) z).
-
-(* notion 5663 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t2 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.z)) z (l_e_st_eq_landau_n_rt_rp_r_c_ts z l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t1 z) (l_e_st_eq_landau_n_rt_rp_r_c_satz222a z) : l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z l_e_st_eq_landau_n_1).
-
-(* notion 5664 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t3 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) x (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) z)).
-
-(* notion 5665 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t4 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0)) z (l_e_st_eq_landau_n_rt_rp_r_c_ts z l_e_st_eq_landau_n_rt_rp_r_c_1c) p (l_e_st_eq_landau_n_rt_rp_r_c_satz222a z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z l_e_st_eq_landau_n_rt_rp_r_c_1c))).
-
-(* notion 5666 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t5 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_distpt2 z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c))).
-
-(* notion 5667 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t6 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_plis12a (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0))).
-
-(* notion 5668 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t7 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satzr155b x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 5669 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t8 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t6 z x p) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t7 z x p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 5670 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t9 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0) z (l_e_st_eq_landau_n_rt_rp_r_c_8279_t8 z x p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0))).
-
-(* notion 5671 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t10 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t3 z x p) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t4 z x p) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t5 z x p) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t9 z x p) : l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 5672 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t11 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z t) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t10 z x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z (l_e_st_eq_landau_n_suc x)).
-
-(* notion 5673 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz279 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z t) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t2 z) (λu:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z u.l_e_st_eq_landau_n_rt_rp_r_c_8279_t11 z u t) x : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) l_e_st_eq_landau_n_rt_rp_r_0))).
-
-(* notion 5674 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_satz18a l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_2).
-
-(* notion 5675 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_t1 q f) f : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5676 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q l_e_st_eq_landau_n_1 f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
-
-(* notion 5677 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5678 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5679 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t1 q f)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t4 q f) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_left1to l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_t1 q f) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5680 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_left1to l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_t1 q f) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t5 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5681 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t3 q f) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t6 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))).
-
-(* notion 5682 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t7 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (q (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
-
-(* notion 5683 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz280 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (q (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t2 q f) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t8 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 f) (q (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
-
-(* notion 5684 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_assoc ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.(Πx:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πy:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πz:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (q (q x y) z) (q x (q y z)) : Prop).
-
-(* notion 5685 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_assocp1 ≝ (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_asspl1 x y z : l_e_st_eq_landau_n_rt_rp_r_c_assoc (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl x y)).
-
-(* notion 5686 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_assocts ≝ (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_assts1 x y z : l_e_st_eq_landau_n_rt_rp_r_c_assoc (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts x y)).
-
-(* notion 5687 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_assq1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.(a z u v : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q z u) v) (q z (q u v))).
-
-(* notion 5688 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_assq2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (q (q z u) v) (q z (q u v)) (l_e_st_eq_landau_n_rt_rp_r_c_assq1 q a z u v) : l_e_st_eq_landau_n_rt_rp_r_c_is (q z (q u v)) (q (q z u) v)).
-
-(* notion 5689 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_satz18a x y) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_pl x y)).
-
-(* notion 5690 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x y) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x y) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5691 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx x y f : Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5692 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_prop1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl x y) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y f))) : Prop).
-
-(* notion 5693 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_all (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx) (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8281_prop1 q a x y u) : Prop).
-
-(* notion 5694 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x f0 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f0) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0)) (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
-
-(* notion 5695 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5696 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5697 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_ispl2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t4 q a x f0) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
-
-(* notion 5698 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t5 q a x f0) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_right1to x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5699 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_c_cx f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_right1to x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t6 q a x f0) : l_e_st_eq_landau_n_rt_rp_r_c_is (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5700 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t7 q a x f0) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t3 q a x f0) : l_e_st_eq_landau_n_rt_rp_r_c_is (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0))).
-
-(* notion 5701 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0))) (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t8 q a x f0) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0)) (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0)))).
-
-(* notion 5702 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f0) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0)) (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t2 q a x f0) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t9 q a x f0) : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop1 q a x l_e_st_eq_landau_n_1 f0).
-
-(* notion 5703 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8281_t10 q a x u : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x l_e_st_eq_landau_n_1).
-
-(* notion 5704 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
-
-(* notion 5705 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl x y : l_e_st_eq_landau_n_nat).
-
-(* notion 5706 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) : l_e_st_eq_landau_n_nat).
-
-(* notion 5707 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
-
-(* notion 5708 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_asspl1 x y l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)).
-
-(* notion 5709 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))).
-
-(* notion 5710 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_asspl2 x y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t13 q a x y p f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))).
-
-(* notion 5711 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t14 q a x y p f) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))).
-
-(* notion 5712 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t16 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t15 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))).
-
-(* notion 5713 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_fr ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) f : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5714 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t17 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz275f q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) f : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f))).
-
-(* notion 5715 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t18 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fise (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t17 q a x y p f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f))).
-
-(* notion 5716 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_satz18a (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)).
-
-(* notion 5717 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_frr ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5718 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t20 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))))).
-
-(* notion 5719 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t21 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.q u (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (p (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))))).
-
-(* notion 5720 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t22 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_assq1 q a (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))))).
-
-(* notion 5721 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t23 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 y (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_satz18a y l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)).
-
-(* notion 5722 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_fy ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) y (l_e_st_eq_landau_n_rt_rp_r_c_8281_t23 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f) : Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5723 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t24 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
-
-(* notion 5724 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t25 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))).
-
-(* notion 5725 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t26 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t25 q a x y p f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
-
-(* notion 5726 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t27 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t14 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t26 q a x y p f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
-
-(* notion 5727 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t28 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) x (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t27 q a x y p f) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_right1to x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))).
-
-(* notion 5728 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t29 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_right1to x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t28 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))).
-
-(* notion 5729 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t30 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t29 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
-
-(* notion 5730 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_rt_rp_r_c_inn y n : l_e_st_eq_landau_n_nat).
-
-(* notion 5731 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) y (l_e_st_eq_landau_n_rt_rp_r_c_8281_t23 q a x y p f) n : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)).
-
-(* notion 5732 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t31 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n) y (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_1top y n) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t23 q a x y p f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n))).
-
-(* notion 5733 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t32 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n)) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t31 q a x y p f n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n)))).
-
-(* notion 5734 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_right1to x y n : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y)).
-
-(* notion 5735 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)).
-
-(* notion 5736 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t33 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 q a x y p f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n))).
-
-(* notion 5737 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t34 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n) y x (l_e_st_eq_landau_n_1top y n)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n))).
-
-(* notion 5738 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t35 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t34 q a x y p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t33 q a x y p f n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n))).
-
-(* notion 5739 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t36 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t32 q a x y p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t35 q a x y p f n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n))).
-
-(* notion 5740 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t37 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n))) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) x (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t36 q a x y p f n) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_right1to x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n))).
-
-(* notion 5741 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t38 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_right1to x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t37 q a x y p f n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f) n)).
-
-(* notion 5742 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t39 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fisi (l_e_st_eq_landau_n_1to y) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (λu:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_8281_t38 q a x y p f u) : l_e_is (Πu:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))).
-
-(* notion 5743 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t40 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (Πu:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:Πu:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q y t) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t39 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))).
-
-(* notion 5744 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t41 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t40 q a x y p f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
-
-(* notion 5745 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t41a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t30 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t41 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
-
-(* notion 5746 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t42 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t41a q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t24 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f))).
-
-(* notion 5747 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t43 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t42 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)))).
-
-(* notion 5748 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_inn x m : l_e_st_eq_landau_n_nat).
-
-(* notion 5749 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x y) m : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y)).
-
-(* notion 5750 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)).
-
-(* notion 5751 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t44 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 q a x y p f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m))).
-
-(* notion 5752 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t45 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_1top x m) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m))).
-
-(* notion 5753 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t46 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t45 q a x y p f m) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t44 q a x y p f m) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m))).
-
-(* notion 5754 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t47 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_1top x m) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t46 q a x y p f m) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)) m) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m))).
-
-(* notion 5755 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t48 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)) m) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t47 q a x y p f m) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f m) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f) m)).
-
-(* notion 5756 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t49 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fisi (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (λu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8281_t48 q a x y p f u) : l_e_is (Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))).
-
-(* notion 5757 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t50 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q x t) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t49 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))).
-
-(* notion 5758 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t51 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t50 q a x y p f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)))).
-
-(* notion 5759 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t52 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t16 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t18 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t20 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t21 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))))).
-
-(* notion 5760 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t53 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t52 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t22 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t43 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t51 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f).
-
-(* notion 5761 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t54 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8281_t53 q a x y p u : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)).
-
-(* notion 5762 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t55 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x t) (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t54 q a x y p) (l_e_st_eq_landau_n_satz4a y) : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x (l_e_st_eq_landau_n_suc y)).
-
-(* notion 5763 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t56 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x t) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t11 q a x) (λz:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x z.l_e_st_eq_landau_n_rt_rp_r_c_8281_t55 q a x z t) y : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y).
-
-(* notion 5764 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz281 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8281_t56 q a x y f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl x y) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x y) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_satz18a x y)) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx x y f)))).
-
-(* notion 5765 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_commut ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.(Πx:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (q x y) (q y x) : Prop).
-
-(* notion 5766 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_commutpl ≝ (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_compl x y : l_e_st_eq_landau_n_rt_rp_r_c_commut (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl x y)).
-
-(* notion 5767 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_commutts ≝ (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_comts x y : l_e_st_eq_landau_n_rt_rp_r_c_commut (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts x y)).
-
-(* notion 5768 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_comq ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.(c z u : l_e_st_eq_landau_n_rt_rp_r_c_is (q z u) (q u z)).
-
-(* notion 5769 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_prop1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (λt:l_e_st_eq_landau_n_1to x.q (f t) (g t))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x g)) : Prop).
-
-(* notion 5770 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_all (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_all (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λv:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8282_prop1 q a c x u v)) : Prop).
-
-(* notion 5771 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λf0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.q (f0 t) (g0 t)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.q (f0 t) (g0 t))) (q (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
-
-(* notion 5772 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λf0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 g0) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_satz277 q g0) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 g0)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
-
-(* notion 5773 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λf0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_satz277 q f0) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (q (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
-
-(* notion 5774 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λf0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 g0)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (q (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t2 q a c f0 g0) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t3 q a c f0 g0) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 g0)) (q (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
-
-(* notion 5775 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λf0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.q (f0 t) (g0 t))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 g0)) (q (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t1 q a c f0 g0) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t4 q a c f0 g0) : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop1 q a c l_e_st_eq_landau_n_1 f0 g0).
-
-(* notion 5776 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.(λu:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8282_t5 q a c u v : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c l_e_st_eq_landau_n_1).
-
-(* notion 5777 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
-
-(* notion 5778 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_assq2 q a (q u v) w z : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q u v) (q w z)) (q (q (q u v) w) z)).
-
-(* notion 5779 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_comq q c (q u v) w : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q u v) w) (q w (q u v))).
-
-(* notion 5780 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_assq2 q a w u v : l_e_st_eq_landau_n_rt_rp_r_c_is (q w (q u v)) (q (q w u) v)).
-
-(* notion 5781 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (q (q u v) w) (q w (q u v)) (q (q w u) v) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t8 q a c u v w z) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t9 q a c u v w z) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q u v) w) (q (q w u) v)).
-
-(* notion 5782 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t z) (q (q u v) w) (q (q w u) v) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t10 q a c u v w z) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (q u v) w) z) (q (q (q w u) v) z)).
-
-(* notion 5783 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_assq1 q a (q w u) v z : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (q w u) v) z) (q (q w u) (q v z))).
-
-(* notion 5784 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_comq q c w u : l_e_st_eq_landau_n_rt_rp_r_c_is (q w u) (q u w)).
-
-(* notion 5785 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (q v z)) (q w u) (q u w) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t13 q a c u v w z) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q w u) (q v z)) (q (q u w) (q v z))).
-
-(* notion 5786 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (q (q u v) (q w z)) (q (q (q u v) w) z) (q (q (q w u) v) z) (q (q w u) (q v z)) (q (q u w) (q v z)) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t7 q a c u v w z) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t11 q a c u v w z) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t12 q a c u v w z) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t14 q a c u v w z) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q u v) (q w z)) (q (q u w) (q v z))).
-
-(* notion 5787 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)).
-
-(* notion 5788 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 q a c x p f g) f) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5789 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 q a c x p f g) g) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5790 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_h ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).q (f t) (g t) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5791 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_shx ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g)) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5792 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t17 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_shx q a c x p f g) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))))).
-
-(* notion 5793 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t18 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(p (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 q a c x p f g) f) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 q a c x p f g) g) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8282_shx q a c x p f g) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g))).
-
-(* notion 5794 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t19 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (l_e_st_eq_landau_n_rt_rp_r_c_8282_shx q a c x p f g) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g)) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t18 q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_shx q a c x p f g) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g)) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))))).
-
-(* notion 5795 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t20 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8282_t15 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g)) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))))).
-
-(* notion 5796 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t21 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f)).
-
-(* notion 5797 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t22 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t21 q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))))).
-
-(* notion 5798 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t23 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) g) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x g) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) g)).
-
-(* notion 5799 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t24 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t23 q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) g))).
-
-(* notion 5800 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t25 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_shx q a c x p f g) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g)) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t17 q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t19 q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t20 q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g)) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))))).
-
-(* notion 5801 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t26 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g)) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) g)) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t25 q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t22 q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t24 q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f g).
-
-(* notion 5802 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t27 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8282_t26 q a c x p u v : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)).
-
-(* notion 5803 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t28 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c t) (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t27 q a c x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c (l_e_st_eq_landau_n_suc x)).
-
-(* notion 5804 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t29 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c t) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t6 q a c) (λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c y.l_e_st_eq_landau_n_rt_rp_r_c_8282_t28 q a c y t) x : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x).
-
-(* notion 5805 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz282 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8282_t29 q a c x f g : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (λt:l_e_st_eq_landau_n_1to x.q (f t) (g t))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x g))).
-
-(* notion 5806 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λs:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to x.f (s t) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5807 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λs:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c x s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f) : Prop).
-
-(* notion 5808 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_all (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x) (λu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x.l_all (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λv:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_imp (l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c x u v))) : Prop).
-
-(* notion 5809 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (s (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1o (l_e_st_eq_landau_n_singlet_th1 (s (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_singlet_th1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (s (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)).
-
-(* notion 5810 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5811 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_rt_rp_r_c_cx f (s (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t1 q a c s f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5812 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_satz277 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f)).
-
-(* notion 5813 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t2 q a c s f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t3 q a c s f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t4 q a c s f) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c l_e_st_eq_landau_n_1 s f).
-
-(* notion 5814 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.(λu:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λv:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_bijective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) u.l_e_st_eq_landau_n_rt_rp_r_c_8283_t5 q a c u v : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c l_e_st_eq_landau_n_1).
-
-(* notion 5815 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
-
-(* notion 5816 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5817 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.(l_ande1 (l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s) (l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s) b : l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s).
-
-(* notion 5818 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) u : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5819 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) : l_e_st_eq_landau_n_nat).
-
-(* notion 5820 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) (l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) case1) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 5821 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t9 q a c x p s f b case1 u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5822 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t10 q a c x p s f b case1 u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5823 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_st_eq_landau_n_satz16a (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5824 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t12 q a c x p s f b case1 u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t11 q a c x p s f b case1 u i) : l_con).
-
-(* notion 5825 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u))) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_t13 q a c x p s f b case1 u t) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5826 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_satz26 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t14 q a c x p s f b case1 u) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) x).
-
-(* notion 5827 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 q a c x p s f b case1 u) : l_e_st_eq_landau_n_1to x).
-
-(* notion 5828 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 t : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x).
-
-(* notion 5829 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t16 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 v).(l_e_st_eq_landau_n_isoutne x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 v) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 q a c x p s f b case1 v) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 v)).
-
-(* notion 5830 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t17 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 v).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p s f b (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 v) (l_e_st_eq_landau_n_isinne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 v)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t16 q a c x p s f b case1 u v i)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 v)).
-
-(* notion 5831 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t18 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 v).(l_e_st_eq_landau_n_thleft1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) u v (l_e_st_eq_landau_n_rt_rp_r_c_8283_t17 q a c x p s f b case1 u v i) : l_e_is (l_e_st_eq_landau_n_1to x) u v).
-
-(* notion 5832 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_invf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5833 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) : l_e_st_eq_landau_n_nat).
-
-(* notion 5834 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t19 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5835 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t20 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t19 q a c x p s f b case1 u i)) case1 : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5836 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t21 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t20 q a c x p s f b case1 u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5837 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t22 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_st_eq_landau_n_satz16a (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5838 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t23 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t22 q a c x p s f b case1 u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t21 q a c x p s f b case1 u i) : l_con).
-
-(* notion 5839 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t24 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_t23 q a c x p s f b case1 u t) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5840 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t25 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_satz26 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t24 q a c x p s f b case1 u) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) x).
-
-(* notion 5841 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t25 q a c x p s f b case1 u) : l_e_st_eq_landau_n_1to x).
-
-(* notion 5842 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t26 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t25 q a c x p s f b case1 u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))).
-
-(* notion 5843 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t27 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t26 q a c x p s f b case1 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))).
-
-(* notion 5844 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t28 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))) (l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t27 q a c x p s f b case1 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)))).
-
-(* notion 5845 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t29 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x))) (l_e_st_eq_landau_n_isinni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t28 q a c x p s f b case1 u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))).
-
-(* notion 5846 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t30 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_1top x u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_isoutinn x u) (l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t29 q a c x p s f b case1 u)) : l_e_is (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))).
-
-(* notion 5847 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t31 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_somei (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_is (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 t)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t30 q a c x p s f b case1 u) : l_e_image (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1) u).
-
-(* notion 5848 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t32 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_andi (l_e_injective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1)) (l_e_surjective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1)) (λt:l_e_st_eq_landau_n_1to x.λu:l_e_st_eq_landau_n_1to x.λv:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1 t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1 u).l_e_st_eq_landau_n_rt_rp_r_c_8283_t18 q a c x p s f b case1 t u v) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_t31 q a c x p s f b case1 t) : l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1)).
-
-(* notion 5849 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5850 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t33 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t32 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c x (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)).
-
-(* notion 5851 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5852 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c x (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5853 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t33a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u))))).
-
-(* notion 5854 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t34 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 q a c x p s f b case1 u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u))).
-
-(* notion 5855 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t35 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t34 q a c x p s f b case1 u) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)))) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u))).
-
-(* notion 5856 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t36 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)))) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t33a q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t35 q a c x p s f b case1 u) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u))).
-
-(* notion 5857 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t37 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t36 q a c x p s f b case1 u) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1 u)).
-
-(* notion 5858 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t38 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_fisi (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_t37 q a c x p s f b case1 t) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1)).
-
-(* notion 5859 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t39 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t38 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1))).
-
-(* notion 5860 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t40 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t39 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t33 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1))).
-
-(* notion 5861 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t41 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) case1 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 5862 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t42 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
-
-(* notion 5863 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t43 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t41 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
-
-(* notion 5864 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t44 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t40 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
-
-(* notion 5865 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t45 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
-
-(* notion 5866 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t46 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t42 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t43 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t44 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t45 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 5867 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1px ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.(l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 x : l_e_st_eq_landau_n_nat).
-
-(* notion 5868 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x u : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b)).
-
-(* notion 5869 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_compl l_e_st_eq_landau_n_1 x) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5870 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) s : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5871 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) : l_e_st_eq_landau_n_nat).
-
-(* notion 5872 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t48 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) (l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) case2) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 5873 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t49 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p s f b) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t48 q a c x p s f b case2 u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5874 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t50 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t49 q a c x p s f b case2 u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1).
-
-(* notion 5875 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t51 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top x u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))).
-
-(* notion 5876 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t52 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t51 q a c x p s f b case2 u i) (l_e_st_eq_landau_n_satz18 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1).
-
-(* notion 5877 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t53 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_ec3e21 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t52 q a c x p s f b case2 u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t50 q a c x p s f b case2 u i) : l_con).
-
-(* notion 5878 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz24 (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u)) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_8283_t53 q a c x p s f b case2 u t) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1).
-
-(* notion 5879 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_mn (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 u) : l_e_st_eq_landau_n_nat).
-
-(* notion 5880 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t54a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_islessis1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_mn_th1c (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5881 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_or_th9 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) x) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54a q a c x p s f b case2 u) (λt:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_satz20c (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) x l_e_st_eq_landau_n_1 t) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_satz20b (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) x l_e_st_eq_landau_n_1 t) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) x).
-
-(* notion 5882 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 q a c x p s f b case2 u) : l_e_st_eq_landau_n_1to x).
-
-(* notion 5883 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 t : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x).
-
-(* notion 5884 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t56 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_st_eq_landau_n_isoutne x (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 v) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 q a c x p s f b case2 v) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 v)).
-
-(* notion 5885 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t57 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 v) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 v) (l_e_st_eq_landau_n_mn_th1c (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 v) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t56 q a c x p s f b case2 u v i)) (l_e_st_eq_landau_n_mn_th1d (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 v) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 v)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 v)).
-
-(* notion 5886 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t58 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_st_eq_landau_n_isinne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t57 q a c x p s f b case2 u v i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v))).
-
-(* notion 5887 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t59 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p s f b) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t58 q a c x p s f b case2 u v i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v))).
-
-(* notion 5888 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t60 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_st_eq_landau_n_thleft1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t59 q a c x p s f b case2 u v i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v)).
-
-(* notion 5889 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t61 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_st_eq_landau_n_thright1 l_e_st_eq_landau_n_1 x u v (l_e_st_eq_landau_n_rt_rp_r_c_8283_t60 q a c x p s f b case2 u v i) : l_e_is (l_e_st_eq_landau_n_1to x) u v).
-
-(* notion 5890 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s04 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_invf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5891 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_8283_s04 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5892 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) : l_e_st_eq_landau_n_nat).
-
-(* notion 5893 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t62 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5894 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t63 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t62 q a c x p s f b case2 u i)) case2 : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5895 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t64 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t63 q a c x p s f b case2 u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1).
-
-(* notion 5896 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t65 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top x u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t64 q a c x p s f b case2 u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) l_e_st_eq_landau_n_1).
-
-(* notion 5897 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t66 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_ec3e21 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t65 q a c x p s f b case2 u i) : l_con).
-
-(* notion 5898 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t67 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz24 (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u)) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_8283_t66 q a c x p s f b case2 u t) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1).
-
-(* notion 5899 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_mn (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t67 q a c x p s f b case2 u) : l_e_st_eq_landau_n_nat).
-
-(* notion 5900 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t68 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_islessis1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_mn_th1c (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t67 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5901 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t69 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_or_th9 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) x) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t68 q a c x p s f b case2 u) (λt:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_satz20c (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) x l_e_st_eq_landau_n_1 t) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_satz20b (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) x l_e_st_eq_landau_n_1 t) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) x).
-
-(* notion 5902 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t69 q a c x p s f b case2 u) : l_e_st_eq_landau_n_1to x).
-
-(* notion 5903 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t70 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t69 q a c x p s f b case2 u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))).
-
-(* notion 5904 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t71 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_mn_th1a (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t67 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t70 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)))).
-
-(* notion 5905 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t72 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t71 q a c x p s f b case2 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)))).
-
-(* notion 5906 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t73 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t72 q a c x p s f b case2 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)))).
-
-(* notion 5907 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t74 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top x u))) (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2))) (l_e_st_eq_landau_n_isinni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t73 q a c x p s f b case2 u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))).
-
-(* notion 5908 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t75 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_mn_th1e (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t74 q a c x p s f b case2 u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))).
-
-(* notion 5909 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t76 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_1top x u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_isoutinn x u) (l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t75 q a c x p s f b case2 u)) : l_e_is (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))).
-
-(* notion 5910 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t77 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_somei (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_is (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 t)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t76 q a c x p s f b case2 u) : l_e_image (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2) u).
-
-(* notion 5911 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t78 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_andi (l_e_injective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2)) (l_e_surjective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2)) (λt:l_e_st_eq_landau_n_1to x.λu:l_e_st_eq_landau_n_1to x.λv:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2 t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2 u).l_e_st_eq_landau_n_rt_rp_r_c_8283_t61 q a c x p s f b case2 t u v) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_t77 q a c x p s f b case2 t) : l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2)).
-
-(* notion 5912 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) f : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5913 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5914 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t79 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t78 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c x (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2)).
-
-(* notion 5915 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5916 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5917 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c x (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5918 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t80 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_mn_th1a (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u)) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u)))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u)))).
-
-(* notion 5919 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t81 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)))) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t80 q a c x p s f b case2 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u)))).
-
-(* notion 5920 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t82 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t81 q a c x p s f b case2 u) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2 u)).
-
-(* notion 5921 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t83 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_fisi (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_t82 q a c x p s f b case2 t) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2)).
-
-(* notion 5922 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t85 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t83 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2))).
-
-(* notion 5923 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t86 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t85 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t79 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))).
-
-(* notion 5924 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t87 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_lessisi1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_satz18a l_e_st_eq_landau_n_1 x) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b)).
-
-(* notion 5925 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2) : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5926 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2) : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 5927 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t87a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 5928 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1d ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87 q a c x p s f b case2) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b)).
-
-(* notion 5929 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t87b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87 q a c x p s f b case2)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2))).
-
-(* notion 5930 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t88 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87a q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87b q a c x p s f b case2) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2))).
-
-(* notion 5931 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1e ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5932 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t88a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t88 q a c x p s f b case2) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)).
-
-(* notion 5933 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t88b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t88a q a c x p s f b case2)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 5934 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t89 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t88b q a c x p s f b case2) case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t88a q a c x p s f b case2) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)).
-
-(* notion 5935 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t89a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t89 q a c x p s f b case2)) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2))).
-
-(* notion 5936 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t90 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_satz281 q a l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2)))).
-
-(* notion 5937 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t91 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t86 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2)))).
-
-(* notion 5938 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t92 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t89a q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2)))).
-
-(* notion 5939 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t93 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (l_e_st_eq_landau_n_rt_rp_r_c_satz281 q a l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2)) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2))).
-
-(* notion 5940 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t94 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t90 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t91 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t92 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t93 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2))).
-
-(* notion 5941 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t95 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_compl l_e_st_eq_landau_n_1 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
-
-(* notion 5942 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t96 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_compl l_e_st_eq_landau_n_1 x)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2))).
-
-(* notion 5943 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t97 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t96 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t94 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t95 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 5944 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5945 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_invf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5946 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2))).
-
-(* notion 5947 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t99 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(not2 : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 5948 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t100 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_symnotis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_notis_th3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 q a c x p s f b not1 not2)) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
-
-(* notion 5949 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t101 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t100 q a c x p s f b not1 not2) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 5950 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_changef (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5951 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t102 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_changef1 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u i : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2))).
-
-(* notion 5952 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t103 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t102 q a c x p s f b not1 not2 u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 q a c x p s f b not1 not2) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5953 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t104 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).(l_e_changef2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u i : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2)).
-
-(* notion 5954 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t105 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_changef3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u n o : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (s u)).
-
-(* notion 5955 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t106 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_wissel_th6 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) b : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2)).
-
-(* notion 5956 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_wissel (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5957 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t107 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_wissel_th3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha)).
-
-(* notion 5958 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t108 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_iswissel1 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t103 q a c x p s f b not1 not2 u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2)).
-
-(* notion 5959 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t109 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t108 q a c x p s f b not1 not2 alpha u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))).
-
-(* notion 5960 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t110 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).(l_e_iswissel2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t104 q a c x p s f b not1 not2 u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5961 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t111 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 q a c x p s f b not1 not2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t110 q a c x p s f b not1 not2 alpha u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))).
-
-(* notion 5962 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t112 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_t106 q a c x p s f b not1 not2)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i (l_e_st_eq_landau_n_rt_rp_r_c_8283_t103 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5963 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t113 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) n (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t112 q a c x p s f b not1 not2 alpha u n o t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 5964 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t114 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2).(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_t106 q a c x p s f b not1 not2)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) i (l_e_st_eq_landau_n_rt_rp_r_c_8283_t104 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)))) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).
-
-(* notion 5965 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t115 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) o (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2).l_e_st_eq_landau_n_rt_rp_r_c_8283_t114 q a c x p s f b not1 not2 alpha u n o t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2))).
-
-(* notion 5966 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t116 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_iswissel3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t113 q a c x p s f b not1 not2 alpha u n o) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t115 q a c x p s f b not1 not2 alpha u n o) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)).
-
-(* notion 5967 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t117 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (s u) (l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t116 q a c x p s f b not1 not2 alpha u n o) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t105 q a c x p s f b not1 not2 u n o)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))).
-
-(* notion 5968 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t118 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).l_e_st_eq_landau_n_rt_rp_r_c_8283_t111 q a c x p s f b not1 not2 alpha u t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t117 q a c x p s f b not1 not2 alpha u n t) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))).
-
-(* notion 5969 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t119 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t109 q a c x p s f b not1 not2 alpha u t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t118 q a c x p s f b not1 not2 alpha u t) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))).
-
-(* notion 5970 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t120 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 t)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_t119 q a c x p s f b not1 not2 alpha t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 t))).
-
-(* notion 5971 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t121 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t103 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5972 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t121a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_ec3e21 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_compl l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_satz18 l_e_st_eq_landau_n_1 x)) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1).
-
-(* notion 5973 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t122 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t121a q a c x p s f b not1 not2) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 5974 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t123 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_symnotis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) alpha : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2))).
-
-(* notion 5975 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t124 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_iswissel3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t122 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t123 q a c x p s f b not1 not2 alpha) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5976 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t125 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) u f)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 t)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t120 q a c x p s f b not1 not2 alpha) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f)))).
-
-(* notion 5977 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t126 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t97 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t106 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t121 q a c x p s f b not1 not2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f))).
-
-(* notion 5978 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t127 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t46 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_t107 q a c x p s f b not1 not2 alpha) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t124 q a c x p s f b not1 not2 alpha) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
-
-(* notion 5979 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t128 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t125 q a c x p s f b not1 not2 alpha) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t126 q a c x p s f b not1 not2 alpha) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t127 q a c x p s f b not1 not2 alpha) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 5980 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_wissel (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 5981 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t129 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_wissel_th3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta)).
-
-(* notion 5982 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t130 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t104 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u) (l_e_iswissel1 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2)).
-
-(* notion 5983 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t131 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t130 q a c x p s f b not1 not2 i3 beta u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))).
-
-(* notion 5984 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t132 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t103 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u) (l_e_iswissel2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5985 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t133 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) i) (l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t132 q a c x p s f b not1 not2 i3 beta u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 q a c x p s f b not1 not2)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))).
-
-(* notion 5986 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t134 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_iswissel3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u n o : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u) u).
-
-(* notion 5987 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t135 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_t134 q a c x p s f b not1 not2 i3 beta u n o) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)).
-
-(* notion 5988 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t136 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t105 q a c x p s f b not1 not2 u n o : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (s u)).
-
-(* notion 5989 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t139 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (s u) (l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t135 q a c x p s f b not1 not2 i3 beta u n o) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t136 q a c x p s f b not1 not2 i3 beta u n o)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))).
-
-(* notion 5990 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t140 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).l_e_st_eq_landau_n_rt_rp_r_c_8283_t133 q a c x p s f b not1 not2 i3 beta u t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t139 q a c x p s f b not1 not2 i3 beta u n t) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))).
-
-(* notion 5991 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t141 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t131 q a c x p s f b not1 not2 i3 beta u t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t140 q a c x p s f b not1 not2 i3 beta u t) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))).
-
-(* notion 5992 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t142 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta t)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_t141 q a c x p s f b not1 not2 i3 beta t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta t))).
-
-(* notion 5993 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t143 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_symnotis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) beta : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2))).
-
-(* notion 5994 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t144 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_iswissel3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t122 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t143 q a c x p s f b not1 not2 i3 beta) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 5995 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t145 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) u f)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta t)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t142 q a c x p s f b not1 not2 i3 beta) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f)))).
-
-(* notion 5996 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t146 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t46 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t129 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t144 q a c x p s f b not1 not2 i3 beta) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f))).
-
-(* notion 5997 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t147 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t97 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_t106 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t121 q a c x p s f b not1 not2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
-
-(* notion 5998 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t148 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t145 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t146 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t147 q a c x p s f b not1 not2 i3 beta) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 5999 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t149 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_ispl1 l_e_st_eq_landau_n_1 x l_e_st_eq_landau_n_1 (l_e_symis l_e_st_eq_landau_n_nat x l_e_st_eq_landau_n_1 i) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 6000 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t149 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 6001 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) f : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6002 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) s : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 6003 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6004 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t151 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t149 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
-
-(* notion 6005 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t152 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t149 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f))).
-
-(* notion 6006 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t153 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz280 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
-
-(* notion 6007 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t154 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz280 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
-
-(* notion 6008 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t155 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t149 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 6009 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t156 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t155 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 6010 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t157 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t156 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6011 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t158 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_symis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_2)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) l_e_st_eq_landau_n_1).
-
-(* notion 6012 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t159 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t158 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 6013 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t160 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t159 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 q a c x p s f b not1 not2) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) gamma) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6014 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t161 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t157 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t160 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))).
-
-(* notion 6015 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t163 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t159 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6016 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t164 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t163 q a c x p s f b not1 not2 i3 gamma i) i3 : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 6017 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t165 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t164 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t156 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))).
-
-(* notion 6018 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t166 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t161 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))).
-
-(* notion 6019 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t167 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t165 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))).
-
-(* notion 6020 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t168 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t166 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)))).
-
-(* notion 6021 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t169 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_comq q c (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)))).
-
-(* notion 6022 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t170 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t167 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
-
-(* notion 6023 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t171 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t152 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t154 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t168 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t169 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)))).
-
-(* notion 6024 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t172 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t171 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t170 q a c x p s f b not1 not2 i3 gamma i) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t153 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t151 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 6025 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_trivial ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_8283_t172 q a c x p s f b not1 not2 i3 gamma i : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 6026 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t173 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_ore1 (l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz24 x) n : l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1).
-
-(* notion 6027 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_mn x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t173 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_nat).
-
-(* notion 6028 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_changef (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 6029 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t174 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_wissel_th6 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) b : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n)).
-
-(* notion 6030 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t175 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_changef2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6031 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t176 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i3 : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6032 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t177 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t175 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t176 q a c x p s f b not1 not2 i3 gamma n) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
-
-(* notion 6033 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 6034 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6035 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t179 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
-
-(* notion 6036 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t180 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_mn_th1b x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t173 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) x).
-
-(* notion 6037 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t180 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) x).
-
-(* notion 6038 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6039 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t182 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_issmpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t180 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n))).
-
-(* notion 6040 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6041 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t183 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_lessisi1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_satz18a l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n))).
-
-(* notion 6042 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t183 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6043 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t184 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz281 q a l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)))).
-
-(* notion 6044 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t185 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 6045 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t186 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 6046 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t183 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n))).
-
-(* notion 6047 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t187 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t183 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n))).
-
-(* notion 6048 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left1to x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_1to x).
-
-(* notion 6049 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t188 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) x (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n))).
-
-(* notion 6050 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t189 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t186 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t187 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t188 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n))).
-
-(* notion 6051 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1c ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 6052 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t190 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t189 q a c x p s f b not1 not2 i3 gamma n) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1c q a c x p s f b not1 not2 i3 gamma n)).
-
-(* notion 6053 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t191 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1c q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t190 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 6054 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t192 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t185 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t191 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6055 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t193 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t175 q a c x p s f b not1 not2 i3 gamma n) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6056 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t194 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t193 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6057 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t195 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t192 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t194 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6058 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t196 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t195 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)))).
-
-(* notion 6059 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t197 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t182 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t184 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t196 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)))).
-
-(* notion 6060 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t198 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t197 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
-
-(* notion 6061 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t199 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_assq1 q a (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))))).
-
-(* notion 6062 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t200 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_comq q c (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
-
-(* notion 6063 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6064 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6065 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6066 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_satz18a l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6067 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t201 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
-
-(* notion 6068 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t202 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_issmpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t180 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n))).
-
-(* notion 6069 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t203 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz281 q a l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)))).
-
-(* notion 6070 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t204 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 6071 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t205 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1c q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t190 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 6072 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t206 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t204 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t205 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6073 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t207 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_changef1 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6074 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t208 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t207 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6075 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t209 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t206 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t208 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6076 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t210 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t209 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)))).
-
-(* notion 6077 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t211 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t202 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t203 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t210 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)))).
-
-(* notion 6078 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_ua ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n))).
-
-(* notion 6079 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_ub ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(l_e_st_eq_landau_n_left1to x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u) : l_e_st_eq_landau_n_1to x).
-
-(* notion 6080 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_uc ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 6081 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t212 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 6082 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t213 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_satz16a (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 6083 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t214 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t213 q a c x p s f b not1 not2 i3 gamma n u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t212 q a c x p s f b not1 not2 i3 gamma n u i) : l_con).
-
-(* notion 6084 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t215 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t214 q a c x p s f b not1 not2 i3 gamma n u t : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6085 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t216 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) l_e_st_eq_landau_n_1).
-
-(* notion 6086 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t217 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) x (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u))).
-
-(* notion 6087 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t218 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u))).
-
-(* notion 6088 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t219 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t218 q a c x p s f b not1 not2 i3 gamma n u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t217 q a c x p s f b not1 not2 i3 gamma n u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t216 q a c x p s f b not1 not2 i3 gamma n u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1).
-
-(* notion 6089 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t220 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_satz18 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1).
-
-(* notion 6090 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t221 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_ec3e21 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t220 q a c x p s f b not1 not2 i3 gamma n u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t219 q a c x p s f b not1 not2 i3 gamma n u i) : l_con).
-
-(* notion 6091 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t222 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t221 q a c x p s f b not1 not2 i3 gamma n u t : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
-
-(* notion 6092 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t223 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(l_e_changef3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t222 q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t215 q a c x p s f b not1 not2 i3 gamma n u) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u))).
-
-(* notion 6093 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t224 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t223 q a c x p s f b not1 not2 i3 gamma n u) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n u)).
-
-(* notion 6094 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t225 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t224 q a c x p s f b not1 not2 i3 gamma n t)) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)).
-
-(* notion 6095 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t226 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t225 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))).
-
-(* notion 6096 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t227 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_comq q c (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)))).
-
-(* notion 6097 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t228 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t226 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)))).
-
-(* notion 6098 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t229 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t227 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t228 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)))).
-
-(* notion 6099 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t230 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t229 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t211 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n))).
-
-(* notion 6100 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t231 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t230 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
-
-(* notion 6101 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t232 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t201 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f))).
-
-(* notion 6102 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t233 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_8283_t46 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_t174 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t177 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
-
-(* notion 6103 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t234 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t179 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t198 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t199 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t200 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
-
-(* notion 6104 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t235 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t234 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t231 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t232 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t233 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 6105 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t236 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_imp_th1 (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (λt:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_8283_t172 q a c x p s f b not1 not2 i3 gamma t) (λt:l_not (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_8283_t235 q a c x p s f b not1 not2 i3 gamma t) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 6106 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t237 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t236 q a c x p s f b not1 not2 i3 t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t148 q a c x p s f b not1 not2 i3 t) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 6107 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t238 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t237 q a c x p s f b not1 not2 t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t128 q a c x p s f b not1 not2 t) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 6108 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t239 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t97 q a c x p s f b t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t238 q a c x p s f b not1 t) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 6109 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t240 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t46 q a c x p s f b t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t239 q a c x p s f b t) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
-
-(* notion 6110 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t241 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λv:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u.l_e_st_eq_landau_n_rt_rp_r_c_8283_t240 q a c x p u v w : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
-
-(* notion 6111 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t242 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t241 q a c x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c (l_e_st_eq_landau_n_suc x)).
-
-(* notion 6112 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t243 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t6 q a c) (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c t.l_e_st_eq_landau_n_rt_rp_r_c_8283_t242 q a c t u) x : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x).
-
-(* notion 6113 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz283 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λs:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x.λb:l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) s.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8283_t243 q a c x s f b : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (λt:l_e_st_eq_landau_n_1to x.f (s t))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f)).
-
-(* notion 6114 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_shiftl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly : l_e_st_eq_landau_n_nat).
-
-(* notion 6115 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_shiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6116 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_intshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly n : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n)).
-
-(* notion 6117 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_shiftrls ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) x).
-
-(* notion 6118 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly n : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n)).
-
-(* notion 6119 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_iseshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly m).(l_e_st_eq_landau_n_rt_rp_r_iseshiftr x ix y iy ly n m i : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly)) n m).
-
-(* notion 6120 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_shiftl1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly)).
-
-(* notion 6121 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_shiftinv1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_rt_rp_r_shiftinv1 x ix y iy ly u a : l_e_st_eq_landau_n_rt_rp_r_is u (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_shiftl1 x ix y iy ly u a))).
-
-(* notion 6122 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_shiftinv2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_rt_rp_r_shiftinv2 x ix y iy ly u a : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_shiftl1 x ix y iy ly u a)) u).
-
-(* notion 6123 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_shiftf ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_shiftf x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6124 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_smpri ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6125 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λlv:l_e_st_eq_landau_n_rt_rp_r_lessis y v.λkv:l_e_st_eq_landau_n_rt_rp_r_lessis v u.(l_e_st_eq_landau_n_rt_rp_r_lessisi1 v x (l_e_st_eq_landau_n_rt_rp_r_satz172a v u x kv k) : l_e_st_eq_landau_n_rt_rp_r_lessis v x).
-
-(* notion 6126 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_lft ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(λt:l_e_st_eq_landau_n_rt_rp_r_real.λv:l_e_st_eq_landau_n_rt_rp_r_intrl t.λlt:l_e_st_eq_landau_n_rt_rp_r_lessis y t.λkt:l_e_st_eq_landau_n_rt_rp_r_lessis t u.f t v lt (l_e_st_eq_landau_n_rt_rp_r_c_8284_t1 x ix y iy ly f pi q a u iu l k t v lt kt) : Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πv:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πlt:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πkt:l_e_st_eq_landau_n_rt_rp_r_lessis t u.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6127 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_pl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl x y : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6128 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_mn ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_mn x y : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6129 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6130 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λlv:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) v.λkv:l_e_st_eq_landau_n_rt_rp_r_lessis v x.(l_e_st_eq_landau_n_rt_rp_r_satz190c u u l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_lessisi2 u u (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real u)) (l_e_st_eq_landau_n_rt_rp_r_lemma1 l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz169a l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_natpos l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_natrl1))) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl u l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)).
-
-(* notion 6131 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λlv:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) v.λkv:l_e_st_eq_landau_n_rt_rp_r_lessis v x.(l_e_st_eq_landau_n_rt_rp_r_isless1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl u l_e_st_eq_landau_n_rt_rp_r_0) u (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_pl02 u l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t2 x ix y iy ly f pi q a u iu l k v iv lv kv) : l_e_st_eq_landau_n_rt_rp_r_less u (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)).
-
-(* notion 6132 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λlv:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) v.λkv:l_e_st_eq_landau_n_rt_rp_r_lessis v x.(l_e_st_eq_landau_n_rt_rp_r_lessisi1 y v (l_e_st_eq_landau_n_rt_rp_r_satz172b y (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) v (l_e_st_eq_landau_n_rt_rp_r_satz172a y u (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) l (l_e_st_eq_landau_n_rt_rp_r_c_8284_t3 x ix y iy ly f pi q a u iu l k v iv lv kv)) lv) : l_e_st_eq_landau_n_rt_rp_r_lessis y v).
-
-(* notion 6133 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_rgt ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(λt:l_e_st_eq_landau_n_rt_rp_r_real.λv:l_e_st_eq_landau_n_rt_rp_r_intrl t.λlt:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) t.λkt:l_e_st_eq_landau_n_rt_rp_r_lessis t x.f t v (l_e_st_eq_landau_n_rt_rp_r_c_8284_t4 x ix y iy ly f pi q a u iu l k t v lt kt) kt : Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πv:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πlt:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) t.Πkt:l_e_st_eq_landau_n_rt_rp_r_lessis t x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6134 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_intpl u iu l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)).
-
-(* notion 6135 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_satzr25 u iu x ix k : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) x).
-
-(* notion 6136 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) y) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) y (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) y)).
-
-(* notion 6137 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly : l_e_st_eq_landau_n_nat).
-
-(* notion 6138 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_suy ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_c_shiftl u iu y iy l : l_e_st_eq_landau_n_nat).
-
-(* notion 6139 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_nat).
-
-(* notion 6140 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_satzr155a (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt2 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 u iu y iy l)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt2 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k)))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t7 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k))).
-
-(* notion 6141 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_isntirl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t8 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k)).
-
-(* notion 6142 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t9 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k)).
-
-(* notion 6143 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6144 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t9 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q)).
-
-(* notion 6145 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_fr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6146 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_lessisi1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_satz18a (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k))).
-
-(* notion 6147 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_fl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6148 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t12a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_c_satz281 q a (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k)))).
-
-(* notion 6149 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))).
-
-(* notion 6150 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)))).
-
-(* notion 6151 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k)).
-
-(* notion 6152 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t13 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t14 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))).
-
-(* notion 6153 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_isnterl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t15 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)))).
-
-(* notion 6154 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_satzr155b (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)))).
-
-(* notion 6155 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 u iu y iy l)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)))).
-
-(* notion 6156 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t18 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t17 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t16 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)))).
-
-(* notion 6157 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) y (l_e_st_eq_landau_n_rt_rp_r_c_8284_t19 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) y)).
-
-(* notion 6158 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y)) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) y)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y)) y (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)))) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) y) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))).
-
-(* notion 6159 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t22 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t20 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t21 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))).
-
-(* notion 6160 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t23 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8284_t22 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n)).
-
-(* notion 6161 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t24 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))).
-
-(* notion 6162 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t25 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))).
-
-(* notion 6163 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t26 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)) x).
-
-(* notion 6164 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t27 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n)).
-
-(* notion 6165 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t28 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n)).
-
-(* notion 6166 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t29 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n) x).
-
-(* notion 6167 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t30 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_8284_t4 x ix y iy ly f pi q a u iu l k (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t27 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t28 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t29 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n)).
-
-(* notion 6168 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t31 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(pi (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t24 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t25 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t26 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t27 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t30 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t29 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t23 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) n)).
-
-(* notion 6169 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t32 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_8284_t31 x ix y iy ly f pi q a u iu l k t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k))).
-
-(* notion 6170 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t33 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λv:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) v) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t32 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)).
-
-(* notion 6171 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t34 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t33 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q))).
-
-(* notion 6172 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t35 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n))).
-
-(* notion 6173 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t36 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)))).
-
-(* notion 6174 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k)).
-
-(* notion 6175 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t37 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t35 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t36 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))).
-
-(* notion 6176 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t38 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_isnterl (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t37 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n)))).
-
-(* notion 6177 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t39 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))) y (l_e_st_eq_landau_n_rt_rp_r_c_8284_t38 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n)) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))) y)).
-
-(* notion 6178 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t40 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n)) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))) y) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8284_t39 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))).
-
-(* notion 6179 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t41 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr u iu y iy l n : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n)).
-
-(* notion 6180 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t42 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr u iu y iy l n : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n)).
-
-(* notion 6181 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t43 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls u iu y iy l n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n) u).
-
-(* notion 6182 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t44 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_8284_t1 x ix y iy ly f pi q a u iu l k (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t41 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t42 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t43 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n) x).
-
-(* notion 6183 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t45 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))).
-
-(* notion 6184 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t46 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))).
-
-(* notion 6185 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t47 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n)) x).
-
-(* notion 6186 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t48 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(pi (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t41 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t42 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t44 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t45 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t46 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t47 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t40 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k n)).
-
-(* notion 6187 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t49 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t48 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) n)).
-
-(* notion 6188 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t50 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_8284_t49 x ix y iy ly f pi q a u iu l k t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k))).
-
-(* notion 6189 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t51 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λv:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) v) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t50 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q)).
-
-(* notion 6190 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t52 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t51 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q))).
-
-(* notion 6191 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t53 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12a x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t34 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t52 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q))).
-
-(* notion 6192 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz284 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_intpl u iu l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1) (l_e_st_eq_landau_n_rt_rp_r_satzr25 u iu x ix k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t11 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t53 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_intpl u iu l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1) (l_e_st_eq_landau_n_rt_rp_r_satzr25 u iu x ix k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q))).
-
-(* notion 6193 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_pl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl x y : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6194 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_mn ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_mn x y : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6195 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6196 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λw:l_e_st_eq_landau_n_rt_rp_r_real.λiw:l_e_st_eq_landau_n_rt_rp_r_intrl w.λlw:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) w.λkw:l_e_st_eq_landau_n_rt_rp_r_lessis w (l_e_st_eq_landau_n_rt_rp_r_pl x v).(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v)) lw (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w.l_e_st_eq_landau_n_rt_rp_r_satz188f (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w (l_e_st_eq_landau_n_rt_rp_r_m0 v) t) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w.l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w v t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v)).
-
-(* notion 6197 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λw:l_e_st_eq_landau_n_rt_rp_r_real.λiw:l_e_st_eq_landau_n_rt_rp_r_intrl w.λlw:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) w.λkw:l_e_st_eq_landau_n_rt_rp_r_lessis w (l_e_st_eq_landau_n_rt_rp_r_pl x v).(l_e_st_eq_landau_n_rt_rp_r_islessis1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v) y (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) (l_e_st_eq_landau_n_rt_rp_r_mnpl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t1 x ix y iy ly f pi q v iv w iw lw kw) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v)).
-
-(* notion 6198 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λw:l_e_st_eq_landau_n_rt_rp_r_real.λiw:l_e_st_eq_landau_n_rt_rp_r_intrl w.λlw:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) w.λkw:l_e_st_eq_landau_n_rt_rp_r_lessis w (l_e_st_eq_landau_n_rt_rp_r_pl x v).(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_is w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v)) kw (λt:l_e_st_eq_landau_n_rt_rp_r_less w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v).l_e_st_eq_landau_n_rt_rp_r_satz188f w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_m0 v) t) (λt:l_e_st_eq_landau_n_rt_rp_r_is w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v).l_e_st_eq_landau_n_rt_rp_r_ismn1 w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v)).
-
-(* notion 6199 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λw:l_e_st_eq_landau_n_rt_rp_r_real.λiw:l_e_st_eq_landau_n_rt_rp_r_intrl w.λlw:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) w.λkw:l_e_st_eq_landau_n_rt_rp_r_lessis w (l_e_st_eq_landau_n_rt_rp_r_pl x v).(l_e_st_eq_landau_n_rt_rp_r_islessis2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v) x (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) (l_e_st_eq_landau_n_rt_rp_r_mnpl x v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t3 x ix y iy ly f pi q v iv w iw lw kw) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) x).
-
-(* notion 6200 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_sft ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(λt:l_e_st_eq_landau_n_rt_rp_r_real.λw:l_e_st_eq_landau_n_rt_rp_r_intrl t.λlt:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) t.λkt:l_e_st_eq_landau_n_rt_rp_r_lessis t (l_e_st_eq_landau_n_rt_rp_r_pl x v).f (l_e_st_eq_landau_n_rt_rp_r_mn t v) (l_e_st_eq_landau_n_rt_rp_r_intmn t w v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t2 x ix y iy ly f pi q v iv t w lt kt) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t4 x ix y iy ly f pi q v iv t w lt kt) : Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πw:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πlt:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) t.Πkt:l_e_st_eq_landau_n_rt_rp_r_lessis t (l_e_st_eq_landau_n_rt_rp_r_pl x v).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6201 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl v y)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl v y) (l_e_st_eq_landau_n_rt_rp_r_compl y v)) (l_e_st_eq_landau_n_rt_rp_r_satz180 v y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 y))).
-
-(* notion 6202 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl x) (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x) (l_e_st_eq_landau_n_rt_rp_r_asspl1 l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_m0 v)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v) x l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mnpl x v)) (l_e_st_eq_landau_n_rt_rp_r_compl l_e_st_eq_landau_n_rt_rp_r_1rl x) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x)).
-
-(* notion 6203 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 y))) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) v) y) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x) y) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t5 x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x) y (l_e_st_eq_landau_n_rt_rp_r_c_8285_t6 x ix y iy ly f pi q v iv)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x) y)).
-
-(* notion 6204 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less y x) (l_e_st_eq_landau_n_rt_rp_r_is y x) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) ly (λt:l_e_st_eq_landau_n_rt_rp_r_less y x.l_e_st_eq_landau_n_rt_rp_r_satz188f y x v t) (λt:l_e_st_eq_landau_n_rt_rp_r_is y x.l_e_st_eq_landau_n_rt_rp_r_ispl1 y x v t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)).
-
-(* notion 6205 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly : l_e_st_eq_landau_n_nat).
-
-(* notion 6206 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_sv ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_rt_rp_r_c_shiftl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_nat).
-
-(* notion 6207 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_rt_rp_r_isrlent (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t7 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv)).
-
-(* notion 6208 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t9 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv)).
-
-(* notion 6209 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t10 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6210 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t9 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q)).
-
-(* notion 6211 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t10 x ix y iy ly f pi q v iv)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t10 x ix y iy ly f pi q v iv) n))).
-
-(* notion 6212 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t10 x ix y iy ly f pi q v iv) n : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv)).
-
-(* notion 6213 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_isnterl (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t12 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n)))).
-
-(* notion 6214 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n))) y) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_m0 v)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n))) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v) y (l_e_st_eq_landau_n_rt_rp_r_c_8285_t13 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_mnpl y v)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n))) y)).
-
-(* notion 6215 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6216 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_stv ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_shiftr (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) n : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6217 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 v))) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl))) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) v) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 v)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 v))) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n))) y) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_t14 x ix y iy ly f pi q v iv n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n)).
-
-(* notion 6218 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n)).
-
-(* notion 6219 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n) x).
-
-(* notion 6220 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n)).
-
-(* notion 6221 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) n : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n)).
-
-(* notion 6222 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)).
-
-(* notion 6223 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n)).
-
-(* notion 6224 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t22 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_intmn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t19 x ix y iy ly f pi q v iv n) v iv : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v)).
-
-(* notion 6225 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t23 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_8285_t2 x ix y iy ly f pi q v iv (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t19 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t21 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t20 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v)).
-
-(* notion 6226 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t24 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_8285_t4 x ix y iy ly f pi q v iv (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t19 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t21 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t20 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v) x).
-
-(* notion 6227 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t25 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(pi (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t22 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t23 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t24 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t16 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t18 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t17 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t15 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftf (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv n)).
-
-(* notion 6228 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t26 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_shiftf (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).l_e_st_eq_landau_n_rt_rp_r_c_8285_t25 x ix y iy ly f pi q v iv t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv)).
-
-(* notion 6229 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t27 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λw:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) w) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t26 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpri (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv))).
-
-(* notion 6230 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_lemma285 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) (l_e_st_eq_landau_n_rt_rp_r_pl x v)).
-
-(* notion 6231 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz285 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpri (l_e_st_eq_landau_n_rt_rp_r_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_lemma285 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t27 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t11 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpri (l_e_st_eq_landau_n_rt_rp_r_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_lemma285 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q)).
-
-(* notion 6232 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_us ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(s u iu lu ul : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6233 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(ins u iu lu ul : l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul)) (l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul)) (l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) x)).
-
-(* notion 6234 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_inseqe1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t1 x ix y iy ly s ins f u iu lu ul) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul)).
-
-(* notion 6235 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_inseqe2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t1 x ix y iy ly s ins f u iu lu ul) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul)).
-
-(* notion 6236 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_inseqe3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t1 x ix y iy ly s ins f u iu lu ul) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) x).
-
-(* notion 6237 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_usf ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(f (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_inseqe1 x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_inseqe2 x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_inseqe3 x ix y iy ly s ins f u iu lu ul) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6238 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_permseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_intrl t.λv:l_e_st_eq_landau_n_rt_rp_r_lessis y t.λw:l_e_st_eq_landau_n_rt_rp_r_lessis t x.l_e_st_eq_landau_n_rt_rp_r_c_usf x ix y iy ly s ins f t u v w : Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πv:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πw:l_e_st_eq_landau_n_rt_rp_r_lessis t x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6239 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_ss ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly)).
-
-(* notion 6240 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_e_st_eq_landau_n_rt_rp_r_c_satz283 q a c (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps) (l_e_st_eq_landau_n_rt_rp_r_bijshiftseq x ix y iy ly s ins pri ps) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t))) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q)).
-
-(* notion 6241 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_ns ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6242 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_shiftinv1 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n))).
-
-(* notion 6243 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_inseqe1 x ix y iy ly s ins f (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n)).
-
-(* notion 6244 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_inseqe2 x ix y iy ly s ins f (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n)).
-
-(* notion 6245 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_inseqe3 x ix y iy ly s ins f (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n) x).
-
-(* notion 6246 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n))).
-
-(* notion 6247 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n))).
-
-(* notion 6248 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n)) x).
-
-(* notion 6249 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(pi (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t4 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t5 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t6 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n)) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t7 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t8 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t9 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t3 x ix y iy ly f pi q a c s ins pri ps n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f) n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n))).
-
-(* notion 6250 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_8286_t10 x ix y iy ly f pi q a c s ins pri ps t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t))).
-
-(* notion 6251 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) u) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t)) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t11 x ix y iy ly f pi q a c s ins pri ps) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t)))).
-
-(* notion 6252 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz286 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t))) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t12 x ix y iy ly f pi q a c s ins pri ps) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t2 x ix y iy ly f pi q a c s ins pri ps) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q)).
-
-(* notion 6253 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_modf ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (f t)) l_e_st_eq_landau_n_rt_rp_r_0 : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6254 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x f)) r : Prop).
-
-(* notion 6255 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_modf x f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) : Prop).
-
-(* notion 6256 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_and (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 x f r) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 x f r) : Prop).
-
-(* notion 6257 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_some (Πt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x f t) : Prop).
-
-(* notion 6258 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 ≝ λx:l_e_st_eq_landau_n_nat.(Πu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 x u : Prop).
-
-(* notion 6259 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t1 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 6260 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t2 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t1 f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
-
-(* notion 6261 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t3 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t2 f) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 l_e_st_eq_landau_n_1 f (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
-
-(* notion 6262 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t4 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) (l_e_st_eq_landau_n_rt_rp_r_c_modf l_e_st_eq_landau_n_1 f) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 l_e_st_eq_landau_n_1 f (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
-
-(* notion 6263 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t5 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_andi (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 l_e_st_eq_landau_n_1 f (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 l_e_st_eq_landau_n_1 f (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t3 f) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t4 f) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 l_e_st_eq_landau_n_1 f (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
-
-(* notion 6264 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t6 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (Πt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 l_e_st_eq_landau_n_1 f t) (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t5 f) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 l_e_st_eq_landau_n_1 f).
-
-(* notion 6265 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t7 ≝ (Πu:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8287_t6 u : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 l_e_st_eq_landau_n_1).
-
-(* notion 6266 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t8 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 6267 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_lf ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8287_t8 x p f) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6268 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t9 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r) pr : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r).
-
-(* notion 6269 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t10 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r) pr : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r).
-
-(* notion 6270 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t11 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
-
-(* notion 6271 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t12 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t11 x p f r pr)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f))).
-
-(* notion 6272 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_m ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6273 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t13 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_islessis1 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t12 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_satz271 (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))).
-
-(* notion 6274 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t14 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t9 x p f r pr) (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r.l_e_st_eq_landau_n_rt_rp_r_satz188f (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) t) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r.l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))).
-
-(* notion 6275 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t13 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t14 x p f r pr) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))).
-
-(* notion 6276 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_lmf ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8287_t8 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6277 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) x (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lmf x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0))).
-
-(* notion 6278 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lmf x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t10 x p f r pr) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lmf x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0))).
-
-(* notion 6279 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_plis12a r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0))).
-
-(* notion 6280 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t19 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 6281 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lmf x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t16 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t17 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t18 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t19 x p f r pr) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))).
-
-(* notion 6282 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_andi (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t15 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t20 x p f r pr) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))).
-
-(* notion 6283 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (Πt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t21 x p f r pr) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
-
-(* notion 6284 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t23 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_someapp l_e_st_eq_landau_n_rt_rp_r_real (Πt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) t) (p (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) t.l_e_st_eq_landau_n_rt_rp_r_c_8287_t22 x p f t u) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
-
-(* notion 6285 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t25 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8287_t23 x p u : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 6286 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t26 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.(l_e_isp l_e_st_eq_landau_n_nat (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 t) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t25 x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 6287 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz287 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_induction (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 t) l_e_st_eq_landau_n_rt_rp_r_c_8287_t7 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 t.l_e_st_eq_landau_n_rt_rp_r_c_8287_t26 t u) x f : l_e_st_eq_landau_n_rt_rp_r_some (Πt:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x f)) t) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_modf x f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli t l_e_st_eq_landau_n_rt_rp_r_0)))).
-
-(* notion 6288 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_modf x f)) : Prop).
-
-(* notion 6289 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 ≝ λx:l_e_st_eq_landau_n_nat.(Πu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8288_prop1 x u : Prop).
-
-(* notion 6290 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t1 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 6291 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t2 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t1 f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
-
-(* notion 6292 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t3 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_t2 f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 6293 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t4 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) (l_e_st_eq_landau_n_rt_rp_r_c_modf l_e_st_eq_landau_n_1 f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_modf l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 6294 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t5 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_modf l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t3 f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t4 f) : l_e_st_eq_landau_n_rt_rp_r_c_8288_prop1 l_e_st_eq_landau_n_1 f).
-
-(* notion 6295 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t6 ≝ (Πu:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8288_t5 u : l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 l_e_st_eq_landau_n_1).
-
-(* notion 6296 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t7 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 6297 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_lf ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8288_t7 x p f) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6298 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t8 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
-
-(* notion 6299 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_m ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) : l_e_st_eq_landau_n_rt_rp_r_real).
-
-(* notion 6300 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t9 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t8 x p f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))))).
-
-(* notion 6301 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t10 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz268 (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))).
-
-(* notion 6302 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t11 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t9 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t10 x p f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))).
-
-(* notion 6303 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t12 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_t11 x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 6304 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8288_t7 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6305 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t13 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) x (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0))).
-
-(* notion 6306 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t14 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (p (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 6307 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t14 x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0))).
-
-(* notion 6308 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_tsis12a (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))))).
-
-(* notion 6309 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ismn2 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))).
-
-(* notion 6310 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts02 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))) l_e_st_eq_landau_n_rt_rp_r_0).
-
-(* notion 6311 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t19 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_t17 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t18 x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 6312 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t13 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t15 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t16 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t19 x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0)).
-
-(* notion 6313 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t12 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t20 x p f) : l_e_st_eq_landau_n_rt_rp_r_c_8288_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
-
-(* notion 6314 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t21a ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8288_t21 x p u : l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 6315 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.(l_e_isp l_e_st_eq_landau_n_nat (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 t) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t21a x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 6316 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz288 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_induction (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 t) l_e_st_eq_landau_n_rt_rp_r_c_8288_t6 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 t.l_e_st_eq_landau_n_rt_rp_r_c_8288_t22 t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_modf x f))).
-
-(* notion 6317 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x f) l_e_st_eq_landau_n_rt_rp_r_c_0c : Prop).
-
-(* notion 6318 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_some (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) : Prop).
-
-(* notion 6319 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_prop3 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_iff (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x f) : Prop).
-
-(* notion 6320 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 ≝ λx:l_e_st_eq_landau_n_nat.(Πu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8289_prop3 x u : Prop).
-
-(* notion 6321 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t1 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
-
-(* notion 6322 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t2 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t1 f) p : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 6323 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t3 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f.(l_somei (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t2 f p) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f).
-
-(* notion 6324 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t4 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f.λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f u) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_singlet_th1 u : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) u (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)).
-
-(* notion 6325 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t5 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f.λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f u) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (f u) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_8289_t1 f) (l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) u (l_e_symis (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) u (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t4 f p u i))) i : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f).
-
-(* notion 6326 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t6 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f.(l_someapp (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) p (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_8289_t5 f p t u) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f).
-
-(* notion 6327 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t7 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_iffi (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f.l_e_st_eq_landau_n_rt_rp_r_c_8289_t3 f t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f.l_e_st_eq_landau_n_rt_rp_r_c_8289_t6 f t) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop3 l_e_st_eq_landau_n_1 f).
-
-(* notion 6328 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t8 ≝ (Πu:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8289_t7 u : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 l_e_st_eq_landau_n_1).
-
-(* notion 6329 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 6330 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_lf ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6331 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t10 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
-
-(* notion 6332 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t11 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t10 x p f) q : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 6333 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t12 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.(l_e_st_eq_landau_n_rt_rp_r_c_satz221c (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t11 x p f q) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c)).
-
-(* notion 6334 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t13 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_iff_th3 (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (p (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) i : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)).
-
-(* notion 6335 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t14 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_1to x.λj:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_somei (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) n) j : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
-
-(* notion 6336 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_someapp (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t13 x p f q i) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (λt:l_e_st_eq_landau_n_1to x.λu:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f t) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_8289_t14 x p f q i t u) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
-
-(* notion 6337 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_somei (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) i : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
-
-(* notion 6338 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.(l_orapp (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t12 x p f q) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_8289_t15 x p f q t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_8289_t16 x p f q t) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
-
-(* notion 6339 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c (f n) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_c_cx f n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) j) i : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 6340 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).(l_e_st_eq_landau_n_rt_rp_r_c_satz221b (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t18 x p f q n i j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 6341 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n : l_e_st_eq_landau_n_nat).
-
-(* notion 6342 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) j : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).
-
-(* notion 6343 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t21 x p f q n i m j) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).
-
-(* notion 6344 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t23 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) m (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_8289_t22 x p f q n i m t) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 6345 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t24 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t23 x p f q n i m) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 6346 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t25 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_satz26 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t24 x p f q n i m) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) x).
-
-(* notion 6347 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t25 x p f q n i m) : l_e_st_eq_landau_n_1to x).
-
-(* notion 6348 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t26 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t25 x p f q n i m) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m))).
-
-(* notion 6349 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t27 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t26 x p f q n i m) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m))).
-
-(* notion 6350 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t28 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t27 x p f q n i m) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m))).
-
-(* notion 6351 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t29 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_c_cx f n (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t28 x p f q n i m) : l_e_st_eq_landau_n_rt_rp_r_c_is (f n) (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m))).
-
-(* notion 6352 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t30 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) l_e_st_eq_landau_n_rt_rp_r_c_0c (f n) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t29 x p f q n i m) i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 6353 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t31 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_somei (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t30 x p f q n i m) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)).
-
-(* notion 6354 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t32 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_iff_th4 (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (p (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t31 x p f q n i m) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)).
-
-(* notion 6355 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t34 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_rt_rp_r_c_satz221a (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t32 x p f q n i m) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 6356 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t35 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).l_e_st_eq_landau_n_rt_rp_r_c_8289_t20 x p f q n i t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).l_e_st_eq_landau_n_rt_rp_r_c_8289_t34 x p f q n i t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 6357 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t36 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_8289_t10 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t35 x p f q n i) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
-
-(* notion 6358 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t37 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.(l_someapp (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) q (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λu:l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_8289_t36 x p f q t u) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
-
-(* notion 6359 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t38 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_iffi (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.l_e_st_eq_landau_n_rt_rp_r_c_8289_t17 x p f t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.l_e_st_eq_landau_n_rt_rp_r_c_8289_t37 x p f t) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop3 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
-
-(* notion 6360 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t39 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8289_t38 x p u : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
-
-(* notion 6361 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t40 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.(l_e_isp l_e_st_eq_landau_n_nat (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 t) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t39 x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 (l_e_st_eq_landau_n_suc x)).
-
-(* notion 6362 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz289 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_induction (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 t) l_e_st_eq_landau_n_rt_rp_r_c_8289_t8 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 t.l_e_st_eq_landau_n_rt_rp_r_c_8289_t40 t u) x f : l_iff (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x f) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_some (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c))).
-
-(* notion 6363 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz289a ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x f) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_iff_th3 (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x f) (l_e_st_eq_landau_n_rt_rp_r_c_satz289 x f) i : l_some (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c)).
-
-(* notion 6364 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t41 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_somei (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) n i : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x f).
-
-(* notion 6365 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_satz289b ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_iff_th4 (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x f) (l_e_st_eq_landau_n_rt_rp_r_c_satz289 x f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t41 x f n i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x f) l_e_st_eq_landau_n_rt_rp_r_c_0c).
-
-(* notion 6366 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_posintnatrl m p mi : l_e_st_eq_landau_n_rt_rp_r_natrl m).
-
-(* notion 6367 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_ntofrl m (l_e_st_eq_landau_n_rt_rp_r_c_v9_t1 x m mi o p) : l_e_st_eq_landau_n_nat).
-
-(* notion 6368 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).x) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
-
-(* notion 6369 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi1 ox mp : l_e_st_eq_landau_n_nat).
-
-(* notion 6370 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 y n ni1 oy np : l_e_st_eq_landau_n_nat).
-
-(* notion 6371 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_isrlent m (l_e_st_eq_landau_n_rt_rp_r_c_v9_t1 x m mi1 ox mp) n (l_e_st_eq_landau_n_rt_rp_r_c_v9_t1 y n ni1 oy np) j : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np)).
-
-(* notion 6372 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t2 x y m n i j mi1 ni1 ox oy mp np) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np)).
-
-(* notion 6373 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t2 x y m n i j mi1 ni1 ox oy mp np) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y))) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 y n ni1 oy np)).
-
-(* notion 6374 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np)) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).x) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).i) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).l_e_st_eq_landau_n_rt_rp_r_c_cx) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).x) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y))).
-
-(* notion 6375 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) u) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).x) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t5 x y m n i j mi1 ni1 ox oy mp np) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi1 ox mp) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y)))).
-
-(* notion 6376 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi1 ox mp) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y))) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 y n ni1 oy np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t6 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t4 x y m n i j mi1 ni1 ox oy mp np) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi1 ox mp) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 y n ni1 oy np)).
-
-(* notion 6377 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.λp1:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t7 x x m m (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real m) mi mi o o p p1 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o p) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o p1)).
-
-(* notion 6378 *)
-definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_some_th5 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).l_e_st_eq_landau_n_rt_rp_r_c_is ((?u:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).x) t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).n) : l_not (l_some (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).l_e_st_eq_landau_n_rt_rp_r_c_is ((?u:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).x) t) l_e_st_eq_landau_n_rt_rp_r_c_0c))).
-
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file is generated by Helena 0.8.2 M - November 2014: do not edit **)
+
+include "basics/pts.ma".
+
+(* notion 1 *)
+definition l_imp ≝ λa:Prop.λb:Prop.(Πx:a.b : Prop).
+
+(* notion 2 *)
+definition l_mp ≝ λa:Prop.λb:Prop.λa1:a.λi:l_imp a b.(i a1 : b).
+
+(* notion 3 *)
+definition l_refimp ≝ λa:Prop.(λx:a.x : l_imp a a).
+
+(* notion 4 *)
+definition l_trimp ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_imp a b.λj:l_imp b c.(λx:a.j (i x) : l_imp a c).
+
+(* notion 5 *)
+axiom l_con : Prop.
+
+(* notion 6 *)
+definition l_not ≝ λa:Prop.(l_imp a l_con : Prop).
+
+(* notion 7 *)
+definition l_wel ≝ λa:Prop.(l_not (l_not a) : Prop).
+
+(* notion 8 *)
+definition l_weli ≝ λa:Prop.λa1:a.(λx:l_not a.x a1 : l_wel a).
+
+(* notion 9 *)
+axiom l_et : Πa:Prop.Πw:l_wel a.a.
+
+(* notion 10 *)
+definition l_cone ≝ λa:Prop.λc1:l_con.(l_et a (λx:l_not a.c1) : a).
+
+(* notion 11 *)
+definition l_imp_th1 ≝ λa:Prop.λb:Prop.λi:l_imp a b.λj:l_imp (l_not a) b.(l_et b (λx:l_not b.x (j (l_trimp a b l_con i x))) : b).
+
+(* notion 12 *)
+definition l_imp_th2 ≝ λa:Prop.λb:Prop.λn:l_not a.(l_trimp a l_con b n (λx:l_con.l_cone b x) : l_imp a b).
+
+(* notion 13 *)
+definition l_imp_th3 ≝ λa:Prop.λb:Prop.λn:l_not b.λi:l_imp a b.(l_trimp a b l_con i n : l_not a).
+
+(* notion 14 *)
+definition l_imp_th4 ≝ λa:Prop.λb:Prop.λa1:a.λn:l_not b.(λx:l_imp a b.l_imp_th3 a b n x a1 : l_not (l_imp a b)).
+
+(* notion 15 *)
+definition l_imp_th5 ≝ λa:Prop.λb:Prop.λn:l_not (l_imp a b).(l_et a (λx:l_not a.n (l_imp_th2 a b x)) : a).
+
+(* notion 16 *)
+definition l_imp_th6 ≝ λa:Prop.λb:Prop.λn:l_not (l_imp a b).(λx:b.n (λy:a.x) : l_not b).
+
+(* notion 17 *)
+definition l_imp_th7 ≝ λa:Prop.λb:Prop.λn:l_not b.λi:l_imp (l_not a) b.(l_et a (l_imp_th3 (l_not a) b n i) : a).
+
+(* notion 18 *)
+definition l_cp ≝ λa:Prop.λb:Prop.λi:l_imp (l_not b) (l_not a).(λx:a.l_imp_th7 b (l_not a) (l_weli a x) i : l_imp a b).
+
+(* notion 19 *)
+definition l_obvious ≝ (l_imp l_con l_con : Prop).
+
+(* notion 20 *)
+definition l_obviousi ≝ (l_refimp l_con : l_obvious).
+
+(* notion 21 *)
+definition l_ec ≝ λa:Prop.λb:Prop.(l_imp a (l_not b) : Prop).
+
+(* notion 22 *)
+definition l_eci1 ≝ λa:Prop.λb:Prop.λn:l_not a.(l_imp_th2 a (l_not b) n : l_ec a b).
+
+(* notion 23 *)
+definition l_eci2 ≝ λa:Prop.λb:Prop.λn:l_not b.(λx:a.n : l_ec a b).
+
+(* notion 24 *)
+definition l_ec_th1 ≝ λa:Prop.λb:Prop.λi:l_imp a (l_not b).(i : l_ec a b).
+
+(* notion 25 *)
+definition l_ec_th2 ≝ λa:Prop.λb:Prop.λi:l_imp b (l_not a).(λx:a.λy:b.i y x : l_ec a b).
+
+(* notion 26 *)
+definition l_comec ≝ λa:Prop.λb:Prop.λe:l_ec a b.(l_ec_th2 b a e : l_ec b a).
+
+(* notion 27 *)
+definition l_ece1 ≝ λa:Prop.λb:Prop.λe:l_ec a b.λa1:a.(e a1 : l_not b).
+
+(* notion 28 *)
+definition l_ece2 ≝ λa:Prop.λb:Prop.λe:l_ec a b.λb1:b.(l_imp_th3 a (l_not b) (l_weli b b1) e : l_not a).
+
+(* notion 29 *)
+definition l_ec_th3 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec a b.λi:l_imp c a.(l_trimp c a (l_not b) i e : l_ec c b).
+
+(* notion 30 *)
+definition l_ec_th4 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec a b.λi:l_imp c b.(l_comec c a (l_ec_th3 b a c (l_comec a b e) i) : l_ec a c).
+
+(* notion 31 *)
+definition l_and ≝ λa:Prop.λb:Prop.(l_not (l_ec a b) : Prop).
+
+(* notion 32 *)
+definition l_andi ≝ λa:Prop.λb:Prop.λa1:a.λb1:b.(l_imp_th4 a (l_not b) a1 (l_weli b b1) : l_and a b).
+
+(* notion 33 *)
+definition l_ande1 ≝ λa:Prop.λb:Prop.λa1:l_and a b.(l_imp_th5 a (l_not b) a1 : a).
+
+(* notion 34 *)
+definition l_ande2 ≝ λa:Prop.λb:Prop.λa1:l_and a b.(l_et b (l_imp_th6 a (l_not b) a1) : b).
+
+(* notion 35 *)
+definition l_comand ≝ λa:Prop.λb:Prop.λa1:l_and a b.(l_andi b a (l_ande2 a b a1) (l_ande1 a b a1) : l_and b a).
+
+(* notion 36 *)
+definition l_and_th1 ≝ λa:Prop.λb:Prop.λn:l_not a.(l_weli (l_ec a b) (l_eci1 a b n) : l_not (l_and a b)).
+
+(* notion 37 *)
+definition l_and_th2 ≝ λa:Prop.λb:Prop.λn:l_not b.(l_weli (l_ec a b) (l_eci2 a b n) : l_not (l_and a b)).
+
+(* notion 38 *)
+definition l_and_th3 ≝ λa:Prop.λb:Prop.λn:l_not (l_and a b).λa1:a.(l_ece1 a b (l_et (l_ec a b) n) a1 : l_not b).
+
+(* notion 39 *)
+definition l_and_th4 ≝ λa:Prop.λb:Prop.λn:l_not (l_and a b).λb1:b.(l_ece2 a b (l_et (l_ec a b) n) b1 : l_not a).
+
+(* notion 40 *)
+definition l_and_th5 ≝ λa:Prop.λb:Prop.λn:l_not (l_and a b).(l_imp_th3 (l_and b a) (l_and a b) n (λx:l_and b a.l_comand b a x) : l_not (l_and b a)).
+
+(* notion 41 *)
+definition l_and_th6 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and a b.λi:l_imp a c.(l_andi c b (i (l_ande1 a b a1)) (l_ande2 a b a1) : l_and c b).
+
+(* notion 42 *)
+definition l_and_th7 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and a b.λi:l_imp b c.(l_andi a c (l_ande1 a b a1) (i (l_ande2 a b a1)) : l_and a c).
+
+(* notion 43 *)
+definition l_or ≝ λa:Prop.λb:Prop.(l_imp (l_not a) b : Prop).
+
+(* notion 44 *)
+definition l_ori1 ≝ λa:Prop.λb:Prop.λa1:a.(l_imp_th2 (l_not a) b (l_weli a a1) : l_or a b).
+
+(* notion 45 *)
+definition l_ori2 ≝ λa:Prop.λb:Prop.λb1:b.(λx:l_not a.b1 : l_or a b).
+
+(* notion 46 *)
+definition l_or_th1 ≝ λa:Prop.λb:Prop.λi:l_imp (l_not a) b.(i : l_or a b).
+
+(* notion 47 *)
+definition l_or_th2 ≝ λa:Prop.λb:Prop.λi:l_imp (l_not b) a.(λx:l_not a.l_et b (l_imp_th3 (l_not b) a x i) : l_or a b).
+
+(* notion 48 *)
+definition l_ore2 ≝ λa:Prop.λb:Prop.λo:l_or a b.λn:l_not a.(o n : b).
+
+(* notion 49 *)
+definition l_ore1 ≝ λa:Prop.λb:Prop.λo:l_or a b.λn:l_not b.(l_et a (l_imp_th3 (l_not a) b n o) : a).
+
+(* notion 50 *)
+definition l_comor ≝ λa:Prop.λb:Prop.λo:l_or a b.(λx:l_not b.l_ore1 a b o x : l_or b a).
+
+(* notion 51 *)
+definition l_or_th3 ≝ λa:Prop.λb:Prop.λn:l_not a.λm:l_not b.(l_imp_th4 (l_not a) b n m : l_not (l_or a b)).
+
+(* notion 52 *)
+definition l_or_th4 ≝ λa:Prop.λb:Prop.λn:l_not (l_or a b).(l_imp_th5 (l_not a) b n : l_not a).
+
+(* notion 53 *)
+definition l_or_th5 ≝ λa:Prop.λb:Prop.λn:l_not (l_or a b).(l_imp_th6 (l_not a) b n : l_not b).
+
+(* notion 54 *)
+definition l_or_th6 ≝ λa:Prop.(l_refimp (l_not a) : l_or a (l_not a)).
+
+(* notion 55 *)
+definition l_orapp ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or a b.λi:l_imp a c.λj:l_imp b c.(l_imp_th1 a c i (l_trimp (l_not a) b c o j) : c).
+
+(* notion 56 *)
+definition l_or_th7 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or a b.λi:l_imp a c.(l_trimp (l_not c) (l_not a) b (λx:l_not c.l_imp_th3 a c x i) o : l_or c b).
+
+(* notion 57 *)
+definition l_or_th8 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or a b.λi:l_imp b c.(l_trimp (l_not a) b c o i : l_or a c).
+
+(* notion 58 *)
+definition l_or_th9 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λo:l_or a b.λi:l_imp a c.λj:l_imp b d.(l_or_th7 a d c (l_or_th8 a b d o j) i : l_or c d).
+
+(* notion 59 *)
+definition l_or_th10 ≝ λa:Prop.λb:Prop.λo:l_or a b.(o : l_imp (l_not a) b).
+
+(* notion 60 *)
+definition l_or_th11 ≝ λa:Prop.λb:Prop.λo:l_or a b.(l_comor a b o : l_imp (l_not b) a).
+
+(* notion 61 *)
+definition l_or_th12 ≝ λa:Prop.λb:Prop.λo:l_or (l_not a) b.(l_trimp a (l_wel a) b (λx:a.l_weli a x) o : l_imp a b).
+
+(* notion 62 *)
+definition l_or_th13 ≝ λa:Prop.λb:Prop.λi:l_imp a b.(l_trimp (l_wel a) a b (λx:l_wel a.l_et a x) i : l_or (l_not a) b).
+
+(* notion 63 *)
+definition l_or_th14 ≝ λa:Prop.λb:Prop.λo:l_or (l_not a) (l_not b).(l_weli (l_ec a b) (l_or_th12 a (l_not b) o) : l_not (l_and a b)).
+
+(* notion 64 *)
+definition l_or_th15 ≝ λa:Prop.λb:Prop.λn:l_not (l_and a b).(l_or_th13 a (l_not b) (l_et (l_ec a b) n) : l_or (l_not a) (l_not b)).
+
+(* notion 65 *)
+definition l_or_th16 ≝ λa:Prop.λb:Prop.λa1:l_and (l_not a) (l_not b).(l_or_th3 a b (l_ande1 (l_not a) (l_not b) a1) (l_ande2 (l_not a) (l_not b) a1) : l_not (l_or a b)).
+
+(* notion 66 *)
+definition l_or_th17 ≝ λa:Prop.λb:Prop.λn:l_not (l_or a b).(l_andi (l_not a) (l_not b) (l_or_th4 a b n) (l_or_th5 a b n) : l_and (l_not a) (l_not b)).
+
+(* notion 67 *)
+definition l_orec ≝ λa:Prop.λb:Prop.(l_and (l_or a b) (l_ec a b) : Prop).
+
+(* notion 68 *)
+definition l_oreci ≝ λa:Prop.λb:Prop.λo:l_or a b.λe:l_ec a b.(l_andi (l_or a b) (l_ec a b) o e : l_orec a b).
+
+(* notion 69 *)
+definition l_orec_th1 ≝ λa:Prop.λb:Prop.λa1:a.λn:l_not b.(l_oreci a b (l_ori1 a b a1) (l_eci2 a b n) : l_orec a b).
+
+(* notion 70 *)
+definition l_orec_th2 ≝ λa:Prop.λb:Prop.λn:l_not a.λb1:b.(l_oreci a b (l_ori2 a b b1) (l_eci1 a b n) : l_orec a b).
+
+(* notion 71 *)
+definition l_orece1 ≝ λa:Prop.λb:Prop.λo:l_orec a b.(l_ande1 (l_or a b) (l_ec a b) o : l_or a b).
+
+(* notion 72 *)
+definition l_orece2 ≝ λa:Prop.λb:Prop.λo:l_orec a b.(l_ande2 (l_or a b) (l_ec a b) o : l_ec a b).
+
+(* notion 73 *)
+definition l_comorec ≝ λa:Prop.λb:Prop.λo:l_orec a b.(l_oreci b a (l_comor a b (l_orece1 a b o)) (l_comec a b (l_orece2 a b o)) : l_orec b a).
+
+(* notion 74 *)
+definition l_orec_th3 ≝ λa:Prop.λb:Prop.λo:l_orec a b.λa1:a.(l_ece1 a b (l_orece2 a b o) a1 : l_not b).
+
+(* notion 75 *)
+definition l_orec_th4 ≝ λa:Prop.λb:Prop.λo:l_orec a b.λb1:b.(l_ece2 a b (l_orece2 a b o) b1 : l_not a).
+
+(* notion 76 *)
+definition l_orec_th5 ≝ λa:Prop.λb:Prop.λo:l_orec a b.λn:l_not a.(l_ore2 a b (l_orece1 a b o) n : b).
+
+(* notion 77 *)
+definition l_orec_th6 ≝ λa:Prop.λb:Prop.λo:l_orec a b.λn:l_not b.(l_ore1 a b (l_orece1 a b o) n : a).
+
+(* notion 78 *)
+definition l_iff ≝ λa:Prop.λb:Prop.(l_and (l_imp a b) (l_imp b a) : Prop).
+
+(* notion 79 *)
+definition l_iffi ≝ λa:Prop.λb:Prop.λi:l_imp a b.λj:l_imp b a.(l_andi (l_imp a b) (l_imp b a) i j : l_iff a b).
+
+(* notion 80 *)
+definition l_iff_th1 ≝ λa:Prop.λb:Prop.λa1:a.λb1:b.(l_iffi a b (λx:a.b1) (λx:b.a1) : l_iff a b).
+
+(* notion 81 *)
+definition l_iff_th2 ≝ λa:Prop.λb:Prop.λn:l_not a.λm:l_not b.(l_iffi a b (l_imp_th2 a b n) (l_imp_th2 b a m) : l_iff a b).
+
+(* notion 82 *)
+definition l_iffe1 ≝ λa:Prop.λb:Prop.λi:l_iff a b.(l_ande1 (l_imp a b) (l_imp b a) i : l_imp a b).
+
+(* notion 83 *)
+definition l_iffe2 ≝ λa:Prop.λb:Prop.λi:l_iff a b.(l_ande2 (l_imp a b) (l_imp b a) i : l_imp b a).
+
+(* notion 84 *)
+definition l_comiff ≝ λa:Prop.λb:Prop.λi:l_iff a b.(l_iffi b a (l_iffe2 a b i) (l_iffe1 a b i) : l_iff b a).
+
+(* notion 85 *)
+definition l_iff_th3 ≝ λa:Prop.λb:Prop.λi:l_iff a b.λa1:a.(l_iffe1 a b i a1 : b).
+
+(* notion 86 *)
+definition l_iff_th4 ≝ λa:Prop.λb:Prop.λi:l_iff a b.λb1:b.(l_iffe2 a b i b1 : a).
+
+(* notion 87 *)
+definition l_iff_th5 ≝ λa:Prop.λb:Prop.λi:l_iff a b.λn:l_not a.(l_imp_th3 b a n (l_iffe2 a b i) : l_not b).
+
+(* notion 88 *)
+definition l_iff_th6 ≝ λa:Prop.λb:Prop.λi:l_iff a b.λn:l_not b.(l_imp_th3 a b n (l_iffe1 a b i) : l_not a).
+
+(* notion 89 *)
+definition l_iff_th7 ≝ λa:Prop.λb:Prop.λa1:a.λn:l_not b.(l_and_th1 (l_imp a b) (l_imp b a) (l_imp_th4 a b a1 n) : l_not (l_iff a b)).
+
+(* notion 90 *)
+definition l_iff_th8 ≝ λa:Prop.λb:Prop.λn:l_not a.λb1:b.(l_and_th2 (l_imp a b) (l_imp b a) (l_imp_th4 b a b1 n) : l_not (l_iff a b)).
+
+(* notion 91 *)
+definition l_refiff ≝ λa:Prop.(l_iffi a a (l_refimp a) (l_refimp a) : l_iff a a).
+
+(* notion 92 *)
+definition l_symiff ≝ λa:Prop.λb:Prop.λi:l_iff a b.(l_comiff a b i : l_iff b a).
+
+(* notion 93 *)
+definition l_triff ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λj:l_iff b c.(l_iffi a c (l_trimp a b c (l_iffe1 a b i) (l_iffe1 b c j)) (l_trimp c b a (l_iffe2 b c j) (l_iffe2 a b i)) : l_iff a c).
+
+(* notion 94 *)
+definition l_iff_th9 ≝ λa:Prop.λb:Prop.λi:l_iff a b.(λx:l_not a.l_iff_th5 a b i x : l_imp (l_not a) (l_not b)).
+
+(* notion 95 *)
+definition l_iff_th10 ≝ λa:Prop.λb:Prop.λi:l_iff a b.(λx:l_not b.l_iff_th6 a b i x : l_imp (l_not b) (l_not a)).
+
+(* notion 96 *)
+definition l_iff_th11 ≝ λa:Prop.λb:Prop.λi:l_iff a b.(l_iffi (l_not a) (l_not b) (l_iff_th9 a b i) (l_iff_th10 a b i) : l_iff (l_not a) (l_not b)).
+
+(* notion 97 *)
+definition l_iff_th12 ≝ λa:Prop.λb:Prop.λi:l_imp (l_not a) (l_not b).λj:l_imp (l_not b) (l_not a).(l_iffi a b (l_cp a b j) (l_cp b a i) : l_iff a b).
+
+(* notion 98 *)
+definition l_iff_th13 ≝ λa:Prop.λb:Prop.λo:l_orec a b.(l_iffi a (l_not b) (l_orece2 a b o) (l_comor a b (l_orece1 a b o)) : l_iff a (l_not b)).
+
+(* notion 99 *)
+definition l_iff_th14 ≝ λa:Prop.λb:Prop.λo:l_orec a b.(l_iff_th13 b a (l_comorec a b o) : l_iff b (l_not a)).
+
+(* notion 100 *)
+definition l_iff_th15 ≝ λa:Prop.λb:Prop.λi:l_iff a (l_not b).(l_oreci a b (l_comor b a (l_iffe2 a (l_not b) i)) (l_iffe1 a (l_not b) i) : l_orec a b).
+
+(* notion 101 *)
+definition l_iff_th16 ≝ λa:Prop.λb:Prop.λi:l_iff b (l_not a).(l_comorec b a (l_iff_th15 b a i) : l_orec a b).
+
+(* notion 102 *)
+definition l_iff_thimp1 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λj:l_imp a c.(l_trimp b a c (l_iffe2 a b i) j : l_imp b c).
+
+(* notion 103 *)
+definition l_iff_thimp2 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λj:l_imp c a.(l_trimp c a b j (l_iffe1 a b i) : l_imp c b).
+
+(* notion 104 *)
+definition l_iff_thec1 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λe:l_ec a c.(l_ec_th3 a c b e (l_iffe2 a b i) : l_ec b c).
+
+(* notion 105 *)
+definition l_iff_thec2 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λe:l_ec c a.(l_ec_th4 c a b e (l_iffe2 a b i) : l_ec c b).
+
+(* notion 106 *)
+definition l_iff_thand1 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λa1:l_and a c.(l_and_th6 a c b a1 (l_iffe1 a b i) : l_and b c).
+
+(* notion 107 *)
+definition l_iff_thand2 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λa1:l_and c a.(l_and_th7 c a b a1 (l_iffe1 a b i) : l_and c b).
+
+(* notion 108 *)
+definition l_iff_thor1 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λo:l_or a c.(l_or_th7 a c b o (l_iffe1 a b i) : l_or b c).
+
+(* notion 109 *)
+definition l_iff_thor2 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λo:l_or c a.(l_or_th8 c a b o (l_iffe1 a b i) : l_or c b).
+
+(* notion 110 *)
+definition l_iff_thorec1 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λo:l_orec a c.(l_oreci b c (l_iff_thor1 a b c i (l_orece1 a c o)) (l_iff_thec1 a b c i (l_orece2 a c o)) : l_orec b c).
+
+(* notion 111 *)
+definition l_iff_thorec2 ≝ λa:Prop.λb:Prop.λc:Prop.λi:l_iff a b.λo:l_orec c a.(l_oreci c b (l_iff_thor2 a b c i (l_orece1 c a o)) (l_iff_thec2 a b c i (l_orece2 c a o)) : l_orec c b).
+
+(* notion 112 *)
+definition l_all ≝ λsigma:Type[0].λp:Πx:sigma.Prop.(Πx:sigma.p x : Prop).
+
+(* notion 113 *)
+definition l_alle ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λa1:l_all sigma p.λs:sigma.(a1 s : p s).
+
+(* notion 114 *)
+definition l_all_th1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λn:l_not (p s).(λx:l_all sigma p.n (x s) : l_not (l_all sigma p)).
+
+(* notion 115 *)
+definition l_non ≝ λsigma:Type[0].λp:Πx:sigma.Prop.(λx:sigma.l_not (p x) : Πx:sigma.Prop).
+
+(* notion 116 *)
+definition l_some ≝ λsigma:Type[0].λp:Πx:sigma.Prop.(l_not (l_non sigma p) : Prop).
+
+(* notion 117 *)
+definition l_somei ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λsp:p s.(l_all_th1 sigma (l_non sigma p) s (l_weli (p s) sp) : l_some sigma p).
+
+(* notion 118 *)
+definition l_some_t1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_not (l_all sigma p).λm:l_non sigma (l_non sigma p).λs:sigma.(l_et (p s) (m s) : p s).
+
+(* notion 119 *)
+definition l_some_t2 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_not (l_all sigma p).λm:l_non sigma (l_non sigma p).(n (λx:sigma.l_some_t1 sigma p n m x) : l_con).
+
+(* notion 120 *)
+definition l_some_th1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_not (l_all sigma p).(λx:l_non sigma (l_non sigma p).l_some_t2 sigma p n x : l_some sigma (l_non sigma p)).
+
+(* notion 121 *)
+definition l_some_t3 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma (l_non sigma p).λa1:l_all sigma p.λt:sigma.(l_weli (p t) (a1 t) : l_not (l_not (p t))).
+
+(* notion 122 *)
+definition l_some_t4 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma (l_non sigma p).λa1:l_all sigma p.(s (λx:sigma.l_some_t3 sigma p s a1 x) : l_con).
+
+(* notion 123 *)
+definition l_some_th2 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma (l_non sigma p).(λx:l_all sigma p.l_some_t4 sigma p s x : l_not (l_all sigma p)).
+
+(* notion 124 *)
+definition l_some_th3 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_not (l_some sigma p).(l_et (l_non sigma p) n : l_non sigma p).
+
+(* notion 125 *)
+definition l_some_th4 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_not (l_some sigma p).λs:sigma.(l_some_th3 sigma p n s : l_not (p s)).
+
+(* notion 126 *)
+definition l_some_th5 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λn:l_non sigma p.(l_weli (l_non sigma p) n : l_not (l_some sigma p)).
+
+(* notion 127 *)
+definition l_some_t5 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma p.λx:Prop.λi:Πy:sigma.l_imp (p y) x.λn:l_not x.λt:sigma.(l_imp_th3 (p t) x n (i t) : l_not (p t)).
+
+(* notion 128 *)
+definition l_some_t6 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma p.λx:Prop.λi:Πy:sigma.l_imp (p y) x.λn:l_not x.(l_mp (l_some sigma p) l_con s (l_some_th5 sigma p (λy:sigma.l_some_t5 sigma p s x i n y)) : l_con).
+
+(* notion 129 *)
+definition l_someapp ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:l_some sigma p.λx:Prop.λi:Πy:sigma.l_imp (p y) x.(l_et x (λy:l_not x.l_some_t6 sigma p s x i y) : x).
+
+(* notion 130 *)
+definition l_some_th6 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λq:Πx:sigma.Prop.λs:l_some sigma p.λi:Πx:sigma.l_imp (p x) (q x).(l_someapp sigma p s (l_some sigma q) (λx:sigma.λy:p x.l_somei sigma q x (l_mp (p x) (q x) y (i x))) : l_some sigma q).
+
+(* notion 131 *)
+definition l_or3 ≝ λa:Prop.λb:Prop.λc:Prop.(l_or a (l_or b c) : Prop).
+
+(* notion 132 *)
+definition l_or3_th1 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not a.(l_ore2 a (l_or b c) o n : l_or b c).
+
+(* notion 133 *)
+definition l_or3e3 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not a.λm:l_not b.(l_ore2 b c (l_or3_th1 a b c o n) m : c).
+
+(* notion 134 *)
+definition l_or3_th2 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not b.(l_or_th2 c a (λx:l_not a.l_or3e3 a b c o x n) : l_or c a).
+
+(* notion 135 *)
+definition l_or3e1 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not b.λm:l_not c.(l_ore2 c a (l_or3_th2 a b c o n) m : a).
+
+(* notion 136 *)
+definition l_or3_th3 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not c.(l_or_th2 a b (λx:l_not b.l_or3e1 a b c o x n) : l_or a b).
+
+(* notion 137 *)
+definition l_or3e2 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λn:l_not c.λm:l_not a.(l_ore2 a b (l_or3_th3 a b c o n) m : b).
+
+(* notion 138 *)
+definition l_or3_th4 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.(l_or_th1 b (l_or c a) (λx:l_not b.l_or3_th2 a b c o x) : l_or3 b c a).
+
+(* notion 139 *)
+definition l_or3_th5 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.(l_or3_th4 b c a (l_or3_th4 a b c o) : l_or3 c a b).
+
+(* notion 140 *)
+definition l_or3i1 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:a.(l_ori1 a (l_or b c) a1 : l_or3 a b c).
+
+(* notion 141 *)
+definition l_or3i2 ≝ λa:Prop.λb:Prop.λc:Prop.λb1:b.(l_ori2 a (l_or b c) (l_ori1 b c b1) : l_or3 a b c).
+
+(* notion 142 *)
+definition l_or3i3 ≝ λa:Prop.λb:Prop.λc:Prop.λc1:c.(l_ori2 a (l_or b c) (l_ori2 b c c1) : l_or3 a b c).
+
+(* notion 143 *)
+definition l_or3_th6 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or a b.(l_or3_th4 c a b (l_ori2 c (l_or a b) o) : l_or3 a b c).
+
+(* notion 144 *)
+definition l_or3_th7 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or b c.(l_ori2 a (l_or b c) o : l_or3 a b c).
+
+(* notion 145 *)
+definition l_or3_th8 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or c a.(l_or3_th4 c a b (l_or3_th6 c a b o) : l_or3 a b c).
+
+(* notion 146 *)
+definition l_or3app ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λo:l_or3 a b c.λi:l_imp a d.λj:l_imp b d.λk:l_imp c d.(l_orapp a (l_or b c) d o i (λx:l_or b c.l_orapp b c d x j k) : d).
+
+(* notion 147 *)
+definition l_and3 ≝ λa:Prop.λb:Prop.λc:Prop.(l_and a (l_and b c) : Prop).
+
+(* notion 148 *)
+definition l_and3e1 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_ande1 a (l_and b c) a1 : a).
+
+(* notion 149 *)
+definition l_and3e2 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_ande1 b c (l_ande2 a (l_and b c) a1) : b).
+
+(* notion 150 *)
+definition l_and3e3 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_ande2 b c (l_ande2 a (l_and b c) a1) : c).
+
+(* notion 151 *)
+definition l_and3i ≝ λa:Prop.λb:Prop.λc:Prop.λa1:a.λb1:b.λc1:c.(l_andi a (l_and b c) a1 (l_andi b c b1 c1) : l_and3 a b c).
+
+(* notion 152 *)
+definition l_and3_th1 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_and3i b c a (l_and3e2 a b c a1) (l_and3e3 a b c a1) (l_and3e1 a b c a1) : l_and3 b c a).
+
+(* notion 153 *)
+definition l_and3_th2 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_and3_th1 b c a (l_and3_th1 a b c a1) : l_and3 c a b).
+
+(* notion 154 *)
+definition l_and3_th3 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_andi a b (l_and3e1 a b c a1) (l_and3e2 a b c a1) : l_and a b).
+
+(* notion 155 *)
+definition l_and3_th4 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_ande2 a (l_and b c) a1 : l_and b c).
+
+(* notion 156 *)
+definition l_and3_th5 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_and3_th3 c a b (l_and3_th2 a b c a1) : l_and c a).
+
+(* notion 157 *)
+definition l_and3_th6 ≝ λa:Prop.λb:Prop.λc:Prop.λa1:l_and3 a b c.(l_and3i c b a (l_and3e3 a b c a1) (l_and3e2 a b c a1) (l_and3e1 a b c a1) : l_and3 c b a).
+
+(* notion 158 *)
+definition l_ec3 ≝ λa:Prop.λb:Prop.λc:Prop.(l_and3 (l_ec a b) (l_ec b c) (l_ec c a) : Prop).
+
+(* notion 159 *)
+definition l_ec3_th1 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_and3e1 (l_ec a b) (l_ec b c) (l_ec c a) e : l_ec a b).
+
+(* notion 160 *)
+definition l_ec3_th2 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_and3e2 (l_ec a b) (l_ec b c) (l_ec c a) e : l_ec b c).
+
+(* notion 161 *)
+definition l_ec3_th3 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_and3e3 (l_ec a b) (l_ec b c) (l_ec c a) e : l_ec c a).
+
+(* notion 162 *)
+definition l_ec3_th4 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_and3_th1 (l_ec a b) (l_ec b c) (l_ec c a) e : l_ec3 b c a).
+
+(* notion 163 *)
+definition l_ec3_th5 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_ec3_th4 b c a (l_ec3_th4 a b c e) : l_ec3 c a b).
+
+(* notion 164 *)
+definition l_ec3_th5a ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.(l_and3i (l_ec c b) (l_ec b a) (l_ec a c) (l_comec b c (l_ec3_th2 a b c e)) (l_comec a b (l_ec3_th1 a b c e)) (l_comec c a (l_ec3_th3 a b c e)) : l_ec3 c b a).
+
+(* notion 165 *)
+definition l_ec3e12 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λa1:a.(l_ece1 a b (l_ec3_th1 a b c e) a1 : l_not b).
+
+(* notion 166 *)
+definition l_ec3e13 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λa1:a.(l_ece2 c a (l_ec3_th3 a b c e) a1 : l_not c).
+
+(* notion 167 *)
+definition l_ec3e23 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λb1:b.(l_ec3e12 b c a (l_ec3_th4 a b c e) b1 : l_not c).
+
+(* notion 168 *)
+definition l_ec3e21 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λb1:b.(l_ec3e13 b c a (l_ec3_th4 a b c e) b1 : l_not a).
+
+(* notion 169 *)
+definition l_ec3e31 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λc1:c.(l_ec3e12 c a b (l_ec3_th5 a b c e) c1 : l_not a).
+
+(* notion 170 *)
+definition l_ec3e32 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λc1:c.(l_ec3e13 c a b (l_ec3_th5 a b c e) c1 : l_not b).
+
+(* notion 171 *)
+definition l_ec3_th6 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec a b.λf:l_ec b c.λg:l_ec c a.(l_and3i (l_ec a b) (l_ec b c) (l_ec c a) e f g : l_ec3 a b c).
+
+(* notion 172 *)
+definition l_ec3_th7 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λo:l_or a b.(l_orapp a b (l_not c) o (λx:a.l_ece2 c a (l_ec3_th3 a b c e) x) (λx:b.l_ece1 b c (l_ec3_th2 a b c e) x) : l_not c).
+
+(* notion 173 *)
+definition l_ec3_th8 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λo:l_or b c.(l_ec3_th7 b c a (l_ec3_th4 a b c e) o : l_not a).
+
+(* notion 174 *)
+definition l_ec3_th9 ≝ λa:Prop.λb:Prop.λc:Prop.λe:l_ec3 a b c.λo:l_or c a.(l_ec3_th7 c a b (l_ec3_th5 a b c e) o : l_not b).
+
+(* notion 175 *)
+definition l_ec3i1 ≝ λa:Prop.λb:Prop.λc:Prop.λn:l_not a.λm:l_not b.(l_ec3_th6 a b c (l_eci1 a b n) (l_eci1 b c m) (l_eci2 c a n) : l_ec3 a b c).
+
+(* notion 176 *)
+definition l_ec3i2 ≝ λa:Prop.λb:Prop.λc:Prop.λn:l_not b.λm:l_not c.(l_ec3_th6 a b c (l_eci2 a b n) (l_eci1 b c n) (l_eci1 c a m) : l_ec3 a b c).
+
+(* notion 177 *)
+definition l_ec3i3 ≝ λa:Prop.λb:Prop.λc:Prop.λn:l_not c.λm:l_not a.(l_ec3_th6 a b c (l_eci1 a b m) (l_eci2 b c n) (l_eci1 c a n) : l_ec3 a b c).
+
+(* notion 178 *)
+definition l_ec3_t1 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λe:Prop.λf:Prop.λo1:l_or3 a b c.λp1:l_ec3 d e f.λi:l_imp a d.λj:l_imp b e.λk:l_imp c f.λd1:d.(λx:b.l_mp e l_con (j x) (l_ec3e12 d e f p1 d1) : l_not b).
+
+(* notion 179 *)
+definition l_ec3_t2 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λe:Prop.λf:Prop.λo1:l_or3 a b c.λp1:l_ec3 d e f.λi:l_imp a d.λj:l_imp b e.λk:l_imp c f.λd1:d.(λx:c.l_mp f l_con (k x) (l_ec3e13 d e f p1 d1) : l_not c).
+
+(* notion 180 *)
+definition l_ec3_th10 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λe:Prop.λf:Prop.λo1:l_or3 a b c.λp1:l_ec3 d e f.λi:l_imp a d.λj:l_imp b e.λk:l_imp c f.λd1:d.(l_or3e1 a b c o1 (l_ec3_t1 a b c d e f o1 p1 i j k d1) (l_ec3_t2 a b c d e f o1 p1 i j k d1) : a).
+
+(* notion 181 *)
+definition l_ec3_th11 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λe:Prop.λf:Prop.λo1:l_or3 a b c.λp1:l_ec3 d e f.λi:l_imp a d.λj:l_imp b e.λk:l_imp c f.λe1:e.(l_ec3_th10 b c a e f d (l_or3_th4 a b c o1) (l_ec3_th4 d e f p1) j k i e1 : b).
+
+(* notion 182 *)
+definition l_ec3_th12 ≝ λa:Prop.λb:Prop.λc:Prop.λd:Prop.λe:Prop.λf:Prop.λo1:l_or3 a b c.λp1:l_ec3 d e f.λi:l_imp a d.λj:l_imp b e.λk:l_imp c f.λf1:f.(l_ec3_th10 c a b f d e (l_or3_th5 a b c o1) (l_ec3_th5 d e f p1) k i j f1 : c).
+
+(* notion 183 *)
+definition l_orec3 ≝ λa:Prop.λb:Prop.λc:Prop.(l_and (l_or3 a b c) (l_ec3 a b c) : Prop).
+
+(* notion 184 *)
+definition l_orec3e1 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_orec3 a b c.(l_ande1 (l_or3 a b c) (l_ec3 a b c) o : l_or3 a b c).
+
+(* notion 185 *)
+definition l_orec3e2 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_orec3 a b c.(l_ande2 (l_or3 a b c) (l_ec3 a b c) o : l_ec3 a b c).
+
+(* notion 186 *)
+definition l_orec3i ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_or3 a b c.λe:l_ec3 a b c.(l_andi (l_or3 a b c) (l_ec3 a b c) o e : l_orec3 a b c).
+
+(* notion 187 *)
+definition l_orec3_th1 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_orec3 a b c.(l_orec3i b c a (l_or3_th4 a b c (l_orec3e1 a b c o)) (l_ec3_th4 a b c (l_orec3e2 a b c o)) : l_orec3 b c a).
+
+(* notion 188 *)
+definition l_orec3_th2 ≝ λa:Prop.λb:Prop.λc:Prop.λo:l_orec3 a b c.(l_orec3i c a b (l_or3_th5 a b c (l_orec3e1 a b c o)) (l_ec3_th5 a b c (l_orec3e2 a b c o)) : l_orec3 c a b).
+
+(* notion 189 *)
+axiom l_e_is : Πsigma:Type[0].Πs:sigma.Πt:sigma.Prop.
+
+(* notion 190 *)
+axiom l_e_refis : Πsigma:Type[0].Πs:sigma.l_e_is sigma s s.
+
+(* notion 191 *)
+axiom l_e_isp : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πs:sigma.Πt:sigma.Πsp:p s.Πi:l_e_is sigma s t.p t.
+
+(* notion 192 *)
+definition l_e_symis ≝ λsigma:Type[0].λs:sigma.λt:sigma.λi:l_e_is sigma s t.(l_e_isp sigma (λx:sigma.l_e_is sigma x s) s t (l_e_refis sigma s) i : l_e_is sigma t s).
+
+(* notion 193 *)
+definition l_e_tris ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λi:l_e_is sigma s t.λj:l_e_is sigma t u.(l_e_isp sigma (λx:sigma.l_e_is sigma x u) t s j (l_e_symis sigma s t i) : l_e_is sigma s u).
+
+(* notion 194 *)
+definition l_e_tris1 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λi:l_e_is sigma u s.λj:l_e_is sigma u t.(l_e_tris sigma s u t (l_e_symis sigma u s i) j : l_e_is sigma s t).
+
+(* notion 195 *)
+definition l_e_tris2 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λi:l_e_is sigma s u.λj:l_e_is sigma t u.(l_e_tris sigma s u t i (l_e_symis sigma t u j) : l_e_is sigma s t).
+
+(* notion 196 *)
+definition l_e_isp1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λt:sigma.λsp:p s.λi:l_e_is sigma t s.(l_e_isp sigma p s t sp (l_e_symis sigma t s i) : p t).
+
+(* notion 197 *)
+definition l_e_symnotis ≝ λsigma:Type[0].λs:sigma.λt:sigma.λn:l_not (l_e_is sigma s t).(l_imp_th3 (l_e_is sigma t s) (l_e_is sigma s t) n (λx:l_e_is sigma t s.l_e_symis sigma t s x) : l_not (l_e_is sigma t s)).
+
+(* notion 198 *)
+definition l_e_notis_th1 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λn:l_not (l_e_is sigma s t).λi:l_e_is sigma s u.(l_e_isp sigma (λx:sigma.l_not (l_e_is sigma x t)) s u n i : l_not (l_e_is sigma u t)).
+
+(* notion 199 *)
+definition l_e_notis_th2 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λn:l_not (l_e_is sigma s t).λi:l_e_is sigma u s.(l_e_notis_th1 sigma s t u n (l_e_symis sigma u s i) : l_not (l_e_is sigma u t)).
+
+(* notion 200 *)
+definition l_e_notis_th3 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λn:l_not (l_e_is sigma s t).λi:l_e_is sigma t u.(l_e_isp sigma (λx:sigma.l_not (l_e_is sigma s x)) t u n i : l_not (l_e_is sigma s u)).
+
+(* notion 201 *)
+definition l_e_notis_th4 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λn:l_not (l_e_is sigma s t).λi:l_e_is sigma u t.(l_e_notis_th3 sigma s t u n (l_e_symis sigma u t i) : l_not (l_e_is sigma s u)).
+
+(* notion 202 *)
+definition l_e_notis_th5 ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λv:sigma.λn:l_not (l_e_is sigma s t).λi:l_e_is sigma s u.λj:l_e_is sigma t v.(l_e_notis_th3 sigma u t v (l_e_notis_th1 sigma s t u n i) j : l_not (l_e_is sigma u v)).
+
+(* notion 203 *)
+definition l_e_tr3is ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λv:sigma.λi:l_e_is sigma s t.λj:l_e_is sigma t u.λk:l_e_is sigma u v.(l_e_tris sigma s u v (l_e_tris sigma s t u i j) k : l_e_is sigma s v).
+
+(* notion 204 *)
+definition l_e_tr4is ≝ λsigma:Type[0].λs:sigma.λt:sigma.λu:sigma.λv:sigma.λw:sigma.λi:l_e_is sigma s t.λj:l_e_is sigma t u.λk:l_e_is sigma u v.λl:l_e_is sigma v w.(l_e_tris sigma s v w (l_e_tr3is sigma s t u v i j k) l : l_e_is sigma s w).
+
+(* notion 205 *)
+definition l_e_amone ≝ λsigma:Type[0].λp:Πx:sigma.Prop.(Πx:sigma.Πy:sigma.Πu:p x.Πv:p y.l_e_is sigma x y : Prop).
+
+(* notion 206 *)
+definition l_e_amonee ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λa1:l_e_amone sigma p.λs:sigma.λt:sigma.λsp:p s.λtp:p t.(a1 s t sp tp : l_e_is sigma s t).
+
+(* notion 207 *)
+definition l_e_one ≝ λsigma:Type[0].λp:Πx:sigma.Prop.(l_and (l_e_amone sigma p) (l_some sigma p) : Prop).
+
+(* notion 208 *)
+definition l_e_onei ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λa1:l_e_amone sigma p.λs:l_some sigma p.(l_andi (l_e_amone sigma p) (l_some sigma p) a1 s : l_e_one sigma p).
+
+(* notion 209 *)
+definition l_e_onee1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_one sigma p.(l_ande1 (l_e_amone sigma p) (l_some sigma p) o1 : l_e_amone sigma p).
+
+(* notion 210 *)
+definition l_e_onee2 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_one sigma p.(l_ande2 (l_e_amone sigma p) (l_some sigma p) o1 : l_some sigma p).
+
+(* notion 211 *)
+axiom l_e_ind : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πo1:l_e_one sigma p.sigma.
+
+(* notion 212 *)
+axiom l_e_oneax : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πo1:l_e_one sigma p.p (l_e_ind sigma p o1).
+
+(* notion 213 *)
+definition l_e_one_th1 ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_one sigma p.λs:sigma.λsp:p s.(l_e_amonee sigma p (l_e_onee1 sigma p o1) (l_e_ind sigma p o1) s (l_e_oneax sigma p o1) sp : l_e_is sigma (l_e_ind sigma p o1) s).
+
+(* notion 214 *)
+definition l_e_isf ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs:sigma.λt:sigma.λi:l_e_is sigma s t.(l_e_isp sigma (λx:sigma.l_e_is tau (f s) (f x)) s t (l_e_refis tau (f s)) i : l_e_is tau (f s) (f t)).
+
+(* notion 215 *)
+definition l_e_injective ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.(l_all sigma (λx:sigma.l_all sigma (λy:sigma.l_imp (l_e_is tau (f x) (f y)) (l_e_is sigma x y))) : Prop).
+
+(* notion 216 *)
+definition l_e_isfe ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λs:sigma.λt:sigma.λj:l_e_is tau (f s) (f t).(i s t j : l_e_is sigma s t).
+
+(* notion 217 *)
+definition l_e_image ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λt0:tau.(l_some sigma (λx:sigma.l_e_is tau t0 (f x)) : Prop).
+
+(* notion 218 *)
+definition l_e_tofs ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs:sigma.(f s : tau).
+
+(* notion 219 *)
+definition l_e_imagei ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs:sigma.(l_somei sigma (λx:sigma.l_e_is tau (l_e_tofs sigma tau f s) (f x)) s (l_e_refis tau (l_e_tofs sigma tau f s)) : l_e_image sigma tau f (l_e_tofs sigma tau f s)).
+
+(* notion 220 *)
+definition l_e_inj_t1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λta:tau.λtb:tau.λj:l_e_is tau ta tb.λsa:sigma.λsb:sigma.λja:l_e_is tau ta (l_e_tofs sigma tau f sa).λjb:l_e_is tau tb (l_e_tofs sigma tau f sb).(l_e_tr3is tau (l_e_tofs sigma tau f sa) ta tb (l_e_tofs sigma tau f sb) (l_e_symis tau ta (l_e_tofs sigma tau f sa) ja) j jb : l_e_is tau (l_e_tofs sigma tau f sa) (l_e_tofs sigma tau f sb)).
+
+(* notion 221 *)
+definition l_e_inj_th1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λta:tau.λtb:tau.λj:l_e_is tau ta tb.λsa:sigma.λsb:sigma.λja:l_e_is tau ta (l_e_tofs sigma tau f sa).λjb:l_e_is tau tb (l_e_tofs sigma tau f sb).(l_e_isfe sigma tau f i sa sb (l_e_inj_t1 sigma tau f i ta tb j sa sb ja jb) : l_e_is sigma sa sb).
+
+(* notion 222 *)
+definition l_e_inj_th2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λt0:tau.(λx:sigma.λy:sigma.λu:l_e_is tau t0 (f x).λv:l_e_is tau t0 (f y).l_e_inj_th1 sigma tau f i t0 t0 (l_e_refis tau t0) x y u v : l_e_amone sigma (λx:sigma.l_e_is tau t0 (f x))).
+
+(* notion 223 *)
+definition l_e_inj_th3 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λt0:tau.λj:l_e_image sigma tau f t0.(l_e_onei sigma (λx:sigma.l_e_is tau t0 (f x)) (l_e_inj_th2 sigma tau f i t0) j : l_e_one sigma (λx:sigma.l_e_is tau t0 (f x))).
+
+(* notion 224 *)
+definition l_e_soft ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λt0:tau.λj:l_e_image sigma tau f t0.(l_e_ind sigma (λx:sigma.l_e_is tau t0 (f x)) (l_e_inj_th3 sigma tau f i t0 j) : sigma).
+
+(* notion 225 *)
+definition l_e_inverse ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.(λx:tau.λu:l_e_image sigma tau f x.l_e_soft sigma tau f i x u : Πx:tau.Πu:l_e_image sigma tau f x.sigma).
+
+(* notion 226 *)
+definition l_e_ists1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λt0:tau.λj:l_e_image sigma tau f t0.(l_e_oneax sigma (λx:sigma.l_e_is tau t0 (f x)) (l_e_inj_th3 sigma tau f i t0 j) : l_e_is tau t0 (l_e_tofs sigma tau f (l_e_soft sigma tau f i t0 j))).
+
+(* notion 227 *)
+definition l_e_ists2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λt0:tau.λj:l_e_image sigma tau f t0.(l_e_symis tau t0 (l_e_tofs sigma tau f (l_e_soft sigma tau f i t0 j)) (l_e_ists1 sigma tau f i t0 j) : l_e_is tau (l_e_tofs sigma tau f (l_e_soft sigma tau f i t0 j)) t0).
+
+(* notion 228 *)
+definition l_e_isinv ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λta:tau.λja:l_e_image sigma tau f ta.λtb:tau.λjb:l_e_image sigma tau f tb.λj:l_e_is tau ta tb.(l_e_inj_th1 sigma tau f i ta tb j (l_e_soft sigma tau f i ta ja) (l_e_soft sigma tau f i tb jb) (l_e_ists1 sigma tau f i ta ja) (l_e_ists1 sigma tau f i tb jb) : l_e_is sigma (l_e_soft sigma tau f i ta ja) (l_e_soft sigma tau f i tb jb)).
+
+(* notion 229 *)
+definition l_e_isinve ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λta:tau.λja:l_e_image sigma tau f ta.λtb:tau.λjb:l_e_image sigma tau f tb.λj:l_e_is sigma (l_e_soft sigma tau f i ta ja) (l_e_soft sigma tau f i tb jb).(l_e_tr3is tau ta (l_e_tofs sigma tau f (l_e_soft sigma tau f i ta ja)) (l_e_tofs sigma tau f (l_e_soft sigma tau f i tb jb)) tb (l_e_ists1 sigma tau f i ta ja) (l_e_isf sigma tau f (l_e_soft sigma tau f i ta ja) (l_e_soft sigma tau f i tb jb) j) (l_e_ists2 sigma tau f i tb jb) : l_e_is tau ta tb).
+
+(* notion 230 *)
+definition l_e_isst1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λs:sigma.(l_e_isfe sigma tau f i s (l_e_soft sigma tau f i (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s)) (l_e_ists1 sigma tau f i (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s)) : l_e_is sigma s (l_e_soft sigma tau f i (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s))).
+
+(* notion 231 *)
+definition l_e_isst2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λi:l_e_injective sigma tau f.λs:sigma.(l_e_symis sigma s (l_e_soft sigma tau f i (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s)) (l_e_isst1 sigma tau f i s) : l_e_is sigma (l_e_soft sigma tau f i (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s)) s).
+
+(* notion 232 *)
+definition l_e_surjective ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.(l_all tau (λx:tau.l_e_image sigma tau f x) : Prop).
+
+(* notion 233 *)
+definition l_e_bijective ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.(l_and (l_e_injective sigma tau f) (l_e_surjective sigma tau f) : Prop).
+
+(* notion 234 *)
+definition l_e_inj_t2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.(l_ande1 (l_e_injective sigma tau f) (l_e_surjective sigma tau f) b : l_e_injective sigma tau f).
+
+(* notion 235 *)
+definition l_e_inj_t3 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.(l_ande2 (l_e_injective sigma tau f) (l_e_surjective sigma tau f) b : l_e_surjective sigma tau f).
+
+(* notion 236 *)
+definition l_e_inj_so ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.λt:tau.(l_e_soft sigma tau f (l_e_inj_t2 sigma tau f b) t (l_e_inj_t3 sigma tau f b t) : sigma).
+
+(* notion 237 *)
+definition l_e_invf ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.(λx:tau.l_e_inj_so sigma tau f b x : Πx:tau.sigma).
+
+(* notion 238 *)
+definition l_e_thinvf1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.λs:sigma.(l_e_tris sigma s (l_e_soft sigma tau f (l_e_inj_t2 sigma tau f b) (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s)) (l_e_invf sigma tau f b (f s)) (l_e_isst1 sigma tau f (l_e_inj_t2 sigma tau f b) s) (l_e_isinv sigma tau f (l_e_inj_t2 sigma tau f b) (l_e_tofs sigma tau f s) (l_e_imagei sigma tau f s) (l_e_tofs sigma tau f s) (l_e_inj_t3 sigma tau f b (l_e_tofs sigma tau f s)) (l_e_refis tau (l_e_tofs sigma tau f s))) : l_e_is sigma s (l_e_invf sigma tau f b (f s))).
+
+(* notion 239 *)
+definition l_e_thinvf2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λb:l_e_bijective sigma tau f.λt:tau.(l_e_ists1 sigma tau f (l_e_inj_t2 sigma tau f b) t (l_e_inj_t3 sigma tau f b t) : l_e_is tau t (f (l_e_invf sigma tau f b t))).
+
+(* notion 240 *)
+definition l_e_inj_h ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λif:l_e_injective sigma tau f.λig:l_e_injective tau upsilon g.(λx:sigma.g (f x) : Πx:sigma.upsilon).
+
+(* notion 241 *)
+definition l_e_inj_t4 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λif:l_e_injective sigma tau f.λig:l_e_injective tau upsilon g.λs:sigma.λt:sigma.λi:l_e_is upsilon (l_e_inj_h sigma tau upsilon f g if ig s) (l_e_inj_h sigma tau upsilon f g if ig t).(l_e_isfe tau upsilon g ig (f s) (f t) i : l_e_is tau (f s) (f t)).
+
+(* notion 242 *)
+definition l_e_inj_t5 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λif:l_e_injective sigma tau f.λig:l_e_injective tau upsilon g.λs:sigma.λt:sigma.λi:l_e_is upsilon (l_e_inj_h sigma tau upsilon f g if ig s) (l_e_inj_h sigma tau upsilon f g if ig t).(l_e_isfe sigma tau f if s t (l_e_inj_t4 sigma tau upsilon f g if ig s t i) : l_e_is sigma s t).
+
+(* notion 243 *)
+definition l_e_inj_th4 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λif:l_e_injective sigma tau f.λig:l_e_injective tau upsilon g.(λx:sigma.λy:sigma.λv:l_e_is upsilon (l_e_inj_h sigma tau upsilon f g if ig x) (l_e_inj_h sigma tau upsilon f g if ig y).l_e_inj_t5 sigma tau upsilon f g if ig x y v : l_e_injective sigma upsilon (λx:sigma.g (f x))).
+
+(* notion 244 *)
+definition l_e_surj_h ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.(λx:sigma.g (f x) : Πx:sigma.upsilon).
+
+(* notion 245 *)
+definition l_e_surj_t1 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.(sg u : l_e_image tau upsilon g u).
+
+(* notion 246 *)
+definition l_e_surj_t2 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.λt:tau.λi:l_e_is upsilon u (g t).(sf t : l_e_image sigma tau f t).
+
+(* notion 247 *)
+definition l_e_surj_t3 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.λt:tau.λi:l_e_is upsilon u (g t).λs:sigma.λj:l_e_is tau t (f s).(l_e_tris upsilon u (g t) (l_e_surj_h sigma tau upsilon f g sf sg s) i (l_e_isf tau upsilon g t (f s) j) : l_e_is upsilon u (l_e_surj_h sigma tau upsilon f g sf sg s)).
+
+(* notion 248 *)
+definition l_e_surj_t4 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.λt:tau.λi:l_e_is upsilon u (g t).λs:sigma.λj:l_e_is tau t (f s).(l_somei sigma (λx:sigma.l_e_is upsilon u (l_e_surj_h sigma tau upsilon f g sf sg x)) s (l_e_surj_t3 sigma tau upsilon f g sf sg u t i s j) : l_e_image sigma upsilon (l_e_surj_h sigma tau upsilon f g sf sg) u).
+
+(* notion 249 *)
+definition l_e_surj_t5 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.λt:tau.λi:l_e_is upsilon u (g t).(l_someapp sigma (λx:sigma.l_e_is tau t (f x)) (l_e_surj_t2 sigma tau upsilon f g sf sg u t i) (l_e_image sigma upsilon (l_e_surj_h sigma tau upsilon f g sf sg) u) (λx:sigma.λv:l_e_is tau t (f x).l_e_surj_t4 sigma tau upsilon f g sf sg u t i x v) : l_e_image sigma upsilon (l_e_surj_h sigma tau upsilon f g sf sg) u).
+
+(* notion 250 *)
+definition l_e_surj_t6 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.λu:upsilon.(l_someapp tau (λx:tau.l_e_is upsilon u (g x)) (l_e_surj_t1 sigma tau upsilon f g sf sg u) (l_e_image sigma upsilon (l_e_surj_h sigma tau upsilon f g sf sg) u) (λx:tau.λv:l_e_is upsilon u (g x).l_e_surj_t5 sigma tau upsilon f g sf sg u x v) : l_e_image sigma upsilon (l_e_surj_h sigma tau upsilon f g sf sg) u).
+
+(* notion 251 *)
+definition l_e_surj_th1 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λsf:l_e_surjective sigma tau f.λsg:l_e_surjective tau upsilon g.(λx:upsilon.l_e_surj_t6 sigma tau upsilon f g sf sg x : l_e_surjective sigma upsilon (λx:sigma.g (f x))).
+
+(* notion 252 *)
+definition l_e_bij_h ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λbf:l_e_bijective sigma tau f.λbg:l_e_bijective tau upsilon g.(λx:sigma.g (f x) : Πx:sigma.upsilon).
+
+(* notion 253 *)
+definition l_e_bij_t1 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λbf:l_e_bijective sigma tau f.λbg:l_e_bijective tau upsilon g.(l_e_inj_th4 sigma tau upsilon f g (l_ande1 (l_e_injective sigma tau f) (l_e_surjective sigma tau f) bf) (l_ande1 (l_e_injective tau upsilon g) (l_e_surjective tau upsilon g) bg) : l_e_injective sigma upsilon (l_e_bij_h sigma tau upsilon f g bf bg)).
+
+(* notion 254 *)
+definition l_e_bij_t2 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λbf:l_e_bijective sigma tau f.λbg:l_e_bijective tau upsilon g.(l_e_surj_th1 sigma tau upsilon f g (l_ande2 (l_e_injective sigma tau f) (l_e_surjective sigma tau f) bf) (l_ande2 (l_e_injective tau upsilon g) (l_e_surjective tau upsilon g) bg) : l_e_surjective sigma upsilon (l_e_bij_h sigma tau upsilon f g bf bg)).
+
+(* notion 255 *)
+definition l_e_bij_th1 ≝ λsigma:Type[0].λtau:Type[0].λupsilon:Type[0].λf:Πx:sigma.tau.λg:Πx:tau.upsilon.λbf:l_e_bijective sigma tau f.λbg:l_e_bijective tau upsilon g.(l_andi (l_e_injective sigma upsilon (l_e_bij_h sigma tau upsilon f g bf bg)) (l_e_surjective sigma upsilon (l_e_bij_h sigma tau upsilon f g bf bg)) (l_e_bij_t1 sigma tau upsilon f g bf bg) (l_e_bij_t2 sigma tau upsilon f g bf bg) : l_e_bijective sigma upsilon (λx:sigma.g (f x))).
+
+(* notion 256 *)
+definition l_e_fise ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λg:Πx:sigma.tau.λi:l_e_is (Πx:sigma.tau) f g.λs:sigma.(l_e_isp (Πx:sigma.tau) (λy:Πx:sigma.tau.l_e_is tau (f s) (y s)) f g (l_e_refis tau (f s)) i : l_e_is tau (f s) (g s)).
+
+(* notion 257 *)
+axiom l_e_fisi : Πsigma:Type[0].Πtau:Type[0].Πf:Πx:sigma.tau.Πg:Πx:sigma.tau.Πi:Πx:sigma.l_e_is tau (f x) (g x).l_e_is (Πx:sigma.tau) f g.
+
+(* notion 258 *)
+definition l_e_fis_th1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λg:Πx:sigma.tau.λi:l_e_is (Πx:sigma.tau) f g.λs:sigma.λt:sigma.λj:l_e_is sigma s t.(l_e_tris tau (f s) (f t) (g t) (l_e_isf sigma tau f s t j) (l_e_fise sigma tau f g i t) : l_e_is tau (f s) (g t)).
+
+(* notion 259 *)
+axiom l_e_ot : Πsigma:Type[0].Πp:Πx:sigma.Prop.Type[0].
+
+(* notion 260 *)
+axiom l_e_in : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πo1:l_e_ot sigma p.sigma.
+
+(* notion 261 *)
+axiom l_e_inp : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πo1:l_e_ot sigma p.p (l_e_in sigma p o1).
+
+(* notion 262 *)
+axiom l_e_otax1 : Πsigma:Type[0].Πp:Πx:sigma.Prop.l_e_injective (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x).
+
+(* notion 263 *)
+axiom l_e_otax2 : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πs:sigma.Πsp:p s.l_e_image (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) s.
+
+(* notion 264 *)
+definition l_e_isini ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_ot sigma p.λo2:l_e_ot sigma p.λi:l_e_is (l_e_ot sigma p) o1 o2.(l_e_isf (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) o1 o2 i : l_e_is sigma (l_e_in sigma p o1) (l_e_in sigma p o2)).
+
+(* notion 265 *)
+definition l_e_isine ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_ot sigma p.λo2:l_e_ot sigma p.λi:l_e_is sigma (l_e_in sigma p o1) (l_e_in sigma p o2).(l_e_isfe (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) o1 o2 i : l_e_is (l_e_ot sigma p) o1 o2).
+
+(* notion 266 *)
+definition l_e_out ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λsp:p s.(l_e_soft (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) s (l_e_otax2 sigma p s sp) : l_e_ot sigma p).
+
+(* notion 267 *)
+definition l_e_isouti ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λsp:p s.λt:sigma.λtp:p t.λi:l_e_is sigma s t.(l_e_isinv (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) s (l_e_otax2 sigma p s sp) t (l_e_otax2 sigma p t tp) i : l_e_is (l_e_ot sigma p) (l_e_out sigma p s sp) (l_e_out sigma p t tp)).
+
+(* notion 268 *)
+definition l_e_isoute ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λsp:p s.λt:sigma.λtp:p t.λi:l_e_is (l_e_ot sigma p) (l_e_out sigma p s sp) (l_e_out sigma p t tp).(l_e_isinve (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) s (l_e_otax2 sigma p s sp) t (l_e_otax2 sigma p t tp) i : l_e_is sigma s t).
+
+(* notion 269 *)
+definition l_e_isoutin ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λo1:l_e_ot sigma p.(l_e_tris (l_e_ot sigma p) o1 (l_e_soft (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) (l_e_in sigma p o1) (l_e_imagei (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) o1)) (l_e_out sigma p (l_e_in sigma p o1) (l_e_inp sigma p o1)) (l_e_isst1 (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) o1) (l_e_isinv (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) (l_e_in sigma p o1) (l_e_imagei (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) o1) (l_e_in sigma p o1) (l_e_otax2 sigma p (l_e_in sigma p o1) (l_e_inp sigma p o1)) (l_e_refis sigma (l_e_in sigma p o1))) : l_e_is (l_e_ot sigma p) o1 (l_e_out sigma p (l_e_in sigma p o1) (l_e_inp sigma p o1))).
+
+(* notion 270 *)
+definition l_e_isinout ≝ λsigma:Type[0].λp:Πx:sigma.Prop.λs:sigma.λsp:p s.(l_e_ists1 (l_e_ot sigma p) sigma (λx:l_e_ot sigma p.l_e_in sigma p x) (l_e_otax1 sigma p) s (l_e_otax2 sigma p s sp) : l_e_is sigma s (l_e_in sigma p (l_e_out sigma p s sp))).
+
+(* notion 271 *)
+axiom l_e_pairtype : Πsigma:Type[0].Πtau:Type[0].Type[0].
+
+(* notion 272 *)
+axiom l_e_pair : Πsigma:Type[0].Πtau:Type[0].Πs:sigma.Πt:tau.l_e_pairtype sigma tau.
+
+(* notion 273 *)
+axiom l_e_first : Πsigma:Type[0].Πtau:Type[0].Πp1:l_e_pairtype sigma tau.sigma.
+
+(* notion 274 *)
+axiom l_e_second : Πsigma:Type[0].Πtau:Type[0].Πp1:l_e_pairtype sigma tau.tau.
+
+(* notion 275 *)
+axiom l_e_pairis1 : Πsigma:Type[0].Πtau:Type[0].Πp1:l_e_pairtype sigma tau.l_e_is (l_e_pairtype sigma tau) (l_e_pair sigma tau (l_e_first sigma tau p1) (l_e_second sigma tau p1)) p1.
+
+(* notion 276 *)
+definition l_e_pairis2 ≝ λsigma:Type[0].λtau:Type[0].λp1:l_e_pairtype sigma tau.(l_e_symis (l_e_pairtype sigma tau) (l_e_pair sigma tau (l_e_first sigma tau p1) (l_e_second sigma tau p1)) p1 (l_e_pairis1 sigma tau p1) : l_e_is (l_e_pairtype sigma tau) p1 (l_e_pair sigma tau (l_e_first sigma tau p1) (l_e_second sigma tau p1))).
+
+(* notion 277 *)
+axiom l_e_firstis1 : Πsigma:Type[0].Πtau:Type[0].Πs:sigma.Πt:tau.l_e_is sigma (l_e_first sigma tau (l_e_pair sigma tau s t)) s.
+
+(* notion 278 *)
+definition l_e_firstis2 ≝ λsigma:Type[0].λtau:Type[0].λs:sigma.λt:tau.(l_e_symis sigma (l_e_first sigma tau (l_e_pair sigma tau s t)) s (l_e_firstis1 sigma tau s t) : l_e_is sigma s (l_e_first sigma tau (l_e_pair sigma tau s t))).
+
+(* notion 279 *)
+axiom l_e_secondis1 : Πsigma:Type[0].Πtau:Type[0].Πs:sigma.Πt:tau.l_e_is tau (l_e_second sigma tau (l_e_pair sigma tau s t)) t.
+
+(* notion 280 *)
+definition l_e_secondis2 ≝ λsigma:Type[0].λtau:Type[0].λs:sigma.λt:tau.(l_e_symis tau (l_e_second sigma tau (l_e_pair sigma tau s t)) t (l_e_secondis1 sigma tau s t) : l_e_is tau t (l_e_second sigma tau (l_e_pair sigma tau s t))).
+
+(* notion 281 *)
+definition l_e_ite_prop1 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λz:ksi.(l_and (l_imp a (l_e_is ksi z x)) (l_imp (l_not a) (l_e_is ksi z y)) : Prop).
+
+(* notion 282 *)
+definition l_e_ite_t1 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_ande1 (l_imp a (l_e_is ksi x1 x)) (l_imp (l_not a) (l_e_is ksi x1 y)) px1 : l_imp a (l_e_is ksi x1 x)).
+
+(* notion 283 *)
+definition l_e_ite_t2 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_mp a (l_e_is ksi x1 x) a1 (l_e_ite_t1 a ksi x y a1 x1 y1 px1 py1) : l_e_is ksi x1 x).
+
+(* notion 284 *)
+definition l_e_ite_t3 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_e_ite_t2 a ksi x y a1 y1 x1 py1 px1 : l_e_is ksi y1 x).
+
+(* notion 285 *)
+definition l_e_ite_t4 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_e_tris2 ksi x1 y1 x (l_e_ite_t2 a ksi x y a1 x1 y1 px1 py1) (l_e_ite_t3 a ksi x y a1 x1 y1 px1 py1) : l_e_is ksi x1 y1).
+
+(* notion 286 *)
+definition l_e_ite_t5 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(λs:ksi.λt:ksi.λps:l_e_ite_prop1 a ksi x y s.λpt:l_e_ite_prop1 a ksi x y t.l_e_ite_t4 a ksi x y a1 s t ps pt : l_e_amone ksi (λt:ksi.l_e_ite_prop1 a ksi x y t)).
+
+(* notion 287 *)
+definition l_e_ite_t6 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(λx1:a.l_e_refis ksi x : l_imp a (l_e_is ksi x x)).
+
+(* notion 288 *)
+definition l_e_ite_t7 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(l_imp_th2 (l_not a) (l_e_is ksi x y) (l_weli a a1) : l_imp (l_not a) (l_e_is ksi x y)).
+
+(* notion 289 *)
+definition l_e_ite_t8 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(l_andi (l_imp a (l_e_is ksi x x)) (l_imp (l_not a) (l_e_is ksi x y)) (l_e_ite_t6 a ksi x y a1) (l_e_ite_t7 a ksi x y a1) : l_e_ite_prop1 a ksi x y x).
+
+(* notion 290 *)
+definition l_e_ite_t9 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(l_somei ksi (λt:ksi.l_e_ite_prop1 a ksi x y t) x (l_e_ite_t8 a ksi x y a1) : l_some ksi (λt:ksi.l_e_ite_prop1 a ksi x y t)).
+
+(* notion 291 *)
+definition l_e_ite_t10 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(l_e_onei ksi (λt:ksi.l_e_ite_prop1 a ksi x y t) (l_e_ite_t5 a ksi x y a1) (l_e_ite_t9 a ksi x y a1) : l_e_one ksi (λt:ksi.l_e_ite_prop1 a ksi x y t)).
+
+(* notion 292 *)
+definition l_e_ite_t11 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_ande2 (l_imp a (l_e_is ksi x1 x)) (l_imp (l_not a) (l_e_is ksi x1 y)) px1 : l_imp (l_not a) (l_e_is ksi x1 y)).
+
+(* notion 293 *)
+definition l_e_ite_t12 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_mp (l_not a) (l_e_is ksi x1 y) n (l_e_ite_t11 a ksi x y n x1 y1 px1 py1) : l_e_is ksi x1 y).
+
+(* notion 294 *)
+definition l_e_ite_t13 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_e_ite_t12 a ksi x y n y1 x1 py1 px1 : l_e_is ksi y1 y).
+
+(* notion 295 *)
+definition l_e_ite_t14 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_e_ite_prop1 a ksi x y x1.λpy1:l_e_ite_prop1 a ksi x y y1.(l_e_tris2 ksi x1 y1 y (l_e_ite_t12 a ksi x y n x1 y1 px1 py1) (l_e_ite_t13 a ksi x y n x1 y1 px1 py1) : l_e_is ksi x1 y1).
+
+(* notion 296 *)
+definition l_e_ite_t15 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(λs:ksi.λt:ksi.λps:l_e_ite_prop1 a ksi x y s.λpt:l_e_ite_prop1 a ksi x y t.l_e_ite_t14 a ksi x y n s t ps pt : l_e_amone ksi (λt:ksi.l_e_ite_prop1 a ksi x y t)).
+
+(* notion 297 *)
+definition l_e_ite_t16 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(λx1:l_not a.l_e_refis ksi y : l_imp (l_not a) (l_e_is ksi y y)).
+
+(* notion 298 *)
+definition l_e_ite_t17 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(l_imp_th2 a (l_e_is ksi y x) n : l_imp a (l_e_is ksi y x)).
+
+(* notion 299 *)
+definition l_e_ite_t18 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(l_andi (l_imp a (l_e_is ksi y x)) (l_imp (l_not a) (l_e_is ksi y y)) (l_e_ite_t17 a ksi x y n) (l_e_ite_t16 a ksi x y n) : l_e_ite_prop1 a ksi x y y).
+
+(* notion 300 *)
+definition l_e_ite_t19 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(l_somei ksi (λt:ksi.l_e_ite_prop1 a ksi x y t) y (l_e_ite_t18 a ksi x y n) : l_some ksi (λt:ksi.l_e_ite_prop1 a ksi x y t)).
+
+(* notion 301 *)
+definition l_e_ite_t20 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(l_e_onei ksi (λt:ksi.l_e_ite_prop1 a ksi x y t) (l_e_ite_t15 a ksi x y n) (l_e_ite_t19 a ksi x y n) : l_e_one ksi (λt:ksi.l_e_ite_prop1 a ksi x y t)).
+
+(* notion 302 *)
+definition l_e_ite_t21 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.(l_imp_th1 a (l_e_one ksi (λt:ksi.l_e_ite_prop1 a ksi x y t)) (λt:a.l_e_ite_t10 a ksi x y t) (λt:l_not a.l_e_ite_t20 a ksi x y t) : l_e_one ksi (λt:ksi.l_e_ite_prop1 a ksi x y t)).
+
+(* notion 303 *)
+definition l_e_ite ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.(l_e_ind ksi (λt:ksi.l_e_ite_prop1 a ksi x y t) (l_e_ite_t21 a ksi x y) : ksi).
+
+(* notion 304 *)
+definition l_e_ite_t22 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.(l_e_oneax ksi (λt:ksi.l_e_ite_prop1 a ksi x y t) (l_e_ite_t21 a ksi x y) : l_e_ite_prop1 a ksi x y (l_e_ite a ksi x y)).
+
+(* notion 305 *)
+definition l_e_ite_t23 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.(l_ande1 (l_imp a (l_e_is ksi (l_e_ite a ksi x y) x)) (l_imp (l_not a) (l_e_is ksi (l_e_ite a ksi x y) y)) (l_e_ite_t22 a ksi x y) : l_imp a (l_e_is ksi (l_e_ite a ksi x y) x)).
+
+(* notion 306 *)
+definition l_e_ite_t24 ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.(l_ande2 (l_imp a (l_e_is ksi (l_e_ite a ksi x y) x)) (l_imp (l_not a) (l_e_is ksi (l_e_ite a ksi x y) y)) (l_e_ite_t22 a ksi x y) : l_imp (l_not a) (l_e_is ksi (l_e_ite a ksi x y) y)).
+
+(* notion 307 *)
+definition l_e_itet ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λa1:a.(l_mp a (l_e_is ksi (l_e_ite a ksi x y) x) a1 (l_e_ite_t23 a ksi x y) : l_e_is ksi (l_e_ite a ksi x y) x).
+
+(* notion 308 *)
+definition l_e_itef ≝ λa:Prop.λksi:Type[0].λx:ksi.λy:ksi.λn:l_not a.(l_mp (l_not a) (l_e_is ksi (l_e_ite a ksi x y) y) n (l_e_ite_t24 a ksi x y) : l_e_is ksi (l_e_ite a ksi x y) y).
+
+(* notion 309 *)
+definition l_e_wissel_wa ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.(l_e_ite (l_e_is sigma s s0) sigma t0 s : sigma).
+
+(* notion 310 *)
+definition l_e_wissel_t1 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_e_itet (l_e_is sigma s s0) sigma t0 s i : l_e_is sigma (l_e_wissel_wa sigma s0 t0 s) t0).
+
+(* notion 311 *)
+definition l_e_wissel_t2 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).(l_e_itef (l_e_is sigma s s0) sigma t0 s n : l_e_is sigma (l_e_wissel_wa sigma s0 t0 s) s).
+
+(* notion 312 *)
+definition l_e_wissel_wb ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.(l_e_ite (l_e_is sigma s t0) sigma s0 (l_e_wissel_wa sigma s0 t0 s) : sigma).
+
+(* notion 313 *)
+definition l_e_wissel_t3 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s t0.(l_e_itet (l_e_is sigma s t0) sigma s0 (l_e_wissel_wa sigma s0 t0 s) i : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) s0).
+
+(* notion 314 *)
+definition l_e_wissel_t4 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s t0).(l_e_itef (l_e_is sigma s t0) sigma s0 (l_e_wissel_wa sigma s0 t0 s) n : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wa sigma s0 t0 s)).
+
+(* notion 315 *)
+definition l_e_wissel_t5 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.λj:l_e_is sigma s0 t0.(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) s0 t0 (l_e_wissel_t3 sigma s0 t0 s (l_e_tris sigma s s0 t0 i j)) j : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t0).
+
+(* notion 316 *)
+definition l_e_wissel_t6 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.λn:l_not (l_e_is sigma s0 t0).(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wa sigma s0 t0 s) t0 (l_e_wissel_t4 sigma s0 t0 s (l_e_notis_th2 sigma s0 t0 s n i)) (l_e_wissel_t1 sigma s0 t0 s i) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t0).
+
+(* notion 317 *)
+definition l_e_wissel_t7 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_imp_th1 (l_e_is sigma s0 t0) (l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t0) (λt:l_e_is sigma s0 t0.l_e_wissel_t5 sigma s0 t0 s i t) (λt:l_not (l_e_is sigma s0 t0).l_e_wissel_t6 sigma s0 t0 s i t) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t0).
+
+(* notion 318 *)
+definition l_e_wissel_t8 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).λo:l_not (l_e_is sigma s t0).(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wa sigma s0 t0 s) s (l_e_wissel_t4 sigma s0 t0 s o) (l_e_wissel_t2 sigma s0 t0 s n) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) s).
+
+(* notion 319 *)
+definition l_e_wissel ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.(λx:sigma.l_e_wissel_wb sigma s0 t0 x : Πx:sigma.sigma).
+
+(* notion 320 *)
+definition l_e_iswissel1 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_e_wissel_t7 sigma s0 t0 s i : l_e_is sigma (l_e_wissel sigma s0 t0 s) t0).
+
+(* notion 321 *)
+definition l_e_iswissel2 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s t0.(l_e_wissel_t3 sigma s0 t0 s i : l_e_is sigma (l_e_wissel sigma s0 t0 s) s0).
+
+(* notion 322 *)
+definition l_e_iswissel3 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).λo:l_not (l_e_is sigma s t0).(l_e_wissel_t8 sigma s0 t0 s n o : l_e_is sigma (l_e_wissel sigma s0 t0 s) s).
+
+(* notion 323 *)
+definition l_e_wissel_t9 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.(l_e_symnotis sigma s0 t (l_e_notis_th1 sigma s t s0 n j) : l_not (l_e_is sigma t s0)).
+
+(* notion 324 *)
+definition l_e_wissel_t10 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.λk:l_e_is sigma s0 t0.(l_e_notis_th3 sigma t s0 t0 (l_e_wissel_t9 sigma s0 t0 s t i n j) k : l_not (l_e_is sigma t t0)).
+
+(* notion 325 *)
+definition l_e_wissel_t11 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.λk:l_e_is sigma s0 t0.(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) t i (l_e_wissel_t8 sigma s0 t0 t (l_e_wissel_t9 sigma s0 t0 s t i n j) (l_e_wissel_t10 sigma s0 t0 s t i n j k)) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t).
+
+(* notion 326 *)
+definition l_e_wissel_t12 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.λk:l_e_is sigma s0 t0.(l_e_wissel_t10 sigma s0 t0 s t i n j k (l_e_tris1 sigma t t0 (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_t11 sigma s0 t0 s t i n j k) (l_e_wissel_t7 sigma s0 t0 s j)) : l_con).
+
+(* notion 327 *)
+definition l_e_wissel_t13 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.(λv:l_e_is sigma s0 t0.l_e_wissel_t12 sigma s0 t0 s t i n j v : l_not (l_e_is sigma s0 t0)).
+
+(* notion 328 *)
+definition l_e_wissel_t14 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.λk:l_e_is sigma t t0.(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) s0 i (l_e_wissel_t3 sigma s0 t0 t k) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) s0).
+
+(* notion 329 *)
+definition l_e_wissel_t15 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.λk:l_e_is sigma t t0.(l_e_wissel_t12 sigma s0 t0 s t i n j (l_e_tris1 sigma s0 t0 (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_t14 sigma s0 t0 s t i n j k) (l_e_wissel_t7 sigma s0 t0 s j)) : l_con).
+
+(* notion 330 *)
+definition l_e_wissel_t16 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.(λv:l_e_is sigma t t0.l_e_wissel_t15 sigma s0 t0 s t i n j v : l_not (l_e_is sigma t t0)).
+
+(* notion 331 *)
+definition l_e_wissel_t17 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) t i (l_e_wissel_t8 sigma s0 t0 t (l_e_wissel_t9 sigma s0 t0 s t i n j) (l_e_wissel_t16 sigma s0 t0 s t i n j)) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t).
+
+(* notion 332 *)
+definition l_e_wissel_t18 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s s0.(l_e_wissel_t15 sigma s0 t0 s t i n j (l_e_tris1 sigma t t0 (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_t17 sigma s0 t0 s t i n j) (l_e_wissel_t7 sigma s0 t0 s j)) : l_con).
+
+(* notion 333 *)
+definition l_e_wissel_t19 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(λv:l_e_is sigma s s0.l_e_wissel_t18 sigma s0 t0 s t i n v : l_not (l_e_is sigma s s0)).
+
+(* notion 334 *)
+definition l_e_wissel_t20 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(l_e_wissel_t19 sigma s0 t0 t s (l_e_symis sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) i) (l_e_symnotis sigma s t n) : l_not (l_e_is sigma t s0)).
+
+(* notion 335 *)
+definition l_e_wissel_t21 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s t0.(l_e_symnotis sigma t0 t (l_e_notis_th1 sigma s t t0 n j) : l_not (l_e_is sigma t t0)).
+
+(* notion 336 *)
+definition l_e_wissel_t22 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s t0.(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) t i (l_e_wissel_t8 sigma s0 t0 t (l_e_wissel_t20 sigma s0 t0 s t i n) (l_e_wissel_t21 sigma s0 t0 s t i n j)) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t).
+
+(* notion 337 *)
+definition l_e_wissel_t23 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).λj:l_e_is sigma s t0.(l_e_wissel_t20 sigma s0 t0 s t i n (l_e_tris1 sigma t s0 (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_t22 sigma s0 t0 s t i n j) (l_e_wissel_t3 sigma s0 t0 s j)) : l_con).
+
+(* notion 338 *)
+definition l_e_wissel_t24 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(λv:l_e_is sigma s t0.l_e_wissel_t23 sigma s0 t0 s t i n v : l_not (l_e_is sigma s t0)).
+
+(* notion 339 *)
+definition l_e_wissel_t25 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(l_e_wissel_t24 sigma s0 t0 t s (l_e_symis sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) i) (l_e_symnotis sigma s t n) : l_not (l_e_is sigma t t0)).
+
+(* notion 340 *)
+definition l_e_wissel_t26 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(l_e_tris sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t) t i (l_e_wissel_t8 sigma s0 t0 t (l_e_wissel_t20 sigma s0 t0 s t i n) (l_e_wissel_t25 sigma s0 t0 s t i n)) : l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) t).
+
+(* notion 341 *)
+definition l_e_wissel_t27 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).λn:l_not (l_e_is sigma s t).(n (l_e_tris1 sigma s t (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_t8 sigma s0 t0 s (l_e_wissel_t19 sigma s0 t0 s t i n) (l_e_wissel_t24 sigma s0 t0 s t i n)) (l_e_wissel_t26 sigma s0 t0 s t i n)) : l_con).
+
+(* notion 342 *)
+definition l_e_wissel_t28 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λt:sigma.λi:l_e_is sigma (l_e_wissel_wb sigma s0 t0 s) (l_e_wissel_wb sigma s0 t0 t).(l_et (l_e_is sigma s t) (λv:l_not (l_e_is sigma s t).l_e_wissel_t27 sigma s0 t0 s t i v) : l_e_is sigma s t).
+
+(* notion 343 *)
+definition l_e_wissel_th1 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.(λx:sigma.λy:sigma.λv:l_e_is sigma (l_e_wissel_wb sigma s0 t0 x) (l_e_wissel_wb sigma s0 t0 y).l_e_wissel_t28 sigma s0 t0 x y v : l_e_injective sigma sigma (l_e_wissel sigma s0 t0)).
+
+(* notion 344 *)
+definition l_e_wissel_t29 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_e_tris2 sigma s (l_e_wissel_wb sigma s0 t0 t0) s0 i (l_e_wissel_t3 sigma s0 t0 t0 (l_e_refis sigma t0)) : l_e_is sigma s (l_e_wissel_wb sigma s0 t0 t0)).
+
+(* notion 345 *)
+definition l_e_wissel_t30 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_somei sigma (λx:sigma.l_e_is sigma s (l_e_wissel_wb sigma s0 t0 x)) t0 (l_e_wissel_t29 sigma s0 t0 s i) : l_e_image sigma sigma (l_e_wissel sigma s0 t0) s).
+
+(* notion 346 *)
+definition l_e_wissel_t31 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s t0.(l_e_tris2 sigma s (l_e_wissel_wb sigma s0 t0 s0) t0 i (l_e_wissel_t7 sigma s0 t0 s0 (l_e_refis sigma s0)) : l_e_is sigma s (l_e_wissel_wb sigma s0 t0 s0)).
+
+(* notion 347 *)
+definition l_e_wissel_t32 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s t0.(l_somei sigma (λx:sigma.l_e_is sigma s (l_e_wissel_wb sigma s0 t0 x)) s0 (l_e_wissel_t31 sigma s0 t0 s i) : l_e_image sigma sigma (l_e_wissel sigma s0 t0) s).
+
+(* notion 348 *)
+definition l_e_wissel_t33 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).λo:l_not (l_e_is sigma s t0).(l_e_symis sigma (l_e_wissel_wb sigma s0 t0 s) s (l_e_wissel_t8 sigma s0 t0 s n o) : l_e_is sigma s (l_e_wissel_wb sigma s0 t0 s)).
+
+(* notion 349 *)
+definition l_e_wissel_t34 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).λo:l_not (l_e_is sigma s t0).(l_somei sigma (λx:sigma.l_e_is sigma s (l_e_wissel_wb sigma s0 t0 x)) s (l_e_wissel_t33 sigma s0 t0 s n o) : l_e_image sigma sigma (l_e_wissel sigma s0 t0) s).
+
+(* notion 350 *)
+definition l_e_wissel_t35 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).(l_imp_th1 (l_e_is sigma s t0) (l_e_image sigma sigma (l_e_wissel sigma s0 t0) s) (λv:l_e_is sigma s t0.l_e_wissel_t32 sigma s0 t0 s v) (λv:l_not (l_e_is sigma s t0).l_e_wissel_t34 sigma s0 t0 s n v) : l_e_image sigma sigma (l_e_wissel sigma s0 t0) s).
+
+(* notion 351 *)
+definition l_e_wissel_t36 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.λs:sigma.(l_imp_th1 (l_e_is sigma s s0) (l_e_image sigma sigma (l_e_wissel sigma s0 t0) s) (λv:l_e_is sigma s s0.l_e_wissel_t30 sigma s0 t0 s v) (λv:l_not (l_e_is sigma s s0).l_e_wissel_t35 sigma s0 t0 s v) : l_e_image sigma sigma (l_e_wissel sigma s0 t0) s).
+
+(* notion 352 *)
+definition l_e_wissel_th2 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.(λx:sigma.l_e_wissel_t36 sigma s0 t0 x : l_e_surjective sigma sigma (l_e_wissel sigma s0 t0)).
+
+(* notion 353 *)
+definition l_e_wissel_th3 ≝ λsigma:Type[0].λs0:sigma.λt0:sigma.(l_andi (l_e_injective sigma sigma (l_e_wissel sigma s0 t0)) (l_e_surjective sigma sigma (l_e_wissel sigma s0 t0)) (l_e_wissel_th1 sigma s0 t0) (l_e_wissel_th2 sigma s0 t0) : l_e_bijective sigma sigma (l_e_wissel sigma s0 t0)).
+
+(* notion 354 *)
+definition l_e_changef ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.(λx:sigma.f (l_e_wissel sigma s0 t0 x) : Πx:sigma.tau).
+
+(* notion 355 *)
+definition l_e_changef1 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s s0.(l_e_isf sigma tau f (l_e_wissel sigma s0 t0 s) t0 (l_e_iswissel1 sigma s0 t0 s i) : l_e_is tau (l_e_changef sigma tau f s0 t0 s) (f t0)).
+
+(* notion 356 *)
+definition l_e_changef2 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λs:sigma.λi:l_e_is sigma s t0.(l_e_isf sigma tau f (l_e_wissel sigma s0 t0 s) s0 (l_e_iswissel2 sigma s0 t0 s i) : l_e_is tau (l_e_changef sigma tau f s0 t0 s) (f s0)).
+
+(* notion 357 *)
+definition l_e_changef3 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λs:sigma.λn:l_not (l_e_is sigma s s0).λo:l_not (l_e_is sigma s t0).(l_e_isf sigma tau f (l_e_wissel sigma s0 t0 s) s (l_e_iswissel3 sigma s0 t0 s n o) : l_e_is tau (l_e_changef sigma tau f s0 t0 s) (f s)).
+
+(* notion 358 *)
+definition l_e_wissel_th4 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λi:l_e_injective sigma tau f.(l_e_inj_th4 sigma sigma tau (l_e_wissel sigma s0 t0) f (l_e_wissel_th1 sigma s0 t0) i : l_e_injective sigma tau (l_e_changef sigma tau f s0 t0)).
+
+(* notion 359 *)
+definition l_e_wissel_th5 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λs:l_e_surjective sigma tau f.(l_e_surj_th1 sigma sigma tau (l_e_wissel sigma s0 t0) f (l_e_wissel_th2 sigma s0 t0) s : l_e_surjective sigma tau (l_e_changef sigma tau f s0 t0)).
+
+(* notion 360 *)
+definition l_e_wissel_th6 ≝ λsigma:Type[0].λtau:Type[0].λf:Πx:sigma.tau.λs0:sigma.λt0:sigma.λb:l_e_bijective sigma tau f.(l_e_bij_th1 sigma sigma tau (l_e_wissel sigma s0 t0) f (l_e_wissel_th3 sigma s0 t0) b : l_e_bijective sigma tau (l_e_changef sigma tau f s0 t0)).
+
+(* notion 361 *)
+definition l_r_imp ≝ λa:Prop.λb:Πx:a.Prop.(Πx:a.b x : Prop).
+
+(* notion 362 *)
+definition l_r_mp ≝ λa:Prop.λb:Πx:a.Prop.λa1:a.λi:l_r_imp a b.(i a1 : b a1).
+
+(* notion 363 *)
+definition l_r_imp_th2 ≝ λa:Prop.λb:Πx:a.Prop.λn:l_not a.(λx:a.l_cone (b x) (l_mp a l_con x n) : l_r_imp a b).
+
+(* notion 364 *)
+definition l_r_ec ≝ λa:Prop.λb:Πx:a.Prop.(Πx:a.l_not (b x) : Prop).
+
+(* notion 365 *)
+definition l_r_eci1 ≝ λa:Prop.λb:Πx:a.Prop.λn:l_not a.(λx:a.l_cone (l_not (b x)) (l_mp a l_con x n) : l_r_ec a b).
+
+(* notion 366 *)
+definition l_r_ande2 ≝ λa:Prop.λb:Πx:a.Prop.λa1:l_and a b.(l_ande2 a b a1 (l_ande1 a b a1) : b (l_ande1 a b a1)).
+
+(* notion 367 *)
+definition l_r_ite_is ≝ λa:Prop.λksi:Type[0].λx1:ksi.λy1:ksi.(l_e_is ksi x1 y1 : Prop).
+
+(* notion 368 *)
+definition l_r_ite_prop1 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λz:ksi.(l_and (l_r_imp a (λt:a.l_r_ite_is a ksi z (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi z (y t))) : Prop).
+
+(* notion 369 *)
+definition l_r_ite_t1 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_ande1 (l_r_imp a (λt:a.l_r_ite_is a ksi x1 (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi x1 (y t))) px1 : l_r_imp a (λt:a.l_r_ite_is a ksi x1 (x t))).
+
+(* notion 370 *)
+definition l_r_ite_t2 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_r_mp a (λt:a.l_r_ite_is a ksi x1 (x t)) a1 (l_r_ite_t1 a ksi x y i j a1 x1 y1 px1 py1) : l_r_ite_is a ksi x1 (x a1)).
+
+(* notion 371 *)
+definition l_r_ite_t3 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_r_ite_t2 a ksi x y i j a1 y1 x1 py1 px1 : l_r_ite_is a ksi y1 (x a1)).
+
+(* notion 372 *)
+definition l_r_ite_t4 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_e_tris2 ksi x1 y1 (x a1) (l_r_ite_t2 a ksi x y i j a1 x1 y1 px1 py1) (l_r_ite_t3 a ksi x y i j a1 x1 y1 px1 py1) : l_r_ite_is a ksi x1 y1).
+
+(* notion 373 *)
+definition l_r_ite_t5 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(λs:ksi.λt:ksi.λps:l_r_ite_prop1 a ksi x y i j s.λpt:l_r_ite_prop1 a ksi x y i j t.l_r_ite_t4 a ksi x y i j a1 s t ps pt : l_e_amone ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t)).
+
+(* notion 374 *)
+definition l_r_ite_t6 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(i a1 : l_r_imp a (λt:a.l_r_ite_is a ksi (x a1) (x t))).
+
+(* notion 375 *)
+definition l_r_ite_t7 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(l_r_imp_th2 (l_not a) (λt:l_not a.l_r_ite_is a ksi (x a1) (y t)) (l_weli a a1) : l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (x a1) (y t))).
+
+(* notion 376 *)
+definition l_r_ite_t8 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(l_andi (l_r_imp a (λt:a.l_r_ite_is a ksi (x a1) (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (x a1) (y t))) (l_r_ite_t6 a ksi x y i j a1) (l_r_ite_t7 a ksi x y i j a1) : l_r_ite_prop1 a ksi x y i j (x a1)).
+
+(* notion 377 *)
+definition l_r_ite_t9 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(l_somei ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t) (x a1) (l_r_ite_t8 a ksi x y i j a1) : l_some ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t)).
+
+(* notion 378 *)
+definition l_r_ite_t10 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(l_e_onei ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t) (l_r_ite_t5 a ksi x y i j a1) (l_r_ite_t9 a ksi x y i j a1) : l_e_one ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t)).
+
+(* notion 379 *)
+definition l_r_ite_t11 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_ande2 (l_r_imp a (λt:a.l_r_ite_is a ksi x1 (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi x1 (y t))) px1 : l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi x1 (y t))).
+
+(* notion 380 *)
+definition l_r_ite_t12 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_r_mp (l_not a) (λt:l_not a.l_r_ite_is a ksi x1 (y t)) n (l_r_ite_t11 a ksi x y i j n x1 y1 px1 py1) : l_r_ite_is a ksi x1 (y n)).
+
+(* notion 381 *)
+definition l_r_ite_t13 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_r_ite_t12 a ksi x y i j n y1 x1 py1 px1 : l_r_ite_is a ksi y1 (y n)).
+
+(* notion 382 *)
+definition l_r_ite_t14 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.λx1:ksi.λy1:ksi.λpx1:l_r_ite_prop1 a ksi x y i j x1.λpy1:l_r_ite_prop1 a ksi x y i j y1.(l_e_tris2 ksi x1 y1 (y n) (l_r_ite_t12 a ksi x y i j n x1 y1 px1 py1) (l_r_ite_t13 a ksi x y i j n x1 y1 px1 py1) : l_r_ite_is a ksi x1 y1).
+
+(* notion 383 *)
+definition l_r_ite_t15 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(λs:ksi.λt:ksi.λps:l_r_ite_prop1 a ksi x y i j s.λpt:l_r_ite_prop1 a ksi x y i j t.l_r_ite_t14 a ksi x y i j n s t ps pt : l_e_amone ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t)).
+
+(* notion 384 *)
+definition l_r_ite_t16 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(j n : l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (y n) (y t))).
+
+(* notion 385 *)
+definition l_r_ite_t17 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(l_r_imp_th2 a (λt:a.l_r_ite_is a ksi (y n) (x t)) n : l_r_imp a (λt:a.l_r_ite_is a ksi (y n) (x t))).
+
+(* notion 386 *)
+definition l_r_ite_t18 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(l_andi (l_r_imp a (λt:a.l_r_ite_is a ksi (y n) (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (y n) (y t))) (l_r_ite_t17 a ksi x y i j n) (l_r_ite_t16 a ksi x y i j n) : l_r_ite_prop1 a ksi x y i j (y n)).
+
+(* notion 387 *)
+definition l_r_ite_t19 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(l_somei ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t) (y n) (l_r_ite_t18 a ksi x y i j n) : l_some ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t)).
+
+(* notion 388 *)
+definition l_r_ite_t20 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(l_e_onei ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t) (l_r_ite_t15 a ksi x y i j n) (l_r_ite_t19 a ksi x y i j n) : l_e_one ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t)).
+
+(* notion 389 *)
+definition l_r_ite_t21 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).(l_imp_th1 a (l_e_one ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t)) (λt:a.l_r_ite_t10 a ksi x y i j t) (λt:l_not a.l_r_ite_t20 a ksi x y i j t) : l_e_one ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t)).
+
+(* notion 390 *)
+definition l_r_ite ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).(l_e_ind ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t) (l_r_ite_t21 a ksi x y i j) : ksi).
+
+(* notion 391 *)
+definition l_r_ite_t22 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).(l_e_oneax ksi (λt:ksi.l_r_ite_prop1 a ksi x y i j t) (l_r_ite_t21 a ksi x y i j) : l_r_ite_prop1 a ksi x y i j (l_r_ite a ksi x y i j)).
+
+(* notion 392 *)
+definition l_r_ite_t23 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).(l_ande1 (l_r_imp a (λt:a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (y t))) (l_r_ite_t22 a ksi x y i j) : l_r_imp a (λt:a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (x t))).
+
+(* notion 393 *)
+definition l_r_ite_t24 ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).(l_ande2 (l_r_imp a (λt:a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (x t))) (l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (y t))) (l_r_ite_t22 a ksi x y i j) : l_r_imp (l_not a) (λt:l_not a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (y t))).
+
+(* notion 394 *)
+definition l_r_itet ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λa1:a.(l_r_mp a (λt:a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (x t)) a1 (l_r_ite_t23 a ksi x y i j) : l_r_ite_is a ksi (l_r_ite a ksi x y i j) (x a1)).
+
+(* notion 395 *)
+definition l_r_itef ≝ λa:Prop.λksi:Type[0].λx:Πt:a.ksi.λy:Πt:l_not a.ksi.λi:Πt:a.Πu:a.l_r_ite_is a ksi (x t) (x u).λj:Πt:l_not a.Πu:l_not a.l_r_ite_is a ksi (y t) (y u).λn:l_not a.(l_r_mp (l_not a) (λt:l_not a.l_r_ite_is a ksi (l_r_ite a ksi x y i j) (y t)) n (l_r_ite_t24 a ksi x y i j) : l_r_ite_is a ksi (l_r_ite a ksi x y i j) (y n)).
+
+(* notion 396 *)
+axiom l_e_st_set : Πsigma:Type[0].Type[0].
+
+(* notion 397 *)
+axiom l_e_st_esti : Πsigma:Type[0].Πs:sigma.Πs0:l_e_st_set sigma.Prop.
+
+(* notion 398 *)
+axiom l_e_st_setof : Πsigma:Type[0].Πp:Πx:sigma.Prop.l_e_st_set sigma.
+
+(* notion 399 *)
+axiom l_e_st_estii : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πs:sigma.Πsp:p s.l_e_st_esti sigma s (l_e_st_setof sigma p).
+
+(* notion 400 *)
+axiom l_e_st_estie : Πsigma:Type[0].Πp:Πx:sigma.Prop.Πs:sigma.Πe:l_e_st_esti sigma s (l_e_st_setof sigma p).p s.
+
+(* notion 401 *)
+definition l_e_st_empty ≝ λsigma:Type[0].λs0:l_e_st_set sigma.(l_non sigma (λx:sigma.l_e_st_esti sigma x s0) : Prop).
+
+(* notion 402 *)
+definition l_e_st_nonempty ≝ λsigma:Type[0].λs0:l_e_st_set sigma.(l_some sigma (λx:sigma.l_e_st_esti sigma x s0) : Prop).
+
+(* notion 403 *)
+definition l_e_st_emptyi ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λn:Πx:sigma.l_not (l_e_st_esti sigma x s0).(n : l_e_st_empty sigma s0).
+
+(* notion 404 *)
+definition l_e_st_emptye ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λe:l_e_st_empty sigma s0.λs:sigma.(e s : l_not (l_e_st_esti sigma s s0)).
+
+(* notion 405 *)
+definition l_e_st_nonemptyi ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_somei sigma (λx:sigma.l_e_st_esti sigma x s0) s ses0 : l_e_st_nonempty sigma s0).
+
+(* notion 406 *)
+definition l_e_st_nonemptyapp ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λn:l_e_st_nonempty sigma s0.λx:Prop.λx1:Πy:sigma.Πz:l_e_st_esti sigma y s0.x.(l_someapp sigma (λy:sigma.l_e_st_esti sigma y s0) n x x1 : x).
+
+(* notion 407 *)
+definition l_e_st_incl ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.(l_all sigma (λx:sigma.l_imp (l_e_st_esti sigma x s0) (l_e_st_esti sigma x t0)) : Prop).
+
+(* notion 408 *)
+definition l_e_st_incli ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λe:Πx:sigma.Πy:l_e_st_esti sigma x s0.l_e_st_esti sigma x t0.(e : l_e_st_incl sigma s0 t0).
+
+(* notion 409 *)
+definition l_e_st_incle ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λi:l_e_st_incl sigma s0 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.(i s ses0 : l_e_st_esti sigma s t0).
+
+(* notion 410 *)
+definition l_e_st_refincl ≝ λsigma:Type[0].λs0:l_e_st_set sigma.(λx:sigma.λy:l_e_st_esti sigma x s0.y : l_e_st_incl sigma s0 s0).
+
+(* notion 411 *)
+definition l_e_st_disj ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.(l_all sigma (λx:sigma.l_ec (l_e_st_esti sigma x s0) (l_e_st_esti sigma x t0)) : Prop).
+
+(* notion 412 *)
+definition l_e_st_disji1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:Πx:sigma.Πy:l_e_st_esti sigma x s0.l_not (l_e_st_esti sigma x t0).(n : l_e_st_disj sigma s0 t0).
+
+(* notion 413 *)
+definition l_e_st_disji2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:Πx:sigma.Πy:l_e_st_esti sigma x t0.l_not (l_e_st_esti sigma x s0).(λx:sigma.l_ec_th2 (l_e_st_esti sigma x s0) (l_e_st_esti sigma x t0) (n x) : l_e_st_disj sigma s0 t0).
+
+(* notion 414 *)
+definition l_e_st_disje1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λd:l_e_st_disj sigma s0 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_ece1 (l_e_st_esti sigma s s0) (l_e_st_esti sigma s t0) (d s) ses0 : l_not (l_e_st_esti sigma s t0)).
+
+(* notion 415 *)
+definition l_e_st_disje2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λd:l_e_st_disj sigma s0 t0.λs:sigma.λset0:l_e_st_esti sigma s t0.(l_ece2 (l_e_st_esti sigma s s0) (l_e_st_esti sigma s t0) (d s) set0 : l_not (l_e_st_esti sigma s s0)).
+
+(* notion 416 *)
+definition l_e_st_symdisj ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λd:l_e_st_disj sigma s0 t0.(λx:sigma.λy:l_e_st_esti sigma x t0.l_e_st_disje2 sigma s0 t0 d x y : l_e_st_disj sigma t0 s0).
+
+(* notion 417 *)
+definition l_e_st_disj_th1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.λses0:l_e_st_esti sigma s s0.λset0:l_e_st_esti sigma s t0.(l_all_th1 sigma (λx:sigma.l_ec (l_e_st_esti sigma x s0) (l_e_st_esti sigma x t0)) s (l_imp_th4 (l_e_st_esti sigma s s0) (l_not (l_e_st_esti sigma s t0)) ses0 (l_weli (l_e_st_esti sigma s t0) set0)) : l_not (l_e_st_disj sigma s0 t0)).
+
+(* notion 418 *)
+definition l_e_st_disj_th2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.λses0:l_e_st_esti sigma s s0.λset0:l_e_st_esti sigma s t0.(l_e_st_disj_th1 sigma t0 s0 s set0 ses0 : l_not (l_e_st_disj sigma t0 s0)).
+
+(* notion 419 *)
+definition l_e_st_issete1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_e_isp (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_esti sigma s x) s0 t0 ses0 i : l_e_st_esti sigma s t0).
+
+(* notion 420 *)
+definition l_e_st_issete2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.λs:sigma.λset0:l_e_st_esti sigma s t0.(l_e_isp1 (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_esti sigma s x) t0 s0 set0 i : l_e_st_esti sigma s s0).
+
+(* notion 421 *)
+definition l_e_st_isset_th1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.(λx:sigma.λy:l_e_st_esti sigma x s0.l_e_st_issete1 sigma s0 t0 i x y : l_e_st_incl sigma s0 t0).
+
+(* notion 422 *)
+definition l_e_st_isset_th2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.(λx:sigma.λy:l_e_st_esti sigma x t0.l_e_st_issete2 sigma s0 t0 i x y : l_e_st_incl sigma t0 s0).
+
+(* notion 423 *)
+axiom l_e_st_isseti : Πsigma:Type[0].Πs0:l_e_st_set sigma.Πt0:l_e_st_set sigma.Πi:l_e_st_incl sigma s0 t0.Πj:l_e_st_incl sigma t0 s0.l_e_is (l_e_st_set sigma) s0 t0.
+
+(* notion 424 *)
+definition l_e_st_isset_th3 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.λses0:l_e_st_esti sigma s s0.λn:l_not (l_e_st_esti sigma s t0).(l_imp_th3 (l_e_is (l_e_st_set sigma) s0 t0) (l_e_st_esti sigma s t0) n (λt:l_e_is (l_e_st_set sigma) s0 t0.l_e_st_issete1 sigma s0 t0 t s ses0) : l_not (l_e_is (l_e_st_set sigma) s0 t0)).
+
+(* notion 425 *)
+definition l_e_st_isset_th4 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.λses0:l_e_st_esti sigma s s0.λn:l_not (l_e_st_esti sigma s t0).(l_e_symnotis (l_e_st_set sigma) s0 t0 (l_e_st_isset_th3 sigma s0 t0 s ses0 n) : l_not (l_e_is (l_e_st_set sigma) t0 s0)).
+
+(* notion 426 *)
+definition l_e_st_isset_nissetprop ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.(l_and (l_e_st_esti sigma s s0) (l_not (l_e_st_esti sigma s t0)) : Prop).
+
+(* notion 427 *)
+definition l_e_st_isset_t1 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λs:sigma.λn:l_not (l_e_st_isset_nissetprop sigma s0 t0 s).λe:l_e_st_esti sigma s s0.(l_et (l_e_st_esti sigma s t0) (l_and_th3 (l_e_st_esti sigma s s0) (l_not (l_e_st_esti sigma s t0)) n e) : l_e_st_esti sigma s t0).
+
+(* notion 428 *)
+definition l_e_st_isset_t2 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:l_not (l_e_is (l_e_st_set sigma) s0 t0).λm:l_not (l_some sigma (λx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)).λl:l_non sigma (λx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x).λs:sigma.(l_some_th4 sigma (λx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x) m s : l_not (l_e_st_isset_nissetprop sigma s0 t0 s)).
+
+(* notion 429 *)
+definition l_e_st_isset_t3 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:l_not (l_e_is (l_e_st_set sigma) s0 t0).λm:l_not (l_some sigma (λx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)).λl:l_non sigma (λx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x).λs:sigma.(l s : l_not (l_e_st_isset_nissetprop sigma t0 s0 s)).
+
+(* notion 430 *)
+definition l_e_st_isset_t4 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:l_not (l_e_is (l_e_st_set sigma) s0 t0).λm:l_not (l_some sigma (λx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)).λl:l_non sigma (λx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x).(l_e_st_isseti sigma s0 t0 (λx:sigma.λy:l_e_st_esti sigma x s0.l_e_st_isset_t1 sigma s0 t0 x (l_e_st_isset_t2 sigma s0 t0 n m l x) y) (λx:sigma.λy:l_e_st_esti sigma x t0.l_e_st_isset_t1 sigma t0 s0 x (l_e_st_isset_t3 sigma s0 t0 n m l x) y) : l_e_is (l_e_st_set sigma) s0 t0).
+
+(* notion 431 *)
+definition l_e_st_isset_t5 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:l_not (l_e_is (l_e_st_set sigma) s0 t0).λm:l_not (l_some sigma (λx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)).(l_imp_th3 (l_non sigma (λx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x)) (l_e_is (l_e_st_set sigma) s0 t0) n (λy:l_non sigma (λx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x).l_e_st_isset_t4 sigma s0 t0 n m y) : l_some sigma (λx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x)).
+
+(* notion 432 *)
+definition l_e_st_isset_th5 ≝ λsigma:Type[0].λs0:l_e_st_set sigma.λt0:l_e_st_set sigma.λn:l_not (l_e_is (l_e_st_set sigma) s0 t0).(l_or_th1 (l_some sigma (λx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)) (l_some sigma (λx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x)) (λy:l_not (l_some sigma (λx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)).l_e_st_isset_t5 sigma s0 t0 n y) : l_or (l_some sigma (λx:sigma.l_e_st_isset_nissetprop sigma s0 t0 x)) (l_some sigma (λx:sigma.l_e_st_isset_nissetprop sigma t0 s0 x))).
+
+(* notion 433 *)
+definition l_e_st_unmore ≝ λsigma:Type[0].λalpha:Type[0].λsa:Πx:alpha.l_e_st_set sigma.(l_e_st_setof sigma (λx:sigma.l_some alpha (λy:alpha.l_e_st_esti sigma x (sa y))) : l_e_st_set sigma).
+
+(* notion 434 *)
+definition l_e_st_eunmore1 ≝ λsigma:Type[0].λalpha:Type[0].λsa:Πx:alpha.l_e_st_set sigma.λs:sigma.λa:alpha.λseasa:l_e_st_esti sigma s (sa a).(l_e_st_estii sigma (λx:sigma.l_some alpha (λy:alpha.l_e_st_esti sigma x (sa y))) s (l_somei alpha (λy:alpha.l_e_st_esti sigma s (sa y)) a seasa) : l_e_st_esti sigma s (l_e_st_unmore sigma alpha sa)).
+
+(* notion 435 *)
+definition l_e_st_unmoreapp ≝ λsigma:Type[0].λalpha:Type[0].λsa:Πx:alpha.l_e_st_set sigma.λs:sigma.λseun:l_e_st_esti sigma s (l_e_st_unmore sigma alpha sa).λx:Prop.λx1:Πy:alpha.Πz:l_e_st_esti sigma s (sa y).x.(l_someapp alpha (λy:alpha.l_e_st_esti sigma s (sa y)) (l_e_st_estie sigma (λz:sigma.l_some alpha (λy:alpha.l_e_st_esti sigma z (sa y))) s seun) x x1 : x).
+
+(* notion 436 *)
+definition l_e_st_eq_refr ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(refr1 s : r s s).
+
+(* notion 437 *)
+definition l_e_st_eq_symr ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λtsr:r s t.(symr1 s t tsr : r t s).
+
+(* notion 438 *)
+definition l_e_st_eq_trr ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λu:sigma.λtsr:r s t.λutr:r t u.(trr1 s t u tsr utr : r s u).
+
+(* notion 439 *)
+definition l_e_st_eq_tr1r ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λu:sigma.λsur:r u s.λtur:r u t.(l_e_st_eq_trr sigma r refr1 symr1 trr1 s u t (l_e_st_eq_symr sigma r refr1 symr1 trr1 u s sur) tur : r s t).
+
+(* notion 440 *)
+definition l_e_st_eq_tr2r ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λu:sigma.λusr:r s u.λutr:r t u.(l_e_st_eq_trr sigma r refr1 symr1 trr1 s u t usr (l_e_st_eq_symr sigma r refr1 symr1 trr1 t u utr) : r s t).
+
+(* notion 441 *)
+definition l_e_st_eq_ecelt ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_setof sigma (r s) : l_e_st_set sigma).
+
+(* notion 442 *)
+definition l_e_st_eq_1_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_estii sigma (r s) s (l_e_st_eq_refr sigma r refr1 symr1 trr1 s) : l_e_st_esti sigma s (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
+
+(* notion 443 *)
+definition l_e_st_eq_1_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λtsr:r s t.(l_e_st_estii sigma (r s) t tsr : l_e_st_esti sigma t (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
+
+(* notion 444 *)
+definition l_e_st_eq_1_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λe:l_e_st_esti sigma t (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s).(l_e_st_estie sigma (r s) t e : r s t).
+
+(* notion 445 *)
+definition l_e_st_eq_1_t1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λe:l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s).(l_e_st_eq_1_th2 sigma r refr1 symr1 trr1 t u (l_e_st_eq_tr1r sigma r refr1 symr1 trr1 t u s tsr (l_e_st_eq_1_th3 sigma r refr1 symr1 trr1 s u e)) : l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)).
+
+(* notion 446 *)
+definition l_e_st_eq_1_th4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λtsr:r s t.(l_e_st_isseti sigma (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) (λx:sigma.λy:l_e_st_esti sigma x (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s).l_e_st_eq_1_t1 sigma r refr1 symr1 trr1 s t tsr x y) (λx:sigma.λy:l_e_st_esti sigma x (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t).l_e_st_eq_1_t1 sigma r refr1 symr1 trr1 t s (l_e_st_eq_symr sigma r refr1 symr1 trr1 s t tsr) x y) : l_e_is (l_e_st_set sigma) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)).
+
+(* notion 447 *)
+definition l_e_st_eq_1_t2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λn:l_not (r s t).λu:sigma.λe:l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s).(l_imp_th3 (l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)) (r s t) n (λx:l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t).l_e_st_eq_tr2r sigma r refr1 symr1 trr1 s t u (l_e_st_eq_1_th3 sigma r refr1 symr1 trr1 s u e) (l_e_st_eq_1_th3 sigma r refr1 symr1 trr1 t u x)) : l_not (l_e_st_esti sigma u (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t))).
+
+(* notion 448 *)
+definition l_e_st_eq_1_th5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λn:l_not (r s t).(λx:sigma.λy:l_e_st_esti sigma x (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s).l_e_st_eq_1_t2 sigma r refr1 symr1 trr1 s t n x y : l_e_st_disj sigma (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)).
+
+(* notion 449 *)
+definition l_e_st_eq_1_th6 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_nonemptyi sigma (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) s (l_e_st_eq_1_th1 sigma r refr1 symr1 trr1 s) : l_e_st_nonempty sigma (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
+
+(* notion 450 *)
+definition l_e_st_eq_ecp ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λs:sigma.(l_e_is (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) : Prop).
+
+(* notion 451 *)
+definition l_e_st_eq_anec ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.(l_some sigma (λx:sigma.l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 x) : Prop).
+
+(* notion 452 *)
+definition l_e_st_eq_2_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_somei sigma (λx:sigma.l_e_st_eq_ecp sigma r refr1 symr1 trr1 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) x) s (l_e_refis (l_e_st_set sigma) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)) : l_e_st_eq_anec sigma r refr1 symr1 trr1 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
+
+(* notion 453 *)
+definition l_e_st_eq_2_t1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λe:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 t.(l_e_st_issete1 sigma s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) e s ses0 : l_e_st_esti sigma s (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)).
+
+(* notion 454 *)
+definition l_e_st_eq_2_t2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λe:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 t.(l_e_st_eq_1_th4 sigma r refr1 symr1 trr1 t s (l_e_st_eq_1_th3 sigma r refr1 symr1 trr1 t s (l_e_st_eq_2_t1 sigma r refr1 symr1 trr1 s0 ecs0 s ses0 t e)) : l_e_is (l_e_st_set sigma) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
+
+(* notion 455 *)
+definition l_e_st_eq_2_t3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λe:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 t.(l_e_tris (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) e (l_e_st_eq_2_t2 sigma r refr1 symr1 trr1 s0 ecs0 s ses0 t e) : l_e_is (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
+
+(* notion 456 *)
+definition l_e_st_eq_2_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_someapp sigma (λx:sigma.l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 x) ecs0 (l_e_is (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)) (λx:sigma.λy:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 x.l_e_st_eq_2_t3 sigma r refr1 symr1 trr1 s0 ecs0 s ses0 x y) : l_e_is (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s)).
+
+(* notion 457 *)
+definition l_e_st_eq_2_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λtes0:l_e_st_esti sigma t s0.(l_e_st_eq_1_th3 sigma r refr1 symr1 trr1 s t (l_e_st_issete1 sigma s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 s0 ecs0 s ses0) t tes0) : r s t).
+
+(* notion 458 *)
+definition l_e_st_eq_2_th4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λtsr:r s t.(l_e_st_issete2 sigma s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 s0 ecs0 s ses0) t (l_e_st_eq_1_th2 sigma r refr1 symr1 trr1 s t tsr) : l_e_st_esti sigma t s0).
+
+(* notion 459 *)
+definition l_e_st_eq_2_t4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λs:sigma.λe:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 s.(l_e_isp (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_nonempty sigma x) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) s0 (l_e_st_eq_1_th6 sigma r refr1 symr1 trr1 s) (l_e_symis (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) e) : l_e_st_nonempty sigma s0).
+
+(* notion 460 *)
+definition l_e_st_eq_2_th5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.(l_someapp sigma (λx:sigma.l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 x) ecs0 (l_e_st_nonempty sigma s0) (λx:sigma.λy:l_e_st_eq_ecp sigma r refr1 symr1 trr1 s0 x.l_e_st_eq_2_t4 sigma r refr1 symr1 trr1 s0 ecs0 x y) : l_e_st_nonempty sigma s0).
+
+(* notion 461 *)
+definition l_e_st_eq_3_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λect0:l_e_st_eq_anec sigma r refr1 symr1 trr1 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λtet0:l_e_st_esti sigma t t0.λtsr:r s t.(l_e_tr3is (l_e_st_set sigma) s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) t0 (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 s0 ecs0 s ses0) (l_e_st_eq_1_th4 sigma r refr1 symr1 trr1 s t tsr) (l_e_symis (l_e_st_set sigma) t0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 t0 ect0 t tet0)) : l_e_is (l_e_st_set sigma) s0 t0).
+
+(* notion 462 *)
+definition l_e_st_eq_3_t1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λect0:l_e_st_eq_anec sigma r refr1 symr1 trr1 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λtet0:l_e_st_esti sigma t t0.λn:l_not (r s t).(l_e_isp1 (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_disj sigma x (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) s0 (l_e_st_eq_1_th5 sigma r refr1 symr1 trr1 s t n) (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 s0 ecs0 s ses0) : l_e_st_disj sigma s0 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t)).
+
+(* notion 463 *)
+definition l_e_st_eq_3_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λect0:l_e_st_eq_anec sigma r refr1 symr1 trr1 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.λt:sigma.λtet0:l_e_st_esti sigma t t0.λn:l_not (r s t).(l_e_isp1 (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_disj sigma s0 x) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) t0 (l_e_st_eq_3_t1 sigma r refr1 symr1 trr1 s0 ecs0 t0 ect0 s ses0 t tet0 n) (l_e_st_eq_2_th2 sigma r refr1 symr1 trr1 t0 ect0 t tet0) : l_e_st_disj sigma s0 t0).
+
+(* notion 464 *)
+definition l_e_st_eq_3_t2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_e_st_issete1 sigma s0 t0 i s ses0 : l_e_st_esti sigma s t0).
+
+(* notion 465 *)
+definition l_e_st_eq_3_t3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.λs:sigma.λses0:l_e_st_esti sigma s s0.(l_e_st_disj_th1 sigma s0 t0 s ses0 (l_e_st_eq_3_t2 sigma r refr1 symr1 trr1 s0 ecs0 t0 i s ses0) : l_not (l_e_st_disj sigma s0 t0)).
+
+(* notion 466 *)
+definition l_e_st_eq_3_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.λt0:l_e_st_set sigma.λi:l_e_is (l_e_st_set sigma) s0 t0.(l_e_st_nonemptyapp sigma s0 (l_e_st_eq_2_th5 sigma r refr1 symr1 trr1 s0 ecs0) (l_not (l_e_st_disj sigma s0 t0)) (λx:sigma.λy:l_e_st_esti sigma x s0.l_e_st_eq_3_t3 sigma r refr1 symr1 trr1 s0 ecs0 t0 i x y) : l_not (l_e_st_disj sigma s0 t0)).
+
+(* notion 467 *)
+definition l_e_st_eq_ect ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.(l_e_ot (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) : Type[0]).
+
+(* notion 468 *)
+definition l_e_st_eq_ectset ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs0:l_e_st_set sigma.λecs0:l_e_st_eq_anec sigma r refr1 symr1 trr1 s0.(l_e_out (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) s0 ecs0 : l_e_st_eq_ect sigma r refr1 symr1 trr1).
+
+(* notion 469 *)
+definition l_e_st_eq_ectelt ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_eq_ectset sigma r refr1 symr1 trr1 (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_2_th1 sigma r refr1 symr1 trr1 s) : l_e_st_eq_ect sigma r refr1 symr1 trr1).
+
+(* notion 470 *)
+definition l_e_st_eq_ecect ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_in (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) e : l_e_st_set sigma).
+
+(* notion 471 *)
+definition l_e_st_eq_4_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_inp (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) e : l_e_st_eq_anec sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)).
+
+(* notion 472 *)
+definition l_e_st_eq_4_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_st_eq_2_th5 sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 e) : l_e_st_nonempty sigma (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)).
+
+(* notion 473 *)
+definition l_e_st_eq_4_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λx:Prop.λx1:Πy:sigma.Πz:l_e_st_esti sigma y (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).x.(l_e_st_nonemptyapp sigma (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_4_th2 sigma r refr1 symr1 trr1 e) x x1 : x).
+
+(* notion 474 *)
+definition l_e_st_eq_4_th4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_isinout (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_2_th1 sigma r refr1 symr1 trr1 s) : l_e_is (l_e_st_set sigma) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s))).
+
+(* notion 475 *)
+definition l_e_st_eq_4_th5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_issete1 sigma (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s)) (l_e_st_eq_4_th4 sigma r refr1 symr1 trr1 s) s (l_e_st_eq_1_th1 sigma r refr1 symr1 trr1 s) : l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s))).
+
+(* notion 476 *)
+definition l_e_st_eq_4_th6 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.(l_e_st_eunmore1 sigma (l_e_st_eq_ect sigma r refr1 symr1 trr1) (λx:l_e_st_eq_ect sigma r refr1 symr1 trr1.l_e_st_eq_ecect sigma r refr1 symr1 trr1 x) s (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_4_th5 sigma r refr1 symr1 trr1 s) : l_e_st_esti sigma s (l_e_st_unmore sigma (l_e_st_eq_ect sigma r refr1 symr1 trr1) (λx:l_e_st_eq_ect sigma r refr1 symr1 trr1.l_e_st_eq_ecect sigma r refr1 symr1 trr1 x))).
+
+(* notion 477 *)
+definition l_e_st_eq_4_th7 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtee:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_st_eq_2_th3 sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 e) s see t tee : r s t).
+
+(* notion 478 *)
+definition l_e_st_eq_4_th8 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtsr:r s t.(l_e_st_eq_2_th4 sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 e) s see t tsr : l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)).
+
+(* notion 479 *)
+definition l_e_st_eq_5_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λi:l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) e f.(l_e_isini (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) e f i : l_e_is (l_e_st_set sigma) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f)).
+
+(* notion 480 *)
+definition l_e_st_eq_5_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λi:l_e_is (l_e_st_set sigma) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).(l_e_isine (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) e f i : l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) e f).
+
+(* notion 481 *)
+definition l_e_st_eq_5_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).λtsr:r s t.(l_e_st_eq_5_th2 sigma r refr1 symr1 trr1 e f (l_e_st_eq_3_th1 sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 e) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 f) s see t tef tsr) : l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) e f).
+
+(* notion 482 *)
+definition l_e_st_eq_5_th4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λi:l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) e f.(l_e_st_issete1 sigma (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e) (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f) (l_e_st_eq_5_th1 sigma r refr1 symr1 trr1 e f i) s see : l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f)).
+
+(* notion 483 *)
+definition l_e_st_eq_5_th5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).λi:l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) e f.(l_e_st_eq_2_th3 sigma r refr1 symr1 trr1 (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f) (l_e_st_eq_4_th1 sigma r refr1 symr1 trr1 f) s (l_e_st_eq_5_th4 sigma r refr1 symr1 trr1 e f s see i) t tef : r s t).
+
+(* notion 484 *)
+definition l_e_st_eq_5_th6 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λs:sigma.λt:sigma.λtsr:r s t.(l_e_isouti (l_e_st_set sigma) (λx:l_e_st_set sigma.l_e_st_eq_anec sigma r refr1 symr1 trr1 x) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_2_th1 sigma r refr1 symr1 trr1 s) (l_e_st_eq_ecelt sigma r refr1 symr1 trr1 t) (l_e_st_eq_2_th1 sigma r refr1 symr1 trr1 t) (l_e_st_eq_1_th4 sigma r refr1 symr1 trr1 s t tsr) : l_e_is (l_e_st_eq_ect sigma r refr1 symr1 trr1) (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 t)).
+
+(* notion 485 *)
+definition l_e_st_eq_fixfu ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.(Πx:sigma.Πy:sigma.Πz:r x y.l_e_is alpha (fu x) (fu y) : Prop).
+
+(* notion 486 *)
+definition l_e_st_eq_10_prop1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λs:sigma.(l_and (l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu s) a1) : Prop).
+
+(* notion 487 *)
+definition l_e_st_eq_10_prop2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.(l_some sigma (λx:sigma.l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 x) : Prop).
+
+(* notion 488 *)
+definition l_e_st_eq_10_t1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_andi (l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu s) (fu s)) see (l_e_refis alpha (fu s)) : l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e (fu s) s).
+
+(* notion 489 *)
+definition l_e_st_eq_10_t2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_somei sigma (λx:sigma.l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e (fu s) x) s (l_e_st_eq_10_t1 sigma r refr1 symr1 trr1 alpha fu ff e s see) : l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e (fu s)).
+
+(* notion 490 *)
+definition l_e_st_eq_10_t3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_somei alpha (λx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x) (fu s) (l_e_st_eq_10_t2 sigma r refr1 symr1 trr1 alpha fu ff e s see) : l_some alpha (λx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x)).
+
+(* notion 491 *)
+definition l_e_st_eq_10_t4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_st_eq_4_th3 sigma r refr1 symr1 trr1 e (l_some alpha (λx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x)) (λx:sigma.λy:l_e_st_esti sigma x (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).l_e_st_eq_10_t3 sigma r refr1 symr1 trr1 alpha fu ff e x y) : l_some alpha (λx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x)).
+
+(* notion 492 *)
+definition l_e_st_eq_10_t5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_ande1 (l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu s) a1) pa1s : l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)).
+
+(* notion 493 *)
+definition l_e_st_eq_10_t6 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_ande1 (l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu t) b1) pb1t : l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)).
+
+(* notion 494 *)
+definition l_e_st_eq_10_t7 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_e_st_eq_4_th7 sigma r refr1 symr1 trr1 e s (l_e_st_eq_10_t5 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s t pb1t) t (l_e_st_eq_10_t6 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s t pb1t) : r s t).
+
+(* notion 495 *)
+definition l_e_st_eq_10_t8 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_ande2 (l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu s) a1) pa1s : l_e_is alpha (fu s) a1).
+
+(* notion 496 *)
+definition l_e_st_eq_10_t9 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_ande2 (l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu t) b1) pb1t : l_e_is alpha (fu t) b1).
+
+(* notion 497 *)
+definition l_e_st_eq_10_t10 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.λt:sigma.λpb1t:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 t.(l_e_tr3is alpha a1 (fu s) (fu t) b1 (l_e_symis alpha (fu s) a1 (l_e_st_eq_10_t8 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s t pb1t)) (ff s t (l_e_st_eq_10_t7 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s t pb1t)) (l_e_st_eq_10_t9 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s t pb1t) : l_e_is alpha a1 b1).
+
+(* notion 498 *)
+definition l_e_st_eq_10_t11 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.λs:sigma.λpa1s:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 s.(l_someapp sigma (λx:sigma.l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 x) pb1 (l_e_is alpha a1 b1) (λx:sigma.λy:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e b1 x.l_e_st_eq_10_t10 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 s pa1s x y) : l_e_is alpha a1 b1).
+
+(* notion 499 *)
+definition l_e_st_eq_10_t12 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λa1:alpha.λb1:alpha.λpa1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e a1.λpb1:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e b1.(l_someapp sigma (λx:sigma.l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 x) pa1 (l_e_is alpha a1 b1) (λx:sigma.λy:l_e_st_eq_10_prop1 sigma r refr1 symr1 trr1 alpha fu ff e a1 x.l_e_st_eq_10_t11 sigma r refr1 symr1 trr1 alpha fu ff e a1 b1 pa1 pb1 x y) : l_e_is alpha a1 b1).
+
+(* notion 500 *)
+definition l_e_st_eq_10_t13 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(λx:alpha.λy:alpha.λu:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x.λv:l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e y.l_e_st_eq_10_t12 sigma r refr1 symr1 trr1 alpha fu ff e x y u v : l_e_amone alpha (λx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x)).
+
+(* notion 501 *)
+definition l_e_st_eq_10_t14 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_onei alpha (λx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x) (l_e_st_eq_10_t13 sigma r refr1 symr1 trr1 alpha fu ff e) (l_e_st_eq_10_t4 sigma r refr1 symr1 trr1 alpha fu ff e) : l_e_one alpha (λx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x)).
+
+(* notion 502 *)
+definition l_e_st_eq_indeq ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_ind alpha (λx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x) (l_e_st_eq_10_t14 sigma r refr1 symr1 trr1 alpha fu ff e) : alpha).
+
+(* notion 503 *)
+definition l_e_st_eq_10_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_oneax alpha (λx:alpha.l_e_st_eq_10_prop2 sigma r refr1 symr1 trr1 alpha fu ff e x) (l_e_st_eq_10_t14 sigma r refr1 symr1 trr1 alpha fu ff e) : l_some sigma (λx:sigma.l_and (l_e_st_esti sigma x (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e)) (l_e_is alpha (fu x) (l_e_st_eq_indeq sigma r refr1 symr1 trr1 alpha fu ff e)))).
+
+(* notion 504 *)
+definition l_e_st_eq_10_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_st_eq_10_t12 sigma r refr1 symr1 trr1 alpha fu ff e (fu s) (l_e_st_eq_indeq sigma r refr1 symr1 trr1 alpha fu ff e) (l_e_st_eq_10_t2 sigma r refr1 symr1 trr1 alpha fu ff e s see) (l_e_st_eq_10_th1 sigma r refr1 symr1 trr1 alpha fu ff e) : l_e_is alpha (fu s) (l_e_st_eq_indeq sigma r refr1 symr1 trr1 alpha fu ff e)).
+
+(* notion 505 *)
+definition l_e_st_eq_10_th3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu:Πx:sigma.alpha.λff:l_e_st_eq_fixfu sigma r refr1 symr1 trr1 alpha fu.λs:sigma.(l_e_st_eq_10_th2 sigma r refr1 symr1 trr1 alpha fu ff (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s) s (l_e_st_eq_4_th5 sigma r refr1 symr1 trr1 s) : l_e_is alpha (fu s) (l_e_st_eq_indeq sigma r refr1 symr1 trr1 alpha fu ff (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s))).
+
+(* notion 506 *)
+definition l_e_st_eq_fixfu2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.(Πx:sigma.Πy:sigma.Πz:sigma.Πu:sigma.Πv:r x y.Πw:r z u.l_e_is alpha (fu2 x z) (fu2 y u) : Prop).
+
+(* notion 507 *)
+definition l_e_st_eq_11_t1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.(ff2 s t u u tsr (l_e_st_eq_refr sigma r refr1 symr1 trr1 u) : l_e_is alpha (fu2 s u) (fu2 t u)).
+
+(* notion 508 *)
+definition l_e_st_eq_11_t2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λs:sigma.λt:sigma.λtsr:r s t.(l_e_fisi sigma alpha (fu2 s) (fu2 t) (λx:sigma.l_e_st_eq_11_t1 sigma r refr1 symr1 trr1 alpha fu2 ff2 s t tsr x) : l_e_is (Πx:sigma.alpha) (fu2 s) (fu2 t)).
+
+(* notion 509 *)
+definition l_e_st_eq_11_i ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_st_eq_indeq sigma r refr1 symr1 trr1 (Πx:sigma.alpha) fu2 (λx:sigma.λy:sigma.λz:r x y.l_e_st_eq_11_t2 sigma r refr1 symr1 trr1 alpha fu2 ff2 x y z) e : Πx:sigma.alpha).
+
+(* notion 510 *)
+definition l_e_st_eq_11_t3 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λuee:l_e_st_esti sigma u (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_st_eq_10_th2 sigma r refr1 symr1 trr1 (Πx:sigma.alpha) fu2 (λx:sigma.λy:sigma.λz:r x y.l_e_st_eq_11_t2 sigma r refr1 symr1 trr1 alpha fu2 ff2 x y z) e u uee : l_e_is (Πx:sigma.alpha) (fu2 u) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e)).
+
+(* notion 511 *)
+definition l_e_st_eq_11_t4 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λuee:l_e_st_esti sigma u (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_fise sigma alpha (fu2 u) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e) (l_e_st_eq_11_t3 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr u uee) s : l_e_is alpha (fu2 u s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s)).
+
+(* notion 512 *)
+definition l_e_st_eq_11_t5 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λuee:l_e_st_esti sigma u (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_fise sigma alpha (fu2 u) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e) (l_e_st_eq_11_t3 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr u uee) t : l_e_is alpha (fu2 u t) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t)).
+
+(* notion 513 *)
+definition l_e_st_eq_11_t6 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λuee:l_e_st_esti sigma u (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(ff2 u u s t (l_e_st_eq_refr sigma r refr1 symr1 trr1 u) tsr : l_e_is alpha (fu2 u s) (fu2 u t)).
+
+(* notion 514 *)
+definition l_e_st_eq_11_t7 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.λu:sigma.λuee:l_e_st_esti sigma u (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).(l_e_tr3is alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s) (fu2 u s) (fu2 u t) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t) (l_e_symis alpha (fu2 u s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s) (l_e_st_eq_11_t4 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr u uee)) (l_e_st_eq_11_t6 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr u uee) (l_e_st_eq_11_t5 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr u uee) : l_e_is alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t)).
+
+(* notion 515 *)
+definition l_e_st_eq_11_t8 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λt:sigma.λtsr:r s t.(l_e_st_eq_4_th3 sigma r refr1 symr1 trr1 e (l_e_is alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t)) (λx:sigma.λy:l_e_st_esti sigma x (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).l_e_st_eq_11_t7 sigma r refr1 symr1 trr1 alpha fu2 ff2 e s t tsr x y) : l_e_is alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t)).
+
+(* notion 516 *)
+definition l_e_st_eq_indeq2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.(l_e_st_eq_indeq sigma r refr1 symr1 trr1 alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e) (λx:sigma.λy:sigma.λz:r x y.l_e_st_eq_11_t8 sigma r refr1 symr1 trr1 alpha fu2 ff2 e x y z) f : alpha).
+
+(* notion 517 *)
+definition l_e_st_eq_11_t9 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).(l_e_st_eq_10_th2 sigma r refr1 symr1 trr1 alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e) (λx:sigma.λy:sigma.λz:r x y.l_e_st_eq_11_t8 sigma r refr1 symr1 trr1 alpha fu2 ff2 e x y z) f t tef : l_e_is alpha (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t) (l_e_st_eq_indeq2 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f)).
+
+(* notion 518 *)
+definition l_e_st_eq_11_t10 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).(l_e_st_eq_10_th2 sigma r refr1 symr1 trr1 (Πx:sigma.alpha) fu2 (λx:sigma.λy:sigma.λz:r x y.l_e_st_eq_11_t2 sigma r refr1 symr1 trr1 alpha fu2 ff2 x y z) e s see : l_e_is (Πx:sigma.alpha) (fu2 s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e)).
+
+(* notion 519 *)
+definition l_e_st_eq_11_t11 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).(l_e_fise sigma alpha (fu2 s) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e) (l_e_st_eq_11_t10 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f s see t tef) t : l_e_is alpha (fu2 s t) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t)).
+
+(* notion 520 *)
+definition l_e_st_eq_11_th1 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λe:l_e_st_eq_ect sigma r refr1 symr1 trr1.λf:l_e_st_eq_ect sigma r refr1 symr1 trr1.λs:sigma.λsee:l_e_st_esti sigma s (l_e_st_eq_ecect sigma r refr1 symr1 trr1 e).λt:sigma.λtef:l_e_st_esti sigma t (l_e_st_eq_ecect sigma r refr1 symr1 trr1 f).(l_e_tris alpha (fu2 s t) (l_e_st_eq_11_i sigma r refr1 symr1 trr1 alpha fu2 ff2 e t) (l_e_st_eq_indeq2 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f) (l_e_st_eq_11_t11 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f s see t tef) (l_e_st_eq_11_t9 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f s see t tef) : l_e_is alpha (fu2 s t) (l_e_st_eq_indeq2 sigma r refr1 symr1 trr1 alpha fu2 ff2 e f)).
+
+(* notion 521 *)
+definition l_e_st_eq_11_th2 ≝ λsigma:Type[0].λr:Πx:sigma.Πy:sigma.Prop.λrefr1:Πx:sigma.r x x.λsymr1:Πx:sigma.Πy:sigma.Πt:r x y.r y x.λtrr1:Πx:sigma.Πy:sigma.Πz:sigma.Πt:r x y.Πu:r y z.r x z.λalpha:Type[0].λfu2:Πx:sigma.Πy:sigma.alpha.λff2:l_e_st_eq_fixfu2 sigma r refr1 symr1 trr1 alpha fu2.λs:sigma.λt:sigma.(l_e_st_eq_11_th1 sigma r refr1 symr1 trr1 alpha fu2 ff2 (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 t) s (l_e_st_eq_4_th5 sigma r refr1 symr1 trr1 s) t (l_e_st_eq_4_th5 sigma r refr1 symr1 trr1 t) : l_e_is alpha (fu2 s t) (l_e_st_eq_indeq2 sigma r refr1 symr1 trr1 alpha fu2 ff2 (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 s) (l_e_st_eq_ectelt sigma r refr1 symr1 trr1 t))).
+
+(* notion 522 *)
+axiom l_e_st_eq_landau_n_nat : Type[0].
+
+(* notion 523 *)
+definition l_e_st_eq_landau_n_is ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_is l_e_st_eq_landau_n_nat x y : Prop).
+
+(* notion 524 *)
+definition l_e_st_eq_landau_n_nis ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_not (l_e_st_eq_landau_n_is x y) : Prop).
+
+(* notion 525 *)
+definition l_e_st_eq_landau_n_in ≝ λx:l_e_st_eq_landau_n_nat.λs:l_e_st_set l_e_st_eq_landau_n_nat.(l_e_st_esti l_e_st_eq_landau_n_nat x s : Prop).
+
+(* notion 526 *)
+definition l_e_st_eq_landau_n_some ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.(l_some l_e_st_eq_landau_n_nat p : Prop).
+
+(* notion 527 *)
+definition l_e_st_eq_landau_n_all ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.(l_all l_e_st_eq_landau_n_nat p : Prop).
+
+(* notion 528 *)
+definition l_e_st_eq_landau_n_one ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.(l_e_one l_e_st_eq_landau_n_nat p : Prop).
+
+(* notion 529 *)
+axiom l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat.
+
+(* notion 530 *)
+axiom l_e_st_eq_landau_n_suc : Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.
+
+(* notion 531 *)
+definition l_e_st_eq_landau_n_ax2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_suc x y i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y)).
+
+(* notion 532 *)
+axiom l_e_st_eq_landau_n_ax3 : Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc x) l_e_st_eq_landau_n_1.
+
+(* notion 533 *)
+axiom l_e_st_eq_landau_n_ax4 : Πx:l_e_st_eq_landau_n_nat.Πy:l_e_st_eq_landau_n_nat.Πu:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y).l_e_st_eq_landau_n_is x y.
+
+(* notion 534 *)
+definition l_e_st_eq_landau_n_cond1 ≝ λs:l_e_st_set l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_in l_e_st_eq_landau_n_1 s : Prop).
+
+(* notion 535 *)
+definition l_e_st_eq_landau_n_cond2 ≝ λs:l_e_st_set l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λx:l_e_st_eq_landau_n_nat.l_imp (l_e_st_eq_landau_n_in x s) (l_e_st_eq_landau_n_in (l_e_st_eq_landau_n_suc x) s)) : Prop).
+
+(* notion 536 *)
+axiom l_e_st_eq_landau_n_ax5 : Πs:l_e_st_set l_e_st_eq_landau_n_nat.Πu:l_e_st_eq_landau_n_cond1 s.Πv:l_e_st_eq_landau_n_cond2 s.Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_in x s.
+
+(* notion 537 *)
+definition l_e_st_eq_landau_n_i1_s ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.(l_e_st_setof l_e_st_eq_landau_n_nat p : l_e_st_set l_e_st_eq_landau_n_nat).
+
+(* notion 538 *)
+definition l_e_st_eq_landau_n_i1_t1 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.(l_e_st_estii l_e_st_eq_landau_n_nat p l_e_st_eq_landau_n_1 1p : l_e_st_eq_landau_n_cond1 (l_e_st_eq_landau_n_i1_s p 1p xsp x)).
+
+(* notion 539 *)
+definition l_e_st_eq_landau_n_i1_t2 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λyes:l_e_st_eq_landau_n_in y (l_e_st_eq_landau_n_i1_s p 1p xsp x).(l_e_st_estie l_e_st_eq_landau_n_nat p y yes : p y).
+
+(* notion 540 *)
+definition l_e_st_eq_landau_n_i1_t3 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λyes:l_e_st_eq_landau_n_in y (l_e_st_eq_landau_n_i1_s p 1p xsp x).(l_e_st_estii l_e_st_eq_landau_n_nat p (l_e_st_eq_landau_n_suc y) (xsp y (l_e_st_eq_landau_n_i1_t2 p 1p xsp x y yes)) : l_e_st_eq_landau_n_in (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_i1_s p 1p xsp x)).
+
+(* notion 541 *)
+definition l_e_st_eq_landau_n_i1_t4 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ax5 (l_e_st_eq_landau_n_i1_s p 1p xsp x) (l_e_st_eq_landau_n_i1_t1 p 1p xsp x) (λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_in y (l_e_st_eq_landau_n_i1_s p 1p xsp x).l_e_st_eq_landau_n_i1_t3 p 1p xsp x y u) x : l_e_st_eq_landau_n_in x (l_e_st_eq_landau_n_i1_s p 1p xsp x)).
+
+(* notion 542 *)
+definition l_e_st_eq_landau_n_induction ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λ1p:p l_e_st_eq_landau_n_1.λxsp:Πx:l_e_st_eq_landau_n_nat.Πy:p x.p (l_e_st_eq_landau_n_suc x).λx:l_e_st_eq_landau_n_nat.(l_e_st_estie l_e_st_eq_landau_n_nat p x (l_e_st_eq_landau_n_i1_t4 p 1p xsp x) : p x).
+
+(* notion 543 *)
+definition l_e_st_eq_landau_n_21_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x y.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y).(l_e_st_eq_landau_n_ax4 x y i : l_e_st_eq_landau_n_is x y).
+
+(* notion 544 *)
+definition l_e_st_eq_landau_n_satz1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x y.(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_is x y) n (λu:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y).l_e_st_eq_landau_n_21_t1 x y n u) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc y)).
+
+(* notion 545 *)
+definition l_e_st_eq_landau_n_22_prop1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc x) x : Prop).
+
+(* notion 546 *)
+definition l_e_st_eq_landau_n_22_t1 ≝ (l_e_st_eq_landau_n_ax3 l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_22_prop1 l_e_st_eq_landau_n_1).
+
+(* notion 547 *)
+definition l_e_st_eq_landau_n_22_t2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_22_prop1 x.(l_e_st_eq_landau_n_satz1 (l_e_st_eq_landau_n_suc x) x p : l_e_st_eq_landau_n_22_prop1 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 548 *)
+definition l_e_st_eq_landau_n_satz2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_22_prop1 y) l_e_st_eq_landau_n_22_t1 (λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_22_prop1 y.l_e_st_eq_landau_n_22_t2 y u) x : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc x) x).
+
+(* notion 549 *)
+definition l_e_st_eq_landau_n_23_prop1 ≝ λx:l_e_st_eq_landau_n_nat.(l_or (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u))) : Prop).
+
+(* notion 550 *)
+definition l_e_st_eq_landau_n_23_t1 ≝ (l_ori1 (l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_suc u))) (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_23_prop1 l_e_st_eq_landau_n_1).
+
+(* notion 551 *)
+definition l_e_st_eq_landau_n_23_t2 ≝ λx:l_e_st_eq_landau_n_nat.(l_somei l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc u)) x (l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc x)) : l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc u))).
+
+(* notion 552 *)
+definition l_e_st_eq_landau_n_23_t3 ≝ λx:l_e_st_eq_landau_n_nat.(l_ori2 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_suc u))) (l_e_st_eq_landau_n_23_t2 x) : l_e_st_eq_landau_n_23_prop1 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 553 *)
+definition l_e_st_eq_landau_n_23_t4 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_23_prop1 y) l_e_st_eq_landau_n_23_t1 (λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_23_prop1 y.l_e_st_eq_landau_n_23_t3 y) x : l_e_st_eq_landau_n_23_prop1 x).
+
+(* notion 554 *)
+definition l_e_st_eq_landau_n_satz3 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_ore2 (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u))) (l_e_st_eq_landau_n_23_t4 x) n : l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u))).
+
+(* notion 555 *)
+definition l_e_st_eq_landau_n_23_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc y).λj:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc z).(l_e_st_eq_landau_n_ax4 y z (l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc z) x i j) : l_e_st_eq_landau_n_is y z).
+
+(* notion 556 *)
+definition l_e_st_eq_landau_n_23_t6 ≝ λx:l_e_st_eq_landau_n_nat.(λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc y).λv:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc z).l_e_st_eq_landau_n_23_t5 x y z u v : l_e_amone l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u))).
+
+(* notion 557 *)
+definition l_e_st_eq_landau_n_satz3a ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_onei l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_23_t6 x) (l_e_st_eq_landau_n_satz3 x n) : l_e_st_eq_landau_n_one (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u))).
+
+(* notion 558 *)
+definition l_e_st_eq_landau_n_24_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (f y))) : Prop).
+
+(* notion 559 *)
+definition l_e_st_eq_landau_n_24_prop2 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_and (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x f) : Prop).
+
+(* notion 560 *)
+definition l_e_st_eq_landau_n_24_prop3 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (a y) (b y) : Prop).
+
+(* notion 561 *)
+definition l_e_st_eq_landau_n_24_t1 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.(l_ande1 (l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x a) pa : l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)).
+
+(* notion 562 *)
+definition l_e_st_eq_landau_n_24_t2 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.(l_ande1 (l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x b) pb : l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)).
+
+(* notion 563 *)
+definition l_e_st_eq_landau_n_24_t3 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.(l_e_tris2 l_e_st_eq_landau_n_nat (a l_e_st_eq_landau_n_1) (b l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_24_t1 x a b pa pb) (l_e_st_eq_landau_n_24_t2 x a b pa pb) : l_e_st_eq_landau_n_24_prop3 x a b pa pb l_e_st_eq_landau_n_1).
+
+(* notion 564 *)
+definition l_e_st_eq_landau_n_24_t4 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_e_st_eq_landau_n_ax2 (a y) (b y) p : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (a y)) (l_e_st_eq_landau_n_suc (b y))).
+
+(* notion 565 *)
+definition l_e_st_eq_landau_n_24_t5 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_ande2 (l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x a) pa : l_e_st_eq_landau_n_24_prop1 x a).
+
+(* notion 566 *)
+definition l_e_st_eq_landau_n_24_t6 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_ande2 (l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x b) pb : l_e_st_eq_landau_n_24_prop1 x b).
+
+(* notion 567 *)
+definition l_e_st_eq_landau_n_24_t7 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_e_st_eq_landau_n_24_t5 x a b pa pb y p y : l_e_st_eq_landau_n_is (a (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (a y))).
+
+(* notion 568 *)
+definition l_e_st_eq_landau_n_24_t8 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_e_st_eq_landau_n_24_t6 x a b pa pb y p y : l_e_st_eq_landau_n_is (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (b y))).
+
+(* notion 569 *)
+definition l_e_st_eq_landau_n_24_t9 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop3 x a b pa pb y.(l_e_tr3is l_e_st_eq_landau_n_nat (a (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (a y)) (l_e_st_eq_landau_n_suc (b y)) (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_24_t7 x a b pa pb y p) (l_e_st_eq_landau_n_24_t4 x a b pa pb y p) (l_e_symis l_e_st_eq_landau_n_nat (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (b y)) (l_e_st_eq_landau_n_24_t8 x a b pa pb y p)) : l_e_st_eq_landau_n_24_prop3 x a b pa pb (l_e_st_eq_landau_n_suc y)).
+
+(* notion 570 *)
+definition l_e_st_eq_landau_n_24_t10 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop3 x a b pa pb z) (l_e_st_eq_landau_n_24_t3 x a b pa pb) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_24_prop3 x a b pa pb z.l_e_st_eq_landau_n_24_t9 x a b pa pb z u) y : l_e_st_eq_landau_n_24_prop3 x a b pa pb y).
+
+(* notion 571 *)
+definition l_e_st_eq_landau_n_24_t11 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_24_prop2 x a.λpb:l_e_st_eq_landau_n_24_prop2 x b.(l_e_fisi l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat a b (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_t10 x a b pa pb y) : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) a b).
+
+(* notion 572 *)
+definition l_e_st_eq_landau_n_24_aa ≝ λx:l_e_st_eq_landau_n_nat.(λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λu:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_24_prop2 x z.λw:l_e_st_eq_landau_n_24_prop2 x u.l_e_st_eq_landau_n_24_t11 x z u v w : l_e_amone (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z)).
+
+(* notion 573 *)
+definition l_e_st_eq_landau_n_24_prop4 ≝ λx:l_e_st_eq_landau_n_nat.(l_some (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z) : Prop).
+
+(* notion 574 *)
+definition l_e_st_eq_landau_n_24_t12 ≝ (λx:l_e_st_eq_landau_n_nat.l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_suc x)) : l_e_st_eq_landau_n_24_prop1 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_suc).
+
+(* notion 575 *)
+definition l_e_st_eq_landau_n_24_t13 ≝ (l_andi (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_24_prop1 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_suc) (l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_24_t12 : l_e_st_eq_landau_n_24_prop2 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_suc).
+
+(* notion 576 *)
+definition l_e_st_eq_landau_n_24_t14 ≝ (l_somei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 l_e_st_eq_landau_n_1 z) l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_24_t13 : l_e_st_eq_landau_n_24_prop4 l_e_st_eq_landau_n_1).
+
+(* notion 577 *)
+definition l_e_st_eq_landau_n_24_g ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_suc (f y) : Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
+
+(* notion 578 *)
+definition l_e_st_eq_landau_n_24_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_24_g x p f pf y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_24_g x p f pf y) (l_e_st_eq_landau_n_suc (f y))).
+
+(* notion 579 *)
+definition l_e_st_eq_landau_n_24_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(l_ande1 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x f) pf : l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)).
+
+(* notion 580 *)
+definition l_e_st_eq_landau_n_24_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_24_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (f l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_t15 x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ax2 (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_24_t16 x p f pf)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_24_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_suc x))).
+
+(* notion 581 *)
+definition l_e_st_eq_landau_n_24_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_ande2 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x f) pf : l_e_st_eq_landau_n_24_prop1 x f).
+
+(* notion 582 *)
+definition l_e_st_eq_landau_n_24_t19 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_24_t18 x p f pf y y : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (f y))).
+
+(* notion 583 *)
+definition l_e_st_eq_landau_n_24_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_nat (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_24_g x p f pf y) (l_e_st_eq_landau_n_suc (f y)) (l_e_st_eq_landau_n_24_t19 x p f pf y) (l_e_st_eq_landau_n_24_t15 x p f pf y) : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_24_g x p f pf y)).
+
+(* notion 584 *)
+definition l_e_st_eq_landau_n_24_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_24_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (f (l_e_st_eq_landau_n_suc y))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_24_g x p f pf y)) (l_e_st_eq_landau_n_24_t15 x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_ax2 (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_24_g x p f pf y) (l_e_st_eq_landau_n_24_t20 x p f pf y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_24_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_24_g x p f pf y))).
+
+(* notion 585 *)
+definition l_e_st_eq_landau_n_24_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_t21 x p f pf y : l_e_st_eq_landau_n_24_prop1 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_24_g x p f pf)).
+
+(* notion 586 *)
+definition l_e_st_eq_landau_n_24_t23 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(l_andi (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_24_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_suc x))) (l_e_st_eq_landau_n_24_prop1 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_24_g x p f pf)) (l_e_st_eq_landau_n_24_t17 x p f pf) (l_e_st_eq_landau_n_24_t22 x p f pf) : l_e_st_eq_landau_n_24_prop2 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_24_g x p f pf)).
+
+(* notion 587 *)
+definition l_e_st_eq_landau_n_24_t24 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_24_prop2 x f.(l_somei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 (l_e_st_eq_landau_n_suc x) z) (l_e_st_eq_landau_n_24_g x p f pf) (l_e_st_eq_landau_n_24_t23 x p f pf) : l_e_st_eq_landau_n_24_prop4 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 588 *)
+definition l_e_st_eq_landau_n_24_t25 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_24_prop4 x.(l_someapp (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z) p (l_e_st_eq_landau_n_24_prop4 (l_e_st_eq_landau_n_suc x)) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_24_prop2 x z.l_e_st_eq_landau_n_24_t24 x p z u) : l_e_st_eq_landau_n_24_prop4 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 589 *)
+definition l_e_st_eq_landau_n_24_bb ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop4 y) l_e_st_eq_landau_n_24_t14 (λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_24_prop4 y.l_e_st_eq_landau_n_24_t25 y u) x : l_e_st_eq_landau_n_24_prop4 x).
+
+(* notion 590 *)
+definition l_e_st_eq_landau_n_satz4 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_onei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z) (l_e_st_eq_landau_n_24_aa x) (l_e_st_eq_landau_n_24_bb x) : l_e_one (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_is (z l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_all (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (z (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (z y)))))).
+
+(* notion 591 *)
+definition l_e_st_eq_landau_n_plus ≝ λx:l_e_st_eq_landau_n_nat.(l_e_ind (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z) (l_e_st_eq_landau_n_satz4 x) : Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
+
+(* notion 592 *)
+definition l_e_st_eq_landau_n_pl ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_plus x y : l_e_st_eq_landau_n_nat).
+
+(* notion 593 *)
+definition l_e_st_eq_landau_n_24_t26 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_oneax (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_24_prop2 x z) (l_e_st_eq_landau_n_satz4 x) : l_e_st_eq_landau_n_24_prop2 x (l_e_st_eq_landau_n_plus x)).
+
+(* notion 594 *)
+definition l_e_st_eq_landau_n_satz4a ≝ λx:l_e_st_eq_landau_n_nat.(l_ande1 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_plus x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x (l_e_st_eq_landau_n_plus x)) (l_e_st_eq_landau_n_24_t26 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)).
+
+(* notion 595 *)
+definition l_e_st_eq_landau_n_24_t27 ≝ λx:l_e_st_eq_landau_n_nat.(l_ande2 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_plus x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_prop1 x (l_e_st_eq_landau_n_plus x)) (l_e_st_eq_landau_n_24_t26 x) : l_e_st_eq_landau_n_24_prop1 x (l_e_st_eq_landau_n_plus x)).
+
+(* notion 596 *)
+definition l_e_st_eq_landau_n_satz4b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_24_t27 x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y))).
+
+(* notion 597 *)
+definition l_e_st_eq_landau_n_24_t28 ≝ (l_e_st_eq_landau_n_24_t11 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_plus l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_24_t26 l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_24_t13 : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (l_e_st_eq_landau_n_plus l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_suc).
+
+(* notion 598 *)
+definition l_e_st_eq_landau_n_satz4c ≝ λx:l_e_st_eq_landau_n_nat.(l_e_fise l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_plus l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_24_t28 x : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_suc x)).
+
+(* notion 599 *)
+definition l_e_st_eq_landau_n_24_t29 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_24_t11 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_plus (l_e_st_eq_landau_n_suc x)) (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_plus x y)) (l_e_st_eq_landau_n_24_t26 (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_24_t23 x (l_e_st_eq_landau_n_24_bb x) (l_e_st_eq_landau_n_plus x) (l_e_st_eq_landau_n_24_t26 x)) : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (l_e_st_eq_landau_n_plus (l_e_st_eq_landau_n_suc x)) (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_plus x y))).
+
+(* notion 600 *)
+definition l_e_st_eq_landau_n_satz4d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_fise l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_plus (l_e_st_eq_landau_n_suc x)) (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_plus x z)) (l_e_st_eq_landau_n_24_t29 x) y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y))).
+
+(* notion 601 *)
+definition l_e_st_eq_landau_n_satz4e ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 602 *)
+definition l_e_st_eq_landau_n_satz4f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_satz4b x y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y))).
+
+(* notion 603 *)
+definition l_e_st_eq_landau_n_satz4g ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_satz4c x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 x)).
+
+(* notion 604 *)
+definition l_e_st_eq_landau_n_satz4h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_satz4d x y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y)).
+
+(* notion 605 *)
+definition l_e_st_eq_landau_n_ispl1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl u z) x y i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
+
+(* notion 606 *)
+definition l_e_st_eq_landau_n_ispl2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl z u) x y i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
+
+(* notion 607 *)
+definition l_e_st_eq_landau_n_ispl12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_ispl1 x y z i) (l_e_st_eq_landau_n_ispl2 z u y j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 608 *)
+definition l_e_st_eq_landau_n_25_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z)) : Prop).
+
+(* notion 609 *)
+definition l_e_st_eq_landau_n_25_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz4a (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_satz4f x y) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_satz4e y)) : l_e_st_eq_landau_n_25_prop1 x y l_e_st_eq_landau_n_1).
+
+(* notion 610 *)
+definition l_e_st_eq_landau_n_25_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_25_prop1 x y z.(l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z)) p : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z)))).
+
+(* notion 611 *)
+definition l_e_st_eq_landau_n_25_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_25_prop1 x y z.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_suc z)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z))) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y z))) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_satz4b (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_25_t2 x y z p) (l_e_st_eq_landau_n_satz4f x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z)) x (l_e_st_eq_landau_n_satz4f y z)) : l_e_st_eq_landau_n_25_prop1 x y (l_e_st_eq_landau_n_suc z)).
+
+(* notion 612 *)
+definition l_e_st_eq_landau_n_satz5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_25_prop1 x y u) (l_e_st_eq_landau_n_25_t1 x y) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_25_prop1 x y u.l_e_st_eq_landau_n_25_t3 x y u v) z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z))).
+
+(* notion 613 *)
+definition l_e_st_eq_landau_n_asspl1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz5 x y z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z))).
+
+(* notion 614 *)
+definition l_e_st_eq_landau_n_asspl2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_satz5 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x y) z)).
+
+(* notion 615 *)
+definition l_e_st_eq_landau_n_26_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x) : Prop).
+
+(* notion 616 *)
+definition l_e_st_eq_landau_n_26_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz4a y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y)).
+
+(* notion 617 *)
+definition l_e_st_eq_landau_n_26_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz4c y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_suc y)).
+
+(* notion 618 *)
+definition l_e_st_eq_landau_n_26_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_26_t2 x y) (l_e_st_eq_landau_n_26_t1 x y) : l_e_st_eq_landau_n_26_prop1 l_e_st_eq_landau_n_1 y).
+
+(* notion 619 *)
+definition l_e_st_eq_landau_n_26_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_26_prop1 x y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y x)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x) p) (l_e_st_eq_landau_n_satz4f y x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x))).
+
+(* notion 620 *)
+definition l_e_st_eq_landau_n_26_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_26_prop1 x y.(l_e_st_eq_landau_n_satz4d x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y))).
+
+(* notion 621 *)
+definition l_e_st_eq_landau_n_26_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_26_prop1 x y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_26_t5 x y p) (l_e_st_eq_landau_n_26_t4 x y p) : l_e_st_eq_landau_n_26_prop1 (l_e_st_eq_landau_n_suc x) y).
+
+(* notion 622 *)
+definition l_e_st_eq_landau_n_satz6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_26_prop1 z y) (l_e_st_eq_landau_n_26_t3 x y) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_26_prop1 z y.l_e_st_eq_landau_n_26_t6 z y u) x : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x)).
+
+(* notion 623 *)
+definition l_e_st_eq_landau_n_compl ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz6 x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x)).
+
+(* notion 624 *)
+definition l_e_st_eq_landau_n_26_t7 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_satz4a x) (l_e_st_eq_landau_n_satz4g x) : l_e_st_eq_landau_n_26_prop1 x l_e_st_eq_landau_n_1).
+
+(* notion 625 *)
+definition l_e_st_eq_landau_n_26_t8 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_26_prop1 x y.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y x)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc y) x) (l_e_st_eq_landau_n_satz4b x y) (l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x) p) (l_e_st_eq_landau_n_satz4h y x) : l_e_st_eq_landau_n_26_prop1 x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 626 *)
+definition l_e_st_eq_landau_n_26_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_26_prop1 x z) (l_e_st_eq_landau_n_26_t7 x) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_26_prop1 x z.l_e_st_eq_landau_n_26_t8 x z u) y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl y x)).
+
+(* notion 627 *)
+definition l_e_st_eq_landau_n_27_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_nis y (l_e_st_eq_landau_n_pl x y) : Prop).
+
+(* notion 628 *)
+definition l_e_st_eq_landau_n_27_t1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symnotis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_ax3 x) : l_e_st_eq_landau_n_nis l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 629 *)
+definition l_e_st_eq_landau_n_27_t2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_notis_th4 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_27_t1 x) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_27_prop1 x l_e_st_eq_landau_n_1).
+
+(* notion 630 *)
+definition l_e_st_eq_landau_n_27_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_27_prop1 x y.(l_e_st_eq_landau_n_satz1 y (l_e_st_eq_landau_n_pl x y) p : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y))).
+
+(* notion 631 *)
+definition l_e_st_eq_landau_n_27_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_27_prop1 x y.(l_e_notis_th4 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_27_t3 x y p) (l_e_st_eq_landau_n_satz4b x y) : l_e_st_eq_landau_n_27_prop1 x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 632 *)
+definition l_e_st_eq_landau_n_satz7 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_27_prop1 x z) (l_e_st_eq_landau_n_27_t2 x) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_27_prop1 x z.l_e_st_eq_landau_n_27_t4 x z u) y : l_e_st_eq_landau_n_nis y (l_e_st_eq_landau_n_pl x y)).
+
+(* notion 633 *)
+definition l_e_st_eq_landau_n_28_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.(l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z) : Prop).
+
+(* notion 634 *)
+definition l_e_st_eq_landau_n_28_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.(l_e_st_eq_landau_n_satz1 y z n : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc z)).
+
+(* notion 635 *)
+definition l_e_st_eq_landau_n_28_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.(l_e_notis_th5 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc z) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 z) (l_e_st_eq_landau_n_28_t1 x y z n) (l_e_st_eq_landau_n_satz4g y) (l_e_st_eq_landau_n_satz4g z) : l_e_st_eq_landau_n_28_prop1 l_e_st_eq_landau_n_1 y z n).
+
+(* notion 636 *)
+definition l_e_st_eq_landau_n_28_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.λp:l_e_st_eq_landau_n_28_prop1 x y z n.(l_e_st_eq_landau_n_satz1 (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z) p : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x z))).
+
+(* notion 637 *)
+definition l_e_st_eq_landau_n_28_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.λp:l_e_st_eq_landau_n_28_prop1 x y z n.(l_e_notis_th5 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) z) (l_e_st_eq_landau_n_28_t3 x y z n p) (l_e_st_eq_landau_n_satz4h x y) (l_e_st_eq_landau_n_satz4h x z) : l_e_st_eq_landau_n_28_prop1 (l_e_st_eq_landau_n_suc x) y z n).
+
+(* notion 638 *)
+definition l_e_st_eq_landau_n_satz8 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis y z.(l_e_st_eq_landau_n_induction (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_28_prop1 u y z n) (l_e_st_eq_landau_n_28_t2 x y z n) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_28_prop1 u y z n.l_e_st_eq_landau_n_28_t4 u y z n v) x : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z)).
+
+(* notion 639 *)
+definition l_e_st_eq_landau_n_satz8a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z).(l_imp_th7 (l_e_st_eq_landau_n_is y z) (l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z)) (l_weli (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x z)) i) (λu:l_e_st_eq_landau_n_nis y z.l_e_st_eq_landau_n_satz8 x y z u) : l_e_st_eq_landau_n_is y z).
+
+(* notion 640 *)
+definition l_e_st_eq_landau_n_diffprop ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl y z) : Prop).
+
+(* notion 641 *)
+definition l_e_st_eq_landau_n_28_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λdv:l_e_st_eq_landau_n_diffprop x y v.(l_e_st_eq_landau_n_satz8a y u v (l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl y v) x du dv) : l_e_st_eq_landau_n_is u v).
+
+(* notion 642 *)
+definition l_e_st_eq_landau_n_satz8b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λdv:l_e_st_eq_landau_n_diffprop x y v.l_e_st_eq_landau_n_28_t5 x y u v du dv : l_e_amone l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl y z))).
+
+(* notion 643 *)
+definition l_e_st_eq_landau_n_29_i ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is x y : Prop).
+
+(* notion 644 *)
+definition l_e_st_eq_landau_n_29_ii ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) : Prop).
+
+(* notion 645 *)
+definition l_e_st_eq_landau_n_29_iii ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_some (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v) : Prop).
+
+(* notion 646 *)
+definition l_e_st_eq_landau_n_29_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λone1:l_e_st_eq_landau_n_29_i x y.λu:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl u x) (l_e_st_eq_landau_n_pl x u) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_compl u x) (l_e_st_eq_landau_n_ispl1 x y u one1) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl u x) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 647 *)
+definition l_e_st_eq_landau_n_29_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λone1:l_e_st_eq_landau_n_29_i x y.λu:l_e_st_eq_landau_n_nat.(l_e_notis_th3 l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl u x) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_satz7 u x) (l_e_st_eq_landau_n_29_t1 x y one1 u) : l_e_st_eq_landau_n_nis x (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 648 *)
+definition l_e_st_eq_landau_n_29_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λone1:l_e_st_eq_landau_n_29_i x y.(l_some_th5 l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_29_t2 x y one1 u) : l_not (l_e_st_eq_landau_n_29_ii x y)).
+
+(* notion 649 *)
+definition l_e_st_eq_landau_n_29_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_ec_th1 (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (λz:l_e_st_eq_landau_n_29_i x y.l_e_st_eq_landau_n_29_t3 x y z) : l_ec (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y)).
+
+(* notion 650 *)
+definition l_e_st_eq_landau_n_29_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λone1:l_e_st_eq_landau_n_29_i x y.(l_e_st_eq_landau_n_29_t3 y x (l_e_symis l_e_st_eq_landau_n_nat x y one1) : l_not (l_e_st_eq_landau_n_29_iii x y)).
+
+(* notion 651 *)
+definition l_e_st_eq_landau_n_29_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_ec_th2 (l_e_st_eq_landau_n_29_iii x y) (l_e_st_eq_landau_n_29_i x y) (λz:l_e_st_eq_landau_n_29_i x y.l_e_st_eq_landau_n_29_t5 x y z) : l_ec (l_e_st_eq_landau_n_29_iii x y) (l_e_st_eq_landau_n_29_i x y)).
+
+(* notion 652 *)
+definition l_e_st_eq_landau_n_29_t6a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λtwo1:l_e_st_eq_landau_n_29_ii x y.λthree1:l_e_st_eq_landau_n_29_iii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.(l_e_tr4is l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x v) u) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl v u)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl v u) x) du (l_e_st_eq_landau_n_ispl1 y (l_e_st_eq_landau_n_pl x v) u dv) (l_e_st_eq_landau_n_asspl1 x v u) (l_e_st_eq_landau_n_compl x (l_e_st_eq_landau_n_pl v u)) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl v u) x)).
+
+(* notion 653 *)
+definition l_e_st_eq_landau_n_29_t7 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λtwo1:l_e_st_eq_landau_n_29_ii x y.λthree1:l_e_st_eq_landau_n_29_iii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.(l_mp (l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl v u) x)) l_con (l_e_st_eq_landau_n_29_t6a x y two1 three1 u du v dv) (l_e_st_eq_landau_n_satz7 (l_e_st_eq_landau_n_pl v u) x) : l_con).
+
+(* notion 654 *)
+definition l_e_st_eq_landau_n_29_t8 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λtwo1:l_e_st_eq_landau_n_29_ii x y.λthree1:l_e_st_eq_landau_n_29_iii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v) three1 l_con (λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.l_e_st_eq_landau_n_29_t7 x y two1 three1 u du v dv) : l_con).
+
+(* notion 655 *)
+definition l_e_st_eq_landau_n_29_t9 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λtwo1:l_e_st_eq_landau_n_29_ii x y.λthree1:l_e_st_eq_landau_n_29_iii x y.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) two1 l_con (λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.l_e_st_eq_landau_n_29_t8 x y two1 three1 u du) : l_con).
+
+(* notion 656 *)
+definition l_e_st_eq_landau_n_29_t10 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λtwo1:l_e_st_eq_landau_n_29_ii x y.(λz:l_e_st_eq_landau_n_29_iii x y.l_e_st_eq_landau_n_29_t9 x y two1 z : l_not (l_e_st_eq_landau_n_29_iii x y)).
+
+(* notion 657 *)
+definition l_e_st_eq_landau_n_29_t11 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_ec_th1 (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y) (λz:l_e_st_eq_landau_n_29_ii x y.l_e_st_eq_landau_n_29_t10 x y z) : l_ec (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y)).
+
+(* notion 658 *)
+definition l_e_st_eq_landau_n_29_a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_ec3_th6 (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y) (l_e_st_eq_landau_n_29_t4 x y) (l_e_st_eq_landau_n_29_t11 x y) (l_e_st_eq_landau_n_29_t6 x y) : l_ec3 (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y)).
+
+(* notion 659 *)
+definition l_e_st_eq_landau_n_29_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_or3 (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y) : Prop).
+
+(* notion 660 *)
+definition l_e_st_eq_landau_n_29_t12 ≝ λx:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_or3i1 (l_e_st_eq_landau_n_29_i x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_ii x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_iii x l_e_st_eq_landau_n_1) j : l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1).
+
+(* notion 661 *)
+definition l_e_st_eq_landau_n_29_t13 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_suc u) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u) j (l_e_st_eq_landau_n_satz4g u) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u)).
+
+(* notion 662 *)
+definition l_e_st_eq_landau_n_29_t14 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_somei l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x l_e_st_eq_landau_n_1 z) u (l_e_st_eq_landau_n_29_t13 x n u j) : l_e_st_eq_landau_n_29_ii x l_e_st_eq_landau_n_1).
+
+(* notion 663 *)
+definition l_e_st_eq_landau_n_29_t15 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_someapp l_e_st_eq_landau_n_nat (λu1:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u1)) (l_e_st_eq_landau_n_satz3 x n) (l_e_st_eq_landau_n_29_ii x l_e_st_eq_landau_n_1) (λu1:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u1).l_e_st_eq_landau_n_29_t14 x n u1 z) : l_e_st_eq_landau_n_29_ii x l_e_st_eq_landau_n_1).
+
+(* notion 664 *)
+definition l_e_st_eq_landau_n_29_t16 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_or3i2 (l_e_st_eq_landau_n_29_i x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_ii x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_iii x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_t15 x n u j) : l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1).
+
+(* notion 665 *)
+definition l_e_st_eq_landau_n_29_t16a ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_satz3 x n) (l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).l_e_st_eq_landau_n_29_t16 x n u v) : l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1).
+
+(* notion 666 *)
+definition l_e_st_eq_landau_n_29_t17 ≝ λx:l_e_st_eq_landau_n_nat.(l_imp_th1 (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1) (λz:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_29_t12 x z) (λz:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_29_t16a x z) : l_e_st_eq_landau_n_29_prop1 x l_e_st_eq_landau_n_1).
+
+(* notion 667 *)
+definition l_e_st_eq_landau_n_29_t18 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λone1:l_e_st_eq_landau_n_29_i x y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz4e y) (l_e_st_eq_landau_n_ispl1 y x l_e_st_eq_landau_n_1 (l_e_symis l_e_st_eq_landau_n_nat x y one1)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 668 *)
+definition l_e_st_eq_landau_n_29_t19 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λone1:l_e_st_eq_landau_n_29_i x y.(l_somei l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_suc y) x z) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_29_t18 x y p one1) : l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 669 *)
+definition l_e_st_eq_landau_n_29_t20 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λone1:l_e_st_eq_landau_n_29_i x y.(l_or3i3 (l_e_st_eq_landau_n_29_i x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_t19 x y p one1) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 670 *)
+definition l_e_st_eq_landau_n_29_t21 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λj:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y) du (l_e_st_eq_landau_n_ispl2 u l_e_st_eq_landau_n_1 y j) (l_e_st_eq_landau_n_satz4a y) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 671 *)
+definition l_e_st_eq_landau_n_29_t22 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λj:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_or3i1 (l_e_st_eq_landau_n_29_i x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_t21 x y p two1 u du j) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 672 *)
+definition l_e_st_eq_landau_n_29_t23 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λn:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.λw:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_suc w).(l_e_tris l_e_st_eq_landau_n_nat u (l_e_st_eq_landau_n_suc w) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 w) j (l_e_st_eq_landau_n_satz4g w) : l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 w)).
+
+(* notion 673 *)
+definition l_e_st_eq_landau_n_29_t24 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λn:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.λw:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_suc w).(l_e_tr4is l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) w) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc y) w) du (l_e_st_eq_landau_n_ispl2 u (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 w) y (l_e_st_eq_landau_n_29_t23 x y p two1 u du n w j)) (l_e_st_eq_landau_n_asspl2 y l_e_st_eq_landau_n_1 w) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y) w (l_e_st_eq_landau_n_satz4a y)) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc y) w)).
+
+(* notion 674 *)
+definition l_e_st_eq_landau_n_29_t25 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λn:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.λw:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_suc w).(l_somei l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x (l_e_st_eq_landau_n_suc y) z) w (l_e_st_eq_landau_n_29_t24 x y p two1 u du n w j) : l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 675 *)
+definition l_e_st_eq_landau_n_29_t26 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λn:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.(l_someapp l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_suc z)) (l_e_st_eq_landau_n_satz3 u n) (l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)) (λz:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_is u (l_e_st_eq_landau_n_suc z).l_e_st_eq_landau_n_29_t25 x y p two1 u du n z v) : l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 676 *)
+definition l_e_st_eq_landau_n_29_t27 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.λn:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.(l_or3i2 (l_e_st_eq_landau_n_29_i x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_t26 x y p two1 u du n) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 677 *)
+definition l_e_st_eq_landau_n_29_t28 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_imp_th1 (l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)) (λz:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_29_t22 x y p two1 u du z) (λz:l_e_st_eq_landau_n_nis u l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_29_t27 x y p two1 u du z) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 678 *)
+definition l_e_st_eq_landau_n_29_t28a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λtwo1:l_e_st_eq_landau_n_29_ii x y.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) two1 (l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)) (λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.l_e_st_eq_landau_n_29_t28 x y p two1 u du) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 679 *)
+definition l_e_st_eq_landau_n_29_t29 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λthree1:l_e_st_eq_landau_n_29_iii x y.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x v)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc v)) (l_e_st_eq_landau_n_ax2 y (l_e_st_eq_landau_n_pl x v) dv) (l_e_st_eq_landau_n_satz4f x v) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc v))).
+
+(* notion 680 *)
+definition l_e_st_eq_landau_n_29_t30 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λthree1:l_e_st_eq_landau_n_29_iii x y.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.(l_somei l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_suc y) x z) (l_e_st_eq_landau_n_suc v) (l_e_st_eq_landau_n_29_t29 x y p three1 v dv) : l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 681 *)
+definition l_e_st_eq_landau_n_29_t31 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λthree1:l_e_st_eq_landau_n_29_iii x y.(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v) three1 (l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)) (λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.l_e_st_eq_landau_n_29_t30 x y p three1 v dv) : l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 682 *)
+definition l_e_st_eq_landau_n_29_t32 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.λthree1:l_e_st_eq_landau_n_29_iii x y.(l_or3i3 (l_e_st_eq_landau_n_29_i x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_ii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_iii x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_29_t31 x y p three1) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 683 *)
+definition l_e_st_eq_landau_n_29_t33 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_29_prop1 x y.(l_or3app (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y) (l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)) p (λz:l_e_st_eq_landau_n_29_i x y.l_e_st_eq_landau_n_29_t20 x y p z) (λz:l_e_st_eq_landau_n_29_ii x y.l_e_st_eq_landau_n_29_t28a x y p z) (λz:l_e_st_eq_landau_n_29_iii x y.l_e_st_eq_landau_n_29_t32 x y p z) : l_e_st_eq_landau_n_29_prop1 x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 684 *)
+definition l_e_st_eq_landau_n_29_b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_29_prop1 x z) (l_e_st_eq_landau_n_29_t17 x) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_29_prop1 x z.l_e_st_eq_landau_n_29_t33 x z u) y : l_or3 (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y)).
+
+(* notion 685 *)
+definition l_e_st_eq_landau_n_satz9 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_orec3i (l_e_st_eq_landau_n_29_i x y) (l_e_st_eq_landau_n_29_ii x y) (l_e_st_eq_landau_n_29_iii x y) (l_e_st_eq_landau_n_29_b x y) (l_e_st_eq_landau_n_29_a x y) : l_orec3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl y u))) (l_e_st_eq_landau_n_some (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is y (l_e_st_eq_landau_n_pl x v)))).
+
+(* notion 686 *)
+definition l_e_st_eq_landau_n_satz9a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_29_b x y : l_or3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u)) (l_e_st_eq_landau_n_some (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v))).
+
+(* notion 687 *)
+definition l_e_st_eq_landau_n_satz9b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_29_a x y : l_ec3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u)) (l_e_st_eq_landau_n_some (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v))).
+
+(* notion 688 *)
+definition l_e_st_eq_landau_n_more ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) : Prop).
+
+(* notion 689 *)
+definition l_e_st_eq_landau_n_less ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_some (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v) : Prop).
+
+(* notion 690 *)
+definition l_e_st_eq_landau_n_satz10 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz9 x y : l_orec3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y)).
+
+(* notion 691 *)
+definition l_e_st_eq_landau_n_satz10a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz9a x y : l_or3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y)).
+
+(* notion 692 *)
+definition l_e_st_eq_landau_n_satz10b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz9b x y : l_ec3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y)).
+
+(* notion 693 *)
+definition l_e_st_eq_landau_n_satz11 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(m : l_e_st_eq_landau_n_less y x).
+
+(* notion 694 *)
+definition l_e_st_eq_landau_n_satz12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l : l_e_st_eq_landau_n_more y x).
+
+(* notion 695 *)
+definition l_e_st_eq_landau_n_moreis ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_or (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) : Prop).
+
+(* notion 696 *)
+definition l_e_st_eq_landau_n_lessis ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_or (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) : Prop).
+
+(* notion 697 *)
+definition l_e_st_eq_landau_n_satz13 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_or_th9 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_less y x) (l_e_st_eq_landau_n_is y x) m (λz:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz11 x y z) (λz:l_e_st_eq_landau_n_is x y.l_e_symis l_e_st_eq_landau_n_nat x y z) : l_e_st_eq_landau_n_lessis y x).
+
+(* notion 698 *)
+definition l_e_st_eq_landau_n_satz14 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_or_th9 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more y x) (l_e_st_eq_landau_n_is y x) l (λz:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz12 x y z) (λz:l_e_st_eq_landau_n_is x y.l_e_symis l_e_st_eq_landau_n_nat x y z) : l_e_st_eq_landau_n_moreis y x).
+
+(* notion 699 *)
+definition l_e_st_eq_landau_n_ismore1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more x z.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_more u z) x y m i : l_e_st_eq_landau_n_more y z).
+
+(* notion 700 *)
+definition l_e_st_eq_landau_n_ismore2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more z x.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_more z u) x y m i : l_e_st_eq_landau_n_more z y).
+
+(* notion 701 *)
+definition l_e_st_eq_landau_n_isless1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less x z.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_less u z) x y l i : l_e_st_eq_landau_n_less y z).
+
+(* notion 702 *)
+definition l_e_st_eq_landau_n_isless2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less z x.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_less z u) x y l i : l_e_st_eq_landau_n_less z y).
+
+(* notion 703 *)
+definition l_e_st_eq_landau_n_ismoreis1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_moreis x z.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_moreis u z) x y m i : l_e_st_eq_landau_n_moreis y z).
+
+(* notion 704 *)
+definition l_e_st_eq_landau_n_ismoreis2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_moreis z x.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_moreis z u) x y m i : l_e_st_eq_landau_n_moreis z y).
+
+(* notion 705 *)
+definition l_e_st_eq_landau_n_islessis1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_lessis x z.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis u z) x y l i : l_e_st_eq_landau_n_lessis y z).
+
+(* notion 706 *)
+definition l_e_st_eq_landau_n_islessis2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_lessis z x.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis z u) x y l i : l_e_st_eq_landau_n_lessis z y).
+
+(* notion 707 *)
+definition l_e_st_eq_landau_n_moreisi2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_ori2 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) i : l_e_st_eq_landau_n_moreis x y).
+
+(* notion 708 *)
+definition l_e_st_eq_landau_n_lessisi2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_ori2 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) i : l_e_st_eq_landau_n_lessis x y).
+
+(* notion 709 *)
+definition l_e_st_eq_landau_n_moreisi1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_ori1 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) m : l_e_st_eq_landau_n_moreis x y).
+
+(* notion 710 *)
+definition l_e_st_eq_landau_n_lessisi1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_ori1 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) l : l_e_st_eq_landau_n_lessis x y).
+
+(* notion 711 *)
+definition l_e_st_eq_landau_n_ismore12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.λm:l_e_st_eq_landau_n_more x z.(l_e_st_eq_landau_n_ismore2 z u y j (l_e_st_eq_landau_n_ismore1 x y z i m) : l_e_st_eq_landau_n_more y u).
+
+(* notion 712 *)
+definition l_e_st_eq_landau_n_isless12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.λl:l_e_st_eq_landau_n_less x z.(l_e_st_eq_landau_n_isless2 z u y j (l_e_st_eq_landau_n_isless1 x y z i l) : l_e_st_eq_landau_n_less y u).
+
+(* notion 713 *)
+definition l_e_st_eq_landau_n_ismoreis12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.λm:l_e_st_eq_landau_n_moreis x z.(l_e_st_eq_landau_n_ismoreis2 z u y j (l_e_st_eq_landau_n_ismoreis1 x y z i m) : l_e_st_eq_landau_n_moreis y u).
+
+(* notion 714 *)
+definition l_e_st_eq_landau_n_islessis12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.λl:l_e_st_eq_landau_n_lessis x z.(l_e_st_eq_landau_n_islessis2 z u y j (l_e_st_eq_landau_n_islessis1 x y z i l) : l_e_st_eq_landau_n_lessis y u).
+
+(* notion 715 *)
+definition l_e_st_eq_landau_n_satz10c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_ec3_th7 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) (l_comor (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) m) : l_not (l_e_st_eq_landau_n_less x y)).
+
+(* notion 716 *)
+definition l_e_st_eq_landau_n_satz10d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_ec3_th9 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) l : l_not (l_e_st_eq_landau_n_more x y)).
+
+(* notion 717 *)
+definition l_e_st_eq_landau_n_satz10e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_not (l_e_st_eq_landau_n_more x y).(l_or3_th2 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10a x y) n : l_e_st_eq_landau_n_lessis x y).
+
+(* notion 718 *)
+definition l_e_st_eq_landau_n_satz10f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_not (l_e_st_eq_landau_n_less x y).(l_comor (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_or3_th3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10a x y) n) : l_e_st_eq_landau_n_moreis x y).
+
+(* notion 719 *)
+definition l_e_st_eq_landau_n_satz10g ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_or_th3 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) (l_ec3e23 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) m) (l_ec3e21 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) m) : l_not (l_e_st_eq_landau_n_lessis x y)).
+
+(* notion 720 *)
+definition l_e_st_eq_landau_n_satz10h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_or_th3 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_ec3e32 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) l) (l_ec3e31 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10b x y) l) : l_not (l_e_st_eq_landau_n_moreis x y)).
+
+(* notion 721 *)
+definition l_e_st_eq_landau_n_satz10j ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_not (l_e_st_eq_landau_n_moreis x y).(l_or3e3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10a x y) (l_or_th5 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) n) (l_or_th4 (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) n) : l_e_st_eq_landau_n_less x y).
+
+(* notion 722 *)
+definition l_e_st_eq_landau_n_satz10k ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λn:l_not (l_e_st_eq_landau_n_lessis x y).(l_or3e2 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_satz10a x y) (l_or_th4 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) n) (l_or_th5 (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) n) : l_e_st_eq_landau_n_more x y).
+
+(* notion 723 *)
+definition l_e_st_eq_landau_n_315_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less y z.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.λw:l_e_st_eq_landau_n_nat.λdw:l_e_st_eq_landau_n_diffprop z y w.(l_e_tr3is l_e_st_eq_landau_n_nat z (l_e_st_eq_landau_n_pl y w) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl x v) w) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl v w)) dw (l_e_st_eq_landau_n_ispl1 y (l_e_st_eq_landau_n_pl x v) w dv) (l_e_st_eq_landau_n_asspl1 x v w) : l_e_st_eq_landau_n_is z (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_pl v w))).
+
+(* notion 724 *)
+definition l_e_st_eq_landau_n_315_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less y z.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.λw:l_e_st_eq_landau_n_nat.λdw:l_e_st_eq_landau_n_diffprop z y w.(l_somei l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop z x u) (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_315_t1 x y z l k v dv w dw) : l_e_st_eq_landau_n_less x z).
+
+(* notion 725 *)
+definition l_e_st_eq_landau_n_315_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less y z.λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.(l_someapp l_e_st_eq_landau_n_nat (λw:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop z y w) k (l_e_st_eq_landau_n_less x z) (λw:l_e_st_eq_landau_n_nat.λdw:l_e_st_eq_landau_n_diffprop z y w.l_e_st_eq_landau_n_315_t2 x y z l k v dv w dw) : l_e_st_eq_landau_n_less x z).
+
+(* notion 726 *)
+definition l_e_st_eq_landau_n_satz15 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less y z.(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x v) l (l_e_st_eq_landau_n_less x z) (λv:l_e_st_eq_landau_n_nat.λdv:l_e_st_eq_landau_n_diffprop y x v.l_e_st_eq_landau_n_315_t3 x y z l k v dv) : l_e_st_eq_landau_n_less x z).
+
+(* notion 727 *)
+definition l_e_st_eq_landau_n_trless ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less y z.(l_e_st_eq_landau_n_satz15 x y z l k : l_e_st_eq_landau_n_less x z).
+
+(* notion 728 *)
+definition l_e_st_eq_landau_n_trmore ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more y z.(l_e_st_eq_landau_n_satz15 z y x n m : l_e_st_eq_landau_n_more x z).
+
+(* notion 729 *)
+definition l_e_st_eq_landau_n_315_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more y z.(l_e_st_eq_landau_n_satz12 z x (l_e_st_eq_landau_n_satz15 z y x (l_e_st_eq_landau_n_satz11 y z n) (l_e_st_eq_landau_n_satz11 x y m)) : l_e_st_eq_landau_n_more x z).
+
+(* notion 730 *)
+definition l_e_st_eq_landau_n_satz16a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_less y z.(l_orapp (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_less x z) l (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_trless x y z u k) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_isless1 y x z (l_e_symis l_e_st_eq_landau_n_nat x y u) k) : l_e_st_eq_landau_n_less x z).
+
+(* notion 731 *)
+definition l_e_st_eq_landau_n_satz16b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_lessis y z.(l_orapp (l_e_st_eq_landau_n_less y z) (l_e_st_eq_landau_n_is y z) (l_e_st_eq_landau_n_less x z) k (λu:l_e_st_eq_landau_n_less y z.l_e_st_eq_landau_n_trless x y z l u) (λu:l_e_st_eq_landau_n_is y z.l_e_st_eq_landau_n_isless2 y z x u l) : l_e_st_eq_landau_n_less x z).
+
+(* notion 732 *)
+definition l_e_st_eq_landau_n_satz16c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_more y z.(l_e_st_eq_landau_n_satz16b z y x n (l_e_st_eq_landau_n_satz13 x y m) : l_e_st_eq_landau_n_more x z).
+
+(* notion 733 *)
+definition l_e_st_eq_landau_n_satz16d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_moreis y z.(l_e_st_eq_landau_n_satz16a z y x (l_e_st_eq_landau_n_satz13 y z n) m : l_e_st_eq_landau_n_more x z).
+
+(* notion 734 *)
+definition l_e_st_eq_landau_n_317_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is y z.(l_e_st_eq_landau_n_lessisi2 x z (l_e_tris l_e_st_eq_landau_n_nat x y z i j) : l_e_st_eq_landau_n_lessis x z).
+
+(* notion 735 *)
+definition l_e_st_eq_landau_n_317_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_less y z.(l_e_st_eq_landau_n_lessisi1 x z (l_e_st_eq_landau_n_satz16a x y z l j) : l_e_st_eq_landau_n_lessis x z).
+
+(* notion 736 *)
+definition l_e_st_eq_landau_n_317_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λi:l_e_st_eq_landau_n_is x y.(l_orapp (l_e_st_eq_landau_n_less y z) (l_e_st_eq_landau_n_is y z) (l_e_st_eq_landau_n_lessis x z) k (λu:l_e_st_eq_landau_n_less y z.l_e_st_eq_landau_n_317_t2 x y z l k i u) (λu:l_e_st_eq_landau_n_is y z.l_e_st_eq_landau_n_317_t1 x y z l k i u) : l_e_st_eq_landau_n_lessis x z).
+
+(* notion 737 *)
+definition l_e_st_eq_landau_n_317_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λj:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_lessisi1 x z (l_e_st_eq_landau_n_satz16b x y z j k) : l_e_st_eq_landau_n_lessis x z).
+
+(* notion 738 *)
+definition l_e_st_eq_landau_n_satz17 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.(l_orapp (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_lessis x z) l (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_317_t4 x y z l k u) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_317_t3 x y z l k u) : l_e_st_eq_landau_n_lessis x z).
+
+(* notion 739 *)
+definition l_e_st_eq_landau_n_317_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λj:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_lessisi1 x z (l_e_st_eq_landau_n_satz16b x y z j k) : l_e_st_eq_landau_n_lessis x z).
+
+(* notion 740 *)
+definition l_e_st_eq_landau_n_317_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_islessis1 y x z (l_e_symis l_e_st_eq_landau_n_nat x y i) k : l_e_st_eq_landau_n_lessis x z).
+
+(* notion 741 *)
+definition l_e_st_eq_landau_n_317_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.(l_orapp (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_lessis x z) l (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_317_t5 x y z l k u) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_317_t6 x y z l k u) : l_e_st_eq_landau_n_lessis x z).
+
+(* notion 742 *)
+definition l_e_st_eq_landau_n_trlessis ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis y z.(l_e_st_eq_landau_n_satz17 x y z l k : l_e_st_eq_landau_n_lessis x z).
+
+(* notion 743 *)
+definition l_e_st_eq_landau_n_trmoreis ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis y z.(l_e_st_eq_landau_n_satz14 z x (l_e_st_eq_landau_n_satz17 z y x (l_e_st_eq_landau_n_satz13 y z n) (l_e_st_eq_landau_n_satz13 x y m)) : l_e_st_eq_landau_n_moreis x z).
+
+(* notion 744 *)
+definition l_e_st_eq_landau_n_satz18 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_somei l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_pl x y) x u) y (l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x y)) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x y) x).
+
+(* notion 745 *)
+definition l_e_st_eq_landau_n_satz18a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz18 x y : l_e_st_eq_landau_n_less x (l_e_st_eq_landau_n_pl x y)).
+
+(* notion 746 *)
+definition l_e_st_eq_landau_n_satz18b ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) x (l_e_st_eq_landau_n_satz4a x) (l_e_st_eq_landau_n_satz18 x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc x) x).
+
+(* notion 747 *)
+definition l_e_st_eq_landau_n_satz18c ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz18b x : l_e_st_eq_landau_n_less x (l_e_st_eq_landau_n_suc x)).
+
+(* notion 748 *)
+definition l_e_st_eq_landau_n_319_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl u y) du (l_e_st_eq_landau_n_compl y u) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl u y)).
+
+(* notion 749 *)
+definition l_e_st_eq_landau_n_319_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl u y) z) (l_e_st_eq_landau_n_pl u (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl y z) u) (l_e_st_eq_landau_n_ispl1 x (l_e_st_eq_landau_n_pl u y) z (l_e_st_eq_landau_n_319_t1 x y z m u du)) (l_e_st_eq_landau_n_asspl1 u y z) (l_e_st_eq_landau_n_compl u (l_e_st_eq_landau_n_pl y z)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl y z) u)).
+
+(* notion 750 *)
+definition l_e_st_eq_landau_n_319_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_somei l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) v) u (l_e_st_eq_landau_n_319_t2 x y z m u du) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
+
+(* notion 751 *)
+definition l_e_st_eq_landau_n_satz19a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) m (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_diffprop x y u.l_e_st_eq_landau_n_319_t3 x y z m u v) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
+
+(* notion 752 *)
+definition l_e_st_eq_landau_n_satz19b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ispl1 x y z i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
+
+(* notion 753 *)
+definition l_e_st_eq_landau_n_satz19c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz11 (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_satz19a y x z (l_e_st_eq_landau_n_satz12 x y l)) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
+
+(* notion 754 *)
+definition l_e_st_eq_landau_n_319_anders1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz19a y x z l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
+
+(* notion 755 *)
+definition l_e_st_eq_landau_n_satz19d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_compl x z) (l_e_st_eq_landau_n_compl y z) (l_e_st_eq_landau_n_satz19a x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
+
+(* notion 756 *)
+definition l_e_st_eq_landau_n_satz19e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ispl2 x y z i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
+
+(* notion 757 *)
+definition l_e_st_eq_landau_n_satz19f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_compl x z) (l_e_st_eq_landau_n_compl y z) (l_e_st_eq_landau_n_satz19c x y z l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
+
+(* notion 758 *)
+definition l_e_st_eq_landau_n_319_anders2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz19d y x z l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
+
+(* notion 759 *)
+definition l_e_st_eq_landau_n_satz19g ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore2 (l_e_st_eq_landau_n_pl x u) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_ispl1 x y u i) (l_e_st_eq_landau_n_satz19d z u x m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 760 *)
+definition l_e_st_eq_landau_n_satz19h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl u y) (l_e_st_eq_landau_n_compl x z) (l_e_st_eq_landau_n_compl y u) (l_e_st_eq_landau_n_satz19g x y z u i m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl u y)).
+
+(* notion 761 *)
+definition l_e_st_eq_landau_n_satz19j ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_pl x u) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_ispl1 x y u i) (l_e_st_eq_landau_n_satz19f z u x l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 762 *)
+definition l_e_st_eq_landau_n_satz19k ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl u y) (l_e_st_eq_landau_n_compl x z) (l_e_st_eq_landau_n_compl y u) (l_e_st_eq_landau_n_satz19j x y z u i l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl u y)).
+
+(* notion 763 *)
+definition l_e_st_eq_landau_n_319_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_satz19a x y z n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
+
+(* notion 764 *)
+definition l_e_st_eq_landau_n_319_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_moreisi2 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_ispl1 x y z i) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
+
+(* notion 765 *)
+definition l_e_st_eq_landau_n_satz19l ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) m (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_319_t4 x y z m u) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_319_t5 x y z m u) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
+
+(* notion 766 *)
+definition l_e_st_eq_landau_n_satz19m ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_e_st_eq_landau_n_ismoreis12 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_compl x z) (l_e_st_eq_landau_n_compl y z) (l_e_st_eq_landau_n_satz19l x y z m) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
+
+(* notion 767 *)
+definition l_e_st_eq_landau_n_satz19n ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_satz19l y x z (l_e_st_eq_landau_n_satz14 x y l)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
+
+(* notion 768 *)
+definition l_e_st_eq_landau_n_satz19o ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_satz19m y x z (l_e_st_eq_landau_n_satz14 x y l)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
+
+(* notion 769 *)
+definition l_e_st_eq_landau_n_320_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz10a x y : l_or3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y)).
+
+(* notion 770 *)
+definition l_e_st_eq_landau_n_320_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) : l_ec3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z))).
+
+(* notion 771 *)
+definition l_e_st_eq_landau_n_satz20a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_ec3_th11 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_320_t1 x y z) (l_e_st_eq_landau_n_320_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz19b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz19a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz19c x y z u) m : l_e_st_eq_landau_n_more x y).
+
+(* notion 772 *)
+definition l_e_st_eq_landau_n_satz20b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_ec3_th10 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_320_t1 x y z) (l_e_st_eq_landau_n_320_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz19b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz19a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz19c x y z u) i : l_e_st_eq_landau_n_is x y).
+
+(* notion 773 *)
+definition l_e_st_eq_landau_n_satz20c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_ec3_th12 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_320_t1 x y z) (l_e_st_eq_landau_n_320_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz19b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz19a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz19c x y z u) l : l_e_st_eq_landau_n_less x y).
+
+(* notion 774 *)
+definition l_e_st_eq_landau_n_320_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_compl z x) i (l_e_st_eq_landau_n_compl y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y)).
+
+(* notion 775 *)
+definition l_e_st_eq_landau_n_320_andersb ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_e_st_eq_landau_n_satz8a z x y (l_e_st_eq_landau_n_320_t3 x y z i) : l_e_st_eq_landau_n_is x y).
+
+(* notion 776 *)
+definition l_e_st_eq_landau_n_320_andersc ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z).(l_e_st_eq_landau_n_satz20a y x z l : l_e_st_eq_landau_n_less x y).
+
+(* notion 777 *)
+definition l_e_st_eq_landau_n_satz20d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y).(l_e_st_eq_landau_n_satz20a x y z (l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_compl z x) (l_e_st_eq_landau_n_compl z y) m) : l_e_st_eq_landau_n_more x y).
+
+(* notion 778 *)
+definition l_e_st_eq_landau_n_satz20e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y).(l_e_st_eq_landau_n_satz20b x y z (l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_compl x z) i (l_e_st_eq_landau_n_compl z y)) : l_e_st_eq_landau_n_is x y).
+
+(* notion 779 *)
+definition l_e_st_eq_landau_n_satz20f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl z y).(l_e_st_eq_landau_n_satz20c x y z (l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_pl z x) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_compl z x) (l_e_st_eq_landau_n_compl z y) l) : l_e_st_eq_landau_n_less x y).
+
+(* notion 780 *)
+definition l_e_st_eq_landau_n_321_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_satz19a x y z m : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z)).
+
+(* notion 781 *)
+definition l_e_st_eq_landau_n_321_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl z y) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl u y) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_compl z y) (l_e_st_eq_landau_n_compl u y) (l_e_st_eq_landau_n_satz19a z u y n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 782 *)
+definition l_e_st_eq_landau_n_satz21 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_trmore (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_321_t1 x y z u m n) (l_e_st_eq_landau_n_321_t2 x y z u m n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 783 *)
+definition l_e_st_eq_landau_n_321_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_trmore (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_satz19a x y z m) (l_e_st_eq_landau_n_satz19d z u y n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 784 *)
+definition l_e_st_eq_landau_n_satz21a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz21 y x u z l k : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 785 *)
+definition l_e_st_eq_landau_n_321_andersa ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz11 (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_satz21 y x u z (l_e_st_eq_landau_n_satz12 x y l) (l_e_st_eq_landau_n_satz12 z u k)) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 786 *)
+definition l_e_st_eq_landau_n_satz22a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_more z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz21 x y z u v n) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz19g x y z u v n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 787 *)
+definition l_e_st_eq_landau_n_satz22b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more z u) (l_e_st_eq_landau_n_is z u) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)) n (λv:l_e_st_eq_landau_n_more z u.l_e_st_eq_landau_n_satz21 x y z u m v) (λv:l_e_st_eq_landau_n_is z u.l_e_st_eq_landau_n_satz19h z u x y v m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 788 *)
+definition l_e_st_eq_landau_n_satz22c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz22a y x u z (l_e_st_eq_landau_n_satz14 x y l) k : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 789 *)
+definition l_e_st_eq_landau_n_satz22d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_lessis z u.(l_e_st_eq_landau_n_satz22b y x u z l (l_e_st_eq_landau_n_satz14 z u k) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 790 *)
+definition l_e_st_eq_landau_n_323_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_st_eq_landau_n_moreisi2 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_ispl1 x y z i) (l_e_st_eq_landau_n_ispl2 z u y j)) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 791 *)
+definition l_e_st_eq_landau_n_323_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.λo:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_satz22a x y z u m o) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 792 *)
+definition l_e_st_eq_landau_n_323_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.(l_orapp (l_e_st_eq_landau_n_more z u) (l_e_st_eq_landau_n_is z u) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)) n (λv:l_e_st_eq_landau_n_more z u.l_e_st_eq_landau_n_323_t2 x y z u m n i v) (λv:l_e_st_eq_landau_n_is z u.l_e_st_eq_landau_n_323_t1 x y z u m n i v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 793 *)
+definition l_e_st_eq_landau_n_323_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λo:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_satz22b x y z u o n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 794 *)
+definition l_e_st_eq_landau_n_satz23 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_323_t4 x y z u m n v) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_323_t3 x y z u m n v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 795 *)
+definition l_e_st_eq_landau_n_323_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λo:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_satz22b x y z u o n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 796 *)
+definition l_e_st_eq_landau_n_323_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ismoreis2 (l_e_st_eq_landau_n_pl x u) (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_ispl1 x y u i) (l_e_st_eq_landau_n_satz19m z u x n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 797 *)
+definition l_e_st_eq_landau_n_323_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_323_t5 x y z u m n v) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_323_t6 x y z u m n v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 798 *)
+definition l_e_st_eq_landau_n_satz23a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis z u.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_pl y u) (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_satz23 y x u z (l_e_st_eq_landau_n_satz14 x y l) (l_e_st_eq_landau_n_satz14 z u k)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl x z) (l_e_st_eq_landau_n_pl y u)).
+
+(* notion 799 *)
+definition l_e_st_eq_landau_n_324_t1 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_suc u) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u) i (l_e_st_eq_landau_n_satz4g u) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u)).
+
+(* notion 800 *)
+definition l_e_st_eq_landau_n_324_t2 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u) x l_e_st_eq_landau_n_1 (l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 u) (l_e_st_eq_landau_n_324_t1 x n u i)) (l_e_st_eq_landau_n_satz18 l_e_st_eq_landau_n_1 u) : l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1).
+
+(* notion 801 *)
+definition l_e_st_eq_landau_n_324_t3 ≝ λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_satz3 x n) (l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_suc u).l_e_st_eq_landau_n_324_t2 x n u v) : l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1).
+
+(* notion 802 *)
+definition l_e_st_eq_landau_n_satz24 ≝ λx:l_e_st_eq_landau_n_nat.(l_or_th2 (l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (λu:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_324_t3 x u) : l_e_st_eq_landau_n_moreis x l_e_st_eq_landau_n_1).
+
+(* notion 803 *)
+definition l_e_st_eq_landau_n_satz24a ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz13 x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24 x) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x).
+
+(* notion 804 *)
+definition l_e_st_eq_landau_n_satz24b ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_324_t3 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_ax3 x) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc x) l_e_st_eq_landau_n_1).
+
+(* notion 805 *)
+definition l_e_st_eq_landau_n_satz24c ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz24b x : l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 806 *)
+definition l_e_st_eq_landau_n_325_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more y x.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop y x u.(l_e_st_eq_landau_n_satz19m u l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_satz24 u) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_pl x u) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 807 *)
+definition l_e_st_eq_landau_n_325_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more y x.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop y x u.(l_e_st_eq_landau_n_ismoreis1 (l_e_st_eq_landau_n_pl x u) y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_symis l_e_st_eq_landau_n_nat y (l_e_st_eq_landau_n_pl x u) du) (l_e_st_eq_landau_n_325_t1 x y m u du) : l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 808 *)
+definition l_e_st_eq_landau_n_satz25 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more y x.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop y x u) m (l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_diffprop y x u.l_e_st_eq_landau_n_325_t2 x y m u v) : l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 809 *)
+definition l_e_st_eq_landau_n_satz25a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more y x.(l_e_st_eq_landau_n_ismoreis2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) y (l_e_st_eq_landau_n_satz4a x) (l_e_st_eq_landau_n_satz25 x y m) : l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_suc x)).
+
+(* notion 810 *)
+definition l_e_st_eq_landau_n_satz25b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y x.(l_e_st_eq_landau_n_satz13 x (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz25 y x l) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) x).
+
+(* notion 811 *)
+definition l_e_st_eq_landau_n_satz25c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y x.(l_e_st_eq_landau_n_islessis1 (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y) x (l_e_st_eq_landau_n_satz4a y) (l_e_st_eq_landau_n_satz25b x y l) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc y) x).
+
+(* notion 812 *)
+definition l_e_st_eq_landau_n_326_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λm:l_e_st_eq_landau_n_more y x.(l_e_st_eq_landau_n_satz25 x y m : l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 813 *)
+definition l_e_st_eq_landau_n_326_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).(l_imp_th3 (l_e_st_eq_landau_n_more y x) (l_e_st_eq_landau_n_moreis y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz10h y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) l) (λv:l_e_st_eq_landau_n_more y x.l_e_st_eq_landau_n_326_t1 x y l v) : l_not (l_e_st_eq_landau_n_more y x)).
+
+(* notion 814 *)
+definition l_e_st_eq_landau_n_satz26 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).(l_e_st_eq_landau_n_satz10e y x (l_e_st_eq_landau_n_326_t2 x y l) : l_e_st_eq_landau_n_lessis y x).
+
+(* notion 815 *)
+definition l_e_st_eq_landau_n_satz26a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less y (l_e_st_eq_landau_n_suc x).(l_e_st_eq_landau_n_satz26 x y (l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) y (l_e_st_eq_landau_n_satz4e x) l) : l_e_st_eq_landau_n_lessis y x).
+
+(* notion 816 *)
+definition l_e_st_eq_landau_n_satz26b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) x.(l_e_st_eq_landau_n_satz14 x y (l_e_st_eq_landau_n_satz26 y x m) : l_e_st_eq_landau_n_moreis y x).
+
+(* notion 817 *)
+definition l_e_st_eq_landau_n_satz26c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc y) x.(l_e_st_eq_landau_n_satz26b x y (l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_satz4e y) m) : l_e_st_eq_landau_n_moreis y x).
+
+(* notion 818 *)
+definition l_e_st_eq_landau_n_327_lbprop ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.(l_imp (p m) (l_e_st_eq_landau_n_lessis n m) : Prop).
+
+(* notion 819 *)
+definition l_e_st_eq_landau_n_lb ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_lbprop p n x) : Prop).
+
+(* notion 820 *)
+definition l_e_st_eq_landau_n_min ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.(l_and (l_e_st_eq_landau_n_lb p n) (p n) : Prop).
+
+(* notion 821 *)
+definition l_e_st_eq_landau_n_327_t1 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λn:l_e_st_eq_landau_n_nat.(λx:p n.l_e_st_eq_landau_n_satz24a n : l_e_st_eq_landau_n_327_lbprop p l_e_st_eq_landau_n_1 n).
+
+(* notion 822 *)
+definition l_e_st_eq_landau_n_327_t2 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.(λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_t1 p s x : l_e_st_eq_landau_n_lb p l_e_st_eq_landau_n_1).
+
+(* notion 823 *)
+definition l_e_st_eq_landau_n_327_t3 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.λy:l_e_st_eq_landau_n_nat.λyp:p y.(l_e_st_eq_landau_n_satz18 y l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) y).
+
+(* notion 824 *)
+definition l_e_st_eq_landau_n_327_t4 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.λy:l_e_st_eq_landau_n_nat.λyp:p y.(l_e_st_eq_landau_n_satz10g (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) y (l_e_st_eq_landau_n_327_t3 p s l y yp) : l_not (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) y)).
+
+(* notion 825 *)
+definition l_e_st_eq_landau_n_327_t5 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.λy:l_e_st_eq_landau_n_nat.λyp:p y.(l_imp_th4 (p y) (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) y) yp (l_e_st_eq_landau_n_327_t4 p s l y yp) : l_not (l_e_st_eq_landau_n_327_lbprop p (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) y)).
+
+(* notion 826 *)
+definition l_e_st_eq_landau_n_327_t6 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.λy:l_e_st_eq_landau_n_nat.λyp:p y.(l_all_th1 l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_lbprop p (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) x) y (l_e_st_eq_landau_n_327_t5 p s l y yp) : l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1))).
+
+(* notion 827 *)
+definition l_e_st_eq_landau_n_327_t7 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.λy:l_e_st_eq_landau_n_nat.λyp:p y.(l_mp (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1)) l_con (l (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_327_t6 p s l y yp) : l_con).
+
+(* notion 828 *)
+definition l_e_st_eq_landau_n_327_t8 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λl:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x.(l_someapp l_e_st_eq_landau_n_nat p s l_con (λx:l_e_st_eq_landau_n_nat.λy:p x.l_e_st_eq_landau_n_327_t7 p s l x y) : l_con).
+
+(* notion 829 *)
+definition l_e_st_eq_landau_n_327_t9 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))).λm:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p m.(n m : l_not (l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))))).
+
+(* notion 830 *)
+definition l_e_st_eq_landau_n_327_t10 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))).λm:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p m.(l_et (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1)) (l_and_th3 (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_327_t9 p s n m l) l) : l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1)).
+
+(* notion 831 *)
+definition l_e_st_eq_landau_n_327_t11 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))).λm:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p m.(l_e_isp l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x) (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc m) (l_e_st_eq_landau_n_327_t10 p s n m l) (l_e_st_eq_landau_n_satz4a m) : l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_suc m)).
+
+(* notion 832 *)
+definition l_e_st_eq_landau_n_327_t12 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))).(λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_induction (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p y) (l_e_st_eq_landau_n_327_t2 p s) (λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_lb p y.l_e_st_eq_landau_n_327_t11 p s n y z) x : Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x).
+
+(* notion 833 *)
+definition l_e_st_eq_landau_n_327_t13 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.(λx:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))).l_e_st_eq_landau_n_327_t8 p s (l_e_st_eq_landau_n_327_t12 p s x) : l_e_st_eq_landau_n_some (λx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
+
+(* notion 834 *)
+definition l_e_st_eq_landau_n_327_t14 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).(l_ande1 (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))) a : l_e_st_eq_landau_n_lb p m).
+
+(* notion 835 *)
+definition l_e_st_eq_landau_n_327_t15 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).(l_ande2 (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))) a : l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).
+
+(* notion 836 *)
+definition l_e_st_eq_landau_n_327_t16 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).λn:l_e_st_eq_landau_n_nat.λnp:p n.(l_mp (p n) (l_e_st_eq_landau_n_lessis m n) np (l_e_st_eq_landau_n_327_t14 p s m a n) : l_e_st_eq_landau_n_lessis m n).
+
+(* notion 837 *)
+definition l_e_st_eq_landau_n_327_t17 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).λn:l_e_st_eq_landau_n_nat.λnp:p n.(l_imp_th3 (l_e_st_eq_landau_n_is m n) (p m) nmp (λx:l_e_st_eq_landau_n_is m n.l_e_isp l_e_st_eq_landau_n_nat p n m np (l_e_symis l_e_st_eq_landau_n_nat m n x)) : l_not (l_e_st_eq_landau_n_is m n)).
+
+(* notion 838 *)
+definition l_e_st_eq_landau_n_327_t18 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).λn:l_e_st_eq_landau_n_nat.λnp:p n.(l_ore1 (l_e_st_eq_landau_n_less m n) (l_e_st_eq_landau_n_is m n) (l_e_st_eq_landau_n_327_t16 p s m a nmp n np) (l_e_st_eq_landau_n_327_t17 p s m a nmp n np) : l_e_st_eq_landau_n_less m n).
+
+(* notion 839 *)
+definition l_e_st_eq_landau_n_327_t19 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).λn:l_e_st_eq_landau_n_nat.λnp:p n.(l_e_st_eq_landau_n_satz25b n m (l_e_st_eq_landau_n_327_t18 p s m a nmp n np) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1) n).
+
+(* notion 840 *)
+definition l_e_st_eq_landau_n_327_t20 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).(λx:l_e_st_eq_landau_n_nat.λy:p x.l_e_st_eq_landau_n_327_t19 p s m a nmp x y : l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1)).
+
+(* notion 841 *)
+definition l_e_st_eq_landau_n_327_t21 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).λnmp:l_not (p m).(l_mp (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1)) l_con (l_e_st_eq_landau_n_327_t20 p s m a nmp) (l_e_st_eq_landau_n_327_t15 p s m a) : l_con).
+
+(* notion 842 *)
+definition l_e_st_eq_landau_n_327_t22 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).(l_et (p m) (λx:l_not (p m).l_e_st_eq_landau_n_327_t21 p s m a x) : p m).
+
+(* notion 843 *)
+definition l_e_st_eq_landau_n_327_t23 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λm:l_e_st_eq_landau_n_nat.λa:l_and (l_e_st_eq_landau_n_lb p m) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl m l_e_st_eq_landau_n_1))).(l_andi (l_e_st_eq_landau_n_lb p m) (p m) (l_e_st_eq_landau_n_327_t14 p s m a) (l_e_st_eq_landau_n_327_t22 p s m a) : l_e_st_eq_landau_n_min p m).
+
+(* notion 844 *)
+definition l_e_st_eq_landau_n_satz27 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.(l_some_th6 l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x) (l_e_st_eq_landau_n_327_t13 p s) (λx:l_e_st_eq_landau_n_nat.λy:l_and (l_e_st_eq_landau_n_lb p x) (l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).l_e_st_eq_landau_n_327_t23 p s x y) : l_e_st_eq_landau_n_some (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)).
+
+(* notion 845 *)
+definition l_e_st_eq_landau_n_327_t24 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.(λx:p u.l_e_st_eq_landau_n_satz24a u : l_e_st_eq_landau_n_327_lbprop p l_e_st_eq_landau_n_1 u).
+
+(* notion 846 *)
+definition l_e_st_eq_landau_n_327_t25 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).(λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_t24 p n x : l_e_st_eq_landau_n_lb p l_e_st_eq_landau_n_1).
+
+(* notion 847 *)
+definition l_e_st_eq_landau_n_327_t26 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.(n u : l_not (l_e_st_eq_landau_n_min p u)).
+
+(* notion 848 *)
+definition l_e_st_eq_landau_n_327_t27 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.(l_and_th3 (l_e_st_eq_landau_n_lb p u) (p u) (l_e_st_eq_landau_n_327_t26 p n u l) l : l_not (p u)).
+
+(* notion 849 *)
+definition l_e_st_eq_landau_n_327_t28 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.λv:l_e_st_eq_landau_n_nat.λvp:p v.(l_imp_th3 (l_e_st_eq_landau_n_is u v) (p u) (l_e_st_eq_landau_n_327_t27 p n u l) (λx:l_e_st_eq_landau_n_is u v.l_e_isp1 l_e_st_eq_landau_n_nat p v u vp x) : l_e_st_eq_landau_n_nis u v).
+
+(* notion 850 *)
+definition l_e_st_eq_landau_n_327_t29 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.λv:l_e_st_eq_landau_n_nat.λvp:p v.(l_mp (p v) (l_e_st_eq_landau_n_lessis u v) vp (l v) : l_e_st_eq_landau_n_lessis u v).
+
+(* notion 851 *)
+definition l_e_st_eq_landau_n_327_t30 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.λv:l_e_st_eq_landau_n_nat.λvp:p v.(l_ore1 (l_e_st_eq_landau_n_less u v) (l_e_st_eq_landau_n_is u v) (l_e_st_eq_landau_n_327_t29 p n u l v vp) (l_e_st_eq_landau_n_327_t28 p n u l v vp) : l_e_st_eq_landau_n_less u v).
+
+(* notion 852 *)
+definition l_e_st_eq_landau_n_327_t31 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.λv:l_e_st_eq_landau_n_nat.λvp:p v.(l_e_st_eq_landau_n_satz25c v u (l_e_st_eq_landau_n_327_t30 p n u l v vp) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) v).
+
+(* notion 853 *)
+definition l_e_st_eq_landau_n_327_t32 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.λv:l_e_st_eq_landau_n_nat.(λx:p v.l_e_st_eq_landau_n_327_t31 p n u l v x : l_e_st_eq_landau_n_327_lbprop p (l_e_st_eq_landau_n_suc u) v).
+
+(* notion 854 *)
+definition l_e_st_eq_landau_n_327_t33 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lb p u.(λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_t32 p n u l x : l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_suc u)).
+
+(* notion 855 *)
+definition l_e_st_eq_landau_n_327_t34 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lb p x) (l_e_st_eq_landau_n_327_t25 p n) (λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_lb p x.l_e_st_eq_landau_n_327_t33 p n x y) u : l_e_st_eq_landau_n_lb p u).
+
+(* notion 856 *)
+definition l_e_st_eq_landau_n_327_t35 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λu:l_e_st_eq_landau_n_nat.λup:p u.(l_e_st_eq_landau_n_satz10g (l_e_st_eq_landau_n_suc u) u (l_e_st_eq_landau_n_satz18b u) : l_not (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) u)).
+
+(* notion 857 *)
+definition l_e_st_eq_landau_n_327_t36 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λu:l_e_st_eq_landau_n_nat.λup:p u.(l_imp_th4 (p u) (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) u) up (l_e_st_eq_landau_n_327_t35 p s u up) : l_not (l_e_st_eq_landau_n_327_lbprop p (l_e_st_eq_landau_n_suc u) u)).
+
+(* notion 858 *)
+definition l_e_st_eq_landau_n_327_t37 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λu:l_e_st_eq_landau_n_nat.λup:p u.(l_all_th1 l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_327_lbprop p (l_e_st_eq_landau_n_suc u) x) u (l_e_st_eq_landau_n_327_t36 p s u up) : l_not (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_suc u))).
+
+(* notion 859 *)
+definition l_e_st_eq_landau_n_327_t38 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.λu:l_e_st_eq_landau_n_nat.λup:p u.(λy:l_non l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x).l_mp (l_e_st_eq_landau_n_lb p (l_e_st_eq_landau_n_suc u)) l_con (l_e_st_eq_landau_n_327_t34 p y (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_327_t37 p s u up) : l_e_st_eq_landau_n_some (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)).
+
+(* notion 860 *)
+definition l_e_st_eq_landau_n_327_anders ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.(l_someapp l_e_st_eq_landau_n_nat p s (l_e_st_eq_landau_n_some (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)) (λx:l_e_st_eq_landau_n_nat.λy:p x.l_e_st_eq_landau_n_327_t38 p s x y) : l_e_st_eq_landau_n_some (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)).
+
+(* notion 861 *)
+definition l_e_st_eq_landau_n_327_t39 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_ande1 (l_e_st_eq_landau_n_lb p n) (p n) mn : l_e_st_eq_landau_n_lb p n).
+
+(* notion 862 *)
+definition l_e_st_eq_landau_n_327_t40 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_ande1 (l_e_st_eq_landau_n_lb p m) (p m) mm : l_e_st_eq_landau_n_lb p m).
+
+(* notion 863 *)
+definition l_e_st_eq_landau_n_327_t41 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_ande2 (l_e_st_eq_landau_n_lb p n) (p n) mn : p n).
+
+(* notion 864 *)
+definition l_e_st_eq_landau_n_327_t42 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_ande2 (l_e_st_eq_landau_n_lb p m) (p m) mm : p m).
+
+(* notion 865 *)
+definition l_e_st_eq_landau_n_327_t43 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_e_st_eq_landau_n_327_t39 p n m mn mm m : l_e_st_eq_landau_n_327_lbprop p n m).
+
+(* notion 866 *)
+definition l_e_st_eq_landau_n_327_t44 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_e_st_eq_landau_n_327_t40 p n m mn mm n : l_e_st_eq_landau_n_327_lbprop p m n).
+
+(* notion 867 *)
+definition l_e_st_eq_landau_n_327_t45 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_mp (p m) (l_e_st_eq_landau_n_lessis n m) (l_e_st_eq_landau_n_327_t42 p n m mn mm) (l_e_st_eq_landau_n_327_t43 p n m mn mm) : l_e_st_eq_landau_n_lessis n m).
+
+(* notion 868 *)
+definition l_e_st_eq_landau_n_327_t46 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_mp (p n) (l_e_st_eq_landau_n_lessis m n) (l_e_st_eq_landau_n_327_t41 p n m mn mm) (l_e_st_eq_landau_n_327_t44 p n m mn mm) : l_e_st_eq_landau_n_lessis m n).
+
+(* notion 869 *)
+definition l_e_st_eq_landau_n_327_t47 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λmn:l_e_st_eq_landau_n_min p n.λmm:l_e_st_eq_landau_n_min p m.(l_ore2 (l_e_st_eq_landau_n_more n m) (l_e_st_eq_landau_n_is n m) (l_e_st_eq_landau_n_satz14 m n (l_e_st_eq_landau_n_327_t46 p n m mn mm)) (l_e_st_eq_landau_n_satz10d n m (l_e_st_eq_landau_n_327_t45 p n m mn mm)) : l_e_st_eq_landau_n_is n m).
+
+(* notion 870 *)
+definition l_e_st_eq_landau_n_327_t48 ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.(λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_min p x.λv:l_e_st_eq_landau_n_min p y.l_e_st_eq_landau_n_327_t47 p x y u v : l_e_amone l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)).
+
+(* notion 871 *)
+definition l_e_st_eq_landau_n_satz27a ≝ λp:Πx:l_e_st_eq_landau_n_nat.Prop.λs:l_e_st_eq_landau_n_some p.(l_e_onei l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x) (l_e_st_eq_landau_n_327_t48 p) (l_e_st_eq_landau_n_satz27 p s) : l_e_st_eq_landau_n_one (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min p x)).
+
+(* notion 872 *)
+definition l_e_st_eq_landau_n_428_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) x)) : Prop).
+
+(* notion 873 *)
+definition l_e_st_eq_landau_n_428_prop2 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_and (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x f) : Prop).
+
+(* notion 874 *)
+definition l_e_st_eq_landau_n_428_prop3 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (a y) (b y) : Prop).
+
+(* notion 875 *)
+definition l_e_st_eq_landau_n_428_t1 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.(l_ande1 (l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x a) pa : l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) x).
+
+(* notion 876 *)
+definition l_e_st_eq_landau_n_428_t2 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.(l_ande1 (l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x b) pb : l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) x).
+
+(* notion 877 *)
+definition l_e_st_eq_landau_n_428_t3 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.(l_e_tris2 l_e_st_eq_landau_n_nat (a l_e_st_eq_landau_n_1) (b l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_428_t1 x a b pa pb) (l_e_st_eq_landau_n_428_t2 x a b pa pb) : l_e_st_eq_landau_n_428_prop3 x a b pa pb l_e_st_eq_landau_n_1).
+
+(* notion 878 *)
+definition l_e_st_eq_landau_n_428_t4 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_e_st_eq_landau_n_ispl1 (a y) (b y) x p : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (a y) x) (l_e_st_eq_landau_n_pl (b y) x)).
+
+(* notion 879 *)
+definition l_e_st_eq_landau_n_428_t5 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_ande2 (l_e_st_eq_landau_n_is (a l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x a) pa : l_e_st_eq_landau_n_428_prop1 x a).
+
+(* notion 880 *)
+definition l_e_st_eq_landau_n_428_t6 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_ande2 (l_e_st_eq_landau_n_is (b l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x b) pb : l_e_st_eq_landau_n_428_prop1 x b).
+
+(* notion 881 *)
+definition l_e_st_eq_landau_n_428_t7 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_e_st_eq_landau_n_428_t5 x a b pa pb y p y : l_e_st_eq_landau_n_is (a (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (a y) x)).
+
+(* notion 882 *)
+definition l_e_st_eq_landau_n_428_t8 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_e_st_eq_landau_n_428_t6 x a b pa pb y p y : l_e_st_eq_landau_n_is (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (b y) x)).
+
+(* notion 883 *)
+definition l_e_st_eq_landau_n_428_t9 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop3 x a b pa pb y.(l_e_tr3is l_e_st_eq_landau_n_nat (a (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (a y) x) (l_e_st_eq_landau_n_pl (b y) x) (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_428_t7 x a b pa pb y p) (l_e_st_eq_landau_n_428_t4 x a b pa pb y p) (l_e_symis l_e_st_eq_landau_n_nat (b (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (b y) x) (l_e_st_eq_landau_n_428_t8 x a b pa pb y p)) : l_e_st_eq_landau_n_428_prop3 x a b pa pb (l_e_st_eq_landau_n_suc y)).
+
+(* notion 884 *)
+definition l_e_st_eq_landau_n_428_t10 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop3 x a b pa pb z) (l_e_st_eq_landau_n_428_t3 x a b pa pb) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_428_prop3 x a b pa pb z.l_e_st_eq_landau_n_428_t9 x a b pa pb z u) y : l_e_st_eq_landau_n_428_prop3 x a b pa pb y).
+
+(* notion 885 *)
+definition l_e_st_eq_landau_n_428_t11 ≝ λx:l_e_st_eq_landau_n_nat.λa:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λb:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpa:l_e_st_eq_landau_n_428_prop2 x a.λpb:l_e_st_eq_landau_n_428_prop2 x b.(l_e_fisi l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat a b (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_t10 x a b pa pb y) : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) a b).
+
+(* notion 886 *)
+definition l_e_st_eq_landau_n_428_a1 ≝ λx:l_e_st_eq_landau_n_nat.(λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λu:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_428_prop2 x z.λw:l_e_st_eq_landau_n_428_prop2 x u.l_e_st_eq_landau_n_428_t11 x z u v w : l_e_amone (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z)).
+
+(* notion 887 *)
+definition l_e_st_eq_landau_n_428_prop4 ≝ λx:l_e_st_eq_landau_n_nat.(l_some (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z) : Prop).
+
+(* notion 888 *)
+definition l_e_st_eq_landau_n_428_id ≝ (λy:l_e_st_eq_landau_n_nat.y : Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
+
+(* notion 889 *)
+definition l_e_st_eq_landau_n_428_t12 ≝ (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_satz4e x : l_e_st_eq_landau_n_428_prop1 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_428_id).
+
+(* notion 890 *)
+definition l_e_st_eq_landau_n_428_t13 ≝ (l_andi (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_428_id l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_428_prop1 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_428_id) (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_428_t12 : l_e_st_eq_landau_n_428_prop2 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_428_id).
+
+(* notion 891 *)
+definition l_e_st_eq_landau_n_428_t14 ≝ (l_somei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 l_e_st_eq_landau_n_1 z) l_e_st_eq_landau_n_428_id l_e_st_eq_landau_n_428_t13 : l_e_st_eq_landau_n_428_prop4 l_e_st_eq_landau_n_1).
+
+(* notion 892 *)
+definition l_e_st_eq_landau_n_428_g ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl (f y) y : Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
+
+(* notion 893 *)
+definition l_e_st_eq_landau_n_428_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(l_ande1 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x f) pf : l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) x).
+
+(* notion 894 *)
+definition l_e_st_eq_landau_n_428_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_428_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_ispl1 (f l_e_st_eq_landau_n_1) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_428_t15 x p f pf)) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_428_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)).
+
+(* notion 895 *)
+definition l_e_st_eq_landau_n_428_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_ande2 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x f) pf : l_e_st_eq_landau_n_428_prop1 x f).
+
+(* notion 896 *)
+definition l_e_st_eq_landau_n_428_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_428_t17 x p f pf y y : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) x)).
+
+(* notion 897 *)
+definition l_e_st_eq_landau_n_428_t19 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_428_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (f y) x) (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y))) (l_e_st_eq_landau_n_ispl1 (f (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) x) (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_428_t18 x p f pf y)) (l_e_st_eq_landau_n_asspl1 (f y) x (l_e_st_eq_landau_n_suc y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_428_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)))).
+
+(* notion 898 *)
+definition l_e_st_eq_landau_n_428_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_satz4b x y) (l_e_st_eq_landau_n_satz4h x y) (l_e_st_eq_landau_n_compl (l_e_st_eq_landau_n_suc x) y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x))).
+
+(* notion 899 *)
+definition l_e_st_eq_landau_n_428_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.λy:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_428_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (f y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y))) (l_e_st_eq_landau_n_pl (f y) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_428_g x p f pf y) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_428_t19 x p f pf y) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc x)) (f y) (l_e_st_eq_landau_n_428_t20 x p f pf y)) (l_e_st_eq_landau_n_asspl2 (f y) y (l_e_st_eq_landau_n_suc x)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_428_g x p f pf (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_428_g x p f pf y) (l_e_st_eq_landau_n_suc x))).
+
+(* notion 900 *)
+definition l_e_st_eq_landau_n_428_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_t21 x p f pf y : l_e_st_eq_landau_n_428_prop1 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_428_g x p f pf)).
+
+(* notion 901 *)
+definition l_e_st_eq_landau_n_428_t23 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(l_andi (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_428_g x p f pf l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_428_prop1 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_428_g x p f pf)) (l_e_st_eq_landau_n_428_t16 x p f pf) (l_e_st_eq_landau_n_428_t22 x p f pf) : l_e_st_eq_landau_n_428_prop2 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_428_g x p f pf)).
+
+(* notion 902 *)
+definition l_e_st_eq_landau_n_428_t24 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.λf:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λpf:l_e_st_eq_landau_n_428_prop2 x f.(l_somei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 (l_e_st_eq_landau_n_suc x) z) (l_e_st_eq_landau_n_428_g x p f pf) (l_e_st_eq_landau_n_428_t23 x p f pf) : l_e_st_eq_landau_n_428_prop4 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 903 *)
+definition l_e_st_eq_landau_n_428_t25 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_428_prop4 x.(l_someapp (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z) p (l_e_st_eq_landau_n_428_prop4 (l_e_st_eq_landau_n_suc x)) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_428_prop2 x z.l_e_st_eq_landau_n_428_t24 x p z u) : l_e_st_eq_landau_n_428_prop4 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 904 *)
+definition l_e_st_eq_landau_n_428_b1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop4 y) l_e_st_eq_landau_n_428_t14 (λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_428_prop4 y.l_e_st_eq_landau_n_428_t25 y u) x : l_e_st_eq_landau_n_428_prop4 x).
+
+(* notion 905 *)
+definition l_e_st_eq_landau_n_satz28 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_onei (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z) (l_e_st_eq_landau_n_428_a1 x) (l_e_st_eq_landau_n_428_b1 x) : l_e_one (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_and (l_e_st_eq_landau_n_is (z l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_all (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (z (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (z y) x))))).
+
+(* notion 906 *)
+definition l_e_st_eq_landau_n_times ≝ λx:l_e_st_eq_landau_n_nat.(l_e_ind (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z) (l_e_st_eq_landau_n_satz28 x) : Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
+
+(* notion 907 *)
+definition l_e_st_eq_landau_n_ts ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_times x y : l_e_st_eq_landau_n_nat).
+
+(* notion 908 *)
+definition l_e_st_eq_landau_n_428_t26 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_oneax (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λz:Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_428_prop2 x z) (l_e_st_eq_landau_n_satz28 x) : l_e_st_eq_landau_n_428_prop2 x (l_e_st_eq_landau_n_times x)).
+
+(* notion 909 *)
+definition l_e_st_eq_landau_n_satz28a ≝ λx:l_e_st_eq_landau_n_nat.(l_ande1 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_times x l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x (l_e_st_eq_landau_n_times x)) (l_e_st_eq_landau_n_428_t26 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1) x).
+
+(* notion 910 *)
+definition l_e_st_eq_landau_n_428_t27 ≝ λx:l_e_st_eq_landau_n_nat.(l_ande2 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_times x l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_428_prop1 x (l_e_st_eq_landau_n_times x)) (l_e_st_eq_landau_n_428_t26 x) : l_e_st_eq_landau_n_428_prop1 x (l_e_st_eq_landau_n_times x)).
+
+(* notion 911 *)
+definition l_e_st_eq_landau_n_satz28b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_428_t27 x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) x)).
+
+(* notion 912 *)
+definition l_e_st_eq_landau_n_428_t28 ≝ (l_e_st_eq_landau_n_428_t11 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_times l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_428_id (l_e_st_eq_landau_n_428_t26 l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_428_t13 : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (l_e_st_eq_landau_n_times l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_428_id).
+
+(* notion 913 *)
+definition l_e_st_eq_landau_n_satz28c ≝ λx:l_e_st_eq_landau_n_nat.(l_e_fise l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_times l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_428_id l_e_st_eq_landau_n_428_t28 x : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 x) x).
+
+(* notion 914 *)
+definition l_e_st_eq_landau_n_428_t29 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_428_t11 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_times (l_e_st_eq_landau_n_suc x)) (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_times x y) y) (l_e_st_eq_landau_n_428_t26 (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_428_t23 x (l_e_st_eq_landau_n_428_b1 x) (l_e_st_eq_landau_n_times x) (l_e_st_eq_landau_n_428_t26 x)) : l_e_is (Πy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (l_e_st_eq_landau_n_times (l_e_st_eq_landau_n_suc x)) (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_times x y) y)).
+
+(* notion 915 *)
+definition l_e_st_eq_landau_n_satz28d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_fise l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_times (l_e_st_eq_landau_n_suc x)) (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_times x z) z) (l_e_st_eq_landau_n_428_t29 x) y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y)).
+
+(* notion 916 *)
+definition l_e_st_eq_landau_n_satz28e ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_satz28a x) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1)).
+
+(* notion 917 *)
+definition l_e_st_eq_landau_n_satz28f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) x) (l_e_st_eq_landau_n_satz28b x y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) x) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc y))).
+
+(* notion 918 *)
+definition l_e_st_eq_landau_n_satz28g ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 x) x (l_e_st_eq_landau_n_satz28c x) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 x)).
+
+(* notion 919 *)
+definition l_e_st_eq_landau_n_satz28h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y) (l_e_st_eq_landau_n_satz28d x y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc x) y)).
+
+(* notion 920 *)
+definition l_e_st_eq_landau_n_ists1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_ts u z) x y i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
+
+(* notion 921 *)
+definition l_e_st_eq_landau_n_ists2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_ts z u) x y i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
+
+(* notion 922 *)
+definition l_e_st_eq_landau_n_ists12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ists1 x y z i) (l_e_st_eq_landau_n_ists2 z u y j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 923 *)
+definition l_e_st_eq_landau_n_429_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x) : Prop).
+
+(* notion 924 *)
+definition l_e_st_eq_landau_n_429_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz28a y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts y l_e_st_eq_landau_n_1) y).
+
+(* notion 925 *)
+definition l_e_st_eq_landau_n_429_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz28c y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 y) y).
+
+(* notion 926 *)
+definition l_e_st_eq_landau_n_429_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_ts y l_e_st_eq_landau_n_1) y (l_e_st_eq_landau_n_429_t2 x y) (l_e_st_eq_landau_n_429_t1 x y) : l_e_st_eq_landau_n_429_prop1 l_e_st_eq_landau_n_1 y).
+
+(* notion 927 *)
+definition l_e_st_eq_landau_n_429_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_429_prop1 x y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y x) y) (l_e_st_eq_landau_n_ts y (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x) y p) (l_e_st_eq_landau_n_satz28f y x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y) (l_e_st_eq_landau_n_ts y (l_e_st_eq_landau_n_suc x))).
+
+(* notion 928 *)
+definition l_e_st_eq_landau_n_429_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_429_prop1 x y.(l_e_st_eq_landau_n_satz28d x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y)).
+
+(* notion 929 *)
+definition l_e_st_eq_landau_n_429_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_429_prop1 x y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc x) y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) y) (l_e_st_eq_landau_n_ts y (l_e_st_eq_landau_n_suc x)) (l_e_st_eq_landau_n_429_t5 x y p) (l_e_st_eq_landau_n_429_t4 x y p) : l_e_st_eq_landau_n_429_prop1 (l_e_st_eq_landau_n_suc x) y).
+
+(* notion 930 *)
+definition l_e_st_eq_landau_n_satz29 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_429_prop1 z y) (l_e_st_eq_landau_n_429_t3 x y) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_429_prop1 z y.l_e_st_eq_landau_n_429_t6 z y u) x : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x)).
+
+(* notion 931 *)
+definition l_e_st_eq_landau_n_comts ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz29 x y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x)).
+
+(* notion 932 *)
+definition l_e_st_eq_landau_n_429_t7 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_satz28a x) (l_e_st_eq_landau_n_satz28g x) : l_e_st_eq_landau_n_429_prop1 x l_e_st_eq_landau_n_1).
+
+(* notion 933 *)
+definition l_e_st_eq_landau_n_429_t8 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_429_prop1 x y.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y x) x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc y) x) (l_e_st_eq_landau_n_satz28b x y) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x) x p) (l_e_st_eq_landau_n_satz28h y x) : l_e_st_eq_landau_n_429_prop1 x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 934 *)
+definition l_e_st_eq_landau_n_429_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_429_prop1 x z) (l_e_st_eq_landau_n_429_t7 x) (λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_429_prop1 x z.l_e_st_eq_landau_n_429_t8 x z u) y : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts y x)).
+
+(* notion 935 *)
+definition l_e_st_eq_landau_n_430_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) : Prop).
+
+(* notion 936 *)
+definition l_e_st_eq_landau_n_430_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc y) x (l_e_st_eq_landau_n_satz4a y)) (l_e_st_eq_landau_n_satz28b x y) (l_e_st_eq_landau_n_ispl2 x (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_satz28e x)) : l_e_st_eq_landau_n_430_prop1 x y l_e_st_eq_landau_n_1).
+
+(* notion 937 *)
+definition l_e_st_eq_landau_n_430_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_430_prop1 x y z.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) x) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_pl y z)) x (l_e_st_eq_landau_n_satz4b y z)) (l_e_st_eq_landau_n_satz28b x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) x p) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) x)).
+
+(* notion 938 *)
+definition l_e_st_eq_landau_n_430_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_430_prop1 x y z.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) x)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_430_t2 x y z p) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z) x) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) x) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_suc z)) (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_satz28f x z)) : l_e_st_eq_landau_n_430_prop1 x y (l_e_st_eq_landau_n_suc z)).
+
+(* notion 939 *)
+definition l_e_st_eq_landau_n_satz30 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_430_prop1 x y u) (l_e_st_eq_landau_n_430_t1 x y) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_430_prop1 x y u.l_e_st_eq_landau_n_430_t3 x y u v) z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z))).
+
+(* notion 940 *)
+definition l_e_st_eq_landau_n_disttp1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_ts z (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_satz30 z x y) (l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_comts z x) (l_e_st_eq_landau_n_comts z y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z))).
+
+(* notion 941 *)
+definition l_e_st_eq_landau_n_disttp2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz30 x y z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z))).
+
+(* notion 942 *)
+definition l_e_st_eq_landau_n_distpt1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x y) z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_disttp1 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x y) z)).
+
+(* notion 943 *)
+definition l_e_st_eq_landau_n_distpt2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) (l_e_st_eq_landau_n_disttp2 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x z)) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl y z))).
+
+(* notion 944 *)
+definition l_e_st_eq_landau_n_431_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z)) : Prop).
+
+(* notion 945 *)
+definition l_e_st_eq_landau_n_431_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz28a (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_ists2 y (l_e_st_eq_landau_n_ts y l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_satz28e y)) : l_e_st_eq_landau_n_431_prop1 x y l_e_st_eq_landau_n_1).
+
+(* notion 946 *)
+definition l_e_st_eq_landau_n_431_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_431_prop1 x y z.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_suc z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y z) y)) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y (l_e_st_eq_landau_n_suc z))) (l_e_st_eq_landau_n_satz28b (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_ts x y) p) (l_e_st_eq_landau_n_distpt2 x (l_e_st_eq_landau_n_ts y z) y) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y z) y) (l_e_st_eq_landau_n_ts y (l_e_st_eq_landau_n_suc z)) x (l_e_st_eq_landau_n_satz28f y z)) : l_e_st_eq_landau_n_431_prop1 x y (l_e_st_eq_landau_n_suc z)).
+
+(* notion 947 *)
+definition l_e_st_eq_landau_n_satz31 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_431_prop1 x y u) (l_e_st_eq_landau_n_431_t1 x y) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_431_prop1 x y u.l_e_st_eq_landau_n_431_t2 x y u v) z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z))).
+
+(* notion 948 *)
+definition l_e_st_eq_landau_n_assts1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz31 x y z : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z))).
+
+(* notion 949 *)
+definition l_e_st_eq_landau_n_assts2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z) (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_assts1 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x y) z)).
+
+(* notion 950 *)
+definition l_e_st_eq_landau_n_432_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl y u) z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts u z)) (l_e_st_eq_landau_n_ists1 x (l_e_st_eq_landau_n_pl y u) z du) (l_e_st_eq_landau_n_disttp1 y u z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts u z))).
+
+(* notion 951 *)
+definition l_e_st_eq_landau_n_432_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λu:l_e_st_eq_landau_n_nat.λdu:l_e_st_eq_landau_n_diffprop x y u.(l_somei l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) v) (l_e_st_eq_landau_n_ts u z) (l_e_st_eq_landau_n_432_t1 x y z m u du) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
+
+(* notion 952 *)
+definition l_e_st_eq_landau_n_satz32a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y u) m (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_diffprop x y u.l_e_st_eq_landau_n_432_t2 x y z m u v) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
+
+(* notion 953 *)
+definition l_e_st_eq_landau_n_satz32b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ists1 x y z i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
+
+(* notion 954 *)
+definition l_e_st_eq_landau_n_satz32c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz11 (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_satz32a y x z (l_e_st_eq_landau_n_satz12 x y l)) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
+
+(* notion 955 *)
+definition l_e_st_eq_landau_n_432_anders1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz32a y x z l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
+
+(* notion 956 *)
+definition l_e_st_eq_landau_n_satz32d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_comts x z) (l_e_st_eq_landau_n_comts y z) (l_e_st_eq_landau_n_satz32a x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
+
+(* notion 957 *)
+definition l_e_st_eq_landau_n_satz32e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ists2 x y z i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
+
+(* notion 958 *)
+definition l_e_st_eq_landau_n_satz32f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_comts x z) (l_e_st_eq_landau_n_comts y z) (l_e_st_eq_landau_n_satz32c x y z l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
+
+(* notion 959 *)
+definition l_e_st_eq_landau_n_432_anders2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_satz32d y x z l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
+
+(* notion 960 *)
+definition l_e_st_eq_landau_n_satz32g ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore2 (l_e_st_eq_landau_n_ts x u) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ists1 x y u i) (l_e_st_eq_landau_n_satz32d z u x m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 961 *)
+definition l_e_st_eq_landau_n_satz32h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λm:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts u y) (l_e_st_eq_landau_n_comts x z) (l_e_st_eq_landau_n_comts y u) (l_e_st_eq_landau_n_satz32g x y z u i m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts u y)).
+
+(* notion 962 *)
+definition l_e_st_eq_landau_n_satz32j ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_ts x u) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ists1 x y u i) (l_e_st_eq_landau_n_satz32f z u x l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 963 *)
+definition l_e_st_eq_landau_n_satz32k ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.λl:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts u y) (l_e_st_eq_landau_n_comts x z) (l_e_st_eq_landau_n_comts y u) (l_e_st_eq_landau_n_satz32j x y z u i l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts u y)).
+
+(* notion 964 *)
+definition l_e_st_eq_landau_n_432_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_satz32a x y z n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
+
+(* notion 965 *)
+definition l_e_st_eq_landau_n_432_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_moreisi2 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ists1 x y z i) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
+
+(* notion 966 *)
+definition l_e_st_eq_landau_n_satz32l ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) m (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_432_t3 x y z m u) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_432_t4 x y z m u) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
+
+(* notion 967 *)
+definition l_e_st_eq_landau_n_satz32m ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.(l_e_st_eq_landau_n_ismoreis12 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_comts x z) (l_e_st_eq_landau_n_comts y z) (l_e_st_eq_landau_n_satz32l x y z m) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
+
+(* notion 968 *)
+definition l_e_st_eq_landau_n_satz32n ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_satz32l y x z (l_e_st_eq_landau_n_satz14 x y l)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
+
+(* notion 969 *)
+definition l_e_st_eq_landau_n_satz32o ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_satz32m y x z (l_e_st_eq_landau_n_satz14 x y l)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_ts z x) (l_e_st_eq_landau_n_ts z y)).
+
+(* notion 970 *)
+definition l_e_st_eq_landau_n_433_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz10a x y : l_or3 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y)).
+
+(* notion 971 *)
+definition l_e_st_eq_landau_n_433_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) : l_ec3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z))).
+
+(* notion 972 *)
+definition l_e_st_eq_landau_n_satz33a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z).(l_ec3_th11 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_433_t1 x y z) (l_e_st_eq_landau_n_433_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz32b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz32a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz32c x y z u) m : l_e_st_eq_landau_n_more x y).
+
+(* notion 973 *)
+definition l_e_st_eq_landau_n_satz33b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z).(l_ec3_th10 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_433_t1 x y z) (l_e_st_eq_landau_n_433_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz32b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz32a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz32c x y z u) i : l_e_st_eq_landau_n_is x y).
+
+(* notion 974 *)
+definition l_e_st_eq_landau_n_satz33c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z).(l_ec3_th12 (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_less x y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)) (l_e_st_eq_landau_n_433_t1 x y z) (l_e_st_eq_landau_n_433_t2 x y z) (λu:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz32b x y z u) (λu:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz32a x y z u) (λu:l_e_st_eq_landau_n_less x y.l_e_st_eq_landau_n_satz32c x y z u) l : l_e_st_eq_landau_n_less x y).
+
+(* notion 975 *)
+definition l_e_st_eq_landau_n_433_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z).(l_e_st_eq_landau_n_satz33a y x z l : l_e_st_eq_landau_n_less x y).
+
+(* notion 976 *)
+definition l_e_st_eq_landau_n_434_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_satz32a x y z m : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z)).
+
+(* notion 977 *)
+definition l_e_st_eq_landau_n_434_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts z y) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts u y) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_comts z y) (l_e_st_eq_landau_n_comts u y) (l_e_st_eq_landau_n_satz32a z u y n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 978 *)
+definition l_e_st_eq_landau_n_satz34 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_trmore (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_434_t1 x y z u m n) (l_e_st_eq_landau_n_434_t2 x y z u m n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 979 *)
+definition l_e_st_eq_landau_n_434_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_trmore (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_satz32a x y z m) (l_e_st_eq_landau_n_satz32d z u y n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 980 *)
+definition l_e_st_eq_landau_n_satz34a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz34 y x u z l k : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 981 *)
+definition l_e_st_eq_landau_n_434_andersa ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz11 (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_satz34 y x u z (l_e_st_eq_landau_n_satz12 x y l) (l_e_st_eq_landau_n_satz12 z u k)) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 982 *)
+definition l_e_st_eq_landau_n_satz35a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_more z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_satz34 x y z u v n) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_satz32g x y z u v n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 983 *)
+definition l_e_st_eq_landau_n_satz35b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more z u) (l_e_st_eq_landau_n_is z u) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)) n (λv:l_e_st_eq_landau_n_more z u.l_e_st_eq_landau_n_satz34 x y z u m v) (λv:l_e_st_eq_landau_n_is z u.l_e_st_eq_landau_n_satz32h z u x y v m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 984 *)
+definition l_e_st_eq_landau_n_satz35c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_less z u.(l_e_st_eq_landau_n_satz35a y x u z (l_e_st_eq_landau_n_satz14 x y l) k : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 985 *)
+definition l_e_st_eq_landau_n_satz35d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λk:l_e_st_eq_landau_n_lessis z u.(l_e_st_eq_landau_n_satz35b y x u z l (l_e_st_eq_landau_n_satz14 z u k) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 986 *)
+definition l_e_st_eq_landau_n_436_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_st_eq_landau_n_moreisi2 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ists1 x y z i) (l_e_st_eq_landau_n_ists2 z u y j)) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 987 *)
+definition l_e_st_eq_landau_n_436_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.λo:l_e_st_eq_landau_n_more z u.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_satz35a x y z u m o) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 988 *)
+definition l_e_st_eq_landau_n_436_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.(l_orapp (l_e_st_eq_landau_n_more z u) (l_e_st_eq_landau_n_is z u) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)) n (λv:l_e_st_eq_landau_n_more z u.l_e_st_eq_landau_n_436_t2 x y z u m n i v) (λv:l_e_st_eq_landau_n_is z u.l_e_st_eq_landau_n_436_t1 x y z u m n i v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 989 *)
+definition l_e_st_eq_landau_n_436_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λo:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_satz35b x y z u o n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 990 *)
+definition l_e_st_eq_landau_n_satz36 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_436_t4 x y z u m n v) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_436_t3 x y z u m n v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 991 *)
+definition l_e_st_eq_landau_n_436_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λo:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_moreisi1 (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_satz35b x y z u o n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 992 *)
+definition l_e_st_eq_landau_n_436_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_ismoreis2 (l_e_st_eq_landau_n_ts x u) (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ists1 x y u i) (l_e_st_eq_landau_n_satz32m z u x n) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 993 *)
+definition l_e_st_eq_landau_n_436_anders ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moreis x y.λn:l_e_st_eq_landau_n_moreis z u.(l_orapp (l_e_st_eq_landau_n_more x y) (l_e_st_eq_landau_n_is x y) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)) m (λv:l_e_st_eq_landau_n_more x y.l_e_st_eq_landau_n_436_t5 x y z u m n v) (λv:l_e_st_eq_landau_n_is x y.l_e_st_eq_landau_n_436_t6 x y z u m n v) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 994 *)
+definition l_e_st_eq_landau_n_satz36a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x y.λk:l_e_st_eq_landau_n_lessis z u.(l_e_st_eq_landau_n_satz13 (l_e_st_eq_landau_n_ts y u) (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_satz36 y x u z (l_e_st_eq_landau_n_satz14 x y l) (l_e_st_eq_landau_n_satz14 z u k)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_ts x z) (l_e_st_eq_landau_n_ts y u)).
+
+(* notion 995 *)
+definition l_e_st_eq_landau_n_mn_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_onei l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y z) (l_e_st_eq_landau_n_satz8b x y) m : l_e_st_eq_landau_n_one (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y z)).
+
+(* notion 996 *)
+definition l_e_st_eq_landau_n_mn ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_ind l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y z) (l_e_st_eq_landau_n_mn_t1 x y m) : l_e_st_eq_landau_n_nat).
+
+(* notion 997 *)
+definition l_e_st_eq_landau_n_mn_th1a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_oneax l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x y z) (l_e_st_eq_landau_n_mn_t1 x y m) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_mn x y m))).
+
+(* notion 998 *)
+definition l_e_st_eq_landau_n_mn_th1b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_mn x y m)) (l_e_st_eq_landau_n_mn_th1a x y m) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_mn x y m)) x).
+
+(* notion 999 *)
+definition l_e_st_eq_landau_n_mn_th1c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl y (l_e_st_eq_landau_n_mn x y m)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_mn x y m) y) (l_e_st_eq_landau_n_mn_th1a x y m) (l_e_st_eq_landau_n_compl y (l_e_st_eq_landau_n_mn x y m)) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_mn x y m) y)).
+
+(* notion 1000 *)
+definition l_e_st_eq_landau_n_mn_th1d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_mn x y m) y) (l_e_st_eq_landau_n_mn_th1c x y m) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_mn x y m) y) x).
+
+(* notion 1001 *)
+definition l_e_st_eq_landau_n_mn_th1e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl y z) x.(l_e_st_eq_landau_n_satz8b x y z (l_e_st_eq_landau_n_mn x y m) (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl y z) x i) (l_e_st_eq_landau_n_mn_th1a x y m) : l_e_st_eq_landau_n_is z (l_e_st_eq_landau_n_mn x y m)).
+
+(* notion 1002 *)
+definition l_e_st_eq_landau_n_mn_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x z.λn:l_e_st_eq_landau_n_more y u.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl u (l_e_st_eq_landau_n_mn x z m)) (l_e_st_eq_landau_n_pl z (l_e_st_eq_landau_n_mn x z m)) x y (l_e_st_eq_landau_n_ispl1 u z (l_e_st_eq_landau_n_mn x z m) (l_e_symis l_e_st_eq_landau_n_nat z u j)) (l_e_st_eq_landau_n_mn_th1b x z m) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl u (l_e_st_eq_landau_n_mn x z m)) y).
+
+(* notion 1003 *)
+definition l_e_st_eq_landau_n_ismn12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λz:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x z.λn:l_e_st_eq_landau_n_more y u.λi:l_e_st_eq_landau_n_is x y.λj:l_e_st_eq_landau_n_is z u.(l_e_st_eq_landau_n_mn_th1e y u (l_e_st_eq_landau_n_mn x z m) n (l_e_st_eq_landau_n_mn_t2 x y z u m n i j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_mn x z m) (l_e_st_eq_landau_n_mn y u n)).
+
+(* notion 1004 *)
+definition l_e_st_eq_landau_n_1to ≝ λn:l_e_st_eq_landau_n_nat.(l_e_ot l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis x n) : Type[0]).
+
+(* notion 1005 *)
+definition l_e_st_eq_landau_n_outn ≝ λn:l_e_st_eq_landau_n_nat.λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x n.(l_e_out l_e_st_eq_landau_n_nat (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis y n) x l : l_e_st_eq_landau_n_1to n).
+
+(* notion 1006 *)
+definition l_e_st_eq_landau_n_inn ≝ λn:l_e_st_eq_landau_n_nat.λxn:l_e_st_eq_landau_n_1to n.(l_e_in l_e_st_eq_landau_n_nat (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis y n) xn : l_e_st_eq_landau_n_nat).
+
+(* notion 1007 *)
+definition l_e_st_eq_landau_n_1top ≝ λn:l_e_st_eq_landau_n_nat.λxn:l_e_st_eq_landau_n_1to n.(l_e_inp l_e_st_eq_landau_n_nat (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis y n) xn : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_inn n xn) n).
+
+(* notion 1008 *)
+definition l_e_st_eq_landau_n_isoutni ≝ λn:l_e_st_eq_landau_n_nat.λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x n.λy:l_e_st_eq_landau_n_nat.λk:l_e_st_eq_landau_n_lessis y n.λi:l_e_st_eq_landau_n_is x y.(l_e_isouti l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis z n) x l y k i : l_e_is (l_e_st_eq_landau_n_1to n) (l_e_st_eq_landau_n_outn n x l) (l_e_st_eq_landau_n_outn n y k)).
+
+(* notion 1009 *)
+definition l_e_st_eq_landau_n_isoutne ≝ λn:l_e_st_eq_landau_n_nat.λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x n.λy:l_e_st_eq_landau_n_nat.λk:l_e_st_eq_landau_n_lessis y n.λi:l_e_is (l_e_st_eq_landau_n_1to n) (l_e_st_eq_landau_n_outn n x l) (l_e_st_eq_landau_n_outn n y k).(l_e_isoute l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis z n) x l y k i : l_e_st_eq_landau_n_is x y).
+
+(* notion 1010 *)
+definition l_e_st_eq_landau_n_isinni ≝ λn:l_e_st_eq_landau_n_nat.λxn:l_e_st_eq_landau_n_1to n.λyn:l_e_st_eq_landau_n_1to n.λi:l_e_is (l_e_st_eq_landau_n_1to n) xn yn.(l_e_isini l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis z n) xn yn i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_inn n xn) (l_e_st_eq_landau_n_inn n yn)).
+
+(* notion 1011 *)
+definition l_e_st_eq_landau_n_isinne ≝ λn:l_e_st_eq_landau_n_nat.λxn:l_e_st_eq_landau_n_1to n.λyn:l_e_st_eq_landau_n_1to n.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_inn n xn) (l_e_st_eq_landau_n_inn n yn).(l_e_isine l_e_st_eq_landau_n_nat (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis z n) xn yn i : l_e_is (l_e_st_eq_landau_n_1to n) xn yn).
+
+(* notion 1012 *)
+definition l_e_st_eq_landau_n_isoutinn ≝ λn:l_e_st_eq_landau_n_nat.λxn:l_e_st_eq_landau_n_1to n.(l_e_isoutin l_e_st_eq_landau_n_nat (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis y n) xn : l_e_is (l_e_st_eq_landau_n_1to n) xn (l_e_st_eq_landau_n_outn n (l_e_st_eq_landau_n_inn n xn) (l_e_st_eq_landau_n_1top n xn))).
+
+(* notion 1013 *)
+definition l_e_st_eq_landau_n_isinoutn ≝ λn:l_e_st_eq_landau_n_nat.λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x n.(l_e_isinout l_e_st_eq_landau_n_nat (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis y n) x l : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_inn n (l_e_st_eq_landau_n_outn n x l))).
+
+(* notion 1014 *)
+definition l_e_st_eq_landau_n_1o ≝ (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1).
+
+(* notion 1015 *)
+definition l_e_st_eq_landau_n_singlet_u0 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_inn l_e_st_eq_landau_n_1 u : l_e_st_eq_landau_n_nat).
+
+(* notion 1016 *)
+definition l_e_st_eq_landau_n_singlet_t1 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_1 u : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_singlet_u0 u) l_e_st_eq_landau_n_1).
+
+(* notion 1017 *)
+definition l_e_st_eq_landau_n_singlet_t2 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_ore2 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_singlet_u0 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_singlet_u0 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz24 (l_e_st_eq_landau_n_singlet_u0 u)) (l_e_st_eq_landau_n_satz10d (l_e_st_eq_landau_n_singlet_u0 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_singlet_t1 u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_singlet_u0 u) l_e_st_eq_landau_n_1).
+
+(* notion 1018 *)
+definition l_e_st_eq_landau_n_singlet_th1 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_tris (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) u (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_singlet_u0 u) (l_e_st_eq_landau_n_singlet_t1 u)) l_e_st_eq_landau_n_1o (l_e_st_eq_landau_n_isoutinn l_e_st_eq_landau_n_1 u) (l_e_st_eq_landau_n_isoutni l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_singlet_u0 u) (l_e_st_eq_landau_n_singlet_t1 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_singlet_t2 u)) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) u l_e_st_eq_landau_n_1o).
+
+(* notion 1019 *)
+definition l_e_st_eq_landau_n_2 ≝ (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
+
+(* notion 1020 *)
+definition l_e_st_eq_landau_n_pair_t1 ≝ λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x l_e_st_eq_landau_n_2.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_2.(l_e_st_eq_landau_n_satz26 l_e_st_eq_landau_n_1 x (l_ore1 (l_e_st_eq_landau_n_less x l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_2) l n) : l_e_st_eq_landau_n_lessis x l_e_st_eq_landau_n_1).
+
+(* notion 1021 *)
+definition l_e_st_eq_landau_n_pair_t2 ≝ λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x l_e_st_eq_landau_n_2.λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_2.(l_ore2 (l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz24 x) (l_e_st_eq_landau_n_satz10d x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pair_t1 x l n)) : l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1).
+
+(* notion 1022 *)
+definition l_e_st_eq_landau_n_pair_th1 ≝ λx:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis x l_e_st_eq_landau_n_2.(l_or_th2 (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_2) (λt:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_pair_t2 x l t) : l_or (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_2)).
+
+(* notion 1023 *)
+definition l_e_st_eq_landau_n_pair_th2 ≝ (l_e_notis_th1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_ax3 l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz4e l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_nis l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1).
+
+(* notion 1024 *)
+definition l_e_st_eq_landau_n_1t ≝ (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_2) : l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2).
+
+(* notion 1025 *)
+definition l_e_st_eq_landau_n_2t ≝ (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_2)) : l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2).
+
+(* notion 1026 *)
+definition l_e_st_eq_landau_n_pair_u0 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.(l_e_st_eq_landau_n_inn l_e_st_eq_landau_n_2 u : l_e_st_eq_landau_n_nat).
+
+(* notion 1027 *)
+definition l_e_st_eq_landau_n_pair_t3 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.(l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_2 u : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_2).
+
+(* notion 1028 *)
+definition l_e_st_eq_landau_n_pair_t4 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutni l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_2) i : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u)) l_e_st_eq_landau_n_1t).
+
+(* notion 1029 *)
+definition l_e_st_eq_landau_n_pair_t5 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_1.(l_e_tris (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u)) l_e_st_eq_landau_n_1t (l_e_st_eq_landau_n_isoutinn l_e_st_eq_landau_n_2 u) (l_e_st_eq_landau_n_pair_t4 u i) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t).
+
+(* notion 1030 *)
+definition l_e_st_eq_landau_n_pair_t6 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_2.(l_e_st_eq_landau_n_isoutni l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_2)) i : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u)) l_e_st_eq_landau_n_2t).
+
+(* notion 1031 *)
+definition l_e_st_eq_landau_n_pair_t7 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_2.(l_e_tris (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u (l_e_st_eq_landau_n_outn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u)) l_e_st_eq_landau_n_2t (l_e_st_eq_landau_n_isoutinn l_e_st_eq_landau_n_2 u) (l_e_st_eq_landau_n_pair_t6 u i) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t).
+
+(* notion 1032 *)
+definition l_e_st_eq_landau_n_pair_th3 ≝ λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.(l_or_th9 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_2) (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t) (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t) (l_e_st_eq_landau_n_pair_th1 (l_e_st_eq_landau_n_pair_u0 u) (l_e_st_eq_landau_n_pair_t3 u)) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_pair_t5 u t) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 u) l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_pair_t7 u t) : l_or (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t) (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t)).
+
+(* notion 1033 *)
+definition l_e_st_eq_landau_n_pair_t9 ≝ λi:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t.(l_e_isini l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_lessis x l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pair_u0 l_e_st_eq_landau_n_2t) (l_e_st_eq_landau_n_pair_u0 l_e_st_eq_landau_n_1t)).
+
+(* notion 1034 *)
+definition l_e_st_eq_landau_n_pair_t10 ≝ λi:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t.(l_e_tr3is l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_pair_u0 l_e_st_eq_landau_n_2t) (l_e_st_eq_landau_n_pair_u0 l_e_st_eq_landau_n_1t) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_pair_t9 i) (l_e_symis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pair_u0 l_e_st_eq_landau_n_1t) (l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_2))) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1).
+
+(* notion 1035 *)
+definition l_e_st_eq_landau_n_pair_th4 ≝ (l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t) (l_e_st_eq_landau_n_is l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_pair_th2 (λt:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t.l_e_st_eq_landau_n_pair_t10 t) : l_not (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t)).
+
+(* notion 1036 *)
+definition l_e_st_eq_landau_n_pair1type ≝ λalpha:Type[0].(Πx:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.alpha : Type[0]).
+
+(* notion 1037 *)
+definition l_e_st_eq_landau_n_pair1 ≝ λalpha:Type[0].λa:alpha.λb:alpha.(λx:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_ite (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) x l_e_st_eq_landau_n_1t) alpha a b : l_e_st_eq_landau_n_pair1type alpha).
+
+(* notion 1038 *)
+definition l_e_st_eq_landau_n_first1 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(p l_e_st_eq_landau_n_1t : alpha).
+
+(* notion 1039 *)
+definition l_e_st_eq_landau_n_second1 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(p l_e_st_eq_landau_n_2t : alpha).
+
+(* notion 1040 *)
+definition l_e_st_eq_landau_n_first1is1 ≝ λalpha:Type[0].λa:alpha.λb:alpha.(l_e_itet (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_1t l_e_st_eq_landau_n_1t) alpha a b (l_e_refis (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_1t) : l_e_is alpha (l_e_st_eq_landau_n_first1 alpha (l_e_st_eq_landau_n_pair1 alpha a b)) a).
+
+(* notion 1041 *)
+definition l_e_st_eq_landau_n_first1is2 ≝ λalpha:Type[0].λa:alpha.λb:alpha.(l_e_symis alpha (l_e_st_eq_landau_n_first1 alpha (l_e_st_eq_landau_n_pair1 alpha a b)) a (l_e_st_eq_landau_n_first1is1 alpha a b) : l_e_is alpha a (l_e_st_eq_landau_n_first1 alpha (l_e_st_eq_landau_n_pair1 alpha a b))).
+
+(* notion 1042 *)
+definition l_e_st_eq_landau_n_second1is1 ≝ λalpha:Type[0].λa:alpha.λb:alpha.(l_e_itef (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_2t l_e_st_eq_landau_n_1t) alpha a b l_e_st_eq_landau_n_pair_th4 : l_e_is alpha (l_e_st_eq_landau_n_second1 alpha (l_e_st_eq_landau_n_pair1 alpha a b)) b).
+
+(* notion 1043 *)
+definition l_e_st_eq_landau_n_second1is2 ≝ λalpha:Type[0].λa:alpha.λb:alpha.(l_e_symis alpha (l_e_st_eq_landau_n_second1 alpha (l_e_st_eq_landau_n_pair1 alpha a b)) b (l_e_st_eq_landau_n_second1is1 alpha a b) : l_e_is alpha b (l_e_st_eq_landau_n_second1 alpha (l_e_st_eq_landau_n_pair1 alpha a b))).
+
+(* notion 1044 *)
+definition l_e_st_eq_landau_n_pair_t11 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu1:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t.(l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) alpha p u l_e_st_eq_landau_n_1t u1 : l_e_is alpha (p u) (l_e_st_eq_landau_n_first1 alpha p)).
+
+(* notion 1045 *)
+definition l_e_st_eq_landau_n_pair_t12 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu1:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t.(l_e_symis alpha (q u) (l_e_st_eq_landau_n_first1 alpha q) (l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) alpha q u l_e_st_eq_landau_n_1t u1) : l_e_is alpha (l_e_st_eq_landau_n_first1 alpha q) (q u)).
+
+(* notion 1046 *)
+definition l_e_st_eq_landau_n_pair_t13 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu1:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t.(l_e_tr3is alpha (p u) (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q) (q u) (l_e_st_eq_landau_n_pair_t11 alpha p q i j u u1) i (l_e_st_eq_landau_n_pair_t12 alpha p q i j u u1) : l_e_is alpha (p u) (q u)).
+
+(* notion 1047 *)
+definition l_e_st_eq_landau_n_pair_t14 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu2:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t.(l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) alpha p u l_e_st_eq_landau_n_2t u2 : l_e_is alpha (p u) (l_e_st_eq_landau_n_second1 alpha p)).
+
+(* notion 1048 *)
+definition l_e_st_eq_landau_n_pair_t15 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu2:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t.(l_e_symis alpha (q u) (l_e_st_eq_landau_n_second1 alpha q) (l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) alpha q u l_e_st_eq_landau_n_2t u2) : l_e_is alpha (l_e_st_eq_landau_n_second1 alpha q) (q u)).
+
+(* notion 1049 *)
+definition l_e_st_eq_landau_n_pair_t16 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.λu2:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t.(l_e_tr3is alpha (p u) (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q) (q u) (l_e_st_eq_landau_n_pair_t14 alpha p q i j u u2) j (l_e_st_eq_landau_n_pair_t15 alpha p q i j u u2) : l_e_is alpha (p u) (q u)).
+
+(* notion 1050 *)
+definition l_e_st_eq_landau_n_pair_t17 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.(l_orapp (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t) (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t) (l_e_is alpha (p u) (q u)) (l_e_st_eq_landau_n_pair_th3 u) (λt:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_1t.l_e_st_eq_landau_n_pair_t13 alpha p q i j u t) (λt:l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) u l_e_st_eq_landau_n_2t.l_e_st_eq_landau_n_pair_t16 alpha p q i j u t) : l_e_is alpha (p u) (q u)).
+
+(* notion 1051 *)
+definition l_e_st_eq_landau_n_pair_th5 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.λq:l_e_st_eq_landau_n_pair1type alpha.λi:l_e_is alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_first1 alpha q).λj:l_e_is alpha (l_e_st_eq_landau_n_second1 alpha p) (l_e_st_eq_landau_n_second1 alpha q).(l_e_fisi (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) alpha p q (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_pair_t17 alpha p q i j t) : l_e_is (l_e_st_eq_landau_n_pair1type alpha) p q).
+
+(* notion 1052 *)
+definition l_e_st_eq_landau_n_pair_q0 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(l_e_st_eq_landau_n_pair1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p) : l_e_st_eq_landau_n_pair1type alpha).
+
+(* notion 1053 *)
+definition l_e_st_eq_landau_n_pair_t18 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(l_e_st_eq_landau_n_first1is1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p) : l_e_is alpha (l_e_st_eq_landau_n_first1 alpha (l_e_st_eq_landau_n_pair_q0 alpha p)) (l_e_st_eq_landau_n_first1 alpha p)).
+
+(* notion 1054 *)
+definition l_e_st_eq_landau_n_pair_t19 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(l_e_st_eq_landau_n_second1is1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p) : l_e_is alpha (l_e_st_eq_landau_n_second1 alpha (l_e_st_eq_landau_n_pair_q0 alpha p)) (l_e_st_eq_landau_n_second1 alpha p)).
+
+(* notion 1055 *)
+definition l_e_st_eq_landau_n_pair1is1 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(l_e_st_eq_landau_n_pair_th5 alpha (l_e_st_eq_landau_n_pair_q0 alpha p) p (l_e_st_eq_landau_n_pair_t18 alpha p) (l_e_st_eq_landau_n_pair_t19 alpha p) : l_e_is (l_e_st_eq_landau_n_pair1type alpha) (l_e_st_eq_landau_n_pair1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p)) p).
+
+(* notion 1056 *)
+definition l_e_st_eq_landau_n_pair1is2 ≝ λalpha:Type[0].λp:l_e_st_eq_landau_n_pair1type alpha.(l_e_symis (l_e_st_eq_landau_n_pair1type alpha) (l_e_st_eq_landau_n_pair1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p)) p (l_e_st_eq_landau_n_pair1is1 alpha p) : l_e_is (l_e_st_eq_landau_n_pair1type alpha) p (l_e_st_eq_landau_n_pair1 alpha (l_e_st_eq_landau_n_first1 alpha p) (l_e_st_eq_landau_n_second1 alpha p))).
+
+(* notion 1057 *)
+definition l_e_st_eq_landau_n_lessisi3 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_lessisi2 x x (l_e_refis l_e_st_eq_landau_n_nat x) : l_e_st_eq_landau_n_lessis x x).
+
+(* notion 1058 *)
+definition l_e_st_eq_landau_n_1out ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a x) : l_e_st_eq_landau_n_1to x).
+
+(* notion 1059 *)
+definition l_e_st_eq_landau_n_xout ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_outn x x (l_e_st_eq_landau_n_lessisi3 x) : l_e_st_eq_landau_n_1to x).
+
+(* notion 1060 *)
+definition l_e_st_eq_landau_n_left_ui ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_inn y u : l_e_st_eq_landau_n_nat).
+
+(* notion 1061 *)
+definition l_e_st_eq_landau_n_left_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_1top y u : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_left_ui x y l u) y).
+
+(* notion 1062 *)
+definition l_e_st_eq_landau_n_left_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_left_ui x y l u) y x (l_e_st_eq_landau_n_left_t1 x y l u) l : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_left_ui x y l u) x).
+
+(* notion 1063 *)
+definition l_e_st_eq_landau_n_left1to ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_left_ui x y l u) (l_e_st_eq_landau_n_left_t2 x y l u) : l_e_st_eq_landau_n_1to x).
+
+(* notion 1064 *)
+definition l_e_st_eq_landau_n_left_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l u) (l_e_st_eq_landau_n_left1to x y l v).(l_e_st_eq_landau_n_isoutne x (l_e_st_eq_landau_n_left_ui x y l u) (l_e_st_eq_landau_n_left_t2 x y l u) (l_e_st_eq_landau_n_left_ui x y l v) (l_e_st_eq_landau_n_left_t2 x y l v) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_left_ui x y l u) (l_e_st_eq_landau_n_left_ui x y l v)).
+
+(* notion 1065 *)
+definition l_e_st_eq_landau_n_thleft1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l u) (l_e_st_eq_landau_n_left1to x y l v).(l_e_st_eq_landau_n_isinne y u v (l_e_st_eq_landau_n_left_t3 x y l u v i) : l_e_is (l_e_st_eq_landau_n_1to y) u v).
+
+(* notion 1066 *)
+definition l_e_st_eq_landau_n_thleft2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.(λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λt:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l u) (l_e_st_eq_landau_n_left1to x y l v).l_e_st_eq_landau_n_thleft1 x y l u v t : l_e_injective (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_left1to x y l t)).
+
+(* notion 1067 *)
+definition l_e_st_eq_landau_n_right_ui ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_inn y u : l_e_st_eq_landau_n_nat).
+
+(* notion 1068 *)
+definition l_e_st_eq_landau_n_right_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_1top y u : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_right_ui x y u) y).
+
+(* notion 1069 *)
+definition l_e_st_eq_landau_n_right_t5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_right_ui x y u) y x (l_e_st_eq_landau_n_right_t4 x y u) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y u)) (l_e_st_eq_landau_n_pl x y)).
+
+(* notion 1070 *)
+definition l_e_st_eq_landau_n_right1to ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y u)) (l_e_st_eq_landau_n_right_t5 x y u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y)).
+
+(* notion 1071 *)
+definition l_e_st_eq_landau_n_right_t6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_right1to x y u) (l_e_st_eq_landau_n_right1to x y v).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y u)) (l_e_st_eq_landau_n_right_t5 x y u) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y v)) (l_e_st_eq_landau_n_right_t5 x y v) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y u)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_right_ui x y v))).
+
+(* notion 1072 *)
+definition l_e_st_eq_landau_n_right_t7 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_right1to x y u) (l_e_st_eq_landau_n_right1to x y v).(l_e_st_eq_landau_n_satz20e (l_e_st_eq_landau_n_right_ui x y u) (l_e_st_eq_landau_n_right_ui x y v) x (l_e_st_eq_landau_n_right_t6 x y u v i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_right_ui x y u) (l_e_st_eq_landau_n_right_ui x y v)).
+
+(* notion 1073 *)
+definition l_e_st_eq_landau_n_thright1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to y.λv:l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_right1to x y u) (l_e_st_eq_landau_n_right1to x y v).(l_e_st_eq_landau_n_isinne y u v (l_e_st_eq_landau_n_right_t7 x y u v i) : l_e_is (l_e_st_eq_landau_n_1to y) u v).
+
+(* notion 1074 *)
+definition l_e_st_eq_landau_n_left ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.alpha.(λt:l_e_st_eq_landau_n_1to y.f (l_e_st_eq_landau_n_left1to x y l t) : Πt:l_e_st_eq_landau_n_1to y.alpha).
+
+(* notion 1075 *)
+definition l_e_st_eq_landau_n_right ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).alpha.(λt:l_e_st_eq_landau_n_1to y.f (l_e_st_eq_landau_n_right1to x y t) : Πt:l_e_st_eq_landau_n_1to y.alpha).
+
+(* notion 1076 *)
+definition l_e_st_eq_landau_n_left_t4 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.(l_e_st_eq_landau_n_lessisi2 y x i : l_e_st_eq_landau_n_lessis y x).
+
+(* notion 1077 *)
+definition l_e_st_eq_landau_n_left_t5 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.(l_e_st_eq_landau_n_lessisi2 x y (l_e_symis l_e_st_eq_landau_n_nat y x i) : l_e_st_eq_landau_n_lessis x y).
+
+(* notion 1078 *)
+definition l_e_st_eq_landau_n_left_f1 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.(l_e_st_eq_landau_n_left alpha y x (l_e_st_eq_landau_n_left_t5 alpha x y i f) f : Πt:l_e_st_eq_landau_n_1to x.alpha).
+
+(* notion 1079 *)
+definition l_e_st_eq_landau_n_left_f2 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.(l_e_st_eq_landau_n_left alpha x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) (l_e_st_eq_landau_n_left_f1 alpha x y i f) : Πt:l_e_st_eq_landau_n_1to y.alpha).
+
+(* notion 1080 *)
+definition l_e_st_eq_landau_n_left_t6 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.λu:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_inn y u) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_inn y u) y x (l_e_st_eq_landau_n_1top y u) (l_e_st_eq_landau_n_left_t4 alpha x y i f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_inn y u) (l_e_st_eq_landau_n_inn x (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u))).
+
+(* notion 1081 *)
+definition l_e_st_eq_landau_n_left_t7 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.λu:l_e_st_eq_landau_n_1to y.(l_e_tris (l_e_st_eq_landau_n_1to y) u (l_e_st_eq_landau_n_outn y (l_e_st_eq_landau_n_inn y u) (l_e_st_eq_landau_n_1top y u)) (l_e_st_eq_landau_n_left1to y x (l_e_st_eq_landau_n_left_t5 alpha x y i f) (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u)) (l_e_st_eq_landau_n_isoutinn y u) (l_e_st_eq_landau_n_isoutni y (l_e_st_eq_landau_n_inn y u) (l_e_st_eq_landau_n_1top y u) (l_e_st_eq_landau_n_inn x (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_inn x (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u)) x y (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u)) (l_e_st_eq_landau_n_left_t5 alpha x y i f)) (l_e_st_eq_landau_n_left_t6 alpha x y i f u)) : l_e_is (l_e_st_eq_landau_n_1to y) u (l_e_st_eq_landau_n_left1to y x (l_e_st_eq_landau_n_left_t5 alpha x y i f) (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u))).
+
+(* notion 1082 *)
+definition l_e_st_eq_landau_n_left_t8 ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.λu:l_e_st_eq_landau_n_1to y.(l_e_isf (l_e_st_eq_landau_n_1to y) alpha f u (l_e_st_eq_landau_n_left1to y x (l_e_st_eq_landau_n_left_t5 alpha x y i f) (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_left_t4 alpha x y i f) u)) (l_e_st_eq_landau_n_left_t7 alpha x y i f u) : l_e_is alpha (f u) (l_e_st_eq_landau_n_left_f2 alpha x y i f u)).
+
+(* notion 1083 *)
+definition l_e_st_eq_landau_n_thleft ≝ λalpha:Type[0].λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.λf:Πt:l_e_st_eq_landau_n_1to y.alpha.(l_e_fisi (l_e_st_eq_landau_n_1to y) alpha f (l_e_st_eq_landau_n_left_f2 alpha x y i f) (λt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_left_t8 alpha x y i f t) : l_e_is (Πt:l_e_st_eq_landau_n_1to y.alpha) f (l_e_st_eq_landau_n_left alpha x y (l_e_st_eq_landau_n_lessisi2 y x i) (l_e_st_eq_landau_n_left alpha y x (l_e_st_eq_landau_n_lessisi2 x y (l_e_symis l_e_st_eq_landau_n_nat y x i)) f))).
+
+(* notion 1084 *)
+definition l_e_st_eq_landau_n_frac ≝ (l_e_st_eq_landau_n_pair1type l_e_st_eq_landau_n_nat : Type[0]).
+
+(* notion 1085 *)
+definition l_e_st_eq_landau_n_fr ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pair1 l_e_st_eq_landau_n_nat x1 x2 : l_e_st_eq_landau_n_frac).
+
+(* notion 1086 *)
+definition l_e_st_eq_landau_n_num ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_first1 l_e_st_eq_landau_n_nat x : l_e_st_eq_landau_n_nat).
+
+(* notion 1087 *)
+definition l_e_st_eq_landau_n_den ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_second1 l_e_st_eq_landau_n_nat x : l_e_st_eq_landau_n_nat).
+
+(* notion 1088 *)
+definition l_e_st_eq_landau_n_numis ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_first1is1 l_e_st_eq_landau_n_nat x1 x2 : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) x1).
+
+(* notion 1089 *)
+definition l_e_st_eq_landau_n_isnum ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_first1is2 l_e_st_eq_landau_n_nat x1 x2 : l_e_st_eq_landau_n_is x1 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2))).
+
+(* notion 1090 *)
+definition l_e_st_eq_landau_n_denis ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_second1is1 l_e_st_eq_landau_n_nat x1 x2 : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) x2).
+
+(* notion 1091 *)
+definition l_e_st_eq_landau_n_isden ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_second1is2 l_e_st_eq_landau_n_nat x1 x2 : l_e_st_eq_landau_n_is x2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))).
+
+(* notion 1092 *)
+definition l_e_st_eq_landau_n_1x ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_num x : l_e_st_eq_landau_n_nat).
+
+(* notion 1093 *)
+definition l_e_st_eq_landau_n_2x ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_den x : l_e_st_eq_landau_n_nat).
+
+(* notion 1094 *)
+definition l_e_st_eq_landau_n_fris ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_pair1is1 l_e_st_eq_landau_n_nat x : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) x).
+
+(* notion 1095 *)
+definition l_e_st_eq_landau_n_isfr ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_pair1is2 l_e_st_eq_landau_n_nat x : l_e_is l_e_st_eq_landau_n_frac x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1096 *)
+definition l_e_st_eq_landau_n_12isnd ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists12 x1 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) y2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_isnum x1 x2) (l_e_st_eq_landau_n_isden y1 y2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2)))).
+
+(* notion 1097 *)
+definition l_e_st_eq_landau_n_ndis12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_12isnd x1 x2 y1 y2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x1 y2)).
+
+(* notion 1098 *)
+definition l_e_st_eq_landau_n_1disnd ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists1 n1 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_isnum n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1099 *)
+definition l_e_st_eq_landau_n_ndis1d ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_1disnd x n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1100 *)
+definition l_e_st_eq_landau_n_n2isnd ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists2 n2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_isden n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)))).
+
+(* notion 1101 *)
+definition l_e_st_eq_landau_n_ndisn2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_n2isnd x n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)).
+
+(* notion 1102 *)
+definition l_e_st_eq_landau_n_isn ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x1 n.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_fr t x2) x1 n i : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr n x2)).
+
+(* notion 1103 *)
+definition l_e_st_eq_landau_n_isd ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x2 n.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_fr x1 t) x2 n i : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr x1 n)).
+
+(* notion 1104 *)
+definition l_e_st_eq_landau_n_isnd ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x1 y1.λj:l_e_st_eq_landau_n_is x2 y2.(l_e_tris l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 x2) (l_e_st_eq_landau_n_fr y1 y2) (l_e_st_eq_landau_n_isn x1 x2 y1 i) (l_e_st_eq_landau_n_isd y1 x2 y2 j) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)).
+
+(* notion 1105 *)
+definition l_e_st_eq_landau_n_1y ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_num y : l_e_st_eq_landau_n_nat).
+
+(* notion 1106 *)
+definition l_e_st_eq_landau_n_2y ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_den y : l_e_st_eq_landau_n_nat).
+
+(* notion 1107 *)
+definition l_e_st_eq_landau_n_eq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : Prop).
+
+(* notion 1108 *)
+definition l_e_st_eq_landau_n_eqi12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_ndis12 x1 x2 y1 y2) i (l_e_st_eq_landau_n_12isnd y1 y2 x1 x2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)).
+
+(* notion 1109 *)
+definition l_e_st_eq_landau_n_eqi1 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)).(l_e_isp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq t (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) x (l_e_st_eq_landau_n_eqi12 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x) n1 n2 i) (l_e_st_eq_landau_n_fris x) : l_e_st_eq_landau_n_eq x (l_e_st_eq_landau_n_fr n1 n2)).
+
+(* notion 1110 *)
+definition l_e_st_eq_landau_n_eqi2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2).(l_e_isp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr n1 n2) t) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) x (l_e_st_eq_landau_n_eqi12 n1 n2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x) i) (l_e_st_eq_landau_n_fris x) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr n1 n2) x).
+
+(* notion 1111 *)
+definition l_e_st_eq_landau_n_satz37 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) : l_e_st_eq_landau_n_eq x x).
+
+(* notion 1112 *)
+definition l_e_st_eq_landau_n_refeq ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz37 x : l_e_st_eq_landau_n_eq x x).
+
+(* notion 1113 *)
+definition l_e_st_eq_landau_n_refeq1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λi:l_e_is l_e_st_eq_landau_n_frac x y.(l_e_isp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq x t) x y (l_e_st_eq_landau_n_refeq x) i : l_e_st_eq_landau_n_eq x y).
+
+(* notion 1114 *)
+definition l_e_st_eq_landau_n_refeq2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λi:l_e_is l_e_st_eq_landau_n_frac x y.(l_e_isp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq t x) x y (l_e_st_eq_landau_n_refeq x) i : l_e_st_eq_landau_n_eq y x).
+
+(* notion 1115 *)
+definition l_e_st_eq_landau_n_eqnd ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x1 y1.λj:l_e_st_eq_landau_n_is x2 y2.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2) (l_e_st_eq_landau_n_isnd x1 x2 y1 y2 i j) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)).
+
+(* notion 1116 *)
+definition l_e_st_eq_landau_n_eqn ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x1 n.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr n x2) (l_e_st_eq_landau_n_isn x1 x2 n i) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr n x2)).
+
+(* notion 1117 *)
+definition l_e_st_eq_landau_n_eqd ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x2 n.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr x1 n) (l_e_st_eq_landau_n_isd x1 x2 n i) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr x1 n)).
+
+(* notion 1118 *)
+definition l_e_st_eq_landau_n_satz38 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) e : l_e_st_eq_landau_n_eq y x).
+
+(* notion 1119 *)
+definition l_e_st_eq_landau_n_symeq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_satz38 x y e : l_e_st_eq_landau_n_eq y x).
+
+(* notion 1120 *)
+definition l_e_st_eq_landau_n_ii1_t1 ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts b c) d) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts b c)) (l_e_st_eq_landau_n_assts2 b c d) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_ts b c) d) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts b c))).
+
+(* notion 1121 *)
+definition l_e_st_eq_landau_n_stets ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_nat.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d))) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts b c))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_ts b c)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_ts c b)) (l_e_st_eq_landau_n_assts1 a b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts b c)) a (l_e_st_eq_landau_n_ii1_t1 a b c d)) (l_e_st_eq_landau_n_assts2 a d (l_e_st_eq_landau_n_ts b c)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts b c) (l_e_st_eq_landau_n_ts c b) (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_comts b c)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_ts c b))).
+
+(* notion 1122 *)
+definition l_e_st_eq_landau_n_ii1_t2 ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts c d) b) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts d c) b) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts c b)) (l_e_st_eq_landau_n_comts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_ts c d) (l_e_st_eq_landau_n_ts d c) b (l_e_st_eq_landau_n_comts c d)) (l_e_st_eq_landau_n_assts1 d c b) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts c b))).
+
+(* notion 1123 *)
+definition l_e_st_eq_landau_n_ii1_anders ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d))) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts c b))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_ts c b)) (l_e_st_eq_landau_n_assts1 a b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts b (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts d (l_e_st_eq_landau_n_ts c b)) a (l_e_st_eq_landau_n_ii1_t2 a b c d)) (l_e_st_eq_landau_n_assts2 a d (l_e_st_eq_landau_n_ts c b)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a d) (l_e_st_eq_landau_n_ts c b))).
+
+(* notion 1124 *)
+definition l_e_st_eq_landau_n_1z ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_num z : l_e_st_eq_landau_n_nat).
+
+(* notion 1125 *)
+definition l_e_st_eq_landau_n_2z ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_den z : l_e_st_eq_landau_n_nat).
+
+(* notion 1126 *)
+definition l_e_st_eq_landau_n_139_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) e f : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1127 *)
+definition l_e_st_eq_landau_n_139_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1128 *)
+definition l_e_st_eq_landau_n_139_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1129 *)
+definition l_e_st_eq_landau_n_139_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_139_t2 x y z e f)) (l_e_st_eq_landau_n_139_t1 x y z e f) (l_e_st_eq_landau_n_139_t3 x y z e f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1130 *)
+definition l_e_st_eq_landau_n_satz39 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_st_eq_landau_n_satz33b (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_139_t4 x y z e f) : l_e_st_eq_landau_n_eq x z).
+
+(* notion 1131 *)
+definition l_e_st_eq_landau_n_139_anders ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) e f) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1132 *)
+definition l_e_st_eq_landau_n_treq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_e_st_eq_landau_n_satz39 x y z e f : l_e_st_eq_landau_n_eq x z).
+
+(* notion 1133 *)
+definition l_e_st_eq_landau_n_treq1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq z x.λf:l_e_st_eq_landau_n_eq z y.(l_e_st_eq_landau_n_treq x z y (l_e_st_eq_landau_n_symeq z x e) f : l_e_st_eq_landau_n_eq x y).
+
+(* notion 1134 *)
+definition l_e_st_eq_landau_n_treq2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y z.(l_e_st_eq_landau_n_treq x z y e (l_e_st_eq_landau_n_symeq y z f) : l_e_st_eq_landau_n_eq x y).
+
+(* notion 1135 *)
+definition l_e_st_eq_landau_n_tr3eq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.λg:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_treq x y u e (l_e_st_eq_landau_n_treq y z u f g) : l_e_st_eq_landau_n_eq x u).
+
+(* notion 1136 *)
+definition l_e_st_eq_landau_n_tr4eq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.λg:l_e_st_eq_landau_n_eq z u.λh:l_e_st_eq_landau_n_eq u v.(l_e_st_eq_landau_n_tr3eq x y z v e f (l_e_st_eq_landau_n_treq z u v g h) : l_e_st_eq_landau_n_eq x v).
+
+(* notion 1137 *)
+definition l_e_st_eq_landau_n_satz40 ≝ λx:l_e_st_eq_landau_n_frac.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_eqi1 x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts n (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n) (l_e_st_eq_landau_n_ts n (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2x x) n)) (l_e_st_eq_landau_n_assts2 (l_e_st_eq_landau_n_1x x) n (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_eq x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n))).
+
+(* notion 1138 *)
+definition l_e_st_eq_landau_n_satz40a ≝ λx:l_e_st_eq_landau_n_frac.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_symeq x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n)) (l_e_st_eq_landau_n_satz40 x n) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n)) x).
+
+(* notion 1139 *)
+definition l_e_st_eq_landau_n_satz40b ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_eqi12 x1 x2 (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x1 (l_e_st_eq_landau_n_ts x2 n)) (l_e_st_eq_landau_n_ts x1 (l_e_st_eq_landau_n_ts n x2)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x1 n) x2) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts x2 n) (l_e_st_eq_landau_n_ts n x2) x1 (l_e_st_eq_landau_n_comts x2 n)) (l_e_st_eq_landau_n_assts2 x1 n x2)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n))).
+
+(* notion 1140 *)
+definition l_e_st_eq_landau_n_satz40c ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n)) (l_e_st_eq_landau_n_satz40b x1 x2 n) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n)) (l_e_st_eq_landau_n_fr x1 x2)).
+
+(* notion 1141 *)
+definition l_e_st_eq_landau_n_moref ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : Prop).
+
+(* notion 1142 *)
+definition l_e_st_eq_landau_n_lessf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : Prop).
+
+(* notion 1143 *)
+definition l_e_st_eq_landau_n_morefi12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2).(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts y1 x2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_12isnd x1 x2 y1 y2) (l_e_st_eq_landau_n_12isnd y1 y2 x1 x2) m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)).
+
+(* notion 1144 *)
+definition l_e_st_eq_landau_n_lessfi12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2).(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts y1 x2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_12isnd x1 x2 y1 y2) (l_e_st_eq_landau_n_12isnd y1 y2 x1 x2) l : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)).
+
+(* notion 1145 *)
+definition l_e_st_eq_landau_n_morefi1 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)).(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_n2isnd x n1 n2) (l_e_st_eq_landau_n_1disnd x n1 n2) m : l_e_st_eq_landau_n_moref x (l_e_st_eq_landau_n_fr n1 n2)).
+
+(* notion 1146 *)
+definition l_e_st_eq_landau_n_morefi2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2).(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_1disnd x n1 n2) (l_e_st_eq_landau_n_n2isnd x n1 n2) m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr n1 n2) x).
+
+(* notion 1147 *)
+definition l_e_st_eq_landau_n_lessfi1 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)).(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_n2isnd x n1 n2) (l_e_st_eq_landau_n_1disnd x n1 n2) l : l_e_st_eq_landau_n_lessf x (l_e_st_eq_landau_n_fr n1 n2)).
+
+(* notion 1148 *)
+definition l_e_st_eq_landau_n_lessfi2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2).(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_1disnd x n1 n2) (l_e_st_eq_landau_n_n2isnd x n1 n2) l : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr n1 n2) x).
+
+(* notion 1149 *)
+definition l_e_st_eq_landau_n_satz41 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz10 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : l_orec3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y)).
+
+(* notion 1150 *)
+definition l_e_st_eq_landau_n_satz41a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz10a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : l_or3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y)).
+
+(* notion 1151 *)
+definition l_e_st_eq_landau_n_satz41b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : l_ec3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y)).
+
+(* notion 1152 *)
+definition l_e_st_eq_landau_n_satz42 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz11 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) m : l_e_st_eq_landau_n_lessf y x).
+
+(* notion 1153 *)
+definition l_e_st_eq_landau_n_satz43 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_satz12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) l : l_e_st_eq_landau_n_moref y x).
+
+(* notion 1154 *)
+definition l_e_st_eq_landau_n_1u ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_num u : l_e_st_eq_landau_n_nat).
+
+(* notion 1155 *)
+definition l_e_st_eq_landau_n_2u ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_den u : l_e_st_eq_landau_n_nat).
+
+(* notion 1156 *)
+definition l_e_st_eq_landau_n_244_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) f (l_e_st_eq_landau_n_symeq x z e) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)))).
+
+(* notion 1157 *)
+definition l_e_st_eq_landau_n_244_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_244_t1 x y z u m e f) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1158 *)
+definition l_e_st_eq_landau_n_244_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_244_t2 x y z u m e f)) (l_e_st_eq_landau_n_satz32d (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1159 *)
+definition l_e_st_eq_landau_n_satz44 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_e_st_eq_landau_n_satz33a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_244_t3 x y z u m e f)) : l_e_st_eq_landau_n_moref z u).
+
+(* notion 1160 *)
+definition l_e_st_eq_landau_n_eqmoref12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.λm:l_e_st_eq_landau_n_moref x z.(l_e_st_eq_landau_n_satz44 x z y u m e f : l_e_st_eq_landau_n_moref y u).
+
+(* notion 1161 *)
+definition l_e_st_eq_landau_n_eqmoref1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref x z.(l_e_st_eq_landau_n_satz44 x z y z m e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_moref y z).
+
+(* notion 1162 *)
+definition l_e_st_eq_landau_n_eqmoref2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref z x.(l_e_st_eq_landau_n_satz44 z x z y m (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_moref z y).
+
+(* notion 1163 *)
+definition l_e_st_eq_landau_n_satz45 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_e_st_eq_landau_n_satz42 u z (l_e_st_eq_landau_n_satz44 y x u z (l_e_st_eq_landau_n_satz43 x y l) f e) : l_e_st_eq_landau_n_lessf z u).
+
+(* notion 1164 *)
+definition l_e_st_eq_landau_n_eqlessf12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.λl:l_e_st_eq_landau_n_lessf x z.(l_e_st_eq_landau_n_satz45 x z y u l e f : l_e_st_eq_landau_n_lessf y u).
+
+(* notion 1165 *)
+definition l_e_st_eq_landau_n_eqlessf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf x z.(l_e_st_eq_landau_n_satz45 x z y z l e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_lessf y z).
+
+(* notion 1166 *)
+definition l_e_st_eq_landau_n_eqlessf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf z x.(l_e_st_eq_landau_n_satz45 z x z y l (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_lessf z y).
+
+(* notion 1167 *)
+definition l_e_st_eq_landau_n_moreq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_or (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) : Prop).
+
+(* notion 1168 *)
+definition l_e_st_eq_landau_n_lesseq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_or (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) : Prop).
+
+(* notion 1169 *)
+definition l_e_st_eq_landau_n_moreqi2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_ori2 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) e : l_e_st_eq_landau_n_moreq x y).
+
+(* notion 1170 *)
+definition l_e_st_eq_landau_n_lesseqi2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_ori2 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) e : l_e_st_eq_landau_n_lesseq x y).
+
+(* notion 1171 *)
+definition l_e_st_eq_landau_n_moreqi1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_ori1 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) m : l_e_st_eq_landau_n_moreq x y).
+
+(* notion 1172 *)
+definition l_e_st_eq_landau_n_lesseqi1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_ori1 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) l : l_e_st_eq_landau_n_lesseq x y).
+
+(* notion 1173 *)
+definition l_e_st_eq_landau_n_satz41c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.(l_ec3_th7 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) (l_comor (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) m) : l_not (l_e_st_eq_landau_n_lessf x y)).
+
+(* notion 1174 *)
+definition l_e_st_eq_landau_n_satz41d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.(l_ec3_th9 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) l : l_not (l_e_st_eq_landau_n_moref x y)).
+
+(* notion 1175 *)
+definition l_e_st_eq_landau_n_satz41e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λn:l_not (l_e_st_eq_landau_n_moref x y).(l_or3_th2 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41a x y) n : l_e_st_eq_landau_n_lesseq x y).
+
+(* notion 1176 *)
+definition l_e_st_eq_landau_n_satz41f ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λn:l_not (l_e_st_eq_landau_n_lessf x y).(l_comor (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_or3_th3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41a x y) n) : l_e_st_eq_landau_n_moreq x y).
+
+(* notion 1177 *)
+definition l_e_st_eq_landau_n_satz41g ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_or_th3 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_ec3e23 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) m) (l_ec3e21 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) m) : l_not (l_e_st_eq_landau_n_lesseq x y)).
+
+(* notion 1178 *)
+definition l_e_st_eq_landau_n_satz41h ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_or_th3 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_ec3e32 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) l) (l_ec3e31 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41b x y) l) : l_not (l_e_st_eq_landau_n_moreq x y)).
+
+(* notion 1179 *)
+definition l_e_st_eq_landau_n_satz41j ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λn:l_not (l_e_st_eq_landau_n_moreq x y).(l_or3e3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41a x y) (l_or_th5 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) n) (l_or_th4 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) n) : l_e_st_eq_landau_n_lessf x y).
+
+(* notion 1180 *)
+definition l_e_st_eq_landau_n_satz41k ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λn:l_not (l_e_st_eq_landau_n_lesseq x y).(l_or3e2 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_satz41a x y) (l_or_th4 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) n) (l_or_th5 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) n) : l_e_st_eq_landau_n_moref x y).
+
+(* notion 1181 *)
+definition l_e_st_eq_landau_n_246_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.λn:l_e_st_eq_landau_n_moref x y.(l_ori1 (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_satz44 x y z u n e f) : l_e_st_eq_landau_n_moreq z u).
+
+(* notion 1182 *)
+definition l_e_st_eq_landau_n_246_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.λg:l_e_st_eq_landau_n_eq x y.(l_ori2 (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_tr3eq z x y u (l_e_st_eq_landau_n_symeq x z e) g f) : l_e_st_eq_landau_n_moreq z u).
+
+(* notion 1183 *)
+definition l_e_st_eq_landau_n_satz46 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_orapp (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moreq z u) m (λt:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_246_t1 x y z u m e f t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_246_t2 x y z u m e f t) : l_e_st_eq_landau_n_moreq z u).
+
+(* notion 1184 *)
+definition l_e_st_eq_landau_n_eqmoreq12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.λm:l_e_st_eq_landau_n_moreq x z.(l_e_st_eq_landau_n_satz46 x z y u m e f : l_e_st_eq_landau_n_moreq y u).
+
+(* notion 1185 *)
+definition l_e_st_eq_landau_n_eqmoreq1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moreq x z.(l_e_st_eq_landau_n_satz46 x z y z m e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_moreq y z).
+
+(* notion 1186 *)
+definition l_e_st_eq_landau_n_eqmoreq2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moreq z x.(l_e_st_eq_landau_n_satz46 z x z y m (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_moreq z y).
+
+(* notion 1187 *)
+definition l_e_st_eq_landau_n_247_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.λk:l_e_st_eq_landau_n_lessf x y.(l_ori1 (l_e_st_eq_landau_n_lessf z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_satz45 x y z u k e f) : l_e_st_eq_landau_n_lesseq z u).
+
+(* notion 1188 *)
+definition l_e_st_eq_landau_n_247_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.λg:l_e_st_eq_landau_n_eq x y.(l_ori2 (l_e_st_eq_landau_n_lessf z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_tr3eq z x y u (l_e_st_eq_landau_n_symeq x z e) g f) : l_e_st_eq_landau_n_lesseq z u).
+
+(* notion 1189 *)
+definition l_e_st_eq_landau_n_satz47 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λe:l_e_st_eq_landau_n_eq x z.λf:l_e_st_eq_landau_n_eq y u.(l_orapp (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_lesseq z u) l (λt:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_247_t1 x y z u l e f t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_247_t2 x y z u l e f t) : l_e_st_eq_landau_n_lesseq z u).
+
+(* notion 1190 *)
+definition l_e_st_eq_landau_n_eqlesseq12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.λl:l_e_st_eq_landau_n_lesseq x z.(l_e_st_eq_landau_n_satz47 x z y u l e f : l_e_st_eq_landau_n_lesseq y u).
+
+(* notion 1191 *)
+definition l_e_st_eq_landau_n_eqlesseq1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lesseq x z.(l_e_st_eq_landau_n_satz47 x z y z l e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_lesseq y z).
+
+(* notion 1192 *)
+definition l_e_st_eq_landau_n_eqlesseq2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lesseq z x.(l_e_st_eq_landau_n_satz47 z x z y l (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_lesseq z y).
+
+(* notion 1193 *)
+definition l_e_st_eq_landau_n_satz48 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.(l_or_th9 (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_lessf y x) (l_e_st_eq_landau_n_eq y x) m (λt:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz42 x y t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz38 x y t) : l_e_st_eq_landau_n_lesseq y x).
+
+(* notion 1194 *)
+definition l_e_st_eq_landau_n_satz49 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.(l_or_th9 (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref y x) (l_e_st_eq_landau_n_eq y x) l (λt:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz43 x y t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz38 x y t) : l_e_st_eq_landau_n_moreq y x).
+
+(* notion 1195 *)
+definition l_e_st_eq_landau_n_250_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf y z.(l_e_st_eq_landau_n_satz34a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) l k : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1196 *)
+definition l_e_st_eq_landau_n_250_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf y z.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)))) (l_e_st_eq_landau_n_250_t1 x y z l k) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1197 *)
+definition l_e_st_eq_landau_n_satz50 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf y z.(l_e_st_eq_landau_n_satz33c (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_250_t2 x y z l k) : l_e_st_eq_landau_n_lessf x z).
+
+(* notion 1198 *)
+definition l_e_st_eq_landau_n_trlessf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf y z.(l_e_st_eq_landau_n_satz50 x y z l k : l_e_st_eq_landau_n_lessf x z).
+
+(* notion 1199 *)
+definition l_e_st_eq_landau_n_trmoref ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref y z.(l_e_st_eq_landau_n_satz43 z x (l_e_st_eq_landau_n_satz50 z y x (l_e_st_eq_landau_n_satz42 y z n) (l_e_st_eq_landau_n_satz42 x y m)) : l_e_st_eq_landau_n_moref x z).
+
+(* notion 1200 *)
+definition l_e_st_eq_landau_n_satz51a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lessf y z.(l_orapp (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_lessf x z) l (λt:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz50 x y z t k) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_eqlessf1 y x z (l_e_st_eq_landau_n_symeq x y t) k) : l_e_st_eq_landau_n_lessf x z).
+
+(* notion 1201 *)
+definition l_e_st_eq_landau_n_satz51b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lesseq y z.(l_orapp (l_e_st_eq_landau_n_lessf y z) (l_e_st_eq_landau_n_eq y z) (l_e_st_eq_landau_n_lessf x z) k (λt:l_e_st_eq_landau_n_lessf y z.l_e_st_eq_landau_n_satz50 x y z l t) (λt:l_e_st_eq_landau_n_eq y z.l_e_st_eq_landau_n_eqlessf2 y z x t l) : l_e_st_eq_landau_n_lessf x z).
+
+(* notion 1202 *)
+definition l_e_st_eq_landau_n_satz51c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moref y z.(l_e_st_eq_landau_n_satz43 z x (l_e_st_eq_landau_n_satz51b z y x (l_e_st_eq_landau_n_satz42 y z n) (l_e_st_eq_landau_n_satz48 x y m)) : l_e_st_eq_landau_n_moref x z).
+
+(* notion 1203 *)
+definition l_e_st_eq_landau_n_satz51d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moreq y z.(l_e_st_eq_landau_n_satz43 z x (l_e_st_eq_landau_n_satz51a z y x (l_e_st_eq_landau_n_satz48 y z n) (l_e_st_eq_landau_n_satz42 x y m)) : l_e_st_eq_landau_n_moref x z).
+
+(* notion 1204 *)
+definition l_e_st_eq_landau_n_252_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq y z.(l_ori2 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_eq x z) (l_e_st_eq_landau_n_treq x y z e f) : l_e_st_eq_landau_n_lesseq x z).
+
+(* notion 1205 *)
+definition l_e_st_eq_landau_n_252_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λe:l_e_st_eq_landau_n_eq x y.λj:l_e_st_eq_landau_n_lessf y z.(l_ori1 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_eq x z) (l_e_st_eq_landau_n_satz51a x y z l j) : l_e_st_eq_landau_n_lesseq x z).
+
+(* notion 1206 *)
+definition l_e_st_eq_landau_n_252_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λe:l_e_st_eq_landau_n_eq x y.(l_orapp (l_e_st_eq_landau_n_lessf y z) (l_e_st_eq_landau_n_eq y z) (l_e_st_eq_landau_n_lesseq x z) k (λt:l_e_st_eq_landau_n_lessf y z.l_e_st_eq_landau_n_252_t2 x y z l k e t) (λt:l_e_st_eq_landau_n_eq y z.l_e_st_eq_landau_n_252_t1 x y z l k e t) : l_e_st_eq_landau_n_lesseq x z).
+
+(* notion 1207 *)
+definition l_e_st_eq_landau_n_252_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λj:l_e_st_eq_landau_n_lessf x y.(l_ori1 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_eq x z) (l_e_st_eq_landau_n_satz51b x y z j k) : l_e_st_eq_landau_n_lesseq x z).
+
+(* notion 1208 *)
+definition l_e_st_eq_landau_n_satz52 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.(l_orapp (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_lesseq x z) l (λt:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_252_t4 x y z l k t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_252_t3 x y z l k t) : l_e_st_eq_landau_n_lesseq x z).
+
+(* notion 1209 *)
+definition l_e_st_eq_landau_n_trlesseq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.(l_e_st_eq_landau_n_satz52 x y z l k : l_e_st_eq_landau_n_lesseq x z).
+
+(* notion 1210 *)
+definition l_e_st_eq_landau_n_252_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λj:l_e_st_eq_landau_n_lessf x y.(l_ori1 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_eq x z) (l_e_st_eq_landau_n_satz51b x y z j k) : l_e_st_eq_landau_n_lesseq x z).
+
+(* notion 1211 *)
+definition l_e_st_eq_landau_n_252_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqlesseq1 y x z (l_e_st_eq_landau_n_symeq x y e) k : l_e_st_eq_landau_n_lesseq x z).
+
+(* notion 1212 *)
+definition l_e_st_eq_landau_n_252_anders ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq y z.(l_orapp (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_lesseq x z) l (λt:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_252_t5 x y z l k t) (λt:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_252_t6 x y z l k t) : l_e_st_eq_landau_n_lesseq x z).
+
+(* notion 1213 *)
+definition l_e_st_eq_landau_n_trmoreq ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq y z.(l_e_st_eq_landau_n_satz49 z x (l_e_st_eq_landau_n_satz52 z y x (l_e_st_eq_landau_n_satz48 y z n) (l_e_st_eq_landau_n_satz48 x y m)) : l_e_st_eq_landau_n_moreq x z).
+
+(* notion 1214 *)
+definition l_e_st_eq_landau_n_253_t1 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_satz18 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1215 *)
+definition l_e_st_eq_landau_n_253_t2 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_morefi2 x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_253_t1 x) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_2x x)) x).
+
+(* notion 1216 *)
+definition l_e_st_eq_landau_n_satz53 ≝ λx:l_e_st_eq_landau_n_frac.(l_somei l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_moref t x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_253_t2 x) : l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_moref t x)).
+
+(* notion 1217 *)
+definition l_e_st_eq_landau_n_254_t1 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_distpt2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_satz18a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1218 *)
+definition l_e_st_eq_landau_n_254_t2 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_lessfi2 x (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_254_t1 x) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x))) x).
+
+(* notion 1219 *)
+definition l_e_st_eq_landau_n_satz54 ≝ λx:l_e_st_eq_landau_n_frac.(l_somei l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_lessf t x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_254_t2 x) : l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_lessf t x)).
+
+(* notion 1220 *)
+definition l_e_st_eq_landau_n_255_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_satz19f (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1221 *)
+definition l_e_st_eq_landau_n_255_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_satz19c (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1222 *)
+definition l_e_st_eq_landau_n_255_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_distpt2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_255_t1 x y l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1223 *)
+definition l_e_st_eq_landau_n_255_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_lessfi1 x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_255_t3 x y l) : l_e_st_eq_landau_n_lessf x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1224 *)
+definition l_e_st_eq_landau_n_255_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_distpt2 (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_255_t2 x y l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1225 *)
+definition l_e_st_eq_landau_n_255_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_lessfi2 y (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_255_t5 x y l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) y).
+
+(* notion 1226 *)
+definition l_e_st_eq_landau_n_255_t7 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_andi (l_e_st_eq_landau_n_lessf x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) y) (l_e_st_eq_landau_n_255_t4 x y l) (l_e_st_eq_landau_n_255_t6 x y l) : l_and (l_e_st_eq_landau_n_lessf x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) y)).
+
+(* notion 1227 *)
+definition l_e_st_eq_landau_n_satz55 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_somei l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_and (l_e_st_eq_landau_n_lessf x t) (l_e_st_eq_landau_n_lessf t y)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_255_t7 x y l) : l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_and (l_e_st_eq_landau_n_lessf x t) (l_e_st_eq_landau_n_lessf t y))).
+
+(* notion 1228 *)
+definition l_e_st_eq_landau_n_pf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_frac).
+
+(* notion 1229 *)
+definition l_e_st_eq_landau_n_ii3_t1 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_ts y1 x2) (l_e_st_eq_landau_n_ndis12 x1 x2 y1 y2) (l_e_st_eq_landau_n_ndis12 y1 y2 x1 x2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2))).
+
+(* notion 1230 *)
+definition l_e_st_eq_landau_n_ii3_t2 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) x2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2)) y2 (l_e_st_eq_landau_n_denis x1 x2) (l_e_st_eq_landau_n_denis y1 y2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x2 y2)).
+
+(* notion 1231 *)
+definition l_e_st_eq_landau_n_pf12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2) (l_e_st_eq_landau_n_ii3_t1 x1 x2 y1 y2) (l_e_st_eq_landau_n_ii3_t2 x1 x2 y1 y2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2))).
+
+(* notion 1232 *)
+definition l_e_st_eq_landau_n_ii3_t3 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ndisn2 x n1 n2) (l_e_st_eq_landau_n_ndis1d x n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1233 *)
+definition l_e_st_eq_landau_n_ii3_t4 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) n2 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_denis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)).
+
+(* notion 1234 *)
+definition l_e_st_eq_landau_n_pf1 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2) (l_e_st_eq_landau_n_ii3_t3 x n1 n2) (l_e_st_eq_landau_n_ii3_t4 x n1 n2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2))).
+
+(* notion 1235 *)
+definition l_e_st_eq_landau_n_ii3_t5 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ndis1d x n1 n2) (l_e_st_eq_landau_n_ndisn2 x n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2))).
+
+(* notion 1236 *)
+definition l_e_st_eq_landau_n_ii3_t6 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) n2 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_denis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1237 *)
+definition l_e_st_eq_landau_n_pf2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ii3_t5 x n1 n2) (l_e_st_eq_landau_n_ii3_t6 x n1 n2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1238 *)
+definition l_e_st_eq_landau_n_pfeq12a ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_pf12 x1 x2 y1 y2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2))).
+
+(* notion 1239 *)
+definition l_e_st_eq_landau_n_pfeq12b ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_pf12 x1 x2 y1 y2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 y2) (l_e_st_eq_landau_n_ts y1 x2)) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2))).
+
+(* notion 1240 *)
+definition l_e_st_eq_landau_n_pfeq1a ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_pf1 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2))).
+
+(* notion 1241 *)
+definition l_e_st_eq_landau_n_pfeq1b ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_pf1 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_fr n1 n2))).
+
+(* notion 1242 *)
+definition l_e_st_eq_landau_n_pfeq2a ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pf2 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1243 *)
+definition l_e_st_eq_landau_n_pfeq2b ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pf2 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n2)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr n1 n2) x)).
+
+(* notion 1244 *)
+definition l_e_st_eq_landau_n_356_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u)) e : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u)))).
+
+(* notion 1245 *)
+definition l_e_st_eq_landau_n_356_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_356_t1 z u x y f e : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1246 *)
+definition l_e_st_eq_landau_n_356_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2u x y z u) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u)))).
+
+(* notion 1247 *)
+definition l_e_st_eq_landau_n_356_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_356_t3 x y z u e f) (l_e_st_eq_landau_n_356_t1 x y z u e f) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
+
+(* notion 1248 *)
+definition l_e_st_eq_landau_n_356_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_356_t2 x y z u e f) (l_e_st_eq_landau_n_stets (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
+
+(* notion 1249 *)
+definition l_e_st_eq_landau_n_356_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_356_t4 x y z u e f) (l_e_st_eq_landau_n_356_t5 x y z u e f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))))).
+
+(* notion 1250 *)
+definition l_e_st_eq_landau_n_356_t7 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_disttp1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_356_t6 x y z u e f) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
+
+(* notion 1251 *)
+definition l_e_st_eq_landau_n_satz56 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_eqi12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_356_t7 x y z u e f) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1252 *)
+definition l_e_st_eq_landau_n_eqpf12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_satz56 x y z u e f : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1253 *)
+definition l_e_st_eq_landau_n_eqpf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqpf12 x y z z e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
+
+(* notion 1254 *)
+definition l_e_st_eq_landau_n_eqpf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqpf12 z z x y (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y)).
+
+(* notion 1255 *)
+definition l_e_st_eq_landau_n_satz57 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 n) (l_e_st_eq_landau_n_fr x2 n)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n)) (l_e_st_eq_landau_n_ts n n)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x1 x2) n) (l_e_st_eq_landau_n_ts n n)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x1 x2) n) (l_e_st_eq_landau_n_pfeq12a x1 n x2 n) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x1 n) (l_e_st_eq_landau_n_ts x2 n)) (l_e_st_eq_landau_n_ts n n) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl x1 x2) n) (l_e_st_eq_landau_n_distpt1 x1 x2 n)) (l_e_st_eq_landau_n_satz40c (l_e_st_eq_landau_n_pl x1 x2) n n) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 n) (l_e_st_eq_landau_n_fr x2 n)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x1 x2) n)).
+
+(* notion 1256 *)
+definition l_e_st_eq_landau_n_satz57a ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 n) (l_e_st_eq_landau_n_fr x2 n)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x1 x2) n) (l_e_st_eq_landau_n_satz57 x1 x2 n) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x1 x2) n) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x1 n) (l_e_st_eq_landau_n_fr x2 n))).
+
+(* notion 1257 *)
+definition l_e_st_eq_landau_n_satz58 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_compl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x y) (l_e_st_eq_landau_n_pf y x)).
+
+(* notion 1258 *)
+definition l_e_st_eq_landau_n_compf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz58 x y : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x y) (l_e_st_eq_landau_n_pf y x)).
+
+(* notion 1259 *)
+definition l_e_st_eq_landau_n_359_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1260 *)
+definition l_e_st_eq_landau_n_359_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_359_t1 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1261 *)
+definition l_e_st_eq_landau_n_359_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_disttp1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_359_t2 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1262 *)
+definition l_e_st_eq_landau_n_359_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_assts2 (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1263 *)
+definition l_e_st_eq_landau_n_359_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_359_t3 x y z) (l_e_st_eq_landau_n_359_t4 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1264 *)
+definition l_e_st_eq_landau_n_359_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1265 *)
+definition l_e_st_eq_landau_n_359_t7 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_359_t5 x y z) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_359_t6 x y z) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1266 *)
+definition l_e_st_eq_landau_n_satz59 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pfeq2a z (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_359_t7 x y z) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pfeq1b x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z))).
+
+(* notion 1267 *)
+definition l_e_st_eq_landau_n_asspf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz59 x y z : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z))).
+
+(* notion 1268 *)
+definition l_e_st_eq_landau_n_asspf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_asspf1 x y z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z)).
+
+(* notion 1269 *)
+definition l_e_st_eq_landau_n_stets1 ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) c) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts b c)) (l_e_st_eq_landau_n_ts a (l_e_st_eq_landau_n_ts c b)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a c) b) (l_e_st_eq_landau_n_assts1 a b c) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts b c) (l_e_st_eq_landau_n_ts c b) a (l_e_st_eq_landau_n_comts b c)) (l_e_st_eq_landau_n_assts2 a c b) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) c) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a c) b)).
+
+(* notion 1270 *)
+definition l_e_st_eq_landau_n_359_t8 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_disttp1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_stets1 (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1271 *)
+definition l_e_st_eq_landau_n_359_t9 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_assts2 (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_stets1 (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1272 *)
+definition l_e_st_eq_landau_n_359_anderst7 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_359_t8 x y z) (l_e_st_eq_landau_n_359_t9 x y z)) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1273 *)
+definition l_e_st_eq_landau_n_360_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz18 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y))).
+
+(* notion 1274 *)
+definition l_e_st_eq_landau_n_360_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz32a (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_360_t1 x y) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1275 *)
+definition l_e_st_eq_landau_n_360_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1276 *)
+definition l_e_st_eq_landau_n_360_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_ismore2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_360_t3 x y) (l_e_st_eq_landau_n_360_t2 x y) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1277 *)
+definition l_e_st_eq_landau_n_satz60 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_morefi2 x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_360_t4 x y) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x y) x).
+
+(* notion 1278 *)
+definition l_e_st_eq_landau_n_satz60a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_pf x y) x (l_e_st_eq_landau_n_satz60 x y) : l_e_st_eq_landau_n_lessf x (l_e_st_eq_landau_n_pf x y)).
+
+(* notion 1279 *)
+definition l_e_st_eq_landau_n_361_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz32a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z) m : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z))).
+
+(* notion 1280 *)
+definition l_e_st_eq_landau_n_361_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_stets1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_stets1 (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_361_t1 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1281 *)
+definition l_e_st_eq_landau_n_361_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_stets1 (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1282 *)
+definition l_e_st_eq_landau_n_361_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz19h (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_361_t3 x y z m) (l_e_st_eq_landau_n_361_t2 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1283 *)
+definition l_e_st_eq_landau_n_361_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_distpt1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_361_t4 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1284 *)
+definition l_e_st_eq_landau_n_361_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz32a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_361_t5 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z))).
+
+(* notion 1285 *)
+definition l_e_st_eq_landau_n_361_t7 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_361_t6 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
+
+(* notion 1286 *)
+definition l_e_st_eq_landau_n_satz61 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_morefi12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_361_t7 x y z m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
+
+(* notion 1287 *)
+definition l_e_st_eq_landau_n_satz62a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz61 x y z m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
+
+(* notion 1288 *)
+definition l_e_st_eq_landau_n_satz62b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqpf1 x y z e : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
+
+(* notion 1289 *)
+definition l_e_st_eq_landau_n_satz62c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_satz61 y x z (l_e_st_eq_landau_n_satz43 x y l)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
+
+(* notion 1290 *)
+definition l_e_st_eq_landau_n_satz62d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_compf x z) (l_e_st_eq_landau_n_compf y z) (l_e_st_eq_landau_n_satz62a x y z m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y)).
+
+(* notion 1291 *)
+definition l_e_st_eq_landau_n_satz62e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqpf2 x y z e : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y)).
+
+(* notion 1292 *)
+definition l_e_st_eq_landau_n_satz62f ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_compf x z) (l_e_st_eq_landau_n_compf y z) (l_e_st_eq_landau_n_satz62c x y z l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y)).
+
+(* notion 1293 *)
+definition l_e_st_eq_landau_n_satz62g ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref2 (l_e_st_eq_landau_n_pf x u) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_eqpf1 x y u e) (l_e_st_eq_landau_n_satz62d z u x m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1294 *)
+definition l_e_st_eq_landau_n_satz62h ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf u y) (l_e_st_eq_landau_n_compf x z) (l_e_st_eq_landau_n_compf y u) (l_e_st_eq_landau_n_satz62g x y z u e m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf u y)).
+
+(* notion 1295 *)
+definition l_e_st_eq_landau_n_satz62j ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_eqlessf2 (l_e_st_eq_landau_n_pf x u) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_eqpf1 x y u e) (l_e_st_eq_landau_n_satz62f z u x l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1296 *)
+definition l_e_st_eq_landau_n_satz62k ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf u y) (l_e_st_eq_landau_n_compf x z) (l_e_st_eq_landau_n_compf y u) (l_e_st_eq_landau_n_satz62j x y z u e l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf u y)).
+
+(* notion 1297 *)
+definition l_e_st_eq_landau_n_363_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz41a x y : l_or3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y)).
+
+(* notion 1298 *)
+definition l_e_st_eq_landau_n_363_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz41b (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) : l_ec3 (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z))).
+
+(* notion 1299 *)
+definition l_e_st_eq_landau_n_satz63a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z).(l_ec3_th11 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_363_t1 x y z) (l_e_st_eq_landau_n_363_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz62b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz62a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz62c x y z u) m : l_e_st_eq_landau_n_moref x y).
+
+(* notion 1300 *)
+definition l_e_st_eq_landau_n_satz63b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z).(l_ec3_th10 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_363_t1 x y z) (l_e_st_eq_landau_n_363_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz62b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz62a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz62c x y z u) e : l_e_st_eq_landau_n_eq x y).
+
+(* notion 1301 *)
+definition l_e_st_eq_landau_n_satz63c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z).(l_ec3_th12 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_363_t1 x y z) (l_e_st_eq_landau_n_363_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz62b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz62a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz62c x y z u) l : l_e_st_eq_landau_n_lessf x y).
+
+(* notion 1302 *)
+definition l_e_st_eq_landau_n_satz63d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y).(l_e_st_eq_landau_n_satz63a x y z (l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_compf z x) (l_e_st_eq_landau_n_compf z y) m) : l_e_st_eq_landau_n_moref x y).
+
+(* notion 1303 *)
+definition l_e_st_eq_landau_n_satz63e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y).(l_e_st_eq_landau_n_satz63b x y z (l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_compf x z) e (l_e_st_eq_landau_n_compf z y)) : l_e_st_eq_landau_n_eq x y).
+
+(* notion 1304 *)
+definition l_e_st_eq_landau_n_satz63f ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λf:l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf z y).(l_e_st_eq_landau_n_satz63c x y z (l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_pf z x) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_compf z x) (l_e_st_eq_landau_n_compf z y) f) : l_e_st_eq_landau_n_lessf x y).
+
+(* notion 1305 *)
+definition l_e_st_eq_landau_n_364_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_satz61 x y z m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z)).
+
+(* notion 1306 *)
+definition l_e_st_eq_landau_n_364_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_pf z y) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf u y) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_compf z y) (l_e_st_eq_landau_n_compf u y) (l_e_st_eq_landau_n_satz61 z u y n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1307 *)
+definition l_e_st_eq_landau_n_satz64 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_trmoref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_364_t1 x y z u m n) (l_e_st_eq_landau_n_364_t2 x y z u m n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1308 *)
+definition l_e_st_eq_landau_n_satz64a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_satz64 y x u z (l_e_st_eq_landau_n_satz43 x y l) (l_e_st_eq_landau_n_satz43 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1309 *)
+definition l_e_st_eq_landau_n_satz65a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moref z u.(l_orapp (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)) m (λv:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz64 x y z u v n) (λv:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz62g x y z u v n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1310 *)
+definition l_e_st_eq_landau_n_satz65b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moreq z u.(l_orapp (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)) n (λv:l_e_st_eq_landau_n_moref z u.l_e_st_eq_landau_n_satz64 x y z u m v) (λv:l_e_st_eq_landau_n_eq z u.l_e_st_eq_landau_n_eqmoref2 (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_eqpf2 z u y v) (l_e_st_eq_landau_n_satz61 x y z m)) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1311 *)
+definition l_e_st_eq_landau_n_satz65c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_satz65a y x u z (l_e_st_eq_landau_n_satz49 x y l) (l_e_st_eq_landau_n_satz43 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1312 *)
+definition l_e_st_eq_landau_n_satz65d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lesseq z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_satz65b y x u z (l_e_st_eq_landau_n_satz43 x y l) (l_e_st_eq_landau_n_satz49 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1313 *)
+definition l_e_st_eq_landau_n_366_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_moreqi2 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_satz56 x y z u e f) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1314 *)
+definition l_e_st_eq_landau_n_366_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.λo:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_moreqi1 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_satz65a x y z u m o) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1315 *)
+definition l_e_st_eq_landau_n_366_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.(l_orapp (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)) n (λv:l_e_st_eq_landau_n_moref z u.l_e_st_eq_landau_n_366_t2 x y z u m n e v) (λv:l_e_st_eq_landau_n_eq z u.l_e_st_eq_landau_n_366_t1 x y z u m n e v) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1316 *)
+definition l_e_st_eq_landau_n_366_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λo:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_moreqi1 (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_satz65b x y z u o n) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1317 *)
+definition l_e_st_eq_landau_n_satz66 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.(l_orapp (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)) m (λv:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_366_t4 x y z u m n v) (λv:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_366_t3 x y z u m n v) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1318 *)
+definition l_e_st_eq_landau_n_satz66a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq z u.(l_e_st_eq_landau_n_satz48 (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_satz66 y x u z (l_e_st_eq_landau_n_satz49 x y l) (l_e_st_eq_landau_n_satz49 z u k)) : l_e_st_eq_landau_n_lesseq (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u)).
+
+(* notion 1319 *)
+definition l_e_st_eq_landau_n_367_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.(l_e_st_eq_landau_n_eqmoref1 (l_e_st_eq_landau_n_pf y v) x y e (l_e_st_eq_landau_n_satz60 y v) : l_e_st_eq_landau_n_moref x y).
+
+(* notion 1320 *)
+definition l_e_st_eq_landau_n_367_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λv:l_e_st_eq_landau_n_frac.(l_imp_th3 (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_satz41d x y l) (λt:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.l_e_st_eq_landau_n_367_t1 x y l v t) : l_not (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x)).
+
+(* notion 1321 *)
+definition l_e_st_eq_landau_n_vorbemerkung67 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.(l_some_th5 l_e_st_eq_landau_n_frac (λv:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x) (λv:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_367_t2 x y l v) : l_not (l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y t) x))).
+
+(* notion 1322 *)
+definition l_e_st_eq_landau_n_satz67b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.λf:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y w) x.(l_e_st_eq_landau_n_satz63e v w y (l_e_st_eq_landau_n_treq2 (l_e_st_eq_landau_n_pf y v) (l_e_st_eq_landau_n_pf y w) x e f) : l_e_st_eq_landau_n_eq v w).
+
+(* notion 1323 *)
+definition l_e_st_eq_landau_n_367_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_onei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) t) (l_e_st_eq_landau_n_satz8b (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x))) m : l_e_st_eq_landau_n_one (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) t)).
+
+(* notion 1324 *)
+definition l_e_st_eq_landau_n_367_vo ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_ind l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) t) (l_e_st_eq_landau_n_367_t3 x y m) : l_e_st_eq_landau_n_nat).
+
+(* notion 1325 *)
+definition l_e_st_eq_landau_n_367_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_oneax l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) t) (l_e_st_eq_landau_n_367_t3 x y m) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_367_vo x y m))).
+
+(* notion 1326 *)
+definition l_e_st_eq_landau_n_367_w ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_367_vo x y m) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_frac).
+
+(* notion 1327 *)
+definition l_e_st_eq_landau_n_367_t5 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_treq y (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_satz40 y (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_eqd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x))) : l_e_st_eq_landau_n_eq y (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))).
+
+(* notion 1328 *)
+definition l_e_st_eq_landau_n_367_t6 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_tr4eq (l_e_st_eq_landau_n_pf y (l_e_st_eq_landau_n_367_w x y m)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_367_vo x y m) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_367_vo x y m)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) x (l_e_st_eq_landau_n_eqpf1 y (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_367_w x y m) (l_e_st_eq_landau_n_367_t5 x y m)) (l_e_st_eq_landau_n_satz57 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_367_vo x y m) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_367_vo x y m)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_367_vo x y m)) (l_e_st_eq_landau_n_367_t4 x y m))) (l_e_st_eq_landau_n_satz40a x (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y (l_e_st_eq_landau_n_367_w x y m)) x).
+
+(* notion 1329 *)
+definition l_e_st_eq_landau_n_satz67a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_somei l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y t) x) (l_e_st_eq_landau_n_367_w x y m) (l_e_st_eq_landau_n_367_t6 x y m) : l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y t) x)).
+
+(* notion 1330 *)
+definition l_e_st_eq_landau_n_mf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_367_w x y m : l_e_st_eq_landau_n_frac).
+
+(* notion 1331 *)
+definition l_e_st_eq_landau_n_satz67c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_367_t6 x y m : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y (l_e_st_eq_landau_n_mf x y m)) x).
+
+(* notion 1332 *)
+definition l_e_st_eq_landau_n_satz67d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_pf y (l_e_st_eq_landau_n_mf x y m)) x (l_e_st_eq_landau_n_satz67c x y m) : l_e_st_eq_landau_n_eq x (l_e_st_eq_landau_n_pf y (l_e_st_eq_landau_n_mf x y m))).
+
+(* notion 1333 *)
+definition l_e_st_eq_landau_n_satz67e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.(l_e_st_eq_landau_n_satz67b x y v (l_e_st_eq_landau_n_mf x y m) e (l_e_st_eq_landau_n_satz67c x y m) : l_e_st_eq_landau_n_eq v (l_e_st_eq_landau_n_mf x y m)).
+
+(* notion 1334 *)
+definition l_e_st_eq_landau_n_tf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_frac).
+
+(* notion 1335 *)
+definition l_e_st_eq_landau_n_ii4_t1 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) x1 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2)) y1 (l_e_st_eq_landau_n_numis x1 x2) (l_e_st_eq_landau_n_numis y1 y2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x1 y1)).
+
+(* notion 1336 *)
+definition l_e_st_eq_landau_n_ii4_t2 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) x2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2)) y2 (l_e_st_eq_landau_n_denis x1 x2) (l_e_st_eq_landau_n_denis y1 y2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x2 y2)).
+
+(* notion 1337 *)
+definition l_e_st_eq_landau_n_tf12 ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y1 y2))) (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2) (l_e_st_eq_landau_n_ii4_t1 x1 x2 y1 y2) (l_e_st_eq_landau_n_ii4_t2 x1 x2 y1 y2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2))).
+
+(* notion 1338 *)
+definition l_e_st_eq_landau_n_ii4_t3 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) n1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_numis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1)).
+
+(* notion 1339 *)
+definition l_e_st_eq_landau_n_ii4_t4 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) n2 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_denis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)).
+
+(* notion 1340 *)
+definition l_e_st_eq_landau_n_tf1 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2) (l_e_st_eq_landau_n_ii4_t3 x n1 n2) (l_e_st_eq_landau_n_ii4_t4 x n1 n2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2))).
+
+(* notion 1341 *)
+definition l_e_st_eq_landau_n_ii4_t5 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) n1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_numis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x))).
+
+(* notion 1342 *)
+definition l_e_st_eq_landau_n_ii4_t6 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_ists1 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) n2 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_denis n1 n2) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))).
+
+(* notion 1343 *)
+definition l_e_st_eq_landau_n_tf2 ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ii4_t5 x n1 n2) (l_e_st_eq_landau_n_ii4_t6 x n1 n2) : l_e_is l_e_st_eq_landau_n_frac (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1344 *)
+definition l_e_st_eq_landau_n_tfeq12a ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_tf12 x1 x2 y1 y2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2))).
+
+(* notion 1345 *)
+definition l_e_st_eq_landau_n_tfeq12b ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.λy1:l_e_st_eq_landau_n_nat.λy2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_tf12 x1 x2 y1 y2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x1 y1) (l_e_st_eq_landau_n_ts x2 y2)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x1 x2) (l_e_st_eq_landau_n_fr y1 y2))).
+
+(* notion 1346 *)
+definition l_e_st_eq_landau_n_tfeq1a ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_tf1 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2))).
+
+(* notion 1347 *)
+definition l_e_st_eq_landau_n_tfeq1b ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr n1 n2)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_tf1 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) n1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) n2)) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr n1 n2))).
+
+(* notion 1348 *)
+definition l_e_st_eq_landau_n_tfeq2a ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_tf2 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x)))).
+
+(* notion 1349 *)
+definition l_e_st_eq_landau_n_tfeq2b ≝ λx:l_e_st_eq_landau_n_frac.λn1:l_e_st_eq_landau_n_nat.λn2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_refeq2 (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr n1 n2) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_tf2 x n1 n2) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts n1 (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts n2 (l_e_st_eq_landau_n_2x x))) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr n1 n2) x)).
+
+(* notion 1350 *)
+definition l_e_st_eq_landau_n_468_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) e f : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)))).
+
+(* notion 1351 *)
+definition l_e_st_eq_landau_n_stets2 ≝ λa:l_e_st_eq_landau_n_nat.λb:l_e_st_eq_landau_n_nat.λc:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts d c)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a c) (l_e_st_eq_landau_n_ts d b)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a c) (l_e_st_eq_landau_n_ts b d)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts c d) (l_e_st_eq_landau_n_ts d c) (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_comts c d)) (l_e_st_eq_landau_n_stets a b d c) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts d b) (l_e_st_eq_landau_n_ts b d) (l_e_st_eq_landau_n_ts a c) (l_e_st_eq_landau_n_comts d b)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a b) (l_e_st_eq_landau_n_ts c d)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts a c) (l_e_st_eq_landau_n_ts b d))).
+
+(* notion 1352 *)
+definition l_e_st_eq_landau_n_468_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_stets2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_468_t1 x y z u e f) (l_e_st_eq_landau_n_stets2 (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1u x y z u) (l_e_st_eq_landau_n_2z x y z)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
+
+(* notion 1353 *)
+definition l_e_st_eq_landau_n_satz68 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_eqi12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1u x y z u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2u x y z u)) (l_e_st_eq_landau_n_468_t2 x y z u e f) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1354 *)
+definition l_e_st_eq_landau_n_eqtf12 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_satz68 x y z u e f : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1355 *)
+definition l_e_st_eq_landau_n_eqtf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqtf12 x y z z e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)).
+
+(* notion 1356 *)
+definition l_e_st_eq_landau_n_eqtf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqtf12 z z x y (l_e_st_eq_landau_n_refeq z) e : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y)).
+
+(* notion 1357 *)
+definition l_e_st_eq_landau_n_satz69 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf y x)).
+
+(* notion 1358 *)
+definition l_e_st_eq_landau_n_comtf ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz69 x y : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf y x)).
+
+(* notion 1359 *)
+definition l_e_st_eq_landau_n_satz70 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_tfeq2a z (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_tfeq1b x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z))).
+
+(* notion 1360 *)
+definition l_e_st_eq_landau_n_asstf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz70 x y z : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z))).
+
+(* notion 1361 *)
+definition l_e_st_eq_landau_n_asstf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_asstf1 x y z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z)).
+
+(* notion 1362 *)
+definition l_e_st_eq_landau_n_471_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))))) (l_e_st_eq_landau_n_tfeq1a x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_disttp2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_satz57a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))))).
+
+(* notion 1363 *)
+definition l_e_st_eq_landau_n_471_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_treq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_assts2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_assts2 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_satz40c (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2z x y z)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_tf x y)).
+
+(* notion 1364 *)
+definition l_e_st_eq_landau_n_471_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_treq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2y x y)))) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_eqd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2z x y z) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_471_t2 x z y) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_tf x z)).
+
+(* notion 1365 *)
+definition l_e_st_eq_landau_n_satz71 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_treq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))))) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_471_t1 x y z) (l_e_st_eq_landau_n_eqpf12 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)))) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_471_t2 x y z) (l_e_st_eq_landau_n_471_t3 x y z)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z))).
+
+(* notion 1366 *)
+definition l_e_st_eq_landau_n_disttpf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_tf z (l_e_st_eq_landau_n_pf x y)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_comtf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_satz71 z x y) (l_e_st_eq_landau_n_eqpf12 (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_comtf z x) (l_e_st_eq_landau_n_comtf z y)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z))).
+
+(* notion 1367 *)
+definition l_e_st_eq_landau_n_disttpf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz71 x y z : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z))).
+
+(* notion 1368 *)
+definition l_e_st_eq_landau_n_distptf1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_disttpf1 x y z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_pf x y) z)).
+
+(* notion 1369 *)
+definition l_e_st_eq_landau_n_distptf2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_symeq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_disttpf2 x y z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z))).
+
+(* notion 1370 *)
+definition l_e_st_eq_landau_n_472_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_satz32a (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z)) m : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z)))).
+
+(* notion 1371 *)
+definition l_e_st_eq_landau_n_472_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_stets2 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_stets2 (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1z x y z) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_472_t1 x y z m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)))).
+
+(* notion 1372 *)
+definition l_e_st_eq_landau_n_satz72a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_morefi12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_1z x y z)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_2z x y z)) (l_e_st_eq_landau_n_472_t2 x y z m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)).
+
+(* notion 1373 *)
+definition l_e_st_eq_landau_n_satz72b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_satz68 x y z z e (l_e_st_eq_landau_n_refeq z) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)).
+
+(* notion 1374 *)
+definition l_e_st_eq_landau_n_satz72c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_satz72a y x z (l_e_st_eq_landau_n_satz43 x y l)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)).
+
+(* notion 1375 *)
+definition l_e_st_eq_landau_n_satz72d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_comtf x z) (l_e_st_eq_landau_n_comtf y z) (l_e_st_eq_landau_n_satz72a x y z m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y)).
+
+(* notion 1376 *)
+definition l_e_st_eq_landau_n_satz72e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_landau_n_eqtf2 x y z e : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y)).
+
+(* notion 1377 *)
+definition l_e_st_eq_landau_n_satz72f ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.(l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_comtf x z) (l_e_st_eq_landau_n_comtf y z) (l_e_st_eq_landau_n_satz72c x y z l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y)).
+
+(* notion 1378 *)
+definition l_e_st_eq_landau_n_satz72g ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref2 (l_e_st_eq_landau_n_tf x u) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_eqtf1 x y u e) (l_e_st_eq_landau_n_satz72d z u x m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1379 *)
+definition l_e_st_eq_landau_n_satz72h ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λm:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf u y) (l_e_st_eq_landau_n_comtf x z) (l_e_st_eq_landau_n_comtf y u) (l_e_st_eq_landau_n_satz72g x y z u e m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf u y)).
+
+(* notion 1380 *)
+definition l_e_st_eq_landau_n_satz72j ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_eqlessf2 (l_e_st_eq_landau_n_tf x u) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_eqtf1 x y u e) (l_e_st_eq_landau_n_satz72f z u x l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1381 *)
+definition l_e_st_eq_landau_n_satz72k ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λl:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf u y) (l_e_st_eq_landau_n_comtf x z) (l_e_st_eq_landau_n_comtf y u) (l_e_st_eq_landau_n_satz72j x y z u e l) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf u y)).
+
+(* notion 1382 *)
+definition l_e_st_eq_landau_n_473_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz41a x y : l_or3 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y)).
+
+(* notion 1383 *)
+definition l_e_st_eq_landau_n_473_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_satz41b (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) : l_ec3 (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z))).
+
+(* notion 1384 *)
+definition l_e_st_eq_landau_n_satz73a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z).(l_ec3_th11 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_473_t1 x y z) (l_e_st_eq_landau_n_473_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz72b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz72a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz72c x y z u) m : l_e_st_eq_landau_n_moref x y).
+
+(* notion 1385 *)
+definition l_e_st_eq_landau_n_satz73b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z).(l_ec3_th10 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_473_t1 x y z) (l_e_st_eq_landau_n_473_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz72b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz72a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz72c x y z u) e : l_e_st_eq_landau_n_eq x y).
+
+(* notion 1386 *)
+definition l_e_st_eq_landau_n_satz73c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z).(l_ec3_th12 (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_lessf x y) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_473_t1 x y z) (l_e_st_eq_landau_n_473_t2 x y z) (λu:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz72b x y z u) (λu:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz72a x y z u) (λu:l_e_st_eq_landau_n_lessf x y.l_e_st_eq_landau_n_satz72c x y z u) l : l_e_st_eq_landau_n_lessf x y).
+
+(* notion 1387 *)
+definition l_e_st_eq_landau_n_satz73d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y).(l_e_st_eq_landau_n_satz73a x y z (l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_comtf z x) (l_e_st_eq_landau_n_comtf z y) m) : l_e_st_eq_landau_n_moref x y).
+
+(* notion 1388 *)
+definition l_e_st_eq_landau_n_satz73e ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y).(l_e_st_eq_landau_n_satz73b x y z (l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_comtf x z) e (l_e_st_eq_landau_n_comtf z y)) : l_e_st_eq_landau_n_eq x y).
+
+(* notion 1389 *)
+definition l_e_st_eq_landau_n_satz73f ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf z y).(l_e_st_eq_landau_n_satz73c x y z (l_e_st_eq_landau_n_eqlessf12 (l_e_st_eq_landau_n_tf z x) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_comtf z x) (l_e_st_eq_landau_n_comtf z y) l) : l_e_st_eq_landau_n_lessf x y).
+
+(* notion 1390 *)
+definition l_e_st_eq_landau_n_474_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_satz72a x y z m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z)).
+
+(* notion 1391 *)
+definition l_e_st_eq_landau_n_474_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_eqmoref12 (l_e_st_eq_landau_n_tf z y) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf u y) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_comtf z y) (l_e_st_eq_landau_n_comtf u y) (l_e_st_eq_landau_n_satz72a z u y n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1392 *)
+definition l_e_st_eq_landau_n_satz74 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_trmoref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_474_t1 x y z u m n) (l_e_st_eq_landau_n_474_t2 x y z u m n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1393 *)
+definition l_e_st_eq_landau_n_satz74a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_satz74 y x u z (l_e_st_eq_landau_n_satz43 x y l) (l_e_st_eq_landau_n_satz43 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1394 *)
+definition l_e_st_eq_landau_n_satz75a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moref z u.(l_orapp (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)) m (λv:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_satz74 x y z u v n) (λv:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_satz72g x y z u v n) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1395 *)
+definition l_e_st_eq_landau_n_satz75b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref x y.λn:l_e_st_eq_landau_n_moreq z u.(l_orapp (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)) n (λv:l_e_st_eq_landau_n_moref z u.l_e_st_eq_landau_n_satz74 x y z u m v) (λv:l_e_st_eq_landau_n_eq z u.l_e_st_eq_landau_n_eqmoref2 (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_eqtf2 z u y v) (l_e_st_eq_landau_n_satz72a x y z m)) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1396 *)
+definition l_e_st_eq_landau_n_satz75c ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lessf z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_satz75a y x u z (l_e_st_eq_landau_n_satz49 x y l) (l_e_st_eq_landau_n_satz43 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1397 *)
+definition l_e_st_eq_landau_n_satz75d ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf x y.λk:l_e_st_eq_landau_n_lesseq z u.(l_e_st_eq_landau_n_satz42 (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_satz75b y x u z (l_e_st_eq_landau_n_satz43 x y l) (l_e_st_eq_landau_n_satz49 z u k)) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1398 *)
+definition l_e_st_eq_landau_n_476_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_moreqi2 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_satz68 x y z u e f) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1399 *)
+definition l_e_st_eq_landau_n_476_t2 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.λo:l_e_st_eq_landau_n_moref z u.(l_e_st_eq_landau_n_moreqi1 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_satz75a x y z u m o) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1400 *)
+definition l_e_st_eq_landau_n_476_t3 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λe:l_e_st_eq_landau_n_eq x y.(l_orapp (l_e_st_eq_landau_n_moref z u) (l_e_st_eq_landau_n_eq z u) (l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)) n (λv:l_e_st_eq_landau_n_moref z u.l_e_st_eq_landau_n_476_t2 x y z u m n e v) (λv:l_e_st_eq_landau_n_eq z u.l_e_st_eq_landau_n_476_t1 x y z u m n e v) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1401 *)
+definition l_e_st_eq_landau_n_476_t4 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.λo:l_e_st_eq_landau_n_moref x y.(l_e_st_eq_landau_n_moreqi1 (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_satz75b x y z u o n) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1402 *)
+definition l_e_st_eq_landau_n_satz76 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moreq x y.λn:l_e_st_eq_landau_n_moreq z u.(l_orapp (l_e_st_eq_landau_n_moref x y) (l_e_st_eq_landau_n_eq x y) (l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)) m (λv:l_e_st_eq_landau_n_moref x y.l_e_st_eq_landau_n_476_t4 x y z u m n v) (λv:l_e_st_eq_landau_n_eq x y.l_e_st_eq_landau_n_476_t3 x y z u m n v) : l_e_st_eq_landau_n_moreq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1403 *)
+definition l_e_st_eq_landau_n_satz76a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lesseq x y.λk:l_e_st_eq_landau_n_lesseq z u.(l_e_st_eq_landau_n_satz48 (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_satz76 y x u z (l_e_st_eq_landau_n_satz49 x y l) (l_e_st_eq_landau_n_satz49 z u k)) : l_e_st_eq_landau_n_lesseq (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u)).
+
+(* notion 1404 *)
+definition l_e_st_eq_landau_n_satz77b ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y v) x.λf:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y w) x.(l_e_st_eq_landau_n_satz73e v w y (l_e_st_eq_landau_n_treq2 (l_e_st_eq_landau_n_tf y v) (l_e_st_eq_landau_n_tf y w) x e f) : l_e_st_eq_landau_n_eq v w).
+
+(* notion 1405 *)
+definition l_e_st_eq_landau_n_477_v ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y)) : l_e_st_eq_landau_n_frac).
+
+(* notion 1406 *)
+definition l_e_st_eq_landau_n_477_t1 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr4eq (l_e_st_eq_landau_n_tf y (l_e_st_eq_landau_n_477_v x y)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_477_v x y) y) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)))) x (l_e_st_eq_landau_n_comtf y (l_e_st_eq_landau_n_477_v x y)) (l_e_st_eq_landau_n_tfeq2a y (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y))) (l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y)) (l_e_st_eq_landau_n_1x x) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_2y x y) (l_e_st_eq_landau_n_1y x y)))) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_2x x) (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) (l_e_st_eq_landau_n_satz40a x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_1y x y) (l_e_st_eq_landau_n_2y x y))) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y (l_e_st_eq_landau_n_477_v x y)) x).
+
+(* notion 1407 *)
+definition l_e_st_eq_landau_n_satz77a ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.(l_somei l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y t) x) (l_e_st_eq_landau_n_477_v x y) (l_e_st_eq_landau_n_477_t1 x y) : l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y t) x)).
+
+(* notion 1408 *)
+definition l_e_st_eq_landau_n_rt_eq ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq x y : Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Prop).
+
+(* notion 1409 *)
+definition l_e_st_eq_landau_n_rt_refeq ≝ (λx:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_refeq x : Πx:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_eq x x).
+
+(* notion 1410 *)
+definition l_e_st_eq_landau_n_rt_symeq ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λt:l_e_st_eq_landau_n_rt_eq x y.l_e_st_eq_landau_n_symeq x y t : Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πt:l_e_st_eq_landau_n_rt_eq x y.l_e_st_eq_landau_n_rt_eq y x).
+
+(* notion 1411 *)
+definition l_e_st_eq_landau_n_rt_treq ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λt:l_e_st_eq_landau_n_rt_eq x y.λu:l_e_st_eq_landau_n_rt_eq y z.l_e_st_eq_landau_n_treq x y z t u : Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πz:l_e_st_eq_landau_n_frac.Πt:l_e_st_eq_landau_n_rt_eq x y.Πu:l_e_st_eq_landau_n_rt_eq y z.l_e_st_eq_landau_n_rt_eq x z).
+
+(* notion 1412 *)
+definition l_e_st_eq_landau_n_rt_inf ≝ λx:l_e_st_eq_landau_n_frac.λs:l_e_st_set l_e_st_eq_landau_n_frac.(l_e_st_esti l_e_st_eq_landau_n_frac x s : Prop).
+
+(* notion 1413 *)
+definition l_e_st_eq_landau_n_rt_rat ≝ (l_e_st_eq_ect l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq : Type[0]).
+
+(* notion 1414 *)
+definition l_e_st_eq_landau_n_rt_is ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_is l_e_st_eq_landau_n_rt_rat x0 y0 : Prop).
+
+(* notion 1415 *)
+definition l_e_st_eq_landau_n_rt_nis ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_not (l_e_st_eq_landau_n_rt_is x0 y0) : Prop).
+
+(* notion 1416 *)
+definition l_e_st_eq_landau_n_rt_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_rat.Prop.(l_some l_e_st_eq_landau_n_rt_rat p : Prop).
+
+(* notion 1417 *)
+definition l_e_st_eq_landau_n_rt_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_rat.Prop.(l_all l_e_st_eq_landau_n_rt_rat p : Prop).
+
+(* notion 1418 *)
+definition l_e_st_eq_landau_n_rt_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_rat.Prop.(l_e_one l_e_st_eq_landau_n_rt_rat p : Prop).
+
+(* notion 1419 *)
+definition l_e_st_eq_landau_n_rt_in ≝ λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_e_st_esti l_e_st_eq_landau_n_rt_rat x0 s : Prop).
+
+(* notion 1420 *)
+definition l_e_st_eq_landau_n_rt_ratof ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_ectelt l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 1421 *)
+definition l_e_st_eq_landau_n_rt_class ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_ecect l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x0 : l_e_st_set l_e_st_eq_landau_n_frac).
+
+(* notion 1422 *)
+definition l_e_st_eq_landau_n_rt_inclass ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_4_th5 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x : l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ratof x))).
+
+(* notion 1423 *)
+definition l_e_st_eq_landau_n_rt_lemmaeq1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λe:l_e_st_eq_landau_n_eq x y.(l_e_st_eq_4_th8 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x0 x xix0 y e : l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class x0)).
+
+(* notion 1424 *)
+definition l_e_st_eq_landau_n_rt_ratapp1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).a.(l_e_st_eq_4_th3 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x0 a a1 : a).
+
+(* notion 1425 *)
+definition l_e_st_eq_landau_n_rt_ii5_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).a.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_rt_ratapp1 y0 a (λy:l_e_st_eq_landau_n_frac.λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).a1 x y xix0 yi) : a).
+
+(* notion 1426 *)
+definition l_e_st_eq_landau_n_rt_ratapp2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).a.(l_e_st_eq_landau_n_rt_ratapp1 x0 a (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_ii5_t1 x0 y0 a a1 x xi) : a).
+
+(* notion 1427 *)
+definition l_e_st_eq_landau_n_rt_ii5_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πz:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).Πzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).a.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_rt_ratapp2 y0 z0 a (λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).a1 x y z xix0 yi zi) : a).
+
+(* notion 1428 *)
+definition l_e_st_eq_landau_n_rt_ratapp3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πz:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).Πzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).a.(l_e_st_eq_landau_n_rt_ratapp1 x0 a (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_ii5_t2 x0 y0 z0 a a1 x xi) : a).
+
+(* notion 1429 *)
+definition l_e_st_eq_landau_n_rt_ii5_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πz:l_e_st_eq_landau_n_frac.Πu:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).Πzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).Πui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).a.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_rt_ratapp3 y0 z0 u0 a (λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).a1 x y z u xix0 yi zi ui) : a).
+
+(* notion 1430 *)
+definition l_e_st_eq_landau_n_rt_ratapp4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λa:Prop.λa1:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.Πz:l_e_st_eq_landau_n_frac.Πu:l_e_st_eq_landau_n_frac.Πxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).Πyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).Πzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).Πui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).a.(l_e_st_eq_landau_n_rt_ratapp1 x0 a (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_ii5_t3 x0 y0 z0 u0 a a1 x xi) : a).
+
+(* notion 1431 *)
+definition l_e_st_eq_landau_n_rt_isi ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λe:l_e_st_eq_landau_n_eq x1 y1.(l_e_st_eq_5_th3 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x0 y0 x1 x1ix0 y1 y1iy0 e : l_e_st_eq_landau_n_rt_is x0 y0).
+
+(* notion 1432 *)
+definition l_e_st_eq_landau_n_rt_ise ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_5_th5 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq x0 y0 x1 x1ix0 y1 y1iy0 i : l_e_st_eq_landau_n_eq x1 y1).
+
+(* notion 1433 *)
+definition l_e_st_eq_landau_n_rt_nisi ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λn:l_not (l_e_st_eq_landau_n_eq x1 y1).(l_imp_th3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_eq x1 y1) n (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_ise x0 y0 x1 y1 x1ix0 y1iy0 t) : l_e_st_eq_landau_n_rt_nis x0 y0).
+
+(* notion 1434 *)
+definition l_e_st_eq_landau_n_rt_nise ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λn:l_e_st_eq_landau_n_rt_nis x0 y0.(l_imp_th3 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_rt_is x0 y0) n (λt:l_e_st_eq_landau_n_eq x1 y1.l_e_st_eq_landau_n_rt_isi x0 y0 x1 y1 x1ix0 y1iy0 t) : l_not (l_e_st_eq_landau_n_eq x1 y1)).
+
+(* notion 1435 *)
+definition l_e_st_eq_landau_n_rt_fixf ≝ λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.alpha.(l_e_st_eq_fixfu2 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq alpha f : Prop).
+
+(* notion 1436 *)
+definition l_e_st_eq_landau_n_rt_indrat ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.alpha.λff:l_e_st_eq_landau_n_rt_fixf alpha f.(l_e_st_eq_indeq2 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq alpha f ff x0 y0 : alpha).
+
+(* notion 1437 *)
+definition l_e_st_eq_landau_n_rt_isindrat ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.alpha.λff:l_e_st_eq_landau_n_rt_fixf alpha f.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_11_th1 l_e_st_eq_landau_n_frac l_e_st_eq_landau_n_rt_eq l_e_st_eq_landau_n_rt_refeq l_e_st_eq_landau_n_rt_symeq l_e_st_eq_landau_n_rt_treq alpha f ff x0 y0 x xix0 y yiy0 : l_e_is alpha (f x y) (l_e_st_eq_landau_n_rt_indrat x0 y0 alpha f ff)).
+
+(* notion 1438 *)
+definition l_e_st_eq_landau_n_rt_satz78 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_refis l_e_st_eq_landau_n_rt_rat x0 : l_e_st_eq_landau_n_rt_is x0 x0).
+
+(* notion 1439 *)
+definition l_e_st_eq_landau_n_rt_satz79 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_symis l_e_st_eq_landau_n_rt_rat x0 y0 i : l_e_st_eq_landau_n_rt_is y0 x0).
+
+(* notion 1440 *)
+definition l_e_st_eq_landau_n_rt_satz80 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is y0 z0.(l_e_tris l_e_st_eq_landau_n_rt_rat x0 y0 z0 i j : l_e_st_eq_landau_n_rt_is x0 z0).
+
+(* notion 1441 *)
+definition l_e_st_eq_landau_n_rt_more ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_some l_e_st_eq_landau_n_frac (λx:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (λy:l_e_st_eq_landau_n_frac.l_and3 (l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref x y))) : Prop).
+
+(* notion 1442 *)
+definition l_e_st_eq_landau_n_rt_ii5_propm ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.(l_and3 (l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref x1 y1) : Prop).
+
+(* notion 1443 *)
+definition l_e_st_eq_landau_n_rt_ii5_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u.(l_and3e1 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref t u) p : l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)).
+
+(* notion 1444 *)
+definition l_e_st_eq_landau_n_rt_ii5_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u.(l_and3e2 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref t u) p : l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)).
+
+(* notion 1445 *)
+definition l_e_st_eq_landau_n_rt_ii5_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u.(l_and3e3 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref t u) p : l_e_st_eq_landau_n_moref t u).
+
+(* notion 1446 *)
+definition l_e_st_eq_landau_n_rt_ii5_t7 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u.(l_e_st_eq_landau_n_satz44 t u x y (l_e_st_eq_landau_n_rt_ii5_t6 x0 y0 m x y xix0 yiy0 t s u p) (l_e_st_eq_landau_n_rt_ise x0 x0 t x (l_e_st_eq_landau_n_rt_ii5_t4 x0 y0 m x y xix0 yiy0 t s u p) xix0 (l_e_refis l_e_st_eq_landau_n_rt_rat x0)) (l_e_st_eq_landau_n_rt_ise y0 y0 u y (l_e_st_eq_landau_n_rt_ii5_t5 x0 y0 m x y xix0 yiy0 t s u p) yiy0 (l_e_refis l_e_st_eq_landau_n_rt_rat y0)) : l_e_st_eq_landau_n_moref x y).
+
+(* notion 1447 *)
+definition l_e_st_eq_landau_n_rt_ii5_t8 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).(l_someapp l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u) s (l_e_st_eq_landau_n_moref x y) (λu:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u.l_e_st_eq_landau_n_rt_ii5_t7 x0 y0 m x y xix0 yiy0 t s u v) : l_e_st_eq_landau_n_moref x y).
+
+(* notion 1448 *)
+definition l_e_st_eq_landau_n_rt_also18 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_someapp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u)) m (l_e_st_eq_landau_n_moref x y) (λt:l_e_st_eq_landau_n_frac.λv:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 t u).l_e_st_eq_landau_n_rt_ii5_t8 x0 y0 m x y xix0 yiy0 t v) : l_e_st_eq_landau_n_moref x y).
+
+(* notion 1449 *)
+definition l_e_st_eq_landau_n_rt_ii5_t9 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_moref x1 y1.(l_and3i (l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_moref x1 y1) x1ix0 y1iy0 m : l_e_st_eq_landau_n_rt_ii5_propm x0 y0 x1 y1).
+
+(* notion 1450 *)
+definition l_e_st_eq_landau_n_rt_ii5_t10 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_moref x1 y1.(l_somei l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 x1 t) y1 (l_e_st_eq_landau_n_rt_ii5_t9 x0 y0 x1 y1 x1ix0 y1iy0 m) : l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 x1 t)).
+
+(* notion 1451 *)
+definition l_e_st_eq_landau_n_rt_morei ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_moref x1 y1.(l_somei l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propm x0 y0 u t)) x1 (l_e_st_eq_landau_n_rt_ii5_t10 x0 y0 x1 y1 x1ix0 y1iy0 m) : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 1452 *)
+definition l_e_st_eq_landau_n_rt_moree ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_also18 x0 y0 m x1 y1 x1ix0 y1iy0 : l_e_st_eq_landau_n_moref x1 y1).
+
+(* notion 1453 *)
+definition l_e_st_eq_landau_n_rt_ismore1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λm:l_e_st_eq_landau_n_rt_more x0 z0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t z0) x0 y0 m i : l_e_st_eq_landau_n_rt_more y0 z0).
+
+(* notion 1454 *)
+definition l_e_st_eq_landau_n_rt_ismore2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λm:l_e_st_eq_landau_n_rt_more z0 x0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more z0 t) x0 y0 m i : l_e_st_eq_landau_n_rt_more z0 y0).
+
+(* notion 1455 *)
+definition l_e_st_eq_landau_n_rt_ismore12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.λm:l_e_st_eq_landau_n_rt_more x0 z0.(l_e_st_eq_landau_n_rt_ismore2 z0 u0 y0 j (l_e_st_eq_landau_n_rt_ismore1 x0 y0 z0 i m) : l_e_st_eq_landau_n_rt_more y0 u0).
+
+(* notion 1456 *)
+definition l_e_st_eq_landau_n_rt_less ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_some l_e_st_eq_landau_n_frac (λx:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (λy:l_e_st_eq_landau_n_frac.l_and3 (l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf x y))) : Prop).
+
+(* notion 1457 *)
+definition l_e_st_eq_landau_n_rt_ii5_propl ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.(l_and3 (l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf x1 y1) : Prop).
+
+(* notion 1458 *)
+definition l_e_st_eq_landau_n_rt_ii5_t11 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u.(l_and3e1 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf t u) p : l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)).
+
+(* notion 1459 *)
+definition l_e_st_eq_landau_n_rt_ii5_t12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u.(l_and3e2 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf t u) p : l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)).
+
+(* notion 1460 *)
+definition l_e_st_eq_landau_n_rt_ii5_t13 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u.(l_and3e3 (l_e_st_eq_landau_n_rt_inf t (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf t u) p : l_e_st_eq_landau_n_lessf t u).
+
+(* notion 1461 *)
+definition l_e_st_eq_landau_n_rt_ii5_t14 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).λu:l_e_st_eq_landau_n_frac.λp:l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u.(l_e_st_eq_landau_n_satz45 t u x y (l_e_st_eq_landau_n_rt_ii5_t13 x0 y0 l x y xix0 yiy0 t s u p) (l_e_st_eq_landau_n_rt_ise x0 x0 t x (l_e_st_eq_landau_n_rt_ii5_t11 x0 y0 l x y xix0 yiy0 t s u p) xix0 (l_e_refis l_e_st_eq_landau_n_rt_rat x0)) (l_e_st_eq_landau_n_rt_ise y0 y0 u y (l_e_st_eq_landau_n_rt_ii5_t12 x0 y0 l x y xix0 yiy0 t s u p) yiy0 (l_e_refis l_e_st_eq_landau_n_rt_rat y0)) : l_e_st_eq_landau_n_lessf x y).
+
+(* notion 1462 *)
+definition l_e_st_eq_landau_n_rt_ii5_t15 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λt:l_e_st_eq_landau_n_frac.λs:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).(l_someapp l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u) s (l_e_st_eq_landau_n_lessf x y) (λu:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u.l_e_st_eq_landau_n_rt_ii5_t14 x0 y0 l x y xix0 yiy0 t s u v) : l_e_st_eq_landau_n_lessf x y).
+
+(* notion 1463 *)
+definition l_e_st_eq_landau_n_rt_also19 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_someapp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u)) l (l_e_st_eq_landau_n_lessf x y) (λt:l_e_st_eq_landau_n_frac.λv:l_some l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 t u).l_e_st_eq_landau_n_rt_ii5_t15 x0 y0 l x y xix0 yiy0 t v) : l_e_st_eq_landau_n_lessf x y).
+
+(* notion 1464 *)
+definition l_e_st_eq_landau_n_rt_ii5_t16 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_lessf x1 y1.(l_and3i (l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0)) (l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0)) (l_e_st_eq_landau_n_lessf x1 y1) x1ix0 y1iy0 l : l_e_st_eq_landau_n_rt_ii5_propl x0 y0 x1 y1).
+
+(* notion 1465 *)
+definition l_e_st_eq_landau_n_rt_ii5_t17 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_lessf x1 y1.(l_somei l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 x1 t) y1 (l_e_st_eq_landau_n_rt_ii5_t16 x0 y0 x1 y1 x1ix0 y1iy0 l) : l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 x1 t)).
+
+(* notion 1466 *)
+definition l_e_st_eq_landau_n_rt_lessi ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_lessf x1 y1.(l_somei l_e_st_eq_landau_n_frac (λu:l_e_st_eq_landau_n_frac.l_some l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ii5_propl x0 y0 u t)) x1 (l_e_st_eq_landau_n_rt_ii5_t17 x0 y0 x1 y1 x1ix0 y1iy0 l) : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 1467 *)
+definition l_e_st_eq_landau_n_rt_lesse ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_also19 x0 y0 l x1 y1 x1ix0 y1iy0 : l_e_st_eq_landau_n_lessf x1 y1).
+
+(* notion 1468 *)
+definition l_e_st_eq_landau_n_rt_isless1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λl:l_e_st_eq_landau_n_rt_less x0 z0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t z0) x0 y0 l i : l_e_st_eq_landau_n_rt_less y0 z0).
+
+(* notion 1469 *)
+definition l_e_st_eq_landau_n_rt_isless2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λl:l_e_st_eq_landau_n_rt_less z0 x0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less z0 t) x0 y0 l i : l_e_st_eq_landau_n_rt_less z0 y0).
+
+(* notion 1470 *)
+definition l_e_st_eq_landau_n_rt_isless12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.λl:l_e_st_eq_landau_n_rt_less x0 z0.(l_e_st_eq_landau_n_rt_isless2 z0 u0 y0 j (l_e_st_eq_landau_n_rt_isless1 x0 y0 z0 i l) : l_e_st_eq_landau_n_rt_less y0 u0).
+
+(* notion 1471 *)
+definition l_e_st_eq_landau_n_rt_581_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_satz41a x1 y1 : l_or3 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1)).
+
+(* notion 1472 *)
+definition l_e_st_eq_landau_n_rt_581_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λe:l_e_st_eq_landau_n_eq x1 y1.(l_or3i1 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_isi x0 y0 x1 y1 x1ix0 y1iy0 e) : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1473 *)
+definition l_e_st_eq_landau_n_rt_581_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_moref x1 y1.(l_or3i2 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_morei x0 y0 x1 y1 x1ix0 y1iy0 m) : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1474 *)
+definition l_e_st_eq_landau_n_rt_581_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_lessf x1 y1.(l_or3i3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_lessi x0 y0 x1 y1 x1ix0 y1iy0 l) : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1475 *)
+definition l_e_st_eq_landau_n_rt_581_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_or3app (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1) (l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)) (l_e_st_eq_landau_n_rt_581_t1 x0 y0 x1 y1 x1ix0 y1iy0) (λt:l_e_st_eq_landau_n_eq x1 y1.l_e_st_eq_landau_n_rt_581_t2 x0 y0 x1 y1 x1ix0 y1iy0 t) (λt:l_e_st_eq_landau_n_moref x1 y1.l_e_st_eq_landau_n_rt_581_t3 x0 y0 x1 y1 x1ix0 y1iy0 t) (λt:l_e_st_eq_landau_n_lessf x1 y1.l_e_st_eq_landau_n_rt_581_t4 x0 y0 x1 y1 x1ix0 y1iy0 t) : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1476 *)
+definition l_e_st_eq_landau_n_rt_581_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_satz41b x1 y1 : l_ec3 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1)).
+
+(* notion 1477 *)
+definition l_e_st_eq_landau_n_rt_581_t7 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_imp_th3 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_moref x1 y1) (l_ec3e12 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1) (l_e_st_eq_landau_n_rt_581_t6 x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_ise x0 y0 x1 y1 x1ix0 y1iy0 i)) (λt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_moree x0 y0 x1 y1 x1ix0 y1iy0 t) : l_not (l_e_st_eq_landau_n_rt_more x0 y0)).
+
+(* notion 1478 *)
+definition l_e_st_eq_landau_n_rt_581_t8 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_imp_th3 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_lessf x1 y1) (l_ec3e23 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1) (l_e_st_eq_landau_n_rt_581_t6 x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_moree x0 y0 x1 y1 x1ix0 y1iy0 m)) (λt:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_lesse x0 y0 x1 y1 x1ix0 y1iy0 t) : l_not (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1479 *)
+definition l_e_st_eq_landau_n_rt_581_t9 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_imp_th3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_eq x1 y1) (l_ec3e31 (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_lessf x1 y1) (l_e_st_eq_landau_n_rt_581_t6 x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_lesse x0 y0 x1 y1 x1ix0 y1iy0 l)) (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_ise x0 y0 x1 y1 x1ix0 y1iy0 t) : l_e_st_eq_landau_n_rt_nis x0 y0).
+
+(* notion 1480 *)
+definition l_e_st_eq_landau_n_rt_581_t10 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_ec3_th6 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_ec_th1 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_581_t7 x0 y0 x1 y1 x1ix0 y1iy0 t)) (l_ec_th1 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (λt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_581_t8 x0 y0 x1 y1 x1ix0 y1iy0 t)) (l_ec_th1 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (λt:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_581_t9 x0 y0 x1 y1 x1ix0 y1iy0 t)) : l_ec3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1481 *)
+definition l_e_st_eq_landau_n_rt_581_t11 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_orec3i (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_581_t5 x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_581_t10 x0 y0 x1 y1 x1ix0 y1iy0) : l_orec3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1482 *)
+definition l_e_st_eq_landau_n_rt_satz81 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_orec3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_581_t11 x0 y0 x y xi yi) : l_orec3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1483 *)
+definition l_e_st_eq_landau_n_rt_satz81a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_orec3e1 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81 x0 y0) : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1484 *)
+definition l_e_st_eq_landau_n_rt_satz81b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_orec3e2 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81 x0 y0) : l_ec3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1485 *)
+definition l_e_st_eq_landau_n_rt_582_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_lessi y0 x0 y x yiy0 xix0 (l_e_st_eq_landau_n_satz42 x y (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m)) : l_e_st_eq_landau_n_rt_less y0 x0).
+
+(* notion 1486 *)
+definition l_e_st_eq_landau_n_rt_satz82 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_less y0 x0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_582_t1 x0 y0 m x y xi yi) : l_e_st_eq_landau_n_rt_less y0 x0).
+
+(* notion 1487 *)
+definition l_e_st_eq_landau_n_rt_583_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_morei y0 x0 y x yiy0 xix0 (l_e_st_eq_landau_n_satz43 x y (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xix0 yiy0 l)) : l_e_st_eq_landau_n_rt_more y0 x0).
+
+(* notion 1488 *)
+definition l_e_st_eq_landau_n_rt_satz83 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_more y0 x0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_583_t1 x0 y0 l x y xi yi) : l_e_st_eq_landau_n_rt_more y0 x0).
+
+(* notion 1489 *)
+definition l_e_st_eq_landau_n_rt_moreis ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_or (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) : Prop).
+
+(* notion 1490 *)
+definition l_e_st_eq_landau_n_rt_moreisi1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_ori1 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) m : l_e_st_eq_landau_n_rt_moreis x0 y0).
+
+(* notion 1491 *)
+definition l_e_st_eq_landau_n_rt_moreisi2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_ori2 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) i : l_e_st_eq_landau_n_rt_moreis x0 y0).
+
+(* notion 1492 *)
+definition l_e_st_eq_landau_n_rt_moreisi ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_moreq x1 y1.(l_orapp (l_e_st_eq_landau_n_moref x1 y1) (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_rt_moreis x0 y0) m (λt:l_e_st_eq_landau_n_moref x1 y1.l_e_st_eq_landau_n_rt_moreisi1 x0 y0 (l_e_st_eq_landau_n_rt_morei x0 y0 x1 y1 x1ix0 y1iy0 t)) (λt:l_e_st_eq_landau_n_eq x1 y1.l_e_st_eq_landau_n_rt_moreisi2 x0 y0 (l_e_st_eq_landau_n_rt_isi x0 y0 x1 y1 x1ix0 y1iy0 t)) : l_e_st_eq_landau_n_rt_moreis x0 y0).
+
+(* notion 1493 *)
+definition l_e_st_eq_landau_n_rt_moreise ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λm:l_e_st_eq_landau_n_rt_moreis x0 y0.(l_orapp (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_moreq x1 y1) m (λt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_moreqi1 x1 y1 (l_e_st_eq_landau_n_rt_moree x0 y0 x1 y1 x1ix0 y1iy0 t)) (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_moreqi2 x1 y1 (l_e_st_eq_landau_n_rt_ise x0 y0 x1 y1 x1ix0 y1iy0 t)) : l_e_st_eq_landau_n_moreq x1 y1).
+
+(* notion 1494 *)
+definition l_e_st_eq_landau_n_rt_ismoreis1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λm:l_e_st_eq_landau_n_rt_moreis x0 z0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_moreis t z0) x0 y0 m i : l_e_st_eq_landau_n_rt_moreis y0 z0).
+
+(* notion 1495 *)
+definition l_e_st_eq_landau_n_rt_ismoreis2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λm:l_e_st_eq_landau_n_rt_moreis z0 x0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_moreis z0 t) x0 y0 m i : l_e_st_eq_landau_n_rt_moreis z0 y0).
+
+(* notion 1496 *)
+definition l_e_st_eq_landau_n_rt_ismoreis12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.λm:l_e_st_eq_landau_n_rt_moreis x0 z0.(l_e_st_eq_landau_n_rt_ismoreis2 z0 u0 y0 j (l_e_st_eq_landau_n_rt_ismoreis1 x0 y0 z0 i m) : l_e_st_eq_landau_n_rt_moreis y0 u0).
+
+(* notion 1497 *)
+definition l_e_st_eq_landau_n_rt_lessis ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_or (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) : Prop).
+
+(* notion 1498 *)
+definition l_e_st_eq_landau_n_rt_lessisi1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_ori1 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) l : l_e_st_eq_landau_n_rt_lessis x0 y0).
+
+(* notion 1499 *)
+definition l_e_st_eq_landau_n_rt_lessisi2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_ori2 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) i : l_e_st_eq_landau_n_rt_lessis x0 y0).
+
+(* notion 1500 *)
+definition l_e_st_eq_landau_n_rt_lessisi ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_lesseq x1 y1.(l_orapp (l_e_st_eq_landau_n_lessf x1 y1) (l_e_st_eq_landau_n_eq x1 y1) (l_e_st_eq_landau_n_rt_lessis x0 y0) l (λt:l_e_st_eq_landau_n_lessf x1 y1.l_e_st_eq_landau_n_rt_lessisi1 x0 y0 (l_e_st_eq_landau_n_rt_lessi x0 y0 x1 y1 x1ix0 y1iy0 t)) (λt:l_e_st_eq_landau_n_eq x1 y1.l_e_st_eq_landau_n_rt_lessisi2 x0 y0 (l_e_st_eq_landau_n_rt_isi x0 y0 x1 y1 x1ix0 y1iy0 t)) : l_e_st_eq_landau_n_rt_lessis x0 y0).
+
+(* notion 1501 *)
+definition l_e_st_eq_landau_n_rt_lessise ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λl:l_e_st_eq_landau_n_rt_lessis x0 y0.(l_orapp (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_lesseq x1 y1) l (λt:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_lesseqi1 x1 y1 (l_e_st_eq_landau_n_rt_lesse x0 y0 x1 y1 x1ix0 y1iy0 t)) (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_lesseqi2 x1 y1 (l_e_st_eq_landau_n_rt_ise x0 y0 x1 y1 x1ix0 y1iy0 t)) : l_e_st_eq_landau_n_lesseq x1 y1).
+
+(* notion 1502 *)
+definition l_e_st_eq_landau_n_rt_islessis1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λl:l_e_st_eq_landau_n_rt_lessis x0 z0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lessis t z0) x0 y0 l i : l_e_st_eq_landau_n_rt_lessis y0 z0).
+
+(* notion 1503 *)
+definition l_e_st_eq_landau_n_rt_islessis2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λl:l_e_st_eq_landau_n_rt_lessis z0 x0.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lessis z0 t) x0 y0 l i : l_e_st_eq_landau_n_rt_lessis z0 y0).
+
+(* notion 1504 *)
+definition l_e_st_eq_landau_n_rt_islessis12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.λl:l_e_st_eq_landau_n_rt_lessis x0 z0.(l_e_st_eq_landau_n_rt_islessis2 z0 u0 y0 j (l_e_st_eq_landau_n_rt_islessis1 x0 y0 z0 i l) : l_e_st_eq_landau_n_rt_lessis y0 u0).
+
+(* notion 1505 *)
+definition l_e_st_eq_landau_n_rt_satz81c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.(l_ec3_th7 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) (l_comor (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) m) : l_not (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1506 *)
+definition l_e_st_eq_landau_n_rt_satz81d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.(l_ec3_th9 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) l : l_not (l_e_st_eq_landau_n_rt_more x0 y0)).
+
+(* notion 1507 *)
+definition l_e_st_eq_landau_n_rt_satz81e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_more x0 y0).(l_or3_th2 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81a x0 y0) n : l_e_st_eq_landau_n_rt_lessis x0 y0).
+
+(* notion 1508 *)
+definition l_e_st_eq_landau_n_rt_satz81f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_less x0 y0).(l_comor (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_or3_th3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81a x0 y0) n) : l_e_st_eq_landau_n_rt_moreis x0 y0).
+
+(* notion 1509 *)
+definition l_e_st_eq_landau_n_rt_satz81g ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_or_th3 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (l_ec3e23 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) m) (l_ec3e21 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) m) : l_not (l_e_st_eq_landau_n_rt_lessis x0 y0)).
+
+(* notion 1510 *)
+definition l_e_st_eq_landau_n_rt_satz81h ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_or_th3 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (l_ec3e32 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) l) (l_ec3e31 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) l) : l_not (l_e_st_eq_landau_n_rt_moreis x0 y0)).
+
+(* notion 1511 *)
+definition l_e_st_eq_landau_n_rt_satz81j ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_moreis x0 y0).(l_or3e3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81a x0 y0) (l_or_th5 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) n) (l_or_th4 (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) n) : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 1512 *)
+definition l_e_st_eq_landau_n_rt_satz81k ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_lessis x0 y0).(l_or3e2 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81a x0 y0) (l_or_th4 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) n) (l_or_th5 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) n) : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 1513 *)
+definition l_e_st_eq_landau_n_rt_584_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_lessisi y0 x0 y x yiy0 xix0 (l_e_st_eq_landau_n_satz48 x y (l_e_st_eq_landau_n_rt_moreise x0 y0 x y xix0 yiy0 m)) : l_e_st_eq_landau_n_rt_lessis y0 x0).
+
+(* notion 1514 *)
+definition l_e_st_eq_landau_n_rt_satz84 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_lessis y0 x0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_584_t1 x0 y0 m x y xi yi) : l_e_st_eq_landau_n_rt_lessis y0 x0).
+
+(* notion 1515 *)
+definition l_e_st_eq_landau_n_rt_585_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_moreisi y0 x0 y x yiy0 xix0 (l_e_st_eq_landau_n_satz49 x y (l_e_st_eq_landau_n_rt_lessise x0 y0 x y xix0 yiy0 l)) : l_e_st_eq_landau_n_rt_moreis y0 x0).
+
+(* notion 1516 *)
+definition l_e_st_eq_landau_n_rt_satz85 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_moreis y0 x0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_585_t1 x0 y0 l x y xi yi) : l_e_st_eq_landau_n_rt_moreis y0 x0).
+
+(* notion 1517 *)
+definition l_e_st_eq_landau_n_rt_586_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_less y0 z0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi x0 z0 x z xix0 ziz0 (l_e_st_eq_landau_n_satz50 x y z (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xix0 yiy0 l) (l_e_st_eq_landau_n_rt_lesse y0 z0 y z yiy0 ziz0 k)) : l_e_st_eq_landau_n_rt_less x0 z0).
+
+(* notion 1518 *)
+definition l_e_st_eq_landau_n_rt_satz86 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_less y0 z0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less x0 z0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_586_t1 x0 y0 z0 l k x y z xi yi zi) : l_e_st_eq_landau_n_rt_less x0 z0).
+
+(* notion 1519 *)
+definition l_e_st_eq_landau_n_rt_trless ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_less y0 z0.(l_e_st_eq_landau_n_rt_satz86 x0 y0 z0 l k : l_e_st_eq_landau_n_rt_less x0 z0).
+
+(* notion 1520 *)
+definition l_e_st_eq_landau_n_rt_trmore ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_more y0 z0.(l_e_st_eq_landau_n_rt_satz83 z0 x0 (l_e_st_eq_landau_n_rt_satz86 z0 y0 x0 (l_e_st_eq_landau_n_rt_satz82 y0 z0 n) (l_e_st_eq_landau_n_rt_satz82 x0 y0 m)) : l_e_st_eq_landau_n_rt_more x0 z0).
+
+(* notion 1521 *)
+definition l_e_st_eq_landau_n_rt_587_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_less y0 z0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi x0 z0 x z xix0 ziz0 (l_e_st_eq_landau_n_satz51a x y z (l_e_st_eq_landau_n_rt_lessise x0 y0 x y xix0 yiy0 l) (l_e_st_eq_landau_n_rt_lesse y0 z0 y z yiy0 ziz0 k)) : l_e_st_eq_landau_n_rt_less x0 z0).
+
+(* notion 1522 *)
+definition l_e_st_eq_landau_n_rt_satz87a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_less y0 z0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less x0 z0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_587_t1 x0 y0 z0 l k x y z xi yi zi) : l_e_st_eq_landau_n_rt_less x0 z0).
+
+(* notion 1523 *)
+definition l_e_st_eq_landau_n_rt_587_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_lessis y0 z0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi x0 z0 x z xix0 ziz0 (l_e_st_eq_landau_n_satz51b x y z (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xix0 yiy0 l) (l_e_st_eq_landau_n_rt_lessise y0 z0 y z yiy0 ziz0 k)) : l_e_st_eq_landau_n_rt_less x0 z0).
+
+(* notion 1524 *)
+definition l_e_st_eq_landau_n_rt_satz87b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_lessis y0 z0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less x0 z0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_587_t2 x0 y0 z0 l k x y z xi yi zi) : l_e_st_eq_landau_n_rt_less x0 z0).
+
+(* notion 1525 *)
+definition l_e_st_eq_landau_n_rt_satz87c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_more y0 z0.(l_e_st_eq_landau_n_rt_satz83 z0 x0 (l_e_st_eq_landau_n_rt_satz87b z0 y0 x0 (l_e_st_eq_landau_n_rt_satz82 y0 z0 n) (l_e_st_eq_landau_n_rt_satz84 x0 y0 m)) : l_e_st_eq_landau_n_rt_more x0 z0).
+
+(* notion 1526 *)
+definition l_e_st_eq_landau_n_rt_satz87d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_moreis y0 z0.(l_e_st_eq_landau_n_rt_satz83 z0 x0 (l_e_st_eq_landau_n_rt_satz87a z0 y0 x0 (l_e_st_eq_landau_n_rt_satz84 y0 z0 n) (l_e_st_eq_landau_n_rt_satz82 x0 y0 m)) : l_e_st_eq_landau_n_rt_more x0 z0).
+
+(* notion 1527 *)
+definition l_e_st_eq_landau_n_rt_588_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_lessis y0 z0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessisi x0 z0 x z xix0 ziz0 (l_e_st_eq_landau_n_satz52 x y z (l_e_st_eq_landau_n_rt_lessise x0 y0 x y xix0 yiy0 l) (l_e_st_eq_landau_n_rt_lessise y0 z0 y z yiy0 ziz0 k)) : l_e_st_eq_landau_n_rt_lessis x0 z0).
+
+(* notion 1528 *)
+definition l_e_st_eq_landau_n_rt_satz88 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_lessis y0 z0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_lessis x0 z0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_588_t1 x0 y0 z0 l k x y z xi yi zi) : l_e_st_eq_landau_n_rt_lessis x0 z0).
+
+(* notion 1529 *)
+definition l_e_st_eq_landau_n_rt_trlessis ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_lessis y0 z0.(l_e_st_eq_landau_n_rt_satz88 x0 y0 z0 l k : l_e_st_eq_landau_n_rt_lessis x0 z0).
+
+(* notion 1530 *)
+definition l_e_st_eq_landau_n_rt_trmoreis ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_moreis y0 z0.(l_e_st_eq_landau_n_rt_satz85 z0 x0 (l_e_st_eq_landau_n_rt_satz88 z0 y0 x0 (l_e_st_eq_landau_n_rt_satz84 y0 z0 n) (l_e_st_eq_landau_n_rt_satz84 x0 y0 m)) : l_e_st_eq_landau_n_rt_moreis x0 z0).
+
+(* notion 1531 *)
+definition l_e_st_eq_landau_n_rt_589_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λz:l_e_st_eq_landau_n_frac.λm:l_e_st_eq_landau_n_moref z x.(l_somei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0) (l_e_st_eq_landau_n_rt_ratof z) (l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_ratof z) x0 z x (l_e_st_eq_landau_n_rt_inclass z) xix0 m) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0)).
+
+(* notion 1532 *)
+definition l_e_st_eq_landau_n_rt_589_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_someapp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_moref t x) (l_e_st_eq_landau_n_satz53 x) (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0)) (λt:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_moref t x.l_e_st_eq_landau_n_rt_589_t1 x0 x xix0 t u) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0)).
+
+(* notion 1533 *)
+definition l_e_st_eq_landau_n_rt_satz89 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp1 x0 (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0)) (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_589_t2 x0 x xi) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t x0)).
+
+(* notion 1534 *)
+definition l_e_st_eq_landau_n_rt_590_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λz:l_e_st_eq_landau_n_frac.λl:l_e_st_eq_landau_n_lessf z x.(l_somei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0) (l_e_st_eq_landau_n_rt_ratof z) (l_e_st_eq_landau_n_rt_lessi (l_e_st_eq_landau_n_rt_ratof z) x0 z x (l_e_st_eq_landau_n_rt_inclass z) xix0 l) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0)).
+
+(* notion 1535 *)
+definition l_e_st_eq_landau_n_rt_590_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_someapp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_lessf t x) (l_e_st_eq_landau_n_satz54 x) (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0)) (λt:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_lessf t x.l_e_st_eq_landau_n_rt_590_t1 x0 x xix0 t u) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0)).
+
+(* notion 1536 *)
+definition l_e_st_eq_landau_n_rt_satz90 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp1 x0 (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0)) (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_590_t2 x0 x xi) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less t x0)).
+
+(* notion 1537 *)
+definition l_e_st_eq_landau_n_rt_591_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λz:l_e_st_eq_landau_n_frac.λa:l_and (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y).(l_e_st_eq_landau_n_rt_lessi x0 (l_e_st_eq_landau_n_rt_ratof z) x z xix0 (l_e_st_eq_landau_n_rt_inclass z) (l_ande1 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y) a) : l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_ratof z)).
+
+(* notion 1538 *)
+definition l_e_st_eq_landau_n_rt_591_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λz:l_e_st_eq_landau_n_frac.λa:l_and (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y).(l_e_st_eq_landau_n_rt_lessi (l_e_st_eq_landau_n_rt_ratof z) y0 z y (l_e_st_eq_landau_n_rt_inclass z) yiy0 (l_ande2 (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y) a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ratof z) y0).
+
+(* notion 1539 *)
+definition l_e_st_eq_landau_n_rt_591_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λz:l_e_st_eq_landau_n_frac.λa:l_and (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y).(l_andi (l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_ratof z)) (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ratof z) y0) (l_e_st_eq_landau_n_rt_591_t1 x0 y0 l x y xix0 yiy0 z a) (l_e_st_eq_landau_n_rt_591_t2 x0 y0 l x y xix0 yiy0 z a) : l_and (l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_ratof z)) (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ratof z) y0)).
+
+(* notion 1540 *)
+definition l_e_st_eq_landau_n_rt_591_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λz:l_e_st_eq_landau_n_frac.λa:l_and (l_e_st_eq_landau_n_lessf x z) (l_e_st_eq_landau_n_lessf z y).(l_somei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0)) (l_e_st_eq_landau_n_rt_ratof z) (l_e_st_eq_landau_n_rt_591_t3 x0 y0 l x y xix0 yiy0 z a) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0))).
+
+(* notion 1541 *)
+definition l_e_st_eq_landau_n_rt_591_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_someapp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_and (l_e_st_eq_landau_n_lessf x t) (l_e_st_eq_landau_n_lessf t y)) (l_e_st_eq_landau_n_satz55 x y (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xix0 yiy0 l)) (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0))) (λt:l_e_st_eq_landau_n_frac.λu:l_and (l_e_st_eq_landau_n_lessf x t) (l_e_st_eq_landau_n_lessf t y).l_e_st_eq_landau_n_rt_591_t4 x0 y0 l x y xix0 yiy0 t u) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0))).
+
+(* notion 1542 *)
+definition l_e_st_eq_landau_n_rt_satz91 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0))) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_591_t5 x0 y0 l x y xi yi) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 t) (l_e_st_eq_landau_n_rt_less t y0))).
+
+(* notion 1543 *)
+definition l_e_st_eq_landau_n_rt_plusfrt ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_pf x y) : Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_rat).
+
+(* notion 1544 *)
+definition l_e_st_eq_landau_n_rt_ii5_t18 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_pf x z)) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_pf y u)) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_pf x z)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_pf y u)) (l_e_st_eq_landau_n_satz56 x y z u e f) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_plusfrt x z) (l_e_st_eq_landau_n_rt_plusfrt y u)).
+
+(* notion 1545 *)
+definition l_e_st_eq_landau_n_rt_fplusfrt ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_rt_eq x y.λw:l_e_st_eq_landau_n_rt_eq z u.l_e_st_eq_landau_n_rt_ii5_t18 x y z u v w : l_e_st_eq_landau_n_rt_fixf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_plusfrt).
+
+(* notion 1546 *)
+definition l_e_st_eq_landau_n_rt_pl ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_indrat x0 y0 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_plusfrt l_e_st_eq_landau_n_rt_fplusfrt : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 1547 *)
+definition l_e_st_eq_landau_n_rt_ii5_t19 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_isindrat x0 y0 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_plusfrt l_e_st_eq_landau_n_rt_fplusfrt x1 y1 x1ix0 y1iy0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_pf x1 y1)) (l_e_st_eq_landau_n_rt_pl x0 y0)).
+
+(* notion 1548 *)
+definition l_e_st_eq_landau_n_rt_picp ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_pf x1 y1) (l_e_st_eq_landau_n_rt_class t)) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_pf x1 y1)) (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_pf x1 y1)) (l_e_st_eq_landau_n_rt_ii5_t19 x0 y0 x1 y1 x1ix0 y1iy0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_pf x1 y1) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl x0 y0))).
+
+(* notion 1549 *)
+definition l_e_st_eq_landau_n_rt_ispl1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_pl t z0) x0 y0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1550 *)
+definition l_e_st_eq_landau_n_rt_ispl2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_pl z0 t) x0 y0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl z0 y0)).
+
+(* notion 1551 *)
+definition l_e_st_eq_landau_n_rt_ispl12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_ispl1 x0 y0 z0 i) (l_e_st_eq_landau_n_rt_ispl2 z0 u0 y0 j) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1552 *)
+definition l_e_st_eq_landau_n_rt_592_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0) (l_e_st_eq_landau_n_pf x1 y1) (l_e_st_eq_landau_n_pf y1 x1) (l_e_st_eq_landau_n_rt_picp x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_picp y0 x0 y1 x1 y1iy0 x1ix0) (l_e_st_eq_landau_n_satz58 x1 y1) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0)).
+
+(* notion 1553 *)
+definition l_e_st_eq_landau_n_rt_satz92 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_592_t1 x0 y0 x y xi yi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0)).
+
+(* notion 1554 *)
+definition l_e_st_eq_landau_n_rt_compl ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz92 x0 y0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0)).
+
+(* notion 1555 *)
+definition l_e_st_eq_landau_n_rt_593_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_picp (l_e_st_eq_landau_n_rt_pl x0 y0) z0 (l_e_st_eq_landau_n_pf x y) z (l_e_st_eq_landau_n_rt_picp x0 y0 x y xix0 yiy0) ziz0 : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0))).
+
+(* notion 1556 *)
+definition l_e_st_eq_landau_n_rt_593_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_picp x0 (l_e_st_eq_landau_n_rt_pl y0 z0) x (l_e_st_eq_landau_n_pf y z) xix0 (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)))).
+
+(* notion 1557 *)
+definition l_e_st_eq_landau_n_rt_593_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_pf x y) z) (l_e_st_eq_landau_n_pf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_rt_593_t1 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_rt_593_t2 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_satz59 x y z) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0))).
+
+(* notion 1558 *)
+definition l_e_st_eq_landau_n_rt_satz93 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0))) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_593_t3 x0 y0 z0 x y z xi yi zi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0))).
+
+(* notion 1559 *)
+definition l_e_st_eq_landau_n_rt_asspl1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz93 x0 y0 z0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0))).
+
+(* notion 1560 *)
+definition l_e_st_eq_landau_n_rt_asspl2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_satz93 x0 y0 z0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0)).
+
+(* notion 1561 *)
+definition l_e_st_eq_landau_n_rt_594_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 y0) x0 (l_e_st_eq_landau_n_pf x1 y1) x1 (l_e_st_eq_landau_n_rt_picp x0 y0 x1 y1 x1ix0 y1iy0) x1ix0 (l_e_st_eq_landau_n_satz60 x1 y1) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 y0) x0).
+
+(* notion 1562 *)
+definition l_e_st_eq_landau_n_rt_satz94 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 y0) x0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_594_t1 x0 y0 x y xi yi) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 y0) x0).
+
+(* notion 1563 *)
+definition l_e_st_eq_landau_n_rt_satz94a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_pl x0 y0) x0 (l_e_st_eq_landau_n_rt_satz94 x0 y0) : l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
+
+(* notion 1564 *)
+definition l_e_st_eq_landau_n_rt_595_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz61 x y z (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1565 *)
+definition l_e_st_eq_landau_n_rt_satz95 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_595_t1 x0 y0 z0 m x y z xi yi zi) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1566 *)
+definition l_e_st_eq_landau_n_rt_596_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz62a x y z (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1567 *)
+definition l_e_st_eq_landau_n_rt_satz96a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_596_t1 x0 y0 z0 m x y z xi yi zi) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1568 *)
+definition l_e_st_eq_landau_n_rt_596_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz62b x y z (l_e_st_eq_landau_n_rt_ise x0 y0 x y xix0 yiy0 i)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1569 *)
+definition l_e_st_eq_landau_n_rt_satz96b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_596_t2 x0 y0 z0 i x y z xi yi zi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1570 *)
+definition l_e_st_eq_landau_n_rt_596_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz62c x y z (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xix0 yiy0 l)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1571 *)
+definition l_e_st_eq_landau_n_rt_satz96c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_596_t3 x0 y0 z0 l x y z xi yi zi) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1572 *)
+definition l_e_st_eq_landau_n_rt_596_andersa ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_satz95 x0 y0 z0 m : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1573 *)
+definition l_e_st_eq_landau_n_rt_596_andersb ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ispl1 x0 y0 z0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1574 *)
+definition l_e_st_eq_landau_n_rt_596_andersc ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_satz95 y0 x0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 1575 *)
+definition l_e_st_eq_landau_n_rt_satz96d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ismore12 (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl z0 y0) (l_e_st_eq_landau_n_rt_compl x0 z0) (l_e_st_eq_landau_n_rt_compl y0 z0) (l_e_st_eq_landau_n_rt_satz96a x0 y0 z0 m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl z0 y0)).
+
+(* notion 1576 *)
+definition l_e_st_eq_landau_n_rt_satz96e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ispl2 x0 y0 z0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl z0 y0)).
+
+(* notion 1577 *)
+definition l_e_st_eq_landau_n_rt_satz96f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl z0 y0) (l_e_st_eq_landau_n_rt_compl x0 z0) (l_e_st_eq_landau_n_rt_compl y0 z0) (l_e_st_eq_landau_n_rt_satz96c x0 y0 z0 l) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl z0 x0) (l_e_st_eq_landau_n_rt_pl z0 y0)).
+
+(* notion 1578 *)
+definition l_e_st_eq_landau_n_rt_597_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_morei x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz63a x y z (l_e_st_eq_landau_n_rt_moree (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) m)) : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 1579 *)
+definition l_e_st_eq_landau_n_rt_satz97a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_more x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_597_t1 x0 y0 z0 m x y z xi yi zi) : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 1580 *)
+definition l_e_st_eq_landau_n_rt_597_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz63b x y z (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) i)) : l_e_st_eq_landau_n_rt_is x0 y0).
+
+(* notion 1581 *)
+definition l_e_st_eq_landau_n_rt_satz97b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_597_t2 x0 y0 z0 i x y z xi yi zi) : l_e_st_eq_landau_n_rt_is x0 y0).
+
+(* notion 1582 *)
+definition l_e_st_eq_landau_n_rt_597_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz63c x y z (l_e_st_eq_landau_n_rt_lesse (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y z) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) l)) : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 1583 *)
+definition l_e_st_eq_landau_n_rt_satz97c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_597_t3 x0 y0 z0 l x y z xi yi zi) : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 1584 *)
+definition l_e_st_eq_landau_n_rt_597_anders ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_satz82 y0 x0 (l_e_st_eq_landau_n_rt_satz97a y0 x0 z0 (l_e_st_eq_landau_n_rt_satz83 (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 z0) l)) : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 1585 *)
+definition l_e_st_eq_landau_n_rt_598_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz64 x y z u (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moree z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1586 *)
+definition l_e_st_eq_landau_n_rt_satz98 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_598_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1587 *)
+definition l_e_st_eq_landau_n_rt_satz98a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_satz98 y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l) (l_e_st_eq_landau_n_rt_satz83 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1588 *)
+definition l_e_st_eq_landau_n_rt_599_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz65a x y z u (l_e_st_eq_landau_n_rt_moreise x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moree z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1589 *)
+definition l_e_st_eq_landau_n_rt_satz99a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_599_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1590 *)
+definition l_e_st_eq_landau_n_rt_599_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz65b x y z u (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moreise z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1591 *)
+definition l_e_st_eq_landau_n_rt_satz99b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_599_t2 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1592 *)
+definition l_e_st_eq_landau_n_rt_satz99c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_satz99a y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz85 x0 y0 l) (l_e_st_eq_landau_n_rt_satz83 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1593 *)
+definition l_e_st_eq_landau_n_rt_satz99d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_lessis z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_satz99b y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l) (l_e_st_eq_landau_n_rt_satz85 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1594 *)
+definition l_e_st_eq_landau_n_rt_5100_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_moreisi (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_pf x z) (l_e_st_eq_landau_n_pf y u) (l_e_st_eq_landau_n_rt_picp x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_picp y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz66 x y z u (l_e_st_eq_landau_n_rt_moreise x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moreise z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1595 *)
+definition l_e_st_eq_landau_n_rt_satz100 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5100_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1596 *)
+definition l_e_st_eq_landau_n_rt_satz100a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_lessis z0 u0.(l_e_st_eq_landau_n_rt_satz84 (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_satz100 y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz85 x0 y0 l) (l_e_st_eq_landau_n_rt_satz85 z0 u0 k)) : l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_pl y0 u0)).
+
+(* notion 1597 *)
+definition l_e_st_eq_landau_n_rt_5101_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λv0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0.(l_e_st_eq_landau_n_rt_ismore1 (l_e_st_eq_landau_n_rt_pl y0 v0) x0 y0 i (l_e_st_eq_landau_n_rt_satz94 y0 v0) : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 1598 *)
+definition l_e_st_eq_landau_n_rt_5101_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λv0:l_e_st_eq_landau_n_rt_rat.(l_imp_th3 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_satz81d x0 y0 l) (λt:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0.l_e_st_eq_landau_n_rt_5101_t1 x0 y0 l v0 t) : l_e_st_eq_landau_n_rt_nis (l_e_st_eq_landau_n_rt_pl y0 v0) x0).
+
+(* notion 1599 *)
+definition l_e_st_eq_landau_n_rt_vorbemerkung101 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.(l_some_th5 l_e_st_eq_landau_n_rt_rat (λv:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v) x0) (λv:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_5101_t2 x0 y0 l v) : l_not (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0))).
+
+(* notion 1600 *)
+definition l_e_st_eq_landau_n_rt_5101_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_ratof v)) x0 (l_e_st_eq_landau_n_pf y v) x (l_e_st_eq_landau_n_rt_picp y0 (l_e_st_eq_landau_n_rt_ratof v) y v yiy0 (l_e_st_eq_landau_n_rt_inclass v)) xix0 e : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_ratof v)) x0).
+
+(* notion 1601 *)
+definition l_e_st_eq_landau_n_rt_5101_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y v) x.(l_somei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0) (l_e_st_eq_landau_n_rt_ratof v) (l_e_st_eq_landau_n_rt_5101_t3 x0 y0 m x y xix0 yiy0 v e) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)).
+
+(* notion 1602 *)
+definition l_e_st_eq_landau_n_rt_5101_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).(l_someapp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y t) x) (l_e_st_eq_landau_n_satz67a x y (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m)) (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)) (λt:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf y t) x.l_e_st_eq_landau_n_rt_5101_t4 x0 y0 m x y xix0 yiy0 t u) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)).
+
+(* notion 1603 *)
+definition l_e_st_eq_landau_n_rt_satz101a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_5101_t5 x0 y0 m x y xi yi) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)).
+
+(* notion 1604 *)
+definition l_e_st_eq_landau_n_rt_5101_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λw0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0.λj:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 w0) x0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λviv0:l_e_st_eq_landau_n_rt_inf v (l_e_st_eq_landau_n_rt_class v0).λwiw0:l_e_st_eq_landau_n_rt_inf w (l_e_st_eq_landau_n_rt_class w0).(l_e_st_eq_landau_n_rt_isi v0 w0 v w viv0 wiw0 (l_e_st_eq_landau_n_satz67b x y v w (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_pl y0 v0) x0 (l_e_st_eq_landau_n_pf y v) x (l_e_st_eq_landau_n_rt_picp y0 v0 y v yiy0 viv0) xix0 i) (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_pl y0 w0) x0 (l_e_st_eq_landau_n_pf y w) x (l_e_st_eq_landau_n_rt_picp y0 w0 y w yiy0 wiw0) xix0 j)) : l_e_st_eq_landau_n_rt_is v0 w0).
+
+(* notion 1605 *)
+definition l_e_st_eq_landau_n_rt_satz101b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λw0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0.λj:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 w0) x0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 v0 w0 (l_e_st_eq_landau_n_rt_is v0 w0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λvi:l_e_st_eq_landau_n_rt_inf v (l_e_st_eq_landau_n_rt_class v0).λwi:l_e_st_eq_landau_n_rt_inf w (l_e_st_eq_landau_n_rt_class w0).l_e_st_eq_landau_n_rt_5101_t6 x0 y0 v0 w0 i j x y v w xi yi vi wi) : l_e_st_eq_landau_n_rt_is v0 w0).
+
+(* notion 1606 *)
+definition l_e_st_eq_landau_n_rt_5101_t7 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(λt:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_rat.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0.λw:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 u) x0.l_e_st_eq_landau_n_rt_satz101b x0 y0 t u v w : l_e_amone l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)).
+
+(* notion 1607 *)
+definition l_e_st_eq_landau_n_rt_satz101 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_onei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0) (l_e_st_eq_landau_n_rt_5101_t7 x0 y0) (l_e_st_eq_landau_n_rt_satz101a x0 y0 m) : l_e_st_eq_landau_n_rt_one (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0)).
+
+(* notion 1608 *)
+definition l_e_st_eq_landau_n_rt_mn ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_ind l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0) (l_e_st_eq_landau_n_rt_satz101 x0 y0 m) : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 1609 *)
+definition l_e_st_eq_landau_n_rt_satz101c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_oneax l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 t) x0) (l_e_st_eq_landau_n_rt_satz101 x0 y0 m) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 m)) x0).
+
+(* notion 1610 *)
+definition l_e_st_eq_landau_n_rt_satz101d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 m)) x0 (l_e_st_eq_landau_n_rt_satz101c x0 y0 m) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 m))).
+
+(* notion 1611 *)
+definition l_e_st_eq_landau_n_rt_satz101e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 m)) x0 (l_e_st_eq_landau_n_rt_compl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) (l_e_st_eq_landau_n_rt_satz101c x0 y0 m) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) x0).
+
+(* notion 1612 *)
+definition l_e_st_eq_landau_n_rt_satz101f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) x0 (l_e_st_eq_landau_n_rt_satz101e x0 y0 m) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0)).
+
+(* notion 1613 *)
+definition l_e_st_eq_landau_n_rt_satz101g ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 v0) x0.(l_e_st_eq_landau_n_rt_satz101b x0 y0 v0 (l_e_st_eq_landau_n_rt_mn x0 y0 m) i (l_e_st_eq_landau_n_rt_satz101c x0 y0 m) : l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_mn x0 y0 m)).
+
+(* notion 1614 *)
+definition l_e_st_eq_landau_n_rt_timesfrt ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_tf x y) : Πx:l_e_st_eq_landau_n_frac.Πy:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_rt_rat).
+
+(* notion 1615 *)
+definition l_e_st_eq_landau_n_rt_ii5_t20 ≝ λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq x y.λf:l_e_st_eq_landau_n_eq z u.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_tf y u)) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_tf y u)) (l_e_st_eq_landau_n_satz68 x y z u e f) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_timesfrt x z) (l_e_st_eq_landau_n_rt_timesfrt y u)).
+
+(* notion 1616 *)
+definition l_e_st_eq_landau_n_rt_ftimesfrt ≝ (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_rt_eq x y.λw:l_e_st_eq_landau_n_rt_eq z u.l_e_st_eq_landau_n_rt_ii5_t20 x y z u v w : l_e_st_eq_landau_n_rt_fixf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_timesfrt).
+
+(* notion 1617 *)
+definition l_e_st_eq_landau_n_rt_ts ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_indrat x0 y0 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_timesfrt l_e_st_eq_landau_n_rt_ftimesfrt : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 1618 *)
+definition l_e_st_eq_landau_n_rt_ii5_t21 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_isindrat x0 y0 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_timesfrt l_e_st_eq_landau_n_rt_ftimesfrt x1 y1 x1ix0 y1iy0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_tf x1 y1)) (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 1619 *)
+definition l_e_st_eq_landau_n_rt_tict ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_tf x1 y1) (l_e_st_eq_landau_n_rt_class t)) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_tf x1 y1)) (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_tf x1 y1)) (l_e_st_eq_landau_n_rt_ii5_t21 x0 y0 x1 y1 x1ix0 y1iy0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_tf x1 y1) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ts x0 y0))).
+
+(* notion 1620 *)
+definition l_e_st_eq_landau_n_rt_ists1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_ts t z0) x0 y0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
+
+(* notion 1621 *)
+definition l_e_st_eq_landau_n_rt_ists2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_ts z0 t) x0 y0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts z0 y0)).
+
+(* notion 1622 *)
+definition l_e_st_eq_landau_n_rt_ists12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 u0.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_rt_ists1 x0 y0 z0 i) (l_e_st_eq_landau_n_rt_ists2 z0 u0 y0 j) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1623 *)
+definition l_e_st_eq_landau_n_rt_5102_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0) (l_e_st_eq_landau_n_tf x1 y1) (l_e_st_eq_landau_n_tf y1 x1) (l_e_st_eq_landau_n_rt_tict x0 y0 x1 y1 x1ix0 y1iy0) (l_e_st_eq_landau_n_rt_tict y0 x0 y1 x1 y1iy0 x1ix0) (l_e_st_eq_landau_n_satz69 x1 y1) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0)).
+
+(* notion 1624 *)
+definition l_e_st_eq_landau_n_rt_satz102 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_5102_t1 x0 y0 x y xi yi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0)).
+
+(* notion 1625 *)
+definition l_e_st_eq_landau_n_rt_comts ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz102 x0 y0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0)).
+
+(* notion 1626 *)
+definition l_e_st_eq_landau_n_rt_5103_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_tict (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_tf x y) z (l_e_st_eq_landau_n_rt_tict x0 y0 x y xix0 yiy0) ziz0 : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0))).
+
+(* notion 1627 *)
+definition l_e_st_eq_landau_n_rt_5103_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_tict x0 (l_e_st_eq_landau_n_rt_ts y0 z0) x (l_e_st_eq_landau_n_tf y z) xix0 (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)))).
+
+(* notion 1628 *)
+definition l_e_st_eq_landau_n_rt_5103_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_tf x y) z) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_tf y z)) (l_e_st_eq_landau_n_rt_5103_t1 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_rt_5103_t2 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_satz70 x y z) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0))).
+
+(* notion 1629 *)
+definition l_e_st_eq_landau_n_rt_satz103 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0))) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5103_t3 x0 y0 z0 x y z xi yi zi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0))).
+
+(* notion 1630 *)
+definition l_e_st_eq_landau_n_rt_assts1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz103 x0 y0 z0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0))).
+
+(* notion 1631 *)
+definition l_e_st_eq_landau_n_rt_assts2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_satz103 x0 y0 z0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0)).
+
+(* notion 1632 *)
+definition l_e_st_eq_landau_n_rt_5104_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_tict x0 (l_e_st_eq_landau_n_rt_pl y0 z0) x (l_e_st_eq_landau_n_pf y z) xix0 (l_e_st_eq_landau_n_rt_picp y0 z0 y z yiy0 ziz0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)))).
+
+(* notion 1633 *)
+definition l_e_st_eq_landau_n_rt_5104_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_picp (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_rt_tict x0 y0 x y xix0 yiy0) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0)))).
+
+(* notion 1634 *)
+definition l_e_st_eq_landau_n_rt_5104_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0)) (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_pf y z)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_tf x y) (l_e_st_eq_landau_n_tf x z)) (l_e_st_eq_landau_n_rt_5104_t1 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_rt_5104_t2 x0 y0 z0 x y z xix0 yiy0 ziz0) (l_e_st_eq_landau_n_satz71 x y z) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0))).
+
+(* notion 1635 *)
+definition l_e_st_eq_landau_n_rt_satz104 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0))) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5104_t3 x0 y0 z0 x y z xi yi zi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0))).
+
+(* notion 1636 *)
+definition l_e_st_eq_landau_n_rt_disttp1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_ts z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts z0 y0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_comts (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_satz104 z0 x0 y0) (l_e_st_eq_landau_n_rt_ispl12 (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts z0 y0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_comts z0 x0) (l_e_st_eq_landau_n_rt_comts z0 y0)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0))).
+
+(* notion 1637 *)
+definition l_e_st_eq_landau_n_rt_disttp2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz104 x0 y0 z0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0))).
+
+(* notion 1638 *)
+definition l_e_st_eq_landau_n_rt_distpt1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_disttp1 x0 y0 z0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) z0)).
+
+(* notion 1639 *)
+definition l_e_st_eq_landau_n_rt_distpt2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0)) (l_e_st_eq_landau_n_rt_disttp2 x0 y0 z0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0)) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0))).
+
+(* notion 1640 *)
+definition l_e_st_eq_landau_n_rt_5105_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz72a x y z (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
+
+(* notion 1641 *)
+definition l_e_st_eq_landau_n_rt_satz105a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5105_t1 x0 y0 z0 m x y z xi yi zi) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
+
+(* notion 1642 *)
+definition l_e_st_eq_landau_n_rt_5105_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) (l_e_st_eq_landau_n_satz72b x y z (l_e_st_eq_landau_n_rt_ise x0 y0 x y xix0 yiy0 i)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
+
+(* notion 1643 *)
+definition l_e_st_eq_landau_n_rt_satz105b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5105_t2 x0 y0 z0 i x y z xi yi zi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
+
+(* notion 1644 *)
+definition l_e_st_eq_landau_n_rt_5105_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xi zi) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yi zi) (l_e_st_eq_landau_n_satz72c x y z (l_e_st_eq_landau_n_rt_lesse x0 y0 x y xi yi l)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
+
+(* notion 1645 *)
+definition l_e_st_eq_landau_n_rt_satz105c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5105_t3 x0 y0 z0 l x y z xi yi zi) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
+
+(* notion 1646 *)
+definition l_e_st_eq_landau_n_rt_5105_andersb ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ists1 x0 y0 z0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
+
+(* notion 1647 *)
+definition l_e_st_eq_landau_n_rt_5105_andersc ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_satz105a y0 x0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0)).
+
+(* notion 1648 *)
+definition l_e_st_eq_landau_n_rt_satz105d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_ismore12 (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_ts z0 y0) (l_e_st_eq_landau_n_rt_comts x0 z0) (l_e_st_eq_landau_n_rt_comts y0 z0) (l_e_st_eq_landau_n_rt_satz105a x0 y0 z0 m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts z0 y0)).
+
+(* notion 1649 *)
+definition l_e_st_eq_landau_n_rt_satz105e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ists2 x0 y0 z0 i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts z0 y0)).
+
+(* notion 1650 *)
+definition l_e_st_eq_landau_n_rt_satz105f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_ts z0 y0) (l_e_st_eq_landau_n_rt_comts x0 z0) (l_e_st_eq_landau_n_rt_comts y0 z0) (l_e_st_eq_landau_n_rt_satz105c x0 y0 z0 l) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts z0 x0) (l_e_st_eq_landau_n_rt_ts z0 y0)).
+
+(* notion 1651 *)
+definition l_e_st_eq_landau_n_rt_5106_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_morei x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz73a x y z (l_e_st_eq_landau_n_rt_moree (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) m)) : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 1652 *)
+definition l_e_st_eq_landau_n_rt_satz106a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_more x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5106_t1 x0 y0 z0 m x y z xi yi zi) : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 1653 *)
+definition l_e_st_eq_landau_n_rt_5106_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_isi x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz73b x y z (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) i)) : l_e_st_eq_landau_n_rt_is x0 y0).
+
+(* notion 1654 *)
+definition l_e_st_eq_landau_n_rt_satz106b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_is x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5106_t2 x0 y0 z0 i x y z xi yi zi) : l_e_st_eq_landau_n_rt_is x0 y0).
+
+(* notion 1655 *)
+definition l_e_st_eq_landau_n_rt_5106_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).(l_e_st_eq_landau_n_rt_lessi x0 y0 x y xix0 yiy0 (l_e_st_eq_landau_n_satz73c x y z (l_e_st_eq_landau_n_rt_lesse (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y z) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 z0 y z yiy0 ziz0) l)) : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 1656 *)
+definition l_e_st_eq_landau_n_rt_satz106c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_ratapp3 x0 y0 z0 (l_e_st_eq_landau_n_rt_less x0 y0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).l_e_st_eq_landau_n_rt_5106_t3 x0 y0 z0 l x y z xi yi zi) : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 1657 *)
+definition l_e_st_eq_landau_n_rt_5106_anders ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_satz82 y0 x0 (l_e_st_eq_landau_n_rt_satz106a y0 x0 z0 (l_e_st_eq_landau_n_rt_satz83 (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 z0) l)) : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 1658 *)
+definition l_e_st_eq_landau_n_rt_5107_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz74 x y z u (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moree z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1659 *)
+definition l_e_st_eq_landau_n_rt_satz107 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5107_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1660 *)
+definition l_e_st_eq_landau_n_rt_satz107a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_satz107 y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l) (l_e_st_eq_landau_n_rt_satz83 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1661 *)
+definition l_e_st_eq_landau_n_rt_5108_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz75a x y z u (l_e_st_eq_landau_n_rt_moreise x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moree z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1662 *)
+definition l_e_st_eq_landau_n_rt_satz108a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_more z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5108_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1663 *)
+definition l_e_st_eq_landau_n_rt_5108_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz75b x y z u (l_e_st_eq_landau_n_rt_moree x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moreise z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1664 *)
+definition l_e_st_eq_landau_n_rt_satz108b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5108_t2 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1665 *)
+definition l_e_st_eq_landau_n_rt_satz108c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_satz108a y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz85 x0 y0 l) (l_e_st_eq_landau_n_rt_satz83 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1666 *)
+definition l_e_st_eq_landau_n_rt_satz108d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.λk:l_e_st_eq_landau_n_rt_lessis z0 u0.(l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_satz108b y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l) (l_e_st_eq_landau_n_rt_satz85 z0 u0 k)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1667 *)
+definition l_e_st_eq_landau_n_rt_5109_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λziz0:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_moreisi (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_tf x z) (l_e_st_eq_landau_n_tf y u) (l_e_st_eq_landau_n_rt_tict x0 z0 x z xix0 ziz0) (l_e_st_eq_landau_n_rt_tict y0 u0 y u yiy0 uiu0) (l_e_st_eq_landau_n_satz76 x y z u (l_e_st_eq_landau_n_rt_moreise x0 y0 x y xix0 yiy0 m) (l_e_st_eq_landau_n_rt_moreise z0 u0 z u ziz0 uiu0 n)) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1668 *)
+definition l_e_st_eq_landau_n_rt_satz109 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.λn:l_e_st_eq_landau_n_rt_moreis z0 u0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 z0 u0 (l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λz:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λzi:l_e_st_eq_landau_n_rt_inf z (l_e_st_eq_landau_n_rt_class z0).λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5109_t1 x0 y0 z0 u0 m n x y z u xi yi zi ui) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1669 *)
+definition l_e_st_eq_landau_n_rt_satz109a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.λk:l_e_st_eq_landau_n_rt_lessis z0 u0.(l_e_st_eq_landau_n_rt_satz84 (l_e_st_eq_landau_n_rt_ts y0 u0) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_satz109 y0 x0 u0 z0 (l_e_st_eq_landau_n_rt_satz85 x0 y0 l) (l_e_st_eq_landau_n_rt_satz85 z0 u0 k)) : l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_ts y0 u0)).
+
+(* notion 1670 *)
+definition l_e_st_eq_landau_n_rt_5110_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y1 v) x1.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ratof v)) x0 (l_e_st_eq_landau_n_tf y1 v) x1 (l_e_st_eq_landau_n_rt_tict y0 (l_e_st_eq_landau_n_rt_ratof v) y1 v y1iy0 (l_e_st_eq_landau_n_rt_inclass v)) x1ix0 e : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ratof v)) x0).
+
+(* notion 1671 *)
+definition l_e_st_eq_landau_n_rt_5110_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).λv:l_e_st_eq_landau_n_frac.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y1 v) x1.(l_somei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0) (l_e_st_eq_landau_n_rt_ratof v) (l_e_st_eq_landau_n_rt_5110_t1 x0 y0 x1 y1 x1ix0 y1iy0 v e) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)).
+
+(* notion 1672 *)
+definition l_e_st_eq_landau_n_rt_5110_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx1:l_e_st_eq_landau_n_frac.λy1:l_e_st_eq_landau_n_frac.λx1ix0:l_e_st_eq_landau_n_rt_inf x1 (l_e_st_eq_landau_n_rt_class x0).λy1iy0:l_e_st_eq_landau_n_rt_inf y1 (l_e_st_eq_landau_n_rt_class y0).(l_someapp l_e_st_eq_landau_n_frac (λt:l_e_st_eq_landau_n_frac.l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y1 t) x1) (l_e_st_eq_landau_n_satz77a x1 y1) (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)) (λt:l_e_st_eq_landau_n_frac.λu:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf y1 t) x1.l_e_st_eq_landau_n_rt_5110_t2 x0 y0 x1 y1 x1ix0 y1iy0 t u) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)).
+
+(* notion 1673 *)
+definition l_e_st_eq_landau_n_rt_satz110a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp2 x0 y0 (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).l_e_st_eq_landau_n_rt_5110_t3 x0 y0 x y xi yi) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)).
+
+(* notion 1674 *)
+definition l_e_st_eq_landau_n_rt_5110_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λw0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 v0) x0.λj:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 w0) x0.λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyiy0:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λviv0:l_e_st_eq_landau_n_rt_inf v (l_e_st_eq_landau_n_rt_class v0).λwiw0:l_e_st_eq_landau_n_rt_inf w (l_e_st_eq_landau_n_rt_class w0).(l_e_st_eq_landau_n_rt_isi v0 w0 v w viv0 wiw0 (l_e_st_eq_landau_n_satz77b x y v w (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_ts y0 v0) x0 (l_e_st_eq_landau_n_tf y v) x (l_e_st_eq_landau_n_rt_tict y0 v0 y v yiy0 viv0) xix0 i) (l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_ts y0 w0) x0 (l_e_st_eq_landau_n_tf y w) x (l_e_st_eq_landau_n_rt_tict y0 w0 y w yiy0 wiw0) xix0 j)) : l_e_st_eq_landau_n_rt_is v0 w0).
+
+(* notion 1675 *)
+definition l_e_st_eq_landau_n_rt_satz110b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λw0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 v0) x0.λj:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 w0) x0.(l_e_st_eq_landau_n_rt_ratapp4 x0 y0 v0 w0 (l_e_st_eq_landau_n_rt_is v0 w0) (λx:l_e_st_eq_landau_n_frac.λy:l_e_st_eq_landau_n_frac.λv:l_e_st_eq_landau_n_frac.λw:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).λyi:l_e_st_eq_landau_n_rt_inf y (l_e_st_eq_landau_n_rt_class y0).λvi:l_e_st_eq_landau_n_rt_inf v (l_e_st_eq_landau_n_rt_class v0).λwi:l_e_st_eq_landau_n_rt_inf w (l_e_st_eq_landau_n_rt_class w0).l_e_st_eq_landau_n_rt_5110_t4 x0 y0 v0 w0 i j x y v w xi yi vi wi) : l_e_st_eq_landau_n_rt_is v0 w0).
+
+(* notion 1676 *)
+definition l_e_st_eq_landau_n_rt_5110_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(λt:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_rat.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0.λw:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 u) x0.l_e_st_eq_landau_n_rt_satz110b x0 y0 t u v w : l_e_amone l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)).
+
+(* notion 1677 *)
+definition l_e_st_eq_landau_n_rt_satz110 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_onei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0) (l_e_st_eq_landau_n_rt_5110_t5 x0 y0) (l_e_st_eq_landau_n_rt_satz110a x0 y0) : l_e_st_eq_landau_n_rt_one (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0)).
+
+(* notion 1678 *)
+definition l_e_st_eq_landau_n_5111_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_ts x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_ndis12 x l_e_st_eq_landau_n_1 y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz28a x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) x).
+
+(* notion 1679 *)
+definition l_e_st_eq_landau_n_5111_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) x (l_e_st_eq_landau_n_5111_t1 x y) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)))).
+
+(* notion 1680 *)
+definition l_e_st_eq_landau_n_satz111a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1).(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) y (l_e_st_eq_landau_n_5111_t1 x y) (l_e_st_eq_landau_n_5111_t1 y x) m : l_e_st_eq_landau_n_more x y).
+
+(* notion 1681 *)
+definition l_e_st_eq_landau_n_satz111b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λe:l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1).(l_e_tr3is l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) y (l_e_st_eq_landau_n_5111_t2 x y) e (l_e_st_eq_landau_n_5111_t1 y x) : l_e_st_eq_landau_n_is x y).
+
+(* notion 1682 *)
+definition l_e_st_eq_landau_n_satz111c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1).(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) y (l_e_st_eq_landau_n_5111_t1 x y) (l_e_st_eq_landau_n_5111_t1 y x) l : l_e_st_eq_landau_n_less x y).
+
+(* notion 1683 *)
+definition l_e_st_eq_landau_n_satz111d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_ismore12 x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) y (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_5111_t2 x y) (l_e_st_eq_landau_n_5111_t2 y x) m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)).
+
+(* notion 1684 *)
+definition l_e_st_eq_landau_n_satz111e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) x y (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_5111_t1 x y) i (l_e_st_eq_landau_n_5111_t2 y x) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)).
+
+(* notion 1685 *)
+definition l_e_st_eq_landau_n_satz111f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_isless12 x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) y (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_5111_t2 x y) (l_e_st_eq_landau_n_5111_t2 y x) l : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)).
+
+(* notion 1686 *)
+definition l_e_st_eq_landau_n_rt_natprop ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_class x0) : Prop).
+
+(* notion 1687 *)
+definition l_e_st_eq_landau_n_rt_natrt ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_some (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t) : Prop).
+
+(* notion 1688 *)
+definition l_e_st_eq_landau_n_rt_ii5_t22 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λnpx:l_e_st_eq_landau_n_rt_natprop x0 x.λnpy:l_e_st_eq_landau_n_rt_natprop y0 y.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_satz111b x y (l_e_st_eq_landau_n_rt_ise x0 y0 (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1) npx npy i) : l_e_st_eq_landau_n_is x y).
+
+(* notion 1689 *)
+definition l_e_st_eq_landau_n_rt_ii5_t23 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_rt_natprop x0 t.λw:l_e_st_eq_landau_n_rt_natprop x0 u.l_e_st_eq_landau_n_rt_ii5_t22 x0 x0 t u v w (l_e_refis l_e_st_eq_landau_n_rt_rat x0) : l_e_amone l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t)).
+
+(* notion 1690 *)
+definition l_e_st_eq_landau_n_rt_satz111g ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_onei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t) (l_e_st_eq_landau_n_rt_ii5_t23 x0) nx0 : l_e_st_eq_landau_n_one (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t)).
+
+(* notion 1691 *)
+definition l_e_st_eq_landau_n_rt_nofrt ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_ind l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t) (l_e_st_eq_landau_n_rt_satz111g x0 nx0) : l_e_st_eq_landau_n_nat).
+
+(* notion 1692 *)
+definition l_e_st_eq_landau_n_rt_inclassn ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_oneax l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop x0 t) (l_e_st_eq_landau_n_rt_satz111g x0 nx0) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_class x0)).
+
+(* notion 1693 *)
+definition l_e_st_eq_landau_n_rt_isrten ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_ii5_t22 x0 y0 (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclassn y0 ny0) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)).
+
+(* notion 1694 *)
+definition l_e_st_eq_landau_n_rt_isrtin ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0).(l_e_st_eq_landau_n_rt_isi x0 y0 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclassn y0 ny0) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_nofrt y0 ny0) i) : l_e_st_eq_landau_n_rt_is x0 y0).
+
+(* notion 1695 *)
+definition l_e_st_eq_landau_n_rt_rtofn ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 1696 *)
+definition l_e_st_eq_landau_n_rt_natrti ≝ λx:l_e_st_eq_landau_n_nat.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop (l_e_st_eq_landau_n_rt_rtofn x) t) x (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rtofn x)).
+
+(* notion 1697 *)
+definition l_e_st_eq_landau_n_rt_isnert ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rtofn t) x y i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)).
+
+(* notion 1698 *)
+definition l_e_st_eq_landau_n_rt_isnirt ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y).(l_e_st_eq_landau_n_rt_ii5_t22 (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) x y (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) i : l_e_st_eq_landau_n_is x y).
+
+(* notion 1699 *)
+definition l_e_st_eq_landau_n_rt_isrtn1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_st_eq_landau_n_rt_isi x0 (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_nofrt x0 nx0)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_refeq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_nofrt x0 nx0))).
+
+(* notion 1700 *)
+definition l_e_st_eq_landau_n_rt_isnrt1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_ii5_t22 (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn x) x (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x)) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rtofn x)) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x))).
+
+(* notion 1701 *)
+definition l_e_st_eq_landau_n_satz112a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_satz57 x y l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x y) l_e_st_eq_landau_n_1)).
+
+(* notion 1702 *)
+definition l_e_st_eq_landau_n_satz112b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_treq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x y) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_tfeq12a x l_e_st_eq_landau_n_1 y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_eqd (l_e_st_eq_landau_n_ts x y) (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz28a l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x y) l_e_st_eq_landau_n_1)).
+
+(* notion 1703 *)
+definition l_e_st_eq_landau_n_rt_satz112c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.(l_e_st_eq_landau_n_rt_lemmaeq1 (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_picp x0 y0 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclassn y0 ny0)) (l_e_st_eq_landau_n_satz112a (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl x0 y0))).
+
+(* notion 1704 *)
+definition l_e_st_eq_landau_n_rt_satz112d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop (l_e_st_eq_landau_n_rt_pl x0 y0) t) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) (l_e_st_eq_landau_n_rt_satz112c x0 nx0 y0 ny0) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_pl x0 y0)).
+
+(* notion 1705 *)
+definition l_e_st_eq_landau_n_rt_satz112e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.(l_e_st_eq_landau_n_rt_lemmaeq1 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_tict x0 y0 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclassn y0 ny0)) (l_e_st_eq_landau_n_satz112b (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_ts x0 y0))).
+
+(* notion 1706 *)
+definition l_e_st_eq_landau_n_rt_satz112f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_natprop (l_e_st_eq_landau_n_rt_ts x0 y0) t) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)) (l_e_st_eq_landau_n_rt_satz112e x0 nx0 y0 ny0) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 1707 *)
+definition l_e_st_eq_landau_n_rt_5112_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_satz111a (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_moree x0 y0 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt y0 ny0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_inclassn y0 ny0) m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0)).
+
+(* notion 1708 *)
+definition l_e_st_eq_landau_n_rt_5112_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λz:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) z.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt y0 ny0) z) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z))) d (l_e_st_eq_landau_n_ispl2 z (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z)) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_isnrt1 z)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z)))).
+
+(* notion 1709 *)
+definition l_e_st_eq_landau_n_rt_5112_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λz:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) z.(l_e_st_eq_landau_n_rt_isi x0 (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_rtofn z)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z))) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn x0 nx0) (l_e_st_eq_landau_n_rt_satz112c y0 ny0 (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z)) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_rt_nofrt x0 nx0) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nofrt y0 ny0) (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_natrti z))) (l_e_st_eq_landau_n_rt_5112_t2 x0 nx0 y0 ny0 m z d)) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_rtofn z))).
+
+(* notion 1710 *)
+definition l_e_st_eq_landau_n_rt_5112_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λz:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) z.(l_e_st_eq_landau_n_rt_satz101g x0 y0 (l_e_st_eq_landau_n_rt_rtofn z) m (l_e_symis l_e_st_eq_landau_n_rt_rat x0 (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_rtofn z)) (l_e_st_eq_landau_n_rt_5112_t3 x0 nx0 y0 ny0 m z d)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_mn x0 y0 m)).
+
+(* notion 1711 *)
+definition l_e_st_eq_landau_n_rt_5112_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λz:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) z.(l_e_isp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_rtofn z) (l_e_st_eq_landau_n_rt_mn x0 y0 m) (l_e_st_eq_landau_n_rt_natrti z) (l_e_st_eq_landau_n_rt_5112_t4 x0 nx0 y0 ny0 m z d) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)).
+
+(* notion 1712 *)
+definition l_e_st_eq_landau_n_rt_satz112g ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_someapp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) t) (l_e_st_eq_landau_n_rt_5112_t1 x0 nx0 y0 ny0 m) (l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nofrt x0 nx0) (l_e_st_eq_landau_n_rt_nofrt y0 ny0) t.l_e_st_eq_landau_n_rt_5112_t5 x0 nx0 y0 ny0 m t u) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)).
+
+(* notion 1713 *)
+definition l_e_st_eq_landau_n_rt_satz112h ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_pf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x y) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_picp (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl x y) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz112a x y) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl x y))).
+
+(* notion 1714 *)
+definition l_e_st_eq_landau_n_rt_satz112j ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x y) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_tict (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x y) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz112b x y) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_ts x y))).
+
+(* notion 1715 *)
+definition l_e_st_eq_landau_n_rt_nt_natt ≝ (l_e_ot l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) : Type[0]).
+
+(* notion 1716 *)
+definition l_e_st_eq_landau_n_rt_nt_ntofrt ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_out l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) x0 nx0 : l_e_st_eq_landau_n_rt_nt_natt).
+
+(* notion 1717 *)
+definition l_e_st_eq_landau_n_rt_nt_is ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_is l_e_st_eq_landau_n_rt_nt_natt xt yt : Prop).
+
+(* notion 1718 *)
+definition l_e_st_eq_landau_n_rt_nt_nis ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_not (l_e_st_eq_landau_n_rt_nt_is xt yt) : Prop).
+
+(* notion 1719 *)
+definition l_e_st_eq_landau_n_rt_nt_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.(l_all l_e_st_eq_landau_n_rt_nt_natt p : Prop).
+
+(* notion 1720 *)
+definition l_e_st_eq_landau_n_rt_nt_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.(l_some l_e_st_eq_landau_n_rt_nt_natt p : Prop).
+
+(* notion 1721 *)
+definition l_e_st_eq_landau_n_rt_nt_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.(l_e_one l_e_st_eq_landau_n_rt_nt_natt p : Prop).
+
+(* notion 1722 *)
+definition l_e_st_eq_landau_n_rt_nt_in ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_esti l_e_st_eq_landau_n_rt_nt_natt xt st : Prop).
+
+(* notion 1723 *)
+definition l_e_st_eq_landau_n_rt_nt_rtofnt ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_in l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) xt : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 1724 *)
+definition l_e_st_eq_landau_n_rt_nt_natrti ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_inp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) xt : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_nt_rtofnt xt)).
+
+(* notion 1725 *)
+definition l_e_st_eq_landau_n_rt_nt_isrtent ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isouti l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) x0 nx0 y0 ny0 i : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofrt x0 nx0) (l_e_st_eq_landau_n_rt_nt_ntofrt y0 ny0)).
+
+(* notion 1726 *)
+definition l_e_st_eq_landau_n_rt_nt_isrtint ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.λy0:l_e_st_eq_landau_n_rt_rat.λny0:l_e_st_eq_landau_n_rt_natrt y0.λi:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofrt x0 nx0) (l_e_st_eq_landau_n_rt_nt_ntofrt y0 ny0).(l_e_isoute l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) x0 nx0 y0 ny0 i : l_e_st_eq_landau_n_rt_is x0 y0).
+
+(* notion 1727 *)
+definition l_e_st_eq_landau_n_rt_nt_isntert ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_nt_is xt yt.(l_e_isini l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) xt yt i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)).
+
+(* notion 1728 *)
+definition l_e_st_eq_landau_n_rt_nt_isntirt ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt).(l_e_isine l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) xt yt i : l_e_st_eq_landau_n_rt_nt_is xt yt).
+
+(* notion 1729 *)
+definition l_e_st_eq_landau_n_rt_nt_isrtnt1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λnx0:l_e_st_eq_landau_n_rt_natrt x0.(l_e_isinout l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) x0 nx0 : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_nt_rtofnt (l_e_st_eq_landau_n_rt_nt_ntofrt x0 nx0))).
+
+(* notion 1730 *)
+definition l_e_st_eq_landau_n_rt_nt_isntrt1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_isoutin l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_natrt t) xt : l_e_st_eq_landau_n_rt_nt_is xt (l_e_st_eq_landau_n_rt_nt_ntofrt (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt))).
+
+(* notion 1731 *)
+definition l_e_st_eq_landau_n_rt_nt_ntofn ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_ntofrt (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x) : l_e_st_eq_landau_n_rt_nt_natt).
+
+(* notion 1732 *)
+definition l_e_st_eq_landau_n_rt_nt_isnent ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_rt_nt_isrtent (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_rt_natrti y) (l_e_st_eq_landau_n_rt_isnert x y i) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofn x) (l_e_st_eq_landau_n_rt_nt_ntofn y)).
+
+(* notion 1733 *)
+definition l_e_st_eq_landau_n_rt_nt_isnint ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofn x) (l_e_st_eq_landau_n_rt_nt_ntofn y).(l_e_st_eq_landau_n_rt_isnirt x y (l_e_st_eq_landau_n_rt_nt_isrtint (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_rt_natrti y) i) : l_e_st_eq_landau_n_is x y).
+
+(* notion 1734 *)
+definition l_e_st_eq_landau_n_rt_nt_nofnt ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) : l_e_st_eq_landau_n_nat).
+
+(* notion 1735 *)
+definition l_e_st_eq_landau_n_rt_nt_isnten ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_nt_is xt yt.(l_e_st_eq_landau_n_rt_isrten (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) (l_e_st_eq_landau_n_rt_nt_isntert xt yt i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
+
+(* notion 1736 *)
+definition l_e_st_eq_landau_n_rt_nt_isntin ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_e_st_eq_landau_n_rt_nt_isntirt xt yt (l_e_st_eq_landau_n_rt_isrtin (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) i) : l_e_st_eq_landau_n_rt_nt_is xt yt).
+
+(* notion 1737 *)
+definition l_e_st_eq_landau_n_rt_nt_ii5_t24 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_isrtnt1 (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_nt_rtofnt (l_e_st_eq_landau_n_rt_nt_ntofn x))).
+
+(* notion 1738 *)
+definition l_e_st_eq_landau_n_rt_nt_ii5_t25 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_isrten (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x) (l_e_st_eq_landau_n_rt_nt_rtofnt (l_e_st_eq_landau_n_rt_nt_ntofn x)) (l_e_st_eq_landau_n_rt_nt_natrti (l_e_st_eq_landau_n_rt_nt_ntofn x)) (l_e_st_eq_landau_n_rt_nt_ii5_t24 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x))).
+
+(* notion 1739 *)
+definition l_e_st_eq_landau_n_rt_nt_isnnt1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_natrti x)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x)) (l_e_st_eq_landau_n_rt_isnrt1 x) (l_e_st_eq_landau_n_rt_nt_ii5_t25 x) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x))).
+
+(* notion 1740 *)
+definition l_e_st_eq_landau_n_rt_nt_ii5_t26 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_isrtn1 (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_nt_nofnt xt))).
+
+(* notion 1741 *)
+definition l_e_st_eq_landau_n_rt_nt_ii5_t27 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_isrtent (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_rt_natrti (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_rt_nt_ii5_t26 xt) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofrt (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt))).
+
+(* notion 1742 *)
+definition l_e_st_eq_landau_n_rt_nt_isntn1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_tris l_e_st_eq_landau_n_rt_nt_natt xt (l_e_st_eq_landau_n_rt_nt_ntofrt (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_rt_nt_isntrt1 xt) (l_e_st_eq_landau_n_rt_nt_ii5_t27 xt) : l_e_st_eq_landau_n_rt_nt_is xt (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt))).
+
+(* notion 1743 *)
+definition l_e_st_eq_landau_n_rt_nt_isnnt2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x)) (l_e_st_eq_landau_n_rt_nt_isnnt1 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x)) x).
+
+(* notion 1744 *)
+definition l_e_st_eq_landau_n_rt_nt_isntn2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_symis l_e_st_eq_landau_n_rt_nt_natt xt (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_rt_nt_isntn1 xt) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) xt).
+
+(* notion 1745 *)
+definition l_e_st_eq_landau_n_rt_nt_1t ≝ (l_e_st_eq_landau_n_rt_nt_ntofn l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_rt_nt_natt).
+
+(* notion 1746 *)
+definition l_e_st_eq_landau_n_rt_nt_suct ≝ (λx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt x)) : Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt).
+
+(* notion 1747 *)
+definition l_e_st_eq_landau_n_rt_nt_5113_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) l_e_st_eq_landau_n_rt_nt_1t.(l_e_st_eq_landau_n_rt_nt_isnint (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) l_e_st_eq_landau_n_1 i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) l_e_st_eq_landau_n_1).
+
+(* notion 1748 *)
+definition l_e_st_eq_landau_n_rt_nt_satz113a ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_imp_th3 (l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ax3 (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (λt:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) l_e_st_eq_landau_n_rt_nt_1t.l_e_st_eq_landau_n_rt_nt_5113_t1 xt t) : l_e_st_eq_landau_n_rt_nt_nis (l_e_st_eq_landau_n_rt_nt_suct xt) l_e_st_eq_landau_n_rt_nt_1t).
+
+(* notion 1749 *)
+definition l_e_st_eq_landau_n_rt_nt_5113_t2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_suct yt).(l_e_st_eq_landau_n_rt_nt_isnint (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt yt)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt yt))).
+
+(* notion 1750 *)
+definition l_e_st_eq_landau_n_rt_nt_satz113b ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λi:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_suct yt).(l_e_st_eq_landau_n_rt_nt_isntin xt yt (l_e_st_eq_landau_n_ax4 (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_5113_t2 xt yt i)) : l_e_st_eq_landau_n_rt_nt_is xt yt).
+
+(* notion 1751 *)
+definition l_e_st_eq_landau_n_rt_nt_cond1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_in l_e_st_eq_landau_n_rt_nt_1t st : Prop).
+
+(* notion 1752 *)
+definition l_e_st_eq_landau_n_rt_nt_cond2 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_all (λx:l_e_st_eq_landau_n_rt_nt_natt.l_imp (l_e_st_eq_landau_n_rt_nt_in x st) (l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_suct x) st)) : Prop).
+
+(* notion 1753 *)
+definition l_e_st_eq_landau_n_rt_nt_5113_prop1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_ntofn x) st : Prop).
+
+(* notion 1754 *)
+definition l_e_st_eq_landau_n_rt_nt_5113_t3 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 x.(c2 (l_e_st_eq_landau_n_rt_nt_ntofn x) : l_imp (l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_ntofn x) st) (l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_ntofn x)) st)).
+
+(* notion 1755 *)
+definition l_e_st_eq_landau_n_rt_nt_5113_t4 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 x.(l_mp (l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_ntofn x) st) (l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_ntofn x)) st) p (l_e_st_eq_landau_n_rt_nt_5113_t3 st c1 c2 x p) : l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_ntofn x)) st).
+
+(* notion 1756 *)
+definition l_e_st_eq_landau_n_rt_nt_5113_t5 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_suc t)) st) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn x)) x (l_e_st_eq_landau_n_rt_nt_5113_t4 st c1 c2 x p) (l_e_st_eq_landau_n_rt_nt_isnnt2 x) : l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 1757 *)
+definition l_e_st_eq_landau_n_rt_nt_5113_t6 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 t) c1 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_nt_5113_prop1 st c1 c2 t.l_e_st_eq_landau_n_rt_nt_5113_t5 st c1 c2 t u) (l_e_st_eq_landau_n_rt_nt_nofnt xt) : l_e_st_eq_landau_n_rt_nt_in (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) st).
+
+(* notion 1758 *)
+definition l_e_st_eq_landau_n_rt_nt_satz113c ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_isp l_e_st_eq_landau_n_rt_nt_natt (λt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_in t st) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt xt)) xt (l_e_st_eq_landau_n_rt_nt_5113_t6 st c1 c2 xt) (l_e_st_eq_landau_n_rt_nt_isntn2 xt) : l_e_st_eq_landau_n_rt_nt_in xt st).
+
+(* notion 1759 *)
+definition l_e_st_eq_landau_n_rt_nt_ax3t ≝ (λx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_satz113a x : Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_nis (l_e_st_eq_landau_n_rt_nt_suct x) l_e_st_eq_landau_n_rt_nt_1t).
+
+(* notion 1760 *)
+definition l_e_st_eq_landau_n_rt_nt_ax4t ≝ (λx:l_e_st_eq_landau_n_rt_nt_natt.λy:l_e_st_eq_landau_n_rt_nt_natt.λu:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct x) (l_e_st_eq_landau_n_rt_nt_suct y).l_e_st_eq_landau_n_rt_nt_satz113b x y u : Πx:l_e_st_eq_landau_n_rt_nt_natt.Πy:l_e_st_eq_landau_n_rt_nt_natt.Πu:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct x) (l_e_st_eq_landau_n_rt_nt_suct y).l_e_st_eq_landau_n_rt_nt_is x y).
+
+(* notion 1761 *)
+definition l_e_st_eq_landau_n_rt_nt_ax5t ≝ (λs:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λu:l_e_st_eq_landau_n_rt_nt_cond1 s.λv:l_e_st_eq_landau_n_rt_nt_cond2 s.λx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_satz113c s u v x : Πs:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.Πu:l_e_st_eq_landau_n_rt_nt_cond1 s.Πv:l_e_st_eq_landau_n_rt_nt_cond2 s.Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_in x s).
+
+(* notion 1762 *)
+definition l_e_st_eq_landau_n_rt_nt_51_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λn:l_e_st_eq_landau_n_rt_nt_nis xt yt.(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_is xt yt) n (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).l_e_st_eq_landau_n_rt_nt_isntin xt yt t) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
+
+(* notion 1763 *)
+definition l_e_st_eq_landau_n_rt_nt_51_t2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λn:l_e_st_eq_landau_n_rt_nt_nis xt yt.(l_e_st_eq_landau_n_satz1 (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_51_t1 xt yt n) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt yt))).
+
+(* notion 1764 *)
+definition l_e_st_eq_landau_n_rt_nt_satz1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λn:l_e_st_eq_landau_n_rt_nt_nis xt yt.(l_imp_th3 (l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_suct yt)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_51_t2 xt yt n) (λt:l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_suct yt).l_e_st_eq_landau_n_rt_nt_isnint (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt yt)) t) : l_e_st_eq_landau_n_rt_nt_nis (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_suct yt)).
+
+(* notion 1765 *)
+definition l_e_st_eq_landau_n_rt_nt_54_x ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_nofnt xt : l_e_st_eq_landau_n_nat).
+
+(* notion 1766 *)
+definition l_e_st_eq_landau_n_rt_nt_54_prop1t ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_all (λt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_is (ft (l_e_st_eq_landau_n_rt_nt_suct t)) (l_e_st_eq_landau_n_rt_nt_suct (ft t))) : Prop).
+
+(* notion 1767 *)
+definition l_e_st_eq_landau_n_rt_nt_54_prop2t ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.(l_and (l_e_st_eq_landau_n_rt_nt_is (ft l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt ft) : Prop).
+
+(* notion 1768 *)
+definition l_e_st_eq_landau_n_rt_nt_54_prop1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc t)) (l_e_st_eq_landau_n_suc (f t))) : Prop).
+
+(* notion 1769 *)
+definition l_e_st_eq_landau_n_rt_nt_54_prop2 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(l_and (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))) (l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt f) : Prop).
+
+(* notion 1770 *)
+definition l_e_st_eq_landau_n_rt_nt_54_g ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.(λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_nofnt (ft (l_e_st_eq_landau_n_rt_nt_ntofn t)) : Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat).
+
+(* notion 1771 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.(l_ande1 (l_e_st_eq_landau_n_rt_nt_is (ft l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt ft) p : l_e_st_eq_landau_n_rt_nt_is (ft l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)).
+
+(* notion 1772 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t2 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt)) (l_e_st_eq_landau_n_rt_nt_isnten (ft l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt) (l_e_st_eq_landau_n_rt_nt_54_t1 st c1 c2 xt ft p)) (l_e_st_eq_landau_n_rt_nt_isnnt2 (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))).
+
+(* notion 1773 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t3 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.(l_ande2 (l_e_st_eq_landau_n_rt_nt_is (ft l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt ft) p : l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt ft).
+
+(* notion 1774 *)
+definition l_e_st_eq_landau_n_rt_nt_54_ut ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_ntofn u : l_e_st_eq_landau_n_rt_nt_natt).
+
+(* notion 1775 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t4 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_suc u (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)) (l_e_st_eq_landau_n_rt_nt_isnnt1 u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc u) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))).
+
+(* notion 1776 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t5 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft) (l_e_st_eq_landau_n_suc u) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))) (l_e_st_eq_landau_n_rt_nt_54_t4 st c1 c2 xt ft p u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_rt_nt_nofnt (ft (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))))).
+
+(* notion 1777 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t6 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_54_t3 st c1 c2 xt ft p (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u) : l_e_st_eq_landau_n_rt_nt_is (ft (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))) (l_e_st_eq_landau_n_rt_nt_suct (ft (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))).
+
+(* notion 1778 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t7 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_isnten (ft (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))) (l_e_st_eq_landau_n_rt_nt_suct (ft (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))) (l_e_st_eq_landau_n_rt_nt_54_t6 st c1 c2 xt ft p u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt (ft (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct (ft (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u))))).
+
+(* notion 1779 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t8 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_nt_isnnt2 (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct (ft (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft u))).
+
+(* notion 1780 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t9 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.λu:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_rt_nt_nofnt (ft (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct (ft (l_e_st_eq_landau_n_rt_nt_54_ut st c1 c2 xt ft p u)))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft u)) (l_e_st_eq_landau_n_rt_nt_54_t5 st c1 c2 xt ft p u) (l_e_st_eq_landau_n_rt_nt_54_t7 st c1 c2 xt ft p u) (l_e_st_eq_landau_n_rt_nt_54_t8 st c1 c2 xt ft p u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft u))).
+
+(* notion 1781 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t10 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.(λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_t9 st c1 c2 xt ft p u : l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft)).
+
+(* notion 1782 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t11 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λft:Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λp:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt ft.(l_andi (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))) (l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft)) (l_e_st_eq_landau_n_rt_nt_54_t2 st c1 c2 xt ft p) (l_e_st_eq_landau_n_rt_nt_54_t10 st c1 c2 xt ft p) : l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt ft)).
+
+(* notion 1783 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t12 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.(l_e_onee1 (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u) (l_e_st_eq_landau_n_satz4 (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt)) : l_e_amone (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u)).
+
+(* notion 1784 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t13 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.(l_e_st_eq_landau_n_rt_nt_54_t12 st c1 c2 xt a b pa pb (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt a) (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt b) (l_e_st_eq_landau_n_rt_nt_54_t11 st c1 c2 xt a pa) (l_e_st_eq_landau_n_rt_nt_54_t11 st c1 c2 xt b pb) : l_e_is (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt a) (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt b)).
+
+(* notion 1785 *)
+definition l_e_st_eq_landau_n_rt_nt_54_y ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_nofnt yt : l_e_st_eq_landau_n_nat).
+
+(* notion 1786 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t14 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_fise l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt a) (l_e_st_eq_landau_n_rt_nt_54_g st c1 c2 xt b) (l_e_st_eq_landau_n_rt_nt_54_t13 st c1 c2 xt a b pa pb) (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt (a (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt)))) (l_e_st_eq_landau_n_rt_nt_nofnt (b (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))))).
+
+(* notion 1787 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t15 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_isntin (a (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))) (b (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))) (l_e_st_eq_landau_n_rt_nt_54_t14 st c1 c2 xt a b pa pb yt) : l_e_st_eq_landau_n_rt_nt_is (a (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))) (b (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt)))).
+
+(* notion 1788 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t16 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_tr3is l_e_st_eq_landau_n_rt_nt_natt (a yt) (a (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))) (b (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt))) (b yt) (l_e_isf l_e_st_eq_landau_n_rt_nt_natt l_e_st_eq_landau_n_rt_nt_natt a yt (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt)) (l_e_st_eq_landau_n_rt_nt_isntn1 yt)) (l_e_st_eq_landau_n_rt_nt_54_t15 st c1 c2 xt a b pa pb yt) (l_e_isf l_e_st_eq_landau_n_rt_nt_natt l_e_st_eq_landau_n_rt_nt_natt b (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_54_y st c1 c2 xt a b pa pb yt)) yt (l_e_st_eq_landau_n_rt_nt_isntn2 yt)) : l_e_st_eq_landau_n_rt_nt_is (a yt) (b yt)).
+
+(* notion 1789 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t17 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λa:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λb:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λpa:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt a.λpb:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt b.(l_e_fisi l_e_st_eq_landau_n_rt_nt_natt l_e_st_eq_landau_n_rt_nt_natt a b (λt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_t16 st c1 c2 xt a b pa pb t) : l_e_is (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) a b).
+
+(* notion 1790 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t18 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(λu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λv:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.λw:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u.λz:l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt v.l_e_st_eq_landau_n_rt_nt_54_t17 st c1 c2 xt u v w z : l_e_amone (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (λu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u)).
+
+(* notion 1791 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t19 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_onee2 (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u) (l_e_st_eq_landau_n_satz4 (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt)) : l_some (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u)).
+
+(* notion 1792 *)
+definition l_e_st_eq_landau_n_rt_nt_54_gt ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.(λt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_ntofn (f (l_e_st_eq_landau_n_rt_nt_nofnt t)) : Πx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt).
+
+(* notion 1793 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t20 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_ande1 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))) (l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt f) p : l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))).
+
+(* notion 1794 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t21 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat f (l_e_st_eq_landau_n_rt_nt_nofnt l_e_st_eq_landau_n_rt_nt_1t) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_nt_isnnt2 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_rt_nt_nofnt l_e_st_eq_landau_n_rt_nt_1t)) (f l_e_st_eq_landau_n_1)).
+
+(* notion 1795 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t22 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_e_st_eq_landau_n_rt_nt_isnent (f (l_e_st_eq_landau_n_rt_nt_nofnt l_e_st_eq_landau_n_rt_nt_1t)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt)) (l_e_tris l_e_st_eq_landau_n_nat (f (l_e_st_eq_landau_n_rt_nt_nofnt l_e_st_eq_landau_n_rt_nt_1t)) (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt)) (l_e_st_eq_landau_n_rt_nt_54_t21 st c1 c2 xt f p) (l_e_st_eq_landau_n_rt_nt_54_t20 st c1 c2 xt f p)) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)).
+
+(* notion 1796 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t23 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_ande2 (l_e_st_eq_landau_n_is (f l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_x st c1 c2 xt))) (l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt f) p : l_e_st_eq_landau_n_rt_nt_54_prop1 st c1 c2 xt f).
+
+(* notion 1797 *)
+definition l_e_st_eq_landau_n_rt_nt_54_z ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_nofnt zt : l_e_st_eq_landau_n_nat).
+
+(* notion 1798 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t24 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat f (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct zt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt)) (l_e_st_eq_landau_n_rt_nt_isnnt2 (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct zt))) (f (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt)))).
+
+(* notion 1799 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t25 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_54_t23 st c1 c2 xt f p (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt) : l_e_st_eq_landau_n_is (f (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) (l_e_st_eq_landau_n_suc (f (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt)))).
+
+(* notion 1800 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t26 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_suc (f (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f zt)) (l_e_st_eq_landau_n_rt_nt_isnnt1 (f (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (f (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f zt)))).
+
+(* notion 1801 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t27 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_isnent (f (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct zt))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f zt))) (l_e_tr3is l_e_st_eq_landau_n_nat (f (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_suct zt))) (f (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) (l_e_st_eq_landau_n_suc (f (l_e_st_eq_landau_n_rt_nt_54_z st c1 c2 xt f p zt))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f zt))) (l_e_st_eq_landau_n_rt_nt_54_t24 st c1 c2 xt f p zt) (l_e_st_eq_landau_n_rt_nt_54_t25 st c1 c2 xt f p zt) (l_e_st_eq_landau_n_rt_nt_54_t26 st c1 c2 xt f p zt)) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f (l_e_st_eq_landau_n_rt_nt_suct zt)) (l_e_st_eq_landau_n_rt_nt_suct (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f zt))).
+
+(* notion 1802 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t28 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_t27 st c1 c2 xt f p u : l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f)).
+
+(* notion 1803 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t29 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_andi (l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_rt_nt_54_prop1t st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f)) (l_e_st_eq_landau_n_rt_nt_54_t22 st c1 c2 xt f p) (l_e_st_eq_landau_n_rt_nt_54_t28 st c1 c2 xt f p) : l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f)).
+
+(* notion 1804 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t30 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.λf:Πx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt f.(l_somei (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (λu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u) (l_e_st_eq_landau_n_rt_nt_54_gt st c1 c2 xt f) (l_e_st_eq_landau_n_rt_nt_54_t29 st c1 c2 xt f p) : l_some (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (λu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u)).
+
+(* notion 1805 *)
+definition l_e_st_eq_landau_n_rt_nt_54_t31 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_someapp (Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat) (λu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u) (l_e_st_eq_landau_n_rt_nt_54_t19 st c1 c2 xt) (l_some (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (λu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u)) (λu:Πt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_rt_nt_54_prop2 st c1 c2 xt u.l_e_st_eq_landau_n_rt_nt_54_t30 st c1 c2 xt u v) : l_some (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (λu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u)).
+
+(* notion 1806 *)
+definition l_e_st_eq_landau_n_rt_nt_satz4 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_nt_natt.λc1:l_e_st_eq_landau_n_rt_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_onei (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (λu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_54_prop2t st c1 c2 xt u) (l_e_st_eq_landau_n_rt_nt_54_t18 st c1 c2 xt) (l_e_st_eq_landau_n_rt_nt_54_t31 st c1 c2 xt) : l_e_one (Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt) (λu:Πt:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_natt.l_and (l_e_st_eq_landau_n_rt_nt_is (u l_e_st_eq_landau_n_rt_nt_1t) (l_e_st_eq_landau_n_rt_nt_suct xt)) (l_e_st_eq_landau_n_rt_nt_all (λv:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_is (u (l_e_st_eq_landau_n_rt_nt_suct v)) (l_e_st_eq_landau_n_rt_nt_suct (u v)))))).
+
+(* notion 1807 *)
+definition l_e_st_eq_landau_n_rt_nt_pl ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_ntofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_satz112d (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) : l_e_st_eq_landau_n_rt_nt_natt).
+
+(* notion 1808 *)
+definition l_e_st_eq_landau_n_rt_nt_ii5_t28 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_satz112c (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) : l_e_st_eq_landau_n_rt_inf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_class (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)))).
+
+(* notion 1809 *)
+definition l_e_st_eq_landau_n_rt_nt_ii5_t29 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_nt_ii5_t28 xt yt) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_refeq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)))).
+
+(* notion 1810 *)
+definition l_e_st_eq_landau_n_rt_nt_isplnt ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_isrtent (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_satz112d (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_natrti (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_ii5_t29 xt yt) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_pl xt yt) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)))).
+
+(* notion 1811 *)
+definition l_e_st_eq_landau_n_rt_nt_isntpl ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_symis l_e_st_eq_landau_n_rt_nt_natt (l_e_st_eq_landau_n_rt_nt_pl xt yt) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_isplnt xt yt) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_pl xt yt)).
+
+(* notion 1812 *)
+definition l_e_st_eq_landau_n_rt_nt_ispln ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)))) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_isnnt1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_isnten (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))) (l_e_st_eq_landau_n_rt_nt_pl xt yt) (l_e_st_eq_landau_n_rt_nt_isntpl xt yt)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt))).
+
+(* notion 1813 *)
+definition l_e_st_eq_landau_n_rt_nt_isnpl ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_ispln xt yt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt))).
+
+(* notion 1814 *)
+definition l_e_st_eq_landau_n_rt_nt_55_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt) (l_e_st_eq_landau_n_rt_nt_isnpl xt yt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt))).
+
+(* notion 1815 *)
+definition l_e_st_eq_landau_n_rt_nt_55_t2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)) (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_ispln yt zt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)))).
+
+(* notion 1816 *)
+definition l_e_st_eq_landau_n_rt_nt_55_t3 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt))) (l_e_st_eq_landau_n_rt_nt_55_t1 xt yt zt) (l_e_st_eq_landau_n_satz5 (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_rt_nt_55_t2 xt yt zt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)))).
+
+(* notion 1817 *)
+definition l_e_st_eq_landau_n_rt_nt_satz5 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_tr3is l_e_st_eq_landau_n_rt_nt_natt (l_e_st_eq_landau_n_rt_nt_pl (l_e_st_eq_landau_n_rt_nt_pl xt yt) zt) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt))) (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)))) (l_e_st_eq_landau_n_rt_nt_pl xt (l_e_st_eq_landau_n_rt_nt_pl yt zt)) (l_e_st_eq_landau_n_rt_nt_isplnt (l_e_st_eq_landau_n_rt_nt_pl xt yt) zt) (l_e_st_eq_landau_n_rt_nt_isnent (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt yt)) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt))) (l_e_st_eq_landau_n_rt_nt_55_t3 xt yt zt)) (l_e_st_eq_landau_n_rt_nt_isntpl xt (l_e_st_eq_landau_n_rt_nt_pl yt zt)) : l_e_st_eq_landau_n_rt_nt_is (l_e_st_eq_landau_n_rt_nt_pl (l_e_st_eq_landau_n_rt_nt_pl xt yt) zt) (l_e_st_eq_landau_n_rt_nt_pl xt (l_e_st_eq_landau_n_rt_nt_pl yt zt))).
+
+(* notion 1818 *)
+definition l_e_st_eq_landau_n_rt_nt_diffprop ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_is xt (l_e_st_eq_landau_n_rt_nt_pl yt zt) : Prop).
+
+(* notion 1819 *)
+definition l_e_st_eq_landau_n_rt_nt_diffprope ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λd:l_e_st_eq_landau_n_rt_nt_diffprop xt yt zt.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_rt_nt_isnten xt (l_e_st_eq_landau_n_rt_nt_pl yt zt) d) (l_e_st_eq_landau_n_rt_nt_isnpl yt zt) : l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)).
+
+(* notion 1820 *)
+definition l_e_st_eq_landau_n_rt_nt_ii5_t30 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt)) d (l_e_st_eq_landau_n_rt_nt_ispln yt zt) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt zt))).
+
+(* notion 1821 *)
+definition l_e_st_eq_landau_n_rt_nt_diffpropi ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt).(l_e_st_eq_landau_n_rt_nt_isntin xt (l_e_st_eq_landau_n_rt_nt_pl yt zt) (l_e_st_eq_landau_n_rt_nt_ii5_t30 xt yt zt d) : l_e_st_eq_landau_n_rt_nt_diffprop xt yt zt).
+
+(* notion 1822 *)
+definition l_e_st_eq_landau_n_rt_nt_59_it ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_is xt yt : Prop).
+
+(* notion 1823 *)
+definition l_e_st_eq_landau_n_rt_nt_59_iit ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_some (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_diffprop xt yt u) : Prop).
+
+(* notion 1824 *)
+definition l_e_st_eq_landau_n_rt_nt_59_iiit ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_some (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_diffprop yt xt u) : Prop).
+
+(* notion 1825 *)
+definition l_e_st_eq_landau_n_rt_nt_59_i ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) : Prop).
+
+(* notion 1826 *)
+definition l_e_st_eq_landau_n_rt_nt_59_ii ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) u) : Prop).
+
+(* notion 1827 *)
+definition l_e_st_eq_landau_n_rt_nt_59_iii ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt xt) u) : Prop).
+
+(* notion 1828 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λone:l_e_st_eq_landau_n_rt_nt_59_i xt yt.(l_or3i1 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_isntin xt yt one) : l_or3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
+
+(* notion 1829 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwo:l_e_st_eq_landau_n_rt_nt_59_ii xt yt.λv:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) v.(l_e_isp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) u) v (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn v)) d (l_e_st_eq_landau_n_rt_nt_isnnt1 v) : l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn v))).
+
+(* notion 1830 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t3 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwo:l_e_st_eq_landau_n_rt_nt_59_ii xt yt.λv:l_e_st_eq_landau_n_nat.λd:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) v.(l_somei l_e_st_eq_landau_n_rt_nt_natt (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_diffprop xt yt u) (l_e_st_eq_landau_n_rt_nt_ntofn v) (l_e_st_eq_landau_n_rt_nt_diffpropi xt yt (l_e_st_eq_landau_n_rt_nt_ntofn v) (l_e_st_eq_landau_n_rt_nt_59_t2 xt yt two v d)) : l_e_st_eq_landau_n_rt_nt_59_iit xt yt).
+
+(* notion 1831 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t4 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwo:l_e_st_eq_landau_n_rt_nt_59_ii xt yt.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) u) two (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) u.l_e_st_eq_landau_n_rt_nt_59_t3 xt yt two u v) : l_e_st_eq_landau_n_rt_nt_59_iit xt yt).
+
+(* notion 1832 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t5 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwo:l_e_st_eq_landau_n_rt_nt_59_ii xt yt.(l_or3i2 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_t4 xt yt two) : l_or3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
+
+(* notion 1833 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t6 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λthree:l_e_st_eq_landau_n_rt_nt_59_iii xt yt.(l_or3i3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_t4 yt xt three) : l_or3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
+
+(* notion 1834 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t7 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_or3app (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt) (l_or3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)) (l_e_st_eq_landau_n_satz9a (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (λu:l_e_st_eq_landau_n_rt_nt_59_i xt yt.l_e_st_eq_landau_n_rt_nt_59_t1 xt yt u) (λu:l_e_st_eq_landau_n_rt_nt_59_ii xt yt.l_e_st_eq_landau_n_rt_nt_59_t5 xt yt u) (λu:l_e_st_eq_landau_n_rt_nt_59_iii xt yt.l_e_st_eq_landau_n_rt_nt_59_t6 xt yt u) : l_or3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
+
+(* notion 1835 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t8 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λonet:l_e_st_eq_landau_n_rt_nt_59_it xt yt.(l_e_st_eq_landau_n_rt_nt_isnten xt yt onet : l_e_st_eq_landau_n_rt_nt_59_i xt yt).
+
+(* notion 1836 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t9 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwot:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.λvt:l_e_st_eq_landau_n_rt_nt_natt.λd:l_e_st_eq_landau_n_rt_nt_diffprop xt yt vt.(l_somei l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) u) (l_e_st_eq_landau_n_rt_nt_nofnt vt) (l_e_st_eq_landau_n_rt_nt_diffprope xt yt vt d) : l_e_st_eq_landau_n_rt_nt_59_ii xt yt).
+
+(* notion 1837 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t10 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwot:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.(l_someapp l_e_st_eq_landau_n_rt_nt_natt (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_diffprop xt yt u) twot (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (λu:l_e_st_eq_landau_n_rt_nt_natt.λv:l_e_st_eq_landau_n_rt_nt_diffprop xt yt u.l_e_st_eq_landau_n_rt_nt_59_t9 xt yt twot u v) : l_e_st_eq_landau_n_rt_nt_59_ii xt yt).
+
+(* notion 1838 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t11 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λthreet:l_e_st_eq_landau_n_rt_nt_59_iiit xt yt.(l_e_st_eq_landau_n_rt_nt_59_t10 yt xt threet : l_e_st_eq_landau_n_rt_nt_59_iii xt yt).
+
+(* notion 1839 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t12 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_satz9b (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) : l_ec3 (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt)).
+
+(* notion 1840 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t13 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λonet:l_e_st_eq_landau_n_rt_nt_59_it xt yt.(l_ec3e12 (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt) (l_e_st_eq_landau_n_rt_nt_59_t12 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t8 xt yt onet) : l_not (l_e_st_eq_landau_n_rt_nt_59_ii xt yt)).
+
+(* notion 1841 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t14 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λonet:l_e_st_eq_landau_n_rt_nt_59_it xt yt.(l_imp_th3 (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_t13 xt yt onet) (λx:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.l_e_st_eq_landau_n_rt_nt_59_t10 xt yt x) : l_not (l_e_st_eq_landau_n_rt_nt_59_iit xt yt)).
+
+(* notion 1842 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t15 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_ec_th1 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (λx:l_e_st_eq_landau_n_rt_nt_59_it xt yt.l_e_st_eq_landau_n_rt_nt_59_t14 xt yt x) : l_ec (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt)).
+
+(* notion 1843 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t16 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwot:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.(l_ec3e23 (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt) (l_e_st_eq_landau_n_rt_nt_59_t12 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t10 xt yt twot) : l_not (l_e_st_eq_landau_n_rt_nt_59_iii xt yt)).
+
+(* notion 1844 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t17 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λtwot:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.(l_imp_th3 (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt) (l_e_st_eq_landau_n_rt_nt_59_t16 xt yt twot) (λx:l_e_st_eq_landau_n_rt_nt_59_iiit xt yt.l_e_st_eq_landau_n_rt_nt_59_t11 xt yt x) : l_not (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
+
+(* notion 1845 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t18 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_ec_th1 (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (λx:l_e_st_eq_landau_n_rt_nt_59_iit xt yt.l_e_st_eq_landau_n_rt_nt_59_t17 xt yt x) : l_ec (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
+
+(* notion 1846 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t19 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λthreet:l_e_st_eq_landau_n_rt_nt_59_iiit xt yt.(l_ec3e31 (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_ii xt yt) (l_e_st_eq_landau_n_rt_nt_59_iii xt yt) (l_e_st_eq_landau_n_rt_nt_59_t12 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t11 xt yt threet) : l_not (l_e_st_eq_landau_n_rt_nt_59_i xt yt)).
+
+(* notion 1847 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t20 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λthreet:l_e_st_eq_landau_n_rt_nt_59_iiit xt yt.(l_imp_th3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_i xt yt) (l_e_st_eq_landau_n_rt_nt_59_t19 xt yt threet) (λx:l_e_st_eq_landau_n_rt_nt_59_it xt yt.l_e_st_eq_landau_n_rt_nt_59_t8 xt yt x) : l_not (l_e_st_eq_landau_n_rt_nt_59_it xt yt)).
+
+(* notion 1848 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t21 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_ec_th1 (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (λx:l_e_st_eq_landau_n_rt_nt_59_iiit xt yt.l_e_st_eq_landau_n_rt_nt_59_t20 xt yt x) : l_ec (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_it xt yt)).
+
+(* notion 1849 *)
+definition l_e_st_eq_landau_n_rt_nt_59_t22 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_ec3_th6 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_t15 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t18 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t21 xt yt) : l_ec3 (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt)).
+
+(* notion 1850 *)
+definition l_e_st_eq_landau_n_rt_nt_satz9 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_orec3i (l_e_st_eq_landau_n_rt_nt_59_it xt yt) (l_e_st_eq_landau_n_rt_nt_59_iit xt yt) (l_e_st_eq_landau_n_rt_nt_59_iiit xt yt) (l_e_st_eq_landau_n_rt_nt_59_t7 xt yt) (l_e_st_eq_landau_n_rt_nt_59_t22 xt yt) : l_orec3 (l_e_st_eq_landau_n_rt_nt_is xt yt) (l_e_st_eq_landau_n_rt_nt_some (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_is xt (l_e_st_eq_landau_n_rt_nt_pl yt u))) (l_e_st_eq_landau_n_rt_nt_some (λu:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_is yt (l_e_st_eq_landau_n_rt_nt_pl xt u)))).
+
+(* notion 1851 *)
+definition l_e_st_eq_landau_n_rt_nt_more ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) : Prop).
+
+(* notion 1852 *)
+definition l_e_st_eq_landau_n_rt_nt_ii5_t31 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_more xt yt.(l_e_st_eq_landau_n_rt_moree (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1)).
+
+(* notion 1853 *)
+definition l_e_st_eq_landau_n_rt_nt_moree ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_more xt yt.(l_e_st_eq_landau_n_satz111a (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_ii5_t31 xt yt m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
+
+(* notion 1854 *)
+definition l_e_st_eq_landau_n_rt_nt_ii5_t32 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_e_st_eq_landau_n_satz111d (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1)).
+
+(* notion 1855 *)
+definition l_e_st_eq_landau_n_rt_nt_morei ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) (l_e_st_eq_landau_n_rt_nt_ii5_t32 xt yt m) : l_e_st_eq_landau_n_rt_nt_more xt yt).
+
+(* notion 1856 *)
+definition l_e_st_eq_landau_n_rt_nt_less ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) : Prop).
+
+(* notion 1857 *)
+definition l_e_st_eq_landau_n_rt_nt_ii5_t33 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_rt_nt_less xt yt.(l_e_st_eq_landau_n_rt_lesse (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) l : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1)).
+
+(* notion 1858 *)
+definition l_e_st_eq_landau_n_rt_nt_lesse ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_rt_nt_less xt yt.(l_e_st_eq_landau_n_satz111c (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_ii5_t33 xt yt l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
+
+(* notion 1859 *)
+definition l_e_st_eq_landau_n_rt_nt_ii5_t34 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_e_st_eq_landau_n_satz111f (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) l : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1)).
+
+(* notion 1860 *)
+definition l_e_st_eq_landau_n_rt_nt_lessi ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_e_st_eq_landau_n_rt_lessi (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt xt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_nt_nofnt yt) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt)) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt)) (l_e_st_eq_landau_n_rt_nt_ii5_t34 xt yt l) : l_e_st_eq_landau_n_rt_nt_less xt yt).
+
+(* notion 1861 *)
+definition l_e_st_eq_landau_n_rt_nt_moreis ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) : Prop).
+
+(* notion 1862 *)
+definition l_e_st_eq_landau_n_rt_nt_moreise ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_moreis xt yt.(l_or_th9 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) m (λu:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt).l_e_st_eq_landau_n_rt_nt_moree xt yt u) (λu:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt).l_e_st_eq_landau_n_rt_isrten (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) u) : l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
+
+(* notion 1863 *)
+definition l_e_st_eq_landau_n_rt_nt_moreisi ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_or_th9 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) m (λu:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).l_e_st_eq_landau_n_rt_nt_morei xt yt u) (λu:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).l_e_st_eq_landau_n_rt_isrtin (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) u) : l_e_st_eq_landau_n_rt_nt_moreis xt yt).
+
+(* notion 1864 *)
+definition l_e_st_eq_landau_n_rt_nt_lessis ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) : Prop).
+
+(* notion 1865 *)
+definition l_e_st_eq_landau_n_rt_nt_lessise ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_rt_nt_lessis xt yt.(l_or_th9 (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) l (λu:l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt).l_e_st_eq_landau_n_rt_nt_lesse xt yt u) (λu:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt).l_e_st_eq_landau_n_rt_isrten (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) u) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)).
+
+(* notion 1866 *)
+definition l_e_st_eq_landau_n_rt_nt_lessisi ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).(l_or_th9 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt)) (l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt)) l (λu:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).l_e_st_eq_landau_n_rt_nt_lessi xt yt u) (λu:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt).l_e_st_eq_landau_n_rt_isrtin (l_e_st_eq_landau_n_rt_nt_rtofnt xt) (l_e_st_eq_landau_n_rt_nt_natrti xt) (l_e_st_eq_landau_n_rt_nt_rtofnt yt) (l_e_st_eq_landau_n_rt_nt_natrti yt) u) : l_e_st_eq_landau_n_rt_nt_lessis xt yt).
+
+(* notion 1867 *)
+definition l_e_st_eq_landau_n_rt_nt_515_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_rt_nt_less xt yt.λk:l_e_st_eq_landau_n_rt_nt_less yt zt.(l_e_st_eq_landau_n_satz15 (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt) (l_e_st_eq_landau_n_rt_nt_lesse xt yt l) (l_e_st_eq_landau_n_rt_nt_lesse yt zt k) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)).
+
+(* notion 1868 *)
+definition l_e_st_eq_landau_n_rt_nt_satz15 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λl:l_e_st_eq_landau_n_rt_nt_less xt yt.λk:l_e_st_eq_landau_n_rt_nt_less yt zt.(l_e_st_eq_landau_n_rt_nt_lessi xt zt (l_e_st_eq_landau_n_rt_nt_515_t1 xt yt zt l k) : l_e_st_eq_landau_n_rt_nt_less xt zt).
+
+(* notion 1869 *)
+definition l_e_st_eq_landau_n_rt_nt_521_t1 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λut:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_more xt yt.λn:l_e_st_eq_landau_n_rt_nt_more zt ut.(l_e_st_eq_landau_n_satz21 (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt zt) (l_e_st_eq_landau_n_rt_nt_nofnt ut) (l_e_st_eq_landau_n_rt_nt_moree xt yt m) (l_e_st_eq_landau_n_rt_nt_moree zt ut n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt ut))).
+
+(* notion 1870 *)
+definition l_e_st_eq_landau_n_rt_nt_521_t2 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λut:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_more xt yt.λn:l_e_st_eq_landau_n_rt_nt_more zt ut.(l_e_st_eq_landau_n_ismore12 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt xt) (l_e_st_eq_landau_n_rt_nt_nofnt zt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt zt)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_nt_nofnt yt) (l_e_st_eq_landau_n_rt_nt_nofnt ut)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt ut)) (l_e_st_eq_landau_n_rt_nt_ispln xt zt) (l_e_st_eq_landau_n_rt_nt_ispln yt ut) (l_e_st_eq_landau_n_rt_nt_521_t1 xt yt zt ut m n) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl xt zt)) (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_pl yt ut))).
+
+(* notion 1871 *)
+definition l_e_st_eq_landau_n_rt_nt_satz21 ≝ λxt:l_e_st_eq_landau_n_rt_nt_natt.λyt:l_e_st_eq_landau_n_rt_nt_natt.λzt:l_e_st_eq_landau_n_rt_nt_natt.λut:l_e_st_eq_landau_n_rt_nt_natt.λm:l_e_st_eq_landau_n_rt_nt_more xt yt.λn:l_e_st_eq_landau_n_rt_nt_more zt ut.(l_e_st_eq_landau_n_rt_nt_morei (l_e_st_eq_landau_n_rt_nt_pl xt zt) (l_e_st_eq_landau_n_rt_nt_pl yt ut) (l_e_st_eq_landau_n_rt_nt_521_t2 xt yt zt ut m n) : l_e_st_eq_landau_n_rt_nt_more (l_e_st_eq_landau_n_rt_nt_pl xt zt) (l_e_st_eq_landau_n_rt_nt_pl yt ut)).
+
+(* notion 1872 *)
+definition l_e_st_eq_landau_n_rt_nt_lb ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λn:l_e_st_eq_landau_n_rt_nt_natt.(l_e_st_eq_landau_n_rt_nt_all (λx:l_e_st_eq_landau_n_rt_nt_natt.l_imp (p x) (l_e_st_eq_landau_n_rt_nt_lessis n x)) : Prop).
+
+(* notion 1873 *)
+definition l_e_st_eq_landau_n_rt_nt_min ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λn:l_e_st_eq_landau_n_rt_nt_natt.(l_and (l_e_st_eq_landau_n_rt_nt_lb p n) (p n) : Prop).
+
+(* notion 1874 *)
+definition l_e_st_eq_landau_n_rt_nt_527_q ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.(λx:l_e_st_eq_landau_n_nat.p (l_e_st_eq_landau_n_rt_nt_ntofn x) : Πx:l_e_st_eq_landau_n_nat.Prop).
+
+(* notion 1875 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t1 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λn:l_e_st_eq_landau_n_rt_nt_natt.λnp:p n.(l_e_isp l_e_st_eq_landau_n_rt_nt_natt p n (l_e_st_eq_landau_n_rt_nt_ntofn (l_e_st_eq_landau_n_rt_nt_nofnt n)) np (l_e_st_eq_landau_n_rt_nt_isntn1 n) : l_e_st_eq_landau_n_rt_nt_527_q p s (l_e_st_eq_landau_n_rt_nt_nofnt n)).
+
+(* notion 1876 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t2 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λn:l_e_st_eq_landau_n_rt_nt_natt.λnp:p n.(l_somei l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_nt_527_q p s) (l_e_st_eq_landau_n_rt_nt_nofnt n) (l_e_st_eq_landau_n_rt_nt_527_t1 p s n np) : l_e_st_eq_landau_n_some (l_e_st_eq_landau_n_rt_nt_527_q p s)).
+
+(* notion 1877 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t3 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.(l_someapp l_e_st_eq_landau_n_rt_nt_natt p s (l_e_st_eq_landau_n_some (l_e_st_eq_landau_n_rt_nt_527_q p s)) (λu:l_e_st_eq_landau_n_rt_nt_natt.λv:p u.l_e_st_eq_landau_n_rt_nt_527_t2 p s u v) : l_e_st_eq_landau_n_some (l_e_st_eq_landau_n_rt_nt_527_q p s)).
+
+(* notion 1878 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t4 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.(l_e_st_eq_landau_n_satz27 (l_e_st_eq_landau_n_rt_nt_527_q p s) (l_e_st_eq_landau_n_rt_nt_527_t3 p s) : l_e_st_eq_landau_n_some (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) x)).
+
+(* notion 1879 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t5 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.(l_ande1 (l_e_st_eq_landau_n_lb (l_e_st_eq_landau_n_rt_nt_527_q p s) m) (l_e_st_eq_landau_n_rt_nt_527_q p s m) mqm : l_e_st_eq_landau_n_lb (l_e_st_eq_landau_n_rt_nt_527_q p s) m).
+
+(* notion 1880 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t6 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.λn:l_e_st_eq_landau_n_nat.λnq:l_e_st_eq_landau_n_rt_nt_527_q p s n.(l_mp (l_e_st_eq_landau_n_rt_nt_527_q p s n) (l_e_st_eq_landau_n_lessis m n) nq (l_e_st_eq_landau_n_rt_nt_527_t5 p s m mqm n) : l_e_st_eq_landau_n_lessis m n).
+
+(* notion 1881 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t7 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.λn:l_e_st_eq_landau_n_rt_nt_natt.λnp:p n.(l_e_st_eq_landau_n_rt_nt_527_t6 p s m mqm (l_e_st_eq_landau_n_rt_nt_nofnt n) (l_e_st_eq_landau_n_rt_nt_527_t1 p s n np) : l_e_st_eq_landau_n_lessis m (l_e_st_eq_landau_n_rt_nt_nofnt n)).
+
+(* notion 1882 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t8 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.λn:l_e_st_eq_landau_n_rt_nt_natt.λnp:p n.(l_e_st_eq_landau_n_islessis1 m (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn m)) (l_e_st_eq_landau_n_rt_nt_nofnt n) (l_e_st_eq_landau_n_rt_nt_isnnt1 m) (l_e_st_eq_landau_n_rt_nt_527_t7 p s m mqm n np) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_nt_nofnt (l_e_st_eq_landau_n_rt_nt_ntofn m)) (l_e_st_eq_landau_n_rt_nt_nofnt n)).
+
+(* notion 1883 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t9 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.λn:l_e_st_eq_landau_n_rt_nt_natt.λnp:p n.(l_e_st_eq_landau_n_rt_nt_lessisi (l_e_st_eq_landau_n_rt_nt_ntofn m) n (l_e_st_eq_landau_n_rt_nt_527_t8 p s m mqm n np) : l_e_st_eq_landau_n_rt_nt_lessis (l_e_st_eq_landau_n_rt_nt_ntofn m) n).
+
+(* notion 1884 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t10 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.λn:l_e_st_eq_landau_n_rt_nt_natt.(λu:p n.l_e_st_eq_landau_n_rt_nt_527_t9 p s m mqm n u : l_imp (p n) (l_e_st_eq_landau_n_rt_nt_lessis (l_e_st_eq_landau_n_rt_nt_ntofn m) n)).
+
+(* notion 1885 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t11 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.(λx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_527_t10 p s m mqm x : l_e_st_eq_landau_n_rt_nt_lb p (l_e_st_eq_landau_n_rt_nt_ntofn m)).
+
+(* notion 1886 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t12 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.(l_ande2 (l_e_st_eq_landau_n_lb (l_e_st_eq_landau_n_rt_nt_527_q p s) m) (l_e_st_eq_landau_n_rt_nt_527_q p s m) mqm : p (l_e_st_eq_landau_n_rt_nt_ntofn m)).
+
+(* notion 1887 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t13 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.(l_andi (l_e_st_eq_landau_n_rt_nt_lb p (l_e_st_eq_landau_n_rt_nt_ntofn m)) (p (l_e_st_eq_landau_n_rt_nt_ntofn m)) (l_e_st_eq_landau_n_rt_nt_527_t11 p s m mqm) (l_e_st_eq_landau_n_rt_nt_527_t12 p s m mqm) : l_e_st_eq_landau_n_rt_nt_min p (l_e_st_eq_landau_n_rt_nt_ntofn m)).
+
+(* notion 1888 *)
+definition l_e_st_eq_landau_n_rt_nt_527_t14 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.λm:l_e_st_eq_landau_n_nat.λmqm:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) m.(l_somei l_e_st_eq_landau_n_rt_nt_natt (λx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_min p x) (l_e_st_eq_landau_n_rt_nt_ntofn m) (l_e_st_eq_landau_n_rt_nt_527_t13 p s m mqm) : l_e_st_eq_landau_n_rt_nt_some (λx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_min p x)).
+
+(* notion 1889 *)
+definition l_e_st_eq_landau_n_rt_nt_satz27 ≝ λp:Πx:l_e_st_eq_landau_n_rt_nt_natt.Prop.λs:l_e_st_eq_landau_n_rt_nt_some p.(l_someapp l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) x) (l_e_st_eq_landau_n_rt_nt_527_t4 p s) (l_e_st_eq_landau_n_rt_nt_some (λx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_min p x)) (λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_min (l_e_st_eq_landau_n_rt_nt_527_q p s) x.l_e_st_eq_landau_n_rt_nt_527_t14 p s x y) : l_e_st_eq_landau_n_rt_nt_some (λx:l_e_st_eq_landau_n_rt_nt_natt.l_e_st_eq_landau_n_rt_nt_min p x)).
+
+(* notion 1890 *)
+definition l_e_st_eq_landau_n_rt_1rt ≝ (l_e_st_eq_landau_n_rt_rtofn l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 1891 *)
+definition l_e_st_eq_landau_n_rt_ii5_t35 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x (l_e_st_eq_landau_n_tfeq1a x l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_eqnd (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_satz28a (l_e_st_eq_landau_n_num x)) (l_e_st_eq_landau_n_satz28a (l_e_st_eq_landau_n_den x))) (l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x (l_e_st_eq_landau_n_fris x)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) x).
+
+(* notion 1892 *)
+definition l_e_st_eq_landau_n_rt_ii5_t36 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0 (l_e_st_eq_landau_n_tf x (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) x (l_e_st_eq_landau_n_rt_tict x0 l_e_st_eq_landau_n_rt_1rt x (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) xix0 (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1))) xix0 (l_e_st_eq_landau_n_rt_ii5_t35 x0 x xix0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0).
+
+(* notion 1893 *)
+definition l_e_st_eq_landau_n_rt_example1a ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ratapp1 x0 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0) (λx:l_e_st_eq_landau_n_frac.λxi:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_ii5_t36 x0 x xi) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0).
+
+(* notion 1894 *)
+definition l_e_st_eq_landau_n_rt_example1b ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0 (l_e_st_eq_landau_n_rt_example1a x0) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt)).
+
+(* notion 1895 *)
+definition l_e_st_eq_landau_n_rt_example1c ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0 (l_e_st_eq_landau_n_rt_comts l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_example1a x0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) x0).
+
+(* notion 1896 *)
+definition l_e_st_eq_landau_n_rt_example1d ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) x0 (l_e_st_eq_landau_n_rt_example1c x0) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0)).
+
+(* notion 1897 *)
+definition l_e_st_eq_landau_n_rt_5114_t1 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_tr3eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_num x)) (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_den x))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_den x))) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_tfeq2a x (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_eqn (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_num x)) (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_num x))) (l_e_st_eq_landau_n_satz40c (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_den x)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1)).
+
+(* notion 1898 *)
+definition l_e_st_eq_landau_n_rt_satz114 ≝ λx:l_e_st_eq_landau_n_frac.(l_e_st_eq_landau_n_rt_isi (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_rt_ratof x)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_num x)) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_tict (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_rt_ratof x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_den x) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass x)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_5114_t1 x) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_rt_ratof x)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_num x))).
+
+(* notion 1899 *)
+definition l_e_st_eq_landau_n_rt_satz114a ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x2) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_rtofn x2) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_rt_isnert x2 (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_isden x1 x2))) (l_e_st_eq_landau_n_rt_satz114 (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_rt_isnert (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr x1 x2)) x1 (l_e_st_eq_landau_n_numis x1 x2)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x2) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2))) (l_e_st_eq_landau_n_rt_rtofn x1)).
+
+(* notion 1900 *)
+definition l_e_st_eq_landau_n_rt_ov ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_ind l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0) (l_e_st_eq_landau_n_rt_satz110 x0 y0) : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 1901 *)
+definition l_e_st_eq_landau_n_rt_satz110c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_oneax l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 t) x0) (l_e_st_eq_landau_n_rt_satz110 x0 y0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov x0 y0)) x0).
+
+(* notion 1902 *)
+definition l_e_st_eq_landau_n_rt_satz110d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov x0 y0)) x0 (l_e_st_eq_landau_n_rt_satz110c x0 y0) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov x0 y0))).
+
+(* notion 1903 *)
+definition l_e_st_eq_landau_n_rt_satz110e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov x0 y0)) x0 (l_e_st_eq_landau_n_rt_comts (l_e_st_eq_landau_n_rt_ov x0 y0) y0) (l_e_st_eq_landau_n_rt_satz110c x0 y0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0) x0).
+
+(* notion 1904 *)
+definition l_e_st_eq_landau_n_rt_satz110f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0) x0 (l_e_st_eq_landau_n_rt_satz110e x0 y0) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0)).
+
+(* notion 1905 *)
+definition l_e_st_eq_landau_n_rt_satz110g ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 v0) x0.(l_e_st_eq_landau_n_rt_satz110b x0 y0 v0 (l_e_st_eq_landau_n_rt_ov x0 y0) i (l_e_st_eq_landau_n_rt_satz110c x0 y0) : l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ov x0 y0)).
+
+(* notion 1906 *)
+definition l_e_st_eq_landau_n_rt_satz114b ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_satz110b (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2)) (l_e_st_eq_landau_n_rt_satz114a x1 x2) (l_e_st_eq_landau_n_rt_satz110c (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2))).
+
+(* notion 1907 *)
+definition l_e_st_eq_landau_n_rt_satz114c ≝ λx1:l_e_st_eq_landau_n_nat.λx2:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2)) (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2)) (l_e_st_eq_landau_n_rt_satz114b x1 x2) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn x1) (l_e_st_eq_landau_n_rt_rtofn x2)) (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr x1 x2))).
+
+(* notion 1908 *)
+definition l_e_st_eq_landau_n_rt_5115_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz89 (l_e_st_eq_landau_n_rt_ov y0 x0) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t (l_e_st_eq_landau_n_rt_ov y0 x0))).
+
+(* notion 1909 *)
+definition l_e_st_eq_landau_n_rt_5115_z ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_num u : l_e_st_eq_landau_n_nat).
+
+(* notion 1910 *)
+definition l_e_st_eq_landau_n_rt_5115_v ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_den u : l_e_st_eq_landau_n_nat).
+
+(* notion 1911 *)
+definition l_e_st_eq_landau_n_rt_5115_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_ismore1 u0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ov y0 x0) (l_e_tris l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_isi u0 (l_e_st_eq_landau_n_rt_ratof (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) u (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) uiu0 (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_refeq1 u (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_isfr u))) (l_e_st_eq_landau_n_rt_satz114b (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) m : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ov y0 x0)).
+
+(* notion 1912 *)
+definition l_e_st_eq_landau_n_rt_5115_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_moreisi (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_or_th9 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz24 (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) (λt:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_satz111d (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1 t) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_satz111e (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0) l_e_st_eq_landau_n_1 t)) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 1913 *)
+definition l_e_st_eq_landau_n_rt_5115_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_comts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ists2 (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) x0 (l_e_st_eq_landau_n_rt_satz110f (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_assts2 x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))).
+
+(* notion 1914 *)
+definition l_e_st_eq_landau_n_rt_5115_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).λn:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt.(l_e_st_eq_landau_n_rt_ismore1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_5115_t4 x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_satz105d (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) n) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt)).
+
+(* notion 1915 *)
+definition l_e_st_eq_landau_n_rt_5115_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).λn:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt.(l_e_st_eq_landau_n_rt_moreisi1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_5115_t5 x0 y0 u0 m u uiu0 n) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt)).
+
+(* notion 1916 *)
+definition l_e_st_eq_landau_n_rt_5115_t7 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt.(l_e_st_eq_landau_n_rt_moreisi2 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) (l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_5115_t4 x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_ists2 (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) i)) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt)).
+
+(* notion 1917 *)
+definition l_e_st_eq_landau_n_rt_5115_t8 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_orapp (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt)) (l_e_st_eq_landau_n_rt_5115_t3 x0 y0 u0 m u uiu0) (λt:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt.l_e_st_eq_landau_n_rt_5115_t6 x0 y0 u0 m u uiu0 t) (λt:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)) l_e_st_eq_landau_n_rt_1rt.l_e_st_eq_landau_n_rt_5115_t7 x0 y0 u0 m u uiu0 t) : l_e_st_eq_landau_n_rt_moreis (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt)).
+
+(* notion 1918 *)
+definition l_e_st_eq_landau_n_rt_5115_t9 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_ismore12 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov y0 x0)) y0 (l_e_st_eq_landau_n_rt_example1b (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))))) (l_e_st_eq_landau_n_rt_satz110c y0 x0) (l_e_st_eq_landau_n_rt_satz105d (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_ov y0 x0) x0 (l_e_st_eq_landau_n_rt_5115_t2 x0 y0 u0 m u uiu0)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) y0).
+
+(* notion 1919 *)
+definition l_e_st_eq_landau_n_rt_5115_t10 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_e_st_eq_landau_n_rt_satz87c (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_v x0 y0 u0 m u uiu0)))) l_e_st_eq_landau_n_rt_1rt) y0 (l_e_st_eq_landau_n_rt_5115_t8 x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_t9 x0 y0 u0 m u uiu0) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) y0).
+
+(* notion 1920 *)
+definition l_e_st_eq_landau_n_rt_5115_t11 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0) (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0) (l_e_st_eq_landau_n_rt_5115_t10 x0 y0 u0 m u uiu0) : l_e_st_eq_landau_n_some (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0)).
+
+(* notion 1921 *)
+definition l_e_st_eq_landau_n_rt_5115_t12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).(l_e_st_eq_landau_n_rt_ratapp1 u0 (l_e_st_eq_landau_n_some (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0)) (λu:l_e_st_eq_landau_n_frac.λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5115_t11 x0 y0 u0 m u ui) : l_e_st_eq_landau_n_some (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0)).
+
+(* notion 1922 *)
+definition l_e_st_eq_landau_n_rt_satz115 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_someapp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t (l_e_st_eq_landau_n_rt_ov y0 x0)) (l_e_st_eq_landau_n_rt_5115_t1 x0 y0) (l_e_st_eq_landau_n_some (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0)) (λt:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_more t (l_e_st_eq_landau_n_rt_ov y0 x0).l_e_st_eq_landau_n_rt_5115_t12 x0 y0 t u) : l_e_st_eq_landau_n_some (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn t) x0) y0)).
+
+(* notion 1923 *)
+definition l_e_st_eq_landau_n_rt_5115_t13 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_andi (l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) y0) (l_e_st_eq_landau_n_rt_natrti (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_5115_t10 x0 y0 u0 m u uiu0) : l_and (l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0))) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) x0) y0)).
+
+(* notion 1924 *)
+definition l_e_st_eq_landau_n_rt_5115_t14 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).λu:l_e_st_eq_landau_n_frac.λuiu0:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).(l_somei l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_5115_z x0 y0 u0 m u uiu0)) (l_e_st_eq_landau_n_rt_5115_t13 x0 y0 u0 m u uiu0) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0))).
+
+(* notion 1925 *)
+definition l_e_st_eq_landau_n_rt_5115_t15 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more u0 (l_e_st_eq_landau_n_rt_ov y0 x0).(l_e_st_eq_landau_n_rt_ratapp1 u0 (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0))) (λu:l_e_st_eq_landau_n_frac.λui:l_e_st_eq_landau_n_rt_inf u (l_e_st_eq_landau_n_rt_class u0).l_e_st_eq_landau_n_rt_5115_t14 x0 y0 u0 m u ui) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0))).
+
+(* notion 1926 *)
+definition l_e_st_eq_landau_n_rt_satz115a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_someapp l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_more t (l_e_st_eq_landau_n_rt_ov y0 x0)) (l_e_st_eq_landau_n_rt_5115_t1 x0 y0) (l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0))) (λt:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_more t (l_e_st_eq_landau_n_rt_ov y0 x0).l_e_st_eq_landau_n_rt_5115_t15 x0 y0 t u) : l_e_st_eq_landau_n_rt_some (λt:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_natrt t) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts t x0) y0))).
+
+(* notion 1927 *)
+definition l_e_st_eq_landau_n_rt_cutprop1a ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_e_st_nonempty l_e_st_eq_landau_n_rt_rat s : Prop).
+
+(* notion 1928 *)
+definition l_e_st_eq_landau_n_rt_cutprop1b ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_not (l_e_st_eq_landau_n_rt_all (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_in x s)) : Prop).
+
+(* notion 1929 *)
+definition l_e_st_eq_landau_n_rt_cutprop1 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_cutprop1a s) (l_e_st_eq_landau_n_rt_cutprop1b s) : Prop).
+
+(* notion 1930 *)
+definition l_e_st_eq_landau_n_rt_cutprop2a ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_all (λx:l_e_st_eq_landau_n_rt_rat.l_imp (l_not (l_e_st_eq_landau_n_rt_in x s)) (l_e_st_eq_landau_n_rt_less x0 x)) : Prop).
+
+(* notion 1931 *)
+definition l_e_st_eq_landau_n_rt_cutprop2 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_all (λx:l_e_st_eq_landau_n_rt_rat.l_imp (l_e_st_eq_landau_n_rt_in x s) (l_e_st_eq_landau_n_rt_cutprop2a s x)) : Prop).
+
+(* notion 1932 *)
+definition l_e_st_eq_landau_n_rt_iii1_ubprop ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_imp (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_moreis x0 y0) : Prop).
+
+(* notion 1933 *)
+definition l_e_st_eq_landau_n_rt_ub ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_all (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_iii1_ubprop s x0 x) : Prop).
+
+(* notion 1934 *)
+definition l_e_st_eq_landau_n_rt_max ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_ub s x0) (l_e_st_eq_landau_n_rt_in x0 s) : Prop).
+
+(* notion 1935 *)
+definition l_e_st_eq_landau_n_rt_cutprop3 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_not (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_max s x)) : Prop).
+
+(* notion 1936 *)
+definition l_e_st_eq_landau_n_rt_cutprop ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_cutprop1 s) (l_e_st_eq_landau_n_rt_cutprop2 s) (l_e_st_eq_landau_n_rt_cutprop3 s) : Prop).
+
+(* notion 1937 *)
+definition l_e_st_eq_landau_n_rt_iii1_lbprop ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_imp (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_lessis x0 y0) : Prop).
+
+(* notion 1938 *)
+definition l_e_st_eq_landau_n_rt_lb ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_all (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_iii1_lbprop s x0 x) : Prop).
+
+(* notion 1939 *)
+definition l_e_st_eq_landau_n_rt_min ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_lb s x0) (l_e_st_eq_landau_n_rt_in x0 s) : Prop).
+
+(* notion 1940 *)
+definition l_e_st_eq_landau_n_rt_cut ≝ (l_e_ot (l_e_st_set l_e_st_eq_landau_n_rt_rat) (λx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) : Type[0]).
+
+(* notion 1941 *)
+definition l_e_st_eq_landau_n_rt_lcl ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_in (l_e_st_set l_e_st_eq_landau_n_rt_rat) (λx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) ksi : l_e_st_set l_e_st_eq_landau_n_rt_rat).
+
+(* notion 1942 *)
+definition l_e_st_eq_landau_n_rt_lrt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_lcl ksi) : Prop).
+
+(* notion 1943 *)
+definition l_e_st_eq_landau_n_rt_urt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.(l_not (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_lcl ksi)) : Prop).
+
+(* notion 1944 *)
+definition l_e_st_eq_landau_n_rt_clcl ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_inp (l_e_st_set l_e_st_eq_landau_n_rt_rat) (λx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) ksi : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_lcl ksi)).
+
+(* notion 1945 *)
+definition l_e_st_eq_landau_n_rt_clcl1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_and3e1 (l_e_st_eq_landau_n_rt_cutprop1 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop2 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop3 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_clcl ksi) : l_e_st_eq_landau_n_rt_cutprop1 (l_e_st_eq_landau_n_rt_lcl ksi)).
+
+(* notion 1946 *)
+definition l_e_st_eq_landau_n_rt_clcl2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_and3e2 (l_e_st_eq_landau_n_rt_cutprop1 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop2 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop3 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_clcl ksi) : l_e_st_eq_landau_n_rt_cutprop2 (l_e_st_eq_landau_n_rt_lcl ksi)).
+
+(* notion 1947 *)
+definition l_e_st_eq_landau_n_rt_clcl3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_and3e3 (l_e_st_eq_landau_n_rt_cutprop1 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop2 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop3 (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_clcl ksi) : l_e_st_eq_landau_n_rt_cutprop3 (l_e_st_eq_landau_n_rt_lcl ksi)).
+
+(* notion 1948 *)
+definition l_e_st_eq_landau_n_rt_clcl1a ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_ande1 (l_e_st_eq_landau_n_rt_cutprop1a (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop1b (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_clcl1 ksi) : l_e_st_eq_landau_n_rt_cutprop1a (l_e_st_eq_landau_n_rt_lcl ksi)).
+
+(* notion 1949 *)
+definition l_e_st_eq_landau_n_rt_clcl1b ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_ande2 (l_e_st_eq_landau_n_rt_cutprop1a (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_cutprop1b (l_e_st_eq_landau_n_rt_lcl ksi)) (l_e_st_eq_landau_n_rt_clcl1 ksi) : l_e_st_eq_landau_n_rt_cutprop1b (l_e_st_eq_landau_n_rt_lcl ksi)).
+
+(* notion 1950 *)
+definition l_e_st_eq_landau_n_rt_cutapp1a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.p.(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_clcl1a ksi) p p1 : p).
+
+(* notion 1951 *)
+definition l_e_st_eq_landau_n_rt_iii1_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_some_th1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_clcl1b ksi) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)).
+
+(* notion 1952 *)
+definition l_e_st_eq_landau_n_rt_cutapp1b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_iii1_t1 ksi) p p1 : p).
+
+(* notion 1953 *)
+definition l_e_st_eq_landau_n_rt_iii1_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_mp (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_cutprop2a (l_e_st_eq_landau_n_rt_lcl ksi) x0) lx (l_e_st_eq_landau_n_rt_clcl2 ksi x0) : l_e_st_eq_landau_n_rt_cutprop2a (l_e_st_eq_landau_n_rt_lcl ksi) x0).
+
+(* notion 1954 *)
+definition l_e_st_eq_landau_n_rt_cutapp2a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_mp (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_less x0 y0) uy (l_e_st_eq_landau_n_rt_iii1_t2 ksi x0 lx y0) : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 1955 *)
+definition l_e_st_eq_landau_n_rt_cutapp2b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_eq_landau_n_rt_satz83 x0 y0 (l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx y0 uy) : l_e_st_eq_landau_n_rt_more y0 x0).
+
+(* notion 1956 *)
+definition l_e_st_eq_landau_n_rt_iii1_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_some_th4 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_max (l_e_st_eq_landau_n_rt_lcl ksi) x) (l_e_st_eq_landau_n_rt_clcl3 ksi) x0 : l_not (l_e_st_eq_landau_n_rt_max (l_e_st_eq_landau_n_rt_lcl ksi) x0)).
+
+(* notion 1957 *)
+definition l_e_st_eq_landau_n_rt_iii1_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_and_th4 (l_e_st_eq_landau_n_rt_ub (l_e_st_eq_landau_n_rt_lcl ksi) x0) (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_iii1_t3 ksi x0 lx) lx : l_not (l_e_st_eq_landau_n_rt_ub (l_e_st_eq_landau_n_rt_lcl ksi) x0)).
+
+(* notion 1958 *)
+definition l_e_st_eq_landau_n_rt_iii1_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_some_th1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 x) (l_e_st_eq_landau_n_rt_iii1_t4 ksi x0 lx) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 x))).
+
+(* notion 1959 *)
+definition l_e_st_eq_landau_n_rt_iii1_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λp:Prop.λp1:Πy:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi y.Πu:l_e_st_eq_landau_n_rt_less x0 y.p.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y0).(l_imp_th5 (l_e_st_eq_landau_n_rt_lrt ksi y0) (l_e_st_eq_landau_n_rt_moreis x0 y0) n : l_e_st_eq_landau_n_rt_lrt ksi y0).
+
+(* notion 1960 *)
+definition l_e_st_eq_landau_n_rt_iii1_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λp:Prop.λp1:Πy:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi y.Πu:l_e_st_eq_landau_n_rt_less x0 y.p.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y0).(l_imp_th6 (l_e_st_eq_landau_n_rt_lrt ksi y0) (l_e_st_eq_landau_n_rt_moreis x0 y0) n : l_not (l_e_st_eq_landau_n_rt_moreis x0 y0)).
+
+(* notion 1961 *)
+definition l_e_st_eq_landau_n_rt_iii1_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λp:Prop.λp1:Πy:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi y.Πu:l_e_st_eq_landau_n_rt_less x0 y.p.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y0).(l_e_st_eq_landau_n_rt_satz81j x0 y0 (l_e_st_eq_landau_n_rt_iii1_t7 ksi x0 lx p p1 y0 n) : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 1962 *)
+definition l_e_st_eq_landau_n_rt_iii1_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λp:Prop.λp1:Πy:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi y.Πu:l_e_st_eq_landau_n_rt_less x0 y.p.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y0).(p1 y0 (l_e_st_eq_landau_n_rt_iii1_t6 ksi x0 lx p p1 y0 n) (l_e_st_eq_landau_n_rt_iii1_t8 ksi x0 lx p p1 y0 n) : p).
+
+(* notion 1963 *)
+definition l_e_st_eq_landau_n_rt_cutapp3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λp:Prop.λp1:Πy:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi y.Πu:l_e_st_eq_landau_n_rt_less x0 y.p.(l_someapp l_e_st_eq_landau_n_rt_rat (Πy:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y)) (l_e_st_eq_landau_n_rt_iii1_t5 ksi x0 lx) p (λy:l_e_st_eq_landau_n_rt_rat.λt:l_not (l_e_st_eq_landau_n_rt_iii1_ubprop (l_e_st_eq_landau_n_rt_lcl ksi) x0 y).l_e_st_eq_landau_n_rt_iii1_t9 ksi x0 lx p p1 y t) : p).
+
+(* notion 1964 *)
+definition l_e_st_eq_landau_n_rt_iii1_t10 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_andi (l_e_st_eq_landau_n_rt_cutprop1a s) (l_e_st_eq_landau_n_rt_cutprop1b s) (l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rat s x0 i) (l_all_th1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_in x s) y0 n) : l_e_st_eq_landau_n_rt_cutprop1 s).
+
+(* notion 1965 *)
+definition l_e_st_eq_landau_n_rt_iii1_t11 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λn:Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_max s x).(l_some_th5 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_max s x) n : l_e_st_eq_landau_n_rt_cutprop3 s).
+
+(* notion 1966 *)
+definition l_e_st_eq_landau_n_rt_cut1 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).λl:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_not (l_e_st_eq_landau_n_rt_in y s).l_e_st_eq_landau_n_rt_less x y.λm:Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_max s x).(l_and3i (l_e_st_eq_landau_n_rt_cutprop1 s) (l_e_st_eq_landau_n_rt_cutprop2 s) (l_e_st_eq_landau_n_rt_cutprop3 s) (l_e_st_eq_landau_n_rt_iii1_t10 s x0 i y0 n) l (l_e_st_eq_landau_n_rt_iii1_t11 s m) : l_e_st_eq_landau_n_rt_cutprop s).
+
+(* notion 1967 *)
+definition l_e_st_eq_landau_n_rt_rp_is ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_is l_e_st_eq_landau_n_rt_cut ksi eta : Prop).
+
+(* notion 1968 *)
+definition l_e_st_eq_landau_n_rt_rp_nis ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta) : Prop).
+
+(* notion 1969 *)
+definition l_e_st_eq_landau_n_rt_rp_ise ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isini (l_e_st_set l_e_st_eq_landau_n_rt_rat) (λx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) ksi eta i : l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta)).
+
+(* notion 1970 *)
+definition l_e_st_eq_landau_n_rt_rp_ise1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_issete1 l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta) (l_e_st_eq_landau_n_rt_rp_ise ksi eta i) x0 lx : l_e_st_eq_landau_n_rt_lrt eta x0).
+
+(* notion 1971 *)
+definition l_e_st_eq_landau_n_rt_rp_isi ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta).(l_e_isine (l_e_st_set l_e_st_eq_landau_n_rt_rat) (λx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) ksi eta i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
+
+(* notion 1972 *)
+definition l_e_st_eq_landau_n_rt_rp_isi1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_lrt eta x.λk:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_lrt ksi x.(l_e_st_eq_landau_n_rt_rp_isi ksi eta (l_e_st_isseti l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta) l k) : l_e_st_eq_landau_n_rt_rp_is ksi eta).
+
+(* notion 1973 *)
+definition l_e_st_eq_landau_n_rt_rp_cutof ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λcs:l_e_st_eq_landau_n_rt_cutprop s.(l_e_out (l_e_st_set l_e_st_eq_landau_n_rt_rat) (λx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) s cs : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 1974 *)
+definition l_e_st_eq_landau_n_rt_rp_ine ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λcs:l_e_st_eq_landau_n_rt_cutprop s.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.(l_e_st_issete1 l_e_st_eq_landau_n_rt_rat s (l_e_st_eq_landau_n_rt_lcl (l_e_st_eq_landau_n_rt_rp_cutof s cs)) (l_e_isinout (l_e_st_set l_e_st_eq_landau_n_rt_rat) (λx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) s cs) x0 i : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_cutof s cs) x0).
+
+(* notion 1975 *)
+definition l_e_st_eq_landau_n_rt_rp_ini ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λcs:l_e_st_eq_landau_n_rt_cutprop s.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_cutof s cs) x0.(l_e_st_issete2 l_e_st_eq_landau_n_rt_rat s (l_e_st_eq_landau_n_rt_lcl (l_e_st_eq_landau_n_rt_rp_cutof s cs)) (l_e_isinout (l_e_st_set l_e_st_eq_landau_n_rt_rat) (λx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) s cs) x0 lx : l_e_st_eq_landau_n_rt_in x0 s).
+
+(* notion 1976 *)
+definition l_e_st_eq_landau_n_rt_rp_isi2 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λt:l_e_st_set l_e_st_eq_landau_n_rt_rat.λcs:l_e_st_eq_landau_n_rt_cutprop s.λct:l_e_st_eq_landau_n_rt_cutprop t.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_in x t.λj:Πx:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_in x t.l_e_st_eq_landau_n_rt_in x s.(l_e_isouti (l_e_st_set l_e_st_eq_landau_n_rt_rat) (λx:l_e_st_set l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_cutprop x) s cs t ct (l_e_st_isseti l_e_st_eq_landau_n_rt_rat s t i j) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_cutof s cs) (l_e_st_eq_landau_n_rt_rp_cutof t ct)).
+
+(* notion 1977 *)
+definition l_e_st_eq_landau_n_rt_rp_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_cut.Prop.(l_all l_e_st_eq_landau_n_rt_cut p : Prop).
+
+(* notion 1978 *)
+definition l_e_st_eq_landau_n_rt_rp_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_cut.Prop.(l_some l_e_st_eq_landau_n_rt_cut p : Prop).
+
+(* notion 1979 *)
+definition l_e_st_eq_landau_n_rt_rp_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_cut.Prop.(l_e_one l_e_st_eq_landau_n_rt_cut p : Prop).
+
+(* notion 1980 *)
+definition l_e_st_eq_landau_n_rt_rp_satz116 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_refis l_e_st_eq_landau_n_rt_cut ksi : l_e_st_eq_landau_n_rt_rp_is ksi ksi).
+
+(* notion 1981 *)
+definition l_e_st_eq_landau_n_rt_rp_satz117 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_symis l_e_st_eq_landau_n_rt_cut ksi eta i : l_e_st_eq_landau_n_rt_rp_is eta ksi).
+
+(* notion 1982 *)
+definition l_e_st_eq_landau_n_rt_rp_satz118 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is eta zeta.(l_e_tris l_e_st_eq_landau_n_rt_cut ksi eta zeta i j : l_e_st_eq_landau_n_rt_rp_is ksi zeta).
+
+(* notion 1983 *)
+definition l_e_st_eq_landau_n_rt_rp_1119_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_ec3e23 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) m : l_not (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 1984 *)
+definition l_e_st_eq_landau_n_rt_rp_satz119 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more y0 x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_lrt ksi y0) (l_e_st_eq_landau_n_rt_less y0 x0) (l_e_st_eq_landau_n_rt_rp_1119_t1 y0 x0 m) (λt:l_e_st_eq_landau_n_rt_lrt ksi y0.l_e_st_eq_landau_n_rt_cutapp2a ksi y0 t x0 ux) : l_e_st_eq_landau_n_rt_urt ksi y0).
+
+(* notion 1985 *)
+definition l_e_st_eq_landau_n_rt_rp_satz119a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_rp_satz119 ksi x0 ux y0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l) : l_e_st_eq_landau_n_rt_urt ksi y0).
+
+(* notion 1986 *)
+definition l_e_st_eq_landau_n_rt_rp_1120_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_ec3e32 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) l : l_not (l_e_st_eq_landau_n_rt_more x0 y0)).
+
+(* notion 1987 *)
+definition l_e_st_eq_landau_n_rt_rp_satz120 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_imp_th7 (l_e_st_eq_landau_n_rt_lrt ksi y0) (l_e_st_eq_landau_n_rt_more y0 x0) (l_e_st_eq_landau_n_rt_rp_1120_t1 y0 x0 l) (λt:l_e_st_eq_landau_n_rt_urt ksi y0.l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx y0 t) : l_e_st_eq_landau_n_rt_lrt ksi y0).
+
+(* notion 1988 *)
+definition l_e_st_eq_landau_n_rt_rp_satz120a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_rp_satz120 ksi x0 lx y0 (l_e_st_eq_landau_n_rt_satz82 x0 y0 m) : l_e_st_eq_landau_n_rt_lrt ksi y0).
+
+(* notion 1989 *)
+definition l_e_st_eq_landau_n_rt_iii1_t12 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(i x0 j y0 : Πu:l_e_st_eq_landau_n_rt_less y0 x0.l_e_st_eq_landau_n_rt_in y0 s).
+
+(* notion 1990 *)
+definition l_e_st_eq_landau_n_rt_iii1_t13 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_imp_th3 (l_e_st_eq_landau_n_rt_less y0 x0) (l_e_st_eq_landau_n_rt_in y0 s) n (l_e_st_eq_landau_n_rt_iii1_t12 s i x0 j y0 n) : l_not (l_e_st_eq_landau_n_rt_less y0 x0)).
+
+(* notion 1991 *)
+definition l_e_st_eq_landau_n_rt_iii1_t14 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_e_st_eq_landau_n_rt_satz81f y0 x0 (l_e_st_eq_landau_n_rt_iii1_t13 s i x0 j y0 n) : l_e_st_eq_landau_n_rt_moreis y0 x0).
+
+(* notion 1992 *)
+definition l_e_st_eq_landau_n_rt_iii1_t15 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).λk:l_e_st_eq_landau_n_rt_is y0 x0.(l_e_isp1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_in x s) x0 y0 j k : l_e_st_eq_landau_n_rt_in y0 s).
+
+(* notion 1993 *)
+definition l_e_st_eq_landau_n_rt_iii1_t16 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_imp_th3 (l_e_st_eq_landau_n_rt_is y0 x0) (l_e_st_eq_landau_n_rt_in y0 s) n (λt:l_e_st_eq_landau_n_rt_is y0 x0.l_e_st_eq_landau_n_rt_iii1_t15 s i x0 j y0 n t) : l_e_st_eq_landau_n_rt_nis y0 x0).
+
+(* notion 1994 *)
+definition l_e_st_eq_landau_n_rt_iii1_t17 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_ore1 (l_e_st_eq_landau_n_rt_more y0 x0) (l_e_st_eq_landau_n_rt_is y0 x0) (l_e_st_eq_landau_n_rt_iii1_t14 s i x0 j y0 n) (l_e_st_eq_landau_n_rt_iii1_t16 s i x0 j y0 n) : l_e_st_eq_landau_n_rt_more y0 x0).
+
+(* notion 1995 *)
+definition l_e_st_eq_landau_n_rt_iii1_t18 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λx0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).(l_e_st_eq_landau_n_rt_satz82 y0 x0 (l_e_st_eq_landau_n_rt_iii1_t17 s i x0 j y0 n) : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 1996 *)
+definition l_e_st_eq_landau_n_rt_iii1_t19 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λi:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.(λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x s.λy:l_e_st_eq_landau_n_rt_rat.λu:l_not (l_e_st_eq_landau_n_rt_in y s).l_e_st_eq_landau_n_rt_iii1_t18 s i x t y u : l_e_st_eq_landau_n_rt_cutprop2 s).
+
+(* notion 1997 *)
+definition l_e_st_eq_landau_n_rt_iii1_t20 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.(s1 x0 i : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x0))).
+
+(* notion 1998 *)
+definition l_e_st_eq_landau_n_rt_iii1_t21 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_ande1 (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0) a : l_e_st_eq_landau_n_rt_in y0 s).
+
+(* notion 1999 *)
+definition l_e_st_eq_landau_n_rt_iii1_t22 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_ande2 (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0) a : l_e_st_eq_landau_n_rt_more y0 x0).
+
+(* notion 2000 *)
+definition l_e_st_eq_landau_n_rt_iii1_t23 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_e_st_eq_landau_n_rt_satz81g y0 x0 (l_e_st_eq_landau_n_rt_iii1_t22 s s1 x0 i y0 a) : l_not (l_e_st_eq_landau_n_rt_lessis y0 x0)).
+
+(* notion 2001 *)
+definition l_e_st_eq_landau_n_rt_iii1_t24 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_imp_th3 (l_e_st_eq_landau_n_rt_moreis x0 y0) (l_e_st_eq_landau_n_rt_lessis y0 x0) (l_e_st_eq_landau_n_rt_iii1_t23 s s1 x0 i y0 a) (λt:l_e_st_eq_landau_n_rt_moreis x0 y0.l_e_st_eq_landau_n_rt_satz84 x0 y0 t) : l_not (l_e_st_eq_landau_n_rt_moreis x0 y0)).
+
+(* notion 2002 *)
+definition l_e_st_eq_landau_n_rt_iii1_t25 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_imp_th4 (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_moreis x0 y0) (l_e_st_eq_landau_n_rt_iii1_t21 s s1 x0 i y0 a) (l_e_st_eq_landau_n_rt_iii1_t24 s s1 x0 i y0 a) : l_not (l_e_st_eq_landau_n_rt_iii1_ubprop s x0 y0)).
+
+(* notion 2003 *)
+definition l_e_st_eq_landau_n_rt_iii1_t26 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_all_th1 l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_iii1_ubprop s x0 y) y0 (l_e_st_eq_landau_n_rt_iii1_t25 s s1 x0 i y0 a) : l_not (l_e_st_eq_landau_n_rt_ub s x0)).
+
+(* notion 2004 *)
+definition l_e_st_eq_landau_n_rt_iii1_t27 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_in y0 s) (l_e_st_eq_landau_n_rt_more y0 x0).(l_and_th1 (l_e_st_eq_landau_n_rt_ub s x0) (l_e_st_eq_landau_n_rt_in x0 s) (l_e_st_eq_landau_n_rt_iii1_t26 s s1 x0 i y0 a) : l_not (l_e_st_eq_landau_n_rt_max s x0)).
+
+(* notion 2005 *)
+definition l_e_st_eq_landau_n_rt_iii1_t28 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.(l_someapp l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x0)) (l_e_st_eq_landau_n_rt_iii1_t20 s s1 x0 i) (l_not (l_e_st_eq_landau_n_rt_max s x0)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x0).l_e_st_eq_landau_n_rt_iii1_t27 s s1 x0 i y t) : l_not (l_e_st_eq_landau_n_rt_max s x0)).
+
+(* notion 2006 *)
+definition l_e_st_eq_landau_n_rt_iii1_t29 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in x0 s).(l_and_th2 (l_e_st_eq_landau_n_rt_ub s x0) (l_e_st_eq_landau_n_rt_in x0 s) n : l_not (l_e_st_eq_landau_n_rt_max s x0)).
+
+(* notion 2007 *)
+definition l_e_st_eq_landau_n_rt_iii1_t30 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).λx0:l_e_st_eq_landau_n_rt_rat.(l_imp_th1 (l_e_st_eq_landau_n_rt_in x0 s) (l_not (l_e_st_eq_landau_n_rt_max s x0)) (λu:l_e_st_eq_landau_n_rt_in x0 s.l_e_st_eq_landau_n_rt_iii1_t28 s s1 x0 u) (λu:l_not (l_e_st_eq_landau_n_rt_in x0 s).l_e_st_eq_landau_n_rt_iii1_t29 s s1 x0 u) : l_not (l_e_st_eq_landau_n_rt_max s x0)).
+
+(* notion 2008 *)
+definition l_e_st_eq_landau_n_rt_iii1_t31 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).(l_e_st_eq_landau_n_rt_iii1_t11 s (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_iii1_t30 s s1 x) : l_e_st_eq_landau_n_rt_cutprop3 s).
+
+(* notion 2009 *)
+definition l_e_st_eq_landau_n_rt_cut2 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 s.λy0:l_e_st_eq_landau_n_rt_rat.λn:l_not (l_e_st_eq_landau_n_rt_in y0 s).λj:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_in y s.λs1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_in x s.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y s) (l_e_st_eq_landau_n_rt_more y x)).(l_and3i (l_e_st_eq_landau_n_rt_cutprop1 s) (l_e_st_eq_landau_n_rt_cutprop2 s) (l_e_st_eq_landau_n_rt_cutprop3 s) (l_e_st_eq_landau_n_rt_iii1_t10 s x0 i y0 n) (l_e_st_eq_landau_n_rt_iii1_t19 s j) (l_e_st_eq_landau_n_rt_iii1_t31 s s1) : l_e_st_eq_landau_n_rt_cutprop s).
+
+(* notion 2010 *)
+definition l_e_st_eq_landau_n_rt_rp_more ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt eta x)) : Prop).
+
+(* notion 2011 *)
+definition l_e_st_eq_landau_n_rt_rp_iii2_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πu:l_e_st_eq_landau_n_rt_urt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta x0).(l_ande1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta x0) a : l_e_st_eq_landau_n_rt_lrt ksi x0).
+
+(* notion 2012 *)
+definition l_e_st_eq_landau_n_rt_rp_iii2_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πu:l_e_st_eq_landau_n_rt_urt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta x0).(l_ande2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta x0) a : l_e_st_eq_landau_n_rt_urt eta x0).
+
+(* notion 2013 *)
+definition l_e_st_eq_landau_n_rt_rp_iii2_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πu:l_e_st_eq_landau_n_rt_urt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta x0).(p1 x0 (l_e_st_eq_landau_n_rt_rp_iii2_t1 ksi eta m p p1 x0 a) (l_e_st_eq_landau_n_rt_rp_iii2_t2 ksi eta m p p1 x0 a) : p).
+
+(* notion 2014 *)
+definition l_e_st_eq_landau_n_rt_rp_moreapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πu:l_e_st_eq_landau_n_rt_urt eta x.p.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt eta x)) m p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt eta x).l_e_st_eq_landau_n_rt_rp_iii2_t3 ksi eta m p p1 x t) : p).
+
+(* notion 2015 *)
+definition l_e_st_eq_landau_n_rt_rp_less ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_lrt eta x)) : Prop).
+
+(* notion 2016 *)
+definition l_e_st_eq_landau_n_rt_rp_iii2_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πu:l_e_st_eq_landau_n_rt_lrt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta x0).(l_ande1 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta x0) a : l_e_st_eq_landau_n_rt_urt ksi x0).
+
+(* notion 2017 *)
+definition l_e_st_eq_landau_n_rt_rp_iii2_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πu:l_e_st_eq_landau_n_rt_lrt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta x0).(l_ande2 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta x0) a : l_e_st_eq_landau_n_rt_lrt eta x0).
+
+(* notion 2018 *)
+definition l_e_st_eq_landau_n_rt_rp_iii2_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πu:l_e_st_eq_landau_n_rt_lrt eta x.p.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta x0).(p1 x0 (l_e_st_eq_landau_n_rt_rp_iii2_t4 ksi eta l p p1 x0 a) (l_e_st_eq_landau_n_rt_rp_iii2_t5 ksi eta l p p1 x0 a) : p).
+
+(* notion 2019 *)
+definition l_e_st_eq_landau_n_rt_rp_lessapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πu:l_e_st_eq_landau_n_rt_lrt eta x.p.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_lrt eta x)) l p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_lrt eta x).l_e_st_eq_landau_n_rt_rp_iii2_t6 ksi eta l p p1 x t) : p).
+
+(* notion 2020 *)
+definition l_e_st_eq_landau_n_rt_rp_2121_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.(l_andi (l_e_st_eq_landau_n_rt_urt eta x0) (l_e_st_eq_landau_n_rt_lrt ksi x0) ux lx : l_and (l_e_st_eq_landau_n_rt_urt eta x0) (l_e_st_eq_landau_n_rt_lrt ksi x0)).
+
+(* notion 2021 *)
+definition l_e_st_eq_landau_n_rt_rp_2121_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt eta x) (l_e_st_eq_landau_n_rt_lrt ksi x)) x0 (l_e_st_eq_landau_n_rt_rp_2121_t1 ksi eta m x0 lx ux) : l_e_st_eq_landau_n_rt_rp_less eta ksi).
+
+(* notion 2022 *)
+definition l_e_st_eq_landau_n_rt_rp_satz121 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m (l_e_st_eq_landau_n_rt_rp_less eta ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_2121_t2 ksi eta m x t u) : l_e_st_eq_landau_n_rt_rp_less eta ksi).
+
+(* notion 2023 *)
+definition l_e_st_eq_landau_n_rt_rp_2122_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_andi (l_e_st_eq_landau_n_rt_lrt eta x0) (l_e_st_eq_landau_n_rt_urt ksi x0) lx ux : l_and (l_e_st_eq_landau_n_rt_lrt eta x0) (l_e_st_eq_landau_n_rt_urt ksi x0)).
+
+(* notion 2024 *)
+definition l_e_st_eq_landau_n_rt_rp_2122_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt eta x) (l_e_st_eq_landau_n_rt_urt ksi x)) x0 (l_e_st_eq_landau_n_rt_rp_2122_t1 ksi eta l x0 ux lx) : l_e_st_eq_landau_n_rt_rp_more eta ksi).
+
+(* notion 2025 *)
+definition l_e_st_eq_landau_n_rt_rp_satz122 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_lessapp ksi eta l (l_e_st_eq_landau_n_rt_rp_more eta ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λu:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_2122_t2 ksi eta l x t u) : l_e_st_eq_landau_n_rt_rp_more eta ksi).
+
+(* notion 2026 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.(l_e_st_isset_th3 l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta) x0 lx ux : l_not (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta))).
+
+(* notion 2027 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta)) (l_e_st_eq_landau_n_rt_rp_2123_t1 ksi eta m x0 lx ux) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_ise ksi eta t) : l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)).
+
+(* notion 2028 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m (l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_2123_t2 ksi eta m x t u) : l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)).
+
+(* notion 2029 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_ec_th2 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t3 ksi eta t) : l_ec (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta)).
+
+(* notion 2030 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_e_st_isset_th4 l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl eta) (l_e_st_eq_landau_n_rt_lcl ksi) x0 lx ux : l_not (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta))).
+
+(* notion 2031 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta)) (l_e_st_eq_landau_n_rt_rp_2123_t5 ksi eta l x0 ux lx) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_ise ksi eta t) : l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)).
+
+(* notion 2032 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_lessapp ksi eta l (l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λu:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_2123_t6 ksi eta l x t u) : l_not (l_e_st_eq_landau_n_rt_rp_is ksi eta)).
+
+(* notion 2033 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_ec_th1 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t7 ksi eta t) : l_ec (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta)).
+
+(* notion 2034 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx y0 uy : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 2035 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_cutapp2b eta y0 ly x0 ux : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 2036 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_mp (l_e_st_eq_landau_n_rt_less x0 y0) l_con (l_e_st_eq_landau_n_rt_rp_2123_t9 ksi eta m l x0 lx ux y0 uy ly) (l_ec3e23 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_satz81b x0 y0) (l_e_st_eq_landau_n_rt_rp_2123_t10 ksi eta m l x0 lx ux y0 uy ly)) : l_con).
+
+(* notion 2037 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λux:l_e_st_eq_landau_n_rt_urt eta x0.(l_e_st_eq_landau_n_rt_rp_lessapp ksi eta l l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λu:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_2123_t11 ksi eta m l x0 lx ux x t u) : l_con).
+
+(* notion 2038 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_2123_t12 ksi eta m l x t u) : l_con).
+
+(* notion 2039 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t13 ksi eta m t : l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2040 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_ec_th1 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t14 ksi eta t) : l_ec (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2041 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_ec3_th6 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_t4 ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_t15 ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_t8 ksi eta) : l_ec3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2042 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_or3i1 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) i : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2043 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis ksi eta.(l_imp_th3 (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta)) (l_e_st_eq_landau_n_rt_rp_is ksi eta) n (λt:l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta).l_e_st_eq_landau_n_rt_rp_isi ksi eta t) : l_not (l_e_is (l_e_st_set l_e_st_eq_landau_n_rt_rat) (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta))).
+
+(* notion 2044 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis ksi eta.(l_e_st_isset_th5 l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_lcl ksi) (l_e_st_eq_landau_n_rt_lcl eta) (l_e_st_eq_landau_n_rt_rp_2123_t17 ksi eta n) : l_or (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_more eta ksi)).
+
+(* notion 2045 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis ksi eta.(l_or_th8 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_more eta ksi) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_t18 ksi eta n) (λt:l_e_st_eq_landau_n_rt_rp_more eta ksi.l_e_st_eq_landau_n_rt_rp_satz121 eta ksi t) : l_or (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2046 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis ksi eta.(l_or3_th7 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_t19 ksi eta n) : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2047 *)
+definition l_e_st_eq_landau_n_rt_rp_2123_b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t16 ksi eta t) (λt:l_e_st_eq_landau_n_rt_rp_nis ksi eta.l_e_st_eq_landau_n_rt_rp_2123_t20 ksi eta t) : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2048 *)
+definition l_e_st_eq_landau_n_rt_rp_satz123 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_orec3i (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_b ksi eta) (l_e_st_eq_landau_n_rt_rp_2123_a ksi eta) : l_orec3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2049 *)
+definition l_e_st_eq_landau_n_rt_rp_satz123a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_orec3e1 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123 ksi eta) : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2050 *)
+definition l_e_st_eq_landau_n_rt_rp_satz123b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_orec3e2 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123 ksi eta) : l_ec3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2051 *)
+definition l_e_st_eq_landau_n_rt_rp_moreis ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_or (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) : Prop).
+
+(* notion 2052 *)
+definition l_e_st_eq_landau_n_rt_rp_lessis ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_or (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) : Prop).
+
+(* notion 2053 *)
+definition l_e_st_eq_landau_n_rt_rp_satz124 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_less eta ksi) (l_e_st_eq_landau_n_rt_rp_is eta ksi) m (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz121 ksi eta t) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_symis l_e_st_eq_landau_n_rt_cut ksi eta t) : l_e_st_eq_landau_n_rt_rp_lessis eta ksi).
+
+(* notion 2054 *)
+definition l_e_st_eq_landau_n_rt_rp_satz125 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more eta ksi) (l_e_st_eq_landau_n_rt_rp_is eta ksi) l (λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz122 ksi eta t) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_symis l_e_st_eq_landau_n_rt_cut ksi eta t) : l_e_st_eq_landau_n_rt_rp_moreis eta ksi).
+
+(* notion 2055 *)
+definition l_e_st_eq_landau_n_rt_rp_ismore1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi zeta.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_more u zeta) ksi eta m i : l_e_st_eq_landau_n_rt_rp_more eta zeta).
+
+(* notion 2056 *)
+definition l_e_st_eq_landau_n_rt_rp_ismore2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more zeta ksi.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_more zeta u) ksi eta m i : l_e_st_eq_landau_n_rt_rp_more zeta eta).
+
+(* notion 2057 *)
+definition l_e_st_eq_landau_n_rt_rp_isless1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less ksi zeta.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_less u zeta) ksi eta l i : l_e_st_eq_landau_n_rt_rp_less eta zeta).
+
+(* notion 2058 *)
+definition l_e_st_eq_landau_n_rt_rp_isless2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less zeta ksi.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_less zeta u) ksi eta l i : l_e_st_eq_landau_n_rt_rp_less zeta eta).
+
+(* notion 2059 *)
+definition l_e_st_eq_landau_n_rt_rp_ismoreis1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi zeta.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_moreis u zeta) ksi eta m i : l_e_st_eq_landau_n_rt_rp_moreis eta zeta).
+
+(* notion 2060 *)
+definition l_e_st_eq_landau_n_rt_rp_ismoreis2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_moreis zeta ksi.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_moreis zeta u) ksi eta m i : l_e_st_eq_landau_n_rt_rp_moreis zeta eta).
+
+(* notion 2061 *)
+definition l_e_st_eq_landau_n_rt_rp_islessis1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi zeta.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_lessis u zeta) ksi eta l i : l_e_st_eq_landau_n_rt_rp_lessis eta zeta).
+
+(* notion 2062 *)
+definition l_e_st_eq_landau_n_rt_rp_islessis2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_lessis zeta ksi.(l_e_isp l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_lessis zeta u) ksi eta l i : l_e_st_eq_landau_n_rt_rp_lessis zeta eta).
+
+(* notion 2063 *)
+definition l_e_st_eq_landau_n_rt_rp_moreisi2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_ori2 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) i : l_e_st_eq_landau_n_rt_rp_moreis ksi eta).
+
+(* notion 2064 *)
+definition l_e_st_eq_landau_n_rt_rp_lessisi2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_ori2 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) i : l_e_st_eq_landau_n_rt_rp_lessis ksi eta).
+
+(* notion 2065 *)
+definition l_e_st_eq_landau_n_rt_rp_moreisi1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_ori1 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) m : l_e_st_eq_landau_n_rt_rp_moreis ksi eta).
+
+(* notion 2066 *)
+definition l_e_st_eq_landau_n_rt_rp_lessisi1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_ori1 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) l : l_e_st_eq_landau_n_rt_rp_lessis ksi eta).
+
+(* notion 2067 *)
+definition l_e_st_eq_landau_n_rt_rp_ismore12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.λm:l_e_st_eq_landau_n_rt_rp_more ksi zeta.(l_e_st_eq_landau_n_rt_rp_ismore2 zeta upsilon eta j (l_e_st_eq_landau_n_rt_rp_ismore1 ksi eta zeta i m) : l_e_st_eq_landau_n_rt_rp_more eta upsilon).
+
+(* notion 2068 *)
+definition l_e_st_eq_landau_n_rt_rp_isless12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.λl:l_e_st_eq_landau_n_rt_rp_less ksi zeta.(l_e_st_eq_landau_n_rt_rp_isless2 zeta upsilon eta j (l_e_st_eq_landau_n_rt_rp_isless1 ksi eta zeta i l) : l_e_st_eq_landau_n_rt_rp_less eta upsilon).
+
+(* notion 2069 *)
+definition l_e_st_eq_landau_n_rt_rp_ismoreis12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi zeta.(l_e_st_eq_landau_n_rt_rp_ismoreis2 zeta upsilon eta j (l_e_st_eq_landau_n_rt_rp_ismoreis1 ksi eta zeta i m) : l_e_st_eq_landau_n_rt_rp_moreis eta upsilon).
+
+(* notion 2070 *)
+definition l_e_st_eq_landau_n_rt_rp_islessis12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi zeta.(l_e_st_eq_landau_n_rt_rp_islessis2 zeta upsilon eta j (l_e_st_eq_landau_n_rt_rp_islessis1 ksi eta zeta i l) : l_e_st_eq_landau_n_rt_rp_lessis eta upsilon).
+
+(* notion 2071 *)
+definition l_e_st_eq_landau_n_rt_rp_satz123c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.(l_ec3_th7 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) (l_comor (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) m) : l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2072 *)
+definition l_e_st_eq_landau_n_rt_rp_satz123d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.(l_ec3_th9 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) l : l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta)).
+
+(* notion 2073 *)
+definition l_e_st_eq_landau_n_rt_rp_satz123e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta).(l_or3_th2 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123a ksi eta) n : l_e_st_eq_landau_n_rt_rp_lessis ksi eta).
+
+(* notion 2074 *)
+definition l_e_st_eq_landau_n_rt_rp_satz123f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta).(l_comor (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_or3_th3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123a ksi eta) n) : l_e_st_eq_landau_n_rt_rp_moreis ksi eta).
+
+(* notion 2075 *)
+definition l_e_st_eq_landau_n_rt_rp_satz123g ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_or_th3 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_ec3e23 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) m) (l_ec3e21 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) m) : l_not (l_e_st_eq_landau_n_rt_rp_lessis ksi eta)).
+
+(* notion 2076 *)
+definition l_e_st_eq_landau_n_rt_rp_satz123h ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_or_th3 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_ec3e32 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) l) (l_ec3e31 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123b ksi eta) l) : l_not (l_e_st_eq_landau_n_rt_rp_moreis ksi eta)).
+
+(* notion 2077 *)
+definition l_e_st_eq_landau_n_rt_rp_satz123j ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_moreis ksi eta).(l_or3e3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123a ksi eta) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) n) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) n) : l_e_st_eq_landau_n_rt_rp_less ksi eta).
+
+(* notion 2078 *)
+definition l_e_st_eq_landau_n_rt_rp_satz123k ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_lessis ksi eta).(l_or3e2 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123a ksi eta) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) n) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) n) : l_e_st_eq_landau_n_rt_rp_more ksi eta).
+
+(* notion 2079 *)
+definition l_e_st_eq_landau_n_rt_rp_2126_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λly:l_e_st_eq_landau_n_rt_lrt zeta y0.(l_e_st_eq_landau_n_rt_cutapp2a eta x0 lx y0 uy : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 2080 *)
+definition l_e_st_eq_landau_n_rt_rp_2126_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λly:l_e_st_eq_landau_n_rt_lrt zeta y0.(l_e_st_eq_landau_n_rt_rp_satz119a ksi x0 ux y0 (l_e_st_eq_landau_n_rt_rp_2126_t1 ksi eta zeta l k x0 ux lx y0 uy ly) : l_e_st_eq_landau_n_rt_urt ksi y0).
+
+(* notion 2081 *)
+definition l_e_st_eq_landau_n_rt_rp_2126_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λly:l_e_st_eq_landau_n_rt_lrt zeta y0.(l_andi (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_lrt zeta y0) (l_e_st_eq_landau_n_rt_rp_2126_t2 ksi eta zeta l k x0 ux lx y0 uy ly) ly : l_and (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_lrt zeta y0)).
+
+(* notion 2082 *)
+definition l_e_st_eq_landau_n_rt_rp_2126_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λly:l_e_st_eq_landau_n_rt_lrt zeta y0.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_lrt zeta x)) y0 (l_e_st_eq_landau_n_rt_rp_2126_t3 ksi eta zeta l k x0 ux lx y0 uy ly) : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
+
+(* notion 2083 *)
+definition l_e_st_eq_landau_n_rt_rp_2126_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_e_st_eq_landau_n_rt_rp_lessapp eta zeta k (l_e_st_eq_landau_n_rt_rp_less ksi zeta) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt eta x.λu:l_e_st_eq_landau_n_rt_lrt zeta x.l_e_st_eq_landau_n_rt_rp_2126_t4 ksi eta zeta l k x0 ux lx x t u) : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
+
+(* notion 2084 *)
+definition l_e_st_eq_landau_n_rt_rp_satz126 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.(l_e_st_eq_landau_n_rt_rp_lessapp ksi eta l (l_e_st_eq_landau_n_rt_rp_less ksi zeta) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λu:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_2126_t5 ksi eta zeta l k x t u) : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
+
+(* notion 2085 *)
+definition l_e_st_eq_landau_n_rt_rp_trless ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.(l_e_st_eq_landau_n_rt_rp_satz126 ksi eta zeta l k : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
+
+(* notion 2086 *)
+definition l_e_st_eq_landau_n_rt_rp_trmore ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more eta zeta.(l_e_st_eq_landau_n_rt_rp_satz122 zeta ksi (l_e_st_eq_landau_n_rt_rp_satz126 zeta eta ksi (l_e_st_eq_landau_n_rt_rp_satz121 eta zeta n) (l_e_st_eq_landau_n_rt_rp_satz121 ksi eta m)) : l_e_st_eq_landau_n_rt_rp_more ksi zeta).
+
+(* notion 2087 *)
+definition l_e_st_eq_landau_n_rt_rp_satz127a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less eta zeta.(l_orapp (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi zeta) l (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_trless ksi eta zeta u k) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_isless1 eta ksi zeta (l_e_symis l_e_st_eq_landau_n_rt_cut ksi eta u) k) : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
+
+(* notion 2088 *)
+definition l_e_st_eq_landau_n_rt_rp_satz127b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.(l_orapp (l_e_st_eq_landau_n_rt_rp_less eta zeta) (l_e_st_eq_landau_n_rt_rp_is eta zeta) (l_e_st_eq_landau_n_rt_rp_less ksi zeta) k (λu:l_e_st_eq_landau_n_rt_rp_less eta zeta.l_e_st_eq_landau_n_rt_rp_trless ksi eta zeta l u) (λu:l_e_st_eq_landau_n_rt_rp_is eta zeta.l_e_st_eq_landau_n_rt_rp_isless2 eta zeta ksi u l) : l_e_st_eq_landau_n_rt_rp_less ksi zeta).
+
+(* notion 2089 *)
+definition l_e_st_eq_landau_n_rt_rp_satz127c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more eta zeta.(l_e_st_eq_landau_n_rt_rp_satz122 zeta ksi (l_e_st_eq_landau_n_rt_rp_satz127b zeta eta ksi (l_e_st_eq_landau_n_rt_rp_satz121 eta zeta n) (l_e_st_eq_landau_n_rt_rp_satz124 ksi eta m)) : l_e_st_eq_landau_n_rt_rp_more ksi zeta).
+
+(* notion 2090 *)
+definition l_e_st_eq_landau_n_rt_rp_satz127d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis eta zeta.(l_e_st_eq_landau_n_rt_rp_satz122 zeta ksi (l_e_st_eq_landau_n_rt_rp_satz127a zeta eta ksi (l_e_st_eq_landau_n_rt_rp_satz124 eta zeta n) (l_e_st_eq_landau_n_rt_rp_satz121 ksi eta m)) : l_e_st_eq_landau_n_rt_rp_more ksi zeta).
+
+(* notion 2091 *)
+definition l_e_st_eq_landau_n_rt_rp_2128_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is eta zeta.(l_e_st_eq_landau_n_rt_rp_lessisi2 ksi zeta (l_e_tris l_e_st_eq_landau_n_rt_cut ksi eta zeta i j) : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
+
+(* notion 2092 *)
+definition l_e_st_eq_landau_n_rt_rp_2128_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_less eta zeta.(l_e_st_eq_landau_n_rt_rp_lessisi1 ksi zeta (l_e_st_eq_landau_n_rt_rp_satz127a ksi eta zeta l j) : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
+
+(* notion 2093 *)
+definition l_e_st_eq_landau_n_rt_rp_2128_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_orapp (l_e_st_eq_landau_n_rt_rp_less eta zeta) (l_e_st_eq_landau_n_rt_rp_is eta zeta) (l_e_st_eq_landau_n_rt_rp_lessis ksi zeta) k (λt:l_e_st_eq_landau_n_rt_rp_less eta zeta.l_e_st_eq_landau_n_rt_rp_2128_t2 ksi eta zeta l k i t) (λt:l_e_st_eq_landau_n_rt_rp_is eta zeta.l_e_st_eq_landau_n_rt_rp_2128_t1 ksi eta zeta l k i t) : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
+
+(* notion 2094 *)
+definition l_e_st_eq_landau_n_rt_rp_2128_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.λj:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_lessisi1 ksi zeta (l_e_st_eq_landau_n_rt_rp_satz127b ksi eta zeta j k) : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
+
+(* notion 2095 *)
+definition l_e_st_eq_landau_n_rt_rp_satz128 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.(l_orapp (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_lessis ksi zeta) l (λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_2128_t4 ksi eta zeta l k t) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_2128_t3 ksi eta zeta l k t) : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
+
+(* notion 2096 *)
+definition l_e_st_eq_landau_n_rt_rp_trlessis ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis eta zeta.(l_e_st_eq_landau_n_rt_rp_satz128 ksi eta zeta l k : l_e_st_eq_landau_n_rt_rp_lessis ksi zeta).
+
+(* notion 2097 *)
+definition l_e_st_eq_landau_n_rt_rp_trmoreis ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis eta zeta.(l_e_st_eq_landau_n_rt_rp_satz125 zeta ksi (l_e_st_eq_landau_n_rt_rp_satz128 zeta eta ksi (l_e_st_eq_landau_n_rt_rp_satz124 eta zeta n) (l_e_st_eq_landau_n_rt_rp_satz124 ksi eta m)) : l_e_st_eq_landau_n_rt_rp_moreis ksi zeta).
+
+(* notion 2098 *)
+definition l_e_st_eq_landau_n_rt_rp_sumprop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) : Prop).
+
+(* notion 2099 *)
+definition l_e_st_eq_landau_n_rt_rp_sumprop ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x y)) : Prop).
+
+(* notion 2100 *)
+definition l_e_st_eq_landau_n_rt_rp_sum ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (λz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop ksi eta z) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2101 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_and3i (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) lx ly i : l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y0).
+
+(* notion 2102 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y) y0 (l_e_st_eq_landau_n_rt_rp_iii3_t1 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y)).
+
+(* notion 2103 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x y)) x0 (l_e_st_eq_landau_n_rt_rp_iii3_t2 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_rp_sumprop ksi eta z0).
+
+(* notion 2104 *)
+definition l_e_st_eq_landau_n_rt_rp_sum1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop ksi eta z) z0 (l_e_st_eq_landau_n_rt_rp_iii3_t3 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
+
+(* notion 2105 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop ksi eta z) z0 i : l_e_st_eq_landau_n_rt_rp_sumprop ksi eta z0).
+
+(* notion 2106 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y0.(l_and3e1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) py : l_e_st_eq_landau_n_rt_lrt ksi x0).
+
+(* notion 2107 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y0.(l_and3e2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) py : l_e_st_eq_landau_n_rt_lrt eta y0).
+
+(* notion 2108 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y0.(l_and3e3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) py : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
+
+(* notion 2109 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y0.(p1 x0 (l_e_st_eq_landau_n_rt_rp_iii3_t5 ksi eta z0 i p p1 x0 px y0 py) y0 (l_e_st_eq_landau_n_rt_rp_iii3_t6 ksi eta z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_iii3_t7 ksi eta z0 i p p1 x0 px y0 py) : p).
+
+(* notion 2110 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y).(l_someapp l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y) px p (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x0 y.l_e_st_eq_landau_n_rt_rp_iii3_t8 ksi eta z0 i p p1 x0 px y t) : p).
+
+(* notion 2111 *)
+definition l_e_st_eq_landau_n_rt_rp_sumapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x y)) (l_e_st_eq_landau_n_rt_rp_iii3_t4 ksi eta z0 i p p1) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_sumprop1 ksi eta z0 x y).l_e_st_eq_landau_n_rt_rp_iii3_t9 ksi eta z0 i p p1 x t) : p).
+
+(* notion 2112 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx x1 ux : l_e_st_eq_landau_n_rt_less x0 x1).
+
+(* notion 2113 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_cutapp2a eta y0 ly y1 uy : l_e_st_eq_landau_n_rt_less y0 y1).
+
+(* notion 2114 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_pl x0 y0) z0 (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl x0 y0) j) (l_e_st_eq_landau_n_rt_satz98a x0 x1 y0 y1 (l_e_st_eq_landau_n_rt_rp_3129_t1 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_rp_3129_t2 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j)) : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_pl x1 y1)).
+
+(* notion 2115 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_ec3e31 (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_e_st_eq_landau_n_rt_more z0 (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_e_st_eq_landau_n_rt_satz81b z0 (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_e_st_eq_landau_n_rt_rp_3129_t3 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_pl x1 y1)).
+
+(* notion 2116 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).(l_e_st_eq_landau_n_rt_rp_sumapp ksi eta z0 i (l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_pl x1 y1)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3129_t4 ksi eta x1 ux y1 uy z0 i x t y u v) : l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_pl x1 y1)).
+
+(* notion 2117 *)
+definition l_e_st_eq_landau_n_rt_rp_satz129a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.(l_imp_th3 (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_nis (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_weli (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_pl x1 y1)) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl x1 y1))) (λt:l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_rp_sum ksi eta).l_e_st_eq_landau_n_rt_rp_3129_t5 ksi eta x1 ux y1 uy (l_e_st_eq_landau_n_rt_pl x1 y1) t) : l_not (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_rp_sum ksi eta))).
+
+(* notion 2118 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_isless2 u0 (l_e_st_eq_landau_n_rt_pl x0 y0) z0 j l : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
+
+(* notion 2119 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_z1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_ov z0 (l_e_st_eq_landau_n_rt_pl x0 y0) : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2120 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_isless12 z0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_satz110f z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_example1d (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_rp_3129_t6 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0))).
+
+(* notion 2121 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_satz106c (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_3129_t7 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2122 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_example1a x0) (l_e_st_eq_landau_n_rt_satz105f (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) l_e_st_eq_landau_n_rt_1rt x0 (l_e_st_eq_landau_n_rt_rp_3129_t8 ksi eta u0 i z0 l x0 lx y0 ly j)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) x0).
+
+(* notion 2123 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_ts y0 l_e_st_eq_landau_n_rt_1rt) y0 (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_example1a y0) (l_e_st_eq_landau_n_rt_satz105f (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j) l_e_st_eq_landau_n_rt_1rt y0 (l_e_st_eq_landau_n_rt_rp_3129_t8 ksi eta u0 i z0 l x0 lx y0 ly j)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) y0).
+
+(* notion 2124 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_satz120 ksi x0 lx (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_rp_3129_t9 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j))).
+
+(* notion 2125 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_satz120 eta y0 ly (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_rp_3129_t10 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_lrt eta (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j))).
+
+(* notion 2126 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j))) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) z0 (l_e_st_eq_landau_n_rt_distpt1 x0 y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_satz110c z0 (l_e_st_eq_landau_n_rt_pl x0 y0)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j))) z0).
+
+(* notion 2127 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j))) z0 (l_e_st_eq_landau_n_rt_rp_3129_t13 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)))).
+
+(* notion 2128 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_sum1 ksi eta z0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_rp_3129_t11 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_3129_z1 ksi eta u0 i z0 l x0 lx y0 ly j)) (l_e_st_eq_landau_n_rt_rp_3129_t12 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_rp_3129_t14 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
+
+(* notion 2129 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_rp_sumapp ksi eta u0 i (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3129_t15 ksi eta u0 i z0 l x t y u v) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
+
+(* notion 2130 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_rp_sum1 ksi eta (l_e_st_eq_landau_n_rt_pl x1 y0) x1 lx1 y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl x1 y0)) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
+
+(* notion 2131 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_satz96a x1 x0 y0 (l_e_st_eq_landau_n_rt_satz83 x0 x1 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_st_eq_landau_n_rt_pl x0 y0)).
+
+(* notion 2132 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_ismore2 (l_e_st_eq_landau_n_rt_pl x0 y0) z0 (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl x0 y0) j) (l_e_st_eq_landau_n_rt_rp_3129_t18 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x1 y0) z0).
+
+(* notion 2133 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_andi (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x1 y0) z0) (l_e_st_eq_landau_n_rt_rp_3129_t17 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) (l_e_st_eq_landau_n_rt_rp_3129_t19 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_and (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x1 y0) z0)).
+
+(* notion 2134 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0)) (l_e_st_eq_landau_n_rt_pl x1 y0) (l_e_st_eq_landau_n_rt_rp_3129_t20 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
+
+(* notion 2135 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_cutapp3 ksi x0 lx (l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_less x0 x.l_e_st_eq_landau_n_rt_rp_3129_t21 ksi eta z0 i x0 lx y0 ly j x t u) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
+
+(* notion 2136 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta).(l_e_st_eq_landau_n_rt_rp_sumapp ksi eta z0 i (l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3129_t22 ksi eta z0 i x t y u v) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
+
+(* notion 2137 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_sum ksi eta) (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_sum1 ksi eta (l_e_st_eq_landau_n_rt_pl x0 y0) x0 lx y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl x0 y0))) (l_e_st_eq_landau_n_rt_pl x1 y1) (l_e_st_eq_landau_n_rt_rp_satz129a ksi eta x1 ux y1 uy) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_sum ksi eta).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_3129_t16 ksi eta x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_sum ksi eta).l_e_st_eq_landau_n_rt_rp_3129_t23 ksi eta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
+
+(* notion 2138 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.(l_e_st_eq_landau_n_rt_cutapp1b eta (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt eta y.l_e_st_eq_landau_n_rt_rp_3129_t24 ksi eta x0 lx y0 ly x1 ux y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
+
+(* notion 2139 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_cutapp1b ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.l_e_st_eq_landau_n_rt_rp_3129_t25 ksi eta x0 lx y0 ly x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
+
+(* notion 2140 *)
+definition l_e_st_eq_landau_n_rt_rp_3129_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_cutapp1a eta (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta y.l_e_st_eq_landau_n_rt_rp_3129_t26 ksi eta x0 lx y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
+
+(* notion 2141 *)
+definition l_e_st_eq_landau_n_rt_rp_satz129 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_cutapp1a ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_3129_t27 ksi eta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
+
+(* notion 2142 *)
+definition l_e_st_eq_landau_n_rt_rp_pl ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_sum ksi eta) (l_e_st_eq_landau_n_rt_rp_satz129 ksi eta) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2143 *)
+definition l_e_st_eq_landau_n_rt_rp_lrtpl ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_sum ksi eta) (l_e_st_eq_landau_n_rt_rp_satz129 ksi eta) z0 (l_e_st_eq_landau_n_rt_rp_sum1 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0).
+
+(* notion 2144 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_isp1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_sum ksi eta))) (l_e_st_eq_landau_n_rt_pl x0 y0) z0 (l_e_st_eq_landau_n_rt_rp_satz129a ksi eta x0 ux y0 uy) i : l_not (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta))).
+
+(* notion 2145 *)
+definition l_e_st_eq_landau_n_rt_rp_urtpl ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_imp_th3 (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0) (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)) (l_e_st_eq_landau_n_rt_rp_iii3_t10 ksi eta z0 x0 ux y0 uy i) (λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_sum ksi eta) (l_e_st_eq_landau_n_rt_rp_satz129 ksi eta) z0 t) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0).
+
+(* notion 2146 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.(l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_sum ksi eta) (l_e_st_eq_landau_n_rt_rp_satz129 ksi eta) z0 lz : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_sum ksi eta)).
+
+(* notion 2147 *)
+definition l_e_st_eq_landau_n_rt_rp_plapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).p.(l_e_st_eq_landau_n_rt_rp_sumapp ksi eta z0 (l_e_st_eq_landau_n_rt_rp_iii3_t11 ksi eta z0 lz p p1) p p1 : p).
+
+(* notion 2148 *)
+definition l_e_st_eq_landau_n_rt_rp_ispl1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_pl u zeta) ksi eta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
+
+(* notion 2149 *)
+definition l_e_st_eq_landau_n_rt_rp_ispl2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_pl zeta u) ksi eta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta)).
+
+(* notion 2150 *)
+definition l_e_st_eq_landau_n_rt_rp_ispl12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_ispl1 ksi eta zeta i) (l_e_st_eq_landau_n_rt_rp_ispl2 zeta upsilon eta j) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2151 *)
+definition l_e_st_eq_landau_n_rt_rp_3130_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_tris l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_pl y0 x0) i (l_e_st_eq_landau_n_rt_compl x0 y0) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y0 x0)).
+
+(* notion 2152 *)
+definition l_e_st_eq_landau_n_rt_rp_3130_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtpl eta ksi z0 y0 ly x0 lx (l_e_st_eq_landau_n_rt_rp_3130_t1 ksi eta z0 lz x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta ksi) z0).
+
+(* notion 2153 *)
+definition l_e_st_eq_landau_n_rt_rp_3130_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) z0.(l_e_st_eq_landau_n_rt_rp_plapp ksi eta z0 lz (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta ksi) z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3130_t2 ksi eta z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta ksi) z0).
+
+(* notion 2154 *)
+definition l_e_st_eq_landau_n_rt_rp_satz130 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_pl eta ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) x.l_e_st_eq_landau_n_rt_rp_3130_t3 ksi eta x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta ksi) x.l_e_st_eq_landau_n_rt_rp_3130_t3 eta ksi x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_pl eta ksi)).
+
+(* notion 2155 *)
+definition l_e_st_eq_landau_n_rt_rp_compl ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz130 ksi eta : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_pl eta ksi)).
+
+(* notion 2156 *)
+definition l_e_st_eq_landau_n_rt_rp_3131_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_pl v0 z0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) i (l_e_st_eq_landau_n_rt_ispl1 v0 (l_e_st_eq_landau_n_rt_pl x0 y0) z0 j) (l_e_st_eq_landau_n_rt_asspl1 x0 y0 z0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0))).
+
+(* notion 2157 *)
+definition l_e_st_eq_landau_n_rt_rp_3131_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtpl eta zeta (l_e_st_eq_landau_n_rt_pl y0 z0) y0 ly z0 lz (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y0 z0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 2158 *)
+definition l_e_st_eq_landau_n_rt_rp_3131_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtpl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta) u0 x0 lx (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_rp_3131_t2 ksi eta zeta u0 lu v0 lv z0 lz i x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_rp_3131_t1 ksi eta zeta u0 lu v0 lv z0 lz i x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
+
+(* notion 2159 *)
+definition l_e_st_eq_landau_n_rt_rp_3131_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 z0).(l_e_st_eq_landau_n_rt_rp_plapp ksi eta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3131_t3 ksi eta zeta u0 lu v0 lv z0 lz i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
+
+(* notion 2160 *)
+definition l_e_st_eq_landau_n_rt_rp_3131_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0.(l_e_st_eq_landau_n_rt_rp_plapp (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3131_t4 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
+
+(* notion 2161 *)
+definition l_e_st_eq_landau_n_rt_rp_3131_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_pl x0 v0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0) i (l_e_st_eq_landau_n_rt_ispl2 v0 (l_e_st_eq_landau_n_rt_pl y0 z0) x0 j) (l_e_st_eq_landau_n_rt_asspl2 x0 y0 z0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl x0 y0) z0)).
+
+(* notion 2162 *)
+definition l_e_st_eq_landau_n_rt_rp_3131_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtpl ksi eta (l_e_st_eq_landau_n_rt_pl x0 y0) x0 lx y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl x0 y0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_pl x0 y0)).
+
+(* notion 2163 *)
+definition l_e_st_eq_landau_n_rt_rp_3131_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtpl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta u0 (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_3131_t7 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) z0 lz (l_e_st_eq_landau_n_rt_rp_3131_t6 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0).
+
+(* notion 2164 *)
+definition l_e_st_eq_landau_n_rt_rp_3131_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 v0).(l_e_st_eq_landau_n_rt_rp_plapp eta zeta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3131_t8 ksi eta zeta u0 lu x0 lx v0 lv i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0).
+
+(* notion 2165 *)
+definition l_e_st_eq_landau_n_rt_rp_3131_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.(l_e_st_eq_landau_n_rt_rp_plapp ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta) u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3131_t9 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) u0).
+
+(* notion 2166 *)
+definition l_e_st_eq_landau_n_rt_rp_satz131 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) x.l_e_st_eq_landau_n_rt_rp_3131_t5 ksi eta zeta x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) x.l_e_st_eq_landau_n_rt_rp_3131_t10 ksi eta zeta x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta))).
+
+(* notion 2167 *)
+definition l_e_st_eq_landau_n_rt_rp_asspl1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz131 ksi eta zeta : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta))).
+
+(* notion 2168 *)
+definition l_e_st_eq_landau_n_rt_rp_asspl2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_satz131 ksi eta zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta)).
+
+(* notion 2169 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_prop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi y0) : Prop).
+
+(* notion 2170 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λp:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0.(l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_ande1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi y0) p) y0 (l_ande2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi y0) p) : l_e_st_eq_landau_n_rt_more y0 x0).
+
+(* notion 2171 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_prop2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λp:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0.(l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 y0 p)) a0 : Prop).
+
+(* notion 2172 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_prop3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0) (Πt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0.l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 y0 t) : Prop).
+
+(* notion 2173 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_prop4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x y)) : Prop).
+
+(* notion 2174 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx y0 uy : l_e_st_eq_landau_n_rt_more y0 x0).
+
+(* notion 2175 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)).(l_e_st_eq_landau_n_rt_satz96d (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)) x0 m : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0)) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)))).
+
+(* notion 2176 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)).(l_e_st_eq_landau_n_rt_ismore2 (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy))) y0 (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0)) (l_e_st_eq_landau_n_rt_satz101c y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)) (l_e_st_eq_landau_n_rt_rp_3132_t3 ksi a0 x0 lx y0 uy n m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0)) y0).
+
+(* notion 2177 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)).(l_e_st_eq_landau_n_rt_rp_satz119 ksi y0 uy (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0)) (l_e_st_eq_landau_n_rt_rp_3132_t4 ksi a0 x0 lx y0 uy n m) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0))).
+
+(* notion 2178 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn n) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)).(l_somei l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) n (l_e_st_eq_landau_n_rt_rp_3132_t5 ksi a0 x0 lx y0 uy n m) : l_e_st_eq_landau_n_some (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0)))).
+
+(* notion 2179 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_someapp l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy))) (l_e_st_eq_landau_n_rt_satz115 a0 (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy))) (l_e_st_eq_landau_n_some (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0)))) (λx:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t2 ksi a0 x0 lx y0 uy)).l_e_st_eq_landau_n_rt_rp_3132_t6 ksi a0 x0 lx y0 uy x t) : l_e_st_eq_landau_n_some (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0)))).
+
+(* notion 2180 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.(l_ande1 (l_e_st_eq_landau_n_lb (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u) (l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0))) m : l_e_st_eq_landau_n_lb (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u).
+
+(* notion 2181 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.(l_ande2 (l_e_st_eq_landau_n_lb (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u) (l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0))) m : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0))).
+
+(* notion 2182 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_u0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_pl x0 a0 : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2183 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt a0) (l_e_st_eq_landau_n_rt_ts a0 l_e_st_eq_landau_n_rt_1rt) a0 (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt a0 (l_e_st_eq_landau_n_rt_isnert u l_e_st_eq_landau_n_1 i)) (l_e_st_eq_landau_n_rt_comts l_e_st_eq_landau_n_rt_1rt a0) (l_e_st_eq_landau_n_rt_example1a a0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) a0).
+
+(* notion 2184 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_e_isp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 x)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) a0 (l_e_st_eq_landau_n_rt_rp_3132_t9 ksi a0 x0 lx y0 uy u m) (l_e_st_eq_landau_n_rt_rp_3132_t10 ksi a0 x0 lx y0 uy u m i) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i)).
+
+(* notion 2185 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_andi (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i)) lx (l_e_st_eq_landau_n_rt_rp_3132_t11 ksi a0 x0 lx y0 uy u m i) : l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i)).
+
+(* notion 2186 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.λp:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i).(l_e_symis l_e_st_eq_landau_n_rt_rat a0 (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) x0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) p)) (l_e_st_eq_landau_n_rt_satz101g (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) x0 a0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) p) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i))) : l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) p).
+
+(* notion 2187 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_andi (l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i)) (Πt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i).l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) t) (l_e_st_eq_landau_n_rt_rp_3132_t12 ksi a0 x0 lx y0 uy u m i) (λt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i).l_e_st_eq_landau_n_rt_rp_3132_t13 ksi a0 x0 lx y0 uy u m i t) : l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i)).
+
+(* notion 2188 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y) (l_e_st_eq_landau_n_rt_rp_3132_u0 ksi a0 x0 lx y0 uy u m i) (l_e_st_eq_landau_n_rt_rp_3132_t14 ksi a0 x0 lx y0 uy u m i) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y)).
+
+(* notion 2189 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λi:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x y)) x0 (l_e_st_eq_landau_n_rt_rp_3132_t15 ksi a0 x0 lx y0 uy u m i) : l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0).
+
+(* notion 2190 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_fr u l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr u l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_satz111d u l_e_st_eq_landau_n_1 o) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2191 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_um10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_3132_t17 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2192 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_satz112g (l_e_st_eq_landau_n_rt_rtofn u) (l_e_st_eq_landau_n_rt_natrti u) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_natrti l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_3132_t17 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o)).
+
+(* notion 2193 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_um1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t18 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_nat).
+
+(* notion 2194 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_v0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2195 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_w0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2196 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_rtofn u) (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_satz101e (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_3132_t17 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_satz94a (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_rt_1rt) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rtofn u)).
+
+(* notion 2197 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_lesse (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rtofn u) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr u l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclassn (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t18 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr u l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_3132_t19 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_lessf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr u l_e_st_eq_landau_n_1)).
+
+(* notion 2198 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_satz111c (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) u (l_e_st_eq_landau_n_rt_rp_3132_t20 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) u).
+
+(* notion 2199 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_imp_th3 (l_e_st_eq_landau_n_lessis u (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) u) (l_e_st_eq_landau_n_satz10h (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) u (l_e_st_eq_landau_n_rt_rp_3132_t21 ksi a0 x0 lx y0 uy u m o)) (λt:l_e_st_eq_landau_n_lessis u (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o).l_e_st_eq_landau_n_satz14 u (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o) t) : l_not (l_e_st_eq_landau_n_lessis u (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o))).
+
+(* notion 2200 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_et (l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) a0))) (l_imp_th3 (l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) a0))) (l_e_st_eq_landau_n_lessis u (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_rp_3132_t22 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t8 ksi a0 x0 lx y0 uy u m (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o))) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) a0))).
+
+(* notion 2201 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_isp1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts x a0))) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_3132_um1 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t23 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_isrtn1 (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t18 ksi a0 x0 lx y0 uy u m o)) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o)).
+
+(* notion 2202 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_andi (l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o)) (l_e_st_eq_landau_n_rt_rp_3132_t24 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t9 ksi a0 x0 lx y0 uy u m) : l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o)).
+
+(* notion 2203 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) a0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt a0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_rt_1rt) a0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) (l_e_st_eq_landau_n_rt_ispl2 a0 (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt a0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) (l_e_st_eq_landau_n_rt_example1d a0)) (l_e_st_eq_landau_n_rt_distpt1 (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_rt_1rt a0) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) l_e_st_eq_landau_n_rt_1rt) (l_e_st_eq_landau_n_rt_rtofn u) a0 (l_e_st_eq_landau_n_rt_satz101e (l_e_st_eq_landau_n_rt_rtofn u) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_3132_t17 ksi a0 x0 lx y0 uy u m o))) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) a0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0)).
+
+(* notion 2204 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) a0) (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) a0)) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_asspl1 x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) a0) (l_e_st_eq_landau_n_rt_ispl2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_3132_um10 ksi a0 x0 lx y0 uy u m o) a0) a0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn u) a0) x0 (l_e_st_eq_landau_n_rt_rp_3132_t26 ksi a0 x0 lx y0 uy u m o)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) a0) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o)).
+
+(* notion 2205 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t28 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.λp:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o).(l_e_symis l_e_st_eq_landau_n_rt_rat a0 (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) p)) (l_e_st_eq_landau_n_rt_satz101g (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) a0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) p) (l_e_st_eq_landau_n_rt_rp_3132_t27 ksi a0 x0 lx y0 uy u m o)) : l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) p).
+
+(* notion 2206 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t29 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_andi (l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o)) (Πt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o).l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) t) (l_e_st_eq_landau_n_rt_rp_3132_t25 ksi a0 x0 lx y0 uy u m o) (λt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o).l_e_st_eq_landau_n_rt_rp_3132_t28 ksi a0 x0 lx y0 uy u m o t) : l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o)).
+
+(* notion 2207 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t30 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) y) (l_e_st_eq_landau_n_rt_rp_3132_w0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t29 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) y)).
+
+(* notion 2208 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t31 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.λo:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x y)) (l_e_st_eq_landau_n_rt_rp_3132_v0 ksi a0 x0 lx y0 uy u m o) (l_e_st_eq_landau_n_rt_rp_3132_t30 ksi a0 x0 lx y0 uy u m o) : l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0).
+
+(* notion 2209 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t32 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λu:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_min (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) a0))) u.(l_orapp (l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0) (l_e_st_eq_landau_n_satz24 u) (λt:l_e_st_eq_landau_n_more u l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_3132_t31 ksi a0 x0 lx y0 uy u m t) (λt:l_e_st_eq_landau_n_is u l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_3132_t16 ksi a0 x0 lx y0 uy u m t) : l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0).
+
+(* notion 2210 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t34 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_someapp l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn y) a0))) x) (l_e_st_eq_landau_n_satz27 (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn y) a0))) (l_e_st_eq_landau_n_rt_rp_3132_t7 ksi a0 x0 lx y0 uy)) (l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0) (λx:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_min (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn y) a0))) x.l_e_st_eq_landau_n_rt_rp_3132_t32 ksi a0 x0 lx y0 uy x t) : l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0).
+
+(* notion 2211 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t35 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_cutapp1b ksi (l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi y.l_e_st_eq_landau_n_rt_rp_3132_t34 ksi a0 x0 lx y t) : l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0).
+
+(* notion 2212 *)
+definition l_e_st_eq_landau_n_rt_rp_satz132 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λa0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_cutapp1a ksi (l_e_st_eq_landau_n_rt_rp_3132_prop4 ksi a0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_3132_t35 ksi a0 x t) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_and (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt ksi y)) (Πt:l_and (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt ksi y).l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x (l_ande1 (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt ksi y) t) y (l_ande2 (l_e_st_eq_landau_n_rt_lrt ksi x) (l_e_st_eq_landau_n_rt_urt ksi y) t))) a0)))).
+
+(* notion 2213 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t36 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_ande1 (l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0) (Πt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0.l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 y0 t) p3 : l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0).
+
+(* notion 2214 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t37 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_r_ande2 (l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0) (Πt:l_e_st_eq_landau_n_rt_rp_3132_prop1 ksi a0 x0 y0.l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 y0 t) p3 : l_e_st_eq_landau_n_rt_rp_3132_prop2 ksi a0 x0 y0 (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3)).
+
+(* notion 2215 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t38 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_ande1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3) : l_e_st_eq_landau_n_rt_lrt ksi x0).
+
+(* notion 2216 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t39 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_ande2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3) : l_e_st_eq_landau_n_rt_urt ksi y0).
+
+(* notion 2217 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t40 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_e_st_eq_landau_n_rt_satz101g y0 x0 (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3))) (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 y0 (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3)) (l_e_st_eq_landau_n_rt_satz101c y0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3))) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3))) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 y0 (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3)))).
+
+(* notion 2218 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t41 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3))) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_3132_t1 ksi a0 x0 y0 (l_e_st_eq_landau_n_rt_rp_3132_t36 ksi p a0 p1 x0 s y0 p3))) a0 (l_e_st_eq_landau_n_rt_rp_3132_t40 ksi p a0 p1 x0 s y0 p3) (l_e_st_eq_landau_n_rt_rp_3132_t37 ksi p a0 p1 x0 s y0 p3) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3))) a0).
+
+(* notion 2219 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t42 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λp3:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y0.(p1 x0 (l_e_st_eq_landau_n_rt_rp_3132_t38 ksi p a0 p1 x0 s y0 p3) y0 (l_e_st_eq_landau_n_rt_rp_3132_t39 ksi p a0 p1 x0 s y0 p3) (l_e_st_eq_landau_n_rt_rp_3132_t41 ksi p a0 p1 x0 s y0 p3) : p).
+
+(* notion 2220 *)
+definition l_e_st_eq_landau_n_rt_rp_3132_t43 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y).(l_someapp l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y) s p (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x0 y.l_e_st_eq_landau_n_rt_rp_3132_t42 ksi p a0 p1 x0 s y t) : p).
+
+(* notion 2221 *)
+definition l_e_st_eq_landau_n_rt_rp_satz132app ≝ λksi:l_e_st_eq_landau_n_rt_cut.λp:Prop.λa0:l_e_st_eq_landau_n_rt_rat.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) a0.p.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x y)) (l_e_st_eq_landau_n_rt_rp_satz132 ksi a0) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_3132_prop3 ksi a0 x y).l_e_st_eq_landau_n_rt_rp_3132_t43 ksi p a0 p1 x t) : p).
+
+(* notion 2222 *)
+definition l_e_st_eq_landau_n_rt_rp_3133_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt ksi u0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) y0.(l_e_tris l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_pl x0 (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu))) (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_satz101d u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) (l_e_st_eq_landau_n_rt_ispl2 (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) y0 x0 i) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
+
+(* notion 2223 *)
+definition l_e_st_eq_landau_n_rt_rp_3133_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt ksi u0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) y0.(l_e_st_eq_landau_n_rt_rp_lrtpl ksi eta u0 x0 lx y0 ly (l_e_st_eq_landau_n_rt_rp_3133_t1 ksi eta y0 ly x0 lx u0 uu i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) u0).
+
+(* notion 2224 *)
+definition l_e_st_eq_landau_n_rt_rp_3133_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt ksi u0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) y0.(l_andi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) u0) (l_e_st_eq_landau_n_rt_urt ksi u0) (l_e_st_eq_landau_n_rt_rp_3133_t2 ksi eta y0 ly x0 lx u0 uu i) uu : l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) u0) (l_e_st_eq_landau_n_rt_urt ksi u0)).
+
+(* notion 2225 *)
+definition l_e_st_eq_landau_n_rt_rp_3133_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt ksi u0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn u0 x0 (l_e_st_eq_landau_n_rt_cutapp2b ksi x0 lx u0 uu)) y0.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi eta) x) (l_e_st_eq_landau_n_rt_urt ksi x)) u0 (l_e_st_eq_landau_n_rt_rp_3133_t3 ksi eta y0 ly x0 lx u0 uu i) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi).
+
+(* notion 2226 *)
+definition l_e_st_eq_landau_n_rt_rp_3133_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_rp_satz132app ksi (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi) y0 (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) y0.l_e_st_eq_landau_n_rt_rp_3133_t4 ksi eta y0 ly x t y u v) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi).
+
+(* notion 2227 *)
+definition l_e_st_eq_landau_n_rt_rp_satz133 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_cutapp1a eta (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_3133_t5 ksi eta x t) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi).
+
+(* notion 2228 *)
+definition l_e_st_eq_landau_n_rt_rp_satz133a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl ksi eta) ksi (l_e_st_eq_landau_n_rt_rp_satz133 ksi eta) : l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_pl ksi eta)).
+
+(* notion 2229 *)
+definition l_e_st_eq_landau_n_rt_rp_3134_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_satz119a eta y0 uy x0 l : l_e_st_eq_landau_n_rt_urt eta x0).
+
+(* notion 2230 *)
+definition l_e_st_eq_landau_n_rt_rp_3134_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_satz83 y0 x0 l : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 2231 *)
+definition l_e_st_eq_landau_n_rt_rp_3134_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_e_tris l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) u0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0) (l_e_st_eq_landau_n_rt_satz101f z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_ispl1 (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0 i) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0)).
+
+(* notion 2232 *)
+definition l_e_st_eq_landau_n_rt_rp_3134_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l))) u0) (l_e_st_eq_landau_n_rt_pl x0 u0) (l_e_st_eq_landau_n_rt_ispl2 z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0) y0 (l_e_st_eq_landau_n_rt_rp_3134_t3 ksi eta zeta m y0 ly uy x0 lx l u0 lu z0 uz i)) (l_e_st_eq_landau_n_rt_asspl2 y0 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) u0) (l_e_st_eq_landau_n_rt_ispl1 (l_e_st_eq_landau_n_rt_pl y0 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l))) x0 u0 (l_e_st_eq_landau_n_rt_satz101c x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l))) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_pl x0 u0)).
+
+(* notion 2233 *)
+definition l_e_st_eq_landau_n_rt_rp_3134_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_rp_lrtpl ksi zeta (l_e_st_eq_landau_n_rt_pl y0 z0) x0 lx u0 lu (l_e_st_eq_landau_n_rt_rp_3134_t4 ksi eta zeta m y0 ly uy x0 lx l u0 lu z0 uz i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 2234 *)
+definition l_e_st_eq_landau_n_rt_rp_3134_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_rp_urtpl eta zeta (l_e_st_eq_landau_n_rt_pl y0 z0) y0 uy z0 uz (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y0 z0)) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 2235 *)
+definition l_e_st_eq_landau_n_rt_rp_3134_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_andi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_rp_3134_t5 ksi eta zeta m y0 ly uy x0 lx l u0 lu z0 uz i) (l_e_st_eq_landau_n_rt_rp_3134_t6 ksi eta zeta m y0 ly uy x0 lx l u0 lu z0 uz i) : l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_pl y0 z0))).
+
+(* notion 2236 *)
+definition l_e_st_eq_landau_n_rt_rp_3134_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt zeta u0.λz0:l_e_st_eq_landau_n_rt_rat.λuz:l_e_st_eq_landau_n_rt_urt zeta z0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn z0 u0 (l_e_st_eq_landau_n_rt_cutapp2b zeta u0 lu z0 uz)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) x) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) x)) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_rp_3134_t7 ksi eta zeta m y0 ly uy x0 lx l u0 lu z0 uz i) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
+
+(* notion 2237 *)
+definition l_e_st_eq_landau_n_rt_rp_3134_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_satz132app zeta (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt zeta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt zeta y.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b zeta x t y u)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta zeta m y0 ly uy x0 lx l)).l_e_st_eq_landau_n_rt_rp_3134_t8 ksi eta zeta m y0 ly uy x0 lx l x t y u v) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
+
+(* notion 2238 *)
+definition l_e_st_eq_landau_n_rt_rp_3134_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.(l_e_st_eq_landau_n_rt_cutapp3 ksi y0 ly (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_less y0 x.l_e_st_eq_landau_n_rt_rp_3134_t9 ksi eta zeta m y0 ly uy x t u) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
+
+(* notion 2239 *)
+definition l_e_st_eq_landau_n_rt_rp_satz134 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_3134_t10 ksi eta zeta m x t u) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
+
+(* notion 2240 *)
+definition l_e_st_eq_landau_n_rt_rp_satz135a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_satz134 ksi eta zeta m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
+
+(* notion 2241 *)
+definition l_e_st_eq_landau_n_rt_rp_satz135b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ispl1 ksi eta zeta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
+
+(* notion 2242 *)
+definition l_e_st_eq_landau_n_rt_rp_satz135c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz134 eta ksi zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
+
+(* notion 2243 *)
+definition l_e_st_eq_landau_n_rt_rp_satz135d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_compl ksi zeta) (l_e_st_eq_landau_n_rt_rp_compl eta zeta) (l_e_st_eq_landau_n_rt_rp_satz135a ksi eta zeta m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta)).
+
+(* notion 2244 *)
+definition l_e_st_eq_landau_n_rt_rp_satz135e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ispl2 ksi eta zeta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta)).
+
+(* notion 2245 *)
+definition l_e_st_eq_landau_n_rt_rp_satz135f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_compl ksi zeta) (l_e_st_eq_landau_n_rt_rp_compl eta zeta) (l_e_st_eq_landau_n_rt_rp_satz135c ksi eta zeta l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta)).
+
+(* notion 2246 *)
+definition l_e_st_eq_landau_n_rt_rp_satz135g ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore2 (l_e_st_eq_landau_n_rt_rp_pl ksi upsilon) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_ispl1 ksi eta upsilon i) (l_e_st_eq_landau_n_rt_rp_satz135d zeta upsilon ksi m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2247 *)
+definition l_e_st_eq_landau_n_rt_rp_satz135h ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl upsilon eta) (l_e_st_eq_landau_n_rt_rp_compl ksi zeta) (l_e_st_eq_landau_n_rt_rp_compl eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz135g ksi eta zeta upsilon i m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl upsilon eta)).
+
+(* notion 2248 *)
+definition l_e_st_eq_landau_n_rt_rp_satz135j ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl ksi upsilon) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_ispl1 ksi eta upsilon i) (l_e_st_eq_landau_n_rt_rp_satz135f zeta upsilon ksi l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2249 *)
+definition l_e_st_eq_landau_n_rt_rp_satz135k ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl upsilon eta) (l_e_st_eq_landau_n_rt_rp_compl ksi zeta) (l_e_st_eq_landau_n_rt_rp_compl eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz135j ksi eta zeta upsilon i l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl upsilon eta)).
+
+(* notion 2250 *)
+definition l_e_st_eq_landau_n_rt_rp_3136_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz123a ksi eta : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2251 *)
+definition l_e_st_eq_landau_n_rt_rp_3136_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) : l_ec3 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta))).
+
+(* notion 2252 *)
+definition l_e_st_eq_landau_n_rt_rp_satz136a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta).(l_ec3_th11 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_3136_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_3136_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz135b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz135a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz135c ksi eta zeta u) m : l_e_st_eq_landau_n_rt_rp_more ksi eta).
+
+(* notion 2253 *)
+definition l_e_st_eq_landau_n_rt_rp_satz136b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta).(l_ec3_th10 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_3136_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_3136_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz135b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz135a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz135c ksi eta zeta u) i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
+
+(* notion 2254 *)
+definition l_e_st_eq_landau_n_rt_rp_satz136c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta).(l_ec3_th12 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_3136_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_3136_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz135b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz135a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz135c ksi eta zeta u) l : l_e_st_eq_landau_n_rt_rp_less ksi eta).
+
+(* notion 2255 *)
+definition l_e_st_eq_landau_n_rt_rp_satz136d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta).(l_e_st_eq_landau_n_rt_rp_satz136a ksi eta zeta (l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_compl zeta ksi) (l_e_st_eq_landau_n_rt_rp_compl zeta eta) m) : l_e_st_eq_landau_n_rt_rp_more ksi eta).
+
+(* notion 2256 *)
+definition l_e_st_eq_landau_n_rt_rp_satz136e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta).(l_e_st_eq_landau_n_rt_rp_satz136b ksi eta zeta (l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_compl ksi zeta) i (l_e_st_eq_landau_n_rt_rp_compl zeta eta)) : l_e_st_eq_landau_n_rt_rp_is ksi eta).
+
+(* notion 2257 *)
+definition l_e_st_eq_landau_n_rt_rp_satz136f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl zeta eta).(l_e_st_eq_landau_n_rt_rp_satz136c ksi eta zeta (l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl zeta ksi) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_compl zeta ksi) (l_e_st_eq_landau_n_rt_rp_compl zeta eta) l) : l_e_st_eq_landau_n_rt_rp_less ksi eta).
+
+(* notion 2258 *)
+definition l_e_st_eq_landau_n_rt_rp_3137_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz134 ksi eta zeta m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta)).
+
+(* notion 2259 *)
+definition l_e_st_eq_landau_n_rt_rp_3137_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl zeta eta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl upsilon eta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_compl zeta eta) (l_e_st_eq_landau_n_rt_rp_compl upsilon eta) (l_e_st_eq_landau_n_rt_rp_satz134 zeta upsilon eta n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2260 *)
+definition l_e_st_eq_landau_n_rt_rp_satz137 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_trmore (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_3137_t1 ksi eta zeta upsilon m n) (l_e_st_eq_landau_n_rt_rp_3137_t2 ksi eta zeta upsilon m n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2261 *)
+definition l_e_st_eq_landau_n_rt_rp_satz137a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz137 eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz122 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2262 *)
+definition l_e_st_eq_landau_n_rt_rp_satz138a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)) m (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz137 ksi eta zeta upsilon t n) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz135g ksi eta zeta upsilon t n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2263 *)
+definition l_e_st_eq_landau_n_rt_rp_satz138b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more zeta upsilon) (l_e_st_eq_landau_n_rt_rp_is zeta upsilon) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)) n (λt:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.l_e_st_eq_landau_n_rt_rp_satz137 ksi eta zeta upsilon m t) (λt:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.l_e_st_eq_landau_n_rt_rp_satz135h zeta upsilon ksi eta t m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2264 *)
+definition l_e_st_eq_landau_n_rt_rp_satz138c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz138a eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz125 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz122 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2265 *)
+definition l_e_st_eq_landau_n_rt_rp_satz138d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz138b eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz125 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2266 *)
+definition l_e_st_eq_landau_n_rt_rp_3139_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_ispl12 ksi eta zeta upsilon i j) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2267 *)
+definition l_e_st_eq_landau_n_rt_rp_3139_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λo:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz138a ksi eta zeta upsilon m o) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2268 *)
+definition l_e_st_eq_landau_n_rt_rp_3139_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_orapp (l_e_st_eq_landau_n_rt_rp_more zeta upsilon) (l_e_st_eq_landau_n_rt_rp_is zeta upsilon) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)) n (λt:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.l_e_st_eq_landau_n_rt_rp_3139_t2 ksi eta zeta upsilon m n i t) (λt:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.l_e_st_eq_landau_n_rt_rp_3139_t1 ksi eta zeta upsilon m n i t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2269 *)
+definition l_e_st_eq_landau_n_rt_rp_3139_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λo:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz138b ksi eta zeta upsilon o n) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2270 *)
+definition l_e_st_eq_landau_n_rt_rp_satz139 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)) m (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_3139_t4 ksi eta zeta upsilon m n t) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_3139_t3 ksi eta zeta upsilon m n t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2271 *)
+definition l_e_st_eq_landau_n_rt_rp_satz139a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz124 (l_e_st_eq_landau_n_rt_rp_pl eta upsilon) (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz139 eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz125 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz125 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_pl ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl eta upsilon)).
+
+(* notion 2272 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λphi:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi.(l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi eta i (l_e_st_eq_landau_n_rt_rp_satz133 eta phi) : l_e_st_eq_landau_n_rt_rp_more ksi eta).
+
+(* notion 2273 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λphi:l_e_st_eq_landau_n_rt_cut.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_satz123d ksi eta l) (λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi.l_e_st_eq_landau_n_rt_rp_3140_t1 ksi eta l phi t) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi).
+
+(* notion 2274 *)
+definition l_e_st_eq_landau_n_rt_rp_vorbemerkung140 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.(l_some_th5 l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi) (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_3140_t2 ksi eta l a) : l_not (l_e_st_eq_landau_n_rt_rp_some (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi))).
+
+(* notion 2275 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more phi psi.(l_e_st_eq_landau_n_rt_rp_satz135d phi psi eta m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)).
+
+(* notion 2276 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more phi psi.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_3140_t3 ksi eta phi psi m) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)).
+
+(* notion 2277 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less phi psi.(l_e_st_eq_landau_n_rt_rp_satz135f phi psi eta l : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)).
+
+(* notion 2278 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less phi psi.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_3140_t5 ksi eta phi psi l) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)).
+
+(* notion 2279 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis phi psi.(l_or3_th1 (l_e_st_eq_landau_n_rt_rp_is phi psi) (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi) (l_e_st_eq_landau_n_rt_rp_satz123a phi psi) n : l_or (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi)).
+
+(* notion 2280 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis phi psi.(l_orapp (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi) (l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_st_eq_landau_n_rt_rp_3140_t7 ksi eta phi psi n) (λt:l_e_st_eq_landau_n_rt_rp_more phi psi.l_e_st_eq_landau_n_rt_rp_3140_t4 ksi eta phi psi t) (λt:l_e_st_eq_landau_n_rt_rp_less phi psi.l_e_st_eq_landau_n_rt_rp_3140_t6 ksi eta phi psi t) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)).
+
+(* notion 2281 *)
+definition l_e_st_eq_landau_n_rt_rp_satz140b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta psi) ksi.(l_imp_th7 (l_e_st_eq_landau_n_rt_rp_is phi psi) (l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_weli (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi)) (l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl eta phi) (l_e_st_eq_landau_n_rt_rp_pl eta psi) ksi i j)) (λt:l_e_st_eq_landau_n_rt_rp_nis phi psi.l_e_st_eq_landau_n_rt_rp_3140_t8 ksi eta phi psi t) : l_e_st_eq_landau_n_rt_rp_is phi psi).
+
+(* notion 2282 *)
+definition l_e_st_eq_landau_n_rt_rp_diffprop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_more x0 y0) (Πt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 t)) : Prop).
+
+(* notion 2283 *)
+definition l_e_st_eq_landau_n_rt_rp_diffprop2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta y0) (l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0) : Prop).
+
+(* notion 2284 *)
+definition l_e_st_eq_landau_n_rt_rp_diffprop ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x y)) : Prop).
+
+(* notion 2285 *)
+definition l_e_st_eq_landau_n_rt_rp_diff ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (λz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop ksi eta z) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2286 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t11a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).λm1:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_tris l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m) (l_e_st_eq_landau_n_rt_mn x0 y0 m1) i (l_e_st_eq_landau_n_rt_satz101g x0 y0 (l_e_st_eq_landau_n_rt_mn x0 y0 m) m1 (l_e_st_eq_landau_n_rt_satz101c x0 y0 m)) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m1)).
+
+(* notion 2287 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).(l_andi (l_e_st_eq_landau_n_rt_more x0 y0) (Πt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 t)) m (λt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_rp_iii3_t11a ksi eta z0 x0 lx y0 uy m i t) : l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0).
+
+(* notion 2288 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).(l_and3i (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta y0) (l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0) lx uy (l_e_st_eq_landau_n_rt_rp_iii3_t12 ksi eta z0 x0 lx y0 uy m i) : l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0).
+
+(* notion 2289 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y) y0 (l_e_st_eq_landau_n_rt_rp_iii3_t13 ksi eta z0 x0 lx y0 uy m i) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y)).
+
+(* notion 2290 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x y)) x0 (l_e_st_eq_landau_n_rt_rp_iii3_t14 ksi eta z0 x0 lx y0 uy m i) : l_e_st_eq_landau_n_rt_rp_diffprop ksi eta z0).
+
+(* notion 2291 *)
+definition l_e_st_eq_landau_n_rt_rp_diff1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λm:l_e_st_eq_landau_n_rt_more x0 y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 m).(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop ksi eta z) z0 (l_e_st_eq_landau_n_rt_rp_iii3_t15 ksi eta z0 x0 lx y0 uy m i) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
+
+(* notion 2292 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop ksi eta z) z0 i : l_e_st_eq_landau_n_rt_rp_diffprop ksi eta z0).
+
+(* notion 2293 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(l_and3e1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta y0) (l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0) py : l_e_st_eq_landau_n_rt_lrt ksi x0).
+
+(* notion 2294 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(l_and3e2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta y0) (l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0) py : l_e_st_eq_landau_n_rt_urt eta y0).
+
+(* notion 2295 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(l_and3e3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_urt eta y0) (l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0) py : l_e_st_eq_landau_n_rt_rp_diffprop1 ksi eta z0 x0 y0).
+
+(* notion 2296 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(l_ande1 (l_e_st_eq_landau_n_rt_more x0 y0) (Πt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 t)) (l_e_st_eq_landau_n_rt_rp_iii3_t19 ksi eta z0 i p p1 x0 px y0 py) : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 2297 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(l_r_ande2 (l_e_st_eq_landau_n_rt_more x0 y0) (Πt:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 t)) (l_e_st_eq_landau_n_rt_rp_iii3_t19 ksi eta z0 i p p1 x0 px y0 py) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_iii3_t20 ksi eta z0 i p p1 x0 px y0 py))).
+
+(* notion 2298 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y0.(p1 x0 (l_e_st_eq_landau_n_rt_rp_iii3_t17 ksi eta z0 i p p1 x0 px y0 py) y0 (l_e_st_eq_landau_n_rt_rp_iii3_t18 ksi eta z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_iii3_t20 ksi eta z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_iii3_t21 ksi eta z0 i p p1 x0 px y0 py) : p).
+
+(* notion 2299 *)
+definition l_e_st_eq_landau_n_rt_rp_iii3_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y).(l_someapp l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y) px p (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x0 y.l_e_st_eq_landau_n_rt_rp_iii3_t22 ksi eta z0 i p p1 x0 px y t) : p).
+
+(* notion 2300 *)
+definition l_e_st_eq_landau_n_rt_rp_diffapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt eta y.Πv:l_e_st_eq_landau_n_rt_more x y.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).p.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x y)) (l_e_st_eq_landau_n_rt_rp_iii3_t16 ksi eta z0 i p p1) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_diffprop2 ksi eta z0 x y).l_e_st_eq_landau_n_rt_rp_iii3_t23 ksi eta z0 i p p1 x t) : p).
+
+(* notion 2301 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_3134_t2 ksi eta eta m y0 ly uy x0 lx l : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 2302 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_diff1 ksi eta (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t9 ksi eta m y0 ly uy x0 lx l)) x0 lx y0 uy (l_e_st_eq_landau_n_rt_rp_3140_t9 ksi eta m y0 ly uy x0 lx l) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t9 ksi eta m y0 ly uy x0 lx l))) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t9 ksi eta m y0 ly uy x0 lx l)) (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
+
+(* notion 2303 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_mn x0 y0 n) z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0) x0 (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n) j) (l_e_st_eq_landau_n_rt_satz101e x0 y0 n) (l_e_st_eq_landau_n_rt_satz94a (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0) : l_e_st_eq_landau_n_rt_less z0 x0).
+
+(* notion 2304 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_trless z0 x0 x1 (l_e_st_eq_landau_n_rt_rp_3140_t11 ksi eta m x1 ux z0 i x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx x1 ux) : l_e_st_eq_landau_n_rt_less z0 x1).
+
+(* notion 2305 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_ec3e31 (l_e_st_eq_landau_n_rt_is z0 x1) (l_e_st_eq_landau_n_rt_more z0 x1) (l_e_st_eq_landau_n_rt_less z0 x1) (l_e_st_eq_landau_n_rt_satz81b z0 x1) (l_e_st_eq_landau_n_rt_rp_3140_t12 ksi eta m x1 ux z0 i x0 lx y0 uy n j) : l_e_st_eq_landau_n_rt_nis z0 x1).
+
+(* notion 2306 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).(l_e_st_eq_landau_n_rt_rp_diffapp ksi eta z0 i (l_e_st_eq_landau_n_rt_nis z0 x1) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt eta y.λv:l_e_st_eq_landau_n_rt_more x y.λw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).l_e_st_eq_landau_n_rt_rp_3140_t13 ksi eta m x1 ux z0 i x t y u v w) : l_e_st_eq_landau_n_rt_nis z0 x1).
+
+(* notion 2307 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.(l_imp_th3 (l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_nis x1 x1) (l_weli (l_e_st_eq_landau_n_rt_is x1 x1) (l_e_refis l_e_st_eq_landau_n_rt_rat x1)) (λt:l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).l_e_st_eq_landau_n_rt_rp_3140_t14 ksi eta m x1 ux x1 t) : l_not (l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_rp_diff ksi eta))).
+
+(* notion 2308 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl z0 y0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0) x0 (l_e_st_eq_landau_n_rt_ispl1 z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0 j) (l_e_st_eq_landau_n_rt_satz101e x0 y0 n) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl z0 y0) x0).
+
+(* notion 2309 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_x2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_pl u0 y0 : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2310 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_pl z0 y0) x0 (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_rp_3140_t16 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_satz96c u0 z0 y0 l) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) x0).
+
+(* notion 2311 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_rp_satz120 ksi x0 lx (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_rp_3140_t17 ksi eta m z0 i u0 l x0 lx y0 uy n j) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j)).
+
+(* notion 2312 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_ismore1 (l_e_st_eq_landau_n_rt_pl y0 u0) (l_e_st_eq_landau_n_rt_pl u0 y0) y0 (l_e_st_eq_landau_n_rt_compl y0 u0) (l_e_st_eq_landau_n_rt_satz94 y0 u0) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) y0).
+
+(* notion 2313 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_satz101g (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) y0 u0 (l_e_st_eq_landau_n_rt_rp_3140_t19 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_compl y0 u0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) y0 (l_e_st_eq_landau_n_rt_rp_3140_t19 ksi eta m z0 i u0 l x0 lx y0 uy n j))).
+
+(* notion 2314 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_rp_diff1 ksi eta u0 (l_e_st_eq_landau_n_rt_rp_3140_x2 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_rp_3140_t18 ksi eta m z0 i u0 l x0 lx y0 uy n j) y0 uy (l_e_st_eq_landau_n_rt_rp_3140_t19 ksi eta m z0 i u0 l x0 lx y0 uy n j) (l_e_st_eq_landau_n_rt_rp_3140_t20 ksi eta m z0 i u0 l x0 lx y0 uy n j) : l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
+
+(* notion 2315 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.(l_e_st_eq_landau_n_rt_rp_diffapp ksi eta z0 i (l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt eta y.λv:l_e_st_eq_landau_n_rt_more x y.λw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).l_e_st_eq_landau_n_rt_rp_3140_t21 ksi eta m z0 i u0 l x t y u v w) : l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
+
+(* notion 2316 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_satz83 x0 x3 l : l_e_st_eq_landau_n_rt_more x3 x0).
+
+(* notion 2317 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_trmore x3 x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t23 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) n : l_e_st_eq_landau_n_rt_more x3 y0).
+
+(* notion 2318 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_ismore12 x3 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) y0) x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0) (l_e_st_eq_landau_n_rt_satz101f x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_satz101f x0 y0 n) (l_e_st_eq_landau_n_rt_rp_3140_t23 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) y0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0)).
+
+(* notion 2319 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_satz97a (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_mn x0 y0 n) y0 (l_e_st_eq_landau_n_rt_rp_3140_t25 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_mn x0 y0 n)).
+
+(* notion 2320 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_ismore2 (l_e_st_eq_landau_n_rt_mn x0 y0 n) z0 (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n) j) (l_e_st_eq_landau_n_rt_rp_3140_t26 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) z0).
+
+(* notion 2321 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t28 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_e_st_eq_landau_n_rt_rp_diff1 ksi eta (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) x3 lx3 y0 uy (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l))) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
+
+(* notion 2322 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t29 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_andi (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) z0) (l_e_st_eq_landau_n_rt_rp_3140_t28 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) (l_e_st_eq_landau_n_rt_rp_3140_t27 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) : l_and (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) z0)).
+
+(* notion 2323 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t30 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).λx3:l_e_st_eq_landau_n_rt_rat.λlx3:l_e_st_eq_landau_n_rt_lrt ksi x3.λl:l_e_st_eq_landau_n_rt_less x0 x3.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0)) (l_e_st_eq_landau_n_rt_mn x3 y0 (l_e_st_eq_landau_n_rt_rp_3140_t24 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l)) (l_e_st_eq_landau_n_rt_rp_3140_t29 ksi eta m z0 i x0 lx y0 uy n j x3 lx3 l) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0))).
+
+(* notion 2324 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t31 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λn:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x0 y0 n).(l_e_st_eq_landau_n_rt_cutapp3 ksi x0 lx (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0))) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi y.λu:l_e_st_eq_landau_n_rt_less x0 y.l_e_st_eq_landau_n_rt_rp_3140_t30 ksi eta m z0 i x0 lx y0 uy n j y t u) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0))).
+
+(* notion 2325 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t32 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_diff ksi eta).(l_e_st_eq_landau_n_rt_rp_diffapp ksi eta z0 i (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt eta y.λv:l_e_st_eq_landau_n_rt_more x y.λw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_mn x y v).l_e_st_eq_landau_n_rt_rp_3140_t31 ksi eta m z0 i x t y u v w) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (l_e_st_eq_landau_n_rt_more x z0))).
+
+(* notion 2326 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t33 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_diff ksi eta) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t9 ksi eta m y0 ly uy x0 lx l)) (l_e_st_eq_landau_n_rt_rp_3140_t10 ksi eta m y0 ly uy x0 lx l) x1 (l_e_st_eq_landau_n_rt_rp_3140_t15 ksi eta m x1 ux1) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_3140_t22 ksi eta m x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_diff ksi eta).l_e_st_eq_landau_n_rt_rp_3140_t32 ksi eta m x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
+
+(* notion 2327 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t34 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_cutapp1b ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.l_e_st_eq_landau_n_rt_rp_3140_t33 ksi eta m y0 ly uy x0 lx l x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
+
+(* notion 2328 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t35 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.(l_e_st_eq_landau_n_rt_cutapp3 ksi y0 ly (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_less y0 x.l_e_st_eq_landau_n_rt_rp_3140_t34 ksi eta m y0 ly uy x t u) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
+
+(* notion 2329 *)
+definition l_e_st_eq_landau_n_rt_rp_satz140h ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt ksi x.λv:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_3140_t35 ksi eta m x u v) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_diff ksi eta)).
+
+(* notion 2330 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_chi ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_diff ksi eta) (l_e_st_eq_landau_n_rt_rp_satz140h ksi eta m) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2331 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t36 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_st_eq_landau_n_rt_cutapp2b eta y1 ly y0 uy : l_e_st_eq_landau_n_rt_more y0 y1).
+
+(* notion 2332 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t37 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) (l_e_st_eq_landau_n_rt_pl y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j)))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y0) x0 (l_e_st_eq_landau_n_rt_asspl1 (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) (l_e_st_eq_landau_n_rt_ispl2 (l_e_st_eq_landau_n_rt_pl y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) y0 (l_e_st_eq_landau_n_rt_mn x0 y0 o) (l_e_st_eq_landau_n_rt_satz101c y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) (l_e_st_eq_landau_n_rt_satz101e x0 y0 o) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) x0).
+
+(* notion 2333 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t38 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_rp_3140_t37 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j) (l_e_st_eq_landau_n_rt_satz94a (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t36 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j))) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) x0).
+
+(* notion 2334 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t39 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_tr3is l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl y1 u0) (l_e_st_eq_landau_n_rt_pl u0 y1) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) i (l_e_st_eq_landau_n_rt_compl y1 u0) (l_e_st_eq_landau_n_rt_ispl1 u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1 j) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1)).
+
+(* notion 2335 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t40 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) z0 x0 (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 o) y1) (l_e_st_eq_landau_n_rt_rp_3140_t39 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j)) (l_e_st_eq_landau_n_rt_rp_3140_t38 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j) : l_e_st_eq_landau_n_rt_less z0 x0).
+
+(* notion 2336 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t41 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λo:l_e_st_eq_landau_n_rt_more x0 y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x0 y0 o).(l_e_st_eq_landau_n_rt_rp_satz120 ksi x0 lx z0 (l_e_st_eq_landau_n_rt_rp_3140_t40 ksi eta m z0 lz y1 ly u0 lu i x0 lx y0 uy o j) : l_e_st_eq_landau_n_rt_lrt ksi z0).
+
+(* notion 2337 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t42 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.λy1:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y1.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl y1 u0).(l_e_st_eq_landau_n_rt_rp_diffapp ksi eta u0 (l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_diff ksi eta) (l_e_st_eq_landau_n_rt_rp_satz140h ksi eta m) u0 lu) (l_e_st_eq_landau_n_rt_lrt ksi z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt eta y.λv:l_e_st_eq_landau_n_rt_more x y.λw:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_mn x y v).l_e_st_eq_landau_n_rt_rp_3140_t41 ksi eta m z0 lz y1 ly u0 lu i x t y u v w) : l_e_st_eq_landau_n_rt_lrt ksi z0).
+
+(* notion 2338 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) z0.(l_e_st_eq_landau_n_rt_rp_plapp eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) z0 lz (l_e_st_eq_landau_n_rt_lrt ksi z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_3140_t42 ksi eta m z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt ksi z0).
+
+(* notion 2339 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t43 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_satz83 y0 x0 l : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 2340 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t44 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.(l_e_st_eq_landau_n_rt_cutapp2b eta y1 ly1 y2 uy2 : l_e_st_eq_landau_n_rt_more y2 y1).
+
+(* notion 2341 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t45 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_cutapp2b eta y1 ly1 y0 uy : l_e_st_eq_landau_n_rt_more y0 y1).
+
+(* notion 2342 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t46 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_tris l_e_st_eq_landau_n_rt_rat y2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) y1) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1) (l_e_st_eq_landau_n_rt_satz101f y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_ispl1 (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1 i) : l_e_st_eq_landau_n_rt_is y2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1)).
+
+(* notion 2343 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t47 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_tr4is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y2 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) (l_e_st_eq_landau_n_rt_pl y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y0) x0 (l_e_st_eq_landau_n_rt_ispl1 y2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1) (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_rp_3140_t46 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_asspl1 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) (l_e_st_eq_landau_n_rt_ispl2 (l_e_st_eq_landau_n_rt_pl y1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) y0 (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) (l_e_st_eq_landau_n_rt_satz101c y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) (l_e_st_eq_landau_n_rt_satz101e x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl y2 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) x0).
+
+(* notion 2344 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t48 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_ismore1 (l_e_st_eq_landau_n_rt_pl y2 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t47 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) (l_e_st_eq_landau_n_rt_satz94 y2 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) : l_e_st_eq_landau_n_rt_more x0 y2).
+
+(* notion 2345 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t49 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_satz101g x0 y2 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) (l_e_st_eq_landau_n_rt_rp_3140_t47 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))).
+
+(* notion 2346 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t50 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_tris l_e_st_eq_landau_n_rt_rat y0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1) (l_e_st_eq_landau_n_rt_satz101f y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_ispl1 (l_e_st_eq_landau_n_rt_mn y0 y1 (l_e_st_eq_landau_n_rt_rp_3140_t45 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1 (l_e_st_eq_landau_n_rt_rp_3140_t49 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) : l_e_st_eq_landau_n_rt_is y0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1)).
+
+(* notion 2347 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t51 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_diff ksi eta) (l_e_st_eq_landau_n_rt_rp_satz140h ksi eta m) (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_rp_diff1 ksi eta (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) x0 lx y2 uy2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)))) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))).
+
+(* notion 2348 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t52 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt eta y1.λy2:l_e_st_eq_landau_n_rt_rat.λuy2:l_e_st_eq_landau_n_rt_urt eta y2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y2 y1 (l_e_st_eq_landau_n_rt_rp_3140_t44 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).(l_e_st_eq_landau_n_rt_rp_lrtpl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) y0 y1 ly1 (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) (l_e_st_eq_landau_n_rt_rp_3140_t51 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) (l_e_tris l_e_st_eq_landau_n_rt_rat y0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1) (l_e_st_eq_landau_n_rt_pl y1 (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i))) (l_e_st_eq_landau_n_rt_rp_3140_t50 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i) (l_e_st_eq_landau_n_rt_compl (l_e_st_eq_landau_n_rt_mn x0 y2 (l_e_st_eq_landau_n_rt_rp_3140_t48 ksi eta m y0 ly uy x0 lx l y1 ly1 y2 uy2 i)) y1)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
+
+(* notion 2349 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t53 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_satz132app eta (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt eta y.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b eta x t y u)) (l_e_st_eq_landau_n_rt_mn x0 y0 (l_e_st_eq_landau_n_rt_rp_3140_t43 ksi eta m y0 ly uy x0 lx l)).l_e_st_eq_landau_n_rt_rp_3140_t52 ksi eta m y0 ly uy x0 lx l x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
+
+(* notion 2350 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t54 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λuy:l_e_st_eq_landau_n_rt_urt eta y0.(l_e_st_eq_landau_n_rt_cutapp3 ksi y0 ly (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_less y0 x.l_e_st_eq_landau_n_rt_rp_3140_t53 ksi eta m y0 ly uy x t u) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
+
+(* notion 2351 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t55 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λly0:l_e_st_eq_landau_n_rt_lrt eta y0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt ksi y1.λuy1:l_e_st_eq_landau_n_rt_urt eta y1.(l_e_st_eq_landau_n_rt_rp_3140_t54 ksi eta m y1 ly1 uy1 : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y1).
+
+(* notion 2352 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t56 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λly0:l_e_st_eq_landau_n_rt_lrt eta y0.λy1:l_e_st_eq_landau_n_rt_rat.λly1:l_e_st_eq_landau_n_rt_lrt ksi y1.λuy1:l_e_st_eq_landau_n_rt_urt eta y1.(l_e_st_eq_landau_n_rt_rp_satz120 (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y1 (l_e_st_eq_landau_n_rt_rp_3140_t55 ksi eta m y0 ly ly0 y1 ly1 uy1) y0 (l_e_st_eq_landau_n_rt_cutapp2a eta y0 ly0 y1 uy1) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
+
+(* notion 2353 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t57 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.λly0:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_rp_moreapp ksi eta m (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_urt eta x.l_e_st_eq_landau_n_rt_rp_3140_t56 ksi eta m y0 ly ly0 x t u) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
+
+(* notion 2354 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.(l_imp_th1 (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0) (λt:l_e_st_eq_landau_n_rt_lrt eta y0.l_e_st_eq_landau_n_rt_rp_3140_t57 ksi eta m y0 ly t) (λt:l_e_st_eq_landau_n_rt_urt eta y0.l_e_st_eq_landau_n_rt_rp_3140_t54 ksi eta m y0 ly t) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) y0).
+
+(* notion 2355 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t58 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) ksi (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) x.l_e_st_eq_landau_n_rt_rp_3140_a ksi eta m x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_3140_b ksi eta m x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m)) ksi).
+
+(* notion 2356 *)
+definition l_e_st_eq_landau_n_rt_rp_satz140a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_somei l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi) (l_e_st_eq_landau_n_rt_rp_3140_chi ksi eta m) (l_e_st_eq_landau_n_rt_rp_3140_t58 ksi eta m) : l_e_st_eq_landau_n_rt_rp_some (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi)).
+
+(* notion 2357 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t59 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(λc:l_e_st_eq_landau_n_rt_cut.λd:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta c) ksi.λu:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta d) ksi.l_e_st_eq_landau_n_rt_rp_satz140b ksi eta c d t u : l_e_amone l_e_st_eq_landau_n_rt_cut (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta c) ksi)).
+
+(* notion 2358 *)
+definition l_e_st_eq_landau_n_rt_rp_satz140 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_onei l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi) (l_e_st_eq_landau_n_rt_rp_3140_t59 ksi eta) (l_e_st_eq_landau_n_rt_rp_satz140a ksi eta m) : l_e_st_eq_landau_n_rt_rp_one (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi)).
+
+(* notion 2359 *)
+definition l_e_st_eq_landau_n_rt_rp_mn ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_ind l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi) (l_e_st_eq_landau_n_rt_rp_satz140 ksi eta m) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2360 *)
+definition l_e_st_eq_landau_n_rt_rp_satz140c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_oneax l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta a) ksi) (l_e_st_eq_landau_n_rt_rp_satz140 ksi eta m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_mn ksi eta m)) ksi).
+
+(* notion 2361 *)
+definition l_e_st_eq_landau_n_rt_rp_satz140d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_mn ksi eta m)) ksi (l_e_st_eq_landau_n_rt_rp_satz140c ksi eta m) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_mn ksi eta m))).
+
+(* notion 2362 *)
+definition l_e_st_eq_landau_n_rt_rp_satz140e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) eta) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_mn ksi eta m)) ksi (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) eta) (l_e_st_eq_landau_n_rt_rp_satz140c ksi eta m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) eta) ksi).
+
+(* notion 2363 *)
+definition l_e_st_eq_landau_n_rt_rp_satz140f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) eta) ksi (l_e_st_eq_landau_n_rt_rp_satz140e ksi eta m) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) eta)).
+
+(* notion 2364 *)
+definition l_e_st_eq_landau_n_rt_rp_satz140g ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta phi) ksi.(l_e_st_eq_landau_n_rt_rp_satz140b ksi eta phi (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) i (l_e_st_eq_landau_n_rt_rp_satz140c ksi eta m) : l_e_st_eq_landau_n_rt_rp_is phi (l_e_st_eq_landau_n_rt_rp_mn ksi eta m)).
+
+(* notion 2365 *)
+definition l_e_st_eq_landau_n_rt_rp_3140_t60 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi zeta.λn:l_e_st_eq_landau_n_rt_rp_more eta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl upsilon (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m)) (l_e_st_eq_landau_n_rt_rp_pl zeta (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m)) ksi eta (l_e_st_eq_landau_n_rt_rp_ispl1 upsilon zeta (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m) (l_e_symis l_e_st_eq_landau_n_rt_cut zeta upsilon j)) (l_e_st_eq_landau_n_rt_rp_satz140c ksi zeta m) i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl upsilon (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m)) eta).
+
+(* notion 2366 *)
+definition l_e_st_eq_landau_n_rt_rp_ismn12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi zeta.λn:l_e_st_eq_landau_n_rt_rp_more eta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz140g eta upsilon (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m) n (l_e_st_eq_landau_n_rt_rp_3140_t60 ksi eta zeta upsilon m n i j) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m) (l_e_st_eq_landau_n_rt_rp_mn eta upsilon n)).
+
+(* notion 2367 *)
+definition l_e_st_eq_landau_n_rt_rp_ismn1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi zeta.λn:l_e_st_eq_landau_n_rt_rp_more eta zeta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ismn12 ksi eta zeta zeta m n i (l_e_refis l_e_st_eq_landau_n_rt_cut zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn ksi zeta m) (l_e_st_eq_landau_n_rt_rp_mn eta zeta n)).
+
+(* notion 2368 *)
+definition l_e_st_eq_landau_n_rt_rp_ismn2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more zeta ksi.λn:l_e_st_eq_landau_n_rt_rp_more zeta eta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ismn12 zeta zeta ksi eta m n (l_e_refis l_e_st_eq_landau_n_rt_cut zeta) i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn zeta ksi m) (l_e_st_eq_landau_n_rt_rp_mn zeta eta n)).
+
+(* notion 2369 *)
+definition l_e_st_eq_landau_n_rt_rp_prodprop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)) : Prop).
+
+(* notion 2370 *)
+definition l_e_st_eq_landau_n_rt_rp_prodprop ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x y)) : Prop).
+
+(* notion 2371 *)
+definition l_e_st_eq_landau_n_rt_rp_prod ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (λz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop ksi eta z) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2372 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_and3i (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)) lx ly i : l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y0).
+
+(* notion 2373 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y) y0 (l_e_st_eq_landau_n_rt_rp_iii4_t1 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y)).
+
+(* notion 2374 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x y)) x0 (l_e_st_eq_landau_n_rt_rp_iii4_t2 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_rp_prodprop ksi eta z0).
+
+(* notion 2375 *)
+definition l_e_st_eq_landau_n_rt_rp_prod1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop ksi eta z) z0 (l_e_st_eq_landau_n_rt_rp_iii4_t3 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
+
+(* notion 2376 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop ksi eta z) z0 i : l_e_st_eq_landau_n_rt_rp_prodprop ksi eta z0).
+
+(* notion 2377 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y0.(l_and3e1 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)) py : l_e_st_eq_landau_n_rt_lrt ksi x0).
+
+(* notion 2378 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y0.(l_and3e2 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)) py : l_e_st_eq_landau_n_rt_lrt eta y0).
+
+(* notion 2379 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y0.(l_and3e3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_lrt eta y0) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)) py : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 2380 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y).λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y0.(p1 x0 (l_e_st_eq_landau_n_rt_rp_iii4_t5 ksi eta z0 i p p1 x0 px y0 py) y0 (l_e_st_eq_landau_n_rt_rp_iii4_t6 ksi eta z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_iii4_t7 ksi eta z0 i p p1 x0 px y0 py) : p).
+
+(* notion 2381 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y).(l_someapp l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y) px p (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x0 y.l_e_st_eq_landau_n_rt_rp_iii4_t8 ksi eta z0 i p p1 x0 px y t) : p).
+
+(* notion 2382 *)
+definition l_e_st_eq_landau_n_rt_rp_prodapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x y)) (l_e_st_eq_landau_n_rt_rp_iii4_t4 ksi eta z0 i p p1) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_prodprop1 ksi eta z0 x y).l_e_st_eq_landau_n_rt_rp_iii4_t9 ksi eta z0 i p p1 x t) : p).
+
+(* notion 2383 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx x1 ux : l_e_st_eq_landau_n_rt_less x0 x1).
+
+(* notion 2384 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_cutapp2a eta y0 ly y1 uy : l_e_st_eq_landau_n_rt_less y0 y1).
+
+(* notion 2385 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 y0) j) (l_e_st_eq_landau_n_rt_satz107a x0 x1 y0 y1 (l_e_st_eq_landau_n_rt_rp_4141_t1 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_rp_4141_t2 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j)) : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_ts x1 y1)).
+
+(* notion 2386 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_ec3e31 (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_e_st_eq_landau_n_rt_more z0 (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_e_st_eq_landau_n_rt_satz81b z0 (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_e_st_eq_landau_n_rt_rp_4141_t3 ksi eta x1 ux y1 uy z0 i x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_ts x1 y1)).
+
+(* notion 2387 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).(l_e_st_eq_landau_n_rt_rp_prodapp ksi eta z0 i (l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_ts x1 y1)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4141_t4 ksi eta x1 ux y1 uy z0 i x t y u v) : l_e_st_eq_landau_n_rt_nis z0 (l_e_st_eq_landau_n_rt_ts x1 y1)).
+
+(* notion 2388 *)
+definition l_e_st_eq_landau_n_rt_rp_satz141a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.(l_imp_th3 (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_nis (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_weli (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_ts x1 y1)) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x1 y1))) (λt:l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_rp_prod ksi eta).l_e_st_eq_landau_n_rt_rp_4141_t5 ksi eta x1 ux y1 uy (l_e_st_eq_landau_n_rt_ts x1 y1) t) : l_not (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_rp_prod ksi eta))).
+
+(* notion 2389 *)
+definition l_e_st_eq_landau_n_rt_4141_v0 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0) x0 : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2390 *)
+definition l_e_st_eq_landau_n_rt_4141_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_4141_v0 x0 y0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0)) x0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) x0 (l_e_st_eq_landau_n_rt_assts2 y0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0) x0) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0)) l_e_st_eq_landau_n_rt_1rt x0 (l_e_st_eq_landau_n_rt_satz110c l_e_st_eq_landau_n_rt_1rt y0)) (l_e_st_eq_landau_n_rt_example1c x0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_4141_v0 x0 y0)) x0).
+
+(* notion 2391 *)
+definition l_e_st_eq_landau_n_rt_satz141b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz110g x0 y0 (l_e_st_eq_landau_n_rt_4141_v0 x0 y0) (l_e_st_eq_landau_n_rt_4141_t6 x0 y0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0) x0) (l_e_st_eq_landau_n_rt_ov x0 y0)).
+
+(* notion 2392 *)
+definition l_e_st_eq_landau_n_rt_satz141c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0) x0) (l_e_st_eq_landau_n_rt_ov x0 y0) (l_e_st_eq_landau_n_rt_satz141b x0 y0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov x0 y0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt y0) x0)).
+
+(* notion 2393 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_isless2 u0 (l_e_st_eq_landau_n_rt_ts x0 y0) z0 j l : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 2394 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ts x0 y0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) y0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt y0) y0 (l_e_st_eq_landau_n_rt_assts2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0 y0) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) l_e_st_eq_landau_n_rt_1rt y0 (l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_example1c y0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ts x0 y0)) y0).
+
+(* notion 2395 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) z0) (l_e_st_eq_landau_n_rt_ov z0 x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ts x0 y0)) y0 (l_e_st_eq_landau_n_rt_satz141b z0 x0) (l_e_st_eq_landau_n_rt_rp_4141_t8 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_satz105f z0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_rp_4141_t7 ksi eta u0 i z0 l x0 lx y0 ly j)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ov z0 x0) y0).
+
+(* notion 2396 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_satz120 eta y0 ly (l_e_st_eq_landau_n_rt_ov z0 x0) (l_e_st_eq_landau_n_rt_rp_4141_t9 ksi eta u0 i z0 l x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_lrt eta (l_e_st_eq_landau_n_rt_ov z0 x0)).
+
+(* notion 2397 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_prod1 ksi eta z0 x0 lx (l_e_st_eq_landau_n_rt_ov z0 x0) (l_e_st_eq_landau_n_rt_rp_4141_t10 ksi eta u0 i z0 l x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_satz110d z0 x0) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
+
+(* notion 2398 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λz0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less z0 u0.(l_e_st_eq_landau_n_rt_rp_prodapp ksi eta u0 i (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4141_t11 ksi eta u0 i z0 l x t y u v) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
+
+(* notion 2399 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_rp_prod1 ksi eta (l_e_st_eq_landau_n_rt_ts x1 y0) x1 lx1 y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x1 y0)) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
+
+(* notion 2400 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_satz105a x1 x0 y0 (l_e_st_eq_landau_n_rt_satz83 x0 x1 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 2401 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_ismore2 (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 y0) j) (l_e_st_eq_landau_n_rt_rp_4141_t14 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x1 y0) z0).
+
+(* notion 2402 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_andi (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x1 y0) z0) (l_e_st_eq_landau_n_rt_rp_4141_t13 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) (l_e_st_eq_landau_n_rt_rp_4141_t15 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_and (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts x1 y0) z0)).
+
+(* notion 2403 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0)) (l_e_st_eq_landau_n_rt_ts x1 y0) (l_e_st_eq_landau_n_rt_rp_4141_t16 ksi eta z0 i x0 lx y0 ly j x1 lx1 l) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
+
+(* notion 2404 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_cutapp3 ksi x0 lx (l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λu:l_e_st_eq_landau_n_rt_less x0 x.l_e_st_eq_landau_n_rt_rp_4141_t17 ksi eta z0 i x0 lx y0 ly j x t u) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
+
+(* notion 2405 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta).(l_e_st_eq_landau_n_rt_rp_prodapp ksi eta z0 i (l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4141_t18 ksi eta z0 i x t y u v) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_more y z0))).
+
+(* notion 2406 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λy1:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y1.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_prod ksi eta) (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_rp_prod1 ksi eta (l_e_st_eq_landau_n_rt_ts x0 y0) x0 lx y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 y0))) (l_e_st_eq_landau_n_rt_ts x1 y1) (l_e_st_eq_landau_n_rt_rp_satz141a ksi eta x1 ux y1 uy) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_prod ksi eta).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_4141_t12 ksi eta x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_prod ksi eta).l_e_st_eq_landau_n_rt_rp_4141_t19 ksi eta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
+
+(* notion 2407 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.(l_e_st_eq_landau_n_rt_cutapp1b eta (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt eta y.l_e_st_eq_landau_n_rt_rp_4141_t20 ksi eta x0 lx y0 ly x1 ux y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
+
+(* notion 2408 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.(l_e_st_eq_landau_n_rt_cutapp1b ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.l_e_st_eq_landau_n_rt_rp_4141_t21 ksi eta x0 lx y0 ly x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
+
+(* notion 2409 *)
+definition l_e_st_eq_landau_n_rt_rp_4141_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_cutapp1a eta (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta y.l_e_st_eq_landau_n_rt_rp_4141_t22 ksi eta x0 lx y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
+
+(* notion 2410 *)
+definition l_e_st_eq_landau_n_rt_rp_satz141 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_cutapp1a ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_4141_t23 ksi eta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
+
+(* notion 2411 *)
+definition l_e_st_eq_landau_n_rt_rp_ts ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_prod ksi eta) (l_e_st_eq_landau_n_rt_rp_satz141 ksi eta) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2412 *)
+definition l_e_st_eq_landau_n_rt_rp_lrtts ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_prod ksi eta) (l_e_st_eq_landau_n_rt_rp_satz141 ksi eta) z0 (l_e_st_eq_landau_n_rt_rp_prod1 ksi eta z0 x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0).
+
+(* notion 2413 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_isp1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_not (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_prod ksi eta))) (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_rt_rp_satz141a ksi eta x0 ux y0 uy) i : l_not (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta))).
+
+(* notion 2414 *)
+definition l_e_st_eq_landau_n_rt_rp_urtts ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_imp_th3 (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0) (l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)) (l_e_st_eq_landau_n_rt_rp_iii4_t10 ksi eta z0 x0 ux y0 uy i) (λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_prod ksi eta) (l_e_st_eq_landau_n_rt_rp_satz141 ksi eta) z0 t) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0).
+
+(* notion 2415 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.(l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_prod ksi eta) (l_e_st_eq_landau_n_rt_rp_satz141 ksi eta) z0 lz : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_prod ksi eta)).
+
+(* notion 2416 *)
+definition l_e_st_eq_landau_n_rt_rp_tsapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_lrt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_lrt eta y.Πv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).p.(l_e_st_eq_landau_n_rt_rp_prodapp ksi eta z0 (l_e_st_eq_landau_n_rt_rp_iii4_t11 ksi eta z0 lz p p1) p p1 : p).
+
+(* notion 2417 *)
+definition l_e_st_eq_landau_n_rt_rp_ists1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ts u zeta) ksi eta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)).
+
+(* notion 2418 *)
+definition l_e_st_eq_landau_n_rt_rp_ists2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_cut (λu:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ts zeta u) ksi eta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta)).
+
+(* notion 2419 *)
+definition l_e_st_eq_landau_n_rt_rp_ists12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ists1 ksi eta zeta i) (l_e_st_eq_landau_n_rt_rp_ists2 zeta upsilon eta j) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2420 *)
+definition l_e_st_eq_landau_n_rt_rp_4142_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_tris l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts y0 x0) i (l_e_st_eq_landau_n_rt_comts x0 y0) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts y0 x0)).
+
+(* notion 2421 *)
+definition l_e_st_eq_landau_n_rt_rp_4142_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtts eta ksi z0 y0 ly x0 lx (l_e_st_eq_landau_n_rt_rp_4142_t1 ksi eta z0 lz x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta ksi) z0).
+
+(* notion 2422 *)
+definition l_e_st_eq_landau_n_rt_rp_4142_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) z0.(l_e_st_eq_landau_n_rt_rp_tsapp ksi eta z0 lz (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta ksi) z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4142_t2 ksi eta z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta ksi) z0).
+
+(* notion 2423 *)
+definition l_e_st_eq_landau_n_rt_rp_satz142 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) x.l_e_st_eq_landau_n_rt_rp_4142_t3 ksi eta x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta ksi) x.l_e_st_eq_landau_n_rt_rp_4142_t3 eta ksi x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta ksi)).
+
+(* notion 2424 *)
+definition l_e_st_eq_landau_n_rt_rp_comts ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz142 ksi eta : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta ksi)).
+
+(* notion 2425 *)
+definition l_e_st_eq_landau_n_rt_rp_4143_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ts v0 z0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)) i (l_e_st_eq_landau_n_rt_ists1 v0 (l_e_st_eq_landau_n_rt_ts x0 y0) z0 j) (l_e_st_eq_landau_n_rt_assts1 x0 y0 z0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0))).
+
+(* notion 2426 *)
+definition l_e_st_eq_landau_n_rt_rp_4143_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtts eta zeta (l_e_st_eq_landau_n_rt_ts y0 z0) y0 ly z0 lz (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts y0 z0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_ts y0 z0)).
+
+(* notion 2427 *)
+definition l_e_st_eq_landau_n_rt_rp_4143_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts v0 z0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta) u0 x0 lx (l_e_st_eq_landau_n_rt_ts y0 z0) (l_e_st_eq_landau_n_rt_rp_4143_t2 ksi eta zeta u0 lu v0 lv z0 lz i x0 lx y0 ly j) (l_e_st_eq_landau_n_rt_rp_4143_t1 ksi eta zeta u0 lu v0 lv z0 lz i x0 lx y0 ly j) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0).
+
+(* notion 2428 *)
+definition l_e_st_eq_landau_n_rt_rp_4143_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts v0 z0).(l_e_st_eq_landau_n_rt_rp_tsapp ksi eta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4143_t3 ksi eta zeta u0 lu v0 lv z0 lz i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0).
+
+(* notion 2429 *)
+definition l_e_st_eq_landau_n_rt_rp_4143_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0.(l_e_st_eq_landau_n_rt_rp_tsapp (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4143_t4 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0).
+
+(* notion 2430 *)
+definition l_e_st_eq_landau_n_rt_rp_4143_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ts x0 v0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ts y0 z0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0) i (l_e_st_eq_landau_n_rt_ists2 v0 (l_e_st_eq_landau_n_rt_ts y0 z0) x0 j) (l_e_st_eq_landau_n_rt_assts2 x0 y0 z0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x0 y0) z0)).
+
+(* notion 2431 *)
+definition l_e_st_eq_landau_n_rt_rp_4143_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi eta (l_e_st_eq_landau_n_rt_ts x0 y0) x0 lx y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 y0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 2432 *)
+definition l_e_st_eq_landau_n_rt_rp_4143_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta u0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_rp_4143_t7 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) z0 lz (l_e_st_eq_landau_n_rt_rp_4143_t6 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0).
+
+(* notion 2433 *)
+definition l_e_st_eq_landau_n_rt_rp_4143_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).(l_e_st_eq_landau_n_rt_rp_tsapp eta zeta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4143_t8 ksi eta zeta u0 lu x0 lx v0 lv i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0).
+
+(* notion 2434 *)
+definition l_e_st_eq_landau_n_rt_rp_4143_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) u0.(l_e_st_eq_landau_n_rt_rp_tsapp ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta) u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts eta zeta) y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4143_t9 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) u0).
+
+(* notion 2435 *)
+definition l_e_st_eq_landau_n_rt_rp_satz143 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) x.l_e_st_eq_landau_n_rt_rp_4143_t5 ksi eta zeta x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) x.l_e_st_eq_landau_n_rt_rp_4143_t10 ksi eta zeta x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta))).
+
+(* notion 2436 *)
+definition l_e_st_eq_landau_n_rt_rp_assts1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz143 ksi eta zeta : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta))).
+
+(* notion 2437 *)
+definition l_e_st_eq_landau_n_rt_rp_assts2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_satz143 ksi eta zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts ksi eta) zeta)).
+
+(* notion 2438 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ts x0 v0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0)) i (l_e_st_eq_landau_n_rt_ists2 v0 (l_e_st_eq_landau_n_rt_pl y0 z0) x0 j) (l_e_st_eq_landau_n_rt_disttp2 x0 y0 z0) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x0 z0))).
+
+(* notion 2439 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi eta (l_e_st_eq_landau_n_rt_ts x0 y0) x0 lx y0 ly (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 y0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 2440 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi zeta (l_e_st_eq_landau_n_rt_ts x0 z0) x0 lx z0 lz (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 z0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_ts x0 z0)).
+
+(* notion 2441 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl y0 z0).(l_e_st_eq_landau_n_rt_rp_lrtpl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) u0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_rp_4144_t2 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) (l_e_st_eq_landau_n_rt_ts x0 z0) (l_e_st_eq_landau_n_rt_rp_4144_t3 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) (l_e_st_eq_landau_n_rt_rp_4144_t1 ksi eta zeta u0 lu x0 lx v0 lv i y0 ly z0 lz j) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0).
+
+(* notion 2442 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) v0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x0 v0).(l_e_st_eq_landau_n_rt_rp_plapp eta zeta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_4144_t4 ksi eta zeta u0 lu x0 lx v0 lv i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0).
+
+(* notion 2443 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0.(l_e_st_eq_landau_n_rt_rp_tsapp ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta) u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4144_t5 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0).
+
+(* notion 2444 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_tris l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_pl v0 w0) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x1 z0)) i (l_e_st_eq_landau_n_rt_ispl12 v0 (l_e_st_eq_landau_n_rt_ts x0 y0) w0 (l_e_st_eq_landau_n_rt_ts x1 z0) j k) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x1 z0))).
+
+(* notion 2445 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_x2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_ite (l_e_st_eq_landau_n_rt_moreis x0 x1) l_e_st_eq_landau_n_rt_rat x0 x1 : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2446 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λm:l_e_st_eq_landau_n_rt_moreis x0 x1.(l_e_itet (l_e_st_eq_landau_n_rt_moreis x0 x1) l_e_st_eq_landau_n_rt_rat x0 x1 m : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) x0).
+
+(* notion 2447 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λm:l_e_st_eq_landau_n_rt_moreis x0 x1.(l_e_isp1 l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt ksi t) x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) lx (l_e_st_eq_landau_n_rt_rp_4144_t8 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k m) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
+
+(* notion 2448 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λm:l_e_st_eq_landau_n_rt_moreis x0 x1.(l_e_st_eq_landau_n_rt_lessisi2 x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) x0 (l_e_st_eq_landau_n_rt_rp_4144_t8 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k m)) : l_e_st_eq_landau_n_rt_lessis x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
+
+(* notion 2449 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λm:l_e_st_eq_landau_n_rt_moreis x0 x1.(l_e_st_eq_landau_n_rt_satz88 x1 x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_satz84 x0 x1 m) (l_e_st_eq_landau_n_rt_rp_4144_t10 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k m) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
+
+(* notion 2450 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λn:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).(l_e_itef (l_e_st_eq_landau_n_rt_moreis x0 x1) l_e_st_eq_landau_n_rt_rat x0 x1 n : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) x1).
+
+(* notion 2451 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λn:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).(l_e_isp1 l_e_st_eq_landau_n_rt_rat (λt:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt ksi t) x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) lx1 (l_e_st_eq_landau_n_rt_rp_4144_t12 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k n) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
+
+(* notion 2452 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λn:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).(l_e_st_eq_landau_n_rt_lessisi2 x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) x1 (l_e_st_eq_landau_n_rt_rp_4144_t12 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k n)) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
+
+(* notion 2453 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).λn:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).(l_e_st_eq_landau_n_rt_lessisi1 x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_satz87b x0 x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_satz81j x0 x1 n) (l_e_st_eq_landau_n_rt_rp_4144_t14 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k n)) : l_e_st_eq_landau_n_rt_lessis x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
+
+(* notion 2454 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_imp_th1 (l_e_st_eq_landau_n_rt_moreis x0 x1) (l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)) (λt:l_e_st_eq_landau_n_rt_moreis x0 x1.l_e_st_eq_landau_n_rt_rp_4144_t9 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) (λt:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).l_e_st_eq_landau_n_rt_rp_4144_t13 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) : l_e_st_eq_landau_n_rt_lrt ksi (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
+
+(* notion 2455 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_imp_th1 (l_e_st_eq_landau_n_rt_moreis x0 x1) (l_e_st_eq_landau_n_rt_lessis x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)) (λt:l_e_st_eq_landau_n_rt_moreis x0 x1.l_e_st_eq_landau_n_rt_rp_4144_t10 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) (λt:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).l_e_st_eq_landau_n_rt_rp_4144_t15 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) : l_e_st_eq_landau_n_rt_lessis x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
+
+(* notion 2456 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_imp_th1 (l_e_st_eq_landau_n_rt_moreis x0 x1) (l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)) (λt:l_e_st_eq_landau_n_rt_moreis x0 x1.l_e_st_eq_landau_n_rt_rp_4144_t11 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) (λt:l_not (l_e_st_eq_landau_n_rt_moreis x0 x1).l_e_st_eq_landau_n_rt_rp_4144_t14 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k t) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)).
+
+(* notion 2457 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_st_eq_landau_n_rt_rp_lrtpl eta zeta (l_e_st_eq_landau_n_rt_pl y0 z0) y0 ly z0 lz (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl y0 z0)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_pl y0 z0)).
+
+(* notion 2458 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_rp_4144_t16 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0) (l_e_st_eq_landau_n_rt_rp_4144_t19 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0))) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0))).
+
+(* notion 2459 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_st_eq_landau_n_rt_satz109a x0 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) y0 y0 (l_e_st_eq_landau_n_rt_rp_4144_t17 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_lessisi2 y0 y0 (l_e_refis l_e_st_eq_landau_n_rt_rat y0)) : l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) y0)).
+
+(* notion 2460 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_st_eq_landau_n_rt_satz109a x1 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) z0 z0 (l_e_st_eq_landau_n_rt_rp_4144_t18 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_lessisi2 z0 z0 (l_e_refis l_e_st_eq_landau_n_rt_rat z0)) : l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_ts x1 z0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) z0)).
+
+(* notion 2461 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_e_st_eq_landau_n_rt_islessis12 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x1 z0)) u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) y0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) z0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_symis l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts x1 z0)) (l_e_st_eq_landau_n_rt_rp_4144_t7 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)) (l_e_st_eq_landau_n_rt_distpt2 (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) y0 z0) (l_e_st_eq_landau_n_rt_satz100a (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) y0) (l_e_st_eq_landau_n_rt_ts x1 z0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) z0) (l_e_st_eq_landau_n_rt_rp_4144_t21 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_rp_4144_t22 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k)) : l_e_st_eq_landau_n_rt_lessis u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0))).
+
+(* notion 2462 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt zeta z0.λk:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x1 z0).(l_orapp (l_e_st_eq_landau_n_rt_less u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0))) (l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0))) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (l_e_st_eq_landau_n_rt_rp_4144_t23 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (λt:l_e_st_eq_landau_n_rt_less u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)).l_e_st_eq_landau_n_rt_rp_satz120 (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)) (l_e_st_eq_landau_n_rt_rp_4144_t20 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) u0 t) (λt:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)).l_e_isp1 l_e_st_eq_landau_n_rt_rat (λu:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_4144_x2 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) (l_e_st_eq_landau_n_rt_pl y0 z0)) u0 (l_e_st_eq_landau_n_rt_rp_4144_t20 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x1 lx1 z0 lz k) t) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
+
+(* notion 2463 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt eta y0.λj:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_tsapp ksi zeta w0 lw (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt zeta y.λv:l_e_st_eq_landau_n_rt_is w0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4144_t24 ksi eta zeta u0 lu v0 lv w0 lw i x0 lx y0 ly j x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
+
+(* notion 2464 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) v0.λw0:l_e_st_eq_landau_n_rt_rat.λlw:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) w0.λi:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl v0 w0).(l_e_st_eq_landau_n_rt_rp_tsapp ksi eta v0 lv (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt eta y.λv:l_e_st_eq_landau_n_rt_is v0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4144_t25 ksi eta zeta u0 lu v0 lv w0 lw i x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
+
+(* notion 2465 *)
+definition l_e_st_eq_landau_n_rt_rp_4144_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) u0.(l_e_st_eq_landau_n_rt_rp_plapp (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) u0 lu (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi eta) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) y.λv:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_4144_t26 ksi eta zeta u0 lu x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) u0).
+
+(* notion 2466 *)
+definition l_e_st_eq_landau_n_rt_rp_satz144 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) x.l_e_st_eq_landau_n_rt_rp_4144_t6 ksi eta zeta x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) x.l_e_st_eq_landau_n_rt_rp_4144_t27 ksi eta zeta x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta))).
+
+(* notion 2467 *)
+definition l_e_st_eq_landau_n_rt_rp_disttp1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta (l_e_st_eq_landau_n_rt_rp_pl ksi eta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_satz144 zeta ksi eta) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_comts zeta ksi) (l_e_st_eq_landau_n_rt_rp_comts zeta eta)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta))).
+
+(* notion 2468 *)
+definition l_e_st_eq_landau_n_rt_rp_disttp2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz144 ksi eta zeta : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta))).
+
+(* notion 2469 *)
+definition l_e_st_eq_landau_n_rt_rp_distpt1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_disttp1 ksi eta zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi eta) zeta)).
+
+(* notion 2470 *)
+definition l_e_st_eq_landau_n_rt_rp_distpt2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) (l_e_st_eq_landau_n_rt_rp_disttp2 ksi eta zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta)) (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_pl eta zeta))).
+
+(* notion 2471 *)
+definition l_e_st_eq_landau_n_rt_rp_4145_phi ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_mn ksi eta m : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2472 *)
+definition l_e_st_eq_landau_n_rt_rp_4145_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_satz140d ksi eta m : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m))).
+
+(* notion 2473 *)
+definition l_e_st_eq_landau_n_rt_rp_4145_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m)) zeta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta)) (l_e_st_eq_landau_n_rt_rp_ists1 ksi (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m)) zeta (l_e_st_eq_landau_n_rt_rp_4145_t1 ksi eta zeta m)) (l_e_st_eq_landau_n_rt_rp_disttp1 eta (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta))).
+
+(* notion 2474 *)
+definition l_e_st_eq_landau_n_rt_rp_satz145a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta)) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta)) (l_e_st_eq_landau_n_rt_rp_4145_t2 ksi eta zeta m)) (l_e_st_eq_landau_n_rt_rp_satz133 (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_4145_phi ksi eta zeta m) zeta)) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)).
+
+(* notion 2475 *)
+definition l_e_st_eq_landau_n_rt_rp_satz145b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ists1 ksi eta zeta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)).
+
+(* notion 2476 *)
+definition l_e_st_eq_landau_n_rt_rp_satz145c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz145a eta ksi zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)).
+
+(* notion 2477 *)
+definition l_e_st_eq_landau_n_rt_rp_satz145d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_comts ksi zeta) (l_e_st_eq_landau_n_rt_rp_comts eta zeta) (l_e_st_eq_landau_n_rt_rp_satz145a ksi eta zeta m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta)).
+
+(* notion 2478 *)
+definition l_e_st_eq_landau_n_rt_rp_satz145e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_st_eq_landau_n_rt_rp_ists2 ksi eta zeta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta)).
+
+(* notion 2479 *)
+definition l_e_st_eq_landau_n_rt_rp_satz145f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_comts ksi zeta) (l_e_st_eq_landau_n_rt_rp_comts eta zeta) (l_e_st_eq_landau_n_rt_rp_satz145c ksi eta zeta l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta)).
+
+(* notion 2480 *)
+definition l_e_st_eq_landau_n_rt_rp_satz145g ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore2 (l_e_st_eq_landau_n_rt_rp_ts ksi upsilon) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ists1 ksi eta upsilon i) (l_e_st_eq_landau_n_rt_rp_satz145d zeta upsilon ksi m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2481 *)
+definition l_e_st_eq_landau_n_rt_rp_satz145h ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λm:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts upsilon eta) (l_e_st_eq_landau_n_rt_rp_comts ksi zeta) (l_e_st_eq_landau_n_rt_rp_comts eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz145g ksi eta zeta upsilon i m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts upsilon eta)).
+
+(* notion 2482 *)
+definition l_e_st_eq_landau_n_rt_rp_satz145j ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_ts ksi upsilon) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ists1 ksi eta upsilon i) (l_e_st_eq_landau_n_rt_rp_satz145f zeta upsilon ksi l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2483 *)
+definition l_e_st_eq_landau_n_rt_rp_satz145k ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λl:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts upsilon eta) (l_e_st_eq_landau_n_rt_rp_comts ksi zeta) (l_e_st_eq_landau_n_rt_rp_comts eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz145j ksi eta zeta upsilon i l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts upsilon eta)).
+
+(* notion 2484 *)
+definition l_e_st_eq_landau_n_rt_rp_4146_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz123a ksi eta : l_or3 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta)).
+
+(* notion 2485 *)
+definition l_e_st_eq_landau_n_rt_rp_4146_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) : l_ec3 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta))).
+
+(* notion 2486 *)
+definition l_e_st_eq_landau_n_rt_rp_satz146a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta).(l_ec3_th11 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_4146_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_4146_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz145b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz145a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz145c ksi eta zeta u) m : l_e_st_eq_landau_n_rt_rp_more ksi eta).
+
+(* notion 2487 *)
+definition l_e_st_eq_landau_n_rt_rp_satz146b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta).(l_ec3_th10 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_4146_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_4146_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz145b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz145a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz145c ksi eta zeta u) i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
+
+(* notion 2488 *)
+definition l_e_st_eq_landau_n_rt_rp_satz146c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta).(l_ec3_th12 (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)) (l_e_st_eq_landau_n_rt_rp_4146_t1 ksi eta zeta) (l_e_st_eq_landau_n_rt_rp_4146_t2 ksi eta zeta) (λu:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz145b ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz145a ksi eta zeta u) (λu:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_satz145c ksi eta zeta u) l : l_e_st_eq_landau_n_rt_rp_less ksi eta).
+
+(* notion 2489 *)
+definition l_e_st_eq_landau_n_rt_rp_satz146d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta).(l_e_st_eq_landau_n_rt_rp_satz146a ksi eta zeta (l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_comts zeta ksi) (l_e_st_eq_landau_n_rt_rp_comts zeta eta) m) : l_e_st_eq_landau_n_rt_rp_more ksi eta).
+
+(* notion 2490 *)
+definition l_e_st_eq_landau_n_rt_rp_satz146e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta).(l_e_st_eq_landau_n_rt_rp_satz146b ksi eta zeta (l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_comts ksi zeta) i (l_e_st_eq_landau_n_rt_rp_comts zeta eta)) : l_e_st_eq_landau_n_rt_rp_is ksi eta).
+
+(* notion 2491 *)
+definition l_e_st_eq_landau_n_rt_rp_satz146f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts zeta eta).(l_e_st_eq_landau_n_rt_rp_satz146c ksi eta zeta (l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_ts zeta ksi) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_comts zeta ksi) (l_e_st_eq_landau_n_rt_rp_comts zeta eta) l) : l_e_st_eq_landau_n_rt_rp_less ksi eta).
+
+(* notion 2492 *)
+definition l_e_st_eq_landau_n_rt_rp_4147_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz145a ksi eta zeta m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta)).
+
+(* notion 2493 *)
+definition l_e_st_eq_landau_n_rt_rp_4147_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_ts zeta eta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts upsilon eta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_comts zeta eta) (l_e_st_eq_landau_n_rt_rp_comts upsilon eta) (l_e_st_eq_landau_n_rt_rp_satz145a zeta upsilon eta n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2494 *)
+definition l_e_st_eq_landau_n_rt_rp_satz147 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_trmore (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_4147_t1 ksi eta zeta upsilon m n) (l_e_st_eq_landau_n_rt_rp_4147_t2 ksi eta zeta upsilon m n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2495 *)
+definition l_e_st_eq_landau_n_rt_rp_satz147a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz147 eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz122 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2496 *)
+definition l_e_st_eq_landau_n_rt_rp_satz148a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)) m (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_satz147 ksi eta zeta upsilon t n) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_satz145g ksi eta zeta upsilon t n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2497 *)
+definition l_e_st_eq_landau_n_rt_rp_satz148b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more zeta upsilon) (l_e_st_eq_landau_n_rt_rp_is zeta upsilon) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)) n (λt:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.l_e_st_eq_landau_n_rt_rp_satz147 ksi eta zeta upsilon m t) (λt:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.l_e_st_eq_landau_n_rt_rp_satz145h zeta upsilon ksi eta t m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2498 *)
+definition l_e_st_eq_landau_n_rt_rp_satz148c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_less zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz148a eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz125 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz122 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2499 *)
+definition l_e_st_eq_landau_n_rt_rp_satz148d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz148b eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz122 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz125 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2500 *)
+definition l_e_st_eq_landau_n_rt_rp_4149_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λj:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.(l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ists12 ksi eta zeta upsilon i j) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2501 *)
+definition l_e_st_eq_landau_n_rt_rp_4149_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.λo:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz148a ksi eta zeta upsilon m o) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2502 *)
+definition l_e_st_eq_landau_n_rt_rp_4149_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_orapp (l_e_st_eq_landau_n_rt_rp_more zeta upsilon) (l_e_st_eq_landau_n_rt_rp_is zeta upsilon) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)) n (λt:l_e_st_eq_landau_n_rt_rp_more zeta upsilon.l_e_st_eq_landau_n_rt_rp_4149_t2 ksi eta zeta upsilon m n i t) (λt:l_e_st_eq_landau_n_rt_rp_is zeta upsilon.l_e_st_eq_landau_n_rt_rp_4149_t1 ksi eta zeta upsilon m n i t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2503 *)
+definition l_e_st_eq_landau_n_rt_rp_4149_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.λo:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_satz148b ksi eta zeta upsilon o n) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2504 *)
+definition l_e_st_eq_landau_n_rt_rp_satz149 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis ksi eta.λn:l_e_st_eq_landau_n_rt_rp_moreis zeta upsilon.(l_orapp (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_is ksi eta) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)) m (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_4149_t4 ksi eta zeta upsilon m n t) (λt:l_e_st_eq_landau_n_rt_rp_is ksi eta.l_e_st_eq_landau_n_rt_rp_4149_t3 ksi eta zeta upsilon m n t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2505 *)
+definition l_e_st_eq_landau_n_rt_rp_satz149a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λzeta:l_e_st_eq_landau_n_rt_cut.λupsilon:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessis ksi eta.λk:l_e_st_eq_landau_n_rt_rp_lessis zeta upsilon.(l_e_st_eq_landau_n_rt_rp_satz124 (l_e_st_eq_landau_n_rt_rp_ts eta upsilon) (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_satz149 eta ksi upsilon zeta (l_e_st_eq_landau_n_rt_rp_satz125 ksi eta l) (l_e_st_eq_landau_n_rt_rp_satz125 zeta upsilon k)) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_ts ksi zeta) (l_e_st_eq_landau_n_rt_rp_ts eta upsilon)).
+
+(* notion 2506 *)
+definition l_e_st_eq_landau_n_rt_ratset ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2507 *)
+definition l_e_st_eq_landau_n_rt_4150_t1 ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz90 r0 : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0)).
+
+(* notion 2508 *)
+definition l_e_st_eq_landau_n_rt_4150_t2 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 r0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0) x0 l : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0)).
+
+(* notion 2509 *)
+definition l_e_st_eq_landau_n_rt_4150_t3 ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_ec3e13 (l_e_st_eq_landau_n_rt_is r0 r0) (l_e_st_eq_landau_n_rt_more r0 r0) (l_e_st_eq_landau_n_rt_less r0 r0) (l_e_st_eq_landau_n_rt_satz81b r0 r0) (l_e_refis l_e_st_eq_landau_n_rt_rat r0) : l_not (l_e_st_eq_landau_n_rt_less r0 r0)).
+
+(* notion 2510 *)
+definition l_e_st_eq_landau_n_rt_4150_t4 ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_imp_th3 (l_e_st_eq_landau_n_rt_in r0 (l_e_st_eq_landau_n_rt_ratset r0)) (l_e_st_eq_landau_n_rt_less r0 r0) (l_e_st_eq_landau_n_rt_4150_t3 r0) (λt:l_e_st_eq_landau_n_rt_in r0 (l_e_st_eq_landau_n_rt_ratset r0).l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0) r0 t) : l_not (l_e_st_eq_landau_n_rt_in r0 (l_e_st_eq_landau_n_rt_ratset r0))).
+
+(* notion 2511 *)
+definition l_e_st_eq_landau_n_rt_4150_t5 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0) x0 i : l_e_st_eq_landau_n_rt_less x0 r0).
+
+(* notion 2512 *)
+definition l_e_st_eq_landau_n_rt_4150_t6 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).λx1:l_e_st_eq_landau_n_rt_rat.λk:l_e_st_eq_landau_n_rt_less x1 x0.(l_e_st_eq_landau_n_rt_4150_t2 r0 x1 (l_e_st_eq_landau_n_rt_trless x1 x0 r0 k (l_e_st_eq_landau_n_rt_4150_t5 r0 x0 i)) : l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_ratset r0)).
+
+(* notion 2513 *)
+definition l_e_st_eq_landau_n_rt_4150_t7 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).(l_e_st_eq_landau_n_rt_satz91 x0 r0 (l_e_st_eq_landau_n_rt_4150_t5 r0 x0 i) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 x) (l_e_st_eq_landau_n_rt_less x r0))).
+
+(* notion 2514 *)
+definition l_e_st_eq_landau_n_rt_4150_t8 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).λx1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x0 x1) (l_e_st_eq_landau_n_rt_less x1 r0).(l_ande1 (l_e_st_eq_landau_n_rt_less x0 x1) (l_e_st_eq_landau_n_rt_less x1 r0) a : l_e_st_eq_landau_n_rt_less x0 x1).
+
+(* notion 2515 *)
+definition l_e_st_eq_landau_n_rt_4150_t9 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).λx1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x0 x1) (l_e_st_eq_landau_n_rt_less x1 r0).(l_ande2 (l_e_st_eq_landau_n_rt_less x0 x1) (l_e_st_eq_landau_n_rt_less x1 r0) a : l_e_st_eq_landau_n_rt_less x1 r0).
+
+(* notion 2516 *)
+definition l_e_st_eq_landau_n_rt_4150_t10 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).λx1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x0 x1) (l_e_st_eq_landau_n_rt_less x1 r0).(l_andi (l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_ratset r0)) (l_e_st_eq_landau_n_rt_more x1 x0) (l_e_st_eq_landau_n_rt_4150_t2 r0 x1 (l_e_st_eq_landau_n_rt_4150_t9 r0 x0 i x1 a)) (l_e_st_eq_landau_n_rt_satz83 x0 x1 (l_e_st_eq_landau_n_rt_4150_t8 r0 x0 i x1 a)) : l_and (l_e_st_eq_landau_n_rt_in x1 (l_e_st_eq_landau_n_rt_ratset r0)) (l_e_st_eq_landau_n_rt_more x1 x0)).
+
+(* notion 2517 *)
+definition l_e_st_eq_landau_n_rt_4150_t11 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_ratset r0).(l_some_th6 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x0 x) (l_e_st_eq_landau_n_rt_less x r0)) (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_ratset r0)) (l_e_st_eq_landau_n_rt_more x x0)) (l_e_st_eq_landau_n_rt_4150_t7 r0 x0 i) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_less x0 x) (l_e_st_eq_landau_n_rt_less x r0).l_e_st_eq_landau_n_rt_4150_t10 r0 x0 i x t) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_ratset r0)) (l_e_st_eq_landau_n_rt_more x x0))).
+
+(* notion 2518 *)
+definition l_e_st_eq_landau_n_rt_4150_t12 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 r0.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_ratset r0) x0 (l_e_st_eq_landau_n_rt_4150_t2 r0 x0 l) r0 (l_e_st_eq_landau_n_rt_4150_t4 r0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_ratset r0).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_4150_t6 r0 x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_ratset r0).l_e_st_eq_landau_n_rt_4150_t11 r0 x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_ratset r0)).
+
+(* notion 2519 *)
+definition l_e_st_eq_landau_n_rt_satz150 ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_less x r0) (l_e_st_eq_landau_n_rt_4150_t1 r0) (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_ratset r0)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_less x r0.l_e_st_eq_landau_n_rt_4150_t12 r0 x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_ratset r0)).
+
+(* notion 2520 *)
+definition l_e_st_eq_landau_n_rt_rp_rpofrt ≝ λr0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_ratset r0) (l_e_st_eq_landau_n_rt_satz150 r0) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2521 *)
+definition l_e_st_eq_landau_n_rt_rp_lrtrpofrt ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 r0.(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_ratset r0) (l_e_st_eq_landau_n_rt_satz150 r0) x0 (l_e_st_eq_landau_n_rt_4150_t2 r0 x0 l) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt r0) x0).
+
+(* notion 2522 *)
+definition l_e_st_eq_landau_n_rt_rp_lrtrpofrte ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt r0) x0.(l_e_st_eq_landau_n_rt_4150_t5 r0 x0 (l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_ratset r0) (l_e_st_eq_landau_n_rt_satz150 r0) x0 lx) : l_e_st_eq_landau_n_rt_less x0 r0).
+
+(* notion 2523 *)
+definition l_e_st_eq_landau_n_rt_rp_iii4_t12 ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 r0.(l_e_st_eq_landau_n_rt_satz81c x0 r0 m : l_not (l_e_st_eq_landau_n_rt_less x0 r0)).
+
+(* notion 2524 *)
+definition l_e_st_eq_landau_n_rt_rp_urtrpofrt ≝ λr0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 r0.(l_imp_th3 (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt r0) x0) (l_e_st_eq_landau_n_rt_less x0 r0) (l_e_st_eq_landau_n_rt_rp_iii4_t12 r0 x0 m) (λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt r0) x0.l_e_st_eq_landau_n_rt_rp_lrtrpofrte r0 x0 t) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt r0) x0).
+
+(* notion 2525 *)
+definition l_e_st_eq_landau_n_rt_rp_1rp ≝ (l_e_st_eq_landau_n_rt_rp_rpofrt l_e_st_eq_landau_n_rt_1rt : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2526 *)
+definition l_e_st_eq_landau_n_rt_rp_4151_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrte l_e_st_eq_landau_n_rt_1rt y0 ly : l_e_st_eq_landau_n_rt_less y0 l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2527 *)
+definition l_e_st_eq_landau_n_rt_rp_4151_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_rt_ts x0 l_e_st_eq_landau_n_rt_1rt) x0 (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 y0) i) (l_e_st_eq_landau_n_rt_example1a x0) (l_e_st_eq_landau_n_rt_satz105f y0 l_e_st_eq_landau_n_rt_1rt x0 (l_e_st_eq_landau_n_rt_rp_4151_t1 ksi z0 lz x0 lx y0 ly i)) : l_e_st_eq_landau_n_rt_less z0 x0).
+
+(* notion 2528 *)
+definition l_e_st_eq_landau_n_rt_rp_4151_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp y0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 y0).(l_e_st_eq_landau_n_rt_rp_satz120 ksi x0 lx z0 (l_e_st_eq_landau_n_rt_rp_4151_t2 ksi z0 lz x0 lx y0 ly i) : l_e_st_eq_landau_n_rt_lrt ksi z0).
+
+(* notion 2529 *)
+definition l_e_st_eq_landau_n_rt_rp_4151_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) z0.(l_e_st_eq_landau_n_rt_rp_tsapp ksi l_e_st_eq_landau_n_rt_rp_1rp z0 lz (l_e_st_eq_landau_n_rt_lrt ksi z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4151_t3 ksi z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt ksi z0).
+
+(* notion 2530 *)
+definition l_e_st_eq_landau_n_rt_rp_4151_y1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x0 : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2531 *)
+definition l_e_st_eq_landau_n_rt_rp_4151_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x1) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l) (l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_satz105f x0 x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) l) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l) l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2532 *)
+definition l_e_st_eq_landau_n_rt_rp_4151_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_rp_lrtrpofrt l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l) (l_e_st_eq_landau_n_rt_rp_4151_t5 ksi x0 lx x1 lx1 l) : l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l)).
+
+(* notion 2533 *)
+definition l_e_st_eq_landau_n_rt_rp_4151_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) x0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) x0 (l_e_st_eq_landau_n_rt_assts2 x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x0) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) l_e_st_eq_landau_n_rt_1rt x0 (l_e_st_eq_landau_n_rt_satz110c l_e_st_eq_landau_n_rt_1rt x1)) (l_e_st_eq_landau_n_rt_example1c x0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l)) x0).
+
+(* notion 2534 *)
+definition l_e_st_eq_landau_n_rt_rp_4151_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λl:l_e_st_eq_landau_n_rt_less x0 x1.(l_e_st_eq_landau_n_rt_rp_lrtts ksi l_e_st_eq_landau_n_rt_rp_1rp x0 x1 lx1 (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l) (l_e_st_eq_landau_n_rt_rp_4151_t6 ksi x0 lx x1 lx1 l) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_rp_4151_y1 ksi x0 lx x1 lx1 l)) x0 (l_e_st_eq_landau_n_rt_rp_4151_t7 ksi x0 lx x1 lx1 l)) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) x0).
+
+(* notion 2535 *)
+definition l_e_st_eq_landau_n_rt_rp_4151_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_cutapp3 ksi x0 lx (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) x0) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi y.λu:l_e_st_eq_landau_n_rt_less x0 y.l_e_st_eq_landau_n_rt_rp_4151_t8 ksi x0 lx y t u) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) x0).
+
+(* notion 2536 *)
+definition l_e_st_eq_landau_n_rt_rp_satz151 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) ksi (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) x.l_e_st_eq_landau_n_rt_rp_4151_t4 ksi x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_4151_t9 ksi x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) ksi).
+
+(* notion 2537 *)
+definition l_e_st_eq_landau_n_rt_rp_satz151a ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) ksi (l_e_st_eq_landau_n_rt_rp_satz151 ksi) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp)).
+
+(* notion 2538 *)
+definition l_e_st_eq_landau_n_rt_rp_satz151b ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp ksi) (l_e_st_eq_landau_n_rt_rp_ts ksi l_e_st_eq_landau_n_rt_rp_1rp) ksi (l_e_st_eq_landau_n_rt_rp_comts l_e_st_eq_landau_n_rt_rp_1rp ksi) (l_e_st_eq_landau_n_rt_rp_satz151 ksi) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp ksi) ksi).
+
+(* notion 2539 *)
+definition l_e_st_eq_landau_n_rt_rp_satz151c ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp ksi) ksi (l_e_st_eq_landau_n_rt_rp_satz151b ksi) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp ksi)).
+
+(* notion 2540 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_invprop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_and (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_less y0 x0) : Prop).
+
+(* notion 2541 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_invprop2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) : Prop).
+
+(* notion 2542 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_invprop ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x) : Prop).
+
+(* notion 2543 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_inv ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (λz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop ksi z) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2544 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_andi (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_less y0 x0) uy l : l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 y0).
+
+(* notion 2545 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x) y0 (l_e_st_eq_landau_n_rt_rp_4152_t1 ksi z0 x0 ux y0 uy l i) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)).
+
+(* notion 2546 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_and3i (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) ux (l_e_st_eq_landau_n_rt_rp_4152_t2 ksi z0 x0 ux y0 uy l i) i : l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0).
+
+(* notion 2547 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x) x0 (l_e_st_eq_landau_n_rt_rp_4152_t3 ksi z0 x0 ux y0 uy l i) : l_e_st_eq_landau_n_rt_rp_4152_invprop ksi z0).
+
+(* notion 2548 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_inv1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.λl:l_e_st_eq_landau_n_rt_less y0 x0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λz:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop ksi z) z0 (l_e_st_eq_landau_n_rt_rp_4152_t4 ksi z0 x0 ux y0 uy l i) : l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
+
+(* notion 2549 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop ksi x) z0 i : l_e_st_eq_landau_n_rt_rp_4152_invprop ksi z0).
+
+(* notion 2550 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.(l_and3e1 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) px : l_e_st_eq_landau_n_rt_urt ksi x0).
+
+(* notion 2551 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.(l_and3e2 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) px : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)).
+
+(* notion 2552 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.(l_and3e3 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x)) (l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) px : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)).
+
+(* notion 2553 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 y0.(l_ande1 (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_less y0 x0) py : l_e_st_eq_landau_n_rt_urt ksi y0).
+
+(* notion 2554 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 y0.(l_ande2 (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_less y0 x0) py : l_e_st_eq_landau_n_rt_less y0 x0).
+
+(* notion 2555 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.λy0:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 y0.(p1 x0 (l_e_st_eq_landau_n_rt_rp_4152_t6 ksi z0 i p p1 x0 px) y0 (l_e_st_eq_landau_n_rt_rp_4152_t9 ksi z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_4152_t10 ksi z0 i p p1 x0 px y0 py) (l_e_st_eq_landau_n_rt_rp_4152_t8 ksi z0 i p p1 x0 px) : p).
+
+(* notion 2556 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.λx0:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x0.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x) (l_e_st_eq_landau_n_rt_rp_4152_t7 ksi z0 i p p1 x0 px) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_4152_invprop1 ksi x0 x.l_e_st_eq_landau_n_rt_rp_4152_t11 ksi z0 i p p1 x0 px x t) : p).
+
+(* notion 2557 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_invapp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_urt ksi x.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_urt ksi y.Πv:l_e_st_eq_landau_n_rt_less y x.Πw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).p.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x) (l_e_st_eq_landau_n_rt_rp_4152_t5 ksi z0 i p p1) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_4152_invprop2 ksi z0 x.l_e_st_eq_landau_n_rt_rp_4152_t12 ksi z0 i p p1 x t) : p).
+
+(* notion 2558 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_2x0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_pl x0 x0 : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2559 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_satz94a x0 x0 : l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux)).
+
+(* notion 2560 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_rp_satz119a ksi x0 ux (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux) (l_e_st_eq_landau_n_rt_rp_4152_t13 ksi x0 ux) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux)).
+
+(* notion 2561 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_rp_4152_inv1 ksi (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux)) (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux) (l_e_st_eq_landau_n_rt_rp_4152_t14 ksi x0 ux) x0 ux (l_e_st_eq_landau_n_rt_rp_4152_t13 ksi x0 ux) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux))) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4152_2x0 ksi x0 ux)) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
+
+(* notion 2562 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_is x0 x1) (l_e_st_eq_landau_n_rt_lrt ksi x0) ux (λt:l_e_st_eq_landau_n_rt_is x0 x1.l_e_isp1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt ksi x) x1 x0 lx t) : l_e_st_eq_landau_n_rt_nis x0 x1).
+
+(* notion 2563 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt x0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2564 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt x1 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x1) l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2565 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x1) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x1) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x1 i) (l_e_st_eq_landau_n_rt_rp_4152_t18 ksi x1 lx x0 ux) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x1) l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2566 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_st_eq_landau_n_rt_satz110b l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0 x1 (l_e_st_eq_landau_n_rt_rp_4152_t17 ksi x1 lx x0 ux) (l_e_st_eq_landau_n_rt_rp_4152_t19 ksi x1 lx x0 ux i) : l_e_st_eq_landau_n_rt_is x0 x1).
+
+(* notion 2567 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) (l_e_st_eq_landau_n_rt_is x0 x1) (l_e_st_eq_landau_n_rt_rp_4152_t16 ksi x1 lx x0 ux) (λt:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).l_e_st_eq_landau_n_rt_rp_4152_t20 ksi x1 lx x0 ux t) : l_e_st_eq_landau_n_rt_nis (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)).
+
+(* notion 2568 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.λi:l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).(l_e_st_eq_landau_n_rt_rp_4152_invapp ksi (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) i l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_less y x.λw:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).l_e_st_eq_landau_n_rt_rp_4152_t21 ksi x1 lx x t (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x) w)) : l_con).
+
+(* notion 2569 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx1:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x1.(λt:l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).l_e_st_eq_landau_n_rt_rp_4152_t22 ksi x1 lx t : l_not (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi))).
+
+(* notion 2570 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_isless2 z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) u0 j l : l_e_st_eq_landau_n_rt_less u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)).
+
+(* notion 2571 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)) (l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_satz110d l_e_st_eq_landau_n_rt_1rt u0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) (l_e_st_eq_landau_n_rt_ts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0))).
+
+(* notion 2572 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0) (l_e_st_eq_landau_n_rt_ts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)) (l_e_st_eq_landau_n_rt_ts u0 x0) (l_e_st_eq_landau_n_rt_rp_4152_t25 ksi z0 i u0 l x0 ux j) (l_e_st_eq_landau_n_rt_satz105c u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x0 (l_e_st_eq_landau_n_rt_rp_4152_t24 ksi z0 i u0 l x0 ux j)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts u0 x0) (l_e_st_eq_landau_n_rt_ts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0))).
+
+(* notion 2573 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts u0 x0) (l_e_st_eq_landau_n_rt_ts x0 u0) (l_e_st_eq_landau_n_rt_ts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0) (l_e_st_eq_landau_n_rt_comts u0 x0) (l_e_st_eq_landau_n_rt_comts u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)) (l_e_st_eq_landau_n_rt_rp_4152_t26 ksi z0 i u0 l x0 ux j) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 u0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0)).
+
+(* notion 2574 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t28 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_satz106c x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0 (l_e_st_eq_landau_n_rt_rp_4152_t27 ksi z0 i u0 l x0 ux j) : l_e_st_eq_landau_n_rt_less x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)).
+
+(* notion 2575 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t29 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_rp_satz119a ksi x0 ux (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_rp_4152_t28 ksi z0 i u0 l x0 ux j) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0)).
+
+(* notion 2576 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t30 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt u0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0) l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2577 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t31 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_satz110g l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0 (l_e_st_eq_landau_n_rt_rp_4152_t30 ksi z0 i u0 l x0 ux j) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0))).
+
+(* notion 2578 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t32 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_rp_4152_inv1 ksi u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_rp_4152_t29 ksi z0 i u0 l x0 ux j) x0 ux (l_e_st_eq_landau_n_rt_rp_4152_t28 ksi z0 i u0 l x0 ux j) (l_e_st_eq_landau_n_rt_rp_4152_t31 ksi z0 i u0 l x0 ux j) : l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
+
+(* notion 2579 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t33 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λu0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less u0 z0.(l_e_st_eq_landau_n_rt_rp_4152_invapp ksi z0 i (l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_less y x.λw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).l_e_st_eq_landau_n_rt_rp_4152_t32 ksi z0 i u0 l x t w) : l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
+
+(* notion 2580 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t34 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_e_st_eq_landau_n_rt_satz91 x1 x0 l : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x1 x) (l_e_st_eq_landau_n_rt_less x x0))).
+
+(* notion 2581 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t35 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_ande1 (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0) a : l_e_st_eq_landau_n_rt_less x1 x2).
+
+(* notion 2582 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t36 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_rp_satz119a ksi x1 ux1 x2 (l_e_st_eq_landau_n_rt_rp_4152_t35 ksi z0 i x0 ux x1 ux1 l j x2 a) : l_e_st_eq_landau_n_rt_urt ksi x2).
+
+(* notion 2583 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t37 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_rp_4152_inv1 ksi (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) x2 (l_e_st_eq_landau_n_rt_rp_4152_t36 ksi z0 i x0 ux x1 ux1 l j x2 a) x1 ux1 (l_e_st_eq_landau_n_rt_rp_4152_t35 ksi z0 i x0 ux x1 ux1 l j x2 a) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
+
+(* notion 2584 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t38 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_ande2 (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0) a : l_e_st_eq_landau_n_rt_less x2 x0).
+
+(* notion 2585 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t39 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_tris l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)) (l_e_st_eq_landau_n_rt_satz110c l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_satz110d l_e_st_eq_landau_n_rt_1rt x2) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2))).
+
+(* notion 2586 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t40 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)) (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_rp_4152_t39 ksi z0 i x0 ux x1 ux1 l j x2 a) (l_e_st_eq_landau_n_rt_satz105c x2 x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_rp_4152_t38 ksi z0 i x0 ux x1 ux1 l j x2 a)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2))).
+
+(* notion 2587 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t41 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x2) (l_e_st_eq_landau_n_rt_ts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) x2) (l_e_st_eq_landau_n_rt_comts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0)) (l_e_st_eq_landau_n_rt_comts x2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)) (l_e_st_eq_landau_n_rt_rp_4152_t40 ksi z0 i x0 ux x1 ux1 l j x2 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) x2) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) x2)).
+
+(* notion 2588 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t42 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_satz106c (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) x2 (l_e_st_eq_landau_n_rt_rp_4152_t41 ksi z0 i x0 ux x1 ux1 l j x2 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2)).
+
+(* notion 2589 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t43 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_e_st_eq_landau_n_rt_ismore2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) j) (l_e_st_eq_landau_n_rt_satz83 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_st_eq_landau_n_rt_rp_4152_t42 ksi z0 i x0 ux x1 ux1 l j x2 a)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) z0).
+
+(* notion 2590 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t44 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_andi (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) z0) (l_e_st_eq_landau_n_rt_rp_4152_t37 ksi z0 i x0 ux x1 ux1 l j x2 a) (l_e_st_eq_landau_n_rt_rp_4152_t43 ksi z0 i x0 ux x1 ux1 l j x2 a) : l_and (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) z0)).
+
+(* notion 2591 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t45 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).λx2:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less x1 x2) (l_e_st_eq_landau_n_rt_less x2 x0).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0)) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x2) (l_e_st_eq_landau_n_rt_rp_4152_t44 ksi z0 i x0 ux x1 ux1 l j x2 a) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0))).
+
+(* notion 2592 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t46 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λux1:l_e_st_eq_landau_n_rt_urt ksi x1.λl:l_e_st_eq_landau_n_rt_less x1 x0.λj:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0).(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less x1 x) (l_e_st_eq_landau_n_rt_less x x0)) (l_e_st_eq_landau_n_rt_rp_4152_t34 ksi z0 i x0 ux x1 ux1 l j) (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_less x1 x) (l_e_st_eq_landau_n_rt_less x x0).l_e_st_eq_landau_n_rt_rp_4152_t45 ksi z0 i x0 ux x1 ux1 l j x t) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0))).
+
+(* notion 2593 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t47 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in z0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).(l_e_st_eq_landau_n_rt_rp_4152_invapp ksi z0 i (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_less y x.λw:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).l_e_st_eq_landau_n_rt_rp_4152_t46 ksi z0 i x t y u v w) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (l_e_st_eq_landau_n_rt_more x z0))).
+
+(* notion 2594 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t48 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl y0 y0)) (l_e_st_eq_landau_n_rt_rp_4152_t15 ksi y0 uy) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x0) (l_e_st_eq_landau_n_rt_rp_4152_t23 ksi x0 lx) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_4152_t33 ksi x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_4152_inv ksi).l_e_st_eq_landau_n_rt_rp_4152_t47 ksi x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
+
+(* notion 2595 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t49 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_cutapp1b ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.l_e_st_eq_landau_n_rt_rp_4152_t48 ksi x0 lx x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
+
+(* notion 2596 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t50 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_cutapp1a ksi (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_4152_t49 ksi x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
+
+(* notion 2597 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_chi ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_4152_inv ksi) (l_e_st_eq_landau_n_rt_rp_4152_t50 ksi) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2598 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t51 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_tris l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 u0) (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) i (l_e_st_eq_landau_n_rt_ists2 u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) x0 j) : l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1))).
+
+(* notion 2599 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t52 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx x1 ux : l_e_st_eq_landau_n_rt_less x0 x1).
+
+(* notion 2600 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t53 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) z0 (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) l_e_st_eq_landau_n_rt_1rt (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1)) (l_e_st_eq_landau_n_rt_rp_4152_t51 ksi z0 lz x0 lx u0 lu i x1 ux j)) (l_e_st_eq_landau_n_rt_satz110c l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_satz105c x0 x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1) (l_e_st_eq_landau_n_rt_rp_4152_t52 ksi z0 lz x0 lx u0 lu i x1 ux j)) : l_e_st_eq_landau_n_rt_less z0 l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2601 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t54 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).λx1:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x1.λj:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x1).(l_e_st_eq_landau_n_rt_rp_lrtrpofrt l_e_st_eq_landau_n_rt_1rt z0 (l_e_st_eq_landau_n_rt_rp_4152_t53 ksi z0 lz x0 lx u0 lu i x1 ux j) : l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp z0).
+
+(* notion 2602 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_r1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).(l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_4152_inv ksi) (l_e_st_eq_landau_n_rt_rp_4152_t50 ksi) u0 lu : l_e_st_eq_landau_n_rt_in u0 (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
+
+(* notion 2603 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_r2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x0 u0).(l_e_st_eq_landau_n_rt_rp_4152_invapp ksi u0 (l_e_st_eq_landau_n_rt_rp_4152_r1 ksi z0 lz x0 lx u0 lu i) (l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_less y x.λw:l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt x).l_e_st_eq_landau_n_rt_rp_4152_t54 ksi z0 lz x0 lx u0 lu i x t w) : l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp z0).
+
+(* notion 2604 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_r3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) z0.(l_e_st_eq_landau_n_rt_rp_tsapp ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) z0 lz (l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_4152_r2 ksi z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp z0).
+
+(* notion 2605 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t55 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrte l_e_st_eq_landau_n_rt_1rt u0 lu : l_e_st_eq_landau_n_rt_less u0 l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2606 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t56 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.(l_e_st_eq_landau_n_rt_satz83 u0 l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_rp_4152_t55 ksi u0 lu) : l_e_st_eq_landau_n_rt_more l_e_st_eq_landau_n_rt_1rt u0).
+
+(* notion 2607 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t57 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.(l_e_st_eq_landau_n_rt_cutapp2b ksi x1 lx1 x2 ux2 : l_e_st_eq_landau_n_rt_more x2 x1).
+
+(* notion 2608 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t58 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_cutapp2a ksi x0 lx x2 ux2 : l_e_st_eq_landau_n_rt_less x0 x2).
+
+(* notion 2609 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t59 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_satz105f x0 x2 (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) (l_e_st_eq_landau_n_rt_rp_4152_t58 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2)).
+
+(* notion 2610 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t60 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0) (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0) i) (l_e_st_eq_landau_n_rt_rp_4152_t59 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2)).
+
+(* notion 2611 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t61 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_tr4is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) u0) x2) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x2) x2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1) (l_e_st_eq_landau_n_rt_distpt1 (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) u0 x2) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) u0) l_e_st_eq_landau_n_rt_1rt x2 (l_e_st_eq_landau_n_rt_satz101e l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu))) (l_e_st_eq_landau_n_rt_example1c x2) (l_e_st_eq_landau_n_rt_satz101f x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1)).
+
+(* notion 2612 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t62 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_satz96c (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_st_eq_landau_n_rt_ts u0 x2) (l_e_st_eq_landau_n_rt_rp_4152_t60 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_st_eq_landau_n_rt_ts u0 x2))).
+
+(* notion 2613 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t63 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_isless2 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x2) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_rp_4152_t61 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) (l_e_st_eq_landau_n_rt_rp_4152_t62 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1)).
+
+(* notion 2614 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t64 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts u0 x2) (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2))) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1) (l_e_st_eq_landau_n_rt_pl x1 (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2))) (l_e_st_eq_landau_n_rt_compl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_compl (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) x1) (l_e_st_eq_landau_n_rt_rp_4152_t63 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts u0 x2) (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2))) (l_e_st_eq_landau_n_rt_pl x1 (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)))).
+
+(* notion 2615 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t65 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_satz97c (l_e_st_eq_landau_n_rt_ts u0 x2) x1 (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_rp_4152_t64 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts u0 x2) x1).
+
+(* notion 2616 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t66 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_ts u0 x2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0) x2) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x2) x2 (l_e_st_eq_landau_n_rt_assts2 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0 x2) (l_e_st_eq_landau_n_rt_ists1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) u0) l_e_st_eq_landau_n_rt_1rt x2 (l_e_st_eq_landau_n_rt_satz110e l_e_st_eq_landau_n_rt_1rt u0)) (l_e_st_eq_landau_n_rt_example1c x2) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_ts u0 x2)) x2).
+
+(* notion 2617 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t67 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_ts u0 x2)) x2 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) x1) (l_e_st_eq_landau_n_rt_ov x1 u0) (l_e_st_eq_landau_n_rt_rp_4152_t66 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) (l_e_st_eq_landau_n_rt_satz141b x1 u0) (l_e_st_eq_landau_n_rt_satz105f (l_e_st_eq_landau_n_rt_ts u0 x2) x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt u0) (l_e_st_eq_landau_n_rt_rp_4152_t65 ksi u0 lu x0 lx x1 lx1 x2 ux2 i)) : l_e_st_eq_landau_n_rt_less x2 (l_e_st_eq_landau_n_rt_ov x1 u0)).
+
+(* notion 2618 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t68 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_rp_satz119a ksi x2 ux2 (l_e_st_eq_landau_n_rt_ov x1 u0) (l_e_st_eq_landau_n_rt_rp_4152_t67 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_ov x1 u0)).
+
+(* notion 2619 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t69 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_satz110e x1 u0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x1 u0) u0) x1).
+
+(* notion 2620 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t70 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ov x1 (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) x1) (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0))) (l_e_st_eq_landau_n_rt_satz110g x1 (l_e_st_eq_landau_n_rt_ov x1 u0) u0 (l_e_st_eq_landau_n_rt_rp_4152_t69 ksi u0 lu x0 lx x1 lx1 x2 ux2 i)) (l_e_st_eq_landau_n_rt_satz141c x1 (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_comts (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) x1) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts x1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)))).
+
+(* notion 2621 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t71 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_rp_4152_inv1 ksi (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_ov x1 u0) (l_e_st_eq_landau_n_rt_rp_4152_t68 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) x2 ux2 (l_e_st_eq_landau_n_rt_rp_4152_t67 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0))) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_rp_4152_inv ksi)).
+
+(* notion 2622 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t72 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_4152_inv ksi) (l_e_st_eq_landau_n_rt_rp_4152_t50 ksi) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_rp_4152_t71 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0))).
+
+(* notion 2623 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t73 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt ksi x1.λx2:l_e_st_eq_landau_n_rt_rat.λux2:l_e_st_eq_landau_n_rt_urt ksi x2.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn x2 x1 (l_e_st_eq_landau_n_rt_rp_4152_t57 ksi u0 lu x0 lx x1 lx1 x2 ux2)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).(l_e_st_eq_landau_n_rt_rp_lrtts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) u0 x1 lx1 (l_e_st_eq_landau_n_rt_ov l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_ov x1 u0)) (l_e_st_eq_landau_n_rt_rp_4152_t72 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) (l_e_st_eq_landau_n_rt_rp_4152_t70 ksi u0 lu x0 lx x1 lx1 x2 ux2 i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) u0).
+
+(* notion 2624 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t74 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_rp_satz132app ksi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) u0) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_urt ksi y.λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn y x (l_e_st_eq_landau_n_rt_cutapp2b ksi x t y u)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_mn l_e_st_eq_landau_n_rt_1rt u0 (l_e_st_eq_landau_n_rt_rp_4152_t56 ksi u0 lu)) x0).l_e_st_eq_landau_n_rt_rp_4152_t73 ksi u0 lu x0 lx x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) u0).
+
+(* notion 2625 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t75 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp u0.(l_e_st_eq_landau_n_rt_cutapp1a ksi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_4152_t74 ksi u0 lu x t) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) u0).
+
+(* notion 2626 *)
+definition l_e_st_eq_landau_n_rt_rp_4152_t76 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) l_e_st_eq_landau_n_rt_rp_1rp (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) x.l_e_st_eq_landau_n_rt_rp_4152_r3 ksi x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt l_e_st_eq_landau_n_rt_rp_1rp x.l_e_st_eq_landau_n_rt_rp_4152_t75 ksi x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_4152_chi ksi)) l_e_st_eq_landau_n_rt_rp_1rp).
+
+(* notion 2627 *)
+definition l_e_st_eq_landau_n_rt_rp_satz152 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_somei l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi t) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_4152_chi ksi) (l_e_st_eq_landau_n_rt_rp_4152_t76 ksi) : l_e_st_eq_landau_n_rt_rp_some (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi c) l_e_st_eq_landau_n_rt_rp_1rp)).
+
+(* notion 2628 *)
+definition l_e_st_eq_landau_n_rt_rp_4153_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more phi psi.(l_e_st_eq_landau_n_rt_rp_satz145d phi psi eta m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)).
+
+(* notion 2629 *)
+definition l_e_st_eq_landau_n_rt_rp_4153_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more phi psi.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_4153_t1 ksi eta phi psi m) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)).
+
+(* notion 2630 *)
+definition l_e_st_eq_landau_n_rt_rp_4153_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less phi psi.(l_e_st_eq_landau_n_rt_rp_satz145f phi psi eta l : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)).
+
+(* notion 2631 *)
+definition l_e_st_eq_landau_n_rt_rp_4153_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less phi psi.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_4153_t3 ksi eta phi psi l) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)).
+
+(* notion 2632 *)
+definition l_e_st_eq_landau_n_rt_rp_4153_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis phi psi.(l_or3_th1 (l_e_st_eq_landau_n_rt_rp_is phi psi) (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi) (l_e_st_eq_landau_n_rt_rp_satz123a phi psi) n : l_or (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi)).
+
+(* notion 2633 *)
+definition l_e_st_eq_landau_n_rt_rp_4153_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_nis phi psi.(l_orapp (l_e_st_eq_landau_n_rt_rp_more phi psi) (l_e_st_eq_landau_n_rt_rp_less phi psi) (l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_st_eq_landau_n_rt_rp_4153_t5 ksi eta phi psi n) (λt:l_e_st_eq_landau_n_rt_rp_more phi psi.l_e_st_eq_landau_n_rt_rp_4153_t2 ksi eta phi psi t) (λt:l_e_st_eq_landau_n_rt_rp_less phi psi.l_e_st_eq_landau_n_rt_rp_4153_t4 ksi eta phi psi t) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)).
+
+(* notion 2634 *)
+definition l_e_st_eq_landau_n_rt_rp_satz153b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λpsi:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta phi) ksi.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta psi) ksi.(l_imp_th7 (l_e_st_eq_landau_n_rt_rp_is phi psi) (l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_weli (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi)) (l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts eta phi) (l_e_st_eq_landau_n_rt_rp_ts eta psi) ksi i j)) (λt:l_e_st_eq_landau_n_rt_rp_nis phi psi.l_e_st_eq_landau_n_rt_rp_4153_t6 ksi eta phi psi t) : l_e_st_eq_landau_n_rt_rp_is phi psi).
+
+(* notion 2635 *)
+definition l_e_st_eq_landau_n_rt_rp_4153_chi ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λtau:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta tau) l_e_st_eq_landau_n_rt_rp_1rp.(l_e_st_eq_landau_n_rt_rp_ts tau ksi : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2636 *)
+definition l_e_st_eq_landau_n_rt_rp_4153_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λtau:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta tau) l_e_st_eq_landau_n_rt_rp_1rp.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_4153_chi ksi eta tau i)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts eta tau) ksi) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp ksi) ksi (l_e_st_eq_landau_n_rt_rp_assts2 eta tau ksi) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_ts eta tau) l_e_st_eq_landau_n_rt_rp_1rp ksi i) (l_e_st_eq_landau_n_rt_rp_satz151b ksi) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_4153_chi ksi eta tau i)) ksi).
+
+(* notion 2637 *)
+definition l_e_st_eq_landau_n_rt_rp_4153_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λtau:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta tau) l_e_st_eq_landau_n_rt_rp_1rp.(l_somei l_e_st_eq_landau_n_rt_cut (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi) (l_e_st_eq_landau_n_rt_rp_4153_chi ksi eta tau i) (l_e_st_eq_landau_n_rt_rp_4153_t7 ksi eta tau i) : l_e_st_eq_landau_n_rt_rp_some (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi)).
+
+(* notion 2638 *)
+definition l_e_st_eq_landau_n_rt_rp_satz153a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_someapp l_e_st_eq_landau_n_rt_cut (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_satz152 eta) (l_e_st_eq_landau_n_rt_rp_some (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi)) (λc:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) l_e_st_eq_landau_n_rt_rp_1rp.l_e_st_eq_landau_n_rt_rp_4153_t8 ksi eta c t) : l_e_st_eq_landau_n_rt_rp_some (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi)).
+
+(* notion 2639 *)
+definition l_e_st_eq_landau_n_rt_rp_4153_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(λc:l_e_st_eq_landau_n_rt_cut.λd:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi.λu:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta d) ksi.l_e_st_eq_landau_n_rt_rp_satz153b ksi eta c d t u : l_e_amone l_e_st_eq_landau_n_rt_cut (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi)).
+
+(* notion 2640 *)
+definition l_e_st_eq_landau_n_rt_rp_satz153 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_onei l_e_st_eq_landau_n_rt_cut (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi) (l_e_st_eq_landau_n_rt_rp_4153_t9 ksi eta) (l_e_st_eq_landau_n_rt_rp_satz153a ksi eta) : l_e_st_eq_landau_n_rt_rp_one (λc:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta c) ksi)).
+
+(* notion 2641 *)
+definition l_e_st_eq_landau_n_rt_rp_ov ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_ind l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta a) ksi) (l_e_st_eq_landau_n_rt_rp_satz153 ksi eta) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2642 *)
+definition l_e_st_eq_landau_n_rt_rp_satz153c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_oneax l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta a) ksi) (l_e_st_eq_landau_n_rt_rp_satz153 ksi eta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_ov ksi eta)) ksi).
+
+(* notion 2643 *)
+definition l_e_st_eq_landau_n_rt_rp_satz153d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_ov ksi eta)) ksi (l_e_st_eq_landau_n_rt_rp_satz153c ksi eta) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_ov ksi eta))).
+
+(* notion 2644 *)
+definition l_e_st_eq_landau_n_rt_rp_satz153e ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ov ksi eta) eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_ov ksi eta)) ksi (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_ov ksi eta) eta) (l_e_st_eq_landau_n_rt_rp_satz153c ksi eta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ov ksi eta) eta) ksi).
+
+(* notion 2645 *)
+definition l_e_st_eq_landau_n_rt_rp_satz153f ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ov ksi eta) eta) ksi (l_e_st_eq_landau_n_rt_rp_satz153e ksi eta) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ov ksi eta) eta)).
+
+(* notion 2646 *)
+definition l_e_st_eq_landau_n_rt_rp_satz153g ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λphi:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts eta phi) ksi.(l_e_st_eq_landau_n_rt_rp_satz153b ksi eta phi (l_e_st_eq_landau_n_rt_rp_ov ksi eta) i (l_e_st_eq_landau_n_rt_rp_satz153c ksi eta) : l_e_st_eq_landau_n_rt_rp_is phi (l_e_st_eq_landau_n_rt_rp_ov ksi eta)).
+
+(* notion 2647 *)
+definition l_e_st_eq_landau_n_rt_rp_ratrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_image l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi : Prop).
+
+(* notion 2648 *)
+definition l_e_st_eq_landau_n_rt_rp_ratrpi ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_imagei l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) x0 : l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).
+
+(* notion 2649 *)
+definition l_e_st_eq_landau_n_rt_rp_rpofnt ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rtofn x) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2650 *)
+definition l_e_st_eq_landau_n_rt_rp_natrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) ksi : Prop).
+
+(* notion 2651 *)
+definition l_e_st_eq_landau_n_rt_rp_natrpi ≝ λx:l_e_st_eq_landau_n_nat.(l_e_imagei l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt y) x : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofnt x)).
+
+(* notion 2652 *)
+definition l_e_st_eq_landau_n_rt_rp_iii5_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp ksi.λx:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofnt x).(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofrt y)) (l_e_st_eq_landau_n_rt_rtofn x) i : l_e_st_eq_landau_n_rt_rp_ratrp ksi).
+
+(* notion 2653 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmaiii5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_someapp l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofnt x)) n (l_e_st_eq_landau_n_rt_rp_ratrp ksi) (λx:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofnt x).l_e_st_eq_landau_n_rt_rp_iii5_t1 ksi n x t) : l_e_st_eq_landau_n_rt_rp_ratrp ksi).
+
+(* notion 2654 *)
+definition l_e_st_eq_landau_n_rt_rp_5154_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrt x0 y0 (l_e_st_eq_landau_n_rt_satz82 x0 y0 m) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0).
+
+(* notion 2655 *)
+definition l_e_st_eq_landau_n_rt_rp_5154_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_rp_urtrpofrt y0 y0 (l_e_st_eq_landau_n_rt_moreisi2 y0 y0 (l_e_refis l_e_st_eq_landau_n_rt_rat y0)) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) y0).
+
+(* notion 2656 *)
+definition l_e_st_eq_landau_n_rt_rp_5154_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_andi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) y0) (l_e_st_eq_landau_n_rt_rp_5154_t1 x0 y0 m) (l_e_st_eq_landau_n_rt_rp_5154_t2 x0 y0 m) : l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) y0)).
+
+(* notion 2657 *)
+definition l_e_st_eq_landau_n_rt_rp_satz154a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) x) (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) x)) y0 (l_e_st_eq_landau_n_rt_rp_5154_t3 x0 y0 m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
+
+(* notion 2658 *)
+definition l_e_st_eq_landau_n_rt_rp_satz154b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_isf l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) x0 y0 i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
+
+(* notion 2659 *)
+definition l_e_st_eq_landau_n_rt_rp_satz154c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_satz154a y0 x0 (l_e_st_eq_landau_n_rt_satz83 x0 y0 l)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
+
+(* notion 2660 *)
+definition l_e_st_eq_landau_n_rt_rp_5154_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz81a x0 y0 : l_or3 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0)).
+
+(* notion 2661 *)
+definition l_e_st_eq_landau_n_rt_rp_5154_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) : l_ec3 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
+
+(* notion 2662 *)
+definition l_e_st_eq_landau_n_rt_rp_satz154d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_ec3_th11 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_5154_t4 x0 y0) (l_e_st_eq_landau_n_rt_rp_5154_t5 x0 y0) (λu:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_rp_satz154b x0 y0 u) (λu:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_rp_satz154a x0 y0 u) (λu:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_rp_satz154c x0 y0 u) m : l_e_st_eq_landau_n_rt_more x0 y0).
+
+(* notion 2663 *)
+definition l_e_st_eq_landau_n_rt_rp_satz154e ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_ec3_th10 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_5154_t4 x0 y0) (l_e_st_eq_landau_n_rt_rp_5154_t5 x0 y0) (λu:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_rp_satz154b x0 y0 u) (λu:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_rp_satz154a x0 y0 u) (λu:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_rp_satz154c x0 y0 u) i : l_e_st_eq_landau_n_rt_is x0 y0).
+
+(* notion 2664 *)
+definition l_e_st_eq_landau_n_rt_rp_satz154f ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_ec3_th12 (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_more x0 y0) (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_5154_t4 x0 y0) (l_e_st_eq_landau_n_rt_rp_5154_t5 x0 y0) (λu:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_rp_satz154b x0 y0 u) (λu:l_e_st_eq_landau_n_rt_more x0 y0.l_e_st_eq_landau_n_rt_rp_satz154a x0 y0 u) (λu:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_rp_satz154c x0 y0 u) l : l_e_st_eq_landau_n_rt_less x0 y0).
+
+(* notion 2665 *)
+definition l_e_st_eq_landau_n_rt_rp_iii5_t2 ≝ (λx:l_e_st_eq_landau_n_rt_rat.λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt y).l_e_st_eq_landau_n_rt_rp_satz154e x y t : l_e_injective l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x)).
+
+(* notion 2666 *)
+definition l_e_st_eq_landau_n_rt_rp_isrterp ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_rp_satz154b x0 y0 i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
+
+(* notion 2667 *)
+definition l_e_st_eq_landau_n_rt_rp_isrtirp ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_st_eq_landau_n_rt_rp_satz154e x0 y0 i : l_e_st_eq_landau_n_rt_is x0 y0).
+
+(* notion 2668 *)
+definition l_e_st_eq_landau_n_rt_rp_rtofrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_soft l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 ksi rtksi : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2669 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpert ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λrteta:l_e_st_eq_landau_n_rt_rp_ratrp eta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isinv l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 ksi rtksi eta rteta i : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi) (l_e_st_eq_landau_n_rt_rp_rtofrp eta rteta)).
+
+(* notion 2670 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpirt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λrteta:l_e_st_eq_landau_n_rt_rp_ratrp eta.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi) (l_e_st_eq_landau_n_rt_rp_rtofrp eta rteta).(l_e_isinve l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 ksi rtksi eta rteta i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
+
+(* notion 2671 *)
+definition l_e_st_eq_landau_n_rt_rp_isrtrp1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_isst1 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 x0 : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_rp_rtofrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0))).
+
+(* notion 2672 *)
+definition l_e_st_eq_landau_n_rt_rp_isrtrp2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_isst2 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 x0 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtofrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0)) x0).
+
+(* notion 2673 *)
+definition l_e_st_eq_landau_n_rt_rp_isrprt1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_ists1 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 ksi rtksi : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi))).
+
+(* notion 2674 *)
+definition l_e_st_eq_landau_n_rt_rp_isrprt2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_ists2 l_e_st_eq_landau_n_rt_rat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_rpofrt x) l_e_st_eq_landau_n_rt_rp_iii5_t2 ksi rtksi : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi)) ksi).
+
+(* notion 2675 *)
+definition l_e_st_eq_landau_n_rt_rp_isnterp ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (λz:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt z) x y i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)).
+
+(* notion 2676 *)
+definition l_e_st_eq_landau_n_rt_rp_isntirp ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y).(l_e_st_eq_landau_n_rt_isnirt x y (l_e_st_eq_landau_n_rt_rp_isrtirp (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) i) : l_e_st_eq_landau_n_is x y).
+
+(* notion 2677 *)
+definition l_e_st_eq_landau_n_rt_rp_iii5_t3 ≝ (λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y).l_e_st_eq_landau_n_rt_rp_isntirp x y t : l_e_injective l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x)).
+
+(* notion 2678 *)
+definition l_e_st_eq_landau_n_rt_rp_ntofrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λntksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_e_soft l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) l_e_st_eq_landau_n_rt_rp_iii5_t3 ksi ntksi : l_e_st_eq_landau_n_nat).
+
+(* notion 2679 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpent ≝ λksi:l_e_st_eq_landau_n_rt_cut.λntksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λnteta:l_e_st_eq_landau_n_rt_rp_natrp eta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isinv l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) l_e_st_eq_landau_n_rt_rp_iii5_t3 ksi ntksi eta nteta i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_ntofrp ksi ntksi) (l_e_st_eq_landau_n_rt_rp_ntofrp eta nteta)).
+
+(* notion 2680 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpint ≝ λksi:l_e_st_eq_landau_n_rt_cut.λntksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λnteta:l_e_st_eq_landau_n_rt_rp_natrp eta.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_ntofrp ksi ntksi) (l_e_st_eq_landau_n_rt_rp_ntofrp eta nteta).(l_e_isinve l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) l_e_st_eq_landau_n_rt_rp_iii5_t3 ksi ntksi eta nteta i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
+
+(* notion 2681 *)
+definition l_e_st_eq_landau_n_rt_rp_isntrp1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_isst1 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt y) l_e_st_eq_landau_n_rt_rp_iii5_t3 x : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x))).
+
+(* notion 2682 *)
+definition l_e_st_eq_landau_n_rt_rp_isntrp2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_isst2 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt y) l_e_st_eq_landau_n_rt_rp_iii5_t3 x : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x)) x).
+
+(* notion 2683 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpnt1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λntksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_e_ists1 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) l_e_st_eq_landau_n_rt_rp_iii5_t3 ksi ntksi : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_ntofrp ksi ntksi))).
+
+(* notion 2684 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpnt2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λntksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_e_ists2 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_rpofnt x) l_e_st_eq_landau_n_rt_rp_iii5_t3 ksi ntksi : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_ntofrp ksi ntksi)) ksi).
+
+(* notion 2685 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrte x0 u0 lu : l_e_st_eq_landau_n_rt_less u0 x0).
+
+(* notion 2686 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t2 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrte y0 v0 lv : l_e_st_eq_landau_n_rt_less v0 y0).
+
+(* notion 2687 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t3 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl u0 v0).(l_e_st_eq_landau_n_rt_satz98a u0 x0 v0 y0 (l_e_st_eq_landau_n_rt_rp_5155_t1 x0 y0 z0 lz u0 lu v0 lv i) (l_e_st_eq_landau_n_rt_rp_5155_t2 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_pl u0 v0) (l_e_st_eq_landau_n_rt_pl x0 y0)).
+
+(* notion 2688 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t4 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl u0 v0).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_pl u0 v0) z0 (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_pl u0 v0) i) (l_e_st_eq_landau_n_rt_rp_5155_t3 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
+
+(* notion 2689 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t5 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrt (l_e_st_eq_landau_n_rt_pl x0 y0) z0 (l_e_st_eq_landau_n_rt_rp_5155_t4 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) z0).
+
+(* notion 2690 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t6 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.(l_e_st_eq_landau_n_rt_rp_plapp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) z0 lz (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_pl x y).l_e_st_eq_landau_n_rt_rp_5155_t5 x0 y0 z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) z0).
+
+(* notion 2691 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t7 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrte (l_e_st_eq_landau_n_rt_pl x0 y0) u0 lu : l_e_st_eq_landau_n_rt_less u0 (l_e_st_eq_landau_n_rt_pl x0 y0)).
+
+(* notion 2692 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_u01 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_st_eq_landau_n_rt_ov u0 (l_e_st_eq_landau_n_rt_pl x0 y0) : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2693 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t8 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_st_eq_landau_n_rt_isless12 u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_satz110f u0 (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_example1d (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_rp_5155_t7 x0 y0 u0 lu) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0))).
+
+(* notion 2694 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t9 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_st_eq_landau_n_rt_satz106c (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) l_e_st_eq_landau_n_rt_1rt (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_5155_t8 x0 y0 u0 lu) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2695 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t10 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_tris l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_pl x0 y0) (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu))) (l_e_st_eq_landau_n_rt_satz110d u0 (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_disttp1 x0 y0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)))).
+
+(* notion 2696 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t11 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 l_e_st_eq_landau_n_rt_1rt.(l_e_st_eq_landau_n_rt_isless12 (l_e_st_eq_landau_n_rt_ts y0 x0) (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt x0) x0 (l_e_st_eq_landau_n_rt_comts y0 x0) (l_e_st_eq_landau_n_rt_example1c x0) (l_e_st_eq_landau_n_rt_satz105c y0 l_e_st_eq_landau_n_rt_1rt x0 l) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts x0 y0) x0).
+
+(* notion 2697 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t12 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 l_e_st_eq_landau_n_rt_1rt.(l_e_st_eq_landau_n_rt_rp_lrtrpofrt x0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_rp_5155_t11 x0 y0 l) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 2698 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t13 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) u0.(l_e_st_eq_landau_n_rt_rp_lrtpl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) u0 (l_e_st_eq_landau_n_rt_ts x0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_rp_5155_t12 x0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) (l_e_st_eq_landau_n_rt_rp_5155_t9 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_rp_5155_t12 y0 (l_e_st_eq_landau_n_rt_rp_5155_u01 x0 y0 u0 lu) (l_e_st_eq_landau_n_rt_rp_5155_t9 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_rp_5155_t10 x0 y0 u0 lu) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) u0).
+
+(* notion 2699 *)
+definition l_e_st_eq_landau_n_rt_rp_satz155a ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) x.l_e_st_eq_landau_n_rt_rp_5155_t13 x0 y0 x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) x.l_e_st_eq_landau_n_rt_rp_5155_t6 x0 y0 x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 y0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
+
+(* notion 2700 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t14 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_satz101f x0 y0 m : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0)).
+
+(* notion 2701 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t15 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_isrterp x0 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) (l_e_st_eq_landau_n_rt_rp_5155_t14 x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_satz155a (l_e_st_eq_landau_n_rt_mn x0 y0 m) y0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
+
+(* notion 2702 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t16 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m))) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m))) (l_e_st_eq_landau_n_rt_rp_5155_t15 x0 y0 m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m))) (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).
+
+(* notion 2703 *)
+definition l_e_st_eq_landau_n_rt_rp_satz155b ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_more x0 y0.(l_e_st_eq_landau_n_rt_rp_satz140g (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_satz154a x0 y0 m) (l_e_st_eq_landau_n_rt_rp_5155_t16 x0 y0 m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn x0 y0 m)) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_satz154a x0 y0 m))).
+
+(* notion 2704 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t17 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrte x0 u0 lu : l_e_st_eq_landau_n_rt_less u0 x0).
+
+(* notion 2705 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t18 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrte y0 v0 lv : l_e_st_eq_landau_n_rt_less v0 y0).
+
+(* notion 2706 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t19 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts u0 v0).(l_e_st_eq_landau_n_rt_satz107a u0 x0 v0 y0 (l_e_st_eq_landau_n_rt_rp_5155_t17 x0 y0 z0 lz u0 lu v0 lv i) (l_e_st_eq_landau_n_rt_rp_5155_t18 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts u0 v0) (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 2707 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t20 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts u0 v0).(l_e_st_eq_landau_n_rt_isless1 (l_e_st_eq_landau_n_rt_ts u0 v0) z0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_symis l_e_st_eq_landau_n_rt_rat z0 (l_e_st_eq_landau_n_rt_ts u0 v0) i) (l_e_st_eq_landau_n_rt_rp_5155_t19 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_less z0 (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 2708 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t21 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) u0.λv0:l_e_st_eq_landau_n_rt_rat.λlv:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) v0.λi:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts u0 v0).(l_e_st_eq_landau_n_rt_rp_lrtrpofrt (l_e_st_eq_landau_n_rt_ts x0 y0) z0 (l_e_st_eq_landau_n_rt_rp_5155_t20 x0 y0 z0 lz u0 lu v0 lv i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) z0).
+
+(* notion 2709 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t22 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) z0.(l_e_st_eq_landau_n_rt_rp_tsapp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) z0 lz (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt y0) y.λv:l_e_st_eq_landau_n_rt_is z0 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_5155_t21 x0 y0 z0 lz x t y u v) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) z0).
+
+(* notion 2710 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t23 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrte (l_e_st_eq_landau_n_rt_ts x0 y0) u0 lu : l_e_st_eq_landau_n_rt_less u0 (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 2711 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t24 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_ande1 (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)) a : l_e_st_eq_landau_n_rt_less u0 u1).
+
+(* notion 2712 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t25 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_ande2 (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)) a : l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 2713 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t26 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_st_eq_landau_n_rt_isless12 u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u0 u1) u1) u1 (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt u1) (l_e_st_eq_landau_n_rt_satz110f u0 u1) (l_e_st_eq_landau_n_rt_example1d u1) (l_e_st_eq_landau_n_rt_rp_5155_t24 x0 y0 u0 lu u1 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u0 u1) u1) (l_e_st_eq_landau_n_rt_ts l_e_st_eq_landau_n_rt_1rt u1)).
+
+(* notion 2714 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t27 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_st_eq_landau_n_rt_satz106c (l_e_st_eq_landau_n_rt_ov u0 u1) l_e_st_eq_landau_n_rt_1rt u1 (l_e_st_eq_landau_n_rt_rp_5155_t26 x0 y0 u0 lu u1 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ov u0 u1) l_e_st_eq_landau_n_rt_1rt).
+
+(* notion 2715 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t28 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_st_eq_landau_n_rt_isless1 u1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) y0) (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_satz110f u1 y0) (l_e_st_eq_landau_n_rt_rp_5155_t25 x0 y0 u0 lu u1 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) y0) (l_e_st_eq_landau_n_rt_ts x0 y0)).
+
+(* notion 2716 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t29 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_st_eq_landau_n_rt_satz106c (l_e_st_eq_landau_n_rt_ov u1 y0) x0 y0 (l_e_st_eq_landau_n_rt_rp_5155_t28 x0 y0 u0 lu u1 a) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ov u1 y0) x0).
+
+(* notion 2717 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t30 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_tr3is l_e_st_eq_landau_n_rt_rat u0 (l_e_st_eq_landau_n_rt_ts u1 (l_e_st_eq_landau_n_rt_ov u0 u1)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) y0) (l_e_st_eq_landau_n_rt_ov u0 u1)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov u0 u1))) (l_e_st_eq_landau_n_rt_satz110d u0 u1) (l_e_st_eq_landau_n_rt_ists1 u1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) y0) (l_e_st_eq_landau_n_rt_ov u0 u1) (l_e_st_eq_landau_n_rt_satz110f u1 y0)) (l_e_st_eq_landau_n_rt_assts1 (l_e_st_eq_landau_n_rt_ov u1 y0) y0 (l_e_st_eq_landau_n_rt_ov u0 u1)) : l_e_st_eq_landau_n_rt_is u0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov u1 y0) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov u0 u1)))).
+
+(* notion 2718 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t31 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.λu1:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_less u0 u1) (l_e_st_eq_landau_n_rt_less u1 (l_e_st_eq_landau_n_rt_ts x0 y0)).(l_e_st_eq_landau_n_rt_rp_lrtts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) u0 (l_e_st_eq_landau_n_rt_ov u1 y0) (l_e_st_eq_landau_n_rt_rp_lrtrpofrt x0 (l_e_st_eq_landau_n_rt_ov u1 y0) (l_e_st_eq_landau_n_rt_rp_5155_t29 x0 y0 u0 lu u1 a)) (l_e_st_eq_landau_n_rt_ts y0 (l_e_st_eq_landau_n_rt_ov u0 u1)) (l_e_st_eq_landau_n_rt_rp_5155_t12 y0 (l_e_st_eq_landau_n_rt_ov u0 u1) (l_e_st_eq_landau_n_rt_rp_5155_t27 x0 y0 u0 lu u1 a)) (l_e_st_eq_landau_n_rt_rp_5155_t30 x0 y0 u0 lu u1 a) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) u0).
+
+(* notion 2719 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t32 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) u0.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_less u0 x) (l_e_st_eq_landau_n_rt_less x (l_e_st_eq_landau_n_rt_ts x0 y0))) (l_e_st_eq_landau_n_rt_satz91 u0 (l_e_st_eq_landau_n_rt_ts x0 y0) (l_e_st_eq_landau_n_rt_rp_5155_t23 x0 y0 u0 lu)) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) u0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_less u0 x) (l_e_st_eq_landau_n_rt_less x (l_e_st_eq_landau_n_rt_ts x0 y0)).l_e_st_eq_landau_n_rt_rp_5155_t31 x0 y0 u0 lu x t) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) u0).
+
+(* notion 2720 *)
+definition l_e_st_eq_landau_n_rt_rp_satz155c ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_isi1 (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) x.l_e_st_eq_landau_n_rt_rp_5155_t32 x0 y0 x t) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) x.l_e_st_eq_landau_n_rt_rp_5155_t22 x0 y0 x t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x0 y0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
+
+(* notion 2721 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t33 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_satz110f x0 y0 : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0)).
+
+(* notion 2722 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t34 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_isrterp x0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_ov x0 y0) y0) (l_e_st_eq_landau_n_rt_rp_5155_t33 x0 y0)) (l_e_st_eq_landau_n_rt_rp_satz155c (l_e_st_eq_landau_n_rt_ov x0 y0) y0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
+
+(* notion 2723 *)
+definition l_e_st_eq_landau_n_rt_rp_5155_t35 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0))) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0))) (l_e_st_eq_landau_n_rt_rp_5155_t34 x0 y0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0))) (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).
+
+(* notion 2724 *)
+definition l_e_st_eq_landau_n_rt_rp_satz155d ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_satz153g (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0)) (l_e_st_eq_landau_n_rt_rp_5155_t35 x0 y0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ov x0 y0)) (l_e_st_eq_landau_n_rt_rp_ov (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0))).
+
+(* notion 2725 *)
+definition l_e_st_eq_landau_n_rt_rp_satz155e ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)) (l_e_st_eq_landau_n_rt_rp_isrterp (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_satz112h x y))) (l_e_st_eq_landau_n_rt_rp_satz155a (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y))).
+
+(* notion 2726 *)
+definition l_e_st_eq_landau_n_rt_rp_satz155f ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)) (l_e_st_eq_landau_n_rt_rp_isrterp (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_satz112j x y))) (l_e_st_eq_landau_n_rt_rp_satz155c (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y))).
+
+(* notion 2727 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_natt ≝ (l_e_ot l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) : Type[0]).
+
+(* notion 2728 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_nttofrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_e_out l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) ksi nksi : l_e_st_eq_landau_n_rt_rp_nt_natt).
+
+(* notion 2729 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_is ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_is l_e_st_eq_landau_n_rt_rp_nt_natt xt yt : Prop).
+
+(* notion 2730 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_nis ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_not (l_e_st_eq_landau_n_rt_rp_nt_is xt yt) : Prop).
+
+(* notion 2731 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.Prop.(l_all l_e_st_eq_landau_n_rt_rp_nt_natt p : Prop).
+
+(* notion 2732 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.Prop.(l_some l_e_st_eq_landau_n_rt_rp_nt_natt p : Prop).
+
+(* notion 2733 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.Prop.(l_e_one l_e_st_eq_landau_n_rt_rp_nt_natt p : Prop).
+
+(* notion 2734 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_in ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_esti l_e_st_eq_landau_n_rt_rp_nt_natt xt st : Prop).
+
+(* notion 2735 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_rpofntt ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_in l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) xt : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2736 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_natrpi ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_inp l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) xt : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt)).
+
+(* notion 2737 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isrpentt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λneta:l_e_st_eq_landau_n_rt_rp_natrp eta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isouti l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) ksi nksi eta neta i : l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofrp ksi nksi) (l_e_st_eq_landau_n_rt_rp_nt_nttofrp eta neta)).
+
+(* notion 2738 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isrpintt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λneta:l_e_st_eq_landau_n_rt_rp_natrp eta.λi:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofrp ksi nksi) (l_e_st_eq_landau_n_rt_rp_nt_nttofrp eta neta).(l_e_isoute l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) ksi nksi eta neta i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
+
+(* notion 2739 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isntterp ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_rt_rp_nt_is xt yt.(l_e_isini l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) xt yt i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt yt)).
+
+(* notion 2740 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isnttirp ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt yt).(l_e_isine l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) xt yt i : l_e_st_eq_landau_n_rt_rp_nt_is xt yt).
+
+(* notion 2741 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isrpntt1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnksi:l_e_st_eq_landau_n_rt_rp_natrp ksi.(l_e_isinout l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) ksi nksi : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_nt_rpofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofrp ksi nksi))).
+
+(* notion 2742 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isnttrp1 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_isoutin l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) xt : l_e_st_eq_landau_n_rt_rp_nt_is xt (l_e_st_eq_landau_n_rt_rp_nt_nttofrp (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt))).
+
+(* notion 2743 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_nttofnt ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_nt_nttofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x) : l_e_st_eq_landau_n_rt_rp_nt_natt).
+
+(* notion 2744 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isntentt ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_st_eq_landau_n_rt_rp_nt_isrpentt (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) (l_e_st_eq_landau_n_rt_rp_natrpi y) (l_e_st_eq_landau_n_rt_rp_isnterp x y i) : l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x) (l_e_st_eq_landau_n_rt_rp_nt_nttofnt y)).
+
+(* notion 2745 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isntintt ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x) (l_e_st_eq_landau_n_rt_rp_nt_nttofnt y).(l_e_st_eq_landau_n_rt_rp_isntirp x y (l_e_st_eq_landau_n_rt_rp_nt_isrpintt (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) (l_e_st_eq_landau_n_rt_rp_natrpi y) i) : l_e_st_eq_landau_n_is x y).
+
+(* notion 2746 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_ntofntt ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt) : l_e_st_eq_landau_n_nat).
+
+(* notion 2747 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isnttent ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_rt_rp_nt_is xt yt.(l_e_st_eq_landau_n_rt_rp_isrpent (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt yt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi yt) (l_e_st_eq_landau_n_rt_rp_nt_isntterp xt yt i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt yt)).
+
+(* notion 2748 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isnttint ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt yt).(l_e_st_eq_landau_n_rt_rp_nt_isnttirp xt yt (l_e_st_eq_landau_n_rt_rp_isrpint (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt yt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi yt) i) : l_e_st_eq_landau_n_rt_rp_nt_is xt yt).
+
+(* notion 2749 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_iii5_t5 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_nt_isrpntt1 (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x))).
+
+(* notion 2750 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_iii5_t6 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_isrpent (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x) (l_e_st_eq_landau_n_rt_rp_nt_rpofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) (l_e_st_eq_landau_n_rt_rp_nt_natrpi (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) (l_e_st_eq_landau_n_rt_rp_nt_iii5_t5 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x)) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x))).
+
+(* notion 2751 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isntntt1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_natrpi x)) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) (l_e_st_eq_landau_n_rt_rp_isntrp1 x) (l_e_st_eq_landau_n_rt_rp_nt_iii5_t6 x) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x))).
+
+(* notion 2752 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_iii5_t7 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_rt_rp_isrpnt1 (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt))).
+
+(* notion 2753 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_iii5_t8 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_rt_rp_nt_isrpentt (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_rt_rp_natrpi (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_rt_rp_nt_iii5_t7 xt) : l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofrp (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt)) (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt))).
+
+(* notion 2754 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isnttnt1 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_tris l_e_st_eq_landau_n_rt_rp_nt_natt xt (l_e_st_eq_landau_n_rt_rp_nt_nttofrp (l_e_st_eq_landau_n_rt_rp_nt_rpofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_natrpi xt)) (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_rt_rp_nt_isnttrp1 xt) (l_e_st_eq_landau_n_rt_rp_nt_iii5_t8 xt) : l_e_st_eq_landau_n_rt_rp_nt_is xt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt))).
+
+(* notion 2755 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isntntt2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) (l_e_st_eq_landau_n_rt_rp_nt_isntntt1 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) x).
+
+(* notion 2756 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_isnttnt2 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_symis l_e_st_eq_landau_n_rt_rp_nt_natt xt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_rt_rp_nt_isnttnt1 xt) : l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) xt).
+
+(* notion 2757 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_1t ≝ (l_e_st_eq_landau_n_rt_rp_nt_nttofnt l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_rt_rp_nt_natt).
+
+(* notion 2758 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_suct ≝ (λx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt x)) : Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_natt).
+
+(* notion 2759 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_5156_t1 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λj:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct xt) l_e_st_eq_landau_n_rt_rp_nt_1t.(l_e_st_eq_landau_n_rt_rp_nt_isntintt (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) l_e_st_eq_landau_n_1 j : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) l_e_st_eq_landau_n_1).
+
+(* notion 2760 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_satz156a ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct xt) l_e_st_eq_landau_n_rt_rp_nt_1t) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ax3 (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (λt:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct xt) l_e_st_eq_landau_n_rt_rp_nt_1t.l_e_st_eq_landau_n_rt_rp_nt_5156_t1 xt t) : l_e_st_eq_landau_n_rt_rp_nt_nis (l_e_st_eq_landau_n_rt_rp_nt_suct xt) l_e_st_eq_landau_n_rt_rp_nt_1t).
+
+(* notion 2761 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_5156_t2 ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct xt) (l_e_st_eq_landau_n_rt_rp_nt_suct yt).(l_e_st_eq_landau_n_rt_rp_nt_isntintt (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt yt)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_nt_ntofntt yt))).
+
+(* notion 2762 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_satz156b ≝ λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.λyt:l_e_st_eq_landau_n_rt_rp_nt_natt.λi:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct xt) (l_e_st_eq_landau_n_rt_rp_nt_suct yt).(l_e_st_eq_landau_n_rt_rp_nt_isnttint xt yt (l_e_st_eq_landau_n_ax4 (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt yt) (l_e_st_eq_landau_n_rt_rp_nt_5156_t2 xt yt i)) : l_e_st_eq_landau_n_rt_rp_nt_is xt yt).
+
+(* notion 2763 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_cond1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_rt_rp_nt_in l_e_st_eq_landau_n_rt_rp_nt_1t st : Prop).
+
+(* notion 2764 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_cond2 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_rt_rp_nt_all (λx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_imp (l_e_st_eq_landau_n_rt_rp_nt_in x st) (l_e_st_eq_landau_n_rt_rp_nt_in (l_e_st_eq_landau_n_rt_rp_nt_suct x) st)) : Prop).
+
+(* notion 2765 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λc1:l_e_st_eq_landau_n_rt_rp_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_rp_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_nt_in (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x) st : Prop).
+
+(* notion 2766 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_5156_t3 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λc1:l_e_st_eq_landau_n_rt_rp_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_rp_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 st c1 c2 x.(c2 (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x) p : l_e_st_eq_landau_n_rt_rp_nt_in (l_e_st_eq_landau_n_rt_rp_nt_suct (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) st).
+
+(* notion 2767 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_5156_t4 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λc1:l_e_st_eq_landau_n_rt_rp_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_rp_nt_cond2 st.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 st c1 c2 x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_nt_in (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_suc t)) st) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt (l_e_st_eq_landau_n_rt_rp_nt_nttofnt x)) x (l_e_st_eq_landau_n_rt_rp_nt_5156_t3 st c1 c2 x p) (l_e_st_eq_landau_n_rt_rp_nt_isntntt2 x) : l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 st c1 c2 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 2768 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_5156_t5 ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λc1:l_e_st_eq_landau_n_rt_rp_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_rp_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 st c1 c2 t) c1 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_nt_5156_prop1 st c1 c2 t.l_e_st_eq_landau_n_rt_rp_nt_5156_t4 st c1 c2 t u) (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt) : l_e_st_eq_landau_n_rt_rp_nt_in (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) st).
+
+(* notion 2769 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_satz156c ≝ λst:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λc1:l_e_st_eq_landau_n_rt_rp_nt_cond1 st.λc2:l_e_st_eq_landau_n_rt_rp_nt_cond2 st.λxt:l_e_st_eq_landau_n_rt_rp_nt_natt.(l_e_isp l_e_st_eq_landau_n_rt_rp_nt_natt (λt:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_in t st) (l_e_st_eq_landau_n_rt_rp_nt_nttofnt (l_e_st_eq_landau_n_rt_rp_nt_ntofntt xt)) xt (l_e_st_eq_landau_n_rt_rp_nt_5156_t5 st c1 c2 xt) (l_e_st_eq_landau_n_rt_rp_nt_isnttnt2 xt) : l_e_st_eq_landau_n_rt_rp_nt_in xt st).
+
+(* notion 2770 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_ax3t ≝ (λx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_satz156a x : Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_nis (l_e_st_eq_landau_n_rt_rp_nt_suct x) l_e_st_eq_landau_n_rt_rp_nt_1t).
+
+(* notion 2771 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_ax4t ≝ (λx:l_e_st_eq_landau_n_rt_rp_nt_natt.λy:l_e_st_eq_landau_n_rt_rp_nt_natt.λu:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct x) (l_e_st_eq_landau_n_rt_rp_nt_suct y).l_e_st_eq_landau_n_rt_rp_nt_satz156b x y u : Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.Πy:l_e_st_eq_landau_n_rt_rp_nt_natt.Πu:l_e_st_eq_landau_n_rt_rp_nt_is (l_e_st_eq_landau_n_rt_rp_nt_suct x) (l_e_st_eq_landau_n_rt_rp_nt_suct y).l_e_st_eq_landau_n_rt_rp_nt_is x y).
+
+(* notion 2772 *)
+definition l_e_st_eq_landau_n_rt_rp_nt_ax5t ≝ (λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.λu:l_e_st_eq_landau_n_rt_rp_nt_cond1 s.λv:l_e_st_eq_landau_n_rt_rp_nt_cond2 s.λx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_satz156c s u v x : Πs:l_e_st_set l_e_st_eq_landau_n_rt_rp_nt_natt.Πu:l_e_st_eq_landau_n_rt_rp_nt_cond1 s.Πv:l_e_st_eq_landau_n_rt_rp_nt_cond2 s.Πx:l_e_st_eq_landau_n_rt_rp_nt_natt.l_e_st_eq_landau_n_rt_rp_nt_in x s).
+
+(* notion 2773 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_ratt ≝ (l_e_ot l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) : Type[0]).
+
+(* notion 2774 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_rttofrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_out l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) ksi rtksi : l_e_st_eq_landau_n_rt_rp_rtt_ratt).
+
+(* notion 2775 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_is ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_is l_e_st_eq_landau_n_rt_rp_rtt_ratt x0t y0t : Prop).
+
+(* notion 2776 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_nis ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_not (l_e_st_eq_landau_n_rt_rp_rtt_is x0t y0t) : Prop).
+
+(* notion 2777 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_rtt_ratt.Prop.(l_all l_e_st_eq_landau_n_rt_rp_rtt_ratt p : Prop).
+
+(* notion 2778 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_rtt_ratt.Prop.(l_some l_e_st_eq_landau_n_rt_rp_rtt_ratt p : Prop).
+
+(* notion 2779 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_rtt_ratt.Prop.(l_e_one l_e_st_eq_landau_n_rt_rp_rtt_ratt p : Prop).
+
+(* notion 2780 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_in l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) x0t : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2781 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_ratrpi ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_inp l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) x0t : l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t)).
+
+(* notion 2782 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrpertt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λrteta:l_e_st_eq_landau_n_rt_rp_ratrp eta.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isouti l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) ksi rtksi eta rteta i : l_e_st_eq_landau_n_rt_rp_rtt_is (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp ksi rtksi) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp eta rteta)).
+
+(* notion 2783 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrpirtt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λrteta:l_e_st_eq_landau_n_rt_rp_ratrp eta.λi:l_e_st_eq_landau_n_rt_rp_rtt_is (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp ksi rtksi) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp eta rteta).(l_e_isoute l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) ksi rtksi eta rteta i : l_e_st_eq_landau_n_rt_rp_is ksi eta).
+
+(* notion 2784 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrtterp ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λi:l_e_st_eq_landau_n_rt_rp_rtt_is x0t y0t.(l_e_isini l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) x0t y0t i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt y0t)).
+
+(* notion 2785 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrttirp ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt y0t).(l_e_isine l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) x0t y0t i : l_e_st_eq_landau_n_rt_rp_rtt_is x0t y0t).
+
+(* notion 2786 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrprtt1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_isinout l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) ksi rtksi : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp ksi rtksi))).
+
+(* notion 2787 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrttrp1 ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_isoutin l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) x0t : l_e_st_eq_landau_n_rt_rp_rtt_is x0t (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t))).
+
+(* notion 2788 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_rttofrt ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rtt_rttofrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) : l_e_st_eq_landau_n_rt_rp_rtt_ratt).
+
+(* notion 2789 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrtertt ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is x0 y0.(l_e_st_eq_landau_n_rt_rp_rtt_isrpertt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_ratrpi y0) (l_e_st_eq_landau_n_rt_rp_isrterp x0 y0 i) : l_e_st_eq_landau_n_rt_rp_rtt_is (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt y0)).
+
+(* notion 2790 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrtirtt ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_rp_rtt_is (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt y0).(l_e_st_eq_landau_n_rt_rp_isrtirp x0 y0 (l_e_st_eq_landau_n_rt_rp_rtt_isrpirtt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_ratrpi y0) i) : l_e_st_eq_landau_n_rt_is x0 y0).
+
+(* notion 2791 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_st_eq_landau_n_rt_rp_rtofrp (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t) : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2792 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrttert ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λi:l_e_st_eq_landau_n_rt_rp_rtt_is x0t y0t.(l_e_st_eq_landau_n_rt_rp_isrpert (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt y0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi y0t) (l_e_st_eq_landau_n_rt_rp_rtt_isrtterp x0t y0t i) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt y0t)).
+
+(* notion 2793 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrttirt ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λy0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt y0t).(l_e_st_eq_landau_n_rt_rp_rtt_isrttirp x0t y0t (l_e_st_eq_landau_n_rt_rp_isrpirt (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt y0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi y0t) i) : l_e_st_eq_landau_n_rt_rp_rtt_is x0t y0t).
+
+(* notion 2794 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_iii5_t9 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rtt_isrprtt1 (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0))).
+
+(* notion 2795 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_iii5_t10 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_isrpert (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0)) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0)) (l_e_st_eq_landau_n_rt_rp_rtt_iii5_t9 x0) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_rp_rtofrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0)) (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0))).
+
+(* notion 2796 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrtrtt1 ≝ λx0:l_e_st_eq_landau_n_rt_rat.(l_e_tris l_e_st_eq_landau_n_rt_rat x0 (l_e_st_eq_landau_n_rt_rp_rtofrp (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_ratrpi x0)) (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0)) (l_e_st_eq_landau_n_rt_rp_isrtrp1 x0) (l_e_st_eq_landau_n_rt_rp_rtt_iii5_t10 x0) : l_e_st_eq_landau_n_rt_is x0 (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt x0))).
+
+(* notion 2797 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_iii5_t11 ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_st_eq_landau_n_rt_rp_isrprt1 (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t))).
+
+(* notion 2798 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_iii5_t12 ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_st_eq_landau_n_rt_rp_rtt_isrpertt (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t)) (l_e_st_eq_landau_n_rt_rp_ratrpi (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t)) (l_e_st_eq_landau_n_rt_rp_rtt_iii5_t11 x0t) : l_e_st_eq_landau_n_rt_rp_rtt_is (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t)) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t))).
+
+(* notion 2799 *)
+definition l_e_st_eq_landau_n_rt_rp_rtt_isrttrt1 ≝ λx0t:l_e_st_eq_landau_n_rt_rp_rtt_ratt.(l_e_tris l_e_st_eq_landau_n_rt_rp_rtt_ratt x0t (l_e_st_eq_landau_n_rt_rp_rtt_rttofrp (l_e_st_eq_landau_n_rt_rp_rtt_rpofrtt x0t) (l_e_st_eq_landau_n_rt_rp_rtt_ratrpi x0t)) (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t)) (l_e_st_eq_landau_n_rt_rp_rtt_isrttrp1 x0t) (l_e_st_eq_landau_n_rt_rp_rtt_iii5_t12 x0t) : l_e_st_eq_landau_n_rt_rp_rtt_is x0t (l_e_st_eq_landau_n_rt_rp_rtt_rttofrt (l_e_st_eq_landau_n_rt_rp_rtt_rtofrtt x0t))).
+
+(* notion 2800 *)
+definition l_e_st_eq_landau_n_rt_rp_example2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_satz153c l_e_st_eq_landau_n_rt_rp_1rp ksi : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi (l_e_st_eq_landau_n_rt_rp_ov l_e_st_eq_landau_n_rt_rp_1rp ksi)) l_e_st_eq_landau_n_rt_rp_1rp).
+
+(* notion 2801 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_x01 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2802 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_s1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2803 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) y0 i : l_e_st_eq_landau_n_rt_urt ksi y0).
+
+(* notion 2804 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0 (l_e_st_eq_landau_n_rt_satz82 (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0 m) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) y0).
+
+(* notion 2805 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).λm:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0.(l_e_isp l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_lrt x y0) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) ksi (l_e_st_eq_landau_n_rt_rp_5157_t2 ksi rtksi y0 i m) (l_e_st_eq_landau_n_rt_rp_isrprt2 ksi rtksi) : l_e_st_eq_landau_n_rt_lrt ksi y0).
+
+(* notion 2806 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).(l_imp_th3 (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0) (l_e_st_eq_landau_n_rt_lrt ksi y0) (l_e_st_eq_landau_n_rt_rp_5157_t1 ksi rtksi y0 i) (λt:l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0.l_e_st_eq_landau_n_rt_rp_5157_t3 ksi rtksi y0 i t) : l_not (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0)).
+
+(* notion 2807 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.λy0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).(l_e_st_eq_landau_n_rt_satz81e (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0 (l_e_st_eq_landau_n_rt_rp_5157_t4 ksi rtksi y0 i) : l_e_st_eq_landau_n_rt_lessis (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) y0).
+
+(* notion 2808 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi).l_e_st_eq_landau_n_rt_rp_5157_t5 ksi rtksi x t : l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)).
+
+(* notion 2809 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_st_eq_landau_n_rt_rp_urtrpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_moreisi2 (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_refis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi))) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)).
+
+(* notion 2810 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_isp l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_urt x (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) ksi (l_e_st_eq_landau_n_rt_rp_5157_t7 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_isrprt2 ksi rtksi) : l_e_st_eq_landau_n_rt_urt ksi (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)).
+
+(* notion 2811 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_t8 ksi rtksi) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)).
+
+(* notion 2812 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_andi (l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)) (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)) (l_e_st_eq_landau_n_rt_rp_5157_t6 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_t9 ksi rtksi) : l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi)).
+
+(* notion 2813 *)
+definition l_e_st_eq_landau_n_rt_rp_satz157a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_e_st_eq_landau_n_rt_rp_5157_t10 ksi rtksi : l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) (l_e_st_eq_landau_n_rt_rp_rtofrp ksi rtksi)).
+
+(* notion 2814 *)
+definition l_e_st_eq_landau_n_rt_rp_satz157b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λrtksi:l_e_st_eq_landau_n_rt_rp_ratrp ksi.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x) (l_e_st_eq_landau_n_rt_rp_5157_x01 ksi rtksi) (l_e_st_eq_landau_n_rt_rp_5157_t10 ksi rtksi) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi y)) x)).
+
+(* notion 2815 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.(l_ande1 (l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x0) (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)) m : l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x0).
+
+(* notion 2816 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.(l_ande2 (l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x0) (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)) m : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)).
+
+(* notion 2817 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) x0 (l_e_st_eq_landau_n_rt_rp_5157_t12 ksi x0 m) : l_e_st_eq_landau_n_rt_urt ksi x0).
+
+(* notion 2818 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.(l_e_st_eq_landau_n_rt_cutapp2a ksi y0 ly x0 (l_e_st_eq_landau_n_rt_rp_5157_t13 ksi x0 m) : l_e_st_eq_landau_n_rt_less y0 x0).
+
+(* notion 2819 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt ksi y0.(l_e_st_eq_landau_n_rt_rp_lrtrpofrt x0 y0 (l_e_st_eq_landau_n_rt_rp_5157_t14 ksi x0 m y0 ly) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0).
+
+(* notion 2820 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) y0 uy : l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi)).
+
+(* notion 2821 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_eq_landau_n_rt_satz85 x0 y0 (l_e_st_eq_landau_n_rt_rp_5157_t11 ksi x0 m y0 (l_e_st_eq_landau_n_rt_rp_5157_t17 ksi x0 m y0 uy)) : l_e_st_eq_landau_n_rt_moreis y0 x0).
+
+(* notion 2822 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt ksi y0.(l_e_st_eq_landau_n_rt_rp_urtrpofrt x0 y0 (l_e_st_eq_landau_n_rt_rp_5157_t18 ksi x0 m y0 uy) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0).
+
+(* notion 2823 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.λy0:l_e_st_eq_landau_n_rt_rat.(l_cp (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0) (l_e_st_eq_landau_n_rt_lrt ksi y0) (λt:l_e_st_eq_landau_n_rt_urt ksi y0.l_e_st_eq_landau_n_rt_rp_5157_t19 ksi x0 m y0 t) : l_imp (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) y0) (l_e_st_eq_landau_n_rt_lrt ksi y0)).
+
+(* notion 2824 *)
+definition l_e_st_eq_landau_n_rt_rp_satz157c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x)) x0.(l_e_st_eq_landau_n_rt_rp_isi1 ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt ksi x.l_e_st_eq_landau_n_rt_rp_5157_t15 ksi x0 m x t) (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5157_t20 ksi x0 m x) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).
+
+(* notion 2825 *)
+definition l_e_st_eq_landau_n_rt_rp_5157_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi y)) x).λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x0.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) x0 (l_e_st_eq_landau_n_rt_rp_satz157c ksi x0 m) : l_e_st_eq_landau_n_rt_rp_ratrp ksi).
+
+(* notion 2826 *)
+definition l_e_st_eq_landau_n_rt_rp_satz157d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_min (l_e_st_setof l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi y)) x).(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x) s (l_e_st_eq_landau_n_rt_rp_ratrp ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5157_s1 ksi) x.l_e_st_eq_landau_n_rt_rp_5157_t21 ksi s x t) : l_e_st_eq_landau_n_rt_rp_ratrp ksi).
+
+(* notion 2827 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_xr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2828 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_e_st_eq_landau_n_rt_rp_urtrpofrt x0 x0 (l_e_st_eq_landau_n_rt_moreisi2 x0 x0 (l_e_refis l_e_st_eq_landau_n_rt_rat x0)) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) x0).
+
+(* notion 2829 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_andi (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) x0) (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_rp_5158_t1 ksi x0 lx) lx : l_and (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) x0) (l_e_st_eq_landau_n_rt_lrt ksi x0)).
+
+(* notion 2830 *)
+definition l_e_st_eq_landau_n_rt_rp_satz158a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt ksi x0.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_rpofrt x0) x) (l_e_st_eq_landau_n_rt_lrt ksi x)) x0 (l_e_st_eq_landau_n_rt_rp_5158_t2 ksi x0 lx) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi).
+
+(* notion 2831 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_s1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2832 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λm:l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0.(l_e_symis l_e_st_eq_landau_n_rt_cut ksi (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) (l_e_st_eq_landau_n_rt_rp_satz157c ksi x0 m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi).
+
+(* notion 2833 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λm:l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0.(l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi (l_e_st_eq_landau_n_rt_rp_5158_t3 ksi x0 ux m) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi).
+
+(* notion 2834 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) x0 ux : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)).
+
+(* notion 2835 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).(l_and_th4 (l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0) (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) n (l_e_st_eq_landau_n_rt_rp_5158_t5 ksi x0 ux n) : l_not (l_e_st_eq_landau_n_rt_lb (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0)).
+
+(* notion 2836 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).(l_some_th1 l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_imp (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 x)) (l_e_st_eq_landau_n_rt_rp_5158_t6 ksi x0 ux n) : l_e_st_eq_landau_n_rt_some (Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_imp (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 x)))).
+
+(* notion 2837 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_imp_th5 (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0) o : l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)).
+
+(* notion 2838 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_urt ksi x) y0 (l_e_st_eq_landau_n_rt_rp_5158_t8 ksi x0 ux n y0 o) : l_e_st_eq_landau_n_rt_urt ksi y0).
+
+(* notion 2839 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_imp_th6 (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0) o : l_not (l_e_st_eq_landau_n_rt_lessis x0 y0)).
+
+(* notion 2840 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_e_st_eq_landau_n_rt_satz82 x0 y0 (l_e_st_eq_landau_n_rt_satz81k x0 y0 (l_e_st_eq_landau_n_rt_rp_5158_t10 ksi x0 ux n y0 o)) : l_e_st_eq_landau_n_rt_less y0 x0).
+
+(* notion 2841 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_e_st_eq_landau_n_rt_rp_lrtrpofrt x0 y0 (l_e_st_eq_landau_n_rt_rp_5158_t11 ksi x0 ux n y0 o) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) y0).
+
+(* notion 2842 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_andi (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) y0) (l_e_st_eq_landau_n_rt_urt ksi y0) (l_e_st_eq_landau_n_rt_rp_5158_t12 ksi x0 ux n y0 o) (l_e_st_eq_landau_n_rt_rp_5158_t9 ksi x0 ux n y0 o) : l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) y0) (l_e_st_eq_landau_n_rt_urt ksi y0)).
+
+(* notion 2843 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).λy0:l_e_st_eq_landau_n_rt_rat.λo:l_not (l_imp (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 y0)).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) x) (l_e_st_eq_landau_n_rt_urt ksi x)) y0 (l_e_st_eq_landau_n_rt_rp_5158_t13 ksi x0 ux n y0 o) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi).
+
+(* notion 2844 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).(l_someapp l_e_st_eq_landau_n_rt_rat (Πx:l_e_st_eq_landau_n_rt_rat.l_not (l_imp (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 x))) (l_e_st_eq_landau_n_rt_rp_5158_t7 ksi x0 ux n) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_not (l_imp (l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux)) (l_e_st_eq_landau_n_rt_lessis x0 x)).l_e_st_eq_landau_n_rt_rp_5158_t14 ksi x0 ux n x t) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi).
+
+(* notion 2845 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λn:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi (l_e_st_eq_landau_n_rt_rp_5158_t15 ksi x0 ux n) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi).
+
+(* notion 2846 *)
+definition l_e_st_eq_landau_n_rt_rp_satz158b ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.(l_imp_th1 (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi) (λt:l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0.l_e_st_eq_landau_n_rt_rp_5158_t4 ksi x0 ux t) (λt:l_not (l_e_st_eq_landau_n_rt_min (l_e_st_eq_landau_n_rt_rp_5158_s1 ksi x0 ux) x0).l_e_st_eq_landau_n_rt_rp_5158_t16 ksi x0 ux t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi).
+
+(* notion 2847 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi.(l_e_st_eq_landau_n_rt_rp_satz123h (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi l : l_not (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi)).
+
+(* notion 2848 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi.(l_imp_th3 (l_e_st_eq_landau_n_rt_urt ksi x0) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi) (l_e_st_eq_landau_n_rt_rp_5158_t17 ksi x0 l) (λt:l_e_st_eq_landau_n_rt_urt ksi x0.l_e_st_eq_landau_n_rt_rp_satz158b ksi x0 t) : l_not (l_e_st_eq_landau_n_rt_urt ksi x0)).
+
+(* notion 2849 *)
+definition l_e_st_eq_landau_n_rt_rp_satz158c ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi.(l_et (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_rp_5158_t18 ksi x0 l) : l_e_st_eq_landau_n_rt_lrt ksi x0).
+
+(* notion 2850 *)
+definition l_e_st_eq_landau_n_rt_rp_5158_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi.(l_e_st_eq_landau_n_rt_rp_satz123c (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi m : l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5158_xr ksi x0) ksi)).
+
+(* notion 2851 *)
+definition l_e_st_eq_landau_n_rt_rp_satz158d ≝ λksi:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi.(l_imp_th3 (l_e_st_eq_landau_n_rt_lrt ksi x0) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) ksi) (l_e_st_eq_landau_n_rt_rp_5158_t19 ksi x0 m) (λt:l_e_st_eq_landau_n_rt_lrt ksi x0.l_e_st_eq_landau_n_rt_rp_satz158a ksi x0 t) : l_e_st_eq_landau_n_rt_urt ksi x0).
+
+(* notion 2852 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_xr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2853 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_zr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2854 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt eta z0.λk:l_e_st_eq_landau_n_rt_less x0 z0.(l_e_st_eq_landau_n_rt_rp_satz127a ksi (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0) (l_e_st_eq_landau_n_rt_rp_satz124 (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) ksi (l_e_st_eq_landau_n_rt_rp_satz158b ksi x0 ux)) (l_e_st_eq_landau_n_rt_rp_satz154c x0 z0 k) : l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0)).
+
+(* notion 2855 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt eta z0.λk:l_e_st_eq_landau_n_rt_less x0 z0.(l_andi (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0) eta) (l_e_st_eq_landau_n_rt_rp_5159_t1 ksi eta l x0 ux lx z0 lz k) (l_e_st_eq_landau_n_rt_rp_satz158a eta z0 lz) : l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_zr ksi eta l x0 ux lx z0) eta)).
+
+(* notion 2856 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt eta z0.λk:l_e_st_eq_landau_n_rt_less x0 z0.(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta)) z0 (l_e_st_eq_landau_n_rt_rp_5159_t2 ksi eta l x0 ux lx z0 lz k) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta))).
+
+(* notion 2857 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt ksi x0.λlx:l_e_st_eq_landau_n_rt_lrt eta x0.(l_e_st_eq_landau_n_rt_cutapp3 eta x0 lx (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt eta x.λu:l_e_st_eq_landau_n_rt_less x0 x.l_e_st_eq_landau_n_rt_rp_5159_t3 ksi eta l x0 ux lx x t u) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta))).
+
+(* notion 2858 *)
+definition l_e_st_eq_landau_n_rt_rp_satz159 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_lessapp ksi eta l (l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt ksi x.λu:l_e_st_eq_landau_n_rt_lrt eta x.l_e_st_eq_landau_n_rt_rp_5159_t4 ksi eta l x t u) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta))).
+
+(* notion 2859 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) eta).(l_andi (l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) eta)) (l_e_st_eq_landau_n_rt_rp_ratrpi x0) a : l_and3 (l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) eta)).
+
+(* notion 2860 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λx0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) eta).(l_somei l_e_st_eq_landau_n_rt_cut (λc:l_e_st_eq_landau_n_rt_cut.l_and3 (l_e_st_eq_landau_n_rt_rp_ratrp c) (l_e_st_eq_landau_n_rt_rp_less ksi c) (l_e_st_eq_landau_n_rt_rp_less c eta)) (l_e_st_eq_landau_n_rt_rp_5159_xr ksi eta l x0) (l_e_st_eq_landau_n_rt_rp_5159_t5 ksi eta l x0 a) : l_e_st_eq_landau_n_rt_rp_some (λc:l_e_st_eq_landau_n_rt_cut.l_and3 (l_e_st_eq_landau_n_rt_rp_ratrp c) (l_e_st_eq_landau_n_rt_rp_less ksi c) (l_e_st_eq_landau_n_rt_rp_less c eta))).
+
+(* notion 2861 *)
+definition l_e_st_eq_landau_n_rt_rp_satz159a ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta)) (l_e_st_eq_landau_n_rt_rp_satz159 ksi eta l) (l_e_st_eq_landau_n_rt_rp_some (λa:l_e_st_eq_landau_n_rt_cut.l_and3 (l_e_st_eq_landau_n_rt_rp_ratrp a) (l_e_st_eq_landau_n_rt_rp_less ksi a) (l_e_st_eq_landau_n_rt_rp_less a eta))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta).l_e_st_eq_landau_n_rt_rp_5159_t6 ksi eta l x t) : l_e_st_eq_landau_n_rt_rp_some (λa:l_e_st_eq_landau_n_rt_cut.l_and3 (l_e_st_eq_landau_n_rt_rp_ratrp a) (l_e_st_eq_landau_n_rt_rp_less ksi a) (l_e_st_eq_landau_n_rt_rp_less a eta))).
+
+(* notion 2862 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_yr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).Πu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta.p.λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt y0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2863 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).Πu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta.p.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta).(l_ande1 (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta) a : l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)).
+
+(* notion 2864 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).Πu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta.p.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta).(l_ande2 (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta) a : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta).
+
+(* notion 2865 *)
+definition l_e_st_eq_landau_n_rt_rp_5159_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).Πu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta.p.λy0:l_e_st_eq_landau_n_rt_rat.λa:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5159_yr ksi eta l p p1 y0) eta).(p1 y0 (l_e_st_eq_landau_n_rt_rp_5159_t7 ksi eta l p p1 y0 a) (l_e_st_eq_landau_n_rt_rp_5159_t8 ksi eta l p p1 y0 a) : p).
+
+(* notion 2866 *)
+definition l_e_st_eq_landau_n_rt_rp_satz159app ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).Πu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta.p.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta)) (l_e_st_eq_landau_n_rt_rp_satz159 ksi eta l) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_and (l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) eta).l_e_st_eq_landau_n_rt_rp_5159_t9 ksi eta l p p1 x t) : p).
+
+(* notion 2867 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_zr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_st_eq_landau_n_rt_rp_rpofrt z0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2868 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_nm ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_5160_zr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) m : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2869 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_dn ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2870 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_fr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_st_eq_landau_n_rt_rp_ov (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2871 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_zeta ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_ite (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2872 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp.(l_e_itet (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp l : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m)).
+
+(* notion 2873 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp.(l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_t1 ksi eta z0 m l) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m)).
+
+(* notion 2874 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp.(l_e_st_eq_landau_n_rt_rp_lessisi1 (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_satz127a (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5160_t2 ksi eta z0 m l) l) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).
+
+(* notion 2875 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λn:l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).(l_e_itef (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp n : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).
+
+(* notion 2876 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λn:l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).(l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5160_t4 ksi eta z0 m n) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).
+
+(* notion 2877 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λn:l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).(l_e_st_eq_landau_n_rt_rp_trlessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_t5 ksi eta z0 m n) (l_e_st_eq_landau_n_rt_rp_satz124 (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_satz123f (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp n)) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m)).
+
+(* notion 2878 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) (λt:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp.l_e_st_eq_landau_n_rt_rp_5160_t3 ksi eta z0 m t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).l_e_st_eq_landau_n_rt_rp_5160_t5 ksi eta z0 m t) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).
+
+(* notion 2879 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m)) (λt:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp.l_e_st_eq_landau_n_rt_rp_5160_t2 ksi eta z0 m t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp).l_e_st_eq_landau_n_rt_rp_5160_t6 ksi eta z0 m t) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m)).
+
+(* notion 2880 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_zr1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z1 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2881 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_zr2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z2 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2882 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_disttp2 (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_satz147a (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) l2 l4) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
+
+(* notion 2883 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) eta)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_disttp1 ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) eta) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) eta))) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
+
+(* notion 2884 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz149a (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_satz139a ksi ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_lessisi2 ksi ksi (l_e_refis l_e_st_eq_landau_n_rt_cut ksi)) (l_e_st_eq_landau_n_rt_rp_5160_t7 ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))).
+
+(* notion 2885 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz139a (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_t10 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t11 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
+
+(* notion 2886 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz127b (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_5160_t9 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t12 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
+
+(* notion 2887 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl eta ksi) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl ksi eta) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_asspl2 eta ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl eta ksi) (l_e_st_eq_landau_n_rt_rp_pl ksi eta) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_compl eta ksi)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)).
+
+(* notion 2888 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_distpt1 eta (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_t14 ksi eta z0 m z1 l1 l2 z2 l3 l4)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))).
+
+(* notion 2889 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_5160_t15 ksi eta z0 m z1 l1 l2 z2 l3 l4)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
+
+(* notion 2890 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl ksi l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_5160_t16 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t13 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)))).
+
+(* notion 2891 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_islessis12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_satz153e (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_satz149a (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_fr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_t8 ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m)))) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m)).
+
+(* notion 2892 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t19 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz139a (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi eta))) (l_e_st_eq_landau_n_rt_rp_5160_t18 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m))).
+
+(* notion 2893 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz127b (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_dn ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_t17 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t19 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m))).
+
+(* notion 2894 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_5160_nm ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_zr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_satz140c (l_e_st_eq_landau_n_rt_rp_5160_zr ksi eta z0 m) (l_e_st_eq_landau_n_rt_rp_ts ksi eta) m) (l_e_st_eq_landau_n_rt_rp_5160_t20 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_5160_zr ksi eta z0 m)).
+
+(* notion 2895 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz154f (l_e_st_eq_landau_n_rt_ts z1 z2) z0 (l_e_st_eq_landau_n_rt_rp_isless1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts z1 z2)) (l_e_st_eq_landau_n_rt_rp_5160_zr ksi eta z0 m) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts z1 z2)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2)) (l_e_st_eq_landau_n_rt_rp_satz155c z1 z2)) (l_e_st_eq_landau_n_rt_rp_5160_t21 ksi eta z0 m z1 l1 l2 z2 l3 l4)) : l_e_st_eq_landau_n_rt_less (l_e_st_eq_landau_n_rt_ts z1 z2) z0).
+
+(* notion 2896 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_x0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_ov z0 z2 : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2897 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_xr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2898 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_y0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(z2 : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2899 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_yr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5160_y0 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2900 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_satz110e z0 z2 : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_y0 ksi eta z0 m z1 l1 l2 z2 l3 l4)) z0).
+
+(* notion 2901 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_ismore1 z0 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z2) (l_e_st_eq_landau_n_rt_ts z1 z2) (l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z2) z0 (l_e_st_eq_landau_n_rt_rp_5160_t23 ksi eta z0 m z1 l1 l2 z2 l3 l4)) (l_e_st_eq_landau_n_rt_satz83 (l_e_st_eq_landau_n_rt_ts z1 z2) z0 (l_e_st_eq_landau_n_rt_rp_5160_t22 ksi eta z0 m z1 l1 l2 z2 l3 l4)) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z2) (l_e_st_eq_landau_n_rt_ts z1 z2)).
+
+(* notion 2902 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_satz106a (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z1 z2 (l_e_st_eq_landau_n_rt_rp_5160_t24 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z1).
+
+(* notion 2903 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t26 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_trmore (l_e_st_eq_landau_n_rt_rp_5160_xr ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) ksi (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) z1 (l_e_st_eq_landau_n_rt_rp_5160_t25 ksi eta z0 m z1 l1 l2 z2 l3 l4)) (l_e_st_eq_landau_n_rt_rp_satz122 ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) l1) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr ksi eta z0 m z1 l1 l2 z2 l3 l4) ksi).
+
+(* notion 2904 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t27 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz122 eta (l_e_st_eq_landau_n_rt_rp_5160_yr ksi eta z0 m z1 l1 l2 z2 l3 l4) l3 : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr ksi eta z0 m z1 l1 l2 z2 l3 l4) eta).
+
+(* notion 2905 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_ur ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt u0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2906 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_vr ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt v0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2907 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_prop1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λu0:l_e_st_eq_landau_n_rt_rat.λv0:l_e_st_eq_landau_n_rt_rat.(l_and3 (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_ur ksi eta z0 u0) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_vr ksi eta z0 u0 v0) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts u0 v0) z0) : Prop).
+
+(* notion 2908 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_prop2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x y)) : Prop).
+
+(* notion 2909 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t28 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_and3i (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr ksi eta z0 m z1 l1 l2 z2 l3 l4) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr ksi eta z0 m z1 l1 l2 z2 l3 l4) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_y0 ksi eta z0 m z1 l1 l2 z2 l3 l4)) z0) (l_e_st_eq_landau_n_rt_rp_5160_t26 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t27 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t23 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_y0 ksi eta z0 m z1 l1 l2 z2 l3 l4)).
+
+(* notion 2910 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t29 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) y) (l_e_st_eq_landau_n_rt_rp_5160_y0 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t28 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) y)).
+
+(* notion 2911 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t30 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr2 ksi eta z0 m z1 l1 l2 z2) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x y)) (l_e_st_eq_landau_n_rt_rp_5160_x0 ksi eta z0 m z1 l1 l2 z2 l3 l4) (l_e_st_eq_landau_n_rt_rp_5160_t29 ksi eta z0 m z1 l1 l2 z2 l3 l4) : l_e_st_eq_landau_n_rt_rp_5160_prop2 ksi eta z0).
+
+(* notion 2912 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t31 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5160_zr1 ksi eta z0 m z1) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).(l_e_st_eq_landau_n_rt_rp_satz159app eta (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_satz133a eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_prop2 ksi eta z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_less eta (l_e_st_eq_landau_n_rt_rp_rpofrt x).λu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_pl eta (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).l_e_st_eq_landau_n_rt_rp_5160_t30 ksi eta z0 m z1 l1 l2 x t u) : l_e_st_eq_landau_n_rt_rp_5160_prop2 ksi eta z0).
+
+(* notion 2913 *)
+definition l_e_st_eq_landau_n_rt_rp_satz160 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).(l_e_st_eq_landau_n_rt_rp_satz159app ksi (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_satz133a ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)) (l_e_st_eq_landau_n_rt_rp_5160_prop2 ksi eta z0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_less ksi (l_e_st_eq_landau_n_rt_rp_rpofrt x).λu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_pl ksi (l_e_st_eq_landau_n_rt_rp_5160_zeta ksi eta z0 m)).l_e_st_eq_landau_n_rt_rp_5160_t31 ksi eta z0 m x t u) : l_e_st_eq_landau_n_rt_some (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and3 (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0)))).
+
+(* notion 2914 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_xr1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x1 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2915 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_yr1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).λy1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt y1 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2916 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t32 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).λy1:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y1.(l_and3e1 (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr1 ksi eta z0 m p p1 x1) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr1 ksi eta z0 m p p1 x1 px y1) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 y1) z0) py : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr1 ksi eta z0 m p p1 x1) ksi).
+
+(* notion 2917 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t33 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).λy1:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y1.(l_and3e2 (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr1 ksi eta z0 m p p1 x1) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr1 ksi eta z0 m p p1 x1 px y1) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 y1) z0) py : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr1 ksi eta z0 m p p1 x1 px y1) eta).
+
+(* notion 2918 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t34 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).λy1:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y1.(l_and3e3 (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_xr1 ksi eta z0 m p p1 x1) ksi) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5160_yr1 ksi eta z0 m p p1 x1 px y1) eta) (l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 y1) z0) py : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x1 y1) z0).
+
+(* notion 2919 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t35 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).λy1:l_e_st_eq_landau_n_rt_rat.λpy:l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y1.(p1 x1 (l_e_st_eq_landau_n_rt_rp_5160_t32 ksi eta z0 m p p1 x1 px y1 py) y1 (l_e_st_eq_landau_n_rt_rp_5160_t33 ksi eta z0 m p p1 x1 px y1 py) (l_e_st_eq_landau_n_rt_rp_5160_t34 ksi eta z0 m p p1 x1 px y1 py) : p).
+
+(* notion 2920 *)
+definition l_e_st_eq_landau_n_rt_rp_5160_t36 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.λx1:l_e_st_eq_landau_n_rt_rat.λpx:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y).(l_someapp l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y) px p (λy:l_e_st_eq_landau_n_rt_rat.λv:l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x1 y.l_e_st_eq_landau_n_rt_rp_5160_t35 ksi eta z0 m p p1 x1 px y v) : p).
+
+(* notion 2921 *)
+definition l_e_st_eq_landau_n_rt_rp_satz160app ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λz0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt z0) (l_e_st_eq_landau_n_rt_rp_ts ksi eta).λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rat.Πt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) ksi.Πy:l_e_st_eq_landau_n_rt_rat.Πu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) eta.Πv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z0.p.(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x y)) (l_e_st_eq_landau_n_rt_rp_satz160 ksi eta z0 m) p (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5160_prop1 ksi eta z0 x y).l_e_st_eq_landau_n_rt_rp_5160_t36 ksi eta z0 m p p1 x t) : p).
+
+(* notion 2922 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_min ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_ite (l_e_st_eq_landau_n_rt_rp_less ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2923 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_max ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.(l_e_ite (l_e_st_eq_landau_n_rt_rp_more ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2924 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_ur ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt u0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2925 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.(l_e_st_eq_landau_n_rt_rp_satz158a (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0 lu : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta)).
+
+(* notion 2926 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) ksi (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_itet (l_e_st_eq_landau_n_rt_rp_less ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta l) (l_e_st_eq_landau_n_rt_rp_5161_t1 ksi eta u0 lu) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
+
+(* notion 2927 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.λl:l_e_st_eq_landau_n_rt_rp_less ksi eta.(l_e_st_eq_landau_n_rt_rp_trless (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi eta (l_e_st_eq_landau_n_rt_rp_5161_t2 ksi eta u0 lu l) l : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
+
+(* notion 2928 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.λn:l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta).(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) eta (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_itef (l_e_st_eq_landau_n_rt_rp_less ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta n) (l_e_st_eq_landau_n_rt_rp_5161_t1 ksi eta u0 lu) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
+
+(* notion 2929 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.λn:l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta).(l_e_st_eq_landau_n_rt_rp_satz127b (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta ksi (l_e_st_eq_landau_n_rt_rp_5161_t4 ksi eta u0 lu n) (l_e_st_eq_landau_n_rt_rp_satz124 ksi eta (l_e_st_eq_landau_n_rt_rp_satz123f ksi eta n)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
+
+(* notion 2930 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi) (λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_5161_t2 ksi eta u0 lu t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta).l_e_st_eq_landau_n_rt_rp_5161_t5 ksi eta u0 lu t) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
+
+(* notion 2931 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λlu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min ksi eta) u0.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_less ksi eta) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta) (λt:l_e_st_eq_landau_n_rt_rp_less ksi eta.l_e_st_eq_landau_n_rt_rp_5161_t3 ksi eta u0 lu t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_less ksi eta).l_e_st_eq_landau_n_rt_rp_5161_t4 ksi eta u0 lu t) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
+
+(* notion 2932 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.(l_e_st_eq_landau_n_rt_rp_satz158b (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0 uu : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta)).
+
+(* notion 2933 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismoreis2 (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) ksi (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_itet (l_e_st_eq_landau_n_rt_rp_more ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta m) (l_e_st_eq_landau_n_rt_rp_5161_t8 ksi eta u0 uu) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
+
+(* notion 2934 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_trmoreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi eta (l_e_st_eq_landau_n_rt_rp_5161_t9 ksi eta u0 uu m) (l_e_st_eq_landau_n_rt_rp_moreisi1 ksi eta m) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
+
+(* notion 2935 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.λn:l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta).(l_e_st_eq_landau_n_rt_rp_ismoreis2 (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) eta (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) (l_e_itef (l_e_st_eq_landau_n_rt_rp_more ksi eta) l_e_st_eq_landau_n_rt_cut ksi eta n) (l_e_st_eq_landau_n_rt_rp_5161_t8 ksi eta u0 uu) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
+
+(* notion 2936 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.λn:l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta).(l_e_st_eq_landau_n_rt_rp_trmoreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta ksi (l_e_st_eq_landau_n_rt_rp_5161_t11 ksi eta u0 uu n) (l_e_st_eq_landau_n_rt_rp_satz125 ksi eta (l_e_st_eq_landau_n_rt_rp_satz123e ksi eta n)) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
+
+(* notion 2937 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi) (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_5161_t9 ksi eta u0 uu t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta).l_e_st_eq_landau_n_rt_rp_5161_t12 ksi eta u0 uu t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) ksi).
+
+(* notion 2938 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λu0:l_e_st_eq_landau_n_rt_rat.λuu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max ksi eta) u0.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_more ksi eta) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta) (λt:l_e_st_eq_landau_n_rt_rp_more ksi eta.l_e_st_eq_landau_n_rt_rp_5161_t10 ksi eta u0 uu t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_more ksi eta).l_e_st_eq_landau_n_rt_rp_5161_t11 ksi eta u0 uu t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_ur ksi eta u0) eta).
+
+(* notion 2939 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t15 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi1 ksi2.(l_e_st_eq_landau_n_rt_rp_satz147 ksi1 ksi2 ksi1 ksi2 m m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts ksi1 ksi1) (l_e_st_eq_landau_n_rt_rp_ts ksi2 ksi2)).
+
+(* notion 2940 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_sq1 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ts ksi1 ksi1 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2941 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_sq2 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ts ksi2 ksi2 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2942 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t16 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more ksi1 ksi2.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)) (l_e_st_eq_landau_n_rt_rp_5161_t15 zeta ksi1 ksi2 m) : l_e_st_eq_landau_n_rt_rp_nis (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)).
+
+(* notion 2943 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t17 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) zeta.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) zeta.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) zeta i j : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2)).
+
+(* notion 2944 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t18 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) zeta.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) zeta.(λt:l_e_st_eq_landau_n_rt_rp_more ksi1 ksi2.l_e_st_eq_landau_n_rt_rp_5161_t16 zeta ksi1 ksi2 t (l_e_st_eq_landau_n_rt_rp_5161_t17 zeta ksi1 ksi2 i j) : l_not (l_e_st_eq_landau_n_rt_rp_more ksi1 ksi2)).
+
+(* notion 2945 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t19 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) zeta.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) zeta.(λt:l_e_st_eq_landau_n_rt_rp_less ksi1 ksi2.l_e_st_eq_landau_n_rt_rp_5161_t16 zeta ksi2 ksi1 (l_e_st_eq_landau_n_rt_rp_satz122 ksi1 ksi2 t) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_t17 zeta ksi1 ksi2 i j)) : l_not (l_e_st_eq_landau_n_rt_rp_less ksi1 ksi2)).
+
+(* notion 2946 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t20 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi1:l_e_st_eq_landau_n_rt_cut.λksi2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq1 zeta ksi1 ksi2) zeta.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_sq2 zeta ksi1 ksi2) zeta.(l_or3e1 (l_e_st_eq_landau_n_rt_rp_is ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_more ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_less ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_satz123a ksi1 ksi2) (l_e_st_eq_landau_n_rt_rp_5161_t18 zeta ksi1 ksi2 i j) (l_e_st_eq_landau_n_rt_rp_5161_t19 zeta ksi1 ksi2 i j) : l_e_st_eq_landau_n_rt_rp_is ksi1 ksi2).
+
+(* notion 2947 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t21 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(λa:l_e_st_eq_landau_n_rt_cut.λb:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta.λu:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts b b) zeta.l_e_st_eq_landau_n_rt_rp_5161_t20 zeta a b t u : l_e_amone l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta)).
+
+(* notion 2948 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_sqrtset ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
+
+(* notion 2949 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_xr ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2950 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t22 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_5161_t6 l_e_st_eq_landau_n_rt_rp_1rp zeta x0 lx : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp).
+
+(* notion 2951 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t23 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_5161_t7 l_e_st_eq_landau_n_rt_rp_1rp zeta x0 lx : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) zeta).
+
+(* notion 2952 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t24 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_isless1 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta (l_e_st_eq_landau_n_rt_rp_satz151a (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_t23 zeta x0 lx) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta).
+
+(* notion 2953 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t25 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_trless (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta (l_e_st_eq_landau_n_rt_rp_satz148c (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0))) (l_e_st_eq_landau_n_rt_rp_5161_t22 zeta x0 lx)) (l_e_st_eq_landau_n_rt_rp_5161_t24 zeta x0 lx) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta).
+
+(* notion 2954 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t26 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) x0 (l_e_st_eq_landau_n_rt_rp_5161_t25 zeta x0 lx) : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
+
+(* notion 2955 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t27 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_5161_t13 l_e_st_eq_landau_n_rt_rp_1rp zeta x0 ux : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp).
+
+(* notion 2956 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t28 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_5161_t14 l_e_st_eq_landau_n_rt_rp_1rp zeta x0 ux : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) zeta).
+
+(* notion 2957 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t29 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_ismoreis1 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta (l_e_st_eq_landau_n_rt_rp_satz151a (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_t28 zeta x0 ux) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta).
+
+(* notion 2958 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t30 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_trmoreis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) zeta (l_e_st_eq_landau_n_rt_rp_satz149 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0))) (l_e_st_eq_landau_n_rt_rp_5161_t27 zeta x0 ux)) (l_e_st_eq_landau_n_rt_rp_5161_t29 zeta x0 ux) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta).
+
+(* notion 2959 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t31 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_rp_satz123c (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta (l_e_st_eq_landau_n_rt_rp_5161_t30 zeta x0 ux) : l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta)).
+
+(* notion 2960 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t32 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta) (l_e_st_eq_landau_n_rt_rp_5161_t31 zeta x0 ux) (λt:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) x0 t) : l_not (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta))).
+
+(* notion 2961 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_yr ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λy0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt y0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2962 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t33 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) x0 i : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta).
+
+(* notion 2963 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t34 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_satz154c y0 x0 l : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)).
+
+(* notion 2964 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t35 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_eq_landau_n_rt_rp_trless (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0) (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta (l_e_st_eq_landau_n_rt_rp_satz147a (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_t34 zeta x0 i y0 l) (l_e_st_eq_landau_n_rt_rp_5161_t34 zeta x0 i y0 l)) (l_e_st_eq_landau_n_rt_rp_5161_t33 zeta x0 i) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0) (l_e_st_eq_landau_n_rt_rp_5161_yr zeta x0 i y0)) zeta).
+
+(* notion 2965 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t36 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) y0 (l_e_st_eq_landau_n_rt_rp_5161_t35 zeta x0 i y0 l) : l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
+
+(* notion 2966 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t37 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) zeta (l_e_st_eq_landau_n_rt_rp_5161_t33 zeta x0 i) : l_e_st_eq_landau_n_rt_rp_more zeta (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0))).
+
+(* notion 2967 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_nm ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_eq_landau_n_rt_rp_mn zeta (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_t37 zeta x0 i) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2968 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_dn ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2969 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_fr ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_eq_landau_n_rt_rp_ov (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2970 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_zr ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2971 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t38 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_5161_t6 l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i) z0 lz : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) l_e_st_eq_landau_n_rt_rp_1rp).
+
+(* notion 2972 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t39 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_5161_t7 l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i) z0 lz : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)).
+
+(* notion 2973 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t40 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_satz94 x0 z0 : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) x0).
+
+(* notion 2974 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t41 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ists12 (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_satz155a x0 z0) (l_e_st_eq_landau_n_rt_rp_satz155a x0 z0)) (l_e_st_eq_landau_n_rt_rp_disttp2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))).
+
+(* notion 2975 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t42 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_5161_t41 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)))).
+
+(* notion 2976 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t43 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_disttp1 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)))) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))).
+
+(* notion 2977 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t44 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_satz145c (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_satz138c (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0))) (l_e_st_eq_landau_n_rt_rp_5161_t38 zeta x0 i z0 lz)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))).
+
+(* notion 2978 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t45 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_satz138c (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_t43 zeta x0 i z0 lz) (l_e_st_eq_landau_n_rt_rp_5161_t44 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))).
+
+(* notion 2979 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t46 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_distpt1 (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))).
+
+(* notion 2980 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t47 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_5161_t42 zeta x0 i z0 lz) (l_e_st_eq_landau_n_rt_rp_5161_t46 zeta x0 i z0 lz) (l_e_st_eq_landau_n_rt_rp_5161_t45 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)))).
+
+(* notion 2981 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t48 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_satz153c (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i)) (l_e_st_eq_landau_n_rt_rp_satz148c (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0) (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i) (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i))) (l_e_st_eq_landau_n_rt_rp_5161_t39 zeta x0 i z0 lz)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i)).
+
+(* notion 2982 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t49 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_satz138c (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0)) (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i) (l_e_st_eq_landau_n_rt_rp_lessisi2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)))) (l_e_st_eq_landau_n_rt_rp_5161_t48 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i))).
+
+(* notion 2983 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t50 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_nm zeta x0 i)) zeta (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) (l_e_st_eq_landau_n_rt_rp_satz140c zeta (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_5161_t37 zeta x0 i)) (l_e_st_eq_landau_n_rt_rp_5161_t49 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) zeta).
+
+(* notion 2984 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t51 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_eq_landau_n_rt_rp_trless (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0) (l_e_st_eq_landau_n_rt_rp_5161_xr zeta x0)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_dn zeta x0 i) (l_e_st_eq_landau_n_rt_rp_5161_zr zeta x0 i z0))) zeta (l_e_st_eq_landau_n_rt_rp_5161_t47 zeta x0 i z0 lz) (l_e_st_eq_landau_n_rt_rp_5161_t50 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl x0 z0))) zeta).
+
+(* notion 2985 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t52 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_rp_5161_t51 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
+
+(* notion 2986 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t53 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_andi (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) x0) (l_e_st_eq_landau_n_rt_rp_5161_t52 zeta x0 i z0 lz) (l_e_st_eq_landau_n_rt_rp_5161_t40 zeta x0 i z0 lz) : l_and (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_pl x0 z0) x0)).
+
+(* notion 2987 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t54 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λz0:l_e_st_eq_landau_n_rt_rat.λlz:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) z0.(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more y x0)) (l_e_st_eq_landau_n_rt_pl x0 z0) (l_e_st_eq_landau_n_rt_rp_5161_t53 zeta x0 i z0 lz) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more y x0))).
+
+(* notion 2988 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t55 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).(l_e_st_eq_landau_n_rt_cutapp1a (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) (l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more y x0))) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_5161_fr zeta x0 i)) x.l_e_st_eq_landau_n_rt_rp_5161_t54 zeta x0 i x t) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_more y x0))).
+
+(* notion 2989 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t56 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) y0.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta) x0 (l_e_st_eq_landau_n_rt_rp_5161_t26 zeta x0 lx) y0 (l_e_st_eq_landau_n_rt_rp_5161_t32 zeta y0 uy) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_5161_t36 zeta x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).l_e_st_eq_landau_n_rt_rp_5161_t55 zeta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
+
+(* notion 2990 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t57 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x0.(l_e_st_eq_landau_n_rt_cutapp1b (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_max l_e_st_eq_landau_n_rt_rp_1rp zeta) y.l_e_st_eq_landau_n_rt_rp_5161_t56 zeta x0 lx y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
+
+(* notion 2991 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t58 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_cutapp1a (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_min l_e_st_eq_landau_n_rt_rp_1rp zeta) x.l_e_st_eq_landau_n_rt_rp_5161_t57 zeta x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
+
+(* notion 2992 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_rtc ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta) (l_e_st_eq_landau_n_rt_rp_5161_t58 zeta) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2993 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t59 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_lessis x0 y0.(l_or_th9 (l_e_st_eq_landau_n_rt_less x0 y0) (l_e_st_eq_landau_n_rt_is x0 y0) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)) l (λt:l_e_st_eq_landau_n_rt_less x0 y0.l_e_st_eq_landau_n_rt_rp_satz154c x0 y0 t) (λt:l_e_st_eq_landau_n_rt_is x0 y0.l_e_st_eq_landau_n_rt_rp_satz154b x0 y0 t) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
+
+(* notion 2994 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t60 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λy0:l_e_st_eq_landau_n_rt_rat.λm:l_e_st_eq_landau_n_rt_moreis x0 y0.(l_e_st_eq_landau_n_rt_rp_satz125 (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_5161_t59 y0 x0 (l_e_st_eq_landau_n_rt_satz84 x0 y0 m)) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
+
+(* notion 2995 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t61 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta m : l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta))).
+
+(* notion 2996 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_zr1 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z1 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2997 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t62 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).(l_e_st_eq_landau_n_rt_rp_satz158c (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) z1 l2 : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) z1).
+
+(* notion 2998 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_xr1 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x1 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 2999 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_xr2 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x2 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3000 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_xm ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_ite (l_e_st_eq_landau_n_rt_more x1 x2) l_e_st_eq_landau_n_rt_rat x1 x2 : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 3001 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_xrm ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3002 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t63 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λo:l_e_st_eq_landau_n_rt_more x1 x2.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) x1 (l_e_itet (l_e_st_eq_landau_n_rt_more x1 x2) l_e_st_eq_landau_n_rt_rat x1 x2 o) : l_e_st_eq_landau_n_rt_is x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3003 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t64 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λo:l_e_st_eq_landau_n_rt_more x1 x2.(l_e_isp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x) x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) lx1 (l_e_st_eq_landau_n_rt_rp_5161_t63 zeta m z1 l1 l2 x1 lx1 x2 lx2 i o) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3004 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t65 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λo:l_e_st_eq_landau_n_rt_more x1 x2.(l_e_st_eq_landau_n_rt_lessisi2 x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t63 zeta m z1 l1 l2 x1 lx1 x2 lx2 i o) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3005 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t66 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λo:l_e_st_eq_landau_n_rt_more x1 x2.(l_e_st_eq_landau_n_rt_lessisi1 x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_satz87b x2 x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_satz82 x1 x2 o) (l_e_st_eq_landau_n_rt_rp_5161_t65 zeta m z1 l1 l2 x1 lx1 x2 lx2 i o)) : l_e_st_eq_landau_n_rt_lessis x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3006 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t67 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λn:l_not (l_e_st_eq_landau_n_rt_more x1 x2).(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) x2 (l_e_itef (l_e_st_eq_landau_n_rt_more x1 x2) l_e_st_eq_landau_n_rt_rat x1 x2 n) : l_e_st_eq_landau_n_rt_is x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3007 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t68 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λn:l_not (l_e_st_eq_landau_n_rt_more x1 x2).(l_e_isp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x) x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) lx2 (l_e_st_eq_landau_n_rt_rp_5161_t67 zeta m z1 l1 l2 x1 lx1 x2 lx2 i n) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3008 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t69 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λn:l_not (l_e_st_eq_landau_n_rt_more x1 x2).(l_e_st_eq_landau_n_rt_lessisi2 x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t67 zeta m z1 l1 l2 x1 lx1 x2 lx2 i n) : l_e_st_eq_landau_n_rt_lessis x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3009 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t70 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).λn:l_not (l_e_st_eq_landau_n_rt_more x1 x2).(l_e_st_eq_landau_n_rt_satz88 x1 x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_satz81e x1 x2 n) (l_e_st_eq_landau_n_rt_rp_5161_t69 zeta m z1 l1 l2 x1 lx1 x2 lx2 i n) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3010 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t71 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_imp_th1 (l_e_st_eq_landau_n_rt_more x1 x2) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) (λt:l_e_st_eq_landau_n_rt_more x1 x2.l_e_st_eq_landau_n_rt_rp_5161_t64 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_more x1 x2).l_e_st_eq_landau_n_rt_rp_5161_t68 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3011 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t72 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_imp_th1 (l_e_st_eq_landau_n_rt_more x1 x2) (l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) (λt:l_e_st_eq_landau_n_rt_more x1 x2.l_e_st_eq_landau_n_rt_rp_5161_t65 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_more x1 x2).l_e_st_eq_landau_n_rt_rp_5161_t70 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) : l_e_st_eq_landau_n_rt_lessis x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3012 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t73 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_imp_th1 (l_e_st_eq_landau_n_rt_more x1 x2) (l_e_st_eq_landau_n_rt_lessis x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) (λt:l_e_st_eq_landau_n_rt_more x1 x2.l_e_st_eq_landau_n_rt_rp_5161_t66 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_more x1 x2).l_e_st_eq_landau_n_rt_rp_5161_t69 zeta m z1 l1 l2 x1 lx1 x2 lx2 i t) : l_e_st_eq_landau_n_rt_lessis x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3013 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t74 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta) (l_e_st_eq_landau_n_rt_rp_5161_t58 zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t71 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)).
+
+(* notion 3014 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t75 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_5161_t59 x1 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t72 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3015 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t76 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_5161_t59 x2 (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t73 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)).
+
+(* notion 3016 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t77 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts x1 x2)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2)) (l_e_st_eq_landau_n_rt_rp_satz154b z1 (l_e_st_eq_landau_n_rt_ts x1 x2) i) (l_e_st_eq_landau_n_rt_rp_satz155c x1 x2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2))).
+
+(* notion 3017 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t78 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_islessis1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2)) (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2)) (l_e_st_eq_landau_n_rt_rp_5161_t77 zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) (l_e_st_eq_landau_n_rt_rp_satz149a (l_e_st_eq_landau_n_rt_rp_5161_xr1 zeta m z1 l1 l2 x1) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_xr2 zeta m z1 l1 l2 x1 lx1 x2) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t75 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t76 zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) : l_e_st_eq_landau_n_rt_rp_lessis (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i))).
+
+(* notion 3018 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t79 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) (l_e_st_eq_landau_n_rt_rp_5161_xm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t74 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) zeta).
+
+(* notion 3019 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t80 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_satz127a (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_xrm zeta m z1 l1 l2 x1 lx1 x2 lx2 i)) zeta (l_e_st_eq_landau_n_rt_rp_5161_t78 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) (l_e_st_eq_landau_n_rt_rp_5161_t79 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) zeta).
+
+(* notion 3020 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t81 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_ec3e23 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) zeta) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) zeta) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) zeta) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) zeta) (l_e_st_eq_landau_n_rt_rp_satz122 zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) l1) (l_e_st_eq_landau_n_rt_rp_5161_t80 zeta m z1 l1 l2 x1 lx1 x2 lx2 i) : l_con).
+
+(* notion 3021 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t82 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).λx1:l_e_st_eq_landau_n_rt_rat.λlx1:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x1.λx2:l_e_st_eq_landau_n_rt_rat.λlx2:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x2.λi:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x1 x2).(l_e_st_eq_landau_n_rt_rp_tsapp (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) z1 (l_e_st_eq_landau_n_rt_rp_5161_t62 zeta m z1 l1 l2) l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) y.λv:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_5161_t81 zeta m z1 l1 l2 x t y u v) : l_con).
+
+(* notion 3022 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t82a ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz1:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr1 zeta m z1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).(l_e_st_eq_landau_n_rt_rp_tsapp (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) z1 (l_e_st_eq_landau_n_rt_rp_5161_t62 zeta m z1 l1 l2) l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) x.λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) y.λv:l_e_st_eq_landau_n_rt_is z1 (l_e_st_eq_landau_n_rt_ts x y).l_e_st_eq_landau_n_rt_rp_5161_t82 zeta m z1 l1 l2 x t y u v) : l_con).
+
+(* notion 3023 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t83 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.(l_e_st_eq_landau_n_rt_rp_satz159app zeta (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_t61 zeta m) l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_less zeta (l_e_st_eq_landau_n_rt_rp_rpofrt x).λu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).l_e_st_eq_landau_n_rt_rp_5161_t82a zeta m x t u) : l_con).
+
+(* notion 3024 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_zr2 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt z2 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3025 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t84 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.(l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) l3 : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta))).
+
+(* notion 3026 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_yr1 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt y1 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3027 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_yr2 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt y2 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3028 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_ym ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_ite (l_e_st_eq_landau_n_rt_less y1 y2) l_e_st_eq_landau_n_rt_rat y1 y2 : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 3029 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_yrm ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3030 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t85 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λk:l_e_st_eq_landau_n_rt_less y1 y2.(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) y1 (l_e_itet (l_e_st_eq_landau_n_rt_less y1 y2) l_e_st_eq_landau_n_rt_rat y1 y2 k) : l_e_st_eq_landau_n_rt_is y1 (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i)).
+
+(* notion 3031 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t86 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λk:l_e_st_eq_landau_n_rt_less y1 y2.(l_e_st_eq_landau_n_rt_rp_satz154b y1 (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t85 zeta l z2 l3 l4 y1 m1 y2 m2 i k) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
+
+(* notion 3032 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t87 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λk:l_e_st_eq_landau_n_rt_less y1 y2.(l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_t86 zeta l z2 l3 l4 y1 m1 y2 m2 i k) m1 : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).
+
+(* notion 3033 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t88 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λk:l_e_st_eq_landau_n_rt_less y1 y2.(l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t86 zeta l z2 l3 l4 y1 m1 y2 m2 i k) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
+
+(* notion 3034 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t89 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λk:l_e_st_eq_landau_n_rt_less y1 y2.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_satz127d (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_satz154c y1 y2 k)) (l_e_st_eq_landau_n_rt_rp_5161_t88 zeta l z2 l3 l4 y1 m1 y2 m2 i k)) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
+
+(* notion 3035 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t90 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λn:l_not (l_e_st_eq_landau_n_rt_less y1 y2).(l_e_symis l_e_st_eq_landau_n_rt_rat (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) y2 (l_e_itef (l_e_st_eq_landau_n_rt_less y1 y2) l_e_st_eq_landau_n_rt_rat y1 y2 n) : l_e_st_eq_landau_n_rt_is y2 (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i)).
+
+(* notion 3036 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t91 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λn:l_not (l_e_st_eq_landau_n_rt_less y1 y2).(l_e_st_eq_landau_n_rt_rp_satz154b y2 (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t90 zeta l z2 l3 l4 y1 m1 y2 m2 i n) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
+
+(* notion 3037 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t92 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λn:l_not (l_e_st_eq_landau_n_rt_less y1 y2).(l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_t91 zeta l z2 l3 l4 y1 m1 y2 m2 i n) m2 : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).
+
+(* notion 3038 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t93 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λn:l_not (l_e_st_eq_landau_n_rt_less y1 y2).(l_e_st_eq_landau_n_rt_rp_moreisi2 (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t91 zeta l z2 l3 l4 y1 m1 y2 m2 i n) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
+
+(* notion 3039 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t94 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.λn:l_not (l_e_st_eq_landau_n_rt_less y1 y2).(l_e_st_eq_landau_n_rt_rp_trmoreis (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t60 y1 y2 (l_e_st_eq_landau_n_rt_satz81f y1 y2 n)) (l_e_st_eq_landau_n_rt_rp_5161_t93 zeta l z2 l3 l4 y1 m1 y2 m2 i n) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
+
+(* notion 3040 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t95 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_imp_th1 (l_e_st_eq_landau_n_rt_less y1 y2) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (λt:l_e_st_eq_landau_n_rt_less y1 y2.l_e_st_eq_landau_n_rt_rp_5161_t87 zeta l z2 l3 l4 y1 m1 y2 m2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_less y1 y2).l_e_st_eq_landau_n_rt_rp_5161_t92 zeta l z2 l3 l4 y1 m1 y2 m2 i t) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)).
+
+(* notion 3041 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t96 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_imp_th1 (l_e_st_eq_landau_n_rt_less y1 y2) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) (λt:l_e_st_eq_landau_n_rt_less y1 y2.l_e_st_eq_landau_n_rt_rp_5161_t88 zeta l z2 l3 l4 y1 m1 y2 m2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_less y1 y2).l_e_st_eq_landau_n_rt_rp_5161_t94 zeta l z2 l3 l4 y1 m1 y2 m2 i t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
+
+(* notion 3042 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t97 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_imp_th1 (l_e_st_eq_landau_n_rt_less y1 y2) (l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) (λt:l_e_st_eq_landau_n_rt_less y1 y2.l_e_st_eq_landau_n_rt_rp_5161_t89 zeta l z2 l3 l4 y1 m1 y2 m2 i t) (λt:l_not (l_e_st_eq_landau_n_rt_less y1 y2).l_e_st_eq_landau_n_rt_rp_5161_t93 zeta l z2 l3 l4 y1 m1 y2 m2 i t) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)).
+
+(* notion 3043 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t98 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_satz158d (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_t95 zeta l z2 l3 l4 y1 m1 y2 m2 i)) : l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i)).
+
+(* notion 3044 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t99 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_imp_th3 (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i)) (l_e_st_eq_landau_n_rt_rp_5161_t98 zeta l z2 l3 l4 y1 m1 y2 m2 i) (λt:l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta).l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta) (l_e_st_eq_landau_n_rt_rp_5161_t58 zeta) (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) t) : l_not (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta))).
+
+(* notion 3045 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t100 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta) (l_e_st_eq_landau_n_rt_in (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_sqrtset zeta)) (l_e_st_eq_landau_n_rt_rp_5161_t99 zeta l z2 l3 l4 y1 m1 y2 m2 i) (λt:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta.l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) zeta) (l_e_st_eq_landau_n_rt_rp_5161_ym zeta l z2 l3 l4 y1 m1 y2 m2 i) t) : l_not (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta)).
+
+(* notion 3046 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t101 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_satz123f (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta (l_e_st_eq_landau_n_rt_rp_5161_t100 zeta l z2 l3 l4 y1 m1 y2 m2 i) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta).
+
+(* notion 3047 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t101a ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_satz149 (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t96 zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t97 zeta l z2 l3 l4 y1 m1 y2 m2 i) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i))).
+
+(* notion 3048 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t102 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_ismoreis1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts y1 y2)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts y1 y2)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2)) (l_e_st_eq_landau_n_rt_rp_satz155c y1 y2)) (l_e_st_eq_landau_n_rt_rp_satz154b (l_e_st_eq_landau_n_rt_ts y1 y2) z2 i)) (l_e_st_eq_landau_n_rt_rp_5161_t101a zeta l z2 l3 l4 y1 m1 y2 m2 i) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i))).
+
+(* notion 3049 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t103 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_trmoreis (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_yrm zeta l z2 l3 l4 y1 m1 y2 m2 i)) zeta (l_e_st_eq_landau_n_rt_rp_5161_t102 zeta l z2 l3 l4 y1 m1 y2 m2 i) (l_e_st_eq_landau_n_rt_rp_5161_t101 zeta l z2 l3 l4 y1 m1 y2 m2 i) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta).
+
+(* notion 3050 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t104 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.λy1:l_e_st_eq_landau_n_rt_rat.λm1:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr1 zeta l z2 l3 l4 y1) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy2:l_e_st_eq_landau_n_rt_rat.λm2:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5161_yr2 zeta l z2 l3 l4 y1 m1 y2) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts y1 y2) z2.(l_e_st_eq_landau_n_rt_rp_satz123c (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta (l_e_st_eq_landau_n_rt_rp_5161_t103 zeta l z2 l3 l4 y1 m1 y2 m2 i) l4 : l_con).
+
+(* notion 3051 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t105 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.λz2:l_e_st_eq_landau_n_rt_rat.λl3:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2).λl4:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5161_zr2 zeta l z2) zeta.(l_e_st_eq_landau_n_rt_rp_satz160app (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) z2 (l_e_st_eq_landau_n_rt_rp_5161_t84 zeta l z2 l3 l4) l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt x) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta).λv:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x y) z2.l_e_st_eq_landau_n_rt_rp_5161_t104 zeta l z2 l3 l4 x t y u v) : l_con).
+
+(* notion 3052 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t106 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.(l_e_st_eq_landau_n_rt_rp_satz159app (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta l l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) (l_e_st_eq_landau_n_rt_rp_rpofrt x).λu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) zeta.l_e_st_eq_landau_n_rt_rp_5161_t105 zeta l x t u) : l_con).
+
+(* notion 3053 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t107 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_or3e1 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta) (l_e_st_eq_landau_n_rt_rp_satz123a (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta) (λt:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.l_e_st_eq_landau_n_rt_rp_5161_t83 zeta t) (λt:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta.l_e_st_eq_landau_n_rt_rp_5161_t106 zeta t) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta)) zeta).
+
+(* notion 3054 *)
+definition l_e_st_eq_landau_n_rt_rp_5161_t108 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_somei l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta) (l_e_st_eq_landau_n_rt_rp_5161_rtc zeta) (l_e_st_eq_landau_n_rt_rp_5161_t107 zeta) : l_e_st_eq_landau_n_rt_rp_some (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta)).
+
+(* notion 3055 *)
+definition l_e_st_eq_landau_n_rt_rp_satz161 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_onei l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta) (l_e_st_eq_landau_n_rt_rp_5161_t21 zeta) (l_e_st_eq_landau_n_rt_rp_5161_t108 zeta) : l_e_st_eq_landau_n_rt_rp_one (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta)).
+
+(* notion 3056 *)
+definition l_e_st_eq_landau_n_rt_rp_irratrp ≝ λksi:l_e_st_eq_landau_n_rt_cut.(l_not (l_e_st_eq_landau_n_rt_rp_ratrp ksi) : Prop).
+
+(* notion 3057 *)
+definition l_e_st_eq_landau_n_5162_t1 ≝ λv:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl v v) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 v) v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) v) (l_e_st_eq_landau_n_ispl1 v (l_e_st_eq_landau_n_ts l_e_st_eq_landau_n_1 v) v (l_e_st_eq_landau_n_satz28g v)) (l_e_st_eq_landau_n_satz28h l_e_st_eq_landau_n_1 v) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) v)).
+
+(* notion 3058 *)
+definition l_e_st_eq_landau_n_5162_t2 ≝ λv:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_pl v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) v) v (l_e_st_eq_landau_n_5162_t1 v) (l_e_st_eq_landau_n_satz18a v v) : l_e_st_eq_landau_n_less v (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) v)).
+
+(* notion 3059 *)
+definition l_e_st_eq_landau_n_5162_t3 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts w w).(l_e_st_eq_landau_n_satz10j v w (l_imp_th3 (l_e_st_eq_landau_n_moreis v w) (l_e_st_eq_landau_n_moreis (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_satz10h (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts w w) l) (λt:l_e_st_eq_landau_n_moreis v w.l_e_st_eq_landau_n_satz36 v w v w t t)) : l_e_st_eq_landau_n_less v w).
+
+(* notion 3060 *)
+definition l_e_st_eq_landau_n_5162_t4 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) v) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts w v)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_disttp1 v w v) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_ts w v) (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_comts w v)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) v) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w))).
+
+(* notion 3061 *)
+definition l_e_st_eq_landau_n_5162_t5 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts w w))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_disttp2 (l_e_st_eq_landau_n_pl v w) v w) (l_e_st_eq_landau_n_ispl12 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) v) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) w) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_5162_t4 v w) (l_e_st_eq_landau_n_disttp1 v w w)) (l_e_st_eq_landau_n_asspl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts w w)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts w w))).
+
+(* notion 3062 *)
+definition l_e_st_eq_landau_n_5162_t6 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v w) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_5162_t1 (l_e_st_eq_landau_n_ts v w))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w)))).
+
+(* notion 3063 *)
+definition l_e_st_eq_landau_n_5162_nun ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_5162_t5 v w) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_ts v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_ts w w) (l_e_st_eq_landau_n_5162_t6 v w)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_ts w w))).
+
+(* notion 3064 *)
+definition l_e_st_eq_landau_n_5162_nun1 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_5162_nun v w) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts v v) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts v w))) (l_e_st_eq_landau_n_ts w w)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl v w) (l_e_st_eq_landau_n_pl v w))).
+
+(* notion 3065 *)
+definition l_e_st_eq_landau_n_5162_prop1 ≝ λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr w v) (l_e_st_eq_landau_n_fr w v)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) : Prop).
+
+(* notion 3066 *)
+definition l_e_st_eq_landau_n_5162_prop2 ≝ λv:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_some (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop1 v t) : Prop).
+
+(* notion 3067 *)
+definition l_e_st_eq_landau_n_5162_prop3 ≝ (l_e_st_eq_landau_n_some (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) : Prop).
+
+(* notion 3068 *)
+definition l_e_st_eq_landau_n_5162_y ≝ λp:l_e_st_eq_landau_n_5162_prop3.(l_e_ind l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) t) (l_e_st_eq_landau_n_satz27a (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) p) : l_e_st_eq_landau_n_nat).
+
+(* notion 3069 *)
+definition l_e_st_eq_landau_n_5162_t7 ≝ λp:l_e_st_eq_landau_n_5162_prop3.(l_e_oneax l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_min (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) t) (l_e_st_eq_landau_n_satz27a (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) p) : l_e_st_eq_landau_n_min (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) (l_e_st_eq_landau_n_5162_y p)).
+
+(* notion 3070 *)
+definition l_e_st_eq_landau_n_5162_t8 ≝ λp:l_e_st_eq_landau_n_5162_prop3.(l_ande1 (l_e_st_eq_landau_n_lb (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_prop2 (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t7 p) : l_e_st_eq_landau_n_lb (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) (l_e_st_eq_landau_n_5162_y p)).
+
+(* notion 3071 *)
+definition l_e_st_eq_landau_n_5162_t9 ≝ λp:l_e_st_eq_landau_n_5162_prop3.(l_ande2 (l_e_st_eq_landau_n_lb (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 u) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_prop2 (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t7 p) : l_e_st_eq_landau_n_5162_prop2 (l_e_st_eq_landau_n_5162_y p)).
+
+(* notion 3072 *)
+definition l_e_st_eq_landau_n_5162_t10 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_st_eq_landau_n_treq1 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr x (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_fr x (l_e_st_eq_landau_n_5162_y p))) q (l_e_st_eq_landau_n_tfeq12a x (l_e_st_eq_landau_n_5162_y p) x (l_e_st_eq_landau_n_5162_y p)) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)))).
+
+(* notion 3073 *)
+definition l_e_st_eq_landau_n_5162_t11 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)))) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts x x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_12isnd (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_5162_t10 p x q) (l_e_st_eq_landau_n_ndis12 (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz28a (l_e_st_eq_landau_n_ts x x)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x)).
+
+(* notion 3074 *)
+definition l_e_st_eq_landau_n_5162_t12 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t11 p x q) (l_e_st_eq_landau_n_5162_t2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts x x)).
+
+(* notion 3075 *)
+definition l_e_st_eq_landau_n_5162_t13 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_st_eq_landau_n_isless1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p))) (l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_assts1 (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t11 p x q)) (l_e_st_eq_landau_n_satz35c (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)))) (l_e_st_eq_landau_n_5162_t2 (l_e_st_eq_landau_n_5162_y p))) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)))).
+
+(* notion 3076 *)
+definition l_e_st_eq_landau_n_5162_t14 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_st_eq_landau_n_5162_t3 (l_e_st_eq_landau_n_5162_y p) x (l_e_st_eq_landau_n_5162_t12 p x q) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_5162_y p) x).
+
+(* notion 3077 *)
+definition l_e_st_eq_landau_n_5162_t15 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_e_st_eq_landau_n_5162_t3 x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t13 p x q) : l_e_st_eq_landau_n_less x (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p))).
+
+(* notion 3078 *)
+definition l_e_st_eq_landau_n_5162_t16 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).(l_e_st_eq_landau_n_isless12 x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) i (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t1 (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_5162_t15 p x q) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))).
+
+(* notion 3079 *)
+definition l_e_st_eq_landau_n_5162_t17 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).(l_e_st_eq_landau_n_satz20f u (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_t16 p x q u i) : l_e_st_eq_landau_n_less u (l_e_st_eq_landau_n_5162_y p)).
+
+(* notion 3080 *)
+definition l_e_st_eq_landau_n_5162_t18 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t) j : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl u t) (l_e_st_eq_landau_n_5162_y p)).
+
+(* notion 3081 *)
+definition l_e_st_eq_landau_n_5162_t19 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ists12 x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u) x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u) i i) (l_e_st_eq_landau_n_5162_nun (l_e_st_eq_landau_n_5162_y p) u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_ts u u))).
+
+(* notion 3082 *)
+definition l_e_st_eq_landau_n_5162_t20 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_5162_t19 p x q u i t j)) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)))).
+
+(* notion 3083 *)
+definition l_e_st_eq_landau_n_5162_t21 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_ts u (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts u (l_e_st_eq_landau_n_pl u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_comts (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t) u j) (l_e_st_eq_landau_n_disttp2 u u t) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts u t))).
+
+(* notion 3084 *)
+definition l_e_st_eq_landau_n_5162_t22 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_ists2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_5162_t21 p x q u i t j)) (l_e_st_eq_landau_n_disttp2 (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts u t)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)))).
+
+(* notion 3085 *)
+definition l_e_st_eq_landau_n_5162_t23 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_5162_t22 p x q u i t j)) (l_e_st_eq_landau_n_asspl2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)))).
+
+(* notion 3086 *)
+definition l_e_st_eq_landau_n_5162_t24 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)))) (l_e_st_eq_landau_n_5162_t20 p x q u i t j) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_5162_t23 p x q u i t j)) (l_e_st_eq_landau_n_asspl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))))).
+
+(* notion 3087 *)
+definition l_e_st_eq_landau_n_5162_t25 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_pl u t) (l_e_st_eq_landau_n_pl u t)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_asspl2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t))) (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_compl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_5162_nun1 u t) (l_e_st_eq_landau_n_ists12 (l_e_st_eq_landau_n_pl u t) (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t) (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_t18 p x q u i t j) (l_e_st_eq_landau_n_5162_t18 p x q u i t j)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))).
+
+(* notion 3088 *)
+definition l_e_st_eq_landau_n_5162_t26 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_5162_t24 p x q u i t j) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_ts t t))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_5162_t25 p x q u i t j)) (l_e_st_eq_landau_n_compl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_asspl2 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)))).
+
+(* notion 3089 *)
+definition l_e_st_eq_landau_n_5162_t27 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_5162_t1 (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_5162_t11 p x q) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x)).
+
+(* notion 3090 *)
+definition l_e_st_eq_landau_n_5162_t28 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_5162_t26 p x q u i t j) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p)) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_y p))) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_5162_t27 p x q u i t j)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)))).
+
+(* notion 3091 *)
+definition l_e_st_eq_landau_n_5162_t29 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_st_eq_landau_n_satz20e (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts x x) (l_e_st_eq_landau_n_5162_t28 p x q u i t j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u))).
+
+(* notion 3092 *)
+definition l_e_st_eq_landau_n_5162_t30 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_tr4is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u)))) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_ts t t) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_num (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u))) (l_e_st_eq_landau_n_den (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_ndis12 (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u)) (l_e_symis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_5162_t29 p x q u i t j)) (l_e_st_eq_landau_n_satz28e (l_e_st_eq_landau_n_ts t t)) (l_e_st_eq_landau_n_12isnd (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u) (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u))).
+
+(* notion 3093 *)
+definition l_e_st_eq_landau_n_5162_t31 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_st_eq_landau_n_treq2 (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr t u) (l_e_st_eq_landau_n_fr t u)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_ts t t) (l_e_st_eq_landau_n_ts u u)) (l_e_st_eq_landau_n_tfeq12a t u t u) (l_e_st_eq_landau_n_5162_t30 p x q u i t j) : l_e_st_eq_landau_n_5162_prop1 u t).
+
+(* notion 3094 *)
+definition l_e_st_eq_landau_n_5162_t32 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_somei l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop1 u v) t (l_e_st_eq_landau_n_5162_t31 p x q u i t j) : l_e_st_eq_landau_n_5162_prop2 u).
+
+(* notion 3095 *)
+definition l_e_st_eq_landau_n_5162_t33 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_st_eq_landau_n_5162_t8 p u (l_e_st_eq_landau_n_5162_t32 p x q u i t j) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_5162_y p) u).
+
+(* notion 3096 *)
+definition l_e_st_eq_landau_n_5162_t34 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).λt:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_pl u t).(l_e_st_eq_landau_n_satz10g (l_e_st_eq_landau_n_5162_y p) u (l_e_st_eq_landau_n_satz12 u (l_e_st_eq_landau_n_5162_y p) (l_e_st_eq_landau_n_5162_t17 p x q u i)) (l_e_st_eq_landau_n_5162_t33 p x q u i t j) : l_con).
+
+(* notion 3097 *)
+definition l_e_st_eq_landau_n_5162_t35 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.λu:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_5162_y p) u).(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_5162_y p) u v) (l_e_st_eq_landau_n_5162_t17 p x q u i) l_con (λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_diffprop (l_e_st_eq_landau_n_5162_y p) u v.l_e_st_eq_landau_n_5162_t34 p x q u i v w) : l_con).
+
+(* notion 3098 *)
+definition l_e_st_eq_landau_n_5162_t36 ≝ λp:l_e_st_eq_landau_n_5162_prop3.λx:l_e_st_eq_landau_n_nat.λq:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) x.(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_diffprop x (l_e_st_eq_landau_n_5162_y p) v) (l_e_st_eq_landau_n_5162_t14 p x q) l_con (λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_diffprop x (l_e_st_eq_landau_n_5162_y p) v.l_e_st_eq_landau_n_5162_t35 p x q v w) : l_con).
+
+(* notion 3099 *)
+definition l_e_st_eq_landau_n_5162_t37 ≝ λp:l_e_st_eq_landau_n_5162_prop3.(l_someapp l_e_st_eq_landau_n_nat (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) v) (l_e_st_eq_landau_n_5162_t9 p) l_con (λv:l_e_st_eq_landau_n_nat.λw:l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_5162_y p) v.l_e_st_eq_landau_n_5162_t36 p v w) : l_con).
+
+(* notion 3100 *)
+definition l_e_st_eq_landau_n_rt_5162_t38 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_rt_ise (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_tf x x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_tict x0 x0 x x xix0 xix0) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1)) i : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf x x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1)).
+
+(* notion 3101 *)
+definition l_e_st_eq_landau_n_rt_5162_t39 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_refeq1 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x (l_e_st_eq_landau_n_fris x) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x).
+
+(* notion 3102 *)
+definition l_e_st_eq_landau_n_rt_5162_t40 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_eqtf12 (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) x (l_e_st_eq_landau_n_rt_5162_t39 x0 i x xix0) (l_e_st_eq_landau_n_rt_5162_t39 x0 i x xix0) : l_e_st_eq_landau_n_eq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x))) (l_e_st_eq_landau_n_tf x x)).
+
+(* notion 3103 *)
+definition l_e_st_eq_landau_n_rt_5162_t41 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_treq (l_e_st_eq_landau_n_tf (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x)) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_den x))) (l_e_st_eq_landau_n_tf x x) (l_e_st_eq_landau_n_fr (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_5162_t40 x0 i x xix0) (l_e_st_eq_landau_n_rt_5162_t38 x0 i x xix0) : l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_num x)).
+
+(* notion 3104 *)
+definition l_e_st_eq_landau_n_rt_5162_t42 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop1 (l_e_st_eq_landau_n_den x) t) (l_e_st_eq_landau_n_num x) (l_e_st_eq_landau_n_rt_5162_t41 x0 i x xix0) : l_e_st_eq_landau_n_5162_prop2 (l_e_st_eq_landau_n_den x)).
+
+(* notion 3105 *)
+definition l_e_st_eq_landau_n_rt_5162_t43 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_5162_prop2 t) (l_e_st_eq_landau_n_den x) (l_e_st_eq_landau_n_rt_5162_t42 x0 i x xix0) : l_e_st_eq_landau_n_5162_prop3).
+
+(* notion 3106 *)
+definition l_e_st_eq_landau_n_rt_5162_t44 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).λx:l_e_st_eq_landau_n_frac.λxix0:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).(l_e_st_eq_landau_n_5162_t37 (l_e_st_eq_landau_n_rt_5162_t43 x0 i x xix0) : l_con).
+
+(* notion 3107 *)
+definition l_e_st_eq_landau_n_rt_5162_t45 ≝ λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts x0 x0) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)).(l_e_st_eq_landau_n_rt_ratapp1 x0 l_con (λx:l_e_st_eq_landau_n_frac.λt:l_e_st_eq_landau_n_rt_inf x (l_e_st_eq_landau_n_rt_class x0).l_e_st_eq_landau_n_rt_5162_t44 x0 i x t) : l_con).
+
+(* notion 3108 *)
+definition l_e_st_eq_landau_n_rt_rp_5162_ksi ≝ (l_e_ind l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_satz161 (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3109 *)
+definition l_e_st_eq_landau_n_rt_rp_5162_t46 ≝ (l_e_oneax l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_satz161 (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_5162_ksi l_e_st_eq_landau_n_rt_rp_5162_ksi) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))).
+
+(* notion 3110 *)
+definition l_e_st_eq_landau_n_rt_rp_5162_x0 ≝ λr:l_e_st_eq_landau_n_rt_rp_ratrp l_e_st_eq_landau_n_rt_rp_5162_ksi.(l_e_st_eq_landau_n_rt_rp_rtofrp l_e_st_eq_landau_n_rt_rp_5162_ksi r : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 3111 *)
+definition l_e_st_eq_landau_n_rt_rp_5162_t47 ≝ λr:l_e_st_eq_landau_n_rt_rp_ratrp l_e_st_eq_landau_n_rt_rp_5162_ksi.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_x0 r))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5162_x0 r))) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_5162_ksi l_e_st_eq_landau_n_rt_rp_5162_ksi) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_satz155c (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) (l_e_st_eq_landau_n_rt_rp_ists12 (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) l_e_st_eq_landau_n_rt_rp_5162_ksi (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) l_e_st_eq_landau_n_rt_rp_5162_ksi (l_e_st_eq_landau_n_rt_rp_isrprt2 l_e_st_eq_landau_n_rt_rp_5162_ksi r) (l_e_st_eq_landau_n_rt_rp_isrprt2 l_e_st_eq_landau_n_rt_rp_5162_ksi r)) l_e_st_eq_landau_n_rt_rp_5162_t46 : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_x0 r))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))).
+
+(* notion 3112 *)
+definition l_e_st_eq_landau_n_rt_rp_5162_t48 ≝ λr:l_e_st_eq_landau_n_rt_rp_ratrp l_e_st_eq_landau_n_rt_rp_5162_ksi.(l_e_st_eq_landau_n_rt_rp_isrtirp (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_5162_t47 r) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_x0 r)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_suc l_e_st_eq_landau_n_1))).
+
+(* notion 3113 *)
+definition l_e_st_eq_landau_n_rt_rp_5162_t49 ≝ λr:l_e_st_eq_landau_n_rt_rp_ratrp l_e_st_eq_landau_n_rt_rp_5162_ksi.(l_e_st_eq_landau_n_rt_5162_t45 (l_e_st_eq_landau_n_rt_rp_5162_x0 r) (l_e_st_eq_landau_n_rt_rp_5162_t48 r) : l_con).
+
+(* notion 3114 *)
+definition l_e_st_eq_landau_n_rt_rp_satz162 ≝ (l_somei l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_irratrp a) l_e_st_eq_landau_n_rt_rp_5162_ksi (λt:l_e_st_eq_landau_n_rt_rp_ratrp l_e_st_eq_landau_n_rt_rp_5162_ksi.l_e_st_eq_landau_n_rt_rp_5162_t49 t) : l_e_st_eq_landau_n_rt_rp_some (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_irratrp a)).
+
+(* notion 3115 *)
+definition l_e_st_eq_landau_n_rt_rp_sqrt ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_ind l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta) (l_e_st_eq_landau_n_rt_rp_satz161 zeta) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3116 *)
+definition l_e_st_eq_landau_n_rt_rp_thsqrt1 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.(l_e_oneax l_e_st_eq_landau_n_rt_cut (λa:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts a a) zeta) (l_e_st_eq_landau_n_rt_rp_satz161 zeta) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_sqrt zeta) (l_e_st_eq_landau_n_rt_rp_sqrt zeta)) zeta).
+
+(* notion 3117 *)
+definition l_e_st_eq_landau_n_rt_rp_thsqrt2 ≝ λzeta:l_e_st_eq_landau_n_rt_cut.λksi:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi ksi) zeta.(l_e_st_eq_landau_n_rt_rp_5161_t20 zeta ksi (l_e_st_eq_landau_n_rt_rp_sqrt zeta) i (l_e_st_eq_landau_n_rt_rp_thsqrt1 zeta) : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_sqrt zeta)).
+
+(* notion 3118 *)
+definition l_e_st_eq_landau_n_rt_rp_issqrt ≝ λksi:l_e_st_eq_landau_n_rt_cut.λeta:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is ksi eta.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_sqrt t) ksi eta i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_sqrt ksi) (l_e_st_eq_landau_n_rt_rp_sqrt eta)).
+
+(* notion 3119 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_x ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_ntofrp ksi nx : l_e_st_eq_landau_n_nat).
+
+(* notion 3120 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_y ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_ntofrp eta ny : l_e_st_eq_landau_n_nat).
+
+(* notion 3121 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t1 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_isrpnt1 ksi nx : l_e_st_eq_landau_n_rt_rp_is ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny))).
+
+(* notion 3122 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t2 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_isrpnt1 eta ny : l_e_st_eq_landau_n_rt_rp_is eta (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))).
+
+(* notion 3123 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t3 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_ispl12 ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) eta (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t1 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t2 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)))).
+
+(* notion 3124 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_x0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny) : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 3125 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_y0 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny) : l_e_st_eq_landau_n_rt_rat).
+
+(* notion 3126 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t4 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_natrti (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny)).
+
+(* notion 3127 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t5 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_natrti (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)).
+
+(* notion 3128 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t6 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_satz155a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)))).
+
+(* notion 3129 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t7 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_satz112d (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t4 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t5 ksi nx eta ny) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))).
+
+(* notion 3130 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_xpy ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t7 ksi nx eta ny) : l_e_st_eq_landau_n_nat).
+
+(* notion 3131 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t8 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_isrtn1 (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t7 ksi nx eta ny) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny))).
+
+(* notion 3132 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t9 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_isrterp (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t8 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny))).
+
+(* notion 3133 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t10 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_pl (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t3 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t6 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t9 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny))).
+
+(* notion 3134 *)
+definition l_e_st_eq_landau_n_rt_rp_natpl ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl ksi eta) (l_e_st_eq_landau_n_rt_rp_rpofnt t)) (l_e_st_eq_landau_n_rt_rp_iiia_xpy ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t10 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_pl ksi eta)).
+
+(* notion 3135 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t11 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_ists12 ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) eta (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t1 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t2 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)))).
+
+(* notion 3136 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t12 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_satz155c (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)))).
+
+(* notion 3137 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t13 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_satz112f (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t4 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t5 ksi nx eta ny) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))).
+
+(* notion 3138 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_xty ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t13 ksi nx eta ny) : l_e_st_eq_landau_n_nat).
+
+(* notion 3139 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t14 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_isrtn1 (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t13 ksi nx eta ny) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny))).
+
+(* notion 3140 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t15 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_st_eq_landau_n_rt_rp_isrterp (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t14 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny))).
+
+(* notion 3141 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t16 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_ts (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t11 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t12 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t15 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny))).
+
+(* notion 3142 *)
+definition l_e_st_eq_landau_n_rt_rp_natts ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts ksi eta) (l_e_st_eq_landau_n_rt_rp_rpofnt t)) (l_e_st_eq_landau_n_rt_rp_iiia_xty ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t16 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_ts ksi eta)).
+
+(* notion 3143 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t17 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismore12 ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) eta (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_iiia_t1 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t2 ksi nx eta ny) m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny))).
+
+(* notion 3144 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t18 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_satz154d (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t17 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny)).
+
+(* notion 3145 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t20 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_ismn12 ksi (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) eta (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) m (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rp_iiia_t1 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t2 ksi nx eta ny) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)))).
+
+(* notion 3146 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t21 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_satz155b (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)))).
+
+(* notion 3147 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t22 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_satz112g (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t4 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t5 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_natrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))).
+
+(* notion 3148 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_xmy ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_nofrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rp_iiia_t22 ksi nx eta ny m) : l_e_st_eq_landau_n_nat).
+
+(* notion 3149 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t23 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_isrtn1 (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rp_iiia_t22 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_is (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m))).
+
+(* notion 3150 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t24 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_st_eq_landau_n_rt_rp_isrterp (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rtofn (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rp_iiia_t23 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m))).
+
+(* notion 3151 *)
+definition l_e_st_eq_landau_n_rt_rp_iiia_t25 ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_x ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_y ksi nx eta ny)) (l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn (l_e_st_eq_landau_n_rt_rp_iiia_x0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_y0 ksi nx eta ny) (l_e_st_eq_landau_n_rt_rp_iiia_t18 ksi nx eta ny m))) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m)) (l_e_st_eq_landau_n_rt_rp_iiia_t20 ksi nx eta ny m) (l_e_st_eq_landau_n_rt_rp_iiia_t21 ksi nx eta ny m) (l_e_st_eq_landau_n_rt_rp_iiia_t24 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m))).
+
+(* notion 3152 *)
+definition l_e_st_eq_landau_n_rt_rp_natmn ≝ λksi:l_e_st_eq_landau_n_rt_cut.λnx:l_e_st_eq_landau_n_rt_rp_natrp ksi.λeta:l_e_st_eq_landau_n_rt_cut.λny:l_e_st_eq_landau_n_rt_rp_natrp eta.λm:l_e_st_eq_landau_n_rt_rp_more ksi eta.(l_somei l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_mn ksi eta m) (l_e_st_eq_landau_n_rt_rp_rpofnt t)) (l_e_st_eq_landau_n_rt_rp_iiia_xmy ksi nx eta ny m) (l_e_st_eq_landau_n_rt_rp_iiia_t25 ksi nx eta ny m) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_mn ksi eta m)).
+
+(* notion 3153 *)
+definition l_e_st_eq_landau_n_rt_rp_3pl13 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl q r) p) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r q) p) (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl q p)) (l_e_st_eq_landau_n_rt_rp_compl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl q r) (l_e_st_eq_landau_n_rt_rp_pl r q) p (l_e_st_eq_landau_n_rt_rp_compl q r)) (l_e_st_eq_landau_n_rt_rp_asspl1 r q p) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl q p))).
+
+(* notion 3154 *)
+definition l_e_st_eq_landau_n_rt_rp_4pl24 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl r s))) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_pl r q))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p s) (l_e_st_eq_landau_n_rt_rp_pl r q)) (l_e_st_eq_landau_n_rt_rp_asspl1 p q (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_pl r q)) p (l_e_st_eq_landau_n_rt_rp_3pl13 q r s)) (l_e_st_eq_landau_n_rt_rp_asspl2 p s (l_e_st_eq_landau_n_rt_rp_pl r q)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p s) (l_e_st_eq_landau_n_rt_rp_pl r q))).
+
+(* notion 3155 *)
+definition l_e_st_eq_landau_n_rt_rp_3pl12 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl q p) r) (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl p r)) (l_e_st_eq_landau_n_rt_rp_asspl2 p q r) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl p q) (l_e_st_eq_landau_n_rt_rp_pl q p) r (l_e_st_eq_landau_n_rt_rp_compl p q)) (l_e_st_eq_landau_n_rt_rp_asspl1 q p r) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl p r))).
+
+(* notion 3156 *)
+definition l_e_st_eq_landau_n_rt_rp_4pl23 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl r s))) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl q s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p r) (l_e_st_eq_landau_n_rt_rp_pl q s)) (l_e_st_eq_landau_n_rt_rp_asspl1 p q (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl q (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl q s)) p (l_e_st_eq_landau_n_rt_rp_3pl12 q r s)) (l_e_st_eq_landau_n_rt_rp_asspl2 p r (l_e_st_eq_landau_n_rt_rp_pl q s)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p r) (l_e_st_eq_landau_n_rt_rp_pl q s))).
+
+(* notion 3157 *)
+definition l_e_st_eq_landau_n_rt_rp_3pl23 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) r) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl p (l_e_st_eq_landau_n_rt_rp_pl r q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p r) q) (l_e_st_eq_landau_n_rt_rp_asspl1 p q r) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl q r) (l_e_st_eq_landau_n_rt_rp_pl r q) p (l_e_st_eq_landau_n_rt_rp_compl q r)) (l_e_st_eq_landau_n_rt_rp_asspl2 p r q) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p q) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl p r) q)).
+
+(* notion 3158 *)
+definition l_e_st_eq_landau_n_rt_rp_a2isapa ≝ λp:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl p p) (l_e_st_eq_landau_n_rt_rp_disttp2 p l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts p l_e_st_eq_landau_n_rt_rp_1rp) p (l_e_st_eq_landau_n_rt_rp_ts p l_e_st_eq_landau_n_rt_rp_1rp) p (l_e_st_eq_landau_n_rt_rp_satz151 p) (l_e_st_eq_landau_n_rt_rp_satz151 p)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl p p)).
+
+(* notion 3159 *)
+definition l_e_st_eq_landau_n_rt_rp_dif ≝ (l_e_st_eq_landau_n_pair1type l_e_st_eq_landau_n_rt_cut : Type[0]).
+
+(* notion 3160 *)
+definition l_e_st_eq_landau_n_rt_rp_df ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_pair1 l_e_st_eq_landau_n_rt_cut a1 a2 : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3161 *)
+definition l_e_st_eq_landau_n_rt_rp_stm ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_first1 l_e_st_eq_landau_n_rt_cut a : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3162 *)
+definition l_e_st_eq_landau_n_rt_rp_std ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_second1 l_e_st_eq_landau_n_rt_cut a : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3163 *)
+definition l_e_st_eq_landau_n_rt_rp_stmis ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_first1is1 l_e_st_eq_landau_n_rt_cut a1 a2 : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1).
+
+(* notion 3164 *)
+definition l_e_st_eq_landau_n_rt_rp_isstm ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_first1is2 l_e_st_eq_landau_n_rt_cut a1 a2 : l_e_st_eq_landau_n_rt_rp_is a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))).
+
+(* notion 3165 *)
+definition l_e_st_eq_landau_n_rt_rp_stdis ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_second1is1 l_e_st_eq_landau_n_rt_cut a1 a2 : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2).
+
+(* notion 3166 *)
+definition l_e_st_eq_landau_n_rt_rp_isstd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_second1is2 l_e_st_eq_landau_n_rt_cut a1 a2 : l_e_st_eq_landau_n_rt_rp_is a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))).
+
+(* notion 3167 *)
+definition l_e_st_eq_landau_n_rt_rp_1a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stm a : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3168 *)
+definition l_e_st_eq_landau_n_rt_rp_2a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_std a : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3169 *)
+definition l_e_st_eq_landau_n_rt_rp_dfis ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_pair1is1 l_e_st_eq_landau_n_rt_cut a : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) a).
+
+(* notion 3170 *)
+definition l_e_st_eq_landau_n_rt_rp_isdf ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_pair1is2 l_e_st_eq_landau_n_rt_cut a : l_e_is l_e_st_eq_landau_n_rt_rp_dif a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a))).
+
+(* notion 3171 *)
+definition l_e_st_eq_landau_n_rt_rp_12issmsd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl12 a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) b2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_isstm a1 a2) (l_e_st_eq_landau_n_rt_rp_isstd b1 b2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)))).
+
+(* notion 3172 *)
+definition l_e_st_eq_landau_n_rt_rp_smsdis12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_12issmsd a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl a1 b2)).
+
+(* notion 3173 *)
+definition l_e_st_eq_landau_n_rt_rp_1sdissmsd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl1 r1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_isstm r1 r2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a))).
+
+(* notion 3174 *)
+definition l_e_st_eq_landau_n_rt_rp_smsdis1sd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_1sdissmsd a r1 r2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a))).
+
+(* notion 3175 *)
+definition l_e_st_eq_landau_n_rt_rp_sm2issmsd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl2 r2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_isstd r1 r2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)))).
+
+(* notion 3176 *)
+definition l_e_st_eq_landau_n_rt_rp_smsdissm2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_sm2issmsd a r1 r2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2)).
+
+(* notion 3177 *)
+definition l_e_st_eq_landau_n_rt_rp_issm ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a1 r.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_dif (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_df t a2) a1 r i : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df r a2)).
+
+(* notion 3178 *)
+definition l_e_st_eq_landau_n_rt_rp_issd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a2 r.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_dif (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_df a1 t) a2 r i : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df a1 r)).
+
+(* notion 3179 *)
+definition l_e_st_eq_landau_n_rt_rp_issmsd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a1 b1.λj:l_e_st_eq_landau_n_rt_rp_is a2 b2.(l_e_tris l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2) (l_e_st_eq_landau_n_rt_rp_issm a1 a2 b1 i) (l_e_st_eq_landau_n_rt_rp_issd b1 a2 b2 j) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)).
+
+(* notion 3180 *)
+definition l_e_st_eq_landau_n_rt_rp_1b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stm b : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3181 *)
+definition l_e_st_eq_landau_n_rt_rp_2b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_std b : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3182 *)
+definition l_e_st_eq_landau_n_rt_rp_eq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : Prop).
+
+(* notion 3183 *)
+definition l_e_st_eq_landau_n_rt_rp_eqi12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2).(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_smsdis12 a1 a2 b1 b2) i (l_e_st_eq_landau_n_rt_rp_12issmsd b1 b2 a1 a2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)).
+
+(* notion 3184 *)
+definition l_e_st_eq_landau_n_rt_rp_eqi1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)).(l_e_isp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq x (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) a (l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) r1 r2 i) (l_e_st_eq_landau_n_rt_rp_dfis a) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_df r1 r2)).
+
+(* notion 3185 *)
+definition l_e_st_eq_landau_n_rt_rp_eqi2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2).(l_e_isp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df r1 r2) x) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) a (l_e_st_eq_landau_n_rt_rp_eqi12 r1 r2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) i) (l_e_st_eq_landau_n_rt_rp_dfis a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df r1 r2) a).
+
+(* notion 3186 *)
+definition l_e_st_eq_landau_n_rt_rp_eqe12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2).(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_pl b1 a2) (l_e_st_eq_landau_n_rt_rp_12issmsd a1 a2 b1 b2) e (l_e_st_eq_landau_n_rt_rp_smsdis12 b1 b2 a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2)).
+
+(* notion 3187 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd163 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_eq a a).
+
+(* notion 3188 *)
+definition l_e_st_eq_landau_n_rt_rp_refeq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd163 a : l_e_st_eq_landau_n_rt_rp_eq a a).
+
+(* notion 3189 *)
+definition l_e_st_eq_landau_n_rt_rp_refeq1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_is l_e_st_eq_landau_n_rt_rp_dif a b.(l_e_isp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq a x) a b (l_e_st_eq_landau_n_rt_rp_refeq a) i : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3190 *)
+definition l_e_st_eq_landau_n_rt_rp_refeq2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_is l_e_st_eq_landau_n_rt_rp_dif a b.(l_e_isp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq x a) a b (l_e_st_eq_landau_n_rt_rp_refeq a) i : l_e_st_eq_landau_n_rt_rp_eq b a).
+
+(* notion 3191 *)
+definition l_e_st_eq_landau_n_rt_rp_eqsmsd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a1 b1.λj:l_e_st_eq_landau_n_rt_rp_is a2 b2.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2) (l_e_st_eq_landau_n_rt_rp_issmsd a1 a2 b1 b2 i j) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)).
+
+(* notion 3192 *)
+definition l_e_st_eq_landau_n_rt_rp_eqsm ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a1 r.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df r a2) (l_e_st_eq_landau_n_rt_rp_issm a1 a2 r i) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df r a2)).
+
+(* notion 3193 *)
+definition l_e_st_eq_landau_n_rt_rp_eqsd ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a2 r.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df a1 r) (l_e_st_eq_landau_n_rt_rp_issd a1 a2 r i) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df a1 r)).
+
+(* notion 3194 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd164 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) e : l_e_st_eq_landau_n_rt_rp_eq b a).
+
+(* notion 3195 *)
+definition l_e_st_eq_landau_n_rt_rp_symeq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_satzd164 a b e : l_e_st_eq_landau_n_rt_rp_eq b a).
+
+(* notion 3196 *)
+definition l_e_st_eq_landau_n_rt_rp_1c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stm c : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3197 *)
+definition l_e_st_eq_landau_n_rt_rp_2c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_std c : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3198 *)
+definition l_e_st_eq_landau_n_rt_rp_1d165_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq b c.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)) e f : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)))).
+
+(* notion 3199 *)
+definition l_e_st_eq_landau_n_rt_rp_1d165_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq b c.(l_e_tr4is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_1d165_t1 a b c e f) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)))).
+
+(* notion 3200 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd165 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq b c.(l_e_st_eq_landau_n_rt_rp_satz136b (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_1d165_t2 a b c e f) : l_e_st_eq_landau_n_rt_rp_eq a c).
+
+(* notion 3201 *)
+definition l_e_st_eq_landau_n_rt_rp_treq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq b c.(l_e_st_eq_landau_n_rt_rp_satzd165 a b c e f : l_e_st_eq_landau_n_rt_rp_eq a c).
+
+(* notion 3202 *)
+definition l_e_st_eq_landau_n_rt_rp_treq1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq c a.λf:l_e_st_eq_landau_n_rt_rp_eq c b.(l_e_st_eq_landau_n_rt_rp_treq a c b (l_e_st_eq_landau_n_rt_rp_symeq c a e) f : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3203 *)
+definition l_e_st_eq_landau_n_rt_rp_treq2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a c.λf:l_e_st_eq_landau_n_rt_rp_eq b c.(l_e_st_eq_landau_n_rt_rp_treq a c b e (l_e_st_eq_landau_n_rt_rp_symeq b c f) : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3204 *)
+definition l_e_st_eq_landau_n_rt_rp_tr3eq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe1:l_e_st_eq_landau_n_rt_rp_eq a b.λe2:l_e_st_eq_landau_n_rt_rp_eq b c.λe3:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_treq a b d e1 (l_e_st_eq_landau_n_rt_rp_treq b c d e2 e3) : l_e_st_eq_landau_n_rt_rp_eq a d).
+
+(* notion 3205 *)
+definition l_e_st_eq_landau_n_rt_rp_tr4eq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_dif.λe1:l_e_st_eq_landau_n_rt_rp_eq a b.λe2:l_e_st_eq_landau_n_rt_rp_eq b c.λe3:l_e_st_eq_landau_n_rt_rp_eq c d.λe4:l_e_st_eq_landau_n_rt_rp_eq d e.(l_e_st_eq_landau_n_rt_rp_tr3eq a b c e e1 e2 (l_e_st_eq_landau_n_rt_rp_treq c d e e3 e4) : l_e_st_eq_landau_n_rt_rp_eq a e).
+
+(* notion 3206 *)
+definition l_e_st_eq_landau_n_rt_rp_posd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) : Prop).
+
+(* notion 3207 *)
+definition l_e_st_eq_landau_n_rt_rp_zero ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) : Prop).
+
+(* notion 3208 *)
+definition l_e_st_eq_landau_n_rt_rp_negd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) : Prop).
+
+(* notion 3209 *)
+definition l_e_st_eq_landau_n_rt_rp_posdi ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more a1 a2.(l_e_st_eq_landau_n_rt_rp_ismore12 a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_isstm a1 a2) (l_e_st_eq_landau_n_rt_rp_isstd a1 a2) m : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_df a1 a2)).
+
+(* notion 3210 *)
+definition l_e_st_eq_landau_n_rt_rp_zeroi ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is a1 a2.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1 a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) i (l_e_st_eq_landau_n_rt_rp_isstd a1 a2) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_df a1 a2)).
+
+(* notion 3211 *)
+definition l_e_st_eq_landau_n_rt_rp_negdi ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less a1 a2.(l_e_st_eq_landau_n_rt_rp_isless12 a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_isstm a1 a2) (l_e_st_eq_landau_n_rt_rp_isstd a1 a2) l : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_df a1 a2)).
+
+(* notion 3212 *)
+definition l_e_st_eq_landau_n_rt_rp_axrde ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) : l_ec3 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a)).
+
+(* notion 3213 *)
+definition l_e_st_eq_landau_n_rt_rp_axrdo ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satz123a (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) : l_or3 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a)).
+
+(* notion 3214 *)
+definition l_e_st_eq_landau_n_rt_rp_axrd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_orec3i (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrdo a) (l_e_st_eq_landau_n_rt_rp_axrde a) : l_orec3 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a)).
+
+(* notion 3215 *)
+definition l_e_st_eq_landau_n_rt_rp_rappd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:Prop.λp1:Πt:l_e_st_eq_landau_n_rt_rp_posd a.p.λp2:Πt:l_e_st_eq_landau_n_rt_rp_zero a.p.λp3:Πt:l_e_st_eq_landau_n_rt_rp_negd a.p.(l_or3app (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) p (l_e_st_eq_landau_n_rt_rp_axrdo a) p2 p1 p3 : p).
+
+(* notion 3216 *)
+definition l_e_st_eq_landau_n_rt_rp_pnot0d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) p : l_not (l_e_st_eq_landau_n_rt_rp_zero a)).
+
+(* notion 3217 *)
+definition l_e_st_eq_landau_n_rt_rp_pnotnd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_ec3e23 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) p : l_not (l_e_st_eq_landau_n_rt_rp_negd a)).
+
+(* notion 3218 *)
+definition l_e_st_eq_landau_n_rt_rp_0notpd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_ec3e12 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) z : l_not (l_e_st_eq_landau_n_rt_rp_posd a)).
+
+(* notion 3219 *)
+definition l_e_st_eq_landau_n_rt_rp_0notnd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_ec3e13 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) z : l_not (l_e_st_eq_landau_n_rt_rp_negd a)).
+
+(* notion 3220 *)
+definition l_e_st_eq_landau_n_rt_rp_nnotpd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_ec3e32 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) n : l_not (l_e_st_eq_landau_n_rt_rp_posd a)).
+
+(* notion 3221 *)
+definition l_e_st_eq_landau_n_rt_rp_nnot0d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrde a) n : l_not (l_e_st_eq_landau_n_rt_rp_zero a)).
+
+(* notion 3222 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) e (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_satz135a (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) p) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a))).
+
+(* notion 3223 *)
+definition l_e_st_eq_landau_n_rt_rp_eqposd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_satz136a (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv1d_t1 a b e p) : l_e_st_eq_landau_n_rt_rp_posd b).
+
+(* notion 3224 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_symeq a b e) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) z) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a))).
+
+(* notion 3225 *)
+definition l_e_st_eq_landau_n_rt_rp_eqzero ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_satz136b (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv1d_t2 a b e z) : l_e_st_eq_landau_n_rt_rp_zero b).
+
+(* notion 3226 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) e (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_satz135c (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) n) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a))).
+
+(* notion 3227 *)
+definition l_e_st_eq_landau_n_rt_rp_eqnegd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_satz136c (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv1d_t3 a b e n) : l_e_st_eq_landau_n_rt_rp_negd b).
+
+(* notion 3228 *)
+definition l_e_st_eq_landau_n_rt_rp_zeroeq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.λy:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) z (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) y)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3229 *)
+definition l_e_st_eq_landau_n_rt_rp_pdofrp ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3230 *)
+definition l_e_st_eq_landau_n_rt_rp_ndofrp ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3231 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpepd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r s.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s) (l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_pdofrp x) r s i) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)).
+
+(* notion 3232 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpend ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r s.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_ndofrp s) (l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ndofrp x) r s i) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_ndofrp s)).
+
+(* notion 3233 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t4 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz136b (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_eqe12 (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp e) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp)).
+
+(* notion 3234 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpipd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz136b r s l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv1d_t4 r s e) : l_e_st_eq_landau_n_rt_rp_is r s).
+
+(* notion 3235 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t5 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_ndofrp s).(l_e_st_eq_landau_n_rt_rp_satz136e (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_eqe12 l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) e) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp)).
+
+(* notion 3236 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpind ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_ndofrp s).(l_e_symis l_e_st_eq_landau_n_rt_cut s r (l_e_st_eq_landau_n_rt_rp_satz136b s r l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv1d_t5 r s e)) : l_e_st_eq_landau_n_rt_rp_is r s).
+
+(* notion 3237 *)
+definition l_e_st_eq_landau_n_rt_rp_posdirp ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_compl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_satz133 l_e_st_eq_landau_n_rt_rp_1rp r)) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
+
+(* notion 3238 *)
+definition l_e_st_eq_landau_n_rt_rp_negdirp ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_negdi l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_compl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_satz133a l_e_st_eq_landau_n_rt_rp_1rp r)) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
+
+(* notion 3239 *)
+definition l_e_st_eq_landau_n_rt_rp_rpofpd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) p : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3240 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_tr4is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_2a a)) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_2a a)) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_satz140f (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) p)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_rpofpd a p) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_rpofpd a p) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a))).
+
+(* notion 3241 *)
+definition l_e_st_eq_landau_n_rt_rp_eqpdrp1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_eqi1 a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofpd a p) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv1d_t6 a p) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd a p))).
+
+(* notion 3242 *)
+definition l_e_st_eq_landau_n_rt_rp_eqpdrp2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_symeq a (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd a p)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 a p) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd a p)) a).
+
+(* notion 3243 *)
+definition l_e_st_eq_landau_n_rt_rp_rpofnd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) n) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3244 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnd a n) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_rpofnd a n)) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_rpofnd a n) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_rpofnd a n)) (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_satz140c (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) n))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnd a n) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_2a a))).
+
+(* notion 3245 *)
+definition l_e_st_eq_landau_n_rt_rp_eqndrp1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_eqi1 a l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnd a n) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_iv1d_t7 a n) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd a n))).
+
+(* notion 3246 *)
+definition l_e_st_eq_landau_n_rt_rp_eqndrp2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_symeq a (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd a n)) (l_e_st_eq_landau_n_rt_rp_eqndrp1 a n) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd a n)) a).
+
+(* notion 3247 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t8 ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λq:l_e_st_eq_landau_n_rt_rp_posd k.λe:l_e_st_eq_landau_n_rt_rp_eq h k.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd h p)) h k (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd k q)) (l_e_st_eq_landau_n_rt_rp_eqpdrp2 h p) e (l_e_st_eq_landau_n_rt_rp_eqpdrp1 k q) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd h p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd k q))).
+
+(* notion 3248 *)
+definition l_e_st_eq_landau_n_rt_rp_eqpderp ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λq:l_e_st_eq_landau_n_rt_rp_posd k.λe:l_e_st_eq_landau_n_rt_rp_eq h k.(l_e_st_eq_landau_n_rt_rp_isrpipd (l_e_st_eq_landau_n_rt_rp_rpofpd h p) (l_e_st_eq_landau_n_rt_rp_rpofpd k q) (l_e_st_eq_landau_n_rt_rp_iv1d_t8 h p k q e) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd h p) (l_e_st_eq_landau_n_rt_rp_rpofpd k q)).
+
+(* notion 3249 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t9 ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λq:l_e_st_eq_landau_n_rt_rp_posd k.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd h p) (l_e_st_eq_landau_n_rt_rp_rpofpd k q).(l_e_st_eq_landau_n_rt_rp_isrpepd (l_e_st_eq_landau_n_rt_rp_rpofpd h p) (l_e_st_eq_landau_n_rt_rp_rpofpd k q) i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd h p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd k q))).
+
+(* notion 3250 *)
+definition l_e_st_eq_landau_n_rt_rp_eqpdirp ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λq:l_e_st_eq_landau_n_rt_rp_posd k.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd h p) (l_e_st_eq_landau_n_rt_rp_rpofpd k q).(l_e_st_eq_landau_n_rt_rp_tr3eq h (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd h p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd k q)) k (l_e_st_eq_landau_n_rt_rp_eqpdrp1 h p) (l_e_st_eq_landau_n_rt_rp_iv1d_t9 h p k q i) (l_e_st_eq_landau_n_rt_rp_eqpdrp2 k q) : l_e_st_eq_landau_n_rt_rp_eq h k).
+
+(* notion 3251 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t10 ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λo:l_e_st_eq_landau_n_rt_rp_negd k.λe:l_e_st_eq_landau_n_rt_rp_eq h k.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd h n)) h k (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd k o)) (l_e_st_eq_landau_n_rt_rp_eqndrp2 h n) e (l_e_st_eq_landau_n_rt_rp_eqndrp1 k o) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd h n)) (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd k o))).
+
+(* notion 3252 *)
+definition l_e_st_eq_landau_n_rt_rp_eqnderp ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λo:l_e_st_eq_landau_n_rt_rp_negd k.λe:l_e_st_eq_landau_n_rt_rp_eq h k.(l_e_st_eq_landau_n_rt_rp_isrpind (l_e_st_eq_landau_n_rt_rp_rpofnd h n) (l_e_st_eq_landau_n_rt_rp_rpofnd k o) (l_e_st_eq_landau_n_rt_rp_iv1d_t10 h n k o e) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnd h n) (l_e_st_eq_landau_n_rt_rp_rpofnd k o)).
+
+(* notion 3253 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t11 ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λo:l_e_st_eq_landau_n_rt_rp_negd k.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnd h n) (l_e_st_eq_landau_n_rt_rp_rpofnd k o).(l_e_st_eq_landau_n_rt_rp_isrpend (l_e_st_eq_landau_n_rt_rp_rpofnd h n) (l_e_st_eq_landau_n_rt_rp_rpofnd k o) i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd h n)) (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd k o))).
+
+(* notion 3254 *)
+definition l_e_st_eq_landau_n_rt_rp_eqndirp ≝ λh:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd h.λk:l_e_st_eq_landau_n_rt_rp_dif.λo:l_e_st_eq_landau_n_rt_rp_negd k.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnd h n) (l_e_st_eq_landau_n_rt_rp_rpofnd k o).(l_e_st_eq_landau_n_rt_rp_tr3eq h (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd h n)) (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd k o)) k (l_e_st_eq_landau_n_rt_rp_eqndrp1 h n) (l_e_st_eq_landau_n_rt_rp_iv1d_t11 h n k o i) (l_e_st_eq_landau_n_rt_rp_eqndrp2 k o) : l_e_st_eq_landau_n_rt_rp_eq h k).
+
+(* notion 3255 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t12 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r)))).
+
+(* notion 3256 *)
+definition l_e_st_eq_landau_n_rt_rp_isrppd1 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isrpipd r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r)) (l_e_st_eq_landau_n_rt_rp_iv1d_t12 r) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r))).
+
+(* notion 3257 *)
+definition l_e_st_eq_landau_n_rt_rp_isrppd2 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r)) (l_e_st_eq_landau_n_rt_rp_isrppd1 r) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_posdirp r)) r).
+
+(* notion 3258 *)
+definition l_e_st_eq_landau_n_rt_rp_iv1d_t13 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqndrp1 (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_rpofnd (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r)))).
+
+(* notion 3259 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpnd1 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_isrpind r (l_e_st_eq_landau_n_rt_rp_rpofnd (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r)) (l_e_st_eq_landau_n_rt_rp_iv1d_t13 r) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofnd (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r))).
+
+(* notion 3260 *)
+definition l_e_st_eq_landau_n_rt_rp_isrpnd2 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofnd (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r)) (l_e_st_eq_landau_n_rt_rp_isrpnd1 r) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnd (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_negdirp r)) r).
+
+(* notion 3261 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmad1 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqi12 a1 a2 (l_e_st_eq_landau_n_rt_rp_pl a1 r) (l_e_st_eq_landau_n_rt_rp_pl a2 r) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl a1 (l_e_st_eq_landau_n_rt_rp_pl a2 r)) (l_e_st_eq_landau_n_rt_rp_pl a1 (l_e_st_eq_landau_n_rt_rp_pl r a2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl a1 r) a2) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl a2 r) (l_e_st_eq_landau_n_rt_rp_pl r a2) a1 (l_e_st_eq_landau_n_rt_rp_compl a2 r)) (l_e_st_eq_landau_n_rt_rp_asspl2 a1 r a2)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 r) (l_e_st_eq_landau_n_rt_rp_pl a2 r))).
+
+(* notion 3262 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmad2 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 r) (l_e_st_eq_landau_n_rt_rp_pl a2 r)) (l_e_st_eq_landau_n_rt_rp_lemmad1 a1 a2 r) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 r) (l_e_st_eq_landau_n_rt_rp_pl a2 r)) (l_e_st_eq_landau_n_rt_rp_df a1 a2)).
+
+(* notion 3263 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmad3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r)) (l_e_st_eq_landau_n_rt_rp_refeq1 a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_isdf a)) (l_e_st_eq_landau_n_rt_rp_lemmad1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) r) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r))).
+
+(* notion 3264 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmad4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_symeq a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r)) (l_e_st_eq_landau_n_rt_rp_lemmad3 a r) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r)) a).
+
+(* notion 3265 *)
+definition l_e_st_eq_landau_n_rt_rp_absd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_ite (l_e_st_eq_landau_n_rt_rp_negd a) l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) a : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3266 *)
+definition l_e_st_eq_landau_n_rt_rp_absnd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_itet (l_e_st_eq_landau_n_rt_rp_negd a) l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) a n) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))).
+
+(* notion 3267 *)
+definition l_e_st_eq_landau_n_rt_rp_absnnd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_itef (l_e_st_eq_landau_n_rt_rp_negd a) l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) a n) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) a).
+
+(* notion 3268 *)
+definition l_e_st_eq_landau_n_rt_rp_absdeql ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less a1 a2.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_df a2 a1) (l_e_st_eq_landau_n_rt_rp_absnd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_negdi a1 a2 l)) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 a1 (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) (l_e_st_eq_landau_n_rt_rp_stmis a1 a2)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_df a2 a1)).
+
+(* notion 3269 *)
+definition l_e_st_eq_landau_n_rt_rp_absdeqm ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_moreis a1 a2.(l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_less a1 a2) (l_e_st_eq_landau_n_rt_rp_satz123c a1 a2 m) (λt:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_df a1 a2).l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) t)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_df a1 a2)).
+
+(* notion 3270 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_symeq a b e) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a))).
+
+(* notion 3271 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absnd a n) (l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_iv2d_t1 a b e n)) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_absnd b (l_e_st_eq_landau_n_rt_rp_eqnegd a b e n))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).
+
+(* notion 3272 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd a) a b (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absnnd a n) e (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd b) b (l_e_st_eq_landau_n_rt_rp_absnnd b (l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_negd a) n (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_eqnegd b a (l_e_st_eq_landau_n_rt_rp_symeq a b e) t)))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).
+
+(* notion 3273 *)
+definition l_e_st_eq_landau_n_rt_rp_eqabsd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_iv2d_t2 a b e t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_negd a).l_e_st_eq_landau_n_rt_rp_iv2d_t3 a b e t) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).
+
+(* notion 3274 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd166a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_eqposd a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p))) p : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3275 *)
+definition l_e_st_eq_landau_n_rt_rp_2d166_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))).
+
+(* notion 3276 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd166b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_absnd a n)) (l_e_st_eq_landau_n_rt_rp_2d166_t1 a n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3277 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd166c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b).(l_e_st_eq_landau_n_rt_rp_tr3eq a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) b (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p))) e (l_e_st_eq_landau_n_rt_rp_absnnd b (l_e_st_eq_landau_n_rt_rp_pnotnd b q)) : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3278 *)
+definition l_e_st_eq_landau_n_rt_rp_2d166_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b).(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_absnd a n)) e (l_e_st_eq_landau_n_rt_rp_absnd b o) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b))).
+
+(* notion 3279 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd166d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b).(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_eqe12 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d166_t2 a b n o e))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3280 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd166e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_rappd a (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_satzd166a a t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)) n) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_satzd166b a t) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3281 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd166f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_eqzero a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_0notnd a z))) z : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3282 *)
+definition l_e_st_eq_landau_n_rt_rp_mored ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : Prop).
+
+(* notion 3283 *)
+definition l_e_st_eq_landau_n_rt_rp_moredi12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2).(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl b1 a2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_12issmsd a1 a2 b1 b2) (l_e_st_eq_landau_n_rt_rp_12issmsd b1 b2 a1 a2) m : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)).
+
+(* notion 3284 *)
+definition l_e_st_eq_landau_n_rt_rp_moredi1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)).(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_sm2issmsd a r1 r2) (l_e_st_eq_landau_n_rt_rp_1sdissmsd a r1 r2) m : l_e_st_eq_landau_n_rt_rp_mored a (l_e_st_eq_landau_n_rt_rp_df r1 r2)).
+
+(* notion 3285 *)
+definition l_e_st_eq_landau_n_rt_rp_moredi2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2).(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_1sdissmsd a r1 r2) (l_e_st_eq_landau_n_rt_rp_sm2issmsd a r1 r2) m : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_df r1 r2) a).
+
+(* notion 3286 *)
+definition l_e_st_eq_landau_n_rt_rp_morede12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2).(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_pl b1 a2) (l_e_st_eq_landau_n_rt_rp_smsdis12 a1 a2 b1 b2) (l_e_st_eq_landau_n_rt_rp_smsdis12 b1 b2 a1 a2) m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2)).
+
+(* notion 3287 *)
+definition l_e_st_eq_landau_n_rt_rp_lessd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : Prop).
+
+(* notion 3288 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmad5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) m : l_e_st_eq_landau_n_rt_rp_lessd b a).
+
+(* notion 3289 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmad6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) l : l_e_st_eq_landau_n_rt_rp_mored b a).
+
+(* notion 3290 *)
+definition l_e_st_eq_landau_n_rt_rp_lessdi12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2).(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_df b1 b2) (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_moredi12 b1 b2 a1 a2 (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2) l)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)).
+
+(* notion 3291 *)
+definition l_e_st_eq_landau_n_rt_rp_lessdi1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)).(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_df r1 r2) a (l_e_st_eq_landau_n_rt_rp_moredi2 a r1 r2 (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) l)) : l_e_st_eq_landau_n_rt_rp_lessd a (l_e_st_eq_landau_n_rt_rp_df r1 r2)).
+
+(* notion 3292 *)
+definition l_e_st_eq_landau_n_rt_rp_lessdi2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2).(l_e_st_eq_landau_n_rt_rp_lemmad5 a (l_e_st_eq_landau_n_rt_rp_df r1 r2) (l_e_st_eq_landau_n_rt_rp_moredi1 a r1 r2 (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) l)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a).
+
+(* notion 3293 *)
+definition l_e_st_eq_landau_n_rt_rp_lessde12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2).(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_pl b1 a2) (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_morede12 b1 b2 a1 a2 (l_e_st_eq_landau_n_rt_rp_lemmad6 (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2) l)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl b1 a2)).
+
+(* notion 3294 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd167 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satz123 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_orec3 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b)).
+
+(* notion 3295 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd167a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satz123a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_or3 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b)).
+
+(* notion 3296 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd167b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_ec3 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b)).
+
+(* notion 3297 *)
+definition l_e_st_eq_landau_n_rt_rp_1d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stm d : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3298 *)
+definition l_e_st_eq_landau_n_rt_rp_2d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_std d : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3299 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λm:l_e_st_eq_landau_n_rt_rp_mored a c.(l_e_tr4is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2d a b c d))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_symeq a b e) f) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))).
+
+(* notion 3300 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λm:l_e_st_eq_landau_n_rt_rp_mored a c.(l_e_st_eq_landau_n_rt_rp_ismore2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_iv2d_t4 a b c d e f m) (l_e_st_eq_landau_n_rt_rp_satz135d (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))).
+
+(* notion 3301 *)
+definition l_e_st_eq_landau_n_rt_rp_eqmored12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λm:l_e_st_eq_landau_n_rt_rp_mored a c.(l_e_st_eq_landau_n_rt_rp_satz136a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2d a b c d)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1d a b c d) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_iv2d_t5 a b c d e f m) : l_e_st_eq_landau_n_rt_rp_mored b d).
+
+(* notion 3302 *)
+definition l_e_st_eq_landau_n_rt_rp_eqlessd12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λl:l_e_st_eq_landau_n_rt_rp_lessd a c.(l_e_st_eq_landau_n_rt_rp_lemmad5 d b (l_e_st_eq_landau_n_rt_rp_eqmored12 c d a b f e (l_e_st_eq_landau_n_rt_rp_lemmad6 a c l)) : l_e_st_eq_landau_n_rt_rp_lessd b d).
+
+(* notion 3303 *)
+definition l_e_st_eq_landau_n_rt_rp_eqmored1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_mored a c.(l_e_st_eq_landau_n_rt_rp_eqmored12 a b c c e (l_e_st_eq_landau_n_rt_rp_refeq c) m : l_e_st_eq_landau_n_rt_rp_mored b c).
+
+(* notion 3304 *)
+definition l_e_st_eq_landau_n_rt_rp_eqmored2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_mored c a.(l_e_st_eq_landau_n_rt_rp_eqmored12 c c a b (l_e_st_eq_landau_n_rt_rp_refeq c) e m : l_e_st_eq_landau_n_rt_rp_mored c b).
+
+(* notion 3305 *)
+definition l_e_st_eq_landau_n_rt_rp_eqlessd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lessd a c.(l_e_st_eq_landau_n_rt_rp_eqlessd12 a b c c e (l_e_st_eq_landau_n_rt_rp_refeq c) l : l_e_st_eq_landau_n_rt_rp_lessd b c).
+
+(* notion 3306 *)
+definition l_e_st_eq_landau_n_rt_rp_eqlessd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lessd c a.(l_e_st_eq_landau_n_rt_rp_eqlessd12 c c a b (l_e_st_eq_landau_n_rt_rp_refeq c) e l : l_e_st_eq_landau_n_rt_rp_lessd c b).
+
+(* notion 3307 *)
+definition l_e_st_eq_landau_n_rt_rp_moreq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_or (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) : Prop).
+
+(* notion 3308 *)
+definition l_e_st_eq_landau_n_rt_rp_lesseq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_or (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) : Prop).
+
+(* notion 3309 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd168a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_lessd b a) (l_e_st_eq_landau_n_rt_rp_eq b a) m (λt:l_e_st_eq_landau_n_rt_rp_mored a b.l_e_st_eq_landau_n_rt_rp_lemmad5 a b t) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_symeq a b t) : l_e_st_eq_landau_n_rt_rp_lesseq b a).
+
+(* notion 3310 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd168b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored b a) (l_e_st_eq_landau_n_rt_rp_eq b a) l (λt:l_e_st_eq_landau_n_rt_rp_lessd a b.l_e_st_eq_landau_n_rt_rp_lemmad6 a b t) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_symeq a b t) : l_e_st_eq_landau_n_rt_rp_moreq b a).
+
+(* notion 3311 *)
+definition l_e_st_eq_landau_n_rt_rp_eqmoreq1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_moreq a c.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_mored a c) (l_e_st_eq_landau_n_rt_rp_eq a c) (l_e_st_eq_landau_n_rt_rp_mored b c) (l_e_st_eq_landau_n_rt_rp_eq b c) m (λt:l_e_st_eq_landau_n_rt_rp_mored a c.l_e_st_eq_landau_n_rt_rp_eqmored1 a b c e t) (λt:l_e_st_eq_landau_n_rt_rp_eq a c.l_e_st_eq_landau_n_rt_rp_treq1 b c a e t) : l_e_st_eq_landau_n_rt_rp_moreq b c).
+
+(* notion 3312 *)
+definition l_e_st_eq_landau_n_rt_rp_eqmoreq2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_moreq c a.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_mored c a) (l_e_st_eq_landau_n_rt_rp_eq c a) (l_e_st_eq_landau_n_rt_rp_mored c b) (l_e_st_eq_landau_n_rt_rp_eq c b) m (λt:l_e_st_eq_landau_n_rt_rp_mored c a.l_e_st_eq_landau_n_rt_rp_eqmored2 a b c e t) (λt:l_e_st_eq_landau_n_rt_rp_eq c a.l_e_st_eq_landau_n_rt_rp_treq c a b t e) : l_e_st_eq_landau_n_rt_rp_moreq c b).
+
+(* notion 3313 *)
+definition l_e_st_eq_landau_n_rt_rp_eqlesseq1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lesseq a c.(l_e_st_eq_landau_n_rt_rp_satzd168a c b (l_e_st_eq_landau_n_rt_rp_eqmoreq2 a b c e (l_e_st_eq_landau_n_rt_rp_satzd168b a c l)) : l_e_st_eq_landau_n_rt_rp_lesseq b c).
+
+(* notion 3314 *)
+definition l_e_st_eq_landau_n_rt_rp_eqlesseq2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lesseq c a.(l_e_st_eq_landau_n_rt_rp_satzd168a b c (l_e_st_eq_landau_n_rt_rp_eqmoreq1 a b c e (l_e_st_eq_landau_n_rt_rp_satzd168b c a l)) : l_e_st_eq_landau_n_rt_rp_lesseq c b).
+
+(* notion 3315 *)
+definition l_e_st_eq_landau_n_rt_rp_eqmoreq12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λm:l_e_st_eq_landau_n_rt_rp_moreq a c.(l_e_st_eq_landau_n_rt_rp_eqmoreq1 a b d e (l_e_st_eq_landau_n_rt_rp_eqmoreq2 c d a f m) : l_e_st_eq_landau_n_rt_rp_moreq b d).
+
+(* notion 3316 *)
+definition l_e_st_eq_landau_n_rt_rp_eqlesseq12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.λl:l_e_st_eq_landau_n_rt_rp_lesseq a c.(l_e_st_eq_landau_n_rt_rp_eqlesseq1 a b d e (l_e_st_eq_landau_n_rt_rp_eqlesseq2 c d a f l) : l_e_st_eq_landau_n_rt_rp_lesseq b d).
+
+(* notion 3317 *)
+definition l_e_st_eq_landau_n_rt_rp_moreqi1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_ori1 (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) m : l_e_st_eq_landau_n_rt_rp_moreq a b).
+
+(* notion 3318 *)
+definition l_e_st_eq_landau_n_rt_rp_lesseqi1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_ori1 (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) l : l_e_st_eq_landau_n_rt_rp_lesseq a b).
+
+(* notion 3319 *)
+definition l_e_st_eq_landau_n_rt_rp_moreqi2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_ori2 (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) e : l_e_st_eq_landau_n_rt_rp_moreq a b).
+
+(* notion 3320 *)
+definition l_e_st_eq_landau_n_rt_rp_lesseqi2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_ori2 (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) e : l_e_st_eq_landau_n_rt_rp_lesseq a b).
+
+(* notion 3321 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd167c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.(l_ec3_th7 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167b a b) (l_comor (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) m) : l_not (l_e_st_eq_landau_n_rt_rp_lessd a b)).
+
+(* notion 3322 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd167d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.(l_ec3_th9 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167b a b) l : l_not (l_e_st_eq_landau_n_rt_rp_mored a b)).
+
+(* notion 3323 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd167e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_mored a b).(l_or3_th2 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167a a b) n : l_e_st_eq_landau_n_rt_rp_lesseq a b).
+
+(* notion 3324 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd167f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_lessd a b).(l_comor (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_or3_th3 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167a a b) n) : l_e_st_eq_landau_n_rt_rp_moreq a b).
+
+(* notion 3325 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd167g ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_lesseq a b) (l_not (l_e_st_eq_landau_n_rt_rp_mored a b)) (l_weli (l_e_st_eq_landau_n_rt_rp_mored a b) m) (λt:l_e_st_eq_landau_n_rt_rp_lesseq a b.l_e_st_eq_landau_n_rt_rp_satzd167d a b t) : l_not (l_e_st_eq_landau_n_rt_rp_lesseq a b)).
+
+(* notion 3326 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd167h ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_moreq a b) (l_not (l_e_st_eq_landau_n_rt_rp_lessd a b)) (l_weli (l_e_st_eq_landau_n_rt_rp_lessd a b) l) (λt:l_e_st_eq_landau_n_rt_rp_moreq a b.l_e_st_eq_landau_n_rt_rp_satzd167c a b t) : l_not (l_e_st_eq_landau_n_rt_rp_moreq a b)).
+
+(* notion 3327 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd167j ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_moreq a b).(l_or3e3 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167a a b) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) n) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) n) : l_e_st_eq_landau_n_rt_rp_lessd a b).
+
+(* notion 3328 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd167k ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_lesseq a b).(l_or3e2 (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_satzd167a a b) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) n) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) n) : l_e_st_eq_landau_n_rt_rp_mored a b).
+
+(* notion 3329 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd169a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a) z) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_satz135a (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) p) : l_e_st_eq_landau_n_rt_rp_mored a b).
+
+(* notion 3330 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd169b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_satz136d (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a) z) m) : l_e_st_eq_landau_n_rt_rp_posd a).
+
+(* notion 3331 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd169c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a) z) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_satz135c (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) n) : l_e_st_eq_landau_n_rt_rp_lessd a b).
+
+(* notion 3332 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd169d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_satz136f (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a) z) l) : l_e_st_eq_landau_n_rt_rp_negd a).
+
+(* notion 3333 *)
+definition l_e_st_eq_landau_n_rt_rp_2d170_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_moreqi1 (l_e_st_eq_landau_n_rt_rp_absd a) b (l_e_st_eq_landau_n_rt_rp_satzd169a (l_e_st_eq_landau_n_rt_rp_absd a) b z (l_e_st_eq_landau_n_rt_rp_satzd166a a p)) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b).
+
+(* notion 3334 *)
+definition l_e_st_eq_landau_n_rt_rp_2d170_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λy:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_moreqi2 (l_e_st_eq_landau_n_rt_rp_absd a) b (l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_absd a) a b (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_0notnd a y)) (l_e_st_eq_landau_n_rt_rp_zeroeq a b y z)) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b).
+
+(* notion 3335 *)
+definition l_e_st_eq_landau_n_rt_rp_2d170_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_moreqi1 (l_e_st_eq_landau_n_rt_rp_absd a) b (l_e_st_eq_landau_n_rt_rp_satzd169a (l_e_st_eq_landau_n_rt_rp_absd a) b z (l_e_st_eq_landau_n_rt_rp_satzd166b a n)) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b).
+
+(* notion 3336 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd170 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_rappd a (l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_2d170_t1 a b z t) (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_2d170_t2 a b z t) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_2d170_t3 a b z t) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b).
+
+(* notion 3337 *)
+definition l_e_st_eq_landau_n_rt_rp_2d171_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lessd b c.(l_e_st_eq_landau_n_rt_rp_satz137a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)) l k : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)))).
+
+(* notion 3338 *)
+definition l_e_st_eq_landau_n_rt_rp_2d171_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lessd b c.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_2d171_t1 a b c l k) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)))).
+
+(* notion 3339 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd171 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lessd b c.(l_e_st_eq_landau_n_rt_rp_satz136c (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_2d171_t2 a b c l k) : l_e_st_eq_landau_n_rt_rp_lessd a c).
+
+(* notion 3340 *)
+definition l_e_st_eq_landau_n_rt_rp_trlessd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lessd b c.(l_e_st_eq_landau_n_rt_rp_satzd171 a b c l k : l_e_st_eq_landau_n_rt_rp_lessd a c).
+
+(* notion 3341 *)
+definition l_e_st_eq_landau_n_rt_rp_trmored ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_mored b c.(l_e_st_eq_landau_n_rt_rp_lemmad6 c a (l_e_st_eq_landau_n_rt_rp_trlessd c b a (l_e_st_eq_landau_n_rt_rp_lemmad5 b c n) (l_e_st_eq_landau_n_rt_rp_lemmad5 a b m)) : l_e_st_eq_landau_n_rt_rp_mored a c).
+
+(* notion 3342 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd172a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lessd b c.(l_orapp (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_lessd a c) l (λt:l_e_st_eq_landau_n_rt_rp_lessd a b.l_e_st_eq_landau_n_rt_rp_trlessd a b c t k) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_eqlessd1 b a c (l_e_st_eq_landau_n_rt_rp_symeq a b t) k) : l_e_st_eq_landau_n_rt_rp_lessd a c).
+
+(* notion 3343 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd172b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq b c.(l_orapp (l_e_st_eq_landau_n_rt_rp_lessd b c) (l_e_st_eq_landau_n_rt_rp_eq b c) (l_e_st_eq_landau_n_rt_rp_lessd a c) k (λt:l_e_st_eq_landau_n_rt_rp_lessd b c.l_e_st_eq_landau_n_rt_rp_trlessd a b c l t) (λt:l_e_st_eq_landau_n_rt_rp_eq b c.l_e_st_eq_landau_n_rt_rp_eqlessd2 b c a t l) : l_e_st_eq_landau_n_rt_rp_lessd a c).
+
+(* notion 3344 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd172c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_mored b c.(l_e_st_eq_landau_n_rt_rp_lemmad6 c a (l_e_st_eq_landau_n_rt_rp_satzd172b c b a (l_e_st_eq_landau_n_rt_rp_lemmad5 b c n) (l_e_st_eq_landau_n_rt_rp_satzd168a a b m)) : l_e_st_eq_landau_n_rt_rp_mored a c).
+
+(* notion 3345 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd172d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_moreq b c.(l_e_st_eq_landau_n_rt_rp_lemmad6 c a (l_e_st_eq_landau_n_rt_rp_satzd172a c b a (l_e_st_eq_landau_n_rt_rp_satzd168a b c n) (l_e_st_eq_landau_n_rt_rp_lemmad5 a b m)) : l_e_st_eq_landau_n_rt_rp_mored a c).
+
+(* notion 3346 *)
+definition l_e_st_eq_landau_n_rt_rp_2d173_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq b c.λj:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_lesseqi1 a c (l_e_st_eq_landau_n_rt_rp_satzd172b a b c j k) : l_e_st_eq_landau_n_rt_rp_lesseq a c).
+
+(* notion 3347 *)
+definition l_e_st_eq_landau_n_rt_rp_2d173_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq b c.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqlesseq1 b a c (l_e_st_eq_landau_n_rt_rp_symeq a b e) k : l_e_st_eq_landau_n_rt_rp_lesseq a c).
+
+(* notion 3348 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd173 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq b c.(l_orapp (l_e_st_eq_landau_n_rt_rp_lessd a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_lesseq a c) l (λt:l_e_st_eq_landau_n_rt_rp_lessd a b.l_e_st_eq_landau_n_rt_rp_2d173_t1 a b c l k t) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_2d173_t2 a b c l k t) : l_e_st_eq_landau_n_rt_rp_lesseq a c).
+
+(* notion 3349 *)
+definition l_e_st_eq_landau_n_rt_rp_trlesseq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq b c.(l_e_st_eq_landau_n_rt_rp_satzd173 a b c l k : l_e_st_eq_landau_n_rt_rp_lesseq a c).
+
+(* notion 3350 *)
+definition l_e_st_eq_landau_n_rt_rp_trmoreq ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq b c.(l_e_st_eq_landau_n_rt_rp_satzd168b c a (l_e_st_eq_landau_n_rt_rp_trlesseq c b a (l_e_st_eq_landau_n_rt_rp_satzd168a b c n) (l_e_st_eq_landau_n_rt_rp_satzd168a a b m)) : l_e_st_eq_landau_n_rt_rp_moreq a c).
+
+(* notion 3351 *)
+definition l_e_st_eq_landau_n_rt_rp_ratd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(Πt:l_not (l_e_st_eq_landau_n_rt_rp_zero a).l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a t)) : Prop).
+
+(* notion 3352 *)
+definition l_e_st_eq_landau_n_rt_rp_irratd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_not (l_e_st_eq_landau_n_rt_rp_ratd a) : Prop).
+
+(* notion 3353 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λr:l_e_st_eq_landau_n_rt_rp_ratd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_zero b) n (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_eqzero a b e t) : l_not (l_e_st_eq_landau_n_rt_rp_zero a)).
+
+(* notion 3354 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λr:l_e_st_eq_landau_n_rt_rp_ratd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a (l_e_st_eq_landau_n_rt_rp_iv2d_t6 a b e r n)) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166e b n) (l_e_st_eq_landau_n_rt_rp_eqabsd a b e) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a (l_e_st_eq_landau_n_rt_rp_iv2d_t6 a b e r n))) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166e b n))).
+
+(* notion 3355 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λr:l_e_st_eq_landau_n_rt_rp_ratd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_e_isp l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp t) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a (l_e_st_eq_landau_n_rt_rp_iv2d_t6 a b e r n))) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166e b n)) (r (l_e_st_eq_landau_n_rt_rp_iv2d_t6 a b e r n)) (l_e_st_eq_landau_n_rt_rp_iv2d_t7 a b e r n) : l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166e b n))).
+
+(* notion 3356 *)
+definition l_e_st_eq_landau_n_rt_rp_eqratd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λr:l_e_st_eq_landau_n_rt_rp_ratd a.(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero b).l_e_st_eq_landau_n_rt_rp_iv2d_t8 a b e r t : l_e_st_eq_landau_n_rt_rp_ratd b).
+
+(* notion 3357 *)
+definition l_e_st_eq_landau_n_rt_rp_eqirratd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λi:l_e_st_eq_landau_n_rt_rp_irratd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_ratd b) (l_e_st_eq_landau_n_rt_rp_ratd a) i (λt:l_e_st_eq_landau_n_rt_rp_ratd b.l_e_st_eq_landau_n_rt_rp_eqratd b a (l_e_st_eq_landau_n_rt_rp_symeq a b e) t) : l_e_st_eq_landau_n_rt_rp_irratd b).
+
+(* notion 3358 *)
+definition l_e_st_eq_landau_n_rt_rp_ratdi0 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_r_imp_th2 (l_not (l_e_st_eq_landau_n_rt_rp_zero a)) (λt:l_not (l_e_st_eq_landau_n_rt_rp_zero a).l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a t))) (l_weli (l_e_st_eq_landau_n_rt_rp_zero a) z) : l_e_st_eq_landau_n_rt_rp_ratd a).
+
+(* notion 3359 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t9 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r) (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r) j : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r) (l_e_st_eq_landau_n_rt_rp_rpofrt y0)).
+
+(* notion 3360 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t10 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_st_eq_landau_n_rt_rp_ismore1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r) (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_iv2d_t9 r i x0 s y0 j) (l_e_st_eq_landau_n_rt_rp_satz133 (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).
+
+(* notion 3361 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t11 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_st_eq_landau_n_rt_rp_satz154d y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t10 r i x0 s y0 j) : l_e_st_eq_landau_n_rt_more y0 x0).
+
+(* notion 3362 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t12 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_st_eq_landau_n_rt_rp_satz155b y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j))) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_satz154a y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j)))).
+
+(* notion 3363 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t13 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_st_eq_landau_n_rt_rp_satz140g (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r (l_e_st_eq_landau_n_rt_rp_satz154a y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j)) (l_e_st_eq_landau_n_rt_rp_iv2d_t9 r i x0 s y0 j) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_satz154a y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j)))).
+
+(* notion 3364 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t14 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_e_tris2 l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j))) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_rpofrt y0) (l_e_st_eq_landau_n_rt_rp_rpofrt x0) (l_e_st_eq_landau_n_rt_rp_satz154a y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j))) (l_e_st_eq_landau_n_rt_rp_iv2d_t13 r i x0 s y0 j) (l_e_st_eq_landau_n_rt_rp_iv2d_t12 r i x0 s y0 j) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofrt (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j)))).
+
+(* notion 3365 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t15 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).λy0:l_e_st_eq_landau_n_rt_rat.λj:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt y0).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofrt x)) (l_e_st_eq_landau_n_rt_mn y0 x0 (l_e_st_eq_landau_n_rt_rp_iv2d_t11 r i x0 s y0 j)) (l_e_st_eq_landau_n_rt_rp_iv2d_t14 r i x0 s y0 j) : l_e_st_eq_landau_n_rt_rp_ratrp r).
+
+(* notion 3366 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t16 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.λs:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).(l_someapp l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt x)) s l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)) (l_e_st_eq_landau_n_rt_rp_rpofrt x).i (l_e_st_eq_landau_n_rt_rp_iv2d_t15 r i x0 s x t)) : l_con).
+
+(* notion 3367 *)
+definition l_e_st_eq_landau_n_rt_rp_remark1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.λx0:l_e_st_eq_landau_n_rt_rat.(λt:l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0)).l_e_st_eq_landau_n_rt_rp_iv2d_t16 r i x0 t : l_e_st_eq_landau_n_rt_rp_irratrp (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_rpofrt x0))).
+
+(* notion 3368 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_rp ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdofrp r : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3369 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_rn ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ndofrp r : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3370 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t17 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_posdirp r : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)).
+
+(* notion 3371 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t18 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pnot0d (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_iv2d_rp r))).
+
+(* notion 3372 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t19 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_nnot0d (l_e_st_eq_landau_n_rt_rp_iv2d_rn r) (l_e_st_eq_landau_n_rt_rp_negdirp r) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_iv2d_rn r))).
+
+(* notion 3373 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t20 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)).(l_e_tris2 l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) n)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r)) (l_e_st_eq_landau_n_rt_rp_isrppd1 r) (l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) n) (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r) (l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r)))) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) n))).
+
+(* notion 3374 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t21 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_iv2d_rn r))) (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_absnd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r) (l_e_st_eq_landau_n_rt_rp_negdirp r)) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_stdis l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_stmis l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_iv2d_rp r)).
+
+(* notion 3375 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t22 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)).(l_e_tris2 l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rn r) n)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r)) (l_e_st_eq_landau_n_rt_rp_isrppd1 r) (l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rn r) n) (l_e_st_eq_landau_n_rt_rp_iv2d_rp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t17 r) (l_e_st_eq_landau_n_rt_rp_iv2d_t21 r)) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_iv2d_rn r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_iv2d_rn r) n))).
+
+(* notion 3376 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t23 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r s.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r.(l_e_isp l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp x) r s rr i : l_e_st_eq_landau_n_rt_rp_ratrp s).
+
+(* notion 3377 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t24 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r s.λrs:l_e_st_eq_landau_n_rt_rp_ratrp s.(l_e_isp1 l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_ratrp x) s r rs i : l_e_st_eq_landau_n_rt_rp_ratrp r).
+
+(* notion 3378 *)
+definition l_e_st_eq_landau_n_rt_rp_remark2a ≝ λr:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r.(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pdofrp r)).l_e_st_eq_landau_n_rt_rp_iv2d_t23 r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_pdofrp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_pdofrp r) t)) (l_e_st_eq_landau_n_rt_rp_iv2d_t20 r t) rr : l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
+
+(* notion 3379 *)
+definition l_e_st_eq_landau_n_rt_rp_remark2b ≝ λr:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r.(l_e_st_eq_landau_n_rt_rp_iv2d_t17 r : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
+
+(* notion 3380 *)
+definition l_e_st_eq_landau_n_rt_rp_remark3a ≝ λr:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r.(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_ndofrp r)).l_e_st_eq_landau_n_rt_rp_iv2d_t23 r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_ndofrp r) t)) (l_e_st_eq_landau_n_rt_rp_iv2d_t22 r t) rr : l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
+
+(* notion 3381 *)
+definition l_e_st_eq_landau_n_rt_rp_remark3b ≝ λr:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r.(l_e_st_eq_landau_n_rt_rp_negdirp r : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
+
+(* notion 3382 *)
+definition l_e_st_eq_landau_n_rt_rp_remark4a ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_pdofrp r)) (l_e_st_eq_landau_n_rt_rp_ratrp r) i (λt:l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_pdofrp r).l_e_st_eq_landau_n_rt_rp_iv2d_t24 r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_pdofrp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t18 r))) (l_e_st_eq_landau_n_rt_rp_iv2d_t20 r (l_e_st_eq_landau_n_rt_rp_iv2d_t18 r)) (t (l_e_st_eq_landau_n_rt_rp_iv2d_t18 r))) : l_e_st_eq_landau_n_rt_rp_irratd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
+
+(* notion 3383 *)
+definition l_e_st_eq_landau_n_rt_rp_remark4b ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.(l_e_st_eq_landau_n_rt_rp_iv2d_t17 r : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
+
+(* notion 3384 *)
+definition l_e_st_eq_landau_n_rt_rp_remark5a ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_ratrp r) i (λt:l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_ndofrp r).l_e_st_eq_landau_n_rt_rp_iv2d_t24 r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_ndofrp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t19 r))) (l_e_st_eq_landau_n_rt_rp_iv2d_t22 r (l_e_st_eq_landau_n_rt_rp_iv2d_t19 r)) (t (l_e_st_eq_landau_n_rt_rp_iv2d_t19 r))) : l_e_st_eq_landau_n_rt_rp_irratd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
+
+(* notion 3385 *)
+definition l_e_st_eq_landau_n_rt_rp_remark5b ≝ λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_irratrp r.(l_e_st_eq_landau_n_rt_rp_negdirp r : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
+
+(* notion 3386 *)
+definition l_e_st_eq_landau_n_rt_rp_natd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_posd a) (Πt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a t)) : Prop).
+
+(* notion 3387 *)
+definition l_e_st_eq_landau_n_rt_rp_natposd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_ande1 (l_e_st_eq_landau_n_rt_rp_posd a) (Πt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a t)) n : l_e_st_eq_landau_n_rt_rp_posd a).
+
+(* notion 3388 *)
+definition l_e_st_eq_landau_n_rt_rp_natderp ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_r_ande2 (l_e_st_eq_landau_n_rt_rp_posd a) (Πt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a t)) n : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a (l_e_st_eq_landau_n_rt_rp_natposd a n))).
+
+(* notion 3389 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t25 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_e_st_eq_landau_n_rt_rp_eqposd a b e (l_e_st_eq_landau_n_rt_rp_natposd a n) : l_e_st_eq_landau_n_rt_rp_posd b).
+
+(* notion 3390 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t26 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_natd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_eqpderp a (l_e_st_eq_landau_n_rt_rp_natposd a n) b p e : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd a (l_e_st_eq_landau_n_rt_rp_natposd a n)) (l_e_st_eq_landau_n_rt_rp_rpofpd b p)).
+
+(* notion 3391 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t27 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_natd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_isp l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) (l_e_st_eq_landau_n_rt_rp_rpofpd a (l_e_st_eq_landau_n_rt_rp_natposd a n)) (l_e_st_eq_landau_n_rt_rp_rpofpd b p) (l_e_st_eq_landau_n_rt_rp_natderp a n) (l_e_st_eq_landau_n_rt_rp_iv2d_t26 a b e n p) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd b p)).
+
+(* notion 3392 *)
+definition l_e_st_eq_landau_n_rt_rp_eqnatd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_andi (l_e_st_eq_landau_n_rt_rp_posd b) (Πt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd b t)) (l_e_st_eq_landau_n_rt_rp_iv2d_t25 a b e n) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_iv2d_t27 a b e n t) : l_e_st_eq_landau_n_rt_rp_natd b).
+
+(* notion 3393 *)
+definition l_e_st_eq_landau_n_rt_rp_pdofnt ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_rpofnt x) : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3394 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t28 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_rpofnt x) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x)).
+
+(* notion 3395 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t29 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).(l_e_st_eq_landau_n_rt_rp_isrppd1 (l_e_st_eq_landau_n_rt_rp_rpofnt x) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) (l_e_st_eq_landau_n_rt_rp_iv2d_t28 x))).
+
+(* notion 3396 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t30 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).(l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_pdofnt x) (l_e_st_eq_landau_n_rt_rp_iv2d_t28 x) (l_e_st_eq_landau_n_rt_rp_pdofnt x) p (l_e_st_eq_landau_n_rt_rp_refeq (l_e_st_eq_landau_n_rt_rp_pdofnt x)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) (l_e_st_eq_landau_n_rt_rp_iv2d_t28 x)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) p)).
+
+(* notion 3397 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t31 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) (l_e_st_eq_landau_n_rt_rp_iv2d_t28 x)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) p) (l_e_st_eq_landau_n_rt_rp_iv2d_t29 x p) (l_e_st_eq_landau_n_rt_rp_iv2d_t30 x p) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) p)).
+
+(* notion 3398 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t32 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).(l_e_isp l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) p) (l_e_st_eq_landau_n_rt_rp_natrpi x) (l_e_st_eq_landau_n_rt_rp_iv2d_t31 x p) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) p)).
+
+(* notion 3399 *)
+definition l_e_st_eq_landau_n_rt_rp_natdi ≝ λx:l_e_st_eq_landau_n_nat.(l_andi (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x)) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofnt x) t)) (l_e_st_eq_landau_n_rt_rp_iv2d_t28 x) (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofnt x).l_e_st_eq_landau_n_rt_rp_iv2d_t32 x t) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_pdofnt x)).
+
+(* notion 3400 *)
+definition l_e_st_eq_landau_n_rt_rp_intd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_or (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) : Prop).
+
+(* notion 3401 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t33 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λi:l_e_st_eq_landau_n_rt_rp_intd a.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_eqzero a b e z : l_e_st_eq_landau_n_rt_rp_zero b).
+
+(* notion 3402 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t34 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).(l_e_st_eq_landau_n_rt_rp_eqnatd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_eqabsd a b e) n : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd b)).
+
+(* notion 3403 *)
+definition l_e_st_eq_landau_n_rt_rp_eqintd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λi:l_e_st_eq_landau_n_rt_rp_intd a.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd b)) i (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_iv2d_t33 a b e i t) (λt:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).l_e_st_eq_landau_n_rt_rp_iv2d_t34 a b e i t) : l_e_st_eq_landau_n_rt_rp_intd b).
+
+(* notion 3404 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t34a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a (l_e_st_eq_landau_n_rt_rp_natposd a n))) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3405 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t35 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_e_st_eq_landau_n_rt_rp_eqnatd a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_iv2d_t34a a n) n : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3406 *)
+definition l_e_st_eq_landau_n_rt_rp_natintd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_natd a.(l_ori2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_iv2d_t35 a n) : l_e_st_eq_landau_n_rt_rp_intd a).
+
+(* notion 3407 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t36 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λi:l_e_st_eq_landau_n_rt_rp_intd a.(l_ore2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) i (l_e_st_eq_landau_n_rt_rp_pnot0d a p) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3408 *)
+definition l_e_st_eq_landau_n_rt_rp_posintnatd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λi:l_e_st_eq_landau_n_rt_rp_intd a.(l_e_st_eq_landau_n_rt_rp_eqnatd (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p)) (l_e_st_eq_landau_n_rt_rp_iv2d_t36 a p i) : l_e_st_eq_landau_n_rt_rp_natd a).
+
+(* notion 3409 *)
+definition l_e_st_eq_landau_n_rt_rp_intdi0 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_ori1 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) z : l_e_st_eq_landau_n_rt_rp_intd a).
+
+(* notion 3410 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t37 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_e_st_eq_landau_n_rt_rp_posdirp r : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
+
+(* notion 3411 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t38 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r).(l_e_tris l_e_st_eq_landau_n_rt_cut r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t37 r n)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) p) (l_e_st_eq_landau_n_rt_rp_isrppd1 r) (l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t37 r n) (l_e_st_eq_landau_n_rt_rp_pdofrp r) p (l_e_st_eq_landau_n_rt_rp_refeq (l_e_st_eq_landau_n_rt_rp_pdofrp r))) : l_e_st_eq_landau_n_rt_rp_is r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) p)).
+
+(* notion 3412 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t39 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r).(l_e_isp l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) r (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) p) n (l_e_st_eq_landau_n_rt_rp_iv2d_t38 r n p) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) p)).
+
+(* notion 3413 *)
+definition l_e_st_eq_landau_n_rt_rp_remark6a ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_andi (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r)) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp r) t)) (l_e_st_eq_landau_n_rt_rp_iv2d_t37 r n) (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp r).l_e_st_eq_landau_n_rt_rp_iv2d_t39 r n t) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
+
+(* notion 3414 *)
+definition l_e_st_eq_landau_n_rt_rp_remark6 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_e_st_eq_landau_n_rt_rp_natintd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_remark6a r n) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
+
+(* notion 3415 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t40 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_e_st_eq_landau_n_rt_rp_absdeql l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_isless2 (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_compl l_e_st_eq_landau_n_rt_rp_1rp r) (l_e_st_eq_landau_n_rt_rp_satz133a l_e_st_eq_landau_n_rt_rp_1rp r)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_pdofrp r)).
+
+(* notion 3416 *)
+definition l_e_st_eq_landau_n_rt_rp_iv2d_t41 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_e_st_eq_landau_n_rt_rp_eqnatd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_iv2d_t40 r n)) (l_e_st_eq_landau_n_rt_rp_remark6a r n) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r))).
+
+(* notion 3417 *)
+definition l_e_st_eq_landau_n_rt_rp_remark7 ≝ λr:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r.(l_ori2 (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_ndofrp r)) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_ndofrp r))) (l_e_st_eq_landau_n_rt_rp_iv2d_t41 r n) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_ndofrp r)).
+
+(* notion 3418 *)
+definition l_e_st_eq_landau_n_rt_rp_2d174_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_ore2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) i n : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3419 *)
+definition l_e_st_eq_landau_n_rt_rp_2d174_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_ande2 (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) t)) (l_e_st_eq_landau_n_rt_rp_2d174_t1 a i n) : Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) t)).
+
+(* notion 3420 *)
+definition l_e_st_eq_landau_n_rt_rp_2d174_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_lemmaiii5 (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a n)) (l_e_st_eq_landau_n_rt_rp_2d174_t2 a i n (l_e_st_eq_landau_n_rt_rp_satzd166e a n)) : l_e_st_eq_landau_n_rt_rp_ratrp (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd166e a n))).
+
+(* notion 3421 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd174 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero a).l_e_st_eq_landau_n_rt_rp_2d174_t3 a i t : l_e_st_eq_landau_n_rt_rp_ratd a).
+
+(* notion 3422 *)
+definition l_e_st_eq_landau_n_rt_rp_pd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3423 *)
+definition l_e_st_eq_landau_n_rt_rp_pd12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) b1 (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) (l_e_st_eq_landau_n_rt_rp_stmis b1 b2)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)) b2 (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) (l_e_st_eq_landau_n_rt_rp_stdis b1 b2)) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2))).
+
+(* notion 3424 *)
+definition l_e_st_eq_landau_n_rt_rp_pd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) r1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stmis r1 r2)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) r2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_stdis r1 r2)) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2))).
+
+(* notion 3425 *)
+definition l_e_st_eq_landau_n_rt_rp_pd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) r1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stmis r1 r2)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) r2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_stdis r1 r2)) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3426 *)
+definition l_e_st_eq_landau_n_rt_rp_pdeq12a ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2)) (l_e_st_eq_landau_n_rt_rp_pd12 a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2))).
+
+(* notion 3427 *)
+definition l_e_st_eq_landau_n_rt_rp_pdeq12b ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2)) (l_e_st_eq_landau_n_rt_rp_pd12 a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b1) (l_e_st_eq_landau_n_rt_rp_pl a2 b2)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2))).
+
+(* notion 3428 *)
+definition l_e_st_eq_landau_n_rt_rp_pdeq1a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pd1 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2))).
+
+(* notion 3429 *)
+definition l_e_st_eq_landau_n_rt_rp_pdeq1b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pd1 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r1 r2))).
+
+(* notion 3430 *)
+definition l_e_st_eq_landau_n_rt_rp_pdeq2a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pd2 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3431 *)
+definition l_e_st_eq_landau_n_rt_rp_pdeq2b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pd2 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df r1 r2) a)).
+
+(* notion 3432 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd175 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd b a)).
+
+(* notion 3433 *)
+definition l_e_st_eq_landau_n_rt_rp_compd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd175 a b : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd b a)).
+
+(* notion 3434 *)
+definition l_e_st_eq_landau_n_rt_rp_iv3d_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_4pl23 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c)) e) (l_e_st_eq_landau_n_rt_rp_4pl23 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))).
+
+(* notion 3435 *)
+definition l_e_st_eq_landau_n_rt_rp_eqpd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_iv3d_t1 a b c e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)).
+
+(* notion 3436 *)
+definition l_e_st_eq_landau_n_rt_rp_eqpd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_compd c a) (l_e_st_eq_landau_n_rt_rp_eqpd1 a b c e) (l_e_st_eq_landau_n_rt_rp_compd b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b)).
+
+(* notion 3437 *)
+definition l_e_st_eq_landau_n_rt_rp_eqpd12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_eqpd1 a b c e) (l_e_st_eq_landau_n_rt_rp_eqpd2 c d b f) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3438 *)
+definition l_e_st_eq_landau_n_rt_rp_iv3d_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_tr4is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) z (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_1b a b)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)))).
+
+(* notion 3439 *)
+definition l_e_st_eq_landau_n_rt_rp_pd01 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_eqi2 b (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_iv3d_t2 a b z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) b).
+
+(* notion 3440 *)
+definition l_e_st_eq_landau_n_rt_rp_pd02 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd b a) a (l_e_st_eq_landau_n_rt_rp_compd a b) (l_e_st_eq_landau_n_rt_rp_pd01 b a z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) a).
+
+(* notion 3441 *)
+definition l_e_st_eq_landau_n_rt_rp_ppd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_satz137 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) p q) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3442 *)
+definition l_e_st_eq_landau_n_rt_rp_npd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_negdi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_satz137a (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) n o) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3443 *)
+definition l_e_st_eq_landau_n_rt_rp_m0d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3444 *)
+definition l_e_st_eq_landau_n_rt_rp_m0deqa ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 a1 (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_df a2 a1)).
+
+(* notion 3445 *)
+definition l_e_st_eq_landau_n_rt_rp_m0deqb ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_df a2 a1) (l_e_st_eq_landau_n_rt_rp_m0deqa a1 a2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df a2 a1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_df a1 a2))).
+
+(* notion 3446 *)
+definition l_e_st_eq_landau_n_rt_rp_iv3d_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_symeq a b e) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a))).
+
+(* notion 3447 *)
+definition l_e_st_eq_landau_n_rt_rp_eqm0d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_iv3d_t3 a b e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)).
+
+(* notion 3448 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd176a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_negdi (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) p) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_m0d a)).
+
+(* notion 3449 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd176b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_zeroi (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) z) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_m0d a)).
+
+(* notion 3450 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd176c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d a)).
+
+(* notion 3451 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd176d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_m0d a).(l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stmis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_stdis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) n) : l_e_st_eq_landau_n_rt_rp_posd a).
+
+(* notion 3452 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd176e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_m0d a).(l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_isstm (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) z (l_e_st_eq_landau_n_rt_rp_stdis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) : l_e_st_eq_landau_n_rt_rp_zero a).
+
+(* notion 3453 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd176f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d a).(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stmis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_stdis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) p) : l_e_st_eq_landau_n_rt_rp_negd a).
+
+(* notion 3454 *)
+definition l_e_st_eq_landau_n_rt_rp_m0d0 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_m0d a) a (l_e_st_eq_landau_n_rt_rp_satzd176b a z) z : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) a).
+
+(* notion 3455 *)
+definition l_e_st_eq_landau_n_rt_rp_3d177_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) a (l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_stdis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_stmis (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_dfis a) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a).
+
+(* notion 3456 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd177 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a (l_e_st_eq_landau_n_rt_rp_3d177_t1 a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a).
+
+(* notion 3457 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd177a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a (l_e_st_eq_landau_n_rt_rp_satzd177 a) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a))).
+
+(* notion 3458 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd177b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_m0d b).(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b (l_e_st_eq_landau_n_rt_rp_eqm0d a (l_e_st_eq_landau_n_rt_rp_m0d b) e) (l_e_st_eq_landau_n_rt_rp_satzd177 b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) b).
+
+(* notion 3459 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd177c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_m0d b).(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d a) b (l_e_st_eq_landau_n_rt_rp_satzd177b a b e) : l_e_st_eq_landau_n_rt_rp_eq b (l_e_st_eq_landau_n_rt_rp_m0d a)).
+
+(* notion 3460 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd177d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) b.(l_e_st_eq_landau_n_rt_rp_satzd177c b a (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d a) b e) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_m0d b)).
+
+(* notion 3461 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd177e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) b.(l_e_st_eq_landau_n_rt_rp_symeq a (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_satzd177d a b e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d b) a).
+
+(* notion 3462 *)
+definition l_e_st_eq_landau_n_rt_rp_3d178_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absnd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_satzd176a a p)) (l_e_st_eq_landau_n_rt_rp_satzd177 a) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3463 *)
+definition l_e_st_eq_landau_n_rt_rp_3d178_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_m0d a) a (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_0notnd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_satzd176b a z))) (l_e_st_eq_landau_n_rt_rp_m0d0 a z) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_0notnd a z))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3464 *)
+definition l_e_st_eq_landau_n_rt_rp_3d178_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_satzd176c a n))) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_absnd a n)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3465 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd178 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_rappd a (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_3d178_t1 a t) (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_3d178_t2 a t) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_3d178_t3 a t) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3466 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd178a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_satzd178 a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a))).
+
+(* notion 3467 *)
+definition l_e_st_eq_landau_n_rt_rp_3d179_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_pdeq1b a (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_m0d a))).
+
+(* notion 3468 *)
+definition l_e_st_eq_landau_n_rt_rp_3d179_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_zeroi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)))).
+
+(* notion 3469 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd179 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_3d179_t1 a) (l_e_st_eq_landau_n_rt_rp_3d179_t2 a) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_m0d a))).
+
+(* notion 3470 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd179a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) a) (l_e_st_eq_landau_n_rt_rp_compd a (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_satzd179 a) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) a)).
+
+(* notion 3471 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd180 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0deqa (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pdeq12b (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b))).
+
+(* notion 3472 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd180a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd180 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b))).
+
+(* notion 3473 *)
+definition l_e_st_eq_landau_n_rt_rp_md ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_m0d b) : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3474 *)
+definition l_e_st_eq_landau_n_rt_rp_mdeq12a ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b2 b1)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl a2 b1)) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df b2 b1) (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_m0deqa b1 b2)) (l_e_st_eq_landau_n_rt_rp_pdeq12a a1 a2 b2 b1) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl a2 b1))).
+
+(* notion 3475 *)
+definition l_e_st_eq_landau_n_rt_rp_mdeq12b ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl a2 b1)) (l_e_st_eq_landau_n_rt_rp_mdeq12a a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl a1 b2) (l_e_st_eq_landau_n_rt_rp_pl a2 b1)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2))).
+
+(* notion 3476 *)
+definition l_e_st_eq_landau_n_rt_rp_mdeq1a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_df r2 r1)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r1)) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df r2 r1) a (l_e_st_eq_landau_n_rt_rp_m0deqa r1 r2)) (l_e_st_eq_landau_n_rt_rp_pdeq1a a r2 r1) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r1))).
+
+(* notion 3477 *)
+definition l_e_st_eq_landau_n_rt_rp_mdeq1b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r1)) (l_e_st_eq_landau_n_rt_rp_mdeq1a a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) r1)) (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_df r1 r2))).
+
+(* notion 3478 *)
+definition l_e_st_eq_landau_n_rt_rp_mdeq2a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdeq12a r1 r2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_1a a)))).
+
+(* notion 3479 *)
+definition l_e_st_eq_landau_n_rt_rp_mdeq2b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdeq12b r1 r2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl r2 (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_df r1 r2) a)).
+
+(* notion 3480 *)
+definition l_e_st_eq_landau_n_rt_rp_eqmd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqpd1 a b (l_e_st_eq_landau_n_rt_rp_m0d c) e : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a c) (l_e_st_eq_landau_n_rt_rp_md b c)).
+
+(* notion 3481 *)
+definition l_e_st_eq_landau_n_rt_rp_eqmd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) c (l_e_st_eq_landau_n_rt_rp_eqm0d a b e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md c a) (l_e_st_eq_landau_n_rt_rp_md c b)).
+
+(* notion 3482 *)
+definition l_e_st_eq_landau_n_rt_rp_eqmd12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md a c) (l_e_st_eq_landau_n_rt_rp_md b c) (l_e_st_eq_landau_n_rt_rp_md b d) (l_e_st_eq_landau_n_rt_rp_eqmd1 a b c e) (l_e_st_eq_landau_n_rt_rp_eqmd2 c d b f) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a c) (l_e_st_eq_landau_n_rt_rp_md b d)).
+
+(* notion 3483 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd181 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_md b a) (l_e_st_eq_landau_n_rt_rp_satzd180 a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_satzd177 b)) (l_e_st_eq_landau_n_rt_rp_compd (l_e_st_eq_landau_n_rt_rp_m0d a) b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_md b a)).
+
+(* notion 3484 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd181a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_md b a)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_satzd181 b a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_md b a))).
+
+(* notion 3485 *)
+definition l_e_st_eq_landau_n_rt_rp_3d182_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pdeq1a a (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_eqsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3486 *)
+definition l_e_st_eq_landau_n_rt_rp_3d182_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_3d182_t1 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3487 *)
+definition l_e_st_eq_landau_n_rt_rp_3d182_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stmis (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))).
+
+(* notion 3488 *)
+definition l_e_st_eq_landau_n_rt_rp_3d182_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_stdis (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))).
+
+(* notion 3489 *)
+definition l_e_st_eq_landau_n_rt_rp_3d182_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_3d182_t1 a b) p : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3490 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd182a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_3d182_t3 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t4 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t5 a b p) : l_e_st_eq_landau_n_rt_rp_mored a b).
+
+(* notion 3491 *)
+definition l_e_st_eq_landau_n_rt_rp_3d182_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_3d182_t1 a b) z : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3492 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd182b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_isstm (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_3d182_t6 a b z) (l_e_st_eq_landau_n_rt_rp_3d182_t4 a b) : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3493 *)
+definition l_e_st_eq_landau_n_rt_rp_3d182_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_3d182_t1 a b) n : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3494 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd182c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md a b).(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_3d182_t3 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t4 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t7 a b n) : l_e_st_eq_landau_n_rt_rp_lessd a b).
+
+(* notion 3495 *)
+definition l_e_st_eq_landau_n_rt_rp_3d182_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) m : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3496 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd182d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d182_t2 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t8 a b m) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3497 *)
+definition l_e_st_eq_landau_n_rt_rp_3d182_t9 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_zeroi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) e : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3498 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd182e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d182_t2 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t9 a b e) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3499 *)
+definition l_e_st_eq_landau_n_rt_rp_3d182_t10 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_negdi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) l : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3500 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd182f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d182_t2 a b) (l_e_st_eq_landau_n_rt_rp_3d182_t10 a b l) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3501 *)
+definition l_e_st_eq_landau_n_rt_rp_3d183_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_12issmsd (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a)))).
+
+(* notion 3502 *)
+definition l_e_st_eq_landau_n_rt_rp_3d183_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_3d183_t1 b a : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d b)))).
+
+(* notion 3503 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd183a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_isless12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a))) (l_e_st_eq_landau_n_rt_rp_3d183_t2 a b) (l_e_st_eq_landau_n_rt_rp_3d183_t1 a b) (l_e_st_eq_landau_n_rt_rp_lemmad5 a b m) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)).
+
+(* notion 3504 *)
+definition l_e_st_eq_landau_n_rt_rp_staz183b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqm0d a b e : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)).
+
+(* notion 3505 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd183c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_m0d a))) (l_e_st_eq_landau_n_rt_rp_3d183_t2 a b) (l_e_st_eq_landau_n_rt_rp_3d183_t1 a b) (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)).
+
+(* notion 3506 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd183d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b).(l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b (l_e_st_eq_landau_n_rt_rp_satzd177 a) (l_e_st_eq_landau_n_rt_rp_satzd177 b) (l_e_st_eq_landau_n_rt_rp_satzd183c (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) l) : l_e_st_eq_landau_n_rt_rp_mored a b).
+
+(* notion 3507 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd183e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b).(l_e_st_eq_landau_n_rt_rp_tr3eq a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b (l_e_st_eq_landau_n_rt_rp_satzd177a a) (l_e_st_eq_landau_n_rt_rp_eqm0d (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) e) (l_e_st_eq_landau_n_rt_rp_satzd177 b) : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3508 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd183f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b).(l_e_st_eq_landau_n_rt_rp_eqlessd12 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a)) a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b (l_e_st_eq_landau_n_rt_rp_satzd177 a) (l_e_st_eq_landau_n_rt_rp_satzd177 b) (l_e_st_eq_landau_n_rt_rp_satzd183a (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) m) : l_e_st_eq_landau_n_rt_rp_lessd a b).
+
+(* notion 3509 *)
+definition l_e_st_eq_landau_n_rt_rp_3d184_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq a (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_lemmad3 a (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_3pl12 (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_mdeq12b (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3510 *)
+definition l_e_st_eq_landau_n_rt_rp_3d184_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_and3i (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_3d184_t1 a) : l_and3 (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a))))).
+
+(* notion 3511 *)
+definition l_e_st_eq_landau_n_rt_rp_3d184_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_posd x) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) x))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_3d184_t2 a) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_posd x) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) x)))).
+
+(* notion 3512 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd184 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (λy:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_posd x) (l_e_st_eq_landau_n_rt_rp_posd y) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md x y)))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_3d184_t3 a) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (λy:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_posd x) (l_e_st_eq_landau_n_rt_rp_posd y) (l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_md x y))))).
+
+(* notion 3513 *)
+definition l_e_st_eq_landau_n_rt_rp_asspd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pdeq2a c (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pdeq1b a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c))).
+
+(* notion 3514 *)
+definition l_e_st_eq_landau_n_rt_rp_asspd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_asspd1 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c)).
+
+(* notion 3515 *)
+definition l_e_st_eq_landau_n_rt_rp_3pd23 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd c b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) b) (l_e_st_eq_landau_n_rt_rp_asspd1 a b c) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd c b) a (l_e_st_eq_landau_n_rt_rp_compd b c)) (l_e_st_eq_landau_n_rt_rp_asspd2 a c b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) b)).
+
+(* notion 3516 *)
+definition l_e_st_eq_landau_n_rt_rp_4pd23 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd c d)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) d) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) b) d) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)) (l_e_st_eq_landau_n_rt_rp_asspd2 (l_e_st_eq_landau_n_rt_rp_pd a b) c d) (l_e_st_eq_landau_n_rt_rp_eqpd1 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) b) d (l_e_st_eq_landau_n_rt_rp_3pd23 a b c)) (l_e_st_eq_landau_n_rt_rp_asspd1 (l_e_st_eq_landau_n_rt_rp_pd a c) b d) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd c d)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d))).
+
+(* notion 3517 *)
+definition l_e_st_eq_landau_n_rt_rp_pdmd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) b) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) b)) a (l_e_st_eq_landau_n_rt_rp_asspd1 a (l_e_st_eq_landau_n_rt_rp_m0d b) b) (l_e_st_eq_landau_n_rt_rp_pd02 a (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) b) (l_e_st_eq_landau_n_rt_rp_satzd179a b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) b) a).
+
+(* notion 3518 *)
+definition l_e_st_eq_landau_n_rt_rp_mdpd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a b) b) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b (l_e_st_eq_landau_n_rt_rp_m0d b))) a (l_e_st_eq_landau_n_rt_rp_asspd1 a b (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_pd02 a (l_e_st_eq_landau_n_rt_rp_pd b (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd179 b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a b) b) a).
+
+(* notion 3519 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd185 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md c d)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_m0d d))) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)) (l_e_st_eq_landau_n_rt_rp_4pd23 a (l_e_st_eq_landau_n_rt_rp_m0d b) c (l_e_st_eq_landau_n_rt_rp_m0d d)) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_m0d d)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd b d)) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd180a b d)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md c d)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d))).
+
+(* notion 3520 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd186 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_asspd1 a b c : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd a (l_e_st_eq_landau_n_rt_rp_pd b c))).
+
+(* notion 3521 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd187a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd b (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) b) a (l_e_st_eq_landau_n_rt_rp_compd b (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_pdmd a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd b (l_e_st_eq_landau_n_rt_rp_md a b)) a).
+
+(* notion 3522 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd187c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λx:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd b x) a.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd x b) b) x (l_e_st_eq_landau_n_rt_rp_eqmd1 a (l_e_st_eq_landau_n_rt_rp_pd x b) b (l_e_st_eq_landau_n_rt_rp_treq1 a (l_e_st_eq_landau_n_rt_rp_pd x b) (l_e_st_eq_landau_n_rt_rp_pd b x) e (l_e_st_eq_landau_n_rt_rp_compd b x))) (l_e_st_eq_landau_n_rt_rp_mdpd x b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a b) x).
+
+(* notion 3523 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd187d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λx:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd b x) a.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md a b) x (l_e_st_eq_landau_n_rt_rp_satzd187c a b x e) : l_e_st_eq_landau_n_rt_rp_eq x (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3524 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd187e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λx:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd x b) a.(l_e_st_eq_landau_n_rt_rp_satzd187c a b x (l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd b x) (l_e_st_eq_landau_n_rt_rp_pd x b) a (l_e_st_eq_landau_n_rt_rp_compd b x) e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a b) x).
+
+(* notion 3525 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd187f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λx:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd x b) a.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md a b) x (l_e_st_eq_landau_n_rt_rp_satzd187e a b x e) : l_e_st_eq_landau_n_rt_rp_eq x (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3526 *)
+definition l_e_st_eq_landau_n_rt_rp_3d188_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_m0d c))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md c c)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_m0d c)) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd180 b c)) (l_e_st_eq_landau_n_rt_rp_4pd23 a c (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_m0d c)) (l_e_st_eq_landau_n_rt_rp_pd02 (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md c c) (l_e_st_eq_landau_n_rt_rp_satzd179 c)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3527 *)
+definition l_e_st_eq_landau_n_rt_rp_3d188_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d188_t1 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c))).
+
+(* notion 3528 *)
+definition l_e_st_eq_landau_n_rt_rp_3d188_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d188_t1 a b c) (l_e_st_eq_landau_n_rt_rp_satzd182d (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) m) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3529 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_satzd182a a b (l_e_st_eq_landau_n_rt_rp_3d188_t3 a b c m) : l_e_st_eq_landau_n_rt_rp_mored a b).
+
+(* notion 3530 *)
+definition l_e_st_eq_landau_n_rt_rp_3d188_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d188_t1 a b c) (l_e_st_eq_landau_n_rt_rp_satzd182e (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) e) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3531 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_satzd182b a b (l_e_st_eq_landau_n_rt_rp_3d188_t4 a b c e) : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3532 *)
+definition l_e_st_eq_landau_n_rt_rp_3d188_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_3d188_t1 a b c) (l_e_st_eq_landau_n_rt_rp_satzd182f (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) l) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3533 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c).(l_e_st_eq_landau_n_rt_rp_satzd182c a b (l_e_st_eq_landau_n_rt_rp_3d188_t5 a b c l) : l_e_st_eq_landau_n_rt_rp_lessd a b).
+
+(* notion 3534 *)
+definition l_e_st_eq_landau_n_rt_rp_3d188_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_3d188_t2 a b c) (l_e_st_eq_landau_n_rt_rp_satzd182d a b m) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c))).
+
+(* notion 3535 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_satzd182a (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_3d188_t6 a b c m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)).
+
+(* notion 3536 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqpd1 a b c e : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)).
+
+(* notion 3537 *)
+definition l_e_st_eq_landau_n_rt_rp_3d188_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_3d188_t2 a b c) (l_e_st_eq_landau_n_rt_rp_satzd182f a b l) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c))).
+
+(* notion 3538 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_satzd182c (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_3d188_t7 a b c l) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c)).
+
+(* notion 3539 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188g ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b).(l_e_st_eq_landau_n_rt_rp_satzd188a a b c (l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_compd c a) (l_e_st_eq_landau_n_rt_rp_compd c b) m) : l_e_st_eq_landau_n_rt_rp_mored a b).
+
+(* notion 3540 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188h ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b).(l_e_st_eq_landau_n_rt_rp_satzd188b a b c (l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_compd a c) e (l_e_st_eq_landau_n_rt_rp_compd c b)) : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3541 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188j ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b).λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b).(l_e_st_eq_landau_n_rt_rp_satzd188c a b c (l_e_st_eq_landau_n_rt_rp_eqlessd12 (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_compd c a) (l_e_st_eq_landau_n_rt_rp_compd c b) l) : l_e_st_eq_landau_n_rt_rp_lessd a b).
+
+(* notion 3542 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188k ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_compd a c) (l_e_st_eq_landau_n_rt_rp_compd b c) (l_e_st_eq_landau_n_rt_rp_satzd188d a b c m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b)).
+
+(* notion 3543 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188l ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqpd2 a b c e : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b)).
+
+(* notion 3544 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188m ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.(l_e_st_eq_landau_n_rt_rp_eqlessd12 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd c b) (l_e_st_eq_landau_n_rt_rp_compd a c) (l_e_st_eq_landau_n_rt_rp_compd b c) (l_e_st_eq_landau_n_rt_rp_satzd188f a b c l) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd c b)).
+
+(* notion 3545 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188n ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_mored c d.(l_e_st_eq_landau_n_rt_rp_eqmored2 (l_e_st_eq_landau_n_rt_rp_pd a d) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_eqpd1 a b d e) (l_e_st_eq_landau_n_rt_rp_satzd188k c d a m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3546 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188o ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λm:l_e_st_eq_landau_n_rt_rp_mored c d.(l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd d b) (l_e_st_eq_landau_n_rt_rp_compd a c) (l_e_st_eq_landau_n_rt_rp_compd b d) (l_e_st_eq_landau_n_rt_rp_satzd188n a b c d e m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd d b)).
+
+(* notion 3547 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188p ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lessd c d.(l_e_st_eq_landau_n_rt_rp_eqlessd2 (l_e_st_eq_landau_n_rt_rp_pd a d) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_eqpd1 a b d e) (l_e_st_eq_landau_n_rt_rp_satzd188m c d a l) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3548 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd188q ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λl:l_e_st_eq_landau_n_rt_rp_lessd c d.(l_e_st_eq_landau_n_rt_rp_eqlessd12 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd d b) (l_e_st_eq_landau_n_rt_rp_compd a c) (l_e_st_eq_landau_n_rt_rp_compd b d) (l_e_st_eq_landau_n_rt_rp_satzd188p a b c d e l) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd d b)).
+
+(* notion 3549 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd189 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_mored c d.(l_e_st_eq_landau_n_rt_rp_trmored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_satzd188d a b c m) (l_e_st_eq_landau_n_rt_rp_satzd188k c d b n) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3550 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd189a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lessd c d.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd189 b a d c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) (l_e_st_eq_landau_n_rt_rp_lemmad6 c d k)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3551 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd190a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_mored c d.(l_orapp (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)) m (λt:l_e_st_eq_landau_n_rt_rp_mored a b.l_e_st_eq_landau_n_rt_rp_satzd189 a b c d t n) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_satzd188n a b c d t n) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3552 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd190b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.(l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_pd c a) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd d b) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_compd c a) (l_e_st_eq_landau_n_rt_rp_compd d b) (l_e_st_eq_landau_n_rt_rp_satzd190a c d a b n m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3553 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd190c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lessd c d.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd190a b a d c (l_e_st_eq_landau_n_rt_rp_satzd168b a b l) (l_e_st_eq_landau_n_rt_rp_lemmad6 c d k)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3554 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd190d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq c d.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd190b b a d c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) (l_e_st_eq_landau_n_rt_rp_satzd168b c d k)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3555 *)
+definition l_e_st_eq_landau_n_rt_rp_3d191_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_moreqi2 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_eqpd12 a b c d e f) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3556 *)
+definition l_e_st_eq_landau_n_rt_rp_3d191_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λo:l_e_st_eq_landau_n_rt_rp_mored c d.(l_e_st_eq_landau_n_rt_rp_moreqi1 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_satzd190a a b c d m o) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3557 *)
+definition l_e_st_eq_landau_n_rt_rp_3d191_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_orapp (l_e_st_eq_landau_n_rt_rp_mored c d) (l_e_st_eq_landau_n_rt_rp_eq c d) (l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)) n (λt:l_e_st_eq_landau_n_rt_rp_mored c d.l_e_st_eq_landau_n_rt_rp_3d191_t2 a b c d m n e t) (λt:l_e_st_eq_landau_n_rt_rp_eq c d.l_e_st_eq_landau_n_rt_rp_3d191_t1 a b c d m n e t) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3558 *)
+definition l_e_st_eq_landau_n_rt_rp_3d191_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.λo:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_moreqi1 (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_satzd190b a b c d o n) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3559 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd191 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_moreq a b.λn:l_e_st_eq_landau_n_rt_rp_moreq c d.(l_orapp (l_e_st_eq_landau_n_rt_rp_mored a b) (l_e_st_eq_landau_n_rt_rp_eq a b) (l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)) m (λt:l_e_st_eq_landau_n_rt_rp_mored a b.l_e_st_eq_landau_n_rt_rp_3d191_t4 a b c d m n t) (λt:l_e_st_eq_landau_n_rt_rp_eq a b.l_e_st_eq_landau_n_rt_rp_3d191_t3 a b c d m n t) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3560 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd191a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lesseq a b.λk:l_e_st_eq_landau_n_rt_rp_lesseq c d.(l_e_st_eq_landau_n_rt_rp_satzd168a (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_satzd191 b a d c (l_e_st_eq_landau_n_rt_rp_satzd168b a b l) (l_e_st_eq_landau_n_rt_rp_satzd168b c d k)) : l_e_st_eq_landau_n_rt_rp_lesseq (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d)).
+
+(* notion 3561 *)
+definition l_e_st_eq_landau_n_rt_rp_td ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3562 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t1 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1 r (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts a1 r)).
+
+(* notion 3563 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t2 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ists2 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a1 r (l_e_st_eq_landau_n_rt_rp_stmis a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts r a1)).
+
+(* notion 3564 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t3 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 r (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts a2 r)).
+
+(* notion 3565 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t4 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ists2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) a2 r (l_e_st_eq_landau_n_rt_rp_stdis a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts r a2)).
+
+(* notion 3566 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t5 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts a1 r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) s) (l_e_st_eq_landau_n_rt_rp_ts a2 s) (l_e_st_eq_landau_n_rt_rp_iv4d_t1 a1 a2 r) (l_e_st_eq_landau_n_rt_rp_iv4d_t3 a1 a2 s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 r) (l_e_st_eq_landau_n_rt_rp_ts a2 s))).
+
+(* notion 3567 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t6 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts r a1) (l_e_st_eq_landau_n_rt_rp_ts s (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts s a2) (l_e_st_eq_landau_n_rt_rp_iv4d_t2 a1 a2 r) (l_e_st_eq_landau_n_rt_rp_iv4d_t4 a1 a2 s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts s (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r a1) (l_e_st_eq_landau_n_rt_rp_ts s a2))).
+
+(* notion 3568 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t7 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts a2 r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) s) (l_e_st_eq_landau_n_rt_rp_ts a1 s) (l_e_st_eq_landau_n_rt_rp_iv4d_t3 a1 a2 r) (l_e_st_eq_landau_n_rt_rp_iv4d_t1 a1 a2 s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a2 r) (l_e_st_eq_landau_n_rt_rp_ts a1 s))).
+
+(* notion 3569 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t8 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts r a2) (l_e_st_eq_landau_n_rt_rp_ts s (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts s a1) (l_e_st_eq_landau_n_rt_rp_iv4d_t4 a1 a2 r) (l_e_st_eq_landau_n_rt_rp_iv4d_t2 a1 a2 s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2))) (l_e_st_eq_landau_n_rt_rp_ts s (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r a2) (l_e_st_eq_landau_n_rt_rp_ts s a1))).
+
+(* notion 3570 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t9 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_iv4d_t5 a1 a2 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_iv4d_t6 b1 b2 a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2))).
+
+(* notion 3571 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t10 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts a2 (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1)) (l_e_st_eq_landau_n_rt_rp_iv4d_t5 a1 a2 (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_iv4d_t8 b1 b2 a1 a2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1))).
+
+(* notion 3572 *)
+definition l_e_st_eq_landau_n_rt_rp_td12 ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df b1 b2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df a1 a2)) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df b1 b2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1)) (l_e_st_eq_landau_n_rt_rp_iv4d_t9 a1 a2 b1 b2) (l_e_st_eq_landau_n_rt_rp_iv4d_t10 a1 a2 b1 b2) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1)))).
+
+(* notion 3573 *)
+definition l_e_st_eq_landau_n_rt_rp_td1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1)) (l_e_st_eq_landau_n_rt_rp_iv4d_t6 r1 r2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_iv4d_t8 r1 r2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1)))).
+
+(* notion 3574 *)
+definition l_e_st_eq_landau_n_rt_rp_td2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_issmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_iv4d_t5 r1 r2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_iv4d_t5 r1 r2 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) : l_e_is l_e_st_eq_landau_n_rt_rp_dif (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a))))).
+
+(* notion 3575 *)
+definition l_e_st_eq_landau_n_rt_rp_tdeq12a ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1))) (l_e_st_eq_landau_n_rt_rp_td12 a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1)))).
+
+(* notion 3576 *)
+definition l_e_st_eq_landau_n_rt_rp_tdeq12b ≝ λa1:l_e_st_eq_landau_n_rt_cut.λa2:l_e_st_eq_landau_n_rt_cut.λb1:l_e_st_eq_landau_n_rt_cut.λb2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1))) (l_e_st_eq_landau_n_rt_rp_td12 a1 a2 b1 b2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b1) (l_e_st_eq_landau_n_rt_rp_ts a2 b2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts a1 b2) (l_e_st_eq_landau_n_rt_rp_ts a2 b1))) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df a1 a2) (l_e_st_eq_landau_n_rt_rp_df b1 b2))).
+
+(* notion 3577 *)
+definition l_e_st_eq_landau_n_rt_rp_tdeq1a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1))) (l_e_st_eq_landau_n_rt_rp_td1 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1)))).
+
+(* notion 3578 *)
+definition l_e_st_eq_landau_n_rt_rp_tdeq1b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_df r1 r2)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1))) (l_e_st_eq_landau_n_rt_rp_td1 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r1) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r2) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r1))) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_df r1 r2))).
+
+(* notion 3579 *)
+definition l_e_st_eq_landau_n_rt_rp_tdeq2a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq1 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a)))) (l_e_st_eq_landau_n_rt_rp_td2 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a))))).
+
+(* notion 3580 *)
+definition l_e_st_eq_landau_n_rt_rp_tdeq2b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_refeq2 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df r1 r2) a) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a)))) (l_e_st_eq_landau_n_rt_rp_td2 a r1 r2) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r1 (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts r2 (l_e_st_eq_landau_n_rt_rp_1a a)))) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_df r1 r2) a)).
+
+(* notion 3581 *)
+definition l_e_st_eq_landau_n_rt_rp_4d194_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3582 *)
+definition l_e_st_eq_landau_n_rt_rp_4d194_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_comts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a)))).
+
+(* notion 3583 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd194 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_4d194_t1 a b) (l_e_st_eq_landau_n_rt_rp_4d194_t2 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td b a)).
+
+(* notion 3584 *)
+definition l_e_st_eq_landau_n_rt_rp_comtd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd194 a b : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td b a)).
+
+(* notion 3585 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t11 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) r)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r)) (l_e_st_eq_landau_n_rt_rp_distpt1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) r) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a)) r e) (l_e_st_eq_landau_n_rt_rp_disttp1 (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2a a) r) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) r)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) r))).
+
+(* notion 3586 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_iv4d_t11 a b c e (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_iv4d_t11 b a c (l_e_st_eq_landau_n_rt_rp_symeq a b e) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c))))).
+
+(* notion 3587 *)
+definition l_e_st_eq_landau_n_rt_rp_eqtd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_iv4d_t12 a b c e) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
+
+(* notion 3588 *)
+definition l_e_st_eq_landau_n_rt_rp_eqtd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_comtd c a) (l_e_st_eq_landau_n_rt_rp_eqtd1 a b c e) (l_e_st_eq_landau_n_rt_rp_comtd b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
+
+(* notion 3589 *)
+definition l_e_st_eq_landau_n_rt_rp_eqtd12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td b d) (l_e_st_eq_landau_n_rt_rp_eqtd1 a b c e) (l_e_st_eq_landau_n_rt_rp_eqtd2 c d b f) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b d)).
+
+(* notion 3590 *)
+definition l_e_st_eq_landau_n_rt_rp_4d192_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) z) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_symis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) z))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))).
+
+(* notion 3591 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd192a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_zeroi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_4d192_t1 a b z) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).
+
+(* notion 3592 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd192b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_comtd b a) (l_e_st_eq_landau_n_rt_rp_satzd192a b a z) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).
+
+(* notion 3593 *)
+definition l_e_st_eq_landau_n_rt_rp_td01 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_satzd192a a b z : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).
+
+(* notion 3594 *)
+definition l_e_st_eq_landau_n_rt_rp_td02 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_satzd192b a b z : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).
+
+(* notion 3595 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd197a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)))) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_tdeq2a b (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))) (l_e_st_eq_landau_n_rt_rp_m0deqb (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3596 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd197b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d b) a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_comtd a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd197a b a) (l_e_st_eq_landau_n_rt_rp_eqm0d (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_comtd b a)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3597 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd197c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_satzd197a a b) (l_e_st_eq_landau_n_rt_rp_satzd197b a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b))).
+
+(* notion 3598 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd197d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd197c a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b)).
+
+(* notion 3599 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd197e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_satzd197a a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) b)).
+
+(* notion 3600 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd197f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_satzd197b a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b))).
+
+(* notion 3601 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd198 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b))) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_satzd197c a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_eqtd2 (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) b a (l_e_st_eq_landau_n_rt_rp_satzd177 b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td a b)).
+
+(* notion 3602 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd198a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_satzd198 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b))).
+
+(* notion 3603 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t13 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_distpt2 r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ists2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_1b a b) r (l_e_st_eq_landau_n_rt_rp_satz140e (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b))).
+
+(* notion 3604 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t14 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b)) s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b))) s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) s) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b)) s) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) s (l_e_st_eq_landau_n_rt_rp_iv4d_t13 a b p q r)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b)) s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) s)).
+
+(* notion 3605 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t15 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b)) s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) s) (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_iv4d_t14 a b p q r s) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)) s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_2b a b)) s)) (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_1b a b)))).
+
+(* notion 3606 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t16 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_satz135h (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_satz145a (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q) p) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))))).
+
+(* notion 3607 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t17 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) q)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_iv4d_t14 a b p q (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_iv4d_t15 a b p q (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_iv4d_t16 a b p q) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))).
+
+(* notion 3608 *)
+definition l_e_st_eq_landau_n_rt_rp_ptdpp ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_posdi (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_iv4d_t17 a b p q) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a b)).
+
+(* notion 3609 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t18 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_satzd197b a b) (l_e_st_eq_landau_n_rt_rp_ptdpp a (l_e_st_eq_landau_n_rt_rp_m0d b) p (l_e_st_eq_landau_n_rt_rp_satzd176c b n)) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3610 *)
+definition l_e_st_eq_landau_n_rt_rp_ntdpn ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_satzd176f (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_iv4d_t18 a b p n) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a b)).
+
+(* notion 3611 *)
+definition l_e_st_eq_landau_n_rt_rp_ntdnp ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_comtd b a) (l_e_st_eq_landau_n_rt_rp_ntdpn b a p n) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a b)).
+
+(* notion 3612 *)
+definition l_e_st_eq_landau_n_rt_rp_ptdnn ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_satzd198 a b) (l_e_st_eq_landau_n_rt_rp_ptdpp (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_satzd176c a n) (l_e_st_eq_landau_n_rt_rp_satzd176c b o)) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a b)).
+
+(* notion 3613 *)
+definition l_e_st_eq_landau_n_rt_rp_4d192_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_pnot0d (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ptdpp a b p q) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3614 *)
+definition l_e_st_eq_landau_n_rt_rp_4d192_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λm:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_nnot0d (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ntdpn a b p m) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3615 *)
+definition l_e_st_eq_landau_n_rt_rp_4d192_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_rappd b (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_4d192_t2 a b n o p t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) o) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_4d192_t3 a b n o p t) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3616 *)
+definition l_e_st_eq_landau_n_rt_rp_4d192_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λm:l_e_st_eq_landau_n_rt_rp_negd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_nnot0d (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ntdnp a b m p) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3617 *)
+definition l_e_st_eq_landau_n_rt_rp_4d192_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λm:l_e_st_eq_landau_n_rt_rp_negd a.λl:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_pnot0d (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ptdnn a b m l) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3618 *)
+definition l_e_st_eq_landau_n_rt_rp_4d192_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_rappd b (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_4d192_t5 a b n o m t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) o) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_4d192_t6 a b n o m t) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3619 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd192d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_e_st_eq_landau_n_rt_rp_rappd a (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_4d192_t4 a b n o t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) n) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_4d192_t7 a b n o t) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3620 *)
+definition l_e_st_eq_landau_n_rt_rp_4d192_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b).λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_et (l_e_st_eq_landau_n_rt_rp_zero b) (l_imp_th3 (l_not (l_e_st_eq_landau_n_rt_rp_zero b)) (l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b))) (l_weli (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)) z) (λt:l_not (l_e_st_eq_landau_n_rt_rp_zero b).l_e_st_eq_landau_n_rt_rp_satzd192d a b n t)) : l_e_st_eq_landau_n_rt_rp_zero b).
+
+(* notion 3621 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd192c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b).(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero a).l_e_st_eq_landau_n_rt_rp_4d192_t8 a b z t : l_or (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_zero b)).
+
+(* notion 3622 *)
+definition l_e_st_eq_landau_n_rt_rp_4d193_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ptdpp a b p q))) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absd b) b (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p)) (l_e_st_eq_landau_n_rt_rp_absnnd b (l_e_st_eq_landau_n_rt_rp_pnotnd b q))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3623 *)
+definition l_e_st_eq_landau_n_rt_rp_4d193_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_absnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ntdpn a b p n)) (l_e_st_eq_landau_n_rt_rp_satzd197f a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b))).
+
+(* notion 3624 *)
+definition l_e_st_eq_landau_n_rt_rp_4d193_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_4d193_t2 a b p n) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p)) (l_e_st_eq_landau_n_rt_rp_absnd b n)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3625 *)
+definition l_e_st_eq_landau_n_rt_rp_4d193_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_satzd166f (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td01 a b z)) (l_e_st_eq_landau_n_rt_rp_td01 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166f a z)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3626 *)
+definition l_e_st_eq_landau_n_rt_rp_4d193_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_satzd166f (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td02 a b z)) (l_e_st_eq_landau_n_rt_rp_td02 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166f b z)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3627 *)
+definition l_e_st_eq_landau_n_rt_rp_4d193_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_eqabsd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_comtd a b)) (l_e_st_eq_landau_n_rt_rp_4d193_t3 b a p n) (l_e_st_eq_landau_n_rt_rp_comtd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absd a)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3628 *)
+definition l_e_st_eq_landau_n_rt_rp_4d193_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_absnd a n) (l_e_st_eq_landau_n_rt_rp_absnd b o)) (l_e_st_eq_landau_n_rt_rp_satzd198 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a b)).
+
+(* notion 3629 *)
+definition l_e_st_eq_landau_n_rt_rp_4d193_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_absnnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_ptdnn a b n o))) (l_e_st_eq_landau_n_rt_rp_4d193_t7 a b n o) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3630 *)
+definition l_e_st_eq_landau_n_rt_rp_4d193_t9 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_rappd b (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_4d193_t1 a b p t) (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_4d193_t5 a b t) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_4d193_t3 a b p t) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3631 *)
+definition l_e_st_eq_landau_n_rt_rp_4d193_t10 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_rappd b (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_4d193_t6 a b n t) (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_4d193_t5 a b t) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_4d193_t8 a b n t) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3632 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd193 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_rappd a (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_4d193_t9 a b t) (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_4d193_t4 a b t) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_4d193_t10 a b t) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3633 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd103a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_satzd193 a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3634 *)
+definition l_e_st_eq_landau_n_rt_rp_1df ≝ (l_e_st_eq_landau_n_rt_rp_pdofrp l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3635 *)
+definition l_e_st_eq_landau_n_rt_rp_4d195_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_a2isapa (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_satz151 (l_e_st_eq_landau_n_rt_rp_2a a)))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3636 *)
+definition l_e_st_eq_landau_n_rt_rp_4d195_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_satz151 (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_a2isapa (l_e_st_eq_landau_n_rt_rp_2a a))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a)))).
+
+(* notion 3637 *)
+definition l_e_st_eq_landau_n_rt_rp_4d195_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_4d195_t1 a) (l_e_st_eq_landau_n_rt_rp_4d195_t2 a) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp))))).
+
+(* notion 3638 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd195 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td a l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)))) a (l_e_st_eq_landau_n_rt_rp_tdeq1a a (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_eqi2 a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_4d195_t3 a)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a l_e_st_eq_landau_n_rt_rp_1df) a).
+
+(* notion 3639 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd195a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a l_e_st_eq_landau_n_rt_rp_1df) a (l_e_st_eq_landau_n_rt_rp_satzd195 a) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_td a l_e_st_eq_landau_n_rt_rp_1df)).
+
+(* notion 3640 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd195b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td l_e_st_eq_landau_n_rt_rp_1df a) (l_e_st_eq_landau_n_rt_rp_td a l_e_st_eq_landau_n_rt_rp_1df) a (l_e_st_eq_landau_n_rt_rp_comtd l_e_st_eq_landau_n_rt_rp_1df a) (l_e_st_eq_landau_n_rt_rp_satzd195 a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td l_e_st_eq_landau_n_rt_rp_1df a) a).
+
+(* notion 3641 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd195c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td l_e_st_eq_landau_n_rt_rp_1df a) a (l_e_st_eq_landau_n_rt_rp_satzd195b a) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_td l_e_st_eq_landau_n_rt_rp_1df a)).
+
+(* notion 3642 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd196a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_absd b) b (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p)) (l_e_st_eq_landau_n_rt_rp_absnnd b (l_e_st_eq_landau_n_rt_rp_pnotnd b q))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3643 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd196b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λo:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd198a a b) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_absnd a n) (l_e_st_eq_landau_n_rt_rp_absnd b o)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3644 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd196c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_treq1 (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_absd b))) (l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) a (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_absd b)) b (l_e_st_eq_landau_n_rt_rp_absnnd a (l_e_st_eq_landau_n_rt_rp_pnotnd a p)) (l_e_st_eq_landau_n_rt_rp_satzd177b (l_e_st_eq_landau_n_rt_rp_absd b) b (l_e_st_eq_landau_n_rt_rp_absnd b n))) (l_e_st_eq_landau_n_rt_rp_satzd197b (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)))).
+
+(* notion 3645 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd196d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λp:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absd a))) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (l_e_st_eq_landau_n_rt_rp_comtd a b) (l_e_st_eq_landau_n_rt_rp_satzd196c b a p n) (l_e_st_eq_landau_n_rt_rp_eqm0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_comtd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_absd a))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)))).
+
+(* notion 3646 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_p1p2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) : Prop).
+
+(* notion 3647 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_p1n2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd b) : Prop).
+
+(* notion 3648 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_n1p2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_posd b) : Prop).
+
+(* notion 3649 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_n1n2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_negd b) : Prop).
+
+(* notion 3650 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_e_st_eq_landau_n_rt_rp_ptdpp (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_satzd166e a n) (l_e_st_eq_landau_n_rt_rp_satzd166e b o) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).
+
+(* notion 3651 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).(l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) e) (l_e_st_eq_landau_n_rt_rp_4d196_t1 a b n o)) : l_not (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3652 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_4d196_t2 a b n o e) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_ntdpn a b p t) : l_not (l_e_st_eq_landau_n_rt_rp_negd b)).
+
+(* notion 3653 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_or3e2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_axrdo b) (l_e_st_eq_landau_n_rt_rp_4d196_t3 a b n o e p) o : l_e_st_eq_landau_n_rt_rp_posd b).
+
+(* notion 3654 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_andi (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) p (l_e_st_eq_landau_n_rt_rp_4d196_t4 a b n o e p) : l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b).
+
+(* notion 3655 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_ori1 (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_t5 a b n o e p) : l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b)).
+
+(* notion 3656 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_4d196_t2 a b n o e) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_ntdnp a b m t) : l_not (l_e_st_eq_landau_n_rt_rp_posd b)).
+
+(* notion 3657 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_or3e3 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_axrdo b) o (l_e_st_eq_landau_n_rt_rp_4d196_t7 a b n o e m) : l_e_st_eq_landau_n_rt_rp_negd b).
+
+(* notion 3658 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t9 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_andi (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_negd b) m (l_e_st_eq_landau_n_rt_rp_4d196_t8 a b n o e m) : l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b).
+
+(* notion 3659 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t10 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_ori2 (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_t9 a b n o e m) : l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b)).
+
+(* notion 3660 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd196e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)).(l_e_st_eq_landau_n_rt_rp_rappd a (l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_4d196_t6 a b n o e t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1n2 a b)) n) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_4d196_t10 a b n o e t) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_negd b))).
+
+(* notion 3661 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t11 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_e_st_eq_landau_n_rt_rp_satzd176a (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_4d196_t1 a b n o) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)))).
+
+(* notion 3662 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).(l_e_st_eq_landau_n_rt_rp_nnotpd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))) e) (l_e_st_eq_landau_n_rt_rp_4d196_t11 a b n o)) : l_not (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3663 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t13 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_4d196_t12 a b n o e) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_ptdpp a b p t) : l_not (l_e_st_eq_landau_n_rt_rp_posd b)).
+
+(* notion 3664 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t14 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_or3e3 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_axrdo b) o (l_e_st_eq_landau_n_rt_rp_4d196_t13 a b n o e p) : l_e_st_eq_landau_n_rt_rp_negd b).
+
+(* notion 3665 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t15 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_andi (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd b) p (l_e_st_eq_landau_n_rt_rp_4d196_t14 a b n o e p) : l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b).
+
+(* notion 3666 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t16 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_ori1 (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_t15 a b n o e p) : l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b)).
+
+(* notion 3667 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t17 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_4d196_t12 a b n o e) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_ptdnn a b m t) : l_not (l_e_st_eq_landau_n_rt_rp_negd b)).
+
+(* notion 3668 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t18 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_or3e2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_axrdo b) (l_e_st_eq_landau_n_rt_rp_4d196_t17 a b n o e m) o : l_e_st_eq_landau_n_rt_rp_posd b).
+
+(* notion 3669 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t19 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_andi (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_posd b) m (l_e_st_eq_landau_n_rt_rp_4d196_t18 a b n o e m) : l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b).
+
+(* notion 3670 *)
+definition l_e_st_eq_landau_n_rt_rp_4d196_t20 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).λm:l_e_st_eq_landau_n_rt_rp_negd a.(l_ori2 (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_t19 a b n o e m) : l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b)).
+
+(* notion 3671 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd196f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b))).(l_e_st_eq_landau_n_rt_rp_rappd a (l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_4d196_t16 a b n o e t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_or (l_e_st_eq_landau_n_rt_rp_4d196_p1n2 a b) (l_e_st_eq_landau_n_rt_rp_4d196_n1p2 a b)) n) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_4d196_t20 a b n o e t) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd b)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_posd b))).
+
+(* notion 3672 *)
+definition l_e_st_eq_landau_n_rt_rp_4d199_t1 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) t) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts p r) t) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts q s) t)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_disttp1 (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s) t) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts p r) t) (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ts q s) t) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_assts1 p r t) (l_e_st_eq_landau_n_rt_rp_assts1 q s t)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) t) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)))).
+
+(* notion 3673 *)
+definition l_e_st_eq_landau_n_rt_rp_4d199_t2 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_distpt2 q (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t)))).
+
+(* notion 3674 *)
+definition l_e_st_eq_landau_n_rt_rp_4d199_t3 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) t) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p s) (l_e_st_eq_landau_n_rt_rp_ts q r)) u)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts s u)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts s u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r t) (l_e_st_eq_landau_n_rt_rp_ts s u))) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t)))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) t) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p s) (l_e_st_eq_landau_n_rt_rp_ts q r)) u) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts s u)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_4d199_t1 p q r s t u) (l_e_st_eq_landau_n_rt_rp_4d199_t1 p q s r u t)) (l_e_st_eq_landau_n_rt_rp_4pl23 (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts s u)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts r t)) (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_ts s u))) (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r t) (l_e_st_eq_landau_n_rt_rp_ts s u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts s t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_ts r u))) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t))) (l_e_st_eq_landau_n_rt_rp_distpt2 p (l_e_st_eq_landau_n_rt_rp_ts r t) (l_e_st_eq_landau_n_rt_rp_ts s u)) (l_e_st_eq_landau_n_rt_rp_4d199_t2 p q r s t u)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) t) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p s) (l_e_st_eq_landau_n_rt_rp_ts q r)) u)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r t) (l_e_st_eq_landau_n_rt_rp_ts s u))) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r u) (l_e_st_eq_landau_n_rt_rp_ts s t))))).
+
+(* notion 3675 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd199 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a b) c) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))))) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_tdeq2a c (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b)))) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))))) (l_e_st_eq_landau_n_rt_rp_4d199_t3 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_4d199_t3 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_tdeq1b a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a b) c) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_td b c))).
+
+(* notion 3676 *)
+definition l_e_st_eq_landau_n_rt_rp_asstd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd199 a b c : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a b) c) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_td b c))).
+
+(* notion 3677 *)
+definition l_e_st_eq_landau_n_rt_rp_asstd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a b) c) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_satzd199 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a b) c)).
+
+(* notion 3678 *)
+definition l_e_st_eq_landau_n_rt_rp_4d201_t1 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl s u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts p t)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q s) (l_e_st_eq_landau_n_rt_rp_ts q u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p t) (l_e_st_eq_landau_n_rt_rp_ts q u))) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl r t)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts p t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl s u)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q s) (l_e_st_eq_landau_n_rt_rp_ts q u)) (l_e_st_eq_landau_n_rt_rp_disttp2 p r t) (l_e_st_eq_landau_n_rt_rp_disttp2 q s u)) (l_e_st_eq_landau_n_rt_rp_4pl23 (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts p t) (l_e_st_eq_landau_n_rt_rp_ts q s) (l_e_st_eq_landau_n_rt_rp_ts q u)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p (l_e_st_eq_landau_n_rt_rp_pl r t)) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl s u))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p r) (l_e_st_eq_landau_n_rt_rp_ts q s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts p t) (l_e_st_eq_landau_n_rt_rp_ts q u)))).
+
+(* notion 3679 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd201 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c))))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_tdeq1a a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) (l_e_st_eq_landau_n_rt_rp_4d201_t1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1c a b c) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_4d201_t1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b) (l_e_st_eq_landau_n_rt_rp_1b a b) (l_e_st_eq_landau_n_rt_rp_2c a b c) (l_e_st_eq_landau_n_rt_rp_1c a b c))) (l_e_st_eq_landau_n_rt_rp_pdeq12b (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2b a b)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1b a b))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_2c a b c))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2c a b c)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1c a b c)))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c))).
+
+(* notion 3680 *)
+definition l_e_st_eq_landau_n_rt_rp_disttpd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_td c (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_comtd (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_satzd201 c a b) (l_e_st_eq_landau_n_rt_rp_eqpd12 (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_comtd c a) (l_e_st_eq_landau_n_rt_rp_comtd c b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c))).
+
+(* notion 3681 *)
+definition l_e_st_eq_landau_n_rt_rp_disttpd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd201 a b c : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c))).
+
+(* notion 3682 *)
+definition l_e_st_eq_landau_n_rt_rp_distptd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_disttpd1 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) c)).
+
+(* notion 3683 *)
+definition l_e_st_eq_landau_n_rt_rp_distptd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_pd b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_disttpd2 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_pd b c))).
+
+(* notion 3684 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd202 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d c))) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_disttpd2 a b (l_e_st_eq_landau_n_rt_rp_m0d c)) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d c)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_satzd197b a c)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c))).
+
+(* notion 3685 *)
+definition l_e_st_eq_landau_n_rt_rp_disttmd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d b) c)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_disttpd1 a (l_e_st_eq_landau_n_rt_rp_m0d b) c) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d b) c) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_satzd197a b c)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c))).
+
+(* notion 3686 *)
+definition l_e_st_eq_landau_n_rt_rp_disttmd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd202 a b c : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c))).
+
+(* notion 3687 *)
+definition l_e_st_eq_landau_n_rt_rp_distmtd1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_disttmd1 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c)).
+
+(* notion 3688 *)
+definition l_e_st_eq_landau_n_rt_rp_distmtd2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_disttmd2 a b c) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c))).
+
+(* notion 3689 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd200 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_landau_n_rt_rp_satzd202 a b c : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md b c)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_td a c))).
+
+(* notion 3690 *)
+definition l_e_st_eq_landau_n_rt_rp_4d203_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.(l_e_st_eq_landau_n_rt_rp_satzd182d a b m : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3691 *)
+definition l_e_st_eq_landau_n_rt_rp_4d203_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λp:l_e_st_eq_landau_n_rt_rp_posd c.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_disttmd1 a b c) (l_e_st_eq_landau_n_rt_rp_ptdpp (l_e_st_eq_landau_n_rt_rp_md a b) c (l_e_st_eq_landau_n_rt_rp_4d203_t1 a b c m) p) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c))).
+
+(* notion 3692 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λp:l_e_st_eq_landau_n_rt_rp_posd c.(l_e_st_eq_landau_n_rt_rp_satzd182a (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_4d203_t2 a b c m p) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
+
+(* notion 3693 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td02 a c z) (l_e_st_eq_landau_n_rt_rp_td02 b c z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
+
+(* notion 3694 *)
+definition l_e_st_eq_landau_n_rt_rp_4d203_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_negd c.(l_e_st_eq_landau_n_rt_rp_eqnegd (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_md a b) c) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)) (l_e_st_eq_landau_n_rt_rp_disttmd1 a b c) (l_e_st_eq_landau_n_rt_rp_ntdpn (l_e_st_eq_landau_n_rt_rp_md a b) c (l_e_st_eq_landau_n_rt_rp_4d203_t1 a b c m) n) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c))).
+
+(* notion 3695 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203c ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_negd c.(l_e_st_eq_landau_n_rt_rp_satzd182c (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_4d203_t3 a b c m n) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
+
+(* notion 3696 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λp:l_e_st_eq_landau_n_rt_rp_posd c.(l_e_st_eq_landau_n_rt_rp_eqmored12 (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_comtd a c) (l_e_st_eq_landau_n_rt_rp_comtd b c) (l_e_st_eq_landau_n_rt_rp_satzd203a a b c m p) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
+
+(* notion 3697 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203e ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_td01 c a z) (l_e_st_eq_landau_n_rt_rp_td01 c b z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
+
+(* notion 3698 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203f ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λm:l_e_st_eq_landau_n_rt_rp_mored a b.λn:l_e_st_eq_landau_n_rt_rp_negd c.(l_e_st_eq_landau_n_rt_rp_eqlessd12 (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_comtd a c) (l_e_st_eq_landau_n_rt_rp_comtd b c) (l_e_st_eq_landau_n_rt_rp_satzd203c a b c m n) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
+
+(* notion 3699 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203g ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λp:l_e_st_eq_landau_n_rt_rp_posd c.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_satzd203a b a c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) p) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
+
+(* notion 3700 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203h ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td02 a c z) (l_e_st_eq_landau_n_rt_rp_td02 b c z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
+
+(* notion 3701 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203j ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λn:l_e_st_eq_landau_n_rt_rp_negd c.(l_e_st_eq_landau_n_rt_rp_lemmad6 (l_e_st_eq_landau_n_rt_rp_td b c) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_satzd203c b a c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) n) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b c)).
+
+(* notion 3702 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203k ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λp:l_e_st_eq_landau_n_rt_rp_posd c.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_satzd203d b a c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) p) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
+
+(* notion 3703 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203l ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_td01 c a z) (l_e_st_eq_landau_n_rt_rp_td01 c b z) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
+
+(* notion 3704 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd203m ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λl:l_e_st_eq_landau_n_rt_rp_lessd a b.λn:l_e_st_eq_landau_n_rt_rp_negd c.(l_e_st_eq_landau_n_rt_rp_lemmad6 (l_e_st_eq_landau_n_rt_rp_td c b) (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_satzd203f b a c (l_e_st_eq_landau_n_rt_rp_lemmad6 a b l) n) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_td c a) (l_e_st_eq_landau_n_rt_rp_td c b)).
+
+(* notion 3705 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t19 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_ts q l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) q) (l_e_st_eq_landau_n_rt_rp_disttp2 q p l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts q l_e_st_eq_landau_n_rt_rp_1rp) q (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_satz151 q)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) q)).
+
+(* notion 3706 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t20 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) q) r) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) q) (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp) r (l_e_st_eq_landau_n_rt_rp_iv4d_t19 p q) (l_e_st_eq_landau_n_rt_rp_satz151 r)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ts q p) q r) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_pl q r))).
+
+(* notion 3707 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t21 ≝ λp:l_e_st_eq_landau_n_rt_cut.λq:l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_pl q r)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_pl r q)) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_iv4d_t20 p q r) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl q r) (l_e_st_eq_landau_n_rt_rp_pl r q) (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_compl q r)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts q (l_e_st_eq_landau_n_rt_rp_pl p l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts q p) (l_e_st_eq_landau_n_rt_rp_pl r q))).
+
+(* notion 3708 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_arp ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_rpofpd a p : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3709 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_arpi ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_ov l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3710 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_ai ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3711 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t22 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_iv4d_ai a p)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) l_e_st_eq_landau_n_rt_rp_1rp)))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)))) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p))) (l_e_st_eq_landau_n_rt_rp_tdeq1a a (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_eqsmsd (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) l_e_st_eq_landau_n_rt_rp_1rp))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a))) (l_e_st_eq_landau_n_rt_rp_iv4d_t20 (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a)) (l_e_st_eq_landau_n_rt_rp_iv4d_t21 (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_1a a))) (l_e_st_eq_landau_n_rt_rp_lemmad2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a))) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_iv4d_ai a p)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)))).
+
+(* notion 3712 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t23 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p)) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ists1 (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p)) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p) (l_e_st_eq_landau_n_rt_rp_satz140d (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_2a a) p)) (l_e_st_eq_landau_n_rt_rp_disttp1 (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_satz153c l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv4d_arp a p))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp)).
+
+(* notion 3713 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t24 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p))) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv4d_t23 a p)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_compl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)))).
+
+(* notion 3714 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t25 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv4d_t24 a p) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p))) l_e_st_eq_landau_n_rt_rp_1df).
+
+(* notion 3715 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t26 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_iv4d_ai a p)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_1a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_2a a) (l_e_st_eq_landau_n_rt_rp_iv4d_arpi a p))) l_e_st_eq_landau_n_rt_rp_1df (l_e_st_eq_landau_n_rt_rp_iv4d_t22 a p) (l_e_st_eq_landau_n_rt_rp_iv4d_t25 a p) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_iv4d_ai a p)) l_e_st_eq_landau_n_rt_rp_1df).
+
+(* notion 3716 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t27 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_iv4d_ai a p) (l_e_st_eq_landau_n_rt_rp_iv4d_t26 a p) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)).
+
+(* notion 3717 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t28 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_satzd176c a n : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d a)).
+
+(* notion 3718 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t29 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λh:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) h) l_e_st_eq_landau_n_rt_rp_1df.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d h)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) h) l_e_st_eq_landau_n_rt_rp_1df (l_e_st_eq_landau_n_rt_rp_satzd197d a h) e : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_m0d h)) l_e_st_eq_landau_n_rt_rp_1df).
+
+(* notion 3719 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t30 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.λh:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) h) l_e_st_eq_landau_n_rt_rp_1df.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_m0d h) (l_e_st_eq_landau_n_rt_rp_iv4d_t29 a n h e) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)).
+
+(* notion 3720 *)
+definition l_e_st_eq_landau_n_rt_rp_iv4d_t31 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) x) l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_iv4d_t27 (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_iv4d_t28 a n)) (l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a) x) l_e_st_eq_landau_n_rt_rp_1df.l_e_st_eq_landau_n_rt_rp_iv4d_t30 a n x t) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)).
+
+(* notion 3721 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmad7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_rappd a (l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_iv4d_t27 a t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)) n) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_iv4d_t31 a t) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a x) l_e_st_eq_landau_n_rt_rp_1df)).
+
+(* notion 3722 *)
+definition l_e_st_eq_landau_n_rt_rp_4d204_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λk:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) a.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b k) a.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_td b h) (l_e_st_eq_landau_n_rt_rp_td b k) a e f : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) (l_e_st_eq_landau_n_rt_rp_td b k)).
+
+(* notion 3723 *)
+definition l_e_st_eq_landau_n_rt_rp_4d204_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λk:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) a.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b k) a.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td b h) (l_e_st_eq_landau_n_rt_rp_td b k)) (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_md h k)) (l_e_st_eq_landau_n_rt_rp_distmtd2 b h k) (l_e_st_eq_landau_n_rt_rp_satzd182e (l_e_st_eq_landau_n_rt_rp_td b h) (l_e_st_eq_landau_n_rt_rp_td b k) (l_e_st_eq_landau_n_rt_rp_4d204_t1 a b n h k e f)) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_md h k))).
+
+(* notion 3724 *)
+definition l_e_st_eq_landau_n_rt_rp_4d204_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λk:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) a.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b k) a.(l_ore2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md h k)) (l_e_st_eq_landau_n_rt_rp_satzd192c b (l_e_st_eq_landau_n_rt_rp_md h k) (l_e_st_eq_landau_n_rt_rp_4d204_t2 a b n h k e f)) n : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md h k)).
+
+(* notion 3725 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd204b ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λk:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) a.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b k) a.(l_e_st_eq_landau_n_rt_rp_satzd182b h k (l_e_st_eq_landau_n_rt_rp_4d204_t3 a b n h k e f) : l_e_st_eq_landau_n_rt_rp_eq h k).
+
+(* notion 3726 *)
+definition l_e_st_eq_landau_n_rt_rp_4d204_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) l_e_st_eq_landau_n_rt_rp_1df.(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_td h a)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td b h) a) (l_e_st_eq_landau_n_rt_rp_td l_e_st_eq_landau_n_rt_rp_1df a) a (l_e_st_eq_landau_n_rt_rp_asstd2 b h a) (l_e_st_eq_landau_n_rt_rp_eqtd1 (l_e_st_eq_landau_n_rt_rp_td b h) l_e_st_eq_landau_n_rt_rp_1df a e) (l_e_st_eq_landau_n_rt_rp_satzd195b a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_td h a)) a).
+
+(* notion 3727 *)
+definition l_e_st_eq_landau_n_rt_rp_4d204_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).λh:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b h) l_e_st_eq_landau_n_rt_rp_1df.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) a) (l_e_st_eq_landau_n_rt_rp_td h a) (l_e_st_eq_landau_n_rt_rp_4d204_t4 a b n h e) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) a)).
+
+(* notion 3728 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd204a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero b).(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_lemmad7 b n) (l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) a)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) l_e_st_eq_landau_n_rt_rp_1df.l_e_st_eq_landau_n_rt_rp_4d204_t5 a b n x t) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b x) a)).
+
+(* notion 3729 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_t1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r s.(l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_asspl2 r l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_asspl2 s l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_satz134 r s (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp)).
+
+(* notion 3730 *)
+definition l_e_st_eq_landau_n_rt_rp_morerpepd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r s.(l_e_st_eq_landau_n_rt_rp_moredi12 (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_iv5d_t1 r s m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)).
+
+(* notion 3731 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_t2 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_morede12 (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp)).
+
+(* notion 3732 *)
+definition l_e_st_eq_landau_n_rt_rp_morerpipd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz136a r s (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ismore12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl r (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_asspl1 r l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_asspl1 s l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_iv5d_t2 r s m)) : l_e_st_eq_landau_n_rt_rp_more r s).
+
+(* notion 3733 *)
+definition l_e_st_eq_landau_n_rt_rp_lessrpepd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r s.(l_e_st_eq_landau_n_rt_rp_lemmad5 (l_e_st_eq_landau_n_rt_rp_pdofrp s) (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_morerpepd s r (l_e_st_eq_landau_n_rt_rp_satz122 r s l)) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)).
+
+(* notion 3734 *)
+definition l_e_st_eq_landau_n_rt_rp_lessrpipd ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz121 s r (l_e_st_eq_landau_n_rt_rp_morerpipd s r (l_e_st_eq_landau_n_rt_rp_lemmad6 (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s) l)) : l_e_st_eq_landau_n_rt_rp_less r s).
+
+(* notion 3735 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_i ≝ (l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3736 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_2 ≝ (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3737 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_rp1 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_iv5d_i : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3738 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_sp1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_iv5d_i : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3739 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_rps ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl r s : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3740 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_rs ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ts r s : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3741 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_t3 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_2) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_4pl23 r l_e_st_eq_landau_n_rt_rp_iv5d_i s l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_3pl23 (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2 l_e_st_eq_landau_n_rt_rp_iv5d_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_2)).
+
+(* notion 3742 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_t4 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) l_e_st_eq_landau_n_rt_rp_iv5d_2) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) (l_e_st_eq_landau_n_rt_rp_pdeq12a (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) l_e_st_eq_landau_n_rt_rp_iv5d_2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_t3 r s)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s))).
+
+(* notion 3743 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmad8 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_iv5d_t4 r s : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r s))).
+
+(* notion 3744 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_t5 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) (l_e_st_eq_landau_n_rt_rp_disttp2 r s l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts r l_e_st_eq_landau_n_rt_rp_iv5d_i) r (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_satz151 r)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r)).
+
+(* notion 3745 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_t6 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr4is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_disttp1 r l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts r (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s) (l_e_st_eq_landau_n_rt_rp_iv5d_t5 r s) (l_e_st_eq_landau_n_rt_rp_satz151b (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) s l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r) s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) r s)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i)).
+
+(* notion 3746 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_t7 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_t6 r s) (l_e_st_eq_landau_n_rt_rp_satz151 l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s)) l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2))).
+
+(* notion 3747 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_t8 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s) (l_e_st_eq_landau_n_rt_rp_satz151 (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r)) (l_e_st_eq_landau_n_rt_rp_satz151b (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_4pl23 r l_e_st_eq_landau_n_rt_rp_iv5d_i s l_e_st_eq_landau_n_rt_rp_iv5d_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)).
+
+(* notion 3748 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_t9 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_iv5d_t8 r s)) (l_e_st_eq_landau_n_rt_rp_3pl23 (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) l_e_st_eq_landau_n_rt_rp_iv5d_i)).
+
+(* notion 3749 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_t10 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rps r s) l_e_st_eq_landau_n_rt_rp_iv5d_2)) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_t7 r s)) (l_e_st_eq_landau_n_rt_rp_iv5d_t9 r s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))))).
+
+(* notion 3750 *)
+definition l_e_st_eq_landau_n_rt_rp_iv5d_t11 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s)) (l_e_st_eq_landau_n_rt_rp_tdeq12a (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i l_e_st_eq_landau_n_rt_rp_iv5d_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_iv5d_rp1 r) l_e_st_eq_landau_n_rt_rp_iv5d_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_sp1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s) l_e_st_eq_landau_n_rt_rp_iv5d_i) l_e_st_eq_landau_n_rt_rp_iv5d_i (l_e_st_eq_landau_n_rt_rp_iv5d_t10 r s)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_iv5d_rs r s))).
+
+(* notion 3751 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmad9 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_iv5d_t11 r s : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r s))).
+
+(* notion 3752 *)
+definition l_e_st_eq_landau_n_rt_rp_in ≝ λr:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.(l_e_st_esti l_e_st_eq_landau_n_rt_cut r s0 : Prop).
+
+(* notion 3753 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_prop1 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_less x r.l_e_st_eq_landau_n_rt_rp_in x s0) : Prop).
+
+(* notion 3754 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_prop2 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_more x r.l_e_st_eq_landau_n_rt_rp_in x t0) : Prop).
+
+(* notion 3755 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_prop3 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λr:l_e_st_eq_landau_n_rt_cut.(l_and (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 r) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 r) : Prop).
+
+(* notion 3756 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t1 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.(l_ande2 (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 r1) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 r1) pr1 : l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 r1).
+
+(* notion 3757 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t2 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.(l_ande1 (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 r2) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 r2) pr2 : l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 r2).
+
+(* notion 3758 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_rx ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.λl:l_e_st_eq_landau_n_rt_rp_less r1 r2.λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_rpofrt x0 : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3759 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t3 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.λl:l_e_st_eq_landau_n_rt_rp_less r1 r2.λx0:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less r1 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) r2.(l_e_st_eq_landau_n_rt_rp_5p205_t2 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) l2 : l_e_st_eq_landau_n_rt_rp_in (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) s0).
+
+(* notion 3760 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t4 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.λl:l_e_st_eq_landau_n_rt_rp_less r1 r2.λx0:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less r1 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) r2.(l_e_st_eq_landau_n_rt_rp_5p205_t1 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_satz122 r1 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) l1) : l_e_st_eq_landau_n_rt_rp_in (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) t0).
+
+(* notion 3761 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t5 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.λl:l_e_st_eq_landau_n_rt_rp_less r1 r2.λx0:l_e_st_eq_landau_n_rt_rat.λl1:l_e_st_eq_landau_n_rt_rp_less r1 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0).λl2:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) r2.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0)) (l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0)) (l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0)) (l_e_st_eq_landau_n_rt_rp_satz123b (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0)) (p2 (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_t3 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0 l1 l2) (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0) (l_e_st_eq_landau_n_rt_rp_5p205_t4 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0 l1 l2)) (l_e_refis l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_5p205_rx s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x0)) : l_con).
+
+(* notion 3762 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t6 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.λl:l_e_st_eq_landau_n_rt_rp_less r1 r2.(l_e_st_eq_landau_n_rt_rp_satz159app r1 r2 l l_con (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_rp_less r1 (l_e_st_eq_landau_n_rt_rp_rpofrt x).λu:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_rpofrt x) r2.l_e_st_eq_landau_n_rt_rp_5p205_t5 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 l x t u) : l_con).
+
+(* notion 3763 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t7 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.(λt:l_e_st_eq_landau_n_rt_rp_less r1 r2.l_e_st_eq_landau_n_rt_rp_5p205_t6 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2 t : l_not (l_e_st_eq_landau_n_rt_rp_less r1 r2)).
+
+(* notion 3764 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t8 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.(λt:l_e_st_eq_landau_n_rt_rp_more r1 r2.l_e_st_eq_landau_n_rt_rp_5p205_t6 s0 t0 p0 p1a p1b p2 r2 r1 pr2 pr1 (l_e_st_eq_landau_n_rt_rp_satz121 r1 r2 t) : l_not (l_e_st_eq_landau_n_rt_rp_more r1 r2)).
+
+(* notion 3765 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t9 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr1:l_e_st_eq_landau_n_rt_cut.λr2:l_e_st_eq_landau_n_rt_cut.λpr1:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r1.λpr2:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 r2.(l_or3e1 (l_e_st_eq_landau_n_rt_rp_is r1 r2) (l_e_st_eq_landau_n_rt_rp_more r1 r2) (l_e_st_eq_landau_n_rt_rp_less r1 r2) (l_e_st_eq_landau_n_rt_rp_satz123a r1 r2) (l_e_st_eq_landau_n_rt_rp_5p205_t8 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2) (l_e_st_eq_landau_n_rt_rp_5p205_t7 s0 t0 p0 p1a p1b p2 r1 r2 pr1 pr2) : l_e_st_eq_landau_n_rt_rp_is r1 r2).
+
+(* notion 3766 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t10 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(λx:l_e_st_eq_landau_n_rt_cut.λy:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x.λu:l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 y.l_e_st_eq_landau_n_rt_rp_5p205_t9 s0 t0 p0 p1a p1b p2 x y t u : l_e_amone l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x)).
+
+(* notion 3767 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_schnittprop ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.(l_e_st_eq_landau_n_rt_rp_some (λy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) : Prop).
+
+(* notion 3768 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_schnittset ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_e_st_setof l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) : l_e_st_set l_e_st_eq_landau_n_rt_rat).
+
+(* notion 3769 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t11 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.(l_andi (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) i lx : l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0)).
+
+(* notion 3770 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t12 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.(l_somei l_e_st_eq_landau_n_rt_cut (λy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) r (l_e_st_eq_landau_n_rt_rp_5p205_t11 s0 t0 p0 p1a p1b p2 r i x0 lx) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0).
+
+(* notion 3771 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t13 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t12 s0 t0 p0 p1a p1b p2 r i x0 lx) : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
+
+(* notion 3772 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t14 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s s0.(l_e_st_eq_landau_n_rt_rp_satz122 s r (p2 s j r i) : l_e_st_eq_landau_n_rt_rp_more r s).
+
+(* notion 3773 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t15 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s s0.(l_e_st_eq_landau_n_rt_rp_satz158b r x0 ux : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r).
+
+(* notion 3774 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t16 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s s0.(l_e_st_eq_landau_n_rt_rp_moreisi1 (l_e_st_eq_landau_n_rt_rp_rpofrt x0) s (l_e_st_eq_landau_n_rt_rp_satz127c (l_e_st_eq_landau_n_rt_rp_rpofrt x0) r s (l_e_st_eq_landau_n_rt_rp_5p205_t15 s0 t0 p0 p1a p1b p2 r i x0 ux s j) (l_e_st_eq_landau_n_rt_rp_5p205_t14 s0 t0 p0 p1a p1b p2 r i x0 ux s j)) : l_e_st_eq_landau_n_rt_rp_moreis (l_e_st_eq_landau_n_rt_rp_rpofrt x0) s).
+
+(* notion 3775 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t17 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s s0.(l_e_st_eq_landau_n_rt_rp_satz158d s x0 (l_e_st_eq_landau_n_rt_rp_5p205_t16 s0 t0 p0 p1a p1b p2 r i x0 ux s j) : l_e_st_eq_landau_n_rt_urt s x0).
+
+(* notion 3776 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t18 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λs:l_e_st_eq_landau_n_rt_cut.(l_weli (l_ec (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0)) (λt:l_e_st_eq_landau_n_rt_rp_in s s0.l_e_st_eq_landau_n_rt_rp_5p205_t17 s0 t0 p0 p1a p1b p2 r i x0 ux s t) : l_not (l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0))).
+
+(* notion 3777 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t19 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.(l_some_th5 l_e_st_eq_landau_n_rt_cut (λy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) (λy:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_t18 s0 t0 p0 p1a p1b p2 r i x0 ux y) : l_not (l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0)).
+
+(* notion 3778 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t20 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r t0.λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0) (l_e_st_eq_landau_n_rt_rp_5p205_t19 s0 t0 p0 p1a p1b p2 r i x0 ux) (λt:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) x0 t) : l_not (l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2))).
+
+(* notion 3779 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t21 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) x0 i : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0).
+
+(* notion 3780 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t22 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_ande1 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) a : l_e_st_eq_landau_n_rt_rp_in r s0).
+
+(* notion 3781 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t23 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_ande2 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) a : l_e_st_eq_landau_n_rt_lrt r x0).
+
+(* notion 3782 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t24 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_e_st_eq_landau_n_rt_rp_satz120 r x0 (l_e_st_eq_landau_n_rt_rp_5p205_t23 s0 t0 p0 p1a p1b p2 x0 i y0 l r a) y0 l : l_e_st_eq_landau_n_rt_lrt r y0).
+
+(* notion 3783 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t25 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_andi (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r y0) (l_e_st_eq_landau_n_rt_rp_5p205_t22 s0 t0 p0 p1a p1b p2 x0 i y0 l r a) (l_e_st_eq_landau_n_rt_rp_5p205_t24 s0 t0 p0 p1a p1b p2 x0 i y0 l r a) : l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r y0)).
+
+(* notion 3784 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t26 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_somei l_e_st_eq_landau_n_rt_cut (λy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y y0)) r (l_e_st_eq_landau_n_rt_rp_5p205_t25 s0 t0 p0 p1a p1b p2 x0 i y0 l r a) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 y0).
+
+(* notion 3785 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t27 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_someapp l_e_st_eq_landau_n_rt_cut (λy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) (l_e_st_eq_landau_n_rt_rp_5p205_t21 s0 t0 p0 p1a p1b p2 x0 i) (l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 y0) (λy:l_e_st_eq_landau_n_rt_cut.λr:l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0).l_e_st_eq_landau_n_rt_rp_5p205_t26 s0 t0 p0 p1a p1b p2 x0 i y0 l y r) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 y0).
+
+(* notion 3786 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t28 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy0:l_e_st_eq_landau_n_rt_rat.λl:l_e_st_eq_landau_n_rt_less y0 x0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) y0 (l_e_st_eq_landau_n_rt_rp_5p205_t27 s0 t0 p0 p1a p1b p2 x0 i y0 l) : l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
+
+(* notion 3787 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t29 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_ande1 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) a : l_e_st_eq_landau_n_rt_rp_in r s0).
+
+(* notion 3788 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t30 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_ande2 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) a : l_e_st_eq_landau_n_rt_lrt r x0).
+
+(* notion 3789 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t31 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_andi (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r y0) (l_e_st_eq_landau_n_rt_rp_5p205_t29 s0 t0 p0 p1a p1b p2 x0 i r a) ly : l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r y0)).
+
+(* notion 3790 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t32 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_somei l_e_st_eq_landau_n_rt_cut (λy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y y0)) r (l_e_st_eq_landau_n_rt_rp_5p205_t31 s0 t0 p0 p1a p1b p2 x0 i r a y0 ly l) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 y0).
+
+(* notion 3791 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t33 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) y0 (l_e_st_eq_landau_n_rt_rp_5p205_t32 s0 t0 p0 p1a p1b p2 x0 i r a y0 ly l) : l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
+
+(* notion 3792 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t34 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_e_st_eq_landau_n_rt_satz83 x0 y0 l : l_e_st_eq_landau_n_rt_more y0 x0).
+
+(* notion 3793 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t35 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_andi (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y0 x0) (l_e_st_eq_landau_n_rt_rp_5p205_t33 s0 t0 p0 p1a p1b p2 x0 i r a y0 ly l) (l_e_st_eq_landau_n_rt_rp_5p205_t34 s0 t0 p0 p1a p1b p2 x0 i r a y0 ly l) : l_and (l_e_st_eq_landau_n_rt_in y0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y0 x0)).
+
+(* notion 3794 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t36 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).λy0:l_e_st_eq_landau_n_rt_rat.λly:l_e_st_eq_landau_n_rt_lrt r y0.λl:l_e_st_eq_landau_n_rt_less x0 y0.(l_somei l_e_st_eq_landau_n_rt_rat (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0)) y0 (l_e_st_eq_landau_n_rt_rp_5p205_t35 s0 t0 p0 p1a p1b p2 x0 i r a y0 ly l) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0))).
+
+(* notion 3795 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t37 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λr:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0).(l_e_st_eq_landau_n_rt_cutapp3 r x0 (l_e_st_eq_landau_n_rt_rp_5p205_t30 s0 t0 p0 p1a p1b p2 x0 i r a) (l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0))) (λy:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt r y.λu:l_e_st_eq_landau_n_rt_less x0 y.l_e_st_eq_landau_n_rt_rp_5p205_t36 s0 t0 p0 p1a p1b p2 x0 i r a y t u) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0))).
+
+(* notion 3796 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t38 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λx0:l_e_st_eq_landau_n_rt_rat.λi:l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).(l_someapp l_e_st_eq_landau_n_rt_cut (λy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) (l_e_st_eq_landau_n_rt_rp_5p205_t21 s0 t0 p0 p1a p1b p2 x0 i) (l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0))) (λy:l_e_st_eq_landau_n_rt_cut.λt:l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0).l_e_st_eq_landau_n_rt_rp_5p205_t37 s0 t0 p0 p1a p1b p2 x0 i y t) : l_e_st_eq_landau_n_rt_some (λy:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_in y (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_more y x0))).
+
+(* notion 3797 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t39 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s t0.λy0:l_e_st_eq_landau_n_rt_rat.λuy:l_e_st_eq_landau_n_rt_urt s y0.(l_e_st_eq_landau_n_rt_cut2 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t13 s0 t0 p0 p1a p1b p2 r i x0 lx) y0 (l_e_st_eq_landau_n_rt_rp_5p205_t20 s0 t0 p0 p1a p1b p2 s j y0 uy) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).λy:l_e_st_eq_landau_n_rt_rat.λu:l_e_st_eq_landau_n_rt_less y x.l_e_st_eq_landau_n_rt_rp_5p205_t28 s0 t0 p0 p1a p1b p2 x t y u) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_in x (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2).l_e_st_eq_landau_n_rt_rp_5p205_t38 s0 t0 p0 p1a p1b p2 x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
+
+(* notion 3798 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t40 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λs:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s t0.(l_e_st_eq_landau_n_rt_cutapp1b s (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt s x.l_e_st_eq_landau_n_rt_rp_5p205_t39 s0 t0 p0 p1a p1b p2 r i x0 lx s j x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
+
+(* notion 3799 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t41 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_cut t0 p1b (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (λy:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_5p205_t40 s0 t0 p0 p1a p1b p2 r i x0 lx y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
+
+(* notion 3800 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t42 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r s0.(l_e_st_eq_landau_n_rt_cutapp1a r (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt r x.l_e_st_eq_landau_n_rt_rp_5p205_t41 s0 t0 p0 p1a p1b p2 r i x t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
+
+(* notion 3801 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t43 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_cut s0 p1a (l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)) (λy:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_in y s0.l_e_st_eq_landau_n_rt_rp_5p205_t42 s0 t0 p0 p1a p1b p2 y t) : l_e_st_eq_landau_n_rt_cutprop (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
+
+(* notion 3802 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_snt ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_e_st_eq_landau_n_rt_rp_cutof (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_5p205_t43 s0 t0 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3803 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t44 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.(l_e_st_eq_landau_n_rt_rp_ini (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_5p205_t43 s0 t0 p0 p1a p1b p2) x0 lx : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
+
+(* notion 3804 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t45 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.(l_e_st_estie l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t44 s0 t0 p0 p1a p1b p2 r l x0 ux lx) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0).
+
+(* notion 3805 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t46 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_ande1 (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0) a : l_e_st_eq_landau_n_rt_rp_in s s0).
+
+(* notion 3806 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t47 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_ande2 (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0) a : l_e_st_eq_landau_n_rt_lrt s x0).
+
+(* notion 3807 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t48 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_andi (l_e_st_eq_landau_n_rt_urt r x0) (l_e_st_eq_landau_n_rt_lrt s x0) ux (l_e_st_eq_landau_n_rt_rp_5p205_t47 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a) : l_and (l_e_st_eq_landau_n_rt_urt r x0) (l_e_st_eq_landau_n_rt_lrt s x0)).
+
+(* notion 3808 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t49 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_somei l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_and (l_e_st_eq_landau_n_rt_urt r x) (l_e_st_eq_landau_n_rt_lrt s x)) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t48 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a) : l_e_st_eq_landau_n_rt_rp_less r s).
+
+(* notion 3809 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t50 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_ec3e23 (l_e_st_eq_landau_n_rt_rp_is s r) (l_e_st_eq_landau_n_rt_rp_more s r) (l_e_st_eq_landau_n_rt_rp_less s r) (l_e_st_eq_landau_n_rt_rp_satz123b s r) (l_e_st_eq_landau_n_rt_rp_satz122 r s (l_e_st_eq_landau_n_rt_rp_5p205_t49 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a)) : l_not (l_e_st_eq_landau_n_rt_rp_less s r)).
+
+(* notion 3810 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t51 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_in r t0) (l_e_st_eq_landau_n_rt_rp_less s r) (l_e_st_eq_landau_n_rt_rp_5p205_t50 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a) (p2 s (l_e_st_eq_landau_n_rt_rp_5p205_t46 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a) r) : l_not (l_e_st_eq_landau_n_rt_rp_in r t0)).
+
+(* notion 3811 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t52 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λs:l_e_st_eq_landau_n_rt_cut.λa:l_and (l_e_st_eq_landau_n_rt_rp_in s s0) (l_e_st_eq_landau_n_rt_lrt s x0).(l_ore1 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_rp_in r t0) (p0 r) (l_e_st_eq_landau_n_rt_rp_5p205_t51 s0 t0 p0 p1a p1b p2 r l x0 ux lx s a) : l_e_st_eq_landau_n_rt_rp_in r s0).
+
+(* notion 3812 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t53 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λux:l_e_st_eq_landau_n_rt_urt r x0.λlx:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.(l_someapp l_e_st_eq_landau_n_rt_cut (λy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) (l_e_st_eq_landau_n_rt_rp_5p205_t45 s0 t0 p0 p1a p1b p2 r l x0 ux lx) (l_e_st_eq_landau_n_rt_rp_in r s0) (λy:l_e_st_eq_landau_n_rt_cut.λt:l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0).l_e_st_eq_landau_n_rt_rp_5p205_t52 s0 t0 p0 p1a p1b p2 r l x0 ux lx y t) : l_e_st_eq_landau_n_rt_rp_in r s0).
+
+(* notion 3813 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t54 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).(l_e_st_eq_landau_n_rt_rp_lessapp r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) l (l_e_st_eq_landau_n_rt_rp_in r s0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_urt r x.λu:l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x.l_e_st_eq_landau_n_rt_rp_5p205_t53 s0 t0 p0 p1a p1b p2 r l x t u) : l_e_st_eq_landau_n_rt_rp_in r s0).
+
+(* notion 3814 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t55 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λi:l_e_st_eq_landau_n_rt_rp_in r s0.(l_andi (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0) i lx : l_and (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt r x0)).
+
+(* notion 3815 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t56 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λi:l_e_st_eq_landau_n_rt_rp_in r s0.(l_somei l_e_st_eq_landau_n_rt_cut (λy:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_in y s0) (l_e_st_eq_landau_n_rt_lrt y x0)) r (l_e_st_eq_landau_n_rt_rp_5p205_t55 s0 t0 p0 p1a p1b p2 r m x0 lx ux i) : l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x0).
+
+(* notion 3816 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t57 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λi:l_e_st_eq_landau_n_rt_rp_in r s0.(l_e_st_estii l_e_st_eq_landau_n_rt_rat (λx:l_e_st_eq_landau_n_rt_rat.l_e_st_eq_landau_n_rt_rp_5p205_schnittprop s0 t0 p0 p1a p1b p2 x) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t56 s0 t0 p0 p1a p1b p2 r m x0 lx ux i) : l_e_st_eq_landau_n_rt_in x0 (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2)).
+
+(* notion 3817 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t58 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.λi:l_e_st_eq_landau_n_rt_rp_in r s0.(l_e_st_eq_landau_n_rt_rp_ine (l_e_st_eq_landau_n_rt_rp_5p205_schnittset s0 t0 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_5p205_t43 s0 t0 p0 p1a p1b p2) x0 (l_e_st_eq_landau_n_rt_rp_5p205_t57 s0 t0 p0 p1a p1b p2 r m x0 lx ux i) : l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0).
+
+(* notion 3818 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t59 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_lrt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0) ux (λt:l_e_st_eq_landau_n_rt_rp_in r s0.l_e_st_eq_landau_n_rt_rp_5p205_t58 s0 t0 p0 p1a p1b p2 r m x0 lx ux t) : l_not (l_e_st_eq_landau_n_rt_rp_in r s0)).
+
+(* notion 3819 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t60 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).λx0:l_e_st_eq_landau_n_rt_rat.λlx:l_e_st_eq_landau_n_rt_lrt r x0.λux:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x0.(l_ore2 (l_e_st_eq_landau_n_rt_rp_in r s0) (l_e_st_eq_landau_n_rt_rp_in r t0) (p0 r) (l_e_st_eq_landau_n_rt_rp_5p205_t59 s0 t0 p0 p1a p1b p2 r m x0 lx ux) : l_e_st_eq_landau_n_rt_rp_in r t0).
+
+(* notion 3820 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t61 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).λr:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).(l_e_st_eq_landau_n_rt_rp_moreapp r (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) m (l_e_st_eq_landau_n_rt_rp_in r t0) (λx:l_e_st_eq_landau_n_rt_rat.λt:l_e_st_eq_landau_n_rt_lrt r x.λu:l_e_st_eq_landau_n_rt_urt (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) x.l_e_st_eq_landau_n_rt_rp_5p205_t60 s0 t0 p0 p1a p1b p2 r m x t u) : l_e_st_eq_landau_n_rt_rp_in r t0).
+
+(* notion 3821 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t62 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_andi (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2)) (λx:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_less x (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).l_e_st_eq_landau_n_rt_rp_5p205_t54 s0 t0 p0 p1a p1b p2 x t) (λx:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_more x (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2).l_e_st_eq_landau_n_rt_rp_5p205_t61 s0 t0 p0 p1a p1b p2 x t) : l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2)).
+
+(* notion 3822 *)
+definition l_e_st_eq_landau_n_rt_rp_5p205_t63 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_somei l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x) (l_e_st_eq_landau_n_rt_rp_5p205_snt s0 t0 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_5p205_t62 s0 t0 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x)).
+
+(* notion 3823 *)
+definition l_e_st_eq_landau_n_rt_rp_satzp205 ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_e_onei l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x) (l_e_st_eq_landau_n_rt_rp_5p205_t10 s0 t0 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_5p205_t63 s0 t0 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_rp_one (λx:l_e_st_eq_landau_n_rt_cut.l_and (l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_less y x.l_e_st_eq_landau_n_rt_rp_in y s0)) (l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_more y x.l_e_st_eq_landau_n_rt_rp_in y t0)))).
+
+(* notion 3824 *)
+definition l_e_st_eq_landau_n_rt_rp_schnitt ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_e_ind l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x) (l_e_st_eq_landau_n_rt_rp_satzp205 s0 t0 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3825 *)
+definition l_e_st_eq_landau_n_rt_rp_satzp205a ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_ande1 (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2)) (l_e_oneax l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x) (l_e_st_eq_landau_n_rt_rp_satzp205 s0 t0 p0 p1a p1b p2)) : l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_less x (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2).l_e_st_eq_landau_n_rt_rp_in x s0)).
+
+(* notion 3826 *)
+definition l_e_st_eq_landau_n_rt_rp_satzp205b ≝ λs0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λt0:l_e_st_set l_e_st_eq_landau_n_rt_cut.λp0:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.l_or (l_e_st_eq_landau_n_rt_rp_in x s0) (l_e_st_eq_landau_n_rt_rp_in x t0)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut s0.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_cut t0.λp2:l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_in x s0.l_e_st_eq_landau_n_rt_rp_all (λy:l_e_st_eq_landau_n_rt_cut.Πu:l_e_st_eq_landau_n_rt_rp_in y t0.l_e_st_eq_landau_n_rt_rp_less x y)).(l_ande2 (l_e_st_eq_landau_n_rt_rp_5p205_prop1 s0 t0 (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_5p205_prop2 s0 t0 (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2)) (l_e_oneax l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_5p205_prop3 s0 t0 x) (l_e_st_eq_landau_n_rt_rp_satzp205 s0 t0 p0 p1a p1b p2)) : l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_more x (l_e_st_eq_landau_n_rt_rp_schnitt s0 t0 p0 p1a p1b p2).l_e_st_eq_landau_n_rt_rp_in x t0)).
+
+(* notion 3827 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_i ≝ (l_e_st_eq_landau_n_rt_rp_1rp : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3828 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_r1 ≝ λr:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_ivad_i : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3829 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_s1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_ivad_i : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3830 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_rps ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pl r s : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3831 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_2 ≝ (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3832 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdeq12a (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) l_e_st_eq_landau_n_rt_rp_ivad_i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_2)).
+
+(* notion 3833 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t2 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_4pl23 r l_e_st_eq_landau_n_rt_rp_ivad_i s l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_asspl2 (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i)).
+
+(* notion 3834 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t3 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t2 r s) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i)).
+
+(* notion 3835 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t4 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_2) (l_e_st_eq_landau_n_rt_rp_ivad_t3 r s) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_2)).
+
+(* notion 3836 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t5 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t4 r s) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) l_e_st_eq_landau_n_rt_rp_ivad_2) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ivad_rps r s))).
+
+(* notion 3837 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmaivad1 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r s)) (l_e_st_eq_landau_n_rt_rp_ivad_t1 r s) (l_e_st_eq_landau_n_rt_rp_ivad_t5 r s) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r s))).
+
+(* notion 3838 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_rs ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_ts r s : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3839 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t6 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_tdeq12a (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) l_e_st_eq_landau_n_rt_rp_ivad_i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))))).
+
+(* notion 3840 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t7 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) s) (l_e_st_eq_landau_n_rt_rp_disttp1 r l_e_st_eq_landau_n_rt_rp_ivad_i s) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i s) s (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) (l_e_st_eq_landau_n_rt_rp_satz151b s)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) s)).
+
+(* notion 3841 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t8 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) s) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) s) (l_e_st_eq_landau_n_rt_rp_ivad_r1 r)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_rps r s)) (l_e_st_eq_landau_n_rt_rp_disttp2 (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) s l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) s) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) s) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_t7 r s) (l_e_st_eq_landau_n_rt_rp_satz151 (l_e_st_eq_landau_n_rt_rp_ivad_r1 r))) (l_e_st_eq_landau_n_rt_rp_4pl24 (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) s r l_e_st_eq_landau_n_rt_rp_ivad_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_rps r s))).
+
+(* notion 3842 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t9 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_rps r s)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_rps r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t8 r s) (l_e_st_eq_landau_n_rt_rp_satz151 l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i))).
+
+(* notion 3843 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t10 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_ispl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t9 r s)) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i))).
+
+(* notion 3844 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t11 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tr3is l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_2) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))) (l_e_st_eq_landau_n_rt_rp_asspl1 (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_4pl23 r s l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ispl12 (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_satz151a (l_e_st_eq_landau_n_rt_rp_ivad_r1 r)) (l_e_st_eq_landau_n_rt_rp_satz151c (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)))).
+
+(* notion 3845 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t12 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)))) (l_e_st_eq_landau_n_rt_rp_ivad_t10 r s) (l_e_st_eq_landau_n_rt_rp_ispl2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rps r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ivad_t11 r s)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))))).
+
+(* notion 3846 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t13 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_eqi12 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_rs r s) l_e_st_eq_landau_n_rt_rp_ivad_i) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t12 r s) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i l_e_st_eq_landau_n_rt_rp_ivad_i)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ivad_rs r s))).
+
+(* notion 3847 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmaivad2 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_df (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_pl r l_e_st_eq_landau_n_rt_rp_1rp) l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_ts l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_pl s l_e_st_eq_landau_n_rt_rp_1rp)))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r s)) (l_e_st_eq_landau_n_rt_rp_ivad_t6 r s) (l_e_st_eq_landau_n_rt_rp_ivad_t13 r s) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r s))).
+
+(* notion 3848 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t14 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_morede12 (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) l_e_st_eq_landau_n_rt_rp_ivad_i m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) l_e_st_eq_landau_n_rt_rp_ivad_i) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) l_e_st_eq_landau_n_rt_rp_ivad_i)).
+
+(* notion 3849 *)
+definition l_e_st_eq_landau_n_rt_rp_ivad_t15 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz136a (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s) l_e_st_eq_landau_n_rt_rp_ivad_i (l_e_st_eq_landau_n_rt_rp_ivad_t14 r s m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_ivad_r1 r) (l_e_st_eq_landau_n_rt_rp_ivad_s1 r s)).
+
+(* notion 3850 *)
+definition l_e_st_eq_landau_n_rt_rp_lemmaivad3 ≝ λr:l_e_st_eq_landau_n_rt_cut.λs:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp r) (l_e_st_eq_landau_n_rt_rp_pdofrp s).(l_e_st_eq_landau_n_rt_rp_satz136a r s l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_ivad_t15 r s m) : l_e_st_eq_landau_n_rt_rp_more r s).
+
+(* notion 3851 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t1 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_e_st_eq_landau_n_rt_rp_treq2 (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b) c e f : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b)).
+
+(* notion 3852 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t2 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_eqpd2 (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td a b) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_comtd b a)) (l_e_st_eq_landau_n_rt_rp_pdmd (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_td a a)).
+
+(* notion 3853 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t3 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_e_st_eq_landau_n_rt_rp_tr4eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_md a b))) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td b b))) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_td b b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b)) (l_e_st_eq_landau_n_rt_rp_disttpd1 a b (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_eqpd12 (l_e_st_eq_landau_n_rt_rp_td a (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_td b b)) (l_e_st_eq_landau_n_rt_rp_disttmd2 a a b) (l_e_st_eq_landau_n_rt_rp_disttmd2 b a b)) (l_e_st_eq_landau_n_rt_rp_asspd2 (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b a) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td b b))) (l_e_st_eq_landau_n_rt_rp_eqmd1 (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td b a)) (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b) (l_e_st_eq_landau_n_rt_rp_d161_t2 c a b n o e f)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b))).
+
+(* notion 3854 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t4 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b)) (l_e_st_eq_landau_n_rt_rp_d161_t3 c a b n o e f)) (l_e_st_eq_landau_n_rt_rp_satzd182e (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b) (l_e_st_eq_landau_n_rt_rp_d161_t1 c a b n o e f)) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b))).
+
+(* notion 3855 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t5 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_e_st_eq_landau_n_rt_rp_satzd192c (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a b) (l_e_st_eq_landau_n_rt_rp_d161_t4 c a b n o e f) : l_or (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b))).
+
+(* notion 3856 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t6 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_td a a) (l_e_st_eq_landau_n_rt_rp_td b b) (l_e_st_eq_landau_n_rt_rp_d161_t1 c a b n o e f) (l_e_st_eq_landau_n_rt_rp_td01 a a z) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td b b)).
+
+(* notion 3857 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t7 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_zero b) (l_refimp (l_e_st_eq_landau_n_rt_rp_zero b)) (l_e_st_eq_landau_n_rt_rp_satzd192c b b (l_e_st_eq_landau_n_rt_rp_d161_t6 c a b n o e f z)) : l_e_st_eq_landau_n_rt_rp_zero b).
+
+(* notion 3858 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t8 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_zeroeq a b z (l_e_st_eq_landau_n_rt_rp_d161_t7 c a b n o e f z) : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3859 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t9 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_or3e2 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_negd a) (l_e_st_eq_landau_n_rt_rp_axrdo a) n p : l_e_st_eq_landau_n_rt_rp_posd a).
+
+(* notion 3860 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t10 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_zero a) p (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_d161_t7 c b a o n f e t) : l_not (l_e_st_eq_landau_n_rt_rp_zero b)).
+
+(* notion 3861 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t11 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_d161_t9 c b a o n f e (l_e_st_eq_landau_n_rt_rp_d161_t10 c a b n o e f p) : l_e_st_eq_landau_n_rt_rp_posd b).
+
+(* notion 3862 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t12 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_pnot0d (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_ppd a b (l_e_st_eq_landau_n_rt_rp_d161_t9 c a b n o e f p) (l_e_st_eq_landau_n_rt_rp_d161_t11 c a b n o e f p)) : l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a b))).
+
+(* notion 3863 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t13 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_ore2 (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b)) (l_e_st_eq_landau_n_rt_rp_d161_t5 c a b n o e f) (l_e_st_eq_landau_n_rt_rp_d161_t12 c a b n o e f p) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3864 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t14 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.λp:l_not (l_e_st_eq_landau_n_rt_rp_zero a).(l_e_st_eq_landau_n_rt_rp_satzd182b a b (l_e_st_eq_landau_n_rt_rp_d161_t13 c a b n o e f p) : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3865 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd161b ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd a).λo:l_not (l_e_st_eq_landau_n_rt_rp_negd b).λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a a) c.λf:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b b) c.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_eq a b) (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_d161_t8 c a b n o e f t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_zero a).l_e_st_eq_landau_n_rt_rp_d161_t14 c a b n o e f t) : l_e_st_eq_landau_n_rt_rp_eq a b).
+
+(* notion 3866 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t15 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_e_st_eq_landau_n_rt_rp_zeroeq (l_e_st_eq_landau_n_rt_rp_td c c) c (l_e_st_eq_landau_n_rt_rp_td01 c c z) z : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c c) c).
+
+(* notion 3867 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t16 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_andi (l_not (l_e_st_eq_landau_n_rt_rp_negd c)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c c) c) n (l_e_st_eq_landau_n_rt_rp_d161_t15 c n z) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd c)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td c c) c)).
+
+(* notion 3868 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t17 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λz:l_e_st_eq_landau_n_rt_rp_zero c.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c)) c (l_e_st_eq_landau_n_rt_rp_d161_t16 c n z) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c))).
+
+(* notion 3869 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t18 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_or3e2 (l_e_st_eq_landau_n_rt_rp_zero c) (l_e_st_eq_landau_n_rt_rp_posd c) (l_e_st_eq_landau_n_rt_rp_negd c) (l_e_st_eq_landau_n_rt_rp_axrdo c) n o : l_e_st_eq_landau_n_rt_rp_posd c).
+
+(* notion 3870 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_crp ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_e_st_eq_landau_n_rt_rp_rpofpd c (l_e_st_eq_landau_n_rt_rp_d161_t18 c n o) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3871 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_srp ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_e_st_eq_landau_n_rt_rp_sqrt (l_e_st_eq_landau_n_rt_rp_d161_crp c n o) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3872 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_s ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_d161_srp c n o) : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3873 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t19 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_d161_s c n o)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_d161_srp c n o) (l_e_st_eq_landau_n_rt_rp_d161_srp c n o))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_d161_crp c n o)) c (l_e_st_eq_landau_n_rt_rp_lemmaivad2 (l_e_st_eq_landau_n_rt_rp_d161_srp c n o) (l_e_st_eq_landau_n_rt_rp_d161_srp c n o)) (l_e_st_eq_landau_n_rt_rp_isrpepd (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_d161_srp c n o) (l_e_st_eq_landau_n_rt_rp_d161_srp c n o)) (l_e_st_eq_landau_n_rt_rp_d161_crp c n o) (l_e_st_eq_landau_n_rt_rp_thsqrt1 (l_e_st_eq_landau_n_rt_rp_d161_crp c n o))) (l_e_st_eq_landau_n_rt_rp_eqpdrp2 c (l_e_st_eq_landau_n_rt_rp_d161_t18 c n o)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_d161_s c n o)) c).
+
+(* notion 3874 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t20 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_andi (l_not (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_d161_s c n o))) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_d161_s c n o)) c) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_d161_srp c n o))) (l_e_st_eq_landau_n_rt_rp_d161_t19 c n o) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_d161_s c n o))) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_d161_s c n o)) c)).
+
+(* notion 3875 *)
+definition l_e_st_eq_landau_n_rt_rp_d161_t21 ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).λo:l_not (l_e_st_eq_landau_n_rt_rp_zero c).(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c)) (l_e_st_eq_landau_n_rt_rp_d161_s c n o) (l_e_st_eq_landau_n_rt_rp_d161_t20 c n o) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c))).
+
+(* notion 3876 *)
+definition l_e_st_eq_landau_n_rt_rp_satzd161a ≝ λc:l_e_st_eq_landau_n_rt_rp_dif.λn:l_not (l_e_st_eq_landau_n_rt_rp_negd c).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_zero c) (l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c))) (λt:l_e_st_eq_landau_n_rt_rp_zero c.l_e_st_eq_landau_n_rt_rp_d161_t17 c n t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_zero c).l_e_st_eq_landau_n_rt_rp_d161_t21 c n t) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c))).
+
+(* notion 3877 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_ori1 (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_absd a))) (l_e_st_eq_landau_n_rt_rp_satzd166f a z) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3878 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).(l_e_st_eq_landau_n_rt_rp_natintd (l_e_st_eq_landau_n_rt_rp_absd a) n : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3879 *)
+definition l_e_st_eq_landau_n_rt_rp_intabsd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.(l_orapp (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_absd a)) i (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_intd_t1 a i t) (λt:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).l_e_st_eq_landau_n_rt_rp_intd_t2 a i t) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3880 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λn:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).(l_e_st_eq_landau_n_rt_rp_eqnatd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_satzd178a a) n : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a))).
+
+(* notion 3881 *)
+definition l_e_st_eq_landau_n_rt_rp_intm0d ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a))) i (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_satzd176b a t) (λt:l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd a).l_e_st_eq_landau_n_rt_rp_intd_t4 a i t) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_m0d a)).
+
+(* notion 3882 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_pd a b) b (l_e_st_eq_landau_n_rt_rp_pd01 a b z) : l_e_st_eq_landau_n_rt_rp_eq b (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3883 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λz:l_e_st_eq_landau_n_rt_rp_zero a.(l_e_st_eq_landau_n_rt_rp_eqintd b (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_intd_t5 a b i j z) j : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3884 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t7 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_pd a b) a (l_e_st_eq_landau_n_rt_rp_pd02 a b z) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3885 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t8 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λz:l_e_st_eq_landau_n_rt_rp_zero b.(l_e_st_eq_landau_n_rt_rp_eqintd a (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_intd_t7 a b i j z) i : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3886 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t9 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_ande2 (l_e_st_eq_landau_n_rt_rp_posd a) (Πt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a t)) (l_e_st_eq_landau_n_rt_rp_posintnatd a p i) p : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_rpofpd a p)).
+
+(* notion 3887 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_apb1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pd a b) pp : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3888 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_a1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_rpofpd a p : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3889 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_b1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_rpofpd b q : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3890 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t10 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_natpl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_t9 a i p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q) (l_e_st_eq_landau_n_rt_rp_intd_t9 b j q) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))).
+
+(* notion 3891 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t11 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_eqpd12 a (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)) b (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 a p) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 b q) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)))).
+
+(* notion 3892 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t12 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_treq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) (l_e_st_eq_landau_n_rt_rp_intd_t11 a b i j pp p q) (l_e_st_eq_landau_n_rt_rp_lemmaivad1 (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)))).
+
+(* notion 3893 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t13 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)))) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)) (l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_pd a b) pp (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) (l_e_st_eq_landau_n_rt_rp_intd_t12 a b i j pp p q)) (l_e_st_eq_landau_n_rt_rp_isrppd2 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q))).
+
+(* notion 3894 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t14 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_isp1 l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b1 a b i j pp p q)) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_intd_t10 a b i j pp p q) (l_e_st_eq_landau_n_rt_rp_intd_t13 a b i j pp p q) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)).
+
+(* notion 3895 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t15 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_andi (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b)) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j t)) pp (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_intd_t14 a b i j t p q) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3896 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t16 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λq:l_e_st_eq_landau_n_rt_rp_posd b.(l_e_st_eq_landau_n_rt_rp_natintd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_intd_t15 a b i j pp p q) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3897 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t17 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_satzd176c b n : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d b)).
+
+(* notion 3898 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_b2 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intd_t17 a b i j pp p n) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3899 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t18 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqpd2 b (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d b)) a (l_e_st_eq_landau_n_rt_rp_satzd177a b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_m0d b))).
+
+(* notion 3900 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t19 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_intd_t18 a b i j pp p n) pp : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a (l_e_st_eq_landau_n_rt_rp_m0d b))).
+
+(* notion 3901 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t20 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_satzd182a a (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intd_t19 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_mored a (l_e_st_eq_landau_n_rt_rp_m0d b)).
+
+(* notion 3902 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t21 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqmored12 a (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 a p) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intd_t17 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_intd_t20 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n))).
+
+(* notion 3903 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t22 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_lemmaivad3 (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t21 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n)).
+
+(* notion 3904 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t23 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_natmn (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_t9 a i p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t9 (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intm0d b j) (l_e_st_eq_landau_n_rt_rp_intd_t17 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_intd_t22 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t22 a b i j pp p n))).
+
+(* notion 3905 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t24 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_eqpd12 (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intd_t17 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_pd a b) pp) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)))).
+
+(* notion 3906 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t25 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_tr4eq a (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a b) b) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a b) b) a (l_e_st_eq_landau_n_rt_rp_mdpd a b)) (l_e_st_eq_landau_n_rt_rp_compd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_intd_t24 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_lemmaivad1 (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)) : l_e_st_eq_landau_n_rt_rp_eq a (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)))).
+
+(* notion 3907 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t26 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)) (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)))) (l_e_st_eq_landau_n_rt_rp_isrppd1 (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_eqpderp a p (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp))) (l_e_st_eq_landau_n_rt_rp_intd_t25 a b i j pp p n)) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)) (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p)).
+
+(* notion 3908 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t27 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_satz140g (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_intd_t22 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t26 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t22 a b i j pp p n))).
+
+(* notion 3909 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t28 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_isp1 l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) (l_e_st_eq_landau_n_rt_rp_mn (l_e_st_eq_landau_n_rt_rp_intd_a1 a b i j pp p) (l_e_st_eq_landau_n_rt_rp_intd_b2 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t22 a b i j pp p n)) (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp) (l_e_st_eq_landau_n_rt_rp_intd_t23 a b i j pp p n) (l_e_st_eq_landau_n_rt_rp_intd_t27 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j pp)).
+
+(* notion 3910 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t29 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_andi (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b)) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_apb1 a b i j t)) pp (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_intd_t28 a b i j t p n) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3911 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t30 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.λn:l_e_st_eq_landau_n_rt_rp_negd b.(l_e_st_eq_landau_n_rt_rp_natintd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_intd_t29 a b i j pp p n) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3912 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t31 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λp:l_e_st_eq_landau_n_rt_rp_posd a.(l_e_st_eq_landau_n_rt_rp_rappd b (l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)) (λt:l_e_st_eq_landau_n_rt_rp_posd b.l_e_st_eq_landau_n_rt_rp_intd_t16 a b i j pp p t) (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_intd_t8 a b i j t) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_intd_t30 a b i j pp p t) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3913 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t31a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_pd a b) pp) (λt:l_e_st_eq_landau_n_rt_rp_negd b.l_e_st_eq_landau_n_rt_rp_npd a b n t) : l_not (l_e_st_eq_landau_n_rt_rp_negd b)).
+
+(* notion 3914 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t32 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pnotnd (l_e_st_eq_landau_n_rt_rp_pd a b) pp) (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_eqnegd a (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_symeq (l_e_st_eq_landau_n_rt_rp_pd a b) a (l_e_st_eq_landau_n_rt_rp_pd02 a b t)) n) : l_not (l_e_st_eq_landau_n_rt_rp_zero b)).
+
+(* notion 3915 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t33 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_or3e2 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_negd b) (l_e_st_eq_landau_n_rt_rp_axrdo b) (l_e_st_eq_landau_n_rt_rp_intd_t31a a b i j pp n) (l_e_st_eq_landau_n_rt_rp_intd_t32 a b i j pp n) : l_e_st_eq_landau_n_rt_rp_posd b).
+
+(* notion 3916 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t34 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_pd b a) (l_e_st_eq_landau_n_rt_rp_compd a b) pp : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd b a)).
+
+(* notion 3917 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t35 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_intd_t30 b a j i (l_e_st_eq_landau_n_rt_rp_intd_t34 a b i j pp n) (l_e_st_eq_landau_n_rt_rp_intd_t33 a b i j pp n) n : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd b a)).
+
+(* notion 3918 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t36 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).λn:l_e_st_eq_landau_n_rt_rp_negd a.(l_e_st_eq_landau_n_rt_rp_eqintd (l_e_st_eq_landau_n_rt_rp_pd b a) (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_compd b a) (l_e_st_eq_landau_n_rt_rp_intd_t35 a b i j pp n) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3919 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t37 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λpp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_rappd a (l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)) (λt:l_e_st_eq_landau_n_rt_rp_posd a.l_e_st_eq_landau_n_rt_rp_intd_t31 a b i j pp t) (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_intd_t6 a b i j t) (λt:l_e_st_eq_landau_n_rt_rp_negd a.l_e_st_eq_landau_n_rt_rp_intd_t36 a b i j pp t) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3920 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t38 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λ0p:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_intdi0 (l_e_st_eq_landau_n_rt_rp_pd a b) 0p : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3921 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t39 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_satzd176c (l_e_st_eq_landau_n_rt_rp_pd a b) np : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b))).
+
+(* notion 3922 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t40 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_eqposd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_satzd180 a b) (l_e_st_eq_landau_n_rt_rp_intd_t39 a b i j np) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b))).
+
+(* notion 3923 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t41 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_intd_t37 (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_intm0d a i) (l_e_st_eq_landau_n_rt_rp_intm0d b j) (l_e_st_eq_landau_n_rt_rp_intd_t40 a b i j np) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b))).
+
+(* notion 3924 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t42 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_eqintd (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_satzd180a a b) (l_e_st_eq_landau_n_rt_rp_intd_t41 a b i j np) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b))).
+
+(* notion 3925 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t43 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_intm0d (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_intd_t42 a b i j np) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b)))).
+
+(* notion 3926 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t44 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λnp:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).(l_e_st_eq_landau_n_rt_rp_eqintd (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a b))) (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_satzd177 (l_e_st_eq_landau_n_rt_rp_pd a b)) (l_e_st_eq_landau_n_rt_rp_intd_t43 a b i j np) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3927 *)
+definition l_e_st_eq_landau_n_rt_rp_intpd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.(l_e_st_eq_landau_n_rt_rp_rappd (l_e_st_eq_landau_n_rt_rp_pd a b) (l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)) (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_intd_t37 a b i j t) (λt:l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_intd_t38 a b i j t) (λt:l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a b).l_e_st_eq_landau_n_rt_rp_intd_t44 a b i j t) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a b)).
+
+(* notion 3928 *)
+definition l_e_st_eq_landau_n_rt_rp_intmd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.(l_e_st_eq_landau_n_rt_rp_intpd a (l_e_st_eq_landau_n_rt_rp_m0d b) i (l_e_st_eq_landau_n_rt_rp_intm0d b j) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 3929 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t45 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero a) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)) n (λt:l_e_st_eq_landau_n_rt_rp_zero a.l_e_st_eq_landau_n_rt_rp_td01 a b t) : l_not (l_e_st_eq_landau_n_rt_rp_zero a)).
+
+(* notion 3930 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t46 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero b) (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)) n (λt:l_e_st_eq_landau_n_rt_rp_zero b.l_e_st_eq_landau_n_rt_rp_td02 a b t) : l_not (l_e_st_eq_landau_n_rt_rp_zero b)).
+
+(* notion 3931 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t47 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_satzd166e a (l_e_st_eq_landau_n_rt_rp_intd_t45 a b i j n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a)).
+
+(* notion 3932 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_a3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_intd_t47 a b i j n) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3933 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t48 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_satzd166e b (l_e_st_eq_landau_n_rt_rp_intd_t46 a b i j n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd b)).
+
+(* notion 3934 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_b3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_intd_t48 a b i j n) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3935 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t49 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_natts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_t9 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_intabsd a i) (l_e_st_eq_landau_n_rt_rp_intd_t47 a b i j n)) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_t9 (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_intabsd b j) (l_e_st_eq_landau_n_rt_rp_intd_t48 a b i j n)) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))).
+
+(* notion 3936 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t50 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_satzd166e (l_e_st_eq_landau_n_rt_rp_td a b) n : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3937 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_atb3 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) p : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 3938 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t51 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_eqtd12 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_intd_t47 a b i j n)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_intd_t48 a b i j n)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)))).
+
+(* notion 3939 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t52 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_st_eq_landau_n_rt_rp_tr3eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) (l_e_st_eq_landau_n_rt_rp_satzd193 a b) (l_e_st_eq_landau_n_rt_rp_intd_t51 a b i j n p) (l_e_st_eq_landau_n_rt_rp_lemmaivad2 (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)))).
+
+(* notion 3940 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t53 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_tris2 l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_intd_atb3 a b i j n p) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_rpofpd (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)))) (l_e_st_eq_landau_n_rt_rp_eqpderp (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)) p (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) (l_e_st_eq_landau_n_rt_rp_posdirp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) (l_e_st_eq_landau_n_rt_rp_intd_t52 a b i j n p)) (l_e_st_eq_landau_n_rt_rp_isrppd1 (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_intd_atb3 a b i j n p) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n))).
+
+(* notion 3941 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t54 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).λp:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).(l_e_isp1 l_e_st_eq_landau_n_rt_cut (λt:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_natrp t) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_intd_a3 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_b3 a b i j n)) (l_e_st_eq_landau_n_rt_rp_intd_atb3 a b i j n p) (l_e_st_eq_landau_n_rt_rp_intd_t49 a b i j n) (l_e_st_eq_landau_n_rt_rp_intd_t53 a b i j n p) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_atb3 a b i j n p)).
+
+(* notion 3942 *)
+definition l_e_st_eq_landau_n_rt_rp_intd_t55 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.λn:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).(l_andi (l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b))) (Πt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_intd_atb3 a b i j n t)) (l_e_st_eq_landau_n_rt_rp_intd_t50 a b i j n) (λt:l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b)).l_e_st_eq_landau_n_rt_rp_intd_t54 a b i j n t) : l_e_st_eq_landau_n_rt_rp_natd (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a b))).
+
+(* notion 3943 *)
+definition l_e_st_eq_landau_n_rt_rp_inttd ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λi:l_e_st_eq_landau_n_rt_rp_intd a.λj:l_e_st_eq_landau_n_rt_rp_intd b.(λt:l_not (l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a b)).l_e_st_eq_landau_n_rt_rp_intd_t55 a b i j t : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_td a b)).
+
+(* notion 3944 *)
+definition l_e_st_eq_landau_n_rt_rp_r_eq ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq x y : Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Prop).
+
+(* notion 3945 *)
+definition l_e_st_eq_landau_n_rt_rp_r_refeq ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_refeq x : Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_eq x x).
+
+(* notion 3946 *)
+definition l_e_st_eq_landau_n_rt_rp_r_symeq ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.l_e_st_eq_landau_n_rt_rp_symeq x y t : Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πt:l_e_st_eq_landau_n_rt_rp_r_eq x y.l_e_st_eq_landau_n_rt_rp_r_eq y x).
+
+(* notion 3947 *)
+definition l_e_st_eq_landau_n_rt_rp_r_treq ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.λu:l_e_st_eq_landau_n_rt_rp_r_eq y z.l_e_st_eq_landau_n_rt_rp_treq x y z t u : Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πz:l_e_st_eq_landau_n_rt_rp_dif.Πt:l_e_st_eq_landau_n_rt_rp_r_eq x y.Πu:l_e_st_eq_landau_n_rt_rp_r_eq y z.l_e_st_eq_landau_n_rt_rp_r_eq x z).
+
+(* notion 3948 *)
+definition l_e_st_eq_landau_n_rt_rp_r_inn ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_esti l_e_st_eq_landau_n_rt_rp_dif a s : Prop).
+
+(* notion 3949 *)
+definition l_e_st_eq_landau_n_rt_rp_r_real ≝ (l_e_st_eq_ect l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq : Type[0]).
+
+(* notion 3950 *)
+definition l_e_st_eq_landau_n_rt_rp_r_is ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_is l_e_st_eq_landau_n_rt_rp_r_real r s : Prop).
+
+(* notion 3951 *)
+definition l_e_st_eq_landau_n_rt_rp_r_nis ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_not (l_e_st_eq_landau_n_rt_rp_r_is r s) : Prop).
+
+(* notion 3952 *)
+definition l_e_st_eq_landau_n_rt_rp_r_some ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_r_real.Prop.(l_some l_e_st_eq_landau_n_rt_rp_r_real p : Prop).
+
+(* notion 3953 *)
+definition l_e_st_eq_landau_n_rt_rp_r_all ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_r_real.Prop.(l_all l_e_st_eq_landau_n_rt_rp_r_real p : Prop).
+
+(* notion 3954 *)
+definition l_e_st_eq_landau_n_rt_rp_r_one ≝ λp:Πx:l_e_st_eq_landau_n_rt_rp_r_real.Prop.(l_e_one l_e_st_eq_landau_n_rt_rp_r_real p : Prop).
+
+(* notion 3955 *)
+definition l_e_st_eq_landau_n_rt_rp_r_in ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs0:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_esti l_e_st_eq_landau_n_rt_rp_r_real r s0 : Prop).
+
+(* notion 3956 *)
+definition l_e_st_eq_landau_n_rt_rp_r_realof ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_ectelt l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq a : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 3957 *)
+definition l_e_st_eq_landau_n_rt_rp_r_class ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_ecect l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq r : l_e_st_set l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 3958 *)
+definition l_e_st_eq_landau_n_rt_rp_r_innclass ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.(l_e_st_eq_4_th5 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq a : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_realof a))).
+
+(* notion 3959 *)
+definition l_e_st_eq_landau_n_rt_rp_r_eqinn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_4_th8 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq r a air b e : l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class r)).
+
+(* notion 3960 *)
+definition l_e_st_eq_landau_n_rt_rp_r_realapp1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).p.(l_e_st_eq_4_th3 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq r p p1 : p).
+
+(* notion 3961 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).p.λa:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_realapp1 s p (λy:l_e_st_eq_landau_n_rt_rp_dif.p1 a y air) : p).
+
+(* notion 3962 *)
+definition l_e_st_eq_landau_n_rt_rp_r_realapp2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).p.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r p (λx:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t1 r s p p1 x xi) : p).
+
+(* notion 3963 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πz:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).Πzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).p.λa:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_realapp2 s t p (λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.p1 a y z air) : p).
+
+(* notion 3964 *)
+definition l_e_st_eq_landau_n_rt_rp_r_realapp3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πz:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).Πzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).p.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r p (λx:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t2 r s t p p1 x xi) : p).
+
+(* notion 3965 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πz:l_e_st_eq_landau_n_rt_rp_dif.Πv:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).Πzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).Πvi:l_e_st_eq_landau_n_rt_rp_r_inn v (l_e_st_eq_landau_n_rt_rp_r_class u).p.λa:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_realapp3 s t u p (λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.p1 a y z v air) : p).
+
+(* notion 3966 *)
+definition l_e_st_eq_landau_n_rt_rp_r_realapp4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.Πz:l_e_st_eq_landau_n_rt_rp_dif.Πv:l_e_st_eq_landau_n_rt_rp_dif.Πxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).Πyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).Πzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).Πvi:l_e_st_eq_landau_n_rt_rp_r_inn v (l_e_st_eq_landau_n_rt_rp_r_class u).p.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r p (λx:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t3 r s t u p p1 x xi) : p).
+
+(* notion 3967 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λe:l_e_st_eq_landau_n_rt_rp_eq a1 b1.(l_e_st_eq_5_th3 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq r s a1 a1ir b1 b1is e : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 3968 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_5_th5 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq r s a1 a1ir b1 b1is i : l_e_st_eq_landau_n_rt_rp_eq a1 b1).
+
+(* notion 3969 *)
+definition l_e_st_eq_landau_n_rt_rp_r_nisin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_eq a1 b1).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_eq a1 b1) n (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is t) : l_e_st_eq_landau_n_rt_rp_r_nis r s).
+
+(* notion 3970 *)
+definition l_e_st_eq_landau_n_rt_rp_r_nisex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_nis r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_r_is r s) n (λt:l_e_st_eq_landau_n_rt_rp_eq a1 b1.l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is t) : l_not (l_e_st_eq_landau_n_rt_rp_eq a1 b1)).
+
+(* notion 3971 *)
+definition l_e_st_eq_landau_n_rt_rp_r_fixf ≝ λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_rt_rp_dif.alpha.(l_e_st_eq_fixfu l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha f : Prop).
+
+(* notion 3972 *)
+definition l_e_st_eq_landau_n_rt_rp_r_indreal ≝ λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_rt_rp_dif.alpha.λff:l_e_st_eq_landau_n_rt_rp_r_fixf alpha f.λr0:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_indeq l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha f ff r0 : alpha).
+
+(* notion 3973 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isindreal ≝ λalpha:Type[0].λf:Πx:l_e_st_eq_landau_n_rt_rp_dif.alpha.λff:l_e_st_eq_landau_n_rt_rp_r_fixf alpha f.λr0:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r0).(l_e_st_eq_10_th2 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha f ff r0 a air : l_e_is alpha (f a) (l_e_st_eq_landau_n_rt_rp_r_indreal alpha f ff r0)).
+
+(* notion 3974 *)
+definition l_e_st_eq_landau_n_rt_rp_r_fixf2 ≝ λalpha:Type[0].λg:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.alpha.(l_e_st_eq_fixfu2 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha g : Prop).
+
+(* notion 3975 *)
+definition l_e_st_eq_landau_n_rt_rp_r_indreal2 ≝ λalpha:Type[0].λg:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.alpha.λff2:l_e_st_eq_landau_n_rt_rp_r_fixf2 alpha g.λr0:l_e_st_eq_landau_n_rt_rp_r_real.λs0:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_indeq2 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha g ff2 r0 s0 : alpha).
+
+(* notion 3976 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isindreal2 ≝ λalpha:Type[0].λg:Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.alpha.λff2:l_e_st_eq_landau_n_rt_rp_r_fixf2 alpha g.λr0:l_e_st_eq_landau_n_rt_rp_r_real.λs0:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r0).λbis:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s0).(l_e_st_eq_11_th1 l_e_st_eq_landau_n_rt_rp_dif l_e_st_eq_landau_n_rt_rp_r_eq l_e_st_eq_landau_n_rt_rp_r_refeq l_e_st_eq_landau_n_rt_rp_r_symeq l_e_st_eq_landau_n_rt_rp_r_treq alpha g ff2 r0 s0 a air b bis : l_e_is alpha (g a b) (l_e_st_eq_landau_n_rt_rp_r_indreal2 alpha g ff2 r0 s0)).
+
+(* notion 3977 *)
+definition l_e_st_eq_landau_n_rt_rp_r_0 ≝ (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 3978 *)
+definition l_e_st_eq_landau_n_rt_rp_r_0in ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λz:l_e_st_eq_landau_n_rt_rp_zero a0.(l_e_st_eq_landau_n_rt_rp_r_isin r l_e_st_eq_landau_n_rt_rp_r_0 a0 (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) a0ir (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_zeroeq a0 (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) z (l_e_st_eq_landau_n_rt_rp_zeroi l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp (l_e_refis l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_1rp))) : l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 3979 *)
+definition l_e_st_eq_landau_n_rt_rp_r_0ex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_eqzero (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) a0 (l_e_st_eq_landau_n_rt_rp_r_isex l_e_st_eq_landau_n_rt_rp_r_0 r (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) a0 (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) a0ir (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r l_e_st_eq_landau_n_rt_rp_r_0 i)) (l_e_tris l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_stm (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) l_e_st_eq_landau_n_rt_rp_1rp (l_e_st_eq_landau_n_rt_rp_std (l_e_st_eq_landau_n_rt_rp_df l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) (l_e_st_eq_landau_n_rt_rp_stmis l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp) (l_e_st_eq_landau_n_rt_rp_isstd l_e_st_eq_landau_n_rt_rp_1rp l_e_st_eq_landau_n_rt_rp_1rp)) : l_e_st_eq_landau_n_rt_rp_zero a0).
+
+(* notion 3980 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_propp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_posd a0) : Prop).
+
+(* notion 3981 *)
+definition l_e_st_eq_landau_n_rt_rp_r_pos ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r x) : Prop).
+
+(* notion 3982 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_posd a0.(l_andi (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_posd a0) a0ir p : l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r a0).
+
+(* notion 3983 *)
+definition l_e_st_eq_landau_n_rt_rp_r_posin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_posd a0.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r x) a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t4 r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_r_pos r).
+
+(* notion 3984 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λa:l_e_st_eq_landau_n_rt_rp_dif.λq1:l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r a.(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_posd a) q1 : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
+
+(* notion 3985 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λa:l_e_st_eq_landau_n_rt_rp_dif.λq1:l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r a.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_posd a) q1 : l_e_st_eq_landau_n_rt_rp_posd a).
+
+(* notion 3986 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λa:l_e_st_eq_landau_n_rt_rp_dif.λq1:l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r a.(l_e_st_eq_landau_n_rt_rp_eqposd a a0 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t5 r a0 a0ir p a q1) a0ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t6 r a0 a0ir p a q1) : l_e_st_eq_landau_n_rt_rp_posd a0).
+
+(* notion 3987 *)
+definition l_e_st_eq_landau_n_rt_rp_r_posex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r x) p (l_e_st_eq_landau_n_rt_rp_posd a0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_ivr1_propp r x.l_e_st_eq_landau_n_rt_rp_r_ivr1_t7 r a0 a0ir p x t) : l_e_st_eq_landau_n_rt_rp_posd a0).
+
+(* notion 3988 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_propn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.(l_and (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_negd a0) : Prop).
+
+(* notion 3989 *)
+definition l_e_st_eq_landau_n_rt_rp_r_neg ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r x) : Prop).
+
+(* notion 3990 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_negd a0.(l_andi (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_negd a0) a0ir n : l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r a0).
+
+(* notion 3991 *)
+definition l_e_st_eq_landau_n_rt_rp_r_negin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_negd a0.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r x) a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t8 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_neg r).
+
+(* notion 3992 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λa:l_e_st_eq_landau_n_rt_rp_dif.λpl:l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r a.(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_negd a) pl : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
+
+(* notion 3993 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λa:l_e_st_eq_landau_n_rt_rp_dif.λpl:l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r a.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_negd a) pl : l_e_st_eq_landau_n_rt_rp_negd a).
+
+(* notion 3994 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λa:l_e_st_eq_landau_n_rt_rp_dif.λpl:l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r a.(l_e_st_eq_landau_n_rt_rp_eqnegd a a0 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t9 r a0 a0ir n a pl) a0ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t10 r a0 a0ir n a pl) : l_e_st_eq_landau_n_rt_rp_negd a0).
+
+(* notion 3995 *)
+definition l_e_st_eq_landau_n_rt_rp_r_negex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r x) n (l_e_st_eq_landau_n_rt_rp_negd a0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_ivr1_propn r x.l_e_st_eq_landau_n_rt_rp_r_ivr1_t11 r a0 a0ir n x t) : l_e_st_eq_landau_n_rt_rp_negd a0).
+
+(* notion 3996 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_posd a0.(l_or3i2 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_posin r a0 a0ir p) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
+
+(* notion 3997 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t13 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λz:l_e_st_eq_landau_n_rt_rp_zero a0.(l_or3i1 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_0in r a0 a0ir z) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
+
+(* notion 3998 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t14 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_negd a0.(l_or3i3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_negin r a0 a0ir n) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
+
+(* notion 3999 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t15 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_rappd a0 (l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)) (λt:l_e_st_eq_landau_n_rt_rp_posd a0.l_e_st_eq_landau_n_rt_rp_r_ivr1_t12 r a0 a0ir t) (λt:l_e_st_eq_landau_n_rt_rp_zero a0.l_e_st_eq_landau_n_rt_rp_r_ivr1_t13 r a0 a0ir t) (λt:l_e_st_eq_landau_n_rt_rp_negd a0.l_e_st_eq_landau_n_rt_rp_r_ivr1_t14 r a0 a0ir t) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
+
+(* notion 4000 *)
+definition l_e_st_eq_landau_n_rt_rp_r_axrlo ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t15 r x xi) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
+
+(* notion 4001 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t16 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_posd a0) (l_e_st_eq_landau_n_rt_rp_0notpd a0 (l_e_st_eq_landau_n_rt_rp_r_0ex r a0 a0ir i)) (λt:l_e_st_eq_landau_n_rt_rp_r_pos r.l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir t) : l_not (l_e_st_eq_landau_n_rt_rp_r_pos r)).
+
+(* notion 4002 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t17 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_negd a0) (l_e_st_eq_landau_n_rt_rp_pnotnd a0 (l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir p)) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir t) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)).
+
+(* notion 4003 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t18 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_zero a0) (l_e_st_eq_landau_n_rt_rp_nnot0d a0 (l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir n)) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_0ex r a0 a0ir t) : l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 4004 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t19 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_ec3_th6 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_ivr1_t16 r a0 a0ir t) (λt:l_e_st_eq_landau_n_rt_rp_r_pos r.l_e_st_eq_landau_n_rt_rp_r_ivr1_t17 r a0 a0ir t) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_ivr1_t18 r a0 a0ir t) : l_ec3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
+
+(* notion 4005 *)
+definition l_e_st_eq_landau_n_rt_rp_r_axrle ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_ec3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t19 r x xi) : l_ec3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
+
+(* notion 4006 *)
+definition l_e_st_eq_landau_n_rt_rp_r_axrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_orec3i (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrlo r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) : l_orec3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r)).
+
+(* notion 4007 *)
+definition l_e_st_eq_landau_n_rt_rp_r_rapp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:Prop.λp1:Πt:l_e_st_eq_landau_n_rt_rp_r_pos r.p.λp2:Πt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.p.λp3:Πt:l_e_st_eq_landau_n_rt_rp_r_neg r.p.(l_or3app (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) p (l_e_st_eq_landau_n_rt_rp_r_axrlo r) p2 p1 p3 : p).
+
+(* notion 4008 *)
+definition l_e_st_eq_landau_n_rt_rp_r_pnotn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_ec3e23 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) p : l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)).
+
+(* notion 4009 *)
+definition l_e_st_eq_landau_n_rt_rp_r_pnot0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) p : l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4010 *)
+definition l_e_st_eq_landau_n_rt_rp_r_0notp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_ec3e12 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) i : l_not (l_e_st_eq_landau_n_rt_rp_r_pos r)).
+
+(* notion 4011 *)
+definition l_e_st_eq_landau_n_rt_rp_r_0notn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_ec3e13 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) i : l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)).
+
+(* notion 4012 *)
+definition l_e_st_eq_landau_n_rt_rp_r_nnotp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_ec3e32 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) n : l_not (l_e_st_eq_landau_n_rt_rp_r_pos r)).
+
+(* notion 4013 *)
+definition l_e_st_eq_landau_n_rt_rp_r_nnot0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_axrle r) n : l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4014 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ispos ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_pos x) r s p i : l_e_st_eq_landau_n_rt_rp_r_pos s).
+
+(* notion 4015 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isneg ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_neg x) r s n i : l_e_st_eq_landau_n_rt_rp_r_neg s).
+
+(* notion 4016 *)
+definition l_e_st_eq_landau_n_rt_rp_r_pofrp ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pdofrp r0) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4017 *)
+definition l_e_st_eq_landau_n_rt_rp_r_nofrp ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_ndofrp r0) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4018 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrpep ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r0 s0.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_pofrp x) r0 s0 i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
+
+(* notion 4019 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrpen ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_is r0 s0.(l_e_isf l_e_st_eq_landau_n_rt_cut l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_nofrp x) r0 s0 i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_nofrp s0)).
+
+(* notion 4020 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t20 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp s0)) i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0)).
+
+(* notion 4021 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrpip ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_isrpipd r0 s0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t20 r0 s0 i) : l_e_st_eq_landau_n_rt_rp_is r0 s0).
+
+(* notion 4022 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t21 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_nofrp s0).(l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_nofrp s0) (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp s0)) i : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp s0)).
+
+(* notion 4023 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrpin ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_nofrp s0).(l_e_st_eq_landau_n_rt_rp_isrpind r0 s0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t21 r0 s0 i) : l_e_st_eq_landau_n_rt_rp_is r0 s0).
+
+(* notion 4024 *)
+definition l_e_st_eq_landau_n_rt_rp_r_posi ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_posdirp r0) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)).
+
+(* notion 4025 *)
+definition l_e_st_eq_landau_n_rt_rp_r_negi ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_negin (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) (l_e_st_eq_landau_n_rt_rp_negdirp r0) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)).
+
+(* notion 4026 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t22 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp r0).λj:l_e_st_eq_landau_n_rt_rp_r_is s (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).λk:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_isrpip r0 s0 (l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) r s (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) i) k j) : l_e_st_eq_landau_n_rt_rp_is r0 s0).
+
+(* notion 4027 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t23 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_cut.λy:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x).λu:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp y).l_e_st_eq_landau_n_rt_rp_r_ivr1_t22 r r x y t u (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r) : l_e_amone l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x))).
+
+(* notion 4028 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t24 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp1:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir p1 : l_e_st_eq_landau_n_rt_rp_posd a0).
+
+(* notion 4029 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_pr ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp1:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_rpofpd a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t24 r a0 a0ir p1) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4030 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t25 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp1:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_isin r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_pr r a0 a0ir p1)) a0 (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_pr r a0 a0ir p1)) a0ir (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_pr r a0 a0ir p1))) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t24 r a0 a0ir p1)) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_pr r a0 a0ir p1))).
+
+(* notion 4031 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t26 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp1:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_somei l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_pr r a0 a0ir p1) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t25 r a0 a0ir p1) : l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x))).
+
+(* notion 4032 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t27 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t26 r x t p) : l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x))).
+
+(* notion 4033 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t28 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_onei l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t23 r) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t27 r p) : l_e_st_eq_landau_n_rt_rp_one (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x))).
+
+(* notion 4034 *)
+definition l_e_st_eq_landau_n_rt_rp_r_rpofp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_ind l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t28 r p) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4035 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isprp1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_oneax l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t28 r p) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p))).
+
+(* notion 4036 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isprp2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) (l_e_st_eq_landau_n_rt_rp_r_isprp1 r p) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) r).
+
+(* notion 4037 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isperp ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λq:l_e_st_eq_landau_n_rt_rp_r_pos s1.λi:l_e_st_eq_landau_n_rt_rp_r_is r1 s1.(l_e_st_eq_landau_n_rt_rp_r_ivr1_t22 r1 s1 (l_e_st_eq_landau_n_rt_rp_r_rpofp r1 p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s1 q) (l_e_st_eq_landau_n_rt_rp_r_isprp1 r1 p) (l_e_st_eq_landau_n_rt_rp_r_isprp1 s1 q) i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofp r1 p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s1 q)).
+
+(* notion 4038 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ispirp ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λq:l_e_st_eq_landau_n_rt_rp_r_pos s1.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofp r1 p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s1 q).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real r1 (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r1 p)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp s1 q)) s1 (l_e_st_eq_landau_n_rt_rp_r_isprp1 r1 p) (l_e_st_eq_landau_n_rt_rp_r_isrpep (l_e_st_eq_landau_n_rt_rp_r_rpofp r1 p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s1 q) i) (l_e_st_eq_landau_n_rt_rp_r_isprp2 s1 q) : l_e_st_eq_landau_n_rt_rp_r_is r1 s1).
+
+(* notion 4039 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrpp1 ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_ivr1_t22 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) r0 (l_e_st_eq_landau_n_rt_rp_r_rpofp (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_posi r0)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_isprp1 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_posi r0)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)) : l_e_st_eq_landau_n_rt_rp_is r0 (l_e_st_eq_landau_n_rt_rp_r_rpofp (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_posi r0))).
+
+(* notion 4040 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrpp2 ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut r0 (l_e_st_eq_landau_n_rt_rp_r_rpofp (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_posi r0)) (l_e_st_eq_landau_n_rt_rp_r_isrpp1 r0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofp (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_posi r0)) r0).
+
+(* notion 4041 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t29 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp r0).λj:l_e_st_eq_landau_n_rt_rp_r_is s (l_e_st_eq_landau_n_rt_rp_r_nofrp s0).λk:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_isrpin r0 s0 (l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) r s (l_e_st_eq_landau_n_rt_rp_r_nofrp s0) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) i) k j) : l_e_st_eq_landau_n_rt_rp_is r0 s0).
+
+(* notion 4042 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t30 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_cut.λy:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x).λu:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp y).l_e_st_eq_landau_n_rt_rp_r_ivr1_t29 r r x y t u (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r) : l_e_amone l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x))).
+
+(* notion 4043 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t31 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn1:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir n1 : l_e_st_eq_landau_n_rt_rp_negd a0).
+
+(* notion 4044 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_nr ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn1:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_rpofnd a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t31 r a0 a0ir n1) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4045 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t32 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn1:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_isin r (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_nr r a0 a0ir n1)) a0 (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_nr r a0 a0ir n1)) a0ir (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_nr r a0 a0ir n1))) (l_e_st_eq_landau_n_rt_rp_eqndrp1 a0 (l_e_st_eq_landau_n_rt_rp_r_ivr1_t31 r a0 a0ir n1)) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_ivr1_nr r a0 a0ir n1))).
+
+(* notion 4046 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t33 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn1:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_somei l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_nr r a0 a0ir n1) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t32 r a0 a0ir n1) : l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x))).
+
+(* notion 4047 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t34 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr1_t33 r x t n) : l_e_st_eq_landau_n_rt_rp_some (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x))).
+
+(* notion 4048 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr1_t35 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_onei l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t30 r) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t34 r n) : l_e_st_eq_landau_n_rt_rp_one (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x))).
+
+(* notion 4049 *)
+definition l_e_st_eq_landau_n_rt_rp_r_rpofn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_ind l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t35 r n) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4050 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isnrp1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_oneax l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp x)) (l_e_st_eq_landau_n_rt_rp_r_ivr1_t35 r n) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_rpofn r n))).
+
+(* notion 4051 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isnrp2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_rpofn r n)) (l_e_st_eq_landau_n_rt_rp_r_isnrp1 r n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_rpofn r n)) r).
+
+(* notion 4052 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isnerp ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_neg s1.λi:l_e_st_eq_landau_n_rt_rp_r_is r1 s1.(l_e_st_eq_landau_n_rt_rp_r_ivr1_t29 r1 s1 (l_e_st_eq_landau_n_rt_rp_r_rpofn r1 n) (l_e_st_eq_landau_n_rt_rp_r_rpofn s1 m) (l_e_st_eq_landau_n_rt_rp_r_isnrp1 r1 n) (l_e_st_eq_landau_n_rt_rp_r_isnrp1 s1 m) i : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofn r1 n) (l_e_st_eq_landau_n_rt_rp_r_rpofn s1 m)).
+
+(* notion 4053 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isnirp ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_neg s1.λi:l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofn r1 n) (l_e_st_eq_landau_n_rt_rp_r_rpofn s1 m).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real r1 (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_rpofn r1 n)) (l_e_st_eq_landau_n_rt_rp_r_nofrp (l_e_st_eq_landau_n_rt_rp_r_rpofn s1 m)) s1 (l_e_st_eq_landau_n_rt_rp_r_isnrp1 r1 n) (l_e_st_eq_landau_n_rt_rp_r_isrpen (l_e_st_eq_landau_n_rt_rp_r_rpofn r1 n) (l_e_st_eq_landau_n_rt_rp_r_rpofn s1 m) i) (l_e_st_eq_landau_n_rt_rp_r_isnrp2 s1 m) : l_e_st_eq_landau_n_rt_rp_r_is r1 s1).
+
+(* notion 4054 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrpn1 ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_ivr1_t29 (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) r0 (l_e_st_eq_landau_n_rt_rp_r_rpofn (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_negi r0)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_isnrp1 (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_negi r0)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)) : l_e_st_eq_landau_n_rt_rp_is r0 (l_e_st_eq_landau_n_rt_rp_r_rpofn (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_negi r0))).
+
+(* notion 4055 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrpn2 ≝ λr0:l_e_st_eq_landau_n_rt_cut.(l_e_symis l_e_st_eq_landau_n_rt_cut r0 (l_e_st_eq_landau_n_rt_rp_r_rpofn (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_negi r0)) (l_e_st_eq_landau_n_rt_rp_r_isrpn1 r0) : l_e_st_eq_landau_n_rt_rp_is (l_e_st_eq_landau_n_rt_rp_r_rpofn (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_r_negi r0)) r0).
+
+(* notion 4056 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz163 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r : l_e_st_eq_landau_n_rt_rp_r_is r r).
+
+(* notion 4057 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz164 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r s i : l_e_st_eq_landau_n_rt_rp_r_is s r).
+
+(* notion 4058 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz165 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is s t.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real r s t i j : l_e_st_eq_landau_n_rt_rp_r_is r t).
+
+(* notion 4059 *)
+definition l_e_st_eq_landau_n_rt_rp_r_absdr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_absd x) : Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4060 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_absd a) (l_e_st_eq_landau_n_rt_rp_absd b) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_absd a)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_absd b)) (l_e_st_eq_landau_n_rt_rp_eqabsd a b e) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_absdr a) (l_e_st_eq_landau_n_rt_rp_r_absdr b)).
+
+(* notion 4061 *)
+definition l_e_st_eq_landau_n_rt_rp_r_fabsdr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.l_e_st_eq_landau_n_rt_rp_r_ivr2_t1 x y t : l_e_st_eq_landau_n_rt_rp_r_fixf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_absdr).
+
+(* notion 4062 *)
+definition l_e_st_eq_landau_n_rt_rp_r_abs ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_indreal l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_absdr l_e_st_eq_landau_n_rt_rp_r_fabsdr r : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4063 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_isindreal l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_absdr l_e_st_eq_landau_n_rt_rp_r_fabsdr r a0 a0ir : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_absd a0)) (l_e_st_eq_landau_n_rt_rp_r_abs r)).
+
+(* notion 4064 *)
+definition l_e_st_eq_landau_n_rt_rp_r_aica ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_class x)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_absd a0)) (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_absd a0)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t2 r a0 a0ir) : l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_abs r))).
+
+(* notion 4065 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isabs ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_abs x) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).
+
+(* notion 4066 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r166_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_satzd166a a0 (l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a0)).
+
+(* notion 4067 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r166_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_2r166_t1 r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)).
+
+(* notion 4068 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz166a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_2r166_t2 r x t p) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)).
+
+(* notion 4069 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r166_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_satzd166b a0 (l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_absd a0)).
+
+(* notion 4070 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r166_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_2r166_t3 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)).
+
+(* notion 4071 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz166b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_2r166_t4 r x t n) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)).
+
+(* notion 4072 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r166_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_satzd166c a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex r a1 a1ir p) (l_e_st_eq_landau_n_rt_rp_r_posex s b1 b1is q) (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is) i) : l_e_st_eq_landau_n_rt_rp_eq a1 b1).
+
+(* notion 4073 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r166_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is (l_e_st_eq_landau_n_rt_rp_r_2r166_t5 r s a1 b1 a1ir b1is p q i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4074 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz166c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_2r166_t6 r s x y t u p q i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4075 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r166_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_satzd166d a1 b1 (l_e_st_eq_landau_n_rt_rp_r_negex r a1 a1ir n) (l_e_st_eq_landau_n_rt_rp_r_negex s b1 b1is o) (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is) i) : l_e_st_eq_landau_n_rt_rp_eq a1 b1).
+
+(* notion 4076 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r166_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is (l_e_st_eq_landau_n_rt_rp_r_2r166_t7 r s a1 b1 a1ir b1is n o i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4077 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz166d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_2r166_t8 r s x y t u n o i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4078 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz166e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_rapp r (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)) (λt:l_e_st_eq_landau_n_rt_rp_r_pos r.l_e_st_eq_landau_n_rt_rp_r_satz166a r t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)) n) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_satz166b r t) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs r)).
+
+(* notion 4079 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r166_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd166f a0 (l_e_st_eq_landau_n_rt_rp_r_0ex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_absd a0)).
+
+(* notion 4080 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r166_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_2r166_t9 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4081 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz166f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_2r166_t10 r x t i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4082 *)
+definition l_e_st_eq_landau_n_rt_rp_r_more ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (λy:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored x y))) : Prop).
+
+(* notion 4083 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_propm ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.(l_and3 (l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) : Prop).
+
+(* notion 4084 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_mored a1 b1.(l_and3i (l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) a1ir b1is m : l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a1 b1).
+
+(* notion 4085 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_mored a1 b1.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a1 x) b1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t3 r s a1 b1 a1ir b1is m) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a1 x)).
+
+(* notion 4086 *)
+definition l_e_st_eq_landau_n_rt_rp_r_morein ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_mored a1 b1.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (λy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s x y)) a1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t4 r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_r_more r s).
+
+(* notion 4087 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a b.(l_and3e1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored a b) p2 : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
+
+(* notion 4088 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a b.(l_and3e2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored a b) p2 : l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)).
+
+(* notion 4089 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a b.(l_and3e3 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_mored a b) p2 : l_e_st_eq_landau_n_rt_rp_mored a b).
+
+(* notion 4090 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a b.(l_e_st_eq_landau_n_rt_rp_eqmored12 a a1 b b1 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t5 r s a1 b1 a1ir b1is m a sa b p2) a1ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_isex s s b b1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t6 r s a1 b1 a1ir b1is m a sa b p2) b1is (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real s)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t7 r s a1 b1 a1ir b1is m a sa b p2) : l_e_st_eq_landau_n_rt_rp_mored a1 b1).
+
+(* notion 4091 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x).(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x) sa (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s a x.l_e_st_eq_landau_n_rt_rp_r_ivr2_t8 r s a1 b1 a1ir b1is m a sa x t) : l_e_st_eq_landau_n_rt_rp_mored a1 b1).
+
+(* notion 4092 *)
+definition l_e_st_eq_landau_n_rt_rp_r_moreex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (λy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s x y)) m (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_some l_e_st_eq_landau_n_rt_rp_dif (λy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propm r s x y).l_e_st_eq_landau_n_rt_rp_r_ivr2_t9 r s a1 b1 a1ir b1is m x t) : l_e_st_eq_landau_n_rt_rp_mored a1 b1).
+
+(* notion 4093 *)
+definition l_e_st_eq_landau_n_rt_rp_r_less ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (λy:l_e_st_eq_landau_n_rt_rp_dif.l_and3 (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd x y))) : Prop).
+
+(* notion 4094 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_propl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.(l_and3 (l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) : Prop).
+
+(* notion 4095 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.(l_and3i (l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) a1ir b1is l : l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a1 b1).
+
+(* notion 4096 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a1 x) b1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t10 r s a1 b1 a1ir b1is l) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a1 x)).
+
+(* notion 4097 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lessin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (λy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s x y)) a1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t11 r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4098 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a b.(l_and3e1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd a b) p2 : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
+
+(* notion 4099 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t13 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a b.(l_and3e2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd a b) p2 : l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)).
+
+(* notion 4100 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t14 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a b.(l_and3e3 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s)) (l_e_st_eq_landau_n_rt_rp_lessd a b) p2 : l_e_st_eq_landau_n_rt_rp_lessd a b).
+
+(* notion 4101 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t15 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x).λb:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a b.(l_e_st_eq_landau_n_rt_rp_eqlessd12 a a1 b b1 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t12 r s a1 b1 a1ir b1is l a sa b p2) a1ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_isex s s b b1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t13 r s a1 b1 a1ir b1is l a sa b p2) b1is (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real s)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t14 r s a1 b1 a1ir b1is l a sa b p2) : l_e_st_eq_landau_n_rt_rp_lessd a1 b1).
+
+(* notion 4102 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t16 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λa:l_e_st_eq_landau_n_rt_rp_dif.λsa:l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x).(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x) sa (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s a x.l_e_st_eq_landau_n_rt_rp_r_ivr2_t15 r s a1 b1 a1ir b1is l a sa x t) : l_e_st_eq_landau_n_rt_rp_lessd a1 b1).
+
+(* notion 4103 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lessex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_some l_e_st_eq_landau_n_rt_rp_dif (λy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s x y)) l (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_some l_e_st_eq_landau_n_rt_rp_dif (λy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_ivr2_propl r s x y).l_e_st_eq_landau_n_rt_rp_r_ivr2_t16 r s a1 b1 a1ir b1is l x t) : l_e_st_eq_landau_n_rt_rp_lessd a1 b1).
+
+(* notion 4104 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ismore1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_more r t.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x t) r s m i : l_e_st_eq_landau_n_rt_rp_r_more s t).
+
+(* notion 4105 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ismore2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_more t r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more t x) r s m i : l_e_st_eq_landau_n_rt_rp_r_more t s).
+
+(* notion 4106 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isless1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_less r t.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x t) r s l i : l_e_st_eq_landau_n_rt_rp_r_less s t).
+
+(* notion 4107 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isless2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_less t r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less t x) r s l i : l_e_st_eq_landau_n_rt_rp_r_less t s).
+
+(* notion 4108 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ismore12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.λm:l_e_st_eq_landau_n_rt_rp_r_more r t.(l_e_st_eq_landau_n_rt_rp_r_ismore2 t u s j (l_e_st_eq_landau_n_rt_rp_r_ismore1 r s t i m) : l_e_st_eq_landau_n_rt_rp_r_more s u).
+
+(* notion 4109 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isless12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.λl:l_e_st_eq_landau_n_rt_rp_r_less r t.(l_e_st_eq_landau_n_rt_rp_r_isless2 t u s j (l_e_st_eq_landau_n_rt_rp_r_isless1 r s t i l) : l_e_st_eq_landau_n_rt_rp_r_less s u).
+
+(* notion 4110 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t17 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_lemmad5 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_lessd b1 a1).
+
+(* notion 4111 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t18 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_lessin s r b1 a1 b1is a1ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t17 r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_r_less s r).
+
+(* notion 4112 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_less s r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr2_t18 r s x y t u m) : l_e_st_eq_landau_n_rt_rp_r_less s r).
+
+(* notion 4113 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t19 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_lemmad6 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_mored b1 a1).
+
+(* notion 4114 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t20 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_morein s r b1 a1 b1is a1ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t19 r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_r_more s r).
+
+(* notion 4115 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_more s r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr2_t20 r s x y t u l) : l_e_st_eq_landau_n_rt_rp_r_more s r).
+
+(* notion 4116 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r167_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd167a a1 b1 : l_or3 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1)).
+
+(* notion 4117 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r167_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λe:l_e_st_eq_landau_n_rt_rp_eq a1 b1.(l_or3i1 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is e) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
+
+(* notion 4118 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r167_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_mored a1 b1.(l_or3i2 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_morein r s a1 b1 a1ir b1is m) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
+
+(* notion 4119 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r167_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.(l_or3i3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_lessin r s a1 b1 a1ir b1is l) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
+
+(* notion 4120 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r167_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_or3app (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)) (l_e_st_eq_landau_n_rt_rp_r_2r167_t1 r s a1 b1 a1ir b1is) (λt:l_e_st_eq_landau_n_rt_rp_eq a1 b1.l_e_st_eq_landau_n_rt_rp_r_2r167_t2 r s a1 b1 a1ir b1is t) (λt:l_e_st_eq_landau_n_rt_rp_mored a1 b1.l_e_st_eq_landau_n_rt_rp_r_2r167_t3 r s a1 b1 a1ir b1is t) (λt:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.l_e_st_eq_landau_n_rt_rp_r_2r167_t4 r s a1 b1 a1ir b1is t) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
+
+(* notion 4121 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r167_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd167b a1 b1 : l_ec3 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1)).
+
+(* notion 4122 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r167_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_ec3e12 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_2r167_t6 r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is i)) (λt:l_e_st_eq_landau_n_rt_rp_r_more r s.l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is t) : l_not (l_e_st_eq_landau_n_rt_rp_r_more r s)).
+
+(* notion 4123 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r167_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_ec3e23 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_2r167_t6 r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is m)) (λt:l_e_st_eq_landau_n_rt_rp_r_less r s.l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is t) : l_not (l_e_st_eq_landau_n_rt_rp_r_less r s)).
+
+(* notion 4124 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r167_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_ec3e31 (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_2r167_t6 r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is l)) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is t) : l_not (l_e_st_eq_landau_n_rt_rp_r_is r s)).
+
+(* notion 4125 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r167_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_ec3_th6 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_ec_th1 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_r_2r167_t7 r s a1 b1 a1ir b1is t)) (l_ec_th1 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (λt:l_e_st_eq_landau_n_rt_rp_r_more r s.l_e_st_eq_landau_n_rt_rp_r_2r167_t8 r s a1 b1 a1ir b1is t)) (l_ec_th1 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (λt:l_e_st_eq_landau_n_rt_rp_r_less r s.l_e_st_eq_landau_n_rt_rp_r_2r167_t9 r s a1 b1 a1ir b1is t)) : l_ec3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
+
+(* notion 4126 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r167_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_orec3i (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_2r167_t5 r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_2r167_t10 r s a1 b1 a1ir b1is) : l_orec3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
+
+(* notion 4127 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz167 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_orec3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_2r167_t11 r s x y t u) : l_orec3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
+
+(* notion 4128 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz167a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_orec3e1 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167 r s) : l_or3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
+
+(* notion 4129 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz167b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_orec3e2 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167 r s) : l_ec3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s)).
+
+(* notion 4130 *)
+definition l_e_st_eq_landau_n_rt_rp_r_moreis ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_or (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) : Prop).
+
+(* notion 4131 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lessis ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_or (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) : Prop).
+
+(* notion 4132 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz168a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_less s r) (l_e_st_eq_landau_n_rt_rp_r_is s r) m (λt:l_e_st_eq_landau_n_rt_rp_r_more r s.l_e_st_eq_landau_n_rt_rp_r_lemma1 r s t) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r s t) : l_e_st_eq_landau_n_rt_rp_r_lessis s r).
+
+(* notion 4133 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz168b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more s r) (l_e_st_eq_landau_n_rt_rp_r_is s r) l (λt:l_e_st_eq_landau_n_rt_rp_r_less r s.l_e_st_eq_landau_n_rt_rp_r_lemma2 r s t) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r s t) : l_e_st_eq_landau_n_rt_rp_r_moreis s r).
+
+(* notion 4134 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ismoreis1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r t.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x t) r s m i : l_e_st_eq_landau_n_rt_rp_r_moreis s t).
+
+(* notion 4135 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ismoreis2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_moreis t r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis t x) r s m i : l_e_st_eq_landau_n_rt_rp_r_moreis t s).
+
+(* notion 4136 *)
+definition l_e_st_eq_landau_n_rt_rp_r_islessis1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r t.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x t) r s l i : l_e_st_eq_landau_n_rt_rp_r_lessis s t).
+
+(* notion 4137 *)
+definition l_e_st_eq_landau_n_rt_rp_r_islessis2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_lessis t r.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis t x) r s l i : l_e_st_eq_landau_n_rt_rp_r_lessis t s).
+
+(* notion 4138 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ismoreis12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r t.(l_e_st_eq_landau_n_rt_rp_r_ismoreis2 t u s j (l_e_st_eq_landau_n_rt_rp_r_ismoreis1 r s t i m) : l_e_st_eq_landau_n_rt_rp_r_moreis s u).
+
+(* notion 4139 *)
+definition l_e_st_eq_landau_n_rt_rp_r_islessis12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r t.(l_e_st_eq_landau_n_rt_rp_r_islessis2 t u s j (l_e_st_eq_landau_n_rt_rp_r_islessis1 r s t i l) : l_e_st_eq_landau_n_rt_rp_r_lessis s u).
+
+(* notion 4140 *)
+definition l_e_st_eq_landau_n_rt_rp_r_moreisi1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) m : l_e_st_eq_landau_n_rt_rp_r_moreis r s).
+
+(* notion 4141 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lessisi1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) l : l_e_st_eq_landau_n_rt_rp_r_lessis r s).
+
+(* notion 4142 *)
+definition l_e_st_eq_landau_n_rt_rp_r_moreisi2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) i : l_e_st_eq_landau_n_rt_rp_r_moreis r s).
+
+(* notion 4143 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lessisi2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) i : l_e_st_eq_landau_n_rt_rp_r_lessis r s).
+
+(* notion 4144 *)
+definition l_e_st_eq_landau_n_rt_rp_r_moreisin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_moreq a1 b1.(l_orapp (l_e_st_eq_landau_n_rt_rp_mored a1 b1) (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_r_moreis r s) m (λt:l_e_st_eq_landau_n_rt_rp_mored a1 b1.l_e_st_eq_landau_n_rt_rp_r_moreisi1 r s (l_e_st_eq_landau_n_rt_rp_r_morein r s a1 b1 a1ir b1is t)) (λt:l_e_st_eq_landau_n_rt_rp_eq a1 b1.l_e_st_eq_landau_n_rt_rp_r_moreisi2 r s (l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is t)) : l_e_st_eq_landau_n_rt_rp_r_moreis r s).
+
+(* notion 4145 *)
+definition l_e_st_eq_landau_n_rt_rp_r_moreisex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.(l_orapp (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_moreq a1 b1) m (λt:l_e_st_eq_landau_n_rt_rp_r_more r s.l_e_st_eq_landau_n_rt_rp_moreqi1 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is t)) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_moreqi2 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is t)) : l_e_st_eq_landau_n_rt_rp_moreq a1 b1).
+
+(* notion 4146 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lessisin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_lesseq a1 b1.(l_orapp (l_e_st_eq_landau_n_rt_rp_lessd a1 b1) (l_e_st_eq_landau_n_rt_rp_eq a1 b1) (l_e_st_eq_landau_n_rt_rp_r_lessis r s) l (λt:l_e_st_eq_landau_n_rt_rp_lessd a1 b1.l_e_st_eq_landau_n_rt_rp_r_lessisi1 r s (l_e_st_eq_landau_n_rt_rp_r_lessin r s a1 b1 a1ir b1is t)) (λt:l_e_st_eq_landau_n_rt_rp_eq a1 b1.l_e_st_eq_landau_n_rt_rp_r_lessisi2 r s (l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is t)) : l_e_st_eq_landau_n_rt_rp_r_lessis r s).
+
+(* notion 4147 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lessisex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.(l_orapp (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_lesseq a1 b1) l (λt:l_e_st_eq_landau_n_rt_rp_r_less r s.l_e_st_eq_landau_n_rt_rp_lesseqi1 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is t)) (λt:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_lesseqi2 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is t)) : l_e_st_eq_landau_n_rt_rp_lesseq a1 b1).
+
+(* notion 4148 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz167c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.(l_ec3_th7 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167b r s) (l_comor (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) m) : l_not (l_e_st_eq_landau_n_rt_rp_r_less r s)).
+
+(* notion 4149 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz167d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.(l_ec3_th9 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167b r s) l : l_not (l_e_st_eq_landau_n_rt_rp_r_more r s)).
+
+(* notion 4150 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz167e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_more r s).(l_or3_th2 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167a r s) n : l_e_st_eq_landau_n_rt_rp_r_lessis r s).
+
+(* notion 4151 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz167f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_less r s).(l_comor (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_or3_th3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167a r s) n) : l_e_st_eq_landau_n_rt_rp_r_moreis r s).
+
+(* notion 4152 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz167g ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_lessis r s) (l_not (l_e_st_eq_landau_n_rt_rp_r_more r s)) (l_weli (l_e_st_eq_landau_n_rt_rp_r_more r s) m) (λt:l_e_st_eq_landau_n_rt_rp_r_lessis r s.l_e_st_eq_landau_n_rt_rp_r_satz167d r s t) : l_not (l_e_st_eq_landau_n_rt_rp_r_lessis r s)).
+
+(* notion 4153 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz167h ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_moreis r s) (l_not (l_e_st_eq_landau_n_rt_rp_r_less r s)) (l_weli (l_e_st_eq_landau_n_rt_rp_r_less r s) l) (λt:l_e_st_eq_landau_n_rt_rp_r_moreis r s.l_e_st_eq_landau_n_rt_rp_r_satz167c r s t) : l_not (l_e_st_eq_landau_n_rt_rp_r_moreis r s)).
+
+(* notion 4154 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz167j ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_moreis r s).(l_or3e3 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167a r s) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) n) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) n) : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4155 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz167k ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_lessis r s).(l_or3e2 (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_satz167a r s) (l_or_th4 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) n) (l_or_th5 (l_e_st_eq_landau_n_rt_rp_r_less r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) n) : l_e_st_eq_landau_n_rt_rp_r_more r s).
+
+(* notion 4156 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r169_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_satzd169a a b (l_e_st_eq_landau_n_rt_rp_r_0ex l_e_st_eq_landau_n_rt_rp_r_0 b bi0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_posex r a air p) : l_e_st_eq_landau_n_rt_rp_mored a b).
+
+(* notion 4157 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r169_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_r_morein r l_e_st_eq_landau_n_rt_rp_r_0 a b air bi0 (l_e_st_eq_landau_n_rt_rp_r_2r169_t1 r p a b air bi0) : l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4158 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz169a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).l_e_st_eq_landau_n_rt_rp_r_2r169_t2 r p x y t u) : l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4159 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r169_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_satzd169b a b (l_e_st_eq_landau_n_rt_rp_r_0ex l_e_st_eq_landau_n_rt_rp_r_0 b bi0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_moreex r l_e_st_eq_landau_n_rt_rp_r_0 a b air bi0 m) : l_e_st_eq_landau_n_rt_rp_posd a).
+
+(* notion 4160 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r169_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_r_posin r a air (l_e_st_eq_landau_n_rt_rp_r_2r169_t3 r m a b air bi0) : l_e_st_eq_landau_n_rt_rp_r_pos r).
+
+(* notion 4161 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz169b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pos r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).l_e_st_eq_landau_n_rt_rp_r_2r169_t4 r m x y t u) : l_e_st_eq_landau_n_rt_rp_r_pos r).
+
+(* notion 4162 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r169_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_satzd169c a b (l_e_st_eq_landau_n_rt_rp_r_0ex l_e_st_eq_landau_n_rt_rp_r_0 b bi0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_negex r a air n) : l_e_st_eq_landau_n_rt_rp_lessd a b).
+
+(* notion 4163 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r169_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_r_lessin r l_e_st_eq_landau_n_rt_rp_r_0 a b air bi0 (l_e_st_eq_landau_n_rt_rp_r_2r169_t5 r n a b air bi0) : l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4164 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz169c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).l_e_st_eq_landau_n_rt_rp_r_2r169_t6 r n x y t u) : l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4165 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r169_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_satzd169d a b (l_e_st_eq_landau_n_rt_rp_r_0ex l_e_st_eq_landau_n_rt_rp_r_0 b bi0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_lessex r l_e_st_eq_landau_n_rt_rp_r_0 a b air bi0 l) : l_e_st_eq_landau_n_rt_rp_negd a).
+
+(* notion 4166 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r169_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_r_negin r a air (l_e_st_eq_landau_n_rt_rp_r_2r169_t7 r l a b air bi0) : l_e_st_eq_landau_n_rt_rp_r_neg r).
+
+(* notion 4167 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz169d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_neg r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).l_e_st_eq_landau_n_rt_rp_r_2r169_t8 r l x y t u) : l_e_st_eq_landau_n_rt_rp_r_neg r).
+
+(* notion 4168 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r170_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_satzd170 a b (l_e_st_eq_landau_n_rt_rp_r_0ex l_e_st_eq_landau_n_rt_rp_r_0 b bi0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_absd a) b).
+
+(* notion 4169 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r170_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbi0:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).(l_e_st_eq_landau_n_rt_rp_r_moreisin (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_absd a) b (l_e_st_eq_landau_n_rt_rp_r_aica r a air) bi0 (l_e_st_eq_landau_n_rt_rp_r_2r170_t1 r a b air bi0) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4170 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz170 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class l_e_st_eq_landau_n_rt_rp_r_0).l_e_st_eq_landau_n_rt_rp_r_2r170_t2 r x y t u) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4171 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz170a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_abs r)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz167c (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz170 r)) (λt:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_abs r).l_e_st_eq_landau_n_rt_rp_r_satz169c (l_e_st_eq_landau_n_rt_rp_r_abs r) t) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_abs r))).
+
+(* notion 4172 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r171_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbis:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s).λcit:l_e_st_eq_landau_n_rt_rp_r_inn c (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_satzd171 a b c (l_e_st_eq_landau_n_rt_rp_r_lessex r s a b air bis l) (l_e_st_eq_landau_n_rt_rp_r_lessex s t b c bis cit k) : l_e_st_eq_landau_n_rt_rp_lessd a c).
+
+(* notion 4173 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r171_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r).λbis:l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class s).λcit:l_e_st_eq_landau_n_rt_rp_r_inn c (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_r_lessin r t a c air cit (l_e_st_eq_landau_n_rt_rp_r_2r171_t1 r s t l k a b c air bis cit) : l_e_st_eq_landau_n_rt_rp_r_less r t).
+
+(* notion 4174 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz171 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less r t) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λw:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λv:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_2r171_t2 r s t l k x y z w u v) : l_e_st_eq_landau_n_rt_rp_r_less r t).
+
+(* notion 4175 *)
+definition l_e_st_eq_landau_n_rt_rp_r_trless ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.(l_e_st_eq_landau_n_rt_rp_r_satz171 r s t l k : l_e_st_eq_landau_n_rt_rp_r_less r t).
+
+(* notion 4176 *)
+definition l_e_st_eq_landau_n_rt_rp_r_trmore ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_more s t.(l_e_st_eq_landau_n_rt_rp_r_lemma2 t r (l_e_st_eq_landau_n_rt_rp_r_trless t s r (l_e_st_eq_landau_n_rt_rp_r_lemma1 s t n) (l_e_st_eq_landau_n_rt_rp_r_lemma1 r s m)) : l_e_st_eq_landau_n_rt_rp_r_more r t).
+
+(* notion 4177 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r172_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.(l_e_st_eq_landau_n_rt_rp_satzd172a a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_lessisex r s a2 b2 a2ir b2is l) (l_e_st_eq_landau_n_rt_rp_r_lessex s t b2 c2 b2is c2it k) : l_e_st_eq_landau_n_rt_rp_lessd a2 c2).
+
+(* notion 4178 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r172_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.(l_e_st_eq_landau_n_rt_rp_r_lessin r t a2 c2 a2ir c2it (l_e_st_eq_landau_n_rt_rp_r_2r172_t1 r s t a2 b2 c2 a2ir b2is c2it l k) : l_e_st_eq_landau_n_rt_rp_r_less r t).
+
+(* notion 4179 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz172a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_less s t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less r t) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_2r172_t2 r s t x y z u v w l k) : l_e_st_eq_landau_n_rt_rp_r_less r t).
+
+(* notion 4180 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r172_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_satzd172b a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a2 b2 a2ir b2is l) (l_e_st_eq_landau_n_rt_rp_r_lessisex s t b2 c2 b2is c2it k) : l_e_st_eq_landau_n_rt_rp_lessd a2 c2).
+
+(* notion 4181 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r172_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_r_lessin r t a2 c2 a2ir c2it (l_e_st_eq_landau_n_rt_rp_r_2r172_t3 r s t a2 b2 c2 a2ir b2is c2it l k) : l_e_st_eq_landau_n_rt_rp_r_less r t).
+
+(* notion 4182 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz172b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less r t) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_2r172_t4 r s t x y z u v w l k) : l_e_st_eq_landau_n_rt_rp_r_less r t).
+
+(* notion 4183 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz172c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_more s t.(l_e_st_eq_landau_n_rt_rp_r_lemma2 t r (l_e_st_eq_landau_n_rt_rp_r_satz172b t s r (l_e_st_eq_landau_n_rt_rp_r_lemma1 s t n) (l_e_st_eq_landau_n_rt_rp_r_satz168a r s m)) : l_e_st_eq_landau_n_rt_rp_r_more r t).
+
+(* notion 4184 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz172d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis s t.(l_e_st_eq_landau_n_rt_rp_r_lemma2 t r (l_e_st_eq_landau_n_rt_rp_r_satz172a t s r (l_e_st_eq_landau_n_rt_rp_r_satz168a s t n) (l_e_st_eq_landau_n_rt_rp_r_lemma1 r s m)) : l_e_st_eq_landau_n_rt_rp_r_more r t).
+
+(* notion 4185 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r173_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_satzd173 a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_lessisex r s a2 b2 a2ir b2is l) (l_e_st_eq_landau_n_rt_rp_r_lessisex s t b2 c2 b2is c2it k) : l_e_st_eq_landau_n_rt_rp_lesseq a2 c2).
+
+(* notion 4186 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r173_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_r_lessisin r t a2 c2 a2ir c2it (l_e_st_eq_landau_n_rt_rp_r_2r173_t1 r s t a2 b2 c2 a2ir b2is c2it l k) : l_e_st_eq_landau_n_rt_rp_r_lessis r t).
+
+(* notion 4187 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz173 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_lessis r t) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_2r173_t2 r s t x y z u v w l k) : l_e_st_eq_landau_n_rt_rp_r_lessis r t).
+
+(* notion 4188 *)
+definition l_e_st_eq_landau_n_rt_rp_r_trlessis ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis s t.(l_e_st_eq_landau_n_rt_rp_r_satz173 r s t l k : l_e_st_eq_landau_n_rt_rp_r_lessis r t).
+
+(* notion 4189 *)
+definition l_e_st_eq_landau_n_rt_rp_r_trmoreis ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis s t.(l_e_st_eq_landau_n_rt_rp_r_satz168b t r (l_e_st_eq_landau_n_rt_rp_r_trlessis t s r (l_e_st_eq_landau_n_rt_rp_r_satz168a s t n) (l_e_st_eq_landau_n_rt_rp_r_satz168a r s m)) : l_e_st_eq_landau_n_rt_rp_r_moreis r t).
+
+(* notion 4190 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ratrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd x)) : Prop).
+
+(* notion 4191 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t21 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λr1:l_e_st_eq_landau_n_rt_rp_ratd a0.(l_andi (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a0) a0ir r1 : l_and (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a0)).
+
+(* notion 4192 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ratrlin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λr1:l_e_st_eq_landau_n_rt_rp_ratd a0.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd x)) a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t21 r a0 a0ir r1) : l_e_st_eq_landau_n_rt_rp_r_ratrl r).
+
+(* notion 4193 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t22 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λrr:l_e_st_eq_landau_n_rt_rp_r_ratrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a) b : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
+
+(* notion 4194 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t23 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λrr:l_e_st_eq_landau_n_rt_rp_r_ratrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a) b : l_e_st_eq_landau_n_rt_rp_ratd a).
+
+(* notion 4195 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t24 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λrr:l_e_st_eq_landau_n_rt_rp_r_ratrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd a).(l_e_st_eq_landau_n_rt_rp_eqratd a a0 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t22 r a0 a0ir rr a b) a0ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t23 r a0 a0ir rr a b) : l_e_st_eq_landau_n_rt_rp_ratd a0).
+
+(* notion 4196 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ratrlex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λrr:l_e_st_eq_landau_n_rt_rp_r_ratrl r.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd x)) rr (l_e_st_eq_landau_n_rt_rp_ratd a0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_ratd x).l_e_st_eq_landau_n_rt_rp_r_ivr2_t24 r a0 a0ir rr x t) : l_e_st_eq_landau_n_rt_rp_ratd a0).
+
+(* notion 4197 *)
+definition l_e_st_eq_landau_n_rt_rp_r_irratrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_not (l_e_st_eq_landau_n_rt_rp_r_ratrl r) : Prop).
+
+(* notion 4198 *)
+definition l_e_st_eq_landau_n_rt_rp_r_remark2 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r0.(l_e_st_eq_landau_n_rt_rp_r_ratrlin (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark2a r0 rr) : l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)).
+
+(* notion 4199 *)
+definition l_e_st_eq_landau_n_rt_rp_r_remark3 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λrr:l_e_st_eq_landau_n_rt_rp_ratrp r0.(l_e_st_eq_landau_n_rt_rp_r_ratrlin (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark3a r0 rr) : l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)).
+
+(* notion 4200 *)
+definition l_e_st_eq_landau_n_rt_rp_r_remark4 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λir:l_e_st_eq_landau_n_rt_rp_irratrp r0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)) (l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark4a r0 ir) (λt:l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0).l_e_st_eq_landau_n_rt_rp_r_ratrlex (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) t) : l_e_st_eq_landau_n_rt_rp_r_irratrl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)).
+
+(* notion 4201 *)
+definition l_e_st_eq_landau_n_rt_rp_r_remark5 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λir:l_e_st_eq_landau_n_rt_rp_irratrp r0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)) (l_e_st_eq_landau_n_rt_rp_ratd (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark5a r0 ir) (λt:l_e_st_eq_landau_n_rt_rp_r_ratrl (l_e_st_eq_landau_n_rt_rp_r_nofrp r0).l_e_st_eq_landau_n_rt_rp_r_ratrlex (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) t) : l_e_st_eq_landau_n_rt_rp_r_irratrl (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)).
+
+(* notion 4202 *)
+definition l_e_st_eq_landau_n_rt_rp_r_natrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd x)) : Prop).
+
+(* notion 4203 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t25 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_natd a0.(l_andi (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a0) a0ir n : l_and (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a0)).
+
+(* notion 4204 *)
+definition l_e_st_eq_landau_n_rt_rp_r_natrlin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_natd a0.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd x)) a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t25 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_natrl r).
+
+(* notion 4205 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t26 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a) b : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
+
+(* notion 4206 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t27 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a) b : l_e_st_eq_landau_n_rt_rp_natd a).
+
+(* notion 4207 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t28 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd a).(l_e_st_eq_landau_n_rt_rp_eqnatd a a0 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t26 r a0 a0ir n a b) a0ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t27 r a0 a0ir n a b) : l_e_st_eq_landau_n_rt_rp_natd a0).
+
+(* notion 4208 *)
+definition l_e_st_eq_landau_n_rt_rp_r_natrlex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd x)) n (l_e_st_eq_landau_n_rt_rp_natd a0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_natd x).l_e_st_eq_landau_n_rt_rp_r_ivr2_t28 r a0 a0ir n x t) : l_e_st_eq_landau_n_rt_rp_natd a0).
+
+(* notion 4209 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t29 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_natposd a0 (l_e_st_eq_landau_n_rt_rp_r_natrlex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_posd a0).
+
+(* notion 4210 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t30 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_posin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t29 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_pos r).
+
+(* notion 4211 *)
+definition l_e_st_eq_landau_n_rt_rp_r_natpos ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_pos r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr2_t30 r x t n) : l_e_st_eq_landau_n_rt_rp_r_pos r).
+
+(* notion 4212 *)
+definition l_e_st_eq_landau_n_rt_rp_r_rlofnt ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pdofnt x) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4213 *)
+definition l_e_st_eq_landau_n_rt_rp_r_natrli ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_natrlin (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_pdofnt x) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofnt x)) (l_e_st_eq_landau_n_rt_rp_natdi x) : l_e_st_eq_landau_n_rt_rp_r_natrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x)).
+
+(* notion 4214 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isnterl ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is x y.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) x y i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)).
+
+(* notion 4215 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isntirl ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).(l_e_st_eq_landau_n_rt_rp_isntirp x y (l_e_st_eq_landau_n_rt_rp_r_isrpip (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) i) : l_e_st_eq_landau_n_is x y).
+
+(* notion 4216 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 ≝ (λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).l_e_st_eq_landau_n_rt_rp_r_isntirl x y t : l_e_injective l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x)).
+
+(* notion 4217 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t32 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_natposd a0 (l_e_st_eq_landau_n_rt_rp_r_natrlex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_posd a0).
+
+(* notion 4218 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_ap ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_rpofpd a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t32 r a0 a0ir n) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4219 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t33 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_natderp a0 (l_e_st_eq_landau_n_rt_rp_r_natrlex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_natrp (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n)).
+
+(* notion 4220 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_ntofrp (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t33 r a0 a0ir n) : l_e_st_eq_landau_n_nat).
+
+(* notion 4221 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t34 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_isrpepd (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n) (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n)) (l_e_st_eq_landau_n_rt_rp_isrpnt1 (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t33 r a0 a0ir n)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n)) (l_e_st_eq_landau_n_rt_rp_pdofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n))).
+
+(* notion 4222 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t35 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_treq a0 (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_r_ivr2_ap r a0 a0ir n)) (l_e_st_eq_landau_n_rt_rp_pdofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n)) (l_e_st_eq_landau_n_rt_rp_eqpdrp1 a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t32 r a0 a0ir n)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t34 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_pdofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n))).
+
+(* notion 4223 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t36 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_isin r (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n)) a0 (l_e_st_eq_landau_n_rt_rp_pdofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n)) a0ir (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n))) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t35 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n))).
+
+(* notion 4224 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t37 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_somei l_e_st_eq_landau_n_nat (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt x)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_x0 r a0 a0ir n) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t36 r a0 a0ir n) : l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r).
+
+(* notion 4225 *)
+definition l_e_st_eq_landau_n_rt_rp_r_natimage ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr2_t37 r x t n) : l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r).
+
+(* notion 4226 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t38 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r.λx:l_e_st_eq_landau_n_nat.λj:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt x).(l_e_isp1 l_e_st_eq_landau_n_rt_rp_r_real (λu:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_natrl u) (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r (l_e_st_eq_landau_n_rt_rp_r_natrli x) j : l_e_st_eq_landau_n_rt_rp_r_natrl r).
+
+(* notion 4227 *)
+definition l_e_st_eq_landau_n_rt_rp_r_imagenat ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) r.(l_someapp l_e_st_eq_landau_n_nat (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt u)) i (l_e_st_eq_landau_n_rt_rp_r_natrl r) (λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt u).l_e_st_eq_landau_n_rt_rp_r_ivr2_t38 r i u v) : l_e_st_eq_landau_n_rt_rp_r_natrl r).
+
+(* notion 4228 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ntofrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_soft l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 r (l_e_st_eq_landau_n_rt_rp_r_natimage r n) : l_e_st_eq_landau_n_nat).
+
+(* notion 4229 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrlent ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_natrl s1.λi:l_e_st_eq_landau_n_rt_rp_r_is r1 s1.(l_e_isinv l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 r1 (l_e_st_eq_landau_n_rt_rp_r_natimage r1 n) s1 (l_e_st_eq_landau_n_rt_rp_r_natimage s1 m) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_ntofrl r1 n) (l_e_st_eq_landau_n_rt_rp_r_ntofrl s1 m)).
+
+(* notion 4230 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrlint ≝ λr1:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r1.λs1:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_natrl s1.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_ntofrl r1 n) (l_e_st_eq_landau_n_rt_rp_r_ntofrl s1 m).(l_e_isinve l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 r1 (l_e_st_eq_landau_n_rt_rp_r_natimage r1 n) s1 (l_e_st_eq_landau_n_rt_rp_r_natimage s1 m) i : l_e_st_eq_landau_n_rt_rp_r_is r1 s1).
+
+(* notion 4231 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrlnt1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_ists1 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt x) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 r (l_e_st_eq_landau_n_rt_rp_r_natimage r n) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n))).
+
+(* notion 4232 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isrlnt2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 r n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n)) r).
+
+(* notion 4233 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_xn ≝ λx:l_e_st_eq_landau_n_nat.(l_e_soft l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_imagei l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) x) : l_e_st_eq_landau_n_nat).
+
+(* notion 4234 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t39 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_isinv l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_imagei l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natimage (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt x)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_ivr2_xn x) (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x))).
+
+(* notion 4235 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isntrl1 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_rp_r_ivr2_xn x) (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x)) (l_e_isst1 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_real (λu:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_rlofnt u) l_e_st_eq_landau_n_rt_rp_r_ivr2_t31 x) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t39 x) : l_e_st_eq_landau_n_is x (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x))).
+
+(* notion 4236 *)
+definition l_e_st_eq_landau_n_rt_rp_r_isntrl2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat x (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x)) (l_e_st_eq_landau_n_rt_rp_r_isntrl1 x) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_natrli x)) x).
+
+(* notion 4237 *)
+definition l_e_st_eq_landau_n_rt_rp_r_intrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd x)) : Prop).
+
+(* notion 4238 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t40 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_intd a0.(l_andi (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a0) a0ir i : l_and (l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a0)).
+
+(* notion 4239 *)
+definition l_e_st_eq_landau_n_rt_rp_r_intrlin ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_intd a0.(l_somei l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd x)) a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t40 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_intrl r).
+
+(* notion 4240 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t41 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a) b : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)).
+
+(* notion 4241 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t42 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a) b : l_e_st_eq_landau_n_rt_rp_intd a).
+
+(* notion 4242 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t43 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_and (l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd a).(l_e_st_eq_landau_n_rt_rp_eqintd a a0 (l_e_st_eq_landau_n_rt_rp_r_isex r r a a0 (l_e_st_eq_landau_n_rt_rp_r_ivr2_t41 r a0 a0ir i a b) a0ir (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) (l_e_st_eq_landau_n_rt_rp_r_ivr2_t42 r a0 a0ir i a b) : l_e_st_eq_landau_n_rt_rp_intd a0).
+
+(* notion 4243 *)
+definition l_e_st_eq_landau_n_rt_rp_r_intrlex ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd x)) i (l_e_st_eq_landau_n_rt_rp_intd a0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_and (l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r)) (l_e_st_eq_landau_n_rt_rp_intd x).l_e_st_eq_landau_n_rt_rp_r_ivr2_t43 r a0 a0ir i x t) : l_e_st_eq_landau_n_rt_rp_intd a0).
+
+(* notion 4244 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t44 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_natintd a0 (l_e_st_eq_landau_n_rt_rp_r_natrlex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_intd a0).
+
+(* notion 4245 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t45 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_intrlin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t44 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_intrl r).
+
+(* notion 4246 *)
+definition l_e_st_eq_landau_n_rt_rp_r_natintrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_intrl r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr2_t45 r x t n) : l_e_st_eq_landau_n_rt_rp_r_intrl r).
+
+(* notion 4247 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t46 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_posintnatd a0 (l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir p) (l_e_st_eq_landau_n_rt_rp_r_intrlex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_natd a0).
+
+(* notion 4248 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t47 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_natrlin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t46 r a0 a0ir p i) : l_e_st_eq_landau_n_rt_rp_r_natrl r).
+
+(* notion 4249 *)
+definition l_e_st_eq_landau_n_rt_rp_r_posintnatrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_natrl r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr2_t47 r x t p i) : l_e_st_eq_landau_n_rt_rp_r_natrl r).
+
+(* notion 4250 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t48 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi2:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_intdi0 a0 (l_e_st_eq_landau_n_rt_rp_r_0ex r a0 a0ir i2) : l_e_st_eq_landau_n_rt_rp_intd a0).
+
+(* notion 4251 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr2_t49 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi2:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_intrlin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_ivr2_t48 r a0 a0ir i2) : l_e_st_eq_landau_n_rt_rp_r_intrl r).
+
+(* notion 4252 *)
+definition l_e_st_eq_landau_n_rt_rp_r_intrli0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_intrl r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr2_t49 r x t i) : l_e_st_eq_landau_n_rt_rp_r_intrl r).
+
+(* notion 4253 *)
+definition l_e_st_eq_landau_n_rt_rp_r_remark6 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r0.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark6 r0 n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)).
+
+(* notion 4254 *)
+definition l_e_st_eq_landau_n_rt_rp_r_remark7 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λn:l_e_st_eq_landau_n_rt_rp_natrp r0.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_nofrp r0) (l_e_st_eq_landau_n_rt_rp_ndofrp r0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_ndofrp r0)) (l_e_st_eq_landau_n_rt_rp_remark7 r0 n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_nofrp r0)).
+
+(* notion 4255 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r174_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_satzd174 a0 (l_e_st_eq_landau_n_rt_rp_r_intrlex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_ratd a0).
+
+(* notion 4256 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2r174_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_ratrlin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_2r174_t1 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_ratrl r).
+
+(* notion 4257 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz174 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_ratrl r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_2r174_t2 r x t i) : l_e_st_eq_landau_n_rt_rp_r_ratrl r).
+
+(* notion 4258 *)
+definition l_e_st_eq_landau_n_rt_rp_r_plusdr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pd x y) : Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4259 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pd a c)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pd b d)) (l_e_st_eq_landau_n_rt_rp_pd a c) (l_e_st_eq_landau_n_rt_rp_pd b d) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pd a c)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pd b d)) (l_e_st_eq_landau_n_rt_rp_eqpd12 a b c d e f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_plusdr a c) (l_e_st_eq_landau_n_rt_rp_r_plusdr b d)).
+
+(* notion 4260 *)
+definition l_e_st_eq_landau_n_rt_rp_r_fplusdr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.λu:l_e_st_eq_landau_n_rt_rp_r_eq z v.l_e_st_eq_landau_n_rt_rp_r_ivr3_t1 x y z v t u : l_e_st_eq_landau_n_rt_rp_r_fixf2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_plusdr).
+
+(* notion 4261 *)
+definition l_e_st_eq_landau_n_rt_rp_r_pl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_indreal2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_plusdr l_e_st_eq_landau_n_rt_rp_r_fplusdr r s : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4262 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isindreal2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_plusdr l_e_st_eq_landau_n_rt_rp_r_fplusdr r s a1 b1 a1ir b1is : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pd a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
+
+(* notion 4263 *)
+definition l_e_st_eq_landau_n_rt_rp_r_picp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_class x)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_pd a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pd a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_ivr3_t2 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_pl r s))).
+
+(* notion 4264 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ispl1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_pl x t) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
+
+(* notion 4265 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ispl2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_pl t x) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s)).
+
+(* notion 4266 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ispl12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_ispl1 r s t i) (l_e_st_eq_landau_n_rt_rp_r_ispl2 t u s j) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4267 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r175_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd175 a1 b1 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_pd b1 a1)).
+
+(* notion 4268 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r175_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r) (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_pd b1 a1) (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_picp s r b1 a1 b1is a1ir) (l_e_st_eq_landau_n_rt_rp_r_3r175_t1 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r)).
+
+(* notion 4269 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz175 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r175_t2 r s x y t u) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r)).
+
+(* notion 4270 *)
+definition l_e_st_eq_landau_n_rt_rp_r_compl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz175 r s : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r)).
+
+(* notion 4271 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_pd01 a1 b1 (l_e_st_eq_landau_n_rt_rp_r_0ex r a1 a1ir i) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd a1 b1) b1).
+
+(* notion 4272 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_pl r s) s (l_e_st_eq_landau_n_rt_rp_pd a1 b1) b1 (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is) b1is (l_e_st_eq_landau_n_rt_rp_r_ivr3_t3 r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) s).
+
+(* notion 4273 *)
+definition l_e_st_eq_landau_n_rt_rp_r_pl01 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr3_t4 r s x y t u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) s).
+
+(* notion 4274 *)
+definition l_e_st_eq_landau_n_rt_rp_r_pl02 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s r) r (l_e_st_eq_landau_n_rt_rp_r_compl r s) (l_e_st_eq_landau_n_rt_rp_r_pl01 s r i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r s) r).
+
+(* notion 4275 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_ppd a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex r a1 a1ir p) (l_e_st_eq_landau_n_rt_rp_r_posex s b1 b1is q) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_pd a1 b1)).
+
+(* notion 4276 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_ivr3_t5 r s a1 b1 a1ir b1is p q) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
+
+(* notion 4277 *)
+definition l_e_st_eq_landau_n_rt_rp_r_pospl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr3_t6 r s x y t u p q) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
+
+(* notion 4278 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_npd a1 b1 (l_e_st_eq_landau_n_rt_rp_r_negex r a1 a1ir n) (l_e_st_eq_landau_n_rt_rp_r_negex s b1 b1is o) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_pd a1 b1)).
+
+(* notion 4279 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_negin (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_ivr3_t7 r s a1 b1 a1ir b1is n o) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
+
+(* notion 4280 *)
+definition l_e_st_eq_landau_n_rt_rp_r_negpl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr3_t8 r s x y t u n o) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
+
+(* notion 4281 *)
+definition l_e_st_eq_landau_n_rt_rp_r_m0dr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_m0d x) : Πx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4282 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t5a ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_m0d a) (l_e_st_eq_landau_n_rt_rp_m0d b) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_m0d a)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_m0d b)) (l_e_st_eq_landau_n_rt_rp_eqm0d a b e) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0dr a) (l_e_st_eq_landau_n_rt_rp_r_m0dr b)).
+
+(* notion 4283 *)
+definition l_e_st_eq_landau_n_rt_rp_r_fm0dr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.l_e_st_eq_landau_n_rt_rp_r_ivr3_t5a x y t : l_e_st_eq_landau_n_rt_rp_r_fixf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_m0dr).
+
+(* notion 4284 *)
+definition l_e_st_eq_landau_n_rt_rp_r_m0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_indreal l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_m0dr l_e_st_eq_landau_n_rt_rp_r_fm0dr r : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4285 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t6a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_isindreal l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_m0dr l_e_st_eq_landau_n_rt_rp_r_fm0dr r a0 a0ir : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_m0d a0)) (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4286 *)
+definition l_e_st_eq_landau_n_rt_rp_r_micm0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_class x)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_m0d a0)) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_m0d a0)) (l_e_st_eq_landau_n_rt_rp_r_ivr3_t6a r a0 a0ir) : l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_m0 r))).
+
+(* notion 4287 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ism0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_m0 x) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
+
+(* notion 4288 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t7a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_absnd a0 (l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_m0d a0)).
+
+(* notion 4289 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t8a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_ivr3_t7a r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4290 *)
+definition l_e_st_eq_landau_n_rt_rp_r_absn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr3_t8a r x t n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4291 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λnn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).(l_e_st_eq_landau_n_rt_rp_absnnd a0 (l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd a0) (l_e_st_eq_landau_n_rt_rp_r_neg r) nn (λt:l_e_st_eq_landau_n_rt_rp_negd a0.l_e_st_eq_landau_n_rt_rp_r_negin r a0 a0ir t)) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd a0) a0).
+
+(* notion 4292 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr3_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λnn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_abs r) r (l_e_st_eq_landau_n_rt_rp_absd a0) a0 (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) a0ir (l_e_st_eq_landau_n_rt_rp_r_ivr3_t9 r a0 a0ir nn) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r).
+
+(* notion 4293 *)
+definition l_e_st_eq_landau_n_rt_rp_r_absnn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λnn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_ivr3_t10 r x t nn) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r).
+
+(* notion 4294 *)
+definition l_e_st_eq_landau_n_rt_rp_r_absp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_absnn r (l_e_st_eq_landau_n_rt_rp_r_pnotn r p) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r).
+
+(* notion 4295 *)
+definition l_e_st_eq_landau_n_rt_rp_r_abs0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs r) r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_absnn r (l_e_st_eq_landau_n_rt_rp_r_0notn r i)) i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4296 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_satzd176a a0 (l_e_st_eq_landau_n_rt_rp_r_posex r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_m0d a0)).
+
+(* notion 4297 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_negin (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_3r176_t1 r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4298 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz176a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t2 r x t p) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4299 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd176b a0 (l_e_st_eq_landau_n_rt_rp_r_0ex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_m0d a0)).
+
+(* notion 4300 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_3r176_t3 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4301 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz176b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t4 r x t i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4302 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_satzd176c a0 (l_e_st_eq_landau_n_rt_rp_r_negex r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_m0d a0)).
+
+(* notion 4303 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_3r176_t5 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4304 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz176c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t6 r x t n) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4305 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_satzd176d a0 (l_e_st_eq_landau_n_rt_rp_r_negex (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) n) : l_e_st_eq_landau_n_rt_rp_posd a0).
+
+(* notion 4306 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_posin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_3r176_t7 r a0 a0ir n) : l_e_st_eq_landau_n_rt_rp_r_pos r).
+
+(* notion 4307 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz176d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_pos r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t8 r x t n) : l_e_st_eq_landau_n_rt_rp_r_pos r).
+
+(* notion 4308 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd176e a0 (l_e_st_eq_landau_n_rt_rp_r_0ex (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) i) : l_e_st_eq_landau_n_rt_rp_zero a0).
+
+(* notion 4309 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_0in r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_3r176_t9 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4310 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz176e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t10 r x t i) : l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4311 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_satzd176f a0 (l_e_st_eq_landau_n_rt_rp_r_posex (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) p) : l_e_st_eq_landau_n_rt_rp_negd a0).
+
+(* notion 4312 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r176_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_negin r a0 a0ir (l_e_st_eq_landau_n_rt_rp_r_3r176_t11 r a0 a0ir p) : l_e_st_eq_landau_n_rt_rp_r_neg r).
+
+(* notion 4313 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz176f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_neg r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r176_t12 r x t p) : l_e_st_eq_landau_n_rt_rp_r_neg r).
+
+(* notion 4314 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r177_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_m0d a0)) a0 (l_e_st_eq_landau_n_rt_rp_r_micm0 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir)) a0ir (l_e_st_eq_landau_n_rt_rp_satzd177 a0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r).
+
+(* notion 4315 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz177 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r177_t1 r x t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r).
+
+(* notion 4316 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz177a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_r_satz177 r) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r))).
+
+(* notion 4317 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz177b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_ism0 r (l_e_st_eq_landau_n_rt_rp_r_m0 s) i) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) s).
+
+(* notion 4318 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz177c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 r) s (l_e_st_eq_landau_n_rt_rp_r_satz177b r s i) : l_e_st_eq_landau_n_rt_rp_r_is s (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4319 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz177d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) s.(l_e_st_eq_landau_n_rt_rp_r_satz177c s r (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 r) s i) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
+
+(* notion 4320 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz177e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) s.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_satz177d r s i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 s) r).
+
+(* notion 4321 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r178_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_m0d a0)) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_aica (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir)) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_satzd178 a0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_abs r)).
+
+(* notion 4322 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz178 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_abs r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r178_t1 r x t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_abs r)).
+
+(* notion 4323 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz178a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_satz178 r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_m0 r))).
+
+(* notion 4324 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r179_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_pd a0 (l_e_st_eq_landau_n_rt_rp_m0d a0)) (l_e_st_eq_landau_n_rt_rp_r_picp r (l_e_st_eq_landau_n_rt_rp_r_m0 r) a0 (l_e_st_eq_landau_n_rt_rp_m0d a0) a0ir (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir)) (l_e_st_eq_landau_n_rt_rp_satzd179 a0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 r)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4325 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz179 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 r)) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r179_t1 r x t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 r)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4326 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz179a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) r) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 r)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_m0 r) r) (l_e_st_eq_landau_n_rt_rp_r_satz179 r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) r) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4327 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r180_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_pd a1 b1)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1)) (l_e_st_eq_landau_n_rt_rp_r_micm0 (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is)) (l_e_st_eq_landau_n_rt_rp_r_picp (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_micm0 s b1 b1is)) (l_e_st_eq_landau_n_rt_rp_satzd180 a1 b1) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s))).
+
+(* notion 4328 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz180 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r180_t1 r s x y t u) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s))).
+
+(* notion 4329 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz180a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_satz180 r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl r s))).
+
+(* notion 4330 *)
+definition l_e_st_eq_landau_n_rt_rp_r_mn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_m0 s) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4331 *)
+definition l_e_st_eq_landau_n_rt_rp_r_micmn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_picp r (l_e_st_eq_landau_n_rt_rp_r_m0 s) a1 (l_e_st_eq_landau_n_rt_rp_m0d b1) a1ir (l_e_st_eq_landau_n_rt_rp_r_micm0 s b1 b1is) : l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_mn r s))).
+
+(* notion 4332 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ismn1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_ispl1 r s (l_e_st_eq_landau_n_rt_rp_r_m0 t) i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r t) (l_e_st_eq_landau_n_rt_rp_r_mn s t)).
+
+(* notion 4333 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ismn2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) t (l_e_st_eq_landau_n_rt_rp_r_ism0 r s i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn t r) (l_e_st_eq_landau_n_rt_rp_r_mn t s)).
+
+(* notion 4334 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ismn12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.(l_e_st_eq_landau_n_rt_rp_r_ispl12 r s (l_e_st_eq_landau_n_rt_rp_r_m0 t) (l_e_st_eq_landau_n_rt_rp_r_m0 u) i (l_e_st_eq_landau_n_rt_rp_r_ism0 t u j) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r t) (l_e_st_eq_landau_n_rt_rp_r_mn s u)).
+
+(* notion 4335 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz181 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_mn s r) (l_e_st_eq_landau_n_rt_rp_r_satz180 r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_satz177 s)) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (l_e_st_eq_landau_n_rt_rp_r_mn s r)).
+
+(* notion 4336 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz181a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn s r)) (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_satz181 s r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn s r))).
+
+(* notion 4337 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_satzd182a a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) p) : l_e_st_eq_landau_n_rt_rp_mored a1 b1).
+
+(* notion 4338 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_r_morein r s a1 b1 a1ir b1is (l_e_st_eq_landau_n_rt_rp_r_3r182_t1 r s a1 b1 a1ir b1is p) : l_e_st_eq_landau_n_rt_rp_r_more r s).
+
+(* notion 4339 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz182a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_more r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t2 r s x y t u p) : l_e_st_eq_landau_n_rt_rp_r_more r s).
+
+(* notion 4340 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd182b a1 b1 (l_e_st_eq_landau_n_rt_rp_r_0ex (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) i) : l_e_st_eq_landau_n_rt_rp_eq a1 b1).
+
+(* notion 4341 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_isin r s a1 b1 a1ir b1is (l_e_st_eq_landau_n_rt_rp_r_3r182_t3 r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4342 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz182b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t4 r s x y t u i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4343 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_satzd182c a1 b1 (l_e_st_eq_landau_n_rt_rp_r_negex (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) n) : l_e_st_eq_landau_n_rt_rp_lessd a1 b1).
+
+(* notion 4344 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_r_lessin r s a1 b1 a1ir b1is (l_e_st_eq_landau_n_rt_rp_r_3r182_t5 r s a1 b1 a1ir b1is n) : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4345 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz182c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_less r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t6 r s x y t u n) : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4346 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_satzd182d a1 b1 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_md a1 b1)).
+
+(* notion 4347 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_3r182_t7 r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
+
+(* notion 4348 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz182d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t8 r s x y t u m) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
+
+(* notion 4349 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_satzd182e a1 b1 (l_e_st_eq_landau_n_rt_rp_r_isex r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_md a1 b1)).
+
+(* notion 4350 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_3r182_t9 r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4351 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz182e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t10 r s x y t u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4352 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_satzd182f a1 b1 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_md a1 b1)).
+
+(* notion 4353 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r182_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_negin (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_md a1 b1) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_3r182_t11 r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
+
+(* notion 4354 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz182f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r182_t12 r s x y t u l) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
+
+(* notion 4355 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r183_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_satzd183a a1 b1 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1)).
+
+(* notion 4356 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r183_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_lessin (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_micm0 s b1 b1is) (l_e_st_eq_landau_n_rt_rp_r_3r183_t1 r s a1 b1 a1ir b1is m) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
+
+(* notion 4357 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz183a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r183_t2 r s x y t u m) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
+
+(* notion 4358 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz183b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_ism0 r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
+
+(* notion 4359 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r183_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_satzd183c a1 b1 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1)).
+
+(* notion 4360 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r183_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_morein (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_m0d a1) (l_e_st_eq_landau_n_rt_rp_m0d b1) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_micm0 s b1 b1is) (l_e_st_eq_landau_n_rt_rp_r_3r183_t3 r s a1 b1 a1ir b1is l) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
+
+(* notion 4361 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz183c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_3r183_t4 r s x y t u l) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)).
+
+(* notion 4362 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz183d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_satz177 r) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) (l_e_st_eq_landau_n_rt_rp_r_satz183c (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) l) : l_e_st_eq_landau_n_rt_rp_r_more r s).
+
+(* notion 4363 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz183e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_satz177a r) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) i) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4364 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz183f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_e_st_eq_landau_n_rt_rp_r_isless12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_satz177 r) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) (l_e_st_eq_landau_n_rt_rp_r_satz183a (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) m) : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4365 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_prop1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_and3 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos t) (l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) : Prop).
+
+(* notion 4366 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_3r184_prop1 r s x) : Prop).
+
+(* notion 4367 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_prop3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 r x) : Prop).
+
+(* notion 4368 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.(l_and3 (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_md a b)) : Prop).
+
+(* notion 4369 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.(l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a x) : Prop).
+
+(* notion 4370 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_and3e1 (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_md a b)) p1 : l_e_st_eq_landau_n_rt_rp_posd a).
+
+(* notion 4371 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_and3e2 (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_md a b)) p1 : l_e_st_eq_landau_n_rt_rp_posd b).
+
+(* notion 4372 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_and3e3 (l_e_st_eq_landau_n_rt_rp_posd a) (l_e_st_eq_landau_n_rt_rp_posd b) (l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_md a b)) p1 : l_e_st_eq_landau_n_rt_rp_eq a0 (l_e_st_eq_landau_n_rt_rp_md a b)).
+
+(* notion 4373 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_ra ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.(l_e_st_eq_landau_n_rt_rp_r_realof a : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4374 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_rb ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_e_st_eq_landau_n_rt_rp_r_realof b : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4375 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_e_st_eq_landau_n_rt_rp_r_innclass a : l_e_st_eq_landau_n_rt_rp_r_inn a (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2))).
+
+(* notion 4376 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_e_st_eq_landau_n_rt_rp_r_innclass b : l_e_st_eq_landau_n_rt_rp_r_inn b (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1))).
+
+(* notion 4377 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_e_st_eq_landau_n_rt_rp_r_isin r (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1)) a0 (l_e_st_eq_landau_n_rt_rp_md a b) a0ir (l_e_st_eq_landau_n_rt_rp_r_micmn (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1) a b (l_e_st_eq_landau_n_rt_rp_r_3r184_t4 r a0 a0ir a p2 b p1) (l_e_st_eq_landau_n_rt_rp_r_3r184_t5 r a0 a0ir a p2 b p1)) (l_e_st_eq_landau_n_rt_rp_r_3r184_t3 r a0 a0ir a p2 b p1) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1))).
+
+(* notion 4378 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_and3i (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1)) (l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1))) (l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) a (l_e_st_eq_landau_n_rt_rp_r_3r184_t4 r a0 a0ir a p2 b p1) (l_e_st_eq_landau_n_rt_rp_r_3r184_t1 r a0 a0ir a p2 b p1)) (l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1) b (l_e_st_eq_landau_n_rt_rp_r_3r184_t5 r a0 a0ir a p2 b p1) (l_e_st_eq_landau_n_rt_rp_r_3r184_t2 r a0 a0ir a p2 b p1)) (l_e_st_eq_landau_n_rt_rp_r_3r184_t6 r a0 a0ir a p2 b p1) : l_e_st_eq_landau_n_rt_rp_r_3r184_prop1 r (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1)).
+
+(* notion 4379 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.λb:l_e_st_eq_landau_n_rt_rp_dif.λp1:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a b.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_3r184_prop1 r (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) x) (l_e_st_eq_landau_n_rt_rp_r_3r184_rb r a0 a0ir a p2 b p1) (l_e_st_eq_landau_n_rt_rp_r_3r184_t7 r a0 a0ir a p2 b p1) : l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 r (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2)).
+
+(* notion 4380 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a x) p2 (l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 r (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_3r184_prop1d r a0 a0ir a x.l_e_st_eq_landau_n_rt_rp_r_3r184_t8 r a0 a0ir a p2 x t) : l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 r (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2)).
+
+(* notion 4381 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λa:l_e_st_eq_landau_n_rt_rp_dif.λp2:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir a.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_3r184_prop2 r x) (l_e_st_eq_landau_n_rt_rp_r_3r184_ra r a0 a0ir a p2) (l_e_st_eq_landau_n_rt_rp_r_3r184_t9 r a0 a0ir a p2) : l_e_st_eq_landau_n_rt_rp_r_3r184_prop3 r).
+
+(* notion 4382 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r184_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir x) (l_e_st_eq_landau_n_rt_rp_satzd184 a0) (l_e_st_eq_landau_n_rt_rp_r_3r184_prop3 r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_3r184_prop2d r a0 a0ir x.l_e_st_eq_landau_n_rt_rp_r_3r184_t10 r a0 a0ir x t) : l_e_st_eq_landau_n_rt_rp_r_3r184_prop3 r).
+
+(* notion 4383 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz184 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_3r184_prop3 r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_3r184_t11 r x t) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_some (λy:l_e_st_eq_landau_n_rt_rp_r_real.l_and3 (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_pos y) (l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_mn x y))))).
+
+(* notion 4384 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r185_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).(l_e_st_eq_landau_n_rt_rp_satzd185 a3 b3 c3 d3 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a3 b3) (l_e_st_eq_landau_n_rt_rp_md c3 d3)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a3 c3) (l_e_st_eq_landau_n_rt_rp_pd b3 d3))).
+
+(* notion 4385 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r185_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn t u)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_md a3 b3) (l_e_st_eq_landau_n_rt_rp_md c3 d3)) (l_e_st_eq_landau_n_rt_rp_md (l_e_st_eq_landau_n_rt_rp_pd a3 c3) (l_e_st_eq_landau_n_rt_rp_pd b3 d3)) (l_e_st_eq_landau_n_rt_rp_r_picp (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn t u) (l_e_st_eq_landau_n_rt_rp_md a3 b3) (l_e_st_eq_landau_n_rt_rp_md c3 d3) (l_e_st_eq_landau_n_rt_rp_r_micmn r s a3 b3 a3ir b3is) (l_e_st_eq_landau_n_rt_rp_r_micmn t u c3 d3 c3it d3iu)) (l_e_st_eq_landau_n_rt_rp_r_micmn (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_pd a3 c3) (l_e_st_eq_landau_n_rt_rp_pd b3 d3) (l_e_st_eq_landau_n_rt_rp_r_picp r t a3 c3 a3ir c3it) (l_e_st_eq_landau_n_rt_rp_r_picp s u b3 d3 b3is d3iu)) (l_e_st_eq_landau_n_rt_rp_r_3r185_t1 r s t u a3 b3 c3 d3 a3ir b3is c3it d3iu) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn t u)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u))).
+
+(* notion 4386 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz185 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp4 r s t u (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn t u)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).λvi:l_e_st_eq_landau_n_rt_rp_r_inn v (l_e_st_eq_landau_n_rt_rp_r_class u).l_e_st_eq_landau_n_rt_rp_r_3r185_t2 r s t u x y z v xi yi zi vi) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn t u)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u))).
+
+(* notion 4387 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r186_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_satzd186 a2 b2 c2 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a2 b2) c2) (l_e_st_eq_landau_n_rt_rp_pd a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2))).
+
+(* notion 4388 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r186_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pd a2 b2) c2) (l_e_st_eq_landau_n_rt_rp_pd a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2)) (l_e_st_eq_landau_n_rt_rp_r_picp (l_e_st_eq_landau_n_rt_rp_r_pl r s) t (l_e_st_eq_landau_n_rt_rp_pd a2 b2) c2 (l_e_st_eq_landau_n_rt_rp_r_picp r s a2 b2 a2ir b2is) c2it) (l_e_st_eq_landau_n_rt_rp_r_picp r (l_e_st_eq_landau_n_rt_rp_r_pl s t) a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2) a2ir (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it)) (l_e_st_eq_landau_n_rt_rp_r_3r186_t1 r s t a2 b2 c2 a2ir b2is c2it) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t))).
+
+(* notion 4389 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz186 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r186_t2 r s t x y z u v w) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t))).
+
+(* notion 4390 *)
+definition l_e_st_eq_landau_n_rt_rp_r_asspl1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz186 r s t : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t))).
+
+(* notion 4391 *)
+definition l_e_st_eq_landau_n_rt_rp_r_asspl2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_satz186 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl r s) t)).
+
+(* notion 4392 *)
+definition l_e_st_eq_landau_n_rt_rp_r_plmn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) s) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 s) s)) r (l_e_st_eq_landau_n_rt_rp_r_asspl1 r (l_e_st_eq_landau_n_rt_rp_r_m0 s) s) (l_e_st_eq_landau_n_rt_rp_r_pl02 r (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 s) s) (l_e_st_eq_landau_n_rt_rp_r_satz179a s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) s) r).
+
+(* notion 4393 *)
+definition l_e_st_eq_landau_n_rt_rp_r_mnpl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r s) s) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_m0 s))) r (l_e_st_eq_landau_n_rt_rp_r_asspl1 r s (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_pl02 r (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_satz179 s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl r s) s) r).
+
+(* notion 4394 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz187a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn r s) s) r (l_e_st_eq_landau_n_rt_rp_r_compl s (l_e_st_eq_landau_n_rt_rp_r_mn r s)) (l_e_st_eq_landau_n_rt_rp_r_plmn r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_mn r s)) r).
+
+(* notion 4395 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz187b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r) (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_satz187a r s) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r)).
+
+(* notion 4396 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz187c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x s) s) x (l_e_st_eq_landau_n_rt_rp_r_ismn1 r (l_e_st_eq_landau_n_rt_rp_r_pl x s) s (l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_pl x s) (l_e_st_eq_landau_n_rt_rp_r_pl s x) i (l_e_st_eq_landau_n_rt_rp_r_compl s x))) (l_e_st_eq_landau_n_rt_rp_r_mnpl x s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) x).
+
+(* notion 4397 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz187d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn r s) x (l_e_st_eq_landau_n_rt_rp_r_satz187c r s x i) : l_e_st_eq_landau_n_rt_rp_r_is x (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
+
+(* notion 4398 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz187e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl x s) r.(l_e_st_eq_landau_n_rt_rp_r_satz187c r s x (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl s x) (l_e_st_eq_landau_n_rt_rp_r_pl x s) r (l_e_st_eq_landau_n_rt_rp_r_compl s x) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn r s) x).
+
+(* notion 4399 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz187f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl x s) r.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn r s) x (l_e_st_eq_landau_n_rt_rp_r_satz187e r s x i) : l_e_st_eq_landau_n_rt_rp_r_is x (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
+
+(* notion 4400 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r187_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s y) r.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real x y (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_satz187c r s x i) (l_e_st_eq_landau_n_rt_rp_r_satz187c r s y j) : l_e_st_eq_landau_n_rt_rp_r_is x y).
+
+(* notion 4401 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r187_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r.λu:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s y) r.l_e_st_eq_landau_n_rt_rp_r_3r187_t1 r s x y t u : l_e_amone l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r)).
+
+(* notion 4402 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz187 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_onei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r) (l_e_st_eq_landau_n_rt_rp_r_3r187_t2 r s) (l_e_st_eq_landau_n_rt_rp_r_satz187b r s) : l_e_st_eq_landau_n_rt_rp_r_one (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl s x) r)).
+
+(* notion 4403 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r188_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_satzd188a a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_moreex (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2) (l_e_st_eq_landau_n_rt_rp_r_picp r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it) m) : l_e_st_eq_landau_n_rt_rp_mored a2 b2).
+
+(* notion 4404 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r188_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_morein r s a2 b2 a2ir b2is (l_e_st_eq_landau_n_rt_rp_r_3r188_t1 r s t a2 b2 c2 a2ir b2is c2it m) : l_e_st_eq_landau_n_rt_rp_r_more r s).
+
+(* notion 4405 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_more r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r188_t2 r s t x y z u v w m) : l_e_st_eq_landau_n_rt_rp_r_more r s).
+
+(* notion 4406 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r188_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_satzd188b a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2) (l_e_st_eq_landau_n_rt_rp_r_picp r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it) i) : l_e_st_eq_landau_n_rt_rp_eq a2 b2).
+
+(* notion 4407 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r188_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_isin r s a2 b2 a2ir b2is (l_e_st_eq_landau_n_rt_rp_r_3r188_t3 r s t a2 b2 c2 a2ir b2is c2it i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4408 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_is r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r188_t4 r s t x y z u v w i) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4409 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r188_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_satzd188c a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_lessex (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2) (l_e_st_eq_landau_n_rt_rp_r_picp r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it) l) : l_e_st_eq_landau_n_rt_rp_lessd a2 b2).
+
+(* notion 4410 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r188_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_lessin r s a2 b2 a2ir b2is (l_e_st_eq_landau_n_rt_rp_r_3r188_t5 r s t a2 b2 c2 a2ir b2is c2it l) : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4411 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t).(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r188_t6 r s t x y z u v w l) : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4412 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r188_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_satzd188d a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a2 b2 a2ir b2is m) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2)).
+
+(* notion 4413 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r188_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_morein (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2) (l_e_st_eq_landau_n_rt_rp_r_picp r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it) (l_e_st_eq_landau_n_rt_rp_r_3r188_t7 r s t a2 b2 c2 a2ir b2is c2it m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
+
+(* notion 4414 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r188_t8 r s t x y z u v w m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
+
+(* notion 4415 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_ispl1 r s t i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
+
+(* notion 4416 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r188_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_satzd188f a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_lessex r s a2 b2 a2ir b2is l) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2)).
+
+(* notion 4417 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r188_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_lessin (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_pd a2 c2) (l_e_st_eq_landau_n_rt_rp_pd b2 c2) (l_e_st_eq_landau_n_rt_rp_r_picp r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it) (l_e_st_eq_landau_n_rt_rp_r_3r188_t9 r s t a2 b2 c2 a2ir b2is c2it l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
+
+(* notion 4418 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_3r188_t10 r s t x y z u v w l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t)).
+
+(* notion 4419 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188g ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s).(l_e_st_eq_landau_n_rt_rp_r_satz188a r s t (l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t s) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_compl t r) (l_e_st_eq_landau_n_rt_rp_r_compl t s) m) : l_e_st_eq_landau_n_rt_rp_r_more r s).
+
+(* notion 4420 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188h ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s).(l_e_st_eq_landau_n_rt_rp_r_satz188b r s t (l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_compl r t) i (l_e_st_eq_landau_n_rt_rp_r_compl t s)) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4421 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188j ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s).(l_e_st_eq_landau_n_rt_rp_r_satz188c r s t (l_e_st_eq_landau_n_rt_rp_r_isless12 (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t s) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_compl t r) (l_e_st_eq_landau_n_rt_rp_r_compl t s) l) : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4422 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188k ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_pl t s) (l_e_st_eq_landau_n_rt_rp_r_compl r t) (l_e_st_eq_landau_n_rt_rp_r_compl s t) (l_e_st_eq_landau_n_rt_rp_r_satz188d r s t m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s)).
+
+(* notion 4423 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188l ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_ispl2 r s t i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s)).
+
+(* notion 4424 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188m ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_isless12 (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_pl t s) (l_e_st_eq_landau_n_rt_rp_r_compl r t) (l_e_st_eq_landau_n_rt_rp_r_compl s t) (l_e_st_eq_landau_n_rt_rp_r_satz188f r s t l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl t s)).
+
+(* notion 4425 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188n ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_more t u.(l_e_st_eq_landau_n_rt_rp_r_ismore2 (l_e_st_eq_landau_n_rt_rp_r_pl r u) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_ispl1 r s u i) (l_e_st_eq_landau_n_rt_rp_r_satz188k t u r m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4426 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188o ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λm:l_e_st_eq_landau_n_rt_rp_r_more t u.(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl u s) (l_e_st_eq_landau_n_rt_rp_r_compl r t) (l_e_st_eq_landau_n_rt_rp_r_compl s u) (l_e_st_eq_landau_n_rt_rp_r_satz188n r s t u i m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl u s)).
+
+(* notion 4427 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188p ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_less t u.(l_e_st_eq_landau_n_rt_rp_r_isless2 (l_e_st_eq_landau_n_rt_rp_r_pl r u) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_ispl1 r s u i) (l_e_st_eq_landau_n_rt_rp_r_satz188m t u r l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4428 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz188q ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λl:l_e_st_eq_landau_n_rt_rp_r_less t u.(l_e_st_eq_landau_n_rt_rp_r_isless12 (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl u s) (l_e_st_eq_landau_n_rt_rp_r_compl r t) (l_e_st_eq_landau_n_rt_rp_r_compl s u) (l_e_st_eq_landau_n_rt_rp_r_satz188p r s t u i l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl u s)).
+
+(* notion 4429 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz189 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_more t u.(l_e_st_eq_landau_n_rt_rp_r_trmore (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s t) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_satz188d r s t m) (l_e_st_eq_landau_n_rt_rp_r_satz188k t u s n) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4430 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz189a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_less t u.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_satz189 s r u t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) (l_e_st_eq_landau_n_rt_rp_r_lemma2 t u k)) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4431 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz190a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_more t u.(l_orapp (l_e_st_eq_landau_n_rt_rp_r_more r s) (l_e_st_eq_landau_n_rt_rp_r_is r s) (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)) m (λv:l_e_st_eq_landau_n_rt_rp_r_more r s.l_e_st_eq_landau_n_rt_rp_r_satz189 r s t u v n) (λv:l_e_st_eq_landau_n_rt_rp_r_is r s.l_e_st_eq_landau_n_rt_rp_r_satz188n r s t u v n) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4432 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz190b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis t u.(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pl t r) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl u s) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_compl t r) (l_e_st_eq_landau_n_rt_rp_r_compl u s) (l_e_st_eq_landau_n_rt_rp_r_satz190a t u r s n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4433 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz190c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_less t u.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_satz190a s r u t (l_e_st_eq_landau_n_rt_rp_r_satz168b r s l) (l_e_st_eq_landau_n_rt_rp_r_lemma2 t u k)) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4434 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz190d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis t u.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_satz190b s r u t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) (l_e_st_eq_landau_n_rt_rp_r_satz168b t u k)) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4435 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r191_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis t u.(l_e_st_eq_landau_n_rt_rp_satzd191 a3 b3 c3 d3 (l_e_st_eq_landau_n_rt_rp_r_moreisex r s a3 b3 a3ir b3is m) (l_e_st_eq_landau_n_rt_rp_r_moreisex t u c3 d3 c3it d3iu n) : l_e_st_eq_landau_n_rt_rp_moreq (l_e_st_eq_landau_n_rt_rp_pd a3 c3) (l_e_st_eq_landau_n_rt_rp_pd b3 d3)).
+
+(* notion 4436 *)
+definition l_e_st_eq_landau_n_rt_rp_r_3r191_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis t u.(l_e_st_eq_landau_n_rt_rp_r_moreisin (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_pd a3 c3) (l_e_st_eq_landau_n_rt_rp_pd b3 d3) (l_e_st_eq_landau_n_rt_rp_r_picp r t a3 c3 a3ir c3it) (l_e_st_eq_landau_n_rt_rp_r_picp s u b3 d3 b3is d3iu) (l_e_st_eq_landau_n_rt_rp_r_3r191_t1 r s t u a3 b3 c3 d3 a3ir b3is c3it d3iu m n) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4437 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz191 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis t u.(l_e_st_eq_landau_n_rt_rp_r_realapp4 r s t u (l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.λxi:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λyi:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).λvi:l_e_st_eq_landau_n_rt_rp_r_inn v (l_e_st_eq_landau_n_rt_rp_r_class u).l_e_st_eq_landau_n_rt_rp_r_3r191_t2 r s t u x y z v xi yi zi vi m n) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4438 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz191a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_lessis r s.λk:l_e_st_eq_landau_n_rt_rp_r_lessis t u.(l_e_st_eq_landau_n_rt_rp_r_satz168a (l_e_st_eq_landau_n_rt_rp_r_pl s u) (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_satz191 s r u t (l_e_st_eq_landau_n_rt_rp_r_satz168b r s l) (l_e_st_eq_landau_n_rt_rp_r_satz168b t u k)) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl r t) (l_e_st_eq_landau_n_rt_rp_r_pl s u)).
+
+(* notion 4439 *)
+definition l_e_st_eq_landau_n_rt_rp_r_timesdr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_td x y) : Πx:l_e_st_eq_landau_n_rt_rp_dif.Πy:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4440 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_dif.λb:l_e_st_eq_landau_n_rt_rp_dif.λc:l_e_st_eq_landau_n_rt_rp_dif.λd:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq a b.λf:l_e_st_eq_landau_n_rt_rp_eq c d.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_td b d)) (l_e_st_eq_landau_n_rt_rp_td a c) (l_e_st_eq_landau_n_rt_rp_td b d) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_td a c)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_td b d)) (l_e_st_eq_landau_n_rt_rp_eqtd12 a b c d e f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_timesdr a c) (l_e_st_eq_landau_n_rt_rp_r_timesdr b d)).
+
+(* notion 4441 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ftimesdr ≝ (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_eq x y.λu:l_e_st_eq_landau_n_rt_rp_r_eq z v.l_e_st_eq_landau_n_rt_rp_r_ivr4_t1 x y z v t u : l_e_st_eq_landau_n_rt_rp_r_fixf2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_timesdr).
+
+(* notion 4442 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ts ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_indreal2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_timesdr l_e_st_eq_landau_n_rt_rp_r_ftimesdr r s : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4443 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isindreal2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_timesdr l_e_st_eq_landau_n_rt_rp_r_ftimesdr r s a1 b1 a1ir b1is : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 4444 *)
+definition l_e_st_eq_landau_n_rt_rp_r_tict ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_class x)) (l_e_st_eq_landau_n_rt_rp_r_realof (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_ivr4_t2 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_inn (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_class (l_e_st_eq_landau_n_rt_rp_r_ts r s))).
+
+(* notion 4445 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ists1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_ts x t) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
+
+(* notion 4446 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ists2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_ts t x) r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
+
+(* notion 4447 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ists12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.λj:l_e_st_eq_landau_n_rt_rp_r_is t u.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_ts s u) (l_e_st_eq_landau_n_rt_rp_r_ists1 r s t i) (l_e_st_eq_landau_n_rt_rp_r_ists2 t u s j) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s u)).
+
+(* notion 4448 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r192_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd192a a1 b1 (l_e_st_eq_landau_n_rt_rp_r_0ex r a1 a1ir i) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a1 b1)).
+
+(* notion 4449 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r192_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_4r192_t1 r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4450 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz192a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r192_t2 r s x y t u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4451 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r192_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd192b a1 b1 (l_e_st_eq_landau_n_rt_rp_r_0ex s b1 b1is i) : l_e_st_eq_landau_n_rt_rp_zero (l_e_st_eq_landau_n_rt_rp_td a1 b1)).
+
+(* notion 4452 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r192_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_0in (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_4r192_t3 r s a1 b1 a1ir b1is i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4453 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz192b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r192_t4 r s x y t u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4454 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r192_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd192c a1 b1 (l_e_st_eq_landau_n_rt_rp_r_0ex (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) i) : l_or (l_e_st_eq_landau_n_rt_rp_zero a1) (l_e_st_eq_landau_n_rt_rp_zero b1)).
+
+(* notion 4455 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r192_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_zero a1) (l_e_st_eq_landau_n_rt_rp_zero b1) (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_4r192_t5 r s a1 b1 a1ir b1is i) (λt:l_e_st_eq_landau_n_rt_rp_zero a1.l_e_st_eq_landau_n_rt_rp_r_0in r a1 a1ir t) (λt:l_e_st_eq_landau_n_rt_rp_zero b1.l_e_st_eq_landau_n_rt_rp_r_0in s b1 b1is t) : l_or (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 4456 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz192c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_or (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r192_t6 r s x y t u i) : l_or (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 4457 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz192d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.λo:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_or (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0)) (l_or_th3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0) n o) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_satz192c r s t) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4458 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ts01 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz192a r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4459 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ts02 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz192b r s i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4460 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r193_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd193 a1 b1 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1))).
+
+(* notion 4461 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r193_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_absd (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)) (l_e_st_eq_landau_n_rt_rp_r_aica (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is)) (l_e_st_eq_landau_n_rt_rp_r_4r193_t1 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
+
+(* notion 4462 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz193 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r193_t2 r s x y t u) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
+
+(* notion 4463 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz193a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_satz193 r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s))).
+
+(* notion 4464 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r194_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd194 a1 b1 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_td b1 a1)).
+
+(* notion 4465 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r194_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_td b1 a1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_tict s r b1 a1 b1is a1ir) (l_e_st_eq_landau_n_rt_rp_r_4r194_t1 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r)).
+
+(* notion 4466 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz194 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r194_t2 r s x y t u) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r)).
+
+(* notion 4467 *)
+definition l_e_st_eq_landau_n_rt_rp_r_comts ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz194 r s : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r)).
+
+(* notion 4468 *)
+definition l_e_st_eq_landau_n_rt_rp_r_1rl ≝ (l_e_st_eq_landau_n_rt_rp_r_realof l_e_st_eq_landau_n_rt_rp_1df : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4469 *)
+definition l_e_st_eq_landau_n_rt_rp_r_pos1 ≝ (l_e_st_eq_landau_n_rt_rp_r_posin l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_1df (l_e_st_eq_landau_n_rt_rp_r_innclass l_e_st_eq_landau_n_rt_rp_1df) (l_e_st_eq_landau_n_rt_rp_posdirp l_e_st_eq_landau_n_rt_rp_1rp) : l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_1rl).
+
+(* notion 4470 *)
+definition l_e_st_eq_landau_n_rt_rp_r_natrl1 ≝ (l_e_st_eq_landau_n_rt_rp_r_natrli l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_rt_rp_r_natrl l_e_st_eq_landau_n_rt_rp_r_1rl).
+
+(* notion 4471 *)
+definition l_e_st_eq_landau_n_rt_rp_r_intrl1 ≝ (l_e_st_eq_landau_n_rt_rp_r_natintrl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_natrl1 : l_e_st_eq_landau_n_rt_rp_r_intrl l_e_st_eq_landau_n_rt_rp_r_1rl).
+
+(* notion 4472 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r195_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_satzd195 a0 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 l_e_st_eq_landau_n_rt_rp_1df) a0).
+
+(* notion 4473 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r195_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r (l_e_st_eq_landau_n_rt_rp_td a0 l_e_st_eq_landau_n_rt_rp_1df) a0 (l_e_st_eq_landau_n_rt_rp_r_tict r l_e_st_eq_landau_n_rt_rp_r_1rl a0 l_e_st_eq_landau_n_rt_rp_1df a0ir (l_e_st_eq_landau_n_rt_rp_r_innclass l_e_st_eq_landau_n_rt_rp_1df)) a0ir (l_e_st_eq_landau_n_rt_rp_r_4r195_t1 r a0 a0ir) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r).
+
+(* notion 4474 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz195 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_4r195_t2 r x t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r).
+
+(* notion 4475 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz195a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r (l_e_st_eq_landau_n_rt_rp_r_satz195 r) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl)).
+
+(* notion 4476 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz195b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_1rl) r (l_e_st_eq_landau_n_rt_rp_r_comts l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_satz195 r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) r).
+
+(* notion 4477 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz195c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) r (l_e_st_eq_landau_n_rt_rp_r_satz195b r) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r)).
+
+(* notion 4478 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz196a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_abs r) r (l_e_st_eq_landau_n_rt_rp_r_abs s) s (l_e_st_eq_landau_n_rt_rp_r_absp r p) (l_e_st_eq_landau_n_rt_rp_r_absp s q)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
+
+(* notion 4479 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_satzd196b a1 b1 (l_e_st_eq_landau_n_rt_rp_r_negex r a1 a1ir n) (l_e_st_eq_landau_n_rt_rp_r_negex s b1 b1is o) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1))).
+
+(* notion 4480 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is)) (l_e_st_eq_landau_n_rt_rp_r_4r196_t1 r s a1 b1 a1ir b1is n o) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
+
+(* notion 4481 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz196b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r196_t2 r s x y t u n o) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
+
+(* notion 4482 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t1a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_satzd196c a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex r a1 a1ir p) (l_e_st_eq_landau_n_rt_rp_r_negex s b1 b1is n) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)))).
+
+(* notion 4483 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t2a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1))) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_micm0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is))) (l_e_st_eq_landau_n_rt_rp_r_4r196_t1a r s a1 b1 a1ir b1is p n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)))).
+
+(* notion 4484 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz196c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r196_t2a r s x y t u p n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)))).
+
+(* notion 4485 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz196d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts s r) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_abs r))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))) (l_e_st_eq_landau_n_rt_rp_r_comts r s) (l_e_st_eq_landau_n_rt_rp_r_satz196c s r p n) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_abs r)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_abs r))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)))).
+
+(* notion 4486 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero a0) (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) n (λt:l_e_st_eq_landau_n_rt_rp_zero a0.l_e_st_eq_landau_n_rt_rp_r_0in r a0 a0ir t) : l_not (l_e_st_eq_landau_n_rt_rp_zero a0)).
+
+(* notion 4487 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).(l_e_st_eq_landau_n_rt_rp_satzd196e a1 b1 (l_e_st_eq_landau_n_rt_rp_r_4r196_t3 r a1 a1ir n) (l_e_st_eq_landau_n_rt_rp_r_4r196_t3 s b1 b1is o) (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is)) i) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1))).
+
+(* notion 4488 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).λa:l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1).(l_andi (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_posin r a1 a1ir (l_ande1 (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1) a)) (l_e_st_eq_landau_n_rt_rp_r_posin s b1 b1is (l_ande2 (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1) a)) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)).
+
+(* notion 4489 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).λa:l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1).(l_andi (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_negin r a1 a1ir (l_ande1 (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1) a)) (l_e_st_eq_landau_n_rt_rp_r_negin s b1 b1is (l_ande2 (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1) a)) : l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s)).
+
+(* notion 4490 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).(l_or_th9 (l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_4r196_t4 r s a1 b1 a1ir b1is n o i) (λt:l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_posd b1).l_e_st_eq_landau_n_rt_rp_r_4r196_t5 r s a1 b1 a1ir b1is n o i t) (λt:l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_negd b1).l_e_st_eq_landau_n_rt_rp_r_4r196_t6 r s a1 b1 a1ir b1is n o i t) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s))).
+
+(* notion 4491 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz196e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r196_t7 r s x y t u n o i) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s))).
+
+(* notion 4492 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).(l_e_st_eq_landau_n_rt_rp_satzd196f a1 b1 (l_e_st_eq_landau_n_rt_rp_r_4r196_t3 r a1 a1ir n) (l_e_st_eq_landau_n_rt_rp_r_4r196_t3 s b1 b1is o) (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1))) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_micm0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_absd a1) (l_e_st_eq_landau_n_rt_rp_absd b1) (l_e_st_eq_landau_n_rt_rp_r_aica r a1 a1ir) (l_e_st_eq_landau_n_rt_rp_r_aica s b1 b1is))) i) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1))).
+
+(* notion 4493 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).λa:l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1).(l_andi (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_posin r a1 a1ir (l_ande1 (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1) a)) (l_e_st_eq_landau_n_rt_rp_r_negin s b1 b1is (l_ande2 (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1) a)) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)).
+
+(* notion 4494 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).λa:l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1).(l_andi (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_negin r a1 a1ir (l_ande1 (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1) a)) (l_e_st_eq_landau_n_rt_rp_r_posin s b1 b1is (l_ande2 (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1) a)) : l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s)).
+
+(* notion 4495 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).(l_or_th9 (l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1)) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_e_st_eq_landau_n_rt_rp_r_4r196_t8 r s a1 b1 a1ir b1is n o i) (λt:l_and (l_e_st_eq_landau_n_rt_rp_posd a1) (l_e_st_eq_landau_n_rt_rp_negd b1).l_e_st_eq_landau_n_rt_rp_r_4r196_t9 r s a1 b1 a1ir b1is n o i t) (λt:l_and (l_e_st_eq_landau_n_rt_rp_negd a1) (l_e_st_eq_landau_n_rt_rp_posd b1).l_e_st_eq_landau_n_rt_rp_r_4r196_t10 r s a1 b1 a1ir b1is n o i t) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s))).
+
+(* notion 4496 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz196f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r196_t11 r s x y t u n o i) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s))).
+
+(* notion 4497 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_ts r s) p) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_ts01 r s t) : l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4498 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t13 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_ts r s) p) (λt:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_ts02 r s t) : l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4499 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t14 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_absp (l_e_st_eq_landau_n_rt_rp_r_ts r s) p) (l_e_st_eq_landau_n_rt_rp_r_satz193 r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s))).
+
+(* notion 4500 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz196g ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_e_st_eq_landau_n_rt_rp_r_satz196e r s (l_e_st_eq_landau_n_rt_rp_r_4r196_t12 r s p) (l_e_st_eq_landau_n_rt_rp_r_4r196_t13 r s p) (l_e_st_eq_landau_n_rt_rp_r_4r196_t14 r s p) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_pos s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_neg s))).
+
+(* notion 4501 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t15 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_nnot0 (l_e_st_eq_landau_n_rt_rp_r_ts r s) n) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_ts01 r s t) : l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4502 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t16 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_nnot0 (l_e_st_eq_landau_n_rt_rp_r_ts r s) n) (λt:l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_ts02 r s t) : l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4503 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r196_t17 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_e_st_eq_landau_n_rt_rp_r_satz177c (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_satz193a r s) (l_e_st_eq_landau_n_rt_rp_r_absn (l_e_st_eq_landau_n_rt_rp_r_ts r s) n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs s)))).
+
+(* notion 4504 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz196h ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s).(l_e_st_eq_landau_n_rt_rp_r_satz196f r s (l_e_st_eq_landau_n_rt_rp_r_4r196_t15 r s n) (l_e_st_eq_landau_n_rt_rp_r_4r196_t16 r s n) (l_e_st_eq_landau_n_rt_rp_r_4r196_t17 r s n) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_pos s))).
+
+(* notion 4505 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r197_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_satzd197a a1 b1 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a1) b1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a1 b1))).
+
+(* notion 4506 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r197_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_m0d a1) b1) (l_e_st_eq_landau_n_rt_rp_m0d (l_e_st_eq_landau_n_rt_rp_td a1 b1)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_m0 r) s (l_e_st_eq_landau_n_rt_rp_m0d a1) b1 (l_e_st_eq_landau_n_rt_rp_r_micm0 r a1 a1ir) b1is) (l_e_st_eq_landau_n_rt_rp_r_micm0 (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is)) (l_e_st_eq_landau_n_rt_rp_r_4r197_t1 r s a1 b1 a1ir b1is) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s))).
+
+(* notion 4507 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz197a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r197_t2 r s x y t u) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s))).
+
+(* notion 4508 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz197b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 s) r) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts s r)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_comts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_satz197a s r) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_ts s r) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_comts s r)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s))).
+
+(* notion 4509 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz197c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_satz197a r s) (l_e_st_eq_landau_n_rt_rp_r_satz197b r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s))).
+
+(* notion 4510 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz197d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_satz197c r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s)).
+
+(* notion 4511 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz197e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_satz197a r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) s)).
+
+(* notion 4512 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz197f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_satz197b r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 s))).
+
+(* notion 4513 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz198 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s))) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_satz197c r (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s r (l_e_st_eq_landau_n_rt_rp_r_satz177 s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 4514 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz198a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_satz198 r s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s))).
+
+(* notion 4515 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_ptdpp a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex r a1 a1ir p) (l_e_st_eq_landau_n_rt_rp_r_posex s b1 b1is q) : l_e_st_eq_landau_n_rt_rp_posd (l_e_st_eq_landau_n_rt_rp_td a1 b1)).
+
+(* notion 4516 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_posin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_ivr4_t3 r s a1 b1 a1ir b1is p q) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 4517 *)
+definition l_e_st_eq_landau_n_rt_rp_r_postspp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr4_t4 r s x y t u p q) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 4518 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_ntdpn a1 b1 (l_e_st_eq_landau_n_rt_rp_r_posex r a1 a1ir p) (l_e_st_eq_landau_n_rt_rp_r_negex s b1 b1is n) : l_e_st_eq_landau_n_rt_rp_negd (l_e_st_eq_landau_n_rt_rp_td a1 b1)).
+
+(* notion 4519 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr4_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_negin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_ivr4_t5 r s a1 b1 a1ir b1is p n) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 4520 *)
+definition l_e_st_eq_landau_n_rt_rp_r_negtspn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λn:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_ivr4_t6 r s x y t u p n) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 4521 *)
+definition l_e_st_eq_landau_n_rt_rp_r_negtsnp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_isneg (l_e_st_eq_landau_n_rt_rp_r_ts s r) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_comts s r) (l_e_st_eq_landau_n_rt_rp_r_negtspn s r p n) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 4522 *)
+definition l_e_st_eq_landau_n_rt_rp_r_postsnn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.λo:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_e_st_eq_landau_n_rt_rp_r_ispos (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_satz198 r s) (l_e_st_eq_landau_n_rt_rp_r_postspp (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_satz176c r n) (l_e_st_eq_landau_n_rt_rp_r_satz176c s o)) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 4523 *)
+definition l_e_st_eq_landau_n_rt_rp_r_possq ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_rapp r (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r r)) (λt:l_e_st_eq_landau_n_rt_rp_r_pos r.l_e_st_eq_landau_n_rt_rp_r_postspp r r t t) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r r)) n) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_postsnn r r t t) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts r r)).
+
+(* notion 4524 *)
+definition l_e_st_eq_landau_n_rt_rp_r_nnegsq ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r r))) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_0notn (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_satz192a r r t)) (λt:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_pnotn (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_possq r t)) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r r))).
+
+(* notion 4525 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r199_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_satzd199 a2 b2 c2 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a2 b2) c2) (l_e_st_eq_landau_n_rt_rp_td a2 (l_e_st_eq_landau_n_rt_rp_td b2 c2))).
+
+(* notion 4526 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r199_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_td a2 b2) c2) (l_e_st_eq_landau_n_rt_rp_td a2 (l_e_st_eq_landau_n_rt_rp_td b2 c2)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_ts r s) t (l_e_st_eq_landau_n_rt_rp_td a2 b2) c2 (l_e_st_eq_landau_n_rt_rp_r_tict r s a2 b2 a2ir b2is) c2it) (l_e_st_eq_landau_n_rt_rp_r_tict r (l_e_st_eq_landau_n_rt_rp_r_ts s t) a2 (l_e_st_eq_landau_n_rt_rp_td b2 c2) a2ir (l_e_st_eq_landau_n_rt_rp_r_tict s t b2 c2 b2is c2it)) (l_e_st_eq_landau_n_rt_rp_r_4r199_t1 r s t a2 b2 c2 a2ir b2is c2it) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t))).
+
+(* notion 4527 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz199 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_4r199_t2 r s t x y z u v w) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t))).
+
+(* notion 4528 *)
+definition l_e_st_eq_landau_n_rt_rp_r_assts1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz199 r s t : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t))).
+
+(* notion 4529 *)
+definition l_e_st_eq_landau_n_rt_rp_r_assts2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_satz199 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r s) t)).
+
+(* notion 4530 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r201_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_satzd201 a2 b2 c2 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a2 b2) (l_e_st_eq_landau_n_rt_rp_td a2 c2))).
+
+(* notion 4531 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r201_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_td a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_td a2 b2) (l_e_st_eq_landau_n_rt_rp_td a2 c2)) (l_e_st_eq_landau_n_rt_rp_r_tict r (l_e_st_eq_landau_n_rt_rp_r_pl s t) a2 (l_e_st_eq_landau_n_rt_rp_pd b2 c2) a2ir (l_e_st_eq_landau_n_rt_rp_r_picp s t b2 c2 b2is c2it)) (l_e_st_eq_landau_n_rt_rp_r_picp (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_td a2 b2) (l_e_st_eq_landau_n_rt_rp_td a2 c2) (l_e_st_eq_landau_n_rt_rp_r_tict r s a2 b2 a2ir b2is) (l_e_st_eq_landau_n_rt_rp_r_tict r t a2 c2 a2ir c2it)) (l_e_st_eq_landau_n_rt_rp_r_4r201_t1 r s t a2 b2 c2 a2ir b2is c2it) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
+
+(* notion 4532 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz201 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_4r201_t2 r s t x y z u v w) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
+
+(* notion 4533 *)
+definition l_e_st_eq_landau_n_rt_rp_r_disttp1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_satz201 t r s) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts t s) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_comts t r) (l_e_st_eq_landau_n_rt_rp_r_comts t s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t))).
+
+(* notion 4534 *)
+definition l_e_st_eq_landau_n_rt_rp_r_disttp2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz201 r s t : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
+
+(* notion 4535 *)
+definition l_e_st_eq_landau_n_rt_rp_r_distpt1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pl r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pl r s) t)).
+
+(* notion 4536 *)
+definition l_e_st_eq_landau_n_rt_rp_r_distpt2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_disttp2 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_pl s t))).
+
+(* notion 4537 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz202 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 t))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_disttp2 r s (l_e_st_eq_landau_n_rt_rp_r_m0 t)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_m0 t)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_satz197b r t)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
+
+(* notion 4538 *)
+definition l_e_st_eq_landau_n_rt_rp_r_disttm1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_mn r s) t) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 s) t)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 r (l_e_st_eq_landau_n_rt_rp_r_m0 s) t) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 s) t) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_satz197a s t)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_mn r s) t) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t))).
+
+(* notion 4539 *)
+definition l_e_st_eq_landau_n_rt_rp_r_disttm2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz202 r s t : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
+
+(* notion 4540 *)
+definition l_e_st_eq_landau_n_rt_rp_r_distmt1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_mn r s) t) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_disttm1 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_mn r s) t)).
+
+(* notion 4541 *)
+definition l_e_st_eq_landau_n_rt_rp_r_distmt2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_disttm2 r s t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t))).
+
+(* notion 4542 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz200 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz202 r s t : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_mn s t)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r t))).
+
+(* notion 4543 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r203_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_satzd203a a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a2 b2 a2ir b2is m) (l_e_st_eq_landau_n_rt_rp_r_posex t c2 c2it p) : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_td a2 c2) (l_e_st_eq_landau_n_rt_rp_td b2 c2)).
+
+(* notion 4544 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r203_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_r_morein (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_td a2 c2) (l_e_st_eq_landau_n_rt_rp_td b2 c2) (l_e_st_eq_landau_n_rt_rp_r_tict r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_tict s t b2 c2 b2is c2it) (l_e_st_eq_landau_n_rt_rp_r_4r203_t1 r s t a2 b2 c2 a2ir b2is c2it m p) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
+
+(* notion 4545 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_4r203_t2 r s t x y z u v w m p) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
+
+(* notion 4546 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λi:l_e_st_eq_landau_n_rt_rp_r_is t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts02 r t i) (l_e_st_eq_landau_n_rt_rp_r_ts02 s t i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
+
+(* notion 4547 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r203_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_satzd203c a2 b2 c2 (l_e_st_eq_landau_n_rt_rp_r_moreex r s a2 b2 a2ir b2is m) (l_e_st_eq_landau_n_rt_rp_r_negex t c2 c2it n) : l_e_st_eq_landau_n_rt_rp_lessd (l_e_st_eq_landau_n_rt_rp_td a2 c2) (l_e_st_eq_landau_n_rt_rp_td b2 c2)).
+
+(* notion 4548 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r203_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λa2:l_e_st_eq_landau_n_rt_rp_dif.λb2:l_e_st_eq_landau_n_rt_rp_dif.λc2:l_e_st_eq_landau_n_rt_rp_dif.λa2ir:l_e_st_eq_landau_n_rt_rp_r_inn a2 (l_e_st_eq_landau_n_rt_rp_r_class r).λb2is:l_e_st_eq_landau_n_rt_rp_r_inn b2 (l_e_st_eq_landau_n_rt_rp_r_class s).λc2it:l_e_st_eq_landau_n_rt_rp_r_inn c2 (l_e_st_eq_landau_n_rt_rp_r_class t).λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_r_lessin (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_td a2 c2) (l_e_st_eq_landau_n_rt_rp_td b2 c2) (l_e_st_eq_landau_n_rt_rp_r_tict r t a2 c2 a2ir c2it) (l_e_st_eq_landau_n_rt_rp_r_tict s t b2 c2 b2is c2it) (l_e_st_eq_landau_n_rt_rp_r_4r203_t3 r s t a2 b2 c2 a2ir b2is c2it m n) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
+
+(* notion 4549 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_r_realapp3 r s t (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_4r203_t4 r s t x y z u v w m n) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
+
+(* notion 4550 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_ts t s) (l_e_st_eq_landau_n_rt_rp_r_comts r t) (l_e_st_eq_landau_n_rt_rp_r_comts s t) (l_e_st_eq_landau_n_rt_rp_r_satz203a r s t m p) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
+
+(* notion 4551 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λi:l_e_st_eq_landau_n_rt_rp_r_is t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 t r i) (l_e_st_eq_landau_n_rt_rp_r_ts01 t s i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
+
+(* notion 4552 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_r_isless12 (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_ts t s) (l_e_st_eq_landau_n_rt_rp_r_comts r t) (l_e_st_eq_landau_n_rt_rp_r_comts s t) (l_e_st_eq_landau_n_rt_rp_r_satz203c r s t m n) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
+
+(* notion 4553 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203g ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_satz203a s r t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) p) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
+
+(* notion 4554 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203h ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λi:l_e_st_eq_landau_n_rt_rp_r_is t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts02 r t i) (l_e_st_eq_landau_n_rt_rp_r_ts02 s t i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
+
+(* notion 4555 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203j ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_r_lemma2 (l_e_st_eq_landau_n_rt_rp_r_ts s t) (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_satz203c s r t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) n) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts r t) (l_e_st_eq_landau_n_rt_rp_r_ts s t)).
+
+(* notion 4556 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203k ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos t.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_ts t s) (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_satz203d s r t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) p) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
+
+(* notion 4557 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203l ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λi:l_e_st_eq_landau_n_rt_rp_r_is t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 t r i) (l_e_st_eq_landau_n_rt_rp_r_ts01 t s i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
+
+(* notion 4558 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz203m ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λn:l_e_st_eq_landau_n_rt_rp_r_neg t.(l_e_st_eq_landau_n_rt_rp_r_lemma2 (l_e_st_eq_landau_n_rt_rp_r_ts t s) (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_satz203f s r t (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) n) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts t r) (l_e_st_eq_landau_n_rt_rp_r_ts t s)).
+
+(* notion 4559 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λn1:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_zero a0) (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) n1 (λt:l_e_st_eq_landau_n_rt_rp_zero a0.l_e_st_eq_landau_n_rt_rp_r_0in r a0 a0ir t) : l_not (l_e_st_eq_landau_n_rt_rp_zero a0)).
+
+(* notion 4560 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s t) r.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s u) r.(l_e_st_eq_landau_n_rt_rp_satzd204b a3 b3 (l_e_st_eq_landau_n_rt_rp_r_4r204_t1 s b3 b3is n1) c3 d3 (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts s t) r (l_e_st_eq_landau_n_rt_rp_td b3 c3) a3 (l_e_st_eq_landau_n_rt_rp_r_tict s t b3 c3 b3is c3it) a3ir i) (l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts s u) r (l_e_st_eq_landau_n_rt_rp_td b3 d3) a3 (l_e_st_eq_landau_n_rt_rp_r_tict s u b3 d3 b3is d3iu) a3ir j) : l_e_st_eq_landau_n_rt_rp_eq c3 d3).
+
+(* notion 4561 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa3:l_e_st_eq_landau_n_rt_rp_dif.λb3:l_e_st_eq_landau_n_rt_rp_dif.λc3:l_e_st_eq_landau_n_rt_rp_dif.λd3:l_e_st_eq_landau_n_rt_rp_dif.λa3ir:l_e_st_eq_landau_n_rt_rp_r_inn a3 (l_e_st_eq_landau_n_rt_rp_r_class r).λb3is:l_e_st_eq_landau_n_rt_rp_r_inn b3 (l_e_st_eq_landau_n_rt_rp_r_class s).λc3it:l_e_st_eq_landau_n_rt_rp_r_inn c3 (l_e_st_eq_landau_n_rt_rp_r_class t).λd3iu:l_e_st_eq_landau_n_rt_rp_r_inn d3 (l_e_st_eq_landau_n_rt_rp_r_class u).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s t) r.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s u) r.(l_e_st_eq_landau_n_rt_rp_r_isin t u c3 d3 c3it d3iu (l_e_st_eq_landau_n_rt_rp_r_4r204_t2 r s t u a3 b3 c3 d3 a3ir b3is c3it d3iu n1 i j) : l_e_st_eq_landau_n_rt_rp_r_is t u).
+
+(* notion 4562 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz204b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s y) r.(l_e_st_eq_landau_n_rt_rp_r_realapp4 r s x y (l_e_st_eq_landau_n_rt_rp_r_is x y) (λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_dif.λw:l_e_st_eq_landau_n_rt_rp_dif.λzi:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class r).λui:l_e_st_eq_landau_n_rt_rp_r_inn u (l_e_st_eq_landau_n_rt_rp_r_class s).λvi:l_e_st_eq_landau_n_rt_rp_r_inn v (l_e_st_eq_landau_n_rt_rp_r_class x).λwi:l_e_st_eq_landau_n_rt_rp_r_inn w (l_e_st_eq_landau_n_rt_rp_r_class y).l_e_st_eq_landau_n_rt_rp_r_4r204_t3 r s x y z u v w zi ui vi wi n i j) : l_e_st_eq_landau_n_rt_rp_r_is x y).
+
+(* notion 4563 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_satzd204a a1 b1 (l_e_st_eq_landau_n_rt_rp_r_4r204_t1 s b1 b1is n1) : l_some l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 x) a1)).
+
+(* notion 4564 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_ar ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 a) a1.(l_e_st_eq_landau_n_rt_rp_r_realof a : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4565 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 a) a1.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ar r s a1 b1 a1ir b1is n1 a e)) r (l_e_st_eq_landau_n_rt_rp_td b1 a) a1 (l_e_st_eq_landau_n_rt_rp_r_tict s (l_e_st_eq_landau_n_rt_rp_r_4r204_ar r s a1 b1 a1ir b1is n1 a e) b1 a b1is (l_e_st_eq_landau_n_rt_rp_r_innclass a)) a1ir e : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ar r s a1 b1 a1ir b1is n1 a e)) r).
+
+(* notion 4566 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λa:l_e_st_eq_landau_n_rt_rp_dif.λe:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 a) a1.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r) (l_e_st_eq_landau_n_rt_rp_r_4r204_ar r s a1 b1 a1ir b1is n1 a e) (l_e_st_eq_landau_n_rt_rp_r_4r204_t5 r s a1 b1 a1ir b1is n1 a e) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)).
+
+(* notion 4567 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λn1:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 x) a1) (l_e_st_eq_landau_n_rt_rp_r_4r204_t4 r s a1 b1 a1ir b1is n1) (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b1 x) a1.l_e_st_eq_landau_n_rt_rp_r_4r204_t6 r s a1 b1 a1ir b1is n1 x t) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)).
+
+(* notion 4568 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz204a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_4r204_t7 r s x y t u n) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)).
+
+(* notion 4569 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz204 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_onei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r.λu:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s y) r.l_e_st_eq_landau_n_rt_rp_r_satz204b r s n x y t u) (l_e_st_eq_landau_n_rt_rp_r_satz204a r s n) : l_e_st_eq_landau_n_rt_rp_r_one (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r)).
+
+(* notion 4570 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ov ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_ind l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r) (l_e_st_eq_landau_n_rt_rp_r_satz204 r s n) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4571 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz204c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_oneax l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r) (l_e_st_eq_landau_n_rt_rp_r_satz204 r s n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) r).
+
+(* notion 4572 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz204d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) r (l_e_st_eq_landau_n_rt_rp_r_satz204c r s n) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_ov r s n))).
+
+(* notion 4573 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz204e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov r s n) s) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) r (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_ov r s n) s) (l_e_st_eq_landau_n_rt_rp_r_satz204c r s n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov r s n) s) r).
+
+(* notion 4574 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz204f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov r s n) s) r (l_e_st_eq_landau_n_rt_rp_r_satz204e r s n) : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov r s n) s)).
+
+(* notion 4575 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz204g ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λx:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s x) r.(l_e_st_eq_landau_n_rt_rp_r_satz204b r s n x (l_e_st_eq_landau_n_rt_rp_r_ov r s n) i (l_e_st_eq_landau_n_rt_rp_r_satz204c r s n) : l_e_st_eq_landau_n_rt_rp_r_is x (l_e_st_eq_landau_n_rt_rp_r_ov r s n)).
+
+(* notion 4576 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_ros ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_ov r s n : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4577 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_ispos r (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_satz204d r s n) p : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
+
+(* notion 4578 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_and_th1 (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_pnotn s q) : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)))).
+
+(* notion 4579 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_ore1 (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_e_st_eq_landau_n_rt_rp_r_satz196g s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n) (l_e_st_eq_landau_n_rt_rp_r_4r204_t8 r s n p)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t9 r s n p q) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
+
+(* notion 4580 *)
+definition l_e_st_eq_landau_n_rt_rp_r_posovpp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t10 r s n p q) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ov r s n)).
+
+(* notion 4581 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λm:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_and_th1 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_nnotp s m) : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)))).
+
+(* notion 4582 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λm:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_ore2 (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_e_st_eq_landau_n_rt_rp_r_satz196g s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n) (l_e_st_eq_landau_n_rt_rp_r_4r204_t8 r s n p)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t11 r s n p m) : l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
+
+(* notion 4583 *)
+definition l_e_st_eq_landau_n_rt_rp_r_negovpn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λm:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t12 r s n p m) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ov r s n)).
+
+(* notion 4584 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t13 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_isneg r (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_satz204d r s n) m : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
+
+(* notion 4585 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t14 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_and_th1 (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_pnotn s p) : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)))).
+
+(* notion 4586 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t15 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_ore1 (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_e_st_eq_landau_n_rt_rp_r_satz196h s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n) (l_e_st_eq_landau_n_rt_rp_r_4r204_t13 r s n m)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t14 r s n m p) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
+
+(* notion 4587 *)
+definition l_e_st_eq_landau_n_rt_rp_r_negovnp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t15 r s n m p) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ov r s n)).
+
+(* notion 4588 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t16 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λl:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_and_th1 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)) (l_e_st_eq_landau_n_rt_rp_r_nnotp s l) : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n)))).
+
+(* notion 4589 *)
+definition l_e_st_eq_landau_n_rt_rp_r_4r204_t17 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λl:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_ore2 (l_and (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))) (l_e_st_eq_landau_n_rt_rp_r_satz196h s (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n) (l_e_st_eq_landau_n_rt_rp_r_4r204_t13 r s n m)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t16 r s n m l) : l_and (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_4r204_ros r s n))).
+
+(* notion 4590 *)
+definition l_e_st_eq_landau_n_rt_rp_r_posovnn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λm:l_e_st_eq_landau_n_rt_rp_r_neg r.λl:l_e_st_eq_landau_n_rt_rp_r_neg s.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) (l_e_st_eq_landau_n_rt_rp_r_4r204_t17 r s n m l) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ov r s n)).
+
+(* notion 4591 *)
+definition l_e_st_eq_landau_n_rt_rp_r_morerpep ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_e_st_eq_landau_n_rt_rp_r_morein (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp s0)) (l_e_st_eq_landau_n_rt_rp_morerpepd r0 s0 m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
+
+(* notion 4592 *)
+definition l_e_st_eq_landau_n_rt_rp_r_morerpip ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_morerpipd r0 s0 (l_e_st_eq_landau_n_rt_rp_r_moreex (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp s0)) m) : l_e_st_eq_landau_n_rt_rp_more r0 s0).
+
+(* notion 4593 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lessrpep ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_less r0 s0.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_morerpep s0 r0 (l_e_st_eq_landau_n_rt_rp_satz122 r0 s0 l)) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
+
+(* notion 4594 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lessrpip ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_satz121 s0 r0 (l_e_st_eq_landau_n_rt_rp_r_morerpip s0 r0 (l_e_st_eq_landau_n_rt_rp_r_lemma2 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) l)) : l_e_st_eq_landau_n_rt_rp_less r0 s0).
+
+(* notion 4595 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_ismore12 r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) s (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp s q)) (l_e_st_eq_landau_n_rt_rp_r_isprp1 r p) (l_e_st_eq_landau_n_rt_rp_r_isprp1 s q) m : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp s q))).
+
+(* notion 4596 *)
+definition l_e_st_eq_landau_n_rt_rp_r_moreperp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λm:l_e_st_eq_landau_n_rt_rp_r_more r s.(l_e_st_eq_landau_n_rt_rp_r_morerpip (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t1 r s p q m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q)).
+
+(* notion 4597 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q).(l_e_st_eq_landau_n_rt_rp_r_morerpep (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q) m : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp s q))).
+
+(* notion 4598 *)
+definition l_e_st_eq_landau_n_rt_rp_r_morepirp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λm:l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q).(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp r p)) r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_rpofp s q)) s (l_e_st_eq_landau_n_rt_rp_r_isprp2 r p) (l_e_st_eq_landau_n_rt_rp_r_isprp2 s q) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t2 r s p q m) : l_e_st_eq_landau_n_rt_rp_r_more r s).
+
+(* notion 4599 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lessperp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_satz121 (l_e_st_eq_landau_n_rt_rp_r_rpofp s q) (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_moreperp s r q p (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l)) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q)).
+
+(* notion 4600 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lesspirp ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.λq:l_e_st_eq_landau_n_rt_rp_r_pos s.λl:l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q).(l_e_st_eq_landau_n_rt_rp_r_lemma1 s r (l_e_st_eq_landau_n_rt_rp_r_morepirp s r q p (l_e_st_eq_landau_n_rt_rp_satz122 (l_e_st_eq_landau_n_rt_rp_r_rpofp r p) (l_e_st_eq_landau_n_rt_rp_r_rpofp s q) l)) : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4601 *)
+definition l_e_st_eq_landau_n_rt_rp_r_s01 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x r) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4602 *)
+definition l_e_st_eq_landau_n_rt_rp_r_s02 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x r) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4603 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s01 r)).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_lessis s r) (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s01 r)) n (λt:l_e_st_eq_landau_n_rt_rp_r_lessis s r.l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x r) s t) : l_not (l_e_st_eq_landau_n_rt_rp_r_lessis s r)).
+
+(* notion 4604 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s01 r)).(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x r) s (l_e_st_eq_landau_n_rt_rp_r_satz167k s r (l_e_st_eq_landau_n_rt_rp_r_5r205_t1 r s n)) : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s02 r)).
+
+(* notion 4605 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb00 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_not (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s01 r)).l_e_st_eq_landau_n_rt_rp_r_5r205_t2 r x t : l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s01 r)) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s02 r)))).
+
+(* notion 4606 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x r) r (l_e_st_eq_landau_n_rt_rp_r_lessisi2 r r (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) : l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_s01 r)).
+
+(* notion 4607 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb01a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s01 r) r (l_e_st_eq_landau_n_rt_rp_r_5r205_t3 r) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s01 r)).
+
+(* notion 4608 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ismore2 (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_0) r (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl02 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_satz188k l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 r (l_e_st_eq_landau_n_rt_rp_r_satz169a l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_pos1)) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) r).
+
+(* notion 4609 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x r) (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_5r205_t4 r) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_s02 r)).
+
+(* notion 4610 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb01b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s02 r) (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_5r205_t5 r) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s02 r)).
+
+(* notion 4611 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s01 r).λt:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_in t (l_e_st_eq_landau_n_rt_rp_r_s02 r).(l_e_st_eq_landau_n_rt_rp_r_satz172a s r t (l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x r) s i) (l_e_st_eq_landau_n_rt_rp_r_lemma1 t r (l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x r) t j)) : l_e_st_eq_landau_n_rt_rp_r_less s t).
+
+(* notion 4612 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb02 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s01 r).λy:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_in y (l_e_st_eq_landau_n_rt_rp_r_s02 r).l_e_st_eq_landau_n_rt_rp_r_5r205_t6 r x t y u : l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s01 r).l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y (l_e_st_eq_landau_n_rt_rp_r_s02 r).l_e_st_eq_landau_n_rt_rp_r_less x y))).
+
+(* notion 4613 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb03a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s r.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_lessis x r) s (l_e_st_eq_landau_n_rt_rp_r_lessisi1 s r l) : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s01 r)).
+
+(* notion 4614 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb03b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s r.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_more x r) s m : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s02 r)).
+
+(* notion 4615 *)
+definition l_e_st_eq_landau_n_rt_rp_r_s11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x r) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4616 *)
+definition l_e_st_eq_landau_n_rt_rp_r_s12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x r) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4617 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s11 r)).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_less s r) (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s11 r)) n (λt:l_e_st_eq_landau_n_rt_rp_r_less s r.l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x r) s t) : l_not (l_e_st_eq_landau_n_rt_rp_r_less s r)).
+
+(* notion 4618 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s11 r)).(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x r) s (l_e_st_eq_landau_n_rt_rp_r_satz167f s r (l_e_st_eq_landau_n_rt_rp_r_5r205_t7 r s n)) : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s12 r)).
+
+(* notion 4619 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_not (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s11 r)).l_e_st_eq_landau_n_rt_rp_r_5r205_t8 r x t : l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s11 r)) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s12 r)))).
+
+(* notion 4620 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_isless2 (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_0) r (l_e_st_eq_landau_n_rt_rp_r_mn r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl02 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_satz188m (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) l_e_st_eq_landau_n_rt_rp_r_0 r (l_e_st_eq_landau_n_rt_rp_r_satz169c (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_satz176a l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_pos1))) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_mn r l_e_st_eq_landau_n_rt_rp_r_1rl) r).
+
+(* notion 4621 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x r) (l_e_st_eq_landau_n_rt_rp_r_mn r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_5r205_t9 r) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_mn r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_s11 r)).
+
+(* notion 4622 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb11a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s11 r) (l_e_st_eq_landau_n_rt_rp_r_mn r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_5r205_t10 r) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s11 r)).
+
+(* notion 4623 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x r) r (l_e_st_eq_landau_n_rt_rp_r_moreisi2 r r (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real r)) : l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_s12 r)).
+
+(* notion 4624 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb11b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s12 r) r (l_e_st_eq_landau_n_rt_rp_r_5r205_t11 r) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_s12 r)).
+
+(* notion 4625 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s11 r).λt:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_in t (l_e_st_eq_landau_n_rt_rp_r_s12 r).(l_e_st_eq_landau_n_rt_rp_r_satz172b s r t (l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x r) s i) (l_e_st_eq_landau_n_rt_rp_r_satz168a t r (l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x r) t j)) : l_e_st_eq_landau_n_rt_rp_r_less s t).
+
+(* notion 4626 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s11 r).λy:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_in y (l_e_st_eq_landau_n_rt_rp_r_s12 r).l_e_st_eq_landau_n_rt_rp_r_5r205_t12 r x t y u : l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_s11 r).l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y (l_e_st_eq_landau_n_rt_rp_r_s12 r).l_e_st_eq_landau_n_rt_rp_r_less x y))).
+
+(* notion 4627 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb13a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s r.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_less x r) s l : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s11 r)).
+
+(* notion 4628 *)
+definition l_e_st_eq_landau_n_rt_rp_r_vb13b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s r.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_moreis x r) s (l_e_st_eq_landau_n_rt_rp_r_moreisi1 s r m) : l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_s12 r)).
+
+(* notion 4629 *)
+definition l_e_st_eq_landau_n_rt_rp_r_2rl ≝ (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4630 *)
+definition l_e_st_eq_landau_n_rt_rp_r_pos2 ≝ (l_e_st_eq_landau_n_rt_rp_r_pospl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_pos1 l_e_st_eq_landau_n_rt_rp_r_pos1 : l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_2rl).
+
+(* notion 4631 *)
+definition l_e_st_eq_landau_n_rt_rp_r_half ≝ (l_e_st_eq_landau_n_rt_rp_r_ov l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_2rl (l_e_st_eq_landau_n_rt_rp_r_pnot0 l_e_st_eq_landau_n_rt_rp_r_2rl l_e_st_eq_landau_n_rt_rp_r_pos2) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4632 *)
+definition l_e_st_eq_landau_n_rt_rp_r_poshalf ≝ (l_e_st_eq_landau_n_rt_rp_r_posovpp l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_2rl (l_e_st_eq_landau_n_rt_rp_r_pnot0 l_e_st_eq_landau_n_rt_rp_r_2rl l_e_st_eq_landau_n_rt_rp_r_pos2) l_e_st_eq_landau_n_rt_rp_r_pos1 l_e_st_eq_landau_n_rt_rp_r_pos2 : l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_half).
+
+(* notion 4633 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl r r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_2rl r) (l_e_st_eq_landau_n_rt_rp_r_ispl12 r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_satz195c r) (l_e_st_eq_landau_n_rt_rp_r_satz195c r)) (l_e_st_eq_landau_n_rt_rp_r_distpt1 l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl r r) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_2rl r)).
+
+(* notion 4634 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r r)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_2rl r)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half l_e_st_eq_landau_n_rt_rp_r_2rl) r) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl r) r (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_pl r r) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_2rl r) l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_ivr5_t3 r)) (l_e_st_eq_landau_n_rt_rp_r_assts2 l_e_st_eq_landau_n_rt_rp_r_half l_e_st_eq_landau_n_rt_rp_r_2rl r) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half l_e_st_eq_landau_n_rt_rp_r_2rl) l_e_st_eq_landau_n_rt_rp_r_1rl r (l_e_st_eq_landau_n_rt_rp_r_satz204e l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_2rl (l_e_st_eq_landau_n_rt_rp_r_pnot0 l_e_st_eq_landau_n_rt_rp_r_2rl l_e_st_eq_landau_n_rt_rp_r_pos2))) (l_e_st_eq_landau_n_rt_rp_r_satz195b r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r r)) r).
+
+(* notion 4635 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_satz203k (l_e_st_eq_landau_n_rt_rp_r_pl r r) (l_e_st_eq_landau_n_rt_rp_r_pl r s) l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_satz188m r s r l) l_e_st_eq_landau_n_rt_rp_r_poshalf : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r r)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s))).
+
+(* notion 4636 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_isless1 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r r)) r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t4 r) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t5 r s l) : l_e_st_eq_landau_n_rt_rp_r_less r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s))).
+
+(* notion 4637 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr5_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_satz203k (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl s s) l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_satz188f r s s l) l_e_st_eq_landau_n_rt_rp_r_poshalf : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl s s))).
+
+(* notion 4638 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_isless2 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl s s)) s (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t4 s) (l_e_st_eq_landau_n_rt_rp_r_ivr5_t6 r s l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl r s)) s).
+
+(* notion 4639 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_satz169b s (l_e_st_eq_landau_n_rt_rp_r_trmore s r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) (l_e_st_eq_landau_n_rt_rp_r_satz169a r p)) : l_e_st_eq_landau_n_rt_rp_r_pos s).
+
+(* notion 4640 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_less x r.l_e_st_eq_landau_n_rt_rp_r_in x s1) : Prop).
+
+(* notion 4641 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_more x r.l_e_st_eq_landau_n_rt_rp_r_in x s2) : Prop).
+
+(* notion 4642 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_and (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 r) : Prop).
+
+(* notion 4643 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_mxy ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_half (l_e_st_eq_landau_n_rt_rp_r_pl x y) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4644 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t13 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_e_st_eq_landau_n_rt_rp_r_lemma2 x (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_lemma3 x y l) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) x).
+
+(* notion 4645 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t14 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_e_st_eq_landau_n_rt_rp_r_lemma4 x y l : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) y).
+
+(* notion 4646 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t15 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 y) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 y) py (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_t14 s1 s2 p0 p1a p1b p2 x y px py l) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) s1).
+
+(* notion 4647 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t16 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 x) px (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_t13 s1 s2 p0 p1a p1b p2 x y px py l) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) s2).
+
+(* notion 4648 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t17 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(p2 (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_t15 s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_t16 s1 s2 p0 p1a p1b p2 x y px py l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)).
+
+(* notion 4649 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t18 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.λl:l_e_st_eq_landau_n_rt_rp_r_less x y.(l_ec3e31 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)) (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)) (l_e_st_eq_landau_n_rt_rp_r_satz167b (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l) (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)) (l_e_st_eq_landau_n_rt_rp_r_5r205_t17 s1 s2 p0 p1a p1b p2 x y px py l) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_mxy s1 s2 p0 p1a p1b p2 x y px py l)) : l_con).
+
+(* notion 4650 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t19 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.(λt:l_e_st_eq_landau_n_rt_rp_r_less x y.l_e_st_eq_landau_n_rt_rp_r_5r205_t18 s1 s2 p0 p1a p1b p2 x y px py t : l_not (l_e_st_eq_landau_n_rt_rp_r_less x y)).
+
+(* notion 4651 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t20 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.(λt:l_e_st_eq_landau_n_rt_rp_r_more x y.l_e_st_eq_landau_n_rt_rp_r_5r205_t18 s1 s2 p0 p1a p1b p2 y x py px (l_e_st_eq_landau_n_rt_rp_r_lemma1 x y t) : l_not (l_e_st_eq_landau_n_rt_rp_r_more x y)).
+
+(* notion 4652 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t21 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λpx:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λpy:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.(l_or3e1 (l_e_st_eq_landau_n_rt_rp_r_is x y) (l_e_st_eq_landau_n_rt_rp_r_more x y) (l_e_st_eq_landau_n_rt_rp_r_less x y) (l_e_st_eq_landau_n_rt_rp_r_satz167a x y) (l_e_st_eq_landau_n_rt_rp_r_5r205_t20 s1 s2 p0 p1a p1b p2 x y px py) (l_e_st_eq_landau_n_rt_rp_r_5r205_t19 s1 s2 p0 p1a p1b p2 x y px py) : l_e_st_eq_landau_n_rt_rp_r_is x y).
+
+(* notion 4653 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t22 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x.λu:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 y.l_e_st_eq_landau_n_rt_rp_r_5r205_t21 s1 s2 p0 p1a p1b p2 x y t u : l_e_amone l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
+
+(* notion 4654 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t23 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1) a : l_e_st_eq_landau_n_rt_rp_r_pos r).
+
+(* notion 4655 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t24 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1) a : l_e_st_eq_landau_n_rt_rp_r_in r s1).
+
+(* notion 4656 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_setof l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s1) : l_e_st_set l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4657 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_setof l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s2) : l_e_st_set l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4658 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t25 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s1.(l_e_st_estii l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s1) r0 i : l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a)).
+
+(* notion 4659 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t26 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_estie l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s1) r0 i : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s1).
+
+(* notion 4660 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t27 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s2.(l_e_st_estii l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s2) r0 i : l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)).
+
+(* notion 4661 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t28 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_estie l_e_st_eq_landau_n_rt_cut (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp x) s2) r0 i : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s2).
+
+(* notion 4662 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t29 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s1) (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s2) (l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a)) (l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)) (p0 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0)) (λt:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s1.l_e_st_eq_landau_n_rt_rp_r_5r205_t25 s1 s2 p0 p1a p1b p2 case1 r a r0 t) (λt:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) s2.l_e_st_eq_landau_n_rt_rp_r_5r205_t27 s1 s2 p0 p1a p1b p2 case1 r a r0 t) : l_or (l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a)) (l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a))).
+
+(* notion 4663 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_pr1 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_r_rpofp r (l_e_st_eq_landau_n_rt_rp_r_5r205_t23 s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4664 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t30 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s1) r (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_pr1 s1 s2 p0 p1a p1b p2 case1 r a)) (l_e_st_eq_landau_n_rt_rp_r_5r205_t24 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_isprp1 r (l_e_st_eq_landau_n_rt_rp_r_5r205_t23 s1 s2 p0 p1a p1b p2 case1 r a)) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_pr1 s1 s2 p0 p1a p1b p2 case1 r a)) s1).
+
+(* notion 4665 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t31 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_pr1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t25 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_pr1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t30 s1 s2 p0 p1a p1b p2 case1 r a)) : l_e_st_nonempty l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a)).
+
+(* notion 4666 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t32 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(p2 r (l_e_st_eq_landau_n_rt_rp_r_5r205_t24 s1 s2 p0 p1a p1b p2 case1 r a) s i : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4667 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t33 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(l_e_st_eq_landau_n_rt_rp_r_lemma5 r s (l_e_st_eq_landau_n_rt_rp_r_5r205_t32 s1 s2 p0 p1a p1b p2 case1 r a s i) (l_e_st_eq_landau_n_rt_rp_r_5r205_t23 s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_rp_r_pos s).
+
+(* notion 4668 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_ps1 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(l_e_st_eq_landau_n_rt_rp_r_rpofp s (l_e_st_eq_landau_n_rt_rp_r_5r205_t33 s1 s2 p0 p1a p1b p2 case1 r a s i) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4669 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t34 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s2) s (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps1 s1 s2 p0 p1a p1b p2 case1 r a s i)) i (l_e_st_eq_landau_n_rt_rp_r_isprp1 s (l_e_st_eq_landau_n_rt_rp_r_5r205_t33 s1 s2 p0 p1a p1b p2 case1 r a s i)) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps1 s1 s2 p0 p1a p1b p2 case1 r a s i)) s2).
+
+(* notion 4670 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t35 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_ps1 s1 s2 p0 p1a p1b p2 case1 r a s i) (l_e_st_eq_landau_n_rt_rp_r_5r205_t27 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_ps1 s1 s2 p0 p1a p1b p2 case1 r a s i) (l_e_st_eq_landau_n_rt_rp_r_5r205_t34 s1 s2 p0 p1a p1b p2 case1 r a s i)) : l_e_st_nonempty l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)).
+
+(* notion 4671 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t36 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_rp_r_real s2 p1b (l_e_st_nonempty l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x s2.l_e_st_eq_landau_n_rt_rp_r_5r205_t35 s1 s2 p0 p1a p1b p2 case1 r a x t) : l_e_st_nonempty l_e_st_eq_landau_n_rt_cut (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)).
+
+(* notion 4672 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t37 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).λs0:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).(p2 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_5r205_t26 s1 s2 p0 p1a p1b p2 case1 r a r0 i) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_r_5r205_t28 s1 s2 p0 p1a p1b p2 case1 r a s0 j) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
+
+(* notion 4673 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t38 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λr0:l_e_st_eq_landau_n_rt_cut.λi:l_e_st_eq_landau_n_rt_rp_in r0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).λs0:l_e_st_eq_landau_n_rt_cut.λj:l_e_st_eq_landau_n_rt_rp_in s0 (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_eq_landau_n_rt_rp_r_lessrpip r0 s0 (l_e_st_eq_landau_n_rt_rp_r_5r205_t37 s1 s2 p0 p1a p1b p2 case1 r a r0 i s0 j) : l_e_st_eq_landau_n_rt_rp_less r0 s0).
+
+(* notion 4674 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_stc ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_schnitt (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_5r205_t29 s1 s2 p0 p1a p1b p2 case1 r a x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t31 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t36 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).λy:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_rp_in y (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_r_5r205_t38 s1 s2 p0 p1a p1b p2 case1 r a x t y u) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4675 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t39 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_satzp205a (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_5r205_t29 s1 s2 p0 p1a p1b p2 case1 r a x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t31 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t36 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).λy:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_rp_in y (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_r_5r205_t38 s1 s2 p0 p1a p1b p2 case1 r a x t y u) : l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_less x (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a))).
+
+(* notion 4676 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t40 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_satzp205b (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.l_e_st_eq_landau_n_rt_rp_r_5r205_t29 s1 s2 p0 p1a p1b p2 case1 r a x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t31 s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t36 s1 s2 p0 p1a p1b p2 case1 r a) (λx:l_e_st_eq_landau_n_rt_cut.λt:l_e_st_eq_landau_n_rt_rp_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a).λy:l_e_st_eq_landau_n_rt_cut.λu:l_e_st_eq_landau_n_rt_rp_in y (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_r_5r205_t38 s1 s2 p0 p1a p1b p2 case1 r a x t y u) : l_e_st_eq_landau_n_rt_rp_all (λx:l_e_st_eq_landau_n_rt_cut.Πt:l_e_st_eq_landau_n_rt_rp_more x (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a))).
+
+(* notion 4677 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_stp ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4678 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t41 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_e_st_eq_landau_n_rt_rp_r_posi (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a)).
+
+(* notion 4679 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_rpofp s p : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4680 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t42 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_lessrpip (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p) (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_isless1 s (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p)) (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_isprp1 s p) l) : l_e_st_eq_landau_n_rt_rp_less (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p) (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a)).
+
+(* notion 4681 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t43 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_st_eq_landau_n_rt_rp_r_5r205_t39 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p) (l_e_st_eq_landau_n_rt_rp_r_5r205_t42 s1 s2 p0 p1a p1b p2 case1 r a s l p) : l_e_st_eq_landau_n_rt_rp_in (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p) (l_e_st_eq_landau_n_rt_rp_r_5r205_sc1 s1 s2 p0 p1a p1b p2 case1 r a)).
+
+(* notion 4682 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t44 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λp:l_e_st_eq_landau_n_rt_rp_r_pos s.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p)) s (l_e_st_eq_landau_n_rt_rp_r_5r205_t26 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_ps2 s1 s2 p0 p1a p1b p2 case1 r a s l p) (l_e_st_eq_landau_n_rt_rp_r_5r205_t43 s1 s2 p0 p1a p1b p2 case1 r a s l p)) (l_e_st_eq_landau_n_rt_rp_r_isprp2 s p) : l_e_st_eq_landau_n_rt_rp_r_in s s1).
+
+(* notion 4683 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t45 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_pos s).λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(p2 r (l_e_st_eq_landau_n_rt_rp_r_5r205_t24 s1 s2 p0 p1a p1b p2 case1 r a) s i : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4684 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t46 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_pos s).λi:l_e_st_eq_landau_n_rt_rp_r_in s s2.(n (l_e_st_eq_landau_n_rt_rp_r_lemma5 r s (l_e_st_eq_landau_n_rt_rp_r_5r205_t45 s1 s2 p0 p1a p1b p2 case1 r a s l n i) (l_e_st_eq_landau_n_rt_rp_r_5r205_t23 s1 s2 p0 p1a p1b p2 case1 r a)) : l_con).
+
+(* notion 4685 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t47 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_pos s).(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_in s s1) (l_e_st_eq_landau_n_rt_rp_r_in s s2) (p0 s) (λt:l_e_st_eq_landau_n_rt_rp_r_in s s2.l_e_st_eq_landau_n_rt_rp_r_5r205_t46 s1 s2 p0 p1a p1b p2 case1 r a s l n t) : l_e_st_eq_landau_n_rt_rp_r_in s s1).
+
+(* notion 4686 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t48 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_pos s) (l_e_st_eq_landau_n_rt_rp_r_in s s1) (λt:l_e_st_eq_landau_n_rt_rp_r_pos s.l_e_st_eq_landau_n_rt_rp_r_5r205_t44 s1 s2 p0 p1a p1b p2 case1 r a s l t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_pos s).l_e_st_eq_landau_n_rt_rp_r_5r205_t47 s1 s2 p0 p1a p1b p2 case1 r a s l t) : l_e_st_eq_landau_n_rt_rp_r_in s s1).
+
+(* notion 4687 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t49 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_eq_landau_n_rt_rp_r_lemma5 (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a) s (l_e_st_eq_landau_n_rt_rp_r_lemma1 s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a) m) (l_e_st_eq_landau_n_rt_rp_r_5r205_t41 s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_rp_r_pos s).
+
+(* notion 4688 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_eq_landau_n_rt_rp_r_rpofp s (l_e_st_eq_landau_n_rt_rp_r_5r205_t49 s1 s2 p0 p1a p1b p2 case1 r a s m) : l_e_st_eq_landau_n_rt_cut).
+
+(* notion 4689 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t50 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_eq_landau_n_rt_rp_r_morerpip (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m) (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_ismore1 s (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m)) (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_isprp1 s (l_e_st_eq_landau_n_rt_rp_r_5r205_t49 s1 s2 p0 p1a p1b p2 case1 r a s m)) m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m) (l_e_st_eq_landau_n_rt_rp_r_5r205_stc s1 s2 p0 p1a p1b p2 case1 r a)).
+
+(* notion 4690 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t51 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_e_st_eq_landau_n_rt_rp_r_5r205_t40 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m) (l_e_st_eq_landau_n_rt_rp_r_5r205_t50 s1 s2 p0 p1a p1b p2 case1 r a s m) : l_e_st_eq_landau_n_rt_rp_in (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m) (l_e_st_eq_landau_n_rt_rp_r_5r205_sc2 s1 s2 p0 p1a p1b p2 case1 r a)).
+
+(* notion 4691 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t52 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s2) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m)) s (l_e_st_eq_landau_n_rt_rp_r_5r205_t28 s1 s2 p0 p1a p1b p2 case1 r a (l_e_st_eq_landau_n_rt_rp_r_5r205_ps3 s1 s2 p0 p1a p1b p2 case1 r a s m) (l_e_st_eq_landau_n_rt_rp_r_5r205_t51 s1 s2 p0 p1a p1b p2 case1 r a s m)) (l_e_st_eq_landau_n_rt_rp_r_isprp2 s (l_e_st_eq_landau_n_rt_rp_r_5r205_t49 s1 s2 p0 p1a p1b p2 case1 r a s m)) : l_e_st_eq_landau_n_rt_rp_r_in s s2).
+
+(* notion 4692 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t53 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_andi (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a)) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_less x (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_r_5r205_t48 s1 s2 p0 p1a p1b p2 case1 r a x t) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_more x (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a).l_e_st_eq_landau_n_rt_rp_r_5r205_t52 s1 s2 p0 p1a p1b p2 case1 r a x t) : l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a)).
+
+(* notion 4693 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t54 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1).(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_5r205_stp s1 s2 p0 p1a p1b p2 case1 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t53 s1 s2 p0 p1a p1b p2 case1 r a) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
+
+(* notion 4694 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t55 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase1:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).(l_someapp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)) case1 (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1).l_e_st_eq_landau_n_rt_rp_r_5r205_t54 s1 s2 p0 p1a p1b p2 case1 x t) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
+
+(* notion 4695 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s1) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4696 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_e_st_setof l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s2) : l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4697 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t56 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s1.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s1) r i : l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)).
+
+(* notion 4698 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t57 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2).(l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s1) r i : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s1).
+
+(* notion 4699 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t58 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s2.(l_e_st_estii l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s2) r i : l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)).
+
+(* notion 4700 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t59 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2).(l_e_st_estie l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 x) s2) r i : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s2).
+
+(* notion 4701 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t60 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_comor (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)) (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)) (l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s1) (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s2) (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)) (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)) (p0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λt:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s1.l_e_st_eq_landau_n_rt_rp_r_5r205_t56 s1 s2 p0 p1a p1b p2 case2 r t) (λt:l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) s2.l_e_st_eq_landau_n_rt_rp_r_5r205_t58 s1 s2 p0 p1a p1b p2 case2 r t)) : l_or (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)) (l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2))).
+
+(* notion 4702 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t61 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r s2.(l_e_st_eq_landau_n_rt_rp_r_5r205_t58 s1 s2 p0 p1a p1b p2 case2 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s2) r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) i (l_e_st_eq_landau_n_rt_rp_r_satz177a r)) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)).
+
+(* notion 4703 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t62 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r s2.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t61 s1 s2 p0 p1a p1b p2 case2 r i) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)).
+
+(* notion 4704 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t63 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_rp_r_real s2 p1b (l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x s2.l_e_st_eq_landau_n_rt_rp_r_5r205_t62 s1 s2 p0 p1a p1b p2 case2 x t) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)).
+
+(* notion 4705 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t64 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r s1.(l_e_st_eq_landau_n_rt_rp_r_5r205_t56 s1 s2 p0 p1a p1b p2 case2 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s1) r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) i (l_e_st_eq_landau_n_rt_rp_r_satz177a r)) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)).
+
+(* notion 4706 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t65 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r s1.(l_e_st_nonemptyi l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t64 s1 s2 p0 p1a p1b p2 case2 r i) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)).
+
+(* notion 4707 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t66 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_e_st_nonemptyapp l_e_st_eq_landau_n_rt_rp_r_real s1 p1a (l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_5r205_t65 s1 s2 p0 p1a p1b p2 case2 x t) : l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)).
+
+(* notion 4708 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t67 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2).λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2).(p2 (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_t57 s1 s2 p0 p1a p1b p2 case2 s j) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t59 s1 s2 p0 p1a p1b p2 case2 r i) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4709 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t68 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_in r (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2).λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_in s (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2).(l_e_st_eq_landau_n_rt_rp_r_lemma1 s r (l_e_st_eq_landau_n_rt_rp_r_satz183d s r (l_e_st_eq_landau_n_rt_rp_r_5r205_t67 s1 s2 p0 p1a p1b p2 case2 r i s j)) : l_e_st_eq_landau_n_rt_rp_r_less r s).
+
+(* notion 4710 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t69 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2).(l_e_st_eq_landau_n_rt_rp_r_satz176c r (l_ande1 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2) a) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4711 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t70 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s2) r (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_ande2 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2) a) (l_e_st_eq_landau_n_rt_rp_r_satz177a r) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) s2).
+
+(* notion 4712 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t71 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2).(l_andi (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)) (l_e_st_eq_landau_n_rt_rp_r_5r205_t69 s1 s2 p0 p1a p1b p2 case2 r a) (l_e_st_eq_landau_n_rt_rp_r_5r205_t58 s1 s2 p0 p1a p1b p2 case2 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t70 s1 s2 p0 p1a p1b p2 case2 r a)) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2))).
+
+(* notion 4713 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t72 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2).(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2))) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t71 s1 s2 p0 p1a p1b p2 case2 r a) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)))).
+
+(* notion 4714 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t73 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_someapp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)) case2 (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)))) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2).l_e_st_eq_landau_n_rt_rp_r_5r205_t72 s1 s2 p0 p1a p1b p2 case2 x t) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)))).
+
+(* notion 4715 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t74 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_e_st_eq_landau_n_rt_rp_r_5r205_t55 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_t60 s1 s2 p0 p1a p1b p2 case2 x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t63 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_t66 s1 s2 p0 p1a p1b p2 case2) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_in x (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2).λy:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_in y (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2).l_e_st_eq_landau_n_rt_rp_r_5r205_t68 s1 s2 p0 p1a p1b p2 case2 x t y u) (l_e_st_eq_landau_n_rt_rp_r_5r205_t73 s1 s2 p0 p1a p1b p2 case2) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) x)).
+
+(* notion 4716 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t75 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_ismore2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_satz177 r) (l_e_st_eq_landau_n_rt_rp_r_satz183c s (l_e_st_eq_landau_n_rt_rp_r_m0 r) l) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_m0 s) r).
+
+(* notion 4717 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t76 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r) p (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_t75 s1 s2 p0 p1a p1b p2 case2 r p s l) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2)).
+
+(* notion 4718 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t77 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_5r205_t57 s1 s2 p0 p1a p1b p2 case2 (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_t76 s1 s2 p0 p1a p1b p2 case2 r p s l)) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) : l_e_st_eq_landau_n_rt_rp_r_in s s1).
+
+(* notion 4719 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t78 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_isless2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) r (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_satz177 r) (l_e_st_eq_landau_n_rt_rp_r_satz183a s (l_e_st_eq_landau_n_rt_rp_r_m0 r) m) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_m0 s) r).
+
+(* notion 4720 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t79 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r) p (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_t78 s1 s2 p0 p1a p1b p2 case2 r p s m) : l_e_st_eq_landau_n_rt_rp_r_in (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2)).
+
+(* notion 4721 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t80 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more s (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_in x s2) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 s)) s (l_e_st_eq_landau_n_rt_rp_r_5r205_t59 s1 s2 p0 p1a p1b p2 case2 (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_5r205_t79 s1 s2 p0 p1a p1b p2 case2 r p s m)) (l_e_st_eq_landau_n_rt_rp_r_satz177 s) : l_e_st_eq_landau_n_rt_rp_r_in s s2).
+
+(* notion 4722 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t81 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.(l_andi (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_less x (l_e_st_eq_landau_n_rt_rp_r_m0 r).l_e_st_eq_landau_n_rt_rp_r_5r205_t77 s1 s2 p0 p1a p1b p2 case2 r p x t) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_more x (l_e_st_eq_landau_n_rt_rp_r_m0 r).l_e_st_eq_landau_n_rt_rp_r_5r205_t80 s1 s2 p0 p1a p1b p2 case2 r p x t) : l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4723 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t82 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) r.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t81 s1 s2 p0 p1a p1b p2 case2 r p) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
+
+(* notion 4724 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t83 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λcase2:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).(l_someapp l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t74 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 (l_e_st_eq_landau_n_rt_rp_r_5r205_sp2 s1 s2 p0 p1a p1b p2 case2) (l_e_st_eq_landau_n_rt_rp_r_5r205_sp1 s1 s2 p0 p1a p1b p2 case2) x.l_e_st_eq_landau_n_rt_rp_r_5r205_t82 s1 s2 p0 p1a p1b p2 case2 x t) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
+
+(* notion 4725 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t84 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.(l_some_th4 l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)) notcase2 r : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2))).
+
+(* notion 4726 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t85 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.(l_and_th3 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_in r s2) (l_e_st_eq_landau_n_rt_rp_r_5r205_t84 s1 s2 p0 p1a p1b p2 notcase1 notcase2 r l) (l_e_st_eq_landau_n_rt_rp_r_satz169d r l) : l_not (l_e_st_eq_landau_n_rt_rp_r_in r s2)).
+
+(* notion 4727 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t86 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r l_e_st_eq_landau_n_rt_rp_r_0.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_in r s1) (l_e_st_eq_landau_n_rt_rp_r_in r s2) (p0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t85 s1 s2 p0 p1a p1b p2 notcase1 notcase2 r l) : l_e_st_eq_landau_n_rt_rp_r_in r s1).
+
+(* notion 4728 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t87 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.(l_some_th4 l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)) notcase1 r : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1))).
+
+(* notion 4729 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t88 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.(l_and_th3 (l_e_st_eq_landau_n_rt_rp_r_pos r) (l_e_st_eq_landau_n_rt_rp_r_in r s1) (l_e_st_eq_landau_n_rt_rp_r_5r205_t87 s1 s2 p0 p1a p1b p2 notcase1 notcase2 r m) (l_e_st_eq_landau_n_rt_rp_r_satz169b r m) : l_not (l_e_st_eq_landau_n_rt_rp_r_in r s1)).
+
+(* notion 4730 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t89 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.(l_ore2 (l_e_st_eq_landau_n_rt_rp_r_in r s1) (l_e_st_eq_landau_n_rt_rp_r_in r s2) (p0 r) (l_e_st_eq_landau_n_rt_rp_r_5r205_t88 s1 s2 p0 p1a p1b p2 notcase1 notcase2 r m) : l_e_st_eq_landau_n_rt_rp_r_in r s2).
+
+(* notion 4731 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t90 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).(l_andi (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 l_e_st_eq_landau_n_rt_rp_r_0) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_less x l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_5r205_t86 s1 s2 p0 p1a p1b p2 notcase1 notcase2 x t) (λx:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_more x l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_5r205_t89 s1 s2 p0 p1a p1b p2 notcase1 notcase2 x t) : l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4732 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t91 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).λnotcase2:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_5r205_t90 s1 s2 p0 p1a p1b p2 notcase1 notcase2) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
+
+(* notion 4733 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t92 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λnotcase1:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))) (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)) (λt:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).l_e_st_eq_landau_n_rt_rp_r_5r205_t83 s1 s2 p0 p1a p1b p2 t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_neg x) (l_e_st_eq_landau_n_rt_rp_r_in x s2))).l_e_st_eq_landau_n_rt_rp_r_5r205_t91 s1 s2 p0 p1a p1b p2 notcase1 t) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
+
+(* notion 4734 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t93 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))) (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)) (λt:l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1)).l_e_st_eq_landau_n_rt_rp_r_5r205_t55 s1 s2 p0 p1a p1b p2 t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_pos x) (l_e_st_eq_landau_n_rt_rp_r_in x s1))).l_e_st_eq_landau_n_rt_rp_r_5r205_t92 s1 s2 p0 p1a p1b p2 t) : l_e_st_eq_landau_n_rt_rp_r_some (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
+
+(* notion 4735 *)
+definition l_e_st_eq_landau_n_rt_rp_r_5r205_t94 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(l_e_onei l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_5r205_t22 s1 s2 p0 p1a p1b p2) (l_e_st_eq_landau_n_rt_rp_r_5r205_t93 s1 s2 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_rp_r_one (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x)).
+
+(* notion 4736 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz205 ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(l_e_st_eq_landau_n_rt_rp_r_5r205_t94 s1 s2 p0 p1a p1b p2 : l_e_st_eq_landau_n_rt_rp_r_one (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_less y x.l_e_st_eq_landau_n_rt_rp_r_in y s1)) (l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_more y x.l_e_st_eq_landau_n_rt_rp_r_in y s2)))).
+
+(* notion 4737 *)
+definition l_e_st_eq_landau_n_rt_rp_r_dedekind ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(l_e_st_eq_landau_n_rt_rp_r_satz205 s1 s2 p0 p1a p1b p2 : l_e_st_eq_landau_n_rt_rp_r_one (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_less y x.l_e_st_eq_landau_n_rt_rp_r_in y s1)) (l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_more y x.l_e_st_eq_landau_n_rt_rp_r_in y s2)))).
+
+(* notion 4738 *)
+definition l_e_st_eq_landau_n_rt_rp_r_schnitt ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).(l_e_ind l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_satz205 s1 s2 p0 p1a p1b p2) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4739 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz205a ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λl:l_e_st_eq_landau_n_rt_rp_r_less r (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2)) (l_e_oneax l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_satz205 s1 s2 p0 p1a p1b p2)) r l : l_e_st_eq_landau_n_rt_rp_r_in r s1).
+
+(* notion 4740 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satz205b ≝ λs1:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λs2:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_real.λp0:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_or (l_e_st_eq_landau_n_rt_rp_r_in x s1) (l_e_st_eq_landau_n_rt_rp_r_in x s2)).λp1a:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s1.λp1b:l_e_st_nonempty l_e_st_eq_landau_n_rt_rp_r_real s2.λp2:l_e_st_eq_landau_n_rt_rp_r_all (λx:l_e_st_eq_landau_n_rt_rp_r_real.Πt:l_e_st_eq_landau_n_rt_rp_r_in x s1.l_e_st_eq_landau_n_rt_rp_r_all (λy:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_in y s2.l_e_st_eq_landau_n_rt_rp_r_less x y)).λr:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_more r (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_5r205_prop1 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2)) (l_e_st_eq_landau_n_rt_rp_r_5r205_prop2 s1 s2 (l_e_st_eq_landau_n_rt_rp_r_schnitt s1 s2 p0 p1a p1b p2)) (l_e_oneax l_e_st_eq_landau_n_rt_rp_r_real (λx:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_5r205_prop3 s1 s2 x) (l_e_st_eq_landau_n_rt_rp_r_satz205 s1 s2 p0 p1a p1b p2)) r m : l_e_st_eq_landau_n_rt_rp_r_in r s2).
+
+(* notion 4741 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_dr ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdofrp r0 : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 4742 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_ds ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_pdofrp s0 : l_e_st_eq_landau_n_rt_rp_dif).
+
+(* notion 4743 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t1 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_lemmaivad1 r0 s0 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_r_iva_dr r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_ds r0 s0)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r0 s0))).
+
+(* notion 4744 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva1 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_pl r0 s0)) (l_e_st_eq_landau_n_rt_rp_pd (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r0 s0)) (l_e_st_eq_landau_n_rt_rp_r_picp (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp s0))) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_pl r0 s0))) (l_e_st_eq_landau_n_rt_rp_r_iva_t1 r0 s0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_pl r0 s0))).
+
+(* notion 4745 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t2 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_lemmaivad2 r0 s0 : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_r_iva_dr r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_ds r0 s0)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r0 s0))).
+
+(* notion 4746 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva2 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_ts r0 s0)) (l_e_st_eq_landau_n_rt_rp_td (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0)) (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r0 s0)) (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_pdofrp r0) (l_e_st_eq_landau_n_rt_rp_pdofrp s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp r0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp s0))) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_pdofrp (l_e_st_eq_landau_n_rt_rp_ts r0 s0))) (l_e_st_eq_landau_n_rt_rp_r_iva_t2 r0 s0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_ts r0 s0))).
+
+(* notion 4747 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t3 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_r_moreex (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) (l_e_st_eq_landau_n_rt_rp_r_iva_dr r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_ds r0 s0) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_r_iva_dr r0 s0)) (l_e_st_eq_landau_n_rt_rp_r_innclass (l_e_st_eq_landau_n_rt_rp_r_iva_ds r0 s0)) m : l_e_st_eq_landau_n_rt_rp_mored (l_e_st_eq_landau_n_rt_rp_r_iva_dr r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_ds r0 s0)).
+
+(* notion 4748 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva3 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_lemmaivad3 r0 s0 (l_e_st_eq_landau_n_rt_rp_r_iva_t3 r0 s0 m) : l_e_st_eq_landau_n_rt_rp_more r0 s0).
+
+(* notion 4749 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t4 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.λl:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).(l_e_st_eq_landau_n_rt_rp_satz121 s0 r0 (l_e_st_eq_landau_n_rt_rp_r_lemmaiva3 s0 r0 (l_e_st_eq_landau_n_rt_rp_r_lemma2 (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0) l)) : l_e_st_eq_landau_n_rt_rp_less r0 s0).
+
+(* notion 4750 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t5 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_ec3e23 (l_e_st_eq_landau_n_rt_rp_is r0 s0) (l_e_st_eq_landau_n_rt_rp_more r0 s0) (l_e_st_eq_landau_n_rt_rp_less r0 s0) (l_e_st_eq_landau_n_rt_rp_satz123b r0 s0) m : l_not (l_e_st_eq_landau_n_rt_rp_less r0 s0)).
+
+(* notion 4751 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t6 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_less r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_t5 r0 s0 m) (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).l_e_st_eq_landau_n_rt_rp_r_iva_t4 r0 s0 m t) : l_not (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0))).
+
+(* notion 4752 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t7 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_ec3e21 (l_e_st_eq_landau_n_rt_rp_is r0 s0) (l_e_st_eq_landau_n_rt_rp_more r0 s0) (l_e_st_eq_landau_n_rt_rp_less r0 s0) (l_e_st_eq_landau_n_rt_rp_satz123b r0 s0) m : l_e_st_eq_landau_n_rt_rp_nis r0 s0).
+
+(* notion 4753 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t8 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_is r0 s0) (l_e_st_eq_landau_n_rt_rp_r_iva_t7 r0 s0 m) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0).l_e_st_eq_landau_n_rt_rp_r_isrpip r0 s0 t) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
+
+(* notion 4754 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva4 ≝ λr0:l_e_st_eq_landau_n_rt_cut.λs0:l_e_st_eq_landau_n_rt_cut.λm:l_e_st_eq_landau_n_rt_rp_more r0 s0.(l_or3e2 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_satz167a (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)) (l_e_st_eq_landau_n_rt_rp_r_iva_t6 r0 s0 m) (l_e_st_eq_landau_n_rt_rp_r_iva_t8 r0 s0 m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pofrp r0) (l_e_st_eq_landau_n_rt_rp_r_pofrp s0)).
+
+(* notion 4755 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t9 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).(l_e_st_eq_landau_n_rt_rp_r_lemmaiva3 (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) m : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)).
+
+(* notion 4756 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t10 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).(l_e_st_eq_landau_n_rt_rp_satz154d (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_rt_rp_r_iva_t9 x y m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)).
+
+(* notion 4757 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t11 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).(l_e_st_eq_landau_n_rt_moree (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_iva_t10 x y m) : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)).
+
+(* notion 4758 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva5 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y).(l_e_st_eq_landau_n_satz111a x y (l_e_st_eq_landau_n_rt_rp_r_iva_t11 x y m) : l_e_st_eq_landau_n_more x y).
+
+(* notion 4759 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t12 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_satz111d x y m : l_e_st_eq_landau_n_moref (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)).
+
+(* notion 4760 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t13 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_rt_morei (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_inclass (l_e_st_eq_landau_n_fr y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_iva_t12 x y m) : l_e_st_eq_landau_n_rt_more (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y)).
+
+(* notion 4761 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iva_t14 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_rt_rp_satz154a (l_e_st_eq_landau_n_rt_rtofn x) (l_e_st_eq_landau_n_rt_rtofn y) (l_e_st_eq_landau_n_rt_rp_r_iva_t13 x y m) : l_e_st_eq_landau_n_rt_rp_more (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)).
+
+(* notion 4762 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemmaiva6 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_more x y.(l_e_st_eq_landau_n_rt_rp_r_lemmaiva4 (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) (l_e_st_eq_landau_n_rt_rp_r_iva_t14 x y m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)).
+
+(* notion 4763 *)
+definition l_e_st_eq_landau_n_rt_rp_r_int_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_intabsd a0 (l_e_st_eq_landau_n_rt_rp_r_intrlex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_absd a0)).
+
+(* notion 4764 *)
+definition l_e_st_eq_landau_n_rt_rp_r_int_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_absd a0) (l_e_st_eq_landau_n_rt_rp_r_aica r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_int_t1 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_abs r)).
+
+(* notion 4765 *)
+definition l_e_st_eq_landau_n_rt_rp_r_intabs ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_abs r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_int_t2 r x t i) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_abs r)).
+
+(* notion 4766 *)
+definition l_e_st_eq_landau_n_rt_rp_r_int_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_intm0d a0 (l_e_st_eq_landau_n_rt_rp_r_intrlex r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_m0d a0)).
+
+(* notion 4767 *)
+definition l_e_st_eq_landau_n_rt_rp_r_int_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λa0:l_e_st_eq_landau_n_rt_rp_dif.λa0ir:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_m0d a0) (l_e_st_eq_landau_n_rt_rp_r_micm0 r a0 a0ir) (l_e_st_eq_landau_n_rt_rp_r_int_t3 r a0 a0ir i) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4768 *)
+definition l_e_st_eq_landau_n_rt_rp_r_intm0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.(l_e_st_eq_landau_n_rt_rp_r_realapp1 r (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).l_e_st_eq_landau_n_rt_rp_r_int_t4 r x t i) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_m0 r)).
+
+(* notion 4769 *)
+definition l_e_st_eq_landau_n_rt_rp_r_int_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_intpd a1 b1 (l_e_st_eq_landau_n_rt_rp_r_intrlex r a1 a1ir i) (l_e_st_eq_landau_n_rt_rp_r_intrlex s b1 b1is j) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_pd a1 b1)).
+
+(* notion 4770 *)
+definition l_e_st_eq_landau_n_rt_rp_r_int_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_pd a1 b1) (l_e_st_eq_landau_n_rt_rp_r_picp r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_int_t5 r s a1 b1 a1ir b1is i j) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
+
+(* notion 4771 *)
+definition l_e_st_eq_landau_n_rt_rp_r_intpl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_pl r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_int_t6 r s x y t u i j) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
+
+(* notion 4772 *)
+definition l_e_st_eq_landau_n_rt_rp_r_intmn ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_r_intpl r i (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_intm0 s j) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_mn r s)).
+
+(* notion 4773 *)
+definition l_e_st_eq_landau_n_rt_rp_r_int_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_inttd a1 b1 (l_e_st_eq_landau_n_rt_rp_r_intrlex r a1 a1ir i) (l_e_st_eq_landau_n_rt_rp_r_intrlex s b1 b1is j) : l_e_st_eq_landau_n_rt_rp_intd (l_e_st_eq_landau_n_rt_rp_td a1 b1)).
+
+(* notion 4774 *)
+definition l_e_st_eq_landau_n_rt_rp_r_int_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa1:l_e_st_eq_landau_n_rt_rp_dif.λb1:l_e_st_eq_landau_n_rt_rp_dif.λa1ir:l_e_st_eq_landau_n_rt_rp_r_inn a1 (l_e_st_eq_landau_n_rt_rp_r_class r).λb1is:l_e_st_eq_landau_n_rt_rp_r_inn b1 (l_e_st_eq_landau_n_rt_rp_r_class s).λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_r_intrlin (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_td a1 b1) (l_e_st_eq_landau_n_rt_rp_r_tict r s a1 b1 a1ir b1is) (l_e_st_eq_landau_n_rt_rp_r_int_t7 r s a1 b1 a1ir b1is i j) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 4775 *)
+definition l_e_st_eq_landau_n_rt_rp_r_intts ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.(l_e_st_eq_landau_n_rt_rp_r_realapp2 r s (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_ts r s)) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λt:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class r).λu:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_int_t8 r s x y t u i j) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 4776 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr24_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n)).
+
+(* notion 4777 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr24_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_more l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_more l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n)) (l_e_st_eq_landau_n_satz10d l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n) (l_e_st_eq_landau_n_rt_rp_r_ivr24_t1 r n)) (λt:l_e_st_eq_landau_n_rt_rp_r_more l_e_st_eq_landau_n_rt_rp_r_1rl r.l_e_st_eq_landau_n_rt_rp_r_lemmaiva5 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n) (l_e_st_eq_landau_n_rt_rp_r_ismore2 r (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl r n)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 r n) t)) : l_not (l_e_st_eq_landau_n_rt_rp_r_more l_e_st_eq_landau_n_rt_rp_r_1rl r)).
+
+(* notion 4778 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satzr24 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_natrl r.(l_e_st_eq_landau_n_rt_rp_r_satz167e l_e_st_eq_landau_n_rt_rp_r_1rl r (l_e_st_eq_landau_n_rt_rp_r_ivr24_t2 r n) : l_e_st_eq_landau_n_rt_rp_r_lessis l_e_st_eq_landau_n_rt_rp_r_1rl r).
+
+(* notion 4779 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr25_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_satz182d s r (l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn s r)).
+
+(* notion 4780 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr25_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_intmn s j r i : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_mn s r)).
+
+(* notion 4781 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr25_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_posintnatrl (l_e_st_eq_landau_n_rt_rp_r_mn s r) (l_e_st_eq_landau_n_rt_rp_r_ivr25_t1 r i s j l) (l_e_st_eq_landau_n_rt_rp_r_ivr25_t2 r i s j l) : l_e_st_eq_landau_n_rt_rp_r_natrl (l_e_st_eq_landau_n_rt_rp_r_mn s r)).
+
+(* notion 4782 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr25_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_satzr24 (l_e_st_eq_landau_n_rt_rp_r_mn s r) (l_e_st_eq_landau_n_rt_rp_r_ivr25_t3 r i s j l) : l_e_st_eq_landau_n_rt_rp_r_lessis l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r)).
+
+(* notion 4783 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr25_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r)) (l_e_st_eq_landau_n_rt_rp_r_is l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r)) (l_e_st_eq_landau_n_rt_rp_r_ivr25_t4 r i s j l) (λt:l_e_st_eq_landau_n_rt_rp_r_less l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r).l_e_st_eq_landau_n_rt_rp_r_satz188f l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r t) (λt:l_e_st_eq_landau_n_rt_rp_r_is l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r).l_e_st_eq_landau_n_rt_rp_r_ispl1 l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r)).
+
+(* notion 4784 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satzr25 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_intrl r.λs:l_e_st_eq_landau_n_rt_rp_r_real.λj:l_e_st_eq_landau_n_rt_rp_r_intrl s.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_islessis12 (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn s r) r) s (l_e_st_eq_landau_n_rt_rp_r_compl l_e_st_eq_landau_n_rt_rp_r_1rl r) (l_e_st_eq_landau_n_rt_rp_r_plmn s r) (l_e_st_eq_landau_n_rt_rp_r_ivr25_t5 r i s j l) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_1rl) s).
+
+(* notion 4785 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr155_t1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_lemmaiva1 (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)))).
+
+(* notion 4786 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr155_t2 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_isrpep (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)) (l_e_st_eq_landau_n_rt_rp_satz155e x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)))).
+
+(* notion 4787 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satzr155a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_pl (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y))) (l_e_st_eq_landau_n_rt_rp_r_ivr155_t2 x y) (l_e_st_eq_landau_n_rt_rp_r_ivr155_t1 x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y))).
+
+(* notion 4788 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satzr155b ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_satzr155a x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x y))).
+
+(* notion 4789 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr155_t3 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_lemmaiva2 (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)))).
+
+(* notion 4790 *)
+definition l_e_st_eq_landau_n_rt_rp_r_ivr155_t4 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_isrpep (l_e_st_eq_landau_n_rt_rp_rpofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)) (l_e_st_eq_landau_n_rt_rp_satz155f x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y)))).
+
+(* notion 4791 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satzr155c ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_pofrp (l_e_st_eq_landau_n_rt_rp_ts (l_e_st_eq_landau_n_rt_rp_rpofnt x) (l_e_st_eq_landau_n_rt_rp_rpofnt y))) (l_e_st_eq_landau_n_rt_rp_r_ivr155_t4 x y) (l_e_st_eq_landau_n_rt_rp_r_ivr155_t3 x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y))).
+
+(* notion 4792 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satzr155d ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_satzr155c x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) (l_e_st_eq_landau_n_rt_rp_r_rlofnt y)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_ts x y))).
+
+(* notion 4793 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t1 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λb0:l_e_st_eq_landau_n_rt_rp_dif.λbis:l_e_st_eq_landau_n_rt_rp_r_inn b0 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd a0) (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_ande1 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t) a) (λu:l_e_st_eq_landau_n_rt_rp_negd a0.l_e_st_eq_landau_n_rt_rp_r_negin r a0 air u) : l_not (l_e_st_eq_landau_n_rt_rp_negd a0)).
+
+(* notion 4794 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t2 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λb0:l_e_st_eq_landau_n_rt_rp_dif.λbis:l_e_st_eq_landau_n_rt_rp_r_inn b0 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd b0) (l_e_st_eq_landau_n_rt_rp_r_neg s) (l_ande1 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t) b) (λu:l_e_st_eq_landau_n_rt_rp_negd b0.l_e_st_eq_landau_n_rt_rp_r_negin s b0 bis u) : l_not (l_e_st_eq_landau_n_rt_rp_negd b0)).
+
+(* notion 4795 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t3 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λb0:l_e_st_eq_landau_n_rt_rp_dif.λbis:l_e_st_eq_landau_n_rt_rp_r_inn b0 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts r r) t (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0 (l_e_st_eq_landau_n_rt_rp_r_tict r r a0 a0 air air) cit (l_ande2 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t) a) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).
+
+(* notion 4796 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t4 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λb0:l_e_st_eq_landau_n_rt_rp_dif.λbis:l_e_st_eq_landau_n_rt_rp_r_inn b0 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isex (l_e_st_eq_landau_n_rt_rp_r_ts s s) t (l_e_st_eq_landau_n_rt_rp_td b0 b0) c0 (l_e_st_eq_landau_n_rt_rp_r_tict s s b0 b0 bis bis) cit (l_ande2 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t) b) : l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td b0 b0) c0).
+
+(* notion 4797 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t5 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λair:l_e_st_eq_landau_n_rt_rp_r_inn a0 (l_e_st_eq_landau_n_rt_rp_r_class r).λb0:l_e_st_eq_landau_n_rt_rp_dif.λbis:l_e_st_eq_landau_n_rt_rp_r_inn b0 (l_e_st_eq_landau_n_rt_rp_r_class s).(l_e_st_eq_landau_n_rt_rp_r_isin r s a0 b0 air bis (l_e_st_eq_landau_n_rt_rp_satzd161b c0 a0 b0 (l_e_st_eq_landau_n_rt_rp_r_7r161_t1 t r s a b c0 cit a0 air b0 bis) (l_e_st_eq_landau_n_rt_rp_r_7r161_t2 t r s a b c0 cit a0 air b0 bis) (l_e_st_eq_landau_n_rt_rp_r_7r161_t3 t r s a b c0 cit a0 air b0 bis) (l_e_st_eq_landau_n_rt_rp_r_7r161_t4 t r s a b c0 cit a0 air b0 bis)) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4798 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satzr161b ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) t).(l_e_st_eq_landau_n_rt_rp_r_realapp3 t r s (l_e_st_eq_landau_n_rt_rp_r_is r s) (λx:l_e_st_eq_landau_n_rt_rp_dif.λy:l_e_st_eq_landau_n_rt_rp_dif.λz:l_e_st_eq_landau_n_rt_rp_dif.λu:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class t).λv:l_e_st_eq_landau_n_rt_rp_r_inn y (l_e_st_eq_landau_n_rt_rp_r_class r).λw:l_e_st_eq_landau_n_rt_rp_r_inn z (l_e_st_eq_landau_n_rt_rp_r_class s).l_e_st_eq_landau_n_rt_rp_r_7r161_t5 t r s a b x u y v z w) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 4799 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t6 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_negd c0) (l_e_st_eq_landau_n_rt_rp_r_neg t) n (λu:l_e_st_eq_landau_n_rt_rp_negd c0.l_e_st_eq_landau_n_rt_rp_r_negin t c0 cit u) : l_not (l_e_st_eq_landau_n_rt_rp_negd c0)).
+
+(* notion 4800 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_ar ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).(l_e_st_eq_landau_n_rt_rp_r_realof a0 : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4801 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t7 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a)) (l_e_st_eq_landau_n_rt_rp_negd a0) (l_ande1 (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0) a) (λu:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a).l_e_st_eq_landau_n_rt_rp_r_negex (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) a0 (l_e_st_eq_landau_n_rt_rp_r_innclass a0) u) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a))).
+
+(* notion 4802 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t8 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).(l_e_st_eq_landau_n_rt_rp_r_isin (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a)) t (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0 (l_e_st_eq_landau_n_rt_rp_r_tict (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) a0 a0 (l_e_st_eq_landau_n_rt_rp_r_innclass a0) (l_e_st_eq_landau_n_rt_rp_r_innclass a0)) cit (l_ande2 (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0) a) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a)) t).
+
+(* notion 4803 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t9 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).(l_andi (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a)) t) (l_e_st_eq_landau_n_rt_rp_r_7r161_t7 t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_t8 t n c0 cit a0 a) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a)) t)).
+
+(* notion 4804 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t10 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).λa0:l_e_st_eq_landau_n_rt_rp_dif.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd a0)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td a0 a0) c0).(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t)) (l_e_st_eq_landau_n_rt_rp_r_7r161_ar t n c0 cit a0 a) (l_e_st_eq_landau_n_rt_rp_r_7r161_t9 t n c0 cit a0 a) : l_e_st_eq_landau_n_rt_rp_r_some (λu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))).
+
+(* notion 4805 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t11 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λc0:l_e_st_eq_landau_n_rt_rp_dif.λcit:l_e_st_eq_landau_n_rt_rp_r_inn c0 (l_e_st_eq_landau_n_rt_rp_r_class t).(l_someapp l_e_st_eq_landau_n_rt_rp_dif (λx:l_e_st_eq_landau_n_rt_rp_dif.l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c0)) (l_e_st_eq_landau_n_rt_rp_satzd161a c0 (l_e_st_eq_landau_n_rt_rp_r_7r161_t6 t n c0 cit)) (l_e_st_eq_landau_n_rt_rp_r_some (λu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λv:l_and (l_not (l_e_st_eq_landau_n_rt_rp_negd x)) (l_e_st_eq_landau_n_rt_rp_eq (l_e_st_eq_landau_n_rt_rp_td x x) c0).l_e_st_eq_landau_n_rt_rp_r_7r161_t10 t n c0 cit x v) : l_e_st_eq_landau_n_rt_rp_r_some (λu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))).
+
+(* notion 4806 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satzr161a ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_e_st_eq_landau_n_rt_rp_r_realapp1 t (l_e_st_eq_landau_n_rt_rp_r_some (λu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))) (λx:l_e_st_eq_landau_n_rt_rp_dif.λv:l_e_st_eq_landau_n_rt_rp_r_inn x (l_e_st_eq_landau_n_rt_rp_r_class t).l_e_st_eq_landau_n_rt_rp_r_7r161_t11 t n x v) : l_e_st_eq_landau_n_rt_rp_r_some (λu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))).
+
+(* notion 4807 *)
+definition l_e_st_eq_landau_n_rt_rp_r_satzr161 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_e_onei l_e_st_eq_landau_n_rt_rp_r_real (λu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t)) (λu:l_e_st_eq_landau_n_rt_rp_r_real.λv:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t).λb:l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg v)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts v v) t).l_e_st_eq_landau_n_rt_rp_r_satzr161b t u v a b) (l_e_st_eq_landau_n_rt_rp_r_satzr161a t n) : l_e_st_eq_landau_n_rt_rp_r_one (λu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t))).
+
+(* notion 4808 *)
+definition l_e_st_eq_landau_n_rt_rp_r_sqrt ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_e_ind l_e_st_eq_landau_n_rt_rp_r_real (λu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t)) (l_e_st_eq_landau_n_rt_rp_r_satzr161 t n) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4809 *)
+definition l_e_st_eq_landau_n_rt_rp_r_7r161_t12 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_e_oneax l_e_st_eq_landau_n_rt_rp_r_real (λu:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg u)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts u u) t)) (l_e_st_eq_landau_n_rt_rp_r_satzr161 t n) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_sqrt t n))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_e_st_eq_landau_n_rt_rp_r_sqrt t n)) t)).
+
+(* notion 4810 *)
+definition l_e_st_eq_landau_n_rt_rp_r_thsqrt1a ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_ande1 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_sqrt t n))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_e_st_eq_landau_n_rt_rp_r_sqrt t n)) t) (l_e_st_eq_landau_n_rt_rp_r_7r161_t12 t n) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_sqrt t n))).
+
+(* notion 4811 *)
+definition l_e_st_eq_landau_n_rt_rp_r_thsqrt1b ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).(l_ande2 (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_sqrt t n))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_e_st_eq_landau_n_rt_rp_r_sqrt t n)) t) (l_e_st_eq_landau_n_rt_rp_r_7r161_t12 t n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_e_st_eq_landau_n_rt_rp_r_sqrt t n)) t).
+
+(* notion 4812 *)
+definition l_e_st_eq_landau_n_rt_rp_r_thsqrt2 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λx:l_e_st_eq_landau_n_rt_rp_r_real.λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg x).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts x x) t.(l_e_st_eq_landau_n_rt_rp_r_satzr161b t x (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_andi (l_not (l_e_st_eq_landau_n_rt_rp_r_neg x)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts x x) t) o i) (l_e_st_eq_landau_n_rt_rp_r_7r161_t12 t n) : l_e_st_eq_landau_n_rt_rp_r_is x (l_e_st_eq_landau_n_rt_rp_r_sqrt t n)).
+
+(* notion 4813 *)
+definition l_e_st_eq_landau_n_rt_rp_r_thsqrt3 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg t).λx:l_e_st_eq_landau_n_rt_rp_r_real.λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg x).λi:l_e_st_eq_landau_n_rt_rp_r_is t (l_e_st_eq_landau_n_rt_rp_r_ts x x).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real x (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) (l_e_st_eq_landau_n_rt_rp_r_thsqrt2 t n x o (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real t (l_e_st_eq_landau_n_rt_rp_r_ts x x) i)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt t n) x).
+
+(* notion 4814 *)
+definition l_e_st_eq_landau_n_rt_rp_r_issqrt ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_thsqrt2 s o (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) (l_e_st_eq_landau_n_rt_rp_r_thsqrt1a r n) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)) r s (l_e_st_eq_landau_n_rt_rp_r_thsqrt1b r n) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) (l_e_st_eq_landau_n_rt_rp_r_sqrt s o)).
+
+(* notion 4815 *)
+definition l_e_st_eq_landau_n_rt_rp_r_sqrt0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_thsqrt3 r n l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_0notn l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 i (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4816 *)
+definition l_e_st_eq_landau_n_rt_rp_r_sqrt_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) o (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) l_e_st_eq_landau_n_rt_rp_r_0.l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)) (l_e_st_eq_landau_n_rt_rp_r_thsqrt1b r n) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) t)) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4817 *)
+definition l_e_st_eq_landau_n_rt_rp_r_sqrtnot0 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_or3e2 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_sqrt r n) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)) (l_e_st_eq_landau_n_rt_rp_r_axrlo (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)) (l_e_st_eq_landau_n_rt_rp_r_thsqrt1a r n) (l_e_st_eq_landau_n_rt_rp_r_sqrt_t1 r n o) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_sqrt r n)).
+
+(* notion 4818 *)
+definition l_e_st_eq_landau_n_rt_rp_r_v0_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) t) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov s t n) t)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_comts t (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_assts1 r (l_e_st_eq_landau_n_rt_rp_r_ov s t n) t) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ov s t n) t) s r (l_e_st_eq_landau_n_rt_rp_r_satz204e s t n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 4819 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz204g (l_e_st_eq_landau_n_rt_rp_r_ts r s) t (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) n (l_e_st_eq_landau_n_rt_rp_r_v0_t1 r s t n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_ts r s) t n)).
+
+(* notion 4820 *)
+definition l_e_st_eq_landau_n_rt_rp_r_v0_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ov r t n) (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ov r t n)) (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_disttp2 t (l_e_st_eq_landau_n_rt_rp_r_ov r t n) (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ov r t n)) r (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) s (l_e_st_eq_landau_n_rt_rp_r_satz204c r t n) (l_e_st_eq_landau_n_rt_rp_r_satz204c s t n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts t (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ov r t n) (l_e_st_eq_landau_n_rt_rp_r_ov s t n))) (l_e_st_eq_landau_n_rt_rp_r_pl r s)).
+
+(* notion 4821 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis t l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz204g (l_e_st_eq_landau_n_rt_rp_r_pl r s) t (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ov r t n) (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) n (l_e_st_eq_landau_n_rt_rp_r_v0_t2 r s t n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ov r t n) (l_e_st_eq_landau_n_rt_rp_r_ov s t n)) (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_pl r s) t n)).
+
+(* notion 4822 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz204b r r n (l_e_st_eq_landau_n_rt_rp_r_ov r r n) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_satz204c r r n) (l_e_st_eq_landau_n_rt_rp_r_satz195 r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ov r r n) l_e_st_eq_landau_n_rt_rp_r_1rl).
+
+(* notion 4823 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.(l_ore2 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ov l_e_st_eq_landau_n_rt_rp_r_0 r n) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz192c r (l_e_st_eq_landau_n_rt_rp_r_ov l_e_st_eq_landau_n_rt_rp_r_0 r n) (l_e_st_eq_landau_n_rt_rp_r_satz204c l_e_st_eq_landau_n_rt_rp_r_0 r n)) n : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ov l_e_st_eq_landau_n_rt_rp_r_0 r n) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4824 *)
+definition l_e_st_eq_landau_n_rt_rp_r_v0_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 r).λp:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_pnotn (l_e_st_eq_landau_n_rt_rp_r_m0 r) p (l_e_st_eq_landau_n_rt_rp_r_isneg r (l_e_st_eq_landau_n_rt_rp_r_m0 r) i (l_e_st_eq_landau_n_rt_rp_r_satz176f r p)) : l_con).
+
+(* notion 4825 *)
+definition l_e_st_eq_landau_n_rt_rp_r_v0_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 r).λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_nnotp (l_e_st_eq_landau_n_rt_rp_r_m0 r) n (l_e_st_eq_landau_n_rt_rp_r_ispos r (l_e_st_eq_landau_n_rt_rp_r_m0 r) i (l_e_st_eq_landau_n_rt_rp_r_satz176d r n)) : l_con).
+
+(* notion 4826 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_m0 r).(l_e_st_eq_landau_n_rt_rp_r_satz176e r (l_or3e1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_axrlo (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (λt:l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 r).l_e_st_eq_landau_n_rt_rp_r_v0_t3 r i t) (λt:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_m0 r).l_e_st_eq_landau_n_rt_rp_r_v0_t4 r i t)) : l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4827 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_satz167f (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0 (l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts r r)) (l_e_st_eq_landau_n_rt_rp_r_nnegsq r) (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_satz169d (l_e_st_eq_landau_n_rt_rp_r_ts r r) t)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4828 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lemma12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_rapp r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs r))) (λt:l_e_st_eq_landau_n_rt_rp_r_pos r.l_e_st_eq_landau_n_rt_rp_r_satz196a r r t t) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs r)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 r r t) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs0 r t))) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_satz196b r r t t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_abs r))).
+
+(* notion 4829 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_satz190a x x l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_moreisi2 x x (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real x)) (l_e_st_eq_landau_n_rt_rp_r_satz169a l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_natpos l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_natrl1)) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 4830 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_ismore2 (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_0) x (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl02 x l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_shift_t1 x ix y iy ly) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) x).
+
+(* notion 4831 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_satz172d (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) x y (l_e_st_eq_landau_n_rt_rp_r_shift_t2 x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_satz168b y x ly) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y).
+
+(* notion 4832 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_satz182d (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y (l_e_st_eq_landau_n_rt_rp_r_shift_t3 x ix y iy ly) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
+
+(* notion 4833 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_intmn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1) y iy : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
+
+(* notion 4834 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_posintnatrl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t4 x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_t5 x ix y iy ly) : l_e_st_eq_landau_n_rt_rp_r_natrl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
+
+(* notion 4835 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shiftl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly) : l_e_st_eq_landau_n_nat).
+
+(* notion 4836 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_n1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_inn (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) n : l_e_st_eq_landau_n_nat).
+
+(* notion 4837 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) n : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
+
+(* notion 4838 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_n2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4839 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_natintrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n)).
+
+(* notion 4840 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4841 *)
+definition l_e_st_eq_landau_n_rt_rp_r_intshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_intmn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_t8 x ix y iy ly n) y iy) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n)).
+
+(* notion 4842 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t8a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) l_e_st_eq_landau_n_rt_rp_r_1rl) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) y (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_mnpl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n)).
+
+(* notion 4843 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t9a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m).(l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m) l_e_st_eq_landau_n_rt_rp_r_1rl) y (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m) l_e_st_eq_landau_n_rt_rp_r_1rl i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m) l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
+
+(* notion 4844 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t10a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly m) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_t8a x ix y iy ly n)) (l_e_st_eq_landau_n_rt_rp_r_shift_t9a x ix y iy ly n m i) (l_e_st_eq_landau_n_rt_rp_r_shift_t8a x ix y iy ly m) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly m)).
+
+(* notion 4845 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t11a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m).(l_e_st_eq_landau_n_rt_rp_r_isntirl (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_shift_t10a x ix y iy ly n m i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly m)).
+
+(* notion 4846 *)
+definition l_e_st_eq_landau_n_rt_rp_r_iseshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m).(l_e_st_eq_landau_n_isinne (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) n m (l_e_st_eq_landau_n_rt_rp_r_shift_t11a x ix y iy ly n m i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) n m).
+
+(* notion 4847 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_satz188d (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x l_e_st_eq_landau_n_rt_rp_r_1rl m : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl)).
+
+(* notion 4848 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_ismore1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_shift_t9 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl)).
+
+(* notion 4849 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_satz188d (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 y) (l_e_st_eq_landau_n_rt_rp_r_shift_t10 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
+
+(* notion 4850 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_ismore1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mnpl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t11 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
+
+(* notion 4851 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly))) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n))) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shift_t12 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly))).
+
+(* notion 4852 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_rt_rp_r_lemmaiva5 (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n))) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_t13 x ix y iy ly n m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n))) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
+
+(* notion 4853 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n))) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_isntrl2 (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)) (l_e_st_eq_landau_n_rt_rp_r_shift_t14 x ix y iy ly n m) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
+
+(* notion 4854 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_satz10d (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_t7 x ix y iy ly n)) (λt:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x.l_e_st_eq_landau_n_rt_rp_r_shift_t15 x ix y iy ly n t) : l_not (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x)).
+
+(* notion 4855 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shiftrls ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_satz167e (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x (l_e_st_eq_landau_n_rt_rp_r_shift_t16 x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) x).
+
+(* notion 4856 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n).(l_e_st_eq_landau_n_rt_rp_r_satz188d y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl m : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl y l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl)).
+
+(* notion 4857 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n).(l_e_st_eq_landau_n_rt_rp_r_ismore12 (l_e_st_eq_landau_n_rt_rp_r_pl y l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_compl y l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_shift_t17 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_1rl y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y)).
+
+(* notion 4858 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n).(l_e_st_eq_landau_n_rt_rp_r_satz188a l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y (l_e_st_eq_landau_n_rt_rp_r_shift_t18 x ix y iy ly n m) : l_e_st_eq_landau_n_rt_rp_r_more l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n)).
+
+(* notion 4859 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n).(l_e_st_eq_landau_n_rt_rp_r_lemmaiva5 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_t19 x ix y iy ly n m) : l_e_st_eq_landau_n_more l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)).
+
+(* notion 4860 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n)) (l_e_st_eq_landau_n_more l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n)) (l_e_st_eq_landau_n_satz10d l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n))) (λt:l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n).l_e_st_eq_landau_n_rt_rp_r_shift_t20 x ix y iy ly n t) : l_not (l_e_st_eq_landau_n_rt_rp_r_more y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n))).
+
+(* notion 4861 *)
+definition l_e_st_eq_landau_n_rt_rp_r_lsshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_satz167e y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_t21 x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n)).
+
+(* notion 4862 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t22 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_and3e1 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x) a : l_e_st_eq_landau_n_rt_rp_r_intrl u).
+
+(* notion 4863 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t23 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_and3e2 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x) a : l_e_st_eq_landau_n_rt_rp_r_lessis y u).
+
+(* notion 4864 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t24 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_and3e3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x) a : l_e_st_eq_landau_n_rt_rp_r_lessis u x).
+
+(* notion 4865 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t25 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).λl:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_satz188f (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 y) (l_e_st_eq_landau_n_rt_rp_r_satz188f u x l_e_st_eq_landau_n_rt_rp_r_1rl l) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
+
+(* notion 4866 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t26 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).λi:l_e_st_eq_landau_n_rt_rp_r_is u x.(l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y (l_e_st_eq_landau_n_rt_rp_r_ispl1 u x l_e_st_eq_landau_n_rt_rp_r_1rl i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
+
+(* notion 4867 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t27 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less u x) (l_e_st_eq_landau_n_rt_rp_r_is u x) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly u a) (λt:l_e_st_eq_landau_n_rt_rp_r_less u x.l_e_st_eq_landau_n_rt_rp_r_shift_t25 x ix y iy ly u a t) (λt:l_e_st_eq_landau_n_rt_rp_r_is u x.l_e_st_eq_landau_n_rt_rp_r_shift_t26 x ix y iy ly u a t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
+
+(* notion 4868 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_ul ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_rt_rp_r_shiftl u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u a) y iy (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u a) : l_e_st_eq_landau_n_nat).
+
+(* notion 4869 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t28 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_rt_rp_r_islessis12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u a) y iy (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u a))) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shift_t27 x ix y iy ly u a) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly))).
+
+(* notion 4870 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t29 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_imp_th3 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly))) (l_e_st_eq_landau_n_rt_rp_r_satz167d (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shift_t28 x ix y iy ly u a)) (λt:l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_lemmaiva6 (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) t) : l_not (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly))).
+
+(* notion 4871 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t30 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_satz10e (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_t29 x ix y iy ly u a) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
+
+(* notion 4872 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shiftl1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shift_t30 x ix y iy ly u a) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
+
+(* notion 4873 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t31 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shift_t30 x ix y iy ly u a) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a))).
+
+(* notion 4874 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t32 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u a) y iy (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u a))) (l_e_st_eq_landau_n_rt_rp_r_isnterl (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_shift_t31 x ix y iy ly u a)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a))).
+
+(* notion 4875 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t33 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) y) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) l_e_st_eq_landau_n_rt_rp_r_1rl) u (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) y) (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y)) (l_e_st_eq_landau_n_rt_rp_r_mnpl u l_e_st_eq_landau_n_rt_rp_r_1rl) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) y) l_e_st_eq_landau_n_rt_rp_r_1rl) u).
+
+(* notion 4876 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shiftinv1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real u (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) y) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_shift_t33 x ix y iy ly u a) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) y) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) y (l_e_st_eq_landau_n_rt_rp_r_shift_t32 x ix y iy ly u a))) : l_e_st_eq_landau_n_rt_rp_r_is u (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a))).
+
+(* notion 4877 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shiftinv2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real u (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) (l_e_st_eq_landau_n_rt_rp_r_shiftinv1 x ix y iy ly u a) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a)) u).
+
+(* notion 4878 *)
+definition l_e_st_eq_landau_n_rt_rp_r_seq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λalpha:Type[0].(Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πv:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πw:l_e_st_eq_landau_n_rt_rp_r_lessis t x.alpha : Type[0]).
+
+(* notion 4879 *)
+definition l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λalpha:Type[0].λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly alpha.(Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πit:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πlt:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πtl:l_e_st_eq_landau_n_rt_rp_r_lessis t x.Πu:l_e_st_eq_landau_n_rt_rp_r_real.Πiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.Πlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.Πul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.Πv:l_e_st_eq_landau_n_rt_rp_r_is t u.l_e_is alpha (s t it lt tl) (s u iu lu ul) : Prop).
+
+(* notion 4880 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shiftf ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λalpha:Type[0].λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly alpha.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).f (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly t) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly t) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly t) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly t) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).alpha).
+
+(* notion 4881 *)
+definition l_e_st_eq_landau_n_rt_rp_r_inseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.(Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πv:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πw:l_e_st_eq_landau_n_rt_rp_r_lessis t x.l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl (s t u v w)) (l_e_st_eq_landau_n_rt_rp_r_lessis y (s t u v w)) (l_e_st_eq_landau_n_rt_rp_r_lessis (s t u v w) x) : Prop).
+
+(* notion 4882 *)
+definition l_e_st_eq_landau_n_rt_rp_r_injseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.(Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πit:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πlt:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πtl:l_e_st_eq_landau_n_rt_rp_r_lessis t x.Πu:l_e_st_eq_landau_n_rt_rp_r_real.Πiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.Πlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.Πul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.Πv:l_e_st_eq_landau_n_rt_rp_r_is (s t it lt tl) (s u iu lu ul).l_e_st_eq_landau_n_rt_rp_r_is t u : Prop).
+
+(* notion 4883 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_prop1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λv:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl v) (l_e_st_eq_landau_n_rt_rp_r_lessis y v) (l_e_st_eq_landau_n_rt_rp_r_lessis v x).(l_e_st_eq_landau_n_rt_rp_r_is u (s v (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly v a) (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly v a) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly v a)) : Prop).
+
+(* notion 4884 *)
+definition l_e_st_eq_landau_n_rt_rp_r_improp ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λv:l_e_st_eq_landau_n_rt_rp_r_real.(l_and (l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl v) (l_e_st_eq_landau_n_rt_rp_r_lessis y v) (l_e_st_eq_landau_n_rt_rp_r_lessis v x)) (Πt:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl v) (l_e_st_eq_landau_n_rt_rp_r_lessis y v) (l_e_st_eq_landau_n_rt_rp_r_lessis v x).l_e_st_eq_landau_n_rt_rp_r_shift_prop1 x ix y iy ly s u v t) : Prop).
+
+(* notion 4885 *)
+definition l_e_st_eq_landau_n_rt_rp_r_imseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_some (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s u t) : Prop).
+
+(* notion 4886 *)
+definition l_e_st_eq_landau_n_rt_rp_r_surjseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.(Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πv:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πw:l_e_st_eq_landau_n_rt_rp_r_lessis t x.l_e_st_eq_landau_n_rt_rp_r_imseq x ix y iy ly s t : Prop).
+
+(* notion 4887 *)
+definition l_e_st_eq_landau_n_rt_rp_r_perm ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.(l_and (l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s) (l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s) : Prop).
+
+(* notion 4888 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_ns ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4889 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t34 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(ins (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly n) : l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n)) (l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n)) (l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) x)).
+
+(* notion 4890 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shiftseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins t) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins t) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
+
+(* notion 4891 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t35 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n)) (l_e_st_eq_landau_n_rt_rp_r_shift_t30 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n)) (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins m)) (l_e_st_eq_landau_n_rt_rp_r_shift_t30 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins m)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n)) (l_e_st_eq_landau_n_rt_rp_r_shift_ul x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins m))).
+
+(* notion 4892 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t36 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_rt_rp_r_isrlint (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n)) y iy (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins m)) y iy (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins m))) (l_e_st_eq_landau_n_rt_rp_r_shift_t35 x ix y iy ly s ins js n m i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) l_e_st_eq_landau_n_rt_rp_r_1rl) y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) l_e_st_eq_landau_n_rt_rp_r_1rl) y)).
+
+(* notion 4893 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t37 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_rt_rp_r_satz188b (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_satz188b (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 y) (l_e_st_eq_landau_n_rt_rp_r_shift_t36 x ix y iy ly s ins js n m i)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins m)).
+
+(* notion 4894 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t38 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(js (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_shift_t37 x ix y iy ly s ins js n m i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly m)).
+
+(* notion 4895 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t39 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_rt_rp_r_satz188b (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly m) y (l_e_st_eq_landau_n_rt_rp_r_satz188b (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly m) y) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_shift_t38 x ix y iy ly s ins js n m i)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n2 x ix y iy ly m)).
+
+(* notion 4896 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t40 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_rt_rp_r_isntirl (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly m) (l_e_st_eq_landau_n_rt_rp_r_shift_t39 x ix y iy ly s ins js n m i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shift_n1 x ix y iy ly m)).
+
+(* notion 4897 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t41 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins n) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins m).(l_e_st_eq_landau_n_isinne (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly) n m (l_e_st_eq_landau_n_rt_rp_r_shift_t40 x ix y iy ly s ins js n m i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) n m).
+
+(* notion 4898 *)
+definition l_e_st_eq_landau_n_rt_rp_r_injshiftseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λjs:l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λv:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins t) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins u).l_e_st_eq_landau_n_rt_rp_r_shift_t41 x ix y iy ly s ins js t u v : l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins)).
+
+(* notion 4899 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t42 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(ss (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_imseq x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n)).
+
+(* notion 4900 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t43 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_ande1 (l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x)) (Πt:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).l_e_st_eq_landau_n_rt_rp_r_shift_prop1 x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u t) p : l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x)).
+
+(* notion 4901 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t44 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_r_ande2 (l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x)) (Πt:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).l_e_st_eq_landau_n_rt_rp_r_shift_prop1 x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u t) p : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (s u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)))).
+
+(* notion 4902 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_ul1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)).
+
+(* notion 4903 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t45 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(pri u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shiftinv1 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) : l_e_st_eq_landau_n_rt_rp_r_is (s u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p))) (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p))).
+
+(* notion 4904 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t46 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_e_st_eq_landau_n_rt_rp_r_shiftinv1 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)))).
+
+(* notion 4905 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t47 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (s u (l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly u (l_e_st_eq_landau_n_rt_rp_r_shift_t43 x ix y iy ly s ins pri ss n u p))) (l_e_st_eq_landau_n_rt_rp_r_shift_ns x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p))) (l_e_st_eq_landau_n_rt_rp_r_shift_t44 x ix y iy ly s ins pri ss n u p) (l_e_st_eq_landau_n_rt_rp_r_shift_t45 x ix y iy ly s ins pri ss n u p) (l_e_st_eq_landau_n_rt_rp_r_shift_t46 x ix y iy ly s ins pri ss n u p) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)))).
+
+(* notion 4906 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t48 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_e_st_eq_landau_n_rt_rp_r_iseshiftr x ix y iy ly n (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p)) (l_e_st_eq_landau_n_rt_rp_r_shift_t47 x ix y iy ly s ins pri ss n u p) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) n (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p))).
+
+(* notion 4907 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t49 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).λu:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) u.(l_somei (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) n (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins t)) (l_e_st_eq_landau_n_rt_rp_r_shift_ul1 x ix y iy ly s ins pri ss n u p) (l_e_st_eq_landau_n_rt_rp_r_shift_t48 x ix y iy ly s ins pri ss n u p) : l_e_image (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins) n).
+
+(* notion 4908 *)
+definition l_e_st_eq_landau_n_rt_rp_r_shift_t50 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).(l_someapp l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) t) (l_e_st_eq_landau_n_rt_rp_r_shift_t42 x ix y iy ly s ins pri ss n) (l_e_image (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins) n) (λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_improp x ix y iy ly s (l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n) t.l_e_st_eq_landau_n_rt_rp_r_shift_t49 x ix y iy ly s ins pri ss n t u) : l_e_image (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins) n).
+
+(* notion 4909 *)
+definition l_e_st_eq_landau_n_rt_rp_r_surjshiftseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λss:l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_shift_t50 x ix y iy ly s ins pri ss t : l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins)).
+
+(* notion 4910 *)
+definition l_e_st_eq_landau_n_rt_rp_r_bijshiftseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_andi (l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins)) (l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins)) (l_e_st_eq_landau_n_rt_rp_r_injshiftseq x ix y iy ly s ins (l_ande1 (l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s) (l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s) ps)) (l_e_st_eq_landau_n_rt_rp_r_surjshiftseq x ix y iy ly s ins pri (l_ande2 (l_e_st_eq_landau_n_rt_rp_r_injseq x ix y iy ly s) (l_e_st_eq_landau_n_rt_rp_r_surjseq x ix y iy ly s) ps)) : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly)) (l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins)).
+
+(* notion 4911 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_complex ≝ (l_e_st_eq_landau_n_pair1type l_e_st_eq_landau_n_rt_rp_r_real : Type[0]).
+
+(* notion 4912 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_cx ≝ (l_e_st_eq_landau_n_rt_rp_r_c_complex : Type[0]).
+
+(* notion 4913 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_is ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_is l_e_st_eq_landau_n_rt_rp_r_c_cx x y : Prop).
+
+(* notion 4914 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_nis ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_not (l_e_st_eq_landau_n_rt_rp_r_c_is x y) : Prop).
+
+(* notion 4915 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_some ≝ λp:Πt:l_e_st_eq_landau_n_rt_rp_r_c_complex.Prop.(l_some l_e_st_eq_landau_n_rt_rp_r_c_cx p : Prop).
+
+(* notion 4916 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_all ≝ λp:Πt:l_e_st_eq_landau_n_rt_rp_r_c_complex.Prop.(l_all l_e_st_eq_landau_n_rt_rp_r_c_cx p : Prop).
+
+(* notion 4917 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_one ≝ λp:Πt:l_e_st_eq_landau_n_rt_rp_r_c_complex.Prop.(l_e_one l_e_st_eq_landau_n_rt_rp_r_c_cx p : Prop).
+
+(* notion 4918 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_pli ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_pair1 l_e_st_eq_landau_n_rt_rp_r_real a b : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 4919 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_re ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_first1 l_e_st_eq_landau_n_rt_rp_r_real x : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4920 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_im ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_second1 l_e_st_eq_landau_n_rt_rp_r_real x : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 4921 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_reis ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_first1is1 l_e_st_eq_landau_n_rt_rp_r_real a b : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a).
+
+(* notion 4922 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isre ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_first1is2 l_e_st_eq_landau_n_rt_rp_r_real a b : l_e_st_eq_landau_n_rt_rp_r_is a (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))).
+
+(* notion 4923 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_imis ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_second1is1 l_e_st_eq_landau_n_rt_rp_r_real a b : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b).
+
+(* notion 4924 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isim ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_second1is2 l_e_st_eq_landau_n_rt_rp_r_real a b : l_e_st_eq_landau_n_rt_rp_r_is b (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))).
+
+(* notion 4925 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_pliis ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_pair1is1 l_e_st_eq_landau_n_rt_rp_r_real x : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x).
+
+(* notion 4926 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ispli ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_pair1is2 l_e_st_eq_landau_n_rt_rp_r_real x : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))).
+
+(* notion 4927 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscere ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_re t) x y i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)).
+
+(* notion 4928 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isceim ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_im t) x y i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)).
+
+(* notion 4929 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is a b.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_pli t c) a b i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli a c) (l_e_st_eq_landau_n_rt_rp_r_c_pli b c)).
+
+(* notion 4930 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is a b.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_pli c t) a b i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli c a) (l_e_st_eq_landau_n_rt_rp_r_c_pli c b)).
+
+(* notion 4931 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is a b.λj:l_e_st_eq_landau_n_rt_rp_r_is c d.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pli a c) (l_e_st_eq_landau_n_rt_rp_r_c_pli b c) (l_e_st_eq_landau_n_rt_rp_r_c_pli b d) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 a b c i) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 c d b j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli a c) (l_e_st_eq_landau_n_rt_rp_r_c_pli b d)).
+
+(* notion 4932 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz206 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x : l_e_st_eq_landau_n_rt_rp_r_c_is x x).
+
+(* notion 4933 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz207 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx x y i : l_e_st_eq_landau_n_rt_rp_r_c_is y x).
+
+(* notion 4934 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz208 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_c_is y z.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx x y z i j : l_e_st_eq_landau_n_rt_rp_r_c_is x z).
+
+(* notion 4935 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_0c ≝ (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 4936 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_1c ≝ (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 4937 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_pl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 4938 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_plis12a ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_pl b d) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) c (l_e_st_eq_landau_n_rt_rp_r_c_reis a b) (l_e_st_eq_landau_n_rt_rp_r_c_reis c d)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) d (l_e_st_eq_landau_n_rt_rp_r_c_imis a b) (l_e_st_eq_landau_n_rt_rp_r_c_imis c d)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl b d))).
+
+(* notion 4939 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_plis12b ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl b d)) (l_e_st_eq_landau_n_rt_rp_r_c_plis12a a b c d) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl b d)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))).
+
+(* notion 4940 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_plis1a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
+
+(* notion 4941 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_plis1b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_plis1a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x)).
+
+(* notion 4942 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_plis2a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) s) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) s))).
+
+(* notion 4943 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_plis2b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_c_plis2a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))).
+
+(* notion 4944 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ispl1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t z) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)).
+
+(* notion 4945 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ispl2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl z t) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y)).
+
+(* notion 4946 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ispl12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_c_is z u.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) (l_e_st_eq_landau_n_rt_rp_r_c_ispl1 x y z i) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 z u y j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)).
+
+(* notion 4947 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz209 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y x)).
+
+(* notion 4948 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_compl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz209 x y : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y x)).
+
+(* notion 4949 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz210 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_plis2a x l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x l_e_st_eq_landau_n_rt_rp_r_c_0c) x).
+
+(* notion 4950 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz210a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl x l_e_st_eq_landau_n_rt_rp_r_c_0c) x (l_e_st_eq_landau_n_rt_rp_r_c_satz210 x) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_pl x l_e_st_eq_landau_n_rt_rp_r_c_0c)).
+
+(* notion 4951 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz210b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl l_e_st_eq_landau_n_rt_rp_r_c_0c x) (l_e_st_eq_landau_n_rt_rp_r_c_pl x l_e_st_eq_landau_n_rt_rp_r_c_0c) x (l_e_st_eq_landau_n_rt_rp_r_c_compl l_e_st_eq_landau_n_rt_rp_r_c_0c x) (l_e_st_eq_landau_n_rt_rp_r_c_satz210 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl l_e_st_eq_landau_n_rt_rp_r_c_0c x) x).
+
+(* notion 4952 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz210c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl l_e_st_eq_landau_n_rt_rp_r_c_0c x) x (l_e_st_eq_landau_n_rt_rp_r_c_satz210b x) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_pl l_e_st_eq_landau_n_rt_rp_r_c_0c x)).
+
+(* notion 4953 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz211 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_plis1a z (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_c_plis2b x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
+
+(* notion 4954 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_asspl1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz211 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
+
+(* notion 4955 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_asspl2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z)).
+
+(* notion 4956 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2212_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re u)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_isre (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re u)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im u))) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re u)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)).
+
+(* notion 4957 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2212_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im u)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_isim (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re u)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im u))) (l_e_st_eq_landau_n_rt_rp_r_c_isceim (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im u)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)).
+
+(* notion 4958 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2212_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_st_eq_landau_n_rt_rp_r_satz187d (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re u) (l_e_st_eq_landau_n_rt_rp_r_c_2212_t1 x y u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re u) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))).
+
+(* notion 4959 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2212_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_st_eq_landau_n_rt_rp_r_satz187d (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im u) (l_e_st_eq_landau_n_rt_rp_r_c_2212_t2 x y u i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im u) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))).
+
+(* notion 4960 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz212a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx u (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re u) (l_e_st_eq_landau_n_rt_rp_r_c_im u)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_ispli u) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re u) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im u) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_2212_t3 x y u i) (l_e_st_eq_landau_n_rt_rp_r_c_2212_t4 x y u i)) : l_e_st_eq_landau_n_rt_rp_r_c_is u (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))).
+
+(* notion 4961 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz212b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_plis2a y (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_satz187a (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz187a (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) x).
+
+(* notion 4962 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz212c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_somei l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y t) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_satz212b x y) : l_e_st_eq_landau_n_rt_rp_r_c_some (λt:l_e_st_eq_landau_n_rt_rp_r_c_complex.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y t) x)).
+
+(* notion 4963 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz212 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_onei l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y t) x) (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y t) x.λw:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx t u (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_satz212a x y t v) (l_e_st_eq_landau_n_rt_rp_r_c_satz212a x y u w)) (l_e_st_eq_landau_n_rt_rp_r_c_satz212c x y) : l_e_st_eq_landau_n_rt_rp_r_c_one (λt:l_e_st_eq_landau_n_rt_rp_r_c_complex.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y t) x)).
+
+(* notion 4964 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_mn ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 4965 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_mnis12a ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_mn b d) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) c (l_e_st_eq_landau_n_rt_rp_r_c_reis a b) (l_e_st_eq_landau_n_rt_rp_r_c_reis c d)) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) d (l_e_st_eq_landau_n_rt_rp_r_c_imis a b) (l_e_st_eq_landau_n_rt_rp_r_c_imis c d)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn b d))).
+
+(* notion 4966 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_mnis12b ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn b d)) (l_e_st_eq_landau_n_rt_rp_r_c_mnis12a a b c d) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn b d)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))).
+
+(* notion 4967 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_mnis1a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_mn s (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn s (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
+
+(* notion 4968 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_mnis1b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_mnis1a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x)).
+
+(* notion 4969 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_mnis2a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) s) (l_e_st_eq_landau_n_rt_rp_r_ismn2 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ismn2 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) s))).
+
+(* notion 4970 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_mnis2b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_c_mnis2a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))).
+
+(* notion 4971 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ismn1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_mn t z) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)).
+
+(* notion 4972 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ismn2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_mn z t) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn z x) (l_e_st_eq_landau_n_rt_rp_r_c_mn z y)).
+
+(* notion 4973 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ismn12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_c_is z u.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn y u) (l_e_st_eq_landau_n_rt_rp_r_c_ismn1 x y z i) (l_e_st_eq_landau_n_rt_rp_r_c_ismn2 z u y j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) (l_e_st_eq_landau_n_rt_rp_r_c_mn y u)).
+
+(* notion 4974 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz212d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_st_eq_landau_n_rt_rp_r_c_satz212a x y u i : l_e_st_eq_landau_n_rt_rp_r_c_is u (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
+
+(* notion 4975 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz212e ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx u (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz212d x y u i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) u).
+
+(* notion 4976 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz212f ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl u y) x.(l_e_st_eq_landau_n_rt_rp_r_c_satz212d x y u (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y) x (l_e_st_eq_landau_n_rt_rp_r_c_compl y u) i) : l_e_st_eq_landau_n_rt_rp_r_c_is u (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
+
+(* notion 4977 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz212g ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl u y) x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx u (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz212f x y u i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) u).
+
+(* notion 4978 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz212h ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212b x y : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) x).
+
+(* notion 4979 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_0c) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isre (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_reis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4980 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_im l_e_st_eq_landau_n_rt_rp_r_c_0c) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isim (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_isceim (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_imis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4981 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_satz182b (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_2213_t1 x y i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)).
+
+(* notion 4982 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_satz182b (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_2213_t2 x y i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)).
+
+(* notion 4983 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz213a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) y (l_e_st_eq_landau_n_rt_rp_r_c_ispli x) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_2213_t3 x y i) (l_e_st_eq_landau_n_rt_rp_r_c_2213_t4 x y i)) (l_e_st_eq_landau_n_rt_rp_r_c_pliis y) : l_e_st_eq_landau_n_rt_rp_r_c_is x y).
+
+(* notion 4984 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_st_eq_landau_n_rt_rp_r_satz182e (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_iscere x y i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4985 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2213_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_st_eq_landau_n_rt_rp_r_satz182e (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_isceim x y i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 4986 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz213b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_2213_t5 x y i) (l_e_st_eq_landau_n_rt_rp_r_c_2213_t6 x y i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 4987 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_m0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_mn l_e_st_eq_landau_n_rt_rp_r_c_0c x : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 4988 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz214 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_im l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_pl01 (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_reis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl01 (l_e_st_eq_landau_n_rt_rp_r_c_im l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_imis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
+
+(* notion 4989 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz214a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)).
+
+(* notion 4990 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_m0isa ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 a) (l_e_st_eq_landau_n_rt_rp_r_m0 b)) (l_e_st_eq_landau_n_rt_rp_r_c_satz214 (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))) (l_e_st_eq_landau_n_rt_rp_r_m0 a) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))) (l_e_st_eq_landau_n_rt_rp_r_m0 b) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_c_reis a b)) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_imis a b))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 a) (l_e_st_eq_landau_n_rt_rp_r_m0 b))).
+
+(* notion 4991 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_m0isb ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 a) (l_e_st_eq_landau_n_rt_rp_r_m0 b)) (l_e_st_eq_landau_n_rt_rp_r_c_m0isa a b) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 a) (l_e_st_eq_landau_n_rt_rp_r_m0 b)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))).
+
+(* notion 4992 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ism0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_m0 t) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)).
+
+(* notion 4993 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz215 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x)) (l_e_st_eq_landau_n_rt_rp_r_c_m0isa (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_satz177 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_satz177 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) x).
+
+(* notion 4994 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz215a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) x (l_e_st_eq_landau_n_rt_rp_r_c_satz215 x) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))).
+
+(* notion 4995 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz215b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) y (l_e_st_eq_landau_n_rt_rp_r_c_ism0 x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) i) (l_e_st_eq_landau_n_rt_rp_r_c_satz215 y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y).
+
+(* notion 4996 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz215c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y (l_e_st_eq_landau_n_rt_rp_r_c_satz215b x y i) : l_e_st_eq_landau_n_rt_rp_r_c_is y (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)).
+
+(* notion 4997 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz215d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y.(l_e_st_eq_landau_n_rt_rp_r_c_satz215c y x (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y i) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)).
+
+(* notion 4998 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz215e ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) (l_e_st_eq_landau_n_rt_rp_r_c_satz215d x y i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) x).
+
+(* notion 4999 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz216 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) x (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x)) (l_e_st_eq_landau_n_rt_rp_r_c_plis2a x (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz179 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_satz179 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5000 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2216_anders ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212h l_e_st_eq_landau_n_rt_rp_r_c_0c x : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5001 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz216a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) x) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_compl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) x) (l_e_st_eq_landau_n_rt_rp_r_c_satz216 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) x) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5002 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz217 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0isa (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_satz180 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz180 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_plis12b (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) (l_e_st_eq_landau_n_rt_rp_r_c_satz214a x) (l_e_st_eq_landau_n_rt_rp_r_c_satz214a y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))).
+
+(* notion 5003 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz217a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz217 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
+
+(* notion 5004 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz218 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_plis2b x (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) x (l_e_st_eq_landau_n_rt_rp_r_c_satz214a y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))).
+
+(* notion 5005 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz218a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz218 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
+
+(* notion 5006 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_2219_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz218 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz217 x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) y (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz215 y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y)).
+
+(* notion 5007 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz219 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_mn y x) (l_e_st_eq_landau_n_rt_rp_r_c_2219_t1 x y) (l_e_st_eq_landau_n_rt_rp_r_c_compl (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz218a y x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn y x)).
+
+(* notion 5008 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz219a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn y x)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz219 y x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn y x))).
+
+(* notion 5009 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ts ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 5010 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_rets ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5011 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_imts ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5012 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_ts b d) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) c (l_e_st_eq_landau_n_rt_rp_r_c_reis a b) (l_e_st_eq_landau_n_rt_rp_r_c_reis c d)) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) d (l_e_st_eq_landau_n_rt_rp_r_c_imis a b) (l_e_st_eq_landau_n_rt_rp_r_c_imis c d)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts b d))).
+
+(* notion 5013 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))) (l_e_st_eq_landau_n_rt_rp_r_ts b c) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) d (l_e_st_eq_landau_n_rt_rp_r_c_reis a b) (l_e_st_eq_landau_n_rt_rp_r_c_imis c d)) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) c (l_e_st_eq_landau_n_rt_rp_r_c_imis a b) (l_e_st_eq_landau_n_rt_rp_r_c_reis c d)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts b c))).
+
+(* notion 5014 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_tsis12a ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts b d)) (l_e_st_eq_landau_n_rt_rp_r_c_imts (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts b c)) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t1 a b c d) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t2 a b c d) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts b d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts b c)))).
+
+(* notion 5015 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_tsis12b ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts b d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts b c))) (l_e_st_eq_landau_n_rt_rp_r_c_tsis12a a b c d) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts a c) (l_e_st_eq_landau_n_rt_rp_r_ts b d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts a d) (l_e_st_eq_landau_n_rt_rp_r_ts b c))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli a b) (l_e_st_eq_landau_n_rt_rp_r_c_pli c d))).
+
+(* notion 5016 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
+
+(* notion 5017 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x)))).
+
+(* notion 5018 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_tsis1a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_imts (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t3 x r s) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t4 x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x))))).
+
+(* notion 5019 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_tsis1b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x)))) (l_e_st_eq_landau_n_rt_rp_r_c_tsis1a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_c_re x)))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) x)).
+
+(* notion 5020 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s))).
+
+(* notion 5021 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) s (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_imis r s)) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) r (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_reis r s)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r))).
+
+(* notion 5022 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_tsis2a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_c_imts x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r)) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t5 x r s) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t6 x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r)))).
+
+(* notion 5023 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_tsis2b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r))) (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a x r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) s)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) s) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) r))) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pli r s))).
+
+(* notion 5024 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ists1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t z) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)).
+
+(* notion 5025 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ists2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts z t) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y)).
+
+(* notion 5026 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ists12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_c_is z u.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 x y z i) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 z u y j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)).
+
+(* notion 5027 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3220_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets y x)).
+
+(* notion 5028 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3220_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_imts y x) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts y x)).
+
+(* notion 5029 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz220 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets y x) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts y x) (l_e_st_eq_landau_n_rt_rp_r_c_3220_t1 x y) (l_e_st_eq_landau_n_rt_rp_r_c_3220_t2 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y x)).
+
+(* notion 5030 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_comts ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz220 x y : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y x)).
+
+(* notion 5031 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_0c) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_iscere x l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_reis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5032 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im l_e_st_eq_landau_n_rt_rp_r_c_0c) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isceim x l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_imis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5033 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_mod2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5034 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma1 x i)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma2 x i))) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5035 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5036 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5037 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) n (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_ispli x) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 i t)) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5038 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_ispos (l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 x) (l_e_st_eq_landau_n_rt_rp_r_pl01 (l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 x) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) i))) (l_e_st_eq_landau_n_rt_rp_r_possq (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_t7 x n i)) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
+
+(* notion 5039 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_ispos (l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 x) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 x) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x) i))) (l_e_st_eq_landau_n_rt_rp_r_possq (l_e_st_eq_landau_n_rt_rp_r_c_re x) o) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
+
+(* notion 5040 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.λp:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_pospl (l_e_st_eq_landau_n_rt_rp_r_c_v3_re2 x) (l_e_st_eq_landau_n_rt_rp_r_c_v3_im2 x) (l_e_st_eq_landau_n_rt_rp_r_possq (l_e_st_eq_landau_n_rt_rp_r_c_re x) o) (l_e_st_eq_landau_n_rt_rp_r_possq (l_e_st_eq_landau_n_rt_rp_r_c_im x) p) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
+
+(* notion 5041 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v3_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_v3_t9 x n o t) (λt:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_v3_t10 x n o t) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
+
+(* notion 5042 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_v3_t8 x n t) (λt:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_v3_t11 x n t) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
+
+(* notion 5043 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x))) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_0notn (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma3 x t)) (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_pnotn (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma4 x t)) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x))).
+
+(* notion 5044 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma1 x i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5045 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma2 x i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5046 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_mn l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t1 x y i)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t2 x y i))) (l_e_st_eq_landau_n_rt_rp_r_satz187c l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl02 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5047 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t1 x y i)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t2 x y i))) (l_e_st_eq_landau_n_rt_rp_r_pl02 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5048 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz221a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_3221_t3 x y i) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t4 x y i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5049 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz221b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_comts x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz221a y x i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5050 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma4 y n : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y)).
+
+(* notion 5051 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_reis (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma1 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5052 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_imis (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma2 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5053 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t6 x y i n)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t7 x y i n))) (l_e_st_eq_landau_n_rt_rp_r_pl02 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5054 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_ii1r ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re y) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5055 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ir ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5056 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_ir1i ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5057 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5058 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_rr1r ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re y) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5059 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5060 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_ri1r ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re y) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5061 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ir ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5062 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_ri1i ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5063 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5064 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_3221_ii1r x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ir x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_3221_ii1r x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)).
+
+(* notion 5065 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_rr1r x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_ii1r x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_disttm1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_3221_rr1r x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_ii1r x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t9 x y i n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y))).
+
+(* notion 5066 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_ri1i x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_ir1i x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_3221_ri1i x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_ir1i x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y))).
+
+(* notion 5067 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t10 x y i n) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t11 x y i n)) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y)) (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1ii x y) (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_c_3221_r1rr x y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_i1ri x y))) (l_e_st_eq_landau_n_rt_rp_r_distpt2 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y))).
+
+(* notion 5068 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t12 x y i n) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t8 x y i n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5069 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz192c (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t13 x y i n)) (l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t5 x y i n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5070 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz182b (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t6 x y i n)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t14 x y i n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5071 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_pl01 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t14 x y i n))) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t7 x y i n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5072 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_c_v3_t7 y n j : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_im y) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5073 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λj:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz192c (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t15 x y i n)) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t17 x y i n j) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5074 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz192c (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t16 x y i n)) o : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5075 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_3221_t18 x y i n t) (λt:l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_re y) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_3221_t19 x y i n t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5076 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3221_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_ispli x) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_3221_t14 x y i n) (l_e_st_eq_landau_n_rt_rp_r_c_3221_t20 x y i n)) : l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5077 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz221c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_or_th2 (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c) (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_3221_t21 x y i t) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c)).
+
+(* notion 5078 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz221d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_or (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_or_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c) n o) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_satz221c x y t) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5079 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3222_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz195 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts02 (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_re x)).
+
+(* notion 5080 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3222_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_ts02 (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_satz195 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)).
+
+(* notion 5081 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz222 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a x l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_3222_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_3222_t2 x)) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x l_e_st_eq_landau_n_rt_rp_r_c_1c) x).
+
+(* notion 5082 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz222a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x l_e_st_eq_landau_n_rt_rp_r_c_1c) x (l_e_st_eq_landau_n_rt_rp_r_c_satz222 x) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_ts x l_e_st_eq_landau_n_rt_rp_r_c_1c)).
+
+(* notion 5083 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz222b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x l_e_st_eq_landau_n_rt_rp_r_c_1c) x (l_e_st_eq_landau_n_rt_rp_r_c_comts l_e_st_eq_landau_n_rt_rp_r_c_1c x) (l_e_st_eq_landau_n_rt_rp_r_c_satz222 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c x) x).
+
+(* notion 5084 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz222c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c x) x (l_e_st_eq_landau_n_rt_rp_r_c_satz222b x) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c x)).
+
+(* notion 5085 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3223_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_satz197b (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_satz195 (l_e_st_eq_landau_n_rt_rp_r_c_re x)))) (l_e_st_eq_landau_n_rt_rp_r_ts02 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)))) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))).
+
+(* notion 5086 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3223_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl))) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts02 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_satz197b (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_satz195 (l_e_st_eq_landau_n_rt_rp_r_c_im x))))) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))).
+
+(* notion 5087 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz223 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) x (l_e_st_eq_landau_n_rt_rp_r_c_m0isa l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a x (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_3223_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_3223_t2 x)) (l_e_st_eq_landau_n_rt_rp_r_c_satz214a x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)).
+
+(* notion 5088 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz223a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz223 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c))).
+
+(* notion 5089 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz223b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) x) (l_e_st_eq_landau_n_rt_rp_r_c_satz223 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)).
+
+(* notion 5090 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz223c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz223b x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) x)).
+
+(* notion 5091 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5092 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5093 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5094 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5095 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3224_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y))) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y)) (l_e_st_eq_landau_n_rt_rp_r_satz197a (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz197a (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y))) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_satz177 (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y))) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y)) (l_e_st_eq_landau_n_rt_rp_r_satz181a (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxry x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixiy x y)))).
+
+(* notion 5096 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3224_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy x y)) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry x y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry x y))) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry x y)) (l_e_st_eq_landau_n_rt_rp_r_satz197a (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_satz197a (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_satz180a (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry x y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3224_rxiy x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_ixry x y)))).
+
+(* notion 5097 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz224a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) y) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))))) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) y (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x)) (l_e_st_eq_landau_n_rt_rp_r_c_tsis1a y (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3224_t1 x y) (l_e_st_eq_landau_n_rt_rp_r_c_3224_t2 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0isb (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y))).
+
+(* notion 5098 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz224b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 y) x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts y x)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_comts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz224a y x) (l_e_st_eq_landau_n_rt_rp_r_c_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_comts y x)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y))).
+
+(* notion 5099 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz224c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz224a x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz224b x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))).
+
+(* notion 5100 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz224d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz224c x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y)).
+
+(* notion 5101 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz224e ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz224a x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) y)).
+
+(* notion 5102 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz224f ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz224b x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))).
+
+(* notion 5103 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz225 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz224c x (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) y x (l_e_st_eq_landau_n_rt_rp_r_c_satz215 y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)).
+
+(* notion 5104 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz225a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz225 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_m0 y))).
+
+(* notion 5105 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5106 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iir ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5107 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rii ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5108 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iri ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5109 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rri ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5110 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iii ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5111 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rir ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5112 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_irr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5113 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)) (l_e_st_eq_landau_n_rt_rp_r_disttm1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_satz180a (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))))).
+
+(* notion 5114 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_disttm1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z))) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z))).
+
+(* notion 5115 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_tsis1a z (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t2 x y z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)))).
+
+(* notion 5116 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts a b) c) (l_e_st_eq_landau_n_rt_rp_r_ts a (l_e_st_eq_landau_n_rt_rp_r_ts b c)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts b c) a) (l_e_st_eq_landau_n_rt_rp_r_assts1 a b c) (l_e_st_eq_landau_n_rt_rp_r_comts a (l_e_st_eq_landau_n_rt_rp_r_ts b c)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts a b) c) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_ts b c) a)).
+
+(* notion 5117 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t5 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_pl c (l_e_st_eq_landau_n_rt_rp_r_pl a b)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl c a) b) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_asspl2 c a b) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl c a) b)).
+
+(* notion 5118 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t6 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl a (l_e_st_eq_landau_n_rt_rp_r_pl b c)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl b c) a) (l_e_st_eq_landau_n_rt_rp_r_pl b (l_e_st_eq_landau_n_rt_rp_r_pl c a)) (l_e_st_eq_landau_n_rt_rp_r_compl a (l_e_st_eq_landau_n_rt_rp_r_pl b c)) (l_e_st_eq_landau_n_rt_rp_r_asspl1 b c a) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl a (l_e_st_eq_landau_n_rt_rp_r_pl b c)) (l_e_st_eq_landau_n_rt_rp_r_pl b (l_e_st_eq_landau_n_rt_rp_r_pl c a))).
+
+(* notion 5119 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr y z x : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5120 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_iir y z x : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5121 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_rii y z x : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5122 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_iri y z x : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5123 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_rri y z x : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5124 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_iii y z x : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5125 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_rir y z x : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5126 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_irr y z x : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5127 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t6 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))).
+
+(* notion 5128 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t5 (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z))).
+
+(* notion 5129 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t7 x y z) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z))))).
+
+(* notion 5130 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t8 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t4 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z))).
+
+(* notion 5131 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t3 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii x y z)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t9 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t10 x y z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z)))).
+
+(* notion 5132 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_comts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t3 y z x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z)))).
+
+(* notion 5133 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3226_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_3226_rrr1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_iir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rii1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iri1 x y z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3226_rir1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_irr1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_rri1 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_3226_iii1 x y z))) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t11 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3226_t12 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
+
+(* notion 5134 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz226 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3226_t13 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
+
+(* notion 5135 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_assts1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz226 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
+
+(* notion 5136 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_assts2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z)).
+
+(* notion 5137 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t1 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_pl a (l_e_st_eq_landau_n_rt_rp_r_pl b c)) (l_e_st_eq_landau_n_rt_rp_r_pl a (l_e_st_eq_landau_n_rt_rp_r_pl c b)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) b) (l_e_st_eq_landau_n_rt_rp_r_asspl1 a b c) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_pl b c) (l_e_st_eq_landau_n_rt_rp_r_pl c b) a (l_e_st_eq_landau_n_rt_rp_r_compl b c)) (l_e_st_eq_landau_n_rt_rp_r_asspl2 a c b) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) b)).
+
+(* notion 5138 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t2 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_pl c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) d) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) b) d) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl b d)) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_pl a b) c d) (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) c) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) b) d (l_e_st_eq_landau_n_rt_rp_r_c_3227_t1 a b c)) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_pl a c) b d) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_pl c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a c) (l_e_st_eq_landau_n_rt_rp_r_pl b d))).
+
+(* notion 5139 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t3 ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.λc:l_e_st_eq_landau_n_rt_rp_r_real.λd:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_pl c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 c) (l_e_st_eq_landau_n_rt_rp_r_m0 d))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn b d)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 c) (l_e_st_eq_landau_n_rt_rp_r_m0 d)) (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_satz180 c d)) (l_e_st_eq_landau_n_rt_rp_r_c_3227_t2 a b (l_e_st_eq_landau_n_rt_rp_r_m0 c) (l_e_st_eq_landau_n_rt_rp_r_m0 d)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl a b) (l_e_st_eq_landau_n_rt_rp_r_pl c d)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn a c) (l_e_st_eq_landau_n_rt_rp_r_mn b d))).
+
+(* notion 5140 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets x z)) (l_e_st_eq_landau_n_rt_rp_r_ismn12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_disttp2 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_disttp2 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_c_3227_t3 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets x z))).
+
+(* notion 5141 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x z)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_disttp2 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_disttp2 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_c_3227_t2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im z)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x z))).
+
+(* notion 5142 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3227_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets x z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x z))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets x z)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im z))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re z)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_3227_t4 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_3227_t5 x y z)) (l_e_st_eq_landau_n_rt_rp_r_c_plis12b (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y) (l_e_st_eq_landau_n_rt_rp_r_c_rets x z) (l_e_st_eq_landau_n_rt_rp_r_c_imts x z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
+
+(* notion 5143 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz227 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_3227_t6 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
+
+(* notion 5144 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_disttp1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_satz227 z x y) (l_e_st_eq_landau_n_rt_rp_r_c_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_comts z x) (l_e_st_eq_landau_n_rt_rp_r_c_comts z y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
+
+(* notion 5145 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_disttp2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz227 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
+
+(* notion 5146 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_distpt1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_disttp1 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z)).
+
+(* notion 5147 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_distpt2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_disttp2 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
+
+(* notion 5148 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz228 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_m0 z))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 z))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_m0 z)) x (l_e_st_eq_landau_n_rt_rp_r_c_satz218 y z)) (l_e_st_eq_landau_n_rt_rp_r_c_disttp2 x y (l_e_st_eq_landau_n_rt_rp_r_c_m0 z)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_m0 z)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz224b x z)) (l_e_st_eq_landau_n_rt_rp_r_c_satz218a (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
+
+(* notion 5149 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_disttm1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_satz228 z x y) (l_e_st_eq_landau_n_rt_rp_r_c_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_comts z x) (l_e_st_eq_landau_n_rt_rp_r_c_comts z y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
+
+(* notion 5150 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_disttm2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz228 x y z : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
+
+(* notion 5151 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_distmt1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_disttm1 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)).
+
+(* notion 5152 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_distmt2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_disttm2 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z))).
+
+(* notion 5153 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λu1:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu2:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) x.λj:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) x.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) x i j : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2)).
+
+(* notion 5154 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λu1:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu2:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) x.λj:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_mn u1 u2)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_disttm2 y u1 u2) (l_e_st_eq_landau_n_rt_rp_r_c_satz213b (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t1 x y n u1 u2 i j)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_mn u1 u2)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5155 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λu1:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu2:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) x.λj:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) x.(l_ore2 (l_e_st_eq_landau_n_rt_rp_r_c_is y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn u1 u2) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_satz221c y (l_e_st_eq_landau_n_rt_rp_r_c_mn u1 u2) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t2 x y n u1 u2 i j)) n : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn u1 u2) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5156 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz229b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λu1:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu2:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u1) x.λj:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u2) x.(l_e_st_eq_landau_n_rt_rp_r_c_satz213a u1 u2 (l_e_st_eq_landau_n_rt_rp_r_c_3229_t3 x y n u1 u2 i j) : l_e_st_eq_landau_n_rt_rp_r_c_is u1 u2).
+
+(* notion 5157 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_lemma4 y n) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5158 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_u ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)))) x : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 5159 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_dd ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λv:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_ov v (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5160 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_satz197b (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_satz177 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_lemma6 (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))).
+
+(* notion 5161 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_lemma6 (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t5 x y n)) (l_e_st_eq_landau_n_rt_rp_r_lemma7 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) (l_e_st_eq_landau_n_rt_rp_r_lemma8 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) l_e_st_eq_landau_n_rt_rp_r_1rl).
+
+(* notion 5162 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_satz197d (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_lemma6 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))).
+
+(* notion 5163 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t7 x y n) (l_e_st_eq_landau_n_rt_rp_r_lemma6 (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n))) (l_e_st_eq_landau_n_rt_rp_r_lemma7 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))))).
+
+(* notion 5164 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz197a (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_satz182e (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5165 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_t8 x y n) (l_e_isf l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n t) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_t9 x y n)) (l_e_st_eq_landau_n_rt_rp_r_lemma9 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5166 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))))) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a y (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im y) (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_t6 x y n) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t10 x y n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 5167 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_3229_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_3229_u x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c x) x (l_e_st_eq_landau_n_rt_rp_r_c_assts2 y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) x) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_3229_dd x y n (l_e_st_eq_landau_n_rt_rp_r_c_im y))))) l_e_st_eq_landau_n_rt_rp_r_c_1c x (l_e_st_eq_landau_n_rt_rp_r_c_3229_t11 x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_satz222b x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_3229_u x y n)) x).
+
+(* notion 5168 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz229a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_somei l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x) (l_e_st_eq_landau_n_rt_rp_r_c_3229_u x y n) (l_e_st_eq_landau_n_rt_rp_r_c_3229_t12 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_some (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x)).
+
+(* notion 5169 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz229 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_onei l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x) (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x.λw:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) x.l_e_st_eq_landau_n_rt_rp_r_c_satz229b x y n t u v w) (l_e_st_eq_landau_n_rt_rp_r_c_satz229a x y n) : l_e_st_eq_landau_n_rt_rp_r_c_one (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x)).
+
+(* notion 5170 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ov ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_ind l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x) (l_e_st_eq_landau_n_rt_rp_r_c_satz229 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 5171 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz229c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_oneax l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y t) x) (l_e_st_eq_landau_n_rt_rp_r_c_satz229 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x).
+
+(* notion 5172 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz229d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n))).
+
+(* notion 5173 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz229e ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x).
+
+(* notion 5174 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz229f ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x (l_e_st_eq_landau_n_rt_rp_r_c_satz229e x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y)).
+
+(* notion 5175 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz229g ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) x.(l_e_st_eq_landau_n_rt_rp_r_c_satz229b x y n u (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) i (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is u (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)).
+
+(* notion 5176 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz229h ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx u (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz229g x y u n i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) u).
+
+(* notion 5177 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz229j ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts u y) x.(l_e_st_eq_landau_n_rt_rp_r_c_satz229g x y u n (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y) x (l_e_st_eq_landau_n_rt_rp_r_c_comts y u) i) : l_e_st_eq_landau_n_rt_rp_r_c_is u (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)).
+
+(* notion 5178 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz229k ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts u y) x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx u (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz229j x y u n i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) u).
+
+(* notion 5179 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isov1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ov t z n) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)).
+
+(* notion 5180 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isov2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229h z x (l_e_st_eq_landau_n_rt_rp_r_c_ov z y o) n (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov z y o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y o)) z (l_e_st_eq_landau_n_rt_rp_r_c_ists1 x y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y o) i) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c z y o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov z x n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y o)).
+
+(* notion 5181 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isov12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_c_is z u.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y u o) (l_e_st_eq_landau_n_rt_rp_r_c_isov1 x y z i n) (l_e_st_eq_landau_n_rt_rp_r_c_isov2 z u y j n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y u o)).
+
+(* notion 5182 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz230 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) x (l_e_st_eq_landau_n_rt_rp_r_c_compl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz212h x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x).
+
+(* notion 5183 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz231 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212e (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) y x (l_e_st_eq_landau_n_rt_rp_r_c_compl y x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) y) x).
+
+(* notion 5184 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz232 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212e x (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) y).
+
+(* notion 5185 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_4233_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) z) y) (l_e_st_eq_landau_n_rt_rp_r_c_compl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_compl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) z y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) z) y)).
+
+(* notion 5186 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_4233_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) z) y) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x (l_e_st_eq_landau_n_rt_rp_r_c_4233_t1 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y (l_e_st_eq_landau_n_rt_rp_r_c_satz230 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)) x).
+
+(* notion 5187 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz233 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212d x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_4233_t2 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
+
+(* notion 5188 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz234 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212g (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) z) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) z) y x (l_e_st_eq_landau_n_rt_rp_r_c_satz230 y z))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z))).
+
+(* notion 5189 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz234a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_satz234 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z)).
+
+(* notion 5190 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz234b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl y x) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y) (l_e_st_eq_landau_n_rt_rp_r_c_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y x) z (l_e_st_eq_landau_n_rt_rp_r_c_compl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz234 y x z) (l_e_st_eq_landau_n_rt_rp_r_c_compl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y)).
+
+(* notion 5191 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz234c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz234b x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z)).
+
+(* notion 5192 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz235 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212f x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl z (l_e_st_eq_landau_n_rt_rp_r_c_mn y z))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl z (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz212h y z)) (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z))).
+
+(* notion 5193 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz235a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_satz235 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z)).
+
+(* notion 5194 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz235b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz235a x y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz234c x z y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) y)).
+
+(* notion 5195 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz235c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) y) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz235b x y z) (l_e_st_eq_landau_n_rt_rp_r_c_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) y (l_e_st_eq_landau_n_rt_rp_r_c_compl x z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x (l_e_st_eq_landau_n_rt_rp_r_c_mn y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) y)).
+
+(* notion 5196 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz236 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212g (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y z) (l_e_st_eq_landau_n_rt_rp_r_c_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x z (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
+
+(* notion 5197 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz236a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_compl z x) (l_e_st_eq_landau_n_rt_rp_r_c_compl z y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz236 x y z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl z x) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
+
+(* notion 5198 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_4237_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) u) y) (l_e_st_eq_landau_n_rt_rp_r_c_pl z y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) u y) (l_e_st_eq_landau_n_rt_rp_r_c_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) u) z y (l_e_st_eq_landau_n_rt_rp_r_c_satz230 z u)) (l_e_st_eq_landau_n_rt_rp_r_c_compl z y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)).
+
+(* notion 5199 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_4237_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_compl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_pl u y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_4237_t1 x y z u)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
+
+(* notion 5200 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_4237_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_4237_t2 x y z u) (l_e_st_eq_landau_n_rt_rp_r_c_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y z) (l_e_st_eq_landau_n_rt_rp_r_c_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x z (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl x z)).
+
+(* notion 5201 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz237 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212f (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_4237_t3 x y z u) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_pl y u))).
+
+(* notion 5202 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_4238_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl u z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl z u)) (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 x u z) (l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_pl u z) (l_e_st_eq_landau_n_rt_rp_r_c_pl z u) x (l_e_st_eq_landau_n_rt_rp_r_c_compl u z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl z u))).
+
+(* notion 5203 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_4238_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_pl z u))) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz237 (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) z u) (l_e_st_eq_landau_n_rt_rp_r_c_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl x (l_e_st_eq_landau_n_rt_rp_r_c_pl z u)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_pl z u)) (l_e_st_eq_landau_n_rt_rp_r_c_4238_t1 x y z u) (l_e_st_eq_landau_n_rt_rp_r_c_asspl1 y z u)) (l_e_st_eq_landau_n_rt_rp_r_c_satz236 x y (l_e_st_eq_landau_n_rt_rp_r_c_pl z u)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)).
+
+(* notion 5204 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz238 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212g (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) (l_e_st_eq_landau_n_rt_rp_r_c_4238_t2 x y z u) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z))).
+
+(* notion 5205 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_4239_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_satz238 x y z u) (l_e_st_eq_landau_n_rt_rp_r_c_satz213b (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5206 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz239a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u).(l_e_st_eq_landau_n_rt_rp_r_c_satz213a (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) (l_e_st_eq_landau_n_rt_rp_r_c_4239_t1 x y z u i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)).
+
+(* notion 5207 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_4239_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_satz238 x y z u) (l_e_st_eq_landau_n_rt_rp_r_c_satz213b (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z) i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5208 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz239b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x u) (l_e_st_eq_landau_n_rt_rp_r_c_pl y z).(l_e_st_eq_landau_n_rt_rp_r_c_satz213a (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u) (l_e_st_eq_landau_n_rt_rp_r_c_4239_t2 x y z u i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) (l_e_st_eq_landau_n_rt_rp_r_c_mn z u)).
+
+(* notion 5209 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz240 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x).
+
+(* notion 5210 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz241 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229h (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) y x n (l_e_st_eq_landau_n_rt_rp_r_c_comts y x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) y n) x).
+
+(* notion 5211 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) n (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx x l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y o) (l_e_st_eq_landau_n_rt_rp_r_c_satz221b y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) t)) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5212 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz242 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229h x (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) y (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 x y n o) (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov x y o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 x y n o)) y).
+
+(* notion 5213 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5243_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) z) y) (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) (l_e_st_eq_landau_n_rt_rp_r_c_comts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) z y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) z) y)).
+
+(* notion 5214 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5243_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) z) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x (l_e_st_eq_landau_n_rt_rp_r_c_5243_t1 x y z n o) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) z) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y (l_e_st_eq_landau_n_rt_rp_r_c_satz240 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o)) x).
+
+(* notion 5215 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz243 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229g x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o) (l_e_st_eq_landau_n_rt_rp_r_c_5243_t2 x y z n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z o) (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o))).
+
+(* notion 5216 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz244 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229k (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) n (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n) z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n) z) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n) z) y x (l_e_st_eq_landau_n_rt_rp_r_c_satz240 y z n))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n))).
+
+(* notion 5217 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz244a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_satz244 x y z n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n)).
+
+(* notion 5218 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz244b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) y) (l_e_st_eq_landau_n_rt_rp_r_c_isov1 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) z (l_e_st_eq_landau_n_rt_rp_r_c_comts x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_satz244 y x z n) (l_e_st_eq_landau_n_rt_rp_r_c_comts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) y)).
+
+(* notion 5219 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz244c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) y) (l_e_st_eq_landau_n_rt_rp_r_c_satz244b x y z n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) y) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z n)).
+
+(* notion 5220 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz245 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229j x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o) (l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x (l_e_st_eq_landau_n_rt_rp_r_c_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o)) y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c y z o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z) (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o))).
+
+(* notion 5221 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz245a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z) (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz245 x y z n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z)).
+
+(* notion 5222 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz245b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) z) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz245a x y z n o) (l_e_st_eq_landau_n_rt_rp_r_c_satz244c x z y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) y n)).
+
+(* notion 5223 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz245c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz245b x y z n o) (l_e_st_eq_landau_n_rt_rp_r_c_isov1 (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) y (l_e_st_eq_landau_n_rt_rp_r_c_comts x z) n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_ov y z o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) y n)).
+
+(* notion 5224 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz246 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229k (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y z) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x z (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y n))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)).
+
+(* notion 5225 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz246a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z y o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_isov12 (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_comts z x) (l_e_st_eq_landau_n_rt_rp_r_c_comts z y) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z y o n) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz246 x y z n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts z x) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z y o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)).
+
+(* notion 5226 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5247_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) u) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts z y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) u y) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) u) z y (l_e_st_eq_landau_n_rt_rp_r_c_satz240 z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_comts z y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)).
+
+(* notion 5227 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5247_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_comts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ts u y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_5247_t1 x y z u n o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z))).
+
+(* notion 5228 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5247_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_5247_t2 x y z u n o) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y z) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x z (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)).
+
+(* notion 5229 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz247 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229j (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o) (l_e_st_eq_landau_n_rt_rp_r_c_5247_t3 x y z u n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o))).
+
+(* notion 5230 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5248_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts u z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 x u z) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts u z) (l_e_st_eq_landau_n_rt_rp_r_c_ts z u) x (l_e_st_eq_landau_n_rt_rp_r_c_comts u z)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts z u))).
+
+(* notion 5231 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5248_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u p)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) u (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o) p)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u) n (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z u o p))) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz247 (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) z u (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o) p) (l_e_st_eq_landau_n_rt_rp_r_c_isov12 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_5248_t1 x y z u n o p) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 y z u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) u (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o) p) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u) n (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z u o p))) (l_e_st_eq_landau_n_rt_rp_r_c_satz246 x y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u) n (l_e_st_eq_landau_n_rt_rp_r_c_satz221d z u o p)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u p)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)).
+
+(* notion 5232 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz248 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229k (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u p) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u o p) (l_e_st_eq_landau_n_rt_rp_r_c_5248_t2 x y z u n o p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u p) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u o p)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n o))).
+
+(* notion 5233 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz249 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229h l_e_st_eq_landau_n_rt_rp_r_c_0c x l_e_st_eq_landau_n_rt_rp_r_c_0c n (l_e_st_eq_landau_n_rt_rp_r_c_satz221b x l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_0c)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_0c x n) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5234 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz250 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229h x x l_e_st_eq_landau_n_rt_rp_r_c_1c n (l_e_st_eq_landau_n_rt_rp_r_c_satz222 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x x n) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 5235 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz251a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov x x (l_e_notis_th2 l_e_st_eq_landau_n_rt_rp_r_c_cx y l_e_st_eq_landau_n_rt_rp_r_c_0c x n i)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_isov2 y x x (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx x y i) n (l_e_notis_th2 l_e_st_eq_landau_n_rt_rp_r_c_cx y l_e_st_eq_landau_n_rt_rp_r_c_0c x n i)) (l_e_st_eq_landau_n_rt_rp_r_c_satz250 x (l_e_notis_th2 l_e_st_eq_landau_n_rt_rp_r_c_cx y l_e_st_eq_landau_n_rt_rp_r_c_0c x n i)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 5236 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz251b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) l_e_st_eq_landau_n_rt_rp_r_c_1c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y l_e_st_eq_landau_n_rt_rp_r_c_1c) y (l_e_st_eq_landau_n_rt_rp_r_c_satz229d x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) l_e_st_eq_landau_n_rt_rp_r_c_1c y i) (l_e_st_eq_landau_n_rt_rp_r_c_satz222 y) : l_e_st_eq_landau_n_rt_rp_r_c_is x y).
+
+(* notion 5237 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_0c u o) l_e_st_eq_landau_n_rt_rp_r_c_0c i (l_e_st_eq_landau_n_rt_rp_r_c_isov1 z l_e_st_eq_landau_n_rt_rp_r_c_0c u j o) (l_e_st_eq_landau_n_rt_rp_r_c_satz249 u o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5238 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_satz229d x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz221b y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_5252_t1 x y z u n o i j)) : l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5239 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_satz221a x u (l_e_st_eq_landau_n_rt_rp_r_c_5252_t2 x y z u n o i j)) (l_e_st_eq_landau_n_rt_rp_r_c_satz221b y z j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)).
+
+(* notion 5240 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n p)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u p o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz248 x y z u n p o) (l_e_st_eq_landau_n_rt_rp_r_c_satz251a (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u p o) i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n p)) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 5241 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz251b (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n p) (l_e_st_eq_landau_n_rt_rp_r_c_5252_t4 x y z u n o i p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)).
+
+(* notion 5242 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz252a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_5252_t3 x y z u n o i t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_5252_t5 x y z u n o i t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)).
+
+(* notion 5243 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) l_e_st_eq_landau_n_rt_rp_r_c_0c i (l_e_st_eq_landau_n_rt_rp_r_c_satz221b y z j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5244 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is u l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_satz221c x u (l_e_st_eq_landau_n_rt_rp_r_c_5252_t6 x y z u n o i j)) o : l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5245 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).λj:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_0c y n) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_isov1 x l_e_st_eq_landau_n_rt_rp_r_c_0c y (l_e_st_eq_landau_n_rt_rp_r_c_5252_t7 x y z u n o i j) n) (l_e_st_eq_landau_n_rt_rp_r_c_satz249 y n)) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_0c u o) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_isov1 z l_e_st_eq_landau_n_rt_rp_r_c_0c u j o) (l_e_st_eq_landau_n_rt_rp_r_c_satz249 u o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)).
+
+(* notion 5246 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u p o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n p)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_satz248 x y z u n p o) (l_e_st_eq_landau_n_rt_rp_r_c_satz251a (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y z n p) i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u p o)) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 5247 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_5252_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz251b (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma6 z u p o) (l_e_st_eq_landau_n_rt_rp_r_c_5252_t9 x y z u n o i p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)).
+
+(* notion 5248 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz252b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is z l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_5252_t8 x y z u n o i t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_5252_t10 x y z u n o i t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)).
+
+(* notion 5249 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz253 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229g (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) y (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) n (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n))) (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) (l_e_st_eq_landau_n_rt_rp_r_c_disttp2 y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) z (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c z y n))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl x z) y n)).
+
+(* notion 5250 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_distop ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_satz253 x z y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n))).
+
+(* notion 5251 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_distpo ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz253 x z y n : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) z n)).
+
+(* notion 5252 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz254 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o))) (l_e_st_eq_landau_n_rt_rp_r_c_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_satz246 x y u n o) (l_e_st_eq_landau_n_rt_rp_r_c_satz246a z u y o n)) (l_e_st_eq_landau_n_rt_rp_r_c_satz253 (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o))).
+
+(* notion 5253 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz255 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229g (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) n (l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n))) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n))) (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) (l_e_st_eq_landau_n_rt_rp_r_c_disttm2 y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) z (l_e_st_eq_landau_n_rt_rp_r_c_satz229c x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz229c z y n))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn x z) y n)).
+
+(* notion 5254 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_distom ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_satz255 x z y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z n) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n))).
+
+(* notion 5255 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_distmo ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis z l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz255 x z y n : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x z n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y z n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) z n)).
+
+(* notion 5256 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz256 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis u l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o))) (l_e_st_eq_landau_n_rt_rp_r_c_ismn12 (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o) (l_e_st_eq_landau_n_rt_rp_r_c_satz246 x y u n o) (l_e_st_eq_landau_n_rt_rp_r_c_satz246a z u y o n)) (l_e_st_eq_landau_n_rt_rp_r_c_satz255 (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) (l_e_st_eq_landau_n_rt_rp_r_c_ov z u o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts x u) (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u) (l_e_st_eq_landau_n_rt_rp_r_c_satz221d y u n o))).
+
+(* notion 5257 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_conj ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 5258 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_conjisa ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) a (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))) (l_e_st_eq_landau_n_rt_rp_r_m0 b) (l_e_st_eq_landau_n_rt_rp_r_c_reis a b) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) b (l_e_st_eq_landau_n_rt_rp_r_c_imis a b)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_pli a (l_e_st_eq_landau_n_rt_rp_r_m0 b))).
+
+(* notion 5259 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_conjisb ≝ λa:l_e_st_eq_landau_n_rt_rp_r_real.λb:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pli a b)) (l_e_st_eq_landau_n_rt_rp_r_c_pli a (l_e_st_eq_landau_n_rt_rp_r_m0 b)) (l_e_st_eq_landau_n_rt_rp_r_c_conjisa a b) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli a (l_e_st_eq_landau_n_rt_rp_r_m0 b)) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pli a b))).
+
+(* notion 5260 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isconj ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_conj t) x y i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)).
+
+(* notion 5261 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz257 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_conjisa (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_satz177 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) x).
+
+(* notion 5262 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz258a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_isconj x l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_conjisa l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5263 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6258_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isre (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma1 (l_e_st_eq_landau_n_rt_rp_r_c_conj x) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5264 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6258_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_satz176e (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isim (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma2 (l_e_st_eq_landau_n_rt_rp_r_c_conj x) i)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5265 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz258b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_ispli x) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_re x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_6258_t1 x i) (l_e_st_eq_landau_n_rt_rp_r_c_6258_t2 x i)) : l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5266 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6258_anders ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx x l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_satz257 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz258a (l_e_st_eq_landau_n_rt_rp_r_c_conj x) i) : l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5267 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz258c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) n (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_satz258b x t) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_conj x) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5268 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6259_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_isim (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isceim (l_e_st_eq_landau_n_rt_rp_r_c_conj x) x i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x)).
+
+(* notion 5269 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz259a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) x.(l_e_st_eq_landau_n_rt_rp_r_lemma10 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_6259_t1 x i)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5270 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz259b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) x (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz176b (l_e_st_eq_landau_n_rt_rp_r_c_im x) i) i)) (l_e_st_eq_landau_n_rt_rp_r_c_pliis x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) x).
+
+(* notion 5271 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz269c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_conj x).(l_e_st_eq_landau_n_rt_rp_r_c_satz259a x (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_conj x) i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5272 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz269d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im x) l_e_st_eq_landau_n_rt_rp_r_0.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) x (l_e_st_eq_landau_n_rt_rp_r_c_satz259b x i) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)).
+
+(* notion 5273 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz260 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_conjisa (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz180 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_plis12b (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
+
+(* notion 5274 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz260a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz260 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
+
+(* notion 5275 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6261_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_satz180 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz197f (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_satz197e (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))).
+
+(* notion 5276 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz261 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y)))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_conjisa (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_c_rets x y) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_imts x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y))) (l_e_st_eq_landau_n_rt_rp_r_ismn2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_satz198a (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_6261_t1 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_tsis12b (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im y))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
+
+(* notion 5277 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz261a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz261 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y))).
+
+(* notion 5278 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6262_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) x (l_e_st_eq_landau_n_rt_rp_r_c_satz230 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y)).
+
+(* notion 5279 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6262_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_isconj x (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) (l_e_st_eq_landau_n_rt_rp_r_c_6262_t1 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz260 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y) y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
+
+(* notion 5280 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz262 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz212f (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_6262_t2 x y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
+
+(* notion 5281 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz262a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz262 x y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_mn x y))).
+
+(* notion 5282 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6263_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229f x y n : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y)).
+
+(* notion 5283 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6263_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_isconj x (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_6263_t1 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y))).
+
+(* notion 5284 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6263_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz261 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
+
+(* notion 5285 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6263_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_6263_t2 x y n) (l_e_st_eq_landau_n_rt_rp_r_c_6263_t3 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))).
+
+(* notion 5286 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_6263_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz258c y n : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_conj y) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 5287 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz263 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229j (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_6263_t5 x y n) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_6263_t4 x y n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y) (l_e_st_eq_landau_n_rt_rp_r_c_satz258c y n))).
+
+(* notion 5288 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz263a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y) (l_e_st_eq_landau_n_rt_rp_r_c_satz258c y n)) (l_e_st_eq_landau_n_rt_rp_r_c_satz263 x y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y) (l_e_st_eq_landau_n_rt_rp_r_c_satz258c y n)) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n))).
+
+(* notion 5289 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_mod ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_sqrt (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5290 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ismod ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_mod t) x y i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)).
+
+(* notion 5291 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz264a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_sqrtnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x) (l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma4 x n)) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod x)).
+
+(* notion 5292 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz264b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_sqrt0 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma3 x i) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5293 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz264c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_thsqrt1a (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod x))).
+
+(* notion 5294 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz264d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_satz167f (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0 (l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_c_satz264c x) (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_satz169d (l_e_st_eq_landau_n_rt_rp_r_c_mod x) t)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5295 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_thsqrt1b (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x))).
+
+(* notion 5296 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_lemma12 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)))).
+
+(* notion 5297 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_satz191 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_moreisi2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)))) (l_e_st_eq_landau_n_rt_rp_r_lemma11 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 5298 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismoreis12 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t2 x) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t3 x) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)))).
+
+(* notion 5299 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_lemma12 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
+
+(* notion 5300 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_satz191 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_lemma11 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_moreisi2 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
+
+(* notion 5301 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismoreis12 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t5 x) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t6 x) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)))).
+
+(* notion 5302 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_lemma2 r s l : l_e_st_eq_landau_n_rt_rp_r_more s r).
+
+(* notion 5303 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_satz169b s (l_e_st_eq_landau_n_rt_rp_r_satz172d s r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_7265_t8 r s m n l) n) : l_e_st_eq_landau_n_rt_rp_r_pos s).
+
+(* notion 5304 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λo:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_trmore (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_satz203a s r s (l_e_st_eq_landau_n_rt_rp_r_c_7265_t8 r s m n l) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t9 r s m n l)) (l_e_st_eq_landau_n_rt_rp_r_satz203d s r r (l_e_st_eq_landau_n_rt_rp_r_c_7265_t8 r s m n l) (l_e_st_eq_landau_n_rt_rp_r_satz169b r o)) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts r r)).
+
+(* notion 5305 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_ismore2 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 r r i)) (l_e_st_eq_landau_n_rt_rp_r_satz169a (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_possq s (l_e_st_eq_landau_n_rt_rp_r_pnot0 s (l_e_st_eq_landau_n_rt_rp_r_c_7265_t9 r s m n l)))) : l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts r r)).
+
+(* notion 5306 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.λl:l_e_st_eq_landau_n_rt_rp_r_less r s.(l_e_st_eq_landau_n_rt_rp_r_lemma1 (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_orapp (l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts r r)) n (λt:l_e_st_eq_landau_n_rt_rp_r_more r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_7265_t10 r s m n l t) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_7265_t11 r s m n l t)) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s)).
+
+(* notion 5307 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7265_t13 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s).λn:l_e_st_eq_landau_n_rt_rp_r_moreis r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_satz167f r s (λt:l_e_st_eq_landau_n_rt_rp_r_less r s.l_e_st_eq_landau_n_rt_rp_r_satz167c (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s) m (l_e_st_eq_landau_n_rt_rp_r_c_7265_t12 r s m n t)) : l_e_st_eq_landau_n_rt_rp_r_moreis r s).
+
+(* notion 5308 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz265a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_7265_t13 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t4 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz264d x) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x))).
+
+(* notion 5309 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz265b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_7265_t13 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_7265_t7 x) (l_e_st_eq_landau_n_rt_rp_r_c_satz264d x) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_im x))).
+
+(* notion 5310 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t1 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts t t) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_satz176b (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts t t) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts t t)).
+
+(* notion 5311 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t2 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 t)) (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 t) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 t (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_ts02 t l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 t)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5312 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t3 ≝ λt:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli t l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts t t) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 t))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts t t) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_tsis12a t l_e_st_eq_landau_n_rt_rp_r_0 t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts t t) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts t t) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 t)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_7266_t1 t) (l_e_st_eq_landau_n_rt_rp_r_c_7266_t2 t)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli t l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli t l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts t t) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 5313 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts s s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_7266_t3 r)) i (l_e_st_eq_landau_n_rt_rp_r_c_7266_t3 s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts s s) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 5314 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts s s) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_c_isre (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts s s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_7266_t4 r s i n o)) (l_e_st_eq_landau_n_rt_rp_r_c_reis (l_e_st_eq_landau_n_rt_rp_r_ts s s) l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s)).
+
+(* notion 5315 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).(l_andi (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s)) n (l_e_st_eq_landau_n_rt_rp_r_c_7266_t5 r s i n o) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts s s))).
+
+(* notion 5316 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7266_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).(l_andi (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts s s)) o (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts s s)) : l_and (l_not (l_e_st_eq_landau_n_rt_rp_r_neg s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts s s) (l_e_st_eq_landau_n_rt_rp_r_ts s s))).
+
+(* notion 5317 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz266 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_neg s).(l_e_st_eq_landau_n_rt_rp_r_satzr161b (l_e_st_eq_landau_n_rt_rp_r_ts s s) r s (l_e_st_eq_landau_n_rt_rp_r_c_7266_t6 r s i n o) (l_e_st_eq_landau_n_rt_rp_r_c_7266_t7 r s i n o) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 5318 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7267_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_7266_t3 (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_thsqrt1b (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 5319 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7267_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_satz197e (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_satz198 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
+
+(* notion 5320 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7267_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_satz197b (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_satz179a (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x))) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5321 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7267_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_tsis2a x (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_re x))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_7267_t2 x) (l_e_st_eq_landau_n_rt_rp_r_c_7267_t3 x)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 5322 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz267 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_7267_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_7267_t4 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x))).
+
+(* notion 5323 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz267a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_satz267 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 5324 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts x z)) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 x y z) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts y x) z (l_e_st_eq_landau_n_rt_rp_r_c_comts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 y x z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts x z))).
+
+(* notion 5325 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λu:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u))) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_ts y u))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 x y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) x (l_e_st_eq_landau_n_rt_rp_r_c_7268_t1 y z u)) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 x z (l_e_st_eq_landau_n_rt_rp_r_c_ts y u)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts z u)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x z) (l_e_st_eq_landau_n_rt_rp_r_c_ts y u))).
+
+(* notion 5326 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_conj y))) (l_e_st_eq_landau_n_rt_rp_r_c_satz267 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_conj (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz261 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t2 x y (l_e_st_eq_landau_n_rt_rp_r_c_conj x) (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_conj y)))).
+
+(* notion 5327 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_conj y))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t3 x y) (l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_conj x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts y (l_e_st_eq_landau_n_rt_rp_r_c_conj y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_satz267a x) (l_e_st_eq_landau_n_rt_rp_r_c_satz267a y)) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t2 (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)))).
+
+(* notion 5328 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_satz176b (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 5329 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 s (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_ts02 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5330 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_tsis12a r l_e_st_eq_landau_n_rt_rp_r_0 s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_7268_t5 r s) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t6 r s)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 5331 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t4 x y) (l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t7 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t7 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 5332 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7268_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)).(l_orapp (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) (l_and (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) l_con (l_e_st_eq_landau_n_rt_rp_r_satz196h (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) n) (λt:l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod y)).l_e_st_eq_landau_n_rt_rp_r_c_satz264c y (l_ande2 (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) t)) (λt:l_and (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod y)).l_e_st_eq_landau_n_rt_rp_r_c_satz264c x (l_ande1 (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) t)) : l_con).
+
+(* notion 5333 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz268 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz266 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7268_t8 x y) (l_e_st_eq_landau_n_rt_rp_r_c_satz264c (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (λt:l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)).l_e_st_eq_landau_n_rt_rp_r_c_7268_t9 x y t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))).
+
+(* notion 5334 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz268a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz268 x y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts x y))).
+
+(* notion 5335 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7269_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_satz264a y n) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5336 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7269_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz268 (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n) y) x (l_e_st_eq_landau_n_rt_rp_r_c_satz240 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)).
+
+(* notion 5337 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7269_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_satz204g (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_7269_t1 x y n) (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_comts (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n))) (l_e_st_eq_landau_n_rt_rp_r_c_7269_t2 x y n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_7269_t1 x y n))).
+
+(* notion 5338 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz269 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_7269_t3 x y n : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x y n)) (l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_satz264a y n)))).
+
+(* notion 5339 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7270_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_abs r) r) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_moreisi1 (l_e_st_eq_landau_n_rt_rp_r_abs r) r (l_e_st_eq_landau_n_rt_rp_r_trmore (l_e_st_eq_landau_n_rt_rp_r_abs r) l_e_st_eq_landau_n_rt_rp_r_0 r (l_e_st_eq_landau_n_rt_rp_r_satz169a (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_satz166b r t)) (l_e_st_eq_landau_n_rt_rp_r_lemma2 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz169c r t)))) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).l_e_st_eq_landau_n_rt_rp_r_moreisi2 (l_e_st_eq_landau_n_rt_rp_r_abs r) r (l_e_st_eq_landau_n_rt_rp_r_absnn r t)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_abs r) r).
+
+(* notion 5340 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7270_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_trmoreis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_satz265a x) (l_e_st_eq_landau_n_rt_rp_r_c_7270_t1 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)).
+
+(* notion 5341 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7270_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_1c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_1c) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_isre (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im y))) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_1c i) (l_e_st_eq_landau_n_rt_rp_r_c_reis l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_1rl).
+
+(* notion 5342 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz270 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_1c.(l_e_st_eq_landau_n_rt_rp_r_ismoreis2 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re y)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7270_t3 x y i) (l_e_st_eq_landau_n_rt_rp_r_satz191 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_re y) (l_e_st_eq_landau_n_rt_rp_r_c_7270_t2 x) (l_e_st_eq_landau_n_rt_rp_r_c_7270_t2 y)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) l_e_st_eq_landau_n_rt_rp_r_1rl).
+
+(* notion 5343 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz264b (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5344 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ismoreis2 (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t1 x y i)) (l_e_st_eq_landau_n_rt_rp_r_satz191 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_mod y) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_satz264d x) (l_e_st_eq_landau_n_rt_rp_r_c_satz264d y)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
+
+(* notion 5345 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_pnot0 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz264a (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) : l_e_st_eq_landau_n_rt_rp_r_nis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 5346 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_satz253 x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz250 (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 5347 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz270 (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t4 x y n) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n))) l_e_st_eq_landau_n_rt_rp_r_1rl).
+
+(* notion 5348 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_fx ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t3 x y n) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5349 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_fy ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ov (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t3 x y n) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5350 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ismoreis1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ov y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n) (l_e_st_eq_landau_n_rt_rp_r_c_satz269 x (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_satz269 y (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t5 x y n) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl).
+
+(* notion 5351 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_prl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5352 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_prr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5353 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_orapp (l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t6 x y n) (λt:l_e_st_eq_landau_n_rt_rp_r_more (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl.l_e_st_eq_landau_n_rt_rp_r_moreisi1 (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n) (l_e_st_eq_landau_n_rt_rp_r_satz203a (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) t (l_e_st_eq_landau_n_rt_rp_r_c_satz264a (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) n))) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl.l_e_st_eq_landau_n_rt_rp_r_moreisi2 (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n) (l_e_st_eq_landau_n_rt_rp_r_ists1 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) t)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n)).
+
+(* notion 5354 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)))) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_disttp1 (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_7271_fx x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))) (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_7271_fy x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_satz204e (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t3 x y n)) (l_e_st_eq_landau_n_rt_rp_r_satz204e (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t3 x y n))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))).
+
+(* notion 5355 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_satz195b (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
+
+(* notion 5356 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ismoreis12 (l_e_st_eq_landau_n_rt_rp_r_c_7271_prl x y n) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_prr x y n) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t8 x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t9 x y n) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t7 x y n) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
+
+(* notion 5357 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7271_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_7271_t2 x y t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pl x y) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_7271_t10 x y t) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
+
+(* notion 5358 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz271 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_satz168a (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_c_7271_t11 x y) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))).
+
+(* notion 5359 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz271a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_7271_t11 x y : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl x y))).
+
+(* notion 5360 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7272_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x)) (l_e_st_eq_landau_n_rt_rp_r_c_reis (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))).
+
+(* notion 5361 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7272_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t1 x)) (l_e_st_eq_landau_n_rt_rp_r_satz198 (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x))).
+
+(* notion 5362 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7272_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_isceim (l_e_st_eq_landau_n_rt_rp_r_c_m0 x) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_c_satz214 x)) (l_e_st_eq_landau_n_rt_rp_r_c_imis (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))).
+
+(* notion 5363 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7272_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t3 x) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t3 x)) (l_e_st_eq_landau_n_rt_rp_r_satz198 (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x))).
+
+(* notion 5364 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7272_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t2 x) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t4 x) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x)).
+
+(* notion 5365 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz272 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_issqrt (l_e_st_eq_landau_n_rt_rp_r_c_mod2 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod2 x) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 x) (l_e_st_eq_landau_n_rt_rp_r_c_7272_t5 x) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)).
+
+(* notion 5366 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz272a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_m0 x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_satz272 x) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_m0 x))).
+
+(* notion 5367 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7273_sum ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5368 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_islessis1 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y))) (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_pl y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) x (l_e_st_eq_landau_n_rt_rp_r_c_satz212h x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz271 y (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y)).
+
+(* notion 5369 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t1 x y) (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y).l_e_st_eq_landau_n_rt_rp_r_satz188f (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) t) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y).l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))).
+
+(* notion 5370 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)))) (l_e_st_eq_landau_n_rt_rp_r_mnpl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y))).
+
+(* notion 5371 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_satz168b (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_islessis2 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_7273_sum x y) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t3 x y) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t2 x y)) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))).
+
+(* notion 5372 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ismoreis12 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn y x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y))) (l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn y x)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y))) (l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_c_mn y x) (l_e_st_eq_landau_n_rt_rp_r_c_satz219 x y)) (l_e_st_eq_landau_n_rt_rp_r_c_satz272 (l_e_st_eq_landau_n_rt_rp_r_c_mn x y))) (l_e_st_eq_landau_n_rt_rp_r_satz181a (l_e_st_eq_landau_n_rt_rp_r_c_mod y) (l_e_st_eq_landau_n_rt_rp_r_c_mod x)) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t4 y x) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)))).
+
+(* notion 5373 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_neg r) (l_not (l_e_st_eq_landau_n_rt_rp_r_neg r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r) (l_or_th6 (l_e_st_eq_landau_n_rt_rp_r_neg r)) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_absn r t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_neg r).l_e_st_eq_landau_n_rt_rp_r_absnn r t) : l_or (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_m0 r)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) r)).
+
+(* notion 5374 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_7273_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λm:l_e_st_eq_landau_n_rt_rp_r_moreis r s.λn:l_e_st_eq_landau_n_rt_rp_r_moreis r (l_e_st_eq_landau_n_rt_rp_r_m0 s).(l_orapp (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_m0 s)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs s) s) (l_e_st_eq_landau_n_rt_rp_r_moreis r (l_e_st_eq_landau_n_rt_rp_r_abs s)) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t6 s) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_m0 s).l_e_st_eq_landau_n_rt_rp_r_ismoreis2 (l_e_st_eq_landau_n_rt_rp_r_m0 s) (l_e_st_eq_landau_n_rt_rp_r_abs s) r (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs s) (l_e_st_eq_landau_n_rt_rp_r_m0 s) t) n) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs s) s.l_e_st_eq_landau_n_rt_rp_r_ismoreis2 s (l_e_st_eq_landau_n_rt_rp_r_abs s) r (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs s) s t) m) : l_e_st_eq_landau_n_rt_rp_r_moreis r (l_e_st_eq_landau_n_rt_rp_r_abs s)).
+
+(* notion 5375 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz273 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_7273_t7 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t4 x y) (l_e_st_eq_landau_n_rt_rp_r_c_7273_t5 x y) : l_e_st_eq_landau_n_rt_rp_r_moreis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_mn x y)) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_mod x) (l_e_st_eq_landau_n_rt_rp_r_c_mod y)))).
+
+(* notion 5376 *)
+definition l_e_st_eq_landau_n_8274_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_some (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y) (λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y.l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to y) f) : Prop).
+
+(* notion 5377 *)
+definition l_e_st_eq_landau_n_8274_prop2 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_all (λy:l_e_st_eq_landau_n_nat.l_imp (l_e_st_eq_landau_n_less x y) (l_not (l_e_st_eq_landau_n_8274_prop1 x y))) : Prop).
+
+(* notion 5378 *)
+definition l_e_st_eq_landau_n_8274_1y ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_1out y : l_e_st_eq_landau_n_1to y).
+
+(* notion 5379 *)
+definition l_e_st_eq_landau_n_8274_yy ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_xout y : l_e_st_eq_landau_n_1to y).
+
+(* notion 5380 *)
+definition l_e_st_eq_landau_n_8274_t1 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_yy y l f).(l_e_st_eq_landau_n_isoutne y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a y) y (l_e_st_eq_landau_n_lessisi3 y) i : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 y).
+
+(* notion 5381 *)
+definition l_e_st_eq_landau_n_8274_t2 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_ec3e31 (l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_more l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_satz10b l_e_st_eq_landau_n_1 y) l : l_e_st_eq_landau_n_nis l_e_st_eq_landau_n_1 y).
+
+(* notion 5382 *)
+definition l_e_st_eq_landau_n_8274_t3 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_yy y l f)) (l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 y) (l_e_st_eq_landau_n_8274_t2 y l f) (λt:l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_yy y l f).l_e_st_eq_landau_n_8274_t1 y l f t) : l_not (l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_yy y l f))).
+
+(* notion 5383 *)
+definition l_e_st_eq_landau_n_8274_t4 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f u l_e_st_eq_landau_n_1o (l_e_st_eq_landau_n_singlet_th1 u) : l_e_is (l_e_st_eq_landau_n_1to y) (f u) (f l_e_st_eq_landau_n_1o)).
+
+(* notion 5384 *)
+definition l_e_st_eq_landau_n_8274_t5 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_notis_th2 (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_yy y l f) (f u) (l_e_st_eq_landau_n_8274_t3 y l f) (l_e_tris (l_e_st_eq_landau_n_1to y) (f u) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_t4 y l f u) i) : l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f u) (l_e_st_eq_landau_n_8274_yy y l f))).
+
+(* notion 5385 *)
+definition l_e_st_eq_landau_n_8274_t6 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f).(l_some_th5 (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_yy y l f) (f u)) (λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_symnotis (l_e_st_eq_landau_n_1to y) (f u) (l_e_st_eq_landau_n_8274_yy y l f) (l_e_st_eq_landau_n_8274_t5 y l f i u)) : l_not (l_e_image (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_yy y l f))).
+
+(* notion 5386 *)
+definition l_e_st_eq_landau_n_8274_t7 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f).(l_all_th1 (l_e_st_eq_landau_n_1to y) (λu:l_e_st_eq_landau_n_1to y.l_e_image (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f u) (l_e_st_eq_landau_n_8274_yy y l f) (l_e_st_eq_landau_n_8274_t6 y l f i) : l_not (l_e_surjective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f)).
+
+(* notion 5387 *)
+definition l_e_st_eq_landau_n_8274_t8 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f)).λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.(l_e_notis_th2 (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f) (f u) n (l_e_st_eq_landau_n_8274_t4 y l f u) : l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f u) (l_e_st_eq_landau_n_8274_1y y l f))).
+
+(* notion 5388 *)
+definition l_e_st_eq_landau_n_8274_t9 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f)).(l_some_th5 (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_1y y l f) (f u)) (λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_symnotis (l_e_st_eq_landau_n_1to y) (f u) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_t8 y l f n u)) : l_not (l_e_image (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_1y y l f))).
+
+(* notion 5389 *)
+definition l_e_st_eq_landau_n_8274_t10 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f)).(l_all_th1 (l_e_st_eq_landau_n_1to y) (λu:l_e_st_eq_landau_n_1to y.l_e_image (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f u) (l_e_st_eq_landau_n_8274_1y y l f) (l_e_st_eq_landau_n_8274_t9 y l f n) : l_not (l_e_surjective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f)).
+
+(* notion 5390 *)
+definition l_e_st_eq_landau_n_8274_t11 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f)) (l_not (l_e_surjective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f)) (λt:l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f).l_e_st_eq_landau_n_8274_t7 y l f t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f l_e_st_eq_landau_n_1o) (l_e_st_eq_landau_n_8274_1y y l f)).l_e_st_eq_landau_n_8274_t10 y l f t) : l_not (l_e_surjective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f)).
+
+(* notion 5391 *)
+definition l_e_st_eq_landau_n_8274_t12 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.(l_and_th2 (l_e_injective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f) (l_e_surjective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f) (l_e_st_eq_landau_n_8274_t11 y l f) : l_not (l_e_bijective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f)).
+
+(* notion 5392 *)
+definition l_e_st_eq_landau_n_8274_t13 ≝ λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.(l_some_th5 (Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y) (λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.l_e_bijective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to y) f) (λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_8274_t12 y l f) : l_not (l_e_st_eq_landau_n_8274_prop1 l_e_st_eq_landau_n_1 y)).
+
+(* notion 5393 *)
+definition l_e_st_eq_landau_n_8274_t14 ≝ (λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y.l_e_st_eq_landau_n_8274_t13 y t : l_e_st_eq_landau_n_8274_prop2 l_e_st_eq_landau_n_1).
+
+(* notion 5394 *)
+definition l_e_st_eq_landau_n_8274_xs ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_suc x : l_e_st_eq_landau_n_nat).
+
+(* notion 5395 *)
+definition l_e_st_eq_landau_n_8274_xxs ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_8274_xs x) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_suc x)).
+
+(* notion 5396 *)
+definition l_e_st_eq_landau_n_8274_yy1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_xout y : l_e_st_eq_landau_n_1to y).
+
+(* notion 5397 *)
+definition l_e_st_eq_landau_n_8274_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_trless l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_suc x) y (l_e_st_eq_landau_n_satz24c x) l : l_e_st_eq_landau_n_less l_e_st_eq_landau_n_1 y).
+
+(* notion 5398 *)
+definition l_e_st_eq_landau_n_8274_ym1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_mn y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_8274_t15 x p y l) : l_e_st_eq_landau_n_nat).
+
+(* notion 5399 *)
+definition l_e_st_eq_landau_n_8274_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_isless12 (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) y (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz4e x) (l_e_st_eq_landau_n_mn_th1c y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_8274_t15 x p y l)) l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1)).
+
+(* notion 5400 *)
+definition l_e_st_eq_landau_n_8274_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_satz20c x (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_8274_t16 x p y l) : l_e_st_eq_landau_n_less x (l_e_st_eq_landau_n_8274_ym1 x p y l)).
+
+(* notion 5401 *)
+definition l_e_st_eq_landau_n_8274_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_e_st_eq_landau_n_isless2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1) y (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_mn_th1d y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_8274_t15 x p y l)) (l_e_st_eq_landau_n_satz18a (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_ym1 x p y l) y).
+
+(* notion 5402 *)
+definition l_e_st_eq_landau_n_8274_t19 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.(l_ande1 (l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f) (l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f) b : l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f).
+
+(* notion 5403 *)
+definition l_e_st_eq_landau_n_8274_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.(l_ande2 (l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f) (l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f) b : l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f).
+
+(* notion 5404 *)
+definition l_e_st_eq_landau_n_8274_u1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_inn x u : l_e_st_eq_landau_n_nat).
+
+(* notion 5405 *)
+definition l_e_st_eq_landau_n_8274_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_satz16a (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) x (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_satz18c x) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)).
+
+(* notion 5406 *)
+definition l_e_st_eq_landau_n_8274_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_t21 x p y l f b i u) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)).
+
+(* notion 5407 *)
+definition l_e_st_eq_landau_n_8274_t23 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_lessisi1 (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_t21 x p y l f b i u) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)).
+
+(* notion 5408 *)
+definition l_e_st_eq_landau_n_8274_u2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t23 x p y l f b i u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)).
+
+(* notion 5409 *)
+definition l_e_st_eq_landau_n_8274_t24 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_t22 x p y l f b i u) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l).l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t23 x p y l f b i u) (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_8274_xs x)) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l))).
+
+(* notion 5410 *)
+definition l_e_st_eq_landau_n_8274_t25 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(l_e_tris2 (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l) j i : l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (f (l_e_st_eq_landau_n_8274_xxs x p y l))).
+
+(* notion 5411 *)
+definition l_e_st_eq_landau_n_8274_t26 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_t19 x p y l f b) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l) (l_e_st_eq_landau_n_8274_t25 x p y l f b i u j) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l)).
+
+(* notion 5412 *)
+definition l_e_st_eq_landau_n_8274_t27 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_t24 x p y l f b i u) (λt:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l).l_e_st_eq_landau_n_8274_t26 x p y l f b i u t) : l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l))).
+
+(* notion 5413 *)
+definition l_e_st_eq_landau_n_8274_w1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_inn y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) : l_e_st_eq_landau_n_nat).
+
+(* notion 5414 *)
+definition l_e_st_eq_landau_n_8274_t28 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y.(l_e_tris (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_outn y (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_1top y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)))) (l_e_st_eq_landau_n_8274_yy1 x p y l) (l_e_st_eq_landau_n_isoutinn y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u))) (l_e_st_eq_landau_n_isoutni y (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_1top y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u))) y (l_e_st_eq_landau_n_lessisi3 y) j) : l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).
+
+(* notion 5415 *)
+definition l_e_st_eq_landau_n_8274_t29 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y) (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (l_e_st_eq_landau_n_8274_yy1 x p y l)) (l_e_st_eq_landau_n_8274_t27 x p y l f b i u) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y.l_e_st_eq_landau_n_8274_t28 x p y l f b i u t) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y).
+
+(* notion 5416 *)
+definition l_e_st_eq_landau_n_8274_t30 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y) (l_e_st_eq_landau_n_1top y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u))) (l_e_st_eq_landau_n_8274_t29 x p y l f b i u) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) y).
+
+(* notion 5417 *)
+definition l_e_st_eq_landau_n_8274_t31 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_islessis2 y (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_mn_th1c y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_8274_t15 x p y l)) (l_e_st_eq_landau_n_satz25b y (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t30 x p y l f b i u)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1)).
+
+(* notion 5418 *)
+definition l_e_st_eq_landau_n_8274_t32 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_or_th9 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_t31 x p y l f b i u) (λt:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_satz20c (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1 t) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_satz20b (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_ym1 x p y l) l_e_st_eq_landau_n_1 t) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_ym1 x p y l)).
+
+(* notion 5419 *)
+definition l_e_st_eq_landau_n_8274_w2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t32 x p y l f b i u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)).
+
+(* notion 5420 *)
+definition l_e_st_eq_landau_n_8274_f1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_8274_w2 x p y l f b i t : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)).
+
+(* notion 5421 *)
+definition l_e_st_eq_landau_n_8274_t33 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t32 x p y l f b i u) (l_e_st_eq_landau_n_8274_w1 x p y l f b i v) (l_e_st_eq_landau_n_8274_t32 x p y l f b i v) j : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w1 x p y l f b i u) (l_e_st_eq_landau_n_8274_w1 x p y l f b i v)).
+
+(* notion 5422 *)
+definition l_e_st_eq_landau_n_8274_t34 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).(l_e_st_eq_landau_n_isinne y (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t33 x p y l f b i u v j) : l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i u)) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i v))).
+
+(* notion 5423 *)
+definition l_e_st_eq_landau_n_8274_t35 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).(l_e_st_eq_landau_n_8274_t19 x p y l f b (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_u2 x p y l f b i v) (l_e_st_eq_landau_n_8274_t34 x p y l f b i u v j) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_u2 x p y l f b i u) (l_e_st_eq_landau_n_8274_u2 x p y l f b i v)).
+
+(* notion 5424 *)
+definition l_e_st_eq_landau_n_8274_t36 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_t23 x p y l f b i u) (l_e_st_eq_landau_n_8274_u1 x p y l f b i v) (l_e_st_eq_landau_n_8274_t23 x p y l f b i v) (l_e_st_eq_landau_n_8274_t35 x p y l f b i u v j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_u1 x p y l f b i u) (l_e_st_eq_landau_n_8274_u1 x p y l f b i v)).
+
+(* notion 5425 *)
+definition l_e_st_eq_landau_n_8274_t37 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).(l_e_st_eq_landau_n_isinne x u v (l_e_st_eq_landau_n_8274_t36 x p y l f b i u v j) : l_e_is (l_e_st_eq_landau_n_1to x) u v).
+
+(* notion 5426 *)
+definition l_e_st_eq_landau_n_8274_v1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_inn (l_e_st_eq_landau_n_8274_ym1 x p y l) v : l_e_st_eq_landau_n_nat).
+
+(* notion 5427 *)
+definition l_e_st_eq_landau_n_8274_t38 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_satz16a (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_8274_ym1 x p y l) y (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_ym1 x p y l) v) (l_e_st_eq_landau_n_8274_t18 x p y l) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y).
+
+(* notion 5428 *)
+definition l_e_st_eq_landau_n_8274_t39 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y) (l_e_st_eq_landau_n_8274_t38 x p y l f b i v) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y).
+
+(* notion 5429 *)
+definition l_e_st_eq_landau_n_8274_t40 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_lessisi1 (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y (l_e_st_eq_landau_n_8274_t38 x p y l f b i v) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y).
+
+(* notion 5430 *)
+definition l_e_st_eq_landau_n_8274_v2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_outn y (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_8274_t40 x p y l f b i v) : l_e_st_eq_landau_n_1to y).
+
+(* notion 5431 *)
+definition l_e_st_eq_landau_n_8274_w3 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_invf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f b (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)).
+
+(* notion 5432 *)
+definition l_e_st_eq_landau_n_8274_t41 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f b (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v))).
+
+(* notion 5433 *)
+definition l_e_st_eq_landau_n_8274_t42 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l) j : l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (f (l_e_st_eq_landau_n_8274_xxs x p y l))).
+
+(* notion 5434 *)
+definition l_e_st_eq_landau_n_8274_t43 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l).(l_e_tr3is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l) (l_e_st_eq_landau_n_8274_t41 x p y l f b i v) (l_e_st_eq_landau_n_8274_t42 x p y l f b i v j) i : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (l_e_st_eq_landau_n_8274_yy1 x p y l)).
+
+(* notion 5435 *)
+definition l_e_st_eq_landau_n_8274_t44 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l).(l_e_st_eq_landau_n_isoutne y (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_8274_t40 x p y l f b i v) y (l_e_st_eq_landau_n_lessisi3 y) (l_e_st_eq_landau_n_8274_t43 x p y l f b i v j) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y).
+
+(* notion 5436 *)
+definition l_e_st_eq_landau_n_8274_t45 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) y) (l_e_st_eq_landau_n_8274_t39 x p y l f b i v) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l).l_e_st_eq_landau_n_8274_t44 x p y l f b i v t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l))).
+
+(* notion 5437 *)
+definition l_e_st_eq_landau_n_8274_w4 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_inn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) : l_e_st_eq_landau_n_nat).
+
+(* notion 5438 *)
+definition l_e_st_eq_landau_n_8274_t46 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v))) (l_e_st_eq_landau_n_8274_xxs x p y l) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_8274_xs x)) j) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l)).
+
+(* notion 5439 *)
+definition l_e_st_eq_landau_n_8274_t47 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_t45 x p y l f b i v) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_8274_t46 x p y l f b i v t) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x)).
+
+(* notion 5440 *)
+definition l_e_st_eq_landau_n_8274_t48 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t47 x p y l f b i v) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_xs x)).
+
+(* notion 5441 *)
+definition l_e_st_eq_landau_n_8274_t49 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_satz26a x (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_t48 x p y l f b i v) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) x).
+
+(* notion 5442 *)
+definition l_e_st_eq_landau_n_8274_w5 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_t49 x p y l f b i v) : l_e_st_eq_landau_n_1to x).
+
+(* notion 5443 *)
+definition l_e_st_eq_landau_n_8274_t50 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_t49 x p y l f b i v) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_8274_u1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))).
+
+(* notion 5444 *)
+definition l_e_st_eq_landau_n_8274_t51 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v))) (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w4 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_xs x) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (l_e_st_eq_landau_n_8274_u1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t23 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t50 x p y l f b i v)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))).
+
+(* notion 5445 *)
+definition l_e_st_eq_landau_n_8274_t52 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v) (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t51 x p y l f b i v) : l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)))).
+
+(* notion 5446 *)
+definition l_e_st_eq_landau_n_8274_t53 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_tris (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (f (l_e_st_eq_landau_n_8274_w3 x p y l f b i v)) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))) (l_e_st_eq_landau_n_8274_t41 x p y l f b i v) (l_e_st_eq_landau_n_8274_t52 x p y l f b i v) : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)))).
+
+(* notion 5447 *)
+definition l_e_st_eq_landau_n_8274_t54 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_inn y (l_e_st_eq_landau_n_8274_v2 x p y l f b i v)) (l_e_st_eq_landau_n_8274_w1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_isinoutn y (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_8274_t40 x p y l f b i v)) (l_e_st_eq_landau_n_isinni y (l_e_st_eq_landau_n_8274_v2 x p y l f b i v) (f (l_e_st_eq_landau_n_8274_u2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))) (l_e_st_eq_landau_n_8274_t53 x p y l f b i v)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_8274_w1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))).
+
+(* notion 5448 *)
+definition l_e_st_eq_landau_n_8274_t55 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) v (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_ym1 x p y l) v)) (l_e_st_eq_landau_n_8274_w2 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_8274_ym1 x p y l) v) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_8274_v1 x p y l f b i v) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_8274_ym1 x p y l) v) (l_e_st_eq_landau_n_8274_w1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t32 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v)) (l_e_st_eq_landau_n_8274_t54 x p y l f b i v)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) v (l_e_st_eq_landau_n_8274_f1 x p y l f b i (l_e_st_eq_landau_n_8274_w5 x p y l f b i v))).
+
+(* notion 5449 *)
+definition l_e_st_eq_landau_n_8274_t56 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).λv:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).(l_somei (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) v (l_e_st_eq_landau_n_8274_f1 x p y l f b i t)) (l_e_st_eq_landau_n_8274_w5 x p y l f b i v) (l_e_st_eq_landau_n_8274_t55 x p y l f b i v) : l_e_image (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i) v).
+
+(* notion 5450 *)
+definition l_e_st_eq_landau_n_8274_t57 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(l_andi (l_e_injective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i)) (l_e_surjective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i)) (λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i u) (l_e_st_eq_landau_n_8274_f1 x p y l f b i v).l_e_st_eq_landau_n_8274_t37 x p y l f b i u v t) (λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).l_e_st_eq_landau_n_8274_t56 x p y l f b i u) : l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (l_e_st_eq_landau_n_8274_f1 x p y l f b i)).
+
+(* notion 5451 *)
+definition l_e_st_eq_landau_n_8274_t58 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(l_somei (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l).l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_ym1 x p y l)) g) (l_e_st_eq_landau_n_8274_f1 x p y l f b i) (l_e_st_eq_landau_n_8274_t57 x p y l f b i) : l_e_st_eq_landau_n_8274_prop1 x (l_e_st_eq_landau_n_8274_ym1 x p y l)).
+
+(* notion 5452 *)
+definition l_e_st_eq_landau_n_8274_t59 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λi:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).(p (l_e_st_eq_landau_n_8274_ym1 x p y l) (l_e_st_eq_landau_n_8274_t17 x p y l) (l_e_st_eq_landau_n_8274_t58 x p y l f b i) : l_con).
+
+(* notion 5453 *)
+definition l_e_st_eq_landau_n_8274_m0 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_invf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f b (l_e_st_eq_landau_n_8274_yy1 x p y l) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)).
+
+(* notion 5454 *)
+definition l_e_st_eq_landau_n_8274_t60 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f b (l_e_st_eq_landau_n_8274_yy1 x p y l) : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_yy1 x p y l) (f (l_e_st_eq_landau_n_8274_m0 x p y l f b n))).
+
+(* notion 5455 *)
+definition l_e_st_eq_landau_n_8274_f2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_changef (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_m0 x p y l f b n) (l_e_st_eq_landau_n_8274_xxs x p y l) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y).
+
+(* notion 5456 *)
+definition l_e_st_eq_landau_n_8274_t61 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_changef2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_m0 x p y l f b n) (l_e_st_eq_landau_n_8274_xxs x p y l) (l_e_st_eq_landau_n_8274_xxs x p y l) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_8274_xxs x p y l)) : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_f2 x p y l f b n (l_e_st_eq_landau_n_8274_xxs x p y l)) (f (l_e_st_eq_landau_n_8274_m0 x p y l f b n))).
+
+(* notion 5457 *)
+definition l_e_st_eq_landau_n_8274_t62 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_tris2 (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_f2 x p y l f b n (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l) (f (l_e_st_eq_landau_n_8274_m0 x p y l f b n)) (l_e_st_eq_landau_n_8274_t61 x p y l f b n) (l_e_st_eq_landau_n_8274_t60 x p y l f b n) : l_e_is (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_f2 x p y l f b n (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).
+
+(* notion 5458 *)
+definition l_e_st_eq_landau_n_8274_t63 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_wissel_th6 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f (l_e_st_eq_landau_n_8274_m0 x p y l f b n) (l_e_st_eq_landau_n_8274_xxs x p y l) b : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) (l_e_st_eq_landau_n_8274_f2 x p y l f b n)).
+
+(* notion 5459 *)
+definition l_e_st_eq_landau_n_8274_t64 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.λn:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).(l_e_st_eq_landau_n_8274_t59 x p y l (l_e_st_eq_landau_n_8274_f2 x p y l f b n) (l_e_st_eq_landau_n_8274_t63 x p y l f b n) (l_e_st_eq_landau_n_8274_t62 x p y l f b n) : l_con).
+
+(* notion 5460 *)
+definition l_e_st_eq_landau_n_8274_t65 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)) l_con (λt:l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l).l_e_st_eq_landau_n_8274_t59 x p y l f b t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to y) (f (l_e_st_eq_landau_n_8274_xxs x p y l)) (l_e_st_eq_landau_n_8274_yy1 x p y l)).l_e_st_eq_landau_n_8274_t64 x p y l f b t) : l_con).
+
+(* notion 5461 *)
+definition l_e_st_eq_landau_n_8274_t65a ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_suc x) y.(l_some_th5 (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y) (λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f) (λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x).l_e_st_eq_landau_n_1to y.λt:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_8274_xs x)) (l_e_st_eq_landau_n_1to y) f.l_e_st_eq_landau_n_8274_t65 x p y l f t) : l_not (l_e_st_eq_landau_n_8274_prop1 (l_e_st_eq_landau_n_8274_xs x) y)).
+
+(* notion 5462 *)
+definition l_e_st_eq_landau_n_8274_t66 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_8274_prop2 x.(λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_8274_xs x) y.l_e_st_eq_landau_n_8274_t65a x p y t : l_e_st_eq_landau_n_8274_prop2 (l_e_st_eq_landau_n_8274_xs x)).
+
+(* notion 5463 *)
+definition l_e_st_eq_landau_n_8274_t67 ≝ λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_8274_prop2 t) l_e_st_eq_landau_n_8274_t14 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_8274_prop2 t.l_e_st_eq_landau_n_8274_t66 t u) x : l_e_st_eq_landau_n_8274_prop2 x).
+
+(* notion 5464 *)
+definition l_e_st_eq_landau_n_satz274 ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.(l_e_st_eq_landau_n_8274_t67 x y l : l_not (l_some (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y) (λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y.l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to y) f))).
+
+(* notion 5465 *)
+definition l_e_st_eq_landau_n_satz274a ≝ λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_less x y.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y.(l_some_th4 (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to y.l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to y) g) (l_e_st_eq_landau_n_satz274 x y l) f : l_not (l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to y) f)).
+
+(* notion 5466 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_inn ≝ λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_inn x u : l_e_st_eq_landau_n_nat).
+
+(* notion 5467 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)).(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x) (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)) o (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x.l_e_tris (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n)) (l_e_st_eq_landau_n_xout x) (l_e_st_eq_landau_n_isoutinn x n) (l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n) x (l_e_st_eq_landau_n_lessisi3 x) t)) : l_not (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x)).
+
+(* notion 5468 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)).(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x) (l_e_st_eq_landau_n_1top x n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t1 q x n o) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x).
+
+(* notion 5469 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma275 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)).(l_e_st_eq_landau_n_satz25c x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t2 q x n o) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x n)) x).
+
+(* notion 5470 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_recprop ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_and (l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_1out x)) (f (l_e_st_eq_landau_n_1out x))) (Πt:l_e_st_eq_landau_n_1to x.Πu:l_not (l_e_is (l_e_st_eq_landau_n_1to x) t (l_e_st_eq_landau_n_xout x)).l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x t)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x t u))) (q (g t) (f (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x t)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x t u))))) : Prop).
+
+(* notion 5471 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_1o ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_1out x : l_e_st_eq_landau_n_1to x).
+
+(* notion 5472 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_xo ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_xout x : l_e_st_eq_landau_n_1to x).
+
+(* notion 5473 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_st_eq_landau_n_satz16b u (l_e_st_eq_landau_n_suc u) x (l_e_st_eq_landau_n_satz18c u) l : l_e_st_eq_landau_n_less u x).
+
+(* notion 5474 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_st_eq_landau_n_lessisi1 u x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t11 q x u l) : l_e_st_eq_landau_n_lessis u x).
+
+(* notion 5475 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_ux ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_st_eq_landau_n_outn x u (l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 q x u l) : l_e_st_eq_landau_n_1to x).
+
+(* notion 5476 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_ec3e31 (l_e_st_eq_landau_n_is u x) (l_e_st_eq_landau_n_more u x) (l_e_st_eq_landau_n_less u x) (l_e_st_eq_landau_n_satz10b u x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t11 q x u l) : l_e_st_eq_landau_n_nis u x).
+
+(* notion 5477 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_st_eq_landau_n_is u x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t13 q x u l) (λt:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x).l_e_st_eq_landau_n_isoutne x u (l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 q x u l) x (l_e_st_eq_landau_n_lessisi3 x) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x))).
+
+(* notion 5478 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_isf l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_suc u (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (l_e_st_eq_landau_n_isinoutn x u (l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 q x u l)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc u) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)))).
+
+(* notion 5479 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t16 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_suc u) l (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t15 q x u l) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l) (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))).
+
+(* notion 5480 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_ns ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)).(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x n o) : l_e_st_eq_landau_n_1to x).
+
+(* notion 5481 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) : Prop).
+
+(* notion 5482 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(Πt:l_e_st_eq_landau_n_1to x.Πu:l_not (l_e_is (l_e_st_eq_landau_n_1to x) t (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)).l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x t u)) (q (g t) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x t u))) : Prop).
+
+(* notion 5483 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q x f g) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q x f g) pg : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q x f g).
+
+(* notion 5484 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q x f g) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q x f g) pg n o : l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x n o)) (q (g n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x n o)))).
+
+(* notion 5485 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t17 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t16 q x u l) : l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))).
+
+(* notion 5486 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t18 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l))) (q (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t17 q x f g pg u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t4 q x f g pg (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)) : l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (q (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l))))).
+
+(* notion 5487 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis u x.(l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x u l)) (h (l_e_st_eq_landau_n_outn x u l)) : Prop).
+
+(* notion 5488 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_nat.(l_and (l_e_st_eq_landau_n_lessis u x) (Πt:l_e_st_eq_landau_n_lessis u x.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h u t) : Prop).
+
+(* notion 5489 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_nat.(l_or (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h u) (l_e_st_eq_landau_n_more u x) : Prop).
+
+(* notion 5490 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λl:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.(l_e_st_eq_landau_n_isoutni x l_e_st_eq_landau_n_1 l l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a x) (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)).
+
+(* notion 5491 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λl:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx g (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t5 q x f g h pg ph l) : l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l)) (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
+
+(* notion 5492 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λl:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (g (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l)) (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t6 q x f g h pg ph l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t3 q x f g pg) : l_e_st_eq_landau_n_rt_rp_r_c_is (g (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
+
+(* notion 5493 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λl:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (g (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l)) (h (l_e_st_eq_landau_n_outn x l_e_st_eq_landau_n_1 l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t7 q x f g h pg ph l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t7 q x f h g ph pg l) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h l_e_st_eq_landau_n_1 l).
+
+(* notion 5494 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.(l_andi (l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x) (Πt:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h l_e_st_eq_landau_n_1 t) (l_e_st_eq_landau_n_satz24a x) (λt:l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 x.l_e_st_eq_landau_n_rt_rp_r_c_8275_t8 q x f g h pg ph t) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h l_e_st_eq_landau_n_1).
+
+(* notion 5495 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_more l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t9 q x f g h pg ph) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h l_e_st_eq_landau_n_1).
+
+(* notion 5496 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t19 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_ec3e32 (l_e_st_eq_landau_n_is u x) (l_e_st_eq_landau_n_more u x) (l_e_st_eq_landau_n_less u x) (l_e_st_eq_landau_n_satz10b u x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t11 q x u l) : l_not (l_e_st_eq_landau_n_more u x)).
+
+(* notion 5497 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t20 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h u) (l_e_st_eq_landau_n_more u x) p (l_e_st_eq_landau_n_rt_rp_r_c_8275_t19 q x f g h pg ph u p l) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h u).
+
+(* notion 5498 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t21 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_ande2 (l_e_st_eq_landau_n_lessis u x) (Πt:l_e_st_eq_landau_n_lessis u x.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h u t) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t20 q x f g h pg ph u p l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 q x u l) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h u (l_e_st_eq_landau_n_rt_rp_r_c_8275_t12 q x u l)).
+
+(* notion 5499 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t22 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (h (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t21 q x f g h pg ph u p l) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (q (h (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l))))).
+
+(* notion 5500 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t23 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (q (h (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t18 q x f h ph u l) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (h (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l))).
+
+(* notion 5501 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t24 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (q (g (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (q (h (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ux q x u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t14 q x u l)))) (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_suc u) l)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t18 q x f g pg u l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t22 q x f g h pg ph u p l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t23 q x f g h pg ph u p l) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h (l_e_st_eq_landau_n_suc u) l).
+
+(* notion 5502 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t25 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_andi (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x) (Πt:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h (l_e_st_eq_landau_n_suc u) t) l (λt:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.l_e_st_eq_landau_n_rt_rp_r_c_8275_t24 q x f g h pg ph u p t) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h (l_e_st_eq_landau_n_suc u)).
+
+(* notion 5503 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t26 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λl:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc u) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t25 q x f g h pg ph u p l) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h (l_e_st_eq_landau_n_suc u)).
+
+(* notion 5504 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t27 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λn:l_not (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x).(l_e_st_eq_landau_n_satz10k (l_e_st_eq_landau_n_suc u) x n : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc u) x).
+
+(* notion 5505 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t28 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.λn:l_not (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x).(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h (l_e_st_eq_landau_n_suc u)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_suc u) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t27 q x f g h pg ph u p n) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h (l_e_st_eq_landau_n_suc u)).
+
+(* notion 5506 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t29 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u.(l_imp_th1 (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h (l_e_st_eq_landau_n_suc u)) (λt:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x.l_e_st_eq_landau_n_rt_rp_r_c_8275_t26 q x f g h pg ph u p t) (λt:l_not (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_suc u) x).l_e_st_eq_landau_n_rt_rp_r_c_8275_t28 q x f g h pg ph u p t) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h (l_e_st_eq_landau_n_suc u)).
+
+(* notion 5507 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t30 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λu:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λv:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h v) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t10 q x f g h pg ph) (λv:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h v.l_e_st_eq_landau_n_rt_rp_r_c_8275_t29 q x f g h pg ph v t) u : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop5 q x f g h u).
+
+(* notion 5508 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t31 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx g n (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n)) (l_e_st_eq_landau_n_isoutinn x n) : l_e_st_eq_landau_n_rt_rp_r_c_is (g n) (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n)))).
+
+(* notion 5509 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t32 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_satz10d (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x (l_e_st_eq_landau_n_1top x n) : l_not (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x)).
+
+(* notion 5510 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t33 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h (l_e_st_eq_landau_n_rt_rp_r_c_inn x n)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t30 q x f g h pg ph (l_e_st_eq_landau_n_rt_rp_r_c_inn x n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t32 q x f g h pg ph n) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop4 q x f g h (l_e_st_eq_landau_n_rt_rp_r_c_inn x n)).
+
+(* notion 5511 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t34 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_ande2 (l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x) (Πt:l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) t) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t33 q x f g h pg ph n) (l_e_st_eq_landau_n_1top x n) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop3 q x f g h (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n)).
+
+(* notion 5512 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t35 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (h n) (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t31 q x f h g ph pg n) : l_e_st_eq_landau_n_rt_rp_r_c_is (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n))) (h n)).
+
+(* notion 5513 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t36 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.λn:l_e_st_eq_landau_n_1to x.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (g n) (g (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n))) (h (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_1top x n))) (h n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t31 q x f g h pg ph n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t34 q x f g h pg ph n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t35 q x f g h pg ph n) : l_e_st_eq_landau_n_rt_rp_r_c_is (g n) (h n)).
+
+(* notion 5514 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t37 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λpg:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λph:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.(l_e_fisi (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx g h (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8275_t36 q x f g h pg ph t) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) g h).
+
+(* notion 5515 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_some (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g) : Prop).
+
+(* notion 5516 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.(l_all (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop6 q x f) : Prop).
+
+(* notion 5517 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t38 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q l_e_st_eq_landau_n_1 f f).
+
+(* notion 5518 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t39 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) n (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q l_e_st_eq_landau_n_1)).(o (l_e_st_eq_landau_n_singlet_th1 n) : l_con).
+
+(* notion 5519 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t40 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) n (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q l_e_st_eq_landau_n_1)).(l_cone (l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q l_e_st_eq_landau_n_1 n o)) (q (f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q l_e_st_eq_landau_n_1 n o)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t39 q f n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q l_e_st_eq_landau_n_1 n o)) (q (f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q l_e_st_eq_landau_n_1 n o)))).
+
+(* notion 5520 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t41 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_andi (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q l_e_st_eq_landau_n_1 f f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q l_e_st_eq_landau_n_1 f f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t38 q f) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λu:l_not (l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) t (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q l_e_st_eq_landau_n_1)).l_e_st_eq_landau_n_rt_rp_r_c_8275_t40 q f t u) : l_e_st_eq_landau_n_rt_rp_r_c_recprop q l_e_st_eq_landau_n_1 f f).
+
+(* notion 5521 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t42 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_somei (Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q l_e_st_eq_landau_n_1 f g) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_t41 q f) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop6 q l_e_st_eq_landau_n_1 f).
+
+(* notion 5522 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t43 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.(λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8275_t42 q f : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q l_e_st_eq_landau_n_1).
+
+(* notion 5523 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_xs ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.(l_e_st_eq_landau_n_suc x : l_e_st_eq_landau_n_nat).
+
+(* notion 5524 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x)) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5525 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t44 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_onei (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g.λv:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) h.l_e_st_eq_landau_n_rt_rp_r_c_8275_t37 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g h u v) (p (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f)) : l_e_one (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g)).
+
+(* notion 5526 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_ind (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t44 q x p f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5527 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t45 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_oneax (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) g) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t44 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_recprop q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f)).
+
+(* notion 5528 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).(l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) n (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) : Prop).
+
+(* notion 5529 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_e_st_eq_landau_n_satz26a x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t2 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) x).
+
+(* notion 5530 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o) : l_e_st_eq_landau_n_1to x).
+
+(* notion 5531 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5532 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t47 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o1) (l_e_refis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o1)).
+
+(* notion 5533 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t48 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t47 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o1)).
+
+(* notion 5534 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(q (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5535 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_c ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).(l_r_ite (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.λu:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f)) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_t48 q x p f n t u) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5536 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t49 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λi:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.(l_r_itet (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.λu:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f)) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_t48 q x p f n t u) i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f)).
+
+(* notion 5537 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t50 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_r_itef (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.λu:l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n.l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f)) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).l_e_st_eq_landau_n_rt_rp_r_c_8275_t48 q x p f n t u) o : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o)).
+
+(* notion 5538 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f t : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5539 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_symnotis l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_ax3 x)) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)))).
+
+(* notion 5540 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t52 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t50 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f))).
+
+(* notion 5541 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t53 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)))).
+
+(* notion 5542 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t54 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a x) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t53 q x p f) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f))).
+
+(* notion 5543 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t55 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t54 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f))).
+
+(* notion 5544 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t56 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t51 q x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t52 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t55 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
+
+(* notion 5545 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t57 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t56 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t3 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t45 q x p f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
+
+(* notion 5546 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t58 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a x) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
+
+(* notion 5547 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t59 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t58 q x p f) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
+
+(* notion 5548 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t60 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t59 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x))).
+
+(* notion 5549 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t61 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_1o q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t57 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t60 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f)).
+
+(* notion 5550 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t62 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).
+
+(* notion 5551 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t63 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_st_eq_landau_n_ax4 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t62 q x p f n o i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) x).
+
+(* notion 5552 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t64 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o) x (l_e_st_eq_landau_n_lessisi3 x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t63 q x p f n o i) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)).
+
+(* notion 5553 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t65 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_symis (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t64 q x p f n o i)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o)).
+
+(* notion 5554 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t66 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t65 q x p f n o i) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t50 q x p f n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n)).
+
+(* notion 5555 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t67 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t66 q x p f n o i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))))).
+
+(* notion 5556 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t68 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) i) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))).
+
+(* notion 5557 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t69 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t68 q x p f n o i) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))).
+
+(* notion 5558 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t70 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_a q x p f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t49 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) i) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t67 q x p f n o i) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t69 q x p f n o i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))).
+
+(* notion 5559 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t71 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x).(l_e_st_eq_landau_n_isoutne x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o) x (l_e_st_eq_landau_n_lessisi3 x) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) x).
+
+(* notion 5560 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t72 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x).(l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t71 q x p f n o o1 i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).
+
+(* notion 5561 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t73 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x).(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t72 q x p f n o o1 i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).
+
+(* notion 5562 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) o1 (λt:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x).l_e_st_eq_landau_n_rt_rp_r_c_8275_t73 q x p f n o o1 t) : l_not (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q x))).
+
+(* notion 5563 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t75 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f n o) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))).
+
+(* notion 5564 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t76 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t75 q x p f n o o1) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o)))).
+
+(* notion 5565 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t77 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))).
+
+(* notion 5566 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t78 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t77 q x p f n o o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t76 q x p f n o o1) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o)))).
+
+(* notion 5567 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t79 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t46 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t78 q x p f n o o1) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))).
+
+(* notion 5568 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t80 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t79 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))).
+
+(* notion 5569 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t81 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))).
+
+(* notion 5570 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t82 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o))) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t76 q x p f n o o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t81 q x p f n o o1) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))).
+
+(* notion 5571 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t83 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t82 q x p f n o o1) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))).
+
+(* notion 5572 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t84 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) (l_e_st_eq_landau_n_satz18c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t83 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))).
+
+(* notion 5573 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t85 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o)) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t84 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))))).
+
+(* notion 5574 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t86 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t50 q x p f n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))).
+
+(* notion 5575 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t87 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t50 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t80 q x p f n o o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t4 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t45 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))))).
+
+(* notion 5576 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t88 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t86 q x p f n o o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t85 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1))))).
+
+(* notion 5577 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t89 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).λo1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_b q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_n1 q x p f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t74 q x p f n o o1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t87 q x p f n o o1) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t88 q x p f n o o1) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))).
+
+(* notion 5578 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t90 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λo:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f n).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).l_e_st_eq_landau_n_rt_rp_r_c_8275_t70 q x p f n o t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_xo q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p))).l_e_st_eq_landau_n_rt_rp_r_c_8275_t89 q x p f n o t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_c q x p f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) n o)))).
+
+(* notion 5579 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t91 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_c_8275_nxs q x p f t).l_e_st_eq_landau_n_rt_rp_r_c_8275_t90 q x p f t u : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f)).
+
+(* notion 5580 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t92 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_andi (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t61 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t91 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_recprop q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f)).
+
+(* notion 5581 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t93 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_somei (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f g) (l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t92 q x p f) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop6 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p) f).
+
+(* notion 5582 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t94 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x.(λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8275_t93 q x p f : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q (l_e_st_eq_landau_n_rt_rp_r_c_8275_xs q x p)).
+
+(* notion 5583 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λy:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q y) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t43 q) (λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q y.l_e_st_eq_landau_n_rt_rp_r_c_8275_t94 q y t) x : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop7 q x).
+
+(* notion 5584 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t96 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x f : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop6 q x f).
+
+(* notion 5585 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t97 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_onei (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λh:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λv:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f h.l_e_st_eq_landau_n_rt_rp_r_c_8275_t37 q x f g h u v) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t96 q x f) : l_e_one (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g)).
+
+(* notion 5586 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz275 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t97 q x f : l_e_one (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g)).
+
+(* notion 5587 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_recf ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_ind (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g) (l_e_st_eq_landau_n_rt_rp_r_c_satz275 q x f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5588 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz275a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_oneax (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g) (l_e_st_eq_landau_n_rt_rp_r_c_satz275 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f)).
+
+(* notion 5589 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_rec ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_recf q x f n : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5590 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz275b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t3 q x f (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f) (l_e_st_eq_landau_n_rt_rp_r_c_satz275a q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_rec q x f (l_e_st_eq_landau_n_1out x)) (f (l_e_st_eq_landau_n_1out x))).
+
+(* notion 5591 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_sucx ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)).(l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x n o : l_e_st_eq_landau_n_1to x).
+
+(* notion 5592 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz275c ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to x) n (l_e_st_eq_landau_n_xout x)).(l_e_st_eq_landau_n_rt_rp_r_c_8275_t4 q x f (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f) (l_e_st_eq_landau_n_rt_rp_r_c_satz275a q x f) n o : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_rec q x f (l_e_st_eq_landau_n_rt_rp_r_c_sucx q x f n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_rec q x f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_sucx q x f n o)))).
+
+(* notion 5593 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz275d ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t37 q x f g (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f) r (l_e_st_eq_landau_n_rt_rp_r_c_satz275a q x f) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) g (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f)).
+
+(* notion 5594 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz275e ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_c_recprop q x f g.λn:l_e_st_eq_landau_n_1to x.(l_e_fise (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx g (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f) (l_e_st_eq_landau_n_rt_rp_r_c_satz275d q x f g r) n : l_e_st_eq_landau_n_rt_rp_r_c_is (g n) (l_e_st_eq_landau_n_rt_rp_r_c_rec q x f n)).
+
+(* notion 5595 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_fl ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y l f : Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5596 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_rf ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_recf q x f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5597 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y l (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f) : Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5598 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t98 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn y l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a y) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_1out y))).
+
+(* notion 5599 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t99 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a x) (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_1out y)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_1out y)) y x (l_e_st_eq_landau_n_1top y (l_e_st_eq_landau_n_1out y)) l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t98 q x y l f) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1out x) (l_e_st_eq_landau_n_left1to x y l (l_e_st_eq_landau_n_1out y))).
+
+(* notion 5600 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t100 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isp (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f t) (f t)) (l_e_st_eq_landau_n_1out x) (l_e_st_eq_landau_n_left1to x y l (l_e_st_eq_landau_n_1out y)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t3 q x f (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_satz275a q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t99 q x y l f) : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f)).
+
+(* notion 5601 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t100a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y) (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)) o (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y.l_e_tris (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_outn y (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_1top y n)) (l_e_st_eq_landau_n_xout y) (l_e_st_eq_landau_n_isoutinn y n) (l_e_st_eq_landau_n_isoutni y (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_1top y n) y (l_e_st_eq_landau_n_lessisi3 y) t)) : l_not (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y)).
+
+(* notion 5602 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t100b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y) (l_e_st_eq_landau_n_1top y n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t100a q x y l f n o) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y).
+
+(* notion 5603 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t101 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_satz16b (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t100b q x y l f n o) l : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x).
+
+(* notion 5604 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t102 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t101 q x y l f n o) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x).
+
+(* notion 5605 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t102 q x y l f n o) (λt:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_xout x).l_e_st_eq_landau_n_isoutne x (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y x (l_e_st_eq_landau_n_1top y n) l) x (l_e_st_eq_landau_n_lessisi3 x) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_xout x))).
+
+(* notion 5606 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t104 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_rt_rp_r_c_8275_t4 q x f (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_satz275a q x f) (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f n) (f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o))))).
+
+(* notion 5607 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t105 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) y x (l_e_st_eq_landau_n_1top y n) l) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n))).
+
+(* notion 5608 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t106 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_ax2 (l_e_st_eq_landau_n_rt_rp_r_c_inn y n) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t105 q x y l f n o) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn y n)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n)))).
+
+(* notion 5609 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t107 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_isinoutn y (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn y n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q y n o) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn y n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o))).
+
+(* notion 5610 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t108 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n))) (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn y n)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t106 q x y l f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t107 q x y l f n o) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n))) (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o))).
+
+(* notion 5611 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t109 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_left1to x y l n))) (l_e_st_eq_landau_n_rt_rp_r_c_lemma275 q x (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o)) (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) y x (l_e_st_eq_landau_n_1top y (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) l) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t108 q x y l f n o) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o)) (l_e_st_eq_landau_n_left1to x y l (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o))).
+
+(* notion 5612 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t110 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.λo:l_not (l_e_is (l_e_st_eq_landau_n_1to y) n (l_e_st_eq_landau_n_xout y)).(l_e_isp (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_rf q x y l f t) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f n) (f t))) (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q x (l_e_st_eq_landau_n_left1to x y l n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t103 q x y l f n o)) (l_e_st_eq_landau_n_left1to x y l (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t104 q x y l f n o) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t109 q x y l f n o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f n) (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f (l_e_st_eq_landau_n_rt_rp_r_c_8275_ns q y n o)))).
+
+(* notion 5613 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t111 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to y.λu:l_not (l_e_is (l_e_st_eq_landau_n_1to y) t (l_e_st_eq_landau_n_xout y)).l_e_st_eq_landau_n_rt_rp_r_c_8275_t110 q x y l f t u : l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f)).
+
+(* notion 5614 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8275_t112 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_andi (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop1 q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_prop2 q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f)) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t100 q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t111 q x y l f) : l_e_st_eq_landau_n_rt_rp_r_c_recprop q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f)).
+
+(* notion 5615 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz275f ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λl:l_e_st_eq_landau_n_lessis y x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz275d q y (l_e_st_eq_landau_n_rt_rp_r_c_8275_fl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_rfl q x y l f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t112 q x y l f) : l_e_is (Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y l (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q y (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y l f))).
+
+(* notion 5616 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_xs ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_suc x : l_e_st_eq_landau_n_nat).
+
+(* notion 5617 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
+
+(* notion 5618 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)).
+
+(* notion 5619 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_satz18c x) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)).
+
+(* notion 5620 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_satz4e x) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)).
+
+(* notion 5621 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_fx ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t1 q x f) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5622 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) f : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5623 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_f1 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5624 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_g2 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5625 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_g1 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5626 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_g ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5627 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8275_t49 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))))).
+
+(* notion 5628 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz275d q (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t92 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f)) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f))).
+
+(* notion 5629 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz275f q (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) f : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f))).
+
+(* notion 5630 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t6 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t5 q x f) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f)).
+
+(* notion 5631 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fise (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t7 q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)))).
+
+(* notion 5632 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t8 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t4 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_g q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))))).
+
+(* notion 5633 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_1top x n) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n))).
+
+(* notion 5634 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x n) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_1top x n) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t1 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t10 q x f n) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t1 q x f) n) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n))).
+
+(* notion 5635 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t1 q x f) n) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) x (l_e_st_eq_landau_n_rt_rp_r_c_8276_t2 q x f) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t11 q x f n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f n) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f n)).
+
+(* notion 5636 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fisi (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8276_t12 q x f t) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f)).
+
+(* notion 5637 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_recf q x u) (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t13 q x f) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f))).
+
+(* notion 5638 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz275d q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8275_t45 q x (l_e_st_eq_landau_n_rt_rp_r_c_8275_t95 q x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1 q x f)) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f))).
+
+(* notion 5639 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t16 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_f1x q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t15 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t14 q x f) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f))).
+
+(* notion 5640 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t17 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fise (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t16 q x f) (l_e_st_eq_landau_n_xout x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_xout x))).
+
+(* notion 5641 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t18 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)))).
+
+(* notion 5642 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t19 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_satz4a x) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t18 q x f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)))).
+
+(* notion 5643 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t20 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t19 q x f) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f)))).
+
+(* notion 5644 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t21 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isp1 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f).l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) f t) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (f t))) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t3 q x f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_xs q x f))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t9 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t20 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f))))).
+
+(* notion 5645 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8276_t22 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_xout x)) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t17 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8276_x1 q x f))))).
+
+(* notion 5646 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz276 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8276_g1x q x f (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_rt_rp_r_c_8276_fx q x f) (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t21 q x f) (l_e_st_eq_landau_n_rt_rp_r_c_8276_t22 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (q (l_e_st_eq_landau_n_rt_rp_r_c_recf q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1)) f) (l_e_st_eq_landau_n_xout x)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
+
+(* notion 5647 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_smpr ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_rec q x f (l_e_st_eq_landau_n_xout x) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5648 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_sum ≝ λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5649 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_prod ≝ λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5650 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8277_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_1) (l_e_refis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)).
+
+(* notion 5651 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz277 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isp (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_rec q l_e_st_eq_landau_n_1 f t) (f t)) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_satz275b q l_e_st_eq_landau_n_1 f) (l_e_st_eq_landau_n_rt_rp_r_c_8277_t1 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5652 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz278 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz276 q x f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1)) f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
+
+(* notion 5653 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_st_eq_landau_n_lessisi2 y x i : l_e_st_eq_landau_n_lessis y x).
+
+(* notion 5654 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v8_f0 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) f : Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5655 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v8_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_fise (l_e_st_eq_landau_n_1to y) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q y (l_e_st_eq_landau_n_rt_rp_r_c_v8_f0 q x f y i)) (l_e_st_eq_landau_n_rt_rp_r_c_satz275f q x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) f) (l_e_st_eq_landau_n_xout y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_xout y))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_v8_f0 q x f y i))).
+
+(* notion 5656 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v8_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_xout y)) x y (l_e_st_eq_landau_n_isinoutn y y (l_e_st_eq_landau_n_lessisi3 y)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_xout y)) x).
+
+(* notion 5657 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v8_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_xout y)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn y (l_e_st_eq_landau_n_xout y)) y x (l_e_st_eq_landau_n_1top y (l_e_st_eq_landau_n_xout y)) (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i)) x (l_e_st_eq_landau_n_lessisi3 x) (l_e_st_eq_landau_n_rt_rp_r_c_v8_t3 q x f y i) : l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_xout y)) (l_e_st_eq_landau_n_xout x)).
+
+(* notion 5658 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v8_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_isf (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f) (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_xout y)) (l_e_st_eq_landau_n_xout x) (l_e_st_eq_landau_n_rt_rp_r_c_v8_t4 q x f y i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_xout y))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f)).
+
+(* notion 5659 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_issmpr ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λx:l_e_st_eq_landau_n_nat.λf:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is y x.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_v8_f0 q x f y i)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f) (l_e_st_eq_landau_n_rt_rp_r_c_recf q x f (l_e_st_eq_landau_n_left1to x y (l_e_st_eq_landau_n_rt_rp_r_c_v8_t1 q x f y i) (l_e_st_eq_landau_n_xout y))) (l_e_st_eq_landau_n_rt_rp_r_c_v8_t2 q x f y i) (l_e_st_eq_landau_n_rt_rp_r_c_v8_t5 q x f y i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x y (l_e_st_eq_landau_n_lessisi2 y x i) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f)).
+
+(* notion 5660 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_xr ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_rlofnt x : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 5661 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0)) : Prop).
+
+(* notion 5662 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t1 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.z)) z).
+
+(* notion 5663 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t2 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.z)) z (l_e_st_eq_landau_n_rt_rp_r_c_ts z l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t1 z) (l_e_st_eq_landau_n_rt_rp_r_c_satz222a z) : l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z l_e_st_eq_landau_n_1).
+
+(* notion 5664 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t3 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) x (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) z)).
+
+(* notion 5665 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t4 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0)) z (l_e_st_eq_landau_n_rt_rp_r_c_ts z l_e_st_eq_landau_n_rt_rp_r_c_1c) p (l_e_st_eq_landau_n_rt_rp_r_c_satz222a z) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z l_e_st_eq_landau_n_rt_rp_r_c_1c))).
+
+(* notion 5666 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t5 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_distpt2 z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c))).
+
+(* notion 5667 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t6 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_plis12a (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 5668 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t7 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satzr155b x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 5669 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t8 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t6 z x p) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t7 z x p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 5670 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t9 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0) z (l_e_st_eq_landau_n_rt_rp_r_c_8279_t8 z x p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 5671 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t10 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).z)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) z) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8279_xr z x) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t3 z x p) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t4 z x p) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t5 z x p) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t9 z x p) : l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 5672 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8279_t11 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z t) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t10 z x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z (l_e_st_eq_landau_n_suc x)).
+
+(* notion 5673 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz279 ≝ λz:l_e_st_eq_landau_n_rt_rp_r_c_complex.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z t) (l_e_st_eq_landau_n_rt_rp_r_c_8279_t2 z) (λu:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_c_8279_prop1 z u.l_e_st_eq_landau_n_rt_rp_r_c_8279_t11 z u t) x : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum x (λt:l_e_st_eq_landau_n_1to x.z)) (l_e_st_eq_landau_n_rt_rp_r_c_ts z (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_rlofnt x) l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 5674 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_satz18a l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_2).
+
+(* notion 5675 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_t1 q f) f : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5676 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q l_e_st_eq_landau_n_1 f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
+
+(* notion 5677 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5678 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5679 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t1 q f)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t4 q f) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_left1to l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_t1 q f) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5680 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2) (l_e_st_eq_landau_n_left1to l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_t1 q f) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t5 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5681 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t3 q f) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t6 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))).
+
+(* notion 5682 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8280_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t7 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (q (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
+
+(* notion 5683 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz280 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8280_f1 q f)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (q (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t2 q f) (l_e_st_eq_landau_n_rt_rp_r_c_8280_t8 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 f) (q (f (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
+
+(* notion 5684 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_assoc ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.(Πx:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πy:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πz:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (q (q x y) z) (q x (q y z)) : Prop).
+
+(* notion 5685 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_assocp1 ≝ (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_asspl1 x y z : l_e_st_eq_landau_n_rt_rp_r_c_assoc (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl x y)).
+
+(* notion 5686 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_assocts ≝ (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_assts1 x y z : l_e_st_eq_landau_n_rt_rp_r_c_assoc (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts x y)).
+
+(* notion 5687 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_assq1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.(a z u v : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q z u) v) (q z (q u v))).
+
+(* notion 5688 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_assq2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (q (q z u) v) (q z (q u v)) (l_e_st_eq_landau_n_rt_rp_r_c_assq1 q a z u v) : l_e_st_eq_landau_n_rt_rp_r_c_is (q z (q u v)) (q (q z u) v)).
+
+(* notion 5689 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_satz18a x y) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_pl x y)).
+
+(* notion 5690 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x y) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x y) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5691 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx x y f : Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5692 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_prop1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl x y) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y f))) : Prop).
+
+(* notion 5693 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_all (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx) (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8281_prop1 q a x y u) : Prop).
+
+(* notion 5694 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x f0 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f0) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0)) (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
+
+(* notion 5695 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5696 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5697 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_ispl2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t4 q a x f0) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
+
+(* notion 5698 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t5 q a x f0) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_right1to x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5699 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_c_cx f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_right1to x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t6 q a x f0) : l_e_st_eq_landau_n_rt_rp_r_c_is (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5700 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t7 q a x f0) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t3 q a x f0) : l_e_st_eq_landau_n_rt_rp_r_c_is (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0))).
+
+(* notion 5701 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0))) (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t8 q a x f0) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0)) (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0)))).
+
+(* notion 5702 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λf0:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f0) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0)) (f0 (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x l_e_st_eq_landau_n_1 f0))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t2 q a x f0) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t9 q a x f0) : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop1 q a x l_e_st_eq_landau_n_1 f0).
+
+(* notion 5703 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8281_t10 q a x u : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x l_e_st_eq_landau_n_1).
+
+(* notion 5704 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl y l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
+
+(* notion 5705 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl x y : l_e_st_eq_landau_n_nat).
+
+(* notion 5706 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) : l_e_st_eq_landau_n_nat).
+
+(* notion 5707 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
+
+(* notion 5708 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_asspl1 x y l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)).
+
+(* notion 5709 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))).
+
+(* notion 5710 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_asspl2 x y l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t13 q a x y p f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))).
+
+(* notion 5711 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t14 q a x y p f) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))).
+
+(* notion 5712 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t16 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t15 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))).
+
+(* notion 5713 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_fr ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) f : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5714 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t17 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz275f q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) f : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f))).
+
+(* notion 5715 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t18 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fise (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t17 q a x y p f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f))).
+
+(* notion 5716 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_satz18a (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)).
+
+(* notion 5717 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_frr ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5718 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t20 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))))).
+
+(* notion 5719 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t21 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.q u (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (p (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))))).
+
+(* notion 5720 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t22 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_assq1 q a (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))))).
+
+(* notion 5721 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t23 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 y (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_satz18a y l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)).
+
+(* notion 5722 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_fy ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) y (l_e_st_eq_landau_n_rt_rp_r_c_8281_t23 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f) : Πt:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5723 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t24 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
+
+(* notion 5724 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t25 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))).
+
+(* notion 5725 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t26 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t25 q a x y p f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
+
+(* notion 5726 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t27 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t14 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t26 q a x y p f) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
+
+(* notion 5727 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t28 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) x (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t27 q a x y p f) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_right1to x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))).
+
+(* notion 5728 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t29 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_right1to x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t28 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))).
+
+(* notion 5729 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t30 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t29 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
+
+(* notion 5730 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_rt_rp_r_c_inn y n : l_e_st_eq_landau_n_nat).
+
+(* notion 5731 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) y (l_e_st_eq_landau_n_rt_rp_r_c_8281_t23 q a x y p f) n : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)).
+
+(* notion 5732 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t31 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n) y (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_1top y n) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t23 q a x y p f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n))).
+
+(* notion 5733 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t32 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n)) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t31 q a x y p f n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n)))).
+
+(* notion 5734 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_right1to x y n : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y)).
+
+(* notion 5735 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)).
+
+(* notion 5736 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t33 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 q a x y p f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n))).
+
+(* notion 5737 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t34 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n) y x (l_e_st_eq_landau_n_1top y n)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n))).
+
+(* notion 5738 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t35 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxpy q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t34 q a x y p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t33 q a x y p f n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n))).
+
+(* notion 5739 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t36 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_8281_n0 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t32 q a x y p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t35 q a x y p f n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n))).
+
+(* notion 5740 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t37 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_pl x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n))) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) x (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t36 q a x y p f n) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_right1to x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n))).
+
+(* notion 5741 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t38 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to y.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_right1to x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nyp1 q a x y p f n)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_nxyp1 q a x y p f n)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t37 q a x y p f n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f n) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f) n)).
+
+(* notion 5742 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t39 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fisi (l_e_st_eq_landau_n_1to y) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (λu:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_8281_t38 q a x y p f u) : l_e_is (Πu:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))).
+
+(* notion 5743 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t40 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (Πu:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:Πu:l_e_st_eq_landau_n_1to y.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q y t) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t39 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))).
+
+(* notion 5744 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t41 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t40 q a x y p f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
+
+(* notion 5745 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t41a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t30 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t41 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))))).
+
+(* notion 5746 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t42 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_fy q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t41a q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t24 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f))).
+
+(* notion 5747 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t43 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t42 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)))).
+
+(* notion 5748 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_inn x m : l_e_st_eq_landau_n_nat).
+
+(* notion 5749 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x y) m : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y)).
+
+(* notion 5750 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)).
+
+(* notion 5751 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t44 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t19 q a x y p f)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m))).
+
+(* notion 5752 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t45 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_1top x m) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x y)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m))).
+
+(* notion 5753 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t46 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxpy q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t45 q a x y p f m) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t44 q a x y p f m) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m))).
+
+(* notion 5754 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t47 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_8281_m0 q a x y p f m) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_1top x m) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t46 q a x y p f m) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)) m) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m))).
+
+(* notion 5755 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t48 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_1to x.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) x (l_e_st_eq_landau_n_rt_rp_r_c_8281_t1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)) m) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_mxyp1 q a x y p f m)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t47 q a x y p f m) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f m) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f) m)).
+
+(* notion 5756 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t49 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_fisi (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (λu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8281_t48 q a x y p f u) : l_e_is (Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))).
+
+(* notion 5757 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t50 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:Πu:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q x t) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t49 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))).
+
+(* notion 5758 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t51 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t50 q a x y p f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)))).
+
+(* notion 5759 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t52 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t12 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_recf q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t16 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t18 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t20 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t21 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))))).
+
+(* notion 5760 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t53 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y) f) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_fr q a x y p f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8281_xyp1 q a x y))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x y (l_e_st_eq_landau_n_rt_rp_r_c_8281_frr q a x y p f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8281_f1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_f2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f))) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t52 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t22 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t43 q a x y p f) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t51 q a x y p f) : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop1 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) f).
+
+(* notion 5761 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t54 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8281_xpy1 q a x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8281_t53 q a x y p u : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y)).
+
+(* notion 5762 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t55 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x t) (l_e_st_eq_landau_n_rt_rp_r_c_8281_yp1 q a x y) (l_e_st_eq_landau_n_suc y) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t54 q a x y p) (l_e_st_eq_landau_n_satz4a y) : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x (l_e_st_eq_landau_n_suc y)).
+
+(* notion 5763 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8281_t56 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x t) (l_e_st_eq_landau_n_rt_rp_r_c_8281_t11 q a x) (λz:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x z.l_e_st_eq_landau_n_rt_rp_r_c_8281_t55 q a x z t) y : l_e_st_eq_landau_n_rt_rp_r_c_8281_prop2 q a x y).
+
+(* notion 5764 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz281 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λx:l_e_st_eq_landau_n_nat.λy:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x y).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8281_t56 q a x y f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl x y) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x y) x (l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x y) (l_e_st_eq_landau_n_satz18a x y)) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q y (l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx x y f)))).
+
+(* notion 5765 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_commut ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.(Πx:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_is (q x y) (q y x) : Prop).
+
+(* notion 5766 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_commutpl ≝ (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_compl x y : l_e_st_eq_landau_n_rt_rp_r_c_commut (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl x y)).
+
+(* notion 5767 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_commutts ≝ (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_comts x y : l_e_st_eq_landau_n_rt_rp_r_c_commut (λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts x y)).
+
+(* notion 5768 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_comq ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.(c z u : l_e_st_eq_landau_n_rt_rp_r_c_is (q z u) (q u z)).
+
+(* notion 5769 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_prop1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (λt:l_e_st_eq_landau_n_1to x.q (f t) (g t))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x g)) : Prop).
+
+(* notion 5770 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_all (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_all (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λv:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8282_prop1 q a c x u v)) : Prop).
+
+(* notion 5771 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λf0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.q (f0 t) (g0 t)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.q (f0 t) (g0 t))) (q (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
+
+(* notion 5772 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λf0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 g0) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_satz277 q g0) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 g0)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
+
+(* notion 5773 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λf0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_satz277 q f0) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (q (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
+
+(* notion 5774 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λf0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 g0)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (q (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t2 q a c f0 g0) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t3 q a c f0 g0) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 g0)) (q (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
+
+(* notion 5775 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λf0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg0:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.q (f0 t) (g0 t))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f0) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 g0)) (q (f0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (g0 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t1 q a c f0 g0) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t4 q a c f0 g0) : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop1 q a c l_e_st_eq_landau_n_1 f0 g0).
+
+(* notion 5776 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.(λu:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8282_t5 q a c u v : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c l_e_st_eq_landau_n_1).
+
+(* notion 5777 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
+
+(* notion 5778 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_assq2 q a (q u v) w z : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q u v) (q w z)) (q (q (q u v) w) z)).
+
+(* notion 5779 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_comq q c (q u v) w : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q u v) w) (q w (q u v))).
+
+(* notion 5780 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_assq2 q a w u v : l_e_st_eq_landau_n_rt_rp_r_c_is (q w (q u v)) (q (q w u) v)).
+
+(* notion 5781 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (q (q u v) w) (q w (q u v)) (q (q w u) v) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t8 q a c u v w z) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t9 q a c u v w z) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q u v) w) (q (q w u) v)).
+
+(* notion 5782 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t z) (q (q u v) w) (q (q w u) v) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t10 q a c u v w z) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (q u v) w) z) (q (q (q w u) v) z)).
+
+(* notion 5783 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_assq1 q a (q w u) v z : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (q w u) v) z) (q (q w u) (q v z))).
+
+(* notion 5784 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_comq q c w u : l_e_st_eq_landau_n_rt_rp_r_c_is (q w u) (q u w)).
+
+(* notion 5785 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (q v z)) (q w u) (q u w) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t13 q a c u v w z) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q w u) (q v z)) (q (q u w) (q v z))).
+
+(* notion 5786 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_st_eq_landau_n_rt_rp_r_c_cx.λz:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (q (q u v) (q w z)) (q (q (q u v) w) z) (q (q (q w u) v) z) (q (q w u) (q v z)) (q (q u w) (q v z)) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t7 q a c u v w z) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t11 q a c u v w z) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t12 q a c u v w z) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t14 q a c u v w z) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q u v) (q w z)) (q (q u w) (q v z))).
+
+(* notion 5787 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)).
+
+(* notion 5788 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 q a c x p f g) f) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5789 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 q a c x p f g) g) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5790 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_h ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).q (f t) (g t) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5791 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_shx ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g)) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5792 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t17 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_shx q a c x p f g) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))))).
+
+(* notion 5793 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t18 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(p (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 q a c x p f g) f) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8282_t16 q a c x p f g) g) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8282_shx q a c x p f g) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g))).
+
+(* notion 5794 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t19 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (l_e_st_eq_landau_n_rt_rp_r_c_8282_shx q a c x p f g) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g)) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t18 q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_shx q a c x p f g) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g)) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))))).
+
+(* notion 5795 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t20 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8282_t15 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g)) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))))).
+
+(* notion 5796 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t21 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f)).
+
+(* notion 5797 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t22 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t21 q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))))).
+
+(* notion 5798 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t23 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) g) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x g) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) g)).
+
+(* notion 5799 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t24 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t23 q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) g))).
+
+(* notion 5800 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t25 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_shx q a c x p f g) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g)) (q (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t17 q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t19 q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t20 q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g)) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))))).
+
+(* notion 5801 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t26 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8282_h q a c x p f g)) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sfx q a c x p f g) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_8282_sgx q a c x p f g) (g (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x))))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) g)) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t25 q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t22 q a c x p f g) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t24 q a c x p f g) : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) f g).
+
+(* notion 5802 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t27 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8282_t26 q a c x p u v : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x)).
+
+(* notion 5803 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t28 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c t) (l_e_st_eq_landau_n_rt_rp_r_c_8282_xp1 q a c x) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t27 q a c x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c (l_e_st_eq_landau_n_suc x)).
+
+(* notion 5804 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8282_t29 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c t) (l_e_st_eq_landau_n_rt_rp_r_c_8282_t6 q a c) (λy:l_e_st_eq_landau_n_nat.λt:l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c y.l_e_st_eq_landau_n_rt_rp_r_c_8282_t28 q a c y t) x : l_e_st_eq_landau_n_rt_rp_r_c_8282_prop2 q a c x).
+
+(* notion 5805 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz282 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λg:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8282_t29 q a c x f g : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (λt:l_e_st_eq_landau_n_1to x.q (f t) (g t))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x g))).
+
+(* notion 5806 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λs:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to x.f (s t) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5807 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λs:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c x s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f) : Prop).
+
+(* notion 5808 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_all (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x) (λu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x.l_all (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (λv:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_imp (l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c x u v))) : Prop).
+
+(* notion 5809 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (s (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_1o (l_e_st_eq_landau_n_singlet_th1 (s (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_singlet_th1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (s (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)).
+
+(* notion 5810 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5811 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_rt_rp_r_c_cx f (s (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t1 q a c s f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5812 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_satz277 q f) : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f)).
+
+(* notion 5813 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c l_e_st_eq_landau_n_1 s f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t2 q a c s f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t3 q a c s f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t4 q a c s f) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c l_e_st_eq_landau_n_1 s f).
+
+(* notion 5814 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.(λu:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λv:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_bijective (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) u.l_e_st_eq_landau_n_rt_rp_r_c_8283_t5 q a c u v : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c l_e_st_eq_landau_n_1).
+
+(* notion 5815 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
+
+(* notion 5816 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5817 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.(l_ande1 (l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s) (l_e_surjective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s) b : l_e_injective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s).
+
+(* notion 5818 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) u : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5819 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) : l_e_st_eq_landau_n_nat).
+
+(* notion 5820 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) (l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) case1) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 5821 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t9 q a c x p s f b case1 u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5822 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t10 q a c x p s f b case1 u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5823 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_st_eq_landau_n_satz16a (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5824 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t12 q a c x p s f b case1 u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t11 q a c x p s f b case1 u i) : l_con).
+
+(* notion 5825 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u))) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_t13 q a c x p s f b case1 u t) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5826 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_satz26 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t14 q a c x p s f b case1 u) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) x).
+
+(* notion 5827 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 q a c x p s f b case1 u) : l_e_st_eq_landau_n_1to x).
+
+(* notion 5828 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 t : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x).
+
+(* notion 5829 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t16 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 v).(l_e_st_eq_landau_n_isoutne x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 v) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 q a c x p s f b case1 v) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 v)).
+
+(* notion 5830 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t17 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 v).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p s f b (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 v) (l_e_st_eq_landau_n_isinne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 v)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t16 q a c x p s f b case1 u v i)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 v)).
+
+(* notion 5831 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t18 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 v).(l_e_st_eq_landau_n_thleft1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) u v (l_e_st_eq_landau_n_rt_rp_r_c_8283_t17 q a c x p s f b case1 u v i) : l_e_is (l_e_st_eq_landau_n_1to x) u v).
+
+(* notion 5832 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_invf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5833 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) : l_e_st_eq_landau_n_nat).
+
+(* notion 5834 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t19 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5835 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t20 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t19 q a c x p s f b case1 u i)) case1 : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5836 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t21 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t20 q a c x p s f b case1 u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5837 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t22 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_e_st_eq_landau_n_satz16a (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5838 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t23 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t22 q a c x p s f b case1 u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t21 q a c x p s f b case1 u i) : l_con).
+
+(* notion 5839 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t24 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_t23 q a c x p s f b case1 u t) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5840 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t25 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_satz26 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t24 q a c x p s f b case1 u) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) x).
+
+(* notion 5841 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t25 q a c x p s f b case1 u) : l_e_st_eq_landau_n_1to x).
+
+(* notion 5842 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t26 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t25 q a c x p s f b case1 u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))).
+
+(* notion 5843 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t27 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t26 q a c x p s f b case1 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))).
+
+(* notion 5844 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t28 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))) (l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t27 q a c x p s f b case1 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)))).
+
+(* notion 5845 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t29 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x))) (l_e_st_eq_landau_n_isinni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t28 q a c x p s f b case1 u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))).
+
+(* notion 5846 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t30 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_1top x u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_isoutinn x u) (l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t29 q a c x p s f b case1 u)) : l_e_is (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u))).
+
+(* notion 5847 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t31 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_somei (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_is (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 t)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w2 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t30 q a c x p s f b case1 u) : l_e_image (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1) u).
+
+(* notion 5848 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t32 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_andi (l_e_injective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1)) (l_e_surjective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1)) (λt:l_e_st_eq_landau_n_1to x.λu:l_e_st_eq_landau_n_1to x.λv:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1 t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1 u).l_e_st_eq_landau_n_rt_rp_r_c_8283_t18 q a c x p s f b case1 t u v) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_t31 q a c x p s f b case1 t) : l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1)).
+
+(* notion 5849 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5850 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t33 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t32 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c x (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)).
+
+(* notion 5851 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5852 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c x (l_e_st_eq_landau_n_rt_rp_r_c_8283_s01 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5853 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t33a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u))))).
+
+(* notion 5854 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t34 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t15 q a c x p s f b case1 u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u))).
+
+(* notion 5855 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t35 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t34 q a c x p s f b case1 u) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)))) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u))).
+
+(* notion 5856 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t36 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)))) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t33a q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t35 q a c x p s f b case1 u) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u))).
+
+(* notion 5857 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t37 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t7 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w1 q a c x p s f b case1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t36 q a c x p s f b case1 u) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1 u)).
+
+(* notion 5858 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t38 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_fisi (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_t37 q a c x p s f b case1 t) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1)).
+
+(* notion 5859 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t39 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t38 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1))).
+
+(* notion 5860 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t40 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g2 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t39 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t33 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1))).
+
+(* notion 5861 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t41 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) case1 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 5862 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t42 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
+
+(* notion 5863 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t43 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t41 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
+
+(* notion 5864 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t44 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t40 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
+
+(* notion 5865 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t45 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x f) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
+
+(* notion 5866 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t46 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase1:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g1 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f01 q a c x p s f b case1)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t42 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t43 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t44 q a c x p s f b case1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t45 q a c x p s f b case1) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 5867 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1px ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.(l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 x : l_e_st_eq_landau_n_nat).
+
+(* notion 5868 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x u : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b)).
+
+(* notion 5869 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_compl l_e_st_eq_landau_n_1 x) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5870 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) s : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5871 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) : l_e_st_eq_landau_n_nat).
+
+(* notion 5872 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t48 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) (l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) case2) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 5873 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t49 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p s f b) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t48 q a c x p s f b case2 u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5874 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t50 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t49 q a c x p s f b case2 u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1).
+
+(* notion 5875 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t51 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top x u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))).
+
+(* notion 5876 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t52 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t51 q a c x p s f b case2 u i) (l_e_st_eq_landau_n_satz18 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1).
+
+(* notion 5877 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t53 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_ec3e21 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t52 q a c x p s f b case2 u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t50 q a c x p s f b case2 u i) : l_con).
+
+(* notion 5878 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz24 (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u)) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_8283_t53 q a c x p s f b case2 u t) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1).
+
+(* notion 5879 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_mn (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 u) : l_e_st_eq_landau_n_nat).
+
+(* notion 5880 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t54a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_islessis1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_mn_th1c (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5881 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_or_th9 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) x) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54a q a c x p s f b case2 u) (λt:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_satz20c (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) x l_e_st_eq_landau_n_1 t) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_satz20b (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) x l_e_st_eq_landau_n_1 t) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) x).
+
+(* notion 5882 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 q a c x p s f b case2 u) : l_e_st_eq_landau_n_1to x).
+
+(* notion 5883 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 t : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x).
+
+(* notion 5884 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t56 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_st_eq_landau_n_isoutne x (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 v) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 q a c x p s f b case2 v) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 v)).
+
+(* notion 5885 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t57 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 v) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 v) (l_e_st_eq_landau_n_mn_th1c (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 v) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t56 q a c x p s f b case2 u v i)) (l_e_st_eq_landau_n_mn_th1d (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 v) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 v)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 v)).
+
+(* notion 5886 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t58 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_st_eq_landau_n_isinne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t57 q a c x p s f b case2 u v i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v))).
+
+(* notion 5887 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t59 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p s f b) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t58 q a c x p s f b case2 u v i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v))).
+
+(* notion 5888 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t60 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_st_eq_landau_n_thleft1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t59 q a c x p s f b case2 u v i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 v)).
+
+(* notion 5889 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t61 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λv:l_e_st_eq_landau_n_1to x.λi:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 v).(l_e_st_eq_landau_n_thright1 l_e_st_eq_landau_n_1 x u v (l_e_st_eq_landau_n_rt_rp_r_c_8283_t60 q a c x p s f b case2 u v i) : l_e_is (l_e_st_eq_landau_n_1to x) u v).
+
+(* notion 5890 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s04 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_invf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5891 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_8283_s04 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5892 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) : l_e_st_eq_landau_n_nat).
+
+(* notion 5893 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t62 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5894 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t63 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t62 q a c x p s f b case2 u i)) case2 : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5895 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t64 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t63 q a c x p s f b case2 u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1).
+
+(* notion 5896 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t65 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top x u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t64 q a c x p s f b case2 u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) l_e_st_eq_landau_n_1).
+
+(* notion 5897 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t66 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.(l_ec3e21 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t65 q a c x p s f b case2 u i) : l_con).
+
+(* notion 5898 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t67 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_ore1 (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz24 (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u)) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_8283_t66 q a c x p s f b case2 u t) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1).
+
+(* notion 5899 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_mn (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t67 q a c x p s f b case2 u) : l_e_st_eq_landau_n_nat).
+
+(* notion 5900 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t68 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_islessis1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_mn_th1c (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t67 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5901 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t69 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_or_th9 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) x) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t68 q a c x p s f b case2 u) (λt:l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_satz20c (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) x l_e_st_eq_landau_n_1 t) (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_satz20b (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) x l_e_st_eq_landau_n_1 t) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) x).
+
+(* notion 5902 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t69 q a c x p s f b case2 u) : l_e_st_eq_landau_n_1to x).
+
+(* notion 5903 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t70 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t69 q a c x p s f b case2 u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))).
+
+(* notion 5904 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t71 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_mn_th1a (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t67 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm2 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t70 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)))).
+
+(* notion 5905 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t72 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t71 q a c x p s f b case2 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)))).
+
+(* notion 5906 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t73 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_u4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t72 q a c x p s f b case2 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)))).
+
+(* notion 5907 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t74 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top x u))) (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2))) (l_e_st_eq_landau_n_isinni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t73 q a c x p s f b case2 u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))).
+
+(* notion 5908 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t75 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_st_eq_landau_n_mn_th1e (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t74 q a c x p s f b case2 u) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))).
+
+(* notion 5909 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t76 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_1top x u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_isoutinn x u) (l_e_st_eq_landau_n_isoutni x (l_e_st_eq_landau_n_rt_rp_r_c_inn x u) (l_e_st_eq_landau_n_1top x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t75 q a c x p s f b case2 u)) : l_e_is (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u))).
+
+(* notion 5910 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t77 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_somei (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_is (l_e_st_eq_landau_n_1to x) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 t)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_w4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t76 q a c x p s f b case2 u) : l_e_image (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2) u).
+
+(* notion 5911 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t78 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_andi (l_e_injective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2)) (l_e_surjective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2)) (λt:l_e_st_eq_landau_n_1to x.λu:l_e_st_eq_landau_n_1to x.λv:l_e_is (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2 t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2 u).l_e_st_eq_landau_n_rt_rp_r_c_8283_t61 q a c x p s f b case2 t u v) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_t77 q a c x p s f b case2 t) : l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2)).
+
+(* notion 5912 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) f : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5913 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5914 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t79 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t78 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c x (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2)).
+
+(* notion 5915 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5916 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5917 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c x (l_e_st_eq_landau_n_rt_rp_r_c_8283_s03 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5918 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t80 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_mn_th1a (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t54 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_nm1 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t55 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u)) x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u)))) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u)))).
+
+(* notion 5919 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t81 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)))) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_n3 q a c x p s f b case2 u) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t80 q a c x p s f b case2 u)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u)))).
+
+(* notion 5920 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t82 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λu:l_e_st_eq_landau_n_1to x.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8283_s02 q a c x p s f b case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_u3 q a c x p s f b case2 u)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_w3 q a c x p s f b case2 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t81 q a c x p s f b case2 u) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2 u)).
+
+(* notion 5921 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t83 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_fisi (l_e_st_eq_landau_n_1to x) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_8283_t82 q a c x p s f b case2 t) : l_e_is (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2)).
+
+(* notion 5922 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t85 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf (Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q x u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t83 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2))).
+
+(* notion 5923 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t86 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g5 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t85 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t79 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))).
+
+(* notion 5924 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t87 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_lessisi1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_satz18a l_e_st_eq_landau_n_1 x) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b)).
+
+(* notion 5925 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2) : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5926 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2) : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 5927 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t87a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 5928 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1d ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87 q a c x p s f b case2) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b)).
+
+(* notion 5929 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t87b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87 q a c x p s f b case2)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2))).
+
+(* notion 5930 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t88 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87a q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t87b q a c x p s f b case2) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2))).
+
+(* notion 5931 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1e ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5932 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t88a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1d q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t47 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t88 q a c x p s f b case2) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)).
+
+(* notion 5933 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t88b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t88a q a c x p s f b case2)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 5934 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t89 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t88b q a c x p s f b case2) case2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t88a q a c x p s f b case2) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)).
+
+(* notion 5935 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t89a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1e q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t89 q a c x p s f b case2)) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2))).
+
+(* notion 5936 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t90 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_satz281 q a l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2)))).
+
+(* notion 5937 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t91 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t86 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2)))).
+
+(* notion 5938 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t92 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t89a q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2)))).
+
+(* notion 5939 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t93 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (l_e_st_eq_landau_n_rt_rp_r_c_satz281 q a l_e_st_eq_landau_n_1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2)) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2))).
+
+(* notion 5940 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t94 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g4 q a c x p s f b case2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g6 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f04 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_f03 q a c x p s f b case2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t90 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t91 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t92 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t93 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2))).
+
+(* notion 5941 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t95 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_compl l_e_st_eq_landau_n_1 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
+
+(* notion 5942 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t96 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_compl l_e_st_eq_landau_n_1 x)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2))).
+
+(* notion 5943 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t97 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λcase2:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g3 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f02 q a c x p s f b case2)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t96 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t94 q a c x p s f b case2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t95 q a c x p s f b case2) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 5944 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5945 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_invf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5946 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_thinvf2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s b (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2))).
+
+(* notion 5947 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t99 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(not2 : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 5948 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t100 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_symnotis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_notis_th3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 q a c x p s f b not1 not2)) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
+
+(* notion 5949 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t101 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t100 q a c x p s f b not1 not2) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 5950 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_changef (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5951 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t102 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_changef1 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u i : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2))).
+
+(* notion 5952 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t103 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t102 q a c x p s f b not1 not2 u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 q a c x p s f b not1 not2) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5953 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t104 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).(l_e_changef2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u i : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2)).
+
+(* notion 5954 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t105 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_changef3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u n o : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (s u)).
+
+(* notion 5955 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t106 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_wissel_th6 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) b : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2)).
+
+(* notion 5956 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_wissel (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5957 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t107 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_wissel_th3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha)).
+
+(* notion 5958 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t108 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_iswissel1 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t103 q a c x p s f b not1 not2 u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2)).
+
+(* notion 5959 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t109 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t108 q a c x p s f b not1 not2 alpha u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))).
+
+(* notion 5960 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t110 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).(l_e_iswissel2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t104 q a c x p s f b not1 not2 u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5961 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t111 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 q a c x p s f b not1 not2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t110 q a c x p s f b not1 not2 alpha u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))).
+
+(* notion 5962 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t112 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_t106 q a c x p s f b not1 not2)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i (l_e_st_eq_landau_n_rt_rp_r_c_8283_t103 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5963 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t113 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) n (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t112 q a c x p s f b not1 not2 alpha u n o t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 5964 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t114 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2).(l_e_isfe (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t8 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_t106 q a c x p s f b not1 not2)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) i (l_e_st_eq_landau_n_rt_rp_r_c_8283_t104 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)))) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).
+
+(* notion 5965 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t115 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) o (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2).l_e_st_eq_landau_n_rt_rp_r_c_8283_t114 q a c x p s f b not1 not2 alpha u n o t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2))).
+
+(* notion 5966 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t116 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_iswissel3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t113 q a c x p s f b not1 not2 alpha u n o) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t115 q a c x p s f b not1 not2 alpha u n o) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)).
+
+(* notion 5967 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t117 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (s u) (l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t116 q a c x p s f b not1 not2 alpha u n o) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t105 q a c x p s f b not1 not2 u n o)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))).
+
+(* notion 5968 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t118 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).l_e_st_eq_landau_n_rt_rp_r_c_8283_t111 q a c x p s f b not1 not2 alpha u t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t117 q a c x p s f b not1 not2 alpha u n t) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))).
+
+(* notion 5969 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t119 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t109 q a c x p s f b not1 not2 alpha u t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t118 q a c x p s f b not1 not2 alpha u t) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u))).
+
+(* notion 5970 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t120 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 t)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_t119 q a c x p s f b not1 not2 alpha t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 t))).
+
+(* notion 5971 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t121 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t103 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5972 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t121a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_ec3e21 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ismore1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_1px q a c x p s f b) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_compl l_e_st_eq_landau_n_1 x) (l_e_st_eq_landau_n_satz18 l_e_st_eq_landau_n_1 x)) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1).
+
+(* notion 5973 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t122 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th3 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t121a q a c x p s f b not1 not2) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) t) : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 5974 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t123 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_symnotis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) alpha : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2))).
+
+(* notion 5975 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t124 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_iswissel3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t122 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t123 q a c x p s f b not1 not2 alpha) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5976 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t125 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) u f)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 t)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t120 q a c x p s f b not1 not2 alpha) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f)))).
+
+(* notion 5977 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t126 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t97 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t106 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t121 q a c x p s f b not1 not2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f))).
+
+(* notion 5978 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t127 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t46 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_t107 q a c x p s f b not1 not2 alpha) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t124 q a c x p s f b not1 not2 alpha) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
+
+(* notion 5979 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t128 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λalpha:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s2 q a c x p s f b not1 not2 alpha) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t125 q a c x p s f b not1 not2 alpha) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t126 q a c x p s f b not1 not2 alpha) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t127 q a c x p s f b not1 not2 alpha) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 5980 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_wissel (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 5981 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t129 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_wissel_th3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta)).
+
+(* notion 5982 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t130 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t104 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u) (l_e_iswissel1 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2)).
+
+(* notion 5983 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t131 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t130 q a c x p s f b not1 not2 i3 beta u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))).
+
+(* notion 5984 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t132 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t103 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u) (l_e_iswissel2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5985 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t133 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) i) (l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t132 q a c x p s f b not1 not2 i3 beta u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 q a c x p s f b not1 not2)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))).
+
+(* notion 5986 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t134 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_iswissel3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) u n o : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u) u).
+
+(* notion 5987 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t135 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_t134 q a c x p s f b not1 not2 i3 beta u n o) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u)).
+
+(* notion 5988 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t136 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t105 q a c x p s f b not1 not2 u n o : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (s u)).
+
+(* notion 5989 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t139 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λo:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).(l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (s u) (l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 u) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t135 q a c x p s f b not1 not2 i3 beta u n o) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t136 q a c x p s f b not1 not2 i3 beta u n o)) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))).
+
+(* notion 5990 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t140 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λn:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2).l_e_st_eq_landau_n_rt_rp_r_c_8283_t133 q a c x p s f b not1 not2 i3 beta u t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t139 q a c x p s f b not1 not2 i3 beta u n t) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))).
+
+(* notion 5991 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t141 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t131 q a c x p s f b not1 not2 i3 beta u t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t140 q a c x p s f b not1 not2 i3 beta u t) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta u))).
+
+(* notion 5992 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t142 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta t)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_t141 q a c x p s f b not1 not2 i3 beta t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta t))).
+
+(* notion 5993 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t143 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_symnotis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) beta : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2))).
+
+(* notion 5994 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t144 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_iswissel3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t122 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t143 q a c x p s f b not1 not2 i3 beta) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 5995 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t145 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) u f)) s (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta t)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t142 q a c x p s f b not1 not2 i3 beta) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f)))).
+
+(* notion 5996 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t146 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t46 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t129 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t144 q a c x p s f b not1 not2 i3 beta) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f))).
+
+(* notion 5997 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t147 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_st_eq_landau_n_rt_rp_r_c_8283_t97 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_t106 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t121 q a c x p s f b not1 not2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
+
+(* notion 5998 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t148 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λbeta:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s3 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s1 q a c x p s f b not1 not2) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t145 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t146 q a c x p s f b not1 not2 i3 beta) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t147 q a c x p s f b not1 not2 i3 beta) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 5999 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t149 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_ispl1 l_e_st_eq_landau_n_1 x l_e_st_eq_landau_n_1 (l_e_symis l_e_st_eq_landau_n_nat x l_e_st_eq_landau_n_1 i) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 6000 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t149 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 6001 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) f : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6002 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) s : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 6003 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_2.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6004 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t151 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t149 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
+
+(* notion 6005 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t152 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t149 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f))).
+
+(* notion 6006 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t153 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz280 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
+
+(* notion 6007 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t154 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz280 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
+
+(* notion 6008 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t155 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tris1 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t149 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 6009 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t156 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t155 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 6010 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t157 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t156 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6011 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t158 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_symis l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a l_e_st_eq_landau_n_2)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) l_e_st_eq_landau_n_1).
+
+(* notion 6012 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t159 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t158 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 6013 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t160 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tr3is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t159 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t98 q a c x p s f b not1 not2) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) gamma) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6014 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t161 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t157 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t160 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))).
+
+(* notion 6015 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t163 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t159 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6016 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t164 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t163 q a c x p s f b not1 not2 i3 gamma i) i3 : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 6017 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t165 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t164 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t156 q a c x p s f b not1 not2 i3 gamma i) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))).
+
+(* notion 6018 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t166 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t161 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))).
+
+(* notion 6019 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t167 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8283_s05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t150 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t165 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))).
+
+(* notion 6020 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t168 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t166 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)))).
+
+(* notion 6021 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t169 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_comq q c (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)))).
+
+(* notion 6022 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t170 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t167 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2)))).
+
+(* notion 6023 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t171 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t152 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t154 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t168 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t169 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)))).
+
+(* notion 6024 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t172 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g7 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t171 q a c x p s f b not1 not2 i3 gamma i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t170 q a c x p s f b not1 not2 i3 gamma i) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_2 (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_1out l_e_st_eq_landau_n_2)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_f05 q a c x p s f b not1 not2 i3 gamma i (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_2))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t153 q a c x p s f b not1 not2 i3 gamma i)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t151 q a c x p s f b not1 not2 i3 gamma i) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 6025 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_trivial ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λi:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_8283_t172 q a c x p s f b not1 not2 i3 gamma i : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 6026 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t173 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_ore1 (l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz24 x) n : l_e_st_eq_landau_n_more x l_e_st_eq_landau_n_1).
+
+(* notion 6027 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_mn x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t173 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_nat).
+
+(* notion 6028 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_changef (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 6029 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t174 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_wissel_th6 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) b : l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n)).
+
+(* notion 6030 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t175 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_changef2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6031 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t176 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i3 : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6032 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t177 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris2 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t175 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t176 q a c x p s f b not1 not2 i3 gamma n) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).
+
+(* notion 6033 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 6034 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6035 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t179 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
+
+(* notion 6036 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t180 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_mn_th1b x l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t173 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) x).
+
+(* notion 6037 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t180 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) x).
+
+(* notion 6038 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6039 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t182 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_issmpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t180 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n))).
+
+(* notion 6040 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6041 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t183 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_lessisi1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_satz18a l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n))).
+
+(* notion 6042 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t183 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6043 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t184 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz281 q a l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)))).
+
+(* notion 6044 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t185 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 6045 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t186 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isinoutn l_e_st_eq_landau_n_1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi3 l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 6046 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1a ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t183 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n))).
+
+(* notion 6047 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t187 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_1top l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t183 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n))).
+
+(* notion 6048 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1b ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left1to x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_1to x).
+
+(* notion 6049 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t188 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) x (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n))).
+
+(* notion 6050 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t189 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1a q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t186 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t187 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t188 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n))).
+
+(* notion 6051 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_1c ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 6052 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t190 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_1b q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t189 q a c x p s f b not1 not2 i3 gamma n) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1c q a c x p s f b not1 not2 i3 gamma n)).
+
+(* notion 6053 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t191 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1c q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t190 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 6054 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t192 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t185 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t191 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6055 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t193 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_symis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t175 q a c x p s f b not1 not2 i3 gamma n) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6056 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t194 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t193 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6057 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t195 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t192 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t194 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6058 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t196 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t195 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)))).
+
+(* notion 6059 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t197 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g9 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g11 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t182 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t184 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t196 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)))).
+
+(* notion 6060 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t198 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t197 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
+
+(* notion 6061 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t199 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_assq1 q a (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))))).
+
+(* notion 6062 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t200 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_comq q c (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
+
+(* notion 6063 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6064 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6065 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6066 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_lessisi1 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_satz18a l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n) : Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6067 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t201 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
+
+(* notion 6068 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t202 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_issmpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t180 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n))).
+
+(* notion 6069 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t203 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz281 q a l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)))).
+
+(* notion 6070 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t204 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 6071 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t205 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_1c q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t190 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 6072 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t206 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t204 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t205 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6073 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t207 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_changef1 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_refis (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6074 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t208 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t207 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6075 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t209 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t206 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t208 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6076 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t210 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t209 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)))).
+
+(* notion 6077 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t211 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g13 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_g15 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t202 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t203 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t210 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)))).
+
+(* notion 6078 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_ua ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(l_e_st_eq_landau_n_right1to l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n))).
+
+(* notion 6079 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_ub ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(l_e_st_eq_landau_n_left1to x (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u) : l_e_st_eq_landau_n_1to x).
+
+(* notion 6080 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_uc ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 6081 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t212 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 6082 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t213 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_satz16a (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 6083 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t214 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_ec3e31 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t213 q a c x p s f b not1 not2 i3 gamma n u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t212 q a c x p s f b not1 not2 i3 gamma n u i) : l_con).
+
+(* notion 6084 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t215 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t214 q a c x p s f b not1 not2 i3 gamma n u t : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6085 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t216 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isoutne (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) x (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t178 q a c x p s f b not1 not2 i3 gamma n)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_satz24a (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) l_e_st_eq_landau_n_1).
+
+(* notion 6086 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t217 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) x (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t181 q a c x p s f b not1 not2 i3 gamma n)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u))).
+
+(* notion 6087 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t218 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u))).
+
+(* notion 6088 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t219 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_tr3is l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_ua q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8283_ub q a c x p s f b not1 not2 i3 gamma n u)) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_8283_t218 q a c x p s f b not1 not2 i3 gamma n u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t217 q a c x p s f b not1 not2 i3 gamma n u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t216 q a c x p s f b not1 not2 i3 gamma n u i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1).
+
+(* notion 6089 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t220 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_e_st_eq_landau_n_satz18 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u) : l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1).
+
+(* notion 6090 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t221 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).λi:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_ec3e21 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_more (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz10b (l_e_st_eq_landau_n_pl l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t220 q a c x p s f b not1 not2 i3 gamma n u i) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t219 q a c x p s f b not1 not2 i3 gamma n u i) : l_con).
+
+(* notion 6091 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t222 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t221 q a c x p s f b not1 not2 i3 gamma n u t : l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))).
+
+(* notion 6092 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t223 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(l_e_changef3 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t222 q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t215 q a c x p s f b not1 not2 i3 gamma n u) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u))).
+
+(* notion 6093 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t224 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u)) (s (l_e_st_eq_landau_n_rt_rp_r_c_8283_uc q a c x p s f b not1 not2 i3 gamma n u)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t223 q a c x p s f b not1 not2 i3 gamma n u) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n u)).
+
+(* notion 6094 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t225 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t224 q a c x p s f b not1 not2 i3 gamma n t)) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)).
+
+(* notion 6095 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t226 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) u) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t225 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))).
+
+(* notion 6096 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t227 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_comq q c (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)))).
+
+(* notion 6097 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t228 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t226 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)))).
+
+(* notion 6098 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t229 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t227 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t228 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n)))).
+
+(* notion 6099 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t230 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g14 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t229 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t211 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n))).
+
+(* notion 6100 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t231 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t230 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
+
+(* notion 6101 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t232 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t201 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f))).
+
+(* notion 6102 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t233 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_st_eq_landau_n_rt_rp_r_c_8283_t46 q a c x p (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_rt_rp_r_c_8283_t174 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t177 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f)).
+
+(* notion 6103 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t234 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g8 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t179 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t198 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t199 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t200 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))))).
+
+(* notion 6104 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t235 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λn:l_e_st_eq_landau_n_nis x l_e_st_eq_landau_n_1.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f)) (q (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xm1 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g10 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (l_e_st_eq_landau_n_rt_rp_r_c_8283_g12 q a c x p s f b not1 not2 i3 gamma n)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_g q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_s4 q a c x p s f b not1 not2 i3 gamma n) f)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) f) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t234 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t231 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t232 q a c x p s f b not1 not2 i3 gamma n) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t233 q a c x p s f b not1 not2 i3 gamma n) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 6105 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t236 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).λgamma:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_imp_th1 (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (λt:l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_8283_t172 q a c x p s f b not1 not2 i3 gamma t) (λt:l_not (l_e_st_eq_landau_n_is x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_8283_t235 q a c x p s f b not1 not2 i3 gamma t) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 6106 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t237 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λi3:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t236 q a c x p s f b not1 not2 i3 t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_b0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t148 q a c x p s f b not1 not2 i3 t) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 6107 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t238 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).λnot2:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t237 q a c x p s f b not1 not2 t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_rt_rp_r_c_8283_a0 q a c x p s f b not1 not2) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t128 q a c x p s f b not1 not2 t) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 6108 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t239 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.λnot1:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t97 q a c x p s f b t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_1out (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t238 q a c x p s f b not1 t) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 6109 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t240 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.λs:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λb:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) s.(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).l_e_st_eq_landau_n_rt_rp_r_c_8283_t46 q a c x p s f b t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (s (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x))).l_e_st_eq_landau_n_rt_rp_r_c_8283_t239 q a c x p s f b t) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop1 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) s f).
+
+(* notion 6110 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t241 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).λv:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x).l_e_st_eq_landau_n_rt_rp_r_c_cx.λw:l_e_bijective (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)) u.l_e_st_eq_landau_n_rt_rp_r_c_8283_t240 q a c x p u v w : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x)).
+
+(* notion 6111 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t242 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_xp1 q a c x) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t241 q a c x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c (l_e_st_eq_landau_n_suc x)).
+
+(* notion 6112 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8283_t243 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c t) (l_e_st_eq_landau_n_rt_rp_r_c_8283_t6 q a c) (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c t.l_e_st_eq_landau_n_rt_rp_r_c_8283_t242 q a c t u) x : l_e_st_eq_landau_n_rt_rp_r_c_8283_prop2 q a c x).
+
+(* notion 6113 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz283 ≝ λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λx:l_e_st_eq_landau_n_nat.λs:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_1to x.λb:l_e_bijective (l_e_st_eq_landau_n_1to x) (l_e_st_eq_landau_n_1to x) s.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_8283_t243 q a c x s f b : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x (λt:l_e_st_eq_landau_n_1to x.f (s t))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q x f)).
+
+(* notion 6114 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_shiftl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.(l_e_st_eq_landau_n_rt_rp_r_shiftl x ix y iy ly : l_e_st_eq_landau_n_nat).
+
+(* notion 6115 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_shiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_shiftr x ix y iy ly n : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6116 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_intshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_intshiftr x ix y iy ly n : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n)).
+
+(* notion 6117 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_shiftrls ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_shiftrls x ix y iy ly n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) x).
+
+(* notion 6118 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_lsshiftr x ix y iy ly n : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n)).
+
+(* notion 6119 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iseshiftr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).λm:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly m).(l_e_st_eq_landau_n_rt_rp_r_iseshiftr x ix y iy ly n m i : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly)) n m).
+
+(* notion 6120 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_shiftl1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_rt_rp_r_shiftl1 x ix y iy ly u a : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly)).
+
+(* notion 6121 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_shiftinv1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_rt_rp_r_shiftinv1 x ix y iy ly u a : l_e_st_eq_landau_n_rt_rp_r_is u (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_shiftl1 x ix y iy ly u a))).
+
+(* notion 6122 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_shiftinv2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λu:l_e_st_eq_landau_n_rt_rp_r_real.λa:l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl u) (l_e_st_eq_landau_n_rt_rp_r_lessis y u) (l_e_st_eq_landau_n_rt_rp_r_lessis u x).(l_e_st_eq_landau_n_rt_rp_r_shiftinv2 x ix y iy ly u a : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_shiftl1 x ix y iy ly u a)) u).
+
+(* notion 6123 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_shiftf ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_shiftf x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6124 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_smpri ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6125 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λlv:l_e_st_eq_landau_n_rt_rp_r_lessis y v.λkv:l_e_st_eq_landau_n_rt_rp_r_lessis v u.(l_e_st_eq_landau_n_rt_rp_r_lessisi1 v x (l_e_st_eq_landau_n_rt_rp_r_satz172a v u x kv k) : l_e_st_eq_landau_n_rt_rp_r_lessis v x).
+
+(* notion 6126 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lft ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(λt:l_e_st_eq_landau_n_rt_rp_r_real.λv:l_e_st_eq_landau_n_rt_rp_r_intrl t.λlt:l_e_st_eq_landau_n_rt_rp_r_lessis y t.λkt:l_e_st_eq_landau_n_rt_rp_r_lessis t u.f t v lt (l_e_st_eq_landau_n_rt_rp_r_c_8284_t1 x ix y iy ly f pi q a u iu l k t v lt kt) : Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πv:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πlt:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πkt:l_e_st_eq_landau_n_rt_rp_r_lessis t u.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6127 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_pl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl x y : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6128 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_mn ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_mn x y : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6129 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6130 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λlv:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) v.λkv:l_e_st_eq_landau_n_rt_rp_r_lessis v x.(l_e_st_eq_landau_n_rt_rp_r_satz190c u u l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_lessisi2 u u (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real u)) (l_e_st_eq_landau_n_rt_rp_r_lemma1 l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz169a l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_natpos l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_natrl1))) : l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl u l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)).
+
+(* notion 6131 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λlv:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) v.λkv:l_e_st_eq_landau_n_rt_rp_r_lessis v x.(l_e_st_eq_landau_n_rt_rp_r_isless1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl u l_e_st_eq_landau_n_rt_rp_r_0) u (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_pl02 u l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t2 x ix y iy ly f pi q a u iu l k v iv lv kv) : l_e_st_eq_landau_n_rt_rp_r_less u (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)).
+
+(* notion 6132 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λlv:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) v.λkv:l_e_st_eq_landau_n_rt_rp_r_lessis v x.(l_e_st_eq_landau_n_rt_rp_r_lessisi1 y v (l_e_st_eq_landau_n_rt_rp_r_satz172b y (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) v (l_e_st_eq_landau_n_rt_rp_r_satz172a y u (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) l (l_e_st_eq_landau_n_rt_rp_r_c_8284_t3 x ix y iy ly f pi q a u iu l k v iv lv kv)) lv) : l_e_st_eq_landau_n_rt_rp_r_lessis y v).
+
+(* notion 6133 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_rgt ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(λt:l_e_st_eq_landau_n_rt_rp_r_real.λv:l_e_st_eq_landau_n_rt_rp_r_intrl t.λlt:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) t.λkt:l_e_st_eq_landau_n_rt_rp_r_lessis t x.f t v (l_e_st_eq_landau_n_rt_rp_r_c_8284_t4 x ix y iy ly f pi q a u iu l k t v lt kt) kt : Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πv:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πlt:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) t.Πkt:l_e_st_eq_landau_n_rt_rp_r_lessis t x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6134 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_intpl u iu l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)).
+
+(* notion 6135 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_satzr25 u iu x ix k : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) x).
+
+(* notion 6136 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) y) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) y (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) y)).
+
+(* notion 6137 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly : l_e_st_eq_landau_n_nat).
+
+(* notion 6138 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_suy ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_c_shiftl u iu y iy l : l_e_st_eq_landau_n_nat).
+
+(* notion 6139 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_nat).
+
+(* notion 6140 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_satzr155a (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt2 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 u iu y iy l)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt2 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k)))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t7 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 x) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k))).
+
+(* notion 6141 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_isntirl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t8 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k)).
+
+(* notion 6142 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t9 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k)).
+
+(* notion 6143 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6144 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t9 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q)).
+
+(* notion 6145 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_fr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6146 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_lessisi1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_satz18a (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k))).
+
+(* notion 6147 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_fl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6148 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t12a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_st_eq_landau_n_rt_rp_r_c_satz281 q a (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k)))).
+
+(* notion 6149 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_satz19o (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))).
+
+(* notion 6150 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)))).
+
+(* notion 6151 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k)).
+
+(* notion 6152 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_right1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t13 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t14 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))).
+
+(* notion 6153 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_isnterl (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t15 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)))).
+
+(* notion 6154 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_satzr155b (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)))).
+
+(* notion 6155 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 u iu y iy l)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)))).
+
+(* notion 6156 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t18 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t17 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t16 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)))).
+
+(* notion 6157 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) y (l_e_st_eq_landau_n_rt_rp_r_c_8284_t19 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) y)).
+
+(* notion 6158 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y)) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) y)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y)) y (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)))) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) y) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_plmn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))).
+
+(* notion 6159 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t22 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_mn (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) y) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t20 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t21 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u))).
+
+(* notion 6160 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t23 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u)) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8284_t22 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n)).
+
+(* notion 6161 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t24 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))).
+
+(* notion 6162 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t25 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n))).
+
+(* notion 6163 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t26 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)) x).
+
+(* notion 6164 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t27 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n)).
+
+(* notion 6165 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t28 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n)).
+
+(* notion 6166 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t29 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n) x).
+
+(* notion 6167 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t30 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_8284_t4 x ix y iy ly f pi q a u iu l k (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t27 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t28 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t29 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n)).
+
+(* notion 6168 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t31 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).(pi (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n1 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t24 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t25 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t26 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t27 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t30 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t29 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t23 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) n)).
+
+(* notion 6169 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t32 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_8284_t31 x ix y iy ly f pi q a u iu l k t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k))).
+
+(* notion 6170 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t33 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λv:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) v) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t32 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)).
+
+(* notion 6171 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t34 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k))) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t33 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q))).
+
+(* notion 6172 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t35 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n))).
+
+(* notion 6173 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t36 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)))).
+
+(* notion 6174 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t10 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n) : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k)).
+
+(* notion 6175 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t37 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_tris l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12 x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t35 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t36 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))).
+
+(* notion 6176 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t38 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_isnterl (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t37 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n)))).
+
+(* notion 6177 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t39 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))) y (l_e_st_eq_landau_n_rt_rp_r_c_8284_t38 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n)) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))) y)).
+
+(* notion 6178 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t40 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) n)) y) (l_e_st_eq_landau_n_rt_rp_r_c_8284_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))) y) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8284_t39 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))).
+
+(* notion 6179 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t41 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr u iu y iy l n : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n)).
+
+(* notion 6180 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t42 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr u iu y iy l n : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n)).
+
+(* notion 6181 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t43 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls u iu y iy l n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n) u).
+
+(* notion 6182 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t44 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_8284_t1 x ix y iy ly f pi q a u iu l k (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t41 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t42 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t43 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n) x).
+
+(* notion 6183 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t45 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))).
+
+(* notion 6184 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t46 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n))).
+
+(* notion 6185 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t47 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n)) x).
+
+(* notion 6186 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t48 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(pi (l_e_st_eq_landau_n_rt_rp_r_c_shiftr u iu y iy l n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t41 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t42 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t44 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8284_n2 x ix y iy ly f pi q a u iu l k n)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t45 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t46 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t47 x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t40 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k n)).
+
+(* notion 6187 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t49 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t48 x ix y iy ly f pi q a u iu l k n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) n)).
+
+(* notion 6188 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t50 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_8284_t49 x ix y iy ly f pi q a u iu l k t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k))).
+
+(* notion 6189 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t51 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λv:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) v) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t50 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q)).
+
+(* notion 6190 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t52 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_isf l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.q t (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t51 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q))).
+
+(* notion 6191 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8284_t53 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fr x ix y iy ly f pi q a u iu l k))) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_fl x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t12a x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t34 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t52 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k)) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_c_8284_p1 u) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t5 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t6 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q))).
+
+(* notion 6192 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz284 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λl:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λk:l_e_st_eq_landau_n_rt_rp_r_less u x.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_intpl u iu l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1) (l_e_st_eq_landau_n_rt_rp_r_satzr25 u iu x ix k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q)) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_8284_suy x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_sxu x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_f1 x ix y iy ly f pi q a u iu l k)) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t11 x ix y iy ly f pi q a u iu l k) (l_e_st_eq_landau_n_rt_rp_r_c_8284_t53 x ix y iy ly f pi q a u iu l k) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q) (q (l_e_st_eq_landau_n_rt_rp_r_c_smpri u iu y iy l (l_e_st_eq_landau_n_rt_rp_r_c_lft x ix y iy ly f pi q a u iu l k) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix (l_e_st_eq_landau_n_rt_rp_r_pl u l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_intpl u iu l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1) (l_e_st_eq_landau_n_rt_rp_r_satzr25 u iu x ix k) (l_e_st_eq_landau_n_rt_rp_r_c_rgt x ix y iy ly f pi q a u iu l k) q))).
+
+(* notion 6193 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_pl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl x y : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6194 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_mn ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λy:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_mn x y : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6195 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl x l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6196 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λw:l_e_st_eq_landau_n_rt_rp_r_real.λiw:l_e_st_eq_landau_n_rt_rp_r_intrl w.λlw:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) w.λkw:l_e_st_eq_landau_n_rt_rp_r_lessis w (l_e_st_eq_landau_n_rt_rp_r_pl x v).(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v)) lw (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w.l_e_st_eq_landau_n_rt_rp_r_satz188f (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w (l_e_st_eq_landau_n_rt_rp_r_m0 v) t) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w.l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) w v t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v)).
+
+(* notion 6197 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λw:l_e_st_eq_landau_n_rt_rp_r_real.λiw:l_e_st_eq_landau_n_rt_rp_r_intrl w.λlw:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) w.λkw:l_e_st_eq_landau_n_rt_rp_r_lessis w (l_e_st_eq_landau_n_rt_rp_r_pl x v).(l_e_st_eq_landau_n_rt_rp_r_islessis1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v) y (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) (l_e_st_eq_landau_n_rt_rp_r_mnpl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t1 x ix y iy ly f pi q v iv w iw lw kw) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v)).
+
+(* notion 6198 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λw:l_e_st_eq_landau_n_rt_rp_r_real.λiw:l_e_st_eq_landau_n_rt_rp_r_intrl w.λlw:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) w.λkw:l_e_st_eq_landau_n_rt_rp_r_lessis w (l_e_st_eq_landau_n_rt_rp_r_pl x v).(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_is w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v)) kw (λt:l_e_st_eq_landau_n_rt_rp_r_less w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v).l_e_st_eq_landau_n_rt_rp_r_satz188f w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_m0 v) t) (λt:l_e_st_eq_landau_n_rt_rp_r_is w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v).l_e_st_eq_landau_n_rt_rp_r_ismn1 w (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v)).
+
+(* notion 6199 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λw:l_e_st_eq_landau_n_rt_rp_r_real.λiw:l_e_st_eq_landau_n_rt_rp_r_intrl w.λlw:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) w.λkw:l_e_st_eq_landau_n_rt_rp_r_lessis w (l_e_st_eq_landau_n_rt_rp_r_pl x v).(l_e_st_eq_landau_n_rt_rp_r_islessis2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v) x (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) (l_e_st_eq_landau_n_rt_rp_r_mnpl x v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t3 x ix y iy ly f pi q v iv w iw lw kw) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn w v) x).
+
+(* notion 6200 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_sft ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(λt:l_e_st_eq_landau_n_rt_rp_r_real.λw:l_e_st_eq_landau_n_rt_rp_r_intrl t.λlt:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) t.λkt:l_e_st_eq_landau_n_rt_rp_r_lessis t (l_e_st_eq_landau_n_rt_rp_r_pl x v).f (l_e_st_eq_landau_n_rt_rp_r_mn t v) (l_e_st_eq_landau_n_rt_rp_r_intmn t w v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t2 x ix y iy ly f pi q v iv t w lt kt) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t4 x ix y iy ly f pi q v iv t w lt kt) : Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πw:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πlt:l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) t.Πkt:l_e_st_eq_landau_n_rt_rp_r_lessis t (l_e_st_eq_landau_n_rt_rp_r_pl x v).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6201 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl v y)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl v y) (l_e_st_eq_landau_n_rt_rp_r_compl y v)) (l_e_st_eq_landau_n_rt_rp_r_satz180 v y) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 y))).
+
+(* notion 6202 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl x) (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x) (l_e_st_eq_landau_n_rt_rp_r_asspl1 l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_m0 v)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) v) x l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_mnpl x v)) (l_e_st_eq_landau_n_rt_rp_r_compl l_e_st_eq_landau_n_rt_rp_r_1rl x) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x)).
+
+(* notion 6203 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 y))) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) v) y) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x) y) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t5 x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 y)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x) y (l_e_st_eq_landau_n_rt_rp_r_c_8285_t6 x ix y iy ly f pi q v iv)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x) y)).
+
+(* notion 6204 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less y x) (l_e_st_eq_landau_n_rt_rp_r_is y x) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) ly (λt:l_e_st_eq_landau_n_rt_rp_r_less y x.l_e_st_eq_landau_n_rt_rp_r_satz188f y x v t) (λt:l_e_st_eq_landau_n_rt_rp_r_is y x.l_e_st_eq_landau_n_rt_rp_r_ispl1 y x v t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)).
+
+(* notion 6205 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly : l_e_st_eq_landau_n_nat).
+
+(* notion 6206 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_sv ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_rt_rp_r_c_shiftl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_nat).
+
+(* notion 6207 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_rt_rp_r_isrlent (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_p1 x) y) (l_e_st_eq_landau_n_rt_rp_r_shift_t6 x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t7 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv)).
+
+(* notion 6208 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t9 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv)).
+
+(* notion 6209 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t10 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6210 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr q (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t9 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q)).
+
+(* notion 6211 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_isinoutn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t10 x ix y iy ly f pi q v iv)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t10 x ix y iy ly f pi q v iv) n))).
+
+(* notion 6212 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t10 x ix y iy ly f pi q v iv) n : l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv)).
+
+(* notion 6213 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_isnterl (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t12 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n)))).
+
+(* notion 6214 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n))) y) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_m0 v)) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n))) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) v) y (l_e_st_eq_landau_n_rt_rp_r_c_8285_t13 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_mnpl y v)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n))) y)).
+
+(* notion 6215 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6216 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_stv ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_shiftr (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) n : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6217 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 v))) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl))) (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) v) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_asspl1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 v)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 v)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_compl (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_m0 v))) (l_e_st_eq_landau_n_rt_rp_r_asspl2 (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) (l_e_st_eq_landau_n_rt_rp_r_m0 v) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ismn1 (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) n)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v)) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_rt_rp_r_c_8285_s0 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n))) y) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_8285_t14 x ix y iy ly f pi q v iv n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n)).
+
+(* notion 6218 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n)).
+
+(* notion 6219 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n) x).
+
+(* notion 6220 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8285_n1 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n)).
+
+(* notion 6221 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) n : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n)).
+
+(* notion 6222 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v)).
+
+(* notion 6223 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) n : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n)).
+
+(* notion 6224 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t22 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_intmn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t19 x ix y iy ly f pi q v iv n) v iv : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v)).
+
+(* notion 6225 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t23 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_8285_t2 x ix y iy ly f pi q v iv (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t19 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t21 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t20 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v)).
+
+(* notion 6226 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t24 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(l_e_st_eq_landau_n_rt_rp_r_c_8285_t4 x ix y iy ly f pi q v iv (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t19 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t21 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t20 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v) x).
+
+(* notion 6227 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t25 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).(pi (l_e_st_eq_landau_n_rt_rp_r_c_8285_mn (l_e_st_eq_landau_n_rt_rp_r_c_8285_stv x ix y iy ly f pi q v iv n) v) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t22 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t23 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t24 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_st0 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t16 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t18 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t17 x ix y iy ly f pi q v iv n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t15 x ix y iy ly f pi q v iv n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftf (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv) n) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv n)).
+
+(* notion 6228 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t26 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_shiftf (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).l_e_st_eq_landau_n_rt_rp_r_c_8285_t25 x ix y iy ly f pi q v iv t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv)).
+
+(* notion 6229 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8285_t27 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λw:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) w) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t26 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpri (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv))).
+
+(* notion 6230 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma285 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_st_eq_landau_n_rt_rp_r_c_8285_t8 x ix y iy ly f pi q v iv : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl y v) (l_e_st_eq_landau_n_rt_rp_r_pl x v)).
+
+(* notion 6231 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz285 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λv:l_e_st_eq_landau_n_rt_rp_r_real.λiv:l_e_st_eq_landau_n_rt_rp_r_intrl v.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpri (l_e_st_eq_landau_n_rt_rp_r_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_lemma285 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_8285_sv x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_f1 x ix y iy ly f pi q v iv)) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t27 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_8285_t11 x ix y iy ly f pi q v iv) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpri (l_e_st_eq_landau_n_rt_rp_r_pl x v) (l_e_st_eq_landau_n_rt_rp_r_intpl x ix v iv) (l_e_st_eq_landau_n_rt_rp_r_pl y v) (l_e_st_eq_landau_n_rt_rp_r_intpl y iy v iv) (l_e_st_eq_landau_n_rt_rp_r_c_lemma285 x ix y iy ly f pi q v iv) (l_e_st_eq_landau_n_rt_rp_r_c_sft x ix y iy ly f pi q v iv) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q)).
+
+(* notion 6232 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_us ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(s u iu lu ul : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6233 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(ins u iu lu ul : l_and3 (l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul)) (l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul)) (l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) x)).
+
+(* notion 6234 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_inseqe1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(l_e_st_eq_landau_n_rt_rp_r_shift_t22 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t1 x ix y iy ly s ins f u iu lu ul) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul)).
+
+(* notion 6235 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_inseqe2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(l_e_st_eq_landau_n_rt_rp_r_shift_t23 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t1 x ix y iy ly s ins f u iu lu ul) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul)).
+
+(* notion 6236 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_inseqe3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(l_e_st_eq_landau_n_rt_rp_r_shift_t24 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t1 x ix y iy ly s ins f u iu lu ul) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) x).
+
+(* notion 6237 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_usf ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_real.λiu:l_e_st_eq_landau_n_rt_rp_r_intrl u.λlu:l_e_st_eq_landau_n_rt_rp_r_lessis y u.λul:l_e_st_eq_landau_n_rt_rp_r_lessis u x.(f (l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_inseqe1 x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_inseqe2 x ix y iy ly s ins f u iu lu ul) (l_e_st_eq_landau_n_rt_rp_r_c_inseqe3 x ix y iy ly s ins f u iu lu ul) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6238 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_permseq ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_intrl t.λv:l_e_st_eq_landau_n_rt_rp_r_lessis y t.λw:l_e_st_eq_landau_n_rt_rp_r_lessis t x.l_e_st_eq_landau_n_rt_rp_r_c_usf x ix y iy ly s ins f t u v w : Πt:l_e_st_eq_landau_n_rt_rp_r_real.Πu:l_e_st_eq_landau_n_rt_rp_r_intrl t.Πv:l_e_st_eq_landau_n_rt_rp_r_lessis y t.Πw:l_e_st_eq_landau_n_rt_rp_r_lessis t x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6239 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_ss ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_e_st_eq_landau_n_rt_rp_r_shiftseq x ix y iy ly s ins : Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly)).
+
+(* notion 6240 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_e_st_eq_landau_n_rt_rp_r_c_satz283 q a c (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps) (l_e_st_eq_landau_n_rt_rp_r_bijshiftseq x ix y iy ly s ins pri ps) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t))) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q)).
+
+(* notion 6241 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_ns ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_us x ix y iy ly s ins f (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6242 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_shiftinv1 x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_shift_t34 x ix y iy ly s ins n) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n))).
+
+(* notion 6243 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_inseqe1 x ix y iy ly s ins f (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n)).
+
+(* notion 6244 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_inseqe2 x ix y iy ly s ins f (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n)).
+
+(* notion 6245 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_inseqe3 x ix y iy ly s ins f (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n) x).
+
+(* notion 6246 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_intshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n))).
+
+(* notion 6247 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_lsshiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n) : l_e_st_eq_landau_n_rt_rp_r_lessis y (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n))).
+
+(* notion 6248 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(l_e_st_eq_landau_n_rt_rp_r_c_shiftrls x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n)) x).
+
+(* notion 6249 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).(pi (l_e_st_eq_landau_n_rt_rp_r_c_8286_ns x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t4 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t5 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t6 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftr x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n)) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t7 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t8 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t9 x ix y iy ly f pi q a c s ins pri ps n) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t3 x ix y iy ly f pi q a c s ins pri ps n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f) n) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps n))).
+
+(* notion 6250 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly)) l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_8286_t10 x ix y iy ly f pi q a c s ins pri ps t) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_cx) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t))).
+
+(* notion 6251 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8286_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) u) (l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t)) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t11 x ix y iy ly f pi q a c s ins pri ps) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t)))).
+
+(* notion 6252 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz286 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_real.λix:l_e_st_eq_landau_n_rt_rp_r_intrl x.λy:l_e_st_eq_landau_n_rt_rp_r_real.λiy:l_e_st_eq_landau_n_rt_rp_r_intrl y.λly:l_e_st_eq_landau_n_rt_rp_r_lessis y x.λf:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx.λpi:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_c_cx f.λq:Πt:l_e_st_eq_landau_n_rt_rp_r_c_cx.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_cx.λa:l_e_st_eq_landau_n_rt_rp_r_c_assoc q.λc:l_e_st_eq_landau_n_rt_rp_r_c_commut q.λs:l_e_st_eq_landau_n_rt_rp_r_seq x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real.λins:l_e_st_eq_landau_n_rt_rp_r_inseq x ix y iy ly s.λpri:l_e_st_eq_landau_n_rt_rp_r_proofsirrelevant x ix y iy ly l_e_st_eq_landau_n_rt_rp_r_real s.λps:l_e_st_eq_landau_n_rt_rp_r_perm x ix y iy ly s.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpr q (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_shiftl x ix y iy ly).l_e_st_eq_landau_n_rt_rp_r_c_shiftf x ix y iy ly f (l_e_st_eq_landau_n_rt_rp_r_c_8286_ss x ix y iy ly f pi q a c s ins pri ps t))) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t12 x ix y iy ly f pi q a c s ins pri ps) (l_e_st_eq_landau_n_rt_rp_r_c_8286_t2 x ix y iy ly f pi q a c s ins pri ps) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly (l_e_st_eq_landau_n_rt_rp_r_c_permseq x ix y iy ly s ins f) q) (l_e_st_eq_landau_n_rt_rp_r_c_smpri x ix y iy ly f q)).
+
+(* notion 6253 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_modf ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (f t)) l_e_st_eq_landau_n_rt_rp_r_0 : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6254 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x f)) r : Prop).
+
+(* notion 6255 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_modf x f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) : Prop).
+
+(* notion 6256 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_and (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 x f r) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 x f r) : Prop).
+
+(* notion 6257 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_some (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x f t) : Prop).
+
+(* notion 6258 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 ≝ λx:l_e_st_eq_landau_n_nat.(Πu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 x u : Prop).
+
+(* notion 6259 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t1 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 6260 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t2 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t1 f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
+
+(* notion 6261 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t3 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t2 f) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 l_e_st_eq_landau_n_1 f (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
+
+(* notion 6262 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t4 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) (l_e_st_eq_landau_n_rt_rp_r_c_modf l_e_st_eq_landau_n_1 f) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 l_e_st_eq_landau_n_1 f (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
+
+(* notion 6263 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t5 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_andi (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 l_e_st_eq_landau_n_1 f (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 l_e_st_eq_landau_n_1 f (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t3 f) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t4 f) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 l_e_st_eq_landau_n_1 f (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
+
+(* notion 6264 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t6 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 l_e_st_eq_landau_n_1 f t) (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t5 f) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 l_e_st_eq_landau_n_1 f).
+
+(* notion 6265 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t7 ≝ (λu:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8287_t6 u : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 l_e_st_eq_landau_n_1).
+
+(* notion 6266 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t8 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 6267 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_lf ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8287_t8 x p f) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6268 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t9 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r) pr : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r).
+
+(* notion 6269 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t10 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r) pr : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r).
+
+(* notion 6270 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t11 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
+
+(* notion 6271 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t12 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t11 x p f r pr)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f))).
+
+(* notion 6272 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_m ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6273 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t13 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_islessis1 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t12 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_satz271 (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))).
+
+(* notion 6274 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t14 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r) (l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))) (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t9 x p f r pr) (λt:l_e_st_eq_landau_n_rt_rp_r_less (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r.l_e_st_eq_landau_n_rt_rp_r_satz188f (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) t) (λt:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r.l_e_st_eq_landau_n_rt_rp_r_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) t) : l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))).
+
+(* notion 6275 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t13 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t14 x p f r pr) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))).
+
+(* notion 6276 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_lmf ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8287_t8 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6277 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_pl t u) x (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lmf x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 6278 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_ispl1 (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lmf x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t10 x p f r pr) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lmf x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 6279 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_plis12a r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 6280 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t19 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6281 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_sum (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lmf x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t16 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t17 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t18 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t19 x p f r pr) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))).
+
+(* notion 6282 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_andi (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t15 x p f r pr) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t20 x p f r pr) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr))).
+
+(* notion 6283 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λr:l_e_st_eq_landau_n_rt_rp_r_real.λpr:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) r.(l_somei l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f t) (l_e_st_eq_landau_n_rt_rp_r_pl r (l_e_st_eq_landau_n_rt_rp_r_c_8287_m x p f r pr)) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t21 x p f r pr) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
+
+(* notion 6284 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t23 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_someapp l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) t) (p (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop3 x (l_e_st_eq_landau_n_rt_rp_r_c_8287_lf x p f) t.l_e_st_eq_landau_n_rt_rp_r_c_8287_t22 x p f t u) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop4 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
+
+(* notion 6285 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t25 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8287_t23 x p u : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 6286 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8287_t26 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 t) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8287_t25 x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 6287 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz287 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 t) l_e_st_eq_landau_n_rt_rp_r_c_8287_t7 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_r_c_8287_prop5 t.l_e_st_eq_landau_n_rt_rp_r_c_8287_t26 t u) x f : l_e_st_eq_landau_n_rt_rp_r_some (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_and (l_e_st_eq_landau_n_rt_rp_r_lessis (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_sum x f)) t) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_sum x (l_e_st_eq_landau_n_rt_rp_r_c_modf x f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli t l_e_st_eq_landau_n_rt_rp_r_0)))).
+
+(* notion 6288 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_modf x f)) : Prop).
+
+(* notion 6289 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 ≝ λx:l_e_st_eq_landau_n_nat.(Πu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8288_prop1 x u : Prop).
+
+(* notion 6290 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t1 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 6291 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t2 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t1 f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)))).
+
+(* notion 6292 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t3 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_t2 f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6293 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t4 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) (l_e_st_eq_landau_n_rt_rp_r_c_modf l_e_st_eq_landau_n_1 f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_modf l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6294 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t5 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_modf l_e_st_eq_landau_n_1 f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t3 f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t4 f) : l_e_st_eq_landau_n_rt_rp_r_c_8288_prop1 l_e_st_eq_landau_n_1 f).
+
+(* notion 6295 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t6 ≝ (λu:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8288_t5 u : l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 l_e_st_eq_landau_n_1).
+
+(* notion 6296 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t7 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 6297 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_lf ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8288_t7 x p f) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6298 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t8 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
+
+(* notion 6299 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_m ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_mod (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6300 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t9 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_ismod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t8 x p f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))))).
+
+(* notion 6301 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t10 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz268 (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))).
+
+(* notion 6302 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t11 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t9 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t10 x p f) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))).
+
+(* notion 6303 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t12 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_t11 x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6304 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8288_t7 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6305 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t13 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) x (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 6306 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t14 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (p (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6307 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t14 x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 6308 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_tsis12a (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))))).
+
+(* notion 6309 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ismn2 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))).
+
+(* notion 6310 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts02 (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 6311 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t19 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f))) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_t17 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t18 x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6312 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lmf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t13 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t15 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t16 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t19 x p f) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6313 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_modf (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8288_lf x p f))) (l_e_st_eq_landau_n_rt_rp_r_c_8288_m x p f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t12 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t20 x p f) : l_e_st_eq_landau_n_rt_rp_r_c_8288_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
+
+(* notion 6314 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t21a ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8288_t21 x p u : l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 6315 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8288_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 t) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8288_t21a x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 6316 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz288 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 t) l_e_st_eq_landau_n_rt_rp_r_c_8288_t6 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_r_c_8288_prop2 t.l_e_st_eq_landau_n_rt_rp_r_c_8288_t22 t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_prod x f)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_modf x f))).
+
+(* notion 6317 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x f) l_e_st_eq_landau_n_rt_rp_r_c_0c : Prop).
+
+(* notion 6318 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_some (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) : Prop).
+
+(* notion 6319 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_prop3 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_iff (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x f) : Prop).
+
+(* notion 6320 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 ≝ λx:l_e_st_eq_landau_n_nat.(Πu:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8289_prop3 x u : Prop).
+
+(* notion 6321 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t1 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1))).
+
+(* notion 6322 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t2 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t1 f) p : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6323 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t3 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f.(l_somei (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t2 f p) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f).
+
+(* notion 6324 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t4 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f.λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f u) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_singlet_th1 u : l_e_is (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) u (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)).
+
+(* notion 6325 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t5 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f.λu:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f u) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 f) (f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1)) (f u) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_8289_t1 f) (l_e_isf (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) l_e_st_eq_landau_n_rt_rp_r_c_cx f (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) u (l_e_symis (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) u (l_e_st_eq_landau_n_xout l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t4 f p u i))) i : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f).
+
+(* notion 6326 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t6 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f.(l_someapp (l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) p (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f) (λt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.λu:l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_8289_t5 f p t u) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f).
+
+(* notion 6327 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t7 ≝ λf:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_iffi (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 l_e_st_eq_landau_n_1 f.l_e_st_eq_landau_n_rt_rp_r_c_8289_t3 f t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 l_e_st_eq_landau_n_1 f.l_e_st_eq_landau_n_rt_rp_r_c_8289_t6 f t) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop3 l_e_st_eq_landau_n_1 f).
+
+(* notion 6328 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t8 ≝ (λu:Πt:l_e_st_eq_landau_n_1to l_e_st_eq_landau_n_1.l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8289_t7 u : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 l_e_st_eq_landau_n_1).
+
+(* notion 6329 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_lessisi1 x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_satz18a x l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 6330 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_lf ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) f : Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6331 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t10 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) x f : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))))).
+
+(* notion 6332 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t11 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t10 x p f) q : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6333 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t12 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.(l_e_st_eq_landau_n_rt_rp_r_c_satz221c (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t11 x p f q) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c)).
+
+(* notion 6334 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t13 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_iff_th3 (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (p (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) i : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)).
+
+(* notion 6335 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t14 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_1to x.λj:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_somei (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) n) j : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
+
+(* notion 6336 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t15 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_someapp (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t13 x p f q i) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (λt:l_e_st_eq_landau_n_1to x.λu:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f t) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_8289_t14 x p f q i t u) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
+
+(* notion 6337 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t16 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_somei (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) i : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
+
+(* notion 6338 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t17 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.(l_orapp (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t12 x p f q) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_8289_t15 x p f q t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_8289_t16 x p f q t) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
+
+(* notion 6339 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t18 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c (f n) (l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_c_cx f n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) j) i : l_e_st_eq_landau_n_rt_rp_r_c_is (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6340 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t20 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λj:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).(l_e_st_eq_landau_n_rt_rp_r_c_satz221b (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t18 x p f q n i j) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6341 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_rt_rp_r_c_inn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n : l_e_st_eq_landau_n_nat).
+
+(* notion 6342 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t21 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_lessisi3 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) j : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).
+
+(* notion 6343 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t22 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).λj:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n)) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t21 x p f q n i m j) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).
+
+(* notion 6344 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t23 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_imp_th3 (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) m (λt:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_8289_t22 x p f q n i m t) : l_e_st_eq_landau_n_nis (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 6345 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t24 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_ore1 (l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t23 x p f q n i m) : l_e_st_eq_landau_n_less (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 6346 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t25 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_satz26 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t24 x p f q n i m) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) x).
+
+(* notion 6347 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_outn x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t25 x p f q n i m) : l_e_st_eq_landau_n_1to x).
+
+(* notion 6348 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t26 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_isinoutn x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t25 x p f q n i m) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m))).
+
+(* notion 6349 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t27 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_isoutni (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n) (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) (l_e_st_eq_landau_n_trlessis (l_e_st_eq_landau_n_rt_rp_r_c_inn x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) x (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_1top x (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t26 x p f q n i m) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m))).
+
+(* notion 6350 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t28 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_tris (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_outn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n1 x p f q n i m) (l_e_st_eq_landau_n_1top (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n)) (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) (l_e_st_eq_landau_n_isoutinn (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) n) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t27 x p f q n i m) : l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m))).
+
+(* notion 6351 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t29 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_isf (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) l_e_st_eq_landau_n_rt_rp_r_c_cx f n (l_e_st_eq_landau_n_left1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_8289_t9 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t28 x p f q n i m) : l_e_st_eq_landau_n_rt_rp_r_c_is (f n) (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m))).
+
+(* notion 6352 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t30 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) l_e_st_eq_landau_n_rt_rp_r_c_0c (f n) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t29 x p f q n i m) i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6353 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t31 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_somei (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_8289_n2 x p f q n i m) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t30 x p f q n i m) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)).
+
+(* notion 6354 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t32 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_iff_th4 (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (p (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t31 x p f q n i m) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)).
+
+(* notion 6355 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t34 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.λm:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).(l_e_st_eq_landau_n_rt_rp_r_c_satz221a (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t32 x p f q n i m) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6356 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t35 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th1 (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c) (λt:l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).l_e_st_eq_landau_n_rt_rp_r_c_8289_t20 x p f q n i t) (λt:l_not (l_e_is (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) n (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1))).l_e_st_eq_landau_n_rt_rp_r_c_8289_t34 x p f q n i t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6357 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t36 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.λn:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod x (l_e_st_eq_landau_n_rt_rp_r_c_8289_lf x p f)) (f (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)))) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_8289_t10 x p f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t35 x p f q n i) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
+
+(* notion 6358 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t37 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.λq:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.(l_someapp (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) q (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).λu:l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_8289_t36 x p f q t u) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
+
+(* notion 6359 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t38 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.λf:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_iffi (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.l_e_st_eq_landau_n_rt_rp_r_c_8289_t17 x p f t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f.l_e_st_eq_landau_n_rt_rp_r_c_8289_t37 x p f t) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop3 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) f).
+
+(* notion 6360 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t39 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.(λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_8289_t38 x p u : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1)).
+
+(* notion 6361 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t40 ≝ λx:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 x.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 t) (l_e_st_eq_landau_n_pl x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_suc x) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t39 x p) (l_e_st_eq_landau_n_satz4a x) : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 (l_e_st_eq_landau_n_suc x)).
+
+(* notion 6362 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz289 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 t) l_e_st_eq_landau_n_rt_rp_r_c_8289_t8 (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_r_c_8289_prop4 t.l_e_st_eq_landau_n_rt_rp_r_c_8289_t40 t u) x f : l_iff (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x f) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_some (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c))).
+
+(* notion 6363 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz289a ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x f) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_iff_th3 (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x f) (l_e_st_eq_landau_n_rt_rp_r_c_satz289 x f) i : l_some (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c)).
+
+(* notion 6364 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_8289_t41 ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_somei (l_e_st_eq_landau_n_1to x) (λt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_is (f t) l_e_st_eq_landau_n_rt_rp_r_c_0c) n i : l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x f).
+
+(* notion 6365 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz289b ≝ λx:l_e_st_eq_landau_n_nat.λf:Πt:l_e_st_eq_landau_n_1to x.l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_1to x.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (f n) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_iff_th4 (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop1 x f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_prop2 x f) (l_e_st_eq_landau_n_rt_rp_r_c_satz289 x f) (l_e_st_eq_landau_n_rt_rp_r_c_8289_t41 x f n i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod x f) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6366 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_posintnatrl m p mi : l_e_st_eq_landau_n_rt_rp_r_natrl m).
+
+(* notion 6367 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_ntofrl m (l_e_st_eq_landau_n_rt_rp_r_c_v9_t1 x m mi o p) : l_e_st_eq_landau_n_nat).
+
+(* notion 6368 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).x) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6369 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi1 ox mp : l_e_st_eq_landau_n_nat).
+
+(* notion 6370 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 y n ni1 oy np : l_e_st_eq_landau_n_nat).
+
+(* notion 6371 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_isrlent m (l_e_st_eq_landau_n_rt_rp_r_c_v9_t1 x m mi1 ox mp) n (l_e_st_eq_landau_n_rt_rp_r_c_v9_t1 y n ni1 oy np) j : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np)).
+
+(* notion 6372 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t2 x y m n i j mi1 ni1 ox oy mp np) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np)).
+
+(* notion 6373 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t2 x y m n i j mi1 ni1 ox oy mp np) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y))) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 y n ni1 oy np)).
+
+(* notion 6374 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_fisi (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np)) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).x) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).i) : l_e_is (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).l_e_st_eq_landau_n_rt_rp_r_c_cx) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).x) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y))).
+
+(* notion 6375 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_isf (Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).l_e_st_eq_landau_n_rt_rp_r_c_cx) l_e_st_eq_landau_n_rt_rp_r_c_cx (λu:Πt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) u) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np).x) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t5 x y m n i j mi1 ni1 ox oy mp np) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi1 ox mp) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y)))).
+
+(* notion 6376 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.λnp:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi1 ox mp) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_m0 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t3 x y m n i j mi1 ni1 ox oy mp np) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_n0 x y m n i j mi1 ni1 ox oy mp np).y))) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 y n ni1 oy np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t6 x y m n i j mi1 ni1 ox oy mp np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t4 x y m n i j mi1 ni1 ox oy mp np) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi1 ox mp) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 y n ni1 oy np)).
+
+(* notion 6377 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.λp1:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t7 x x m m (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real m) mi mi o o p p1 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o p) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o p1)).
+
+(* notion 6378 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_some_th5 (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).l_e_st_eq_landau_n_rt_rp_r_c_is ((λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).x) t) l_e_st_eq_landau_n_rt_rp_r_c_0c) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).n) : l_not (l_some (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).l_e_st_eq_landau_n_rt_rp_r_c_is ((λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).x) t) l_e_st_eq_landau_n_rt_rp_r_c_0c))).
+
+(* notion 6379 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o p) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_some (l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).l_e_st_eq_landau_n_rt_rp_r_c_is ((λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).x) t) l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t9 x m mi o p n) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o p) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_satz289a (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p) (λu:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_v9_m1 x m mi o p).x) t) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o p) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6380 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.(l_e_st_eq_landau_n_rt_rp_r_intabs m mi : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_abs m)).
+
+(* notion 6381 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_satz166b m n : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m)).
+
+(* notion 6382 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 x m mi o n) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m))).
+
+(* notion 6383 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m) o (l_e_st_eq_landau_n_rt_rp_r_nnotp m n) : l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6384 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t10 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t14 x m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 x m mi o n)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6385 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 x m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t15 x m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6386 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_pwm ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi1) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi1 ox nm) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 x m mi1 ox nm) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6387 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_pwn ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 y (l_e_st_eq_landau_n_rt_rp_r_abs n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 y n ni1) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 y n ni1 oy nn) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 y n ni1 oy nn) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6388 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t7 x y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_abs n) i (l_e_st_eq_landau_n_rt_rp_r_isabs m n j) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi1) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 y n ni1) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi1 ox nm) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 y n ni1 oy nn) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 x m mi1 ox nm) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 y n ni1 oy nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pwm x y m n i j mi1 ni1 ox oy nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pwn x y m n i j mi1 ni1 ox oy nm nn)).
+
+(* notion 6389 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_isov2 (l_e_st_eq_landau_n_rt_rp_r_c_v9_pwm x y m n i j mi1 ni1 ox oy nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pwn x y m n i j mi1 ni1 ox oy nm nn) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_v9_t16 x y m n i j mi1 ni1 ox oy nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t15 x m mi1 ox nm) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t15 y n ni1 oy nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi1 ox nm) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 y n ni1 oy nn)).
+
+(* notion 6390 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.λn1:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t17 x x m m (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real m) mi mi o o n n1 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi o n1)).
+
+(* notion 6391 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_r_ite (l_e_st_eq_landau_n_rt_rp_r_neg m) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_neg m.l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi o t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).l_e_st_eq_landau_n_rt_rp_r_c_1c) (λt:l_e_st_eq_landau_n_rt_rp_r_neg m.λu:l_e_st_eq_landau_n_rt_rp_r_neg m.l_e_st_eq_landau_n_rt_rp_r_c_v9_t18 x m mi o t u) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_1c) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6392 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_r_itet (l_e_st_eq_landau_n_rt_rp_r_neg m) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_neg m.l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi o t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).l_e_st_eq_landau_n_rt_rp_r_c_1c) (λt:l_e_st_eq_landau_n_rt_rp_r_neg m.λu:l_e_st_eq_landau_n_rt_rp_r_neg m.l_e_st_eq_landau_n_rt_rp_r_c_v9_t18 x m mi o t u) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_1c) n : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi o n)).
+
+(* notion 6393 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λnn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).(l_r_itef (l_e_st_eq_landau_n_rt_rp_r_neg m) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_neg m.l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi o t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).l_e_st_eq_landau_n_rt_rp_r_c_1c) (λt:l_e_st_eq_landau_n_rt_rp_r_neg m.λu:l_e_st_eq_landau_n_rt_rp_r_neg m.l_e_st_eq_landau_n_rt_rp_r_c_v9_t18 x m mi o t u) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_1c) nn : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 6394 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_neg t) m n nm j : l_e_st_eq_landau_n_rt_rp_r_neg n).
+
+(* notion 6395 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t22 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t19 x m mi1 ox nm : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi1 ox nm)).
+
+(* notion 6396 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t23 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 y n ni1 oy (l_e_st_eq_landau_n_rt_rp_r_c_v9_t21 x y m n i j mi1 ni1 ox oy nm)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t19 y n ni1 oy (l_e_st_eq_landau_n_rt_rp_r_c_v9_t21 x y m n i j mi1 ni1 ox oy nm)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 y n ni1 oy (l_e_st_eq_landau_n_rt_rp_r_c_v9_t21 x y m n i j mi1 ni1 ox oy nm)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy)).
+
+(* notion 6397 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t24 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi1 ox nm) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 y n ni1 oy (l_e_st_eq_landau_n_rt_rp_r_c_v9_t21 x y m n i j mi1 ni1 ox oy nm)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t22 x y m n i j mi1 ni1 ox oy nm) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t17 x y m n i j mi1 ni1 ox oy nm (l_e_st_eq_landau_n_rt_rp_r_c_v9_t21 x y m n i j mi1 ni1 ox oy nm)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t23 x y m n i j mi1 ni1 ox oy nm) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy)).
+
+(* notion 6398 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t25 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_not (l_e_st_eq_landau_n_rt_rp_r_neg t)) m n nn j : l_not (l_e_st_eq_landau_n_rt_rp_r_neg n)).
+
+(* notion 6399 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t26 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).(l_e_st_eq_landau_n_rt_rp_r_c_v9_t20 x m mi1 ox nn : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi1 ox) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 6400 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t27 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).(l_e_st_eq_landau_n_rt_rp_r_c_v9_t20 y n ni1 oy (l_e_st_eq_landau_n_rt_rp_r_c_v9_t25 x y m n i j mi1 ni1 ox oy nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 6401 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t28 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnn:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_v9_t26 x y m n i j mi1 ni1 ox oy nn) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t27 x y m n i j mi1 ni1 ox oy nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy)).
+
+(* notion 6402 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t29 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_neg m) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy)) (λt:l_e_st_eq_landau_n_rt_rp_r_neg m.l_e_st_eq_landau_n_rt_rp_r_c_v9_t24 x y m n i j mi1 ni1 ox oy t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_neg m).l_e_st_eq_landau_n_rt_rp_r_c_v9_t28 x y m n i j mi1 ni1 ox oy t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy)).
+
+(* notion 6403 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_pw ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_r_ite (l_e_st_eq_landau_n_rt_rp_r_pos m) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_pos m.l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi o) (λt:l_e_st_eq_landau_n_rt_rp_r_pos m.λu:l_e_st_eq_landau_n_rt_rp_r_pos m.l_e_st_eq_landau_n_rt_rp_r_c_v9_t8 x m mi o t u) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi o)) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6404 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t30 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_r_itet (l_e_st_eq_landau_n_rt_rp_r_pos m) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_pos m.l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi o) (λt:l_e_st_eq_landau_n_rt_rp_r_pos m.λu:l_e_st_eq_landau_n_rt_rp_r_pos m.l_e_st_eq_landau_n_rt_rp_r_c_v9_t8 x m mi o t u) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi o)) p : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o p)).
+
+(* notion 6405 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t31 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_r_itef (l_e_st_eq_landau_n_rt_rp_r_pos m) l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_pos m.l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi o) (λt:l_e_st_eq_landau_n_rt_rp_r_pos m.λu:l_e_st_eq_landau_n_rt_rp_r_pos m.l_e_st_eq_landau_n_rt_rp_r_c_v9_t8 x m mi o t u) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).λu:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi o)) n : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi o)).
+
+(* notion 6406 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t32 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λi:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_v9_t31 x m mi o (l_e_st_eq_landau_n_rt_rp_r_0notp m i)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t20 x m mi o (l_e_st_eq_landau_n_rt_rp_r_0notn m i)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 6407 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t33 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t31 x m mi o (l_e_st_eq_landau_n_rt_rp_r_nnotp m n)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t19 x m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi o n)).
+
+(* notion 6408 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_posexp ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t30 x m mi o p : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_ntofrl m (l_e_st_eq_landau_n_rt_rp_r_posintnatrl m p mi)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_ntofrl m (l_e_st_eq_landau_n_rt_rp_r_posintnatrl m p mi)).x))).
+
+(* notion 6409 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_notis_th2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi o p) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t10 x m mi o p n) (l_e_st_eq_landau_n_rt_rp_r_c_posexp x m mi o p) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6410 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_0exp ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λi:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t32 x m mi o i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 6411 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t14 x m mi o n : l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6412 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m))).
+
+(* notion 6413 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t34 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t30 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 x m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 x m mi o n))).
+
+(* notion 6414 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t35 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_isov2 (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 x m mi o n)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_v9_t34 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t14 x m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t15 x m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t11 x m mi) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t13 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t12 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t14 x m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi o n)).
+
+(* notion 6415 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_negexp ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_intabs m mi) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_intabs m mi) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_satz166b m n) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 x m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw2 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t33 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t35 x m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_intabs m mi) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_intabs m mi) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x m mi o n) (l_e_st_eq_landau_n_rt_rp_r_satz166b m n) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 x m mi o n)))).
+
+(* notion 6416 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t36 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_pos t) m n mp j : l_e_st_eq_landau_n_rt_rp_r_pos n).
+
+(* notion 6417 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t37 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_c_v9_t30 x m mi1 ox mp : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi1 ox mp)).
+
+(* notion 6418 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t38 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw y n ni1 oy) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 y n ni1 oy (l_e_st_eq_landau_n_rt_rp_r_c_v9_t36 x y m n i j mi1 ni1 ox oy mp)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t30 y n ni1 oy (l_e_st_eq_landau_n_rt_rp_r_c_v9_t36 x y m n i j mi1 ni1 ox oy mp)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 y n ni1 oy (l_e_st_eq_landau_n_rt_rp_r_c_v9_t36 x y m n i j mi1 ni1 ox oy mp)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y n ni1 oy)).
+
+(* notion 6419 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t39 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λmp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 x m mi1 ox mp) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw1 y n ni1 oy (l_e_st_eq_landau_n_rt_rp_r_c_v9_t36 x y m n i j mi1 ni1 ox oy mp)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y n ni1 oy) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t37 x y m n i j mi1 ni1 ox oy mp) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t7 x y m n i j mi1 ni1 ox oy mp (l_e_st_eq_landau_n_rt_rp_r_c_v9_t36 x y m n i j mi1 ni1 ox oy mp)) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t38 x y m n i j mi1 ni1 ox oy mp) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_pw y n ni1 oy)).
+
+(* notion 6420 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t40 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnp:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_not (l_e_st_eq_landau_n_rt_rp_r_pos t)) m n np j : l_not (l_e_st_eq_landau_n_rt_rp_r_pos n)).
+
+(* notion 6421 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t41 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnp:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_e_st_eq_landau_n_rt_rp_r_c_v9_t31 x m mi1 ox np : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi1 ox)).
+
+(* notion 6422 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t42 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnp:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw y n ni1 oy) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t31 y n ni1 oy (l_e_st_eq_landau_n_rt_rp_r_c_v9_t40 x y m n i j mi1 ni1 ox oy np)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy) (l_e_st_eq_landau_n_rt_rp_r_c_pw y n ni1 oy)).
+
+(* notion 6423 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v9_t43 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).λnp:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_v9_pw3 y n ni1 oy) (l_e_st_eq_landau_n_rt_rp_r_c_pw y n ni1 oy) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t41 x y m n i j mi1 ni1 ox oy np) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t29 x y m n i j mi1 ni1 ox oy) (l_e_st_eq_landau_n_rt_rp_r_c_v9_t42 x y m n i j mi1 ni1 ox oy np) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_pw y n ni1 oy)).
+
+(* notion 6424 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ispw12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λj:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi1:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni1:l_e_st_eq_landau_n_rt_rp_r_intrl n.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_pw y n ni1 oy)) (λt:l_e_st_eq_landau_n_rt_rp_r_pos m.l_e_st_eq_landau_n_rt_rp_r_c_v9_t39 x y m n i j mi1 ni1 ox oy t) (λt:l_not (l_e_st_eq_landau_n_rt_rp_r_pos m).l_e_st_eq_landau_n_rt_rp_r_c_v9_t43 x y m n i j mi1 ni1 ox oy t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi1 ox) (l_e_st_eq_landau_n_rt_rp_r_c_pw y n ni1 oy)).
+
+(* notion 6425 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ispw1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λox:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λoy:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_e_st_eq_landau_n_rt_rp_r_c_ispw12 x y m m i (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real m) mi mi ox oy : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi ox) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi oy)).
+
+(* notion 6426 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ispw2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is m n.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λom:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λon:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_rt_rp_r_c_ispw12 x x m n (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) i mi ni om on : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi om) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni on)).
+
+(* notion 6427 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9290_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x m mi o p n : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6428 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9290_t2 ≝ λi:l_e_st_eq_landau_n_rt_rp_r_c_is l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_0c) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isre l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_iscere l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_reis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 6429 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_1not0 ≝ (l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_is l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pnot0 l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_pos1) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_9290_t2 t) : l_e_st_eq_landau_n_rt_rp_r_c_nis l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6430 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9290_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.(l_e_notis_th2 l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_1not0 (l_e_st_eq_landau_n_rt_rp_r_c_0exp x m mi o i) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6431 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_intabs m mi) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x m mi o nm) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6432 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9290_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_intabs m mi) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x m mi o nm) (l_e_st_eq_landau_n_rt_rp_r_satz166b m nm) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 x m mi o nm) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6433 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9290_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm) (l_e_st_eq_landau_n_rt_rp_r_c_9290_t5 x m mi o n nm)) (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm) (l_e_st_eq_landau_n_rt_rp_r_c_9290_t5 x m mi o n nm)) (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm) (l_e_st_eq_landau_n_rt_rp_r_c_negexp x m mi o nm)) (l_e_st_eq_landau_n_rt_rp_r_c_satz229e l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm) (l_e_st_eq_landau_n_rt_rp_r_c_9290_t5 x m mi o n nm)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm)) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 6434 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9290_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_notis_th2 l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm)) l_e_st_eq_landau_n_rt_rp_r_c_1not0 (l_e_st_eq_landau_n_rt_rp_r_c_9290_t6 x m mi o n nm) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6435 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9290_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm)) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_9290_t7 x m mi o n nm) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_satz221a (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_9290_p0 x m mi o n nm) t) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6436 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz290 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_rapp m (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_0c) (λt:l_e_st_eq_landau_n_rt_rp_r_pos m.l_e_st_eq_landau_n_rt_rp_r_c_9290_t1 x m mi o n t) (λt:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_9290_t4 x m mi o n t) (λt:l_e_st_eq_landau_n_rt_rp_r_neg m.l_e_st_eq_landau_n_rt_rp_r_c_9290_t8 x m mi o n t) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6437 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma291 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_1rl) l_e_st_eq_landau_n_rt_rp_r_pos1 : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_1rl)).
+
+(* notion 6438 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9291_1a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_ntofrl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_posintnatrl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_pos1 l_e_st_eq_landau_n_rt_rp_r_intrl1) : l_e_st_eq_landau_n_nat).
+
+(* notion 6439 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9291_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_posexp x l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 x) l_e_st_eq_landau_n_rt_rp_r_pos1 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 x)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x).x))).
+
+(* notion 6440 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9291_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_ntofrl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_natrl1) (l_e_st_eq_landau_n_rt_rp_r_ntofrl l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_posintnatrl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_pos1 l_e_st_eq_landau_n_rt_rp_r_intrl1)) (l_e_st_eq_landau_n_rt_rp_r_isntrl1 l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_isrlent l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_natrl1 l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_posintnatrl l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_pos1 l_e_st_eq_landau_n_rt_rp_r_intrl1) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_1rl)) : l_e_st_eq_landau_n_is l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x)).
+
+(* notion 6441 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9291_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_lessisi2 l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x) (l_e_st_eq_landau_n_rt_rp_r_c_9291_t2 x) : l_e_st_eq_landau_n_lessis l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x)).
+
+(* notion 6442 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9291_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x).x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_9291_t2 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_9291_t3 x) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x).x))) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x).x))).
+
+(* notion 6443 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9291_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_st_eq_landau_n_rt_rp_r_c_satz277 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_9291_t3 x) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x).x)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_9291_t3 x) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x).x))) x).
+
+(* notion 6444 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9291_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris1 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x).x)) x (l_e_st_eq_landau_n_rt_rp_r_c_prod l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x) l_e_st_eq_landau_n_1 (l_e_st_eq_landau_n_rt_rp_r_c_9291_t3 x) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x).x))) (l_e_st_eq_landau_n_rt_rp_r_c_9291_t4 x) (l_e_st_eq_landau_n_rt_rp_r_c_9291_t5 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x).x)) x).
+
+(* notion 6445 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz291 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 x)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9291_1a x).x)) x (l_e_st_eq_landau_n_rt_rp_r_c_9291_t1 x) (l_e_st_eq_landau_n_rt_rp_r_c_9291_t6 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 x)) x).
+
+(* notion 6446 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) a : l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6447 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) a : l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6448 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c).(l_e_st_eq_landau_n_rt_rp_r_c_satz221d x y (l_e_st_eq_landau_n_rt_rp_r_c_9292_t1 x y m mi o a) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t2 x y m mi o a) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6449 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma292a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_or_th7 (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) o (λt:l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c).l_e_st_eq_landau_n_rt_rp_r_c_9292_t1 x y m mi o t) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6450 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma292b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_or_th7 (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) o (λt:l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c).l_e_st_eq_landau_n_rt_rp_r_c_9292_t2 x y m mi o t) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6451 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma292c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_or_th7 (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c) o (λt:l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c).l_e_st_eq_landau_n_rt_rp_r_c_9292_t3 x y m mi o t) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6452 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_nr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_rlofnt n : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6453 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_natintrl (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_natrli n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n)).
+
+(* notion 6454 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n)) (l_e_st_eq_landau_n_rt_rp_r_natpos (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_natrli n)) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n))).
+
+(* notion 6455 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t4 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t5 x n) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6456 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_pw x l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 x)) x (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9292_t5 x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 x)) (l_e_st_eq_landau_n_rt_rp_r_c_satz291 x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x l_e_st_eq_landau_n_1) x).
+
+(* notion 6457 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_posintnatrl (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_natpos (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_natrli n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t4 x n)) : l_e_st_eq_landau_n_nat).
+
+(* notion 6458 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat n (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_natrli n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n) (l_e_st_eq_landau_n_rt_rp_r_isntrl1 n) (l_e_st_eq_landau_n_rt_rp_r_isrlent (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_natrli n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_posintnatrl (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_natpos (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_natrli n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t4 x n)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n))) : l_e_st_eq_landau_n_is n (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n)).
+
+(* notion 6459 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_lessisi2 n (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t7 x n) : l_e_st_eq_landau_n_lessis n (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n)).
+
+(* notion 6460 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_posexp x (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t4 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t5 x n) (l_e_st_eq_landau_n_rt_rp_r_natpos (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x n) (l_e_st_eq_landau_n_rt_rp_r_natrli n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n).x))).
+
+(* notion 6461 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_issmpr (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n).x) n (l_e_st_eq_landau_n_rt_rp_r_c_9292_t7 x n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod n (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n) n (l_e_st_eq_landau_n_rt_rp_r_c_9292_t8 x n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n).x))) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n).x))).
+
+(* notion 6462 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_prod n (λt:l_e_st_eq_landau_n_1to n.x)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9292_n0 x n).x)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t9 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t10 x n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_prod n (λt:l_e_st_eq_landau_n_1to n.x))).
+
+(* notion 6463 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_pl n l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
+
+(* notion 6464 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_lessisi1 n (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n) (l_e_st_eq_landau_n_satz18a n l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_lessis n (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)).
+
+(* notion 6465 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_satz278 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) n (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n).x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n).x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod n (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n) n (l_e_st_eq_landau_n_rt_rp_r_c_9292_t12 x n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n).x))) x)).
+
+(* notion 6466 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_prod n (λt:l_e_st_eq_landau_n_1to n.x)) x (l_e_st_eq_landau_n_rt_rp_r_c_9292_t11 x n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod n (λt:l_e_st_eq_landau_n_1to n.x)) x)).
+
+(* notion 6467 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n).x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod n (λt:l_e_st_eq_landau_n_1to n.x)) x) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t13 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t14 x n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n).x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x)).
+
+(* notion 6468 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λn:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n).x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t11 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t15 x n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x)).
+
+(* notion 6469 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) : Prop).
+
+(* notion 6470 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x l_e_st_eq_landau_n_1) x (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y l_e_st_eq_landau_n_1) y (l_e_st_eq_landau_n_rt_rp_r_c_9292_t6 x) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t6 y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)).
+
+(* notion 6471 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t6 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t17 x y) : l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y l_e_st_eq_landau_n_1).
+
+(* notion 6472 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y n.(l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) p : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y))).
+
+(* notion 6473 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y n.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) x) (l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts x (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) x)) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n))).
+
+(* notion 6474 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y n.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) x) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) y) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) y)) (l_e_st_eq_landau_n_rt_rp_r_c_assts2 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) x y) (l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) y (l_e_st_eq_landau_n_rt_rp_r_c_9292_t20 x y n p)) (l_e_st_eq_landau_n_rt_rp_r_c_assts1 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) y) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) y))).
+
+(* notion 6475 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t22 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y n.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts x y)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) y)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t16 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t19 x y n p) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t21 x y n p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) y))).
+
+(* notion 6476 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t23 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y n.(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) y) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t16 x n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t16 y n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) y))).
+
+(* notion 6477 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t24 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y n.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x n) x) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y n) y)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t22 x y n p) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t23 x y n p) : l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n)).
+
+(* notion 6478 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t25 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y n.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y t) (l_e_st_eq_landau_n_rt_rp_r_c_9292_n1 x n) (l_e_st_eq_landau_n_suc n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t24 x y n p) (l_e_st_eq_landau_n_satz4a n) : l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y (l_e_st_eq_landau_n_suc n)).
+
+(* notion 6479 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t26 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y t) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t18 x y) (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y t.l_e_st_eq_landau_n_rt_rp_r_c_9292_t25 x y t u) n : l_e_st_eq_landau_n_rt_rp_r_c_9292_prop1 x y n).
+
+(* notion 6480 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_prop2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o))) : Prop).
+
+(* notion 6481 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t28 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_posintnatrl m p mi : l_e_st_eq_landau_n_rt_rp_r_natrl m).
+
+(* notion 6482 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_ntofrl m (l_e_st_eq_landau_n_rt_rp_r_c_9292_t28 x y m mi o p) : l_e_st_eq_landau_n_nat).
+
+(* notion 6483 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t29 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_isrlnt1 m (l_e_st_eq_landau_n_rt_rp_r_c_9292_t28 x y m mi o p) : l_e_st_eq_landau_n_rt_rp_r_is m (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p))).
+
+(* notion 6484 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t30 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_isrlnt2 m (l_e_st_eq_landau_n_rt_rp_r_c_9292_t28 x y m mi o p) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) m).
+
+(* notion 6485 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t31 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t29 x y m mi o p) mi (l_e_st_eq_landau_n_rt_rp_r_c_9292_t4 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t5 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p))).
+
+(* notion 6486 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t32 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) m (l_e_st_eq_landau_n_rt_rp_r_c_9292_t30 x y m mi o p) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t4 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) mi (l_e_st_eq_landau_n_rt_rp_r_c_9292_t5 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw2 y (l_e_st_eq_landau_n_rt_rp_r_c_9292_nr x (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) m (l_e_st_eq_landau_n_rt_rp_r_c_9292_t30 x y m mi o p) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t4 y (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) mi (l_e_st_eq_landau_n_rt_rp_r_c_9292_t5 y (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o)))).
+
+(* notion 6487 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t33 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λp:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 x (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_p0 y (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o))) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t31 x y m mi o p) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t26 x y (l_e_st_eq_landau_n_rt_rp_r_c_9292_m0 x y m mi o p)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t32 x y m mi o p) : l_e_st_eq_landau_n_rt_rp_r_c_9292_prop2 x y m mi o).
+
+(* notion 6488 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t34 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λi:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_0exp x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o) i) (l_e_st_eq_landau_n_rt_rp_r_c_0exp y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o) i)) (l_e_st_eq_landau_n_rt_rp_r_c_satz222 l_e_st_eq_landau_n_rt_rp_r_c_1c) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o))) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 6489 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t35 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λi:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o))) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_0exp (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o) i) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t34 x y m mi o i) : l_e_st_eq_landau_n_rt_rp_r_c_9292_prop2 x y m mi o).
+
+(* notion 6490 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_intabs m mi : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_abs m)).
+
+(* notion 6491 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t37 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_ori2 (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m)) (l_e_st_eq_landau_n_rt_rp_r_satz166b m n) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m))).
+
+(* notion 6492 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t38 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t37 x y m mi o n) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m))).
+
+(* notion 6493 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t39 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t37 x y m mi o n) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m))).
+
+(* notion 6494 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t40 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t37 x y m mi o n) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m))).
+
+(* notion 6495 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o) n : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m))).
+
+(* notion 6496 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o) n : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m))).
+
+(* notion 6497 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t43 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o) n : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_abs m))).
+
+(* notion 6498 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t44 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs m)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t43 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t40 x y m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t43 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t40 x y m mi o n))).
+
+(* notion 6499 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t45 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_9292_t33 x y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t37 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_satz166b m n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t40 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t38 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t39 x y m mi o n)))).
+
+(* notion 6500 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t46 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t38 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t39 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs m)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t38 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw2 y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs m)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t39 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t38 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t39 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n)))).
+
+(* notion 6501 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t47 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t43 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t40 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t38 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t39 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t44 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t45 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t46 x y m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t43 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n)))).
+
+(* notion 6502 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t48 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_satz166b m n) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o) n) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6503 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t49 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_satz166b m n) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o) n) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6504 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t50 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t43 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_satz166b m n) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o) n) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t43 x y m mi o n)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6505 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t51 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_satz221d (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t48 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t49 x y m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6506 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t52 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_negexp (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o) n : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t43 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t50 x y m mi o n))).
+
+(* notion 6507 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t53 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_isov12 l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t43 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_satz222a l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t47 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t50 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t51 x y m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t43 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t50 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t51 x y m mi o n))).
+
+(* notion 6508 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t54 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t43 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t50 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t51 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t52 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t53 x y m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t51 x y m mi o n))).
+
+(* notion 6509 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t55 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t48 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t49 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_negexp x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o) n) (l_e_st_eq_landau_n_rt_rp_r_c_negexp y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o) n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t48 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t49 x y m mi o n)))).
+
+(* notion 6510 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t56 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_c_satz247 l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t48 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t49 x y m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t48 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t49 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t51 x y m mi o n))).
+
+(* notion 6511 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t57 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t48 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t49 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t51 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t55 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t56 x y m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t51 x y m mi o n))).
+
+(* notion 6512 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9292_t58 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).λn:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t41 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y (l_e_st_eq_landau_n_rt_rp_r_abs m) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t36 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t42 x y m mi o n))) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t51 x y m mi o n)) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t54 x y m mi o n) (l_e_st_eq_landau_n_rt_rp_r_c_9292_t57 x y m mi o n) : l_e_st_eq_landau_n_rt_rp_r_c_9292_prop2 x y m mi o).
+
+(* notion 6513 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz292 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis y l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m).(l_e_st_eq_landau_n_rt_rp_r_rapp m (l_e_st_eq_landau_n_rt_rp_r_c_9292_prop2 x y m mi o) (λt:l_e_st_eq_landau_n_rt_rp_r_pos m.l_e_st_eq_landau_n_rt_rp_r_c_9292_t33 x y m mi o t) (λt:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_9292_t35 x y m mi o t) (λt:l_e_st_eq_landau_n_rt_rp_r_neg m.l_e_st_eq_landau_n_rt_rp_r_c_9292_t58 x y m mi o t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts x y) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a x y m mi o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw y m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b x y m mi o)))).
+
+(* notion 6514 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma293 ≝ λm:l_e_st_eq_landau_n_rt_rp_r_real.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m) l_e_st_eq_landau_n_rt_rp_r_c_1not0 : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6515 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 ≝ λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.(l_ori1 (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_andi (l_e_st_eq_landau_n_rt_rp_r_c_nis l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c) l_e_st_eq_landau_n_rt_rp_r_c_1not0 l_e_st_eq_landau_n_rt_rp_r_c_1not0) : l_or (l_and (l_e_st_eq_landau_n_rt_rp_r_c_nis l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_nis l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_0c)) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6516 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9293_1m ≝ λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.(l_e_st_eq_landau_n_rt_rp_r_c_pw l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma293 m) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6517 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9293_t2 ≝ λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.(l_e_st_eq_landau_n_rt_rp_r_c_satz222 (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi)).
+
+(* notion 6518 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9293_t3 ≝ λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.(l_e_st_eq_landau_n_rt_rp_r_c_ispw1 l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) m (l_e_st_eq_landau_n_rt_rp_r_c_satz222a l_e_st_eq_landau_n_rt_rp_r_c_1c) mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma293 m) (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi)))).
+
+(* notion 6519 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9293_t4 ≝ λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.(l_e_st_eq_landau_n_rt_rp_r_c_satz292 l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi))) (l_e_st_eq_landau_n_rt_rp_r_c_pw l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi))))).
+
+(* notion 6520 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9293_t5 ≝ λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_pw l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi))) (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_pw l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi))) (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_1c) mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma293 m)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx l_e_st_eq_landau_n_rt_rp_r_c_1c) mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma293 m)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi))) (l_e_st_eq_landau_n_rt_rp_r_c_pw l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi)))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi))).
+
+(* notion 6521 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9293_t6 ≝ λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292c l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292a l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi))) (l_e_st_eq_landau_n_rt_rp_r_c_pw l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma292b l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_9293_t1 m mi)))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi)) (l_e_st_eq_landau_n_rt_rp_r_c_9293_t2 m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9293_t3 m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9293_t4 m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9293_t5 m mi) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi))).
+
+(* notion 6522 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9293_t7 ≝ λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c)) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_disttm2 (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_satz213b (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi)) (l_e_st_eq_landau_n_rt_rp_r_c_9293_t6 m mi))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6523 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9293_t8 ≝ λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.(l_ore2 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_satz221c (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_9293_t7 m mi)) (l_e_st_eq_landau_n_rt_rp_r_c_satz290 l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma293 m) l_e_st_eq_landau_n_rt_rp_r_c_1not0) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6524 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz293 ≝ λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.(l_e_st_eq_landau_n_rt_rp_r_c_satz213a (l_e_st_eq_landau_n_rt_rp_r_c_9293_1m m mi) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_9293_t8 m mi) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw l_e_st_eq_landau_n_rt_rp_r_c_1c m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma293 m)) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 6525 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_ande1 (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n) a : l_e_st_eq_landau_n_rt_rp_r_pos m).
+
+(* notion 6526 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n) a : l_e_st_eq_landau_n_rt_rp_r_pos n).
+
+(* notion 6527 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_rt_rp_r_pospl m n (l_e_st_eq_landau_n_rt_rp_r_c_9294_t1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t2 x m n mi ni o a) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl m n)).
+
+(* notion 6528 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma294a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_or_th8 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)) (l_e_st_eq_landau_n_rt_rp_r_pos m) o (λt:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).l_e_st_eq_landau_n_rt_rp_r_c_9294_t1 x m n mi ni o t) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6529 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma294b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_or_th8 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)) (l_e_st_eq_landau_n_rt_rp_r_pos n) o (λt:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).l_e_st_eq_landau_n_rt_rp_r_c_9294_t2 x m n mi ni o t) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n)).
+
+(* notion 6530 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma294c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_or_th8 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl m n)) o (λt:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).l_e_st_eq_landau_n_rt_rp_r_c_9294_t3 x m n mi ni o t) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl m n))).
+
+(* notion 6531 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) : Prop).
+
+(* notion 6532 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_rt_rp_r_ntofrl m (l_e_st_eq_landau_n_rt_rp_r_posintnatrl m (l_e_st_eq_landau_n_rt_rp_r_c_9294_t1 x m n mi ni o a) mi) : l_e_st_eq_landau_n_nat).
+
+(* notion 6533 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_rt_rp_r_ntofrl n (l_e_st_eq_landau_n_rt_rp_r_posintnatrl n (l_e_st_eq_landau_n_rt_rp_r_c_9294_t2 x m n mi ni o a) ni) : l_e_st_eq_landau_n_nat).
+
+(* notion 6534 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a).x)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a).x)) (l_e_st_eq_landau_n_rt_rp_r_c_posexp x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t1 x m n mi ni o a)) (l_e_st_eq_landau_n_rt_rp_r_c_posexp x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t2 x m n mi ni o a)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a).x)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a).x)))).
+
+(* notion 6535 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_posintnatrl (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t3 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni)) : l_e_st_eq_landau_n_nat).
+
+(* notion 6536 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_rt_rp_r_c_posexp x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t3 x m n mi ni o a) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a).x))).
+
+(* notion 6537 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a))) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a))) (l_e_st_eq_landau_n_rt_rp_r_ispl12 m (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a)) n (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 m (l_e_st_eq_landau_n_rt_rp_r_posintnatrl m (l_e_st_eq_landau_n_rt_rp_r_c_9294_t1 x m n mi ni o a) mi)) (l_e_st_eq_landau_n_rt_rp_r_isrlnt1 n (l_e_st_eq_landau_n_rt_rp_r_posintnatrl n (l_e_st_eq_landau_n_rt_rp_r_c_9294_t2 x m n mi ni o a) ni))) (l_e_st_eq_landau_n_rt_rp_r_satzr155b (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)))).
+
+(* notion 6538 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_tris2 l_e_st_eq_landau_n_nat (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_ntofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a))) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)))) (l_e_st_eq_landau_n_rt_rp_r_isntrl1 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a))) (l_e_st_eq_landau_n_rt_rp_r_isrlent (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_posintnatrl (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t3 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni)) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a))) (l_e_st_eq_landau_n_rt_rp_r_natrli (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t6 x m n mi ni o a)) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a)).
+
+(* notion 6539 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_lessisi2 (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t7 x m n mi ni o a) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a)).
+
+(* notion 6540 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_rt_rp_r_c_issmpr (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a).x) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t7 x m n mi ni o a) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t8 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a).x))) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a).x))).
+
+(* notion 6541 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)).x)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_p1 x m n mi ni o a).x)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t5 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t9 x m n mi ni o a) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)).x))).
+
+(* notion 6542 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_lessisi1 (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (l_e_st_eq_landau_n_satz18a (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) : l_e_st_eq_landau_n_lessis (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a))).
+
+(* notion 6543 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_rt_rp_r_c_satz281 (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.λu:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_ts t u) l_e_st_eq_landau_n_rt_rp_r_c_assocts (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)).x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)).x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_left l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t11 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)).x))) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a) (l_e_st_eq_landau_n_right l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)).x))))).
+
+(* notion 6544 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a)).x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a).x)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a).x))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t10 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t12 x m n mi ni o a) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a).x)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a).x)))).
+
+(* notion 6545 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_m1 x m n mi ni o a).x)) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9294_n1 x m n mi ni o a).x))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t4 x m n mi ni o a) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t13 x m n mi ni o a) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6546 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_ore1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)) o na : l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6547 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_or_th15 (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n) na : l_or (l_not (l_e_st_eq_landau_n_rt_rp_r_pos m)) (l_not (l_e_st_eq_landau_n_rt_rp_r_pos n))).
+
+(* notion 6548 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_am ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_abs m : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6549 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_an ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_abs n : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6550 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_ap ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_pl m n) : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6551 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_intabs m mi : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o)).
+
+(* notion 6552 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_intabs n ni : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)).
+
+(* notion 6553 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_intabs (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o)).
+
+(* notion 6554 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_andi (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_satz166e m (l_e_st_eq_landau_n_rt_rp_r_nnot0 m nm)) (l_e_st_eq_landau_n_rt_rp_r_satz166e n (l_e_st_eq_landau_n_rt_rp_r_nnot0 n nn)) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))).
+
+(* notion 6555 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t20 x m n mi ni o na nm nn) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)))).
+
+(* notion 6556 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) nm : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o))).
+
+(* notion 6557 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o) nn : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))).
+
+(* notion 6558 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t24 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t21 x m n mi ni o na nm nn) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o))).
+
+(* notion 6559 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t25 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t21 x m n mi ni o na nm nn) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))).
+
+(* notion 6560 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t26 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t24 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t25 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t24 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t25 x m n mi ni o na nm nn)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t24 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t25 x m n mi ni o na nm nn)))).
+
+(* notion 6561 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t27 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t21 x m n mi ni o na nm nn) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)))).
+
+(* notion 6562 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t28 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_9294_t14 x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t21 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t20 x m n mi ni o na nm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t24 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t25 x m n mi ni o na nm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t27 x m n mi ni o na nm nn))).
+
+(* notion 6563 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t29 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_m0 m) (l_e_st_eq_landau_n_rt_rp_r_m0 n)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl m n)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_ispl12 (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_m0 m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_m0 n) (l_e_st_eq_landau_n_rt_rp_r_absn m nm) (l_e_st_eq_landau_n_rt_rp_r_absn n nn)) (l_e_st_eq_landau_n_rt_rp_r_satz180a m n) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_pl m n)) (l_e_st_eq_landau_n_rt_rp_r_absn (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_negpl m n nm nn))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o)).
+
+(* notion 6564 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_negpl m n nm nn) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o))).
+
+(* notion 6565 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t31 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t29 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t27 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 x m n mi ni o na nm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t27 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 x m n mi ni o na nm nn))).
+
+(* notion 6566 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t32 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t24 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t25 x m n mi ni o na nm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t27 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t26 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t28 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t31 x m n mi ni o na nm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 x m n mi ni o na nm nn))).
+
+(* notion 6567 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t33 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_satz166b m nm) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) nm) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6568 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t34 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_satz166b n nn) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o) nn) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6569 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t35 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_satz166b (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_negpl m n nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_negpl m n nm nn)) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 x m n mi ni o na nm nn)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6570 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t36 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t33 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t34 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_negexp x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) nm) (l_e_st_eq_landau_n_rt_rp_r_c_negexp x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o) nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t33 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t34 x m n mi ni o na nm nn)))).
+
+(* notion 6571 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t37 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_satz221d (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t33 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t34 x m n mi ni o na nm nn) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6572 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t38 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_satz247 l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t33 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t34 x m n mi ni o na nm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t33 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t34 x m n mi ni o na nm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t37 x m n mi ni o na nm nn))).
+
+(* notion 6573 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t39 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_isov12 (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_satz222 l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t32 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t37 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t35 x m n mi ni o na nm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t37 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t35 x m n mi ni o na nm nn))).
+
+(* notion 6574 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t40 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t35 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_negexp x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_negpl m n nm nn)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t35 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o))).
+
+(* notion 6575 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t41 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t33 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t34 x m n mi ni o na nm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_am x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t17 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t22 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t23 x m n mi ni o na nm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t37 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t30 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t35 x m n mi ni o na nm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t36 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t38 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t39 x m n mi ni o na nm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t40 x m n mi ni o na nm nn) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6576 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o) nn : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))).
+
+(* notion 6577 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn) (l_e_st_eq_landau_n_rt_rp_r_satz166b n nn) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o) nn) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6578 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t44 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_ists2 (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_negexp x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o) nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn)))).
+
+(* notion 6579 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t45 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_satz244a (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn))).
+
+(* notion 6580 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t46 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_isov1 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_satz222 (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn))).
+
+(* notion 6581 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t47 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t44 x m n mi ni o na pm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t45 x m n mi ni o na pm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t46 x m n mi ni o na pm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn))).
+
+(* notion 6582 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t48 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_satz182d m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) casea : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))).
+
+(* notion 6583 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t49 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_satz166e n (l_e_st_eq_landau_n_rt_rp_r_nnot0 n nn) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)).
+
+(* notion 6584 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t50 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_andi (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t49 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t48 x m n mi ni o na pm nn casea) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)))).
+
+(* notion 6585 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t51 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t50 x m n mi ni o na pm nn casea) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))))).
+
+(* notion 6586 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_intmn m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))).
+
+(* notion 6587 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t51 x m n mi ni o na pm nn casea) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))).
+
+(* notion 6588 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t51 x m n mi ni o na pm nn casea) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)))).
+
+(* notion 6589 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t55 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t51 x m n mi ni o na pm nn casea) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))))).
+
+(* notion 6590 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t56 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)))).
+
+(* notion 6591 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t57 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_9294_t14 x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t51 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t50 x m n mi ni o na pm nn casea) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t56 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t55 x m n mi ni o na pm nn casea))).
+
+(* notion 6592 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t58 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_satz187a m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))) m).
+
+(* notion 6593 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t59 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))) m (l_e_st_eq_landau_n_rt_rp_r_c_9294_t58 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t56 x m n mi ni o na pm nn casea) mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t55 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t56 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t55 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o))).
+
+(* notion 6594 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t60 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t56 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t55 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t57 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t59 x m n mi ni o na pm nn casea) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o))).
+
+(* notion 6595 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t61 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn))).
+
+(* notion 6596 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t62 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_isp1 l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_nis t l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t61 x m n mi ni o na pm nn casea) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6597 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t63 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_isov12 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t60 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t61 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t62 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t62 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn))).
+
+(* notion 6598 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t64 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t62 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t47 x m n mi ni o na pm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t63 x m n mi ni o na pm nn casea) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t62 x m n mi ni o na pm nn casea))).
+
+(* notion 6599 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t65 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_satz229h (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t62 x m n mi ni o na pm nn casea) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea)))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t62 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea))).
+
+(* notion 6600 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t66 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_m0 n)) (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_ismn2 (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_m0 n) m (l_e_st_eq_landau_n_rt_rp_r_absn n nn)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 n)) n m (l_e_st_eq_landau_n_rt_rp_r_satz177 n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pl m n)).
+
+(* notion 6601 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t67 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t66 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o))).
+
+(* notion 6602 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t68 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasea:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t53 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t62 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t52 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t54 x m n mi ni o na pm nn casea)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t64 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t65 x m n mi ni o na pm nn casea) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t67 x m n mi ni o na pm nn casea) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6603 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t69 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcaseb:l_e_st_eq_landau_n_rt_rp_r_is m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) caseb mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn))).
+
+(* notion 6604 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t70 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcaseb:l_e_st_eq_landau_n_rt_rp_r_is m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_satz251a (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t69 x m n mi ni o na pm nn caseb) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn)) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 6605 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t71 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcaseb:l_e_st_eq_landau_n_rt_rp_r_is m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_m0 n)) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ispl2 n (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 n)) m (l_e_st_eq_landau_n_rt_rp_r_satz177a n)) (l_e_st_eq_landau_n_rt_rp_r_ismn2 (l_e_st_eq_landau_n_rt_rp_r_m0 n) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_m0 n) (l_e_st_eq_landau_n_rt_rp_r_absn n nn))) (l_e_st_eq_landau_n_rt_rp_r_satz182e m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) caseb) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl m n) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 6606 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t72 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcaseb:l_e_st_eq_landau_n_rt_rp_r_is m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_0exp x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t71 x m n mi ni o na pm nn caseb)) : l_e_st_eq_landau_n_rt_rp_r_c_is l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o))).
+
+(* notion 6607 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t73 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcaseb:l_e_st_eq_landau_n_rt_rp_r_is m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t47 x m n mi ni o na pm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t70 x m n mi ni o na pm nn caseb) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t72 x m n mi ni o na pm nn caseb) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6608 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t74 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_satz182d (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m (l_e_st_eq_landau_n_rt_rp_r_lemma2 m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) casec) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m)).
+
+(* notion 6609 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t75 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_andi (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m)) pm (l_e_st_eq_landau_n_rt_rp_r_c_9294_t74 x m n mi ni o na pm nn casec) : l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m))).
+
+(* notion 6610 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t76 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t75 x m n mi ni o na pm nn casec) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m)))).
+
+(* notion 6611 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_intmn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) m mi : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m)).
+
+(* notion 6612 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t76 x m n mi ni o na pm nn casec) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6613 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t76 x m n mi ni o na pm nn casec) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m))).
+
+(* notion 6614 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t80 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t76 x m n mi ni o na pm nn casec) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl m (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m)))).
+
+(* notion 6615 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t81 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_intpl m mi (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_pl m (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m))).
+
+(* notion 6616 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t81a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_9294_t14 x m (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t76 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t75 x m n mi ni o na pm nn casec) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t81 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t80 x m n mi ni o na pm nn casec))).
+
+(* notion 6617 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t82 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_satz187a (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl m (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)).
+
+(* notion 6618 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t83 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_pl m (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t82 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t81 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t80 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t81 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t80 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn))).
+
+(* notion 6619 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t84 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t81 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t80 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t81a x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t83 x m n mi ni o na pm nn casec) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn))).
+
+(* notion 6620 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t85 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_satz290 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t15 x m n mi ni o na) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6621 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t86 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_satz290 x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t15 x m n mi ni o na) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6622 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t87 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_satz221d (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t85 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t86 x m n mi ni o na pm nn casec) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec))) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6623 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t88 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_satz222 (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec))).
+
+(* notion 6624 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t89 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x m (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o))).
+
+(* notion 6625 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t90 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t88 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t89 x m n mi ni o na pm nn casec) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o))).
+
+(* notion 6626 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t91 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_isov12 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t90 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t84 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t87 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t87 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn))).
+
+(* notion 6627 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t92 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t87 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t18 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t42 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t43 x m n mi ni o na pm nn)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t47 x m n mi ni o na pm nn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t91 x m n mi ni o na pm nn casec) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t87 x m n mi ni o na pm nn casec))).
+
+(* notion 6628 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t93 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_satz246a l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t86 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t85 x m n mi ni o na pm nn casec) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t87 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t86 x m n mi ni o na pm nn casec))).
+
+(* notion 6629 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t94 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_satz182f m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) casec : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))).
+
+(* notion 6630 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t94a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_m0 n)) (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_ismn2 (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_m0 n) m (l_e_st_eq_landau_n_rt_rp_r_absn n nn)) (l_e_st_eq_landau_n_rt_rp_r_ispl2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_m0 n)) n m (l_e_st_eq_landau_n_rt_rp_r_satz177 n)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pl m n)).
+
+(* notion 6631 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t95 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_satz181a (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_abs (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_absn (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t94 x m n mi ni o na pm nn casec))) (l_e_st_eq_landau_n_rt_rp_r_isabs (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t94a x m n mi ni o na pm nn casec)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o)).
+
+(* notion 6632 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t96 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_isp l_e_st_eq_landau_n_rt_rp_r_real (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_neg t) (l_e_st_eq_landau_n_rt_rp_r_mn m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t94 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t94a x m n mi ni o na pm nn casec) : l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_pl m n)).
+
+(* notion 6633 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t97 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw3 x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t96 x m n mi ni o na pm nn casec) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o))).
+
+(* notion 6634 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t98 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_lemmapw1 x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t97 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_satz166b (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t96 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_lemmapw2 x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t96 x m n mi ni o na pm nn casec)) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t97 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6635 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t99 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t95 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t97 x m n mi ni o na pm nn casec) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t97 x m n mi ni o na pm nn casec))).
+
+(* notion 6636 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t100 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_st_eq_landau_n_rt_rp_r_c_isov2 (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t97 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_9294_t99 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t86 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t98 x m n mi ni o na pm nn casec) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t86 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t97 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t98 x m n mi ni o na pm nn casec))).
+
+(* notion 6637 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t101 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t97 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t98 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_negexp x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t96 x m n mi ni o na pm nn casec)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t97 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t98 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o))).
+
+(* notion 6638 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t102 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.λcasec:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) l_e_st_eq_landau_n_rt_rp_r_c_1c) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t78 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec))) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t87 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o) m) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t77 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t79 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t86 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_c_9294_ap x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t19 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t97 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t98 x m n mi ni o na pm nn casec)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t92 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t93 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t100 x m n mi ni o na pm nn casec) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t101 x m n mi ni o na pm nn casec) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6639 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t103 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.λnn:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_or3app (l_e_st_eq_landau_n_rt_rp_r_is m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_satz167a m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o)) (λt:l_e_st_eq_landau_n_rt_rp_r_is m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).l_e_st_eq_landau_n_rt_rp_r_c_9294_t73 x m n mi ni o na pm nn t) (λt:l_e_st_eq_landau_n_rt_rp_r_more m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).l_e_st_eq_landau_n_rt_rp_r_c_9294_t68 x m n mi ni o na pm nn t) (λt:l_e_st_eq_landau_n_rt_rp_r_less m (l_e_st_eq_landau_n_rt_rp_r_c_9294_an x m n mi ni o).l_e_st_eq_landau_n_rt_rp_r_c_9294_t102 x m n mi ni o na pm nn t) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6640 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t104 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos n) (l_e_st_eq_landau_n_rt_rp_r_pos m)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t15 x m n mi ni o na) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos n) (l_e_st_eq_landau_n_rt_rp_r_pos m))).
+
+(* notion 6641 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t104a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_and_th5 (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n) na : l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos n) (l_e_st_eq_landau_n_rt_rp_r_pos m))).
+
+(* notion 6642 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x n m ni mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t104 x m n mi ni o na) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n)).
+
+(* notion 6643 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x n m ni mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t104 x m n mi ni o na) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6644 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t107 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x n m ni mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t104 x m n mi ni o na) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl n m))).
+
+(* notion 6645 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t108 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x m (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x n (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na)))).
+
+(* notion 6646 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t109 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_c_comts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na)))).
+
+(* notion 6647 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t110 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λqn:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_c_9294_t103 x n m ni mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t104 x m n mi ni o na) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t104a x m n mi ni o na) qn nm : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl n m) (l_e_st_eq_landau_n_rt_rp_r_intpl n ni m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t107 x m n mi ni o na))).
+
+(* notion 6648 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t111 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_pl n m) (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_compl n m) (l_e_st_eq_landau_n_rt_rp_r_intpl n ni m mi) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t107 x m n mi ni o na) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl n m) (l_e_st_eq_landau_n_rt_rp_r_intpl n ni m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t107 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o))).
+
+(* notion 6649 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t112 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.λqn:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl n m) (l_e_st_eq_landau_n_rt_rp_r_intpl n ni m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t107 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t108 x m n mi ni o na) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t109 x m n mi ni o na) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t110 x m n mi ni o na nm qn) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t111 x m n mi ni o na) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6650 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t113 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λi:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_c_ists1 (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_0exp x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o)))).
+
+(* notion 6651 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t114 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λi:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_c_satz222b (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))).
+
+(* notion 6652 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t115 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λi:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl m n) n (l_e_st_eq_landau_n_rt_rp_r_pl01 m n i) : l_e_st_eq_landau_n_rt_rp_r_is n (l_e_st_eq_landau_n_rt_rp_r_pl m n)).
+
+(* notion 6653 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t116 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λi:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x n (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t115 x m n mi ni o na i) ni (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o))).
+
+(* notion 6654 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t117 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λi:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t113 x m n mi ni o na i) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t114 x m n mi ni o na i) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t116 x m n mi ni o na i) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6655 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t118 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λi:l_e_st_eq_landau_n_rt_rp_r_is n l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_c_9294_t117 x n m ni mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t104 x m n mi ni o na) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t104a x m n mi ni o na) i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl n m) (l_e_st_eq_landau_n_rt_rp_r_intpl n ni m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t107 x m n mi ni o na))).
+
+(* notion 6656 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t119 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λi:l_e_st_eq_landau_n_rt_rp_r_is n l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9294_t105 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9294_t106 x m n mi ni o na))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl n m) (l_e_st_eq_landau_n_rt_rp_r_intpl n ni m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t107 x m n mi ni o na)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t108 x m n mi ni o na) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t109 x m n mi ni o na) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t118 x m n mi ni o na i) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t111 x m n mi ni o na) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6657 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t120 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_ore2 (l_not (l_e_st_eq_landau_n_rt_rp_r_pos m)) (l_not (l_e_st_eq_landau_n_rt_rp_r_pos n)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t16 x m n mi ni o na) (l_weli (l_e_st_eq_landau_n_rt_rp_r_pos m) pm) : l_not (l_e_st_eq_landau_n_rt_rp_r_pos n)).
+
+(* notion 6658 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t121 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λpm:l_e_st_eq_landau_n_rt_rp_r_pos m.(l_e_st_eq_landau_n_rt_rp_r_rapp n (l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o) (l_imp_th2 (l_e_st_eq_landau_n_rt_rp_r_pos n) (l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9294_t120 x m n mi ni o na pm)) (λt:l_e_st_eq_landau_n_rt_rp_r_is n l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_9294_t119 x m n mi ni o na t) (λt:l_e_st_eq_landau_n_rt_rp_r_neg n.l_e_st_eq_landau_n_rt_rp_r_c_9294_t103 x m n mi ni o na pm t) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6659 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t122 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λnm:l_e_st_eq_landau_n_rt_rp_r_neg m.(l_e_st_eq_landau_n_rt_rp_r_rapp n (l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o) (λt:l_e_st_eq_landau_n_rt_rp_r_pos n.l_e_st_eq_landau_n_rt_rp_r_c_9294_t112 x m n mi ni o na nm t) (λt:l_e_st_eq_landau_n_rt_rp_r_is n l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_9294_t119 x m n mi ni o na t) (λt:l_e_st_eq_landau_n_rt_rp_r_neg n.l_e_st_eq_landau_n_rt_rp_r_c_9294_t41 x m n mi ni o na nm t) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6660 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9294_t123 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λna:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_rapp m (l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o) (λt:l_e_st_eq_landau_n_rt_rp_r_pos m.l_e_st_eq_landau_n_rt_rp_r_c_9294_t121 x m n mi ni o na t) (λt:l_e_st_eq_landau_n_rt_rp_r_is m l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_9294_t117 x m n mi ni o na t) (λt:l_e_st_eq_landau_n_rt_rp_r_neg m.l_e_st_eq_landau_n_rt_rp_r_c_9294_t122 x m n mi ni o na t) : l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o).
+
+(* notion 6661 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz294 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_imp_th1 (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)) (l_e_st_eq_landau_n_rt_rp_r_c_9294_prop1 x m n mi ni o) (λt:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).l_e_st_eq_landau_n_rt_rp_r_c_9294_t14 x m n mi ni o t) (λt:l_not (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).l_e_st_eq_landau_n_rt_rp_r_c_9294_t123 x m n mi ni o t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl m n) (l_e_st_eq_landau_n_rt_rp_r_intpl m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x m n mi ni o))).
+
+(* notion 6662 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma295a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m) o : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6663 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma295b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n) o : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n)).
+
+(* notion 6664 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma295c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn m n)) o : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn m n))).
+
+(* notion 6665 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9295_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn m n)) (l_e_st_eq_landau_n_rt_rp_r_pos n)) o : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn m n)) (l_e_st_eq_landau_n_rt_rp_r_pos n))).
+
+(* notion 6666 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_intmn m mi n ni : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_mn m n)).
+
+(* notion 6667 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9295_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x (l_e_st_eq_landau_n_rt_rp_r_mn m n) n (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) ni (l_e_st_eq_landau_n_rt_rp_r_c_9295_t1 x m n mi ni o) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn m n))).
+
+(* notion 6668 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9295_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x (l_e_st_eq_landau_n_rt_rp_r_mn m n) n (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) ni (l_e_st_eq_landau_n_rt_rp_r_c_9295_t1 x m n mi ni o) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n)).
+
+(* notion 6669 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9295_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x (l_e_st_eq_landau_n_rt_rp_r_mn m n) n (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) ni (l_e_st_eq_landau_n_rt_rp_r_c_9295_t1 x m n mi ni o) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn m n) n))).
+
+(* notion 6670 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9295_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma295c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t3 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma295b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9295_t4 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma295c x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t3 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x n (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma295b x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t4 x m n mi ni o)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma295c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma295b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t3 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9295_t4 x m n mi ni o)))).
+
+(* notion 6671 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9295_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz294 x (l_e_st_eq_landau_n_rt_rp_r_mn m n) n (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) ni (l_e_st_eq_landau_n_rt_rp_r_c_9295_t1 x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t3 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9295_t4 x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn m n) n) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) n ni) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t5 x m n mi ni o))).
+
+(* notion 6672 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9295_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_plmn m n : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn m n) n) m).
+
+(* notion 6673 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9295_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn m n) n) m (l_e_st_eq_landau_n_rt_rp_r_c_9295_t8 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) n ni) mi (l_e_st_eq_landau_n_rt_rp_r_c_9295_t5 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma295a x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn m n) n) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) n ni) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t5 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma295a x m n mi ni o))).
+
+(* notion 6674 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9295_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma295c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma295b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t3 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_9295_t4 x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_mn m n) n) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) n ni) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t5 x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma295a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t6 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t7 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t9 x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma295c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma295b x m n mi ni o))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma295a x m n mi ni o))).
+
+(* notion 6675 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9295_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz290 x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma295b x m n mi ni o) o : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma295b x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6676 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz295 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz229k (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma295a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma295b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t2 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_lemma295c x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t11 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9295_t10 x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma295a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma295b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_satz290 x n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma295b x m n mi ni o) o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn m n) (l_e_st_eq_landau_n_rt_rp_r_intmn m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma295c x m n mi ni o))).
+
+(* notion 6677 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma296 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m) n : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6678 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_intrli0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_intrl l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 6679 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma295a x l_e_st_eq_landau_n_rt_rp_r_0 m (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) mi n : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6680 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma295b x l_e_st_eq_landau_n_rt_rp_r_0 m (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) mi n : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6681 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma295c x l_e_st_eq_landau_n_rt_rp_r_0 m (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) mi n : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_mn l_e_st_eq_landau_n_rt_rp_r_0 m))).
+
+(* notion 6682 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz290 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x m mi n) n : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x m mi n)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6683 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz290 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9296_t3 x m mi n) n : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9296_t3 x m mi n)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6684 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t2 x m mi n)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_0exp x l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t2 x m mi n) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_c_is l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t2 x m mi n))).
+
+(* notion 6685 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x m (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t3 x m mi n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9296_t3 x m mi n))).
+
+(* notion 6686 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_isov12 l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t2 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9296_t3 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t7 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t8 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t5 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t6 x m mi n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t5 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t2 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9296_t3 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t6 x m mi n))).
+
+(* notion 6687 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz295 x l_e_st_eq_landau_n_rt_rp_r_0 m (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) mi n : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t2 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9296_t3 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t6 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn l_e_st_eq_landau_n_rt_rp_r_0 m) (l_e_st_eq_landau_n_rt_rp_r_intmn l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t4 x m mi n))).
+
+(* notion 6688 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_m0 m) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn l_e_st_eq_landau_n_rt_rp_r_0 m) (l_e_st_eq_landau_n_rt_rp_r_m0 m)).
+
+(* notion 6689 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x (l_e_st_eq_landau_n_rt_rp_r_m0 m) (l_e_st_eq_landau_n_rt_rp_r_intm0 m mi) n : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 m))).
+
+(* notion 6690 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_mn l_e_st_eq_landau_n_rt_rp_r_0 m) (l_e_st_eq_landau_n_rt_rp_r_m0 m) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t11 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_intmn l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) m mi) (l_e_st_eq_landau_n_rt_rp_r_intm0 m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t4 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t12 x m mi n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn l_e_st_eq_landau_n_rt_rp_r_0 m) (l_e_st_eq_landau_n_rt_rp_r_intmn l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t4 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_m0 m) (l_e_st_eq_landau_n_rt_rp_r_intm0 m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t12 x m mi n))).
+
+(* notion 6691 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9296_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t5 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pw x l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t2 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9296_t3 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t6 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_mn l_e_st_eq_landau_n_rt_rp_r_0 m) (l_e_st_eq_landau_n_rt_rp_r_intmn l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_9296_t1 x m mi n) m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t4 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_m0 m) (l_e_st_eq_landau_n_rt_rp_r_intm0 m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t12 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t9 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t10 x m mi n) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t13 x m mi n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t5 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_m0 m) (l_e_st_eq_landau_n_rt_rp_r_intm0 m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9296_t12 x m mi n))).
+
+(* notion 6692 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz296 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λn:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_9296_t14 x m mi n : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x m mi n)) (l_e_st_eq_landau_n_rt_rp_r_c_satz290 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x m mi n) n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_m0 m) (l_e_st_eq_landau_n_rt_rp_r_intm0 m mi) (l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x (l_e_st_eq_landau_n_rt_rp_r_m0 m) (l_e_st_eq_landau_n_rt_rp_r_intm0 m mi) n))).
+
+(* notion 6693 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz290 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) p : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6694 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_ande2 (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n) a : l_e_st_eq_landau_n_rt_rp_r_pos n).
+
+(* notion 6695 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t3 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λa:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).(l_e_st_eq_landau_n_rt_rp_r_postspp m n (l_ande1 (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n) a) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t2 x m n mi ni o a) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts m n)).
+
+(* notion 6696 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma297a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_or_th9 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)) (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n) o (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_9297_t1 x m n mi ni o t) (λt:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).l_e_st_eq_landau_n_rt_rp_r_c_9297_t2 x m n mi ni o t) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos n)).
+
+(* notion 6697 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma297b ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_or_th8 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts m n)) o (λt:l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n).l_e_st_eq_landau_n_rt_rp_r_c_9297_t3 x m n mi ni o t) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts m n))).
+
+(* notion 6698 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t4 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_ore2 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m) o (l_weli (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) i) : l_e_st_eq_landau_n_rt_rp_r_pos m).
+
+(* notion 6699 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_m1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_ntofrl m (l_e_st_eq_landau_n_rt_rp_r_posintnatrl m (l_e_st_eq_landau_n_rt_rp_r_c_9297_t4 x m mi o i) mi) : l_e_st_eq_landau_n_nat).
+
+(* notion 6700 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t5 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_posexp x m mi o (l_e_st_eq_landau_n_rt_rp_r_c_9297_t4 x m mi o i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9297_m1 x m mi o i) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9297_m1 x m mi o i).x))).
+
+(* notion 6701 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t6 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz289b (l_e_st_eq_landau_n_rt_rp_r_c_9297_m1 x m mi o i) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9297_m1 x m mi o i).x) (l_e_st_eq_landau_n_xout (l_e_st_eq_landau_n_rt_rp_r_c_9297_m1 x m mi o i)) i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9297_m1 x m mi o i) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9297_m1 x m mi o i).x)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6702 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t7 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) (l_e_st_eq_landau_n_rt_rp_r_c_prod (l_e_st_eq_landau_n_rt_rp_r_c_9297_m1 x m mi o i) (λt:l_e_st_eq_landau_n_1to (l_e_st_eq_landau_n_rt_rp_r_c_9297_m1 x m mi o i).x)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_9297_t5 x m mi o i) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t6 x m mi o i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6703 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_pw0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m).λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_9297_t7 x m mi o i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi o) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6704 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.(l_e_st_eq_landau_n_rt_rp_r_intts m mi n ni : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_ts m n)).
+
+(* notion 6705 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_prop1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o)) : Prop).
+
+(* notion 6706 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t9 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_pw0 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6707 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t10 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_pw0 (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t9 x m n mi ni o i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6708 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t11 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_pw0 x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o) i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6709 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t12 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λi:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_0c (l_e_st_eq_landau_n_rt_rp_r_c_9297_t10 x m n mi ni o i) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t11 x m n mi ni o i) : l_e_st_eq_landau_n_rt_rp_r_c_9297_prop1 x m n mi ni o).
+
+(* notion 6710 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t13 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m) p : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6711 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t13 x m mi p) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6712 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_nr ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_rlofnt n : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6713 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_natintrl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_natrli n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)).
+
+(* notion 6714 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.(l_ori2 (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_natpos (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_natrli n)) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n))).
+
+(* notion 6715 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n))) p : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)))).
+
+(* notion 6716 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_intts m mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n))).
+
+(* notion 6717 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p n)) : Prop).
+
+(* notion 6718 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t18 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_ispw1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p)) l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p)))).
+
+(* notion 6719 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t19 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_satz291 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p)).
+
+(* notion 6720 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t20 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x m (l_e_st_eq_landau_n_rt_rp_r_ts m l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_satz195a m) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t13 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p l_e_st_eq_landau_n_1) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p l_e_st_eq_landau_n_1))).
+
+(* notion 6721 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t21 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p l_e_st_eq_landau_n_1)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t18 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t19 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t20 x m mi p) : l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p l_e_st_eq_landau_n_1).
+
+(* notion 6722 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_pl n l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_nat).
+
+(* notion 6723 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t22 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_satz290 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t13 x m mi p) p : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6724 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t23 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t22 x m mi p n p2) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_1rl))).
+
+(* notion 6725 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t24 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294a (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t23 x m mi p n p2) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n))).
+
+(* notion 6726 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t25 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294b (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t23 x m mi p n p2) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos l_e_st_eq_landau_n_rt_rp_r_1rl)).
+
+(* notion 6727 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t26 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294c (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t23 x m mi p n p2) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl))).
+
+(* notion 6728 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t27 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_satzr155a n l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t26 x m mi p n p2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t26 x m mi p n p2))).
+
+(* notion 6729 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t27a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_satz294 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t23 x m mi p n p2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t24 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t25 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t26 x m mi p n p2))).
+
+(* notion 6730 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t28 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t24 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t25 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t26 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t27 x m mi p n p2) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t27a x m mi p n p2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t24 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t25 x m mi p n p2)))).
+
+(* notion 6731 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t29 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n))) (l_e_st_eq_landau_n_rt_rp_r_pos m)) p : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n))) (l_e_st_eq_landau_n_rt_rp_r_pos m))).
+
+(* notion 6732 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t30 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) m (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t29 x m mi p n p2) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)))).
+
+(* notion 6733 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t31 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294b x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) m (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t29 x m mi p n p2) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6734 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t32 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294c x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) m (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t29 x m mi p n p2) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) m))).
+
+(* notion 6735 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t33 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t24 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t30 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t24 x m mi p n p2) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p n)) p2 (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t30 x m mi p n p2)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t24 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t30 x m mi p n p2))).
+
+(* notion 6736 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t34 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t25 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t31 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p)) l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t25 x m mi p n p2) (l_e_st_eq_landau_n_rt_rp_r_c_lemma291 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t19 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x m (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t13 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t31 x m mi p n p2)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t25 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t31 x m mi p n p2))).
+
+(* notion 6737 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t35 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t24 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t30 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t25 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t31 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t33 x m mi p n p2) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t34 x m mi p n p2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t24 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t25 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t30 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t31 x m mi p n p2)))).
+
+(* notion 6738 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t36 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_satz294 x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) m (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t29 x m mi p n p2) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t30 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t31 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) m) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t32 x m mi p n p2))).
+
+(* notion 6739 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t37 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) m) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_ts m l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_ispl2 m (l_e_st_eq_landau_n_rt_rp_r_ts m l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_satz195a m)) (l_e_st_eq_landau_n_rt_rp_r_distpt2 m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) m (l_e_st_eq_landau_n_rt_rp_r_satzr155b n l_e_st_eq_landau_n_1)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) m) (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)))).
+
+(* notion 6740 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t38 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) m) (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t37 x m mi p n p2) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t32 x m mi p n p2) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) m) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t32 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)))).
+
+(* notion 6741 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t39 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t24 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_intrl1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_t25 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t30 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t31 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) m) (l_e_st_eq_landau_n_rt_rp_r_intpl (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p n)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p n) m mi) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t32 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_nr x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t28 x m mi p n p2) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t35 x m mi p n p2) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t36 x m mi p n p2) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t38 x m mi p n p2) : l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2)).
+
+(* notion 6742 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t40 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.λp2:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p t) (l_e_st_eq_landau_n_rt_rp_r_c_9297_n1 x m mi p n p2) (l_e_st_eq_landau_n_suc n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t39 x m mi p n p2) (l_e_st_eq_landau_n_satz4a n) : l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p (l_e_st_eq_landau_n_suc n)).
+
+(* notion 6743 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t41 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p t) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t21 x m mi p) (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p t.l_e_st_eq_landau_n_rt_rp_r_c_9297_t40 x m mi p t u) n : l_e_st_eq_landau_n_rt_rp_r_c_9297_prop2 x m mi p n).
+
+(* notion 6744 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t42 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_posintnatrl n q ni : l_e_st_eq_landau_n_rt_rp_r_natrl n).
+
+(* notion 6745 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_ntofrl n (l_e_st_eq_landau_n_rt_rp_r_c_9297_t42 x m n mi ni o p q) : l_e_st_eq_landau_n_nat).
+
+(* notion 6746 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t43 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_isrlnt1 n (l_e_st_eq_landau_n_rt_rp_r_c_9297_t42 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_is n (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q))).
+
+(* notion 6747 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t44 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_isrlnt2 n (l_e_st_eq_landau_n_rt_rp_r_c_9297_t42 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) n).
+
+(* notion 6748 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6749 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t44a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x m m (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real m) mi mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t13 x m mi p) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p)).
+
+(* notion 6750 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t45 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_c_ispw12 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) n (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t44a x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t43 x m n mi ni o p q) ni (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)))).
+
+(* notion 6751 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t46 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_c_9297_t41 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)))).
+
+(* notion 6752 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t47 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) n m (l_e_st_eq_landau_n_rt_rp_r_c_9297_t44 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_ts m n)).
+
+(* notion 6753 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t48 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t47 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o))).
+
+(* notion 6754 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t49 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_pos n.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p0 x m mi p) (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t14 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t15 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_rlofnt (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t17 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t16 x m mi p (l_e_st_eq_landau_n_rt_rp_r_c_9297_n0 x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t45 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t46 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t48 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_9297_prop1 x m n mi ni o).
+
+(* notion 6755 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t50 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_is n l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_c_0exp (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o) i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 6756 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t51 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_is n l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_ts02 m n i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts m n) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 6757 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t52 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_is n l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_c_0exp x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t51 x m n mi ni o p i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_1c).
+
+(* notion 6758 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t53 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λi:l_e_st_eq_landau_n_rt_rp_r_is n l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_9297_t50 x m n mi ni o p i) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t52 x m n mi ni o p i) : l_e_st_eq_landau_n_rt_rp_r_c_9297_prop1 x m n mi ni o).
+
+(* notion 6759 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_an ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_abs n : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6760 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_intabs n ni : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)).
+
+(* notion 6761 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t55 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_ori1 (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))) p : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)))).
+
+(* notion 6762 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t55 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6763 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t56 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_satz166e n (l_e_st_eq_landau_n_rt_rp_r_nnot0 n q) : l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)).
+
+(* notion 6764 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t56a ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t55 x m n mi ni o p q) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos m)).
+
+(* notion 6765 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t57 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t55 x m n mi ni o p q) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))).
+
+(* notion 6766 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t58 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t55 x m n mi ni o p q) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)))).
+
+(* notion 6767 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t59 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_9297_t49 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t55 x m n mi ni o p q) p (l_e_st_eq_landau_n_rt_rp_r_c_9297_t56 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t57 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t58 x m n mi ni o p q))).
+
+(* notion 6768 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t60 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_satz177c (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) n (l_e_st_eq_landau_n_rt_rp_r_absn n q) : l_e_st_eq_landau_n_rt_rp_r_is n (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))).
+
+(* notion 6769 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t61 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_intm0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))).
+
+(* notion 6770 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t62 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_satz290 x m mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t56a x m n mi ni o p q) p : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6771 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma296 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t62 x m n mi ni o p q) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))).
+
+(* notion 6772 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t64 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_satz290 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t62 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6773 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t65 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma296 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t61 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t62 x m n mi ni o p q) : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)))).
+
+(* notion 6774 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t66 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_satz296 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t62 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t64 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t61 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t65 x m n mi ni o p q))).
+
+(* notion 6775 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t67 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x m (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t56a x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q)).
+
+(* notion 6776 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t68 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_ispw12 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) n (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t67 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t60 x m n mi ni o p q) ni (l_e_st_eq_landau_n_rt_rp_r_c_9297_t61 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t65 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t61 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t65 x m n mi ni o p q))).
+
+(* notion 6777 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t69 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t64 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t61 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t65 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t68 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t66 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t64 x m n mi ni o p q))).
+
+(* notion 6778 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t70 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_satz197f m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_ists2 (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) n m (l_e_symis l_e_st_eq_landau_n_rt_rp_r_real n (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t60 x m n mi ni o p q))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_ts m n)).
+
+(* notion 6779 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t71 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_intm0 (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) : l_e_st_eq_landau_n_rt_rp_r_intrl (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)))).
+
+(* notion 6780 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t72 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) p : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)))).
+
+(* notion 6781 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t73 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_satz290 x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t72 x m n mi ni o p q) p : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t72 x m n mi ni o p q)) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6782 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t74 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_lemma296 x (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t71 x m n mi ni o p q) p : l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_pos (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))))).
+
+(* notion 6783 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t75 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_satz296 x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) p : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t72 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t73 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t71 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t74 x m n mi ni o p q))).
+
+(* notion 6784 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t76 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_ispw2 x (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t70 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t71 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t74 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t71 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t74 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o))).
+
+(* notion 6785 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t77 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_ispw1 (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t57 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t57 x m n mi ni o p q))).
+
+(* notion 6786 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t78 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_ispw1 x x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_refis l_e_st_eq_landau_n_rt_rp_r_c_cx x) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t58 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t72 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t58 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t72 x m n mi ni o p q))).
+
+(* notion 6787 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t79 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t57 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t58 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t72 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t77 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t59 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t78 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t72 x m n mi ni o p q))).
+
+(* notion 6788 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t80 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_st_eq_landau_n_rt_rp_r_c_isov2 (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t72 x m n mi ni o p q)) l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_9297_t79 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t64 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t73 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t64 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t72 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t73 x m n mi ni o p q))).
+
+(* notion 6789 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t81 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.λq:l_e_st_eq_landau_n_rt_rp_r_neg n.(l_e_tr4is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1 x m n mi ni o) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_9297_p1t55 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t63 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t64 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_ov l_e_st_eq_landau_n_rt_rp_r_c_1c (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q) mi (l_e_st_eq_landau_n_rt_rp_r_c_9297_t54 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t72 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t73 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts m (l_e_st_eq_landau_n_rt_rp_r_c_9297_an x m n mi ni o p q))) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t71 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t74 x m n mi ni o p q)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t8 x m n mi ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t69 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t80 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t75 x m n mi ni o p q) (l_e_st_eq_landau_n_rt_rp_r_c_9297_t76 x m n mi ni o p q) : l_e_st_eq_landau_n_rt_rp_r_c_9297_prop1 x m n mi ni o).
+
+(* notion 6790 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_9297_t82 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).λp:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_st_eq_landau_n_rt_rp_r_rapp n (l_e_st_eq_landau_n_rt_rp_r_c_9297_prop1 x m n mi ni o) (λt:l_e_st_eq_landau_n_rt_rp_r_pos n.l_e_st_eq_landau_n_rt_rp_r_c_9297_t49 x m n mi ni o p t) (λt:l_e_st_eq_landau_n_rt_rp_r_is n l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_9297_t53 x m n mi ni o p t) (λt:l_e_st_eq_landau_n_rt_rp_r_neg n.l_e_st_eq_landau_n_rt_rp_r_c_9297_t81 x m n mi ni o p t) : l_e_st_eq_landau_n_rt_rp_r_c_9297_prop1 x m n mi ni o).
+
+(* notion 6791 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz297 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.λm:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_real.λmi:l_e_st_eq_landau_n_rt_rp_r_intrl m.λni:l_e_st_eq_landau_n_rt_rp_r_intrl n.λo:l_or (l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_and (l_e_st_eq_landau_n_rt_rp_r_pos m) (l_e_st_eq_landau_n_rt_rp_r_pos n)).(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_c_9297_prop1 x m n mi ni o) (λt:l_e_st_eq_landau_n_rt_rp_r_c_is x l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_9297_t12 x m n mi ni o t) (λt:l_e_st_eq_landau_n_rt_rp_r_c_nis x l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_9297_t82 x m n mi ni o t) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pw (l_e_st_eq_landau_n_rt_rp_r_c_pw x m mi (l_e_st_eq_landau_n_rt_rp_r_c_lemma294a x m n mi ni o)) n ni (l_e_st_eq_landau_n_rt_rp_r_c_lemma297a x m n mi ni o)) (l_e_st_eq_landau_n_rt_rp_r_c_pw x (l_e_st_eq_landau_n_rt_rp_r_ts m n) (l_e_st_eq_landau_n_rt_rp_r_intts m mi n ni) (l_e_st_eq_landau_n_rt_rp_r_c_lemma297b x m n mi ni o))).
+
+(* notion 6792 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_plis12a r l_e_st_eq_landau_n_rt_rp_r_0 s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl r s) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r s) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6793 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t1 r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 6794 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_10298_t1 r s : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r s) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6795 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_mn l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_mnis12a r l_e_st_eq_landau_n_rt_rp_r_0 s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_mn l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_mn r s) (l_e_st_eq_landau_n_rt_rp_r_pl02 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6796 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298c ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t2 r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 6797 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298d ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_10298_t2 r s : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_mn (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn r s) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6798 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_satz176b (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts r s)).
+
+(* notion 6799 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s)) (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 s (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_ts02 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 6800 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s))) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_tsis12a r l_e_st_eq_landau_n_rt_rp_r_0 s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts r s) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 s)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_10298_t3 r s) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t4 r s)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6801 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t5 r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 6802 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_10298_t5 r s : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts r s) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6803 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_0c.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real s (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_re l_e_st_eq_landau_n_rt_rp_r_c_0c) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_c_isre s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_0c i) (l_e_st_eq_landau_n_rt_rp_r_c_reis l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 6804 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_lemma298 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_imp_th3 (l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_0c) (l_e_st_eq_landau_n_rt_rp_r_is s l_e_st_eq_landau_n_rt_rp_r_0) n (λt:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_0c.l_e_st_eq_landau_n_rt_rp_r_c_10298_t6 r s n t) : l_e_st_eq_landau_n_rt_rp_r_c_nis (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_c_0c).
+
+(* notion 6805 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ov r s n) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t5 s (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 (l_e_st_eq_landau_n_rt_rp_r_ts s (l_e_st_eq_landau_n_rt_rp_r_ov r s n)) r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_satz204c r s n)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ov r s n) l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6806 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298g ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_c_satz229g (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ov r s n) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_lemma298 r s n) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t7 r s n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ov r s n) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_lemma298 r s n))).
+
+(* notion 6807 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298h ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_nis s l_e_st_eq_landau_n_rt_rp_r_0.(l_e_st_eq_landau_n_rt_rp_r_c_satz229h (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ov r s n) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_lemma298 r s n) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t7 r s n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ov (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_pli s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_lemma298 r s n)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_ov r s n) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6808 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_m0isa r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_isrecx2 (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_m0 r) (l_e_st_eq_landau_n_rt_rp_r_satz176b l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6809 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298j ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t8 r) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 6810 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298k ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_10298_t8 r : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_m0 (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_m0 r) l_e_st_eq_landau_n_rt_rp_r_0)).
+
+(* notion 6811 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod2 (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_imis r l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_ists12 (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) r (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) r (l_e_st_eq_landau_n_rt_rp_r_c_reis r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_reis r l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod2 (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts r r)).
+
+(* notion 6812 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_ar ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_abs r : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6813 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t10 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λp:l_e_st_eq_landau_n_rt_rp_r_pos r.(l_e_st_eq_landau_n_rt_rp_r_satz196a r r p p : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r))).
+
+(* notion 6814 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t11 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.(l_e_tris2 l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_ts01 r r i) (l_e_st_eq_landau_n_rt_rp_r_ts01 (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_abs0 r i)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r))).
+
+(* notion 6815 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t12 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λn:l_e_st_eq_landau_n_rt_rp_r_neg r.(l_e_st_eq_landau_n_rt_rp_r_satz196b r r n n : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r))).
+
+(* notion 6816 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t13 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_rapp r (l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r))) (λt:l_e_st_eq_landau_n_rt_rp_r_pos r.l_e_st_eq_landau_n_rt_rp_r_c_10298_t10 r t) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_c_10298_t11 r t) (λt:l_e_st_eq_landau_n_rt_rp_r_neg r.l_e_st_eq_landau_n_rt_rp_r_c_10298_t12 r t) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r))).
+
+(* notion 6817 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t14 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod2 (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts r r) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r)) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t9 r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t13 r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod2 (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r))).
+
+(* notion 6818 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10298_t15 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_imp_th1 (l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0) (l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r))) (λt:l_e_st_eq_landau_n_rt_rp_r_is r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_0notn (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_abs0 r t)) (λt:l_e_st_eq_landau_n_rt_rp_r_nis r l_e_st_eq_landau_n_rt_rp_r_0.l_e_st_eq_landau_n_rt_rp_r_pnotn (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r) (l_e_st_eq_landau_n_rt_rp_r_satz166e r t)) : l_not (l_e_st_eq_landau_n_rt_rp_r_neg (l_e_st_eq_landau_n_rt_rp_r_c_10298_ar r))).
+
+(* notion 6819 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298l ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_thsqrt3 (l_e_st_eq_landau_n_rt_rp_r_c_mod2 (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_c_lemma5 (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t15 r) (l_e_st_eq_landau_n_rt_rp_r_c_10298_t14 r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_abs r)).
+
+(* notion 6820 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz298m ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_c_satz298l r) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_abs r) (l_e_st_eq_landau_n_rt_rp_r_c_mod (l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0))).
+
+(* notion 6821 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_cofrl ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_pli r l_e_st_eq_landau_n_rt_rp_r_0 : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 6822 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isrlic ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s)) s (l_e_st_eq_landau_n_rt_rp_r_c_isre r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) i) (l_e_st_eq_landau_n_rt_rp_r_c_reis s l_e_st_eq_landau_n_rt_rp_r_0) : l_e_st_eq_landau_n_rt_rp_r_is r s).
+
+(* notion 6823 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isrlec ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_is r s.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx1 r s l_e_st_eq_landau_n_rt_rp_r_0 i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s)).
+
+(* notion 6824 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v10_t1 ≝ (λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λv:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) (l_e_st_eq_landau_n_rt_rp_r_c_cofrl u).l_e_st_eq_landau_n_rt_rp_r_c_isrlic t u v : l_e_injective l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_cofrl t)).
+
+(* notion 6825 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_realc ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_image l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) x : Prop).
+
+(* notion 6826 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_reali ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_imagei l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) r : l_e_st_eq_landau_n_rt_rp_r_c_realc (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r)).
+
+(* notion 6827 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_rlofc ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λrx:l_e_st_eq_landau_n_rt_rp_r_c_realc x.(l_e_soft l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t1 x rx : l_e_st_eq_landau_n_rt_rp_r_real).
+
+(* notion 6828 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscirl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λrx:l_e_st_eq_landau_n_rt_rp_r_c_realc x.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λry:l_e_st_eq_landau_n_rt_rp_r_c_realc y.λi:l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rlofc x rx) (l_e_st_eq_landau_n_rt_rp_r_c_rlofc y ry).(l_e_isinve l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t1 x rx y ry i : l_e_st_eq_landau_n_rt_rp_r_c_is x y).
+
+(* notion 6829 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscerl ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λrx:l_e_st_eq_landau_n_rt_rp_r_c_realc x.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λry:l_e_st_eq_landau_n_rt_rp_r_c_realc y.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isinv l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t1 x rx y ry i : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rlofc x rx) (l_e_st_eq_landau_n_rt_rp_r_c_rlofc y ry)).
+
+(* notion 6830 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isrlc1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_isst1 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t1 r : l_e_st_eq_landau_n_rt_rp_r_is r (l_e_st_eq_landau_n_rt_rp_r_c_rlofc (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_reali r))).
+
+(* notion 6831 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isrlc2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_isst2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t1 r : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_c_rlofc (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_reali r)) r).
+
+(* notion 6832 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscrl1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λrx:l_e_st_eq_landau_n_rt_rp_r_c_realc x.(l_e_ists1 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t1 x rx : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_c_rlofc x rx))).
+
+(* notion 6833 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscrl2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λrx:l_e_st_eq_landau_n_rt_rp_r_c_realc x.(l_e_ists2 l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_real.l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t1 x rx : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_c_rlofc x rx)) x).
+
+(* notion 6834 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_cofn ≝ λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_rlofnt n) : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 6835 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isnec ≝ λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is n m.(l_e_st_eq_landau_n_rt_rp_r_c_isrlec (l_e_st_eq_landau_n_rt_rp_r_rlofnt n) (l_e_st_eq_landau_n_rt_rp_r_rlofnt m) (l_e_st_eq_landau_n_rt_rp_r_isnterl n m i) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofn n) (l_e_st_eq_landau_n_rt_rp_r_c_cofn m)).
+
+(* notion 6836 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isnic ≝ λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofn n) (l_e_st_eq_landau_n_rt_rp_r_c_cofn m).(l_e_st_eq_landau_n_rt_rp_r_isntirl n m (l_e_st_eq_landau_n_rt_rp_r_c_isrlic (l_e_st_eq_landau_n_rt_rp_r_rlofnt n) (l_e_st_eq_landau_n_rt_rp_r_rlofnt m) i) : l_e_st_eq_landau_n_is n m).
+
+(* notion 6837 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v10_t2 ≝ (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_nat.λv:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofn t) (l_e_st_eq_landau_n_rt_rp_r_c_cofn u).l_e_st_eq_landau_n_rt_rp_r_c_isnic t u v : l_e_injective l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_cofn t)).
+
+(* notion 6838 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_natc ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.(l_e_image l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_cofn t) x : Prop).
+
+(* notion 6839 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_nati ≝ λn:l_e_st_eq_landau_n_nat.(l_e_imagei l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_cofn t) n : l_e_st_eq_landau_n_rt_rp_r_c_natc (l_e_st_eq_landau_n_rt_rp_r_c_cofn n)).
+
+(* notion 6840 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_nofc ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λnx:l_e_st_eq_landau_n_rt_rp_r_c_natc x.(l_e_soft l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_cofn t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t2 x nx : l_e_st_eq_landau_n_nat).
+
+(* notion 6841 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscen ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λnx:l_e_st_eq_landau_n_rt_rp_r_c_natc x.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λny:l_e_st_eq_landau_n_rt_rp_r_c_natc y.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isinv l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_cofn t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t2 x nx y ny i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_nofc x nx) (l_e_st_eq_landau_n_rt_rp_r_c_nofc y ny)).
+
+(* notion 6842 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscin ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λnx:l_e_st_eq_landau_n_rt_rp_r_c_natc x.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λny:l_e_st_eq_landau_n_rt_rp_r_c_natc y.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_nofc x nx) (l_e_st_eq_landau_n_rt_rp_r_c_nofc y ny).(l_e_isinve l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_cofn t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t2 x nx y ny i : l_e_st_eq_landau_n_rt_rp_r_c_is x y).
+
+(* notion 6843 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isnc1 ≝ λn:l_e_st_eq_landau_n_nat.(l_e_isst1 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_cofn t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t2 n : l_e_st_eq_landau_n_is n (l_e_st_eq_landau_n_rt_rp_r_c_nofc (l_e_st_eq_landau_n_rt_rp_r_c_cofn n) (l_e_st_eq_landau_n_rt_rp_r_c_nati n))).
+
+(* notion 6844 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isnc2 ≝ λn:l_e_st_eq_landau_n_nat.(l_e_isst2 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_cofn t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t2 n : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_nofc (l_e_st_eq_landau_n_rt_rp_r_c_cofn n) (l_e_st_eq_landau_n_rt_rp_r_c_nati n)) n).
+
+(* notion 6845 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscn1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λnx:l_e_st_eq_landau_n_rt_rp_r_c_natc x.(l_e_ists1 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_cofn t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t2 x nx : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_cofn (l_e_st_eq_landau_n_rt_rp_r_c_nofc x nx))).
+
+(* notion 6846 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscn2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λnx:l_e_st_eq_landau_n_rt_rp_r_c_natc x.(l_e_ists2 l_e_st_eq_landau_n_nat l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_cofn t) l_e_st_eq_landau_n_rt_rp_r_c_v10_t2 x nx : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofn (l_e_st_eq_landau_n_rt_rp_r_c_nofc x nx)) x).
+
+(* notion 6847 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_natt ≝ (l_e_ot l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_natc t) : Type[0]).
+
+(* notion 6848 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_cofnt ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_e_in l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_natc t) nt : l_e_st_eq_landau_n_rt_rp_r_c_cx).
+
+(* notion 6849 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_natti ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_e_inp l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_natc t) nt : l_e_st_eq_landau_n_rt_rp_r_c_natc (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt)).
+
+(* notion 6850 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isntec ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λmt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λi:l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt nt mt.(l_e_isini l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_natc t) nt mt i : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_cofnt mt)).
+
+(* notion 6851 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isntic ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λmt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_cofnt mt).(l_e_isine l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_natc t) nt mt i : l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt nt mt).
+
+(* notion 6852 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ntofc ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λnx:l_e_st_eq_landau_n_rt_rp_r_c_natc x.(l_e_out l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_natc t) x nx : l_e_st_eq_landau_n_rt_rp_r_c_natt).
+
+(* notion 6853 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscent ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λnx:l_e_st_eq_landau_n_rt_rp_r_c_natc x.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λny:l_e_st_eq_landau_n_rt_rp_r_c_natc y.λi:l_e_st_eq_landau_n_rt_rp_r_c_is x y.(l_e_isouti l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_natc t) x nx y ny i : l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_ntofc x nx) (l_e_st_eq_landau_n_rt_rp_r_c_ntofc y ny)).
+
+(* notion 6854 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscint ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λnx:l_e_st_eq_landau_n_rt_rp_r_c_natc x.λy:l_e_st_eq_landau_n_rt_rp_r_c_cx.λny:l_e_st_eq_landau_n_rt_rp_r_c_natc y.λi:l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_ntofc x nx) (l_e_st_eq_landau_n_rt_rp_r_c_ntofc y ny).(l_e_isoute l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_natc t) x nx y ny i : l_e_st_eq_landau_n_rt_rp_r_c_is x y).
+
+(* notion 6855 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isntc1 ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_e_isoutin l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_natc t) nt : l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt nt (l_e_st_eq_landau_n_rt_rp_r_c_ntofc (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_natti nt))).
+
+(* notion 6856 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isntc2 ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_natt nt (l_e_st_eq_landau_n_rt_rp_r_c_ntofc (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_natti nt)) (l_e_st_eq_landau_n_rt_rp_r_c_isntc1 nt) : l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_ntofc (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_natti nt)) nt).
+
+(* notion 6857 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscnt1 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λnx:l_e_st_eq_landau_n_rt_rp_r_c_natc x.(l_e_isinout l_e_st_eq_landau_n_rt_rp_r_c_cx (λt:l_e_st_eq_landau_n_rt_rp_r_c_cx.l_e_st_eq_landau_n_rt_rp_r_c_natc t) x nx : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_cofnt (l_e_st_eq_landau_n_rt_rp_r_c_ntofc x nx))).
+
+(* notion 6858 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_iscnt2 ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_cx.λnx:l_e_st_eq_landau_n_rt_rp_r_c_natc x.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_cofnt (l_e_st_eq_landau_n_rt_rp_r_c_ntofc x nx)) (l_e_st_eq_landau_n_rt_rp_r_c_iscnt1 x nx) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofnt (l_e_st_eq_landau_n_rt_rp_r_c_ntofc x nx)) x).
+
+(* notion 6859 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ntofn ≝ λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_ntofc (l_e_st_eq_landau_n_rt_rp_r_c_cofn n) (l_e_st_eq_landau_n_rt_rp_r_c_nati n) : l_e_st_eq_landau_n_rt_rp_r_c_natt).
+
+(* notion 6860 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isnent ≝ λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λi:l_e_st_eq_landau_n_is n m.(l_e_st_eq_landau_n_rt_rp_r_c_iscent (l_e_st_eq_landau_n_rt_rp_r_c_cofn n) (l_e_st_eq_landau_n_rt_rp_r_c_nati n) (l_e_st_eq_landau_n_rt_rp_r_c_cofn m) (l_e_st_eq_landau_n_rt_rp_r_c_nati m) (l_e_st_eq_landau_n_rt_rp_r_c_isnec n m i) : l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n) (l_e_st_eq_landau_n_rt_rp_r_c_ntofn m)).
+
+(* notion 6861 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isnint ≝ λn:l_e_st_eq_landau_n_nat.λm:l_e_st_eq_landau_n_nat.λi:l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n) (l_e_st_eq_landau_n_rt_rp_r_c_ntofn m).(l_e_st_eq_landau_n_rt_rp_r_c_isnic n m (l_e_st_eq_landau_n_rt_rp_r_c_iscint (l_e_st_eq_landau_n_rt_rp_r_c_cofn n) (l_e_st_eq_landau_n_rt_rp_r_c_nati n) (l_e_st_eq_landau_n_rt_rp_r_c_cofn m) (l_e_st_eq_landau_n_rt_rp_r_c_nati m) i) : l_e_st_eq_landau_n_is n m).
+
+(* notion 6862 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_nofnt ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_e_st_eq_landau_n_rt_rp_r_c_nofc (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_natti nt) : l_e_st_eq_landau_n_nat).
+
+(* notion 6863 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isnter ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λmt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λi:l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt nt mt.(l_e_st_eq_landau_n_rt_rp_r_c_iscen (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_natti nt) (l_e_st_eq_landau_n_rt_rp_r_c_cofnt mt) (l_e_st_eq_landau_n_rt_rp_r_c_natti mt) (l_e_st_eq_landau_n_rt_rp_r_c_isntec nt mt i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_nofnt mt)).
+
+(* notion 6864 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isntin ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λmt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λi:l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_nofnt mt).(l_e_st_eq_landau_n_rt_rp_r_c_isntic nt mt (l_e_st_eq_landau_n_rt_rp_r_c_iscin (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_natti nt) (l_e_st_eq_landau_n_rt_rp_r_c_cofnt mt) (l_e_st_eq_landau_n_rt_rp_r_c_natti mt) i) : l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt nt mt).
+
+(* notion 6865 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v10_t3 ≝ λn:l_e_st_eq_landau_n_nat.(l_e_st_eq_landau_n_rt_rp_r_c_iscnt1 (l_e_st_eq_landau_n_rt_rp_r_c_cofn n) (l_e_st_eq_landau_n_rt_rp_r_c_nati n) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofn n) (l_e_st_eq_landau_n_rt_rp_r_c_cofnt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n))).
+
+(* notion 6866 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isnnt1 ≝ λn:l_e_st_eq_landau_n_nat.(l_e_tris l_e_st_eq_landau_n_nat n (l_e_st_eq_landau_n_rt_rp_r_c_nofc (l_e_st_eq_landau_n_rt_rp_r_c_cofn n) (l_e_st_eq_landau_n_rt_rp_r_c_nati n)) (l_e_st_eq_landau_n_rt_rp_r_c_nofnt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n)) (l_e_st_eq_landau_n_rt_rp_r_c_isnc1 n) (l_e_st_eq_landau_n_rt_rp_r_c_iscen (l_e_st_eq_landau_n_rt_rp_r_c_cofn n) (l_e_st_eq_landau_n_rt_rp_r_c_nati n) (l_e_st_eq_landau_n_rt_rp_r_c_cofnt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n)) (l_e_st_eq_landau_n_rt_rp_r_c_natti (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n)) (l_e_st_eq_landau_n_rt_rp_r_c_v10_t3 n)) : l_e_st_eq_landau_n_is n (l_e_st_eq_landau_n_rt_rp_r_c_nofnt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n))).
+
+(* notion 6867 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isnnt2 ≝ λn:l_e_st_eq_landau_n_nat.(l_e_symis l_e_st_eq_landau_n_nat n (l_e_st_eq_landau_n_rt_rp_r_c_nofnt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n)) (l_e_st_eq_landau_n_rt_rp_r_c_isnnt1 n) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_nofnt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n)) n).
+
+(* notion 6868 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_v10_t4 ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_e_st_eq_landau_n_rt_rp_r_c_iscn1 (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_natti nt) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_cofn (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt))).
+
+(* notion 6869 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isntn1 ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_natt nt (l_e_st_eq_landau_n_rt_rp_r_c_ntofc (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_natti nt)) (l_e_st_eq_landau_n_rt_rp_r_c_ntofn (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)) (l_e_st_eq_landau_n_rt_rp_r_c_isntc1 nt) (l_e_st_eq_landau_n_rt_rp_r_c_iscent (l_e_st_eq_landau_n_rt_rp_r_c_cofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_natti nt) (l_e_st_eq_landau_n_rt_rp_r_c_cofn (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)) (l_e_st_eq_landau_n_rt_rp_r_c_nati (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)) (l_e_st_eq_landau_n_rt_rp_r_c_v10_t4 nt)) : l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt nt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt))).
+
+(* notion 6870 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_isntn2 ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_natt nt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)) (l_e_st_eq_landau_n_rt_rp_r_c_isntn1 nt) : l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)) nt).
+
+(* notion 6871 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_1t ≝ (l_e_st_eq_landau_n_rt_rp_r_c_ntofn l_e_st_eq_landau_n_1 : l_e_st_eq_landau_n_rt_rp_r_c_natt).
+
+(* notion 6872 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_suct ≝ (λt:l_e_st_eq_landau_n_rt_rp_r_c_natt.l_e_st_eq_landau_n_rt_rp_r_c_ntofn (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_nofnt t)) : Πt:l_e_st_eq_landau_n_rt_rp_r_c_natt.l_e_st_eq_landau_n_rt_rp_r_c_natt).
+
+(* notion 6873 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10299_t1 ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λi:l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_suct nt) l_e_st_eq_landau_n_rt_rp_r_c_1t.(l_e_st_eq_landau_n_rt_rp_r_c_isnint (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)) l_e_st_eq_landau_n_1 i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)) l_e_st_eq_landau_n_1).
+
+(* notion 6874 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz299a ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_imp_th3 (l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_suct nt) l_e_st_eq_landau_n_rt_rp_r_c_1t) (l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)) l_e_st_eq_landau_n_1) (l_e_st_eq_landau_n_ax3 (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)) (λt:l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_suct nt) l_e_st_eq_landau_n_rt_rp_r_c_1t.l_e_st_eq_landau_n_rt_rp_r_c_10299_t1 nt t) : l_not (l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_suct nt) l_e_st_eq_landau_n_rt_rp_r_c_1t)).
+
+(* notion 6875 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ax3t ≝ (λt:l_e_st_eq_landau_n_rt_rp_r_c_natt.l_e_st_eq_landau_n_rt_rp_r_c_satz299a t : Πt:l_e_st_eq_landau_n_rt_rp_r_c_natt.l_not (l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_suct t) l_e_st_eq_landau_n_rt_rp_r_c_1t)).
+
+(* notion 6876 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10299_t2 ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λmt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λi:l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_suct nt) (l_e_st_eq_landau_n_rt_rp_r_c_suct mt).(l_e_st_eq_landau_n_rt_rp_r_c_isnint (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_nofnt mt)) i : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)) (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_nofnt mt))).
+
+(* notion 6877 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10299_t3 ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λmt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λi:l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_suct nt) (l_e_st_eq_landau_n_rt_rp_r_c_suct mt).(l_e_st_eq_landau_n_ax4 (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_nofnt mt) (l_e_st_eq_landau_n_rt_rp_r_c_10299_t2 nt mt i) : l_e_st_eq_landau_n_is (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt) (l_e_st_eq_landau_n_rt_rp_r_c_nofnt mt)).
+
+(* notion 6878 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz299b ≝ λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λmt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λi:l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_suct nt) (l_e_st_eq_landau_n_rt_rp_r_c_suct mt).(l_e_st_eq_landau_n_rt_rp_r_c_isntin nt mt (l_e_st_eq_landau_n_rt_rp_r_c_10299_t3 nt mt i) : l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt nt mt).
+
+(* notion 6879 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ax4t ≝ (λt:l_e_st_eq_landau_n_rt_rp_r_c_natt.λu:l_e_st_eq_landau_n_rt_rp_r_c_natt.λv:l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_suct t) (l_e_st_eq_landau_n_rt_rp_r_c_suct u).l_e_st_eq_landau_n_rt_rp_r_c_satz299b t u v : Πt:l_e_st_eq_landau_n_rt_rp_r_c_natt.Πu:l_e_st_eq_landau_n_rt_rp_r_c_natt.Πv:l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_suct t) (l_e_st_eq_landau_n_rt_rp_r_c_suct u).l_e_is l_e_st_eq_landau_n_rt_rp_r_c_natt t u).
+
+(* notion 6880 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_cond1t ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_e_st_esti l_e_st_eq_landau_n_rt_rp_r_c_natt l_e_st_eq_landau_n_rt_rp_r_c_1t s : Prop).
+
+(* notion 6881 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_cond2t ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_all l_e_st_eq_landau_n_rt_rp_r_c_natt (λt:l_e_st_eq_landau_n_rt_rp_r_c_natt.l_imp (l_e_st_esti l_e_st_eq_landau_n_rt_rp_r_c_natt t s) (l_e_st_esti l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_suct t) s)) : Prop).
+
+(* notion 6882 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10299_prop1 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_c_natt.λc1:l_e_st_eq_landau_n_rt_rp_r_c_cond1t s.λc2:l_e_st_eq_landau_n_rt_rp_r_c_cond2t s.λn:l_e_st_eq_landau_n_nat.(l_e_st_esti l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n) s : Prop).
+
+(* notion 6883 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10299_t4 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_c_natt.λc1:l_e_st_eq_landau_n_rt_rp_r_c_cond1t s.λc2:l_e_st_eq_landau_n_rt_rp_r_c_cond2t s.(c1 : l_e_st_eq_landau_n_rt_rp_r_c_10299_prop1 s c1 c2 l_e_st_eq_landau_n_1).
+
+(* notion 6884 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10299_t5 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_c_natt.λc1:l_e_st_eq_landau_n_rt_rp_r_c_cond1t s.λc2:l_e_st_eq_landau_n_rt_rp_r_c_cond2t s.λn:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_10299_prop1 s c1 c2 n.(c2 (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n) p : l_e_st_esti l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn (l_e_st_eq_landau_n_suc (l_e_st_eq_landau_n_rt_rp_r_c_nofnt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n)))) s).
+
+(* notion 6885 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10299_t6 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_c_natt.λc1:l_e_st_eq_landau_n_rt_rp_r_c_cond1t s.λc2:l_e_st_eq_landau_n_rt_rp_r_c_cond2t s.λn:l_e_st_eq_landau_n_nat.λp:l_e_st_eq_landau_n_rt_rp_r_c_10299_prop1 s c1 c2 n.(l_e_isp l_e_st_eq_landau_n_nat (λt:l_e_st_eq_landau_n_nat.l_e_st_esti l_e_st_eq_landau_n_rt_rp_r_c_natt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn (l_e_st_eq_landau_n_suc t)) s) (l_e_st_eq_landau_n_rt_rp_r_c_nofnt (l_e_st_eq_landau_n_rt_rp_r_c_ntofn n)) n (l_e_st_eq_landau_n_rt_rp_r_c_10299_t5 s c1 c2 n p) (l_e_st_eq_landau_n_rt_rp_r_c_isnnt2 n) : l_e_st_eq_landau_n_rt_rp_r_c_10299_prop1 s c1 c2 (l_e_st_eq_landau_n_suc n)).
+
+(* notion 6886 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10299_t7 ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_c_natt.λc1:l_e_st_eq_landau_n_rt_rp_r_c_cond1t s.λc2:l_e_st_eq_landau_n_rt_rp_r_c_cond2t s.λnt:l_e_st_eq_landau_n_rt_rp_r_c_natt.(l_e_st_eq_landau_n_induction (λt:l_e_st_eq_landau_n_nat.l_e_st_eq_landau_n_rt_rp_r_c_10299_prop1 s c1 c2 t) (l_e_st_eq_landau_n_rt_rp_r_c_10299_t4 s c1 c2) (λt:l_e_st_eq_landau_n_nat.λu:l_e_st_eq_landau_n_rt_rp_r_c_10299_prop1 s c1 c2 t.l_e_st_eq_landau_n_rt_rp_r_c_10299_t6 s c1 c2 t u) (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt) : l_e_st_eq_landau_n_rt_rp_r_c_10299_prop1 s c1 c2 (l_e_st_eq_landau_n_rt_rp_r_c_nofnt nt)).
+
+(* notion 6887 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz299c ≝ λs:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_c_natt.λc1:l_e_st_eq_landau_n_rt_rp_r_c_cond1t s.λc2:l_e_st_eq_landau_n_rt_rp_r_c_cond2t s.(λt:l_e_st_eq_landau_n_rt_rp_r_c_natt.l_e_isp l_e_st_eq_landau_n_rt_rp_r_c_natt (λu:l_e_st_eq_landau_n_rt_rp_r_c_natt.l_e_st_esti l_e_st_eq_landau_n_rt_rp_r_c_natt u s) (l_e_st_eq_landau_n_rt_rp_r_c_ntofn (l_e_st_eq_landau_n_rt_rp_r_c_nofnt t)) t (l_e_st_eq_landau_n_rt_rp_r_c_10299_t7 s c1 c2 t) (l_e_st_eq_landau_n_rt_rp_r_c_isntn2 t) : Πt:l_e_st_eq_landau_n_rt_rp_r_c_natt.l_e_st_esti l_e_st_eq_landau_n_rt_rp_r_c_natt t s).
+
+(* notion 6888 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ax5t ≝ (λt:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_c_natt.λu:l_e_st_eq_landau_n_rt_rp_r_c_cond1t t.λv:l_e_st_eq_landau_n_rt_rp_r_c_cond2t t.l_e_st_eq_landau_n_rt_rp_r_c_satz299c t u v : Πt:l_e_st_set l_e_st_eq_landau_n_rt_rp_r_c_natt.Πu:l_e_st_eq_landau_n_rt_rp_r_c_cond1t t.Πv:l_e_st_eq_landau_n_rt_rp_r_c_cond2t t.Πw:l_e_st_eq_landau_n_rt_rp_r_c_natt.l_e_st_esti l_e_st_eq_landau_n_rt_rp_r_c_natt w t).
+
+(* notion 6889 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_ic ≝ (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_c_complex).
+
+(* notion 6890 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10300_t1 ≝ (l_e_st_eq_landau_n_rt_rp_r_c_tsis12a l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_ic l_e_st_eq_landau_n_rt_rp_r_c_ic) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0)))).
+
+(* notion 6891 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10300_t2 ≝ (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl01 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_ism0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl) l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_st_eq_landau_n_rt_rp_r_satz195 l_e_st_eq_landau_n_rt_rp_r_1rl)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)).
+
+(* notion 6892 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10300_t3 ≝ (l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl01 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_ts02 l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 6893 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10300_t4 ≝ (l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0)) l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_c_10300_t2 l_e_st_eq_landau_n_rt_rp_r_c_10300_t3 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl))).
+
+(* notion 6894 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10300_t5 ≝ (l_e_st_eq_landau_n_rt_rp_r_c_satz298j l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c)).
+
+(* notion 6895 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz2300 ≝ (l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_ic l_e_st_eq_landau_n_rt_rp_r_c_ic) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_1rl l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_m0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c) l_e_st_eq_landau_n_rt_rp_r_c_10300_t1 l_e_st_eq_landau_n_rt_rp_r_c_10300_t4 l_e_st_eq_landau_n_rt_rp_r_c_10300_t5 : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts l_e_st_eq_landau_n_rt_rp_r_c_ic l_e_st_eq_landau_n_rt_rp_r_c_ic) (l_e_st_eq_landau_n_rt_rp_r_c_m0 l_e_st_eq_landau_n_rt_rp_r_c_1c)).
+
+(* notion 6896 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10301_t1 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_tsis12a s l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)))).
+
+(* notion 6897 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10301_t2 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl01 (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_m0 (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_ts02 s l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_satz176b (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl)) l_e_st_eq_landau_n_rt_rp_r_0).
+
+(* notion 6898 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10301_t3 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_real (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_1rl) s (l_e_st_eq_landau_n_rt_rp_r_pl02 (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts01 l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_satz195 s) : l_e_st_eq_landau_n_rt_rp_r_is (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) s).
+
+(* notion 6899 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10301_t4 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl)) l_e_st_eq_landau_n_rt_rp_r_0 (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0)) s (l_e_st_eq_landau_n_rt_rp_r_c_10301_t2 r s) (l_e_st_eq_landau_n_rt_rp_r_c_10301_t3 r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 s)).
+
+(* notion 6900 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10301_t5 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_mn (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_1rl)) (l_e_st_eq_landau_n_rt_rp_r_pl (l_e_st_eq_landau_n_rt_rp_r_ts s l_e_st_eq_landau_n_rt_rp_r_1rl) (l_e_st_eq_landau_n_rt_rp_r_ts l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0))) (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 s) (l_e_st_eq_landau_n_rt_rp_r_c_10301_t1 r s) (l_e_st_eq_landau_n_rt_rp_r_c_10301_t4 r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic) (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 s)).
+
+(* notion 6901 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10301_t6 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_ispl2 (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic) (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 s) (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_10301_t5 r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 s))).
+
+(* notion 6902 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10301_t7 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_plis12a r l_e_st_eq_landau_n_rt_rp_r_0 l_e_st_eq_landau_n_rt_rp_r_0 s : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 s))).
+
+(* notion 6903 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10301_t8 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_st_eq_landau_n_rt_rp_r_c_isrecx12 (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_0) r (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 s) s (l_e_st_eq_landau_n_rt_rp_r_pl02 r l_e_st_eq_landau_n_rt_rp_r_0 (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) (l_e_st_eq_landau_n_rt_rp_r_pl01 l_e_st_eq_landau_n_rt_rp_r_0 s (l_e_refis l_e_st_eq_landau_n_rt_rp_r_real l_e_st_eq_landau_n_rt_rp_r_0)) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)).
+
+(* notion 6904 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz301a ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_pli l_e_st_eq_landau_n_rt_rp_r_0 s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_pl r l_e_st_eq_landau_n_rt_rp_r_0) (l_e_st_eq_landau_n_rt_rp_r_pl l_e_st_eq_landau_n_rt_rp_r_0 s)) (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) (l_e_st_eq_landau_n_rt_rp_r_c_10301_t6 r s) (l_e_st_eq_landau_n_rt_rp_r_c_10301_t7 r s) (l_e_st_eq_landau_n_rt_rp_r_c_10301_t8 r s) : l_e_is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic)) (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)).
+
+(* notion 6905 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz301b ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic)) (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) (l_e_st_eq_landau_n_rt_rp_r_c_satz301a r s) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic))).
+
+(* notion 6906 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz301c ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_tris l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_pli (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_c_ic)) (l_e_st_eq_landau_n_rt_rp_r_c_ispli x) (l_e_st_eq_landau_n_rt_rp_r_c_satz301b (l_e_st_eq_landau_n_rt_rp_r_c_re x) (l_e_st_eq_landau_n_rt_rp_r_c_im x)) : l_e_st_eq_landau_n_rt_rp_r_c_is x (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_c_ic))).
+
+(* notion 6907 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz301d ≝ λx:l_e_st_eq_landau_n_rt_rp_r_c_complex.(l_e_symis l_e_st_eq_landau_n_rt_rp_r_c_cx x (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_c_ic)) (l_e_st_eq_landau_n_rt_rp_r_c_satz301c x) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_c_re x)) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl (l_e_st_eq_landau_n_rt_rp_r_c_im x)) l_e_st_eq_landau_n_rt_rp_r_c_ic)) x).
+
+(* notion 6908 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_10301_t9 ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl u) l_e_st_eq_landau_n_rt_rp_r_c_ic)).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_c_cx (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl u) l_e_st_eq_landau_n_rt_rp_r_c_ic)) (l_e_st_eq_landau_n_rt_rp_r_c_pli t u) (l_e_st_eq_landau_n_rt_rp_r_c_satz301b r s) i (l_e_st_eq_landau_n_rt_rp_r_c_satz301a t u) : l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) (l_e_st_eq_landau_n_rt_rp_r_c_pli t u)).
+
+(* notion 6909 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz301e ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl u) l_e_st_eq_landau_n_rt_rp_r_c_ic)).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real r (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_re (l_e_st_eq_landau_n_rt_rp_r_c_pli t u)) t (l_e_st_eq_landau_n_rt_rp_r_c_isre r s) (l_e_st_eq_landau_n_rt_rp_r_c_iscere (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) (l_e_st_eq_landau_n_rt_rp_r_c_pli t u) (l_e_st_eq_landau_n_rt_rp_r_c_10301_t9 r s t u i)) (l_e_st_eq_landau_n_rt_rp_r_c_reis t u) : l_e_st_eq_landau_n_rt_rp_r_is r t).
+
+(* notion 6910 *)
+definition l_e_st_eq_landau_n_rt_rp_r_c_satz301f ≝ λr:l_e_st_eq_landau_n_rt_rp_r_real.λs:l_e_st_eq_landau_n_rt_rp_r_real.λt:l_e_st_eq_landau_n_rt_rp_r_real.λu:l_e_st_eq_landau_n_rt_rp_r_real.λi:l_e_st_eq_landau_n_rt_rp_r_c_is (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl r) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl s) l_e_st_eq_landau_n_rt_rp_r_c_ic)) (l_e_st_eq_landau_n_rt_rp_r_c_pl (l_e_st_eq_landau_n_rt_rp_r_c_cofrl t) (l_e_st_eq_landau_n_rt_rp_r_c_ts (l_e_st_eq_landau_n_rt_rp_r_c_cofrl u) l_e_st_eq_landau_n_rt_rp_r_c_ic)).(l_e_tr3is l_e_st_eq_landau_n_rt_rp_r_real s (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli r s)) (l_e_st_eq_landau_n_rt_rp_r_c_im (l_e_st_eq_landau_n_rt_rp_r_c_pli t u)) u (l_e_st_eq_landau_n_rt_rp_r_c_isim r s) (l_e_st_eq_landau_n_rt_rp_r_c_isceim (l_e_st_eq_landau_n_rt_rp_r_c_pli r s) (l_e_st_eq_landau_n_rt_rp_r_c_pli t u) (l_e_st_eq_landau_n_rt_rp_r_c_10301_t9 r s t u i)) (l_e_st_eq_landau_n_rt_rp_r_c_imis t u) : l_e_st_eq_landau_n_rt_rp_r_is s u).
+
--- /dev/null
+baseuri=cic:/matita/automath/
+++ /dev/null
-baseuri=cic:/matita/automath/
\ / This software is distributed as is, NO WARRANTY.
V_______________________________________________________________ *)
-module U = NUri
-module K = U.UriHash
-module C = Cps
-module N = Level
-module E = Entity
-module G = Options
-module S = Status
-module A = Aut
-module D = Crg
+module U = NUri
+module UH = U.UriHash
+module C = Cps
+module G = Options
+module N = Level
+module E = Entity
+module S = Status
+module A = Aut
+module D = Crg
(* qualified identifier: uri, name, qualifiers *)
type qid = D.uri * D.id * D.id list
let henv_size, hcnt_size = 7000, 4300 (* hash tables initial sizes *)
-let henv = K.create henv_size (* optimized global environment *)
+let henv = UH.create henv_size (* optimized global environment *)
-let hcnt = K.create hcnt_size (* optimized context *)
+let hcnt = UH.create hcnt_size (* optimized context *)
(* Internal functions *******************************************************)
| Some qid -> let f qid = f (Some qid) in relax_qid f lst qid
let resolve_gref err f lst qid =
- try let a, cnt = K.find henv (uri_of_qid qid) in f qid a cnt
+ try let a, cnt = UH.find henv (uri_of_qid qid) in f qid a cnt
with Not_found -> err qid
let resolve_gref_relaxed f lst qid =
let get_cnt err f lst = function
| None -> f empty_cnt
| Some qid as node ->
- try let cnt = K.find hcnt (uri_of_qid qid) in f cnt
+ try let cnt = UH.find hcnt (uri_of_qid qid) in f cnt
with Not_found -> err node
let get_cnt_relaxed f lst =
let f _ vv = xlate_term (f vv) st lst y lenv t in
xlate_term f st lst false lenv v
| A.Abst (name, w, t) ->
- let f d ww =
+ let f dw ww =
let a = E.node_attrs ~name:(name, true) () in
- let f d tt =
- let l = if !G.cc then match y, d with
+ let f dt tt =
+(* let a = {a with E.n_degr = dt} in *)
+ let l = if !G.cc then match y, dt with
| true, _ -> N.one
| _ , 0 -> N.one
| _ , 1 -> N.unknown st.S.lenv
else N.infinite
in
let b = D.Abst (l, ww) in
- f d (D.TBind (a, b, tt))
+ f dt (D.TBind (a, b, tt))
in
let f lenv = xlate_term f st lst y lenv t in
- push_abst f {a with E.n_degr = succ d} ww lenv
+ push_abst f {a with E.n_degr = succ dw} ww lenv
in
xlate_term f st lst true lenv w
| A.GRef (name, args) ->
let gref = D.TGRef (a, uri_of_qid qid) in
if cnt = D.ESort then f a.E.n_degr gref else
let f = function
- | D.EAppl (D.ESort, a, v) -> f a.E.n_degr (D.TAppl (a, v, gref))
+ | D.EAppl (D.ESort, b, v) -> f a.E.n_degr (D.TAppl (b, v, gref))
| args -> f a.E.n_degr (D.TProj (E.empty_node, args, gref))
in
let f args = C.list_fold_right f map2 args D.ESort in
let f qid =
let f cnt =
let f d ww =
- K.add hcnt (uri_of_qid qid) (add_abst cnt name d ww);
+ UH.add hcnt (uri_of_qid qid) (add_abst cnt name d ww);
err {lst with node = Some qid}
in
xlate_term f st lst true cnt w
let f qid =
let f d ww =
let a = E.node_attrs ~apix:lst.line ~degr:(succ d) () in
- K.add henv (uri_of_qid qid) (a, lenv);
+ UH.add henv (uri_of_qid qid) (a, lenv);
let t = add_proj lenv ww in
(*
print_newline (); CrgOutput.pp_term print_string t;
let f _ ww =
let f d vv =
let na = E.node_attrs ~apix:lst.line ~degr:d () in
- K.add henv (uri_of_qid qid) (na, lenv);
+ UH.add henv (uri_of_qid qid) (na, lenv);
let t = add_proj lenv (D.TCast (E.empty_node, ww, vv)) in
(*
print_newline (); CrgOutput.pp_term print_string t;
(* Interface functions ******************************************************)
let initial_status () =
- K.clear henv; K.clear hcnt; {
+ UH.clear henv; UH.clear hcnt; {
path = []; node = None; nodes = []; line = 1; mk_uri = G.get_mk_uri ();
}
V_______________________________________________________________ *)
module P = Printf
+
module C = Cps
module L = Log
module A = Aut
V_______________________________________________________________ *)
module C = Cps
-module E = Entity
module J = Marks
module N = Level
+module E = Entity
module D = Crg
module Z = Bag
\ / This software is distributed as is, NO WARRANTY.
V_______________________________________________________________ *)
-module U = NUri
-module L = Log
-module K = U.UriHash
-module E = Entity
-module Z = Bag
+module U = NUri
+module UH = U.UriHash
+module L = Log
+module E = Entity
+module Z = Bag
exception ObjectNotFound of Z.message
let hsize = 7000
-let env = K.create hsize
+let env = UH.create hsize
(* Internal functions *******************************************************)
let set_entity f (ra, na, uri, b) =
let age = get_age () in
let entry = ra, {na with E.n_apix = Some age}, uri, b in
- K.add env uri entry; f entry
+ UH.add env uri entry; f entry
let get_entity f uri =
- try f (K.find env uri) with Not_found -> error uri
+ try f (UH.find env uri) with Not_found -> error uri
V_______________________________________________________________ *)
module P = Printf
+
module U = NUri
module L = Log
module G = Options
-module E = Entity
module J = Marks
module H = Hierarchy
+module E = Entity
module XD = XmlCrg
module Z = Bag
module ZD = BagCrg
module U = NUri
module C = Cps
module L = Log
-module E = Entity
module G = Options
module J = Marks
+module E = Entity
module S = Status
module Z = Bag
module ZO = BagOutput
module C = Cps
module W = Share
module L = Log
+module G = Options
module H = Hierarchy
module E = Entity
-module G = Options
module S = Status
module Z = Bag
module ZO = BagOutput
(* kernel version: basic, relative, global *)
(* note : ufficial basic \lambda\delta *)
-module E = Entity
module N = Level
+module E = Entity
type uri = E.uri
type attrs = E.node_attrs
V_______________________________________________________________ *)
module C = Cps
-module E = Entity
module N = Level
+module E = Entity
module D = Crg
module B = Brg
\ / This software is distributed as is, NO WARRANTY.
V_______________________________________________________________ *)
-module U = NUri
-module K = U.UriHash
-module E = Entity
+module U = NUri
+module UH = U.UriHash
+module E = Entity
let hsize = 7000
-let env = K.create hsize
+let env = UH.create hsize
(* Interface functions ******************************************************)
(* decps *)
let set_entity entity =
let _, _, uri, _ = entity in
- K.add env uri entity; entity
+ UH.add env uri entity; entity
let get_entity uri =
- try K.find env uri with Not_found -> E.empty_root, E.empty_node, uri, E.Void
+ try UH.find env uri with Not_found -> E.empty_root, E.empty_node, uri, E.Void
\ / This software is distributed as is, NO WARRANTY.
V_______________________________________________________________ *)
+module F = Filename
module P = Printf
module U = NUri
let ok = ref true
+let base = "matita"
+
+let ext = ".ma"
+
let width = 70
let out_preamble och =
(* Interface functions ******************************************************)
let open_out fname =
- let och = open_out (fname ^ ".ma") in
+ let dir = F.concat !G.ma_dir base in
+ let path = F.concat dir fname in
+ let och = open_out (path ^ ext) in
out_preamble och;
out_top_comment och (P.sprintf "This file is generated by %s: do not edit" G.version_string);
out_include och "basics/pts";
V_______________________________________________________________ *)
module P = Printf
-module C = Cps
+
module U = NUri
+module C = Cps
module L = Log
module G = Options
-module E = Entity
module H = Hierarchy
module N = Level
+module E = Entity
module XD = XmlCrg
module B = Brg
module BD = BrgCrg
module U = NUri
module W = Share
module L = Log
+module G = Options
module H = Hierarchy
module N = Level
module E = Entity
-module G = Options
module O = Output
module S = Status
module B = Brg
module C = Cps
module W = Share
module L = Log
+module G = Options
module H = Hierarchy
module N = Level
module E = Entity
-module G = Options
module S = Status
module B = Brg
module BE = BrgEnvironment
V_______________________________________________________________ *)
module L = Log
-module E = Entity
module G = Options
+module E = Entity
module S = Status
module B = Brg
module BE = BrgEnvironment
module K = Hashtbl
module P = Scanf
+
module C = Cps
type graph = string * (int -> int)
V_______________________________________________________________ *)
module F = Filename
+
module C = Cps
type uri_generator = string -> string
let debug_lexer = ref false (* output lexer debug information *)
-let ma_preamble = ref "" (* location of Matita preamble file *)
+let ma_dir = ref "" (* directory for grafite output *)
+
+let ma_preamble = ref "" (* location of grafite preamble file *)
let kernel_id () =
let id = match !kernel with
xdir := ""; kernel := Brg; si := false; cover := "";
expand := false; indexes := false; icm := 0; unquote := false;
debug_parser := false; debug_lexer := false;
- ma_preamble := ""
+ ma_dir := ""; ma_preamble := ""
V_______________________________________________________________ *)
module P = Printf
+
module L = Log
module G = Options
\ / This software is distributed as is, NO WARRANTY.
V_______________________________________________________________ *)
-module N = Level
module G = Options
+module N = Level
type status = {
delta: bool; (* global delta-expansion *)
(* note : fragment of complete \lambda\delta serving as abstract layer *)
module C = Cps
-module E = Entity
module N = Level
+module E = Entity
type uri = E.uri
type id = E.id
V_______________________________________________________________ *)
module P = Printf
+
module U = NUri
module C = Cps
module L = Log
V_______________________________________________________________ *)
module P = Printf
+
module L = Log
let level = 1
-(* free = F I M P Q U V *)
+(* free = F I K M P Q U V *)
module U = NUri
-module K = NUri.UriHash
+module UH = NUri.UriHash
module C = Cps
module W = Share (**)
V_______________________________________________________________ *)
module U = NUri
-module H = Hierarchy
module C = Cps
module G = Options
+module H = Hierarchy
module E = Entity
module T = Txt
module TT = TxtTxt
module F = Filename
module P = Printf
+
module U = NUri
module C = Cps
module L = Log
module Y = Time
module G = Options
module H = Hierarchy
-module O = Output
module E = Entity
+module O = Output
module S = Status
module DO = CrgOutput
module TD = TxtCrg
if !G.trace >= 2 then begin preprocess := true; G.summary := true end
in
let set_stage i = G.stage := i in
+ let set_madir s = G.ma_dir := s in
let set_xdir s = G.xdir := s in
let set_root s = root := s in
let clear_options () =
if !G.trace >= 1 then Y.utime_stamp "at exit"
in
let help =
- "Usage: helena [ -LPVXdgilopqtx1 | -Ts <number> | -O <dir> | -m <file> | -hkr <string> ]* [ <file> ]*\n\n" ^
+ "Usage: helena [ -LPVXdgilopqtx1 | -Ts <number> | -MO <dir> | -m <file> | -hkr <string> ]* [ <file> ]*\n\n" ^
"Trace levels: 0 just errors (default), 1 time stamps, 2 processed files, \
3 typing information, 4 reduction information\n\n" ^
"Stages: 0 parsing, 1 to intermediate, 2 to untrusted, 3 to trusted (default)\n"
in
let help_L = " show lexer debug information" in
+ let help_M = "<dir> set location of output directory (Grafite) to <dir> (default: current directory)" in
let help_O = "<dir> set location of output directory (XML) to <dir> (default: current directory)" in
let help_P = " show parser debug information" in
let help_T = "<number> set trace level (see above)" in
let help_i = " show local references by index" in
let help_k = "<string> set kernel version (default: \"brg\")" in
let help_l = " disambiguate binders level (Automath)" in
- let help_m = "<file> set location of Matita preamble to <file> (default: empty)" in
+ let help_m = "<file> export kernel entities (Grafite) setting location of preamble to <file> (default: empty)" in
let help_o = " activate sort inclusion (default: false)" in
let help_p = " preprocess source (Automath)" in
let help_q = " disable quotation of identifiers" in
let help_1 = " parse files with streaming policy" in
at_exit exit;
Arg.parse [
- ("-L", Arg.Set G.debug_lexer, help_L);
+ ("-L", Arg.Set G.debug_lexer, help_L);
+ ("-M", Arg.String set_madir, help_M);
("-O", Arg.String set_xdir, help_O);
("-P", Arg.Set G.debug_parser, help_P);
("-T", Arg.Int set_trace, help_T);
V_______________________________________________________________ *)
module F = Filename
+
module U = NUri
module C = Cps
-module H = Hierarchy
module G = Options
-module E = Entity
+module H = Hierarchy
module N = Level
+module E = Entity
(* internal functions *******************************************************)
let level st n =
"level", N.to_string st n
+let degr a =
+ "degr", string_of_int a.E.n_degr
+
let meta a =
let map = function
| E.Main -> "Main"
val apix: Entity.node_attrs -> attr
+val degr: Entity.node_attrs -> attr
+
val meta: Entity.root_attrs -> attr
val info: Entity.root_attrs -> attr list
projects / helm.git / commitdiff